LMFDB - Embedded newform 475.2.bb.b.32.4

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			32.4
Character	$\chi$	$=$	475.32
Dual form			475.2.bb.b.193.4

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{18}\right)$

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	$0.930579\pi$
$3$	−0.344068	−	0.737855i	−0.198648	−	0.426001i	0.781599	−	0.623781i	$-0.214404\pi$
$3$	−0.344068	−	0.737855i	−0.198648	−	0.426001i	−0.980246	+	0.197780i	$0.936627\pi$
$4$	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	0.554605	−	0.832114i	$-0.312869\pi$
$7$	3.83889	−	1.02863i	1.45096	−	0.388784i	0.896359	+	0.443329i	$0.146203\pi$
$8$	−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	−0.952223	−	0.305403i	$-0.901209\pi$
$11$	−2.45629	−	4.25442i	−0.740599	−	1.28275i	0.211624	−	0.977351i	$-0.432125\pi$
$12$	−0.269070	−	1.00418i	−0.0776737	−	0.289882i
$13$	−1.10589	−	0.515684i	−0.306718	−	0.143025i	0.263165	−	0.964751i	$-0.415234\pi$
$13$	−1.10589	−	0.515684i	−0.306718	−	0.143025i	−0.569883	+	0.821726i	$0.693012\pi$
$14$	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	$0.473154\pi$
$18$	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	0.899315	−	0.437302i	$-0.144066\pi$
$23$	0.867092	+	1.23834i	0.180801	+	0.258211i	−0.718513	+	0.695513i	$0.755177\pi$
$24$	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	0.781943	−	0.623350i	$-0.214229\pi$
$29$	1.63627	+	1.37299i	0.303847	+	0.254958i	−0.478096	+	0.878307i	$0.658673\pi$
$30$		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
$33$	−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	0.116021	−	0.993247i	$-0.462986\pi$
$37$	6.74741	−	6.74741i	1.10927	−	1.10927i	0.993247	−	0.116021i	$-0.0370139\pi$
$38$	−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	−0.863377	−	0.504559i	$-0.831655\pi$
$41$	0.783311	−	2.15213i	0.122333	−	0.336106i	0.985710	+	0.168453i	$0.0538772\pi$
$42$	2.25375	−	1.57810i	0.347762	−	0.243506i
$43$	1.09842	+	0.769121i	0.167507	+	0.117290i	0.654324	−	0.756214i	$-0.272953\pi$
$43$	1.09842	+	0.769121i	0.167507	+	0.117290i	−0.486817	+	0.873504i	$0.661842\pi$
$44$	−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	$0.853742\pi$
$48$	−0.0130907	−	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	−0.963944	−	0.266105i	$-0.914263\pi$
$53$	−7.59734	+	5.31972i	−1.04358	+	0.730719i	−0.0796315	+	0.996824i	$0.525374\pi$
$54$	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	−0.233952	+	0.972248i	$0.575166\pi$
$59$	−9.46359	+	7.94090i	−1.23205	+	1.03382i	−0.998103	+	0.0615685i	$0.980390\pi$
$60$		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
$63$	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	−0.608631	−	0.793453i	$-0.708281\pi$
$67$	−8.76025	+	0.766422i	−1.07023	+	0.0936334i	−0.461603	+	0.887087i	$0.652726\pi$
$68$	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	−0.330094	−	0.943948i	$-0.607081\pi$
$71$	−2.67473	+	0.471627i	−0.317432	+	0.0559718i	0.0126621	+	0.999920i	$0.495969\pi$
$72$	3.73542	+	5.33473i	0.440223	+	0.628704i
$73$	0.139300	−	0.0649566i	0.0163038	−	0.00760259i	−0.414449	−	0.910072i	$-0.636026\pi$
$73$	0.139300	−	0.0649566i	0.0163038	−	0.00760259i	0.430753	+	0.902470i	$0.358248\pi$
$74$	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	0.429290	−	0.903167i	$-0.358764\pi$
$79$	1.57856	+	0.574548i	0.177602	+	0.0646417i	−0.251689	+	0.967808i	$0.580986\pi$
