LMFDB - Embedded newform 13.7.f.a.2.2

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			2.2
Character	$\chi$	$=$	13.2
Dual form			13.7.f.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.37184 - 2.51118i) q^{2} +(10.4091 + 18.0291i) q^{3} +(26.0998 + 15.0687i) q^{4} +(160.035 - 160.035i) q^{5} +(-52.2782 - 195.105i) q^{6} +(162.036 - 43.4174i) q^{7} +(232.320 + 232.320i) q^{8} +(147.801 - 255.999i) q^{9} +O(q^{10})$	\(q+(-9.37184 - 2.51118i) q^{2} +(10.4091 + 18.0291i) q^{3} +(26.0998 + 15.0687i) q^{4} +(160.035 - 160.035i) q^{5} +(-52.2782 - 195.105i) q^{6} +(162.036 - 43.4174i) q^{7} +(232.320 + 232.320i) q^{8} +(147.801 - 255.999i) q^{9} +(-1901.70 + 1097.95i) q^{10} +(-264.307 + 986.407i) q^{11} +627.408i q^{12} +(189.333 - 2188.83i) q^{13} -1627.60 q^{14} +(4551.12 + 1219.47i) q^{15} +(-2558.27 - 4431.05i) q^{16} +(1836.32 + 1060.20i) q^{17} +(-2028.03 + 2028.03i) q^{18} +(334.793 + 1249.46i) q^{19} +(6588.42 - 1765.36i) q^{20} +(2469.42 + 2469.42i) q^{21} +(4954.09 - 8580.73i) q^{22} +(-11932.9 + 6889.45i) q^{23} +(-1770.27 + 6606.75i) q^{24} -35597.7i q^{25} +(-7270.93 + 20037.9i) q^{26} +21330.4 q^{27} +(4883.35 + 1308.49i) q^{28} +(12087.9 + 20936.9i) q^{29} +(-39590.1 - 22857.3i) q^{30} +(-26370.1 + 26370.1i) q^{31} +(7406.29 + 27640.6i) q^{32} +(-20535.2 + 5502.40i) q^{33} +(-14547.4 - 14547.4i) q^{34} +(18983.1 - 32879.8i) q^{35} +(7715.15 - 4454.34i) q^{36} +(-7417.14 + 27681.1i) q^{37} -12550.5i q^{38} +(41433.4 - 19370.2i) q^{39} +74358.7 q^{40} +(83471.8 + 22366.2i) q^{41} +(-16941.9 - 29344.2i) q^{42} +(-102720. - 59305.2i) q^{43} +(-21762.3 + 21762.3i) q^{44} +(-17315.5 - 64622.2i) q^{45} +(129134. - 34601.3i) q^{46} +(2437.23 + 2437.23i) q^{47} +(53258.5 - 92246.5i) q^{48} +(-77516.5 + 44754.2i) q^{49} +(-89392.1 + 333616. i) q^{50} +44143.0i q^{51} +(37924.4 - 54274.9i) q^{52} -262002. q^{53} +(-199905. - 53564.4i) q^{54} +(115562. + 200159. i) q^{55} +(47730.8 + 27557.4i) q^{56} +(-19041.8 + 19041.8i) q^{57} +(-60709.8 - 226572. i) q^{58} +(148193. - 39708.1i) q^{59} +(100408. + 100408. i) q^{60} +(14741.0 - 25532.2i) q^{61} +(313357. - 180917. i) q^{62} +(12834.3 - 47898.1i) q^{63} +49815.7i q^{64} +(-319990. - 380590. i) q^{65} +206271. q^{66} +(86045.8 + 23055.9i) q^{67} +(31951.7 + 55342.1i) q^{68} +(-248421. - 143426. i) q^{69} +(-260474. + 260474. i) q^{70} +(172572. + 644048. i) q^{71} +(93810.6 - 25136.5i) q^{72} +(46511.6 + 46511.6i) q^{73} +(139025. - 240798. i) q^{74} +(641794. - 370540. i) q^{75} +(-10089.8 + 37655.7i) q^{76} +171309. i q^{77} +(-436949. + 77488.2i) q^{78} +169972. q^{79} +(-1.11854e6 - 299711. i) q^{80} +(114283. + 197945. i) q^{81} +(-726119. - 419225. i) q^{82} +(378696. - 378696. i) q^{83} +(27240.4 + 101663. i) q^{84} +(463546. - 124207. i) q^{85} +(813746. + 813746. i) q^{86} +(-251649. + 435869. i) q^{87} +(-290565. + 167758. i) q^{88} +(37362.9 - 139440. i) q^{89} +649112. i q^{90} +(-64354.3 - 362889. i) q^{91} -415261. q^{92} +(-749920. - 200940. i) q^{93} +(-16721.0 - 28961.6i) q^{94} +(253537. + 146380. i) q^{95} +(-421243. + 421243. i) q^{96} +(-54694.5 - 204123. i) q^{97} +(838858. - 224771. i) q^{98} +(213454. + 213454. 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 $

$2$	−9.37184	−	2.51118i	−1.17148	−	0.313897i	−0.379938	−	0.925012i	$-0.624055\pi$
$2$	−9.37184	−	2.51118i	−1.17148	−	0.313897i	−0.791542	+	0.611115i	$0.790721\pi$
$3$	10.4091	+	18.0291i	0.385523	+	0.667745i	0.991842	−	0.127477i	$-0.0406879\pi$
$3$	10.4091	+	18.0291i	0.385523	+	0.667745i	−0.606319	+	0.795222i	$0.707355\pi$
$4$	26.0998	+	15.0687i	0.407809	+	0.235449i
$5$	160.035	−	160.035i	1.28028	−	1.28028i	0.339777	−	0.940506i	$-0.389648\pi$
$5$	160.035	−	160.035i	1.28028	−	1.28028i	0.940506	−	0.339777i	$-0.110352\pi$
$6$	−52.2782	−	195.105i	−0.242029	−	0.903264i
$7$	162.036	−	43.4174i	0.472408	−	0.126581i	−0.0147576	−	0.999891i	$-0.504698\pi$
$7$	162.036	−	43.4174i	0.472408	−	0.126581i	0.487165	+	0.873310i	$0.338031\pi$
$8$	232.320	+	232.320i	0.453749	+	0.453749i
$9$	147.801	−	255.999i	0.202745	−	0.351164i
$10$	−1901.70	+	1097.95i	−1.90170	+	1.09795i
$11$	−264.307	+	986.407i	−0.198578	+	0.741102i	0.792734	+	0.609568i	$0.208657\pi$
$11$	−264.307	+	986.407i	−0.198578	+	0.741102i	−0.991312	+	0.131534i	$0.958010\pi$
$12$			627.408i			0.363083i
$13$	189.333	−	2188.83i	0.0861780	−	0.996280i
$13$	189.333	−	2188.83i	0.0861780	−	0.996280i
$14$	−1627.60			−0.593150
$15$	4551.12	+	1219.47i	1.34848	+	0.361324i
$16$	−2558.27	−	4431.05i	−0.624577	−	1.08180i
$17$	1836.32	+	1060.20i	0.373768	+	0.215795i	0.675103	−	0.737723i	$-0.264099\pi$
$17$	1836.32	+	1060.20i	0.373768	+	0.215795i	−0.301335	+	0.953518i	$0.597432\pi$
$18$	−2028.03	+	2028.03i	−0.347741	+	0.347741i
$19$	334.793	+	1249.46i	0.0488108	+	0.182164i	0.986027	−	0.166584i	$-0.0532736\pi$
$19$	334.793	+	1249.46i	0.0488108	+	0.182164i	−0.937217	+	0.348748i	$0.886607\pi$
$20$	6588.42	−	1765.36i	0.823553	−	0.220670i
$21$	2469.42	+	2469.42i	0.266648	+	0.266648i
$22$	4954.09	−	8580.73i	0.465260	−	0.805854i
$23$	−11932.9	+	6889.45i	−0.980758	+	0.566241i	−0.902499	−	0.430692i	$-0.858269\pi$
$23$	−11932.9	+	6889.45i	−0.980758	+	0.566241i	−0.0782591	+	0.996933i	$0.524936\pi$
$24$	−1770.27	+	6606.75i	−0.128058	+	0.477919i
$25$		−	35597.7i		−	2.27825i
$26$	−7270.93	+	20037.9i	−0.413685	+	1.14007i
$27$	21330.4			1.08370
$28$	4883.35	+	1308.49i	0.222456	+	0.0596068i
$29$	12087.9	+	20936.9i	0.495630	+	0.858456i	0.999987	−	0.00503870i	$-0.00160387\pi$
$29$	12087.9	+	20936.9i	0.495630	+	0.858456i	−0.504357	+	0.863495i	$0.668271\pi$
$30$	−39590.1	−	22857.3i	−1.46630	−	0.846568i
$31$	−26370.1	+	26370.1i	−0.885171	+	0.885171i	−0.994055	−	0.108883i	$-0.965273\pi$
$31$	−26370.1	+	26370.1i	−0.885171	+	0.885171i	0.108883	+	0.994055i	$0.465273\pi$
$32$	7406.29	+	27640.6i	0.226022	+	0.843525i
$33$	−20535.2	+	5502.40i	−0.571423	+	0.153112i
$34$	−14547.4	−	14547.4i	−0.370124	−	0.370124i
$35$	18983.1	−	32879.8i	0.442756	−	0.766875i
$36$	7715.15	−	4454.34i	0.165362	−	0.0954720i
$37$	−7417.14	+	27681.1i	−0.146430	+	0.546486i	0.853257	+	0.521490i	$0.174624\pi$
$37$	−7417.14	+	27681.1i	−0.146430	+	0.546486i	−0.999688	+	0.0249953i	$0.992043\pi$
$38$		−	12550.5i		−	0.228723i
$39$	41433.4	−	19370.2i	0.698484	−	0.326543i
$40$	74358.7			1.16186
$41$	83471.8	+	22366.2i	1.21112	+	0.324519i	0.807202	−	0.590275i	$-0.200981\pi$
$41$	83471.8	+	22366.2i	1.21112	+	0.324519i	0.403920	+	0.914794i	$0.367647\pi$
$42$	−16941.9	−	29344.2i	−0.228673	−	0.396072i
$43$	−102720.	−	59305.2i	−1.29196	−	0.745912i	−0.312956	−	0.949768i	$-0.601319\pi$
$43$	−102720.	−	59305.2i	−1.29196	−	0.745912i	−0.979001	+	0.203856i	$0.934653\pi$
$44$	−21762.3	+	21762.3i	−0.255474	+	0.255474i
$45$	−17315.5	−	64622.2i	−0.190019	−	0.709160i
$46$	129134.	−	34601.3i	1.32668	−	0.355483i
$47$	2437.23	+	2437.23i	0.0234748	+	0.0234748i	0.718747	−	0.695272i	$-0.244716\pi$
$47$	2437.23	+	2437.23i	0.0234748	+	0.0234748i	−0.695272	+	0.718747i	$0.744716\pi$
$48$	53258.5	−	92246.5i	0.481577	−	0.834115i
$49$	−77516.5	+	44754.2i	−0.658879	+	0.380404i
$50$	−89392.1	+	333616.i	−0.715137	+	2.66893i
$51$			44143.0i			0.332775i
$52$	37924.4	−	54274.9i	0.269717	−	0.386002i
$53$	−262002.			−1.75986			−0.879928	−	0.475108i	$-0.842409\pi$
$53$	−262002.			−1.75986			−0.879928	+	0.475108i	$0.842409\pi$
$54$	−199905.	−	53564.4i	−1.26953	−	0.340169i
$55$	115562.	+	200159.i	0.694585	+	1.20306i
$56$	47730.8	+	27557.4i	0.271791	+	0.156918i
$57$	−19041.8	+	19041.8i	−0.102822	+	0.102822i
$58$	−60709.8	−	226572.i	−0.311154	−	1.16124i
$59$	148193.	−	39708.1i	0.721557	−	0.193341i	0.120691	−	0.992690i	$-0.461489\pi$
$59$	148193.	−	39708.1i	0.721557	−	0.193341i	0.600866	+	0.799350i	$0.294822\pi$
$60$	100408.	+	100408.i	0.464850	+	0.464850i
$61$	14741.0	−	25532.2i	0.0649439	−	0.112486i	−0.831725	−	0.555188i	$-0.812646\pi$
$61$	14741.0	−	25532.2i	0.0649439	−	0.112486i	0.896669	+	0.442701i	$0.145980\pi$
$62$	313357.	−	180917.i	1.31481	−	0.759108i
$63$	12834.3	−	47898.1i	0.0513274	−	0.191556i
$64$			49815.7i			0.190032i
$65$	−319990.	−	380590.i	−1.16519	−	1.38585i
$66$	206271.			0.717473
$67$	86045.8	+	23055.9i	0.286092	+	0.0766580i	0.399011	−	0.916946i	$-0.369354\pi$
$67$	86045.8	+	23055.9i	0.286092	+	0.0766580i	−0.112919	+	0.993604i	$0.536020\pi$
$68$	31951.7	+	55342.1i	0.101617	+	0.176006i
$69$	−248421.	−	143426.i	−0.756209	−	0.436597i
$70$	−260474.	+	260474.i	−0.759400	+	0.759400i
$71$	172572.	+	644048.i	0.482165	+	1.79946i	0.592501	+	0.805569i	$0.298140\pi$
$71$	172572.	+	644048.i	0.482165	+	1.79946i	−0.110337	+	0.993894i	$0.535193\pi$
$72$	93810.6	−	25136.5i	0.251336	−	0.0673452i
$73$	46511.6	+	46511.6i	0.119562	+	0.119562i	0.764356	−	0.644794i	$-0.223057\pi$
$73$	46511.6	+	46511.6i	0.119562	+	0.119562i	−0.644794	+	0.764356i	$0.723057\pi$
$74$	139025.	−	240798.i	0.343081	−	0.594233i
$75$	641794.	−	370540.i	1.52129	−	0.878317i
$76$	−10089.8	+	37655.7i	−0.0229849	+	0.0857807i
$77$			171309.i			0.375239i
$78$	−436949.	+	77488.2i	−0.920761	+	0.163287i
$79$	169972.			0.344743			0.172371	−	0.985032i	$-0.444857\pi$
$79$	169972.			0.344743			0.172371	+	0.985032i	$0.444857\pi$
$80$	−1.11854e6	−	299711.i	−2.18464	−	0.585373i
$81$	114283.	+	197945.i	0.215044	+	0.372468i
$82$	−726119.	−	419225.i	−1.31694	−	0.760336i
