LMFDB - Embedded newform 475.2.bb.b.193.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(32,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([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("475.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
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			193.4
Character	$\chi$	$=$	475.193
Dual form			475.2.bb.b.32.4

$q$-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} +(-0.344068 + 0.737855i) q^{3} +(1.25755 - 0.221740i) q^{4} +(0.650528 + 0.236773i) q^{6} +(3.83889 + 1.02863i) q^{7} +(-0.721192 - 2.69152i) q^{8} +(1.50231 + 1.79039i) q^{9} +(-2.45629 + 4.25442i) q^{11} +(-0.269070 + 1.00418i) q^{12} +(-1.10589 + 0.515684i) q^{13} +(0.586836 - 3.32811i) q^{14} +(0.173363 - 0.0630990i) q^{16} +(1.40281 - 0.122730i) q^{17} +(1.40528 - 1.40528i) q^{18} +(-4.22304 - 1.07980i) q^{19} +(-2.07982 + 2.47863i) q^{21} +(3.78591 + 1.76540i) q^{22} +(0.867092 - 1.23834i) q^{23} +(2.23409 + 0.393931i) q^{24} +(0.518789 + 0.898569i) q^{26} +(-4.19712 + 1.12462i) q^{27} +(5.05567 + 0.442314i) q^{28} +(1.63627 - 1.37299i) q^{29} +(8.01543 - 4.62771i) q^{31} +(-2.42153 - 5.19298i) q^{32} +(-2.29401 - 3.27619i) q^{33} +(-0.207926 - 1.17921i) q^{34} +(2.28623 + 1.91838i) q^{36} +(6.74741 + 6.74741i) q^{37} +(-0.601718 + 3.65731i) q^{38} -0.993416i q^{39} +(0.783311 + 2.15213i) q^{41} +(2.25375 + 1.57810i) q^{42} +(1.09842 - 0.769121i) q^{43} +(-2.14553 + 5.89479i) q^{44} +(-1.11324 - 0.642730i) q^{46} +(0.434606 - 4.96757i) q^{47} +(-0.0130907 + 0.149627i) q^{48} +(7.61681 + 4.39757i) q^{49} +(-0.392104 + 1.07730i) q^{51} +(-1.27636 + 0.893717i) q^{52} +(-7.59734 - 5.31972i) q^{53} +(1.26370 + 3.47199i) q^{54} -11.0743i q^{56} +(2.24975 - 2.74446i) q^{57} +(-1.28431 - 1.28431i) q^{58} +(-9.46359 - 7.94090i) q^{59} +(-1.09383 - 6.20343i) q^{61} +(-4.51411 - 6.44682i) q^{62} +(3.92558 + 8.41843i) q^{63} +(-3.89991 + 2.25161i) q^{64} +(-2.60522 + 2.18604i) q^{66} +(-8.76025 - 0.766422i) q^{67} +(1.73688 - 0.465396i) q^{68} +(0.615374 + 1.06586i) q^{69} +(-2.67473 - 0.471627i) q^{71} +(3.73542 - 5.33473i) q^{72} +(0.139300 + 0.0649566i) q^{73} +(5.21560 - 6.21571i) q^{74} +(-5.55010 - 0.421490i) q^{76} +(-13.8056 + 13.8056i) q^{77} +(-0.841512 + 0.0736228i) q^{78} +(1.57856 - 0.574548i) q^{79} +(-0.603254 + 3.42123i) q^{81} +(1.76499 - 0.823030i) q^{82} +(-0.200296 + 0.747516i) q^{83} +(-2.06586 + 3.57817i) q^{84} +(-0.732919 - 0.873459i) q^{86} +(0.450082 + 1.67973i) q^{87} +(13.2223 + 3.54291i) q^{88} +(-3.86114 - 1.40534i) q^{89} +(-4.77583 + 0.842108i) q^{91} +(0.815821 - 1.74953i) q^{92} +(0.656731 + 7.50647i) q^{93} -4.24019 q^{94} +4.66483 q^{96} +(-0.860973 - 9.84096i) q^{97} +(3.16065 - 6.77803i) q^{98} +(-11.3072 + 1.99376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

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	−0.976312	−	0.216367i	$-0.930579\pi$
$2$	−0.0741107	−	0.847089i	−0.0524042	−	0.598983i	0.923908	−	0.382615i	$-0.124976\pi$
$3$	−0.344068	+	0.737855i	−0.198648	+	0.426001i	−0.980246	−	0.197780i	$-0.936627\pi$
$3$	−0.344068	+	0.737855i	−0.198648	+	0.426001i	0.781599	+	0.623781i	$0.214404\pi$
$4$	1.25755	−	0.221740i	0.628774	−	0.110870i
$5$		0			0
$5$		0			0
$6$	0.650528	+	0.236773i	0.265577	+	0.0966622i
$7$	3.83889	+	1.02863i	1.45096	+	0.388784i	0.896359	−	0.443329i	$-0.146203\pi$
$7$	3.83889	+	1.02863i	1.45096	+	0.388784i	0.554605	+	0.832114i	$0.312869\pi$
$8$	−0.721192	−	2.69152i	−0.254980	−	0.951597i
$9$	1.50231	+	1.79039i	0.500772	+	0.596796i
$10$		0			0
$11$	−2.45629	+	4.25442i	−0.740599	+	1.28275i	0.211624	+	0.977351i	$0.432125\pi$
$11$	−2.45629	+	4.25442i	−0.740599	+	1.28275i	−0.952223	+	0.305403i	$0.901209\pi$
$12$	−0.269070	+	1.00418i	−0.0776737	+	0.289882i
$13$	−1.10589	+	0.515684i	−0.306718	+	0.143025i	−0.569883	−	0.821726i	$-0.693012\pi$
$13$	−1.10589	+	0.515684i	−0.306718	+	0.143025i	0.263165	+	0.964751i	$0.415234\pi$
$14$	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	0.0842397	−	0.996446i	$-0.473154\pi$
$17$	1.40281	−	0.122730i	0.340231	−	0.0297663i	0.255991	+	0.966679i	$0.417598\pi$
$18$	1.40528	−	1.40528i	0.331228	−	0.331228i
$19$	−4.22304	−	1.07980i	−0.968831	−	0.247724i
$19$	−4.22304	−	1.07980i	−0.968831	−	0.247724i
$20$		0			0
$21$	−2.07982	+	2.47863i	−0.453853	+	0.540881i
$22$	3.78591	+	1.76540i	0.807158	+	0.376384i
$23$	0.867092	−	1.23834i	0.180801	−	0.258211i	−0.718513	−	0.695513i	$-0.755177\pi$
$23$	0.867092	−	1.23834i	0.180801	−	0.258211i	0.899315	+	0.437302i	$0.144066\pi$
$24$	2.23409	+	0.393931i	0.456032	+	0.0804108i
$25$		0			0
$26$	0.518789	+	0.898569i	0.101743	+	0.176224i
$27$	−4.19712	+	1.12462i	−0.807737	+	0.216432i
$28$	5.05567	+	0.442314i	0.955432	+	0.0835895i
$29$	1.63627	−	1.37299i	0.303847	−	0.254958i	−0.478096	−	0.878307i	$-0.658673\pi$
$29$	1.63627	−	1.37299i	0.303847	−	0.254958i	0.781943	+	0.623350i	$0.214229\pi$
$30$		0			0
$31$	8.01543	−	4.62771i	1.43961	−	0.831161i	0.441791	−	0.897118i	$-0.354343\pi$
$31$	8.01543	−	4.62771i	1.43961	−	0.831161i	0.997823	+	0.0659564i	$0.0210098\pi$
$32$	−2.42153	−	5.19298i	−0.428069	−	0.917997i
$33$	−2.29401	−	3.27619i	−0.399337	−	0.570312i
$34$	−0.207926	−	1.17921i	−0.0356590	−	0.202232i
$35$		0			0
$36$	2.28623	+	1.91838i	0.381039	+	0.319729i
$37$	6.74741	+	6.74741i	1.10927	+	1.10927i	0.993247	+	0.116021i	$0.0370139\pi$
$37$	6.74741	+	6.74741i	1.10927	+	1.10927i	0.116021	+	0.993247i	$0.462986\pi$
$38$	−0.601718	+	3.65731i	−0.0976115	+	0.593294i
$39$		−	0.993416i		−	0.159074i
$40$		0			0
$41$	0.783311	+	2.15213i	0.122333	+	0.336106i	0.985710	−	0.168453i	$-0.0538772\pi$
$41$	0.783311	+	2.15213i	0.122333	+	0.336106i	−0.863377	+	0.504559i	$0.831655\pi$
$42$	2.25375	+	1.57810i	0.347762	+	0.243506i
$43$	1.09842	−	0.769121i	0.167507	−	0.117290i	−0.486817	−	0.873504i	$-0.661842\pi$
$43$	1.09842	−	0.769121i	0.167507	−	0.117290i	0.654324	+	0.756214i	$0.272953\pi$
$44$	−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	−0.896282	−	0.443485i	$-0.853742\pi$
$47$	0.434606	−	4.96757i	0.0633939	−	0.724595i	0.959676	−	0.281110i	$-0.0907026\pi$
$48$	−0.0130907	+	0.149627i	−0.00188948	+	0.0215968i
$49$	7.61681	+	4.39757i	1.08812	+	0.628224i
$50$		0			0
$51$	−0.392104	+	1.07730i	−0.0549055	+	0.150852i
$52$	−1.27636	+	0.893717i	−0.176999	+	0.123936i
$53$	−7.59734	−	5.31972i	−1.04358	−	0.730719i	−0.0796315	−	0.996824i	$-0.525374\pi$
$53$	−7.59734	−	5.31972i	−1.04358	−	0.730719i	−0.963944	+	0.266105i	$0.914263\pi$
$54$	1.26370	+	3.47199i	0.171968	+	0.472478i
$55$		0			0
$56$		−	11.0743i		−	1.47987i
$57$	2.24975	−	2.74446i	0.297986	−	0.363513i
$58$	−1.28431	−	1.28431i	−0.168638	−	0.168638i
$59$	−9.46359	−	7.94090i	−1.23205	−	1.03382i	−0.998103	−	0.0615685i	$-0.980390\pi$
$59$	−9.46359	−	7.94090i	−1.23205	−	1.03382i	−0.233952	−	0.972248i	$-0.575166\pi$
$60$		0			0
$61$	−1.09383	−	6.20343i	−0.140051	−	0.794268i	−0.971209	−	0.238231i	$-0.923432\pi$
$61$	−1.09383	−	6.20343i	−0.140051	−	0.794268i	0.831158	−	0.556037i	$-0.187679\pi$
$62$	−4.51411	−	6.44682i	−0.573293	−	0.818747i
$63$	3.92558	+	8.41843i	0.494576	+	1.06062i
$64$	−3.89991	+	2.25161i	−0.487489	+	0.281452i
$65$		0			0
$66$	−2.60522	+	2.18604i	−0.320680	+	0.269082i
$67$	−8.76025	−	0.766422i	−1.07023	−	0.0936334i	−0.461603	−	0.887087i	$-0.652726\pi$
$67$	−8.76025	−	0.766422i	−1.07023	−	0.0936334i	−0.608631	+	0.793453i	$0.708281\pi$
$68$	1.73688	−	0.465396i	0.210628	−	0.0564376i
$69$	0.615374	+	1.06586i	0.0740823	+	0.128314i
$70$		0			0
$71$	−2.67473	−	0.471627i	−0.317432	−	0.0559718i	0.0126621	−	0.999920i	$-0.495969\pi$
$71$	−2.67473	−	0.471627i	−0.317432	−	0.0559718i	−0.330094	+	0.943948i	$0.607081\pi$
