LMFDB - Embedded newform 690.2.m.d.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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			301.1
Root			$3.40070 - 0.998536i$ of defining polynomial
Character	$\chi$	$=$	690.301
Dual form			690.2.m.d.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.67997 + 1.93879i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(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} +(-1.67997 + 1.93879i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.654861 + 0.755750i) q^{10} +(-2.76610 + 1.77766i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-0.430994 - 0.497394i) q^{13} +(-2.46147 + 0.722751i) q^{14} +(-0.142315 + 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.0578863 - 0.126753i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(1.15549 + 2.53016i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-2.15814 - 1.38695i) q^{21} -3.28807 q^{22} +(0.901053 + 4.71042i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.0936640 - 0.651448i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-2.46147 - 0.722751i) q^{28} +(1.89762 - 4.15522i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(0.109859 - 0.764087i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-2.15323 - 2.48495i) q^{33} +(0.117225 - 0.0753360i) q^{34} +(-2.15814 + 1.38695i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(3.95770 - 1.16208i) q^{37} +(-0.395852 + 2.75321i) q^{38} +(0.430994 - 0.497394i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-1.26148 - 0.370403i) q^{41} +(-1.06570 - 2.33355i) q^{42} +(0.230800 + 1.60525i) q^{43} +(-2.76610 - 1.77766i) q^{44} -1.00000 q^{45} +(-1.78863 + 4.44981i) q^{46} +11.5007 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.0596044 + 0.414558i) q^{49} +(0.415415 + 0.909632i) q^{50} +(0.133701 + 0.0392582i) q^{51} +(0.273404 - 0.598671i) q^{52} +(-1.71849 + 1.98324i) q^{53} +(0.142315 - 0.989821i) q^{54} +(-3.15488 + 0.926355i) q^{55} +(-1.67997 - 1.93879i) q^{56} +(-2.33997 + 1.50381i) q^{57} +(3.84286 - 2.46966i) q^{58} +(-2.61938 - 3.02292i) q^{59} +(-0.959493 + 0.281733i) q^{60} +(-0.0859029 + 0.597468i) q^{61} +(0.505516 - 0.583396i) q^{62} +(1.06570 - 2.33355i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.273404 - 0.598671i) q^{65} +(-0.467941 - 3.25460i) q^{66} +(9.14743 + 5.87870i) q^{67} +0.139346 q^{68} +(-4.53425 + 1.56225i) q^{69} -2.56538 q^{70} +(-9.47019 - 6.08612i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-0.989072 - 2.16577i) q^{73} +(3.95770 + 1.16208i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(-1.82151 + 2.10214i) q^{76} +(1.20045 - 8.34928i) q^{77} +(0.631487 - 0.185421i) q^{78} +(7.89859 + 9.11546i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-0.860967 - 0.993609i) q^{82} +(-1.26997 + 0.372896i) q^{83} +(0.365092 - 2.53927i) q^{84} +(0.0912520 - 0.105310i) q^{85} +(-0.673701 + 1.47520i) q^{86} +(4.38298 + 1.28696i) q^{87} +(-1.36591 - 2.99093i) q^{88} +(-2.22071 - 15.4454i) q^{89} +(-0.841254 - 0.540641i) q^{90} +1.68840 q^{91} +(-3.91044 + 2.77641i) q^{92} +0.771944 q^{93} +(9.67499 + 6.21774i) q^{94} +(0.395852 + 2.75321i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(14.2780 + 4.19239i) q^{97} +(-0.173984 + 0.380973i) q^{98} +(2.15323 - 2.48495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * 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
$7$	−1.67997	+	1.93879i	−0.634968	+	0.732792i	−0.978477	−	0.206357i	$-0.933839\pi$
$7$	−1.67997	+	1.93879i	−0.634968	+	0.732792i	0.343509	+	0.939149i	$0.388384\pi$
$8$	−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
$11$	−2.76610	+	1.77766i	−0.834010	+	0.535985i	−0.886550	−	0.462633i	$-0.846905\pi$
$11$	−2.76610	+	1.77766i	−0.834010	+	0.535985i	0.0525400	+	0.998619i	$0.483268\pi$
$12$	−0.841254	+	0.540641i	−0.242849	+	0.156070i
$13$	−0.430994	−	0.497394i	−0.119536	−	0.137952i	0.692827	−	0.721104i	$-0.256365\pi$
$13$	−0.430994	−	0.497394i	−0.119536	−	0.137952i	−0.812363	+	0.583151i	$0.801819\pi$
$14$	−2.46147	+	0.722751i	−0.657854	+	0.193163i
$15$	−0.142315	+	0.989821i	−0.0367455	+	0.255571i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	0.0578863	−	0.126753i	0.0140395	−	0.0307422i	−0.902482	−	0.430727i	$-0.858257\pi$
$17$	0.0578863	−	0.126753i	0.0140395	−	0.0307422i	0.916522	+	0.399985i	$0.130985\pi$
$18$	−0.959493	−	0.281733i	−0.226155	−	0.0664050i
$19$	1.15549	+	2.53016i	0.265087	+	0.580459i	0.994632	−	0.103473i	$-0.0329956\pi$
$19$	1.15549	+	2.53016i	0.265087	+	0.580459i	−0.729545	+	0.683932i	$0.760268\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−2.15814	−	1.38695i	−0.470944	−	0.302657i
$22$	−3.28807			−0.701018
$23$	0.901053	+	4.71042i	0.187883	+	0.982192i
$23$	0.901053	+	4.71042i	0.187883	+	0.982192i
$24$	−1.00000			−0.204124
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.0936640	−	0.651448i	−0.0183690	−	0.127759i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−2.46147	−	0.722751i	−0.465173	−	0.136587i
$29$	1.89762	−	4.15522i	0.352380	−	0.771605i	−0.647574	−	0.762003i	$-0.724216\pi$
$29$	1.89762	−	4.15522i	0.352380	−	0.771605i	0.999954	−	0.00960200i	$-0.00305646\pi$
$30$	−0.654861	+	0.755750i	−0.119561	+	0.137980i
$31$	0.109859	−	0.764087i	0.0197313	−	0.137234i	−0.977575	−	0.210589i	$-0.932462\pi$
$31$	0.109859	−	0.764087i	0.0197313	−	0.137234i	0.997306	+	0.0733555i	$0.0233708\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−2.15323	−	2.48495i	−0.374828	−	0.432575i
$34$	0.117225	−	0.0753360i	0.0201039	−	0.0129200i
$35$	−2.15814	+	1.38695i	−0.364792	+	0.234437i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	3.95770	−	1.16208i	0.650641	−	0.191046i	0.0602760	−	0.998182i	$-0.480802\pi$
$37$	3.95770	−	1.16208i	0.650641	−	0.191046i	0.590365	+	0.807136i	$0.298984\pi$
$38$	−0.395852	+	2.75321i	−0.0642157	+	0.446630i
$39$	0.430994	−	0.497394i	0.0690143	−	0.0796468i
$40$	−0.415415	+	0.909632i	−0.0656829	+	0.143825i
$41$	−1.26148	−	0.370403i	−0.197010	−	0.0578472i	0.181739	−	0.983347i	$-0.441827\pi$
$41$	−1.26148	−	0.370403i	−0.197010	−	0.0578472i	−0.378749	+	0.925500i	$0.623646\pi$
$42$	−1.06570	−	2.33355i	−0.164441	−	0.360075i
$43$	0.230800	+	1.60525i	0.0351966	+	0.244798i	0.999823	−	0.0188236i	$-0.00599208\pi$
$43$	0.230800	+	1.60525i	0.0351966	+	0.244798i	−0.964626	+	0.263622i	$0.915083\pi$
$44$	−2.76610	−	1.77766i	−0.417005	−	0.267993i
$45$	−1.00000			−0.149071
$46$	−1.78863	+	4.44981i	−0.263720	+	0.656088i
$47$	11.5007			1.67755			0.838774	−	0.544480i	$-0.183273\pi$
$47$	11.5007			1.67755			0.838774	+	0.544480i	$0.183273\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	0.0596044	+	0.414558i	0.00851491	+	0.0592225i
$50$	0.415415	+	0.909632i	0.0587486	+	0.128641i
$51$	0.133701	+	0.0392582i	0.0187219	+	0.00549725i
$52$	0.273404	−	0.598671i	0.0379143	−	0.0830208i
$53$	−1.71849	+	1.98324i	−0.236053	+	0.272420i	−0.861400	−	0.507927i	$-0.830412\pi$
$53$	−1.71849	+	1.98324i	−0.236053	+	0.272420i	0.625347	+	0.780347i	$0.284957\pi$
$54$	0.142315	−	0.989821i	0.0193666	−	0.134698i
$55$	−3.15488	+	0.926355i	−0.425403	+	0.124910i
$56$	−1.67997	−	1.93879i	−0.224495	−	0.259081i
$57$	−2.33997	+	1.50381i	−0.309936	+	0.199184i
$58$	3.84286	−	2.46966i	0.504593	−	0.324282i
$59$	−2.61938	−	3.02292i	−0.341014	−	0.393551i	0.559176	−	0.829049i	$-0.311118\pi$
$59$	−2.61938	−	3.02292i	−0.341014	−	0.393551i	−0.900190	+	0.435498i	$0.856572\pi$
$60$	−0.959493	+	0.281733i	−0.123870	+	0.0363715i
$61$	−0.0859029	+	0.597468i	−0.0109987	+	0.0764980i	−0.994582	−	0.103960i	$-0.966849\pi$
$61$	−0.0859029	+	0.597468i	−0.0109987	+	0.0764980i	0.983583	+	0.180458i	$0.0577578\pi$
$62$	0.505516	−	0.583396i	0.0642006	−	0.0740914i
$63$	1.06570	−	2.33355i	0.134265	−	0.294000i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−0.273404	−	0.598671i	−0.0339116	−	0.0742560i
$66$	−0.467941	−	3.25460i	−0.0575995	−	0.400613i
$67$	9.14743	+	5.87870i	1.11754	+	0.718197i	0.962923	−	0.269778i	$-0.0869503\pi$
$67$	9.14743	+	5.87870i	1.11754	+	0.718197i	0.154614	+	0.987975i	$0.450587\pi$
$68$	0.139346			0.0168982
$69$	−4.53425	+	1.56225i	−0.545859	+	0.188072i
$70$	−2.56538			−0.306622
$71$	−9.47019	−	6.08612i	−1.12390	−	0.722290i	−0.159626	−	0.987178i	$-0.551029\pi$
$71$	−9.47019	−	6.08612i	−1.12390	−	0.722290i	−0.964279	+	0.264888i	$0.914665\pi$
$72$	−0.142315	−	0.989821i	−0.0167720	−	0.116652i
$73$	−0.989072	−	2.16577i	−0.115762	−	0.253484i	0.842878	−	0.538105i	$-0.180860\pi$
$73$	−0.989072	−	2.16577i	−0.115762	−	0.253484i	−0.958640	+	0.284621i	$0.908132\pi$
$74$	3.95770	+	1.16208i	0.460073	+	0.135090i
$75$	−0.415415	+	0.909632i	−0.0479680	+	0.105035i
$76$	−1.82151	+	2.10214i	−0.208942	+	0.241132i
$77$	1.20045	−	8.34928i	0.136804	−	0.951489i
$78$	0.631487	−	0.185421i	0.0715018	−	0.0209948i
$79$	7.89859	+	9.11546i	0.888661	+	1.02557i	0.999496	+	0.0317308i	$0.0101019\pi$
$79$	7.89859	+	9.11546i	0.888661	+	1.02557i	−0.110835	+	0.993839i	$0.535353\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	−0.860967	−	0.993609i	−0.0950779	−	0.109726i
$83$	−1.26997	+	0.372896i	−0.139397	+	0.0409307i	−0.350687	−	0.936493i	$-0.614052\pi$
