LMFDB - Embedded newform 855.2.dl.a.127.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	855.127
Dual form			855.2.dl.a.478.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0741107 + 0.847089i) q^{2} +(1.25755 + 0.221740i) q^{4} +(-0.654653 - 2.13809i) q^{5} +(-3.83889 + 1.02863i) q^{7} +(-0.721192 + 2.69152i) q^{8} +(1.85967 - 0.396094i) q^{10} +(2.45629 + 4.25442i) q^{11} +(1.10589 + 0.515684i) q^{13} +(-0.586836 - 3.32811i) q^{14} +(0.173363 + 0.0630990i) q^{16} +(1.40281 + 0.122730i) q^{17} +(-4.22304 + 1.07980i) q^{19} +(-0.349158 - 2.83391i) q^{20} +(-3.78591 + 1.76540i) q^{22} +(0.867092 + 1.23834i) q^{23} +(-4.14286 + 2.79941i) q^{25} +(-0.518789 + 0.898569i) q^{26} +(-5.05567 + 0.442314i) q^{28} +(-1.63627 - 1.37299i) q^{29} +(8.01543 + 4.62771i) q^{31} +(-2.42153 + 5.19298i) q^{32} +(-0.207926 + 1.17921i) q^{34} +(4.71244 + 7.53450i) q^{35} +(-6.74741 + 6.74741i) q^{37} +(-0.601718 - 3.65731i) q^{38} +(6.22685 - 0.220040i) q^{40} +(-0.783311 + 2.15213i) q^{41} +(-1.09842 - 0.769121i) q^{43} +(2.14553 + 5.89479i) q^{44} +(-1.11324 + 0.642730i) q^{46} +(0.434606 + 4.96757i) q^{47} +(7.61681 - 4.39757i) q^{49} +(-2.06432 - 3.71684i) q^{50} +(1.27636 + 0.893717i) q^{52} +(-7.59734 + 5.31972i) q^{53} +(7.48831 - 8.03693i) q^{55} -11.0743i q^{56} +(1.28431 - 1.28431i) q^{58} +(9.46359 - 7.94090i) q^{59} +(-1.09383 + 6.20343i) q^{61} +(-4.51411 + 6.44682i) q^{62} +(-3.89991 - 2.25161i) q^{64} +(0.378607 - 2.70208i) q^{65} +(8.76025 - 0.766422i) q^{67} +(1.73688 + 0.465396i) q^{68} +(-6.73163 + 3.43347i) q^{70} +(2.67473 - 0.471627i) q^{71} +(-0.139300 + 0.0649566i) q^{73} +(-5.21560 - 6.21571i) q^{74} +(-5.55010 + 0.421490i) q^{76} +(-13.8056 - 13.8056i) q^{77} +(1.57856 + 0.574548i) q^{79} +(0.0214188 - 0.411974i) q^{80} +(-1.76499 - 0.823030i) q^{82} +(-0.200296 - 0.747516i) q^{83} +(-0.655944 - 3.07967i) q^{85} +(0.732919 - 0.873459i) q^{86} +(-13.2223 + 3.54291i) q^{88} +(3.86114 - 1.40534i) q^{89} +(-4.77583 - 0.842108i) q^{91} +(0.815821 + 1.74953i) q^{92} -4.24019 q^{94} +(5.07334 + 8.32233i) q^{95} +(0.860973 - 9.84096i) q^{97} +(3.16065 + 6.77803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.0741107	+	0.847089i	−0.0524042	+	0.598983i	0.923908	+	0.382615i	$0.124976\pi$
$2$	−0.0741107	+	0.847089i	−0.0524042	+	0.598983i	−0.976312	+	0.216367i	$0.930579\pi$
$3$		0			0
$3$		0			0
$4$	1.25755	+	0.221740i	0.628774	+	0.110870i
$5$	−0.654653	−	2.13809i	−0.292770	−	0.956183i
$5$	−0.654653	−	2.13809i	−0.292770	−	0.956183i
$6$		0			0
$7$	−3.83889	+	1.02863i	−1.45096	+	0.388784i	−0.896359	−	0.443329i	$-0.853797\pi$
$7$	−3.83889	+	1.02863i	−1.45096	+	0.388784i	−0.554605	+	0.832114i	$0.687131\pi$
$8$	−0.721192	+	2.69152i	−0.254980	+	0.951597i
$9$		0			0
$10$	1.85967	−	0.396094i	0.588079	−	0.125256i
$11$	2.45629	+	4.25442i	0.740599	+	1.28275i	0.952223	+	0.305403i	$0.0987913\pi$
$11$	2.45629	+	4.25442i	0.740599	+	1.28275i	−0.211624	+	0.977351i	$0.567875\pi$
$12$		0			0
$13$	1.10589	+	0.515684i	0.306718	+	0.143025i	0.569883	−	0.821726i	$-0.306988\pi$
$13$	1.10589	+	0.515684i	0.306718	+	0.143025i	−0.263165	+	0.964751i	$0.584766\pi$
$14$	−0.586836	−	3.32811i	−0.156839	−	0.889476i
$15$		0			0
$16$	0.173363	+	0.0630990i	0.0433408	+	0.0157748i
$17$	1.40281	+	0.122730i	0.340231	+	0.0297663i	0.255991	−	0.966679i	$-0.417598\pi$
$17$	1.40281	+	0.122730i	0.340231	+	0.0297663i	0.0842397	+	0.996446i	$0.473154\pi$
$18$		0			0
$19$	−4.22304	+	1.07980i	−0.968831	+	0.247724i
$19$	−4.22304	+	1.07980i	−0.968831	+	0.247724i
$20$	−0.349158	−	2.83391i	−0.0780740	−	0.633682i
$21$		0			0
$22$	−3.78591	+	1.76540i	−0.807158	+	0.376384i
$23$	0.867092	+	1.23834i	0.180801	+	0.258211i	0.899315	−	0.437302i	$-0.144066\pi$
$23$	0.867092	+	1.23834i	0.180801	+	0.258211i	−0.718513	+	0.695513i	$0.755177\pi$
$24$		0			0
$25$	−4.14286	+	2.79941i	−0.828572	+	0.559882i
$26$	−0.518789	+	0.898569i	−0.101743	+	0.176224i
$27$		0			0
$28$	−5.05567	+	0.442314i	−0.955432	+	0.0835895i
$29$	−1.63627	−	1.37299i	−0.303847	−	0.254958i	0.478096	−	0.878307i	$-0.341327\pi$
$29$	−1.63627	−	1.37299i	−0.303847	−	0.254958i	−0.781943	+	0.623350i	$0.785771\pi$
$30$		0			0
$31$	8.01543	+	4.62771i	1.43961	+	0.831161i	0.997823	−	0.0659564i	$-0.0210098\pi$
$31$	8.01543	+	4.62771i	1.43961	+	0.831161i	0.441791	+	0.897118i	$0.354343\pi$
$32$	−2.42153	+	5.19298i	−0.428069	+	0.917997i
$33$		0			0
$34$	−0.207926	+	1.17921i	−0.0356590	+	0.202232i
$35$	4.71244	+	7.53450i	0.796547	+	1.27356i
$36$		0			0
$37$	−6.74741	+	6.74741i	−1.10927	+	1.10927i	−0.116021	+	0.993247i	$0.537014\pi$
$37$	−6.74741	+	6.74741i	−1.10927	+	1.10927i	−0.993247	+	0.116021i	$0.962986\pi$
$38$	−0.601718	−	3.65731i	−0.0976115	−	0.593294i
$39$		0			0
$40$	6.22685	−	0.220040i	0.984552	−	0.0347914i
$41$	−0.783311	+	2.15213i	−0.122333	+	0.336106i	−0.985710	−	0.168453i	$-0.946123\pi$
$41$	−0.783311	+	2.15213i	−0.122333	+	0.336106i	0.863377	+	0.504559i	$0.168345\pi$
$42$		0			0
$43$	−1.09842	−	0.769121i	−0.167507	−	0.117290i	0.486817	−	0.873504i	$-0.338158\pi$
$43$	−1.09842	−	0.769121i	−0.167507	−	0.117290i	−0.654324	+	0.756214i	$0.727047\pi$
$44$	2.14553	+	5.89479i	0.323450	+	0.888672i
$45$		0			0
$46$	−1.11324	+	0.642730i	−0.164138	+	0.0947654i
$47$	0.434606	+	4.96757i	0.0633939	+	0.724595i	0.959676	+	0.281110i	$0.0907026\pi$
$47$	0.434606	+	4.96757i	0.0633939	+	0.724595i	−0.896282	+	0.443485i	$0.853742\pi$
$48$		0			0
$49$	7.61681	−	4.39757i	1.08812	−	0.628224i
$50$	−2.06432	−	3.71684i	−0.291939	−	0.525640i
$51$		0			0
$52$	1.27636	+	0.893717i	0.176999	+	0.123936i
$53$	−7.59734	+	5.31972i	−1.04358	+	0.730719i	−0.963944	−	0.266105i	$-0.914263\pi$
$53$	−7.59734	+	5.31972i	−1.04358	+	0.730719i	−0.0796315	+	0.996824i	$0.525374\pi$
$54$		0			0
$55$	7.48831	−	8.03693i	1.00972	−	1.08370i
$56$		−	11.0743i		−	1.47987i
$57$		0			0
$58$	1.28431	−	1.28431i	0.168638	−	0.168638i
$59$	9.46359	−	7.94090i	1.23205	−	1.03382i	0.233952	−	0.972248i	$-0.424834\pi$
$59$	9.46359	−	7.94090i	1.23205	−	1.03382i	0.998103	−	0.0615685i	$-0.0196103\pi$
$60$		0			0
$61$	−1.09383	+	6.20343i	−0.140051	+	0.794268i	0.831158	+	0.556037i	$0.187679\pi$
$61$	−1.09383	+	6.20343i	−0.140051	+	0.794268i	−0.971209	+	0.238231i	$0.923432\pi$
$62$	−4.51411	+	6.44682i	−0.573293	+	0.818747i
$63$		0			0
$64$	−3.89991	−	2.25161i	−0.487489	−	0.281452i
$65$	0.378607	−	2.70208i	0.0469604	−	0.335152i
$66$		0			0
$67$	8.76025	−	0.766422i	1.07023	−	0.0936334i	0.461603	−	0.887087i	$-0.347274\pi$
$67$	8.76025	−	0.766422i	1.07023	−	0.0936334i	0.608631	+	0.793453i	$0.291719\pi$
$68$	1.73688	+	0.465396i	0.210628	+	0.0564376i
$69$		0			0
$70$	−6.73163	+	3.43347i	−0.804584	+	0.410378i
$71$	2.67473	−	0.471627i	0.317432	−	0.0559718i	−0.0126621	−	0.999920i	$-0.504031\pi$
$71$	2.67473	−	0.471627i	0.317432	−	0.0559718i	0.330094	+	0.943948i	$0.392919\pi$
$72$		0			0
$73$	−0.139300	+	0.0649566i	−0.0163038	+	0.00760259i	−0.430753	−	0.902470i	$-0.641752\pi$
$73$	−0.139300	+	0.0649566i	−0.0163038	+	0.00760259i	0.414449	+	0.910072i	$0.363974\pi$
$74$	−5.21560	−	6.21571i	−0.606302	−	0.722562i
$75$		0			0
$76$	−5.55010	+	0.421490i	−0.636640	+	0.0483482i
$77$	−13.8056	−	13.8056i	−1.57330	−	1.57330i
$78$		0			0
$79$	1.57856	+	0.574548i	0.177602	+	0.0646417i	0.429290	−	0.903167i	$-0.358764\pi$
$79$	1.57856	+	0.574548i	0.177602	+	0.0646417i	−0.251689	+	0.967808i	$0.580986\pi$
$80$	0.0214188	−	0.411974i	0.00239469	−	0.0460601i
$81$		0			0
$82$	−1.76499	−	0.823030i	−0.194911	−	0.0908885i
$83$	−0.200296	−	0.747516i	−0.0219854	−	0.0820505i	0.954062	−	0.299611i	$-0.0968568\pi$
$83$	−0.200296	−	0.747516i	−0.0219854	−	0.0820505i	−0.976047	+	0.217560i	$0.930190\pi$
