LMFDB - Embedded newform 684.2.bt.a.439.72

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(67,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 6, 17]))

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

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

chi := DirichletCharacter("684.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bt (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			439.72
Character	$\chi$	$=$	684.439
Dual form			684.2.bt.a.67.72

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.432441 + 1.34647i) q^{2} +(0.497535 + 1.65905i) q^{3} +(-1.62599 + 1.16454i) q^{4} +(0.976110 + 0.819053i) q^{5} +(-2.01872 + 1.38736i) q^{6} +4.59654i q^{7} +(-2.27117 - 1.68576i) q^{8} +(-2.50492 + 1.65088i) q^{9} +(-0.680724 + 1.66850i) q^{10} +(3.45262 - 1.99337i) q^{11} +(-2.74103 - 2.11820i) q^{12} +(-1.14724 + 3.15202i) q^{13} +(-6.18912 + 1.98773i) q^{14} +(-0.873204 + 2.02693i) q^{15} +(1.28768 - 3.78707i) q^{16} +(0.907723 - 5.14795i) q^{17} +(-3.30609 - 2.65890i) q^{18} +(3.53893 - 2.54479i) q^{19} +(-2.54097 - 0.195050i) q^{20} +(-7.62590 + 2.28694i) q^{21} +(4.17708 + 3.78685i) q^{22} +(5.76138 - 1.01589i) q^{23} +(1.66677 - 4.60672i) q^{24} +(-0.586299 - 3.32507i) q^{25} +(-4.74023 - 0.181668i) q^{26} +(-3.98518 - 3.33442i) q^{27} +(-5.35287 - 7.47392i) q^{28} +(-2.91865 + 8.01892i) q^{29} +(-3.10681 - 0.299220i) q^{30} +(-2.87788 + 4.98464i) q^{31} +(5.65604 + 0.0961414i) q^{32} +(5.02491 + 4.73631i) q^{33} +(7.32413 - 1.00396i) q^{34} +(-3.76481 + 4.48673i) q^{35} +(2.15045 - 5.60139i) q^{36} -9.63493i q^{37} +(4.95688 + 3.66461i) q^{38} +(-5.80017 - 0.335094i) q^{39} +(-0.836190 - 3.50569i) q^{40} +(2.14382 + 0.378013i) q^{41} +(-6.37707 - 9.27912i) q^{42} +(-1.55813 - 0.274740i) q^{43} +(-3.29256 + 7.26193i) q^{44} +(-3.79723 - 0.440225i) q^{45} +(3.85932 + 7.31824i) q^{46} +(0.915437 - 2.51514i) q^{47} +(6.92361 + 0.252127i) q^{48} -14.1282 q^{49} +(4.22358 - 2.22733i) q^{50} +(8.99235 - 1.05533i) q^{51} +(-1.80526 - 6.46117i) q^{52} +(-3.50418 + 9.62766i) q^{53} +(2.76636 - 6.80788i) q^{54} +(5.00282 + 0.882131i) q^{55} +(7.74864 - 10.4395i) q^{56} +(5.98268 + 4.60516i) q^{57} +(-12.0594 - 0.462172i) q^{58} +(2.22644 - 0.810357i) q^{59} +(-0.940623 - 4.31264i) q^{60} +(-1.47705 + 1.23939i) q^{61} +(-7.95621 - 1.71943i) q^{62} +(-7.58831 - 11.5140i) q^{63} +(2.31645 + 7.65729i) q^{64} +(-3.70151 + 2.13707i) q^{65} +(-4.20434 + 8.81409i) q^{66} +(9.08956 - 7.62705i) q^{67} +(4.51907 + 9.42760i) q^{68} +(4.55190 + 9.05299i) q^{69} +(-7.66933 - 3.12898i) q^{70} +(-1.12853 + 0.410751i) q^{71} +(8.47207 + 0.473255i) q^{72} +(-2.96881 - 2.49113i) q^{73} +(12.9732 - 4.16654i) q^{74} +(5.22476 - 2.62704i) q^{75} +(-2.79075 + 8.25904i) q^{76} +(9.16261 + 15.8701i) q^{77} +(-2.05704 - 7.95469i) q^{78} +(9.29621 - 3.38354i) q^{79} +(4.35873 - 2.64192i) q^{80} +(3.54922 - 8.27061i) q^{81} +(0.418091 + 3.05007i) q^{82} +6.43480i q^{83} +(9.73639 - 12.5992i) q^{84} +(5.10249 - 4.28149i) q^{85} +(-0.303869 - 2.21679i) q^{86} +(-14.7559 - 0.852497i) q^{87} +(-11.2018 - 1.29299i) q^{88} +(2.58961 + 3.08618i) q^{89} +(-1.04933 - 5.30325i) q^{90} +(-14.4884 - 5.27335i) q^{91} +(-8.18489 + 8.36119i) q^{92} +(-9.70164 - 2.29453i) q^{93} +(3.78245 + 0.144961i) q^{94} +(5.53871 + 0.414583i) q^{95} +(2.65457 + 9.43150i) q^{96} +(1.41601 - 1.68753i) q^{97} +(-6.10961 - 19.0232i) q^{98} +(-5.35772 + 10.6931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 18 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} + 21 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} + 24 q^{21} - 15 q^{22} - 39 q^{24} - 6 q^{25} - 30 q^{26}+ \cdots - 63 q^{98}+O(q^{100}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 18 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 + 21 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 + 24 * q^21 - 15 * q^22 - 39 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 + 42 * q^30 - 3 * q^32 - 36 * q^33 - 21 * q^34 + 54 * q^36 - 3 * q^38 + 12 * q^40 - 36 * q^41 + 66 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 - 564 * q^49 - 9 * q^50 - 3 * q^52 - 24 * q^53 + 66 * q^54 + 63 * q^56 - 12 * q^57 - 6 * q^58 - 9 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 18 * q^65 + 6 * q^66 - 6 * q^68 - 18 * q^69 + 18 * q^70 + 12 * q^72 - 60 * q^73 - 60 * q^74 - 3 * q^76 + 72 * q^77 + 9 * q^78 - 12 * q^80 + 18 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 + 105 * q^86 - 24 * q^89 - 141 * q^90 - 171 * q^92 + 6 * q^93 + 15 * q^96 - 24 * q^97 - 63 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.432441	+	1.34647i	0.305782	+	0.952101i
$2$	0.432441	+	1.34647i	0.305782	+	0.952101i
$3$	0.497535	+	1.65905i	0.287252	+	0.957855i
$3$	0.497535	+	1.65905i	0.287252	+	0.957855i
$4$	−1.62599	+	1.16454i	−0.812994	+	0.582272i
$5$	0.976110	+	0.819053i	0.436530	+	0.366292i	0.834409	−	0.551146i	$-0.185809\pi$
$5$	0.976110	+	0.819053i	0.436530	+	0.366292i	−0.397879	+	0.917438i	$0.630254\pi$
$6$	−2.01872	+	1.38736i	−0.824138	+	0.566388i
$7$			4.59654i			1.73733i	0.495401	+	0.868664i	$0.335021\pi$
$7$			4.59654i			1.73733i	−0.495401	+	0.868664i	$0.664979\pi$
$8$	−2.27117	−	1.68576i	−0.802981	−	0.596005i
$9$	−2.50492	+	1.65088i	−0.834972	+	0.550292i
$10$	−0.680724	+	1.66850i	−0.215264	+	0.527626i
$11$	3.45262	−	1.99337i	1.04100	−	0.601024i	0.120887	−	0.992666i	$-0.461426\pi$
$11$	3.45262	−	1.99337i	1.04100	−	0.601024i	0.920118	+	0.391642i	$0.128093\pi$
$12$	−2.74103	−	2.11820i	−0.791266	−	0.611472i
$13$	−1.14724	+	3.15202i	−0.318188	+	0.874214i	0.672747	+	0.739872i	$0.265114\pi$
$13$	−1.14724	+	3.15202i	−0.318188	+	0.874214i	−0.990935	+	0.134341i	$0.957108\pi$
$14$	−6.18912	+	1.98773i	−1.65411	+	0.531244i
$15$	−0.873204	+	2.02693i	−0.225460	+	0.523350i
$16$	1.28768	−	3.78707i	0.321920	−	0.946767i
$17$	0.907723	−	5.14795i	0.220155	−	1.24856i	−0.651578	−	0.758581i	$-0.725893\pi$
$17$	0.907723	−	5.14795i	0.220155	−	1.24856i	0.871733	−	0.489980i	$-0.162996\pi$
$18$	−3.30609	−	2.65890i	−0.779253	−	0.626709i
$19$	3.53893	−	2.54479i	0.811887	−	0.583815i
$19$	3.53893	−	2.54479i	0.811887	−	0.583815i
$20$	−2.54097	−	0.195050i	−0.568177	−	0.0436144i
$21$	−7.62590	+	2.28694i	−1.66411	+	0.499051i
$22$	4.17708	+	3.78685i	0.890557	+	0.807359i
$23$	5.76138	−	1.01589i	1.20133	−	0.211827i	0.463057	−	0.886329i	$-0.346753\pi$
$23$	5.76138	−	1.01589i	1.20133	−	0.211827i	0.738273	+	0.674502i	$0.235642\pi$
$24$	1.66677	−	4.60672i	0.340228	−	0.940343i
$25$	−0.586299	−	3.32507i	−0.117260	−	0.665013i
$26$	−4.74023	−	0.181668i	−0.929636	−	0.0356280i
$27$	−3.98518	−	3.33442i	−0.766947	−	0.641710i
$28$	−5.35287	−	7.47392i	−1.01160	−	1.41244i
$29$	−2.91865	+	8.01892i	−0.541979	+	1.48908i	0.302322	+	0.953206i	$0.402238\pi$
$29$	−2.91865	+	8.01892i	−0.541979	+	1.48908i	−0.844301	+	0.535870i	$0.819984\pi$
$30$	−3.10681	−	0.299220i	−0.567224	−	0.0546299i
$31$	−2.87788	+	4.98464i	−0.516883	+	0.895268i	0.482924	+	0.875662i	$0.339575\pi$
$31$	−2.87788	+	4.98464i	−0.516883	+	0.895268i	−0.999808	+	0.0196062i	$0.993759\pi$
$32$	5.65604	+	0.0961414i	0.999856	+	0.0169956i
$33$	5.02491	+	4.73631i	0.874725	+	0.824486i
$34$	7.32413	−	1.00396i	1.25608	−	0.172178i
$35$	−3.76481	+	4.48673i	−0.636369	+	0.758395i
$36$	2.15045	−	5.60139i	0.358409	−	0.933565i
$37$		−	9.63493i		−	1.58397i	−0.610539	−	0.791986i	$-0.709047\pi$
$37$		−	9.63493i		−	1.58397i	0.610539	−	0.791986i	$-0.290953\pi$
$38$	4.95688	+	3.66461i	0.804111	+	0.594479i
$39$	−5.80017	−	0.335094i	−0.928770	−	0.0536580i
$40$	−0.836190	−	3.50569i	−0.132213	−	0.554299i
$41$	2.14382	+	0.378013i	0.334808	+	0.0590358i	0.338525	−	0.940957i	$-0.390072\pi$
$41$	2.14382	+	0.378013i	0.334808	+	0.0590358i	−0.00371673	+	0.999993i	$0.501183\pi$
$42$	−6.37707	−	9.27912i	−0.984003	−	1.43180i
$43$	−1.55813	−	0.274740i	−0.237613	−	0.0418975i	0.0535737	−	0.998564i	$-0.482939\pi$
$43$	−1.55813	−	0.274740i	−0.237613	−	0.0418975i	−0.291186	+	0.956666i	$0.594050\pi$
$44$	−3.29256	+	7.26193i	−0.496371	+	1.09478i
$45$	−3.79723	−	0.440225i	−0.566058	−	0.0656249i
$46$	3.85932	+	7.31824i	0.569026	+	1.07901i
$47$	0.915437	−	2.51514i	0.133530	−	0.366871i	−0.854850	−	0.518876i	$-0.826351\pi$
$47$	0.915437	−	2.51514i	0.133530	−	0.366871i	0.988380	+	0.152005i	$0.0485729\pi$
$48$	6.92361	+	0.252127i	0.999338	+	0.0363915i
$49$	−14.1282			−2.01831
$50$	4.22358	−	2.22733i	0.597304	−	0.314993i
$51$	8.99235	−	1.05533i	1.25918	−	0.147775i
$52$	−1.80526	−	6.46117i	−0.250345	−	0.896003i
$53$	−3.50418	+	9.62766i	−0.481336	+	1.32246i	0.427012	+	0.904246i	$0.359566\pi$
$53$	−3.50418	+	9.62766i	−0.481336	+	1.32246i	−0.908348	+	0.418215i	$0.862656\pi$
$54$	2.76636	−	6.80788i	0.376454	−	0.926435i
$55$	5.00282	+	0.882131i	0.674579	+	0.118947i
$56$	7.74864	−	10.4395i	1.03546	−	1.39504i
$57$	5.98268	+	4.60516i	0.792426	+	0.609968i
$58$	−12.0594	−	0.462172i	−1.58348	−	0.0606862i
$59$	2.22644	−	0.810357i	0.289858	−	0.105500i	−0.192999	−	0.981199i	$-0.561821\pi$
$59$	2.22644	−	0.810357i	0.289858	−	0.105500i	0.482857	+	0.875699i	$0.339599\pi$
$60$	−0.940623	−	4.31264i	−0.121434	−	0.556760i
$61$	−1.47705	+	1.23939i	−0.189117	+	0.158688i	−0.732430	−	0.680842i	$-0.761614\pi$
$61$	−1.47705	+	1.23939i	−0.189117	+	0.158688i	0.543313	+	0.839530i	$0.317170\pi$
$62$	−7.95621	−	1.71943i	−1.01044	−	0.218368i
$63$	−7.58831	−	11.5140i	−0.956038	−	1.45062i
$64$	2.31645	+	7.65729i	0.289557	+	0.957161i
$65$	−3.70151	+	2.13707i	−0.459116	+	0.265071i
$66$	−4.20434	+	8.81409i	−0.517519	+	1.08494i
