LMFDB - Embedded newform 13.7.f.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(2,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99070308706$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	13.2
Dual form			13.7.f.a.7.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.48669 + 0.666306i) q^{2} +(-16.9072 - 29.2841i) q^{3} +(-49.6860 - 28.6862i) q^{4} +(34.0715 - 34.0715i) q^{5} +(-22.5307 - 84.0857i) q^{6} +(190.342 - 51.0019i) q^{7} +(-220.944 - 220.944i) q^{8} +(-207.205 + 358.889i) q^{9} +O(q^{10})$	\(q+(2.48669 + 0.666306i) q^{2} +(-16.9072 - 29.2841i) q^{3} +(-49.6860 - 28.6862i) q^{4} +(34.0715 - 34.0715i) q^{5} +(-22.5307 - 84.0857i) q^{6} +(190.342 - 51.0019i) q^{7} +(-220.944 - 220.944i) q^{8} +(-207.205 + 358.889i) q^{9} +(107.427 - 62.0232i) q^{10} +(-120.972 + 451.473i) q^{11} +1940.01i q^{12} +(2156.00 - 422.473i) q^{13} +507.303 q^{14} +(-1573.81 - 421.700i) q^{15} +(1433.71 + 2483.27i) q^{16} +(-1343.96 - 775.937i) q^{17} +(-754.384 + 754.384i) q^{18} +(-3123.25 - 11656.1i) q^{19} +(-2670.26 + 715.494i) q^{20} +(-4711.68 - 4711.68i) q^{21} +(-601.639 + 1042.07i) q^{22} +(17806.4 - 10280.5i) q^{23} +(-2734.61 + 10205.7i) q^{24} +13303.3i q^{25} +(5642.79 + 385.995i) q^{26} -10637.7 q^{27} +(-10920.4 - 2926.10i) q^{28} +(11154.3 + 19319.8i) q^{29} +(-3632.59 - 2097.27i) q^{30} +(1680.77 - 1680.77i) q^{31} +(7086.34 + 26446.6i) q^{32} +(15266.3 - 4090.58i) q^{33} +(-2825.00 - 2825.00i) q^{34} +(4747.52 - 8222.94i) q^{35} +(20590.3 - 11887.8i) q^{36} +(-7659.24 + 28584.7i) q^{37} -31066.2i q^{38} +(-48823.6 - 55993.6i) q^{39} -15055.8 q^{40} +(-19684.5 - 5274.43i) q^{41} +(-8577.06 - 14855.9i) q^{42} +(-60100.8 - 34699.2i) q^{43} +(18961.7 - 18961.7i) q^{44} +(5168.12 + 19287.7i) q^{45} +(51129.0 - 13700.0i) q^{46} +(133594. + 133594. i) q^{47} +(48480.1 - 83970.0i) q^{48} +(-68258.3 + 39409.0i) q^{49} +(-8864.04 + 33081.1i) q^{50} +52475.6i q^{51} +(-119242. - 40856.4i) q^{52} +106247. q^{53} +(-26452.6 - 7087.94i) q^{54} +(11260.7 + 19504.1i) q^{55} +(-53323.4 - 30786.3i) q^{56} +(-288533. + 288533. i) q^{57} +(14864.4 + 55474.6i) q^{58} +(365659. - 97978.2i) q^{59} +(66099.1 + 66099.1i) q^{60} +(100762. - 174526. i) q^{61} +(5299.47 - 3059.65i) q^{62} +(-21135.7 + 78879.4i) q^{63} -113029. i q^{64} +(59063.8 - 87852.5i) q^{65} +40688.0 q^{66} +(-225048. - 60301.4i) q^{67} +(44517.4 + 77106.3i) q^{68} +(-602112. - 347630. i) q^{69} +(17284.6 - 17284.6i) q^{70} +(-84973.0 - 317124. i) q^{71} +(125075. - 33513.8i) q^{72} +(-40750.8 - 40750.8i) q^{73} +(-38092.3 + 65977.7i) q^{74} +(389574. - 224921. i) q^{75} +(-179188. + 668740. i) q^{76} +92103.9i q^{77} +(-84100.1 - 171770. i) q^{78} +435228. q^{79} +(133458. + 35759.8i) q^{80} +(330905. + 573145. i) q^{81} +(-45434.7 - 26231.7i) q^{82} +(-256625. + 256625. i) q^{83} +(98944.1 + 369265. i) q^{84} +(-72228.2 + 19353.5i) q^{85} +(-126332. - 126332. i) q^{86} +(377176. - 653287. i) q^{87} +(126478. - 73022.3i) q^{88} +(-242124. + 903619. i) q^{89} +51406.1i q^{90} +(388829. - 190374. i) q^{91} -1.17964e6 q^{92} +(-77637.0 - 20802.8i) q^{93} +(243192. + 421220. i) q^{94} +(-503556. - 290728. i) q^{95} +(654654. - 654654. i) q^{96} +(-90722.7 - 338582. i) q^{97} +(-195996. + 52516.9i) q^{98} +(-136963. - 136963. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.48669	+	0.666306i	0.310836	+	0.0832883i	0.410865	−	0.911696i	$-0.365227\pi$
$2$	2.48669	+	0.666306i	0.310836	+	0.0832883i	−0.100029	+	0.994985i	$0.531893\pi$
$3$	−16.9072	−	29.2841i	−0.626192	−	1.08460i	−0.988309	−	0.152463i	$-0.951279\pi$
$3$	−16.9072	−	29.2841i	−0.626192	−	1.08460i	0.362118	−	0.932132i	$-0.382054\pi$
$4$	−49.6860	−	28.6862i	−0.776343	−	0.448222i
$5$	34.0715	−	34.0715i	0.272572	−	0.272572i	−0.557563	−	0.830135i	$-0.688263\pi$
$5$	34.0715	−	34.0715i	0.272572	−	0.272572i	0.830135	+	0.557563i	$0.188263\pi$
$6$	−22.5307	−	84.0857i	−0.104309	−	0.389286i
$7$	190.342	−	51.0019i	0.554932	−	0.148693i	0.0295548	−	0.999563i	$-0.490591\pi$
$7$	190.342	−	51.0019i	0.554932	−	0.148693i	0.525377	+	0.850870i	$0.323924\pi$
$8$	−220.944	−	220.944i	−0.431532	−	0.431532i
$9$	−207.205	+	358.889i	−0.284232	+	0.492304i
$10$	107.427	−	62.0232i	0.107427	−	0.0620232i
$11$	−120.972	+	451.473i	−0.0908880	+	0.339198i	−0.996364	−	0.0851990i	$-0.972847\pi$
$11$	−120.972	+	451.473i	−0.0908880	+	0.339198i	0.905476	+	0.424397i	$0.139514\pi$
$12$			1940.01i			1.12269i
$13$	2156.00	−	422.473i	0.981337	−	0.192296i
$13$	2156.00	−	422.473i	0.981337	−	0.192296i
$14$	507.303			0.184877
$15$	−1573.81	−	421.700i	−0.466313	−	0.124948i
$16$	1433.71	+	2483.27i	0.350028	+	0.606266i
$17$	−1343.96	−	775.937i	−0.273552	−	0.157935i	0.356949	−	0.934124i	$-0.383817\pi$
$17$	−1343.96	−	775.937i	−0.273552	−	0.157935i	−0.630501	+	0.776189i	$0.717150\pi$
$18$	−754.384	+	754.384i	−0.129353	+	0.129353i
$19$	−3123.25	−	11656.1i	−0.455350	−	1.69939i	−0.687056	−	0.726604i	$-0.741097\pi$
$19$	−3123.25	−	11656.1i	−0.455350	−	1.69939i	0.231706	−	0.972786i	$-0.425569\pi$
$20$	−2670.26	+	715.494i	−0.333783	+	0.0894368i
$21$	−4711.68	−	4711.68i	−0.508766	−	0.508766i
$22$	−601.639	+	1042.07i	−0.0565025	+	0.0978652i
$23$	17806.4	−	10280.5i	1.46350	−	0.844953i	0.464330	−	0.885662i	$-0.346295\pi$
$23$	17806.4	−	10280.5i	1.46350	−	0.844953i	0.999171	+	0.0407095i	$0.0129618\pi$
$24$	−2734.61	+	10205.7i	−0.197816	+	0.738259i
$25$			13303.3i			0.851409i
$26$	5642.79	+	385.995i	0.321051	+	0.0219615i
$27$	−10637.7			−0.540449
$28$	−10920.4	−	2926.10i	−0.497465	−	0.133295i
$29$	11154.3	+	19319.8i	0.457350	+	0.792154i	0.998820	−	0.0485666i	$-0.0154653\pi$
$29$	11154.3	+	19319.8i	0.457350	+	0.792154i	−0.541470	+	0.840720i	$0.682132\pi$
$30$	−3632.59	−	2097.27i	−0.134540	−	0.0776768i
$31$	1680.77	−	1680.77i	0.0564188	−	0.0564188i	−0.678334	−	0.734753i	$-0.737298\pi$
$31$	1680.77	−	1680.77i	0.0564188	−	0.0564188i	0.734753	+	0.678334i	$0.237298\pi$
$32$	7086.34	+	26446.6i	0.216258	+	0.807086i
$33$	15266.3	−	4090.58i	0.424806	−	0.113827i
$34$	−2825.00	−	2825.00i	−0.0718757	−	0.0718757i
$35$	4747.52	−	8222.94i	0.110729	−	0.191789i
$36$	20590.3	−	11887.8i	0.441323	−	0.254798i
$37$	−7659.24	+	28584.7i	−0.151210	+	0.564323i	0.848190	+	0.529692i	$0.177692\pi$
$37$	−7659.24	+	28584.7i	−0.151210	+	0.564323i	−0.999400	+	0.0346313i	$0.988974\pi$
$38$		−	31066.2i		−	0.566157i
$39$	−48823.6	−	55993.6i	−0.823068	−	0.943940i
$40$	−15055.8			−0.235247
$41$	−19684.5	−	5274.43i	−0.285609	−	0.0765287i	0.113170	−	0.993576i	$-0.463899\pi$
$41$	−19684.5	−	5274.43i	−0.285609	−	0.0765287i	−0.398779	+	0.917047i	$0.630566\pi$
$42$	−8577.06	−	14855.9i	−0.115769	−	0.200517i
$43$	−60100.8	−	34699.2i	−0.755918	−	0.436429i	0.0719102	−	0.997411i	$-0.477090\pi$
$43$	−60100.8	−	34699.2i	−0.755918	−	0.436429i	−0.827828	+	0.560982i	$0.810424\pi$
$44$	18961.7	−	18961.7i	0.222596	−	0.222596i
$45$	5168.12	+	19287.7i	0.0567147	+	0.211662i
$46$	51129.0	−	13700.0i	0.525284	−	0.140749i
$47$	133594.	+	133594.i	1.28675	+	1.28675i	0.936752	+	0.349993i	$0.113816\pi$
$47$	133594.	+	133594.i	1.28675	+	1.28675i	0.349993	+	0.936752i	$0.386184\pi$
$48$	48480.1	−	83970.0i	0.438369	−	0.759277i
$49$	−68258.3	+	39409.0i	−0.580186	+	0.334971i
$50$	−8864.04	+	33081.1i	−0.0709124	+	0.264649i
$51$			52475.6i			0.395591i
$52$	−119242.	−	40856.4i	−0.848046	−	0.290569i
$53$	106247.			0.713654			0.356827	−	0.934170i	$-0.383859\pi$
$53$	106247.			0.713654			0.356827	+	0.934170i	$0.383859\pi$
$54$	−26452.6	−	7087.94i	−0.167991	−	0.0450131i
$55$	11260.7	+	19504.1i	0.0676826	+	0.117230i
$56$	−53323.4	−	30786.3i	−0.303636	−	0.175305i
$57$	−288533.	+	288533.i	−1.55801	+	1.55801i
$58$	14864.4	+	55474.6i	0.0761838	+	0.284322i
$59$	365659.	−	97978.2i	1.78041	−	0.477060i	0.789754	−	0.613424i	$-0.210208\pi$
$59$	365659.	−	97978.2i	1.78041	−	0.477060i	0.990659	+	0.136363i	$0.0435415\pi$
$60$	66099.1	+	66099.1i	0.306015	+	0.306015i
$61$	100762.	−	174526.i	0.443924	−	0.768899i	−0.554052	−	0.832482i	$-0.686919\pi$
$61$	100762.	−	174526.i	0.443924	−	0.768899i	0.997977	+	0.0635826i	$0.0202526\pi$
$62$	5299.47	−	3059.65i	0.0222360	−	0.0128380i
$63$	−21135.7	+	78879.4i	−0.0845268	+	0.315458i
$64$		−	113029.i		−	0.431173i
$65$	59063.8	−	87852.5i	0.215071	−	0.319900i
$66$	40688.0			0.141526
$67$	−225048.	−	60301.4i	−0.748257	−	0.200495i	−0.135512	−	0.990776i	$-0.543268\pi$
$67$	−225048.	−	60301.4i	−0.748257	−	0.200495i	−0.612745	+	0.790281i	$0.709935\pi$
$68$	44517.4	+	77106.3i	0.141580	+	0.245224i
$69$	−602112.	−	347630.i	−1.83286	−	1.05820i
$70$	17284.6	−	17284.6i	0.0503924	−	0.0503924i
$71$	−84973.0	−	317124.i	−0.237414	−	0.886041i	−0.977046	−	0.213029i	$-0.931667\pi$
$71$	−84973.0	−	317124.i	−0.237414	−	0.886041i	0.739632	−	0.673012i	$-0.235000\pi$
$72$	125075.	−	33513.8i	0.335100	−	0.0897896i
$73$	−40750.8	−	40750.8i	−0.104753	−	0.104753i	0.652788	−	0.757541i	$-0.273599\pi$
$73$	−40750.8	−	40750.8i	−0.104753	−	0.104753i	−0.757541	+	0.652788i	$0.773599\pi$
$74$	−38092.3	+	65977.7i	−0.0940030	+	0.162818i
$75$	389574.	−	224921.i	0.923434	−	0.533145i
$76$	−179188.	+	668740.i	−0.408196	+	1.52341i
$77$			92103.9i			0.201746i
$78$	−84100.1	−	171770.i	−0.177220	−	0.361962i
$79$	435228.			0.882745			0.441373	−	0.897324i	$-0.354492\pi$
$79$	435228.			0.882745			0.441373	+	0.897324i	$0.354492\pi$
$80$	133458.	+	35759.8i	0.260659	+	0.0698434i
$81$	330905.	+	573145.i	0.622656	+	1.07847i
