LMFDB - Embedded newform 825.2.n.o.751.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.4
Character	$\chi$	$=$	825.751
Dual form			825.2.n.o.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.233654 - 0.169760i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.592258 + 1.82278i) q^{4} +(-0.233654 - 0.169760i) q^{6} +(-1.13329 + 3.48791i) q^{7} +(0.349548 + 1.07580i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.233654 - 0.169760i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.592258 + 1.82278i) q^{4} +(-0.233654 - 0.169760i) q^{6} +(-1.13329 + 3.48791i) q^{7} +(0.349548 + 1.07580i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.25682 - 3.06927i) q^{11} +1.91659 q^{12} +(-3.90406 + 2.83647i) q^{13} +(0.327309 + 1.00735i) q^{14} +(-2.83680 - 2.06106i) q^{16} +(-3.10673 - 2.25717i) q^{17} +(-0.0892481 + 0.274677i) q^{18} +(-2.15132 - 6.62109i) q^{19} +3.66740 q^{21} +(-0.227376 - 0.930506i) q^{22} -1.20633 q^{23} +(0.915128 - 0.664879i) q^{24} +(-0.430683 + 1.32551i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-5.68650 - 4.13148i) q^{28} +(1.52862 - 4.70461i) q^{29} +(-5.96190 + 4.33158i) q^{31} -3.27504 q^{32} +(-3.30743 - 0.246854i) q^{33} -1.10908 q^{34} +(-0.592258 - 1.82278i) q^{36} +(-0.737599 + 2.27010i) q^{37} +(-1.62666 - 1.18184i) q^{38} +(3.90406 + 2.83647i) q^{39} +(1.33051 + 4.09490i) q^{41} +(0.856905 - 0.622578i) q^{42} +0.772454 q^{43} +(4.85024 + 4.10871i) q^{44} +(-0.281864 + 0.204786i) q^{46} +(-1.99955 - 6.15398i) q^{47} +(-1.08356 + 3.33486i) q^{48} +(-5.21803 - 3.79112i) q^{49} +(-1.18667 + 3.65218i) q^{51} +(-2.85805 - 8.79618i) q^{52} +(-8.70198 + 6.32236i) q^{53} +0.288813 q^{54} -4.14842 q^{56} +(-5.63224 + 4.09206i) q^{57} +(-0.441485 - 1.35875i) q^{58} +(-4.48008 + 13.7883i) q^{59} +(1.48124 + 1.07618i) q^{61} +(-0.657697 + 2.02418i) q^{62} +(-1.13329 - 3.48791i) q^{63} +(4.90838 - 3.56615i) q^{64} +(-0.814701 + 0.503790i) q^{66} +6.10784 q^{67} +(5.95433 - 4.32607i) q^{68} +(0.372776 + 1.14729i) q^{69} +(2.66254 + 1.93445i) q^{71} +(-0.915128 - 0.664879i) q^{72} +(0.0591833 - 0.182147i) q^{73} +(0.213028 + 0.655633i) q^{74} +13.3429 q^{76} +(9.28097 + 7.86205i) q^{77} +1.39372 q^{78} +(2.55645 - 1.85737i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.00603 + 0.730924i) q^{82} +(-1.23813 - 0.899554i) q^{83} +(-2.17205 + 6.68488i) q^{84} +(0.180487 - 0.131132i) q^{86} -4.94672 q^{87} +(3.74123 + 0.279232i) q^{88} -3.04594 q^{89} +(-5.46890 - 16.8315i) q^{91} +(0.714458 - 2.19888i) q^{92} +(5.96190 + 4.33158i) q^{93} +(-1.51190 - 1.09846i) q^{94} +(1.01204 + 3.11475i) q^{96} +(-11.1459 + 8.09794i) q^{97} -1.86280 q^{98} +(0.787278 + 3.22183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	0.233654	−	0.169760i	0.165219	−	0.120038i	−0.502104	−	0.864807i	$-0.667440\pi$
$2$	0.233654	−	0.169760i	0.165219	−	0.120038i	0.667322	+	0.744769i	$0.267440\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.592258	+	1.82278i	−0.296129	+	0.911391i
$5$		0			0
$5$		0			0
$6$	−0.233654	−	0.169760i	−0.0953890	−	0.0693042i
$7$	−1.13329	+	3.48791i	−0.428343	+	1.31830i	0.471413	+	0.881912i	$0.343744\pi$
$7$	−1.13329	+	3.48791i	−0.428343	+	1.31830i	−0.899756	+	0.436392i	$0.856256\pi$
$8$	0.349548	+	1.07580i	0.123584	+	0.380352i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.25682	−	3.06927i	0.378946	−	0.925419i
$11$	1.25682	−	3.06927i	0.378946	−	0.925419i
$12$	1.91659			0.553271
$13$	−3.90406	+	2.83647i	−1.08279	+	0.786695i	−0.978168	−	0.207817i	$-0.933364\pi$
$13$	−3.90406	+	2.83647i	−1.08279	+	0.786695i	−0.104625	+	0.994512i	$0.533364\pi$
$14$	0.327309	+	1.00735i	0.0874769	+	0.269226i
$15$		0			0
$16$	−2.83680	−	2.06106i	−0.709201	−	0.515264i
$17$	−3.10673	−	2.25717i	−0.753494	−	0.547445i	0.143414	−	0.989663i	$-0.454192\pi$
$17$	−3.10673	−	2.25717i	−0.753494	−	0.547445i	−0.896908	+	0.442218i	$0.854192\pi$
$18$	−0.0892481	+	0.274677i	−0.0210360	+	0.0647421i
$19$	−2.15132	−	6.62109i	−0.493547	−	1.51898i	−0.819209	−	0.573496i	$-0.805587\pi$
$19$	−2.15132	−	6.62109i	−0.493547	−	1.51898i	0.325661	−	0.945486i	$-0.394413\pi$
$20$		0			0
$21$	3.66740			0.800293
$22$	−0.227376	−	0.930506i	−0.0484767	−	0.198385i
$23$	−1.20633			−0.251537			−0.125769	−	0.992060i	$-0.540140\pi$
$23$	−1.20633			−0.251537			−0.125769	+	0.992060i	$0.540140\pi$
$24$	0.915128	−	0.664879i	0.186800	−	0.135718i
$25$		0			0
$26$	−0.430683	+	1.32551i	−0.0844639	+	0.259953i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−5.68650	−	4.13148i	−1.07465	−	0.780777i
$29$	1.52862	−	4.70461i	0.283858	−	0.873624i	−0.702881	−	0.711308i	$-0.748103\pi$
$29$	1.52862	−	4.70461i	0.283858	−	0.873624i	0.986739	−	0.162317i	$-0.0518967\pi$
$30$		0			0
$31$	−5.96190	+	4.33158i	−1.07079	+	0.777974i	−0.976054	−	0.217529i	$-0.930200\pi$
$31$	−5.96190	+	4.33158i	−1.07079	+	0.777974i	−0.0947353	+	0.995502i	$0.530200\pi$
$32$	−3.27504			−0.578950
$33$	−3.30743	−	0.246854i	−0.575749	−	0.0429718i
$34$	−1.10908			−0.190206
$35$		0			0
$36$	−0.592258	−	1.82278i	−0.0987097	−	0.303797i
$37$	−0.737599	+	2.27010i	−0.121261	+	0.373201i	−0.993201	−	0.116410i	$-0.962861\pi$
$37$	−0.737599	+	2.27010i	−0.121261	+	0.373201i	0.871941	+	0.489611i	$0.162861\pi$
$38$	−1.62666	−	1.18184i	−0.263879	−	0.191720i
$39$	3.90406	+	2.83647i	0.625150	+	0.454198i
$40$		0			0
$41$	1.33051	+	4.09490i	0.207791	+	0.639516i	0.999587	+	0.0287302i	$0.00914637\pi$
$41$	1.33051	+	4.09490i	0.207791	+	0.639516i	−0.791796	+	0.610786i	$0.790854\pi$
$42$	0.856905	−	0.622578i	0.132223	−	0.0960658i
$43$	0.772454			0.117798			0.0588990	−	0.998264i	$-0.481241\pi$
$43$	0.772454			0.117798			0.0588990	+	0.998264i	$0.481241\pi$
$44$	4.85024	+	4.10871i	0.731202	+	0.619412i
$45$		0			0
$46$	−0.281864	+	0.204786i	−0.0415586	+	0.0301941i
$47$	−1.99955	−	6.15398i	−0.291664	−	0.897651i	−0.984322	−	0.176384i	$-0.943560\pi$
$47$	−1.99955	−	6.15398i	−0.291664	−	0.897651i	0.692657	−	0.721267i	$-0.256440\pi$
$48$	−1.08356	+	3.33486i	−0.156399	+	0.481346i
$49$	−5.21803	−	3.79112i	−0.745433	−	0.541589i
$50$		0			0
$51$	−1.18667	+	3.65218i	−0.166167	+	0.511408i
$52$	−2.85805	−	8.79618i	−0.396340	−	1.21981i
$53$	−8.70198	+	6.32236i	−1.19531	+	0.868443i	−0.993815	−	0.111047i	$-0.964580\pi$
$53$	−8.70198	+	6.32236i	−1.19531	+	0.868443i	−0.201494	+	0.979490i	$0.564580\pi$
$54$	0.288813			0.0393024
$55$		0			0
$56$	−4.14842			−0.554356
$57$	−5.63224	+	4.09206i	−0.746008	+	0.542006i
$58$	−0.441485	−	1.35875i	−0.0579699	−	0.178413i
$59$	−4.48008	+	13.7883i	−0.583257	+	1.79508i	0.0229023	+	0.999738i	$0.492709\pi$
$59$	−4.48008	+	13.7883i	−0.583257	+	1.79508i	−0.606159	+	0.795343i	$0.707291\pi$
$60$		0			0
$61$	1.48124	+	1.07618i	0.189653	+	0.137791i	0.678560	−	0.734545i	$-0.262604\pi$
$61$	1.48124	+	1.07618i	0.189653	+	0.137791i	−0.488907	+	0.872336i	$0.662604\pi$
$62$	−0.657697	+	2.02418i	−0.0835276	+	0.257072i
$63$	−1.13329	−	3.48791i	−0.142781	−	0.439435i
$64$	4.90838	−	3.56615i	0.613547	−	0.445768i
$65$		0			0
$66$	−0.814701	+	0.503790i	−0.100283	+	0.0620122i
$67$	6.10784			0.746191			0.373096	−	0.927793i	$-0.378296\pi$
$67$	6.10784			0.746191			0.373096	+	0.927793i	$0.378296\pi$
$68$	5.95433	−	4.32607i	0.722068	−	0.524613i
$69$	0.372776	+	1.14729i	0.0448770	+	0.138117i
$70$		0			0
$71$	2.66254	+	1.93445i	0.315985	+	0.229576i	0.734460	−	0.678652i	$-0.237435\pi$
$71$	2.66254	+	1.93445i	0.315985	+	0.229576i	−0.418475	+	0.908228i	$0.637435\pi$
$72$	−0.915128	−	0.664879i	−0.107849	−	0.0783568i
$73$	0.0591833	−	0.182147i	0.00692688	−	0.0213187i	−0.947533	−	0.319657i	$-0.896432\pi$
$73$	0.0591833	−	0.182147i	0.00692688	−	0.0213187i	0.954460	+	0.298338i	$0.0964323\pi$
$74$	0.213028	+	0.655633i	0.0247640	+	0.0762158i
$75$		0			0
$76$	13.3429			1.53054
$77$	9.28097	+	7.86205i	1.05766	+	0.895964i
$78$	1.39372			0.157808
$79$	2.55645	−	1.85737i	0.287623	−	0.208970i	−0.434613	−	0.900618i	$-0.643115\pi$
$79$	2.55645	−	1.85737i	0.287623	−	0.208970i	0.722235	+	0.691647i	$0.243115\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.00603	+	0.730924i	0.111097	+	0.0807170i
