LMFDB - Embedded newform 43.6.e.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	43.11
Dual form			43.6.e.a.4.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97079 + 2.47129i) q^{2} +(-9.09722 + 11.4076i) q^{3} +(4.89739 - 21.4569i) q^{4} +(83.4030 - 40.1648i) q^{5} -46.1201 q^{6} -19.6284 q^{7} +(153.810 - 74.0710i) q^{8} +(6.69973 + 29.3534i) q^{9} +O(q^{10})$	\(q+(1.97079 + 2.47129i) q^{2} +(-9.09722 + 11.4076i) q^{3} +(4.89739 - 21.4569i) q^{4} +(83.4030 - 40.1648i) q^{5} -46.1201 q^{6} -19.6284 q^{7} +(153.810 - 74.0710i) q^{8} +(6.69973 + 29.3534i) q^{9} +(263.629 + 126.957i) q^{10} +(126.479 + 554.139i) q^{11} +(200.218 + 251.065i) q^{12} +(556.520 - 268.006i) q^{13} +(-38.6834 - 48.5074i) q^{14} +(-300.554 + 1316.81i) q^{15} +(-148.354 - 71.4435i) q^{16} +(-311.046 - 149.792i) q^{17} +(-59.3372 + 74.4065i) q^{18} +(681.631 - 2986.42i) q^{19} +(-453.354 - 1986.27i) q^{20} +(178.563 - 223.911i) q^{21} +(-1120.18 + 1404.66i) q^{22} +(1112.17 + 4872.72i) q^{23} +(-554.275 + 2428.44i) q^{24} +(3394.45 - 4256.51i) q^{25} +(1759.11 + 847.141i) q^{26} +(-3590.24 - 1728.97i) q^{27} +(-96.1278 + 421.163i) q^{28} +(-494.258 - 619.780i) q^{29} +(-3846.56 + 1852.41i) q^{30} +(1526.28 + 1913.90i) q^{31} +(-1331.43 - 5833.38i) q^{32} +(-7471.97 - 3598.31i) q^{33} +(-242.827 - 1063.89i) q^{34} +(-1637.06 + 788.369i) q^{35} +662.644 q^{36} -11541.9 q^{37} +(8723.68 - 4201.10i) q^{38} +(-2005.49 + 8786.64i) q^{39} +(9853.18 - 12355.5i) q^{40} +(-2268.39 - 2844.47i) q^{41} +905.262 q^{42} +(-9959.33 + 6915.22i) q^{43} +12509.5 q^{44} +(1737.75 + 2179.07i) q^{45} +(-9850.07 + 12351.6i) q^{46} +(-403.647 + 1768.49i) q^{47} +(2164.61 - 1042.42i) q^{48} -16421.7 q^{49} +17208.8 q^{50} +(4538.41 - 2185.58i) q^{51} +(-3025.08 - 13253.7i) q^{52} +(-3972.93 - 1913.26i) q^{53} +(-2802.83 - 12280.0i) q^{54} +(32805.6 + 41136.9i) q^{55} +(-3019.04 + 1453.89i) q^{56} +(27866.8 + 34943.9i) q^{57} +(557.579 - 2442.91i) q^{58} +(-9224.60 - 4442.33i) q^{59} +(26782.8 + 12897.9i) q^{60} +(13045.0 - 16357.9i) q^{61} +(-1721.82 + 7543.79i) q^{62} +(-131.505 - 576.159i) q^{63} +(8506.77 - 10667.2i) q^{64} +(35651.1 - 44705.0i) q^{65} +(-5833.21 - 25557.0i) q^{66} +(-7469.34 + 32725.3i) q^{67} +(-4737.38 + 5940.48i) q^{68} +(-65703.4 - 31641.1i) q^{69} +(-5174.60 - 2491.96i) q^{70} +(-1479.38 + 6481.60i) q^{71} +(3204.72 + 4018.60i) q^{72} +(29621.2 - 14264.8i) q^{73} +(-22746.6 - 28523.4i) q^{74} +(17676.3 + 77444.8i) q^{75} +(-60741.1 - 29251.4i) q^{76} +(-2482.57 - 10876.8i) q^{77} +(-25666.8 + 12360.5i) q^{78} -52745.8 q^{79} -15242.7 q^{80} +(45792.8 - 22052.6i) q^{81} +(2559.00 - 11211.7i) q^{82} +(-36581.0 + 45871.1i) q^{83} +(-3929.95 - 4928.00i) q^{84} -31958.5 q^{85} +(-36717.3 - 10984.0i) q^{86} +11566.6 q^{87} +(60499.3 + 75863.7i) q^{88} +(-27405.9 + 34366.0i) q^{89} +(-1960.38 + 8588.99i) q^{90} +(-10923.6 + 5260.52i) q^{91} +110000. q^{92} -35717.8 q^{93} +(-5165.96 + 2487.80i) q^{94} +(-63098.9 - 276454. i) q^{95} +(78656.9 + 37879.2i) q^{96} +(9296.13 + 40729.0i) q^{97} +(-32363.8 - 40582.9i) q^{98} +(-15418.5 + 7425.16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) $ 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	1.97079	+	2.47129i	0.348390	+	0.436867i	0.924893	−	0.380228i	$-0.124154\pi$
$2$	1.97079	+	2.47129i	0.348390	+	0.436867i	−0.576503	+	0.817095i	$0.695583\pi$
$3$	−9.09722	+	11.4076i	−0.583587	+	0.731795i	−0.982720	−	0.185098i	$-0.940740\pi$
$3$	−9.09722	+	11.4076i	−0.583587	+	0.731795i	0.399133	+	0.916893i	$0.369311\pi$
$4$	4.89739	−	21.4569i	0.153044	−	0.670528i
$5$	83.4030	−	40.1648i	1.49196	−	0.718490i	0.502672	−	0.864477i	$-0.332350\pi$
$5$	83.4030	−	40.1648i	1.49196	−	0.718490i	0.989286	+	0.145987i	$0.0466359\pi$
$6$	−46.1201			−0.523013
$7$	−19.6284			−0.151404			−0.0757022	−	0.997130i	$-0.524120\pi$
$7$	−19.6284			−0.151404			−0.0757022	+	0.997130i	$0.524120\pi$
$8$	153.810	−	74.0710i	0.849688	−	0.409188i
$9$	6.69973	+	29.3534i	0.0275709	+	0.120796i
$10$	263.629	+	126.957i	0.833668	+	0.401473i
$11$	126.479	+	554.139i	0.315163	+	1.38082i	0.845926	+	0.533300i	$0.179048\pi$
$11$	126.479	+	554.139i	0.315163	+	1.38082i	−0.530763	+	0.847520i	$0.678095\pi$
$12$	200.218	+	251.065i	0.401375	+	0.503308i
$13$	556.520	−	268.006i	0.913319	−	0.439831i	0.0826379	−	0.996580i	$-0.473665\pi$
$13$	556.520	−	268.006i	0.913319	−	0.439831i	0.830681	+	0.556748i	$0.187951\pi$
$14$	−38.6834	−	48.5074i	−0.0527478	−	0.0661436i
$15$	−300.554	+	1316.81i	−0.344901	+	1.51111i
$16$	−148.354	−	71.4435i	−0.144877	−	0.0697691i
$17$	−311.046	−	149.792i	−0.261037	−	0.125709i	0.298788	−	0.954319i	$-0.403418\pi$
$17$	−311.046	−	149.792i	−0.261037	−	0.125709i	−0.559825	+	0.828611i	$0.689132\pi$
$18$	−59.3372	+	74.4065i	−0.0431664	+	0.0541289i
$19$	681.631	−	2986.42i	0.433177	−	1.89787i	−0.00702723	−	0.999975i	$-0.502237\pi$
$19$	681.631	−	2986.42i	0.433177	−	1.89787i	0.440204	−	0.897898i	$-0.354906\pi$
$20$	−453.354	−	1986.27i	−0.253432	−	1.11036i
$21$	178.563	−	223.911i	0.0883577	−	0.110797i
$22$	−1120.18	+	1404.66i	−0.493435	+	0.618748i
$23$	1112.17	+	4872.72i	0.438379	+	1.92066i	0.387256	+	0.921972i	$0.373423\pi$
$23$	1112.17	+	4872.72i	0.438379	+	1.92066i	0.0511229	+	0.998692i	$0.483720\pi$
$24$	−554.275	+	2428.44i	−0.196425	+	0.860595i
$25$	3394.45	−	4256.51i	1.08622	−	1.36208i
$26$	1759.11	+	847.141i	0.510339	+	0.245766i
$27$	−3590.24	−	1728.97i	−0.947796	−	0.456434i
$28$	−96.1278	+	421.163i	−0.0231715	+	0.101521i
$29$	−494.258	−	619.780i	−0.109134	−	0.136849i	0.724265	−	0.689522i	$-0.242179\pi$
$29$	−494.258	−	619.780i	−0.109134	−	0.136849i	−0.833398	+	0.552673i	$0.813608\pi$
$30$	−3846.56	+	1852.41i	−0.780314	+	0.375779i
$31$	1526.28	+	1913.90i	0.285254	+	0.357697i	0.903727	−	0.428109i	$-0.140820\pi$
$31$	1526.28	+	1913.90i	0.285254	+	0.357697i	−0.618474	+	0.785806i	$0.712249\pi$
$32$	−1331.43	−	5833.38i	−0.229850	−	1.00704i
$33$	−7471.97	−	3598.31i	−1.19440	−	0.575194i
$34$	−242.827	−	1063.89i	−0.0360246	−	0.157834i
$35$	−1637.06	+	788.369i	−0.225889	+	0.108783i
$36$	662.644			0.0852166
$37$	−11541.9			−1.38603			−0.693015	−	0.720924i	$-0.743718\pi$
$37$	−11541.9			−1.38603			−0.693015	+	0.720924i	$0.743718\pi$
$38$	8723.68	−	4201.10i	0.980033	−	0.471959i
$39$	−2005.49	+	8786.64i	−0.211135	+	0.925042i
$40$	9853.18	−	12355.5i	0.973703	−	1.22098i
$41$	−2268.39	−	2844.47i	−0.210746	−	0.264267i	0.665212	−	0.746654i	$-0.268341\pi$
$41$	−2268.39	−	2844.47i	−0.210746	−	0.264267i	−0.875958	+	0.482388i	$0.839770\pi$
$42$	905.262			0.0791865
$43$	−9959.33	+	6915.22i	−0.821408	+	0.570341i
$43$	−9959.33	+	6915.22i	−0.821408	+	0.570341i
$44$	12509.5			0.974112
$45$	1737.75	+	2179.07i	0.127925	+	0.160413i
$46$	−9850.07	+	12351.6i	−0.686348	+	0.860654i
$47$	−403.647	+	1768.49i	−0.0266536	+	0.116777i	−0.986505	−	0.163733i	$-0.947646\pi$
$47$	−403.647	+	1768.49i	−0.0266536	+	0.116777i	0.959851	+	0.280510i	$0.0905036\pi$
$48$	2164.61	−	1042.42i	0.135605	−	0.0653039i
$49$	−16421.7			−0.977077
$50$	17208.8			0.973478
$51$	4538.41	−	2185.58i	0.244331	−	0.117664i
$52$	−3025.08	−	13253.7i	−0.155141	−	0.679719i
$53$	−3972.93	−	1913.26i	−0.194277	−	0.0935587i	0.334216	−	0.942496i	$-0.391528\pi$
$53$	−3972.93	−	1913.26i	−0.194277	−	0.0935587i	−0.528493	+	0.848938i	$0.677243\pi$
$54$	−2802.83	−	12280.0i	−0.130801	−	0.573078i
$55$	32805.6	+	41136.9i	1.46231	+	1.83368i
$56$	−3019.04	+	1453.89i	−0.128647	+	0.0619530i
$57$	27866.8	+	34943.9i	1.13606	+	1.42457i
$58$	557.579	−	2442.91i	0.0217639	−	0.0953539i
$59$	−9224.60	−	4442.33i	−0.344999	−	0.166143i	0.253358	−	0.967373i	$-0.418465\pi$
$59$	−9224.60	−	4442.33i	−0.344999	−	0.166143i	−0.598356	+	0.801230i	$0.704179\pi$
$60$	26782.8	+	12897.9i	0.960456	+	0.462531i
$61$	13045.0	−	16357.9i	0.448867	−	0.562862i	−0.504989	−	0.863126i	$-0.668503\pi$
$61$	13045.0	−	16357.9i	0.448867	−	0.562862i	0.953856	+	0.300264i	$0.0970748\pi$
$62$	−1721.82	+	7543.79i	−0.0568864	+	0.249236i
$63$	−131.505	−	576.159i	−0.00417436	−	0.0182891i
$64$	8506.77	−	10667.2i	0.259606	−	0.325536i
$65$	35651.1	−	44705.0i	1.04662	−	1.31242i
$66$	−5833.21	−	25557.0i	−0.164834	−	0.722187i
$67$	−7469.34	+	32725.3i	−0.203280	+	0.890629i	0.765643	+	0.643266i	$0.222421\pi$
$67$	−7469.34	+	32725.3i	−0.203280	+	0.890629i	−0.968923	+	0.247363i	$0.920436\pi$
$68$	−4737.38	+	5940.48i	−0.124241	+	0.155794i
$69$	−65703.4	−	31641.1i	−1.66136	−	0.800071i
$70$	−5174.60	−	2491.96i	−0.126221	−	0.0607849i
$71$	−1479.38	+	6481.60i	−0.0348285	+	0.152594i	−0.989352	−	0.145542i	$-0.953508\pi$
$71$	−1479.38	+	6481.60i	−0.0348285	+	0.152594i	0.954524	+	0.298135i	$0.0963647\pi$
$72$	3204.72	+	4018.60i	0.0728550	+	0.0913573i
$73$	29621.2	−	14264.8i	0.650573	−	0.313299i	−0.0793319	−	0.996848i	$-0.525279\pi$
$73$	29621.2	−	14264.8i	0.650573	−	0.313299i	0.729905	+	0.683549i	$0.239564\pi$
$74$	−22746.6	−	28523.4i	−0.482879	−	0.605511i
$75$	17676.3	+	77444.8i	0.362858	+	1.58979i
$76$	−60741.1	−	29251.4i	−1.20628	−	0.580915i
$77$	−2482.57	−	10876.8i	−0.0477171	−	0.209062i
$78$	−25666.8	+	12360.5i	−0.477678	+	0.230037i
$79$	−52745.8			−0.950867			−0.475434	−	0.879752i	$-0.657709\pi$