$83$	378696.	−	378696.i	0.662302	−	0.662302i	−0.293620	−	0.955922i	$-0.594860\pi$
$83$	378696.	−	378696.i	0.662302	−	0.662302i	0.955922	+	0.293620i	$0.0948601\pi$
$84$	27240.4	+	101663.i	0.0459595	+	0.171523i
$85$	463546.	−	124207.i	0.754807	−	0.202250i
$86$	813746.	+	813746.i	1.27936	+	1.27936i
$87$	−251649.	+	435869.i	−0.382153	+	0.661909i
$88$	−290565.	+	167758.i	−0.426379	+	0.246170i
$89$	37362.9	−	139440.i	0.0529993	−	0.197796i	−0.934350	−	0.356357i	$-0.884019\pi$
$89$	37362.9	−	139440.i	0.0529993	−	0.197796i	0.987349	+	0.158561i	$0.0506854\pi$
$90$			649112.i			0.890414i
$91$	−64354.3	−	362889.i	−0.0853991	−	0.481559i
$92$	−415261.			−0.533283
$93$	−749920.	−	200940.i	−0.932322	−	0.249815i
$94$	−16721.0	−	28961.6i	−0.0201316	−	0.0348690i
$95$	253537.	+	146380.i	0.295713	+	0.170730i
$96$	−421243.	+	421243.i	−0.476123	+	0.476123i
$97$	−54694.5	−	204123.i	−0.0599278	−	0.223654i	0.929467	−	0.368905i	$-0.120267\pi$
$97$	−54694.5	−	204123.i	−0.0599278	−	0.223654i	−0.989395	+	0.145252i	$0.953601\pi$
$98$	838858.	−	224771.i	0.891272	−	0.238816i
$99$	213454.	+	213454.i	0.219988	+	0.219988i
$100$	536412.	−	929092.i	0.536412	−	0.929092i
$101$	−523979.	+	302519.i	−0.508569	+	0.293622i	−0.732245	−	0.681041i	$-0.761527\pi$
$101$	−523979.	+	302519.i	−0.508569	+	0.293622i	0.223677	+	0.974663i	$0.428194\pi$
$102$	110851.	−	413701.i	0.104457	−	0.389840i
$103$		−	603662.i		−	0.552436i	−0.961095	−	0.276218i	$-0.910919\pi$
$103$		−	603662.i		−	0.552436i	0.961095	−	0.276218i	$-0.0890812\pi$
$104$	552493.	−	464521.i	0.491164	−	0.412958i
$105$	790391.			0.682769
$106$	2.45544e6	+	657933.i	2.06164	+	0.552414i
$107$	−548498.	−	950027.i	−0.447738	−	0.775505i	0.550500	−	0.834835i	$-0.314437\pi$
$107$	−548498.	−	950027.i	−0.447738	−	0.775505i	−0.998238	+	0.0593298i	$0.981104\pi$
$108$	556719.	+	321422.i	0.441941	+	0.255155i
$109$	−639560.	+	639560.i	−0.493857	+	0.493857i	−0.909519	−	0.415662i	$-0.863550\pi$
$109$	−639560.	+	639560.i	−0.493857	+	0.493857i	0.415662	+	0.909519i	$0.363550\pi$
$110$	−580391.	−	2.16605e6i	−0.436057	−	1.62739i
$111$	−576272.	+	154412.i	−0.421365	+	0.112904i
$112$	−606915.	−	606915.i	−0.431990	−	0.431990i
$113$	−226130.	+	391669.i	−0.156720	+	0.271447i	−0.933684	−	0.358098i	$-0.883425\pi$
$113$	−226130.	+	391669.i	−0.156720	+	0.271447i	0.776964	+	0.629545i	$0.216759\pi$
$114$	226274.	−	130640.i	0.152729	−	0.0881780i
$115$	−807127.	+	3.01224e6i	−0.530699	+	1.98060i
$116$			728598.i			0.466782i
$117$	−532353.	−	371980.i	−0.332386	−	0.232253i
$118$	−1.48855e6			−0.905979
$119$	343581.	+	92062.2i	0.203886	+	0.0546312i
$120$	774008.	+	1.34062e6i	0.447921	+	0.775822i
$121$	631076.	+	364352.i	0.356226	+	0.205667i
$122$	−202267.	+	202267.i	−0.111390	+	0.111390i
$123$	465624.	+	1.73773e6i	0.250219	+	0.933830i
$124$	−1.08562e6	+	290891.i	−0.569394	+	0.152569i
$125$	−3.19633e6	−	3.19633e6i	−1.63652	−	1.63652i
$126$	−240561.	+	416664.i	−0.120258	+	0.208293i
$127$	−1.83707e6	+	1.06063e6i	−0.896840	+	0.517791i	−0.876174	−	0.481996i	$-0.839912\pi$
$127$	−1.83707e6	+	1.06063e6i	−0.896840	+	0.517791i	−0.0206664	+	0.999786i	$0.506579\pi$
$128$	599099.	−	2.23587e6i	0.285672	−	1.06614i
$129$		−	2.46926e6i		−	1.15026i
$130$	2.04317e6	+	4.37038e6i	0.929980	+	1.98925i
$131$	1.82952e6			0.813811			0.406906	−	0.913470i	$-0.366608\pi$
$131$	1.82952e6			0.813811			0.406906	+	0.913470i	$0.366608\pi$
$132$	−618880.	−	165828.i	−0.269082	−	0.0721003i
$133$	108497.	+	187922.i	0.0461171	+	0.0798772i
$134$	−748510.	−	432152.i	−0.311088	−	0.179607i
$135$	3.41362e6	−	3.41362e6i	1.38744	−	1.38744i
$136$	180308.	+	672919.i	0.0716801	+	0.267514i
$137$	−1.12688e6	+	301946.i	−0.438244	+	0.117427i	−0.471193	−	0.882030i	$-0.656177\pi$
$137$	−1.12688e6	+	301946.i	−0.438244	+	0.117427i	0.0329497	+	0.999457i	$0.489510\pi$
$138$	1.96800e6	+	1.96800e6i	0.748837	+	0.748837i
$139$	273227.	−	473243.i	0.101737	−	0.176214i	−0.810663	−	0.585513i	$-0.800893\pi$
$139$	273227.	−	473243.i	0.101737	−	0.176214i	0.912400	+	0.409299i	$0.134227\pi$
$140$	990913.	−	572104.i	0.361120	−	0.208493i
$141$	−18571.7	+	69310.4i	−0.00662511	+	0.0247253i
$142$		−	6.46927e6i		−	2.25939i
$143$	2.10903e6	+	765282.i	0.721232	+	0.261706i
$144$	−1.51246e6			−0.506518
$145$	5.28514e6	+	1.41615e6i	1.73361	+	0.464521i
$146$	−319100.	−	552698.i	−0.102534	−	0.177594i
$147$	−1.61376e6	−	931702.i	−0.508026	−	0.293309i
$148$	−610705.	+	610705.i	−0.188385	+	0.188385i
$149$	668891.	+	2.49633e6i	0.202207	+	0.754647i	0.990283	+	0.139069i	$0.0444109\pi$
$149$	668891.	+	2.49633e6i	0.202207	+	0.754647i	−0.788076	+	0.615578i	$0.788922\pi$
$150$	−6.94528e6	+	1.86098e6i	−2.05786	+	0.551403i
$151$	−3.30562e6	−	3.30562e6i	−0.960113	−	0.960113i	0.0391212	−	0.999234i	$-0.487544\pi$
$151$	−3.30562e6	−	3.30562e6i	−0.960113	−	0.960113i	−0.999234	+	0.0391212i	$0.987544\pi$
$152$	−212496.	+	368054.i	−0.0605090	+	0.104805i
$153$	542820.	−	313397.i	0.151559	−	0.0875026i
$154$	430187.	−	1.60548e6i	0.117786	−	0.439585i
$155$			8.44031e6i			2.26654i
$156$	1.37329e6	+	118789.i	0.361733	+	0.0312898i
$157$	3.52959e6			0.912064			0.456032	−	0.889963i	$-0.349270\pi$
$157$	3.52959e6			0.912064			0.456032	+	0.889963i	$0.349270\pi$
$158$	−1.59295e6	−	426829.i	−0.403859	−	0.108214i
$159$	−2.72721e6	−	4.72366e6i	−0.678464	−	1.17513i
$160$	5.60875e6	+	3.23821e6i	1.36932	+	0.790579i
$161$	−1.63443e6	+	1.63443e6i	−0.391642	+	0.391642i
$162$	−573972.	−	2.14209e6i	−0.135004	−	0.503841i
$163$	326202.	−	87405.5i	0.0753223	−	0.0201825i	−0.220961	−	0.975283i	$-0.570919\pi$
$163$	326202.	−	87405.5i	0.0753223	−	0.0201825i	0.296283	+	0.955100i	$0.404253\pi$
$164$	1.84157e6	+	1.84157e6i	0.417500	+	0.417500i
$165$	−2.40579e6	+	4.16694e6i	−0.535556	+	0.927611i
$166$	−4.50005e6	+	2.59810e6i	−0.983768	+	0.567979i
$167$	1.80514e6	−	6.73689e6i	0.387581	−	1.44647i	−0.446477	−	0.894795i	$-0.647322\pi$
$167$	1.80514e6	−	6.73689e6i	0.387581	−	1.44647i	0.834058	−	0.551677i	$-0.186012\pi$
$168$			1.14739e6i			0.241982i
$169$	−4.75511e6	−	828835.i	−0.985147	−	0.171715i
$170$	−4.65619e6			−0.947728
$171$	369344.	+	98965.4i	0.0738657	+	0.0197922i
$172$	−1.78731e6	−	3.09571e6i	−0.351248	−	0.608380i
$173$	5.61268e6	+	3.24048e6i	1.08401	+	0.625851i	0.931974	−	0.362524i	$-0.118085\pi$
$173$	5.61268e6	+	3.24048e6i	1.08401	+	0.625851i	0.152032	+	0.988376i	$0.451418\pi$
$174$	3.45296e6	−	3.45296e6i	0.655456	−	0.655456i
$175$	−1.54556e6	−	5.76810e6i	−0.288384	−	1.07626i
$176$	5.04698e6	−	1.35234e6i	0.925750	−	0.248054i
$177$	2.25845e6	+	2.25845e6i	0.407278	+	0.407278i
$178$	−700318.	+	1.21299e6i	−0.124175	+	0.215078i
$179$	−4.32238e6	+	2.49553e6i	−0.753640	+	0.435114i	−0.827008	−	0.562191i	$-0.809959\pi$
$179$	−4.32238e6	+	2.49553e6i	−0.753640	+	0.435114i	0.0733676	+	0.997305i	$0.476625\pi$
$180$	521844.	−	1.94755e6i	0.0894795	−	0.333942i
$181$		−	833309.i		−	0.140530i	−0.997528	−	0.0702652i	$-0.977615\pi$
$181$		−	833309.i		−	0.140530i	0.997528	−	0.0702652i	$-0.0223846\pi$
$182$	−308159.	+	3.56254e6i	−0.0511165	+	0.590943i
$183$	613764.			0.100149
$184$	−4.37280e6	−	1.17169e6i	−0.701950	−	0.188087i
$185$	3.24296e6	+	5.61697e6i	0.512184	+	0.887129i
$186$	6.52353e6	+	3.76636e6i	1.01378	+	0.585306i
$187$	−1.53114e6	+	1.53114e6i	−0.234148	+	0.234148i
$188$	26885.2	+	100337.i	0.00404613	+	0.0151004i
$189$	3.45629e6	−	926109.i	0.511946	−	0.137176i
$190$	−2.00853e6	−	2.00853e6i	−0.292831	−	0.292831i
$191$	−2.97799e6	+	5.15804e6i	−0.427389	+	0.740260i	−0.996640	−	0.0819036i	$-0.973900\pi$
$191$	−2.97799e6	+	5.15804e6i	−0.427389	+	0.740260i	0.569251	+	0.822164i	$0.307233\pi$
$192$	−898133.	+	518537.i	−0.126893	+	0.0732616i
$193$	2.45986e6	−	9.18032e6i	0.342167	−	1.27699i	−0.553720	−	0.832703i	$-0.686792\pi$
$193$	2.45986e6	−	9.18032e6i	0.342167	−	1.27699i	0.895887	−	0.444282i	$-0.146541\pi$
$194$			2.05035e6i			0.280817i
$195$	3.53088e6	−	9.73073e6i	0.476189	−	1.31233i
$196$	−2.69755e6			−0.358263
$197$	−1.92518e6	−	515850.i	−0.251810	−	0.0674722i	0.130706	−	0.991421i	$-0.458276\pi$
$197$	−1.92518e6	−	515850.i	−0.251810	−	0.0674722i	−0.382516	+	0.923949i	$0.624942\pi$
$198$	−1.46444e6	−	2.53648e6i	−0.188658	−	0.326765i
$199$	−2.21118e6	−	1.27662e6i	−0.280585	−	0.161996i	0.353103	−	0.935584i	$-0.385126\pi$
$199$	−2.21118e6	−	1.27662e6i	−0.280585	−	0.161996i	−0.633688	+	0.773589i	$0.718460\pi$
$200$	8.27004e6	−	8.27004e6i	1.03375	−	1.03375i
$201$	479983.	+	1.79132e6i	0.0591068	+	0.220590i
$202$	5.67033e6	−	1.51936e6i	0.687945	−	0.184334i
$203$	2.86770e6	+	2.86770e6i	0.342804	+	0.342804i
$204$	−665178.	+	1.15212e6i	−0.0783516	+	0.135709i
$205$	1.69378e7	−	9.77906e6i	1.96606	−	1.13510i
$206$	−1.51590e6	+	5.65742e6i	−0.173408	+	0.647168i
$207$			4.07307e6i			0.459209i
$208$	−1.01832e7	+	4.76066e6i	−1.13160	+	0.529026i
$209$	−1.32097e6			−0.144695
$210$	−7.40742e6	−	1.98481e6i	−0.799851	−	0.214319i
$211$	−1.57657e6	−	2.73070e6i	−0.167829	−	0.290688i	0.769827	−	0.638252i	$-0.220342\pi$
$211$	−1.57657e6	−	2.73070e6i	−0.167829	−	0.290688i	−0.937656	+	0.347564i	$0.887009\pi$
$212$	−6.83820e6	−	3.94804e6i	−0.717685	−	0.414356i
$213$	−9.81528e6	+	9.81528e6i	−1.01570	+	1.01570i
$214$	2.75475e6	+	1.02809e7i	0.281087	+	1.04903i
$215$	−2.59297e7	+	6.94785e6i	−2.60905	+	0.699093i
$216$	4.95547e6	+	4.95547e6i	0.491726	+	0.491726i
$217$	−3.12798e6	+	5.41783e6i	−0.306116	+	0.530208i
$218$	7.59990e6	−	4.38780e6i	0.733565	−	0.423524i
