LMFDB - Embedded newform 690.2.m.h.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			301.1
Character	$\chi$	$=$	690.301
Dual form			690.2.m.h.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.50479 + 1.73662i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.50479 + 1.73662i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.853274 + 0.548366i) q^{11} +(0.841254 - 0.540641i) q^{12} +(0.709976 + 0.819356i) q^{13} +(2.20479 - 0.647385i) q^{14} +(0.142315 - 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.38738 + 3.03795i) q^{17} +(0.959493 + 0.281733i) q^{18} +(1.74564 + 3.82241i) q^{19} +(0.142315 + 0.989821i) q^{20} +(1.93309 + 1.24232i) q^{21} +1.01429 q^{22} +(-4.48412 + 1.70080i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.154292 - 1.07313i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.20479 - 0.647385i) q^{28} +(2.28915 - 5.01253i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(-1.47850 + 10.2832i) q^{31} +(0.959493 - 0.281733i) q^{32} +(0.664218 + 0.766548i) q^{33} +(2.80958 - 1.80561i) q^{34} +(-1.93309 + 1.24232i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-9.82859 + 2.88593i) q^{37} +(0.598028 - 4.15938i) q^{38} +(0.709976 - 0.819356i) q^{39} +(0.415415 - 0.909632i) q^{40} +(7.18638 + 2.11011i) q^{41} +(-0.954571 - 2.09022i) q^{42} +(0.0393378 + 0.273600i) q^{43} +(-0.853274 - 0.548366i) q^{44} -1.00000 q^{45} +(4.69180 + 0.993494i) q^{46} +2.17758 q^{47} +(0.841254 + 0.540641i) q^{48} +(0.244751 + 1.70228i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(3.20447 + 0.940917i) q^{51} +(-0.450378 + 0.986189i) q^{52} +(8.32572 - 9.60839i) q^{53} +(0.142315 - 0.989821i) q^{54} +(-0.973203 + 0.285758i) q^{55} +(1.50479 + 1.73662i) q^{56} +(3.53507 - 2.27185i) q^{57} +(-4.63573 + 2.97920i) q^{58} +(2.87562 + 3.31865i) q^{59} +(0.959493 - 0.281733i) q^{60} +(-0.477322 + 3.31985i) q^{61} +(6.80330 - 7.85143i) q^{62} +(0.954571 - 2.09022i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.450378 + 0.986189i) q^{65} +(-0.144348 - 1.00396i) q^{66} +(-1.08341 - 0.696264i) q^{67} -3.33975 q^{68} +(2.32164 + 4.19642i) q^{69} +2.29787 q^{70} +(12.1616 + 7.81579i) q^{71} +(0.142315 + 0.989821i) q^{72} +(3.01367 + 6.59901i) q^{73} +(9.82859 + 2.88593i) q^{74} +(0.415415 - 0.909632i) q^{75} +(-2.75182 + 3.17577i) q^{76} +(0.331694 - 2.30698i) q^{77} +(-1.04025 + 0.305444i) q^{78} +(-2.02018 - 2.33141i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-4.90475 - 5.66039i) q^{82} +(-14.2484 + 4.18372i) q^{83} +(-0.327021 + 2.27448i) q^{84} +(-2.18707 + 2.52402i) q^{85} +(0.114826 - 0.251435i) q^{86} +(-5.28729 - 1.55249i) q^{87} +(0.421351 + 0.922629i) q^{88} +(-0.698556 - 4.85857i) q^{89} +(0.841254 + 0.540641i) q^{90} -2.49127 q^{91} +(-3.40987 - 3.37236i) q^{92} +10.3889 q^{93} +(-1.83190 - 1.17729i) q^{94} +(0.598028 + 4.15938i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(14.1518 + 4.15536i) q^{97} +(0.714424 - 1.56437i) q^{98} +(0.664218 - 0.766548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−1.50479	+	1.73662i	−0.568756	+	0.656379i	−0.965149	−	0.261702i	$-0.915716\pi$
$7$	−1.50479	+	1.73662i	−0.568756	+	0.656379i	0.396393	+	0.918081i	$0.370262\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−0.654861	−	0.755750i	−0.207085	−	0.238989i
$11$	−0.853274	+	0.548366i	−0.257272	+	0.165338i	−0.662919	−	0.748691i	$-0.730683\pi$
$11$	−0.853274	+	0.548366i	−0.257272	+	0.165338i	0.405647	+	0.914030i	$0.367046\pi$
$12$	0.841254	−	0.540641i	0.242849	−	0.156070i
$13$	0.709976	+	0.819356i	0.196912	+	0.227248i	0.845615	−	0.533793i	$-0.179234\pi$
$13$	0.709976	+	0.819356i	0.196912	+	0.227248i	−0.648703	+	0.761041i	$0.724688\pi$
$14$	2.20479	−	0.647385i	0.589255	−	0.173021i
$15$	0.142315	−	0.989821i	0.0367455	−	0.255571i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.38738	+	3.03795i	−0.336490	+	0.736810i	−0.999935	−	0.0114150i	$-0.996366\pi$
$17$	−1.38738	+	3.03795i	−0.336490	+	0.736810i	0.663445	+	0.748225i	$0.269094\pi$
$18$	0.959493	+	0.281733i	0.226155	+	0.0664050i
$19$	1.74564	+	3.82241i	0.400476	+	0.876921i	0.997222	+	0.0744904i	$0.0237330\pi$
$19$	1.74564	+	3.82241i	0.400476	+	0.876921i	−0.596745	+	0.802431i	$0.703540\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	1.93309	+	1.24232i	0.421835	+	0.271097i
$22$	1.01429			0.216247
$23$	−4.48412	+	1.70080i	−0.935003	+	0.354641i
$23$	−4.48412	+	1.70080i	−0.935003	+	0.354641i
$24$	−1.00000			−0.204124
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.154292	−	1.07313i	−0.0302592	−	0.210458i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−2.20479	−	0.647385i	−0.416667	−	0.122344i
$29$	2.28915	−	5.01253i	0.425084	−	0.930804i	−0.569015	−	0.822327i	$-0.692675\pi$
$29$	2.28915	−	5.01253i	0.425084	−	0.930804i	0.994099	−	0.108477i	$-0.0345973\pi$
$30$	−0.654861	+	0.755750i	−0.119561	+	0.137980i
$31$	−1.47850	+	10.2832i	−0.265546	+	1.84691i	0.223559	+	0.974690i	$0.428232\pi$
$31$	−1.47850	+	10.2832i	−0.265546	+	1.84691i	−0.489106	+	0.872225i	$0.662677\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	0.664218	+	0.766548i	0.115625	+	0.133439i
$34$	2.80958	−	1.80561i	0.481839	−	0.309659i
$35$	−1.93309	+	1.24232i	−0.326752	+	0.209991i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−9.82859	+	2.88593i	−1.61581	+	0.474445i	−0.959888	−	0.280384i	$-0.909538\pi$
$37$	−9.82859	+	2.88593i	−1.61581	+	0.474445i	−0.655922	+	0.754829i	$0.727720\pi$
$38$	0.598028	−	4.15938i	0.0970130	−	0.674740i
$39$	0.709976	−	0.819356i	0.113687	−	0.131202i
$40$	0.415415	−	0.909632i	0.0656829	−	0.143825i
$41$	7.18638	+	2.11011i	1.12232	+	0.329544i	0.789686	−	0.613511i	$-0.210243\pi$
$41$	7.18638	+	2.11011i	1.12232	+	0.329544i	0.332637	+	0.943055i	$0.392061\pi$
$42$	−0.954571	−	2.09022i	−0.147293	−	0.322528i
$43$	0.0393378	+	0.273600i	0.00599896	+	0.0417237i	0.992601	−	0.121421i	$-0.0387452\pi$
$43$	0.0393378	+	0.273600i	0.00599896	+	0.0417237i	−0.986602	+	0.163145i	$0.947836\pi$
$44$	−0.853274	−	0.548366i	−0.128636	−	0.0826692i
$45$	−1.00000			−0.149071
$46$	4.69180	+	0.993494i	0.691768	+	0.146483i
$47$	2.17758			0.317633			0.158816	−	0.987308i	$-0.449232\pi$
$47$	2.17758			0.317633			0.158816	+	0.987308i	$0.449232\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	0.244751	+	1.70228i	0.0349644	+	0.243183i
$50$	−0.415415	−	0.909632i	−0.0587486	−	0.128641i
$51$	3.20447	+	0.940917i	0.448715	+	0.131755i
$52$	−0.450378	+	0.986189i	−0.0624561	+	0.136760i
$53$	8.32572	−	9.60839i	1.14363	−	1.31981i	0.203464	−	0.979082i	$-0.434780\pi$
$53$	8.32572	−	9.60839i	1.14363	−	1.31981i	0.940161	−	0.340731i	$-0.110675\pi$
$54$	0.142315	−	0.989821i	0.0193666	−	0.134698i
$55$	−0.973203	+	0.285758i	−0.131227	+	0.0385316i
$56$	1.50479	+	1.73662i	0.201086	+	0.232065i
$57$	3.53507	−	2.27185i	0.468232	−	0.300914i
$58$	−4.63573	+	2.97920i	−0.608702	+	0.391189i
$59$	2.87562	+	3.31865i	0.374374	+	0.432051i	0.911404	−	0.411512i	$-0.134999\pi$
$59$	2.87562	+	3.31865i	0.374374	+	0.432051i	−0.537030	+	0.843563i	$0.680454\pi$
$60$	0.959493	−	0.281733i	0.123870	−	0.0363715i
$61$	−0.477322	+	3.31985i	−0.0611148	+	0.425063i	0.936178	+	0.351527i	$0.114337\pi$
$61$	−0.477322	+	3.31985i	−0.0611148	+	0.425063i	−0.997293	+	0.0735358i	$0.976572\pi$
$62$	6.80330	−	7.85143i	0.864020	−	0.997133i
$63$	0.954571	−	2.09022i	0.120265	−	0.263343i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.450378	+	0.986189i	0.0558625	+	0.122322i
$66$	−0.144348	−	1.00396i	−0.0177680	−	0.123579i
$67$	−1.08341	−	0.696264i	−0.132359	−	0.0850622i	0.472786	−	0.881177i	$-0.343248\pi$
$67$	−1.08341	−	0.696264i	−0.132359	−	0.0850622i	−0.605145	+	0.796115i	$0.706885\pi$
$68$	−3.33975			−0.405005
$69$	2.32164	+	4.19642i	0.279493	+	0.505190i
$70$	2.29787			0.274648
$71$	12.1616	+	7.81579i	1.44332	+	0.927563i	0.999506	+	0.0314429i	$0.0100102\pi$
$71$	12.1616	+	7.81579i	1.44332	+	0.927563i	0.443811	+	0.896120i	$0.353626\pi$
$72$	0.142315	+	0.989821i	0.0167720	+	0.116652i
$73$	3.01367	+	6.59901i	0.352723	+	0.772355i	0.999949	+	0.0100577i	$0.00320151\pi$
$73$	3.01367	+	6.59901i	0.352723	+	0.772355i	−0.647227	+	0.762298i	$0.724071\pi$
$74$	9.82859	+	2.88593i	1.14255	+	0.335483i
$75$	0.415415	−	0.909632i	0.0479680	−	0.105035i
$76$	−2.75182	+	3.17577i	−0.315656	+	0.364286i
$77$	0.331694	−	2.30698i	0.0378000	−	0.262905i
$78$	−1.04025	+	0.305444i	−0.117785	+	0.0345847i
$79$	−2.02018	−	2.33141i	−0.227288	−	0.262304i	0.630639	−	0.776077i	$-0.282793\pi$
$79$	−2.02018	−	2.33141i	−0.227288	−	0.262304i	−0.857926	+	0.513773i	$0.828248\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	−4.90475	−	5.66039i	−0.541639	−	0.625085i
$83$	−14.2484	+	4.18372i	−1.56397	+	0.459222i	−0.945238	−	0.326381i	$-0.894171\pi$
$83$	−14.2484	+	4.18372i	−1.56397	+	0.459222i	−0.618730	+	0.785604i	$0.712352\pi$
$84$	−0.327021	+	2.27448i	−0.0356809	+	0.248166i
$85$	−2.18707	+	2.52402i	−0.237221	+	0.273768i
$86$	0.114826	−	0.251435i	0.0123821	−	0.0271129i
$87$	−5.28729	−	1.55249i	−0.566857	−	0.166444i
$88$	0.421351	+	0.922629i	0.0449161	+	0.0983526i