$82$	−45434.7	−	26231.7i	−0.0824036	−	0.0475757i
$83$	−256625.	+	256625.i	−0.448813	+	0.448813i	−0.894960	−	0.446147i	$-0.852796\pi$
$83$	−256625.	+	256625.i	−0.448813	+	0.448813i	0.446147	+	0.894960i	$0.352796\pi$
$84$	98944.1	+	369265.i	0.166937	+	0.623017i
$85$	−72228.2	+	19353.5i	−0.117612	+	0.0315139i
$86$	−126332.	−	126332.i	−0.198617	−	0.198617i
$87$	377176.	−	653287.i	0.572777	−	0.992080i
$88$	126478.	−	73022.3i	0.185596	−	0.107154i
$89$	−242124.	+	903619.i	−0.343453	+	1.28178i	0.550956	+	0.834535i	$0.314263\pi$
$89$	−242124.	+	903619.i	−0.343453	+	1.28178i	−0.894409	+	0.447250i	$0.852403\pi$
$90$			51406.1i			0.0705158i
$91$	388829.	−	190374.i	0.515982	−	0.252629i
$92$	−1.17964e6			−1.51491
$93$	−77637.0	−	20802.8i	−0.0965206	−	0.0258626i
$94$	243192.	+	421220.i	0.292796	+	0.507138i
$95$	−503556.	−	290728.i	−0.587323	−	0.339091i
$96$	654654.	−	654654.i	0.739943	−	0.739943i
$97$	−90722.7	−	338582.i	−0.0994033	−	0.370978i	0.898247	−	0.439491i	$-0.144841\pi$
$97$	−90722.7	−	338582.i	−0.0994033	−	0.370978i	−0.997650	+	0.0685131i	$0.978175\pi$
$98$	−195996.	+	52516.9i	−0.208242	+	0.0557982i
$99$	−136963.	−	136963.i	−0.141155	−	0.141155i
$100$	381620.	−	660985.i	0.381620	−	0.660985i
$101$	701692.	−	405122.i	0.681056	−	0.393208i	−0.119197	−	0.992871i	$-0.538032\pi$
$101$	701692.	−	405122.i	0.681056	−	0.393208i	0.800253	+	0.599663i	$0.204699\pi$
$102$	−34964.8	+	130490.i	−0.0329481	+	0.122964i
$103$			87516.3i			0.0800898i	0.999198	+	0.0400449i	$0.0127501\pi$
$103$			87516.3i			0.0800898i	−0.999198	+	0.0400449i	$0.987250\pi$
$104$	−569698.	−	383012.i	−0.506460	−	0.340496i
$105$	−321068.			−0.277351
$106$	264202.	+	70792.8i	0.221829	+	0.0594390i
$107$	−617565.	−	1.06965e6i	−0.504117	−	0.873156i	−0.999989	−	0.00476029i	$-0.998485\pi$
$107$	−617565.	−	1.06965e6i	−0.504117	−	0.873156i	0.495872	−	0.868396i	$-0.334849\pi$
$108$	528543.	+	305154.i	0.419574	+	0.242241i
$109$	−711838.	+	711838.i	−0.549670	+	0.549670i	−0.926345	−	0.376676i	$-0.877067\pi$
$109$	−711838.	+	711838.i	−0.549670	+	0.549670i	0.376676	+	0.926345i	$0.377067\pi$
$110$	15006.1	+	56003.6i	0.0112743	+	0.0420764i
$111$	966571.	−	258992.i	0.706749	−	0.189373i
$112$	399547.	+	399547.i	0.284389	+	0.284389i
$113$	−1.00864e6	+	1.74702e6i	−0.699041	+	1.21077i	0.269759	+	0.962928i	$0.413056\pi$
$113$	−1.00864e6	+	1.74702e6i	−0.699041	+	1.21077i	−0.968799	+	0.247846i	$0.920277\pi$
$114$	−909744.	+	525241.i	−0.614051	+	0.354523i
$115$	256418.	−	956966.i	0.168599	−	0.629221i
$116$		−	1.27990e6i		−	0.819977i
$117$	−295112.	+	861303.i	−0.184259	+	0.537772i
$118$	974565.			0.593150
$119$	−295386.	−	79148.4i	−0.175287	−	0.0469679i
$120$	254551.	+	440896.i	0.147310	+	0.255148i
$121$	1.34502e6	+	776549.i	0.759230	+	0.438342i
$122$	366852.	−	366852.i	0.202028	−	0.202028i
$123$	178351.	+	665617.i	0.0958432	+	0.357692i
$124$	−131726.	+	35295.8i	−0.0690885	+	0.0185122i
$125$	985630.	+	985630.i	0.504643	+	0.504643i
$126$	−105116.	+	182066.i	−0.0525479	+	0.0910157i
$127$	−1.74129e6	+	1.00533e6i	−0.850080	+	0.490794i	−0.860678	−	0.509150i	$-0.829960\pi$
$127$	−1.74129e6	+	1.00533e6i	−0.850080	+	0.490794i	0.0105981	+	0.999944i	$0.496626\pi$
$128$	528838.	−	1.97365e6i	0.252170	−	0.941110i
$129$			2.34666e6i			1.09315i
$130$	205410.	−	179107.i	0.0934957	−	0.0815235i
$131$	2.68360e6			1.19372			0.596862	−	0.802344i	$-0.296414\pi$
$131$	2.68360e6			1.19372			0.596862	+	0.802344i	$0.296414\pi$
$132$	−875863.	−	234687.i	−0.380815	−	0.102039i
$133$	−1.18897e6	−	2.05935e6i	−0.505377	−	0.875338i
$134$	−519445.	−	299902.i	−0.215886	−	0.124642i
$135$	−362442.	+	362442.i	−0.147312	+	0.147312i
$136$	125502.	+	468379.i	0.0498923	+	0.186200i
$137$	−2.58680e6	+	693130.i	−1.00601	+	0.269559i	−0.723960	−	0.689842i	$-0.757680\pi$
$137$	−2.58680e6	+	693130.i	−1.00601	+	0.269559i	−0.282046	+	0.959401i	$0.591013\pi$
$138$	−1.26564e6	−	1.26564e6i	−0.481584	−	0.481584i
$139$	−188967.	+	327300.i	−0.0703625	+	0.121871i	−0.899060	−	0.437825i	$-0.855749\pi$
$139$	−188967.	+	327300.i	−0.0703625	+	0.121871i	0.828698	+	0.559696i	$0.189082\pi$
$140$	−471770.	+	272377.i	−0.171928	+	0.0992626i
$141$	1.65348e6	−	6.17086e6i	0.589849	−	2.20135i
$142$		−	845206.i		−	0.295187i
$143$	−70079.6	+	1.02448e6i	−0.0239653	+	0.350345i
$144$	−1.18829e6			−0.397956
$145$	1.03830e6	+	278212.i	0.340580	+	0.0912582i
$146$	−74181.9	−	128487.i	−0.0238363	−	0.0412858i
$147$	2.30811e6	+	1.33259e6i	0.726615	+	0.419511i
$148$	1.20054e6	−	1.20054e6i	0.370333	−	0.370333i
$149$	−592234.	−	2.21025e6i	−0.179033	−	0.668162i	−0.995829	−	0.0912352i	$-0.970918\pi$
$149$	−592234.	−	2.21025e6i	−0.179033	−	0.668162i	0.816796	−	0.576927i	$-0.195748\pi$
$150$	1.11861e6	−	299732.i	0.331441	−	0.0888094i
$151$	−10900.0	−	10900.0i	−0.00316587	−	0.00316587i	0.705522	−	0.708688i	$-0.250713\pi$
$151$	−10900.0	−	10900.0i	−0.00316587	−	0.00316587i	−0.708688	+	0.705522i	$0.750713\pi$
$152$	−1.88529e6	+	3.26541e6i	−0.536843	+	0.929839i
$153$	556951.	−	321556.i	0.155504	−	0.0897805i
$154$	−61369.4	+	229034.i	−0.0168031	+	0.0627101i
$155$		−	114533.i		−	0.0307564i
$156$	819603.	+	4.18266e6i	0.215889	+	1.10174i
$157$	−3.15946e6			−0.816420			−0.408210	−	0.912888i	$-0.633847\pi$
$157$	−3.15946e6			−0.816420			−0.408210	+	0.912888i	$0.633847\pi$
$158$	1.08228e6	+	289995.i	0.274389	+	0.0735223i
$159$	−1.79633e6	−	3.11134e6i	−0.446884	−	0.774026i
$160$	1.14252e6	+	659633.i	0.278935	+	0.161043i
$161$	2.86497e6	−	2.86497e6i	0.686504	−	0.686504i
$162$	440968.	+	1.64572e6i	0.103720	+	0.387088i
$163$	−6.90788e6	+	1.85096e6i	−1.59508	+	0.427400i	−0.943551	−	0.331226i	$-0.892538\pi$
$163$	−6.90788e6	+	1.85096e6i	−1.59508	+	0.427400i	−0.651526	+	0.758626i	$0.725871\pi$
$164$	826738.	+	826738.i	0.187429	+	0.187429i
$165$	380773.	−	659518.i	0.0847645	−	0.146816i
$166$	−809138.	+	467156.i	−0.176888	+	0.102126i
$167$	−1.36920e6	+	5.10994e6i	−0.293981	+	1.09715i	0.648043	+	0.761604i	$0.275588\pi$
$167$	−1.36920e6	+	5.10994e6i	−0.293981	+	1.09715i	−0.942023	+	0.335547i	$0.891079\pi$
$168$			2.08204e6i			0.439097i
$169$	4.46984e6	−	1.82170e6i	0.926045	−	0.377414i
$170$	−192504.			−0.0391826
$171$	4.83041e6	+	1.29430e6i	0.966041	+	0.258850i
$172$	1.99078e6	+	3.44813e6i	0.391235	+	0.677638i
$173$	7.51531e6	+	4.33897e6i	1.45147	+	0.838008i	0.998565	−	0.0535501i	$-0.0170537\pi$
$173$	7.51531e6	+	4.33897e6i	1.45147	+	0.838008i	0.452907	+	0.891558i	$0.350387\pi$
$174$	1.37321e6	−	1.37321e6i	0.260668	−	0.260668i
$175$	678491.	+	2.53216e6i	0.126599	+	0.472474i
$176$	−1.29457e6	+	346878.i	−0.237458	+	0.0636267i
$177$	−9.05147e6	−	9.05147e6i	−1.63230	−	1.63230i
$178$	−1.20417e6	+	2.08569e6i	−0.213515	+	0.369819i
$179$	3.85702e6	−	2.22685e6i	0.672500	−	0.388268i	−0.124523	−	0.992217i	$-0.539740\pi$
$179$	3.85702e6	−	2.22685e6i	0.672500	−	0.388268i	0.797023	+	0.603949i	$0.206407\pi$
$180$	296508.	−	1.10658e6i	0.0508415	−	0.189743i
$181$		−	5.91755e6i		−	0.997943i	−0.866618	−	0.498972i	$-0.833711\pi$
$181$		−	5.91755e6i		−	0.997943i	0.866618	−	0.498972i	$-0.166289\pi$
$182$	1.09374e6	−	214322.i	0.181427	−	0.0355511i
$183$	−6.81442e6			−1.11193
$184$	−6.20565e6	−	1.66280e6i	−0.996171	−	0.266923i
$185$	712961.	+	1.23489e6i	0.112603	+	0.195034i
$186$	−179198.	−	103460.i	−0.0278480	−	0.0160781i
$187$	512896.	−	512896.i	0.0784340	−	0.0784340i
$188$	−2.80544e6	−	1.04700e7i	−0.422209	−	1.57570i
$189$	−2.02479e6	+	542541.i	−0.299912	+	0.0803613i
$190$	−1.05847e6	−	1.05847e6i	−0.154319	−	0.154319i
$191$	−368146.	+	637647.i	−0.0528348	+	0.0915125i	−0.891233	−	0.453545i	$-0.850159\pi$
$191$	−368146.	+	637647.i	−0.0528348	+	0.0915125i	0.838398	+	0.545058i	$0.183492\pi$
$192$	−3.30996e6	+	1.91101e6i	−0.467648	+	0.269997i
$193$	301583.	−	1.12552e6i	0.0419502	−	0.156560i	−0.941774	−	0.336248i	$-0.890842\pi$
$193$	301583.	−	1.12552e6i	0.0419502	−	0.156560i	0.983724	+	0.179688i	$0.0575087\pi$
$194$		−	902396.i		−	0.123592i
$195$	−3.57128e6	−	244293.i	−0.481637	−	0.0329464i
$196$	4.52197e6			0.600565
$197$	1.08614e7	+	2.91029e6i	1.42064	+	0.380660i	0.885712	−	0.464235i	$-0.153671\pi$
$197$	1.08614e7	+	2.91029e6i	1.42064	+	0.380660i	0.534932	+	0.844895i	$0.320337\pi$
$198$	−249325.	−	431843.i	−0.0321196	−	0.0556328i
$199$	−3.79899e6	−	2.19335e6i	−0.482069	−	0.278322i	0.239210	−	0.970968i	$-0.423112\pi$
$199$	−3.79899e6	−	2.19335e6i	−0.482069	−	0.278322i	−0.721278	+	0.692646i	$0.756445\pi$
$200$	2.93928e6	−	2.93928e6i	0.367410	−	0.367410i
$201$	2.03905e6	+	7.60985e6i	0.251096	+	0.937104i
$202$	2.01483e6	−	539871.i	0.244446	−	0.0654992i
$203$	3.10848e6	+	3.10848e6i	0.371586	+	0.371586i
$204$	1.50533e6	−	2.60730e6i	0.177313	−	0.307115i
$205$	−850388.	+	490971.i	−0.0987087	+	0.0569895i
$206$	−58312.7	+	217626.i	−0.00667054	+	0.0248948i
$207$			8.52071e6i			0.960649i
$208$	4.14020e6	+	4.74821e6i	0.460078	+	0.527643i
$209$	5.64025e6			0.617816
$210$	−798397.	−	213930.i	−0.0862107	−	0.0231001i
$211$	−1.42125e6	−	2.46167e6i	−0.151294	−	0.262049i	0.780409	−	0.625269i	$-0.215011\pi$
$211$	−1.42125e6	−	2.46167e6i	−0.151294	−	0.262049i	−0.931703	+	0.363220i	$0.881677\pi$
$212$	−5.27897e6	−	3.04782e6i	−0.554041	−	0.319876i
$213$	−7.85002e6	+	7.85002e6i	−0.812329	+	0.812329i
$214$	−822974.	−	3.07138e6i	−0.0839740	−	0.313395i
$215$	−3.22998e6	+	865471.i	−0.325001	+	0.0870837i
$216$	2.35033e6	+	2.35033e6i	0.233221	+	0.233221i
$217$	234198.	−	405644.i	0.0229195	−	0.0396977i
