LMFDB - Embedded newform 845.2.b.d.339.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(339,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("845.339");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.49843600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} + 10x^{2} + 1 $ x^6 + 8x^4 + 10x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.3
Root			$-0.330837i$ of defining polynomial
Character	$\chi$	$=$	845.339
Dual form			845.2.b.d.339.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.330837i q^{2} -2.69180i q^{3} +1.89055 q^{4} +(-2.12291 - 0.702335i) q^{5} -0.890547 q^{6} -3.35348i q^{7} -1.28714i q^{8} -4.24581 q^{9} +O(q^{10})$	\(q-0.330837i q^{2} -2.69180i q^{3} +1.89055 q^{4} +(-2.12291 - 0.702335i) q^{5} -0.890547 q^{6} -3.35348i q^{7} -1.28714i q^{8} -4.24581 q^{9} +(-0.232358 + 0.702335i) q^{10} -3.24581 q^{11} -5.08898i q^{12} -1.10945 q^{14} +(-1.89055 + 5.71445i) q^{15} +3.35526 q^{16} +1.94881i q^{17} +1.40467i q^{18} +1.24581 q^{19} +(-4.01345 - 1.32780i) q^{20} -9.02690 q^{21} +1.07383i q^{22} +2.69180i q^{23} -3.46472 q^{24} +(4.01345 + 2.98198i) q^{25} +3.35348i q^{27} -6.33991i q^{28} -3.00000 q^{29} +(1.89055 + 0.625462i) q^{30} +3.78109 q^{31} -3.68431i q^{32} +8.73709i q^{33} +0.644737 q^{34} +(-2.35526 + 7.11911i) q^{35} -8.02690 q^{36} -1.94881i q^{37} -0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +2.78109 q^{41} +2.98643i q^{42} -8.73709i q^{43} -6.13636 q^{44} +(9.01345 + 2.98198i) q^{45} +0.890547 q^{46} +6.86960i q^{47} -9.03171i q^{48} -4.24581 q^{49} +(0.986548 - 1.32780i) q^{50} +5.24581 q^{51} -12.8336i q^{53} +1.10945 q^{54} +(6.89055 + 2.27964i) q^{55} -4.31638 q^{56} -3.35348i q^{57} +0.992510i q^{58} +2.53528 q^{59} +(-3.57417 + 10.8034i) q^{60} -7.49162 q^{61} -1.25092i q^{62} +14.2382i q^{63} +5.49162 q^{64} +2.89055 q^{66} +4.01515i q^{67} +3.68431i q^{68} +7.24581 q^{69} +(2.35526 + 0.779207i) q^{70} +5.24581 q^{71} +5.46493i q^{72} -5.46493i q^{73} -0.644737 q^{74} +(8.02690 - 10.8034i) q^{75} +2.35526 q^{76} +10.8848i q^{77} -13.7811 q^{79} +(-7.12291 - 2.35652i) q^{80} -3.71053 q^{81} -0.920088i q^{82} +8.61955i q^{83} -17.0658 q^{84} +(1.36872 - 4.13713i) q^{85} -2.89055 q^{86} +8.07541i q^{87} +4.17780i q^{88} -10.3164 q^{89} +(0.986548 - 2.98198i) q^{90} +5.08898i q^{92} -10.1780i q^{93} +2.27271 q^{94} +(-2.64474 - 0.874976i) q^{95} -9.91745 q^{96} +5.26607i q^{97} +1.40467i q^{98} +13.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9	$ 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9} - 7 q^{10} - 22 q^{14} + 4 q^{15} + 16 q^{16} - 12 q^{19} + q^{20} - 4 q^{21} - 32 q^{24} - q^{25} - 18 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{36} + 35 q^{40} - 14 q^{41} - 2 q^{44} + 29 q^{45} - 10 q^{46} - 6 q^{49} + 31 q^{50} + 12 q^{51} + 22 q^{54} + 26 q^{55} + 16 q^{56} + 4 q^{59} - 48 q^{60} - 6 q^{61} - 6 q^{64} + 2 q^{66} + 24 q^{69} + 10 q^{70} + 12 q^{71} - 8 q^{74} - 2 q^{75} + 10 q^{76} - 52 q^{79} - 33 q^{80} - 14 q^{81} - 90 q^{84} - 21 q^{85} - 2 q^{86} - 20 q^{89} + 31 q^{90} - 56 q^{94} - 20 q^{95} + 6 q^{96} + 52 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9 - 7 * q^10 - 22 * q^14 + 4 * q^15 + 16 * q^16 - 12 * q^19 + q^20 - 4 * q^21 - 32 * q^24 - q^25 - 18 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^36 + 35 * q^40 - 14 * q^41 - 2 * q^44 + 29 * q^45 - 10 * q^46 - 6 * q^49 + 31 * q^50 + 12 * q^51 + 22 * q^54 + 26 * q^55 + 16 * q^56 + 4 * q^59 - 48 * q^60 - 6 * q^61 - 6 * q^64 + 2 * q^66 + 24 * q^69 + 10 * q^70 + 12 * q^71 - 8 * q^74 - 2 * q^75 + 10 * q^76 - 52 * q^79 - 33 * q^80 - 14 * q^81 - 90 * q^84 - 21 * q^85 - 2 * q^86 - 20 * q^89 + 31 * q^90 - 56 * q^94 - 20 * q^95 + 6 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.330837i		−	0.233937i	−0.993136	−	0.116968i	$-0.962682\pi$
$2$		−	0.330837i		−	0.233937i	0.993136	−	0.116968i	$-0.0373176\pi$
$3$		−	2.69180i		−	1.55411i	−0.629430	−	0.777057i	$-0.716712\pi$
$3$		−	2.69180i		−	1.55411i	0.629430	−	0.777057i	$-0.283288\pi$
$4$	1.89055			0.945274
$5$	−2.12291	−	0.702335i	−0.949392	−	0.314094i
$5$	−2.12291	−	0.702335i	−0.949392	−	0.314094i
$6$	−0.890547			−0.363564
$7$		−	3.35348i		−	1.26750i	−0.773540	−	0.633748i	$-0.781516\pi$
$7$		−	3.35348i		−	1.26750i	0.773540	−	0.633748i	$-0.218484\pi$
$8$		−	1.28714i		−	0.455071i
$9$	−4.24581			−1.41527
$10$	−0.232358	+	0.702335i	−0.0734780	+	0.222098i
$11$	−3.24581			−0.978649			−0.489324	−	0.872102i	$-0.662757\pi$
$11$	−3.24581			−0.978649			−0.489324	+	0.872102i	$0.662757\pi$
$12$		−	5.08898i		−	1.46906i
$13$		0			0
$13$		0			0
$14$	−1.10945			−0.296514
$15$	−1.89055	+	5.71445i	−0.488137	+	1.47546i
$16$	3.35526			0.838816
$17$			1.94881i			0.472655i	0.971673	+	0.236328i	$0.0759439\pi$
$17$			1.94881i			0.472655i	−0.971673	+	0.236328i	$0.924056\pi$
$18$			1.40467i			0.331084i
$19$	1.24581			0.285808			0.142904	−	0.989737i	$-0.454356\pi$
$19$	1.24581			0.285808			0.142904	+	0.989737i	$0.454356\pi$
$20$	−4.01345	−	1.32780i	−0.897435	−	0.296904i
$21$	−9.02690			−1.96983
$22$			1.07383i			0.228942i
$23$			2.69180i			0.561280i	0.959813	+	0.280640i	$0.0905467\pi$
$23$			2.69180i			0.561280i	−0.959813	+	0.280640i	$0.909453\pi$
$24$	−3.46472			−0.707232
$25$	4.01345	+	2.98198i	0.802690	+	0.596396i
$26$		0			0
$27$			3.35348i			0.645377i
$28$		−	6.33991i		−	1.19813i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	1.89055	+	0.625462i	0.345165	+	0.114193i
$31$	3.78109			0.679105			0.339552	−	0.940587i	$-0.389724\pi$
$31$	3.78109			0.679105			0.339552	+	0.940587i	$0.389724\pi$
$32$		−	3.68431i		−	0.651301i
$33$			8.73709i			1.52093i
$34$	0.644737			0.110571
$35$	−2.35526	+	7.11911i	−0.398112	+	1.20335i
$36$	−8.02690			−1.33782
$37$		−	1.94881i		−	0.320382i	−0.987086	−	0.160191i	$-0.948789\pi$
$37$		−	1.94881i		−	0.320382i	0.987086	−	0.160191i	$-0.0512110\pi$
$38$		−	0.412160i		−	0.0668611i
$39$		0			0
$40$	−0.904000	+	2.73247i	−0.142935	+	0.432041i
$41$	2.78109			0.434334			0.217167	−	0.976134i	$-0.430318\pi$
$41$	2.78109			0.434334			0.217167	+	0.976134i	$0.430318\pi$
$42$			2.98643i			0.460816i
$43$		−	8.73709i		−	1.33239i	−0.745776	−	0.666197i	$-0.767921\pi$
$43$		−	8.73709i		−	1.33239i	0.745776	−	0.666197i	$-0.232079\pi$
$44$	−6.13636			−0.925091
$45$	9.01345	+	2.98198i	1.34365	+	0.444527i
$46$	0.890547			0.131304
$47$			6.86960i			1.00203i	0.865437	+	0.501017i	$0.167041\pi$
$47$			6.86960i			1.00203i	−0.865437	+	0.501017i	$0.832959\pi$
$48$		−	9.03171i		−	1.30362i
$49$	−4.24581			−0.606544
$50$	0.986548	−	1.32780i	0.139519	−	0.187779i
$51$	5.24581			0.734560
$52$		0			0
$53$		−	12.8336i		−	1.76282i	−0.472347	−	0.881412i	$-0.656593\pi$
$53$		−	12.8336i		−	1.76282i	0.472347	−	0.881412i	$-0.343407\pi$
$54$	1.10945			0.150977
$55$	6.89055	+	2.27964i	0.929121	+	0.307387i
$56$	−4.31638			−0.576800
$57$		−	3.35348i		−	0.444179i
$58$			0.992510i			0.130323i
$59$	2.53528			0.330066			0.165033	−	0.986288i	$-0.447227\pi$
$59$	2.53528			0.330066			0.165033	+	0.986288i	$0.447227\pi$
$60$	−3.57417	+	10.8034i	−0.461423	+	1.39472i
$61$	−7.49162			−0.959204			−0.479602	−	0.877486i	$-0.659219\pi$
$61$	−7.49162			−0.959204			−0.479602	+	0.877486i	$0.659219\pi$