$83$	−1.23813	−	0.899554i	−0.135902	−	0.0987389i	0.517757	−	0.855528i	$-0.326767\pi$
$83$	−1.23813	−	0.899554i	−0.135902	−	0.0987389i	−0.653659	+	0.756789i	$0.726767\pi$
$84$	−2.17205	+	6.68488i	−0.236990	+	0.729380i
$85$		0			0
$86$	0.180487	−	0.131132i	0.0194624	−	0.0141403i
$87$	−4.94672			−0.530344
$88$	3.74123	+	0.279232i	0.398816	+	0.0297662i
$89$	−3.04594			−0.322869			−0.161434	−	0.986883i	$-0.551612\pi$
$89$	−3.04594			−0.322869			−0.161434	+	0.986883i	$0.551612\pi$
$90$		0			0
$91$	−5.46890	−	16.8315i	−0.573297	−	1.76443i
$92$	0.714458	−	2.19888i	0.0744874	−	0.229249i
$93$	5.96190	+	4.33158i	0.618220	+	0.449163i
$94$	−1.51190	−	1.09846i	−0.155941	−	0.113298i
$95$		0			0
$96$	1.01204	+	3.11475i	0.103291	+	0.317897i
$97$	−11.1459	+	8.09794i	−1.13169	+	0.822221i	−0.985940	−	0.167100i	$-0.946560\pi$
$97$	−11.1459	+	8.09794i	−1.13169	+	0.822221i	−0.145750	+	0.989321i	$0.546560\pi$
$98$	−1.86280			−0.188171
$99$	0.787278	+	3.22183i	0.0791245	+	0.323806i
$100$		0			0
$101$	3.76944	−	2.73866i	0.375073	−	0.272507i	−0.384238	−	0.923234i	$-0.625536\pi$
$101$	3.76944	−	2.73866i	0.375073	−	0.272507i	0.759312	+	0.650727i	$0.225536\pi$
$102$	0.342725	+	1.05480i	0.0339348	+	0.104441i
$103$	−3.03362	+	9.33653i	−0.298912	+	0.919956i	0.682968	+	0.730449i	$0.260689\pi$
$103$	−3.03362	+	9.33653i	−0.298912	+	0.919956i	−0.981879	+	0.189507i	$0.939311\pi$
$104$	−4.41612	−	3.20850i	−0.433036	−	0.314619i
$105$		0			0
$106$	−0.959973	+	2.95449i	−0.0932409	+	0.286966i
$107$	3.64690	+	11.2240i	0.352559	+	1.08506i	0.957411	+	0.288727i	$0.0932321\pi$
$107$	3.64690	+	11.2240i	0.352559	+	1.08506i	−0.604852	+	0.796338i	$0.706768\pi$
$108$	−1.55055	+	1.12654i	−0.149202	+	0.108402i
$109$	−10.4450			−1.00045			−0.500226	−	0.865895i	$-0.666750\pi$
$109$	−10.4450			−1.00045			−0.500226	+	0.865895i	$0.666750\pi$
$110$		0			0
$111$	2.38692			0.226556
$112$	10.4037	−	7.55873i	0.983057	−	0.714233i
$113$	−3.97563	−	12.2357i	−0.373996	−	1.15104i	−0.944153	−	0.329506i	$-0.893118\pi$
$113$	−3.97563	−	12.2357i	−0.373996	−	1.15104i	0.570157	−	0.821536i	$-0.306882\pi$
$114$	−0.621329	+	1.91226i	−0.0581928	+	0.179099i
$115$		0			0
$116$	7.67015	+	5.57269i	0.712155	+	0.517411i
$117$	1.49122	−	4.58950i	0.137863	−	0.424300i
$118$	1.29391	+	3.98223i	0.119114	+	0.366594i
$119$	11.3936	−	8.27797i	1.04445	−	0.758840i
$120$		0			0
$121$	−7.84079	−	7.71505i	−0.712799	−	0.701368i
$122$	0.528791			0.0478745
$123$	3.48333	−	2.53079i	0.314081	−	0.228193i
$124$	−4.36454	−	13.4327i	−0.391947	−	1.20629i
$125$		0			0
$126$	−0.856905	−	0.622578i	−0.0763392	−	0.0554636i
$127$	−0.150412	−	0.109281i	−0.0133469	−	0.00969709i	0.581092	−	0.813838i	$-0.302626\pi$
$127$	−0.150412	−	0.109281i	−0.0133469	−	0.00969709i	−0.594439	+	0.804141i	$0.702626\pi$
$128$	2.56556	−	7.89598i	0.226766	−	0.697913i
$129$	−0.238701	−	0.734647i	−0.0210165	−	0.0646821i
$130$		0			0
$131$	−9.27143			−0.810048			−0.405024	−	0.914306i	$-0.632737\pi$
$131$	−9.27143			−0.810048			−0.405024	+	0.914306i	$0.632737\pi$
$132$	2.40881	−	5.88252i	0.209660	−	0.512007i
$133$	25.5318			2.21389
$134$	1.42712	−	1.03687i	0.123285	−	0.0895716i
$135$		0			0
$136$	1.34231	−	4.13121i	0.115102	−	0.354248i
$137$	−0.354431	−	0.257509i	−0.0302811	−	0.0220005i	0.572542	−	0.819876i	$-0.305957\pi$
$137$	−0.354431	−	0.257509i	−0.0302811	−	0.0220005i	−0.602823	+	0.797875i	$0.705957\pi$
$138$	0.281864	+	0.204786i	0.0239939	+	0.0174326i
$139$	2.65888	−	8.18320i	0.225524	−	0.694090i	−0.772714	−	0.634754i	$-0.781102\pi$
$139$	2.65888	−	8.18320i	0.225524	−	0.694090i	0.998238	−	0.0593365i	$-0.0188985\pi$
$140$		0			0
$141$	−5.23489	+	3.80337i	−0.440857	+	0.320302i
$142$	0.950505			0.0797646
$143$	3.79916	+	15.5475i	0.317702	+	1.30015i
$144$	3.50648			0.292207
$145$		0			0
$146$	−0.0170929	−	0.0526065i	−0.00141462	−	0.00435374i
$147$	−1.99311	+	6.13416i	−0.164389	+	0.505937i
$148$	−3.70104	−	2.68897i	−0.304224	−	0.221032i
$149$	12.3975	+	9.00729i	1.01564	+	0.737906i	0.965385	−	0.260830i	$-0.0839963\pi$
$149$	12.3975	+	9.00729i	1.01564	+	0.737906i	0.0502560	+	0.998736i	$0.483996\pi$
$150$		0			0
$151$	−0.324650	−	0.999170i	−0.0264197	−	0.0813113i	0.936977	−	0.349390i	$-0.113611\pi$
$151$	−0.324650	−	0.999170i	−0.0264197	−	0.0813113i	−0.963397	+	0.268079i	$0.913611\pi$
$152$	6.37096	−	4.62877i	0.516753	−	0.375443i
$153$	3.84013			0.310456
$154$	3.50320	+	0.261466i	0.282296	+	0.0210695i
$155$		0			0
$156$	−7.48248	+	5.43634i	−0.599078	+	0.435255i
$157$	1.52614	+	4.69697i	0.121799	+	0.374859i	0.993304	−	0.115527i	$-0.0368557\pi$
$157$	1.52614	+	4.69697i	0.121799	+	0.374859i	−0.871505	+	0.490386i	$0.836856\pi$
$158$	0.282019	−	0.867965i	0.0224362	−	0.0690516i
$159$	8.70198	+	6.32236i	0.690112	+	0.501396i
$160$		0			0
$161$	1.36712	−	4.20757i	0.107744	−	0.331603i
$162$	−0.0892481	−	0.274677i	−0.00701199	−	0.0215807i
$163$	7.78967	−	5.65953i	0.610134	−	0.443288i	−0.239328	−	0.970939i	$-0.576927\pi$
$163$	7.78967	−	5.65953i	0.610134	−	0.443288i	0.849461	+	0.527651i	$0.176927\pi$
$164$	−8.25212			−0.644382
$165$		0			0
$166$	−0.442003			−0.0343061
$167$	7.55958	−	5.49236i	0.584978	−	0.425011i	−0.255537	−	0.966799i	$-0.582252\pi$
$167$	7.55958	−	5.49236i	0.584978	−	0.425011i	0.840515	+	0.541788i	$0.182252\pi$
$168$	1.28193	+	3.94538i	0.0989032	+	0.304393i
$169$	3.17894	−	9.78376i	0.244534	−	0.752597i
$170$		0			0
$171$	5.63224	+	4.09206i	0.430708	+	0.312928i
$172$	−0.457492	+	1.40802i	−0.0348834	+	0.107360i
$173$	0.106516	+	0.327824i	0.00809829	+	0.0249240i	0.955024	−	0.296528i	$-0.0958290\pi$
$173$	0.106516	+	0.327824i	0.00809829	+	0.0249240i	−0.946926	+	0.321452i	$0.895829\pi$
$174$	−1.15582	+	0.839755i	−0.0876227	+	0.0636617i
$175$		0			0
$176$	−9.89129	+	6.11652i	−0.745584	+	0.461050i
$177$	14.4979			1.08973
$178$	−0.711697	+	0.517078i	−0.0533440	+	0.0387567i
$179$	4.96714	+	15.2873i	0.371261	+	1.14262i	0.945967	+	0.324264i	$0.105117\pi$
$179$	4.96714	+	15.2873i	0.371261	+	1.14262i	−0.574705	+	0.818360i	$0.694883\pi$
$180$		0			0
$181$	8.68475	+	6.30984i	0.645532	+	0.469007i	0.861746	−	0.507339i	$-0.169371\pi$
$181$	8.68475	+	6.30984i	0.645532	+	0.469007i	−0.216214	+	0.976346i	$0.569371\pi$
$182$	−4.13515	−	3.00437i	−0.306518	−	0.222698i
$183$	0.565783	−	1.74130i	0.0418239	−	0.128721i
$184$	−0.421670	−	1.29777i	−0.0310859	−	0.0956726i
$185$		0			0
$186$	2.12835			0.156058
$187$	−10.8325	+	6.69853i	−0.792150	+	0.489845i
$188$	12.4016			0.904481
$189$	−2.96699	+	2.15564i	−0.215817	+	0.156800i
$190$		0			0
$191$	−4.20217	+	12.9330i	−0.304059	+	0.935796i	0.675968	+	0.736931i	$0.263726\pi$
$191$	−4.20217	+	12.9330i	−0.304059	+	0.935796i	−0.980027	+	0.198865i	$0.936274\pi$
$192$	−4.90838	−	3.56615i	−0.354232	−	0.257364i
$193$	−20.9601	−	15.2284i	−1.50874	−	1.09616i	−0.966733	−	0.255786i	$-0.917666\pi$
$193$	−20.9601	−	15.2284i	−1.50874	−	1.09616i	−0.542004	−	0.840376i	$-0.682334\pi$
$194$	−1.22957	+	3.78424i	−0.0882783	+	0.271693i
$195$		0			0
$196$	10.0008	−	7.26601i	0.714343	−	0.519001i
$197$	1.18346			0.0843177			0.0421588	−	0.999111i	$-0.486576\pi$
$197$	1.18346			0.0843177			0.0421588	+	0.999111i	$0.486576\pi$
$198$	0.730889	+	0.619147i	0.0519420	+	0.0440008i
$199$	3.13466			0.222210			0.111105	−	0.993809i	$-0.464561\pi$
$199$	3.13466			0.222210			0.111105	+	0.993809i	$0.464561\pi$
$200$		0			0
$201$	−1.88743	−	5.80890i	−0.133129	−	0.409728i
$202$	0.415832	−	1.27980i	0.0292578	−	0.0900464i
$203$	14.6769	+	10.6634i	1.03011	+	0.748422i
$204$	−5.95433	−	4.32607i	−0.416886	−	0.302886i
$205$		0			0
$206$	0.876149	+	2.69651i	0.0610442	+	0.187875i
$207$	0.975941	−	0.709063i	0.0678326	−	0.0492833i
$208$	16.9212			1.17327
$209$	−23.0257	−	1.71856i	−1.59272	−	0.118875i
$210$		0			0
$211$	2.44569	−	1.77690i	0.168368	−	0.122327i	−0.500410	−	0.865788i	$-0.666818\pi$
$211$	2.44569	−	1.77690i	0.168368	−	0.122327i	0.668778	+	0.743462i	$0.266818\pi$
$212$	−6.37047	−	19.6063i	−0.437526	−	1.34657i
$213$	1.01700	−	3.13000i	0.0696836	−	0.214464i
$214$	2.75750	+	2.00344i	0.188499	+	0.136952i
$215$		0			0
$216$	−0.349548	+	1.07580i	−0.0237837	+	0.0731988i