$79$	−52745.8			−0.950867			−0.475434	+	0.879752i	$0.657709\pi$
$80$	−15242.7			−0.266279
$81$	45792.8	−	22052.6i	0.775505	−	0.373464i
$82$	2559.00	−	11211.7i	0.0420278	−	0.184136i
$83$	−36581.0	+	45871.1i	−0.582855	+	0.730877i	−0.982597	−	0.185751i	$-0.940528\pi$
$83$	−36581.0	+	45871.1i	−0.582855	+	0.730877i	0.399742	+	0.916628i	$0.369100\pi$
$84$	−3929.95	−	4928.00i	−0.0607699	−	0.0762030i
$85$	−31958.5			−0.479777
$86$	−36717.3	−	10984.0i	−0.535334	−	0.160145i
$87$	11566.6			0.163835
$88$	60499.3	+	75863.7i	0.832806	+	1.04431i
$89$	−27405.9	+	34366.0i	−0.366750	+	0.459889i	−0.930627	−	0.365969i	$-0.880738\pi$
$89$	−27405.9	+	34366.0i	−0.366750	+	0.459889i	0.563877	+	0.825858i	$0.309309\pi$
$90$	−1960.38	+	8588.99i	−0.0255114	+	0.111773i
$91$	−10923.6	+	5260.52i	−0.138281	+	0.0665924i
$92$	110000.			1.35495
$93$	−35717.8			−0.428231
$94$	−5165.96	+	2487.80i	−0.0603020	+	0.0290399i
$95$	−63098.9	−	276454.i	−0.717319	−	3.14278i
$96$	78656.9	+	37879.2i	0.871082	+	0.419491i
$97$	9296.13	+	40729.0i	0.100317	+	0.439516i	0.999996	+	0.00296364i	$0.000943357\pi$
$97$	9296.13	+	40729.0i	0.100317	+	0.439516i	−0.899679	+	0.436552i	$0.856199\pi$
$98$	−32363.8	−	40582.9i	−0.340404	−	0.426853i
$99$	−15418.5	+	7425.16i	−0.158108	+	0.0761409i
$100$	−74707.4	−	93680.1i	−0.747074	−	0.936801i
$101$	−35982.8	+	157651.i	−0.350987	+	1.53777i	0.423921	+	0.905699i	$0.360654\pi$
$101$	−35982.8	+	157651.i	−0.350987	+	1.53777i	−0.774907	+	0.632075i	$0.782204\pi$
$102$	14345.5	+	6908.42i	0.136526	+	0.0657473i
$103$	−43784.1	−	21085.3i	−0.406652	−	0.195833i	0.219364	−	0.975643i	$-0.429602\pi$
$103$	−43784.1	−	21085.3i	−0.406652	−	0.195833i	−0.626017	+	0.779809i	$0.715316\pi$
$104$	65746.9	−	82444.0i	0.596063	−	0.747439i
$105$	5899.38	−	25846.9i	0.0522195	−	0.228789i
$106$	−3101.58	−	13588.9i	−0.0268113	−	0.117468i
$107$	116372.	−	145925.i	0.982624	−	1.23217i	0.00996112	−	0.999950i	$-0.496829\pi$
$107$	116372.	−	145925.i	0.982624	−	1.23217i	0.972663	−	0.232221i	$-0.0745993\pi$
$108$	−54681.2	+	68568.0i	−0.451106	+	0.565669i
$109$	−25043.4	−	109722.i	−0.201896	−	0.884562i	−0.969781	−	0.243976i	$-0.921548\pi$
$109$	−25043.4	−	109722.i	−0.201896	−	0.884562i	0.767886	−	0.640587i	$-0.221309\pi$
$110$	−37008.4	+	162144.i	−0.291621	+	1.27767i
$111$	104999.	−	131665.i	0.808869	−	1.01429i
$112$	2911.94	+	1402.32i	0.0219350	+	0.0105634i
$113$	82153.4	+	39563.0i	0.605242	+	0.291469i	0.711298	−	0.702891i	$-0.248108\pi$
$113$	82153.4	+	39563.0i	0.605242	+	0.291469i	−0.106055	+	0.994360i	$0.533822\pi$
$114$	−31436.9	+	137734.i	−0.226557	+	0.992612i
$115$	288470.	+	361729.i	2.03402	+	2.55058i
$116$	−15719.1	+	7569.94i	−0.108463	+	0.0522333i
$117$	11595.4	+	14540.2i	0.0783109	+	0.0981988i
$118$	−7201.45	−	31551.6i	−0.0476118	−	0.208601i
$119$	6105.32	+	2940.17i	0.0395222	+	0.0190329i
$120$	51309.4	+	224801.i	0.325270	+	1.42510i
$121$	−145971.	+	70296.0i	−0.906367	+	0.436483i
$122$	66134.0			0.402277
$123$	53084.5			0.316377
$124$	48541.1	−	23376.2i	0.283502	−	0.136527i
$125$	47774.4	−	209313.i	0.273477	−	1.19818i
$126$	1164.69	−	1460.48i	0.00653558	−	0.00819536i
$127$	77140.4	+	96731.0i	0.424397	+	0.532178i	0.947357	−	0.320180i	$-0.103743\pi$
$127$	77140.4	+	96731.0i	0.424397	+	0.532178i	−0.522959	+	0.852358i	$0.675172\pi$
$128$	−148342.			−0.800275
$129$	11716.4	−	176521.i	0.0619899	−	0.933946i
$130$	180740.			0.937985
$131$	−144698.	−	181446.i	−0.736690	−	0.923779i	0.262463	−	0.964942i	$-0.415465\pi$
$131$	−144698.	−	181446.i	−0.736690	−	0.923779i	−0.999152	+	0.0411626i	$0.986894\pi$
$132$	−113802.	+	142703.i	−0.568479	+	0.712850i
$133$	−13379.3	+	58618.5i	−0.0655850	+	0.287346i
$134$	−95594.4	+	46035.8i	−0.459907	+	0.221480i
$135$	−368881.			−1.74202
$136$	−58937.2			−0.273239
$137$	290157.	−	139732.i	1.32078	−	0.636056i	0.365242	−	0.930913i	$-0.380986\pi$
$137$	290157.	−	139732.i	1.32078	−	0.636056i	0.955541	+	0.294857i	$0.0952720\pi$
$138$	−51293.2	−	224730.i	−0.229278	−	1.00453i
$139$	51128.1	+	24622.0i	0.224451	+	0.108090i	0.542730	−	0.839907i	$-0.317391\pi$
$139$	51128.1	+	24622.0i	0.224451	+	0.108090i	−0.318279	+	0.947997i	$0.603105\pi$
$140$	8898.59	+	38987.2i	0.0383708	+	0.168113i
$141$	−16502.1	−	20693.0i	−0.0699023	−	0.0876547i
$142$	−18933.5	+	9117.89i	−0.0787970	+	0.0379466i
$143$	218900.	+	274493.i	0.895172	+	1.12251i
$144$	1103.18	−	4833.35i	0.00443344	−	0.0194242i
$145$	−66116.0	−	31839.8i	−0.261148	−	0.125762i
$146$	93629.8	+	45089.8i	0.363523	+	0.175064i
$147$	149392.	−	187332.i	0.570209	−	0.715020i
$148$	−56525.2	+	247653.i	−0.212123	+	0.929371i
$149$	−77958.3	−	341558.i	−0.287671	−	1.26037i	−0.887711	−	0.460401i	$-0.847706\pi$
$149$	−77958.3	−	341558.i	−0.287671	−	1.26037i	0.600040	−	0.799970i	$-0.295151\pi$
$150$	−156553.	+	196311.i	−0.568109	+	0.712387i
$151$	−163319.	+	204796.i	−0.582901	+	0.730935i	−0.982605	−	0.185710i	$-0.940542\pi$
$151$	−163319.	+	204796.i	−0.582901	+	0.730935i	0.399704	+	0.916644i	$0.369113\pi$
$152$	−116366.	−	509831.i	−0.408522	−	1.78985i
$153$	2312.98	−	10133.8i	0.00798809	−	0.0349981i
$154$	21987.2	−	27571.1i	0.0747083	−	0.0936812i
$155$	204168.	+	98322.1i	0.682588	+	0.328717i
$156$	178712.	+	86063.3i	0.587954	+	0.283144i
$157$	−60483.2	+	264994.i	−0.195833	+	0.858001i	0.777551	+	0.628820i	$0.216462\pi$
$157$	−60483.2	+	264994.i	−0.195833	+	0.858001i	−0.973384	+	0.229181i	$0.926395\pi$
$158$	−103951.	−	130350.i	−0.331273	−	0.415403i
$159$	57968.2	−	27916.0i	0.181843	−	0.0875710i
$160$	−345342.	−	433045.i	−1.06647	−	1.33731i
$161$	−21830.0	−	95643.4i	−0.0663726	−	0.290797i
$162$	144747.	+	69706.3i	0.433332	+	0.208682i
$163$	−8901.17	−	38998.6i	−0.0262409	−	0.114969i	0.960111	−	0.279618i	$-0.0902079\pi$
$163$	−8901.17	−	38998.6i	−0.0262409	−	0.114969i	−0.986352	+	0.164649i	$0.947351\pi$
$164$	−72142.8	+	34742.1i	−0.209451	+	0.100866i
$165$	−767711.			−2.19527
$166$	−185455.			−0.522357
$167$	392151.	−	188850.i	1.08808	−	0.523994i	0.198191	−	0.980163i	$-0.436493\pi$
$167$	392151.	−	188850.i	1.08808	−	0.523994i	0.889893	+	0.456170i	$0.150779\pi$
$168$	10879.5	−	47666.2i	0.0297396	−	0.130298i
$169$	6390.15	−	8013.00i	0.0172105	−	0.0215813i
$170$	−62983.6	−	78978.9i	−0.167149	−	0.209599i
$171$	92228.5			0.241199
$172$	99604.4	+	247563.i	0.256719	+	0.638064i
$173$	221697.			0.563177			0.281588	−	0.959535i	$-0.409139\pi$
$173$	221697.			0.563177			0.281588	+	0.959535i	$0.409139\pi$
$174$	22795.3	+	28584.3i	0.0570783	+	0.0715740i
$175$	−66627.5	+	83548.2i	−0.164459	+	0.206225i
$176$	20826.0	−	91244.8i	0.0506786	−	0.222038i
$177$	134594.	−	64817.2i	0.322919	−	0.155510i
$178$	−138940.			−0.328682
$179$	−303880.			−0.708876			−0.354438	−	0.935080i	$-0.615328\pi$
$179$	−303880.			−0.708876			−0.354438	+	0.935080i	$0.615328\pi$
$180$	55266.6	−	26615.0i	0.127140	−	0.0612272i
$181$	−27198.6	−	119165.i	−0.0617092	−	0.270366i	0.934656	−	0.355554i	$-0.115708\pi$
$181$	−27198.6	−	119165.i	−0.0617092	−	0.270366i	−0.996365	+	0.0851885i	$0.972851\pi$
$182$	−34528.4	−	16628.0i	−0.0772676	−	0.0372101i
$183$	67930.3	+	297622.i	0.149946	+	0.656958i
$184$	531989.	+	667093.i	1.15840	+	1.45259i
$185$	−962628.	+	463577.i	−2.06790	+	0.995847i
$186$	−70392.4	−	88269.3i	−0.149191	−	0.187080i
$187$	43664.8	−	191308.i	0.0913119	−	0.400064i
$188$	35969.5	+	17322.0i	0.0742232	+	0.0357440i
$189$	70470.6	+	33936.8i	0.143500	+	0.0691062i
$190$	558845.	−	700769.i	1.12307	−	1.40829i
$191$	−7348.60	+	32196.3i	−0.0145754	+	0.0638591i	−0.981693	−	0.190472i	$-0.938998\pi$
$191$	−7348.60	+	32196.3i	−0.0145754	+	0.0638591i	0.967117	+	0.254331i	$0.0818553\pi$
$192$	44298.1	+	194083.i	0.0867226	+	0.379957i
$193$	274927.	−	344748.i	0.531281	−	0.666205i	−0.441681	−	0.897172i	$-0.645618\pi$
$193$	274927.	−	344748.i	0.531281	−	0.666205i	0.972962	+	0.230967i	$0.0741890\pi$
$194$	−82332.6	+	103242.i	−0.157061	+	0.196948i
$195$	185649.	+	813383.i	0.349629	+	1.53182i
$196$	−80423.7	+	352359.i	−0.149535	+	0.655157i
$197$	−43814.2	+	54941.3i	−0.0804358	+	0.100863i	−0.820421	−	0.571760i	$-0.806261\pi$
$197$	−43814.2	+	54941.3i	−0.0804358	+	0.100863i	0.739985	+	0.672623i	$0.234832\pi$
$198$	−48736.4	−	23470.2i	−0.0883468	−	0.0425456i
$199$	807968.	+	389097.i	1.44631	+	0.696507i	0.981950	−	0.189140i	$-0.0605699\pi$
$199$	807968.	+	389097.i	1.44631	+	0.696507i	0.464361	+	0.885646i	$0.346284\pi$
$200$	206817.	−	906124.i	0.365604	−	1.60182i
$201$	−305366.	−	382916.i	−0.533126	−	0.668519i
$202$	−460516.	+	221773.i	−0.794083	+	0.382410i
$203$	9701.48	+	12165.3i	0.0165233	+	0.0207196i
$204$	−24669.4	−	108084.i	−0.0415034	−	0.181838i
$205$	−303438.	−	146128.i	−0.504297	−	0.242856i
$206$	−34181.3	−	149758.i	−0.0561204	−	0.245880i
$207$	−135580.	+	65291.8i	−0.219922	+	0.105909i
$208$	−101709.			−0.163006
$209$	1.74110e6			2.75714
$210$	75501.6	−	36359.7i	0.118143	−	0.0568947i
$211$	148293.	−	649714.i	0.229305	−	1.00465i	−0.720903	−	0.693036i	$-0.756272\pi$
$211$	148293.	−	649714.i	0.229305	−	1.00465i	0.950208	−	0.311616i	$-0.100870\pi$
$212$	−60509.6	+	75876.6i	−0.0924665	+	0.115949i
$213$	−60480.9	−	75840.7i	−0.0913418	−	0.114539i
$214$	589968.			0.880632
$215$	−552890.	+	976765.i	−0.815722	+	1.44110i
$216$	−680282.			−0.992098