$62$		−	1.25092i		−	0.158868i
$63$			14.2382i			1.79385i
$64$	5.49162			0.686453
$65$		0			0
$66$	2.89055			0.355802
$67$			4.01515i			0.490529i	0.969456	+	0.245264i	$0.0788748\pi$
$67$			4.01515i			0.490529i	−0.969456	+	0.245264i	$0.921125\pi$
$68$			3.68431i			0.446789i
$69$	7.24581			0.872293
$70$	2.35526	+	0.779207i	0.281508	+	0.0931331i
$71$	5.24581			0.622563			0.311282	−	0.950318i	$-0.399242\pi$
$71$	5.24581			0.622563			0.311282	+	0.950318i	$0.399242\pi$
$72$			5.46493i			0.644048i
$73$		−	5.46493i		−	0.639622i	−0.947481	−	0.319811i	$-0.896381\pi$
$73$		−	5.46493i		−	0.639622i	0.947481	−	0.319811i	$-0.103619\pi$
$74$	−0.644737			−0.0749491
$75$	8.02690	−	10.8034i	0.926867	−	1.24747i
$76$	2.35526			0.270167
$77$			10.8848i			1.24043i
$78$		0			0
$79$	−13.7811			−1.55049			−0.775247	−	0.631658i	$-0.782375\pi$
$79$	−13.7811			−1.55049			−0.775247	+	0.631658i	$0.782375\pi$
$80$	−7.12291	−	2.35652i	−0.796365	−	0.263467i
$81$	−3.71053			−0.412281
$82$		−	0.920088i		−	0.101607i
$83$			8.61955i			0.946119i	0.881031	+	0.473059i	$0.156850\pi$
$83$			8.61955i			0.946119i	−0.881031	+	0.473059i	$0.843150\pi$
$84$	−17.0658			−1.86203
$85$	1.36872	−	4.13713i	0.148458	−	0.448735i
$86$	−2.89055			−0.311696
$87$			8.07541i			0.865775i
$88$			4.17780i			0.445355i
$89$	−10.3164			−1.09353			−0.546767	−	0.837285i	$-0.684142\pi$
$89$	−10.3164			−1.09353			−0.546767	+	0.837285i	$0.684142\pi$
$90$	0.986548	−	2.98198i	0.103991	−	0.314328i
$91$		0			0
$92$			5.08898i			0.530563i
$93$		−	10.1780i		−	1.05541i
$94$	2.27271			0.234413
$95$	−2.64474	−	0.874976i	−0.271344	−	0.0897706i
$96$	−9.91745			−1.01220
$97$			5.26607i			0.534689i	0.963601	+	0.267344i	$0.0861461\pi$
$97$			5.26607i			0.534689i	−0.963601	+	0.267344i	$0.913854\pi$
$98$			1.40467i			0.141893i
$99$	13.7811			1.38505
$100$	7.58762	+	5.63757i	0.758762	+	0.563757i
$101$	5.71053			0.568219			0.284109	−	0.958792i	$-0.408302\pi$
$101$	5.71053			0.568219			0.284109	+	0.958792i	$0.408302\pi$
$102$		−	1.73551i		−	0.171841i
$103$		−	7.36863i		−	0.726052i	−0.931779	−	0.363026i	$-0.881744\pi$
$103$		−	7.36863i		−	0.726052i	0.931779	−	0.363026i	$-0.118256\pi$
$104$		0			0
$105$	19.1633	+	6.33991i	1.87014	+	0.618712i
$106$	−4.24581			−0.412390
$107$		−	8.57444i		−	0.828922i	−0.910067	−	0.414461i	$-0.863970\pi$
$107$		−	8.57444i		−	0.828922i	0.910067	−	0.414461i	$-0.136030\pi$
$108$			6.33991i			0.610058i
$109$	8.49162			0.813350			0.406675	−	0.913573i	$-0.366688\pi$
$109$	8.49162			0.813350			0.406675	+	0.913573i	$0.366688\pi$
$110$	0.754190	−	2.27964i	0.0719092	−	0.217356i
$111$	−5.24581			−0.497910
$112$		−	11.2518i		−	1.06320i
$113$		−	7.33242i		−	0.689776i	−0.938644	−	0.344888i	$-0.887917\pi$
$113$		−	7.33242i		−	0.689776i	0.938644	−	0.344888i	$-0.112083\pi$
$114$	−1.10945			−0.103910
$115$	1.89055	−	5.71445i	0.176294	−	0.532875i
$116$	−5.67164			−0.526599
$117$		0			0
$118$		−	0.838765i		−	0.0772145i
$119$	6.53528			0.599089
$120$	7.35526	+	2.43339i	0.671441	+	0.222137i
$121$	−0.464716			−0.0422469
$122$			2.47850i			0.224393i
$123$		−	7.48616i		−	0.675004i
$124$	7.14834			0.641940
$125$	−6.42583	−	9.14925i	−0.574744	−	0.818333i
$126$	4.71053			0.419647
$127$			9.16369i			0.813146i	0.913618	+	0.406573i	$0.133276\pi$
$127$			9.16369i			0.813146i	−0.913618	+	0.406573i	$0.866724\pi$
$128$		−	9.18546i		−	0.811887i
$129$	−23.5185			−2.07069
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$			16.5179i			1.43770i
$133$		−	4.17780i		−	0.362261i
$134$	1.32836			0.114753
$135$	2.35526	−	7.11911i	0.202709	−	0.612716i
$136$	2.50838			0.215092
$137$		−	16.8487i		−	1.43948i	−0.694242	−	0.719741i	$-0.744260\pi$
$137$		−	16.8487i		−	1.43948i	0.694242	−	0.719741i	$-0.255740\pi$
$138$		−	2.39718i		−	0.204061i
$139$	1.02690			0.0871009			0.0435505	−	0.999051i	$-0.486133\pi$
$139$	1.02690			0.0871009			0.0435505	+	0.999051i	$0.486133\pi$
$140$	−4.45274	+	13.4590i	−0.376325	+	1.13749i
$141$	18.4916			1.55728
$142$		−	1.73551i		−	0.145640i
$143$		0			0
$144$	−14.2458			−1.18715
$145$	6.36872	+	2.10700i	0.528893	+	0.174977i
$146$	−1.80800			−0.149631
$147$			11.4289i			0.942639i
$148$		−	3.68431i		−	0.302849i
$149$	−15.8517			−1.29862			−0.649309	−	0.760524i	$-0.724942\pi$
$149$	−15.8517			−1.29862			−0.649309	+	0.760524i	$0.724942\pi$
$150$	−3.57417	−	2.65559i	−0.291830	−	0.216828i
$151$	14.5454			1.18369			0.591845	−	0.806052i	$-0.298400\pi$
$151$	14.5454			1.18369			0.591845	+	0.806052i	$0.298400\pi$
$152$		−	1.60353i		−	0.130063i
$153$		−	8.27427i		−	0.668935i
$154$	3.60107			0.290183
$155$	−8.02690	−	2.65559i	−0.644736	−	0.213302i
$156$		0			0
$157$		−	10.9210i		−	0.871588i	−0.900047	−	0.435794i	$-0.856468\pi$
$157$		−	10.9210i		−	0.871588i	0.900047	−	0.435794i	$-0.143532\pi$
$158$			4.55929i			0.362718i
$159$	−34.5454			−2.73963
$160$	−2.58762	+	7.82145i	−0.204569	+	0.618340i
$161$	9.02690			0.711420
$162$			1.22758i			0.0964476i
$163$		−	4.17780i		−	0.327230i	−0.986524	−	0.163615i	$-0.947684\pi$
$163$		−	4.17780i		−	0.327230i	0.986524	−	0.163615i	$-0.0523155\pi$
$164$	5.25779			0.410564
$165$	6.13636	−	18.5480i	0.477715	−	1.44396i
$166$	2.85166			0.221332
$167$			3.35348i			0.259500i	0.991547	+	0.129750i	$0.0414175\pi$
$167$			3.35348i			0.259500i	−0.991547	+	0.129750i	$0.958583\pi$
$168$			11.6188i			0.896413i
$169$		0			0
$170$	−1.36872	−	0.452821i	−0.104976	−	0.0347298i
$171$	−5.28947			−0.404496
$172$		−	16.5179i		−	1.25948i
$173$			8.73709i			0.664268i	0.943232	+	0.332134i	$0.107769\pi$
$173$			8.73709i			0.664268i	−0.943232	+	0.332134i	$0.892231\pi$
$174$	2.67164			0.202537
$175$	10.0000	−	13.4590i	0.755929	−	1.01741i
$176$	−10.8905			−0.820906
$177$		−	6.82449i		−	0.512960i
$178$			3.41303i			0.255818i
$179$	18.0101			1.34614			0.673071	−	0.739578i	$-0.264975\pi$
$179$	18.0101			1.34614			0.673071	+	0.739578i	$0.264975\pi$
$180$	17.0404	+	5.63757i	1.27011	+	0.420200i
$181$	1.04366			0.0775749			0.0387875	−	0.999247i	$-0.487650\pi$
$181$	1.04366			0.0775749			0.0387875	+	0.999247i	$0.487650\pi$
$182$		0			0
$183$			20.1660i			1.49071i
$184$	3.46472			0.255422
$185$	−1.36872	+	4.13713i	−0.100630	+	0.304168i
$186$	−3.36724			−0.246898
$187$		−	6.32546i		−	0.462564i
$188$			12.9873i			0.947197i
$189$	11.2458			0.818012
$190$	−0.289474	+	0.874976i	−0.0210006	+	0.0634774i
$191$	25.5185			1.84646			0.923228	−	0.384253i	$-0.125541\pi$
$191$	25.5185			1.84646			0.923228	+	0.384253i	$0.125541\pi$
$192$		−	14.7824i		−	1.06683i
$193$		−	19.8207i		−	1.42672i	−0.700795	−	0.713362i	$-0.747171\pi$
$193$		−	19.8207i		−	1.42672i	0.700795	−	0.713362i	$-0.252829\pi$
$194$	1.74221			0.125083
$195$		0			0
$196$	−8.02690			−0.573350
$197$		−	21.6520i		−	1.54264i	−0.636448	−	0.771319i	$-0.719597\pi$
$197$		−	21.6520i		−	1.54264i	0.636448	−	0.771319i	$-0.280403\pi$
$198$		−	4.55929i		−	0.324015i
$199$	−18.2291			−1.29222			−0.646112	−	0.763243i	$-0.723606\pi$
$199$	−18.2291			−1.29222			−0.646112	+	0.763243i	$0.723606\pi$
$200$	3.83821	−	5.16586i	0.271402	−	0.365281i
$201$	10.8080			0.762337
$202$		−	1.88925i		−	0.132927i
$203$			10.0604i			0.706104i
$204$	9.91745			0.694361
$205$	−5.90400	−	1.95326i	−0.412353	−	0.136422i
