LMFDB - Embedded newform 961.2.d.p.388.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (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:	$7.67362363425$
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} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.3
Root			$-2.16544i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.p.374.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.49685 - 1.08752i) q^{2} +(-0.403986 - 0.293513i) q^{3} +(0.439812 - 1.35360i) q^{4} +1.20736 q^{5} -0.923909 q^{6} +(1.15357 - 3.55033i) q^{7} +(0.329747 + 1.01486i) q^{8} +(-0.849996 - 2.61602i) q^{9} +(1.80724 - 1.31303i) q^{10} +(-0.573693 + 1.76565i) q^{11} +(-0.574979 + 0.417746i) q^{12} +(4.19432 + 3.04736i) q^{13} +(-2.13435 - 6.56885i) q^{14} +(-0.487757 - 0.354376i) q^{15} +(3.90015 + 2.83362i) q^{16} +(-1.75135 - 5.39009i) q^{17} +(-4.11730 - 2.99139i) q^{18} +(1.16376 - 0.845521i) q^{19} +(0.531013 - 1.63429i) q^{20} +(-1.50810 + 1.09570i) q^{21} +(1.06145 + 3.26681i) q^{22} +(-1.09533 - 3.37109i) q^{23} +(0.164660 - 0.506773i) q^{24} -3.54228 q^{25} +9.59234 q^{26} +(-0.887376 + 2.73106i) q^{27} +(-4.29839 - 3.12296i) q^{28} +(-1.11046 + 0.806795i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(0.750004 - 0.544910i) q^{33} +(-8.48335 - 6.16352i) q^{34} +(1.39278 - 4.28654i) q^{35} -3.91489 q^{36} +4.50281 q^{37} +(0.822447 - 2.53123i) q^{38} +(-0.800011 - 2.46218i) q^{39} +(0.398123 + 1.22530i) q^{40} +(3.81784 - 2.77382i) q^{41} +(-1.06580 + 3.28018i) q^{42} +(-5.30652 + 3.85541i) q^{43} +(2.13767 + 1.55311i) q^{44} +(-1.02625 - 3.15848i) q^{45} +(-5.30569 - 3.85481i) q^{46} +(3.42131 + 2.48572i) q^{47} +(-0.743900 - 2.28949i) q^{48} +(-5.61102 - 4.07665i) q^{49} +(-5.30225 + 3.85231i) q^{50} +(-0.874543 + 2.69157i) q^{51} +(5.96963 - 4.33719i) q^{52} +(-4.00588 - 12.3288i) q^{53} +(1.64183 + 5.05303i) q^{54} +(-0.692655 + 2.13177i) q^{55} +3.98346 q^{56} -0.718314 q^{57} +(-0.784779 + 2.41530i) q^{58} +(1.76492 + 1.28229i) q^{59} +(-0.694207 + 0.504371i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(2.35642 - 1.71204i) q^{64} +(5.06407 + 3.67926i) q^{65} +(0.530040 - 1.63130i) q^{66} +2.88300 q^{67} -8.06631 q^{68} +(-0.546960 + 1.68337i) q^{69} +(-2.57693 - 7.93098i) q^{70} +(2.78166 + 8.56106i) q^{71} +(2.37460 - 1.72525i) q^{72} +(-1.29912 + 3.99829i) q^{73} +(6.74003 - 4.89692i) q^{74} +(1.43103 + 1.03971i) q^{75} +(-0.632664 - 1.94714i) q^{76} +(5.60683 + 4.07360i) q^{77} +(-3.87517 - 2.81548i) q^{78} +(3.47079 + 10.6820i) q^{79} +(4.70889 + 3.42121i) q^{80} +(-5.51587 + 4.00751i) q^{81} +(2.69813 - 8.30399i) q^{82} +(8.47642 - 6.15848i) q^{83} +(0.819859 + 2.52327i) q^{84} +(-2.11451 - 6.50779i) q^{85} +(-3.75020 + 11.5419i) q^{86} +0.685415 q^{87} -1.98105 q^{88} +(-0.834882 + 2.56950i) q^{89} +(-4.97107 - 3.61169i) q^{90} +(15.6576 - 11.3759i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(1.40508 - 1.02085i) q^{95} +(-2.74121 - 1.99160i) q^{96} +(-2.56277 + 7.88740i) q^{97} -12.8323 q^{98} +5.10660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.49685	−	1.08752i	1.05843	−	0.768996i	0.0846340	−	0.996412i	$-0.473028\pi$
$2$	1.49685	−	1.08752i	1.05843	−	0.768996i	0.973798	+	0.227417i	$0.0730279\pi$
$3$	−0.403986	−	0.293513i	−0.233242	−	0.169460i	0.465025	−	0.885297i	$-0.346045\pi$
$3$	−0.403986	−	0.293513i	−0.233242	−	0.169460i	−0.698267	+	0.715837i	$0.746045\pi$
$4$	0.439812	−	1.35360i	0.219906	−	0.676802i
$5$	1.20736			0.539948			0.269974	−	0.962868i	$-0.412985\pi$
$5$	1.20736			0.539948			0.269974	+	0.962868i	$0.412985\pi$
$6$	−0.923909			−0.377184
$7$	1.15357	−	3.55033i	0.436010	−	1.34190i	−0.456038	−	0.889960i	$-0.650732\pi$
$7$	1.15357	−	3.55033i	0.436010	−	1.34190i	0.892048	−	0.451940i	$-0.149268\pi$
$8$	0.329747	+	1.01486i	0.116583	+	0.358806i
$9$	−0.849996	−	2.61602i	−0.283332	−	0.872006i
$10$	1.80724	−	1.31303i	0.571499	−	0.415218i
$11$	−0.573693	+	1.76565i	−0.172975	+	0.532362i	−0.999535	−	0.0304861i	$-0.990294\pi$
$11$	−0.573693	+	1.76565i	−0.172975	+	0.532362i	0.826560	+	0.562848i	$0.190294\pi$
$12$	−0.574979	+	0.417746i	−0.165982	+	0.120593i
$13$	4.19432	+	3.04736i	1.16330	+	0.845184i	0.990191	−	0.139719i	$-0.0446199\pi$
$13$	4.19432	+	3.04736i	1.16330	+	0.845184i	0.173105	+	0.984903i	$0.444620\pi$
$14$	−2.13435	−	6.56885i	−0.570429	−	1.75560i
$15$	−0.487757	−	0.354376i	−0.125938	−	0.0914996i
$16$	3.90015	+	2.83362i	0.975037	+	0.708406i
$17$	−1.75135	−	5.39009i	−0.424764	−	1.30729i	−0.903220	−	0.429177i	$-0.858804\pi$
$17$	−1.75135	−	5.39009i	−0.424764	−	1.30729i	0.478456	−	0.878111i	$-0.341196\pi$
$18$	−4.11730	−	2.99139i	−0.970457	−	0.705078i
$19$	1.16376	−	0.845521i	0.266985	−	0.193976i	−0.446236	−	0.894915i	$-0.647236\pi$
$19$	1.16376	−	0.845521i	0.266985	−	0.193976i	0.713221	+	0.700940i	$0.247236\pi$
$20$	0.531013	−	1.63429i	0.118738	−	0.365438i
$21$	−1.50810	+	1.09570i	−0.329094	+	0.239101i
$22$	1.06145	+	3.26681i	0.226302	+	0.696486i
$23$	−1.09533	−	3.37109i	−0.228393	−	0.702921i	−0.997929	−	0.0643183i	$-0.979513\pi$
$23$	−1.09533	−	3.37109i	−0.228393	−	0.702921i	0.769537	−	0.638603i	$-0.220487\pi$
$24$	0.164660	−	0.506773i	0.0336112	−	0.103445i
$25$	−3.54228			−0.708456
$26$	9.59234			1.88121
$27$	−0.887376	+	2.73106i	−0.170776	+	0.525593i
$28$	−4.29839	−	3.12296i	−0.812319	−	0.590184i
$29$	−1.11046	+	0.806795i	−0.206207	+	0.149818i	−0.686096	−	0.727511i	$-0.740677\pi$
$29$	−1.11046	+	0.806795i	−0.206207	+	0.149818i	0.479889	+	0.877329i	$0.340677\pi$
$30$	−1.11549			−0.203660
$31$		0			0
$31$		0			0
$32$	6.78540			1.19950
$33$	0.750004	−	0.544910i	0.130559	−	0.0948567i
$34$	−8.48335	−	6.16352i	−1.45488	−	1.05703i
$35$	1.39278	−	4.28654i	0.235423	−	0.724557i
$36$	−3.91489			−0.652482
$37$	4.50281			0.740258			0.370129	−	0.928980i	$-0.379313\pi$
$37$	4.50281			0.740258			0.370129	+	0.928980i	$0.379313\pi$
$38$	0.822447	−	2.53123i	0.133419	−	0.410620i
$39$	−0.800011	−	2.46218i	−0.128104	−	0.394264i
$40$	0.398123	+	1.22530i	0.0629488	+	0.193737i
$41$	3.81784	−	2.77382i	0.596247	−	0.433198i	−0.248298	−	0.968684i	$-0.579871\pi$
$41$	3.81784	−	2.77382i	0.596247	−	0.433198i	0.844545	+	0.535485i	$0.179871\pi$
$42$	−1.06580	+	3.28018i	−0.164456	+	0.506143i
$43$	−5.30652	+	3.85541i	−0.809237	+	0.587945i	−0.913609	−	0.406593i	$-0.866717\pi$
$43$	−5.30652	+	3.85541i	−0.809237	+	0.587945i	0.104372	+	0.994538i	$0.466717\pi$
$44$	2.13767	+	1.55311i	0.322265	+	0.234140i
$45$	−1.02625	−	3.15848i	−0.152985	−	0.470838i
$46$	−5.30569	−	3.85481i	−0.782281	−	0.568361i
$47$	3.42131	+	2.48572i	0.499049	+	0.362580i	0.808654	−	0.588285i	$-0.200197\pi$
$47$	3.42131	+	2.48572i	0.499049	+	0.362580i	−0.309605	+	0.950865i	$0.600197\pi$
$48$	−0.743900	−	2.28949i	−0.107373	−	0.330459i
$49$	−5.61102	−	4.07665i	−0.801575	−	0.582378i
$50$	−5.30225	+	3.85231i	−0.749852	+	0.544799i
$51$	−0.874543	+	2.69157i	−0.122460	+	0.376895i
$52$	5.96963	−	4.33719i	0.827838	−	0.601460i
$53$	−4.00588	−	12.3288i	−0.550250	−	1.69350i	−0.708168	−	0.706044i	$-0.750478\pi$
$53$	−4.00588	−	12.3288i	−0.550250	−	1.69350i	0.157918	−	0.987452i	$-0.449522\pi$
$54$	1.64183	+	5.05303i	0.223425	+	0.687630i
$55$	−0.692655	+	2.13177i	−0.0933976	+	0.287448i
$56$	3.98346			0.532313
$57$	−0.718314			−0.0951431
$58$	−0.784779	+	2.41530i	−0.103047	+	0.317145i
$59$	1.76492	+	1.28229i	0.229773	+	0.166940i	0.696715	−	0.717348i	$-0.254644\pi$
$59$	1.76492	+	1.28229i	0.229773	+	0.166940i	−0.466942	+	0.884288i	$0.654644\pi$
$60$	−0.694207	+	0.504371i	−0.0896218	+	0.0651140i
$61$	−2.68087			−0.343251			−0.171625	−	0.985162i	$-0.554902\pi$
$61$	−2.68087			−0.343251			−0.171625	+	0.985162i	$0.554902\pi$
$62$		0			0
$63$	−10.2683			−1.29368
$64$	2.35642	−	1.71204i	0.294552	−	0.214005i
$65$	5.06407	+	3.67926i	0.628120	+	0.456356i
$66$	0.530040	−	1.63130i	0.0652434	−	0.200799i
$67$	2.88300			0.352214			0.176107	−	0.984371i	$-0.443649\pi$
$67$	2.88300			0.352214			0.176107	+	0.984371i	$0.443649\pi$
$68$	−8.06631			−0.978184
$69$	−0.546960	+	1.68337i	−0.0658462	+	0.202654i
$70$	−2.57693	−	7.93098i	−0.308002	−	0.947933i
$71$	2.78166	+	8.56106i	0.330122	+	1.01601i	0.969075	+	0.246766i	$0.0793678\pi$
$71$	2.78166	+	8.56106i	0.330122	+	1.01601i	−0.638953	+	0.769246i	$0.720632\pi$
$72$	2.37460	−	1.72525i	0.279849	−	0.203322i
$73$	−1.29912	+	3.99829i	−0.152051	+	0.467965i	−0.997850	−	0.0655368i	$-0.979124\pi$
$73$	−1.29912	+	3.99829i	−0.152051	+	0.467965i	0.845799	+	0.533501i	$0.179124\pi$
$74$	6.74003	−	4.89692i	0.783512	−	0.569255i
$75$	1.43103	+	1.03971i	0.165241	+	0.120055i
$76$	−0.632664	−	1.94714i	−0.0725715	−	0.223352i
$77$	5.60683	+	4.07360i	0.638958	+	0.464230i
$78$	−3.87517	−	2.81548i	−0.438777	−	0.318790i
$79$	3.47079	+	10.6820i	0.390494	+	1.20182i	0.932416	+	0.361388i	$0.117697\pi$
$79$	3.47079	+	10.6820i	0.390494	+	1.20182i	−0.541922	+	0.840429i	$0.682303\pi$
$80$	4.70889	+	3.42121i	0.526470	+	0.382503i