$217$	−29958.4	−	37566.7i	−0.0431887	−	0.0541569i
$218$	221801.	−	278129.i	0.316098	−	0.396374i
$219$	−106744.	+	467676.i	−0.150395	+	0.658923i
$220$	1.04333e6	−	502442.i	1.45333	−	0.699889i
$221$	−213248.			−0.293701
$222$	532313.			0.724911
$223$	−266622.	+	128398.i	−0.359032	+	0.172901i	−0.604700	−	0.796453i	$-0.706707\pi$
$223$	−266622.	+	128398.i	−0.359032	+	0.172901i	0.245668	+	0.969354i	$0.420993\pi$
$224$	26133.8	+	114500.i	0.0348003	+	0.152470i
$225$	147685.	+	71121.3i	0.194482	+	0.0936577i
$226$	64135.4	+	280995.i	0.0835269	+	0.365955i
$227$	127053.	+	159319.i	0.163652	+	0.205213i	0.856895	−	0.515491i	$-0.172390\pi$
$227$	127053.	+	159319.i	0.163652	+	0.205213i	−0.693244	+	0.720703i	$0.743819\pi$
$228$	886262.	−	426801.i	1.12908	−	0.543736i
$229$	−702929.	−	881445.i	−0.885773	−	1.11072i	−0.993189	−	0.116510i	$-0.962829\pi$
$229$	−702929.	−	881445.i	−0.885773	−	1.11072i	0.107416	−	0.994214i	$-0.465742\pi$
$230$	−325426.	+	1.42579e6i	−0.405633	+	1.77719i
$231$	146663.	+	70629.0i	0.180838	+	0.0870869i
$232$	−121930.	−	58718.2i	−0.148727	−	0.0716231i
$233$	−626233.	+	785272.i	−0.755695	+	0.947611i	−0.999755	−	0.0221488i	$-0.992949\pi$
$233$	−626233.	+	785272.i	−0.755695	+	0.947611i	0.244060	+	0.969760i	$0.421521\pi$
$234$	−13081.0	+	57311.4i	−0.0156171	+	0.0684229i
$235$	37365.7	+	163710.i	0.0441371	+	0.193377i
$236$	−140495.	+	176175.i	−0.164203	+	0.205904i
$237$	479840.	−	601700.i	0.554914	−	0.695840i
$238$	4766.29	+	20882.5i	0.00545429	+	0.0238968i
$239$	−154702.	+	677792.i	−0.175186	+	0.767541i	0.808624	+	0.588326i	$0.200213\pi$
$239$	−154702.	+	677792.i	−0.175186	+	0.767541i	−0.983810	+	0.179215i	$0.942644\pi$
$240$	138666.	−	173882.i	0.155397	−	0.194861i
$241$	−232619.	−	112023.i	−0.257990	−	0.124241i	0.300419	−	0.953807i	$-0.402874\pi$
$241$	−232619.	−	112023.i	−0.257990	−	0.124241i	−0.558409	+	0.829566i	$0.688588\pi$
$242$	−461401.	−	222199.i	−0.506454	−	0.243895i
$243$	50451.9	−	221044.i	0.0548102	−	0.240139i
$244$	−287102.	−	360015.i	−0.308718	−	0.387120i
$245$	−1.36962e6	+	659575.i	−1.45776	+	0.702019i
$246$	104619.	+	131188.i	0.110223	+	0.138215i
$247$	−421037.	−	1.84469e6i	−0.439115	−	1.92389i
$248$	376522.	+	181324.i	0.388742	+	0.187208i
$249$	−190492.	−	834600.i	−0.194706	−	0.853061i
$250$	611428.	−	294448.i	0.618722	−	0.297961i
$251$	234073.			0.234513			0.117257	−	0.993102i	$-0.462590\pi$
$251$	234073.			0.234513			0.117257	+	0.993102i	$0.462590\pi$
$252$	−13006.6			−0.0129022
$253$	−2.55950e6	+	1.23259e6i	−2.51393	+	1.21065i
$254$	−87023.2	+	381273.i	−0.0846351	+	0.370811i
$255$	290734.	−	364568.i	0.279991	−	0.351098i
$256$	−564568.	−	707945.i	−0.538414	−	0.675149i
$257$	137217.			0.129592			0.0647958	−	0.997899i	$-0.479360\pi$
$257$	137217.			0.129592			0.0647958	+	0.997899i	$0.479360\pi$
$258$	459325.	−	318931.i	0.429607	−	0.298296i
$259$	226548.			0.209851
$260$	−784633.	−	983899.i	−0.719836	−	0.902646i
$261$	14881.3	−	18660.5i	0.0135219	−	0.0169560i
$262$	163236.	−	715183.i	0.146914	−	0.643671i
$263$	371761.	−	179031.i	0.331417	−	0.159602i	−0.260774	−	0.965400i	$-0.583978\pi$
$263$	371761.	−	179031.i	0.331417	−	0.159602i	0.592190	+	0.805798i	$0.298263\pi$
$264$	−1.41580e6			−1.25023
$265$	−408200.			−0.357074
$266$	−171231.	+	82460.7i	−0.148381	+	0.0714567i
$267$	−142714.	−	625269.i	−0.122514	−	0.536771i
$268$	665603.	+	320538.i	0.566081	+	0.272610i
$269$	−427706.	−	1.87390e6i	−0.360383	−	1.57894i	−0.752223	−	0.658909i	$-0.771018\pi$
$269$	−427706.	−	1.87390e6i	−0.360383	−	1.57894i	0.391840	−	0.920033i	$-0.371839\pi$
$270$	−726987.	−	911613.i	−0.606900	−	0.761029i
$271$	−608089.	+	292840.i	−0.502972	+	0.242219i	−0.668125	−	0.744049i	$-0.732903\pi$
$271$	−608089.	+	292840.i	−0.502972	+	0.242219i	0.165152	+	0.986268i	$0.447188\pi$
$272$	35443.2	+	44444.4i	0.0290477	+	0.0364246i
$273$	39364.5	−	172467.i	0.0319668	−	0.140056i
$274$	917158.	+	441680.i	0.738019	+	0.355411i
$275$	2.78802e6	+	1.34264e6i	2.22313	+	1.07060i
$276$	−1.00069e6	+	1.25483e6i	−0.790731	+	0.991545i
$277$	−172051.	+	753803.i	−0.134728	+	0.590280i	0.861817	+	0.507219i	$0.169327\pi$
$277$	−172051.	+	753803.i	−0.134728	+	0.590280i	−0.996544	+	0.0830606i	$0.973530\pi$
$278$	39914.6	+	174877.i	0.0309756	+	0.135713i
$279$	−45953.8	+	57624.3i	−0.0353436	+	0.0443195i
$280$	−193402.	+	242518.i	−0.147423	+	0.184863i
$281$	383600.	+	1.68066e6i	0.289810	+	1.26974i	0.884786	+	0.465997i	$0.154304\pi$
$281$	383600.	+	1.68066e6i	0.289810	+	1.26974i	−0.594976	+	0.803743i	$0.702839\pi$
$282$	18616.2	−	81563.0i	0.0139402	−	0.0610760i
$283$	−1.12303e6	+	1.40823e6i	−0.833537	+	1.04522i	0.164727	+	0.986339i	$0.447326\pi$
$283$	−1.12303e6	+	1.40823e6i	−0.833537	+	1.04522i	−0.998265	+	0.0588837i	$0.981246\pi$
$284$	131830.	+	63485.9i	0.0969880	+	0.0467069i
$285$	3.72769e6	+	1.79516e6i	2.71849	+	1.30916i
$286$	−246945.	+	1.08193e6i	−0.178519	+	0.782143i
$287$	44524.8	+	55832.3i	0.0319078	+	0.0400111i
$288$	162309.	−	78164.1i	0.115309	−	0.0555298i
$289$	−810954.	−	1.01690e6i	−0.571152	−	0.716202i
$290$	−51615.3	−	226142.i	−0.0360399	−	0.157901i
$291$	−549187.	−	264475.i	−0.380179	−	0.183084i
$292$	−161012.	−	705440.i	−0.110510	−	0.484176i
$293$	2.24383e6	−	1.08057e6i	1.52693	−	0.735333i	0.533083	−	0.846063i	$-0.321033\pi$
$293$	2.24383e6	−	1.08057e6i	1.52693	−	0.735333i	0.993850	+	0.110730i	$0.0353190\pi$
$294$	757372.			0.511024
$295$	−947785.			−0.634095
$296$	−1.77526e6	+	854919.i	−1.17769	+	0.567147i
$297$	504001.	−	2.20817e6i	0.331543	−	1.45259i
$298$	690450.	−	865797.i	0.450393	−	0.564775i
$299$	1.92486e6	+	2.41370e6i	1.24515	+	1.56137i
$300$	1.74829e6			1.12153
$301$	195485.	−	135734.i	0.124365	−	0.0863522i
$302$	−827978.			−0.522398
$303$	−1.47107e6	−	1.84466e6i	−0.920504	−	1.15428i
$304$	−314483.	+	394350.i	−0.195170	+	0.244736i
$305$	430979.	−	1.88824e6i	0.265281	−	1.16227i
$306$	29602.1	−	14255.6i	0.0180725	−	0.00870326i
$307$	1.45326e6			0.880027			0.440013	−	0.897991i	$-0.354974\pi$
$307$	1.45326e6			0.880027			0.440013	+	0.897991i	$0.354974\pi$
$308$	−245541.			−0.147485
$309$	638845.	−	307652.i	0.380627	−	0.183300i
$310$	159390.	+	698332.i	0.0942011	+	0.412722i
$311$	−2.76588e6	−	1.33198e6i	−1.62155	−	0.780900i	−0.621558	−	0.783368i	$-0.713500\pi$
$311$	−2.76588e6	−	1.33198e6i	−1.62155	−	0.780900i	−0.999997	+	0.00246857i	$0.999214\pi$
$312$	342370.	+	1.50002e6i	0.199118	+	0.872391i
$313$	826749.	+	1.03671e6i	0.476994	+	0.598131i	0.960868	−	0.277006i	$-0.0893423\pi$
$313$	826749.	+	1.03671e6i	0.476994	+	0.598131i	−0.483874	+	0.875137i	$0.660771\pi$
$314$	−774079.	+	372777.i	−0.443059	+	0.213366i
$315$	−34109.2	−	42771.6i	−0.0193685	−	0.0242873i
$316$	−258317.	+	1.13176e6i	−0.145524	+	0.637583i
$317$	370713.	+	178526.i	0.207200	+	0.0997823i	0.534606	−	0.845102i	$-0.320460\pi$
$317$	370713.	+	178526.i	0.207200	+	0.0997823i	−0.327406	+	0.944884i	$0.606174\pi$
$318$	183232.	+	88239.8i	0.101609	+	0.0489324i
$319$	280931.	−	352277.i	0.154569	−	0.193824i
$320$	281047.	−	1.23135e6i	0.153428	−	0.672210i
$321$	605993.	+	2.65503e6i	0.328250	+	1.43816i
$322$	193341.	−	242441.i	0.103916	−	0.130307i
$323$	−659360.	+	826811.i	−0.351655	+	0.440961i
$324$	−248916.	−	1.09057e6i	−0.131732	−	0.577154i
$325$	748311.	−	3.27857e6i	0.392983	−	1.72177i
$326$	78834.6	−	98855.5i	0.0410840	−	0.0515177i
$327$	1.47949e6	+	712484.i	0.765142	+	0.368473i
$328$	−559594.	−	269486.i	−0.287203	−	0.138310i
$329$	7922.92	−	34712.6i	0.00403548	−	0.0176806i
$330$	−1.51300e6	−	1.89724e6i	−0.764810	−	0.959041i
$331$	2.37405e6	−	1.14328e6i	1.19102	−	0.573567i	0.269920	−	0.962883i	$-0.413003\pi$
$331$	2.37405e6	−	1.14328e6i	1.19102	−	0.573567i	0.921104	+	0.389316i	$0.127289\pi$
$332$	805100.	+	1.00956e6i	0.400871	+	0.502676i
$333$	−77327.5	−	338794.i	−0.0382141	−	0.167427i
$334$	1.23955e6	+	596937.i	0.607993	+	0.292794i
$335$	691440.	+	3.02939e6i	0.336622	+	1.47484i
$336$	−42487.6	+	20461.0i	−0.0205312	+	0.00988730i
$337$	475817.			0.228226			0.114113	−	0.993468i	$-0.463597\pi$
$337$	475817.			0.228226			0.114113	+	0.993468i	$0.463597\pi$
$338$	32396.1			0.0154242
$339$	−1.19868e6	+	577256.i	−0.566507	+	0.272815i
$340$	−156513.	+	685730.i	−0.0734268	+	0.321704i
$341$	−867524.	+	1.08784e6i	−0.404013	+	0.506616i
$342$	181763.	+	227924.i	0.0840311	+	0.105372i
$343$	652225.			0.299338
$344$	−1.01963e6	+	1.80133e6i	−0.464564	+	0.820723i
$345$	−6.75072e6			−3.05353
$346$	436919.	+	547879.i	0.196205	+	0.246034i
$347$	−1.26691e6	+	1.58866e6i	−0.564837	+	0.708284i	−0.979444	−	0.201717i	$-0.935348\pi$
$347$	−1.26691e6	+	1.58866e6i	−0.564837	+	0.708284i	0.414606	+	0.910001i	$0.363919\pi$
$348$	56646.0	−	248182.i	0.0250738	−	0.109856i
$349$	1.56721e6	−	754729.i	0.688754	−	0.331686i	−0.0565611	−	0.998399i	$-0.518014\pi$
$349$	1.56721e6	−	754729.i	0.688754	−	0.331686i	0.745315	+	0.666713i	$0.232299\pi$
$350$	−337781.			−0.147389
$351$	−2.46142e6			−1.06639
$352$	3.06411e6	−	1.47560e6i	1.31810	−	0.634762i
$353$	326400.	+	1.43005e6i	0.139416	+	0.610823i	0.995564	+	0.0940908i	$0.0299944\pi$
$353$	326400.	+	1.43005e6i	0.139416	+	0.610823i	−0.856147	+	0.516732i	$0.827148\pi$
$354$	425440.	+	204881.i	0.180439	+	0.0868947i
$355$	136947.	+	600004.i	0.0576742	+	0.252687i