$67$	9.08956	−	7.62705i	1.11047	−	0.931792i	0.112383	−	0.993665i	$-0.464152\pi$
$67$	9.08956	−	7.62705i	1.11047	−	0.931792i	0.998084	+	0.0618728i	$0.0197073\pi$
$68$	4.51907	+	9.42760i	0.548017	+	1.14326i
$69$	4.55190	+	9.05299i	0.547984	+	1.08985i
$70$	−7.66933	−	3.12898i	−0.916660	−	0.373984i
$71$	−1.12853	+	0.410751i	−0.133932	+	0.0487471i	−0.408116	−	0.912930i	$-0.633814\pi$
$71$	−1.12853	+	0.410751i	−0.133932	+	0.0487471i	0.274185	+	0.961677i	$0.411592\pi$
$72$	8.47207	+	0.473255i	0.998443	+	0.0557736i
$73$	−2.96881	−	2.49113i	−0.347473	−	0.291564i	0.452302	−	0.891865i	$-0.350603\pi$
$73$	−2.96881	−	2.49113i	−0.347473	−	0.291564i	−0.799774	+	0.600301i	$0.795048\pi$
$74$	12.9732	−	4.16654i	1.50810	−	0.484351i
$75$	5.22476	−	2.62704i	0.603303	−	0.303344i
$76$	−2.79075	+	8.25904i	−0.320121	+	0.947377i
$77$	9.16261	+	15.8701i	1.04418	+	1.80857i
$78$	−2.05704	−	7.95469i	−0.232914	−	0.900691i
$79$	9.29621	−	3.38354i	1.04590	−	0.380678i	0.238789	−	0.971071i	$-0.423250\pi$
$79$	9.29621	−	3.38354i	1.04590	−	0.380678i	0.807116	+	0.590393i	$0.201027\pi$
$80$	4.35873	−	2.64192i	0.487320	−	0.295375i
$81$	3.54922	−	8.27061i	0.394358	−	0.918957i
$82$	0.418091	+	3.05007i	0.0461705	+	0.336824i
$83$			6.43480i			0.706312i	0.935565	+	0.353156i	$0.114891\pi$
$83$			6.43480i			0.706312i	−0.935565	+	0.353156i	$0.885109\pi$
$84$	9.73639	−	12.5992i	1.06233	−	1.37469i
$85$	5.10249	−	4.28149i	0.553442	−	0.464393i
$86$	−0.303869	−	2.21679i	−0.0327670	−	0.239043i
$87$	−14.7559	−	0.852497i	−1.58200	−	0.0913973i
$88$	−11.2018	−	1.29299i	−1.19412	−	0.137833i
$89$	2.58961	+	3.08618i	0.274499	+	0.327135i	0.885627	−	0.464396i	$-0.153729\pi$
$89$	2.58961	+	3.08618i	0.274499	+	0.327135i	−0.611129	+	0.791531i	$0.709284\pi$
$90$	−1.04933	−	5.30325i	−0.110609	−	0.559011i
$91$	−14.4884	−	5.27335i	−1.51880	−	0.552797i
$92$	−8.18489	+	8.36119i	−0.853334	+	0.871714i
$93$	−9.70164	−	2.29453i	−1.00601	−	0.237932i
$94$	3.78245	+	0.144961i	0.390130	+	0.0149516i
$95$	5.53871	+	0.414583i	0.568259	+	0.0425353i
$96$	2.65457	+	9.43150i	0.270931	+	0.962599i
$97$	1.41601	−	1.68753i	0.143774	−	0.171343i	−0.689352	−	0.724427i	$-0.742105\pi$
$97$	1.41601	−	1.68753i	0.143774	−	0.171343i	0.833126	+	0.553084i	$0.186549\pi$
$98$	−6.10961	−	19.0232i	−0.617164	−	1.92164i
$99$	−5.35772	+	10.6931i	−0.538471	+	1.07469i
$100$	4.82550	+	4.72375i	0.482550	+	0.472375i
$101$	−2.58387	−	14.6538i	−0.257105	−	1.45811i	−0.790612	−	0.612317i	$-0.790238\pi$
$101$	−2.58387	−	14.6538i	−0.257105	−	1.45811i	0.533508	−	0.845795i	$-0.320874\pi$
$102$	5.30964	+	11.6516i	0.525733	+	1.15368i
$103$	−8.19148			−0.807130			−0.403565	−	0.914951i	$-0.632229\pi$
$103$	−8.19148			−0.807130			−0.403565	+	0.914951i	$0.632229\pi$
$104$	7.91913	−	5.22482i	0.776534	−	0.512336i
$105$	−9.31685	−	4.01372i	−0.909231	−	0.391699i
$106$	−14.4788	−	0.554893i	−1.40630	−	0.0538959i
$107$	6.23185	+	10.7939i	0.602456	+	1.04348i	0.992448	+	0.122666i	$0.0391445\pi$
$107$	6.23185	+	10.7939i	0.602456	+	1.04348i	−0.389992	+	0.920818i	$0.627522\pi$
$108$	10.3629	+	0.780824i	0.997173	+	0.0751348i
$109$	5.37314	+	14.7626i	0.514654	+	1.41400i	0.876337	+	0.481698i	$0.159980\pi$
$109$	5.37314	+	14.7626i	0.514654	+	1.41400i	−0.361683	+	0.932301i	$0.617798\pi$
$110$	0.975657	+	7.11763i	0.0930253	+	0.678640i
$111$	15.9849	−	4.79372i	1.51722	−	0.455000i
$112$	17.4074	+	5.91887i	1.64485	+	0.559280i
$113$	−10.6693	+	6.15990i	−1.00368	+	0.579475i	−0.909335	−	0.416064i	$-0.863409\pi$
$113$	−10.6693	+	6.15990i	−1.00368	+	0.579475i	−0.0943452	+	0.995540i	$0.530076\pi$
$114$	−3.61357	+	10.0470i	−0.338442	+	0.940987i
$115$	6.45580	+	3.72726i	0.602006	+	0.347569i
$116$	−4.59269	−	16.4376i	−0.426420	−	1.52619i
$117$	−2.32985	−	9.78951i	−0.215395	−	0.905041i
$118$	2.05393	+	2.64741i	0.189080	+	0.243714i
$119$	23.6628	+	4.17238i	2.16916	+	0.382482i
$120$	5.40010	−	3.13149i	0.492960	−	0.285865i
$121$	2.44706	−	4.23844i	0.222460	−	0.385312i
$122$	−2.30755	−	1.45285i	−0.208916	−	0.131535i
$123$	0.439482	+	3.74479i	0.0396268	+	0.337656i
$124$	−1.12542	−	11.4564i	−0.101066	−	1.02881i
$125$	5.33667	−	9.24338i	0.477326	−	0.826753i
$126$	12.2217	−	15.1966i	1.08880	−	1.35382i
$127$	4.41115	−	3.70140i	0.391426	−	0.328446i	−0.425742	−	0.904845i	$-0.639987\pi$
$127$	4.41115	−	3.70140i	0.391426	−	0.328446i	0.817169	+	0.576399i	$0.195542\pi$
$128$	−9.30861	+	6.43037i	−0.822773	+	0.568370i
$129$	−0.319416	−	2.72171i	−0.0281230	−	0.239633i
$130$	−4.47819	−	4.05983i	−0.392764	−	0.356071i
$131$	2.67032	+	7.33663i	0.233307	+	0.641005i	0.999999	−	0.00100944i	$-0.000321314\pi$
$131$	2.67032	+	7.33663i	0.233307	+	0.641005i	−0.766693	+	0.642014i	$0.778099\pi$
$132$	−13.6861	−	1.84946i	−1.19122	−	0.160975i
$133$	11.6972	+	16.2668i	1.01428	+	1.41051i
$134$	14.2003	+	8.94061i	1.22672	+	0.772351i
$135$	−1.15890	−	6.51883i	−0.0997422	−	0.561052i
$136$	−10.7398	+	10.1617i	−0.920929	+	0.871358i
$137$	3.48428	−	2.92366i	0.297682	−	0.249785i	−0.481697	−	0.876338i	$-0.659979\pi$
$137$	3.48428	−	2.92366i	0.297682	−	0.249785i	0.779379	+	0.626553i	$0.215535\pi$
$138$	−10.2212	+	10.0439i	−0.870086	+	0.854994i
$139$	−5.91348	+	16.2471i	−0.501575	+	1.37806i	0.388162	+	0.921591i	$0.373110\pi$
$139$	−5.91348	+	16.2471i	−0.501575	+	1.37806i	−0.889737	+	0.456474i	$0.849112\pi$
$140$	0.896553	−	11.6797i	0.0757726	−	0.987111i
$141$	4.62822	+	0.267387i	0.389766	+	0.0225180i
$142$	−1.04109	−	1.34191i	−0.0873661	−	0.112611i
$143$	2.32216	+	13.1696i	0.194189	+	1.10130i
$144$	3.02645	+	11.6121i	0.252204	+	0.967674i
$145$	−9.41684	+	5.43682i	−0.782026	+	0.451503i
$146$	2.07040	−	5.07469i	0.171348	−	0.419985i
$147$	−7.02927	−	23.4394i	−0.579764	−	1.93325i
$148$	11.2203	+	15.6663i	0.922302	+	1.28776i
$149$	2.63342	−	14.9349i	0.215738	−	1.22351i	−0.663883	−	0.747836i	$-0.731093\pi$
$149$	2.63342	−	14.9349i	0.215738	−	1.22351i	0.879621	−	0.475675i	$-0.157796\pi$
$150$	5.79665	+	5.89897i	0.473294	+	0.481649i
$151$	−5.48369	+	9.49802i	−0.446256	+	0.772938i	−0.998139	−	0.0609836i	$-0.980576\pi$
$151$	−5.48369	+	9.49802i	−0.446256	+	0.772938i	0.551883	+	0.833922i	$0.313910\pi$
$152$	−12.3274	−	0.186124i	−0.999886	−	0.0150967i
$153$	6.22486	+	14.3937i	0.503250	+	1.16366i
$154$	−17.4064	+	19.2001i	−1.40265	+	1.54719i
$155$	−6.89182	+	2.50842i	−0.553564	+	0.201481i
$156$	9.82124	−	6.20969i	0.786328	−	0.497173i
$157$	−9.90389	−	8.31035i	−0.790417	−	0.663238i	0.155432	−	0.987847i	$-0.450323\pi$
$157$	−9.90389	−	8.31035i	−0.790417	−	0.663238i	−0.945849	+	0.324608i	$0.894768\pi$
$158$	8.57592	+	11.0539i	0.682264	+	0.879403i
$159$	−17.7163	−	1.02352i	−1.40499	−	0.0811707i
$160$	5.44217	+	4.72644i	0.430241	+	0.373658i
$161$	4.66956	+	26.4824i	0.368013	+	2.08710i
$162$	12.6710	+	1.20238i	0.995528	+	0.0944678i
$163$	−11.6802	−	6.74355i	−0.914862	−	0.528196i	−0.0328695	−	0.999460i	$-0.510465\pi$
$163$	−11.6802	−	6.74355i	−0.914862	−	0.528196i	−0.881992	+	0.471264i	$0.843798\pi$
$164$	−3.92604	+	1.88193i	−0.306572	+	0.146954i
$165$	1.02557	+	8.73883i	0.0798409	+	0.680317i
$166$	−8.66430	+	2.78268i	−0.672480	+	0.215978i
$167$	1.19685	+	6.78769i	0.0926153	+	0.525247i	0.995452	+	0.0952640i	$0.0303695\pi$
$167$	1.19685	+	6.78769i	0.0926153	+	0.525247i	−0.902837	+	0.429983i	$0.858519\pi$
$168$	21.1750	+	7.66138i	1.63368	+	0.591088i
$169$	1.33950	+	1.12397i	0.103038	+	0.0864593i
$170$	7.97145	+	5.01887i	0.611382	+	0.384930i
$171$	−4.66361	+	12.2168i	−0.356635	+	0.934244i
$172$	2.85345	−	1.36778i	0.217573	−	0.104293i
$173$	10.2706	−	12.2400i	0.780859	−	0.930592i	−0.218113	−	0.975924i	$-0.569990\pi$
$173$	10.2706	−	12.2400i	0.780859	−	0.930592i	0.998972	+	0.0453317i	$0.0144345\pi$
$174$	−5.23322	−	20.2372i	−0.396729	−	1.53418i
$175$	15.2838	−	2.69495i	1.15535	−	0.203719i
$176$	−3.10317	−	15.6421i	−0.233910	−	1.17907i
$177$	2.45216	+	3.29060i	0.184315	+	0.247337i
$178$	−3.03561	+	4.82144i	−0.227529	+	0.361382i
$179$	−5.09090	+	8.81769i	−0.380511	+	0.659065i	−0.991135	−	0.132855i	$-0.957585\pi$
$179$	−5.09090	+	8.81769i	−0.380511	+	0.659065i	0.610624	+	0.791921i	$0.290919\pi$
$180$	6.68691	−	3.70624i	0.498413	−	0.276247i
$181$	−1.35904	+	0.239636i	−0.101017	+	0.0178120i	−0.223928	−	0.974606i	$-0.571888\pi$
$181$	−1.35904	+	0.239636i	−0.101017	+	0.0178120i	0.122911	+	0.992418i	$0.460777\pi$
$182$	0.835042	−	21.7887i	0.0618975	−	1.61508i
$183$	−2.79110	−	1.83386i	−0.206324	−	0.135563i
$184$	−14.7976	−	7.40502i	−1.09089	−	0.545905i
$185$	7.89152	−	9.40475i	0.580196	−	0.691451i
$186$	−1.10587	−	14.0553i	−0.0810860	−	1.03058i
$187$	−7.12776	−	19.5834i	−0.521233	−	1.43208i
$188$	1.44050	+	5.15566i	0.105059	+	0.376015i
$189$	15.3268	−	18.3180i	1.11486	−	1.33244i
$190$	1.83694	+	7.63701i	0.133266	+	0.554047i
$191$	10.4254	+	6.01912i	0.754357	+	0.435528i	0.827266	−	0.561811i	$-0.189895\pi$
$191$	10.4254	+	6.01912i	0.754357	+	0.435528i	−0.0729094	+	0.997339i	$0.523228\pi$
$192$	−11.5513	+	7.65289i	−0.833646	+	0.552300i
$193$	−6.97797	−	1.23040i	−0.502285	−	0.0885665i	−0.0832359	−	0.996530i	$-0.526526\pi$
$193$	−6.97797	−	1.23040i	−0.502285	−	0.0885665i	−0.419049	+	0.907963i	$0.637637\pi$
$194$	2.88456	+	1.17686i	0.207099	+	0.0844935i
$195$	−5.38714	−	5.07774i	−0.385781	−	0.363624i
$196$	22.9723	−	16.4529i	1.64088	−	1.17520i
$197$	−4.90137	−	8.48943i	−0.349208	−	0.604847i	0.636901	−	0.770946i	$-0.280216\pi$
$197$	−4.90137	−	8.48943i	−0.349208	−	0.604847i	−0.986109	+	0.166099i	$0.946883\pi$
$198$	−16.7149	−	2.58991i	−1.18787	−	0.184057i
$199$	−6.44302	+	1.13608i	−0.456734	+	0.0805345i	−0.397282	−	0.917697i	$-0.630046\pi$
$199$	−6.44302	+	1.13608i	−0.456734	+	0.0805345i	−0.0594520	+	0.998231i	$0.518935\pi$
