LMFDB - Embedded newform 755.2.h.d.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(321,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.321"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 14 x^{14} - 22 x^{13} + 54 x^{12} - 181 x^{11} + 697 x^{10} - 1743 x^{9} + 3507 x^{8} + \cdots + 16 $ x^16 - 5x^15 + 14x^14 - 22x^13 + 54x^12 - 181x^11 + 697x^10 - 1743x^9 + 3507x^8 - 5479x^7 + 7616x^6 - 7799x^5 + 6803x^4 - 3330x^3 + 948x^2 - 136*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.3
Root			$-2.13654 + 1.55228i$ of defining polynomial
Character	$\chi$	$=$	755.361
Dual form			755.2.h.d.366.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.40610 q^{2} +(-1.06077 - 0.770696i) q^{3} -0.0228706 q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.49156 - 1.08368i) q^{6} +(1.62510 + 5.00155i) q^{7} -2.84437 q^{8} +(-0.395787 - 1.21811i) q^{9} +(-0.434510 - 1.33728i) q^{10} +(-0.993622 + 0.721909i) q^{11} +(0.0242605 + 0.0176263i) q^{12} +(3.92067 + 2.84854i) q^{13} +(2.28506 + 7.03270i) q^{14} +(-0.405179 + 1.24701i) q^{15} -3.95374 q^{16} +(-1.97896 + 6.09062i) q^{17} +(-0.556517 - 1.71278i) q^{18} -1.39043 q^{19} +(0.00706741 + 0.0217513i) q^{20} +(2.13081 - 6.55796i) q^{21} +(-1.39714 + 1.01508i) q^{22} +7.39532 q^{23} +(3.01722 + 2.19214i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(5.51288 + 4.00534i) q^{26} +(-1.73449 + 5.33820i) q^{27} +(-0.0371671 - 0.114389i) q^{28} +(-2.02051 + 1.46799i) q^{29} +(-0.569723 + 1.75343i) q^{30} +(1.30724 - 4.02328i) q^{31} +0.129369 q^{32} +1.61038 q^{33} +(-2.78263 + 8.56404i) q^{34} +(4.25457 - 3.09113i) q^{35} +(0.00905189 + 0.0278588i) q^{36} +(5.91595 + 4.29819i) q^{37} -1.95509 q^{38} +(-1.96358 - 6.04329i) q^{39} +(0.878958 + 2.70515i) q^{40} +(4.73550 + 3.44054i) q^{41} +(2.99614 - 9.22117i) q^{42} +(-1.04723 + 3.22304i) q^{43} +(0.0227248 - 0.0165105i) q^{44} +(-1.03618 + 0.752831i) q^{45} +10.3986 q^{46} +(-6.03524 - 4.38486i) q^{47} +(4.19401 + 3.04713i) q^{48} +(-16.7114 + 12.1415i) q^{49} +(-1.13756 + 0.826487i) q^{50} +(6.79324 - 4.93558i) q^{51} +(-0.0896682 - 0.0651478i) q^{52} +(-6.10190 + 4.43329i) q^{53} +(-2.43887 + 7.50606i) q^{54} +(0.993622 + 0.721909i) q^{55} +(-4.62239 - 14.2262i) q^{56} +(1.47493 + 1.07160i) q^{57} +(-2.84105 + 2.06415i) q^{58} +2.83242 q^{59} +(0.00926669 - 0.0285199i) q^{60} +(-8.32476 + 6.04829i) q^{61} +(1.83812 - 5.65715i) q^{62} +(5.44922 - 3.95909i) q^{63} +8.08938 q^{64} +(1.49756 - 4.60903i) q^{65} +2.26436 q^{66} +(2.03629 - 6.26705i) q^{67} +(0.0452601 - 0.139296i) q^{68} +(-7.84474 - 5.69954i) q^{69} +(5.98237 - 4.34645i) q^{70} +(-3.50336 - 10.7822i) q^{71} +(1.12576 + 3.46474i) q^{72} +(-1.04071 - 3.20296i) q^{73} +(8.31845 + 6.04371i) q^{74} +1.31119 q^{75} +0.0318001 q^{76} +(-5.22540 - 3.79647i) q^{77} +(-2.76100 - 8.49750i) q^{78} +(1.99600 + 6.14307i) q^{79} +(1.22177 + 3.76023i) q^{80} +(2.84547 - 2.06735i) q^{81} +(6.65861 + 4.83776i) q^{82} +(3.00648 - 9.25300i) q^{83} +(-0.0487329 + 0.149985i) q^{84} +6.40405 q^{85} +(-1.47251 + 4.53192i) q^{86} +3.27468 q^{87} +(2.82623 - 2.05337i) q^{88} +(1.43761 - 4.42451i) q^{89} +(-1.45698 + 1.05856i) q^{90} +(-7.87560 + 24.2386i) q^{91} -0.169136 q^{92} +(-4.48741 + 3.26029i) q^{93} +(-8.48617 - 6.16557i) q^{94} +(0.429667 + 1.32238i) q^{95} +(-0.137231 - 0.0997044i) q^{96} +(-2.17458 + 6.69267i) q^{97} +(-23.4980 + 17.0723i) q^{98} +(1.27262 + 0.924615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	1.40610			0.994266			0.497133	−	0.867674i	$-0.334386\pi$
$2$	1.40610			0.994266			0.497133	+	0.867674i	$0.334386\pi$
$3$	−1.06077	−	0.770696i	−0.612437	−	0.444961i	0.237835	−	0.971306i	$-0.423562\pi$
$3$	−1.06077	−	0.770696i	−0.612437	−	0.444961i	−0.850272	+	0.526344i	$0.823562\pi$
$4$	−0.0228706			−0.0114353
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−1.49156	−	1.08368i	−0.608925	−	0.442410i
$7$	1.62510	+	5.00155i	0.614231	+	1.89041i	0.412465	+	0.910974i	$0.364668\pi$
$7$	1.62510	+	5.00155i	0.614231	+	1.89041i	0.201766	+	0.979434i	$0.435332\pi$
$8$	−2.84437			−1.00564
$9$	−0.395787	−	1.21811i	−0.131929	−	0.406035i
$10$	−0.434510	−	1.33728i	−0.137404	−	0.422887i
$11$	−0.993622	+	0.721909i	−0.299588	+	0.217664i	−0.727416	−	0.686197i	$-0.759279\pi$
$11$	−0.993622	+	0.721909i	−0.299588	+	0.217664i	0.427828	+	0.903860i	$0.359279\pi$
$12$	0.0242605	+	0.0176263i	0.00700340	+	0.00508827i
$13$	3.92067	+	2.84854i	1.08740	+	0.790042i	0.978958	−	0.204061i	$-0.0654142\pi$
$13$	3.92067	+	2.84854i	1.08740	+	0.790042i	0.108441	+	0.994103i	$0.465414\pi$
$14$	2.28506	+	7.03270i	0.610709	+	1.87957i
$15$	−0.405179	+	1.24701i	−0.104617	+	0.321977i
$16$	−3.95374			−0.988434
$17$	−1.97896	+	6.09062i	−0.479969	+	1.47719i	0.359169	+	0.933272i	$0.383060\pi$
$17$	−1.97896	+	6.09062i	−0.479969	+	1.47719i	−0.839138	+	0.543919i	$0.816940\pi$
$18$	−0.556517	−	1.71278i	−0.131172	−	0.403707i
$19$	−1.39043			−0.318987			−0.159494	−	0.987199i	$-0.550986\pi$
$19$	−1.39043			−0.318987			−0.159494	+	0.987199i	$0.550986\pi$
$20$	0.00706741	+	0.0217513i	0.00158032	+	0.00486373i
$21$	2.13081	−	6.55796i	0.464981	−	1.43106i
$22$	−1.39714	+	1.01508i	−0.297870	+	0.216416i
$23$	7.39532			1.54203			0.771015	−	0.636817i	$-0.219749\pi$
$23$	7.39532			1.54203			0.771015	+	0.636817i	$0.219749\pi$
$24$	3.01722	+	2.19214i	0.615888	+	0.447469i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	5.51288	+	4.00534i	1.08116	+	0.785512i
$27$	−1.73449	+	5.33820i	−0.333802	+	1.02734i
$28$	−0.0371671	−	0.114389i	−0.00702392	−	0.0216174i
$29$	−2.02051	+	1.46799i	−0.375200	+	0.272599i	−0.759364	−	0.650666i	$-0.774490\pi$
$29$	−2.02051	+	1.46799i	−0.375200	+	0.272599i	0.384164	+	0.923265i	$0.374490\pi$
$30$	−0.569723	+	1.75343i	−0.104017	+	0.320131i
$31$	1.30724	−	4.02328i	0.234788	−	0.722603i	−0.762362	−	0.647151i	$-0.775960\pi$
$31$	1.30724	−	4.02328i	0.234788	−	0.722603i	0.997149	−	0.0754514i	$-0.0240398\pi$
$32$	0.129369			0.0228695
$33$	1.61038			0.280331
$34$	−2.78263	+	8.56404i	−0.477216	+	1.46872i
$35$	4.25457	−	3.09113i	0.719154	−	0.522496i
$36$	0.00905189	+	0.0278588i	0.00150865	+	0.00464314i
$37$	5.91595	+	4.29819i	0.972577	+	0.706619i	0.956037	−	0.293245i	$-0.0947351\pi$
$37$	5.91595	+	4.29819i	0.972577	+	0.706619i	0.0165395	+	0.999863i	$0.494735\pi$
$38$	−1.95509			−0.317158
$39$	−1.96358	−	6.04329i	−0.314425	−	0.967701i
$40$	0.878958	+	2.70515i	0.138975	+	0.427722i
$41$	4.73550	+	3.44054i	0.739561	+	0.537323i	0.892574	−	0.450902i	$-0.148898\pi$
$41$	4.73550	+	3.44054i	0.739561	+	0.537323i	−0.153013	+	0.988224i	$0.548898\pi$
$42$	2.99614	−	9.22117i	0.462315	−	1.42286i
$43$	−1.04723	+	3.22304i	−0.159701	+	0.491508i	−0.998607	−	0.0527679i	$-0.983196\pi$
$43$	−1.04723	+	3.22304i	−0.159701	+	0.491508i	0.838906	+	0.544276i	$0.183196\pi$
$44$	0.0227248	−	0.0165105i	0.00342589	−	0.00248905i
$45$	−1.03618	+	0.752831i	−0.154465	+	0.112225i
$46$	10.3986			1.53319
$47$	−6.03524	−	4.38486i	−0.880330	−	0.639597i	0.0530089	−	0.998594i	$-0.483119\pi$
$47$	−6.03524	−	4.38486i	−0.880330	−	0.639597i	−0.933339	+	0.358997i	$0.883119\pi$
$48$	4.19401	+	3.04713i	0.605353	+	0.439815i
$49$	−16.7114	+	12.1415i	−2.38734	+	1.73451i
$50$	−1.13756	+	0.826487i	−0.160876	+	0.116883i
$51$	6.79324	−	4.93558i	0.951243	−	0.691119i
$52$	−0.0896682	−	0.0651478i	−0.0124347	−	0.00903437i
$53$	−6.10190	+	4.43329i	−0.838161	+	0.608959i	−0.921856	−	0.387532i	$-0.873328\pi$
$53$	−6.10190	+	4.43329i	−0.838161	+	0.608959i	0.0836956	+	0.996491i	$0.473328\pi$
$54$	−2.43887	+	7.50606i	−0.331888	+	1.02145i
$55$	0.993622	+	0.721909i	0.133980	+	0.0973422i
$56$	−4.62239	−	14.2262i	−0.617692	−	1.90106i
$57$	1.47493	+	1.07160i	0.195359	+	0.141937i
$58$	−2.84105	+	2.06415i	−0.373049	+	0.271036i
$59$	2.83242			0.368750			0.184375	−	0.982856i	$-0.440974\pi$
$59$	2.83242			0.368750			0.184375	+	0.982856i	$0.440974\pi$
$60$	0.00926669	−	0.0285199i	0.00119632	−	0.00368191i
$61$	−8.32476	+	6.04829i	−1.06588	+	0.774404i	−0.975166	−	0.221473i	$-0.928913\pi$
$61$	−8.32476	+	6.04829i	−1.06588	+	0.774404i	−0.0907095	+	0.995877i	$0.528913\pi$
$62$	1.83812	−	5.65715i	0.233442	−	0.718459i
$63$	5.44922	−	3.95909i	0.686537	−	0.498799i
$64$	8.08938			1.01117
$65$	1.49756	−	4.60903i	0.185750	−	0.571680i
$66$	2.26436			0.278723
$67$	2.03629	−	6.26705i	0.248772	−	0.765642i	−0.746221	−	0.665698i	$-0.768134\pi$
$67$	2.03629	−	6.26705i	0.248772	−	0.765642i	0.994993	−	0.0999435i	$-0.0318662\pi$
$68$	0.0452601	−	0.139296i	0.00548859	−	0.0168921i
$69$	−7.84474	−	5.69954i	−0.944396	−	0.686144i
$70$	5.98237	−	4.34645i	0.715030	−	0.519500i
$71$	−3.50336	−	10.7822i	−0.415772	−	1.27961i	−0.911559	−	0.411170i	$-0.865120\pi$
$71$	−3.50336	−	10.7822i	−0.415772	−	1.27961i	0.495787	−	0.868444i	$-0.334880\pi$
$72$	1.12576	+	3.46474i	0.132672	+	0.408324i