$80$		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	0.954062	−	0.299611i	$-0.0968568\pi$
$83$	−0.200296	−	0.747516i	−0.0219854	−	0.0820505i	−0.976047	+	0.217560i	$0.930190\pi$
$84$	−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	−0.538452	−	0.842656i	$-0.680991\pi$
$89$	−3.86114	+	1.40534i	−0.409280	+	0.148966i	0.129171	+	0.991622i	$0.458768\pi$
$90$		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	0.818152	+	0.575002i	$0.194999\pi$
$97$	−0.860973	+	9.84096i	−0.0874185	+	0.999198i	−0.905570	+	0.424196i	$0.860557\pi$
$98$	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	0.0993398	−	0.995054i	$-0.468327\pi$
$101$	8.19112	−	2.98132i	0.815047	−	0.296653i	0.715707	+	0.698401i	$0.246105\pi$
$102$	0.941625	−	0.252308i	0.0932348	−	0.0249822i
$103$	−0.0994278	+	0.371070i	−0.00979691	+	0.0365626i	−0.970651	−	0.240491i	$-0.922691\pi$
$103$	−0.0994278	+	0.371070i	−0.00979691	+	0.0365626i	0.960854	+	0.277054i	$0.0893581\pi$
$104$	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	$-0.219446\pi$
$108$	−5.02871	−	2.34493i	−0.483888	−	0.225641i
$109$	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	$0.844807\pi$
$110$		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	−0.996677	−	0.0814546i	$-0.974043\pi$
$113$	−11.4607	−	11.4607i	−1.07813	−	1.07813i	−0.0814546	−	0.996677i	$-0.525957\pi$
$114$	−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	−0.964094	−	0.265561i	$-0.914443\pi$
$127$	−1.58848	+	3.40651i	−0.140955	+	0.302279i	0.823139	+	0.567840i	$0.192221\pi$
$128$	−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	−0.891052	−	0.453902i	$-0.850032\pi$
$131$	−6.85330	+	5.75060i	−0.598775	+	0.502432i	0.292277	+	0.956334i	$0.405587\pi$
$132$	−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	−0.356415	−	0.934328i	$-0.616001\pi$
$137$	4.67796	−	3.27554i	0.399665	−	0.279848i	0.756080	+	0.654479i	$0.227112\pi$
$138$	0.857272	+	0.600268i	0.0729758	+	0.0510982i
$139$	−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	$-0.250517\pi$
$140$		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	−0.866419	−	0.499318i	$-0.833584\pi$
$149$	1.44345	−	3.96584i	0.118252	−	0.324894i	0.984671	+	0.174424i	$0.0558062\pi$
$150$		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
$153$	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	−0.996522	−	0.0833309i	$-0.973444\pi$
$157$	−7.23463	+	10.3321i	−0.577386	+	0.824593i	0.419136	+	0.907923i	$0.362333\pi$
$158$	−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	−0.168251	−	0.985744i	$-0.553812\pi$
$163$	−10.3009	−	2.76013i	−0.806833	−	0.216190i	−0.638582	+	0.769554i	$0.720479\pi$
$164$	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	$0.776655\pi$
$168$	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	0.554986	−	0.831860i	$-0.312724\pi$
$173$	12.5886	+	1.10136i	0.957090	+	0.0837345i	0.402104	+	0.915594i	$0.368279\pi$
$174$	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	0.964667	−	0.263473i	$-0.0848681\pi$
$179$	3.40041	+	5.88969i	0.254159	+	0.440216i	−0.710508	+	0.703689i	$0.751535\pi$
$180$		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
$183$	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	0.959676	+	0.281108i	$0.0907018\pi$
$193$	7.75406	+	16.6286i	0.558149	+	1.19696i	−0.401527	+	0.915847i	$0.631520\pi$
$194$	−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	$0.284623\pi$
$198$	2.52688	−	9.43043i	0.179577	−	0.670191i