$218$	−2.24442e6	+	1.29582e6i	−0.216638	+	0.125076i
$219$	−504368.	+	1.88233e6i	−0.0480193	+	0.179210i
$220$		−	1.29211e6i		−	0.121347i
$221$	−3.22539e6	−	1.10513e6i	−0.298817	−	0.102385i
$222$	2.57613e6			0.235455
$223$	−7.01335e6	−	1.87922e6i	−0.632428	−	0.169459i	−0.0716567	−	0.997429i	$-0.522829\pi$
$223$	−7.01335e6	−	1.87922e6i	−0.632428	−	0.169459i	−0.560771	+	0.827971i	$0.689495\pi$
$224$	2.69765e6	+	4.67247e6i	0.240017	+	0.415721i
$225$	−4.77440e6	−	2.75650e6i	−0.419152	−	0.241997i
$226$	−3.67223e6	+	3.67223e6i	−0.318130	+	0.318130i
$227$	1.86595e6	+	6.96381e6i	0.159522	+	0.595346i	0.998676	+	0.0514505i	$0.0163844\pi$
$227$	1.86595e6	+	6.96381e6i	0.159522	+	0.595346i	−0.839153	+	0.543895i	$0.816949\pi$
$228$	2.26130e7	−	6.05913e6i	1.90789	−	0.511218i
$229$	1.17933e7	+	1.17933e7i	0.982037	+	0.982037i	0.999841	−	0.0178049i	$-0.00566779\pi$
$229$	1.17933e7	+	1.17933e7i	0.982037	+	0.982037i	−0.0178049	+	0.999841i	$0.505668\pi$
$230$	1.27526e6	−	2.20882e6i	0.104813	−	0.181542i
$231$	2.69718e6	−	1.55722e6i	0.218813	−	0.126332i
$232$	1.80412e6	−	6.73309e6i	0.144478	−	0.539200i
$233$		−	9.60469e6i		−	0.759304i	−0.925129	−	0.379652i	$-0.876044\pi$
$233$		−	9.60469e6i		−	0.759304i	0.925129	−	0.379652i	$-0.123956\pi$
$234$	−1.30774e6	+	1.94516e6i	−0.102065	+	0.151812i
$235$	9.10349e6			0.701462
$236$	−2.09788e7	−	5.62124e6i	−1.59604	−	0.427658i
$237$	−7.35847e6	−	1.27452e7i	−0.552768	−	0.957422i
$238$	−681796.	−	393635.i	−0.0505735	−	0.0291986i
$239$	−1.02477e7	+	1.02477e7i	−0.750644	+	0.750644i	−0.974599	−	0.223955i	$-0.928103\pi$
$239$	−1.02477e7	+	1.02477e7i	−0.750644	+	0.750644i	0.223955	+	0.974599i	$0.428103\pi$
$240$	−1.20920e6	−	4.51278e6i	−0.0874707	−	0.326445i
$241$	1.89066e6	−	506602.i	0.135071	−	0.0361922i	−0.190650	−	0.981658i	$-0.561060\pi$
$241$	1.89066e6	−	506602.i	0.135071	−	0.0361922i	0.325721	+	0.945466i	$0.394393\pi$
$242$	2.82723e6	+	2.82723e6i	0.199487	+	0.199487i
$243$	7.31191e6	−	1.26646e7i	0.509580	−	0.882618i
$244$	−1.00130e7	+	5.78098e6i	−0.689275	+	0.397953i
$245$	−982942.	+	3.66839e6i	−0.0668389	+	0.249446i
$246$			1.77402e6i			0.119166i
$247$	−1.16581e7	−	2.38111e7i	−0.773637	−	1.58011i
$248$	−742714.			−0.0486930
$249$	1.18538e7	+	3.17623e6i	0.767823	+	0.205738i
$250$	1.79422e6	+	3.10769e6i	0.114830	+	0.198892i
$251$	−1.37625e7	−	7.94579e6i	−0.870315	−	0.502476i	−0.00286188	−	0.999996i	$-0.500911\pi$
$251$	−1.37625e7	−	7.94579e6i	−0.870315	−	0.502476i	−0.867453	+	0.497519i	$0.834244\pi$
$252$	3.31290e6	−	3.31290e6i	0.207017	−	0.207017i
$253$	2.48731e6	+	9.28278e6i	0.153592	+	0.573213i
$254$	−4.99990e6	+	1.33972e6i	−0.305113	+	0.0817547i
$255$	1.78792e6	+	1.78792e6i	0.107827	+	0.107827i
$256$	−986829.	+	1.70924e6i	−0.0588196	+	0.101879i
$257$	1.36068e7	−	7.85587e6i	0.801596	−	0.462802i	−0.0424327	−	0.999099i	$-0.513511\pi$
$257$	1.36068e7	−	7.85587e6i	0.801596	−	0.462802i	0.844029	+	0.536297i	$0.180177\pi$
$258$	−1.56359e6	+	5.83541e6i	−0.0910469	+	0.339792i
$259$			5.83148e6i			0.335645i
$260$	−5.45480e6	+	2.67072e6i	−0.310355	+	0.151953i
$261$	−9.24491e6			−0.519973
$262$	6.67328e6	+	1.78810e6i	0.371053	+	0.0994232i
$263$	6.89603e6	+	1.19443e7i	0.379081	+	0.656587i	0.990929	−	0.134388i	$-0.0429070\pi$
$263$	6.89603e6	+	1.19443e7i	0.379081	+	0.656587i	−0.611848	+	0.790975i	$0.709574\pi$
$264$	−4.27678e6	−	2.46920e6i	−0.232437	−	0.134198i
$265$	3.61999e6	−	3.61999e6i	0.194522	−	0.194522i
$266$	−1.58443e6	−	5.91318e6i	−0.0841839	−	0.314178i
$267$	3.05553e7	−	8.18726e6i	1.60529	−	0.430135i
$268$	9.45191e6	+	9.45191e6i	0.491038	+	0.491038i
$269$	−2.59768e6	+	4.49932e6i	−0.133453	+	0.231148i	−0.925006	−	0.379954i	$-0.875940\pi$
$269$	−2.59768e6	+	4.49932e6i	−0.133453	+	0.231148i	0.791552	+	0.611102i	$0.209273\pi$
$270$	−1.14278e6	+	659782.i	−0.0580590	+	0.0335204i
$271$	−8.57768e6	+	3.20123e7i	−0.430985	+	1.60846i	0.319511	+	0.947583i	$0.396481\pi$
$271$	−8.57768e6	+	3.20123e7i	−0.430985	+	1.60846i	−0.750496	+	0.660875i	$0.770185\pi$
$272$		−	4.44989e6i		−	0.221127i
$273$	−1.21489e7	−	8.16781e6i	−0.597104	−	0.401437i
$274$	−6.89440e6			−0.335154
$275$	−6.00607e6	−	1.60932e6i	−0.288797	−	0.0773828i
$276$	1.99444e7	+	3.45446e7i	0.948621	+	1.64306i
$277$	5.55508e6	+	3.20723e6i	0.261367	+	0.150900i	0.624958	−	0.780658i	$-0.285116\pi$
$277$	5.55508e6	+	3.20723e6i	0.261367	+	0.150900i	−0.363591	+	0.931559i	$0.618449\pi$
$278$	−687983.	+	687983.i	−0.0320216	+	0.0320216i
$279$	254947.	+	951476.i	0.0117392	+	0.0438112i
$280$	−2.86575e6	+	767875.i	−0.130546	+	0.0349797i
$281$	−2.21347e7	−	2.21347e7i	−0.997598	−	0.997598i	0.00239922	−	0.999997i	$-0.499236\pi$
$281$	−2.21347e7	−	2.21347e7i	−0.997598	−	0.997598i	−0.999997	+	0.00239922i	$0.999236\pi$
$282$	8.22337e6	−	1.42433e7i	0.366693	−	0.635131i
$283$	2.71144e7	−	1.56545e7i	1.19630	−	0.690684i	0.236571	−	0.971614i	$-0.423976\pi$
$283$	2.71144e7	−	1.56545e7i	1.19630	−	0.690684i	0.959728	+	0.280930i	$0.0906430\pi$
$284$	−4.87511e6	+	1.81942e7i	−0.212828	+	0.794286i
$285$			1.96616e7i			0.849343i
$286$	−856885.	+	2.50087e6i	−0.0366290	+	0.106904i
$287$	−4.01577e6			−0.169873
$288$	−1.09597e7	−	2.93665e6i	−0.458799	−	0.122935i
$289$	−1.08646e7	−	1.88181e7i	−0.450113	−	0.779618i
$290$	2.39656e6	+	1.38365e6i	0.0982638	+	0.0567327i
$291$	−8.38119e6	+	8.38119e6i	−0.340116	+	0.340116i
$292$	855756.	+	3.19373e6i	0.0343717	+	0.128277i
$293$	−1.82967e7	+	4.90260e6i	−0.727396	+	0.194905i	−0.603469	−	0.797386i	$-0.706215\pi$
$293$	−1.82967e7	+	4.90260e6i	−0.727396	+	0.194905i	−0.123927	+	0.992291i	$0.539549\pi$
$294$	4.85164e6	+	4.85164e6i	0.190918	+	0.190918i
$295$	9.12031e6	−	1.57968e7i	0.355258	−	0.615325i
$296$	8.00788e6	−	4.62335e6i	0.308775	−	0.178271i
$297$	1.28686e6	−	4.80262e6i	0.0491203	−	0.183320i
$298$		−	5.89080e6i		−	0.222600i
$299$	3.40473e7	−	2.96876e7i	1.27371	−	1.11061i
$300$	−2.58085e7			−0.955869
$301$	−1.32094e7	−	3.53945e6i	−0.484377	−	0.129788i
$302$	−19842.1	−	34367.5i	−0.000720388	−	0.00124775i
$303$	−2.37273e7	−	1.36989e7i	−0.852943	−	0.492447i
$304$	2.44674e7	−	2.44674e7i	0.870898	−	0.870898i
$305$	−2.51322e6	−	9.37948e6i	−0.0885792	−	0.330582i
$306$	1.59922e6	−	428509.i	0.0558140	−	0.0149553i
$307$	2.71510e6	+	2.71510e6i	0.0938363	+	0.0938363i	0.752467	−	0.658630i	$-0.228864\pi$
$307$	2.71510e6	+	2.71510e6i	0.0938363	+	0.0938363i	−0.658630	+	0.752467i	$0.728864\pi$
$308$	2.64211e6	−	4.57627e6i	0.0904272	−	0.156624i
$309$	2.56283e6	−	1.47965e6i	0.0868651	−	0.0501516i
$310$	76314.1	−	284808.i	0.00256165	−	0.00956020i
$311$			5.23932e6i			0.174178i	0.996201	+	0.0870891i	$0.0277565\pi$
$311$			5.23932e6i			0.174178i	−0.996201	+	0.0870891i	$0.972244\pi$
$312$	−1.58417e6	+	2.31587e7i	−0.0521601	+	0.762520i
$313$	3.09546e7			1.00947			0.504734	−	0.863275i	$-0.331590\pi$
$313$	3.09546e7			1.00947			0.504734	+	0.863275i	$0.331590\pi$
$314$	−7.85659e6	−	2.10517e6i	−0.253773	−	0.0679982i
$315$	1.96742e6	+	3.40767e6i	0.0629455	+	0.109025i
$316$	−2.16247e7	−	1.24850e7i	−0.685314	−	0.395666i
$317$	−2.16477e7	+	2.16477e7i	−0.679571	+	0.679571i	−0.959903	−	0.280332i	$-0.909555\pi$
$317$	−2.16477e7	+	2.16477e7i	−0.679571	+	0.679571i	0.280332	+	0.959903i	$0.409555\pi$
$318$	−2.39381e6	−	8.93383e6i	−0.0744404	−	0.277815i
$319$	−1.00717e7	+	2.69872e6i	−0.310265	+	0.0831352i
$320$	−3.85108e6	−	3.85108e6i	−0.117526	−	0.117526i
$321$	−2.08825e7	+	3.61696e7i	−0.631347	+	1.09353i
$322$	9.03325e6	−	5.21535e6i	0.270568	−	0.156212i
$323$	−4.84688e6	+	1.80888e7i	−0.143832	+	0.536788i
$324$		−	3.79697e7i		−	1.11635i
$325$	5.62027e6	+	2.86818e7i	0.163722	+	0.835519i
$326$	−1.84110e7			−0.531405
$327$	3.28807e7	+	8.81036e6i	0.940368	+	0.251971i
$328$	3.18381e6	+	5.51452e6i	0.0902247	+	0.156274i
$329$	3.22420e7	+	1.86149e7i	0.905386	+	0.522725i
$330$	1.38630e6	−	1.38630e6i	0.0385759	−	0.0385759i
$331$	−5.23754e6	−	1.95468e7i	−0.144425	−	0.539002i	−0.999780	−	0.0209602i	$-0.993328\pi$
$331$	−5.23754e6	−	1.95468e7i	−0.144425	−	0.539002i	0.855355	−	0.518042i	$-0.173339\pi$
$332$	2.01123e7	−	5.38907e6i	0.549601	−	0.147265i
$333$	−8.67170e6	−	8.67170e6i	−0.234840	−	0.234840i
$334$	−6.80957e6	+	1.17945e7i	−0.182760	+	0.316549i
$335$	−9.72229e6	+	5.61317e6i	−0.258603	+	0.149305i
$336$	4.94515e6	−	1.84556e7i	0.130365	−	0.486530i
$337$			5.57292e7i			1.45611i	0.685521	+	0.728053i	$0.259574\pi$
$337$			5.57292e7i			1.45611i	−0.685521	+	0.728053i	$0.740426\pi$
$338$	1.23289e7	−	1.55173e6i	0.319282	−	0.0401851i
$339$	6.82132e7			1.75093
$340$	4.14391e6	+	1.11036e6i	0.105432	+	0.0282505i
$341$	555498.	+	962150.i	0.0140094	+	0.0242650i
$342$	1.11493e7	+	6.43706e6i	0.278721	+	0.160920i
$343$	−2.73756e7	+	2.73756e7i	−0.678394	+	0.678394i
$344$	5.61233e6	+	2.09455e7i	0.137869	+	0.514536i
$345$	−3.23592e7	+	8.67061e6i	−0.788025	+	0.211151i
$346$	1.57972e7	+	1.57972e7i	0.381374	+	0.381374i
$347$	6.81417e6	−	1.18025e7i	0.163089	−	0.282478i	−0.772886	−	0.634545i	$-0.781188\pi$
$347$	6.81417e6	−	1.18025e7i	0.163089	−	0.282478i	0.935975	+	0.352066i	$0.114521\pi$
$348$	−3.74807e7	+	2.16395e7i	−0.889344	+	0.513463i
$349$	2.02019e7	−	7.53945e7i	0.475243	−	1.77363i	−0.145225	−	0.989399i	$-0.546391\pi$
$349$	2.02019e7	−	7.53945e7i	0.475243	−	1.77363i	0.620468	−	0.784232i	$-0.286943\pi$
$350$			6.74878e6i			0.157406i
$351$	−2.29348e7	+	4.49413e6i	−0.530363	+	0.103926i
$352$	−1.27972e7			−0.293418
$353$	1.63820e7	+	4.38955e6i	0.372429	+	0.0997920i	0.440178	−	0.897910i	$-0.354915\pi$
