LMFDB - Embedded newform 475.2.l.b.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.3
Root			$0.785237 - 1.36007i$ of defining polynomial
Character	$\chi$	$=$	475.301
Dual form			475.2.l.b.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20305 + 1.00948i) q^{2} +(2.14722 - 0.781523i) q^{3} +(0.0809872 + 0.459301i) q^{4} +(3.37214 + 1.22736i) q^{6} +(-2.00668 - 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +(1.70162 - 1.42783i) q^{9} +O(q^{10})$	\(q+(1.20305 + 1.00948i) q^{2} +(2.14722 - 0.781523i) q^{3} +(0.0809872 + 0.459301i) q^{4} +(3.37214 + 1.22736i) q^{6} +(-2.00668 - 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +(1.70162 - 1.42783i) q^{9} +(-1.38310 + 2.39560i) q^{11} +(0.532851 + 0.922925i) q^{12} +(2.61923 + 0.953321i) q^{13} +(1.09448 - 6.20713i) q^{14} +(4.43089 - 1.61271i) q^{16} +(2.76292 + 2.31836i) q^{17} +3.48851 q^{18} +(1.79089 + 3.97401i) q^{19} +(-7.02510 - 5.89476i) q^{21} +(-4.08226 + 1.48582i) q^{22} +(-0.237457 - 1.34669i) q^{23} +(0.955667 - 5.41986i) q^{24} +(2.18871 + 3.79096i) q^{26} +(-0.889658 + 1.54093i) q^{27} +(1.43387 - 1.20316i) q^{28} +(-7.28463 + 6.11253i) q^{29} +(-0.776853 - 1.34555i) q^{31} +(2.43210 + 0.885212i) q^{32} +(-1.09760 + 6.22480i) q^{33} +(0.983591 + 5.57822i) q^{34} +(0.793615 + 0.665922i) q^{36} -8.51183 q^{37} +(-1.85715 + 6.58880i) q^{38} +6.36909 q^{39} +(6.21041 - 2.26041i) q^{41} +(-2.50092 - 14.1834i) q^{42} +(1.08613 - 6.15974i) q^{43} +(-1.21232 - 0.441247i) q^{44} +(1.07378 - 1.85984i) q^{46} +(-6.97857 + 5.85572i) q^{47} +(8.25371 - 6.92568i) q^{48} +(-4.55356 + 7.88699i) q^{49} +(7.74443 + 2.81874i) q^{51} +(-0.225738 + 1.28022i) q^{52} +(0.684965 + 3.88463i) q^{53} +(-2.62585 + 0.955730i) q^{54} -9.66619 q^{56} +(6.95120 + 7.13343i) q^{57} -14.9343 q^{58} +(2.76682 + 2.32164i) q^{59} +(-1.30047 - 7.37531i) q^{61} +(0.423711 - 2.40298i) q^{62} +(-8.37730 - 3.04909i) q^{63} +(-2.68292 - 4.64695i) q^{64} +(-7.60428 + 6.38075i) q^{66} +(11.1628 - 9.36668i) q^{67} +(-0.841066 + 1.45677i) q^{68} +(-1.56234 - 2.70605i) q^{69} +(-0.576318 + 3.26846i) q^{71} +(-0.929023 - 5.26875i) q^{72} +(-9.40420 + 3.42285i) q^{73} +(-10.2402 - 8.59253i) q^{74} +(-1.68023 + 1.14440i) q^{76} +11.1018 q^{77} +(7.66235 + 6.42947i) q^{78} +(1.82991 - 0.666034i) q^{79} +(-1.86319 + 10.5667i) q^{81} +(9.75329 + 3.54991i) q^{82} +(0.809339 + 1.40182i) q^{83} +(2.13853 - 3.70404i) q^{84} +(7.52481 - 6.31406i) q^{86} +(-10.8646 + 18.8180i) q^{87} +(3.33120 + 5.76980i) q^{88} +(11.5122 + 4.19008i) q^{89} +(-1.94252 - 11.0166i) q^{91} +(0.599304 - 0.218129i) q^{92} +(-2.71965 - 2.28205i) q^{93} -14.3068 q^{94} +5.91406 q^{96} +(8.87934 + 7.45065i) q^{97} +(-13.4399 + 4.89173i) q^{98} +(1.06700 + 6.05125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.20305	+	1.00948i	0.850687	+	0.713811i	0.959941	−	0.280203i	$-0.0904018\pi$
$2$	1.20305	+	1.00948i	0.850687	+	0.713811i	−0.109254	+	0.994014i	$0.534846\pi$
$3$	2.14722	−	0.781523i	1.23970	−	0.451212i	0.362788	−	0.931872i	$-0.381825\pi$
$3$	2.14722	−	0.781523i	1.23970	−	0.451212i	0.876907	+	0.480659i	$0.159603\pi$
$4$	0.0809872	+	0.459301i	0.0404936	+	0.229651i
$5$		0			0
$5$		0			0
$6$	3.37214	+	1.22736i	1.37667	+	0.501068i
$7$	−2.00668	−	3.47568i	−0.758455	−	1.31368i	−0.943638	−	0.330979i	$-0.892621\pi$
$7$	−2.00668	−	3.47568i	−0.758455	−	1.31368i	0.185183	−	0.982704i	$-0.440712\pi$
$8$	1.20425	−	2.08582i	0.425766	−	0.737449i
$9$	1.70162	−	1.42783i	0.567208	−	0.475944i
$10$		0			0
$11$	−1.38310	+	2.39560i	−0.417021	+	0.722301i	−0.995638	−	0.0932980i	$-0.970259\pi$
$11$	−1.38310	+	2.39560i	−0.417021	+	0.722301i	0.578618	+	0.815599i	$0.303592\pi$
$12$	0.532851	+	0.922925i	0.153821	+	0.266426i
$13$	2.61923	+	0.953321i	0.726443	+	0.264404i	0.678659	−	0.734454i	$-0.262562\pi$
$13$	2.61923	+	0.953321i	0.726443	+	0.264404i	0.0477847	+	0.998858i	$0.484784\pi$
$14$	1.09448	−	6.20713i	0.292513	−	1.65893i
$15$		0			0
$16$	4.43089	−	1.61271i	1.10772	−	0.403178i
$17$	2.76292	+	2.31836i	0.670106	+	0.562286i	0.913097	−	0.407743i	$-0.133684\pi$
$17$	2.76292	+	2.31836i	0.670106	+	0.562286i	−0.242991	+	0.970029i	$0.578129\pi$
$18$	3.48851			0.822250
$19$	1.79089	+	3.97401i	0.410858	+	0.911699i
$19$	1.79089	+	3.97401i	0.410858	+	0.911699i
$20$		0			0
$21$	−7.02510	−	5.89476i	−1.53300	−	1.28634i
$22$	−4.08226	+	1.48582i	−0.870340	+	0.316778i
$23$	−0.237457	−	1.34669i	−0.0495133	−	0.280804i	0.949991	−	0.312276i	$-0.101091\pi$
$23$	−0.237457	−	1.34669i	−0.0495133	−	0.280804i	−0.999505	+	0.0314725i	$0.989980\pi$
$24$	0.955667	−	5.41986i	0.195075	−	1.10632i
$25$		0			0
$26$	2.18871	+	3.79096i	0.429241	+	0.743468i
$27$	−0.889658	+	1.54093i	−0.171215	+	0.296553i
$28$	1.43387	−	1.20316i	0.270975	−	0.227375i
$29$	−7.28463	+	6.11253i	−1.35272	+	1.13507i	−0.374564	+	0.927201i	$0.622208\pi$
$29$	−7.28463	+	6.11253i	−1.35272	+	1.13507i	−0.978157	+	0.207866i	$0.933348\pi$
$30$		0			0
$31$	−0.776853	−	1.34555i	−0.139527	−	0.241668i	0.787791	−	0.615943i	$-0.211225\pi$
$31$	−0.776853	−	1.34555i	−0.139527	−	0.241668i	−0.927318	+	0.374275i	$0.877891\pi$
$32$	2.43210	+	0.885212i	0.429939	+	0.156485i
$33$	−1.09760	+	6.22480i	−0.191068	+	1.08360i
$34$	0.983591	+	5.57822i	0.168685	+	0.956658i
$35$		0			0
$36$	0.793615	+	0.665922i	0.132269	+	0.110987i
$37$	−8.51183			−1.39934			−0.699668	−	0.714468i	$-0.746669\pi$
$37$	−8.51183			−1.39934			−0.699668	+	0.714468i	$0.746669\pi$
$38$	−1.85715	+	6.58880i	−0.301269	+	1.06885i
$39$	6.36909			1.01987
$40$		0			0
$41$	6.21041	−	2.26041i	0.969904	−	0.353016i	0.191997	−	0.981396i	$-0.438504\pi$
$41$	6.21041	−	2.26041i	0.969904	−	0.353016i	0.777907	+	0.628379i	$0.216281\pi$
$42$	−2.50092	−	14.1834i	−0.385900	−	2.18855i
$43$	1.08613	−	6.15974i	0.165633	−	0.939351i	−0.782776	−	0.622303i	$-0.786197\pi$
$43$	1.08613	−	6.15974i	0.165633	−	0.939351i	0.948409	−	0.317048i	$-0.102692\pi$
$44$	−1.21232	−	0.441247i	−0.182764	−	0.0665205i
$45$		0			0
$46$	1.07378	−	1.85984i	0.158320	−	0.274219i
$47$	−6.97857	+	5.85572i	−1.01793	+	0.854144i	−0.989366	−	0.145448i	$-0.953538\pi$
$47$	−6.97857	+	5.85572i	−1.01793	+	0.854144i	−0.0285637	+	0.999592i	$0.509093\pi$
$48$	8.25371	−	6.92568i	1.19132	−	0.999636i
$49$	−4.55356	+	7.88699i	−0.650508	+	1.12671i
$50$		0			0
$51$	7.74443	+	2.81874i	1.08444	+	0.394703i
$52$	−0.225738	+	1.28022i	−0.0313042	+	0.177535i
$53$	0.684965	+	3.88463i	0.0940872	+	0.533595i	0.995023	+	0.0996432i	$0.0317701\pi$
$53$	0.684965	+	3.88463i	0.0940872	+	0.533595i	−0.900936	+	0.433952i	$0.857119\pi$
$54$	−2.62585	+	0.955730i	−0.357333	+	0.130058i
$55$		0			0
$56$	−9.66619			−1.29170
$57$	6.95120	+	7.13343i	0.920709	+	0.944845i
$58$	−14.9343			−1.96096
$59$	2.76682	+	2.32164i	0.360209	+	0.302251i	0.804874	−	0.593446i	$-0.202233\pi$
$59$	2.76682	+	2.32164i	0.360209	+	0.302251i	−0.444665	+	0.895697i	$0.646677\pi$
$60$		0			0
$61$	−1.30047	−	7.37531i	−0.166508	−	0.944311i	−0.947496	−	0.319766i	$-0.896396\pi$
$61$	−1.30047	−	7.37531i	−0.166508	−	0.944311i	0.780989	−	0.624545i	$-0.214716\pi$
$62$	0.423711	−	2.40298i	0.0538113	−	0.305179i
$63$	−8.37730	−	3.04909i	−1.05544	−	0.384149i
$64$	−2.68292	−	4.64695i	−0.335365	−	0.580869i
$65$		0			0
$66$	−7.60428	+	6.38075i	−0.936023	+	0.785416i
$67$	11.1628	−	9.36668i	1.36375	−	1.14432i	0.388946	−	0.921261i	$-0.372839\pi$
$67$	11.1628	−	9.36668i	1.36375	−	1.14432i	0.974804	−	0.223061i	$-0.0716051\pi$
$68$	−0.841066	+	1.45677i	−0.101994	+	0.176659i
$69$	−1.56234	−	2.70605i	−0.188084	−	0.325770i
$70$		0			0
$71$	−0.576318	+	3.26846i	−0.0683964	+	0.387895i	0.931323	+	0.364195i	$0.118656\pi$
$71$	−0.576318	+	3.26846i	−0.0683964	+	0.387895i	−0.999719	+	0.0237002i	$0.992455\pi$
$72$	−0.929023	−	5.26875i	−0.109486	−	0.620928i
$73$	−9.40420	+	3.42285i	−1.10068	+	0.400614i	−0.827566	−	0.561368i	$-0.810275\pi$
$73$	−9.40420	+	3.42285i	−1.10068	+	0.400614i	−0.273112	+	0.961982i	$0.588053\pi$
$74$	−10.2402	−	8.59253i	−1.19040	−	0.998862i
$75$		0			0
$76$	−1.68023	+	1.14440i	−0.192735	+	0.131272i
$77$	11.1018			1.26517
$78$	7.66235	+	6.42947i	0.867590	+	0.727995i
$79$	1.82991	−	0.666034i	0.205881	−	0.0749347i	−0.237021	−	0.971505i	$-0.576171\pi$