$219$	−354418.	+	1.32271e6i	−0.0337430	+	0.125930i
$220$			6.96547e6i			0.654157i
$221$	2.66827e6	−	3.81866e6i	0.247203	−	0.353781i
$222$	5.78849e6			0.529061
$223$	−1.35490e6	−	363044.i	−0.122178	−	0.0327374i	0.197212	−	0.980361i	$-0.436811\pi$
$223$	−1.35490e6	−	363044.i	−0.122178	−	0.0327374i	−0.319390	+	0.947623i	$0.603478\pi$
$224$	2.40017e6	+	4.15721e6i	0.213549	+	0.369878i
$225$	−9.11296e6	−	5.26137e6i	−0.800040	−	0.461903i
$226$	3.10281e6	−	3.10281e6i	0.268800	−	0.268800i
$227$	3.83117e6	+	1.42981e7i	0.327532	+	1.22237i	0.911742	+	0.410763i	$0.134738\pi$
$227$	3.83117e6	+	1.42981e7i	0.327532	+	1.22237i	−0.584210	+	0.811602i	$0.698596\pi$
$228$	−783924.	+	210052.i	−0.0661408	+	0.0177224i
$229$	−5.86941e6	−	5.86941e6i	−0.488752	−	0.488752i	0.419161	−	0.907912i	$-0.362324\pi$
$229$	−5.86941e6	−	5.86941e6i	−0.488752	−	0.488752i	−0.907912	+	0.419161i	$0.862324\pi$
$230$	1.51285e7	−	2.62034e7i	1.24341	−	2.15365i
$231$	−3.08854e6	+	1.78317e6i	−0.250564	+	0.144663i
$232$	−2.05579e6	+	7.67231e6i	−0.164632	+	0.614416i
$233$		−	5.82716e6i		−	0.460669i	−0.973112	−	0.230334i	$-0.926018\pi$
$233$		−	5.82716e6i		−	0.460669i	0.973112	−	0.230334i	$-0.0739820\pi$
$234$	4.05502e6	+	4.82297e6i	0.316480	+	0.376415i
$235$	780085.			0.0601088
$236$	4.46615e6	+	1.19670e6i	0.339779	+	0.0910436i
$237$	1.76925e6	+	3.06443e6i	0.132906	+	0.230200i
$238$	−2.98880e6	−	1.72559e6i	−0.221700	−	0.127999i
$239$	5.26700e6	−	5.26700e6i	0.385806	−	0.385806i	−0.487382	−	0.873189i	$-0.662048\pi$
$239$	5.26700e6	−	5.26700e6i	0.385806	−	0.385806i	0.873189	+	0.487382i	$0.162048\pi$
$240$	−6.23945e6	−	2.32860e7i	−0.451349	−	1.68446i
$241$	2.42770e7	−	6.50501e6i	1.73438	−	0.464726i	0.753195	−	0.657797i	$-0.228512\pi$
$241$	2.42770e7	−	6.50501e6i	1.73438	−	0.464726i	0.981185	+	0.193071i	$0.0618449\pi$
$242$	−4.99939e6	−	4.99939e6i	−0.352753	−	0.352753i
$243$	5.39575e6	−	9.34571e6i	0.376039	−	0.651319i
$244$	769476.	−	444257.i	0.0529695	−	0.0305819i
$245$	−5.24313e6	+	1.95676e7i	−0.356527	+	1.33058i
$246$		−	1.74550e7i		−	1.17251i
$247$	2.79825e6	−	496239.i	0.185693	−	0.0329306i
$248$	−1.22526e7			−0.803291
$249$	1.07694e7	+	2.88566e6i	0.697581	+	0.186916i
$250$	2.19290e7	+	3.79821e7i	1.40345	+	2.43085i
$251$	−1.43021e7	−	8.25732e6i	−0.904437	−	0.522177i	−0.0258001	−	0.999667i	$-0.508213\pi$
$251$	−1.43021e7	−	8.25732e6i	−0.904437	−	0.522177i	−0.878637	+	0.477490i	$0.841547\pi$
$252$	1.05673e6	−	1.05673e6i	0.0660335	−	0.0660335i
$253$	−3.64186e6	−	1.35916e7i	−0.224886	−	0.839285i
$254$	1.98802e7	−	5.32688e6i	1.21316	−	0.325066i
$255$	7.06444e6	+	7.06444e6i	0.426047	+	0.426047i
$256$	−9.63521e6	+	1.66887e7i	−0.574303	+	0.994723i
$257$	−136082.	+	78566.9i	−0.00801680	+	0.00462850i	−0.504003	−	0.863702i	$-0.668140\pi$
$257$	−136082.	+	78566.9i	−0.00801680	+	0.00462850i	0.495986	+	0.868330i	$0.334807\pi$
$258$	−6.20075e6	+	2.31415e7i	−0.361064	+	1.34751i
$259$			4.80737e6i			0.276699i
$260$	−2.61667e6	−	1.47552e7i	−0.148877	−	0.839506i
$261$	7.14642e6			0.401946
$262$	−1.71460e7	−	4.59426e6i	−0.953364	−	0.255453i
$263$	−1.65537e7	−	2.86719e7i	−0.909974	−	1.57612i	−0.814098	−	0.580727i	$-0.802768\pi$
$263$	−1.65537e7	−	2.86719e7i	−0.909974	−	1.57612i	−0.0958757	−	0.995393i	$-0.530565\pi$
$264$	−6.04905e6	−	3.49242e6i	−0.328758	−	0.189808i
$265$	−4.19296e7	+	4.19296e7i	−2.25311	+	2.25311i
$266$	−544910.	−	2.03363e6i	−0.0289521	−	0.108051i
$267$	2.90290e6	−	777829.i	0.152510	−	0.0408649i
$268$	1.89835e6	+	1.89835e6i	0.0986218	+	0.0986218i
$269$	9.93564e6	−	1.72090e7i	0.510433	−	0.884096i	−0.489494	−	0.872007i	$-0.662818\pi$
$269$	9.93564e6	−	1.72090e7i	0.510433	−	0.884096i	0.999927	−	0.0120895i	$-0.00384830\pi$
$270$	−4.05641e7	+	2.34197e7i	−2.06087	+	1.18984i
$271$	−192013.	+	716602.i	−0.00964767	+	0.0360056i	−0.970582	−	0.240771i	$-0.922600\pi$
$271$	−192013.	+	716602.i	−0.00964767	+	0.0360056i	0.960934	+	0.276777i	$0.0892663\pi$
$272$		−	1.08491e7i		−	0.539122i
$273$	5.87269e6	−	4.93760e6i	0.288635	−	0.242677i
$274$	1.13192e7			0.550254
$275$	3.51138e7	+	9.40871e6i	1.68842	+	0.452410i
$276$	−4.32250e6	−	7.48679e6i	−0.205593	−	0.356097i
$277$	2.30529e7	+	1.33096e7i	1.08464	+	0.626219i	0.932145	−	0.362085i	$-0.117935\pi$
$277$	2.30529e7	+	1.33096e7i	1.08464	+	0.626219i	0.152498	+	0.988304i	$0.451268\pi$
$278$	−3.74904e6	+	3.74904e6i	−0.174496	+	0.174496i
$279$	2.85319e6	+	1.06483e7i	0.131377	+	0.490304i
$280$	1.20488e7	−	3.22846e6i	0.548869	−	0.147069i
$281$	−1.31657e7	−	1.31657e7i	−0.593371	−	0.593371i	0.345169	−	0.938540i	$-0.387821\pi$
$281$	−1.31657e7	−	1.31657e7i	−0.593371	−	0.593371i	−0.938540	+	0.345169i	$0.887821\pi$
$282$	348101.	−	602929.i	0.0155224	−	0.0268856i
$283$	1.85879e7	−	1.07318e7i	0.820110	−	0.473491i	−0.0303444	−	0.999540i	$-0.509660\pi$
$283$	1.85879e7	−	1.07318e7i	0.820110	−	0.473491i	0.850454	+	0.526049i	$0.176327\pi$
$284$	−5.20088e6	+	1.94100e7i	−0.227050	+	0.847363i
$285$			6.09473e6i			0.263281i
$286$	−1.78438e7	−	1.24683e7i	−0.762761	−	0.532976i
$287$	1.44965e7			0.613222
$288$	8.17062e6	+	2.18931e6i	0.342041	+	0.0916495i
$289$	−9.82073e6	−	1.70100e7i	−0.406865	−	0.704711i
$290$	−4.59753e7	−	2.65438e7i	−1.88508	−	1.08835i
$291$	3.11083e6	−	3.11083e6i	0.126240	−	0.126240i
$292$	513072.	+	1.91481e6i	0.0206077	+	0.0769091i
$293$	2.02819e6	−	543451.i	0.0806316	−	0.0216052i	−0.218278	−	0.975887i	$-0.570044\pi$
$293$	2.02819e6	−	543451.i	0.0806316	−	0.0216052i	0.298909	+	0.954282i	$0.403377\pi$
$294$	1.27842e7	+	1.27842e7i	0.503073	+	0.503073i
$295$	1.73614e7	−	3.00708e7i	0.676266	−	1.17133i
$296$	−8.15402e6	+	4.70772e6i	−0.314410	+	0.181525i
$297$	−5.63777e6	+	2.10404e7i	−0.215198	+	0.803129i
$298$		−	2.50750e7i		−	0.947527i
$299$	1.28205e7	+	2.74234e7i	0.479615	+	1.02591i
$300$	2.23343e7			0.827195
$301$	−1.92191e7	−	5.14975e6i	−0.704749	−	0.188837i
$302$	2.26788e7	+	3.92808e7i	0.823377	+	1.42613i
$303$	−1.09083e7	−	6.29791e6i	−0.392129	−	0.226396i
$304$	4.67994e6	−	4.67994e6i	0.166579	−	0.166579i
$305$	−1.72697e6	−	6.44515e6i	−0.0608675	−	0.227161i
$306$	−5.87422e6	+	1.57399e6i	−0.205015	+	0.0549336i
$307$	2.33578e7	+	2.33578e7i	0.807267	+	0.807267i	0.984219	−	0.176953i	$-0.0566240\pi$
$307$	2.33578e7	+	2.33578e7i	0.807267	+	0.807267i	−0.176953	+	0.984219i	$0.556624\pi$
$308$	−2.58141e6	+	4.47113e6i	−0.0883495	+	0.153026i
$309$	1.08835e7	−	6.28358e6i	0.368886	−	0.212977i
$310$	2.11951e7	−	7.91013e7i	0.711461	−	2.65521i
$311$			1.99611e7i			0.663596i	0.943350	+	0.331798i	$0.107655\pi$
$311$			1.99611e7i			0.663596i	−0.943350	+	0.331798i	$0.892345\pi$
$312$	1.41259e7	+	5.12570e6i	0.465105	+	0.168768i
$313$	−3.23854e7			−1.05613			−0.528063	−	0.849205i	$-0.677081\pi$
$313$	−3.23854e7			−1.05613			−0.528063	+	0.849205i	$0.677081\pi$
$314$	−3.30788e7	−	8.86343e6i	−1.06847	−	0.286294i
$315$	−5.61145e6	−	9.71932e6i	−0.179533	−	0.310960i
$316$	4.43622e6	+	2.56125e6i	0.140589	+	0.0811693i
$317$	1.49729e7	−	1.49729e7i	0.470031	−	0.470031i	−0.431893	−	0.901925i	$-0.642154\pi$
$317$	1.49729e7	−	1.49729e7i	0.470031	−	0.470031i	0.901925	+	0.431893i	$0.142154\pi$
$318$	1.36970e7	+	5.11179e7i	0.425936	+	1.58961i
$319$	−2.38472e7	+	6.38984e6i	−0.734625	+	0.196842i
$320$	7.97228e6	+	7.97228e6i	0.243295	+	0.243295i
$321$	1.14188e7	−	1.97779e7i	0.345226	−	0.597949i
$322$	1.94220e7	−	1.12133e7i	0.581736	−	0.335866i
$323$	−709895.	+	2.64937e6i	−0.0210662	+	0.0786202i
$324$			6.88842e6i			0.202528i
$325$	−7.79171e7	−	6.73982e6i	−2.26978	−	0.196335i
$326$	−3.27660e6			−0.0945738
$327$	−1.81879e7	−	4.87344e6i	−0.520164	−	0.139377i
$328$	1.41960e7	+	2.45882e7i	0.402296	+	0.696796i
$329$	500736.	+	289100.i	0.0140612	+	0.00811821i
$330$	3.30106e7	−	3.30106e7i	0.918568	−	0.918568i
$331$	4.20969e6	+	1.57108e7i	0.116082	+	0.433225i	0.999366	−	0.0356146i	$-0.0113389\pi$
$331$	4.20969e6	+	1.57108e7i	0.116082	+	0.433225i	−0.883283	+	0.468840i	$0.844672\pi$
$332$	1.55903e7	−	4.17742e6i	0.426031	−	0.114155i
$333$	5.99008e6	+	5.99008e6i	0.162218	+	0.162218i
$334$	−3.38351e7	+	5.86040e7i	−0.908087	+	1.57285i
$335$	1.74601e7	−	1.00806e7i	0.464422	−	0.268134i
$336$	4.62469e6	−	1.72596e7i	0.121917	−	0.455001i
$337$		−	1.54316e7i		−	0.403201i	−0.979468	−	0.201600i	$-0.935386\pi$
$337$		−	1.54316e7i		−	0.403201i	0.979468	−	0.201600i	$-0.0646142\pi$
$338$	4.24828e7	+	1.97086e7i	1.10018	+	0.510395i
$339$	−9.41527e6			−0.241676
$340$	1.39701e7	+	3.74328e6i	0.355437	+	0.0952391i
$341$	−1.90419e7	−	3.29815e7i	−0.480227	−	0.831778i
$342$	−3.21291e6	−	1.85498e6i	−0.0803195	−	0.0463725i
$343$	−2.45727e7	+	2.45727e7i	−0.608934	+	0.608934i
$344$	−1.00860e7	−	3.76416e7i	−0.247768	−	0.924682i
$345$	−6.27095e7	+	1.68030e7i	−1.52713	+	0.409193i
$346$	−4.44637e7	−	4.44637e7i	−1.07344	−	1.07344i
$347$	−3.75387e7	+	6.50189e7i	−0.898443	+	1.55615i	−0.0689584	+	0.997620i	$0.521968\pi$
$347$	−3.75387e7	+	6.50189e7i	−0.898443	+	1.55615i	−0.829485	+	0.558530i	$0.811366\pi$
$348$	−1.31360e7	+	7.58406e6i	−0.311691	+	0.179955i
$349$	−5.00643e6	+	1.86843e7i	−0.117775	+	0.439541i	−0.999479	−	0.0322604i	$-0.989729\pi$
$349$	−5.00643e6	+	1.86843e7i	−0.117775	+	0.439541i	0.881705	+	0.471801i	$0.156396\pi$
$350$			5.79389e7i			1.35134i
$351$	4.03855e6	−	4.66885e7i	0.0933908	−	1.07966i
$352$	−2.92225e7			−0.670022
$353$	5.05743e6	+	1.35513e6i	0.114976	+	0.0308076i	0.315848	−	0.948810i	$-0.397711\pi$