$83$	−1.26997	+	0.372896i	−0.139397	+	0.0409307i	0.211290	+	0.977423i	$0.432234\pi$
$84$	0.365092	−	2.53927i	0.0398348	−	0.277057i
$85$	0.0912520	−	0.105310i	0.00989767	−	0.0114225i
$86$	−0.673701	+	1.47520i	−0.0726471	+	0.159075i
$87$	4.38298	+	1.28696i	0.469905	+	0.137977i
$88$	−1.36591	−	2.99093i	−0.145607	−	0.318834i
$89$	−2.22071	−	15.4454i	−0.235395	−	1.63721i	−0.674145	−	0.738599i	$-0.735488\pi$
$89$	−2.22071	−	15.4454i	−0.235395	−	1.63721i	0.438750	−	0.898609i	$-0.355421\pi$
$90$	−0.841254	−	0.540641i	−0.0886759	−	0.0569885i
$91$	1.68840			0.176992
$92$	−3.91044	+	2.77641i	−0.407692	+	0.289461i
$93$	0.771944			0.0800469
$94$	9.67499	+	6.21774i	0.997899	+	0.641311i
$95$	0.395852	+	2.75321i	0.0406136	+	0.282474i
$96$	−0.415415	−	0.909632i	−0.0423981	−	0.0928389i
$97$	14.2780	+	4.19239i	1.44971	+	0.425673i	0.909445	−	0.415824i	$-0.136507\pi$
$97$	14.2780	+	4.19239i	1.44971	+	0.425673i	0.540263	+	0.841496i	$0.318325\pi$
$98$	−0.173984	+	0.380973i	−0.0175751	+	0.0384840i
$99$	2.15323	−	2.48495i	0.216407	−	0.249747i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	−0.403921	+	0.118602i	−0.0401917	+	0.0118013i	−0.301767	−	0.953382i	$-0.597576\pi$
$101$	−0.403921	+	0.118602i	−0.0401917	+	0.0118013i	0.261575	+	0.965183i	$0.415758\pi$
$102$	0.0912520	+	0.105310i	0.00903530	+	0.0104273i
$103$	−9.44613	+	6.07066i	−0.930755	+	0.598160i	−0.915759	−	0.401728i	$-0.868410\pi$
$103$	−9.44613	+	6.07066i	−0.930755	+	0.598160i	−0.0149958	+	0.999888i	$0.504773\pi$
$104$	0.553668	−	0.355821i	0.0542916	−	0.0348911i
$105$	−1.67997	−	1.93879i	−0.163948	−	0.189206i
$106$	−2.51791	+	0.739325i	−0.244561	+	0.0718096i
$107$	1.65305	−	11.4972i	0.159806	−	1.11148i	−0.739182	−	0.673506i	$-0.764788\pi$
$107$	1.65305	−	11.4972i	0.159806	−	1.11148i	0.898988	−	0.437973i	$-0.144303\pi$
$108$	0.654861	−	0.755750i	0.0630140	−	0.0727220i
$109$	2.09921	−	4.59662i	0.201067	−	0.440276i	−0.782059	−	0.623205i	$-0.785830\pi$
$109$	2.09921	−	4.59662i	0.201067	−	0.440276i	0.983126	+	0.182928i	$0.0585577\pi$
$110$	−3.15488	−	0.926355i	−0.300806	−	0.0883245i
$111$	1.71350	+	3.75203i	0.162638	+	0.356127i
$112$	−0.365092	−	2.53927i	−0.0344979	−	0.239938i
$113$	4.60488	+	2.95938i	0.433191	+	0.278395i	0.739009	−	0.673695i	$-0.235294\pi$
$113$	4.60488	+	2.95938i	0.433191	+	0.278395i	−0.305819	+	0.952090i	$0.598930\pi$
$114$	−2.78152			−0.260514
$115$	−0.462526	+	4.77348i	−0.0431308	+	0.445129i
$116$	4.56802			0.424130
$117$	0.553668	+	0.355821i	0.0511866	+	0.0328957i
$118$	−0.569245	−	3.95919i	−0.0524033	−	0.364473i
$119$	0.148500	+	0.325171i	0.0136130	+	0.0298083i
$120$	−0.959493	−	0.281733i	−0.0875893	−	0.0257185i
$121$	−0.0783560	+	0.171576i	−0.00712328	+	0.0155978i
$122$	−0.395282	+	0.456180i	−0.0357871	+	0.0413006i
$123$	0.187106	−	1.30135i	0.0168708	−	0.117339i
$124$	0.740675	−	0.217482i	0.0665146	−	0.0195304i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	2.15814	−	1.38695i	0.192262	−	0.123559i
$127$	9.15551	−	5.88389i	0.812421	−	0.522111i	−0.0672266	−	0.997738i	$-0.521415\pi$
$127$	9.15551	−	5.88389i	0.812421	−	0.522111i	0.879647	+	0.475627i	$0.157779\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−1.55606	+	0.456901i	−0.137004	+	0.0402279i
$130$	0.0936640	−	0.651448i	0.00821488	−	0.0571357i
$131$	1.83950	−	2.12289i	0.160718	−	0.185478i	−0.669679	−	0.742651i	$-0.733568\pi$
$131$	1.83950	−	2.12289i	0.160718	−	0.185478i	0.830397	+	0.557173i	$0.188114\pi$
$132$	1.36591	−	2.99093i	0.118887	−	0.260327i
$133$	−6.84663	−	2.01035i	−0.593678	−	0.174319i
$134$	4.51704	+	9.89095i	0.390213	+	0.854448i
$135$	−0.142315	−	0.989821i	−0.0122485	−	0.0851903i
$136$	0.117225	+	0.0753360i	0.0100520	+	0.00646001i
$137$	11.1059			0.948843			0.474422	−	0.880298i	$-0.342657\pi$
$137$	11.1059			0.948843			0.474422	+	0.880298i	$0.342657\pi$
$138$	−4.65906	−	1.13715i	−0.396606	−	0.0968010i
$139$	15.3683			1.30352			0.651760	−	0.758425i	$-0.274031\pi$
$139$	15.3683			1.30352			0.651760	+	0.758425i	$0.274031\pi$
$140$	−2.15814	−	1.38695i	−0.182396	−	0.117219i
$141$	1.63672	+	11.3836i	0.137837	+	0.958674i
$142$	−4.67642	−	10.2399i	−0.392437	−	0.859317i
$143$	2.07637	+	0.609678i	0.173635	+	0.0509838i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	2.99142	−	3.45228i	0.248424	−	0.286696i
$146$	0.338841	−	2.35669i	0.0280427	−	0.195041i
$147$	−0.401855	+	0.117995i	−0.0331445	+	0.00973209i
$148$	2.70116	+	3.11730i	0.222034	+	0.256240i
$149$	7.42977	−	4.77482i	0.608671	−	0.391169i	−0.199688	−	0.979860i	$-0.563993\pi$
$149$	7.42977	−	4.77482i	0.608671	−	0.391169i	0.808358	+	0.588691i	$0.200356\pi$
$150$	−0.841254	+	0.540641i	−0.0686881	+	0.0441431i
$151$	0.727083	+	0.839099i	0.0591692	+	0.0682849i	0.784563	−	0.620050i	$-0.212888\pi$
$151$	0.727083	+	0.839099i	0.0591692	+	0.0682849i	−0.725393	+	0.688335i	$0.758342\pi$
$152$	−2.66885	+	0.783646i	−0.216473	+	0.0635621i
$153$	−0.0198310	+	0.137927i	−0.00160324	+	0.0111508i
$154$	5.52384	−	6.37486i	0.445124	−	0.513700i
$155$	0.320677	−	0.702185i	0.0257574	−	0.0564009i
$156$	0.631487	+	0.185421i	0.0505594	+	0.0148456i
$157$	3.07285	+	6.72860i	0.245240	+	0.537001i	0.991722	−	0.128405i	$-0.0409858\pi$
$157$	3.07285	+	6.72860i	0.245240	+	0.537001i	−0.746482	+	0.665406i	$0.768259\pi$
$158$	1.71653	+	11.9387i	0.136560	+	0.949793i
$159$	−2.20762	−	1.41875i	−0.175076	−	0.112515i
$160$	−1.00000			−0.0790569
$161$	−10.6462	−	6.16641i	−0.839042	−	0.485981i
$162$	1.00000			0.0785674
$163$	15.7121	+	10.0975i	1.23066	+	0.790900i	0.983994	−	0.178199i	$-0.0570272\pi$
$163$	15.7121	+	10.0975i	1.23066	+	0.790900i	0.246670	+	0.969099i	$0.420664\pi$
$164$	−0.187106	−	1.30135i	−0.0146105	−	0.101618i
$165$	−1.36591	−	2.99093i	−0.106336	−	0.232844i
$166$	−1.26997	−	0.372896i	−0.0985686	−	0.0289424i
$167$	7.03416	−	15.4027i	0.544320	−	1.19189i	−0.415065	−	0.909792i	$-0.636241\pi$
$167$	7.03416	−	15.4027i	0.544320	−	1.19189i	0.959384	−	0.282102i	$-0.0910317\pi$
$168$	1.67997	−	1.93879i	0.129612	−	0.149581i
$169$	1.78845	−	12.4389i	0.137573	−	0.956841i
$170$	0.133701	−	0.0392582i	0.0102544	−	0.00301097i
$171$	−1.82151	−	2.10214i	−0.139294	−	0.160754i
$172$	−1.36431	+	0.876787i	−0.104027	+	0.0668544i
$173$	1.25843	−	0.808746i	0.0956770	−	0.0614878i	−0.491927	−	0.870636i	$-0.663707\pi$
$173$	1.25843	−	0.808746i	0.0956770	−	0.0614878i	0.587604	+	0.809148i	$0.300071\pi$
$174$	2.99142	+	3.45228i	0.226779	+	0.261717i
$175$	−2.46147	+	0.722751i	−0.186069	+	0.0546349i
$176$	0.467941	−	3.25460i	0.0352723	−	0.245325i
$177$	2.61938	−	3.02292i	0.196884	−	0.227217i
$178$	6.48223	−	14.1941i	0.485864	−	1.06389i
$179$	−21.5425	−	6.32546i	−1.61016	−	0.472787i	−0.651813	−	0.758379i	$-0.725992\pi$
$179$	−21.5425	−	6.32546i	−1.61016	−	0.472787i	−0.958351	+	0.285592i	$0.907810\pi$
$180$	−0.415415	−	0.909632i	−0.0309632	−	0.0678000i
$181$	1.29533	+	9.00920i	0.0962810	+	0.669649i	0.979612	+	0.200899i	$0.0643863\pi$
$181$	1.29533	+	9.00920i	0.0962810	+	0.669649i	−0.883331	+	0.468750i	$0.844705\pi$
$182$	1.42037	+	0.912816i	0.105285	+	0.0676625i
$183$	−0.603612			−0.0446203
$184$	−4.79071	+	0.221518i	−0.353176	+	0.0163305i
$185$	4.12478			0.303260
$186$	0.649401	+	0.417344i	0.0476164	+	0.0306012i
$187$	0.0652055	+	0.453514i	0.00476830	+	0.0331643i
$188$	4.77756	+	10.4614i	0.348439	+	0.762975i
$189$	2.46147	+	0.722751i	0.179045	+	0.0525724i
$190$	−1.15549	+	2.53016i	−0.0838278	+	0.183557i
$191$	−13.8138	+	15.9420i	−0.999532	+	1.15352i	−0.0113962	+	0.999935i	$0.503628\pi$
$191$	−13.8138	+	15.9420i	−0.999532	+	1.15352i	−0.988135	+	0.153586i	$0.950918\pi$
$192$	0.142315	−	0.989821i	0.0102707	−	0.0714342i
$193$	−17.7636	+	5.21586i	−1.27865	+	0.375446i	−0.849405	−	0.527742i	$-0.823039\pi$
$193$	−17.7636	+	5.21586i	−1.27865	+	0.375446i	−0.429246	+	0.903188i	$0.641221\pi$
$194$	9.74482	+	11.2461i	0.699637	+	0.807424i
$195$	0.553668	−	0.355821i	0.0396490	−	0.0254809i
$196$	−0.352334	+	0.226431i	−0.0251667	+	0.0161737i
$197$	−3.73869	−	4.31468i	−0.266371	−	0.307408i	0.606769	−	0.794878i	$-0.292465\pi$
$197$	−3.73869	−	4.31468i	−0.266371	−	0.307408i	−0.873140	+	0.487470i	$0.837920\pi$
$198$	3.15488	−	0.926355i	0.224207	−	0.0658332i
$199$	0.194025	−	1.34947i	0.0137541	−	0.0956617i	−0.981788	−	0.189979i	$-0.939158\pi$
$199$	0.194025	−	1.34947i	0.0137541	−	0.0956617i	0.995542	+	0.0943177i	$0.0300670\pi$
$200$	−0.654861	+	0.755750i	−0.0463056	+	0.0534396i
$201$	−4.51704	+	9.89095i	−0.318608	+	0.697654i
$202$	−0.403921	−	0.118602i	−0.0284198	−	0.00834480i
$203$	4.86813	+	10.6597i	0.341676	+	0.748166i
$204$	0.0198310	+	0.137927i	0.00138845	+	0.00965685i
$205$	−1.10602	−	0.710798i	−0.0772480	−	0.0496443i
$206$	−11.2286			−0.782336
$207$	−2.19163	−	4.26576i	−0.152329	−	0.296491i
$208$	0.658147			0.0456343
$209$	−7.69397	−	4.94461i	−0.532203	−	0.342026i
$210$	−0.365092	−	2.53927i	−0.0251937	−	0.175226i
$211$	−4.52174	−	9.90123i	−0.311289	−	0.681629i	0.687727	−	0.725969i	$-0.258609\pi$
$211$	−4.52174	−	9.90123i	−0.311289	−	0.681629i	−0.999016	+	0.0443407i	$0.985881\pi$
$212$	−2.51791	−	0.739325i	−0.172931	−	0.0507771i
$213$	4.67642	−	10.2399i	0.320423	−	0.701629i
$214$	7.60650	−	8.77837i	0.519970	−	0.600077i
