LMFDB - Embedded newform 531.2.i.a.262.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(19,531)] 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("531.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([0, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,26] 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 59)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			262.4
Character	$\chi$	$=$	531.262
Dual form			531.2.i.a.379.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.19893 - 1.67159i) q^{2} +(1.50605 - 5.42431i) q^{4} +(-0.330311 + 0.312887i) q^{5} +(-0.362135 - 0.426338i) q^{7} +(-3.71073 - 9.31322i) q^{8} +(-0.203314 + 1.24016i) q^{10} +(-1.66508 + 1.00184i) q^{11} +(-0.146364 + 0.215870i) q^{13} +(-1.50897 - 0.332149i) q^{14} +(-14.0801 - 8.47172i) q^{16} +(3.05473 - 3.59631i) q^{17} +(4.22025 + 1.95250i) q^{19} +(1.19973 + 2.26293i) q^{20} +(-1.98672 + 4.98630i) q^{22} +(3.34811 - 1.12811i) q^{23} +(-0.259488 + 4.78597i) q^{25} +(0.0390017 + 0.719343i) q^{26} +(-2.85798 + 1.32224i) q^{28} +(4.87493 + 3.70583i) q^{29} +(0.386926 - 0.179011i) q^{31} +(-25.1895 + 2.73952i) q^{32} +(0.705614 - 13.0143i) q^{34} +(0.253012 + 0.0275168i) q^{35} +(-3.25905 + 8.17960i) q^{37} +(12.5438 - 2.76110i) q^{38} +(4.13968 + 1.91522i) q^{40} +(-3.15602 - 1.06339i) q^{41} +(3.43733 + 2.06817i) q^{43} +(2.92661 + 10.5407i) q^{44} +(5.47654 - 8.07730i) q^{46} +(-1.40614 - 1.33196i) q^{47} +(1.08185 - 6.59900i) q^{49} +(7.42956 + 10.9578i) q^{50} +(0.950515 + 1.11903i) q^{52} +(1.36486 + 8.32531i) q^{53} +(0.236529 - 0.851900i) q^{55} +(-2.62679 + 4.95466i) q^{56} +16.9142 q^{58} +(-6.86593 - 3.44368i) q^{59} +(-0.900340 + 0.684420i) q^{61} +(0.551592 - 1.04041i) q^{62} +(-26.9511 + 25.5294i) q^{64} +(-0.0191975 - 0.117099i) q^{65} +(-1.70447 - 4.27791i) q^{67} +(-14.9069 - 21.9860i) q^{68} +(0.602354 - 0.362424i) q^{70} +(1.83446 + 1.73769i) q^{71} +(-10.5528 - 2.32285i) q^{73} +(6.50647 + 23.4342i) q^{74} +(16.9469 - 19.9514i) q^{76} +(1.03011 + 0.347083i) q^{77} +(1.15299 + 2.17477i) q^{79} +(7.30150 - 1.60718i) q^{80} +(-8.71741 + 2.93724i) q^{82} +(8.28172 + 0.900691i) q^{83} +(0.116227 + 2.14369i) q^{85} +(11.0156 - 1.19802i) q^{86} +(15.5090 + 11.7897i) q^{88} +(10.7195 + 8.14876i) q^{89} +(0.145037 - 0.0157737i) q^{91} +(-1.07679 - 19.8602i) q^{92} +(-5.31849 - 0.578420i) q^{94} +(-2.00491 + 0.675531i) q^{95} +(2.50354 - 0.551071i) q^{97} +(-8.65188 - 16.3192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8} - 3 q^{10} + 15 q^{11} - 23 q^{13} - 13 q^{14} - 8 q^{16} + 10 q^{17} - 15 q^{19} - 7 q^{20} - q^{22} - 3 q^{23} - 5 q^{25} - 5 q^{26} + 29 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) $ 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8 - 3 * q^10 + 15 * q^11 - 23 * q^13 - 13 * q^14 - 8 * q^16 + 10 * q^17 - 15 * q^19 - 7 * q^20 - q^22 - 3 * q^23 - 5 * q^25 - 5 * q^26 + 29 * q^28 + 13 * q^29 + 3 * q^31 - 36 * q^32 + 27 * q^34 - 28 * q^35 - 9 * q^37 - 31 * q^38 + 79 * q^40 - 23 * q^41 + 19 * q^43 - 43 * q^44 - 31 * q^46 - 10 * q^47 - 31 * q^49 + 60 * q^50 - 75 * q^52 + 23 * q^53 - 24 * q^55 + 103 * q^56 + 12 * q^58 + 33 * q^59 - 47 * q^61 + 39 * q^62 - 152 * q^64 + 16 * q^65 - 19 * q^67 + 5 * q^68 + 23 * q^70 + 18 * q^71 + 24 * q^73 - 19 * q^74 + 97 * q^76 - 65 * q^77 + 41 * q^79 - 107 * q^80 + 145 * q^82 - 49 * q^83 + 39 * q^85 - 111 * q^86 + 175 * q^88 - 51 * q^89 + 77 * q^91 - 135 * q^92 + 151 * q^94 - 65 * q^95 + 91 * q^97 - 31 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{23}{29}\right)$

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 $

$2$	2.19893	−	1.67159i	1.55488	−	1.18199i	0.647205	−	0.762316i	$-0.275938\pi$
$2$	2.19893	−	1.67159i	1.55488	−	1.18199i	0.907675	−	0.419673i	$-0.137855\pi$
$3$		0			0
$3$		0			0
$4$	1.50605	−	5.42431i	0.753025	−	2.71215i
$5$	−0.330311	+	0.312887i	−0.147719	+	0.139927i	−0.757991	−	0.652265i	$-0.773819\pi$
$5$	−0.330311	+	0.312887i	−0.147719	+	0.139927i	0.610272	+	0.792192i	$0.291060\pi$
$6$		0			0
$7$	−0.362135	−	0.426338i	−0.136874	−	0.161141i	0.689454	−	0.724329i	$-0.257850\pi$
$7$	−0.362135	−	0.426338i	−0.136874	−	0.161141i	−0.826328	+	0.563189i	$0.809574\pi$
$8$	−3.71073	−	9.31322i	−1.31194	−	3.29272i
$9$		0			0
$10$	−0.203314	+	1.24016i	−0.0642935	+	0.392173i
$11$	−1.66508	+	1.00184i	−0.502039	+	0.302067i	−0.743954	−	0.668230i	$-0.767052\pi$
$11$	−1.66508	+	1.00184i	−0.502039	+	0.302067i	0.241915	+	0.970297i	$0.422224\pi$
$12$		0			0
$13$	−0.146364	+	0.215870i	−0.0405940	+	0.0598716i	−0.847444	−	0.530884i	$-0.821860\pi$
$13$	−0.146364	+	0.215870i	−0.0405940	+	0.0598716i	0.806850	+	0.590756i	$0.201170\pi$
$14$	−1.50897	−	0.332149i	−0.403289	−	0.0887706i
$15$		0			0
$16$	−14.0801	−	8.47172i	−3.52003	−	2.11793i
$17$	3.05473	−	3.59631i	0.740882	−	0.872233i	−0.254614	−	0.967043i	$-0.581948\pi$
$17$	3.05473	−	3.59631i	0.740882	−	0.872233i	0.995495	+	0.0948096i	$0.0302242\pi$
$18$		0			0
$19$	4.22025	+	1.95250i	0.968193	+	0.447934i	0.839266	−	0.543721i	$-0.182985\pi$
$19$	4.22025	+	1.95250i	0.968193	+	0.447934i	0.128926	+	0.991654i	$0.458847\pi$
$20$	1.19973	+	2.26293i	0.268268	+	0.506007i
$21$		0			0
$22$	−1.98672	+	4.98630i	−0.423571	+	1.06308i
$23$	3.34811	−	1.12811i	0.698130	−	0.235227i	0.0522141	−	0.998636i	$-0.483372\pi$
$23$	3.34811	−	1.12811i	0.698130	−	0.235227i	0.645916	+	0.763408i	$0.276476\pi$
$24$		0			0
$25$	−0.259488	+	4.78597i	−0.0518975	+	0.957193i
$26$	0.0390017	+	0.719343i	0.00764885	+	0.141075i
$27$		0			0
$28$	−2.85798	+	1.32224i	−0.540107	+	0.249880i
$29$	4.87493	+	3.70583i	0.905252	+	0.688155i	0.950468	−	0.310823i	$-0.100605\pi$
$29$	4.87493	+	3.70583i	0.905252	+	0.688155i	−0.0452161	+	0.998977i	$0.514398\pi$
$30$		0			0
$31$	0.386926	−	0.179011i	0.0694940	−	0.0321514i	−0.384834	−	0.922986i	$-0.625741\pi$
$31$	0.386926	−	0.179011i	0.0694940	−	0.0321514i	0.454328	+	0.890834i	$0.349879\pi$
$32$	−25.1895	+	2.73952i	−4.45291	+	0.484283i
$33$		0			0
$34$	0.705614	−	13.0143i	0.121012	−	2.23193i
$35$	0.253012	+	0.0275168i	0.0427669	+	0.00465118i
$36$		0			0
$37$	−3.25905	+	8.17960i	−0.535785	+	1.34472i	0.373147	+	0.927772i	$0.378279\pi$
$37$	−3.25905	+	8.17960i	−0.535785	+	1.34472i	−0.908931	+	0.416946i	$0.863100\pi$
$38$	12.5438	−	2.76110i	2.03488	−	0.447910i
$39$		0			0
$40$	4.13968	+	1.91522i	0.654540	+	0.302823i
$41$	−3.15602	−	1.06339i	−0.492887	−	0.166073i	0.0618719	−	0.998084i	$-0.480293\pi$
$41$	−3.15602	−	1.06339i	−0.492887	−	0.166073i	−0.554759	+	0.832011i	$0.687190\pi$
$42$		0			0
$43$	3.43733	+	2.06817i	0.524188	+	0.315393i	0.752938	−	0.658092i	$-0.228636\pi$
$43$	3.43733	+	2.06817i	0.524188	+	0.315393i	−0.228750	+	0.973485i	$0.573464\pi$
$44$	2.92661	+	10.5407i	0.441204	+	1.58907i
$45$		0			0
$46$	5.47654	−	8.07730i	0.807472	−	1.19093i
$47$	−1.40614	−	1.33196i	−0.205106	−	0.194287i	0.578251	−	0.815859i	$-0.303736\pi$
$47$	−1.40614	−	1.33196i	−0.205106	−	0.194287i	−0.783357	+	0.621572i	$0.786494\pi$
$48$		0			0
$49$	1.08185	−	6.59900i	0.154550	−	0.942715i
$50$	7.42956	+	10.9578i	1.05070	+	1.54966i
$51$		0			0
$52$	0.950515	+	1.11903i	0.131813	+	0.155182i
$53$	1.36486	+	8.32531i	0.187479	+	1.14357i	0.898034	+	0.439927i	$0.144996\pi$
$53$	1.36486	+	8.32531i	0.187479	+	1.14357i	−0.710555	+	0.703642i	$0.751556\pi$
$54$		0			0
$55$	0.236529	−	0.851900i	0.0318936	−	0.114870i
$56$	−2.62679	+	4.95466i	−0.351020	+	0.662094i
$57$		0			0
$58$	16.9142			2.22095
$59$	−6.86593	−	3.44368i	−0.893868	−	0.448329i
$59$	−6.86593	−	3.44368i	−0.893868	−	0.448329i
$60$		0			0
$61$	−0.900340	+	0.684420i	−0.115277	+	0.0876310i	−0.661224	−	0.750188i	$-0.729963\pi$
$61$	−0.900340	+	0.684420i	−0.115277	+	0.0876310i	0.545948	+	0.837819i	$0.316170\pi$
$62$	0.551592	−	1.04041i	0.0700523	−	0.132133i
$63$		0			0
$64$	−26.9511	+	25.5294i	−3.36889	+	3.19118i
$65$	−0.0191975	−	0.117099i	−0.00238116	−	0.0145244i
$66$		0			0
$67$	−1.70447	−	4.27791i	−0.208235	−	0.522630i	0.787349	−	0.616508i	$-0.211453\pi$