$217$	−8.35157	−	25.7035i	−0.566942	−	1.74487i
$218$	−2.44053	+	1.77315i	−0.165294	+	0.120093i
$219$	−0.191521			−0.0129418
$220$		0			0
$221$	18.5313			1.24655
$222$	0.557715	−	0.405203i	0.0374314	−	0.0271955i
$223$	0.0142058	+	0.0437208i	0.000951288	+	0.00292776i	0.951531	−	0.307553i	$-0.0995101\pi$
$223$	0.0142058	+	0.0437208i	0.000951288	+	0.00292776i	−0.950580	+	0.310481i	$0.899510\pi$
$224$	3.71157	−	11.4230i	0.247989	−	0.763233i
$225$		0			0
$226$	−3.00606	−	2.18403i	−0.199960	−	0.145280i
$227$	−1.89918	+	5.84506i	−0.126053	+	0.387951i	−0.994091	−	0.108546i	$-0.965380\pi$
$227$	−1.89918	+	5.84506i	−0.126053	+	0.387951i	0.868039	+	0.496497i	$0.165380\pi$
$228$	−4.12320	−	12.6899i	−0.273065	−	0.840409i
$229$	−9.49504	+	6.89855i	−0.627450	+	0.455869i	−0.855516	−	0.517777i	$-0.826760\pi$
$229$	−9.49504	+	6.89855i	−0.627450	+	0.455869i	0.228066	+	0.973646i	$0.426760\pi$
$230$		0			0
$231$	4.60927	−	11.2562i	0.303268	−	0.740606i
$232$	5.59554			0.367365
$233$	8.62313	−	6.26507i	0.564920	−	0.410439i	−0.268336	−	0.963325i	$-0.586474\pi$
$233$	8.62313	−	6.26507i	0.564920	−	0.410439i	0.833256	+	0.552887i	$0.186474\pi$
$234$	−0.430683	−	1.32551i	−0.0281546	−	0.0866511i
$235$		0			0
$236$	−22.4797	−	16.3324i	−1.46330	−	1.06315i
$237$	−2.55645	−	1.85737i	−0.166059	−	0.120649i
$238$	1.25691	−	3.86837i	0.0814733	−	0.250749i
$239$	1.41940	+	4.36847i	0.0918134	+	0.282573i	0.986410	−	0.164302i	$-0.0525371\pi$
$239$	1.41940	+	4.36847i	0.0918134	+	0.282573i	−0.894597	+	0.446874i	$0.852537\pi$
$240$		0			0
$241$	−18.8716			−1.21563			−0.607814	−	0.794079i	$-0.707953\pi$
$241$	−18.8716			−1.21563			−0.607814	+	0.794079i	$0.707953\pi$
$242$	−3.14174	−	0.471603i	−0.201959	−	0.0303158i
$243$	−1.00000			−0.0641500
$244$	−2.83893	+	2.06260i	−0.181744	+	0.132044i
$245$		0			0
$246$	0.384269	−	1.18266i	0.0245001	−	0.0754036i
$247$	27.1794	+	19.7470i	1.72938	+	1.25647i
$248$	−6.74387	−	4.89971i	−0.428236	−	0.311132i
$249$	−0.472924	+	1.45551i	−0.0299703	+	0.0922392i
$250$		0			0
$251$	15.7683	−	11.4563i	0.995285	−	0.723117i	0.0342128	−	0.999415i	$-0.489108\pi$
$251$	15.7683	−	11.4563i	0.995285	−	0.723117i	0.961072	+	0.276298i	$0.0891076\pi$
$252$	7.02890			0.442779
$253$	−1.51614	+	3.70255i	−0.0953191	+	0.232777i
$254$	−0.0536959			−0.00336918
$255$		0			0
$256$	3.00870	+	9.25983i	0.188044	+	0.578739i
$257$	−4.07328	+	12.5363i	−0.254084	+	0.781991i	0.739924	+	0.672690i	$0.234861\pi$
$257$	−4.07328	+	12.5363i	−0.254084	+	0.781991i	−0.994009	+	0.109301i	$0.965139\pi$
$258$	−0.180487	−	0.131132i	−0.0112366	−	0.00816390i
$259$	−7.08197	−	5.14535i	−0.440052	−	0.319717i
$260$		0			0
$261$	1.52862	+	4.70461i	0.0946193	+	0.291208i
$262$	−2.16631	+	1.57392i	−0.133835	+	0.0972369i
$263$	29.8396			1.83999			0.919993	−	0.391935i	$-0.128194\pi$
$263$	29.8396			1.83999			0.919993	+	0.391935i	$0.128194\pi$
$264$	−0.890538	−	3.64441i	−0.0548088	−	0.224298i
$265$		0			0
$266$	5.96562	−	4.33428i	0.365776	−	0.265752i
$267$	0.941247	+	2.89686i	0.0576034	+	0.177285i
$268$	−3.61742	+	11.1333i	−0.220969	+	0.680072i
$269$	−0.203757	−	0.148038i	−0.0124233	−	0.00902604i	0.581556	−	0.813506i	$-0.302444\pi$
$269$	−0.203757	−	0.148038i	−0.0124233	−	0.00902604i	−0.593980	+	0.804480i	$0.702444\pi$
$270$		0			0
$271$	−3.73594	+	11.4980i	−0.226942	+	0.698456i	0.771147	+	0.636658i	$0.219684\pi$
$271$	−3.73594	+	11.4980i	−0.226942	+	0.698456i	−0.998089	+	0.0617983i	$0.980316\pi$
$272$	4.16102	+	12.8063i	0.252299	+	0.776497i
$273$	−14.3178	+	10.4025i	−0.866551	+	0.629586i
$274$	−0.126529			−0.00764391
$275$		0			0
$276$	−2.31204			−0.139168
$277$	−13.3209	+	9.67819i	−0.800375	+	0.581506i	−0.911024	−	0.412353i	$-0.864707\pi$
$277$	−13.3209	+	9.67819i	−0.800375	+	0.581506i	0.110649	+	0.993860i	$0.464707\pi$
$278$	−0.767920	−	2.36341i	−0.0460568	−	0.141748i
$279$	2.27724	−	7.00864i	0.136335	−	0.419596i
$280$		0			0
$281$	−10.1950	−	7.40711i	−0.608183	−	0.441871i	0.240591	−	0.970627i	$-0.422659\pi$
$281$	−10.1950	−	7.40711i	−0.608183	−	0.441871i	−0.848774	+	0.528756i	$0.822659\pi$
$282$	−0.577496	+	1.77735i	−0.0343894	+	0.105840i
$283$	5.51529	+	16.9743i	0.327850	+	1.00902i	0.970138	+	0.242554i	$0.0779853\pi$
$283$	5.51529	+	16.9743i	0.327850	+	1.00902i	−0.642288	+	0.766463i	$0.722015\pi$
$284$	−5.10298	+	3.70753i	−0.302806	+	0.220002i
$285$		0			0
$286$	3.52704	+	2.98781i	0.208558	+	0.176673i
$287$	−15.7905			−0.932083
$288$	2.64956	−	1.92502i	0.156127	−	0.113433i
$289$	−0.696329	−	2.14308i	−0.0409605	−	0.126063i
$290$		0			0
$291$	11.1459	+	8.09794i	0.653382	+	0.474710i
$292$	0.296963	+	0.215756i	0.0173785	+	0.0126262i
$293$	3.06135	−	9.42187i	0.178846	−	0.550431i	−0.820942	−	0.571011i	$-0.806551\pi$
$293$	3.06135	−	9.42187i	0.178846	−	0.550431i	0.999788	+	0.0205799i	$0.00655124\pi$
$294$	0.575636	+	1.77162i	0.0335717	+	0.103323i
$295$		0			0
$296$	−2.69999			−0.156934
$297$	2.82086	−	1.74435i	0.163683	−	0.101217i
$298$	4.42580			0.256380
$299$	4.70959	−	3.42172i	0.272362	−	0.197883i
$300$		0			0
$301$	−0.875414	+	2.69425i	−0.0504580	+	0.155294i
$302$	−0.245475	−	0.178348i	−0.0141255	−	0.0102628i
$303$	−3.76944	−	2.73866i	−0.216549	−	0.157332i
$304$	−7.54357	+	23.2167i	−0.432653	+	1.33157i
$305$		0			0
$306$	0.897265	−	0.651901i	0.0512932	−	0.0372667i
$307$	23.2505			1.32698			0.663489	−	0.748186i	$-0.269075\pi$
$307$	23.2505			1.32698			0.663489	+	0.748186i	$0.269075\pi$
$308$	−19.8275	+	12.2608i	−1.12978	+	0.698626i
$309$	9.81701			0.558470
$310$		0			0
$311$	9.22810	+	28.4012i	0.523278	+	1.61048i	0.767696	+	0.640814i	$0.221403\pi$
$311$	9.22810	+	28.4012i	0.523278	+	1.61048i	−0.244419	+	0.969670i	$0.578597\pi$
$312$	−1.68681	+	5.19146i	−0.0954967	+	0.293909i
$313$	−20.7405	−	15.0688i	−1.17232	−	0.851740i	−0.181035	−	0.983477i	$-0.557945\pi$
$313$	−20.7405	−	15.0688i	−1.17232	−	0.851740i	−0.991285	+	0.131737i	$0.957945\pi$
$314$	1.15395	+	0.838392i	0.0651210	+	0.0473132i
$315$		0			0
$316$	1.87150	+	5.75989i	0.105280	+	0.324019i
$317$	−0.906665	+	0.658731i	−0.0509234	+	0.0369980i	−0.612956	−	0.790117i	$-0.710020\pi$
$317$	−0.906665	+	0.658731i	−0.0509234	+	0.0369980i	0.562032	+	0.827115i	$0.310020\pi$
$318$	3.10654			0.174206
$319$	−12.5185	−	10.6046i	−0.700901	−	0.593744i
$320$		0			0
$321$	9.54770	−	6.93681i	0.532901	−	0.387175i
$322$	−0.394842	−	1.21520i	−0.0220037	−	0.0677204i
$323$	−8.26137	+	25.4259i	−0.459675	+	1.41473i
$324$	1.55055	+	1.12654i	0.0861418	+	0.0625856i
$325$		0			0
$326$	0.859330	−	2.64475i	0.0475939	−	0.146479i
$327$	3.22769	+	9.93382i	0.178492	+	0.549341i
$328$	−3.94021	+	2.86273i	−0.217561	+	0.158068i
$329$	23.7306			1.30831
$330$		0			0
$331$	−10.9379			−0.601200			−0.300600	−	0.953750i	$-0.597187\pi$
$331$	−10.9379			−0.601200			−0.300600	+	0.953750i	$0.597187\pi$
$332$	2.37298	−	1.72407i	0.130234	−	0.0946209i
$333$	−0.737599	−	2.27010i	−0.0404202	−	0.124400i
$334$	0.833948	−	2.56663i	0.0456316	−	0.140440i
$335$		0			0
$336$	−10.4037	−	7.55873i	−0.567568	−	0.412362i
$337$	6.74151	−	20.7482i	0.367234	−	1.13023i	−0.581337	−	0.813663i	$-0.697470\pi$
$337$	6.74151	−	20.7482i	0.367234	−	1.13023i	0.948571	−	0.316566i	$-0.102530\pi$
$338$	−0.918118	−	2.82568i	−0.0499390	−	0.153697i
$339$	−10.4083	+	7.56211i	−0.565304	+	0.410717i
$340$		0			0
$341$	5.80170	+	23.7427i	0.314180	+	1.28574i
$342$	2.01066			0.108724
$343$	−1.63233	+	1.18595i	−0.0881373	+	0.0640355i
$344$	0.270010	+	0.831004i	0.0145579	+	0.0448047i
$345$		0			0
$346$	0.0805393	+	0.0585152i	0.00432982	+	0.00314580i
$347$	−20.5376	−	14.9215i	−1.10252	−	0.801026i	−0.121049	−	0.992647i	$-0.538626\pi$
$347$	−20.5376	−	14.9215i	−1.10252	−	0.801026i	−0.981469	+	0.191620i	$0.938626\pi$
$348$	2.92974	−	9.01680i	0.157050	−	0.483351i
$349$	9.94686	+	30.6133i	0.532443	+	1.63869i	0.749110	+	0.662446i	$0.230482\pi$
$349$	9.94686	+	30.6133i	0.532443	+	1.63869i	−0.216666	+	0.976246i	$0.569518\pi$
$350$		0			0
$351$	−4.82569			−0.257576
$352$	−4.11614	+	10.0520i	−0.219391	+	0.535771i
$353$	−10.2135			−0.543611			−0.271806	−	0.962352i	$-0.587621\pi$
$353$	−10.2135			−0.543611			−0.271806	+	0.962352i	$0.587621\pi$