$215$	−0.230800	+	1.60525i	−0.0157404	+	0.109477i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	1.29684	+	1.49663i	0.0880353	+	0.101598i
$218$	4.25108	−	2.73201i	0.287920	−	0.185035i
$219$	2.00296	−	1.28723i	0.135348	−	0.0869826i
$220$	−2.15323	−	2.48495i	−0.145170	−	0.167536i
$221$	−0.0879950	+	0.0258377i	−0.00591919	+	0.00173803i
$222$	−0.587017	+	4.08279i	−0.0393980	+	0.274019i
$223$	0.609548	−	0.703456i	0.0408183	−	0.0471069i	−0.734973	−	0.678096i	$-0.762805\pi$
$223$	0.609548	−	0.703456i	0.0408183	−	0.0471069i	0.775792	+	0.630989i	$0.217351\pi$
$224$	1.06570	−	2.33355i	0.0712049	−	0.155917i
$225$	−0.959493	−	0.281733i	−0.0639662	−	0.0187822i
$226$	2.27391	+	4.97917i	0.151258	+	0.331210i
$227$	2.17190	+	15.1059i	0.144154	+	1.00261i	0.925563	+	0.378594i	$0.123592\pi$
$227$	2.17190	+	15.1059i	0.144154	+	1.00261i	−0.781409	+	0.624020i	$0.785498\pi$
$228$	−2.33997	−	1.50381i	−0.154968	−	0.0995920i
$229$	−0.346499			−0.0228973			−0.0114487	−	0.999934i	$-0.503644\pi$
$229$	−0.346499			−0.0228973			−0.0114487	+	0.999934i	$0.503644\pi$
$230$	−2.96984	+	3.76564i	−0.195825	+	0.248299i
$231$	8.43514			0.554992
$232$	3.84286	+	2.46966i	0.252296	+	0.162141i
$233$	−2.49449	−	17.3496i	−0.163419	−	1.13661i	−0.892128	−	0.451783i	$-0.850788\pi$
$233$	−2.49449	−	17.3496i	−0.163419	−	1.13661i	0.728709	−	0.684824i	$-0.240121\pi$
$234$	0.273404	+	0.598671i	0.0178730	+	0.0391364i
$235$	11.0348	+	3.24012i	0.719833	+	0.211362i
$236$	1.66162	−	3.63844i	0.108162	−	0.236842i
$237$	−7.89859	+	9.11546i	−0.513069	+	0.592113i
$238$	−0.0508740	+	0.353836i	−0.00329767	+	0.0229358i
$239$	−19.3808	+	5.69073i	−1.25364	+	0.368103i	−0.840124	−	0.542394i	$-0.817518\pi$
$239$	−19.3808	+	5.69073i	−1.25364	+	0.368103i	−0.413518	+	0.910496i	$0.635700\pi$
$240$	−0.654861	−	0.755750i	−0.0422711	−	0.0487834i
$241$	−15.6564	+	10.0617i	−1.00852	+	0.648134i	−0.937009	−	0.349306i	$-0.886417\pi$
$241$	−15.6564	+	10.0617i	−1.00852	+	0.648134i	−0.0715078	+	0.997440i	$0.522781\pi$
$242$	−0.158678	+	0.101976i	−0.0102002	+	0.00655528i
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$	−0.579161	+	0.170057i	−0.0370770	+	0.0108868i
$245$	−0.0596044	+	0.414558i	−0.00380798	+	0.0264851i
$246$	0.860967	−	0.993609i	0.0548932	−	0.0633502i
$247$	0.760480	−	1.66522i	0.0483882	−	0.105955i
$248$	0.740675	+	0.217482i	0.0470329	+	0.0138101i
$249$	−0.549836	−	1.20397i	−0.0348444	−	0.0762987i
$250$	0.142315	+	0.989821i	0.00900078	+	0.0626018i
$251$	−8.95597	−	5.75565i	−0.565296	−	0.363294i	0.226564	−	0.973996i	$-0.427251\pi$
$251$	−8.95597	−	5.75565i	−0.565296	−	0.363294i	−0.791860	+	0.610703i	$0.790887\pi$
$252$	2.56538			0.161604
$253$	−10.8659	−	11.4277i	−0.683136	−	0.718455i
$254$	10.8832			0.682872
$255$	0.117225	+	0.0753360i	0.00734092	+	0.00471772i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−10.2930	−	22.5384i	−0.642057	−	1.40591i	−0.898337	−	0.439306i	$-0.855224\pi$
$257$	−10.2930	−	22.5384i	−0.642057	−	1.40591i	0.256280	−	0.966602i	$-0.417503\pi$
$258$	−1.55606	−	0.456901i	−0.0968762	−	0.0284454i
$259$	−4.39577	+	9.62539i	−0.273140	+	0.598093i
$260$	0.430994	−	0.497394i	0.0267291	−	0.0308471i
$261$	−0.650097	+	4.52153i	−0.0402400	+	0.279875i
$262$	2.69520	−	0.791384i	0.166510	−	0.0488918i
$263$	11.2635	+	12.9988i	0.694537	+	0.801539i	0.988004	−	0.154430i	$-0.0493543\pi$
$263$	11.2635	+	12.9988i	0.694537	+	0.801539i	−0.293466	+	0.955969i	$0.594809\pi$
$264$	2.76610	−	1.77766i	0.170242	−	0.109408i
$265$	−2.20762	+	1.41875i	−0.135613	+	0.0871534i
$266$	−4.67287	−	5.39278i	−0.286512	−	0.330653i
$267$	14.9721	−	4.39622i	0.916280	−	0.269044i
$268$	−1.54747	+	10.7629i	−0.0945268	+	0.657448i
$269$	−1.58979	+	1.83471i	−0.0969310	+	0.111864i	−0.802142	−	0.597133i	$-0.796307\pi$
$269$	−1.58979	+	1.83471i	−0.0969310	+	0.111864i	0.705212	+	0.708997i	$0.250852\pi$
$270$	0.415415	−	0.909632i	0.0252814	−	0.0553584i
$271$	2.23992	+	0.657701i	0.136066	+	0.0399525i	0.349056	−	0.937102i	$-0.386502\pi$
$271$	2.23992	+	0.657701i	0.136066	+	0.0399525i	−0.212991	+	0.977054i	$0.568320\pi$
$272$	0.0578863	+	0.126753i	0.00350987	+	0.00768555i
$273$	0.240284	+	1.67121i	0.0145426	+	0.101146i
$274$	9.34290	+	6.00432i	0.564425	+	0.362734i
$275$	−3.28807			−0.198278
$276$	−3.30466	−	3.47552i	−0.198917	−	0.209201i
$277$	−8.57936			−0.515484			−0.257742	−	0.966214i	$-0.582978\pi$
$277$	−8.57936			−0.515484			−0.257742	+	0.966214i	$0.582978\pi$
$278$	12.9286	+	8.30872i	0.775407	+	0.498324i
$279$	0.109859	+	0.764087i	0.00657709	+	0.0457447i
$280$	−1.06570	−	2.33355i	−0.0636876	−	0.139456i
$281$	−15.6516	−	4.59572i	−0.933696	−	0.274158i	−0.220713	−	0.975339i	$-0.570838\pi$
$281$	−15.6516	−	4.59572i	−0.933696	−	0.274158i	−0.712983	+	0.701181i	$0.752656\pi$
$282$	−4.77756	+	10.4614i	−0.284499	+	0.622967i
$283$	3.78537	−	4.36855i	0.225017	−	0.259683i	−0.632004	−	0.774965i	$-0.717767\pi$
$283$	3.78537	−	4.36855i	0.225017	−	0.259683i	0.857021	+	0.515282i	$0.172313\pi$
$284$	1.60207	−	11.1427i	0.0950655	−	0.661195i
$285$	−2.66885	+	0.783646i	−0.158089	+	0.0464192i
$286$	1.41714	+	1.63546i	0.0837971	+	0.0967071i
$287$	2.83737	−	1.82347i	0.167485	−	0.107636i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	11.1199	+	12.8331i	0.654113	+	0.754886i
$290$	4.38298	−	1.28696i	0.257378	−	0.0755729i
$291$	−2.11775	+	14.7293i	−0.124145	+	0.863446i
$292$	1.55917	−	1.79938i	0.0912438	−	0.105301i
$293$	5.24002	−	11.4740i	0.306125	−	0.670321i	−0.692572	−	0.721349i	$-0.743522\pi$
$293$	5.24002	−	11.4740i	0.306125	−	0.670321i	0.998697	+	0.0510279i	$0.0162498\pi$
$294$	−0.401855	−	0.117995i	−0.0234367	−	0.00688163i
$295$	−1.66162	−	3.63844i	−0.0967432	−	0.211838i
$296$	0.587017	+	4.08279i	0.0341197	+	0.237308i
$297$	2.76610	+	1.77766i	0.160505	+	0.103150i
$298$	8.83179			0.511612
$299$	1.95459	−	2.47835i	0.113037	−	0.143326i
$300$	−1.00000			−0.0577350
$301$	−3.49997	−	2.24929i	−0.201735	−	0.129647i
$302$	0.158010	+	1.09899i	0.00909247	+	0.0632395i
$303$	−0.174879	−	0.382931i	−0.0100465	−	0.0219988i
$304$	−2.66885	−	0.783646i	−0.153069	−	0.0449452i
$305$	−0.250749	+	0.549065i	−0.0143579	+	0.0314394i
$306$	−0.0912520	+	0.105310i	−0.00521653	+	0.00602020i
$307$	0.916320	−	6.37314i	0.0522971	−	0.363735i	−0.946822	−	0.321759i	$-0.895726\pi$
$307$	0.916320	−	6.37314i	0.0522971	−	0.363735i	0.999119	−	0.0419753i	$-0.0133651\pi$
$308$	8.09346	−	2.37645i	0.461168	−	0.135411i
$309$	−7.35319	−	8.48604i	−0.418309	−	0.482754i
$310$	0.649401	−	0.417344i	0.0368835	−	0.0237036i
$311$	−3.43757	+	2.20919i	−0.194927	+	0.125272i	−0.634464	−	0.772953i	$-0.718779\pi$
$311$	−3.43757	+	2.20919i	−0.194927	+	0.125272i	0.439537	+	0.898225i	$0.355143\pi$
$312$	0.430994	+	0.497394i	0.0244003	+	0.0281594i
$313$	5.61542	−	1.64884i	0.317402	−	0.0931978i	−0.119151	−	0.992876i	$-0.538017\pi$
$313$	5.61542	−	1.64884i	0.317402	−	0.0931978i	0.436553	+	0.899678i	$0.356199\pi$
$314$	−1.05271	+	7.32177i	−0.0594079	+	0.413191i
$315$	1.67997	−	1.93879i	0.0946554	−	0.109238i
$316$	−5.01052	+	10.9715i	−0.281864	+	0.617196i
$317$	−2.20295	−	0.646846i	−0.123730	−	0.0363305i	0.219281	−	0.975662i	$-0.429629\pi$
$317$	−2.20295	−	0.646846i	−0.123730	−	0.0363305i	−0.343011	+	0.939331i	$0.611447\pi$
$318$	−1.09014	−	2.38706i	−0.0611318	−	0.133860i
$319$	2.13756	+	14.8671i	0.119681	+	0.832396i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	11.6155			0.648311
$322$	−5.62238	−	10.9433i	−0.313323	−	0.609847i
$323$	0.387594			0.0215663
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	−0.0936640	−	0.651448i	−0.00519555	−	0.0361358i
$326$	7.75870	+	16.9892i	0.429715	+	0.940944i
$327$	4.84858	+	1.42367i	0.268127	+	0.0787292i
$328$	0.546160	−	1.19592i	0.0301566	−	0.0660338i
$329$	−19.3208	+	22.2974i	−1.06519	+	1.22929i
$330$	0.467941	−	3.25460i	0.0257593	−	0.179160i
$331$	−20.9406	+	6.14871i	−1.15100	+	0.337964i	−0.800929	−	0.598760i	$-0.795661\pi$
$331$	−20.9406	+	6.14871i	−1.15100	+	0.337964i	−0.350070	+	0.936723i	$0.613842\pi$
$332$	−0.866762	−	1.00030i	−0.0475698	−	0.0548984i
$333$	−3.46998	+	2.23002i	−0.190154	+	0.122205i
$334$	14.2448	−	9.15459i	0.779442	−	0.500917i
$335$	7.12067	+	8.21770i	0.389044	+	0.448981i
$336$	2.46147	−	0.722751i	0.134284	−	0.0394293i
$337$	2.25560	−	15.6881i	0.122871	−	0.854584i	−0.831407	−	0.555663i	$-0.812464\pi$
$337$	2.25560	−	15.6881i	0.122871	−	0.854584i	0.954278	−	0.298920i	$-0.0966265\pi$
$338$	8.22953	−	9.49739i	0.447628	−	0.516590i
$339$	−2.27391	+	4.97917i	−0.123502	+	0.270431i
$340$	0.133701	+	0.0392582i	0.00725097	+	0.00212908i
$341$	1.05441	+	2.30883i	0.0570994	+	0.125030i
$342$	−0.395852	−	2.75321i	−0.0214052	−	0.148877i
$343$	−16.0108	−	10.2895i	−0.864503	−	0.555582i
$344$	−1.62176			−0.0874392
$345$	−4.79071	+	0.221518i	−0.257923	+	0.0119261i
$346$	1.49590			0.0804203
$347$	−1.44116	−	0.926179i	−0.0773657	−	0.0497199i	0.501386	−	0.865224i	$-0.332824\pi$
$347$	−1.44116	−	0.926179i	−0.0773657	−	0.0497199i	−0.578752	+	0.815504i	$0.696460\pi$
$348$	0.650097	+	4.52153i	0.0348489	+	0.242379i
$349$	1.33770	+	2.92916i	0.0716055	+	0.156794i	0.942050	−	0.335472i	$-0.108896\pi$
$349$	1.33770	+	2.92916i	0.0716055	+	0.156794i	−0.870445	+	0.492266i	$0.836169\pi$
$350$	−2.46147	−	0.722751i	−0.131571	−	0.0386327i