$79$	1.82991	−	0.666034i	0.205881	−	0.0749347i	0.442902	+	0.896570i	$0.353949\pi$
$80$		0			0
$81$	−1.86319	+	10.5667i	−0.207022	+	1.17408i
$82$	9.75329	+	3.54991i	1.07707	+	0.392022i
$83$	0.809339	+	1.40182i	0.0888365	+	0.153869i	0.907020	−	0.421088i	$-0.138352\pi$
$83$	0.809339	+	1.40182i	0.0888365	+	0.153869i	−0.818183	+	0.574958i	$0.805018\pi$
$84$	2.13853	−	3.70404i	0.233332	−	0.404144i
$85$		0			0
$86$	7.52481	−	6.31406i	0.811421	−	0.680863i
$87$	−10.8646	+	18.8180i	−1.16481	+	2.01750i
$88$	3.33120	+	5.76980i	0.355107	+	0.615063i
$89$	11.5122	+	4.19008i	1.22029	+	0.444148i	0.870260	−	0.492593i	$-0.163951\pi$
$89$	11.5122	+	4.19008i	1.22029	+	0.444148i	0.350025	+	0.936740i	$0.386173\pi$
$90$		0			0
$91$	−1.94252	−	11.0166i	−0.203632	−	1.15485i
$92$	0.599304	−	0.218129i	0.0624818	−	0.0227415i
$93$	−2.71965	−	2.28205i	−0.282014	−	0.236638i
$94$	−14.3068			−1.47564
$95$		0			0
$96$	5.91406			0.603601
$97$	8.87934	+	7.45065i	0.901560	+	0.756499i	0.970495	−	0.241122i	$-0.0775155\pi$
$97$	8.87934	+	7.45065i	0.901560	+	0.756499i	−0.0689344	+	0.997621i	$0.521960\pi$
$98$	−13.4399	+	4.89173i	−1.35764	+	0.494140i
$99$	1.06700	+	6.05125i	0.107237	+	0.608173i
$100$		0			0
$101$	6.56131	+	2.38812i	0.652874	+	0.237627i	0.647157	−	0.762357i	$-0.275958\pi$
$101$	6.56131	+	2.38812i	0.652874	+	0.237627i	0.00571740	+	0.999984i	$0.498180\pi$
$102$	6.47149	+	11.2090i	0.640773	+	1.10985i
$103$	5.06688	−	8.77610i	0.499255	−	0.864735i	−0.500745	−	0.865595i	$-0.666940\pi$
$103$	5.06688	−	8.77610i	0.499255	−	0.864735i	1.00000		0.000860217i	$0.000273816\pi$
$104$	5.14266	−	4.31521i	0.504279	−	0.423141i
$105$		0			0
$106$	−3.09741	+	5.36487i	−0.300847	+	0.521083i
$107$	−5.89176	−	10.2048i	−0.569578	−	0.986538i	−0.996608	−	0.0823003i	$-0.973773\pi$
$107$	−5.89176	−	10.2048i	−0.569578	−	0.986538i	0.427030	−	0.904238i	$-0.359560\pi$
$108$	−0.779803	−	0.283825i	−0.0750366	−	0.0273111i
$109$	−0.278545	+	1.57971i	−0.0266797	+	0.151308i	−0.995237	−	0.0974809i	$-0.968922\pi$
$109$	−0.278545	+	1.57971i	−0.0266797	+	0.151308i	0.968558	+	0.248789i	$0.0800326\pi$
$110$		0			0
$111$	−18.2767	+	6.65219i	−1.73475	+	0.631398i
$112$	−14.4967	−	12.1641i	−1.36981	−	1.14940i
$113$	−12.9449			−1.21775			−0.608876	−	0.793266i	$-0.708379\pi$
$113$	−12.9449			−1.21775			−0.608876	+	0.793266i	$0.708379\pi$
$114$	1.16160	+	15.5990i	0.108794	+	1.46098i
$115$		0			0
$116$	−3.39745	−	2.85080i	−0.315445	−	0.264690i
$117$	5.81812	−	2.11762i	0.537886	−	0.195774i
$118$	0.984981	+	5.58610i	0.0906748	+	0.514242i
$119$	2.51358	−	14.2552i	0.230420	−	1.30677i
$120$		0			0
$121$	1.67406	+	2.89956i	0.152187	+	0.263596i
$122$	5.88070	−	10.1857i	0.532414	−	0.922168i
$123$	11.5685	−	9.70716i	1.04310	−	0.875265i
$124$	0.555097	−	0.465781i	0.0498492	−	0.0418284i
$125$		0			0
$126$	−7.00034	−	12.1249i	−0.623640	−	1.08018i
$127$	−7.79759	−	2.83809i	−0.691924	−	0.251840i	−0.0279654	−	0.999609i	$-0.508903\pi$
$127$	−7.79759	−	2.83809i	−0.691924	−	0.251840i	−0.663959	+	0.747769i	$0.731125\pi$
$128$	2.36218	−	13.3966i	0.208790	−	1.18410i
$129$	−2.48182	−	14.0751i	−0.218512	−	1.23925i
$130$		0			0
$131$	−4.98836	−	4.18573i	−0.435835	−	0.365709i	0.398313	−	0.917250i	$-0.369596\pi$
$131$	−4.98836	−	4.18573i	−0.435835	−	0.365709i	−0.834148	+	0.551540i	$0.814040\pi$
$132$	−2.94795			−0.256586
$133$	10.2186	−	14.1991i	0.886066	−	1.23122i
$134$	22.8849			1.97695
$135$		0			0
$136$	8.16293	−	2.97106i	0.699966	−	0.254767i
$137$	−2.58191	−	14.6427i	−0.220587	−	1.25101i	−0.870943	−	0.491384i	$-0.836491\pi$
$137$	−2.58191	−	14.6427i	−0.220587	−	1.25101i	0.650356	−	0.759630i	$-0.274620\pi$
$138$	0.852130	−	4.83267i	0.0725382	−	0.411384i
$139$	−9.35768	−	3.40592i	−0.793708	−	0.288886i	−0.0868313	−	0.996223i	$-0.527674\pi$
$139$	−9.35768	−	3.40592i	−0.793708	−	0.288886i	−0.706876	+	0.707337i	$0.749896\pi$
$140$		0			0
$141$	−10.4081	+	18.0274i	−0.876522	+	1.51818i
$142$	−3.99279	+	3.35035i	−0.335068	+	0.281155i
$143$	−5.90644	+	4.95609i	−0.493921	+	0.414449i
$144$	5.23703	−	9.07080i	0.436419	−	0.755900i
$145$		0			0
$146$	−14.7690	−	5.37549i	−1.22229	−	0.444879i
$147$	−3.61361	+	20.4938i	−0.298045	+	1.69030i
$148$	−0.689349	−	3.90949i	−0.0566642	−	0.321358i
$149$	1.34529	−	0.489644i	0.110210	−	0.0401132i	−0.286326	−	0.958132i	$-0.592434\pi$
$149$	1.34529	−	0.489644i	0.110210	−	0.0401132i	0.396537	+	0.918019i	$0.370212\pi$
$150$		0			0
$151$	−8.18383			−0.665990			−0.332995	−	0.942929i	$-0.608059\pi$
$151$	−8.18383			−0.665990			−0.332995	+	0.942929i	$0.608059\pi$
$152$	10.4457	+	1.05022i	0.847262	+	0.0851841i
$153$	8.01168			0.647706
$154$	13.3560	+	11.2070i	1.07626	+	0.903089i
$155$		0			0
$156$	0.515815	+	2.92533i	0.0412982	+	0.234214i
$157$	1.36055	−	7.71609i	0.108584	−	0.615811i	−0.881144	−	0.472848i	$-0.843226\pi$
$157$	1.36055	−	7.71609i	0.108584	−	0.615811i	0.989728	−	0.142963i	$-0.0456629\pi$
$158$	2.87383	+	1.04599i	0.228630	+	0.0832144i
$159$	4.50670	+	7.80583i	0.357404	+	0.619042i
$160$		0			0
$161$	−4.20415	+	3.52770i	−0.331333	+	0.278022i
$162$	−12.9084	+	10.8314i	−1.01418	+	0.850998i
$163$	−9.64968	+	16.7137i	−0.755821	+	1.30912i	0.189144	+	0.981949i	$0.439429\pi$
$163$	−9.64968	+	16.7137i	−0.755821	+	1.30912i	−0.944965	+	0.327171i	$0.893905\pi$
$164$	1.54117	+	2.66939i	0.120345	+	0.208444i
$165$		0			0
$166$	−0.441429	+	2.50347i	−0.0342616	+	0.194307i
$167$	−1.63050	−	9.24703i	−0.126172	−	0.715556i	−0.980605	−	0.195995i	$-0.937206\pi$
$167$	−1.63050	−	9.24703i	−0.126172	−	0.715556i	0.854433	−	0.519562i	$-0.173905\pi$
$168$	−20.7554	+	7.55435i	−1.60131	+	0.582830i
$169$	−4.00704	−	3.36231i	−0.308234	−	0.258639i
$170$		0			0
$171$	8.72163	+	4.20517i	0.666960	+	0.321578i
$172$	2.91714			0.222430
$173$	−6.36647	−	5.34210i	−0.484034	−	0.406153i	0.367849	−	0.929886i	$-0.380094\pi$
$173$	−6.36647	−	5.34210i	−0.484034	−	0.406153i	−0.851882	+	0.523733i	$0.824539\pi$
$174$	−32.0671	+	11.6715i	−2.43100	+	0.884811i
$175$		0			0
$176$	−2.26495	+	12.8452i	−0.170727	+	0.968243i
$177$	7.75537	+	2.82272i	0.582929	+	0.212169i
$178$	9.61991	+	16.6622i	0.721043	+	1.24888i
$179$	9.26593	−	16.0491i	0.692568	−	1.19956i	−0.278425	−	0.960458i	$-0.589813\pi$
$179$	9.26593	−	16.0491i	0.692568	−	1.19956i	0.970994	−	0.239105i	$-0.0768541\pi$
$180$		0			0
$181$	8.67868	−	7.28228i	0.645081	−	0.541288i	−0.260493	−	0.965476i	$-0.583885\pi$
$181$	8.67868	−	7.28228i	0.645081	−	0.541288i	0.905574	+	0.424188i	$0.139441\pi$
$182$	8.78409	−	15.2145i	0.651120	−	1.12777i
$183$	−8.55635	−	14.8200i	−0.632503	−	1.09553i
$184$	−3.09491	−	1.12645i	−0.228160	−	0.0830433i
$185$		0			0
$186$	−0.968187	−	5.49086i	−0.0709909	−	0.402610i
$187$	−9.37527	+	3.41232i	−0.685587	+	0.249533i
$188$	−3.25471	−	2.73103i	−0.237374	−	0.199181i
$189$	7.14105			0.519435
$190$		0			0
$191$	11.8879			0.860175			0.430088	−	0.902787i	$-0.358483\pi$
$191$	11.8879			0.860175			0.430088	+	0.902787i	$0.358483\pi$
$192$	−9.39250	−	7.88124i	−0.677845	−	0.568780i
$193$	−0.900069	+	0.327598i	−0.0647884	+	0.0235810i	−0.374211	−	0.927344i	$-0.622086\pi$
$193$	−0.900069	+	0.327598i	−0.0647884	+	0.0235810i	0.309423	+	0.950925i	$0.399864\pi$
$194$	3.16102	+	17.9270i	0.226948	+	1.28709i
$195$		0			0
$196$	−3.99128	−	1.45271i	−0.285092	−	0.103765i
$197$	7.13881	+	12.3648i	0.508619	+	0.880955i	0.999950	+	0.00998159i	$0.00317729\pi$
$197$	7.13881	+	12.3648i	0.508619	+	0.880955i	−0.491331	+	0.870973i	$0.663489\pi$
$198$	−4.82496	+	8.35708i	−0.342895	+	0.593912i
$199$	−5.94888	+	4.99170i	−0.421705	+	0.353852i	−0.828811	−	0.559528i	$-0.810982\pi$
$199$	−5.94888	+	4.99170i	−0.421705	+	0.353852i	0.407106	+	0.913381i	$0.366538\pi$
$200$		0			0
$201$	16.6486	−	28.8362i	1.17430	−	2.03395i
$202$	5.48283	+	9.49655i	0.385771	+	0.668175i
$203$	35.8631	+	13.0531i	2.51710	+	0.916148i
$204$	−0.667452	+	3.78531i	−0.0467310	+	0.265025i
$205$		0			0
$206$	14.9550	−	5.44319i	1.04197	−	0.379245i
$207$	−2.32691	−	1.95251i	−0.161731	−	0.135709i
$208$	13.1430			0.911300
$209$	−11.9971	−	1.20620i	−0.829858	−	0.0834343i
$210$		0			0
$211$	5.83936	+	4.89980i	0.401998	+	0.337316i	0.821265	−	0.570546i	$-0.193269\pi$
$211$	5.83936	+	4.89980i	0.401998	+	0.337316i	−0.419267	+	0.907863i	$0.637713\pi$
