LMFDB - Embedded newform 820.2.u.b.221.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.4
Character	$\chi$	$=$	820.221
Dual form			820.2.u.b.141.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.355750 q^{3} +(0.809017 + 0.587785i) q^{5} +(0.307592 + 0.946670i) q^{7} -2.87344 q^{9} +(3.39225 - 2.46462i) q^{11} +(-1.59331 + 4.90370i) q^{13} +(-0.287808 - 0.209105i) q^{15} +(2.28447 - 1.65977i) q^{17} +(2.17078 + 6.68097i) q^{19} +(-0.109426 - 0.336778i) q^{21} +(-0.101413 + 0.312117i) q^{23} +(0.309017 + 0.951057i) q^{25} +2.08948 q^{27} +(3.80723 + 2.76611i) q^{29} +(-2.25881 + 1.64112i) q^{31} +(-1.20679 + 0.876788i) q^{33} +(-0.307592 + 0.946670i) q^{35} +(-6.30447 - 4.58047i) q^{37} +(0.566819 - 1.74449i) q^{39} +(6.39530 + 0.316543i) q^{41} +(-3.73793 + 11.5042i) q^{43} +(-2.32466 - 1.68897i) q^{45} +(-1.76202 + 5.42294i) q^{47} +(4.86155 - 3.53212i) q^{49} +(-0.812702 + 0.590462i) q^{51} +(8.16912 + 5.93522i) q^{53} +4.19306 q^{55} +(-0.772254 - 2.37675i) q^{57} +(-1.06083 + 3.26489i) q^{59} +(-4.03007 - 12.4033i) q^{61} +(-0.883847 - 2.72020i) q^{63} +(-4.17133 + 3.03065i) q^{65} +(7.67956 + 5.57953i) q^{67} +(0.0360776 - 0.111035i) q^{69} +(-11.8629 + 8.61891i) q^{71} +6.31718 q^{73} +(-0.109933 - 0.338338i) q^{75} +(3.37661 + 2.45325i) q^{77} +8.58590 q^{79} +7.87699 q^{81} +3.73133 q^{83} +2.82376 q^{85} +(-1.35442 - 0.984045i) q^{87} +(-4.09886 - 12.6150i) q^{89} -5.13227 q^{91} +(0.803571 - 0.583829i) q^{93} +(-2.17078 + 6.68097i) q^{95} +(9.84725 + 7.15445i) q^{97} +(-9.74745 + 7.08193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.355750			−0.205392			−0.102696	−	0.994713i	$-0.532747\pi$
$3$	−0.355750			−0.205392			−0.102696	+	0.994713i	$0.532747\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	0.307592	+	0.946670i	0.116259	+	0.357808i	0.992207	−	0.124597i	$-0.0397636\pi$
$7$	0.307592	+	0.946670i	0.116259	+	0.357808i	−0.875949	+	0.482404i	$0.839764\pi$
$8$		0			0
$9$	−2.87344			−0.957814
$10$		0			0
$11$	3.39225	−	2.46462i	1.02280	−	0.743110i	0.0559475	−	0.998434i	$-0.482182\pi$
$11$	3.39225	−	2.46462i	1.02280	−	0.743110i	0.966856	+	0.255324i	$0.0821821\pi$
$12$		0			0
$13$	−1.59331	+	4.90370i	−0.441904	+	1.36004i	0.443939	+	0.896057i	$0.353581\pi$
$13$	−1.59331	+	4.90370i	−0.441904	+	1.36004i	−0.885843	+	0.463984i	$0.846419\pi$
$14$		0			0
$15$	−0.287808	−	0.209105i	−0.0743117	−	0.0539906i
$16$		0			0
$17$	2.28447	−	1.65977i	0.554066	−	0.402553i	−0.275216	−	0.961382i	$-0.588749\pi$
$17$	2.28447	−	1.65977i	0.554066	−	0.402553i	0.829282	+	0.558830i	$0.188749\pi$
$18$		0			0
$19$	2.17078	+	6.68097i	0.498010	+	1.53272i	0.812212	+	0.583362i	$0.198263\pi$
$19$	2.17078	+	6.68097i	0.498010	+	1.53272i	−0.314201	+	0.949356i	$0.601737\pi$
$20$		0			0
$21$	−0.109426	−	0.336778i	−0.0238787	−	0.0734910i
$22$		0			0
$23$	−0.101413	+	0.312117i	−0.0211460	+	0.0650808i	−0.961073	−	0.276296i	$-0.910893\pi$
$23$	−0.101413	+	0.312117i	−0.0211460	+	0.0650808i	0.939927	+	0.341376i	$0.110893\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	2.08948			0.402120
$28$		0			0
$29$	3.80723	+	2.76611i	0.706985	+	0.513655i	0.882200	−	0.470876i	$-0.156062\pi$
$29$	3.80723	+	2.76611i	0.706985	+	0.513655i	−0.175215	+	0.984530i	$0.556062\pi$
$30$		0			0
$31$	−2.25881	+	1.64112i	−0.405694	+	0.294754i	−0.771856	−	0.635797i	$-0.780672\pi$
$31$	−2.25881	+	1.64112i	−0.405694	+	0.294754i	0.366162	+	0.930551i	$0.380672\pi$
$32$		0			0
$33$	−1.20679	+	0.876788i	−0.210076	+	0.152629i
$34$		0			0
$35$	−0.307592	+	0.946670i	−0.0519925	+	0.160016i
$36$		0			0
$37$	−6.30447	−	4.58047i	−1.03645	−	0.753024i	−0.0668598	−	0.997762i	$-0.521298\pi$
$37$	−6.30447	−	4.58047i	−1.03645	−	0.753024i	−0.969589	+	0.244738i	$0.921298\pi$
$38$		0			0
$39$	0.566819	−	1.74449i	0.0907638	−	0.279342i
$40$		0			0
$41$	6.39530	+	0.316543i	0.998777	+	0.0494357i
$41$	6.39530	+	0.316543i	0.998777	+	0.0494357i
$42$		0			0
$43$	−3.73793	+	11.5042i	−0.570029	+	1.75437i	0.0824843	+	0.996592i	$0.473715\pi$
$43$	−3.73793	+	11.5042i	−0.570029	+	1.75437i	−0.652514	+	0.757777i	$0.726285\pi$
$44$		0			0
$45$	−2.32466	−	1.68897i	−0.346540	−	0.251776i
$46$		0			0
$47$	−1.76202	+	5.42294i	−0.257017	+	0.791017i	0.736408	+	0.676537i	$0.236520\pi$
$47$	−1.76202	+	5.42294i	−0.257017	+	0.791017i	−0.993426	+	0.114480i	$0.963480\pi$
$48$		0			0
$49$	4.86155	−	3.53212i	0.694507	−	0.504589i
$50$		0			0
$51$	−0.812702	+	0.590462i	−0.113801	+	0.0826813i
$52$		0			0
$53$	8.16912	+	5.93522i	1.12212	+	0.815265i	0.984528	−	0.175225i	$-0.0560653\pi$
$53$	8.16912	+	5.93522i	1.12212	+	0.815265i	0.137587	+	0.990490i	$0.456065\pi$
$54$		0			0
$55$	4.19306			0.565392
$56$		0			0
$57$	−0.772254	−	2.37675i	−0.102288	−	0.314809i
$58$		0			0
$59$	−1.06083	+	3.26489i	−0.138108	+	0.425053i	−0.996061	−	0.0886762i	$-0.971736\pi$
$59$	−1.06083	+	3.26489i	−0.138108	+	0.425053i	0.857952	+	0.513729i	$0.171736\pi$
$60$		0			0
$61$	−4.03007	−	12.4033i	−0.515997	−	1.58808i	−0.781460	−	0.623955i	$-0.785525\pi$
$61$	−4.03007	−	12.4033i	−0.515997	−	1.58808i	0.265463	−	0.964121i	$-0.414475\pi$
$62$		0			0
$63$	−0.883847	−	2.72020i	−0.111354	−	0.342713i
$64$		0			0
$65$	−4.17133	+	3.03065i	−0.517390	+	0.375906i
$66$		0			0
$67$	7.67956	+	5.57953i	0.938208	+	0.681648i	0.947989	−	0.318304i	$-0.103113\pi$
$67$	7.67956	+	5.57953i	0.938208	+	0.681648i	−0.00978079	+	0.999952i	$0.503113\pi$
$68$		0			0
$69$	0.0360776	−	0.111035i	0.00434323	−	0.0133671i
$70$		0			0
$71$	−11.8629	+	8.61891i	−1.40787	+	1.02288i	−0.414240	+	0.910168i	$0.635953\pi$
$71$	−11.8629	+	8.61891i	−1.40787	+	1.02288i	−0.993628	+	0.112709i	$0.964047\pi$
$72$		0			0
$73$	6.31718			0.739370			0.369685	−	0.929157i	$-0.379466\pi$
$73$	6.31718			0.739370			0.369685	+	0.929157i	$0.379466\pi$
$74$		0			0
$75$	−0.109933	−	0.338338i	−0.0126939	−	0.0390680i
$76$		0			0
$77$	3.37661	+	2.45325i	0.384800	+	0.279574i
$78$		0			0
$79$	8.58590			0.965989			0.482994	−	0.875623i	$-0.339549\pi$
$79$	8.58590			0.965989			0.482994	+	0.875623i	$0.339549\pi$