$67$	−1.70447	−	4.27791i	−0.208235	−	0.522630i	−0.995584	+	0.0938778i	$0.970074\pi$
$68$	−14.9069	−	21.9860i	−1.80773	−	2.66620i
$69$		0			0
$70$	0.602354	−	0.362424i	0.0719951	−	0.0433180i
$71$	1.83446	+	1.73769i	0.217710	+	0.206226i	0.788780	−	0.614675i	$-0.210713\pi$
$71$	1.83446	+	1.73769i	0.217710	+	0.206226i	−0.571070	+	0.820901i	$0.693472\pi$
$72$		0			0
$73$	−10.5528	−	2.32285i	−1.23511	−	0.271869i	−0.451021	−	0.892513i	$-0.648940\pi$
$73$	−10.5528	−	2.32285i	−1.23511	−	0.271869i	−0.784092	+	0.620644i	$0.786871\pi$
$74$	6.50647	+	23.4342i	0.756361	+	2.72417i
$75$		0			0
$76$	16.9469	−	19.9514i	1.94394	−	2.28858i
$77$	1.03011	+	0.347083i	0.117391	+	0.0395538i
$78$		0			0
$79$	1.15299	+	2.17477i	0.129721	+	0.244680i	0.939861	−	0.341556i	$-0.110954\pi$
$79$	1.15299	+	2.17477i	0.129721	+	0.244680i	−0.810140	+	0.586236i	$0.800609\pi$
$80$	7.30150	−	1.60718i	0.816333	−	0.179688i
$81$		0			0
$82$	−8.71741	+	2.93724i	−0.962677	+	0.324364i
$83$	8.28172	+	0.900691i	0.909037	+	0.0988637i	0.550676	−	0.834719i	$-0.314370\pi$
$83$	8.28172	+	0.900691i	0.909037	+	0.0988637i	0.358361	+	0.933583i	$0.383336\pi$
$84$		0			0
$85$	0.116227	+	2.14369i	0.0126066	+	0.232515i
$86$	11.0156	−	1.19802i	1.18784	−	0.129185i
$87$		0			0
$88$	15.5090	+	11.7897i	1.65327	+	1.25678i
$89$	10.7195	+	8.14876i	1.13627	+	0.863766i	0.992058	−	0.125781i	$-0.0401437\pi$
$89$	10.7195	+	8.14876i	1.13627	+	0.863766i	0.144207	+	0.989548i	$0.453937\pi$
$90$		0			0
$91$	0.145037	−	0.0157737i	0.0152040	−	0.00165353i
$92$	−1.07679	−	19.8602i	−0.112263	−	2.07057i
$93$		0			0
$94$	−5.31849	−	0.578420i	−0.548560	−	0.0596595i
$95$	−2.00491	+	0.675531i	−0.205699	+	0.0693081i
$96$		0			0
$97$	2.50354	−	0.551071i	0.254196	−	0.0559528i	−0.0860442	−	0.996291i	$-0.527423\pi$
$97$	2.50354	−	0.551071i	0.254196	−	0.0559528i	0.340240	+	0.940339i	$0.389492\pi$
$98$	−8.65188	−	16.3192i	−0.873971	−	1.64848i
$99$		0			0
$100$	25.5697	+	8.61545i	2.55697	+	0.861545i
$101$	8.69776	−	10.2398i	0.865460	−	1.01890i	−0.134150	−	0.990961i	$-0.542830\pi$
$101$	8.69776	−	10.2398i	0.865460	−	1.01890i	0.999610	−	0.0279367i	$-0.00889369\pi$
$102$		0			0
$103$	−2.91301	−	10.4917i	−0.287028	−	1.03378i	−0.956689	−	0.291113i	$-0.905974\pi$
$103$	−2.91301	−	10.4917i	−0.287028	−	1.03378i	0.669661	−	0.742667i	$-0.266439\pi$
$104$	2.55356	+	0.562081i	0.250397	+	0.0551166i
$105$		0			0
$106$	16.9177	+	16.0253i	1.64319	+	1.55651i
$107$	−12.5150	+	7.53003i	−1.20987	+	0.727955i	−0.970060	−	0.242864i	$-0.921913\pi$
$107$	−12.5150	+	7.53003i	−1.20987	+	0.727955i	−0.239811	+	0.970820i	$0.577085\pi$
$108$		0			0
$109$	4.90864	+	7.23970i	0.470163	+	0.693438i	0.986650	−	0.162857i	$-0.0520709\pi$
$109$	4.90864	+	7.23970i	0.470163	+	0.693438i	−0.516487	+	0.856295i	$0.672761\pi$
$110$	−0.903912	−	2.26865i	−0.0861847	−	0.216307i
$111$		0			0
$112$	1.48708	+	9.07079i	0.140516	+	0.857109i
$113$	−7.28399	+	6.89976i	−0.685220	+	0.649075i	−0.948915	−	0.315531i	$-0.897817\pi$
$113$	−7.28399	+	6.89976i	−0.685220	+	0.649075i	0.263695	+	0.964606i	$0.415059\pi$
$114$		0			0
$115$	−0.752947	+	1.42021i	−0.0702127	+	0.132435i
$116$	27.4434	−	20.8619i	2.54806	−	1.93698i
$117$		0			0
$118$	−20.8541	+	3.90456i	−1.91978	+	0.359444i
$119$	−2.63947			−0.241960
$120$		0			0
$121$	−3.38370	+	6.38234i	−0.307609	+	0.580213i
$122$	−0.835719	+	3.00999i	−0.0756625	+	0.272512i
$123$		0			0
$124$	−0.388281	−	2.36841i	−0.0348686	−	0.212689i
$125$	−2.88448	−	3.39587i	−0.257996	−	0.303736i
$126$		0			0
$127$	−9.87131	−	14.5591i	−0.875937	−	1.29191i	−0.955473	−	0.295078i	$-0.904654\pi$
$127$	−9.87131	−	14.5591i	−0.875937	−	1.29191i	0.0795362	−	0.996832i	$-0.474656\pi$
$128$	−8.39056	+	51.1801i	−0.741627	+	4.52373i
$129$		0			0
$130$	−0.237956	−	0.225404i	−0.0208701	−	0.0197692i
$131$	0.103723	−	0.152980i	0.00906230	−	0.0133659i	−0.823131	−	0.567852i	$-0.807775\pi$
$131$	0.103723	−	0.152980i	0.00906230	−	0.0133659i	0.832193	+	0.554486i	$0.187085\pi$
$132$		0			0
$133$	−0.695876	−	2.50632i	−0.0603401	−	0.217325i
$134$	−10.8989	−	6.55766i	−0.941523	−	0.566495i
$135$		0			0
$136$	−44.8285	−	15.1045i	−3.84401	−	1.29520i
$137$	−11.0931	−	5.13221i	−0.947748	−	0.438475i	−0.115765	−	0.993277i	$-0.536932\pi$
$137$	−11.0931	−	5.13221i	−0.947748	−	0.438475i	−0.831982	+	0.554802i	$0.812794\pi$
$138$		0			0
$139$	−19.0817	+	4.20020i	−1.61849	+	0.356257i	−0.929589	−	0.368598i	$-0.879838\pi$
$139$	−19.0817	+	4.20020i	−1.61849	+	0.356257i	−0.688902	+	0.724855i	$0.741907\pi$
$140$	0.530309	−	1.33097i	0.0448193	−	0.112488i
$141$		0			0
$142$	6.93856	+	0.754614i	0.582271	+	0.0633258i
$143$	0.0274385	−	0.506074i	0.00229452	−	0.0423200i
$144$		0			0
$145$	−2.76975	+	0.301228i	−0.230015	+	0.0250156i
$146$	−27.0878	+	12.5321i	−2.24180	+	1.03717i
$147$		0			0
$148$	39.4604	+	29.9970i	3.24362	+	2.46574i
$149$	4.77405	−	2.20871i	0.391106	−	0.180945i	−0.214474	−	0.976730i	$-0.568804\pi$
$149$	4.77405	−	2.20871i	0.391106	−	0.180945i	0.605579	+	0.795785i	$0.292941\pi$
$150$		0			0
$151$	−0.295991	−	5.45922i	−0.0240874	−	0.444265i	−0.985556	−	0.169350i	$-0.945833\pi$
$151$	−0.295991	−	5.45922i	−0.0240874	−	0.444265i	0.961469	−	0.274915i	$-0.0886497\pi$
$152$	2.52383	−	46.5493i	0.204710	−	3.77565i
$153$		0			0
$154$	2.84531	−	0.958697i	0.229282	−	0.0772540i
$155$	−0.0717957	+	0.180194i	−0.00576677	+	0.0144735i
$156$		0			0
$157$	−3.99154	−	7.52885i	−0.318560	−	0.600867i	0.671583	−	0.740929i	$-0.265615\pi$
$157$	−3.99154	−	7.52885i	−0.318560	−	0.600867i	−0.990143	+	0.140062i	$0.955270\pi$
$158$	6.17065	+	2.85485i	0.490910	+	0.227119i
$159$		0			0
$160$	7.46319	−	8.78635i	0.590017	−	0.694622i
$161$	−1.69342	−	1.01890i	−0.133461	−	0.0803005i
$162$		0			0
$163$	4.77394	+	1.05082i	0.373924	+	0.0823069i	0.397957	−	0.917404i	$-0.369719\pi$
$163$	4.77394	+	1.05082i	0.373924	+	0.0823069i	−0.0240324	+	0.999711i	$0.507651\pi$
$164$	−10.5213	+	15.5177i	−0.821572	+	1.21173i
$165$		0			0
$166$	19.7165	−	11.8630i	1.53030	−	0.920750i
$167$	−2.13245	+	13.0074i	−0.165014	+	1.00654i	0.766343	+	0.642432i	$0.222074\pi$
$167$	−2.13245	+	13.0074i	−0.165014	+	1.00654i	−0.931357	+	0.364108i	$0.881374\pi$
$168$		0			0
$169$	4.78662	+	12.0135i	0.368201	+	0.924116i
$170$	3.83893	+	4.51954i	0.294432	+	0.346633i
$171$		0			0
$172$	16.3952	−	15.5303i	1.25012	−	1.18418i
$173$	3.68273	−	13.2640i	0.279993	−	1.00844i	−0.681094	−	0.732196i	$-0.738495\pi$
$173$	3.68273	−	13.2640i	0.279993	−	1.00844i	0.961087	−	0.276247i	$-0.0890908\pi$
$174$		0			0
$175$	2.13441	−	1.62253i	0.161346	−	0.122652i
$176$	31.9318			2.40695
$177$		0			0
$178$	37.1928			2.78772
$179$	3.76889	−	2.86504i	0.281700	−	0.214143i	−0.454777	−	0.890605i	$-0.650281\pi$
$179$	3.76889	−	2.86504i	0.281700	−	0.214143i	0.736477	+	0.676462i	$0.236488\pi$
$180$		0			0
$181$	−5.11465	+	18.4213i	−0.380169	+	1.36925i	0.487942	+	0.872876i	$0.337748\pi$
$181$	−5.11465	+	18.4213i	−0.380169	+	1.36925i	−0.868111	+	0.496370i	$0.834666\pi$
$182$	0.292559	−	0.277127i	0.0216859	−	0.0205420i
$183$		0			0
$184$	−22.9303	−	26.9956i	−1.69044	−	1.99014i
$185$	−1.48279	−	3.72153i	−0.109017	−	0.273612i
$186$		0			0
$187$	−1.48343	+	9.04849i	−0.108479	+	0.661691i
$188$	−9.34268	+	5.62131i	−0.681385	+	0.409976i
$189$		0			0
$190$	−3.27944	+	4.83682i	−0.237916	+	0.350900i
$191$	−18.1216	−	3.98886i	−1.31123	−	0.288624i	−0.496285	−	0.868160i	$-0.665303\pi$
$191$	−18.1216	−	3.98886i	−1.31123	−	0.288624i	−0.814947	+	0.579536i	$0.803234\pi$
$192$		0			0
$193$	2.66195	+	1.60164i	0.191611	+	0.115289i	0.608127	−	0.793840i	$-0.291921\pi$
$193$	2.66195	+	1.60164i	0.191611	+	0.115289i	−0.416516	+	0.909129i	$0.636749\pi$
$194$	4.58396	−	5.39665i	0.329109	−	0.387457i
$195$		0			0
$196$	−34.1657	−	15.8067i	−2.44041	−	1.12905i
$197$	−3.01537	−	5.68760i	−0.214837	−	0.405225i	0.752548	−	0.658538i	$-0.228825\pi$
$197$	−3.01537	−	5.68760i	−0.214837	−	0.405225i	−0.967384	+	0.253313i	$0.918480\pi$