$89$	−0.698556	−	4.85857i	−0.0740468	−	0.515007i	−0.992763	−	0.120089i	$-0.961682\pi$
$89$	−0.698556	−	4.85857i	−0.0740468	−	0.515007i	0.918716	−	0.394918i	$-0.129227\pi$
$90$	0.841254	+	0.540641i	0.0886759	+	0.0569885i
$91$	−2.49127			−0.261156
$92$	−3.40987	−	3.37236i	−0.355503	−	0.351593i
$93$	10.3889			1.07728
$94$	−1.83190	−	1.17729i	−0.188946	−	0.121428i
$95$	0.598028	+	4.15938i	0.0613564	+	0.426743i
$96$	−0.415415	−	0.909632i	−0.0423981	−	0.0928389i
$97$	14.1518	+	4.15536i	1.43690	+	0.421912i	0.905188	−	0.425012i	$-0.139730\pi$
$97$	14.1518	+	4.15536i	1.43690	+	0.421912i	0.531714	+	0.846924i	$0.321548\pi$
$98$	0.714424	−	1.56437i	0.0721677	−	0.158025i
$99$	0.664218	−	0.766548i	0.0667564	−	0.0770410i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	1.31470	−	0.386029i	0.130817	−	0.0384114i	−0.215669	−	0.976467i	$-0.569193\pi$
$101$	1.31470	−	0.386029i	0.130817	−	0.0384114i	0.346486	+	0.938055i	$0.387375\pi$
$102$	−2.18707	−	2.52402i	−0.216553	−	0.249915i
$103$	−2.86055	+	1.83836i	−0.281858	+	0.181139i	−0.673930	−	0.738795i	$-0.735395\pi$
$103$	−2.86055	+	1.83836i	−0.281858	+	0.181139i	0.392071	+	0.919935i	$0.371759\pi$
$104$	0.912056	−	0.586143i	0.0894344	−	0.0574760i
$105$	1.50479	+	1.73662i	0.146852	+	0.169476i
$106$	−12.1987	+	3.58187i	−1.18484	+	0.347902i
$107$	0.903619	−	6.28481i	0.0873562	−	0.607575i	−0.898373	−	0.439234i	$-0.855250\pi$
$107$	0.903619	−	6.28481i	0.0873562	−	0.607575i	0.985729	−	0.168341i	$-0.0538411\pi$
$108$	−0.654861	+	0.755750i	−0.0630140	+	0.0727220i
$109$	6.18177	−	13.5362i	0.592106	−	1.29653i	−0.342055	−	0.939680i	$-0.611123\pi$
$109$	6.18177	−	13.5362i	0.592106	−	1.29653i	0.934161	−	0.356851i	$-0.116150\pi$
$110$	0.973203	+	0.285758i	0.0927912	+	0.0272460i
$111$	4.25531	+	9.31783i	0.403896	+	0.884410i
$112$	−0.327021	−	2.27448i	−0.0309006	−	0.214918i
$113$	−16.2862	−	10.4665i	−1.53208	−	0.984605i	−0.989489	−	0.144606i	$-0.953809\pi$
$113$	−16.2862	−	10.4665i	−1.53208	−	0.984605i	−0.542587	−	0.840000i	$-0.682555\pi$
$114$	−4.20215			−0.393567
$115$	−4.78165	+	0.368582i	−0.445891	+	0.0343705i
$116$	5.51051			0.511638
$117$	−0.912056	−	0.586143i	−0.0843196	−	0.0541889i
$118$	−0.624933	−	4.34650i	−0.0575297	−	0.400128i
$119$	−3.18803	−	6.98081i	−0.292246	−	0.639930i
$120$	−0.959493	−	0.281733i	−0.0875893	−	0.0257185i
$121$	−4.14219	+	9.07014i	−0.376563	+	0.824558i
$122$	2.19639	−	2.53477i	0.198852	−	0.229487i
$123$	1.06590	−	7.41353i	0.0961094	−	0.668456i
$124$	−9.96811	+	2.92690i	−0.895162	+	0.262843i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	−1.93309	+	1.24232i	−0.172214	+	0.110675i
$127$	−0.230067	+	0.147855i	−0.0204151	+	0.0131200i	−0.550809	−	0.834632i	$-0.685681\pi$
$127$	−0.230067	+	0.147855i	−0.0204151	+	0.0131200i	0.530393	+	0.847752i	$0.322044\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	0.265217	−	0.0778748i	0.0233511	−	0.00685649i
$130$	0.154292	−	1.07313i	0.0135323	−	0.0941195i
$131$	−1.49341	+	1.72348i	−0.130480	+	0.150582i	−0.817230	−	0.576312i	$-0.804491\pi$
$131$	−1.49341	+	1.72348i	−0.130480	+	0.150582i	0.686750	+	0.726894i	$0.259037\pi$
$132$	−0.421351	+	0.922629i	−0.0366739	+	0.0803046i
$133$	−9.26487	−	2.72041i	−0.803366	−	0.235890i
$134$	0.534992	+	1.17147i	0.0462163	+	0.101200i
$135$	0.142315	+	0.989821i	0.0122485	+	0.0851903i
$136$	2.80958	+	1.80561i	0.240919	+	0.154830i
$137$	−13.4057			−1.14532			−0.572662	−	0.819792i	$-0.694089\pi$
$137$	−13.4057			−1.14532			−0.572662	+	0.819792i	$0.694089\pi$
$138$	0.315669	−	4.78543i	0.0268715	−	0.407363i
$139$	−17.9224			−1.52016			−0.760078	−	0.649832i	$-0.774839\pi$
$139$	−17.9224			−1.52016			−0.760078	+	0.649832i	$0.774839\pi$
$140$	−1.93309	−	1.24232i	−0.163376	−	0.104995i
$141$	−0.309902	−	2.15541i	−0.0260984	−	0.181519i
$142$	−6.00546	−	13.1501i	−0.503967	−	1.10353i
$143$	−1.05511	−	0.309808i	−0.0882327	−	0.0259075i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	3.60861	−	4.16456i	0.299679	−	0.345848i
$146$	1.03244	−	7.18075i	0.0854450	−	0.594283i
$147$	1.65012	−	0.484519i	0.136100	−	0.0399625i
$148$	−6.70808	−	7.74154i	−0.551401	−	0.636350i
$149$	−0.0526004	+	0.0338042i	−0.00430919	+	0.00276935i	−0.542794	−	0.839866i	$-0.682633\pi$
$149$	−0.0526004	+	0.0338042i	−0.00430919	+	0.00276935i	0.538484	+	0.842635i	$0.318997\pi$
$150$	−0.841254	+	0.540641i	−0.0686881	+	0.0441431i
$151$	−0.210554	−	0.242992i	−0.0171346	−	0.0197744i	0.747118	−	0.664692i	$-0.231437\pi$
$151$	−0.210554	−	0.242992i	−0.0171346	−	0.0197744i	−0.764252	+	0.644917i	$0.776892\pi$
$152$	4.03193	−	1.18388i	0.327033	−	0.0960256i
$153$	0.475296	−	3.30576i	0.0384254	−	0.267255i
$154$	−1.52629	+	1.76143i	−0.122992	+	0.141940i
$155$	−4.31572	+	9.45010i	−0.346647	+	0.759051i
$156$	1.04025	+	0.305444i	0.0832864	+	0.0244551i
$157$	−0.720738	−	1.57820i	−0.0575212	−	0.125954i	0.878689	−	0.477395i	$-0.158419\pi$
$157$	−0.720738	−	1.57820i	−0.0575212	−	0.125954i	−0.936210	+	0.351441i	$0.885692\pi$
$158$	0.439027	+	3.05350i	0.0349271	+	0.242923i
$159$	−10.6955	−	6.87356i	−0.848205	−	0.545108i
$160$	1.00000			0.0790569
$161$	3.79400	−	10.3465i	0.299009	−	0.815420i
$162$	−1.00000			−0.0785674
$163$	11.4080	+	7.33150i	0.893547	+	0.574248i	0.904870	−	0.425688i	$-0.139968\pi$
$163$	11.4080	+	7.33150i	0.893547	+	0.574248i	−0.0113231	+	0.999936i	$0.503604\pi$
$164$	1.06590	+	7.41353i	0.0832332	+	0.578900i
$165$	0.421351	+	0.922629i	0.0328021	+	0.0718266i
$166$	14.2484	+	4.18372i	1.10589	+	0.324719i
$167$	0.425939	−	0.932675i	0.0329601	−	0.0721726i	−0.892436	−	0.451174i	$-0.851005\pi$
$167$	0.425939	−	0.932675i	0.0329601	−	0.0721726i	0.925396	+	0.379002i	$0.123733\pi$
$168$	1.50479	−	1.73662i	0.116097	−	0.133983i
$169$	1.68281	−	11.7042i	0.129447	−	0.900326i
$170$	3.20447	−	0.940917i	0.245772	−	0.0721651i
$171$	−2.75182	−	3.17577i	−0.210437	−	0.242857i
$172$	−0.232534	+	0.149441i	−0.0177306	+	0.0113947i
$173$	−0.225469	+	0.144900i	−0.0171421	+	0.0110165i	−0.549184	−	0.835702i	$-0.685061\pi$
$173$	−0.225469	+	0.144900i	−0.0171421	+	0.0110165i	0.532042	+	0.846718i	$0.321425\pi$
$174$	3.60861	+	4.16456i	0.273568	+	0.315715i
$175$	−2.20479	+	0.647385i	−0.166667	+	0.0489377i
$176$	0.144348	−	1.00396i	0.0108807	−	0.0756767i
$177$	2.87562	−	3.31865i	0.216145	−	0.249445i
$178$	−2.03908	+	4.46495i	−0.152835	+	0.334662i
$179$	−13.2939	−	3.90343i	−0.993630	−	0.291756i	−0.255790	−	0.966732i	$-0.582336\pi$
$179$	−13.2939	−	3.90343i	−0.993630	−	0.291756i	−0.737840	+	0.674976i	$0.764154\pi$
$180$	−0.415415	−	0.909632i	−0.0309632	−	0.0678000i
$181$	−0.901850	−	6.27251i	−0.0670340	−	0.466232i	−0.995496	−	0.0948042i	$-0.969777\pi$
$181$	−0.901850	−	6.27251i	−0.0670340	−	0.466232i	0.928462	−	0.371428i	$-0.121132\pi$
$182$	2.09579	+	1.34688i	0.155350	+	0.0998375i
$183$	3.35398			0.247934
$184$	1.04533	+	4.68052i	0.0770627	+	0.345053i
$185$	−10.2435			−0.753119
$186$	−8.73973	−	5.61668i	−0.640828	−	0.411835i
$187$	−0.482088	−	3.35299i	−0.0352537	−	0.245195i
$188$	0.904599	+	1.98080i	0.0659747	+	0.144464i
$189$	−2.20479	−	0.647385i	−0.160375	−	0.0470904i
$190$	1.74564	−	3.82241i	0.126642	−	0.277307i
$191$	−6.38638	+	7.37028i	−0.462102	+	0.533294i	−0.938198	−	0.346099i	$-0.887506\pi$
$191$	−6.38638	+	7.37028i	−0.462102	+	0.533294i	0.476096	+	0.879393i	$0.342052\pi$
$192$	−0.142315	+	0.989821i	−0.0102707	+	0.0714342i
$193$	0.475253	−	0.139547i	0.0342094	−	0.0100448i	−0.264583	−	0.964363i	$-0.585234\pi$
$193$	0.475253	−	0.139547i	0.0342094	−	0.0100448i	0.298793	+	0.954318i	$0.403416\pi$
$194$	−9.65873	−	11.1468i	−0.693457	−	0.800292i
$195$	0.912056	−	0.586143i	0.0653137	−	0.0419746i
$196$	−1.44677	+	0.929785i	−0.103341	+	0.0664132i
$197$	−8.60988	−	9.93633i	−0.613429	−	0.707934i	0.361017	−	0.932559i	$-0.382430\pi$
$197$	−8.60988	−	9.93633i	−0.613429	−	0.707934i	−0.974445	+	0.224625i	$0.927884\pi$
$198$	−0.973203	+	0.285758i	−0.0691625	+	0.0203079i
$199$	2.66497	−	18.5352i	0.188914	−	1.31393i	−0.645911	−	0.763413i	$-0.723522\pi$
$199$	2.66497	−	18.5352i	0.188914	−	1.31393i	0.834825	−	0.550515i	$-0.185569\pi$
$200$	0.654861	−	0.755750i	0.0463056	−	0.0534396i
$201$	−0.534992	+	1.17147i	−0.0377354	+	0.0826291i
$202$	−1.31470	−	0.386029i	−0.0925017	−	0.0271609i
$203$	5.26017	+	11.5182i	0.369191	+	0.808416i
$204$	0.475296	+	3.30576i	0.0332774	+	0.231449i
$205$	6.30079	+	4.04927i	0.440066	+	0.282814i
$206$	3.40034			0.236913
$207$	3.82331	−	2.89522i	0.265738	−	0.201232i
$208$	−1.08416			−0.0751732
$209$	−3.58558	−	2.30432i	−0.248020	−	0.159393i
$210$	−0.327021	−	2.27448i	−0.0225666	−	0.156954i
$211$	7.29326	+	15.9700i	0.502089	+	1.09942i	0.975785	+	0.218732i	$0.0701921\pi$
$211$	7.29326	+	15.9700i	0.502089	+	1.09942i	−0.473696	+	0.880688i	$0.657081\pi$
$212$	12.1987	+	3.58187i	0.837812	+	0.246004i
$213$	6.00546	−	13.1501i	0.411487	−	0.901031i
$214$	−4.15800	+	4.79858i	−0.284235	+	0.328024i
$215$	−0.0393378	+	0.273600i	−0.00268282	+	0.0186594i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−15.6331	−	18.0416i	−1.06125	−	1.22474i
$218$	−12.5186	+	8.04525i	−0.847870	+	0.544893i
$219$	6.10295	−	3.92213i	0.412399	−	0.265033i