$73$	−1.04071	−	3.20296i	−0.121805	−	0.374879i	0.871500	−	0.490395i	$-0.163148\pi$
$73$	−1.04071	−	3.20296i	−0.121805	−	0.374879i	−0.993306	+	0.115517i	$0.963148\pi$
$74$	8.31845	+	6.04371i	0.967000	+	0.702567i
$75$	1.31119			0.151403
$76$	0.0318001			0.00364772
$77$	−5.22540	−	3.79647i	−0.595489	−	0.432648i
$78$	−2.76100	−	8.49750i	−0.312622	−	0.962152i
$79$	1.99600	+	6.14307i	0.224568	+	0.691149i	0.998335	+	0.0576790i	$0.0183700\pi$
$79$	1.99600	+	6.14307i	0.224568	+	0.691149i	−0.773767	+	0.633470i	$0.781630\pi$
$80$	1.22177	+	3.76023i	0.136598	+	0.420406i
$81$	2.84547	−	2.06735i	0.316163	−	0.229706i
$82$	6.65861	+	4.83776i	0.735320	+	0.534241i
$83$	3.00648	−	9.25300i	0.330004	−	1.01565i	−0.639127	−	0.769102i	$-0.720704\pi$
$83$	3.00648	−	9.25300i	0.330004	−	1.01565i	0.969131	−	0.246547i	$-0.0792960\pi$
$84$	−0.0487329	+	0.149985i	−0.00531720	+	0.0163647i
$85$	6.40405			0.694617
$86$	−1.47251	+	4.53192i	−0.158785	+	0.488690i
$87$	3.27468			0.351082
$88$	2.82623	−	2.05337i	0.301277	−	0.218890i
$89$	1.43761	−	4.42451i	0.152387	−	0.468997i	−0.845500	−	0.533975i	$-0.820698\pi$
$89$	1.43761	−	4.42451i	0.152387	−	0.468997i	0.997887	+	0.0649776i	$0.0206976\pi$
$90$	−1.45698	+	1.05856i	−0.153579	+	0.111582i
$91$	−7.87560	+	24.2386i	−0.825587	+	2.54090i
$92$	−0.169136			−0.0176336
$93$	−4.48741	+	3.26029i	−0.465323	+	0.338077i
$94$	−8.48617	−	6.16557i	−0.875282	−	0.635930i
$95$	0.429667	+	1.32238i	0.0440830	+	0.135673i
$96$	−0.137231	−	0.0997044i	−0.0140061	−	0.0101760i
$97$	−2.17458	+	6.69267i	−0.220795	+	0.679537i	0.777896	+	0.628393i	$0.216287\pi$
$97$	−2.17458	+	6.69267i	−0.220795	+	0.679537i	−0.998691	+	0.0511445i	$0.983713\pi$
$98$	−23.4980	+	17.0723i	−2.37365	+	1.72456i
$99$	1.27262	+	0.924615i	0.127903	+	0.0929273i
$100$	0.0185027	−	0.0134430i	0.00185027	−	0.00134430i
$101$	11.6656	−	8.47553i	1.16077	−	0.843347i	0.170893	−	0.985290i	$-0.445335\pi$
$101$	11.6656	−	8.47553i	1.16077	−	0.843347i	0.989875	+	0.141943i	$0.0453348\pi$
$102$	9.55200	−	6.93993i	0.945789	−	0.687156i
$103$	−2.99052	−	2.17274i	−0.294665	−	0.214086i	0.430624	−	0.902532i	$-0.358294\pi$
$103$	−2.99052	−	2.17274i	−0.294665	−	0.214086i	−0.725288	+	0.688445i	$0.758294\pi$
$104$	−11.1518	−	8.10228i	−1.09353	−	0.794494i
$105$	−6.89544			−0.672926
$106$	−8.57991	+	6.23367i	−0.833355	+	0.605468i
$107$	0.904274	−	0.656993i	0.0874194	−	0.0635139i	−0.543217	−	0.839592i	$-0.682794\pi$
$107$	0.904274	−	0.656993i	0.0874194	−	0.0635139i	0.630636	+	0.776078i	$0.282794\pi$
$108$	0.0396688	−	0.122088i	0.00381713	−	0.0117479i
$109$	−0.0777573	+	0.239312i	−0.00744780	+	0.0229220i	−0.954711	−	0.297534i	$-0.903836\pi$
$109$	−0.0777573	+	0.239312i	−0.00744780	+	0.0229220i	0.947264	+	0.320456i	$0.103836\pi$
$110$	1.39714	+	1.01508i	0.133212	+	0.0967840i
$111$	−2.96288	−	9.11880i	−0.281224	−	0.865518i
$112$	−6.42522	−	19.7748i	−0.607126	−	1.86854i
$113$	−11.3063			−1.06360			−0.531802	−	0.846869i	$-0.678485\pi$
$113$	−11.3063			−1.06360			−0.531802	+	0.846869i	$0.678485\pi$
$114$	2.07391	+	1.50678i	0.194239	+	0.141123i
$115$	−2.28528	−	7.03336i	−0.213103	−	0.655865i
$116$	0.0462104	−	0.0335738i	0.00429053	−	0.00311725i
$117$	1.91807	−	5.90321i	0.177325	−	0.545752i
$118$	3.98268			0.366636
$119$	−33.6785			−3.08731
$120$	1.15248	−	3.54696i	0.105206	−	0.323792i
$121$	−2.93305	+	9.02701i	−0.266641	+	0.820638i
$122$	−11.7055	+	8.50453i	−1.05976	+	0.769964i
$123$	−2.37167	−	7.29926i	−0.213847	−	0.658152i
$124$	−0.0298975	+	0.0920149i	−0.00268487	+	0.00826319i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	7.66217	−	5.56689i	0.682601	−	0.495938i
$127$	−8.71069	−	6.32869i	−0.772949	−	0.561580i	0.129906	−	0.991526i	$-0.458533\pi$
$127$	−8.71069	−	6.32869i	−0.772949	−	0.561580i	−0.902855	+	0.429946i	$0.858533\pi$
$128$	11.1158			0.982505
$129$	3.59485	−	2.61181i	0.316509	−	0.229957i
$130$	2.10573	−	6.48077i	0.184685	−	0.568401i
$131$	5.06610	+	15.5919i	0.442628	+	1.36227i	0.885065	+	0.465468i	$0.154114\pi$
$131$	5.06610	+	15.5919i	0.442628	+	1.36227i	−0.442437	+	0.896799i	$0.645886\pi$
$132$	−0.0368303			−0.00320567
$133$	−2.25959	−	6.95432i	−0.195932	−	0.603016i
$134$	2.86323	−	8.81212i	0.247346	−	0.761252i
$135$	5.61291			0.483083
$136$	5.62889	−	17.3239i	0.482674	−	1.48552i
$137$	−5.30841	−	16.3376i	−0.453528	−	1.39582i	−0.872855	−	0.487980i	$-0.837734\pi$
$137$	−5.30841	−	16.3376i	−0.453528	−	1.39582i	0.419327	−	0.907835i	$-0.362266\pi$
$138$	−11.0305	−	8.01415i	−0.938981	−	0.682209i
$139$	10.5918	+	7.69542i	0.898388	+	0.652717i	0.938051	−	0.346496i	$-0.112629\pi$
$139$	10.5918	+	7.69542i	0.898388	+	0.652717i	−0.0396638	+	0.999213i	$0.512629\pi$
$140$	−0.0973047	+	0.0706960i	−0.00822375	+	0.00597490i
$141$	3.02262	+	9.30266i	0.254550	+	0.783425i
$142$	−4.92609	−	15.1609i	−0.413388	−	1.27228i
$143$	−5.95205			−0.497735
$144$	1.56484	+	4.81607i	0.130403	+	0.401339i
$145$	2.02051	+	1.46799i	0.167795	+	0.121910i
$146$	−1.46334	−	4.50370i	−0.121107	−	0.372729i
$147$	27.0844			2.23389
$148$	−0.135302	−	0.0983023i	−0.0111217	−	0.00808040i
$149$	15.3805			1.26002			0.630010	−	0.776587i	$-0.283051\pi$
$149$	15.3805			1.26002			0.630010	+	0.776587i	$0.283051\pi$
$150$	1.84366			0.150535
$151$	−0.999684	−	12.2475i	−0.0813531	−	0.996685i
$151$	−0.999684	−	12.2475i	−0.0813531	−	0.996685i
$152$	3.95490			0.320785
$153$	8.20226			0.663114
$154$	−7.34745	−	5.33824i	−0.592075	−	0.430167i
$155$	−4.23033			−0.339788
$156$	0.0449084	+	0.138214i	0.00359555	+	0.0110660i
$157$	8.66088	+	6.29250i	0.691214	+	0.502196i	0.877059	−	0.480383i	$-0.159502\pi$
$157$	8.66088	+	6.29250i	0.691214	+	0.502196i	−0.185845	+	0.982579i	$0.559502\pi$
$158$	2.80659	+	8.63779i	0.223280	+	0.687186i
$159$	9.88944			0.784284
$160$	−0.0399773	−	0.123038i	−0.00316049	−	0.00972698i
$161$	12.0181	+	36.9880i	0.947162	+	2.91507i
$162$	4.00103	−	2.90692i	0.314350	−	0.228389i
$163$	3.74374	+	2.71999i	0.293232	+	0.213046i	0.724668	−	0.689098i	$-0.241993\pi$
$163$	3.74374	+	2.71999i	0.293232	+	0.213046i	−0.431436	+	0.902144i	$0.641993\pi$
$164$	−0.108304	−	0.0786874i	−0.00845711	−	0.00614445i
$165$	−0.497634	−	1.53156i	−0.0387408	−	0.119232i
$166$	4.22743	−	13.0107i	0.328112	−	1.00982i
$167$	−20.3575			−1.57531			−0.787657	−	0.616114i	$-0.788706\pi$
$167$	−20.3575			−1.57531			−0.787657	+	0.616114i	$0.788706\pi$
$168$	−6.06080	+	18.6532i	−0.467601	+	1.43913i
$169$	3.24030	+	9.97262i	0.249254	+	0.767125i
$170$	9.00477			0.690634
$171$	0.550315	+	1.69369i	0.0420836	+	0.129520i
$172$	0.0239507	−	0.0737128i	0.00182623	−	0.00562055i
$173$	15.6388	−	11.3622i	1.18899	−	0.863853i	0.195835	−	0.980637i	$-0.437258\pi$
$173$	15.6388	−	11.3622i	1.18899	−	0.863853i	0.993157	+	0.116783i	$0.0372584\pi$
$174$	4.60454			0.349069
$175$	−4.25457	−	3.09113i	−0.321615	−	0.233667i
$176$	3.92852	−	2.85424i	0.296123	−	0.215146i
$177$	−3.00455	−	2.18294i	−0.225836	−	0.164080i
$178$	2.02143	−	6.22133i	0.151513	−	0.466308i
$179$	−4.13868	−	12.7375i	−0.309339	−	0.952049i	−0.978022	−	0.208501i	$-0.933142\pi$
$179$	−4.13868	−	12.7375i	−0.309339	−	0.952049i	0.668683	−	0.743548i	$-0.266858\pi$
$180$	0.0236981	−	0.0172177i	0.00176636	−	0.00128333i
$181$	2.54341	−	7.82782i	0.189050	−	0.581837i	−0.810944	−	0.585123i	$-0.801046\pi$
$181$	2.54341	−	7.82782i	0.189050	−	0.581837i	0.999995	+	0.00328638i	$0.00104609\pi$
$182$	−11.0739	+	34.0820i	−0.820853	+	2.52633i
$183$	13.4921			0.997361
$184$	−21.0350			−1.55072
$185$	2.25969	−	6.95462i	0.166136	−	0.511314i
$186$	−6.30977	+	4.58431i	−0.462655	+	0.336138i
$187$	−2.43053	−	7.48040i	−0.177738	−	0.547021i
$188$	0.138030	+	0.100284i	0.0100668	+	0.00731399i
$189$	−29.5180			−2.14712
$190$	0.604157	+	1.85940i	0.0438302	+	0.134895i
$191$	1.41810	+	4.36447i	0.102610	+	0.315802i	0.989162	−	0.146827i	$-0.0469061\pi$
$191$	1.41810	+	4.36447i	0.102610	+	0.315802i	−0.886552	+	0.462629i	$0.846906\pi$
$192$	−8.58098	−	6.23445i	−0.619279	−	0.449933i
$193$	−6.06476	+	18.6654i	−0.436551	+	1.34357i	0.454938	+	0.890523i	$0.349661\pi$
$193$	−6.06476	+	18.6654i	−0.436551	+	1.34357i	−0.891489	+	0.453042i	$0.850339\pi$
$194$	−3.05768	+	9.41059i	−0.219529	+	0.675641i
$195$	−5.14073	+	3.73496i	−0.368135	+	0.267466i
$196$	0.382200	−	0.277685i	0.0273000	−	0.0198346i
$197$	11.8283			0.842730			0.421365	−	0.906891i	$-0.361551\pi$
$197$	11.8283			0.842730			0.421365	+	0.906891i	$0.361551\pi$
$198$	1.78944	+	1.30011i	0.127170	+	0.0923945i
$199$	13.5068	+	9.81324i	0.957469	+	0.695642i	0.952562	−	0.304346i	$-0.0984379\pi$
$199$	13.5068	+	9.81324i	0.957469	+	0.695642i	0.00490743	+	0.999988i	$0.498438\pi$
$200$	2.30114	−	1.67188i	0.162715	−	0.118220i
$201$	−6.99002	+	5.07855i	−0.493038	+	0.358213i
$202$	16.4030	−	11.9175i	1.15411	−	0.838511i
$203$	−10.6258	−	7.72007i	−0.745782	−	0.541842i
$204$	−0.155366	+	0.112880i	−0.0108778	+	0.00790316i