$80$		0			0
$81$	7.87699			0.875222
$82$		0			0
$83$	3.73133			0.409567			0.204784	−	0.978807i	$-0.434351\pi$
$83$	3.73133			0.409567			0.204784	+	0.978807i	$0.434351\pi$
$84$		0			0
$85$	2.82376			0.306280
$86$		0			0
$87$	−1.35442	−	0.984045i	−0.145209	−	0.105501i
$88$		0			0
$89$	−4.09886	−	12.6150i	−0.434478	−	1.33719i	−0.893621	−	0.448823i	$-0.851843\pi$
$89$	−4.09886	−	12.6150i	−0.434478	−	1.33719i	0.459143	−	0.888363i	$-0.348157\pi$
$90$		0			0
$91$	−5.13227			−0.538009
$92$		0			0
$93$	0.803571	−	0.583829i	0.0833265	−	0.0605402i
$94$		0			0
$95$	−2.17078	+	6.68097i	−0.222717	+	0.685453i
$96$		0			0
$97$	9.84725	+	7.15445i	0.999837	+	0.726424i	0.962053	−	0.272862i	$-0.0879702\pi$
$97$	9.84725	+	7.15445i	0.999837	+	0.726424i	0.0377838	+	0.999286i	$0.487970\pi$
$98$		0			0
$99$	−9.74745	+	7.08193i	−0.979655	+	0.711761i
$100$		0			0
$101$	−3.62369	−	11.1526i	−0.360570	−	1.10972i	−0.952709	−	0.303885i	$-0.901716\pi$
$101$	−3.62369	−	11.1526i	−0.360570	−	1.10972i	0.592139	−	0.805836i	$-0.298284\pi$
$102$		0			0
$103$	−2.91210	−	8.96253i	−0.286938	−	0.883104i	−0.985811	−	0.167859i	$-0.946315\pi$
$103$	−2.91210	−	8.96253i	−0.286938	−	0.883104i	0.698873	−	0.715246i	$-0.253685\pi$
$104$		0			0
$105$	0.109426	−	0.336778i	0.0106789	−	0.0328662i
$106$		0			0
$107$	2.03096	+	6.25066i	0.196341	+	0.604274i	0.999958	+	0.00912850i	$0.00290573\pi$
$107$	2.03096	+	6.25066i	0.196341	+	0.604274i	−0.803618	+	0.595146i	$0.797094\pi$
$108$		0			0
$109$	−8.37152			−0.801846			−0.400923	−	0.916112i	$-0.631311\pi$
$109$	−8.37152			−0.801846			−0.400923	+	0.916112i	$0.631311\pi$
$110$		0			0
$111$	2.24282	+	1.62950i	0.212879	+	0.154665i
$112$		0			0
$113$	−10.0020	+	7.26688i	−0.940909	+	0.683611i	−0.948639	−	0.316359i	$-0.897539\pi$
$113$	−10.0020	+	7.26688i	−0.940909	+	0.683611i	0.00773005	+	0.999970i	$0.497539\pi$
$114$		0			0
$115$	−0.265502	+	0.192899i	−0.0247582	+	0.0179879i
$116$		0			0
$117$	4.57828	−	14.0905i	0.423262	−	1.30267i
$118$		0			0
$119$	2.27394	+	1.65211i	0.208452	+	0.151449i
$120$		0			0
$121$	2.03386	−	6.25959i	0.184897	−	0.569054i
$122$		0			0
$123$	−2.27513	−	0.112610i	−0.205141	−	0.0101537i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−10.7658	−	7.82182i	−0.955312	−	0.694075i	−0.00325465	−	0.999995i	$-0.501036\pi$
$127$	−10.7658	−	7.82182i	−0.955312	−	0.694075i	−0.952057	+	0.305920i	$0.901036\pi$
$128$		0			0
$129$	1.32977	−	4.09261i	0.117080	−	0.360334i
$130$		0			0
$131$	12.6103	−	9.16190i	1.10176	−	0.800479i	0.120418	−	0.992723i	$-0.461577\pi$
$131$	12.6103	−	9.16190i	1.10176	−	0.800479i	0.981347	+	0.192244i	$0.0615766\pi$
$132$		0			0
$133$	−5.65696	+	4.11002i	−0.490521	+	0.356384i
$134$		0			0
$135$	1.69042	+	1.22816i	0.145488	+	0.105704i
$136$		0			0
$137$	−18.7412			−1.60117			−0.800585	−	0.599219i	$-0.795478\pi$
$137$	−18.7412			−1.60117			−0.800585	+	0.599219i	$0.795478\pi$
$138$		0			0
$139$	−6.39792	−	19.6908i	−0.542665	−	1.67015i	−0.726478	−	0.687189i	$-0.758844\pi$
$139$	−6.39792	−	19.6908i	−0.542665	−	1.67015i	0.183813	−	0.982961i	$-0.441156\pi$
$140$		0			0
$141$	0.626839	−	1.92921i	0.0527894	−	0.162469i
$142$		0			0
$143$	6.68083	+	20.5615i	0.558679	+	1.71944i
$144$		0			0
$145$	1.45423	+	4.47567i	0.120767	+	0.371684i
$146$		0			0
$147$	−1.72950	+	1.25655i	−0.142646	+	0.103639i
$148$		0			0
$149$	−0.984161	−	0.715035i	−0.0806256	−	0.0585780i	0.546742	−	0.837301i	$-0.315868\pi$
$149$	−0.984161	−	0.715035i	−0.0806256	−	0.0585780i	−0.627368	+	0.778723i	$0.715868\pi$
$150$		0			0
$151$	6.52755	−	20.0897i	0.531205	−	1.63488i	−0.220505	−	0.975386i	$-0.570770\pi$
$151$	6.52755	−	20.0897i	0.531205	−	1.63488i	0.751709	−	0.659494i	$-0.229230\pi$
$152$		0			0
$153$	−6.56430	+	4.76924i	−0.530692	+	0.385571i
$154$		0			0
$155$	−2.79204			−0.224262
$156$		0			0
$157$	−5.38376	−	16.5695i	−0.429671	−	1.32239i	−0.898450	−	0.439075i	$-0.855306\pi$
$157$	−5.38376	−	16.5695i	−0.429671	−	1.32239i	0.468780	−	0.883315i	$-0.344694\pi$
$158$		0			0
$159$	−2.90617	−	2.11145i	−0.230474	−	0.167449i
$160$		0			0
$161$	−0.326665			−0.0257448
$162$		0			0
$163$	8.26118			0.647066			0.323533	−	0.946217i	$-0.395129\pi$
$163$	8.26118			0.647066			0.323533	+	0.946217i	$0.395129\pi$
$164$		0			0
$165$	−1.49168			−0.116127
$166$		0			0
$167$	−4.54182			−0.351457			−0.175728	−	0.984439i	$-0.556228\pi$
$167$	−4.54182			−0.351457			−0.175728	+	0.984439i	$0.556228\pi$
$168$		0			0
$169$	−10.9904	−	7.98500i	−0.845416	−	0.614231i
$170$		0			0
$171$	−6.23760	−	19.1974i	−0.477001	−	1.46806i
$172$		0			0
$173$	−9.38787			−0.713746			−0.356873	−	0.934153i	$-0.616157\pi$
$173$	−9.38787			−0.713746			−0.356873	+	0.934153i	$0.616157\pi$
$174$		0			0
$175$	−0.805286	+	0.585074i	−0.0608739	+	0.0442275i
$176$		0			0
$177$	0.377390	−	1.16149i	0.0283663	−	0.0873026i
$178$		0			0
$179$	4.12004	+	2.99338i	0.307946	+	0.223736i	0.731015	−	0.682362i	$-0.239047\pi$
$179$	4.12004	+	2.99338i	0.307946	+	0.223736i	−0.423069	+	0.906098i	$0.639047\pi$
$180$		0			0
$181$	5.63403	−	4.09337i	0.418774	−	0.304257i	−0.358370	−	0.933580i	$-0.616667\pi$
$181$	5.63403	−	4.09337i	0.418774	−	0.304257i	0.777145	+	0.629322i	$0.216667\pi$
$182$		0			0
$183$	1.43370	+	4.41246i	0.105982	+	0.326179i
$184$		0			0
$185$	−2.40809	−	7.41135i	−0.177047	−	0.544894i
$186$		0			0
$187$	3.65882	−	11.2607i	0.267560	−	0.823464i
$188$		0			0
$189$	0.642706	+	1.97805i	0.0467500	+	0.143882i
$190$		0			0
$191$	10.9352			0.791247			0.395623	−	0.918413i	$-0.370529\pi$
$191$	10.9352			0.791247			0.395623	+	0.918413i	$0.370529\pi$
$192$		0			0
$193$	−9.14354	−	6.64317i	−0.658166	−	0.478186i	0.207877	−	0.978155i	$-0.433345\pi$
$193$	−9.14354	−	6.64317i	−0.658166	−	0.478186i	−0.866043	+	0.499969i	$0.833345\pi$
$194$		0			0
$195$	1.48395	−	1.07815i	0.106268	−	0.0772083i
$196$		0			0
$197$	18.8265	−	13.6783i	1.34134	−	0.974537i	0.341942	−	0.939721i	$-0.388915\pi$
$197$	18.8265	−	13.6783i	1.34134	−	0.974537i	0.999394	−	0.0348164i	$-0.0110846\pi$
$198$		0			0