$220$	−0.664218	−	0.766548i	−0.0447815	−	0.0516807i
$221$	−3.47417	+	1.02011i	−0.233698	+	0.0686199i
$222$	1.45781	−	10.1393i	0.0978415	−	0.680502i
$223$	7.32456	−	8.45299i	0.490489	−	0.566054i	−0.455507	−	0.890232i	$-0.650542\pi$
$223$	7.32456	−	8.45299i	0.490489	−	0.566054i	0.945996	+	0.324178i	$0.105088\pi$
$224$	−0.954571	+	2.09022i	−0.0637799	+	0.139659i
$225$	−0.959493	−	0.281733i	−0.0639662	−	0.0187822i
$226$	8.04220	+	17.6100i	0.534959	+	1.17140i
$227$	−0.123798	−	0.861032i	−0.00821675	−	0.0571487i	0.985301	−	0.170830i	$-0.0546449\pi$
$227$	−0.123798	−	0.861032i	−0.00821675	−	0.0571487i	−0.993517	+	0.113681i	$0.963736\pi$
$228$	3.53507	+	2.27185i	0.234116	+	0.150457i
$229$	7.57233			0.500394			0.250197	−	0.968195i	$-0.419505\pi$
$229$	7.57233			0.500394			0.250197	+	0.968195i	$0.419505\pi$
$230$	4.22185	+	2.27508i	0.278380	+	0.150015i
$231$	−2.33071			−0.153349
$232$	−4.63573	−	2.97920i	−0.304351	−	0.195594i
$233$	1.20469	+	8.37878i	0.0789216	+	0.548912i	0.990471	+	0.137721i	$0.0439779\pi$
$233$	1.20469	+	8.37878i	0.0789216	+	0.548912i	−0.911549	+	0.411191i	$0.865113\pi$
$234$	0.450378	+	0.986189i	0.0294421	+	0.0644692i
$235$	2.08937	+	0.613495i	0.136296	+	0.0400200i
$236$	−1.82417	+	3.99438i	−0.118743	+	0.260012i
$237$	−2.02018	+	2.33141i	−0.131225	+	0.151441i
$238$	−1.09217	+	7.59621i	−0.0707949	+	0.492389i
$239$	−10.0136	+	2.94025i	−0.647724	+	0.190189i	−0.589061	−	0.808089i	$-0.700502\pi$
$239$	−10.0136	+	2.94025i	−0.647724	+	0.190189i	−0.0586636	+	0.998278i	$0.518684\pi$
$240$	0.654861	+	0.755750i	0.0422711	+	0.0487834i
$241$	−11.5506	+	7.42313i	−0.744041	+	0.478166i	−0.856924	−	0.515442i	$-0.827628\pi$
$241$	−11.5506	+	7.42313i	−0.744041	+	0.478166i	0.112883	+	0.993608i	$0.463991\pi$
$242$	8.38832	−	5.39085i	0.539222	−	0.346537i
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$	−3.21812	+	0.944927i	−0.206019	+	0.0604927i
$245$	−0.244751	+	1.70228i	−0.0156366	+	0.108755i
$246$	−4.90475	+	5.66039i	−0.312716	+	0.360893i
$247$	−1.89255	+	4.14412i	−0.120420	+	0.263684i
$248$	9.96811	+	2.92690i	0.632975	+	0.185858i
$249$	6.16889	+	13.5080i	0.390938	+	0.856034i
$250$	−0.142315	−	0.989821i	−0.00900078	−	0.0626018i
$251$	13.5891	+	8.73318i	0.857736	+	0.551234i	0.893979	−	0.448109i	$-0.147902\pi$
$251$	13.5891	+	8.73318i	0.857736	+	0.551234i	−0.0362424	+	0.999343i	$0.511539\pi$
$252$	2.29787			0.144752
$253$	2.89352	−	3.91018i	0.181914	−	0.245831i
$254$	0.273481			0.0171597
$255$	2.80958	+	1.80561i	0.175943	+	0.113071i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	7.79170	+	17.0614i	0.486033	+	1.06426i	0.980760	+	0.195216i	$0.0625407\pi$
$257$	7.79170	+	17.0614i	0.486033	+	1.06426i	−0.494727	+	0.869048i	$0.664732\pi$
$258$	−0.265217	−	0.0778748i	−0.0165117	−	0.00484827i
$259$	9.77816	−	21.4112i	0.607586	−	1.33043i
$260$	−0.709976	+	0.819356i	−0.0440308	+	0.0508143i
$261$	−0.784227	+	5.45442i	−0.0485424	+	0.337620i
$262$	2.18812	−	0.642490i	0.135183	−	0.0396932i
$263$	−10.6158	−	12.2513i	−0.654598	−	0.755447i	0.327286	−	0.944925i	$-0.393866\pi$
$263$	−10.6158	−	12.2513i	−0.654598	−	0.755447i	−0.981885	+	0.189478i	$0.939320\pi$
$264$	0.853274	−	0.548366i	0.0525154	−	0.0337496i
$265$	10.6955	−	6.87356i	0.657017	−	0.422239i
$266$	6.32334	+	7.29752i	0.387709	+	0.447440i
$267$	−4.70970	+	1.38289i	−0.288229	+	0.0846316i
$268$	0.183280	−	1.27474i	0.0111956	−	0.0778672i
$269$	4.13391	−	4.77078i	0.252049	−	0.290880i	−0.615599	−	0.788060i	$-0.711086\pi$
$269$	4.13391	−	4.77078i	0.252049	−	0.290880i	0.867647	+	0.497180i	$0.165631\pi$
$270$	0.415415	−	0.909632i	0.0252814	−	0.0553584i
$271$	−23.2325	−	6.82168i	−1.41127	−	0.414387i	−0.514734	−	0.857350i	$-0.672109\pi$
$271$	−23.2325	−	6.82168i	−1.41127	−	0.414387i	−0.896540	+	0.442963i	$0.853927\pi$
$272$	−1.38738	−	3.03795i	−0.0841225	−	0.184203i
$273$	0.354544	+	2.46591i	0.0214580	+	0.149244i
$274$	11.2776	+	7.24765i	0.681303	+	0.437847i
$275$	−1.01429			−0.0611639
$276$	−2.85276	+	3.85510i	−0.171716	+	0.232050i
$277$	20.8125			1.25050			0.625250	−	0.780424i	$-0.284997\pi$
$277$	20.8125			1.25050			0.625250	+	0.780424i	$0.284997\pi$
$278$	15.0773	+	9.68957i	0.904274	+	0.581142i
$279$	−1.47850	−	10.2832i	−0.0885154	−	0.615638i
$280$	0.954571	+	2.09022i	0.0570465	+	0.124914i
$281$	11.2821	+	3.31273i	0.673035	+	0.197621i	0.600354	−	0.799734i	$-0.295026\pi$
$281$	11.2821	+	3.31273i	0.673035	+	0.197621i	0.0726811	+	0.997355i	$0.476844\pi$
$282$	−0.904599	+	1.98080i	−0.0538681	+	0.117955i
$283$	−4.02180	+	4.64141i	−0.239071	+	0.275903i	−0.862588	−	0.505907i	$-0.831158\pi$
$283$	−4.02180	+	4.64141i	−0.239071	+	0.275903i	0.623517	+	0.781810i	$0.285703\pi$
$284$	−2.05738	+	14.3094i	−0.122083	+	0.849105i
$285$	4.03193	−	1.18388i	0.238831	−	0.0701272i
$286$	0.720120	+	0.831063i	0.0425816	+	0.0491418i
$287$	−14.4784	+	9.30471i	−0.854634	+	0.549240i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	3.82835	+	4.41815i	0.225197	+	0.259891i
$290$	−5.28729	+	1.55249i	−0.310480	+	0.0911653i
$291$	2.09904	−	14.5992i	0.123048	−	0.855818i
$292$	−4.75075	+	5.48265i	−0.278016	+	0.320848i
$293$	12.1733	−	26.6558i	0.711170	−	1.55725i	−0.114709	−	0.993399i	$-0.536594\pi$
$293$	12.1733	−	26.6558i	0.711170	−	1.55725i	0.825879	−	0.563847i	$-0.190679\pi$
$294$	−1.65012	−	0.484519i	−0.0962370	−	0.0282577i
$295$	1.82417	+	3.99438i	0.106207	+	0.232562i
$296$	1.45781	+	10.1393i	0.0847332	+	0.589332i
$297$	−0.853274	−	0.548366i	−0.0495120	−	0.0318194i
$298$	0.0625262			0.00362204
$299$	−4.57717	−	2.46656i	−0.264705	−	0.142645i
$300$	1.00000			0.0577350
$301$	−0.534334	−	0.343395i	−0.0307985	−	0.0197930i
$302$	0.0457578	+	0.318252i	0.00263306	+	0.0183134i
$303$	−0.569201	−	1.24638i	−0.0326997	−	0.0716024i
$304$	−4.03193	−	1.18388i	−0.231247	−	0.0679003i
$305$	−1.39330	+	3.05089i	−0.0797799	+	0.174694i
$306$	−2.18707	+	2.52402i	−0.125027	+	0.144288i
$307$	−0.469784	+	3.26742i	−0.0268120	+	0.186482i	−0.998826	−	0.0484413i	$-0.984575\pi$
$307$	−0.469784	+	3.26742i	−0.0268120	+	0.186482i	0.972014	+	0.234923i	$0.0754837\pi$
$308$	2.23630	−	0.656635i	0.127425	−	0.0374153i
$309$	2.22675	+	2.56981i	0.126675	+	0.146191i
$310$	8.73973	−	5.61668i	0.496383	−	0.319006i
$311$	22.5074	−	14.4646i	1.27628	−	0.820213i	0.285852	−	0.958274i	$-0.407723\pi$
$311$	22.5074	−	14.4646i	1.27628	−	0.820213i	0.990424	+	0.138061i	$0.0440870\pi$
$312$	−0.709976	−	0.819356i	−0.0401945	−	0.0463869i
$313$	20.7610	−	6.09599i	1.17348	−	0.344566i	0.363825	−	0.931467i	$-0.381471\pi$
$313$	20.7610	−	6.09599i	1.17348	−	0.344566i	0.809658	+	0.586901i	$0.199652\pi$
$314$	−0.246914	+	1.71732i	−0.0139342	+	0.0969142i
$315$	1.50479	−	1.73662i	0.0847851	−	0.0978472i
$316$	1.28151	−	2.80612i	0.0720907	−	0.157857i
$317$	20.7350	+	6.08835i	1.16459	+	0.341956i	0.806216	−	0.591621i	$-0.201512\pi$
$317$	20.7350	+	6.08835i	1.16459	+	0.341956i	0.358378	+	0.933577i	$0.383330\pi$
$318$	5.28147	+	11.5648i	0.296170	+	0.648522i
$319$	0.795432	+	5.53235i	0.0445356	+	0.309752i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	−6.34944			−0.354391
$322$	−8.78547	+	6.65286i	−0.489595	+	0.370749i
$323$	−14.0341			−0.780881
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	0.154292	+	1.07313i	0.00855861	+	0.0595264i
$326$	−5.63335	−	12.3353i	−0.312002	−	0.683189i
$327$	−14.2782	−	4.19245i	−0.789584	−	0.231843i
$328$	3.11136	−	6.81293i	0.171796	−	0.376181i
$329$	−3.27679	+	3.78162i	−0.180655	+	0.208487i
$330$	0.144348	−	1.00396i	0.00794611	−	0.0552664i
$331$	−6.21218	+	1.82406i	−0.341452	+	0.100259i	−0.447963	−	0.894052i	$-0.647850\pi$
$331$	−6.21218	+	1.82406i	−0.341452	+	0.100259i	0.106511	+	0.994312i	$0.466032\pi$
$332$	−9.72465	−	11.2228i	−0.533710	−	0.615934i
$333$	8.61740	−	5.53807i	0.472231	−	0.303484i
$334$	−0.862565	+	0.554337i	−0.0471974	+	0.0303320i
$335$	−0.843362	−	0.973292i	−0.0460778	−	0.0531766i
$336$	−2.20479	+	0.647385i	−0.120281	+	0.0353178i
$337$	−0.960232	+	6.67856i	−0.0523072	+	0.363805i	0.946810	+	0.321793i	$0.104286\pi$
$337$	−0.960232	+	6.67856i	−0.0523072	+	0.363805i	−0.999117	+	0.0420112i	$0.986623\pi$
$338$	−7.74346	+	8.93643i	−0.421189	+	0.486078i
$339$	−8.04220	+	17.6100i	−0.436792	+	0.956442i
$340$	−3.20447	−	0.940917i	−0.173787	−	0.0510284i
$341$	−4.37738	−	9.58513i	−0.237049	−	0.519064i
$342$	0.598028	+	4.15938i	0.0323377	+	0.224913i
$343$	−16.8562	−	10.8328i	−0.910147	−	0.584916i
$344$	0.276414			0.0149032
$345$	1.04533	+	4.68052i	0.0562787	+	0.251991i
$346$	0.268015			0.0144086
$347$	16.9772	+	10.9106i	0.911386	+	0.585713i	0.910146	−	0.414287i	$-0.135969\pi$
$347$	16.9772	+	10.9106i	0.911386	+	0.585713i	0.00124004	+	0.999999i	$0.499605\pi$
$348$	−0.784227	−	5.45442i	−0.0420390	−	0.292387i
$349$	9.64105	+	21.1109i	0.516073	+	1.13004i	0.970905	+	0.239466i	$0.0769722\pi$
$349$	9.64105	+	21.1109i	0.516073	+	1.13004i	−0.454831	+	0.890578i	$0.650300\pi$
$350$	2.20479	+	0.647385i	0.117851	+	0.0346042i
$351$	−0.450378	+	0.986189i	−0.0240394	+	0.0526389i
$352$	−0.664218	+	0.766548i	−0.0354029	+	0.0408571i
$353$	−4.54405	+	31.6045i	−0.241855	+	1.68214i	0.400942	+	0.916103i	$0.368683\pi$