$205$	1.80880	−	5.56692i	0.126332	−	0.388810i
$206$	−4.20498	−	3.05510i	−0.292975	−	0.212859i
$207$	−2.92697	−	9.00828i	−0.203438	−	0.626119i
$208$	−15.5013	−	11.2624i	−1.07482	−	0.780904i
$209$	1.38157	−	1.00377i	0.0955649	−	0.0694319i
$210$	−9.69571			−0.669068
$211$	5.23923	−	16.1247i	0.360684	−	1.11007i	−0.591956	−	0.805970i	$-0.701644\pi$
$211$	5.23923	−	16.1247i	0.360684	−	1.11007i	0.952640	−	0.304100i	$-0.0983557\pi$
$212$	0.139554	−	0.101392i	0.00958463	−	0.00696364i
$213$	−4.59355	+	14.1375i	−0.314745	+	0.968685i
$214$	1.27150	−	0.923801i	0.0869182	−	0.0631497i
$215$	3.38890			0.231121
$216$	4.93351	−	15.1838i	0.335683	−	1.03313i
$217$	22.2470			1.51023
$218$	−0.109335	+	0.336498i	−0.00740510	+	0.0227905i
$219$	−1.36456	+	4.19968i	−0.0922084	+	0.283788i
$220$	−0.0227248	−	0.0165105i	−0.00153210	−	0.00111314i
$221$	−25.1082	+	18.2422i	−1.68896	+	1.22710i
$222$	−4.16612	−	12.8220i	−0.279611	−	0.860555i
$223$	4.15614	+	12.7913i	0.278316	+	0.856568i	0.988323	+	0.152374i	$0.0486917\pi$
$223$	4.15614	+	12.7913i	0.278316	+	0.856568i	−0.710007	+	0.704195i	$0.751308\pi$
$224$	0.210238	+	0.647047i	0.0140471	+	0.0432327i
$225$	1.03618	+	0.752831i	0.0690788	+	0.0501887i
$226$	−15.8978			−1.05750
$227$	23.5399			1.56240			0.781200	−	0.624281i	$-0.214608\pi$
$227$	23.5399			1.56240			0.781200	+	0.624281i	$0.214608\pi$
$228$	−0.0337326	−	0.0245082i	−0.00223400	−	0.00162309i
$229$	0.594987	+	1.83118i	0.0393178	+	0.121008i	0.968789	−	0.247887i	$-0.0797362\pi$
$229$	0.594987	+	1.83118i	0.0393178	+	0.121008i	−0.929471	+	0.368895i	$0.879736\pi$
$230$	−3.21334	−	9.88964i	−0.211881	−	0.652104i
$231$	2.61703	+	8.05438i	0.172188	+	0.529939i
$232$	5.74708	−	4.17550i	0.377314	−	0.274135i
$233$	16.8624	+	12.2512i	1.10469	+	0.802604i	0.981819	−	0.189819i	$-0.0607900\pi$
$233$	16.8624	+	12.2512i	1.10469	+	0.802604i	0.122871	+	0.992423i	$0.460790\pi$
$234$	2.69700	−	8.30052i	0.176309	−	0.542622i
$235$	−2.30526	+	7.09485i	−0.150378	+	0.462817i
$236$	−0.0647793			−0.00421677
$237$	2.61713	−	8.05470i	0.170001	−	0.523209i
$238$	−47.3555			−3.06960
$239$	−3.44970	+	2.50635i	−0.223142	+	0.162122i	−0.693740	−	0.720225i	$-0.744038\pi$
$239$	−3.44970	+	2.50635i	−0.223142	+	0.162122i	0.470598	+	0.882348i	$0.344038\pi$
$240$	1.60197	−	4.93035i	0.103407	−	0.318253i
$241$	−12.5347	+	9.10701i	−0.807432	+	0.586634i	−0.913085	−	0.407769i	$-0.866307\pi$
$241$	−12.5347	+	9.10701i	−0.807432	+	0.586634i	0.105653	+	0.994403i	$0.466307\pi$
$242$	−4.12418	+	12.6929i	−0.265112	+	0.815932i
$243$	12.2270			0.784365
$244$	0.190392	−	0.138328i	0.0121886	−	0.00885555i
$245$	16.7114	+	12.1415i	1.06765	+	0.775695i
$246$	−3.33482	−	10.2635i	−0.212620	−	0.654378i
$247$	−5.45143	−	3.96070i	−0.346866	−	0.252013i
$248$	−3.71828	+	11.4437i	−0.236111	+	0.726675i
$249$	−10.3204	+	7.49824i	−0.654031	+	0.475181i
$250$	1.13756	+	0.826487i	0.0719458	+	0.0522717i
$251$	10.2479	−	7.44551i	0.646840	−	0.469957i	−0.215353	−	0.976536i	$-0.569090\pi$
$251$	10.2479	−	7.44551i	0.646840	−	0.469957i	0.862193	+	0.506580i	$0.169090\pi$
$252$	−0.124627	+	0.0905469i	−0.00785077	+	0.00570392i
$253$	−7.34815	+	5.33874i	−0.461974	+	0.335644i
$254$	−12.2481	−	8.89880i	−0.768517	−	0.558360i
$255$	−6.79324	−	4.93558i	−0.425409	−	0.309078i
$256$	−0.548823			−0.0343014
$257$	5.84957	−	4.24996i	0.364886	−	0.265105i	−0.390201	−	0.920730i	$-0.627594\pi$
$257$	5.84957	−	4.24996i	0.364886	−	0.265105i	0.755087	+	0.655624i	$0.227594\pi$
$258$	5.05473	−	3.67248i	0.314694	−	0.228638i
$259$	−11.8836	+	36.5739i	−0.738410	+	2.27259i
$260$	−0.0342502	+	0.105411i	−0.00212411	+	0.00653733i
$261$	2.58786	+	1.88019i	0.160184	+	0.116381i
$262$	7.12347	+	21.9238i	0.440089	+	1.35446i
$263$	2.90230	+	8.93236i	0.178963	+	0.550793i	0.999792	−	0.0203814i	$-0.00648806\pi$
$263$	2.90230	+	8.93236i	0.178963	+	0.550793i	−0.820829	+	0.571174i	$0.806488\pi$
$264$	−4.58051			−0.281911
$265$	6.10190	+	4.43329i	0.374837	+	0.272335i
$266$	−3.17723	−	9.77850i	−0.194808	−	0.599558i
$267$	−4.93493	+	3.58544i	−0.302013	+	0.219425i
$268$	−0.0465712	+	0.143331i	−0.00284479	+	0.00875535i
$269$	10.3824			0.633026			0.316513	−	0.948588i	$-0.397488\pi$
$269$	10.3824			0.633026			0.316513	+	0.948588i	$0.397488\pi$
$270$	7.89234			0.480313
$271$	4.00957	−	12.3402i	0.243564	−	0.749612i	−0.752306	−	0.658814i	$-0.771058\pi$
$271$	4.00957	−	12.3402i	0.243564	−	0.749612i	0.995869	−	0.0907978i	$-0.0289417\pi$
$272$	7.82429	−	24.0807i	0.474417	−	1.46011i
$273$	27.0348	−	19.6419i	1.63622	−	1.18878i
$274$	−7.46417	−	22.9724i	−0.450927	−	1.38781i
$275$	0.379530	−	1.16807i	0.0228865	−	0.0704374i
$276$	0.179414	+	0.130352i	0.0107995	+	0.00784627i
$277$	8.14480	−	5.91754i	0.489374	−	0.355551i	−0.315570	−	0.948902i	$-0.602196\pi$
$277$	8.14480	−	5.91754i	0.489374	−	0.355551i	0.804943	+	0.593352i	$0.202196\pi$
$278$	14.8932	+	10.8206i	0.893236	+	0.648974i
$279$	−5.41817			−0.324377
$280$	−12.1016	+	8.79230i	−0.723207	+	0.525440i
$281$	0.129817	−	0.399536i	0.00774423	−	0.0238343i	−0.947110	−	0.320910i	$-0.896011\pi$
$281$	0.129817	−	0.399536i	0.00774423	−	0.0238343i	0.954854	+	0.297076i	$0.0960113\pi$
$282$	4.25012	+	13.0805i	0.253091	+	0.778933i
$283$	16.8759			1.00317			0.501585	−	0.865109i	$-0.332751\pi$
$283$	16.8759			1.00317			0.501585	+	0.865109i	$0.332751\pi$
$284$	0.0801240	+	0.246596i	0.00475448	+	0.0146328i
$285$	0.563374	−	1.73389i	0.0333714	−	0.102707i
$286$	−8.36920			−0.494881
$287$	−9.51237	+	29.2761i	−0.561497	+	1.72811i
$288$	−0.0512027	−	0.157586i	−0.00301715	−	0.00928582i
$289$	−19.4260	−	14.1138i	−1.14271	−	0.830226i
$290$	2.84105	+	2.06415i	0.166832	+	0.121211i
$291$	7.46474	−	5.42345i	0.437591	−	0.317928i
$292$	0.0238016	+	0.0732538i	0.00139288	+	0.00428685i
$293$	7.11582	+	21.9002i	0.415711	+	1.27943i	0.911614	+	0.411048i	$0.134837\pi$
$293$	7.11582	+	21.9002i	0.415711	+	1.27943i	−0.495903	+	0.868378i	$0.665163\pi$
$294$	38.0835			2.22108
$295$	−0.875267	−	2.69380i	−0.0509600	−	0.156839i
$296$	−16.8271	−	12.2256i	−0.978058	−	0.710601i
$297$	−2.13027	−	6.55629i	−0.123611	−	0.380435i
$298$	21.6266			1.25279
$299$	28.9946	+	21.0658i	1.67680	+	1.21827i
$300$	−0.0299876			−0.00173134
$301$	−17.8220			−1.02724
$302$	−1.40566	−	17.2212i	−0.0808866	−	0.990970i
$303$	−18.9066			−1.08615
$304$	5.49741			0.315298
$305$	8.32476	+	6.04829i	0.476674	+	0.346324i
$306$	11.5332			0.659311
$307$	0.503138	+	1.54850i	0.0287156	+	0.0883775i	0.964387	−	0.264494i	$-0.0852051\pi$
$307$	0.503138	+	1.54850i	0.0287156	+	0.0883775i	−0.935672	+	0.352872i	$0.885205\pi$
$308$	0.119508	+	0.0868277i	0.00680961	+	0.00494747i
$309$	1.49774	+	4.60956i	0.0852033	+	0.262229i
$310$	−5.94828			−0.337840
$311$	−8.95402	−	27.5576i	−0.507736	−	1.56265i	−0.796122	−	0.605136i	$-0.793119\pi$
$311$	−8.95402	−	27.5576i	−0.507736	−	1.56265i	0.288387	−	0.957514i	$-0.406881\pi$
$312$	5.58515	+	17.1893i	0.316197	+	0.973155i
$313$	8.33829	−	6.05812i	0.471308	−	0.342425i	−0.326643	−	0.945148i	$-0.605917\pi$
$313$	8.33829	−	6.05812i	0.471308	−	0.342425i	0.797951	+	0.602722i	$0.205917\pi$
$314$	12.1781	+	8.84791i	0.687250	+	0.499317i
$315$	−5.44922	−	3.95909i	−0.307029	−	0.223070i
$316$	−0.0456498	−	0.140496i	−0.00256800	−	0.00790350i
$317$	6.14200	−	18.9031i	0.344969	−	1.06171i	−0.616631	−	0.787252i	$-0.711503\pi$
$317$	6.14200	−	18.9031i	0.344969	−	1.06171i	0.961600	−	0.274454i	$-0.0884970\pi$
$318$	13.9056			0.779787
$319$	0.947873	−	2.91725i	0.0530707	−	0.163335i
$320$	−2.49976	−	7.69346i	−0.139741	−	0.430077i
$321$	−1.46557			−0.0818001
$322$	16.8988	+	52.0090i	0.941731	+	2.89835i
$323$	2.75161	−	8.46860i	0.153104	−	0.471205i
$324$	−0.0650777	+	0.0472817i	−0.00361543	+	0.00262676i
$325$	−4.84622			−0.268820
$326$	5.26409	+	3.82459i	0.291551	+	0.211824i
$327$	0.266920	−	0.193929i	0.0147607	−	0.0107243i
$328$	−13.4695	−	9.78617i	−0.743729	−	0.540351i
$329$	12.1232	−	37.3114i	0.668374	−	2.05704i
$330$	−0.699726	−	2.15353i	−0.0385186	−	0.118548i
$331$	15.9942	−	11.6204i	0.879119	−	0.638717i	−0.0538995	−	0.998546i	$-0.517165\pi$
$331$	15.9942	−	11.6204i	0.879119	−	0.638717i	0.933018	+	0.359829i	$0.117165\pi$
$332$	−0.0687601	+	0.211622i	−0.00377370	+	0.0116143i
$333$	2.89420	−	8.90743i	0.158601	−	0.488124i
$334$	−28.6248			−1.56628
$335$	−6.58956			−0.360026
$336$	−8.42466	+	25.9284i	−0.459603	+	1.41451i
$337$	−3.40658	+	2.47502i	−0.185568	+	0.134823i	−0.676691	−	0.736267i	$-0.736587\pi$
$337$	−3.40658	+	2.47502i	−0.185568	+	0.134823i	0.491123	+	0.871090i	$0.336587\pi$
$338$	4.55620	+	14.0225i	0.247825	+	0.762726i
$339$	11.9934	+	8.71369i	0.651390	+	0.473263i
$340$	−0.146465			−0.00794316
$341$	1.60554	+	4.94133i	0.0869446	+	0.267588i
$342$	0.773800	+	2.38151i	0.0418423	+	0.128777i
$343$	−58.1023	−	42.2138i	−3.13723	−	2.27933i
$344$	2.97870	−	9.16750i	0.160601	−	0.494278i