$351$	−0.273404	+	0.598671i	−0.0145932	+	0.0319547i
$352$	2.15323	−	2.48495i	0.114767	−	0.132449i
$353$	−2.99699	+	20.8445i	−0.159514	+	1.10944i	0.740018	+	0.672587i	$0.234817\pi$
$353$	−2.99699	+	20.8445i	−0.159514	+	1.10944i	−0.899532	+	0.436855i	$0.856092\pi$
$354$	3.83788	−	1.12690i	0.203981	−	0.0598942i
$355$	−7.37192	−	8.50765i	−0.391261	−	0.451539i
$356$	13.1271	−	8.43628i	0.695735	−	0.447122i
$357$	−0.300727	+	0.193266i	−0.0159162	+	0.0102287i
$358$	−14.7029	−	16.9681i	−0.777074	−	0.896791i
$359$	−16.0345	+	4.70816i	−0.846270	+	0.248487i	−0.675992	−	0.736909i	$-0.736285\pi$
$359$	−16.0345	+	4.70816i	−0.846270	+	0.248487i	−0.170278	+	0.985396i	$0.554467\pi$
$360$	0.142315	−	0.989821i	0.00750065	−	0.0521682i
$361$	7.37578	−	8.51210i	0.388199	−	0.448005i
$362$	−3.78104	+	8.27933i	−0.198727	+	0.435152i
$363$	−0.180981	−	0.0531407i	−0.00949902	−	0.00278916i
$364$	0.701386	+	1.53582i	0.0367626	+	0.0804988i
$365$	−0.338841	−	2.35669i	−0.0177357	−	0.123355i
$366$	−0.507791	−	0.326337i	−0.0265426	−	0.0170579i
$367$	4.60931			0.240604			0.120302	−	0.992737i	$-0.461614\pi$
$367$	4.60931			0.240604			0.120302	+	0.992737i	$0.461614\pi$
$368$	−4.14997	−	2.40370i	−0.216332	−	0.125302i
$369$	1.31473			0.0684423
$370$	3.46998	+	2.23002i	0.180396	+	0.115933i
$371$	−0.958077	−	6.66357i	−0.0497409	−	0.345955i
$372$	0.320677	+	0.702185i	0.0166263	+	0.0364066i
$373$	−20.7924	−	6.10520i	−1.07659	−	0.316115i	−0.305076	−	0.952328i	$-0.598682\pi$
$373$	−20.7924	−	6.10520i	−1.07659	−	0.316115i	−0.771514	+	0.636213i	$0.780500\pi$
$374$	−0.190334	+	0.416773i	−0.00984194	+	0.0215508i
$375$	−0.654861	+	0.755750i	−0.0338169	+	0.0390267i
$376$	−1.63672	+	11.3836i	−0.0844073	+	0.587066i
$377$	−2.88465	+	0.847009i	−0.148567	+	0.0436232i
$378$	1.67997	+	1.93879i	0.0864082	+	0.0997204i
$379$	−2.25423	+	1.44871i	−0.115792	+	0.0744151i	−0.597255	−	0.802051i	$-0.703742\pi$
$379$	−2.25423	+	1.44871i	−0.115792	+	0.0744151i	0.481463	+	0.876466i	$0.340106\pi$
$380$	−2.33997	+	1.50381i	−0.120038	+	0.0771436i
$381$	7.12697	+	8.22496i	0.365126	+	0.421377i
$382$	−20.2398	+	5.94294i	−1.03556	+	0.304067i
$383$	−2.78514	+	19.3711i	−0.142314	+	0.989817i	0.786055	+	0.618157i	$0.212120\pi$
$383$	−2.78514	+	19.3711i	−0.142314	+	0.989817i	−0.928369	+	0.371660i	$0.878789\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	3.50408	−	7.67288i	0.178585	−	0.391046i
$386$	−17.7636	−	5.21586i	−0.904142	−	0.265480i
$387$	−0.673701	−	1.47520i	−0.0342462	−	0.0749886i
$388$	2.11775	+	14.7293i	0.107513	+	0.747766i
$389$	0.713503	+	0.458540i	0.0361760	+	0.0232489i	0.558604	−	0.829435i	$-0.311337\pi$
$389$	0.713503	+	0.458540i	0.0361760	+	0.0232489i	−0.522428	+	0.852684i	$0.674974\pi$
$390$	0.658147			0.0333266
$391$	0.649221	+	0.158458i	0.0328325	+	0.00801355i
$392$	−0.418821			−0.0211536
$393$	2.36307	+	1.51865i	0.119201	+	0.0766060i
$394$	−0.812496	−	5.65103i	−0.0409329	−	0.284695i
$395$	5.01052	+	10.9715i	0.252107	+	0.552037i
$396$	3.15488	+	0.926355i	0.158539	+	0.0465511i
$397$	−5.52943	+	12.1078i	−0.277514	+	0.607671i	−0.996145	−	0.0877205i	$-0.972042\pi$
$397$	−5.52943	+	12.1078i	−0.277514	+	0.607671i	0.718631	+	0.695392i	$0.244769\pi$
$398$	0.892805	−	1.03035i	0.0447523	−	0.0516469i
$399$	1.01551	−	7.06304i	0.0508392	−	0.353594i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	−7.26629	−	8.38574i	−0.362861	−	0.418764i	0.544735	−	0.838608i	$-0.316630\pi$
$401$	−7.26629	−	8.38574i	−0.362861	−	0.418764i	−0.907596	+	0.419844i	$0.862085\pi$
$402$	−9.14743	+	5.87870i	−0.456232	+	0.293203i
$403$	−0.427401	+	0.274674i	−0.0212904	+	0.0136825i
$404$	−0.275679	−	0.318151i	−0.0137155	−	0.0158286i
$405$	0.959493	−	0.281733i	0.0476776	−	0.0139994i
$406$	−1.66775	+	11.5994i	−0.0827689	+	0.575670i
$407$	−8.88158	+	10.2499i	−0.440244	+	0.508068i
$408$	−0.0578863	+	0.126753i	−0.00286580	+	0.00627522i
$409$	−29.1602	−	8.56220i	−1.44188	−	0.423374i	−0.535031	−	0.844833i	$-0.679700\pi$
$409$	−29.1602	−	8.56220i	−1.44188	−	0.423374i	−0.906848	+	0.421459i	$0.861518\pi$
$410$	−0.546160	−	1.19592i	−0.0269729	−	0.0590624i
$411$	1.58054	+	10.9929i	0.0779622	+	0.542239i
$412$	−9.44613	−	6.07066i	−0.465377	−	0.299080i
$413$	10.2613			0.504924
$414$	0.462526	−	4.77348i	0.0227319	−	0.234604i
$415$	−1.32358			−0.0649721
$416$	0.553668	+	0.355821i	0.0271458	+	0.0174456i
$417$	2.18713	+	15.2119i	0.107104	+	0.744928i
$418$	−3.79932	−	8.31935i	−0.185831	−	0.406912i
$419$	29.6334	+	8.70115i	1.44769	+	0.425079i	0.908776	−	0.417285i	$-0.137018\pi$
$419$	29.6334	+	8.70115i	1.44769	+	0.425079i	0.538910	+	0.842364i	$0.318836\pi$
$420$	1.06570	−	2.33355i	0.0520007	−	0.113866i
$421$	−19.3701	+	22.3543i	−0.944040	+	1.08948i	0.0518266	+	0.998656i	$0.483496\pi$
$421$	−19.3701	+	22.3543i	−0.944040	+	1.08948i	−0.995867	+	0.0908245i	$0.971050\pi$
$422$	1.54908	−	10.7741i	0.0754080	−	0.524474i
$423$	−11.0348	+	3.24012i	−0.536532	+	0.157540i
$424$	−1.71849	−	1.98324i	−0.0834573	−	0.0963149i
$425$	0.117225	−	0.0753360i	0.00568625	−	0.00365433i
$426$	9.47019	−	6.08612i	0.458832	−	0.294874i
$427$	−1.01405	−	1.17027i	−0.0490732	−	0.0566335i
$428$	11.1449	−	3.27245i	0.538711	−	0.158180i
$429$	−0.307974	+	2.14200i	−0.0148691	+	0.103417i
$430$	−1.06202	+	1.22564i	−0.0512153	+	0.0591056i
$431$	−2.42149	+	5.30232i	−0.116639	+	0.255404i	−0.958943	−	0.283599i	$-0.908472\pi$
$431$	−2.42149	+	5.30232i	−0.116639	+	0.255404i	0.842304	+	0.539003i	$0.181199\pi$
$432$	0.959493	+	0.281733i	0.0461636	+	0.0135549i
$433$	−12.0537	−	26.3940i	−0.579266	−	1.26842i	−0.941715	−	0.336412i	$-0.890786\pi$
$433$	−12.0537	−	26.3940i	−0.579266	−	1.26842i	0.362449	−	0.932004i	$-0.381941\pi$
$434$	0.281830	+	1.96017i	0.0135283	+	0.0940913i
$435$	3.84286	+	2.46966i	0.184251	+	0.118411i
$436$	5.05327			0.242008
$437$	−10.8770	+	7.72265i	−0.520317	+	0.369424i
$438$	2.38093			0.113765
$439$	−8.81073	−	5.66231i	−0.420513	−	0.270247i	0.313226	−	0.949679i	$-0.398590\pi$
$439$	−8.81073	−	5.66231i	−0.420513	−	0.270247i	−0.733739	+	0.679431i	$0.762227\pi$
$440$	−0.467941	−	3.25460i	−0.0223082	−	0.155157i
$441$	−0.173984	−	0.380973i	−0.00828497	−	0.0181415i
$442$	−0.0879950	−	0.0258377i	−0.00418550	−	0.00122897i
$443$	13.1399	−	28.7724i	0.624296	−	1.36702i	−0.288057	−	0.957613i	$-0.593009\pi$
$443$	13.1399	−	28.7724i	0.624296	−	1.36702i	0.912353	−	0.409404i	$-0.134263\pi$
$444$	−2.70116	+	3.11730i	−0.128191	+	0.147941i
$445$	2.22071	−	15.4454i	0.105272	−	0.732182i
$446$	0.893101	−	0.262238i	0.0422896	−	0.0124173i
$447$	5.78359	+	6.67462i	0.273554	+	0.315699i
$448$	2.15814	−	1.38695i	0.101962	−	0.0655272i
$449$	15.4097	−	9.90322i	0.727229	−	0.467362i	−0.123916	−	0.992293i	$-0.539545\pi$
$449$	15.4097	−	9.90322i	0.727229	−	0.467362i	0.851145	+	0.524931i	$0.175909\pi$
$450$	−0.654861	−	0.755750i	−0.0308704	−	0.0356264i
$451$	4.14782	−	1.21791i	0.195313	−	0.0573491i
$452$	−0.779007	+	5.41811i	−0.0366414	+	0.254847i
$453$	−0.727083	+	0.839099i	−0.0341614	+	0.0394243i
$454$	−6.33975	+	13.8821i	−0.297539	+	0.651520i
$455$	1.62001	+	0.475676i	0.0759470	+	0.0223001i
$456$	−1.15549	−	2.53016i	−0.0541106	−	0.118486i
$457$	2.23260	+	15.5281i	0.104437	+	0.726373i	0.973002	+	0.230798i	$0.0741336\pi$
$457$	2.23260	+	15.5281i	0.104437	+	0.726373i	−0.868565	+	0.495575i	$0.834957\pi$
$458$	−0.291494	−	0.187332i	−0.0136206	−	0.00875343i
$459$	−0.139346			−0.00650410
$460$	−4.53425	+	1.56225i	−0.211410	+	0.0728401i
$461$	38.0734			1.77325			0.886627	−	0.462486i	$-0.153042\pi$
$461$	38.0734			1.77325			0.886627	+	0.462486i	$0.153042\pi$
$462$	7.09609	+	4.56038i	0.330140	+	0.212168i
$463$	−3.13262	−	21.7879i	−0.145585	−	1.01257i	−0.923336	−	0.383994i	$-0.874548\pi$
$463$	−3.13262	−	21.7879i	−0.145585	−	1.01257i	0.777750	−	0.628573i	$-0.216361\pi$
$464$	1.89762	+	4.15522i	0.0880950	+	0.192901i
$465$	0.740675	+	0.217482i	0.0343480	+	0.0100855i
$466$	7.28138	−	15.9440i	0.337303	−	0.738591i
$467$	−21.8409	+	25.2058i	−1.01068	+	1.16638i	−0.0246681	+	0.999696i	$0.507853\pi$
$467$	−21.8409	+	25.2058i	−1.01068	+	1.16638i	−0.986010	+	0.166689i	$0.946693\pi$
$468$	−0.0936640	+	0.651448i	−0.00432962	+	0.0301132i
$469$	−26.7649	+	7.85889i	−1.23589	+	0.362890i
$470$	7.53135	+	8.69164i	0.347395	+	0.400915i
$471$	−6.22280	+	3.99915i	−0.286731	+	0.184271i
$472$	3.36493	−	2.16251i	0.154883	−	0.0995376i
$473$	−3.49200	−	4.02999i	−0.160563	−	0.185299i
$474$	−11.5729	+	3.39811i	−0.531561	+	0.156080i
$475$	−0.395852	+	2.75321i	−0.0181629	+	0.126326i
$476$	−0.234096	+	0.270161i	−0.0107298	+	0.0123828i
$477$	1.09014	−	2.38706i	0.0499139	−	0.109296i
$478$	−19.3808	−	5.69073i	−0.886459	−	0.260288i
$479$	13.2434	+	28.9989i	0.605104	+	1.32499i	0.925873	+	0.377836i	$0.123332\pi$
$479$	13.2434	+	28.9989i	0.605104	+	1.32499i	−0.320768	+	0.947158i	$0.603941\pi$
$480$	−0.142315	−	0.989821i	−0.00649575	−	0.0451790i
$481$	−2.28376	−	1.46768i	−0.104130	−	0.0669206i
$482$	−18.6108			−0.847698
$483$	4.58853	−	11.4155i	0.208785	−	0.519421i
$484$	−0.188621			−0.00857369
$485$	12.5185	+	8.04514i	0.568435	+	0.365311i
$486$	0.142315	+	0.989821i	0.00645553	+	0.0448992i
$487$	11.9638	+	26.1970i	0.542131	+	1.18710i	0.960361	+	0.278760i	$0.0899235\pi$