$84$		0			0
$85$	−0.655944	−	3.07967i	−0.0711471	−	0.334037i
$86$	0.732919	−	0.873459i	0.0790327	−	0.0941875i
$87$		0			0
$88$	−13.2223	+	3.54291i	−1.40950	+	0.377675i
$89$	3.86114	−	1.40534i	0.409280	−	0.148966i	−0.129171	−	0.991622i	$-0.541232\pi$
$89$	3.86114	−	1.40534i	0.409280	−	0.148966i	0.538452	+	0.842656i	$0.319009\pi$
$90$		0			0
$91$	−4.77583	−	0.842108i	−0.500643	−	0.0882769i
$92$	0.815821	+	1.74953i	0.0850552	+	0.182402i
$93$		0			0
$94$	−4.24019			−0.437342
$95$	5.07334	+	8.32233i	0.520513	+	0.853853i
$96$		0			0
$97$	0.860973	−	9.84096i	0.0874185	−	0.999198i	−0.818152	−	0.575002i	$-0.805001\pi$
$97$	0.860973	−	9.84096i	0.0874185	−	0.999198i	0.905570	−	0.424196i	$-0.139443\pi$
$98$	3.16065	+	6.77803i	0.319273	+	0.684684i
$99$		0			0
$100$	−5.83058	+	2.60176i	−0.583058	+	0.260176i
$101$	−8.19112	+	2.98132i	−0.815047	+	0.296653i	−0.715707	−	0.698401i	$-0.753895\pi$
$101$	−8.19112	+	2.98132i	−0.815047	+	0.296653i	−0.0993398	+	0.995054i	$0.531673\pi$
$102$		0			0
$103$	0.0994278	−	0.371070i	0.00979691	−	0.0365626i	−0.960854	−	0.277054i	$-0.910642\pi$
$103$	0.0994278	−	0.371070i	0.00979691	−	0.0365626i	0.970651	+	0.240491i	$0.0773086\pi$
$104$	−2.18553	+	2.60462i	−0.214309	+	0.255404i
$105$		0			0
$106$	−3.94323	−	6.82988i	−0.383000	−	0.663376i
$107$	−2.22050	−	8.28702i	−0.214664	−	0.801137i	−0.986285	−	0.165054i	$-0.947220\pi$
$107$	−2.22050	−	8.28702i	−0.214664	−	0.801137i	0.771621	−	0.636083i	$-0.219446\pi$
$108$		0			0
$109$	1.11653	+	6.33215i	0.106944	+	0.606510i	0.990426	+	0.138045i	$0.0440818\pi$
$109$	1.11653	+	6.33215i	0.106944	+	0.606510i	−0.883482	+	0.468465i	$0.844807\pi$
$110$	6.25303	+	6.93889i	0.596203	+	0.661597i
$111$		0			0
$112$	−0.730427	−	0.0639041i	−0.0690189	−	0.00603837i
$113$	−11.4607	−	11.4607i	−1.07813	−	1.07813i	−0.996677	−	0.0814546i	$-0.974043\pi$
$113$	−11.4607	−	11.4607i	−1.07813	−	1.07813i	−0.0814546	−	0.996677i	$-0.525957\pi$
$114$		0			0
$115$	2.08003	−	2.66460i	0.193964	−	0.248475i
$116$	−1.75324	−	2.08942i	−0.162784	−	0.193998i
$117$		0			0
$118$	6.02529	+	8.60501i	0.554673	+	0.792156i
$119$	−5.51146	+	0.971819i	−0.505235	+	0.0890865i
$120$		0			0
$121$	−6.56670	+	11.3739i	−0.596973	+	1.03399i
$122$	−5.17379	−	1.38631i	−0.468413	−	0.125511i
$123$		0			0
$124$	9.05364	+	7.59691i	0.813041	+	0.682222i
$125$	8.69753	+	7.02517i	0.777931	+	0.628350i
$126$		0			0
$127$	1.58848	−	3.40651i	0.140955	−	0.302279i	−0.823139	−	0.567840i	$-0.807779\pi$
$127$	1.58848	−	3.40651i	0.140955	−	0.302279i	0.964094	+	0.265561i	$0.0855571\pi$
$128$	−4.37663	+	6.25048i	−0.386843	+	0.552469i
$129$		0			0
$130$	2.26085	+	0.520967i	0.198289	+	0.0456918i
$131$	6.85330	−	5.75060i	0.598775	−	0.502432i	−0.292277	−	0.956334i	$-0.594413\pi$
$131$	6.85330	−	5.75060i	0.598775	−	0.502432i	0.891052	+	0.453902i	$0.149968\pi$
$132$		0			0
$133$	15.1010	−	8.48917i	1.30943	−	0.736105i
$134$			7.47751i			0.645959i
$135$		0			0
$136$	−1.34202	+	3.68718i	−0.115077	+	0.316173i
$137$	4.67796	−	3.27554i	0.399665	−	0.279848i	−0.356415	−	0.934328i	$-0.616001\pi$
$137$	4.67796	−	3.27554i	0.399665	−	0.279848i	0.756080	+	0.654479i	$0.227112\pi$
$138$		0			0
$139$	−3.42015	−	9.39679i	−0.290094	−	0.797026i	−0.996052	−	0.0887722i	$-0.971706\pi$
$139$	−3.42015	−	9.39679i	−0.290094	−	0.797026i	0.705958	−	0.708253i	$-0.250517\pi$
$140$	4.25542	+	10.5199i	0.359648	+	0.889096i
$141$		0			0
$142$	0.201284	+	2.30069i	0.0168914	+	0.193069i
$143$	0.522445	+	5.97158i	0.0436891	+	0.499368i
$144$		0			0
$145$	−1.86439	+	4.39731i	−0.154829	+	0.365177i
$146$	−0.0447004	−	0.122813i	−0.00369943	−	0.0101641i
$147$		0			0
$148$	−9.98136	+	6.98902i	−0.820463	+	0.574494i
$149$	−1.44345	+	3.96584i	−0.118252	+	0.324894i	−0.984671	−	0.174424i	$-0.944194\pi$
$149$	−1.44345	+	3.96584i	−0.118252	+	0.324894i	0.866419	+	0.499318i	$0.166416\pi$
$150$		0			0
$151$		−	16.0056i		−	1.30252i	−0.758856	−	0.651258i	$-0.774242\pi$
$151$		−	16.0056i		−	1.30252i	0.758856	−	0.651258i	$-0.225758\pi$
$152$	0.139302	−	12.1451i	0.0112989	−	0.985101i
$153$		0			0
$154$	12.7177	−	10.6714i	1.02482	−	0.859930i
$155$	4.64714	−	20.1673i	0.373267	−	1.61987i
$156$		0			0
$157$	7.23463	−	10.3321i	0.577386	−	0.824593i	−0.419136	−	0.907923i	$-0.637667\pi$
$157$	7.23463	−	10.3321i	0.577386	−	0.824593i	0.996522	+	0.0833309i	$0.0265558\pi$
$158$	−0.603681	+	1.29460i	−0.0480263	+	0.102993i
$159$		0			0
$160$	12.6883	+	1.77784i	1.00310	+	0.140551i
$161$	−4.60245	−	3.86192i	−0.362724	−	0.304362i
$162$		0			0
$163$	10.3009	+	2.76013i	0.806833	+	0.216190i	0.638582	−	0.769554i	$-0.279521\pi$
$163$	10.3009	+	2.76013i	0.806833	+	0.216190i	0.168251	+	0.985744i	$0.446188\pi$
$164$	−1.46226	+	2.53271i	−0.114184	+	0.197772i
$165$		0			0
$166$	0.648057	−	0.114270i	0.0502990	−	0.00886907i
$167$	1.34413	+	1.91962i	0.104012	+	0.148545i	0.867784	−	0.496941i	$-0.165544\pi$
$167$	1.34413	+	1.91962i	0.104012	+	0.148545i	−0.763772	+	0.645486i	$0.776655\pi$
$168$		0			0
$169$	−7.39918	−	8.81800i	−0.569168	−	0.678308i
$170$	2.65737	−	0.327406i	0.203811	−	0.0251109i
$171$		0			0
$172$	−1.21077	−	1.21077i	−0.0923203	−	0.0923203i
$173$	12.5886	+	1.10136i	0.957090	+	0.0837345i	0.554986	−	0.831860i	$-0.312724\pi$
$173$	12.5886	+	1.10136i	0.957090	+	0.0837345i	0.402104	+	0.915594i	$0.368279\pi$
$174$		0			0
$175$	13.0244	−	15.0081i	0.984554	−	1.13450i
$176$	0.157380	+	0.892548i	0.0118630	+	0.0672784i
$177$		0			0
$178$	0.904298	+	3.37488i	0.0677800	+	0.252958i
$179$	−3.40041	−	5.88969i	−0.254159	−	0.440216i	0.710508	−	0.703689i	$-0.248465\pi$
$179$	−3.40041	−	5.88969i	−0.254159	−	0.440216i	−0.964667	+	0.263473i	$0.915132\pi$
$180$		0			0
$181$	12.5267	−	14.9288i	0.931106	−	1.10965i	−0.0626462	−	0.998036i	$-0.519954\pi$
$181$	12.5267	−	14.9288i	0.931106	−	1.10965i	0.993752	−	0.111613i	$-0.0356016\pi$
$182$	1.06728	−	3.98315i	0.0791121	−	0.295250i
$183$		0			0
$184$	−3.95835	+	1.44072i	−0.291813	+	0.106211i
$185$	18.8438	+	10.0094i	1.38542	+	0.735903i
$186$		0			0
$187$	2.92355	+	6.26958i	0.213791	+	0.458477i
$188$	−0.554970	+	6.34333i	−0.0404753	+	0.462635i
$189$		0			0
$190$	−7.42575	+	3.68080i	−0.538720	+	0.267033i
$191$	18.5918			1.34525			0.672627	−	0.739982i	$-0.265166\pi$
$191$	18.5918			1.34525			0.672627	+	0.739982i	$0.265166\pi$
$192$		0			0
$193$	−7.75406	−	16.6286i	−0.558149	−	1.19696i	−0.959676	−	0.281108i	$-0.909298\pi$
$193$	−7.75406	−	16.6286i	−0.558149	−	1.19696i	0.401527	−	0.915847i	$-0.368480\pi$
$194$	8.27237	+	1.45864i	0.593921	+	0.104724i
$195$		0			0
$196$	10.5536	−	3.84120i	0.753830	−	0.274372i
$197$	10.9281	−	2.92819i	0.778598	−	0.208625i	0.152431	−	0.988314i	$-0.451290\pi$
$197$	10.9281	−	2.92819i	0.778598	−	0.208625i	0.626166	+	0.779690i	$0.284623\pi$
$198$		0			0
$199$	−7.77099	+	9.26110i	−0.550871	+	0.656502i	−0.967588	−	0.252534i	$-0.918736\pi$
$199$	−7.77099	+	9.26110i	−0.550871	+	0.656502i	0.416717	+	0.909036i	$0.363180\pi$
$200$	−4.54689	−	13.1695i	−0.321514	−	0.931226i
$201$		0			0
$202$	−1.91840	−	7.15956i	−0.134978	−	0.503745i
$203$	7.69373	+	3.58765i	0.539994	+	0.251803i
$204$		0			0
$205$	5.11424	+	0.265893i	0.357194	+	0.0185708i
$206$	0.306960	+	0.111724i	0.0213870	+	0.00778421i
$207$		0			0
$208$	0.159181	+	0.159181i	0.0110372	+	0.0110372i
$209$	−14.9669	−	15.3142i	−1.03528	−	1.05931i
$210$		0			0
$211$	4.77188	+	5.68690i	0.328509	+	0.391502i	0.904866	−	0.425696i	$-0.139971\pi$
$211$	4.77188	+	5.68690i	0.328509	+	0.391502i	−0.576357	+	0.817198i	$0.695526\pi$
$212$	−10.7336	+	5.00517i	−0.737188	+	0.343756i
$213$		0			0
$214$	7.18441	−	1.26681i	0.491116	−	0.0865970i
$215$	−0.925368	+	2.85203i	−0.0631096	+	0.194507i
$216$		0			0