$354$	3.38749	−	2.46115i	0.180043	−	0.130809i
$355$		0			0
$356$	1.80398	−	5.55208i	0.0956108	−	0.294260i
$357$	−11.3936	−	8.27797i	−0.603016	−	0.438116i
$358$	3.75576	+	2.72872i	0.198498	+	0.144217i
$359$	9.96844	−	30.6797i	0.526114	−	1.61921i	−0.235988	−	0.971756i	$-0.575833\pi$
$359$	9.96844	−	30.6797i	0.526114	−	1.61921i	0.762102	−	0.647457i	$-0.224167\pi$
$360$		0			0
$361$	−23.8393	+	17.3203i	−1.25470	+	0.911593i
$362$	3.10039			0.162953
$363$	−4.91451	+	9.84112i	−0.257945	+	0.516525i
$364$	33.9193			1.77785
$365$		0			0
$366$	−0.163405	−	0.502910i	−0.00854134	−	0.0262875i
$367$	4.71299	−	14.5051i	0.246016	−	0.757160i	−0.749452	−	0.662059i	$-0.769683\pi$
$367$	4.71299	−	14.5051i	0.246016	−	0.757160i	0.995468	−	0.0951006i	$-0.0303173\pi$
$368$	3.42212	+	2.48631i	0.178390	+	0.129608i
$369$	−3.48333	−	2.53079i	−0.181335	−	0.131748i
$370$		0			0
$371$	−12.1899	−	37.5168i	−0.632870	−	1.94777i
$372$	−11.4265	+	8.30184i	−0.592437	+	0.430430i
$373$	−14.4355			−0.747440			−0.373720	−	0.927542i	$-0.621918\pi$
$373$	−14.4355			−0.747440			−0.373720	+	0.927542i	$0.621918\pi$
$374$	−1.39392	+	3.40406i	−0.0720777	+	0.176020i
$375$		0			0
$376$	5.92150	−	4.30222i	0.305378	−	0.221870i
$377$	7.37665	+	22.7030i	0.379917	+	1.16926i
$378$	−0.327309	+	1.00735i	−0.0168349	+	0.0518126i
$379$	16.2923	+	11.8371i	0.836880	+	0.608029i	0.921497	−	0.388384i	$-0.126967\pi$
$379$	16.2923	+	11.8371i	0.836880	+	0.608029i	−0.0846172	+	0.996414i	$0.526967\pi$
$380$		0			0
$381$	−0.0574523	+	0.176820i	−0.00294337	+	0.00905876i
$382$	1.21364	+	3.73520i	0.0620953	+	0.191110i
$383$	−7.47458	+	5.43060i	−0.381933	+	0.277491i	−0.762142	−	0.647410i	$-0.775852\pi$
$383$	−7.47458	+	5.43060i	−0.381933	+	0.277491i	0.380209	+	0.924901i	$0.375852\pi$
$384$	−8.30233			−0.423676
$385$		0			0
$386$	−7.48258			−0.380853
$387$	−0.624928	+	0.454037i	−0.0317669	+	0.0230800i
$388$	−8.15956	−	25.1125i	−0.414239	−	1.27490i
$389$	6.36140	−	19.5784i	0.322536	−	0.992663i	−0.650005	−	0.759930i	$-0.725233\pi$
$389$	6.36140	−	19.5784i	0.322536	−	0.992663i	0.972541	−	0.232733i	$-0.0747668\pi$
$390$		0			0
$391$	3.74775	+	2.72290i	0.189532	+	0.137703i
$392$	2.25453	−	6.93872i	0.113871	−	0.350458i
$393$	2.86503	+	8.81765i	0.144522	+	0.444792i
$394$	0.276520	−	0.200903i	0.0139309	−	0.0101214i
$395$		0			0
$396$	−6.33897	−	0.473117i	−0.318545	−	0.0237750i
$397$	−20.1311			−1.01035			−0.505176	−	0.863017i	$-0.668572\pi$
$397$	−20.1311			−1.01035			−0.505176	+	0.863017i	$0.668572\pi$
$398$	0.732428	−	0.532140i	0.0367133	−	0.0266738i
$399$	−7.88976	−	24.2822i	−0.394982	−	1.21563i
$400$		0			0
$401$	−0.524993	−	0.381430i	−0.0262169	−	0.0190477i	0.574600	−	0.818435i	$-0.305158\pi$
$401$	−0.524993	−	0.381430i	−0.0262169	−	0.0190477i	−0.600817	+	0.799387i	$0.705158\pi$
$402$	−1.42712	−	1.03687i	−0.0711785	−	0.0517142i
$403$	10.9893	−	33.8215i	0.547414	−	1.68477i
$404$	2.75950	+	8.49286i	0.137290	+	0.422536i
$405$		0			0
$406$	5.23953			0.260034
$407$	6.04050	+	5.11700i	0.299416	+	0.253640i
$408$	−4.34381			−0.215051
$409$	−10.6063	+	7.70595i	−0.524449	+	0.381035i	−0.818277	−	0.574824i	$-0.805071\pi$
$409$	−10.6063	+	7.70595i	−0.524449	+	0.381035i	0.293828	+	0.955858i	$0.405071\pi$
$410$		0			0
$411$	−0.135381	+	0.416659i	−0.00667784	+	0.0205523i
$412$	−15.2218	−	11.0593i	−0.749923	−	0.544851i
$413$	−43.0150	−	31.2522i	−2.11663	−	1.53782i
$414$	0.107663	−	0.331351i	0.00529133	−	0.0162850i
$415$		0			0
$416$	12.7860	−	9.28954i	0.626883	−	0.455457i
$417$	−8.60433			−0.421356
$418$	−5.67180	+	3.50730i	−0.277417	+	0.171547i
$419$	−33.0462			−1.61441			−0.807206	−	0.590270i	$-0.799021\pi$
$419$	−33.0462			−1.61441			−0.807206	+	0.590270i	$0.799021\pi$
$420$		0			0
$421$	2.69395	+	8.29112i	0.131295	+	0.404084i	0.994995	−	0.0999212i	$-0.0318591\pi$
$421$	2.69395	+	8.29112i	0.131295	+	0.404084i	−0.863700	+	0.504006i	$0.831859\pi$
$422$	0.269800	−	0.830359i	0.0131337	−	0.0404212i
$423$	5.23489	+	3.80337i	0.254529	+	0.184926i
$424$	−9.84333	−	7.15160i	−0.478035	−	0.347312i
$425$		0			0
$426$	−0.293722	−	0.903984i	−0.0142309	−	0.0437982i
$427$	−5.43230	+	3.94680i	−0.262888	+	0.190999i
$428$	−22.6188			−1.09332
$429$	13.6126	−	8.41767i	0.657222	−	0.406409i
$430$		0			0
$431$	13.2578	−	9.63233i	0.638604	−	0.463973i	−0.220766	−	0.975327i	$-0.570856\pi$
$431$	13.2578	−	9.63233i	0.638604	−	0.463973i	0.859370	+	0.511354i	$0.170856\pi$
$432$	−1.08356	−	3.33486i	−0.0521329	−	0.160449i
$433$	−10.8117	+	33.2750i	−0.519578	+	1.59910i	0.255217	+	0.966884i	$0.417853\pi$
$433$	−10.8117	+	33.2750i	−0.519578	+	1.59910i	−0.774795	+	0.632212i	$0.782147\pi$
$434$	−6.31480	−	4.58797i	−0.303120	−	0.220230i
$435$		0			0
$436$	6.18616	−	19.0390i	0.296263	−	0.911804i
$437$	2.59520	+	7.98722i	0.124145	+	0.382080i
$438$	−0.0447497	+	0.0325126i	−0.00213823	+	0.00155351i
$439$	18.5657			0.886091			0.443046	−	0.896499i	$-0.353898\pi$
$439$	18.5657			0.886091			0.443046	+	0.896499i	$0.353898\pi$
$440$		0			0
$441$	6.44984			0.307135
$442$	4.32992	−	3.14587i	0.205953	−	0.149634i
$443$	2.73532	+	8.41846i	0.129959	+	0.399973i	0.994772	−	0.102121i	$-0.0325630\pi$
$443$	2.73532	+	8.41846i	0.129959	+	0.399973i	−0.864813	+	0.502094i	$0.832563\pi$
$444$	−1.41367	+	4.35084i	−0.0670899	+	0.206482i
$445$		0			0
$446$	0.0107413	+	0.00780400i	0.000508614	+	0.000369530i
$447$	4.73541	−	14.5741i	0.223977	−	0.689332i
$448$	6.87577	+	21.1614i	0.324850	+	0.999784i
$449$	−2.57355	+	1.86980i	−0.121453	+	0.0882411i	−0.646854	−	0.762614i	$-0.723916\pi$
$449$	−2.57355	+	1.86980i	−0.121453	+	0.0882411i	0.525400	+	0.850855i	$0.323916\pi$
$450$		0			0
$451$	14.2406	+	1.06286i	0.670562	+	0.0500483i
$452$	24.6577			1.15980
$453$	−0.849945	+	0.617521i	−0.0399339	+	0.0290137i
$454$	0.548507	+	1.68813i	0.0257427	+	0.0792278i
$455$		0			0
$456$	−6.37096	−	4.62877i	−0.298348	−	0.216762i
$457$	−2.85384	−	2.07343i	−0.133497	−	0.0969911i	0.519033	−	0.854754i	$-0.326292\pi$
$457$	−2.85384	−	2.07343i	−0.133497	−	0.0969911i	−0.652530	+	0.757763i	$0.726292\pi$
$458$	−1.04746	+	3.22375i	−0.0489446	+	0.150636i
$459$	−1.18667	−	3.65218i	−0.0553889	−	0.170469i
$460$		0			0
$461$	−18.1321			−0.844496			−0.422248	−	0.906480i	$-0.638759\pi$
$461$	−18.1321			−0.844496			−0.422248	+	0.906480i	$0.638759\pi$
$462$	−0.833880	−	3.41254i	−0.0387956	−	0.158766i
$463$	18.0104			0.837013			0.418506	−	0.908214i	$-0.362554\pi$
$463$	18.0104			0.837013			0.418506	+	0.908214i	$0.362554\pi$
$464$	−14.0329	+	10.1955i	−0.651460	+	0.473313i
$465$		0			0
$466$	0.951275	−	2.92772i	0.0440670	−	0.135624i
$467$	−21.6183	−	15.7066i	−1.00038	−	0.726816i	−0.0382073	−	0.999270i	$-0.512165\pi$
$467$	−21.6183	−	15.7066i	−1.00038	−	0.726816i	−0.962169	+	0.272454i	$0.912165\pi$
$468$	7.48248	+	5.43634i	0.345878	+	0.251295i
$469$	−6.92195	+	21.3036i	−0.319626	+	0.983708i
$470$		0			0
$471$	3.99548	−	2.90289i	0.184102	−	0.133758i
$472$	−16.3994			−0.754844
$473$	0.970838	−	2.37087i	0.0446392	−	0.109013i
$474$	−0.912632			−0.0419186
$475$		0			0
$476$	8.34096	+	25.6708i	0.382307	+	1.17662i
$477$	3.32386	−	10.2298i	0.152189	−	0.468390i
$478$	1.07324	+	0.779755i	0.0490889	+	0.0356651i
$479$	−18.4202	−	13.3831i	−0.841642	−	0.611489i	0.0811869	−	0.996699i	$-0.474129\pi$
$479$	−18.4202	−	13.3831i	−0.841642	−	0.611489i	−0.922829	+	0.385210i	$0.874129\pi$
$480$		0			0
$481$	−3.55942	−	10.9548i	−0.162296	−	0.499495i
$482$	−4.40944	+	3.20364i	−0.200844	+	0.145922i
$483$	−4.42410			−0.201303
$484$	18.7066	−	9.72276i	0.850301	−	0.441944i
$485$		0			0
$486$	−0.233654	+	0.169760i	−0.0105988	+	0.00770047i
$487$	−4.18739	−	12.8875i	−0.189749	−	0.583986i	0.810249	−	0.586086i	$-0.199332\pi$
$487$	−4.18739	−	12.8875i	−0.189749	−	0.583986i	−0.999998	+	0.00209933i	$0.999332\pi$
$488$	−0.639992	+	1.96969i	−0.0289711	+	0.0891638i
$489$	−7.78967	−	5.65953i	−0.352261	−	0.255933i
$490$		0			0
$491$	5.88248	−	18.1044i	0.265473	−	0.817041i	−0.726111	−	0.687577i	$-0.758674\pi$
$491$	5.88248	−	18.1044i	0.265473	−	0.817041i	0.991584	−	0.129464i	$-0.0413257\pi$
$492$	2.55005	+	7.84823i	0.114965	+	0.353826i
