LMFDB - Embedded newform 845.2.n.g.484.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,10,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.1
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.g.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.31673 + 1.33757i) q^{2} +(0.416726 - 0.240597i) q^{3} +(2.57816 - 4.46551i) q^{4} +(-1.67513 + 1.48119i) q^{5} +(-0.643629 + 1.11480i) q^{6} +(0.698071 + 0.403032i) q^{7} +8.44358i q^{8} +(-1.38423 + 2.39755i) q^{9} +(1.89963 - 5.67213i) q^{10} +(-1.83757 - 3.18276i) q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.341700 + 1.02028i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(1.16936 + 0.675131i) q^{17} -7.40597i q^{18} +(0.837565 - 1.45071i) q^{19} +(2.29553 + 11.2991i) q^{20} +0.387873 q^{21} +(8.51429 + 4.91573i) q^{22} +(-5.61288 + 3.24060i) q^{23} +(2.03150 + 3.51866i) q^{24} +(0.612127 - 4.96239i) q^{25} +2.77575i q^{27} +(3.59948 - 2.07816i) q^{28} +(1.20910 + 2.09421i) q^{29} +(-0.573070 - 2.82077i) q^{30} +5.28726 q^{31} +(13.8133 + 7.97508i) q^{32} +(-1.53152 - 0.884226i) q^{33} -3.61213 q^{34} +(-1.76633 + 0.358849i) q^{35} +(7.13752 + 12.3625i) q^{36} +(-3.26358 + 1.88423i) q^{37} +4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +(-4.15633 - 7.19897i) q^{41} +(-0.898598 + 0.518806i) q^{42} +(-5.88364 - 3.39692i) q^{43} -18.9502 q^{44} +(-1.23248 - 6.06652i) q^{45} +(8.66902 - 15.0152i) q^{46} -3.19394i q^{47} +(-5.11533 - 2.95334i) q^{48} +(-3.17513 - 5.49949i) q^{49} +(5.21939 + 12.3153i) q^{50} +0.649738 q^{51} -5.73813i q^{53} +(-3.71274 - 6.43066i) q^{54} +(7.79244 + 2.60974i) q^{55} +(-3.40303 + 5.89422i) q^{56} -0.806063i q^{57} +(-5.60230 - 3.23449i) q^{58} +(-2.99389 + 5.18557i) q^{59} +(3.67513 + 4.15633i) q^{60} +(0.884226 - 1.53152i) q^{61} +(-12.2492 + 7.07205i) q^{62} +(-1.93258 + 1.11577i) q^{63} -18.1187 q^{64} +4.73084 q^{66} +(-8.56885 + 4.94723i) q^{67} +(6.02961 - 3.48119i) q^{68} +(-1.55936 + 2.70089i) q^{69} +(3.61213 - 3.19394i) q^{70} +(4.28115 - 7.41517i) q^{71} +(-20.2439 - 11.6878i) q^{72} -11.7685i q^{73} +(5.04055 - 8.73049i) q^{74} +(-0.938847 - 2.21523i) q^{75} +(-4.31876 - 7.48031i) q^{76} -2.96239i q^{77} +2.26187 q^{79} +(26.0270 + 8.71661i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(19.2582 + 11.1187i) q^{82} +3.84367i q^{83} +(1.00000 - 1.73205i) q^{84} +(-2.95883 + 0.601118i) q^{85} +18.1744 q^{86} +(1.00772 + 0.581810i) q^{87} +(26.8739 - 15.5156i) q^{88} +(-1.38787 - 2.40387i) q^{89} +(10.9697 + 12.4060i) q^{90} +33.4191i q^{92} +(2.20334 - 1.27210i) q^{93} +(4.27210 + 7.39949i) q^{94} +(0.745746 + 3.67072i) q^{95} +7.67513 q^{96} +(-1.62292 - 0.936996i) q^{97} +(14.7119 + 8.49389i) q^{98} +10.1744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} + 4 q^{6} + 6 q^{9} - 2 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{15} - 10 q^{16} - 20 q^{20} + 8 q^{21} + 16 q^{24} + 4 q^{25} + 12 q^{29} - 8 q^{30} + 40 q^{31} - 40 q^{34} - 8 q^{35} + 22 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 + 4 * q^6 + 6 * q^9 - 2 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^15 - 10 * q^16 - 20 * q^20 + 8 * q^21 + 16 * q^24 + 4 * q^25 + 12 * q^29 - 8 * q^30 + 40 * q^31 - 40 * q^34 - 8 * q^35 + 22 * q^36 - 68 * q^40 - 8 * q^41 - 80 * q^44 - 4 * q^45 + 32 * q^46 - 18 * q^49 + 16 * q^50 + 48 * q^51 - 68 * q^54 + 16 * q^55 - 40 * q^56 + 16 * q^59 + 24 * q^60 - 12 * q^61 - 132 * q^64 - 32 * q^66 + 24 * q^69 + 40 * q^70 - 24 * q^71 - 4 * q^74 - 16 * q^75 - 20 * q^76 + 64 * q^79 + 48 * q^80 - 46 * q^81 + 12 * q^84 - 12 * q^85 + 64 * q^86 - 20 * q^89 + 140 * q^90 + 32 * q^94 - 16 * q^95 + 72 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.31673	+	1.33757i	−1.63818	+	0.945802i	−0.656716	+	0.754138i	$0.728055\pi$
$2$	−2.31673	+	1.33757i	−1.63818	+	0.945802i	−0.981461	+	0.191663i	$0.938612\pi$
$3$	0.416726	−	0.240597i	0.240597	−	0.138909i	−0.374854	−	0.927084i	$-0.622307\pi$
$3$	0.416726	−	0.240597i	0.240597	−	0.138909i	0.615451	+	0.788175i	$0.288974\pi$
$4$	2.57816	−	4.46551i	1.28908	−	2.23275i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$	−0.643629	+	1.11480i	−0.262760	+	0.455114i
$7$	0.698071	+	0.403032i	0.263846	+	0.152332i	0.626088	−	0.779753i	$-0.284655\pi$
$7$	0.698071	+	0.403032i	0.263846	+	0.152332i	−0.362242	+	0.932084i	$0.617988\pi$
$8$			8.44358i			2.98526i
$9$	−1.38423	+	2.39755i	−0.461409	+	0.799183i
$10$	1.89963	−	5.67213i	0.600717	−	1.79368i
$11$	−1.83757	−	3.18276i	−0.554047	−	0.959637i	−0.997977	−	0.0635759i	$-0.979750\pi$
$11$	−1.83757	−	3.18276i	−0.554047	−	0.959637i	0.443930	−	0.896061i	$-0.353584\pi$
$12$		−	2.48119i		−	0.716259i
$13$		0			0
$13$		0			0
$14$	−2.15633			−0.576302
$15$	−0.341700	+	1.02028i	−0.0882266	+	0.263436i
$16$	−6.13752	−	10.6305i	−1.53438	−	2.65762i
$17$	1.16936	+	0.675131i	0.283612	+	0.163743i	0.635057	−	0.772465i	$-0.280976\pi$
$17$	1.16936	+	0.675131i	0.283612	+	0.163743i	−0.351446	+	0.936208i	$0.614310\pi$
$18$		−	7.40597i		−	1.74560i
$19$	0.837565	−	1.45071i	0.192151	−	0.332815i	−0.753812	−	0.657090i	$-0.771787\pi$
$19$	0.837565	−	1.45071i	0.192151	−	0.332815i	0.945963	+	0.324275i	$0.105120\pi$
$20$	2.29553	+	11.2991i	0.513295	+	2.52655i
$21$	0.387873			0.0846409
$22$	8.51429	+	4.91573i	1.81525	+	1.04804i
$23$	−5.61288	+	3.24060i	−1.17037	+	0.675711i	−0.953766	−	0.300549i	$-0.902830\pi$
$23$	−5.61288	+	3.24060i	−1.17037	+	0.675711i	−0.216600	+	0.976260i	$0.569497\pi$
$24$	2.03150	+	3.51866i	0.414679	+	0.718244i
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$		0			0
$27$			2.77575i			0.534193i
$28$	3.59948	−	2.07816i	0.680238	−	0.392736i
$29$	1.20910	+	2.09421i	0.224523	+	0.388886i	0.956176	−	0.292791i	$-0.0945842\pi$
$29$	1.20910	+	2.09421i	0.224523	+	0.388886i	−0.731653	+	0.681677i	$0.761251\pi$
$30$	−0.573070	−	2.82077i	−0.104628	−	0.515000i
$31$	5.28726			0.949620			0.474810	−	0.880088i	$-0.342517\pi$
$31$	5.28726			0.949620			0.474810	+	0.880088i	$0.342517\pi$
$32$	13.8133	+	7.97508i	2.44186	+	1.40981i
$33$	−1.53152	−	0.884226i	−0.266604	−	0.153924i
$34$	−3.61213			−0.619475
$35$	−1.76633	+	0.358849i	−0.298564	+	0.0606565i
$36$	7.13752	+	12.3625i	1.18959	+	2.06042i
$37$	−3.26358	+	1.88423i	−0.536528	+	0.309765i	−0.743671	−	0.668546i	$-0.766917\pi$
$37$	−3.26358	+	1.88423i	−0.536528	+	0.309765i	0.207142	+	0.978311i	$0.433584\pi$
$38$			4.48119i			0.726946i
$39$		0			0
$40$	−12.5066	−	14.1441i	−1.97747	−	2.23638i
$41$	−4.15633	−	7.19897i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$41$	−4.15633	−	7.19897i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$42$	−0.898598	+	0.518806i	−0.138657	+	0.0800535i
$43$	−5.88364	−	3.39692i	−0.897247	−	0.518026i	−0.0209410	−	0.999781i	$-0.506666\pi$
$43$	−5.88364	−	3.39692i	−0.897247	−	0.518026i	−0.876306	+	0.481755i	$0.840000\pi$
$44$	−18.9502			−2.85685
$45$	−1.23248	−	6.06652i	−0.183727	−	0.904343i
$46$	8.66902	−	15.0152i	1.27818	−	2.21387i
$47$		−	3.19394i		−	0.465884i	−0.972491	−	0.232942i	$-0.925165\pi$
$47$		−	3.19394i		−	0.465884i	0.972491	−	0.232942i	$-0.0748352\pi$
$48$	−5.11533	−	2.95334i	−0.738335	−	0.426278i
$49$	−3.17513	−	5.49949i	−0.453590	−	0.785641i
$50$	5.21939	+	12.3153i	0.738133	+	1.74164i
$51$	0.649738			0.0909816
$52$		0			0
$53$		−	5.73813i		−	0.788193i	−0.919069	−	0.394097i	$-0.871057\pi$
$53$		−	5.73813i		−	0.788193i	0.919069	−	0.394097i	$-0.128943\pi$
$54$	−3.71274	−	6.43066i	−0.505240	−	0.875102i
$55$	7.79244	+	2.60974i	1.05073	+	0.351898i
$56$	−3.40303	+	5.89422i	−0.454749	+	0.787649i
$57$		−	0.806063i		−	0.106766i
$58$	−5.60230	−	3.23449i	−0.735618	−	0.424709i
$59$	−2.99389	+	5.18557i	−0.389771	+	0.675104i	−0.992419	−	0.122904i	$-0.960779\pi$
$59$	−2.99389	+	5.18557i	−0.389771	+	0.675104i	0.602647	+	0.798008i	$0.294113\pi$
$60$	3.67513	+	4.15633i	0.474457	+	0.536579i
$61$	0.884226	−	1.53152i	0.113214	−	0.196092i	−0.803851	−	0.594831i	$-0.797219\pi$
$61$	0.884226	−	1.53152i	0.113214	−	0.196092i	0.917064	+	0.398740i	$0.130552\pi$
$62$	−12.2492	+	7.07205i	−1.55564	+	0.898152i
$63$	−1.93258	+	1.11577i	−0.243482	+	0.140574i
$64$	−18.1187			−2.26484
$65$		0			0
$66$	4.73084			0.582326
$67$	−8.56885	+	4.94723i	−1.04685	+	0.604400i	−0.921766	−	0.387746i	$-0.873254\pi$
$67$	−8.56885	+	4.94723i	−1.04685	+	0.604400i	−0.125086	+	0.992146i	$0.539921\pi$
$68$	6.02961	−	3.48119i	0.731197	−	0.422157i
$69$	−1.55936	+	2.70089i	−0.187725	+	0.325148i
$70$	3.61213	−	3.19394i	0.431732	−	0.381748i
$71$	4.28115	−	7.41517i	0.508079	−	0.880018i	−0.491877	−	0.870664i	$-0.663689\pi$
$71$	4.28115	−	7.41517i	0.508079	−	0.880018i	0.999956	−	0.00935389i	$-0.00297748\pi$