$72$	3.73542	−	5.33473i	0.440223	−	0.628704i
$73$	0.139300	+	0.0649566i	0.0163038	+	0.00760259i	0.430753	−	0.902470i	$-0.358248\pi$
$73$	0.139300	+	0.0649566i	0.0163038	+	0.00760259i	−0.414449	+	0.910072i	$0.636026\pi$
$74$	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
$78$	−0.841512	+	0.0736228i	−0.0952825	+	0.00833614i
$79$	1.57856	−	0.574548i	0.177602	−	0.0646417i	−0.251689	−	0.967808i	$-0.580986\pi$
$79$	1.57856	−	0.574548i	0.177602	−	0.0646417i	0.429290	+	0.903167i	$0.358764\pi$
$80$		0			0
$81$	−0.603254	+	3.42123i	−0.0670283	+	0.380136i
$82$	1.76499	−	0.823030i	0.194911	−	0.0908885i
$83$	−0.200296	+	0.747516i	−0.0219854	+	0.0820505i	−0.976047	−	0.217560i	$-0.930190\pi$
$83$	−0.200296	+	0.747516i	−0.0219854	+	0.0820505i	0.954062	+	0.299611i	$0.0968568\pi$
$84$	−2.06586	+	3.57817i	−0.225403	+	0.390410i
$85$		0			0
$86$	−0.732919	−	0.873459i	−0.0790327	−	0.0941875i
$87$	0.450082	+	1.67973i	0.0482538	+	0.180086i
$88$	13.2223	+	3.54291i	1.40950	+	0.377675i
$89$	−3.86114	−	1.40534i	−0.409280	−	0.148966i	0.129171	−	0.991622i	$-0.458768\pi$
$89$	−3.86114	−	1.40534i	−0.409280	−	0.148966i	−0.538452	+	0.842656i	$0.680991\pi$
$90$		0			0
$91$	−4.77583	+	0.842108i	−0.500643	+	0.0882769i
$92$	0.815821	−	1.74953i	0.0850552	−	0.182402i
$93$	0.656731	+	7.50647i	0.0680999	+	0.778385i
$94$	−4.24019			−0.437342
$95$		0			0
$96$	4.66483			0.476103
$97$	−0.860973	−	9.84096i	−0.0874185	−	0.999198i	−0.905570	−	0.424196i	$-0.860557\pi$
$97$	−0.860973	−	9.84096i	−0.0874185	−	0.999198i	0.818152	−	0.575002i	$-0.194999\pi$
$98$	3.16065	−	6.77803i	0.319273	−	0.684684i
$99$	−11.3072	+	1.99376i	−1.13641	+	0.200380i
$100$		0			0
$101$	8.19112	+	2.98132i	0.815047	+	0.296653i	0.715707	−	0.698401i	$-0.246105\pi$
$101$	8.19112	+	2.98132i	0.815047	+	0.296653i	0.0993398	+	0.995054i	$0.468327\pi$
$102$	0.941625	+	0.252308i	0.0932348	+	0.0249822i
$103$	−0.0994278	−	0.371070i	−0.00979691	−	0.0365626i	0.960854	−	0.277054i	$-0.0893581\pi$
$103$	−0.0994278	−	0.371070i	−0.00979691	−	0.0365626i	−0.970651	+	0.240491i	$0.922691\pi$
$104$	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	0.771621	+	0.636083i	$0.219446\pi$
$107$	−2.22050	+	8.28702i	−0.214664	+	0.801137i	−0.986285	+	0.165054i	$0.947220\pi$
$108$	−5.02871	+	2.34493i	−0.483888	+	0.225641i
$109$	1.11653	−	6.33215i	0.106944	−	0.606510i	−0.883482	−	0.468465i	$-0.844807\pi$
$109$	1.11653	−	6.33215i	0.106944	−	0.606510i	0.990426	−	0.138045i	$-0.0440818\pi$
$110$		0			0
$111$	−7.30018	+	2.65705i	−0.692902	+	0.252196i
$112$	0.730427	−	0.0639041i	0.0690189	−	0.00603837i
$113$	−11.4607	+	11.4607i	−1.07813	+	1.07813i	−0.0814546	+	0.996677i	$0.525957\pi$
$113$	−11.4607	+	11.4607i	−1.07813	+	1.07813i	−0.996677	+	0.0814546i	$0.974043\pi$
$114$	−2.49154	−	1.70234i	−0.233354	−	0.159439i
$115$		0			0
$116$	1.75324	−	2.08942i	0.162784	−	0.193998i
$117$	−2.58467	−	1.20525i	−0.238953	−	0.111425i
$118$	−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
$123$	−1.85747	−	0.162508i	−0.167483	−	0.0146528i
$124$	9.05364	−	7.59691i	0.813041	−	0.682222i
$125$		0			0
$126$	6.84023	−	3.94921i	0.609376	−	0.351824i
$127$	−1.58848	−	3.40651i	−0.140955	−	0.302279i	0.823139	−	0.567840i	$-0.192221\pi$
$127$	−1.58848	−	3.40651i	−0.140955	−	0.302279i	−0.964094	+	0.265561i	$0.914443\pi$
$128$	−4.37663	−	6.25048i	−0.386843	−	0.552469i
$129$	0.189570	+	1.07510i	0.0166907	+	0.0946577i
$130$		0			0
$131$	−6.85330	−	5.75060i	−0.598775	−	0.502432i	0.292277	−	0.956334i	$-0.405587\pi$
$131$	−6.85330	−	5.75060i	−0.598775	−	0.502432i	−0.891052	+	0.453902i	$0.850032\pi$
$132$	−3.61129	−	3.61129i	−0.314323	−	0.314323i
$133$	−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	0.756080	−	0.654479i	$-0.227112\pi$
$137$	4.67796	+	3.27554i	0.399665	+	0.279848i	−0.356415	+	0.934328i	$0.616001\pi$
$138$	0.857272	−	0.600268i	0.0729758	−	0.0510982i
$139$	−3.42015	+	9.39679i	−0.290094	+	0.797026i	0.705958	+	0.708253i	$0.250517\pi$
$139$	−3.42015	+	9.39679i	−0.290094	+	0.797026i	−0.996052	+	0.0887722i	$0.971706\pi$
$140$		0			0
$141$	3.51582	+	2.02986i	0.296085	+	0.170945i
$142$	−0.201284	+	2.30069i	−0.0168914	+	0.193069i
$143$	0.522445	−	5.97158i	0.0436891	−	0.499368i
$144$	0.373418	+	0.215593i	0.0311182	+	0.0179661i
$145$		0			0
$146$	0.0447004	−	0.122813i	0.00369943	−	0.0101641i
$147$	−5.86547	+	4.10704i	−0.483776	+	0.338743i
$148$	9.98136	+	6.98902i	0.820463	+	0.574494i
$149$	1.44345	+	3.96584i	0.118252	+	0.324894i	0.984671	−	0.174424i	$-0.0558062\pi$
$149$	1.44345	+	3.96584i	0.118252	+	0.324894i	−0.866419	+	0.499318i	$0.833584\pi$
$150$		0			0
$151$			16.0056i			1.30252i	0.758856	+	0.651258i	$0.225758\pi$
$151$			16.0056i			1.30252i	−0.758856	+	0.651258i	$0.774242\pi$
$152$	0.139302	+	12.1451i	0.0112989	+	0.985101i
$153$	2.32719	+	2.32719i	0.188142	+	0.188142i
$154$	12.7177	+	10.6714i	1.02482	+	0.859930i
$155$		0			0
$156$	−0.220280	−	1.24927i	−0.0176365	−	0.100021i
$157$	−7.23463	−	10.3321i	−0.577386	−	0.824593i	0.419136	−	0.907923i	$-0.362333\pi$
$157$	−7.23463	−	10.3321i	−0.577386	−	0.824593i	−0.996522	+	0.0833309i	$0.973444\pi$
$158$	−0.603681	−	1.29460i	−0.0480263	−	0.102993i
$159$	6.53918	−	3.77540i	0.518591	−	0.299409i
$160$		0			0
$161$	4.60245	−	3.86192i	0.362724	−	0.304362i
$162$	2.94279	+	0.257461i	0.231208	+	0.0202280i
$163$	−10.3009	+	2.76013i	−0.806833	+	0.216190i	−0.638582	−	0.769554i	$-0.720479\pi$
$163$	−10.3009	+	2.76013i	−0.806833	+	0.216190i	−0.168251	+	0.985744i	$0.553812\pi$
$164$	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	−0.763772	−	0.645486i	$-0.776655\pi$
$167$	1.34413	−	1.91962i	0.104012	−	0.148545i	0.867784	+	0.496941i	$0.165544\pi$
$168$	8.17123	+	3.81031i	0.630424	+	0.293972i
$169$	−7.39918	+	8.81800i	−0.569168	+	0.678308i
$170$		0			0
$171$	−4.41106	−	9.18308i	−0.337322	−	0.702248i
$172$	1.21077	−	1.21077i	0.0923203	−	0.0923203i
$173$	12.5886	−	1.10136i	0.957090	−	0.0837345i	0.402104	−	0.915594i	$-0.368279\pi$
$173$	12.5886	−	1.10136i	0.957090	−	0.0837345i	0.554986	+	0.831860i	$0.312724\pi$
$174$	1.38952	−	0.505745i	0.105340	−	0.0383405i
$175$		0			0
$176$	−0.157380	+	0.892548i	−0.0118630	+	0.0672784i
$177$	9.11535	−	4.25056i	0.685152	−	0.319491i
$178$	−0.904298	+	3.37488i	−0.0677800	+	0.252958i
$179$	3.40041	−	5.88969i	0.254159	−	0.440216i	−0.710508	−	0.703689i	$-0.751535\pi$
$179$	3.40041	−	5.88969i	0.254159	−	0.440216i	0.964667	+	0.263473i	$0.0848681\pi$
$180$		0			0
$181$	12.5267	+	14.9288i	0.931106	+	1.10965i	0.993752	+	0.111613i	$0.0356016\pi$
$181$	12.5267	+	14.9288i	0.931106	+	1.10965i	−0.0626462	+	0.998036i	$0.519954\pi$
$182$	1.06728	+	3.98315i	0.0791121	+	0.295250i
$183$	4.95359	+	1.32731i	0.366180	+	0.0981175i
$184$	−3.95835	−	1.44072i	−0.291813	−	0.106211i
$185$		0			0
$186$	6.30998	−	1.11262i	0.462670	−	0.0815813i
$187$	−2.92355	+	6.26958i	−0.213791	+	0.458477i
$188$	−0.554970	−	6.34333i	−0.0404753	−	0.462635i
$189$	−17.2691			−1.25614
$190$		0			0
$191$	−18.5918			−1.34525			−0.672627	−	0.739982i	$-0.734834\pi$
$191$	−18.5918			−1.34525			−0.672627	+	0.739982i	$0.734834\pi$
$192$	−0.319533	−	3.65228i	−0.0230603	−	0.263580i
$193$	7.75406	−	16.6286i	0.558149	−	1.19696i	−0.401527	−	0.915847i	$-0.631520\pi$
$193$	7.75406	−	16.6286i	0.558149	−	1.19696i	0.959676	−	0.281108i	$-0.0907018\pi$
$194$	−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	0.626166	−	0.779690i	$-0.284623\pi$
$197$	10.9281	+	2.92819i	0.778598	+	0.208625i	0.152431	+	0.988314i	$0.451290\pi$
$198$	2.52688	+	9.43043i	0.179577	+	0.670191i
$199$	−7.77099	−	9.26110i	−0.550871	−	0.656502i	0.416717	−	0.909036i	$-0.363180\pi$
$199$	−7.77099	−	9.26110i	−0.550871	−	0.656502i	−0.967588	+	0.252534i	$0.918736\pi$
$200$		0			0