$353$	5.05743e6	+	1.35513e6i	0.114976	+	0.0308076i	−0.200872	+	0.979617i	$0.564378\pi$
$354$	−1.54945e7	−	2.68373e7i	−0.349275	−	0.604962i
$355$	1.30688e8	+	7.54528e7i	2.92113	+	1.68652i
$356$	3.07635e6	−	3.07635e6i	0.0681845	−	0.0681845i
$357$	1.91657e6	+	7.15274e6i	0.0421231	+	0.157206i
$358$	4.67754e7	−	1.25334e7i	1.01946	−	0.273162i
$359$	−1.77805e7	−	1.77805e7i	−0.384292	−	0.384292i	0.488354	−	0.872646i	$-0.337597\pi$
$359$	−1.77805e7	−	1.77805e7i	−0.384292	−	0.384292i	−0.872646	+	0.488354i	$0.837597\pi$
$360$	1.09903e7	−	1.90357e7i	0.235560	−	0.408002i
$361$	3.92939e7	−	2.26863e7i	0.835224	−	0.482217i
$362$	−2.09259e6	+	7.80965e6i	−0.0441121	+	0.164629i
$363$			1.51703e7i			0.317157i
$364$	3.78863e6	−	1.04411e7i	0.0785558	−	0.216491i
$365$	1.48870e7			0.306146
$366$	−5.75210e6	−	1.54127e6i	−0.117323	−	0.0314366i
$367$	−2.04112e6	−	3.53532e6i	−0.0412924	−	0.0715206i	0.844641	−	0.535334i	$-0.179814\pi$
$367$	−2.04112e6	−	3.53532e6i	−0.0412924	−	0.0715206i	−0.885933	+	0.463813i	$0.846481\pi$
$368$	6.10550e7	+	3.52501e7i	1.22512	+	0.707322i
$369$	1.80629e7	−	1.80629e7i	0.359508	−	0.359508i
$370$	−1.62873e7	−	6.07850e7i	−0.321546	−	1.20003i
$371$	−4.24537e7	+	1.13754e7i	−0.831369	+	0.222765i
$372$	−1.65448e7	−	1.65448e7i	−0.321391	−	0.321391i
$373$	9.66679e6	−	1.67434e7i	0.186275	−	0.322639i	−0.757730	−	0.652568i	$-0.773692\pi$
$373$	9.66679e6	−	1.67434e7i	0.186275	−	0.322639i	0.944006	+	0.329930i	$0.107025\pi$
$374$	1.81946e7	−	1.05047e7i	0.347798	−	0.200802i
$375$	2.43561e7	−	9.08980e7i	0.461863	−	1.72370i
$376$			1.13243e6i			0.0213034i
$377$	4.81159e7	−	2.24943e7i	0.897975	−	0.419806i
$378$	−3.47174e7			−0.642794
$379$	8.33021e6	+	2.23207e6i	0.153016	+	0.0410006i	0.334514	−	0.942391i	$-0.391428\pi$
$379$	8.33021e6	+	2.23207e6i	0.153016	+	0.0410006i	−0.181498	+	0.983391i	$0.558094\pi$
$380$	4.41151e6	+	7.64097e6i	0.0803965	+	0.139251i
$381$	−3.82446e7	−	2.20805e7i	−0.691504	−	0.399240i
$382$	4.08621e7	−	4.08621e7i	0.733044	−	0.733044i
$383$	−1.77683e7	−	6.63122e7i	−0.316264	−	1.18031i	−0.922807	−	0.385262i	$-0.874111\pi$
$383$	−1.77683e7	−	6.63122e7i	−0.316264	−	1.18031i	0.606543	−	0.795051i	$-0.292556\pi$
$384$	4.65467e7	−	1.24722e7i	0.822045	−	0.220266i
$385$	2.74155e7	+	2.74155e7i	0.480412	+	0.480412i
$386$	−4.61068e7	+	7.98594e7i	−0.801684	+	1.38856i
$387$	−3.03641e7	+	1.75307e7i	−0.523875	+	0.302459i
$388$	1.64835e6	−	6.15173e6i	0.0282199	−	0.105318i
$389$			7.51491e7i			1.27666i	0.769763	+	0.638329i	$0.220374\pi$
$389$			7.51491e7i			1.27666i	−0.769763	+	0.638329i	$0.779626\pi$
$390$	−5.75265e7	+	8.23282e7i	−0.969782	+	1.38789i
$391$	−2.92168e7			−0.488768
$392$	−2.84059e7	−	7.61133e6i	−0.471574	−	0.126358i
$393$	1.90437e7	+	3.29846e7i	0.313743	+	0.543418i
$394$	1.67471e7	+	9.66893e6i	0.273811	+	0.158085i
$395$	2.72015e7	−	2.72015e7i	0.441368	−	0.441368i
$396$	2.35463e6	+	8.78759e6i	0.0379173	+	0.141509i
$397$	−3.65718e6	+	979937.i	−0.0584486	+	0.0156613i	−0.287925	−	0.957653i	$-0.592965\pi$
$397$	−3.65718e6	+	979937.i	−0.0584486	+	0.0156613i	0.229476	+	0.973314i	$0.426299\pi$
$398$	1.75170e7	+	1.75170e7i	0.277850	+	0.277850i
$399$	−2.25871e6	+	3.91220e6i	−0.0355584	+	0.0615889i
$400$	−1.57735e8	+	9.10683e7i	−2.46461	+	1.42294i
$401$	3.98812e6	−	1.48839e7i	0.0618494	−	0.230825i	−0.928081	−	0.372377i	$-0.878543\pi$
$401$	3.98812e6	−	1.48839e7i	0.0618494	−	0.230825i	0.989931	+	0.141552i	$0.0452094\pi$
$402$		−	1.79933e7i		−	0.276970i
$403$	5.27269e7	+	6.27124e7i	0.805596	+	0.958160i
$404$	−1.82343e7			−0.276532
$405$	4.99675e7	+	1.33888e7i	0.752182	+	0.201547i
$406$	−1.96743e7	−	3.40769e7i	−0.293983	−	0.509193i
$407$	−2.53445e7	−	1.46326e7i	−0.375924	−	0.217040i
$408$	−1.02553e7	+	1.02553e7i	−0.150997	+	0.150997i
$409$	1.57037e7	+	5.86069e7i	0.229526	+	0.856601i	0.980541	+	0.196316i	$0.0628979\pi$
$409$	1.57037e7	+	5.86069e7i	0.229526	+	0.856601i	−0.751015	+	0.660285i	$0.770435\pi$
$410$	−1.83296e8	+	4.91139e7i	−2.65950	+	0.712612i
$411$	−1.71736e7	−	1.71736e7i	−0.247364	−	0.247364i
$412$	9.09641e6	−	1.57555e7i	0.130070	−	0.225289i
$413$	2.22885e7	−	1.28683e7i	0.316396	−	0.182671i
$414$	1.02282e7	−	3.81722e7i	0.144145	−	0.537955i
$415$		−	1.21209e8i		−	1.69587i
$416$	6.19028e7	−	1.09778e7i	0.859865	−	0.152488i
$417$	1.13762e7			0.156888
$418$	1.23799e7	+	3.31719e6i	0.169507	+	0.0454194i
$419$	−5.54749e6	−	9.60854e6i	−0.0754144	−	0.130622i	0.825852	−	0.563887i	$-0.190695\pi$
$419$	−5.54749e6	−	9.60854e6i	−0.0754144	−	0.130622i	−0.901266	+	0.433265i	$0.857361\pi$
$420$	2.06290e7	+	1.19102e7i	0.278440	+	0.160757i
$421$	−5.69651e7	+	5.69651e7i	−0.763419	+	0.763419i	−0.976939	−	0.213520i	$-0.931507\pi$
$421$	−5.69651e7	+	5.69651e7i	−0.763419	+	0.763419i	0.213520	+	0.976939i	$0.431507\pi$
$422$	7.91810e6	+	2.95508e7i	0.105362	+	0.393216i
$423$	984151.	−	263703.i	0.0130029	−	0.00348412i
$424$	−6.08682e7	−	6.08682e7i	−0.798533	−	0.798533i
$425$	3.77407e7	−	6.53688e7i	0.491635	−	0.851537i
$426$	1.16635e8	−	6.73394e7i	1.50869	−	0.871044i
$427$	1.28003e6	−	4.77715e6i	0.0164414	−	0.0613600i
$428$		−	3.30607e7i		−	0.421678i
$429$	8.15580e6	+	4.59899e7i	0.103299	+	0.582492i
$430$	2.60457e8			3.27589
$431$	9.39536e7	+	2.51748e7i	1.17350	+	0.314437i	0.792344	−	0.610075i	$-0.208861\pi$
$431$	9.39536e7	+	2.51748e7i	1.17350	+	0.314437i	0.381152	+	0.924512i	$0.375527\pi$
$432$	−5.45688e7	−	9.45159e7i	−0.676851	−	1.17234i
$433$	−1.06785e8	−	6.16526e7i	−1.31537	−	0.759430i	−0.332391	−	0.943142i	$-0.607855\pi$
$433$	−1.06785e8	−	6.16526e7i	−1.31537	−	0.759430i	−0.982980	+	0.183712i	$0.941189\pi$
$434$	4.29201e7	−	4.29201e7i	0.525039	−	0.525039i
$435$	2.94817e7	+	1.10027e8i	0.358166	+	1.33669i
$436$	−2.63297e7	+	7.05503e6i	−0.317678	+	0.0851215i
$437$	−1.26032e7	−	1.26032e7i	−0.151020	−	0.151020i
$438$	6.64310e6	−	1.15062e7i	0.0790585	−	0.136933i
$439$	−4.36371e7	+	2.51939e7i	−0.515777	+	0.297784i	−0.735205	−	0.677845i	$-0.762914\pi$
$439$	−4.36371e7	+	2.51939e7i	−0.515777	+	0.297784i	0.219428	+	0.975629i	$0.429581\pi$
$440$	−1.96535e7	+	7.33480e7i	−0.230719	+	0.861054i
$441$			2.64588e7i			0.308500i
$442$	−3.45960e7	+	2.90874e7i	−0.400644	+	0.336851i
$443$	−6.24926e7			−0.718815			−0.359408	−	0.933181i	$-0.617021\pi$
$443$	−6.24926e7			−0.718815			−0.359408	+	0.933181i	$0.617021\pi$
$444$	−1.73674e7	−	4.65357e6i	−0.198420	−	0.0531664i
$445$	−1.63360e7	−	2.82947e7i	−0.185381	−	0.321089i
$446$	1.17862e7	+	6.80478e6i	0.132853	+	0.0767025i
$447$	−3.80441e7	+	3.80441e7i	−0.425956	+	0.425956i
$448$	2.16287e6	+	8.07193e6i	0.0240545	+	0.0897725i
$449$	9.55183e7	−	2.55940e7i	1.05523	−	0.282748i	0.310819	−	0.950469i	$-0.399397\pi$
$449$	9.55183e7	−	2.55940e7i	1.05523	−	0.282748i	0.744412	+	0.667721i	$0.232730\pi$
$450$	7.21930e7	+	7.21930e7i	0.792241	+	0.792241i
$451$	−4.41244e7	+	7.64256e7i	−0.481004	+	0.833124i
$452$	−1.18039e7	+	6.81500e6i	−0.127824	+	0.0737990i
$453$	2.51888e7	−	9.40060e7i	0.270965	−	1.01126i
$454$		−	1.43620e8i		−	1.53479i
$455$	−6.83740e7	−	4.77761e7i	−0.725867	−	0.507196i
$456$	−8.84758e6			−0.0933104
$457$	5.43112e7	+	1.45526e7i	0.569037	+	0.152473i	0.531855	−	0.846836i	$-0.321495\pi$
$457$	5.43112e7	+	1.45526e7i	0.569037	+	0.152473i	0.0371820	+	0.999309i	$0.488162\pi$
$458$	4.02681e7	+	6.97463e7i	0.419145	+	0.725981i
$459$	3.91694e7	+	2.26145e7i	0.405051	+	0.233856i
$460$	−6.64565e7	+	6.64565e7i	−0.682753	+	0.682753i
$461$	8.73835e6	+	3.26120e7i	0.0891921	+	0.332870i	0.996075	−	0.0885132i	$-0.0282116\pi$
$461$	8.73835e6	+	3.26120e7i	0.0891921	+	0.332870i	−0.906883	+	0.421383i	$0.861545\pi$
$462$	3.34232e7	−	8.95572e6i	0.338940	−	0.0908186i
$463$	−6.00127e7	−	6.00127e7i	−0.604645	−	0.604645i	0.336897	−	0.941542i	$-0.390623\pi$
$463$	−6.00127e7	−	6.00127e7i	−0.604645	−	0.604645i	−0.941542	+	0.336897i	$0.890623\pi$
$464$	6.18482e7	−	1.07124e8i	0.619118	−	1.07234i
$465$	−1.52171e8	+	8.78561e7i	−1.51347	+	0.873802i
$466$	−1.46330e7	+	5.46112e7i	−0.144603	+	0.539665i
$467$		−	1.59772e8i		−	1.56873i	−0.620298	−	0.784367i	$-0.712988\pi$
$467$		−	1.59772e8i		−	1.56873i	0.620298	−	0.784367i	$-0.287012\pi$
$468$	−8.28905e6	−	1.77305e7i	−0.0808663	−	0.172975i
$469$	1.49435e7			0.144855
$470$	−7.31084e6	−	1.95893e6i	−0.0704163	−	0.0188680i
$471$	3.67399e7	+	6.36354e7i	0.351621	+	0.609026i
$472$	4.36530e7	+	2.52031e7i	0.415134	+	0.239678i
$473$	8.56486e7	−	8.56486e7i	0.809351	−	0.809351i
$474$	−8.88581e6	−	3.31623e7i	−0.0834377	−	0.311394i
$475$	4.44780e7	−	1.19178e7i	0.415016	−	0.111203i
$476$	7.58013e6	+	7.58013e6i	0.0702839	+	0.0702839i
$477$	−3.87241e7	+	6.70722e7i	−0.356801	+	0.617998i
$478$	−6.25878e7	+	3.61351e7i	−0.573068	+	0.330861i
$479$	−3.96180e7	+	1.47856e8i	−0.360484	+	1.34534i	0.512958	+	0.858414i	$0.328550\pi$
$479$	−3.96180e7	+	1.47856e8i	−0.360484	+	1.34534i	−0.873441	+	0.486929i	$0.838117\pi$
$480$			1.34828e8i			1.21914i
$481$	5.91849e7	+	2.14758e7i	0.531834	+	0.192981i
$482$	−2.43856e8			−2.17767
$483$	−4.64803e7	−	1.24544e7i	−0.412504	−	0.110530i
$484$	1.09806e7	+	1.90190e7i	0.0968482	+	0.167746i
$485$	−4.14199e7	−	2.39138e7i	−0.363064	−	0.209615i
$486$	−7.40368e7	+	7.40368e7i	−0.644969	+	0.644969i
$487$	−5.82216e7	−	2.17286e8i	−0.504077	−	1.88124i	−0.471685	−	0.881767i	$-0.656354\pi$
$487$	−5.82216e7	−	2.17286e8i	−0.504077	−	1.88124i	−0.0323927	−	0.999475i	$-0.510313\pi$
$488$	9.35626e6	−	2.50700e6i	0.0805087	−	0.0215723i