$72$	−20.2439	−	11.6878i	−2.38577	−	1.37742i
$73$		−	11.7685i		−	1.37739i	−0.725050	−	0.688697i	$-0.758183\pi$
$73$		−	11.7685i		−	1.37739i	0.725050	−	0.688697i	$-0.241817\pi$
$74$	5.04055	−	8.73049i	0.585952	−	1.01490i
$75$	−0.938847	−	2.21523i	−0.108409	−	0.255793i
$76$	−4.31876	−	7.48031i	−0.495396	−	0.858051i
$77$		−	2.96239i		−	0.337596i
$78$		0			0
$79$	2.26187			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$79$	2.26187			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$80$	26.0270	+	8.71661i	2.90990	+	0.974547i
$81$	−3.48484	−	6.03592i	−0.387205	−	0.670658i
$82$	19.2582	+	11.1187i	2.12671	+	1.22786i
$83$			3.84367i			0.421898i	0.977497	+	0.210949i	$0.0676554\pi$
$83$			3.84367i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$	−2.95883	+	0.601118i	−0.320930	+	0.0652004i
$86$	18.1744			1.95980
$87$	1.00772	+	0.581810i	0.108039	+	0.0623765i
$88$	26.8739	−	15.5156i	2.86476	−	1.65397i
$89$	−1.38787	−	2.40387i	−0.147114	−	0.254809i	0.783045	−	0.621964i	$-0.213665\pi$
$89$	−1.38787	−	2.40387i	−0.147114	−	0.254809i	−0.930160	+	0.367155i	$0.880332\pi$
$90$	10.9697	+	12.4060i	1.15631	+	1.30770i
$91$		0			0
$92$			33.4191i			3.48419i
$93$	2.20334	−	1.27210i	0.228476	−	0.131911i
$94$	4.27210	+	7.39949i	0.440633	+	0.763199i
$95$	0.745746	+	3.67072i	0.0765119	+	0.376608i
$96$	7.67513			0.783340
$97$	−1.62292	−	0.936996i	−0.164783	−	0.0951375i	0.415341	−	0.909666i	$-0.363662\pi$
$97$	−1.62292	−	0.936996i	−0.164783	−	0.0951375i	−0.580124	+	0.814528i	$0.696996\pi$
$98$	14.7119	+	8.49389i	1.48612	+	0.858013i
$99$	10.1744			1.02257
$100$	−20.5814	−	15.5273i	−2.05814	−	1.55273i
$101$	−5.24965	−	9.09265i	−0.522359	−	0.904753i	−0.999662	−	0.0260137i	$-0.991719\pi$
$101$	−5.24965	−	9.09265i	−0.522359	−	0.904753i	0.477302	−	0.878739i	$-0.341615\pi$
$102$	−1.50527	+	0.869067i	−0.149044	+	0.0860505i
$103$		−	15.3684i		−	1.51429i	−0.653247	−	0.757145i	$-0.726594\pi$
$103$		−	15.3684i		−	1.51429i	0.653247	−	0.757145i	$-0.273406\pi$
$104$		0			0
$105$	−0.649738	+	0.574515i	−0.0634080	+	0.0560670i
$106$	7.67513	+	13.2937i	0.745475	+	1.29120i
$107$	9.63967	−	5.56547i	0.931902	−	0.538034i	0.0444895	−	0.999010i	$-0.485834\pi$
$107$	9.63967	−	5.56547i	0.931902	−	0.538034i	0.887413	+	0.460976i	$0.152501\pi$
$108$	12.3951	+	7.15633i	1.19272	+	0.688618i
$109$	9.58769			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$109$	9.58769			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$110$	−21.5437	+	4.37683i	−2.05411	+	0.417314i
$111$	−0.906679	+	1.57041i	−0.0860581	+	0.149057i
$112$		−	9.89446i		−	0.934939i
$113$	0.497545	+	0.287258i	0.0468051	+	0.0270229i	0.523220	−	0.852198i	$-0.324731\pi$
$113$	0.497545	+	0.287258i	0.0468051	+	0.0270229i	−0.476415	+	0.879221i	$0.658064\pi$
$114$	1.07816	+	1.86743i	0.100979	+	0.174901i
$115$	4.60235	−	13.7422i	0.429172	−	1.28147i
$116$	12.4690			1.15772
$117$		0			0
$118$		−	16.0181i		−	1.47459i
$119$	0.544198	+	0.942579i	0.0498866	+	0.0864061i
$120$	−8.61486	−	2.88517i	−0.786425	−	0.263379i
$121$	−1.25329	+	2.17077i	−0.113936	+	0.197343i
$122$			4.73084i			0.428310i
$123$	−3.46410	−	2.00000i	−0.312348	−	0.180334i
$124$	13.6314	−	23.6103i	1.22414	−	2.12027i
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$	2.98484	−	5.16990i	0.265911	−	0.460571i
$127$	−3.71919	+	2.14728i	−0.330025	+	0.190540i	−0.655852	−	0.754889i	$-0.727691\pi$
$127$	−3.71919	+	2.14728i	−0.330025	+	0.190540i	0.325827	+	0.945429i	$0.394357\pi$
$128$	14.3497	−	8.28480i	1.26835	−	0.732279i
$129$	−3.26916			−0.287833
$130$		0			0
$131$	−0.836381			−0.0730749			−0.0365375	−	0.999332i	$-0.511633\pi$
$131$	−0.836381			−0.0730749			−0.0365375	+	0.999332i	$0.511633\pi$
$132$	−7.89704	+	4.55936i	−0.687349	+	0.396841i
$133$	1.16936	−	0.675131i	0.101396	−	0.0585413i
$134$	13.2345	−	22.9228i	1.14329	−	1.98023i
$135$	−4.11142	−	4.64974i	−0.353855	−	0.400186i
$136$	−5.70052	+	9.87360i	−0.488816	+	0.846654i
$137$	−12.9366	−	7.46898i	−1.10525	−	0.638118i	−0.167657	−	0.985845i	$-0.553620\pi$
$137$	−12.9366	−	7.46898i	−1.10525	−	0.638118i	−0.937596	+	0.347728i	$0.886953\pi$
$138$		−	8.34297i		−	0.710201i
$139$	−4.21933	+	7.30809i	−0.357879	+	0.619864i	−0.987606	−	0.156952i	$-0.949833\pi$
$139$	−4.21933	+	7.30809i	−0.357879	+	0.619864i	0.629727	+	0.776816i	$0.283167\pi$
$140$	−2.95144	+	8.81273i	−0.249442	+	0.744811i
$141$	−0.768452	−	1.33100i	−0.0647153	−	0.112090i
$142$			22.9053i			1.92217i
$143$		0			0
$144$	33.9829			2.83190
$145$	−5.12733	−	1.71718i	−0.425802	−	0.142604i
$146$	15.7411	+	27.2643i	1.30274	+	2.25641i
$147$	−2.64632	−	1.52785i	−0.218265	−	0.126015i
$148$			19.4314i			1.59725i
$149$	5.67513	−	9.82962i	0.464925	−	0.805273i	−0.534273	−	0.845312i	$-0.679415\pi$
$149$	5.67513	−	9.82962i	0.464925	−	0.805273i	0.999198	+	0.0400384i	$0.0127480\pi$
$150$	5.13808	+	3.87633i	0.419522	+	0.316501i
$151$	−13.9878			−1.13831			−0.569155	−	0.822230i	$-0.692729\pi$
$151$	−13.9878			−1.13831			−0.569155	+	0.822230i	$0.692729\pi$
$152$	12.2492	+	7.07205i	0.993538	+	0.573619i
$153$	−3.23732	+	1.86907i	−0.261722	+	0.151105i
$154$	3.96239	+	6.86306i	0.319298	+	0.553041i
$155$	−8.85685	+	7.83146i	−0.711399	+	0.629038i
$156$		0			0
$157$			2.77575i			0.221529i	0.993847	+	0.110764i	$0.0353299\pi$
$157$			2.77575i			0.221529i	−0.993847	+	0.110764i	$0.964670\pi$
$158$	−5.24013	+	3.02539i	−0.416883	+	0.240687i
$159$	−1.38058	−	2.39123i	−0.109487	−	0.189637i
$160$	−34.9517	+	7.10080i	−2.76317	+	0.561368i
$161$	−5.22425			−0.411729
$162$	16.1469	+	9.32241i	1.26862	+	0.732437i
$163$	−1.93258	−	1.11577i	−0.151371	−	0.0873942i	0.422401	−	0.906409i	$-0.361187\pi$
$163$	−1.93258	−	1.11577i	−0.151371	−	0.0873942i	−0.573772	+	0.819015i	$0.694521\pi$
$164$	−42.8627			−3.34702
$165$	3.87521	−	0.787291i	0.301685	−	0.0612905i
$166$	−5.14117	−	8.90476i	−0.399032	−	0.691144i
$167$	13.5907	−	7.84661i	1.05168	−	0.607189i	0.128563	−	0.991701i	$-0.458964\pi$
$167$	13.5907	−	7.84661i	1.05168	−	0.607189i	0.923120	+	0.384512i	$0.125630\pi$
$168$			3.27504i			0.252675i
$169$		0			0
$170$	6.05079	−	5.35026i	0.464074	−	0.410346i
$171$	2.31876	+	4.01621i	0.177320	+	0.307127i
$172$	−30.3380	+	17.5156i	−2.31325	+	1.33555i
$173$	−22.1596	−	12.7938i	−1.68476	−	0.972698i	−0.958418	−	0.285367i	$-0.907885\pi$
$173$	−22.1596	−	12.7938i	−1.68476	−	0.972698i	−0.726344	−	0.687331i	$-0.758782\pi$
$174$	−3.11283			−0.235983
$175$	2.42731	−	3.21740i	0.183487	−	0.243212i
$176$	−22.5562	+	39.0685i	−1.70024	+	2.94490i
$177$			2.88129i			0.216571i
$178$	6.43066	+	3.71274i	0.481998	+	0.278282i
$179$	6.06300	+	10.5014i	0.453170	+	0.784914i	0.998581	−	0.0532551i	$-0.0169596\pi$
$179$	6.06300	+	10.5014i	0.453170	+	0.784914i	−0.545411	+	0.838169i	$0.683626\pi$
$180$	−30.2676	−	10.1368i	−2.25601	−	0.755555i
$181$	−2.73084			−0.202982			−0.101491	−	0.994836i	$-0.532361\pi$
$181$	−2.73084			−0.202982			−0.101491	+	0.994836i	$0.532361\pi$
$182$		0			0
$183$		−	0.850969i		−	0.0629054i
$184$	−27.3623	−	47.3928i	−2.01717	−	3.49384i
$185$	2.67601	−	7.99031i	0.196744	−	0.587460i
$186$	−3.40303	+	5.89422i	−0.249522	+	0.432185i
$187$		−	4.96239i		−	0.362886i
$188$	−14.2626	−	8.23449i	−1.04020	−	0.600562i
$189$	−1.11871	+	1.93767i	−0.0813745	+	0.140945i
$190$	−6.63752	−	7.50659i	−0.481536	−	0.544585i
$191$	−10.3127	+	17.8620i	−0.746197	+	1.29245i	0.203436	+	0.979088i	$0.434789\pi$
$191$	−10.3127	+	17.8620i	−0.746197	+	1.29245i	−0.949633	+	0.313363i	$0.898544\pi$
$192$	−7.55055	+	4.35931i	−0.544914	+	0.314606i
$193$	−18.8698	+	10.8945i	−1.35827	+	0.784200i	−0.989391	−	0.145275i	$-0.953593\pi$
$193$	−18.8698	+	10.8945i	−1.35827	+	0.784200i	−0.368884	+	0.929476i	$0.620260\pi$
$194$	5.01317			0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	−0.560431	−	0.828201i	$-0.689365\pi$
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	0.437028	+	0.899448i	$0.356031\pi$
$198$	−23.5714	+	13.6090i	−1.67515	+	0.967146i
$199$	−8.37565	+	14.5071i	−0.593734	+	1.02838i	0.399990	+	0.916520i	$0.369014\pi$
$199$	−8.37565	+	14.5071i	−0.593734	+	1.02838i	−0.993724	+	0.111859i	$0.964320\pi$
$200$	41.9003	+	5.16854i	2.96280	+	0.365471i
$201$	−2.38058	+	4.12328i	−0.167913	+	0.290834i
$202$	24.3240	+	14.0435i	1.71143	+	0.988097i
$203$			1.94921i			0.136808i
$204$	1.67513	−	2.90141i	0.117283	−	0.203139i
$205$	17.6255	+	5.90289i	1.23102	+	0.412275i
$206$	20.5562	+	35.6044i	1.43222	+	2.48067i
$207$		−	17.9429i		−	1.24712i
$208$		0			0
$209$	−6.15633			−0.425842
$210$	0.736817	−	2.20007i	0.0508452	−	0.151819i
$211$	2.45088	+	4.24504i	0.168725	+	0.292241i	0.937972	−	0.346711i	$-0.112702\pi$