$493$	−15.3681	+	11.1656i	−0.692147	+	0.502874i
$494$	9.70284			0.436551
$495$		0			0
$496$	25.8404			1.16027
$497$	−9.76459	+	7.09439i	−0.438002	+	0.318227i
$498$	0.136586	+	0.420370i	0.00612058	+	0.0188372i
$499$	−7.14118	+	21.9783i	−0.319683	+	0.983884i	0.654100	+	0.756408i	$0.273047\pi$
$499$	−7.14118	+	21.9783i	−0.319683	+	0.983884i	−0.973784	+	0.227476i	$0.926953\pi$
$500$		0			0
$501$	−7.55958	−	5.49236i	−0.337737	−	0.245380i
$502$	1.73950	−	5.35364i	0.0776379	−	0.238945i
$503$	−8.24483	−	25.3750i	−0.367619	−	1.13141i	−0.948325	−	0.317301i	$-0.897224\pi$
$503$	−8.24483	−	25.3750i	−0.367619	−	1.13141i	0.580706	−	0.814113i	$-0.302776\pi$
$504$	3.35614	−	2.43838i	0.149494	−	0.108614i
$505$		0			0
$506$	0.274291	+	1.12250i	0.0121937	+	0.0499011i
$507$	−10.2873			−0.456873
$508$	0.288278	−	0.209446i	0.0127903	−	0.00929266i
$509$	2.68124	+	8.25201i	0.118844	+	0.365764i	0.992729	−	0.120368i	$-0.0384074\pi$
$509$	2.68124	+	8.25201i	0.118844	+	0.365764i	−0.873885	+	0.486132i	$0.838407\pi$
$510$		0			0
$511$	0.568241	+	0.412851i	0.0251375	+	0.0182635i
$512$	15.7084	+	11.4128i	0.694219	+	0.504380i
$513$	2.15132	−	6.62109i	0.0949832	−	0.292328i
$514$	1.17642	+	3.62064i	0.0518895	+	0.159699i
$515$		0			0
$516$	1.48047			0.0651743
$517$	−21.4013	−	1.59731i	−0.941228	−	0.0702498i
$518$	−2.52821			−0.111083
$519$	0.278863	−	0.202606i	0.0122407	−	0.00889342i
$520$		0			0
$521$	−2.01393	+	6.19824i	−0.0882319	+	0.271550i	−0.985431	−	0.170077i	$-0.945598\pi$
$521$	−2.01393	+	6.19824i	−0.0882319	+	0.271550i	0.897199	+	0.441627i	$0.145598\pi$
$522$	1.15582	+	0.839755i	0.0505890	+	0.0367551i
$523$	−29.8210	−	21.6662i	−1.30398	−	0.947398i	−0.303995	−	0.952674i	$-0.598321\pi$
$523$	−29.8210	−	21.6662i	−1.30398	−	0.947398i	−0.999986	+	0.00527594i	$0.998321\pi$
$524$	5.49108	−	16.8998i	0.239879	−	0.738271i
$525$		0			0
$526$	6.97215	−	5.06556i	0.304000	−	0.220869i
$527$	28.2992			1.23273
$528$	8.87373	+	7.51707i	0.386180	+	0.327139i
$529$	−21.5448			−0.936729
$530$		0			0
$531$	−4.48008	−	13.7883i	−0.194419	−	0.598360i
$532$	−15.1214	+	46.5389i	−0.655597	+	2.01772i
$533$	−16.8095	−	12.2128i	−0.728099	−	0.528995i
$534$	0.711697	+	0.517078i	0.0307981	+	0.0223762i
$535$		0			0
$536$	2.13498	+	6.57080i	0.0922172	+	0.283815i
$537$	13.0041	−	9.44806i	0.561170	−	0.407714i
$538$	−0.0727396			−0.00313603
$539$	−18.1941	+	11.2508i	−0.783675	+	0.484604i
$540$		0			0
$541$	−16.4781	+	11.9720i	−0.708449	+	0.514718i	−0.882673	−	0.469988i	$-0.844258\pi$
$541$	−16.4781	+	11.9720i	−0.708449	+	0.514718i	0.174224	+	0.984706i	$0.444258\pi$
$542$	1.07899	+	3.32078i	0.0463465	+	0.142640i
$543$	3.31728	−	10.2095i	0.142358	−	0.438133i
$544$	10.1747	+	7.39233i	0.436235	+	0.316944i
$545$		0			0
$546$	−1.57949	+	4.86117i	−0.0675959	+	0.208039i
$547$	7.43795	+	22.8916i	0.318024	+	0.978776i	0.974492	+	0.224423i	$0.0720496\pi$
$547$	7.43795	+	22.8916i	0.318024	+	0.978776i	−0.656468	+	0.754354i	$0.727950\pi$
$548$	0.679298	−	0.493539i	0.0290182	−	0.0210829i
$549$	−1.83091			−0.0781415
$550$		0			0
$551$	−34.4382			−1.46712
$552$	−1.10395	+	0.802064i	−0.0469871	+	0.0341381i
$553$	3.58113	+	11.0216i	0.152285	+	0.468686i
$554$	−1.46952	+	4.52271i	−0.0624338	+	0.192151i
$555$		0			0
$556$	13.3415	+	9.69314i	0.565804	+	0.411081i
$557$	11.7523	−	36.1699i	0.497961	−	1.53257i	−0.314330	−	0.949314i	$-0.601780\pi$
$557$	11.7523	−	36.1699i	0.497961	−	1.53257i	0.812291	−	0.583253i	$-0.198220\pi$
$558$	−0.657697	−	2.02418i	−0.0278425	−	0.0856905i
$559$	−3.01571	+	2.19104i	−0.127551	+	0.0926711i
$560$		0			0
$561$	9.71810	+	8.23235i	0.410298	+	0.347570i
$562$	−3.63954			−0.153525
$563$	−1.18084	+	0.857930i	−0.0497664	+	0.0361574i	−0.612390	−	0.790556i	$-0.709792\pi$
$563$	−1.18084	+	0.857930i	−0.0497664	+	0.0361574i	0.562624	+	0.826713i	$0.309792\pi$
$564$	−3.83231	−	11.7946i	−0.161369	−	0.496644i
$565$		0			0
$566$	4.17023	+	3.02985i	0.175288	+	0.127354i
$567$	2.96699	+	2.15564i	0.124602	+	0.0905286i
$568$	−1.15039	+	3.54053i	−0.0482692	+	0.148557i
$569$	−0.330277	−	1.01649i	−0.0138459	−	0.0426134i	0.943895	−	0.330246i	$-0.107132\pi$
$569$	−0.330277	−	1.01649i	−0.0138459	−	0.0426134i	−0.957741	+	0.287633i	$0.907132\pi$
$570$		0			0
$571$	−4.25241			−0.177958			−0.0889789	−	0.996034i	$-0.528360\pi$
$571$	−4.25241			−0.177958			−0.0889789	+	0.996034i	$0.528360\pi$
$572$	−30.5899	−	2.28312i	−1.27903	−	0.0954619i
$573$	13.5985			0.568086
$574$	−3.68952	+	2.68059i	−0.153998	+	0.111886i
$575$		0			0
$576$	−1.87483	+	5.77014i	−0.0781181	+	0.240423i
$577$	−2.45662	−	1.78484i	−0.102270	−	0.0743037i	0.535475	−	0.844551i	$-0.320133\pi$
$577$	−2.45662	−	1.78484i	−0.102270	−	0.0743037i	−0.637745	+	0.770247i	$0.720133\pi$
$578$	−0.526509	−	0.382531i	−0.0218999	−	0.0159112i
$579$	−8.00603	+	24.6400i	−0.332719	+	1.02400i
$580$		0			0
$581$	4.54072	−	3.29903i	0.188381	−	0.136867i
$582$	3.97899			0.164934
$583$	8.46815	+	34.6548i	0.350715	+	1.43525i
$584$	0.216641			0.00896467
$585$		0			0
$586$	−0.884157	−	2.72116i	−0.0365242	−	0.112410i
$587$	−0.785738	+	2.41825i	−0.0324309	+	0.0998120i	−0.965962	−	0.258685i	$-0.916711\pi$
$587$	−0.785738	+	2.41825i	−0.0324309	+	0.0998120i	0.933531	+	0.358497i	$0.116711\pi$
$588$	−10.0008	−	7.26601i	−0.412426	−	0.299645i
$589$	41.5057	+	30.1557i	1.71021	+	1.24254i
$590$		0			0
$591$	−0.365708	−	1.12553i	−0.0150432	−	0.0462982i
$592$	6.77122	−	4.91958i	0.278295	−	0.202193i
$593$	40.7468			1.67327			0.836636	−	0.547760i	$-0.184519\pi$
$593$	40.7468			1.67327			0.836636	+	0.547760i	$0.184519\pi$
$594$	0.362987	−	0.886443i	0.0148935	−	0.0363712i
$595$		0			0
$596$	−23.7608	+	17.2633i	−0.973282	+	0.707131i
$597$	−0.968664	−	2.98124i	−0.0396448	−	0.122014i
$598$	0.519546	−	1.59900i	0.0212458	−	0.0653879i
$599$	−5.46985	−	3.97408i	−0.223492	−	0.162376i	0.470405	−	0.882451i	$-0.344108\pi$
$599$	−5.46985	−	3.97408i	−0.223492	−	0.162376i	−0.693897	+	0.720074i	$0.744108\pi$
$600$		0			0
$601$	−4.66421	+	14.3550i	−0.190257	+	0.585551i	−0.999999	−	0.00123468i	$-0.999607\pi$
$601$	−4.66421	+	14.3550i	−0.190257	+	0.585551i	0.809742	+	0.586786i	$0.199607\pi$
$602$	0.252831	+	0.778133i	0.0103046	+	0.0317143i
$603$	−4.94135	+	3.59010i	−0.201227	+	0.146200i
$604$	2.01355			0.0819301
$605$		0			0
$606$	−1.34566			−0.0546637
$607$	6.36404	−	4.62375i	0.258308	−	0.187672i	−0.451093	−	0.892477i	$-0.648966\pi$
$607$	6.36404	−	4.62375i	0.258308	−	0.187672i	0.709401	+	0.704805i	$0.248966\pi$
$608$	7.04566	+	21.6843i	0.285739	+	0.879415i
$609$	5.60607	−	17.2537i	0.227169	−	0.699155i
$610$		0			0
$611$	25.2619	+	18.3539i	1.02199	+	0.742518i
$612$	−2.27435	+	6.99973i	−0.0919352	+	0.282947i
$613$	−8.37440	−	25.7738i	−0.338239	−	1.04099i	−0.965104	−	0.261865i	$-0.915662\pi$
$613$	−8.37440	−	25.7738i	−0.338239	−	1.04099i	0.626865	−	0.779128i	$-0.284338\pi$
$614$	5.43259	−	3.94701i	0.219241	−	0.159288i
$615$		0			0
$616$	−5.21383	+	12.7326i	−0.210071	+	0.513011i
$617$	3.61737			0.145630			0.0728149	−	0.997345i	$-0.476802\pi$
$617$	3.61737			0.145630			0.0728149	+	0.997345i	$0.476802\pi$
$618$	2.29379	−	1.66654i	0.0922697	−	0.0670379i
$619$	−5.11806	−	15.7518i	−0.205712	−	0.633116i	−0.999683	−	0.0251613i	$-0.991990\pi$
$619$	−5.11806	−	15.7518i	−0.205712	−	0.633116i	0.793971	−	0.607955i	$-0.208010\pi$
$620$		0			0
$621$	−0.975941	−	0.709063i	−0.0391632	−	0.0284537i
$622$	6.97757	+	5.06950i	0.279775	+	0.203268i
$623$	3.45193	−	10.6239i	0.138299	−	0.425640i
$624$	−5.22893	−	16.0930i	−0.209325	−	0.644235i
$625$		0			0
$626$	−7.40418			−0.295931
$627$	5.48089	+	22.4298i	0.218886	+	0.895761i
$628$	−9.46543			−0.377712
$629$	7.41553	−	5.38770i	0.295676	−	0.214821i
$630$		0			0
$631$	1.23280	−	3.79417i	0.0490770	−	0.151044i	−0.923515	−	0.383563i	$-0.874697\pi$
$631$	1.23280	−	3.79417i	0.0490770	−	0.151044i	0.972592	+	0.232519i	$0.0746969\pi$
$632$	2.89175	+	2.10098i	0.115028	+	0.0835726i
$633$	−2.44569	−	1.77690i	−0.0972073	−	0.0706252i
$634$	−0.100020	+	0.307831i	−0.00397231	+	0.0122255i
$635$		0			0
$636$	−16.6781	+	12.1173i	−0.661330	+	0.480484i
$637$	31.1249			1.23321
