LMFDB - Embedded newform 847.2.f.o.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.446265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 $ x^8 - x^7 + 4x^6 - 7x^5 + 19x^4 + 21x^3 + 36x^2 + 27x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$-0.711597 - 2.19007i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.o.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86298 - 1.35354i) q^{2} +(-0.711597 + 2.19007i) q^{3} +(1.02061 + 3.14113i) q^{4} +(-2.91695 + 2.11929i) q^{5} +(4.29004 - 3.11689i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-1.86298 - 1.35354i) q^{9} +O(q^{10})$	\(q+(-1.86298 - 1.35354i) q^{2} +(-0.711597 + 2.19007i) q^{3} +(1.02061 + 3.14113i) q^{4} +(-2.91695 + 2.11929i) q^{5} +(4.29004 - 3.11689i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-1.86298 - 1.35354i) q^{9} +8.30278 q^{10} -7.60555 q^{12} +(-5.34400 - 3.88265i) q^{13} +(-0.711597 + 2.19007i) q^{14} +(-2.56570 - 7.89641i) q^{15} +(-0.244951 + 0.177967i) q^{16} +(-2.18210 + 1.58539i) q^{17} +(1.63865 + 5.04324i) q^{18} +(-0.927051 + 2.85317i) q^{19} +(-9.63404 - 6.99954i) q^{20} +2.30278 q^{21} -2.69722 q^{23} +(5.58895 + 4.06061i) q^{24} +(2.47214 - 7.60845i) q^{25} +(4.70049 + 14.4666i) q^{26} +(-1.29892 + 0.943719i) q^{27} +(2.67200 - 1.94132i) q^{28} +(1.45152 + 4.46733i) q^{29} +(-5.90823 + 18.1837i) q^{30} +(-0.809017 - 0.587785i) q^{31} -5.30278 q^{32} +6.21110 q^{34} +(2.91695 + 2.11929i) q^{35} +(2.35024 - 7.23331i) q^{36} +(-1.61032 - 4.95605i) q^{37} +(5.58895 - 4.06061i) q^{38} +(12.3060 - 8.94086i) q^{39} +(3.34253 + 10.2872i) q^{40} +(2.16312 - 6.65740i) q^{41} +(-4.29004 - 3.11689i) q^{42} +1.69722 q^{43} +8.30278 q^{45} +(5.02489 + 3.65079i) q^{46} +(-0.589705 + 1.81493i) q^{47} +(-0.215454 - 0.663100i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-14.9039 + 10.8283i) q^{50} +(-1.91934 - 5.90711i) q^{51} +(6.74172 - 20.7489i) q^{52} +(10.4431 + 7.58732i) q^{53} +3.69722 q^{54} -3.00000 q^{56} +(-5.58895 - 4.06061i) q^{57} +(3.34253 - 10.2872i) q^{58} +(2.06956 + 6.36944i) q^{59} +(22.1850 - 16.1184i) q^{60} +(3.48102 - 2.52911i) q^{61} +(0.711597 + 2.19007i) q^{62} +(-0.711597 + 2.19007i) q^{63} +(10.3689 + 7.53344i) q^{64} +23.8167 q^{65} +8.51388 q^{67} +(-7.20699 - 5.23618i) q^{68} +(1.91934 - 5.90711i) q^{69} +(-2.56570 - 7.89641i) q^{70} +(3.48102 - 2.52911i) q^{71} +(-5.58895 + 4.06061i) q^{72} +(-1.54508 - 4.75528i) q^{73} +(-3.70820 + 11.4127i) q^{74} +(14.9039 + 10.8283i) q^{75} -9.90833 q^{76} -35.0278 q^{78} +(6.71709 + 4.88025i) q^{79} +(0.337346 - 1.03824i) q^{80} +(-3.27730 - 10.0865i) q^{81} +(-13.0409 + 9.47476i) q^{82} +(-2.42705 + 1.76336i) q^{83} +(2.35024 + 7.23331i) q^{84} +(3.00518 - 9.24901i) q^{85} +(-3.16190 - 2.29726i) q^{86} -10.8167 q^{87} -14.7250 q^{89} +(-15.4679 - 11.2381i) q^{90} +(-2.04123 + 6.28225i) q^{91} +(-2.75282 - 8.47232i) q^{92} +(1.86298 - 1.35354i) q^{93} +(3.55518 - 2.58299i) q^{94} +(-3.34253 - 10.2872i) q^{95} +(3.77344 - 11.6134i) q^{96} +(2.91695 + 2.11929i) q^{97} +2.30278 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.86298	−	1.35354i	−1.31733	−	0.957096i	−0.999961	−	0.00879304i	$-0.997201\pi$
$2$	−1.86298	−	1.35354i	−1.31733	−	0.957096i	−0.317368	−	0.948303i	$-0.602799\pi$
$3$	−0.711597	+	2.19007i	−0.410841	+	1.26444i	0.505078	+	0.863074i	$0.331464\pi$
$3$	−0.711597	+	2.19007i	−0.410841	+	1.26444i	−0.915919	+	0.401364i	$0.868536\pi$
$4$	1.02061	+	3.14113i	0.510307	+	1.57056i
$5$	−2.91695	+	2.11929i	−1.30450	+	0.947775i	−0.999989	−	0.00473329i	$-0.998493\pi$
$5$	−2.91695	+	2.11929i	−1.30450	+	0.947775i	−0.304512	+	0.952509i	$0.598493\pi$
$6$	4.29004	−	3.11689i	1.75140	−	1.27247i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.927051	−	2.85317i	0.327762	−	1.00875i
$9$	−1.86298	−	1.35354i	−0.620995	−	0.451179i
$10$	8.30278			2.62557
$11$		0			0
$11$		0			0
$12$	−7.60555			−2.19553
$13$	−5.34400	−	3.88265i	−1.48216	−	1.07685i	−0.976853	−	0.213912i	$-0.931379\pi$
$13$	−5.34400	−	3.88265i	−1.48216	−	1.07685i	−0.505307	−	0.862940i	$-0.668621\pi$
$14$	−0.711597	+	2.19007i	−0.190182	+	0.585321i
$15$	−2.56570	−	7.89641i	−0.662461	−	2.03884i
$16$	−0.244951	+	0.177967i	−0.0612377	+	0.0444918i
$17$	−2.18210	+	1.58539i	−0.529237	+	0.384513i	−0.820072	−	0.572260i	$-0.806067\pi$
$17$	−2.18210	+	1.58539i	−0.529237	+	0.384513i	0.290835	+	0.956773i	$0.406067\pi$
$18$	1.63865	+	5.04324i	0.386233	+	1.18870i
$19$	−0.927051	+	2.85317i	−0.212680	+	0.654562i	0.786630	+	0.617425i	$0.211824\pi$
$19$	−0.927051	+	2.85317i	−0.212680	+	0.654562i	−0.999310	+	0.0371374i	$0.988176\pi$
$20$	−9.63404	−	6.99954i	−2.15424	−	1.56514i
$21$	2.30278			0.502507
$22$		0			0
$23$	−2.69722			−0.562410			−0.281205	−	0.959648i	$-0.590734\pi$
$23$	−2.69722			−0.562410			−0.281205	+	0.959648i	$0.590734\pi$
$24$	5.58895	+	4.06061i	1.14084	+	0.828869i
$25$	2.47214	−	7.60845i	0.494427	−	1.52169i
$26$	4.70049	+	14.4666i	0.921842	+	2.83714i
$27$	−1.29892	+	0.943719i	−0.249977	+	0.181619i
$28$	2.67200	−	1.94132i	0.504961	−	0.366876i
$29$	1.45152	+	4.46733i	0.269541	+	0.829562i	0.990612	+	0.136701i	$0.0436499\pi$
$29$	1.45152	+	4.46733i	0.269541	+	0.829562i	−0.721071	+	0.692861i	$0.756350\pi$
$30$	−5.90823	+	18.1837i	−1.07869	+	3.31987i
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i	0.512758	−	0.858533i	$-0.328624\pi$
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i	−0.658062	+	0.752964i	$0.728624\pi$
$32$	−5.30278			−0.937407
$33$		0			0
$34$	6.21110			1.06520
$35$	2.91695	+	2.11929i	0.493055	+	0.358225i
$36$	2.35024	−	7.23331i	0.391707	−	1.20555i
$37$	−1.61032	−	4.95605i	−0.264735	−	0.814770i	−0.991754	−	0.128153i	$-0.959095\pi$
$37$	−1.61032	−	4.95605i	−0.264735	−	0.814770i	0.727020	−	0.686617i	$-0.240905\pi$
$38$	5.58895	−	4.06061i	0.906648	−	0.658718i
$39$	12.3060	−	8.94086i	1.97054	−	1.43168i
$40$	3.34253	+	10.2872i	0.528500	+	1.62656i
$41$	2.16312	−	6.65740i	0.337822	−	1.03971i	−0.627493	−	0.778623i	$-0.715919\pi$
$41$	2.16312	−	6.65740i	0.337822	−	1.03971i	0.965315	−	0.261088i	$-0.0840813\pi$
$42$	−4.29004	−	3.11689i	−0.661967	−	0.480947i
$43$	1.69722			0.258824			0.129412	−	0.991591i	$-0.458691\pi$
$43$	1.69722			0.258824			0.129412	+	0.991591i	$0.458691\pi$
$44$		0			0
$45$	8.30278			1.23770
$46$	5.02489	+	3.65079i	0.740879	+	0.538280i
$47$	−0.589705	+	1.81493i	−0.0860174	+	0.264734i	−0.984809	−	0.173642i	$-0.944446\pi$
$47$	−0.589705	+	1.81493i	−0.0860174	+	0.264734i	0.898791	+	0.438377i	$0.144446\pi$
$48$	−0.215454	−	0.663100i	−0.0310981	−	0.0957102i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−14.9039	+	10.8283i	−2.10773	+	1.53135i
$51$	−1.91934	−	5.90711i	−0.268761	−	0.827161i
$52$	6.74172	−	20.7489i	0.934908	−	2.87735i
$53$	10.4431	+	7.58732i	1.43446	+	1.04220i	0.989164	+	0.146818i	$0.0469031\pi$
$53$	10.4431	+	7.58732i	1.43446	+	1.04220i	0.445301	+	0.895381i	$0.353097\pi$
$54$	3.69722			0.503129
$55$		0			0
$56$	−3.00000			−0.400892
$57$	−5.58895	−	4.06061i	−0.740275	−	0.537841i
$58$	3.34253	−	10.2872i	0.438896	−	1.35078i
$59$	2.06956	+	6.36944i	0.269433	+	0.829230i	0.990639	+	0.136509i	$0.0435883\pi$
$59$	2.06956	+	6.36944i	0.269433	+	0.829230i	−0.721206	+	0.692721i	$0.756412\pi$
$60$	22.1850	−	16.1184i	2.86408	−	2.08087i
$61$	3.48102	−	2.52911i	0.445699	−	0.323819i	−0.342196	−	0.939628i	$-0.611171\pi$
$61$	3.48102	−	2.52911i	0.445699	−	0.323819i	0.787895	+	0.615809i	$0.211171\pi$
$62$	0.711597	+	2.19007i	0.0903729	+	0.278139i
$63$	−0.711597	+	2.19007i	−0.0896528	+	0.275923i
$64$	10.3689	+	7.53344i	1.29611	+	0.941680i
$65$	23.8167			2.95409
$66$		0			0
$67$	8.51388			1.04014			0.520068	−	0.854125i	$-0.325907\pi$
$67$	8.51388			1.04014			0.520068	+	0.854125i	$0.325907\pi$
$68$	−7.20699	−	5.23618i	−0.873976	−	0.634980i
$69$	1.91934	−	5.90711i	0.231061	−	0.711132i
$70$	−2.56570	−	7.89641i	−0.306660	−	0.943801i
$71$	3.48102	−	2.52911i	0.413121	−	0.300150i	−0.361743	−	0.932278i	$-0.617818\pi$
$71$	3.48102	−	2.52911i	0.413121	−	0.300150i	0.774864	+	0.632128i	$0.217818\pi$
$72$	−5.58895	+	4.06061i	−0.658665	+	0.478548i
$73$	−1.54508	−	4.75528i	−0.180839	−	0.556564i	0.819013	−	0.573774i	$-0.194521\pi$
$73$	−1.54508	−	4.75528i	−0.180839	−	0.556564i	−0.999852	+	0.0172107i	$0.994521\pi$
$74$	−3.70820	+	11.4127i	−0.431070	+	1.32670i
$75$	14.9039	+	10.8283i	1.72095	+	1.25034i