$353$	−4.54405	+	31.6045i	−0.241855	+	1.68214i	−0.642797	+	0.766036i	$0.722226\pi$
$354$	−4.21333	+	1.23714i	−0.223936	+	0.0657535i
$355$	9.46701	+	10.9255i	0.502457	+	0.579866i
$356$	4.12932	−	2.65375i	0.218853	−	0.140648i
$357$	−6.45605	+	4.14905i	−0.341691	+	0.219591i
$358$	9.07316	+	10.4710i	0.479531	+	0.553409i
$359$	−18.7194	+	5.49650i	−0.987970	+	0.290094i	−0.735510	−	0.677513i	$-0.763058\pi$
$359$	−18.7194	+	5.49650i	−0.987970	+	0.290094i	−0.252459	+	0.967607i	$0.581239\pi$
$360$	−0.142315	+	0.989821i	−0.00750065	+	0.0521682i
$361$	0.878777	−	1.01416i	0.0462514	−	0.0533770i
$362$	−2.63249	+	5.76435i	−0.138361	+	0.302967i
$363$	9.56731	+	2.80922i	0.502154	+	0.147446i
$364$	−1.03491	−	2.26614i	−0.0542440	−	0.118778i
$365$	1.03244	+	7.18075i	0.0540402	+	0.375858i
$366$	−2.82155	−	1.81330i	−0.147485	−	0.0947827i
$367$	3.74049			0.195252			0.0976260	−	0.995223i	$-0.468875\pi$
$367$	3.74049			0.195252			0.0976260	+	0.995223i	$0.468875\pi$
$368$	1.65109	−	4.50265i	0.0860692	−	0.234717i
$369$	−7.48977			−0.389902
$370$	8.61740	+	5.53807i	0.447997	+	0.287910i
$371$	4.15766	+	28.9171i	0.215855	+	1.50130i
$372$	4.31572	+	9.45010i	0.223760	+	0.489965i
$373$	28.1402	+	8.26272i	1.45705	+	0.427828i	0.911865	−	0.410490i	$-0.134642\pi$
$373$	28.1402	+	8.26272i	1.45705	+	0.427828i	0.545182	+	0.838318i	$0.316461\pi$
$374$	−1.40721	+	3.08135i	−0.0727649	+	0.159333i
$375$	0.654861	−	0.755750i	0.0338169	−	0.0390267i
$376$	0.309902	−	2.15541i	0.0159820	−	0.111157i
$377$	5.73229	−	1.68315i	0.295228	−	0.0866867i
$378$	1.50479	+	1.73662i	0.0773979	+	0.0893219i
$379$	28.1719	−	18.1050i	1.44709	−	0.929990i	0.447734	−	0.894167i	$-0.352231\pi$
$379$	28.1719	−	18.1050i	1.44709	−	0.929990i	0.999358	−	0.0358231i	$-0.0114053\pi$
$380$	−3.53507	+	2.27185i	−0.181345	+	0.116544i
$381$	0.179092	+	0.206683i	0.00917515	+	0.0105887i
$382$	9.35724	−	2.74753i	0.478758	−	0.140576i
$383$	−1.74270	+	12.1208i	−0.0890479	+	0.619342i	0.895609	+	0.444842i	$0.146740\pi$
$383$	−1.74270	+	12.1208i	−0.0890479	+	0.619342i	−0.984657	+	0.174500i	$0.944169\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	0.968210	−	2.12008i	0.0493445	−	0.108049i
$386$	−0.475253	−	0.139547i	−0.0241897	−	0.00710275i
$387$	−0.114826	−	0.251435i	−0.00583696	−	0.0127812i
$388$	2.09904	+	14.5992i	0.106563	+	0.741160i
$389$	−5.93839	−	3.81637i	−0.301088	−	0.193498i	0.381370	−	0.924423i	$-0.375453\pi$
$389$	−5.93839	−	3.81637i	−0.301088	−	0.193498i	−0.682458	+	0.730925i	$0.739089\pi$
$390$	−1.08416			−0.0548987
$391$	1.05426	−	15.9822i	0.0533160	−	0.808253i
$392$	1.71978			0.0868622
$393$	1.91848	+	1.23293i	0.0967743	+	0.0621931i
$394$	1.87111	+	13.0138i	0.0942650	+	0.655627i
$395$	−1.28151	−	2.80612i	−0.0644799	−	0.141191i
$396$	0.973203	+	0.285758i	0.0489053	+	0.0143599i
$397$	7.85096	−	17.1912i	0.394028	−	0.862801i	−0.603813	−	0.797126i	$-0.706353\pi$
$397$	7.85096	−	17.1912i	0.394028	−	0.862801i	0.997841	−	0.0656752i	$-0.0209201\pi$
$398$	−12.2628	+	14.1520i	−0.614680	+	0.709378i
$399$	−1.37419	+	9.55772i	−0.0687957	+	0.478485i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	−12.2123	−	14.0938i	−0.609855	−	0.703810i	0.363893	−	0.931441i	$-0.381447\pi$
$401$	−12.2123	−	14.0938i	−0.609855	−	0.703810i	−0.973747	+	0.227631i	$0.926902\pi$
$402$	1.08341	−	0.696264i	0.0540355	−	0.0347265i
$403$	−9.47529	+	6.08940i	−0.471998	+	0.303334i
$404$	0.897289	+	1.03553i	0.0446418	+	0.0515194i
$405$	0.959493	−	0.281733i	0.0476776	−	0.0139994i
$406$	1.80205	−	12.5336i	0.0894344	−	0.622030i
$407$	6.80393	−	7.85215i	0.337258	−	0.389217i
$408$	1.38738	−	3.03795i	0.0686857	−	0.150401i
$409$	−5.66911	−	1.66460i	−0.280319	−	0.0823092i	0.138551	−	0.990355i	$-0.455756\pi$
$409$	−5.66911	−	1.66460i	−0.280319	−	0.0823092i	−0.418870	+	0.908046i	$0.637574\pi$
$410$	−3.11136	−	6.81293i	−0.153659	−	0.336467i
$411$	1.90783	+	13.2692i	0.0941061	+	0.654523i
$412$	−2.86055	−	1.83836i	−0.140929	−	0.0905697i
$413$	−10.0904			−0.496517
$414$	−4.78165	+	0.368582i	−0.235005	+	0.0181148i
$415$	−14.8500			−0.728956
$416$	0.912056	+	0.586143i	0.0447172	+	0.0287380i
$417$	2.55062	+	17.7400i	0.124904	+	0.868729i
$418$	1.77058	+	3.87703i	0.0866018	+	0.189632i
$419$	21.7168	+	6.37663i	1.06093	+	0.311519i	0.765227	−	0.643760i	$-0.222627\pi$
$419$	21.7168	+	6.37663i	1.06093	+	0.311519i	0.295707	+	0.955279i	$0.404445\pi$
$420$	−0.954571	+	2.09022i	−0.0465783	+	0.101992i
$421$	1.97767	−	2.28235i	0.0963858	−	0.111235i	−0.705507	−	0.708703i	$-0.749281\pi$
$421$	1.97767	−	2.28235i	0.0963858	−	0.111235i	0.801893	+	0.597467i	$0.203826\pi$
$422$	2.49856	−	17.3779i	0.121628	−	0.845941i
$423$	−2.08937	+	0.613495i	−0.101589	+	0.0298292i
$424$	−8.32572	−	9.60839i	−0.404333	−	0.466625i
$425$	−2.80958	+	1.80561i	−0.136285	+	0.0875848i
$426$	−12.1616	+	7.81579i	−0.589232	+	0.378676i
$427$	−5.04703	−	5.82458i	−0.244243	−	0.281871i
$428$	6.09224	−	1.78884i	0.294480	−	0.0864670i
$429$	−0.156497	+	1.08846i	−0.00755575	+	0.0525514i
$430$	0.181013	−	0.208900i	0.00872920	−	0.0100740i
$431$	4.92716	−	10.7890i	0.237333	−	0.519687i	−0.753063	−	0.657949i	$-0.771424\pi$
$431$	4.92716	−	10.7890i	0.237333	−	0.519687i	0.990396	+	0.138262i	$0.0441516\pi$
$432$	−0.959493	−	0.281733i	−0.0461636	−	0.0135549i
$433$	3.07697	+	6.73761i	0.147870	+	0.323789i	0.969044	−	0.246888i	$-0.0794080\pi$
$433$	3.07697	+	6.73761i	0.147870	+	0.323789i	−0.821174	+	0.570677i	$0.806681\pi$
$434$	3.39740	+	23.6294i	0.163081	+	1.13425i
$435$	−4.63573	−	2.97920i	−0.222266	−	0.142842i
$436$	14.8809			0.712668
$437$	−14.3288	−	14.1712i	−0.685439	−	0.677898i
$438$	−7.25459			−0.346638
$439$	9.84232	+	6.32527i	0.469748	+	0.301889i	0.754016	−	0.656856i	$-0.228114\pi$
$439$	9.84232	+	6.32527i	0.469748	+	0.301889i	−0.284268	+	0.958745i	$0.591750\pi$
$440$	0.144348	+	1.00396i	0.00688153	+	0.0478621i
$441$	−0.714424	−	1.56437i	−0.0340202	−	0.0744938i
$442$	3.47417	+	1.02011i	0.165249	+	0.0485216i
$443$	−13.9484	+	30.5427i	−0.662708	+	1.45113i	0.217270	+	0.976112i	$0.430285\pi$
$443$	−13.9484	+	30.5427i	−0.662708	+	1.45113i	−0.879977	+	0.475016i	$0.842442\pi$
$444$	−6.70808	+	7.74154i	−0.318351	+	0.367397i
$445$	0.698556	−	4.85857i	0.0331147	−	0.230318i
$446$	−10.7318	+	3.15115i	−0.508167	+	0.149211i
$447$	0.0409459	+	0.0472541i	0.00193668	+	0.00223504i
$448$	1.93309	−	1.24232i	0.0913301	−	0.0586943i
$449$	28.8778	−	18.5586i	1.36283	−	0.875835i	0.364363	−	0.931257i	$-0.381287\pi$
$449$	28.8778	−	18.5586i	1.36283	−	0.875835i	0.998463	+	0.0554216i	$0.0176503\pi$
$450$	0.654861	+	0.755750i	0.0308704	+	0.0356264i
$451$	−7.28906	+	2.14026i	−0.343228	+	0.100781i
$452$	2.75513	−	19.1624i	0.129591	−	0.901323i
$453$	−0.210554	+	0.242992i	−0.00989269	+	0.0114168i
$454$	−0.361364	+	0.791277i	−0.0169597	+	0.0371365i
$455$	−2.39035	−	0.701871i	−0.112062	−	0.0329042i
$456$	−1.74564	−	3.82241i	−0.0817469	−	0.179001i
$457$	3.77024	+	26.2226i	0.176364	+	1.22664i	0.865089	+	0.501618i	$0.167262\pi$
$457$	3.77024	+	26.2226i	0.176364	+	1.22664i	−0.688725	+	0.725023i	$0.741829\pi$
$458$	−6.37025	−	4.09391i	−0.297662	−	0.191296i
$459$	−3.33975			−0.155886
$460$	−2.32164	−	4.19642i	−0.108247	−	0.195659i
$461$	−8.81787			−0.410689			−0.205344	−	0.978690i	$-0.565831\pi$
$461$	−8.81787			−0.410689			−0.205344	+	0.978690i	$0.565831\pi$
$462$	1.96071	+	1.26007i	0.0912207	+	0.0586240i
$463$	−3.22291	−	22.4158i	−0.149781	−	1.04175i	−0.916576	−	0.399860i	$-0.869059\pi$
$463$	−3.22291	−	22.4158i	−0.149781	−	1.04175i	0.766795	−	0.641893i	$-0.221850\pi$
$464$	2.28915	+	5.01253i	0.106271	+	0.232701i
$465$	9.96811	+	2.92690i	0.462260	+	0.135732i
$466$	3.51646	−	7.69998i	0.162897	−	0.356695i
$467$	3.67574	−	4.24203i	0.170093	−	0.196298i	−0.664303	−	0.747464i	$-0.731271\pi$
$467$	3.67574	−	4.24203i	0.170093	−	0.196298i	0.834396	+	0.551166i	$0.185817\pi$
$468$	0.154292	−	1.07313i	0.00713217	−	0.0496053i
$469$	2.83944	−	0.833735i	0.131113	−	0.0384983i
$470$	−1.42601	−	1.64570i	−0.0657770	−	0.0759107i
$471$	−1.45956	+	0.938003i	−0.0672530	+	0.0432209i
$472$	3.69411	−	2.37406i	0.170035	−	0.109275i
$473$	−0.183599	−	0.211884i	−0.00844189	−	0.00974246i
$474$	2.95994	−	0.869116i	0.135954	−	0.0399198i
$475$	−0.598028	+	4.15938i	−0.0274394	+	0.190845i
$476$	5.02561	−	5.79987i	0.230349	−	0.265837i
$477$	−5.28147	+	11.5648i	−0.241822	+	0.529516i
$478$	10.0136	+	2.94025i	0.458010	+	0.134484i
$479$	−4.16386	−	9.11759i	−0.190252	−	0.416593i	0.790336	−	0.612674i	$-0.209906\pi$
$479$	−4.16386	−	9.11759i	−0.190252	−	0.416593i	−0.980588	+	0.196080i	$0.937179\pi$
$480$	−0.142315	−	0.989821i	−0.00649575	−	0.0451790i
$481$	−9.34266	−	6.00417i	−0.425989	−	0.273766i
$482$	13.7302			0.625396
$483$	−10.7812	−	2.28292i	−0.490559	−	0.103877i
$484$	−9.97122			−0.453237
$485$	12.4079	+	7.97407i	0.563413	+	0.362084i
$486$	0.142315	+	0.989821i	0.00645553	+	0.0448992i
$487$	15.4367	+	33.8017i	0.699505	+	1.53170i	0.840570	+	0.541703i	$0.182220\pi$
$487$	15.4367	+	33.8017i	0.699505	+	1.53170i	−0.141065	+	0.990000i	$0.545053\pi$
$488$	3.21812	+	0.944927i	0.145678	+	0.0427748i