$201$	3.57963	−	6.20009i	0.252487	−	0.437321i
$202$	1.91840	−	7.15956i	0.134978	−	0.503745i
$203$	7.69373	−	3.58765i	0.539994	−	0.251803i
$204$	−0.254210	+	1.44170i	−0.0177983	+	0.100939i
$205$		0			0
$206$	−0.306960	+	0.111724i	−0.0213870	+	0.00778421i
$207$	3.51975	−	0.307938i	0.244639	−	0.0214032i
$208$	−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	−0.576357	−	0.817198i	$-0.695526\pi$
$211$	4.77188	−	5.68690i	0.328509	−	0.391502i	0.904866	+	0.425696i	$0.139971\pi$
$212$	−10.7336	−	5.00517i	−0.737188	−	0.343756i
$213$	1.26828	−	1.81129i	0.0869011	−	0.124108i
$214$	7.18441	+	1.26681i	0.491116	+	0.0865970i
$215$		0			0
$216$	6.05386	+	10.4856i	0.411913	+	0.713454i
$217$	35.5305	−	9.52038i	2.41197	−	0.646285i
$218$	−5.44664	−	0.476520i	−0.368893	−	0.0322740i
$219$	−0.0958571	+	0.0804337i	−0.00647742	+	0.00543520i
$220$		0			0
$221$	−1.48806	+	0.859131i	−0.100098	+	0.0577914i
$222$	2.79178	+	5.98699i	0.187372	+	0.401820i
$223$	8.33065	+	11.8974i	0.557861	+	0.796708i	0.994699	−	0.102832i	$-0.0327904\pi$
$223$	8.33065	+	11.8974i	0.557861	+	0.796708i	−0.436837	+	0.899540i	$0.643902\pi$
$224$	−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	0.597683	−	0.801733i	$-0.296088\pi$
$227$	−3.07432	−	3.07432i	−0.204050	−	0.204050i	−0.801733	+	0.597683i	$0.796088\pi$
$228$	2.22061	−	3.95015i	0.147063	−	0.261605i
$229$		−	18.5866i		−	1.22824i	−0.789214	−	0.614119i	$-0.789512\pi$
$229$		−	18.5866i		−	1.22824i	0.789214	−	0.614119i	$-0.210488\pi$
$230$		0			0
$231$	−5.43648	−	14.9366i	−0.357694	−	0.982757i
$232$	−4.87549	−	3.41386i	−0.320092	−	0.224131i
$233$	18.0369	−	12.6296i	1.18164	−	0.827390i	0.193519	−	0.981097i	$-0.438010\pi$
$233$	18.0369	−	12.6296i	1.18164	−	0.827390i	0.988116	+	0.153707i	$0.0491211\pi$
$234$	−0.829403	+	2.27877i	−0.0542198	+	0.148968i
$235$		0			0
$236$	−13.6617	−	7.88760i	−0.889303	−	0.513439i
$237$	−0.119197	+	1.36243i	−0.00774269	+	0.0884993i
$238$	0.414760	−	4.74072i	0.0268849	−	0.307295i
$239$	−2.93366	−	1.69375i	−0.189763	−	0.109560i	0.402109	−	0.915592i	$-0.368277\pi$
$239$	−2.93366	−	1.69375i	−0.189763	−	0.109560i	−0.591872	+	0.806032i	$0.701611\pi$
$240$		0			0
$241$	−0.0368288	+	0.101186i	−0.00237235	+	0.00651798i	−0.940873	−	0.338759i	$-0.889993\pi$
$241$	−0.0368288	+	0.101186i	−0.00237235	+	0.00651798i	0.938501	+	0.345277i	$0.112215\pi$
$242$	−9.14801	+	6.40550i	−0.588056	+	0.411761i
$243$	−12.9949	−	9.09913i	−0.833623	−	0.583709i
$244$	−2.75109	−	7.55856i	−0.176121	−	0.483887i
$245$		0			0
$246$			1.58549i			0.101087i
$247$	5.22704	−	0.983611i	0.332589	−	0.0625857i
$248$	−18.2363	−	18.2363i	−1.15800	−	1.15800i
$249$	−0.482643	−	0.404986i	−0.0305863	−	0.0256649i
$250$		0			0
$251$	3.71248	+	21.0545i	0.234330	+	1.32895i	0.844020	+	0.536311i	$0.180183\pi$
$251$	3.71248	+	21.0545i	0.234330	+	1.32895i	−0.609691	+	0.792639i	$0.708706\pi$
$252$	6.80330	+	9.71612i	0.428567	+	0.612058i
$253$	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	0.471892	−	0.881656i	$-0.343571\pi$
$257$	12.5607	+	1.09892i	0.783518	+	0.0685489i	0.311625	+	0.950205i	$0.399127\pi$
$258$	0.896660	−	0.240259i	0.0558236	−	0.0149579i
$259$	18.9620	+	32.8431i	1.17824	+	2.04077i
$260$		0			0
$261$	4.91637	+	0.866889i	0.304316	+	0.0536591i
$262$	−4.36337	+	6.23153i	−0.269570	+	0.384985i
$263$	−24.1482	−	11.2605i	−1.48904	−	0.694351i	−0.503532	−	0.863977i	$-0.667966\pi$
$263$	−24.1482	−	11.2605i	−1.48904	−	0.694351i	−0.985509	+	0.169626i	$0.945744\pi$
$264$	−7.16352	+	8.53715i	−0.440884	+	0.525426i
$265$		0			0
$266$	−6.07194	+	13.4211i	−0.372294	+	0.822899i
$267$	2.36543	−	2.36543i	0.144762	−	0.144762i
$268$	−11.1864	+	0.978681i	−0.683317	+	0.0597825i
$269$	12.1556	−	4.42428i	0.741141	−	0.269753i	0.0562682	−	0.998416i	$-0.482080\pi$
$269$	12.1556	−	4.42428i	0.741141	−	0.269753i	0.684873	+	0.728662i	$0.259858\pi$
$270$		0			0
$271$	3.22437	−	18.2863i	0.195866	−	1.11081i	−0.715313	−	0.698804i	$-0.753716\pi$
$271$	3.22437	−	18.2863i	0.195866	−	1.11081i	0.911180	−	0.412009i	$-0.135173\pi$
$272$	0.235451	−	0.109793i	0.0142763	−	0.00665715i
$273$	1.02185	−	3.81361i	0.0618455	−	0.230810i
$274$	2.42799	−	4.20540i	0.146680	−	0.254058i
$275$		0			0
$276$	1.01021	+	1.20392i	0.0608072	+	0.0724672i
$277$	4.08087	+	15.2300i	0.245195	+	0.915082i	0.973285	+	0.229600i	$0.0737418\pi$
$277$	4.08087	+	15.2300i	0.245195	+	0.915082i	−0.728090	+	0.685482i	$0.759592\pi$
$278$	8.21339	+	2.20077i	0.492607	+	0.131994i
$279$	20.3271	+	7.39846i	1.21695	+	0.442934i
$280$		0			0
$281$	0.225686	−	0.0397945i	0.0134633	−	0.00237394i	−0.166912	−	0.985972i	$-0.553380\pi$
$281$	0.225686	−	0.0397945i	0.0134633	−	0.00237394i	0.180376	+	0.983598i	$0.442269\pi$
$282$	1.45891	−	3.12865i	0.0868769	−	0.186308i
$283$	1.12979	+	12.9136i	0.0671591	+	0.767632i	0.952867	+	0.303389i	$0.0981181\pi$
$283$	1.12979	+	12.9136i	0.0671591	+	0.767632i	−0.885708	+	0.464243i	$0.846326\pi$
$284$	−3.46818			−0.205799
$285$		0			0
$286$	−5.09718			−0.301403
$287$	0.793305	+	9.06752i	0.0468273	+	0.535239i
$288$	5.65956	−	12.1370i	0.333493	−	0.715177i
$289$	−14.7889	+	2.60769i	−0.869937	+	0.153393i
$290$		0			0
$291$	7.55744	+	2.75068i	0.443025	+	0.161248i
$292$	0.189580	+	0.0507977i	0.0110943	+	0.00297271i
$293$	−1.97297	−	7.36321i	−0.115262	−	0.430163i	0.884044	−	0.467403i	$-0.154810\pi$
$293$	−1.97297	−	7.36321i	−0.115262	−	0.430163i	−0.999306	+	0.0372396i	$0.988144\pi$
$294$	3.91373	+	4.66420i	0.228253	+	0.272022i
$295$		0			0
$296$	13.2946	−	23.0270i	0.772735	−	1.33842i
$297$	5.52476	−	20.6187i	0.320579	−	1.19642i
$298$	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
$303$	−5.01808	+	5.01808i	−0.288281	+	0.288281i
$304$	−0.800253	+	0.0792713i	−0.0458977	+	0.00454652i
$305$		0			0
$306$	1.79887	−	2.14381i	0.102835	−	0.122553i
$307$	−24.9542	−	11.6364i	−1.42421	−	0.664122i	−0.450685	−	0.892683i	$-0.648820\pi$
$307$	−24.9542	−	11.6364i	−1.42421	−	0.664122i	−0.973530	+	0.228561i	$0.926598\pi$
$308$	−14.3000	+	20.4225i	−0.814817	+	1.16368i
$309$	0.308006	+	0.0543097i	0.0175218	+	0.00308957i
$310$		0			0
$311$	3.61837	+	6.26721i	0.205179	+	0.355381i	0.950190	−	0.311672i	$-0.100889\pi$
$311$	3.61837	+	6.26721i	0.205179	+	0.355381i	−0.745011	+	0.667053i	$0.767556\pi$
$312$	−2.67380	+	0.716443i	−0.151374	+	0.0405606i
$313$	5.80964	+	0.508278i	0.328381	+	0.0287296i	0.250154	−	0.968206i	$-0.419519\pi$
$313$	5.80964	+	0.508278i	0.328381	+	0.0287296i	0.0782264	+	0.996936i	$0.475074\pi$
$314$	−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	0.938022	−	0.346574i	$-0.112655\pi$
$317$	1.23887	+	2.65676i	0.0695818	+	0.149219i	−0.868441	+	0.495793i	$0.834877\pi$
$318$	−3.68272	−	5.25947i	−0.206517	−	0.294937i
$319$	1.82213	+	10.3338i	0.102020	+	0.578582i
$320$		0			0
$321$	−5.35062	−	4.48970i	−0.298643	−	0.250591i
$322$	−3.61248	−	3.61248i	−0.201316	−	0.201316i
$323$	−6.05663	−	0.996463i	−0.337000	−	0.0554447i
$324$			4.43612i			0.246451i
$325$		0			0
$326$	3.10149	+	8.52127i	0.171776	+	0.471949i
$327$	4.28805	+	3.00253i	0.237130	+	0.166040i
$328$	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	0.683995	−	0.729487i	$-0.260241\pi$
$331$	7.17253	+	4.14106i	0.394238	+	0.227613i	−0.289757	+	0.957100i	$0.593574\pi$
$332$	−0.0861283	+	0.984451i	−0.00472690	+	0.0540288i
$333$	−1.94376	+	22.2172i	−0.106517	+	1.21750i
$334$	−1.72571	−	0.996337i	−0.0944264	−	0.0545171i
$335$		0			0
$336$	−0.204164	+	0.560937i	−0.0111381	+	0.0306016i
$337$	−12.2046	+	8.54575i	−0.664827	+	0.465517i	−0.856640	−	0.515915i	$-0.827452\pi$
$337$	−12.2046	+	8.54575i	−0.664827	+	0.465517i	0.191813	+	0.981431i	$0.438563\pi$
$338$	8.01799	+	5.61426i	0.436121	+	0.305375i
$339$	−4.51308	−	12.3996i	−0.245117	−	0.673453i