$81$	−5.51587	+	4.00751i	−0.612874	+	0.445279i
$82$	2.69813	−	8.30399i	0.297958	−	0.917022i
$83$	8.47642	−	6.15848i	0.930408	−	0.675981i	−0.0156845	−	0.999877i	$-0.504993\pi$
$83$	8.47642	−	6.15848i	0.930408	−	0.675981i	0.946093	+	0.323896i	$0.104993\pi$
$84$	0.819859	+	2.52327i	0.0894540	+	0.275311i
$85$	−2.11451	−	6.50779i	−0.229351	−	0.705869i
$86$	−3.75020	+	11.5419i	−0.404395	+	1.24460i
$87$	0.685415			0.0734842
$88$	−1.98105			−0.211180
$89$	−0.834882	+	2.56950i	−0.0884973	+	0.272367i	−0.985505	−	0.169649i	$-0.945737\pi$
$89$	−0.834882	+	2.56950i	−0.0884973	+	0.272367i	0.897007	+	0.442016i	$0.145737\pi$
$90$	−4.97107	−	3.61169i	−0.523997	−	0.380706i
$91$	15.6576	−	11.3759i	1.64136	−	1.19252i
$92$	−5.04486			−0.525963
$93$		0			0
$94$	7.82446			0.807031
$95$	1.40508	−	1.02085i	0.144158	−	0.104737i
$96$	−2.74121	−	1.99160i	−0.279773	−	0.203267i
$97$	−2.56277	+	7.88740i	−0.260210	+	0.800844i	0.732548	+	0.680715i	$0.238331\pi$
$97$	−2.56277	+	7.88740i	−0.260210	+	0.800844i	−0.992758	+	0.120129i	$0.961669\pi$
$98$	−12.8323			−1.29626
$99$	5.10660			0.513233
$100$	−1.55794	+	4.79484i	−0.155794	+	0.479484i
$101$	0.493946	+	1.52021i	0.0491495	+	0.151267i	0.972619	−	0.232405i	$-0.0746595\pi$
$101$	0.493946	+	1.52021i	0.0491495	+	0.151267i	−0.923470	+	0.383672i	$0.874659\pi$
$102$	1.61808	+	4.97995i	0.160214	+	0.493089i
$103$	−14.8114	+	10.7611i	−1.45941	+	1.06032i	−0.475889	+	0.879505i	$0.657874\pi$
$103$	−14.8114	+	10.7611i	−1.45941	+	1.06032i	−0.983517	+	0.180816i	$0.942126\pi$
$104$	−1.70956	+	5.26149i	−0.167636	+	0.515931i
$105$	−1.82082	+	1.32290i	−0.177694	+	0.129102i
$106$	−19.4041	−	14.0979i	−1.88469	−	1.36931i
$107$	3.57696	+	11.0087i	0.345798	+	1.06426i	0.961155	+	0.276008i	$0.0890115\pi$
$107$	3.57696	+	11.0087i	0.345798	+	1.06426i	−0.615358	+	0.788248i	$0.710989\pi$
$108$	3.30650	+	2.40231i	0.318168	+	0.231163i
$109$	−1.12720	−	0.818958i	−0.107966	−	0.0784419i	0.532492	−	0.846435i	$-0.321256\pi$
$109$	−1.12720	−	0.818958i	−0.107966	−	0.0784419i	−0.640458	+	0.767993i	$0.721256\pi$
$110$	1.28155	+	3.94422i	0.122191	+	0.376066i
$111$	−1.81907	−	1.32164i	−0.172659	−	0.125444i
$112$	14.5594	−	10.5780i	1.37574	−	0.999530i
$113$	−1.00602	+	3.09622i	−0.0946388	+	0.291268i	−0.987159	−	0.159738i	$-0.948935\pi$
$113$	−1.00602	+	3.09622i	−0.0946388	+	0.291268i	0.892521	+	0.451007i	$0.148935\pi$
$114$	−1.07521	+	0.781184i	−0.100702	+	0.0731646i
$115$	−1.32246	−	4.07013i	−0.123320	−	0.379541i
$116$	0.603688	+	1.85796i	0.0560510	+	0.172507i
$117$	4.40678	−	13.5627i	0.407407	−	1.25387i
$118$	4.03633			0.371575
$119$	−21.1569			−1.93945
$120$	0.198805	−	0.611858i	0.0181483	−	0.0558547i
$121$	6.11081	+	4.43976i	0.555528	+	0.403615i
$122$	−4.01286	+	2.91551i	−0.363307	+	0.263958i
$123$	−2.35651			−0.212479
$124$		0			0
$125$	−10.3136			−0.922478
$126$	−15.3700	+	11.1670i	−1.36927	+	0.994835i
$127$	−7.75964	−	5.63771i	−0.688556	−	0.500265i	0.187629	−	0.982240i	$-0.439920\pi$
$127$	−7.75964	−	5.63771i	−0.688556	−	0.500265i	−0.876185	+	0.481975i	$0.839920\pi$
$128$	−2.52829	+	7.78128i	−0.223471	+	0.687774i
$129$	3.27538			0.288381
$130$	11.5814			1.01576
$131$	−3.55128	+	10.9297i	−0.310277	+	0.954933i	0.667379	+	0.744719i	$0.267416\pi$
$131$	−3.55128	+	10.9297i	−0.310277	+	0.954933i	−0.977655	+	0.210215i	$0.932584\pi$
$132$	−0.407731	−	1.25487i	−0.0354884	−	0.109222i
$133$	−1.65940	−	5.10711i	−0.143888	−	0.442842i
$134$	4.31541	−	3.13533i	0.372795	−	0.270851i
$135$	−1.07138	+	3.29738i	−0.0922101	+	0.283793i
$136$	4.89266	−	3.55473i	0.419542	−	0.304815i
$137$	12.7725	+	9.27980i	1.09123	+	0.792827i	0.979607	−	0.200924i	$-0.0643943\pi$
$137$	12.7725	+	9.27980i	1.09123	+	0.792827i	0.111625	+	0.993750i	$0.464394\pi$
$138$	1.01199	+	3.11458i	0.0861462	+	0.265131i
$139$	8.25885	+	6.00040i	0.700506	+	0.508948i	0.880097	−	0.474794i	$-0.157477\pi$
$139$	8.25885	+	6.00040i	0.700506	+	0.508948i	−0.179591	+	0.983741i	$0.557477\pi$
$140$	−5.18971	−	3.77054i	−0.438611	−	0.318669i
$141$	−0.652568	−	2.00840i	−0.0549561	−	0.169138i
$142$	13.4741	+	9.78949i	1.13072	+	0.821516i
$143$	−7.78680	+	5.65744i	−0.651165	+	0.473099i
$144$	4.09770	−	12.6114i	0.341475	−	1.05095i
$145$	−1.34073	+	0.974094i	−0.111341	+	0.0808941i
$146$	2.40365	+	7.39766i	0.198927	+	0.612235i
$147$	1.07023	+	3.29382i	0.0882708	+	0.271670i
$148$	1.98039	−	6.09503i	0.162787	−	0.501008i
$149$	3.82067			0.313001			0.156501	−	0.987678i	$-0.449979\pi$
$149$	3.82067			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$150$	3.27274			0.267218
$151$	−2.74023	+	8.43357i	−0.222997	+	0.686314i	0.775492	+	0.631358i	$0.217502\pi$
$151$	−2.74023	+	8.43357i	−0.222997	+	0.686314i	−0.998489	+	0.0549565i	$0.982498\pi$
$152$	1.24183	+	0.902240i	0.100725	+	0.0731813i
$153$	−12.6119	+	9.16311i	−1.01961	+	0.740794i
$154$	12.8227			1.03328
$155$		0			0
$156$	−3.68467			−0.295010
$157$	4.18837	−	3.04303i	0.334268	−	0.242860i	−0.407971	−	0.912995i	$-0.633764\pi$
$157$	4.18837	−	3.04303i	0.334268	−	0.242860i	0.742240	+	0.670135i	$0.233764\pi$
$158$	16.8122	+	12.2147i	1.33750	+	0.971753i
$159$	−2.00035	+	6.15646i	−0.158638	+	0.488239i
$160$	8.19243			0.647668
$161$	−13.2320			−1.04283
$162$	−3.89815	+	11.9973i	−0.306268	+	0.942595i
$163$	0.171126	+	0.526673i	0.0134036	+	0.0412522i	0.957535	−	0.288318i	$-0.0930961\pi$
$163$	0.171126	+	0.526673i	0.0134036	+	0.0412522i	−0.944131	+	0.329570i	$0.893096\pi$
$164$	−2.07552	−	6.38781i	−0.162071	−	0.498804i
$165$	0.905526	−	0.657903i	0.0704951	−	0.0512177i
$166$	5.99042	−	18.4366i	0.464947	−	1.43096i
$167$	−1.61642	+	1.17440i	−0.125082	+	0.0908776i	−0.648567	−	0.761157i	$-0.724632\pi$
$167$	−1.61642	+	1.17440i	−0.125082	+	0.0908776i	0.523485	+	0.852035i	$0.324632\pi$
$168$	−1.60926	−	1.16920i	−0.124157	−	0.0902056i
$169$	4.28877	+	13.1995i	0.329905	+	1.01534i
$170$	−10.2425	−	7.44159i	−0.785562	−	0.570744i
$171$	−3.20109	−	2.32573i	−0.244793	−	0.177853i
$172$	2.88483	+	8.87858i	0.219966	+	0.676986i
$173$	3.28266	+	2.38499i	0.249576	+	0.181328i	0.705539	−	0.708671i	$-0.250705\pi$
$173$	3.28266	+	2.38499i	0.249576	+	0.181328i	−0.455963	+	0.889999i	$0.650705\pi$
$174$	1.02596	−	0.745405i	0.0777780	−	0.0565090i
$175$	−4.08628	+	12.5763i	−0.308894	+	0.950677i
$176$	−7.24066	+	5.26065i	−0.545785	+	0.396536i
$177$	−0.336634	−	1.03605i	−0.0253030	−	0.0778745i
$178$	1.54470	+	4.75411i	0.115780	+	0.356336i
$179$	−1.22490	+	3.76986i	−0.0915534	+	0.281772i	−0.986340	−	0.164721i	$-0.947327\pi$
$179$	−1.22490	+	3.76986i	−0.0915534	+	0.281772i	0.894787	+	0.446494i	$0.147327\pi$
$180$	−4.72669			−0.352307
$181$	6.39742			0.475517			0.237758	−	0.971324i	$-0.423587\pi$
$181$	6.39742			0.475517			0.237758	+	0.971324i	$0.423587\pi$
$182$	11.0655	−	34.0560i	0.820227	−	2.52440i
$183$	1.08304	+	0.786872i	0.0800603	+	0.0581672i
$184$	3.05999	−	2.22321i	0.225585	−	0.163897i
$185$	5.43652			0.399701
$186$		0			0
$187$	10.5217			0.769425
$188$	4.86942	−	3.53784i	0.355139	−	0.258023i
$189$	8.67253	+	6.30097i	0.630834	+	0.458328i
$190$	0.992991	−	3.05611i	0.0720392	−	0.221714i
$191$	11.6256			0.841202			0.420601	−	0.907246i	$-0.361819\pi$
$191$	11.6256			0.841202			0.420601	+	0.907246i	$0.361819\pi$
$192$	−1.45447			−0.104967
$193$	4.18518	−	12.8807i	0.301256	−	0.927171i	−0.679792	−	0.733405i	$-0.737930\pi$
$193$	4.18518	−	12.8807i	0.301256	−	0.927171i	0.981048	−	0.193765i	$-0.0620701\pi$
$194$	4.74166	+	14.5933i	0.340431	+	1.04774i
$195$	−0.965902	−	2.97274i	−0.0691697	−	0.212882i
$196$	−7.98596	+	5.80214i	−0.570426	+	0.414439i
$197$	7.23233	−	22.2588i	0.515282	−	1.58587i	−0.267487	−	0.963562i	$-0.586193\pi$
$197$	7.23233	−	22.2588i	0.515282	−	1.58587i	0.782769	−	0.622313i	$-0.213807\pi$
$198$	7.64380	−	5.55355i	0.543222	−	0.394674i
$199$	−5.33787	−	3.87819i	−0.378391	−	0.274917i	0.382291	−	0.924042i	$-0.375135\pi$
$199$	−5.33787	−	3.87819i	−0.378391	−	0.274917i	−0.760682	+	0.649125i	$0.775135\pi$
$200$	−1.16805	−	3.59490i	−0.0825939	−	0.254198i
$201$	−1.16469	−	0.846198i	−0.0821510	−	0.0596862i
$202$	2.39263	+	1.73835i	0.168345	+	0.122310i
$203$	1.58340	+	4.87320i	0.111133	+	0.342031i
$204$	3.25868	+	2.36757i	0.228153	+	0.165763i
$205$	4.60951	−	3.34901i	0.321942	−	0.233905i
$206$	−10.4674	+	32.2154i	−0.729300	+	2.24455i
$207$	−7.88781	+	5.73083i	−0.548241	+	0.398320i
$208$	7.72343	+	23.7703i	0.535524	+	1.64817i
$209$	0.825249	+	2.53986i	0.0570837	+	0.175686i
$210$	−1.28680	+	3.96037i	−0.0887978	+	0.273291i
$211$	−19.3651			−1.33315			−0.666574	−	0.745439i	$-0.732240\pi$
$211$	−19.3651			−1.33315			−0.666574	+	0.745439i	$0.732240\pi$
$212$	−18.4502			−1.26716
$213$	1.38903	−	4.27500i	0.0951750	−	0.292918i
$214$	17.3264	+	12.5884i	1.18441	+	0.860525i
$215$	−6.40689	+	4.65488i	−0.436946	+	0.317460i
$216$	−3.06424			−0.208495
$217$		0			0
$218$	−2.57788			−0.174596
$219$	1.69838	−	1.23394i	0.114766	−	0.0833822i