$198$		0			0
$199$	4.71187	−	11.8259i	0.334016	−	0.838316i	−0.662030	−	0.749477i	$-0.730305\pi$
$199$	4.71187	−	11.8259i	0.334016	−	0.838316i	0.996046	−	0.0888392i	$-0.0283157\pi$
$200$	45.5356	−	15.3427i	3.21986	−	1.08490i
$201$		0			0
$202$	2.00910	−	37.0557i	0.141360	−	2.60723i
$203$	−0.185447	−	3.42037i	−0.0130158	−	0.240063i
$204$		0			0
$205$	1.37519	−	0.636229i	0.0960471	−	0.0444361i
$206$	−23.9433	−	18.2012i	−1.66821	−	1.26814i
$207$		0			0
$208$	3.88961	−	1.79952i	0.269696	−	0.124775i
$209$	−8.98314	+	0.976975i	−0.621377	+	0.0675788i
$210$		0			0
$211$	1.38963	−	25.6302i	0.0956662	−	1.76446i	−0.419864	−	0.907587i	$-0.637922\pi$
$211$	1.38963	−	25.6302i	0.0956662	−	1.76446i	0.515530	−	0.856872i	$-0.327595\pi$
$212$	47.2146	+	5.13489i	3.24271	+	0.352666i
$213$		0			0
$214$	−14.9326	+	37.4779i	−1.02077	+	2.56194i
$215$	−1.78249	+	0.392356i	−0.121565	+	0.0267584i
$216$		0			0
$217$	−0.216439	−	0.100135i	−0.0146928	−	0.00679762i
$218$	22.8956	+	7.71441i	1.55068	+	0.522486i
$219$		0			0
$220$	−4.26474	−	2.56601i	−0.287529	−	0.173000i
$221$	0.329234	+	1.18579i	0.0221467	+	0.0797652i
$222$		0			0
$223$	−11.8028	+	17.4078i	−0.790372	+	1.16571i	0.192478	+	0.981301i	$0.438348\pi$
$223$	−11.8028	+	17.4078i	−0.790372	+	1.16571i	−0.982849	+	0.184410i	$0.940963\pi$
$224$	10.2899	+	9.74715i	0.687526	+	0.651259i
$225$		0			0
$226$	−4.48346	+	27.3479i	−0.298236	+	1.81916i
$227$	0.391450	+	0.577346i	0.0259815	+	0.0383198i	0.840458	−	0.541877i	$-0.182286\pi$
$227$	0.391450	+	0.577346i	0.0259815	+	0.0383198i	−0.814476	+	0.580197i	$0.802976\pi$
$228$		0			0
$229$	5.80508	+	6.83426i	0.383610	+	0.451621i	0.919748	−	0.392510i	$-0.128393\pi$
$229$	5.80508	+	6.83426i	0.383610	+	0.451621i	−0.536138	+	0.844131i	$0.680117\pi$
$230$	0.718320	+	4.38156i	0.0473646	+	0.288911i
$231$		0			0
$232$	16.4236	−	59.1526i	1.07826	−	3.88356i
$233$	−5.33325	+	10.0596i	−0.349393	+	0.659025i	−0.994462	−	0.105099i	$-0.966484\pi$
$233$	−5.33325	+	10.0596i	−0.349393	+	0.659025i	0.645069	+	0.764125i	$0.276829\pi$
$234$		0			0
$235$	0.881215			0.0574842
$236$	−29.0200	+	32.0566i	−1.88904	+	2.08670i
$237$		0			0
$238$	−5.80401	+	4.41209i	−0.376218	+	0.285993i
$239$	3.17436	−	5.98747i	0.205332	−	0.387298i	−0.759363	−	0.650668i	$-0.774489\pi$
$239$	3.17436	−	5.98747i	0.205332	−	0.387298i	0.964695	+	0.263370i	$0.0848340\pi$
$240$		0			0
$241$	−8.73229	+	8.27166i	−0.562496	+	0.532825i	−0.915247	−	0.402893i	$-0.868005\pi$
$241$	−8.73229	+	8.27166i	−0.562496	+	0.532825i	0.352751	+	0.935717i	$0.385246\pi$
$242$	3.22809	+	19.6905i	0.207510	+	1.26575i
$243$		0			0
$244$	2.35655	+	5.91449i	0.150863	+	0.378636i
$245$	1.70739	+	2.51822i	0.109081	+	0.160883i
$246$		0			0
$247$	−1.03918	+	0.625252i	−0.0661213	+	0.0397839i
$248$	−3.10295	−	2.93927i	−0.197037	−	0.186644i
$249$		0			0
$250$	−12.0193	−	2.64564i	−0.760166	−	0.167325i
$251$	−2.39913	−	8.64089i	−0.151432	−	0.545408i	−0.999870	−	0.0161139i	$-0.994871\pi$
$251$	−2.39913	−	8.64089i	−0.151432	−	0.545408i	0.848438	−	0.529294i	$-0.177543\pi$
$252$		0			0
$253$	−4.44468	+	5.23268i	−0.279434	+	0.328976i
$254$	−46.0431	−	15.5137i	−2.88900	−	0.973418i
$255$		0			0
$256$	32.3243	+	60.9700i	2.02027	+	3.81063i
$257$	−10.7130	+	2.35810i	−0.668255	+	0.147094i	−0.536126	−	0.844138i	$-0.680113\pi$
$257$	−10.7130	+	2.35810i	−0.668255	+	0.147094i	−0.132130	+	0.991232i	$0.542182\pi$
$258$		0			0
$259$	4.66749	−	1.57266i	0.290024	−	0.0977203i
$260$	−0.664096	−	0.0722248i	−0.0411855	−	0.00447919i
$261$		0			0
$262$	−0.0276391	−	0.509773i	−0.00170755	−	0.0314939i
$263$	17.2455	−	1.87556i	1.06340	−	0.115652i	0.440345	−	0.897829i	$-0.354856\pi$
$263$	17.2455	−	1.87556i	1.06340	−	0.115652i	0.623056	+	0.782177i	$0.285891\pi$
$264$		0			0
$265$	−3.05571	−	2.32289i	−0.187711	−	0.142694i
$266$	−5.71971	−	4.34801i	−0.350698	−	0.266594i
$267$		0			0
$268$	−25.7717	+	2.80284i	−1.57426	+	0.171211i
$269$	1.17735	+	21.7149i	0.0717843	+	1.32398i	0.783445	+	0.621461i	$0.213460\pi$
$269$	1.17735	+	21.7149i	0.0717843	+	1.32398i	−0.711661	+	0.702523i	$0.752057\pi$
$270$		0			0
$271$	20.6243	+	2.24302i	1.25283	+	0.136254i	0.710372	−	0.703826i	$-0.248527\pi$
$271$	20.6243	+	2.24302i	1.25283	+	0.136254i	0.542462	+	0.840080i	$0.317492\pi$
$272$	−73.4779	+	24.7576i	−4.45525	+	1.50115i
$273$		0			0
$274$	−32.9719	+	7.25767i	−1.99191	+	0.438452i
$275$	−4.36272	−	8.22897i	−0.263082	−	0.496225i
$276$		0			0
$277$	3.61404	+	1.21771i	0.217147	+	0.0731652i	0.425772	−	0.904830i	$-0.360002\pi$
$277$	3.61404	+	1.21771i	0.217147	+	0.0731652i	−0.208626	+	0.977996i	$0.566899\pi$
$278$	−34.9384	+	41.1327i	−2.09547	+	2.46697i
$279$		0			0
$280$	−0.682590	−	2.45847i	−0.0407926	−	0.146922i
$281$	−12.8386	−	2.82598i	−0.765885	−	0.168584i	−0.185187	−	0.982703i	$-0.559289\pi$
$281$	−12.8386	−	2.82598i	−0.765885	−	0.168584i	−0.580698	+	0.814119i	$0.697220\pi$
$282$		0			0
$283$	−6.42058	−	6.08189i	−0.381664	−	0.361531i	0.472685	−	0.881232i	$-0.343285\pi$
$283$	−6.42058	−	6.08189i	−0.381664	−	0.361531i	−0.854348	+	0.519701i	$0.826044\pi$
$284$	12.1886	−	7.33362i	0.723259	−	0.435170i
$285$		0			0
$286$	−0.785610	−	1.15869i	−0.0464541	−	0.0685146i
$287$	0.689541	+	1.73062i	0.0407023	+	0.102155i
$288$		0			0
$289$	−0.851755	−	5.19548i	−0.0501033	−	0.305616i
$290$	−5.58696	+	5.29225i	−0.328077	+	0.310771i
$291$		0			0
$292$	−28.4929	+	53.7434i	−1.66742	+	3.14509i
$293$	9.26205	−	7.04083i	0.541095	−	0.411329i	−0.298608	−	0.954376i	$-0.596522\pi$
$293$	9.26205	−	7.04083i	0.541095	−	0.411329i	0.839703	+	0.543046i	$0.182729\pi$
$294$		0			0
$295$	3.34538	−	1.01078i	0.194775	−	0.0588496i
$296$	88.2719			5.13070
$297$		0			0
$298$	6.80577	−	12.8370i	0.394248	−	0.743630i
$299$	−0.246517	+	0.887872i	−0.0142564	+	0.0513470i
$300$		0			0
$301$	−0.363036	−	2.21442i	−0.0209250	−	0.127637i
$302$	−9.77642	−	11.5097i	−0.562570	−	0.662308i
$303$		0			0
$304$	−42.8806	−	63.2442i	−2.45937	−	3.62730i
$305$	0.0832456	−	0.507776i	0.00476663	−	0.0290752i
$306$		0			0
$307$	6.56327	+	6.21706i	0.374586	+	0.354827i	0.851714	−	0.524007i	$-0.175564\pi$
$307$	6.56327	+	6.21706i	0.374586	+	0.354827i	−0.477128	+	0.878834i	$0.658322\pi$
$308$	3.43407	−	5.06488i	0.195675	−	0.288598i
$309$		0			0
$310$	0.143335	+	0.516246i	0.00814088	+	0.0293208i
$311$	−3.65309	−	2.19799i	−0.207148	−	0.124637i	0.408200	−	0.912893i	$-0.366157\pi$
$311$	−3.65309	−	2.19799i	−0.207148	−	0.124637i	−0.615348	+	0.788256i	$0.710984\pi$
$312$		0			0
$313$	−9.74534	−	3.28359i	−0.550839	−	0.185599i	0.0300992	−	0.999547i	$-0.490418\pi$
$313$	−9.74534	−	3.28359i	−0.550839	−	0.185599i	−0.580938	+	0.813948i	$0.697314\pi$
$314$	−21.3622	−	9.88322i	−1.20554	−	0.557743i
$315$		0			0
$316$	13.5331	−	2.97885i	0.761294	−	0.167573i
$317$	−9.25431	+	23.2266i	−0.519774	+	1.30453i	0.401586	+	0.915821i	$0.368459\pi$
$317$	−9.25431	+	23.2266i	−0.519774	+	1.30453i	−0.921359	+	0.388712i	$0.872920\pi$
$318$		0			0
$319$	−11.8298	−	1.28657i	−0.662341	−	0.0720339i
$320$	0.914410	−	16.8653i	0.0511171	−	0.942799i
$321$		0			0
$322$	−5.42690	+	0.590211i	−0.302429	+	0.0328912i
$323$	19.9135	−	9.21298i	1.10802	−	0.512624i
$324$		0			0
$325$	−0.995168	−	0.756507i	−0.0552020	−	0.0419635i
$326$	12.2541	−	5.66936i	0.678693	−	0.313997i
$327$		0			0
$328$	1.80757	+	33.3386i	0.0998062	+	1.84082i
$329$	−0.0586556	+	1.08184i	−0.00323379	+	0.0596437i
$330$		0			0
$331$	3.83599	−	1.29250i	0.210845	−	0.0710420i	−0.211897	−	0.977292i	$-0.567964\pi$
$331$	3.83599	−	1.29250i	0.210845	−	0.0710420i	0.422742	+	0.906250i	$0.361068\pi$
$332$	17.3583	−	43.5661i	0.952661	−	2.39100i
$333$		0			0
$334$	17.0538	+	32.1669i	0.933142	+	1.76009i
$335$	1.90151	+	0.879731i	0.103890	+	0.0480649i
$336$		0			0
$337$	10.4610	−	12.3157i	0.569849	−	0.670878i	−0.399452	−	0.916754i	$-0.630800\pi$
$337$	10.4610	−	12.3157i	0.569849	−	0.670878i	0.969301	+	0.245876i	$0.0790755\pi$
$338$	30.6070	+	18.4156i	1.66480	+	1.00168i
$339$		0			0