$340$		0			0
$341$			45.4680i			2.46223i
$342$	−7.45198	+	4.41713i	−0.402957	+	0.238851i
$343$	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	0.706326	−	0.707887i	$-0.250351\pi$
$347$	−3.73392	−	5.33259i	−0.200447	−	0.286268i	−0.906774	+	0.421618i	$0.861462\pi$
$348$	0.938461	+	2.01254i	0.0503068	+	0.107883i
$349$	21.2321	−	12.2584i	1.13653	−	0.656176i	0.190961	−	0.981598i	$-0.438840\pi$
$349$	21.2321	−	12.2584i	1.13653	−	0.656176i	0.945569	+	0.325422i	$0.105506\pi$
$350$		0			0
$351$	4.06160	−	3.40809i	0.216792	−	0.181910i
$352$	28.0410	+	2.45327i	1.49459	+	0.130760i
$353$	18.5195	−	4.96227i	0.985691	−	0.264115i	0.270251	−	0.962790i	$-0.412893\pi$
$353$	18.5195	−	4.96227i	0.985691	−	0.264115i	0.715440	+	0.698675i	$0.246226\pi$
$354$	−4.27615	−	7.40650i	−0.227275	−	0.393651i
$355$		0			0
$356$	−5.16719	−	0.911116i	−0.273861	−	0.0482890i
$357$	−2.61338	+	3.73229i	−0.138315	+	0.197534i
$358$	−5.24110	−	2.44397i	−0.277001	−	0.129168i
$359$	−12.6054	+	15.0226i	−0.665289	+	0.792860i	−0.988134	−	0.153592i	$-0.950916\pi$
$359$	−12.6054	+	15.0226i	−0.665289	+	0.792860i	0.322846	+	0.946452i	$0.395360\pi$
$360$		0			0
$361$	16.6681	+	9.12009i	0.877266	+	0.480005i
$362$	11.7177	−	11.7177i	0.615866	−	0.615866i
$363$	10.6516	−	0.931899i	0.559067	−	0.0489120i
$364$	−5.81910	+	2.11798i	−0.305004	+	0.111012i
$365$		0			0
$366$	0.757236	−	4.29450i	0.0395813	−	0.224477i
$367$	−12.5944	+	5.87286i	−0.657421	+	0.306561i	−0.722552	−	0.691316i	$-0.757031\pi$
$367$	−12.5944	+	5.87286i	−0.657421	+	0.306561i	0.0651311	+	0.997877i	$0.479253\pi$
$368$	0.0721840	−	0.269394i	0.00376285	−	0.0140431i
$369$	−2.67637	+	4.63561i	−0.139326	+	0.241320i
$370$		0			0
$371$	−23.6934	−	28.2366i	−1.23010	−	1.46597i
$372$	2.49035	+	9.29412i	0.129119	+	0.481878i
$373$	35.6461	+	9.55135i	1.84569	+	0.494550i	0.999278	−	0.0379859i	$-0.0120942\pi$
$373$	35.6461	+	9.55135i	1.84569	+	0.494550i	0.846407	+	0.532536i	$0.178761\pi$
$374$	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
$378$	1.27983	+	14.6285i	0.0658271	+	0.752407i
$379$	−2.15198			−0.110540			−0.0552699	−	0.998471i	$-0.517602\pi$
$379$	−2.15198			−0.110540			−0.0552699	+	0.998471i	$0.517602\pi$
$380$		0			0
$381$	3.06006			0.156771
$382$	1.37785	+	15.7489i	0.0704969	+	0.805783i
$383$	−4.96338	+	10.6440i	−0.253617	+	0.543883i	−0.991355	−	0.131203i	$-0.958116\pi$
$383$	−4.96338	+	10.6440i	−0.253617	+	0.543883i	0.737739	+	0.675086i	$0.235894\pi$
$384$	6.11781	−	1.07873i	0.312198	−	0.0550489i
$385$		0			0
$386$	−14.6606	−	5.33602i	−0.746205	−	0.271596i
$387$	3.02720	+	0.811135i	0.153881	+	0.0412323i
$388$	−3.26484	−	12.1846i	−0.165747	−	0.618578i
$389$	2.20372	+	2.62629i	0.111733	+	0.133158i	0.819012	−	0.573776i	$-0.194522\pi$
$389$	2.20372	+	2.62629i	0.111733	+	0.133158i	−0.707279	+	0.706934i	$0.750078\pi$
$390$		0			0
$391$	1.06438	−	1.84356i	0.0538281	−	0.0932330i
$392$	6.34298	−	23.6723i	0.320369	−	1.19563i
$393$	6.60111	−	3.07815i	0.332982	−	0.155272i
$394$	1.67054	−	9.47412i	0.0841607	−	0.477299i
$395$		0			0
$396$	−13.7772	+	5.01450i	−0.692331	+	0.251988i
$397$	−8.57163	+	0.749921i	−0.430198	+	0.0376375i	−0.300199	−	0.953877i	$-0.597053\pi$
$397$	−8.57163	+	0.749921i	−0.430198	+	0.0376375i	−0.129999	+	0.991514i	$0.541497\pi$
$398$	−7.26907	+	7.26907i	−0.364365	+	0.364365i
$399$	11.4596	−	8.22154i	0.573696	−	0.411592i
$400$		0			0
$401$	−9.47424	+	11.2910i	−0.473121	+	0.563844i	−0.948841	−	0.315753i	$-0.897743\pi$
$401$	−9.47424	+	11.2910i	−0.473121	+	0.563844i	0.475720	+	0.879597i	$0.342187\pi$
$402$	−5.51732	−	2.57277i	−0.275179	−	0.128318i
$403$	−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
$408$	3.18235	+	0.278419i	0.157550	+	0.0137838i
$409$	−28.3413	+	23.7811i	−1.40139	+	1.17590i	−0.440905	+	0.897554i	$0.645342\pi$
$409$	−28.3413	+	23.7811i	−1.40139	+	1.17590i	−0.960480	+	0.278348i	$0.910213\pi$
$410$		0			0
$411$	−4.02641	+	2.32465i	−0.198608	+	0.114666i
$412$	−0.207316	−	0.444591i	−0.0102137	−	0.0219034i
$413$	−28.1615	−	40.2187i	−1.38573	−	1.97903i
$414$	−0.521702	−	2.95872i	−0.0256402	−	0.145413i
$415$		0			0
$416$	5.35587	+	4.49411i	0.262593	+	0.220342i
$417$	−5.75671	−	5.75671i	−0.281907	−	0.281907i
$418$	−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	0.918959	−	0.394353i	$-0.129031\pi$
$421$	−0.789738	−	2.16979i	−0.0384895	−	0.105749i	−0.957449	+	0.288604i	$0.906809\pi$
$422$	−5.17096	−	3.62074i	−0.251718	−	0.176255i
$423$	9.54681	−	6.68475i	0.464182	−	0.325023i
$424$	−8.83901	+	24.2850i	−0.429260	+	1.17938i
$425$		0			0
$426$	−1.62832	−	0.940111i	−0.0788923	−	0.0455485i
$427$	2.18192	−	24.9394i	0.105590	−	1.20690i
$428$	−0.954825	+	10.9137i	−0.0461532	+	0.527534i
$429$	4.22640	+	2.44012i	0.204053	+	0.117810i
$430$		0			0
$431$	6.23851	−	17.1402i	0.300498	−	0.825612i	−0.693915	−	0.720057i	$-0.744116\pi$
$431$	6.23851	−	17.1402i	0.300498	−	0.825612i	0.994413	−	0.105556i	$-0.0336621\pi$
$432$	−0.656664	+	0.459801i	−0.0315938	+	0.0221222i
$433$	−17.8019	−	12.4651i	−0.855507	−	0.599032i	0.0614092	−	0.998113i	$-0.480441\pi$
$433$	−17.8019	−	12.4651i	−0.855507	−	0.599032i	−0.916916	+	0.399080i	$0.869329\pi$
$434$	−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
$438$	0.0752385	+	0.0752385i	0.00359504	+	0.00359504i
$439$	−7.23611	−	6.07181i	−0.345361	−	0.289792i	0.453563	−	0.891224i	$-0.350153\pi$
$439$	−7.23611	−	6.07181i	−0.345361	−	0.289792i	−0.798924	+	0.601432i	$0.794597\pi$
$440$		0			0
$441$	3.56949	+	20.2436i	0.169976	+	0.963980i
$442$	0.838042	+	1.19685i	0.0398616	+	0.0569282i
$443$	14.4220	+	30.9280i	0.685208	+	1.46943i	0.873250	+	0.487273i	$0.162008\pi$
$443$	14.4220	+	30.9280i	0.685208	+	1.46943i	−0.188042	+	0.982161i	$0.560214\pi$
$444$	−8.59115	+	4.96010i	−0.407718	+	0.235396i
$445$		0			0
$446$	9.46077	−	7.93852i	0.447980	−	0.375900i
$447$	−3.42286	−	0.299461i	−0.161896	−	0.0141640i
$448$	−17.2874	+	4.63214i	−0.816752	+	0.218848i
$449$	20.6242	+	35.7221i	0.973316	+	1.68583i	0.685385	+	0.728181i	$0.259634\pi$
$449$	20.6242	+	35.7221i	0.973316	+	1.68583i	0.287931	+	0.957651i	$0.407033\pi$
$450$		0			0
$451$	−11.0801	−	1.95372i	−0.521741	−	0.0919970i
$452$	−11.8711	+	16.9537i	−0.558369	+	0.797433i
$453$	−11.8098	−	5.50700i	−0.554873	−	0.258742i
$454$	−2.37638	+	2.83206i	−0.111529	+	0.132915i
$455$		0			0
$456$	−9.00929	−	4.07597i	−0.421899	−	0.190875i
$457$	12.9398	−	12.9398i	0.605300	−	0.605300i	−0.336414	−	0.941714i	$-0.609214\pi$
$457$	12.9398	−	12.9398i	0.605300	−	0.605300i	0.941714	+	0.336414i	$0.109214\pi$
$458$	−15.7445	+	1.37747i	−0.735693	+	0.0643648i
$459$	−5.74973	+	2.09273i	−0.268374	+	0.0976803i
$460$		0			0
$461$	5.56561	−	31.5641i	0.259216	−	1.47009i	−0.525797	−	0.850610i	$-0.676233\pi$
$461$	5.56561	−	31.5641i	0.259216	−	1.47009i	0.785014	−	0.619479i	$-0.212656\pi$
$462$	−12.2497	+	5.71215i	−0.569910	+	0.265753i
$463$	−9.97438	+	37.2249i	−0.463549	+	1.72999i	0.198108	+	0.980180i	$0.436520\pi$
$463$	−9.97438	+	37.2249i	−0.463549	+	1.72999i	−0.661656	+	0.749807i	$0.730146\pi$
$464$	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	0.882183	−	0.470907i	$-0.156073\pi$
$467$	−2.53409	−	9.45734i	−0.117263	−	0.437633i	−0.999446	+	0.0332738i	$0.989407\pi$
$468$	−3.51760	−	0.942537i	−0.162601	−	0.0435688i
$469$	−32.8412	−	11.9532i	−1.51647	−	0.551949i
$470$		0			0
$471$	10.1128	−	1.78316i	0.465974	−	0.0821637i
$472$	−14.5480	+	31.1984i	−0.669628	+	1.43602i
$473$	0.574128	+	6.56232i	0.0263984	+	0.301736i
$474$	1.16293			0.0534153
$475$		0			0
$476$	7.14642			0.327555
$477$	−1.88924	−	21.5941i	−0.0865023	−	0.988726i
$478$	−1.21734	+	2.61060i	−0.0556800	+	0.119406i
$479$	12.0119	−	2.11802i	0.548837	−	0.0967747i	0.107648	−	0.994189i	$-0.465668\pi$