$217$	−35.5305	−	9.52038i	−2.41197	−	0.646285i
$218$	−5.44664	+	0.476520i	−0.368893	+	0.0322740i
$219$		0			0
$220$	11.1990	−	8.44637i	0.755037	−	0.569454i
$221$	1.48806	+	0.859131i	0.100098	+	0.0577914i
$222$		0			0
$223$	−8.33065	+	11.8974i	−0.557861	+	0.796708i	−0.994699	−	0.102832i	$-0.967210\pi$
$223$	−8.33065	+	11.8974i	−0.557861	+	0.796708i	0.436837	+	0.899540i	$0.356098\pi$
$224$	3.95433	−	22.4261i	0.264210	−	1.49841i
$225$		0			0
$226$	10.5576	−	8.85887i	0.702281	−	0.589283i
$227$	−3.07432	+	3.07432i	−0.204050	+	0.204050i	−0.801733	−	0.597683i	$-0.796088\pi$
$227$	−3.07432	+	3.07432i	−0.204050	+	0.204050i	0.597683	+	0.801733i	$0.296088\pi$
$228$		0			0
$229$			18.5866i			1.22824i	0.789214	+	0.614119i	$0.210488\pi$
$229$			18.5866i			1.22824i	−0.789214	+	0.614119i	$0.789512\pi$
$230$	2.10300	+	1.95945i	0.138668	+	0.129202i
$231$		0			0
$232$	4.87549	−	3.41386i	0.320092	−	0.224131i
$233$	18.0369	+	12.6296i	1.18164	+	0.827390i	0.988116	−	0.153707i	$-0.0491211\pi$
$233$	18.0369	+	12.6296i	1.18164	+	0.827390i	0.193519	+	0.981097i	$0.438010\pi$
$234$		0			0
$235$	10.3366	−	4.18126i	0.674286	−	0.272756i
$236$	13.6617	−	7.88760i	0.889303	−	0.513439i
$237$		0			0
$238$	−0.414760	−	4.74072i	−0.0268849	−	0.307295i
$239$	2.93366	−	1.69375i	0.189763	−	0.109560i	−0.402109	−	0.915592i	$-0.631723\pi$
$239$	2.93366	−	1.69375i	0.189763	−	0.109560i	0.591872	+	0.806032i	$0.298389\pi$
$240$		0			0
$241$	−0.0368288	−	0.101186i	−0.00237235	−	0.00651798i	0.938501	−	0.345277i	$-0.112215\pi$
$241$	−0.0368288	−	0.101186i	−0.00237235	−	0.00651798i	−0.940873	+	0.338759i	$0.889993\pi$
$242$	−9.14801	−	6.40550i	−0.588056	−	0.411761i
$243$		0			0
$244$	−2.75109	+	7.55856i	−0.176121	+	0.483887i
$245$	−14.3888	−	13.4066i	−0.919264	−	0.856513i
$246$		0			0
$247$	−5.22704	−	0.983611i	−0.332589	−	0.0625857i
$248$	−18.2363	+	18.2363i	−1.15800	+	1.15800i
$249$		0			0
$250$	−6.59552	+	6.84694i	−0.417138	+	0.433039i
$251$	−3.71248	+	21.0545i	−0.234330	+	1.32895i	0.609691	+	0.792639i	$0.291294\pi$
$251$	−3.71248	+	21.0545i	−0.234330	+	1.32895i	−0.844020	+	0.536311i	$0.819817\pi$
$252$		0			0
$253$	−3.13857	+	6.73067i	−0.197320	+	0.423154i
$254$	2.76790	+	1.59805i	0.173673	+	0.100270i
$255$		0			0
$256$	−11.8697	−	9.95986i	−0.741856	−	0.622491i
$257$	12.5607	−	1.09892i	0.783518	−	0.0685489i	0.311625	−	0.950205i	$-0.399127\pi$
$257$	12.5607	−	1.09892i	0.783518	−	0.0685489i	0.471892	+	0.881656i	$0.343571\pi$
$258$		0			0
$259$	18.9620	−	32.8431i	1.17824	−	2.04077i
$260$	1.07528	−	3.31405i	0.0666857	−	0.205528i
$261$		0			0
$262$	4.36337	+	6.23153i	0.269570	+	0.384985i
$263$	−24.1482	+	11.2605i	−1.48904	+	0.694351i	−0.985509	−	0.169626i	$-0.945744\pi$
$263$	−24.1482	+	11.2605i	−1.48904	+	0.694351i	−0.503532	+	0.863977i	$0.667966\pi$
$264$		0			0
$265$	16.3477	+	12.7612i	1.00423	+	0.783917i
$266$	6.07194	+	13.4211i	0.372294	+	0.822899i
$267$		0			0
$268$	11.1864	+	0.978681i	0.683317	+	0.0597825i
$269$	−12.1556	−	4.42428i	−0.741141	−	0.269753i	−0.0562682	−	0.998416i	$-0.517920\pi$
$269$	−12.1556	−	4.42428i	−0.741141	−	0.269753i	−0.684873	+	0.728662i	$0.740142\pi$
$270$		0			0
$271$	3.22437	+	18.2863i	0.195866	+	1.11081i	0.911180	+	0.412009i	$0.135173\pi$
$271$	3.22437	+	18.2863i	0.195866	+	1.11081i	−0.715313	+	0.698804i	$0.753716\pi$
$272$	0.235451	+	0.109793i	0.0142763	+	0.00665715i
$273$		0			0
$274$	2.42799	+	4.20540i	0.146680	+	0.254058i
$275$	−22.0859	−	10.7493i	−1.33183	−	0.648206i
$276$		0			0
$277$	−4.08087	+	15.2300i	−0.245195	+	0.915082i	0.728090	+	0.685482i	$0.240408\pi$
$277$	−4.08087	+	15.2300i	−0.245195	+	0.915082i	−0.973285	+	0.229600i	$0.926258\pi$
$278$	8.21339	−	2.20077i	0.492607	−	0.131994i
$279$		0			0
$280$	−23.6778	+	7.24982i	−1.41502	+	0.433259i
$281$	−0.225686	−	0.0397945i	−0.0134633	−	0.00237394i	0.166912	−	0.985972i	$-0.446620\pi$
$281$	−0.225686	−	0.0397945i	−0.0134633	−	0.00237394i	−0.180376	+	0.983598i	$0.557731\pi$
$282$		0			0
$283$	−1.12979	+	12.9136i	−0.0671591	+	0.767632i	0.885708	+	0.464243i	$0.153674\pi$
$283$	−1.12979	+	12.9136i	−0.0671591	+	0.767632i	−0.952867	+	0.303389i	$0.901882\pi$
$284$	3.46818			0.205799
$285$		0			0
$286$	−5.09718			−0.301403
$287$	0.793305	−	9.06752i	0.0468273	−	0.535239i
$288$		0			0
$289$	−14.7889	−	2.60769i	−0.869937	−	0.153393i
$290$	−3.58675	−	1.90519i	−0.210621	−	0.111877i
$291$		0			0
$292$	−0.189580	+	0.0507977i	−0.0110943	+	0.00297271i
$293$	−1.97297	+	7.36321i	−0.115262	+	0.430163i	−0.999306	−	0.0372396i	$-0.988144\pi$
$293$	−1.97297	+	7.36321i	−0.115262	+	0.430163i	0.884044	+	0.467403i	$0.154810\pi$
$294$		0			0
$295$	−23.1737	−	15.0355i	−1.34923	−	0.875400i
$296$	−13.2946	−	23.0270i	−0.772735	−	1.33842i
$297$		0			0
$298$	−3.25244	−	1.51664i	−0.188409	−	0.0878566i
$299$	0.320317	+	1.81661i	0.0185244	+	0.105057i
$300$		0			0
$301$	5.00785	+	1.82271i	0.288648	+	0.105059i
$302$	13.5582	+	1.18619i	0.780184	+	0.0682573i
$303$		0			0
$304$	−0.800253	−	0.0792713i	−0.0458977	−	0.00454652i
$305$	13.9796	−	1.72238i	0.800468	−	0.0986231i
$306$		0			0
$307$	24.9542	−	11.6364i	1.42421	−	0.664122i	0.450685	−	0.892683i	$-0.351180\pi$
$307$	24.9542	−	11.6364i	1.42421	−	0.664122i	0.973530	+	0.228561i	$0.0734022\pi$
$308$	−14.3000	−	20.4225i	−0.814817	−	1.16368i
$309$		0			0
$310$	16.7391	+	5.43115i	0.950715	+	0.308469i
$311$	−3.61837	+	6.26721i	−0.205179	+	0.355381i	−0.950190	−	0.311672i	$-0.899111\pi$
$311$	−3.61837	+	6.26721i	−0.205179	+	0.355381i	0.745011	+	0.667053i	$0.232444\pi$
$312$		0			0
$313$	−5.80964	+	0.508278i	−0.328381	+	0.0287296i	−0.250154	−	0.968206i	$-0.580481\pi$
$313$	−5.80964	+	0.508278i	−0.328381	+	0.0287296i	−0.0782264	+	0.996936i	$0.524926\pi$
$314$	8.21606	+	6.89409i	0.463659	+	0.389056i
$315$		0			0
$316$	1.85771	+	1.07255i	0.104504	+	0.0603356i
$317$	1.23887	−	2.65676i	0.0695818	−	0.149219i	−0.868441	−	0.495793i	$-0.834877\pi$
$317$	1.23887	−	2.65676i	0.0695818	−	0.149219i	0.938022	+	0.346574i	$0.112655\pi$
$318$		0			0
$319$	1.82213	−	10.3338i	0.102020	−	0.578582i
$320$	−2.26107	+	9.81238i	−0.126398	+	0.548529i
$321$		0			0
$322$	3.61248	−	3.61248i	0.201316	−	0.201316i
$323$	−6.05663	+	0.996463i	−0.337000	+	0.0554447i
$324$		0			0
$325$	−6.02516	+	0.959430i	−0.334215	+	0.0532196i
$326$	−3.10149	+	8.52127i	−0.171776	+	0.471949i
$327$		0			0
$328$	−5.22759	−	3.66040i	−0.288645	−	0.202112i
$329$	−6.77819	−	18.6229i	−0.373694	−	1.02671i
$330$		0			0
$331$	7.17253	−	4.14106i	0.394238	−	0.227613i	−0.289757	−	0.957100i	$-0.593574\pi$
$331$	7.17253	−	4.14106i	0.394238	−	0.227613i	0.683995	+	0.729487i	$0.260241\pi$
$332$	−0.0861283	−	0.984451i	−0.00472690	−	0.0540288i
$333$		0			0
$334$	−1.72571	+	0.996337i	−0.0944264	+	0.0545171i
$335$	−7.37360	−	18.2285i	−0.402863	−	0.995927i
$336$		0			0
$337$	12.2046	+	8.54575i	0.664827	+	0.465517i	0.856640	−	0.515915i	$-0.172548\pi$
$337$	12.2046	+	8.54575i	0.664827	+	0.465517i	−0.191813	+	0.981431i	$0.561437\pi$
$338$	8.01799	−	5.61426i	0.436121	−	0.305375i
$339$		0			0
$340$	−0.141995	−	4.01828i	−0.00770078	−	0.217922i
$341$			45.4680i			2.46223i
$342$		0			0
$343$	−5.04480	+	5.04480i	−0.272394	+	0.272394i
$344$	2.86228	−	2.40174i	0.154324	−	0.129493i
$345$		0			0
$346$	−1.86589	+	10.5820i	−0.100311	+	0.568892i
$347$	−3.73392	+	5.33259i	−0.200447	+	0.286268i	−0.906774	−	0.421618i	$-0.861462\pi$
$347$	−3.73392	+	5.33259i	−0.200447	+	0.286268i	0.706326	+	0.707887i	$0.250351\pi$
$348$		0			0
$349$	21.2321	+	12.2584i	1.13653	+	0.656176i	0.945569	−	0.325422i	$-0.105506\pi$
$349$	21.2321	+	12.2584i	1.13653	+	0.656176i	0.190961	+	0.981598i	$0.438840\pi$
$350$	11.7479	+	12.1451i	0.627954	+	0.649184i