$345$	−2.99642	+	9.22205i	−0.161322	+	0.496498i
$346$	21.9897	−	15.9765i	1.18217	−	0.858900i
$347$	−17.0441	+	12.3832i	−0.914973	+	0.664767i	−0.942268	−	0.334861i	$-0.891311\pi$
$347$	−17.0441	+	12.3832i	−0.914973	+	0.664767i	0.0272949	+	0.999627i	$0.491311\pi$
$348$	−0.0748939			−0.00401473
$349$	21.6853	+	15.7553i	1.16079	+	0.843360i	0.989877	−	0.141927i	$-0.0453298\pi$
$349$	21.6853	+	15.7553i	1.16079	+	0.843360i	0.170908	+	0.985287i	$0.445330\pi$
$350$	−5.98237	−	4.34645i	−0.319771	−	0.232327i
$351$	−22.0064	+	15.9886i	−1.17461	+	0.853407i
$352$	−0.128544	+	0.0933929i	−0.00685144	+	0.00497786i
$353$	9.91944	−	7.20690i	0.527959	−	0.383584i	−0.291635	−	0.956530i	$-0.594199\pi$
$353$	9.91944	−	7.20690i	0.527959	−	0.383584i	0.819594	+	0.572945i	$0.194199\pi$
$354$	−4.22472	−	3.06944i	−0.224541	−	0.163139i
$355$	−9.17191	+	6.66378i	−0.486794	+	0.353677i
$356$	−0.0328791	+	0.101191i	−0.00174259	+	0.00536313i
$357$	35.7252	+	25.9559i	1.89078	+	1.37373i
$358$	−5.81941	−	17.9103i	−0.307566	−	0.946589i
$359$	−28.8360	−	20.9506i	−1.52191	−	1.10573i	−0.960532	−	0.278169i	$-0.910272\pi$
$359$	−28.8360	−	20.9506i	−1.52191	−	1.10573i	−0.561375	−	0.827561i	$-0.689728\pi$
$360$	2.94728	−	2.14133i	0.155336	−	0.112858i
$361$	−17.0667			−0.898247
$362$	3.57630	−	11.0067i	0.187966	−	0.578501i
$363$	10.0684	−	7.31511i	0.528453	−	0.383943i
$364$	0.180120	−	0.554352i	0.00944084	−	0.0290559i
$365$	−2.72460	+	1.97954i	−0.142612	+	0.103614i
$366$	18.9712			0.991643
$367$	0.683455	−	2.10346i	0.0356761	−	0.109800i	−0.931633	−	0.363402i	$-0.881615\pi$
$367$	0.683455	−	2.10346i	0.0356761	−	0.109800i	0.967309	+	0.253602i	$0.0816153\pi$
$368$	−29.2391			−1.52420
$369$	2.31670	−	7.13006i	0.120602	−	0.371176i
$370$	3.17736	−	9.77892i	0.165183	−	0.508382i
$371$	−32.0895	−	23.3144i	−1.66601	−	1.21042i
$372$	0.102630	−	0.0745650i	0.00532111	−	0.00386601i
$373$	8.20105	+	25.2402i	0.424634	+	1.30689i	0.903344	+	0.428917i	$0.141105\pi$
$373$	8.20105	+	25.2402i	0.424634	+	1.30689i	−0.478710	+	0.877973i	$0.658895\pi$
$374$	−3.41758	−	10.5182i	−0.176719	−	0.543884i
$375$	−0.405179	−	1.24701i	−0.0209233	−	0.0643954i
$376$	17.1664	+	12.4721i	0.885291	+	0.643202i
$377$	−12.1034			−0.623357
$378$	−41.5053			−2.13480
$379$	12.4879	+	9.07296i	0.641458	+	0.466047i	0.860351	−	0.509702i	$-0.170244\pi$
$379$	12.4879	+	9.07296i	0.641458	+	0.466047i	−0.218893	+	0.975749i	$0.570244\pi$
$380$	−0.00982676	−	0.0302437i	−0.000504102	−	0.00155147i
$381$	4.36256	+	13.4266i	0.223501	+	0.687865i
$382$	1.99400	+	6.13690i	0.102022	+	0.313991i
$383$	−5.25774	+	3.81997i	−0.268658	+	0.195192i	−0.713955	−	0.700191i	$-0.753098\pi$
$383$	−5.25774	+	3.81997i	−0.268658	+	0.195192i	0.445297	+	0.895383i	$0.353098\pi$
$384$	−11.7913	−	8.56688i	−0.601722	−	0.437177i
$385$	−1.99592	+	6.14282i	−0.101722	+	0.313067i
$386$	−8.52768	+	26.2455i	−0.434048	+	1.33586i
$387$	4.34048			0.220639
$388$	0.0497340	−	0.153065i	0.00252486	−	0.00777072i
$389$	−16.7419			−0.848848			−0.424424	−	0.905464i	$-0.639523\pi$
$389$	−16.7419			−0.848848			−0.424424	+	0.905464i	$0.639523\pi$
$390$	−7.22840	+	5.25174i	−0.366024	+	0.265932i
$391$	−14.6350	+	45.0420i	−0.740126	+	2.27787i
$392$	47.5334	−	34.5350i	2.40080	−	1.74428i
$393$	6.64260	−	20.4438i	0.335075	−	1.03125i
$394$	16.6318			0.837898
$395$	5.22560	−	3.79662i	0.262929	−	0.191029i
$396$	−0.0291057	−	0.0211465i	−0.00146262	−	0.00106265i
$397$	0.482135	+	1.48386i	0.0241977	+	0.0744728i	0.962426	−	0.271544i	$-0.0875341\pi$
$397$	0.482135	+	1.48386i	0.0241977	+	0.0744728i	−0.938228	+	0.346016i	$0.887534\pi$
$398$	18.9919	+	13.7984i	0.951979	+	0.691653i
$399$	−2.96275	+	9.11840i	−0.148323	+	0.456491i
$400$	3.19864	−	2.32395i	0.159932	−	0.116197i
$401$	22.6806	+	16.4784i	1.13262	+	0.822895i	0.986074	−	0.166310i	$-0.0531851\pi$
$401$	22.6806	+	16.4784i	1.13262	+	0.822895i	0.146544	+	0.989204i	$0.453185\pi$
$402$	−9.82870	+	7.14097i	−0.490211	+	0.356159i
$403$	16.5857	−	12.0502i	0.826194	−	0.600265i
$404$	−0.266799	+	0.193841i	−0.0132737	+	0.00964394i
$405$	−2.84547	−	2.06735i	−0.141393	−	0.102728i
$406$	−14.9409	−	10.8552i	−0.741506	−	0.538735i
$407$	−8.98113			−0.445178
$408$	−19.3225	+	14.0386i	−0.956604	+	0.695014i
$409$	−8.46905	+	6.15313i	−0.418768	+	0.304252i	−0.777142	−	0.629326i	$-0.783331\pi$
$409$	−8.46905	+	6.15313i	−0.418768	+	0.304252i	0.358374	+	0.933578i	$0.383331\pi$
$410$	2.54336	−	7.82766i	0.125608	−	0.386581i
$411$	−6.96031	+	21.4216i	−0.343327	+	1.05665i
$412$	0.0683950	+	0.0496919i	0.00336958	+	0.00244814i
$413$	4.60298	+	14.1665i	0.226498	+	0.697088i
$414$	−4.11562	−	12.6666i	−0.202272	−	0.622528i
$415$	−9.72918			−0.477587
$416$	0.507215	+	0.368513i	0.0248683	+	0.0180679i
$417$	−5.30469	−	16.3262i	−0.259772	−	0.799495i
$418$	1.94262	−	1.41140i	0.0950169	−	0.0690338i
$419$	0.989435	−	3.04517i	0.0483370	−	0.148766i	−0.923975	−	0.382453i	$-0.875079\pi$
$419$	0.989435	−	3.04517i	0.0483370	−	0.148766i	0.972312	+	0.233687i	$0.0750792\pi$
$420$	0.157703			0.00769512
$421$	−20.9899			−1.02299			−0.511494	−	0.859287i	$-0.670908\pi$
$421$	−20.9899			−1.02299			−0.511494	+	0.859287i	$0.670908\pi$
$422$	7.36691	−	22.6730i	0.358615	−	1.10370i
$423$	−2.95255	+	9.08703i	−0.143558	+	0.441826i
$424$	17.3560	−	12.6099i	0.842884	−	0.612391i
$425$	−1.97896	−	6.09062i	−0.0959937	−	0.295438i
$426$	−6.45901	+	19.8788i	−0.312940	+	0.963131i
$427$	−43.7794	−	31.8076i	−2.11863	−	1.53928i
$428$	−0.0206813	+	0.0150258i	−0.000999668	+	0.000726302i
$429$	6.31377	+	4.58722i	0.304831	+	0.221473i
$430$	4.76515			0.229796
$431$	−1.08747	+	0.790095i	−0.0523817	+	0.0380575i	−0.613668	−	0.789564i	$-0.710307\pi$
$431$	−1.08747	+	0.790095i	−0.0523817	+	0.0380575i	0.561286	+	0.827622i	$0.310307\pi$
$432$	6.85770	−	21.1058i	0.329941	−	1.01545i
$433$	8.11248	+	24.9676i	0.389861	+	1.19987i	0.932892	+	0.360156i	$0.117277\pi$
$433$	8.11248	+	24.9676i	0.389861	+	1.19987i	−0.543031	+	0.839713i	$0.682723\pi$
$434$	31.2817			1.50157
$435$	−1.01193	−	3.11440i	−0.0485184	−	0.149324i
$436$	0.00177836	−	0.00547323i	8.51679e−5	−	0.000262120i
$437$	−10.2827			−0.491888
$438$	−1.91871	+	5.90519i	−0.0916796	+	0.282161i
$439$	5.68814	+	17.5063i	0.271480	+	0.835530i	0.990129	+	0.140157i	$0.0447607\pi$
$439$	5.68814	+	17.5063i	0.271480	+	0.835530i	−0.718649	+	0.695373i	$0.755239\pi$
$440$	−2.82623	−	2.05337i	−0.134735	−	0.0978907i
$441$	21.4038	+	15.5508i	1.01923	+	0.740514i
$442$	−35.3047	+	25.6504i	−1.67928	+	1.22007i
$443$	1.57132	+	4.83602i	0.0746556	+	0.229766i	0.981420	−	0.191871i	$-0.0614555\pi$
$443$	1.57132	+	4.83602i	0.0746556	+	0.229766i	−0.906765	+	0.421637i	$0.861456\pi$
$444$	0.0677629	+	0.208553i	0.00321588	+	0.00989747i
$445$	−4.65221			−0.220536
$446$	5.84397	+	17.9859i	0.276720	+	0.851657i
$447$	−16.3152	−	11.8537i	−0.771682	−	0.560660i
$448$	13.1461	+	40.4594i	0.621093	+	1.91153i
$449$	−8.56071			−0.404005			−0.202002	−	0.979385i	$-0.564745\pi$
$449$	−8.56071			−0.404005			−0.202002	+	0.979385i	$0.564745\pi$
$450$	1.45698	+	1.05856i	0.0686827	+	0.0499009i
$451$	−7.18906			−0.338519
$452$	0.258581			0.0121626
$453$	−8.37864	+	13.7622i	−0.393663	+	0.646606i
$454$	33.0996			1.55344
$455$	25.4860			1.19480
$456$	−4.19525	−	3.04803i	−0.196460	−	0.142737i
$457$	−13.5004			−0.631520			−0.315760	−	0.948839i	$-0.602260\pi$
$457$	−13.5004			−0.631520			−0.315760	+	0.948839i	$0.602260\pi$
$458$	0.836613	+	2.57483i	0.0390924	+	0.120314i
$459$	−29.0804	−	21.1282i	−1.35736	−	0.986179i
$460$	0.0522657	+	0.160857i	0.00243690	+	0.00750002i
$461$	−20.4860			−0.954126			−0.477063	−	0.878869i	$-0.658299\pi$
$461$	−20.4860			−0.954126			−0.477063	+	0.878869i	$0.658299\pi$
$462$	3.67981	+	11.3253i	0.171200	+	0.526901i
$463$	−11.5378	−	35.5098i	−0.536209	−	1.65028i	−0.741021	−	0.671481i	$-0.765658\pi$
$463$	−11.5378	−	35.5098i	−0.536209	−	1.65028i	0.204812	−	0.978801i	$-0.434342\pi$
$464$	7.98858	−	5.80404i	0.370860	−	0.269446i
$465$	4.48741	+	3.26029i	0.208099	+	0.151193i
$466$	23.7102	+	17.2265i	1.09836	+	0.798002i
$467$	−4.59885	−	14.1538i	−0.212809	−	0.654960i	−0.999302	−	0.0373602i	$-0.988105\pi$
$467$	−4.59885	−	14.1538i	−0.212809	−	0.654960i	0.786492	−	0.617600i	$-0.211895\pi$
$468$	−0.0438674	+	0.135010i	−0.00202777	+	0.00624084i
$469$	34.6541			1.60018
$470$	−3.24143	+	9.97610i	−0.149516	+	0.460163i
$471$	−4.33762	−	13.3498i	−0.199867	−	0.615127i
$472$	−8.05645			−0.370828
$473$	−1.28619	−	3.95848i	−0.0591390	−	0.182011i
$474$	3.67996	−	11.3257i	0.169026	−	0.520209i
$475$	1.12488	−	0.817276i	0.0516132	−	0.0374992i
$476$	0.770249			0.0353043
$477$	7.81527	+	5.67813i	0.357837	+	0.259983i
$478$	−4.85063	+	3.52419i	−0.221863	+	0.161193i
$479$	−6.02915	−	4.38043i	−0.275479	−	0.200147i	0.441464	−	0.897279i	$-0.354459\pi$
$479$	−6.02915	−	4.38043i	−0.275479	−	0.200147i	−0.716943	+	0.697132i	$0.754459\pi$