$212$	−1.72874	+	0.629211i	−0.118731	+	0.0432144i
$213$	1.31690	+	7.46850i	0.0902324	+	0.511733i
$214$	3.21348	−	18.2246i	0.219669	−	1.24581i
$215$		0			0
$216$	2.14274	+	3.71134i	0.145795	+	0.252524i
$217$	−3.11779	+	5.40018i	−0.211650	+	0.366588i
$218$	−1.92979	+	1.61928i	−0.130702	+	0.109672i
$219$	−17.5178	+	14.6992i	−1.18374	+	0.993279i
$220$		0			0
$221$	5.02657	+	8.70627i	0.338123	+	0.585647i
$222$	−28.7031	−	10.4471i	−1.92643	−	0.701163i
$223$	1.38976	−	7.88173i	0.0930653	−	0.527799i	−0.902258	−	0.431197i	$-0.858091\pi$
$223$	1.38976	−	7.88173i	0.0930653	−	0.527799i	0.995323	−	0.0966024i	$-0.0307975\pi$
$224$	−1.80374	−	10.2295i	−0.120518	−	0.683490i
$225$		0			0
$226$	−15.5734	−	13.0676i	−1.03592	−	0.869244i
$227$	17.7409			1.17750			0.588752	−	0.808314i	$-0.299619\pi$
$227$	17.7409			1.17750			0.588752	+	0.808314i	$0.299619\pi$
$228$	−2.71343	+	3.77041i	−0.179701	+	0.249701i
$229$	−24.2231			−1.60071			−0.800354	−	0.599528i	$-0.795355\pi$
$229$	−24.2231			−1.60071			−0.800354	+	0.599528i	$0.795355\pi$
$230$		0			0
$231$	23.8379	−	8.67630i	1.56842	−	0.570858i
$232$	3.97713	+	22.5554i	0.261111	+	1.48084i
$233$	−2.37014	+	13.4418i	−0.155273	+	0.880598i	0.803262	+	0.595625i	$0.203096\pi$
$233$	−2.37014	+	13.4418i	−0.155273	+	0.880598i	−0.958536	+	0.284973i	$0.908015\pi$
$234$	9.13721	+	3.32567i	0.597318	+	0.217406i
$235$		0			0
$236$	−0.842254	+	1.45883i	−0.0548260	+	0.0949615i
$237$	3.40870	−	2.86024i	0.221419	−	0.185792i
$238$	17.4144	−	14.6124i	1.12880	−	0.947180i
$239$	−1.86882	+	3.23689i	−0.120884	+	0.209377i	−0.920117	−	0.391645i	$-0.871906\pi$
$239$	−1.86882	+	3.23689i	−0.120884	+	0.209377i	0.799233	+	0.601022i	$0.205240\pi$
$240$		0			0
$241$	4.96295	+	1.80636i	0.319691	+	0.116358i	0.496881	−	0.867819i	$-0.334478\pi$
$241$	4.96295	+	1.80636i	0.319691	+	0.116358i	−0.177190	+	0.984177i	$0.556701\pi$
$242$	−0.913066	+	5.17826i	−0.0586941	+	0.332871i
$243$	3.33051	+	18.8883i	0.213652	+	1.21168i
$244$	3.28217	−	1.19461i	0.210119	−	0.0764771i
$245$		0			0
$246$	23.7168			1.51212
$247$	0.902244	+	12.1161i	0.0574084	+	0.770930i
$248$	−3.74210			−0.237623
$249$	2.83338	+	2.37748i	0.179558	+	0.150667i
$250$		0			0
$251$	−2.17833	−	12.3539i	−0.137495	−	0.779772i	−0.973090	−	0.230426i	$-0.925988\pi$
$251$	−2.17833	−	12.3539i	−0.137495	−	0.779772i	0.835595	−	0.549346i	$-0.185123\pi$
$252$	0.721996	−	4.09464i	0.0454815	−	0.257938i
$253$	3.55455	+	1.29375i	0.223473	+	0.0813375i
$254$	−6.51591	−	11.2859i	−0.408845	−	0.708140i
$255$		0			0
$256$	8.14452	−	6.83406i	0.509032	−	0.427129i
$257$	−6.58784	+	5.52786i	−0.410938	+	0.344818i	−0.824703	−	0.565565i	$-0.808658\pi$
$257$	−6.58784	+	5.52786i	−0.410938	+	0.344818i	0.413765	+	0.910384i	$0.364214\pi$
$258$	11.2228	−	19.4385i	0.698701	−	1.21019i
$259$	17.0806	+	29.5844i	1.06133	+	1.83828i
$260$		0			0
$261$	−3.66803	+	20.8024i	−0.227045	+	1.28764i
$262$	−1.77584	−	10.0713i	−0.109712	−	0.622208i
$263$	25.0807	−	9.12863i	1.54654	−	0.562895i	0.578939	−	0.815371i	$-0.303467\pi$
$263$	25.0807	−	9.12863i	1.54654	−	0.562895i	0.967603	+	0.252475i	$0.0812447\pi$
$264$	11.6620	+	9.78561i	0.717748	+	0.602262i
$265$		0			0
$266$	26.6273	−	6.76679i	1.63262	−	0.414899i
$267$	27.9937			1.71319
$268$	5.20617	+	4.36849i	0.318017	+	0.266848i
$269$	3.10399	−	1.12976i	0.189254	−	0.0688828i	−0.245655	−	0.969357i	$-0.579003\pi$
$269$	3.10399	−	1.12976i	0.189254	−	0.0688828i	0.434909	+	0.900475i	$0.356781\pi$
$270$		0			0
$271$	−3.19296	+	18.1082i	−0.193959	+	1.09999i	0.719935	+	0.694041i	$0.244172\pi$
$271$	−3.19296	+	18.1082i	−0.193959	+	1.09999i	−0.913894	+	0.405953i	$0.866940\pi$
$272$	15.9810	+	5.81662i	0.968993	+	0.352685i
$273$	−12.7807	−	22.1369i	−0.773526	−	1.33979i
$274$	11.6754	−	20.2224i	0.705336	−	1.22168i
$275$		0			0
$276$	1.11636	−	0.936739i	0.0671971	−	0.0563851i
$277$	13.3893	−	23.1910i	0.804488	−	1.39341i	−0.112148	−	0.993691i	$-0.535773\pi$
$277$	13.3893	−	23.1910i	0.804488	−	1.39341i	0.916636	−	0.399722i	$-0.130893\pi$
$278$	−7.81957	−	13.5439i	−0.468987	−	0.812308i
$279$	−3.24313	−	1.18040i	−0.194161	−	0.0706688i
$280$		0			0
$281$	3.74145	+	21.2188i	0.223196	+	1.26581i	0.866103	+	0.499865i	$0.166617\pi$
$281$	3.74145	+	21.2188i	0.223196	+	1.26581i	−0.642907	+	0.765945i	$0.722272\pi$
$282$	−30.7198	+	11.1811i	−1.82934	+	0.665825i
$283$	−14.0547	−	11.7933i	−0.835465	−	0.701038i	0.121074	−	0.992643i	$-0.461366\pi$
$283$	−14.0547	−	11.7933i	−0.835465	−	0.701038i	−0.956539	+	0.291605i	$0.905811\pi$
$284$	−1.54788			−0.0918499
$285$		0			0
$286$	−12.1088			−0.716010
$287$	−20.3188	−	17.0495i	−1.19938	−	1.00640i
$288$	5.40245	−	1.96633i	0.318343	−	0.115867i
$289$	−0.693114	−	3.93084i	−0.0407714	−	0.231226i
$290$		0			0
$291$	24.8887	+	9.05875i	1.45900	+	0.531033i
$292$	−2.33374	−	4.04215i	−0.136572	−	0.236549i
$293$	−4.64436	+	8.04426i	−0.271326	+	0.469951i	−0.969202	−	0.246268i	$-0.920796\pi$
$293$	−4.64436	+	8.04426i	−0.271326	+	0.469951i	0.697875	+	0.716219i	$0.254129\pi$
$294$	−25.0354	+	21.0072i	−1.46010	+	1.22517i
$295$		0			0
$296$	−10.2504	+	17.7542i	−0.595791	+	1.03194i
$297$	−2.46097	−	4.26253i	−0.142800	−	0.247337i
$298$	2.11274	+	0.768973i	0.122388	+	0.0445454i
$299$	0.661871	−	3.75366i	0.0382770	−	0.217079i
$300$		0			0
$301$	−23.5888	+	8.58561i	−1.35963	+	0.494867i
$302$	−9.84557	−	8.26142i	−0.566549	−	0.475391i
$303$	15.9549			0.916585
$304$	14.3442	+	14.7202i	0.822694	+	0.844261i
$305$		0			0
$306$	9.63847	+	8.08764i	0.550995	+	0.462339i
$307$	−10.3508	+	3.76739i	−0.590753	+	0.215017i	−0.620061	−	0.784554i	$-0.712892\pi$
$307$	−10.3508	+	3.76739i	−0.590753	+	0.215017i	0.0293076	+	0.999570i	$0.490670\pi$
$308$	0.899102	+	5.09906i	0.0512311	+	0.290546i
$309$	4.02097	−	22.8041i	0.228745	−	1.29728i
$310$		0			0
$311$	−12.6911	−	21.9816i	−0.719644	−	1.24646i	−0.961141	−	0.276058i	$-0.910972\pi$
$311$	−12.6911	−	21.9816i	−0.719644	−	1.24646i	0.241497	−	0.970402i	$-0.422362\pi$
$312$	7.66997	−	13.2848i	0.434227	−	0.752103i
$313$	−16.1297	+	13.5345i	−0.911707	+	0.765013i	−0.972443	−	0.233141i	$-0.925100\pi$
$313$	−16.1297	+	13.5345i	−0.911707	+	0.765013i	0.0607363	+	0.998154i	$0.480655\pi$
$314$	9.42606	−	7.90940i	0.531943	−	0.446353i
$315$		0			0
$316$	0.454110	+	0.786541i	0.0255457	+	0.0442464i
$317$	3.76804	+	1.37145i	0.211634	+	0.0770285i	0.445662	−	0.895201i	$-0.352968\pi$
$317$	3.76804	+	1.37145i	0.211634	+	0.0770285i	−0.234028	+	0.972230i	$0.575191\pi$
$318$	−2.45804	+	13.9402i	−0.137840	+	0.781730i
$319$	−4.56780	−	25.9053i	−0.255748	−	1.45042i
$320$		0			0
$321$	−20.6262	−	17.3074i	−1.15124	−	0.966006i
$322$	−8.61896			−0.480316
$323$	−4.26511	+	15.1318i	−0.237317	+	0.841955i
$324$	−5.00419			−0.278011
$325$		0			0
$326$	−28.4813	+	10.3663i	−1.57743	+	0.574138i
$327$	0.636480	+	3.60966i	0.0351974	+	0.199614i
$328$	2.76409	−	15.6759i	0.152621	−	0.865557i
$329$	34.3564	+	12.5047i	1.89413	+	0.689406i
$330$		0			0
$331$	16.0680	−	27.8306i	0.883176	−	1.52971i	0.0353860	−	0.999374i	$-0.488734\pi$
$331$	16.0680	−	27.8306i	0.883176	−	1.52971i	0.847790	−	0.530332i	$-0.177933\pi$
$332$	−0.578309	+	0.485259i	−0.0317389	+	0.0266321i
$333$	−14.4839	+	12.1535i	−0.793715	+	0.666006i
$334$	7.37312	−	12.7706i	0.403439	−	0.698777i
$335$		0			0
$336$	−40.6340	−	14.7896i	−2.21677	−	0.806837i
$337$	−4.07164	+	23.0914i	−0.221796	+	1.25787i	0.646920	+	0.762558i	$0.276057\pi$
$337$	−4.07164	+	23.0914i	−0.221796	+	1.25787i	−0.868716	+	0.495310i	$0.835054\pi$
$338$	−1.42650	−	8.09007i	−0.0775912	−	0.440042i
$339$	−27.7954	+	10.1167i	−1.50964	+	0.549464i
$340$		0			0
$341$	4.29786			0.232742
$342$	6.24754	+	13.8634i	0.337828	+	0.749645i
$343$	8.45661			0.456614
$344$	−11.5401	−	9.68333i	−0.622203	−	0.522090i
$345$		0			0
$346$	−2.26645	−	12.8537i	−0.121845	−	0.691017i
$347$	−1.12759	+	6.39487i	−0.0605321	+	0.343295i	0.939468	+	0.342638i	$0.111320\pi$
$347$	−1.12759	+	6.39487i	−0.0605321	+	0.343295i	−1.00000		0.000657202i	$0.999791\pi$
$348$	−9.52303	−	3.46610i	−0.510488	−	0.185802i
$349$	13.6004	+	23.5566i	0.728013	+	1.26096i	0.957722	+	0.287696i	$0.0928893\pi$
$349$	13.6004	+	23.5566i	0.728013	+	1.26096i	−0.229709	+	0.973259i	$0.573777\pi$