$489$	4.97131e6	+	4.97131e6i	0.0425152	+	0.0425152i
$490$	9.82756e7	−	1.70218e8i	0.835329	−	1.44683i
$491$	6.73158e7	−	3.88648e7i	0.568686	−	0.328331i	−0.187939	−	0.982181i	$-0.560181\pi$
$491$	6.73158e7	−	3.88648e7i	0.568686	−	0.328331i	0.756624	+	0.653850i	$0.226847\pi$
$492$	−1.40327e7	+	5.23709e7i	−0.117828	+	0.439739i
$493$			5.12625e7i			0.427818i
$494$	−2.74709e7	−	2.37623e6i	−0.227872	−	0.0197109i
$495$	6.83204e7			0.563294
$496$	1.84309e8	+	4.93855e7i	1.51043	+	0.404720i
$497$	5.59257e7	+	9.68662e7i	0.455557	+	0.789047i
$498$	−9.36830e7	−	5.40879e7i	−0.758530	−	0.437937i
$499$	−4.04648e7	+	4.04648e7i	−0.325668	+	0.325668i	−0.850937	−	0.525268i	$-0.823965\pi$
$499$	−4.04648e7	+	4.04648e7i	−0.325668	+	0.325668i	0.525268	+	0.850937i	$0.323965\pi$
$500$	−3.52590e7	−	1.31588e8i	−0.282072	−	1.05271i
$501$	1.40250e8	−	3.75799e7i	1.11530	−	0.298842i
$502$	1.13301e8	+	1.13301e8i	0.895621	+	0.895621i
$503$	−3.93752e7	+	6.81999e7i	−0.309399	+	0.535895i	−0.978231	−	0.207518i	$-0.933461\pi$
$503$	−3.93752e7	+	6.81999e7i	−0.309399	+	0.535895i	0.668832	+	0.743414i	$0.266795\pi$
$504$	1.41093e7	−	8.14601e6i	0.110208	−	0.0636288i
$505$	−3.54414e7	+	1.32269e8i	−0.275192	+	1.02703i
$506$			1.36524e8i			1.05380i
$507$	−3.45534e7	−	9.43579e7i	−0.265135	−	0.724026i
$508$	−6.39296e7			−0.487653
$509$	−1.98778e8	−	5.32625e7i	−1.50736	−	0.403895i	−0.591800	−	0.806085i	$-0.701583\pi$
$509$	−1.98778e8	−	5.32625e7i	−1.50736	−	0.403895i	−0.915556	+	0.402190i	$0.868249\pi$
$510$	−4.84668e7	−	8.39469e7i	−0.365370	−	0.632840i
$511$	9.55595e6	+	5.51713e6i	0.0716162	+	0.0413476i
$512$	2.74548e7	−	2.74548e7i	0.204554	−	0.204554i
$513$	7.14126e6	+	2.66516e7i	0.0528960	+	0.197411i
$514$	1.47263e6	−	394591.i	0.0108444	−	0.00290575i
$515$	−9.66073e7	−	9.66073e7i	−0.707275	−	0.707275i
$516$	3.72086e7	−	6.44471e7i	0.270828	−	0.469088i
$517$	−3.04827e6	+	1.75992e6i	−0.0220588	+	0.0127357i
$518$	1.20722e7	−	4.50539e7i	0.0868551	−	0.324148i
$519$			1.34922e8i			0.965119i
$520$	1.40786e7	−	1.62758e8i	0.100126	−	1.15753i
$521$	1.40196e8			0.991343			0.495671	−	0.868510i	$-0.334922\pi$
$521$	1.40196e8			0.991343			0.495671	+	0.868510i	$0.334922\pi$
$522$	−6.69752e7	−	1.79459e7i	−0.470871	−	0.126170i
$523$	−2.49046e7	−	4.31361e7i	−0.174091	−	0.301534i	0.765756	−	0.643132i	$-0.222365\pi$
$523$	−2.49046e7	−	4.31361e7i	−0.174091	−	0.301534i	−0.939846	+	0.341598i	$0.889032\pi$
$524$	4.77502e7	+	2.75686e7i	0.331880	+	0.191611i
$525$	8.79057e7	−	8.79057e7i	0.607490	−	0.607490i
$526$	8.31388e7	+	3.10278e8i	0.571276	+	2.13203i
$527$	−7.63817e7	+	2.04664e7i	−0.521864	+	0.139833i
$528$	7.69160e7	+	7.69160e7i	0.522534	+	0.522534i
$529$	2.09112e7	−	3.62192e7i	0.141258	−	0.244665i
$530$	4.98250e8	−	2.87665e8i	3.34672	−	1.93223i
$531$	1.17378e7	−	4.38060e7i	0.0783976	−	0.292584i
$532$			6.53964e6i			0.0434329i
$533$	6.47597e7	−	1.78471e8i	0.427684	−	1.17865i
$534$	−2.91587e7			−0.191490
$535$	−2.39817e8	−	6.42588e7i	−1.56610	−	0.419635i
$536$	1.46338e7	+	2.53465e7i	0.0950303	+	0.164597i
$537$	−8.99843e7	−	5.19524e7i	−0.581090	−	0.335493i
$538$	−1.36330e8	+	1.36330e8i	−0.875478	+	0.875478i
$539$	−2.36577e7	−	8.82917e7i	−0.151080	−	0.563837i
$540$	1.40534e8	−	3.76559e7i	0.892481	−	0.239139i
$541$	1.89076e8	+	1.89076e8i	1.19411	+	1.19411i	0.975901	+	0.218212i	$0.0700226\pi$
$541$	1.89076e8	+	1.89076e8i	1.19411	+	1.19411i	0.218212	+	0.975901i	$0.429977\pi$
$542$	3.59903e6	−	6.23370e6i	0.0226041	−	0.0391515i
$543$	1.50238e7	−	8.67401e6i	0.0938385	−	0.0541777i
$544$	−1.57043e7	+	5.86092e7i	−0.0975488	+	0.364057i
$545$			2.04704e8i			1.26455i
$546$	−6.74371e7	+	3.15270e7i	−0.414306	+	0.193689i
$547$	1.90723e8			1.16531			0.582654	−	0.812721i	$-0.302014\pi$
$547$	1.90723e8			1.16531			0.582654	+	0.812721i	$0.302014\pi$
$548$	−3.39613e7	−	9.09989e6i	−0.206368	−	0.0552961i
$549$	−4.35748e6	−	7.54737e6i	−0.0263341	−	0.0456119i
$550$	−3.05454e8	−	1.76354e8i	−1.83594	−	1.05998i
$551$	−2.21129e7	+	2.21129e7i	−0.132188	+	0.132188i
$552$	−2.43924e7	−	9.10338e7i	−0.145023	−	0.541235i
$553$	2.75415e7	−	7.37972e6i	0.162859	−	0.0436379i
$554$	−1.82626e8	−	1.82626e8i	−1.07407	−	1.07407i
$555$	−6.75126e7	+	1.16935e8i	−0.394917	+	0.684016i
$556$	1.42623e7	−	8.23437e6i	0.0829787	−	0.0479077i
$557$	−2.22742e7	+	8.31285e7i	−0.128895	+	0.481044i	−0.999949	−	0.0101449i	$-0.996771\pi$
$557$	−2.22742e7	+	8.31285e7i	−0.128895	+	0.481044i	0.871053	+	0.491189i	$0.163437\pi$
$558$		−	1.06959e8i		−	0.615621i
$559$	−1.49257e8	+	2.13607e8i	−0.854475	+	1.22287i
$560$	−1.94256e8			−1.10614
$561$	−4.35429e7	−	1.16673e7i	−0.246621	−	0.0660818i
$562$	9.03258e7	+	1.56449e8i	0.508865	+	0.881380i
$563$	−1.30569e7	−	7.53841e6i	−0.0731670	−	0.0422430i	0.462970	−	0.886374i	$-0.346784\pi$
$563$	−1.30569e7	−	7.53841e6i	−0.0731670	−	0.0422430i	−0.536137	+	0.844131i	$0.680117\pi$
$564$	−1.52914e6	+	1.52914e6i	−0.00852332	+	0.00852332i
$565$	2.64921e7	+	9.88699e7i	0.146883	+	0.548174i
$566$	−2.01153e8	+	5.38987e7i	−1.10937	+	0.297255i
$567$	2.71122e7	+	2.71122e7i	0.148736	+	0.148736i
$568$	−1.09533e8	+	1.89717e8i	−0.597723	+	1.03529i
$569$	2.84280e7	−	1.64129e7i	0.154316	−	0.0890941i	−0.420854	−	0.907128i	$-0.638269\pi$
$569$	2.84280e7	−	1.64129e7i	0.154316	−	0.0890941i	0.575169	+	0.818034i	$0.304936\pi$
$570$	1.53050e7	−	5.71189e7i	0.0826433	−	0.308429i
$571$		−	1.33271e8i		−	0.715857i	−0.933749	−	0.357929i	$-0.883483\pi$
$571$		−	1.33271e8i		−	0.715857i	0.933749	−	0.357929i	$-0.116517\pi$
$572$	4.35135e7	+	5.17541e7i	0.232507	+	0.276539i
$573$	−1.23993e8			−0.659073
$574$	−1.35859e8	−	3.64033e7i	−0.718377	−	0.192489i
$575$	2.45248e8	+	4.24783e8i	1.29004	+	2.23441i
$576$	1.27528e7	+	7.36281e6i	0.0667324	+	0.0385280i
$577$	2.45904e8	−	2.45904e8i	1.28008	−	1.28008i	0.339464	−	0.940619i	$-0.389754\pi$
$577$	2.45904e8	−	2.45904e8i	1.28008	−	1.28008i	0.940619	−	0.339464i	$-0.110246\pi$
$578$	4.93232e7	+	1.84077e8i	0.255428	+	0.953269i
$579$	1.91118e8	−	5.12099e7i	0.984613	−	0.263826i
$580$	1.16602e8	+	1.16602e8i	0.597613	+	0.597613i
$581$	4.49203e7	−	7.78042e7i	0.229041	−	0.396711i
$582$	−3.69660e7	+	2.13423e7i	−0.187514	+	0.108261i
$583$	6.92490e7	−	2.58441e8i	0.349468	−	1.30423i
$584$			2.16111e7i			0.108502i
$585$	−1.44725e8	+	2.56654e7i	−0.722898	+	0.128198i
$586$	−2.03726e7			−0.101240
$587$	−2.48817e8	−	6.66704e7i	−1.23017	−	0.329624i	−0.415526	−	0.909581i	$-0.636402\pi$
$587$	−2.48817e8	−	6.66704e7i	−1.23017	−	0.329624i	−0.814647	+	0.579958i	$0.803069\pi$
$588$	−2.80791e7	−	4.86345e7i	−0.138118	−	0.239228i
$589$	−4.17771e7	−	2.41200e7i	−0.204452	−	0.118041i
$590$	−2.38221e8	+	2.38221e8i	−1.15991	+	1.15991i
$591$	−1.07391e7	−	4.00788e7i	−0.0520241	−	0.194157i
$592$	1.41631e8	−	3.79500e7i	0.682644	−	0.182914i
$593$	−1.13225e8	−	1.13225e8i	−0.542972	−	0.542972i	0.381427	−	0.924399i	$-0.375433\pi$
$593$	−1.13225e8	−	1.13225e8i	−0.542972	−	0.542972i	−0.924399	+	0.381427i	$0.875433\pi$
$594$	1.05673e8	−	1.83030e8i	0.504200	−	0.873300i
$595$	6.97183e7	−	4.02519e7i	0.330976	−	0.191089i
$596$	−2.01587e7	+	7.52332e7i	−0.0952189	+	0.355362i
$597$		−	5.31540e7i		−	0.249812i
$598$	−5.12869e7	−	2.89203e8i	−0.239830	−	1.35238i
$599$	3.63641e8			1.69197			0.845985	−	0.533206i	$-0.179013\pi$
$599$	3.63641e8			1.69197			0.845985	+	0.533206i	$0.179013\pi$
$600$	2.35185e8	+	6.30176e7i	1.08882	+	0.291748i
$601$	−1.54068e8	−	2.66854e8i	−0.709724	−	1.22928i	−0.964960	−	0.262398i	$-0.915487\pi$
$601$	−1.54068e8	−	2.66854e8i	−0.709724	−	1.22928i	0.255236	−	0.966879i	$-0.417847\pi$
$602$	1.67187e8	+	9.65253e7i	0.766324	+	0.442437i
$603$	1.86199e7	−	1.86199e7i	0.0849231	−	0.0849231i
$604$	−3.64646e7	−	1.36088e8i	−0.165486	−	0.617601i
$605$	1.59304e8	−	4.26853e7i	0.719382	−	0.192758i
$606$	8.64157e7	+	8.64157e7i	0.388307	+	0.388307i
$607$	1.45142e8	−	2.51393e8i	0.648972	−	1.12405i	−0.334397	−	0.942432i	$-0.608533\pi$
$607$	1.45142e8	−	2.51393e8i	0.648972	−	1.12405i	0.983369	−	0.181620i	$-0.0581340\pi$
$608$	−3.20564e7	+	1.85078e7i	−0.142628	+	0.0823462i
$609$	−2.18519e7	+	8.15523e7i	−0.0967468	+	0.361064i
$610$			6.47396e7i			0.285220i
$611$	5.79611e6	−	4.87322e6i	0.0254105	−	0.0213645i
$612$	1.88900e7			0.0824095
$613$	2.25841e8	+	6.05138e7i	0.980439	+	0.262708i	0.713229	−	0.700931i	$-0.247232\pi$
$613$	2.25841e8	+	6.05138e7i	0.980439	+	0.262708i	0.267209	+	0.963638i	$0.413898\pi$
$614$	−1.60250e8	−	2.77561e8i	−0.692298	−	1.19910i
$615$	3.52615e8	+	2.03583e8i	1.51592	+	0.875216i
$616$	−3.97984e7	+	3.97984e7i	−0.170264	+	0.170264i
$617$	−3.95522e7	−	1.47611e8i	−0.168390	−	0.628439i	−0.997583	−	0.0694778i	$-0.977867\pi$
$617$	−3.95522e7	−	1.47611e8i	−0.168390	−	0.628439i	0.829194	−	0.558961i	$-0.188800\pi$
$618$	−1.17777e8	+	3.15584e7i	−0.498996	+	0.133705i
$619$	1.68000e8	+	1.68000e8i	0.708334	+	0.708334i	0.966185	−	0.257851i	$-0.0830144\pi$
$619$	1.68000e8	+	1.68000e8i	0.708334	+	0.708334i	−0.257851	+	0.966185i	$0.583014\pi$
$620$	−1.27185e8	+	2.20290e8i	−0.533654	+	0.924316i
$621$	−2.54533e8	+	1.46955e8i	−1.06284	+	0.613633i
$622$	5.01259e7	−	1.87072e8i	0.208301	−	0.777390i
$623$		−	2.42165e7i		−	0.100149i
$624$	−1.91828e8	−	1.34039e8i	−0.789511	−	0.551667i
$625$	−4.66840e8			−1.91218
$626$	3.03510e8	+	8.13254e7i	1.23723	+	0.331515i
$627$	−1.37501e7	−	2.38159e7i	−0.0557832	−	0.0966193i
$628$	9.21216e7	+	5.31864e7i	0.371948	+	0.214744i
$629$	−4.29678e7	+	4.29678e7i	−0.172660	+	0.172660i