$199$	−0.657008	+	2.02206i	−0.0465740	+	0.143340i	−0.971639	−	0.236468i	$-0.924010\pi$
$199$	−0.657008	+	2.02206i	−0.0465740	+	0.143340i	0.925065	+	0.379808i	$0.124010\pi$
$200$		0			0
$201$	−2.73200	−	1.98492i	−0.192701	−	0.140005i
$202$		0			0
$203$	−1.44753	+	4.45503i	−0.101596	+	0.312682i
$204$		0			0
$205$	4.98784	+	4.01515i	0.348366	+	0.280430i
$206$		0			0
$207$	0.291404	−	0.896849i	0.0202540	−	0.0623353i
$208$		0			0
$209$	23.8298	+	17.3134i	1.64835	+	1.19759i
$210$		0			0
$211$	0.0356925	−	0.109850i	0.00245717	−	0.00756240i	−0.949820	−	0.312796i	$-0.898734\pi$
$211$	0.0356925	−	0.109850i	0.00245717	−	0.00756240i	0.952278	+	0.305233i	$0.0987345\pi$
$212$		0			0
$213$	4.22023	−	3.06618i	0.289165	−	0.210091i
$214$		0			0
$215$	−9.78603	+	7.10997i	−0.667402	+	0.484896i
$216$		0			0
$217$	−2.24839	−	1.63355i	−0.152631	−	0.110893i
$218$		0			0
$219$	−2.24734			−0.151861
$220$		0			0
$221$	4.49913	+	13.8469i	0.302644	+	0.931443i
$222$		0			0
$223$	−8.61825	+	26.5243i	−0.577121	+	1.77620i	0.0517200	+	0.998662i	$0.483530\pi$
$223$	−8.61825	+	26.5243i	−0.577121	+	1.77620i	−0.628841	+	0.777534i	$0.716470\pi$
$224$		0			0
$225$	−0.887942	−	2.73281i	−0.0591962	−	0.182187i
$226$		0			0
$227$	−0.943262	−	2.90306i	−0.0626065	−	0.192683i	0.914861	−	0.403769i	$-0.132300\pi$
$227$	−0.943262	−	2.90306i	−0.0626065	−	0.192683i	−0.977468	+	0.211086i	$0.932300\pi$
$228$		0			0
$229$	3.02921	−	2.20085i	0.200176	−	0.145436i	−0.483182	−	0.875520i	$-0.660519\pi$
$229$	3.02921	−	2.20085i	0.200176	−	0.145436i	0.683358	+	0.730084i	$0.260519\pi$
$230$		0			0
$231$	−1.20123	−	0.872744i	−0.0790351	−	0.0574223i
$232$		0			0
$233$	−4.36051	+	13.4203i	−0.285667	+	0.879192i	0.700531	+	0.713622i	$0.252946\pi$
$233$	−4.36051	+	13.4203i	−0.285667	+	0.879192i	−0.986198	+	0.165570i	$0.947054\pi$
$234$		0			0
$235$	−4.61303	+	3.35156i	−0.300921	+	0.218632i
$236$		0			0
$237$	−3.05443			−0.198407
$238$		0			0
$239$	−2.97529	−	9.15701i	−0.192456	−	0.592318i	−0.999997	−	0.00250651i	$-0.999202\pi$
$239$	−2.97529	−	9.15701i	−0.192456	−	0.592318i	0.807541	−	0.589811i	$-0.200798\pi$
$240$		0			0
$241$	−4.79254	−	3.48198i	−0.308715	−	0.224294i	0.422630	−	0.906302i	$-0.361107\pi$
$241$	−4.79254	−	3.48198i	−0.308715	−	0.224294i	−0.731345	+	0.682008i	$0.761107\pi$
$242$		0			0
$243$	−9.07067			−0.581884
$244$		0			0
$245$	6.00920			0.383914
$246$		0			0
$247$	−36.2202			−2.30463
$248$		0			0
$249$	−1.32742			−0.0841220
$250$		0			0
$251$	−12.6861	−	9.21698i	−0.800738	−	0.581770i	0.110392	−	0.993888i	$-0.464789\pi$
$251$	−12.6861	−	9.21698i	−0.800738	−	0.581770i	−0.911131	+	0.412118i	$0.864789\pi$
$252$		0			0
$253$	0.425230	+	1.30872i	0.0267340	+	0.0822787i
$254$		0			0
$255$	−1.00455			−0.0629076
$256$		0			0
$257$	22.8082	−	16.5711i	1.42274	−	1.03368i	0.431425	−	0.902149i	$-0.358011\pi$
$257$	22.8082	−	16.5711i	1.42274	−	1.03368i	0.991312	−	0.131531i	$-0.0419892\pi$
$258$		0			0
$259$	2.39699	−	7.37717i	0.148942	−	0.458395i
$260$		0			0
$261$	−10.9399	−	7.94827i	−0.677160	−	0.491986i
$262$		0			0
$263$	7.17870	−	5.21563i	0.442657	−	0.321609i	−0.344033	−	0.938958i	$-0.611793\pi$
$263$	7.17870	−	5.21563i	0.442657	−	0.321609i	0.786690	+	0.617348i	$0.211793\pi$
$264$		0			0
$265$	3.12033	+	9.60338i	0.191680	+	0.589931i
$266$		0			0
$267$	1.45817	+	4.48778i	0.0892385	+	0.274648i
$268$		0			0
$269$	−3.51955	+	10.8321i	−0.214591	+	0.660442i	0.784592	+	0.620013i	$0.212873\pi$
$269$	−3.51955	+	10.8321i	−0.214591	+	0.660442i	−0.999182	+	0.0404293i	$0.987127\pi$
$270$		0			0
$271$	3.10603	+	9.55937i	0.188678	+	0.580690i	0.999992	−	0.00391959i	$-0.00124765\pi$
$271$	3.10603	+	9.55937i	0.188678	+	0.580690i	−0.811315	+	0.584610i	$0.801248\pi$
$272$		0			0
$273$	1.82581			0.110503
$274$		0			0
$275$	3.39225	+	2.46462i	0.204561	+	0.148622i
$276$		0			0
$277$	11.9077	−	8.65144i	0.715463	−	0.519815i	−0.169468	−	0.985536i	$-0.554205\pi$
$277$	11.9077	−	8.65144i	0.715463	−	0.519815i	0.884932	+	0.465721i	$0.154205\pi$
$278$		0			0
$279$	6.49056	−	4.71567i	0.388579	−	0.282319i
$280$		0			0
$281$	5.13225	−	15.7954i	0.306164	−	0.942277i	−0.673076	−	0.739573i	$-0.735027\pi$
$281$	5.13225	−	15.7954i	0.306164	−	0.942277i	0.979240	−	0.202703i	$-0.0649727\pi$
$282$		0			0
$283$	−2.61744	−	1.90168i	−0.155591	−	0.113043i	0.507266	−	0.861790i	$-0.330656\pi$
$283$	−2.61744	−	1.90168i	−0.155591	−	0.113043i	−0.662857	+	0.748746i	$0.730656\pi$
$284$		0			0
$285$	0.772254	−	2.37675i	0.0457444	−	0.140787i
$286$		0			0
$287$	1.66748	+	6.15160i	0.0984282	+	0.363118i
$288$		0			0
$289$	−2.78930	+	8.58457i	−0.164076	+	0.504975i
$290$		0			0
$291$	−3.50316	−	2.54520i	−0.205359	−	0.149202i
$292$		0			0
$293$	0.0617383	−	0.190011i	0.00360679	−	0.0111006i	−0.949237	−	0.314562i	$-0.898142\pi$
$293$	0.0617383	−	0.190011i	0.00360679	−	0.0111006i	0.952844	+	0.303461i	$0.0981424\pi$
$294$		0			0
$295$	−2.77728	+	2.01782i	−0.161700	+	0.117482i
$296$		0			0
$297$	7.08804	−	5.14976i	0.411290	−	0.298819i
$298$		0			0
$299$	−1.36894	−	0.994596i	−0.0791681	−	0.0575190i
$300$		0			0
$301$	−12.0404			−0.693998
$302$		0			0
$303$	1.28913	+	3.96752i	0.0740584	+	0.227928i
$304$		0			0
$305$	4.03007	−	12.4033i	0.230761	−	0.710209i
$306$		0			0
$307$	−0.475445	−	1.46327i	−0.0271351	−	0.0835132i	0.936572	−	0.350476i	$-0.113980\pi$
$307$	−0.475445	−	1.46327i	−0.0271351	−	0.0835132i	−0.963707	+	0.266962i	$0.913980\pi$
$308$		0			0
$309$	1.03598	+	3.18842i	0.0589349	+	0.181383i
$310$		0			0
$311$	−7.77287	+	5.64732i	−0.440759	+	0.320230i	−0.785937	−	0.618307i	$-0.787819\pi$
$311$	−7.77287	+	5.64732i	−0.440759	+	0.320230i	0.345177	+	0.938537i	$0.387819\pi$
$312$		0			0
$313$	−21.5791	−	15.6782i	−1.21973	−	0.886182i	−0.223648	−	0.974670i	$-0.571797\pi$
$313$	−21.5791	−	15.6782i	−1.21973	−	0.886182i	−0.996077	+	0.0884879i	$0.971797\pi$
$314$		0			0
$315$	0.883847	−	2.72020i	0.0497992	−	0.153266i
$316$		0			0
$317$	12.0312	−	8.74117i	0.675739	−	0.490953i	−0.196202	−	0.980563i	$-0.562861\pi$