$220$	2.58094	+	1.87516i	0.174007	+	0.126423i
$221$	9.07980	−	27.9448i	0.610774	−	1.87977i
$222$	−4.16019			−0.279214
$223$	7.05971			0.472753			0.236377	−	0.971662i	$-0.424040\pi$
$223$	7.05971			0.472753			0.236377	+	0.971662i	$0.424040\pi$
$224$	7.82746	−	24.0904i	0.522994	−	1.60961i
$225$	3.01092	+	9.26667i	0.200728	+	0.617778i
$226$	1.86135	+	5.72865i	0.123815	+	0.381064i
$227$	7.29718	−	5.30171i	0.484331	−	0.351887i	−0.318669	−	0.947866i	$-0.603236\pi$
$227$	7.29718	−	5.30171i	0.484331	−	0.351887i	0.803000	+	0.595979i	$0.203236\pi$
$228$	−0.315924	+	0.972313i	−0.0209226	+	0.0643930i
$229$	−14.5250	+	10.5530i	−0.959836	+	0.697362i	−0.953113	−	0.302616i	$-0.902140\pi$
$229$	−14.5250	+	10.5530i	−0.959836	+	0.697362i	−0.00672346	+	0.999977i	$0.502140\pi$
$230$	−6.40589	−	4.65415i	−0.422392	−	0.306885i
$231$	−1.06943	−	3.29136i	−0.0703632	−	0.216556i
$232$	−1.18495	−	0.860917i	−0.0777958	−	0.0565220i
$233$	−11.0409	−	8.02168i	−0.723313	−	0.525518i	0.164128	−	0.986439i	$-0.447519\pi$
$233$	−11.0409	−	8.02168i	−0.723313	−	0.525518i	−0.887441	+	0.460921i	$0.847519\pi$
$234$	−8.15345	−	25.0937i	−0.533008	−	1.64043i
$235$	4.13075	+	3.00117i	0.269461	+	0.195775i
$236$	2.51194	−	1.82503i	0.163514	−	0.118800i
$237$	1.73315	−	5.33410i	0.112580	−	0.346487i
$238$	−31.6687	+	23.0087i	−2.05278	+	1.49143i
$239$	−3.04420	−	9.36908i	−0.196913	−	0.606035i	−0.999949	−	0.0101049i	$-0.996783\pi$
$239$	−3.04420	−	9.36908i	−0.196913	−	0.606035i	0.803036	−	0.595930i	$-0.203217\pi$
$240$	−0.898157	−	2.76424i	−0.0579758	−	0.178431i
$241$	−2.06109	+	6.34337i	−0.132766	+	0.408612i	−0.995236	−	0.0974964i	$-0.968917\pi$
$241$	−2.06109	+	6.34337i	−0.132766	+	0.408612i	0.862470	+	0.506109i	$0.168917\pi$
$242$	13.9753			0.898366
$243$	12.0194			0.771046
$244$	−1.17908	+	3.62884i	−0.0754830	+	0.232313i
$245$	−6.77453	−	4.92199i	−0.432809	−	0.314454i
$246$	−3.52734	+	2.56276i	−0.224895	+	0.163396i
$247$	7.45779			0.474528
$248$		0			0
$249$	−5.23195			−0.331562
$250$	−15.4379	+	11.2163i	−0.976380	+	0.709381i
$251$	23.7187	+	17.2327i	1.49711	+	1.08772i	0.971513	+	0.236984i	$0.0761590\pi$
$251$	23.7187	+	17.2327i	1.49711	+	1.08772i	0.525600	+	0.850732i	$0.323841\pi$
$252$	−4.51612	+	13.8992i	−0.284489	+	0.875566i
$253$	6.58054			0.413715
$254$	−17.7461			−1.11349
$255$	−1.05589	+	3.24969i	−0.0661223	+	0.203504i
$256$	6.47800	+	19.9372i	0.404875	+	1.24608i
$257$	−7.40049	−	22.7764i	−0.461630	−	1.42075i	−0.863172	−	0.504911i	$-0.831525\pi$
$257$	−7.40049	−	22.7764i	−0.461630	−	1.42075i	0.401542	−	0.915841i	$-0.368475\pi$
$258$	4.90274	−	3.56205i	0.305231	−	0.221763i
$259$	5.19433	−	15.9865i	0.322760	−	0.993352i
$260$	7.20750	−	5.23655i	0.446990	−	0.324757i
$261$	3.05448	+	2.21921i	0.189067	+	0.137366i
$262$	6.57060	+	20.2222i	0.405933	+	1.24933i
$263$	−3.19095	−	2.31836i	−0.196762	−	0.142956i	0.485042	−	0.874491i	$-0.338804\pi$
$263$	−3.19095	−	2.31836i	−0.196762	−	0.142956i	−0.681804	+	0.731535i	$0.738804\pi$
$264$	0.800316	+	0.581464i	0.0492561	+	0.0357866i
$265$	−4.83655	−	14.8854i	−0.297107	−	0.914400i
$266$	−8.03797	−	5.83993i	−0.492839	−	0.358069i
$267$	1.09146	−	0.792995i	0.0667965	−	0.0485305i
$268$	1.26798	−	3.90244i	0.0774542	−	0.238379i
$269$	−10.3168	+	7.49558i	−0.629025	+	0.457013i	−0.856062	−	0.516873i	$-0.827096\pi$
$269$	−10.3168	+	7.49558i	−0.629025	+	0.457013i	0.227037	+	0.973886i	$0.427096\pi$
$270$	1.98228	+	6.10083i	0.120638	+	0.371285i
$271$	−1.02674	−	3.15999i	−0.0623703	−	0.191956i	0.915016	−	0.403417i	$-0.132178\pi$
$271$	−1.02674	−	3.15999i	−0.0623703	−	0.191956i	−0.977386	+	0.211461i	$0.932178\pi$
$272$	8.44297	−	25.9848i	0.511931	−	1.57556i
$273$	−9.66443			−0.584918
$274$	29.2106			1.76467
$275$	2.03218	−	6.25441i	0.122545	−	0.377155i
$276$	2.03805	+	1.48073i	0.122676	+	0.0891297i
$277$	−17.0028	+	12.3533i	−1.02160	+	0.742237i	−0.966611	−	0.256250i	$-0.917513\pi$
$277$	−17.0028	+	12.3533i	−1.02160	+	0.742237i	−0.0549911	+	0.998487i	$0.517513\pi$
$278$	18.8878			1.13282
$279$		0			0
$280$	4.80948			0.287421
$281$	7.57793	−	5.50569i	0.452061	−	0.328442i	−0.338348	−	0.941021i	$-0.609868\pi$
$281$	7.57793	−	5.50569i	0.452061	−	0.328442i	0.790409	+	0.612579i	$0.209868\pi$
$282$	−3.16097	−	2.29658i	−0.188233	−	0.136759i
$283$	−3.13131	+	9.63718i	−0.186137	+	0.572871i	−0.999966	−	0.00823329i	$-0.997379\pi$
$283$	−3.13131	+	9.63718i	−0.186137	+	0.572871i	0.813829	+	0.581104i	$0.197379\pi$
$284$	12.8117			0.760234
$285$	−0.867265			−0.0513723
$286$	−5.50306	+	16.9367i	−0.325403	+	1.00149i
$287$	−5.44384	−	16.7544i	−0.321340	−	0.988982i
$288$	−5.76756	−	17.7507i	−0.339857	−	1.04597i
$289$	−12.2326	+	8.88748i	−0.719563	+	0.522793i
$290$	−0.947512	+	2.91614i	−0.0556398	+	0.171242i
$291$	3.35038	−	2.43419i	0.196403	−	0.142695i
$292$	4.84073	+	3.51700i	0.283282	+	0.205817i
$293$	−6.57282	−	20.2291i	−0.383988	−	1.18179i	−0.937212	−	0.348761i	$-0.886602\pi$
$293$	−6.57282	−	20.2291i	−0.383988	−	1.18179i	0.553223	−	0.833033i	$-0.313398\pi$
$294$	5.18407	+	3.76645i	0.302341	+	0.219664i
$295$	2.13089	+	1.54818i	0.124065	+	0.0901388i
$296$	1.48479	+	4.56970i	0.0863015	+	0.265609i
$297$	−4.31301	−	3.13358i	−0.250266	−	0.181829i
$298$	5.71896	−	4.15507i	0.331290	−	0.240697i
$299$	5.67873	−	17.4773i	0.328409	−	1.01074i
$300$	2.03673	−	1.47977i	0.117591	−	0.0854348i
$301$	7.56654	+	23.2874i	0.436128	+	1.34226i
$302$	5.07000	+	15.6038i	0.291746	+	0.897900i
$303$	0.246654	−	0.759123i	0.0141699	−	0.0436105i
$304$	6.93472			0.397734
$305$	−3.23678			−0.185338
$306$	−8.91306	+	27.4316i	−0.509526	+	1.56816i
$307$	−13.1394	−	9.54636i	−0.749907	−	0.544839i	0.145891	−	0.989301i	$-0.453395\pi$
$307$	−13.1394	−	9.54636i	−0.749907	−	0.544839i	−0.895798	+	0.444461i	$0.853395\pi$
$308$	7.98000	−	5.79781i	0.454703	−	0.330361i
$309$	9.14210			0.520076
$310$		0			0
$311$	−10.3858			−0.588924			−0.294462	−	0.955663i	$-0.595141\pi$
$311$	−10.3858			−0.588924			−0.294462	+	0.955663i	$0.595141\pi$
$312$	2.23496	−	1.62379i	0.126529	−	0.0919290i
$313$	−25.9239	−	18.8348i	−1.46530	−	1.06461i	−0.981941	−	0.189186i	$-0.939415\pi$
$313$	−25.9239	−	18.8348i	−1.46530	−	1.06461i	−0.483363	−	0.875420i	$-0.660585\pi$
$314$	2.95999	−	9.10991i	0.167042	−	0.514102i
$315$	−12.3975			−0.698521
$316$	15.9857			0.899264
$317$	7.82267	−	24.0757i	0.439365	−	1.35223i	−0.449181	−	0.893441i	$-0.648284\pi$
$317$	7.82267	−	24.0757i	0.439365	−	1.35223i	0.888547	−	0.458786i	$-0.151716\pi$
$318$	3.70107	+	11.3907i	0.207546	+	0.638760i
$319$	−0.787452	−	2.42353i	−0.0440889	−	0.135692i
$320$	2.84505	−	2.06705i	0.159043	−	0.115551i
$321$	1.78617	−	5.49726i	0.0996943	−	0.306827i
$322$	−19.8064	+	14.3902i	−1.10377	+	0.801933i
$323$	−6.59558	−	4.79197i	−0.366988	−	0.266632i
$324$	2.99863	+	9.22885i	0.166591	+	0.512714i
$325$	−14.8575	−	10.7946i	−0.824144	−	0.598776i
$326$	0.828919	+	0.602245i	0.0459096	+	0.0333553i
$327$	0.214998	+	0.661695i	0.0118894	+	0.0365918i
$328$	4.07395	+	2.95990i	0.224946	+	0.163433i
$329$	12.7719	−	9.27931i	0.704137	−	0.511585i
$330$	0.639950	−	1.96956i	0.0352281	−	0.108421i
$331$	26.6291	−	19.3472i	1.46367	−	1.06342i	0.481278	−	0.876568i	$-0.340173\pi$
$331$	26.6291	−	19.3472i	1.46367	−	1.06342i	0.982389	−	0.186849i	$-0.0598274\pi$
$332$	−4.60811	−	14.1823i	−0.252903	−	0.778354i
$333$	−3.82737	−	11.7794i	−0.209739	−	0.645510i
$334$	−1.14235	+	3.51579i	−0.0625066	+	0.192375i
$335$	3.48082			0.190178
$336$	−8.98660			−0.490259
$337$	1.22083	−	3.75733i	0.0665030	−	0.204675i	−0.912283	−	0.409560i	$-0.865682\pi$
$337$	1.22083	−	3.75733i	0.0665030	−	0.204675i	0.978786	+	0.204885i	$0.0656821\pi$
$338$	20.7744	+	15.0935i	1.12998	+	0.820976i
$339$	1.31520	−	0.955551i	0.0714320	−	0.0518984i
$340$	−9.73895			−0.528169
$341$		0			0
$342$	−7.32083			−0.395865
$343$	0.194480	−	0.141298i	0.0105009	−	0.00762938i
$344$	−5.66249	−	4.11404i	−0.305301	−	0.221814i
$345$	−0.660378	+	2.03244i	−0.0355536	+	0.109423i
$346$	7.50739			0.403600
$347$	−13.6844			−0.734619			−0.367310	−	0.930099i	$-0.619721\pi$
$347$	−13.6844			−0.734619			−0.367310	+	0.930099i	$0.619721\pi$
$348$	0.301454	−	0.927780i	0.0161596	−	0.0497342i
$349$	−1.14488	−	3.52357i	−0.0612839	−	0.188613i	0.915727	−	0.401800i	$-0.131615\pi$
$349$	−1.14488	−	3.52357i	−0.0612839	−	0.188613i	−0.977011	+	0.213188i	$0.931615\pi$
$350$	7.56046	+	23.2687i	0.404123	+	1.24376i
$351$	−12.0445	+	8.75082i	−0.642886	+	0.467084i
$352$	−3.89274	+	11.9806i	−0.207484	+	0.638569i
$353$	12.5329	−	9.10566i	0.667057	−	0.484645i	−0.201982	−	0.979389i	$-0.564738\pi$
$353$	12.5329	−	9.10566i	0.667057	−	0.484645i	0.869039	+	0.494744i	$0.164738\pi$
$354$	−1.63062	−	1.18472i	−0.0866666	−	0.0629670i
$355$	3.35847	+	10.3363i	0.178249	+	0.548594i
$356$	3.11090	+	2.26020i	0.164877	+	0.119790i
$357$	8.54711	+	6.20984i	0.452361	+	0.328659i
$358$	2.26632	+	6.97501i	0.119779	+	0.368641i