$630$	2.81827e7	+	1.05179e8i	0.112710	+	0.420638i
$631$	−2.31363e8	+	6.19936e7i	−0.920887	+	0.246751i	−0.687964	−	0.725744i	$-0.741495\pi$
$631$	−2.31363e8	+	6.19936e7i	−0.920887	+	0.246751i	−0.232922	+	0.972495i	$0.574829\pi$
$632$	3.94877e7	+	3.94877e7i	0.156427	+	0.156427i
$633$	3.28214e7	−	5.68483e7i	0.129403	−	0.224133i
$634$	−1.77923e8	+	1.02724e8i	−0.698174	+	0.403091i
$635$	−1.24258e8	+	4.63736e8i	−0.485290	+	1.81113i
$636$		−	1.64382e8i		−	0.638974i
$637$	8.32827e7	+	1.78144e8i	0.322208	+	0.689211i
$638$	2.39538e8			0.922387
$639$	1.90382e8	+	5.10126e7i	0.729664	+	0.195513i
$640$	−2.61941e8	−	4.53695e8i	−0.999225	−	1.73071i
$641$	−2.43991e8	−	1.40868e8i	−0.926402	−	0.534858i	−0.0407302	−	0.999170i	$-0.512968\pi$
$641$	−2.43991e8	−	1.40868e8i	−0.926402	−	0.534858i	−0.885672	+	0.464312i	$0.846302\pi$
$642$	−1.56681e8	+	1.56681e8i	−0.592120	+	0.592120i
$643$	6.66712e7	+	2.48820e8i	0.250787	+	0.935950i	0.970386	+	0.241560i	$0.0776591\pi$
$643$	6.66712e7	+	2.48820e8i	0.250787	+	0.935950i	−0.719599	+	0.694390i	$0.755674\pi$
$644$	−6.72872e7	+	1.80295e7i	−0.251927	+	0.0675036i
$645$	−3.95169e8	−	3.95169e8i	−1.47266	−	1.47266i
$646$	1.33061e7	−	2.30468e7i	0.0493573	−	0.0854894i
$647$	−3.80998e8	+	2.19969e8i	−1.40673	+	0.812175i	−0.995071	−	0.0991641i	$-0.968383\pi$
$647$	−3.80998e8	+	2.19969e8i	−1.40673	+	0.812175i	−0.411657	+	0.911339i	$0.635050\pi$
$648$	−1.94361e7	+	7.25367e7i	−0.0714307	+	0.266583i
$649$			1.56673e8i			0.573141i
$650$	7.13302e8	+	2.58828e8i	2.59737	+	0.942479i
$651$	−1.30238e8			−0.472058
$652$	9.83089e6	+	2.63418e6i	0.0354691	+	0.00950392i
$653$	2.25913e8	+	3.91293e8i	0.811339	+	1.40528i	0.911927	+	0.410352i	$0.134594\pi$
$653$	2.25913e8	+	3.91293e8i	0.811339	+	1.40528i	−0.100588	+	0.994928i	$0.532072\pi$
$654$	1.58216e8	+	9.13463e7i	0.565611	+	0.326556i
$655$	2.92788e8	−	2.92788e8i	1.04191	−	1.04191i
$656$	−1.14437e8	−	4.27086e8i	−0.405374	−	1.51288i
$657$	1.87814e7	−	5.03245e6i	0.0662263	−	0.0177453i
$658$	−3.96684e6	−	3.96684e6i	−0.0139241	−	0.0139241i
$659$	−6.68129e7	+	1.15723e8i	−0.233456	+	0.404357i	−0.958823	−	0.284005i	$-0.908337\pi$
$659$	−6.68129e7	+	1.15723e8i	−0.233456	+	0.404357i	0.725367	+	0.688362i	$0.241670\pi$
$660$	−1.25581e8	+	7.25043e7i	−0.436810	+	0.252192i
$661$	1.13777e8	−	4.24621e8i	0.393958	−	1.47027i	−0.429590	−	0.903024i	$-0.641342\pi$
$661$	1.13777e8	−	4.24621e8i	0.393958	−	1.47027i	0.823548	−	0.567247i	$-0.191991\pi$
$662$		−	1.57810e8i		−	0.543952i
$663$	9.66213e7	+	8.35773e6i	0.331537	+	0.0286779i
$664$	1.75957e8			0.601038
$665$	4.74375e7	+	1.27108e7i	0.161308	+	0.0432225i
$666$	−4.10959e7	−	7.11802e7i	−0.139116	−	0.240955i
$667$	−2.88487e8	−	1.66558e8i	−0.972186	−	0.561292i
$668$	1.48630e8	−	1.48630e8i	0.498629	−	0.498629i
$669$	−7.55793e6	−	2.82066e7i	−0.0252420	−	0.0942046i
$670$	−1.88948e8	+	5.06284e7i	−0.628228	+	0.168333i
$671$	2.12890e7	+	2.12890e7i	0.0704673	+	0.0704673i
$672$	−4.99672e7	+	8.65457e7i	−0.164656	+	0.285192i
$673$	−2.61519e8	+	1.50988e8i	−0.857944	+	0.495334i	−0.863323	−	0.504652i	$-0.831621\pi$
$673$	−2.61519e8	+	1.50988e8i	−0.857944	+	0.495334i	0.00537952	+	0.999986i	$0.498288\pi$
$674$	−3.87515e7	+	1.44623e8i	−0.126564	+	0.472342i
$675$		−	7.59312e8i		−	2.46893i
$676$	−1.11618e8	−	9.32860e7i	−0.361322	−	0.301979i
$677$	−3.45180e8			−1.11245			−0.556224	−	0.831032i	$-0.687750\pi$
$677$	−3.45180e8			−1.11245			−0.556224	+	0.831032i	$0.687750\pi$
$678$	8.82384e7	+	2.36434e7i	0.283119	+	0.0758614i
$679$	−1.77249e7	−	3.07005e7i	−0.0566207	−	0.0980699i
$680$	1.36547e8	+	7.88352e7i	0.434264	+	0.250722i
$681$	−2.17903e8	+	2.17903e8i	−0.689957	+	0.689957i
$682$	9.56351e7	+	3.56915e8i	0.301484	+	1.12515i
$683$	7.53340e7	−	2.01857e7i	0.236444	−	0.0633551i	−0.138651	−	0.990341i	$-0.544277\pi$
$683$	7.53340e7	−	2.01857e7i	0.236444	−	0.0633551i	0.375095	+	0.926986i	$0.377610\pi$
$684$	8.14852e6	+	8.14852e6i	0.0254631	+	0.0254631i
$685$	−1.32018e8	+	2.28663e8i	−0.410736	+	0.711416i
$686$	2.91998e8	−	1.68585e8i	0.904497	−	0.522211i
$687$	4.47249e7	−	1.66916e8i	0.137936	−	0.514786i
$688$			6.06874e8i			1.86352i
$689$	−4.96057e7	+	5.73477e8i	−0.151661	+	1.75331i
$690$	6.29899e8			1.91745
$691$	−2.78996e6	−	747567.i	−0.00845597	−	0.00226577i	0.254589	−	0.967049i	$-0.418060\pi$
$691$	−2.78996e6	−	747567.i	−0.00845597	−	0.00226577i	−0.263045	+	0.964784i	$0.584727\pi$
$692$	9.76599e7	+	1.69152e8i	0.294712	+	0.510456i
$693$	4.38548e7	+	2.53196e7i	0.131770	+	0.0760776i
$694$	5.15081e8	−	5.15081e8i	1.54098	−	1.54098i
$695$	−3.20096e7	−	1.19462e8i	−0.0953513	−	0.355856i
$696$	−1.59724e8	+	4.27979e7i	−0.473742	+	0.126939i
$697$	1.29568e8	+	1.29568e8i	0.382649	+	0.382649i
$698$	9.38390e7	−	1.62534e8i	0.275941	−	0.477945i
$699$	1.05058e8	−	6.06555e7i	0.307609	−	0.177598i
$700$	4.65791e7	−	1.73836e8i	0.135799	−	0.506810i
$701$		−	2.34962e8i		−	0.682093i	−0.940046	−	0.341047i	$-0.889219\pi$
$701$		−	2.34962e8i		−	0.682093i	0.940046	−	0.341047i	$-0.110781\pi$
$702$	−1.55092e8	+	4.27416e8i	−0.448309	+	1.23549i
$703$	−3.70698e7			−0.106698
$704$	−4.91386e7	−	1.31667e7i	−0.140833	−	0.0377361i
$705$	8.11999e6	+	1.40642e7i	0.0231733	+	0.0401374i
$706$	−4.39944e7	−	2.54002e7i	−0.125021	−	0.0721810i
$707$	−7.17687e7	+	7.17687e7i	−0.203085	+	0.203085i
$708$	2.49132e7	+	9.29772e7i	0.0701987	+	0.261985i
$709$	−2.40296e8	+	6.43870e7i	−0.674228	+	0.180659i	−0.579659	−	0.814859i	$-0.696814\pi$
$709$	−2.40296e8	+	6.43870e7i	−0.674228	+	0.180659i	−0.0945696	+	0.995518i	$0.530147\pi$
$710$	−1.03531e9	−	1.03531e9i	−2.89265	−	2.89265i
$711$	2.51220e7	−	4.35125e7i	0.0698948	−	0.121061i
$712$	4.10748e7	−	2.37146e7i	0.113798	−	0.0657015i
$713$	1.32996e8	−	4.96348e8i	0.366919	−	1.36936i
$714$		−	7.18472e7i		−	0.197386i
$715$	4.59992e8	−	2.15048e8i	1.25844	−	0.588324i
$716$	−1.50418e8			−0.409789
$717$	1.49784e8	+	4.01345e7i	0.406357	+	0.108883i
$718$	1.21986e8	+	2.11286e8i	0.329562	+	0.570818i
$719$	2.69345e8	+	1.55506e8i	0.724640	+	0.418371i	0.816458	−	0.577405i	$-0.195934\pi$
$719$	2.69345e8	+	1.55506e8i	0.724640	+	0.418371i	−0.0918179	+	0.995776i	$0.529268\pi$
$720$	−2.42047e8	+	2.42047e8i	−0.648487	+	0.648487i
$721$	−2.62094e7	−	9.78148e7i	−0.0699280	−	0.260975i
$722$	−4.25225e8	+	1.13939e8i	−1.12982	+	0.302733i
$723$	3.69982e8	+	3.69982e8i	0.978961	+	0.978961i
$724$	1.25569e7	−	2.17492e7i	0.0330877	−	0.0573097i
$725$	7.45305e8	−	4.30302e8i	1.95578	−	1.12917i
$726$	3.80953e7	−	1.42174e8i	0.0995548	−	0.371543i
$727$			2.02898e8i			0.528049i	0.964516	+	0.264025i	$0.0850500\pi$
$727$			2.02898e8i			0.528049i	−0.964516	+	0.264025i	$0.914950\pi$
$728$	6.93554e7	−	9.92569e7i	0.179757	−	0.257257i
$729$	3.91285e8			1.00997
$730$	−1.39519e8	−	3.73839e7i	−0.358644	−	0.0960983i
$731$	−1.25751e8	−	2.17807e8i	−0.321928	−	0.557596i
$732$	1.60191e7	+	9.24864e6i	0.0408418	+	0.0235801i
$733$	−1.28400e8	+	1.28400e8i	−0.326026	+	0.326026i	−0.851073	−	0.525047i	$-0.824048\pi$
$733$	−1.28400e8	+	1.28400e8i	−0.326026	+	0.326026i	0.525047	+	0.851073i	$0.324048\pi$
$734$	1.02512e7	+	3.82581e7i	0.0259232	+	0.0967466i
$735$	−4.07363e8	+	1.09153e8i	−1.02594	+	0.274898i
$736$	−2.78807e8	−	2.78807e8i	−0.699311	−	0.699311i
$737$	−4.54850e7	+	7.87823e7i	−0.113623	+	0.196801i
$738$	−2.14642e8	+	1.23924e8i	−0.534006	+	0.308308i
$739$	−1.53035e8	+	5.71133e8i	−0.379190	+	1.41516i	0.467936	+	0.883763i	$0.344998\pi$
$739$	−1.53035e8	+	5.71133e8i	−0.379190	+	1.41516i	−0.847125	+	0.531393i	$0.821669\pi$
$740$			1.95469e8i			0.482373i
$741$	3.80740e7	+	4.52845e7i	0.0935780	+	0.111300i
$742$	4.26435e8			1.04386
$743$	2.63549e8	+	7.06178e7i	0.642533	+	0.172166i	0.565351	−	0.824851i	$-0.308741\pi$
$743$	2.63549e8	+	7.06178e7i	0.642533	+	0.172166i	0.0771826	+	0.997017i	$0.475408\pi$
$744$	−1.27539e8	−	2.20903e8i	−0.309687	−	0.536394i
$745$	5.06548e8	+	2.92456e8i	1.22504	+	0.707280i
$746$	−1.32641e8	+	1.32641e8i	−0.319493	+	0.319493i
$747$	−4.09740e7	−	1.52917e8i	−0.0982985	−	0.366855i
$748$	−6.30349e7	+	1.68901e7i	−0.150618	+	0.0403579i
$749$	−1.30124e8	−	1.30124e8i	−0.309679	−	0.309679i
$750$	−4.56522e8	+	7.90720e8i	−1.08213	+	1.87430i
$751$	1.40650e7	−	8.12046e6i	0.0332064	−	0.0191717i	−0.483305	−	0.875452i	$-0.660564\pi$
$751$	1.40650e7	−	8.12046e6i	0.0332064	−	0.0191717i	0.516511	+	0.856280i	$0.327230\pi$
$752$	4.56439e6	−	1.70345e7i	0.0107332	−	0.0400568i
$753$		−	3.43805e8i		−	0.805244i
$754$	−5.07422e8	+	8.99857e7i	−1.18374	+	0.209923i
$755$	−1.05803e9			−2.45843
$756$	1.04164e8	+	2.79106e7i	0.241074	+	0.0645956i
$757$	−1.16055e7	−	2.01012e7i	−0.0267531	−	0.0463378i	0.852339	−	0.522990i	$-0.175183\pi$
$757$	−1.16055e7	−	2.01012e7i	−0.0267531	−	0.0463378i	−0.879092	+	0.476652i	$0.841850\pi$
$758$	−7.24643e7	−	4.18373e7i	−0.166386	−	0.0960629i
$759$	2.07136e8	−	2.07136e8i	0.473729	−	0.473729i
$760$	2.48948e7	+	9.29086e7i	0.0567110	+	0.211648i
$761$	3.36905e7	−	9.02735e6i	0.0764458	−	0.0204836i	−0.220393	−	0.975411i	$-0.570734\pi$
$761$	3.36905e7	−	9.02735e6i	0.0764458	−	0.0204836i	0.296839	+	0.954927i	$0.404067\pi$
$762$	3.02974e8	+	3.02974e8i	0.684763	+	0.684763i
$763$	−7.58636e7	+	1.31400e8i	−0.170789	+	0.295815i
$764$	−1.55450e8	+	8.97492e7i	−0.348587	+	0.201257i
$765$	3.67158e7	−	1.37025e8i	0.0820103	−	0.306066i
$766$			6.66087e8i			1.48199i
$767$	−5.88563e7	−	3.31886e8i	−0.130439	−	0.735534i