$317$	12.0312	−	8.74117i	0.675739	−	0.490953i	0.871941	+	0.489610i	$0.162861\pi$
$318$		0			0
$319$	19.7325			1.10481
$320$		0			0
$321$	−0.722515	−	2.22367i	−0.0403269	−	0.124113i
$322$		0			0
$323$	16.0479	+	11.6595i	0.892931	+	0.648752i
$324$		0			0
$325$	−5.15605			−0.286006
$326$		0			0
$327$	2.97817			0.164693
$328$		0			0
$329$	−5.67572			−0.312913
$330$		0			0
$331$	31.6482			1.73954			0.869771	−	0.493455i	$-0.164266\pi$
$331$	31.6482			1.73954			0.869771	+	0.493455i	$0.164266\pi$
$332$		0			0
$333$	18.1155	+	13.1617i	0.992725	+	0.721257i
$334$		0			0
$335$	2.93333	+	9.02787i	0.160265	+	0.493245i
$336$		0			0
$337$	24.7665			1.34912			0.674560	−	0.738220i	$-0.264334\pi$
$337$	24.7665			1.34912			0.674560	+	0.738220i	$0.264334\pi$
$338$		0			0
$339$	3.55821	−	2.58519i	0.193256	−	0.140408i
$340$		0			0
$341$	−3.61772	+	11.1342i	−0.195911	+	0.602951i
$342$		0			0
$343$	10.4761	+	7.61135i	0.565658	+	0.410974i
$344$		0			0
$345$	0.0944524	−	0.0686237i	0.00508515	−	0.00369458i
$346$		0			0
$347$	10.2223	+	31.4611i	0.548764	+	1.68892i	0.711869	+	0.702312i	$0.247849\pi$
$347$	10.2223	+	31.4611i	0.548764	+	1.68892i	−0.163105	+	0.986609i	$0.552151\pi$
$348$		0			0
$349$	−5.18362	−	15.9536i	−0.277473	−	0.853974i	−0.988554	−	0.150865i	$-0.951794\pi$
$349$	−5.18362	−	15.9536i	−0.277473	−	0.853974i	0.711081	−	0.703110i	$-0.248206\pi$
$350$		0			0
$351$	−3.32918	+	10.2462i	−0.177699	+	0.546900i
$352$		0			0
$353$	−4.09224	−	12.5946i	−0.217808	−	0.670344i	−0.998942	−	0.0459811i	$-0.985359\pi$
$353$	−4.09224	−	12.5946i	−0.217808	−	0.670344i	0.781134	−	0.624363i	$-0.214641\pi$
$354$		0			0
$355$	−14.6634			−0.778250
$356$		0			0
$357$	−0.808953	−	0.587739i	−0.0428144	−	0.0311065i
$358$		0			0
$359$	−28.4123	+	20.6427i	−1.49954	+	1.08948i	−0.528982	+	0.848633i	$0.677426\pi$
$359$	−28.4123	+	20.6427i	−1.49954	+	1.08948i	−0.970562	+	0.240849i	$0.922574\pi$
$360$		0			0
$361$	−24.5517	+	17.8379i	−1.29220	+	0.938835i
$362$		0			0
$363$	−0.723547	+	2.22685i	−0.0379764	+	0.116879i
$364$		0			0
$365$	5.11071	+	3.71315i	0.267507	+	0.194355i
$366$		0			0
$367$	−8.54315	+	26.2931i	−0.445949	+	1.37249i	0.435491	+	0.900193i	$0.356575\pi$
$367$	−8.54315	+	26.2931i	−0.445949	+	1.37249i	−0.881440	+	0.472296i	$0.843425\pi$
$368$		0			0
$369$	−18.3765	−	0.909568i	−0.956643	−	0.0473502i
$370$		0			0
$371$	−3.10594	+	9.55909i	−0.161252	+	0.496283i
$372$		0			0
$373$	11.1021	+	8.06615i	0.574845	+	0.417649i	0.836862	−	0.547414i	$-0.184388\pi$
$373$	11.1021	+	8.06615i	0.574845	+	0.417649i	−0.262017	+	0.965063i	$0.584388\pi$
$374$		0			0
$375$	0.109933	−	0.338338i	0.00567691	−	0.0174717i
$376$		0			0
$377$	−19.6303	+	14.2622i	−1.01101	+	0.734543i
$378$		0			0
$379$	14.2556	−	10.3573i	0.732262	−	0.532019i	−0.158016	−	0.987436i	$-0.550510\pi$
$379$	14.2556	−	10.3573i	0.732262	−	0.532019i	0.890278	+	0.455417i	$0.150510\pi$
$380$		0			0
$381$	3.82994	+	2.78261i	0.196214	+	0.142558i
$382$		0			0
$383$	5.29390			0.270506			0.135253	−	0.990811i	$-0.456815\pi$
$383$	5.29390			0.270506			0.135253	+	0.990811i	$0.456815\pi$
$384$		0			0
$385$	1.28975	+	3.96944i	0.0657317	+	0.202302i
$386$		0			0
$387$	10.7407	−	33.0566i	0.545982	−	1.68036i
$388$		0			0
$389$	5.20932	+	16.0327i	0.264123	+	0.812888i	0.991894	+	0.127067i	$0.0405564\pi$
$389$	5.20932	+	16.0327i	0.264123	+	0.812888i	−0.727771	+	0.685820i	$0.759444\pi$
$390$		0			0
$391$	0.286366	+	0.881344i	0.0144821	+	0.0445715i
$392$		0			0
$393$	−4.48611	+	3.25935i	−0.226294	+	0.164412i
$394$		0			0
$395$	6.94614	+	5.04666i	0.349498	+	0.253925i
$396$		0			0
$397$	−10.7901	+	33.2085i	−0.541540	+	1.66669i	0.187538	+	0.982257i	$0.439949\pi$
$397$	−10.7901	+	33.2085i	−0.541540	+	1.66669i	−0.729078	+	0.684431i	$0.760051\pi$
$398$		0			0
$399$	2.01246	−	1.46214i	0.100749	−	0.0731986i
$400$		0			0
$401$	−3.36461			−0.168021			−0.0840104	−	0.996465i	$-0.526773\pi$
$401$	−3.36461			−0.168021			−0.0840104	+	0.996465i	$0.526773\pi$
$402$		0			0
$403$	−4.44858	−	13.6913i	−0.221600	−	0.682014i
$404$		0			0
$405$	6.37262	+	4.62998i	0.316658	+	0.230066i
$406$		0			0
$407$	−32.6755			−1.61966
$408$		0			0
$409$	−14.4700			−0.715494			−0.357747	−	0.933819i	$-0.616455\pi$
$409$	−14.4700			−0.715494			−0.357747	+	0.933819i	$0.616455\pi$
$410$		0			0
$411$	6.66719			0.328868
$412$		0			0
$413$	−3.41708			−0.168144
$414$		0			0
$415$	3.01871	+	2.19322i	0.148183	+	0.107661i
$416$		0			0
$417$	2.27606	+	7.00500i	0.111459	+	0.343036i
$418$		0			0
$419$	40.4142			1.97437			0.987183	−	0.159595i	$-0.0510189\pi$
$419$	40.4142			1.97437			0.987183	+	0.159595i	$0.0510189\pi$
$420$		0			0
$421$	−4.92080	+	3.57517i	−0.239825	+	0.174243i	−0.701205	−	0.712959i	$-0.747354\pi$
$421$	−4.92080	+	3.57517i	−0.239825	+	0.174243i	0.461380	+	0.887203i	$0.347354\pi$
$422$		0			0
$423$	5.06306	−	15.5825i	0.246175	−	0.757648i
$424$		0			0
$425$	2.28447	+	1.65977i	0.110813	+	0.0805105i
$426$		0			0
$427$	10.5022	−	7.63029i	0.508237	−	0.369256i
$428$		0			0
$429$	−2.37671	−	7.31475i	−0.114748	−	0.353159i
$430$		0			0
$431$	1.00239	+	3.08504i	0.0482834	+	0.148601i	0.972291	−	0.233772i	$-0.0751069\pi$
$431$	1.00239	+	3.08504i	0.0482834	+	0.148601i	−0.924008	+	0.382373i	$0.875107\pi$
$432$		0			0
$433$	4.27562	−	13.1590i	0.205473	−	0.632382i	−0.794220	−	0.607630i	$-0.792120\pi$
$433$	4.27562	−	13.1590i	0.205473	−	0.632382i	0.999694	−	0.0247518i	$-0.00787956\pi$
$434$		0			0
$435$	−0.517343	−	1.59222i	−0.0248047	−	0.0763411i
$436$		0			0
$437$	−2.30538			−0.110282
$438$		0			0
$439$	16.0428	+	11.6558i	0.765681	+	0.556300i	0.900648	−	0.434550i	$-0.143093\pi$
$439$	16.0428	+	11.6558i	0.765681	+	0.556300i	−0.134966	+	0.990850i	$0.543093\pi$
$440$		0			0
$441$	−13.9694	+	10.1493i	−0.665208	+	0.483302i
$442$		0			0
$443$	25.0636	−	18.2098i	1.19081	−	0.865174i	0.197460	−	0.980311i	$-0.436731\pi$
$443$	25.0636	−	18.2098i	1.19081	−	0.865174i	0.993350	+	0.115137i	$0.0367308\pi$
$444$		0			0
$445$	4.09886	−	12.6150i	0.194304	−	0.598008i
$446$		0			0