$359$	4.34391	+	3.15604i	0.229263	+	0.166569i	0.696486	−	0.717570i	$-0.254746\pi$
$359$	4.34391	+	3.15604i	0.229263	+	0.166569i	−0.467223	+	0.884139i	$0.654746\pi$
$360$	2.86700	−	2.08300i	0.151104	−	0.109784i
$361$	−5.23189	+	16.1021i	−0.275363	+	0.847479i
$362$	9.57597	−	6.95735i	0.503302	−	0.365670i
$363$	−1.16555	−	3.58720i	−0.0611757	−	0.188279i
$364$	−8.51206	−	26.1974i	−0.446153	−	1.37312i
$365$	−1.56851	+	4.82738i	−0.0820996	+	0.252677i
$366$	2.47688			0.129469
$367$	−14.7209			−0.768425			−0.384212	−	0.923245i	$-0.625527\pi$
$367$	−14.7209			−0.768425			−0.384212	+	0.923245i	$0.625527\pi$
$368$	5.28044	−	16.2515i	0.275262	−	0.847169i
$369$	−10.5015	−	7.62980i	−0.546688	−	0.397192i
$370$	8.13765	−	5.91235i	0.423056	−	0.307368i
$371$	−48.3926			−2.51242
$372$		0			0
$373$	23.8449			1.23464			0.617320	−	0.786712i	$-0.288218\pi$
$373$	23.8449			1.23464			0.617320	+	0.786712i	$0.288218\pi$
$374$	15.7494	−	11.4426i	0.814383	−	0.591684i
$375$	4.16656	+	3.02718i	0.215160	+	0.156323i
$376$	−1.39449	+	4.29179i	−0.0719152	+	0.221332i
$377$	−7.11622			−0.366504
$378$	19.8339			1.02015
$379$	−6.83764	+	21.0441i	−0.351226	+	1.08096i	0.606939	+	0.794748i	$0.292397\pi$
$379$	−6.83764	+	21.0441i	−0.351226	+	1.08096i	−0.958165	+	0.286215i	$0.907603\pi$
$380$	−0.763854	−	2.35090i	−0.0391849	−	0.120599i
$381$	1.48005	+	4.55511i	0.0758250	+	0.233365i
$382$	17.4018	−	12.6432i	0.890354	−	0.646880i
$383$	−7.35417	+	22.6338i	−0.375780	+	1.15653i	0.567170	+	0.823601i	$0.308038\pi$
$383$	−7.35417	+	22.6338i	−0.375780	+	1.15653i	−0.942951	+	0.332933i	$0.891962\pi$
$384$	3.30530	−	2.40144i	0.168673	−	0.122548i
$385$	6.76948	+	4.91831i	0.345004	+	0.250660i
$386$	−7.74345	−	23.8319i	−0.394131	−	1.21301i
$387$	14.5964	+	10.6049i	0.741974	+	0.539076i
$388$	9.54927	+	6.93795i	0.484791	+	0.352221i
$389$	5.27010	+	16.2197i	0.267205	+	0.822372i	0.991177	+	0.132543i	$0.0423143\pi$
$389$	5.27010	+	16.2197i	0.267205	+	0.822372i	−0.723972	+	0.689829i	$0.757686\pi$
$390$	−4.67873	−	3.39930i	−0.236917	−	0.172130i
$391$	−16.2522	+	11.8079i	−0.821908	+	0.597151i
$392$	2.28699	−	7.03864i	0.115511	−	0.355505i
$393$	4.64268	−	3.37311i	0.234192	−	0.170151i
$394$	−13.3813	−	41.1834i	−0.674140	−	2.07479i
$395$	4.19049	+	12.8970i	0.210847	+	0.648919i
$396$	2.24595	−	6.91231i	0.112863	−	0.347357i
$397$	−10.0215			−0.502965			−0.251482	−	0.967862i	$-0.580918\pi$
$397$	−10.0215			−0.502965			−0.251482	+	0.967862i	$0.580918\pi$
$398$	−12.2076			−0.611912
$399$	−0.828628	+	2.55026i	−0.0414833	+	0.127672i
$400$	−13.8154	−	10.0375i	−0.690771	−	0.501874i
$401$	23.1002	−	16.7832i	1.15357	−	0.838115i	0.164615	−	0.986358i	$-0.447362\pi$
$401$	23.1002	−	16.7832i	1.15357	−	0.838115i	0.988951	+	0.148243i	$0.0473617\pi$
$402$	−2.66363			−0.132850
$403$		0			0
$404$	2.27501			0.113186
$405$	−6.65964	+	4.83851i	−0.330920	+	0.240428i
$406$	7.66983	+	5.57245i	0.380647	+	0.276556i
$407$	−2.58323	+	7.95037i	−0.128046	+	0.394085i
$408$	−3.01993			−0.149509
$409$	−23.0102			−1.13778			−0.568891	−	0.822413i	$-0.692628\pi$
$409$	−23.0102			−1.13778			−0.568891	+	0.822413i	$0.692628\pi$
$410$	3.25762	−	10.0259i	0.160882	−	0.495145i
$411$	−2.43619	−	7.49782i	−0.120168	−	0.369840i
$412$	8.05202	+	24.7816i	0.396694	+	1.22090i
$413$	6.58851	−	4.78683i	0.324200	−	0.235545i
$414$	−5.57444	+	17.1564i	−0.273969	+	0.843189i
$415$	10.2341	−	7.43551i	0.502372	−	0.364995i
$416$	28.4602	+	20.6775i	1.39537	+	1.01380i
$417$	−1.57526	−	4.84816i	−0.0771409	−	0.237415i
$418$	3.99743	+	2.90430i	0.195521	+	0.142054i
$419$	−27.1352	−	19.7149i	−1.32564	−	0.963137i	−0.999843	−	0.0176979i	$-0.994366\pi$
$419$	−27.1352	−	19.7149i	−1.32564	−	0.963137i	−0.325800	−	0.945439i	$-0.605634\pi$
$420$	0.989867	+	3.04650i	0.0483005	+	0.148654i
$421$	−7.30321	−	5.30610i	−0.355937	−	0.258603i	0.395419	−	0.918501i	$-0.370600\pi$
$421$	−7.30321	−	5.30610i	−0.355937	−	0.258603i	−0.751355	+	0.659898i	$0.770600\pi$
$422$	−28.9866	+	21.0600i	−1.41104	+	1.02518i
$423$	3.59461	−	11.0631i	0.174776	−	0.537904i
$424$	11.1911	−	8.13078i	0.543486	−	0.394866i
$425$	6.20376	+	19.0932i	0.300926	+	0.926156i
$426$	−2.57000	−	7.90964i	−0.124517	−	0.383223i
$427$	−3.09258	+	9.51800i	−0.149661	+	0.460608i
$428$	16.4747			0.796333
$429$	4.80630			0.232050
$430$	−4.52785	+	13.9353i	−0.218352	+	0.672019i
$431$	−9.14737	−	6.64595i	−0.440613	−	0.320124i	0.345265	−	0.938505i	$-0.387789\pi$
$431$	−9.14737	−	6.64595i	−0.440613	−	0.320124i	−0.785878	+	0.618381i	$0.787789\pi$
$432$	−11.1997	+	8.13706i	−0.538846	+	0.391495i
$433$	9.10433			0.437526			0.218763	−	0.975778i	$-0.429798\pi$
$433$	9.10433			0.437526			0.218763	+	0.975778i	$0.429798\pi$
$434$		0			0
$435$	0.827544			0.0396777
$436$	−1.60430	+	1.16559i	−0.0768321	+	0.0558218i
$437$	−4.12503	−	2.99701i	−0.197327	−	0.143367i
$438$	1.20027	−	3.69406i	0.0573512	−	0.176509i
$439$	−39.6053			−1.89026			−0.945128	−	0.326700i	$-0.894063\pi$
$439$	−39.6053			−1.89026			−0.945128	+	0.326700i	$0.894063\pi$
$440$	−2.39184			−0.114027
$441$	−5.89524	+	18.1437i	−0.280726	+	0.863984i
$442$	−16.7995	−	51.7036i	−0.799071	−	2.45929i
$443$	7.80525	+	24.0221i	0.370839	+	1.14132i	0.946244	+	0.323455i	$0.104844\pi$
$443$	7.80525	+	24.0221i	0.370839	+	1.14132i	−0.575405	+	0.817869i	$0.695156\pi$
$444$	−2.58902	+	1.88103i	−0.122870	+	0.0892699i
$445$	−1.00800	+	3.10232i	−0.0477840	+	0.147064i
$446$	10.5673	−	7.67761i	0.500377	−	0.363545i
$447$	−1.54350	−	1.12142i	−0.0730049	−	0.0530412i
$448$	−3.36000	−	10.3410i	−0.158745	−	0.488568i
$449$	−1.48204	−	1.07677i	−0.0699419	−	0.0508158i	0.552265	−	0.833669i	$-0.313764\pi$
$449$	−1.48204	−	1.07677i	−0.0699419	−	0.0508158i	−0.622207	+	0.782853i	$0.713764\pi$
$450$	14.5846	+	10.5963i	0.687525	+	0.499516i
$451$	2.70732	+	8.33228i	0.127483	+	0.392352i
$452$	3.74860	+	2.72352i	0.176319	+	0.128103i
$453$	3.58238	−	2.60275i	0.168315	−	0.122288i
$454$	5.15703	−	15.8717i	0.242031	−	0.744896i
$455$	18.9044	−	13.7348i	0.886251	−	0.643899i
$456$	−0.236862	−	0.728985i	−0.0110921	−	0.0341379i
$457$	11.1105	+	34.1946i	0.519728	+	1.59956i	0.774512	+	0.632559i	$0.217996\pi$
$457$	11.1105	+	34.1946i	0.519728	+	1.59956i	−0.254784	+	0.966998i	$0.582004\pi$
$458$	−10.2650	+	31.5925i	−0.479653	+	1.47622i
$459$	16.2748			0.759642
$460$	−6.09097			−0.283993
$461$	−0.413073	+	1.27131i	−0.0192387	+	0.0592106i	−0.960215	−	0.279262i	$-0.909910\pi$
$461$	−0.413073	+	1.27131i	−0.0192387	+	0.0592106i	0.940976	+	0.338473i	$0.109910\pi$
$462$	−5.18020	−	3.76364i	−0.241005	−	0.175100i
$463$	9.51938	−	6.91623i	0.442403	−	0.321425i	−0.344186	−	0.938901i	$-0.611845\pi$
$463$	9.51938	−	6.91623i	0.442403	−	0.321425i	0.786589	+	0.617477i	$0.211845\pi$
$464$	−6.61711			−0.307192
$465$		0			0
$466$	−25.2503			−1.16970
$467$	−8.89825	+	6.46496i	−0.411762	+	0.299163i	−0.774315	−	0.632801i	$-0.781905\pi$
$467$	−8.89825	+	6.46496i	−0.411762	+	0.299163i	0.362553	+	0.931963i	$0.381905\pi$
$468$	−16.4203	−	11.9301i	−0.759030	−	0.551468i
$469$	3.32575	−	10.2356i	0.153569	−	0.472637i
$470$	9.44695			0.435755
$471$	−2.58521			−0.119120
$472$	−0.719361	+	2.21397i	−0.0331113	+	0.101906i
$473$	−3.76298	−	11.5813i	−0.173022	−	0.532507i
$474$	−3.20669	−	9.86918i	−0.147288	−	0.453306i
$475$	−4.12236	+	2.99507i	−0.189147	+	0.137423i
$476$	−9.30508	+	28.6381i	−0.426498	+	1.31262i
$477$	−28.8475	+	20.9589i	−1.32084	+	0.959643i
$478$	−14.7458	−	10.7134i	−0.674457	−	0.490022i
$479$	−0.207584	−	0.638877i	−0.00948474	−	0.0291910i	0.946202	−	0.323576i	$-0.104885\pi$
$479$	−0.207584	−	0.638877i	−0.00948474	−	0.0291910i	−0.955687	+	0.294385i	$0.904885\pi$
$480$	−3.30963	−	2.40459i	−0.151063	−	0.109754i
$481$	18.8863	+	13.7217i	0.861139	+	0.625654i
$482$	3.81343	+	11.7365i	0.173697	+	0.534585i
$483$	5.34556	+	3.88378i	0.243232	+	0.176718i
$484$	8.69729	−	6.31895i	0.395331	−	0.287225i
$485$	−3.09419	+	9.52294i	−0.140500	+	0.432415i
$486$	17.9912	−	13.0714i	0.816100	−	0.592931i
$487$	−7.59425	−	23.3727i	−0.344128	−	1.05912i	−0.962049	−	0.272877i	$-0.912025\pi$
$487$	−7.59425	−	23.3727i	−0.344128	−	1.05912i	0.617921	−	0.786241i	$-0.287975\pi$
$488$	−0.884009	−	2.72070i	−0.0400172	−	0.123160i
$489$	0.0854527	−	0.262996i	0.00386430	−	0.0118931i
$490$	−15.4932			−0.699912
$491$	8.63428			0.389660			0.194830	−	0.980837i	$-0.437585\pi$
$491$	8.63428			0.389660			0.194830	+	0.980837i	$0.437585\pi$
$492$	−1.03642	+	3.18978i	−0.0467255	+	0.143806i
$493$	6.29350	+	4.57249i	0.283445	+	0.205935i
$494$	11.1632	−	8.11052i	0.502255	−	0.364910i
$495$	6.16551			0.277119
$496$		0			0
$497$	33.6035			1.50732
$498$	−7.83144	+	5.68987i	−0.350935	+	0.254969i
$499$	−25.1575	−	18.2780i	−1.12620	−	0.818236i	−0.141067	−	0.990000i	$-0.545053\pi$
$499$	−25.1575	−	18.2780i	−1.12620	−	0.818236i	−0.985138	+	0.171764i	$0.945053\pi$
$500$	−4.53606	+	13.9606i	−0.202859	+	0.624335i
$501$	0.997713			0.0445745
$502$	54.2443			2.42104
