LMFDB - Embedded newform 46.2.c.a.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [46,2,Mod(3,46)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	46.25
Dual form			46.2.c.a.35.1

$q$-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} +(-0.0530529 - 0.368991i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-3.26024 - 0.957293i) q^{5} +(0.154861 - 0.339098i) q^{6} +(-0.297176 + 0.342959i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.74514 - 0.806046i) q^{9} +(-2.22514 - 2.56794i) q^{10} +(-2.53833 + 1.63129i) q^{11} +(0.313607 - 0.201543i) q^{12} +(-0.592042 - 0.683252i) q^{13} +(-0.435418 + 0.127850i) q^{14} +(-0.180267 + 1.25379i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.61546 - 5.72706i) q^{17} +(2.74514 + 0.806046i) q^{18} +(2.73616 + 5.99136i) q^{19} +(-0.483568 - 3.36329i) q^{20} +(0.142315 + 0.0914602i) q^{21} -3.01732 q^{22} +(-0.838287 + 4.72200i) q^{23} +0.372786 q^{24} +(5.50648 + 3.53880i) q^{25} +(-0.128663 - 0.894870i) q^{26} +(-0.907644 - 1.98746i) q^{27} +(-0.435418 - 0.127850i) q^{28} +(-0.645699 + 1.41388i) q^{29} +(-0.829499 + 0.957293i) q^{30} +(1.07486 - 7.47584i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(0.736596 + 0.850077i) q^{33} +(5.29655 - 3.40388i) q^{34} +(1.29718 - 0.833644i) q^{35} +(1.87358 + 2.16222i) q^{36} +(-1.19143 + 0.349835i) q^{37} +(-0.937368 + 6.51954i) q^{38} +(-0.220705 + 0.254707i) q^{39} +(1.41153 - 3.09082i) q^{40} +(-7.37121 - 2.16438i) q^{41} +(0.0702757 + 0.153882i) q^{42} +(-0.887042 - 6.16951i) q^{43} +(-2.53833 - 1.63129i) q^{44} -9.72143 q^{45} +(-3.25812 + 3.51919i) q^{46} -10.0111 q^{47} +(0.313607 + 0.201543i) q^{48} +(0.966896 + 6.72491i) q^{49} +(2.71913 + 5.95406i) q^{50} +(-2.25199 - 0.661244i) q^{51} +(0.375565 - 0.822373i) q^{52} +(6.13461 - 7.07971i) q^{53} +(0.310945 - 2.16267i) q^{54} +(9.83719 - 2.88846i) q^{55} +(-0.297176 - 0.342959i) q^{56} +(2.06560 - 1.32748i) q^{57} +(-1.30760 + 0.840343i) q^{58} +(4.43488 + 5.11812i) q^{59} +(-1.21537 + 0.356865i) q^{60} +(-0.447498 + 3.11242i) q^{61} +(4.94597 - 5.70796i) q^{62} +(-0.539348 + 1.18101i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.27612 + 2.79432i) q^{65} +(0.160078 + 1.11336i) q^{66} +(-5.96316 - 3.83229i) q^{67} +6.29602 q^{68} +(1.78685 + 0.0588045i) q^{69} +1.54196 q^{70} +(10.6901 + 6.87011i) q^{71} +(0.407167 + 2.83191i) q^{72} +(-0.587813 - 1.28713i) q^{73} +(-1.19143 - 0.349835i) q^{74} +(1.01365 - 2.21959i) q^{75} +(-4.31329 + 4.97780i) q^{76} +(0.194866 - 1.35532i) q^{77} +(-0.323373 + 0.0949510i) q^{78} +(0.618652 + 0.713962i) q^{79} +(2.85848 - 1.83703i) q^{80} +(6.53535 - 4.20002i) q^{81} +(-5.03090 - 5.80597i) q^{82} +(7.57601 - 2.22452i) q^{83} +(-0.0240754 + 0.167448i) q^{84} +(-14.0095 + 16.1678i) q^{85} +(2.58926 - 5.66969i) q^{86} +(0.555967 + 0.163246i) q^{87} +(-1.25344 - 2.74465i) q^{88} +(1.58232 + 11.0053i) q^{89} +(-8.17819 - 5.25580i) q^{90} +0.410268 q^{91} +(-4.64352 + 1.19906i) q^{92} -2.81554 q^{93} +(-8.42190 - 5.41243i) q^{94} +(-3.18506 - 22.1526i) q^{95} +(0.154861 + 0.339098i) q^{96} +(-1.40353 - 0.412113i) q^{97} +(-2.82236 + 6.18010i) q^{98} +(-5.65318 + 6.52412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots + 20 q^{99}+O(q^{100}) $ 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{11}\right)$

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
$3$	−0.0530529	−	0.368991i	−0.0306301	−	0.213037i	0.968758	−	0.248007i	$-0.0797756\pi$
$3$	−0.0530529	−	0.368991i	−0.0306301	−	0.213037i	−0.999388	+	0.0349698i	$0.988866\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−3.26024	−	0.957293i	−1.45802	−	0.428114i	−0.545838	−	0.837891i	$-0.683788\pi$
$5$	−3.26024	−	0.957293i	−1.45802	−	0.428114i	−0.912186	+	0.409777i	$0.865607\pi$
$6$	0.154861	−	0.339098i	0.0632216	−	0.138436i
$7$	−0.297176	+	0.342959i	−0.112322	+	0.129626i	−0.809126	−	0.587635i	$-0.800059\pi$
$7$	−0.297176	+	0.342959i	−0.112322	+	0.129626i	0.696804	+	0.717261i	$0.254605\pi$
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	2.74514	−	0.806046i	0.915046	−	0.268682i
$10$	−2.22514	−	2.56794i	−0.703650	−	0.812055i
$11$	−2.53833	+	1.63129i	−0.765336	+	0.491851i	−0.864138	−	0.503256i	$-0.832135\pi$
$11$	−2.53833	+	1.63129i	−0.765336	+	0.491851i	0.0988018	+	0.995107i	$0.468499\pi$
$12$	0.313607	−	0.201543i	0.0905306	−	0.0581805i
$13$	−0.592042	−	0.683252i	−0.164203	−	0.189500i	0.667685	−	0.744444i	$-0.267285\pi$
$13$	−0.592042	−	0.683252i	−0.164203	−	0.189500i	−0.831888	+	0.554944i	$0.812740\pi$
$14$	−0.435418	+	0.127850i	−0.116370	+	0.0341694i
$15$	−0.180267	+	1.25379i	−0.0465448	+	0.323726i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	2.61546	−	5.72706i	0.634342	−	1.38902i	−0.270272	−	0.962784i	$-0.587114\pi$
$17$	2.61546	−	5.72706i	0.634342	−	1.38902i	0.904614	−	0.426232i	$-0.140159\pi$
$18$	2.74514	+	0.806046i	0.647035	+	0.189987i
$19$	2.73616	+	5.99136i	0.627719	+	1.37451i	0.909770	+	0.415114i	$0.136258\pi$
$19$	2.73616	+	5.99136i	0.627719	+	1.37451i	−0.282051	+	0.959400i	$0.591015\pi$
$20$	−0.483568	−	3.36329i	−0.108129	−	0.752055i
$21$	0.142315	+	0.0914602i	0.0310556	+	0.0199583i
$22$	−3.01732			−0.643295
$23$	−0.838287	+	4.72200i	−0.174795	+	0.984605i
$23$	−0.838287	+	4.72200i	−0.174795	+	0.984605i
$24$	0.372786			0.0760945
$25$	5.50648	+	3.53880i	1.10130	+	0.707761i
$26$	−0.128663	−	0.894870i	−0.0252329	−	0.175499i
$27$	−0.907644	−	1.98746i	−0.174676	−	0.382487i
$28$	−0.435418	−	0.127850i	−0.0822862	−	0.0241614i
$29$	−0.645699	+	1.41388i	−0.119903	+	0.262551i	−0.960061	−	0.279790i	$-0.909735\pi$
$29$	−0.645699	+	1.41388i	−0.119903	+	0.262551i	0.840158	+	0.542342i	$0.182462\pi$
$30$	−0.829499	+	0.957293i	−0.151445	+	0.174777i
$31$	1.07486	−	7.47584i	0.193051	−	1.34270i	−0.630823	−	0.775927i	$-0.717283\pi$
$31$	1.07486	−	7.47584i	0.193051	−	1.34270i	0.823874	−	0.566773i	$-0.191808\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	0.736596	+	0.850077i	0.128225	+	0.147979i
$34$	5.29655	−	3.40388i	0.908350	−	0.583761i
$35$	1.29718	−	0.833644i	0.219263	−	0.140912i
$36$	1.87358	+	2.16222i	0.312263	+	0.360370i
$37$	−1.19143	+	0.349835i	−0.195870	+	0.0575125i	−0.378196	−	0.925726i	$-0.623455\pi$
$37$	−1.19143	+	0.349835i	−0.195870	+	0.0575125i	0.182326	+	0.983238i	$0.441637\pi$
$38$	−0.937368	+	6.51954i	−0.152061	+	1.05761i
$39$	−0.220705	+	0.254707i	−0.0353410	+	0.0407857i
$40$	1.41153	−	3.09082i	0.223182	−	0.488701i
$41$	−7.37121	−	2.16438i	−1.15119	−	0.338020i	−0.350186	−	0.936680i	$-0.613882\pi$
$41$	−7.37121	−	2.16438i	−1.15119	−	0.338020i	−0.801003	+	0.598660i	$0.795700\pi$
$42$	0.0702757	+	0.153882i	0.0108438	+	0.0237446i
$43$	−0.887042	−	6.16951i	−0.135273	−	0.940841i	−0.938527	−	0.345206i	$-0.887809\pi$
$43$	−0.887042	−	6.16951i	−0.135273	−	0.940841i	0.803255	−	0.595636i	$-0.203100\pi$
$44$	−2.53833	−	1.63129i	−0.382668	−	0.245926i
$45$	−9.72143			−1.44919
$46$	−3.25812	+	3.51919i	−0.480383	+	0.518876i
$47$	−10.0111			−1.46027			−0.730137	−	0.683301i	$-0.760544\pi$
$47$	−10.0111			−1.46027			−0.730137	+	0.683301i	$0.760544\pi$
$48$	0.313607	+	0.201543i	0.0452653	+	0.0290902i
$49$	0.966896	+	6.72491i	0.138128	+	0.960702i
$50$	2.71913	+	5.95406i	0.384543	+	0.842031i
$51$	−2.25199	−	0.661244i	−0.315342	−	0.0925927i
$52$	0.375565	−	0.822373i	0.0520815	−	0.114043i
$53$	6.13461	−	7.07971i	0.842653	−	0.972474i	−0.157233	−	0.987562i	$-0.550257\pi$
$53$	6.13461	−	7.07971i	0.842653	−	0.972474i	0.999886	+	0.0150880i	$0.00480283\pi$
$54$	0.310945	−	2.16267i	0.0423142	−	0.294302i
$55$	9.83719	−	2.88846i	1.32645	−	0.389480i
$56$	−0.297176	−	0.342959i	−0.0397118	−	0.0458298i
$57$	2.06560	−	1.32748i	0.273595	−	0.175829i
$58$	−1.30760	+	0.840343i	−0.171696	+	0.110342i
$59$	4.43488	+	5.11812i	0.577372	+	0.666323i	0.967038	−	0.254634i	$-0.0819549\pi$
$59$	4.43488	+	5.11812i	0.577372	+	0.666323i	−0.389666	+	0.920956i	$0.627409\pi$
$60$	−1.21537	+	0.356865i	−0.156904	+	0.0460711i
$61$	−0.447498	+	3.11242i	−0.0572962	+	0.398504i	0.940911	+	0.338654i	$0.109971\pi$
$61$	−0.447498	+	3.11242i	−0.0572962	+	0.398504i	−0.998207	+	0.0598505i	$0.980938\pi$
$62$	4.94597	−	5.70796i	0.628139	−	0.724912i
$63$	−0.539348	+	1.18101i	−0.0679514	+	0.148793i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	1.27612	+	2.79432i	0.158284	+	0.346593i
$66$	0.160078	+	1.11336i	0.0197042	+	0.137046i
$67$	−5.96316	−	3.83229i	−0.728516	−	0.468189i	0.123074	−	0.992398i	$-0.460725\pi$
$67$	−5.96316	−	3.83229i	−0.728516	−	0.468189i	−0.851590	+	0.524209i	$0.824361\pi$
$68$	6.29602			0.763504
$69$	1.78685	+	0.0588045i	0.215111	+	0.00707924i
$70$	1.54196			0.184299
$71$	10.6901	+	6.87011i	1.26868	+	0.815332i	0.989448	−	0.144891i	$-0.0462833\pi$
$71$	10.6901	+	6.87011i	1.26868	+	0.815332i	0.279234	+	0.960223i	$0.409920\pi$
$72$	0.407167	+	2.83191i	0.0479851	+	0.333744i
$73$	−0.587813	−	1.28713i	−0.0687984	−	0.150647i	0.872109	−	0.489312i	$-0.162752\pi$
$73$	−0.587813	−	1.28713i	−0.0687984	−	0.150647i	−0.940907	+	0.338665i	$0.890025\pi$
$74$	−1.19143	−	0.349835i	−0.138501	−	0.0406675i
$75$	1.01365	−	2.21959i	0.117046	−	0.256296i
$76$	−4.31329	+	4.97780i	−0.494769	+	0.570993i
$77$	0.194866	−	1.35532i	0.0222070	−	0.154453i
$78$	−0.323373	+	0.0949510i	−0.0366148	+	0.0107511i