$351$		0			0
$352$	−28.0410	+	2.45327i	−1.49459	+	0.130760i
$353$	18.5195	+	4.96227i	0.985691	+	0.264115i	0.715440	−	0.698675i	$-0.246226\pi$
$353$	18.5195	+	4.96227i	0.985691	+	0.264115i	0.270251	+	0.962790i	$0.412893\pi$
$354$		0			0
$355$	−2.75940	−	5.41006i	−0.146454	−	0.287136i
$356$	5.16719	−	0.911116i	0.273861	−	0.0482890i
$357$		0			0
$358$	5.24110	−	2.44397i	0.277001	−	0.129168i
$359$	12.6054	+	15.0226i	0.665289	+	0.792860i	0.988134	−	0.153592i	$-0.0490840\pi$
$359$	12.6054	+	15.0226i	0.665289	+	0.792860i	−0.322846	+	0.946452i	$0.604640\pi$
$360$		0			0
$361$	16.6681	−	9.12009i	0.877266	−	0.480005i
$362$	11.7177	+	11.7177i	0.615866	+	0.615866i
$363$		0			0
$364$	−5.81910	−	2.11798i	−0.305004	−	0.111012i
$365$	0.230076	+	0.255312i	0.0120427	+	0.0133636i
$366$		0			0
$367$	12.5944	+	5.87286i	0.657421	+	0.306561i	0.722552	−	0.691316i	$-0.242969\pi$
$367$	12.5944	+	5.87286i	0.657421	+	0.306561i	−0.0651311	+	0.997877i	$0.520747\pi$
$368$	0.0721840	+	0.269394i	0.00376285	+	0.0140431i
$369$		0			0
$370$	−9.87535	+	15.2206i	−0.513395	+	0.791280i
$371$	23.6934	−	28.2366i	1.23010	−	1.46597i
$372$		0			0
$373$	−35.6461	+	9.55135i	−1.84569	+	0.494550i	−0.999278	−	0.0379859i	$-0.987906\pi$
$373$	−35.6461	+	9.55135i	−1.84569	+	0.494550i	−0.846407	+	0.532536i	$0.821239\pi$
$374$	−5.52756	+	2.01187i	−0.285823	+	0.104031i
$375$		0			0
$376$	−13.6838	−	2.41282i	−0.705687	−	0.124432i
$377$	−1.10150	−	2.36217i	−0.0567300	−	0.121658i
$378$		0			0
$379$	−2.15198			−0.110540			−0.0552699	−	0.998471i	$-0.517602\pi$
$379$	−2.15198			−0.110540			−0.0552699	+	0.998471i	$0.517602\pi$
$380$	4.53457	+	11.5907i	0.232619	+	0.594590i
$381$		0			0
$382$	−1.37785	+	15.7489i	−0.0704969	+	0.805783i
$383$	−4.96338	−	10.6440i	−0.253617	−	0.543883i	0.737739	−	0.675086i	$-0.235894\pi$
$383$	−4.96338	−	10.6440i	−0.253617	−	0.543883i	−0.991355	+	0.131203i	$0.958116\pi$
$384$		0			0
$385$	−20.4798	+	38.5555i	−1.04375	+	1.96497i
$386$	14.6606	−	5.33602i	0.746205	−	0.271596i
$387$		0			0
$388$	3.26484	−	12.1846i	0.165747	−	0.618578i
$389$	−2.20372	+	2.62629i	−0.111733	+	0.133158i	−0.819012	−	0.573776i	$-0.805478\pi$
$389$	−2.20372	+	2.62629i	−0.111733	+	0.133158i	0.707279	+	0.706934i	$0.249922\pi$
$390$		0			0
$391$	1.06438	+	1.84356i	0.0538281	+	0.0932330i
$392$	6.34298	+	23.6723i	0.320369	+	1.19563i
$393$		0			0
$394$	1.67054	+	9.47412i	0.0841607	+	0.477299i
$395$	0.195029	−	3.75123i	0.00981296	−	0.188745i
$396$		0			0
$397$	8.57163	+	0.749921i	0.430198	+	0.0376375i	0.300199	−	0.953877i	$-0.402947\pi$
$397$	8.57163	+	0.749921i	0.430198	+	0.0376375i	0.129999	+	0.991514i	$0.458503\pi$
$398$	−7.26907	−	7.26907i	−0.364365	−	0.364365i
$399$		0			0
$400$	−0.894860	+	0.223905i	−0.0447430	+	0.0111952i
$401$	9.47424	+	11.2910i	0.473121	+	0.563844i	0.948841	−	0.315753i	$-0.102257\pi$
$401$	9.47424	+	11.2910i	0.473121	+	0.563844i	−0.475720	+	0.879597i	$0.657813\pi$
$402$		0			0
$403$	6.47774	+	9.25116i	0.322679	+	0.460833i
$404$	−10.9618	+	1.93286i	−0.545370	+	0.0961634i
$405$		0			0
$406$	−3.60924	+	6.25140i	−0.179124	+	0.310252i
$407$	−45.2799	−	12.1327i	−2.24444	−	0.601396i
$408$		0			0
$409$	−28.3413	−	23.7811i	−1.40139	−	1.17590i	−0.960480	−	0.278348i	$-0.910213\pi$
$409$	−28.3413	−	23.7811i	−1.40139	−	1.17590i	−0.440905	−	0.897554i	$-0.645342\pi$
$410$	−0.604255	+	4.31251i	−0.0298420	+	0.212980i
$411$		0			0
$412$	0.207316	−	0.444591i	0.0102137	−	0.0219034i
$413$	−28.1615	+	40.2187i	−1.38573	+	1.97903i
$414$		0			0
$415$	−1.46713	+	0.917615i	−0.0720187	+	0.0450439i
$416$	−5.35587	+	4.49411i	−0.262593	+	0.220342i
$417$		0			0
$418$	14.0817	−	11.5434i	0.688760	−	0.564605i
$419$			9.21192i			0.450032i	0.974355	+	0.225016i	$0.0722434\pi$
$419$			9.21192i			0.450032i	−0.974355	+	0.225016i	$0.927757\pi$
$420$		0			0
$421$	−0.789738	+	2.16979i	−0.0384895	+	0.105749i	−0.957449	−	0.288604i	$-0.906809\pi$
$421$	−0.789738	+	2.16979i	−0.0384895	+	0.105749i	0.918959	+	0.394353i	$0.129031\pi$
$422$	−5.17096	+	3.62074i	−0.251718	+	0.176255i
$423$		0			0
$424$	−8.83901	−	24.2850i	−0.429260	−	1.17938i
$425$	−6.15520	+	3.41858i	−0.298571	+	0.165826i
$426$		0			0
$427$	−2.18192	−	24.9394i	−0.105590	−	1.20690i
$428$	−0.954825	−	10.9137i	−0.0461532	−	0.527534i
$429$		0			0
$430$	−2.34734	−	0.995235i	−0.113199	−	0.0479945i
$431$	−6.23851	−	17.1402i	−0.300498	−	0.825612i	−0.994413	−	0.105556i	$-0.966338\pi$
$431$	−6.23851	−	17.1402i	−0.300498	−	0.825612i	0.693915	−	0.720057i	$-0.255884\pi$
$432$		0			0
$433$	17.8019	−	12.4651i	0.855507	−	0.599032i	−0.0614092	−	0.998113i	$-0.519559\pi$
$433$	17.8019	−	12.4651i	0.855507	−	0.599032i	0.916916	+	0.399080i	$0.130671\pi$
$434$	10.6978	−	29.3920i	0.513511	−	1.41086i
$435$		0			0
$436$			8.21056i			0.393215i
$437$	−4.99892	−	4.29324i	−0.239131	−	0.205374i
$438$		0			0
$439$	−7.23611	+	6.07181i	−0.345361	+	0.289792i	−0.798924	−	0.601432i	$-0.794597\pi$
$439$	−7.23611	+	6.07181i	−0.345361	+	0.289792i	0.453563	+	0.891224i	$0.350153\pi$
$440$	16.2311	+	25.9511i	0.773786	+	1.23717i
$441$		0			0
$442$	−0.838042	+	1.19685i	−0.0398616	+	0.0569282i
$443$	14.4220	−	30.9280i	0.685208	−	1.46943i	−0.188042	−	0.982161i	$-0.560214\pi$
$443$	14.4220	−	30.9280i	0.685208	−	1.46943i	0.873250	−	0.487273i	$-0.162008\pi$
$444$		0			0
$445$	−5.53246	−	7.33546i	−0.262264	−	0.347734i
$446$	−9.46077	−	7.93852i	−0.447980	−	0.375900i
$447$		0			0
$448$	17.2874	+	4.63214i	0.816752	+	0.218848i
$449$	−20.6242	+	35.7221i	−0.973316	+	1.68583i	−0.287931	+	0.957651i	$0.592967\pi$
$449$	−20.6242	+	35.7221i	−0.973316	+	1.68583i	−0.685385	+	0.728181i	$0.740366\pi$
$450$		0			0
$451$	−11.0801	+	1.95372i	−0.521741	+	0.0919970i
$452$	−11.8711	−	16.9537i	−0.558369	−	0.797433i
$453$		0			0
$454$	−2.37638	−	2.83206i	−0.111529	−	0.132915i
$455$	1.32601	+	10.7624i	0.0621642	+	0.504551i
$456$		0			0
$457$	−12.9398	−	12.9398i	−0.605300	−	0.605300i	0.336414	−	0.941714i	$-0.390786\pi$
$457$	−12.9398	−	12.9398i	−0.605300	−	0.605300i	−0.941714	+	0.336414i	$0.890786\pi$
$458$	−15.7445	−	1.37747i	−0.735693	−	0.0643648i
$459$		0			0
$460$	3.20658	−	2.88964i	0.149508	−	0.134730i
$461$	−5.56561	−	31.5641i	−0.259216	−	1.47009i	−0.785014	−	0.619479i	$-0.787344\pi$
$461$	−5.56561	−	31.5641i	−0.259216	−	1.47009i	0.525797	−	0.850610i	$-0.323767\pi$
$462$		0			0
$463$	9.97438	+	37.2249i	0.463549	+	1.72999i	0.661656	+	0.749807i	$0.269854\pi$
$463$	9.97438	+	37.2249i	0.463549	+	1.72999i	−0.198108	+	0.980180i	$0.563480\pi$
$464$	−0.197034	−	0.341273i	−0.00914706	−	0.0158432i
$465$		0			0
$466$	−12.0351	+	14.3429i	−0.557515	+	0.664420i
$467$	−2.53409	+	9.45734i	−0.117263	+	0.437633i	−0.999446	−	0.0332738i	$-0.989407\pi$
$467$	−2.53409	+	9.45734i	−0.117263	+	0.437633i	0.882183	+	0.470907i	$0.156073\pi$
$468$		0			0
$469$	−32.8412	+	11.9532i	−1.51647	+	0.551949i
$470$	2.77585	+	9.06590i	0.128040	+	0.418179i
$471$		0			0
$472$	14.5480	+	31.1984i	0.669628	+	1.43602i
$473$	0.574128	−	6.56232i	0.0263984	−	0.301736i
$474$		0			0
$475$	14.4726	−	16.2955i	0.664050	−	0.747688i
$476$	−7.14642			−0.327555
$477$		0			0
$478$	1.21734	+	2.61060i	0.0556800	+	0.119406i
$479$	−12.0119	−	2.11802i	−0.548837	−	0.0967747i	−0.107648	−	0.994189i	$-0.534332\pi$
$479$	−12.0119	−	2.11802i	−0.548837	−	0.0967747i	−0.441189	+	0.897414i	$0.645443\pi$
$480$		0			0
$481$	−10.9414	+	3.98235i	−0.498886	+	0.181580i
$482$	0.0884433	−	0.0236983i	0.00402848	−	0.00107943i
$483$		0			0
$484$	−10.7800	+	12.8471i	−0.489999	+	0.583958i
$485$	−21.6045	+	4.60157i	−0.981010	+	0.208947i
$486$		0			0
$487$	−2.75407	−	10.2783i	−0.124799	−	0.465756i	0.875034	−	0.484062i	$-0.160839\pi$