$489$	5.63335	−	12.3353i	0.254749	−	0.557822i
$490$	1.12622	−	1.29973i	0.0508774	−	0.0587156i
$491$	4.06635	−	28.2821i	0.183512	−	1.27635i	−0.664867	−	0.746962i	$-0.731512\pi$
$491$	4.06635	−	28.2821i	0.183512	−	1.27635i	0.848378	−	0.529390i	$-0.177579\pi$
$492$	7.18638	−	2.11011i	0.323987	−	0.0951311i
$493$	12.0519	+	13.9086i	0.542789	+	0.626412i
$494$	3.83260	−	2.46306i	0.172437	−	0.110818i
$495$	0.853274	−	0.548366i	0.0383518	−	0.0246472i
$496$	−6.80330	−	7.85143i	−0.305477	−	0.352540i
$497$	−31.8736	+	9.35894i	−1.42973	+	0.419806i
$498$	2.11337	−	14.6988i	0.0947023	−	0.658669i
$499$	21.0598	−	24.3044i	0.942768	−	1.08801i	−0.0532252	−	0.998583i	$-0.516950\pi$
$499$	21.0598	−	24.3044i	0.942768	−	1.08801i	0.995993	−	0.0894297i	$-0.0285044\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	−0.983799	−	0.288870i	−0.0439529	−	0.0129057i
$502$	−6.71036	−	14.6936i	−0.299498	−	0.655809i
$503$	−0.130594	−	0.908298i	−0.00582288	−	0.0404990i	0.986703	−	0.162535i	$-0.0519669\pi$
$503$	−0.130594	−	0.908298i	−0.00582288	−	0.0404990i	−0.992526	+	0.122036i	$0.961058\pi$
$504$	−1.93309	−	1.24232i	−0.0861068	−	0.0553375i
$505$	1.37020			0.0609730
$506$	−4.54819	+	1.72510i	−0.202192	+	0.0766900i
$507$	−11.8246			−0.525149
$508$	−0.230067	−	0.147855i	−0.0102076	−	0.00656000i
$509$	1.03968	+	7.23115i	0.0460831	+	0.320515i	0.999804	+	0.0198203i	$0.00630940\pi$
$509$	1.03968	+	7.23115i	0.0460831	+	0.320515i	−0.953720	+	0.300695i	$0.902782\pi$
$510$	−1.38738	−	3.03795i	−0.0614344	−	0.134523i
$511$	−15.9949	−	4.69652i	−0.707571	−	0.207762i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−2.75182	+	3.17577i	−0.121496	+	0.140214i
$514$	2.66932	−	18.5655i	0.117739	−	0.818890i
$515$	−3.26261	+	0.957988i	−0.143768	+	0.0422140i
$516$	0.181013	+	0.208900i	0.00796863	+	0.00919629i
$517$	−1.85807	+	1.19411i	−0.0817179	+	0.0525169i
$518$	−19.8017	+	12.7258i	−0.870036	+	0.559138i
$519$	0.175513	+	0.202552i	0.00770415	+	0.00889107i
$520$	1.04025	−	0.305444i	0.0456178	−	0.0133946i
$521$	5.92923	−	41.2387i	0.259764	−	1.80670i	−0.274722	−	0.961524i	$-0.588586\pi$
$521$	5.92923	−	41.2387i	0.259764	−	1.80670i	0.534487	−	0.845177i	$-0.320505\pi$
$522$	3.60861	−	4.16456i	0.157945	−	0.182278i
$523$	14.6807	−	32.1462i	0.641940	−	1.40565i	−0.256494	−	0.966546i	$-0.582567\pi$
$523$	14.6807	−	32.1462i	0.641940	−	1.40565i	0.898435	−	0.439107i	$-0.144705\pi$
$524$	−2.18812	−	0.642490i	−0.0955885	−	0.0280673i
$525$	0.954571	+	2.09022i	0.0416609	+	0.0912246i
$526$	2.30703	+	16.0458i	0.100591	+	0.699629i
$527$	−29.1885	−	18.7583i	−1.27147	−	0.817125i
$528$	−1.01429			−0.0441412
$529$	17.2146	−	15.2531i	0.748460	−	0.663180i
$530$	−12.7137			−0.552249
$531$	−3.69411	−	2.37406i	−0.160311	−	0.103026i
$532$	−1.37419	−	9.55772i	−0.0595788	−	0.414380i
$533$	3.37322	+	7.38633i	0.146110	+	0.319937i
$534$	4.70970	+	1.38289i	0.203809	+	0.0598436i
$535$	2.63765	−	5.77565i	0.114036	−	0.249703i
$536$	−0.843362	+	0.973292i	−0.0364277	+	0.0420398i
$537$	−1.97179	+	13.7141i	−0.0850888	+	0.591806i
$538$	−6.05694	+	1.77848i	−0.261133	+	0.0766757i
$539$	−1.14231	−	1.31830i	−0.0492028	−	0.0567831i
$540$	−0.841254	+	0.540641i	−0.0362018	+	0.0232655i
$541$	−2.37637	+	1.52720i	−0.102168	+	0.0656594i	−0.590727	−	0.806871i	$-0.701159\pi$
$541$	−2.37637	+	1.52720i	−0.102168	+	0.0656594i	0.488559	+	0.872531i	$0.337523\pi$
$542$	15.8563	+	18.2992i	0.681088	+	0.786018i
$543$	−6.08032	+	1.78534i	−0.260931	+	0.0766164i
$544$	−0.475296	+	3.30576i	−0.0203782	+	0.141733i
$545$	9.74495	−	11.2463i	0.417428	−	0.481737i
$546$	1.03491	−	2.26614i	0.0442901	−	0.0969817i
$547$	−19.3716	−	5.68802i	−0.828270	−	0.243202i	−0.159996	−	0.987118i	$-0.551148\pi$
$547$	−19.3716	−	5.68802i	−0.828270	−	0.243202i	−0.668274	+	0.743916i	$0.732966\pi$
$548$	−5.56892	−	12.1942i	−0.237892	−	0.520912i
$549$	−0.477322	−	3.31985i	−0.0203716	−	0.141688i
$550$	0.853274	+	0.548366i	0.0363837	+	0.0233824i
$551$	23.1560			0.986478
$552$	4.48412	−	1.70080i	0.190857	−	0.0723907i
$553$	7.08870			0.301442
$554$	−17.5086	−	11.2521i	−0.743868	−	0.478055i
$555$	1.45781	+	10.1393i	0.0618804	+	0.430387i
$556$	−7.44523	−	16.3028i	−0.315748	−	0.691391i
$557$	0.687513	+	0.201872i	0.0291309	+	0.00855360i	0.296266	−	0.955106i	$-0.404259\pi$
$557$	0.687513	+	0.201872i	0.0291309	+	0.00855360i	−0.267135	+	0.963659i	$0.586077\pi$
$558$	−4.31572	+	9.45010i	−0.182699	+	0.400055i
$559$	−0.196247	+	0.226481i	−0.00830037	+	0.00957914i
$560$	0.327021	−	2.27448i	0.0138192	−	0.0961145i
$561$	−3.25026	+	0.954361i	−0.137226	+	0.0402932i
$562$	−7.70013	−	8.88643i	−0.324810	−	0.374851i
$563$	−14.1461	+	9.09116i	−0.596188	+	0.383147i	−0.803655	−	0.595095i	$-0.797114\pi$
$563$	−14.1461	+	9.09116i	−0.596188	+	0.383147i	0.207467	+	0.978242i	$0.433478\pi$
$564$	1.83190	−	1.17729i	0.0771368	−	0.0495728i
$565$	−12.6777	−	14.6309i	−0.533356	−	0.615526i
$566$	5.89269	−	1.73025i	0.247688	−	0.0727278i
$567$	−0.327021	+	2.27448i	−0.0137336	+	0.0955193i
$568$	9.46701	−	10.9255i	0.397227	−	0.458424i
$569$	−16.9603	+	37.1379i	−0.711013	+	1.55690i	0.115072	+	0.993357i	$0.463290\pi$
$569$	−16.9603	+	37.1379i	−0.711013	+	1.55690i	−0.826086	+	0.563545i	$0.809437\pi$
$570$	−4.03193	−	1.18388i	−0.168879	−	0.0495874i
$571$	0.0300680	+	0.0658398i	0.00125831	+	0.00275531i	0.910260	−	0.414037i	$-0.135882\pi$
$571$	0.0300680	+	0.0658398i	0.00125831	+	0.00275531i	−0.909002	+	0.416792i	$0.863154\pi$
$572$	−0.156497	−	1.08846i	−0.00654347	−	0.0455108i
$573$	8.20413	+	5.27248i	0.342733	+	0.220261i
$574$	17.2105			0.718353
$575$	−4.69180	−	0.993494i	−0.195662	−	0.0414316i
$576$	1.00000			0.0416667
$577$	20.7669	+	13.3461i	0.864537	+	0.555605i	0.896077	−	0.443898i	$-0.146405\pi$
$577$	20.7669	+	13.3461i	0.864537	+	0.555605i	−0.0315398	+	0.999502i	$0.510041\pi$
$578$	−0.831980	−	5.78655i	−0.0346058	−	0.240689i
$579$	−0.205762	−	0.450556i	−0.00855118	−	0.0187245i
$580$	5.28729	+	1.55249i	0.219543	+	0.0644636i
$581$	14.1753	−	31.0396i	0.588092	−	1.28774i
$582$	−9.65873	+	11.1468i	−0.400367	+	0.462049i
$583$	−1.83520	+	12.7641i	−0.0760064	+	0.528636i
$584$	6.96073	−	2.04385i	0.288037	−	0.0845753i
$585$	−0.709976	−	0.819356i	−0.0293539	−	0.0338762i
$586$	−24.6520	+	15.8429i	−1.01836	+	0.654463i
$587$	18.2892	−	11.7538i	0.754876	−	0.485129i	−0.105734	−	0.994394i	$-0.533719\pi$
$587$	18.2892	−	11.7538i	0.754876	−	0.485129i	0.860610	+	0.509265i	$0.170083\pi$
$588$	1.12622	+	1.29973i	0.0464445	+	0.0535998i
$589$	−41.8875	+	12.2993i	−1.72594	+	0.506783i
$590$	0.624933	−	4.34650i	0.0257281	−	0.178943i
$591$	−8.60988	+	9.93633i	−0.354163	+	0.408726i
$592$	4.25531	−	9.31783i	0.174892	−	0.382961i
$593$	−15.6660	−	4.59994i	−0.643324	−	0.188897i	−0.0562328	−	0.998418i	$-0.517909\pi$
$593$	−15.6660	−	4.59994i	−0.643324	−	0.188897i	−0.587091	+	0.809521i	$0.699727\pi$
$594$	0.421351	+	0.922629i	0.0172882	+	0.0378559i
$595$	−1.09217	−	7.59621i	−0.0447746	−	0.311414i
$596$	−0.0526004	−	0.0338042i	−0.00215460	−	0.00138467i
$597$	−18.7258			−0.766398
$598$	2.51704	+	4.54961i	0.102929	+	0.186047i
$599$	26.3188			1.07536			0.537678	−	0.843151i	$-0.319302\pi$
$599$	26.3188			1.07536			0.537678	+	0.843151i	$0.319302\pi$
$600$	−0.841254	−	0.540641i	−0.0343440	−	0.0220716i
$601$	−5.57225	−	38.7559i	−0.227297	−	1.58089i	−0.709423	−	0.704783i	$-0.751044\pi$
$601$	−5.57225	−	38.7559i	−0.227297	−	1.58089i	0.482126	−	0.876102i	$-0.339865\pi$
$602$	0.263857	+	0.577765i	0.0107540	+	0.0235480i
$603$	1.23568	+	0.362829i	0.0503209	+	0.0147755i
$604$	0.133566	−	0.292469i	0.00543474	−	0.0119004i
$605$	−6.52976	+	7.53574i	−0.265472	+	0.306372i
$606$	−0.195000	+	1.35625i	−0.00792132	+	0.0550940i
$607$	−24.8654	+	7.30115i	−1.00926	+	0.296344i	−0.744249	−	0.667902i	$-0.767192\pi$
$607$	−24.8654	+	7.30115i	−1.00926	+	0.296344i	−0.265007	+	0.964246i	$0.585374\pi$
$608$	2.75182	+	3.17577i	0.111601	+	0.128795i
$609$	10.6523	−	6.84583i	0.431654	−	0.277407i
$610$	2.82155	−	1.81330i	0.114241	−	0.0734184i
$611$	1.54603	+	1.78421i	0.0625456	+	0.0721815i
$612$	3.20447	−	0.940917i	0.129533	−	0.0380343i
$613$	3.87979	−	26.9845i	0.156703	−	1.08989i	−0.747953	−	0.663752i	$-0.768963\pi$
$613$	3.87979	−	26.9845i	0.156703	−	1.08989i	0.904656	−	0.426143i	$-0.140128\pi$
$614$	2.16171	−	2.49474i	0.0872394	−	0.100680i
$615$	3.11136	−	6.81293i	0.125462	−	0.274724i
$616$	−2.23630	−	0.656635i	−0.0901029	−	0.0264566i
$617$	4.42988	+	9.70007i	0.178340	+	0.390510i	0.977599	−	0.210477i	$-0.0675016\pi$
$617$	4.42988	+	9.70007i	0.178340	+	0.390510i	−0.799259	+	0.600987i	$0.794774\pi$
$618$	−0.483919	−	3.36573i	−0.0194661	−	0.135390i
$619$	10.3164	+	6.62994i	0.414651	+	0.266480i	0.731291	−	0.682066i	$-0.238918\pi$
$619$	10.3164	+	6.62994i	0.414651	+	0.266480i	−0.316640	+	0.948546i	$0.602555\pi$
$620$	−10.3889			−0.417230
$621$	−3.40987	−	3.37236i	−0.136833	−	0.135328i
$622$	−26.7546			−1.07276
$623$	9.48864	+	6.09798i	0.380154	+	0.244310i
$624$	0.154292	+	1.07313i	0.00617664	+	0.0429595i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−20.7610	−	6.09599i	−0.829778	−	0.243645i