$503$	−5.11249	+	15.7346i	−0.227955	+	0.701572i	0.770024	+	0.638015i	$0.220244\pi$
$503$	−5.11249	+	15.7346i	−0.227955	+	0.701572i	−0.997978	+	0.0635567i	$0.979756\pi$
$504$	−3.38593	−	10.4208i	−0.150821	−	0.464180i
$505$	0.596371	+	1.83544i	0.0265382	+	0.0816761i
$506$	9.85007	−	7.15649i	0.437889	−	0.318145i
$507$	2.14161	−	6.59121i	0.0951124	−	0.292726i
$508$	−11.0440	+	8.02394i	−0.489998	+	0.356005i
$509$	−24.9963	−	18.1608i	−1.10794	−	0.804965i	−0.125602	−	0.992081i	$-0.540086\pi$
$509$	−24.9963	−	18.1608i	−1.10794	−	0.804965i	−0.982338	+	0.187115i	$0.940086\pi$
$510$	1.95361	+	6.01260i	0.0865074	+	0.266242i
$511$	12.6966	+	9.22464i	0.561666	+	0.408074i
$512$	18.1405	+	13.1798i	0.801705	+	0.582473i
$513$	1.27648	+	3.92860i	0.0563579	+	0.173452i
$514$	−35.8473	−	26.0446i	−1.58116	−	1.14878i
$515$	−17.8827	+	12.9925i	−0.788004	+	0.572519i
$516$	1.44055	−	4.43356i	0.0634167	−	0.195177i
$517$	−6.35169	+	4.61477i	−0.279347	+	0.202957i
$518$	−9.61058	−	29.5783i	−0.422264	−	1.29960i
$519$	−0.626123	−	1.92701i	−0.0274838	−	0.0845863i
$520$	−2.06406	+	6.35252i	−0.0905149	+	0.278576i
$521$	−14.7219			−0.644980			−0.322490	−	0.946573i	$-0.604520\pi$
$521$	−14.7219			−0.644980			−0.322490	+	0.946573i	$0.604520\pi$
$522$	6.98553			0.305748
$523$	−9.38146	+	28.8732i	−0.410223	+	1.26254i	0.506232	+	0.862397i	$0.331038\pi$
$523$	−9.38146	+	28.8732i	−0.410223	+	1.26254i	−0.916455	+	0.400138i	$0.868962\pi$
$524$	13.2326	+	9.61405i	0.578069	+	0.419992i
$525$	5.34210	−	3.88126i	0.233148	−	0.169392i
$526$	−7.29764			−0.318192
$527$		0			0
$528$	4.46920			0.194497
$529$	8.44289	−	6.13412i	0.367082	−	0.266701i
$530$	−23.4278	−	17.0213i	−1.01764	−	0.739357i
$531$	1.85432	−	5.70700i	0.0804705	−	0.247663i
$532$	−7.64282			−0.331358
$533$	24.4661			1.05974
$534$	0.771355	−	2.37399i	0.0333798	−	0.102732i
$535$	4.31868	+	13.2915i	0.186713	+	0.574643i
$536$	0.950659	+	2.92583i	0.0410622	+	0.126377i
$537$	1.60135	−	1.16345i	0.0691032	−	0.0502064i
$538$	−7.29103	+	22.4395i	−0.314339	+	0.967435i
$539$	10.4169	−	7.56833i	0.448688	−	0.325991i
$540$	3.99214	+	2.90046i	0.171794	+	0.124816i
$541$	−8.37466	−	25.7746i	−0.360055	−	1.10813i	−0.953020	−	0.302907i	$-0.902043\pi$
$541$	−8.37466	−	25.7746i	−0.360055	−	1.10813i	0.592965	−	0.805228i	$-0.297957\pi$
$542$	−4.97345	−	3.61342i	−0.213628	−	0.155210i
$543$	−2.58447	−	1.87773i	−0.110910	−	0.0805810i
$544$	−11.8836	−	36.5739i	−0.509504	−	1.56809i
$545$	−1.36094	−	0.988778i	−0.0582961	−	0.0423546i
$546$	−14.4662	+	10.5103i	−0.619096	+	0.449799i
$547$	10.1551	−	31.2542i	0.434201	−	1.33633i	−0.459703	−	0.888073i	$-0.652044\pi$
$547$	10.1551	−	31.2542i	0.434201	−	1.33633i	0.893904	−	0.448259i	$-0.147956\pi$
$548$	18.1787	−	13.2076i	0.776555	−	0.564200i
$549$	2.27873	+	7.01322i	0.0972539	+	0.299317i
$550$	−3.75995	−	11.5719i	−0.160325	−	0.493429i
$551$	−0.610145	+	1.87783i	−0.0259930	+	0.0799983i
$552$	−1.88873			−0.0803899
$553$	41.9284			1.78298
$554$	−12.0162	+	36.9820i	−0.510519	+	1.57121i
$555$	−2.19628	−	1.59569i	−0.0932269	−	0.0677333i
$556$	11.7545	−	8.54015i	0.498502	−	0.362183i
$557$	−3.79343			−0.160733			−0.0803663	−	0.996765i	$-0.525609\pi$
$557$	−3.79343			−0.160733			−0.0803663	+	0.996765i	$0.525609\pi$
$558$		0			0
$559$	−34.0061			−1.43830
$560$	17.5785	−	12.7715i	0.742826	−	0.539695i
$561$	−4.25063	−	3.08826i	−0.179462	−	0.130387i
$562$	5.35544	−	16.4824i	0.225906	−	0.695266i
$563$	−8.97818			−0.378385			−0.189193	−	0.981940i	$-0.560587\pi$
$563$	−8.97818			−0.378385			−0.189193	+	0.981940i	$0.560587\pi$
$564$	−3.00558			−0.126558
$565$	−1.21464	+	3.73826i	−0.0511001	+	0.157270i
$566$	5.79357	+	17.8308i	0.243522	+	0.749484i
$567$	7.86505	+	24.2061i	0.330301	+	1.01656i
$568$	−7.77100	+	5.64596i	−0.326064	+	0.236899i
$569$	2.93430	−	9.03084i	0.123012	−	0.378592i	−0.870522	−	0.492130i	$-0.836218\pi$
$569$	2.93430	−	9.03084i	0.123012	−	0.378592i	0.993534	+	0.113538i	$0.0362184\pi$
$570$	−1.29816	+	0.943171i	−0.0543741	+	0.0395051i
$571$	−5.18447	−	3.76674i	−0.216963	−	0.157633i	0.473995	−	0.880527i	$-0.342811\pi$
$571$	−5.18447	−	3.76674i	−0.216963	−	0.157633i	−0.690959	+	0.722894i	$0.742811\pi$
$572$	4.23320	+	13.0285i	0.176999	+	0.544747i
$573$	−4.69660	−	3.41228i	−0.196203	−	0.142550i
$574$	−26.3694	−	19.1585i	−1.10064	−	0.799661i
$575$	3.87998	+	11.9413i	0.161806	+	0.497988i
$576$	−6.48167	−	4.70921i	−0.270069	−	0.196217i
$577$	−6.37116	+	4.62892i	−0.265235	+	0.192704i	−0.712452	−	0.701721i	$-0.752415\pi$
$577$	−6.37116	+	4.62892i	−0.265235	+	0.192704i	0.447217	+	0.894426i	$0.352415\pi$
$578$	−8.64495	+	26.6064i	−0.359582	+	1.10668i
$579$	−5.47140	+	3.97521i	−0.227384	+	0.165204i
$580$	0.728869	+	2.24323i	0.0302646	+	0.0931450i
$581$	−12.0865	−	37.1984i	−0.501432	−	1.54325i
$582$	2.36777	−	7.28724i	0.0981471	−	0.302066i
$583$	24.0665			0.996733
$584$	−4.48607			−0.185635
$585$	5.32058	−	16.3750i	0.219979	−	0.677025i
$586$	−31.8381	−	23.1317i	−1.31522	−	0.955563i
$587$	−37.2778	+	27.0839i	−1.53862	+	1.11787i	−0.587426	+	0.809278i	$0.699859\pi$
$587$	−37.2778	+	27.0839i	−1.53862	+	1.11787i	−0.951193	+	0.308595i	$0.900141\pi$
$588$	4.92922			0.203278
$589$		0			0
$590$	4.87331			0.200631
$591$	−9.45501	+	6.86947i	−0.388927	+	0.282572i
$592$	17.5616	+	12.7593i	0.721779	+	0.524403i
$593$	2.65526	−	8.17204i	0.109038	−	0.335586i	−0.881619	−	0.471962i	$-0.843546\pi$
$593$	2.65526	−	8.17204i	0.109038	−	0.335586i	0.990657	+	0.136377i	$0.0435458\pi$
$594$	−9.86377			−0.404715
$595$	−25.5441			−1.04720
$596$	1.68038	−	5.17167i	0.0688309	−	0.211840i
$597$	1.01813	+	3.13347i	0.0416691	+	0.128244i
$598$	−10.5068	−	32.3367i	−0.429656	−	1.32234i
$599$	20.5548	−	14.9339i	0.839846	−	0.610184i	−0.0824816	−	0.996593i	$-0.526285\pi$
$599$	20.5548	−	14.9339i	0.839846	−	0.610184i	0.922328	+	0.386409i	$0.126285\pi$
$600$	−0.583273	+	1.79513i	−0.0238120	+	0.0732859i
$601$	20.3593	−	14.7919i	0.830474	−	0.603375i	−0.0892191	−	0.996012i	$-0.528437\pi$
$601$	20.3593	−	14.7919i	0.830474	−	0.603375i	0.919693	+	0.392637i	$0.128437\pi$
$602$	36.6516	+	26.6289i	1.49381	+	1.08531i
$603$	−2.45054	−	7.54198i	−0.0997936	−	0.307133i
$604$	10.2105	+	7.41838i	0.415460	+	0.301850i
$605$	7.37795	+	5.36040i	0.299956	+	0.217931i
$606$	−0.456361	−	1.40453i	−0.0185384	−	0.0570553i
$607$	−7.59425	−	5.51754i	−0.308241	−	0.223950i	0.422900	−	0.906176i	$-0.361012\pi$
$607$	−7.59425	−	5.51754i	−0.308241	−	0.223950i	−0.731141	+	0.682226i	$0.761012\pi$
$608$	7.89657	−	5.73720i	0.320248	−	0.232674i
$609$	0.790677	−	2.43345i	0.0320398	−	0.0986085i
$610$	−4.84497	+	3.52008i	−0.196167	+	0.142524i
$611$	6.77518	+	20.8519i	0.274095	+	0.843576i
$612$	6.85633	+	21.1016i	0.277151	+	0.852982i
$613$	3.54936	−	10.9238i	0.143357	−	0.441208i	−0.853439	−	0.521193i	$-0.825487\pi$
$613$	3.54936	−	10.9238i	0.143357	−	0.441208i	0.996796	+	0.0799850i	$0.0254872\pi$
$614$	−30.0496			−1.21270
$615$	−2.84516			−0.114728
$616$	−2.28528	+	7.03338i	−0.0920768	+	0.283383i
$617$	1.82303	+	1.32451i	0.0733925	+	0.0533227i	0.623877	−	0.781523i	$-0.285557\pi$
$617$	1.82303	+	1.32451i	0.0733925	+	0.0533227i	−0.550484	+	0.834846i	$0.685557\pi$
$618$	13.6843	−	9.94226i	0.550465	−	0.399936i
$619$	23.6684			0.951314			0.475657	−	0.879631i	$-0.342210\pi$
$619$	23.6684			0.951314			0.475657	+	0.879631i	$0.342210\pi$
$620$		0			0
$621$	10.1786			0.408455
$622$	−15.5460	+	11.2948i	−0.623336	+	0.452880i
$623$	8.15949	+	5.92822i	0.326903	+	0.237509i
$624$	3.85673	−	11.8698i	0.154393	−	0.475172i
$625$	5.25913			0.210365
$626$	−59.2874			−2.36960
$627$	0.412092	−	1.26829i	0.0164574	−	0.0506506i
$628$	−2.27696	−	7.00776i	−0.0908605	−	0.279640i
$629$	−7.88599	−	24.2706i	−0.314435	−	0.967731i
$630$	−18.5572	+	13.4826i	−0.739337	+	0.537160i
$631$	−10.7235	+	33.0035i	−0.426896	+	1.31385i	0.474272	+	0.880379i	$0.342711\pi$
$631$	−10.7235	+	33.0035i	−0.426896	+	1.31385i	−0.901167	+	0.433471i	$0.857289\pi$
$632$	−9.69619	+	7.04469i	−0.385694	+	0.280223i
$633$	7.82323	+	5.68391i	0.310945	+	0.225915i
$634$	−14.4736	−	44.5450i	−0.574819	−	1.76911i
$635$	−9.36869	−	6.80675i	−0.371785	−	0.270118i
$636$	7.45362	+	5.41537i	0.295555	+	0.214734i
$637$	−11.1115	−	34.1976i	−0.440252	−	1.35496i
$638$	−3.81434	−	2.77128i	−0.151011	−	0.109716i
$639$	20.0315	−	14.5537i	0.792434	−	0.575737i
$640$	−3.05256	+	9.39481i	−0.120663	+	0.371363i
$641$	−21.3522	+	15.5133i	−0.843361	+	0.612738i	−0.923307	−	0.384062i	$-0.874525\pi$
$641$	−21.3522	+	15.5133i	−0.843361	+	0.612738i	0.0799466	+	0.996799i	$0.474525\pi$
$642$	−3.30478	−	10.1711i	−0.130429	−	0.401420i
$643$	3.56429	+	10.9698i	0.140562	+	0.432605i	0.996414	−	0.0846161i	$-0.0269664\pi$
$643$	3.56429	+	10.9698i	0.140562	+	0.432605i	−0.855852	+	0.517221i	$0.826966\pi$
$644$	−5.81962	+	17.9109i	−0.229325	+	0.705790i
$645$	3.95456			0.155711
$646$	−15.0840			−0.593471
$647$	13.3022	−	40.9400i	0.522963	−	1.60952i	−0.245345	−	0.969436i	$-0.578901\pi$