$487$	−2.75407	−	10.2783i	−0.124799	−	0.465756i	−0.999832	+	0.0183065i	$0.994173\pi$
$488$	−15.9078	−	7.41794i	−0.720113	−	0.335794i
$489$		0			0
$490$	12.4229	−	11.1950i	0.561210	−	0.505738i
$491$	−36.5384	−	13.2989i	−1.64896	−	0.600171i	−0.660385	−	0.750927i	$-0.729607\pi$
$491$	−36.5384	−	13.2989i	−1.64896	−	0.600171i	−0.988571	+	0.150756i	$0.951829\pi$
$492$		0			0
$493$	−2.12686	−	2.12686i	−0.0957888	−	0.0957888i
$494$	1.22059	−	4.35488i	0.0549168	−	0.195935i
$495$		0			0
$496$	1.09758	+	1.30804i	0.0492826	+	0.0587328i
$497$	−9.78286	+	4.56182i	−0.438821	+	0.204626i
$498$		0			0
$499$	16.0108	−	2.82313i	0.716740	−	0.126381i	0.196627	−	0.980478i	$-0.437001\pi$
$499$	16.0108	−	2.82313i	0.716740	−	0.126381i	0.520113	+	0.854098i	$0.325890\pi$
$500$	9.37980	+	10.7631i	0.419477	+	0.481339i
$501$		0			0
$502$	−17.5599	−	4.70517i	−0.783738	−	0.210002i
$503$	28.6678	−	2.50810i	1.27823	−	0.111831i	0.572261	−	0.820071i	$-0.306066\pi$
$503$	28.6678	−	2.50810i	1.27823	−	0.111831i	0.705971	+	0.708240i	$0.250511\pi$
$504$		0			0
$505$	11.7367	+	15.5616i	0.522275	+	0.692483i
$506$	−5.46888	−	3.15746i	−0.243121	−	0.140366i
$507$		0			0
$508$	2.75295	−	3.93162i	0.122142	−	0.174437i
$509$	3.87905	−	21.9992i	0.171936	−	0.975097i	−0.769686	−	0.638423i	$-0.779587\pi$
$509$	3.87905	−	21.9992i	0.171936	−	0.975097i	0.941621	−	0.336673i	$-0.109302\pi$
$510$		0			0
$511$	0.467940	−	0.392649i	0.0207005	−	0.0173697i
$512$	−1.47449	+	1.47449i	−0.0651637	+	0.0651637i
$513$		0			0
$514$			10.7215i			0.472906i
$515$	−0.858471	+	0.0303360i	−0.0378288	+	0.00133677i
$516$		0			0
$517$	−20.0666	+	14.0508i	−0.882528	+	0.617953i
$518$	26.4158	+	18.4965i	1.16064	+	0.812691i
$519$		0			0
$520$	6.99967	+	2.96775i	0.306956	+	0.130144i
$521$	23.6960	−	13.6809i	1.03814	−	0.599371i	0.118835	−	0.992914i	$-0.462084\pi$
$521$	23.6960	−	13.6809i	1.03814	−	0.599371i	0.919306	+	0.393543i	$0.128751\pi$
$522$		0			0
$523$	−0.813771	−	9.30145i	−0.0355837	−	0.406724i	−0.993009	−	0.118042i	$-0.962338\pi$
$523$	−0.813771	−	9.30145i	−0.0355837	−	0.406724i	0.957425	−	0.288682i	$-0.0932172\pi$
$524$	9.89348	−	5.71200i	0.432199	−	0.249530i
$525$		0			0
$526$	−7.74899	−	21.2902i	−0.337872	−	0.928296i
$527$	10.6761	+	7.47552i	0.465060	+	0.325639i
$528$		0			0
$529$	7.08484	−	19.4654i	0.308036	−	0.846323i
$530$	−12.0214	+	12.9022i	−0.522178	+	0.560435i
$531$		0			0
$532$	20.8727	−	7.32704i	0.904945	−	0.317667i
$533$	−1.97607	+	1.97607i	−0.0855932	+	0.0855932i
$534$		0			0
$535$	−16.2647	+	10.1728i	−0.703186	+	0.439806i
$536$	−4.25497	+	24.1311i	−0.183787	+	1.04231i
$537$		0			0
$538$	4.64863	−	9.96901i	0.200416	−	0.429795i
$539$	37.4182	+	21.6034i	1.61171	+	0.930524i
$540$		0			0
$541$	19.4951	+	16.3584i	0.838162	+	0.703301i	0.957149	−	0.289594i	$-0.0935204\pi$
$541$	19.4951	+	16.3584i	0.838162	+	0.703301i	−0.118988	+	0.992896i	$0.537965\pi$
$542$	−15.7291	+	1.37612i	−0.675622	+	0.0591093i
$543$		0			0
$544$	−4.03426	+	6.98755i	−0.172968	+	0.299589i
$545$	12.8078	−	6.53260i	0.548625	−	0.279826i
$546$		0			0
$547$	17.3018	+	24.7095i	0.739771	+	1.05650i	0.995953	+	0.0898741i	$0.0286465\pi$
$547$	17.3018	+	24.7095i	0.739771	+	1.05650i	−0.256182	+	0.966629i	$0.582465\pi$
$548$	6.60907	−	3.08186i	0.282326	−	0.131651i
$549$		0			0
$550$	10.7424	−	17.9121i	0.458058	−	0.763775i
$551$	8.39256	+	4.03134i	0.357535	+	0.171741i
$552$		0			0
$553$	−6.65090	−	0.581878i	−0.282825	−	0.0247440i
$554$	−12.5987	−	4.58556i	−0.535269	−	0.194822i
$555$		0			0
$556$	−2.21736	−	12.5753i	−0.0940372	−	0.533311i
$557$	26.2184	+	12.2258i	1.11091	+	0.518025i	0.889398	−	0.457133i	$-0.151124\pi$
$557$	26.2184	+	12.2258i	1.11091	+	0.518025i	0.221510	+	0.975158i	$0.428902\pi$
$558$		0			0
$559$	−0.818106	−	1.41700i	−0.0346022	−	0.0599327i
$560$	0.341543	+	1.60355i	0.0144328	+	0.0677625i
$561$		0			0
$562$	0.0504352	−	0.188227i	0.00212748	−	0.00793987i
$563$	18.9758	−	5.08454i	0.799734	−	0.214288i	0.164267	−	0.986416i	$-0.447474\pi$
$563$	18.9758	−	5.08454i	0.799734	−	0.214288i	0.635467	+	0.772128i	$0.280808\pi$
$564$		0			0
$565$	−17.0012	+	32.0068i	−0.715247	+	1.34654i
$566$	−10.8552	−	1.91407i	−0.456279	−	0.0804543i
$567$		0			0
$568$	−0.659597	+	7.53923i	−0.0276761	+	0.316339i
$569$	−28.9346			−1.21300			−0.606501	−	0.795082i	$-0.707428\pi$
$569$	−28.9346			−1.21300			−0.606501	+	0.795082i	$0.707428\pi$
$570$		0			0
$571$	−24.1433			−1.01037			−0.505184	−	0.863012i	$-0.668575\pi$
$571$	−24.1433			−1.01037			−0.505184	+	0.863012i	$0.668575\pi$
$572$	−0.667135	+	7.62539i	−0.0278943	+	0.318834i
$573$		0			0
$574$	7.62220	+	1.34400i	0.318145	+	0.0560975i
$575$	−7.05885	−	2.70290i	−0.294374	−	0.112719i
$576$		0			0
$577$	26.2166	−	7.02471i	1.09141	−	0.292442i	0.332148	−	0.943227i	$-0.392227\pi$
$577$	26.2166	−	7.02471i	1.09141	−	0.292442i	0.759262	+	0.650785i	$0.225560\pi$
$578$	3.30496	−	12.3343i	0.137468	−	0.513039i
$579$		0			0
$580$	−3.31962	+	5.11642i	−0.137840	+	0.212448i
$581$	1.53783	+	2.66360i	0.0638000	+	0.110505i
$582$		0			0
$583$	−41.2936	−	19.2555i	−1.71020	−	0.797481i
$584$	−0.0743703	−	0.421775i	−0.00307746	−	0.0174532i
$585$		0			0
$586$	−6.09108	−	2.21697i	−0.251620	−	0.0915822i
$587$	36.8062	+	3.22012i	1.51915	+	0.132909i	0.815968	−	0.578097i	$-0.196204\pi$
$587$	36.8062	+	3.22012i	1.51915	+	0.132909i	0.703186	+	0.711006i	$0.251760\pi$
$588$		0			0
$589$	−38.8465	−	10.8879i	−1.60064	−	0.448628i
$590$	14.4538	−	18.5159i	0.595054	−	0.762288i
$591$		0			0
$592$	−1.59551	+	0.743997i	−0.0655750	+	0.0305781i
$593$	1.82350	+	2.60423i	0.0748823	+	0.106943i	0.854846	−	0.518882i	$-0.173651\pi$
$593$	1.82350	+	2.60423i	0.0748823	+	0.106943i	−0.779964	+	0.625825i	$0.784763\pi$
$594$		0			0
$595$	5.68593	+	11.1478i	0.233100	+	0.457015i
$596$	−2.69459	+	4.66716i	−0.110375	+	0.191174i
$597$		0			0
$598$	−1.56257	+	0.136707i	−0.0638981	+	0.00559036i
$599$	5.95719	+	4.99867i	0.243404	+	0.204240i	0.756326	−	0.654195i	$-0.226992\pi$
$599$	5.95719	+	4.99867i	0.243404	+	0.204240i	−0.512922	+	0.858435i	$0.671437\pi$
$600$		0			0
$601$	16.9764	+	9.80133i	0.692482	+	0.399805i	0.804541	−	0.593897i	$-0.202411\pi$
$601$	16.9764	+	9.80133i	0.692482	+	0.399805i	−0.112059	+	0.993702i	$0.535745\pi$
$602$	−1.91513	+	4.10701i	−0.0780549	+	0.167389i
$603$		0			0
$604$	3.54907	−	20.1278i	0.144410	−	0.818988i
$605$	28.6172	+	6.59427i	1.16346	+	0.268095i
$606$		0			0
$607$	−16.2338	+	16.2338i	−0.658910	+	0.658910i	−0.955122	−	0.296212i	$-0.904276\pi$
$607$	−16.2338	+	16.2338i	−0.658910	+	0.658910i	0.296212	+	0.955122i	$0.404276\pi$
$608$	4.61879	−	24.5449i	0.187317	−	0.995427i
$609$		0			0
$610$	0.422973	+	11.9696i	0.0171257	+	0.484635i
$611$	−2.08107	+	5.71770i	−0.0841912	+	0.231314i
$612$		0			0
$613$	30.4501	+	21.3214i	1.22987	+	0.861162i	0.993866	−	0.110590i	$-0.0352742\pi$
$613$	30.4501	+	21.3214i	1.22987	+	0.861162i	0.236001	+	0.971753i	$0.424163\pi$
$614$	8.00766	+	22.0009i	0.323163	+	0.887882i
$615$		0			0
$616$	47.1147	−	27.2017i	1.89830	−	1.09599i
$617$	−0.00700337	−	0.0800488i	−0.000281945	−	0.00322264i	0.996052	−	0.0887670i	$-0.0282926\pi$
$617$	−0.00700337	−	0.0800488i	−0.000281945	−	0.00322264i	−0.996334	+	0.0855443i	$0.972737\pi$
$618$		0			0
$619$	−24.9397	+	14.3989i	−1.00241	+	0.578741i	−0.908960	−	0.416883i	$-0.863123\pi$
$619$	−24.9397	+	14.3989i	−1.00241	+	0.578741i	−0.0934491	+	0.995624i	$0.529789\pi$
$620$	10.3159	−	24.3308i	0.414296	−	0.977150i
$621$		0			0
$622$	−5.04072	−	3.52955i	−0.202115	−	0.141522i
$623$	−13.3769	+	9.36663i	−0.535935	+	0.375266i
$624$		0			0
$625$	9.32658	−	23.1951i	0.373063	−	0.927806i
$626$		−	4.95896i		−	0.198200i
$627$		0			0
$628$	11.3889	−	11.3889i	0.454468	−	0.454468i