$627$	−1.77058	+	3.87703i	−0.0707101	+	0.154834i
$628$	1.13617	−	1.31121i	0.0453382	−	0.0523231i
$629$	4.86871	−	33.8626i	0.194128	−	1.35019i
$630$	−2.20479	+	0.647385i	−0.0878410	+	0.0257925i
$631$	−19.8158	−	22.8686i	−0.788854	−	0.910386i	0.208861	−	0.977945i	$-0.433024\pi$
$631$	−19.8158	−	22.8686i	−0.788854	−	0.910386i	−0.997715	+	0.0675594i	$0.978479\pi$
$632$	−2.59518	+	1.66782i	−0.103231	+	0.0663424i
$633$	14.7695	−	9.49179i	0.587036	−	0.377265i
$634$	−14.1518	−	16.3320i	−0.562039	−	0.648628i
$635$	−0.262403	+	0.0770484i	−0.0104131	+	0.00305757i
$636$	1.80935	−	12.5843i	0.0717454	−	0.499000i
$637$	−1.22100	+	1.40911i	−0.0483780	+	0.0558311i
$638$	2.32186	−	5.08415i	0.0919231	−	0.201284i
$639$	−13.8709	−	4.07287i	−0.548726	−	0.161120i
$640$	0.415415	+	0.909632i	0.0164207	+	0.0359564i
$641$	2.82725	+	19.6639i	0.111670	+	0.776679i	0.966296	+	0.257435i	$0.0828774\pi$
$641$	2.82725	+	19.6639i	0.111670	+	0.776679i	−0.854626	+	0.519244i	$0.826214\pi$
$642$	5.34149	+	3.43277i	0.210812	+	0.135480i
$643$	−5.70957			−0.225163			−0.112582	−	0.993642i	$-0.535912\pi$
$643$	−5.70957			−0.225163			−0.112582	+	0.993642i	$0.535912\pi$
$644$	10.9876	−	0.846954i	0.432973	−	0.0333747i
$645$	0.276414			0.0108838
$646$	11.8063	+	7.58743i	0.464512	+	0.298524i
$647$	4.32504	+	30.0813i	0.170035	+	1.18262i	0.878806	+	0.477180i	$0.158341\pi$
$647$	4.32504	+	30.0813i	0.170035	+	1.18262i	−0.708771	+	0.705439i	$0.750750\pi$
$648$	−0.415415	−	0.909632i	−0.0163190	−	0.0357337i
$649$	−4.27353	−	1.25482i	−0.167751	−	0.0492560i
$650$	0.450378	−	0.986189i	0.0176653	−	0.0386815i
$651$	−15.6331	+	18.0416i	−0.612710	+	0.707105i
$652$	−1.92990	+	13.4227i	−0.0755806	+	0.525675i
$653$	−20.4342	+	6.00003i	−0.799653	+	0.234799i	−0.655933	−	0.754819i	$-0.727725\pi$
$653$	−20.4342	+	6.00003i	−0.799653	+	0.234799i	−0.143720	+	0.989618i	$0.545906\pi$
$654$	9.74495	+	11.2463i	0.381058	+	0.439764i
$655$	−1.91848	+	1.23293i	−0.0749611	+	0.0481745i
$656$	−6.30079	+	4.04927i	−0.246005	+	0.158098i
$657$	−4.75075	−	5.48265i	−0.185344	−	0.213899i
$658$	4.80111	−	1.40973i	0.187167	−	0.0549571i
$659$	−4.54374	+	31.6024i	−0.176999	+	1.23105i	0.686660	+	0.726979i	$0.259076\pi$
$659$	−4.54374	+	31.6024i	−0.176999	+	1.23105i	−0.863659	+	0.504076i	$0.831833\pi$
$660$	−0.664218	+	0.766548i	−0.0258546	+	0.0298378i
$661$	−18.9349	+	41.4617i	−0.736482	+	1.61267i	0.0527733	+	0.998607i	$0.483194\pi$
$661$	−18.9349	+	41.4617i	−0.736482	+	1.61267i	−0.789256	+	0.614065i	$0.789533\pi$
$662$	6.21218	+	1.82406i	0.241443	+	0.0708942i
$663$	1.50415	+	3.29363i	0.0584163	+	0.127914i
$664$	2.11337	+	14.6988i	0.0820146	+	0.570424i
$665$	−8.12315	−	5.22043i	−0.315002	−	0.202440i
$666$	−10.2435			−0.396928
$667$	−1.73950	+	26.3701i	−0.0673535	+	1.02106i
$668$	1.02533			0.0396713
$669$	−9.40934	−	6.04702i	−0.363786	−	0.233791i
$670$	0.183280	+	1.27474i	0.00708073	+	0.0492475i
$671$	−1.41320	−	3.09448i	−0.0545561	−	0.119461i
$672$	2.20479	+	0.647385i	0.0850517	+	0.0249734i
$673$	12.2542	−	26.8330i	0.472366	−	1.03434i	−0.512126	−	0.858910i	$-0.671142\pi$
$673$	12.2542	−	26.8330i	0.472366	−	1.03434i	0.984492	−	0.175427i	$-0.0561306\pi$
$674$	4.41850	−	5.09922i	0.170194	−	0.196415i
$675$	−0.142315	+	0.989821i	−0.00547770	+	0.0380982i
$676$	11.3456	−	3.33137i	0.436370	−	0.128130i
$677$	−6.00270	−	6.92749i	−0.230703	−	0.266245i	0.628581	−	0.777744i	$-0.283636\pi$
$677$	−6.00270	−	6.92749i	−0.230703	−	0.266245i	−0.859284	+	0.511499i	$0.829090\pi$
$678$	16.2862	−	10.4665i	0.625467	−	0.401963i
$679$	−28.5118	+	18.3234i	−1.09418	+	0.703187i
$680$	2.18707	+	2.52402i	0.0838704	+	0.0967916i
$681$	−0.834650	+	0.245075i	−0.0319839	+	0.00939131i
$682$	−1.49962	+	10.4301i	−0.0574236	+	0.399390i
$683$	12.0069	−	13.8567i	0.459431	−	0.530211i	−0.478011	−	0.878354i	$-0.658642\pi$
$683$	12.0069	−	13.8567i	0.459431	−	0.530211i	0.937442	+	0.348143i	$0.113187\pi$
$684$	1.74564	−	3.82241i	0.0667461	−	0.146154i
$685$	−12.8626	−	3.77681i	−0.491457	−	0.144305i
$686$	8.32365	+	18.2262i	0.317798	+	0.695881i
$687$	−1.07766	−	7.49526i	−0.0411151	−	0.285962i
$688$	−0.232534	−	0.149441i	−0.00886528	−	0.00569737i
$689$	13.7837			0.525119
$690$	1.65109	−	4.50265i	0.0628561	−	0.171413i
$691$	17.4839			0.665119			0.332559	−	0.943082i	$-0.392088\pi$
$691$	17.4839			0.665119			0.332559	+	0.943082i	$0.392088\pi$
$692$	−0.225469	−	0.144900i	−0.00857104	−	0.00550827i
$693$	0.331694	+	2.30698i	0.0126000	+	0.0876350i
$694$	−8.38345	−	18.3572i	−0.318231	−	0.696829i
$695$	−17.1964	−	5.04932i	−0.652297	−	0.191532i
$696$	−2.28915	+	5.01253i	−0.0867699	+	0.190000i
$697$	−16.3807	+	18.9043i	−0.620462	+	0.716051i
$698$	3.30288	−	22.9720i	0.125016	−	0.869503i
$699$	8.12205	−	2.38485i	0.307204	−	0.0902033i
$700$	−1.50479	−	1.73662i	−0.0568756	−	0.0656379i
$701$	−31.9102	+	20.5074i	−1.20523	+	0.774555i	−0.979854	−	0.199717i	$-0.935998\pi$
$701$	−31.9102	+	20.5074i	−1.20523	+	0.774555i	−0.225377	+	0.974272i	$0.572362\pi$
$702$	0.912056	−	0.586143i	0.0344233	−	0.0221225i
$703$	−28.1884	−	32.5311i	−1.06314	−	1.22693i
$704$	0.973203	−	0.285758i	0.0366790	−	0.0107699i
$705$	0.309902	−	2.15541i	0.0116716	−	0.0811776i
$706$	20.9094	−	24.1307i	0.786935	−	0.908172i
$707$	−1.30795	+	2.86401i	−0.0491906	+	0.107712i
$708$	4.21333	+	1.23714i	0.158346	+	0.0464947i
$709$	4.23898	+	9.28208i	0.159198	+	0.348596i	0.972376	−	0.233420i	$-0.0749916\pi$
$709$	4.23898	+	9.28208i	0.159198	+	0.348596i	−0.813178	+	0.582015i	$0.802264\pi$
$710$	−2.05738	−	14.3094i	−0.0772120	−	0.537021i
$711$	2.59518	+	1.66782i	0.0973269	+	0.0625482i
$712$	−4.90853			−0.183955
$713$	−10.8599	−	48.6256i	−0.406705	−	1.82104i
$714$	7.67433			0.287204
$715$	−0.925088	−	0.594518i	−0.0345963	−	0.0222337i
$716$	−1.97179	−	13.7141i	−0.0736891	−	0.512519i
$717$	4.33540	+	9.49321i	0.161909	+	0.354530i
$718$	18.7194	+	5.49650i	0.698600	+	0.205128i
$719$	0.562608	−	1.23194i	0.0209817	−	0.0459436i	−0.898851	−	0.438254i	$-0.855597\pi$
$719$	0.562608	−	1.23194i	0.0209817	−	0.0459436i	0.919833	+	0.392311i	$0.128324\pi$
$720$	0.654861	−	0.755750i	0.0244052	−	0.0281651i
$721$	1.11198	−	7.73402i	0.0414125	−	0.288030i
$722$	−1.28757	+	0.378065i	−0.0479185	+	0.0140701i
$723$	8.99140	+	10.3766i	0.334394	+	0.385911i
$724$	5.33103	−	3.42605i	0.198126	−	0.127328i
$725$	4.63573	−	2.97920i	0.172167	−	0.110645i
$726$	−6.52976	−	7.53574i	−0.242342	−	0.279678i
$727$	39.2695	−	11.5306i	1.45643	−	0.427645i	0.544765	−	0.838589i	$-0.316619\pi$
$727$	39.2695	−	11.5306i	1.45643	−	0.427645i	0.911661	+	0.410944i	$0.134801\pi$
$728$	−0.354544	+	2.46591i	−0.0131403	+	0.0913927i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	3.01367	−	6.59901i	0.111541	−	0.244240i
$731$	−0.885760	−	0.260083i	−0.0327610	−	0.00961950i
$732$	1.39330	+	3.05089i	0.0514977	+	0.112764i
$733$	5.63260	+	39.1756i	0.208045	+	1.44698i	0.779526	+	0.626369i	$0.215460\pi$
$733$	5.63260	+	39.1756i	0.208045	+	1.44698i	−0.571481	+	0.820615i	$0.693631\pi$
$734$	−3.14670	−	2.02226i	−0.116147	−	0.0746430i
$735$	1.71978			0.0634352
$736$	−3.82331	+	2.89522i	−0.140929	+	0.106719i
$737$	1.30625			0.0481164
$738$	6.30079	+	4.04927i	0.231935	+	0.149056i
$739$	4.16150	+	28.9439i	0.153083	+	1.06472i	0.911012	+	0.412380i	$0.135302\pi$
$739$	4.16150	+	28.9439i	0.153083	+	1.06472i	−0.757929	+	0.652337i	$0.773789\pi$
$740$	−4.25531	−	9.31783i	−0.156428	−	0.342530i
$741$	4.37127	+	1.28352i	0.160583	+	0.0471513i
$742$	12.1361	−	26.5744i	0.445532	−	0.975579i
$743$	−20.2629	+	23.3846i	−0.743372	+	0.857897i	−0.993908	−	0.110210i	$-0.964848\pi$
$743$	−20.2629	+	23.3846i	−0.743372	+	0.857897i	0.250536	+	0.968107i	$0.419393\pi$
$744$	1.47850	−	10.2832i	0.0542044	−	0.377000i
$745$	−0.0599934	+	0.0176157i	−0.00219799	+	0.000645388i
$746$	−19.2059	−	22.1648i	−0.703179	−	0.811511i
$747$	12.4926	−	8.02849i	0.457079	−	0.293747i
$748$	2.84972	−	1.83141i	0.104196	−	0.0669628i
$749$	9.55455	+	11.0265i	0.349116	+	0.402901i
$750$	−0.959493	+	0.281733i	−0.0350357	+	0.0102874i
$751$	4.35044	−	30.2580i	0.158750	−	1.10413i	−0.742191	−	0.670189i	$-0.766213\pi$
$751$	4.35044	−	30.2580i	0.158750	−	1.10413i	0.900941	−	0.433942i	$-0.142878\pi$
$752$	−1.42601	+	1.64570i	−0.0520013	+	0.0600127i
$753$	6.71036	−	14.6936i	0.244539	−	0.535466i
$754$	−5.73229	−	1.68315i	−0.208758	−	0.0612967i
$755$	−0.133566	−	0.292469i	−0.00486097	−	0.0106441i
$756$	−0.327021	−	2.27448i	−0.0118936	−	0.0827222i
$757$	30.8228	+	19.8086i	1.12027	+	0.719956i	0.963508	−	0.267680i	$-0.0862570\pi$
$757$	30.8228	+	19.8086i	1.12027	+	0.719956i	0.156765	+	0.987636i	$0.449893\pi$
$758$	−33.4880			−1.21634
$759$	−4.28217	−	2.30759i	−0.155433	−	0.0837602i
$760$	4.20215			0.152428
$761$	3.05783	+	1.96515i	0.110846	+	0.0712365i	0.594889	−	0.803808i	$-0.297196\pi$
$761$	3.05783	+	1.96515i	0.110846	+	0.0712365i	−0.484043	+	0.875044i	$0.660832\pi$
$762$	−0.0389204	−	0.270697i	−0.00140994	−	0.00980632i
$763$	14.2049	+	31.1044i	0.514252	+	1.12606i
$764$	−9.35724	−	2.74753i	−0.338533	−	0.0994023i
$765$	1.38738	−	3.03795i	0.0501610	−	0.109837i
$766$	8.01903	−	9.25446i	0.289739	−	0.334377i