$340$	11.8030	+	2.59805i	0.640110	+	0.140899i
$341$	−0.464921	+	0.685707i	−0.0251769	+	0.0371331i
$342$		0			0
$343$	−6.56034	+	3.94722i	−0.354225	+	0.213130i
$344$	6.50635	−	39.6870i	0.350799	−	2.13978i
$345$		0			0
$346$	−14.0738	−	35.3226i	−0.756613	−	1.89896i
$347$	2.52185	+	2.96896i	0.135380	+	0.159382i	0.825675	−	0.564147i	$-0.190795\pi$
$347$	2.52185	+	2.96896i	0.135380	+	0.159382i	−0.690294	+	0.723529i	$0.742519\pi$
$348$		0			0
$349$	4.15856	−	3.93920i	0.222603	−	0.210860i	−0.568268	−	0.822843i	$-0.692386\pi$
$349$	4.15856	−	3.93920i	0.222603	−	0.210860i	0.790871	+	0.611983i	$0.209628\pi$
$350$	1.98121	−	7.13569i	0.105900	−	0.381419i
$351$		0			0
$352$	39.1978	−	29.7974i	2.08925	−	1.58821i
$353$	8.94551			0.476121			0.238061	−	0.971250i	$-0.423488\pi$
$353$	8.94551			0.476121			0.238061	+	0.971250i	$0.423488\pi$
$354$		0			0
$355$	−1.14964			−0.0610167
$356$	60.3455	−	45.8734i	3.19830	−	2.43129i
$357$		0			0
$358$	3.49839	−	12.6001i	0.184895	−	0.665933i
$359$	−14.8703	+	14.0859i	−0.784826	+	0.743426i	−0.970997	−	0.239091i	$-0.923151\pi$
$359$	−14.8703	+	14.0859i	−0.784826	+	0.743426i	0.186171	+	0.982517i	$0.440392\pi$
$360$		0			0
$361$	1.69796	+	1.99899i	0.0893661	+	0.105210i
$362$	19.5460	+	49.0568i	1.02732	+	2.57837i
$363$		0			0
$364$	0.132872	−	0.810480i	0.00696436	−	0.0424807i
$365$	4.21250	−	2.53458i	0.220492	−	0.132666i
$366$		0			0
$367$	17.7943	−	26.2447i	0.928857	−	1.36996i	−0.000190189	−	1.00000i	$-0.500061\pi$
$367$	17.7943	−	26.2447i	0.928857	−	1.36996i	0.929047	−	0.369961i	$-0.120629\pi$
$368$	−56.6989	−	12.4804i	−2.95563	−	0.650584i
$369$		0			0
$370$	−9.48140	−	5.70477i	−0.492915	−	0.296577i
$371$	3.05513	−	3.59677i	0.158614	−	0.186735i
$372$		0			0
$373$	16.4416	+	7.60669i	0.851314	+	0.393860i	0.796501	−	0.604637i	$-0.206682\pi$
$373$	16.4416	+	7.60669i	0.851314	+	0.393860i	0.0548126	+	0.998497i	$0.482544\pi$
$374$	11.8634	+	22.3767i	0.613440	+	1.15707i
$375$		0			0
$376$	−7.18707	+	18.0382i	−0.370645	+	0.930249i
$377$	−1.51349	+	0.509954i	−0.0779487	+	0.0262640i
$378$		0			0
$379$	0.733744	−	13.5331i	0.0376899	−	0.695149i	−0.917243	−	0.398328i	$-0.869591\pi$
$379$	0.733744	−	13.5331i	0.0376899	−	0.695149i	0.954933	−	0.296821i	$-0.0959266\pi$
$380$	0.644798	+	11.8926i	0.0330775	+	0.610078i
$381$		0			0
$382$	−46.5159	+	21.5205i	−2.37996	+	1.10109i
$383$	−22.4018	−	17.0294i	−1.14468	−	0.870161i	−0.151695	−	0.988427i	$-0.548473\pi$
$383$	−22.4018	−	17.0294i	−1.14468	−	0.870161i	−0.992982	+	0.118266i	$0.962266\pi$
$384$		0			0
$385$	−0.448852	+	0.207661i	−0.0228756	+	0.0105834i
$386$	8.53072	−	0.927771i	0.434202	−	0.0472223i
$387$		0			0
$388$	0.781283	−	14.4099i	0.0396636	−	0.731553i
$389$	−28.5137	−	3.10105i	−1.44570	−	0.157230i	−0.648626	−	0.761108i	$-0.724656\pi$
$389$	−28.5137	−	3.10105i	−1.44570	−	0.157230i	−0.797077	+	0.603878i	$0.793621\pi$
$390$		0			0
$391$	6.17056	−	15.4869i	0.312059	−	0.783208i
$392$	−65.4724	+	14.4116i	−3.30686	+	0.727894i
$393$		0			0
$394$	−16.1379	−	7.46619i	−0.813016	−	0.376141i
$395$	−1.06130	−	0.357594i	−0.0533998	−	0.0179925i
$396$		0			0
$397$	15.5055	+	9.32933i	0.778197	+	0.468226i	0.848432	−	0.529305i	$-0.177547\pi$
$397$	15.5055	+	9.32933i	0.778197	+	0.468226i	−0.0702345	+	0.997531i	$0.522375\pi$
$398$	−9.40692	−	33.8807i	−0.471526	−	1.69828i
$399$		0			0
$400$	44.1990	−	65.1887i	2.20995	−	3.25943i
$401$	14.0940	+	13.3505i	0.703821	+	0.666694i	0.953417	−	0.301656i	$-0.0975393\pi$
$401$	14.0940	+	13.3505i	0.703821	+	0.666694i	−0.249596	+	0.968350i	$0.580298\pi$
$402$		0			0
$403$	−0.0179888	+	0.109727i	−0.000896084	+	0.00546587i
$404$	−42.4445	−	62.6010i	−2.11169	−	3.11451i
$405$		0			0
$406$	−6.12523	−	7.21118i	−0.303990	−	0.357885i
$407$	−2.76811	−	16.8847i	−0.137210	−	0.836944i
$408$		0			0
$409$	2.52893	−	9.10840i	0.125048	−	0.450381i	−0.874342	−	0.485310i	$-0.838707\pi$
$409$	2.52893	−	9.10840i	0.125048	−	0.450381i	0.999390	+	0.0349289i	$0.0111205\pi$
$410$	1.96043	−	3.69776i	0.0968188	−	0.182620i
$411$		0			0
$412$	−61.2975			−3.01991
$413$	1.01822	+	4.17428i	0.0501033	+	0.205403i
$414$		0			0
$415$	−3.01735	+	2.29373i	−0.148116	+	0.112595i
$416$	3.09544	−	5.83862i	0.151767	−	0.286262i
$417$		0			0
$418$	−18.1202	+	17.1644i	−0.886289	+	0.839537i
$419$	−2.41565	−	14.7348i	−0.118012	−	0.719842i	−0.977855	−	0.209283i	$-0.932887\pi$
$419$	−2.41565	−	14.7348i	−0.118012	−	0.719842i	0.859843	−	0.510559i	$-0.170561\pi$
$420$		0			0
$421$	14.2104	+	35.6655i	0.692575	+	1.73823i	0.674366	+	0.738397i	$0.264417\pi$
$421$	14.2104	+	35.6655i	0.692575	+	1.73823i	0.0182089	+	0.999834i	$0.494204\pi$
$422$	−39.7874	−	58.6821i	−1.93682	−	2.85660i
$423$		0			0
$424$	72.4708	−	43.6042i	3.51949	−	2.11761i
$425$	16.4192	+	15.5530i	0.796446	+	0.754434i
$426$		0			0
$427$	0.617838	+	0.135996i	0.0298993	+	0.00658133i
$428$	21.9969	+	79.2258i	1.06326	+	3.82952i
$429$		0			0
$430$	−3.26372	+	3.84235i	−0.157391	+	0.185294i
$431$	20.7188	+	6.98099i	0.997991	+	0.336262i	0.770446	−	0.637505i	$-0.220034\pi$
$431$	20.7188	+	6.98099i	0.997991	+	0.336262i	0.227545	+	0.973768i	$0.426930\pi$
$432$		0			0
$433$	−6.69581	−	12.6296i	−0.321780	−	0.606942i	0.668868	−	0.743381i	$-0.266779\pi$
$433$	−6.69581	−	12.6296i	−0.321780	−	0.606942i	−0.990648	+	0.136439i	$0.956434\pi$
$434$	−0.643318	+	0.141605i	−0.0308803	+	0.00679726i
$435$		0			0
$436$	46.6630	−	15.7226i	2.23475	−	0.752976i
$437$	16.3325	+	1.77627i	0.781291	+	0.0849705i
$438$		0			0
$439$	−1.01404	−	18.7028i	−0.0483974	−	0.892637i	−0.917434	−	0.397889i	$-0.869743\pi$
$439$	−1.01404	−	18.7028i	−0.0483974	−	0.892637i	0.869036	−	0.494748i	$-0.164740\pi$
$440$	−8.81163	+	0.958322i	−0.420078	+	0.0456862i
$441$		0			0
$442$	2.70612	+	2.05714i	0.128717	+	0.0978481i
$443$	−14.2390	−	10.8242i	−0.676517	−	0.514275i	0.209570	−	0.977794i	$-0.432794\pi$
$443$	−14.2390	−	10.8242i	−0.676517	−	0.514275i	−0.886087	+	0.463519i	$0.846587\pi$
$444$		0			0
$445$	−6.09041	+	0.662372i	−0.288713	+	0.0313994i
$446$	3.14509	+	58.0079i	0.148925	+	2.74675i
$447$		0			0
$448$	20.6441	+	2.24518i	0.975341	+	0.106075i
$449$	17.6640	−	5.95170i	0.833616	−	0.280878i	0.130050	−	0.991507i	$-0.458486\pi$
$449$	17.6640	−	5.95170i	0.833616	−	0.280878i	0.703567	+	0.710629i	$0.251590\pi$
$450$		0			0
$451$	6.32035	−	1.39122i	0.297614	−	0.0655098i
$452$	26.4564	+	49.9020i	1.24440	+	2.34719i
$453$		0			0
$454$	1.82586	+	0.615202i	0.0856917	+	0.0288729i
$455$	−0.0429719	+	0.0505904i	−0.00201455	+	0.00237171i
$456$		0			0
$457$	9.32995	+	33.6034i	0.436437	+	1.57190i	0.775631	+	0.631187i	$0.217432\pi$
$457$	9.32995	+	33.6034i	0.436437	+	1.57190i	−0.339194	+	0.940716i	$0.610154\pi$
$458$	24.1890	+	5.32441i	1.13028	+	0.248793i
$459$		0			0
$460$	6.56967	+	6.22312i	0.306312	+	0.290154i
$461$	28.8377	−	17.3511i	1.34310	−	0.808119i	0.351347	−	0.936245i	$-0.385724\pi$
$461$	28.8377	−	17.3511i	1.34310	−	0.808119i	0.991758	+	0.128126i	$0.0408962\pi$
$462$		0			0
$463$	−12.5141	−	18.4569i	−0.581578	−	0.857764i	0.417116	−	0.908853i	$-0.363041\pi$
$463$	−12.5141	−	18.4569i	−0.581578	−	0.857764i	−0.998694	+	0.0510897i	$0.983731\pi$
$464$	−37.2448	−	93.4775i	−1.72905	−	4.33958i
$465$		0			0
$466$	5.08799	+	31.0353i	0.235696	+	1.43768i
$467$	11.3029	−	10.7067i	0.523038	−	0.495448i	−0.380013	−	0.924981i	$-0.624081\pi$
$467$	11.3029	−	10.7067i	0.523038	−	0.495448i	0.903051	+	0.429533i	$0.141322\pi$
$468$		0			0
$469$	−1.20658	+	2.27586i	−0.0557149	+	0.105089i
$470$	1.93773	−	1.47303i	0.0893810	−	0.0679457i
$471$		0			0
$472$	−6.59418	+	76.7225i	−0.303522	+	3.53144i
$473$	−7.79540			−0.358433
$474$		0			0
$475$	−10.4397	+	19.6913i	−0.479006	+	0.903501i
$476$	−3.97517	+	14.3173i	−0.182202	+	0.656231i
$477$		0			0
$478$	−3.02837	−	18.4723i	−0.138515	−	0.844902i
$479$	6.25544	+	7.36447i	0.285818	+	0.336491i	0.886269	−	0.463170i	$-0.153288\pi$
$479$	6.25544	+	7.36447i	0.285818	+	0.336491i	−0.600451	+	0.799662i	$0.705012\pi$
$480$		0			0