$447$	0.350115	+	0.254374i	0.0165599	+	0.0120315i
$448$		0			0
$449$	1.11295	−	3.42531i	0.0525234	−	0.161650i	−0.921354	−	0.388724i	$-0.872916\pi$
$449$	1.11295	−	3.42531i	0.0525234	−	0.161650i	0.973878	+	0.227074i	$0.0729159\pi$
$450$		0			0
$451$	22.4746	−	14.6882i	1.05829	−	0.691638i
$452$		0			0
$453$	−2.32218	+	7.14693i	−0.109105	+	0.335792i
$454$		0			0
$455$	−4.15210	−	3.01668i	−0.194653	−	0.141424i
$456$		0			0
$457$	−3.20561	+	9.86586i	−0.149952	+	0.461506i	−0.997615	−	0.0690306i	$-0.978009\pi$
$457$	−3.20561	+	9.86586i	−0.149952	+	0.461506i	0.847662	+	0.530536i	$0.178009\pi$
$458$		0			0
$459$	4.77336	−	3.46805i	0.222801	−	0.161875i
$460$		0			0
$461$	26.1878	−	19.0265i	1.21969	−	0.886154i	0.223613	−	0.974678i	$-0.428215\pi$
$461$	26.1878	−	19.0265i	1.21969	−	0.886154i	0.996074	+	0.0885239i	$0.0282150\pi$
$462$		0			0
$463$	−33.8023	−	24.5588i	−1.57093	−	1.14134i	−0.926263	−	0.376878i	$-0.876998\pi$
$463$	−33.8023	−	24.5588i	−1.57093	−	1.14134i	−0.644663	−	0.764467i	$-0.723002\pi$
$464$		0			0
$465$	0.993269			0.0460617
$466$		0			0
$467$	5.70350	+	17.5536i	0.263926	+	0.812282i	0.991939	+	0.126718i	$0.0404443\pi$
$467$	5.70350	+	17.5536i	0.263926	+	0.812282i	−0.728012	+	0.685564i	$0.759556\pi$
$468$		0			0
$469$	−2.91980	+	8.98623i	−0.134824	+	0.414946i
$470$		0			0
$471$	1.91527	+	5.89460i	0.0882511	+	0.271609i
$472$		0			0
$473$	15.6734	+	48.2376i	0.720662	+	2.21797i
$474$		0			0
$475$	−5.68317	+	4.12906i	−0.260762	+	0.189454i
$476$		0			0
$477$	−23.4735	−	17.0545i	−1.07478	−	0.780872i
$478$		0			0
$479$	−4.41028	+	13.5734i	−0.201511	+	0.620186i	0.798328	+	0.602223i	$0.205718\pi$
$479$	−4.41028	+	13.5734i	−0.201511	+	0.620186i	−0.999839	+	0.0179634i	$0.994282\pi$
$480$		0			0
$481$	32.5062	−	23.6171i	1.48216	−	1.07685i
$482$		0			0
$483$	0.116211			0.00528779
$484$		0			0
$485$	3.76132	+	11.5761i	0.170793	+	0.525645i
$486$		0			0
$487$	−9.50916	−	6.90881i	−0.430901	−	0.313068i	0.351108	−	0.936335i	$-0.385805\pi$
$487$	−9.50916	−	6.90881i	−0.430901	−	0.313068i	−0.782009	+	0.623267i	$0.785805\pi$
$488$		0			0
$489$	−2.93892			−0.132902
$490$		0			0
$491$	10.1144			0.456456			0.228228	−	0.973608i	$-0.426707\pi$
$491$	10.1144			0.456456			0.228228	+	0.973608i	$0.426707\pi$
$492$		0			0
$493$	13.2886			0.598490
$494$		0			0
$495$	−12.0485			−0.541540
$496$		0			0
$497$	−11.8082	−	8.57916i	−0.529670	−	0.384828i
$498$		0			0
$499$	−7.40518	−	22.7908i	−0.331501	−	1.02026i	−0.968420	−	0.249325i	$-0.919791\pi$
$499$	−7.40518	−	22.7908i	−0.331501	−	1.02026i	0.636919	−	0.770931i	$-0.280209\pi$
$500$		0			0
$501$	1.61575			0.0721865
$502$		0			0
$503$	−9.38291	+	6.81708i	−0.418363	+	0.303959i	−0.776979	−	0.629527i	$-0.783249\pi$
$503$	−9.38291	+	6.81708i	−0.418363	+	0.303959i	0.358616	+	0.933485i	$0.383249\pi$
$504$		0			0
$505$	3.62369	−	11.1526i	0.161252	−	0.496282i
$506$		0			0
$507$	3.90984	+	2.84066i	0.173642	+	0.126158i
$508$		0			0
$509$	−12.2483	+	8.89889i	−0.542895	+	0.394436i	−0.825159	−	0.564900i	$-0.808915\pi$
$509$	−12.2483	+	8.89889i	−0.542895	+	0.394436i	0.282264	+	0.959337i	$0.408915\pi$
$510$		0			0
$511$	1.94311	+	5.98029i	0.0859583	+	0.264552i
$512$		0			0
$513$	4.53579	+	13.9597i	0.200260	+	0.616337i
$514$		0			0
$515$	2.91210	−	8.96253i	0.128323	−	0.394936i
$516$		0			0
$517$	7.38825	+	22.7387i	0.324935	+	1.00005i
$518$		0			0
$519$	3.33973			0.146598
$520$		0			0
$521$	28.2808	+	20.5472i	1.23900	+	0.900189i	0.997532	−	0.0702183i	$-0.0223696\pi$
$521$	28.2808	+	20.5472i	1.23900	+	0.900189i	0.241473	+	0.970408i	$0.422370\pi$
$522$		0			0
$523$	−25.0138	+	18.1736i	−1.09378	+	0.794676i	−0.980033	−	0.198834i	$-0.936285\pi$
$523$	−25.0138	+	18.1736i	−1.09378	+	0.794676i	−0.113745	+	0.993510i	$0.536285\pi$
$524$		0			0
$525$	0.286480	−	0.208140i	0.0125030	−	0.00908399i
$526$		0			0
$527$	−2.43631	+	7.49819i	−0.106127	+	0.326626i
$528$		0			0
$529$	18.5203	+	13.4558i	0.805229	+	0.585033i
$530$		0			0
$531$	3.04823	−	9.38148i	0.132282	−	0.407122i
$532$		0			0
$533$	−11.7419	+	30.8562i	−0.508598	+	1.33653i
$534$		0			0
$535$	−2.03096	+	6.25066i	−0.0878062	+	0.270240i
$536$		0			0
$537$	−1.46570	−	1.06490i	−0.0632498	−	0.0459537i
$538$		0			0
$539$	7.78628	−	23.9637i	0.335379	−	1.03219i
$540$		0			0
$541$	−25.6891	+	18.6642i	−1.10446	+	0.802437i	−0.981782	−	0.190010i	$-0.939148\pi$
$541$	−25.6891	+	18.6642i	−1.10446	+	0.802437i	−0.122677	+	0.992447i	$0.539148\pi$
$542$		0			0
$543$	−2.00431	+	1.45621i	−0.0860131	+	0.0624922i
$544$		0			0
$545$	−6.77270	−	4.92065i	−0.290111	−	0.210778i
$546$		0			0
$547$	2.46912			0.105572			0.0527859	−	0.998606i	$-0.483190\pi$
$547$	2.46912			0.105572			0.0527859	+	0.998606i	$0.483190\pi$
$548$		0			0
$549$	11.5802	+	35.6401i	0.494229	+	1.52108i
$550$		0			0
$551$	−10.2157	+	31.4406i	−0.435202	+	1.33941i
$552$		0			0
$553$	2.64095	+	8.12801i	0.112305	+	0.345638i
$554$		0			0
$555$	0.856680	+	2.63659i	0.0363640	+	0.111917i
$556$		0			0
$557$	20.0511	−	14.5680i	0.849591	−	0.617264i	−0.0754420	−	0.997150i	$-0.524037\pi$
$557$	20.0511	−	14.5680i	0.849591	−	0.617264i	0.925033	+	0.379886i	$0.124037\pi$
$558$		0			0
$559$	−50.4573	−	36.6594i	−2.13412	−	1.55053i
$560$		0			0
$561$	−1.30163	+	4.00600i	−0.0549547	+	0.169133i
$562$		0			0
$563$	1.26574	−	0.919611i	0.0533444	−	0.0387570i	−0.560794	−	0.827956i	$-0.689504\pi$
$563$	1.26574	−	0.919611i	0.0533444	−	0.0387570i	0.614138	+	0.789199i	$0.289504\pi$
$564$		0			0
$565$	−12.3632			−0.520122
$566$		0			0
$567$	2.42290	+	7.45692i	0.101752	+	0.313161i
$568$		0			0
$569$	13.5794	+	9.86599i	0.569277	+	0.413604i	0.834842	−	0.550489i	$-0.185559\pi$
$569$	13.5794	+	9.86599i	0.569277	+	0.413604i	−0.265566	+	0.964093i	$0.585559\pi$
$570$		0			0
$571$	7.74233			0.324006			0.162003	−	0.986790i	$-0.448205\pi$
$571$	7.74233			0.324006			0.162003	+	0.986790i	$0.448205\pi$
$572$		0			0
$573$	−3.89021			−0.162516
$574$		0			0
$575$	−0.328179			−0.0136860
$576$		0			0
$577$	28.4600			1.18480			0.592402	−	0.805643i	$-0.298180\pi$