$76$	−9.90833			−1.13656
$77$		0			0
$78$	−35.0278			−3.96611
$79$	6.71709	+	4.88025i	0.755731	+	0.549071i	0.897598	−	0.440815i	$-0.145310\pi$
$79$	6.71709	+	4.88025i	0.755731	+	0.549071i	−0.141867	+	0.989886i	$0.545310\pi$
$80$	0.337346	−	1.03824i	0.0377164	−	0.116079i
$81$	−3.27730	−	10.0865i	−0.364144	−	1.12072i
$82$	−13.0409	+	9.47476i	−1.44013	+	1.04631i
$83$	−2.42705	+	1.76336i	−0.266403	+	0.193553i	−0.712965	−	0.701199i	$-0.752648\pi$
$83$	−2.42705	+	1.76336i	−0.266403	+	0.193553i	0.446562	+	0.894753i	$0.352648\pi$
$84$	2.35024	+	7.23331i	0.256433	+	0.789219i
$85$	3.00518	−	9.24901i	0.325958	−	1.00320i
$86$	−3.16190	−	2.29726i	−0.340957	−	0.247720i
$87$	−10.8167			−1.15967
$88$		0			0
$89$	−14.7250			−1.56084			−0.780422	−	0.625253i	$-0.784996\pi$
$89$	−14.7250			−1.56084			−0.780422	+	0.625253i	$0.784996\pi$
$90$	−15.4679	−	11.2381i	−1.63046	−	1.18460i
$91$	−2.04123	+	6.28225i	−0.213979	+	0.658559i
$92$	−2.75282	−	8.47232i	−0.287002	−	0.883301i
$93$	1.86298	−	1.35354i	0.193183	−	0.140355i
$94$	3.55518	−	2.58299i	0.366689	−	0.266415i
$95$	−3.34253	−	10.2872i	−0.342936	−	1.05545i
$96$	3.77344	−	11.6134i	0.385125	−	1.18529i
$97$	2.91695	+	2.11929i	0.296172	+	0.215181i	0.725940	−	0.687758i	$-0.241405\pi$
$97$	2.91695	+	2.11929i	0.296172	+	0.215181i	−0.429769	+	0.902939i	$0.641405\pi$
$98$	2.30278			0.232615
$99$		0			0
$100$	26.4222			2.64222
$101$	4.29004	+	3.11689i	0.426874	+	0.310142i	0.780398	−	0.625283i	$-0.215017\pi$
$101$	4.29004	+	3.11689i	0.426874	+	0.310142i	−0.353523	+	0.935426i	$0.615017\pi$
$102$	−4.41980	+	13.6027i	−0.437625	+	1.34687i
$103$	−4.41980	−	13.6027i	−0.435496	−	1.34032i	−0.892578	−	0.450894i	$-0.851105\pi$
$103$	−4.41980	−	13.6027i	−0.435496	−	1.34032i	0.457082	−	0.889425i	$-0.348895\pi$
$104$	−16.0320	+	11.6479i	−1.57207	+	1.14217i
$105$	−6.71709	+	4.88025i	−0.655521	+	0.476264i
$106$	−9.18552	−	28.2701i	−0.892177	−	2.74584i
$107$	3.83010	−	11.7878i	0.370269	−	1.13957i	−0.576346	−	0.817206i	$-0.695522\pi$
$107$	3.83010	−	11.7878i	0.370269	−	1.13957i	0.946615	−	0.322366i	$-0.104478\pi$
$108$	−4.29004	−	3.11689i	−0.412809	−	0.299923i
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$	12.0000			1.13899
$112$	0.244951	+	0.177967i	0.0231457	+	0.0168163i
$113$	−3.30562	+	10.1737i	−0.310967	+	0.957058i	0.666416	+	0.745580i	$0.267828\pi$
$113$	−3.30562	+	10.1737i	−0.310967	+	0.957058i	−0.977383	+	0.211478i	$0.932172\pi$
$114$	4.91594	+	15.1297i	0.460420	+	1.41703i
$115$	7.86767	−	5.71620i	0.733664	−	0.533038i
$116$	−12.5510	+	9.11883i	−1.16533	+	0.846662i
$117$	4.70049	+	14.4666i	0.434560	+	1.33744i
$118$	4.76572	−	14.6674i	0.438720	−	1.35024i
$119$	2.18210	+	1.58539i	0.200033	+	0.145332i
$120$	−24.9083			−2.27381
$121$		0			0
$122$	−9.90833			−0.897058
$123$	13.0409	+	9.47476i	1.17586	+	0.854311i
$124$	1.02061	−	3.14113i	0.0916538	−	0.282081i
$125$	3.34253	+	10.2872i	0.298965	+	0.920120i
$126$	4.29004	−	3.11689i	0.382187	−	0.277675i
$127$	−1.61803	+	1.17557i	−0.143577	+	0.104315i	−0.657255	−	0.753668i	$-0.728283\pi$
$127$	−1.61803	+	1.17557i	−0.143577	+	0.104315i	0.513678	+	0.857983i	$0.328283\pi$
$128$	−5.84299	−	17.9829i	−0.516453	−	1.58948i
$129$	−1.20774	+	3.71704i	−0.106336	+	0.327267i
$130$	−44.3701	−	32.2367i	−3.89151	−	2.82735i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	3.00000			0.260133
$134$	−15.8612	−	11.5239i	−1.37020	−	0.995509i
$135$	1.78887	−	5.50557i	0.153961	−	0.473844i
$136$	2.50046	+	7.69564i	0.214413	+	0.659896i
$137$	8.18679	−	5.94805i	0.699445	−	0.508176i	−0.180307	−	0.983610i	$-0.557709\pi$
$137$	8.18679	−	5.94805i	0.699445	−	0.508176i	0.879751	+	0.475434i	$0.157709\pi$
$138$	−11.5712	+	8.40696i	−0.985005	+	0.715648i
$139$	6.67648	+	20.5481i	0.566292	+	1.74287i	0.664082	+	0.747660i	$0.268823\pi$
$139$	6.67648	+	20.5481i	0.566292	+	1.74287i	−0.0977898	+	0.995207i	$0.531177\pi$
$140$	−3.67988	+	11.3255i	−0.311006	+	0.957179i
$141$	−3.55518	−	2.58299i	−0.299400	−	0.217527i
$142$	−9.90833			−0.831488
$143$		0			0
$144$	0.697224			0.0581020
$145$	−13.7016	−	9.95478i	−1.13785	−	0.826699i
$146$	−3.55798	+	10.9503i	−0.294461	+	0.906257i
$147$	−0.711597	−	2.19007i	−0.0586915	−	0.180634i
$148$	13.9241	−	10.1164i	1.14455	−	0.831566i
$149$	3.97092	−	2.88504i	0.325310	−	0.236352i	−0.413128	−	0.910673i	$-0.635564\pi$
$149$	3.97092	−	2.88504i	0.325310	−	0.236352i	0.738438	+	0.674321i	$0.235564\pi$
$150$	−13.1092	−	40.3459i	−1.07036	−	3.29423i
$151$	−0.0652343	+	0.200770i	−0.00530869	+	0.0163385i	−0.953676	−	0.300836i	$-0.902734\pi$
$151$	−0.0652343	+	0.200770i	−0.00530869	+	0.0163385i	0.948367	+	0.317175i	$0.102734\pi$
$152$	7.28115	+	5.29007i	0.590579	+	0.429081i
$153$	6.21110			0.502138
$154$		0			0
$155$	3.60555			0.289605
$156$	40.6441	+	29.5297i	3.25413	+	2.36426i
$157$	2.22835	−	6.85817i	0.177842	−	0.547341i	−0.821910	−	0.569618i	$-0.807091\pi$
$157$	2.22835	−	6.85817i	0.177842	−	0.547341i	0.999752	+	0.0222763i	$0.00709134\pi$
$158$	−5.90823	−	18.1837i	−0.470033	−	1.44661i
$159$	−24.0480	+	17.4719i	−1.90713	+	1.38561i
$160$	15.4679	−	11.2381i	1.22285	−	0.888451i
$161$	0.833488	+	2.56521i	0.0656881	+	0.202167i
$162$	−7.54688	+	23.2269i	−0.592939	+	1.82488i
$163$	−2.27872	−	1.65559i	−0.178483	−	0.129676i	0.494957	−	0.868918i	$-0.335184\pi$
$163$	−2.27872	−	1.65559i	−0.178483	−	0.129676i	−0.673440	+	0.739242i	$0.735184\pi$
$164$	23.1194			1.80532
$165$		0			0
$166$	6.90833			0.536190
$167$	4.21587	+	3.06301i	0.326234	+	0.237023i	0.738831	−	0.673891i	$-0.235378\pi$
$167$	4.21587	+	3.06301i	0.326234	+	0.237023i	−0.412597	+	0.910914i	$0.635378\pi$
$168$	2.13479	−	6.57021i	0.164703	−	0.506903i
$169$	9.46621	+	29.1340i	0.728170	+	2.24108i
$170$	−18.1175	+	13.1631i	−1.38955	+	1.00957i
$171$	5.58895	−	4.06061i	0.427398	−	0.310523i
$172$	1.73221	+	5.33120i	0.132080	+	0.406500i
$173$	−0.402580	+	1.23901i	−0.0306076	+	0.0942004i	−0.965193	−	0.261538i	$-0.915770\pi$
$173$	−0.402580	+	1.23901i	−0.0306076	+	0.0942004i	0.934586	+	0.355738i	$0.115770\pi$
$174$	20.1513	+	14.6407i	1.52766	+	1.10991i
$175$	−8.00000			−0.604743
$176$		0			0
$177$	−15.4222			−1.15920
$178$	27.4324	+	19.9308i	2.05615	+	1.49388i
$179$	−1.97599	+	6.08148i	−0.147693	+	0.454551i	−0.997347	−	0.0727880i	$-0.976810\pi$
$179$	−1.97599	+	6.08148i	−0.147693	+	0.454551i	0.849655	+	0.527339i	$0.176810\pi$
$180$	8.47393	+	26.0801i	0.631609	+	1.94389i
$181$	20.3962	−	14.8187i	1.51604	−	1.10147i	0.552631	−	0.833426i	$-0.313624\pi$
$181$	20.3962	−	14.8187i	1.51604	−	1.10147i	0.963408	−	0.268040i	$-0.0863760\pi$
$182$	12.3060	−	8.94086i	0.912184	−	0.662741i
$183$	3.06184	+	9.42338i	0.226338	+	0.696596i
$184$	−2.50046	+	7.69564i	−0.184337	+	0.567330i
$185$	15.2005	+	11.0438i	1.11757	+	0.811959i
$186$	−5.30278			−0.388818
$187$		0			0
$188$	−6.30278			−0.459677
$189$	1.29892	+	0.943719i	0.0944824	+	0.0686455i
$190$	−7.69710	+	23.6892i	−0.558406	+	1.71860i
$191$	−8.28680	−	25.5042i	−0.599612	−	1.84542i	−0.530281	−	0.847822i	$-0.677914\pi$
$191$	−8.28680	−	25.5042i	−0.599612	−	1.84542i	−0.0693311	−	0.997594i	$-0.522086\pi$
$192$	−23.8772	+	17.3478i	−1.72319	+	1.25197i
$193$	1.71465	−	1.24577i	0.123424	−	0.0896724i	−0.524361	−	0.851496i	$-0.675696\pi$
$193$	1.71465	−	1.24577i	0.123424	−	0.0896724i	0.647784	+	0.761824i	$0.275696\pi$
$194$	−2.56570	−	7.89641i	−0.184206	−	0.566929i
$195$	−16.9479	+	52.1601i	−1.21366	+	3.73526i
$196$	−2.67200	−	1.94132i	−0.190857	−	0.138666i
$197$	−10.6056			−0.755614			−0.377807	−	0.925884i	$-0.623322\pi$
$197$	−10.6056			−0.755614			−0.377807	+	0.925884i	$0.623322\pi$
$198$		0			0
$199$	19.4222			1.37680			0.688402	−	0.725330i	$-0.258313\pi$
$199$	19.4222			1.37680			0.688402	+	0.725330i	$0.258313\pi$
$200$	−19.4164	−	14.1068i	−1.37295	−	0.997505i
$201$	−6.05845	+	18.6460i	−0.427330	+	1.31519i
$202$	−3.77344	−	11.6134i	−0.265498	−	0.817119i
$203$	3.80013	−	2.76096i	0.266717	−	0.193781i
$204$	16.5961	−	12.0578i	1.16196	−	0.844212i
$205$	7.79924	+	24.0036i	0.544722	+	1.67648i
$206$	−10.1778	+	31.3241i	−0.709122	+	2.18245i
$207$	5.02489	+	3.65079i	0.349254	+	0.253748i
$208$	2.00000			0.138675
$209$		0			0
$210$	19.1194			1.31937
$211$	−12.5510	−	9.11883i	−0.864046	−	0.627766i	0.0649368	−	0.997889i	$-0.479315\pi$
$211$	−12.5510	−	9.11883i	−0.864046	−	0.627766i	−0.928983	+	0.370123i	$0.879315\pi$