$211$	2.45088	+	4.24504i	0.168725	+	0.292241i	−0.769247	+	0.638952i	$0.779368\pi$
$212$	−25.6237	−	14.7938i	−1.75984	−	1.01605i
$213$		−	4.12013i		−	0.282307i
$214$	−14.8884	+	25.7874i	−1.01775	+	1.76279i
$215$	14.8874	−	3.02453i	1.01531	−	0.206271i
$216$	−23.4372			−1.59470
$217$	3.69088	+	2.13093i	0.250553	+	0.144657i
$218$	−22.2121	+	12.8242i	−1.50439	+	0.868562i
$219$	−2.83146	−	4.90423i	−0.191332	−	0.331397i
$220$	31.7440	−	28.0689i	2.14018	−	1.89240i
$221$		0			0
$222$		−	4.85097i		−	0.325576i
$223$	21.5706	−	12.4538i	1.44448	−	0.833969i	0.446333	−	0.894867i	$-0.352730\pi$
$223$	21.5706	−	12.4538i	1.44448	−	0.833969i	0.998144	+	0.0608976i	$0.0193963\pi$
$224$	6.42842	+	11.1344i	0.429517	+	0.743946i
$225$	11.0503	+	8.33667i	0.736683	+	0.555778i
$226$	−1.53690			−0.102233
$227$	8.62136	+	4.97755i	0.572220	+	0.330371i	0.758036	−	0.652213i	$-0.226159\pi$
$227$	8.62136	+	4.97755i	0.572220	+	0.330371i	−0.185815	+	0.982585i	$0.559493\pi$
$228$	−3.59948	−	2.07816i	−0.238382	−	0.137630i
$229$	5.35026			0.353555			0.176778	−	0.984251i	$-0.443433\pi$
$229$	5.35026			0.353555			0.176778	+	0.984251i	$0.443433\pi$
$230$	7.71866	+	37.9929i	0.508953	+	2.50518i
$231$	−0.712742	−	1.23451i	−0.0468950	−	0.0812245i
$232$	−17.6827	+	10.2091i	−1.16092	+	0.670260i
$233$			10.7612i			0.704987i	0.935814	+	0.352493i	$0.114666\pi$
$233$			10.7612i			0.704987i	−0.935814	+	0.352493i	$0.885334\pi$
$234$		0			0
$235$	4.73084	+	5.35026i	0.308606	+	0.349013i
$236$	15.4375	+	26.7385i	1.00489	+	1.74053i
$237$	0.942579	−	0.544198i	0.0612271	−	0.0353495i
$238$	−2.52152	−	1.45580i	−0.163446	−	0.0943656i
$239$	−11.8618			−0.767274			−0.383637	−	0.923484i	$-0.625329\pi$
$239$	−11.8618			−0.767274			−0.383637	+	0.923484i	$0.625329\pi$
$240$	12.9433	−	2.62957i	0.835488	−	0.169738i
$241$	−14.3127	+	24.7902i	−0.921959	+	1.59688i	−0.125578	+	0.992084i	$0.540079\pi$
$241$	−14.3127	+	24.7902i	−0.921959	+	1.59688i	−0.796381	+	0.604796i	$0.793255\pi$
$242$		−	6.70545i		−	0.431043i
$243$	−10.1161	−	5.84051i	−0.648945	−	0.374669i
$244$	−4.55936	−	7.89704i	−0.291883	−	0.505556i
$245$	13.4646	+	4.50938i	0.860220	+	0.288093i
$246$	10.7005			0.682240
$247$		0			0
$248$			44.6434i			2.83486i
$249$	0.924777	+	1.60176i	0.0586054	+	0.101507i
$250$	−26.9845	−	12.8988i	−1.70665	−	0.815791i
$251$	9.69323	−	16.7892i	0.611831	−	1.05972i	−0.379100	−	0.925356i	$-0.623767\pi$
$251$	9.69323	−	16.7892i	0.611831	−	1.05972i	0.990932	−	0.134367i	$-0.0429002\pi$
$252$			11.5066i			0.724847i
$253$	20.6281	+	11.9096i	1.29688	+	0.748751i
$254$	5.74424	−	9.94932i	0.360426	−	0.624276i
$255$	−1.08840	+	0.962389i	−0.0681580	+	0.0602671i
$256$	−4.04420	+	7.00476i	−0.252762	+	0.437797i
$257$	19.7997	−	11.4314i	1.23507	−	0.713069i	0.266989	−	0.963700i	$-0.413971\pi$
$257$	19.7997	−	11.4314i	1.23507	−	0.713069i	0.968083	+	0.250631i	$0.0806380\pi$
$258$	7.57376	−	4.37271i	0.471522	−	0.272233i
$259$	−3.03761			−0.188748
$260$		0			0
$261$	−6.69464			−0.414388
$262$	1.93767	−	1.11871i	0.119710	−	0.0691144i
$263$	−18.9506	+	10.9411i	−1.16854	+	0.674658i	−0.953336	−	0.301910i	$-0.902376\pi$
$263$	−18.9506	+	10.9411i	−1.16854	+	0.674658i	−0.215206	+	0.976569i	$0.569042\pi$
$264$	7.46604	−	12.9316i	0.459503	−	0.795882i
$265$	8.49929	+	9.61213i	0.522107	+	0.590468i
$266$	−1.80606	+	3.12819i	−0.110737	+	0.191802i
$267$	−1.15673	−	0.667837i	−0.0707905	−	0.0408709i
$268$			51.0191i			3.11648i
$269$	11.3757	−	19.7032i	0.693586	−	1.20133i	−0.277069	−	0.960850i	$-0.589363\pi$
$269$	11.3757	−	19.7032i	0.693586	−	1.20133i	0.970655	−	0.240476i	$-0.0773035\pi$
$270$	15.7444	+	5.27290i	0.958173	+	0.320899i
$271$	0.0618192	+	0.107074i	0.00375525	+	0.00650428i	0.867897	−	0.496744i	$-0.165471\pi$
$271$	0.0618192	+	0.107074i	0.00375525	+	0.00650428i	−0.864142	+	0.503249i	$0.832138\pi$
$272$		−	16.5745i		−	1.00498i
$273$		0			0
$274$	39.9610			2.41413
$275$	−16.9189	+	7.17046i	−1.02025	+	0.432395i
$276$	8.04055	+	13.9266i	0.483984	+	0.838285i
$277$	13.2937	+	7.67513i	0.798742	+	0.461154i	0.843031	−	0.537865i	$-0.180769\pi$
$277$	13.2937	+	7.67513i	0.798742	+	0.461154i	−0.0442891	+	0.999019i	$0.514102\pi$
$278$		−	22.5745i		−	1.35393i
$279$	−7.31876	+	12.6765i	−0.438163	+	0.758920i
$280$	−3.02997	−	14.9141i	−0.181075	−	0.891291i
$281$	−13.9248			−0.830683			−0.415341	−	0.909666i	$-0.636338\pi$
$281$	−13.9248			−0.830683			−0.415341	+	0.909666i	$0.636338\pi$
$282$	3.56059	+	2.05571i	0.212030	+	0.122416i
$283$	−17.6509	+	10.1908i	−1.04924	+	0.605778i	−0.922436	−	0.386150i	$-0.873805\pi$
$283$	−17.6509	+	10.1908i	−1.04924	+	0.605778i	−0.126803	+	0.991928i	$0.540471\pi$
$284$	−22.0750	−	38.2350i	−1.30991	−	2.26883i
$285$	1.19394	+	1.35026i	0.0707227	+	0.0799826i
$286$		0			0
$287$		−	6.70052i		−	0.395519i
$288$	−38.2413	+	22.0786i	−2.25339	+	1.30100i
$289$	−7.58840	−	13.1435i	−0.446376	−	0.773146i
$290$	14.1755	−	2.87990i	0.832413	−	0.169114i
$291$	−0.901754			−0.0528618
$292$	−52.5521	−	30.3410i	−3.07538	−	1.77557i
$293$	−4.65972	−	2.69029i	−0.272224	−	0.157168i	0.357674	−	0.933846i	$-0.383570\pi$
$293$	−4.65972	−	2.69029i	−0.272224	−	0.157168i	−0.629898	+	0.776678i	$0.716903\pi$
$294$	8.17442			0.476742
$295$	−2.66568	−	13.1210i	−0.155202	−	0.763937i
$296$	−15.9096	−	27.5563i	−0.924728	−	1.60168i
$297$	8.83453	−	5.10062i	0.512631	−	0.295968i
$298$			30.3634i			1.75891i
$299$		0			0
$300$	−12.3127	−	1.51881i	−0.710871	−	0.0876883i
$301$	−2.73813	−	4.74259i	−0.157823	−	0.273358i
$302$	32.4059	−	18.7096i	1.86475	−	1.07661i
$303$	−4.37533	−	2.52610i	−0.251356	−	0.145121i
$304$	−20.5623			−1.17933
$305$	0.787291	+	3.87521i	0.0450801	+	0.221894i
$306$	5.00000	−	8.66025i	0.285831	−	0.495074i
$307$			19.1695i			1.09406i	0.837113	+	0.547031i	$0.184242\pi$
$307$			19.1695i			1.09406i	−0.837113	+	0.547031i	$0.815758\pi$
$308$	−13.2286	−	7.63752i	−0.753768	−	0.435188i
$309$	−3.69758	−	6.40440i	−0.210348	−	0.364334i
$310$	10.0439	−	29.9900i	0.570453	−	1.70332i
$311$	−25.2506			−1.43183			−0.715915	−	0.698187i	$-0.753990\pi$
$311$	−25.2506			−1.43183			−0.715915	+	0.698187i	$0.753990\pi$
$312$		0			0
$313$		−	2.81194i		−	0.158940i	−0.996837	−	0.0794702i	$-0.974677\pi$
$313$		−	2.81194i		−	0.158940i	0.996837	−	0.0794702i	$-0.0253229\pi$
$314$	−3.71274	−	6.43066i	−0.209522	−	0.362903i
$315$	1.58464	−	4.73159i	0.0892844	−	0.266595i
$316$	5.83146	−	10.1004i	0.328045	−	0.568191i
$317$			23.7685i			1.33497i	0.744624	+	0.667485i	$0.232629\pi$
$317$			23.7685i			1.33497i	−0.744624	+	0.667485i	$0.767371\pi$
$318$	6.39686	+	3.69323i	0.358718	+	0.207106i
$319$	4.44358	−	7.69651i	0.248793	−	0.430922i
$320$	30.3512	−	26.8373i	1.69668	−	1.50025i
$321$	2.67807	−	4.63855i	0.149475	−	0.258899i
$322$	12.1032	−	6.98778i	0.674485	−	0.389414i
$323$	1.95883	−	1.13093i	0.108992	−	0.0629268i
$324$	−35.9380			−1.99655
$325$		0			0
$326$	5.96968			0.330630
$327$	3.99544	−	2.30677i	0.220949	−	0.127565i
$328$	60.7851	−	35.0943i	3.35629	−	1.93776i
$329$	1.28726	−	2.22960i	0.0709688	−	0.122922i
$330$	−7.92478	+	7.00729i	−0.436245	+	0.385739i
$331$	−5.90057	+	10.2201i	−0.324325	+	0.561747i	−0.981375	−	0.192100i	$-0.938470\pi$
$331$	−5.90057	+	10.2201i	−0.324325	+	0.561747i	0.657051	+	0.753846i	$0.271804\pi$
$332$	17.1640	+	9.90962i	0.941995	+	0.543861i
$333$		−	10.4328i		−	0.571713i
$334$	−20.9907	+	36.3570i	−1.14856	+	1.98937i
$335$	7.02614	−	20.9794i	0.383879	−	1.14623i
$336$	−2.38058	−	4.12328i	−0.129871	−	0.224944i
$337$			16.1114i			0.877645i	0.898574	+	0.438822i	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$		0			0
$339$	0.276454			0.0150149
$340$	−4.94405	+	14.7625i	−0.268129	+	0.800608i
$341$	−9.71568	−	16.8281i	−0.526134	−	0.911290i
$342$	−10.7439	−	6.20299i	−0.580963	−	0.335419i
$343$		−	10.7612i		−	0.581048i
$344$	28.6822	−	49.6790i	1.54644	−	2.67851i
$345$	−1.38841	−	6.83405i	−0.0747494	−	0.367933i
$346$	68.4504			3.67992
$347$	−23.8108	−	13.7472i	−1.27823	−	0.737988i	−0.301709	−	0.953400i	$-0.597557\pi$
$347$	−23.8108	−	13.7472i	−1.27823	−	0.737988i	−0.976523	+	0.215413i	$0.930890\pi$
$348$	5.19615	−	3.00000i	0.278543	−	0.160817i
$349$	8.80114	+	15.2440i	0.471114	+	0.815994i	0.999454	−	0.0330393i	$-0.0105186\pi$
$349$	8.80114	+	15.2440i	0.471114	+	0.815994i	−0.528340	+	0.849033i	$0.677185\pi$
$350$	−1.31994	+	10.7005i	−0.0705540	+	0.571967i
$351$		0			0
$352$		−	58.6190i		−	3.12440i
$353$	13.6559	−	7.88423i	0.726829	−	0.419635i	−0.0904319	−	0.995903i	$-0.528825\pi$
$353$	13.6559	−	7.88423i	0.726829	−	0.419635i	0.817261	+	0.576268i	$0.195491\pi$
$354$	−3.85391	−	6.67517i	−0.204833	−	0.354781i
$355$	3.81182	+	18.7626i	0.202310	+	0.995815i
$356$	−14.3127			−0.758569