$350$		0			0
$351$	−3.79922	+	3.18793i	−0.202787	+	0.170159i
$352$	−5.48446	+	4.60201i	−0.292323	+	0.245288i
$353$	−3.28062	+	5.68221i	−0.174610	+	0.302433i	−0.940026	−	0.341102i	$-0.889200\pi$
$353$	−3.28062	+	5.68221i	−0.174610	+	0.302433i	0.765416	+	0.643536i	$0.222533\pi$
$354$	6.48063	+	11.2248i	0.344442	+	0.596590i
$355$		0			0
$356$	−0.992172	+	5.62689i	−0.0525850	+	0.298224i
$357$	−5.74358	−	32.5735i	−0.303983	−	1.72397i
$358$	27.3486	−	9.95408i	1.44542	−	0.526090i
$359$	−2.09279	−	1.75606i	−0.110453	−	0.0926813i	0.585888	−	0.810392i	$-0.300746\pi$
$359$	−2.09279	−	1.75606i	−0.110453	−	0.0926813i	−0.696342	+	0.717710i	$0.745190\pi$
$360$		0			0
$361$	−12.5854	+	14.2340i	−0.662391	+	0.749158i
$362$	17.7922			0.935139
$363$	5.86064	+	4.91766i	0.307604	+	0.258110i
$364$	4.90262	−	1.78441i	0.256967	−	0.0935284i
$365$		0			0
$366$	4.66680	−	26.4667i	0.243938	−	1.38344i
$367$	6.18227	+	2.25016i	0.322712	+	0.117457i	0.498296	−	0.867007i	$-0.333959\pi$
$367$	6.18227	+	2.25016i	0.322712	+	0.117457i	−0.175584	+	0.984464i	$0.556181\pi$
$368$	−3.22397	−	5.58408i	−0.168061	−	0.291090i
$369$	7.34031	−	12.7138i	0.382121	−	0.661853i
$370$		0			0
$371$	12.1272	−	10.1759i	0.629614	−	0.528309i
$372$	0.827894	−	1.43395i	0.0429243	−	0.0743470i
$373$	−4.27996	−	7.41311i	−0.221608	−	0.383836i	0.733688	−	0.679486i	$-0.237797\pi$
$373$	−4.27996	−	7.41311i	−0.221608	−	0.383836i	−0.955296	+	0.295650i	$0.904464\pi$
$374$	−14.7236	−	5.35896i	−0.761340	−	0.277105i
$375$		0			0
$376$	3.81004	+	21.6078i	0.196488	+	1.11434i
$377$	−24.9073	+	9.06551i	−1.28279	+	0.466898i
$378$	8.59106	+	7.20875i	0.441876	+	0.370778i
$379$	14.2477			0.731856			0.365928	−	0.930643i	$-0.380752\pi$
$379$	14.2477			0.731856			0.365928	+	0.930643i	$0.380752\pi$
$380$		0			0
$381$	−18.9611			−0.971409
$382$	14.3017	+	12.0006i	0.731739	+	0.614002i
$383$	20.0778	−	7.30773i	1.02593	−	0.373408i	0.226399	−	0.974035i	$-0.427305\pi$
$383$	20.0778	−	7.30773i	1.02593	−	0.373408i	0.799529	+	0.600627i	$0.205082\pi$
$384$	−5.39764	−	30.6115i	−0.275447	−	1.56214i
$385$		0			0
$386$	−1.41353	−	0.514485i	−0.0719470	−	0.0261866i
$387$	−6.94689	−	12.0324i	−0.353130	−	0.611640i
$388$	−2.70298	+	4.68170i	−0.137223	+	0.237677i
$389$	11.7148	−	9.82991i	0.593965	−	0.498396i	−0.295534	−	0.955332i	$-0.595498\pi$
$389$	11.7148	−	9.82991i	0.593965	−	0.498396i	0.889500	+	0.456936i	$0.151053\pi$
$390$		0			0
$391$	2.46604	−	4.27130i	0.124713	−	0.216009i
$392$	10.9672	+	18.9958i	0.553929	+	0.959433i
$393$	−13.9823	−	5.08915i	−0.705316	−	0.256714i
$394$	−3.89365	+	22.0820i	−0.196159	+	1.11247i
$395$		0			0
$396$	−2.69293	+	0.980147i	−0.135325	+	0.0492543i
$397$	−24.9746	−	20.9562i	−1.25344	−	1.05176i	−0.996349	−	0.0853727i	$-0.972792\pi$
$397$	−24.9746	−	20.9562i	−1.25344	−	1.05176i	−0.257090	−	0.966387i	$-0.582764\pi$
$398$	−12.1958			−0.611322
$399$	10.8446	−	38.4747i	0.542911	−	1.92614i
$400$		0			0
$401$	−13.2617	−	11.1279i	−0.662258	−	0.555701i	0.248505	−	0.968631i	$-0.420061\pi$
$401$	−13.2617	−	11.1279i	−0.662258	−	0.555701i	−0.910763	+	0.412930i	$0.864505\pi$
$402$	49.1388	−	17.8851i	2.45082	−	0.892026i
$403$	−0.752015	−	4.26489i	−0.0374605	−	0.212449i
$404$	−0.565485	+	3.20702i	−0.0281339	+	0.159555i
$405$		0			0
$406$	29.9683	+	51.9067i	1.48730	+	2.57609i
$407$	11.7727	−	20.3910i	0.583552	−	1.01074i
$408$	15.2056	−	12.7590i	0.752790	−	0.631666i
$409$	−8.29411	+	6.95959i	−0.410117	+	0.344129i	−0.824389	−	0.566024i	$-0.808481\pi$
$409$	−8.29411	+	6.95959i	−0.410117	+	0.344129i	0.414271	+	0.910153i	$0.364036\pi$
$410$		0			0
$411$	−16.9875	−	29.4233i	−0.837934	−	1.45134i
$412$	4.44123	+	1.61647i	0.218803	+	0.0796379i
$413$	2.51713	−	14.2754i	0.123860	−	0.702445i
$414$	−0.828373	−	4.69794i	−0.0407123	−	0.230891i
$415$		0			0
$416$	5.52633	+	4.63715i	0.270951	+	0.227355i
$417$	−22.7547			−1.11430
$418$	−13.2155	−	13.5620i	−0.646392	−	0.663338i
$419$	33.9763			1.65985			0.829925	−	0.557876i	$-0.188383\pi$
$419$	33.9763			1.65985			0.829925	+	0.557876i	$0.188383\pi$
$420$		0			0
$421$	−7.80720	+	2.84159i	−0.380500	+	0.138491i	−0.525187	−	0.850987i	$-0.676005\pi$
$421$	−7.80720	+	2.84159i	−0.380500	+	0.138491i	0.144687	+	0.989477i	$0.453782\pi$
$422$	2.07880	+	11.7894i	0.101194	+	0.573901i
$423$	−3.51393	+	19.9285i	−0.170853	+	0.968955i
$424$	8.92752	+	3.24935i	0.433559	+	0.157802i
$425$		0			0
$426$	−5.95501	+	10.3144i	−0.288521	+	0.499733i
$427$	−23.0246	+	19.3199i	−1.11424	+	0.934956i
$428$	4.20993	−	3.53255i	0.203495	−	0.170752i
$429$	−8.80910	+	15.2578i	−0.425307	+	0.736654i
$430$		0			0
$431$	11.3983	+	4.14863i	0.549035	+	0.199832i	0.601618	−	0.798784i	$-0.294523\pi$
$431$	11.3983	+	4.14863i	0.549035	+	0.199832i	−0.0525827	+	0.998617i	$0.516745\pi$
$432$	−1.45690	+	8.26247i	−0.0700950	+	0.397528i
$433$	0.943849	+	5.35283i	0.0453585	+	0.257241i	0.999052	−	0.0435404i	$-0.0138637\pi$
$433$	0.943849	+	5.35283i	0.0453585	+	0.257241i	−0.953693	+	0.300781i	$0.902753\pi$
$434$	−9.20225	+	3.34934i	−0.441722	+	0.160774i
$435$		0			0
$436$	−0.748119			−0.0358284
$437$	4.92648	−	3.35542i	0.235666	−	0.160512i
$438$	−35.9134			−1.71601
$439$	−19.4428	−	16.3144i	−0.927952	−	0.778644i	0.0474965	−	0.998871i	$-0.484876\pi$
$439$	−19.4428	−	16.3144i	−0.927952	−	0.778644i	−0.975449	+	0.220227i	$0.929320\pi$
$440$		0			0
$441$	3.51286	+	19.9224i	0.167279	+	0.948686i
$442$	−2.74159	+	15.5483i	−0.130404	+	0.739558i
$443$	−4.62446	−	1.68317i	−0.219715	−	0.0799697i	0.229817	−	0.973234i	$-0.426187\pi$
$443$	−4.62446	−	1.68317i	−0.219715	−	0.0799697i	−0.449532	+	0.893264i	$0.648409\pi$
$444$	−4.53554	−	7.85579i	−0.215247	−	0.372819i
$445$		0			0
$446$	9.62841	−	8.07919i	0.455918	−	0.382561i
$447$	2.50595	−	2.10274i	0.118527	−	0.0994563i
$448$	−10.7675	+	18.6499i	−0.508718	+	0.881125i
$449$	−2.03325	−	3.52169i	−0.0959548	−	0.166199i	0.814052	−	0.580792i	$-0.197257\pi$
$449$	−2.03325	−	3.52169i	−0.0959548	−	0.166199i	−0.910007	+	0.414594i	$0.863924\pi$
$450$		0			0
$451$	−3.17460	+	18.0041i	−0.149486	+	0.847778i
$452$	−1.04837	−	5.94560i	−0.0493111	−	0.279657i
$453$	−17.5724	+	6.39585i	−0.825625	+	0.300503i
$454$	21.3432	+	17.9091i	1.00169	+	0.840515i
$455$		0			0
$456$	23.2500	−	5.90854i	1.08878	−	0.276693i
$457$	13.5517			0.633922			0.316961	−	0.948439i	$-0.397338\pi$
$457$	13.5517			0.633922			0.316961	+	0.948439i	$0.397338\pi$
$458$	−29.1417	−	24.4528i	−1.36170	−	1.14260i
$459$	−6.03049	+	2.19492i	−0.281479	+	0.102450i
$460$		0			0
$461$	3.10504	−	17.6096i	0.144616	−	0.820160i	−0.823058	−	0.567957i	$-0.807734\pi$
$461$	3.10504	−	17.6096i	0.144616	−	0.820160i	0.967674	−	0.252203i	$-0.0811549\pi$
$462$	37.4368	+	13.6259i	1.74172	+	0.633934i
$463$	0.653477	+	1.13185i	0.0303696	+	0.0526017i	0.880811	−	0.473468i	$-0.156998\pi$
$463$	0.653477	+	1.13185i	0.0303696	+	0.0526017i	−0.850441	+	0.526070i	$0.823665\pi$
$464$	−22.4196	+	38.8320i	−1.04081	+	1.80273i
$465$		0			0
$466$	−16.4206	+	13.7785i	−0.760669	+	0.638277i
$467$	13.5133	−	23.4057i	0.625321	−	1.08309i	−0.363158	−	0.931728i	$-0.618301\pi$
$467$	13.5133	−	23.4057i	0.625321	−	1.08309i	0.988479	−	0.151360i	$-0.0483653\pi$
$468$	1.44382	+	2.50077i	0.0667406	+	0.115598i
$469$	−54.9557	−	20.0022i	−2.53762	−	0.923618i
$470$		0			0
$471$	−3.10889	−	17.6314i	−0.143250	−	0.812412i
$472$	8.17446	−	2.97526i	0.376260	−	0.136947i
$473$	13.2541	+	11.1215i	0.609422	+	0.511366i
$474$	6.98820			0.320979
$475$		0			0
$476$	6.75101			0.309432
$477$	6.71215	+	5.63217i	0.307328	+	0.257879i
$478$	−5.51587	+	2.00761i	−0.252290	+	0.0918261i
$479$	0.0502667	+	0.285076i	0.00229674	+	0.0130255i	0.985935	−	0.167132i	$-0.0534505\pi$
$479$	0.0502667	+	0.285076i	0.00229674	+	0.0130255i	−0.983638	+	0.180157i	$0.942339\pi$
$480$		0			0
$481$	−22.2944	−	8.11451i	−1.01654	−	0.369990i
$482$	4.14719	+	7.18315i	0.188899	+	0.327184i
$483$	−6.27024	+	10.8604i	−0.285306	+	0.494164i
$484$	−1.19619	+	1.00373i	−0.0543724	+	0.0456239i
$485$		0			0
$486$	−15.0606	+	26.0856i	−0.683161	+	1.18327i
$487$	7.68554	+	13.3117i	0.348265	+	0.603212i	0.985941	−	0.167092i	$-0.0534376\pi$
$487$	7.68554	+	13.3117i	0.348265	+	0.603212i	−0.637676	+	0.770304i	$0.720104\pi$