$79$	0.618652	+	0.713962i	0.0696038	+	0.0803270i	0.789483	−	0.613772i	$-0.210349\pi$
$79$	0.618652	+	0.713962i	0.0696038	+	0.0803270i	−0.719880	+	0.694099i	$0.755803\pi$
$80$	2.85848	−	1.83703i	0.319587	−	0.205386i
$81$	6.53535	−	4.20002i	0.726150	−	0.466669i
$82$	−5.03090	−	5.80597i	−0.555570	−	0.641162i
$83$	7.57601	−	2.22452i	0.831575	−	0.244173i	0.161882	−	0.986810i	$-0.448244\pi$
$83$	7.57601	−	2.22452i	0.831575	−	0.244173i	0.669694	+	0.742638i	$0.266425\pi$
$84$	−0.0240754	+	0.167448i	−0.00262684	+	0.0182701i
$85$	−14.0095	+	16.1678i	−1.51954	+	1.75365i
$86$	2.58926	−	5.66969i	0.279207	−	0.611379i
$87$	0.555967	+	0.163246i	0.0596059	+	0.0175019i
$88$	−1.25344	−	2.74465i	−0.133617	−	0.292581i
$89$	1.58232	+	11.0053i	0.167726	+	1.16656i	0.883571	+	0.468298i	$0.155133\pi$
$89$	1.58232	+	11.0053i	0.167726	+	1.16656i	−0.715845	+	0.698259i	$0.753958\pi$
$90$	−8.17819	−	5.25580i	−0.862057	−	0.554010i
$91$	0.410268			0.0430078
$92$	−4.64352	+	1.19906i	−0.484120	+	0.125010i
$93$	−2.81554			−0.291958
$94$	−8.42190	−	5.41243i	−0.868653	−	0.558249i
$95$	−3.18506	−	22.1526i	−0.326780	−	2.27281i
$96$	0.154861	+	0.339098i	0.0158054	+	0.0346090i
$97$	−1.40353	−	0.412113i	−0.142507	−	0.0418437i	0.209701	−	0.977765i	$-0.432751\pi$
$97$	−1.40353	−	0.412113i	−0.142507	−	0.0418437i	−0.352208	+	0.935922i	$0.614569\pi$
$98$	−2.82236	+	6.18010i	−0.285101	+	0.624284i
$99$	−5.65318	+	6.52412i	−0.568166	+	0.655699i
$100$	−0.931532	+	6.47895i	−0.0931532	+	0.647895i
$101$	−2.29607	+	0.674187i	−0.228467	+	0.0670841i	−0.393962	−	0.919127i	$-0.628896\pi$
$101$	−2.29607	+	0.674187i	−0.228467	+	0.0670841i	0.165495	+	0.986211i	$0.447078\pi$
$102$	−1.53700	−	1.77379i	−0.152186	−	0.175632i
$103$	−9.53126	+	6.12537i	−0.939143	+	0.603551i	−0.918152	−	0.396229i	$-0.870319\pi$
$103$	−9.53126	+	6.12537i	−0.939143	+	0.603551i	−0.0209914	+	0.999780i	$0.506682\pi$
$104$	0.760554	−	0.488779i	0.0745785	−	0.0479287i
$105$	−0.376426	−	0.434419i	−0.0367354	−	0.0423950i
$106$	8.98834	−	2.63922i	0.873025	−	0.256343i
$107$	0.448170	−	3.11709i	0.0433263	−	0.301341i	−0.956624	−	0.291327i	$-0.905903\pi$
$107$	0.448170	−	3.11709i	0.0433263	−	0.301341i	0.999950	−	0.0100140i	$-0.00318761\pi$
$108$	1.43081	−	1.65124i	0.137680	−	0.158891i
$109$	2.06655	−	4.52510i	0.197939	−	0.433426i	−0.784470	−	0.620167i	$-0.787065\pi$
$109$	2.06655	−	4.52510i	0.197939	−	0.433426i	0.982409	+	0.186740i	$0.0597923\pi$
$110$	9.83719	+	2.88846i	0.937939	+	0.275404i
$111$	0.192295	+	0.421067i	0.0182518	+	0.0399659i
$112$	−0.0645824	−	0.449181i	−0.00610247	−	0.0424436i
$113$	7.84875	+	5.04409i	0.738349	+	0.474508i	0.854976	−	0.518668i	$-0.173572\pi$
$113$	7.84875	+	5.04409i	0.738349	+	0.474508i	−0.116627	+	0.993176i	$0.537208\pi$
$114$	2.45538			0.229968
$115$	7.25335	−	14.5924i	0.676378	−	1.36074i
$116$	−1.55435			−0.144317
$117$	−2.17597	−	1.39841i	−0.201168	−	0.129283i
$118$	0.963791	+	6.70331i	0.0887242	+	0.617090i
$119$	1.18689	+	2.59894i	0.108802	+	0.238244i
$120$	−1.21537	−	0.356865i	−0.110948	−	0.0325772i
$121$	−0.787535	+	1.72446i	−0.0715941	+	0.156769i
$122$	−2.05916	+	2.37640i	−0.186427	+	0.215149i
$123$	−0.407574	+	2.83474i	−0.0367497	+	0.255600i
$124$	7.24677	−	2.12785i	0.650780	−	0.191086i
$125$	−3.43911	−	3.96894i	−0.307603	−	0.354993i
$126$	−1.09223	+	0.701933i	−0.0973035	+	0.0625331i
$127$	−2.36859	+	1.52220i	−0.210178	+	0.135073i	−0.641495	−	0.767127i	$-0.721685\pi$
$127$	−2.36859	+	1.52220i	−0.210178	+	0.135073i	0.431317	+	0.902200i	$0.358049\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−2.22943	+	0.654621i	−0.196291	+	0.0576362i
$130$	−0.437181	+	3.04066i	−0.0383433	+	0.266684i
$131$	2.90789	−	3.35588i	0.254063	−	0.293205i	−0.614362	−	0.789024i	$-0.710587\pi$
$131$	2.90789	−	3.35588i	0.254063	−	0.293205i	0.868426	+	0.495819i	$0.165132\pi$
$132$	−0.467264	+	1.02317i	−0.0406701	+	0.0890552i
$133$	−2.86791	−	0.842095i	−0.248680	−	0.0730189i
$134$	−2.94464	−	6.44786i	−0.254378	−	0.557010i
$135$	1.05655	+	7.34848i	0.0909335	+	0.632457i
$136$	5.29655	+	3.40388i	0.454175	+	0.291881i
$137$	8.55865			0.731215			0.365607	−	0.930769i	$-0.380861\pi$
$137$	8.55865			0.731215			0.365607	+	0.930769i	$0.380861\pi$
$138$	1.47140	+	1.01551i	0.125254	+	0.0864462i
$139$	1.44220			0.122326			0.0611629	−	0.998128i	$-0.480519\pi$
$139$	1.44220			0.122326			0.0611629	+	0.998128i	$0.480519\pi$
$140$	1.29718	+	0.833644i	0.109631	+	0.0704558i
$141$	0.531120	+	3.69402i	0.0447284	+	0.311093i
$142$	5.27882	+	11.5590i	0.442989	+	0.970010i
$143$	2.61738	+	0.768532i	0.218876	+	0.0642678i
$144$	−1.18852	+	2.60249i	−0.0990429	+	0.216874i
$145$	3.45863	−	3.99147i	0.287224	−	0.331474i
$146$	0.201376	−	1.40060i	0.0166660	−	0.115914i
$147$	2.43014	−	0.713552i	0.200434	−	0.0588528i
$148$	−0.813159	−	0.938435i	−0.0668412	−	0.0771389i
$149$	2.09196	−	1.34442i	0.171380	−	0.110139i	−0.452139	−	0.891948i	$-0.649339\pi$
$149$	2.09196	−	1.34442i	0.171380	−	0.110139i	0.623519	+	0.781808i	$0.285702\pi$
$150$	2.05274	−	1.31921i	0.167605	−	0.107713i
$151$	−1.68399	−	1.94343i	−0.137041	−	0.158154i	0.683080	−	0.730343i	$-0.260640\pi$
$151$	−1.68399	−	1.94343i	−0.137041	−	0.158154i	−0.820122	+	0.572189i	$0.806094\pi$
$152$	−6.31978	+	1.85565i	−0.512602	+	0.150513i
$153$	2.56353	−	17.8297i	0.207249	−	1.44145i
$154$	0.896674	−	1.03482i	0.0722560	−	0.0833879i
$155$	−10.6609	+	23.3441i	−0.856302	+	1.87504i
$156$	−0.323373	−	0.0949510i	−0.0258906	−	0.00760216i
$157$	−1.98827	−	4.35370i	−0.158681	−	0.347463i	0.813547	−	0.581499i	$-0.197534\pi$
$157$	−1.98827	−	4.35370i	−0.158681	−	0.347463i	−0.972228	+	0.234037i	$0.924806\pi$
$158$	0.134446	+	0.935092i	0.0106959	+	0.0743919i
$159$	−2.93781	−	1.88802i	−0.232984	−	0.149729i
$160$	3.39788			0.268626
$161$	−1.37033	−	1.69076i	−0.107997	−	0.133251i
$162$	7.76859			0.610358
$163$	−13.3604	−	8.58618i	−1.04646	−	0.672521i	−0.0998865	−	0.994999i	$-0.531848\pi$
$163$	−13.3604	−	8.58618i	−1.04646	−	0.672521i	−0.946577	+	0.322477i	$0.895484\pi$
$164$	−1.09332	−	7.60420i	−0.0853739	−	0.593789i
$165$	−1.58771	−	3.47659i	−0.123603	−	0.270652i
$166$	7.57601	+	2.22452i	0.588013	+	0.172656i
$167$	−2.18808	+	4.79122i	−0.169318	+	0.370755i	−0.975201	−	0.221319i	$-0.928964\pi$
$167$	−2.18808	+	4.79122i	−0.169318	+	0.370755i	0.805883	+	0.592075i	$0.201691\pi$
$168$	−0.110783	+	0.127850i	−0.00854708	+	0.00986385i
$169$	1.73377	−	12.0587i	0.133367	−	0.927589i
$170$	−20.5265	+	6.02713i	−1.57431	+	0.462260i
$171$	12.3405	+	14.2417i	0.943699	+	1.08909i
$172$	5.24349	−	3.36979i	0.399813	−	0.256944i
$173$	−1.42274	+	0.914337i	−0.108169	+	0.0695158i	−0.593607	−	0.804755i	$-0.702296\pi$
$173$	−1.42274	+	0.914337i	−0.108169	+	0.0695158i	0.485438	+	0.874271i	$0.338660\pi$
$174$	0.379451	+	0.437910i	0.0287661	+	0.0331979i
$175$	−2.85006	+	0.836852i	−0.215444	+	0.0632601i
$176$	0.429409	−	2.98661i	0.0323680	−	0.225124i
$177$	1.65326	−	1.90796i	0.124267	−	0.143411i
$178$	−4.61877	+	10.1137i	−0.346191	+	0.758053i
$179$	−10.6333	−	3.12221i	−0.794767	−	0.233365i	−0.140949	−	0.990017i	$-0.545015\pi$
$179$	−10.6333	−	3.12221i	−0.794767	−	0.233365i	−0.653818	+	0.756652i	$0.726834\pi$
$180$	−4.03843	−	8.84293i	−0.301007	−	0.659113i
$181$	−0.369064	−	2.56690i	−0.0274323	−	0.190796i	0.971497	−	0.237050i	$-0.0761806\pi$
$181$	−0.369064	−	2.56690i	−0.0274323	−	0.190796i	−0.998930	+	0.0462544i	$0.985272\pi$
$182$	0.345139	+	0.221808i	0.0255834	+	0.0164415i
$183$	1.17220			0.0866512
$184$	−4.55464	−	1.50176i	−0.335772	−	0.110712i
$185$	4.21924			0.310205
$186$	−2.36859	−	1.52220i	−0.173673	−	0.111613i
$187$	2.70357	+	18.8037i	0.197705	+	1.37507i
$188$	−4.15877	−	9.10645i	−0.303310	−	0.664156i
$189$	0.951347	+	0.279341i	0.0692003	+	0.0203191i
$190$	9.29715	−	20.3579i	0.674486	−	1.47692i
$191$	9.41486	−	10.8653i	0.681235	−	0.786188i	−0.304855	−	0.952399i	$-0.598608\pi$
$191$	9.41486	−	10.8653i	0.681235	−	0.786188i	0.986090	+	0.166211i	$0.0531534\pi$
$192$	−0.0530529	+	0.368991i	−0.00382876	+	0.0266296i
$193$	−13.1935	+	3.87395i	−0.949687	+	0.278853i	−0.719657	−	0.694330i	$-0.755701\pi$
$193$	−13.1935	+	3.87395i	−0.949687	+	0.278853i	−0.230031	+	0.973183i	$0.573883\pi$
$194$	−0.957917	−	1.10549i	−0.0687744	−	0.0793699i
$195$	0.963379	−	0.619126i	0.0689890	−	0.0443365i
$196$	−5.71553	+	3.67315i	−0.408252	+	0.262368i
$197$	2.11370	+	2.43934i	0.150595	+	0.173795i	0.826034	−	0.563620i	$-0.190592\pi$
$197$	2.11370	+	2.43934i	0.150595	+	0.173795i	−0.675440	+	0.737415i	$0.736046\pi$
$198$	−8.28296	+	2.43210i	−0.588645	+	0.172842i
$199$	−1.34169	+	9.33168i	−0.0951101	+	0.661506i	0.885370	+	0.464887i	$0.153905\pi$
$199$	−1.34169	+	9.33168i	−0.0951101	+	0.661506i	−0.980480	+	0.196618i	$0.937004\pi$
$200$	−4.28644	+	4.94681i	−0.303097	+	0.349792i
$201$	−1.09772	+	2.40367i	−0.0774271	+	0.169542i
$202$	−2.29607	−	0.674187i	−0.161551	−	0.0474356i
$203$	−0.293018	−	0.641620i	−0.0205658	−	0.0450329i
$204$	−0.334022	−	2.32317i	−0.0233862	−	0.162655i
$205$	21.9600	+	14.1128i	1.53375	+	0.985681i
$206$	−11.3298			−0.789387
$207$	1.50493	+	13.6382i	0.104600	+	0.947923i
$208$	0.904073			0.0626862
$209$	−16.7189	−	10.7446i	−1.15647	−	0.743219i
$210$	−0.0818052	−	0.568968i	−0.00564510	−	0.0392625i
$211$	−11.0770	−	24.2552i	−0.762571	−	1.66980i	−0.742360	−	0.670001i	$-0.766294\pi$