$356$	603169.	+	756350.i	0.252240	+	0.316299i
$357$	−89081.5	+	42899.4i	−0.0369928	+	0.0178148i
$358$	−598885.	−	750978.i	−0.246965	−	0.309684i
$359$	314809.	−	1.37927e6i	0.128917	−	0.564823i	−0.868670	−	0.495392i	$-0.835024\pi$
$359$	314809.	−	1.37927e6i	0.128917	−	0.564823i	0.997587	−	0.0694311i	$-0.0221184\pi$
$360$	428690.	+	206446.i	0.174336	+	0.0839557i
$361$	−6.22321e6	−	2.99694e6i	−2.51331	−	1.21035i
$362$	240889.	−	302065.i	0.0966150	−	0.121151i
$363$	526027.	−	2.30467e6i	0.209528	−	0.918000i
$364$	59377.3	+	260149.i	0.0234891	+	0.102913i
$365$	1.89756e6	−	2.37946e6i	0.745526	−	0.934860i
$366$	−601635.	+	754427.i	−0.234763	+	0.294384i
$367$	2658.95	+	11649.6i	0.00103049	+	0.00451489i	0.975441	−	0.220263i	$-0.0706915\pi$
$367$	2658.95	+	11649.6i	0.00103049	+	0.00451489i	−0.974410	+	0.224778i	$0.927834\pi$
$368$	183130.	−	802344.i	0.0704919	−	0.308845i
$369$	68297.4	−	85642.3i	0.0261119	−	0.0327433i
$370$	−3.04277e6	−	1.46532e6i	−1.15549	−	0.556454i
$371$	77982.0	+	37554.1i	0.0294144	+	0.0141652i
$372$	−174924.	+	766394.i	−0.0655380	+	0.287141i
$373$	980191.	+	1.22912e6i	0.364786	+	0.457427i	0.930023	−	0.367501i	$-0.119787\pi$
$373$	980191.	+	1.22912e6i	0.364786	+	0.457427i	−0.565237	+	0.824929i	$0.691215\pi$
$374$	558833.	−	269120.i	0.206587	−	0.0994870i
$375$	1.95314e6	+	2.44916e6i	0.717224	+	0.899371i
$376$	68909.0	+	301910.i	0.0251366	+	0.110131i
$377$	−441170.	−	212456.i	−0.159865	−	0.0769867i
$378$	55014.9	+	241036.i	0.0198039	+	0.0867665i
$379$	4.60196e6	−	2.21619e6i	1.64568	−	0.792516i	0.646105	−	0.763248i	$-0.276397\pi$
$379$	4.60196e6	−	2.21619e6i	1.64568	−	0.792516i	0.999572	−	0.0292677i	$-0.00931753\pi$
$380$	−6.24087e6			−2.21710
$381$	−1.80523e6			−0.637118
$382$	−94049.2	+	45291.7i	−0.0329759	+	0.0158804i
$383$	883411.	−	3.87048e6i	0.307727	−	1.34824i	−0.550441	−	0.834874i	$-0.685541\pi$
$383$	883411.	−	3.87048e6i	0.307727	−	1.34824i	0.858169	−	0.513368i	$-0.171602\pi$
$384$	1.34950e6	−	1.69222e6i	0.467030	−	0.585637i
$385$	−643919.	−	807449.i	−0.221401	−	0.277628i
$386$	1.39380e6			0.476136
$387$	−269710.	−	246010.i	−0.0915419	−	0.0834980i
$388$	919444.			0.310060
$389$	−1.64961e6	−	2.06855e6i	−0.552723	−	0.693093i	0.424471	−	0.905442i	$-0.360460\pi$
$389$	−1.64961e6	−	2.06855e6i	−0.552723	−	0.693093i	−0.977194	+	0.212348i	$0.931889\pi$
$390$	−1.64423e6	+	2.06180e6i	−0.547396	+	0.686413i
$391$	383958.	−	1.68223e6i	0.127011	−	0.556473i
$392$	−2.52583e6	+	1.21637e6i	−0.830211	+	0.399808i
$393$	3.38620e6			1.10594
$394$	−222125.			−0.0720869
$395$	−4.39916e6	+	2.11852e6i	−1.41865	+	0.683188i
$396$	83810.3	+	367197.i	0.0268571	+	0.117669i
$397$	2.07248e6	+	998052.i	0.659953	+	0.317817i	0.733713	−	0.679459i	$-0.237786\pi$
$397$	2.07248e6	+	998052.i	0.659953	+	0.317817i	−0.0737598	+	0.997276i	$0.523500\pi$
$398$	630764.	+	2.76356e6i	0.199599	+	0.874502i
$399$	−546980.	−	685891.i	−0.172004	−	0.215686i
$400$	−807680.	+	388958.i	−0.252400	+	0.121549i
$401$	1.54726e6	+	1.94021e6i	0.480511	+	0.602542i	0.961710	−	0.274069i	$-0.0883698\pi$
$401$	1.54726e6	+	1.94021e6i	0.480511	+	0.602542i	−0.481198	+	0.876612i	$0.659798\pi$
$402$	344487.	−	1.50930e6i	0.106318	−	0.465810i
$403$	1.36234e6	+	656070.i	0.417854	+	0.201228i
$404$	3.20647e6	+	1.54416e6i	0.977404	+	0.470693i
$405$	2.93352e6	−	3.67852e6i	0.888692	−	1.11438i
$406$	−10944.4	+	47950.4i	−0.00329515	+	0.0144370i
$407$	−1.45980e6	−	6.39581e6i	−0.436825	−	1.91386i
$408$	536165.	−	672329.i	0.159458	−	0.199955i
$409$	479968.	−	601861.i	0.141874	−	0.177905i	−0.705817	−	0.708394i	$-0.749420\pi$
$409$	479968.	−	601861.i	0.141874	−	0.177905i	0.847692	+	0.530489i	$0.177992\pi$
$410$	−236888.	−	1.03787e6i	−0.0695958	−	0.304919i
$411$	−1.04562e6	+	4.58116e6i	−0.305330	+	1.33774i
$412$	−666853.	+	836207.i	−0.193547	+	0.242701i
$413$	181064.	+	87195.7i	0.0522343	+	0.0251547i
$414$	−428554.	−	206381.i	−0.122887	−	0.0591791i
$415$	−1.20856e6	+	5.29506e6i	−0.344468	+	1.50921i
$416$	−2.30435e6	−	2.88956e6i	−0.652852	−	0.818651i
$417$	−746000.	+	359254.i	−0.210087	+	0.101172i
$418$	3.43135e6	+	4.30278e6i	0.960560	+	1.20450i
$419$	−438559.	−	1.92145e6i	−0.122037	−	0.534681i	−0.998576	−	0.0533492i	$-0.983010\pi$
$419$	−438559.	−	1.92145e6i	−0.122037	−	0.534681i	0.876538	−	0.481332i	$-0.159847\pi$
$420$	−525702.	−	253165.i	−0.145417	−	0.0700293i
$421$	1.58917e6	+	6.96260e6i	0.436983	+	1.91455i	0.403185	+	0.915119i	$0.367903\pi$
$421$	1.58917e6	+	6.96260e6i	0.436983	+	1.91455i	0.0337982	+	0.999429i	$0.489240\pi$
$422$	1.89789e6	−	913975.i	0.518788	−	0.249835i
$423$	−54615.6			−0.0148411
$424$	−752793.			−0.203358
$425$	−1.69342e6	+	815508.i	−0.454770	+	0.219006i
$426$	68229.3	−	298932.i	0.0182158	−	0.0798084i
$427$	−256051.	+	321078.i	−0.0679605	+	0.0852198i
$428$	−2.56119e6	−	3.21163e6i	−0.675821	−	0.847453i
$429$	−5.12267e6			−1.34386
$430$	−3.50350e6	+	558646.i	−0.913758	+	0.145702i
$431$	−239512.			−0.0621061			−0.0310530	−	0.999518i	$-0.509886\pi$
$431$	−239512.			−0.0621061			−0.0310530	+	0.999518i	$0.509886\pi$
$432$	409103.	+	513000.i	0.105469	+	0.132254i
$433$	−1.65239e6	+	2.07204e6i	−0.423539	+	0.531101i	−0.947122	−	0.320873i	$-0.896024\pi$
$433$	−1.65239e6	+	2.07204e6i	−0.423539	+	0.531101i	0.523583	+	0.851975i	$0.324595\pi$
$434$	33796.5	−	148072.i	0.00861286	−	0.0377354i
$435$	964686.	−	464568.i	0.244435	−	0.117713i
$436$	−2.47694e6			−0.624022
$437$	1.53101e7			3.83507
$438$	−1.36614e6	+	657896.i	−0.340258	+	0.163860i
$439$	−38103.0	−	166940.i	−0.00943621	−	0.0413427i	0.969991	−	0.243142i	$-0.0781782\pi$
$439$	−38103.0	−	166940.i	−0.00943621	−	0.0413427i	−0.979427	+	0.201800i	$0.935321\pi$
$440$	8.09288e6	+	3.89732e6i	1.99283	+	0.959698i
$441$	−110021.	−	482034.i	−0.0269389	−	0.118027i
$442$	−420268.	−	526999.i	−0.102322	−	0.128308i
$443$	2.60006e6	−	1.25212e6i	0.629470	−	0.303137i	−0.0918143	−	0.995776i	$-0.529267\pi$
$443$	2.60006e6	−	1.25212e6i	0.629470	−	0.303137i	0.721284	+	0.692640i	$0.243552\pi$
$444$	−2.31089e6	−	2.89777e6i	−0.556317	−	0.697599i
$445$	−905437.	+	3.96698e6i	−0.216750	+	0.949642i
$446$	−842765.	−	405854.i	−0.200618	−	0.0966124i
$447$	4.60554e6	+	2.21791e6i	1.09021	+	0.525020i
$448$	−166974.	+	209379.i	−0.0393055	+	0.0492876i
$449$	−828169.	+	3.62845e6i	−0.193867	+	0.849386i	0.780632	+	0.624991i	$0.214898\pi$
$449$	−828169.	+	3.62845e6i	−0.193867	+	0.849386i	−0.974498	+	0.224394i	$0.927960\pi$
$450$	115294.	+	505138.i	0.0268397	+	0.117592i
$451$	1.28933e6	−	1.61677e6i	0.298485	−	0.374289i
$452$	1.25124e6	−	1.56900e6i	0.288067	−	0.361224i
$453$	−850468.	−	3.72614e6i	−0.194721	−	0.853128i
$454$	−143330.	+	627970.i	−0.0326361	+	0.142988i
$455$	−699772.	+	877486.i	−0.158463	+	0.198706i
$456$	6.87452e6	+	3.31060e6i	1.54821	+	0.745580i
$457$	3.44895e6	+	1.66093e6i	0.772497	+	0.372015i	0.778239	−	0.627969i	$-0.216113\pi$
$457$	3.44895e6	+	1.66093e6i	0.772497	+	0.372015i	−0.00574184	+	0.999984i	$0.501828\pi$
$458$	792983.	−	3.47429e6i	0.176645	−	0.773930i
$459$	857745.	+	1.07558e6i	0.190032	+	0.238292i
$460$	9.17434e6	−	4.41813e6i	2.02153	−	0.973517i
$461$	2.74794e6	+	3.44581e6i	0.602219	+	0.755159i	0.985722	−	0.168381i	$-0.0538538\pi$
$461$	2.74794e6	+	3.44581e6i	0.602219	+	0.755159i	−0.383503	+	0.923540i	$0.625282\pi$
$462$	114496.	+	501641.i	0.0249567	+	0.109342i
$463$	−5.94927e6	−	2.86502e6i	−1.28977	−	0.621119i	−0.341886	−	0.939741i	$-0.611066\pi$
$463$	−5.94927e6	−	2.86502e6i	−1.28977	−	0.621119i	−0.947882	+	0.318622i	$0.896780\pi$
$464$	29045.9	+	127258.i	0.00626311	+	0.0274405i
$465$	−2.97898e6	+	1.43460e6i	−0.638903	+	0.307679i
$466$	−3.17481e6			−0.677257
$467$	−5.72300e6			−1.21432			−0.607158	−	0.794581i	$-0.707690\pi$
$467$	−5.72300e6			−1.21432			−0.607158	+	0.794581i	$0.707690\pi$
$468$	368775.	−	177593.i	0.0778300	−	0.0374809i
$469$	146611.	−	642344.i	0.0307775	−	0.134845i
$470$	−330935.	+	414980.i	−0.0691032	+	0.0866527i
$471$	−2.47271e6	−	3.10068e6i	−0.513595	−	0.644028i
$472$	−1.74788e6			−0.361125
$473$	−5.09163e6	−	4.64422e6i	−1.04642	−	0.954465i
$474$	2.43264e6			0.497316
$475$	−1.03980e7	−	1.30386e7i	−2.11453	−	2.65154i
$476$	92986.9	−	116602.i	0.0188107	−	0.0235878i
$477$	29543.2	−	129437.i	0.00594514	−	0.0260473i
$478$	−1.97991e6	+	953473.i	−0.396347	+	0.190871i
$479$	−3.20257e6			−0.637764			−0.318882	−	0.947794i	$-0.603307\pi$
$479$	−3.20257e6			−0.637764			−0.318882	+	0.947794i	$0.603307\pi$
$480$	8.08163e6			1.60102
$481$	−6.42329e6	+	3.09329e6i	−1.26589	+	0.609619i
$482$	−181601.	−	795644.i	−0.0356041	−	0.155992i
$483$	1.28965e6	+	621062.i	0.251538	+	0.121134i
$484$	793456.	+	3.47636e6i	0.153960	+	0.674545i
$485$	2.41120e6	+	3.02354e6i	0.465456	+	0.583663i
$486$	645695.	−	310950.i	0.124004	−	0.0597173i
$487$	4.92101e6	+	6.17075e6i	0.940224	+	1.17900i	0.983676	+	0.179949i	$0.0575931\pi$
$487$	4.92101e6	+	6.17075e6i	0.940224	+	1.17900i	−0.0434516	+	0.999056i	$0.513835\pi$
$488$	794802.	−	3.48226e6i	0.151081	−	0.661929i
$489$	525854.	+	253238.i	0.0994474	+	0.0478913i
$490$	−4.32924e6	−	2.08485e6i	−0.814557	−	0.392270i
$491$	2.85319e6	−	3.57778e6i	0.534105	−	0.669746i	−0.439432	−	0.898276i	$-0.644820\pi$
$491$	2.85319e6	−	3.57778e6i	0.534105	−	0.669746i	0.973537	+	0.228530i	$0.0733918\pi$