$577$	28.4600			1.18480			0.592402	+	0.805643i	$0.298180\pi$
$578$		0			0
$579$	3.25281	+	2.36331i	0.135182	+	0.0982157i
$580$		0			0
$581$	1.14773	+	3.53234i	0.0476158	+	0.146546i
$582$		0			0
$583$	42.3398			1.75353
$584$		0			0
$585$	11.9861	−	8.70840i	0.495564	−	0.360048i
$586$		0			0
$587$	−3.21387	+	9.89128i	−0.132651	+	0.408257i	−0.995217	−	0.0976868i	$-0.968856\pi$
$587$	−3.21387	+	9.89128i	−0.132651	+	0.408257i	0.862566	+	0.505944i	$0.168856\pi$
$588$		0			0
$589$	−15.8676	−	11.5285i	−0.653815	−	0.475024i
$590$		0			0
$591$	−6.69754	+	4.86605i	−0.275500	+	0.200163i
$592$		0			0
$593$	−7.13117	−	21.9475i	−0.292842	−	0.901276i	−0.983938	−	0.178512i	$-0.942872\pi$
$593$	−7.13117	−	21.9475i	−0.292842	−	0.901276i	0.691095	−	0.722763i	$-0.257128\pi$
$594$		0			0
$595$	0.868567	+	2.67317i	0.0356078	+	0.109589i
$596$		0			0
$597$	0.233730	−	0.719349i	0.00956595	−	0.0294410i
$598$		0			0
$599$	5.16025	+	15.8816i	0.210842	+	0.648906i	0.999423	+	0.0339742i	$0.0108164\pi$
$599$	5.16025	+	15.8816i	0.210842	+	0.648906i	−0.788580	+	0.614932i	$0.789184\pi$
$600$		0			0
$601$	−25.2778			−1.03110			−0.515551	−	0.856859i	$-0.672413\pi$
$601$	−25.2778			−1.03110			−0.515551	+	0.856859i	$0.672413\pi$
$602$		0			0
$603$	−22.0668	−	16.0325i	−0.898629	−	0.652892i
$604$		0			0
$605$	5.32473	−	3.86864i	0.216481	−	0.157283i
$606$		0			0
$607$	−6.53243	+	4.74609i	−0.265143	+	0.192638i	−0.712411	−	0.701762i	$-0.752397\pi$
$607$	−6.53243	+	4.74609i	−0.265143	+	0.192638i	0.447268	+	0.894400i	$0.352397\pi$
$608$		0			0
$609$	0.514957	−	1.58488i	0.0208671	−	0.0642224i
$610$		0			0
$611$	−23.7850	−	17.2808i	−0.962239	−	0.699108i
$612$		0			0
$613$	14.8899	−	45.8265i	0.601398	−	1.85091i	0.0815244	−	0.996671i	$-0.474021\pi$
$613$	14.8899	−	45.8265i	0.601398	−	1.85091i	0.519874	−	0.854243i	$-0.325979\pi$
$614$		0			0
$615$	−1.77443	−	1.42839i	−0.0715517	−	0.0575982i
$616$		0			0
$617$	13.0695	−	40.2239i	0.526160	−	1.61935i	−0.235851	−	0.971789i	$-0.575788\pi$
$617$	13.0695	−	40.2239i	0.526160	−	1.61935i	0.762011	−	0.647565i	$-0.224212\pi$
$618$		0			0
$619$	−2.12691	−	1.54529i	−0.0854879	−	0.0621106i	0.544220	−	0.838942i	$-0.316826\pi$
$619$	−2.12691	−	1.54529i	−0.0854879	−	0.0621106i	−0.629708	+	0.776832i	$0.716826\pi$
$620$		0			0
$621$	−0.211900	+	0.652160i	−0.00850325	+	0.0261703i
$622$		0			0
$623$	10.6815	−	7.76053i	0.427944	−	0.310919i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−8.47747	−	6.15924i	−0.338558	−	0.245976i
$628$		0			0
$629$	−22.0049			−0.877393
$630$		0			0
$631$	3.04260	+	9.36417i	0.121124	+	0.372782i	0.993175	−	0.116633i	$-0.0372103\pi$
$631$	3.04260	+	9.36417i	0.121124	+	0.372782i	−0.872051	+	0.489415i	$0.837210\pi$
$632$		0			0
$633$	−0.0126976	+	0.0390792i	−0.000504685	+	0.00155326i
$634$		0			0
$635$	−4.11218	−	12.6560i	−0.163187	−	0.502237i
$636$		0			0
$637$	9.57451	+	29.4673i	0.379356	+	1.16754i
$638$		0			0
$639$	34.0874	−	24.7659i	1.34848	−	0.979725i
$640$		0			0
$641$	27.6805	+	20.1110i	1.09331	+	0.794339i	0.979956	−	0.199216i	$-0.0638394\pi$
$641$	27.6805	+	20.1110i	1.09331	+	0.794339i	0.113358	+	0.993554i	$0.463839\pi$
$642$		0			0
$643$	12.2929	−	37.8338i	0.484786	−	1.49202i	−0.347505	−	0.937678i	$-0.612971\pi$
$643$	12.2929	−	37.8338i	0.484786	−	1.49202i	0.832291	−	0.554339i	$-0.187029\pi$
$644$		0			0
$645$	3.48138	−	2.52937i	0.137079	−	0.0995939i
$646$		0			0
$647$	15.5622			0.611811			0.305906	−	0.952062i	$-0.401041\pi$
$647$	15.5622			0.611811			0.305906	+	0.952062i	$0.401041\pi$
$648$		0			0
$649$	4.44811	+	13.6899i	0.174604	+	0.537375i
$650$		0			0
$651$	0.799865	+	0.581136i	0.0313492	+	0.0227765i
$652$		0			0
$653$	−20.5229			−0.803121			−0.401561	−	0.915832i	$-0.631532\pi$
$653$	−20.5229			−0.803121			−0.401561	+	0.915832i	$0.631532\pi$
$654$		0			0
$655$	15.5872			0.609041
$656$		0			0
$657$	−18.1521			−0.708179
$658$		0			0
$659$	7.97088			0.310501			0.155251	−	0.987875i	$-0.450381\pi$
$659$	7.97088			0.310501			0.155251	+	0.987875i	$0.450381\pi$
$660$		0			0
$661$	−14.4168	−	10.4744i	−0.560748	−	0.407408i	0.270984	−	0.962584i	$-0.412651\pi$
$661$	−14.4168	−	10.4744i	−0.560748	−	0.407408i	−0.831733	+	0.555176i	$0.812651\pi$
$662$		0			0
$663$	−1.60056	−	4.92603i	−0.0621608	−	0.191311i
$664$		0			0
$665$	−6.99239			−0.271153
$666$		0			0
$667$	−1.24945	+	0.907780i	−0.0483790	+	0.0351494i
$668$		0			0
$669$	3.06594	−	9.43601i	0.118536	−	0.364817i
$670$		0			0
$671$	−44.2403	−	32.1425i	−1.70788	−	1.24085i
$672$		0			0
$673$	−12.6471	+	9.18865i	−0.487510	+	0.354196i	−0.804226	−	0.594324i	$-0.797420\pi$
$673$	−12.6471	+	9.18865i	−0.487510	+	0.354196i	0.316716	+	0.948520i	$0.397420\pi$
$674$		0			0
$675$	0.645684	+	1.98721i	0.0248524	+	0.0764878i
$676$		0			0
$677$	−2.51014	−	7.72543i	−0.0964727	−	0.296912i	0.891162	−	0.453685i	$-0.149891\pi$
$677$	−2.51014	−	7.72543i	−0.0964727	−	0.296912i	−0.987635	+	0.156773i	$0.949891\pi$
$678$		0			0
$679$	−3.74397	+	11.5228i	−0.143680	+	0.442203i
$680$		0			0
$681$	0.335566	+	1.03276i	0.0128589	+	0.0395756i
$682$		0			0
$683$	−29.5163			−1.12941			−0.564704	−	0.825293i	$-0.691010\pi$
$683$	−29.5163			−1.12941			−0.564704	+	0.825293i	$0.691010\pi$
$684$		0			0
$685$	−15.1620	−	11.0158i	−0.579309	−	0.420892i
$686$		0			0
$687$	−1.07764	+	0.782952i	−0.0411145	+	0.0298715i
$688$		0			0
$689$	−42.1204	+	30.6023i	−1.60466	+	1.16585i
$690$		0			0
$691$	5.28336	−	16.2605i	0.200988	−	0.618579i	−0.798866	−	0.601509i	$-0.794566\pi$
$691$	5.28336	−	16.2605i	0.200988	−	0.618579i	0.999854	−	0.0170696i	$-0.00543368\pi$
$692$		0			0
$693$	−9.70249	−	7.04927i	−0.368567	−	0.267780i
$694$		0			0
$695$	6.39792	−	19.6908i	0.242687	−	0.746914i
$696$		0			0
$697$	15.1353	−	9.89157i	0.573289	−	0.374670i
$698$		0			0
$699$	1.55125	−	4.77426i	0.0586738	−	0.180579i
$700$		0			0
$701$	−16.2323	−	11.7935i	−0.613086	−	0.445433i	0.237414	−	0.971409i	$-0.423700\pi$
$701$	−16.2323	−	11.7935i	−0.613086	−	0.445433i	−0.850500	+	0.525976i	$0.823700\pi$
$702$		0			0