$211$	−11.0770	−	24.2552i	−0.762571	−	1.66980i	−0.0202106	−	0.999796i	$-0.506434\pi$
$212$	8.98834	+	2.63922i	0.617322	+	0.181262i
$213$	1.96787	−	4.30903i	0.134836	−	0.295250i
$214$	2.06225	−	2.37997i	0.140973	−	0.162691i
$215$	−3.01406	+	20.9632i	−0.205557	+	1.42968i
$216$	2.09640	−	0.615560i	0.142642	−	0.0418835i
$217$	2.24448	+	2.59027i	0.152365	+	0.175839i
$218$	4.18494	−	2.68950i	0.283440	−	0.182156i
$219$	−0.443755	+	0.285184i	−0.0299862	+	0.0192710i
$220$	6.71395	+	7.74831i	0.452654	+	0.522391i
$221$	−5.46149	+	1.60364i	−0.367379	+	0.107872i
$222$	−0.0658773	+	0.458186i	−0.00442139	+	0.0307515i
$223$	17.2361	−	19.8916i	1.15422	−	1.33204i	0.219929	−	0.975516i	$-0.429417\pi$
$223$	17.2361	−	19.8916i	1.15422	−	1.33204i	0.934287	−	0.356521i	$-0.116037\pi$
$224$	0.188515	−	0.412791i	0.0125957	−	0.0275807i
$225$	17.9685	+	5.27603i	1.19790	+	0.351735i
$226$	3.87575	+	8.48671i	0.257811	+	0.564528i
$227$	−0.547746	−	3.80966i	−0.0363552	−	0.252856i	0.963536	−	0.267577i	$-0.0862230\pi$
$227$	−0.547746	−	3.80966i	−0.0363552	−	0.252856i	−0.999892	+	0.0147212i	$0.995314\pi$
$228$	2.06560	+	1.32748i	0.136798	+	0.0879145i
$229$	21.9552			1.45084			0.725422	−	0.688305i	$-0.241645\pi$
$229$	21.9552			1.45084			0.725422	+	0.688305i	$0.241645\pi$
$230$	13.9911	−	8.35442i	0.922548	−	0.550874i
$231$	−0.510440			−0.0335845
$232$	−1.30760	−	0.840343i	−0.0858481	−	0.0551712i
$233$	1.78881	+	12.4414i	0.117189	+	0.815066i	0.960627	+	0.277840i	$0.0896186\pi$
$233$	1.78881	+	12.4414i	0.117189	+	0.815066i	−0.843439	+	0.537226i	$0.819472\pi$
$234$	−1.07450	−	2.35284i	−0.0702425	−	0.153810i
$235$	32.6387	+	9.58358i	2.12911	+	0.625164i
$236$	−2.81329	+	6.16025i	−0.183130	+	0.400998i
$237$	0.230624	−	0.266155i	0.0149807	−	0.0172886i
$238$	−0.406612	+	2.82805i	−0.0263567	+	0.183315i
$239$	−23.4574	+	6.88771i	−1.51733	+	0.445529i	−0.931146	−	0.364647i	$-0.881190\pi$
$239$	−23.4574	+	6.88771i	−1.51733	+	0.445529i	−0.586187	+	0.810176i	$0.699372\pi$
$240$	−0.829499	−	0.957293i	−0.0535439	−	0.0617930i
$241$	−12.1026	+	7.77784i	−0.779594	+	0.501015i	−0.868899	−	0.494990i	$-0.835172\pi$
$241$	−12.1026	+	7.77784i	−0.779594	+	0.501015i	0.0893048	+	0.996004i	$0.471535\pi$
$242$	−1.59483	+	1.02493i	−0.102520	+	0.0658853i
$243$	−6.18892	−	7.14239i	−0.397019	−	0.458185i
$244$	−3.01705	+	0.885886i	−0.193147	+	0.0567130i
$245$	3.28540	−	22.8504i	0.209896	−	1.45986i
$246$	−1.87545	+	2.16438i	−0.119574	+	0.137996i
$247$	2.47369	−	5.41663i	0.157397	−	0.344652i
$248$	7.24677	+	2.12785i	0.460171	+	0.135118i
$249$	−1.22276	−	2.67746i	−0.0774891	−	0.169677i
$250$	−0.747389	−	5.19821i	−0.0472690	−	0.328763i
$251$	−4.96630	−	3.19165i	−0.313470	−	0.201455i	0.374440	−	0.927251i	$-0.377835\pi$
$251$	−4.96630	−	3.19165i	−0.313470	−	0.201455i	−0.687910	+	0.725796i	$0.741471\pi$
$252$	−1.29833			−0.0817874
$253$	−5.57508	−	13.3535i	−0.350503	−	0.839526i
$254$	−2.81554			−0.176663
$255$	6.70903	+	4.31163i	0.420136	+	0.270005i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	0.370120	+	0.810449i	0.0230874	+	0.0505544i	0.920824	−	0.389977i	$-0.127517\pi$
$257$	0.370120	+	0.810449i	0.0230874	+	0.0505544i	−0.897737	+	0.440532i	$0.854790\pi$
$258$	−2.22943	−	0.654621i	−0.138799	−	0.0407549i
$259$	0.234084	−	0.512574i	0.0145453	−	0.0318498i
$260$	−2.01168	+	2.32161i	−0.124759	+	0.143980i
$261$	−0.632879	+	4.40177i	−0.0391742	+	0.272463i
$262$	4.26060	−	1.25102i	0.263221	−	0.0772886i
$263$	3.81112	+	4.39827i	0.235004	+	0.271209i	0.860986	−	0.508628i	$-0.169847\pi$
$263$	3.81112	+	4.39827i	0.235004	+	0.271209i	−0.625982	+	0.779837i	$0.715302\pi$
$264$	−0.946253	+	0.608120i	−0.0582379	+	0.0374272i
$265$	−26.7776	+	17.2089i	−1.64494	+	1.05714i
$266$	−1.95737	−	2.25893i	−0.120014	−	0.138504i
$267$	3.97690	−	1.16772i	0.243383	−	0.0714636i
$268$	1.00879	−	7.01627i	0.0616215	−	0.428587i
$269$	7.98246	−	9.21225i	0.486699	−	0.561681i	−0.458282	−	0.888807i	$-0.651535\pi$
$269$	7.98246	−	9.21225i	0.486699	−	0.561681i	0.944981	+	0.327127i	$0.106080\pi$
$270$	−3.08406	+	6.75315i	−0.187690	+	0.410984i
$271$	−15.0738	−	4.42608i	−0.915670	−	0.268865i	−0.210245	−	0.977649i	$-0.567426\pi$
$271$	−15.0738	−	4.42608i	−0.915670	−	0.268865i	−0.705426	+	0.708784i	$0.749244\pi$
$272$	2.61546	+	5.72706i	0.158586	+	0.347254i
$273$	−0.0217659	−	0.151385i	−0.00131733	−	0.00916225i
$274$	7.19999	+	4.62715i	0.434967	+	0.279537i
$275$	−19.7501			−1.19097
$276$	0.688794	+	1.64980i	0.0414605	+	0.0993065i
$277$	22.1047			1.32814			0.664070	−	0.747670i	$-0.268828\pi$
$277$	22.1047			1.32814			0.664070	+	0.747670i	$0.268828\pi$
$278$	1.21326	+	0.779712i	0.0727662	+	0.0467640i
$279$	−3.07522	−	21.3886i	−0.184108	−	1.28050i
$280$	0.640551	+	1.40261i	0.0382803	+	0.0838221i
$281$	−30.8970	−	9.07217i	−1.84316	−	0.541200i	−0.999994	−	0.00354681i	$-0.998871\pi$
$281$	−30.8970	−	9.07217i	−1.84316	−	0.541200i	−0.843166	−	0.537654i	$-0.819311\pi$
$282$	−1.55033	+	3.39475i	−0.0923209	+	0.202155i
$283$	−16.4016	+	18.9285i	−0.974976	+	1.12518i	0.0171390	+	0.999853i	$0.494544\pi$
$283$	−16.4016	+	18.9285i	−0.974976	+	1.12518i	−0.992115	+	0.125329i	$0.960001\pi$
$284$	−1.80844	+	12.5780i	−0.107311	+	0.746367i
$285$	−8.00513	+	2.35052i	−0.474183	+	0.139233i
$286$	1.78638	+	2.06159i	0.105631	+	0.121904i
$287$	2.93284	−	1.88482i	0.173120	−	0.111257i
$288$	−2.40685	+	1.54679i	−0.141825	+	0.0911455i
$289$	−14.8259	−	17.1100i	−0.872114	−	1.00647i
$290$	5.06754	−	1.48796i	0.297576	−	0.0873763i
$291$	−0.0776047	+	0.539753i	−0.00454927	+	0.0316409i
$292$	0.926630	−	1.06939i	0.0542269	−	0.0625812i
$293$	−3.88510	+	8.50719i	−0.226970	+	0.496995i	−0.988516	−	0.151116i	$-0.951713\pi$
$293$	−3.88510	+	8.50719i	−0.226970	+	0.496995i	0.761546	+	0.648111i	$0.224441\pi$
$294$	2.43014	+	0.713552i	0.141728	+	0.0416152i
$295$	−9.55922	−	20.9318i	−0.556559	−	1.21870i
$296$	−0.176716	−	1.22909i	−0.0102714	−	0.0714393i
$297$	5.54602	+	3.56421i	0.321813	+	0.206816i
$298$	2.48672			0.144052
$299$	3.72262	−	2.22286i	0.215285	−	0.128551i
$300$	2.44009			0.140879
$301$	2.37950	+	1.52921i	0.137152	+	0.0881421i
$302$	−0.365966	−	2.54535i	−0.0210590	−	0.146469i
$303$	0.370582	+	0.811462i	0.0212894	+	0.0466173i
$304$	−6.31978	−	1.85565i	−0.362464	−	0.106429i
$305$	4.43844	−	9.71884i	0.254145	−	0.556499i
$306$	11.7961	−	13.6134i	0.674336	−	0.778226i
$307$	−3.46888	+	24.1266i	−0.197979	+	1.37698i	0.612158	+	0.790736i	$0.290302\pi$
$307$	−3.46888	+	24.1266i	−0.197979	+	1.37698i	−0.810137	+	0.586241i	$0.800607\pi$
$308$	1.31379	−	0.385765i	0.0748604	−	0.0219810i
$309$	2.76587	+	3.19198i	0.157345	+	0.181586i
$310$	−21.5893	+	13.8746i	−1.22619	+	0.788023i
$311$	10.5510	−	6.78069i	0.598290	−	0.384498i	−0.206160	−	0.978518i	$-0.566097\pi$
$311$	10.5510	−	6.78069i	0.598290	−	0.384498i	0.804450	+	0.594021i	$0.202460\pi$
$312$	−0.220705	−	0.254707i	−0.0124949	−	0.0144199i
$313$	−9.63076	+	2.82785i	−0.544363	+	0.159839i	−0.542341	−	0.840159i	$-0.682462\pi$
$313$	−9.63076	+	2.82785i	−0.544363	+	0.159839i	−0.00202200	+	0.999998i	$0.500644\pi$
$314$	0.681150	−	4.73750i	0.0384395	−	0.267353i
$315$	2.88897	−	3.33405i	0.162775	−	0.187853i
$316$	−0.392446	+	0.859336i	−0.0220768	+	0.0483414i
$317$	30.6385	+	8.99628i	1.72083	+	0.505281i	0.985098	−	0.171992i	$-0.0550204\pi$
$317$	30.6385	+	8.99628i	1.72083	+	0.505281i	0.735731	+	0.677273i	$0.236839\pi$
$318$	−1.45071	−	3.17660i	−0.0813515	−	0.178135i
$319$	−0.667451	−	4.64222i	−0.0373701	−	0.259915i
$320$	2.85848	+	1.83703i	0.159794	+	0.102693i
$321$	−1.17396			−0.0655239
$322$	−0.238703	−	2.16322i	−0.0133024	−	0.120551i
$323$	41.4692			2.30741
$324$	6.53535	+	4.20002i	0.363075	+	0.233334i
$325$	−0.842172	−	5.85744i	−0.0467153	−	0.324912i
$326$	−6.59741	−	14.4463i	−0.365397	−	0.800107i
$327$	−1.77936	−	0.522467i	−0.0983988	−	0.0288925i
$328$	3.19138	−	6.98816i	0.176215	−	0.385856i
$329$	2.97506	−	3.43341i	0.164021	−	0.189290i
$330$	0.543924	−	3.78308i	0.0299420	−	0.208251i
$331$	29.4707	−	8.65337i	1.61985	−	0.475632i	0.658875	−	0.752252i	$-0.271032\pi$
$331$	29.4707	−	8.65337i	1.61985	−	0.475632i	0.960979	+	0.276620i	$0.0892143\pi$
$332$	5.17068	+	5.96729i	0.283778	+	0.327497i
$333$	−2.98865	+	1.92069i	−0.163777	+	0.105253i
$334$	−4.43105	+	2.84766i	−0.242456	+	0.155817i
$335$	15.7727	+	18.2027i	0.861755	+	0.994519i
$336$	−0.162317	+	0.0476607i	−0.00885514	+	0.00260010i
$337$	−3.97926	+	27.6764i	−0.216764	+	1.50763i	0.533109	+	0.846047i	$0.321024\pi$
$337$	−3.97926	+	27.6764i	−0.216764	+	1.50763i	−0.749873	+	0.661582i	$0.769885\pi$
$338$	7.97794	−	9.20703i	0.433943	−	0.500797i
$339$	1.44482	−	3.16372i	0.0784721	−	0.171830i
$340$	−20.5265	−	6.02713i	−1.11321	−	0.326867i
$341$	9.46687	+	20.7296i	0.512660	+	1.12257i
$342$	2.68184	+	18.6526i	0.145017	+	1.00862i
$343$	−5.26603	−	3.38427i	−0.284339	−	0.182734i
$344$	6.23295			0.336058
$345$	−5.76926	−	1.90225i	−0.310607	−	0.102414i
$346$	−1.69121			−0.0909200
$347$	−12.6400	−	8.12324i	−0.678551	−	0.436079i	0.155448	−	0.987844i	$-0.450318\pi$
$347$	−12.6400	−	8.12324i	−0.678551	−	0.436079i	−0.833999	+	0.551766i	$0.813954\pi$
$348$	0.0824626	+	0.573540i	0.00442046	+	0.0307450i
$349$	11.6528	+	25.5162i	0.623762	+	1.36585i	0.912751	+	0.408516i	$0.133954\pi$
$349$	11.6528	+	25.5162i	0.623762	+	1.36585i	−0.288989	+	0.957332i	$0.593319\pi$