$481$	−1.28873	−	1.90073i	−0.0587608	−	0.0866657i
$482$	−5.37492	+	32.7856i	−0.244821	+	1.49334i
$483$		0			0
$484$	29.5237	+	27.9664i	1.34199	+	1.27120i
$485$	−0.654524	+	0.965350i	−0.0297204	+	0.0438343i
$486$		0			0
$487$	4.15232	+	14.9553i	0.188159	+	0.677689i	0.996085	+	0.0884041i	$0.0281767\pi$
$487$	4.15232	+	14.9553i	0.188159	+	0.677689i	−0.807925	+	0.589285i	$0.799410\pi$
$488$	9.71507	+	5.84536i	0.439781	+	0.264607i
$489$		0			0
$490$	7.96386	+	2.68334i	0.359771	+	0.121221i
$491$	−18.9172	−	8.75202i	−0.853721	−	0.394973i	−0.0563121	−	0.998413i	$-0.517934\pi$
$491$	−18.9172	−	8.75202i	−0.853721	−	0.394973i	−0.797408	+	0.603440i	$0.793796\pi$
$492$		0			0
$493$	28.2189	−	6.21145i	1.27092	−	0.279750i
$494$	−1.23992	+	3.11196i	−0.0557866	+	0.140014i
$495$		0			0
$496$	−6.96450	−	0.757435i	−0.312715	−	0.0340098i
$497$	0.0765227	−	1.41138i	0.00343251	−	0.0633090i
$498$		0			0
$499$	−4.27293	+	0.464710i	−0.191283	+	0.0208033i	−0.203259	−	0.979125i	$-0.565153\pi$
$499$	−4.27293	+	0.464710i	−0.191283	+	0.0208033i	0.0119761	+	0.999928i	$0.496188\pi$
$500$	−22.7644	+	10.5320i	−1.01806	+	0.471003i
$501$		0			0
$502$	−19.7195	−	14.9904i	−0.880125	−	0.669053i
$503$	38.1484	−	17.6493i	1.70095	−	0.786944i	0.703893	−	0.710306i	$-0.251444\pi$
$503$	38.1484	−	17.6493i	1.70095	−	0.786944i	0.997059	−	0.0766376i	$-0.0244184\pi$
$504$		0			0
$505$	0.330935	+	6.10373i	0.0147264	+	0.271612i
$506$	−1.02668	+	18.9360i	−0.0456414	+	0.841806i
$507$		0			0
$508$	−93.8396	+	31.6183i	−4.16346	+	1.40283i
$509$	−1.99509	+	5.00731i	−0.0884310	+	0.221945i	−0.966540	−	0.256515i	$-0.917426\pi$
$509$	−1.99509	+	5.00731i	−0.0884310	+	0.221945i	0.878109	+	0.478460i	$0.158805\pi$
$510$		0			0
$511$	2.83122	+	5.34025i	0.125246	+	0.236239i
$512$	78.8556	+	36.4825i	3.48496	+	1.61231i
$513$		0			0
$514$	−19.6153	+	23.0929i	−0.865193	+	1.01858i
$515$	4.24492	+	2.55408i	0.187054	+	0.112546i
$516$		0			0
$517$	3.67574	+	0.809092i	0.161659	+	0.0355838i
$518$	7.63466	−	11.2603i	0.335448	−	0.494748i
$519$		0			0
$520$	−1.01934	+	0.613314i	−0.0447009	+	0.0268956i
$521$	1.21887	−	7.43479i	0.0533997	−	0.325724i	−0.946595	−	0.322426i	$-0.895502\pi$
$521$	1.21887	−	7.43479i	0.0533997	−	0.325724i	0.999995	−	0.00329846i	$-0.00104993\pi$
$522$		0			0
$523$	−3.55951	−	8.93369i	−0.155646	−	0.390643i	0.830388	−	0.557186i	$-0.188119\pi$
$523$	−3.55951	−	8.93369i	−0.155646	−	0.390643i	−0.986034	+	0.166543i	$0.946740\pi$
$524$	−0.673596	−	0.793019i	−0.0294262	−	0.0346432i
$525$		0			0
$526$	34.7865	−	32.9515i	1.51676	−	1.43675i
$527$	0.538177	−	1.93834i	0.0234434	−	0.0844353i
$528$		0			0
$529$	−8.37291	+	6.36492i	−0.364039	+	0.276736i
$530$	−10.6022			−0.460530
$531$		0			0
$532$	−14.6431			−0.634858
$533$	0.691479	−	0.525649i	0.0299513	−	0.0227684i
$534$		0			0
$535$	1.77779	−	6.40303i	0.0768607	−	0.276827i
$536$	−33.5163	+	31.7483i	−1.44768	+	1.37132i
$537$		0			0
$538$	38.8873	+	45.7817i	1.67655	+	1.97379i
$539$	4.80980	+	12.0717i	0.207173	+	0.519964i
$540$		0			0
$541$	3.90020	−	23.7902i	0.167683	−	1.02282i	−0.760129	−	0.649772i	$-0.774864\pi$
$541$	3.90020	−	23.7902i	0.167683	−	1.02282i	0.927812	−	0.373048i	$-0.121687\pi$
$542$	49.1007	−	29.5429i	2.10906	−	1.26898i
$543$		0			0
$544$	−67.0950	+	98.9577i	−2.87667	+	4.24277i
$545$	−3.88659	−	0.855502i	−0.166483	−	0.0366457i
$546$		0			0
$547$	10.5455	+	6.34501i	0.450892	+	0.271293i	0.722835	−	0.691020i	$-0.242839\pi$
$547$	10.5455	+	6.34501i	0.450892	+	0.271293i	−0.271943	+	0.962313i	$0.587666\pi$
$548$	−44.5455	+	52.4430i	−1.90289	+	2.24025i
$549$		0			0
$550$	−23.3487	−	10.8023i	−0.995594	−	0.460611i
$551$	13.3378	+	25.1578i	0.568211	+	1.07176i
$552$		0			0
$553$	0.509648	−	1.27912i	0.0216724	−	0.0543937i
$554$	9.98253	−	3.36351i	0.424117	−	0.142902i
$555$		0			0
$556$	−5.95485	+	109.831i	−0.252542	+	4.65786i
$557$	0.276773	+	5.10478i	0.0117273	+	0.216297i	0.998523	+	0.0543278i	$0.0173016\pi$
$557$	0.276773	+	5.10478i	0.0117273	+	0.216297i	−0.986796	+	0.161969i	$0.948216\pi$
$558$		0			0
$559$	−0.949556	+	0.439312i	−0.0401620	+	0.0185809i
$560$	−3.32933	−	2.53089i	−0.140690	−	0.106950i
$561$		0			0
$562$	−32.9550	+	15.2466i	−1.39012	+	0.643140i
$563$	−33.5628	+	3.65018i	−1.41450	+	0.153837i	−0.783234	−	0.621727i	$-0.786431\pi$
$563$	−33.5628	+	3.65018i	−1.41450	+	0.153837i	−0.631270	+	0.775563i	$0.717466\pi$
$564$		0			0
$565$	0.247135	−	4.55813i	0.0103970	−	0.191762i
$566$	−24.2848	−	2.64113i	−1.02077	−	0.111015i
$567$		0			0
$568$	9.37634	−	23.5328i	0.393422	−	0.987416i
$569$	−7.00852	+	1.54269i	−0.293812	+	0.0646730i	−0.359431	−	0.933172i	$-0.617029\pi$
$569$	−7.00852	+	1.54269i	−0.293812	+	0.0646730i	0.0656183	+	0.997845i	$0.479098\pi$
$570$		0			0
$571$	34.0296	+	15.7438i	1.42409	+	0.658856i	0.972401	−	0.233318i	$-0.0749582\pi$
$571$	34.0296	+	15.7438i	1.42409	+	0.658856i	0.451693	+	0.892174i	$0.350820\pi$
$572$	−2.70377	−	0.911008i	−0.113050	−	0.0380911i
$573$		0			0
$574$	4.40913	+	2.65288i	0.184033	+	0.110729i
$575$	4.53031	+	16.3167i	0.188927	+	0.680453i
$576$		0			0
$577$	−4.94090	+	7.28728i	−0.205692	+	0.303373i	−0.916517	−	0.399996i	$-0.869012\pi$
$577$	−4.94090	+	7.28728i	−0.205692	+	0.303373i	0.710825	+	0.703369i	$0.248322\pi$
$578$	−10.5576	−	10.0007i	−0.439140	−	0.415975i
$579$		0			0
$580$	−2.53743	+	15.4776i	−0.105361	+	0.642673i
$581$	−2.61510	−	3.85698i	−0.108493	−	0.160014i
$582$		0			0
$583$	−10.6133	−	12.4949i	−0.439556	−	0.517485i
$584$	17.5254	+	106.900i	0.725206	+	4.42356i
$585$		0			0
$586$	8.59728	−	30.9646i	0.355150	−	1.27914i
$587$	13.7524	−	25.9397i	0.567622	−	1.07065i	−0.419056	−	0.907960i	$-0.637639\pi$
$587$	13.7524	−	25.9397i	0.567622	−	1.07065i	0.986678	−	0.162687i	$-0.0520162\pi$
$588$		0			0
$589$	1.98245			0.0816853
$590$	5.66666	−	7.81471i	0.233293	−	0.321726i
$591$		0			0
$592$	115.183	−	87.5600i	4.73400	−	3.59869i
$593$	11.9254	−	22.4937i	0.489718	−	0.923707i	−0.508324	−	0.861166i	$-0.669735\pi$
$593$	11.9254	−	22.4937i	0.489718	−	0.923707i	0.998042	−	0.0625409i	$-0.0199204\pi$
$594$		0			0
$595$	0.871844	−	0.825855i	0.0357421	−	0.0338567i
$596$	−4.79076	−	29.2224i	−0.196237	−	1.19699i
$597$		0			0
$598$	0.942081	+	2.36444i	0.0385246	+	0.0966893i
$599$	17.6632	+	26.0512i	0.721698	+	1.06442i	0.994741	+	0.102423i	$0.0326595\pi$
$599$	17.6632	+	26.0512i	0.721698	+	1.06442i	−0.273043	+	0.962002i	$0.588030\pi$
$600$		0			0
$601$	−2.99384	+	1.80133i	−0.122121	+	0.0734778i	−0.575304	−	0.817940i	$-0.695116\pi$
$601$	−2.99384	+	1.80133i	−0.122121	+	0.0734778i	0.453183	+	0.891418i	$0.350289\pi$
$602$	−4.49988	−	4.26251i	−0.183401	−	0.173727i
$603$		0			0
$604$	−30.0583	−	6.61633i	−1.22305	−	0.269215i
$605$	−0.879278	−	3.16687i	−0.0357477	−	0.128752i
$606$		0			0
$607$	−3.69432	+	4.34929i	−0.149948	+	0.176532i	−0.832008	−	0.554764i	$-0.812809\pi$
$607$	−3.69432	+	4.34929i	−0.149948	+	0.176532i	0.682060	+	0.731296i	$0.261084\pi$
$608$	−111.655	−	37.6209i	−4.52820	−	1.52573i
$609$		0			0
$610$	−0.665739	−	1.25572i	−0.0269550	−	0.0508425i
$611$	0.493338	−	0.108592i	0.0199583	−	0.00439316i
$612$		0			0
$613$	34.0157	−	11.4612i	1.37388	−	0.462915i	0.466984	−	0.884266i	$-0.345340\pi$
$613$	34.0157	−	11.4612i	1.37388	−	0.462915i	0.906898	+	0.421351i	$0.138444\pi$
$614$	24.8246	+	2.69983i	1.00184	+	0.108956i
$615$		0			0
$616$	−0.589979	−	10.8815i	−0.0237709	−	0.438429i
$617$	−4.59512	+	0.499749i	−0.184992	+	0.0201191i	−0.200146	−	0.979766i	$-0.564142\pi$
$617$	−4.59512	+	0.499749i	−0.184992	+	0.0201191i	0.0151538	+	0.999885i	$0.495176\pi$
$618$		0			0
$619$	28.5385	+	21.6944i	1.14706	+	0.871973i	0.993235	−	0.116125i	$-0.0370474\pi$
$619$	28.5385	+	21.6944i	1.14706	+	0.871973i	0.153826	+	0.988098i	$0.450840\pi$
$620$	0.869297	+	0.660822i	0.0349118	+	0.0265393i
$621$		0			0
$622$	−11.7070	+	1.27322i	−0.469409	+	0.0510513i
$623$	−0.407781	−	7.52107i	−0.0163374	−	0.301325i
$624$		0			0
$625$	−21.8092	−	2.37189i	−0.872368	−	0.0948757i