$479$	12.0119	−	2.11802i	0.548837	−	0.0967747i	0.441189	+	0.897414i	$0.354557\pi$
$480$		0			0
$481$	−10.9414	−	3.98235i	−0.498886	−	0.181580i
$482$	0.0884433	+	0.0236983i	0.00402848	+	0.00107943i
$483$	1.26598	+	4.72470i	0.0576041	+	0.214981i
$484$	−10.7800	−	12.8471i	−0.489999	−	0.583958i
$485$		0			0
$486$	−6.74471	+	11.6822i	−0.305946	+	0.529915i
$487$	2.75407	−	10.2783i	0.124799	−	0.465756i	−0.875034	−	0.484062i	$-0.839161\pi$
$487$	2.75407	−	10.2783i	0.124799	−	0.465756i	0.999832	+	0.0183065i	$0.00582746\pi$
$488$	−15.9078	+	7.41794i	−0.720113	+	0.335794i
$489$	1.50765	−	8.55028i	0.0681781	−	0.386657i
$490$		0			0
$491$	36.5384	−	13.2989i	1.64896	−	0.600171i	0.660385	−	0.750927i	$-0.270393\pi$
$491$	36.5384	−	13.2989i	1.64896	−	0.600171i	0.988571	+	0.150756i	$0.0481709\pi$
$492$	−2.37189	+	0.207514i	−0.106933	+	0.00935544i
$493$	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
$498$	−0.307290	+	0.438856i	−0.0137700	+	0.0196656i
$499$	16.0108	+	2.82313i	0.716740	+	0.126381i	0.520113	−	0.854098i	$-0.325890\pi$
$499$	16.0108	+	2.82313i	0.716740	+	0.126381i	0.196627	+	0.980478i	$0.437001\pi$
$500$		0			0
$501$	0.953931	+	1.65226i	0.0426185	+	0.0738174i
$502$	17.5599	−	4.70517i	0.783738	−	0.210002i
$503$	28.6678	+	2.50810i	1.27823	+	0.111831i	0.705971	−	0.708240i	$-0.250511\pi$
$503$	28.6678	+	2.50810i	1.27823	+	0.111831i	0.572261	+	0.820071i	$0.306066\pi$
$504$	19.8273	−	16.6371i	0.883178	−	0.741074i
$505$		0			0
$506$	5.46888	−	3.15746i	0.243121	−	0.140366i
$507$	−3.96059	−	8.49351i	−0.175896	−	0.377210i
$508$	−2.75295	−	3.93162i	−0.122142	−	0.174437i
$509$	−3.87905	−	21.9992i	−0.171936	−	0.975097i	−0.941621	−	0.336673i	$-0.890698\pi$
$509$	−3.87905	−	21.9992i	−0.171936	−	0.975097i	0.769686	−	0.638423i	$-0.220413\pi$
$510$		0			0
$511$	0.467940	+	0.392649i	0.0207005	+	0.0173697i
$512$	−1.47449	−	1.47449i	−0.0651637	−	0.0651637i
$513$	18.9390	−	0.217225i	0.836176	−	0.00959073i
$514$		−	10.7215i		−	0.472906i
$515$		0			0
$516$	0.476786	+	1.30996i	0.0209893	+	0.0576678i
$517$	20.0666	+	14.0508i	0.882528	+	0.617953i
$518$	26.4158	−	18.4965i	1.16064	−	0.812691i
$519$	−3.51867	+	9.66747i	−0.154453	+	0.424355i
$520$		0			0
$521$	−23.6960	−	13.6809i	−1.03814	−	0.599371i	−0.118835	−	0.992914i	$-0.537916\pi$
$521$	−23.6960	−	13.6809i	−1.03814	−	0.599371i	−0.919306	+	0.393543i	$0.871249\pi$
$522$	0.369976	−	4.22885i	0.0161934	−	0.185092i
$523$	0.813771	−	9.30145i	0.0355837	−	0.406724i	−0.957425	−	0.288682i	$-0.906783\pi$
$523$	0.813771	−	9.30145i	0.0355837	−	0.406724i	0.993009	−	0.118042i	$-0.0376616\pi$
$524$	−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
$528$	−0.604422	−	0.423221i	−0.0263041	−	0.0184183i
$529$	7.08484	+	19.4654i	0.308036	+	0.846323i
$530$		0			0
$531$		−	28.8732i		−	1.25299i
$532$	−20.8727	−	7.32704i	−0.904945	−	0.317667i
$533$	−1.97607	−	1.97607i	−0.0855932	−	0.0855932i
$534$	−2.17904	−	1.82843i	−0.0942962	−	0.0791239i
$535$		0			0
$536$	4.25497	+	24.1311i	0.183787	+	1.04231i
$537$	3.17577	+	4.53547i	0.137044	+	0.195720i
$538$	−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	−0.118988	−	0.992896i	$-0.537965\pi$
$541$	19.4951	−	16.3584i	0.838162	−	0.703301i	0.957149	+	0.289594i	$0.0935204\pi$
$542$	−15.7291	−	1.37612i	−0.675622	−	0.0591093i
$543$	−15.3253	+	4.10641i	−0.657673	+	0.176223i
$544$	−4.03426	−	6.98755i	−0.172968	−	0.299589i
$545$		0			0
$546$	−3.30620	−	0.582973i	−0.141492	−	0.0249489i
$547$	−17.3018	+	24.7095i	−0.739771	+	1.05650i	0.256182	+	0.966629i	$0.417535\pi$
$547$	−17.3018	+	24.7095i	−0.739771	+	1.05650i	−0.995953	+	0.0898741i	$0.971354\pi$
$548$	6.60907	+	3.08186i	0.282326	+	0.131651i
$549$	9.46327	−	11.2779i	0.403883	−	0.481329i
$550$		0			0
$551$	−8.39256	+	4.03134i	−0.357535	+	0.171741i
$552$	2.42498	−	2.42498i	0.103214	−	0.103214i
$553$	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	0.221510	−	0.975158i	$-0.428902\pi$
$557$	26.2184	−	12.2258i	1.11091	−	0.518025i	0.889398	+	0.457133i	$0.151124\pi$
$558$	4.76070	−	17.7672i	0.201537	−	0.752145i
$559$	−0.818106	+	1.41700i	−0.0346022	+	0.0599327i
$560$		0			0
$561$	−3.62014	−	4.31432i	−0.152843	−	0.182151i
$562$	−0.0504352	−	0.188227i	−0.00212748	−	0.00793987i
$563$	18.9758	+	5.08454i	0.799734	+	0.214288i	0.635467	−	0.772128i	$-0.280808\pi$
$563$	18.9758	+	5.08454i	0.799734	+	0.214288i	0.164267	+	0.986416i	$0.447474\pi$
$564$	4.87141	+	1.77305i	0.205123	+	0.0746588i
$565$		0			0
$566$	10.8552	−	1.91407i	0.456279	−	0.0804543i
$567$	−5.83499	+	12.5132i	−0.245047	+	0.525504i
$568$	0.659597	+	7.53923i	0.0276761	+	0.316339i
$569$	28.9346			1.21300			0.606501	−	0.795082i	$-0.292572\pi$
$569$	28.9346			1.21300			0.606501	+	0.795082i	$0.292572\pi$
$570$		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
$573$	6.39683	−	13.7180i	0.267231	−	0.573079i
$574$	7.62220	−	1.34400i	0.318145	−	0.0560975i
$575$		0			0
$576$	−9.89016	−	3.59972i	−0.412090	−	0.149988i
$577$	−26.2166	−	7.02471i	−1.09141	−	0.292442i	−0.332148	−	0.943227i	$-0.607773\pi$
$577$	−26.2166	−	7.02471i	−1.09141	−	0.292442i	−0.759262	+	0.650785i	$0.774440\pi$
$578$	3.30496	+	12.3343i	0.137468	+	0.513039i
$579$	9.60160	+	11.4427i	0.399029	+	0.475544i
$580$		0			0
$581$	−1.53783	+	2.66360i	−0.0638000	+	0.110505i
$582$	1.76999	−	6.60568i	0.0733683	−	0.273814i
$583$	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	0.703186	−	0.711006i	$-0.251760\pi$
$587$	36.8062	−	3.22012i	1.51915	−	0.132909i	0.815968	+	0.578097i	$0.196204\pi$
$588$	−6.46541	+	6.46541i	−0.266629	+	0.266629i
$589$	−38.8465	+	10.8879i	−1.60064	+	0.448628i
$590$		0			0
$591$	−5.92060	+	7.05589i	−0.243541	+	0.290241i
$592$	1.59551	+	0.743997i	0.0655750	+	0.0305781i
$593$	1.82350	−	2.60423i	0.0748823	−	0.106943i	−0.779964	−	0.625825i	$-0.784763\pi$
$593$	1.82350	−	2.60423i	0.0748823	−	0.106943i	0.854846	+	0.518882i	$0.173651\pi$
$594$	−17.8753	−	3.15190i	−0.733433	−	0.129324i
$595$		0			0
$596$	2.69459	+	4.66716i	0.110375	+	0.191174i
$597$	9.50710	−	2.54742i	0.389100	−	0.104259i
$598$	1.56257	+	0.136707i	0.0638981	+	0.00559036i
$599$	−5.95719	+	4.99867i	−0.243404	+	0.204240i	−0.756326	−	0.654195i	$-0.773008\pi$
$599$	−5.95719	+	4.99867i	−0.243404	+	0.204240i	0.512922	+	0.858435i	$0.328563\pi$
$600$		0			0
$601$	16.9764	−	9.80133i	0.692482	−	0.399805i	−0.112059	−	0.993702i	$-0.535745\pi$
$601$	16.9764	−	9.80133i	0.692482	−	0.399805i	0.804541	+	0.593897i	$0.202411\pi$
$602$	−1.91513	−	4.10701i	−0.0780549	−	0.167389i
$603$	−11.7885	−	16.8357i	−0.480063	−	0.685601i
$604$	3.54907	+	20.1278i	0.144410	+	0.818988i
$605$		0			0
$606$	4.62266	+	3.87887i	0.187783	+	0.157568i
$607$	16.2338	+	16.2338i	0.658910	+	0.658910i	0.955122	−	0.296212i	$-0.0957236\pi$
$607$	16.2338	+	16.2338i	0.658910	+	0.658910i	−0.296212	+	0.955122i	$0.595724\pi$
$608$	4.61879	+	24.5449i	0.187317	+	0.995427i
$609$			6.91125i			0.280058i
$610$		0			0
$611$	2.08107	+	5.71770i	0.0841912	+	0.231314i
$612$	3.44258	+	2.41052i	0.139158	+	0.0974396i
$613$	−30.4501	+	21.3214i	−1.22987	+	0.861162i	−0.993866	−	0.110590i	$-0.964726\pi$
$613$	−30.4501	+	21.3214i	−1.22987	+	0.861162i	−0.236001	+	0.971753i	$0.575837\pi$
$614$	−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	−0.996334	−	0.0855443i	$-0.972737\pi$
$617$	−0.00700337	+	0.0800488i	−0.000281945	+	0.00322264i	0.996052	+	0.0887670i	$0.0282926\pi$
$618$	0.0231787	−	0.264933i	0.000932382	−	0.0106572i
$619$	−24.9397	−	14.3989i	−1.00241	−	0.578741i	−0.0934491	−	0.995624i	$-0.529789\pi$
$619$	−24.9397	−	14.3989i	−1.00241	−	0.578741i	−0.908960	+	0.416883i	$0.863123\pi$
$620$		0			0
$621$	−2.24664	+	6.17259i	−0.0901545	+	0.247697i
$622$	5.04072	−	3.52955i	0.202115	−	0.141522i