$350$	−2.85006	−	0.836852i	−0.152342	−	0.0447316i
$351$	−0.820576	+	1.79681i	−0.0437991	+	0.0959066i
$352$	1.97592	−	2.28034i	0.105317	−	0.121542i
$353$	−0.0907651	+	0.631285i	−0.00483094	+	0.0335999i	−0.992094	−	0.125494i	$-0.959948\pi$
$353$	−0.0907651	+	0.631285i	−0.00483094	+	0.0335999i	0.987263	+	0.159094i	$0.0508574\pi$
$354$	2.42233	−	0.711261i	0.128745	−	0.0378031i
$355$	−28.2756	−	32.6318i	−1.50071	−	1.73191i
$356$	−9.35343	+	6.01109i	−0.495731	+	0.318587i
$357$	0.896017	−	0.575835i	0.0474222	−	0.0304764i
$358$	−7.25727	−	8.37534i	−0.383559	−	0.442650i
$359$	9.51233	−	2.79307i	0.502041	−	0.147413i	−0.0208995	−	0.999782i	$-0.506653\pi$
$359$	9.51233	−	2.79307i	0.502041	−	0.147413i	0.522941	+	0.852369i	$0.324835\pi$
$360$	1.38350	−	9.62248i	0.0729171	−	0.507149i
$361$	−15.9675	+	18.4275i	−0.840394	+	0.969867i
$362$	1.07729	−	2.35894i	0.0566212	−	0.123983i
$363$	0.678092	+	0.199106i	0.0355906	+	0.0104503i
$364$	0.170431	+	0.373193i	0.00893303	+	0.0195606i
$365$	0.684251	+	4.75907i	0.0358153	+	0.249101i
$366$	0.986113	+	0.633737i	0.0515450	+	0.0331259i
$367$	7.90826			0.412808			0.206404	−	0.978467i	$-0.433824\pi$
$367$	7.90826			0.412808			0.206404	+	0.978467i	$0.433824\pi$
$368$	−3.01969	−	3.72579i	−0.157412	−	0.194220i
$369$	−21.9796			−1.14421
$370$	3.54945	+	2.28109i	0.184527	+	0.118588i
$371$	0.604996	+	4.20784i	0.0314098	+	0.218460i
$372$	−1.16962	−	2.56111i	−0.0606419	−	0.132787i
$373$	16.4937	+	4.84298i	0.854010	+	0.250760i	0.679300	−	0.733860i	$-0.262283\pi$
$373$	16.4937	+	4.84298i	0.854010	+	0.250760i	0.174709	+	0.984620i	$0.444102\pi$
$374$	−7.89168	+	17.2804i	−0.408069	+	0.893547i
$375$	−1.28205	+	1.47956i	−0.0662047	+	0.0764043i
$376$	1.42473	−	9.90923i	0.0734750	−	0.511030i
$377$	1.34832	−	0.395902i	0.0694420	−	0.0203900i
$378$	0.649301	+	0.749334i	0.0333965	+	0.0385416i
$379$	9.43812	−	6.06551i	0.484804	−	0.311564i	−0.275309	−	0.961356i	$-0.588780\pi$
$379$	9.43812	−	6.06551i	0.484804	−	0.311564i	0.760113	+	0.649791i	$0.225144\pi$
$380$	18.8276	−	12.0998i	0.965835	−	0.620704i
$381$	0.687338	+	0.793230i	0.0352134	+	0.0406384i
$382$	13.7945	−	4.05044i	0.705789	−	0.207238i
$383$	0.780740	−	5.43016i	0.0398939	−	0.277468i	−0.960104	−	0.279644i	$-0.909783\pi$
$383$	0.780740	−	5.43016i	0.0398939	−	0.277468i	0.999998	+	0.00217582i	$0.000692585\pi$
$384$	−0.244123	+	0.281733i	−0.0124578	+	0.0143771i
$385$	−1.93275	+	4.23213i	−0.0985020	+	0.215689i
$386$	−13.1935	−	3.87395i	−0.671530	−	0.197179i
$387$	−7.40796	−	16.2212i	−0.376568	−	0.824568i
$388$	−0.208175	−	1.44789i	−0.0105685	−	0.0735055i
$389$	−15.9542	−	10.2531i	−0.808910	−	0.519855i	0.0696023	−	0.997575i	$-0.477827\pi$
$389$	−15.9542	−	10.2531i	−0.808910	−	0.519855i	−0.878512	+	0.477720i	$0.841463\pi$
$390$	1.14517			0.0579880
$391$	24.8507	+	17.1511i	1.25675	+	0.867369i
$392$	−6.79407			−0.343152
$393$	−1.39256	−	0.894946i	−0.0702455	−	0.0451440i
$394$	0.459350	+	3.19485i	0.0231417	+	0.160954i
$395$	−1.33348	−	2.91992i	−0.0670948	−	0.146917i
$396$	−8.28296	−	2.43210i	−0.416235	−	0.122218i
$397$	5.96204	−	13.0551i	0.299226	−	0.655214i	−0.698976	−	0.715145i	$-0.746361\pi$
$397$	5.96204	−	13.0551i	0.299226	−	0.655214i	0.998203	+	0.0599306i	$0.0190879\pi$
$398$	−6.17379	+	7.12494i	−0.309464	+	0.357141i
$399$	−0.158575	+	1.10291i	−0.00793866	+	0.0552146i
$400$	−6.28043	+	1.84410i	−0.314021	+	0.0922050i
$401$	−5.76089	−	6.64842i	−0.287685	−	0.332006i	0.593450	−	0.804871i	$-0.297765\pi$
$401$	−5.76089	−	6.64842i	−0.287685	−	0.332006i	−0.881135	+	0.472864i	$0.843220\pi$
$402$	−2.22298	+	1.42862i	−0.110872	+	0.0712532i
$403$	−5.74425	+	3.69160i	−0.286141	+	0.183892i
$404$	−1.56708	−	1.80851i	−0.0779653	−	0.0899768i
$405$	−25.3275	+	7.43681i	−1.25853	+	0.369538i
$406$	0.100383	−	0.698182i	0.00498195	−	0.0346502i
$407$	2.45356	−	2.83156i	0.121618	−	0.140355i
$408$	0.975006	−	2.13496i	0.0482700	−	0.105697i
$409$	8.00049	+	2.34916i	0.395599	+	0.116158i	0.473480	−	0.880804i	$-0.342997\pi$
$409$	8.00049	+	2.34916i	0.395599	+	0.116158i	−0.0778817	+	0.996963i	$0.524816\pi$
$410$	10.8439	+	23.7449i	0.535544	+	1.17268i
$411$	−0.454061	−	3.15806i	−0.0223972	−	0.155776i
$412$	−9.53126	−	6.12537i	−0.469572	−	0.301775i
$413$	−3.07324			−0.151224
$414$	−6.10736	+	12.2868i	−0.300160	+	0.603866i
$415$	−26.8291			−1.31699
$416$	0.760554	+	0.488779i	0.0372892	+	0.0239643i
$417$	−0.0765129	−	0.532159i	−0.00374685	−	0.0260599i
$418$	−8.25588	−	18.0779i	−0.403808	−	0.884217i
$419$	3.99590	+	1.17330i	0.195213	+	0.0573196i	0.377877	−	0.925856i	$-0.376654\pi$
$419$	3.99590	+	1.17330i	0.195213	+	0.0573196i	−0.182665	+	0.983175i	$0.558472\pi$
$420$	0.238788	−	0.522874i	0.0116517	−	0.0255136i
$421$	−1.28909	+	1.48769i	−0.0628263	+	0.0725054i	−0.786293	−	0.617854i	$-0.788002\pi$
$421$	−1.28909	+	1.48769i	−0.0628263	+	0.0725054i	0.723466	+	0.690360i	$0.242548\pi$
$422$	3.79480	−	26.3934i	0.184728	−	1.28481i
$423$	−27.4819	+	8.06943i	−1.33622	+	0.392349i
$424$	6.13461	+	7.07971i	0.297923	+	0.343821i
$425$	34.6689	−	22.2804i	1.68169	−	1.08076i
$426$	3.98511	−	2.56108i	0.193079	−	0.124085i
$427$	−0.934445	−	1.07841i	−0.0452210	−	0.0521878i
$428$	3.02158	−	0.887217i	0.146054	−	0.0428853i
$429$	0.144722	−	1.00656i	0.00698724	−	0.0485973i
$430$	−13.8692	+	16.0059i	−0.668831	+	0.771872i
$431$	3.18064	−	6.96463i	0.153206	−	0.335474i	−0.817430	−	0.576028i	$-0.804602\pi$
$431$	3.18064	−	6.96463i	0.153206	−	0.335474i	0.970636	+	0.240554i	$0.0773291\pi$
$432$	2.09640	+	0.615560i	0.100863	+	0.0296161i
$433$	2.61902	+	5.73485i	0.125862	+	0.275599i	0.962065	−	0.272821i	$-0.0879567\pi$
$433$	2.61902	+	5.73485i	0.125862	+	0.275599i	−0.836203	+	0.548420i	$0.815229\pi$
$434$	0.487772	+	3.39253i	0.0234138	+	0.162847i
$435$	−1.65631	−	1.06445i	−0.0794140	−	0.0510362i
$436$	4.97465			0.238243
$437$	−30.5849	+	7.89768i	−1.46307	+	0.377797i
$438$	−0.527493			−0.0252046
$439$	9.67374	+	6.21693i	0.461702	+	0.296718i	0.750738	−	0.660600i	$-0.229698\pi$
$439$	9.67374	+	6.21693i	0.461702	+	0.296718i	−0.289035	+	0.957318i	$0.593335\pi$
$440$	1.45908	+	10.1481i	0.0695589	+	0.483793i
$441$	8.07485	+	17.6815i	0.384517	+	0.841974i
$442$	−5.46149	−	1.60364i	−0.259776	−	0.0762773i
$443$	−6.67161	+	14.6088i	−0.316978	+	0.694085i	−0.999317	−	0.0369509i	$-0.988235\pi$
$443$	−6.67161	+	14.6088i	−0.316978	+	0.694085i	0.682339	+	0.731036i	$0.260963\pi$
$444$	−0.303134	+	0.349835i	−0.0143861	+	0.0166024i
$445$	5.37653	−	37.3946i	0.254872	−	1.77267i
$446$	25.2541	−	7.41528i	1.19582	−	0.351124i
$447$	−0.607064	−	0.700590i	−0.0287132	−	0.0331367i
$448$	0.381761	−	0.245343i	0.0180365	−	0.0115913i
$449$	17.2350	−	11.0763i	0.813370	−	0.522721i	−0.0665837	−	0.997781i	$-0.521210\pi$
$449$	17.2350	−	11.0763i	0.813370	−	0.522721i	0.879953	+	0.475060i	$0.157574\pi$
$450$	12.2636	+	14.1530i	0.578113	+	0.667178i
$451$	22.2413	−	6.53063i	1.04730	−	0.307516i
$452$	−1.32777	+	9.23487i	−0.0624532	+	0.434372i
$453$	−0.627768	+	0.724483i	−0.0294951	+	0.0340392i
$454$	1.59886	−	3.50102i	0.0750384	−	0.164311i
$455$	−1.33757	−	0.392746i	−0.0627063	−	0.0184122i
$456$	1.02000	+	2.23349i	0.0477660	+	0.104593i
$457$	−5.83704	−	40.5975i	−0.273045	−	1.89907i	−0.416039	−	0.909347i	$-0.636582\pi$
$457$	−5.83704	−	40.5975i	−0.273045	−	1.89907i	0.142994	−	0.989724i	$-0.454327\pi$
$458$	18.4699	+	11.8699i	0.863043	+	0.554644i
$459$	−13.7562			−0.642085
$460$	16.2868	+	0.535993i	0.759377	+	0.0249908i
$461$	−30.8859			−1.43850			−0.719250	−	0.694751i	$-0.755514\pi$
$461$	−30.8859			−1.43850			−0.719250	+	0.694751i	$0.755514\pi$
$462$	−0.429409	−	0.275965i	−0.0199779	−	0.0128390i
$463$	−1.32780	−	9.23505i	−0.0617081	−	0.429189i	−0.997133	−	0.0756645i	$-0.975892\pi$
$463$	−1.32780	−	9.23505i	−0.0617081	−	0.429189i	0.935425	−	0.353524i	$-0.115017\pi$
$464$	−0.645699	−	1.41388i	−0.0299758	−	0.0656379i
$465$	9.17934	+	2.69530i	0.425682	+	0.124991i
$466$	−5.22151	+	11.4335i	−0.241882	+	0.529647i
$467$	−18.5135	+	21.3657i	−0.856703	+	0.988688i	−1.00000		0.000992003i	$-0.999684\pi$
$467$	−18.5135	+	21.3657i	−0.856703	+	0.988688i	0.143297	+	0.989680i	$0.454230\pi$
$468$	0.368109	−	2.56025i	0.0170158	−	0.118348i
$469$	3.08642	−	0.906256i	0.142518	−	0.0418470i
$470$	22.2761	+	25.7080i	1.02752	+	1.18582i
$471$	−1.50099	+	0.964629i	−0.0691621	+	0.0444478i
$472$	−5.69718	+	3.66135i	−0.262234	+	0.168527i
$473$	12.3158	+	14.2132i	0.566283	+	0.653526i
$474$	0.337908	−	0.0992187i	0.0155206	−	0.00455726i
$475$	−6.13561	+	42.6741i	−0.281521	+	1.95802i
$476$	−1.87102	+	2.15927i	−0.0857582	+	0.0989702i
$477$	11.1338	−	24.3796i	0.509781	−	1.11626i
$478$	−23.4574	−	6.88771i	−1.07292	−	0.315037i
$479$	−9.60719	−	21.0368i	−0.438964	−	0.961197i	−0.991787	−	0.127898i	$-0.959177\pi$
$479$	−9.60719	−	21.0368i	−0.438964	−	0.961197i	0.552823	−	0.833298i	$-0.313550\pi$
$480$	−0.180267	−	1.25379i	−0.00822804	−	0.0572273i
$481$	0.944401	+	0.606930i	0.0430610	+	0.0276736i
$482$	−14.3863			−0.655280
$483$	−0.551176	+	0.595341i	−0.0250794	+	0.0270889i
$484$	−1.89578			−0.0861717
$485$	4.18132	+	2.68717i	0.189864	+	0.122018i
$486$	−1.34498	−	9.35455i	−0.0610096	−	0.424331i
$487$	15.6023	+	34.1642i	0.707006	+	1.54813i	0.831265	+	0.555877i	$0.187617\pi$