$212$	−13.1744	+	40.5467i	−0.904823	+	2.78476i
$213$	3.06184	+	9.42338i	0.209794	+	0.645679i
$214$	−23.0907	+	16.7764i	−1.57845	+	1.14681i
$215$	−4.95072	+	3.59691i	−0.337636	+	0.245307i
$216$	1.48843	+	4.58091i	0.101275	+	0.311691i
$217$	−0.309017	+	0.951057i	−0.0209774	+	0.0645619i
$218$	14.9039	+	10.8283i	1.00942	+	0.733385i
$219$	11.5139			0.778036
$220$		0			0
$221$	17.8167			1.19848
$222$	−22.3558	−	16.2425i	−1.50042	−	1.09012i
$223$	4.29791	−	13.2276i	0.287809	−	0.885786i	−0.697733	−	0.716358i	$-0.745808\pi$
$223$	4.29791	−	13.2276i	0.287809	−	0.885786i	0.985543	−	0.169428i	$-0.0541921\pi$
$224$	1.63865	+	5.04324i	0.109487	+	0.336966i
$225$	−14.9039	+	10.8283i	−0.993592	+	0.721887i
$226$	19.9288	−	14.4791i	1.32564	−	0.963135i
$227$	2.01290	+	6.19507i	0.133601	+	0.411181i	0.995370	−	0.0961200i	$-0.0306432\pi$
$227$	2.01290	+	6.19507i	0.133601	+	0.411181i	−0.861769	+	0.507301i	$0.830643\pi$
$228$	7.05073	−	21.6999i	0.466946	−	1.43711i
$229$	2.10794	+	1.53150i	0.139296	+	0.101205i	0.655251	−	0.755411i	$-0.272563\pi$
$229$	2.10794	+	1.53150i	0.139296	+	0.101205i	−0.515955	+	0.856616i	$0.672563\pi$
$230$	−22.3944			−1.47665
$231$		0			0
$232$	14.0917			0.925164
$233$	−14.5623	−	10.5801i	−0.954008	−	0.693128i	−0.00225687	−	0.999997i	$-0.500718\pi$
$233$	−14.5623	−	10.5801i	−0.954008	−	0.693128i	−0.951752	+	0.306870i	$0.900718\pi$
$234$	10.8242	−	33.3134i	0.707598	−	2.17776i
$235$	−2.12621	−	6.54381i	−0.138699	−	0.426871i
$236$	−17.8950	+	13.0015i	−1.16486	+	0.846324i
$237$	−15.4679	+	11.2381i	−1.00475	+	0.729994i
$238$	−1.91934	−	5.90711i	−0.124412	−	0.382901i
$239$	8.13658	−	25.0418i	0.526312	−	1.61982i	−0.235396	−	0.971900i	$-0.575639\pi$
$239$	8.13658	−	25.0418i	0.526312	−	1.61982i	0.761707	−	0.647921i	$-0.224361\pi$
$240$	2.03377	+	1.47762i	0.131279	+	0.0953800i
$241$	0.486122			0.0313139			0.0156569	−	0.999877i	$-0.495016\pi$
$241$	0.486122			0.0313139			0.0156569	+	0.999877i	$0.495016\pi$
$242$		0			0
$243$	19.6056			1.25770
$244$	11.4970	+	8.35308i	0.736022	+	0.534751i
$245$	1.11418	−	3.42908i	0.0711821	−	0.219076i
$246$	−11.4705	−	35.3027i	−0.731335	−	2.25082i
$247$	16.0320	−	11.6479i	1.02009	−	0.741140i
$248$	−2.42705	+	1.76336i	−0.154118	+	0.111973i
$249$	−2.13479	−	6.57021i	−0.135287	−	0.416370i
$250$	7.69710	−	23.6892i	0.486807	−	1.49824i
$251$	−3.55518	−	2.58299i	−0.224401	−	0.163037i	0.469904	−	0.882717i	$-0.344288\pi$
$251$	−3.55518	−	2.58299i	−0.224401	−	0.163037i	−0.694306	+	0.719680i	$0.744288\pi$
$252$	−7.60555			−0.479105
$253$		0			0
$254$	4.60555			0.288978
$255$	18.1175	+	13.1631i	1.13456	+	0.824307i
$256$	−5.53398	+	17.0318i	−0.345874	+	1.06449i
$257$	2.00432	+	6.16867i	0.125026	+	0.384791i	0.993906	−	0.110232i	$-0.0351595\pi$
$257$	2.00432	+	6.16867i	0.125026	+	0.384791i	−0.868880	+	0.495023i	$0.835160\pi$
$258$	7.28115	−	5.29007i	0.453305	−	0.329345i
$259$	−4.21587	+	3.06301i	−0.261961	+	0.190326i
$260$	24.3076	+	74.8111i	1.50749	+	4.63959i
$261$	3.34253	−	10.2872i	0.206897	−	0.636765i
$262$	11.1779	+	8.12123i	0.690573	+	0.501731i
$263$	20.2389			1.24798			0.623991	−	0.781432i	$-0.285510\pi$
$263$	20.2389			1.24798			0.623991	+	0.781432i	$0.285510\pi$
$264$		0			0
$265$	−46.5416			−2.85903
$266$	−5.58895	−	4.06061i	−0.342681	−	0.248972i
$267$	10.4782	−	32.2487i	0.641258	−	1.97359i
$268$	8.68938	+	26.7432i	0.530788	+	1.63360i
$269$	−13.0409	+	9.47476i	−0.795117	+	0.577686i	−0.909478	−	0.415753i	$-0.863518\pi$
$269$	−13.0409	+	9.47476i	−0.795117	+	0.577686i	0.114360	+	0.993439i	$0.463518\pi$
$270$	−10.7846	+	7.83549i	−0.656331	+	0.476853i
$271$	−8.81127	−	27.1183i	−0.535247	−	1.64732i	−0.743115	−	0.669163i	$-0.766653\pi$
$271$	−8.81127	−	27.1183i	−0.535247	−	1.64732i	0.207869	−	0.978157i	$-0.433347\pi$
$272$	0.252360	−	0.776684i	0.0153016	−	0.0470934i
$273$	−12.3060	−	8.94086i	−0.744795	−	0.541126i
$274$	−23.3028			−1.40777
$275$		0			0
$276$	20.5139			1.23479
$277$	−24.2188	−	17.5960i	−1.45517	−	1.05724i	−0.984589	−	0.174882i	$-0.944046\pi$
$277$	−24.2188	−	17.5960i	−1.45517	−	1.05724i	−0.470577	−	0.882359i	$-0.655954\pi$
$278$	15.3744	−	47.3177i	0.922098	−	2.83792i
$279$	0.711597	+	2.19007i	0.0426022	+	0.131116i
$280$	8.75086	−	6.35787i	0.522964	−	0.379955i
$281$	−5.17322	+	3.75856i	−0.308608	+	0.224217i	−0.731299	−	0.682057i	$-0.761086\pi$
$281$	−5.17322	+	3.75856i	−0.308608	+	0.224217i	0.422691	+	0.906274i	$0.361086\pi$
$282$	3.12708	+	9.62415i	0.186215	+	0.573110i
$283$	1.35796	−	4.17937i	0.0807223	−	0.248438i	−0.902548	−	0.430589i	$-0.858306\pi$
$283$	1.35796	−	4.17937i	0.0807223	−	0.248438i	0.983271	+	0.182151i	$0.0583060\pi$
$284$	11.4970	+	8.35308i	0.682223	+	0.495664i
$285$	24.9083			1.47544
$286$		0			0
$287$	−7.00000			−0.413197
$288$	9.87899	+	7.17751i	0.582125	+	0.422939i
$289$	−3.00518	+	9.24901i	−0.176776	+	0.544059i
$290$	12.0517	+	37.0912i	0.707698	+	2.17807i
$291$	−6.71709	+	4.88025i	−0.393763	+	0.286085i
$292$	13.3600	−	9.70661i	0.781835	−	0.568037i
$293$	1.48843	+	4.58091i	0.0869549	+	0.267620i	0.985074	−	0.172133i	$-0.0550660\pi$
$293$	1.48843	+	4.58091i	0.0869549	+	0.267620i	−0.898119	+	0.439753i	$0.855066\pi$
$294$	−1.63865	+	5.04324i	−0.0955679	+	0.294128i
$295$	−19.5355	−	14.1934i	−1.13740	−	0.826369i
$296$	−15.6333			−0.908668
$297$		0			0
$298$	−11.3028			−0.654752
$299$	14.4140	+	10.4724i	0.833582	+	0.605633i
$300$	−18.8020	+	57.8665i	−1.08553	+	3.34092i
$301$	−0.524471	−	1.61416i	−0.0302300	−	0.0930384i
$302$	0.393281	−	0.285735i	0.0226308	−	0.0164422i
$303$	−9.87899	+	7.17751i	−0.567533	+	0.412337i
$304$	−0.280688	−	0.863870i	−0.0160986	−	0.0495464i
$305$	−4.79405	+	14.7546i	−0.274507	+	0.844845i
$306$	−11.5712	−	8.40696i	−0.661481	−	0.480594i
$307$	−16.6333			−0.949313			−0.474657	−	0.880171i	$-0.657428\pi$
$307$	−16.6333			−0.949313			−0.474657	+	0.880171i	$0.657428\pi$
$308$		0			0
$309$	32.9361			1.87367
$310$	−6.71709	−	4.88025i	−0.381505	−	0.277180i
$311$	1.97599	−	6.08148i	0.112048	−	0.344849i	−0.879272	−	0.476321i	$-0.841970\pi$
$311$	1.97599	−	6.08148i	0.112048	−	0.344849i	0.991320	+	0.131471i	$0.0419702\pi$
$312$	−14.1015	−	43.3999i	−0.798338	−	2.45703i
$313$	−12.3802	+	8.99475i	−0.699771	+	0.508413i	−0.879857	−	0.475238i	$-0.842362\pi$
$313$	−12.3802	+	8.99475i	−0.699771	+	0.508413i	0.180087	+	0.983651i	$0.442362\pi$
$314$	−13.4342	+	9.76050i	−0.758134	+	0.550817i
$315$	−2.56570	−	7.89641i	−0.144561	−	0.444912i
$316$	−8.47393	+	26.0801i	−0.476696	+	1.46712i
$317$	−13.9982	−	10.1703i	−0.786219	−	0.571222i	0.120620	−	0.992699i	$-0.461512\pi$
$317$	−13.9982	−	10.1703i	−0.786219	−	0.571222i	−0.906839	+	0.421477i	$0.861512\pi$
$318$	68.4500			3.83848
$319$		0			0
$320$	−46.2111			−2.58328
$321$	23.0907	+	16.7764i	1.28880	+	0.936365i
$322$	1.91934	−	5.90711i	0.106960	−	0.329190i
$323$	−2.50046	−	7.69564i	−0.139130	−	0.428197i
$324$	28.3381	−	20.5888i	1.57434	−	1.14382i
$325$	−42.7520	+	31.0612i	−2.37146	+	1.72296i
$326$	2.00432	+	6.16867i	0.111009	+	0.341651i
$327$	5.69277	−	17.5206i	0.314811	−	0.968889i
$328$	−16.9894	−	12.3435i	−0.938080	−	0.681555i
$329$	1.90833			0.105209
$330$		0			0
$331$	23.8167			1.30908			0.654541	−	0.756027i	$-0.272862\pi$
$331$	23.8167			1.30908			0.654541	+	0.756027i	$0.272862\pi$
$332$	−8.01600	−	5.82397i	−0.439935	−	0.319632i
$333$	−3.70820	+	11.4127i	−0.203208	+	0.625411i
$334$	−3.70820	−	11.4127i	−0.202904	−	0.624474i
$335$	−24.8346	+	18.0434i	−1.35686	+	0.985815i
$336$	−0.564066	+	0.409818i	−0.0307723	+	0.0223574i
$337$	3.64297	+	11.2119i	0.198445	+	0.610752i	0.999919	+	0.0127217i	$0.00404957\pi$
$337$	3.64297	+	11.2119i	0.198445	+	0.610752i	−0.801474	+	0.598030i	$0.795950\pi$
$338$	21.7986	−	67.0891i	1.18569	−	3.64916i
$339$	−19.9288	−	14.4791i	−1.08238	−	0.786396i
$340$	32.1194			1.74192
$341$		0			0
$342$	−15.9083			−0.860224
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	1.57341	−	4.84247i	0.0848328	−	0.261088i
$345$	6.92027	+	21.2984i	0.372575	+	1.14667i
$346$	2.42705	−	1.76336i	0.130479	−	0.0947986i
$347$	−7.77105	+	5.64600i	−0.417172	+	0.303093i	−0.776499	−	0.630119i	$-0.783006\pi$
$347$	−7.77105	+	5.64600i	−0.417172	+	0.303093i	0.359327	+	0.933212i	$0.383006\pi$
$348$	−11.0396	−	33.9765i	−0.591786	−	1.82133i
$349$	−1.45152	+	4.46733i	−0.0776982	+	0.239130i	−0.982360	−	0.187000i	$-0.940124\pi$