$353$	1.63820e7	+	4.38955e6i	0.372429	+	0.0997920i	−0.0677495	+	0.997702i	$0.521582\pi$
$354$	−1.64771e7	−	2.85392e7i	−0.371426	−	0.643328i
$355$	−1.37001e7	−	7.90973e6i	−0.306223	−	0.176798i
$356$	3.79516e7	−	3.79516e7i	0.841162	−	0.841162i
$357$	2.67635e6	+	9.98828e6i	0.0588218	+	0.219526i
$358$	1.10750e7	−	2.96753e6i	0.241375	−	0.0646763i
$359$	−2.34840e7	−	2.34840e7i	−0.507561	−	0.507561i	0.406216	−	0.913777i	$-0.366848\pi$
$359$	−2.34840e7	−	2.34840e7i	−0.507561	−	0.507561i	−0.913777	+	0.406216i	$0.866848\pi$
$360$	3.11964e6	−	5.40337e6i	0.0668647	−	0.115813i
$361$	−8.53675e7	+	4.92869e7i	−1.81456	+	1.04764i
$362$	3.94290e6	−	1.47151e7i	0.0831170	−	0.310197i
$363$		−	5.25170e7i		−	1.09794i
$364$	−2.47805e7	−	1.69510e6i	−0.513813	−	0.0351473i
$365$	−2.77688e6			−0.0571056
$366$	−1.69454e7	−	4.54049e6i	−0.345627	−	0.0926104i
$367$	−3.18205e7	−	5.51148e7i	−0.643738	−	1.11499i	−0.984591	−	0.174870i	$-0.944049\pi$
$367$	−3.18205e7	−	5.51148e7i	−0.643738	−	1.11499i	0.340853	−	0.940116i	$-0.389284\pi$
$368$	5.10586e7	+	2.94787e7i	1.02453	+	0.591514i
$369$	5.97165e6	−	5.97165e6i	0.118854	−	0.118854i
$370$	950101.	+	3.54582e6i	0.0187571	+	0.0700023i
$371$	2.02232e7	−	5.41878e6i	0.396029	−	0.106116i
$372$	3.26072e6	+	3.26072e6i	0.0633409	+	0.0633409i
$373$	−1.27798e7	+	2.21353e7i	−0.246263	+	0.426539i	−0.962486	−	0.271332i	$-0.912536\pi$
$373$	−1.27798e7	+	2.21353e7i	−0.246263	+	0.426539i	0.716223	+	0.697871i	$0.245869\pi$
$374$	1.61716e6	−	933667.i	0.0309128	−	0.0178475i
$375$	1.21991e7	−	4.55275e7i	0.231330	−	0.863336i
$376$		−	5.90335e7i		−	1.11054i
$377$	3.22108e7	+	3.69411e7i	0.601142	+	0.689423i
$378$	−5.39652e6			−0.0999167
$379$	3.62432e7	+	9.71133e6i	0.665746	+	0.178386i	0.575838	−	0.817564i	$-0.304676\pi$
$379$	3.62432e7	+	9.71133e6i	0.665746	+	0.178386i	0.0899082	+	0.995950i	$0.471343\pi$
$380$	1.66798e7	+	2.88902e7i	0.303976	+	0.526502i
$381$	5.88805e7	+	3.39947e7i	1.06463	+	0.614662i
$382$	−1.34033e6	+	1.34033e6i	−0.0240449	+	0.0240449i
$383$	3.87209e6	+	1.44508e7i	0.0689206	+	0.257215i	0.991786	−	0.127907i	$-0.0408259\pi$
$383$	3.87209e6	+	1.44508e7i	0.0689206	+	0.257215i	−0.922866	+	0.385122i	$0.874159\pi$
$384$	−6.67377e7	+	1.78823e7i	−1.17863	+	0.315813i
$385$	3.13812e6	+	3.13812e6i	0.0549905	+	0.0549905i
$386$	1.49988e6	−	2.59788e6i	0.0260793	−	0.0451707i
$387$	2.49063e7	−	1.43797e7i	0.429712	−	0.248094i
$388$	−5.20498e6	+	1.94252e7i	−0.0891095	+	0.332561i
$389$			3.23998e6i			0.0550420i	0.999621	+	0.0275210i	$0.00876130\pi$
$389$			3.23998e6i			0.0550420i	−0.999621	+	0.0275210i	$0.991239\pi$
$390$	−8.71789e6	−	2.98705e6i	−0.146966	−	0.0503557i
$391$	−3.19082e7			−0.533792
$392$	2.37885e7	+	6.37410e6i	0.394919	+	0.105818i
$393$	−4.53721e7	−	7.85868e7i	−0.747500	−	1.29471i
$394$	2.50697e7	+	1.44740e7i	0.409883	+	0.236646i
$395$	1.48289e7	−	1.48289e7i	0.240612	−	0.240612i
$396$	2.87619e6	+	1.07341e7i	0.0463161	+	0.172854i
$397$	−4.20284e7	+	1.12615e7i	−0.671693	+	0.179980i	−0.578517	−	0.815670i	$-0.696369\pi$
$397$	−4.20284e7	+	1.12615e7i	−0.671693	+	0.179980i	−0.0931757	+	0.995650i	$0.529702\pi$
$398$	−7.98546e6	−	7.98546e6i	−0.126663	−	0.126663i
$399$	−4.02042e7	+	6.96356e7i	−0.632925	+	1.09626i
$400$	−3.30355e7	+	1.90731e7i	−0.516180	+	0.298017i
$401$	6.35234e6	−	2.37072e7i	0.0985146	−	0.367661i	−0.899014	−	0.437919i	$-0.855716\pi$
$401$	6.35234e6	−	2.37072e7i	0.0985146	−	0.367661i	0.997529	+	0.0702579i	$0.0223822\pi$
$402$			2.02820e7i			0.312199i
$403$	2.91366e6	−	4.33383e6i	0.0445168	−	0.0662150i
$404$	−4.64857e7			−0.704977
$405$	3.08024e7	+	8.25347e6i	0.463681	+	0.124243i
$406$	5.65861e6	+	9.80101e6i	0.0845536	+	0.146451i
$407$	−1.19787e7	−	6.91588e6i	−0.177674	−	0.102580i
$408$	1.15942e7	−	1.15942e7i	0.170710	−	0.170710i
$409$	6.97679e6	+	2.60377e7i	0.101973	+	0.380569i	0.997984	−	0.0634628i	$-0.0202144\pi$
$409$	6.97679e6	+	2.60377e7i	0.101973	+	0.380569i	−0.896011	+	0.444032i	$0.853548\pi$
$410$	−2.44179e6	+	654275.i	−0.0354288	+	0.00949311i
$411$	6.40331e7	+	6.40331e7i	0.922315	+	0.922315i
$412$	2.51051e6	−	4.34833e6i	0.0358980	−	0.0621772i
$413$	6.46031e7	−	3.72986e7i	0.917072	−	0.529472i
$414$	−5.67740e6	+	2.11884e7i	−0.0800108	+	0.298604i
$415$			1.74872e7i			0.244668i
$416$	2.64511e7	+	5.40250e7i	0.367421	+	0.750438i
$417$	1.27796e7			0.176241
$418$	1.40255e7	+	3.75813e6i	0.192040	+	0.0514569i
$419$	3.40584e7	+	5.89909e7i	0.463002	+	0.801943i	0.999109	−	0.0422074i	$-0.0134390\pi$
$419$	3.40584e7	+	5.89909e7i	0.463002	+	0.801943i	−0.536107	+	0.844150i	$0.680106\pi$
$420$	1.59526e7	+	9.21023e6i	0.215320	+	0.124315i
$421$	8.72935e7	−	8.72935e7i	1.16986	−	1.16986i	0.187624	−	0.982241i	$-0.439921\pi$
$421$	8.72935e7	−	8.72935e7i	1.16986	−	1.16986i	0.982241	−	0.187624i	$-0.0600786\pi$
$422$	−1.89397e6	−	7.06839e6i	−0.0252020	−	0.0940553i
$423$	−7.56267e7	+	2.02641e7i	−0.999203	+	0.267736i
$424$	−2.34746e7	−	2.34746e7i	−0.307964	−	0.307964i
$425$	1.03225e7	−	1.78791e7i	0.134468	−	0.232905i
$426$	−2.47511e7	+	1.42900e7i	−0.320159	+	0.184844i
$427$	1.02781e7	−	3.83585e7i	0.132017	−	0.492695i
$428$			7.08624e7i			0.903825i
$429$	3.11859e7	−	1.52689e7i	0.394990	−	0.193391i
$430$	−8.60862e6			−0.108275
$431$	−9.75385e7	−	2.61354e7i	−1.21827	−	0.326435i	−0.408270	−	0.912861i	$-0.633868\pi$
$431$	−9.75385e7	−	2.61354e7i	−1.21827	−	0.326435i	−0.810003	+	0.586426i	$0.800534\pi$
$432$	−1.52514e7	−	2.64162e7i	−0.189172	−	0.327656i
$433$	1.67973e7	+	9.69793e6i	0.206907	+	0.119458i	0.599873	−	0.800095i	$-0.295218\pi$
$433$	1.67973e7	+	9.69793e6i	0.206907	+	0.119458i	−0.392966	+	0.919553i	$0.628551\pi$
$434$	852661.	−	852661.i	0.0104306	−	0.0104306i
$435$	−9.40755e6	−	3.51095e7i	−0.114290	−	0.426537i
$436$	5.57883e7	−	1.49484e7i	0.673107	−	0.180358i
$437$	−1.75445e8	−	1.75445e8i	−2.10231	−	2.10231i
$438$	−2.50841e6	+	4.34470e6i	−0.0298522	+	0.0517056i
$439$	3.41904e7	−	1.97399e7i	0.404121	−	0.233319i	−0.284140	−	0.958783i	$-0.591708\pi$
$439$	3.41904e7	−	1.97399e7i	0.404121	−	0.233319i	0.688260	+	0.725464i	$0.258375\pi$
$440$	1.82133e6	−	6.79730e6i	0.0213811	−	0.0797955i
$441$		−	3.26629e7i		−	0.380837i
$442$	−7.28419e6	−	4.89721e6i	−0.0843557	−	0.0567129i
$443$	−4.31028e7			−0.495786			−0.247893	−	0.968787i	$-0.579738\pi$
$443$	−4.31028e7			−0.495786			−0.247893	+	0.968787i	$0.579738\pi$
$444$	−5.54545e7	−	1.48590e7i	−0.633561	−	0.169762i
$445$	2.25381e7	+	3.90372e7i	0.255763	+	0.442995i
$446$	−1.61879e7	−	9.34608e6i	−0.182467	−	0.105348i
$447$	−5.47120e7	+	5.47120e7i	−0.612576	+	0.612576i
$448$	−5.76471e6	−	2.15142e7i	−0.0641126	−	0.239271i
$449$	−6.71882e7	+	1.80030e7i	−0.742256	+	0.198887i	−0.610081	−	0.792339i	$-0.708863\pi$
$449$	−6.71882e7	+	1.80030e7i	−0.742256	+	0.198887i	−0.132176	+	0.991226i	$0.542196\pi$
$450$	−1.00358e7	−	1.00358e7i	−0.110132	−	0.110132i
$451$	4.76253e6	−	8.24894e6i	0.0519168	−	0.0899226i
$452$	1.00231e8	−	5.78683e7i	1.08539	−	0.626651i
$453$	−134908.	+	503482.i	−0.00145125	+	0.00541614i
$454$			1.85601e7i			0.198341i
$455$	6.76166e6	−	1.97343e7i	0.0717826	−	0.209502i
$456$	1.27500e8			1.34467
$457$	8.40017e7	+	2.25082e7i	0.880115	+	0.235826i	0.670457	−	0.741949i	$-0.266098\pi$
$457$	8.40017e7	+	2.25082e7i	0.880115	+	0.235826i	0.209658	+	0.977775i	$0.432765\pi$
$458$	2.14683e7	+	3.71841e7i	0.223460	+	0.387044i
$459$	1.42966e7	+	8.25415e6i	0.147841	+	0.0853561i
$460$	−4.01921e7	+	4.01921e7i	−0.412921	+	0.412921i
$461$	−3.27309e7	−	1.22153e8i	−0.334083	−	1.24682i	−0.904859	−	0.425711i	$-0.860024\pi$
$461$	−3.27309e7	−	1.22153e8i	−0.334083	−	1.24682i	0.570776	−	0.821106i	$-0.306642\pi$
$462$	7.74462e6	−	2.07517e6i	0.0785370	−	0.0210439i
$463$	4.92350e7	+	4.92350e7i	0.496056	+	0.496056i	0.910208	−	0.414152i	$-0.135922\pi$
$463$	4.92350e7	+	4.92350e7i	0.496056	+	0.496056i	−0.414152	+	0.910208i	$0.635922\pi$
$464$	−3.19842e7	+	5.53983e7i	−0.320171	+	0.554552i
$465$	−3.35400e6	+	1.93643e6i	−0.0333583	+	0.0192594i
$466$	6.39967e6	−	2.38839e7i	0.0632411	−	0.236019i
$467$			1.23464e8i			1.21224i	0.795372	+	0.606121i	$0.207275\pi$
$467$			1.23464e8i			1.21224i	−0.795372	+	0.606121i	$0.792725\pi$
$468$	3.93704e7	−	3.43290e7i	0.384090	−	0.334907i
$469$	−4.59115e7			−0.445044
$470$	2.26375e7	+	6.06571e6i	0.218040	+	0.0584236i
$471$	5.34175e7	+	9.25218e7i	0.511235	+	0.885486i
$472$	−1.02438e8	−	5.91426e7i	−0.974171	−	0.562438i
$473$	2.29363e7	−	2.29363e7i	0.216740	−	0.216740i
$474$	−9.80599e6	−	3.65965e7i	−0.0920781	−	0.343640i
$475$	1.55064e8	−	4.15494e7i	1.44688	−	0.387689i
$476$	1.24061e7	+	1.24061e7i	0.115031	+	0.115031i
$477$	−2.20148e7	+	3.81308e7i	−0.202843	+	0.351335i
$478$	−3.23110e7	+	1.86548e7i	−0.295847	+	0.170807i
$479$	−5.58880e7	+	2.08577e8i	−0.508525	+	1.89784i	−0.0738112	+	0.997272i	$0.523516\pi$
$479$	−5.58880e7	+	2.08577e8i	−0.508525	+	1.89784i	−0.434714	+	0.900569i	$0.643150\pi$
$480$		−	4.46101e7i		−	0.403376i
$481$	−4.43703e6	+	6.48643e7i	−0.0398710	+	0.582868i
$482$	5.03904e6			0.0449994
$483$	−1.32337e8	−	3.54595e7i	−1.17446	−	0.314696i
$484$	−4.45525e7	−	7.71672e7i	−0.392949	−	0.680608i
$485$	−1.46271e7	−	8.44494e6i	−0.128213	−	0.0740238i
$486$	2.66209e7	−	2.66209e7i	0.231907	−	0.231907i
$487$	4.00706e7	+	1.49546e8i	0.346928	+	1.29475i	0.890344	+	0.455289i	$0.150464\pi$
$487$	4.00706e7	+	1.49546e8i	0.346928	+	1.29475i	−0.543416	+	0.839464i	$0.682869\pi$
$488$	−6.08233e7	+	1.62975e7i	−0.523372	+	0.140237i