$199$	−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	$0.363180\pi$
$200$		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	0.904866	−	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
$213$	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	−0.436837	−	0.899540i	$-0.643902\pi$
$223$	8.33065	−	11.8974i	0.557861	−	0.796708i	0.994699	+	0.102832i	$0.0327904\pi$
$224$	−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	$0.296088\pi$
$228$	2.22061	+	3.95015i	0.147063	+	0.261605i
$229$			18.5866i			1.22824i	0.789214	+	0.614119i	$0.210488\pi$
$229$			18.5866i			1.22824i	−0.789214	+	0.614119i	$0.789512\pi$
$230$		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	0.988116	−	0.153707i	$-0.0491211\pi$
$233$	18.0369	+	12.6296i	1.18164	+	0.827390i	0.193519	+	0.981097i	$0.438010\pi$
$234$	−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	−0.591872	−	0.806032i	$-0.701611\pi$
$239$	−2.93366	+	1.69375i	−0.189763	+	0.109560i	0.402109	+	0.915592i	$0.368277\pi$
$240$		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
$243$	−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	−0.609691	−	0.792639i	$-0.708706\pi$
$251$	3.71248	−	21.0545i	0.234330	−	1.32895i	0.844020	−	0.536311i	$-0.180183\pi$
$252$	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	0.311625	−	0.950205i	$-0.399127\pi$
$257$	12.5607	−	1.09892i	0.783518	−	0.0685489i	0.471892	+	0.881656i	$0.343571\pi$
$258$	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	−0.985509	−	0.169626i	$-0.945744\pi$
$263$	−24.1482	+	11.2605i	−1.48904	+	0.694351i	−0.503532	+	0.863977i	$0.667966\pi$
$264$	−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	0.684873	−	0.728662i	$-0.259858\pi$
$269$	12.1556	+	4.42428i	0.741141	+	0.269753i	0.0562682	+	0.998416i	$0.482080\pi$
$270$		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
$273$	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	−0.728090	−	0.685482i	$-0.759592\pi$
$277$	4.08087	−	15.2300i	0.245195	−	0.915082i	0.973285	−	0.229600i	$-0.0737418\pi$
$278$	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	0.180376	−	0.983598i	$-0.442269\pi$
$281$	0.225686	+	0.0397945i	0.0134633	+	0.00237394i	−0.166912	+	0.985972i	$0.553380\pi$
$282$	1.45891	+	3.12865i	0.0868769	+	0.186308i
$283$	1.12979	−	12.9136i	0.0671591	−	0.767632i	−0.885708	−	0.464243i	$-0.846326\pi$
$283$	1.12979	−	12.9136i	0.0671591	−	0.767632i	0.952867	−	0.303389i	$-0.0981181\pi$
$284$	−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	−0.999306	−	0.0372396i	$-0.988144\pi$
$293$	−1.97297	+	7.36321i	−0.115262	+	0.430163i	0.884044	+	0.467403i	$0.154810\pi$
$294$	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	−0.973530	−	0.228561i	$-0.926598\pi$
$307$	−24.9542	+	11.6364i	−1.42421	+	0.664122i	−0.450685	+	0.892683i	$0.648820\pi$
$308$	−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	−0.745011	−	0.667053i	$-0.767556\pi$
$311$	3.61837	−	6.26721i	0.205179	−	0.355381i	0.950190	+	0.311672i	$0.100889\pi$
$312$	−2.67380	−	0.716443i	−0.151374	−	0.0405606i
$313$	5.80964	−	0.508278i	0.328381	−	0.0287296i	0.0782264	−	0.996936i	$-0.475074\pi$
$313$	5.80964	−	0.508278i	0.328381	−	0.0287296i	0.250154	+	0.968206i	$0.419519\pi$
$314$	−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	$0.112655\pi$
$318$	−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	−0.289757	−	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