$487$	11.9638	+	26.1970i	0.542131	+	1.18710i	−0.418230	+	0.908341i	$0.637349\pi$
$488$	−0.579161	−	0.170057i	−0.0262174	−	0.00769813i
$489$	−7.75870	+	16.9892i	−0.350860	+	0.768277i
$490$	−0.274269	+	0.316523i	−0.0123902	+	0.0142991i
$491$	3.78950	−	26.3566i	0.171018	−	1.18946i	−0.705721	−	0.708490i	$-0.749377\pi$
$491$	3.78950	−	26.3566i	0.171018	−	1.18946i	0.876739	−	0.480966i	$-0.159714\pi$
$492$	1.26148	−	0.370403i	0.0568718	−	0.0166991i
$493$	−0.416841	−	0.481060i	−0.0187736	−	0.0216659i
$494$	1.54004	−	0.989725i	0.0692898	−	0.0445298i
$495$	2.76610	−	1.77766i	0.124327	−	0.0799000i
$496$	0.505516	+	0.583396i	0.0226983	+	0.0261953i
$497$	27.7093	−	8.13618i	1.24293	−	0.364958i
$498$	0.188365	−	1.31011i	0.00844086	−	0.0587074i
$499$	6.01384	−	6.94034i	0.269216	−	0.310692i	−0.605003	−	0.796223i	$-0.706828\pi$
$499$	6.01384	−	6.94034i	0.269216	−	0.310692i	0.874220	+	0.485531i	$0.161374\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	16.2470	+	4.77054i	0.725860	+	0.213132i
$502$	−4.42250	−	9.68393i	−0.197386	−	0.432215i
$503$	6.24106	+	43.4075i	0.278275	+	1.93545i	0.347125	+	0.937819i	$0.387158\pi$
$503$	6.24106	+	43.4075i	0.278275	+	1.93545i	−0.0688497	+	0.997627i	$0.521933\pi$
$504$	2.15814	+	1.38695i	0.0961310	+	0.0617796i
$505$	−0.420973			−0.0187331
$506$	−2.96272	−	15.4882i	−0.131709	−	0.688534i
$507$	12.5668			0.558113
$508$	9.15551	+	5.88389i	0.406210	+	0.261055i
$509$	0.910556	+	6.33306i	0.0403597	+	0.280708i	1.00000		0.000522904i	$-0.000166445\pi$
$509$	0.910556	+	6.33306i	0.0403597	+	0.280708i	−0.959640	+	0.281231i	$0.909257\pi$
$510$	0.0578863	+	0.126753i	0.00256325	+	0.00561273i
$511$	5.86056	+	1.72082i	0.259256	+	0.0761245i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.82151	−	2.10214i	0.0804217	−	0.0928116i
$514$	3.52621	−	24.5253i	0.155534	−	1.08177i
$515$	−10.7738	+	3.16347i	−0.474750	+	0.139399i
$516$	−1.06202	−	1.22564i	−0.0467530	−	0.0539558i
$517$	−31.8120	+	20.4443i	−1.39909	+	0.899141i
$518$	−8.90183	+	5.72086i	−0.391124	+	0.251360i
$519$	0.979608	+	1.13053i	0.0430000	+	0.0496247i
$520$	0.631487	−	0.185421i	0.0276925	−	0.00813126i
$521$	3.27874	−	22.8041i	0.143644	−	0.999066i	−0.782703	−	0.622395i	$-0.786160\pi$
$521$	3.27874	−	22.8041i	0.143644	−	0.999066i	0.926347	−	0.376671i	$-0.122931\pi$
$522$	−2.99142	+	3.45228i	−0.130931	+	0.151102i
$523$	5.85864	−	12.8286i	0.256180	−	0.560957i	−0.737220	−	0.675652i	$-0.763862\pi$
$523$	5.85864	−	12.8286i	0.256180	−	0.560957i	0.993401	+	0.114696i	$0.0365893\pi$
$524$	2.69520	+	0.791384i	0.117741	+	0.0345717i
$525$	−1.06570	−	2.33355i	−0.0465109	−	0.101845i
$526$	2.44779	+	17.0248i	0.106729	+	0.742316i
$527$	−0.0904912	−	0.0581552i	−0.00394186	−	0.00253328i
$528$	3.28807			0.143095
$529$	−21.3762	+	8.48869i	−0.929400	+	0.369073i
$530$	−2.62421			−0.113988
$531$	3.36493	+	2.16251i	0.146026	+	0.0938449i
$532$	−1.01551	−	7.06304i	−0.0440280	−	0.306222i
$533$	0.359453	+	0.787093i	0.0155696	+	0.0340928i
$534$	14.9721	+	4.39622i	0.647908	+	0.190243i
$535$	4.82523	−	10.5658i	0.208613	−	0.456799i
$536$	−7.12067	+	8.21770i	−0.307566	+	0.354950i
$537$	3.19525	−	22.2235i	0.137885	−	0.959014i
$538$	−2.32933	+	0.683954i	−0.100425	+	0.0294873i
$539$	−0.901815	−	1.04075i	−0.0388439	−	0.0448283i
$540$	0.841254	−	0.540641i	0.0362018	−	0.0232655i
$541$	24.2279	−	15.5703i	1.04164	−	0.669421i	0.0962474	−	0.995357i	$-0.469316\pi$
$541$	24.2279	−	15.5703i	1.04164	−	0.669421i	0.945392	+	0.325937i	$0.105680\pi$
$542$	1.52876	+	1.76429i	0.0656660	+	0.0757827i
$543$	−8.73316	+	2.56429i	−0.374776	+	0.110044i
$544$	−0.0198310	+	0.137927i	−0.000850246	+	0.00591359i
$545$	3.30919	−	3.81901i	0.141750	−	0.163588i
$546$	−0.701386	+	1.53582i	−0.0300165	+	0.0657270i
$547$	−2.21009	−	0.648942i	−0.0944967	−	0.0277467i	0.234142	−	0.972202i	$-0.424772\pi$
$547$	−2.21009	−	0.648942i	−0.0944967	−	0.0277467i	−0.328639	+	0.944456i	$0.606590\pi$
$548$	4.61357	+	10.1023i	0.197082	+	0.431549i
$549$	−0.0859029	−	0.597468i	−0.00366625	−	0.0254993i
$550$	−2.76610	−	1.77766i	−0.117947	−	0.0757998i
$551$	12.7061			0.541297
$552$	−0.901053	−	4.71042i	−0.0383514	−	0.200489i
$553$	−30.9423			−1.31580
$554$	−7.21742	−	4.63835i	−0.306639	−	0.197065i
$555$	0.587017	+	4.08279i	0.0249175	+	0.173305i
$556$	6.38422	+	13.9795i	0.270751	+	0.592862i
$557$	−9.28734	−	2.72701i	−0.393517	−	0.115547i	0.0789866	−	0.996876i	$-0.474832\pi$
$557$	−9.28734	−	2.72701i	−0.393517	−	0.115547i	−0.472504	+	0.881329i	$0.656650\pi$
$558$	−0.320677	+	0.702185i	−0.0135753	+	0.0297259i
$559$	0.698967	−	0.806651i	0.0295632	−	0.0341177i
$560$	0.365092	−	2.53927i	0.0154279	−	0.107304i
$561$	−0.439619	+	0.129084i	−0.0185607	+	0.00544992i
$562$	−10.6823	−	12.3281i	−0.450607	−	0.520028i
$563$	26.3899	−	16.9598i	1.11220	−	0.714770i	0.150431	−	0.988620i	$-0.451934\pi$
$563$	26.3899	−	16.9598i	1.11220	−	0.714770i	0.961772	+	0.273851i	$0.0882975\pi$
$564$	−9.67499	+	6.21774i	−0.407391	+	0.261814i
$565$	3.58460	+	4.13684i	0.150805	+	0.174038i
$566$	5.54627	−	1.62853i	0.233127	−	0.0684523i
$567$	−0.365092	+	2.53927i	−0.0153324	+	0.106639i
$568$	7.37192	−	8.50765i	0.309319	−	0.356973i
$569$	9.94283	−	21.7718i	0.416825	−	0.912720i	−0.578458	−	0.815712i	$-0.696345\pi$
$569$	9.94283	−	21.7718i	0.416825	−	0.912720i	0.995284	−	0.0970080i	$-0.0309272\pi$
$570$	−2.66885	−	0.783646i	−0.111786	−	0.0328233i
$571$	−12.4050	−	27.1632i	−0.519134	−	1.13674i	−0.969766	−	0.244035i	$-0.921529\pi$
$571$	−12.4050	−	27.1632i	−0.519134	−	1.13674i	0.450633	−	0.892710i	$-0.351198\pi$
$572$	0.307974	+	2.14200i	0.0128770	+	0.0895617i
$573$	−17.7456	−	11.4044i	−0.741334	−	0.476426i
$574$	3.37279			0.140778
$575$	−1.78863	+	4.44981i	−0.0745912	+	0.185570i
$576$	1.00000			0.0416667
$577$	32.6014	+	20.9516i	1.35721	+	0.872228i	0.998133	−	0.0610779i	$-0.0194538\pi$
$577$	32.6014	+	20.9516i	1.35721	+	0.872228i	0.359081	+	0.933306i	$0.383090\pi$
$578$	2.41659	+	16.8077i	0.100517	+	0.699110i
$579$	−7.69079	−	16.8405i	−0.319618	−	0.699866i
$580$	4.38298	+	1.28696i	0.181994	+	0.0534381i
$581$	1.41054	−	3.08865i	0.0585190	−	0.128139i
$582$	−9.74482	+	11.2461i	−0.403936	+	0.466167i
$583$	1.22797	−	8.54075i	0.0508575	−	0.353722i
$584$	2.28448	−	0.670784i	0.0945325	−	0.0277572i
$585$	0.430994	+	0.497394i	0.0178194	+	0.0205647i
$586$	10.6115	−	6.81961i	0.438358	−	0.281716i
$587$	29.7189	−	19.0992i	1.22663	−	0.788309i	0.243269	−	0.969959i	$-0.421780\pi$
$587$	29.7189	−	19.0992i	1.22663	−	0.788309i	0.983363	+	0.181650i	$0.0581439\pi$
$588$	−0.274269	−	0.316523i	−0.0113107	−	0.0130532i
$589$	2.06021	−	0.604931i	0.0848893	−	0.0249257i
$590$	0.569245	−	3.95919i	0.0234355	−	0.162997i
$591$	3.73869	−	4.31468i	0.153789	−	0.177482i
$592$	−1.71350	+	3.75203i	−0.0704242	+	0.154208i
$593$	−8.96521	−	2.63242i	−0.368157	−	0.108101i	0.0924206	−	0.995720i	$-0.470540\pi$
$593$	−8.96521	−	2.63242i	−0.368157	−	0.108101i	−0.460578	+	0.887619i	$0.652358\pi$
$594$	1.36591	+	2.99093i	0.0560440	+	0.122719i
$595$	0.0508740	+	0.353836i	0.00208563	+	0.0145059i
$596$	7.42977	+	4.77482i	0.304335	+	0.195584i
$597$	1.36335			0.0557982
$598$	2.98420	−	1.02819i	0.122033	−	0.0420457i
$599$	−24.0451			−0.982456			−0.491228	−	0.871031i	$-0.663452\pi$
$599$	−24.0451			−0.982456			−0.491228	+	0.871031i	$0.663452\pi$
$600$	−0.841254	−	0.540641i	−0.0343440	−	0.0220716i
$601$	2.19092	+	15.2382i	0.0893696	+	0.621579i	0.984449	+	0.175672i	$0.0562098\pi$
$601$	2.19092	+	15.2382i	0.0893696	+	0.621579i	−0.895079	+	0.445907i	$0.852881\pi$
$602$	−1.72830	−	3.78445i	−0.0704403	−	0.154243i
$603$	−10.4331	−	3.06344i	−0.424869	−	0.124753i
$604$	−0.461230	+	1.00995i	−0.0187672	+	0.0410944i
$605$	−0.123521	+	0.142550i	−0.00502182	+	0.00579549i
$606$	0.0599108	−	0.416689i	0.00243371	−	0.0169268i
$607$	−21.1201	+	6.20142i	−0.857239	+	0.251708i	−0.680679	−	0.732582i	$-0.738315\pi$
$607$	−21.1201	+	6.20142i	−0.857239	+	0.251708i	−0.176560	+	0.984290i	$0.556497\pi$
$608$	−1.82151	−	2.10214i	−0.0738720	−	0.0852529i
$609$	−9.85841	+	6.33562i	−0.399483	+	0.256732i
$610$	−0.507791	+	0.326337i	−0.0205598	+	0.0132130i
$611$	−4.95673	−	5.72037i	−0.200528	−	0.231422i
$612$	−0.133701	+	0.0392582i	−0.00540455	+	0.00158692i
$613$	1.82578	−	12.6986i	0.0737426	−	0.512891i	−0.919153	−	0.393901i	$-0.871125\pi$
$613$	1.82578	−	12.6986i	0.0737426	−	0.512891i	0.992895	−	0.118990i	$-0.0379656\pi$
$614$	4.21644	−	4.86603i	0.170162	−	0.196377i
$615$	0.546160	−	1.19592i	0.0220233	−	0.0482243i
$616$	8.09346	+	2.37645i	0.326095	+	0.0957501i
$617$	5.65209	+	12.3764i	0.227545	+	0.498253i	0.988624	−	0.150405i	$-0.0480577\pi$
$617$	5.65209	+	12.3764i	0.227545	+	0.498253i	−0.761080	+	0.648658i	$0.775330\pi$
$618$	−1.59800	−	11.1143i	−0.0642811	−	0.447085i
$619$	12.2310	+	7.86037i	0.491605	+	0.315935i	0.762850	−	0.646575i	$-0.223799\pi$
$619$	12.2310	+	7.86037i	0.491605	+	0.315935i	−0.271246	+	0.962510i	$0.587436\pi$
$620$	0.771944			0.0310020
$621$	3.91044	−	2.77641i	0.156921	−	0.111413i
$622$	−4.08625			−0.163844
$623$	33.6760	+	21.6423i	1.34920	+	0.867079i
$624$	0.0936640	+	0.651448i	0.00374956	+	0.0260788i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	5.61542	+	1.64884i	0.224437	+	0.0659008i