$200$	−4.27367	+	8.54016i	−0.302194	+	0.603880i
$201$	17.1761	+	11.2853i	1.21151	+	0.796007i
$202$	18.6137	−	9.81605i	1.30965	−	0.690655i
$203$	−36.8593	−	13.4157i	−2.58701	−	0.941596i
$204$	−13.3925	+	12.1879i	−0.937662	+	0.853326i
$205$	1.78299	+	2.12489i	0.124529	+	0.148408i
$206$	−3.54233	−	11.0296i	−0.246806	−	0.768470i
$207$	−12.7547	+	12.0560i	−0.886511	+	0.837952i
$208$	10.4596	+	8.40348i	0.725246	+	0.582676i
$209$	7.14589	−	15.8406i	0.494291	−	1.09572i
$210$	1.37538	−	14.2806i	0.0949101	−	0.985455i
$211$	14.9927	−	5.45688i	1.03214	−	0.375667i	0.230243	−	0.973133i	$-0.426048\pi$
$211$	14.9927	−	5.45688i	1.03214	−	0.375667i	0.801894	+	0.597466i	$0.203826\pi$
$212$	−5.51407	−	19.7352i	−0.378708	−	1.35542i
$213$	−1.24294	−	1.66793i	−0.0851648	−	0.114284i
$214$	−11.8388	+	13.0588i	−0.809283	+	0.892678i
$215$	−1.29588	−	1.54437i	−0.0883782	−	0.105325i
$216$	3.43000	+	14.2911i	0.233382	+	0.972385i
$217$	−22.9121	−	13.2283i	−1.55538	−	0.897996i
$218$	−17.5539	+	13.6188i	−1.18890	+	0.922379i
$219$	2.65582	−	6.16484i	0.179464	−	0.416581i
$220$	−9.16180	+	4.39166i	−0.617689	+	0.296086i
$221$	15.1851	+	8.76711i	1.02146	+	0.589740i
$222$	13.3671	+	19.4502i	0.897144	+	1.30541i
$223$	3.40370	−	19.3034i	0.227929	−	1.29265i	−0.629078	−	0.777342i	$-0.716567\pi$
$223$	3.40370	−	19.3034i	0.227929	−	1.29265i	0.857007	−	0.515306i	$-0.172322\pi$
$224$	−0.441918	+	25.9982i	−0.0295269	+	1.73708i
$225$	6.95790	+	7.36111i	0.463860	+	0.490741i
$226$	−12.9080	−	11.7021i	−0.858627	−	0.778412i
$227$	8.04512	−	13.9345i	0.533973	−	0.924868i	−0.465239	−	0.885185i	$-0.654032\pi$
$227$	8.04512	−	13.9345i	0.533973	−	0.924868i	0.999212	−	0.0396835i	$-0.0126350\pi$
$228$	−15.0907	−	0.520841i	−0.999405	−	0.0344935i
$229$	0.622889	+	1.07887i	0.0411616	+	0.0712940i	0.885872	−	0.463929i	$-0.153561\pi$
$229$	0.622889	+	1.07887i	0.0411616	+	0.0712940i	−0.844711	+	0.535223i	$0.820227\pi$
$230$	−2.22690	+	10.3044i	−0.146838	+	0.679451i
$231$	−21.7706	+	23.0972i	−1.43240	+	1.51968i
$232$	20.1467	−	13.2922i	1.32269	−	0.872677i
$233$	2.37884	−	0.865826i	0.155843	−	0.0567222i	−0.262921	−	0.964817i	$-0.584686\pi$
$233$	2.37884	−	0.865826i	0.155843	−	0.0567222i	0.418764	+	0.908095i	$0.362464\pi$
$234$	12.1738	−	7.37047i	0.795827	−	0.481823i
$235$	2.95360	−	1.70526i	0.192672	−	0.111239i
$236$	−2.67647	+	3.91042i	−0.174223	+	0.254546i
$237$	10.2387	+	13.7395i	0.665073	+	0.892475i
$238$	4.61475	+	33.6656i	0.299130	+	2.18222i
$239$			12.3976i			0.801935i	0.916092	+	0.400968i	$0.131326\pi$
$239$			12.3976i			0.801935i	−0.916092	+	0.400968i	$0.868674\pi$
$240$	6.55170	+	5.91691i	0.422911	+	0.381935i
$241$	8.83276	−	1.55745i	0.568968	−	0.100324i	0.118239	−	0.992985i	$-0.462275\pi$
$241$	8.83276	−	1.55745i	0.568968	−	0.100324i	0.450729	+	0.892661i	$0.351164\pi$
$242$	6.76516	+	1.46203i	0.434881	+	0.0939830i
$243$	15.4873	+	1.77342i	0.993508	+	0.113765i
$244$	0.958341	−	3.73533i	0.0613515	−	0.239130i
$245$	−13.7906	−	11.5717i	−0.881052	−	0.739291i
$246$	−4.85221	+	2.21115i	−0.309366	+	0.140978i
$247$	3.96122	+	14.0743i	0.252046	+	0.895526i
$248$	14.9391	−	6.46957i	0.948632	−	0.410818i
$249$	−10.6757	+	3.20154i	−0.676544	+	0.202890i
$250$	14.7538	+	3.18847i	0.933110	+	0.201656i
$251$	7.20005	−	19.7820i	0.454463	−	1.24863i	−0.475089	−	0.879938i	$-0.657584\pi$
$251$	7.20005	−	19.7820i	0.454463	−	1.24863i	0.929552	−	0.368690i	$-0.120194\pi$
$252$	25.7470	+	9.88463i	1.62191	+	0.622673i
$253$	17.8668	−	14.9920i	1.12328	−	0.942541i
$254$	6.89140	+	4.33887i	0.432405	+	0.272245i
$255$	9.64189	+	6.33510i	0.603799	+	0.396719i
$256$	−12.6838	−	9.75305i	−0.792735	−	0.609566i
$257$	3.01188	+	3.58941i	0.187876	+	0.223901i	0.851758	−	0.523936i	$-0.175537\pi$
$257$	3.01188	+	3.58941i	0.187876	+	0.223901i	−0.663882	+	0.747837i	$0.731092\pi$
$258$	3.52659	−	1.60707i	0.219556	−	0.100052i
$259$	44.2873			2.75188
$260$	3.52991	−	7.78541i	0.218915	−	0.482831i
$261$	−5.92727	−	24.9050i	−0.366889	−	1.54158i
$262$	−8.72384	+	6.76818i	−0.538960	+	0.418139i
$263$	3.37710	+	9.27851i	0.208241	+	0.572137i	0.999211	−	0.0397177i	$-0.0126459\pi$
$263$	3.37710	+	9.27851i	0.208241	+	0.572137i	−0.790970	+	0.611855i	$0.790424\pi$
$264$	−3.42818	−	19.2278i	−0.210990	−	1.18339i
$265$	−11.3060	+	6.52754i	−0.694524	+	0.400984i
$266$	−16.8445	+	22.7845i	−1.03280	+	1.39701i
$267$	−3.83172	+	5.83179i	−0.234497	+	0.356900i
$268$	−5.89750	+	22.9867i	−0.360247	+	1.40413i
$269$	2.10496	−	2.50860i	0.128342	−	0.152952i	−0.698047	−	0.716052i	$-0.745947\pi$
$269$	2.10496	−	2.50860i	0.128342	−	0.152952i	0.826388	+	0.563100i	$0.190392\pi$
$270$	8.27629	−	4.37944i	0.503679	−	0.266524i
$271$	3.16897	+	8.70668i	0.192501	+	0.528893i	0.997966	−	0.0637511i	$-0.0203064\pi$
$271$	3.16897	+	8.70668i	0.192501	+	0.528893i	−0.805465	+	0.592644i	$0.798084\pi$
$272$	−18.3268	−	10.0665i	−1.11122	−	0.610372i
$273$	1.54027	−	26.6607i	0.0932215	−	1.61358i
$274$	5.44338	+	3.42718i	0.328847	+	0.207044i
$275$	−8.65236	−	10.3115i	−0.521757	−	0.621806i
$276$	−17.9439	−	9.41918i	−1.08010	−	0.566968i
$277$	−8.10151	−	14.0322i	−0.486772	−	0.843114i	0.513112	−	0.858322i	$-0.328493\pi$
$277$	−8.10151	−	14.0322i	−0.486772	−	0.843114i	−0.999884	+	0.0152072i	$0.995159\pi$
$278$	−24.4336	−	0.936408i	−1.46543	−	0.0561620i
$279$	−1.02016	−	17.2371i	−0.0610755	−	1.03196i
$280$	16.1141	−	3.84358i	0.963000	−	0.229698i
$281$	−1.98843	−	2.36972i	−0.118620	−	0.141366i	0.703467	−	0.710728i	$-0.251634\pi$
$281$	−1.98843	−	2.36972i	−0.118620	−	0.141366i	−0.822086	+	0.569363i	$0.807190\pi$
$282$	1.64140	+	6.34741i	0.0977442	+	0.377983i
$283$	−5.06888	−	13.9266i	−0.301314	−	0.827853i	−0.994272	−	0.106875i	$-0.965915\pi$
$283$	−5.06888	−	13.9266i	−0.301314	−	0.827853i	0.692959	−	0.720977i	$-0.256307\pi$
$284$	1.35664	−	1.98210i	0.0805016	−	0.117616i
$285$	2.06789	+	9.39528i	0.122491	+	0.556528i
$286$	−16.7284	+	8.82182i	−0.989169	+	0.521645i
$287$	−1.73755	+	9.85415i	−0.102565	+	0.581672i
$288$	−14.3266	+	9.09659i	−0.844204	+	0.536022i
$289$	−9.70268	−	3.53149i	−0.570746	−	0.207735i
$290$	−11.3928	−	10.3284i	−0.669006	−	0.606507i
$291$	3.50422	+	1.50962i	0.205421	+	0.0884957i
$292$	7.72827	+	0.593237i	0.452263	+	0.0347166i
$293$		−	32.5527i		−	1.90175i	−0.309577	−	0.950874i	$-0.600187\pi$
$293$		−	32.5527i		−	1.90175i	0.309577	−	0.950874i	$-0.399813\pi$
$294$	28.5208	−	19.6009i	1.66337	−	1.14315i
$295$	2.83697	+	1.03257i	0.165175	+	0.0601188i
$296$	−16.2421	+	21.8826i	−0.944055	+	1.27190i
$297$	−20.4060	−	3.56856i	−1.18408	−	0.207069i
$298$	21.2482	−	2.91262i	1.23088	−	0.168724i
$299$	−3.40760	+	19.3255i	−0.197067	+	1.11762i
$300$	−5.43610	+	10.3560i	−0.313853	+	0.597904i
$301$	1.26285	−	7.16200i	0.0727897	−	0.412811i
$302$	−15.1602	−	3.27631i	−0.872373	−	0.188530i
$303$	23.0260	−	11.5776i	1.32281	−	0.665115i
$304$	−5.08028	−	16.6791i	−0.291374	−	0.956609i
$305$	−2.45689			−0.140681
$306$	−16.6889	+	14.6061i	−0.954042	+	0.834973i
$307$	−11.8295	−	9.92615i	−0.675147	−	0.566515i	0.239437	−	0.970912i	$-0.423037\pi$
$307$	−11.8295	−	9.92615i	−0.675147	−	0.566515i	−0.914584	+	0.404397i	$0.867482\pi$
$308$	−33.3797	−	15.1344i	−1.90199	−	0.862360i
$309$	−4.07555	−	13.5901i	−0.231850	−	0.773114i
$310$	−6.35783	−	8.19492i	−0.361100	−	0.465440i
$311$	7.92835	+	4.57744i	0.449576	+	0.259563i	0.707651	−	0.706562i	$-0.249755\pi$
$311$	7.92835	+	4.57744i	0.449576	+	0.259563i	−0.258075	+	0.966125i	$0.583088\pi$
$312$	12.6083	+	10.5387i	0.713804	+	0.596638i
$313$	−3.99547	−	1.45423i	−0.225837	−	0.0821981i	0.226623	−	0.973983i	$-0.427231\pi$
$313$	−3.99547	−	1.45423i	−0.225837	−	0.0821981i	−0.452461	+	0.891784i	$0.649454\pi$
$314$	6.90683	−	16.9291i	0.389775	−	0.955364i
$315$	2.02351	−	17.4541i	0.114012	−	0.983428i
$316$	−11.1752	+	16.3274i	−0.628657	+	0.918490i
$317$	10.0840	−	1.77809i	0.566375	−	0.0998672i	0.116874	−	0.993147i	$-0.462713\pi$
$317$	10.0840	−	1.77809i	0.566375	−	0.0998672i	0.449502	+	0.893280i	$0.351602\pi$
$318$	−6.28310	−	24.2971i	−0.352339	−	1.36251i
$319$	5.90770	+	33.5042i	0.330768	+	1.87588i
$320$	−4.01061	+	9.37165i	−0.224200	+	0.523891i
$321$	−14.8071	+	15.7093i	−0.826450	+	0.876809i
$322$	−33.6386	+	17.7395i	−1.87460	+	0.988585i
$323$	−9.88808	−	20.5282i	−0.550187	−	1.14222i
$324$	3.86049	+	17.5811i	0.214472	+	0.976730i
$325$	11.1533	+	1.96663i	0.618674	+	0.109089i
$326$	4.02903	−	18.6432i	0.223147	−	1.03255i
$327$	−21.8186	+	16.2592i	−1.20657	+	0.899138i
$328$	−4.23175	−	4.47249i	−0.233659	−	0.246952i
$329$	11.5610	+	4.20784i	0.637376	+	0.231986i
$330$	−11.3231	+	5.15994i	−0.623317	+	0.284046i
$331$	1.47114	+	2.54809i	0.0808610	+	0.140055i	0.903620	−	0.428335i	$-0.140900\pi$
$331$	1.47114	+	2.54809i	0.0808610	+	0.140055i	−0.822759	+	0.568390i	$0.807566\pi$
$332$	−7.49361	−	10.4629i	−0.411265	−	0.574227i
$333$	15.9061	+	24.1347i	0.871647	+	1.32257i
$334$	−8.62189	+	4.54681i	−0.471769	+	0.248791i
$335$	15.1194			0.826059
$336$	−1.15891	+	31.8247i	−0.0632239	+	1.73618i
$337$	10.6594	−	12.7034i	0.580653	−	0.691996i	−0.393127	−	0.919484i	$-0.628607\pi$
$337$	10.6594	−	12.7034i	0.580653	−	0.691996i	0.973781	+	0.227488i	$0.0730513\pi$
$338$	−0.934144	+	2.28965i	−0.0508108	+	0.124540i
$339$	−15.5279	−	14.6361i	−0.843362	−	0.794925i
$340$	−3.31060	+	12.9037i	−0.179542	+	0.699803i
$341$			22.9468i			1.24264i
$342$	−18.4664	−	0.996367i	−0.998548	−	0.0538774i
$343$		−	32.7649i		−	1.76914i
$344$	3.07564	+	3.25061i	0.165827	+	0.175261i
$345$	−2.97173	+	12.5650i	−0.159993	+	0.676475i
$346$	20.9223	+	8.53601i	1.12479	+	0.458899i