$206$	−2.43781			−0.169850
$207$		−	11.4289i		−	0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$	2.09747	−	6.33991i	0.144739	−	0.437495i
$211$	19.2996			1.32864			0.664320	−	0.747448i	$-0.268721\pi$
$211$	19.2996			1.32864			0.664320	+	0.747448i	$0.268721\pi$
$212$		−	24.2624i		−	1.66635i
$213$		−	14.1207i		−	0.967534i
$214$	−2.83674			−0.193915
$215$	−6.13636	+	18.5480i	−0.418496	+	1.26496i
$216$	4.31638			0.293692
$217$		−	12.6798i		−	0.860762i
$218$		−	2.80934i		−	0.190272i
$219$	−14.7105			−0.994045
$220$	13.0269	+	4.30978i	0.878274	+	0.290565i
$221$		0			0
$222$			1.73551i			0.116480i
$223$			12.3707i			0.828406i	0.910184	+	0.414203i	$0.135940\pi$
$223$			12.3707i			0.828406i	−0.910184	+	0.414203i	$0.864060\pi$
$224$	−12.3553			−0.825521
$225$	−17.0404	−	12.6609i	−1.13602	−	0.844061i
$226$	−2.42583			−0.161364
$227$			6.16282i			0.409040i	0.978862	+	0.204520i	$0.0655634\pi$
$227$			6.16282i			0.409040i	−0.978862	+	0.204520i	$0.934437\pi$
$228$		−	6.33991i		−	0.419871i
$229$	26.9832			1.78310			0.891551	−	0.452920i	$-0.149618\pi$
$229$	26.9832			1.78310			0.891551	+	0.452920i	$0.149618\pi$
$230$	−1.89055	−	0.625462i	−0.124659	−	0.0412417i
$231$	29.2996			1.92777
$232$			3.86141i			0.253514i
$233$			0.824319i			0.0540029i	0.999635	+	0.0270015i	$0.00859588\pi$
$233$			0.824319i			0.0540029i	−0.999635	+	0.0270015i	$0.991404\pi$
$234$		0			0
$235$	4.82476	−	14.5835i	0.314733	−	0.951323i
$236$	4.79307			0.312003
$237$			37.0960i			2.40964i
$238$		−	2.16211i		−	0.140149i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−6.34328	+	19.1735i	−0.409457	+	1.23764i
$241$	22.6938			1.46183			0.730917	−	0.682466i	$-0.239093\pi$
$241$	22.6938			1.46183			0.730917	+	0.682466i	$0.239093\pi$
$242$			0.153745i			0.00988310i
$243$			20.0484i			1.28611i
$244$	−14.1633			−0.906710
$245$	9.01345	+	2.98198i	0.575848	+	0.190512i
$246$	−2.47670			−0.157908
$247$		0			0
$248$		−	4.86678i		−	0.309041i
$249$	23.2021			1.47038
$250$	−3.02690	+	2.12590i	−0.191438	+	0.134454i
$251$	19.0269			1.20097			0.600484	−	0.799637i	$-0.294975\pi$
$251$	19.0269			1.20097			0.600484	+	0.799637i	$0.294975\pi$
$252$			26.9180i			1.69568i
$253$		−	8.73709i		−	0.549296i
$254$	3.03168			0.190225
$255$	−11.1364	−	3.68431i	−0.697386	−	0.230721i
$256$	7.94436			0.496522
$257$			2.11145i			0.131709i	0.997829	+	0.0658544i	$0.0209773\pi$
$257$			2.11145i			0.131709i	−0.997829	+	0.0658544i	$0.979023\pi$
$258$			7.78079i			0.484411i
$259$	−6.53528			−0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$		−	3.30837i		−	0.204391i
$263$			29.9173i			1.84478i	0.386257	+	0.922391i	$0.373768\pi$
$263$			29.9173i			1.84478i	−0.386257	+	0.922391i	$0.626232\pi$
$264$	11.2458			0.692132
$265$	−9.01345	+	27.2444i	−0.553692	+	1.67361i
$266$	−1.38217			−0.0847461
$267$			27.7697i			1.69948i
$268$			7.59083i			0.463684i
$269$	−18.5891			−1.13340			−0.566699	−	0.823925i	$-0.691780\pi$
$269$	−18.5891			−1.13340			−0.566699	+	0.823925i	$0.691780\pi$
$270$	−2.35526	−	0.779207i	−0.143337	−	0.0474210i
$271$	5.82476			0.353829			0.176914	−	0.984226i	$-0.443388\pi$
$271$	5.82476			0.353829			0.176914	+	0.984226i	$0.443388\pi$
$272$			6.53876i			0.396471i
$273$		0			0
$274$	−5.57417			−0.336748
$275$	−13.0269	−	9.67894i	−0.785552	−	0.583662i
$276$	13.6985			0.824556
$277$			13.5403i			0.813560i	0.913526	+	0.406780i	$0.133349\pi$
$277$			13.5403i			0.813560i	−0.913526	+	0.406780i	$0.866651\pi$
$278$		−	0.339738i		−	0.0203761i
$279$	−16.0538			−0.961116
$280$	9.16326	+	3.03154i	0.547610	+	0.181169i
$281$	−0.464716			−0.0277226			−0.0138613	−	0.999904i	$-0.504412\pi$
$281$	−0.464716			−0.0277226			−0.0138613	+	0.999904i	$0.504412\pi$
$282$		−	6.11770i		−	0.364304i
$283$		−	10.0604i		−	0.598031i	−0.954248	−	0.299015i	$-0.903342\pi$
$283$		−	10.0604i		−	0.598031i	0.954248	−	0.299015i	$-0.0966582\pi$
$284$	9.91745			0.588492
$285$	−2.35526	+	7.11911i	−0.139514	+	0.421700i
$286$		0			0
$287$		−	9.32634i		−	0.550516i
$288$			15.6429i			0.921767i
$289$	13.2021			0.776597
$290$	0.697074	−	2.10700i	0.0409336	−	0.123728i
$291$	14.1752			0.830967
$292$		−	10.3317i		−	0.604618i
$293$		−	13.4501i		−	0.785764i	−0.919589	−	0.392882i	$-0.871478\pi$
$293$		−	13.4501i		−	0.785764i	0.919589	−	0.392882i	$-0.128522\pi$
$294$	3.78109			0.220518
$295$	−5.38217	−	1.78062i	−0.313362	−	0.103672i
$296$	−2.50838			−0.145797
$297$		−	10.8848i		−	0.631597i
$298$			5.24431i			0.303795i
$299$		0			0
$300$	15.1752	−	20.4244i	0.876143	−	1.17920i
$301$	−29.2996			−1.68880
$302$		−	4.81216i		−	0.276909i
$303$		−	15.3716i		−	0.883076i
$304$	4.18002			0.239741
$305$	15.9040	+	5.26162i	0.910660	+	0.301280i
$306$	−2.73743			−0.156488
$307$			24.6077i			1.40444i	0.711961	+	0.702219i	$0.247807\pi$
$307$			24.6077i			1.40444i	−0.711961	+	0.702219i	$0.752193\pi$
$308$			20.5781i			1.17255i
$309$	−19.8349			−1.12837
$310$	−0.878567	+	2.65559i	−0.0498993	+	0.150828i
$311$	2.43781			0.138236			0.0691178	−	0.997609i	$-0.477982\pi$
$311$	2.43781			0.138236			0.0691178	+	0.997609i	$0.477982\pi$
$312$		0			0
$313$			19.2965i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$313$			19.2965i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$314$	−3.61305			−0.203896
$315$	10.0000	−	30.2264i	0.563436	−	1.70307i
$316$	−26.0538			−1.46564
$317$		−	28.8217i		−	1.61879i	−0.587265	−	0.809395i	$-0.699795\pi$
$317$		−	28.8217i		−	1.61879i	0.587265	−	0.809395i	$-0.300205\pi$
$318$			11.4289i			0.640900i
$319$	9.73743			0.545191
$320$	−11.6582	−	3.85695i	−0.651713	−	0.215610i
$321$	−23.0807			−1.28824
$322$		−	2.98643i		−	0.166427i
$323$			2.42785i			0.135089i
$324$	−7.01492			−0.389718
$325$		0			0
$326$	−1.38217			−0.0765512
$327$		−	22.8578i		−	1.26404i
$328$		−	3.57964i		−	0.197653i
$329$	23.0371			1.27007
$330$	−6.13636	−	2.03013i	−0.337795	−	0.111755i
$331$	−2.97310			−0.163416			−0.0817081	−	0.996656i	$-0.526038\pi$
$331$	−2.97310			−0.163416			−0.0817081	+	0.996656i	$0.526038\pi$
$332$			16.2957i			0.894341i
$333$			8.27427i			0.453427i
$334$	1.10945			0.0607066
$335$	2.81998	−	8.52378i	0.154072	−	0.465704i
$336$	−30.2876			−1.65233
$337$			1.90370i			0.103701i	0.998655	+	0.0518505i	$0.0165119\pi$
$337$			1.90370i			0.103701i	−0.998655	+	0.0518505i	$0.983488\pi$
$338$		0			0
$339$	−19.7374			−1.07199
$340$	2.58762	−	7.82145i	0.140333	−	0.424178i
$341$	−12.2727			−0.664605
$342$			1.74995i			0.0946265i
$343$		−	9.23611i		−	0.498703i
$344$	−11.2458			−0.606333
$345$	−15.3822	−	5.08898i	−0.828148	−	0.273982i
$346$	2.89055			0.155397
$347$		−	12.6347i		−	0.678266i	−0.940738	−	0.339133i	$-0.889866\pi$
$347$		−	12.6347i		−	0.678266i	0.940738	−	0.339133i	$-0.110134\pi$
$348$			15.2669i			0.818394i
$349$	−8.97310			−0.480319			−0.240159	−	0.970733i	$-0.577200\pi$
$349$	−8.97310			−0.480319			−0.240159	+	0.970733i	$0.577200\pi$
$350$	−4.45274	−	3.30837i	−0.238009	−	0.176840i
$351$		0			0
$352$			11.9586i			0.637395i
$353$			34.2505i			1.82297i	0.411336	+	0.911484i	$0.365062\pi$
$353$			34.2505i			1.82297i	−0.411336	+	0.911484i	$0.634938\pi$
$354$	−2.25779			−0.120000
$355$	−11.1364	−	3.68431i	−0.591056	−	0.195543i
$356$	−19.5036			−1.03369
$357$		−	17.5917i		−	0.931052i