$629$	−10.2934	+	8.63721i	−0.410426	+	0.344388i
$630$		0			0
$631$	−1.03534	+	5.87173i	−0.0412164	+	0.233750i	−0.998456	−	0.0555461i	$-0.982310\pi$
$631$	−1.03534	+	5.87173i	−0.0412164	+	0.233750i	0.957240	+	0.289296i	$0.0934211\pi$
$632$	−2.68485	+	3.83436i	−0.106798	+	0.152523i
$633$		0			0
$634$	2.15870	+	1.24633i	0.0857331	+	0.0494980i
$635$	−8.32333	−	1.16624i	−0.330301	−	0.0462807i
$636$		0			0
$637$	10.6911	−	0.935350i	0.423597	−	0.0370599i
$638$	8.61862	+	2.30935i	0.341214	+	0.0914281i
$639$		0			0
$640$	16.2293	+	5.26574i	0.641518	+	0.208147i
$641$	23.2634	−	4.10197i	0.918850	−	0.162018i	0.305831	−	0.952086i	$-0.401066\pi$
$641$	23.2634	−	4.10197i	0.918850	−	0.162018i	0.613019	+	0.790068i	$0.289955\pi$
$642$		0			0
$643$	−16.0066	+	7.46400i	−0.631239	+	0.294351i	−0.711783	−	0.702400i	$-0.752112\pi$
$643$	−16.0066	+	7.46400i	−0.631239	+	0.294351i	0.0805441	+	0.996751i	$0.474334\pi$
$644$	−4.93146	−	5.87709i	−0.194327	−	0.231590i
$645$		0			0
$646$	−0.395233	−	5.20435i	−0.0155502	−	0.204762i
$647$	−5.50558	−	5.50558i	−0.216447	−	0.216447i	0.590553	−	0.806999i	$-0.298910\pi$
$647$	−5.50558	−	5.50558i	−0.216447	−	0.216447i	−0.806999	+	0.590553i	$0.798910\pi$
$648$		0			0
$649$	57.0292	+	20.7569i	2.23859	+	0.814780i
$650$	−0.366195	−	5.17495i	−0.0143633	−	0.202978i
$651$		0			0
$652$	12.3419	+	5.75512i	0.483346	+	0.225388i
$653$	−0.674379	−	2.51682i	−0.0263905	−	0.0984907i	0.951474	−	0.307728i	$-0.0995686\pi$
$653$	−0.674379	−	2.51682i	−0.0263905	−	0.0984907i	−0.977865	+	0.209237i	$0.932902\pi$
$654$		0			0
$655$	−16.7818	−	10.8883i	−0.655720	−	0.425442i
$656$	−0.271594	+	0.323674i	−0.0106040	+	0.0126373i
$657$		0			0
$658$	16.2776	−	4.36157i	0.634567	−	0.170032i
$659$	−25.1582	+	9.15684i	−0.980025	+	0.356700i	−0.781850	−	0.623467i	$-0.785724\pi$
$659$	−25.1582	+	9.15684i	−0.980025	+	0.356700i	−0.198175	+	0.980167i	$0.563501\pi$
$660$		0			0
$661$	−36.0063	−	6.34888i	−1.40048	−	0.246943i	−0.578140	−	0.815937i	$-0.696221\pi$
$661$	−36.0063	−	6.34888i	−1.40048	−	0.246943i	−0.822341	+	0.568995i	$0.807333\pi$
$662$	2.97629	+	6.38267i	0.115677	+	0.248070i
$663$		0			0
$664$	2.15641			0.0836849
$665$	−28.0366	−	26.7299i	−1.08721	−	1.03654i
$666$		0			0
$667$	0.281429	−	3.21675i	0.0108970	−	0.124553i
$668$	1.26466	+	2.71206i	0.0489310	+	0.104933i
$669$		0			0
$670$	15.9876	−	4.89517i	0.617655	−	0.189117i
$671$	−29.0787	+	10.5838i	−1.12257	+	0.408583i
$672$		0			0
$673$	−4.66494	+	17.4098i	−0.179820	+	0.671098i	0.815860	+	0.578249i	$0.196264\pi$
$673$	−4.66494	+	17.4098i	−0.179820	+	0.671098i	−0.995680	+	0.0928486i	$0.970403\pi$
$674$	−8.14350	+	9.70505i	−0.313676	+	0.373825i
$675$		0			0
$676$	−7.34952	−	12.7297i	−0.282674	−	0.489606i
$677$	−11.0963	−	41.4118i	−0.426464	−	1.59158i	−0.760706	−	0.649097i	$-0.775147\pi$
$677$	−11.0963	−	41.4118i	−0.426464	−	1.59158i	0.334242	−	0.942487i	$-0.391520\pi$
$678$		0			0
$679$	6.81750	+	38.6640i	0.261632	+	1.48379i
$680$	8.76207	+	0.455546i	0.336010	+	0.0174694i
$681$		0			0
$682$	−38.5154	−	3.36966i	−1.47483	−	0.129031i
$683$	17.1640	+	17.1640i	0.656763	+	0.656763i	0.954613	−	0.297850i	$-0.0962696\pi$
$683$	17.1640	+	17.1640i	0.656763	+	0.656763i	−0.297850	+	0.954613i	$0.596270\pi$
$684$		0			0
$685$	−10.0658	−	7.85756i	−0.384596	−	0.300222i
$686$	−3.89953	−	4.64727i	−0.148885	−	0.177434i
$687$		0			0
$688$	−0.141895	−	0.202647i	−0.00540968	−	0.00772583i
$689$	−11.1451	+	1.96518i	−0.424595	+	0.0748675i
$690$		0			0
$691$	6.09079	−	10.5496i	0.231705	−	0.401324i	−0.726605	−	0.687055i	$-0.758903\pi$
$691$	6.09079	−	10.5496i	0.231705	−	0.401324i	0.958310	+	0.285731i	$0.0922363\pi$
$692$	15.5865	+	4.17639i	0.592510	+	0.158762i
$693$		0			0
$694$	−4.24046	−	3.55817i	−0.160966	−	0.135066i
$695$	−17.8522	+	13.4642i	−0.677172	+	0.510727i
$696$		0			0
$697$	−1.36296	+	2.92289i	−0.0516259	+	0.110712i
$698$	−11.9575	+	17.0770i	−0.452597	+	0.646375i
$699$		0			0
$700$	19.7067	−	15.9854i	0.744844	−	0.604190i
$701$	−23.1767	+	19.4476i	−0.875372	+	0.734524i	−0.965222	−	0.261431i	$-0.915806\pi$
$701$	−23.1767	+	19.4476i	−0.875372	+	0.734524i	0.0898504	+	0.995955i	$0.471361\pi$
$702$		0			0
$703$	21.2087	−	35.7804i	0.799900	−	1.34948i
$704$		−	22.1224i		−	0.833771i
$705$		0			0
$706$	−5.57598	+	15.3199i	−0.209855	+	0.576571i
$707$	28.3781	−	19.8706i	1.06727	−	0.747310i
$708$		0			0
$709$	0.671174	+	1.84404i	0.0252065	+	0.0692542i	0.951658	−	0.307161i	$-0.0993789\pi$
$709$	0.671174	+	1.84404i	0.0252065	+	0.0692542i	−0.926451	+	0.376415i	$0.877157\pi$
$710$	4.78731	−	1.93651i	0.179664	−	0.0726761i
$711$		0			0
$712$	0.997885	+	11.4059i	0.0373973	+	0.427453i
$713$	1.21946	+	13.9384i	0.0456690	+	0.521999i
$714$		0			0
$715$	12.4258	−	5.02634i	0.464697	−	0.187975i
$716$	−2.97021	−	8.16057i	−0.111002	−	0.304975i
$717$		0			0
$718$	−13.6596	+	9.56458i	−0.509773	+	0.356947i
$719$	4.78058	−	13.1345i	0.178285	−	0.489835i	−0.818072	−	0.575117i	$-0.804957\pi$
$719$	4.78058	−	13.1345i	0.178285	−	0.489835i	0.996357	+	0.0852814i	$0.0271789\pi$
$720$		0			0
$721$			1.52677i			0.0568599i
$722$	6.49025	+	14.7952i	0.241542	+	0.550621i
$723$		0			0
$724$	19.0633	−	15.9960i	0.708481	−	0.594486i
$725$	10.6224	+	1.10752i	0.394505	+	0.0411323i
$726$		0			0
$727$	13.9674	−	19.9475i	0.518022	−	0.739813i	−0.471865	−	0.881671i	$-0.656419\pi$
$727$	13.9674	−	19.9475i	0.518022	−	0.739813i	0.989887	+	0.141858i	$0.0453078\pi$
$728$	5.71084	−	12.2469i	0.211658	−	0.453902i
$729$		0			0
$730$	−0.233323	+	0.175974i	−0.00863566	+	0.00651307i
$731$	−1.44648	−	1.21374i	−0.0534999	−	0.0448917i
$732$		0			0
$733$	17.2215	+	4.61450i	0.636092	+	0.170440i	0.562433	−	0.826843i	$-0.309866\pi$
$733$	17.2215	+	4.61450i	0.636092	+	0.170440i	0.0736595	+	0.997283i	$0.476532\pi$
$734$	−5.90821	+	10.2333i	−0.218076	+	0.377719i
$735$		0			0
$736$	−8.53033	+	1.50413i	−0.314432	+	0.0554429i
$737$	24.7784	+	35.3872i	0.912723	+	1.30350i
$738$		0			0
$739$	18.5274	+	22.0801i	0.681543	+	0.812231i	0.990305	−	0.138908i	$-0.0443593\pi$
$739$	18.5274	+	22.0801i	0.681543	+	0.812231i	−0.308763	+	0.951139i	$0.599915\pi$
$740$	21.4775	+	16.7657i	0.789528	+	0.616318i
$741$		0			0
$742$	22.1630	+	22.1630i	0.813630	+	0.813630i
$743$	6.33768	+	0.554475i	0.232507	+	0.0203417i	0.202814	−	0.979217i	$-0.434991\pi$
$743$	6.33768	+	0.554475i	0.232507	+	0.0203417i	0.0296933	+	0.999559i	$0.490547\pi$
$744$		0			0
$745$	9.42428	+	0.489974i	0.345279	+	0.0179513i
$746$	−5.44908	−	30.9033i	−0.199505	−	1.13145i
$747$		0			0
$748$	2.28629	+	8.53257i	0.0835952	+	0.311982i
$749$	17.0485	+	29.5289i	0.622939	+	1.07896i
$750$		0			0
$751$	33.4145	−	39.8218i	1.21931	−	1.45312i	0.366891	−	0.930264i	$-0.380422\pi$
$751$	33.4145	−	39.8218i	1.21931	−	1.45312i	0.852421	−	0.522856i	$-0.175133\pi$
$752$	−0.238104	+	0.888618i	−0.00868277	+	0.0324046i
$753$		0			0
$754$	2.08260	−	0.758005i	0.0758439	−	0.0276049i
$755$	−34.2214	+	10.4781i	−1.24544	+	0.381337i
$756$		0			0
$757$	−22.6581	−	48.5905i	−0.823523	−	1.76605i	−0.615871	−	0.787847i	$-0.711196\pi$
$757$	−22.6581	−	48.5905i	−0.823523	−	1.76605i	−0.207652	−	0.978203i	$-0.566582\pi$
$758$	0.159485	−	1.82292i	0.00579275	−	0.0662115i
$759$		0			0
$760$	−26.0586	+	7.65301i	−0.945245	+	0.277604i
$761$	−28.6371			−1.03809			−0.519046	−	0.854746i	$-0.673713\pi$
$761$	−28.6371			−1.03809			−0.519046	+	0.854746i	$0.673713\pi$
$762$		0			0
$763$	−10.7997	−	23.1599i	−0.390974	−	0.838446i
$764$	23.3800	+	4.12253i	0.845860	+	0.149148i
$765$		0			0
$766$	9.38426	−	3.41559i	0.339067	−	0.123410i
$767$	14.5607	−	3.90152i	0.525755	−	0.140876i
$768$		0			0
$769$	−3.77330	+	4.49684i	−0.136069	+	0.162160i	−0.829776	−	0.558097i	$-0.811532\pi$