$480$	−0.0524177	+	0.161325i	−0.00239253	+	0.00736345i
$481$	10.9510	+	33.7036i	0.499321	+	1.53675i
$482$	−17.6251	+	12.8054i	−0.802803	+	0.583270i
$483$	15.7580	−	48.4982i	0.717014	−	2.20674i
$484$	0.0670808	−	0.206453i	0.00304913	−	0.00938425i
$485$	7.03709			0.319538
$486$	17.1925			0.779868
$487$	−10.7150	+	32.9773i	−0.485542	+	1.49435i	0.345652	+	0.938363i	$0.387658\pi$
$487$	−10.7150	+	32.9773i	−0.485542	+	1.49435i	−0.831194	+	0.555983i	$0.812342\pi$
$488$	23.6787	−	17.2036i	1.07188	−	0.778769i
$489$	−1.87497	−	5.77057i	−0.0847892	−	0.260954i
$490$	23.4980	+	17.0723i	1.06153	+	0.771247i
$491$	−39.7907			−1.79573			−0.897864	−	0.440272i	$-0.854882\pi$
$491$	−39.7907			−1.79573			−0.897864	+	0.440272i	$0.854882\pi$
$492$	0.0542416	+	0.166939i	0.00244540	+	0.00752617i
$493$	−4.94244	−	15.2113i	−0.222596	−	0.685081i
$494$	−7.66528	−	5.56916i	−0.344877	−	0.250568i
$495$	0.486099	−	1.49606i	0.0218485	−	0.0672428i
$496$	−5.16849	+	15.9070i	−0.232072	+	0.714245i
$497$	48.2345	−	35.0444i	2.16361	−	1.57196i
$498$	−14.5116	+	10.5433i	−0.650281	+	0.472457i
$499$	−19.8084			−0.886744			−0.443372	−	0.896338i	$-0.646218\pi$
$499$	−19.8084			−0.886744			−0.443372	+	0.896338i	$0.646218\pi$
$500$	−0.0185027	−	0.0134430i	−0.000827467	−	0.000601190i
$501$	21.5947	+	15.6895i	0.964780	+	0.700954i
$502$	14.4096	−	10.4692i	0.643131	−	0.467262i
$503$	30.8969	−	22.4479i	1.37763	−	1.00090i	0.380528	−	0.924770i	$-0.375742\pi$
$503$	30.8969	−	22.4479i	1.37763	−	1.00090i	0.997098	−	0.0761338i	$-0.0242576\pi$
$504$	−15.4996	+	11.2611i	−0.690406	+	0.501610i
$505$	−11.6656	−	8.47553i	−0.519111	−	0.377156i
$506$	−10.3323	+	7.50683i	−0.459325	+	0.333719i
$507$	4.24864	−	13.0760i	0.188689	−	0.580724i
$508$	0.199219	+	0.144741i	0.00883891	+	0.00642185i
$509$	4.03260	+	12.4111i	0.178742	+	0.550110i	0.999785	−	0.0207562i	$-0.00660739\pi$
$509$	4.03260	+	12.4111i	0.178742	+	0.550110i	−0.821043	+	0.570866i	$0.806607\pi$
$510$	−9.55200	−	6.93993i	−0.422970	−	0.307305i
$511$	14.3285	−	10.4103i	0.633857	−	0.460524i
$512$	−23.0032			−1.01661
$513$	2.41169	−	7.42241i	0.106479	−	0.327707i
$514$	8.22511	−	5.97589i	0.362794	−	0.263585i
$515$	−1.14228	+	3.51557i	−0.0503347	+	0.154914i
$516$	−0.0822164	+	0.0597337i	−0.00361938	+	0.00262963i
$517$	9.16221			0.402954
$518$	−16.7096	+	51.4268i	−0.734176	+	2.25956i
$519$	−25.3460			−1.11256
$520$	−4.25962	+	13.1098i	−0.186797	+	0.574901i
$521$	8.06572	−	24.8237i	0.353366	−	1.08755i	−0.603585	−	0.797299i	$-0.706262\pi$
$521$	8.06572	−	24.8237i	0.353366	−	1.08755i	0.956951	−	0.290250i	$-0.0937383\pi$
$522$	3.63880	+	2.64374i	0.159266	+	0.115713i
$523$	14.9436	−	10.8571i	0.653437	−	0.474750i	−0.211003	−	0.977485i	$-0.567673\pi$
$523$	14.9436	−	10.8571i	0.653437	−	0.474750i	0.864440	+	0.502735i	$0.167673\pi$
$524$	−0.115865	−	0.356596i	−0.00506158	−	0.0155780i
$525$	2.13081	+	6.55796i	0.0929962	+	0.286213i
$526$	4.08094	+	12.5598i	0.177937	+	0.547635i
$527$	21.9173	+	15.9238i	0.954732	+	0.693653i
$528$	−6.36701			−0.277088
$529$	31.6907			1.37786
$530$	8.57991	+	6.23367i	0.372688	+	0.270773i
$531$	−1.12104	−	3.45019i	−0.0486488	−	0.149726i
$532$	0.0516783	+	0.159050i	0.00224054	+	0.00689567i
$533$	8.76584	+	26.9785i	0.379691	+	1.16857i
$534$	−6.93903	+	5.04150i	−0.300281	+	0.218167i
$535$	−0.904274	−	0.656993i	−0.0390952	−	0.0284043i
$536$	−5.79195	+	17.8258i	−0.250174	+	0.769957i
$537$	−5.42658	+	16.7013i	−0.234174	+	0.720713i
$538$	14.5987			0.629396
$539$	7.83973	−	24.1282i	0.337681	−	1.03928i
$540$	−0.128371			−0.00552420
$541$	13.7197	−	9.96797i	0.589858	−	0.428557i	−0.252407	−	0.967621i	$-0.581222\pi$
$541$	13.7197	−	9.96797i	0.589858	−	0.428557i	0.842264	+	0.539065i	$0.181222\pi$
$542$	5.63787	−	17.3516i	0.242167	−	0.745314i
$543$	−8.73084	+	6.34333i	−0.374676	+	0.272218i
$544$	−0.256017	+	0.787939i	−0.0109766	+	0.0337826i
$545$	0.251628			0.0107786
$546$	38.0137	−	27.6186i	1.62684	−	1.18197i
$547$	31.9512	+	23.2139i	1.36613	+	0.992554i	0.998028	+	0.0627694i	$0.0199933\pi$
$547$	31.9512	+	23.2139i	1.36613	+	0.992554i	0.368105	+	0.929784i	$0.380007\pi$
$548$	0.121407	+	0.373651i	0.00518623	+	0.0159616i
$549$	10.6623	+	7.74660i	0.455055	+	0.330617i
$550$	0.533659	−	1.64243i	0.0227553	−	0.0700336i
$551$	2.80939	−	2.04114i	0.119684	−	0.0869555i
$552$	22.3133	+	16.2116i	0.949718	+	0.690011i
$553$	−27.4811	+	19.9662i	−1.16862	+	0.849050i
$554$	11.4524	−	8.32068i	0.486568	−	0.353512i
$555$	−7.75691	+	5.63573i	−0.329263	+	0.239223i
$556$	−0.242242	−	0.175999i	−0.0102733	−	0.00746402i
$557$	−9.29518	−	6.75335i	−0.393850	−	0.286148i	0.373182	−	0.927758i	$-0.378267\pi$
$557$	−9.29518	−	6.75335i	−0.393850	−	0.286148i	−0.767031	+	0.641610i	$0.778267\pi$
$558$	−7.61851			−0.322517
$559$	−13.2868	+	9.65340i	−0.561970	+	0.408295i
$560$	−16.8214	+	12.2215i	−0.710836	+	0.516453i
$561$	−3.18688	+	9.80819i	−0.134550	+	0.414102i
$562$	0.182536	−	0.561789i	0.00769983	−	0.0236976i
$563$	−1.76498	−	1.28233i	−0.0743850	−	0.0540438i	0.549971	−	0.835184i	$-0.314639\pi$
$563$	−1.76498	−	1.28233i	−0.0743850	−	0.0540438i	−0.624356	+	0.781140i	$0.714639\pi$
$564$	−0.0691292	−	0.212758i	−0.00291086	−	0.00895871i
$565$	3.49383	+	10.7529i	0.146986	+	0.452378i
$566$	23.7293			0.997417
$567$	14.9642	+	10.8721i	0.628435	+	0.456585i
$568$	9.96483	+	30.6686i	0.418115	+	1.28683i
$569$	17.8884	−	12.9967i	0.749919	−	0.544848i	−0.145882	−	0.989302i	$-0.546602\pi$
$569$	17.8884	−	12.9967i	0.749919	−	0.544848i	0.895802	+	0.444454i	$0.146602\pi$
$570$	0.792162	−	2.43803i	0.0331800	−	0.102118i
$571$	−18.2272			−0.762786			−0.381393	−	0.924413i	$-0.624555\pi$
$571$	−18.2272			−0.762786			−0.381393	+	0.924413i	$0.624555\pi$
$572$	0.136127			0.00569176
$573$	1.85940	−	5.72263i	0.0776774	−	0.239066i
$574$	−13.3754	+	41.1652i	−0.558278	+	1.71820i
$575$	−5.98294	+	4.34686i	−0.249506	+	0.181277i
$576$	−3.20167	−	9.85372i	−0.133403	−	0.410572i
$577$	2.96368	−	9.12127i	0.123380	−	0.379723i	−0.870223	−	0.492658i	$-0.836025\pi$
$577$	2.96368	−	9.12127i	0.123380	−	0.379723i	0.993602	+	0.112935i	$0.0360252\pi$
$578$	−27.3150	−	19.8455i	−1.13616	−	0.825465i
$579$	20.8187	−	15.1256i	0.865194	−	0.628600i
$580$	−0.0462104	−	0.0335738i	−0.00191878	−	0.00139408i
$581$	51.1652			2.12269
$582$	10.4962	−	7.62594i	0.435082	−	0.316105i
$583$	2.86255	−	8.81003i	0.118555	−	0.364874i
$584$	2.96015	+	9.11041i	0.122492	+	0.376991i
$585$	−6.20700			−0.256628
$586$	10.0056	+	30.7940i	0.413327	+	1.27209i
$587$	4.01613	−	12.3604i	0.165764	−	0.510168i	−0.833328	−	0.552779i	$-0.813568\pi$
$587$	4.01613	−	12.3604i	0.165764	−	0.510168i	0.999092	+	0.0426108i	$0.0135676\pi$
$588$	−0.619438			−0.0255452
$589$	−1.81763	+	5.59410i	−0.0748943	+	0.230501i
$590$	−1.23072	−	3.78776i	−0.0506678	−	0.155940i
$591$	−12.5471	−	9.11601i	−0.516119	−	0.374982i
$592$	−23.3901	−	16.9939i	−0.961328	−	0.698446i
$593$	32.7734	−	23.8112i	1.34584	−	0.977810i	0.346633	−	0.938001i	$-0.387325\pi$
$593$	32.7734	−	23.8112i	1.34584	−	0.977810i	0.999207	−	0.0398093i	$-0.0126750\pi$
$594$	−2.99538	−	9.21883i	−0.122902	−	0.378253i
$595$	10.4072	+	32.0302i	0.426655	+	1.31311i
$596$	−0.351762			−0.0144087
$597$	−6.76457	−	20.8192i	−0.276855	−	0.852073i
$598$	40.7695	+	29.6207i	1.66719	+	1.21128i
$599$	2.09159	+	6.43727i	0.0854603	+	0.263020i	0.984650	−	0.174539i	$-0.0558434\pi$
$599$	2.09159	+	6.43727i	0.0854603	+	0.263020i	−0.899190	+	0.437558i	$0.855843\pi$
$600$	−3.72949			−0.152256
$601$	−22.6041	−	16.4228i	−0.922041	−	0.669902i	0.0219906	−	0.999758i	$-0.493000\pi$
$601$	−22.6041	−	16.4228i	−0.922041	−	0.669902i	−0.944031	+	0.329857i	$0.893000\pi$
$602$	−25.0596			−1.02135
$603$	−8.43986			−0.343698
$604$	0.0228634	+	0.280107i	0.000930298	+	0.0113974i
$605$	9.49156			0.385887
$606$	−26.5846			−1.07993
$607$	25.5641	+	18.5734i	1.03762	+	0.753872i	0.969819	−	0.243827i	$-0.0784029\pi$
$607$	25.5641	+	18.5734i	1.03762	+	0.753872i	0.0677973	+	0.997699i	$0.478403\pi$
$608$	−0.179880			−0.00729508
$609$	5.32168	+	16.3784i	0.215645	+	0.663688i
$610$	11.7055	+	8.50453i	0.473941	+	0.344338i
$611$	−11.1718	−	34.3832i	−0.451962	−	1.39099i
$612$	−0.187591			−0.00758291
$613$	−14.0115	−	43.1230i	−0.565919	−	1.74172i	−0.665204	−	0.746661i	$-0.731656\pi$
$613$	−14.0115	−	43.1230i	−0.565919	−	1.74172i	0.0992853	−	0.995059i	$-0.468344\pi$
$614$	0.707464	+	2.17735i	0.0285509	+	0.0878708i
$615$	−6.20912	+	4.51119i	−0.250376	+	0.181909i
$616$	14.8630	+	10.7986i	0.598845	+	0.435087i
$617$	−5.84920	−	4.24969i	−0.235480	−	0.171086i	0.463787	−	0.885947i	$-0.346490\pi$
$617$	−5.84920	−	4.24969i	−0.235480	−	0.171086i	−0.699267	+	0.714860i	$0.746490\pi$
$618$	2.10597	+	6.48152i	0.0847147	+	0.260725i
$619$	0.315999	−	0.972544i	0.0127011	−	0.0390898i	−0.944505	−	0.328497i	$-0.893458\pi$
$619$	0.315999	−	0.972544i	0.0127011	−	0.0390898i	0.957206	+	0.289407i	$0.0934580\pi$