$357$	0.453564	+	0.261865i	0.0240051	+	0.0138594i
$358$	−28.0927	−	16.2193i	−1.48475	−	0.857218i
$359$	−14.8242			−0.782389			−0.391195	−	0.920308i	$-0.627938\pi$
$359$	−14.8242			−0.782389			−0.391195	+	0.920308i	$0.627938\pi$
$360$	51.2231	−	10.4065i	2.69970	−	0.548472i
$361$	8.09697	+	14.0244i	0.426156	+	0.738124i
$362$	6.32662	−	3.65268i	0.332520	−	0.191980i
$363$			1.20616i			0.0633067i
$364$		0			0
$365$	17.4314	+	19.7137i	0.912399	+	1.03186i
$366$	1.13823	+	1.97147i	0.0594961	+	0.103050i
$367$	−23.4098	+	13.5156i	−1.22198	+	0.705510i	−0.965340	−	0.260997i	$-0.915949\pi$
$367$	−23.4098	+	13.5156i	−1.22198	+	0.705510i	−0.256640	+	0.966507i	$0.582616\pi$
$368$	68.8983	+	39.7785i	3.59157	+	2.07360i
$369$	23.0132			1.19802
$370$	4.48797	+	22.0908i	0.233318	+	1.14844i
$371$	2.31265	−	4.00563i	0.120067	−	0.207962i
$372$		−	13.1187i		−	0.680174i
$373$	11.2172	+	6.47627i	0.580806	+	0.335329i	0.761454	−	0.648219i	$-0.224486\pi$
$373$	11.2172	+	6.47627i	0.580806	+	0.335329i	−0.180648	+	0.983548i	$0.557819\pi$
$374$	6.63752	+	11.4965i	0.343218	+	0.594471i
$375$	4.85388	+	2.32019i	0.250654	+	0.119814i
$376$	26.9683			1.39078
$377$		0			0
$378$		−	5.98541i		−	0.307856i
$379$	15.1429	+	26.2283i	0.777840	+	1.34726i	0.933185	+	0.359397i	$0.117018\pi$
$379$	15.1429	+	26.2283i	0.777840	+	1.34726i	−0.155345	+	0.987860i	$0.549649\pi$
$380$	18.3143	+	6.13358i	0.939503	+	0.314646i
$381$	−1.03326	+	1.78965i	−0.0529354	+	0.0916867i
$382$		−	55.1754i		−	2.82302i
$383$	18.2682	+	10.5471i	0.933460	+	0.538934i	0.887904	−	0.460028i	$-0.152161\pi$
$383$	18.2682	+	10.5471i	0.933460	+	0.538934i	0.0455560	+	0.998962i	$0.485494\pi$
$384$	3.98660	−	6.90499i	0.203440	−	0.352369i
$385$	4.38787	+	4.96239i	0.223627	+	0.252907i
$386$	29.1441	−	50.4791i	1.48340	−	2.56932i
$387$	16.2886	−	9.40422i	0.827995	−	0.478043i
$388$	−8.36833	+	4.83146i	−0.424837	+	0.245280i
$389$	6.77575			0.343544			0.171772	−	0.985137i	$-0.445051\pi$
$389$	6.77575			0.343544			0.171772	+	0.985137i	$0.445051\pi$
$390$		0			0
$391$	−8.75131			−0.442573
$392$	46.4354	−	26.8095i	2.34534	−	1.35408i
$393$	−0.348542	+	0.201231i	−0.0175816	+	0.0101508i
$394$	2.67513	−	4.63346i	0.134771	−	0.233430i
$395$	−3.78892	+	3.35026i	−0.190641	+	0.168570i
$396$	26.2313	−	45.4340i	1.31817	−	2.28314i
$397$	9.06640	+	5.23449i	0.455030	+	0.262711i	0.709952	−	0.704250i	$-0.248717\pi$
$397$	9.06640	+	5.23449i	0.455030	+	0.262711i	−0.254922	+	0.966961i	$0.582050\pi$
$398$		−	44.8119i		−	2.24622i
$399$	0.324869	−	0.562690i	0.0162638	−	0.0281697i
$400$	−56.5096	+	23.9495i	−2.82548	+	1.19748i
$401$	2.50659	+	4.34154i	0.125173	+	0.216806i	0.921801	−	0.387664i	$-0.126718\pi$
$401$	2.50659	+	4.34154i	0.125173	+	0.216806i	−0.796628	+	0.604470i	$0.793385\pi$
$402$		−	12.7367i		−	0.635250i
$403$		0			0
$404$	−54.1378			−2.69345
$405$	14.7779	+	4.94923i	0.734322	+	0.245929i
$406$	−2.60720	−	4.51581i	−0.129393	−	0.224116i
$407$	11.9941	+	6.92478i	0.594524	+	0.343248i
$408$			5.48612i			0.271603i
$409$	7.19394	−	12.4603i	0.355717	−	0.616120i	−0.631523	−	0.775357i	$-0.717570\pi$
$409$	7.19394	−	12.4603i	0.355717	−	0.616120i	0.987240	+	0.159237i	$0.0509033\pi$
$410$	−48.7289	+	9.89980i	−2.40655	+	0.488916i
$411$	−7.18806			−0.354561
$412$	−68.6275	−	39.6221i	−3.38104	−	1.95204i
$413$	−4.17990	+	2.41327i	−0.205679	+	0.118749i
$414$	23.9998	+	41.5688i	1.17952	+	2.04300i
$415$	−5.69323	−	6.43866i	−0.279470	−	0.316061i
$416$		0			0
$417$			4.06063i			0.198850i
$418$	14.2626	−	8.23449i	0.697604	−	0.402762i
$419$	8.73084	+	15.1223i	0.426529	+	0.738771i	0.996562	−	0.0828515i	$-0.0264027\pi$
$419$	8.73084	+	15.1223i	0.426529	+	0.738771i	−0.570032	+	0.821622i	$0.693069\pi$
$420$	0.890373	+	4.38261i	0.0434457	+	0.213849i
$421$	−2.88717			−0.140712			−0.0703559	−	0.997522i	$-0.522414\pi$
$421$	−2.88717			−0.140712			−0.0703559	+	0.997522i	$0.522414\pi$
$422$	−11.3560	−	6.55642i	−0.552804	−	0.319161i
$423$	7.65762	+	4.42113i	0.372326	+	0.214963i
$424$	48.4504			2.35296
$425$	4.06606	−	5.38956i	0.197233	−	0.261432i
$426$	5.51094	+	9.54523i	0.267006	+	0.462468i
$427$	1.23451	−	0.712742i	0.0597419	−	0.0344920i
$428$		−	57.3947i		−	2.77428i
$429$		0			0
$430$	−30.4445	+	26.9199i	−1.46817	+	1.29819i
$431$	0.444768	+	0.770360i	0.0214237	+	0.0371070i	0.876538	−	0.481332i	$-0.159847\pi$
$431$	0.444768	+	0.770360i	0.0214237	+	0.0371070i	−0.855115	+	0.518439i	$0.826513\pi$
$432$	29.5076	−	17.0362i	1.41968	−	0.819654i
$433$	−21.8677	−	12.6253i	−1.05089	−	0.606733i	−0.127994	−	0.991775i	$-0.540854\pi$
$433$	−21.8677	−	12.6253i	−1.05089	−	0.606733i	−0.922899	+	0.385042i	$0.874187\pi$
$434$	−11.4010			−0.547268
$435$	−2.54984	+	0.518028i	−0.122256	+	0.0248375i
$436$	24.7186	−	42.8139i	1.18381	−	2.05041i
$437$			10.8568i			0.519354i
$438$	13.1194	+	7.57452i	0.626871	+	0.361924i
$439$	14.4060	+	24.9519i	0.687560	+	1.19089i	0.972625	+	0.232380i	$0.0746513\pi$
$439$	14.4060	+	24.9519i	0.687560	+	1.19089i	−0.285066	+	0.958508i	$0.592015\pi$
$440$	−22.0356	+	65.7961i	−1.05050	+	3.13671i
$441$	17.5804			0.837162
$442$		0			0
$443$		−	36.9805i		−	1.75700i	−0.477746	−	0.878498i	$-0.658546\pi$
$443$		−	36.9805i		−	1.75700i	0.477746	−	0.878498i	$-0.341454\pi$
$444$	4.67513	+	8.09756i	0.221872	+	0.384293i
$445$	5.88546	+	1.97108i	0.278998	+	0.0934382i
$446$	−33.3156	+	57.7043i	−1.57754	+	2.73238i
$447$		−	5.46168i		−	0.258329i
$448$	−12.6482	−	7.30242i	−0.597569	−	0.345007i
$449$	6.34297	−	10.9863i	0.299343	−	0.518478i	−0.676643	−	0.736312i	$-0.736566\pi$
$449$	6.34297	−	10.9863i	0.299343	−	0.518478i	0.975986	+	0.217834i	$0.0698991\pi$
$450$	−36.7513	−	4.53339i	−1.73247	−	0.213706i
$451$	−15.2750	+	26.4571i	−0.719273	+	1.24582i
$452$	2.56550	−	1.48119i	0.120671	−	0.0696695i
$453$	−5.82908	+	3.36542i	−0.273874	+	0.158121i
$454$	−26.6312			−1.24986
$455$		0			0
$456$	6.80606			0.318723
$457$	21.6934	−	12.5247i	1.01477	−	0.585880i	0.102188	−	0.994765i	$-0.467416\pi$
$457$	21.6934	−	12.5247i	1.01477	−	0.585880i	0.912586	+	0.408885i	$0.134082\pi$
$458$	−12.3951	+	7.15633i	−0.579186	+	0.334393i
$459$	−1.87399	+	3.24585i	−0.0874705	+	0.151503i
$460$	−49.5002	−	55.9814i	−2.30796	−	2.61015i
$461$	−18.4436	+	31.9452i	−0.859003	+	1.48784i	0.0138774	+	0.999904i	$0.495583\pi$
$461$	−18.4436	+	31.9452i	−0.859003	+	1.48784i	−0.872881	+	0.487934i	$0.837751\pi$
$462$	3.30246	+	1.90668i	0.153645	+	0.0887067i
$463$		−	39.0191i		−	1.81337i	−0.421809	−	0.906685i	$-0.638605\pi$
$463$		−	39.0191i		−	1.81337i	0.421809	−	0.906685i	$-0.361395\pi$
$464$	14.8417	−	25.7066i	0.689008	−	1.19340i
$465$	−1.80666	+	5.39451i	−0.0837817	+	0.250164i
$466$	−14.3938	−	24.9307i	−0.666778	−	1.15489i
$467$			32.7694i			1.51639i	0.652029	+	0.758194i	$0.273918\pi$
$467$			32.7694i			1.51639i	−0.652029	+	0.758194i	$0.726082\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	−18.1164	−	6.06731i	−0.835648	−	0.279864i
$471$	0.667837	+	1.15673i	0.0307723	+	0.0532992i
$472$	−43.7848	−	25.2792i	−2.01536	−	1.16357i
$473$			24.9683i			1.14804i
$474$	−1.45580	+	2.52152i	−0.0668672	+	0.115817i
$475$	−6.68627	−	5.04434i	−0.306787	−	0.231450i
$476$	5.61213			0.257231
$477$	13.7575	+	7.94288i	0.629911	+	0.363679i
$478$	27.4805	−	15.8659i	1.25693	−	0.725689i
$479$	−8.43747	−	14.6141i	−0.385518	−	0.667737i	0.606323	−	0.795219i	$-0.292644\pi$
$479$	−8.43747	−	14.6141i	−0.385518	−	0.667737i	−0.991841	+	0.127482i	$0.959311\pi$
$480$	−12.8568	+	11.3684i	−0.586832	+	0.518892i
$481$		0			0
$482$		−	76.5764i		−	3.48796i
$483$	−2.17708	+	1.25694i	−0.0990608	+	0.0571928i
$484$	6.46239	+	11.1932i	0.293745	+	0.508781i
$485$	4.10648	−	0.834276i	0.186466	−	0.0378825i
$486$	31.2482			1.41745
$487$	−8.00616	−	4.62236i	−0.362794	−	0.209459i	0.307512	−	0.951544i	$-0.400504\pi$
$487$	−8.00616	−	4.62236i	−0.362794	−	0.209459i	−0.670306	+	0.742085i	$0.733837\pi$
$488$	12.9316	+	7.46604i	0.585384	+	0.337972i
$489$	−1.07381			−0.0485593
$490$	−37.2254	+	7.56273i	−1.68167	+	0.341649i
$491$	12.8749	+	22.3001i	0.581038	+	1.00639i	0.995357	+	0.0962557i	$0.0306867\pi$
$491$	12.8749	+	22.3001i	0.581038	+	1.00639i	−0.414318	+	0.910132i	$0.635980\pi$
$492$	−17.8620	+	10.3127i	−0.805283	+	0.464930i
$493$			3.26519i			0.147057i
$494$		0			0
$495$	−17.0435	+	15.0703i	−0.766048	+	0.677360i
$496$	−32.4506	−	56.2062i	−1.45708	−	2.52373i
$497$	5.97709	−	3.45088i	0.268109	−	0.154793i
$498$	−4.28492	−	2.47390i	−0.192012	−	0.110858i
$499$	−27.7015			−1.24009			−0.620044	−	0.784567i	$-0.712885\pi$
$499$	−27.7015			−1.24009			−0.620044	+	0.784567i	$0.712885\pi$
$500$	57.4755	−	4.47483i	2.57038	−	0.200120i
$501$	3.77575	−	6.53978i	0.168688	−	0.292176i