$488$	−16.9497	−	6.16917i	−0.767275	−	0.279265i
$489$	−7.65778	+	43.4294i	−0.346297	+	1.96395i
$490$		0			0
$491$	−13.6351	+	4.96276i	−0.615342	+	0.223966i	−0.630839	−	0.775914i	$-0.717289\pi$
$491$	−13.6351	+	4.96276i	−0.615342	+	0.223966i	0.0154969	+	0.999880i	$0.495067\pi$
$492$	5.39541	+	4.52729i	0.243244	+	0.204106i
$493$	−34.2979			−1.54470
$494$	−11.1455	+	15.4871i	−0.501462	+	0.696799i
$495$		0			0
$496$	−5.61213	−	4.70914i	−0.251992	−	0.211447i
$497$	12.5166	−	4.55567i	0.561447	−	0.204350i
$498$	1.00867	+	5.72048i	0.0451998	+	0.256341i
$499$	−2.55922	+	14.5140i	−0.114566	+	0.649737i	0.872398	+	0.488797i	$0.162564\pi$
$499$	−2.55922	+	14.5140i	−0.114566	+	0.649737i	−0.986964	+	0.160941i	$0.948547\pi$
$500$		0			0
$501$	−10.7278	−	18.5811i	−0.479282	−	0.830142i
$502$	9.85039	−	17.0614i	0.439644	−	0.761486i
$503$	−3.33423	+	2.79775i	−0.148666	+	0.124746i	−0.714087	−	0.700057i	$-0.753158\pi$
$503$	−3.33423	+	2.79775i	−0.148666	+	0.124746i	0.565421	+	0.824802i	$0.308714\pi$
$504$	−16.4482	+	13.8017i	−0.732662	+	0.614776i
$505$		0			0
$506$	2.97030	+	5.14471i	0.132046	+	0.228710i
$507$	−11.2317	−	4.08801i	−0.498817	−	0.181555i
$508$	0.672034	−	3.81129i	0.0298167	−	0.169099i
$509$	1.49227	+	8.46308i	0.0661437	+	0.375119i	0.999854	+	0.0170899i	$0.00544015\pi$
$509$	1.49227	+	8.46308i	0.0661437	+	0.375119i	−0.933710	+	0.358029i	$0.883449\pi$
$510$		0			0
$511$	30.7680	+	25.8174i	1.36109	+	1.14209i
$512$	−10.5094			−0.464455
$513$	−7.71696	−	0.775866i	−0.340712	−	0.0342553i
$514$	−13.5058			−0.595715
$515$		0			0
$516$	6.26372	−	2.27981i	0.275745	−	0.100363i
$517$	−4.37590	−	24.8169i	−0.192452	−	1.09145i
$518$	−9.31607	+	52.8341i	−0.409325	+	2.32140i
$519$	−17.8452	−	6.49511i	−0.783316	−	0.285104i
$520$		0			0
$521$	−1.03475	+	1.79225i	−0.0453334	+	0.0785197i	−0.887802	−	0.460226i	$-0.847768\pi$
$521$	−1.03475	+	1.79225i	−0.0453334	+	0.0785197i	0.842468	+	0.538746i	$0.181102\pi$
$522$	−25.4125	+	21.3236i	−1.11227	+	0.933309i
$523$	−10.7338	+	9.00674i	−0.469357	+	0.393837i	−0.846560	−	0.532293i	$-0.821330\pi$
$523$	−10.7338	+	9.00674i	−0.469357	+	0.393837i	0.377203	+	0.926131i	$0.376886\pi$
$524$	1.51852	−	2.63015i	0.0663368	−	0.114899i
$525$		0			0
$526$	39.3886	+	14.3363i	1.71742	+	0.625091i
$527$	0.973090	−	5.51866i	0.0423884	−	0.240397i
$528$	5.17546	+	29.3515i	0.225233	+	1.27736i
$529$	19.8557	−	7.22690i	0.863293	−	0.314213i
$530$		0			0
$531$	8.02299			0.348168
$532$	7.34925	+	3.54347i	0.318630	+	0.153629i
$533$	18.4214			0.797919
$534$	33.6779	+	28.2591i	1.45739	+	1.22289i
$535$		0			0
$536$	−6.09446	−	34.5634i	−0.263240	−	1.49291i
$537$	7.35325	−	41.7023i	0.317316	−	1.79959i
$538$	4.87474	+	1.77426i	0.210165	+	0.0764938i
$539$	−12.5961	−	21.8170i	−0.542551	−	0.939725i
$540$		0			0
$541$	−12.7311	+	10.6827i	−0.547354	+	0.459285i	−0.874044	−	0.485847i	$-0.838511\pi$
$541$	−12.7311	+	10.6827i	−0.547354	+	0.459285i	0.326690	+	0.945132i	$0.394067\pi$
$542$	−22.1212	+	18.5619i	−0.950186	+	0.797301i
$543$	12.9437	−	22.4192i	0.555469	−	0.962100i
$544$	4.66745	+	8.08426i	0.200115	+	0.346610i
$545$		0			0
$546$	6.97087	−	39.5338i	0.298326	−	1.69189i
$547$	1.04789	+	5.94288i	0.0448045	+	0.254099i	0.998980	−	0.0451475i	$-0.0143758\pi$
$547$	1.04789	+	5.94288i	0.0448045	+	0.254099i	−0.954176	+	0.299247i	$0.903265\pi$
$548$	6.51632	−	2.37175i	0.278364	−	0.101316i
$549$	−12.7436	−	10.6932i	−0.543884	−	0.456373i
$550$		0			0
$551$	−37.3372	−	18.0023i	−1.59062	−	0.766923i
$552$	−7.52578			−0.320319
$553$	−5.98698	−	5.02367i	−0.254592	−	0.213628i
$554$	39.5190	−	14.3837i	1.67900	−	0.611106i
$555$		0			0
$556$	0.806489	−	4.57383i	0.0342028	−	0.193973i
$557$	−26.4311	−	9.62013i	−1.11992	−	0.407618i	−0.285298	−	0.958439i	$-0.592093\pi$
$557$	−26.4311	−	9.62013i	−1.11992	−	0.407618i	−0.834623	+	0.550821i	$0.814315\pi$
$558$	−2.71006	−	4.69396i	−0.114726	−	0.198711i
$559$	8.71703	−	15.0983i	0.368691	−	0.638591i
$560$		0			0
$561$	−17.4639	+	14.6540i	−0.737327	+	0.618691i
$562$	−16.9188	+	29.3043i	−0.713679	+	1.23613i
$563$	−0.605777	−	1.04924i	−0.0255305	−	0.0442201i	0.852978	−	0.521947i	$-0.174794\pi$
$563$	−0.605777	−	1.04924i	−0.0255305	−	0.0442201i	−0.878508	+	0.477727i	$0.841461\pi$
$564$	−9.12293	−	3.32048i	−0.384145	−	0.139817i
$565$		0			0
$566$	−5.00343	−	28.3759i	−0.210310	−	1.19273i
$567$	40.4653	−	14.7282i	1.69938	−	0.618525i
$568$	6.12340	+	5.13814i	0.256932	+	0.215592i
$569$	−17.5814			−0.737049			−0.368524	−	0.929618i	$-0.620137\pi$
$569$	−17.5814			−0.737049			−0.368524	+	0.929618i	$0.620137\pi$
$570$		0			0
$571$	42.6982			1.78686			0.893432	−	0.449198i	$-0.148290\pi$
$571$	42.6982			1.78686			0.893432	+	0.449198i	$0.148290\pi$
$572$	−2.75468	−	2.31145i	−0.115179	−	0.0966467i
$573$	25.5258	−	9.29063i	1.06636	−	0.388122i
$574$	−7.23343	−	41.0228i	−0.301918	−	1.71226i
$575$		0			0
$576$	−11.2004	−	4.07660i	−0.466682	−	0.169859i
$577$	2.74678	+	4.75757i	0.114350	+	0.198060i	0.917520	−	0.397690i	$-0.130188\pi$
$577$	2.74678	+	4.75757i	0.114350	+	0.198060i	−0.803170	+	0.595750i	$0.796855\pi$
$578$	3.13426	−	5.42869i	0.130368	−	0.225804i
$579$	−1.67662	+	1.40685i	−0.0696778	+	0.0584666i
$580$		0			0
$581$	3.24817	−	5.62600i	0.134757	−	0.233406i
$582$	20.7978	+	36.0228i	0.862096	+	1.49319i
$583$	−10.2534	−	3.73193i	−0.424653	−	0.154561i
$584$	−4.18555	+	23.7374i	−0.173199	+	0.982262i
$585$		0			0
$586$	−13.7079	+	4.98928i	−0.566270	+	0.206105i
$587$	9.51705	+	7.98576i	0.392811	+	0.329607i	0.817707	−	0.575635i	$-0.195245\pi$
$587$	9.51705	+	7.98576i	0.392811	+	0.329607i	−0.424896	+	0.905242i	$0.639689\pi$
$588$	−9.70547			−0.400247
$589$	3.95596	−	5.49694i	0.163002	−	0.226498i
$590$		0			0
$591$	24.9919	+	20.9707i	1.02803	+	0.862620i
$592$	−37.7150	+	13.7271i	−1.55008	+	0.564182i
$593$	0.194097	+	1.10078i	0.00797061	+	0.0452036i	0.988534	−	0.151001i	$-0.0482496\pi$
$593$	0.194097	+	1.10078i	0.00797061	+	0.0452036i	−0.980563	+	0.196204i	$0.937138\pi$
$594$	1.34226	−	7.61236i	0.0550738	−	0.312339i
$595$		0			0
$596$	0.333845	+	0.578237i	0.0136748	+	0.0236855i
$597$	−8.87240	+	15.3674i	−0.363123	+	0.628948i
$598$	4.58551	−	3.84770i	0.187515	−	0.157344i
$599$	−21.0736	+	17.6829i	−0.861044	+	0.722502i	−0.962193	−	0.272370i	$-0.912193\pi$
$599$	−21.0736	+	17.6829i	−0.861044	+	0.722502i	0.101149	+	0.994871i	$0.467748\pi$
$600$		0			0
$601$	−7.02686	−	12.1709i	−0.286631	−	0.496460i	0.686372	−	0.727251i	$-0.259202\pi$
$601$	−7.02686	−	12.1709i	−0.286631	−	0.496460i	−0.973004	+	0.230790i	$0.925869\pi$
$602$	−37.0455	−	13.4835i	−1.50986	−	0.549545i
$603$	5.62080	−	31.8771i	0.228897	−	1.29814i
$604$	−0.662785	−	3.75884i	−0.0269683	−	0.152945i
$605$		0			0
$606$	19.1946	+	16.1062i	0.779727	+	0.654269i
$607$	16.1942			0.657304			0.328652	−	0.944451i	$-0.393406\pi$
$607$	16.1942			0.657304			0.328652	+	0.944451i	$0.393406\pi$
$608$	0.837784	+	11.2505i	0.0339766	+	0.456268i
$609$	87.2071			3.53381
$610$		0			0
$611$	−23.8609	+	8.68464i	−0.965307	+	0.351343i
$612$	0.648843	+	3.67977i	0.0262279	+	0.148746i
$613$	−4.80621	+	27.2574i	−0.194121	+	1.10091i	0.719544	+	0.694447i	$0.244351\pi$
$613$	−4.80621	+	27.2574i	−0.194121	+	1.10091i	−0.913665	+	0.406468i	$0.866760\pi$
$614$	−16.2557	−	5.91659i	−0.656027	−	0.238774i
$615$		0			0
$616$	13.3693	−	23.1563i	0.538665	−	0.932995i
$617$	−4.66949	+	3.91817i	−0.187987	+	0.157739i	−0.731924	−	0.681386i	$-0.761377\pi$
$617$	−4.66949	+	3.91817i	−0.187987	+	0.157739i	0.543937	+	0.839126i	$0.316933\pi$
$618$	27.8577	−	23.3754i	1.12060	−	0.940296i
$619$	5.85935	−	10.1487i	0.235507	−	0.407910i	−0.723913	−	0.689891i	$-0.757658\pi$
$619$	5.85935	−	10.1487i	0.235507	−	0.407910i	0.959420	+	0.281981i	$0.0909916\pi$
$620$		0			0
$621$	2.28641	+	0.832186i	0.0917505	+	0.0333945i
$622$	6.92195	−	39.2564i	0.277545	−	1.57404i
$623$	−8.53787	−	48.4207i	−0.342063	−	1.93993i
$624$	28.2207	−	10.2715i	1.12973	−	0.411190i
$625$		0			0
$626$	−33.0677			−1.32165
$627$	−26.7031	+	6.78605i	−1.06642	+	0.271009i
$628$	3.65419			0.145818
$629$	−23.5175	−	19.7335i	−0.937704	−	0.786827i
$630$		0			0
$631$	3.63291	+	20.6033i	0.144624	+	0.820203i	0.967668	+	0.252226i	$0.0811626\pi$
$631$	3.63291	+	20.6033i	0.144624	+	0.820203i	−0.823045	+	0.567977i	$0.807726\pi$