$492$	259976.	−	1.13903e6i	0.0484195	−	0.212140i
$493$	60899.0	+	266816.i	0.0112848	+	0.0494418i
$494$	3.72898e6	−	4.67600e6i	0.687500	−	0.862098i
$495$	−987720.	+	1.23856e6i	−0.181184	+	0.227198i
$496$	−89694.6	−	392978.i	−0.0163705	−	0.0717239i
$497$	29037.8	−	127223.i	0.00527319	−	0.0231034i
$498$	1.68712e6	−	2.11558e6i	0.304841	−	0.382258i
$499$	−2.58569e6	−	1.24520e6i	−0.464863	−	0.223866i	0.186765	−	0.982405i	$-0.440200\pi$
$499$	−2.58569e6	−	1.24520e6i	−0.464863	−	0.223866i	−0.651629	+	0.758538i	$0.725914\pi$
$500$	−4.25724e6	−	2.05018e6i	−0.761559	−	0.366747i
$501$	−1.41317e6	+	6.19150e6i	−0.251536	+	1.10205i
$502$	461309.	+	578463.i	0.0817020	+	0.102451i
$503$	−1.09200e6	+	525880.i	−0.192444	+	0.0926759i	−0.527624	−	0.849478i	$-0.676917\pi$
$503$	−1.09200e6	+	525880.i	−0.192444	+	0.0926759i	0.335180	+	0.942154i	$0.391203\pi$
$504$	−62903.4	−	78878.4i	−0.0110306	−	0.0138319i
$505$	3.33094e6	+	1.45938e7i	0.581217	+	2.54648i
$506$	−8.09032e6	−	3.89609e6i	−1.40472	−	0.676477i
$507$	33276.1	+	145792.i	0.00574926	+	0.0251892i
$508$	2.45333e6	−	1.18146e6i	0.421791	−	0.203124i
$509$	8.39759e6			1.43668			0.718340	−	0.695692i	$-0.244902\pi$
$509$	8.39759e6			1.43668			0.718340	+	0.695692i	$0.244902\pi$
$510$	1.47393e6			0.250929
$511$	−581416.	+	279995.i	−0.0984996	+	0.0474349i
$512$	−419398.	+	1.83750e6i	−0.0707052	+	0.309780i
$513$	−7.61066e6	+	9.54346e6i	−1.27682	+	1.60108i
$514$	270427.	+	339105.i	0.0451484	+	0.0566143i
$515$	−4.49861e6			−0.747413
$516$	−3.73021e6	−	1.11589e6i	−0.616749	−	0.184500i
$517$	−1.03104e6			−0.169649
$518$	446479.	+	559867.i	0.0731100	+	0.0916770i
$519$	−2.01683e6	+	2.52902e6i	−0.328663	+	0.412130i
$520$	2.17215e6	−	9.51679e6i	0.352274	−	1.54341i
$521$	5.04771e6	−	2.43085e6i	0.814704	−	0.392341i	0.0203476	−	0.999793i	$-0.493523\pi$
$521$	5.04771e6	−	2.43085e6i	0.814704	−	0.392341i	0.794356	+	0.607452i	$0.207808\pi$
$522$	75443.6			0.0121184
$523$	−14715.9			−0.00235252			−0.00117626	−	0.999999i	$-0.500374\pi$
$523$	−14715.9			−0.00235252			−0.00117626	+	0.999999i	$0.500374\pi$
$524$	−4.60190e6	+	2.21616e6i	−0.732165	+	0.352592i
$525$	−346956.	−	1.52011e6i	−0.0549384	−	0.240701i
$526$	1.17510e6	+	565899.i	0.185187	+	0.0891814i
$527$	−188058.	−	823935.i	−0.0294961	−	0.129231i
$528$	851421.	+	1.06765e6i	0.132911	+	0.166665i
$529$	−1.67075e7	+	8.04591e6i	−2.59581	+	1.25007i
$530$	−804476.	−	1.00878e6i	−0.124401	−	0.155994i
$531$	68595.4	−	300536.i	0.0105574	−	0.0462552i
$532$	1.19225e6	+	574156.i	0.182636	+	0.0879531i
$533$	−2.02474e6	−	975064.i	−0.308711	−	0.148667i
$534$	1.26397e6	−	1.58496e6i	0.191815	−	0.240528i
$535$	3.84468e6	−	1.68447e7i	0.580732	−	2.54435i
$536$	1.27514e6	+	5.58674e6i	0.191710	+	0.839937i
$537$	2.76447e6	−	3.46653e6i	0.413691	−	0.518752i
$538$	3.78804e6	−	4.75006e6i	0.564234	−	0.707527i
$539$	−2.07700e6	−	9.09992e6i	−0.307939	−	1.34917i
$540$	−1.80656e6	+	7.91504e6i	−0.266604	+	1.16807i
$541$	4.65992e6	−	5.84335e6i	0.684518	−	0.858359i	−0.311243	−	0.950330i	$-0.600745\pi$
$541$	4.65992e6	−	5.84335e6i	0.684518	−	0.858359i	0.995762	+	0.0919714i	$0.0293168\pi$
$542$	−1.92211e6	−	925640.i	−0.281048	−	0.135345i
$543$	1.60681e6	+	773799.i	0.233865	+	0.112623i
$544$	−459656.	+	2.01389e6i	−0.0665941	+	0.291768i
$545$	−6.49566e6	−	8.14531e6i	−0.936769	−	1.17467i
$546$	503797.	−	242616.i	0.0723226	−	0.0348287i
$547$	1.15803e6	+	1.45213e6i	0.165483	+	0.207509i	0.857658	−	0.514221i	$-0.171919\pi$
$547$	1.15803e6	+	1.45213e6i	0.165483	+	0.207509i	−0.692175	+	0.721730i	$0.743347\pi$
$548$	−1.57721e6	−	6.91019e6i	−0.224356	−	0.982966i
$549$	567557.	+	273321.i	0.0803672	+	0.0387028i
$550$	2.17655e6	+	9.53608e6i	0.306804	+	1.34420i
$551$	−2.18783e6	+	1.05360e6i	−0.306997	+	0.147842i
$552$	−1.24495e7			−1.73902
$553$	1.03531e6			0.143966
$554$	−2.20194e6	+	1.06040e6i	−0.304812	+	0.146790i
$555$	3.46896e6	−	1.51985e7i	0.478043	−	2.09444i
$556$	778705.	−	976465.i	0.106828	−	0.133958i
$557$	7.35765e6	+	9.22620e6i	1.00485	+	1.26004i	0.965387	+	0.260820i	$0.0839929\pi$
$557$	7.35765e6	+	9.22620e6i	1.00485	+	1.26004i	0.0394618	+	0.999221i	$0.487436\pi$
$558$	−232972.			−0.0316751
$559$	−3.68925e6	+	6.51762e6i	−0.499353	+	0.882185i
$560$	299189.			0.0403158
$561$	1.78513e6	+	2.23848e6i	0.239476	+	0.300294i
$562$	−3.39742e6	+	4.26023e6i	−0.453741	+	0.568973i
$563$	−2.34780e6	+	1.02864e7i	−0.312169	+	1.36770i	0.538777	+	0.842448i	$0.318886\pi$
$563$	−2.34780e6	+	1.02864e7i	−0.312169	+	1.36770i	−0.850946	+	0.525253i	$0.823971\pi$
$564$	−524824.	+	252742.i	−0.0694730	+	0.0334564i
$565$	8.44088e6			1.11241
$566$	−5.69342e6			−0.747020
$567$	−898837.	+	432857.i	−0.117415	+	0.0565441i
$568$	252555.	+	1.10651e6i	0.0328462	+	0.143908i
$569$	3.85443e6	+	1.85620e6i	0.499091	+	0.240350i	0.666454	−	0.745546i	$-0.267811\pi$
$569$	3.85443e6	+	1.85620e6i	0.499091	+	0.240350i	−0.167364	+	0.985895i	$0.553525\pi$
$570$	2.91013e6	+	1.27501e7i	0.375167	+	1.64372i
$571$	−4.76809e6	−	5.97899e6i	−0.612004	−	0.767428i	0.375191	−	0.926947i	$-0.377577\pi$
$571$	−4.76809e6	−	5.97899e6i	−0.612004	−	0.767428i	−0.987195	+	0.159519i	$0.949006\pi$
$572$	6.96180e6	−	3.35262e6i	0.889675	−	0.428445i
$573$	−300430.	−	376727.i	−0.0382258	−	0.0479336i
$574$	−50229.0	+	220068.i	−0.00636319	+	0.0278790i
$575$	2.45159e7	+	1.18063e7i	3.09228	+	1.48916i
$576$	370111.	+	178236.i	0.0464810	+	0.0223841i
$577$	9.70771e6	−	1.21731e7i	1.21388	−	1.52216i	0.428014	−	0.903772i	$-0.359213\pi$
$577$	9.70771e6	−	1.21731e7i	1.21388	−	1.52216i	0.785870	−	0.618391i	$-0.212215\pi$
$578$	914849.	−	4.00821e6i	0.113902	−	0.499035i
$579$	1.43165e6	+	6.27249e6i	0.177477	+	0.777577i
$580$	−1.00698e6	+	1.26271e6i	−0.124294	+	0.155860i
$581$	718025.	−	900375.i	0.0882469	−	0.110658i
$582$	−428739.	−	1.87843e6i	−0.0524669	−	0.229872i
$583$	557722.	−	2.44354e6i	0.0679589	−	0.297747i
$584$	3.49943e6	−	4.38815e6i	0.424586	−	0.532414i
$585$	1.55110e6	+	746970.i	0.187391	+	0.0902430i
$586$	7.09252e6	+	3.41558e6i	0.853211	+	0.410885i
$587$	655239.	−	2.87079e6i	0.0784882	−	0.343879i	−0.920402	−	0.390973i	$-0.872139\pi$
$587$	655239.	−	2.87079e6i	0.0784882	−	0.343879i	0.998890	+	0.0470933i	$0.0149958\pi$
$588$	−3.28792e6	−	4.12293e6i	−0.392174	−	0.491770i
$589$	6.75607e6	−	3.25355e6i	0.802428	−	0.386429i
$590$	−1.86789e6	−	2.34225e6i	−0.220912	−	0.277015i
$591$	−228158.	−	999626.i	−0.0268700	−	0.117725i
$592$	1.71228e6	+	824593.i	0.200804	+	0.0967020i
$593$	1.89762e6	+	8.31403e6i	0.221602	+	0.970901i	0.956272	+	0.292477i	$0.0944796\pi$
$593$	1.89762e6	+	8.31403e6i	0.221602	+	0.970901i	−0.734671	+	0.678424i	$0.762663\pi$
$594$	6.45032e6	−	3.10631e6i	0.750093	−	0.361226i
$595$	627293.			0.0726404
$596$	−7.71056e6			−0.889140
$597$	−1.17889e7	+	5.67724e6i	−1.35375	+	0.651931i
$598$	−2.17146e6	+	9.51379e6i	−0.248313	+	1.08793i
$599$	3.89232e6	−	4.88082e6i	0.443243	−	0.555809i	−0.509152	−	0.860677i	$-0.670041\pi$
$599$	3.89232e6	−	4.88082e6i	0.443243	−	0.555809i	0.952395	+	0.304868i	$0.0986123\pi$
$600$	8.45520e6	+	1.06025e7i	0.958839	+	1.20235i
$601$	1.16438e7			1.31495			0.657475	−	0.753477i	$-0.271625\pi$
$601$	1.16438e7			1.31495			0.657475	+	0.753477i	$0.271625\pi$
$602$	720700.	+	215597.i	0.0810519	+	0.0242466i
$603$	−1.01064e6			−0.113189
$604$	3.59444e6	+	4.50729e6i	0.400903	+	0.502716i
$605$	−9.35102e6	+	1.17258e7i	−1.03865	+	1.30243i
$606$	1.65953e6	−	7.27087e6i	0.183571	−	0.804276i
$607$	−1.30031e7	+	6.26197e6i	−1.43244	+	0.689825i	−0.979449	−	0.201691i	$-0.935356\pi$
$607$	−1.30031e7	+	6.26197e6i	−1.43244	+	0.689825i	−0.452988	+	0.891517i	$0.649642\pi$
$608$	−1.83285e7			−2.01079
$609$	−227032.			−0.0248053
$610$	5.51577e6	−	2.65626e6i	0.600180	−	0.289032i
$611$	249329.	+	1.09238e6i	0.0270190	+	0.118378i
$612$	−206113.	−	99258.7i	−0.0222447	−	0.0107125i
$613$	−2.01733e6	−	8.83850e6i	−0.216833	−	0.950008i	−0.959801	−	0.280681i	$-0.909440\pi$
$613$	−2.01733e6	−	8.83850e6i	−0.216833	−	0.950008i	0.742968	−	0.669327i	$-0.233417\pi$
$614$	2.86406e6	+	3.59142e6i	0.306593	+	0.384455i
$615$	4.42741e6	−	2.13213e6i	0.472022	−	0.227314i
$616$	−1.18750e6	−	1.48908e6i	−0.126091	−	0.158113i
$617$	2.99579e6	−	1.31254e7i	0.316809	−	1.38803i	−0.526304	−	0.850296i	$-0.676423\pi$
$617$	2.99579e6	−	1.31254e7i	0.316809	−	1.38803i	0.843114	−	0.537736i	$-0.180720\pi$
$618$	2.01933e6	+	972457.i	0.212684	+	0.102423i
$619$	−4.06771e6	−	1.95891e6i	−0.426701	−	0.205488i	0.208193	−	0.978088i	$-0.433242\pi$
$619$	−4.06771e6	−	1.95891e6i	−0.426701	−	0.205488i	−0.634894	+	0.772599i	$0.718956\pi$
$620$	3.10958e6	−	3.89929e6i	0.324879	−	0.407386i
$621$	4.43184e6	−	1.94171e7i	0.461163	−	2.02049i
$622$	−2.15926e6	−	9.46034e6i	−0.223784	−	0.980462i
$623$	537933.	−	674547.i	0.0555275	−	0.0696293i
$624$	925272.	−	1.16025e6i	0.0951279	−	0.119287i
$625$	−636666.	−	2.78942e6i	−0.0651946	−	0.285636i
$626$	−932666.	+	4.08628e6i	−0.0951241	+	0.416766i
$627$	−1.58392e7	+	1.98617e7i	−1.60903	+	2.01766i
$628$	5.38975e6	+	2.59556e6i	0.545342	+	0.262623i
$629$	3.59005e6	+	1.72888e6i	0.361805	+	0.174236i
$630$	38479.0	−	168588.i	0.00386254	−	0.0169229i
$631$	−564769.	−	708198.i	−0.0564673	−	0.0708078i	0.752796	−	0.658254i	$-0.228705\pi$