$769$	−3.77330	+	4.49684i	−0.136069	+	0.162160i	0.693707	+	0.720257i	$0.255976\pi$
$770$	−31.1422	−	20.2056i	−1.12229	−	0.728159i
$771$		0			0
$772$	−6.06387	−	22.6307i	−0.218244	−	0.814496i
$773$	−41.1245	−	19.1767i	−1.47915	−	0.689738i	−0.495295	−	0.868725i	$-0.664940\pi$
$773$	−41.1245	−	19.1767i	−1.47915	−	0.689738i	−0.983851	+	0.178987i	$0.942718\pi$
$774$		0			0
$775$	−46.1617	+	3.26654i	−1.65818	+	0.117337i
$776$	25.8663	+	9.41455i	0.928544	+	0.337963i
$777$		0			0
$778$	−2.06138	−	2.06138i	−0.0739040	−	0.0739040i
$779$	0.984074	−	9.93434i	0.0352581	−	0.355935i
$780$		0			0
$781$	8.57640	+	10.2210i	0.306888	+	0.365735i
$782$	−1.64054	+	0.764998i	−0.0586658	+	0.0273563i
$783$		0			0
$784$	1.59796	−	0.281763i	0.0570699	−	0.0100630i
$785$	−26.8272	−	8.70434i	−0.957502	−	0.310671i
$786$		0			0
$787$	24.6233	+	6.59781i	0.877728	+	0.235186i	0.669426	−	0.742878i	$-0.266540\pi$
$787$	24.6233	+	6.59781i	0.877728	+	0.235186i	0.208301	+	0.978065i	$0.433207\pi$
$788$	14.3919	−	1.25913i	0.512692	−	0.0448547i
$789$		0			0
$790$	3.16317	+	0.443213i	0.112541	+	0.0157688i
$791$	55.7851	+	32.2076i	1.98349	+	1.14517i
$792$		0			0
$793$	−4.40867	+	6.29623i	−0.156556	+	0.223586i
$794$	−1.27050	+	7.20536i	−0.0450884	+	0.255709i
$795$		0			0
$796$	−11.8259	+	9.92314i	−0.419159	+	0.351716i
$797$	37.6403	−	37.6403i	1.33329	−	1.33329i	0.430880	−	0.902409i	$-0.358203\pi$
$797$	37.6403	−	37.6403i	1.33329	−	1.33329i	0.902409	−	0.430880i	$-0.141797\pi$
$798$		0			0
$799$			7.02189i			0.248417i
$800$	−4.50525	−	28.2926i	−0.159284	−	1.00030i
$801$		0			0
$802$	−10.2666	+	7.18875i	−0.362526	+	0.253844i
$803$	−0.618513	−	0.433087i	−0.0218268	−	0.0152833i
$804$		0			0
$805$	−5.24412	+	12.3687i	−0.184831	+	0.435938i
$806$	−8.31663	+	4.80161i	−0.292941	+	0.169129i
$807$		0			0
$808$	−2.11694	−	24.1967i	−0.0744736	−	0.851237i
$809$	22.8364	−	13.1846i	0.802885	−	0.463546i	−0.0415941	−	0.999135i	$-0.513244\pi$
$809$	22.8364	−	13.1846i	0.802885	−	0.463546i	0.844479	+	0.535589i	$0.179910\pi$
$810$		0			0
$811$	3.15115	+	8.65771i	0.110652	+	0.304013i	0.982643	−	0.185509i	$-0.0593934\pi$
$811$	3.15115	+	8.65771i	0.110652	+	0.304013i	−0.871991	+	0.489522i	$0.837171\pi$
$812$	8.87971	+	6.21764i	0.311617	+	0.218196i
$813$		0			0
$814$	13.6332	−	37.4569i	0.477844	−	1.31286i
$815$	−0.842133	−	23.8313i	−0.0294986	−	0.834774i
$816$		0			0
$817$	5.46916	+	2.06195i	0.191342	+	0.0721385i
$818$	22.2451	−	22.2451i	0.777783	−	0.777783i
$819$		0			0
$820$	6.37244	+	1.46840i	0.222535	+	0.0512788i
$821$	−2.89232	+	16.4031i	−0.100943	+	0.572473i	0.891821	+	0.452388i	$0.149428\pi$
$821$	−2.89232	+	16.4031i	−0.100943	+	0.572473i	−0.992764	+	0.120085i	$0.961683\pi$
$822$		0			0
$823$	11.5057	−	24.6740i	0.401063	−	0.860082i	−0.597252	−	0.802054i	$-0.703741\pi$
$823$	11.5057	−	24.6740i	0.401063	−	0.860082i	0.998315	−	0.0580287i	$-0.0184815\pi$
$824$	0.927036	+	0.535225i	0.0322948	+	0.0186454i
$825$		0			0
$826$	−31.9818	−	26.8359i	−1.11279	−	0.933740i
$827$	−19.3437	+	1.69235i	−0.672646	+	0.0588489i	−0.418361	−	0.908281i	$-0.637395\pi$
$827$	−19.3437	+	1.69235i	−0.672646	+	0.0588489i	−0.254284	+	0.967130i	$0.581840\pi$
$828$		0			0
$829$	−23.2647	+	40.2956i	−0.808016	+	1.39953i	0.106219	+	0.994343i	$0.466125\pi$
$829$	−23.2647	+	40.2956i	−0.808016	+	1.39953i	−0.914236	+	0.405183i	$0.867208\pi$
$830$	−0.668572	−	1.31080i	−0.0232065	−	0.0454984i
$831$		0			0
$832$	−3.15174	−	4.50116i	−0.109267	−	0.156050i
$833$	11.2246	−	5.23413i	0.388910	−	0.181352i
$834$		0			0
$835$	3.22438	−	4.13057i	0.111584	−	0.142944i
$836$	−15.4258	−	22.5771i	−0.533514	−	0.780847i
$837$		0			0
$838$	−7.80332	−	0.682702i	−0.269561	−	0.0235835i
$839$	52.2864	+	19.0307i	1.80513	+	0.657013i	0.997755	+	0.0669723i	$0.0213339\pi$
$839$	52.2864	+	19.0307i	1.80513	+	0.657013i	0.807374	+	0.590041i	$0.200888\pi$
$840$		0			0
$841$	−4.24353	−	24.0663i	−0.146329	−	0.829872i
$842$	−1.77948	−	0.829783i	−0.0613248	−	0.0285962i
$843$		0			0
$844$	4.73985	+	8.20966i	0.163152	+	0.282588i
$845$	−14.0098	+	21.5928i	−0.481951	+	0.742816i
$846$		0			0
$847$	13.5094	−	50.4176i	0.464187	−	1.73237i
$848$	−1.65277	+	0.442858i	−0.0567563	+	0.0152078i
$849$		0			0
$850$	−2.43968	−	5.46736i	−0.0836803	−	0.187529i
$851$	−14.2062	−	2.50493i	−0.486982	−	0.0858680i
$852$		0			0
$853$	0.873658	−	9.98595i	0.0299135	−	0.341913i	−0.966460	−	0.256819i	$-0.917326\pi$
$853$	0.873658	−	9.98595i	0.0299135	−	0.341913i	0.996373	−	0.0850935i	$-0.0271189\pi$
$854$	21.2876			0.728447
$855$		0			0
$856$	23.9061			0.817094
$857$	1.25616	−	14.3580i	0.0429096	−	0.490459i	−0.944085	−	0.329703i	$-0.893051\pi$
$857$	1.25616	−	14.3580i	0.0429096	−	0.490459i	0.986994	−	0.160756i	$-0.0513932\pi$
$858$		0			0
$859$	29.4418	+	5.19139i	1.00454	+	0.177128i	0.651637	−	0.758531i	$-0.274083\pi$
$859$	29.4418	+	5.19139i	1.00454	+	0.177128i	0.352906	+	0.935659i	$0.385194\pi$
$860$	−1.79610	+	3.38137i	−0.0612466	+	0.115304i
$861$		0			0
$862$	14.9816	−	4.01430i	0.510275	−	0.136728i
$863$	10.4833	−	39.1242i	0.356856	−	1.33180i	−0.521278	−	0.853387i	$-0.674544\pi$
$863$	10.4833	−	39.1242i	0.356856	−	1.33180i	0.878133	−	0.478416i	$-0.158789\pi$
$864$		0			0
$865$	−5.88633	−	27.6365i	−0.200141	−	0.939668i
$866$	9.23970	+	16.0036i	0.313978	+	0.543825i
$867$		0			0
$868$	−42.5703	−	19.8509i	−1.44493	−	0.673782i
$869$	1.43303	+	8.12709i	0.0486121	+	0.275693i
$870$		0			0
$871$	10.0831	+	3.66994i	0.341652	+	0.124351i
$872$	−17.8484	−	1.56153i	−0.604422	−	0.0528801i
$873$		0			0
$874$	4.00723	−	3.91635i	0.135547	−	0.132473i
$875$	−40.6151	−	18.0223i	−1.37304	−	0.609265i
$876$		0			0
$877$	−19.2255	+	8.96500i	−0.649199	+	0.302727i	−0.719182	−	0.694822i	$-0.755483\pi$
$877$	−19.2255	+	8.96500i	−0.649199	+	0.302727i	0.0699829	+	0.997548i	$0.477706\pi$
$878$	−4.60710	−	6.57962i	−0.155482	−	0.222051i
$879$		0			0
$880$	1.80532	−	0.920802i	0.0608573	−	0.0310402i
$881$	−6.83139	+	11.8323i	−0.230155	+	0.398641i	−0.957854	−	0.287256i	$-0.907257\pi$
$881$	−6.83139	+	11.8323i	−0.230155	+	0.398641i	0.727698	+	0.685897i	$0.240590\pi$
$882$		0			0
$883$	−14.5546	+	1.27336i	−0.489800	+	0.0428520i	−0.329381	−	0.944197i	$-0.606840\pi$
$883$	−14.5546	+	1.27336i	−0.489800	+	0.0428520i	−0.160419	+	0.987049i	$0.551285\pi$
$884$	1.68080	+	1.41036i	0.0565315	+	0.0474355i
$885$		0			0
$886$	25.1300	+	14.5088i	0.844257	+	0.487432i
$887$	−2.51587	+	5.39531i	−0.0844747	+	0.181157i	−0.944008	−	0.329924i	$-0.892977\pi$
$887$	−2.51587	+	5.39531i	−0.0844747	+	0.181157i	0.859533	+	0.511081i	$0.170755\pi$
$888$		0			0
$889$	−2.59398	+	14.7112i	−0.0869992	+	0.493397i
$890$	6.62381	−	4.14285i	0.222031	−	0.138869i
$891$		0			0
$892$	−13.1143	+	13.1143i	−0.439099	+	0.439099i
$893$	−7.19936	−	20.5090i	−0.240917	−	0.686306i
$894$		0			0
$895$	−10.3666	+	11.1261i	−0.346517	+	0.371904i
$896$	10.3720	−	28.4968i	0.346504	−	0.952012i
$897$		0			0
$898$	−28.7314	−	20.1179i	−0.958778	−	0.671344i
$899$	−6.76157	−	18.5773i	−0.225511	−	0.619586i
$900$		0			0
$901$	−11.3105	+	6.53012i	−0.376807	+	0.217550i
$902$	−0.833821	−	9.53061i	−0.0277632	−	0.317335i
$903$		0			0
$904$	39.1121	−	22.5814i	1.30085	−	0.751045i
$905$	−40.1198	−	17.0101i	−1.33363	−	0.565436i
$906$		0			0
$907$	33.1934	+	23.2423i	1.10217	+	0.771747i	0.975456	−	0.220192i	$-0.0706685\pi$
$907$	33.1934	+	23.2423i	1.10217	+	0.771747i	0.126713	+	0.991939i	$0.459557\pi$
$908$	−4.54780	+	3.18440i	−0.150924	+	0.105678i
$909$		0			0
$910$	−9.21502	+	0.325634i	−0.305475	+	0.0107947i
$911$		−	24.1659i		−	0.800652i	−0.916373	−	0.400326i	$-0.868897\pi$
$911$		−	24.1659i		−	0.800652i	0.916373	−	0.400326i	$-0.131103\pi$