$358$		−	5.95841i		−	0.314912i
$359$	−22.4043			−1.18245			−0.591227	−	0.806505i	$-0.701356\pi$
$359$	−22.4043			−1.18245			−0.591227	+	0.806505i	$0.701356\pi$
$360$	3.83821	−	11.6015i	0.202291	−	0.611454i
$361$	−17.4480			−0.918314
$362$		−	0.345282i		−	0.0181476i
$363$			1.25092i			0.0656565i
$364$		0			0
$365$	−3.83821	+	11.6015i	−0.200901	+	0.607252i
$366$	6.67164			0.348732
$367$		−	13.1951i		−	0.688777i	−0.938827	−	0.344388i	$-0.888086\pi$
$367$		−	13.1951i		−	0.688777i	0.938827	−	0.344388i	$-0.111914\pi$
$368$			9.03171i			0.470811i
$369$	−11.8080			−0.614700
$370$	1.36872	+	0.452821i	0.0711561	+	0.0235410i
$371$	−43.0371			−2.23437
$372$		−	19.2419i		−	0.997647i
$373$			15.2614i			0.790206i	0.918637	+	0.395103i	$0.129291\pi$
$373$			15.2614i			0.790206i	−0.918637	+	0.395103i	$0.870709\pi$
$374$	−2.09269			−0.108211
$375$	−24.6280	+	17.2971i	−1.27178	+	0.893217i
$376$	8.84210			0.455997
$377$		0			0
$378$		−	3.72052i		−	0.191363i
$379$	−18.2291			−0.936363			−0.468182	−	0.883632i	$-0.655091\pi$
$379$	−18.2291			−0.936363			−0.468182	+	0.883632i	$0.655091\pi$
$380$	−5.00000	−	1.65418i	−0.256495	−	0.0848578i
$381$	24.6669			1.26372
$382$		−	8.44246i		−	0.431954i
$383$		−	1.44088i		−	0.0736255i	−0.999322	−	0.0368128i	$-0.988279\pi$
$383$		−	1.44088i		−	0.0736255i	0.999322	−	0.0368128i	$-0.0117205\pi$
$384$	−24.7255			−1.26177
$385$	7.64474	−	23.1073i	0.389612	−	1.17766i
$386$	−6.55741			−0.333763
$387$			37.0960i			1.88570i
$388$			9.95576i			0.505427i
$389$	18.7912			0.952754			0.476377	−	0.879241i	$-0.341950\pi$
$389$	18.7912			0.952754			0.476377	+	0.879241i	$0.341950\pi$
$390$		0			0
$391$	−5.24581			−0.265292
$392$			5.46493i			0.276021i
$393$		−	26.9180i		−	1.35784i
$394$	−7.16326			−0.360880
$395$	29.2560	+	9.67894i	1.47203	+	0.487000i
$396$	26.0538			1.30925
$397$		−	17.0927i		−	0.857857i	−0.903338	−	0.428928i	$-0.858891\pi$
$397$		−	17.0927i		−	0.857857i	0.903338	−	0.428928i	$-0.141109\pi$
$398$			6.03084i			0.302298i
$399$	−11.2458			−0.562995
$400$	13.4662	+	10.0053i	0.673309	+	0.500266i
$401$	22.2021			1.10872			0.554361	−	0.832276i	$-0.312963\pi$
$401$	22.2021			1.10872			0.554361	+	0.832276i	$0.312963\pi$
$402$		−	3.57568i		−	0.178339i
$403$		0			0
$404$	10.7960			0.537122
$405$	7.87709	+	2.60603i	0.391416	+	0.129495i
$406$	3.32836			0.165184
$407$			6.32546i			0.313541i
$408$		−	6.75207i		−	0.334277i
$409$	9.63276			0.476309			0.238155	−	0.971227i	$-0.423458\pi$
$409$	9.63276			0.476309			0.238155	+	0.971227i	$0.423458\pi$
$410$	−0.646209	+	1.95326i	−0.0319140	+	0.0964646i
$411$	−45.3534			−2.23712
$412$		−	13.9307i		−	0.686318i
$413$		−	8.50202i		−	0.418357i
$414$	−3.78109			−0.185831
$415$	6.05381	−	18.2985i	0.297170	−	0.898238i
$416$		0			0
$417$		−	2.76423i		−	0.135365i
$418$			1.33779i			0.0654335i
$419$	1.95634			0.0955733			0.0477866	−	0.998858i	$-0.484783\pi$
$419$	1.95634			0.0955733			0.0477866	+	0.998858i	$0.484783\pi$
$420$	36.2291	+	11.9859i	1.76780	+	0.584852i
$421$	−12.0807			−0.588778			−0.294389	−	0.955686i	$-0.595116\pi$
$421$	−12.0807			−0.588778			−0.294389	+	0.955686i	$0.595116\pi$
$422$		−	6.38502i		−	0.310818i
$423$		−	29.1670i		−	1.41815i
$424$	−16.5185			−0.802210
$425$	−5.81131	+	7.82145i	−0.281890	+	0.379396i
$426$	−4.67164			−0.226342
$427$			25.1230i			1.21579i
$428$		−	16.2104i		−	0.783558i
$429$		0			0
$430$	6.13636	+	2.03013i	0.295921	+	0.0979016i
$431$	24.5891			1.18441			0.592207	−	0.805786i	$-0.298257\pi$
$431$	24.5891			1.18441			0.592207	+	0.805786i	$0.298257\pi$
$432$			11.2518i			0.541352i
$433$			36.0728i			1.73355i	0.498700	+	0.866775i	$0.333811\pi$
$433$			36.0728i			1.73355i	−0.498700	+	0.866775i	$0.666189\pi$
$434$	−4.19495			−0.201364
$435$	5.67164	−	17.1433i	0.271934	−	0.821960i
$436$	16.0538			0.768838
$437$			3.35348i			0.160419i
$438$			4.86678i			0.232544i
$439$	−2.53528			−0.121003			−0.0605013	−	0.998168i	$-0.519270\pi$
$439$	−2.53528			−0.121003			−0.0605013	+	0.998168i	$0.519270\pi$
$440$	2.93421	−	8.86907i	0.139883	−	0.422816i
$441$	18.0269			0.858424
$442$		0			0
$443$			19.3579i			0.919721i	0.887991	+	0.459860i	$0.152101\pi$
$443$			19.3579i			0.919721i	−0.887991	+	0.459860i	$0.847899\pi$
$444$	−9.91745			−0.470661
$445$	21.9007	+	7.24555i	1.03819	+	0.343472i
$446$	4.09269			0.193795
$447$			42.6696i			2.01820i
$448$		−	18.4160i		−	0.870075i
$449$	24.8080			1.17076			0.585381	−	0.810758i	$-0.300945\pi$
$449$	24.8080			1.17076			0.585381	+	0.810758i	$0.300945\pi$
$450$	−4.18869	+	5.63757i	−0.197457	+	0.265758i
$451$	−9.02690			−0.425060
$452$		−	13.8623i		−	0.652027i
$453$		−	39.1534i		−	1.83959i
$454$	2.03888			0.0956896
$455$		0			0
$456$	−4.31638			−0.202133
$457$			7.56748i			0.353992i	0.984212	+	0.176996i	$0.0566380\pi$
$457$			7.56748i			0.353992i	−0.984212	+	0.176996i	$0.943362\pi$
$458$		−	8.92704i		−	0.417133i
$459$	−6.53528			−0.305041
$460$	3.57417	−	10.8034i	0.166646	−	0.503712i
$461$	−12.3433			−0.574884			−0.287442	−	0.957798i	$-0.592805\pi$
$461$	−12.3433			−0.574884			−0.287442	+	0.957798i	$0.592805\pi$
$462$		−	9.69338i		−	0.450977i
$463$		−	22.8578i		−	1.06229i	−0.847281	−	0.531146i	$-0.821762\pi$
$463$		−	22.8578i		−	1.06229i	0.847281	−	0.531146i	$-0.178238\pi$
$464$	−10.0658			−0.467293
$465$	−7.14834	+	21.6069i	−0.331496	+	1.00199i
$466$	0.272715			0.0126333
$467$		−	15.2976i		−	0.707889i	−0.935266	−	0.353945i	$-0.884840\pi$
$467$		−	15.2976i		−	0.707889i	0.935266	−	0.353945i	$-0.115160\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$	−4.82476	−	1.59621i	−0.222549	−	0.0736275i
$471$	−29.3971			−1.35455
$472$		−	3.26325i		−	0.150203i
$473$			28.3589i			1.30394i
$474$	12.2727			0.563704
$475$	5.00000	+	3.71498i	0.229416	+	0.170455i
$476$	12.3553			0.566303
$477$			54.4889i			2.49487i
$478$			1.32335i			0.0605284i
$479$	−24.2829			−1.10951			−0.554756	−	0.832013i	$-0.687188\pi$
$479$	−24.2829			−1.10951			−0.554756	+	0.832013i	$0.687188\pi$
$480$	21.0538	+	6.96537i	0.960971	+	0.317924i
$481$		0			0
$482$		−	7.50793i		−	0.341977i
$483$		−	24.2987i		−	1.10563i
$484$	−0.878567			−0.0399349
$485$	3.69855	−	11.1794i	0.167942	−	0.507629i
$486$	6.63276			0.300868
$487$			36.8883i			1.67157i	0.549060	+	0.835783i	$0.314986\pi$
$487$			36.8883i			1.67157i	−0.549060	+	0.835783i	$0.685014\pi$
$488$			9.64273i			0.436506i
$489$	−11.2458			−0.508553
$490$	0.986548	−	2.98198i	0.0445677	−	0.134712i
$491$	−35.3534			−1.59548			−0.797739	−	0.603003i	$-0.793971\pi$
$491$	−35.3534			−1.59548			−0.797739	+	0.603003i	$0.793971\pi$
$492$		−	14.1529i		−	0.638064i
$493$		−	5.84642i		−	0.263310i
$494$		0			0
$495$	−29.2560	−	9.67894i	−1.31496	−	0.435036i
$496$	12.6866			0.569644
$497$		−	17.5917i		−	0.789096i
$498$		−	7.67612i		−	0.343975i
$499$	−16.2189			−0.726058			−0.363029	−	0.931778i	$-0.618257\pi$
$499$	−16.2189			−0.726058			−0.363029	+	0.931778i	$0.618257\pi$
$500$	−12.1483	−	17.2971i	−0.543290	−	0.773549i
$501$	9.02690			0.403292
$502$		−	6.29480i		−	0.280950i
$503$		−	20.2384i		−	0.902386i	−0.892427	−	0.451193i	$-0.850999\pi$
$503$		−	20.2384i		−	0.902386i	0.892427	−	0.451193i	$-0.149001\pi$
$504$	18.3265			0.816328
$505$	−12.1229	−	4.01070i	−0.539462	−	0.178474i