$626$	−26.9181	+	9.06978i	−1.07587	+	0.362501i
$627$		0			0
$628$	−46.8502	+	10.3125i	−1.86953	+	0.411514i
$629$	19.4609	+	36.7071i	0.775955	+	1.46361i
$630$		0			0
$631$	−5.22943	−	1.76200i	−0.208180	−	0.0701441i	0.213279	−	0.976991i	$-0.431586\pi$
$631$	−5.22943	−	1.76200i	−0.208180	−	0.0701441i	−0.421460	+	0.906847i	$0.638482\pi$
$632$	15.9756	−	18.8080i	0.635477	−	0.748141i
$633$		0			0
$634$	18.4756	+	66.5430i	0.733759	+	2.64276i
$635$	7.81595	+	1.72042i	0.310166	+	0.0682728i
$636$		0			0
$637$	1.26618	+	1.19939i	0.0501680	+	0.0475217i
$638$	−28.1635	+	16.9454i	−1.11500	+	0.670876i
$639$		0			0
$640$	−13.2421	−	19.5306i	−0.523440	−	0.772016i
$641$	12.6621	+	31.7796i	0.500125	+	1.25522i	0.934974	+	0.354715i	$0.115422\pi$
$641$	12.6621	+	31.7796i	0.500125	+	1.25522i	−0.434850	+	0.900503i	$0.643198\pi$
$642$		0			0
$643$	−6.94337	−	42.3527i	−0.273820	−	1.67023i	−0.662659	−	0.748922i	$-0.730572\pi$
$643$	−6.94337	−	42.3527i	−0.273820	−	1.67023i	0.388839	−	0.921306i	$-0.372876\pi$
$644$	−8.07720	+	7.65113i	−0.318286	+	0.301497i
$645$		0			0
$646$	28.3882	−	53.5459i	1.11692	−	2.10673i
$647$	19.9736	−	15.1835i	0.785242	−	0.596925i	−0.133835	−	0.991004i	$-0.542729\pi$
$647$	19.9736	−	15.1835i	0.785242	−	0.596925i	0.919077	+	0.394078i	$0.128936\pi$
$648$		0			0
$649$	14.8823	−	1.14459i	0.584183	−	0.0449292i
$650$	−3.45287			−0.135433
$651$		0			0
$652$	12.8898	−	24.3127i	0.504803	−	0.952160i
$653$	7.01168	−	25.2538i	0.274388	−	0.988257i	−0.690009	−	0.723800i	$-0.742394\pi$
$653$	7.01168	−	25.2538i	0.274388	−	0.988257i	0.964398	−	0.264457i	$-0.0851926\pi$
$654$		0			0
$655$	0.0136046	+	0.0829843i	0.000531575	+	0.00324247i
$656$	35.4284	+	41.7095i	1.38325	+	1.62848i
$657$		0			0
$658$	1.67941	+	2.47694i	0.0654700	+	0.0965611i
$659$	1.20967	−	7.37866i	0.0471221	−	0.287432i	−0.952744	−	0.303773i	$-0.901754\pi$
$659$	1.20967	−	7.37866i	0.0471221	−	0.287432i	0.999866	+	0.0163412i	$0.00520181\pi$
$660$		0			0
$661$	−32.4775	−	30.7643i	−1.26323	−	1.19659i	−0.970689	−	0.240340i	$-0.922741\pi$
$661$	−32.4775	−	30.7643i	−1.26323	−	1.19659i	−0.292540	−	0.956253i	$-0.594500\pi$
$662$	6.27457	−	9.25429i	0.243868	−	0.359678i
$663$		0			0
$664$	−22.3428	−	80.4717i	−0.867071	−	3.12291i
$665$	1.01405	+	0.610134i	0.0393232	+	0.0236600i
$666$		0			0
$667$	20.5024	+	6.90807i	0.793856	+	0.267481i
$668$	67.3443	+	31.1568i	2.60563	+	1.20549i
$669$		0			0
$670$	5.65183	−	1.24406i	0.218349	−	0.0480623i
$671$	0.813452	−	2.04161i	0.0314030	−	0.0788155i
$672$		0			0
$673$	0.342285	+	0.0372257i	0.0131941	+	0.00143495i	0.114714	−	0.993399i	$-0.463405\pi$
$673$	0.342285	+	0.0372257i	0.0131941	+	0.00143495i	−0.101520	+	0.994834i	$0.532370\pi$
$674$	2.41640	−	44.5679i	0.0930763	−	1.71669i
$675$		0			0
$676$	72.3738	−	7.87113i	2.78361	−	0.302736i
$677$	−17.6552	+	8.16815i	−0.678544	+	0.313928i	−0.728719	−	0.684813i	$-0.759884\pi$
$677$	−17.6552	+	8.16815i	−0.678544	+	0.313928i	0.0501756	+	0.998740i	$0.484022\pi$
$678$		0			0
$679$	−1.14156	−	0.867792i	−0.0438091	−	0.0333028i
$680$	19.5333	−	9.03708i	0.749069	−	0.346556i
$681$		0			0
$682$	0.123888	+	2.28498i	0.00474391	+	0.0874963i
$683$	0.744241	−	13.7267i	0.0284776	−	0.525239i	−0.949141	−	0.314852i	$-0.898045\pi$
$683$	0.744241	−	13.7267i	0.0284776	−	0.525239i	0.977618	−	0.210386i	$-0.0674722\pi$
$684$		0			0
$685$	5.26997	−	1.77566i	0.201355	−	0.0678445i
$686$	−7.82762	+	19.6458i	−0.298860	+	0.750082i
$687$		0			0
$688$	−30.8770	−	58.2402i	−1.17717	−	2.22039i
$689$	−1.99695	−	0.923888i	−0.0760778	−	0.0351973i
$690$		0			0
$691$	−12.4402	+	14.6457i	−0.473247	+	0.557149i	−0.946051	−	0.324019i	$-0.894966\pi$
$691$	−12.4402	+	14.6457i	−0.473247	+	0.557149i	0.472804	+	0.881168i	$0.343242\pi$
$692$	−66.4016	−	39.9525i	−2.52421	−	1.51877i
$693$		0			0
$694$	10.5082	+	2.31304i	0.398888	+	0.0878018i
$695$	4.98871	−	7.35779i	0.189232	−	0.279097i
$696$		0			0
$697$	−13.4651	+	8.10165i	−0.510025	+	0.306872i
$698$	2.55969	−	15.6134i	0.0968857	−	0.590977i
$699$		0			0
$700$	−5.58660	−	14.0213i	−0.211153	−	0.529955i
$701$	4.90487	+	5.77446i	0.185254	+	0.218098i	0.846948	−	0.531676i	$-0.178438\pi$
$701$	4.90487	+	5.77446i	0.185254	+	0.218098i	−0.661693	+	0.749775i	$0.730162\pi$
$702$		0			0
$703$	−29.7247	+	28.1567i	−1.12109	+	1.06195i
$704$	19.2991	−	69.5092i	0.727364	−	2.61973i
$705$		0			0
$706$	19.6706	−	14.9532i	0.740311	−	0.562770i
$707$	−7.51537			−0.282645
$708$		0			0
$709$	39.9384			1.49992			0.749960	−	0.661483i	$-0.230073\pi$
$709$	39.9384			1.49992			0.749960	+	0.661483i	$0.230073\pi$
$710$	−2.52799	+	1.92173i	−0.0948737	+	0.0721211i
$711$		0			0
$712$	36.1140	−	130.071i	1.35343	−	4.87461i
$713$	1.09353	−	1.03585i	0.0409530	−	0.0387927i
$714$		0			0
$715$	0.149281	+	0.175747i	0.00558278	+	0.00657255i
$716$	−9.86470	−	24.7585i	−0.368661	−	0.925269i
$717$		0			0
$718$	−9.15303	+	55.8310i	−0.341588	+	2.08359i
$719$	−28.8259	+	17.3440i	−1.07503	+	0.646822i	−0.939012	−	0.343885i	$-0.888257\pi$
$719$	−28.8259	+	17.3440i	−1.07503	+	0.646822i	−0.136014	+	0.990707i	$0.543429\pi$
$720$		0			0
$721$	−3.41811	+	5.04134i	−0.127297	+	0.187749i
$722$	7.07517	+	1.55736i	0.263311	+	0.0579590i
$723$		0			0
$724$	92.2199	+	55.4869i	3.42733	+	2.06215i
$725$	−19.0009	+	22.3696i	−0.705677	+	0.830788i
$726$		0			0
$727$	−16.3607	−	7.56925i	−0.606784	−	0.280728i	0.0923415	−	0.995727i	$-0.470565\pi$
$727$	−16.3607	−	7.56925i	−0.606784	−	0.280728i	−0.699125	+	0.714999i	$0.746427\pi$
$728$	−0.685096	−	1.29223i	−0.0253914	−	0.0478932i
$729$		0			0
$730$	5.02624	−	12.6149i	0.186029	−	0.466899i
$731$	17.9379	−	6.04398i	0.663457	−	0.223545i
$732$		0			0
$733$	1.92477	−	35.5003i	0.0710929	−	1.31123i	−0.717605	−	0.696451i	$-0.754761\pi$
$733$	1.92477	−	35.5003i	0.0710929	−	1.31123i	0.788698	−	0.614781i	$-0.210756\pi$
$734$	−4.74167	−	87.4550i	−0.175018	−	3.22802i
$735$		0			0
$736$	−81.2468	+	37.5888i	−2.99480	+	1.38554i
$737$	7.12387	+	5.41543i	0.262411	+	0.199480i
$738$		0			0
$739$	−28.5154	+	13.1926i	−1.04895	+	0.485298i	−0.867156	−	0.498037i	$-0.834054\pi$
$739$	−28.5154	+	13.1926i	−1.04895	+	0.485298i	−0.181799	+	0.983336i	$0.558192\pi$
$740$	−22.4198	+	2.43831i	−0.824170	+	0.0896339i
$741$		0			0
$742$	0.705705	−	13.0160i	0.0259073	−	0.477831i
$743$	33.4440	+	3.63726i	1.22694	+	0.133438i	0.698550	−	0.715562i	$-0.253829\pi$
$743$	33.4440	+	3.63726i	1.22694	+	0.133438i	0.528393	+	0.849000i	$0.322795\pi$
$744$		0			0
$745$	−0.885844	+	2.22330i	−0.0324548	+	0.0814554i
$746$	48.8692	−	10.7569i	1.78923	−	0.393839i
$747$		0			0
$748$	46.8477	+	21.6740i	1.71292	+	0.792481i
$749$	7.74245	+	2.60873i	0.282903	+	0.0953211i
$750$		0			0
$751$	0.111877	+	0.0673144i	0.00408247	+	0.00245634i	0.517594	−	0.855627i	$-0.326828\pi$
$751$	0.111877	+	0.0673144i	0.00408247	+	0.00245634i	−0.513511	+	0.858083i	$0.671656\pi$
$752$	8.51453	+	30.6666i	0.310493	+	1.11830i
$753$		0			0
$754$	−2.47563	+	3.65128i	−0.0901571	+	0.132972i
$755$	1.80589	+	1.71063i	0.0657230	+	0.0622562i
$756$		0			0
$757$	2.98239	−	18.1918i	0.108397	−	0.661191i	−0.875604	−	0.483029i	$-0.839537\pi$
$757$	2.98239	−	18.1918i	0.108397	−	0.661191i	0.984001	−	0.178162i	$-0.0570152\pi$
$758$	−21.0083	−	30.9849i	−0.763056	−	1.12542i
$759$		0			0
$760$	13.7310	+	16.1654i	0.498077	+	0.586381i
$761$	−2.85579	−	17.4196i	−0.103522	−	0.631459i	−0.986717	−	0.162451i	$-0.948060\pi$
$761$	−2.85579	−	17.4196i	−0.103522	−	0.631459i	0.883194	−	0.469008i	$-0.155388\pi$
$762$		0			0
$763$	1.30897	−	4.71449i	0.0473879	−	0.170676i
$764$	−48.9288	+	92.2896i	−1.77018	+	3.33892i
$765$		0			0
$766$	−77.7261			−2.80836
$767$	1.74831	−	0.978120i	0.0631279	−	0.0353179i
$768$		0			0
$769$	−12.0412	+	9.15349i	−0.434217	+	0.330083i	−0.799343	−	0.600875i	$-0.794819\pi$
$769$	−12.0412	+	9.15349i	−0.434217	+	0.330083i	0.365126	+	0.930958i	$0.381026\pi$
$770$	−0.639873	+	1.20693i	−0.0230594	+	0.0434947i
$771$		0			0
$772$	12.6968	−	12.0271i	0.456968	−	0.432863i