$487$	15.6023	+	34.1642i	0.707006	+	1.54813i	−0.124259	+	0.992250i	$0.539655\pi$
$488$	−3.01705	−	0.885886i	−0.136575	−	0.0401022i
$489$	−2.45942	+	5.38537i	−0.111219	+	0.243535i
$490$	15.1177	−	17.4468i	0.682949	−	0.788165i
$491$	3.77518	−	26.2570i	0.170372	−	1.18496i	−0.707729	−	0.706484i	$-0.750280\pi$
$491$	3.77518	−	26.2570i	0.170372	−	1.18496i	0.878101	−	0.478476i	$-0.158811\pi$
$492$	−2.74788	+	0.806851i	−0.123884	+	0.0363756i
$493$	6.40859	+	7.39591i	0.288628	+	0.333095i
$494$	5.00945	−	3.21938i	0.225386	−	0.144847i
$495$	24.6762	−	15.8584i	1.10911	−	0.712784i
$496$	4.94597	+	5.70796i	0.222081	+	0.256295i
$497$	−5.53300	+	1.62464i	−0.248189	+	0.0728749i
$498$	0.418898	−	2.91350i	0.0187713	−	0.130557i
$499$	−3.79954	+	4.38490i	−0.170091	+	0.196295i	−0.834395	−	0.551167i	$-0.814183\pi$
$499$	−3.79954	+	4.38490i	−0.170091	+	0.196295i	0.664304	+	0.747462i	$0.268728\pi$
$500$	2.18162	−	4.77708i	0.0975649	−	0.213637i
$501$	1.88400	+	0.553192i	0.0841709	+	0.0247148i
$502$	−2.45238	−	5.36997i	−0.109455	−	0.239673i
$503$	3.24700	+	22.5834i	0.144777	+	1.00694i	0.924599	+	0.380943i	$0.124400\pi$
$503$	3.24700	+	22.5834i	0.144777	+	1.00694i	−0.779822	+	0.626001i	$0.784690\pi$
$504$	−1.09223	−	0.701933i	−0.0486517	−	0.0312666i
$505$	8.13113			0.361831
$506$	2.52938	−	14.2478i	0.112445	−	0.633391i
$507$	−4.54152			−0.201696
$508$	−2.36859	−	1.52220i	−0.105089	−	0.0675366i
$509$	5.40977	+	37.6258i	0.239784	+	1.66773i	0.653196	+	0.757189i	$0.273428\pi$
$509$	5.40977	+	37.6258i	0.239784	+	1.66773i	−0.413413	+	0.910544i	$0.635663\pi$
$510$	3.31295	+	7.25435i	0.146700	+	0.321228i
$511$	0.616117	+	0.180908i	0.0272554	+	0.00800291i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	9.42415	−	10.8760i	0.416086	−	0.480189i
$514$	−0.126797	+	0.881895i	−0.00559279	+	0.0388987i
$515$	36.9380	−	10.8460i	1.62768	−	0.477930i
$516$	−1.52160	−	1.75603i	−0.0669849	−	0.0773047i
$517$	25.4116	−	16.3310i	1.11760	−	0.718238i
$518$	0.474043	−	0.304649i	0.0208282	−	0.0133855i
$519$	0.412863	+	0.476469i	0.0181227	+	0.0209147i
$520$	−2.94749	+	0.865462i	−0.129256	+	0.0379530i
$521$	0.983759	−	6.84219i	0.0430993	−	0.299762i	−0.956858	−	0.290555i	$-0.906160\pi$
$521$	0.983759	−	6.84219i	0.0430993	−	0.299762i	0.999958	−	0.00920713i	$-0.00293076\pi$
$522$	−2.91219	+	3.36084i	−0.127463	+	0.147100i
$523$	1.26479	−	2.76949i	0.0553052	−	0.121102i	−0.879962	−	0.475044i	$-0.842432\pi$
$523$	1.26479	−	2.76949i	0.0553052	−	0.121102i	0.935267	+	0.353943i	$0.115159\pi$
$524$	4.26060	+	1.25102i	0.186125	+	0.0546513i
$525$	0.459995	+	1.00725i	0.0200758	+	0.0439599i
$526$	0.828236	+	5.76051i	0.0361128	+	0.251170i
$527$	−40.0033	−	25.7086i	−1.74257	−	1.11988i
$528$	−1.12481			−0.0489512
$529$	−21.5946	−	7.91678i	−0.938894	−	0.344208i
$530$	−31.8307			−1.38264
$531$	16.2998	+	10.4752i	0.707351	+	0.454587i
$532$	−0.425377	−	2.95856i	−0.0184424	−	0.128270i
$533$	2.88524	+	6.31780i	0.124974	+	0.273654i
$534$	3.97690	+	1.16772i	0.172097	+	0.0505324i
$535$	−4.44511	+	9.73344i	−0.192179	+	0.420813i
$536$	4.64193	−	5.35707i	0.200501	−	0.231390i
$537$	−0.587941	+	4.08922i	−0.0253715	+	0.176463i
$538$	11.6958	−	3.43419i	0.504241	−	0.148059i
$539$	−13.4246	−	15.4928i	−0.578237	−	0.667321i
$540$	−6.24551	+	4.01374i	−0.268764	+	0.172724i
$541$	−6.86555	+	4.41222i	−0.295173	+	0.189696i	−0.679842	−	0.733358i	$-0.737952\pi$
$541$	−6.86555	+	4.41222i	−0.295173	+	0.189696i	0.384669	+	0.923054i	$0.374315\pi$
$542$	−10.2880	−	11.8730i	−0.441907	−	0.509988i
$543$	−0.927582	+	0.272363i	−0.0398064	+	0.0116882i
$544$	−0.896017	+	6.23193i	−0.0384164	+	0.267192i
$545$	−11.0693	+	12.7746i	−0.474156	+	0.547205i
$546$	0.0635344	−	0.139121i	0.00271902	−	0.00595382i
$547$	−25.4758	−	7.48036i	−1.08926	−	0.319837i	−0.312686	−	0.949857i	$-0.601229\pi$
$547$	−25.4758	−	7.48036i	−1.08926	−	0.319837i	−0.776579	+	0.630020i	$0.783047\pi$
$548$	3.55539	+	7.78522i	0.151879	+	0.332568i
$549$	1.28031	+	8.90472i	0.0546421	+	0.380044i
$550$	−16.6148	−	10.6777i	−0.708459	−	0.455299i
$551$	−10.2378			−0.436146
$552$	−0.312501	+	1.76029i	−0.0133009	+	0.0749231i
$553$	−0.428708			−0.0182305
$554$	18.5956	+	11.9507i	0.790053	+	0.507736i
$555$	−0.223843	−	1.55686i	−0.00950160	−	0.0660851i
$556$	0.599112	+	1.31187i	0.0254080	+	0.0556357i
$557$	−36.1617	−	10.6180i	−1.53222	−	0.449900i	−0.596490	−	0.802620i	$-0.703439\pi$
$557$	−36.1617	−	10.6180i	−1.53222	−	0.449900i	−0.935729	+	0.352720i	$0.885257\pi$
$558$	8.97651	−	19.6558i	0.380006	−	0.832097i
$559$	−3.69017	+	4.25868i	−0.156077	+	0.180123i
$560$	−0.219443	+	1.52626i	−0.00927317	+	0.0644963i
$561$	6.79498	−	1.99519i	0.286884	−	0.0842368i
$562$	−21.0874	−	24.3362i	−0.889519	−	1.02656i
$563$	1.01476	−	0.652145i	0.0427669	−	0.0274846i	−0.519083	−	0.854724i	$-0.673726\pi$
$563$	1.01476	−	0.652145i	0.0427669	−	0.0274846i	0.561850	+	0.827239i	$0.310090\pi$
$564$	−3.13956	+	2.01767i	−0.132199	+	0.0849594i
$565$	−20.7602	−	23.9585i	−0.873386	−	1.00794i
$566$	−24.0315	+	7.05627i	−1.01012	+	0.296597i
$567$	−0.501714	+	3.48950i	−0.0210700	+	0.146545i
$568$	−8.32154	+	9.60357i	−0.349164	+	0.402957i
$569$	9.10351	−	19.9339i	0.381639	−	0.835673i	−0.617168	−	0.786832i	$-0.711720\pi$
$569$	9.10351	−	19.9339i	0.381639	−	0.835673i	0.998807	−	0.0488411i	$-0.0155528\pi$
$570$	−8.00513	−	2.35052i	−0.335298	−	0.0984524i
$571$	18.2559	+	39.9747i	0.763984	+	1.67289i	0.739468	+	0.673191i	$0.235077\pi$
$571$	18.2559	+	39.9747i	0.763984	+	1.67289i	0.0245151	+	0.999699i	$0.492196\pi$
$572$	0.388217	+	2.70011i	0.0162322	+	0.112897i
$573$	−4.50870	−	2.89756i	−0.188353	−	0.121047i
$574$	3.48627			0.145514
$575$	−21.3262	+	23.0351i	−0.889366	+	0.960629i
$576$	−2.86103			−0.119210
$577$	7.99484	+	5.13797i	0.332830	+	0.213897i	0.696372	−	0.717681i	$-0.254796\pi$
$577$	7.99484	+	5.13797i	0.332830	+	0.213897i	−0.363542	+	0.931578i	$0.618433\pi$
$578$	−3.22198	−	22.4094i	−0.134017	−	0.932107i
$579$	2.12941	+	4.66275i	0.0884952	+	0.193777i
$580$	5.06754	+	1.48796i	0.210418	+	0.0617843i
$581$	−1.48849	+	3.25933i	−0.0617529	+	0.135220i
$582$	−0.357098	+	0.412113i	−0.0148022	+	0.0170826i
$583$	−4.02262	+	27.9780i	−0.166600	+	1.15873i
$584$	1.35769	−	0.398652i	0.0561814	−	0.0164964i
$585$	5.75549	+	6.64219i	0.237960	+	0.274621i
$586$	−7.86769	+	5.05626i	−0.325011	+	0.208872i
$587$	−5.38811	+	3.46273i	−0.222391	+	0.142922i	−0.647093	−	0.762411i	$-0.724015\pi$
$587$	−5.38811	+	3.46273i	−0.222391	+	0.142922i	0.424702	+	0.905333i	$0.360379\pi$
$588$	1.65859	+	1.91411i	0.0683989	+	0.0789365i
$589$	47.7315	−	14.0152i	1.96674	−	0.577487i
$590$	3.27484	−	22.7770i	0.134823	−	0.937716i
$591$	0.787956	−	0.909349i	0.0324122	−	0.0374056i
$592$	0.515832	−	1.12952i	0.0212006	−	0.0464228i
$593$	23.3928	+	6.86874i	0.960626	+	0.282065i	0.724205	−	0.689585i	$-0.242207\pi$
$593$	23.3928	+	6.86874i	0.960626	+	0.282065i	0.236422	+	0.971651i	$0.424025\pi$
$594$	2.73865	+	5.99681i	0.112368	+	0.246052i
$595$	−1.38162	−	9.60936i	−0.0566408	−	0.393945i
$596$	2.09196	+	1.34442i	0.0856900	+	0.0550696i
$597$	3.51449			0.143838
$598$	4.33343	+	0.142612i	0.177207	+	0.00583183i
$599$	26.4384			1.08025			0.540123	−	0.841586i	$-0.318378\pi$
$599$	26.4384			1.08025			0.540123	+	0.841586i	$0.318378\pi$
$600$	2.05274	+	1.31921i	0.0838027	+	0.0538567i
$601$	−0.768802	−	5.34713i	−0.0313601	−	0.218114i	0.968115	−	0.250505i	$-0.0805968\pi$
$601$	−0.768802	−	5.34713i	−0.0313601	−	0.218114i	−0.999475	+	0.0323913i	$0.989688\pi$
$602$	1.17501	+	2.57290i	0.0478897	+	0.104864i
$603$	−19.4587	−	5.71359i	−0.792420	−	0.232675i
$604$	1.06825	−	2.33914i	0.0434665	−	0.0951784i
$605$	4.21836	−	4.86825i	0.171501	−	0.197923i
$606$	−0.126956	+	0.882997i	−0.00515723	+	0.0358693i
$607$	11.1601	−	3.27691i	0.452976	−	0.133006i	−0.0472832	−	0.998882i	$-0.515056\pi$
$607$	11.1601	−	3.27691i	0.452976	−	0.133006i	0.500259	+	0.865876i	$0.333238\pi$
$608$	−4.31329	−	4.97780i	−0.174927	−	0.201877i
$609$	−0.221207	+	0.142161i	−0.00896374	+	0.00576065i
$610$	8.98826	−	5.77640i	0.363924	−	0.233880i
$611$	5.92701	+	6.84013i	0.239781	+	0.276722i
$612$	17.2834	−	5.07488i	0.698642	−	0.205140i
$613$	−2.66100	+	18.5077i	−0.107477	+	0.747519i	0.862804	+	0.505538i	$0.168706\pi$
$613$	−2.66100	+	18.5077i	−0.107477	+	0.747519i	−0.970281	+	0.241980i	$0.922203\pi$
$614$	−15.9620	+	18.4211i	−0.644175	+	0.743417i
$615$	4.04246	−	8.85176i	0.163008	−	0.356937i
$616$	1.31379	+	0.385765i	0.0529343	+	0.0155429i
$617$	−9.06984	−	19.8602i	−0.365138	−	0.799541i	−0.999646	−	0.0266240i	$-0.991524\pi$
$617$	−9.06984	−	19.8602i	−0.365138	−	0.799541i	0.634508	−	0.772917i	$-0.281203\pi$
$618$	0.601081	+	4.18061i	0.0241790	+	0.168169i
$619$	−12.3875	−	7.96098i	−0.497897	−	0.319979i	0.267478	−	0.963564i	$-0.413810\pi$
$619$	−12.3875	−	7.96098i	−0.497897	−	0.319979i	−0.765374	+	0.643585i	$0.777446\pi$
$620$	−25.6632			−1.03066
$621$	10.1457	−	2.61983i	0.407131	−	0.105130i
$622$	12.5420			0.502887
$623$	−4.24458	−	2.72783i	−0.170056	−	0.109288i
$624$	−0.0479637	−	0.333595i	−0.00192008	−	0.0133545i
$625$	−6.18277	−	13.5384i	−0.247311	−	0.541535i
$626$	−9.63076	−	2.82785i	−0.384923	−	0.113023i
$627$	−3.07767	+	6.73917i	−0.122910	+	0.269136i
$628$	3.13431	−	3.61718i	0.125072	−	0.144341i
$629$	−1.11261	+	7.73836i	−0.0443626	+	0.308549i