$347$	−1.90523	+	2.27056i	−0.102278	+	0.121890i	−0.814755	−	0.579805i	$-0.803129\pi$
$347$	−1.90523	+	2.27056i	−0.102278	+	0.121890i	0.712477	+	0.701695i	$0.247573\pi$
$348$	24.9858	−	15.7978i	1.33938	−	0.846850i
$349$	−0.236263			−0.0126469			−0.00632344	−	0.999980i	$-0.502013\pi$
$349$	−0.236263			−0.0126469			−0.00632344	+	0.999980i	$0.502013\pi$
$350$	10.2380	+	19.4138i	0.547246	+	1.03771i
$351$	15.0821	−	8.73597i	0.805025	−	0.466292i
$352$	19.7198	−	10.9426i	1.05107	−	0.583245i
$353$	4.29494	+	7.43906i	0.228597	+	0.395941i	0.957392	−	0.288790i	$-0.0932530\pi$
$353$	4.29494	+	7.43906i	0.228597	+	0.395941i	−0.728796	+	0.684731i	$0.759920\pi$
$354$	−3.37029	+	4.72476i	−0.179129	+	0.251118i
$355$	−1.43799	−	0.523387i	−0.0763208	−	0.0277785i
$356$	−7.80468	−	2.00238i	−0.413647	−	0.106126i
$357$	4.85085	+	41.3337i	0.256734	+	2.18761i
$358$	−14.0743	−	3.04163i	−0.743851	−	0.160755i
$359$	−11.2099	−	1.97660i	−0.591635	−	0.104321i	−0.130188	−	0.991489i	$-0.541558\pi$
$359$	−11.2099	−	1.97660i	−0.591635	−	0.104321i	−0.461446	+	0.887168i	$0.652669\pi$
$360$	7.88205	+	7.40103i	0.415421	+	0.390068i
$361$	6.04810	−	18.0117i	0.318321	−	0.947983i
$362$	−0.910369	−	1.72629i	−0.0478479	−	0.0907316i
$363$	8.24929	+	1.95104i	0.432976	+	0.102403i
$364$	29.6990	−	8.29796i	1.55665	−	0.434931i
$365$	−0.857518	−	4.86323i	−0.0448845	−	0.254553i
$366$	1.26226	−	4.55119i	0.0659795	−	0.237894i
$367$	−33.2351	+	5.86024i	−1.73486	+	0.305902i	−0.949645	−	0.313327i	$-0.898556\pi$
$367$	−33.2351	+	5.86024i	−1.73486	+	0.305902i	−0.785211	+	0.619229i	$0.787445\pi$
$368$	3.57157	−	23.1269i	0.186181	−	1.20557i
$369$	−5.99414	+	2.59229i	−0.312043	+	0.134949i
$370$	16.0759	+	6.55873i	0.835745	+	0.340972i
$371$	−44.2539	−	16.1071i	−2.29755	−	0.836240i
$372$	18.4468	−	7.56710i	0.956424	−	0.392336i
$373$	−22.0209	−	12.7138i	−1.14020	−	0.658294i	−0.193719	−	0.981057i	$-0.562055\pi$
$373$	−22.0209	−	12.7138i	−1.14020	−	0.658294i	−0.946480	+	0.322763i	$0.895388\pi$
$374$	23.2862	−	18.0660i	1.20410	−	0.934171i
$375$	17.9904	+	4.25491i	0.929022	+	0.219723i
$376$	−6.31904	+	4.16912i	−0.325879	+	0.215006i
$377$	−21.9274	−	18.3993i	−1.12932	−	0.947611i
$378$	31.2927	+	12.7157i	1.60952	+	0.654024i
$379$	−28.7120			−1.47483			−0.737417	−	0.675437i	$-0.763955\pi$
$379$	−28.7120			−1.47483			−0.737417	+	0.675437i	$0.763955\pi$
$380$	−9.48867	+	5.77595i	−0.486759	+	0.296300i
$381$	8.33552	+	5.47676i	0.427041	+	0.280583i
$382$	−3.59621	+	16.6405i	−0.183998	+	0.851401i
$383$	−3.06333	+	17.3730i	−0.156529	+	0.887719i	0.800846	+	0.598871i	$0.204384\pi$
$383$	−3.06333	+	17.3730i	−0.156529	+	0.887719i	−0.957375	+	0.288849i	$0.906728\pi$
$384$	−15.2997	−	12.2441i	−0.780760	−	0.624832i
$385$	−4.05475	+	22.9956i	−0.206649	+	1.17197i
$386$	−1.36086	−	9.92774i	−0.0692657	−	0.505309i
$387$	4.35655	−	1.88408i	0.221456	−	0.0957730i
$388$	−0.337208	+	4.39290i	−0.0171191	+	0.223016i
$389$	−27.8889	−	10.1507i	−1.41402	−	0.514662i	−0.481714	−	0.876328i	$-0.659986\pi$
$389$	−27.8889	−	10.1507i	−1.41402	−	0.514662i	−0.932307	+	0.361667i	$0.882208\pi$
$390$	4.50742	−	9.44947i	0.228242	−	0.478493i
$391$		−	30.5814i		−	1.54657i
$392$	32.0875	+	23.8167i	1.62066	+	1.20292i
$393$	−10.8433	+	8.08043i	−0.546972	+	0.407604i
$394$	9.31124	−	10.2708i	0.469094	−	0.517433i
$395$	11.8454	+	4.31138i	0.596008	+	0.216929i
$396$	−3.74096	−	23.6261i	−0.187990	−	1.18726i
$397$	0.867141	−	4.91780i	0.0435206	−	0.246817i	−0.955285	−	0.295688i	$-0.904451\pi$
$397$	0.867141	−	4.91780i	0.0435206	−	0.246817i	0.998805	+	0.0488707i	$0.0155622\pi$
$398$	−4.31593	−	8.18408i	−0.216338	−	0.410231i
$399$	−21.1678	+	27.4996i	−1.05972	+	1.37670i
$400$	−13.3472	−	2.06126i	−0.667361	−	0.103063i
$401$	4.76674	+	13.0965i	0.238040	+	0.654008i	0.999980	+	0.00636100i	$0.00202478\pi$
$401$	4.76674	+	13.0965i	0.238040	+	0.654008i	−0.761940	+	0.647647i	$0.775753\pi$
$402$	−7.76779	+	28.0074i	−0.387422	+	1.39688i
$403$	−12.4101	−	14.7898i	−0.618190	−	0.736730i
$404$	21.2664	+	20.8180i	1.05804	+	1.03573i
$405$	10.2385	−	5.16603i	0.508755	−	0.256702i
$406$	2.12439	−	55.4316i	0.105432	−	2.75102i
$407$	−19.2060	−	33.2658i	−0.952006	−	1.64892i
$408$	−22.2022	−	12.7621i	−1.09917	−	0.631817i
$409$	−16.4234	−	19.5726i	−0.812083	−	0.967803i	0.187813	−	0.982205i	$-0.439860\pi$
$409$	−16.4234	−	19.5726i	−0.812083	−	0.967803i	−0.999896	+	0.0144016i	$0.995416\pi$
$410$	−2.09007	+	3.31964i	−0.103221	+	0.163945i
$411$	6.58406	+	4.32598i	0.324768	+	0.213385i
$412$	13.3192	−	9.53933i	0.656192	−	0.469969i
$413$	3.72484	+	10.2339i	0.183287	+	0.503578i
$414$	−21.7488	−	11.9603i	−1.06889	−	0.587817i
$415$	−5.27045	+	6.28108i	−0.258716	+	0.308326i
$416$	−6.79189	+	17.7177i	−0.333000	+	0.868680i
$417$	−29.8970	−	1.72725i	−1.46406	−	0.0845836i
$418$	24.4191	+	2.77163i	1.19438	+	0.135565i
$419$	10.9977	−	6.34953i	0.537273	−	0.310195i	−0.206700	−	0.978404i	$-0.566272\pi$
$419$	10.9977	−	6.34953i	0.537273	−	0.310195i	0.743973	+	0.668210i	$0.232939\pi$
$420$	19.8232	−	4.32361i	0.967275	−	0.210971i
$421$	−2.76201	−	7.58856i	−0.134612	−	0.369844i	0.854012	−	0.520254i	$-0.174163\pi$
$421$	−2.76201	−	7.58856i	−0.134612	−	0.369844i	−0.988624	+	0.150410i	$0.951941\pi$
$422$	13.8310	+	17.8275i	0.673283	+	0.867827i
$423$	1.85909	+	7.81150i	0.0903923	+	0.379808i
$424$	24.1885	−	15.9589i	1.17470	−	0.775032i
$425$	−17.6495			−0.856126
$426$	1.70832	−	2.39487i	0.0827684	−	0.116032i
$427$	−5.69692	−	6.78932i	−0.275693	−	0.328558i
$428$	−22.7029	−	10.2935i	−1.09738	−	0.497554i
$429$	−20.6938	+	10.4049i	−0.999104	+	0.502355i
$430$	1.51906	−	2.41272i	0.0732556	−	0.116352i
$431$	−0.118084	+	0.0990843i	−0.00568791	+	0.00477272i	−0.645627	−	0.763653i	$-0.723404\pi$
$431$	−0.118084	+	0.0990843i	−0.00568791	+	0.00477272i	0.639939	+	0.768426i	$0.278960\pi$
$432$	−17.7593	+	10.7985i	−0.854445	+	0.519542i
$433$	−2.15615	+	5.92397i	−0.103618	+	0.284688i	−0.980658	−	0.195730i	$-0.937293\pi$
$433$	−2.15615	+	5.92397i	−0.103618	+	0.284688i	0.877040	+	0.480417i	$0.159515\pi$
$434$	7.90344	−	36.5710i	0.379377	−	1.75547i
$435$	−13.7052	−	12.9180i	−0.657113	−	0.619372i
$436$	−25.9283	−	17.7465i	−1.24174	−	0.849905i
$437$	17.8039	−	18.2566i	0.851677	−	0.873333i
$438$	9.44929	+	0.910070i	0.451504	+	0.0434848i
$439$	25.3020	+	21.2309i	1.20760	+	1.01329i	0.999380	+	0.0352116i	$0.0112105\pi$
$439$	25.3020	+	21.2309i	1.20760	+	1.01329i	0.208217	+	0.978083i	$0.433234\pi$
$440$	−9.87520	−	10.4370i	−0.470782	−	0.497564i
$441$	35.3899	−	23.3239i	1.68523	−	1.11066i
$442$	−5.23804	+	24.2376i	−0.249148	+	1.15286i
$443$	19.4402	−	3.42784i	0.923633	−	0.162861i	0.308445	−	0.951242i	$-0.400191\pi$
$443$	19.4402	−	3.42784i	0.923633	−	0.162861i	0.615188	+	0.788381i	$0.289080\pi$
$444$	−20.4087	+	26.4096i	−0.968555	+	1.25334i
$445$			5.13348i			0.243351i
$446$	27.4634	−	3.76457i	1.30043	−	0.178258i
$447$	26.0879	−	3.06164i	1.23392	−	0.144810i
$448$	−35.1970	+	10.6477i	−1.66290	+	0.503055i
$449$	18.7648	−	10.8339i	0.885565	−	0.511281i	0.0130760	−	0.999915i	$-0.495838\pi$
$449$	18.7648	−	10.8339i	0.885565	−	0.511281i	0.872489	+	0.488633i	$0.162504\pi$
$450$	−6.90266	+	12.5519i	−0.325395	+	0.591702i
$451$	8.15532	−	2.96829i	0.384019	−	0.139771i
$452$	10.1746	−	22.4408i	0.478575	−	1.05552i
$453$	−18.4861	−	4.37213i	−0.868551	−	0.205420i
$454$	22.2416	+	4.80667i	1.04385	+	0.225588i
$455$	−9.82311	−	17.0141i	−0.460515	−	0.797635i
$456$	−5.82454	−	20.5445i	−0.272759	−	0.962082i
$457$	−16.6559	+	28.8489i	−0.779130	+	1.34949i	0.153314	+	0.988178i	$0.451005\pi$
$457$	−16.6559	+	28.8489i	−0.779130	+	1.34949i	−0.932444	+	0.361315i	$0.882328\pi$
$458$	−1.18331	+	1.30525i	−0.0552927	+	0.0609905i
$459$	−20.7829	+	17.4888i	−0.970062	+	0.816306i
$460$	−14.8376	+	1.45758i	−0.691807	+	0.0679599i
$461$	−2.46968	+	14.0063i	−0.115024	+	0.652336i	0.871714	+	0.490016i	$0.163009\pi$
$461$	−2.46968	+	14.0063i	−0.115024	+	0.652336i	−0.986738	+	0.162320i	$0.948102\pi$
$462$	−40.5143	−	19.3254i	−1.88490	−	0.899100i
$463$	1.58889	+	0.917348i	0.0738421	+	0.0426328i	0.536466	−	0.843922i	$-0.319759\pi$
$463$	1.58889	+	0.917348i	0.0738421	+	0.0426328i	−0.462624	+	0.886554i	$0.653092\pi$
$464$	26.6099	+	21.3789i	1.23533	+	0.992491i
$465$	−7.59052	−	10.1859i	−0.352002	−	0.472358i
$466$	2.19452	+	2.82863i	0.101659	+	0.131034i
$467$	7.98281	+	4.60888i	0.369400	+	0.213273i	0.673196	−	0.739464i	$-0.264921\pi$
$467$	7.98281	+	4.60888i	0.369400	+	0.213273i	−0.303796	+	0.952737i	$0.598254\pi$
$468$	15.1886	+	13.2044i	0.702094	+	0.610375i
$469$	35.0580	+	41.7805i	1.61883	+	1.92925i
$470$	3.57336	+	3.23953i	0.164827	+	0.149428i
$471$	8.85978	−	20.5658i	0.408237	−	0.947621i
$472$	−6.42269	−	1.91277i	−0.295628	−	0.0880424i
$473$	−5.92729	+	2.15736i	−0.272537	+	0.0991954i
$474$	−14.0722	+	19.7276i	−0.646359	+	0.906120i
$475$	−10.5365	−	10.2752i	−0.483446	−	0.471458i
$476$	−43.3343	+	20.7721i	−1.98623	+	0.952086i
$477$	−7.11639	−	29.9015i	−0.325837	−	1.36909i
$478$	−16.6931	+	5.36125i	−0.763524	+	0.245218i
$479$	−16.8146	−	20.0388i	−0.768277	−	0.915596i	0.230064	−	0.973175i	$-0.426106\pi$
$479$	−16.8146	−	20.0388i	−0.768277	−	0.915596i	−0.998341	+	0.0575790i	$0.981662\pi$
$480$	−5.13375	+	11.3804i	−0.234322	+	0.519443i
$481$	30.3695	+	11.0536i	1.38473	+	0.504001i
$482$	5.91672	+	11.2196i	0.269499	+	0.511038i
$483$	−41.6124	+	20.9230i	−1.89343	+	0.952028i
$484$	0.956946	+	9.74136i	0.0434976	+	0.442789i
$485$	2.76435	−	0.487430i	0.125523	−	0.0221331i
$486$	4.30946	+	21.6201i	0.195481	+	0.980707i
$487$	−0.422073	−	0.731052i	−0.0191260	−	0.0331271i	0.856304	−	0.516472i	$-0.172755\pi$