$620$	0.0967502			0.00388558
$621$	−12.8271	+	39.4777i	−0.514733	+	1.58418i
$622$	−12.5903	−	38.7489i	−0.504824	−	1.55369i
$623$	24.4657			0.980197
$624$	7.76349	+	23.8936i	0.310788	+	0.956508i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	11.7245	−	8.51835i	0.468606	−	0.340462i
$627$	−2.23912			−0.0894220
$628$	−0.198080	−	0.143913i	−0.00790425	−	0.00574277i
$629$	−37.8861	+	27.5259i	−1.51062	+	1.09753i
$630$	−7.66217	−	5.56689i	−0.305268	−	0.221790i
$631$	3.84579	−	11.8361i	0.153099	−	0.471189i	−0.844865	−	0.534980i	$-0.820319\pi$
$631$	3.84579	−	11.8361i	0.153099	−	0.471189i	0.997963	+	0.0637910i	$0.0203191\pi$
$632$	−5.67737	−	17.4731i	−0.225833	−	0.695044i
$633$	−17.9849	+	13.0668i	−0.714834	+	0.519357i
$634$	8.63629	−	26.5798i	0.342991	−	1.05562i
$635$	−3.32719	+	10.2400i	−0.132035	+	0.406363i
$636$	−0.226178			−0.00896853
$637$	−100.106			−3.96633
$638$	1.33281	−	4.10196i	0.0527664	−	0.162398i
$639$	−11.7473	+	8.53492i	−0.464716	+	0.337636i
$640$	−3.43496	−	10.5717i	−0.135779	−	0.417884i
$641$	−3.42749	−	2.49022i	−0.135378	−	0.0983578i	0.518035	−	0.855359i	$-0.326664\pi$
$641$	−3.42749	−	2.49022i	−0.135378	−	0.0983578i	−0.653413	+	0.757001i	$0.726664\pi$
$642$	−2.06074			−0.0813311
$643$	−4.78160	−	14.7162i	−0.188568	−	0.580352i	0.811424	−	0.584458i	$-0.198693\pi$
$643$	−4.78160	−	14.7162i	−0.188568	−	0.580352i	−0.999992	+	0.00410618i	$0.998693\pi$
$644$	−0.274862	−	0.845939i	−0.0108311	−	0.0333347i
$645$	−3.59485	−	2.61181i	−0.141547	−	0.102840i
$646$	3.86906	−	11.9077i	0.152226	−	0.468503i
$647$	−5.47960	+	16.8645i	−0.215425	+	0.663011i	0.783698	+	0.621142i	$0.213331\pi$
$647$	−5.47960	+	16.8645i	−0.215425	+	0.663011i	−0.999123	+	0.0418687i	$0.986669\pi$
$648$	−8.09356	+	5.88032i	−0.317945	+	0.231001i
$649$	−2.81436	+	2.04475i	−0.110473	+	0.0802635i
$650$	−6.81429			−0.267278
$651$	−23.5990	−	17.1457i	−0.924918	−	0.671993i
$652$	−0.0856217	−	0.0622078i	−0.00335320	−	0.00243625i
$653$	−6.23850	+	4.53253i	−0.244131	+	0.177372i	−0.703122	−	0.711069i	$-0.748211\pi$
$653$	−6.23850	+	4.53253i	−0.244131	+	0.177372i	0.458991	+	0.888441i	$0.348211\pi$
$654$	0.375317	−	0.272684i	0.0146761	−	0.0106628i
$655$	13.2632	−	9.63630i	0.518237	−	0.376521i
$656$	−18.7229	−	13.6030i	−0.731007	−	0.531108i
$657$	−3.48965	+	2.53538i	−0.136144	+	0.0989146i
$658$	17.0465	−	52.4637i	0.664541	−	2.04525i
$659$	17.0866	+	12.4141i	0.665599	+	0.483586i	0.868549	−	0.495603i	$-0.165053\pi$
$659$	17.0866	+	12.4141i	0.665599	+	0.483586i	−0.202950	+	0.979189i	$0.565053\pi$
$660$	0.0113812	+	0.0350277i	0.000443013	+	0.00136345i
$661$	−33.8319	−	24.5803i	−1.31591	−	0.956062i	−0.999973	−	0.00728051i	$-0.997683\pi$
$661$	−33.8319	−	24.5803i	−1.31591	−	0.956062i	−0.315933	−	0.948782i	$-0.602317\pi$
$662$	22.4895	−	16.3396i	0.874078	−	0.635055i
$663$	40.6932			1.58039
$664$	−8.55154	+	26.3189i	−0.331864	+	1.02137i
$665$	−5.91570	+	4.29800i	−0.229401	+	0.166669i
$666$	4.06954	−	12.5248i	0.157692	−	0.485325i
$667$	−14.9423	+	10.8562i	−0.578570	+	0.420356i
$668$	0.465590			0.0180142
$669$	5.44947	−	16.7718i	0.210689	−	0.648434i
$670$	−9.26562			−0.357962
$671$	3.90535	−	12.0194i	0.150764	−	0.464005i
$672$	0.275662	−	0.848399i	0.0106339	−	0.0327277i
$673$	−25.7314	−	18.6950i	−0.991874	−	0.720639i	−0.0315434	−	0.999502i	$-0.510042\pi$
$673$	−25.7314	−	18.6950i	−0.991874	−	0.720639i	−0.960331	+	0.278864i	$0.910042\pi$
$674$	−4.79000	+	3.48014i	−0.184504	+	0.134050i
$675$	−1.73449	−	5.33820i	−0.0667604	−	0.205467i
$676$	−0.0741077	−	0.228080i	−0.00285030	−	0.00877231i
$677$	−1.53924	−	4.73731i	−0.0591579	−	0.182069i	0.917111	−	0.398633i	$-0.130515\pi$
$677$	−1.53924	−	4.73731i	−0.0591579	−	0.182069i	−0.976269	+	0.216563i	$0.930515\pi$
$678$	16.8639	+	12.2524i	0.647655	+	0.470549i
$679$	−37.0076			−1.42022
$680$	−18.2155			−0.698532
$681$	−24.9705	−	18.1421i	−0.956871	−	0.695208i
$682$	2.25755	+	6.94803i	0.0864461	+	0.266054i
$683$	1.18900	+	3.65938i	0.0454959	+	0.140022i	0.971224	−	0.238168i	$-0.0765467\pi$
$683$	1.18900	+	3.65938i	0.0454959	+	0.140022i	−0.925728	+	0.378190i	$0.876547\pi$
$684$	−0.0125860	−	0.0387359i	−0.000481239	−	0.00148110i
$685$	−13.8976	+	10.0972i	−0.531000	+	0.385794i
$686$	−81.6979	−	59.3570i	−3.11924	−	2.26626i
$687$	0.780138	−	2.40102i	0.0297641	−	0.0916046i
$688$	4.14046	−	12.7430i	0.157854	−	0.485823i
$689$	−36.5520			−1.39252
$690$	−4.21329	+	12.9672i	−0.160397	+	0.493651i
$691$	46.3058			1.76156			0.880778	−	0.473529i	$-0.157020\pi$
$691$	46.3058			1.76156			0.880778	+	0.473529i	$0.157020\pi$
$692$	−0.357668	+	0.259861i	−0.0135965	+	0.00987843i
$693$	−2.55636	+	7.86768i	−0.0971083	+	0.298868i
$694$	−23.9657	+	17.4121i	−0.909726	+	0.660955i
$695$	4.04572	−	12.4514i	0.153463	−	0.472310i
$696$	−9.31438			−0.353061
$697$	−30.3264	+	22.0334i	−1.14869	+	0.834575i
$698$	30.4917	+	22.1535i	1.15413	+	0.838524i
$699$	−8.44515	−	25.9915i	−0.319425	−	0.983088i
$700$	0.0973047	+	0.0706960i	0.00367777	+	0.00267206i
$701$	11.3280	−	34.8639i	0.427851	−	1.31679i	−0.472386	−	0.881392i	$-0.656607\pi$
$701$	11.3280	−	34.8639i	0.427851	−	1.31679i	0.900238	−	0.435399i	$-0.143393\pi$
$702$	−30.9433	+	22.4816i	−1.16788	+	0.848514i
$703$	−8.22574	−	5.97635i	−0.310240	−	0.225402i
$704$	−8.03779	+	5.83979i	−0.302935	+	0.220095i
$705$	7.91332	−	5.74936i	0.298033	−	0.216533i
$706$	13.9478	−	10.1337i	0.524931	−	0.381385i
$707$	61.3485	+	44.5723i	2.30725	+	1.67631i
$708$	0.0687160	+	0.0499251i	0.00258251	+	0.00187630i
$709$	24.5081			0.920420			0.460210	−	0.887810i	$-0.347774\pi$
$709$	24.5081			0.920420			0.460210	+	0.887810i	$0.347774\pi$
$710$	−12.8967	+	9.36997i	−0.484003	+	0.351649i
$711$	6.69291	−	4.86269i	0.251004	−	0.182365i
$712$	−4.08909	+	12.5849i	−0.153245	+	0.471641i
$713$	9.66748	−	29.7534i	0.362050	−	1.11428i
$714$	50.2334	+	36.4967i	1.87994	+	1.36585i
$715$	1.83928	+	5.66074i	0.0687854	+	0.211700i
$716$	0.0946541	+	0.291316i	0.00353739	+	0.0108870i
$717$	5.59098			0.208799
$718$	−40.5465	−	29.4587i	−1.51318	−	1.09939i
$719$	−4.40290	−	13.5507i	−0.164200	−	0.505357i	0.834776	−	0.550590i	$-0.185597\pi$
$719$	−4.40290	−	13.5507i	−0.164200	−	0.505357i	−0.998976	+	0.0452328i	$0.985597\pi$
$720$	4.09679	−	2.97649i	0.152678	−	0.110927i
$721$	6.00716	−	18.4881i	0.223718	−	0.688535i
$722$	−23.9976			−0.893097
$723$	20.3152			0.755531
$724$	−0.0581694	+	0.179027i	−0.00216185	+	0.00665349i
$725$	0.771768	−	2.37526i	0.0286627	−	0.0882148i
$726$	14.1572	−	10.2858i	0.525423	−	0.381742i
$727$	−12.4772	−	38.4008i	−0.462753	−	1.42421i	−0.861786	−	0.507271i	$-0.830654\pi$
$727$	−12.4772	−	38.4008i	−0.462753	−	1.42421i	0.399033	−	0.916937i	$-0.369346\pi$
$728$	22.4011	−	68.9435i	0.830240	−	2.55521i
$729$	−21.5065	−	15.6254i	−0.796537	−	0.578718i
$730$	−3.83108	+	2.78344i	−0.141795	+	0.103020i
$731$	−17.5578	−	12.7565i	−0.649401	−	0.471817i
$732$	−0.308572			−0.0114051
$733$	26.8233	−	19.4882i	0.990740	−	0.719815i	0.0306568	−	0.999530i	$-0.490240\pi$
$733$	26.8233	−	19.4882i	0.990740	−	0.719815i	0.960083	+	0.279715i	$0.0902401\pi$
$734$	0.961010	−	2.95768i	0.0354715	−	0.109170i
$735$	−8.36955	−	25.7588i	−0.308715	−	0.950128i
$736$	0.956728			0.0352655
$737$	2.50094	+	7.69709i	0.0921232	+	0.283526i
$738$	3.25752	−	10.0256i	0.119911	−	0.369048i
$739$	8.69079			0.319696			0.159848	−	0.987142i	$-0.448900\pi$
$739$	8.69079			0.319696			0.159848	+	0.987142i	$0.448900\pi$
$740$	−0.0516806	+	0.159057i	−0.00189982	+	0.00584703i
$741$	2.73023	+	8.40279i	0.100298	+	0.308684i
$742$	−45.1212	−	32.7825i	−1.65645	−	1.20348i
$743$	8.44929	+	6.13877i	0.309975	+	0.225210i	0.731886	−	0.681428i	$-0.238641\pi$
$743$	8.44929	+	6.13877i	0.309975	+	0.225210i	−0.421911	+	0.906637i	$0.638641\pi$
$744$	12.7638	−	9.27348i	0.467945	−	0.339982i
$745$	−4.75284	−	14.6277i	−0.174130	−	0.535919i
$746$	11.5315	+	35.4904i	0.422199	+	1.29940i
$747$	−12.4611			−0.455926
$748$	0.0555877	+	0.171081i	0.00203249	+	0.00625536i
$749$	4.75552	+	3.45509i	0.173763	+	0.126246i
$750$	−0.569723	−	1.75343i	−0.0208034	−	0.0640262i
$751$	35.7644			1.30506			0.652530	−	0.757763i	$-0.273708\pi$
$751$	35.7644			1.30506			0.652530	+	0.757763i	$0.273708\pi$
$752$	23.8617	+	17.3366i	0.870148	+	0.632199i
$753$	−16.6089			−0.605261
$754$	−17.0186			−0.619782
$755$	−11.3391	+	4.73543i	−0.412673	+	0.172340i
$756$	0.675094			0.0245529
$757$	−26.0082			−0.945286			−0.472643	−	0.881254i	$-0.656700\pi$
$757$	−26.0082			−0.945286			−0.472643	+	0.881254i	$0.656700\pi$
$758$	17.5592	+	12.7575i	0.637780	+	0.463374i
$759$	11.9093			0.432279
$760$	−1.22213	−	3.76134i	−0.0443314	−	0.136438i
$761$	29.0960	+	21.1395i	1.05473	+	0.766307i	0.973106	−	0.230356i	$-0.0739892\pi$
$761$	29.0960	+	21.1395i	1.05473	+	0.766307i	0.0816245	+	0.996663i	$0.473989\pi$
$762$	6.13422	+	18.8792i	0.222219	+	0.683920i