$631$	−564769.	−	708198.i	−0.0564673	−	0.0708078i	−0.809263	+	0.587446i	$0.800133\pi$
$632$	−8.11283e6	+	3.90693e6i	−0.807941	+	0.389084i
$633$	6.06259e6	+	7.60225e6i	0.601380	+	0.754107i
$634$	289408.	+	1.26798e6i	0.0285948	+	0.125282i
$635$	1.03189e7	+	4.96933e6i	1.01555	+	0.489062i
$636$	−315098.	−	1.38053e6i	−0.0308889	−	0.135333i
$637$	−9.13902e6	+	4.40112e6i	−0.892383	+	0.429749i
$638$	1.42424e6			0.138526
$639$	−200169.			−0.0193929
$640$	−1.23722e7	+	5.95812e6i	−1.19398	+	0.574989i
$641$	823850.	−	3.60952e6i	0.0791959	−	0.346980i	−0.919769	−	0.392459i	$-0.871624\pi$
$641$	823850.	−	3.60952e6i	0.0791959	−	0.346980i	0.998965	+	0.0454793i	$0.0144815\pi$
$642$	−5.36707e6	+	6.73010e6i	−0.513925	+	0.644442i
$643$	7.43016e6	+	9.31712e6i	0.708713	+	0.888698i	0.997641	−	0.0686528i	$-0.0218701\pi$
$643$	7.43016e6	+	9.31712e6i	0.708713	+	0.888698i	−0.288927	+	0.957351i	$0.593299\pi$
$644$	−2.15912e6			−0.205145
$645$	−6.11273e6	−	1.51930e7i	−0.578544	−	1.43795i
$646$	−3.34275e6			−0.315154
$647$	−9.92754e6	−	1.24487e7i	−0.932354	−	1.16913i	−0.985351	−	0.170540i	$-0.945449\pi$
$647$	−9.92754e6	−	1.24487e7i	−0.932354	−	1.16913i	0.0529967	−	0.998595i	$-0.483123\pi$
$648$	5.40993e6	−	6.78384e6i	0.506121	−	0.634655i
$649$	1.29496e6	−	5.67357e6i	0.120682	−	0.528743i
$650$	9.57706e6	−	4.61207e6i	0.889097	−	0.428166i
$651$	701082.			0.0648361
$652$	−880381.			−0.0811058
$653$	2.75331e6	−	1.32592e6i	0.252681	−	0.121685i	−0.303256	−	0.952909i	$-0.598074\pi$
$653$	2.75331e6	−	1.32592e6i	0.252681	−	0.121685i	0.555937	+	0.831224i	$0.312360\pi$
$654$	1.15500e6	+	5.06040e6i	0.105594	+	0.462638i
$655$	−1.93560e7	−	9.32135e6i	−1.76284	−	0.848937i
$656$	133306.	+	584051.i	0.0120945	+	0.0529897i
$657$	617176.	+	773914.i	0.0557822	+	0.0699487i
$658$	101399.	−	48831.4i	0.00912999	−	0.00439677i
$659$	−6.91902e6	−	8.67617e6i	−0.620627	−	0.778242i	0.367805	−	0.929903i	$-0.380109\pi$
$659$	−6.91902e6	−	8.67617e6i	−0.620627	−	0.778242i	−0.988433	+	0.151661i	$0.951538\pi$
$660$	−3.75978e6	+	1.64727e7i	−0.335972	+	1.47199i
$661$	−2.31436e6	−	1.11454e6i	−0.206028	−	0.0992180i	0.328024	−	0.944669i	$-0.393617\pi$
$661$	−2.31436e6	−	1.11454e6i	−0.206028	−	0.0992180i	−0.534052	+	0.845451i	$0.679332\pi$
$662$	7.50415e6	+	3.61381e6i	0.665513	+	0.320494i
$663$	1.93997e6	−	2.43264e6i	0.171400	−	0.214929i
$664$	−2.22881e6	+	9.76503e6i	−0.196179	+	0.859515i
$665$	1.23853e6	+	5.42634e6i	0.108605	+	0.475831i
$666$	684863.	−	858791.i	0.0598299	−	0.0750243i
$667$	2.47032e6	−	3.09768e6i	0.215000	−	0.269601i
$668$	−2.13162e6	−	9.33922e6i	−0.184828	−	0.809784i
$669$	960806.	−	4.20957e6i	0.0829986	−	0.363640i
$670$	−6.12384e6	+	7.67905e6i	−0.527032	+	0.660877i
$671$	1.07144e7	+	5.15980e6i	0.918677	+	0.442412i
$672$	−1.54391e6	−	743506.i	−0.131886	−	0.0635128i
$673$	152283.	−	667195.i	0.0129602	−	0.0567826i	−0.968034	−	0.250818i	$-0.919300\pi$
$673$	152283.	−	667195.i	0.0129602	−	0.0567826i	0.980995	+	0.194035i	$0.0621576\pi$
$674$	937737.	+	1.17588e6i	0.0795117	+	0.0997045i
$675$	−1.95463e7	+	9.41299e6i	−1.65122	+	0.795185i
$676$	−140639.	−	176356.i	−0.0118369	−	0.0148430i
$677$	−2.54455e6	−	1.11484e7i	−0.213373	−	0.934849i	−0.962256	−	0.272147i	$-0.912266\pi$
$677$	−2.54455e6	−	1.11484e7i	−0.213373	−	0.934849i	0.748883	−	0.662703i	$-0.230591\pi$
$678$	−3.78892e6	−	1.82465e6i	−0.316550	−	0.152442i
$679$	−182468.	−	799443.i	−0.0151884	−	0.0665446i
$680$	−4.91554e6	+	2.36720e6i	−0.407661	+	0.196319i
$681$	−2.97327e6			−0.245678
$682$	−4.39808e6			−0.362078
$683$	−5.44867e6	+	2.62394e6i	−0.446929	+	0.215230i	−0.643791	−	0.765201i	$-0.722639\pi$
$683$	−5.44867e6	+	2.62394e6i	−0.446929	+	0.215230i	0.196861	+	0.980431i	$0.436925\pi$
$684$	451679.	−	1.97894e6i	0.0369139	−	0.161730i
$685$	1.85877e7	−	2.33082e7i	1.51355	−	1.89794i
$686$	1.28540e6	+	1.61184e6i	0.104286	+	0.130771i
$687$	1.64498e7			1.32975
$688$	1.97155e6	−	314371.i	0.158795	−	0.0253205i
$689$	−2.72378e6			−0.218587
$690$	−1.33043e7	−	1.66830e7i	−1.06382	−	1.33399i
$691$	9.62878e6	−	1.20741e7i	0.767142	−	0.961966i	−0.232802	−	0.972524i	$-0.574789\pi$
$691$	9.62878e6	−	1.20741e7i	0.767142	−	0.961966i	0.999944	+	0.0105582i	$0.00336083\pi$
$692$	1.08574e6	−	4.75693e6i	0.0861906	−	0.377626i
$693$	302640.	−	145744.i	0.0239383	−	0.0115281i
$694$	−6.42287e6			−0.506210
$695$	5.25317e6			0.412534
$696$	1.77905e6	−	856746.i	0.139208	−	0.0670392i
$697$	279495.	+	1.22455e6i	0.0217918	+	0.0954759i
$698$	4.95380e6	+	2.38563e6i	0.384858	+	0.185338i
$699$	−3.26105e6	−	1.42876e7i	−0.252444	−	1.10603i
$700$	1.46638e6	+	1.83879e6i	0.113110	+	0.141836i
$701$	−1.39449e7	+	6.71551e6i	−1.07182	+	0.516160i	−0.884692	−	0.466177i	$-0.845631\pi$
$701$	−1.39449e7	+	6.71551e6i	−1.07182	+	0.516160i	−0.187125	+	0.982336i	$0.559917\pi$
$702$	−4.85094e6	−	6.08289e6i	−0.371521	−	0.465872i
$703$	−7.86731e6	+	3.44689e7i	−0.600396	+	2.63051i
$704$	6.98701e6	+	3.36477e6i	0.531324	+	0.255872i
$705$	−2.20745e6	−	1.06305e6i	−0.167270	−	0.0805531i
$706$	−2.89081e6	+	3.62496e6i	−0.218277	+	0.273711i
$707$	706282.	−	3.09442e6i	0.0531410	−	0.232826i
$708$	−731614.	−	3.20541e6i	−0.0548528	−	0.240326i
$709$	−203889.	+	255669.i	−0.0152327	+	0.0191013i	−0.789390	−	0.613893i	$-0.789603\pi$
$709$	−203889.	+	255669.i	−0.0152327	+	0.0191013i	0.774157	+	0.632994i	$0.218174\pi$
$710$	−1.21289e6	+	1.52092e6i	−0.0902976	+	0.113230i
$711$	−353382.	−	1.54827e6i	−0.0262163	−	0.114861i
$712$	−1.66979e6	+	7.31581e6i	−0.123441	+	0.540832i
$713$	−7.62841e6	+	9.56572e6i	−0.561966	+	0.704683i
$714$	−281578.	−	135601.i	−0.0206706	−	0.00995444i
$715$	2.92819e7	+	1.41014e7i	2.14207	+	1.03157i
$716$	−1.48822e6	+	6.52033e6i	−0.108489	+	0.475321i
$717$	−6.32460e6	−	7.93079e6i	−0.459446	−	0.576128i
$718$	4.02900e6	−	1.94026e6i	0.291666	−	0.140459i
$719$	1.12191e7	+	1.40683e7i	0.809349	+	1.01489i	0.999451	+	0.0331274i	$0.0105467\pi$
$719$	1.12191e7	+	1.40683e7i	0.809349	+	1.01489i	−0.190102	+	0.981764i	$0.560882\pi$
$720$	−102122.	−	447425.i	−0.00734155	−	0.0321654i
$721$	859410.	+	413870.i	0.0615690	+	0.0296501i
$722$	−4.85832e6	−	2.12857e7i	−0.346851	−	1.51966i
$723$	3.39410e6	−	1.63451e6i	0.241479	−	0.116290i
$724$	−2.69011e6			−0.190732
$725$	−4.31583e6			−0.304944
$726$	6.73221e6	−	3.24206e6i	0.474041	−	0.228286i
$727$	−1.94314e6	+	8.51347e6i	−0.136354	+	0.597407i	0.859864	+	0.510523i	$0.170548\pi$
$727$	−1.94314e6	+	8.51347e6i	−0.136354	+	0.597407i	−0.996218	+	0.0868842i	$0.972309\pi$
$728$	−1.29050e6	+	1.61824e6i	−0.0902466	+	0.113166i
$729$	9.76317e6	+	1.22426e7i	0.680412	+	0.853210i
$730$	9.62003e6			0.668143
$731$	4.13365e6	−	659125.i	0.286115	−	0.0456220i
$732$	6.71873e6			0.463457
$733$	5.92742e6	+	7.43275e6i	0.407480	+	0.510963i	0.942651	−	0.333780i	$-0.108324\pi$
$733$	5.92742e6	+	7.43275e6i	0.407480	+	0.510963i	−0.535171	+	0.844744i	$0.679753\pi$
$734$	−23549.4	+	29530.0i	−0.00161339	+	0.00202313i
$735$	4.93561e6	−	2.16243e7i	0.336994	−	1.47647i
$736$	2.69436e7	−	1.29754e7i	1.83342	−	0.882928i
$737$	−1.90791e7			−1.29386
$738$	346247.			0.0234016
$739$	−1.41138e7	+	6.79684e6i	−0.950675	+	0.457821i	−0.843923	−	0.536465i	$-0.819759\pi$
$739$	−1.41138e7	+	6.79684e6i	−0.950675	+	0.457821i	−0.106752	+	0.994286i	$0.534045\pi$
$740$	5.23256e6	+	2.29253e7i	0.351265	+	1.53899i
$741$	2.48736e7	+	1.19785e7i	1.66415	+	0.801414i
$742$	60878.9	+	266728.i	0.00405935	+	0.0177852i
$743$	−1.81317e6	−	2.27364e6i	−0.120494	−	0.151095i	0.717926	−	0.696120i	$-0.245092\pi$
$743$	−1.81317e6	−	2.27364e6i	−0.120494	−	0.151095i	−0.838420	+	0.545025i	$0.816520\pi$
$744$	−5.49376e6	+	2.64566e6i	−0.363863	+	0.175227i
$745$	−2.02205e7	−	2.53558e7i	−1.33476	−	1.67373i
$746$	−1.10577e6	+	4.84468e6i	−0.0727472	+	0.318726i
$747$	−1.59156e6	−	766454.i	−0.104357	−	0.0502556i
$748$	−3.89103e6	−	1.87382e6i	−0.254279	−	0.122454i
$749$	−2.28418e6	+	2.86427e6i	−0.148774	+	0.186556i
$750$	−2.20336e6	+	9.65356e6i	−0.143032	+	0.626663i
$751$	2.23434e6	+	9.78930e6i	0.144561	+	0.633362i	0.994342	+	0.106226i	$0.0338768\pi$
$751$	2.23434e6	+	9.78930e6i	0.144561	+	0.633362i	−0.849781	+	0.527135i	$0.823266\pi$
$752$	186230.	−	233525.i	0.0120089	−	0.0150587i
$753$	−2.12941e6	+	2.67020e6i	−0.136859	+	0.171616i
$754$	−344412.	−	1.50897e6i	−0.0220622	−	0.0966610i
$755$	−5.39574e6	+	2.36403e7i	−0.344495	+	1.50933i
$756$	1.07330e6	−	1.34588e6i	0.0682994	−	0.0856448i
$757$	1.22540e7	+	5.90120e6i	0.777208	+	0.374283i	0.780054	−	0.625713i	$-0.215192\pi$
$757$	1.22540e7	+	5.90120e6i	0.777208	+	0.374283i	−0.00284618	+	0.999996i	$0.500906\pi$
$758$	1.45463e7	+	7.00515e6i	0.919561	+	0.442837i
$759$	9.22348e6	−	4.04107e7i	0.581153	−	2.54620i
$760$	−3.01825e7	−	3.78476e7i	−1.89549	−	2.37687i
$761$	−864147.	+	416151.i	−0.0540911	+	0.0260489i	−0.460734	−	0.887538i	$-0.652414\pi$
$761$	−864147.	+	416151.i	−0.0540911	+	0.0260489i	0.406643	+	0.913587i	$0.366699\pi$
$762$	−3.55773e6	−	4.46125e6i	−0.221965	−	0.278336i
$763$	491560.	+	2.15367e6i	0.0305679	+	0.133927i
$764$	654844.	+	315356.i	0.0405886	+	0.0195465i
$765$	−214113.	−	938092.i	−0.0132279	−	0.0579551i
$766$	1.13061e7	−	5.44473e6i	0.696211	−	0.335278i
$767$	−6.32425e6			−0.388169