$487$	−0.422073	−	0.731052i	−0.0191260	−	0.0331271i	−0.875430	+	0.483345i	$0.839422\pi$
$488$	5.44395	−	0.324928i	0.246436	−	0.0147088i
$489$	5.37661	−	22.7332i	0.243139	−	1.02803i
$490$	9.61739	−	23.5729i	0.434470	−	1.06491i
$491$	−0.783230	−	0.138105i	−0.0353467	−	0.00623257i	0.155947	−	0.987765i	$-0.450157\pi$
$491$	−0.783230	−	0.138105i	−0.0353467	−	0.00623257i	−0.191294	+	0.981533i	$0.561268\pi$
$492$	−5.07556	−	5.57719i	−0.228824	−	0.251439i
$493$	38.6317	+	22.3040i	1.73988	+	1.00452i
$494$	−17.2377	+	11.4200i	−0.775560	+	0.513809i
$495$	−13.9879	+	6.04936i	−0.628711	+	0.271899i
$496$	15.1714	+	17.3174i	0.681215	+	0.777572i
$497$	−1.88803	−	5.18732i	−0.0846898	−	0.232683i
$498$	−8.92741	−	12.9901i	−0.400047	−	0.582099i
$499$	22.1209	−	26.3627i	0.990268	−	1.18016i	0.00663412	−	0.999978i	$-0.497888\pi$
$499$	22.1209	−	26.3627i	0.990268	−	1.18016i	0.983634	−	0.180178i	$-0.0576673\pi$
$500$	2.08695	+	21.2444i	0.0933314	+	0.950079i
$501$	−10.6657	+	5.36276i	−0.476507	+	0.239590i
$502$	29.7496	+	1.14014i	1.32779	+	0.0508869i
$503$	10.3031	−	1.81672i	0.459394	−	0.0810036i	0.0608384	−	0.998148i	$-0.480623\pi$
$503$	10.3031	−	1.81672i	0.459394	−	0.0810036i	0.398556	+	0.917144i	$0.369511\pi$
$504$	−2.17534	+	38.9422i	−0.0968972	+	1.73462i
$505$	9.48014	−	16.4201i	0.421861	−	0.730684i
$506$	27.9127	+	17.5740i	1.24087	+	0.781261i
$507$	−1.19828	+	2.78151i	−0.0532175	+	0.123531i
$508$	−2.86205	+	11.1554i	−0.126983	+	0.494941i
$509$	−14.4880	+	2.55462i	−0.642168	+	0.113232i	−0.485244	−	0.874379i	$-0.661269\pi$
$509$	−14.4880	+	2.55462i	−0.642168	+	0.113232i	−0.156925	+	0.987611i	$0.550158\pi$
$510$	−4.36050	+	15.7221i	−0.193086	+	0.696187i
$511$	11.4506	−	13.6462i	0.506543	−	0.603674i
$512$	7.64725	−	21.2960i	0.337964	−	0.941159i
$513$	−22.5887	−	1.65887i	−0.997314	−	0.0732409i
$514$	−3.53059	+	5.60763i	−0.155728	+	0.247342i
$515$	−7.99578	−	6.70926i	−0.352336	−	0.295645i
$516$	3.68892	+	4.05350i	0.162396	+	0.178445i
$517$	−1.85296	−	10.5086i	−0.0814930	−	0.462170i
$518$	19.1517	+	59.6318i	0.841477	+	2.62007i
$519$	25.4168	+	10.9496i	1.11568	+	0.480635i
$520$	12.0093	+	1.38619i	0.526644	+	0.0607885i
$521$	18.4268	+	10.6387i	0.807292	+	0.466090i	0.846015	−	0.533160i	$-0.178996\pi$
$521$	18.4268	+	10.6387i	0.807292	+	0.466090i	−0.0387225	+	0.999250i	$0.512329\pi$
$522$	30.9708	−	18.7509i	1.35556	−	0.820704i
$523$	0.166394	+	0.943668i	0.00727591	+	0.0412637i	0.988230	−	0.152978i	$-0.0488864\pi$
$523$	0.166394	+	0.943668i	0.00727591	+	0.0412637i	−0.980954	+	0.194242i	$0.937775\pi$
$524$	−12.8857	−	8.81958i	−0.562916	−	0.385285i
$525$	12.0753	+	24.0158i	0.527009	+	1.04814i
$526$	−11.0329	+	8.55959i	−0.481056	+	0.373216i
$527$	23.0484	+	19.3399i	1.00400	+	0.842459i
$528$	24.4072	−	12.9308i	1.06219	−	0.562742i
$529$	10.5485	−	3.83934i	0.458630	−	0.166928i
$530$	−13.6784	−	12.4005i	−0.594150	−	0.538644i
$531$	−4.23924	+	5.70545i	−0.183968	+	0.247595i
$532$	−37.9630	−	12.8278i	−1.64590	−	0.556155i
$533$	−3.65099	+	6.32370i	−0.158142	+	0.273910i
$534$	−9.50936	−	2.63740i	−0.411510	−	0.114131i
$535$	−2.75780	+	15.6402i	−0.119230	+	0.676187i
$536$	−33.5013	+	1.99956i	−1.44704	+	0.0863679i
$537$	−17.1619	−	4.05896i	−0.740592	−	0.175157i
$538$	4.28804	+	1.74946i	0.184871	+	0.0754246i
$539$	−48.7792	+	28.1627i	−2.10107	+	1.21305i
$540$	9.47582	+	9.24996i	0.407774	+	0.398055i
$541$	−0.753655	−	4.27419i	−0.0324022	−	0.183762i	0.964311	−	0.264772i	$-0.0852966\pi$
$541$	−0.753655	−	4.27419i	−0.0324022	−	0.183762i	−0.996713	+	0.0810098i	$0.974185\pi$
$542$	−10.3529	+	8.03207i	−0.444696	+	0.345007i
$543$	−1.07374	−	2.13549i	−0.0460786	−	0.0916428i
$544$	5.62905	−	29.0297i	0.241343	−	1.24464i
$545$	−6.84657	+	18.8108i	−0.293275	+	0.805766i
$546$	36.5640	−	9.45526i	1.56480	−	0.404648i
$547$	25.9967	−	21.8138i	1.11154	−	0.932693i	0.113394	−	0.993550i	$-0.463828\pi$
$547$	25.9967	−	21.8138i	1.11154	−	0.932693i	0.998146	+	0.0608573i	$0.0193835\pi$
$548$	−2.26067	+	8.81143i	−0.0965712	+	0.376406i
$549$	1.65381	−	5.54300i	0.0705827	−	0.236570i
$550$	10.1425	−	16.1093i	0.432478	−	0.686903i
$551$	10.0775	+	35.8058i	0.429318	+	1.52538i
$552$	4.92299	−	28.2343i	0.209536	−	1.20173i
$553$	15.5526	+	42.7304i	0.661363	+	1.81708i
$554$	15.3906	−	16.9766i	0.653884	−	0.721266i
$555$	19.5293	+	8.41326i	0.828972	+	0.357123i
$556$	−9.30525	−	33.3042i	−0.394631	−	1.41241i
$557$	−14.4131	+	12.0941i	−0.610705	+	0.512442i	−0.894866	−	0.446334i	$-0.852729\pi$
$557$	−14.4131	+	12.0941i	−0.610705	+	0.512442i	0.284162	+	0.958776i	$0.408285\pi$
$558$	22.7682	−	8.82768i	0.963856	−	0.373705i
$559$	2.65354	−	4.59607i	0.112233	−	0.194393i
$560$	12.1437	+	20.0351i	0.513164	+	0.846636i
$561$	28.9435	−	21.5688i	1.22200	−	0.910633i
$562$	2.33089	−	3.70214i	0.0983226	−	0.156165i
$563$	−16.2038	+	28.0657i	−0.682907	+	1.18283i	0.291182	+	0.956668i	$0.405951\pi$
$563$	−16.2038	+	28.0657i	−0.682907	+	1.18283i	−0.974090	+	0.226162i	$0.927382\pi$
$564$	−7.83682	+	4.95499i	−0.329990	+	0.208643i
$565$	−15.4597	−	2.72596i	−0.650393	−	0.114682i
$566$	16.5599	−	12.8476i	0.696063	−	0.540024i
$567$	38.0162	+	16.3141i	1.59653	+	0.685129i
$568$	3.25551	+	0.969537i	0.136598	+	0.0406809i
$569$	27.6036	+	15.9369i	1.15720	+	0.668111i	0.950632	−	0.310320i	$-0.100436\pi$
$569$	27.6036	+	15.9369i	1.15720	+	0.668111i	0.206571	+	0.978432i	$0.433770\pi$
$570$	−11.7563	+	6.84727i	−0.492416	+	0.286800i
$571$	19.1356	−	11.0479i	0.800800	−	0.462342i	−0.0429511	−	0.999077i	$-0.513676\pi$
$571$	19.1356	−	11.0479i	0.800800	−	0.462342i	0.843751	+	0.536735i	$0.180343\pi$
$572$	−19.1124	−	18.7094i	−0.799129	−	0.782279i
$573$	−4.79902	+	20.2910i	−0.200482	+	0.847670i
$574$	−14.0198	+	1.92177i	−0.585173	+	0.0802133i
$575$	−6.75578	−	18.5613i	−0.281735	−	0.774062i
$576$	−18.4438	−	15.3567i	−0.768490	−	0.639862i
$577$	−2.71774	−	4.70726i	−0.113141	−	0.195966i	0.803894	−	0.594772i	$-0.202758\pi$
$577$	−2.71774	−	4.70726i	−0.113141	−	0.195966i	−0.917035	+	0.398806i	$0.869425\pi$
$578$	0.559216	−	14.5916i	0.0232603	−	0.606930i
$579$	−1.43048	−	12.1890i	−0.0594487	−	0.506557i
$580$	8.98027	−	19.8065i	0.372885	−	0.822421i
$581$	−29.5778			−1.22710
$582$	−0.517302	+	5.37116i	−0.0214428	+	0.222642i
$583$	7.09289	+	40.2258i	0.293758	+	1.66598i
$584$	2.54325	+	10.6625i	0.105240	+	0.441216i
$585$	5.74394	−	11.4639i	0.237483	−	0.473974i
$586$	43.8314	−	14.0771i	1.81066	−	0.581521i
$587$	12.2566	−	14.6069i	0.505886	−	0.602891i	−0.451298	−	0.892373i	$-0.649039\pi$
$587$	12.2566	−	14.6069i	0.505886	−	0.602891i	0.957183	+	0.289482i	$0.0934832\pi$
$588$	38.7257	+	29.9263i	1.59702	+	1.23414i
$589$	2.50022	+	24.9639i	0.103020	+	1.02862i
$590$	−0.163510	+	4.26644i	−0.00673159	+	0.175647i
$591$	11.6458	−	12.3554i	0.479045	−	0.508235i
$592$	−36.4881	−	12.4067i	−1.49965	−	0.509912i
$593$	8.06213	+	2.93438i	0.331072	+	0.120500i	0.502208	−	0.864747i	$-0.332521\pi$
$593$	8.06213	+	2.93438i	0.331072	+	0.120500i	−0.171135	+	0.985248i	$0.554744\pi$
$594$	−4.01944	−	29.0194i	−0.164920	−	1.19068i
$595$	19.6801	+	23.4538i	0.806804	+	0.961511i
$596$	13.1104	+	27.3506i	0.537022	+	1.12033i
$597$	−5.09045	−	10.1241i	−0.208338	−	0.414351i
$598$	−27.4948	+	3.76888i	−1.12435	+	0.154121i
$599$	−17.6320	+	14.7950i	−0.720426	+	0.604509i	−0.927503	−	0.373816i	$-0.878049\pi$
$599$	−17.6320	+	14.7950i	−0.720426	+	0.604509i	0.207077	+	0.978325i	$0.433605\pi$
$600$	−16.2949	−	2.84121i	−0.665236	−	0.115992i
$601$			0.689668i			0.0281321i	0.999901	+	0.0140661i	$0.00447752\pi$
$601$			0.689668i			0.0281321i	−0.999901	+	0.0140661i	$0.995522\pi$
$602$	10.1896	−	1.39675i	0.415296	−	0.0569271i
$603$	−10.1773	+	34.1109i	−0.414451	+	1.38910i
$604$	−2.14445	−	21.8297i	−0.0872563	−	0.888237i
$605$	5.86011	−	2.13290i	0.238247	−	0.0867149i
$606$	25.5463	+	25.9972i	1.03775	+	1.05607i
$607$	9.12448	+	15.8041i	0.370351	+	0.641467i	0.989620	−	0.143712i	$-0.0459040\pi$
$607$	9.12448	+	15.8041i	0.370351	+	0.641467i	−0.619268	+	0.785179i	$0.712571\pi$
$608$	20.2610	−	14.0532i	0.821692	−	0.569932i
$609$	3.91854	−	67.8263i	0.158787	−	2.74846i
$610$	−1.06246	−	3.30814i	−0.0430178	−	0.133943i
$611$	6.87756	+	5.77096i	0.278236	+	0.233468i
$612$	−26.8837	−	16.1549i	−1.08671	−	0.653024i
$613$	46.0101	−	16.7463i	1.85833	−	0.676376i	0.878110	−	0.478458i	$-0.158804\pi$
$613$	46.0101	−	16.7463i	1.85833	−	0.676376i	0.980219	−	0.197918i	$-0.0634181\pi$
$614$	8.24973	−	20.2206i	0.332932	−	0.816038i
$615$	−2.63820	+	4.01528i	−0.106382	+	0.161912i
$616$	5.94326	−	51.4897i	0.239461	−	2.07458i
$617$	−10.5214	+	8.82851i	−0.423576	+	0.355422i	−0.829521	−	0.558475i	$-0.811387\pi$
$617$	−10.5214	+	8.82851i	−0.423576	+	0.355422i	0.405946	+	0.913897i	$0.366942\pi$
$618$	16.5363	−	11.3645i	0.665187	−	0.457149i
$619$	−24.9292	+	14.3929i	−1.00199	+	0.578499i	−0.908837	−	0.417152i	$-0.863028\pi$
$619$	−24.9292	+	14.3929i	−1.00199	+	0.578499i	−0.0931538	+	0.995652i	$0.529695\pi$
$620$	8.28486	−	12.1045i	0.332728	−	0.486128i
$621$	−26.3475	−	15.1624i	−1.05729	−	0.608445i
$622$	−2.73485	+	12.6548i	−0.109658	+	0.507411i
$623$	−14.1858	+	11.9033i	−0.568340	+	0.476894i
$624$	−8.73778	+	21.5341i	−0.349791	+	0.862055i
$625$	−3.08372	+	1.12238i	−0.123349	+	0.0448952i
$626$	0.230280	−	6.00867i	0.00920384	−	0.240155i
$627$	29.8357	+	3.97415i	1.19152	+	0.158712i
$628$	25.7814	+	1.97903i	1.02879	+	0.0789719i
$629$	−49.6002	−	8.74585i	−1.97769	−	0.348720i
$630$	24.3766	−	4.82328i	0.971186	−	0.192164i
$631$	3.46795	−	9.52812i	0.138057	−	0.379308i	−0.851327	−	0.524636i	$-0.824201\pi$