$506$	−2.89055			−0.128500
$507$		0			0
$508$			17.3244i			0.768646i
$509$	20.0371			0.888127			0.444063	−	0.895995i	$-0.353537\pi$
$509$	20.0371			0.888127			0.444063	+	0.895995i	$0.353537\pi$
$510$	−1.21891	+	3.68431i	−0.0539740	+	0.163144i
$511$	−18.3265			−0.810718
$512$		−	20.9992i		−	0.928042i
$513$			4.17780i			0.184454i
$514$	0.698546			0.0308116
$515$	−5.17524	+	15.6429i	−0.228048	+	0.689308i
$516$	−44.4629			−1.95737
$517$		−	22.2974i		−	0.980639i
$518$			2.16211i			0.0949977i
$519$	23.5185			1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$		−	4.21401i		−	0.184442i
$523$			11.7380i			0.513265i	0.966509	+	0.256633i	$0.0826130\pi$
$523$			11.7380i			0.513265i	−0.966509	+	0.256633i	$0.917387\pi$
$524$	18.9055			0.825889
$525$	−36.2291	−	26.9180i	−1.58117	−	1.17480i
$526$	9.89775			0.431562
$527$			7.36863i			0.320982i
$528$			29.3152i			1.27578i
$529$	15.7542			0.684965
$530$	9.01345	+	2.98198i	0.391519	+	0.129529i
$531$	−10.7643			−0.467132
$532$		−	7.89832i		−	0.342436i
$533$		0			0
$534$	9.18722			0.397570
$535$	−6.02213	+	18.2027i	−0.260359	+	0.786972i
$536$	5.16804			0.223225
$537$		−	48.4798i		−	2.09206i
$538$			6.14995i			0.265143i
$539$	13.7811			0.593594
$540$	4.45274	−	13.4590i	0.191615	−	0.579184i
$541$	−21.8080			−0.937599			−0.468800	−	0.883305i	$-0.655313\pi$
$541$	−21.8080			−0.937599			−0.468800	+	0.883305i	$0.655313\pi$
$542$		−	1.92704i		−	0.0827736i
$543$		−	2.80934i		−	0.120560i
$544$	7.18002			0.307841
$545$	−18.0269	−	5.96396i	−0.772188	−	0.255468i
$546$		0			0
$547$		−	6.30924i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$547$		−	6.30924i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$548$		−	31.8533i		−	1.36070i
$549$	31.8080			1.35753
$550$	−3.20215	+	4.30978i	−0.136540	+	0.183769i
$551$	−3.73743			−0.159220
$552$		−	9.32634i		−	0.396955i
$553$			46.2146i			1.96524i
$554$	4.47964			0.190322
$555$	11.1364	+	3.68431i	0.472712	+	0.156390i
$556$	1.94141			0.0823342
$557$			35.8378i			1.51849i	0.650802	+	0.759247i	$0.274433\pi$
$557$			35.8378i			1.51849i	−0.650802	+	0.759247i	$0.725567\pi$
$558$			5.31119i			0.224840i
$559$		0			0
$560$	−7.90253	+	23.8865i	−0.333943	+	1.00939i
$561$	−17.0269			−0.718876
$562$			0.153745i			0.00648534i
$563$		−	5.00212i		−	0.210814i	−0.994429	−	0.105407i	$-0.966385\pi$
$563$		−	5.00212i		−	0.210814i	0.994429	−	0.105407i	$-0.0336145\pi$
$564$	34.9593			1.47205
$565$	−5.14981	+	15.5660i	−0.216654	+	0.654868i
$566$	−3.32836			−0.139901
$567$			12.4432i			0.522564i
$568$		−	6.75207i		−	0.283310i
$569$	13.1680			0.552033			0.276017	−	0.961153i	$-0.410986\pi$
$569$	13.1680			0.552033			0.276017	+	0.961153i	$0.410986\pi$
$570$	2.35526	+	0.779207i	0.0986511	+	0.0326374i
$571$	19.8349			0.830065			0.415032	−	0.909807i	$-0.363770\pi$
$571$	19.8349			0.830065			0.415032	+	0.909807i	$0.363770\pi$
$572$		0			0
$573$		−	68.6909i		−	2.86960i
$574$	−3.08549			−0.128786
$575$	−8.02690	+	10.8034i	−0.334745	+	0.450534i
$576$	−23.3164			−0.971516
$577$			10.9210i			0.454646i	0.973819	+	0.227323i	$0.0729972\pi$
$577$			10.9210i			0.454646i	−0.973819	+	0.227323i	$0.927003\pi$
$578$		−	4.36775i		−	0.181675i
$579$	−53.3534			−2.21729
$580$	12.0404	+	3.98339i	0.499949	+	0.165401i
$581$	28.9055			1.19920
$582$		−	4.68969i		−	0.194394i
$583$			41.6553i			1.72519i
$584$	−7.03411			−0.291073
$585$		0			0
$586$	−4.44979			−0.183819
$587$			40.4495i			1.66953i	0.550607	+	0.834764i	$0.314396\pi$
$587$			40.4495i			1.66953i	−0.550607	+	0.834764i	$0.685604\pi$
$588$			21.6069i			0.891052i
$589$	4.71053			0.194094
$590$	−0.589093	+	1.78062i	−0.0242526	+	0.0733069i
$591$	−58.2829			−2.39744
$592$		−	6.53876i		−	0.268742i
$593$		−	1.47709i		−	0.0606569i	−0.999540	−	0.0303284i	$-0.990345\pi$
$593$		−	1.47709i		−	0.0606569i	0.999540	−	0.0303284i	$-0.00965532\pi$
$594$	−3.60107			−0.147754
$595$	−13.8738	−	4.58996i	−0.568770	−	0.188170i
$596$	−29.9683			−1.22755
$597$			49.0690i			2.00826i
$598$		0			0
$599$	−2.27271			−0.0928606			−0.0464303	−	0.998922i	$-0.514785\pi$
$599$	−2.27271			−0.0928606			−0.0464303	+	0.998922i	$0.514785\pi$
$600$	−13.9055	−	10.3317i	−0.567689	−	0.421790i
$601$	7.40429			0.302027			0.151014	−	0.988532i	$-0.451746\pi$
$601$	7.40429			0.302027			0.151014	+	0.988532i	$0.451746\pi$
$602$			9.69338i			0.395073i
$603$		−	17.0476i		−	0.694231i
$604$	27.4988			1.11891
$605$	0.986548	+	0.326386i	0.0401089	+	0.0132695i
$606$	−5.08549			−0.206584
$607$		−	10.6932i		−	0.434024i	−0.976169	−	0.217012i	$-0.930369\pi$
$607$		−	10.6932i		−	0.434024i	0.976169	−	0.217012i	$-0.0696311\pi$
$608$		−	4.58996i		−	0.186147i
$609$	27.0807			1.09737
$610$	1.74074	−	5.26162i	0.0704804	−	0.213037i
$611$		0			0
$612$		−	15.6429i		−	0.632327i
$613$		−	6.08149i		−	0.245629i	−0.992430	−	0.122815i	$-0.960808\pi$
$613$		−	6.08149i		−	0.245629i	0.992430	−	0.122815i	$-0.0391920\pi$
$614$	8.14114			0.328550
$615$	−5.25779	+	15.8924i	−0.212015	+	0.640844i
$616$	14.0101			0.564485
$617$			31.8388i			1.28178i	0.767631	+	0.640892i	$0.221435\pi$
$617$			31.8388i			1.28178i	−0.767631	+	0.640892i	$0.778565\pi$
$618$			6.56211i			0.263967i
$619$	26.4043			1.06128			0.530639	−	0.847598i	$-0.321952\pi$
$619$	26.4043			1.06128			0.530639	+	0.847598i	$0.321952\pi$
$620$	−15.1752	−	5.02052i	−0.609452	−	0.201629i
$621$	−9.02690			−0.362237
$622$		−	0.806517i		−	0.0323384i
$623$			34.5957i			1.38605i
$624$		0			0
$625$	7.21560	+	23.9361i	0.288624	+	0.957443i
$626$	6.38400			0.255156
$627$			10.8848i			0.434695i
$628$		−	20.6466i		−	0.823889i
$629$	3.79785			0.151430
$630$	−10.0000	−	3.30837i	−0.398410	−	0.131808i
$631$	35.1680			1.40002			0.700009	−	0.714134i	$-0.253179\pi$
$631$	35.1680			1.40002			0.700009	+	0.714134i	$0.253179\pi$
$632$			17.7381i			0.705585i
$633$		−	51.9508i		−	2.06486i
$634$	−9.53528			−0.378695
$635$	6.43598	−	19.4536i	0.255404	−	0.771994i
$636$	−65.3098			−2.58970
$637$		0			0
$638$		−	3.22150i		−	0.127540i
$639$	−22.2727			−0.881095
$640$	−6.45126	+	19.4999i	−0.255009	+	0.770799i
$641$	5.52514			0.218230			0.109115	−	0.994029i	$-0.465198\pi$
$641$	5.52514			0.218230			0.109115	+	0.994029i	$0.465198\pi$
$642$			7.63594i			0.301367i
$643$			32.1552i			1.26808i	0.773301	+	0.634039i	$0.218604\pi$
$643$			32.1552i			1.26808i	−0.773301	+	0.634039i	$0.781396\pi$
$644$	17.0658			0.672486
$645$	49.9276	+	16.5179i	1.96590	+	0.650391i
$646$	0.803220			0.0316023
$647$		−	13.7843i		−	0.541917i	−0.962591	−	0.270959i	$-0.912659\pi$
$647$		−	13.7843i		−	0.541917i	0.962591	−	0.270959i	$-0.0873407\pi$
$648$			4.77595i			0.187617i
$649$	−8.22905			−0.323019
$650$		0			0
$651$	−34.1316			−1.33772
$652$		−	7.89832i		−	0.309322i
$653$		−	8.50202i		−	0.332710i	−0.986066	−	0.166355i	$-0.946800\pi$
$653$		−	8.50202i		−	0.332710i	0.986066	−	0.166355i	$-0.0531997\pi$
$654$	−7.56219			−0.295705
$655$	−21.2291	−	7.02335i	−0.829488	−	0.274425i
$656$	9.33130			0.364326
$657$			23.2031i			0.905238i
$658$		−	7.62150i		−	0.297117i
$659$	−4.04366			−0.157519			−0.0787594	−	0.996894i	$-0.525096\pi$
$659$	−4.04366			−0.157519			−0.0787594	+	0.996894i	$0.525096\pi$
$660$	11.6011	−	35.0659i	0.451571	−	1.36494i