$632$	0.814445	−	4.61895i	0.0323969	−	0.183732i
$633$	16.3677	+	5.95734i	0.650556	+	0.236783i
$634$	3.14869	+	5.45369i	0.125050	+	0.216594i
$635$		0			0
$636$	−3.22024	+	2.70210i	−0.127691	+	0.107145i
$637$	−19.4456	+	16.3168i	−0.770464	+	0.646496i
$638$	20.6556	−	35.7765i	0.817763	−	1.41641i
$639$	3.68614	+	6.38458i	0.145821	+	0.252570i
$640$		0			0
$641$	−1.64737	+	9.34270i	−0.0650672	+	0.369015i	0.934836	+	0.355081i	$0.115547\pi$
$641$	−1.64737	+	9.34270i	−0.0650672	+	0.369015i	−0.999903	+	0.0139340i	$0.995565\pi$
$642$	−7.34287	−	41.6435i	−0.289800	−	1.64354i
$643$	11.7831	−	4.28868i	0.464678	−	0.169129i	−0.0990618	−	0.995081i	$-0.531584\pi$
$643$	11.7831	−	4.28868i	0.464678	−	0.169129i	0.563740	+	0.825952i	$0.309362\pi$
$644$	−1.96076	−	1.64527i	−0.0772647	−	0.0648328i
$645$		0			0
$646$	−20.4064	+	13.8988i	−0.802879	+	0.546840i
$647$	15.6504			0.615281			0.307640	−	0.951503i	$-0.400461\pi$
$647$	15.6504			0.615281			0.307640	+	0.951503i	$0.400461\pi$
$648$	19.7965	+	16.6112i	0.777680	+	0.652551i
$649$	−9.38851	+	3.41714i	−0.368531	+	0.134134i
$650$		0			0
$651$	−2.47422	+	14.0320i	−0.0969722	+	0.549956i
$652$	−8.45814	−	3.07851i	−0.331246	−	0.120564i
$653$	9.54528	+	16.5329i	0.373536	+	0.646983i	0.990107	−	0.140317i	$-0.0448120\pi$
$653$	9.54528	+	16.5329i	0.373536	+	0.646983i	−0.616571	+	0.787299i	$0.711479\pi$
$654$	−2.87816	+	4.98512i	−0.112545	+	0.194934i
$655$		0			0
$656$	23.8723	−	20.0312i	0.932056	−	0.782088i
$657$	−11.1152	+	19.2520i	−0.433644	+	0.751093i
$658$	28.7093	+	49.7259i	1.11920	+	1.93852i
$659$	9.83688	+	3.58033i	0.383190	+	0.139470i	0.526431	−	0.850218i	$-0.323530\pi$
$659$	9.83688	+	3.58033i	0.383190	+	0.139470i	−0.143240	+	0.989688i	$0.545752\pi$
$660$		0			0
$661$	−5.06045	−	28.6992i	−0.196829	−	1.11627i	−0.909791	−	0.415068i	$-0.863758\pi$
$661$	−5.06045	−	28.6992i	−0.196829	−	1.11627i	0.712962	−	0.701203i	$-0.247353\pi$
$662$	47.4250	−	17.2613i	1.84323	−	0.670880i
$663$	17.5973	+	14.7659i	0.683421	+	0.573458i
$664$	3.89858			0.151294
$665$		0			0
$666$	−29.6936			−1.15060
$667$	9.96145	+	8.35865i	0.385709	+	0.323648i
$668$	4.11512	−	1.49778i	0.159219	−	0.0579509i
$669$	−3.17563	−	18.0099i	−0.122777	−	0.696303i
$670$		0			0
$671$	19.4670	+	7.08540i	0.751514	+	0.273529i
$672$	−11.8676	−	20.5554i	−0.457804	−	0.792940i
$673$	−7.27748	+	12.6050i	−0.280526	+	0.485886i	−0.971514	−	0.236980i	$-0.923842\pi$
$673$	−7.27748	+	12.6050i	−0.280526	+	0.485886i	0.690988	+	0.722866i	$0.257176\pi$
$674$	−28.2087	+	23.6699i	−1.08656	+	0.911731i
$675$		0			0
$676$	1.21979	−	2.11274i	0.0469151	−	0.0812594i
$677$	−5.48999	−	9.50895i	−0.210998	−	0.365459i	0.741029	−	0.671473i	$-0.234338\pi$
$677$	−5.48999	−	9.50895i	−0.210998	−	0.365459i	−0.952027	+	0.306014i	$0.901005\pi$
$678$	−43.6520	−	15.8880i	−1.67644	−	0.610176i
$679$	8.07804	−	45.8128i	0.310007	−	1.75813i
$680$		0			0
$681$	38.0935	−	13.8649i	1.45975	−	0.531304i
$682$	5.17055	+	4.33861i	0.197991	+	0.166134i
$683$	43.3449			1.65854			0.829272	−	0.558844i	$-0.188755\pi$
$683$	43.3449			1.65854			0.829272	+	0.558844i	$0.188755\pi$
$684$	−1.22510	+	4.34642i	−0.0468429	+	0.166190i
$685$		0			0
$686$	10.1737	+	8.53678i	0.388435	+	0.325936i
$687$	−52.0122	+	18.9309i	−1.98439	+	0.722259i
$688$	−5.12137	−	29.0447i	−0.195251	−	1.10732i
$689$	−1.90922	+	10.8277i	−0.0727355	+	0.412504i
$690$		0			0
$691$	−15.2029	−	26.3321i	−0.578344	−	1.00172i	−0.995669	−	0.0929641i	$-0.970366\pi$
$691$	−15.2029	−	26.3321i	−0.578344	−	1.00172i	0.417325	−	0.908757i	$-0.362968\pi$
$692$	1.93803	−	3.35677i	0.0736729	−	0.127605i
$693$	18.8911	−	15.8515i	0.717612	−	0.602148i
$694$	−7.81205	+	6.55509i	−0.296541	+	0.248828i
$695$		0			0
$696$	26.1673	+	45.3232i	0.991870	+	1.71797i
$697$	22.3993	+	8.15268i	0.848434	+	0.308805i
$698$	−7.41793	+	42.0692i	−0.280773	+	1.59234i
$699$	5.41582	+	30.7147i	0.204845	+	1.16174i
$700$		0			0
$701$	16.3694	+	13.7356i	0.618266	+	0.518786i	0.897258	−	0.441507i	$-0.145556\pi$
$701$	16.3694	+	13.7356i	0.618266	+	0.518786i	−0.278992	+	0.960293i	$0.590000\pi$
$702$	−7.78881			−0.293970
$703$	−15.2437	−	33.8261i	−0.574929	−	1.27577i
$704$	14.8430			0.559416
$705$		0			0
$706$	−9.68284	+	3.52427i	−0.364419	+	0.132638i
$707$	−4.86613	−	27.5972i	−0.183010	−	1.03790i
$708$	−0.668395	+	3.79065i	−0.0251198	+	0.142462i
$709$	18.8045	+	6.84427i	0.706217	+	0.257042i	0.670063	−	0.742304i	$-0.266267\pi$
$709$	18.8045	+	6.84427i	0.706217	+	0.257042i	0.0361542	+	0.999346i	$0.488489\pi$
$710$		0			0
$711$	2.16284	−	3.74615i	0.0811129	−	0.140492i
$712$	22.6033	−	18.9664i	0.847093	−	0.710795i
$713$	−1.62756	+	1.36569i	−0.0609527	+	0.0511454i
$714$	25.9725	−	44.9856i	0.971995	−	1.68354i
$715$		0			0
$716$	8.12177	+	2.95608i	0.303525	+	0.110474i
$717$	−1.48306	+	8.41083i	−0.0553858	+	0.314108i
$718$	−0.745028	−	4.22526i	−0.0278042	−	0.157685i
$719$	3.85410	−	1.40278i	0.143734	−	0.0523147i	−0.269152	−	0.963098i	$-0.586743\pi$
$719$	3.85410	−	1.40278i	0.143734	−	0.0523147i	0.412885	+	0.910783i	$0.364521\pi$
$720$		0			0
$721$	−40.6705			−1.51465
$722$	−29.5099	+	4.41950i	−1.09824	+	0.164477i
$723$	12.0682			0.448822
$724$	4.04762	+	3.39636i	0.150429	+	0.126225i
$725$		0			0
$726$	2.08637	+	11.8324i	0.0774326	+	0.439142i
$727$	6.20784	−	35.2064i	0.230236	−	1.30573i	−0.622182	−	0.782872i	$-0.713754\pi$
$727$	6.20784	−	35.2064i	0.230236	−	1.30573i	0.852418	−	0.522861i	$-0.175135\pi$
$728$	−25.3180	−	9.21498i	−0.938346	−	0.341530i
$729$	5.81836	+	10.0777i	0.215495	+	0.373248i
$730$		0			0
$731$	17.2814	−	14.5008i	0.639175	−	0.536332i
$732$	6.11390	−	5.13017i	0.225976	−	0.189617i
$733$	−15.6472	+	27.1018i	−0.577943	+	1.00103i	0.417772	+	0.908552i	$0.362811\pi$
$733$	−15.6472	+	27.1018i	−0.577943	+	1.00103i	−0.995715	+	0.0924752i	$0.970522\pi$
$734$	5.16610	+	8.94794i	0.190684	+	0.330274i
$735$		0			0
$736$	0.614584	−	3.48548i	0.0226539	−	0.128476i
$737$	6.99959	+	39.6966i	0.257833	+	1.46224i
$738$	21.6651	−	7.88545i	0.797504	−	0.290268i
$739$	24.9062	+	20.8988i	0.916188	+	0.768773i	0.973286	−	0.229596i	$-0.0737403\pi$
$739$	24.9062	+	20.8988i	0.916188	+	0.768773i	−0.0570981	+	0.998369i	$0.518185\pi$
$740$		0			0
$741$	11.4063	+	25.3108i	0.419022	+	0.929815i
$742$	24.8621			0.912716
$743$	−29.7586	−	24.9704i	−1.09174	−	0.916076i	−0.0948946	−	0.995487i	$-0.530251\pi$
$743$	−29.7586	−	24.9704i	−1.09174	−	0.916076i	−0.996842	+	0.0794116i	$0.974696\pi$
$744$	−8.03509	+	2.92453i	−0.294581	+	0.107219i
$745$		0			0
$746$	2.33438	−	13.2389i	0.0854676	−	0.484711i
$747$	3.37875	+	1.22976i	0.123622	+	0.0449947i
$748$	−2.32656	−	4.02972i	−0.0850674	−	0.147341i
$749$	−23.6458	+	40.9557i	−0.863998	+	1.49649i
$750$		0			0
$751$	−1.38487	+	1.16204i	−0.0505345	+	0.0424035i	−0.667705	−	0.744426i	$-0.732723\pi$
$751$	−1.38487	+	1.16204i	−0.0505345	+	0.0424035i	0.617171	+	0.786829i	$0.288279\pi$
$752$	−21.4777	+	37.2005i	−0.783212	+	1.35656i
$753$	−14.3322	−	24.8241i	−0.522294	−	0.904640i
$754$	−39.1162	−	14.2371i	−1.42453	−	0.518486i
$755$		0			0
$756$	0.578333	+	3.27989i	0.0210338	+	0.119289i
$757$	21.2025	−	7.71707i	0.770617	−	0.280482i	0.0733625	−	0.997305i	$-0.476627\pi$
$757$	21.2025	−	7.71707i	0.770617	−	0.280482i	0.697254	+	0.716824i	$0.254405\pi$
$758$	17.1408	+	14.3828i	0.622580	+	0.522407i
$759$	8.64349			0.313739
$760$		0			0
$761$	2.85080			0.103341			0.0516707	−	0.998664i	$-0.483545\pi$
$761$	2.85080			0.103341			0.0516707	+	0.998664i	$0.483545\pi$
$762$	−22.8112	−	19.1409i	−0.826364	−	0.693402i
$763$	6.04950	−	2.20184i	0.219006	−	0.0797118i
$764$	0.962764	+	5.46011i	0.0348316	+	0.197540i
$765$		0			0
$766$	31.5317	+	11.4766i	1.13929	+	0.414666i
$767$	5.03367	+	8.71856i	0.181755	+	0.314809i
$768$	12.1471	−	21.0393i	0.438319	−	0.759191i
$769$	4.68799	−	3.93369i	0.169053	−	0.141852i	−0.554336	−	0.832293i	$-0.687028\pi$
$769$	4.68799	−	3.93369i	0.169053	−	0.141852i	0.723389	+	0.690441i	$0.242583\pi$
$770$		0			0
$771$	−9.82538	+	17.0181i	−0.353852	+	0.612890i
$772$	−0.223360	−	0.386872i	−0.00803892	−	0.0139238i
$773$	47.1328	+	17.1549i	1.69525	+	0.617020i	0.995270	−	0.0971441i	$-0.0309708\pi$