$631$	3.46795	−	9.52812i	0.138057	−	0.379308i	0.989384	+	0.145328i	$0.0464236\pi$
$632$	−26.8171	−	7.98653i	−1.06673	−	0.317687i
$633$	16.5126	+	22.1586i	0.656319	+	0.880727i
$634$	6.75490	+	12.8090i	0.268271	+	0.508709i
$635$	7.33741			0.291176
$636$	29.9984	−	18.9671i	1.18951	−	0.752095i
$637$	16.2084	−	44.5323i	0.642202	−	1.76444i
$638$	−42.5579	+	22.4432i	−1.68488	+	0.888534i
$639$	2.14877	−	2.89196i	0.0850041	−	0.114404i
$640$	−14.3530	−	1.34750i	−0.567354	−	0.0532646i
$641$	42.3201	+	7.46218i	1.67155	+	0.294739i	0.927620	−	0.373525i	$-0.121851\pi$
$641$	42.3201	+	7.46218i	1.67155	+	0.294739i	0.743925	+	0.668263i	$0.232962\pi$
$642$	−27.5554	−	13.1440i	−1.08752	−	0.518752i
$643$	−27.7917	−	4.90043i	−1.09600	−	0.193254i	−0.403719	−	0.914883i	$-0.632283\pi$
$643$	−27.7917	−	4.90043i	−1.09600	−	0.193254i	−0.692280	+	0.721629i	$0.743394\pi$
$644$	−38.4325	−	37.6222i	−1.51445	−	1.48252i
$645$	1.91744	−	2.91831i	0.0754993	−	0.114908i
$646$	23.3647	−	22.1913i	0.919273	−	0.873105i
$647$		−	21.8448i		−	0.858807i	−0.903113	−	0.429403i	$-0.858724\pi$
$647$		−	21.8448i		−	0.858807i	0.903113	−	0.429403i	$-0.141276\pi$
$648$	−22.0031	+	12.8009i	−0.864364	+	0.502866i
$649$	6.07170	−	7.23598i	0.238335	−	0.284037i
$650$	2.17514	+	15.8681i	0.0853159	+	0.622398i
$651$	10.5469	−	44.5940i	0.413365	−	1.74778i
$652$	26.8450	−	2.63713i	1.05133	−	0.103278i
$653$	0.361723	−	0.626523i	0.0141553	−	0.0245177i	−0.858861	−	0.512209i	$-0.828827\pi$
$653$	0.361723	−	0.626523i	0.0141553	−	0.0245177i	0.873016	+	0.487691i	$0.162161\pi$
$654$	−31.3279	−	22.3470i	−1.22502	−	0.873837i
$655$	−3.40257	+	9.34849i	−0.132949	+	0.365276i
$656$	4.19211	−	7.63203i	0.163675	−	0.297981i
$657$	11.5492	+	1.33893i	0.450576	+	0.0522367i
$658$	−0.666319	+	17.3862i	−0.0259758	+	0.677784i
$659$	−0.902975	−	5.12103i	−0.0351749	−	0.199487i	0.962156	−	0.272499i	$-0.0878500\pi$
$659$	−0.902975	−	5.12103i	−0.0351749	−	0.199487i	−0.997331	+	0.0730118i	$0.976739\pi$
$660$	−11.8443	−	13.0149i	−0.461039	−	0.506605i
$661$	−40.1474	+	7.07908i	−1.56155	+	0.275344i	−0.886608	−	0.462522i	$-0.846944\pi$
$661$	−40.1474	+	7.07908i	−1.56155	+	0.275344i	−0.674947	+	0.737867i	$0.735833\pi$
$662$	−2.79475	+	3.08275i	−0.108621	+	0.119814i
$663$	−6.98999	+	29.5548i	−0.271469	+	1.14781i
$664$	10.8475	−	14.6146i	0.420965	−	0.567155i
$665$	−1.90565	+	25.4589i	−0.0738978	+	0.987253i
$666$	−25.6183	+	31.8540i	−0.992690	+	1.23432i
$667$	−8.66912	+	49.1650i	−0.335670	+	1.90368i
$668$	−9.85063	−	9.64292i	−0.381132	−	0.373096i
$669$	33.7188	−	3.95718i	1.30364	−	0.152993i
$670$	6.53824	+	20.3578i	0.252594	+	0.786492i
$671$	−2.62913	+	7.22346i	−0.101496	+	0.278859i
$672$	−43.3523	+	12.2019i	−1.67235	+	0.470697i
$673$	−27.4767	+	15.8637i	−1.05915	+	0.611500i	−0.925197	−	0.379488i	$-0.876100\pi$
$673$	−27.4767	+	15.8637i	−1.05915	+	0.611500i	−0.133952	+	0.990988i	$0.542767\pi$
$674$	21.7143	+	8.85913i	0.836404	+	0.341241i
$675$	−8.75067	+	15.2059i	−0.336814	+	0.585277i
$676$	−3.48692	−	0.267663i	−0.134112	−	0.0102947i
$677$			1.68752i			0.0648566i	0.999474	+	0.0324283i	$0.0103241\pi$
$677$			1.68752i			0.0648566i	−0.999474	+	0.0324283i	$0.989676\pi$
$678$	12.9922	−	27.2373i	0.498964	−	1.04604i
$679$	7.75680	+	6.50873i	0.297679	+	0.249782i
$680$	−18.8062	+	1.12247i	−0.721184	+	0.0430446i
$681$	27.1209	+	6.41435i	1.03927	+	0.245798i
$682$	−30.8973	+	9.92314i	−1.18312	+	0.379977i
$683$	39.2471			1.50175			0.750874	−	0.660445i	$-0.229632\pi$
$683$	39.2471			1.50175			0.750874	+	0.660445i	$0.229632\pi$
$684$	−6.64405	−	25.2954i	−0.254041	−	0.967193i
$685$	5.79567			0.221441
$686$	44.1172	−	14.1689i	1.68440	−	0.540972i
$687$	−1.48000	+	1.57018i	−0.0564656	+	0.0599063i
$688$	−3.04683	+	5.54696i	−0.116159	+	0.211476i
$689$	−26.3265	−	22.0905i	−1.00296	−	0.841582i
$690$	−18.2035	+	1.43225i	−0.692995	+	0.0545248i
$691$		−	44.8001i		−	1.70428i	−0.523317	−	0.852138i	$-0.675306\pi$
$691$		−	44.8001i		−	1.70428i	0.523317	−	0.852138i	$-0.324694\pi$
$692$	−2.44584	+	31.8627i	−0.0929770	+	1.21124i
$693$	−49.1512	−	24.6270i	−1.86710	−	0.935502i
$694$	−3.88115	−	1.58345i	−0.147326	−	0.0601071i
$695$	−19.0795	+	11.0155i	−0.723726	+	0.417843i
$696$	32.0762	+	26.8111i	1.21585	+	1.01627i
$697$	3.89199	−	10.6932i	0.147420	−	0.405032i
$698$	−0.102170	−	0.318122i	−0.00386719	−	0.0120411i
$699$	2.62001	+	3.51584i	0.0990978	+	0.132981i
$700$	−21.7129	+	22.1806i	−0.820671	+	0.838348i
$701$	0.441923	−	2.50627i	0.0166912	−	0.0946605i	−0.975324	−	0.220778i	$-0.929140\pi$
$701$	0.441923	−	2.50627i	0.0166912	−	0.0946605i	0.992015	+	0.126117i	$0.0402516\pi$
$702$	18.2849	+	16.5299i	0.690119	+	0.623882i
$703$	−24.5189	−	34.0974i	−0.924746	−	1.28601i
$704$	23.2617	+	21.8202i	0.876707	+	0.822378i
$705$	4.29865	+	4.05176i	0.161896	+	0.152598i
$706$	−8.15919	+	8.99999i	−0.307075	+	0.338719i
$707$	67.3570	−	11.8769i	2.53322	−	0.446675i
$708$	−7.81923	−	2.49483i	−0.293864	−	0.0937616i
$709$	8.36242	+	47.4256i	0.314057	+	1.78111i	0.577458	+	0.816421i	$0.304045\pi$
$709$	8.36242	+	47.4256i	0.314057	+	1.78111i	−0.263400	+	0.964687i	$0.584844\pi$
$710$	0.0828791	−	2.16256i	0.00311040	−	0.0811593i
$711$	−17.7004	+	23.8224i	−0.663818	+	0.893409i
$712$	−0.678912	−	11.3747i	−0.0254433	−	0.426285i
$713$	−11.5167	+	31.6420i	−0.431305	+	1.18500i
$714$	−53.5571	+	24.4060i	−2.00432	+	0.913370i
$715$	−8.51994	+	14.7570i	−0.318628	+	0.551879i
$716$	−1.99084	−	20.2660i	−0.0744013	−	0.757377i
$717$	−20.5683	+	6.16825i	−0.768138	+	0.230358i
$718$	−2.18617	−	15.9486i	−0.0815871	−	0.595196i
$719$	16.2707	−	19.3907i	0.606797	−	0.723152i	−0.371944	−	0.928255i	$-0.621309\pi$
$719$	16.2707	−	19.3907i	0.606797	−	0.723152i	0.978740	+	0.205103i	$0.0657530\pi$
$720$	−6.55677	+	13.8135i	−0.244356	+	0.514799i
$721$		−	37.6524i		−	1.40225i
$722$	26.8677	+	0.354624i	0.999913	+	0.0131977i
$723$	6.97851	+	13.8791i	0.259533	+	0.516170i
$724$	1.93072	−	1.97231i	0.0717546	−	0.0733002i
$725$	28.3746	+	5.00321i	1.05381	+	0.185815i
$726$	0.940317	+	11.9512i	0.0348984	+	0.443550i
$727$	34.5583	+	6.09356i	1.28170	+	0.225998i	0.772700	−	0.634771i	$-0.218906\pi$
$727$	34.5583	+	6.09356i	1.28170	+	0.225998i	0.508996	+	0.860769i	$0.330017\pi$
$728$	24.0161	+	36.4006i	0.890095	+	1.34910i
$729$	4.76325	+	26.5765i	0.176417	+	0.984316i
$730$	6.17738	−	3.25769i	0.228635	−	0.120572i
$731$	−2.82870	+	7.77179i	−0.104623	+	0.287450i
$732$	6.67392	−	0.268518i	0.246675	−	0.00992470i
$733$	19.6291			0.725016			0.362508	−	0.931981i	$-0.381921\pi$
$733$	19.6291			0.725016			0.362508	+	0.931981i	$0.381921\pi$
$734$	−22.2629	−	42.2160i	−0.821738	−	1.55822i
$735$	12.3368	−	28.6368i	0.455049	−	1.05628i
$736$	32.6842	−	5.19198i	1.20476	−	0.191379i
$737$	16.1793	−	44.4522i	0.595971	−	1.63742i
$738$	−6.08257	−	6.94995i	−0.223902	−	0.255831i
$739$	36.6318	+	6.45918i	1.34752	+	0.237605i	0.800409	−	0.599454i	$-0.204615\pi$
$739$	36.6318	+	6.45918i	1.34752	+	0.237605i	0.547114	+	0.837058i	$0.315727\pi$
$740$	−1.87929	+	24.4820i	−0.0690840	+	0.899977i
$741$	−21.3792	+	13.5743i	−0.785383	+	0.498665i
$742$	2.55059	−	66.5522i	0.0936350	−	2.44321i
$743$	18.8055	−	6.84463i	0.689906	−	0.251105i	0.0268111	−	0.999641i	$-0.491465\pi$
$743$	18.8055	−	6.84463i	0.689906	−	0.251105i	0.663095	+	0.748535i	$0.269243\pi$
$744$	18.1661	+	21.5659i	0.666001	+	0.790643i
$745$	14.8029	−	12.4211i	0.542338	−	0.455076i
$746$	7.59602	−	35.1486i	0.278110	−	1.28688i
$747$	−10.6231	−	16.1187i	−0.388678	−	0.589751i
$748$	34.3953	+	23.5417i	1.25762	+	0.860771i
$749$	−49.6145	+	28.6450i	−1.81288	+	1.04666i
$750$	2.05069	+	26.0637i	0.0748805	+	0.951711i
$751$	−7.06756	+	5.93039i	−0.257899	+	0.216403i	−0.762565	−	0.646912i	$-0.776060\pi$
$751$	−7.06756	+	5.93039i	−0.257899	+	0.216403i	0.504666	+	0.863315i	$0.331616\pi$
$752$	−8.34623	−	6.70552i	−0.304356	−	0.244525i
$753$	36.4017	+	2.10304i	1.32655	+	0.0766389i
$754$	15.2918	−	37.4813i	0.556896	−	1.36499i
$755$	−13.1321	+	4.77968i	−0.477925	+	0.173950i
$756$	−3.58909	+	47.6336i	−0.130534	+	1.73242i
$757$	−10.7201	−	8.99521i	−0.389628	−	0.326937i	0.426840	−	0.904327i	$-0.359627\pi$
$757$	−10.7201	−	8.99521i	−0.389628	−	0.326937i	−0.816468	+	0.577390i	$0.804071\pi$
$758$	−12.4162	−	38.6599i	−0.450978	−	1.40419i
$759$	33.7620	+	22.1829i	1.22548	+	0.805189i
$760$	−11.8805	−	10.2785i	−0.430950	−	0.372840i
$761$	5.77291	+	9.99897i	0.209268	+	0.362462i	0.951484	−	0.307698i	$-0.0995586\pi$
$761$	5.77291	+	9.99897i	0.209268	+	0.362462i	−0.742216	+	0.670160i	$0.766225\pi$
$762$	−3.76970	+	13.5919i	−0.136562	+	0.492384i
$763$	−67.8568	+	24.6979i	−2.45658	+	0.894123i
$764$	−23.9611	+	2.35383i	−0.866883	+	0.0851586i
$765$	−5.71309	+	19.1484i	−0.206557	+	0.692310i
$766$	−24.7170	+	3.38811i	−0.893063	+	0.122418i
$767$			7.94746i			0.286966i
$768$	9.87021	−	25.8955i	0.356161	−	0.934425i
$769$	−20.6251	+	17.3065i	−0.743759	+	0.624088i	−0.933844	−	0.357680i	$-0.883568\pi$
$769$	−20.6251	+	17.3065i	−0.743759	+	0.624088i	0.190085	+	0.981768i	$0.439124\pi$
$770$	−32.7165	+	4.48465i	−1.17902	+	0.161615i
$771$	−4.45651	+	6.78272i	−0.160497	+	0.244274i
$772$	12.7790	−	6.12552i	0.459925	−	0.220462i
$773$	8.78429	+	10.4687i	0.315949	+	0.376533i	0.900524	−	0.434806i	$-0.143183\pi$
$773$	8.78429	+	10.4687i	0.315949	+	0.376533i	−0.584575	+	0.811340i	$0.698739\pi$
$774$	4.42081	+	5.05123i	0.158903	+	0.181563i
$775$	18.2616	+	6.64667i	0.655975	+	0.238755i
$776$	−6.06076	+	1.44563i	−0.217568	+	0.0518952i
$777$	22.0345	+	73.4751i	0.790484	+	2.63590i
$778$	1.60738	−	41.9412i	0.0576274	−	1.50367i
$779$	8.54880	−	4.11780i	0.306293	−	0.147536i