$638$	−4.72524	−	0.352675i	−0.187074	−	0.0139625i
$639$	−3.29108			−0.130193
$640$		0			0
$641$	−10.5863	−	32.5812i	−0.418133	−	1.28688i	−0.909418	−	0.415883i	$-0.863473\pi$
$641$	−10.5863	−	32.5812i	−0.418133	−	1.28688i	0.491285	−	0.870999i	$-0.336527\pi$
$642$	1.05327	−	3.24163i	0.0415693	−	0.127937i
$643$	33.6323	+	24.4353i	1.32633	+	0.963634i	0.999830	+	0.0184357i	$0.00586859\pi$
$643$	33.6323	+	24.4353i	1.32633	+	0.963634i	0.326498	+	0.945198i	$0.394131\pi$
$644$	6.85979	+	4.98393i	0.270314	+	0.196394i
$645$		0			0
$646$	2.38599	+	7.34332i	0.0938755	+	0.288919i
$647$	7.98408	−	5.80077i	0.313887	−	0.228052i	−0.419676	−	0.907674i	$-0.637856\pi$
$647$	7.98408	−	5.80077i	0.313887	−	0.228052i	0.733562	+	0.679622i	$0.237856\pi$
$648$	1.13116			0.0444362
$649$	36.6892	+	31.0800i	1.44018	+	1.22000i
$650$		0			0
$651$	−21.8647	+	15.8856i	−0.856945	+	0.622607i
$652$	5.70259	+	17.5508i	0.223331	+	0.687341i
$653$	−6.40677	+	19.7180i	−0.250716	+	0.771625i	0.743927	+	0.668261i	$0.232961\pi$
$653$	−6.40677	+	19.7180i	−0.250716	+	0.771625i	−0.994644	+	0.103365i	$0.967039\pi$
$654$	2.44053	+	1.77315i	0.0954322	+	0.0693356i
$655$		0			0
$656$	4.66542	−	14.3587i	0.182154	−	0.560613i
$657$	0.0591833	+	0.182147i	0.00230896	+	0.00710624i
$658$	5.54476	−	4.02850i	0.216157	−	0.157047i
$659$	26.4580			1.03066			0.515329	−	0.856992i	$-0.327670\pi$
$659$	26.4580			1.03066			0.515329	+	0.856992i	$0.327670\pi$
$660$		0			0
$661$	5.75931			0.224011			0.112006	−	0.993708i	$-0.464273\pi$
$661$	5.75931			0.224011			0.112006	+	0.993708i	$0.464273\pi$
$662$	−2.55568	+	1.85681i	−0.0993294	+	0.0721671i
$663$	−5.72648	−	17.6243i	−0.222398	−	0.684471i
$664$	0.534953	−	1.64641i	0.0207602	−	0.0638933i
$665$		0			0
$666$	−0.557715	−	0.405203i	−0.0216110	−	0.0157013i
$667$	−1.84402	+	5.67531i	−0.0714008	+	0.219749i
$668$	5.53415	+	17.0324i	0.214123	+	0.659002i
$669$	0.0371912	−	0.0270210i	0.00143789	−	0.00104469i
$670$		0			0
$671$	5.16475	−	3.19375i	0.199383	−	0.123293i
$672$	−12.0109			−0.463330
$673$	12.8303	−	9.32174i	0.494571	−	0.359327i	−0.312369	−	0.949961i	$-0.601122\pi$
$673$	12.8303	−	9.32174i	0.494571	−	0.359327i	0.806939	+	0.590634i	$0.201122\pi$
$674$	−1.94704	−	5.99236i	−0.0749970	−	0.230817i
$675$		0			0
$676$	15.9509	+	11.5890i	0.613497	+	0.445732i
$677$	−11.7553	−	8.54071i	−0.451792	−	0.328246i	0.338511	−	0.940962i	$-0.390077\pi$
$677$	−11.7553	−	8.54071i	−0.451792	−	0.328246i	−0.790303	+	0.612716i	$0.790077\pi$
$678$	−1.14821	+	3.53384i	−0.0440969	+	0.135716i
$679$	−15.6134	−	48.0530i	−0.599186	−	1.84411i
$680$		0			0
$681$	6.14586			0.235510
$682$	5.38615	+	4.56269i	0.206246	+	0.174714i
$683$	48.0516			1.83864			0.919321	−	0.393509i	$-0.128739\pi$
$683$	48.0516			1.83864			0.919321	+	0.393509i	$0.128739\pi$
$684$	−10.7947	+	7.84279i	−0.412744	+	0.299876i
$685$		0			0
$686$	−0.180073	+	0.554207i	−0.00687521	+	0.0211597i
$687$	9.49504	+	6.89855i	0.362258	+	0.263196i
$688$	−2.19130	−	1.59207i	−0.0835425	−	0.0606972i
$689$	16.0399	−	49.3658i	0.611072	−	1.88069i
$690$		0			0
$691$	22.8033	−	16.5676i	0.867479	−	0.630260i	−0.0624305	−	0.998049i	$-0.519885\pi$
$691$	22.8033	−	16.5676i	0.867479	−	0.630260i	0.929909	+	0.367789i	$0.119885\pi$
$692$	−0.660636			−0.0251136
$693$	−12.1297	−	0.905313i	−0.460768	−	0.0343900i
$694$	−7.33178			−0.278310
$695$		0			0
$696$	−1.72912	−	5.32167i	−0.0655420	−	0.201717i
$697$	5.10935	−	15.7250i	0.193531	−	0.595626i
$698$	7.52104	+	5.46435i	0.284675	+	0.206829i
$699$	−8.62313	−	6.26507i	−0.326157	−	0.236967i
$700$		0			0
$701$	9.19666	+	28.3044i	0.347353	+	1.06904i	0.960312	+	0.278928i	$0.0899792\pi$
$701$	9.19666	+	28.3044i	0.347353	+	1.06904i	−0.612959	+	0.790115i	$0.710021\pi$
$702$	−1.12754	+	0.819208i	−0.0425564	+	0.0309190i
$703$	16.6173			0.626734
$704$	−4.77649	−	19.5471i	−0.180021	−	0.736710i
$705$		0			0
$706$	−2.38644	+	1.73385i	−0.0898147	+	0.0652542i
$707$	5.28032	+	16.2511i	0.198587	+	0.611187i
$708$	−8.58647	+	26.4264i	−0.322699	+	0.993166i
$709$	2.05148	+	1.49049i	0.0770449	+	0.0559764i	0.625641	−	0.780111i	$-0.284838\pi$
$709$	2.05148	+	1.49049i	0.0770449	+	0.0559764i	−0.548596	+	0.836088i	$0.684838\pi$
$710$		0			0
$711$	−0.976476	+	3.00529i	−0.0366207	+	0.112707i
$712$	−1.06470	−	3.27681i	−0.0399014	−	0.122804i
$713$	7.19202	−	5.22531i	0.269343	−	0.195689i
$714$	−4.06744			−0.152220
$715$		0			0
$716$	−30.8072			−1.15132
$717$	3.71604	−	2.69986i	0.138778	−	0.100828i
$718$	−2.87901	−	8.86069i	−0.107444	−	0.330678i
$719$	−11.7267	+	36.0910i	−0.437331	+	1.34597i	0.453348	+	0.891334i	$0.350230\pi$
$719$	−11.7267	+	36.0910i	−0.437331	+	1.34597i	−0.890679	+	0.454633i	$0.849770\pi$
$720$		0			0
$721$	−29.1270	−	21.1620i	−1.08475	−	0.788114i
$722$	−2.62987	+	8.09392i	−0.0978738	+	0.301224i
$723$	5.83165	+	17.9480i	0.216881	+	0.667493i
$724$	−16.6451	+	12.0934i	−0.618609	+	0.449446i
$725$		0			0
$726$	0.522330	+	3.13371i	0.0193855	+	0.116303i
$727$	10.1521			0.376520			0.188260	−	0.982119i	$-0.439715\pi$
$727$	10.1521			0.376520			0.188260	+	0.982119i	$0.439715\pi$
$728$	16.1957	−	11.7669i	0.600252	−	0.436109i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−2.39981	−	1.74356i	−0.0887601	−	0.0644880i
$732$	2.83893	+	2.06260i	0.104930	+	0.0762359i
$733$	4.28623	−	13.1917i	0.158316	−	0.487246i	−0.840166	−	0.542329i	$-0.817543\pi$
$733$	4.28623	−	13.1917i	0.158316	−	0.487246i	0.998482	+	0.0550837i	$0.0175426\pi$
$734$	−1.36117	−	4.18926i	−0.0502418	−	0.154628i
$735$		0			0
$736$	3.95077			0.145627
$737$	7.67647	−	18.7466i	0.282767	−	0.690539i
$738$	−1.24352			−0.0457747
$739$	−3.14794	+	2.28711i	−0.115799	+	0.0841328i	−0.644177	−	0.764876i	$-0.722800\pi$
$739$	−3.14794	+	2.28711i	−0.115799	+	0.0841328i	0.528379	+	0.849009i	$0.322800\pi$
$740$		0			0
$741$	10.3816	−	31.9513i	0.381378	−	1.17376i
$742$	−9.21707	−	6.69659i	−0.338369	−	0.245840i
$743$	34.0211	+	24.7178i	1.24811	+	0.906807i	0.998111	−	0.0614378i	$-0.0195686\pi$
$743$	34.0211	+	24.7178i	1.24811	+	0.906807i	0.250002	+	0.968245i	$0.419569\pi$
$744$	−2.57593	+	7.92789i	−0.0944381	+	0.290651i
$745$		0			0
$746$	−3.37291	+	2.45056i	−0.123491	+	0.0897215i
$747$	1.53041			0.0559949
$748$	−5.79433	−	23.7125i	−0.211862	−	0.867016i
$749$	−43.2812			−1.58146
$750$		0			0
$751$	−1.54988	−	4.77005i	−0.0565560	−	0.174062i	0.918788	−	0.394751i	$-0.129169\pi$
$751$	−1.54988	−	4.77005i	−0.0565560	−	0.174062i	−0.975344	+	0.220690i	$0.929169\pi$
$752$	−7.01138	+	21.5788i	−0.255679	+	0.786899i
$753$	−15.7683	−	11.4563i	−0.574628	−	0.417492i
$754$	5.57764	+	4.05239i	0.203126	+	0.147579i
$755$		0			0
$756$	−2.17205	−	6.68488i	−0.0789966	−	0.243127i
$757$	28.6845	−	20.8405i	1.04256	−	0.757462i	0.0717736	−	0.997421i	$-0.477134\pi$
$757$	28.6845	−	20.8405i	1.04256	−	0.757462i	0.970783	+	0.239959i	$0.0771341\pi$
$758$	5.81623			0.211255
$759$	3.98985	+	0.297787i	0.144822	+	0.0108090i
$760$		0			0
$761$	−11.5819	+	8.41472i	−0.419842	+	0.305033i	−0.777574	−	0.628791i	$-0.783550\pi$
$761$	−11.5819	+	8.41472i	−0.419842	+	0.305033i	0.357732	+	0.933824i	$0.383550\pi$
$762$	0.0165929	+	0.0510678i	0.000601099	+	0.00184999i
$763$	11.8373	−	36.4313i	0.428537	−	1.31890i
$764$	−21.0852	−	15.3193i	−0.762836	−	0.554233i
$765$		0			0
$766$	−0.824571	+	2.53777i	−0.0297930	+	0.0916933i
$767$	−21.6195	−	66.5379i	−0.780634	−	2.40254i
$768$	7.87688	−	5.72289i	0.284232	−	0.206507i
$769$	−29.6869			−1.07054			−0.535269	−	0.844682i	$-0.679790\pi$
$769$	−29.6869			−1.07054			−0.535269	+	0.844682i	$0.679790\pi$
$770$		0			0
$771$	13.1814			0.474717
$772$	40.1718	−	29.1865i	1.44581	−	1.05045i
$773$	−14.9060	−	45.8758i	−0.536130	−	1.65004i	−0.741194	−	0.671291i	$-0.765740\pi$
$773$	−14.9060	−	45.8758i	−0.536130	−	1.65004i	0.205064	−	0.978749i	$-0.434260\pi$
$774$	−0.0689400	+	0.212176i	−0.00247800	+	0.00762649i
$775$		0			0
$776$	−12.6078	−	9.16007i	−0.452592	−	0.328827i
$777$	−2.70507	+	8.32535i	−0.0970439	+	0.298670i
$778$	−1.83725	−	5.65449i	−0.0658687	−	0.202723i
$779$	24.2503	−	17.6189i	0.868859	−	0.631263i
$780$		0			0
$781$	9.28366	−	5.74078i	0.332196	−	0.205421i