$333$	−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	0.191813	−	0.981431i	$-0.438563\pi$
$337$	−12.2046	−	8.54575i	−0.664827	−	0.465517i	−0.856640	+	0.515915i	$0.827452\pi$
$338$	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	−0.906774	−	0.421618i	$-0.861462\pi$
$347$	−3.73392	+	5.33259i	−0.200447	+	0.286268i	0.706326	+	0.707887i	$0.250351\pi$
$348$	0.938461	−	2.01254i	0.0503068	−	0.107883i
$349$	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	$0.438840\pi$
$350$		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	0.715440	−	0.698675i	$-0.246226\pi$
$353$	18.5195	+	4.96227i	0.985691	+	0.264115i	0.270251	+	0.962790i	$0.412893\pi$
$354$	−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	0.322846	−	0.946452i	$-0.395360\pi$
$359$	−12.6054	−	15.0226i	−0.665289	−	0.792860i	−0.988134	+	0.153592i	$0.950916\pi$
$360$		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	0.0651311	−	0.997877i	$-0.479253\pi$
$367$	−12.5944	−	5.87286i	−0.657421	−	0.306561i	−0.722552	+	0.691316i	$0.757031\pi$
$368$	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	0.846407	−	0.532536i	$-0.178761\pi$
$373$	35.6461	−	9.55135i	1.84569	−	0.494550i	0.999278	+	0.0379859i	$0.0120942\pi$
$374$	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	0.737739	−	0.675086i	$-0.235894\pi$
$383$	−4.96338	−	10.6440i	−0.253617	−	0.543883i	−0.991355	+	0.131203i	$0.958116\pi$
$384$	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	−0.707279	−	0.706934i	$-0.750078\pi$
$389$	2.20372	−	2.62629i	0.111733	−	0.133158i	0.819012	+	0.573776i	$0.194522\pi$
$390$		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	−0.129999	−	0.991514i	$-0.541497\pi$
$397$	−8.57163	−	0.749921i	−0.430198	−	0.0376375i	−0.300199	+	0.953877i	$0.597053\pi$
$398$	−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	0.475720	−	0.879597i	$-0.342187\pi$
$401$	−9.47424	−	11.2910i	−0.473121	−	0.563844i	−0.948841	+	0.315753i	$0.897743\pi$
$402$	−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	−0.960480	−	0.278348i	$-0.910213\pi$
$409$	−28.3413	−	23.7811i	−1.40139	−	1.17590i	−0.440905	−	0.897554i	$-0.645342\pi$
$410$		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	$-0.927757\pi$
$419$		−	9.21192i		−	0.450032i	0.974355	−	0.225016i	$-0.0722434\pi$
$420$		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
$423$	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	0.994413	+	0.105556i	$0.0336621\pi$
$431$	6.23851	+	17.1402i	0.300498	+	0.825612i	−0.693915	+	0.720057i	$0.744116\pi$
$432$	−0.656664	−	0.459801i	−0.0315938	−	0.0221222i
$433$	−17.8019	+	12.4651i	−0.855507	+	0.599032i	−0.916916	−	0.399080i	$-0.869329\pi$
$433$	−17.8019	+	12.4651i	−0.855507	+	0.599032i	0.0614092	+	0.998113i	$0.480441\pi$
$434$	−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	−0.798924	−	0.601432i	$-0.794597\pi$
$439$	−7.23611	+	6.07181i	−0.345361	+	0.289792i	0.453563	+	0.891224i	$0.350153\pi$
$440$		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	−0.188042	−	0.982161i	$-0.560214\pi$
$443$	14.4220	−	30.9280i	0.685208	−	1.46943i	0.873250	−	0.487273i	$-0.162008\pi$
$444$	−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	0.287931	−	0.957651i	$-0.407033\pi$
$449$	20.6242	−	35.7221i	0.973316	−	1.68583i	0.685385	−	0.728181i	$-0.259634\pi$
$450$		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	0.941714	−	0.336414i	$-0.109214\pi$
$457$	12.9398	+	12.9398i	0.605300	+	0.605300i	−0.336414	+	0.941714i	$0.609214\pi$