$630$	4.23288	−	1.24289i	0.168642	−	0.0495178i
$631$	8.25672	+	9.52877i	0.328695	+	0.379334i	0.895910	−	0.444236i	$-0.146525\pi$
$631$	8.25672	+	9.52877i	0.328695	+	0.379334i	−0.567215	+	0.823570i	$0.691979\pi$
$632$	−0.794738	+	0.510747i	−0.0316130	+	0.0203164i
$633$	−8.36229	+	5.37412i	−0.332371	+	0.213602i
$634$	20.9110	+	24.1326i	0.830482	+	0.958427i
$635$	9.17934	−	2.69530i	0.364271	−	0.106960i
$636$	0.496989	−	3.45664i	0.0197069	−	0.137065i
$637$	4.02237	−	4.64206i	0.159372	−	0.183925i
$638$	1.94828	−	4.26614i	0.0771331	−	0.168898i
$639$	34.8834	+	10.2427i	1.37997	+	0.405195i
$640$	1.41153	+	3.09082i	0.0557956	+	0.122175i
$641$	4.74951	+	33.0336i	0.187594	+	1.30475i	0.838213	+	0.545343i	$0.183601\pi$
$641$	4.74951	+	33.0336i	0.187594	+	1.30475i	−0.650619	+	0.759405i	$0.725490\pi$
$642$	−0.987595	−	0.634689i	−0.0389773	−	0.0250492i
$643$	26.4979			1.04498			0.522488	−	0.852646i	$-0.325004\pi$
$643$	26.4979			1.04498			0.522488	+	0.852646i	$0.325004\pi$
$644$	0.968713	−	1.94887i	0.0381726	−	0.0767961i
$645$	7.89515			0.310871
$646$	34.8861	+	22.4199i	1.37258	+	0.882101i
$647$	−3.78374	−	26.3165i	−0.148754	−	1.03461i	−0.918263	−	0.395972i	$-0.870408\pi$
$647$	−3.78374	−	26.3165i	−0.148754	−	1.03461i	0.769508	−	0.638637i	$-0.220501\pi$
$648$	3.22719	+	7.06656i	0.126776	+	0.277601i
$649$	−19.6063	−	5.75693i	−0.769615	−	0.225979i
$650$	2.45829	−	5.38290i	0.0964220	−	0.211135i
$651$	0.836710	−	0.965615i	0.0327933	−	0.0378454i
$652$	2.26017	−	15.7198i	0.0885151	−	0.615636i
$653$	−2.87063	+	0.842893i	−0.112336	+	0.0329850i	−0.337418	−	0.941355i	$-0.609553\pi$
$653$	−2.87063	+	0.842893i	−0.112336	+	0.0329850i	0.225081	+	0.974340i	$0.427735\pi$
$654$	−1.21443	−	1.40152i	−0.0474878	−	0.0548038i
$655$	−12.6930	+	8.15728i	−0.495956	+	0.318731i
$656$	6.46285	−	4.15342i	0.252332	−	0.162164i
$657$	−2.65112	−	3.05955i	−0.103430	−	0.119364i
$658$	4.35902	−	1.27992i	0.169932	−	0.0498967i
$659$	−4.64990	+	32.3408i	−0.181134	+	1.25982i	0.672952	+	0.739686i	$0.265026\pi$
$659$	−4.64990	+	32.3408i	−0.181134	+	1.25982i	−0.854086	+	0.520131i	$0.825883\pi$
$660$	2.50286	−	2.88846i	0.0974238	−	0.112433i
$661$	19.0220	−	41.6524i	0.739871	−	1.62009i	−0.0438951	−	0.999036i	$-0.513977\pi$
$661$	19.0220	−	41.6524i	0.739871	−	1.62009i	0.783766	−	0.621056i	$-0.213296\pi$
$662$	29.4707	+	8.65337i	1.14541	+	0.336323i
$663$	0.881476	+	1.93016i	0.0342337	+	0.0749613i
$664$	1.12370	+	7.81548i	0.0436079	+	0.303300i
$665$	8.54395	+	5.49086i	0.331320	+	0.212927i
$666$	−3.55262			−0.137661
$667$	−6.13507	−	4.23423i	−0.237551	−	0.163950i
$668$	−5.26720			−0.203794
$669$	−8.25423	−	5.30467i	−0.319127	−	0.205091i
$670$	3.42774	+	23.8404i	0.132425	+	0.921036i
$671$	−3.94134	−	8.63034i	−0.152154	−	0.333171i
$672$	−0.162317	−	0.0476607i	−0.00626153	−	0.00183855i
$673$	4.44121	−	9.72489i	0.171196	−	0.374867i	−0.804514	−	0.593934i	$-0.797574\pi$
$673$	4.44121	−	9.72489i	0.171196	−	0.374867i	0.975710	+	0.219067i	$0.0703013\pi$
$674$	−18.3105	+	21.1315i	−0.705296	+	0.813955i
$675$	2.03531	−	14.1559i	0.0783392	−	0.544861i
$676$	11.6892	−	3.43225i	0.449583	−	0.132010i
$677$	−16.1168	−	18.5998i	−0.619418	−	0.714847i	0.356178	−	0.934418i	$-0.384080\pi$
$677$	−16.1168	−	18.5998i	−0.619418	−	0.714847i	−0.975596	+	0.219571i	$0.929534\pi$
$678$	2.92590	−	1.88036i	0.112369	−	0.0722149i
$679$	0.558431	−	0.358882i	0.0214306	−	0.0137726i
$680$	−14.0095	−	16.1678i	−0.537240	−	0.620008i
$681$	−1.37667	+	0.404227i	−0.0527542	+	0.0154900i
$682$	−3.24321	+	22.5570i	−0.124189	+	0.863752i
$683$	7.90989	−	9.12850i	0.302664	−	0.349292i	−0.583961	−	0.811781i	$-0.698498\pi$
$683$	7.90989	−	9.12850i	0.302664	−	0.349292i	0.886625	+	0.462489i	$0.153044\pi$
$684$	−7.82825	+	17.1415i	−0.299321	+	0.655421i
$685$	−27.9032	−	8.19313i	−1.06613	−	0.313043i
$686$	−2.60039	−	5.69406i	−0.0992834	−	0.217400i
$687$	−1.16479	−	8.10129i	−0.0444395	−	0.309084i
$688$	5.24349	+	3.36979i	0.199906	+	0.128472i
$689$	−8.46918			−0.322650
$690$	−3.82498	−	4.71938i	−0.145614	−	0.179664i
$691$	−34.2727			−1.30379			−0.651897	−	0.758307i	$-0.726027\pi$
$691$	−34.2727			−1.30379			−0.651897	+	0.758307i	$0.726027\pi$
$692$	−1.42274	−	0.914337i	−0.0540843	−	0.0347579i
$693$	−0.557517	−	3.87762i	−0.0211783	−	0.147299i
$694$	−6.24170	−	13.6674i	−0.236932	−	0.518808i
$695$	−4.70192	−	1.38061i	−0.178354	−	0.0523694i
$696$	−0.240707	+	0.527075i	−0.00912398	+	0.0199787i
$697$	−31.6746	+	36.5545i	−1.19976	+	1.38460i
$698$	−3.99208	+	27.7656i	−0.151103	+	1.05094i
$699$	4.49588	−	1.32011i	0.170050	−	0.0499311i
$700$	−1.94518	−	2.24486i	−0.0735210	−	0.0848478i
$701$	−29.4880	+	18.9508i	−1.11375	+	0.715761i	−0.962106	−	0.272675i	$-0.912092\pi$
$701$	−29.4880	+	18.9508i	−1.11375	+	0.715761i	−0.151639	+	0.988436i	$0.548455\pi$
$702$	−1.66174	+	1.06794i	−0.0627184	+	0.0403067i
$703$	−5.35593	−	6.18108i	−0.202003	−	0.233124i
$704$	2.89510	−	0.850077i	0.109113	−	0.0320385i
$705$	1.80468	−	12.5518i	0.0679682	−	0.472729i
$706$	−0.417655	+	0.481999i	−0.0157186	+	0.0181403i
$707$	0.451117	−	0.987809i	0.0169660	−	0.0371504i
$708$	2.42233	+	0.711261i	0.0910368	+	0.0267308i
$709$	6.97322	+	15.2692i	0.261885	+	0.573447i	0.994204	−	0.107515i	$-0.0342892\pi$
$709$	6.97322	+	15.2692i	0.261885	+	0.573447i	−0.732319	+	0.680962i	$0.761562\pi$
$710$	−6.14487	−	42.7385i	−0.230613	−	1.60395i
$711$	2.27377	+	1.46126i	0.0852731	+	0.0548017i
$712$	−11.1184			−0.416681
$713$	34.3999	+	11.3424i	1.28828	+	0.424776i
$714$	1.06510			0.0398603
$715$	−7.79757	−	5.01119i	−0.291613	−	0.187408i
$716$	−1.57716	−	10.9694i	−0.0589411	−	0.409944i
$717$	3.78599	+	8.29016i	0.141390	+	0.309602i
$718$	9.51233	+	2.79307i	0.354997	+	0.104236i
$719$	7.35029	−	16.0949i	0.274119	−	0.600238i	−0.721636	−	0.692272i	$-0.756610\pi$
$719$	7.35029	−	16.0949i	0.274119	−	0.600238i	0.995756	+	0.0920344i	$0.0293370\pi$
$720$	6.36618	−	7.34697i	0.237254	−	0.273805i
$721$	0.731708	−	5.08914i	0.0272502	−	0.189530i
$722$	−23.3953	+	6.86949i	−0.870685	+	0.255656i
$723$	3.51203	+	4.05310i	0.130614	+	0.150736i
$724$	2.18162	−	1.40204i	0.0810791	−	0.0521064i
$725$	−8.55898	+	5.50052i	−0.317873	+	0.204284i
$726$	0.462802	+	0.534102i	0.0171762	+	0.0198224i
$727$	−36.0386	+	10.5819i	−1.33660	+	0.392461i	−0.870455	−	0.492249i	$-0.836175\pi$
$727$	−36.0386	+	10.5819i	−1.33660	+	0.392461i	−0.466143	+	0.884709i	$0.654357\pi$
$728$	−0.0583872	+	0.406092i	−0.00216397	+	0.0150508i
$729$	12.9549	−	14.9507i	0.479811	−	0.553731i
$730$	−1.99732	+	4.37352i	−0.0739240	+	0.161871i
$731$	−37.6532	−	11.0560i	−1.39265	−	0.408920i
$732$	0.486948	+	1.06627i	0.0179981	+	0.0394103i
$733$	−1.65421	−	11.5053i	−0.0610995	−	0.424956i	−0.997297	−	0.0734809i	$-0.976589\pi$
$733$	−1.65421	−	11.5053i	−0.0610995	−	0.424956i	0.936197	−	0.351475i	$-0.114320\pi$
$734$	6.65285	+	4.27553i	0.245561	+	0.157813i
$735$	−8.60591			−0.317434
$736$	−0.526011	−	4.76690i	−0.0193890	−	0.175710i
$737$	21.3880			0.787839
$738$	−18.4904	−	11.8831i	−0.680641	−	0.437422i
$739$	2.52893	+	17.5891i	0.0930283	+	0.647026i	0.981974	+	0.189014i	$0.0605292\pi$
$739$	2.52893	+	17.5891i	0.0930283	+	0.647026i	−0.888946	+	0.458012i	$0.848562\pi$
$740$	1.75273	+	3.83795i	0.0644318	+	0.141086i
$741$	−2.12992	−	0.625402i	−0.0782447	−	0.0229747i
$742$	−1.76597	+	3.86694i	−0.0648309	+	0.141960i
$743$	20.1863	−	23.2963i	0.740565	−	0.854658i	−0.253053	−	0.967452i	$-0.581435\pi$
$743$	20.1863	−	23.2963i	0.740565	−	0.854658i	0.993618	+	0.112795i	$0.0359802\pi$
$744$	0.400693	−	2.78688i	0.0146901	−	0.102172i
$745$	−8.10730	+	2.38052i	−0.297028	+	0.0872154i
$746$	11.2570	+	12.9913i	0.412150	+	0.475646i
$747$	19.0041	−	12.2132i	0.695325	−	0.446858i
$748$	−15.9814	+	10.2706i	−0.584337	+	0.375531i
$749$	0.935850	+	1.08003i	0.0341952	+	0.0394634i
$750$	−1.87844	+	0.551560i	−0.0685910	+	0.0201401i
$751$	6.12621	−	42.6087i	0.223548	−	1.55481i	−0.500913	−	0.865498i	$-0.667002\pi$
$751$	6.12621	−	42.6087i	0.223548	−	1.55481i	0.724461	−	0.689316i	$-0.242089\pi$
$752$	6.55590	−	7.56591i	0.239069	−	0.275900i
$753$	−0.914213	+	2.00185i	−0.0333158	+	0.0729514i
$754$	1.34832	+	0.395902i	0.0491029	+	0.0144179i
$755$	3.62979	+	7.94812i	0.132101	+	0.289262i
$756$	0.141107	+	0.981418i	0.00513200	+	0.0356938i
$757$	24.3476	+	15.6472i	0.884927	+	0.568708i	0.902285	−	0.431141i	$-0.141889\pi$
$757$	24.3476	+	15.6472i	0.884927	+	0.568708i	−0.0173572	+	0.999849i	$0.505525\pi$
$758$	11.2191			0.407497
$759$	−4.63154	+	2.76560i	−0.168114	+	0.100385i
$760$	22.3804			0.811822
$761$	33.2323	+	21.3571i	1.20467	+	0.774194i	0.979758	−	0.200186i	$-0.0641546\pi$
$761$	33.2323	+	21.3571i	1.20467	+	0.774194i	0.224911	+	0.974379i	$0.427791\pi$
$762$	0.149373	+	1.03891i	0.00541120	+	0.0376358i
$763$	0.937798	+	2.05349i	0.0339506	+	0.0743413i
$764$	13.7945	+	4.05044i	0.499068	+	0.146540i
$765$	−25.4260	+	55.6752i	−0.919279	+	2.01294i
$766$	3.59257	−	4.14604i	0.129805	−	0.149803i
$767$	0.871337	−	6.06028i	0.0314622	−	0.218824i
$768$	−0.357685	+	0.105026i	−0.0129069	+	0.00378979i
$769$	−15.6751	−	18.0900i	−0.565257	−	0.652341i	0.399112	−	0.916902i	$-0.369318\pi$
$769$	−15.6751	−	18.0900i	−0.565257	−	0.652341i	−0.964369	+	0.264561i	$0.914773\pi$
$770$	−3.91399	+	2.51537i	−0.141051	+	0.0906477i
$771$	0.279413	−	0.179568i	0.0100628	−	0.00646697i