$661$	31.2727			1.21637			0.608184	−	0.793796i	$-0.291898\pi$
$661$	31.2727			1.21637			0.608184	+	0.793796i	$0.291898\pi$
$662$			0.983609i			0.0382290i
$663$		0			0
$664$	11.0945			0.430551
$665$	−2.93421	+	8.86907i	−0.113784	+	0.343928i
$666$	2.73743			0.106073
$667$		−	8.07541i		−	0.312681i
$668$			6.33991i			0.245298i
$669$	33.2996			1.28744
$670$	−2.81998	−	0.932952i	−0.108945	−	0.0360431i
$671$	24.3164			0.938723
$672$			33.2579i			1.28295i
$673$			32.0739i			1.23636i	0.786037	+	0.618179i	$0.212129\pi$
$673$			32.0739i			1.23636i	−0.786037	+	0.618179i	$0.787871\pi$
$674$	0.629812			0.0242595
$675$	−10.0000	+	13.4590i	−0.384900	+	0.518038i
$676$		0			0
$677$			14.2382i			0.547220i	0.961841	+	0.273610i	$0.0882177\pi$
$677$			14.2382i			0.547220i	−0.961841	+	0.273610i	$0.911782\pi$
$678$			6.52986i			0.250778i
$679$	17.6597			0.677716
$680$	−5.32505	−	1.76172i	−0.204206	−	0.0675589i
$681$	16.5891			0.635695
$682$			4.06026i			0.155475i
$683$			25.7847i			0.986622i	0.869853	+	0.493311i	$0.164214\pi$
$683$			25.7847i			0.986622i	−0.869853	+	0.493311i	$0.835786\pi$
$684$	−10.0000			−0.382360
$685$	−11.8334	+	35.7682i	−0.452132	+	1.36663i
$686$	−3.05564			−0.116665
$687$		−	72.6336i		−	2.77114i
$688$		−	29.3152i		−	1.11763i
$689$		0			0
$690$	−1.68362	+	5.08898i	−0.0640944	+	0.193734i
$691$	−0.0436636			−0.00166104			−0.000830522	−	1.00000i	$-0.500264\pi$
$691$	−0.0436636			−0.00166104			−0.000830522		1.00000i	$0.500264\pi$
$692$			16.5179i			0.627915i
$693$		−	46.2146i		−	1.75555i
$694$	−4.18002			−0.158671
$695$	−2.18002	−	0.721231i	−0.0826929	−	0.0273578i
$696$	10.3941			0.393989
$697$			5.41982i			0.205290i
$698$			2.96863i			0.112364i
$699$	2.21891			0.0839267
$700$	18.9055	−	25.4449i	0.714560	−	0.961727i
$701$	−14.5454			−0.549373			−0.274687	−	0.961534i	$-0.588574\pi$
$701$	−14.5454			−0.549373			−0.274687	+	0.961534i	$0.588574\pi$
$702$		0			0
$703$		−	2.42785i		−	0.0915679i
$704$	−17.8248			−0.671796
$705$	−39.2560	−	12.9873i	−1.47846	−	0.489130i
$706$	11.3313			0.426459
$707$		−	19.1501i		−	0.720214i
$708$		−	12.9020i		−	0.484888i
$709$	−19.6328			−0.737324			−0.368662	−	0.929564i	$-0.620184\pi$
$709$	−19.6328			−0.737324			−0.368662	+	0.929564i	$0.620184\pi$
$710$	−1.21891	+	3.68431i	−0.0457447	+	0.138270i
$711$	58.5119			2.19437
$712$			13.2786i			0.497636i
$713$			10.1780i			0.381168i
$714$	−5.81998			−0.217807
$715$		0			0
$716$	34.0490			1.27247
$717$			10.7672i			0.402109i
$718$			7.41216i			0.276619i
$719$	−47.4312			−1.76889			−0.884443	−	0.466649i	$-0.845461\pi$
$719$	−47.4312			−1.76889			−0.884443	+	0.466649i	$0.845461\pi$
$720$	30.2425	+	10.0053i	1.12707	+	0.372876i
$721$	−24.7105			−0.920268
$722$			5.77242i			0.214827i
$723$		−	61.0872i		−	2.27186i
$724$	1.97310			0.0733295
$725$	−12.0404	−	8.94594i	−0.447168	−	0.332244i
$726$	0.413851			0.0153595
$727$			34.0951i			1.26452i	0.774757	+	0.632259i	$0.217872\pi$
$727$			34.0951i			1.26452i	−0.774757	+	0.632259i	$0.782128\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$	3.83821	+	1.26982i	0.142059	+	0.0469982i
$731$	17.0269			0.629763
$732$			38.1247i			1.40913i
$733$			14.3920i			0.531580i	0.964031	+	0.265790i	$0.0856327\pi$
$733$			14.3920i			0.531580i	−0.964031	+	0.265790i	$0.914367\pi$
$734$	−4.36541			−0.161130
$735$	8.02690	−	24.2624i	0.296077	−	0.894934i
$736$	9.91745			0.365562
$737$		−	13.0324i		−	0.480055i
$738$			3.90652i			0.143801i
$739$	34.4480			1.26719			0.633594	−	0.773665i	$-0.281579\pi$
$739$	34.4480			1.26719			0.633594	+	0.773665i	$0.281579\pi$
$740$	−2.58762	+	7.82145i	−0.0951228	+	0.287522i
$741$		0			0
$742$			14.2382i			0.522702i
$743$		−	40.7134i		−	1.49363i	−0.665031	−	0.746816i	$-0.731582\pi$
$743$		−	40.7134i		−	1.49363i	0.665031	−	0.746816i	$-0.268418\pi$
$744$	−13.1004			−0.480285
$745$	33.6516	+	11.1332i	1.23290	+	0.407888i
$746$	5.04903			0.184858
$747$		−	36.5970i		−	1.33901i
$748$		−	11.9586i		−	0.437249i
$749$	−28.7542			−1.05066
$750$	5.72251	+	8.14783i	0.208956	+	0.297517i
$751$	32.5018			1.18601			0.593003	−	0.805200i	$-0.297942\pi$
$751$	32.5018			1.18601			0.593003	+	0.805200i	$0.297942\pi$
$752$			23.0493i			0.840522i
$753$		−	51.2167i		−	1.86644i
$754$		0			0
$755$	−30.8786	−	10.2158i	−1.12379	−	0.371790i
$756$	21.2607			0.773245
$757$		−	13.0324i		−	0.473671i	−0.971550	−	0.236836i	$-0.923890\pi$
$757$		−	13.0324i		−	0.473671i	0.971550	−	0.236836i	$-0.0761103\pi$
$758$			6.03084i			0.219050i
$759$	−23.5185			−0.853668
$760$	−1.12621	+	3.40413i	−0.0408520	+	0.123481i
$761$	−3.98985			−0.144632			−0.0723161	−	0.997382i	$-0.523039\pi$
$761$	−3.98985			−0.144632			−0.0723161	+	0.997382i	$0.523039\pi$
$762$		−	8.16070i		−	0.295631i
$763$		−	28.4765i		−	1.03092i
$764$	48.2440			1.74541
$765$	−5.81131	+	17.5655i	−0.210108	+	0.635082i
$766$	−0.476696			−0.0172237
$767$		0			0
$768$		−	21.3847i		−	0.771652i
$769$	−6.66686			−0.240413			−0.120207	−	0.992749i	$-0.538356\pi$
$769$	−6.66686			−0.240413			−0.120207	+	0.992749i	$0.538356\pi$
$770$	−7.64474	−	2.52916i	−0.275497	−	0.0911445i
$771$	5.68362			0.204691
$772$		−	37.4720i		−	1.34865i
$773$		−	48.3349i		−	1.73849i	−0.494384	−	0.869244i	$-0.664606\pi$
$773$		−	48.3349i		−	1.73849i	0.494384	−	0.869244i	$-0.335394\pi$
$774$	12.2727			0.441134
$775$	15.1752	+	11.2751i	0.545111	+	0.405015i
$776$	6.77815			0.243321
$777$			17.5917i			0.631099i
$778$		−	6.21683i		−	0.222884i
$779$	3.46472			0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$			1.73551i			0.0620616i
$783$		−	10.0604i		−	0.359531i
$784$	−14.2458			−0.508779
$785$	−7.67017	+	23.1842i	−0.273760	+	0.827478i
$786$	−8.90547			−0.317648
$787$		−	27.9612i		−	0.996709i	−0.866973	−	0.498355i	$-0.833938\pi$
$787$		−	27.9612i		−	0.996709i	0.866973	−	0.498355i	$-0.166062\pi$
$788$		−	40.9341i		−	1.45822i
$789$	80.5316			2.86700
$790$	3.20215	−	9.67894i	0.113927	−	0.344361i
$791$	−24.5891			−0.874288
$792$		−	17.7381i		−	0.630297i
$793$		0			0
$794$	−5.65488			−0.200684
$795$	73.3367	+	24.2624i	2.60098	+	0.860500i
$796$	−34.4629			−1.22150
$797$			37.2424i			1.31919i	0.751619	+	0.659597i	$0.229273\pi$
$797$			37.2424i			1.31919i	−0.751619	+	0.659597i	$0.770727\pi$
$798$			3.72052i			0.131705i
$799$	−13.3875			−0.473617
$800$	10.9865	−	14.7868i	0.388433	−	0.522793i
$801$	43.8014			1.54765
$802$		−	7.34528i		−	0.259371i
$803$			17.7381i			0.625965i
$804$	20.4330			0.720617
$805$	−19.1633	−	6.33991i	−0.675416	−	0.223452i
$806$		0			0
$807$			50.0382i			1.76143i
$808$		−	7.35022i		−	0.258580i
$809$	−14.5287			−0.510801			−0.255400	−	0.966835i	$-0.582207\pi$
$809$	−14.5287			−0.510801			−0.255400	+	0.966835i	$0.582207\pi$
$810$	0.862170	−	2.60603i	0.0302936	−	0.0915666i
$811$	44.0538			1.54694			0.773469	−	0.633834i	$-0.218520\pi$
$811$	44.0538			1.54694			0.773469	+	0.633834i	$0.218520\pi$
$812$			19.0197i			0.667461i
$813$		−	15.6791i		−	0.549890i
$814$	2.09269			0.0733489
$815$	−2.93421	+	8.86907i	−0.102781	+	0.310670i
$816$	17.6011			0.616161
$817$		−	10.8848i		−	0.380809i
$818$		−	3.18687i		−	0.111426i
$819$		0			0
$820$	−11.1618	−	3.69273i	−0.389787	−	0.128956i
$821$	27.0269			0.943245			0.471623	−	0.881800i	$-0.343668\pi$
$821$	27.0269			0.943245			0.471623	+	0.881800i	$0.343668\pi$