$627$	3.79932	−	8.31935i	0.151730	−	0.332243i
$628$	−4.84404	+	5.59032i	−0.193298	+	0.223078i
$629$	0.0817983	−	0.568920i	0.00326151	−	0.0226843i
$630$	2.46147	−	0.722751i	0.0980671	−	0.0287951i
$631$	−19.7501	−	22.7929i	−0.786240	−	0.907369i	0.211303	−	0.977421i	$-0.432229\pi$
$631$	−19.7501	−	22.7929i	−0.786240	−	0.907369i	−0.997543	+	0.0700513i	$0.977684\pi$
$632$	−10.1468	+	6.52093i	−0.403617	+	0.259389i
$633$	9.15694	−	5.88481i	0.363956	−	0.233900i
$634$	−1.50353	−	1.73517i	−0.0597129	−	0.0689123i
$635$	10.4423	−	3.06615i	0.414391	−	0.121676i
$636$	0.373464	−	2.59750i	0.0148088	−	0.102998i
$637$	0.180509	−	0.208319i	0.00715204	−	0.00825389i
$638$	−6.23952	+	13.6626i	−0.247025	+	0.540909i
$639$	10.8012	+	3.17153i	0.427290	+	0.125464i
$640$	−0.415415	−	0.909632i	−0.0164207	−	0.0359564i
$641$	1.44690	+	10.0634i	0.0571493	+	0.397482i	0.998239	+	0.0593243i	$0.0188946\pi$
$641$	1.44690	+	10.0634i	0.0571493	+	0.397482i	−0.941090	+	0.338158i	$0.890196\pi$
$642$	9.77154	+	6.27979i	0.385652	+	0.247843i
$643$	13.9998			0.552099			0.276050	−	0.961143i	$-0.410975\pi$
$643$	13.9998			0.552099			0.276050	+	0.961143i	$0.410975\pi$
$644$	1.18656	−	12.2458i	0.0467568	−	0.482551i
$645$	−1.62176			−0.0638565
$646$	0.326064	+	0.209549i	0.0128288	+	0.00824459i
$647$	−0.228368	−	1.58833i	−0.00897805	−	0.0624437i	0.984840	−	0.173466i	$-0.0554966\pi$
$647$	−0.228368	−	1.58833i	−0.00897805	−	0.0624437i	−0.993818	+	0.111022i	$0.964588\pi$
$648$	0.415415	+	0.909632i	0.0163190	+	0.0357337i
$649$	12.6192	+	3.70533i	0.495347	+	0.145447i
$650$	0.273404	−	0.598671i	0.0107238	−	0.0234818i
$651$	−1.29684	+	1.49663i	−0.0508272	+	0.0586577i
$652$	−2.65801	+	18.4869i	−0.104096	+	0.724002i
$653$	22.2252	−	6.52590i	0.869738	−	0.255378i	0.183734	−	0.982976i	$-0.441181\pi$
$653$	22.2252	−	6.52590i	0.869738	−	0.255378i	0.686004	+	0.727598i	$0.259363\pi$
$654$	3.30919	+	3.81901i	0.129400	+	0.149335i
$655$	2.36307	−	1.51865i	0.0923328	−	0.0593387i
$656$	1.10602	−	0.710798i	0.0431830	−	0.0277520i
$657$	1.55917	+	1.79938i	0.0608292	+	0.0702006i
$658$	−28.3085	+	8.31214i	−1.10358	+	0.324041i
$659$	6.81339	−	47.3882i	0.265412	−	1.84598i	−0.224834	−	0.974397i	$-0.572184\pi$
$659$	6.81339	−	47.3882i	0.265412	−	1.84598i	0.490246	−	0.871584i	$-0.336907\pi$
$660$	2.15323	−	2.48495i	0.0838142	−	0.0967267i
$661$	14.9909	−	32.8255i	0.583079	−	1.27677i	−0.356455	−	0.934312i	$-0.616015\pi$
$661$	14.9909	−	32.8255i	0.583079	−	1.27677i	0.939535	−	0.342453i	$-0.111258\pi$
$662$	−20.9406	−	6.14871i	−0.813879	−	0.238977i
$663$	−0.0380977	−	0.0834223i	−0.00147959	−	0.00323985i
$664$	−0.188365	−	1.31011i	−0.00731000	−	0.0508421i
$665$	−6.00291	−	3.85783i	−0.232783	−	0.149600i
$666$	−4.12478			−0.159832
$667$	21.2827	+	5.19455i	0.824070	+	0.201134i
$668$	16.9329			0.655152
$669$	0.783043	+	0.503231i	0.0302742	+	0.0194560i
$670$	1.54747	+	10.7629i	0.0597840	+	0.415807i
$671$	−0.824481	−	1.80536i	−0.0318287	−	0.0696952i
$672$	2.46147	+	0.722751i	0.0949531	+	0.0278807i
$673$	13.9247	−	30.4907i	0.536756	−	1.17533i	−0.425941	−	0.904751i	$-0.640057\pi$
$673$	13.9247	−	30.4907i	0.536756	−	1.17533i	0.962697	−	0.270581i	$-0.0872158\pi$
$674$	10.3791	−	11.9782i	0.399790	−	0.461382i
$675$	0.142315	−	0.989821i	0.00547770	−	0.0380982i
$676$	12.0578	−	3.54049i	0.463761	−	0.136173i
$677$	12.6463	+	14.5946i	0.486037	+	0.560917i	0.944802	−	0.327641i	$-0.106253\pi$
$677$	12.6463	+	14.5946i	0.486037	+	0.560917i	−0.458765	+	0.888558i	$0.651708\pi$
$678$	−4.60488	+	2.95938i	−0.176849	+	0.113654i
$679$	−32.1147	+	20.6388i	−1.23245	+	0.792046i
$680$	0.0912520	+	0.105310i	0.00349936	+	0.00403847i
$681$	−14.6431	+	4.29959i	−0.561123	+	0.164761i
$682$	−0.361224	+	2.51237i	−0.0138320	+	0.0962035i
$683$	−19.8696	+	22.9307i	−0.760288	+	0.877420i	−0.995523	−	0.0945190i	$-0.969869\pi$
$683$	−19.8696	+	22.9307i	−0.760288	+	0.877420i	0.235235	+	0.971939i	$0.424414\pi$
$684$	1.15549	−	2.53016i	0.0441812	−	0.0967432i
$685$	10.6561	+	3.12890i	0.407147	+	0.119549i
$686$	−7.90622	−	17.3122i	−0.301861	−	0.660983i
$687$	−0.0493120	−	0.342972i	−0.00188137	−	0.0130852i
$688$	−1.36431	−	0.876787i	−0.0520137	−	0.0334272i
$689$	1.72711			0.0657978
$690$	−4.14997	−	2.40370i	−0.157987	−	0.0915074i
$691$	51.4730			1.95812			0.979062	−	0.203564i	$-0.0652525\pi$
$691$	51.4730			1.95812			0.979062	+	0.203564i	$0.0652525\pi$
$692$	1.25843	+	0.808746i	0.0478385	+	0.0307439i
$693$	1.20045	+	8.34928i	0.0456012	+	0.317163i
$694$	−0.711653	−	1.55830i	−0.0270140	−	0.0591524i
$695$	14.7458	+	4.32975i	0.559339	+	0.164237i
$696$	−1.89762	+	4.15522i	−0.0719293	+	0.157503i
$697$	−0.119972	+	0.138455i	−0.00454427	+	0.00524436i
$698$	−0.458276	+	3.18738i	−0.0173460	+	0.120644i
$699$	16.8180	−	4.93820i	0.636113	−	0.186780i
$700$	−1.67997	−	1.93879i	−0.0634968	−	0.0732792i
$701$	20.4750	−	13.1585i	0.773331	−	0.496990i	−0.0934834	−	0.995621i	$-0.529800\pi$
$701$	20.4750	−	13.1585i	0.773331	−	0.496990i	0.866814	+	0.498631i	$0.166164\pi$
$702$	−0.553668	+	0.355821i	−0.0208969	+	0.0134296i
$703$	7.51333	+	8.67085i	0.283371	+	0.327027i
$704$	3.15488	−	0.926355i	0.118904	−	0.0349133i
$705$	−1.63672	+	11.3836i	−0.0616424	+	0.428732i
$706$	−13.7906	+	15.9152i	−0.519017	+	0.598977i
$707$	0.448630	−	0.982364i	0.0168725	−	0.0369456i
$708$	3.83788	+	1.12690i	0.144236	+	0.0423516i
$709$	−12.7779	−	27.9796i	−0.479883	−	1.05080i	−0.982496	−	0.186286i	$-0.940355\pi$
$709$	−12.7779	−	27.9796i	−0.479883	−	1.05080i	0.502613	−	0.864512i	$-0.332372\pi$
$710$	−1.60207	−	11.1427i	−0.0601247	−	0.418176i
$711$	−10.1468	−	6.52093i	−0.380533	−	0.244554i
$712$	15.6042			0.584793
$713$	3.69816	−	0.171000i	0.138497	−	0.00640399i
$714$	−0.357475			−0.0133782
$715$	1.82050	+	1.16996i	0.0680828	+	0.0437541i
$716$	−3.19525	−	22.2235i	−0.119412	−	0.830530i
$717$	−8.39098	−	18.3737i	−0.313367	−	0.686178i
$718$	−16.0345	−	4.70816i	−0.598403	−	0.175707i
$719$	15.5114	−	33.9652i	0.578477	−	1.26669i	−0.363682	−	0.931523i	$-0.618480\pi$
$719$	15.5114	−	33.9652i	0.578477	−	1.26669i	0.942159	−	0.335166i	$-0.108792\pi$
$720$	0.654861	−	0.755750i	0.0244052	−	0.0281651i
$721$	4.09948	−	28.5125i	0.152673	−	1.06186i
$722$	10.8069	−	3.17319i	0.402191	−	0.118094i
$723$	−12.1875	−	14.0651i	−0.453257	−	0.523086i
$724$	−7.65696	+	4.92083i	−0.284569	+	0.182881i
$725$	3.84286	−	2.46966i	0.142720	−	0.0917208i
$726$	−0.123521	−	0.142550i	−0.00458428	−	0.00529054i
$727$	−0.985740	+	0.289440i	−0.0365591	+	0.0107347i	−0.299961	−	0.953951i	$-0.596974\pi$
$727$	−0.985740	+	0.289440i	−0.0365591	+	0.0107347i	0.263402	+	0.964686i	$0.415155\pi$
$728$	−0.240284	+	1.67121i	−0.00890552	+	0.0619392i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	0.989072	−	2.16577i	0.0366072	−	0.0801586i
$731$	0.216831	+	0.0636672i	0.00801977	+	0.00235482i
$732$	−0.250749	−	0.549065i	−0.00926797	−	0.0202940i
$733$	2.85882	+	19.8836i	0.105593	+	0.734416i	0.971984	+	0.235049i	$0.0755250\pi$
$733$	2.85882	+	19.8836i	0.105593	+	0.734416i	−0.866391	+	0.499367i	$0.833566\pi$
$734$	3.87760	+	2.49198i	0.143125	+	0.0919806i
$735$	−0.418821			−0.0154484
$736$	−2.19163	−	4.26576i	−0.0807847	−	0.157238i
$737$	−35.7530			−1.31698
$738$	1.10602	+	0.710798i	0.0407133	+	0.0261648i
$739$	−4.65359	−	32.3664i	−0.171185	−	1.19062i	−0.876386	−	0.481610i	$-0.840052\pi$
$739$	−4.65359	−	32.3664i	−0.171185	−	1.19062i	0.705201	−	0.709008i	$-0.250857\pi$
$740$	1.71350	+	3.75203i	0.0629893	+	0.137927i
$741$	1.75650	+	0.515754i	0.0645265	+	0.0189467i
$742$	2.79661	−	6.12373i	0.102667	−	0.224809i
$743$	−32.7565	+	37.8030i	−1.20172	+	1.38686i	−0.300336	+	0.953833i	$0.597099\pi$
$743$	−32.7565	+	37.8030i	−1.20172	+	1.38686i	−0.901383	+	0.433024i	$0.857447\pi$
$744$	−0.109859	+	0.764087i	−0.00402763	+	0.0280128i
$745$	8.47404	−	2.48820i	0.310465	−	0.0911607i
$746$	−14.1910	−	16.3772i	−0.519568	−	0.599613i
$747$	1.11347	−	0.715583i	0.0407397	−	0.0261818i
$748$	−0.385444	+	0.247710i	−0.0140932	+	0.00905716i
$749$	19.5136	+	22.5199i	0.713011	+	0.822858i
$750$	−0.959493	+	0.281733i	−0.0350357	+	0.0102874i
$751$	2.21466	−	15.4033i	0.0808142	−	0.562075i	−0.908679	−	0.417496i	$-0.862908\pi$
$751$	2.21466	−	15.4033i	0.0808142	−	0.562075i	0.989493	−	0.144580i	$-0.0461830\pi$
$752$	−7.53135	+	8.69164i	−0.274640	+	0.316951i
$753$	4.42250	−	9.68393i	0.161165	−	0.352902i
$754$	−2.88465	−	0.847009i	−0.105053	−	0.0308462i
$755$	0.461230	+	1.00995i	0.0167859	+	0.0367559i
$756$	0.365092	+	2.53927i	0.0132783	+	0.0923523i
$757$	4.57289	+	2.93882i	0.166205	+	0.106813i	0.621099	−	0.783732i	$-0.286687\pi$
$757$	4.57289	+	2.93882i	0.166205	+	0.106813i	−0.454894	+	0.890545i	$0.650323\pi$
$758$	−2.67961			−0.0973278
$759$	9.76502	−	12.3817i	0.354448	−	0.449427i
$760$	−2.78152			−0.100896
$761$	8.55111	+	5.49547i	0.309978	+	0.199210i	0.686375	−	0.727248i	$-0.259201\pi$
$761$	8.55111	+	5.49547i	0.309978	+	0.199210i	−0.376397	+	0.926458i	$0.622837\pi$
$762$	1.54884	+	10.7724i	0.0561085	+	0.390243i
$763$	5.38526	+	11.7921i	0.194960	+	0.426902i
$764$	−20.2398	−	5.94294i	−0.732250	−	0.215008i
$765$	−0.0578863	+	0.126753i	−0.00209288	+	0.00458278i
$766$	−12.8158	+	14.7902i	−0.463054	+	0.534393i
$767$	−0.374647	+	2.60573i	−0.0135277	+	0.0940873i