$773$	3.71417	+	22.6555i	0.133590	+	0.814860i	0.965587	+	0.260080i	$0.0837491\pi$
$773$	3.71417	+	22.6555i	0.133590	+	0.814860i	−0.831997	+	0.554779i	$0.812803\pi$
$774$		0			0
$775$	0.756339	+	1.89827i	0.0271685	+	0.0681878i
$776$	−14.4222	−	21.2712i	−0.517727	−	0.763590i
$777$		0			0
$778$	−67.8834	+	40.8441i	−2.43374	+	1.46433i
$779$	−11.2429	−	10.6499i	−0.402820	−	0.381571i
$780$		0			0
$781$	−4.79541	−	1.05555i	−0.171593	−	0.0377706i
$782$	−12.3191	−	44.3693i	−0.440530	−	1.58664i
$783$		0			0
$784$	−71.1375	+	83.7496i	−2.54063	+	2.99106i
$785$	3.67413	+	1.23796i	0.131135	+	0.0441846i
$786$		0			0
$787$	−8.72867	−	16.4640i	−0.311143	−	0.586879i	0.677787	−	0.735258i	$-0.262939\pi$
$787$	−8.72867	−	16.4640i	−0.311143	−	0.586879i	−0.988930	+	0.148380i	$0.952594\pi$
$788$	−35.3926	+	7.79050i	−1.26081	+	0.277525i
$789$		0			0
$790$	−2.93148	+	0.987729i	−0.104297	+	0.0351418i
$791$	5.57941	+	0.606798i	0.198381	+	0.0215752i
$792$		0			0
$793$	−0.0159690	−	0.294531i	−0.000567075	−	0.0104591i
$794$	49.6903	−	5.40414i	1.76344	−	0.191786i
$795$		0			0
$796$	−57.0510	−	43.3690i	−2.02212	−	1.53718i
$797$	1.91562	+	1.45622i	0.0678548	+	0.0515819i	0.638552	−	0.769579i	$-0.279534\pi$
$797$	1.91562	+	1.45622i	0.0678548	+	0.0515819i	−0.570697	+	0.821161i	$0.693327\pi$
$798$		0			0
$799$	−9.08552	+	0.988110i	−0.321423	+	0.0349568i
$800$	−6.57490	−	121.267i	−0.232458	−	4.28743i
$801$		0			0
$802$	53.3083	+	5.79763i	1.88238	+	0.204721i
$803$	19.8984	−	6.70454i	0.702198	−	0.236598i
$804$		0			0
$805$	0.878156	−	0.193297i	0.0309509	−	0.00681282i
$806$	0.143861	+	0.271351i	0.00506730	+	0.00955793i
$807$		0			0
$808$	−127.640	−	43.0071i	−4.49038	−	1.51298i
$809$	−19.3198	+	22.7450i	−0.679247	+	0.799672i	−0.988486	−	0.151313i	$-0.951650\pi$
$809$	−19.3198	+	22.7450i	−0.679247	+	0.799672i	0.309239	+	0.950984i	$0.399926\pi$
$810$		0			0
$811$	−6.09940	−	21.9681i	−0.214179	−	0.771403i	−0.990075	−	0.140542i	$-0.955116\pi$
$811$	−6.09940	−	21.9681i	−0.214179	−	0.771403i	0.775896	−	0.630861i	$-0.217298\pi$
$812$	−18.8324	−	4.14533i	−0.660889	−	0.145473i
$813$		0			0
$814$	−34.3111	−	32.5012i	−1.20260	−	1.13917i
$815$	−1.90567	+	1.14661i	−0.0667529	+	0.0401639i
$816$		0			0
$817$	10.4683	+	15.4396i	0.366239	+	0.540163i
$818$	−9.66450	−	24.2561i	−0.337911	−	0.848094i
$819$		0			0
$820$	−1.38000	−	8.41762i	−0.0481916	−	0.293956i
$821$	−18.2222	+	17.2610i	−0.635961	+	0.602414i	−0.936208	−	0.351448i	$-0.885690\pi$
$821$	−18.2222	+	17.2610i	−0.635961	+	0.602414i	0.300247	+	0.953862i	$0.402931\pi$
$822$		0			0
$823$	14.7380	−	27.7988i	0.513734	−	0.969006i	−0.481950	−	0.876199i	$-0.660071\pi$
$823$	14.7380	−	27.7988i	0.513734	−	0.969006i	0.995684	−	0.0928069i	$-0.0295839\pi$
$824$	−86.9023	+	66.0614i	−3.02739	+	2.30136i
$825$		0			0
$826$	9.21666	+	7.47693i	0.320689	+	0.260156i
$827$	−10.5707			−0.367580			−0.183790	−	0.982966i	$-0.558837\pi$
$827$	−10.5707			−0.367580			−0.183790	+	0.982966i	$0.558837\pi$
$828$		0			0
$829$	−23.5498	+	44.4196i	−0.817919	+	1.54276i	0.0218166	+	0.999762i	$0.493055\pi$
$829$	−23.5498	+	44.4196i	−0.817919	+	1.54276i	−0.839735	+	0.542996i	$0.817290\pi$
$830$	−2.80079	+	10.0875i	−0.0972168	+	0.350143i
$831$		0			0
$832$	−1.56638	−	9.55452i	−0.0543046	−	0.331243i
$833$	−20.4273	−	24.0489i	−0.707764	−	0.833244i
$834$		0			0
$835$	−3.36546	−	4.96369i	−0.116467	−	0.171775i
$836$	−8.22965	+	50.1987i	−0.284629	+	1.73616i
$837$		0			0
$838$	−29.9423	−	28.3629i	−1.03434	−	0.979779i
$839$	−19.2563	+	28.4009i	−0.664801	+	0.980508i	0.334473	+	0.942405i	$0.391442\pi$
$839$	−19.2563	+	28.4009i	−0.664801	+	0.980508i	−0.999274	+	0.0381028i	$0.987869\pi$
$840$		0			0
$841$	2.27348	+	8.18833i	0.0783959	+	0.282356i
$842$	90.8658	+	54.6721i	3.13144	+	1.88413i
$843$		0			0
$844$	−136.933	−	46.1382i	−4.71344	−	1.58814i
$845$	−5.33994	−	2.47052i	−0.183700	−	0.0849885i
$846$		0			0
$847$	3.94639	−	0.868666i	0.135600	−	0.0298477i
$848$	51.3122	−	128.784i	1.76207	−	4.42246i
$849$		0			0
$850$	62.1029	+	6.75409i	2.13011	+	0.231663i
$851$	−1.68418	+	31.0628i	−0.0577328	+	1.06482i
$852$		0			0
$853$	26.8140	−	2.91620i	0.918094	−	0.0998488i	0.363145	−	0.931733i	$-0.381703\pi$
$853$	26.8140	−	2.91620i	0.918094	−	0.0998488i	0.554950	+	0.831884i	$0.312738\pi$
$854$	1.58591	−	0.733722i	0.0542689	−	0.0251075i
$855$		0			0
$856$	116.569	+	88.6131i	3.98423	+	3.02873i
$857$	−52.0485	+	24.0802i	−1.77794	+	0.822564i	−0.804391	+	0.594101i	$0.797508\pi$
$857$	−52.0485	+	24.0802i	−1.77794	+	0.822564i	−0.973552	+	0.228464i	$0.926630\pi$
$858$		0			0
$859$	3.06830	+	56.5914i	0.104689	+	1.93088i	0.307294	+	0.951615i	$0.400576\pi$
$859$	3.06830	+	56.5914i	0.104689	+	1.93088i	−0.202605	+	0.979260i	$0.564941\pi$
$860$	−0.556264	+	10.2597i	−0.0189684	+	0.349852i
$861$		0			0
$862$	57.2286	−	19.2826i	1.94921	−	0.656767i
$863$	8.05576	−	20.2184i	0.274221	−	0.688243i	−0.725779	−	0.687928i	$-0.758520\pi$
$863$	8.05576	−	20.2184i	0.274221	−	0.688243i	1.00000		0.000315051i	$-0.000100284\pi$
$864$		0			0
$865$	2.93369	+	5.53352i	0.0997483	+	0.188145i
$866$	−35.8352	−	16.5791i	−1.21773	−	0.563381i
$867$		0			0
$868$	−0.869131	+	1.02322i	−0.0295002	+	0.0347304i
$869$	−4.09859	−	2.46604i	−0.139035	−	0.0836546i
$870$		0			0
$871$	1.17295	+	0.258185i	0.0397438	+	0.00874826i
$872$	49.2103	−	72.5798i	1.66647	−	2.45786i
$873$		0			0
$874$	38.8833	−	23.3953i	1.31525	−	0.791358i
$875$	−0.403219	+	2.45953i	−0.0136313	+	0.0831472i
$876$		0			0
$877$	10.4297	+	26.1765i	0.352184	+	0.883916i	0.993203	+	0.116391i	$0.0371327\pi$
$877$	10.4297	+	26.1765i	0.352184	+	0.883916i	−0.641019	+	0.767525i	$0.721488\pi$
$878$	−33.4931	−	39.4312i	−1.13034	−	1.33074i
$879$		0			0
$880$	−10.5474	+	9.99104i	−0.355553	+	0.336798i
$881$	8.49212	−	30.5858i	0.286107	−	1.03046i	−0.671173	−	0.741301i	$-0.734209\pi$
$881$	8.49212	−	30.5858i	0.286107	−	1.03046i	0.957280	−	0.289163i	$-0.0933769\pi$
$882$		0			0
$883$	−13.8071	+	10.4959i	−0.464647	+	0.353215i	−0.811155	−	0.584832i	$-0.801161\pi$
$883$	−13.8071	+	10.4959i	−0.464647	+	0.353215i	0.346508	+	0.938047i	$0.387367\pi$
$884$	6.92796			0.233012
$885$		0			0
$886$	−49.4043			−1.65977
$887$	−35.8341	+	27.2404i	−1.20319	+	0.914642i	−0.997945	−	0.0640687i	$-0.979592\pi$
$887$	−35.8341	+	27.2404i	−1.20319	+	0.914642i	−0.205245	+	0.978711i	$0.565799\pi$
$888$		0			0
$889$	−2.63235	+	9.48086i	−0.0882861	+	0.317978i
$890$	−12.2852	+	11.6371i	−0.411800	+	0.390078i
$891$		0			0
$892$	76.6495	+	90.2388i	2.56642	+	3.02142i
$893$	−3.33360	−	8.36670i	−0.111555	−	0.279981i
$894$		0			0
$895$	−0.348473	+	2.12559i	−0.0116482	+	0.0710506i
$896$	24.8585	−	14.9569i	0.830465	−	0.499674i
$897$		0			0
$898$	28.8932	−	42.6143i	0.964179	−	1.42206i
$899$	2.54962	+	0.561214i	0.0850347	+	0.0187176i
$900$		0			0
$901$	34.1097	+	20.5231i	1.13636	+	0.683724i
$902$	11.5725	−	13.6242i	0.385322	−	0.453636i
$903$		0			0
$904$	91.2879	+	42.2343i	3.03619	+	1.40469i
$905$	−4.07436	−	7.68507i	−0.135436	−	0.255460i
$906$		0			0
$907$	10.0941	−	25.3343i	0.335169	−	0.841212i	−0.660720	−	0.750633i	$-0.729749\pi$
$907$	10.0941	−	25.3343i	0.335169	−	0.841212i	0.995889	−	0.0905793i	$-0.0288718\pi$
$908$	3.72125	−	1.25383i	0.123494	−	0.0416099i
$909$		0			0
$910$	−0.00992609	+	0.183076i	−0.000329047	+	0.00606891i
$911$	−2.18840	−	40.3627i	−0.0725050	−	1.33728i	−0.777867	−	0.628429i	$-0.783698\pi$
$911$	−2.18840	−	40.3627i	−0.0725050	−	1.33728i	0.705362	−	0.708847i	$-0.250784\pi$
$912$		0			0
$913$	−14.6920	+	6.79726i	−0.486236	+	0.224957i
$914$	76.6870	+	58.2959i	2.53658	+	1.92826i
$915$		0			0
$916$	45.8139	−	21.1958i	1.51373	−	0.700327i
$917$	−0.102783	+	0.0111783i	−0.00339418	+	0.000369139i
$918$		0			0
$919$	1.90808	−	35.1924i	0.0629417	−	1.16089i	−0.781026	−	0.624498i	$-0.785304\pi$
$919$	1.90808	−	35.1924i	0.0629417	−	1.16089i	0.843968	−	0.536393i	$-0.180214\pi$
$920$	16.0207	+	1.74236i	0.528187	+	0.0574437i
$921$		0			0
$922$	34.4083	−	86.3584i	1.13318	−	2.84406i