$780$	14.6727	+	1.98278i	0.525366	+	0.0709950i
$781$	−3.07760	+	3.66774i	−0.110125	+	0.131242i
$782$	41.1771	−	13.2247i	1.47249	−	0.472914i
$783$	38.3698	−	22.2248i	1.37122	−	0.794249i
$784$	−18.1925	+	53.5044i	−0.649734	+	1.91087i
$785$	−2.86066	−	16.2236i	−0.102101	−	0.579046i
$786$	−15.5692	−	11.1059i	−0.555334	−	0.396134i
$787$	−20.6024			−0.734397			−0.367199	−	0.930143i	$-0.619683\pi$
$787$	−20.6024			−0.734397			−0.367199	+	0.930143i	$0.619683\pi$
$788$	17.8559	+	8.09585i	0.636089	+	0.288403i
$789$	−13.7133	+	10.2192i	−0.488207	+	0.363812i
$790$	−0.682714	+	17.8140i	−0.0242899	+	0.633793i
$791$	−28.3142	−	49.0417i	−1.00674	−	1.74372i
$792$	30.1942	−	15.2540i	1.07291	−	0.542028i
$793$	−2.21206	−	6.07758i	−0.0785525	−	0.215821i
$794$	6.99668	−	0.959078i	0.248303	−	0.0340364i
$795$	−16.4547	−	15.5096i	−0.583588	−	0.550070i
$796$	9.15327	−	9.35043i	0.324429	−	0.331417i
$797$	0.871247	−	0.503015i	0.0308612	−	0.0178177i	−0.484490	−	0.874797i	$-0.660995\pi$
$797$	0.871247	−	0.503015i	0.0308612	−	0.0178177i	0.515351	+	0.856979i	$0.327661\pi$
$798$	−46.1814	−	16.6099i	−1.63480	−	0.587984i
$799$	−12.1169	−	6.99568i	−0.428664	−	0.247489i
$800$	−2.99645	−	18.8631i	−0.105941	−	0.666910i
$801$	−11.5817	−	3.45550i	−0.409218	−	0.122094i
$802$	−15.5728	+	12.0818i	−0.549894	+	0.426622i
$803$	−15.2159	−	2.68298i	−0.536958	−	0.0946802i
$804$	−41.0703	+	1.65242i	−1.44844	+	0.0582764i
$805$	−17.1325	+	29.6743i	−0.603841	+	1.04588i
$806$	14.5474	−	23.1056i	0.512410	−	0.813858i
$807$	5.20919	+	2.24413i	0.183372	+	0.0789972i
$808$	−18.8344	+	37.6372i	−0.662592	+	1.32407i
$809$	20.4127	−	35.3559i	0.717673	−	1.24305i	−0.244246	−	0.969713i	$-0.578541\pi$
$809$	20.4127	−	35.3559i	0.717673	−	1.24305i	0.961919	−	0.273333i	$-0.0881261\pi$
$810$	11.3835	+	11.5519i	0.399975	+	0.405892i
$811$	19.8759	−	16.6778i	0.697936	−	0.585638i	−0.223250	−	0.974761i	$-0.571666\pi$
$811$	19.8759	−	16.6778i	0.697936	−	0.585638i	0.921186	+	0.389123i	$0.127222\pi$
$812$	75.5559	−	21.1105i	2.65149	−	0.740832i
$813$	−12.8682	+	9.58937i	−0.451306	+	0.336314i
$814$	36.4860	−	40.2459i	1.27884	−	1.41062i
$815$	−5.87780	−	16.1491i	−0.205890	−	0.565679i
$816$	7.58266	−	35.4136i	0.265446	−	1.23972i
$817$	−6.21327	+	2.99282i	−0.217375	+	0.104706i
$818$	19.2519	−	30.5777i	0.673126	−	1.06912i
$819$	44.9979	−	10.7092i	1.57235	−	0.374211i
$820$	−5.37364	−	1.37867i	−0.187656	−	0.0481453i
$821$	27.8227	−	23.3460i	0.971018	−	0.814781i	−0.0116923	−	0.999932i	$-0.503722\pi$
$821$	27.8227	−	23.3460i	0.971018	−	0.814781i	0.982710	+	0.185151i	$0.0592774\pi$
$822$	−2.97761	+	10.7360i	−0.103856	+	0.374461i
$823$	−13.8307	+	37.9995i	−0.482107	+	1.32458i	0.425577	+	0.904922i	$0.360071\pi$
$823$	−13.8307	+	37.9995i	−0.482107	+	1.32458i	−0.907683	+	0.419655i	$0.862151\pi$
$824$	18.6043	+	13.8088i	0.648110	+	0.481053i
$825$	12.8024	−	19.4851i	0.445724	−	0.678383i
$826$	−12.1689	+	9.44097i	−0.423411	+	0.328493i
$827$	1.26372	+	7.16693i	0.0439440	+	0.249219i	0.998864	−	0.0476431i	$-0.0151710\pi$
$827$	1.26372	+	7.16693i	0.0439440	+	0.249219i	−0.954920	+	0.296862i	$0.904060\pi$
$828$	6.69918	−	34.4563i	0.232813	−	1.19744i
$829$	−17.8902	+	10.3289i	−0.621353	+	0.358738i	−0.777395	−	0.629012i	$-0.783460\pi$
$829$	−17.8902	+	10.3289i	−0.621353	+	0.358738i	0.156043	+	0.987750i	$0.450126\pi$
$830$	−10.7365	−	4.38033i	−0.372668	−	0.152043i
$831$	19.2494	−	20.4224i	0.667755	−	0.708444i
$832$	−26.7935	−	1.48325i	−0.928897	−	0.0514225i
$833$	−12.8245	+	72.7312i	−0.444342	+	2.51999i
$834$	−10.6030	−	41.0025i	−0.367153	−	1.41980i
$835$	−4.39122	+	7.60582i	−0.151965	+	0.263210i
$836$	6.82793	+	34.0783i	0.236149	+	1.17862i
$837$	28.0898	−	10.2686i	0.970925	−	0.354934i
$838$	13.3053	+	12.0623i	0.459625	+	0.416686i
$839$	15.4027	−	5.60614i	0.531762	−	0.193545i	−0.0621631	−	0.998066i	$-0.519800\pi$
$839$	15.4027	−	5.60614i	0.531762	−	0.193545i	0.593925	+	0.804521i	$0.297578\pi$
$840$	14.3940	+	24.8218i	0.496641	+	0.856433i
$841$	−33.5692	−	28.1679i	−1.15756	−	0.971308i
$842$	9.02340	−	7.00058i	0.310967	−	0.241256i
$843$	2.94218	−	4.47793i	0.101334	−	0.154228i
$844$	−18.0231	+	26.3324i	−0.620382	+	0.906400i
$845$	0.386903	+	2.19424i	0.0133099	+	0.0754841i
$846$	−9.71404	+	5.88124i	−0.333975	+	0.202201i
$847$	19.4821	+	11.2480i	0.669414	+	0.386487i
$848$	31.9483	+	25.6679i	1.09711	+	0.881440i
$849$	20.5831	−	15.3385i	0.706410	−	0.526417i
$850$	−7.63237	−	23.7646i	−0.261788	−	0.815119i
$851$	−9.78799	−	55.5104i	−0.335528	−	1.90287i
$852$	3.96338	+	1.26457i	0.135783	+	0.0433235i
$853$	12.6742	+	10.6349i	0.433955	+	0.364132i	0.833442	−	0.552607i	$-0.186367\pi$
$853$	12.6742	+	10.6349i	0.433955	+	0.364132i	−0.399486	+	0.916739i	$0.630812\pi$
$854$	6.67807	−	10.6067i	0.228519	−	0.362955i
$855$	−14.5584	+	8.10522i	−0.497888	+	0.277193i
$856$	4.04224	−	35.0202i	0.138161	−	1.19696i
$857$	−13.0607	+	15.5652i	−0.446146	+	0.531697i	−0.941508	−	0.336990i	$-0.890591\pi$
$857$	−13.0607	+	15.5652i	−0.446146	+	0.531697i	0.495362	+	0.868687i	$0.335036\pi$
$858$	−22.9588	−	23.3641i	−0.783801	−	0.797637i
$859$	−41.8752	+	7.38372i	−1.42876	+	0.251929i	−0.833908	−	0.551904i	$-0.813902\pi$
$859$	−41.8752	+	7.38372i	−1.42876	+	0.251929i	−0.594855	+	0.803833i	$0.702790\pi$
$860$	3.90557	+	1.00202i	0.133179	+	0.0341685i
$861$	−17.2131	+	2.02010i	−0.586620	+	0.0688447i
$862$	−0.184479	−	0.116149i	−0.00628338	−	0.00395605i
$863$	−3.29970	+	5.71524i	−0.112323	+	0.194549i	−0.916706	−	0.399561i	$-0.869162\pi$
$863$	−3.29970	+	5.71524i	−0.112323	+	0.194549i	0.804383	+	0.594110i	$0.202496\pi$
$864$	−22.2197	−	19.2428i	−0.755930	−	0.654652i
$865$	20.0505	−	3.53544i	0.681736	−	0.120209i
$866$	−8.90888	−	0.341429i	−0.302736	−	0.0116022i
$867$	1.03150	−	17.8543i	0.0350315	−	0.606364i
$868$	52.6598	−	5.17305i	1.78739	−	0.175585i
$869$	25.3516	−	30.2129i	0.859995	−	1.02490i
$870$	11.4671	−	24.0400i	0.388772	−	0.815031i
$871$	13.6127	+	37.4006i	0.461249	+	1.26727i
$872$	12.6828	−	42.5862i	0.429493	−	1.44215i
$873$	−0.761075	+	6.56477i	−0.0257585	+	0.222184i
$874$	32.2812	+	16.0776i	1.09193	+	0.543833i
$875$	42.4876	+	24.5302i	1.43634	+	0.829272i
$876$	2.86088	+	13.1168i	0.0966601	+	0.443175i
$877$	5.29167	+	0.933064i	0.178687	+	0.0315073i	0.262276	−	0.964993i	$-0.415527\pi$
$877$	5.29167	+	0.933064i	0.178687	+	0.0315073i	−0.0835886	+	0.996500i	$0.526638\pi$
$878$	−17.6452	+	43.2496i	−0.595497	+	1.45960i
$879$	54.0067	−	16.1961i	1.82160	−	0.546281i
$880$	9.78271	−	17.8101i	0.329775	−	0.600378i
$881$	−1.89847	−	3.28825i	−0.0639611	−	0.110784i	0.832272	−	0.554368i	$-0.187040\pi$
$881$	−1.89847	−	3.28825i	−0.0639611	−	0.110784i	−0.896233	+	0.443584i	$0.853707\pi$
$882$	46.7091	+	37.5654i	1.57278	+	1.26489i
$883$	−12.6487	+	2.23031i	−0.425663	+	0.0750559i	−0.382376	−	0.924007i	$-0.624894\pi$
$883$	−12.6487	+	2.23031i	−0.425663	+	0.0750559i	−0.0432872	+	0.999063i	$0.513783\pi$
$884$	−34.9005	+	3.42846i	−1.17383	+	0.115312i
$885$	−0.301601	+	5.22043i	−0.0101382	+	0.175483i
$886$	13.0223	+	24.6934i	0.437491	+	0.829592i
$887$	−33.3502	−	12.1385i	−1.11979	−	0.407570i	−0.285214	−	0.958464i	$-0.592065\pi$
$887$	−33.3502	−	12.1385i	−1.11979	−	0.407570i	−0.834575	+	0.550894i	$0.814287\pi$
$888$	−44.3854	−	16.0592i	−1.48948	−	0.538912i
$889$	17.0136	+	20.2760i	0.570618	+	0.680036i
$890$	−6.91211	+	2.21993i	−0.231694	+	0.0744123i
$891$	−4.23230	−	35.6302i	−0.141787	−	1.19366i
$892$	16.9452	+	35.3508i	0.567367	+	1.18363i
$893$	−3.16084	−	11.2305i	−0.105773	−	0.375815i
$894$	15.4039	+	33.8028i	0.515184	+	1.13053i
$895$	−12.1914	+	4.43732i	−0.407515	+	0.148323i
$896$	−29.5575	−	42.7874i	−0.987446	−	1.42943i
$897$	−33.7574	+	3.96171i	−1.12713	+	0.132278i
$898$	22.7022	+	20.5813i	0.757582	+	0.686807i
$899$	−31.5719	−	37.6259i	−1.05298	−	1.25489i
$900$	−19.8858	−	3.86630i	−0.662860	−	0.128877i
$901$	46.3819	+	26.7786i	1.54521	+	0.892125i
$902$	7.52343	+	9.69732i	0.250503	+	0.322885i
$903$	12.5105	−	1.46821i	0.416322	−	0.0488589i
$904$	34.6158	+	3.99557i	1.15131	+	0.132891i
$905$	−1.52285	−	0.879216i	−0.0506212	−	0.0292261i
$906$	−2.10718	−	26.7817i	−0.0700064	−	0.889762i
$907$	−3.68662	+	20.9079i	−0.122412	+	0.694235i	0.860399	+	0.509621i	$0.170214\pi$
$907$	−3.68662	+	20.9079i	−0.122412	+	0.694235i	−0.982811	+	0.184614i	$0.940897\pi$
$908$	3.14612	+	32.0263i	0.104408	+	1.06283i
$909$	30.6641	+	32.4410i	1.01706	+	1.07600i
$910$	18.6612	−	20.5842i	0.618612	−	0.682359i
$911$	7.65229	−	13.2542i	0.253532	−	0.439130i	−0.710964	−	0.703228i	$-0.751741\pi$
$911$	7.65229	−	13.2542i	0.253532	−	0.439130i	0.964496	+	0.264099i	$0.0850745\pi$
$912$	25.1438	−	16.7269i	0.832595	−	0.553882i
$913$	12.8270	+	22.2169i	0.424510	+	0.735274i
$914$	−46.0469	−	9.95130i	−1.52310	−	0.329160i
$915$	−1.22239	−	4.07612i	−0.0404110	−	0.134752i
$916$	−2.26921	−	1.02886i	−0.0749767	−	0.0339944i
$917$	−33.7231	+	12.2742i	−1.11364	+	0.405330i
$918$	−32.5356	−	20.4208i	−1.07383	−	0.673986i
$919$	−20.7553	+	11.9831i	−0.684655	+	0.395286i	−0.801606	−	0.597852i	$-0.796021\pi$
$919$	−20.7553	+	11.9831i	−0.684655	+	0.395286i	0.116952	+	0.993138i	$0.462688\pi$
$920$	−8.37899	−	19.3481i	−0.276247	−	0.637890i
$921$	10.5824	−	24.5644i	0.348702	−	0.809425i
$922$	−19.9271	+	2.73152i	−0.656263	+	0.0899579i
$923$		−	4.02838i		−	0.132596i
$924$	8.50112	−	62.9086i	0.279666	−	2.06954i
$925$	−32.0368	+	5.64895i	−1.05336	+	0.185736i
$926$	−0.548082	+	2.53610i	−0.0180111	+	0.0833415i
$927$	20.5190	−	13.5231i	0.673931	−	0.444157i
$928$	−17.2789	+	45.0747i	−0.567209	+	1.47965i
$929$	−14.1734	−	11.8929i	−0.465015	−	0.390194i	0.379957	−	0.925004i	$-0.375939\pi$