$647$	13.3022	−	40.9400i	0.522963	−	1.60952i	0.768308	−	0.640080i	$-0.221099\pi$
$648$	−5.88588	−	4.27634i	−0.231219	−	0.167991i
$649$	−3.27659	+	2.38058i	−0.128617	+	0.0934459i
$650$	−33.9787			−1.33276
$651$		0			0
$652$	0.788169			0.0308671
$653$	38.6408	−	28.0742i	1.51213	−	1.09863i	0.546908	−	0.837192i	$-0.315805\pi$
$653$	38.6408	−	28.0742i	1.51213	−	1.09863i	0.965221	−	0.261434i	$-0.0841954\pi$
$654$	1.04143	+	0.756642i	0.0407231	+	0.0295871i
$655$	−4.28768	+	13.1961i	−0.167533	+	0.515615i
$656$	22.7501			0.888243
$657$	11.5639			0.451149
$658$	9.02609	−	27.7794i	0.351874	−	1.08296i
$659$	−7.06587	−	21.7465i	−0.275247	−	0.847124i	−0.989154	−	0.146883i	$-0.953076\pi$
$659$	−7.06587	−	21.7465i	−0.275247	−	0.847124i	0.713906	−	0.700241i	$-0.246924\pi$
$660$	−0.492279	−	1.51508i	−0.0191619	−	0.0589743i
$661$	16.1030	−	11.6995i	0.626333	−	0.455058i	−0.228795	−	0.973475i	$-0.573478\pi$
$661$	16.1030	−	11.6995i	0.626333	−	0.455058i	0.855128	+	0.518417i	$0.173478\pi$
$662$	18.8192	−	57.9195i	0.731429	−	2.25111i
$663$	−11.8703	+	8.62426i	−0.461003	+	0.334938i
$664$	9.04504	+	6.57161i	0.351016	+	0.255028i
$665$	−2.00349	−	6.16612i	−0.0776922	−	0.239112i
$666$	−18.5394	−	13.4697i	−0.718388	−	0.521940i
$667$	3.93610	+	2.85975i	0.152407	+	0.110730i
$668$	0.878747	+	2.70451i	0.0339998	+	0.104640i
$669$	−2.85203	−	2.07212i	−0.110266	−	0.0801127i
$670$	5.21026	−	3.78548i	0.201290	−	0.146246i
$671$	1.53800	−	4.73347i	0.0593738	−	0.182734i
$672$	−10.2330	+	7.43474i	−0.394748	+	0.286801i
$673$	5.38525	+	16.5741i	0.207586	+	0.638884i	0.999597	+	0.0283777i	$0.00903410\pi$
$673$	5.38525	+	16.5741i	0.207586	+	0.638884i	−0.792011	+	0.610507i	$0.790966\pi$
$674$	−2.25879	−	6.95184i	−0.0870054	−	0.267775i
$675$	3.14333	−	9.67419i	0.120987	−	0.372360i
$676$	19.7531			0.759734
$677$	31.8257			1.22316			0.611581	−	0.791182i	$-0.290534\pi$
$677$	31.8257			1.22316			0.611581	+	0.791182i	$0.290534\pi$
$678$	0.929475	−	2.86063i	0.0356963	−	0.109862i
$679$	25.0466	+	18.1974i	0.961199	+	0.698352i
$680$	5.90721	−	4.29184i	0.226531	−	0.164585i
$681$	−4.50408			−0.172597
$682$		0			0
$683$	19.9935			0.765031			0.382515	−	0.923949i	$-0.375058\pi$
$683$	19.9935			0.765031			0.382515	+	0.923949i	$0.375058\pi$
$684$	−4.55599	+	3.31012i	−0.174203	+	0.126566i
$685$	15.4211	+	11.2041i	0.589209	+	0.428086i
$686$	0.137442	−	0.423004i	0.00524757	−	0.0161504i
$687$	8.96533			0.342049
$688$	−31.6210			−1.20554
$689$	20.7684	−	63.9185i	0.791212	−	2.43510i
$690$	1.22184	+	3.76042i	0.0465145	+	0.143157i
$691$	−4.40644	−	13.5616i	−0.167629	−	0.515909i	0.831591	−	0.555388i	$-0.187430\pi$
$691$	−4.40644	−	13.5616i	−0.167629	−	0.515909i	−0.999220	+	0.0394789i	$0.987430\pi$
$692$	4.67209	−	3.39447i	0.177606	−	0.129039i
$693$	5.89084	−	18.1301i	0.223774	−	0.688707i
$694$	−20.4835	+	14.8822i	−0.777544	+	0.564919i
$695$	9.97141	+	7.24466i	0.378237	+	0.274805i
$696$	0.226013	+	0.695597i	0.00856701	+	0.0263665i
$697$	−21.6375	−	15.7206i	−0.819579	−	0.595459i
$698$	−5.54568	−	4.02917i	−0.209907	−	0.152506i
$699$	2.10590	+	6.48129i	0.0796525	+	0.245145i
$700$	15.2261	+	11.0624i	0.575492	+	0.418120i
$701$	37.6558	−	27.3585i	1.42224	−	1.03332i	0.430842	−	0.902427i	$-0.358217\pi$
$701$	37.6558	−	27.3585i	1.42224	−	1.03332i	0.991397	−	0.130890i	$-0.0417834\pi$
$702$	−8.51202	+	26.1973i	−0.321265	+	0.988753i
$703$	5.24019	−	3.80722i	0.197638	−	0.143592i
$704$	1.67099	+	5.14278i	0.0629778	+	0.193826i
$705$	−0.787885	−	2.42486i	−0.0296735	−	0.0913255i
$706$	8.85718	−	27.2596i	0.333344	−	1.02593i
$707$	5.96706			0.224414
$708$	−1.55046			−0.0582699
$709$	6.86831	−	21.1385i	0.257945	−	0.793873i	−0.735290	−	0.677752i	$-0.762954\pi$
$709$	6.86831	−	21.1385i	0.257945	−	0.793873i	0.993235	−	0.116120i	$-0.0370458\pi$
$710$	16.2681	+	11.8195i	0.610530	+	0.443576i
$711$	24.9941	−	18.1593i	0.937353	−	0.681027i
$712$	−2.88297			−0.108044
$713$		0			0
$714$	19.5471			0.731531
$715$	−9.40149	+	6.83058i	−0.351596	+	0.255449i
$716$	4.56417	+	3.31606i	0.170571	+	0.123927i
$717$	−1.52013	+	4.67849i	−0.0567704	+	0.174721i
$718$	9.93445			0.370750
$719$	44.0914			1.64433			0.822165	−	0.569249i	$-0.192766\pi$
$719$	44.0914			1.64433			0.822165	+	0.569249i	$0.192766\pi$
$720$	4.94741	−	15.2266i	0.184379	−	0.567460i
$721$	21.1194	+	64.9990i	0.786529	+	2.42069i
$722$	9.68008	+	29.7922i	0.360255	+	1.10875i
$723$	2.69451	−	1.95768i	0.100210	−	0.0728068i
$724$	2.81367	−	8.65957i	0.104569	−	0.321830i
$725$	3.93355	−	2.85789i	0.146089	−	0.106140i
$726$	−5.64583	−	4.10193i	−0.209536	−	0.152237i
$727$	12.0548	+	37.1009i	0.447089	+	1.37600i	0.880177	+	0.474646i	$0.157424\pi$
$727$	12.0548	+	37.1009i	0.447089	+	1.37600i	−0.433088	+	0.901352i	$0.642576\pi$
$728$	16.7079	+	12.1390i	0.619237	+	0.449902i
$729$	11.6919	+	8.49467i	0.433034	+	0.314618i
$730$	2.90207	+	8.93165i	0.107410	+	0.330575i
$731$	30.0746	+	21.8505i	1.11235	+	0.808168i
$732$	1.54145	−	1.11993i	0.0569735	−	0.0413936i
$733$	2.10474	−	6.47772i	0.0777403	−	0.239260i	−0.904632	−	0.426193i	$-0.859855\pi$
$733$	2.10474	−	6.47772i	0.0777403	−	0.239260i	0.982373	+	0.186933i	$0.0598546\pi$
$734$	−22.0350	+	16.0093i	−0.813325	+	0.590915i
$735$	1.29215	+	3.97683i	0.0476617	+	0.146688i
$736$	−7.43228	−	22.8742i	−0.273957	−	0.843154i
$737$	−1.65396	+	5.09036i	−0.0609243	+	0.187506i
$738$	−24.0168			−0.884070
$739$	−33.2004			−1.22130			−0.610649	−	0.791902i	$-0.709091\pi$
$739$	−33.2004			−1.22130			−0.610649	+	0.791902i	$0.709091\pi$
$740$	2.39105	−	7.35890i	0.0878968	−	0.270518i
$741$	−3.01284	−	2.18896i	−0.110680	−	0.0804134i
$742$	−72.4363	+	52.6281i	−2.65922	+	1.93204i
$743$	22.5011			0.825484			0.412742	−	0.910848i	$-0.364571\pi$
$743$	22.5011			0.825484			0.412742	+	0.910848i	$0.364571\pi$
$744$		0			0
$745$	4.61293			0.169005
$746$	35.6922	−	25.9319i	1.30678	−	0.949433i
$747$	−23.3156	−	16.9398i	−0.853074	−	0.619795i
$748$	4.62759	−	14.2422i	0.169201	−	0.520748i
$749$	43.2110			1.57890
$750$	9.52884			0.347944
$751$	1.98220	−	6.10058i	0.0723314	−	0.222613i	−0.908355	−	0.418200i	$-0.862661\pi$
$751$	1.98220	−	6.10058i	0.0723314	−	0.222613i	0.980686	+	0.195587i	$0.0626611\pi$
$752$	6.29999	+	19.3894i	0.229737	+	0.707058i
$753$	−4.52403	−	13.9235i	−0.164865	−	0.507401i
$754$	−10.6519	+	7.73906i	−0.387919	+	0.281840i
$755$	−3.30845	+	10.1824i	−0.120407	+	0.370574i
$756$	12.3433	−	8.96793i	0.448921	−	0.326161i
$757$	20.9324	+	15.2083i	0.760801	+	0.552754i	0.899156	−	0.437628i	$-0.144181\pi$
$757$	20.9324	+	15.2083i	0.760801	+	0.552754i	−0.138355	+	0.990383i	$0.544181\pi$
$758$	12.6511	+	38.9359i	0.459507	+	1.41422i
$759$	−2.65845	−	1.93147i	−0.0964955	−	0.0701081i
$760$	1.49933	+	1.08933i	0.0543866	+	0.0395142i
$761$	−13.8231	−	42.5432i	−0.501088	−	1.54219i	−0.807249	−	0.590211i	$-0.799045\pi$
$761$	−13.8231	−	42.5432i	−0.501088	−	1.54219i	0.306161	−	0.951980i	$-0.400955\pi$
$762$	7.16920	+	5.20873i	0.259713	+	0.188692i
$763$	−4.20788	+	3.05720i	−0.152336	+	0.110678i
$764$	5.11310	−	15.7365i	0.184985	−	0.569327i
$765$	−15.2272	+	11.0632i	−0.550539	+	0.399990i
$766$	13.6067	+	41.8772i	0.491631	+	1.51308i
$767$	3.49505	+	10.7567i	0.126199	+	0.388401i
$768$	3.23482	−	9.95575i	0.116726	−	0.359247i
$769$	12.6875			0.457524			0.228762	−	0.973482i	$-0.426532\pi$
$769$	12.6875			0.457524			0.228762	+	0.973482i	$0.426532\pi$
$770$	15.4817			0.557920
$771$	−3.69547	+	11.3735i	−0.133089	+	0.409606i
$772$	−15.5946	−	11.3302i	−0.561263	−	0.407781i
$773$	−7.44923	+	5.41219i	−0.267930	+	0.194663i	−0.713636	−	0.700517i	$-0.752953\pi$
$773$	−7.44923	+	5.41219i	−0.267930	+	0.194663i	0.445706	+	0.895180i	$0.352953\pi$
$774$	33.3816			1.19988
$775$		0			0
$776$	−8.84964			−0.317683
$777$	−6.79068	+	4.93372i	−0.243614	+	0.176996i
$778$	25.5279	+	18.5471i	0.915218	+	0.664945i
$779$	2.09772	−	6.45613i	0.0751587	−	0.231315i
$780$	−4.44873			−0.159290
$781$	−16.7116			−0.597989
$782$	−11.4857	+	35.3493i	−0.410727	+	1.26409i
$783$	−1.21801	−	3.74866i	−0.0435283	−	0.133966i
$784$	−10.3321	−	31.7990i	−0.369005	−	1.13568i
$785$	5.05688	−	3.67404i	0.180488	−	0.131132i
$786$	3.28106	−	10.0981i	0.117031	−	0.360186i
$787$	37.8259	−	27.4821i	1.34835	−	0.979631i	0.349254	−	0.937028i	$-0.386435\pi$
$787$	37.8259	−	27.4821i	1.34835	−	0.979631i	0.999092	−	0.0426032i	$-0.0135651\pi$
$788$	−26.9487	−	19.5794i	−0.960009	−	0.697487i
$789$	0.608631	+	1.87317i	0.0216678	+	0.0666867i
$790$	20.2983	+	14.7476i	0.722183	+	0.524697i
$791$	9.83211	+	7.14345i	0.349590	+	0.253992i
$792$	1.68388	+	5.18246i	0.0598342	+	0.184151i
$793$	−11.2445	−	8.16957i	−0.399302	−	0.290110i
$794$	−15.0007	+	10.8986i	−0.532354	+	0.386778i
$795$	−2.41515	+	7.43307i	−0.0856566	+	0.263624i
$796$	−7.59719	+	5.51968i	−0.269275	+	0.195640i
$797$	−0.111240	−	0.342360i	−0.00394031	−	0.0121270i	0.949067	−	0.315074i	$-0.102029\pi$