$623$	−13.3769	−	9.36663i	−0.535935	−	0.375266i
$624$	−0.0626836	−	0.172222i	−0.00250935	−	0.00689439i
$625$		0			0
$626$		−	4.95896i		−	0.198200i
$627$	6.15006	+	16.3126i	0.245610	+	0.651461i
$628$	−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	0.957240	−	0.289296i	$-0.0934211\pi$
$631$	−1.03534	−	5.87173i	−0.0412164	−	0.233750i	−0.998456	+	0.0555461i	$0.982310\pi$
$632$	−2.68485	−	3.83436i	−0.106798	−	0.152523i
$633$	2.55426	+	5.47763i	0.101523	+	0.217716i
$634$	2.15870	−	1.24633i	0.0857331	−	0.0494980i
$635$		0			0
$636$	7.38618	−	6.19774i	0.292881	−	0.245756i
$637$	−10.6911	−	0.935350i	−0.423597	−	0.0370599i
$638$	8.61862	−	2.30935i	0.341214	−	0.0914281i
$639$	−3.17389	−	5.49734i	−0.125557	−	0.217471i
$640$		0			0
$641$	−23.2634	−	4.10197i	−0.918850	−	0.162018i	−0.305831	−	0.952086i	$-0.598934\pi$
$641$	−23.2634	−	4.10197i	−0.918850	−	0.162018i	−0.613019	+	0.790068i	$0.710045\pi$
$642$	−3.40664	+	4.86519i	−0.134449	+	0.192014i
$643$	16.0066	+	7.46400i	0.631239	+	0.294351i	0.711783	−	0.702400i	$-0.247888\pi$
$643$	16.0066	+	7.46400i	0.631239	+	0.294351i	−0.0805441	+	0.996751i	$0.525666\pi$
$644$	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	−0.806999	−	0.590553i	$-0.798910\pi$
$647$	−5.50558	+	5.50558i	−0.216447	+	0.216447i	0.590553	+	0.806999i	$0.298910\pi$
$648$	9.64337	−	0.843686i	0.378827	−	0.0331431i
$649$	57.0292	−	20.7569i	2.23859	−	0.814780i
$650$		0			0
$651$	−5.20024	+	29.4920i	−0.203814	+	1.15588i
$652$	−12.3419	+	5.75512i	−0.483346	+	0.225388i
$653$	−0.674379	+	2.51682i	−0.0263905	+	0.0984907i	−0.977865	−	0.209237i	$-0.932902\pi$
$653$	−0.674379	+	2.51682i	−0.0263905	+	0.0984907i	0.951474	+	0.307728i	$0.0995686\pi$
$654$	2.22562	−	3.85488i	0.0870285	−	0.150738i
$655$		0			0
$656$	0.271594	+	0.323674i	0.0106040	+	0.0126373i
$657$	0.0929746	+	0.346986i	0.00362729	+	0.0135372i
$658$	−16.2776	−	4.36157i	−0.634567	−	0.170032i
$659$	25.1582	+	9.15684i	0.980025	+	0.356700i	0.781850	−	0.623467i	$-0.214276\pi$
$659$	25.1582	+	9.15684i	0.980025	+	0.356700i	0.198175	+	0.980167i	$0.436499\pi$
$660$		0			0
$661$	−36.0063	+	6.34888i	−1.40048	+	0.246943i	−0.822341	−	0.568995i	$-0.807333\pi$
$661$	−36.0063	+	6.34888i	−1.40048	+	0.246943i	−0.578140	+	0.815937i	$0.696221\pi$
$662$	2.97629	−	6.38267i	0.115677	−	0.248070i
$663$	−0.121922	−	1.39357i	−0.00473505	−	0.0541218i
$664$	2.15641			0.0836849
$665$		0			0
$666$	18.9640			0.734841
$667$	−0.281429	−	3.21675i	−0.0108970	−	0.124553i
$668$	1.26466	−	2.71206i	0.0489310	−	0.104933i
$669$	−11.6449	+	2.05330i	−0.450216	+	0.0793853i
$670$		0			0
$671$	29.0787	+	10.5838i	1.12257	+	0.408583i
$672$	17.9078	+	4.79837i	0.690808	+	0.185101i
$673$	4.66494	+	17.4098i	0.179820	+	0.671098i	0.995680	+	0.0928486i	$0.0295973\pi$
$673$	4.66494	+	17.4098i	0.179820	+	0.671098i	−0.815860	+	0.578249i	$0.803736\pi$
$674$	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	0.334242	+	0.942487i	$0.391520\pi$
$677$	−11.0963	+	41.4118i	−0.426464	+	1.59158i	−0.760706	+	0.649097i	$0.775147\pi$
$678$	−10.1691	+	4.74193i	−0.390542	+	0.182113i
$679$	6.81750	−	38.6640i	0.261632	−	1.48379i
$680$		0			0
$681$	3.32617	−	1.21063i	0.127459	−	0.0463914i
$682$	38.5154	−	3.36966i	1.47483	−	0.129031i
$683$	17.1640	−	17.1640i	0.656763	−	0.656763i	−0.297850	−	0.954613i	$-0.596270\pi$
$683$	17.1640	−	17.1640i	0.656763	−	0.656763i	0.954613	+	0.297850i	$0.0962696\pi$
$684$	−7.58337	−	10.5701i	−0.289957	−	0.404156i
$685$		0			0
$686$	3.89953	−	4.64727i	0.148885	−	0.177434i
$687$	13.7142	+	6.39505i	0.523230	+	0.243986i
$688$	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	0.958310	−	0.285731i	$-0.0922363\pi$
$691$	6.09079	+	10.5496i	0.231705	+	0.401324i	−0.726605	+	0.687055i	$0.758903\pi$
$692$	15.5865	−	4.17639i	0.592510	−	0.158762i
$693$	−45.4578	−	3.97704i	−1.72680	−	0.151075i
$694$	−4.24046	+	3.55817i	−0.160966	+	0.135066i
$695$		0			0
$696$	4.19643	−	2.42281i	0.159065	−	0.0918364i
$697$	1.36296	+	2.92289i	0.0516259	+	0.110712i
$698$	−11.9575	−	17.0770i	−0.452597	−	0.646375i
$699$	3.11288	+	17.6540i	0.117740	+	0.667737i
$700$		0			0
$701$	23.1767	+	19.4476i	0.875372	+	0.734524i	0.965222	−	0.261431i	$-0.0841944\pi$
$701$	23.1767	+	19.4476i	0.875372	+	0.734524i	−0.0898504	+	0.995955i	$0.528639\pi$
$702$	−3.18797	−	3.18797i	−0.120322	−	0.120322i
$703$	−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
$708$	10.5205	−	7.36651i	0.395383	−	0.276850i
$709$	0.671174	−	1.84404i	0.0252065	−	0.0692542i	−0.926451	−	0.376415i	$-0.877157\pi$
$709$	0.671174	−	1.84404i	0.0252065	−	0.0692542i	0.951658	+	0.307161i	$0.0993789\pi$
$710$		0			0
$711$	3.40015	+	1.96308i	0.127516	+	0.0736212i
$712$	−0.997885	+	11.4059i	−0.0373973	+	0.427453i
$713$	1.21946	−	13.9384i	0.0456690	−	0.521999i
$714$	3.35526	+	1.93716i	0.125568	+	0.0724965i
$715$		0			0
$716$	2.97021	−	8.16057i	0.111002	−	0.304975i
$717$	2.25912	−	1.58185i	0.0843684	−	0.0590754i
$718$	13.6596	+	9.56458i	0.509773	+	0.356947i
$719$	−4.78058	−	13.1345i	−0.178285	−	0.489835i	0.818072	−	0.575117i	$-0.195043\pi$
$719$	−4.78058	−	13.1345i	−0.178285	−	0.489835i	−0.996357	+	0.0852814i	$0.972821\pi$
$720$		0			0
$721$		−	1.52677i		−	0.0568599i
$722$	6.49025	−	14.7952i	0.241542	−	0.550621i
$723$	−0.0619893	−	0.0619893i	−0.00230541	−	0.00230541i
$724$	19.0633	+	15.9960i	0.708481	+	0.594486i
$725$		0			0
$726$	−1.57880	−	8.95383i	−0.0585949	−	0.332308i
$727$	−13.9674	−	19.9475i	−0.518022	−	0.739813i	0.471865	−	0.881671i	$-0.343581\pi$
$727$	−13.9674	−	19.9475i	−0.518022	−	0.739813i	−0.989887	+	0.141858i	$0.954692\pi$
$728$	5.71084	+	12.2469i	0.211658	+	0.453902i
$729$	2.15924	−	1.24664i	0.0799718	−	0.0461717i
$730$		0			0
$731$	1.44648	−	1.21374i	0.0534999	−	0.0448917i
$732$	6.52369	+	0.570749i	0.241122	+	0.0210955i
$733$	−17.2215	+	4.61450i	−0.636092	+	0.170440i	−0.562433	−	0.826843i	$-0.690134\pi$
$733$	−17.2215	+	4.61450i	−0.636092	+	0.170440i	−0.0736595	+	0.997283i	$0.523468\pi$
$734$	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
$738$	4.12512	+	1.92357i	0.151848	+	0.0708078i
$739$	18.5274	−	22.0801i	0.681543	−	0.812231i	−0.308763	−	0.951139i	$-0.599915\pi$
$739$	18.5274	−	22.0801i	0.681543	−	0.812231i	0.990305	+	0.138908i	$0.0443593\pi$
$740$		0			0
$741$	−1.07269	+	4.19523i	−0.0394064	+	0.154116i
$742$	−22.1630	+	22.1630i	−0.813630	+	0.813630i
$743$	6.33768	−	0.554475i	0.232507	−	0.0203417i	0.0296933	−	0.999559i	$-0.490547\pi$
$743$	6.33768	−	0.554475i	0.232507	−	0.0203417i	0.202814	+	0.979217i	$0.434991\pi$
$744$	19.7302	−	7.18121i	0.723345	−	0.263276i
$745$		0			0
$746$	5.44908	−	30.9033i	0.199505	−	1.13145i
$747$	−1.63925	+	0.764396i	−0.0599771	+	0.0279678i
$748$	−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	0.852421	+	0.522856i	$0.175133\pi$
$751$	33.4145	+	39.8218i	1.21931	+	1.45312i	0.366891	+	0.930264i	$0.380422\pi$
$752$	−0.238104	−	0.888618i	−0.00868277	−	0.0324046i
$753$	−16.8125	−	4.50491i	−0.612683	−	0.164168i
$754$	2.08260	+	0.758005i	0.0758439	+	0.0276049i
$755$		0			0
$756$	−21.7167	+	3.82924i	−0.789829	+	0.139268i
$757$	22.6581	−	48.5905i	0.823523	−	1.76605i	0.207652	−	0.978203i	$-0.433418\pi$
$757$	22.6581	−	48.5905i	0.823523	−	1.76605i	0.615871	−	0.787847i	$-0.288804\pi$
$758$	0.159485	+	1.82292i	0.00579275	+	0.0662115i
$759$	−6.04614			−0.219461
$760$		0			0
$761$	28.6371			1.03809			0.519046	−	0.854746i	$-0.326287\pi$
$761$	28.6371			1.03809			0.519046	+	0.854746i	$0.326287\pi$
$762$	−0.226783	−	2.59214i	−0.00821548	−	0.0939034i
$763$	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
$768$	−3.26496	−	12.1850i	−0.117814	−	0.439688i
$769$	−3.77330	−	4.49684i	−0.136069	−	0.162160i	0.693707	−	0.720257i	$-0.255976\pi$