$822$			15.0046i			0.523345i
$823$			39.5963i			1.38024i	0.723695	+	0.690120i	$0.242442\pi$
$823$			39.5963i			1.38024i	−0.723695	+	0.690120i	$0.757558\pi$
$824$	−9.48442			−0.330405
$825$	−26.0538	+	35.0659i	−0.907077	+	1.22084i
$826$	−2.81278			−0.0978691
$827$		−	26.5639i		−	0.923716i	−0.886954	−	0.461858i	$-0.847183\pi$
$827$		−	26.5639i		−	0.923716i	0.886954	−	0.461858i	$-0.152817\pi$
$828$		−	21.6069i		−	0.750890i
$829$	−13.9832			−0.485658			−0.242829	−	0.970069i	$-0.578075\pi$
$829$	−13.9832			−0.485658			−0.242829	+	0.970069i	$0.578075\pi$
$830$	−6.05381	−	2.00282i	−0.210131	−	0.0695189i
$831$	36.4480			1.26437
$832$		0			0
$833$		−	8.27427i		−	0.286686i
$834$	−0.914507			−0.0316668
$835$	2.35526	−	7.11911i	0.0815072	−	0.246367i
$836$	−7.64474			−0.264399
$837$			12.6798i			0.438278i
$838$		−	0.647228i		−	0.0223581i
$839$	−14.3941			−0.496941			−0.248471	−	0.968639i	$-0.579928\pi$
$839$	−14.3941			−0.496941			−0.248471	+	0.968639i	$0.579928\pi$
$840$	8.16032	−	24.6657i	0.281558	−	0.851048i
$841$	−20.0000			−0.689655
$842$			3.99674i			0.137737i
$843$			1.25092i			0.0430841i
$844$	36.4868			1.25593
$845$		0			0
$846$	−9.64952			−0.331757
$847$			1.55841i			0.0535477i
$848$		−	43.0600i		−	1.47869i
$849$	−27.0807			−0.929408
$850$	2.58762	+	1.92259i	0.0887547	+	0.0659444i
$851$	5.24581			0.179824
$852$		−	26.6958i		−	0.914584i
$853$			27.2633i			0.933478i	0.884395	+	0.466739i	$0.154571\pi$
$853$			27.2633i			0.933478i	−0.884395	+	0.466739i	$0.845429\pi$
$854$	8.31160			0.284417
$855$	11.2291	+	3.71498i	0.384025	+	0.127050i
$856$	−11.0365			−0.377219
$857$		−	50.6201i		−	1.72915i	−0.502503	−	0.864575i	$-0.667587\pi$
$857$		−	50.6201i		−	1.72915i	0.502503	−	0.864575i	$-0.332413\pi$
$858$		0			0
$859$	−1.27992			−0.0436702			−0.0218351	−	0.999762i	$-0.506951\pi$
$859$	−1.27992			−0.0436702			−0.0218351	+	0.999762i	$0.506951\pi$
$860$	−11.6011	+	35.0659i	−0.395593	+	1.19574i
$861$	−25.1047			−0.855565
$862$		−	8.13497i		−	0.277078i
$863$		−	8.38448i		−	0.285411i	−0.989765	−	0.142706i	$-0.954420\pi$
$863$		−	8.38448i		−	0.285411i	0.989765	−	0.142706i	$-0.0455802\pi$
$864$	12.3553			0.420335
$865$	6.13636	−	18.5480i	0.208642	−	0.630651i
$866$	11.9342			0.405541
$867$		−	35.5376i		−	1.20692i
$868$		−	23.9718i		−	0.813655i
$869$	44.7308			1.51739
$870$	−5.67164	−	1.87639i	−0.192287	−	0.0636155i
$871$		0			0
$872$		−	10.9299i		−	0.370132i
$873$		−	22.3588i		−	0.756729i
$874$	1.10945			0.0375278
$875$	−30.6818	+	21.5489i	−1.03723	+	0.728485i
$876$	−27.8109			−0.939645
$877$		−	55.8862i		−	1.88714i	−0.331169	−	0.943572i	$-0.607443\pi$
$877$		−	55.8862i		−	1.88714i	0.331169	−	0.943572i	$-0.392557\pi$
$878$			0.838765i			0.0283069i
$879$	−36.2051			−1.22117
$880$	23.1196	+	7.64881i	0.779362	+	0.257841i
$881$	25.1949			0.848839			0.424420	−	0.905466i	$-0.360478\pi$
$881$	25.1949			0.848839			0.424420	+	0.905466i	$0.360478\pi$
$882$		−	5.96396i		−	0.200817i
$883$			30.7868i			1.03606i	0.855363	+	0.518029i	$0.173334\pi$
$883$			30.7868i			1.03606i	−0.855363	+	0.518029i	$0.826666\pi$
$884$		0			0
$885$	−4.79307	+	14.4877i	−0.161117	+	0.487000i
$886$	6.40429			0.215156
$887$		−	12.4721i		−	0.418771i	−0.977833	−	0.209385i	$-0.932854\pi$
$887$		−	12.4721i		−	0.418771i	0.977833	−	0.209385i	$-0.0671463\pi$
$888$			6.75207i			0.226585i
$889$	30.7302			1.03066
$890$	2.39709	−	7.24555i	0.0803507	−	0.242871i
$891$	12.0437			0.403478
$892$			23.3875i			0.783071i
$893$			8.55822i			0.286390i
$894$	14.1167			0.472132
$895$	−38.2338	−	12.6491i	−1.27802	−	0.422814i
$896$	−30.8032			−1.02906
$897$		0			0
$898$		−	8.20739i		−	0.273884i
$899$	−11.3433			−0.378320
$900$	−32.2156	−	23.9361i	−1.07385	−	0.797869i
$901$	25.0101			0.833209
$902$			2.98643i			0.0994372i
$903$			78.8688i			2.62459i
$904$	−9.43781			−0.313897
$905$	−2.21560	−	0.733001i	−0.0736490	−	0.0243658i
$906$	−12.9534			−0.430348
$907$		−	38.8911i		−	1.29136i	−0.763609	−	0.645678i	$-0.776575\pi$
$907$		−	38.8911i		−	1.29136i	0.763609	−	0.645678i	$-0.223425\pi$
$908$			11.6511i			0.386655i
$909$	−24.2458			−0.804183
$910$		0			0
$911$	0.165096			0.00546989			0.00273494	−	0.999996i	$-0.499129\pi$
$911$	0.165096			0.00546989			0.00273494	+	0.999996i	$0.499129\pi$
$912$		−	11.2518i		−	0.372584i
$913$		−	27.9774i		−	0.925918i
$914$	2.50360			0.0828117
$915$	14.1633	−	42.8105i	0.468223	−	1.41527i
$916$	51.0131			1.68552
$917$		−	33.5348i		−	1.10742i
$918$			2.16211i			0.0713603i
$919$	−0.895326			−0.0295341			−0.0147670	−	0.999891i	$-0.504701\pi$
$919$	−0.895326			−0.0295341			−0.0147670	+	0.999891i	$0.504701\pi$
$920$	−7.35526	−	2.43339i	−0.242496	−	0.0802265i
$921$	66.2392			2.18266
$922$			4.08361i			0.134486i
$923$		0			0
$924$	55.3923			1.82227
$925$	5.81131	−	7.82145i	0.191075	−	0.257168i
$926$	−7.56219			−0.248509
$927$			31.2858i			1.02756i
$928$			11.0529i			0.362831i
$929$	12.2895			0.403205			0.201602	−	0.979467i	$-0.435385\pi$
$929$	12.2895			0.403205			0.201602	+	0.979467i	$0.435385\pi$
$930$	7.14834	+	2.36493i	0.234403	+	0.0775491i
$931$	−5.28947			−0.173356
$932$			1.55841i			0.0510476i
$933$		−	6.56211i		−	0.214834i
$934$	−5.06101			−0.165601
$935$	−4.44259	+	13.4284i	−0.145288	+	0.439154i
$936$		0			0
$937$		−	5.77242i		−	0.188577i	−0.995545	−	0.0942884i	$-0.969942\pi$
$937$		−	5.77242i		−	0.188577i	0.995545	−	0.0942884i	$-0.0300576\pi$
$938$		−	4.45462i		−	0.145448i
$939$	51.9425			1.69508
$940$	9.12143	−	27.5708i	0.297508	−	0.899261i
$941$	−55.8887			−1.82192			−0.910960	−	0.412495i	$-0.864658\pi$
$941$	−55.8887			−1.82192			−0.910960	+	0.412495i	$0.864658\pi$
$942$			9.72563i			0.316878i
$943$			7.48616i			0.243783i
$944$	8.50655			0.276864
$945$	−23.8738	−	7.89832i	−0.776614	−	0.256932i
$946$	9.38217			0.305041
$947$		−	1.89638i		−	0.0616239i	−0.999525	−	0.0308120i	$-0.990191\pi$
$947$		−	1.89638i		−	0.0616239i	0.999525	−	0.0308120i	$-0.00980931\pi$
$948$			70.1318i			2.27777i
$949$		0			0
$950$	1.22905	−	1.65418i	0.0398757	−	0.0536688i
$951$	−77.5825			−2.51578
$952$		−	8.41179i		−	0.272628i
$953$		−	33.6523i		−	1.09011i	−0.838402	−	0.545053i	$-0.816510\pi$
$953$		−	33.6523i		−	1.09011i	0.838402	−	0.545053i	$-0.183490\pi$
$954$	18.0269			0.583643
$955$	−54.1734	−	17.9225i	−1.75301	−	0.579960i
$956$	−7.56219			−0.244579
$957$		−	26.2113i		−	0.847290i
$958$			8.03366i			0.259556i
$959$	−56.5018			−1.82454
$960$	−10.3822	+	31.3816i	−0.335083	+	1.01284i
$961$	−16.7033			−0.538817
$962$		0			0
$963$			36.4054i			1.17315i
$964$	42.9036			1.38183
$965$	−13.9208	+	42.0775i	−0.448125	+	1.35452i
$966$	−8.03888			−0.258647
$967$		−	23.0493i		−	0.741216i	−0.928789	−	0.370608i	$-0.879149\pi$
$967$		−	23.0493i		−	0.741216i	0.928789	−	0.370608i	$-0.120851\pi$
$968$			0.598152i			0.0192253i
$969$	6.53528			0.209944
$970$	−3.69855	−	1.22361i	−0.118753	−	0.0392879i
$971$	14.9193			0.478783			0.239391	−	0.970923i	$-0.423052\pi$
$971$	14.9193			0.478783			0.239391	+	0.970923i	$0.423052\pi$
$972$			37.9025i			1.21572i
$973$		−	3.44370i		−	0.110400i
$974$	12.2040			0.391041
$975$		0			0
$976$	−25.1364			−0.804595
$977$		−	23.3641i		−	0.747485i	−0.927533	−	0.373742i	$-0.878074\pi$