$349$	−1.45152	+	4.46733i	−0.0776982	+	0.239130i	0.904662	+	0.426130i	$0.140124\pi$
$350$	14.9039	+	10.8283i	0.796646	+	0.578797i
$351$	10.6056			0.566082
$352$		0			0
$353$	5.09167			0.271002			0.135501	−	0.990777i	$-0.456736\pi$
$353$	5.09167			0.271002			0.135501	+	0.990777i	$0.456736\pi$
$354$	28.7313	+	20.8745i	1.52705	+	1.10947i
$355$	−4.79405	+	14.7546i	−0.254442	+	0.783092i
$356$	−15.0285	−	46.2530i	−0.796510	−	2.45141i
$357$	−5.02489	+	3.65079i	−0.265945	+	0.193221i
$358$	11.9128	−	8.65513i	0.629609	−	0.457438i
$359$	−10.4868	−	32.2751i	−0.553474	−	1.70342i	−0.699941	−	0.714201i	$-0.746790\pi$
$359$	−10.4868	−	32.2751i	−0.553474	−	1.70342i	0.146467	−	0.989216i	$-0.453210\pi$
$360$	7.69710	−	23.6892i	0.405673	−	1.24853i
$361$	8.09017	+	5.87785i	0.425798	+	0.309361i
$362$	−58.0555			−3.05133
$363$		0			0
$364$	−21.8167			−1.14350
$365$	14.5848	+	10.5964i	0.763401	+	0.554644i
$366$	7.05073	−	21.6999i	0.368548	−	1.13427i
$367$	−5.44899	−	16.7703i	−0.284435	−	0.875401i	−0.986567	−	0.163355i	$-0.947769\pi$
$367$	−5.44899	−	16.7703i	−0.284435	−	0.875401i	0.702132	−	0.712046i	$-0.252231\pi$
$368$	0.660687	−	0.480017i	0.0344407	−	0.0250226i
$369$	−13.0409	+	9.47476i	−0.678882	+	0.493236i
$370$	−13.3701	−	41.1490i	−0.695079	−	2.13923i
$371$	3.98889	−	12.2765i	0.207093	−	0.637367i
$372$	6.15302	+	4.47043i	0.319019	+	0.231781i
$373$	−20.1194			−1.04174			−0.520872	−	0.853635i	$-0.674393\pi$
$373$	−20.1194			−1.04174			−0.520872	+	0.853635i	$0.674393\pi$
$374$		0			0
$375$	−24.9083			−1.28626
$376$	4.63161	+	3.36506i	0.238857	+	0.173540i
$377$	9.58810	−	29.5091i	0.493812	−	1.51980i
$378$	−1.14251	−	3.51627i	−0.0587641	−	0.180857i
$379$	12.7959	−	9.29680i	0.657283	−	0.477544i	−0.208461	−	0.978031i	$-0.566845\pi$
$379$	12.7959	−	9.29680i	0.657283	−	0.477544i	0.865744	+	0.500486i	$0.166845\pi$
$380$	28.9021	−	20.9986i	1.48265	−	1.07721i
$381$	−1.42319	−	4.38014i	−0.0729124	−	0.224401i
$382$	−19.0826	+	58.7303i	−0.976353	+	3.00491i
$383$	−31.2550	−	22.7081i	−1.59706	−	1.16033i	−0.892871	−	0.450313i	$-0.851313\pi$
$383$	−31.2550	−	22.7081i	−1.59706	−	1.16033i	−0.704185	−	0.710016i	$-0.748687\pi$
$384$	43.5416			2.22197
$385$		0			0
$386$	−4.88057			−0.248414
$387$	−3.16190	−	2.29726i	−0.160729	−	0.116776i
$388$	−3.67988	+	11.3255i	−0.186817	+	0.574965i
$389$	−2.41548	−	7.43408i	−0.122470	−	0.376923i	0.870962	−	0.491350i	$-0.163497\pi$
$389$	−2.41548	−	7.43408i	−0.122470	−	0.376923i	−0.993432	+	0.114428i	$0.963497\pi$
$390$	102.174	−	74.2340i	5.17380	−	3.75898i
$391$	5.88561	−	4.27615i	0.297648	−	0.216254i
$392$	0.927051	+	2.85317i	0.0468231	+	0.144107i
$393$	4.26958	−	13.1404i	0.215372	−	0.662846i
$394$	19.7580	+	14.3550i	0.995393	+	0.723195i
$395$	−29.9361			−1.50625
$396$		0			0
$397$	30.2111			1.51625			0.758126	−	0.652108i	$-0.226115\pi$
$397$	30.2111			1.51625			0.758126	+	0.652108i	$0.226115\pi$
$398$	−36.1833	−	26.2887i	−1.81370	−	1.31773i
$399$	−2.13479	+	6.57021i	−0.106873	+	0.328922i
$400$	0.748503	+	2.30365i	0.0374251	+	0.115183i
$401$	17.1601	−	12.4676i	0.856937	−	0.622601i	−0.0701132	−	0.997539i	$-0.522336\pi$
$401$	17.1601	−	12.4676i	0.856937	−	0.622601i	0.927050	+	0.374938i	$0.122336\pi$
$402$	36.5248	−	26.5369i	1.82169	−	1.32354i
$403$	2.04123	+	6.28225i	0.101681	+	0.312941i
$404$	−5.41209	+	16.6567i	−0.269261	+	0.828701i
$405$	30.9359	+	22.4762i	1.53722	+	1.11685i
$406$	−10.8167			−0.536822
$407$		0			0
$408$	−18.6333			−0.922486
$409$	−16.6702	−	12.1116i	−0.824290	−	0.598882i	0.0936478	−	0.995605i	$-0.470147\pi$
$409$	−16.6702	−	12.1116i	−0.824290	−	0.598882i	−0.917938	+	0.396723i	$0.870147\pi$
$410$	17.9599	−	55.2749i	0.886976	−	2.72983i
$411$	7.20095	+	22.1623i	0.355197	+	1.09318i
$412$	38.2170	−	27.7663i	1.88282	−	1.36795i
$413$	5.41817	−	3.93653i	0.266611	−	0.193704i
$414$	−4.41980	−	13.6027i	−0.217221	−	0.668539i
$415$	3.34253	−	10.2872i	0.164078	−	0.504981i
$416$	28.3381	+	20.5888i	1.38939	+	1.00945i
$417$	−49.7527			−2.43640
$418$		0			0
$419$	−38.4222			−1.87705			−0.938524	−	0.345215i	$-0.887806\pi$
$419$	−38.4222			−1.87705			−0.938524	+	0.345215i	$0.887806\pi$
$420$	−22.1850	−	16.1184i	−1.08252	−	0.786496i
$421$	−6.74172	+	20.7489i	−0.328571	+	1.01124i	0.641232	+	0.767347i	$0.278424\pi$
$421$	−6.74172	+	20.7489i	−0.328571	+	1.01124i	−0.969803	+	0.243891i	$0.921576\pi$
$422$	11.0396	+	33.9765i	0.537401	+	1.65395i
$423$	3.55518	−	2.58299i	0.172859	−	0.125589i
$424$	31.3292	−	22.7620i	1.52148	−	1.10542i
$425$	6.66791	+	20.5217i	0.323441	+	0.995449i
$426$	7.05073	−	21.6999i	0.341609	−	1.05136i
$427$	−3.48102	−	2.52911i	−0.168458	−	0.122392i
$428$	40.9361			1.97872
$429$		0			0
$430$	14.0917			0.679561
$431$	2.52367	+	1.83355i	0.121561	+	0.0883192i	0.646905	−	0.762571i	$-0.276063\pi$
$431$	2.52367	+	1.83355i	0.121561	+	0.0883192i	−0.525344	+	0.850890i	$0.676063\pi$
$432$	0.150220	−	0.462329i	0.00722746	−	0.0222438i
$433$	9.00698	+	27.7206i	0.432848	+	1.33217i	0.895276	+	0.445511i	$0.146978\pi$
$433$	9.00698	+	27.7206i	0.432848	+	1.33217i	−0.462429	+	0.886657i	$0.653022\pi$
$434$	1.86298	−	1.35354i	0.0894261	−	0.0649719i
$435$	31.5517	−	22.9236i	1.51279	−	1.09910i
$436$	−8.16491	−	25.1290i	−0.391028	−	1.20346i
$437$	2.50046	−	7.69564i	0.119613	−	0.368132i
$438$	−21.4502	−	15.5845i	−1.02493	−	0.744655i
$439$	27.7250			1.32324			0.661621	−	0.749839i	$-0.269869\pi$
$439$	27.7250			1.32324			0.661621	+	0.749839i	$0.269869\pi$
$440$		0			0
$441$	2.30278			0.109656
$442$	−33.1922	−	24.1155i	−1.57879	−	1.14706i
$443$	8.32371	−	25.6177i	0.395471	−	1.21714i	−0.533123	−	0.846038i	$-0.678982\pi$
$443$	8.32371	−	25.6177i	0.395471	−	1.21714i	0.928594	−	0.371097i	$-0.121018\pi$
$444$	12.2474	+	37.6935i	0.581234	+	1.78886i
$445$	42.9521	−	31.2065i	2.03612	−	1.47933i
$446$	−25.9110	+	18.8254i	−1.22692	+	0.891411i
$447$	3.49275	+	10.7496i	0.165201	+	0.508438i
$448$	3.96056	−	12.1894i	0.187119	−	0.575893i
$449$	−32.6281	−	23.7057i	−1.53981	−	1.11874i	−0.950452	−	0.310872i	$-0.899379\pi$
$449$	−32.6281	−	23.7057i	−1.53981	−	1.11874i	−0.589363	−	0.807868i	$-0.700621\pi$
$450$	42.4222			1.99980
$451$		0			0
$452$	−35.3305			−1.66181
$453$	−0.393281	−	0.285735i	−0.0184779	−	0.0134250i
$454$	4.63525	−	14.2658i	0.217543	−	0.669529i
$455$	−7.35975	−	22.6510i	−0.345030	−	1.06189i
$456$	−16.7669	+	12.1818i	−0.785180	+	0.570467i
$457$	−17.0860	+	12.4137i	−0.799248	+	0.580688i	−0.910694	−	0.413083i	$-0.864452\pi$
$457$	−17.0860	+	12.4137i	−0.799248	+	0.580688i	0.111445	+	0.993771i	$0.464452\pi$
$458$	−1.85410	−	5.70634i	−0.0866365	−	0.266640i
$459$	1.33821	−	4.11858i	0.0624622	−	0.192239i
$460$	25.9852	+	18.8793i	1.21156	+	0.880253i
$461$	8.09167			0.376867			0.188433	−	0.982086i	$-0.439659\pi$
$461$	8.09167			0.376867			0.188433	+	0.982086i	$0.439659\pi$
$462$		0			0
$463$	−30.8167			−1.43217			−0.716086	−	0.698012i	$-0.754068\pi$
$463$	−30.8167			−1.43217			−0.716086	+	0.698012i	$0.754068\pi$
$464$	−1.15059	−	0.835951i	−0.0534147	−	0.0388081i
$465$	−2.56570	+	7.89641i	−0.118981	+	0.366187i
$466$	12.8087	+	39.4213i	0.593354	+	1.82615i
$467$	10.9554	−	7.95957i	0.506956	−	0.368325i	−0.304712	−	0.952445i	$-0.598560\pi$
$467$	10.9554	−	7.95957i	0.506956	−	0.368325i	0.811668	+	0.584120i	$0.198560\pi$
$468$	−40.6441	+	29.5297i	−1.87877	+	1.36501i
$469$	−2.63093	−	8.09718i	−0.121485	−	0.373893i
$470$	−4.89619	+	15.0689i	−0.225844	+	0.695078i
$471$	13.4342	+	9.76050i	0.619014	+	0.449740i
$472$	20.0917			0.924794
$473$		0			0
$474$	44.0278			2.02226
$475$	19.4164	+	14.1068i	0.890886	+	0.647266i
$476$	−2.75282	+	8.47232i	−0.126175	+	0.388328i
$477$	−9.18552	−	28.2701i	−0.420576	−	1.29440i
$478$	−49.0534	+	35.6394i	−2.24365	+	1.63011i
$479$	23.1648	−	16.8302i	1.05843	−	0.768993i	0.0846313	−	0.996412i	$-0.473029\pi$
$479$	23.1648	−	16.8302i	1.05843	−	0.768993i	0.973797	+	0.227419i	$0.0730288\pi$
$480$	13.6053	+	41.8729i	0.620995	+	1.91123i
$481$	−10.6370	+	32.7375i	−0.485008	+	1.49270i
$482$	−0.905637	−	0.657984i	−0.0412507	−	0.0299704i
$483$	−6.21110			−0.282615
$484$		0			0
$485$	−13.0000			−0.590300
$486$	−36.5248	−	26.5369i	−1.65680	−	1.20374i
$487$	−0.870394	+	2.67880i	−0.0394413	+	0.121388i	−0.968839	−	0.247693i	$-0.920328\pi$
$487$	−0.870394	+	2.67880i	−0.0394413	+	0.121388i	0.929397	+	0.369081i	$0.120328\pi$
$488$	−3.98889	−	12.2765i	−0.180569	−	0.555733i
$489$	5.24738	−	3.81245i	0.237295	−	0.172405i