$923$	−0.643614	+	0.141670i	−0.0211848	+	0.00466313i
$924$		0			0
$925$	−38.3016	−	17.7202i	−1.25935	−	0.582637i
$926$	−58.3698	−	19.6671i	−1.91815	−	0.646301i
$927$		0			0
$928$	−132.949	−	79.9928i	−4.36427	−	2.62589i
$929$	2.83215	+	10.2005i	0.0929199	+	0.334667i	0.995369	−	0.0961297i	$-0.0306463\pi$
$929$	2.83215	+	10.2005i	0.0929199	+	0.334667i	−0.902449	+	0.430797i	$0.858233\pi$
$930$		0			0
$931$	17.4502	−	25.7372i	0.571908	−	0.843501i
$932$	46.5341	+	44.0794i	1.52428	+	1.44387i
$933$		0			0
$934$	6.95722	−	42.4372i	0.227647	−	1.38859i
$935$	−2.34116	−	3.45296i	−0.0765642	−	0.112924i
$936$		0			0
$937$	−38.5366	−	45.3688i	−1.25894	−	1.48213i	−0.807542	−	0.589810i	$-0.799203\pi$
$937$	−38.5366	−	45.3688i	−1.25894	−	1.48213i	−0.451394	−	0.892325i	$-0.649073\pi$
$938$	1.15110	+	7.02137i	0.0375846	+	0.229256i
$939$		0			0
$940$	1.32716	−	4.77998i	0.0432870	−	0.155906i
$941$	24.0840	−	45.4272i	0.785116	−	1.48089i	−0.0894570	−	0.995991i	$-0.528513\pi$
$941$	24.0840	−	45.4272i	0.785116	−	1.48089i	0.874573	−	0.484895i	$-0.161142\pi$
$942$		0			0
$943$	−11.7663			−0.383164
$944$	67.4992	+	106.654i	2.19691	+	3.47128i
$945$		0			0
$946$	−17.1416	+	13.0307i	−0.557320	+	0.423664i
$947$	−7.34190	+	13.8483i	−0.238580	+	0.450009i	−0.973671	−	0.227960i	$-0.926795\pi$
$947$	−7.34190	+	13.8483i	−0.238580	+	0.450009i	0.735091	+	0.677969i	$0.237139\pi$
$948$		0			0
$949$	2.04598	−	1.93806i	0.0664154	−	0.0629120i
$950$	9.95958	+	60.7508i	0.323132	+	1.97102i
$951$		0			0
$952$	9.79434	+	24.5819i	0.317436	+	0.796705i
$953$	−9.23932	−	13.6270i	−0.299291	−	0.441421i	0.648074	−	0.761578i	$-0.275575\pi$
$953$	−9.23932	−	13.6270i	−0.299291	−	0.441421i	−0.947365	+	0.320156i	$0.896265\pi$
$954$		0			0
$955$	7.23381	−	4.35244i	0.234081	−	0.140842i
$956$	−27.6971	−	26.2361i	−0.895790	−	0.848537i
$957$		0			0
$958$	26.0656	+	5.73748i	0.842142	+	0.185370i
$959$	1.82914	+	6.58796i	0.0590659	+	0.212736i
$960$		0			0
$961$	−19.9513	+	23.4885i	−0.643591	+	0.757693i
$962$	−6.01105	−	2.02536i	−0.193804	−	0.0653002i
$963$		0			0
$964$	31.7167	+	59.8241i	1.02153	+	1.92681i
$965$	−1.38040	+	0.303849i	−0.0444367	+	0.00978126i
$966$		0			0
$967$	−34.0867	+	11.4851i	−1.09615	+	0.369338i	−0.808559	−	0.588415i	$-0.799752\pi$
$967$	−34.0867	+	11.4851i	−1.09615	+	0.369338i	−0.287595	+	0.957752i	$0.592856\pi$
$968$	71.9961	+	7.83005i	2.31404	+	0.251667i
$969$		0			0
$970$	0.174412	+	3.21683i	0.00560002	+	0.103286i
$971$	−8.77295	+	0.954116i	−0.281537	+	0.0306190i	−0.247798	−	0.968812i	$-0.579707\pi$
$971$	−8.77295	+	0.954116i	−0.281537	+	0.0306190i	−0.0337391	+	0.999431i	$0.510742\pi$
$972$		0			0
$973$	8.70085	+	6.61422i	0.278937	+	0.212042i
$974$	34.1297	+	25.9447i	1.09359	+	0.831323i
$975$		0			0
$976$	18.4751	−	2.00929i	0.591374	−	0.0643158i
$977$	−1.18540	−	21.8634i	−0.0379242	−	0.699471i	−0.954245	−	0.299026i	$-0.903338\pi$
$977$	−1.18540	−	21.8634i	−0.0379242	−	0.699471i	0.916321	−	0.400445i	$-0.131145\pi$
$978$		0			0
$979$	−26.0126	−	2.82904i	−0.831365	−	0.0904164i
$980$	16.2310	−	5.46886i	0.518481	−	0.174696i
$981$		0			0
$982$	−56.2274	+	12.3766i	−1.79429	+	0.394952i
$983$	−26.6755	−	50.3153i	−0.850816	−	1.60481i	−0.795192	−	0.606358i	$-0.792630\pi$
$983$	−26.6755	−	50.3153i	−0.850816	−	1.60481i	−0.0556239	−	0.998452i	$-0.517715\pi$
$984$		0			0
$985$	2.77559	+	0.935204i	0.0884375	+	0.0297981i
$986$	51.6685	−	60.8289i	1.64546	−	1.93719i
$987$		0			0
$988$	1.82651	+	6.57848i	0.0581089	+	0.209289i
$989$	13.8417	+	3.04679i	0.440140	+	0.0968822i
$990$		0			0
$991$	19.7502	+	18.7084i	0.627387	+	0.594293i	0.933883	−	0.357579i	$-0.116398\pi$
$991$	19.7502	+	18.7084i	0.627387	+	0.594293i	−0.306496	+	0.951872i	$0.599156\pi$
$992$	−9.25607	+	5.56919i	−0.293880	+	0.176822i
$993$		0			0
$994$	−2.19097	−	3.23144i	−0.0694934	−	0.102495i
$995$	2.14379	+	5.38051i	0.0679627	+	0.170574i
$996$		0			0
$997$	0.497262	+	3.03317i	0.0157485	+	0.0960614i	0.993531	−	0.113560i	$-0.0362253\pi$
$997$	0.497262	+	3.03317i	0.0157485	+	0.0960614i	−0.977783	+	0.209621i	$0.932777\pi$
$998$	−8.61909	+	8.16444i	−0.272833	+	0.258441i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.a.262.4		112
3.2	odd	2		59.2.c.a.26.1	yes	112
12.11	even	2		944.2.m.c.321.1		112
59.25	even	29	inner	531.2.i.a.379.4		112
177.5	odd	58		3481.2.a.p.1.1		56
177.113	even	58		3481.2.a.q.1.56		56
177.143	odd	58		59.2.c.a.25.1	✓	112
708.143	even	58		944.2.m.c.497.1		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.25.1	✓	112	177.143	odd	58
59.2.c.a.26.1	yes	112	3.2	odd	2
531.2.i.a.262.4		112	1.1	even	1	trivial
531.2.i.a.379.4		112	59.25	even	29	inner
944.2.m.c.321.1		112	12.11	even	2
944.2.m.c.497.1		112	708.143	even	58
3481.2.a.p.1.1		56	177.5	odd	58
3481.2.a.q.1.56		56	177.113	even	58

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19893 - 1.67159i) q^{2} +(1.50605 - 5.42431i) q^{4} +(-0.330311 + 0.312887i) q^{5} +(-0.362135 - 0.426338i) q^{7} +(-3.71073 - 9.31322i) q^{8} +(-0.203314 + 1.24016i) q^{10} +(-1.66508 + 1.00184i) q^{11} +(-0.146364 + 0.215870i) q^{13} +(-1.50897 - 0.332149i) q^{14} +(-14.0801 - 8.47172i) q^{16} +(3.05473 - 3.59631i) q^{17} +(4.22025 + 1.95250i) q^{19} +(1.19973 + 2.26293i) q^{20} +(-1.98672 + 4.98630i) q^{22} +(3.34811 - 1.12811i) q^{23} +(-0.259488 + 4.78597i) q^{25} +(0.0390017 + 0.719343i) q^{26} +(-2.85798 + 1.32224i) q^{28} +(4.87493 + 3.70583i) q^{29} +(0.386926 - 0.179011i) q^{31} +(-25.1895 + 2.73952i) q^{32} +(0.705614 - 13.0143i) q^{34} +(0.253012 + 0.0275168i) q^{35} +(-3.25905 + 8.17960i) q^{37} +(12.5438 - 2.76110i) q^{38} +(4.13968 + 1.91522i) q^{40} +(-3.15602 - 1.06339i) q^{41} +(3.43733 + 2.06817i) q^{43} +(2.92661 + 10.5407i) q^{44} +(5.47654 - 8.07730i) q^{46} +(-1.40614 - 1.33196i) q^{47} +(1.08185 - 6.59900i) q^{49} +(7.42956 + 10.9578i) q^{50} +(0.950515 + 1.11903i) q^{52} +(1.36486 + 8.32531i) q^{53} +(0.236529 - 0.851900i) q^{55} +(-2.62679 + 4.95466i) q^{56} +16.9142 q^{58} +(-6.86593 - 3.44368i) q^{59} +(-0.900340 + 0.684420i) q^{61} +(0.551592 - 1.04041i) q^{62} +(-26.9511 + 25.5294i) q^{64} +(-0.0191975 - 0.117099i) q^{65} +(-1.70447 - 4.27791i) q^{67} +(-14.9069 - 21.9860i) q^{68} +(0.602354 - 0.362424i) q^{70} +(1.83446 + 1.73769i) q^{71} +(-10.5528 - 2.32285i) q^{73} +(6.50647 + 23.4342i) q^{74} +(16.9469 - 19.9514i) q^{76} +(1.03011 + 0.347083i) q^{77} +(1.15299 + 2.17477i) q^{79} +(7.30150 - 1.60718i) q^{80} +(-8.71741 + 2.93724i) q^{82} +(8.28172 + 0.900691i) q^{83} +(0.116227 + 2.14369i) q^{85} +(11.0156 - 1.19802i) q^{86} +(15.5090 + 11.7897i) q^{88} +(10.7195 + 8.14876i) q^{89} +(0.145037 - 0.0157737i) q^{91} +(-1.07679 - 19.8602i) q^{92} +(-5.31849 - 0.578420i) q^{94} +(-2.00491 + 0.675531i) q^{95} +(2.50354 - 0.551071i) q^{97} +(-8.65188 - 16.3192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 26 q^{2} - 30 q^{4} + 25 q^{5} - 23 q^{7} + 8 q^{8} - 3 q^{10} + 15 q^{11} - 23 q^{13} - 13 q^{14} - 8 q^{16} + 10 q^{17} - 15 q^{19} - 7 q^{20} - q^{22} - 3 q^{23} - 5 q^{25} - 5 q^{26} + 29 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 112 * q + 26 * q^2 - 30 * q^4 + 25 * q^5 - 23 * q^7 + 8 * q^8 - 3 * q^10 + 15 * q^11 - 23 * q^13 - 13 * q^14 - 8 * q^16 + 10 * q^17 - 15 * q^19 - 7 * q^20 - q^22 - 3 * q^23 - 5 * q^25 - 5 * q^26 + 29 * q^28 + 13 * q^29 + 3 * q^31 - 36 * q^32 + 27 * q^34 - 28 * q^35 - 9 * q^37 - 31 * q^38 + 79 * q^40 - 23 * q^41 + 19 * q^43 - 43 * q^44 - 31 * q^46 - 10 * q^47 - 31 * q^49 + 60 * q^50 - 75 * q^52 + 23 * q^53 - 24 * q^55 + 103 * q^56 + 12 * q^58 + 33 * q^59 - 47 * q^61 + 39 * q^62 - 152 * q^64 + 16 * q^65 - 19 * q^67 + 5 * q^68 + 23 * q^70 + 18 * q^71 + 24 * q^73 - 19 * q^74 + 97 * q^76 - 65 * q^77 + 41 * q^79 - 107 * q^80 + 145 * q^82 - 49 * q^83 + 39 * q^85 - 111 * q^86 + 175 * q^88 - 51 * q^89 + 77 * q^91 - 135 * q^92 + 151 * q^94 - 65 * q^95 + 91 * q^97 - 31 * q^98

Introduction

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