$977$		−	23.3641i		−	0.747485i	0.927533	−	0.373742i	$-0.121926\pi$
$978$			3.72052i			0.118969i
$979$	33.4850			1.07019
$980$	17.0404	+	5.63757i	0.544334	+	0.180086i
$981$	−36.0538			−1.15111
$982$			11.6962i			0.373241i
$983$		−	5.31119i		−	0.169401i	−0.996406	−	0.0847003i	$-0.973007\pi$
$983$		−	5.31119i		−	0.169401i	0.996406	−	0.0847003i	$-0.0269933\pi$
$984$	−9.63570			−0.307175
$985$	−15.2069	+	45.9651i	−0.484533	+	1.46457i
$986$	−1.93421			−0.0615978
$987$		−	62.0112i		−	1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$	−3.20215	+	9.67894i	−0.101771	+	0.307617i
$991$	−24.0879			−0.765178			−0.382589	−	0.923919i	$-0.624967\pi$
$991$	−24.0879			−0.765178			−0.382589	+	0.923919i	$0.624967\pi$
$992$		−	13.9307i		−	0.442301i
$993$			8.00299i			0.253967i
$994$	−5.81998			−0.184599
$995$	38.6985	+	12.8029i	1.22683	+	0.405879i
$996$	43.8648			1.38991
$997$			20.4099i			0.646389i	0.946332	+	0.323195i	$0.104757\pi$
$997$			20.4099i			0.646389i	−0.946332	+	0.323195i	$0.895243\pi$
$998$			5.36581i			0.169852i
$999$	6.53528			0.206767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.b.d.339.3		6
5.2	odd	4		4225.2.a.br.1.4		6
5.3	odd	4		4225.2.a.br.1.3		6
5.4	even	2	inner	845.2.b.d.339.4		6
13.2	odd	12		845.2.l.f.654.8		24
13.3	even	3		65.2.n.a.9.4	yes	12
13.4	even	6		845.2.n.e.484.4		12
13.5	odd	4		845.2.d.d.844.5		12
13.6	odd	12		845.2.l.f.699.7		24
13.7	odd	12		845.2.l.f.699.5		24
13.8	odd	4		845.2.d.d.844.7		12
13.9	even	3		65.2.n.a.29.3	yes	12
13.10	even	6		845.2.n.e.529.3		12
13.11	odd	12		845.2.l.f.654.6		24
13.12	even	2		845.2.b.e.339.4		6
39.29	odd	6		585.2.bs.a.334.3		12
39.35	odd	6		585.2.bs.a.289.4		12
52.3	odd	6		1040.2.dh.a.529.1		12
52.35	odd	6		1040.2.dh.a.289.6		12
65.3	odd	12		325.2.e.e.126.4		12
65.4	even	6		845.2.n.e.484.3		12
65.9	even	6		65.2.n.a.29.4	yes	12
65.12	odd	4		4225.2.a.bq.1.3		6
65.19	odd	12		845.2.l.f.699.6		24
65.22	odd	12		325.2.e.e.276.3		12
65.24	odd	12		845.2.l.f.654.7		24
65.29	even	6		65.2.n.a.9.3	✓	12
65.34	odd	4		845.2.d.d.844.6		12
65.38	odd	4		4225.2.a.bq.1.4		6
65.42	odd	12		325.2.e.e.126.3		12
65.44	odd	4		845.2.d.d.844.8		12
65.48	odd	12		325.2.e.e.276.4		12
65.49	even	6		845.2.n.e.529.4		12
65.54	odd	12		845.2.l.f.654.5		24
65.59	odd	12		845.2.l.f.699.8		24
65.64	even	2		845.2.b.e.339.3		6
195.29	odd	6		585.2.bs.a.334.4		12
195.74	odd	6		585.2.bs.a.289.3		12
260.139	odd	6		1040.2.dh.a.289.1		12
260.159	odd	6		1040.2.dh.a.529.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	65.29	even	6
65.2.n.a.9.4	yes	12	13.3	even	3
65.2.n.a.29.3	yes	12	13.9	even	3
65.2.n.a.29.4	yes	12	65.9	even	6
325.2.e.e.126.3		12	65.42	odd	12
325.2.e.e.126.4		12	65.3	odd	12
325.2.e.e.276.3		12	65.22	odd	12
325.2.e.e.276.4		12	65.48	odd	12
585.2.bs.a.289.3		12	195.74	odd	6
585.2.bs.a.289.4		12	39.35	odd	6
585.2.bs.a.334.3		12	39.29	odd	6
585.2.bs.a.334.4		12	195.29	odd	6
845.2.b.d.339.3		6	1.1	even	1	trivial
845.2.b.d.339.4		6	5.4	even	2	inner
845.2.b.e.339.3		6	65.64	even	2
845.2.b.e.339.4		6	13.12	even	2
845.2.d.d.844.5		12	13.5	odd	4
845.2.d.d.844.6		12	65.34	odd	4
845.2.d.d.844.7		12	13.8	odd	4
845.2.d.d.844.8		12	65.44	odd	4
845.2.l.f.654.5		24	65.54	odd	12
845.2.l.f.654.6		24	13.11	odd	12
845.2.l.f.654.7		24	65.24	odd	12
845.2.l.f.654.8		24	13.2	odd	12
845.2.l.f.699.5		24	13.7	odd	12
845.2.l.f.699.6		24	65.19	odd	12
845.2.l.f.699.7		24	13.6	odd	12
845.2.l.f.699.8		24	65.59	odd	12
845.2.n.e.484.3		12	65.4	even	6
845.2.n.e.484.4		12	13.4	even	6
845.2.n.e.529.3		12	13.10	even	6
845.2.n.e.529.4		12	65.49	even	6
1040.2.dh.a.289.1		12	260.139	odd	6
1040.2.dh.a.289.6		12	52.35	odd	6
1040.2.dh.a.529.1		12	52.3	odd	6
1040.2.dh.a.529.6		12	260.159	odd	6
4225.2.a.bq.1.3		6	65.12	odd	4
4225.2.a.bq.1.4		6	65.38	odd	4
4225.2.a.br.1.3		6	5.3	odd	4
4225.2.a.br.1.4		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.330837i q^{2} -2.69180i q^{3} +1.89055 q^{4} +(-2.12291 - 0.702335i) q^{5} -0.890547 q^{6} -3.35348i q^{7} -1.28714i q^{8} -4.24581 q^{9} +O(q^{10})\)	\(q-0.330837i q^{2} -2.69180i q^{3} +1.89055 q^{4} +(-2.12291 - 0.702335i) q^{5} -0.890547 q^{6} -3.35348i q^{7} -1.28714i q^{8} -4.24581 q^{9} +(-0.232358 + 0.702335i) q^{10} -3.24581 q^{11} -5.08898i q^{12} -1.10945 q^{14} +(-1.89055 + 5.71445i) q^{15} +3.35526 q^{16} +1.94881i q^{17} +1.40467i q^{18} +1.24581 q^{19} +(-4.01345 - 1.32780i) q^{20} -9.02690 q^{21} +1.07383i q^{22} +2.69180i q^{23} -3.46472 q^{24} +(4.01345 + 2.98198i) q^{25} +3.35348i q^{27} -6.33991i q^{28} -3.00000 q^{29} +(1.89055 + 0.625462i) q^{30} +3.78109 q^{31} -3.68431i q^{32} +8.73709i q^{33} +0.644737 q^{34} +(-2.35526 + 7.11911i) q^{35} -8.02690 q^{36} -1.94881i q^{37} -0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +2.78109 q^{41} +2.98643i q^{42} -8.73709i q^{43} -6.13636 q^{44} +(9.01345 + 2.98198i) q^{45} +0.890547 q^{46} +6.86960i q^{47} -9.03171i q^{48} -4.24581 q^{49} +(0.986548 - 1.32780i) q^{50} +5.24581 q^{51} -12.8336i q^{53} +1.10945 q^{54} +(6.89055 + 2.27964i) q^{55} -4.31638 q^{56} -3.35348i q^{57} +0.992510i q^{58} +2.53528 q^{59} +(-3.57417 + 10.8034i) q^{60} -7.49162 q^{61} -1.25092i q^{62} +14.2382i q^{63} +5.49162 q^{64} +2.89055 q^{66} +4.01515i q^{67} +3.68431i q^{68} +7.24581 q^{69} +(2.35526 + 0.779207i) q^{70} +5.24581 q^{71} +5.46493i q^{72} -5.46493i q^{73} -0.644737 q^{74} +(8.02690 - 10.8034i) q^{75} +2.35526 q^{76} +10.8848i q^{77} -13.7811 q^{79} +(-7.12291 - 2.35652i) q^{80} -3.71053 q^{81} -0.920088i q^{82} +8.61955i q^{83} -17.0658 q^{84} +(1.36872 - 4.13713i) q^{85} -2.89055 q^{86} +8.07541i q^{87} +4.17780i q^{88} -10.3164 q^{89} +(0.986548 - 2.98198i) q^{90} +5.08898i q^{92} -10.1780i q^{93} +2.27271 q^{94} +(-2.64474 - 0.874976i) q^{95} -9.91745 q^{96} +5.26607i q^{97} +1.40467i q^{98} +13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9	\( 6 q - 4 q^{4} - 3 q^{5} + 10 q^{6} - 6 q^{9} - 7 q^{10} - 22 q^{14} + 4 q^{15} + 16 q^{16} - 12 q^{19} + q^{20} - 4 q^{21} - 32 q^{24} - q^{25} - 18 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{36} + 35 q^{40} - 14 q^{41} - 2 q^{44} + 29 q^{45} - 10 q^{46} - 6 q^{49} + 31 q^{50} + 12 q^{51} + 22 q^{54} + 26 q^{55} + 16 q^{56} + 4 q^{59} - 48 q^{60} - 6 q^{61} - 6 q^{64} + 2 q^{66} + 24 q^{69} + 10 q^{70} + 12 q^{71} - 8 q^{74} - 2 q^{75} + 10 q^{76} - 52 q^{79} - 33 q^{80} - 14 q^{81} - 90 q^{84} - 21 q^{85} - 2 q^{86} - 20 q^{89} + 31 q^{90} - 56 q^{94} - 20 q^{95} + 6 q^{96} + 52 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 - 3 * q^5 + 10 * q^6 - 6 * q^9 - 7 * q^10 - 22 * q^14 + 4 * q^15 + 16 * q^16 - 12 * q^19 + q^20 - 4 * q^21 - 32 * q^24 - q^25 - 18 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^34 - 10 * q^35 + 2 * q^36 + 35 * q^40 - 14 * q^41 - 2 * q^44 + 29 * q^45 - 10 * q^46 - 6 * q^49 + 31 * q^50 + 12 * q^51 + 22 * q^54 + 26 * q^55 + 16 * q^56 + 4 * q^59 - 48 * q^60 - 6 * q^61 - 6 * q^64 + 2 * q^66 + 24 * q^69 + 10 * q^70 + 12 * q^71 - 8 * q^74 - 2 * q^75 + 10 * q^76 - 52 * q^79 - 33 * q^80 - 14 * q^81 - 90 * q^84 - 21 * q^85 - 2 * q^86 - 20 * q^89 + 31 * q^90 - 56 * q^94 - 20 * q^95 + 6 * q^96 + 52 * q^99

Introduction

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