$773$	47.1328	+	17.1549i	1.69525	+	0.617020i	0.699978	+	0.714164i	$0.253193\pi$
$774$	3.78897	−	21.4883i	0.136192	−	0.772382i
$775$		0			0
$776$	26.2337	−	9.54827i	0.941734	−	0.342763i
$777$	59.7965	+	50.1752i	2.14519	+	1.80003i
$778$	24.0167			0.861039
$779$	20.1050	+	20.6321i	0.720337	+	0.739221i
$780$		0			0
$781$	−7.03283	−	5.90124i	−0.251654	−	0.211163i
$782$	7.27856	−	2.64918i	0.260281	−	0.0947345i
$783$	−2.93817	−	16.6632i	−0.105002	−	0.595493i
$784$	−7.45686	+	42.2900i	−0.266317	+	1.51036i
$785$		0			0
$786$	−11.6841	−	20.2374i	−0.416757	−	0.721845i
$787$	−16.5102	+	28.5964i	−0.588524	+	1.01935i	0.405902	+	0.913917i	$0.366957\pi$
$787$	−16.5102	+	28.5964i	−0.588524	+	1.01935i	−0.994426	+	0.105437i	$0.966376\pi$
$788$	−5.10101	+	4.28025i	−0.181716	+	0.152478i
$789$	46.7194	−	39.2023i	1.66326	−	1.39564i
$790$		0			0
$791$	25.9763	+	44.9922i	0.923610	+	1.59974i
$792$	13.9068	+	5.06165i	0.494155	+	0.179858i
$793$	3.62482	−	20.5574i	0.128721	−	0.730014i
$794$	−8.89089	−	50.4227i	−0.315526	−	1.78944i
$795$		0			0
$796$	−2.77448	−	2.32806i	−0.0983388	−	0.0825160i
$797$	−47.2358			−1.67318			−0.836590	−	0.547830i	$-0.815454\pi$
$797$	−47.2358			−1.67318			−0.836590	+	0.547830i	$0.815454\pi$
$798$	51.8861	−	35.3396i	1.83675	−	1.25101i
$799$	−32.8569			−1.16239
$800$		0			0
$801$	25.5721	−	9.30748i	0.903545	−	0.328864i
$802$	−4.72113	−	26.7749i	−0.166709	−	0.945454i
$803$	4.80718	−	27.2629i	0.169642	−	0.962085i
$804$	14.5928	+	5.31136i	0.514650	+	0.187317i
$805$		0			0
$806$	3.40061	−	5.89003i	0.119781	−	0.207467i
$807$	5.78201	−	4.85168i	0.203536	−	0.170787i
$808$	12.8826	−	10.8098i	0.453210	−	0.380288i
$809$	−2.19118	+	3.79524i	−0.0770378	+	0.133433i	−0.901971	−	0.431797i	$-0.857880\pi$
$809$	−2.19118	+	3.79524i	−0.0770378	+	0.133433i	0.824933	+	0.565231i	$0.191213\pi$
$810$		0			0
$811$	31.9131	+	11.6154i	1.12062	+	0.407873i	0.834879	−	0.550433i	$-0.185537\pi$
$811$	31.9131	+	11.6154i	1.12062	+	0.407873i	0.285743	+	0.958306i	$0.407760\pi$
$812$	−3.09085	+	17.5291i	−0.108468	+	0.615151i
$813$	7.29598	+	41.3776i	0.255881	+	1.45117i
$814$	34.7475	−	12.6471i	1.21790	−	0.443279i
$815$		0			0
$816$	38.8606			1.36039
$817$	26.4240	−	6.71513i	0.924458	−	0.234933i
$818$	−17.0038			−0.594525
$819$	−19.0353	−	15.9725i	−0.665148	−	0.558125i
$820$		0			0
$821$	6.96961	+	39.5266i	0.243241	+	1.37949i	0.824542	+	0.565800i	$0.191433\pi$
$821$	6.96961	+	39.5266i	0.243241	+	1.37949i	−0.581301	+	0.813688i	$0.697456\pi$
$822$	9.26534	−	52.5464i	0.323166	−	1.83276i
$823$	5.93493	+	2.16014i	0.206879	+	0.0752976i	0.443381	−	0.896333i	$-0.353779\pi$
$823$	5.93493	+	2.16014i	0.206879	+	0.0752976i	−0.236502	+	0.971631i	$0.576001\pi$
$824$	−12.2036	−	21.1372i	−0.425132	−	0.736350i
$825$		0			0
$826$	17.4389	−	14.6330i	0.606779	−	0.509148i
$827$	−16.3638	+	13.7308i	−0.569024	+	0.477468i	−0.881322	−	0.472516i	$-0.843346\pi$
$827$	−16.3638	+	13.7308i	−0.569024	+	0.477468i	0.312298	+	0.949984i	$0.398901\pi$
$828$	0.708339	−	1.22688i	0.0246165	−	0.0426370i
$829$	−24.5301	−	42.4874i	−0.851966	−	1.47565i	−0.879432	−	0.476025i	$-0.842077\pi$
$829$	−24.5301	−	42.4874i	−0.851966	−	1.47565i	0.0274658	−	0.999623i	$-0.491256\pi$
$830$		0			0
$831$	10.6255	−	60.2602i	0.368595	−	2.09040i
$832$	−2.59714	−	14.7291i	−0.0900396	−	0.510640i
$833$	−30.8660	+	11.2343i	−1.06944	+	0.389246i
$834$	−27.3752	−	22.9705i	−0.947924	−	0.795403i
$835$		0			0
$836$	−0.417606	−	5.60797i	−0.0144432	−	0.193956i
$837$	2.76453			0.0955562
$838$	40.8752	+	34.2984i	1.41201	+	1.18482i
$839$	6.94430	−	2.52752i	0.239744	−	0.0872597i	−0.219354	−	0.975645i	$-0.570395\pi$
$839$	6.94430	−	2.52752i	0.239744	−	0.0872597i	0.459098	+	0.888386i	$0.348173\pi$
$840$		0			0
$841$	10.6670	−	60.4955i	0.367827	−	2.08605i
$842$	−12.2610	−	4.46264i	−0.422542	−	0.153793i
$843$	24.6167	+	42.6374i	0.847845	+	1.46851i
$844$	−1.77757	+	3.07884i	−0.0611865	+	0.105978i
$845$		0			0
$846$	−24.3448	+	20.4277i	−0.836993	+	0.702320i
$847$	6.71862	−	11.6370i	0.230855	−	0.399852i
$848$	9.29980	+	16.1077i	0.319357	+	0.553142i
$849$	−39.3952	−	14.3387i	−1.35204	−	0.492102i
$850$		0			0
$851$	2.02120	+	11.4628i	0.0692858	+	0.392939i
$852$	−3.32364	+	1.20971i	−0.113866	+	0.0414438i
$853$	−2.10899	−	1.76966i	−0.0722106	−	0.0605919i	0.605968	−	0.795489i	$-0.292786\pi$
$853$	−2.10899	−	1.76966i	−0.0722106	−	0.0605919i	−0.678179	+	0.734897i	$0.737230\pi$
$854$	−47.2028			−1.61525
$855$		0			0
$856$	−28.3806			−0.970029
$857$	33.8025	+	28.3637i	1.15467	+	0.968885i	0.999818	−	0.0190524i	$-0.00606493\pi$
$857$	33.8025	+	28.3637i	1.15467	+	0.968885i	0.154854	+	0.987937i	$0.450509\pi$
$858$	−26.0003	+	9.46332i	−0.887634	+	0.323072i
$859$	−2.04090	−	11.5745i	−0.0696347	−	0.394918i	−0.999626	−	0.0273372i	$-0.991297\pi$
$859$	−2.04090	−	11.5745i	−0.0696347	−	0.394918i	0.929992	−	0.367581i	$-0.119814\pi$
$860$		0			0
$861$	−56.9534	−	20.7293i	−1.94097	−	0.706453i
$862$	9.52474	+	16.4973i	0.324414	+	0.561902i
$863$	−17.1415	+	29.6900i	−0.583504	+	1.01066i	0.411556	+	0.911385i	$0.364986\pi$
$863$	−17.1415	+	29.6900i	−0.583504	+	1.01066i	−0.995060	+	0.0992746i	$0.968348\pi$
$864$	−3.52779	+	2.96017i	−0.120018	+	0.100707i
$865$		0			0
$866$	−4.26808	+	7.39254i	−0.145035	+	0.251209i
$867$	−4.56031	−	7.89868i	−0.154876	−	0.268253i
$868$	−2.73281	−	0.994661i	−0.0927576	−	0.0337610i
$869$	−0.935404	+	5.30494i	−0.0317314	+	0.179958i
$870$		0			0
$871$	38.1673	−	13.8918i	1.29325	−	0.470704i
$872$	2.95955	+	2.48335i	0.100223	+	0.0840970i
$873$	25.7476			0.871423
$874$	9.31406	+	0.936439i	0.315053	+	0.0316755i
$875$		0			0
$876$	−8.17007	−	6.85550i	−0.276041	−	0.231626i
$877$	−22.7444	+	8.27828i	−0.768023	+	0.279537i	−0.696169	−	0.717878i	$-0.745114\pi$
$877$	−22.7444	+	8.27828i	−0.768023	+	0.279537i	−0.0718537	+	0.997415i	$0.522891\pi$
$878$	−6.92157	−	39.2542i	−0.233592	−	1.32476i
$879$	−3.68566	+	20.9024i	−0.124314	+	0.705022i
$880$		0			0
$881$	19.5867	+	33.9251i	0.659892	+	1.14297i	0.980643	+	0.195802i	$0.0627311\pi$
$881$	19.5867	+	33.9251i	0.659892	+	1.14297i	−0.320752	+	0.947163i	$0.603936\pi$
$882$	−15.8851	+	27.5139i	−0.534880	+	0.926440i
$883$	−24.7964	+	20.8067i	−0.834467	+	0.700201i	−0.956312	−	0.292348i	$-0.905563\pi$
$883$	−24.7964	+	20.8067i	−0.834467	+	0.700201i	0.121845	+	0.992549i	$0.461119\pi$
$884$	−3.59171	+	3.01380i	−0.120802	+	0.101365i
$885$		0			0
$886$	−3.86435	−	6.69325i	−0.129825	−	0.224864i
$887$	0.357853	+	0.130248i	0.0120155	+	0.00437329i	0.348021	−	0.937487i	$-0.386854\pi$
$887$	0.357853	+	0.130248i	0.0120155	+	0.00437329i	−0.336005	+	0.941860i	$0.609076\pi$
$888$	−8.13448	+	46.1329i	−0.272975	+	1.54812i
$889$	5.78301	+	32.7971i	0.193956	+	1.09998i
$890$		0			0
$891$	−22.7366	−	19.0783i	−0.761705	−	0.639147i
$892$	3.73264			0.124978
$893$	−35.7685	−	17.2459i	−1.19695	−	0.577114i
$894$	5.13747			0.171823
$895$		0			0
$896$	−51.3024	+	18.6726i	−1.71389	+	0.623807i
$897$	−1.51239	−	8.57717i	−0.0504971	−	0.286384i
$898$	1.10897	−	6.28930i	0.0370069	−	0.209877i
$899$	13.8838	+	5.05328i	0.463050	+	0.168536i
$900$		0			0
$901$	−7.11348	+	12.3209i	−0.236984	+	0.410469i
$902$	−21.9940	+	18.4551i	−0.732319	+	0.614488i
$903$	−43.9403	+	36.8703i	−1.46224	+	1.22697i
$904$	−15.5889	+	27.0007i	−0.518478	+	0.898030i
$905$		0			0
$906$	−27.5971	−	10.0445i	−0.916851	−	0.333706i
$907$	0.855419	−	4.85132i	0.0284037	−	0.161086i	−0.967307	−	0.253609i	$-0.918382\pi$
$907$	0.855419	−	4.85132i	0.0284037	−	0.161086i	0.995710	+	0.0925237i	$0.0294934\pi$
$908$	1.43678	+	8.14841i	0.0476814	+	0.270415i
$909$	14.5747	−	5.30476i	0.483413	−	0.175948i
$910$		0			0
$911$	20.6775			0.685075			0.342537	−	0.939504i	$-0.388714\pi$
$911$	20.6775			0.685075			0.342537	+	0.939504i	$0.388714\pi$
$912$	42.3042	+	20.3972i	1.40083	+	0.675417i
$913$	−4.47759			−0.148187
$914$	16.3034	+	13.6802i	0.539269	+	0.452500i
$915$		0			0
$916$	−1.96176	−	11.1257i	−0.0648184	−	0.367604i
$917$	−4.53819	+	25.7374i	−0.149864	+	0.849923i
$918$	−9.47073	−	3.44706i	−0.312581	−	0.113770i
$919$	30.2934	+	52.4697i	0.999287	+	1.73082i	0.532344	+	0.846528i	$0.321311\pi$
$919$	30.2934	+	52.4697i	0.999287	+	1.73082i	0.466943	+	0.884287i	$0.345355\pi$
$920$		0			0