$772$	−9.00464	−	10.3919i	−0.324084	−	0.374013i
$773$	−39.5324	+	11.6078i	−1.42188	+	0.417502i	−0.900140	−	0.435600i	$-0.856536\pi$
$773$	−39.5324	+	11.6078i	−1.42188	+	0.417502i	−0.521743	+	0.853103i	$0.674718\pi$
$774$	2.53785	−	17.6512i	0.0912213	−	0.634458i
$775$	32.3742	−	37.3619i	1.16292	−	1.34208i
$776$	0.607660	−	1.33059i	0.0218137	−	0.0477654i
$777$	−0.201554	−	0.0591816i	−0.00723071	−	0.00212313i
$778$	−7.87826	−	17.2510i	−0.282449	−	0.618478i
$779$	−7.20124	−	50.0857i	−0.258011	−	1.79451i
$780$	0.963379	+	0.619126i	0.0344945	+	0.0221683i
$781$	−38.3421			−1.37199
$782$	11.6331	+	27.8637i	0.415999	+	0.996404i
$783$	3.39610			0.121367
$784$	−5.71553	−	3.67315i	−0.204126	−	0.131184i
$785$	2.31446	+	16.0974i	0.0826068	+	0.574543i
$786$	−0.687654	−	1.50575i	−0.0245278	−	0.0537084i
$787$	36.2747	+	10.6512i	1.29305	+	0.379675i	0.854697	−	0.519127i	$-0.173743\pi$
$787$	36.2747	+	10.6512i	1.29305	+	0.379675i	0.438356	+	0.898801i	$0.355561\pi$
$788$	−1.34084	+	2.93602i	−0.0477653	+	0.104591i
$789$	1.42073	−	1.63961i	0.0505794	−	0.0583717i
$790$	0.456831	−	3.17733i	0.0162533	−	0.113044i
$791$	−4.06237	+	1.19282i	−0.144441	+	0.0424118i
$792$	−5.65318	−	6.52412i	−0.200877	−	0.231824i
$793$	2.39150	−	1.53693i	0.0849248	−	0.0545778i
$794$	12.0737	−	7.75929i	0.428479	−	0.275367i
$795$	7.77058	+	8.96773i	0.275594	+	0.318053i
$796$	−9.04576	+	2.65607i	−0.320618	+	0.0941421i
$797$	0.768159	−	5.34266i	0.0272096	−	0.189247i	−0.971683	−	0.236286i	$-0.924070\pi$
$797$	0.768159	−	5.34266i	0.0272096	−	0.189247i	0.998893	+	0.0470397i	$0.0149787\pi$
$798$	−0.729680	+	0.842095i	−0.0258304	+	0.0298098i
$799$	−26.1837	+	57.3343i	−0.926313	+	2.02834i
$800$	−6.28043	−	1.84410i	−0.222047	−	0.0651988i
$801$	13.2144	+	28.9356i	0.466909	+	1.02239i
$802$	−1.25196	−	8.70758i	−0.0442083	−	0.307475i
$803$	3.59175	+	2.30827i	0.126750	+	0.0814573i
$804$	−2.64246			−0.0931925
$805$	2.84906	+	6.82409i	0.100416	+	0.240518i
$806$	−6.82820			−0.240513
$807$	−3.82273	−	2.45672i	−0.134566	−	0.0864806i
$808$	−0.340560	−	2.36865i	−0.0119809	−	0.0833287i
$809$	2.99076	+	6.54885i	0.105150	+	0.230245i	0.954892	−	0.296952i	$-0.0959701\pi$
$809$	2.99076	+	6.54885i	0.105150	+	0.230245i	−0.849743	+	0.527197i	$0.823243\pi$
$810$	−25.3275	−	7.43681i	−0.889916	−	0.261303i
$811$	17.2272	−	37.7223i	0.604928	−	1.32461i	−0.321061	−	0.947058i	$-0.604040\pi$
$811$	17.2272	−	37.7223i	0.604928	−	1.32461i	0.925989	−	0.377549i	$-0.123233\pi$
$812$	0.461914	−	0.533077i	0.0162100	−	0.0187073i
$813$	−0.833473	+	5.79693i	−0.0292312	+	0.203307i
$814$	3.59492	−	1.05556i	0.126002	−	0.0369975i
$815$	35.3385	+	40.7828i	1.23785	+	1.42856i
$816$	1.97448	−	1.26892i	0.0691205	−	0.0444210i
$817$	34.5367	−	22.1954i	1.20829	−	0.776518i
$818$	5.46039	+	6.30163i	0.190918	+	0.220331i
$819$	1.12624	−	0.330695i	0.0393541	−	0.0115554i
$820$	−3.71497	+	25.8382i	−0.129732	+	0.902308i
$821$	−24.7854	+	28.6039i	−0.865016	+	0.998282i	0.134956	+	0.990852i	$0.456911\pi$
$821$	−24.7854	+	28.6039i	−0.865016	+	0.998282i	−0.999972	+	0.00743035i	$0.997635\pi$
$822$	1.32540	−	2.90222i	0.0462286	−	0.101226i
$823$	21.7705	+	6.39240i	0.758873	+	0.222825i	0.638204	−	0.769868i	$-0.279678\pi$
$823$	21.7705	+	6.39240i	0.758873	+	0.222825i	0.120669	+	0.992693i	$0.461496\pi$
$824$	−4.70658	−	10.3060i	−0.163962	−	0.359026i
$825$	1.04780	+	7.28761i	0.0364797	+	0.253722i
$826$	−2.58538	−	1.66152i	−0.0899567	−	0.0578117i
$827$	31.6752			1.10145			0.550727	−	0.834685i	$-0.314351\pi$
$827$	31.6752			1.10145			0.550727	+	0.834685i	$0.314351\pi$
$828$	−11.7806	+	7.03447i	−0.409404	+	0.244465i
$829$	26.0097			0.903353			0.451676	−	0.892182i	$-0.350826\pi$
$829$	26.0097			0.903353			0.451676	+	0.892182i	$0.350826\pi$
$830$	−22.5701	−	14.5049i	−0.783420	−	0.503473i
$831$	−1.17272	−	8.15643i	−0.0406811	−	0.282943i
$832$	0.375565	+	0.822373i	0.0130204	+	0.0285107i
$833$	41.0428	+	12.0513i	1.42205	+	0.417552i
$834$	0.223340	−	0.489047i	0.00773364	−	0.0169343i
$835$	11.7202	−	13.5259i	0.405596	−	0.468083i
$836$	2.82834	−	19.6715i	0.0978202	−	0.680354i
$837$	−15.8335	+	4.64915i	−0.547287	+	0.160698i
$838$	2.72723	+	3.14739i	0.0942107	+	0.108725i
$839$	−2.67543	+	1.71939i	−0.0923659	+	0.0593600i	−0.586008	−	0.810305i	$-0.699301\pi$
$839$	−2.67543	+	1.71939i	−0.0923659	+	0.0593600i	0.493643	+	0.869665i	$0.335665\pi$
$840$	0.483568	−	0.310771i	0.0166847	−	0.0107226i
$841$	17.4088	+	20.0909i	0.600304	+	0.692788i
$842$	−1.88875	+	0.554588i	−0.0650907	+	0.0191124i
$843$	−1.70838	+	11.8820i	−0.0588396	+	0.409238i
$844$	17.4618	−	20.1519i	0.601059	−	0.693659i
$845$	−17.1962	+	37.6544i	−0.591566	+	1.29535i
$846$	−27.4819	−	8.06943i	−0.944849	−	0.277433i
$847$	−0.357383	−	0.782560i	−0.0122798	−	0.0268891i
$848$	1.33318	+	9.27245i	0.0457815	+	0.318417i
$849$	7.85460	+	5.04785i	0.269569	+	0.173242i
$850$	41.2110			1.41353
$851$	−0.653162	−	5.91919i	−0.0223901	−	0.202907i
$852$	4.73711			0.162291
$853$	−45.7240	−	29.3850i	−1.56556	−	1.00612i	−0.980823	−	0.194901i	$-0.937561\pi$
$853$	−45.7240	−	29.3850i	−1.56556	−	1.00612i	−0.584737	−	0.811223i	$-0.698802\pi$
$854$	−0.203074	−	1.41241i	−0.00694906	−	0.0483318i
$855$	−26.5994	−	58.2446i	−0.909681	−	1.99192i
$856$	3.02158	+	0.887217i	0.103276	+	0.0303245i
$857$	11.0618	−	24.2219i	0.377863	−	0.827404i	−0.621180	−	0.783668i	$-0.713347\pi$
$857$	11.0618	−	24.2219i	0.377863	−	0.827404i	0.999043	−	0.0437365i	$-0.0139262\pi$
$858$	0.665936	−	0.768532i	0.0227347	−	0.0262372i
$859$	−0.933580	+	6.49319i	−0.0318533	+	0.221545i	−0.999530	−	0.0306484i	$-0.990243\pi$
$859$	−0.933580	+	6.49319i	−0.0318533	+	0.221545i	0.967677	+	0.252193i	$0.0811519\pi$
$860$	−20.3209	+	5.96676i	−0.692938	+	0.203465i
$861$	−0.851078	−	0.982196i	−0.0290046	−	0.0334731i
$862$	6.44109	−	4.13943i	0.219384	−	0.140990i
$863$	−21.7967	+	14.0079i	−0.741969	+	0.476835i	−0.856216	−	0.516618i	$-0.827191\pi$
$863$	−21.7967	+	14.0079i	−0.741969	+	0.476835i	0.114247	+	0.993452i	$0.463555\pi$
$864$	1.43081	+	1.65124i	0.0486772	+	0.0561764i
$865$	5.51375	−	1.61898i	0.187473	−	0.0550471i
$866$	−0.897235	+	6.24041i	−0.0304893	+	0.212058i
$867$	−5.52689	+	6.37837i	−0.187703	+	0.216621i
$868$	−1.42380	+	3.11769i	−0.0483270	+	0.105821i
$869$	−2.73502	−	0.803074i	−0.0927792	−	0.0272424i
$870$	−0.817893	−	1.79094i	−0.0277292	−	0.0607184i
$871$	0.912017	+	6.34322i	0.0309025	+	0.214932i
$872$	4.18494	+	2.68950i	0.141720	+	0.0910780i
$873$	−4.18506			−0.141643
$874$	−29.9995	−	9.89149i	−1.01475	−	0.334585i
$875$	2.38320			0.0805669
$876$	−0.443755	−	0.285184i	−0.0149931	−	0.00963548i
$877$	0.750902	+	5.22264i	0.0253561	+	0.176356i	0.998564	−	0.0535711i	$-0.0170604\pi$
$877$	0.750902	+	5.22264i	0.0253561	+	0.176356i	−0.973208	+	0.229927i	$0.926151\pi$
$878$	4.77694	+	10.4600i	0.161214	+	0.353009i
$879$	3.34519	+	0.982237i	0.112831	+	0.0331300i
$880$	−4.25904	+	9.32599i	−0.143572	+	0.314379i
$881$	35.7720	−	41.2831i	1.20519	−	1.39086i	0.306734	−	0.951795i	$-0.400764\pi$
$881$	35.7720	−	41.2831i	1.20519	−	1.39086i	0.898454	−	0.439067i	$-0.144691\pi$
$882$	−2.76632	+	19.2402i	−0.0931469	+	0.647851i
$883$	−21.9469	+	6.44418i	−0.738571	+	0.216864i	−0.629316	−	0.777150i	$-0.716665\pi$
$883$	−21.9469	+	6.44418i	−0.738571	+	0.216864i	−0.109255	+	0.994014i	$0.534847\pi$
$884$	−3.72750	−	4.30177i	−0.125370	−	0.144684i
$885$	−7.21650	+	4.63776i	−0.242580	+	0.155897i
$886$	−13.5106	+	8.68275i	−0.453898	+	0.291703i
$887$	14.8078	+	17.0891i	0.497196	+	0.573794i	0.947774	−	0.318942i	$-0.103328\pi$
$887$	14.8078	+	17.0891i	0.497196	+	0.573794i	−0.450578	+	0.892737i	$0.648782\pi$
$888$	−0.444147	+	0.130413i	−0.0149046	+	0.00437639i
$889$	0.181835	−	1.26469i	0.00609854	−	0.0424162i
$890$	24.7401	−	28.5515i	0.829289	−	0.957050i
$891$	−9.73746	+	21.3221i	−0.326217	+	0.714316i
$892$	25.2541	+	7.41528i	0.845571	+	0.248282i
$893$	−27.3921	−	59.9803i	−0.916642	−	2.00717i
$894$	−0.131928	−	0.917577i	−0.00441232	−	0.0306884i
$895$	31.6781	+	20.3583i	1.05888	+	0.680502i
$896$	0.453800			0.0151604
$897$	−1.01771	−	1.25568i	−0.0339804	−	0.0419261i
$898$	20.4873			0.683669
$899$	9.87592	+	6.34687i	0.329380	+	0.211680i
$900$	2.66514	+	18.5365i	0.0888380	+	0.617882i
$901$	−24.5011	−	53.6500i	−0.816251	−	1.78734i
$902$	22.2413	+	6.53063i	0.740554	+	0.217446i
$903$	0.438025	−	0.959142i	0.0145766	−	0.0319182i
$904$	−6.10974	+	7.05102i	−0.203207	+	0.234513i
$905$	−1.25403	+	8.72200i	−0.0416855	+	0.289929i
$906$	−0.919797	+	0.270077i	−0.0305582	+	0.00897270i
$907$	−12.0213	−	13.8733i	−0.399162	−	0.460657i	0.520215	−	0.854035i	$-0.325852\pi$
$907$	−12.0213	−	13.8733i	−0.399162	−	0.460657i	−0.919377	+	0.393378i	$0.871306\pi$
$908$	3.23785	−	2.08084i	0.107452	−	0.0690550i
$909$	−5.75960	+	3.70147i	−0.191034	+	0.122770i
$910$	−0.912902	−	1.05354i	−0.0302624	−	0.0349247i
$911$	−0.154132	+	0.0452571i	−0.00510660	+	0.00149943i	−0.284285	−	0.958740i	$-0.591756\pi$
$911$	−0.154132	+	0.0452571i	−0.00510660	+	0.00149943i	0.279178	+	0.960239i	$0.409938\pi$
$912$	−0.349437	+	2.43039i	−0.0115710	+	0.0804782i
$913$	−15.6016	+	18.0052i	−0.516338	+	0.595886i
$914$	17.0382	−	37.3085i	0.563575	−	1.23406i
$915$	−3.82164	−	1.12213i	−0.126339	−	0.0370966i
$916$	9.12054	+	19.9712i	0.301351	+	0.659867i