$767$	−0.677529	+	4.71232i	−0.0244642	+	0.170152i
$768$	−0.959493	+	0.281733i	−0.0346227	+	0.0101661i
$769$	2.43677	+	2.81218i	0.0878721	+	0.101410i	0.797983	−	0.602680i	$-0.205901\pi$
$769$	2.43677	+	2.81218i	0.0878721	+	0.101410i	−0.710111	+	0.704090i	$0.751355\pi$
$770$	−1.96071	+	1.26007i	−0.0706592	+	0.0454099i
$771$	15.7789	−	10.1405i	0.568264	−	0.365201i
$772$	0.324363	+	0.374335i	0.0116741	+	0.0134726i
$773$	−2.33770	+	0.686409i	−0.0840811	+	0.0246884i	−0.323503	−	0.946227i	$-0.604860\pi$
$773$	−2.33770	+	0.686409i	−0.0840811	+	0.0246884i	0.239421	+	0.970916i	$0.423042\pi$
$774$	−0.0393378	+	0.273600i	−0.00141397	+	0.00983436i
$775$	−6.80330	+	7.85143i	−0.244382	+	0.282032i
$776$	6.12708	−	13.4164i	0.219949	−	0.481622i
$777$	−22.5848	−	6.63151i	−0.810226	−	0.237904i
$778$	2.93240	+	6.42107i	0.105132	+	0.230207i
$779$	4.47909	+	31.1528i	0.160480	+	1.11616i
$780$	0.912056	+	0.586143i	0.0326568	+	0.0209873i
$781$	−14.6631			−0.524686
$782$	−9.52750	+	12.8751i	−0.340703	+	0.460412i
$783$	5.51051			0.196929
$784$	−1.44677	−	0.929785i	−0.0516705	−	0.0332066i
$785$	−0.246914	−	1.71732i	−0.00881274	−	0.0612939i
$786$	−0.947353	−	2.07441i	−0.0337909	−	0.0739919i
$787$	7.14301	+	2.09738i	0.254621	+	0.0747634i	0.406552	−	0.913628i	$-0.366731\pi$
$787$	7.14301	+	2.09738i	0.254621	+	0.0747634i	−0.151931	+	0.988391i	$0.548549\pi$
$788$	5.46173	−	11.9595i	0.194566	−	0.426040i
$789$	−10.6158	+	12.2513i	−0.377933	+	0.436157i
$790$	−0.439027	+	3.05350i	−0.0156199	+	0.108639i
$791$	42.6835	−	12.5330i	1.51765	−	0.445623i
$792$	−0.664218	−	0.766548i	−0.0236019	−	0.0272381i
$793$	−3.05902	+	1.96591i	−0.108629	+	0.0698116i
$794$	−15.8989	+	10.2176i	−0.564231	+	0.362609i
$795$	−8.32572	−	9.60839i	−0.295283	−	0.340774i
$796$	17.9673	−	5.27568i	0.636835	−	0.186991i
$797$	1.64838	−	11.4647i	0.0583885	−	0.406101i	−0.939577	−	0.342339i	$-0.888781\pi$
$797$	1.64838	−	11.4647i	0.0583885	−	0.406101i	0.997965	−	0.0637622i	$-0.0203099\pi$
$798$	6.32334	−	7.29752i	0.223844	−	0.258329i
$799$	−3.02114	+	6.61537i	−0.106880	+	0.234035i
$800$	0.959493	+	0.281733i	0.0339232	+	0.00996075i
$801$	2.03908	+	4.46495i	0.0720472	+	0.157761i
$802$	2.65399	+	18.4589i	0.0937158	+	0.651808i
$803$	−6.19015	−	3.97817i	−0.218446	−	0.140387i
$804$	−1.28785			−0.0454189
$805$	6.55527	−	8.85852i	0.231043	−	0.312222i
$806$	11.2633			0.396733
$807$	−5.31054	−	3.41288i	−0.186940	−	0.120139i
$808$	−0.195000	−	1.35625i	−0.00686006	−	0.0477128i
$809$	−12.3721	−	27.0912i	−0.434981	−	0.952476i	−0.992492	−	0.122307i	$-0.960971\pi$
$809$	−12.3721	−	27.0912i	−0.434981	−	0.952476i	0.557511	−	0.830169i	$-0.311756\pi$
$810$	−0.959493	−	0.281733i	−0.0337131	−	0.00989907i
$811$	−4.30884	+	9.43504i	−0.151304	+	0.331309i	−0.970073	−	0.242814i	$-0.921930\pi$
$811$	−4.30884	+	9.43504i	−0.151304	+	0.331309i	0.818769	+	0.574123i	$0.194657\pi$
$812$	−8.29213	+	9.56963i	−0.290997	+	0.335828i
$813$	−3.44591	+	23.9668i	−0.120853	+	0.840554i
$814$	−9.96902	+	2.92717i	−0.349414	+	0.102597i
$815$	8.88041	+	10.2485i	0.311067	+	0.358991i
$816$	−2.80958	+	1.80561i	−0.0983549	+	0.0632089i
$817$	−0.977143	+	0.627972i	−0.0341859	+	0.0219700i
$818$	3.86921	+	4.46530i	0.135284	+	0.156126i
$819$	2.39035	−	0.701871i	0.0835257	−	0.0245254i
$820$	−1.06590	+	7.41353i	−0.0372230	+	0.258892i
$821$	8.42926	−	9.72789i	0.294183	−	0.339506i	−0.589347	−	0.807880i	$-0.700615\pi$
$821$	8.42926	−	9.72789i	0.294183	−	0.339506i	0.883530	+	0.468375i	$0.155160\pi$
$822$	5.56892	−	12.1942i	0.194238	−	0.425323i
$823$	−43.3095	−	12.7168i	−1.50967	−	0.443280i	−0.580915	−	0.813964i	$-0.697305\pi$
$823$	−43.3095	−	12.7168i	−1.50967	−	0.443280i	−0.928759	+	0.370684i	$0.879123\pi$
$824$	1.41255	+	3.09306i	0.0492086	+	0.107752i
$825$	0.144348	+	1.00396i	0.00502556	+	0.0349536i
$826$	8.48860	+	5.45529i	0.295356	+	0.189814i
$827$	52.4940			1.82540			0.912698	−	0.408636i	$-0.133995\pi$
$827$	52.4940			1.82540			0.912698	+	0.408636i	$0.133995\pi$
$828$	4.22185	+	2.27508i	0.146719	+	0.0790646i
$829$	−30.6652			−1.06505			−0.532524	−	0.846415i	$-0.678756\pi$
$829$	−30.6652			−1.06505			−0.532524	+	0.846415i	$0.678756\pi$
$830$	12.4926	+	8.02849i	0.433624	+	0.278673i
$831$	−2.96192	−	20.6006i	−0.102748	−	0.714628i
$832$	−0.450378	−	0.986189i	−0.0156140	−	0.0341900i
$833$	−5.51099	−	1.61817i	−0.190945	−	0.0560664i
$834$	7.44523	−	16.3028i	0.257807	−	0.564519i
$835$	0.671450	−	0.774895i	0.0232365	−	0.0268163i
$836$	0.606573	−	4.21881i	0.0209788	−	0.145911i
$837$	−9.96811	+	2.92690i	−0.344548	+	0.101168i
$838$	−14.8219	−	17.1053i	−0.512013	−	0.590894i
$839$	37.4884	−	24.0923i	1.29424	−	0.831760i	0.301671	−	0.953412i	$-0.402456\pi$
$839$	37.4884	−	24.0923i	1.29424	−	0.831760i	0.992573	+	0.121652i	$0.0388193\pi$
$840$	1.93309	−	1.24232i	0.0666980	−	0.0428642i
$841$	−0.894328	−	1.03211i	−0.0308389	−	0.0355900i
$842$	−2.89766	+	0.850829i	−0.0998598	+	0.0293215i
$843$	1.67340	−	11.6387i	0.0576349	−	0.400860i
$844$	−11.4971	+	13.2684i	−0.395746	+	0.456716i
$845$	4.91211	−	10.7560i	0.168982	−	0.370019i
$846$	2.08937	+	0.613495i	0.0718341	+	0.0210924i
$847$	−9.51823	−	20.8420i	−0.327050	−	0.716140i
$848$	1.80935	+	12.5843i	0.0621334	+	0.432147i
$849$	5.16652	+	3.32032i	0.177315	+	0.113953i
$850$	3.33975			0.114553
$851$	39.1641	−	29.6573i	1.34253	−	1.01664i
$852$	14.4565			0.495272
$853$	28.1057	+	18.0624i	0.962320	+	0.618446i	0.924639	−	0.380844i	$-0.124367\pi$
$853$	28.1057	+	18.0624i	0.962320	+	0.618446i	0.0376810	+	0.999290i	$0.488003\pi$
$854$	1.09682	+	7.62858i	0.0375326	+	0.261045i
$855$	−1.74564	−	3.82241i	−0.0596995	−	0.130724i
$856$	−6.09224	−	1.78884i	−0.208228	−	0.0611414i
$857$	−11.8189	+	25.8797i	−0.403725	+	0.884035i	0.593154	+	0.805089i	$0.297883\pi$
$857$	−11.8189	+	25.8797i	−0.403725	+	0.884035i	−0.996879	+	0.0789455i	$0.974845\pi$
$858$	0.720120	−	0.831063i	0.0245845	−	0.0283720i
$859$	−4.96454	+	34.5291i	−0.169388	+	1.17812i	0.710766	+	0.703429i	$0.248349\pi$
$859$	−4.96454	+	34.5291i	−0.169388	+	1.17812i	−0.880153	+	0.474689i	$0.842560\pi$
$860$	−0.265217	+	0.0778748i	−0.00904383	+	0.00265551i
$861$	11.2705	+	13.0068i	0.384098	+	0.443272i
$862$	−9.97795	+	6.41244i	−0.339850	+	0.218409i
$863$	−11.1953	+	7.19481i	−0.381094	+	0.244914i	−0.717137	−	0.696933i	$-0.754548\pi$
$863$	−11.1953	+	7.19481i	−0.381094	+	0.244914i	0.336043	+	0.941847i	$0.390911\pi$
$864$	0.654861	+	0.755750i	0.0222788	+	0.0257111i
$865$	−0.257159	+	0.0755086i	−0.00874366	+	0.00256737i
$866$	1.05412	−	7.33158i	0.0358205	−	0.249137i
$867$	3.82835	−	4.41815i	0.130018	−	0.150048i
$868$	9.91697	−	21.7151i	0.336604	−	0.737060i
$869$	3.00223	+	0.881534i	0.101844	+	0.0299040i
$870$	2.28915	+	5.01253i	0.0776093	+	0.169941i
$871$	−0.198705	−	1.38203i	−0.00673288	−	0.0468282i
$872$	−12.5186	−	8.04525i	−0.423935	−	0.272446i
$873$	−14.7493			−0.499188
$874$	4.39263	+	19.6683i	0.148583	+	0.665289i
$875$	−2.29787			−0.0776823
$876$	6.10295	+	3.92213i	0.206200	+	0.132516i
$877$	6.43014	+	44.7226i	0.217130	+	1.51018i	0.748557	+	0.663071i	$0.230747\pi$
$877$	6.43014	+	44.7226i	0.217130	+	1.51018i	−0.531426	+	0.847105i	$0.678344\pi$
$878$	−4.86018	−	10.6423i	−0.164023	−	0.359161i
$879$	−28.1169	−	8.25586i	−0.948359	−	0.278463i
$880$	0.421351	−	0.922629i	0.0142037	−	0.0311018i
$881$	−9.10421	+	10.5068i	−0.306729	+	0.353984i	−0.888096	−	0.459657i	$-0.847972\pi$
$881$	−9.10421	+	10.5068i	−0.306729	+	0.353984i	0.581368	+	0.813641i	$0.302518\pi$
$882$	−0.244751	+	1.70228i	−0.00824119	+	0.0573187i
$883$	38.8901	−	11.4192i	1.30876	−	0.384286i	0.448333	−	0.893866i	$-0.352018\pi$
$883$	38.8901	−	11.4192i	1.30876	−	0.384286i	0.860423	+	0.509581i	$0.170200\pi$
$884$	−2.37114	−	2.73645i	−0.0797502	−	0.0920366i
$885$	3.69411	−	2.37406i	0.124176	−	0.0798032i
$886$	28.2468	−	18.1531i	0.948968	−	0.609865i
$887$	14.4916	+	16.7242i	0.486582	+	0.561545i	0.944949	−	0.327218i	$-0.106111\pi$
$887$	14.4916	+	16.7242i	0.486582	+	0.561545i	−0.458367	+	0.888763i	$0.651566\pi$
$888$	9.82859	−	2.88593i	0.329826	−	0.0968456i
$889$	0.0894340	−	0.622027i	0.00299952	−	0.0208621i
$890$	−3.21440	+	3.70962i	−0.107747	+	0.124347i
$891$	−0.421351	+	0.922629i	−0.0141158	+	0.0309092i
$892$	10.7318	+	3.15115i	0.359329	+	0.105508i
$893$	3.80126	+	8.32360i	0.127204	+	0.278539i
$894$	−0.00889840	−	0.0618898i	−0.000297607	−	0.00206990i
$895$	−11.6556	−	7.49063i	−0.389605	−	0.250384i
$896$	−2.29787			−0.0767665
$897$	−1.79005	+	4.88161i	−0.0597682	+	0.162992i
$898$	−34.3271			−1.14551
$899$	48.1603	+	30.9508i	1.60624	+	1.03227i
$900$	−0.142315	−	0.989821i	−0.00474383	−	0.0329940i
$901$	17.6388	+	38.6236i	0.587634	+	1.28674i
$902$	7.28906	+	2.14026i	0.242699	+	0.0712629i
$903$	−0.263857	+	0.577765i	−0.00878059	+	0.0192268i
$904$	−12.6777	+	14.6309i	−0.421655	+	0.486616i
$905$	0.901850	−	6.27251i	0.0299785	−	0.208505i
$906$	0.308501	−	0.0905840i	0.0102493	−	0.00300945i
$907$	14.2575	+	16.4540i	0.473411	+	0.546346i	0.941357	−	0.337411i	$-0.109551\pi$
$907$	14.2575	+	16.4540i	0.473411	+	0.546346i	−0.467946	+	0.883757i	$0.655006\pi$
$908$	0.731795	−	0.470296i	0.0242855	−	0.0156073i