$490$	−6.71709	+	4.88025i	−0.303447	+	0.220467i
$491$	−3.92366	−	12.0758i	−0.177072	−	0.544972i	0.822650	−	0.568548i	$-0.192495\pi$
$491$	−3.92366	−	12.0758i	−0.177072	−	0.544972i	−0.999722	+	0.0235761i	$0.992495\pi$
$492$	−16.4517	+	50.6332i	−0.741700	+	2.28272i
$493$	−10.2498	−	7.44693i	−0.461628	−	0.335393i
$494$	−45.6333			−2.05314
$495$		0			0
$496$	0.302776			0.0135950
$497$	−3.48102	−	2.52911i	−0.156145	−	0.113446i
$498$	−4.91594	+	15.1297i	−0.220289	+	0.677979i
$499$	0.898722	+	2.76598i	0.0402323	+	0.123822i	0.969155	−	0.246450i	$-0.0792642\pi$
$499$	0.898722	+	2.76598i	0.0402323	+	0.123822i	−0.928923	+	0.370273i	$0.879264\pi$
$500$	−28.9021	+	20.9986i	−1.29254	+	0.939087i
$501$	−9.70820	+	7.05342i	−0.433731	+	0.315124i
$502$	3.12708	+	9.62415i	0.139568	+	0.429547i
$503$	1.72363	−	5.30480i	0.0768530	−	0.236529i	−0.905248	−	0.424883i	$-0.860315\pi$
$503$	1.72363	−	5.30480i	0.0768530	−	0.236529i	0.982101	+	0.188354i	$0.0603152\pi$
$504$	5.58895	+	4.06061i	0.248952	+	0.180874i
$505$	−19.1194			−0.850803
$506$		0			0
$507$	−70.5416			−3.13286
$508$	−5.34400	−	3.88265i	−0.237102	−	0.172265i
$509$	6.89194	−	21.2112i	0.305480	−	0.940170i	−0.674018	−	0.738715i	$-0.735433\pi$
$509$	6.89194	−	21.2112i	0.305480	−	0.940170i	0.979498	−	0.201455i	$-0.0645670\pi$
$510$	−15.9358	−	49.0454i	−0.705650	−	2.17177i
$511$	−4.04508	+	2.93893i	−0.178944	+	0.130010i
$512$	2.76862	−	2.01152i	0.122357	−	0.0888975i
$513$	−1.48843	−	4.58091i	−0.0657157	−	0.202252i
$514$	4.61550	−	14.2051i	0.203581	−	0.626558i
$515$	41.7205	+	30.3117i	1.83843	+	1.33569i
$516$	−12.9083			−0.568257
$517$		0			0
$518$	12.0000			0.527250
$519$	−2.42705	−	1.76336i	−0.106536	−	0.0774027i
$520$	22.0793	−	67.9530i	0.968239	−	2.97993i
$521$	2.29359	+	7.05894i	0.100484	+	0.309258i	0.988644	−	0.150277i	$-0.0480164\pi$
$521$	2.29359	+	7.05894i	0.100484	+	0.309258i	−0.888160	+	0.459534i	$0.848016\pi$
$522$	−20.1513	+	14.6407i	−0.881997	+	0.640808i
$523$	36.0349	−	26.1809i	1.57570	−	1.14481i	0.654271	−	0.756260i	$-0.272976\pi$
$523$	36.0349	−	26.1809i	1.57570	−	1.14481i	0.921427	−	0.388551i	$-0.127024\pi$
$524$	−6.12368	−	18.8468i	−0.267514	−	0.823324i
$525$	5.69277	−	17.5206i	0.248453	−	0.764660i
$526$	−37.7047	−	27.3941i	−1.64400	−	1.19444i
$527$	2.69722			0.117493
$528$		0			0
$529$	−15.7250			−0.683695
$530$	86.7063	+	62.9959i	3.76628	+	2.73636i
$531$	4.76572	−	14.6674i	0.206815	−	0.636510i
$532$	3.06184	+	9.42338i	0.132748	+	0.408555i
$533$	−37.4080	+	27.1785i	−1.62032	+	1.17723i
$534$	−63.1707	+	45.8962i	−2.73366	+	1.98612i
$535$	13.8096	+	42.5016i	0.597041	+	1.83750i
$536$	7.89280	−	24.2915i	0.340917	−	1.04923i
$537$	−11.9128	−	8.65513i	−0.514074	−	0.373496i
$538$	37.1194			1.60033
$539$		0			0
$540$	19.1194			0.822769
$541$	26.2077	+	19.0410i	1.12676	+	0.818636i	0.985219	−	0.171297i	$-0.0547959\pi$
$541$	26.2077	+	19.0410i	1.12676	+	0.818636i	0.141536	+	0.989933i	$0.454796\pi$
$542$	−20.2904	+	62.4474i	−0.871547	+	2.68234i
$543$	17.9401	+	55.2141i	0.769885	+	2.36946i
$544$	11.5712	−	8.40696i	0.496111	−	0.360445i
$545$	23.3356	−	16.9543i	0.999588	−	0.726243i
$546$	10.8242	+	33.3134i	0.463232	+	1.42568i
$547$	−9.25076	+	28.4709i	−0.395534	+	1.21733i	0.533011	+	0.846108i	$0.321060\pi$
$547$	−9.25076	+	28.4709i	−0.395534	+	1.21733i	−0.928545	+	0.371220i	$0.878940\pi$
$548$	27.0391	+	19.6451i	1.15505	+	0.839196i
$549$	−9.90833			−0.422877
$550$		0			0
$551$	−14.0917			−0.600325
$552$	−15.0747	−	10.9524i	−0.641620	−	0.466164i
$553$	2.56570	−	7.89641i	0.109105	−	0.335789i
$554$	21.3024	+	65.5621i	0.905053	+	2.78547i
$555$	−35.0034	+	25.4315i	−1.48581	+	1.07951i
$556$	−57.7301	+	41.9433i	−2.44830	+	1.77879i
$557$	2.23693	+	6.88456i	0.0947818	+	0.291708i	0.987197	−	0.159507i	$-0.0509905\pi$
$557$	2.23693	+	6.88456i	0.0947818	+	0.291708i	−0.892415	+	0.451216i	$0.850991\pi$
$558$	1.63865	−	5.04324i	0.0693695	−	0.213497i
$559$	−9.06997	−	6.58972i	−0.383619	−	0.278715i
$560$	−1.09167			−0.0461316
$561$		0			0
$562$	14.7250			0.621136
$563$	0.244951	+	0.177967i	0.0103234	+	0.00750042i	0.592935	−	0.805250i	$-0.297969\pi$
$563$	0.244951	+	0.177967i	0.0103234	+	0.00750042i	−0.582612	+	0.812751i	$0.697969\pi$
$564$	4.48504	−	13.8035i	0.188854	−	0.581233i
$565$	−11.9186	−	36.6817i	−0.501419	−	1.54321i
$566$	−8.18679	+	5.94805i	−0.344116	+	0.250015i
$567$	−8.58007	+	6.23379i	−0.360329	+	0.261794i
$568$	−3.98889	−	12.2765i	−0.167370	−	0.515113i
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$	−46.4038	−	33.7144i	−1.94364	−	1.41214i
$571$	25.8444			1.08155			0.540777	−	0.841166i	$-0.318130\pi$
$571$	25.8444			1.08155			0.540777	+	0.841166i	$0.318130\pi$
$572$		0			0
$573$	61.7527			2.57976
$574$	13.0409	+	9.47476i	0.544316	+	0.395469i
$575$	−6.66791	+	20.5217i	−0.278071	+	0.855814i
$576$	−9.12029	−	28.0694i	−0.380012	−	1.16956i
$577$	−1.78882	+	1.29965i	−0.0744695	+	0.0541053i	−0.624397	−	0.781107i	$-0.714655\pi$
$577$	−1.78882	+	1.29965i	−0.0744695	+	0.0541053i	0.549928	+	0.835212i	$0.314655\pi$
$578$	18.1175	−	13.1631i	0.753588	−	0.547514i
$579$	1.50818	+	4.64170i	0.0626778	+	0.192902i
$580$	17.2852	−	53.1984i	0.717729	−	2.20894i
$581$	2.42705	+	1.76336i	0.100691	+	0.0731563i
$582$	19.1194			0.792526
$583$		0			0
$584$	−15.0000			−0.620704
$585$	−44.3701	−	32.2367i	−1.83448	−	1.33282i
$586$	3.42752	−	10.5488i	0.141589	−	0.435767i
$587$	−4.20435	−	12.9396i	−0.173532	−	0.534076i	0.826031	−	0.563624i	$-0.190593\pi$
$587$	−4.20435	−	12.9396i	−0.173532	−	0.534076i	−0.999563	+	0.0295476i	$0.990593\pi$
$588$	6.15302	−	4.47043i	0.253746	−	0.184357i
$589$	2.42705	−	1.76336i	0.100005	−	0.0726578i
$590$	17.1831	+	52.8840i	0.707415	+	2.17720i
$591$	7.54688	−	23.2269i	0.310437	−	0.955427i
$592$	1.27646	+	0.927405i	0.0524623	+	0.0381161i
$593$	22.6056			0.928299			0.464149	−	0.885757i	$-0.346360\pi$
$593$	22.6056			0.928299			0.464149	+	0.885757i	$0.346360\pi$
$594$		0			0
$595$	−9.72498			−0.398685
$596$	13.1151	+	9.52865i	0.537214	+	0.390309i
$597$	−13.8208	+	42.5360i	−0.565647	+	1.74088i
$598$	−12.6783	−	39.0197i	−0.518453	−	1.59563i
$599$	11.9645	−	8.69270i	0.488855	−	0.355174i	−0.315889	−	0.948796i	$-0.602303\pi$
$599$	11.9645	−	8.69270i	0.488855	−	0.355174i	0.804744	+	0.593622i	$0.202303\pi$
$600$	44.7116	−	32.4849i	1.82534	−	1.32619i
$601$	−1.79744	−	5.53197i	−0.0733193	−	0.225654i	0.907681	−	0.419662i	$-0.137851\pi$
$601$	−1.79744	−	5.53197i	−0.0733193	−	0.225654i	−0.981000	+	0.194008i	$0.937851\pi$
$602$	−1.20774	+	3.71704i	−0.0492238	+	0.151495i
$603$	−15.8612	−	11.5239i	−0.645919	−	0.469288i
$604$	−0.697224			−0.0283697
$605$		0			0
$606$	28.1194			1.14227
$607$	16.6185	+	12.0741i	0.674525	+	0.490071i	0.871537	−	0.490330i	$-0.163124\pi$
$607$	16.6185	+	12.0741i	0.674525	+	0.490071i	−0.197012	+	0.980401i	$0.563124\pi$
$608$	4.91594	−	15.1297i	0.199368	−	0.613591i
$609$	3.34253	+	10.2872i	0.135446	+	0.416860i
$610$	28.9021	−	20.9986i	1.17021	−	0.850209i
$611$	10.1981	−	7.40936i	0.412571	−	0.299751i
$612$	6.33914	+	19.5099i	0.256244	+	0.788639i
$613$	−10.2147	+	31.4377i	−0.412568	+	1.26976i	0.501839	+	0.864961i	$0.332657\pi$
$613$	−10.2147	+	31.4377i	−0.412568	+	1.26976i	−0.914408	+	0.404794i	$0.867343\pi$
$614$	30.9876	+	22.5138i	1.25056	+	0.908583i
$615$	−58.1194			−2.34360
$616$		0			0
$617$	21.6333			0.870924			0.435462	−	0.900207i	$-0.356585\pi$
$617$	21.6333			0.870924			0.435462	+	0.900207i	$0.356585\pi$
$618$	−61.3594	−	44.5802i	−2.46824	−	1.79328i
$619$	12.3040	−	37.8679i	0.494540	−	1.52204i	−0.323131	−	0.946354i	$-0.604736\pi$
$619$	12.3040	−	37.8679i	0.494540	−	1.52204i	0.817672	−	0.575685i	$-0.195264\pi$
$620$	3.67988	+	11.3255i	0.147787	+	0.454843i
$621$	3.50347	−	2.54542i	0.140590	−	0.102144i
$622$	−11.9128	+	8.65513i	−0.477658	+	0.347039i
$623$	4.55027	+	14.0043i	0.182303	+	0.561070i
$624$	−1.42319	+	4.38014i	−0.0569733	+	0.175346i
$625$	0.809017	+	0.587785i	0.0323607	+	0.0235114i
$626$	35.2389			1.40843
$627$		0			0
$628$	23.8167			0.950388
$629$	11.3711	+	8.26162i	0.453397	+	0.329412i
$630$	−5.90823	+	18.1837i	−0.235389	+	0.724454i
$631$	−9.59668	−	29.5355i	−0.382038	−	1.17579i	−0.938606	−	0.344990i	$-0.887882\pi$
$631$	−9.59668	−	29.5355i	−0.382038	−	1.17579i	0.556569	−	0.830802i	$-0.312118\pi$
$632$	20.1513	−	14.6407i	0.801574	−	0.582378i