$489$	1.70996e8	+	1.70996e8i	1.46238	+	1.46238i
$490$	−4.88854e6	+	8.46720e6i	−0.0415519	+	0.0719700i
$491$	−4.67388e6	+	2.69846e6i	−0.0394851	+	0.0227967i	−0.519613	−	0.854402i	$-0.673924\pi$
$491$	−4.67388e6	+	2.69846e6i	−0.0394851	+	0.0227967i	0.480128	+	0.877199i	$0.340590\pi$
$492$	1.02325e7	−	3.81880e7i	0.0859181	−	0.320651i
$493$		−	3.46202e7i		−	0.288927i
$494$	−1.31246e7	−	6.69786e7i	−0.108870	−	0.555591i
$495$	−9.33308e6			−0.0769501
$496$	6.58356e6	+	1.76406e6i	0.0539530	+	0.0144567i
$497$	−3.23478e7	−	5.60280e7i	−0.263497	−	0.456390i
$498$	2.73605e7	+	1.57966e7i	0.221532	+	0.127901i
$499$	−1.25075e8	+	1.25075e8i	−1.00663	+	1.00663i	−0.00665368	+	0.999978i	$0.502118\pi$
$499$	−1.25075e8	+	1.25075e8i	−1.00663	+	1.00663i	−0.999978	+	0.00665368i	$0.997882\pi$
$500$	−2.06980e7	−	7.72460e7i	−0.165584	−	0.617968i
$501$	1.72789e8	−	4.62987e7i	1.37405	−	0.368176i
$502$	−2.89287e7	−	2.89287e7i	−0.228675	−	0.228675i
$503$	7.06862e7	−	1.22432e8i	0.555432	−	0.962036i	−0.442438	−	0.896799i	$-0.645886\pi$
$503$	7.06862e7	−	1.22432e8i	0.555432	−	0.962036i	0.997870	−	0.0652367i	$-0.0207803\pi$
$504$	2.20977e7	−	1.27581e7i	0.172606	−	0.0996542i
$505$	1.01046e7	−	3.77109e7i	0.0784594	−	0.292814i
$506$			2.47407e7i			0.190968i
$507$	−1.28919e8	−	1.00095e8i	−0.989222	−	0.768051i
$508$	1.15357e8			0.879938
$509$	3.61400e7	+	9.68369e6i	0.274053	+	0.0734324i	0.393228	−	0.919441i	$-0.371358\pi$
$509$	3.61400e7	+	9.68369e6i	0.274053	+	0.0734324i	−0.119175	+	0.992873i	$0.538025\pi$
$510$	3.25470e6	+	5.63731e6i	0.0245358	+	0.0424973i
$511$	−9.83493e6	−	5.67820e6i	−0.0737069	−	0.0425547i
$512$	−9.60608e7	+	9.60608e7i	−0.715709	+	0.715709i
$513$	3.32241e7	+	1.23994e8i	0.246094	+	0.918434i
$514$	3.90702e7	−	1.04688e7i	0.287711	−	0.0770919i
$515$	2.98182e6	+	2.98182e6i	0.0218303	+	0.0218303i
$516$	6.73168e7	−	1.16596e8i	0.489976	−	0.848663i
$517$	−7.64751e7	+	4.41529e7i	−0.553412	+	0.319512i
$518$	−3.88555e6	+	1.45011e7i	−0.0279553	+	0.104330i
$519$		−	2.93439e8i		−	2.09901i
$520$	−3.24603e7	+	6.36068e6i	−0.230857	+	0.0452370i
$521$	−2.05966e8			−1.45640			−0.728202	−	0.685363i	$-0.759644\pi$
$521$	−2.05966e8			−1.45640			−0.728202	+	0.685363i	$0.759644\pi$
$522$	−2.29892e7	−	6.15994e6i	−0.161626	−	0.0433077i
$523$	−2.36020e7	−	4.08798e7i	−0.164985	−	0.285762i	0.771665	−	0.636029i	$-0.219424\pi$
$523$	−2.36020e7	−	4.08798e7i	−0.164985	−	0.285762i	−0.936650	+	0.350267i	$0.886091\pi$
$524$	−1.33337e8	−	7.69823e7i	−0.926740	−	0.535054i
$525$	6.26807e7	−	6.26807e7i	0.433168	−	0.433168i
$526$	9.18973e6	+	3.42965e7i	0.0631459	+	0.235664i
$527$	−3.56307e6	+	954721.i	−0.0243440	+	0.00652296i
$528$	3.20455e7	+	3.20455e7i	0.217703	+	0.217703i
$529$	1.37361e8	−	2.37916e8i	0.927890	−	1.60715i
$530$	1.14138e7	−	6.58976e6i	0.0766660	−	0.0442631i
$531$	−4.06031e7	+	1.51533e8i	−0.271191	+	1.01210i
$532$			1.36428e8i			0.906083i
$533$	−4.46679e7	−	3.05551e6i	−0.294995	−	0.0201791i
$534$	8.14367e7			0.534806
$535$	−5.74861e7	−	1.54034e7i	−0.375406	−	0.100590i
$536$	3.63998e7	+	6.30463e7i	0.236377	+	0.409416i
$537$	−1.30422e8	−	7.52994e7i	−0.842228	−	0.486260i
$538$	−9.45756e6	+	9.45756e6i	−0.0607340	+	0.0607340i
$539$	−9.53475e6	−	3.55842e7i	−0.0608896	−	0.227243i
$540$	2.84053e7	−	7.61119e6i	0.180393	−	0.0483360i
$541$	8.56938e7	+	8.56938e7i	0.541200	+	0.541200i	0.923881	−	0.382681i	$-0.124999\pi$
$541$	8.56938e7	+	8.56938e7i	0.541200	+	0.541200i	−0.382681	+	0.923881i	$0.624999\pi$
$542$	−4.26600e7	+	7.38894e7i	−0.267931	+	0.464071i
$543$	−1.73290e8	+	1.00049e8i	−1.08236	+	0.624904i
$544$	1.09971e7	−	4.10417e7i	0.0683096	−	0.254935i
$545$			4.85069e7i			0.299650i
$546$	−2.47683e7	−	2.84057e7i	−0.152166	−	0.174513i
$547$	1.03787e8			0.634132			0.317066	−	0.948404i	$-0.397302\pi$
$547$	1.03787e8			0.634132			0.317066	+	0.948404i	$0.397302\pi$
$548$	1.48411e8	+	3.97666e7i	0.901828	+	0.241644i
$549$	4.17569e7	+	7.23251e7i	0.252355	+	0.437091i
$550$	−1.38629e7	−	8.00376e6i	−0.0833233	−	0.0481067i
$551$	1.90357e8	−	1.90357e8i	1.13792	−	1.13792i
$552$	5.62265e7	+	2.09840e8i	0.334290	+	1.24759i
$553$	8.28420e7	−	2.21974e7i	0.489863	−	0.131258i
$554$	1.16768e7	+	1.16768e7i	0.0686741	+	0.0686741i
$555$	2.41083e7	−	4.17568e7i	0.141022	−	0.244258i
$556$	1.87780e7	−	1.08415e7i	0.109251	−	0.0630760i
$557$	−3.35268e7	+	1.25124e8i	−0.194011	+	0.724058i	0.798510	+	0.601982i	$0.205622\pi$
$557$	−3.35268e7	+	1.25124e8i	−0.194011	+	0.724058i	−0.992521	+	0.122076i	$0.961045\pi$
$558$			2.53590e6i			0.0145958i
$559$	−1.44237e8	−	4.94204e7i	−0.825734	−	0.282925i
$560$	2.72263e7			0.155033
$561$	−2.36913e7	−	6.34807e6i	−0.134184	−	0.0359545i
$562$	−4.02937e7	−	6.97907e7i	−0.227001	−	0.393178i
$563$	−8.47000e7	−	4.89016e7i	−0.474633	−	0.274030i	0.243544	−	0.969890i	$-0.421690\pi$
$563$	−8.47000e7	−	4.89016e7i	−0.474633	−	0.274030i	−0.718177	+	0.695860i	$0.755023\pi$
$564$	−2.59173e8	+	2.59173e8i	−1.44462	+	1.44462i
$565$	2.51577e7	+	9.38898e7i	0.139484	+	0.520563i
$566$	7.78556e7	−	2.08614e7i	0.429379	−	0.115052i
$567$	9.22164e7	+	9.22164e7i	0.505894	+	0.505894i
$568$	−5.12923e7	+	8.88409e7i	−0.279903	+	0.484806i
$569$	2.49325e8	−	1.43948e8i	1.35341	−	0.781392i	0.364685	−	0.931131i	$-0.381177\pi$
$569$	2.49325e8	−	1.43948e8i	1.35341	−	0.781392i	0.988726	+	0.149739i	$0.0478435\pi$
$570$	−1.31006e7	+	4.88922e7i	−0.0707403	+	0.264007i
$571$		−	2.36093e8i		−	1.26816i	−0.773267	−	0.634080i	$-0.781379\pi$
$571$		−	2.36093e8i		−	1.26816i	0.773267	−	0.634080i	$-0.218621\pi$
$572$	3.28705e7	−	4.88921e7i	0.175638	−	0.261246i
$573$	2.48972e7			0.132339
$574$	−9.98598e6	−	2.67574e6i	−0.0528026	−	0.0141484i
$575$	1.36765e8	+	2.36883e8i	0.719400	+	1.24604i
$576$	4.05650e7	+	2.34202e7i	0.212268	+	0.122553i
$577$	−9.29466e7	+	9.29466e7i	−0.483845	+	0.483845i	−0.906357	−	0.422512i	$-0.861148\pi$
$577$	−9.29466e7	+	9.29466e7i	−0.483845	+	0.483845i	0.422512	+	0.906357i	$0.361148\pi$
$578$	−1.44783e7	−	5.40339e7i	−0.0749782	−	0.279823i
$579$	−3.80588e7	+	1.01978e7i	−0.196074	+	0.0525378i
$580$	−4.36081e7	−	4.36081e7i	−0.223503	−	0.223503i
$581$	−3.57581e7	+	6.19348e7i	−0.182325	+	0.315796i
$582$	−2.64258e7	+	1.52570e7i	−0.134048	+	0.0773925i
$583$	−1.28529e7	+	4.79675e7i	−0.0648626	+	0.242070i
$584$			1.80073e7i			0.0904086i
$585$	1.92910e7	+	3.94008e7i	0.0963579	+	0.196806i
$586$	−4.87649e7			−0.242334
$587$	8.08230e7	+	2.16565e7i	0.399596	+	0.107071i	0.453020	−	0.891501i	$-0.350347\pi$
$587$	8.08230e7	+	2.16565e7i	0.399596	+	0.107071i	−0.0534238	+	0.998572i	$0.517013\pi$
$588$	−7.64538e7	−	1.32422e8i	−0.376069	−	0.651370i
$589$	−2.48408e7	−	1.43418e7i	−0.121568	−	0.0701873i
$590$	3.32049e7	−	3.32049e7i	0.161676	−	0.161676i
$591$	−9.84096e7	−	3.67270e8i	−0.476733	−	1.77919i
$592$	−8.19645e7	+	2.19623e7i	−0.395058	+	0.105855i
$593$	−2.03498e8	−	2.03498e8i	−0.975879	−	0.975879i	0.0238368	−	0.999716i	$-0.492412\pi$
$593$	−2.03498e8	−	2.03498e8i	−0.975879	−	0.975879i	−0.999716	+	0.0238368i	$0.992412\pi$
$594$	6.40003e6	−	1.10852e7i	0.0305367	−	0.0528912i
$595$	−1.27610e7	+	7.36754e6i	−0.0605804	+	0.0349761i
$596$	−3.39779e7	+	1.26807e8i	−0.160493	+	0.598970i
$597$			1.48333e8i			0.697133i
$598$	1.04446e8	−	5.11378e7i	0.488415	−	0.239132i
$599$	3.68580e7			0.171495			0.0857474	−	0.996317i	$-0.472672\pi$
$599$	3.68580e7			0.171495			0.0857474	+	0.996317i	$0.472672\pi$
$600$	−1.35769e8	−	3.63792e7i	−0.628560	−	0.168422i
$601$	7.48450e7	+	1.29635e8i	0.344778	+	0.597173i	0.985313	−	0.170756i	$-0.0546209\pi$
$601$	7.48450e7	+	1.29635e8i	0.344778	+	0.597173i	−0.640536	+	0.767929i	$0.721288\pi$
$602$	−3.04893e7	−	1.76030e7i	−0.139752	−	0.0806858i
$603$	6.82726e7	−	6.82726e7i	0.311383	−	0.311383i
$604$	228896.	+	854253.i	0.00103879	+	0.00387682i
$605$	7.22852e7	−	1.93688e7i	0.326425	−	0.0874653i
$606$	−4.98746e7	−	4.98746e7i	−0.224110	−	0.224110i
$607$	6.21691e7	−	1.07680e8i	0.277977	−	0.481470i	−0.692905	−	0.721029i	$-0.743669\pi$
$607$	6.21691e7	−	1.07680e8i	0.277977	−	0.481470i	0.970882	+	0.239559i	$0.0770028\pi$
$608$	2.86132e8	−	1.65198e8i	1.27308	−	0.735013i
$609$	3.84733e7	−	1.43584e8i	0.170337	−	0.635705i
$610$		−	2.49984e7i		−	0.110134i
$611$	3.44468e8	+	2.31588e8i	1.51017	+	1.01530i
$612$	−3.68968e7			−0.160966
$613$	−3.52229e8	−	9.43795e7i	−1.52913	−	0.409728i	−0.606393	−	0.795165i	$-0.707384\pi$
$613$	−3.52229e8	−	9.43795e7i	−1.52913	−	0.409728i	−0.922734	+	0.385436i	$0.874051\pi$
$614$	4.94252e6	+	8.56070e6i	0.0213522	+	0.0369832i
$615$	2.87553e7	+	1.66019e7i	0.123621	+	0.0713727i
$616$	2.03498e7	−	2.03498e7i	0.0870600	−	0.0870600i
$617$	−4.02260e7	−	1.50125e8i	−0.171258	−	0.639144i	−0.997159	−	0.0753284i	$-0.975999\pi$
$617$	−4.02260e7	−	1.50125e8i	−0.171258	−	0.639144i	0.825901	−	0.563816i	$-0.190667\pi$
$618$	7.35887e6	−	1.97180e6i	0.0311778	−	0.00835407i
$619$	−3.74477e7	−	3.74477e7i	−0.157889	−	0.157889i	0.623741	−	0.781631i	$-0.285612\pi$
$619$	−3.74477e7	−	3.74477e7i	−0.157889	−	0.157889i	−0.781631	+	0.623741i	$0.785612\pi$
$620$	−3.28552e6	+	5.69069e6i	−0.0137857	+	0.0238775i
$621$	−1.89419e8	+	1.09361e8i	−0.790948	+	0.456654i
$622$	−3.49099e6	+	1.30286e7i	−0.0145070	+	0.0541409i
$623$			1.84345e8i			0.762372i
$624$	6.90479e7	−	2.01521e8i	0.284182	−	0.829404i
$625$	−1.40700e8			−0.576305
$626$	7.69745e7	+	2.06253e7i	0.313779	+	0.0840769i
$627$	−9.53607e7	−	1.65170e8i	−0.386871	−	0.670081i