$458$	−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	0.785014	+	0.619479i	$0.212656\pi$
$461$	5.56561	+	31.5641i	0.259216	+	1.47009i	−0.525797	+	0.850610i	$0.676233\pi$
$462$	−12.2497	−	5.71215i	−0.569910	−	0.265753i
$463$	−9.97438	−	37.2249i	−0.463549	−	1.72999i	−0.661656	−	0.749807i	$-0.730146\pi$
$463$	−9.97438	−	37.2249i	−0.463549	−	1.72999i	0.198108	−	0.980180i	$-0.436520\pi$
$464$	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	$0.156073\pi$
$468$	−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	0.441189	−	0.897414i	$-0.354557\pi$
$479$	12.0119	+	2.11802i	0.548837	+	0.0967747i	0.107648	+	0.994189i	$0.465668\pi$
$480$		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	0.999832	−	0.0183065i	$-0.00582746\pi$
$487$	2.75407	+	10.2783i	0.124799	+	0.465756i	−0.875034	+	0.484062i	$0.839161\pi$
$488$	−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	0.988571	−	0.150756i	$-0.0481709\pi$
$491$	36.5384	+	13.2989i	1.64896	+	0.600171i	0.660385	+	0.750927i	$0.270393\pi$
$492$	−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	0.196627	−	0.980478i	$-0.437001\pi$
$499$	16.0108	−	2.82313i	0.716740	−	0.126381i	0.520113	+	0.854098i	$0.325890\pi$
$500$		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	0.572261	−	0.820071i	$-0.306066\pi$
$503$	28.6678	−	2.50810i	1.27823	−	0.111831i	0.705971	+	0.708240i	$0.250511\pi$
$504$	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	0.769686	+	0.638423i	$0.220413\pi$
$509$	−3.87905	+	21.9992i	−0.171936	+	0.975097i	−0.941621	+	0.336673i	$0.890698\pi$
$510$		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	−0.919306	−	0.393543i	$-0.871249\pi$
$521$	−23.6960	+	13.6809i	−1.03814	+	0.599371i	−0.118835	+	0.992914i	$0.537916\pi$
$522$	0.369976	+	4.22885i	0.0161934	+	0.185092i
$523$	0.813771	+	9.30145i	0.0355837	+	0.406724i	0.993009	+	0.118042i	$0.0376616\pi$
$523$	0.813771	+	9.30145i	0.0355837	+	0.406724i	−0.957425	+	0.288682i	$0.906783\pi$
$524$	−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	0.957149	−	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
$543$	−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	−0.995953	−	0.0898741i	$-0.971354\pi$
$547$	−17.3018	−	24.7095i	−0.739771	−	1.05650i	0.256182	−	0.966629i	$-0.417535\pi$
$548$	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	0.889398	−	0.457133i	$-0.151124\pi$
$557$	26.2184	+	12.2258i	1.11091	+	0.518025i	0.221510	+	0.975158i	$0.428902\pi$
$558$	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	0.164267	−	0.986416i	$-0.447474\pi$
$563$	18.9758	−	5.08454i	0.799734	−	0.214288i	0.635467	+	0.772128i	$0.280808\pi$
$564$	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	−0.759262	−	0.650785i	$-0.774440\pi$
$577$	−26.2166	+	7.02471i	−1.09141	+	0.292442i	−0.332148	+	0.943227i	$0.607773\pi$
$578$	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	0.815968	−	0.578097i	$-0.196204\pi$
$587$	36.8062	+	3.22012i	1.51915	+	0.132909i	0.703186	+	0.711006i	$0.251760\pi$
$588$	−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	0.854846	−	0.518882i	$-0.173651\pi$
$593$	1.82350	+	2.60423i	0.0748823	+	0.106943i	−0.779964	+	0.625825i	$0.784763\pi$
$594$	−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	0.512922	−	0.858435i	$-0.328563\pi$
$599$	−5.95719	−	4.99867i	−0.243404	−	0.204240i	−0.756326	+	0.654195i	$0.773008\pi$
$600$		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