$769$	−3.77330	−	4.49684i	−0.136069	−	0.162160i	−0.829776	+	0.558097i	$0.811532\pi$
$770$		0			0
$771$	−5.13259	+	8.88991i	−0.184846	+	0.320162i
$772$	6.06387	−	22.6307i	0.218244	−	0.814496i
$773$	−41.1245	+	19.1767i	−1.47915	+	0.689738i	−0.983851	−	0.178987i	$-0.942718\pi$
$773$	−41.1245	+	19.1767i	−1.47915	+	0.689738i	−0.495295	+	0.868725i	$0.664940\pi$
$774$	0.462756	−	2.62442i	0.0166334	−	0.0943329i
$775$		0			0
$776$	−25.8663	+	9.41455i	−0.928544	+	0.337963i
$777$	−30.7577	+	2.69095i	−1.10343	+	0.0965372i
$778$	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
$783$	−5.32352	+	7.60278i	−0.190247	+	0.271701i
$784$	1.59796	+	0.281763i	0.0570699	+	0.0100630i
$785$		0			0
$786$	−3.09668	−	5.36360i	−0.110455	−	0.191313i
$787$	−24.6233	+	6.59781i	−0.877728	+	0.235186i	−0.669426	−	0.742878i	$-0.733460\pi$
$787$	−24.6233	+	6.59781i	−0.877728	+	0.235186i	−0.208301	+	0.978065i	$0.566793\pi$
$788$	14.3919	+	1.25913i	0.512692	+	0.0448547i
$789$	16.6172	−	13.9435i	0.591588	−	0.496402i
$790$		0			0
$791$	−55.7851	+	32.2076i	−1.98349	+	1.14517i
$792$	13.5209	+	28.9956i	0.480444	+	1.03032i
$793$	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	0.902409	+	0.430880i	$0.141797\pi$
$797$	37.6403	+	37.6403i	1.33329	+	1.33329i	0.430880	+	0.902409i	$0.358203\pi$
$798$	−7.81365	−	9.09797i	−0.276600	−	0.322065i
$799$		−	7.02189i		−	0.248417i
$800$		0			0
$801$	−3.28455	−	9.02422i	−0.116054	−	0.318855i
$802$	10.2666	+	7.18875i	0.362526	+	0.253844i
$803$	−0.618513	+	0.433087i	−0.0218268	+	0.0152833i
$804$	3.12674	−	8.59066i	0.110272	−	0.302969i
$805$		0			0
$806$	8.31663	+	4.80161i	0.292941	+	0.169129i
$807$	−0.917874	+	10.4913i	−0.0323107	+	0.369313i
$808$	2.11694	−	24.1967i	0.0744736	−	0.851237i
$809$	−22.8364	−	13.1846i	−0.802885	−	0.463546i	0.0415941	−	0.999135i	$-0.486756\pi$
$809$	−22.8364	−	13.1846i	−0.802885	−	0.463546i	−0.844479	+	0.535589i	$0.820090\pi$
$810$		0			0
$811$	3.15115	−	8.65771i	0.110652	−	0.304013i	−0.871991	−	0.489522i	$-0.837171\pi$
$811$	3.15115	−	8.65771i	0.110652	−	0.304013i	0.982643	+	0.185509i	$0.0593934\pi$
$812$	8.87971	−	6.21764i	0.311617	−	0.218196i
$813$	12.3832	+	8.67084i	0.434299	+	0.304100i
$814$	13.6332	+	37.4569i	0.477844	+	1.31286i
$815$		0			0
$816$			0.211505i			0.00740415i
$817$	−5.46916	+	2.06195i	−0.191342	+	0.0721385i
$818$	22.2451	+	22.2451i	0.777783	+	0.777783i
$819$	−8.68250	−	7.28548i	−0.303391	−	0.254575i
$820$		0			0
$821$	2.89232	+	16.4031i	0.100943	+	0.572473i	0.992764	+	0.120085i	$0.0383168\pi$
$821$	2.89232	+	16.4031i	0.100943	+	0.572473i	−0.891821	+	0.452388i	$0.850572\pi$
$822$	2.26759	+	3.23845i	0.0790911	+	0.112954i
$823$	−11.5057	−	24.6740i	−0.401063	−	0.860082i	−0.998315	−	0.0580287i	$-0.981519\pi$
$823$	−11.5057	−	24.6740i	−0.401063	−	0.860082i	0.597252	−	0.802054i	$-0.296259\pi$
$824$	−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	−0.254284	−	0.967130i	$-0.581840\pi$
$827$	−19.3437	−	1.69235i	−0.672646	−	0.0588489i	−0.418361	+	0.908281i	$0.637395\pi$
$828$	4.35797	−	1.16771i	0.151450	−	0.0405809i
$829$	−23.2647	−	40.2956i	−0.808016	−	1.39953i	−0.914236	−	0.405183i	$-0.867208\pi$
$829$	−23.2647	−	40.2956i	−0.808016	−	1.39953i	0.106219	−	0.994343i	$-0.466125\pi$
$830$		0			0
$831$	−12.6416	−	2.22906i	−0.438533	−	0.0773253i
$832$	3.15174	−	4.50116i	0.109267	−	0.156050i
$833$	11.2246	+	5.23413i	0.388910	+	0.181352i
$834$	−4.44981	+	5.30308i	−0.154084	+	0.183631i
$835$		0			0
$836$	15.4258	−	22.5771i	0.533514	−	0.780847i
$837$	−28.4374	+	28.4374i	−0.982939	+	0.982939i
$838$	7.80332	−	0.682702i	0.269561	−	0.0235835i
$839$	−52.2864	+	19.0307i	−1.80513	+	0.657013i	−0.807374	+	0.590041i	$0.799112\pi$
$839$	−52.2864	+	19.0307i	−1.80513	+	0.657013i	−0.997755	+	0.0669723i	$0.978666\pi$
$840$		0			0
$841$	−4.24353	+	24.0663i	−0.146329	+	0.829872i
$842$	−1.77948	+	0.829783i	−0.0613248	+	0.0285962i
$843$	−0.0482886	+	0.180215i	−0.00166315	+	0.00620695i
$844$	4.73985	−	8.20966i	0.163152	−	0.282588i
$845$		0			0
$846$	−6.37010	−	7.59159i	−0.219008	−	0.261004i
$847$	−13.5094	−	50.4176i	−0.464187	−	1.73237i
$848$	−1.65277	−	0.442858i	−0.0567563	−	0.0152078i
$849$	−9.91707	−	3.60952i	−0.340353	−	0.123878i
$850$		0			0
$851$	14.2062	−	2.50493i	0.486982	−	0.0858680i
$852$	1.19329	−	2.55901i	0.0408814	−	0.0876704i
$853$	−0.873658	−	9.98595i	−0.0299135	−	0.341913i	−0.996373	−	0.0850935i	$-0.972881\pi$
$853$	−0.873658	−	9.98595i	−0.0299135	−	0.341913i	0.966460	−	0.256819i	$-0.0826744\pi$
$854$	−21.2876			−0.728447
$855$		0			0
$856$	23.9061			0.817094
$857$	1.25616	+	14.3580i	0.0429096	+	0.490459i	0.986994	+	0.160756i	$0.0513932\pi$
$857$	1.25616	+	14.3580i	0.0429096	+	0.490459i	−0.944085	+	0.329703i	$0.893051\pi$
$858$	1.75377	−	3.76098i	0.0598729	−	0.128398i
$859$	29.4418	−	5.19139i	1.00454	−	0.177128i	0.352906	−	0.935659i	$-0.385194\pi$
$859$	29.4418	−	5.19139i	1.00454	−	0.177128i	0.651637	+	0.758531i	$0.274083\pi$
$860$		0			0
$861$	−6.96347	−	2.53449i	−0.237314	−	0.0863753i
$862$	−14.9816	−	4.01430i	−0.510275	−	0.136728i
$863$	10.4833	+	39.1242i	0.356856	+	1.33180i	0.878133	+	0.478416i	$0.158789\pi$
$863$	10.4833	+	39.1242i	0.356856	+	1.33180i	−0.521278	+	0.853387i	$0.674544\pi$
$864$	16.0035	+	19.0723i	0.544452	+	0.648852i
$865$		0			0
$866$	−9.23970	+	16.0036i	−0.313978	+	0.543825i
$867$	3.16429	−	11.8093i	0.107465	−	0.401065i
$868$	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
$873$	16.3257	−	16.3257i	0.552541	−	0.552541i
$874$	4.00723	+	3.91635i	0.135547	+	0.132473i
$875$		0			0
$876$	−0.102710	+	0.122404i	−0.00347023	+	0.00413566i
$877$	19.2255	+	8.96500i	0.649199	+	0.302727i	0.719182	−	0.694822i	$-0.244517\pi$
$877$	19.2255	+	8.96500i	0.649199	+	0.302727i	−0.0699829	+	0.997548i	$0.522294\pi$
$878$	−4.60710	+	6.57962i	−0.155482	+	0.222051i
$879$	6.11182	+	1.07768i	0.206146	+	0.0363492i
$880$		0			0
$881$	6.83139	+	11.8323i	0.230155	+	0.398641i	0.957854	−	0.287256i	$-0.0927432\pi$
$881$	6.83139	+	11.8323i	0.230155	+	0.398641i	−0.727698	+	0.685897i	$0.759410\pi$
$882$	16.8836	−	4.52394i	0.568500	−	0.152329i
$883$	14.5546	+	1.27336i	0.489800	+	0.0428520i	0.329381	−	0.944197i	$-0.393160\pi$
$883$	14.5546	+	1.27336i	0.489800	+	0.0428520i	0.160419	+	0.987049i	$0.448715\pi$
$884$	−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	0.859533	−	0.511081i	$-0.170755\pi$
$887$	−2.51587	−	5.39531i	−0.0844747	−	0.181157i	−0.944008	+	0.329924i	$0.892977\pi$
$888$	12.4163	+	17.7324i	0.416665	+	0.595059i
$889$	−2.59398	−	14.7112i	−0.0869992	−	0.493397i
$890$		0			0
$891$	−13.0735	−	10.9700i	−0.437980	−	0.367509i
$892$	13.1143	+	13.1143i	0.439099	+	0.439099i
$893$	−7.19936	+	20.5090i	−0.240917	+	0.686306i
$894$			2.92166i			0.0977149i
$895$		0			0
$896$	−10.3720	−	28.4968i	−0.346504	−	0.952012i
$897$	−1.23018	−	0.861383i	−0.0410746	−	0.0287607i
$898$	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
$903$	−0.378144	+	4.32220i	−0.0125838	+	0.143834i
$904$	39.1121	+	22.5814i	1.30085	+	0.751045i
$905$		0			0
$906$	−3.78969	+	10.4121i	−0.125904	+	0.345918i
$907$	−33.1934	+	23.2423i	−1.10217	+	0.771747i	−0.975456	−	0.220192i	$-0.929332\pi$
$907$	−33.1934	+	23.2423i	−1.10217	+	0.771747i	−0.126713	+	0.991939i	$0.540443\pi$
$908$	−4.54780	−	3.18440i	−0.150924	−	0.105678i
$909$	6.96791	+	19.1442i	0.231111	+	0.634972i
$910$		0			0
$911$		−	24.1659i		−	0.800652i	−0.916373	−	0.400326i	$-0.868897\pi$
$911$		−	24.1659i		−	0.800652i	0.916373	−	0.400326i	$-0.131103\pi$
$912$	0.216850	−	0.617746i	0.00718064	−	0.0204556i
$913$	−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
$918$	2.19885	+	4.71544i	0.0725727	+	0.155633i
$919$	−10.9705	+	6.33379i	−0.361882	+	0.208933i	−0.669906	−	0.742446i	$-0.733666\pi$