$502$			51.8613i			2.31468i
$503$	2.03965	+	1.17759i	0.0909436	+	0.0525063i	0.544782	−	0.838578i	$-0.316612\pi$
$503$	2.03965	+	1.17759i	0.0909436	+	0.0525063i	−0.453839	+	0.891084i	$0.649946\pi$
$504$	−9.42113	−	16.3179i	−0.419650	−	0.726856i
$505$	22.2618	+	7.45564i	0.990639	+	0.331772i
$506$	−63.7196			−2.83268
$507$		0			0
$508$			22.1441i			0.982486i
$509$	−10.7562	−	18.6303i	−0.476762	−	0.825775i	0.522884	−	0.852404i	$-0.324856\pi$
$509$	−10.7562	−	18.6303i	−0.476762	−	0.825775i	−0.999645	+	0.0266286i	$0.991523\pi$
$510$	1.23426	−	3.68540i	0.0546542	−	0.163192i
$511$	4.74306	−	8.21522i	0.209821	−	0.363420i
$512$			11.5017i			0.508306i
$513$	4.02679	+	2.32487i	0.177787	+	0.102645i
$514$	−30.5804	+	52.9668i	−1.34884	+	2.33627i
$515$	22.7635	+	25.7440i	1.00308	+	1.13442i
$516$	−8.42842	+	14.5985i	−0.371041	+	0.642661i
$517$	−10.1655	+	5.86907i	−0.447079	+	0.258121i
$518$	7.03733	−	4.06300i	0.309203	−	0.178518i
$519$	−12.3127			−0.540465
$520$		0			0
$521$	37.7440			1.65360			0.826798	−	0.562499i	$-0.190160\pi$
$521$	37.7440			1.65360			0.826798	+	0.562499i	$0.190160\pi$
$522$	15.5097	−	8.95452i	0.678841	−	0.391929i
$523$	−20.5609	+	11.8708i	−0.899064	+	0.519075i	−0.876896	−	0.480679i	$-0.840390\pi$
$523$	−20.5609	+	11.8708i	−0.899064	+	0.519075i	−0.0221676	+	0.999754i	$0.507057\pi$
$524$	−2.15633	+	3.73486i	−0.0941995	+	0.163158i
$525$	0.237428	−	1.92478i	0.0103622	−	0.0840042i
$526$	29.2689	−	50.6953i	1.27619	−	2.21042i
$527$	6.18271	+	3.56959i	0.269323	+	0.155494i
$528$			21.7078i			0.944712i
$529$	9.50294	−	16.4596i	0.413171	−	0.715634i
$530$	−32.5474	−	10.9004i	−1.41377	−	0.473481i
$531$	−8.28844	−	14.3560i	−0.359688	−	0.622997i
$532$		−	6.96239i		−	0.301858i
$533$		0			0
$534$	3.57310			0.154623
$535$	−7.90417	+	23.6011i	−0.341727	+	1.02036i
$536$	−41.7723	−	72.3518i	−1.80429	−	3.12512i
$537$	5.05323	+	2.91748i	0.218063	+	0.125899i
$538$			60.8627i			2.62398i
$539$	−11.6690	+	20.2113i	−0.502620	+	0.870564i
$540$	−31.3634	+	6.37180i	−1.34966	+	0.274199i
$541$	−13.0376			−0.560531			−0.280265	−	0.959923i	$-0.590422\pi$
$541$	−13.0376			−0.560531			−0.280265	+	0.959923i	$0.590422\pi$
$542$	−0.286437	−	0.165374i	−0.0123035	−	0.00710344i
$543$	−1.13801	+	0.657032i	−0.0488368	+	0.0281960i
$544$	10.7685	+	18.6515i	0.461694	+	0.799677i
$545$	−16.0606	+	14.2012i	−0.687962	+	0.608314i
$546$		0			0
$547$			8.43041i			0.360458i	0.983625	+	0.180229i	$0.0576839\pi$
$547$			8.43041i			0.360458i	−0.983625	+	0.180229i	$0.942316\pi$
$548$	−66.7055	+	38.5125i	−2.84952	+	1.64517i
$549$	2.44794	+	4.23995i	0.104475	+	0.180957i
$550$	29.6056	−	39.2422i	1.26239	−	1.67329i
$551$	4.05079			0.172569
$552$	−22.8051	−	13.1666i	−0.970652	−	0.560406i
$553$	1.57894	+	0.911603i	0.0671435	+	0.0387653i
$554$	−41.0640			−1.74464
$555$	−0.807282	−	3.97362i	−0.0342672	−	0.168671i
$556$	21.7562	+	37.6829i	0.922670	+	1.59811i
$557$	−11.8587	+	6.84661i	−0.502469	+	0.290100i	−0.729732	−	0.683733i	$-0.760355\pi$
$557$	−11.8587	+	6.84661i	−0.502469	+	0.290100i	0.227264	+	0.973833i	$0.427022\pi$
$558$		−	39.1573i		−	1.65766i
$559$		0			0
$560$	14.6556	+	16.5745i	0.619313	+	0.700401i
$561$	−1.19394	−	2.06796i	−0.0504080	−	0.0873093i
$562$	32.2600	−	18.6253i	1.36080	−	0.785661i
$563$	−7.68084	−	4.43453i	−0.323709	−	0.186893i	0.329336	−	0.944213i	$-0.393175\pi$
$563$	−7.68084	−	4.43453i	−0.323709	−	0.186893i	−0.653044	+	0.757320i	$0.726509\pi$
$564$	−7.92478			−0.333693
$565$	−1.25894	+	0.255767i	−0.0529639	+	0.0107602i
$566$	27.2616	−	47.2185i	1.14589	−	1.98474i
$567$		−	5.61801i		−	0.235934i
$568$	62.6106	+	36.1482i	2.62708	+	1.51675i
$569$	−16.3908	−	28.3897i	−0.687139	−	1.19016i	−0.972760	−	0.231816i	$-0.925533\pi$
$569$	−16.3908	−	28.3897i	−0.687139	−	1.19016i	0.285621	−	0.958343i	$-0.407800\pi$
$570$	−4.57209	−	1.53123i	−0.191504	−	0.0641360i
$571$	40.2882			1.68601			0.843005	−	0.537906i	$-0.180785\pi$
$571$	40.2882			1.68601			0.843005	+	0.537906i	$0.180785\pi$
$572$		0			0
$573$			9.92478i			0.414614i
$574$	8.96239	+	15.5233i	0.374083	+	0.647931i
$575$	12.6453	+	29.8369i	0.527346	+	1.24429i
$576$	25.0804	−	43.4405i	1.04502	−	1.81002i
$577$		−	28.8568i		−	1.20133i	−0.799502	−	0.600663i	$-0.794903\pi$
$577$		−	28.8568i		−	1.20133i	0.799502	−	0.600663i	$-0.205097\pi$
$578$	35.1606	+	20.3000i	1.46249	+	0.844367i
$579$	−5.24235	+	9.08002i	−0.217865	+	0.377353i
$580$	−20.8872	+	18.4690i	−0.867292	+	0.766882i
$581$	−1.54912	+	2.68316i	−0.0642684	+	0.111316i
$582$	2.08912	−	1.20616i	0.0865969	−	0.0499967i
$583$	−18.2631	+	10.5442i	−0.756380	+	0.436696i
$584$	99.3679			4.11187
$585$		0			0
$586$	14.3938			0.594600
$587$	−36.0948	+	20.8393i	−1.48979	+	0.860131i	−0.999932	−	0.0116712i	$-0.996285\pi$
$587$	−36.0948	+	20.8393i	−1.48979	+	0.860131i	−0.489858	+	0.871802i	$0.662952\pi$
$588$	−13.6453	+	7.87812i	−0.562723	+	0.324888i
$589$	4.42842	−	7.67026i	0.182470	−	0.316047i
$590$	23.7259	+	26.8324i	0.976781	+	1.10467i
$591$	−0.481194	+	0.833453i	−0.0197937	+	0.0342837i
$592$	40.0605	+	23.1289i	1.64648	+	0.950594i
$593$			22.4993i			0.923935i	0.886897	+	0.461968i	$0.152856\pi$
$593$			22.4993i			0.923935i	−0.886897	+	0.461968i	$0.847144\pi$
$594$	−13.6448	+	23.6335i	−0.559853	+	0.969695i
$595$	−2.30775	−	0.772880i	−0.0946084	−	0.0316850i
$596$	−29.2628	−	50.6847i	−1.19865	−	2.07613i
$597$			8.06063i			0.329900i
$598$		0			0
$599$	−4.15045			−0.169583			−0.0847913	−	0.996399i	$-0.527022\pi$
$599$	−4.15045			−0.169583			−0.0847913	+	0.996399i	$0.527022\pi$
$600$	18.7045	−	7.92723i	0.763609	−	0.323628i
$601$	−13.9624	−	24.1836i	−0.569538	−	0.986468i	−0.996612	−	0.0822515i	$-0.973789\pi$
$601$	−13.9624	−	24.1836i	−0.569538	−	0.986468i	0.427074	−	0.904217i	$-0.359544\pi$
$602$	12.6870	+	7.32487i	0.517085	+	0.298539i
$603$		−	27.3923i		−	1.11550i
$604$	−36.0628	+	62.4626i	−1.46737	+	2.54157i
$605$	−1.11590	−	5.49269i	−0.0453677	−	0.223310i
$606$	13.5153			0.549021
$607$	−7.09698	−	4.09745i	−0.288058	−	0.166310i	0.349008	−	0.937120i	$-0.386519\pi$
$607$	−7.09698	−	4.09745i	−0.288058	−	0.166310i	−0.637066	+	0.770810i	$0.719852\pi$
$608$	23.1390	−	13.3593i	0.938411	−	0.541792i
$609$	0.468976	+	0.812289i	0.0190038	+	0.0329156i
$610$	−7.00729	−	7.92478i	−0.283717	−	0.320865i
$611$		0			0
$612$			19.2750i			0.779147i
$613$	28.6994	−	16.5696i	1.15916	−	0.669239i	0.208055	−	0.978117i	$-0.433287\pi$
$613$	28.6994	−	16.5696i	1.15916	−	0.669239i	0.951102	+	0.308878i	$0.0999534\pi$
$614$	−25.6405	−	44.4106i	−1.03476	−	1.79227i
$615$	8.76521	−	1.78075i	0.353447	−	0.0718066i
$616$	25.0132			1.00781
$617$	−25.1261	−	14.5066i	−1.01154	−	0.584013i	−0.0998982	−	0.994998i	$-0.531852\pi$
$617$	−25.1261	−	14.5066i	−1.01154	−	0.584013i	−0.911642	+	0.410984i	$0.865185\pi$
$618$	17.1326	+	9.89152i	0.689175	+	0.397895i
$619$	12.2134			0.490900			0.245450	−	0.969409i	$-0.421064\pi$
$619$	12.2134			0.490900			0.245450	+	0.969409i	$0.421064\pi$
$620$	12.1370	+	59.7411i	0.487435	+	2.39926i
$621$	−8.99508	−	15.5799i	−0.360960	−	0.625201i
$622$	58.4989	−	33.7743i	2.34559	−	1.35423i
$623$		−	2.23743i		−	0.0896406i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	3.76116	+	6.51452i	0.150326	+	0.260372i
$627$	−2.56550	+	1.48119i	−0.102456	+	0.0591532i
$628$	12.3951	+	7.15633i	0.494619	+	0.285568i
$629$	−5.08840			−0.202888
$630$	2.65762	+	13.0814i	0.105882	+	0.521175i
$631$	−0.610942	+	1.05818i	−0.0243212	+	0.0421256i	−0.877930	−	0.478789i	$-0.841076\pi$
$631$	−0.610942	+	1.05818i	−0.0243212	+	0.0421256i	0.853609	+	0.520915i	$0.174409\pi$
$632$			19.0982i			0.759687i
$633$	2.04269	+	1.17935i	0.0811897	+	0.0468749i
$634$	−31.7919	−	55.0651i	−1.26262	−	2.18692i
$635$	3.04960	−	9.10581i	0.121020	−	0.361353i
$636$	−14.2374			−0.564551
$637$		0			0
$638$			23.7743i			0.941235i
$639$	11.8522	+	20.5285i	0.468864	+	0.812096i
$640$	−11.7662	+	35.1328i	−0.465100	+	1.38875i
$641$	11.0508	−	19.1405i	0.436480	−	0.756005i	−0.560935	−	0.827860i	$-0.689558\pi$
$641$	11.0508	−	19.1405i	0.436480	−	0.756005i	0.997415	+	0.0718545i	$0.0228917\pi$
$642$			14.3284i			0.565496i
$643$	−10.1055	−	5.83440i	−0.398521	−	0.230086i	0.287325	−	0.957833i	$-0.407234\pi$
$643$	−10.1055	−	5.83440i	−0.398521	−	0.230086i	−0.685846	+	0.727747i	$0.740567\pi$
$644$	−13.4690	+	23.3289i	−0.530752	+	0.919289i
$645$	5.47627	−	4.84226i	0.215628	−	0.190664i
$646$	−3.02539	+	5.24013i	−0.119032	+	0.206170i
$647$	10.3555	−	5.97873i	0.407115	−	0.235048i	−0.282434	−	0.959287i	$-0.591142\pi$
$647$	10.3555	−	5.97873i	0.407115	−	0.235048i	0.689550	+	0.724238i	$0.257809\pi$
$648$	50.9648	−	29.4245i	2.00209	−	1.15591i