$603$	−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	−0.296212	−	0.955122i	$-0.595724\pi$
$607$	16.2338	−	16.2338i	0.658910	−	0.658910i	0.955122	+	0.296212i	$0.0957236\pi$
$608$	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	−0.236001	−	0.971753i	$-0.575837\pi$
$613$	−30.4501	−	21.3214i	−1.22987	−	0.861162i	−0.993866	+	0.110590i	$0.964726\pi$
$614$	−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	$0.972737\pi$
$618$	0.0231787	+	0.264933i	0.000932382	+	0.0106572i
$619$	−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	$0.529789\pi$
$620$		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	−0.998456	−	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
$633$	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	−0.613019	−	0.790068i	$-0.710045\pi$
$641$	−23.2634	+	4.10197i	−0.918850	+	0.162018i	−0.305831	+	0.952086i	$0.598934\pi$
$642$	−3.40664	−	4.86519i	−0.134449	−	0.192014i
$643$	16.0066	−	7.46400i	0.631239	−	0.294351i	−0.0805441	−	0.996751i	$-0.525666\pi$
$643$	16.0066	−	7.46400i	0.631239	−	0.294351i	0.711783	+	0.702400i	$0.247888\pi$
$644$	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	$0.798910\pi$
$648$	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	0.951474	−	0.307728i	$-0.0995686\pi$
$653$	−0.674379	−	2.51682i	−0.0263905	−	0.0984907i	−0.977865	+	0.209237i	$0.932902\pi$
$654$	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	0.198175	−	0.980167i	$-0.436499\pi$
$659$	25.1582	−	9.15684i	0.980025	−	0.356700i	0.781850	+	0.623467i	$0.214276\pi$
$660$		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
$663$	−0.121922	+	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	−0.815860	−	0.578249i	$-0.803736\pi$
$673$	4.66494	−	17.4098i	0.179820	−	0.671098i	0.995680	−	0.0928486i	$-0.0295973\pi$
$674$	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	$-0.391520\pi$
$678$	−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	0.954613	−	0.297850i	$-0.0962696\pi$
$683$	17.1640	+	17.1640i	0.656763	+	0.656763i	−0.297850	+	0.954613i	$0.596270\pi$
$684$	−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	−0.726605	−	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
$693$	−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	−0.0898504	−	0.995955i	$-0.528639\pi$
$701$	23.1767	−	19.4476i	0.875372	−	0.734524i	0.965222	+	0.261431i	$0.0841944\pi$
$702$	−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	0.951658	−	0.307161i	$-0.0993789\pi$
$709$	0.671174	+	1.84404i	0.0252065	+	0.0692542i	−0.926451	+	0.376415i	$0.877157\pi$
$710$		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	−0.996357	−	0.0852814i	$-0.972821\pi$
$719$	−4.78058	+	13.1345i	−0.178285	+	0.489835i	0.818072	+	0.575117i	$0.195043\pi$
$720$		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	−0.989887	−	0.141858i	$-0.954692\pi$
$727$	−13.9674	+	19.9475i	−0.518022	+	0.739813i	0.471865	+	0.881671i	$0.343581\pi$
$728$	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	−0.0736595	−	0.997283i	$-0.523468\pi$
$733$	−17.2215	−	4.61450i	−0.636092	−	0.170440i	−0.562433	+	0.826843i	$0.690134\pi$
$734$	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	0.990305	−	0.138908i	$-0.0443593\pi$
$739$	18.5274	+	22.0801i	0.681543	+	0.812231i	−0.308763	+	0.951139i	$0.599915\pi$
$740$		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	0.202814	−	0.979217i	$-0.434991\pi$