$768$	−4.01176e8			−0.885628
$769$	−6.37819e8	−	1.70903e8i	−1.40255	−	0.375812i	−0.523290	−	0.852154i	$-0.675296\pi$
$769$	−6.37819e8	−	1.70903e8i	−1.40255	−	0.375812i	−0.879260	+	0.476342i	$0.841962\pi$
$770$	−1.88088e8	−	3.25779e8i	−0.411993	−	0.713593i
$771$	−2.83298e6	−	1.63562e6i	−0.00618132	−	0.00356878i
$772$	2.02538e8	−	2.02538e8i	0.440204	−	0.440204i
$773$	−3.29568e7	−	1.22996e8i	−0.0713520	−	0.266289i	0.921029	−	0.389493i	$-0.127350\pi$
$773$	−3.29568e7	−	1.22996e8i	−0.0713520	−	0.266289i	−0.992381	+	0.123204i	$0.960683\pi$
$774$	3.28591e8	−	8.80456e7i	0.708651	−	0.189882i
$775$	9.38715e8	+	9.38715e8i	2.01664	+	2.01664i
$776$	3.47151e7	−	6.01283e7i	0.0742904	−	0.128675i
$777$	−8.66725e7	+	5.00404e7i	−0.184764	+	0.106674i
$778$	1.88713e8	−	7.04285e8i	0.400740	−	1.49558i
$779$			1.11783e8i			0.236463i
$780$	2.38785e8	−	2.00764e8i	0.503180	−	0.423060i
$781$	−6.80905e8			−1.42933
$782$	2.73815e8	+	7.33686e7i	0.572582	+	0.153423i
$783$	2.57840e8	+	4.46592e8i	0.537112	+	0.930306i
$784$	3.96616e8	+	2.28986e8i	0.823041	+	0.475183i
$785$	5.64859e8	−	5.64859e8i	1.16770	−	1.16770i
$786$	−9.56442e7	−	3.56949e8i	−0.196966	−	0.735087i
$787$	7.13891e8	−	1.91287e8i	1.46456	−	0.392428i	0.563499	−	0.826117i	$-0.309455\pi$
$787$	7.13891e8	−	1.91287e8i	1.46456	−	0.392428i	0.901063	+	0.433688i	$0.142788\pi$
$788$	−4.24736e7	−	4.24736e7i	−0.0868041	−	0.0868041i
$789$	3.44619e8	−	5.96898e8i	0.701631	−	1.21526i
$790$	−3.23236e8	+	1.86620e8i	−0.655598	+	0.378510i
$791$	−1.96360e7	+	7.32825e7i	−0.0396756	+	0.148071i
$792$			9.91792e7i			0.199639i
$793$	−5.30946e7	−	3.70997e7i	−0.106471	−	0.0743961i
$794$	3.67353e7			0.0733875
$795$	−1.19240e9	−	3.19503e8i	−2.37313	−	0.635878i
$796$	−3.84742e7	−	6.66392e7i	−0.0762834	−	0.132127i
$797$	5.50786e8	+	3.17996e8i	1.08795	+	0.628127i	0.933029	−	0.359801i	$-0.117155\pi$
$797$	5.50786e8	+	3.17996e8i	1.08795	+	0.628127i	0.154918	+	0.987927i	$0.450489\pi$
$798$	3.09925e7	−	3.09925e7i	0.0609885	−	0.0609885i
$799$	1.89158e6	+	7.05948e6i	0.00370839	+	0.0138399i
$800$	9.83942e8	−	2.63647e8i	1.92176	−	0.514935i
$801$	−3.01742e7	−	3.01742e7i	−0.0587136	−	0.0587136i
$802$	−7.47521e7	+	1.29474e8i	−0.144911	+	0.250993i
$803$	−5.81727e7	+	3.35860e7i	−0.112350	+	0.0648652i
$804$	−1.44655e7	+	5.39858e7i	−0.0278332	+	0.103875i
$805$			5.23134e8i			1.00283i
$806$	−3.36666e8	−	7.20137e8i	−0.642976	−	1.37534i
$807$	4.13685e8			0.787134
$808$	−1.92012e8	−	5.14494e7i	−0.363993	−	0.0975317i
$809$	−2.98581e7	−	5.17157e7i	−0.0563918	−	0.0976735i	0.836451	−	0.548041i	$-0.184626\pi$
$809$	−2.98581e7	−	5.17157e7i	−0.0563918	−	0.0976735i	−0.892843	+	0.450368i	$0.851293\pi$
$810$	−4.34666e8	−	2.50955e8i	−0.817902	−	0.472216i
$811$	5.12538e7	−	5.12538e7i	0.0960867	−	0.0960867i	−0.657429	−	0.753516i	$-0.728356\pi$
$811$	5.12538e7	−	5.12538e7i	0.0960867	−	0.0960867i	0.753516	+	0.657429i	$0.228356\pi$
$812$	3.16338e7	+	1.18059e8i	0.0590858	+	0.220511i
$813$	−1.49184e7	+	3.99737e6i	−0.0277619	+	0.00743879i
$814$	2.00779e8	+	2.00779e8i	0.372259	+	0.372259i
$815$	3.82159e7	−	6.61918e7i	0.0705945	−	0.122273i
$816$	1.95600e8	−	1.12929e8i	0.359996	−	0.207844i
$817$	3.97099e7	−	1.48199e8i	0.0728170	−	0.271757i
$818$		−	5.88689e8i		−	1.07554i
$819$	−1.02411e8	−	3.71606e7i	−0.186420	−	0.0676444i
$820$	5.89432e8			1.06904
$821$	9.51547e8	+	2.54966e8i	1.71949	+	0.460737i	0.977720	−	0.209913i	$-0.0673179\pi$
$821$	9.51547e8	+	2.54966e8i	1.71949	+	0.460737i	0.741774	+	0.670650i	$0.233985\pi$
$822$	1.17823e8	+	2.04075e8i	0.212135	+	0.367429i
$823$	−8.53468e8	−	4.92750e8i	−1.53104	−	0.883949i	−0.999314	−	0.0370355i	$-0.988209\pi$
$823$	−8.53468e8	−	4.92750e8i	−1.53104	−	0.883949i	−0.531731	−	0.846914i	$-0.678458\pi$
$824$	1.40242e8	−	1.40242e8i	0.250667	−	0.250667i
$825$	1.95873e8	+	7.31007e8i	0.348828	+	1.30185i
$826$	−2.41199e8	+	6.46290e7i	−0.427991	+	0.114680i
$827$	−1.54563e8	−	1.54563e8i	−0.273268	−	0.273268i	0.557147	−	0.830414i	$-0.311896\pi$
$827$	−1.54563e8	−	1.54563e8i	−0.273268	−	0.273268i	−0.830414	+	0.557147i	$0.811896\pi$
$828$	−6.13760e7	+	1.06306e8i	−0.108120	+	0.187270i
$829$	−1.50146e8	+	8.66869e7i	−0.263542	+	0.152156i	−0.625949	−	0.779864i	$-0.715288\pi$
$829$	−1.50146e8	+	8.66869e7i	−0.263542	+	0.152156i	0.362407	+	0.932020i	$0.381955\pi$
$830$	−3.04378e8	+	1.13596e9i	−0.532328	+	1.98668i
$831$			5.54165e8i			0.965686i
$832$	1.09038e8	+	9.43177e6i	0.189325	+	0.0163766i
$833$	−1.89794e8			−0.328357
$834$	−1.06616e8	−	2.85677e7i	−0.183791	−	0.0492466i
$835$	−7.89254e8	−	1.36703e9i	−1.35568	−	2.34811i
$836$	−3.44770e7	−	1.99053e7i	−0.0590080	−	0.0340683i
$837$	−5.62485e8	+	5.62485e8i	−0.959256	+	0.959256i
$838$	2.78615e7	+	1.03980e8i	0.0473448	+	0.176693i
$839$	−1.13577e9	+	3.04328e8i	−1.92311	+	0.515295i	−0.936958	+	0.349441i	$0.886371\pi$
$839$	−1.13577e9	+	3.04328e8i	−1.92311	+	0.515295i	−0.986150	+	0.165854i	$0.946962\pi$
$840$	1.83623e8	+	1.83623e8i	0.309806	+	0.309806i
$841$	5.17602e6	−	8.96514e6i	0.00870178	−	0.0150719i
$842$	6.76918e8	−	3.90819e8i	1.13396	−	0.654695i
$843$	1.00323e8	−	3.74410e8i	0.167462	−	0.624978i
$844$		−	9.50277e7i		−	0.158060i
$845$	−8.93630e8	+	6.28344e8i	−1.48111	+	1.04142i
$846$	−9.88551e6			−0.0163263
$847$	1.18076e8	+	3.16384e7i	0.194317	+	0.0520672i
$848$	6.70271e8	+	1.16094e9i	1.09916	+	1.90381i
$849$	3.86968e8	+	2.23416e8i	0.632342	+	0.365083i
$850$	−5.17852e8	+	5.17852e8i	−0.843236	+	0.843236i
$851$	−1.02200e8	−	3.81416e8i	−0.165830	−	0.618885i
$852$	−4.04081e8	+	1.08273e8i	−0.653355	+	0.175066i
$853$	−6.47815e8	−	6.47815e8i	−1.04377	−	1.04377i	−0.998997	−	0.0447698i	$-0.985745\pi$
$853$	−6.47815e8	−	6.47815e8i	−1.04377	−	1.04377i	−0.0447698	−	0.998997i	$-0.514255\pi$
$854$	−2.39925e7	+	4.15563e7i	−0.0385215	+	0.0667211i
$855$	7.49461e7	−	4.32701e7i	0.119909	−	0.0692293i
$856$	9.32830e7	−	3.48137e8i	0.148724	−	0.555046i
$857$			7.31054e8i			1.16147i	0.814094	+	0.580734i	$0.197234\pi$
$857$			7.31054e8i			1.16147i	−0.814094	+	0.580734i	$0.802766\pi$
$858$	3.90539e7	−	4.51490e8i	0.0618304	−	0.714804i
$859$	9.64152e8			1.52113			0.760564	−	0.649263i	$-0.224922\pi$
$859$	9.64152e8			1.52113			0.760564	+	0.649263i	$0.224922\pi$
$860$	−7.81456e8	−	2.09390e8i	−1.22860	−	0.329201i
$861$	1.50896e8	+	2.61359e8i	0.236411	+	0.409475i
$862$	−8.17300e8	−	4.71868e8i	−1.27603	−	0.736714i
$863$	−7.39463e8	+	7.39463e8i	−1.15049	+	1.15049i	−0.164040	+	0.986454i	$0.552453\pi$
$863$	−7.39463e8	+	7.39463e8i	−1.15049	+	1.15049i	−0.986454	+	0.164040i	$0.947547\pi$
$864$	1.57979e8	+	5.89585e8i	0.244939	+	0.914125i
$865$	1.41682e9	−	3.79636e8i	2.18910	−	0.586568i
$866$	8.45956e8	+	8.45956e8i	1.30255	+	1.30255i
$867$	2.04450e8	−	3.54118e8i	0.313711	−	0.543364i
$868$	−1.63280e8	+	9.42695e7i	−0.249674	+	0.144149i
$869$	−4.49247e7	+	1.67661e8i	−0.0684582	+	0.255490i
$870$		−	1.10519e9i		−	1.67834i
$871$	6.67567e7	−	1.83974e8i	0.101028	−	0.278421i
$872$	−2.97164e8			−0.448175
$873$	−6.03390e7	−	1.61678e7i	−0.0906892	−	0.0243001i
$874$	8.64661e7	+	1.49764e8i	0.129513	+	0.224322i
$875$	−6.56697e8	−	3.79144e8i	−0.980259	−	0.565953i
$876$	−2.91817e7	+	2.91817e7i	−0.0434109	+	0.0434109i
$877$	−4.11382e7	−	1.53530e8i	−0.0609883	−	0.227611i	0.928704	−	0.370822i	$-0.120924\pi$
$877$	−4.11382e7	−	1.53530e8i	−0.0609883	−	0.227611i	−0.989692	+	0.143211i	$0.954257\pi$
$878$	4.72226e8	−	1.26533e8i	0.697696	−	0.186947i
$879$	3.09096e7	+	3.09096e7i	0.0455120	+	0.0455120i
$880$	5.91275e8	−	1.02412e9i	0.867643	−	1.50280i
$881$	7.19893e8	−	4.15630e8i	1.05279	−	0.607826i	0.129358	−	0.991598i	$-0.458708\pi$
$881$	7.19893e8	−	4.15630e8i	1.05279	−	0.607826i	0.923428	+	0.383772i	$0.125375\pi$
$882$	6.64428e7	−	2.47968e8i	0.0968372	−	0.361401i
$883$		−	1.11009e9i		−	1.61241i	−0.591638	−	0.806204i	$-0.701518\pi$
$883$		−	1.11009e9i		−	1.61241i	0.591638	−	0.806204i	$-0.298482\pi$
$884$	1.27184e8	−	5.94588e7i	0.184109	−	0.0860714i
$885$	7.22865e8			1.04286
$886$	5.85671e8	+	1.56930e8i	0.842078	+	0.225634i
$887$	4.37279e8	+	7.57390e8i	0.626596	+	1.08530i	0.988230	+	0.152977i	$0.0488859\pi$
$887$	4.37279e8	+	7.57390e8i	0.626596	+	1.08530i	−0.361633	+	0.932320i	$0.617781\pi$
$888$	−1.69752e8	−	9.80064e7i	−0.242424	−	0.139964i
$889$	−2.51621e8	+	2.51621e8i	−0.358131	+	0.358131i
$890$	8.20451e7	+	3.06196e8i	0.116381	+	0.434340i
$891$	−2.25460e8	+	6.04118e7i	−0.318740	+	0.0854061i
$892$	−2.98920e7	−	2.98920e7i	−0.0421173	−	0.0421173i
$893$	−2.22926e6	+	3.86119e6i	−0.00313045	+	0.00542210i
$894$	4.52079e8	−	2.61008e8i	0.632706	−	0.365293i
$895$	−2.92361e8	+	1.09111e9i	−0.407803	+	1.52194i
$896$		−	3.88302e8i		−	0.539815i
$897$	−3.60969e8	+	5.16596e8i	−0.500142	+	0.715770i
$898$	−9.59454e8			−1.32494
$899$	−8.70869e8	−	2.33349e8i	−1.19860	−	0.321163i
$900$	−1.58564e8	−	2.74641e8i	−0.217509	−	0.376737i
$901$	−4.81120e8	−	2.77775e8i	−0.657777	−	0.379768i
$902$	6.05445e8	−	6.05445e8i	0.825002	−	0.825002i
$903$	−1.07209e8	−	4.00108e8i	−0.145602	−	0.543393i
$904$	−1.43527e8	+	3.84580e7i	−0.194280	+	0.0520572i
$905$	−1.33359e8	−	1.33359e8i	−0.179919	−	0.179919i
$906$	−4.72132e8	+	8.17756e8i	−0.634861	+	1.09961i
$907$	2.10984e8	−	1.21812e8i	0.282766	−	0.163255i	−0.351909	−	0.936034i	$-0.614467\pi$
$907$	2.10984e8	−	1.21812e8i	0.282766	−	0.163255i	0.634675	+	0.772779i	$0.281134\pi$
$908$	−1.15462e8	+	4.30909e8i	−0.154234	+	0.575609i
$909$			1.78850e8i			0.238121i