$628$	1.56981e8	+	9.06329e7i	0.633822	+	0.365938i
$629$	3.24736e7	−	3.24736e7i	0.130490	−	0.130490i
$630$	2.62180e6	+	9.78471e6i	0.0104852	+	0.0391315i
$631$	−8.23230e7	+	2.20584e7i	−0.327667	+	0.0877981i	−0.418903	−	0.908031i	$-0.637585\pi$
$631$	−8.23230e7	+	2.20584e7i	−0.327667	+	0.0877981i	0.0912354	+	0.995829i	$0.470918\pi$
$632$	−9.61611e7	−	9.61611e7i	−0.380933	−	0.380933i
$633$	−4.80585e7	+	8.32397e7i	−0.189478	+	0.328186i
$634$	−6.82552e7	+	3.94071e7i	−0.267835	+	0.154635i
$635$	−2.50751e7	+	9.35816e7i	−0.0979314	+	0.365485i
$636$			2.06120e8i			0.801213i
$637$	−1.30516e8	+	1.13803e8i	−0.504945	+	0.440286i
$638$	−2.68435e7			−0.103366
$639$	1.31419e8	+	3.52136e7i	0.503682	+	0.134961i
$640$	−4.92270e7	−	8.52636e7i	−0.187786	−	0.325255i
$641$	−6.50975e7	−	3.75841e7i	−0.247167	−	0.142702i	0.371299	−	0.928513i	$-0.378912\pi$
$641$	−6.50975e7	−	3.75841e7i	−0.247167	−	0.142702i	−0.618466	+	0.785811i	$0.712246\pi$
$642$	−7.60284e7	+	7.60284e7i	−0.287323	+	0.287323i
$643$	−2.11559e7	−	7.89549e7i	−0.0795791	−	0.296993i	0.914653	−	0.404239i	$-0.132464\pi$
$643$	−2.11559e7	−	7.89549e7i	−0.0795791	−	0.296993i	−0.994233	+	0.107246i	$0.965797\pi$
$644$	−2.24534e8	+	6.01638e7i	−0.840669	+	0.225257i
$645$	7.99543e7	+	7.99543e7i	0.297963	+	0.297963i
$646$	−2.41054e7	+	4.17517e7i	−0.0894162	+	0.154873i
$647$	3.30237e8	−	1.90663e8i	1.21931	−	0.703968i	0.254538	−	0.967063i	$-0.418077\pi$
$647$	3.30237e8	−	1.90663e8i	1.21931	−	0.703968i	0.964770	+	0.263095i	$0.0847433\pi$
$648$	5.35214e7	−	1.99745e8i	0.196699	−	0.734091i
$649$			1.76938e8i			0.647272i
$650$	−5.13499e6	+	7.50675e7i	−0.0186982	+	0.273346i
$651$	−1.58385e7			−0.0574079
$652$	3.96322e8	+	1.06194e8i	1.42990	+	0.383140i
$653$	1.68195e8	+	2.91323e8i	0.604053	+	1.04625i	0.992200	+	0.124653i	$0.0397817\pi$
$653$	1.68195e8	+	2.91323e8i	0.604053	+	1.04625i	−0.388148	+	0.921597i	$0.626885\pi$
$654$	7.58937e7	+	4.38172e7i	0.271314	+	0.156643i
$655$	9.14344e7	−	9.14344e7i	0.325376	−	0.325376i
$656$	−1.51241e7	−	5.64438e7i	−0.0535743	−	0.199942i
$657$	2.30688e7	−	6.18126e6i	0.0813445	−	0.0217962i
$658$	6.77725e7	+	6.77725e7i	0.237890	+	0.237890i
$659$	−2.61457e8	+	4.52857e8i	−0.913575	+	1.58236i	−0.104601	+	0.994514i	$0.533356\pi$
$659$	−2.61457e8	+	4.52857e8i	−0.913575	+	1.58236i	−0.808974	+	0.587844i	$0.799977\pi$
$660$	−3.78381e7	+	2.18459e7i	−0.131613	+	0.0759866i
$661$	6.57527e7	−	2.45392e8i	0.227672	−	0.849683i	−0.753645	−	0.657282i	$-0.771706\pi$
$661$	6.57527e7	−	2.45392e8i	0.227672	−	0.849683i	0.981316	−	0.192401i	$-0.0616273\pi$
$662$		−	5.20965e7i		−	0.179570i
$663$	2.21695e7	+	1.13137e8i	0.0760704	+	0.388208i
$664$	1.13400e8			0.387354
$665$	−1.10675e8	−	2.96553e7i	−0.376344	−	0.100841i
$666$	−1.57858e7	−	2.73418e7i	−0.0534372	−	0.0925560i
$667$	3.97237e8	+	2.29345e8i	1.33866	+	0.772878i
$668$	2.14615e8	−	2.14615e8i	0.719997	−	0.719997i
$669$	6.35446e7	+	2.37152e8i	0.212227	+	0.792042i
$670$	−2.79164e7	+	7.48018e6i	−0.0928186	+	0.0248707i
$671$	6.66042e7	+	6.66042e7i	0.220462	+	0.220462i
$672$	9.12193e7	−	1.57996e8i	0.300593	−	0.520642i
$673$	−3.64176e8	+	2.10257e8i	−1.19472	+	0.689772i	−0.959373	−	0.282140i	$-0.908956\pi$
$673$	−3.64176e8	+	2.10257e8i	−1.19472	+	0.689772i	−0.235346	+	0.971912i	$0.575622\pi$
$674$	−3.71327e7	+	1.38581e8i	−0.121277	+	0.452610i
$675$		−	1.41516e8i		−	0.460143i
$676$	−2.74346e8	−	3.77097e7i	−0.888094	−	0.122071i
$677$	−1.62659e8			−0.524218			−0.262109	−	0.965038i	$-0.584418\pi$
$677$	−1.62659e8			−0.524218			−0.262109	+	0.965038i	$0.584418\pi$
$678$	1.69625e8	+	4.54509e7i	0.544253	+	0.145832i
$679$	−3.45366e7	−	5.98191e7i	−0.110324	−	0.191087i
$680$	2.02344e7	+	1.16824e7i	0.0643524	+	0.0371538i
$681$	1.72381e8	−	1.72381e8i	0.545818	−	0.545818i
$682$	740263.	+	2.76270e6i	0.00233364	+	0.00870925i
$683$	−3.66101e8	+	9.80965e7i	−1.14905	+	0.307887i	−0.782585	−	0.622544i	$-0.786099\pi$
$683$	−3.66101e8	+	9.80965e7i	−1.14905	+	0.307887i	−0.366466	+	0.930431i	$0.619432\pi$
$684$	−2.02875e8	−	2.02875e8i	−0.633957	−	0.633957i
$685$	−6.45201e7	+	1.11752e8i	−0.200735	+	0.347684i
$686$	−8.63152e7	+	4.98341e7i	−0.267371	+	0.154367i
$687$	1.45964e8	−	5.44746e8i	0.450169	−	1.68006i
$688$		−	1.98995e8i		−	0.611050i
$689$	2.29068e8	−	4.48864e7i	0.700335	−	0.137233i
$690$	−8.62445e7			−0.262533
$691$	−4.82179e8	−	1.29199e8i	−1.46142	−	0.391585i	−0.561437	−	0.827519i	$-0.689751\pi$
$691$	−4.82179e8	−	1.29199e8i	−1.46142	−	0.391585i	−0.899979	+	0.435934i	$0.856418\pi$
$692$	−2.48937e8	−	4.31172e8i	−0.751227	−	1.30116i
$693$	−3.30551e7	−	1.90844e7i	−0.0993205	−	0.0573427i
$694$	2.48088e7	−	2.48088e7i	0.0742211	−	0.0742211i
$695$	4.71323e6	+	1.75900e7i	0.0140399	+	0.0523976i
$696$	−2.27675e8	+	6.10053e7i	−0.675285	+	0.180942i
$697$	2.23625e7	+	2.23625e7i	0.0660423	+	0.0660423i
$698$	1.00472e8	−	1.74022e8i	0.295445	−	0.511726i
$699$	−2.81265e8	+	1.62388e8i	−0.823538	+	0.475470i
$700$	3.89267e7	−	1.45276e8i	0.113489	−	0.423546i
$701$		−	2.54219e8i		−	0.737996i	−0.929430	−	0.368998i	$-0.879701\pi$
$701$		−	2.54219e8i		−	0.737996i	0.929430	−	0.368998i	$-0.120299\pi$
$702$	−6.00261e7	−	4.10608e6i	−0.173512	−	0.0118691i
$703$	3.57108e8			1.02786
$704$	5.10297e7	+	1.36734e7i	0.146253	+	0.0391884i
$705$	−1.53914e8	−	2.66587e8i	−0.439250	−	0.760803i
$706$	3.78122e7	+	2.18309e7i	0.107453	+	0.0620379i
$707$	1.12899e8	−	1.12899e8i	0.319472	−	0.319472i
$708$	1.90079e8	+	7.09383e8i	0.535591	+	1.99885i
$709$	3.25675e8	−	8.72644e7i	0.913789	−	0.244849i	0.228860	−	0.973459i	$-0.426500\pi$
$709$	3.25675e8	−	8.72644e7i	0.913789	−	0.244849i	0.684929	+	0.728610i	$0.259833\pi$
$710$	−2.87975e7	−	2.87975e7i	−0.0804598	−	0.0804598i
$711$	−9.01813e7	+	1.56199e8i	−0.250904	+	0.434579i
$712$	2.53145e8	−	1.46153e8i	0.701342	−	0.404920i
$713$	1.26493e7	−	4.72078e7i	0.0348978	−	0.130240i
$714$			2.66210e7i			0.0731358i
$715$	3.25180e7	+	3.72934e7i	0.0889622	+	0.102027i
$716$	−2.55519e8			−0.696121
$717$	4.73356e8	+	1.26835e8i	1.28419	+	0.344098i
$718$	−4.27498e7	−	7.40448e7i	−0.115494	−	0.200042i
$719$	4.40096e8	+	2.54090e8i	1.18403	+	0.683598i	0.956942	−	0.290278i	$-0.0937476\pi$
$719$	4.40096e8	+	2.54090e8i	1.18403	+	0.683598i	0.227083	+	0.973875i	$0.427081\pi$
$720$	−4.04869e7	+	4.04869e7i	−0.108472	+	0.108472i
$721$	4.46349e6	+	1.66580e7i	0.0119088	+	0.0444444i
$722$	−2.45123e8	+	6.56804e7i	−0.651286	+	0.174512i
$723$	−4.68011e7	−	4.68011e7i	−0.123834	−	0.123834i
$724$	−1.69752e8	+	2.94019e8i	−0.447300	+	0.774747i
$725$	−2.57017e8	+	1.48389e8i	−0.674446	+	0.389392i
$726$	3.49924e7	−	1.30593e8i	0.0914458	−	0.341281i
$727$		−	3.97223e8i		−	1.03379i	−0.856050	−	0.516893i	$-0.827088\pi$
$727$		−	3.97223e8i		−	1.03379i	0.856050	−	0.516893i	$-0.172912\pi$
$728$	−1.27972e8	−	4.38474e7i	−0.331680	−	0.113645i
$729$	−1.20352e7			−0.0310650
$730$	−6.90524e6	−	1.85025e6i	−0.0177505	−	0.00475623i
$731$	5.38487e7	+	9.32688e7i	0.137855	+	0.238772i
$732$	3.38581e8	+	1.95480e8i	0.863236	+	0.498390i
$733$	−2.50473e8	+	2.50473e8i	−0.635989	+	0.635989i	−0.949563	−	0.313575i	$-0.898473\pi$
$733$	−2.50473e8	+	2.50473e8i	−0.635989	+	0.635989i	0.313575	+	0.949563i	$0.398473\pi$
$734$	−4.24044e7	−	1.58255e8i	−0.107232	−	0.400194i
$735$	1.24044e8	−	3.32375e7i	0.312402	−	0.0837080i
$736$	3.98068e8	+	3.98068e8i	0.998443	+	0.998443i
$737$	5.44489e7	−	9.43083e7i	0.136015	−	0.235585i
$738$	1.88286e7	−	1.08707e7i	0.0468434	−	0.0270451i
$739$	1.84240e8	−	6.87591e8i	0.456509	−	1.70372i	−0.227103	−	0.973871i	$-0.572925\pi$
$739$	1.84240e8	−	6.87591e8i	0.456509	−	1.70372i	0.683612	−	0.729845i	$-0.260408\pi$
$740$		−	8.18086e7i		−	0.201885i
$741$	−5.00180e8	+	7.43975e8i	−1.22934	+	1.82854i
$742$	5.38993e7			0.131938
$743$	−2.69928e8	−	7.23271e7i	−0.658085	−	0.176333i	−0.0857035	−	0.996321i	$-0.527314\pi$
$743$	−2.69928e8	−	7.23271e7i	−0.658085	−	0.176333i	−0.572382	+	0.819987i	$0.693980\pi$
$744$	1.25572e7	+	2.17497e7i	0.0304912	+	0.0528122i
$745$	−9.54848e7	−	5.51282e7i	−0.230922	−	0.133323i
$746$	−4.65283e7	+	4.65283e7i	−0.112073	+	0.112073i
$747$	−3.89261e7	−	1.45274e8i	−0.0933854	−	0.348519i
$748$	−4.01968e7	+	1.07707e7i	−0.0960476	+	0.0257359i
$749$	−1.72103e8	−	1.72103e8i	−0.409583	−	0.409583i
$750$	6.06705e7	−	1.05084e8i	0.143812	−	0.249089i
$751$	−3.26160e8	+	1.88309e8i	−0.770037	+	0.444581i	−0.832888	−	0.553442i	$-0.813314\pi$
$751$	−3.26160e8	+	1.88309e8i	−0.770037	+	0.444581i	0.0628509	+	0.998023i	$0.479981\pi$
$752$	−1.40214e8	+	5.23284e8i	−0.329713	+	1.23051i
$753$			5.37363e8i			1.25859i
$754$	5.54841e7	+	1.13323e8i	0.129436	+	0.264366i
$755$	−742756.			−0.00172586
$756$	1.16167e8	+	3.11269e7i	0.268855	+	0.0720394i
$757$	−2.35032e7	−	4.07087e7i	−0.0541800	−	0.0938425i	0.837663	−	0.546187i	$-0.183921\pi$
$757$	−2.35032e7	−	4.07087e7i	−0.0541800	−	0.0938425i	−0.891843	+	0.452344i	$0.850588\pi$
$758$	8.36548e7	+	4.82981e7i	0.192080	+	0.110898i
$759$	2.29784e8	−	2.29784e8i	0.525527	−	0.525527i
$760$	4.70230e7	+	1.75492e8i	0.107120	+	0.399777i
$761$	1.73881e8	−	4.65914e7i	0.394548	−	0.105719i	−0.0560900	−	0.998426i	$-0.517863\pi$
$761$	1.73881e8	−	4.65914e7i	0.394548	−	0.105719i	0.450638	+	0.892707i	$0.351197\pi$
$762$	1.23767e8	+	1.23767e8i	0.279730	+	0.279730i
$763$	−9.91873e7	+	1.71797e8i	−0.223297	+	0.386761i
$764$	3.65834e7	−	2.11214e7i	0.0820358	−	0.0473634i
$765$	8.02027e6	−	2.99321e7i	0.0179145	−	0.0668578i
$766$			3.85147e7i			0.0856921i
$767$	7.46968e8	−	3.65722e8i	1.65545	−	0.810522i