$649$	22.0059			0.863806
$650$		0			0
$651$	2.05079			0.0803766
$652$	−9.96500	+	5.75329i	−0.390259	+	0.225316i
$653$	9.52505	−	5.49929i	0.372744	−	0.215204i	−0.301912	−	0.953336i	$-0.597625\pi$
$653$	9.52505	−	5.49929i	0.372744	−	0.215204i	0.674657	+	0.738132i	$0.264292\pi$
$654$	−6.17091	+	10.6883i	−0.241302	+	0.417947i
$655$	1.40105	−	1.23884i	0.0547434	−	0.0484056i
$656$	−51.0191	+	88.3676i	−1.99196	+	3.45017i
$657$	28.2154	+	16.2902i	1.10079	+	0.635541i
$658$			6.88717i			0.268490i
$659$	−1.31994	+	2.28621i	−0.0514177	+	0.0890581i	−0.890589	−	0.454810i	$-0.849707\pi$
$659$	−1.31994	+	2.28621i	−0.0514177	+	0.0890581i	0.839171	+	0.543868i	$0.183041\pi$
$660$	6.47528	−	19.3346i	0.252050	−	0.752597i
$661$	9.15140	+	15.8507i	0.355948	+	0.616520i	0.987280	−	0.158993i	$-0.0508246\pi$
$661$	9.15140	+	15.8507i	0.355948	+	0.616520i	−0.631332	+	0.775513i	$0.717491\pi$
$662$		−	31.5696i		−	1.22699i
$663$		0			0
$664$	−32.4544			−1.25947
$665$	−0.958833	+	2.86298i	−0.0371819	+	0.111022i
$666$	13.9545	+	24.1699i	0.540727	+	0.936566i
$667$	−13.5730	−	7.83638i	−0.525549	−	0.303426i
$668$		−	80.9194i		−	3.13087i
$669$	5.99271	−	10.3797i	0.231691	−	0.401301i
$670$	11.7836	+	58.0015i	0.455241	+	2.24080i
$671$	−6.49929			−0.250902
$672$	5.35779	+	3.09332i	0.206681	+	0.119327i
$673$	−5.81135	+	3.35519i	−0.224011	+	0.129333i	−0.607806	−	0.794085i	$-0.707950\pi$
$673$	−5.81135	+	3.35519i	−0.224011	+	0.129333i	0.383795	+	0.923418i	$0.374617\pi$
$674$	−21.5501	−	37.3258i	−0.830078	−	1.43774i
$675$	13.7743	+	1.69911i	0.530174	+	0.0653987i
$676$		0			0
$677$		−	1.57593i		−	0.0605679i	−0.999541	−	0.0302840i	$-0.990359\pi$
$677$		−	1.57593i		−	0.0605679i	0.999541	−	0.0302840i	$-0.00964116\pi$
$678$	−0.640469	+	0.369775i	−0.0245971	+	0.0142011i
$679$	−0.755278	−	1.30818i	−0.0289849	−	0.0502033i
$680$	−5.07559	−	24.9831i	−0.194640	−	0.958060i
$681$	4.79033			0.183566
$682$	45.0172	+	25.9907i	1.72380	+	0.995236i
$683$	−13.1583	−	7.59697i	−0.503490	−	0.290690i	0.226664	−	0.973973i	$-0.427218\pi$
$683$	−13.1583	−	7.59697i	−0.503490	−	0.290690i	−0.730154	+	0.683283i	$0.760551\pi$
$684$	23.9126			0.914320
$685$	32.7336	−	6.65017i	1.25069	−	0.254090i
$686$	14.3938	+	24.9307i	0.549556	+	0.951859i
$687$	2.22960	−	1.28726i	0.0850644	−	0.0491119i
$688$			83.3947i			3.17939i
$689$		0			0
$690$	12.3576	+	13.9756i	0.470444	+	0.532041i
$691$	−9.35637	−	16.2057i	−0.355933	−	0.616494i	0.631344	−	0.775503i	$-0.282504\pi$
$691$	−9.35637	−	16.2057i	−0.355933	−	0.616494i	−0.987277	+	0.159009i	$0.949170\pi$
$692$	−114.262	+	65.9692i	−4.34359	+	2.50777i
$693$	7.10247	+	4.10062i	0.269801	+	0.155769i
$694$	73.5510			2.79196
$695$	−3.75678	−	18.4917i	−0.142503	−	0.701429i
$696$	−4.91256	+	8.50880i	−0.186210	+	0.322525i
$697$		−	11.2243i		−	0.425149i
$698$	−40.7797	−	23.5442i	−1.54354	−	0.891161i
$699$	2.58910	+	4.48446i	0.0979289	+	0.169618i
$700$	−8.10931	−	19.1341i	−0.306503	−	0.723202i
$701$	24.3028			0.917904			0.458952	−	0.888461i	$-0.348225\pi$
$701$	24.3028			0.917904			0.458952	+	0.888461i	$0.348225\pi$
$702$		0			0
$703$			6.31265i			0.238086i
$704$	33.2943	+	57.6675i	1.25483	+	2.17342i
$705$	3.25872	+	1.09137i	0.122731	+	0.0411033i
$706$	−21.0913	+	36.5313i	−0.793783	+	1.37487i
$707$		−	8.46310i		−	0.318287i
$708$	12.8664	+	7.42842i	0.483549	+	0.279177i
$709$	4.83146	−	8.36833i	0.181449	−	0.314279i	−0.760925	−	0.648840i	$-0.775255\pi$
$709$	4.83146	−	8.36833i	0.181449	−	0.314279i	0.942374	+	0.334561i	$0.108588\pi$
$710$	−33.9271	−	38.3693i	−1.27326	−	1.43997i
$711$	−3.13093	+	5.42293i	−0.117419	+	0.203376i
$712$	20.2972	−	11.7186i	0.760672	−	0.439174i
$713$	−29.6767	+	17.1339i	−1.11140	+	0.641669i
$714$	−1.40105			−0.0524329
$715$		0			0
$716$	62.5256			2.33669
$717$	−4.94312	+	2.85391i	−0.184604	+	0.106581i
$718$	34.3436	−	19.8283i	1.28169	−	0.739985i
$719$	14.2071	−	24.6074i	0.529836	−	0.917703i	−0.469558	−	0.882901i	$-0.655587\pi$
$719$	14.2071	−	24.6074i	0.529836	−	0.917703i	0.999394	−	0.0348012i	$-0.0110798\pi$
$720$	−56.9257	+	50.3352i	−2.12150	+	1.87588i
$721$	6.19394	−	10.7282i	0.230674	−	0.399540i
$722$	−37.5170	−	21.6604i	−1.39624	−	0.806118i
$723$			13.7743i			0.512273i
$724$	−7.04055	+	12.1946i	−0.261660	+	0.453208i
$725$	11.1324	−	4.71808i	0.413448	−	0.175225i
$726$	−1.61331	−	2.79434i	−0.0598756	−	0.103708i
$727$		−	34.8545i		−	1.29268i	−0.763049	−	0.646341i	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		0			0
$729$	15.2882			0.566230
$730$	−66.7521	−	22.3557i	−2.47061	−	0.827423i
$731$	−4.58673	−	7.94446i	−0.169646	−	0.293836i
$732$	−3.80001	−	2.19394i	−0.140452	−	0.0810902i
$733$			6.25202i			0.230923i	0.993312	+	0.115462i	$0.0368348\pi$
$733$			6.25202i			0.230923i	−0.993312	+	0.115462i	$0.963165\pi$
$734$	36.1561	−	62.6242i	1.33455	−	2.31150i
$735$	6.69599	−	1.36036i	0.246985	−	0.0501777i
$736$	−103.376			−3.81050
$737$	31.4917	+	18.1817i	1.16001	+	0.669732i
$738$	−53.3153	+	30.7816i	−1.96256	+	1.13309i
$739$	16.0423	+	27.7861i	0.590126	+	1.02213i	0.994215	+	0.107408i	$0.0342552\pi$
$739$	16.0423	+	27.7861i	0.590126	+	1.02213i	−0.404089	+	0.914720i	$0.632411\pi$
$740$	−28.7816	−	32.5501i	−1.05803	−	1.19656i
$741$		0			0
$742$			12.3733i			0.454238i
$743$	−26.4521	+	15.2721i	−0.970432	+	0.560279i	−0.899368	−	0.437193i	$-0.855973\pi$
$743$	−26.4521	+	15.2721i	−0.970432	+	0.560279i	−0.0710638	+	0.997472i	$0.522639\pi$
$744$	10.7411	+	18.6041i	0.393787	+	0.682059i
$745$	5.05298	+	24.8719i	0.185127	+	0.911235i
$746$	−34.6497			−1.26862
$747$	−9.21540	−	5.32051i	−0.337174	−	0.194667i
$748$	−22.1596	−	12.7938i	−0.810235	−	0.467789i
$749$	8.97224			0.327838
$750$	−14.3486	+	1.11712i	−0.523935	+	0.0407916i
$751$	−14.0811	−	24.3892i	−0.513827	−	0.889974i	−0.999871	−	0.0160400i	$-0.994894\pi$
$751$	−14.0811	−	24.3892i	−0.513827	−	0.889974i	0.486045	−	0.873934i	$-0.338439\pi$
$752$	−33.9531	+	19.6028i	−1.23814	+	0.714842i
$753$		−	9.32865i		−	0.339955i
$754$		0			0
$755$	23.4314	−	20.7186i	0.852755	−	0.754028i
$756$	5.76845	+	9.99125i	0.209797	+	0.363378i
$757$	30.6667	−	17.7054i	1.11460	−	0.643515i	0.174584	−	0.984642i	$-0.444142\pi$
$757$	30.6667	−	17.7054i	1.11460	−	0.643515i	0.940017	+	0.341127i	$0.110809\pi$
$758$	−70.1642	−	40.5093i	−2.54848	−	1.47136i
$759$	11.4617			0.416033
$760$	−30.9940	+	6.29676i	−1.12427	+	0.228408i
$761$	−9.61942	+	16.6613i	−0.348704	+	0.603973i	−0.986019	−	0.166630i	$-0.946711\pi$
$761$	−9.61942	+	16.6613i	−0.348704	+	0.603973i	0.637316	+	0.770603i	$0.280045\pi$
$762$		−	5.52820i		−	0.200265i
$763$	6.69289	+	3.86414i	0.242299	+	0.139891i
$764$	53.1754	+	92.1025i	1.92382	+	3.33215i
$765$	2.65448	−	7.92603i	0.0959730	−	0.286566i
$766$	−56.4299			−2.03890
$767$		0			0
$768$			3.89209i			0.140444i
$769$	−24.4821	−	42.4043i	−0.882849	−	1.52914i	−0.848159	−	0.529741i	$-0.822289\pi$
$769$	−24.4821	−	42.4043i	−0.882849	−	1.52914i	−0.0346894	−	0.999398i	$-0.511044\pi$
$770$	−16.8030	−	5.62745i	−0.605540	−	0.202799i
$771$	5.50071	−	9.52750i	0.198103	−	0.343125i
$772$			112.351i			4.04359i
$773$	−39.9827	−	23.0840i	−1.43808	−	0.830275i	−0.440363	−	0.897820i	$-0.645150\pi$
$773$	−39.9827	−	23.0840i	−1.43808	−	0.830275i	−0.997716	+	0.0675447i	$0.978483\pi$
$774$	−25.1575	+	43.5741i	−0.904268	+	1.56624i
$775$	3.23647	−	26.2374i	0.116258	−	0.942476i
$776$	7.91160	−	13.7033i	0.284010	−	0.491920i
$777$	−1.26585	+	0.730841i	−0.0454122	+	0.0262188i
$778$	−15.6976	+	9.06300i	−0.562786	+	0.324924i
$779$	−13.9248			−0.498907
$780$		0			0
$781$	−31.4676			−1.12600
$782$	20.2744	−	11.7054i	0.725012	−	0.418586i
$783$	−5.81301	+	3.35614i	−0.207740	+	0.119939i
$784$	−38.9749	+	67.5064i	−1.39196	+	2.41094i
$785$	−4.11142	−	4.64974i	−0.146743	−	0.165956i
$786$	0.538319	−	0.932395i	0.0192012	−	0.0332574i
$787$	−19.6118	−	11.3229i	−0.699086	−	0.403617i	0.107921	−	0.994159i	$-0.465581\pi$
$787$	−19.6118	−	11.3229i	−0.699086	−	0.403617i	−0.807007	+	0.590542i	$0.798914\pi$
$788$			10.3127i			0.367373i
$789$	−5.26480	+	9.11891i	−0.187432	+	0.324642i
$790$	4.29672	−	12.8296i	0.152870	−	0.456456i
$791$	0.231548	+	0.401053i	0.00823290	+	0.0142598i
$792$			85.9086i			3.05263i
$793$		0			0
$794$	−28.0059			−0.993891
$795$	5.85453	+	1.96072i	0.207639	+	0.0695397i
$796$	43.1876	+	74.8031i	1.53074	+	2.65133i
$797$	−7.13382	−	4.11871i	−0.252693	−	0.145892i	0.368304	−	0.929706i	$-0.379939\pi$
$797$	−7.13382	−	4.11871i	−0.252693	−	0.145892i	−0.620997	+	0.783813i	$0.713272\pi$
$798$			1.73813i			0.0615293i
$799$	2.15633	−	3.73486i	0.0762853	−	0.132130i
$800$	48.0309	−	63.6650i	1.69815	−	2.25090i
$801$	7.68452			0.271519
$802$	−11.6142	−	6.70545i	−0.410111	−	0.236778i