$782$	1.33792			0.0478438
$783$	4.00198	−	2.90761i	0.143019	−	0.103909i
$784$	6.98880	+	21.5093i	0.249600	+	0.768190i
$785$		0			0
$786$	2.16631	+	1.57392i	0.0772697	+	0.0561398i
$787$	−41.6109	−	30.2321i	−1.48327	−	1.07766i	−0.976485	−	0.215586i	$-0.930834\pi$
$787$	−41.6109	−	30.2321i	−1.48327	−	1.07766i	−0.506785	−	0.862073i	$-0.669166\pi$
$788$	−0.700911	+	2.15718i	−0.0249689	+	0.0768464i
$789$	−9.22093	−	28.3791i	−0.328274	−	1.01032i
$790$		0			0
$791$	47.1827			1.67762
$792$	−3.19085	+	1.97314i	−0.113382	+	0.0701123i
$793$	−8.83542			−0.313755
$794$	−4.70372	+	3.41745i	−0.166929	+	0.121281i
$795$		0			0
$796$	−1.85653	+	5.71381i	−0.0658029	+	0.202521i
$797$	30.6447	+	22.2646i	1.08549	+	0.788654i	0.978632	−	0.205620i	$-0.0659211\pi$
$797$	30.6447	+	22.2646i	1.08549	+	0.788654i	0.106858	+	0.994274i	$0.465921\pi$
$798$	−5.96562	−	4.33428i	−0.211181	−	0.153432i
$799$	−7.67854	+	23.6321i	−0.271647	+	0.836044i
$800$		0			0
$801$	2.46422	−	1.79036i	0.0870688	−	0.0632592i
$802$	−0.187419			−0.00661798
$803$	−0.484676	−	0.410576i	−0.0171038	−	0.0144889i
$804$	11.7062			0.412846
$805$		0			0
$806$	−3.17384	−	9.76808i	−0.111794	−	0.344066i
$807$	−0.0778282	+	0.239530i	−0.00273968	+	0.00843187i
$808$	4.26384	+	3.09786i	0.150001	+	0.108982i
$809$	27.3621	+	19.8797i	0.962000	+	0.698934i	0.953614	−	0.301031i	$-0.0973307\pi$
$809$	27.3621	+	19.8797i	0.962000	+	0.698934i	0.00838569	+	0.999965i	$0.497331\pi$
$810$		0			0
$811$	−2.72366	−	8.38257i	−0.0956408	−	0.294352i	0.891779	−	0.452470i	$-0.149457\pi$
$811$	−2.72366	−	8.38257i	−0.0956408	−	0.294352i	−0.987420	+	0.158118i	$0.949457\pi$
$812$	−28.1295	+	20.4373i	−0.987152	+	0.717208i
$813$	12.0897			0.424006
$814$	2.28005	+	0.170175i	0.0799157	+	0.00596462i
$815$		0			0
$816$	10.8937	−	7.91474i	0.381356	−	0.277071i
$817$	−1.66180	−	5.11449i	−0.0581389	−	0.178933i
$818$	−1.17006	+	3.60106i	−0.0409100	+	0.125908i
$819$	14.3178	+	10.4025i	0.500303	+	0.363492i
$820$		0			0
$821$	11.9598	−	36.8086i	0.417401	−	1.28463i	−0.492685	−	0.870208i	$-0.663984\pi$
$821$	11.9598	−	36.8086i	0.417401	−	1.28463i	0.910086	−	0.414420i	$-0.136016\pi$
$822$	0.0390997	+	0.120336i	0.00136376	+	0.00419721i
$823$	5.54505	−	4.02872i	0.193288	−	0.140432i	−0.486932	−	0.873440i	$-0.661884\pi$
$823$	5.54505	−	4.02872i	0.193288	−	0.140432i	0.680220	+	0.733008i	$0.261884\pi$
$824$	−11.1046			−0.386848
$825$		0			0
$826$	−15.3560			−0.534304
$827$	−30.8210	+	22.3928i	−1.07175	+	0.778673i	−0.976226	−	0.216754i	$-0.930453\pi$
$827$	−30.8210	+	22.3928i	−1.07175	+	0.778673i	−0.0955254	+	0.995427i	$0.530453\pi$
$828$	0.714458	+	2.19888i	0.0248291	+	0.0764163i
$829$	2.29299	−	7.05711i	0.0796390	−	0.245104i	−0.903308	−	0.428992i	$-0.858869\pi$
$829$	2.29299	−	7.05711i	0.0796390	−	0.245104i	0.982947	+	0.183889i	$0.0588687\pi$
$830$		0			0
$831$	13.3209	+	9.67819i	0.462097	+	0.335733i
$832$	−9.04736	+	27.8449i	−0.313661	+	0.965349i
$833$	7.65381	+	23.5560i	0.265189	+	0.816167i
$834$	−2.01044	+	1.46067i	−0.0696158	+	0.0505789i
$835$		0			0
$836$	16.7697	−	40.9531i	0.579993	−	1.41639i
$837$	−7.36932			−0.254721
$838$	−7.72139	+	5.60992i	−0.266731	+	0.193791i
$839$	17.0553	+	52.4909i	0.588815	+	1.81219i	0.583377	+	0.812202i	$0.301731\pi$
$839$	17.0553	+	52.4909i	0.588815	+	1.81219i	0.00543830	+	0.999985i	$0.498269\pi$
$840$		0			0
$841$	3.66481	+	2.66264i	0.126373	+	0.0918151i
$842$	2.03695	+	1.47993i	0.0701980	+	0.0510018i
$843$	−3.89415	+	11.9849i	−0.134122	+	0.412784i
$844$	1.79042	+	5.51033i	0.0616287	+	0.189674i
$845$		0			0
$846$	1.86882			0.0642512
$847$	35.7953	−	18.6046i	1.22994	−	0.639261i
$848$	37.7165			1.29519
$849$	14.4392	−	10.4907i	0.495552	−	0.360040i
$850$		0			0
$851$	0.889787	−	2.73848i	0.0305015	−	0.0938740i
$852$	5.10298	+	3.70753i	0.174825	+	0.127018i
$853$	2.68717	+	1.95234i	0.0920069	+	0.0668469i	0.632838	−	0.774285i	$-0.281890\pi$
$853$	2.68717	+	1.95234i	0.0920069	+	0.0668469i	−0.540831	+	0.841131i	$0.681890\pi$
$854$	−0.599274	+	1.84437i	−0.0205067	+	0.0631132i
$855$		0			0
$856$	−10.8000	+	7.84665i	−0.369136	+	0.268193i
$857$	−34.6080			−1.18219			−0.591094	−	0.806603i	$-0.701304\pi$
$857$	−34.6080			−1.18219			−0.591094	+	0.806603i	$0.701304\pi$
$858$	1.75166	−	4.27770i	0.0598007	−	0.146038i
$859$	39.0606			1.33273			0.666366	−	0.745625i	$-0.267849\pi$
$859$	39.0606			1.33273			0.666366	+	0.745625i	$0.267849\pi$
$860$		0			0
$861$	4.87953	+	15.0176i	0.166294	+	0.511800i
$862$	1.46255	−	4.50127i	0.0498147	−	0.153314i
$863$	0.421177	+	0.306003i	0.0143370	+	0.0104165i	0.594931	−	0.803777i	$-0.297179\pi$
$863$	0.421177	+	0.306003i	0.0143370	+	0.0104165i	−0.580594	+	0.814193i	$0.697179\pi$
$864$	−2.64956	−	1.92502i	−0.0901399	−	0.0654905i
$865$		0			0
$866$	3.12256	+	9.61026i	0.106109	+	0.326570i
$867$	−1.82301	+	1.32450i	−0.0619127	+	0.0449822i
$868$	51.7982			1.75814
$869$	−2.48776	−	10.1808i	−0.0843913	−	0.345360i
$870$		0			0
$871$	−23.8454	+	17.3247i	−0.807970	+	0.587025i
$872$	−3.65104	−	11.2367i	−0.123640	−	0.380524i
$873$	4.25734	−	13.1027i	0.144089	−	0.443461i
$874$	1.96229	+	1.42569i	0.0663755	+	0.0482246i
$875$		0			0
$876$	0.113430	−	0.349101i	0.00383244	−	0.0117950i
$877$	13.2196	+	40.6857i	0.446394	+	1.37386i	0.880948	+	0.473213i	$0.156906\pi$
$877$	13.2196	+	40.6857i	0.446394	+	1.37386i	−0.434555	+	0.900645i	$0.643094\pi$
$878$	4.33795	−	3.15171i	0.146399	−	0.106365i
$879$	−9.90674			−0.334146
$880$		0			0
$881$	33.2644			1.12071			0.560353	−	0.828254i	$-0.310665\pi$
$881$	33.2644			1.12071			0.560353	+	0.828254i	$0.310665\pi$
$882$	1.50703	−	1.09492i	0.0507445	−	0.0368680i
$883$	11.5207	+	35.4570i	0.387701	+	1.19322i	0.934501	+	0.355959i	$0.115846\pi$
$883$	11.5207	+	35.4570i	0.387701	+	1.19322i	−0.546800	+	0.837263i	$0.684154\pi$
$884$	−10.9753	+	33.7785i	−0.369139	+	1.13609i
$885$		0			0
$886$	2.06824	+	1.50266i	0.0694838	+	0.0504829i
$887$	14.7539	−	45.4077i	0.495386	−	1.52464i	−0.320968	−	0.947090i	$-0.604008\pi$
$887$	14.7539	−	45.4077i	0.495386	−	1.52464i	0.816354	−	0.577551i	$-0.195992\pi$
$888$	0.834343	+	2.56784i	0.0279987	+	0.0861712i
$889$	0.551621	−	0.400776i	0.0185008	−	0.0134416i
$890$		0			0
$891$	−2.53067	−	2.14377i	−0.0847805	−	0.0718188i
$892$	−0.0881070			−0.00295004
$893$	−36.4444	+	26.4784i	−1.21957	+	0.886066i
$894$	−1.36765	−	4.20919i	−0.0457410	−	0.140776i
$895$		0			0
$896$	24.6329	+	17.8969i	0.822928	+	0.597892i
$897$	−4.70959	−	3.42172i	−0.157249	−	0.114248i
$898$	−0.283906	+	0.873772i	−0.00947406	+	0.0291582i
$899$	11.2649	+	34.6698i	0.375705	+	1.15630i
$900$		0			0
$901$	41.3054			1.37608
$902$	3.50780	−	2.16913i	0.116797	−	0.0722242i
$903$	2.83290			0.0942730
$904$	11.7735	−	8.55396i	0.391581	−	0.284500i
$905$		0			0
$906$	−0.0937631	+	0.288573i	−0.00311507	+	0.00958720i
$907$	9.93665	+	7.21940i	0.329941	+	0.239716i	0.740406	−	0.672160i	$-0.234633\pi$
$907$	9.93665	+	7.21940i	0.329941	+	0.239716i	−0.410465	+	0.911877i	$0.634633\pi$
$908$	−9.52948	−	6.92357i	−0.316247	−	0.229767i
$909$	−1.43980	+	4.43124i	−0.0477551	+	0.146975i
$910$		0			0
$911$	−34.9756	+	25.4113i	−1.15879	+	0.841913i	−0.989625	−	0.143674i	$-0.954108\pi$
$911$	−34.9756	+	25.4113i	−1.15879	+	0.841913i	−0.169169	+	0.985587i	$0.554108\pi$
$912$	24.4115			0.808346
$913$	−4.31708	+	2.66957i	−0.142875	+	0.0883499i
$914$	−1.01880			−0.0336988
$915$		0			0
$916$	−6.95104	−	21.3931i	−0.229669	−	0.706848i
$917$	10.5072	−	32.3379i	0.346979	−	1.06789i
$918$	−0.897265	−	0.651901i	−0.0296141	−	0.0215159i
$919$	−44.8612	−	32.5935i	−1.47983	−	1.07516i	−0.977610	−	0.210424i	$-0.932516\pi$
$919$	−44.8612	−	32.5935i	−1.47983	−	1.07516i	−0.502223	−	0.864738i	$-0.667484\pi$
$920$		0			0
$921$	−7.18481	−	22.1126i	−0.236747	−	0.728634i
$922$	−4.23665	+	3.07810i	−0.139527	+	0.101372i
$923$	−15.8817			−0.522753
$924$	17.7878	+	15.0683i	0.585175	+	0.495711i
$925$		0			0
$926$	4.20820	−	3.05744i	0.138290	−	0.100474i
$927$	−3.03362	−	9.33653i	−0.0996373	−	0.306652i
$928$	−5.00629	+	15.4078i	−0.164340	+	0.505785i
$929$	−38.2715	−	27.8058i	−1.25565	−	0.912280i	−0.257110	−	0.966382i	$-0.582770\pi$