$763$	−1.32330			−0.0479065
$764$	−0.0324329	−	0.0998181i	−0.00117338	−	0.00361129i
$765$	−2.53464	−	7.80081i	−0.0916400	−	0.282039i
$766$	−7.39294	+	5.37128i	−0.267118	+	0.194072i
$767$	11.1050	+	8.06826i	0.400979	+	0.291328i
$768$	0.582176	+	0.422975i	0.0210075	+	0.0152628i
$769$	3.56271	+	10.9649i	0.128475	+	0.395405i	0.994518	−	0.104564i	$-0.0333448\pi$
$769$	3.56271	+	10.9649i	0.128475	+	0.395405i	−0.866043	+	0.499969i	$0.833345\pi$
$770$	−2.80648	+	8.63745i	−0.101138	+	0.311272i
$771$	−9.48049			−0.341431
$772$	0.138705	−	0.426889i	0.00499209	−	0.0153641i
$773$	11.0969	+	34.1528i	0.399129	+	1.22839i	0.925699	+	0.378260i	$0.123478\pi$
$773$	11.0969	+	34.1528i	0.399129	+	1.22839i	−0.526571	+	0.850131i	$0.676522\pi$
$774$	6.10316			0.219374
$775$	1.30724	+	4.02328i	0.0469576	+	0.144521i
$776$	6.18530	−	19.0364i	0.222039	−	0.683367i
$777$	40.7931	−	29.6379i	1.46345	−	1.06326i
$778$	−23.5409			−0.843980
$779$	−6.58440	−	4.78384i	−0.235911	−	0.171399i
$780$	0.117572	−	0.0854208i	0.00420974	−	0.00305856i
$781$	11.2648	+	8.18435i	0.403086	+	0.292859i
$782$	−20.5784	+	63.3338i	−0.735882	+	2.26481i
$783$	−4.33186	−	13.3321i	−0.154808	−	0.476451i
$784$	66.0725	−	48.0045i	2.35973	−	1.71445i
$785$	3.30816	−	10.1815i	0.118073	−	0.363393i
$786$	9.34019	−	28.7462i	0.333154	−	1.02534i
$787$	1.78082			0.0634795			0.0317397	−	0.999496i	$-0.489895\pi$
$787$	1.78082			0.0634795			0.0317397	+	0.999496i	$0.489895\pi$
$788$	−0.270520			−0.00963688
$789$	3.80545	−	11.7120i	0.135478	−	0.416958i
$790$	7.34774	−	5.33845i	0.261421	−	0.189933i
$791$	−18.3738	−	56.5488i	−0.653298	−	2.01064i
$792$	−3.61981	−	2.62994i	−0.128624	−	0.0934510i
$793$	−49.8674			−1.77084
$794$	0.677933	+	2.08646i	0.0240589	+	0.0740458i
$795$	−3.05601	−	9.40542i	−0.108385	−	0.333576i
$796$	−0.308908	−	0.224435i	−0.0109490	−	0.00795488i
$797$	−11.8343	+	36.4223i	−0.419193	+	1.29014i	0.489253	+	0.872142i	$0.337270\pi$
$797$	−11.8343	+	36.4223i	−0.419193	+	1.29014i	−0.908446	+	0.418002i	$0.862730\pi$
$798$	−4.16593	+	12.8214i	−0.147472	+	0.453873i
$799$	38.6500	−	28.0809i	1.36734	−	0.993429i
$800$	−0.104662	+	0.0760414i	−0.00370036	+	0.00268847i
$801$	−5.95851			−0.210534
$802$	31.8913	+	23.1704i	1.12612	+	0.818176i
$803$	3.34632	+	2.43124i	0.118089	+	0.0857966i
$804$	0.159866	−	0.116150i	0.00563804	−	0.00409628i
$805$	31.4639	−	22.8599i	1.10896	−	0.805704i
$806$	23.3213	−	16.9439i	0.821457	−	0.596823i
$807$	−11.0133	−	8.00167i	−0.387688	−	0.281672i
$808$	−33.1812	+	24.1075i	−1.16731	+	0.848100i
$809$	−11.5769	+	35.6299i	−0.407021	+	1.25268i	0.512175	+	0.858881i	$0.328840\pi$
$809$	−11.5769	+	35.6299i	−0.407021	+	1.25268i	−0.919196	+	0.393801i	$0.871160\pi$
$810$	−4.00103	−	2.90692i	−0.140582	−	0.102139i
$811$	0.130928	+	0.402955i	0.00459751	+	0.0141497i	0.953329	−	0.301934i	$-0.0976321\pi$
$811$	0.130928	+	0.402955i	0.00459751	+	0.0141497i	−0.948731	+	0.316083i	$0.897632\pi$
$812$	0.243018	+	0.176563i	0.00852825	+	0.00619614i
$813$	−13.7637	+	9.99995i	−0.482716	+	0.350714i
$814$	−12.6284			−0.442625
$815$	1.42998	−	4.40103i	0.0500901	−	0.154161i
$816$	−26.8587	+	19.5140i	−0.940241	+	0.683125i
$817$	1.45610	−	4.48142i	0.0509425	−	0.156785i
$818$	−11.9084	+	8.65194i	−0.416366	+	0.302508i
$819$	32.6422			1.14061
$820$	−0.0413684	+	0.127319i	−0.00144465	+	0.00444617i
$821$	3.72490			0.130000			0.0649999	−	0.997885i	$-0.479295\pi$
$821$	3.72490			0.130000			0.0649999	+	0.997885i	$0.479295\pi$
$822$	−9.78692	+	30.1210i	−0.341358	+	1.05059i
$823$	2.25526	−	6.94099i	0.0786136	−	0.241948i	−0.904024	−	0.427481i	$-0.859401\pi$
$823$	2.25526	−	6.94099i	0.0786136	−	0.241948i	0.982638	+	0.185533i	$0.0594012\pi$
$824$	8.50613	+	6.18007i	0.296325	+	0.215293i
$825$	−1.30282	+	0.946556i	−0.0453585	+	0.0329549i
$826$	6.47227	+	19.9196i	0.225199	+	0.693091i
$827$	−8.96368	−	27.5874i	−0.311698	−	0.959307i	−0.977092	−	0.212815i	$-0.931737\pi$
$827$	−8.96368	−	27.5874i	−0.311698	−	0.959307i	0.665395	−	0.746492i	$-0.268263\pi$
$828$	0.0669416	+	0.206025i	0.00232638	+	0.00715986i
$829$	−14.0589	−	10.2144i	−0.488287	−	0.354761i	0.316238	−	0.948680i	$-0.397580\pi$
$829$	−14.0589	−	10.2144i	−0.488287	−	0.354761i	−0.804525	+	0.593918i	$0.797580\pi$
$830$	−13.6802			−0.474848
$831$	−13.2004			−0.457917
$832$	31.7158	+	23.0429i	1.09955	+	0.798868i
$833$	−40.8783	−	125.810i	−1.41635	−	4.35907i
$834$	−7.45895	−	22.9563i	−0.258282	−	0.794911i
$835$	6.29083	+	19.3612i	0.217703	+	0.670021i
$836$	−0.0315973	+	0.0229568i	−0.00109281	+	0.000793976i
$837$	19.2097	+	13.9566i	0.663983	+	0.482412i
$838$	1.39125	−	4.28182i	0.0480599	−	0.147913i
$839$	1.83262	−	5.64022i	0.0632690	−	0.194722i	−0.914425	−	0.404754i	$-0.867357\pi$
$839$	1.83262	−	5.64022i	0.0632690	−	0.194722i	0.977694	+	0.210033i	$0.0673570\pi$
$840$	19.6132			0.676719
$841$	−7.03401	+	21.6485i	−0.242552	+	0.746498i
$842$	−29.5141			−1.01712
$843$	−0.445627	+	0.323767i	−0.0153482	+	0.0111511i
$844$	−0.119825	+	0.368782i	−0.00412453	+	0.0126940i
$845$	8.48322	−	6.16342i	0.291832	−	0.212028i
$846$	−4.15160	+	12.7773i	−0.142735	+	0.439293i
$847$	−49.9155			−1.71512
$848$	24.1253	−	17.5281i	0.828466	−	0.601916i
$849$	−17.9015	−	13.0062i	−0.614378	−	0.446372i
$850$	−2.78263	−	8.56404i	−0.0954433	−	0.293744i
$851$	43.7504	+	31.7865i	1.49974	+	1.08963i
$852$	0.105057	−	0.323333i	0.00359921	−	0.0110772i
$853$	−0.312847	+	0.227297i	−0.0107117	+	0.00778249i	−0.593128	−	0.805108i	$-0.702107\pi$
$853$	−0.312847	+	0.227297i	−0.0107117	+	0.00778249i	0.582417	+	0.812891i	$0.302107\pi$
$854$	−61.5584	−	44.7248i	−2.10648	−	1.53045i
$855$	1.44074	−	1.04676i	0.0492724	−	0.0357985i
$856$	−2.57209	+	1.86873i	−0.0879121	+	0.0638719i
$857$	−27.6567	+	20.0937i	−0.944734	+	0.686389i	−0.949555	−	0.313599i	$-0.898465\pi$
$857$	−27.6567	+	20.0937i	−0.944734	+	0.686389i	0.00482162	+	0.999988i	$0.498465\pi$
$858$	8.87781	+	6.45011i	0.303084	+	0.220203i
$859$	37.8635	+	27.5094i	1.29189	+	0.938610i	0.999842	−	0.0177945i	$-0.00566447\pi$
$859$	37.8635	+	27.5094i	1.29189	+	0.938610i	0.292044	+	0.956405i	$0.405664\pi$
$860$	−0.0775063			−0.00264294
$861$	32.6534	−	23.7241i	1.11282	−	0.808514i
$862$	−1.52910	+	1.11096i	−0.0520814	+	0.0378393i
$863$	5.45366	−	16.7846i	0.185645	−	0.571356i	−0.814314	−	0.580425i	$-0.802887\pi$
$863$	5.45366	−	16.7846i	0.185645	−	0.571356i	0.999959	+	0.00906851i	$0.00288664\pi$
$864$	−0.224389	+	0.690600i	−0.00763388	+	0.0234947i
$865$	−15.6388	−	11.3622i	−0.531733	−	0.386327i
$866$	11.4070	+	35.1071i	0.387625	+	1.19299i
$867$	9.72911	+	29.9431i	0.330418	+	1.01692i
$868$	−0.508804			−0.0172699
$869$	−6.41801	−	4.66295i	−0.217716	−	0.158180i
$870$	−1.42288	−	4.37917i	−0.0482401	−	0.148468i
$871$	25.8355	−	18.7706i	0.875403	−	0.636018i
$872$	0.221170	−	0.680693i	0.00748978	−	0.0230512i
$873$	9.01304			0.305045
$874$	−14.4585			−0.489067
$875$	−1.62510	+	5.00155i	−0.0549385	+	0.169083i
$876$	0.0312083	−	0.0960493i	0.00105443	−	0.00324521i
$877$	−3.81915	+	2.77477i	−0.128964	+	0.0936975i	−0.650397	−	0.759594i	$-0.725397\pi$
$877$	−3.81915	+	2.77477i	−0.128964	+	0.0936975i	0.521434	+	0.853292i	$0.325397\pi$
$878$	7.99812	+	24.6157i	0.269923	+	0.830739i
$879$	9.33016	−	28.7153i	0.314699	−	0.968543i
$880$	−3.92852	−	2.85424i	−0.132430	−	0.0962163i
$881$	−21.7661	+	15.8140i	−0.733319	+	0.532787i	−0.890612	−	0.454765i	$-0.849723\pi$
$881$	−21.7661	+	15.8140i	−0.733319	+	0.532787i	0.157293	+	0.987552i	$0.449723\pi$
$882$	30.0960	+	21.8660i	1.01339	+	0.736268i
$883$	−51.8325			−1.74430			−0.872150	−	0.489238i	$-0.837275\pi$
$883$	−51.8325			−1.74430			−0.872150	+	0.489238i	$0.837275\pi$
$884$	0.574240	−	0.417210i	0.0193138	−	0.0140323i
$885$	−1.14764	+	3.53207i	−0.0385774	+	0.118729i
$886$	2.20944	+	6.79995i	0.0742276	+	0.228449i
$887$	22.8338			0.766684			0.383342	−	0.923606i	$-0.374773\pi$
$887$	22.8338			0.766684			0.383342	+	0.923606i	$0.374773\pi$
$888$	8.42751	+	25.9372i	0.282809	+	0.870396i
$889$	17.4975	−	53.8517i	0.586847	−	1.80613i
$890$	−6.54149			−0.219271
$891$	−1.33488	+	4.10834i	−0.0447202	+	0.137635i
$892$	−0.0950536	−	0.292545i	−0.00318263	−	0.00979513i
$893$	8.39159	+	6.09685i	0.280814	+	0.204023i
$894$	−22.9409	−	16.6675i	−0.767258	−	0.557445i
$895$	−10.8352	+	7.87223i	−0.362181	+	0.263140i
$896$	18.0643	+	55.5961i	0.603484	+	1.85733i
$897$	−14.5213	−	44.6921i	−0.484853	−	1.49222i
$898$	−12.0372			−0.401688
$899$	3.26483	+	10.0481i	0.108888	+	0.335123i
$900$	−0.0236981	−	0.0172177i	−0.000789938	−	0.000573924i
$901$	−14.9260	−	45.9377i	−0.497259	−	1.53041i
$902$	−10.1086			−0.336578
$903$	18.9051	+	13.7353i	0.629122	+	0.457084i
$904$	32.1592			1.06960
$905$	−8.23065			−0.273596
$906$	−11.7812	+	19.3511i	−0.391405	+	0.642898i
$907$	−6.85182			−0.227511			−0.113756	−	0.993509i	$-0.536288\pi$
$907$	−6.85182			−0.227511			−0.113756	+	0.993509i	$0.536288\pi$