$919$	−10.9705	+	6.33379i	−0.361882	+	0.208933i	0.308024	+	0.951379i	$0.400332\pi$
$920$		0			0
$921$	17.1719	−	14.4089i	0.565833	−	0.474790i
$922$	−27.1501	−	2.37533i	−0.894141	−	0.0782272i
$923$	3.20116	−	0.857749i	0.105368	−	0.0282332i
$924$	−10.1487	−	17.5780i	−0.333867	−	0.578275i
$925$		0			0
$926$	32.2720	+	5.69043i	1.06052	+	0.186999i
$927$	0.514987	−	0.735478i	0.0169144	−	0.0241563i
$928$	−11.0922	−	5.17236i	−0.364118	−	0.169791i
$929$	−7.06706	+	8.42219i	−0.231863	+	0.276323i	−0.869414	−	0.494085i	$-0.835503\pi$
$929$	−7.06706	+	8.42219i	−0.231863	+	0.276323i	0.637551	+	0.770408i	$0.279948\pi$
$930$		0			0
$931$	−27.4176	−	26.7957i	−0.898574	−	0.878195i
$932$	19.8818	−	19.8818i	0.651249	−	0.651249i
$933$	−5.86926	+	0.513493i	−0.192151	+	0.0168110i
$934$	−7.82341	+	2.84749i	−0.255990	+	0.0931726i
$935$		0			0
$936$	−1.37992	+	7.82591i	−0.0451041	+	0.255798i
$937$	45.8065	−	21.3599i	1.49643	−	0.697798i	0.509730	−	0.860334i	$-0.329745\pi$
$937$	45.8065	−	21.3599i	1.49643	−	0.697798i	0.986703	+	0.162536i	$0.0519674\pi$
$938$	−7.69157	+	28.7053i	−0.251139	+	0.937262i
$939$	−2.37395	+	4.11180i	−0.0774708	+	0.134183i
$940$		0			0
$941$	8.30693	+	9.89982i	0.270798	+	0.322725i	0.884256	−	0.467003i	$-0.154666\pi$
$941$	8.30693	+	9.89982i	0.270798	+	0.322725i	−0.613457	+	0.789728i	$0.710222\pi$
$942$	−2.25996	−	8.43430i	−0.0736336	−	0.274804i
$943$	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	−0.692630	−	0.721293i	$-0.743548\pi$
$947$	9.38977	−	20.1364i	0.305126	−	0.654346i	0.997757	+	0.0669472i	$0.0213259\pi$
$948$	0.152209	+	1.73975i	0.00494350	+	0.0565045i
$949$	−0.187547			−0.00608804
$950$		0			0
$951$	−2.38656			−0.0773896
$952$	−1.35915	−	15.5351i	−0.0440501	−	0.503495i
$953$	−0.0877126	+	0.188100i	−0.00284129	+	0.00609316i	−0.907723	−	0.419569i	$-0.862181\pi$
$953$	−0.0877126	+	0.188100i	−0.00284129	+	0.00609316i	0.904882	+	0.425662i	$0.139959\pi$
$954$	−18.1521	+	3.20071i	−0.587696	+	0.103627i
$955$		0			0
$956$	−4.06479	−	1.47946i	−0.131465	−	0.0478493i
$957$	−8.25179	−	2.21106i	−0.266743	−	0.0714734i
$958$	−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
$963$	−18.1729	+	8.47416i	−0.585613	+	0.273076i
$964$	−0.0238770	+	0.135413i	−0.000769025	+	0.00436136i
$965$		0			0
$966$	3.90842	−	1.42255i	0.125751	−	0.0457698i
$967$	−31.7239	+	2.77548i	−1.02017	+	0.0892534i	−0.584949	−	0.811070i	$-0.698886\pi$
$967$	−31.7239	+	2.77548i	−1.02017	+	0.0892534i	−0.435222	+	0.900323i	$0.643330\pi$
$968$	−25.8772	+	25.8772i	−0.831723	+	0.831723i
$969$	2.81913	−	4.12606i	0.0905637	−	0.132548i
$970$		0			0
$971$	8.61657	−	10.2688i	0.276519	−	0.329542i	−0.609855	−	0.792513i	$-0.708772\pi$
$971$	8.61657	−	10.2688i	0.276519	−	0.329542i	0.886373	+	0.462971i	$0.153217\pi$
$972$	−18.3593	−	8.56110i	−0.588876	−	0.274598i
$973$	−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	−0.451951	−	0.892043i	$-0.649272\pi$
$977$	−12.4193	+	3.32775i	−0.397330	+	0.106464i	0.0546207	+	0.998507i	$0.482605\pi$
$978$	−7.35459	−	0.643443i	−0.235174	−	0.0205750i
$979$	15.4630	−	12.9750i	0.494199	−	0.414682i
$980$		0			0
$981$	13.0144	−	7.51386i	0.415518	−	0.239899i
$982$	−13.9732	−	29.9657i	−0.445904	−	0.956244i
$983$	7.59418	+	10.8456i	0.242217	+	0.345921i	0.921792	−	0.387684i	$-0.126725\pi$
$983$	7.59418	+	10.8456i	0.242217	+	0.345921i	−0.679576	+	0.733606i	$0.737836\pi$
$984$	0.902200	+	5.11663i	0.0287611	+	0.163112i
$985$		0			0
$986$	−1.95926	−	1.64402i	−0.0623956	−	0.0523561i
$987$	11.4089	+	11.4089i	0.363148	+	0.363148i
$988$	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	0.937902	−	0.346901i	$-0.112766\pi$
$991$	−0.111950	−	0.307581i	−0.00355622	−	0.00977062i	−0.941458	+	0.337130i	$0.890544\pi$
$992$	−43.4412	−	30.4178i	−1.37926	−	0.965767i
$993$	−5.52334	+	3.86749i	−0.175278	+	0.122731i
$994$	−3.13926	+	8.62504i	−0.0995712	+	0.273570i
$995$		0			0
$996$	−0.696748	−	0.402268i	−0.0220773	−	0.0127463i
$997$	−2.69227	+	30.7728i	−0.0852650	+	0.974584i	0.826246	+	0.563309i	$0.190472\pi$
$997$	−2.69227	+	30.7728i	−0.0852650	+	0.974584i	−0.911511	+	0.411275i	$0.865084\pi$
$998$	1.20487	−	13.7718i	0.0381396	−	0.435938i
$999$	−35.9080	−	20.7315i	−1.13608	−	0.655915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.193.4		96
5.2	odd	4	inner	475.2.bb.b.307.5		96
5.3	odd	4		95.2.r.a.22.4	yes	96
5.4	even	2		95.2.r.a.3.5	✓	96
15.8	even	4		855.2.dl.a.307.5		96
15.14	odd	2		855.2.dl.a.478.4		96
19.13	odd	18	inner	475.2.bb.b.393.5		96
95.13	even	36		95.2.r.a.32.5	yes	96
95.32	even	36	inner	475.2.bb.b.32.4		96
95.89	odd	18		95.2.r.a.13.4	yes	96
285.89	even	18		855.2.dl.a.298.5		96
285.203	odd	36		855.2.dl.a.127.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.5	✓	96	5.4	even	2
95.2.r.a.13.4	yes	96	95.89	odd	18
95.2.r.a.22.4	yes	96	5.3	odd	4
95.2.r.a.32.5	yes	96	95.13	even	36
475.2.bb.b.32.4		96	95.32	even	36	inner
475.2.bb.b.193.4		96	1.1	even	1	trivial
475.2.bb.b.307.5		96	5.2	odd	4	inner
475.2.bb.b.393.5		96	19.13	odd	18	inner
855.2.dl.a.127.4		96	285.203	odd	36
855.2.dl.a.298.5		96	285.89	even	18
855.2.dl.a.307.5		96	15.8	even	4
855.2.dl.a.478.4		96	15.14	odd	2

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0741107 - 0.847089i) q^{2} +(-0.344068 + 0.737855i) q^{3} +(1.25755 - 0.221740i) q^{4} +(0.650528 + 0.236773i) q^{6} +(3.83889 + 1.02863i) q^{7} +(-0.721192 - 2.69152i) q^{8} +(1.50231 + 1.79039i) q^{9} +(-2.45629 + 4.25442i) q^{11} +(-0.269070 + 1.00418i) q^{12} +(-1.10589 + 0.515684i) q^{13} +(0.586836 - 3.32811i) q^{14} +(0.173363 - 0.0630990i) q^{16} +(1.40281 - 0.122730i) q^{17} +(1.40528 - 1.40528i) q^{18} +(-4.22304 - 1.07980i) q^{19} +(-2.07982 + 2.47863i) q^{21} +(3.78591 + 1.76540i) q^{22} +(0.867092 - 1.23834i) q^{23} +(2.23409 + 0.393931i) q^{24} +(0.518789 + 0.898569i) q^{26} +(-4.19712 + 1.12462i) q^{27} +(5.05567 + 0.442314i) q^{28} +(1.63627 - 1.37299i) q^{29} +(8.01543 - 4.62771i) q^{31} +(-2.42153 - 5.19298i) q^{32} +(-2.29401 - 3.27619i) q^{33} +(-0.207926 - 1.17921i) q^{34} +(2.28623 + 1.91838i) q^{36} +(6.74741 + 6.74741i) q^{37} +(-0.601718 + 3.65731i) q^{38} -0.993416i q^{39} +(0.783311 + 2.15213i) q^{41} +(2.25375 + 1.57810i) q^{42} +(1.09842 - 0.769121i) q^{43} +(-2.14553 + 5.89479i) q^{44} +(-1.11324 - 0.642730i) q^{46} +(0.434606 - 4.96757i) q^{47} +(-0.0130907 + 0.149627i) q^{48} +(7.61681 + 4.39757i) q^{49} +(-0.392104 + 1.07730i) q^{51} +(-1.27636 + 0.893717i) q^{52} +(-7.59734 - 5.31972i) q^{53} +(1.26370 + 3.47199i) q^{54} -11.0743i q^{56} +(2.24975 - 2.74446i) q^{57} +(-1.28431 - 1.28431i) q^{58} +(-9.46359 - 7.94090i) q^{59} +(-1.09383 - 6.20343i) q^{61} +(-4.51411 - 6.44682i) q^{62} +(3.92558 + 8.41843i) q^{63} +(-3.89991 + 2.25161i) q^{64} +(-2.60522 + 2.18604i) q^{66} +(-8.76025 - 0.766422i) q^{67} +(1.73688 - 0.465396i) q^{68} +(0.615374 + 1.06586i) q^{69} +(-2.67473 - 0.471627i) q^{71} +(3.73542 - 5.33473i) q^{72} +(0.139300 + 0.0649566i) q^{73} +(5.21560 - 6.21571i) q^{74} +(-5.55010 - 0.421490i) q^{76} +(-13.8056 + 13.8056i) q^{77} +(-0.841512 + 0.0736228i) q^{78} +(1.57856 - 0.574548i) q^{79} +(-0.603254 + 3.42123i) q^{81} +(1.76499 - 0.823030i) q^{82} +(-0.200296 + 0.747516i) q^{83} +(-2.06586 + 3.57817i) q^{84} +(-0.732919 - 0.873459i) q^{86} +(0.450082 + 1.67973i) q^{87} +(13.2223 + 3.54291i) q^{88} +(-3.86114 - 1.40534i) q^{89} +(-4.77583 + 0.842108i) q^{91} +(0.815821 - 1.74953i) q^{92} +(0.656731 + 7.50647i) q^{93} -4.24019 q^{94} +4.66483 q^{96} +(-0.860973 - 9.84096i) q^{97} +(3.16065 - 6.77803i) q^{98} +(-11.3072 + 1.99376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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