$743$	6.33768	+	0.554475i	0.232507	+	0.0203417i	0.0296933	+	0.999559i	$0.490547\pi$
$744$	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	0.366891	−	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
$753$	−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	0.615871	+	0.787847i	$0.288804\pi$
$757$	22.6581	+	48.5905i	0.823523	+	1.76605i	0.207652	+	0.978203i	$0.433418\pi$
$758$	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	−0.829776	−	0.558097i	$-0.811532\pi$
$769$	−3.77330	+	4.49684i	−0.136069	+	0.162160i	0.693707	+	0.720257i	$0.255976\pi$
$770$		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	−0.495295	−	0.868725i	$-0.664940\pi$
$773$	−41.1245	−	19.1767i	−1.47915	−	0.689738i	−0.983851	+	0.178987i	$0.942718\pi$
$774$	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	−0.208301	−	0.978065i	$-0.566793\pi$
$787$	−24.6233	−	6.59781i	−0.877728	−	0.235186i	−0.669426	+	0.742878i	$0.733460\pi$
$788$	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	0.430880	−	0.902409i	$-0.358203\pi$
$797$	37.6403	−	37.6403i	1.33329	−	1.33329i	0.902409	−	0.430880i	$-0.141797\pi$
$798$	−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	−0.844479	−	0.535589i	$-0.820090\pi$
$809$	−22.8364	+	13.1846i	−0.802885	+	0.463546i	0.0415941	+	0.999135i	$0.486756\pi$
$810$		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
$813$	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	−0.891821	−	0.452388i	$-0.850572\pi$
$821$	2.89232	−	16.4031i	0.100943	−	0.572473i	0.992764	−	0.120085i	$-0.0383168\pi$
$822$	2.26759	−	3.23845i	0.0790911	−	0.112954i
$823$	−11.5057	+	24.6740i	−0.401063	+	0.860082i	0.597252	+	0.802054i	$0.296259\pi$
$823$	−11.5057	+	24.6740i	−0.401063	+	0.860082i	−0.998315	+	0.0580287i	$0.981519\pi$
$824$	−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	$0.581840\pi$
$828$	4.35797	+	1.16771i	0.151450	+	0.0405809i
$829$	−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			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	−0.997755	−	0.0669723i	$-0.978666\pi$
$839$	−52.2864	−	19.0307i	−1.80513	−	0.657013i	−0.807374	−	0.590041i	$-0.799112\pi$
$840$		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	0.966460	+	0.256819i	$0.0826744\pi$
$853$	−0.873658	+	9.98595i	−0.0299135	+	0.341913i	−0.996373	+	0.0850935i	$0.972881\pi$
$854$	−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	$-0.0513932\pi$
$858$	1.75377	+	3.76098i	0.0598729	+	0.128398i
$859$	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	$0.385194\pi$
$860$		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	−0.521278	−	0.853387i	$-0.674544\pi$
$863$	10.4833	−	39.1242i	0.356856	−	1.33180i	0.878133	−	0.478416i	$-0.158789\pi$
$864$	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	−0.0699829	−	0.997548i	$-0.522294\pi$
$877$	19.2255	−	8.96500i	0.649199	−	0.302727i	0.719182	+	0.694822i	$0.244517\pi$
$878$	−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	−0.727698	−	0.685897i	$-0.759410\pi$
$881$	6.83139	−	11.8323i	0.230155	−	0.398641i	0.957854	+	0.287256i	$0.0927432\pi$
$882$	16.8836	+	4.52394i	0.568500	+	0.152329i
$883$	14.5546	−	1.27336i	0.489800	−	0.0428520i	0.160419	−	0.987049i	$-0.448715\pi$
$883$	14.5546	−	1.27336i	0.489800	−	0.0428520i	0.329381	+	0.944197i	$0.393160\pi$
$884$	−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	$0.170755\pi$
$888$	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	−0.126713	−	0.991939i	$-0.540443\pi$