$929$	−38.2715	−	27.8058i	−1.25565	−	0.912280i	−0.998535	+	0.0541022i	$0.982770\pi$
$930$		0			0
$931$	−13.8757	+	42.7050i	−0.454757	+	1.39960i
$932$	6.31275	+	19.4286i	0.206781	+	0.636406i
$933$	24.1595	−	17.5529i	0.790946	−	0.574656i
$934$	−7.71757			−0.252527
$935$		0			0
$936$	5.45863			0.178421
$937$	−28.0504	+	20.3798i	−0.916367	+	0.665780i	−0.942617	−	0.333876i	$-0.891643\pi$
$937$	−28.0504	+	20.3798i	−0.916367	+	0.665780i	0.0262500	+	0.999655i	$0.491643\pi$
$938$	1.99915	+	6.15274i	0.0652745	+	0.200894i
$939$	−7.92215	+	24.3819i	−0.258530	+	0.795672i
$940$		0			0
$941$	−17.8414	−	12.9625i	−0.581613	−	0.422566i	0.257692	−	0.966227i	$-0.417038\pi$
$941$	−17.8414	−	12.9625i	−0.581613	−	0.422566i	−0.839305	+	0.543661i	$0.817038\pi$
$942$	0.440769	−	1.35655i	0.0143610	−	0.0441987i
$943$	−1.60504	−	4.93980i	−0.0522672	−	0.160862i
$944$	41.1275	−	29.8809i	1.33859	−	0.972541i
$945$		0			0
$946$	−0.175638	−	0.718773i	−0.00571047	−	0.0233693i
$947$	58.6395			1.90553			0.952764	−	0.303711i	$-0.0982256\pi$
$947$	58.6395			1.90553			0.952764	+	0.303711i	$0.0982256\pi$
$948$	4.89966	−	3.55981i	0.159133	−	0.115617i
$949$	0.285600	+	0.878986i	0.00927096	+	0.0285331i
$950$		0			0
$951$	0.906665	+	0.658731i	0.0294006	+	0.0213608i
$952$	12.8880	+	9.36371i	0.417704	+	0.303480i
$953$	13.4062	−	41.2601i	0.434270	−	1.33654i	−0.459563	−	0.888145i	$-0.651994\pi$
$953$	13.4062	−	41.2601i	0.434270	−	1.33654i	0.893833	−	0.448400i	$-0.148006\pi$
$954$	−0.959973	−	2.95449i	−0.0310803	−	0.0956553i
$955$		0			0
$956$	−8.80342			−0.284723
$957$	−6.21715	+	15.1828i	−0.200972	+	0.490790i
$958$	−6.57588			−0.212457
$959$	1.29984	−	0.944390i	0.0419741	−	0.0304959i
$960$		0			0
$961$	7.20221	−	22.1661i	0.232329	−	0.715036i
$962$	−2.69136	−	1.95538i	−0.0867728	−	0.0630441i
$963$	−9.54770	−	6.93681i	−0.307670	−	0.223536i
$964$	11.1769	−	34.3989i	0.359983	−	1.10791i
$965$		0			0
$966$	−1.03371	+	0.751034i	−0.0332591	+	0.0241641i
$967$	−39.9415			−1.28443			−0.642217	−	0.766523i	$-0.721985\pi$
$967$	−39.9415			−1.28443			−0.642217	+	0.766523i	$0.721985\pi$
$968$	5.55910	−	11.1319i	0.178676	−	0.357792i
$969$	26.7343			0.858831
$970$		0			0
$971$	12.9044	+	39.7158i	0.414123	+	1.27454i	0.913033	+	0.407886i	$0.133734\pi$
$971$	12.9044	+	39.7158i	0.414123	+	1.27454i	−0.498910	+	0.866654i	$0.666266\pi$
$972$	0.592258	−	1.82278i	0.0189967	−	0.0584658i
$973$	25.5290	+	18.5479i	0.818421	+	0.594618i
$974$	−3.16617	−	2.30036i	−0.101451	−	0.0737083i
$975$		0			0
$976$	−1.98391	−	6.10584i	−0.0635034	−	0.195443i
$977$	−25.7168	+	18.6843i	−0.822753	+	0.597765i	−0.917500	−	0.397736i	$-0.869796\pi$
$977$	−25.7168	+	18.6843i	−0.822753	+	0.597765i	0.0947468	+	0.995501i	$0.469796\pi$
$978$	−2.78085			−0.0889218
$979$	−3.82821	+	9.34880i	−0.122350	+	0.298789i
$980$		0			0
$981$	8.45021	−	6.13944i	0.269794	−	0.196017i
$982$	−1.69894	−	5.22879i	−0.0542152	−	0.166857i
$983$	7.41330	−	22.8158i	0.236448	−	0.727711i	−0.760478	−	0.649363i	$-0.775035\pi$
$983$	7.41330	−	22.8158i	0.236448	−	0.727711i	0.996926	−	0.0783479i	$-0.0249645\pi$
$984$	3.94021	+	2.86273i	0.125609	+	0.0912604i
$985$		0			0
$986$	−1.69536	+	5.21779i	−0.0539914	+	0.166168i
$987$	−7.33315	−	22.5691i	−0.233417	−	0.718383i
$988$	−52.0917	+	37.8468i	−1.65726	+	1.20407i
$989$	−0.931834			−0.0296306
$990$		0			0
$991$	−14.1684			−0.450074			−0.225037	−	0.974350i	$-0.572250\pi$
$991$	−14.1684			−0.450074			−0.225037	+	0.974350i	$0.572250\pi$
$992$	19.5255	−	14.1861i	0.619934	−	0.450408i
$993$	3.37999	+	10.4025i	0.107261	+	0.330115i
$994$	−1.07720	+	3.31527i	−0.0341666	+	0.105154i
$995$		0			0
$996$	−2.37298	−	1.72407i	−0.0751909	−	0.0546294i
$997$	−2.25804	+	6.94954i	−0.0715129	+	0.220094i	−0.980425	−	0.196894i	$-0.936914\pi$
$997$	−2.25804	+	6.94954i	−0.0715129	+	0.220094i	0.908912	+	0.416988i	$0.136914\pi$
$998$	2.06247	+	6.34762i	0.0652862	+	0.200930i
$999$	−1.93106	+	1.40300i	−0.0610960	+	0.0443888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.o.751.4		24
5.2	odd	4		165.2.s.a.124.7	yes	48
5.3	odd	4		165.2.s.a.124.6	yes	48
5.4	even	2		825.2.n.p.751.3		24
11.2	odd	10		9075.2.a.dx.1.8		12
11.4	even	5	inner	825.2.n.o.301.4		24
11.9	even	5		9075.2.a.dz.1.5		12
15.2	even	4		495.2.ba.c.289.6		48
15.8	even	4		495.2.ba.c.289.7		48
55.2	even	20		1815.2.c.k.364.13		24
55.4	even	10		825.2.n.p.301.3		24
55.9	even	10		9075.2.a.dy.1.8		12
55.13	even	20		1815.2.c.k.364.12		24
55.24	odd	10		9075.2.a.ea.1.5		12
55.37	odd	20		165.2.s.a.4.6	✓	48
55.42	odd	20		1815.2.c.j.364.12		24
55.48	odd	20		165.2.s.a.4.7	yes	48
55.53	odd	20		1815.2.c.j.364.13		24
165.92	even	20		495.2.ba.c.334.7		48
165.158	even	20		495.2.ba.c.334.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.6	✓	48	55.37	odd	20
165.2.s.a.4.7	yes	48	55.48	odd	20
165.2.s.a.124.6	yes	48	5.3	odd	4
165.2.s.a.124.7	yes	48	5.2	odd	4
495.2.ba.c.289.6		48	15.2	even	4
495.2.ba.c.289.7		48	15.8	even	4
495.2.ba.c.334.6		48	165.158	even	20
495.2.ba.c.334.7		48	165.92	even	20
825.2.n.o.301.4		24	11.4	even	5	inner
825.2.n.o.751.4		24	1.1	even	1	trivial
825.2.n.p.301.3		24	55.4	even	10
825.2.n.p.751.3		24	5.4	even	2
1815.2.c.j.364.12		24	55.42	odd	20
1815.2.c.j.364.13		24	55.53	odd	20
1815.2.c.k.364.12		24	55.13	even	20
1815.2.c.k.364.13		24	55.2	even	20
9075.2.a.dx.1.8		12	11.2	odd	10
9075.2.a.dy.1.8		12	55.9	even	10
9075.2.a.dz.1.5		12	11.9	even	5
9075.2.a.ea.1.5		12	55.24	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.233654 - 0.169760i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.592258 + 1.82278i) q^{4} +(-0.233654 - 0.169760i) q^{6} +(-1.13329 + 3.48791i) q^{7} +(0.349548 + 1.07580i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.233654 - 0.169760i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.592258 + 1.82278i) q^{4} +(-0.233654 - 0.169760i) q^{6} +(-1.13329 + 3.48791i) q^{7} +(0.349548 + 1.07580i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.25682 - 3.06927i) q^{11} +1.91659 q^{12} +(-3.90406 + 2.83647i) q^{13} +(0.327309 + 1.00735i) q^{14} +(-2.83680 - 2.06106i) q^{16} +(-3.10673 - 2.25717i) q^{17} +(-0.0892481 + 0.274677i) q^{18} +(-2.15132 - 6.62109i) q^{19} +3.66740 q^{21} +(-0.227376 - 0.930506i) q^{22} -1.20633 q^{23} +(0.915128 - 0.664879i) q^{24} +(-0.430683 + 1.32551i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-5.68650 - 4.13148i) q^{28} +(1.52862 - 4.70461i) q^{29} +(-5.96190 + 4.33158i) q^{31} -3.27504 q^{32} +(-3.30743 - 0.246854i) q^{33} -1.10908 q^{34} +(-0.592258 - 1.82278i) q^{36} +(-0.737599 + 2.27010i) q^{37} +(-1.62666 - 1.18184i) q^{38} +(3.90406 + 2.83647i) q^{39} +(1.33051 + 4.09490i) q^{41} +(0.856905 - 0.622578i) q^{42} +0.772454 q^{43} +(4.85024 + 4.10871i) q^{44} +(-0.281864 + 0.204786i) q^{46} +(-1.99955 - 6.15398i) q^{47} +(-1.08356 + 3.33486i) q^{48} +(-5.21803 - 3.79112i) q^{49} +(-1.18667 + 3.65218i) q^{51} +(-2.85805 - 8.79618i) q^{52} +(-8.70198 + 6.32236i) q^{53} +0.288813 q^{54} -4.14842 q^{56} +(-5.63224 + 4.09206i) q^{57} +(-0.441485 - 1.35875i) q^{58} +(-4.48008 + 13.7883i) q^{59} +(1.48124 + 1.07618i) q^{61} +(-0.657697 + 2.02418i) q^{62} +(-1.13329 - 3.48791i) q^{63} +(4.90838 - 3.56615i) q^{64} +(-0.814701 + 0.503790i) q^{66} +6.10784 q^{67} +(5.95433 - 4.32607i) q^{68} +(0.372776 + 1.14729i) q^{69} +(2.66254 + 1.93445i) q^{71} +(-0.915128 - 0.664879i) q^{72} +(0.0591833 - 0.182147i) q^{73} +(0.213028 + 0.655633i) q^{74} +13.3429 q^{76} +(9.28097 + 7.86205i) q^{77} +1.39372 q^{78} +(2.55645 - 1.85737i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.00603 + 0.730924i) q^{82} +(-1.23813 - 0.899554i) q^{83} +(-2.17205 + 6.68488i) q^{84} +(0.180487 - 0.131132i) q^{86} -4.94672 q^{87} +(3.74123 + 0.279232i) q^{88} -3.04594 q^{89} +(-5.46890 - 16.8315i) q^{91} +(0.714458 - 2.19888i) q^{92} +(5.96190 + 4.33158i) q^{93} +(-1.51190 - 1.09846i) q^{94} +(1.01204 + 3.11475i) q^{96} +(-11.1459 + 8.09794i) q^{97} -1.86280 q^{98} +(0.787278 + 3.22183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

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