$768$	1.32119e7			0.808282
$769$	−1.93351e7	+	9.31128e6i	−1.17904	+	0.567798i	−0.917633	−	0.397430i	$-0.869902\pi$
$769$	−1.93351e7	+	9.31128e6i	−1.17904	+	0.567798i	−0.261411	+	0.965228i	$0.584188\pi$
$770$	726414.	−	3.18263e6i	0.0441527	−	0.193446i
$771$	−1.24830e6	+	1.56532e6i	−0.0756279	+	0.0948344i
$772$	−6.05078e6	−	7.58744e6i	−0.365400	−	0.458197i
$773$	−1.81457e6			−0.109226			−0.0546128	−	0.998508i	$-0.517392\pi$
$773$	−1.81457e6			−0.109226			−0.0546128	+	0.998508i	$0.517392\pi$
$774$	76421.2	−	1.15137e6i	0.00458523	−	0.0690815i
$775$	1.33274e7			0.797061
$776$	4.44667e6	+	5.57595e6i	0.265082	+	0.332403i
$777$	−2.06096e6	+	2.58436e6i	−0.122466	+	0.153568i
$778$	1.86095e6	−	8.15335e6i	0.110226	−	0.482933i
$779$	−1.00410e7	+	4.83549e6i	−0.592835	+	0.285494i
$780$	1.83619e7			1.08064
$781$	−3.77882e6			−0.221681
$782$	4.91399e6	−	2.36645e6i	0.287354	−	0.138382i
$783$	702926.	+	3.07972e6i	0.0409737	+	0.179518i
$784$	2.43623e6	+	1.17323e6i	0.141556	+	0.0681697i
$785$	5.59896e6	+	2.45306e7i	0.324290	+	1.42081i
$786$	6.67349e6	+	8.36830e6i	0.385298	+	0.483149i
$787$	−1.05621e7	+	5.08645e6i	−0.607875	+	0.292737i	−0.712388	−	0.701786i	$-0.752386\pi$
$787$	−1.05621e7	+	5.08645e6i	−0.607875	+	0.292737i	0.104512	+	0.994524i	$0.466672\pi$
$788$	964294.	+	1.20919e6i	0.0553215	+	0.0693709i
$789$	−1.33969e6	+	5.86956e6i	−0.0766146	+	0.335671i
$790$	−1.39053e7	−	6.69644e6i	−0.792707	−	0.381748i
$791$	−1.61253e6	−	776556.i	−0.0916364	−	0.0441298i
$792$	−1.82153e6	+	2.28413e6i	−0.103187	+	0.129392i
$793$	2.87578e6	−	1.25996e7i	0.162395	−	0.711499i
$794$	1.61794e6	+	7.08865e6i	0.0910774	+	0.399036i
$795$	3.71348e6	−	4.65656e6i	0.208384	−	0.261305i
$796$	1.23058e7	−	1.54309e7i	0.688376	−	0.863196i
$797$	5.95589e6	+	2.60945e7i	0.332125	+	1.45513i	0.815009	+	0.579449i	$0.196732\pi$
$797$	5.95589e6	+	2.60945e7i	0.332125	+	1.45513i	−0.482884	+	0.875684i	$0.660411\pi$
$798$	617055.	−	2.70349e6i	0.0343018	−	0.150286i
$799$	390458.	−	489619.i	0.0216375	−	0.0271326i
$800$	−2.93493e7	−	1.41339e7i	−1.62133	−	0.780794i
$801$	−1.19237e6	−	574216.i	−0.0656644	−	0.0316223i
$802$	−1.74549e6	+	7.64749e6i	−0.0958256	+	0.419839i
$803$	1.16512e7	+	1.46101e7i	0.637647	+	0.799583i
$804$	−9.71169e6	+	4.67690e6i	−0.529852	+	0.255163i
$805$	−5.66218e6	−	7.10015e6i	−0.307960	−	0.386169i
$806$	1.06355e6	+	4.65973e6i	0.0576662	+	0.252652i
$807$	2.52676e7	+	1.21682e7i	1.36578	+	0.657723i
$808$	6.14284e6	+	2.69135e7i	0.331010	+	1.45025i
$809$	1.46111e7	−	7.03635e6i	0.784897	−	0.377987i	0.00188924	−	0.999998i	$-0.499399\pi$
$809$	1.46111e7	−	7.03635e6i	0.784897	−	0.377987i	0.783008	+	0.622012i	$0.213684\pi$
$810$	1.48720e7			0.796449
$811$	2.55916e7			1.36630			0.683149	−	0.730279i	$-0.260610\pi$
$811$	2.55916e7			1.36630			0.683149	+	0.730279i	$0.260610\pi$
$812$	308541.	−	148585.i	0.0164219	−	0.00790835i
$813$	2.19133e6	−	9.60084e6i	0.116274	−	0.509428i
$814$	1.29290e7	−	1.62124e7i	0.683915	−	0.857603i
$815$	−2.30876e6	−	2.89509e6i	−0.121754	−	0.152675i
$816$	−829437.			−0.0436072
$817$	1.38632e7	+	3.44564e7i	0.726620	+	1.80599i
$818$	2.43329e6			0.127148
$819$	−227599.	−	285400.i	−0.0118566	−	0.0148677i
$820$	−4.62152e6	+	5.79520e6i	−0.240021	+	0.300977i
$821$	−992119.	+	4.34676e6i	−0.0513696	+	0.225065i	−0.994096	−	0.108501i	$-0.965395\pi$
$821$	−992119.	+	4.34676e6i	−0.0513696	+	0.225065i	0.942727	+	0.333566i	$0.108252\pi$
$822$	−1.33821e7	+	6.44447e6i	−0.690787	+	0.332665i
$823$	−3.18781e7			−1.64056			−0.820280	−	0.571962i	$-0.806183\pi$
$823$	−3.18781e7			−1.64056			−0.820280	+	0.571962i	$0.806183\pi$
$824$	−8.29624e6			−0.425661
$825$	−4.06795e7	+	1.95902e7i	−2.08085	+	1.00208i
$826$	141353.	+	619306.i	0.00720864	+	0.0315831i
$827$	−2.36280e7	−	1.13787e7i	−1.20133	−	0.578532i	−0.277278	−	0.960790i	$-0.589432\pi$
$827$	−2.36280e7	−	1.13787e7i	−1.20133	−	0.578532i	−0.924056	+	0.382258i	$0.875146\pi$
$828$	736970.	+	3.22888e6i	0.0373572	+	0.163673i
$829$	6.45084e6	+	8.08910e6i	0.326009	+	0.408803i	0.917644	−	0.397403i	$-0.130089\pi$
$829$	6.45084e6	+	8.08910e6i	0.326009	+	0.408803i	−0.591635	+	0.806206i	$0.701517\pi$
$830$	−1.54675e7	+	7.44874e6i	−0.779335	+	0.375308i
$831$	−7.03386e6	−	8.82018e6i	−0.353339	−	0.443073i
$832$	1.87533e6	−	8.21635e6i	0.0939224	−	0.411501i
$833$	5.10791e6	+	2.45984e6i	0.255053	+	0.122827i
$834$	−2.35803e6	−	1.13557e6i	−0.117391	−	0.0565325i
$835$	2.51215e7	−	3.15013e7i	1.24689	−	1.56355i
$836$	8.52688e6	−	3.73587e7i	0.421963	−	1.84874i
$837$	−2.17066e6	−	9.51027e6i	−0.107097	−	0.469223i
$838$	3.88417e6	−	4.87059e6i	0.191068	−	0.239592i
$839$	4.75661e6	−	5.96461e6i	0.233288	−	0.292534i	−0.651383	−	0.758749i	$-0.725811\pi$
$839$	4.75661e6	−	5.96461e6i	0.233288	−	0.292534i	0.884672	+	0.466214i	$0.154382\pi$
$840$	−1.00712e6	−	4.41248e6i	−0.0492473	−	0.215767i
$841$	4.42432e6	−	1.93842e7i	0.215703	−	0.945058i
$842$	−1.40747e7	+	1.76491e7i	−0.684162	+	0.857912i
$843$	−2.26620e7	−	1.09134e7i	−1.09832	−	0.528923i
$844$	−1.32146e7	−	6.36381e6i	−0.638554	−	0.307511i
$845$	211118.	−	924967.i	0.0101715	−	0.0445641i
$846$	−107636.	−	134971.i	−0.00517049	−	0.00648358i
$847$	2.86517e6	−	1.37980e6i	0.137228	−	0.0660855i
$848$	452709.	+	567680.i	0.0216187	+	0.0271090i
$849$	−5.84806e6	−	2.56220e7i	−0.278447	−	1.21996i
$850$	−5.35273e6	−	2.57774e6i	−0.254114	−	0.122375i
$851$	−1.28365e7	−	5.62403e7i	−0.607606	−	2.66210i
$852$	−1.92350e6	+	926311.i	−0.0907808	+	0.0437177i
$853$	2.32789e7			1.09544			0.547721	−	0.836661i	$-0.315496\pi$
$853$	2.32789e7			1.09544			0.547721	+	0.836661i	$0.315496\pi$
$854$	−1.29810e6			−0.0609065
$855$	7.69213e6	−	3.70434e6i	0.359858	−	0.173299i
$856$	7.09028e6	−	3.10645e7i	0.330734	−	1.44904i
$857$	−1.47771e7	+	1.85298e7i	−0.687284	+	0.861826i	−0.996002	−	0.0893270i	$-0.971528\pi$
$857$	−1.47771e7	+	1.85298e7i	−0.687284	+	0.861826i	0.308719	+	0.951153i	$0.400100\pi$
$858$	−1.00957e7	−	1.26596e7i	−0.468187	−	0.587088i
$859$	−3.38681e7			−1.56606			−0.783028	−	0.621986i	$-0.786326\pi$
$859$	−3.38681e7			−1.56606			−0.783028	+	0.621986i	$0.786326\pi$
$860$	1.82506e7	+	1.66469e7i	0.841456	+	0.767515i
$861$	−1.04196e6			−0.0479009
$862$	−472028.	−	591905.i	−0.0216371	−	0.0271321i
$863$	−2.02396e7	+	2.53796e7i	−0.925070	+	1.16000i	0.0617361	+	0.998093i	$0.480336\pi$
$863$	−2.02396e7	+	2.53796e7i	−0.925070	+	1.16000i	−0.986806	+	0.161908i	$0.948235\pi$
$864$	−5.30558e6	+	2.32453e7i	−0.241796	+	1.05938i
$865$	1.84902e7	−	8.90442e6i	0.840237	−	0.404637i
$866$	−8.37713e6			−0.379578
$867$	1.89778e7			0.857430
$868$	−952782.	+	458836.i	−0.0429234	+	0.0206708i
$869$	−6.67121e6	−	2.92285e7i	−0.299678	−	1.31298i
$870$	3.04928e6	+	1.46845e6i	0.136584	+	0.0657752i
$871$	4.61374e6	+	2.02141e7i	0.206067	+	0.902838i
$872$	−1.19792e7	−	1.50214e7i	−0.533501	−	0.668989i
$873$	−1.13325e6	+	545746.i	−0.0503259	+	0.0242357i
$874$	3.01730e7	+	3.78357e7i	1.33610	+	1.67542i
$875$	−937733.	+	4.10848e6i	−0.0414056	+	0.181410i
$876$	9.51211e6	+	4.58079e6i	0.418809	+	0.201688i
$877$	−3.06070e7	−	1.47396e7i	−1.34376	−	0.647121i	−0.382806	−	0.923829i	$-0.625042\pi$
$877$	−3.06070e7	−	1.47396e7i	−1.34376	−	0.647121i	−0.960954	+	0.276708i	$0.910757\pi$
$878$	337465.	−	423167.i	0.0147738	−	0.0185258i
$879$	−8.08592e6	+	3.54267e7i	−0.352986	+	1.54653i
$880$	−1.92787e6	−	8.44657e6i	−0.0839213	−	0.367683i
$881$	−1.10331e7	+	1.38350e7i	−0.478913	+	0.600537i	−0.961328	−	0.275405i	$-0.911188\pi$
$881$	−1.10331e7	+	1.38350e7i	−0.478913	+	0.600537i	0.482416	+	0.875942i	$0.339759\pi$
$882$	974419.	−	1.22188e6i	0.0421769	−	0.0528881i
$883$	−2.92065e6	−	1.27962e7i	−0.126060	−	0.552306i	−0.998030	−	0.0627457i	$-0.980014\pi$
$883$	−2.92065e6	−	1.27962e7i	−0.126060	−	0.552306i	0.871969	−	0.489561i	$-0.162843\pi$
$884$	−1.04436e6	+	4.57565e6i	−0.0449490	+	0.196934i
$885$	8.62221e6	−	1.08119e7i	0.370050	−	0.464028i
$886$	8.21855e6	+	3.95785e6i	0.351731	+	0.169385i
$887$	1.70254e7	+	8.19901e6i	0.726589	+	0.349907i	0.760342	−	0.649523i	$-0.225032\pi$
$887$	1.70254e7	+	8.19901e6i	0.726589	+	0.349907i	−0.0337525	+	0.999430i	$0.510746\pi$
$888$	6.39737e6	−	2.80287e7i	0.272251	−	1.19281i
$889$	−1.51414e6	−	1.89867e6i	−0.0642557	−	0.0805741i
$890$	−1.15880e7	+	5.58048e6i	−0.490381	+	0.236155i
$891$	1.80120e7	+	2.25864e7i	0.760096	+	0.953131i
$892$	1.44927e6	+	6.34969e6i	0.0609872	+	0.267202i
$893$	5.00632e6	+	2.41092e6i	0.210083	+	0.101170i
$894$	3.59545e6	+	1.57527e7i	0.150456	+	0.659190i
$895$	−2.53445e7	+	1.22053e7i	−1.05761	+	0.509320i
$896$	2.91171e6			0.121165
$897$	−4.50453e7			−1.86925
$898$	−1.05991e7	+	5.10426e6i	−0.438610	+	0.211223i
$899$	431819.	−	1.89192e6i	0.0178198	−	0.0780735i
$900$	2.24931e6	−	2.82055e6i	0.0925644	−	0.116072i
$901$	949171.	+	1.19022e6i	0.0389522	+	0.0488446i
$902$	6.53651e6			0.267504
$903$	−229974.	+	3.46481e6i	−0.00938555	+	0.141404i
$904$	1.55665e7			0.633533
$905$	−7.05468e6	−	8.84628e6i	−0.286323	−	0.359037i
$906$	7.53230e6	−	9.44521e6i	0.304865	−	0.382288i
$907$	4.60195e6	−	2.01625e7i	0.185748	−	0.813814i	−0.793078	−	0.609120i	$-0.791523\pi$
$907$	4.60195e6	−	2.01625e7i	0.185748	−	0.813814i	0.978826	−	0.204694i	$-0.0656201\pi$
$908$	4.04073e6	−	1.94591e6i	0.162646	−	0.0783264i