$633$	28.9021	−	20.9986i	1.14876	−	0.834620i
$634$	12.3126	+	37.8943i	0.488996	+	1.50497i
$635$	2.22835	−	6.85817i	0.0884295	−	0.272158i
$636$	−79.4252	−	57.7058i	−3.14941	−	2.28818i
$637$	6.60555			0.261721
$638$		0			0
$639$	−9.90833			−0.391967
$640$	55.1547	+	40.0722i	2.18018	+	1.58399i
$641$	−8.90484	+	27.4063i	−0.351720	+	1.08248i	0.606167	+	0.795337i	$0.292706\pi$
$641$	−8.90484	+	27.4063i	−0.351720	+	1.08248i	−0.957887	+	0.287145i	$0.907294\pi$
$642$	−20.3101	−	62.5082i	−0.801577	−	2.46700i
$643$	1.00226	−	0.728183i	0.0395252	−	0.0287167i	−0.567847	−	0.823134i	$-0.692224\pi$
$643$	1.00226	−	0.728183i	0.0395252	−	0.0287167i	0.607372	+	0.794417i	$0.292224\pi$
$644$	−7.20699	+	5.23618i	−0.283995	+	0.206335i
$645$	−4.35457	−	13.4020i	−0.171461	−	0.527702i
$646$	−5.75801	+	17.7213i	−0.226546	+	0.697236i
$647$	−8.58007	−	6.23379i	−0.337317	−	0.245075i	0.406212	−	0.913779i	$-0.366850\pi$
$647$	−8.58007	−	6.23379i	−0.337317	−	0.245075i	−0.743529	+	0.668704i	$0.766850\pi$
$648$	−31.8167			−1.24988
$649$		0			0
$650$	121.689			4.77303
$651$	−1.86298	−	1.35354i	−0.0730161	−	0.0530493i
$652$	2.87472	−	8.84747i	0.112583	−	0.346493i
$653$	−2.10646	−	6.48302i	−0.0824322	−	0.253700i	0.901343	−	0.433106i	$-0.142582\pi$
$653$	−2.10646	−	6.48302i	−0.0824322	−	0.253700i	−0.983775	+	0.179406i	$0.942582\pi$
$654$	−34.3203	+	24.9351i	−1.34203	+	0.975041i
$655$	17.5017	−	12.7157i	0.683849	−	0.496845i
$656$	0.654940	+	2.01570i	0.0255711	+	0.0786998i
$657$	−3.55798	+	10.9503i	−0.138810	+	0.427214i
$658$	−3.55518	−	2.58299i	−0.138595	−	0.100696i
$659$	4.63331			0.180488			0.0902440	−	0.995920i	$-0.471235\pi$
$659$	4.63331			0.180488			0.0902440	+	0.995920i	$0.471235\pi$
$660$		0			0
$661$	−18.3028			−0.711895			−0.355948	−	0.934506i	$-0.615842\pi$
$661$	−18.3028			−0.711895			−0.355948	+	0.934506i	$0.615842\pi$
$662$	−44.3701	−	32.2367i	−1.72449	−	1.25292i
$663$	−12.6783	+	39.0197i	−0.492383	+	1.51540i
$664$	2.78115	+	8.55951i	0.107930	+	0.332173i
$665$	−8.75086	+	6.35787i	−0.339344	+	0.246548i
$666$	22.3558	−	16.2425i	0.866270	−	0.629382i
$667$	−3.91508	−	12.0494i	−0.151593	−	0.466554i
$668$	−5.31852	+	16.3687i	−0.205780	+	0.633325i
$669$	25.9110	+	18.8254i	1.00178	+	0.727834i
$670$	70.6888			2.73095
$671$		0			0
$672$	−12.2111			−0.471054
$673$	6.81371	+	4.95045i	0.262649	+	0.190826i	0.711314	−	0.702874i	$-0.248100\pi$
$673$	6.81371	+	4.95045i	0.262649	+	0.190826i	−0.448665	+	0.893700i	$0.648100\pi$
$674$	8.38894	−	25.8185i	0.323130	−	0.994492i
$675$	3.96914	+	12.2158i	0.152772	+	0.470185i
$676$	−81.8522	+	59.4691i	−3.14816	+	2.28727i
$677$	−8.33512	+	6.05582i	−0.320345	+	0.232744i	−0.736323	−	0.676631i	$-0.763439\pi$
$677$	−8.33512	+	6.05582i	−0.320345	+	0.232744i	0.415978	+	0.909375i	$0.363439\pi$
$678$	17.5290	+	53.9487i	0.673197	+	2.07189i
$679$	1.11418	−	3.42908i	0.0427582	−	0.131596i
$680$	−23.6030	−	17.1486i	−0.905135	−	0.657619i
$681$	−15.0000			−0.574801
$682$		0			0
$683$	15.6972			0.600638			0.300319	−	0.953839i	$-0.402907\pi$
$683$	15.6972			0.600638			0.300319	+	0.953839i	$0.402907\pi$
$684$	18.4591	+	13.4113i	0.705800	+	0.512794i
$685$	−11.2748	+	34.7004i	−0.430789	+	1.32583i
$686$	−0.711597	−	2.19007i	−0.0271689	−	0.0836173i
$687$	−4.85410	+	3.52671i	−0.185196	+	0.134552i
$688$	−0.415736	+	0.302050i	−0.0158498	+	0.0115155i
$689$	−26.3488	−	81.0934i	−1.00381	−	3.08941i
$690$	15.9358	−	49.0454i	0.606666	−	1.86713i
$691$	13.7757	+	10.0087i	0.524054	+	0.380748i	0.818129	−	0.575035i	$-0.195012\pi$
$691$	13.7757	+	10.0087i	0.524054	+	0.380748i	−0.294075	+	0.955782i	$0.595012\pi$
$692$	−4.30278			−0.163567
$693$		0			0
$694$	22.1194			0.839642
$695$	−63.0224	−	45.7884i	−2.39057	−	1.73685i
$696$	−10.0276	+	30.8617i	−0.380095	+	1.16981i
$697$	5.83442	+	17.9565i	0.220994	+	0.680151i
$698$	8.75086	−	6.35787i	0.331225	−	0.240649i
$699$	33.5337	−	24.3637i	1.26836	−	0.921519i
$700$	−8.16491	−	25.1290i	−0.308605	−	0.949787i
$701$	−9.61643	+	29.5963i	−0.363208	+	1.11784i	0.587888	+	0.808942i	$0.299960\pi$
$701$	−9.61643	+	29.5963i	−0.363208	+	1.11784i	−0.951096	+	0.308896i	$0.900040\pi$
$702$	−19.7580	−	14.3550i	−0.745717	−	0.541795i
$703$	15.6333			0.589621
$704$		0			0
$705$	15.8444			0.596735
$706$	−9.48571	−	6.89177i	−0.356999	−	0.259375i
$707$	1.63865	−	5.04324i	0.0616277	−	0.189671i
$708$	−15.7401	−	48.4431i	−0.591550	−	1.82060i
$709$	−20.4928	+	14.8889i	−0.769624	+	0.559165i	−0.901847	−	0.432055i	$-0.857789\pi$
$709$	−20.4928	+	14.8889i	−0.769624	+	0.559165i	0.132223	+	0.991220i	$0.457789\pi$
$710$	28.9021	−	20.9986i	1.08468	−	0.788064i
$711$	−5.90823	−	18.1837i	−0.221576	−	0.681940i
$712$	−13.6508	+	42.0129i	−0.511586	+	1.57450i
$713$	2.18210	+	1.58539i	0.0817203	+	0.0593733i
$714$	14.3028			0.535268
$715$		0			0
$716$	−21.1194			−0.789270
$717$	49.0534	+	35.6394i	1.83193	+	1.33098i
$718$	−24.1488	+	74.3224i	−0.901226	+	2.77369i
$719$	6.56317	+	20.1994i	0.244765	+	0.753309i	0.995675	+	0.0929045i	$0.0296151\pi$
$719$	6.56317	+	20.1994i	0.244765	+	0.753309i	−0.750910	+	0.660404i	$0.770385\pi$
$720$	−2.03377	+	1.47762i	−0.0757941	+	0.0550677i
$721$	−11.5712	+	8.40696i	−0.430934	+	0.313092i
$722$	−7.11597	−	21.9007i	−0.264829	−	0.815060i
$723$	−0.345923	+	1.06464i	−0.0128650	+	0.0395944i
$724$	67.3641	+	48.9429i	2.50357	+	1.81895i
$725$	37.5778			1.39560
$726$		0			0
$727$	24.1194			0.894540			0.447270	−	0.894399i	$-0.352396\pi$
$727$	24.1194			0.894540			0.447270	+	0.894399i	$0.352396\pi$
$728$	16.0320	+	11.6479i	0.594186	+	0.431701i
$729$	−4.11936	+	12.6781i	−0.152569	+	0.469559i
$730$	−12.8285	−	39.4820i	−0.474804	−	1.46130i
$731$	−3.70351	+	2.69076i	−0.136979	+	0.0995214i
$732$	−26.4751	+	19.2353i	−0.978547	+	0.710956i
$733$	−2.09788	−	6.45663i	−0.0774871	−	0.238481i	0.904808	−	0.425819i	$-0.140014\pi$
$733$	−2.09788	−	6.45663i	−0.0774871	−	0.238481i	−0.982295	+	0.187338i	$0.940014\pi$
$734$	−12.5478	+	38.6182i	−0.463148	+	1.42542i
$735$	6.71709	+	4.88025i	0.247763	+	0.180011i
$736$	14.3028			0.527207
$737$		0			0
$738$	37.1194			1.36639
$739$	34.8844	+	25.3450i	1.28324	+	0.932330i	0.999646	−	0.0266143i	$-0.00847260\pi$
$739$	34.8844	+	25.3450i	1.28324	+	0.932330i	0.283596	+	0.958944i	$0.408473\pi$
$740$	−19.1762	+	59.0183i	−0.704931	+	2.16956i
$741$	14.1015	+	43.3999i	0.518030	+	1.59433i
$742$	−24.0480	+	17.4719i	−0.882830	+	0.641414i
$743$	−36.3541	+	26.4128i	−1.33370	+	0.968990i	−0.334050	+	0.942555i	$0.608416\pi$
$743$	−36.3541	+	26.4128i	−1.33370	+	0.968990i	−0.999651	+	0.0264352i	$0.991584\pi$
$744$	−2.13479	−	6.57021i	−0.0782652	−	0.240876i
$745$	−5.46874	+	16.8311i	−0.200359	+	0.616642i
$746$	37.4822	+	27.2324i	1.37232	+	0.997049i
$747$	6.90833			0.252762
$748$		0			0
$749$	−12.3944			−0.452883
$750$	46.4038	+	33.7144i	1.69443	+	1.23107i
$751$	2.35882	−	7.25971i	0.0860746	−	0.264910i	−0.898750	−	0.438461i	$-0.855524\pi$
$751$	2.35882	−	7.25971i	0.0860746	−	0.264910i	0.984825	+	0.173550i	$0.0555239\pi$
$752$	−0.178548	−	0.549516i	−0.00651099	−	0.0200388i
$753$	8.18679	−	5.94805i	0.298343	−	0.216759i
$754$	−57.8042	+	41.9972i	−2.10511	+	1.52945i
$755$	−0.235206	−	0.723888i	−0.00856001	−	0.0263450i
$756$	−1.63865	+	5.04324i	−0.0595970	+	0.183421i
$757$	19.2681	+	13.9991i	0.700310	+	0.508805i	0.880033	−	0.474912i	$-0.157520\pi$
$757$	19.2681	+	13.9991i	0.700310	+	0.508805i	−0.179723	+	0.983717i	$0.557520\pi$
$758$	−36.4222			−1.32291
$759$		0			0
$760$	−32.4500			−1.17708
$761$	−33.9787	−	24.6870i	−1.23173	−	0.894902i	−0.234709	−	0.972066i	$-0.575414\pi$
$761$	−33.9787	−	24.6870i	−1.23173	−	0.894902i	−0.997018	+	0.0771633i	$0.975414\pi$
$762$	−3.27730	+	10.0865i	−0.118724	+	0.365395i
$763$	2.47214	+	7.60845i	0.0894973	+	0.275444i
$764$	71.6541	−	52.0598i	2.59236	−	1.88346i
$765$	−18.1175	+	13.1631i	−0.655039	+	0.475914i
$766$	27.4913	+	84.6096i	0.993302	+	3.05707i
$767$	13.6706	−	42.0737i	0.493615	−	1.51919i
$768$	−33.3629	−	24.2396i	−1.20388	−	0.874671i
$769$	−39.3305			−1.41830			−0.709148	−	0.705060i	$-0.750920\pi$
$769$	−39.3305			−1.41830			−0.709148	+	0.705060i	$0.750920\pi$
$770$		0			0
$771$	−14.9361			−0.537910
$772$	5.66312	+	4.11450i	0.203820	+	0.148084i
$773$	9.46621	−	29.1340i	0.340476	−	1.04788i	−0.623485	−	0.781835i	$-0.714284\pi$
$773$	9.46621	−	29.1340i	0.340476	−	1.04788i	0.963961	−	0.266042i	$-0.0857161\pi$
$774$	2.78115	+	8.55951i	0.0999665	+	0.307665i