$917$	0.286776	+	1.99457i	0.00947019	+	0.0658666i
$918$	−11.5725	−	7.43717i	−0.381948	−	0.245463i
$919$	−39.6364			−1.30748			−0.653742	−	0.756717i	$-0.726802\pi$
$919$	−39.6364			−1.30748			−0.653742	+	0.756717i	$0.726802\pi$
$920$	13.4116	+	9.25623i	0.442166	+	0.305169i
$921$	9.08653			0.299411
$922$	−25.9829	−	16.6982i	−0.855701	−	0.549925i
$923$	−1.63496	−	11.3714i	−0.0538155	−	0.374295i
$924$	−0.212044	−	0.464313i	−0.00697575	−	0.0152748i
$925$	−7.79858	−	2.28987i	−0.256416	−	0.0752905i
$926$	3.87583	−	8.48688i	0.127368	−	0.278896i
$927$	−21.2273	+	24.4976i	−0.697196	+	0.804608i
$928$	0.221207	−	1.53853i	0.00726146	−	0.0505046i
$929$	−18.6092	+	5.46417i	−0.610550	+	0.179274i	−0.572367	−	0.819997i	$-0.693975\pi$
$929$	−18.6092	+	5.46417i	−0.610550	+	0.179274i	−0.0381821	+	0.999271i	$0.512157\pi$
$930$	6.26497	+	7.23016i	0.205436	+	0.237086i
$931$	−37.6458	+	24.1935i	−1.23379	+	0.792910i
$932$	−10.5740	+	6.79552i	−0.346364	+	0.222595i
$933$	−3.06178	−	3.53348i	−0.100238	−	0.115681i
$934$	−27.1257	+	7.96483i	−0.887581	+	0.260617i
$935$	9.18640	−	63.8928i	0.300427	−	2.08952i
$936$	1.69385	−	1.95481i	0.0553652	−	0.0638948i
$937$	1.72084	−	3.76811i	0.0562173	−	0.123099i	−0.879439	−	0.476012i	$-0.842082\pi$
$937$	1.72084	−	3.76811i	0.0562173	−	0.123099i	0.935656	+	0.352914i	$0.114809\pi$
$938$	3.08642	+	0.906256i	0.100775	+	0.0295903i
$939$	1.55439	+	3.40364i	0.0507256	+	0.111074i
$940$	4.84107	+	33.6704i	0.157898	+	1.09821i
$941$	15.7689	+	10.1340i	0.514050	+	0.330360i	0.771814	−	0.635848i	$-0.219349\pi$
$941$	15.7689	+	10.1340i	0.514050	+	0.330360i	−0.257764	+	0.966208i	$0.582986\pi$
$942$	−1.78423			−0.0581335
$943$	16.3994	−	32.9925i	0.534038	−	1.07438i
$944$	−6.77225			−0.220418
$945$	−2.83421	−	1.82144i	−0.0921968	−	0.0592513i
$946$	2.67649	+	18.6154i	0.0870202	+	0.605238i
$947$	15.9708	+	34.9712i	0.518982	+	1.13641i	0.969824	+	0.243807i	$0.0783965\pi$
$947$	15.9708	+	34.9712i	0.518982	+	1.13641i	−0.450842	+	0.892604i	$0.648876\pi$
$948$	0.337908	+	0.0992187i	0.0109747	+	0.00322247i
$949$	−0.531426	+	1.16366i	−0.0172508	+	0.0377740i
$950$	−28.2330	+	32.5826i	−0.915998	+	1.05712i
$951$	1.69408	−	11.7826i	0.0549344	−	0.382077i
$952$	−2.74140	+	0.804947i	−0.0888492	+	0.0260885i
$953$	−6.59544	−	7.61155i	−0.213647	−	0.246562i	0.638803	−	0.769370i	$-0.279430\pi$
$953$	−6.59544	−	7.61155i	−0.213647	−	0.246562i	−0.852450	+	0.522808i	$0.824884\pi$
$954$	22.5469	−	14.4900i	0.729984	−	0.469132i
$955$	−41.0960	+	26.4108i	−1.32984	+	0.854633i
$956$	−16.0098	−	18.4763i	−0.517795	−	0.597567i
$957$	−1.67753	+	0.492567i	−0.0542268	+	0.0159224i
$958$	3.29128	−	22.8913i	0.106336	−	0.739586i
$959$	−2.54342	+	2.93526i	−0.0821313	+	0.0947846i
$960$	0.526198	−	1.15221i	0.0169830	−	0.0371875i
$961$	−24.9885	−	7.33729i	−0.806081	−	0.236687i
$962$	0.466350	+	1.02116i	0.0150357	+	0.0329236i
$963$	−1.28223	−	8.91810i	−0.0413193	−	0.287382i
$964$	−12.1026	−	7.77784i	−0.389797	−	0.250507i
$965$	46.7224			1.50405
$966$	−0.785544	+	0.202844i	−0.0252745	+	0.00652641i
$967$	−21.0441			−0.676732			−0.338366	−	0.941015i	$-0.609874\pi$
$967$	−21.0441			−0.676732			−0.338366	+	0.941015i	$0.609874\pi$
$968$	−1.59483	−	1.02493i	−0.0512598	−	0.0329427i
$969$	−2.20006	−	15.3018i	−0.0706762	−	0.491564i
$970$	2.06476	+	4.52118i	0.0662953	+	0.145166i
$971$	−0.675805	−	0.198434i	−0.0216876	−	0.00636806i	0.270871	−	0.962616i	$-0.412688\pi$
$971$	−0.675805	−	0.198434i	−0.0216876	−	0.00636806i	−0.292558	+	0.956248i	$0.594507\pi$
$972$	3.92598	−	8.59670i	0.125926	−	0.275739i
$973$	−0.428587	+	0.494615i	−0.0137399	+	0.0158566i
$974$	−5.34509	+	37.1759i	−0.171268	+	1.19119i
$975$	−2.11666	+	0.621508i	−0.0677875	+	0.0199042i
$976$	−2.05916	−	2.37640i	−0.0659121	−	0.0760666i
$977$	−9.51001	+	6.11172i	−0.304252	+	0.195531i	−0.683854	−	0.729619i	$-0.739697\pi$
$977$	−9.51001	+	6.11172i	−0.304252	+	0.195531i	0.379602	+	0.925150i	$0.376061\pi$
$978$	−4.98055	+	3.20080i	−0.159260	+	0.102350i
$979$	−21.9692	−	25.3538i	−0.702139	−	0.810312i
$980$	22.1503	−	6.50391i	0.707565	−	0.207760i
$981$	2.02552	−	14.0878i	0.0646697	−	0.449788i
$982$	17.3715	−	20.0477i	0.554346	−	0.639749i
$983$	−13.8797	+	30.3923i	−0.442694	+	0.969364i	0.548402	+	0.836215i	$0.315236\pi$
$983$	−13.8797	+	30.3923i	−0.442694	+	0.969364i	−0.991096	+	0.133149i	$0.957491\pi$
$984$	−2.74788	−	0.806851i	−0.0875992	−	0.0257215i
$985$	−4.55600	−	9.97624i	−0.145166	−	0.317870i
$986$	1.39272	+	9.68658i	0.0443532	+	0.308484i
$987$	−1.42473	−	0.915620i	−0.0453497	−	0.0291445i
$988$	5.95475			0.189446
$989$	29.8760	+	0.983208i	0.950002	+	0.0312642i
$990$	29.3327			0.932254
$991$	7.60346	+	4.88645i	0.241532	+	0.155223i	0.655807	−	0.754929i	$-0.272329\pi$
$991$	7.60346	+	4.88645i	0.241532	+	0.155223i	−0.414275	+	0.910152i	$0.635965\pi$
$992$	1.07486	+	7.47584i	0.0341269	+	0.237358i
$993$	−4.75652	−	10.4153i	−0.150944	−	0.330521i
$994$	−5.53300	−	1.62464i	−0.175496	−	0.0515303i
$995$	13.3074	−	29.1391i	0.421873	−	0.923773i
$996$	1.92756	−	2.22452i	0.0610769	−	0.0704866i
$997$	−7.67442	+	53.3768i	−0.243051	+	1.69046i	0.393580	+	0.919290i	$0.371236\pi$
$997$	−7.67442	+	53.3768i	−0.243051	+	1.69046i	−0.636631	+	0.771168i	$0.719673\pi$
$998$	−5.56703	+	1.63463i	−0.176221	+	0.0517432i
$999$	1.77668	+	2.05039i	0.0562116	+	0.0648716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.a.25.1	✓	10
3.2	odd	2		414.2.i.f.163.1		10
4.3	odd	2		368.2.m.b.209.1		10
23.9	even	11		1058.2.a.m.1.3		5
23.12	even	11	inner	46.2.c.a.35.1	yes	10
23.14	odd	22		1058.2.a.l.1.3		5
69.14	even	22		9522.2.a.bu.1.5		5
69.32	odd	22		9522.2.a.bp.1.1		5
69.35	odd	22		414.2.i.f.127.1		10
92.35	odd	22		368.2.m.b.81.1		10
92.55	odd	22		8464.2.a.bx.1.3		5
92.83	even	22		8464.2.a.bw.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.25.1	✓	10	1.1	even	1	trivial
46.2.c.a.35.1	yes	10	23.12	even	11	inner
368.2.m.b.81.1		10	92.35	odd	22
368.2.m.b.209.1		10	4.3	odd	2
414.2.i.f.127.1		10	69.35	odd	22
414.2.i.f.163.1		10	3.2	odd	2
1058.2.a.l.1.3		5	23.14	odd	22
1058.2.a.m.1.3		5	23.9	even	11
8464.2.a.bw.1.3		5	92.83	even	22
8464.2.a.bx.1.3		5	92.55	odd	22
9522.2.a.bp.1.1		5	69.32	odd	22
9522.2.a.bu.1.5		5	69.14	even	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.0530529 - 0.368991i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-3.26024 - 0.957293i) q^{5} +(0.154861 - 0.339098i) q^{6} +(-0.297176 + 0.342959i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.74514 - 0.806046i) q^{9} +(-2.22514 - 2.56794i) q^{10} +(-2.53833 + 1.63129i) q^{11} +(0.313607 - 0.201543i) q^{12} +(-0.592042 - 0.683252i) q^{13} +(-0.435418 + 0.127850i) q^{14} +(-0.180267 + 1.25379i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.61546 - 5.72706i) q^{17} +(2.74514 + 0.806046i) q^{18} +(2.73616 + 5.99136i) q^{19} +(-0.483568 - 3.36329i) q^{20} +(0.142315 + 0.0914602i) q^{21} -3.01732 q^{22} +(-0.838287 + 4.72200i) q^{23} +0.372786 q^{24} +(5.50648 + 3.53880i) q^{25} +(-0.128663 - 0.894870i) q^{26} +(-0.907644 - 1.98746i) q^{27} +(-0.435418 - 0.127850i) q^{28} +(-0.645699 + 1.41388i) q^{29} +(-0.829499 + 0.957293i) q^{30} +(1.07486 - 7.47584i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(0.736596 + 0.850077i) q^{33} +(5.29655 - 3.40388i) q^{34} +(1.29718 - 0.833644i) q^{35} +(1.87358 + 2.16222i) q^{36} +(-1.19143 + 0.349835i) q^{37} +(-0.937368 + 6.51954i) q^{38} +(-0.220705 + 0.254707i) q^{39} +(1.41153 - 3.09082i) q^{40} +(-7.37121 - 2.16438i) q^{41} +(0.0702757 + 0.153882i) q^{42} +(-0.887042 - 6.16951i) q^{43} +(-2.53833 - 1.63129i) q^{44} -9.72143 q^{45} +(-3.25812 + 3.51919i) q^{46} -10.0111 q^{47} +(0.313607 + 0.201543i) q^{48} +(0.966896 + 6.72491i) q^{49} +(2.71913 + 5.95406i) q^{50} +(-2.25199 - 0.661244i) q^{51} +(0.375565 - 0.822373i) q^{52} +(6.13461 - 7.07971i) q^{53} +(0.310945 - 2.16267i) q^{54} +(9.83719 - 2.88846i) q^{55} +(-0.297176 - 0.342959i) q^{56} +(2.06560 - 1.32748i) q^{57} +(-1.30760 + 0.840343i) q^{58} +(4.43488 + 5.11812i) q^{59} +(-1.21537 + 0.356865i) q^{60} +(-0.447498 + 3.11242i) q^{61} +(4.94597 - 5.70796i) q^{62} +(-0.539348 + 1.18101i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.27612 + 2.79432i) q^{65} +(0.160078 + 1.11336i) q^{66} +(-5.96316 - 3.83229i) q^{67} +6.29602 q^{68} +(1.78685 + 0.0588045i) q^{69} +1.54196 q^{70} +(10.6901 + 6.87011i) q^{71} +(0.407167 + 2.83191i) q^{72} +(-0.587813 - 1.28713i) q^{73} +(-1.19143 - 0.349835i) q^{74} +(1.01365 - 2.21959i) q^{75} +(-4.31329 + 4.97780i) q^{76} +(0.194866 - 1.35532i) q^{77} +(-0.323373 + 0.0949510i) q^{78} +(0.618652 + 0.713962i) q^{79} +(2.85848 - 1.83703i) q^{80} +(6.53535 - 4.20002i) q^{81} +(-5.03090 - 5.80597i) q^{82} +(7.57601 - 2.22452i) q^{83} +(-0.0240754 + 0.167448i) q^{84} +(-14.0095 + 16.1678i) q^{85} +(2.58926 - 5.66969i) q^{86} +(0.555967 + 0.163246i) q^{87} +(-1.25344 - 2.74465i) q^{88} +(1.58232 + 11.0053i) q^{89} +(-8.17819 - 5.25580i) q^{90} +0.410268 q^{91} +(-4.64352 + 1.19906i) q^{92} -2.81554 q^{93} +(-8.42190 - 5.41243i) q^{94} +(-3.18506 - 22.1526i) q^{95} +(0.154861 + 0.339098i) q^{96} +(-1.40353 - 0.412113i) q^{97} +(-2.82236 + 6.18010i) q^{98} +(-5.65318 + 6.52412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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