$768$	0.959493	−	0.281733i	0.0346227	−	0.0101661i
$769$	17.5044	+	20.2012i	0.631227	+	0.728474i	0.977798	−	0.209549i	$-0.0671997\pi$
$769$	17.5044	+	20.2012i	0.631227	+	0.728474i	−0.346572	+	0.938024i	$0.612654\pi$
$770$	7.09609	−	4.56038i	0.255725	−	0.164345i
$771$	20.8442	−	13.3957i	0.750685	−	0.482436i
$772$	−12.1238	−	13.9916i	−0.436344	−	0.503568i
$773$	25.5782	−	7.51045i	0.919986	−	0.270132i	0.212747	−	0.977107i	$-0.431759\pi$
$773$	25.5782	−	7.51045i	0.919986	−	0.270132i	0.707238	+	0.706975i	$0.249941\pi$
$774$	0.230800	−	1.60525i	0.00829593	−	0.0576994i
$775$	0.505516	−	0.583396i	0.0181587	−	0.0209562i
$776$	−6.18168	+	13.5360i	−0.221910	+	0.485914i
$777$	−10.1530	−	2.98119i	−0.364237	−	0.106950i
$778$	0.352331	+	0.771498i	0.0126317	+	0.0276595i
$779$	−0.520440	−	3.61974i	−0.0186467	−	0.129691i
$780$	0.553668	+	0.355821i	0.0198245	+	0.0127404i
$781$	37.0145			1.32448
$782$	0.460491	+	0.484298i	0.0164671	+	0.0173185i
$783$	−4.56802			−0.163248
$784$	−0.352334	−	0.226431i	−0.0125834	−	0.00808684i
$785$	1.05271	+	7.32177i	0.0375729	+	0.261325i
$786$	1.16690	+	2.55515i	0.0416218	+	0.0911390i
$787$	−13.6593	−	4.01075i	−0.486903	−	0.142968i	0.0290613	−	0.999578i	$-0.490748\pi$
$787$	−13.6593	−	4.01075i	−0.486903	−	0.142968i	−0.515965	+	0.856610i	$0.672566\pi$
$788$	2.37166	−	5.19322i	0.0844870	−	0.185001i
$789$	−11.2635	+	12.9988i	−0.400991	+	0.462769i
$790$	−1.71653	+	11.9387i	−0.0610713	+	0.424760i
$791$	−13.4736	+	3.95622i	−0.479068	+	0.140667i
$792$	2.15323	+	2.48495i	0.0765115	+	0.0882990i
$793$	0.334201	−	0.214778i	0.0118678	−	0.00762698i
$794$	−11.1976	+	7.19626i	−0.397388	+	0.255386i
$795$	−1.71849	−	1.98324i	−0.0609486	−	0.0703384i
$796$	1.30813	−	0.384100i	0.0463653	−	0.0136141i
$797$	3.86802	−	26.9027i	0.137012	−	0.952941i	−0.799090	−	0.601212i	$-0.794685\pi$
$797$	3.86802	−	26.9027i	0.137012	−	0.952941i	0.936102	−	0.351729i	$-0.114406\pi$
$798$	4.67287	−	5.39278i	0.165418	−	0.190902i
$799$	0.665732	−	1.45775i	0.0235519	−	0.0515715i
$800$	−0.959493	−	0.281733i	−0.0339232	−	0.00996075i
$801$	6.48223	+	14.1941i	0.229038	+	0.501524i
$802$	−1.57911	−	10.9830i	−0.0557605	−	0.387823i
$803$	6.58587	+	4.23248i	0.232410	+	0.149361i
$804$	−10.8736			−0.383481
$805$	−8.47772	−	8.91602i	−0.298800	−	0.314248i
$806$	−0.508052			−0.0178954
$807$	−2.04229	−	1.31250i	−0.0718919	−	0.0462021i
$808$	−0.0599108	−	0.416689i	−0.00210765	−	0.0146591i
$809$	5.50077	+	12.0450i	0.193397	+	0.423480i	0.981343	−	0.192264i	$-0.0615830\pi$
$809$	5.50077	+	12.0450i	0.193397	+	0.423480i	−0.787947	+	0.615744i	$0.788856\pi$
$810$	0.959493	+	0.281733i	0.0337131	+	0.00989907i
$811$	10.9742	−	24.0302i	0.385358	−	0.843816i	−0.613189	−	0.789936i	$-0.710114\pi$
$811$	10.9742	−	24.0302i	0.385358	−	0.843816i	0.998547	−	0.0538803i	$-0.0171589\pi$
$812$	−7.67413	+	8.85641i	−0.269309	+	0.310799i
$813$	−0.332232	+	2.31073i	−0.0116519	+	0.0810407i
$814$	−13.0132	+	3.82101i	−0.456111	+	0.133926i
$815$	12.2308	+	14.1151i	0.428427	+	0.494431i
$816$	−0.117225	+	0.0753360i	−0.00410370	+	0.00263729i
$817$	−3.79485	+	2.43880i	−0.132765	+	0.0853230i
$818$	−19.9020	−	22.9682i	−0.695858	−	0.803063i
$819$	−1.62001	+	0.475676i	−0.0566076	+	0.0166215i
$820$	0.187106	−	1.30135i	0.00653402	−	0.0454451i
$821$	19.6659	−	22.6956i	0.686343	−	0.792082i	−0.300497	−	0.953783i	$-0.597152\pi$
$821$	19.6659	−	22.6956i	0.686343	−	0.792082i	0.986840	+	0.161700i	$0.0516978\pi$
$822$	−4.61357	+	10.1023i	−0.160917	+	0.352358i
$823$	46.9918	+	13.7980i	1.63803	+	0.480970i	0.965782	−	0.259354i	$-0.0835098\pi$
$823$	46.9918	+	13.7980i	1.63803	+	0.480970i	0.672250	+	0.740324i	$0.265328\pi$
$824$	−4.66454	−	10.2139i	−0.162497	−	0.355819i
$825$	−0.467941	−	3.25460i	−0.0162916	−	0.113311i
$826$	8.63233	+	5.54766i	0.300357	+	0.193028i
$827$	−31.8309			−1.10687			−0.553435	−	0.832893i	$-0.686683\pi$
$827$	−31.8309			−1.10687			−0.553435	+	0.832893i	$0.686683\pi$
$828$	2.96984	−	3.76564i	0.103209	−	0.130865i
$829$	15.3270			0.532328			0.266164	−	0.963928i	$-0.414244\pi$
$829$	15.3270			0.532328			0.266164	+	0.963928i	$0.414244\pi$
$830$	−1.11347	−	0.715583i	−0.0386491	−	0.0248382i
$831$	−1.22097	−	8.49204i	−0.0423550	−	0.294586i
$832$	0.273404	+	0.598671i	0.00947858	+	0.0207552i
$833$	0.0559968	+	0.0164422i	0.00194017	+	0.000569687i
$834$	−6.38422	+	13.9795i	−0.221067	+	0.484070i
$835$	11.0887	−	12.7970i	0.383739	−	0.442858i
$836$	1.30159	−	9.05274i	0.0450164	−	0.313096i
$837$	−0.740675	+	0.217482i	−0.0256015	+	0.00751727i
$838$	20.2250	+	23.3409i	0.698661	+	0.806298i
$839$	−9.75254	+	6.26758i	−0.336695	+	0.216381i	−0.698053	−	0.716047i	$-0.745950\pi$
$839$	−9.75254	+	6.26758i	−0.336695	+	0.216381i	0.361357	+	0.932427i	$0.382313\pi$
$840$	2.15814	−	1.38695i	0.0744628	−	0.0478543i
$841$	5.32610	+	6.14665i	0.183659	+	0.211953i
$842$	−28.3808	+	8.33335i	−0.978066	+	0.287186i
$843$	2.32149	−	16.1463i	0.0799564	−	0.556109i
$844$	7.12807	−	8.22624i	0.245358	−	0.283159i
$845$	5.22046	−	11.4312i	0.179589	−	0.393245i
$846$	−11.0348	−	3.24012i	−0.379385	−	0.111398i
$847$	−0.201013	−	0.440157i	−0.00690689	−	0.0151240i
$848$	−0.373464	−	2.59750i	−0.0128248	−	0.0891985i
$849$	4.86279	+	3.12513i	0.166891	+	0.107254i
$850$	0.139346			0.00477952
$851$	9.04001	+	17.5953i	0.309887	+	0.603160i
$852$	11.2572			0.385667
$853$	47.0647	+	30.2467i	1.61146	+	1.03563i	0.961175	+	0.275940i	$0.0889889\pi$
$853$	47.0647	+	30.2467i	1.61146	+	1.03563i	0.650290	+	0.759686i	$0.274647\pi$
$854$	−0.220374	−	1.53273i	−0.00754104	−	0.0524491i
$855$	−1.15549	−	2.53016i	−0.0395168	−	0.0865298i
$856$	11.1449	+	3.27245i	0.380926	+	0.111850i
$857$	7.61715	−	16.6792i	0.260197	−	0.569751i	−0.733774	−	0.679393i	$-0.762243\pi$
$857$	7.61715	−	16.6792i	0.260197	−	0.569751i	0.993971	+	0.109642i	$0.0349704\pi$
$858$	−1.41714	+	1.63546i	−0.0483803	+	0.0558338i
$859$	5.19972	−	36.1648i	0.177412	−	1.23393i	−0.685310	−	0.728251i	$-0.740333\pi$
$859$	5.19972	−	36.1648i	0.177412	−	1.23393i	0.862723	−	0.505678i	$-0.168757\pi$
$860$	−1.55606	+	0.456901i	−0.0530613	+	0.0155802i
$861$	2.20871	+	2.54898i	0.0752726	+	0.0868692i
$862$	−4.90374	+	3.15144i	−0.167022	+	0.107339i
$863$	−36.6758	+	23.5701i	−1.24846	+	0.802336i	−0.986661	−	0.162787i	$-0.947952\pi$
$863$	−36.6758	+	23.5701i	−1.24846	+	0.802336i	−0.261798	+	0.965123i	$0.584315\pi$
$864$	0.654861	+	0.755750i	0.0222788	+	0.0257111i
$865$	1.43531	−	0.421445i	0.0488020	−	0.0143295i
$866$	4.12943	−	28.7208i	0.140324	−	0.975973i
$867$	−11.1199	+	12.8331i	−0.377652	+	0.435834i
$868$	−0.822659	+	1.80137i	−0.0279229	+	0.0611426i
$869$	−38.0525	−	11.1732i	−1.29084	−	0.379026i
$870$	1.89762	+	4.15522i	0.0643355	+	0.140875i
$871$	−1.01846	−	7.08356i	−0.0345093	−	0.240017i
$872$	4.25108	+	2.73201i	0.143960	+	0.0925174i
$873$	−14.8807			−0.503637
$874$	−13.3255	+	0.616159i	−0.450741	+	0.0208419i
$875$	−2.56538			−0.0867257
$876$	2.00296	+	1.28723i	0.0676738	+	0.0434913i
$877$	3.77706	+	26.2700i	0.127542	+	0.887076i	0.948656	+	0.316311i	$0.102444\pi$
$877$	3.77706	+	26.2700i	0.127542	+	0.887076i	−0.821113	+	0.570765i	$0.806647\pi$
$878$	−4.35078	−	9.52688i	−0.146832	−	0.321517i
$879$	12.1030	+	3.55376i	0.408224	+	0.119865i
$880$	1.36591	−	2.99093i	0.0460449	−	0.100824i
$881$	−21.6961	+	25.0386i	−0.730959	+	0.843572i	−0.992579	−	0.121599i	$-0.961198\pi$
$881$	−21.6961	+	25.0386i	−0.730959	+	0.843572i	0.261620	+	0.965171i	$0.415743\pi$
$882$	0.0596044	−	0.414558i	0.00200698	−	0.0139589i
$883$	−37.0162	+	10.8689i	−1.24570	+	0.365769i	−0.837152	−	0.546970i	$-0.815781\pi$
$883$	−37.0162	+	10.8689i	−1.24570	+	0.365769i	−0.408543	+	0.912739i	$0.633963\pi$
$884$	−0.0600572	−	0.0693097i	−0.00201994	−	0.00233114i
$885$	3.36493	−	2.16251i	0.113111	−	0.0726919i
$886$	26.6095	−	17.1009i	0.893964	−	0.574516i
$887$	−35.3660	−	40.8146i	−1.18747	−	1.37042i	−0.912556	−	0.408951i	$-0.865895\pi$
$887$	−35.3660	−	40.8146i	−1.18747	−	1.37042i	−0.274918	−	0.961468i	$-0.588651\pi$
$888$	−3.95770	+	1.16208i	−0.132812	+	0.0389970i
$889$	−3.97336	+	27.6353i	−0.133262	+	0.926859i
$890$	10.2186	−	11.7929i	0.342528	−	0.395298i
$891$	−1.36591	+	2.99093i	−0.0457598	+	0.100200i
$892$	0.893101	+	0.262238i	0.0299032	+	0.00878038i
$893$	13.2889	+	29.0986i	0.444696	+	0.973748i
$894$	1.25689	+	8.74189i	0.0420368	+	0.292373i
$895$	−18.8878	−	12.1385i	−0.631350	−	0.405744i
$896$	2.56538			0.0857034
$897$	2.73129	+	1.58199i	0.0911950	+	0.0528211i
$898$	18.3176			0.611265
$899$	−2.96648	−	1.90644i	−0.0989375	−	0.0635833i
$900$	−0.142315	−	0.989821i	−0.00474383	−	0.0329940i
$901$	0.151906	+	0.332627i	0.00506071	+	0.0110814i
$902$	4.14782	+	1.21791i	0.138107	+	0.0405520i
$903$	1.72830	−	3.78445i	0.0575142	−	0.125939i
$904$	−3.58460	+	4.13684i	−0.119222	+	0.137589i
$905$	−1.29533	+	9.00920i	−0.0430582	+	0.299476i
$906$	−1.06531	+	0.312804i	−0.0353926	+	0.0103922i
$907$	−36.5705	−	42.2046i	−1.21430	−	1.40138i	−0.890332	−	0.455312i	$-0.849528\pi$
$907$	−36.5705	−	42.2046i	−1.21430	−	1.40138i	−0.323970	−	0.946067i	$-0.605018\pi$
$908$	−12.8386	+	8.25085i	−0.426063	+	0.273814i
$909$	0.354145	−	0.227595i	0.0117463	−	0.00754886i
$910$	1.10566	+	1.27601i	0.0366524	+	0.0422992i