$775$	−6.47214	+	4.70228i	−0.232486	+	0.168911i
$776$	8.75086	−	6.35787i	0.314137	−	0.228234i
$777$	−3.70820	−	11.4127i	−0.133031	−	0.409428i
$778$	−5.56231	+	17.1190i	−0.199418	+	0.613747i
$779$	16.9894	+	12.3435i	0.608707	+	0.442251i
$780$	−181.139			−6.48581
$781$		0			0
$782$	−16.7527			−0.599077
$783$	−6.10131	−	4.43286i	−0.218043	−	0.158418i
$784$	0.0935628	−	0.287957i	0.00334153	−	0.0102842i
$785$	8.03444	+	24.7275i	0.286762	+	0.882561i
$786$	−25.7402	+	18.7014i	−0.918123	+	0.667055i
$787$	18.1917	−	13.2170i	0.648462	−	0.471136i	−0.214285	−	0.976771i	$-0.568742\pi$
$787$	18.1917	−	13.2170i	0.648462	−	0.471136i	0.862747	+	0.505636i	$0.168742\pi$
$788$	−10.8242	−	33.3134i	−0.385595	−	1.18674i
$789$	−14.4019	+	44.3245i	−0.512721	+	1.57799i
$790$	55.7705	+	40.5196i	1.98422	+	1.44162i
$791$	10.6972			0.380350
$792$		0			0
$793$	−28.4222			−1.00930
$794$	−56.2828	−	40.8919i	−1.99740	−	1.45120i
$795$	33.1189	−	101.929i	1.17461	−	3.61506i
$796$	19.8226	+	61.0076i	0.702592	+	2.16236i
$797$	23.1648	−	16.8302i	0.820540	−	0.596158i	−0.0963268	−	0.995350i	$-0.530709\pi$
$797$	23.1648	−	16.8302i	0.820540	−	0.596158i	0.916867	+	0.399192i	$0.130709\pi$
$798$	12.8701	−	9.35068i	0.455597	−	0.331010i
$799$	−1.59057	−	4.89526i	−0.0562702	−	0.173182i
$800$	−13.1092	+	40.3459i	−0.463480	+	1.42644i
$801$	27.4324	+	19.9308i	0.969277	+	0.704221i
$802$	−48.8444			−1.72476
$803$		0			0
$804$	−64.7527			−2.28365
$805$	−7.86767	−	5.71620i	−0.277299	−	0.201470i
$806$	4.70049	−	14.4666i	0.165568	−	0.509565i
$807$	−11.4705	−	35.3027i	−0.403782	−	1.24271i
$808$	12.8701	−	9.35068i	0.452769	−	0.328956i
$809$	−6.54630	+	4.75617i	−0.230156	+	0.167218i	−0.696886	−	0.717182i	$-0.745432\pi$
$809$	−6.54630	+	4.75617i	−0.230156	+	0.167218i	0.466731	+	0.884400i	$0.345432\pi$
$810$	−27.2106	−	83.7458i	−0.956085	−	2.94253i
$811$	−12.6216	+	38.8453i	−0.443205	+	1.36404i	0.441236	+	0.897391i	$0.354540\pi$
$811$	−12.6216	+	38.8453i	−0.443205	+	1.36404i	−0.884440	+	0.466653i	$0.845460\pi$
$812$	12.5510	+	9.11883i	0.440453	+	0.320008i
$813$	65.6611			2.30283
$814$		0			0
$815$	10.1556			0.355735
$816$	1.52141	+	1.10537i	0.0532601	+	0.0386957i
$817$	−1.57341	+	4.84247i	−0.0550468	+	0.169417i
$818$	14.6628	+	45.1276i	0.512674	+	1.57785i
$819$	12.3060	−	8.94086i	0.430008	−	0.312419i
$820$	−67.4383	+	48.9968i	−2.35505	+	1.71104i
$821$	−8.47393	−	26.0801i	−0.295742	−	0.910201i	−0.982971	−	0.183760i	$-0.941173\pi$
$821$	−8.47393	−	26.0801i	−0.295742	−	0.910201i	0.687229	−	0.726441i	$-0.258827\pi$
$822$	16.5822	−	51.0347i	0.578370	−	1.78004i
$823$	−28.4864	−	20.6966i	−0.992973	−	0.721437i	−0.0324027	−	0.999475i	$-0.510316\pi$
$823$	−28.4864	−	20.6966i	−0.992973	−	0.721437i	−0.960570	+	0.278038i	$0.910316\pi$
$824$	−42.9083			−1.49478
$825$		0			0
$826$	−15.4222			−0.536607
$827$	11.4746	+	8.33676i	0.399010	+	0.289898i	0.769138	−	0.639083i	$-0.220686\pi$
$827$	11.4746	+	8.33676i	0.399010	+	0.289898i	−0.370128	+	0.928981i	$0.620686\pi$
$828$	−6.33914	+	19.5099i	−0.220300	+	0.678014i
$829$	4.10221	+	12.6253i	0.142476	+	0.438495i	0.996678	−	0.0814464i	$-0.0259539\pi$
$829$	4.10221	+	12.6253i	0.142476	+	0.438495i	−0.854202	+	0.519941i	$0.825954\pi$
$830$	−20.1513	+	14.6407i	−0.699460	+	0.508188i
$831$	55.7705	−	40.5196i	1.93466	−	1.40561i
$832$	−26.1617	−	80.5175i	−0.906994	−	2.79144i
$833$	0.833488	−	2.56521i	0.0288787	−	0.0888794i
$834$	92.6886	+	67.3422i	3.20954	+	2.33187i
$835$	−18.7889			−0.650217
$836$		0			0
$837$	1.60555			0.0554960
$838$	71.5800	+	52.0059i	2.47269	+	1.79651i
$839$	13.0439	−	40.1451i	0.450327	−	1.38596i	−0.426208	−	0.904625i	$-0.640151\pi$
$839$	13.0439	−	40.1451i	0.450327	−	1.38596i	0.876535	−	0.481339i	$-0.159849\pi$
$840$	7.69710	+	23.6892i	0.265575	+	0.817356i
$841$	5.61141	−	4.07693i	0.193497	−	0.140584i
$842$	40.6441	−	29.5297i	1.40069	−	1.01766i
$843$	−4.55027	−	14.0043i	−0.156720	−	0.482333i
$844$	15.8337	−	48.7311i	0.545018	−	1.67739i
$845$	−89.3559	−	64.9209i	−3.07394	−	2.23335i
$846$	−10.1194			−0.347913
$847$		0			0
$848$	−3.90833			−0.134212
$849$	8.18679	+	5.94805i	0.280970	+	0.204137i
$850$	15.3547	−	47.2569i	0.526662	−	1.62090i
$851$	4.34339	+	13.3676i	0.148890	+	0.458235i
$852$	−26.4751	+	19.2353i	−0.907021	+	0.658989i
$853$	36.9923	−	26.8765i	1.26659	−	0.920233i	0.267530	−	0.963549i	$-0.413792\pi$
$853$	36.9923	−	26.8765i	1.26659	−	0.920233i	0.999061	+	0.0433166i	$0.0137924\pi$
$854$	3.06184	+	9.42338i	0.104774	+	0.322461i
$855$	−7.69710	+	23.6892i	−0.263235	+	0.810154i
$856$	−30.0820	−	21.8558i	−1.02818	−	0.747017i
$857$	35.3583			1.20782			0.603908	−	0.797054i	$-0.293609\pi$
$857$	35.3583			1.20782			0.603908	+	0.797054i	$0.293609\pi$
$858$		0			0
$859$	−25.3028			−0.863320			−0.431660	−	0.902036i	$-0.642072\pi$
$859$	−25.3028			−0.863320			−0.431660	+	0.902036i	$0.642072\pi$
$860$	−16.3511	−	11.8798i	−0.557569	−	0.405097i
$861$	4.98118	−	15.3305i	0.169758	−	0.522462i
$862$	−2.21978	−	6.83177i	−0.0756059	−	0.232691i
$863$	−25.4211	+	18.4695i	−0.865344	+	0.628709i	−0.929334	−	0.369241i	$-0.879618\pi$
$863$	−25.4211	+	18.4695i	−0.865344	+	0.628709i	0.0639894	+	0.997951i	$0.479618\pi$
$864$	6.88787	−	5.00433i	0.234330	−	0.170251i
$865$	−1.45152	−	4.46733i	−0.0493532	−	0.151894i
$866$	20.7410	−	63.8344i	0.704809	−	2.16918i
$867$	−18.1175	−	13.1631i	−0.615302	−	0.447043i
$868$	−3.30278			−0.112104
$869$		0			0
$870$	−89.8082			−3.04478
$871$	−45.4982	−	33.0564i	−1.54165	−	1.12007i
$872$	−7.41641	+	22.8254i	−0.251151	+	0.772964i
$873$	−2.56570	−	7.89641i	−0.0868357	−	0.267253i
$874$	−15.0747	+	10.9524i	−0.509908	+	0.370470i
$875$	8.75086	−	6.35787i	0.295833	−	0.214935i
$876$	11.7512	+	36.1665i	0.397037	+	1.22195i
$877$	14.5410	−	44.7525i	0.491013	−	1.51118i	−0.332066	−	0.943256i	$-0.607746\pi$
$877$	14.5410	−	44.7525i	0.491013	−	1.51118i	0.823079	−	0.567927i	$-0.192254\pi$
$878$	−51.6512	−	37.5268i	−1.74314	−	1.26647i
$879$	−11.0917			−0.374113
$880$		0			0
$881$	34.3305			1.15663			0.578313	−	0.815815i	$-0.303711\pi$
$881$	34.3305			1.15663			0.578313	+	0.815815i	$0.303711\pi$
$882$	−4.29004	−	3.11689i	−0.144453	−	0.104951i
$883$	−2.38715	+	7.34689i	−0.0803340	+	0.247243i	−0.983155	−	0.182774i	$-0.941492\pi$
$883$	−2.38715	+	7.34689i	−0.0803340	+	0.247243i	0.902821	+	0.430017i	$0.141492\pi$
$884$	18.1839	+	55.9644i	0.611592	+	1.88229i
$885$	44.9858	−	32.6841i	1.51218	−	1.09866i
$886$	−50.1815	+	36.4590i	−1.68588	+	1.22486i
$887$	13.6337	+	41.9601i	0.457773	+	1.40888i	0.867848	+	0.496829i	$0.165503\pi$
$887$	13.6337	+	41.9601i	0.457773	+	1.40888i	−0.410075	+	0.912052i	$0.634497\pi$
$888$	11.1246	−	34.2380i	0.373318	−	1.14895i
$889$	1.61803	+	1.17557i	0.0542671	+	0.0394274i
$890$	−122.258			−4.09810
$891$		0			0
$892$	45.9361			1.53805
$893$	−4.63161	−	3.36506i	−0.154991	−	0.112607i
$894$	8.04302	−	24.7539i	0.268999	−	0.827893i
$895$	−7.12455	−	21.9271i	−0.238147	−	0.732942i
$896$	−15.2972	+	11.1140i	−0.511042	+	0.371294i
$897$	−33.1922	+	24.1155i	−1.10825	+	0.805193i
$898$	28.6991	+	88.3267i	0.957701	+	2.94750i
$899$	1.45152	−	4.46733i	0.0484110	−	0.148994i
$900$	−49.2242	−	35.7634i	−1.64081	−	1.19211i
$901$	−34.8167			−1.15991
$902$		0			0
$903$	3.90833			0.130061
$904$	25.9627	+	18.8630i	0.863507	+	0.627374i
$905$	−28.0896	+	86.4510i	−0.933731	+	2.87373i
$906$	0.345923	+	1.06464i	0.0114925	+	0.0353703i
$907$	−0.319116	+	0.231851i	−0.0105961	+	0.00769849i	−0.593071	−	0.805150i	$-0.702085\pi$
$907$	−0.319116	+	0.231851i	−0.0105961	+	0.00769849i	0.582475	+	0.812849i	$0.302085\pi$
$908$	−17.4051	+	12.6455i	−0.577608	+	0.419657i
$909$	−3.77344	−	11.6134i	−0.125157	−	0.385194i
$910$	−16.9479	+	52.1601i	−0.561816	+	1.72909i
$911$	40.8149	+	29.6537i	1.35226	+	0.982472i	0.998896	+	0.0469855i	$0.0149615\pi$
$911$	40.8149	+	29.6537i	1.35226	+	0.982472i	0.353362	+	0.935487i	$0.385039\pi$
$912$	2.09167			0.0692622
$913$		0			0
$914$	48.6333			1.60865
$915$	−28.9021	−	20.9986i	−0.955474	−	0.694193i
$916$	−2.65926	+	8.18437i	−0.0878645	+	0.270419i
$917$	1.85410	+	5.70634i	0.0612278	+	0.188440i
$918$	−8.06771	+	5.86154i	−0.266274	+	0.193460i
$919$	−44.8824	+	32.6090i	−1.48053	+	1.07567i	−0.503150	+	0.864199i	$0.667826\pi$
$919$	−44.8824	+	32.6090i	−1.48053	+	1.07567i	−0.977384	+	0.211472i	$0.932174\pi$
$920$	−9.01555	−	27.7470i	−0.297234	−	0.914792i