$909$	−1.15268	+	0.740785i	−0.0382321	+	0.0245703i
$910$	1.63143	+	1.88277i	0.0540815	+	0.0624134i
$911$	−30.1732	+	8.85964i	−0.999682	+	0.293533i	−0.740325	−	0.672249i	$-0.765329\pi$
$911$	−30.1732	+	8.85964i	−0.999682	+	0.293533i	−0.259356	+	0.965782i	$0.583510\pi$
$912$	−0.598028	+	4.15938i	−0.0198027	+	0.137731i
$913$	9.86360	−	11.3832i	0.326438	−	0.376729i
$914$	11.0053	−	24.0982i	0.364022	−	0.797098i
$915$	3.21812	+	0.944927i	0.106388	+	0.0312383i
$916$	3.14566	+	6.88804i	0.103936	+	0.227587i
$917$	−0.745771	−	5.18695i	−0.0246275	−	0.171288i
$918$	2.80958	+	1.80561i	0.0927299	+	0.0595939i
$919$	30.3621			1.00155			0.500777	−	0.865576i	$-0.333048\pi$
$919$	30.3621			1.00155			0.500777	+	0.865576i	$0.333048\pi$
$920$	−0.315669	+	4.78543i	−0.0104073	+	0.157771i
$921$	3.30102			0.108772
$922$	7.41806	+	4.76730i	0.244301	+	0.157003i
$923$	2.23053	+	15.5137i	0.0734189	+	0.510640i
$924$	−0.968210	−	2.12008i	−0.0318518	−	0.0697456i
$925$	−9.82859	−	2.88593i	−0.323162	−	0.0948889i
$926$	−9.40764	+	20.5999i	−0.309154	+	0.676953i
$927$	2.22675	−	2.56981i	0.0731361	−	0.0844036i
$928$	0.784227	−	5.45442i	0.0257435	−	0.179050i
$929$	−20.6974	+	6.07731i	−0.679060	+	0.199390i	−0.603033	−	0.797716i	$-0.706041\pi$
$929$	−20.6974	+	6.07731i	−0.679060	+	0.199390i	−0.0760263	+	0.997106i	$0.524223\pi$
$930$	−6.80330	−	7.85143i	−0.223089	−	0.257459i
$931$	−6.07956	+	3.90710i	−0.199250	+	0.128050i
$932$	−7.12116	+	4.57649i	−0.233261	+	0.149908i
$933$	−17.5205	−	20.2197i	−0.573596	−	0.661965i
$934$	−5.38564	+	1.58137i	−0.176224	+	0.0517439i
$935$	0.482088	−	3.35299i	0.0157660	−	0.109655i
$936$	−0.709976	+	0.819356i	−0.0232063	+	0.0267815i
$937$	−8.34585	+	18.2749i	−0.272647	+	0.597014i	−0.995581	−	0.0939029i	$-0.970066\pi$
$937$	−8.34585	+	18.2749i	−0.272647	+	0.597014i	0.722934	+	0.690917i	$0.242793\pi$
$938$	−2.83944	−	0.833735i	−0.0927110	−	0.0272224i
$939$	−8.98855	−	19.6822i	−0.293330	−	0.642304i
$940$	0.309902	+	2.15541i	0.0101079	+	0.0703019i
$941$	6.70492	+	4.30899i	0.218574	+	0.140469i	0.645346	−	0.763890i	$-0.276713\pi$
$941$	6.70492	+	4.30899i	0.218574	+	0.140469i	−0.426772	+	0.904359i	$0.640349\pi$
$942$	1.73498			0.0565288
$943$	−35.8134	+	2.76059i	−1.16625	+	0.0898973i
$944$	−4.39120			−0.142921
$945$	−1.93309	−	1.24232i	−0.0628835	−	0.0404128i
$946$	0.0398999	+	0.277510i	0.00129726	+	0.00902262i
$947$	2.05819	+	4.50680i	0.0668821	+	0.146451i	0.940121	−	0.340841i	$-0.110712\pi$
$947$	2.05819	+	4.50680i	0.0668821	+	0.146451i	−0.873239	+	0.487292i	$0.837985\pi$
$948$	−2.95994	−	0.869116i	−0.0961343	−	0.0282276i
$949$	−3.26730	+	7.15440i	−0.106061	+	0.232242i
$950$	2.75182	−	3.17577i	0.0892809	−	0.103036i
$951$	3.07548	−	21.3904i	0.0997292	−	0.693632i
$952$	−7.36346	+	2.16211i	−0.238651	+	0.0700743i
$953$	19.7509	+	22.7937i	0.639793	+	0.738360i	0.979338	−	0.202229i	$-0.0648186\pi$
$953$	19.7509	+	22.7937i	0.639793	+	0.738360i	−0.339545	+	0.940590i	$0.610273\pi$
$954$	10.6955	−	6.87356i	0.346278	−	0.222540i
$955$	−8.20413	+	5.27248i	−0.265480	+	0.170613i
$956$	−6.83434	−	7.88724i	−0.221038	−	0.255092i
$957$	5.36284	−	1.57467i	0.173356	−	0.0509019i
$958$	−1.42648	+	9.92136i	−0.0460874	+	0.320545i
$959$	20.1727	−	23.2805i	0.651410	−	0.751767i
$960$	−0.415415	+	0.909632i	−0.0134075	+	0.0293582i
$961$	−73.8137	−	21.6737i	−2.38109	−	0.699150i
$962$	4.61345	+	10.1021i	0.148744	+	0.325703i
$963$	0.903619	+	6.28481i	0.0291187	+	0.202525i
$964$	−11.5506	−	7.42313i	−0.372020	−	0.239083i
$965$	0.495317			0.0159448
$966$	7.83544	+	7.74925i	0.252101	+	0.249328i
$967$	45.6742			1.46878			0.734392	−	0.678726i	$-0.237467\pi$
$967$	45.6742			1.46878			0.734392	+	0.678726i	$0.237467\pi$
$968$	8.38832	+	5.39085i	0.269611	+	0.173268i
$969$	1.99727	+	13.8913i	0.0641615	+	0.446253i
$970$	−6.12708	−	13.4164i	−0.196729	−	0.430776i
$971$	24.5862	+	7.21916i	0.789008	+	0.231674i	0.651321	−	0.758802i	$-0.274215\pi$
$971$	24.5862	+	7.21916i	0.789008	+	0.231674i	0.137687	+	0.990476i	$0.456033\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	26.9694	−	31.1243i	0.864598	−	0.997799i
$974$	5.28839	−	36.7816i	0.169451	−	1.17856i
$975$	1.04025	−	0.305444i	0.0333146	−	0.00978204i
$976$	−2.19639	−	2.53477i	−0.0703048	−	0.0811361i
$977$	−13.8088	+	8.87435i	−0.441781	+	0.283916i	−0.742562	−	0.669778i	$-0.766389\pi$
$977$	−13.8088	+	8.87435i	−0.441781	+	0.283916i	0.300780	+	0.953693i	$0.402753\pi$
$978$	−11.4080	+	7.33150i	−0.364789	+	0.234436i
$979$	3.26033	+	3.76262i	0.104201	+	0.120254i
$980$	−1.65012	+	0.484519i	−0.0527112	+	0.0154774i
$981$	−2.11778	+	14.7295i	−0.0676155	+	0.470276i
$982$	−18.7113	+	21.5940i	−0.597101	+	0.689091i
$983$	1.16654	−	2.55437i	0.0372068	−	0.0814716i	−0.890116	−	0.455734i	$-0.849377\pi$
$983$	1.16654	−	2.55437i	0.0372068	−	0.0814716i	0.927323	+	0.374262i	$0.122104\pi$
$984$	−7.18638	−	2.11011i	−0.229093	−	0.0672679i
$985$	−5.46173	−	11.9595i	−0.174025	−	0.381062i
$986$	−2.61912	−	18.2164i	−0.0834099	−	0.580129i
$987$	4.20946	+	2.70526i	0.133989	+	0.0861093i
$988$	−4.55582			−0.144940
$989$	−0.641734	−	1.15995i	−0.0204060	−	0.0368843i
$990$	−1.01429			−0.0322362
$991$	−3.15824	−	2.02968i	−0.100325	−	0.0644749i	0.489516	−	0.871994i	$-0.337173\pi$
$991$	−3.15824	−	2.02968i	−0.100325	−	0.0644749i	−0.589841	+	0.807519i	$0.700810\pi$
$992$	1.47850	+	10.2832i	0.0469424	+	0.326492i
$993$	2.68958	+	5.88936i	0.0853513	+	0.186893i
$994$	31.8736	+	9.35894i	1.01097	+	0.296848i
$995$	7.77900	−	17.0336i	0.246611	−	0.540002i
$996$	−9.72465	+	11.2228i	−0.308137	+	0.355610i
$997$	8.88242	−	61.7786i	0.281309	−	1.95655i	−0.0100997	−	0.999949i	$-0.503215\pi$
$997$	8.88242	−	61.7786i	0.281309	−	1.95655i	0.291409	−	0.956599i	$-0.405876\pi$
$998$	−30.8566	+	9.06031i	−0.976748	+	0.286799i
$999$	−6.70808	−	7.74154i	−0.212234	−	0.244931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.301.1	✓	30
23.12	even	11	inner	690.2.m.h.541.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.301.1	✓	30	1.1	even	1	trivial
690.2.m.h.541.1	yes	30	23.12	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.50479 + 1.73662i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(-0.142315 - 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.50479 + 1.73662i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.853274 + 0.548366i) q^{11} +(0.841254 - 0.540641i) q^{12} +(0.709976 + 0.819356i) q^{13} +(2.20479 - 0.647385i) q^{14} +(0.142315 - 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.38738 + 3.03795i) q^{17} +(0.959493 + 0.281733i) q^{18} +(1.74564 + 3.82241i) q^{19} +(0.142315 + 0.989821i) q^{20} +(1.93309 + 1.24232i) q^{21} +1.01429 q^{22} +(-4.48412 + 1.70080i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.154292 - 1.07313i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.20479 - 0.647385i) q^{28} +(2.28915 - 5.01253i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(-1.47850 + 10.2832i) q^{31} +(0.959493 - 0.281733i) q^{32} +(0.664218 + 0.766548i) q^{33} +(2.80958 - 1.80561i) q^{34} +(-1.93309 + 1.24232i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-9.82859 + 2.88593i) q^{37} +(0.598028 - 4.15938i) q^{38} +(0.709976 - 0.819356i) q^{39} +(0.415415 - 0.909632i) q^{40} +(7.18638 + 2.11011i) q^{41} +(-0.954571 - 2.09022i) q^{42} +(0.0393378 + 0.273600i) q^{43} +(-0.853274 - 0.548366i) q^{44} -1.00000 q^{45} +(4.69180 + 0.993494i) q^{46} +2.17758 q^{47} +(0.841254 + 0.540641i) q^{48} +(0.244751 + 1.70228i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(3.20447 + 0.940917i) q^{51} +(-0.450378 + 0.986189i) q^{52} +(8.32572 - 9.60839i) q^{53} +(0.142315 - 0.989821i) q^{54} +(-0.973203 + 0.285758i) q^{55} +(1.50479 + 1.73662i) q^{56} +(3.53507 - 2.27185i) q^{57} +(-4.63573 + 2.97920i) q^{58} +(2.87562 + 3.31865i) q^{59} +(0.959493 - 0.281733i) q^{60} +(-0.477322 + 3.31985i) q^{61} +(6.80330 - 7.85143i) q^{62} +(0.954571 - 2.09022i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.450378 + 0.986189i) q^{65} +(-0.144348 - 1.00396i) q^{66} +(-1.08341 - 0.696264i) q^{67} -3.33975 q^{68} +(2.32164 + 4.19642i) q^{69} +2.29787 q^{70} +(12.1616 + 7.81579i) q^{71} +(0.142315 + 0.989821i) q^{72} +(3.01367 + 6.59901i) q^{73} +(9.82859 + 2.88593i) q^{74} +(0.415415 - 0.909632i) q^{75} +(-2.75182 + 3.17577i) q^{76} +(0.331694 - 2.30698i) q^{77} +(-1.04025 + 0.305444i) q^{78} +(-2.02018 - 2.33141i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-4.90475 - 5.66039i) q^{82} +(-14.2484 + 4.18372i) q^{83} +(-0.327021 + 2.27448i) q^{84} +(-2.18707 + 2.52402i) q^{85} +(0.114826 - 0.251435i) q^{86} +(-5.28729 - 1.55249i) q^{87} +(0.421351 + 0.922629i) q^{88} +(-0.698556 - 4.85857i) q^{89} +(0.841254 + 0.540641i) q^{90} -2.49127 q^{91} +(-3.40987 - 3.37236i) q^{92} +10.3889 q^{93} +(-1.83190 - 1.17729i) q^{94} +(0.598028 + 4.15938i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(14.1518 + 4.15536i) q^{97} +(0.714424 - 1.56437i) q^{98} +(0.664218 - 0.766548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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