$907$	−33.1934	−	23.2423i	−1.10217	−	0.771747i	−0.975456	+	0.220192i	$0.929332\pi$
$908$	−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	$0.131103\pi$
$911$			24.1659i			0.800652i	−0.916373	+	0.400326i	$0.868897\pi$
$912$	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	0.308024	−	0.951379i	$-0.400332\pi$
$919$	−10.9705	−	6.33379i	−0.361882	−	0.208933i	−0.669906	+	0.742446i	$0.733666\pi$
$920$		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	0.637551	−	0.770408i	$-0.279948\pi$
$929$	−7.06706	−	8.42219i	−0.231863	−	0.276323i	−0.869414	+	0.494085i	$0.835503\pi$
$930$		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	0.986703	−	0.162536i	$-0.0519674\pi$
$937$	45.8065	+	21.3599i	1.49643	+	0.697798i	0.509730	+	0.860334i	$0.329745\pi$
$938$	−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	−0.613457	−	0.789728i	$-0.710222\pi$
$941$	8.30693	−	9.89982i	0.270798	−	0.322725i	0.884256	+	0.467003i	$0.154666\pi$
$942$	−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	0.997757	−	0.0669472i	$-0.0213259\pi$
$947$	9.38977	+	20.1364i	0.305126	+	0.654346i	−0.692630	+	0.721293i	$0.743548\pi$
$948$	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	0.904882	−	0.425662i	$-0.139959\pi$
$953$	−0.0877126	−	0.188100i	−0.00284129	−	0.00609316i	−0.907723	+	0.419569i	$0.862181\pi$
$954$	−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	−0.435222	−	0.900323i	$-0.643330\pi$
$967$	−31.7239	−	2.77548i	−1.02017	−	0.0892534i	−0.584949	+	0.811070i	$0.698886\pi$
$968$	−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	0.886373	−	0.462971i	$-0.153217\pi$
$971$	8.61657	+	10.2688i	0.276519	+	0.329542i	−0.609855	+	0.792513i	$0.708772\pi$
$972$	−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	0.0546207	−	0.998507i	$-0.482605\pi$
$977$	−12.4193	−	3.32775i	−0.397330	−	0.106464i	−0.451951	+	0.892043i	$0.649272\pi$
$978$	−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	−0.679576	−	0.733606i	$-0.737836\pi$
$983$	7.59418	−	10.8456i	0.242217	−	0.345921i	0.921792	+	0.387684i	$0.126725\pi$
$984$	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	−0.941458	−	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
$993$	−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	−0.911511	−	0.411275i	$-0.865084\pi$
$997$	−2.69227	−	30.7728i	−0.0852650	−	0.974584i	0.826246	−	0.563309i	$-0.190472\pi$
$998$	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.32.4		96
5.2	odd	4		95.2.r.a.13.4	yes	96
5.3	odd	4	inner	475.2.bb.b.393.5		96
5.4	even	2		95.2.r.a.32.5	yes	96
15.2	even	4		855.2.dl.a.298.5		96
15.14	odd	2		855.2.dl.a.127.4		96
19.3	odd	18	inner	475.2.bb.b.307.5		96
95.3	even	36	inner	475.2.bb.b.193.4		96
95.22	even	36		95.2.r.a.3.5	✓	96
95.79	odd	18		95.2.r.a.22.4	yes	96
285.212	odd	36		855.2.dl.a.478.4		96
285.269	even	18		855.2.dl.a.307.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.5	✓	96	95.22	even	36
95.2.r.a.13.4	yes	96	5.2	odd	4
95.2.r.a.22.4	yes	96	95.79	odd	18
95.2.r.a.32.5	yes	96	5.4	even	2
475.2.bb.b.32.4		96	1.1	even	1	trivial
475.2.bb.b.193.4		96	95.3	even	36	inner
475.2.bb.b.307.5		96	19.3	odd	18	inner
475.2.bb.b.393.5		96	5.3	odd	4	inner
855.2.dl.a.127.4		96	15.14	odd	2
855.2.dl.a.298.5		96	15.2	even	4
855.2.dl.a.307.5		96	285.269	even	18
855.2.dl.a.478.4		96	285.212	odd	36

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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