$921$	11.8362	−	36.4281i	0.390016	−	1.20035i
$922$	−15.0747	−	10.9524i	−0.496458	−	0.360698i
$923$	−28.4222			−0.935528
$924$		0			0
$925$	−41.6888			−1.37072
$926$	57.4110	+	41.7115i	1.88664	+	1.37072i
$927$	−10.1778	+	31.3241i	−0.334283	+	1.02882i
$928$	−7.69710	−	23.6892i	−0.252670	−	0.777637i
$929$	22.3558	−	16.2425i	0.733471	−	0.532898i	−0.157189	−	0.987569i	$-0.550243\pi$
$929$	22.3558	−	16.2425i	0.733471	−	0.532898i	0.890659	+	0.454671i	$0.150243\pi$
$930$	15.4679	−	11.2381i	0.507214	−	0.368512i
$931$	−0.927051	−	2.85317i	−0.0303829	−	0.0935089i
$932$	18.3710	−	56.5403i	0.601764	−	1.85204i
$933$	11.9128	+	8.65513i	0.390006	+	0.283356i
$934$	−31.1833			−1.02035
$935$		0			0
$936$	45.6333			1.49157
$937$	−25.5694	−	18.5773i	−0.835317	−	0.606893i	0.0857417	−	0.996317i	$-0.472674\pi$
$937$	−25.5694	−	18.5773i	−0.835317	−	0.606893i	−0.921059	+	0.389424i	$0.872674\pi$
$938$	−6.05845	+	18.6460i	−0.197815	+	0.608813i
$939$	−10.8894	−	33.5141i	−0.355362	−	1.09369i
$940$	18.3849	−	13.3574i	0.599649	−	0.435671i
$941$	−30.2752	+	21.9962i	−0.986943	+	0.717056i	−0.959250	−	0.282560i	$-0.908816\pi$
$941$	−30.2752	+	21.9962i	−0.986943	+	0.717056i	−0.0276937	+	0.999616i	$0.508816\pi$
$942$	−11.8165	−	36.3673i	−0.385001	−	1.18491i
$943$	−5.83442	+	17.9565i	−0.189995	+	0.584744i
$944$	−1.64049	−	1.19189i	−0.0533934	−	0.0387926i
$945$	−5.78890			−0.188313
$946$		0			0
$947$	46.6611			1.51628			0.758140	−	0.652091i	$-0.226108\pi$
$947$	46.6611			1.51628			0.758140	+	0.652091i	$0.226108\pi$
$948$	−51.0871	−	37.1170i	−1.65923	−	1.20550i
$949$	−10.2061	+	31.4113i	−0.331305	+	1.01965i
$950$	−17.0783	−	52.5617i	−0.554094	−	1.70533i
$951$	32.2348	−	23.4200i	1.04529	−	0.759444i
$952$	6.54630	−	4.75617i	0.212167	−	0.154148i
$953$	−1.86268	−	5.73274i	−0.0603381	−	0.185702i	0.916344	−	0.400392i	$-0.131126\pi$
$953$	−1.86268	−	5.73274i	−0.0603381	−	0.185702i	−0.976682	+	0.214690i	$0.931126\pi$
$954$	−21.1522	+	65.0998i	−0.684828	+	2.10768i
$955$	78.2229	+	56.8323i	2.53123	+	1.83905i
$956$	86.9638			2.81261
$957$		0			0
$958$	−65.9361			−2.13030
$959$	−8.18679	−	5.94805i	−0.264365	−	0.192073i
$960$	32.8837	−	101.206i	1.06132	−	3.26639i
$961$	−9.27051	−	28.5317i	−0.299049	−	0.920377i
$962$	64.1280	−	46.5917i	2.06757	−	1.50218i
$963$	−23.0907	+	16.7764i	−0.744086	+	0.540610i
$964$	0.496143	+	1.52697i	0.0159797	+	0.0491804i
$965$	−2.36142	+	7.26770i	−0.0760168	+	0.233956i
$966$	11.5712	+	8.40696i	0.372297	+	0.270490i
$967$	40.5139			1.30284			0.651419	−	0.758718i	$-0.274174\pi$
$967$	40.5139			1.30284			0.651419	+	0.758718i	$0.274174\pi$
$968$		0			0
$969$	18.6333			0.598588
$970$	24.2188	+	17.5960i	0.777619	+	0.564973i
$971$	−1.96742	+	6.05508i	−0.0631374	+	0.194317i	−0.977649	−	0.210242i	$-0.932575\pi$
$971$	−1.96742	+	6.05508i	−0.0631374	+	0.194317i	0.914512	+	0.404559i	$0.132575\pi$
$972$	20.0097	+	61.5835i	0.641811	+	1.97529i
$973$	17.4793	−	12.6994i	0.560359	−	0.407125i
$974$	5.24738	−	3.81245i	0.168137	−	0.122159i
$975$	−37.6039	−	115.733i	−1.20429	−	3.70642i
$976$	−0.402580	+	1.23901i	−0.0128863	+	0.0396598i
$977$	−32.3831	−	23.5277i	−1.03603	−	0.752719i	−0.0665220	−	0.997785i	$-0.521190\pi$
$977$	−32.3831	−	23.5277i	−1.03603	−	0.752719i	−0.969506	+	0.245066i	$0.921190\pi$
$978$	−14.9361			−0.477603
$979$		0			0
$980$	11.9083			0.380398
$981$	14.9039	+	10.8283i	0.475844	+	0.345721i
$982$	−9.03530	+	27.8078i	−0.288328	+	0.887383i
$983$	−2.86614	−	8.82107i	−0.0914156	−	0.281348i	0.894887	−	0.446292i	$-0.147256\pi$
$983$	−2.86614	−	8.82107i	−0.0914156	−	0.281348i	−0.986303	+	0.164944i	$0.947256\pi$
$984$	39.1227	−	28.4243i	1.24719	−	0.906133i
$985$	30.9359	−	22.4762i	0.985699	−	0.716152i
$986$	9.01555	+	27.7470i	0.287114	+	0.883645i
$987$	−1.35796	+	4.17937i	−0.0432243	+	0.133031i
$988$	52.9501	+	38.4705i	1.68457	+	1.22391i
$989$	−4.57779			−0.145565
$990$		0			0
$991$	−43.7250			−1.38897			−0.694485	−	0.719507i	$-0.744368\pi$
$991$	−43.7250			−1.38897			−0.694485	+	0.719507i	$0.744368\pi$
$992$	4.29004	+	3.11689i	0.136209	+	0.0989615i
$993$	−16.9479	+	52.1601i	−0.537824	+	1.65525i
$994$	3.06184	+	9.42338i	0.0971157	+	0.298891i
$995$	−56.6536	+	41.1613i	−1.79604	+	1.30490i
$996$	18.4591	−	13.4113i	0.584898	−	0.424953i
$997$	14.1212	+	43.4606i	0.447223	+	1.37641i	0.880027	+	0.474924i	$0.157524\pi$
$997$	14.1212	+	43.4606i	0.447223	+	1.37641i	−0.432803	+	0.901488i	$0.642476\pi$
$998$	2.06956	−	6.36944i	0.0655107	−	0.201621i
$999$	6.76880	+	4.91782i	0.214155	+	0.155593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.o.323.1		8
11.2	odd	10		847.2.f.r.148.1		8
11.3	even	5	inner	847.2.f.o.729.1		8
11.4	even	5	inner	847.2.f.o.372.2		8
11.5	even	5		847.2.a.g.1.2	yes	2
11.6	odd	10		847.2.a.e.1.1	✓	2
11.7	odd	10		847.2.f.r.372.1		8
11.8	odd	10		847.2.f.r.729.2		8
11.9	even	5	inner	847.2.f.o.148.2		8
11.10	odd	2		847.2.f.r.323.2		8
33.5	odd	10		7623.2.a.bc.1.1		2
33.17	even	10		7623.2.a.bs.1.2		2
77.6	even	10		5929.2.a.k.1.1		2
77.27	odd	10		5929.2.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.e.1.1	✓	2	11.6	odd	10
847.2.a.g.1.2	yes	2	11.5	even	5
847.2.f.o.148.2		8	11.9	even	5	inner
847.2.f.o.323.1		8	1.1	even	1	trivial
847.2.f.o.372.2		8	11.4	even	5	inner
847.2.f.o.729.1		8	11.3	even	5	inner
847.2.f.r.148.1		8	11.2	odd	10
847.2.f.r.323.2		8	11.10	odd	2
847.2.f.r.372.1		8	11.7	odd	10
847.2.f.r.729.2		8	11.8	odd	10
5929.2.a.k.1.1		2	77.6	even	10
5929.2.a.p.1.2		2	77.27	odd	10
7623.2.a.bc.1.1		2	33.5	odd	10
7623.2.a.bs.1.2		2	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86298 - 1.35354i) q^{2} +(-0.711597 + 2.19007i) q^{3} +(1.02061 + 3.14113i) q^{4} +(-2.91695 + 2.11929i) q^{5} +(4.29004 - 3.11689i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-1.86298 - 1.35354i) q^{9} +O(q^{10})\)	\(q+(-1.86298 - 1.35354i) q^{2} +(-0.711597 + 2.19007i) q^{3} +(1.02061 + 3.14113i) q^{4} +(-2.91695 + 2.11929i) q^{5} +(4.29004 - 3.11689i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-1.86298 - 1.35354i) q^{9} +8.30278 q^{10} -7.60555 q^{12} +(-5.34400 - 3.88265i) q^{13} +(-0.711597 + 2.19007i) q^{14} +(-2.56570 - 7.89641i) q^{15} +(-0.244951 + 0.177967i) q^{16} +(-2.18210 + 1.58539i) q^{17} +(1.63865 + 5.04324i) q^{18} +(-0.927051 + 2.85317i) q^{19} +(-9.63404 - 6.99954i) q^{20} +2.30278 q^{21} -2.69722 q^{23} +(5.58895 + 4.06061i) q^{24} +(2.47214 - 7.60845i) q^{25} +(4.70049 + 14.4666i) q^{26} +(-1.29892 + 0.943719i) q^{27} +(2.67200 - 1.94132i) q^{28} +(1.45152 + 4.46733i) q^{29} +(-5.90823 + 18.1837i) q^{30} +(-0.809017 - 0.587785i) q^{31} -5.30278 q^{32} +6.21110 q^{34} +(2.91695 + 2.11929i) q^{35} +(2.35024 - 7.23331i) q^{36} +(-1.61032 - 4.95605i) q^{37} +(5.58895 - 4.06061i) q^{38} +(12.3060 - 8.94086i) q^{39} +(3.34253 + 10.2872i) q^{40} +(2.16312 - 6.65740i) q^{41} +(-4.29004 - 3.11689i) q^{42} +1.69722 q^{43} +8.30278 q^{45} +(5.02489 + 3.65079i) q^{46} +(-0.589705 + 1.81493i) q^{47} +(-0.215454 - 0.663100i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-14.9039 + 10.8283i) q^{50} +(-1.91934 - 5.90711i) q^{51} +(6.74172 - 20.7489i) q^{52} +(10.4431 + 7.58732i) q^{53} +3.69722 q^{54} -3.00000 q^{56} +(-5.58895 - 4.06061i) q^{57} +(3.34253 - 10.2872i) q^{58} +(2.06956 + 6.36944i) q^{59} +(22.1850 - 16.1184i) q^{60} +(3.48102 - 2.52911i) q^{61} +(0.711597 + 2.19007i) q^{62} +(-0.711597 + 2.19007i) q^{63} +(10.3689 + 7.53344i) q^{64} +23.8167 q^{65} +8.51388 q^{67} +(-7.20699 - 5.23618i) q^{68} +(1.91934 - 5.90711i) q^{69} +(-2.56570 - 7.89641i) q^{70} +(3.48102 - 2.52911i) q^{71} +(-5.58895 + 4.06061i) q^{72} +(-1.54508 - 4.75528i) q^{73} +(-3.70820 + 11.4127i) q^{74} +(14.9039 + 10.8283i) q^{75} -9.90833 q^{76} -35.0278 q^{78} +(6.71709 + 4.88025i) q^{79} +(0.337346 - 1.03824i) q^{80} +(-3.27730 - 10.0865i) q^{81} +(-13.0409 + 9.47476i) q^{82} +(-2.42705 + 1.76336i) q^{83} +(2.35024 + 7.23331i) q^{84} +(3.00518 - 9.24901i) q^{85} +(-3.16190 - 2.29726i) q^{86} -10.8167 q^{87} -14.7250 q^{89} +(-15.4679 - 11.2381i) q^{90} +(-2.04123 + 6.28225i) q^{91} +(-2.75282 - 8.47232i) q^{92} +(1.86298 - 1.35354i) q^{93} +(3.55518 - 2.58299i) q^{94} +(-3.34253 - 10.2872i) q^{95} +(3.77344 - 11.6134i) q^{96} +(2.91695 + 2.11929i) q^{97} +2.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

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