$803$	−37.4561	+	21.6253i	−1.32180	+	0.763140i
$804$	12.2750	+	21.2610i	0.432907	+	0.749817i
$805$	8.75131	−	7.73813i	0.308443	−	0.272733i
$806$		0			0
$807$		−	10.9478i		−	0.385381i
$808$	76.7746	−	44.3258i	2.70092	−	1.55938i
$809$	22.0659	+	38.2193i	0.775797	+	1.34372i	0.934345	+	0.356369i	$0.115985\pi$
$809$	22.0659	+	38.2193i	0.775797	+	1.34372i	−0.158548	+	0.987351i	$0.550681\pi$
$810$	−40.8564	+	8.30042i	−1.43555	+	0.291647i
$811$	−22.6883			−0.796694			−0.398347	−	0.917235i	$-0.630416\pi$
$811$	−22.6883			−0.796694			−0.398347	+	0.917235i	$0.630416\pi$
$812$	8.70424	+	5.02539i	0.305459	+	0.176357i
$813$	0.0515234	+	0.0297470i	0.00180700	+	0.00104327i
$814$	−37.0494			−1.29858
$815$	4.89000	−	0.993455i	0.171289	−	0.0347992i
$816$	−3.98778	−	6.90704i	−0.139600	−	0.241795i
$817$	−9.85587	+	5.69029i	−0.344813	+	0.199078i
$818$			38.4894i			1.34575i
$819$		0			0
$820$	71.8007	−	63.4880i	2.50739	−	2.21710i
$821$	−25.1368	−	43.5382i	−0.877281	−	1.51949i	−0.854313	−	0.519759i	$-0.826022\pi$
$821$	−25.1368	−	43.5382i	−0.877281	−	1.51949i	−0.0229677	−	0.999736i	$-0.507311\pi$
$822$	16.6528	−	9.61450i	0.580833	−	0.335344i
$823$	4.44352	+	2.56547i	0.154891	+	0.0894265i	0.575442	−	0.817842i	$-0.304830\pi$
$823$	4.44352	+	2.56547i	0.154891	+	0.0894265i	−0.420551	+	0.907269i	$0.638163\pi$
$824$	129.764			4.52054
$825$	−5.32536	+	7.05876i	−0.185405	+	0.245755i
$826$	6.45580	−	11.1818i	0.224626	−	0.389064i
$827$		−	18.6946i		−	0.650076i	−0.945701	−	0.325038i	$-0.894623\pi$
$827$		−	18.6946i		−	0.650076i	0.945701	−	0.325038i	$-0.105377\pi$
$828$	−80.1241	−	46.2597i	−2.78450	−	1.60763i
$829$	−1.72061	−	2.98018i	−0.0597591	−	0.103506i	0.834598	−	0.550859i	$-0.185700\pi$
$829$	−1.72061	−	2.98018i	−0.0597591	−	0.103506i	−0.894357	+	0.447353i	$0.852367\pi$
$830$	21.8018	+	7.30157i	0.756752	+	0.253441i
$831$	7.38646			0.256233
$832$		0			0
$833$		−	8.57452i		−	0.297089i
$834$	−5.43136	−	9.40740i	−0.188073	−	0.325752i
$835$	−11.1439	+	33.2746i	−0.385651	+	1.15152i
$836$	−15.8720	+	27.4911i	−0.548945	+	0.950800i
$837$			14.6761i			0.507280i
$838$	−40.4540	−	23.3561i	−1.39746	−	0.806825i
$839$	26.3124	−	45.5744i	0.908406	−	1.57340i	0.0921263	−	0.995747i	$-0.470634\pi$
$839$	26.3124	−	45.5744i	0.908406	−	1.57340i	0.816279	−	0.577657i	$-0.196033\pi$
$840$	−4.85097	−	5.48612i	−0.167374	−	0.189289i
$841$	11.5762	−	20.0505i	0.399179	−	0.691398i
$842$	6.68879	−	3.86177i	0.230511	−	0.133085i
$843$	−5.80282	+	3.35026i	−0.199860	+	0.115389i
$844$	25.2750			0.870003
$845$		0			0
$846$	−23.6542			−0.813248
$847$	−1.74978	+	1.01023i	−0.0601230	+	0.0347121i
$848$	−60.9992	+	35.2179i	−2.09472	+	1.20939i
$849$	−4.90374	+	8.49353i	−0.168296	+	0.291497i
$850$	−2.21108	+	17.9248i	−0.0758394	+	0.614815i
$851$	12.2120	−	21.1519i	0.418623	−	0.725077i
$852$	−18.3985	−	10.6224i	−0.630321	−	0.363916i
$853$		−	6.31853i		−	0.216342i	−0.994132	−	0.108171i	$-0.965501\pi$
$853$		−	6.31853i		−	0.216342i	0.994132	−	0.108171i	$-0.0344995\pi$
$854$	−1.90668	+	3.30246i	−0.0652452	+	0.113008i
$855$	−9.83301	−	3.29314i	−0.336282	−	0.112623i
$856$	46.9925	+	81.3934i	1.60617	+	2.78197i
$857$		−	0.775746i		−	0.0264990i	−0.999912	−	0.0132495i	$-0.995782\pi$
$857$		−	0.775746i		−	0.0264990i	0.999912	−	0.0132495i	$-0.00421757\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	24.8760	−	74.2774i	0.848265	−	2.53284i
$861$	−1.61213	−	2.79229i	−0.0549411	−	0.0951608i
$862$	−2.06081	−	1.18981i	−0.0701916	−	0.0405252i
$863$		−	19.9208i		−	0.678112i	−0.940766	−	0.339056i	$-0.889892\pi$
$863$		−	19.9208i		−	0.678112i	0.940766	−	0.339056i	$-0.110108\pi$
$864$	−22.1368	+	38.3421i	−0.753110	+	1.30442i
$865$	56.0704	−	11.3913i	1.90645	−	0.387316i
$866$	67.5487			2.29540
$867$	−6.32457	−	3.65149i	−0.214794	−	0.124011i
$868$	19.0314	−	10.9878i	0.645968	−	0.372950i
$869$	−4.15633	−	7.19897i	−0.140994	−	0.244208i
$870$	5.21440	−	4.61071i	0.176785	−	0.156318i
$871$		0			0
$872$			80.9544i			2.74146i
$873$	4.49299	−	2.59403i	0.152065	−	0.0877946i
$874$	−14.5217	−	25.1524i	−0.491205	−	0.850793i
$875$	0.699528	+	8.98487i	0.0236484	+	0.303744i
$876$	−29.1998			−0.986570
$877$	19.1719	+	11.0689i	0.647388	+	0.373770i	0.787455	−	0.616372i	$-0.211398\pi$
$877$	19.1719	+	11.0689i	0.647388	+	0.373770i	−0.140067	+	0.990142i	$0.544732\pi$
$878$	−66.7495	−	38.5379i	−2.25269	−	1.30059i
$879$	−2.58910			−0.0873283
$880$	−20.0834	−	98.8549i	−0.677012	−	3.33240i
$881$	−1.11577	−	1.93258i	−0.0375914	−	0.0651102i	0.846618	−	0.532202i	$-0.178635\pi$
$881$	−1.11577	−	1.93258i	−0.0375914	−	0.0651102i	−0.884209	+	0.467092i	$0.845302\pi$
$882$	−40.7291	+	23.5149i	−1.37142	+	0.791789i
$883$			4.30440i			0.144855i	0.997374	+	0.0724273i	$0.0230745\pi$
$883$			4.30440i			0.144855i	−0.997374	+	0.0724273i	$0.976925\pi$
$884$		0			0
$885$	−4.26774	−	4.82653i	−0.143459	−	0.162242i
$886$	49.4638	+	85.6739i	1.66177	+	2.87827i
$887$	13.7984	−	7.96651i	0.463305	−	0.267489i	−0.250128	−	0.968213i	$-0.580473\pi$
$887$	13.7984	−	7.96651i	0.463305	−	0.267489i	0.713433	+	0.700723i	$0.247139\pi$
$888$	−13.2599	−	7.65562i	−0.444974	−	0.256906i
$889$	−3.46168			−0.116101
$890$	−16.2715	+	3.30573i	−0.545421	+	0.110808i
$891$	−12.8072	+	22.1828i	−0.429059	+	0.743152i
$892$		−	128.432i		−	4.30022i
$893$	−4.63346	−	2.67513i	−0.155053	−	0.0895198i
$894$	7.30536	+	12.6532i	0.244328	+	0.423188i
$895$	−25.7110	−	8.61078i	−0.859423	−	0.287827i
$896$	13.3561			0.446197
$897$		0			0
$898$			33.9365i			1.13248i
$899$	6.39280	+	11.0727i	0.213212	+	0.369294i
$900$	65.7168	−	27.8517i	2.19056	−	0.928390i
$901$	3.87399	−	6.70995i	0.129061	−	0.223541i
$902$		−	81.7255i		−	2.72116i
$903$	−2.28211	−	1.31757i	−0.0759438	−	0.0438461i
$904$	−2.42548	+	4.20106i	−0.0806704	+	0.139725i
$905$	4.57452	−	4.04491i	0.152062	−	0.134457i
$906$	9.00294	−	15.5935i	0.299103	−	0.518061i
$907$	−44.9542	+	25.9543i	−1.49268	+	0.861798i	−0.999965	−	0.00839339i	$-0.997328\pi$
$907$	−44.9542	+	25.9543i	−1.49268	+	0.861798i	−0.492713	+	0.870192i	$0.663995\pi$
$908$	44.4546	−	25.6659i	1.47528	−	0.851751i
$909$	29.0668			0.964085
$910$		0			0
$911$	−9.67750			−0.320630			−0.160315	−	0.987066i	$-0.551251\pi$
$911$	−9.67750			−0.320630			−0.160315	+	0.987066i	$0.551251\pi$
$912$	−8.56885	+	4.94723i	−0.283743	+	0.163819i
$913$	12.2335	−	7.06300i	0.404869	−	0.233751i
$914$	−33.5052	+	58.0327i	−1.10825	+	1.91955i
$915$	1.26045	+	1.42548i	0.0416692	+	0.0471251i
$916$	13.7938	−	23.8916i	0.455761	−	0.789402i
$917$	−0.583853	−	0.337088i	−0.0192805	−	0.0111316i
$918$		−	10.0263i		−	0.330919i
$919$	6.77575	−	11.7359i	0.223511	−	0.387133i	−0.732361	−	0.680917i	$-0.761581\pi$
$919$	6.77575	−	11.7359i	0.223511	−	0.387133i	0.955872	+	0.293784i	$0.0949147\pi$
$920$	116.033	+	38.8603i	3.82550	+	1.28119i
$921$	4.61213	+	7.98844i	0.151975	+	0.263228i
$922$		−	98.6780i		−	3.24979i
$923$		0			0
$924$	−7.35026			−0.241806
$925$	7.35254	+	17.3485i	0.241750	+	0.570416i
$926$	52.1905	+	90.3967i	1.71509	+	2.97062i
$927$	36.8464	+	21.2733i	1.21019	+	0.698706i
$928$			38.5705i			1.26614i
$929$	4.72496	−	8.18387i	0.155021	−	0.268504i	−0.778046	−	0.628208i	$-0.783789\pi$
$929$	4.72496	−	8.18387i	0.155021	−	0.268504i	0.933067	+	0.359704i	$0.117122\pi$
$930$	−3.02997	−	14.9141i	−0.0993565	−	0.489054i
$931$	−10.6375			−0.348631
$932$	48.0540	+	27.7440i	1.57406	+	0.908785i
$933$	−10.5226	+	6.07522i	−0.344494	+	0.198894i
$934$	−43.8312	−	75.9179i	−1.43420	−	2.48411i
$935$	7.35026	+	8.31265i	0.240379	+	0.271853i
$936$		0			0
$937$			16.0409i			0.524035i	0.965063	+	0.262017i	$0.0843877\pi$
$937$			16.0409i			0.524035i	−0.965063	+	0.262017i	$0.915612\pi$
$938$	18.4772	−	10.6678i	0.603303	−	0.348317i
$939$	−0.676545	−	1.17181i	−0.0220782	−	0.0382406i
$940$	36.0885	−	7.33176i	1.17708	−	0.239136i
$941$	21.6747			0.706574			0.353287	−	0.935515i	$-0.385064\pi$
$941$	21.6747			0.706574			0.353287	+	0.935515i	$0.385064\pi$
$942$	−3.09440	−	1.78655i	−0.100821	−	0.0582090i
$943$	46.6579	+	26.9380i	1.51939	+	0.877220i
$944$	73.5002			2.39223
$945$	−0.996072	−	4.90288i	−0.0324022	−	0.159491i
$946$	−33.3967	−	57.8448i	−1.08582	−	1.88070i
$947$	4.01072	−	2.31559i	0.130331	−	0.0752466i	−0.433417	−	0.901193i	$-0.642692\pi$
$947$	4.01072	−	2.31559i	0.130331	−	0.0752466i	0.563748	+	0.825947i	$0.309359\pi$
$948$		−	5.61213i		−	0.182273i
$949$		0			0
$950$	22.2374	+	2.74306i	0.721477	+	0.0889966i
$951$	5.71862	+	9.90494i	0.185439	+	0.321190i
$952$	−7.95874	+	4.59498i	−0.257944	+	0.148924i
$953$	22.7748	+	13.1490i	0.737748	+	0.425939i	0.821250	−	0.570569i	$-0.193277\pi$
$953$	22.7748	+	13.1490i	0.737748	+	0.425939i	−0.0835021	+	0.996508i	$0.526611\pi$