$911$	−3.23392	+	0.949564i	−0.107144	+	0.0314605i	−0.334865	−	0.942266i	$-0.608691\pi$
$911$	−3.23392	+	0.949564i	−0.107144	+	0.0314605i	0.227721	+	0.973726i	$0.426873\pi$
$912$	0.395852	−	2.75321i	0.0131080	−	0.0911680i
$913$	2.84997	−	3.28904i	0.0943203	−	0.108851i
$914$	−6.51693	+	14.2701i	−0.215561	+	0.472012i
$915$	−0.579161	−	0.170057i	−0.0191465	−	0.00562192i
$916$	−0.143941	−	0.315187i	−0.00475594	−	0.0104141i
$917$	1.02554	+	7.13278i	0.0338663	+	0.235545i
$918$	−0.117225	−	0.0753360i	−0.00386900	−	0.00248646i
$919$	−35.2629			−1.16322			−0.581608	−	0.813469i	$-0.697576\pi$
$919$	−35.2629			−1.16322			−0.581608	+	0.813469i	$0.697576\pi$
$920$	−4.65906	−	1.13715i	−0.153605	−	0.0374909i
$921$	6.43868			0.212162
$922$	32.0294	+	20.5840i	1.05483	+	0.677899i
$923$	1.05440	+	7.33350i	0.0347059	+	0.241385i
$924$	3.50408	+	7.67288i	0.115276	+	0.252419i
$925$	3.95770	+	1.16208i	0.130128	+	0.0382091i
$926$	9.14408	−	20.0227i	0.300493	−	0.657988i
$927$	7.35319	−	8.48604i	0.241511	−	0.278718i
$928$	−0.650097	+	4.52153i	−0.0213405	+	0.148426i
$929$	−12.3942	+	3.63926i	−0.406639	+	0.119400i	−0.478654	−	0.878003i	$-0.658875\pi$
$929$	−12.3942	+	3.63926i	−0.406639	+	0.119400i	0.0720149	+	0.997404i	$0.477057\pi$
$930$	0.505516	+	0.583396i	0.0165765	+	0.0191303i
$931$	−0.980026	+	0.629825i	−0.0321191	+	0.0206417i
$932$	14.7455	−	9.47633i	0.483004	−	0.310408i
$933$	−2.67593	−	3.08818i	−0.0876059	−	0.101103i
$934$	−32.0010	+	9.39635i	−1.04711	+	0.307458i
$935$	−0.0652055	+	0.453514i	−0.00213245	+	0.0148315i
$936$	−0.430994	+	0.497394i	−0.0140875	+	0.0162578i
$937$	−8.86363	+	19.4086i	−0.289562	+	0.634053i	−0.997380	−	0.0723424i	$-0.976953\pi$
$937$	−8.86363	+	19.4086i	−0.289562	+	0.634053i	0.707818	+	0.706395i	$0.249680\pi$
$938$	−26.7649	−	7.85889i	−0.873905	−	0.256602i
$939$	2.43121	+	5.32361i	0.0793396	+	0.173730i
$940$	1.63672	+	11.3836i	0.0533839	+	0.371293i
$941$	50.9507	+	32.7440i	1.66095	+	1.06742i	0.916749	+	0.399464i	$0.130804\pi$
$941$	50.9507	+	32.7440i	1.66095	+	1.06742i	0.744196	+	0.667961i	$0.232833\pi$
$942$	−7.39706			−0.241009
$943$	0.608098	−	6.27584i	0.0198024	−	0.204370i
$944$	3.99990			0.130186
$945$	2.15814	+	1.38695i	0.0702042	+	0.0451175i
$946$	−0.758885	−	5.27816i	−0.0246735	−	0.171608i
$947$	0.00768542	+	0.0168287i	0.000249743	+	0.000546860i	0.909757	−	0.415142i	$-0.136268\pi$
$947$	0.00768542	+	0.0168287i	0.000249743	+	0.000546860i	−0.909507	+	0.415688i	$0.863541\pi$
$948$	−11.5729	−	3.39811i	−0.375871	−	0.110366i
$949$	−0.650955	+	1.42539i	−0.0211309	+	0.0462702i
$950$	−1.82151	+	2.10214i	−0.0590976	+	0.0682023i
$951$	0.326749	−	2.27259i	0.0105956	−	0.0736937i
$952$	−0.342995	+	0.100712i	−0.0111165	+	0.00326410i
$953$	−27.3310	−	31.5417i	−0.885339	−	1.02174i	−0.999600	−	0.0282853i	$-0.990995\pi$
$953$	−27.3310	−	31.5417i	−0.885339	−	1.02174i	0.114260	−	0.993451i	$-0.463550\pi$
$954$	2.20762	−	1.41875i	0.0714745	−	0.0459339i
$955$	−17.7456	+	11.4044i	−0.574235	+	0.369038i
$956$	−13.2276	−	15.2654i	−0.427810	−	0.493719i
$957$	−14.4115	+	4.23161i	−0.465859	+	0.136789i
$958$	−4.53697	+	31.5553i	−0.146583	+	1.01951i
$959$	−18.6576	+	21.5320i	−0.602485	+	0.695305i
$960$	0.415415	−	0.909632i	0.0134075	−	0.0293582i
$961$	29.1725	+	8.56583i	0.941049	+	0.276317i
$962$	−1.12773	−	2.46939i	−0.0363595	−	0.0796162i
$963$	1.65305	+	11.4972i	0.0532688	+	0.370493i
$964$	−15.6564	−	10.0617i	−0.504258	−	0.324067i
$965$	−18.5135			−0.595971
$966$	10.0318	−	7.12254i	0.322767	−	0.229164i
$967$	−16.0098			−0.514842			−0.257421	−	0.966299i	$-0.582873\pi$
$967$	−16.0098			−0.514842			−0.257421	+	0.966299i	$0.582873\pi$
$968$	−0.158678	−	0.101976i	−0.00510011	−	0.00327764i
$969$	0.0551603	+	0.383648i	0.00177200	+	0.0123246i
$970$	6.18168	+	13.5360i	0.198482	+	0.434615i
$971$	−17.7177	−	5.20238i	−0.568588	−	0.166952i	−0.0152121	−	0.999884i	$-0.504842\pi$
$971$	−17.7177	−	5.20238i	−0.568588	−	0.166952i	−0.553375	+	0.832932i	$0.686661\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	−25.8182	+	29.7958i	−0.827694	+	0.955210i
$974$	−4.09861	+	28.5065i	−0.131328	+	0.913406i
$975$	0.631487	−	0.185421i	0.0202238	−	0.00593824i
$976$	−0.395282	−	0.456180i	−0.0126527	−	0.0146020i
$977$	−31.2090	+	20.0568i	−0.998464	+	0.641674i	−0.934383	−	0.356271i	$-0.884048\pi$
$977$	−31.2090	+	20.0568i	−0.998464	+	0.641674i	−0.0640815	+	0.997945i	$0.520412\pi$
$978$	−15.7121	+	10.0975i	−0.502417	+	0.322884i
$979$	33.5994	+	38.7758i	1.07384	+	1.23928i
$980$	−0.401855	+	0.117995i	−0.0128368	+	0.00376922i
$981$	−0.719156	+	5.00184i	−0.0229609	+	0.159696i
$982$	17.4374	−	20.1238i	0.556449	−	0.642177i
$983$	−20.8763	+	45.7128i	−0.665852	+	1.45801i	0.211115	+	0.977461i	$0.432290\pi$
$983$	−20.8763	+	45.7128i	−0.665852	+	1.45801i	−0.876967	+	0.480551i	$0.840437\pi$
$984$	1.26148	+	0.370403i	0.0402144	+	0.0118080i
$985$	−2.37166	−	5.19322i	−0.0755675	−	0.165470i
$986$	−0.0905883	−	0.630055i	−0.00288492	−	0.0200650i
$987$	−24.8200	−	15.9509i	−0.790031	−	0.507722i
$988$	1.83065			0.0582408
$989$	−7.35344	+	2.53358i	−0.233826	+	0.0805631i
$990$	3.28807			0.104502
$991$	26.6551	+	17.1302i	0.846726	+	0.544158i	0.890552	−	0.454881i	$-0.150318\pi$
$991$	26.6551	+	17.1302i	0.846726	+	0.544158i	−0.0438261	+	0.999039i	$0.513955\pi$
$992$	0.109859	+	0.764087i	0.00348803	+	0.0242598i
$993$	−9.06629	−	19.8524i	−0.287710	−	0.629997i
$994$	27.7093	+	8.13618i	0.878885	+	0.258064i
$995$	0.566356	−	1.24015i	0.0179547	−	0.0393153i
$996$	0.866762	−	1.00030i	0.0274644	−	0.0316956i
$997$	−0.335605	+	2.33419i	−0.0106287	+	0.0739244i	−0.994445	−	0.105253i	$-0.966435\pi$
$997$	−0.335605	+	2.33419i	−0.0106287	+	0.0739244i	0.983817	+	0.179178i	$0.0573437\pi$
$998$	8.81139	−	2.58726i	0.278920	−	0.0818982i
$999$	−2.70116	−	3.11730i	−0.0854608	−	0.0986270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.301.1	✓	20
23.12	even	11	inner	690.2.m.d.541.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.301.1	✓	20	1.1	even	1	trivial
690.2.m.d.541.1	yes	20	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)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.67997 + 1.93879i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(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} +(-1.67997 + 1.93879i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(0.654861 + 0.755750i) q^{10} +(-2.76610 + 1.77766i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-0.430994 - 0.497394i) q^{13} +(-2.46147 + 0.722751i) q^{14} +(-0.142315 + 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.0578863 - 0.126753i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(1.15549 + 2.53016i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-2.15814 - 1.38695i) q^{21} -3.28807 q^{22} +(0.901053 + 4.71042i) q^{23} -1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.0936640 - 0.651448i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-2.46147 - 0.722751i) q^{28} +(1.89762 - 4.15522i) q^{29} +(-0.654861 + 0.755750i) q^{30} +(0.109859 - 0.764087i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-2.15323 - 2.48495i) q^{33} +(0.117225 - 0.0753360i) q^{34} +(-2.15814 + 1.38695i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(3.95770 - 1.16208i) q^{37} +(-0.395852 + 2.75321i) q^{38} +(0.430994 - 0.497394i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-1.26148 - 0.370403i) q^{41} +(-1.06570 - 2.33355i) q^{42} +(0.230800 + 1.60525i) q^{43} +(-2.76610 - 1.77766i) q^{44} -1.00000 q^{45} +(-1.78863 + 4.44981i) q^{46} +11.5007 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.0596044 + 0.414558i) q^{49} +(0.415415 + 0.909632i) q^{50} +(0.133701 + 0.0392582i) q^{51} +(0.273404 - 0.598671i) q^{52} +(-1.71849 + 1.98324i) q^{53} +(0.142315 - 0.989821i) q^{54} +(-3.15488 + 0.926355i) q^{55} +(-1.67997 - 1.93879i) q^{56} +(-2.33997 + 1.50381i) q^{57} +(3.84286 - 2.46966i) q^{58} +(-2.61938 - 3.02292i) q^{59} +(-0.959493 + 0.281733i) q^{60} +(-0.0859029 + 0.597468i) q^{61} +(0.505516 - 0.583396i) q^{62} +(1.06570 - 2.33355i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.273404 - 0.598671i) q^{65} +(-0.467941 - 3.25460i) q^{66} +(9.14743 + 5.87870i) q^{67} +0.139346 q^{68} +(-4.53425 + 1.56225i) q^{69} -2.56538 q^{70} +(-9.47019 - 6.08612i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-0.989072 - 2.16577i) q^{73} +(3.95770 + 1.16208i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(-1.82151 + 2.10214i) q^{76} +(1.20045 - 8.34928i) q^{77} +(0.631487 - 0.185421i) q^{78} +(7.89859 + 9.11546i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-0.860967 - 0.993609i) q^{82} +(-1.26997 + 0.372896i) q^{83} +(0.365092 - 2.53927i) q^{84} +(0.0912520 - 0.105310i) q^{85} +(-0.673701 + 1.47520i) q^{86} +(4.38298 + 1.28696i) q^{87} +(-1.36591 - 2.99093i) q^{88} +(-2.22071 - 15.4454i) q^{89} +(-0.841254 - 0.540641i) q^{90} +1.68840 q^{91} +(-3.91044 + 2.77641i) q^{92} +0.771944 q^{93} +(9.67499 + 6.21774i) q^{94} +(0.395852 + 2.75321i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(14.2780 + 4.19239i) q^{97} +(-0.173984 + 0.380973i) q^{98} +(2.15323 - 2.48495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more