$703$	16.9163	−	52.0632i	0.638012	−	1.96360i
$704$		0			0
$705$	1.64109	−	1.19232i	0.0618069	−	0.0449053i
$706$		0			0
$707$	9.44318	−	6.86087i	0.355147	−	0.258030i
$708$		0			0
$709$	−16.4213	−	11.9308i	−0.616715	−	0.448070i	0.235057	−	0.971982i	$-0.424472\pi$
$709$	−16.4213	−	11.9308i	−0.616715	−	0.448070i	−0.851773	+	0.523912i	$0.824472\pi$
$710$		0			0
$711$	−24.6711			−0.925238
$712$		0			0
$713$	−0.283149	−	0.871442i	−0.0106040	−	0.0326358i
$714$		0			0
$715$	−6.68083	+	20.5615i	−0.249849	+	0.768956i
$716$		0			0
$717$	1.05846	+	3.25761i	0.0395289	+	0.121658i
$718$		0			0
$719$	−4.81505	−	14.8192i	−0.179571	−	0.552663i	0.820242	−	0.572017i	$-0.193839\pi$
$719$	−4.81505	−	14.8192i	−0.179571	−	0.552663i	−0.999813	+	0.0193543i	$0.993839\pi$
$720$		0			0
$721$	7.58882	−	5.51360i	0.282623	−	0.205337i
$722$		0			0
$723$	1.70495	+	1.23872i	0.0634076	+	0.0460683i
$724$		0			0
$725$	−1.45423	+	4.47567i	−0.0540088	+	0.166222i
$726$		0			0
$727$	−7.61702	+	5.53409i	−0.282500	+	0.205248i	−0.720007	−	0.693967i	$-0.755861\pi$
$727$	−7.61702	+	5.53409i	−0.282500	+	0.205248i	0.437507	+	0.899215i	$0.355861\pi$
$728$		0			0
$729$	−20.4041			−0.755707
$730$		0			0
$731$	10.5550	+	32.4851i	0.390392	+	1.20150i
$732$		0			0
$733$	−16.8148	−	12.2167i	−0.621070	−	0.451234i	0.232225	−	0.972662i	$-0.425399\pi$
$733$	−16.8148	−	12.2167i	−0.621070	−	0.451234i	−0.853295	+	0.521428i	$0.825399\pi$
$734$		0			0
$735$	−2.13777			−0.0788530
$736$		0			0
$737$	39.8024			1.46614
$738$		0			0
$739$	−4.91341			−0.180743			−0.0903714	−	0.995908i	$-0.528805\pi$
$739$	−4.91341			−0.180743			−0.0903714	+	0.995908i	$0.528805\pi$
$740$		0			0
$741$	12.8853			0.473354
$742$		0			0
$743$	−3.32545	−	2.41608i	−0.121999	−	0.0886375i	0.525113	−	0.851033i	$-0.324023\pi$
$743$	−3.32545	−	2.41608i	−0.121999	−	0.0886375i	−0.647112	+	0.762395i	$0.724023\pi$
$744$		0			0
$745$	−0.375916	−	1.15695i	−0.0137725	−	0.0423874i
$746$		0			0
$747$	−10.7218			−0.392289
$748$		0			0
$749$	−5.29261	+	3.84531i	−0.193388	+	0.140504i
$750$		0			0
$751$	11.2026	−	34.4779i	0.408787	−	1.25812i	−0.508904	−	0.860823i	$-0.669949\pi$
$751$	11.2026	−	34.4779i	0.408787	−	1.25812i	0.917691	−	0.397294i	$-0.130051\pi$
$752$		0			0
$753$	4.51307	+	3.27894i	0.164466	+	0.119491i
$754$		0			0
$755$	17.0894	−	12.4161i	0.621945	−	0.451870i
$756$		0			0
$757$	1.33484	+	4.10821i	0.0485155	+	0.149315i	0.972379	−	0.233406i	$-0.0749870\pi$
$757$	1.33484	+	4.10821i	0.0485155	+	0.149315i	−0.923864	+	0.382721i	$0.874987\pi$
$758$		0			0
$759$	−0.151275	−	0.465578i	−0.00549095	−	0.0168994i
$760$		0			0
$761$	−12.7995	+	39.3929i	−0.463982	+	1.42799i	0.396275	+	0.918132i	$0.370303\pi$
$761$	−12.7995	+	39.3929i	−0.463982	+	1.42799i	−0.860258	+	0.509859i	$0.829697\pi$
$762$		0			0
$763$	−2.57501	−	7.92507i	−0.0932216	−	0.286907i
$764$		0			0
$765$	−8.11392			−0.293360
$766$		0			0
$767$	−14.3198	−	10.4040i	−0.517059	−	0.375665i
$768$		0			0
$769$	12.8472	−	9.33407i	0.463284	−	0.336595i	−0.331534	−	0.943443i	$-0.607566\pi$
$769$	12.8472	−	9.33407i	0.463284	−	0.336595i	0.794818	+	0.606848i	$0.207566\pi$
$770$		0			0
$771$	−8.11402	+	5.89518i	−0.292219	+	0.212310i
$772$		0			0
$773$	14.8453	−	45.6891i	0.533948	−	1.64332i	−0.211962	−	0.977278i	$-0.567985\pi$
$773$	14.8453	−	45.6891i	0.533948	−	1.64332i	0.745911	−	0.666046i	$-0.232015\pi$
$774$		0			0
$775$	−2.25881	−	1.64112i	−0.0811388	−	0.0589508i
$776$		0			0
$777$	−0.852729	+	2.62443i	−0.0305915	+	0.0941509i
$778$		0			0
$779$	11.7679	+	43.4139i	0.421631	+	1.55546i
$780$		0			0
$781$	−18.9997	+	58.4751i	−0.679863	+	2.09240i
$782$		0			0
$783$	7.95512	+	5.77973i	0.284293	+	0.206551i
$784$		0			0
$785$	5.38376	−	16.5695i	0.192154	−	0.591391i
$786$		0			0
$787$	−32.3509	+	23.5043i	−1.15318	+	0.837838i	−0.988901	−	0.148575i	$-0.952531\pi$
$787$	−32.3509	+	23.5043i	−1.15318	+	0.837838i	−0.164284	+	0.986413i	$0.552531\pi$
$788$		0			0
$789$	−2.55382	+	1.85546i	−0.0909185	+	0.0660561i
$790$		0			0
$791$	−9.95587	−	7.23337i	−0.353990	−	0.257189i
$792$		0			0
$793$	67.2430			2.38787
$794$		0			0
$795$	−1.11006	−	3.41640i	−0.0393697	−	0.121167i
$796$		0			0
$797$	4.21656	−	12.9772i	0.149358	−	0.459678i	−0.848187	−	0.529696i	$-0.822306\pi$
$797$	4.21656	−	12.9772i	0.149358	−	0.459678i	0.997546	+	0.0700187i	$0.0223059\pi$
$798$		0			0
$799$	4.97553	+	15.3131i	0.176022	+	0.541739i
$800$		0			0
$801$	11.7778	+	36.2484i	0.416149	+	1.28078i
$802$		0			0
$803$	21.4295	−	15.5694i	0.756230	−	0.549433i
$804$		0			0
$805$	−0.264278	−	0.192009i	−0.00931457	−	0.00676743i
$806$		0			0
$807$	1.25208	−	3.85350i	0.0440753	−	0.135650i
$808$		0			0
$809$	1.72763	−	1.25520i	0.0607402	−	0.0441303i	−0.557001	−	0.830512i	$-0.688048\pi$
$809$	1.72763	−	1.25520i	0.0607402	−	0.0441303i	0.617741	+	0.786382i	$0.288048\pi$
$810$		0			0
$811$	11.7951			0.414182			0.207091	−	0.978322i	$-0.433600\pi$
$811$	11.7951			0.414182			0.207091	+	0.978322i	$0.433600\pi$
$812$		0			0
$813$	−1.10497	−	3.40074i	−0.0387530	−	0.119269i
$814$		0			0
$815$	6.68344	+	4.85580i	0.234111	+	0.170091i
$816$		0			0
$817$	−84.9732			−2.97284
$818$		0			0
$819$	14.7473			0.515312
$820$		0			0
$821$	−26.8163			−0.935895			−0.467948	−	0.883756i	$-0.655006\pi$
$821$	−26.8163			−0.935895			−0.467948	+	0.883756i	$0.655006\pi$
$822$		0			0
$823$	15.0940			0.526145			0.263073	−	0.964776i	$-0.415264\pi$
$823$	15.0940			0.526145			0.263073	+	0.964776i	$0.415264\pi$
$824$		0			0
$825$	−1.20679	−	0.876788i	−0.0420152	−	0.0305258i
$826$		0			0
$827$	−14.2878	−	43.9732i	−0.496834	−	1.52910i	−0.814079	−	0.580755i	$-0.802758\pi$
$827$	−14.2878	−	43.9732i	−0.496834	−	1.52910i	0.317244	−	0.948344i	$-0.397242\pi$
$828$		0			0
$829$	7.56345			0.262689			0.131345	−	0.991337i	$-0.458071\pi$
$829$	7.56345			0.262689			0.131345	+	0.991337i	$0.458071\pi$
$830$		0			0
$831$	−4.23616	+	3.07775i	−0.146951	+	0.106766i
$832$		0			0
$833$	5.24358	−	16.1381i	0.181679	−	0.559151i
$834$		0			0
$835$	−3.67441	−	2.66962i	−0.127158	−	0.0923859i