$910$	5.20816e8	+	6.19449e8i	0.691131	+	0.822018i
$911$	9.74837e8			1.28937			0.644684	−	0.764449i	$-0.276989\pi$
$911$	9.74837e8			1.28937			0.644684	+	0.764449i	$0.276989\pi$
$912$	1.33089e8	+	3.56612e7i	0.175452	+	0.0470122i
$913$	2.73456e8	+	4.73640e8i	0.359315	+	0.622352i
$914$	−4.72451e8	−	2.72770e8i	−0.618755	−	0.357238i
$915$	9.82240e7	−	9.82240e7i	0.128220	−	0.128220i
$916$	−6.47459e7	−	2.41635e8i	−0.0842415	−	0.314393i
$917$	2.96448e8	−	7.94330e7i	0.384451	−	0.103013i
$918$	−3.10301e8	−	3.10301e8i	−0.401102	−	0.401102i
$919$	5.55148e8	−	9.61544e8i	0.715257	−	1.23886i	−0.247603	−	0.968861i	$-0.579643\pi$
$919$	5.55148e8	−	9.61544e8i	0.715257	−	1.23886i	0.962860	−	0.270000i	$-0.0870237\pi$
$920$	−8.87314e8	+	5.12291e8i	−1.13950	+	0.657890i
$921$	−1.77986e8	+	6.64254e8i	−0.227828	+	0.850267i
$922$		−	3.27578e8i		−	0.417947i
$923$	1.44238e9	−	2.55791e8i	1.83432	−	0.325297i
$924$	−1.07481e8			−0.136243
$925$	9.85384e8	+	2.64033e8i	1.24503	+	0.333605i
$926$	4.11727e8	+	7.13133e8i	0.518533	+	0.898126i
$927$	−1.54537e8	−	8.92218e7i	−0.193996	−	0.112004i
$928$	−4.89182e8	+	4.89182e8i	−0.612106	+	0.612106i
$929$	−2.85125e8	−	1.06410e9i	−0.355621	−	1.32720i	−0.879701	−	0.475527i	$-0.842257\pi$
$929$	−2.85125e8	−	1.06410e9i	−0.355621	−	1.32720i	0.524080	−	0.851669i	$-0.324409\pi$
$930$	1.64675e9	−	4.41245e8i	2.04728	−	0.548568i
$931$	−8.18707e7	−	8.18707e7i	−0.101456	−	0.101456i
$932$	8.78078e7	−	1.52088e8i	0.108464	−	0.187865i
$933$	−3.59881e8	+	2.07777e8i	−0.443113	+	0.255831i
$934$	−4.01215e8	+	1.49735e9i	−0.492421	+	1.83774i
$935$			4.90074e8i			0.599552i
$936$	−3.72579e7	−	2.10094e8i	−0.0454350	−	0.256204i
$937$	−6.67691e8			−0.811628			−0.405814	−	0.913956i	$-0.633012\pi$
$937$	−6.67691e8			−0.811628			−0.405814	+	0.913956i	$0.633012\pi$
$938$	−1.40048e8	−	3.75258e7i	−0.169695	−	0.0454697i
$939$	−3.37103e8	−	5.83879e8i	−0.407160	−	0.705222i
$940$	2.03601e7	+	1.17549e7i	0.0245130	+	0.0141526i
$941$	−2.95273e8	+	2.95273e8i	−0.354369	+	0.354369i	−0.861732	−	0.507364i	$-0.830620\pi$
$941$	−2.95273e8	+	2.95273e8i	−0.354369	+	0.354369i	0.507364	+	0.861732i	$0.330620\pi$
$942$	−1.84521e8	−	6.88641e8i	−0.220746	−	0.823835i
$943$	−1.15015e9	+	3.08182e8i	−1.37157	+	0.367512i
$944$	−5.55064e8	−	5.55064e8i	−0.659823	−	0.659823i
$945$	4.04918e8	−	7.01338e8i	0.479812	−	0.831060i
$946$	−1.01776e9	+	5.87607e8i	−1.20219	+	0.694086i
$947$	−1.09860e8	+	4.10003e8i	−0.129357	+	0.482767i	−0.999957	−	0.00922382i	$-0.997064\pi$
$947$	−1.09860e8	+	4.10003e8i	−0.129357	+	0.482767i	0.870600	+	0.491991i	$0.163731\pi$
$948$			1.06642e8i			0.125170i
$949$	1.10612e8	−	9.29996e7i	0.129421	−	0.108813i
$950$	−4.46769e8			−0.521089
$951$	4.25801e8	+	1.14093e8i	0.495069	+	0.132653i
$952$	5.84327e7	+	1.01208e8i	0.0677244	+	0.117302i
$953$	2.81572e8	+	1.62566e8i	0.325320	+	0.187824i	0.653761	−	0.756701i	$-0.273190\pi$
$953$	2.81572e8	+	1.62566e8i	0.325320	+	0.187824i	−0.328441	+	0.944524i	$0.606523\pi$
$954$	5.31347e8	−	5.31347e8i	0.611974	−	0.611974i
$955$	3.48884e8	+	1.30205e9i	0.400563	+	1.49492i
$956$	2.16835e8	−	5.81006e7i	0.248173	−	0.0664978i
$957$	−3.63432e8	−	3.63432e8i	−0.414655	−	0.414655i
$958$	7.42587e8	−	1.28620e9i	0.844599	−	1.46289i
$959$	−1.69485e8	+	9.78522e7i	−0.192166	+	0.110947i
$960$	−6.07488e7	+	2.26717e8i	−0.0686632	+	0.256254i
$961$		−	5.03264e8i		−	0.567056i
$962$	−5.00742e8	−	3.49892e8i	−0.562456	−	0.393014i
$963$	−3.24274e8			−0.363106
$964$	7.31648e8	+	1.96044e8i	0.816716	+	0.218838i
$965$	−1.07551e9	−	1.86284e9i	−1.19683	−	2.07297i
$966$	4.04331e8	+	2.33441e8i	0.448545	+	0.258968i
$967$	6.23694e7	−	6.23694e7i	0.0689751	−	0.0689751i	−0.671778	−	0.740753i	$-0.734469\pi$
$967$	6.23694e7	−	6.23694e7i	0.0689751	−	0.0689751i	0.740753	+	0.671778i	$0.234469\pi$
$968$	6.19652e7	+	2.31257e8i	0.0683159	+	0.254958i
$969$	−5.51551e7	+	1.47788e7i	−0.0606197	+	0.0162430i
$970$	3.28129e8	+	3.28129e8i	0.359525	+	0.359525i
$971$	−8.45520e8	+	1.46448e9i	−0.923562	+	1.59966i	−0.129705	+	0.991553i	$0.541403\pi$
$971$	−8.45520e8	+	1.46448e9i	−0.923562	+	1.59966i	−0.793857	+	0.608104i	$0.791930\pi$
$972$	2.81656e8	−	1.62614e8i	0.306704	−	0.177076i
$973$	2.37256e7	−	8.85451e7i	0.0257560	−	0.0961227i
$974$			2.18257e9i			2.36207i
$975$	−6.89535e8	−	1.47493e9i	−0.743948	−	1.59132i
$976$	−1.50846e8			−0.162250
$977$	1.08946e9	+	2.91920e8i	1.16823	+	0.313026i	0.790248	−	0.612787i	$-0.209952\pi$
$977$	1.08946e9	+	2.91920e8i	1.16823	+	0.313026i	0.377981	+	0.925813i	$0.376618\pi$
$978$	−3.41065e7	−	5.90742e7i	−0.0364603	−	0.0631512i
$979$	1.27670e8	+	7.37100e7i	0.136063	+	0.0785558i
$980$	−4.31704e8	+	4.31704e8i	−0.458678	+	0.458678i
$981$	6.91989e7	+	2.58254e8i	0.0732980	+	0.273552i
$982$	−7.28469e8	+	1.95193e8i	−0.769266	+	0.206124i
$983$	9.01160e8	+	9.01160e8i	0.948727	+	0.948727i	0.998748	−	0.0500211i	$-0.0159289\pi$
$983$	9.01160e8	+	9.01160e8i	0.948727	+	0.948727i	−0.0500211	+	0.998748i	$0.515929\pi$
$984$	−2.95536e8	+	5.11883e8i	−0.310188	+	0.537261i
$985$	−3.90651e8	+	2.25542e8i	−0.408771	+	0.236004i
$986$	1.28729e8	−	4.80424e8i	0.134291	−	0.501180i
$987$			1.20371e7i			0.0125190i
$988$	8.05114e7	+	2.92143e7i	0.0834808	+	0.0302918i
$989$	1.63432e9			1.68946
$990$	−6.40289e8	−	1.71565e8i	−0.659888	−	0.176816i
$991$	6.67959e8	+	1.15694e9i	0.686323	+	1.18875i	0.973019	+	0.230725i	$0.0741097\pi$
$991$	6.67959e8	+	1.15694e9i	0.686323	+	1.18875i	−0.286696	+	0.958022i	$0.592557\pi$
$992$	−9.24192e8	−	5.33583e8i	−0.946732	−	0.546596i
$993$	−2.39432e8	+	2.39432e8i	−0.244531	+	0.244531i
$994$	−2.80879e8	−	1.04825e9i	−0.285996	−	1.06735i
$995$	−5.58171e8	+	1.49562e8i	−0.566628	+	0.151828i
$996$	2.37597e8	+	2.37597e8i	0.240471	+	0.240471i
$997$	−7.28910e8	+	1.26251e9i	−0.735510	+	1.27394i	0.218990	+	0.975727i	$0.429724\pi$
$997$	−7.28910e8	+	1.26251e9i	−0.735510	+	1.27394i	−0.954499	+	0.298213i	$0.903610\pi$
$998$	4.80844e8	−	2.77615e8i	0.483740	−	0.279288i
$999$	−1.58210e8	+	5.90449e8i	−0.158686	+	0.592224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.2.2	✓	24
13.7	odd	12	inner	13.7.f.a.7.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.2.2	✓	24	1.1	even	1	trivial
13.7.f.a.7.2	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)

\(f(q)\)	\(=\)	\(q+(-9.37184 - 2.51118i) q^{2} +(10.4091 + 18.0291i) q^{3} +(26.0998 + 15.0687i) q^{4} +(160.035 - 160.035i) q^{5} +(-52.2782 - 195.105i) q^{6} +(162.036 - 43.4174i) q^{7} +(232.320 + 232.320i) q^{8} +(147.801 - 255.999i) q^{9} +O(q^{10})\)	\(q+(-9.37184 - 2.51118i) q^{2} +(10.4091 + 18.0291i) q^{3} +(26.0998 + 15.0687i) q^{4} +(160.035 - 160.035i) q^{5} +(-52.2782 - 195.105i) q^{6} +(162.036 - 43.4174i) q^{7} +(232.320 + 232.320i) q^{8} +(147.801 - 255.999i) q^{9} +(-1901.70 + 1097.95i) q^{10} +(-264.307 + 986.407i) q^{11} +627.408i q^{12} +(189.333 - 2188.83i) q^{13} -1627.60 q^{14} +(4551.12 + 1219.47i) q^{15} +(-2558.27 - 4431.05i) q^{16} +(1836.32 + 1060.20i) q^{17} +(-2028.03 + 2028.03i) q^{18} +(334.793 + 1249.46i) q^{19} +(6588.42 - 1765.36i) q^{20} +(2469.42 + 2469.42i) q^{21} +(4954.09 - 8580.73i) q^{22} +(-11932.9 + 6889.45i) q^{23} +(-1770.27 + 6606.75i) q^{24} -35597.7i q^{25} +(-7270.93 + 20037.9i) q^{26} +21330.4 q^{27} +(4883.35 + 1308.49i) q^{28} +(12087.9 + 20936.9i) q^{29} +(-39590.1 - 22857.3i) q^{30} +(-26370.1 + 26370.1i) q^{31} +(7406.29 + 27640.6i) q^{32} +(-20535.2 + 5502.40i) q^{33} +(-14547.4 - 14547.4i) q^{34} +(18983.1 - 32879.8i) q^{35} +(7715.15 - 4454.34i) q^{36} +(-7417.14 + 27681.1i) q^{37} -12550.5i q^{38} +(41433.4 - 19370.2i) q^{39} +74358.7 q^{40} +(83471.8 + 22366.2i) q^{41} +(-16941.9 - 29344.2i) q^{42} +(-102720. - 59305.2i) q^{43} +(-21762.3 + 21762.3i) q^{44} +(-17315.5 - 64622.2i) q^{45} +(129134. - 34601.3i) q^{46} +(2437.23 + 2437.23i) q^{47} +(53258.5 - 92246.5i) q^{48} +(-77516.5 + 44754.2i) q^{49} +(-89392.1 + 333616. i) q^{50} +44143.0i q^{51} +(37924.4 - 54274.9i) q^{52} -262002. q^{53} +(-199905. - 53564.4i) q^{54} +(115562. + 200159. i) q^{55} +(47730.8 + 27557.4i) q^{56} +(-19041.8 + 19041.8i) q^{57} +(-60709.8 - 226572. i) q^{58} +(148193. - 39708.1i) q^{59} +(100408. + 100408. i) q^{60} +(14741.0 - 25532.2i) q^{61} +(313357. - 180917. i) q^{62} +(12834.3 - 47898.1i) q^{63} +49815.7i q^{64} +(-319990. - 380590. i) q^{65} +206271. q^{66} +(86045.8 + 23055.9i) q^{67} +(31951.7 + 55342.1i) q^{68} +(-248421. - 143426. i) q^{69} +(-260474. + 260474. i) q^{70} +(172572. + 644048. i) q^{71} +(93810.6 - 25136.5i) q^{72} +(46511.6 + 46511.6i) q^{73} +(139025. - 240798. i) q^{74} +(641794. - 370540. i) q^{75} +(-10089.8 + 37655.7i) q^{76} +171309. i q^{77} +(-436949. + 77488.2i) q^{78} +169972. q^{79} +(-1.11854e6 - 299711. i) q^{80} +(114283. + 197945. i) q^{81} +(-726119. - 419225. i) q^{82} +(378696. - 378696. i) q^{83} +(27240.4 + 101663. i) q^{84} +(463546. - 124207. i) q^{85} +(813746. + 813746. i) q^{86} +(-251649. + 435869. i) q^{87} +(-290565. + 167758. i) q^{88} +(37362.9 - 139440. i) q^{89} +649112. i q^{90} +(-64354.3 - 362889. i) q^{91} -415261. q^{92} +(-749920. - 200940. i) q^{93} +(-16721.0 - 28961.6i) q^{94} +(253537. + 146380. i) q^{95} +(-421243. + 421243. i) q^{96} +(-54694.5 - 204123. i) q^{97} +(838858. - 224771. i) q^{98} +(213454. + 213454. 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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