$908$	−0.538373			−0.0178665
$909$	−14.9412	−	10.8554i	−0.495567	−	0.360051i
$910$	35.8359			1.18795
$911$	−8.53787	−	26.2769i	−0.282872	−	0.870591i	−0.987028	−	0.160546i	$-0.948674\pi$
$911$	−8.53787	−	26.2769i	−0.282872	−	0.870591i	0.704156	−	0.710045i	$-0.251326\pi$
$912$	−5.83149	−	4.23683i	−0.193100	−	0.140295i
$913$	3.69251	+	11.3644i	0.122204	+	0.376106i
$914$	−18.9829			−0.627899
$915$	−4.16927	−	12.8317i	−0.137832	−	0.424203i
$916$	−0.0136077	−	0.0418802i	−0.000449612	−	0.00138376i
$917$	−69.7505	+	50.6767i	−2.30337	+	1.67349i
$918$	−40.8901	−	29.7084i	−1.34958	−	0.980524i
$919$	13.4431	+	9.76701i	0.443448	+	0.322184i	0.787004	−	0.616949i	$-0.211631\pi$
$919$	13.4431	+	9.76701i	0.443448	+	0.322184i	−0.343555	+	0.939132i	$0.611631\pi$
$920$	6.50017	+	20.0055i	0.214304	+	0.659561i
$921$	0.659707	−	2.03037i	0.0217381	−	0.0669030i
$922$	−28.8054			−0.948655
$923$	16.9780	−	52.2530i	0.558839	−	1.71993i
$924$	−0.0598530	−	0.184209i	−0.00196902	−	0.00606002i
$925$	−7.31252			−0.240434
$926$	−16.2234	−	49.9306i	−0.533135	−	1.64082i
$927$	−1.46302	+	4.50271i	−0.0480519	+	0.147888i
$928$	−0.261393	+	0.189913i	−0.00858064	+	0.00623420i
$929$	−35.7533			−1.17303			−0.586513	−	0.809940i	$-0.699500\pi$
$929$	−35.7533			−1.17303			−0.586513	+	0.809940i	$0.699500\pi$
$930$	6.30977	+	4.58431i	0.206905	+	0.150326i
$931$	23.2361	−	16.8820i	0.761532	−	0.553286i
$932$	−0.385653	−	0.280193i	−0.0126325	−	0.00917803i
$933$	−11.7404	+	36.1332i	−0.384363	+	1.18295i
$934$	−6.46647	−	19.9017i	−0.211589	−	0.651205i
$935$	−6.36321	+	4.62314i	−0.208099	+	0.151193i
$936$	−5.45569	+	16.7909i	−0.178325	+	0.548827i
$937$	−8.30346	+	25.5554i	−0.271262	+	0.834859i	0.718922	+	0.695091i	$0.244636\pi$
$937$	−8.30346	+	25.5554i	−0.271262	+	0.834859i	−0.990184	+	0.139768i	$0.955364\pi$
$938$	48.7273			1.59100
$939$	−13.5140			−0.441012
$940$	0.0527226	−	0.162264i	0.00171962	−	0.00529245i
$941$	−7.92638	+	5.75885i	−0.258393	+	0.187733i	−0.709438	−	0.704768i	$-0.751051\pi$
$941$	−7.92638	+	5.75885i	−0.258393	+	0.187733i	0.451046	+	0.892501i	$0.351051\pi$
$942$	−6.09914	−	18.7712i	−0.198721	−	0.611600i
$943$	35.0205	+	25.4439i	1.14043	+	0.828568i
$944$	−11.1987			−0.364485
$945$	9.12155	+	28.0733i	0.296724	+	0.913223i
$946$	−1.80852	−	5.56604i	−0.0587999	−	0.180968i
$947$	−23.7437	−	17.2508i	−0.771566	−	0.560575i	0.130870	−	0.991400i	$-0.458223\pi$
$947$	−23.7437	−	17.2508i	−0.771566	−	0.560575i	−0.902436	+	0.430824i	$0.858223\pi$
$948$	−0.0598554	+	0.184216i	−0.00194401	+	0.00598306i
$949$	5.04349	−	15.5223i	0.163719	−	0.503874i
$950$	1.58170	−	1.14918i	0.0513173	−	0.0372842i
$951$	−21.0838	+	15.3183i	−0.683690	+	0.496730i
$952$	95.7941			3.10470
$953$	33.2070	+	24.1263i	1.07568	+	0.781527i	0.976925	−	0.213585i	$-0.0685139\pi$
$953$	33.2070	+	24.1263i	1.07568	+	0.781527i	0.0987552	+	0.995112i	$0.468514\pi$
$954$	10.9891	+	7.98404i	0.355785	+	0.258493i
$955$	3.71264	−	2.69739i	0.120138	−	0.0872855i
$956$	0.0788967	−	0.0573218i	0.00255170	−	0.00185392i
$957$	−3.25379	+	2.36402i	−0.105180	+	0.0764178i
$958$	−8.47762	−	6.15935i	−0.273899	−	0.198999i
$959$	73.0866	−	53.1005i	2.36009	−	1.71470i
$960$	−3.27764	+	10.0875i	−0.105785	+	0.325574i
$961$	10.6016	+	7.70253i	0.341988	+	0.248469i
$962$	15.3982	+	47.3908i	0.496458	+	1.52794i
$963$	−1.15819	−	0.841472i	−0.0373220	−	0.0271161i
$964$	0.286677	−	0.208283i	0.00923324	−	0.00670834i
$965$	19.6260			0.631782
$966$	22.1574	−	68.1935i	0.712903	−	2.19409i
$967$	−22.3061	+	16.2063i	−0.717316	+	0.521160i	−0.885525	−	0.464591i	$-0.846201\pi$
$967$	−22.3061	+	16.2063i	−0.717316	+	0.521160i	0.168210	+	0.985751i	$0.446201\pi$
$968$	8.34268	−	25.6761i	0.268144	−	0.825262i
$969$	−9.44554	+	6.86259i	−0.303435	+	0.220458i
$970$	9.89488			0.317705
$971$	−2.94703	+	9.07003i	−0.0945747	+	0.291071i	−0.987143	−	0.159842i	$-0.948902\pi$
$971$	−2.94703	+	9.07003i	−0.0945747	+	0.291071i	0.892568	+	0.450913i	$0.148902\pi$
$972$	−0.279640			−0.00896946
$973$	−21.2762	+	65.4814i	−0.682083	+	2.09924i
$974$	−15.0664	+	46.3696i	−0.482758	+	1.48578i
$975$	5.14073	+	3.73496i	0.164635	+	0.119614i
$976$	32.9139	−	23.9133i	1.05355	−	0.765447i
$977$	4.88566	+	15.0365i	0.156306	+	0.481061i	0.998291	−	0.0584404i	$-0.0186128\pi$
$977$	4.88566	+	15.0365i	0.156306	+	0.481061i	−0.841985	+	0.539501i	$0.818613\pi$
$978$	−2.63641	−	8.11402i	−0.0843030	−	0.259458i
$979$	1.76565	+	5.43412i	0.0564305	+	0.173675i
$980$	−0.382200	−	0.277685i	−0.0122089	−	0.00887031i
$981$	0.322283			0.0102897
$982$	−55.9499			−1.78543
$983$	40.5602	+	29.4687i	1.29367	+	0.939906i	0.999873	−	0.0159622i	$-0.00508114\pi$
$983$	40.5602	+	29.4687i	1.29367	+	0.939906i	0.293797	+	0.955868i	$0.405081\pi$
$984$	6.74591	+	20.7618i	0.215052	+	0.661861i
$985$	−3.65514	−	11.2494i	−0.116462	−	0.358435i
$986$	−6.94959	−	21.3886i	−0.221320	−	0.681153i
$987$	−41.6156	+	30.2355i	−1.32464	+	0.962408i
$988$	0.124678	+	0.0905836i	0.00396653	+	0.00288185i
$989$	−7.74458	+	23.8354i	−0.246263	+	0.757921i
$990$	0.683506	−	2.10361i	0.0217232	−	0.0668573i
$991$	−38.2967			−1.21654			−0.608268	−	0.793732i	$-0.708135\pi$
$991$	−38.2967			−1.21654			−0.608268	+	0.793732i	$0.708135\pi$
$992$	0.169117	−	0.520489i	0.00536948	−	0.0165256i
$993$	−25.9220			−0.822609
$994$	67.8227	−	49.2761i	2.15121	−	1.56294i
$995$	5.15912	−	15.8782i	0.163555	−	0.503371i
$996$	0.236035	−	0.171489i	0.00747905	−	0.00543385i
$997$	0.997752	−	3.07076i	0.0315991	−	0.0972521i	−0.934013	−	0.357239i	$-0.883718\pi$
$997$	0.997752	−	3.07076i	0.0315991	−	0.0972521i	0.965612	+	0.259987i	$0.0837182\pi$
$998$	−27.8526			−0.881659
$999$	−33.2057	+	24.1254i	−1.05058	+	0.763293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.h.d.361.3	✓	16
151.64	even	5	inner	755.2.h.d.366.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.h.d.361.3	✓	16	1.1	even	1	trivial
755.2.h.d.366.3	yes	16	151.64	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.40610 q^{2} +(-1.06077 - 0.770696i) q^{3} -0.0228706 q^{4} +(-0.309017 - 0.951057i) q^{5} +(-1.49156 - 1.08368i) q^{6} +(1.62510 + 5.00155i) q^{7} -2.84437 q^{8} +(-0.395787 - 1.21811i) q^{9} +(-0.434510 - 1.33728i) q^{10} +(-0.993622 + 0.721909i) q^{11} +(0.0242605 + 0.0176263i) q^{12} +(3.92067 + 2.84854i) q^{13} +(2.28506 + 7.03270i) q^{14} +(-0.405179 + 1.24701i) q^{15} -3.95374 q^{16} +(-1.97896 + 6.09062i) q^{17} +(-0.556517 - 1.71278i) q^{18} -1.39043 q^{19} +(0.00706741 + 0.0217513i) q^{20} +(2.13081 - 6.55796i) q^{21} +(-1.39714 + 1.01508i) q^{22} +7.39532 q^{23} +(3.01722 + 2.19214i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(5.51288 + 4.00534i) q^{26} +(-1.73449 + 5.33820i) q^{27} +(-0.0371671 - 0.114389i) q^{28} +(-2.02051 + 1.46799i) q^{29} +(-0.569723 + 1.75343i) q^{30} +(1.30724 - 4.02328i) q^{31} +0.129369 q^{32} +1.61038 q^{33} +(-2.78263 + 8.56404i) q^{34} +(4.25457 - 3.09113i) q^{35} +(0.00905189 + 0.0278588i) q^{36} +(5.91595 + 4.29819i) q^{37} -1.95509 q^{38} +(-1.96358 - 6.04329i) q^{39} +(0.878958 + 2.70515i) q^{40} +(4.73550 + 3.44054i) q^{41} +(2.99614 - 9.22117i) q^{42} +(-1.04723 + 3.22304i) q^{43} +(0.0227248 - 0.0165105i) q^{44} +(-1.03618 + 0.752831i) q^{45} +10.3986 q^{46} +(-6.03524 - 4.38486i) q^{47} +(4.19401 + 3.04713i) q^{48} +(-16.7114 + 12.1415i) q^{49} +(-1.13756 + 0.826487i) q^{50} +(6.79324 - 4.93558i) q^{51} +(-0.0896682 - 0.0651478i) q^{52} +(-6.10190 + 4.43329i) q^{53} +(-2.43887 + 7.50606i) q^{54} +(0.993622 + 0.721909i) q^{55} +(-4.62239 - 14.2262i) q^{56} +(1.47493 + 1.07160i) q^{57} +(-2.84105 + 2.06415i) q^{58} +2.83242 q^{59} +(0.00926669 - 0.0285199i) q^{60} +(-8.32476 + 6.04829i) q^{61} +(1.83812 - 5.65715i) q^{62} +(5.44922 - 3.95909i) q^{63} +8.08938 q^{64} +(1.49756 - 4.60903i) q^{65} +2.26436 q^{66} +(2.03629 - 6.26705i) q^{67} +(0.0452601 - 0.139296i) q^{68} +(-7.84474 - 5.69954i) q^{69} +(5.98237 - 4.34645i) q^{70} +(-3.50336 - 10.7822i) q^{71} +(1.12576 + 3.46474i) q^{72} +(-1.04071 - 3.20296i) q^{73} +(8.31845 + 6.04371i) q^{74} +1.31119 q^{75} +0.0318001 q^{76} +(-5.22540 - 3.79647i) q^{77} +(-2.76100 - 8.49750i) q^{78} +(1.99600 + 6.14307i) q^{79} +(1.22177 + 3.76023i) q^{80} +(2.84547 - 2.06735i) q^{81} +(6.65861 + 4.83776i) q^{82} +(3.00648 - 9.25300i) q^{83} +(-0.0487329 + 0.149985i) q^{84} +6.40405 q^{85} +(-1.47251 + 4.53192i) q^{86} +3.27468 q^{87} +(2.82623 - 2.05337i) q^{88} +(1.43761 - 4.42451i) q^{89} +(-1.45698 + 1.05856i) q^{90} +(-7.87560 + 24.2386i) q^{91} -0.169136 q^{92} +(-4.48741 + 3.26029i) q^{93} +(-8.48617 - 6.16557i) q^{94} +(0.429667 + 1.32238i) q^{95} +(-0.137231 - 0.0997044i) q^{96} +(-2.17458 + 6.69267i) q^{97} +(-23.4980 + 17.0723i) q^{98} +(1.27262 + 0.924615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

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