$912$		0			0
$913$	2.68826	−	2.68826i	0.0889684	−	0.0889684i
$914$	11.9202	−	10.0022i	0.394284	−	0.330844i
$915$		0			0
$916$	−4.12139	+	23.3735i	−0.136174	+	0.772283i
$917$	−20.3938	+	29.1254i	−0.673463	+	0.961805i
$918$		0			0
$919$	−10.9705	−	6.33379i	−0.361882	−	0.208933i	0.308024	−	0.951379i	$-0.400332\pi$
$919$	−10.9705	−	6.33379i	−0.361882	−	0.208933i	−0.669906	+	0.742446i	$0.733666\pi$
$920$	5.67173	+	7.52013i	0.186991	+	0.247931i
$921$		0			0
$922$	27.1501	−	2.37533i	0.894141	−	0.0782272i
$923$	3.20116	+	0.857749i	0.105368	+	0.0282332i
$924$		0			0
$925$	9.06479	−	46.8424i	0.298049	−	1.54017i
$926$	−32.2720	+	5.69043i	−1.06052	+	0.186999i
$927$		0			0
$928$	11.0922	−	5.17236i	0.364118	−	0.169791i
$929$	7.06706	+	8.42219i	0.231863	+	0.276323i	0.869414	−	0.494085i	$-0.164497\pi$
$929$	7.06706	+	8.42219i	0.231863	+	0.276323i	−0.637551	+	0.770408i	$0.720052\pi$
$930$		0			0
$931$	−27.4176	+	26.7957i	−0.898574	+	0.878195i
$932$	19.8818	+	19.8818i	0.651249	+	0.651249i
$933$		0			0
$934$	−7.82341	−	2.84749i	−0.255990	−	0.0931726i
$935$	11.4910	−	10.3552i	0.375797	−	0.338652i
$936$		0			0
$937$	−45.8065	−	21.3599i	−1.49643	−	0.697798i	−0.509730	−	0.860334i	$-0.670255\pi$
$937$	−45.8065	−	21.3599i	−1.49643	−	0.697798i	−0.986703	+	0.162536i	$0.948033\pi$
$938$	−7.69157	−	28.7053i	−0.251139	−	0.937262i
$939$		0			0
$940$	13.9259	−	2.96610i	0.454214	−	0.0967436i
$941$	−8.30693	+	9.89982i	−0.270798	+	0.322725i	−0.884256	−	0.467003i	$-0.845334\pi$
$941$	−8.30693	+	9.89982i	−0.270798	+	0.322725i	0.613457	+	0.789728i	$0.289778\pi$
$942$		0			0
$943$	−3.34426	+	0.896091i	−0.108904	+	0.0291808i
$944$	2.14170	−	0.779515i	0.0697064	−	0.0253711i
$945$		0			0
$946$	5.51632	+	0.972676i	0.179351	+	0.0316244i
$947$	9.38977	+	20.1364i	0.305126	+	0.654346i	0.997757	−	0.0669472i	$-0.0213259\pi$
$947$	9.38977	+	20.1364i	0.305126	+	0.654346i	−0.692630	+	0.721293i	$0.743548\pi$
$948$		0			0
$949$	−0.187547			−0.00608804
$950$	12.7312	+	13.4673i	0.413053	+	0.436936i
$951$		0			0
$952$	1.35915	−	15.5351i	0.0440501	−	0.503495i
$953$	−0.0877126	−	0.188100i	−0.00284129	−	0.00609316i	0.904882	−	0.425662i	$-0.139959\pi$
$953$	−0.0877126	−	0.188100i	−0.00284129	−	0.00609316i	−0.907723	+	0.419569i	$0.862181\pi$
$954$		0			0
$955$	−12.1712	−	39.7509i	−0.393849	−	1.28631i
$956$	4.06479	−	1.47946i	0.131465	−	0.0478493i
$957$		0			0
$958$	2.68436	−	10.0182i	0.0867277	−	0.323672i
$959$	−14.5888	+	17.3863i	−0.471099	+	0.561433i
$960$		0			0
$961$	27.3314	+	47.3394i	0.881659	+	1.52708i
$962$	−2.56253	−	9.56349i	−0.0826193	−	0.308339i
$963$		0			0
$964$	−0.0238770	−	0.135413i	−0.000769025	−	0.00436136i
$965$	−30.4773	+	27.4649i	−0.981099	+	0.884125i
$966$		0			0
$967$	31.7239	+	2.77548i	1.02017	+	0.0892534i	0.584949	−	0.811070i	$-0.301114\pi$
$967$	31.7239	+	2.77548i	1.02017	+	0.0892534i	0.435222	+	0.900323i	$0.356670\pi$
$968$	−25.8772	−	25.8772i	−0.831723	−	0.831723i
$969$		0			0
$970$	−2.29682	−	18.6420i	−0.0737464	−	0.598558i
$971$	−8.61657	−	10.2688i	−0.276519	−	0.329542i	0.609855	−	0.792513i	$-0.291228\pi$
$971$	−8.61657	−	10.2688i	−0.276519	−	0.329542i	−0.886373	+	0.462971i	$0.846783\pi$
$972$		0			0
$973$	22.7954	+	32.5552i	0.730786	+	1.04367i
$974$	8.91077	−	1.57121i	0.285520	−	0.0503448i
$975$		0			0
$976$	−0.581061	+	1.00643i	−0.0185993	+	0.0322149i
$977$	−12.4193	−	3.32775i	−0.397330	−	0.106464i	0.0546207	−	0.998507i	$-0.482605\pi$
$977$	−12.4193	−	3.32775i	−0.397330	−	0.106464i	−0.451951	+	0.892043i	$0.649272\pi$
$978$		0			0
$979$	15.4630	+	12.9750i	0.494199	+	0.414682i
$980$	−15.1218	−	20.0499i	−0.483048	−	0.640472i
$981$		0			0
$982$	13.9732	−	29.9657i	0.445904	−	0.956244i
$983$	7.59418	−	10.8456i	0.242217	−	0.345921i	−0.679576	−	0.733606i	$-0.737836\pi$
$983$	7.59418	−	10.8456i	0.242217	−	0.345921i	0.921792	+	0.387684i	$0.126725\pi$
$984$		0			0
$985$	−13.4149	−	21.4484i	−0.427433	−	0.683403i
$986$	1.95926	−	1.64402i	0.0623956	−	0.0523561i
$987$		0			0
$988$	−6.35515	−	2.39598i	−0.202184	−	0.0762263i
$989$		−	2.02711i		−	0.0644583i
$990$		0			0
$991$	−0.111950	+	0.307581i	−0.00355622	+	0.00977062i	−0.941458	−	0.337130i	$-0.890544\pi$
$991$	−0.111950	+	0.307581i	−0.00355622	+	0.00977062i	0.937902	+	0.346901i	$0.112766\pi$
$992$	−43.4412	+	30.4178i	−1.37926	+	0.965767i
$993$		0			0
$994$	−3.13926	−	8.62504i	−0.0995712	−	0.273570i
$995$	24.8884	+	10.5523i	0.789014	+	0.334529i
$996$		0			0
$997$	2.69227	+	30.7728i	0.0852650	+	0.974584i	0.911511	+	0.411275i	$0.134916\pi$
$997$	2.69227	+	30.7728i	0.0852650	+	0.974584i	−0.826246	+	0.563309i	$0.809528\pi$
$998$	1.20487	+	13.7718i	0.0381396	+	0.435938i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.127.4		96
3.2	odd	2		95.2.r.a.32.5	yes	96
5.3	odd	4	inner	855.2.dl.a.298.5		96
15.2	even	4		475.2.bb.b.393.5		96
15.8	even	4		95.2.r.a.13.4	yes	96
15.14	odd	2		475.2.bb.b.32.4		96
19.3	odd	18	inner	855.2.dl.a.307.5		96
57.41	even	18		95.2.r.a.22.4	yes	96
95.3	even	36	inner	855.2.dl.a.478.4		96
285.98	odd	36		95.2.r.a.3.5	✓	96
285.212	odd	36		475.2.bb.b.193.4		96
285.269	even	18		475.2.bb.b.307.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.5	✓	96	285.98	odd	36
95.2.r.a.13.4	yes	96	15.8	even	4
95.2.r.a.22.4	yes	96	57.41	even	18
95.2.r.a.32.5	yes	96	3.2	odd	2
475.2.bb.b.32.4		96	15.14	odd	2
475.2.bb.b.193.4		96	285.212	odd	36
475.2.bb.b.307.5		96	285.269	even	18
475.2.bb.b.393.5		96	15.2	even	4
855.2.dl.a.127.4		96	1.1	even	1	trivial
855.2.dl.a.298.5		96	5.3	odd	4	inner
855.2.dl.a.307.5		96	19.3	odd	18	inner
855.2.dl.a.478.4		96	95.3	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0741107 + 0.847089i) q^{2} +(1.25755 + 0.221740i) q^{4} +(-0.654653 - 2.13809i) q^{5} +(-3.83889 + 1.02863i) q^{7} +(-0.721192 + 2.69152i) q^{8} +(1.85967 - 0.396094i) q^{10} +(2.45629 + 4.25442i) q^{11} +(1.10589 + 0.515684i) q^{13} +(-0.586836 - 3.32811i) q^{14} +(0.173363 + 0.0630990i) q^{16} +(1.40281 + 0.122730i) q^{17} +(-4.22304 + 1.07980i) q^{19} +(-0.349158 - 2.83391i) q^{20} +(-3.78591 + 1.76540i) q^{22} +(0.867092 + 1.23834i) q^{23} +(-4.14286 + 2.79941i) q^{25} +(-0.518789 + 0.898569i) q^{26} +(-5.05567 + 0.442314i) q^{28} +(-1.63627 - 1.37299i) q^{29} +(8.01543 + 4.62771i) q^{31} +(-2.42153 + 5.19298i) q^{32} +(-0.207926 + 1.17921i) q^{34} +(4.71244 + 7.53450i) q^{35} +(-6.74741 + 6.74741i) q^{37} +(-0.601718 - 3.65731i) q^{38} +(6.22685 - 0.220040i) q^{40} +(-0.783311 + 2.15213i) q^{41} +(-1.09842 - 0.769121i) q^{43} +(2.14553 + 5.89479i) q^{44} +(-1.11324 + 0.642730i) q^{46} +(0.434606 + 4.96757i) q^{47} +(7.61681 - 4.39757i) q^{49} +(-2.06432 - 3.71684i) q^{50} +(1.27636 + 0.893717i) q^{52} +(-7.59734 + 5.31972i) q^{53} +(7.48831 - 8.03693i) q^{55} -11.0743i q^{56} +(1.28431 - 1.28431i) q^{58} +(9.46359 - 7.94090i) q^{59} +(-1.09383 + 6.20343i) q^{61} +(-4.51411 + 6.44682i) q^{62} +(-3.89991 - 2.25161i) q^{64} +(0.378607 - 2.70208i) q^{65} +(8.76025 - 0.766422i) q^{67} +(1.73688 + 0.465396i) q^{68} +(-6.73163 + 3.43347i) q^{70} +(2.67473 - 0.471627i) q^{71} +(-0.139300 + 0.0649566i) q^{73} +(-5.21560 - 6.21571i) q^{74} +(-5.55010 + 0.421490i) q^{76} +(-13.8056 - 13.8056i) q^{77} +(1.57856 + 0.574548i) q^{79} +(0.0214188 - 0.411974i) q^{80} +(-1.76499 - 0.823030i) q^{82} +(-0.200296 - 0.747516i) q^{83} +(-0.655944 - 3.07967i) q^{85} +(0.732919 - 0.873459i) q^{86} +(-13.2223 + 3.54291i) q^{88} +(3.86114 - 1.40534i) q^{89} +(-4.77583 - 0.842108i) q^{91} +(0.815821 + 1.74953i) q^{92} -4.24019 q^{94} +(5.07334 + 8.32233i) q^{95} +(0.860973 - 9.84096i) q^{97} +(3.16065 + 6.77803i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more