$797$	−0.111240	−	0.342360i	−0.00394031	−	0.0121270i	−0.953007	+	0.302947i	$0.902029\pi$
$798$	1.53313	+	4.71850i	0.0542723	+	0.167033i
$799$	7.40638	−	22.7945i	0.262019	−	0.806412i
$800$	−24.0358			−0.849793
$801$	7.43151			0.262580
$802$	16.3252	−	50.2439i	0.576464	−	1.77417i
$803$	−6.31427	−	4.58758i	−0.222826	−	0.161892i
$804$	−1.65766	+	1.20436i	−0.0584613	+	0.0424746i
$805$	−15.9759			−0.563075
$806$		0			0
$807$	6.36789			0.224160
$808$	−1.37992	+	1.00257i	−0.0485453	+	0.0352702i
$809$	23.2358	+	16.8818i	0.816929	+	0.593533i	0.915831	−	0.401564i	$-0.131533\pi$
$809$	23.2358	+	16.8818i	0.816929	+	0.593533i	−0.0989025	+	0.995097i	$0.531533\pi$
$810$	−4.70648	+	14.4850i	−0.165369	+	0.508953i
$811$	−19.9135			−0.699258			−0.349629	−	0.936888i	$-0.613692\pi$
$811$	−19.9135			−0.699258			−0.349629	+	0.936888i	$0.613692\pi$
$812$	7.29278			0.255926
$813$	−0.512709	+	1.57796i	−0.0179815	+	0.0553413i
$814$	4.77951	+	14.7098i	0.167522	+	0.515579i
$815$	0.206611	+	0.635884i	0.00723728	+	0.0222741i
$816$	−11.0377	+	8.01938i	−0.386398	+	0.280734i
$817$	−2.91568	+	8.97355i	−0.102007	+	0.313945i
$818$	−34.4428	+	25.0242i	−1.20427	+	0.874950i
$819$	−43.0685	−	31.2911i	−1.50493	−	1.09340i
$820$	−2.50591	−	7.71239i	−0.0875101	−	0.269328i
$821$	−37.2415	−	27.0575i	−1.29974	−	0.944315i	−0.299785	−	0.954007i	$-0.596915\pi$
$821$	−37.2415	−	27.0575i	−1.29974	−	0.944315i	−0.999953	+	0.00969217i	$0.996915\pi$
$822$	−11.8007	−	8.57369i	−0.411596	−	0.299042i
$823$	−4.08844	−	12.5829i	−0.142514	−	0.438613i	0.854169	−	0.519996i	$-0.174066\pi$
$823$	−4.08844	−	12.5829i	−0.142514	−	0.438613i	−0.996683	+	0.0813827i	$0.974066\pi$
$824$	−15.8049	−	11.4830i	−0.550591	−	0.400028i
$825$	−2.65672	+	1.93022i	−0.0924953	+	0.0672017i
$826$	4.65621	−	14.3303i	0.162010	−	0.498616i
$827$	−9.22900	+	6.70526i	−0.320924	+	0.233165i	−0.736570	−	0.676362i	$-0.763556\pi$
$827$	−9.22900	+	6.70526i	−0.320924	+	0.233165i	0.415646	+	0.909527i	$0.363556\pi$
$828$	4.28811	+	13.1975i	0.149022	+	0.458643i
$829$	13.3072	+	40.9553i	0.462177	+	1.42244i	0.862498	+	0.506061i	$0.168899\pi$
$829$	13.3072	+	40.9553i	0.462177	+	1.42244i	−0.400321	+	0.916375i	$0.631101\pi$
$830$	7.23261	−	22.2597i	0.251047	−	0.772644i
$831$	10.4948			0.364059
$832$	15.1008			0.523525
$833$	−12.1466	+	37.3835i	−0.420856	+	1.29526i
$834$	−7.63042	−	5.54382i	−0.264220	−	0.191967i
$835$	−1.95160	+	1.41792i	−0.0675380	+	0.0490692i
$836$	3.80091			0.131457
$837$		0			0
$838$	−62.0578			−2.14375
$839$	−35.0876	+	25.4926i	−1.21136	+	0.880102i	−0.995353	−	0.0962904i	$-0.969302\pi$
$839$	−35.0876	+	25.4926i	−1.21136	+	0.880102i	−0.216004	+	0.976393i	$0.569302\pi$
$840$	−1.94296	−	1.41165i	−0.0670386	−	0.0487064i
$841$	−8.37929	+	25.7888i	−0.288941	+	0.889269i
$842$	−16.7023			−0.575600
$843$	−4.67737			−0.161097
$844$	−8.51700	+	26.2126i	−0.293167	+	0.902276i
$845$	5.17809	+	15.9365i	0.178132	+	0.548233i
$846$	−6.65076	−	20.4689i	−0.228658	−	0.703737i
$847$	22.8119	−	16.5738i	0.783826	−	0.569483i
$848$	19.3117	−	59.4354i	0.663168	−	2.04102i
$849$	4.09365	−	2.97421i	0.140494	−	0.102075i
$850$	30.0504	+	21.8329i	1.03072	+	0.748862i
$851$	−4.93208	−	15.1794i	−0.169070	−	0.520343i
$852$	−5.17575	−	3.76040i	−0.177318	−	0.128829i
$853$	−5.46275	−	3.96892i	−0.187041	−	0.135893i	0.490324	−	0.871540i	$-0.336878\pi$
$853$	−5.46275	−	3.96892i	−0.187041	−	0.135893i	−0.677365	+	0.735647i	$0.736878\pi$
$854$	5.72192	+	17.6103i	0.195800	+	0.602611i
$855$	−3.86487	−	2.80799i	−0.132176	−	0.0960314i
$856$	−9.99279	+	7.26019i	−0.341547	+	0.248148i
$857$	−7.67788	+	23.6301i	−0.262271	+	0.807188i	0.730038	+	0.683406i	$0.239502\pi$
$857$	−7.67788	+	23.6301i	−0.262271	+	0.807188i	−0.992309	+	0.123782i	$0.960498\pi$
$858$	7.19430	−	5.22696i	0.245609	−	0.178446i
$859$	0.493769	+	1.51966i	0.0168472	+	0.0518502i	0.959127	−	0.282977i	$-0.0913220\pi$
$859$	0.493769	+	1.51966i	0.0168472	+	0.0518502i	−0.942280	+	0.334827i	$0.891322\pi$
$860$	3.48303	+	10.7197i	0.118770	+	0.365537i
$861$	−2.71841	+	8.36639i	−0.0926430	+	0.285126i
$862$	−20.9198			−0.712533
$863$	−30.7713			−1.04747			−0.523734	−	0.851882i	$-0.675461\pi$
$863$	−30.7713			−1.04747			−0.523734	+	0.851882i	$0.675461\pi$
$864$	−6.02120	+	18.5314i	−0.204845	+	0.630450i
$865$	3.96336	+	2.87955i	0.134758	+	0.0979076i
$866$	13.6278	−	9.90118i	0.463092	−	0.336456i
$867$	7.55038			0.256424
$868$		0			0
$869$	−20.8518			−0.707348
$870$	1.23871	−	0.899974i	0.0419961	−	0.0305120i
$871$	12.0922	+	8.78552i	0.409730	+	0.297686i
$872$	0.459434	−	1.41399i	0.0155584	−	0.0478838i
$873$	22.8119			0.772067
$874$	−9.43387			−0.319105
$875$	−11.8975	+	36.6168i	−0.402209	+	1.23787i
$876$	−0.923304	−	2.84164i	−0.0311955	−	0.0960100i
$877$	2.57438	+	7.92312i	0.0869306	+	0.267545i	0.985067	−	0.172173i	$-0.0550787\pi$
$877$	2.57438	+	7.92312i	0.0869306	+	0.267545i	−0.898136	+	0.439717i	$0.855079\pi$
$878$	−59.2831	+	43.0717i	−2.00071	+	1.45360i
$879$	−3.28217	+	10.1015i	−0.110705	+	0.340714i
$880$	−8.74210	+	6.35151i	−0.294696	+	0.214109i
$881$	−17.6878	−	12.8510i	−0.595919	−	0.432960i	0.248509	−	0.968630i	$-0.420059\pi$
$881$	−17.6878	−	12.8510i	−0.595919	−	0.432960i	−0.844428	+	0.535669i	$0.820059\pi$
$882$	10.9074	+	33.5695i	0.367271	+	1.13035i
$883$	10.0888	+	7.32993i	0.339515	+	0.246672i	0.744457	−	0.667670i	$-0.232708\pi$
$883$	10.0888	+	7.32993i	0.339515	+	0.246672i	−0.404942	+	0.914342i	$0.632708\pi$
$884$	−33.8327	−	24.5809i	−1.13792	−	0.826745i
$885$	−0.406439	−	1.25089i	−0.0136623	−	0.0420482i
$886$	37.8079	+	27.4690i	1.27018	+	0.922840i
$887$	20.0166	−	14.5429i	0.672093	−	0.488304i	−0.198632	−	0.980074i	$-0.563650\pi$
$887$	20.0166	−	14.5429i	0.672093	−	0.488304i	0.870725	+	0.491770i	$0.163650\pi$
$888$	0.741435	−	2.28190i	0.0248809	−	0.0765756i
$889$	−28.9670	+	21.0458i	−0.971524	+	0.705853i
$890$	1.86502	+	5.73993i	0.0625155	+	0.192403i
$891$	−3.91143	−	12.0381i	−0.131038	−	0.403293i
$892$	3.10495	−	9.55605i	0.103961	−	0.319960i
$893$	6.08331			0.203570
$894$	−3.52995			−0.118059
$895$	−1.47890	+	4.55158i	−0.0494341	+	0.152143i
$896$	24.7096	+	17.9525i	0.825489	+	0.599753i
$897$	−7.42395	+	5.39382i	−0.247879	+	0.180094i
$898$	−3.38940			−0.113106
$899$		0			0
$900$	13.8676			0.462255
$901$	−59.4378	+	43.1841i	−1.98016	+	1.43867i
$902$	13.1140	+	9.52788i	0.436648	+	0.317244i
$903$	3.77839	−	11.6287i	0.125737	−	0.386978i
$904$	−3.47395			−0.115542
$905$	7.72400			0.256754
$906$	2.53173	−	7.79185i	0.0841109	−	0.258867i
$907$	−9.71592	−	29.9025i	−0.322612	−	0.992897i	−0.972507	−	0.232873i	$-0.925187\pi$
$907$	−9.71592	−	29.9025i	−0.322612	−	0.992897i	0.649895	−	0.760024i	$-0.274813\pi$
$908$	−3.96702	−	12.2092i	−0.131650	−	0.405178i
$909$	3.55705	−	2.58434i	0.117980	−	0.0857173i
$910$	13.3600	−	41.1179i	0.442880	−	1.36305i
$911$	−6.78267	+	4.92790i	−0.224720	+	0.163269i	−0.694449	−	0.719542i	$-0.744352\pi$
$911$	−6.78267	+	4.92790i	−0.224720	+	0.163269i	0.469729	+	0.882811i	$0.344352\pi$
$912$	−2.80153	−	2.03543i	−0.0927680	−	0.0673999i
$913$	6.01083	+	18.4994i	0.198929	+	0.612242i
$914$	53.8182	+	39.1012i	1.78015	+	1.29335i
$915$	1.30762	+	0.950039i	0.0432285	+	0.0314073i
$916$	7.89632	+	24.3024i	0.260902	+	0.802973i
$917$	34.7075	+	25.2165i	1.14614	+	0.832721i
$918$	24.3609	−	17.6992i	0.804029	−	0.584161i
$919$	−12.4033	+	38.1735i	−0.409148	+	1.25923i	0.508234	+	0.861219i	$0.330298\pi$
$919$	−12.4033	+	38.1735i	−0.409148	+	1.25923i	−0.917382	+	0.398008i	$0.869702\pi$
$920$	3.69451	−	2.68422i	0.121804	−	0.0884961i
$921$	2.50617	+	7.71319i	0.0825810	+	0.254158i
$922$	0.764269	+	2.35218i	0.0251699	+	0.0774649i
$923$	−14.4214	+	44.3846i	−0.474687	+	1.46094i
$924$	−4.92554			−0.162039
$925$	−15.9502			−0.524440
$926$	6.72750	−	20.7051i	0.221079	−	0.680412i
$927$	40.7408	+	29.5999i	1.33810	+	0.972189i
$928$	−7.53491	+	5.47443i	−0.247345	+	0.179707i
$929$	54.6187			1.79198			0.895991	−	0.444072i	$-0.146467\pi$
$929$	54.6187			1.79198			0.895991	+	0.444072i	$0.146467\pi$
$930$		0			0
$931$	−9.97677			−0.326975
$932$	−15.7141	+	11.4170i	−0.514732	+	0.373975i
$933$	4.19572	+	3.04837i	0.137362	+	0.0997991i
$934$	−6.28854	+	19.3541i	−0.205767	+	0.633286i
$935$	12.7035			0.415450
$936$	15.2173			0.497392
$937$	−4.13770	+	12.7345i	−0.135173	+	0.416019i	−0.995617	−	0.0935259i	$-0.970186\pi$
$937$	−4.13770	+	12.7345i	−0.135173	+	0.416019i	0.860444	+	0.509545i	$0.170186\pi$
$938$	−6.15333	−	18.9380i	−0.200913	−	0.618347i
$939$	4.94463	+	15.2180i	0.161362	+	0.496621i
$940$	5.87915	−	4.27145i	0.191757	−	0.139319i
$941$	−11.8513	+	36.4746i	−0.386342	+	1.18904i	0.549160	+	0.835717i	$0.314948\pi$
$941$	−11.8513	+	36.4746i	−0.386342	+	1.18904i	−0.935502	+	0.353321i	$0.885052\pi$
$942$	−3.86967	+	2.81148i	−0.126081	+	0.0916030i
$943$	−13.5326	−	9.83203i	−0.440683	−	0.320175i
$944$	3.24992	+	10.0022i	0.105776	+	0.325545i
$945$	10.4709	+	7.60754i	0.340618	+	0.247473i