$768$	6.67379e7			0.147329
$769$	6.46514e8	+	1.73233e8i	1.42167	+	0.380935i	0.886076	−	0.463540i	$-0.153421\pi$
$769$	6.46514e8	+	1.73233e8i	1.42167	+	0.380935i	0.535594	+	0.844476i	$0.320088\pi$
$770$	5.71258e6	+	9.89448e6i	0.0125130	+	0.0216731i
$771$	−4.60104e8	−	2.65641e8i	−1.00391	−	0.579605i
$772$	−4.72714e7	+	4.72714e7i	−0.102742	+	0.102742i
$773$	−1.51772e8	−	5.66423e8i	−0.328590	−	1.22631i	−0.910653	−	0.413171i	$-0.864421\pi$
$773$	−1.51772e8	−	5.66423e8i	−0.328590	−	1.22631i	0.582063	−	0.813144i	$-0.302246\pi$
$774$	7.15156e7	−	1.91625e7i	0.154233	−	0.0413267i
$775$	2.23598e7	+	2.23598e7i	0.0480355	+	0.0480355i
$776$	−5.47630e7	+	9.48523e7i	−0.117193	+	0.202984i
$777$	1.70770e8	−	9.85939e7i	0.364039	−	0.210178i
$778$	−2.15882e6	+	8.05683e6i	−0.00458435	+	0.0171090i
$779$			2.45918e8i			0.520208i
$780$	1.70435e8	+	1.14584e8i	0.359149	+	0.241458i
$781$	1.53452e8			0.322122
$782$	−7.93457e7	−	2.12606e7i	−0.165922	−	0.0444586i
$783$	−1.18656e8	−	2.05518e8i	−0.247175	−	0.428119i
$784$	−1.95726e8	−	1.13002e8i	−0.406163	−	0.234498i
$785$	−1.07648e8	+	1.07648e8i	−0.222534	+	0.222534i
$786$	−6.04634e7	−	2.25653e8i	−0.124516	−	0.464700i
$787$	−6.86549e8	+	1.83960e8i	−1.40847	+	0.377398i	−0.881379	−	0.472410i	$-0.843384\pi$
$787$	−6.86549e8	+	1.83960e8i	−1.40847	+	0.377398i	−0.527091	+	0.849809i	$0.676717\pi$
$788$	−4.56172e8	−	4.56172e8i	−0.932287	−	0.932287i
$789$	2.33185e8	−	4.03887e8i	0.474754	−	0.822298i
$790$	4.67554e7	−	2.69942e7i	0.0948310	−	0.0547507i
$791$	−1.02885e8	+	3.83974e8i	−0.207886	+	0.775840i
$792$			6.05223e7i			0.121826i
$793$	1.43511e8	−	4.18846e8i	0.287783	−	0.839914i
$794$	−1.12015e8			−0.223777
$795$	−1.67212e8	−	4.48043e7i	−0.332786	−	0.0891698i
$796$	1.25838e8	+	2.17957e8i	0.249500	+	0.432147i
$797$	−2.40443e8	−	1.38820e8i	−0.474938	−	0.274205i	0.243367	−	0.969934i	$-0.421748\pi$
$797$	−2.40443e8	−	1.38820e8i	−0.474938	−	0.274205i	−0.718304	+	0.695729i	$0.755082\pi$
$798$	−1.46374e8	+	1.46374e8i	−0.288041	+	0.288041i
$799$	−7.58846e7	−	2.83205e8i	−0.148769	−	0.555215i
$800$	−3.51826e8	+	9.42714e7i	−0.687160	+	0.184124i
$801$	−2.74130e8	−	2.74130e8i	−0.533407	−	0.533407i
$802$	3.15926e7	−	5.47199e7i	0.0612438	−	0.106077i
$803$	2.33276e7	−	1.34682e7i	0.0450529	−	0.0260113i
$804$	1.16985e8	−	4.36595e8i	0.225094	−	0.840061i
$805$		−	1.95228e8i		−	0.374244i
$806$	1.01330e7	−	8.83548e6i	0.0193524	−	0.0168743i
$807$	1.75678e8			0.334269
$808$	−2.44544e8	−	6.55254e7i	−0.463579	−	0.124216i
$809$	2.10102e8	+	3.63907e8i	0.396812	+	0.687299i	0.993331	−	0.115301i	$-0.0367832\pi$
$809$	2.10102e8	+	3.63907e8i	0.396812	+	0.687299i	−0.596519	+	0.802599i	$0.703450\pi$
$810$	7.10965e7	+	4.10476e7i	0.133781	+	0.0772383i
$811$	8.07659e7	−	8.07659e7i	0.151414	−	0.151414i	−0.627335	−	0.778749i	$-0.715854\pi$
$811$	8.07659e7	−	8.07659e7i	0.151414	−	0.151414i	0.778749	+	0.627335i	$0.215854\pi$
$812$	−6.52773e7	−	2.43618e8i	−0.121925	−	0.455031i
$813$	1.08248e9	−	2.90049e8i	2.01441	−	0.539758i
$814$	−2.51791e7	−	2.51791e7i	−0.0466839	−	0.0466839i
$815$	−1.72297e8	+	2.98427e8i	−0.318277	+	0.551271i
$816$	−1.30311e8	+	7.52350e7i	−0.239834	+	0.138468i
$817$	−2.16748e8	+	8.08916e8i	−0.397457	+	1.48333i
$818$			6.93964e7i			0.126788i
$819$	−1.22440e7	+	1.78993e8i	−0.0222880	+	0.325825i
$820$	5.63364e7			0.102176
$821$	−6.36078e8	−	1.70437e8i	−1.14943	−	0.307988i	−0.366691	−	0.930343i	$-0.619509\pi$
$821$	−6.36078e8	−	1.70437e8i	−1.14943	−	0.307988i	−0.782735	+	0.622355i	$0.786176\pi$
$822$	1.16565e8	+	2.01896e8i	0.209871	+	0.363507i
$823$	4.24768e8	+	2.45240e8i	0.761996	+	0.439938i	0.830012	−	0.557746i	$-0.188334\pi$
$823$	4.24768e8	+	2.45240e8i	0.761996	+	0.439938i	−0.0680160	+	0.997684i	$0.521667\pi$
$824$	1.93362e7	−	1.93362e7i	0.0345613	−	0.0345613i
$825$	5.44181e7	+	2.03091e8i	0.0969129	+	0.361684i
$826$	1.85500e8	−	4.97046e7i	0.329158	−	0.0881975i
$827$	7.31281e7	+	7.31281e7i	0.129291	+	0.129291i	0.768791	−	0.639500i	$-0.220859\pi$
$827$	7.31281e7	+	7.31281e7i	0.129291	+	0.129291i	−0.639500	+	0.768791i	$0.720859\pi$
$828$	2.44427e8	−	4.23360e8i	0.430584	−	0.745794i
$829$	5.22826e8	−	3.01854e8i	0.917684	−	0.529825i	0.0347888	−	0.999395i	$-0.488924\pi$
$829$	5.22826e8	−	3.01854e8i	0.917684	−	0.529825i	0.882896	+	0.469569i	$0.155591\pi$
$830$	−1.16519e7	+	4.34853e7i	−0.0203780	+	0.0760516i
$831$		−	2.16900e8i		−	0.377970i
$832$	−4.77519e7	−	2.43691e8i	−0.0829126	−	0.423126i
$833$	1.22315e8			0.211615
$834$	3.17788e7	+	8.51511e6i	0.0547822	+	0.0146788i
$835$	1.27453e8	+	2.20754e8i	0.218922	+	0.379184i
$836$	−2.80241e8	−	1.61797e8i	−0.479638	−	0.276919i
$837$	−1.78795e7	+	1.78795e7i	−0.0304915	+	0.0304915i
$838$	4.53867e7	+	1.69385e8i	0.0771252	+	0.287835i
$839$	−6.69241e8	+	1.79322e8i	−1.13317	+	0.303633i	−0.776203	−	0.630483i	$-0.782857\pi$
$839$	−6.69241e8	+	1.79322e8i	−1.13317	+	0.303633i	−0.356970	+	0.934116i	$0.616190\pi$
$840$	7.09382e7	+	7.09382e7i	0.119686	+	0.119686i
$841$	4.85743e7	−	8.41332e7i	0.0816618	−	0.141442i
$842$	2.75236e8	−	1.58908e8i	0.461072	−	0.266200i
$843$	−2.73960e8	+	1.02243e9i	−0.457303	+	1.70668i
$844$			1.63081e8i			0.271253i
$845$	9.02261e7	−	2.14363e8i	0.149542	−	0.355287i
$846$	−2.01562e8			−0.332888
$847$	2.95619e8	+	7.92109e7i	0.486500	+	0.130357i
$848$	1.52327e8	+	2.63839e8i	0.249799	+	0.432664i
$849$	−9.16854e8	−	5.29346e8i	−1.49823	−	0.865001i
$850$	3.75817e7	−	3.75817e7i	0.0611956	−	0.0611956i
$851$	1.57482e8	+	5.87731e8i	0.255530	+	0.953653i
$852$	6.15223e8	−	1.64849e8i	0.994750	−	0.266542i
$853$	8.85876e6	+	8.85876e6i	0.0142733	+	0.0142733i	0.714207	−	0.699934i	$-0.246787\pi$
$853$	8.85876e6	+	8.85876e6i	0.0142733	+	0.0142733i	−0.699934	+	0.714207i	$0.746787\pi$
$854$	5.11170e7	−	8.85373e7i	0.0820714	−	0.142152i
$855$	2.08678e8	−	1.20481e8i	0.333871	−	0.192761i
$856$	−9.98864e7	+	3.72781e8i	−0.159252	+	0.594337i
$857$			5.35088e8i			0.850125i	0.905164	+	0.425062i	$0.139748\pi$
$857$			5.35088e8i			0.850125i	−0.905164	+	0.425062i	$0.860252\pi$
$858$	8.77233e7	−	1.71896e7i	0.138884	−	0.0272147i
$859$	−5.32562e8			−0.840215			−0.420108	−	0.907474i	$-0.638008\pi$
$859$	−5.32562e8			−0.840215			−0.420108	+	0.907474i	$0.638008\pi$
$860$	1.85312e8	+	4.96541e7i	0.291345	+	0.0780657i
$861$	6.78954e7	+	1.17598e8i	0.106373	+	0.184243i
$862$	−2.25134e8	−	1.29981e8i	−0.351495	−	0.202936i
$863$	−2.19072e8	+	2.19072e8i	−0.340842	+	0.340842i	−0.856684	−	0.515842i	$-0.827479\pi$
$863$	−2.19072e8	+	2.19072e8i	−0.340842	+	0.340842i	0.515842	+	0.856684i	$0.327479\pi$
$864$	−7.53821e7	−	2.81330e8i	−0.116876	−	0.436189i
$865$	4.03894e8	−	1.08223e8i	0.624049	−	0.167213i
$866$	3.53079e7	+	3.53079e7i	0.0543648	+	0.0543648i
$867$	−3.67380e8	+	6.36321e8i	−0.563714	+	0.976381i
$868$	−2.32728e7	+	1.34365e7i	−0.0355868	+	0.0205460i
$869$	−5.26503e7	+	1.96494e8i	−0.0802309	+	0.299426i
$870$		−	9.35746e7i		−	0.142102i
$871$	−5.10679e8	−	3.49329e7i	−0.772846	−	0.0528665i
$872$	3.14553e8			0.474400
$873$	1.40312e8	+	3.75964e7i	0.210887	+	0.0565071i
$874$	−3.19377e8	−	5.53177e8i	−0.478376	−	0.828572i
$875$	2.37875e8	+	1.37337e8i	0.355079	+	0.205005i
$876$	7.90569e7	−	7.90569e7i	0.117605	−	0.117605i
$877$	4.23496e7	+	1.58051e8i	0.0627842	+	0.234314i	0.990187	−	0.139751i	$-0.0446303\pi$
$877$	4.23496e7	+	1.58051e8i	0.0627842	+	0.234314i	−0.927402	+	0.374065i	$0.877964\pi$
$878$	9.81737e7	−	2.63056e7i	0.145048	−	0.0388655i
$879$	4.52914e8	+	4.52914e8i	0.666883	+	0.666883i
$880$	−3.22892e7	+	5.59266e7i	−0.0473816	+	0.0820673i
$881$	9.86810e8	−	5.69735e8i	1.44313	−	0.833192i	0.445074	−	0.895494i	$-0.353177\pi$
$881$	9.86810e8	−	5.69735e8i	1.44313	−	0.833192i	0.998057	+	0.0623016i	$0.0198441\pi$
$882$	2.17635e7	−	8.12225e7i	0.0317192	−	0.118378i
$883$		−	8.05006e8i		−	1.16928i	−0.811294	−	0.584638i	$-0.801237\pi$
$883$		−	8.05006e8i		−	1.16928i	0.811294	−	0.584638i	$-0.198763\pi$
$884$	1.28555e8	+	1.47434e8i	0.186093	+	0.213422i
$885$	−6.16795e8			−0.889838
$886$	−1.07183e8	−	2.87197e7i	−0.154108	−	0.0412932i
$887$	2.51741e8	+	4.36028e8i	0.360730	+	0.624803i	0.988081	−	0.153934i	$-0.0491942\pi$
$887$	2.51741e8	+	4.36028e8i	0.360730	+	0.624803i	−0.627351	+	0.778737i	$0.715861\pi$
$888$	−2.70781e8	−	1.56336e8i	−0.386705	−	0.223264i
$889$	−2.80166e8	+	2.80166e8i	−0.398758	+	0.398758i
$890$	3.00346e7	+	1.12091e8i	0.0426042	+	0.159001i
$891$	−2.98790e8	+	8.00604e7i	−0.422408	+	0.113184i
$892$	2.94557e8	+	2.94557e8i	0.415026	+	0.415026i
$893$	1.13994e9	−	1.97443e9i	1.60076	−	2.77260i
$894$	−1.72507e8	+	9.95968e7i	−0.241431	+	0.139390i
$895$	5.55423e7	−	2.07287e8i	0.0774738	−	0.289136i
$896$		−	4.02639e8i		−	0.559748i
$897$	−1.44502e9	−	4.95112e8i	−2.00215	−	0.686004i
$898$	−1.79072e8			−0.247285
$899$	5.12201e7	+	1.37244e7i	0.0704955	+	0.0188892i
$900$	1.58147e8	+	2.73919e8i	0.216937	+	0.375746i
$901$	−1.42791e8	−	8.24407e7i	−0.195222	−	0.112711i
$902$	1.73392e7	−	1.73392e7i	0.0236271	−	0.0236271i
$903$	1.19684e8	+	4.46667e8i	0.162545	+	0.606626i
$904$	6.08848e8	−	1.63140e8i	0.824145	−	0.220829i
$905$	−2.01620e8	−	2.01620e8i	−0.272012	−	0.272012i
$906$	−670947.	+	1.16211e6i	−0.000902201	+	0.00156266i
$907$	−8.43987e8	+	4.87276e8i	−1.13113	+	0.653060i	−0.944220	−	0.329316i	$-0.893182\pi$
$907$	−8.43987e8	+	4.87276e8i	−1.13113	+	0.653060i	−0.186914	+	0.982376i	$0.559848\pi$
$908$	1.07054e8	−	3.99531e8i	0.143003	−	0.533694i
$909$			3.35773e8i			0.447048i