$921$	−19.2812	+	16.1788i	−0.635336	+	0.533110i
$922$	21.5121	−	18.0508i	0.708462	−	0.594470i
$923$	−4.62540	+	8.01143i	−0.152247	+	0.263699i
$924$	5.91560	+	10.2461i	0.194609	+	0.337073i
$925$		0			0
$926$	−0.356419	+	2.02135i	−0.0117127	+	0.0664258i
$927$	−3.90887	−	22.1683i	−0.128384	−	0.728102i
$928$	−23.1278	+	8.41784i	−0.759208	+	0.276329i
$929$	−0.222628	−	0.186807i	−0.00730419	−	0.00612894i	0.639128	−	0.769100i	$-0.279295\pi$
$929$	−0.222628	−	0.186807i	−0.00730419	−	0.00612894i	−0.646432	+	0.762971i	$0.723740\pi$
$930$		0			0
$931$	−39.4978	−	3.97113i	−1.29449	−	0.130149i
$932$	−6.36576			−0.208517
$933$	−44.4295	−	37.2808i	−1.45456	−	1.22052i
$934$	39.8848	−	14.5169i	1.30507	−	0.475007i
$935$		0			0
$936$	2.58949	−	14.6857i	0.0846400	−	0.480018i
$937$	4.98587	+	1.81471i	0.162881	+	0.0592839i	0.422174	−	0.906515i	$-0.361267\pi$
$937$	4.98587	+	1.81471i	0.162881	+	0.0592839i	−0.259293	+	0.965799i	$0.583489\pi$
$938$	−45.9227	−	79.5405i	−1.49943	−	2.59709i
$939$	−24.0565	+	41.6671i	−0.785056	+	1.35976i
$940$		0			0
$941$	−21.7752	+	18.2716i	−0.709852	+	0.595637i	−0.924558	−	0.381042i	$-0.875565\pi$
$941$	−21.7752	+	18.2716i	−0.709852	+	0.595637i	0.214706	+	0.976679i	$0.431121\pi$
$942$	14.0584	−	24.3499i	0.458048	−	0.793362i
$943$	−4.51877	−	7.82674i	−0.147151	−	0.254874i
$944$	16.0036	+	5.82484i	0.520873	+	0.189582i
$945$		0			0
$946$	4.71841	+	26.7594i	0.153409	+	0.870024i
$947$	−46.9649	+	17.0938i	−1.52615	+	0.555474i	−0.962676	−	0.270657i	$-0.912759\pi$
$947$	−46.9649	+	17.0938i	−1.52615	+	0.555474i	−0.563478	+	0.826131i	$0.690537\pi$
$948$	1.58977	+	1.33398i	0.0516334	+	0.0433256i
$949$	−27.8948			−0.905504
$950$		0			0
$951$	9.16261			0.297118
$952$	−26.7069	−	22.4097i	−0.865575	−	0.726304i
$953$	−11.3705	+	4.13854i	−0.368328	+	0.134060i	−0.519551	−	0.854439i	$-0.673901\pi$
$953$	−11.3705	+	4.13854i	−0.368328	+	0.134060i	0.151224	+	0.988500i	$0.451679\pi$
$954$	2.38951	+	13.5516i	0.0773632	+	0.438749i
$955$		0			0
$956$	−1.63806	−	0.596205i	−0.0529786	−	0.0192826i
$957$	−30.0536	−	52.0544i	−0.971496	−	1.68268i
$958$	−0.227306	+	0.393705i	−0.00734391	+	0.0127200i
$959$	−45.7124	+	38.3572i	−1.47613	+	1.23862i
$960$		0			0
$961$	14.2930	−	24.7562i	0.461065	−	0.798587i
$962$	−18.6299	−	32.2680i	−0.600653	−	1.04036i
$963$	−24.5963	−	8.95234i	−0.792606	−	0.288485i
$964$	−0.427730	+	2.42578i	−0.0137763	+	0.0781291i
$965$		0			0
$966$	−18.5068	+	6.73591i	−0.595445	+	0.216724i
$967$	−10.0879	−	8.46474i	−0.324404	−	0.272208i	0.466011	−	0.884779i	$-0.345691\pi$
$967$	−10.0879	−	8.46474i	−0.324404	−	0.272208i	−0.790415	+	0.612571i	$0.790135\pi$
$968$	8.06395			0.259185
$969$	2.66772	+	35.8245i	0.0856995	+	1.15085i
$970$		0			0
$971$	−13.4161	−	11.2575i	−0.430544	−	0.361269i	0.401613	−	0.915809i	$-0.368450\pi$
$971$	−13.4161	−	11.2575i	−0.430544	−	0.361269i	−0.832157	+	0.554540i	$0.812894\pi$
$972$	−8.40567	+	3.05941i	−0.269612	+	0.0981307i
$973$	6.94003	+	39.3589i	0.222487	+	1.26179i
$974$	−4.19184	+	23.7731i	−0.134315	+	0.761740i
$975$		0			0
$976$	−17.6565	−	30.5819i	−0.565170	−	0.978903i
$977$	−5.26807	+	9.12457i	−0.168541	+	0.291921i	−0.937907	−	0.346887i	$-0.887239\pi$
$977$	−5.26807	+	9.12457i	−0.168541	+	0.291921i	0.769366	+	0.638808i	$0.220572\pi$
$978$	−53.0539	+	44.5175i	−1.69648	+	1.42351i
$979$	−25.9602	+	21.7832i	−0.829693	+	0.696195i
$980$		0			0
$981$	1.78158	+	3.08578i	0.0568813	+	0.0985213i
$982$	−21.4135	−	7.79388i	−0.683333	−	0.248713i
$983$	−9.02591	+	51.1885i	−0.287882	+	1.63266i	0.406925	+	0.913462i	$0.366601\pi$
$983$	−9.02591	+	51.1885i	−0.287882	+	1.63266i	−0.694807	+	0.719197i	$0.744510\pi$
$984$	−6.31599	−	35.8198i	−0.201346	−	1.14189i
$985$		0			0
$986$	−41.2621	−	34.6230i	−1.31405	−	1.10262i
$987$	83.5433			2.65921
$988$	−5.49188	+	1.39565i	−0.174720	+	0.0444016i
$989$	−8.55315			−0.271974
$990$		0			0
$991$	−6.36762	+	2.31763i	−0.202274	+	0.0736218i	−0.441171	−	0.897423i	$-0.645437\pi$
$991$	−6.36762	+	2.31763i	−0.202274	+	0.0736218i	0.238896	+	0.971045i	$0.423214\pi$
$992$	−0.698288	−	3.96019i	−0.0221707	−	0.125736i
$993$	12.7512	−	72.3157i	0.404647	−	2.29487i
$994$	19.6570	+	7.15456i	0.623482	+	0.226929i
$995$		0			0
$996$	−0.862514	+	1.49392i	−0.0273298	+	0.0473366i
$997$	30.8481	−	25.8846i	0.976968	−	0.819774i	−0.00666090	−	0.999978i	$-0.502120\pi$
$997$	30.8481	−	25.8846i	0.976968	−	0.819774i	0.983629	+	0.180204i	$0.0576758\pi$
$998$	−17.7305	+	14.8777i	−0.561250	+	0.470944i
$999$	7.57262	−	13.1162i	0.239587	−	0.414977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.b.301.3		18
5.2	odd	4		475.2.u.c.149.2		36
5.3	odd	4		475.2.u.c.149.5		36
5.4	even	2		95.2.k.b.16.1	yes	18
15.14	odd	2		855.2.bs.b.586.3		18
19.5	even	9		9025.2.a.ce.1.8		9
19.6	even	9	inner	475.2.l.b.101.3		18
19.14	odd	18		9025.2.a.cd.1.2		9
95.14	odd	18		1805.2.a.u.1.8		9
95.24	even	18		1805.2.a.t.1.2		9
95.44	even	18		95.2.k.b.6.1	✓	18
95.63	odd	36		475.2.u.c.424.2		36
95.82	odd	36		475.2.u.c.424.5		36
285.44	odd	18		855.2.bs.b.766.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.1	✓	18	95.44	even	18
95.2.k.b.16.1	yes	18	5.4	even	2
475.2.l.b.101.3		18	19.6	even	9	inner
475.2.l.b.301.3		18	1.1	even	1	trivial
475.2.u.c.149.2		36	5.2	odd	4
475.2.u.c.149.5		36	5.3	odd	4
475.2.u.c.424.2		36	95.63	odd	36
475.2.u.c.424.5		36	95.82	odd	36
855.2.bs.b.586.3		18	15.14	odd	2
855.2.bs.b.766.3		18	285.44	odd	18
1805.2.a.t.1.2		9	95.24	even	18
1805.2.a.u.1.8		9	95.14	odd	18
9025.2.a.cd.1.2		9	19.14	odd	18
9025.2.a.ce.1.8		9	19.5	even	9

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20305 + 1.00948i) q^{2} +(2.14722 - 0.781523i) q^{3} +(0.0809872 + 0.459301i) q^{4} +(3.37214 + 1.22736i) q^{6} +(-2.00668 - 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +(1.70162 - 1.42783i) q^{9} +O(q^{10})\)	\(q+(1.20305 + 1.00948i) q^{2} +(2.14722 - 0.781523i) q^{3} +(0.0809872 + 0.459301i) q^{4} +(3.37214 + 1.22736i) q^{6} +(-2.00668 - 3.47568i) q^{7} +(1.20425 - 2.08582i) q^{8} +(1.70162 - 1.42783i) q^{9} +(-1.38310 + 2.39560i) q^{11} +(0.532851 + 0.922925i) q^{12} +(2.61923 + 0.953321i) q^{13} +(1.09448 - 6.20713i) q^{14} +(4.43089 - 1.61271i) q^{16} +(2.76292 + 2.31836i) q^{17} +3.48851 q^{18} +(1.79089 + 3.97401i) q^{19} +(-7.02510 - 5.89476i) q^{21} +(-4.08226 + 1.48582i) q^{22} +(-0.237457 - 1.34669i) q^{23} +(0.955667 - 5.41986i) q^{24} +(2.18871 + 3.79096i) q^{26} +(-0.889658 + 1.54093i) q^{27} +(1.43387 - 1.20316i) q^{28} +(-7.28463 + 6.11253i) q^{29} +(-0.776853 - 1.34555i) q^{31} +(2.43210 + 0.885212i) q^{32} +(-1.09760 + 6.22480i) q^{33} +(0.983591 + 5.57822i) q^{34} +(0.793615 + 0.665922i) q^{36} -8.51183 q^{37} +(-1.85715 + 6.58880i) q^{38} +6.36909 q^{39} +(6.21041 - 2.26041i) q^{41} +(-2.50092 - 14.1834i) q^{42} +(1.08613 - 6.15974i) q^{43} +(-1.21232 - 0.441247i) q^{44} +(1.07378 - 1.85984i) q^{46} +(-6.97857 + 5.85572i) q^{47} +(8.25371 - 6.92568i) q^{48} +(-4.55356 + 7.88699i) q^{49} +(7.74443 + 2.81874i) q^{51} +(-0.225738 + 1.28022i) q^{52} +(0.684965 + 3.88463i) q^{53} +(-2.62585 + 0.955730i) q^{54} -9.66619 q^{56} +(6.95120 + 7.13343i) q^{57} -14.9343 q^{58} +(2.76682 + 2.32164i) q^{59} +(-1.30047 - 7.37531i) q^{61} +(0.423711 - 2.40298i) q^{62} +(-8.37730 - 3.04909i) q^{63} +(-2.68292 - 4.64695i) q^{64} +(-7.60428 + 6.38075i) q^{66} +(11.1628 - 9.36668i) q^{67} +(-0.841066 + 1.45677i) q^{68} +(-1.56234 - 2.70605i) q^{69} +(-0.576318 + 3.26846i) q^{71} +(-0.929023 - 5.26875i) q^{72} +(-9.40420 + 3.42285i) q^{73} +(-10.2402 - 8.59253i) q^{74} +(-1.68023 + 1.14440i) q^{76} +11.1018 q^{77} +(7.66235 + 6.42947i) q^{78} +(1.82991 - 0.666034i) q^{79} +(-1.86319 + 10.5667i) q^{81} +(9.75329 + 3.54991i) q^{82} +(0.809339 + 1.40182i) q^{83} +(2.13853 - 3.70404i) q^{84} +(7.52481 - 6.31406i) q^{86} +(-10.8646 + 18.8180i) q^{87} +(3.33120 + 5.76980i) q^{88} +(11.5122 + 4.19008i) q^{89} +(-1.94252 - 11.0166i) q^{91} +(0.599304 - 0.218129i) q^{92} +(-2.71965 - 2.28205i) q^{93} -14.3068 q^{94} +5.91406 q^{96} +(8.87934 + 7.45065i) q^{97} +(-13.4399 + 4.89173i) q^{98} +(1.06700 + 6.05125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Introduction

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