$954$	−42.4965			−1.37587
$955$	−9.18210	−	45.1963i	−0.297126	−	1.46252i
$956$	−30.5816	+	52.9689i	−0.989079	+	1.71314i
$957$		−	4.27645i		−	0.138238i
$958$	39.0947	+	22.5713i	1.26309	+	0.729247i
$959$	−6.02047	−	10.4278i	−0.194411	−	0.336730i
$960$	6.19117	−	18.4862i	0.199819	−	0.596641i
$961$	−3.04491			−0.0982228
$962$		0			0
$963$			30.8155i			0.993014i
$964$	73.8007	+	127.827i	2.37696	+	4.11702i
$965$	15.4725	−	46.1994i	0.498077	−	1.48721i
$966$	3.36248	−	5.82399i	0.108186	−	0.187384i
$967$			11.9405i			0.383981i	0.981397	+	0.191990i	$0.0614942\pi$
$967$			11.9405i			0.383981i	−0.981397	+	0.191990i	$0.938506\pi$
$968$	−18.3291	−	10.5823i	−0.589118	−	0.340128i
$969$	0.544198	−	0.942579i	0.0174822	−	0.0302800i
$970$	−8.39772	+	7.42548i	−0.269635	+	0.238418i
$971$	−15.0762	+	26.1127i	−0.483818	+	0.837997i	−0.999827	−	0.0185861i	$-0.994084\pi$
$971$	−15.0762	+	26.1127i	−0.483818	+	0.837997i	0.516010	+	0.856583i	$0.327417\pi$
$972$	−52.1617	+	30.1155i	−1.67309	+	0.965957i
$973$	−5.89079	+	3.40105i	−0.188850	+	0.109033i
$974$	24.7308			0.792427
$975$		0			0
$976$	−21.7078			−0.694850
$977$	−23.3239	+	13.4660i	−0.746196	+	0.430817i	−0.824318	−	0.566127i	$-0.808441\pi$
$977$	−23.3239	+	13.4660i	−0.746196	+	0.430817i	0.0781216	+	0.996944i	$0.475108\pi$
$978$	2.48772	−	1.43629i	0.0795487	−	0.0459274i
$979$	−5.10062	+	8.83453i	−0.163016	+	0.282353i
$980$	54.8505	−	48.5002i	1.75214	−	1.54928i
$981$	−13.2715	+	22.9870i	−0.423727	+	0.733917i
$982$	−59.6556	−	34.4422i	−1.90369	−	1.09909i
$983$		−	20.5902i		−	0.656727i	−0.944551	−	0.328363i	$-0.893503\pi$
$983$		−	20.5902i		−	0.656727i	0.944551	−	0.328363i	$-0.106497\pi$
$984$	16.8872	−	29.2494i	0.538343	−	0.932438i
$985$	1.42022	−	4.24063i	0.0452519	−	0.135118i
$986$	−4.36741	−	7.56457i	−0.139087	−	0.240905i
$987$		−	1.23884i		−	0.0394328i
$988$		0			0
$989$	44.0322			1.40014
$990$	19.3277	−	57.7106i	0.614274	−	1.83416i
$991$	24.0689	+	41.6885i	0.764573	+	1.32428i	0.940472	+	0.339871i	$0.110384\pi$
$991$	24.0689	+	41.6885i	0.764573	+	1.32428i	−0.175899	+	0.984408i	$0.556283\pi$
$992$	73.0342	+	42.1663i	2.31884	+	1.33878i
$993$			5.67864i			0.180206i
$994$	−9.23155	+	15.9895i	−0.292807	+	0.507156i
$995$	−7.45746	−	36.7072i	−0.236417	−	1.16370i
$996$	9.53690			0.302188
$997$	−28.9473	−	16.7127i	−0.916771	−	0.529298i	−0.0341674	−	0.999416i	$-0.510878\pi$
$997$	−28.9473	−	16.7127i	−0.916771	−	0.529298i	−0.882603	+	0.470118i	$0.844211\pi$
$998$	64.1769	−	37.0525i	2.03148	−	1.17288i
$999$	−5.23013	−	9.05886i	−0.165474	−	0.286610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.g.484.1		12
5.4	even	2	inner	845.2.n.g.484.6		12
13.2	odd	12		845.2.d.a.844.2		6
13.3	even	3		845.2.b.c.339.1		6
13.4	even	6		845.2.n.f.529.1		12
13.5	odd	4		845.2.l.e.699.6		12
13.6	odd	12		845.2.l.e.654.5		12
13.7	odd	12		845.2.l.d.654.1		12
13.8	odd	4		845.2.l.d.699.2		12
13.9	even	3	inner	845.2.n.g.529.6		12
13.10	even	6		65.2.b.a.14.6	yes	6
13.11	odd	12		845.2.d.b.844.6		6
13.12	even	2		845.2.n.f.484.6		12
39.23	odd	6		585.2.c.b.469.1		6
52.23	odd	6		1040.2.d.c.209.3		6
65.3	odd	12		4225.2.a.ba.1.1		3
65.4	even	6		845.2.n.f.529.6		12
65.9	even	6	inner	845.2.n.g.529.1		12
65.19	odd	12		845.2.l.d.654.2		12
65.23	odd	12		325.2.a.k.1.3		3
65.24	odd	12		845.2.d.a.844.1		6
65.29	even	6		845.2.b.c.339.6		6
65.34	odd	4		845.2.l.e.699.5		12
65.42	odd	12		4225.2.a.bh.1.3		3
65.44	odd	4		845.2.l.d.699.1		12
65.49	even	6		65.2.b.a.14.1	✓	6
65.54	odd	12		845.2.d.b.844.5		6
65.59	odd	12		845.2.l.e.654.6		12
65.62	odd	12		325.2.a.j.1.1		3
65.64	even	2		845.2.n.f.484.1		12
195.23	even	12		2925.2.a.bf.1.1		3
195.62	even	12		2925.2.a.bj.1.3		3
195.179	odd	6		585.2.c.b.469.6		6
260.23	even	12		5200.2.a.cb.1.3		3
260.127	even	12		5200.2.a.cj.1.1		3
260.179	odd	6		1040.2.d.c.209.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	65.49	even	6
65.2.b.a.14.6	yes	6	13.10	even	6
325.2.a.j.1.1		3	65.62	odd	12
325.2.a.k.1.3		3	65.23	odd	12
585.2.c.b.469.1		6	39.23	odd	6
585.2.c.b.469.6		6	195.179	odd	6
845.2.b.c.339.1		6	13.3	even	3
845.2.b.c.339.6		6	65.29	even	6
845.2.d.a.844.1		6	65.24	odd	12
845.2.d.a.844.2		6	13.2	odd	12
845.2.d.b.844.5		6	65.54	odd	12
845.2.d.b.844.6		6	13.11	odd	12
845.2.l.d.654.1		12	13.7	odd	12
845.2.l.d.654.2		12	65.19	odd	12
845.2.l.d.699.1		12	65.44	odd	4
845.2.l.d.699.2		12	13.8	odd	4
845.2.l.e.654.5		12	13.6	odd	12
845.2.l.e.654.6		12	65.59	odd	12
845.2.l.e.699.5		12	65.34	odd	4
845.2.l.e.699.6		12	13.5	odd	4
845.2.n.f.484.1		12	65.64	even	2
845.2.n.f.484.6		12	13.12	even	2
845.2.n.f.529.1		12	13.4	even	6
845.2.n.f.529.6		12	65.4	even	6
845.2.n.g.484.1		12	1.1	even	1	trivial
845.2.n.g.484.6		12	5.4	even	2	inner
845.2.n.g.529.1		12	65.9	even	6	inner
845.2.n.g.529.6		12	13.9	even	3	inner
1040.2.d.c.209.3		6	52.23	odd	6
1040.2.d.c.209.4		6	260.179	odd	6
2925.2.a.bf.1.1		3	195.23	even	12
2925.2.a.bj.1.3		3	195.62	even	12
4225.2.a.ba.1.1		3	65.3	odd	12
4225.2.a.bh.1.3		3	65.42	odd	12
5200.2.a.cb.1.3		3	260.23	even	12
5200.2.a.cj.1.1		3	260.127	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.31673 + 1.33757i) q^{2} +(0.416726 - 0.240597i) q^{3} +(2.57816 - 4.46551i) q^{4} +(-1.67513 + 1.48119i) q^{5} +(-0.643629 + 1.11480i) q^{6} +(0.698071 + 0.403032i) q^{7} +8.44358i q^{8} +(-1.38423 + 2.39755i) q^{9} +(1.89963 - 5.67213i) q^{10} +(-1.83757 - 3.18276i) q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.341700 + 1.02028i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(1.16936 + 0.675131i) q^{17} -7.40597i q^{18} +(0.837565 - 1.45071i) q^{19} +(2.29553 + 11.2991i) q^{20} +0.387873 q^{21} +(8.51429 + 4.91573i) q^{22} +(-5.61288 + 3.24060i) q^{23} +(2.03150 + 3.51866i) q^{24} +(0.612127 - 4.96239i) q^{25} +2.77575i q^{27} +(3.59948 - 2.07816i) q^{28} +(1.20910 + 2.09421i) q^{29} +(-0.573070 - 2.82077i) q^{30} +5.28726 q^{31} +(13.8133 + 7.97508i) q^{32} +(-1.53152 - 0.884226i) q^{33} -3.61213 q^{34} +(-1.76633 + 0.358849i) q^{35} +(7.13752 + 12.3625i) q^{36} +(-3.26358 + 1.88423i) q^{37} +4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +(-4.15633 - 7.19897i) q^{41} +(-0.898598 + 0.518806i) q^{42} +(-5.88364 - 3.39692i) q^{43} -18.9502 q^{44} +(-1.23248 - 6.06652i) q^{45} +(8.66902 - 15.0152i) q^{46} -3.19394i q^{47} +(-5.11533 - 2.95334i) q^{48} +(-3.17513 - 5.49949i) q^{49} +(5.21939 + 12.3153i) q^{50} +0.649738 q^{51} -5.73813i q^{53} +(-3.71274 - 6.43066i) q^{54} +(7.79244 + 2.60974i) q^{55} +(-3.40303 + 5.89422i) q^{56} -0.806063i q^{57} +(-5.60230 - 3.23449i) q^{58} +(-2.99389 + 5.18557i) q^{59} +(3.67513 + 4.15633i) q^{60} +(0.884226 - 1.53152i) q^{61} +(-12.2492 + 7.07205i) q^{62} +(-1.93258 + 1.11577i) q^{63} -18.1187 q^{64} +4.73084 q^{66} +(-8.56885 + 4.94723i) q^{67} +(6.02961 - 3.48119i) q^{68} +(-1.55936 + 2.70089i) q^{69} +(3.61213 - 3.19394i) q^{70} +(4.28115 - 7.41517i) q^{71} +(-20.2439 - 11.6878i) q^{72} -11.7685i q^{73} +(5.04055 - 8.73049i) q^{74} +(-0.938847 - 2.21523i) q^{75} +(-4.31876 - 7.48031i) q^{76} -2.96239i q^{77} +2.26187 q^{79} +(26.0270 + 8.71661i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(19.2582 + 11.1187i) q^{82} +3.84367i q^{83} +(1.00000 - 1.73205i) q^{84} +(-2.95883 + 0.601118i) q^{85} +18.1744 q^{86} +(1.00772 + 0.581810i) q^{87} +(26.8739 - 15.5156i) q^{88} +(-1.38787 - 2.40387i) q^{89} +(10.9697 + 12.4060i) q^{90} +33.4191i q^{92} +(2.20334 - 1.27210i) q^{93} +(4.27210 + 7.39949i) q^{94} +(0.745746 + 3.67072i) q^{95} +7.67513 q^{96} +(-1.62292 - 0.936996i) q^{97} +(14.7119 + 8.49389i) q^{98} +10.1744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} + 4 q^{6} + 6 q^{9} - 2 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{15} - 10 q^{16} - 20 q^{20} + 8 q^{21} + 16 q^{24} + 4 q^{25} + 12 q^{29} - 8 q^{30} + 40 q^{31} - 40 q^{34} - 8 q^{35} + 22 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 + 4 * q^6 + 6 * q^9 - 2 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^15 - 10 * q^16 - 20 * q^20 + 8 * q^21 + 16 * q^24 + 4 * q^25 + 12 * q^29 - 8 * q^30 + 40 * q^31 - 40 * q^34 - 8 * q^35 + 22 * q^36 - 68 * q^40 - 8 * q^41 - 80 * q^44 - 4 * q^45 + 32 * q^46 - 18 * q^49 + 16 * q^50 + 48 * q^51 - 68 * q^54 + 16 * q^55 - 40 * q^56 + 16 * q^59 + 24 * q^60 - 12 * q^61 - 132 * q^64 - 32 * q^66 + 24 * q^69 + 40 * q^70 - 24 * q^71 - 4 * q^74 - 16 * q^75 - 20 * q^76 + 64 * q^79 + 48 * q^80 - 46 * q^81 + 12 * q^84 - 12 * q^85 + 64 * q^86 - 20 * q^89 + 140 * q^90 + 32 * q^94 - 16 * q^95 + 72 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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