$929$	−14.1734	−	11.8929i	−0.465015	−	0.390194i	−0.844972	+	0.534810i	$0.820383\pi$
$930$	10.4326	−	14.6252i	0.342097	−	0.479580i
$931$	−49.9987	+	35.9532i	−1.63864	+	1.17832i
$932$	−2.85967	+	4.17808i	−0.0936717	+	0.136858i
$933$	−3.64958	+	15.4310i	−0.119482	+	0.505188i
$934$	−2.75364	+	12.7417i	−0.0901018	+	0.416922i
$935$	9.08234	−	24.9535i	0.297024	−	0.816068i
$936$	−11.2112	+	26.1612i	−0.366451	+	0.855107i
$937$	−23.9866	+	20.1271i	−0.783607	+	0.657524i	−0.944154	−	0.329504i	$-0.893119\pi$
$937$	−23.9866	+	20.1271i	−0.783607	+	0.657524i	0.160547	+	0.987028i	$0.448674\pi$
$938$	−41.0959	+	65.2724i	−1.34183	+	2.13122i
$939$	0.424762	−	7.35223i	0.0138616	−	0.239931i
$940$	−2.81667	+	6.21234i	−0.0918698	+	0.202624i
$941$	−32.1737	−	38.3431i	−1.04883	−	1.24995i	−0.967396	−	0.253270i	$-0.918494\pi$
$941$	−32.1737	−	38.3431i	−1.04883	−	1.24995i	−0.0814358	−	0.996679i	$-0.525951\pi$
$942$	31.5226	+	3.03598i	1.02706	+	0.0989175i
$943$	12.7354			0.414721
$944$	−0.201941	−	9.47515i	−0.00657262	−	0.308390i
$945$	29.9641	−	5.32693i	0.974732	−	0.173285i
$946$	−5.46803	−	7.04802i	−0.177781	−	0.229151i
$947$	−14.6369	−	40.2146i	−0.475636	−	1.30680i	−0.913163	−	0.407594i	$-0.866368\pi$
$947$	−14.6369	−	40.2146i	−0.475636	−	1.30680i	0.437528	−	0.899205i	$-0.355854\pi$
$948$	−32.6482	−	10.4169i	−1.06036	−	0.338324i
$949$	11.2580	−	6.49983i	0.365451	−	0.210993i
$950$	9.27887	−	18.6305i	0.301046	−	0.604453i
$951$	7.96710	+	15.8453i	0.258351	+	0.513818i
$952$	−46.7086	−	49.3659i	−1.51383	−	1.59996i
$953$	3.85186	−	4.59047i	0.124774	−	0.148700i	−0.700041	−	0.714103i	$-0.746835\pi$
$953$	3.85186	−	4.59047i	0.124774	−	0.148700i	0.824815	+	0.565403i	$0.191279\pi$
$954$	37.1841	−	22.5127i	1.20388	−	0.728874i
$955$	5.24637	+	14.4143i	0.169769	+	0.466435i
$956$	−14.4376	−	20.1584i	−0.466944	−	0.651969i
$957$	−52.6460	+	26.4707i	−1.70180	+	0.855677i
$958$	19.7104	−	31.3060i	0.636815	−	1.01145i
$959$	13.4387	+	16.0156i	0.433959	+	0.517172i
$960$	−17.5435	−	1.99110i	−0.566214	−	0.0642623i
$961$	−1.06444	−	1.84366i	−0.0343367	−	0.0594730i
$962$	−1.75035	+	45.6718i	−0.0564337	+	1.47252i
$963$	−33.4296	−	16.7498i	−1.07726	−	0.539754i
$964$	−12.5482	+	12.8185i	−0.404152	+	0.412857i
$965$	−5.80350	−	6.91634i	−0.186821	−	0.222645i
$966$	−46.1672	−	46.9821i	−1.48541	−	1.51163i
$967$	−3.34332	−	9.18571i	−0.107514	−	0.295392i	0.874256	−	0.485465i	$-0.161350\pi$
$967$	−3.34332	−	9.18571i	−0.107514	−	0.295392i	−0.981770	+	0.190073i	$0.939128\pi$
$968$	−12.7027	+	5.50107i	−0.408279	+	0.176811i
$969$	29.1378	−	26.6184i	0.936040	−	0.855105i
$970$	1.85173	+	3.51135i	0.0594556	+	0.112743i
$971$	−2.60667	+	14.7832i	−0.0836521	+	0.474415i	0.913987	+	0.405743i	$0.132987\pi$
$971$	−2.60667	+	14.7832i	−0.0836521	+	0.474415i	−0.997639	+	0.0686717i	$0.978124\pi$
$972$	−27.2473	+	15.1520i	−0.873958	+	0.486001i
$973$	−74.6806	−	27.1815i	−2.39415	−	0.871400i
$974$	0.801821	−	0.884448i	0.0256920	−	0.0283395i
$975$	2.28642	+	19.4824i	0.0732241	+	0.623937i
$976$	2.79170	+	7.18963i	0.0893601	+	0.230134i
$977$		−	23.1539i		−	0.740760i	−0.928880	−	0.370380i	$-0.879228\pi$
$977$		−	23.1539i		−	0.740760i	0.928880	−	0.370380i	$-0.120772\pi$
$978$	32.9347	−	2.59130i	1.05314	−	0.0828606i
$979$	15.0929	+	5.49335i	0.482370	+	0.175568i
$980$	35.8992	+	2.75569i	1.14676	+	0.0880274i
$981$	−37.8305	−	28.1087i	−1.20783	−	0.897441i
$982$	−0.152747	−	1.11432i	−0.00487435	−	0.0355594i
$983$	−1.58170	+	8.97026i	−0.0504484	+	0.286107i	−0.999587	−	0.0287529i	$-0.990846\pi$
$983$	−1.58170	+	8.97026i	−0.0504484	+	0.286107i	0.949138	+	0.314860i	$0.101958\pi$
$984$	5.31466	−	9.24592i	0.169425	−	0.294749i
$985$	2.16902	−	12.3011i	0.0691106	−	0.391946i
$986$	−13.3258	+	61.6618i	−0.424381	+	1.96371i
$987$	−1.22905	+	21.2738i	−0.0391212	+	0.677152i
$988$	−22.8310	−	18.2716i	−0.726351	−	0.581298i
$989$	−9.25607			−0.294326
$990$	−14.1943	−	16.2184i	−0.451124	−	0.515454i
$991$	10.7694	+	9.03661i	0.342102	+	0.287057i	0.797609	−	0.603175i	$-0.206098\pi$
$991$	10.7694	+	9.03661i	0.342102	+	0.287057i	−0.455508	+	0.890232i	$0.650542\pi$
$992$	−16.7567	+	27.9166i	−0.532024	+	0.886354i
$993$	−3.49547	+	3.70846i	−0.110925	+	0.117684i
$994$	6.16814	−	4.78540i	0.195641	−	0.151784i
$995$	−7.21961	−	4.16824i	−0.228877	−	0.132142i
$996$	13.6302	−	17.6380i	0.431890	−	0.558880i
$997$	−29.7282	−	10.8202i	−0.941501	−	0.342678i	−0.174742	−	0.984614i	$-0.555909\pi$
$997$	−29.7282	−	10.8202i	−0.941501	−	0.342678i	−0.766758	+	0.641936i	$0.778131\pi$
$998$	45.0627	+	18.3849i	1.42643	+	0.581965i
$999$	−32.1269	+	38.3969i	−1.01645	+	1.21482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bt.a.439.72	yes	696
4.3	odd	2	inner	684.2.bt.a.439.7	yes	696
9.4	even	3		684.2.cc.a.211.7	yes	696
19.10	odd	18		684.2.cc.a.295.84	yes	696
36.31	odd	6		684.2.cc.a.211.84	yes	696
76.67	even	18		684.2.cc.a.295.7	yes	696
171.67	odd	18	inner	684.2.bt.a.67.7	✓	696
684.67	even	18	inner	684.2.bt.a.67.72	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bt.a.67.7	✓	696	171.67	odd	18	inner
684.2.bt.a.67.72	yes	696	684.67	even	18	inner
684.2.bt.a.439.7	yes	696	4.3	odd	2	inner
684.2.bt.a.439.72	yes	696	1.1	even	1	trivial
684.2.cc.a.211.7	yes	696	9.4	even	3
684.2.cc.a.211.84	yes	696	36.31	odd	6
684.2.cc.a.295.7	yes	696	76.67	even	18
684.2.cc.a.295.84	yes	696	19.10	odd	18

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.432441 + 1.34647i) q^{2} +(0.497535 + 1.65905i) q^{3} +(-1.62599 + 1.16454i) q^{4} +(0.976110 + 0.819053i) q^{5} +(-2.01872 + 1.38736i) q^{6} +4.59654i q^{7} +(-2.27117 - 1.68576i) q^{8} +(-2.50492 + 1.65088i) q^{9} +(-0.680724 + 1.66850i) q^{10} +(3.45262 - 1.99337i) q^{11} +(-2.74103 - 2.11820i) q^{12} +(-1.14724 + 3.15202i) q^{13} +(-6.18912 + 1.98773i) q^{14} +(-0.873204 + 2.02693i) q^{15} +(1.28768 - 3.78707i) q^{16} +(0.907723 - 5.14795i) q^{17} +(-3.30609 - 2.65890i) q^{18} +(3.53893 - 2.54479i) q^{19} +(-2.54097 - 0.195050i) q^{20} +(-7.62590 + 2.28694i) q^{21} +(4.17708 + 3.78685i) q^{22} +(5.76138 - 1.01589i) q^{23} +(1.66677 - 4.60672i) q^{24} +(-0.586299 - 3.32507i) q^{25} +(-4.74023 - 0.181668i) q^{26} +(-3.98518 - 3.33442i) q^{27} +(-5.35287 - 7.47392i) q^{28} +(-2.91865 + 8.01892i) q^{29} +(-3.10681 - 0.299220i) q^{30} +(-2.87788 + 4.98464i) q^{31} +(5.65604 + 0.0961414i) q^{32} +(5.02491 + 4.73631i) q^{33} +(7.32413 - 1.00396i) q^{34} +(-3.76481 + 4.48673i) q^{35} +(2.15045 - 5.60139i) q^{36} -9.63493i q^{37} +(4.95688 + 3.66461i) q^{38} +(-5.80017 - 0.335094i) q^{39} +(-0.836190 - 3.50569i) q^{40} +(2.14382 + 0.378013i) q^{41} +(-6.37707 - 9.27912i) q^{42} +(-1.55813 - 0.274740i) q^{43} +(-3.29256 + 7.26193i) q^{44} +(-3.79723 - 0.440225i) q^{45} +(3.85932 + 7.31824i) q^{46} +(0.915437 - 2.51514i) q^{47} +(6.92361 + 0.252127i) q^{48} -14.1282 q^{49} +(4.22358 - 2.22733i) q^{50} +(8.99235 - 1.05533i) q^{51} +(-1.80526 - 6.46117i) q^{52} +(-3.50418 + 9.62766i) q^{53} +(2.76636 - 6.80788i) q^{54} +(5.00282 + 0.882131i) q^{55} +(7.74864 - 10.4395i) q^{56} +(5.98268 + 4.60516i) q^{57} +(-12.0594 - 0.462172i) q^{58} +(2.22644 - 0.810357i) q^{59} +(-0.940623 - 4.31264i) q^{60} +(-1.47705 + 1.23939i) q^{61} +(-7.95621 - 1.71943i) q^{62} +(-7.58831 - 11.5140i) q^{63} +(2.31645 + 7.65729i) q^{64} +(-3.70151 + 2.13707i) q^{65} +(-4.20434 + 8.81409i) q^{66} +(9.08956 - 7.62705i) q^{67} +(4.51907 + 9.42760i) q^{68} +(4.55190 + 9.05299i) q^{69} +(-7.66933 - 3.12898i) q^{70} +(-1.12853 + 0.410751i) q^{71} +(8.47207 + 0.473255i) q^{72} +(-2.96881 - 2.49113i) q^{73} +(12.9732 - 4.16654i) q^{74} +(5.22476 - 2.62704i) q^{75} +(-2.79075 + 8.25904i) q^{76} +(9.16261 + 15.8701i) q^{77} +(-2.05704 - 7.95469i) q^{78} +(9.29621 - 3.38354i) q^{79} +(4.35873 - 2.64192i) q^{80} +(3.54922 - 8.27061i) q^{81} +(0.418091 + 3.05007i) q^{82} +6.43480i q^{83} +(9.73639 - 12.5992i) q^{84} +(5.10249 - 4.28149i) q^{85} +(-0.303869 - 2.21679i) q^{86} +(-14.7559 - 0.852497i) q^{87} +(-11.2018 - 1.29299i) q^{88} +(2.58961 + 3.08618i) q^{89} +(-1.04933 - 5.30325i) q^{90} +(-14.4884 - 5.27335i) q^{91} +(-8.18489 + 8.36119i) q^{92} +(-9.70164 - 2.29453i) q^{93} +(3.78245 + 0.144961i) q^{94} +(5.53871 + 0.414583i) q^{95} +(2.65457 + 9.43150i) q^{96} +(1.41601 - 1.68753i) q^{97} +(-6.10961 - 19.0232i) q^{98} +(-5.35772 + 10.6931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 18 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} + 21 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} + 24 q^{21} - 15 q^{22} - 39 q^{24} - 6 q^{25} - 30 q^{26}+ \cdots - 63 q^{98}+O(q^{100}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 18 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 + 21 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 + 24 * q^21 - 15 * q^22 - 39 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 + 42 * q^30 - 3 * q^32 - 36 * q^33 - 21 * q^34 + 54 * q^36 - 3 * q^38 + 12 * q^40 - 36 * q^41 + 66 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 - 564 * q^49 - 9 * q^50 - 3 * q^52 - 24 * q^53 + 66 * q^54 + 63 * q^56 - 12 * q^57 - 6 * q^58 - 9 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 18 * q^65 + 6 * q^66 - 6 * q^68 - 18 * q^69 + 18 * q^70 + 12 * q^72 - 60 * q^73 - 60 * q^74 - 3 * q^76 + 72 * q^77 + 9 * q^78 - 12 * q^80 + 18 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 + 105 * q^86 - 24 * q^89 - 141 * q^90 - 171 * q^92 + 6 * q^93 + 15 * q^96 - 24 * q^97 - 63 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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