$909$	−4.86866e6			−0.195434
$910$	−3.54763e6			−0.142015
$911$	2.19051e7	−	1.05489e7i	0.874480	−	0.421127i	0.0578744	−	0.998324i	$-0.481568\pi$
$911$	2.19051e7	−	1.05489e7i	0.874480	−	0.421127i	0.816605	+	0.577197i	$0.195853\pi$
$912$	−1.63764e6	−	7.17497e6i	−0.0651976	−	0.285649i
$913$	−3.00457e7	−	1.44692e7i	−1.19290	−	0.574472i
$914$	2.69252e6	+	1.17967e7i	0.106609	+	0.467085i
$915$	1.76195e7	+	2.20942e7i	0.695731	+	0.872419i
$916$	−2.23556e7	+	1.07659e7i	−0.880333	+	0.423946i
$917$	2.84018e6	+	3.56148e6i	0.111538	+	0.139864i
$918$	−967633.	+	4.23948e6i	−0.0378969	+	0.166037i
$919$	2.42908e7	+	1.16978e7i	0.948751	+	0.456894i	0.843248	−	0.537524i	$-0.180640\pi$
$919$	2.42908e7	+	1.16978e7i	0.948751	+	0.456894i	0.105503	+	0.994419i	$0.466355\pi$
$920$	7.11632e7	+	3.42704e7i	2.77195	+	1.33490i
$921$	−1.32206e7	+	1.65781e7i	−0.513572	+	0.643999i
$922$	−3.09999e6	+	1.35819e7i	−0.120097	+	0.526180i
$923$	913801.	+	4.00362e6i	0.0353059	+	0.154685i
$924$	2.23374e6	−	2.80102e6i	0.0860702	−	0.107929i
$925$	−3.91784e7	+	4.91281e7i	−1.50554	+	1.88789i
$926$	−4.64447e6	−	2.03488e7i	−0.177995	−	0.779849i
$927$	325585.	−	1.42648e6i	0.0124441	−	0.0545213i
$928$	−2.95734e6	+	3.70839e6i	−0.112728	+	0.141356i
$929$	6.95140e6	+	3.34762e6i	0.264261	+	0.127261i	0.561323	−	0.827597i	$-0.310293\pi$
$929$	6.95140e6	+	3.34762e6i	0.264261	+	0.127261i	−0.297062	+	0.954858i	$0.596007\pi$
$930$	−9.41626e6	−	4.53463e6i	−0.357002	−	0.171923i
$931$	−1.11936e7	+	4.90422e7i	−0.423247	+	1.85437i
$932$	1.37826e7	+	1.72828e7i	0.519745	+	0.651740i
$933$	4.03564e7	−	1.94346e7i	1.51778	−	0.730923i
$934$	−1.12788e7	−	1.41432e7i	−0.423055	−	0.530494i
$935$	−4.04207e6	−	1.77095e7i	−0.151208	−	0.662485i
$936$	2.86050e6	+	1.37754e6i	0.106722	+	0.0513944i
$937$	575534.	+	2.52158e6i	0.0214152	+	0.0938261i	0.984506	−	0.175350i	$-0.0561057\pi$
$937$	575534.	+	2.52158e6i	0.0214152	+	0.0938261i	−0.963091	+	0.269176i	$0.913249\pi$
$938$	1.87636e6	−	903607.i	0.0696320	−	0.0335330i
$939$	−1.93474e7			−0.716077
$940$	3.69570e6			0.136420
$941$	3.12432e7	−	1.50459e7i	1.15022	−	0.553918i	0.241121	−	0.970495i	$-0.422485\pi$
$941$	3.12432e7	−	1.50459e7i	1.15022	−	0.553918i	0.909100	+	0.416577i	$0.136770\pi$
$942$	2.78950e6	−	1.22216e7i	0.102423	−	0.448745i
$943$	1.13375e7	−	1.42168e7i	0.415181	−	0.520621i
$944$	1.05113e6	+	1.31808e6i	0.0383907	+	0.0481405i
$945$	7.24053e6			0.263749
$946$	1.44269e6	−	2.17357e7i	0.0524138	−	0.789671i
$947$	5.09432e6			0.184591			0.0922956	−	0.995732i	$-0.470580\pi$
$947$	5.09432e6			0.184591			0.0922956	+	0.995732i	$0.470580\pi$
$948$	−1.05606e7	−	1.32426e7i	−0.381654	−	0.478579i
$949$	1.26618e7	−	1.58773e7i	0.456382	−	0.572285i
$950$	1.17301e7	−	5.13928e7i	0.421689	−	1.84754i
$951$	−5.40901e6	+	2.60484e6i	−0.193939	+	0.0933963i
$952$	1.15684e6			0.0413696
$953$	1.23766e7			0.441438			0.220719	−	0.975337i	$-0.429160\pi$
$953$	1.23766e7			0.441438			0.220719	+	0.975337i	$0.429160\pi$
$954$	378101.	−	182084.i	0.0134505	−	0.00647740i
$955$	680263.	+	2.98043e6i	0.0241362	+	0.105747i
$956$	1.37857e7	+	6.63883e6i	0.487847	+	0.234935i
$957$	1.46292e6	+	6.40948e6i	0.0516346	+	0.226226i
$958$	−6.31160e6	−	7.91449e6i	−0.222190	−	0.278618i
$959$	−5.69530e6	+	2.74271e6i	−0.199972	+	0.0963017i
$960$	1.14899e7	+	1.44079e7i	0.402381	+	0.504570i
$961$	5.03712e6	−	2.20691e7i	0.175944	−	0.770859i
$962$	−2.03034e7	−	9.77760e6i	−0.707345	−	0.340639i
$963$	5.06307e6	+	2.43824e6i	0.175933	+	0.0847250i
$964$	−3.54290e6	+	4.44266e6i	−0.122791	+	0.153975i
$965$	9.08303e6	−	3.97954e7i	0.313988	−	1.37567i
$966$	1.00680e6	+	4.41109e6i	0.0347137	+	0.152091i
$967$	1.99837e7	−	2.50587e7i	0.687241	−	0.861773i	−0.308758	−	0.951141i	$-0.599913\pi$
$967$	1.99837e7	−	2.50587e7i	0.687241	−	0.861773i	0.995999	+	0.0893681i	$0.0284848\pi$
$968$	−1.72449e7	+	2.16245e7i	−0.591525	+	0.741749i
$969$	−3.43355e6	−	1.50434e7i	−0.117472	−	0.514678i
$970$	−2.72010e6	+	1.19175e7i	−0.0928231	+	0.406684i
$971$	1.82026e7	−	2.28253e7i	0.619563	−	0.776907i	−0.368720	−	0.929540i	$-0.620204\pi$
$971$	1.82026e7	−	2.28253e7i	0.619563	−	0.776907i	0.988283	+	0.152634i	$0.0487754\pi$
$972$	−4.49584e6	−	2.16508e6i	−0.152632	−	0.0735036i
$973$	−1.00356e6	−	483289.i	−0.0339829	−	0.0163653i
$974$	−5.55145e6	+	2.43225e7i	−0.187503	+	0.821506i
$975$	3.05929e7	+	3.83622e7i	1.03064	+	1.29239i
$976$	−3.10394e6	+	1.49478e6i	−0.104301	+	0.0502287i
$977$	1.44929e7	+	1.81736e7i	0.485758	+	0.609121i	0.962951	−	0.269677i	$-0.0869171\pi$
$977$	1.44929e7	+	1.81736e7i	0.485758	+	0.609121i	−0.477193	+	0.878799i	$0.658346\pi$
$978$	410523.	+	1.79862e6i	0.0137243	+	0.0601302i
$979$	−2.25098e7	−	1.08401e7i	−0.750610	−	0.361475i
$980$	7.44485e6	+	3.26180e7i	0.247623	+	1.08491i
$981$	3.05294e6	−	1.47022e6i	0.101285	−	0.0487764i
$982$	1.44648e7			0.478667
$983$	825823.			0.0272586			0.0136293	−	0.999907i	$-0.495662\pi$
$983$	825823.			0.0272586			0.0136293	+	0.999907i	$0.495662\pi$
$984$	8.16494e6	−	3.93203e6i	0.268822	−	0.129458i
$985$	−1.44753e6	+	6.34206e6i	−0.0475377	+	0.208276i
$986$	−539361.	+	676337.i	−0.0176680	+	0.0221550i
$987$	323909.	+	406169.i	0.0105835	+	0.0132713i
$988$	−4.16432e7			−1.35722
$989$	−4.47723e7	−	4.08381e7i	−1.45552	−	1.32762i
$990$	−5.00744e6			−0.162378
$991$	3.41028e7	+	4.27635e7i	1.10308	+	1.38321i	0.916148	+	0.400840i	$0.131282\pi$
$991$	3.41028e7	+	4.27635e7i	1.10308	+	1.38321i	0.186927	+	0.982374i	$0.440147\pi$
$992$	9.13236e6	−	1.14516e7i	0.294648	−	0.369477i
$993$	−8.55522e6	+	3.74829e7i	−0.275333	+	1.20631i
$994$	371633.	−	178969.i	0.0119302	−	0.00574529i
$995$	8.30150e7			2.65827
$996$	−1.88408e7			−0.601799
$997$	2.48409e7	−	1.19628e7i	0.791462	−	0.381148i	0.00594057	−	0.999982i	$-0.498109\pi$
$997$	2.48409e7	−	1.19628e7i	0.791462	−	0.381148i	0.785522	+	0.618834i	$0.212395\pi$
$998$	−2.01859e6	−	8.84404e6i	−0.0641538	−	0.281076i
$999$	4.14382e7	+	1.99556e7i	1.31367	+	0.632631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.11.12	yes	108
43.4	even	7	inner	43.6.e.a.4.12	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.12	✓	108	43.4	even	7	inner
43.6.e.a.11.12	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97079 + 2.47129i) q^{2} +(-9.09722 + 11.4076i) q^{3} +(4.89739 - 21.4569i) q^{4} +(83.4030 - 40.1648i) q^{5} -46.1201 q^{6} -19.6284 q^{7} +(153.810 - 74.0710i) q^{8} +(6.69973 + 29.3534i) q^{9} +O(q^{10})\)	\(q+(1.97079 + 2.47129i) q^{2} +(-9.09722 + 11.4076i) q^{3} +(4.89739 - 21.4569i) q^{4} +(83.4030 - 40.1648i) q^{5} -46.1201 q^{6} -19.6284 q^{7} +(153.810 - 74.0710i) q^{8} +(6.69973 + 29.3534i) q^{9} +(263.629 + 126.957i) q^{10} +(126.479 + 554.139i) q^{11} +(200.218 + 251.065i) q^{12} +(556.520 - 268.006i) q^{13} +(-38.6834 - 48.5074i) q^{14} +(-300.554 + 1316.81i) q^{15} +(-148.354 - 71.4435i) q^{16} +(-311.046 - 149.792i) q^{17} +(-59.3372 + 74.4065i) q^{18} +(681.631 - 2986.42i) q^{19} +(-453.354 - 1986.27i) q^{20} +(178.563 - 223.911i) q^{21} +(-1120.18 + 1404.66i) q^{22} +(1112.17 + 4872.72i) q^{23} +(-554.275 + 2428.44i) q^{24} +(3394.45 - 4256.51i) q^{25} +(1759.11 + 847.141i) q^{26} +(-3590.24 - 1728.97i) q^{27} +(-96.1278 + 421.163i) q^{28} +(-494.258 - 619.780i) q^{29} +(-3846.56 + 1852.41i) q^{30} +(1526.28 + 1913.90i) q^{31} +(-1331.43 - 5833.38i) q^{32} +(-7471.97 - 3598.31i) q^{33} +(-242.827 - 1063.89i) q^{34} +(-1637.06 + 788.369i) q^{35} +662.644 q^{36} -11541.9 q^{37} +(8723.68 - 4201.10i) q^{38} +(-2005.49 + 8786.64i) q^{39} +(9853.18 - 12355.5i) q^{40} +(-2268.39 - 2844.47i) q^{41} +905.262 q^{42} +(-9959.33 + 6915.22i) q^{43} +12509.5 q^{44} +(1737.75 + 2179.07i) q^{45} +(-9850.07 + 12351.6i) q^{46} +(-403.647 + 1768.49i) q^{47} +(2164.61 - 1042.42i) q^{48} -16421.7 q^{49} +17208.8 q^{50} +(4538.41 - 2185.58i) q^{51} +(-3025.08 - 13253.7i) q^{52} +(-3972.93 - 1913.26i) q^{53} +(-2802.83 - 12280.0i) q^{54} +(32805.6 + 41136.9i) q^{55} +(-3019.04 + 1453.89i) q^{56} +(27866.8 + 34943.9i) q^{57} +(557.579 - 2442.91i) q^{58} +(-9224.60 - 4442.33i) q^{59} +(26782.8 + 12897.9i) q^{60} +(13045.0 - 16357.9i) q^{61} +(-1721.82 + 7543.79i) q^{62} +(-131.505 - 576.159i) q^{63} +(8506.77 - 10667.2i) q^{64} +(35651.1 - 44705.0i) q^{65} +(-5833.21 - 25557.0i) q^{66} +(-7469.34 + 32725.3i) q^{67} +(-4737.38 + 5940.48i) q^{68} +(-65703.4 - 31641.1i) q^{69} +(-5174.60 - 2491.96i) q^{70} +(-1479.38 + 6481.60i) q^{71} +(3204.72 + 4018.60i) q^{72} +(29621.2 - 14264.8i) q^{73} +(-22746.6 - 28523.4i) q^{74} +(17676.3 + 77444.8i) q^{75} +(-60741.1 - 29251.4i) q^{76} +(-2482.57 - 10876.8i) q^{77} +(-25666.8 + 12360.5i) q^{78} -52745.8 q^{79} -15242.7 q^{80} +(45792.8 - 22052.6i) q^{81} +(2559.00 - 11211.7i) q^{82} +(-36581.0 + 45871.1i) q^{83} +(-3929.95 - 4928.00i) q^{84} -31958.5 q^{85} +(-36717.3 - 10984.0i) q^{86} +11566.6 q^{87} +(60499.3 + 75863.7i) q^{88} +(-27405.9 + 34366.0i) q^{89} +(-1960.38 + 8588.99i) q^{90} +(-10923.6 + 5260.52i) q^{91} +110000. q^{92} -35717.8 q^{93} +(-5165.96 + 2487.80i) q^{94} +(-63098.9 - 276454. i) q^{95} +(78656.9 + 37879.2i) q^{96} +(9296.13 + 40729.0i) q^{97} +(-32363.8 - 40582.9i) q^{98} +(-15418.5 + 7425.16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more