$910$	2.99633e7	−	4.45678e7i	0.0397617	−	0.0591422i
$911$	5.73122e8			0.758039			0.379020	−	0.925389i	$-0.376261\pi$
$911$	5.73122e8			0.758039			0.379020	+	0.925389i	$0.376261\pi$
$912$	−1.13018e9	−	3.02831e8i	−1.48992	−	0.399223i
$913$	−8.48150e7	−	1.46904e8i	−0.111445	−	0.193028i
$914$	1.93889e8	+	1.11942e8i	0.253930	+	0.146606i
$915$	−2.32178e8	+	2.32178e8i	−0.303080	+	0.303080i
$916$	−2.47656e8	−	9.24264e8i	−0.322227	−	1.20257i
$917$	5.10801e8	−	1.36869e8i	0.662435	−	0.177499i
$918$	3.00514e7	+	3.00514e7i	0.0388452	+	0.0388452i
$919$	2.57579e8	−	4.46140e8i	0.331867	−	0.574811i	−0.651011	−	0.759068i	$-0.725655\pi$
$919$	2.57579e8	−	4.46140e8i	0.331867	−	0.574811i	0.982878	+	0.184258i	$0.0589881\pi$
$920$	−2.68090e8	+	1.54782e8i	−0.344284	+	0.198773i
$921$	3.36045e7	−	1.25414e8i	0.0430149	−	0.160534i
$922$		−	3.25566e8i		−	0.415381i
$923$	−3.17178e8	−	6.47819e8i	−0.403365	−	0.823851i
$924$	−1.78683e8			−0.226499
$925$	−3.80269e8	−	1.01893e8i	−0.480470	−	0.128741i
$926$	8.96265e7	+	1.55238e8i	0.112876	+	0.195508i
$927$	−3.14087e7	−	1.81338e7i	−0.0394285	−	0.0227641i
$928$	−4.31900e8	+	4.31900e8i	−0.540430	+	0.540430i
$929$	3.01371e8	+	1.12473e9i	0.375884	+	1.40282i	0.852049	+	0.523462i	$0.175360\pi$
$929$	3.01371e8	+	1.12473e9i	0.375884	+	1.40282i	−0.476165	+	0.879356i	$0.657973\pi$
$930$	−9.63060e6	+	2.58051e6i	−0.0119730	+	0.00320817i
$931$	6.72543e8	+	6.72543e8i	0.833434	+	0.833434i
$932$	−2.75522e8	+	4.77219e8i	−0.340337	+	0.589481i
$933$	1.53429e8	−	8.85821e7i	0.188913	−	0.109069i
$934$	−8.22648e7	+	3.07016e8i	−0.100966	+	0.376809i
$935$		−	3.49503e7i		−	0.0427579i
$936$	2.55503e8	−	1.25097e8i	0.311579	−	0.152552i
$937$	6.47813e8			0.787464			0.393732	−	0.919225i	$-0.371184\pi$
$937$	6.47813e8			0.787464			0.393732	+	0.919225i	$0.371184\pi$
$938$	−1.14167e8	−	3.05911e7i	−0.138336	−	0.0370669i
$939$	−5.23355e8	−	9.06478e8i	−0.632121	−	1.09486i
$940$	−4.52316e8	−	2.61145e8i	−0.544576	−	0.314411i
$941$	1.88790e8	−	1.88790e8i	0.226574	−	0.226574i	−0.584686	−	0.811260i	$-0.698782\pi$
$941$	1.88790e8	−	1.88790e8i	0.226574	−	0.226574i	0.811260	+	0.584686i	$0.198782\pi$
$942$	7.11848e7	+	2.65665e8i	0.0851598	+	0.317821i
$943$	−4.04734e8	+	1.08448e8i	−0.482652	+	0.129326i
$944$	7.67557e8	+	7.67557e8i	0.912420	+	0.912420i
$945$	−5.05025e7	+	8.74729e7i	−0.0598436	+	0.103652i
$946$	7.23179e7	−	4.17528e7i	0.0854225	−	0.0493187i
$947$	3.74774e7	−	1.39867e8i	0.0441285	−	0.164690i	−0.940345	−	0.340222i	$-0.889498\pi$
$947$	3.74774e7	−	1.39867e8i	0.0441285	−	0.164690i	0.984474	+	0.175532i	$0.0561645\pi$
$948$			8.44347e8i			0.991051i
$949$	−1.05075e8	−	7.06424e7i	−0.122942	−	0.0826546i
$950$	4.13281e8			0.482031
$951$	9.99936e8	+	2.67932e8i	1.16260	+	0.311518i
$952$	4.77764e7	+	8.27512e7i	0.0553736	+	0.0959099i
$953$	2.06247e8	+	1.19077e8i	0.238292	+	0.137578i	0.614391	−	0.789001i	$-0.289402\pi$
$953$	2.06247e8	+	1.19077e8i	0.238292	+	0.137578i	−0.376100	+	0.926579i	$0.622735\pi$
$954$	−8.01508e7	+	8.01508e7i	−0.0923130	+	0.0923130i
$955$	9.18233e6	+	3.42689e7i	0.0105425	+	0.0393451i
$956$	8.03137e8	−	2.15200e8i	0.919213	−	0.246302i
$957$	2.49314e8	+	2.49314e8i	0.284453	+	0.284453i
$958$	−2.77952e8	+	4.81427e8i	−0.316136	+	0.547563i
$959$	−4.57024e8	+	2.63863e8i	−0.518183	+	0.299173i
$960$	−4.76645e7	+	1.77886e8i	−0.0538743	+	0.201062i
$961$			8.81854e8i			0.993634i
$962$	−5.42530e7	+	1.58341e8i	−0.0609394	+	0.177856i
$963$	5.11850e8			0.573144
$964$	−1.08472e8	−	2.90650e7i	−0.121084	−	0.0324443i
$965$	−2.80729e7	−	4.86236e7i	−0.0312396	−	0.0541085i
$966$	−3.05453e8	−	1.76354e8i	−0.338855	−	0.195638i
$967$	1.63259e8	−	1.63259e8i	0.180550	−	0.180550i	−0.611045	−	0.791596i	$-0.709251\pi$
$967$	1.63259e8	−	1.63259e8i	0.180550	−	0.180550i	0.791596	+	0.611045i	$0.209251\pi$
$968$	−1.25601e8	−	4.68749e8i	−0.138474	−	0.516790i
$969$	6.11661e8	−	1.63894e8i	0.672264	−	0.180133i
$970$	−3.07460e7	−	3.07460e7i	−0.0336879	−	0.0336879i
$971$	−3.42609e8	+	5.93415e8i	−0.374232	+	0.648188i	−0.990212	−	0.139574i	$-0.955427\pi$
$971$	−3.42609e8	+	5.93415e8i	−0.374232	+	0.648188i	0.615980	+	0.787762i	$0.288760\pi$
$972$	−7.26599e8	+	4.19502e8i	−0.791217	+	0.456810i
$973$	−1.92753e7	+	7.19364e7i	−0.0209249	+	0.0780927i
$974$			3.98573e8i			0.431351i
$975$	7.44897e8	−	6.49513e8i	0.803679	−	0.700767i
$976$	5.77858e8			0.621543
$977$	−4.47010e8	−	1.19776e8i	−0.479328	−	0.128436i	0.0110615	−	0.999939i	$-0.496479\pi$
$977$	−4.47010e8	−	1.19776e8i	−0.479328	−	0.128436i	−0.490390	+	0.871503i	$0.663146\pi$
$978$	3.11279e8	+	5.39151e8i	0.332761	+	0.576360i
$979$	−3.78669e8	−	2.18625e8i	−0.403564	−	0.232998i
$980$	1.54071e8	−	1.54071e8i	0.163697	−	0.163697i
$981$	−1.07975e8	−	4.02968e8i	−0.114371	−	0.426838i
$982$	−1.34205e7	+	3.59601e6i	−0.0141721	+	0.00379740i
$983$	−3.35370e8	−	3.35370e8i	−0.353072	−	0.353072i	0.508179	−	0.861251i	$-0.330319\pi$
$983$	−3.35370e8	−	3.35370e8i	−0.353072	−	0.353072i	−0.861251	+	0.508179i	$0.830319\pi$
$984$	1.07658e8	−	1.86470e8i	0.112996	−	0.195715i
$985$	4.69221e8	−	2.70905e8i	0.490986	−	0.283471i
$986$	2.30676e7	−	8.60895e7i	0.0240642	−	0.0898089i
$987$		−	1.25890e9i		−	1.30930i
$988$	−1.03805e8	+	1.51750e9i	−0.107633	+	1.57347i
$989$	−1.42691e9			−1.47505
$990$	−2.32085e7	−	6.21869e6i	−0.0239189	−	0.00640904i
$991$	−3.61863e8	−	6.26766e8i	−0.371812	−	0.643998i	0.618032	−	0.786153i	$-0.287930\pi$
$991$	−3.61863e8	−	6.26766e8i	−0.371812	−	0.643998i	−0.989844	+	0.142155i	$0.954597\pi$
$992$	5.63612e7	+	3.25402e7i	0.0577359	+	0.0333338i
$993$	−4.83857e8	+	4.83857e8i	−0.494162	+	0.494162i
$994$	−4.31071e7	−	1.60878e8i	−0.0438924	−	0.163809i
$995$	−2.04168e8	+	5.47067e7i	−0.207262	+	0.0555356i
$996$	−4.97856e8	−	4.97856e8i	−0.503878	−	0.503878i
$997$	−1.78717e8	+	3.09547e8i	−0.180335	+	0.312350i	−0.941995	−	0.335628i	$-0.891052\pi$
$997$	−1.78717e8	+	3.09547e8i	−0.180335	+	0.312350i	0.761659	+	0.647978i	$0.224385\pi$
$998$	−3.94362e8	+	2.27685e8i	−0.396738	+	0.229057i
$999$	8.14764e7	−	3.04074e8i	0.0817213	−	0.304988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.2.4	✓	24
13.7	odd	12	inner	13.7.f.a.7.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.2.4	✓	24	1.1	even	1	trivial
13.7.f.a.7.4	yes	24	13.7	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.48669 + 0.666306i) q^{2} +(-16.9072 - 29.2841i) q^{3} +(-49.6860 - 28.6862i) q^{4} +(34.0715 - 34.0715i) q^{5} +(-22.5307 - 84.0857i) q^{6} +(190.342 - 51.0019i) q^{7} +(-220.944 - 220.944i) q^{8} +(-207.205 + 358.889i) q^{9} +O(q^{10})\)	\(q+(2.48669 + 0.666306i) q^{2} +(-16.9072 - 29.2841i) q^{3} +(-49.6860 - 28.6862i) q^{4} +(34.0715 - 34.0715i) q^{5} +(-22.5307 - 84.0857i) q^{6} +(190.342 - 51.0019i) q^{7} +(-220.944 - 220.944i) q^{8} +(-207.205 + 358.889i) q^{9} +(107.427 - 62.0232i) q^{10} +(-120.972 + 451.473i) q^{11} +1940.01i q^{12} +(2156.00 - 422.473i) q^{13} +507.303 q^{14} +(-1573.81 - 421.700i) q^{15} +(1433.71 + 2483.27i) q^{16} +(-1343.96 - 775.937i) q^{17} +(-754.384 + 754.384i) q^{18} +(-3123.25 - 11656.1i) q^{19} +(-2670.26 + 715.494i) q^{20} +(-4711.68 - 4711.68i) q^{21} +(-601.639 + 1042.07i) q^{22} +(17806.4 - 10280.5i) q^{23} +(-2734.61 + 10205.7i) q^{24} +13303.3i q^{25} +(5642.79 + 385.995i) q^{26} -10637.7 q^{27} +(-10920.4 - 2926.10i) q^{28} +(11154.3 + 19319.8i) q^{29} +(-3632.59 - 2097.27i) q^{30} +(1680.77 - 1680.77i) q^{31} +(7086.34 + 26446.6i) q^{32} +(15266.3 - 4090.58i) q^{33} +(-2825.00 - 2825.00i) q^{34} +(4747.52 - 8222.94i) q^{35} +(20590.3 - 11887.8i) q^{36} +(-7659.24 + 28584.7i) q^{37} -31066.2i q^{38} +(-48823.6 - 55993.6i) q^{39} -15055.8 q^{40} +(-19684.5 - 5274.43i) q^{41} +(-8577.06 - 14855.9i) q^{42} +(-60100.8 - 34699.2i) q^{43} +(18961.7 - 18961.7i) q^{44} +(5168.12 + 19287.7i) q^{45} +(51129.0 - 13700.0i) q^{46} +(133594. + 133594. i) q^{47} +(48480.1 - 83970.0i) q^{48} +(-68258.3 + 39409.0i) q^{49} +(-8864.04 + 33081.1i) q^{50} +52475.6i q^{51} +(-119242. - 40856.4i) q^{52} +106247. q^{53} +(-26452.6 - 7087.94i) q^{54} +(11260.7 + 19504.1i) q^{55} +(-53323.4 - 30786.3i) q^{56} +(-288533. + 288533. i) q^{57} +(14864.4 + 55474.6i) q^{58} +(365659. - 97978.2i) q^{59} +(66099.1 + 66099.1i) q^{60} +(100762. - 174526. i) q^{61} +(5299.47 - 3059.65i) q^{62} +(-21135.7 + 78879.4i) q^{63} -113029. i q^{64} +(59063.8 - 87852.5i) q^{65} +40688.0 q^{66} +(-225048. - 60301.4i) q^{67} +(44517.4 + 77106.3i) q^{68} +(-602112. - 347630. i) q^{69} +(17284.6 - 17284.6i) q^{70} +(-84973.0 - 317124. i) q^{71} +(125075. - 33513.8i) q^{72} +(-40750.8 - 40750.8i) q^{73} +(-38092.3 + 65977.7i) q^{74} +(389574. - 224921. i) q^{75} +(-179188. + 668740. i) q^{76} +92103.9i q^{77} +(-84100.1 - 171770. i) q^{78} +435228. q^{79} +(133458. + 35759.8i) q^{80} +(330905. + 573145. i) q^{81} +(-45434.7 - 26231.7i) q^{82} +(-256625. + 256625. i) q^{83} +(98944.1 + 369265. i) q^{84} +(-72228.2 + 19353.5i) q^{85} +(-126332. - 126332. i) q^{86} +(377176. - 653287. i) q^{87} +(126478. - 73022.3i) q^{88} +(-242124. + 903619. i) q^{89} +51406.1i q^{90} +(388829. - 190374. i) q^{91} -1.17964e6 q^{92} +(-77637.0 - 20802.8i) q^{93} +(243192. + 421220. i) q^{94} +(-503556. - 290728. i) q^{95} +(654654. - 654654. i) q^{96} +(-90722.7 - 338582. i) q^{97} +(-195996. + 52516.9i) q^{98} +(-136963. - 136963. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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