$946$	−18.2275	−	13.2431i	−0.592627	−	0.430569i
$947$	13.4384	+	41.3591i	0.436689	+	1.34399i	0.891346	+	0.453323i	$0.149762\pi$
$947$	13.4384	+	41.3591i	0.436689	+	1.34399i	−0.454658	+	0.890666i	$0.650238\pi$
$948$	−6.45799	−	4.69200i	−0.209746	−	0.152389i
$949$	−17.6332	+	12.8112i	−0.572397	+	0.415870i
$950$	−2.91334	+	8.96633i	−0.0945211	+	0.290906i
$951$	−10.2268	+	7.43020i	−0.331626	+	0.240941i
$952$	−6.97642	−	21.4712i	−0.226107	−	0.695886i
$953$	−12.4271	−	38.2466i	−0.402552	−	1.23893i	−0.922922	−	0.384988i	$-0.874206\pi$
$953$	−12.4271	−	38.2466i	−0.402552	−	1.23893i	0.520369	−	0.853941i	$-0.325794\pi$
$954$	−20.3870	+	62.7447i	−0.660053	+	2.03143i
$955$	14.0363			0.454205
$956$	−14.0209			−0.453468
$957$	−0.393218	+	1.21020i	−0.0127109	+	0.0391202i
$958$	−1.00552	−	0.730550i	−0.0324867	−	0.0236030i
$959$	47.6805	−	34.6419i	1.53968	−	1.11864i
$960$	−1.75607			−0.0566768
$961$		0			0
$962$	43.1925			1.39258
$963$	25.7587	−	18.7148i	0.830062	−	0.603075i
$964$	7.67992	+	5.57979i	0.247354	+	0.179713i
$965$	5.05303	−	15.5516i	0.162663	−	0.500624i
$966$	12.2252			0.393339
$967$	43.8720			1.41083			0.705414	−	0.708795i	$-0.250761\pi$
$967$	43.8720			1.41083			0.705414	+	0.708795i	$0.250761\pi$
$968$	−2.49070	+	7.66558i	−0.0800541	+	0.246381i
$969$	1.25802	+	3.87178i	0.0404133	+	0.124379i
$970$	5.72489	+	17.6194i	0.183815	+	0.565725i
$971$	−41.6793	+	30.2818i	−1.33755	+	0.971788i	−0.338022	+	0.941138i	$0.609758\pi$
$971$	−41.6793	+	30.2818i	−1.33755	+	0.971788i	−0.999530	+	0.0306500i	$0.990242\pi$
$972$	5.28629	−	16.2695i	0.169558	−	0.521845i
$973$	30.8306	−	22.3998i	0.988384	−	0.718103i
$974$	−36.7858	−	26.7264i	−1.17869	−	0.856371i
$975$	2.83386	+	8.72172i	0.0907561	+	0.279319i
$976$	−10.4558	−	7.59659i	−0.334682	−	0.243161i
$977$	−11.6299	−	8.44962i	−0.372073	−	0.270327i	0.385997	−	0.922500i	$-0.373858\pi$
$977$	−11.6299	−	8.44962i	−0.372073	−	0.270327i	−0.758070	+	0.652173i	$0.773858\pi$
$978$	−0.158105	−	0.486597i	−0.00505564	−	0.0155597i
$979$	−4.05786	−	2.94821i	−0.129690	−	0.0942252i
$980$	−9.64194	+	7.00528i	−0.308001	+	0.223775i
$981$	−1.18429	+	3.64488i	−0.0378116	+	0.116372i
$982$	12.9242	−	9.38999i	0.412428	−	0.299647i
$983$	−16.5862	−	51.0471i	−0.529018	−	1.62815i	−0.756230	−	0.654306i	$-0.772961\pi$
$983$	−16.5862	−	51.0471i	−0.529018	−	1.62815i	0.227212	−	0.973845i	$-0.427039\pi$
$984$	−0.777051	−	2.39152i	−0.0247715	−	0.0762387i
$985$	8.73203	−	26.8744i	0.278226	−	0.856291i
$986$	14.3931			0.458370
$987$	−7.88326			−0.250927
$988$	3.28003	−	10.0949i	0.104352	−	0.321161i
$989$	18.8094	+	13.6658i	0.598103	+	0.434547i
$990$	9.22883	−	6.70514i	0.293312	−	0.213103i
$991$	−35.5382			−1.12891			−0.564453	−	0.825465i	$-0.690913\pi$
$991$	−35.5382			−1.12891			−0.564453	+	0.825465i	$0.690913\pi$
$992$		0			0
$993$	−16.4364			−0.521594
$994$	50.2993	−	36.5446i	1.59540	−	1.15912i
$995$	−6.44473	−	4.68237i	−0.204312	−	0.148441i
$996$	−2.30108	+	7.08199i	−0.0729125	+	0.224401i
$997$	−30.5225			−0.966658			−0.483329	−	0.875439i	$-0.660573\pi$
$997$	−30.5225			−0.966658			−0.483329	+	0.875439i	$0.660573\pi$
$998$	−57.5347			−1.82123
$999$	−3.99569	+	12.2975i	−0.126418	+	0.389075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.p.388.3		16
31.2	even	5	inner	961.2.d.p.374.3		16
31.3	odd	30		961.2.g.j.547.1		16
31.4	even	5		961.2.d.o.628.2		16
31.5	even	3		961.2.g.s.338.2		16
31.6	odd	6		961.2.g.n.235.2		16
31.7	even	15		31.2.g.a.9.1	yes	16
31.8	even	5		961.2.a.i.1.2		8
31.9	even	15		961.2.c.j.521.2		16
31.10	even	15		961.2.g.t.732.2		16
31.11	odd	30		961.2.g.j.448.1		16
31.12	odd	30		961.2.g.m.816.2		16
31.13	odd	30		961.2.g.l.844.1		16
31.14	even	15		961.2.c.j.439.2		16
31.15	odd	10		961.2.d.n.531.2		16
31.16	even	5		961.2.d.o.531.2		16
31.17	odd	30		961.2.c.i.439.2		16
31.18	even	15		31.2.g.a.7.1	✓	16
31.19	even	15		961.2.g.s.816.2		16
31.20	even	15		961.2.g.k.448.1		16
31.21	odd	30		961.2.g.n.732.2		16
31.22	odd	30		961.2.c.i.521.2		16
31.23	odd	10		961.2.a.j.1.2		8
31.24	odd	30		961.2.g.l.846.1		16
31.25	even	3		961.2.g.t.235.2		16
31.26	odd	6		961.2.g.m.338.2		16
31.27	odd	10		961.2.d.n.628.2		16
31.28	even	15		961.2.g.k.547.1		16
31.29	odd	10		961.2.d.q.374.3		16
31.30	odd	2		961.2.d.q.388.3		16
93.8	odd	10		8649.2.a.bf.1.7		8
93.23	even	10		8649.2.a.be.1.7		8
93.38	odd	30		279.2.y.c.226.2		16
93.80	odd	30		279.2.y.c.100.2		16
124.7	odd	30		496.2.bg.c.257.1		16
124.111	odd	30		496.2.bg.c.193.1		16
155.7	odd	60		775.2.ck.a.474.1		32
155.18	odd	60		775.2.ck.a.224.1		32
155.38	odd	60		775.2.ck.a.474.4		32
155.49	even	30		775.2.bl.a.751.2		16
155.69	even	30		775.2.bl.a.226.2		16
155.142	odd	60		775.2.ck.a.224.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.1	✓	16	31.18	even	15
31.2.g.a.9.1	yes	16	31.7	even	15
279.2.y.c.100.2		16	93.80	odd	30
279.2.y.c.226.2		16	93.38	odd	30
496.2.bg.c.193.1		16	124.111	odd	30
496.2.bg.c.257.1		16	124.7	odd	30
775.2.bl.a.226.2		16	155.69	even	30
775.2.bl.a.751.2		16	155.49	even	30
775.2.ck.a.224.1		32	155.18	odd	60
775.2.ck.a.224.4		32	155.142	odd	60
775.2.ck.a.474.1		32	155.7	odd	60
775.2.ck.a.474.4		32	155.38	odd	60
961.2.a.i.1.2		8	31.8	even	5
961.2.a.j.1.2		8	31.23	odd	10
961.2.c.i.439.2		16	31.17	odd	30
961.2.c.i.521.2		16	31.22	odd	30
961.2.c.j.439.2		16	31.14	even	15
961.2.c.j.521.2		16	31.9	even	15
961.2.d.n.531.2		16	31.15	odd	10
961.2.d.n.628.2		16	31.27	odd	10
961.2.d.o.531.2		16	31.16	even	5
961.2.d.o.628.2		16	31.4	even	5
961.2.d.p.374.3		16	31.2	even	5	inner
961.2.d.p.388.3		16	1.1	even	1	trivial
961.2.d.q.374.3		16	31.29	odd	10
961.2.d.q.388.3		16	31.30	odd	2
961.2.g.j.448.1		16	31.11	odd	30
961.2.g.j.547.1		16	31.3	odd	30
961.2.g.k.448.1		16	31.20	even	15
961.2.g.k.547.1		16	31.28	even	15
961.2.g.l.844.1		16	31.13	odd	30
961.2.g.l.846.1		16	31.24	odd	30
961.2.g.m.338.2		16	31.26	odd	6
961.2.g.m.816.2		16	31.12	odd	30
961.2.g.n.235.2		16	31.6	odd	6
961.2.g.n.732.2		16	31.21	odd	30
961.2.g.s.338.2		16	31.5	even	3
961.2.g.s.816.2		16	31.19	even	15
961.2.g.t.235.2		16	31.25	even	3
961.2.g.t.732.2		16	31.10	even	15
8649.2.a.be.1.7		8	93.23	even	10
8649.2.a.bf.1.7		8	93.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.49685 - 1.08752i) q^{2} +(-0.403986 - 0.293513i) q^{3} +(0.439812 - 1.35360i) q^{4} +1.20736 q^{5} -0.923909 q^{6} +(1.15357 - 3.55033i) q^{7} +(0.329747 + 1.01486i) q^{8} +(-0.849996 - 2.61602i) q^{9} +(1.80724 - 1.31303i) q^{10} +(-0.573693 + 1.76565i) q^{11} +(-0.574979 + 0.417746i) q^{12} +(4.19432 + 3.04736i) q^{13} +(-2.13435 - 6.56885i) q^{14} +(-0.487757 - 0.354376i) q^{15} +(3.90015 + 2.83362i) q^{16} +(-1.75135 - 5.39009i) q^{17} +(-4.11730 - 2.99139i) q^{18} +(1.16376 - 0.845521i) q^{19} +(0.531013 - 1.63429i) q^{20} +(-1.50810 + 1.09570i) q^{21} +(1.06145 + 3.26681i) q^{22} +(-1.09533 - 3.37109i) q^{23} +(0.164660 - 0.506773i) q^{24} -3.54228 q^{25} +9.59234 q^{26} +(-0.887376 + 2.73106i) q^{27} +(-4.29839 - 3.12296i) q^{28} +(-1.11046 + 0.806795i) q^{29} -1.11549 q^{30} +6.78540 q^{32} +(0.750004 - 0.544910i) q^{33} +(-8.48335 - 6.16352i) q^{34} +(1.39278 - 4.28654i) q^{35} -3.91489 q^{36} +4.50281 q^{37} +(0.822447 - 2.53123i) q^{38} +(-0.800011 - 2.46218i) q^{39} +(0.398123 + 1.22530i) q^{40} +(3.81784 - 2.77382i) q^{41} +(-1.06580 + 3.28018i) q^{42} +(-5.30652 + 3.85541i) q^{43} +(2.13767 + 1.55311i) q^{44} +(-1.02625 - 3.15848i) q^{45} +(-5.30569 - 3.85481i) q^{46} +(3.42131 + 2.48572i) q^{47} +(-0.743900 - 2.28949i) q^{48} +(-5.61102 - 4.07665i) q^{49} +(-5.30225 + 3.85231i) q^{50} +(-0.874543 + 2.69157i) q^{51} +(5.96963 - 4.33719i) q^{52} +(-4.00588 - 12.3288i) q^{53} +(1.64183 + 5.05303i) q^{54} +(-0.692655 + 2.13177i) q^{55} +3.98346 q^{56} -0.718314 q^{57} +(-0.784779 + 2.41530i) q^{58} +(1.76492 + 1.28229i) q^{59} +(-0.694207 + 0.504371i) q^{60} -2.68087 q^{61} -10.2683 q^{63} +(2.35642 - 1.71204i) q^{64} +(5.06407 + 3.67926i) q^{65} +(0.530040 - 1.63130i) q^{66} +2.88300 q^{67} -8.06631 q^{68} +(-0.546960 + 1.68337i) q^{69} +(-2.57693 - 7.93098i) q^{70} +(2.78166 + 8.56106i) q^{71} +(2.37460 - 1.72525i) q^{72} +(-1.29912 + 3.99829i) q^{73} +(6.74003 - 4.89692i) q^{74} +(1.43103 + 1.03971i) q^{75} +(-0.632664 - 1.94714i) q^{76} +(5.60683 + 4.07360i) q^{77} +(-3.87517 - 2.81548i) q^{78} +(3.47079 + 10.6820i) q^{79} +(4.70889 + 3.42121i) q^{80} +(-5.51587 + 4.00751i) q^{81} +(2.69813 - 8.30399i) q^{82} +(8.47642 - 6.15848i) q^{83} +(0.819859 + 2.52327i) q^{84} +(-2.11451 - 6.50779i) q^{85} +(-3.75020 + 11.5419i) q^{86} +0.685415 q^{87} -1.98105 q^{88} +(-0.834882 + 2.56950i) q^{89} +(-4.97107 - 3.61169i) q^{90} +(15.6576 - 11.3759i) q^{91} -5.04486 q^{92} +7.82446 q^{94} +(1.40508 - 1.02085i) q^{95} +(-2.74121 - 1.99160i) q^{96} +(-2.56277 + 7.88740i) q^{97} -12.8323 q^{98} +5.10660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

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