$836$		0			0
$837$	−4.71973	+	3.42908i	−0.163138	+	0.118526i
$838$		0			0
$839$	0.517600	+	1.59301i	0.0178695	+	0.0549967i	0.959594	−	0.281389i	$-0.0907953\pi$
$839$	0.517600	+	1.59301i	0.0178695	+	0.0549967i	−0.941724	+	0.336386i	$0.890795\pi$
$840$		0			0
$841$	−2.11788	−	6.51817i	−0.0730304	−	0.224764i
$842$		0			0
$843$	−1.82580	+	5.61923i	−0.0628838	+	0.193536i
$844$		0			0
$845$	−4.19796	−	12.9200i	−0.144414	−	0.444461i
$846$		0			0
$847$	6.55137			0.225108
$848$		0			0
$849$	0.931156	+	0.676524i	0.0319572	+	0.0232183i
$850$		0			0
$851$	2.06899	−	1.50321i	0.0709242	−	0.0515295i
$852$		0			0
$853$	11.4353	−	8.30825i	0.391538	−	0.284469i	−0.374547	−	0.927208i	$-0.622202\pi$
$853$	11.4353	−	8.30825i	0.391538	−	0.284469i	0.766086	+	0.642739i	$0.222202\pi$
$854$		0			0
$855$	6.23760	−	19.1974i	0.213322	−	0.656536i
$856$		0			0
$857$	−6.22133	−	4.52006i	−0.212517	−	0.154402i	0.476435	−	0.879210i	$-0.341929\pi$
$857$	−6.22133	−	4.52006i	−0.212517	−	0.154402i	−0.688952	+	0.724807i	$0.741929\pi$
$858$		0			0
$859$	16.0757	−	49.4758i	0.548495	−	1.68809i	−0.164037	−	0.986454i	$-0.552452\pi$
$859$	16.0757	−	49.4758i	0.548495	−	1.68809i	0.712532	−	0.701640i	$-0.247548\pi$
$860$		0			0
$861$	−0.593206	−	2.18843i	−0.0202164	−	0.0745816i
$862$		0			0
$863$	−5.20911	+	16.0320i	−0.177320	+	0.545735i	−0.999732	−	0.0231577i	$-0.992628\pi$
$863$	−5.20911	+	16.0320i	−0.177320	+	0.545735i	0.822412	+	0.568893i	$0.192628\pi$
$864$		0			0
$865$	−7.59495	−	5.51805i	−0.258236	−	0.187619i
$866$		0			0
$867$	0.992292	−	3.05396i	0.0337000	−	0.103718i
$868$		0			0
$869$	29.1255	−	21.1609i	0.988016	−	0.717836i
$870$		0			0
$871$	−39.5962	+	28.7683i	−1.34167	+	0.974778i
$872$		0			0
$873$	−28.2955	−	20.5579i	−0.957658	−	0.695779i
$874$		0			0
$875$	−0.995388			−0.0336503
$876$		0			0
$877$	17.3724	+	53.4668i	0.586625	+	1.80545i	0.592646	+	0.805463i	$0.298084\pi$
$877$	17.3724	+	53.4668i	0.586625	+	1.80545i	−0.00602082	+	0.999982i	$0.501916\pi$
$878$		0			0
$879$	−0.0219634	+	0.0675965i	−0.000740808	+	0.00227997i
$880$		0			0
$881$	−10.4489	−	32.1583i	−0.352031	−	1.08344i	−0.957711	−	0.287732i	$-0.907099\pi$
$881$	−10.4489	−	32.1583i	−0.352031	−	1.08344i	0.605680	−	0.795708i	$-0.292901\pi$
$882$		0			0
$883$	−12.3611	−	38.0436i	−0.415985	−	1.28027i	−0.911367	−	0.411595i	$-0.864972\pi$
$883$	−12.3611	−	38.0436i	−0.415985	−	1.28027i	0.495382	−	0.868675i	$-0.335028\pi$
$884$		0			0
$885$	0.988019	−	0.717838i	0.0332119	−	0.0241299i
$886$		0			0
$887$	11.2876	+	8.20094i	0.379002	+	0.275361i	0.760934	−	0.648830i	$-0.224741\pi$
$887$	11.2876	+	8.20094i	0.379002	+	0.275361i	−0.381932	+	0.924190i	$0.624741\pi$
$888$		0			0
$889$	4.09321	−	12.5976i	0.137282	−	0.422510i
$890$		0			0
$891$	26.7208	−	19.4138i	0.895179	−	0.650386i
$892$		0			0
$893$	−40.0554			−1.34040
$894$		0			0
$895$	1.57372	+	4.84340i	0.0526035	+	0.161897i
$896$		0			0
$897$	0.487002	+	0.353827i	0.0162605	+	0.0118140i
$898$		0			0
$899$	−13.1393			−0.438221
$900$		0			0
$901$	28.5132			0.949913
$902$		0			0
$903$	4.28338			0.142542
$904$		0			0
$905$	6.96405			0.231493
$906$		0			0
$907$	−11.1460	−	8.09802i	−0.370096	−	0.268890i	0.387155	−	0.922015i	$-0.373458\pi$
$907$	−11.1460	−	8.09802i	−0.370096	−	0.268890i	−0.757251	+	0.653124i	$0.773458\pi$
$908$		0			0
$909$	10.4124	+	32.0462i	0.345359	+	1.06291i
$910$		0			0
$911$	15.1631			0.502376			0.251188	−	0.967938i	$-0.419179\pi$
$911$	15.1631			0.502376			0.251188	+	0.967938i	$0.419179\pi$
$912$		0			0
$913$	12.6576	−	9.19631i	0.418906	−	0.304353i
$914$		0			0
$915$	−1.43370	+	4.41246i	−0.0473965	+	0.145872i
$916$		0			0
$917$	12.5521	+	9.11965i	0.414507	+	0.301157i
$918$		0			0
$919$	22.5381	−	16.3749i	0.743462	−	0.540157i	−0.150332	−	0.988636i	$-0.548034\pi$
$919$	22.5381	−	16.3749i	0.743462	−	0.540157i	0.893793	+	0.448479i	$0.148034\pi$
$920$		0			0
$921$	0.169140	+	0.520558i	0.00557334	+	0.0171530i
$922$		0			0
$923$	−23.3633	−	71.9047i	−0.769011	−	2.36677i
$924$		0			0
$925$	2.40809	−	7.41135i	0.0791777	−	0.243684i
$926$		0			0
$927$	8.36776	+	25.7533i	0.274833	+	0.845850i
$928$		0			0
$929$	−9.42567			−0.309246			−0.154623	−	0.987974i	$-0.549416\pi$
$929$	−9.42567			−0.309246			−0.154623	+	0.987974i	$0.549416\pi$
$930$		0			0
$931$	34.1513	+	24.8124i	1.11926	+	0.813193i
$932$		0			0
$933$	2.76520	−	2.00904i	0.0905286	−	0.0657729i
$934$		0			0
$935$	9.57893	−	6.95950i	0.313264	−	0.227600i
$936$		0			0
$937$	−3.94565	+	12.1435i	−0.128899	+	0.396709i	−0.994591	−	0.103867i	$-0.966878\pi$
$937$	−3.94565	+	12.1435i	−0.128899	+	0.396709i	0.865693	+	0.500576i	$0.166878\pi$
$938$		0			0
$939$	7.67678	+	5.57751i	0.250522	+	0.182015i
$940$		0			0
$941$	6.02259	−	18.5356i	0.196331	−	0.604244i	−0.803628	−	0.595132i	$-0.797100\pi$
$941$	6.02259	−	18.5356i	0.196331	−	0.604244i	0.999958	−	0.00911149i	$-0.00290032\pi$
$942$		0			0
$943$	−0.747363	+	1.96398i	−0.0243375	+	0.0639559i
$944$		0			0
$945$	−0.642706	+	1.97805i	−0.0209072	+	0.0643458i
$946$		0			0
$947$	−26.2856	−	19.0976i	−0.854166	−	0.620588i	0.0721256	−	0.997396i	$-0.477022\pi$
$947$	−26.2856	−	19.0976i	−0.854166	−	0.620588i	−0.926291	+	0.376808i	$0.877022\pi$
$948$		0			0
$949$	−10.0652	+	30.9776i	−0.326731	+	1.00557i
$950$		0			0
$951$	−4.28010	+	3.10967i	−0.138792	+	0.100838i
$952$		0			0
$953$	−28.2440	+	20.5205i	−0.914913	+	0.664723i	−0.942253	−	0.334903i	$-0.891297\pi$
$953$	−28.2440	+	20.5205i	−0.914913	+	0.664723i	0.0273393	+	0.999626i	$0.491297\pi$
$954$		0			0
$955$	8.84680	+	6.42758i	0.286276	+	0.207992i
$956$		0			0
$957$	−7.01984			−0.226919
$958$		0			0
$959$	−5.76464	−	17.7417i	−0.186150	−	0.572911i
$960$		0			0
$961$	−7.17059	+	22.0688i	−0.231309	+	0.711897i
$962$		0			0
$963$	−5.83586	−	17.9609i	−0.188058	−	0.578782i
$964$		0			0
$965$	−3.49252	−	10.7489i	−0.112428	−	0.346018i
$966$		0			0
$967$	−11.3216	+	8.22563i	−0.364079	+	0.264519i	−0.754751	−	0.656011i	$-0.772242\pi$
$967$	−11.3216	+	8.22563i	−0.364079	+	0.264519i	0.390673	+	0.920530i	$0.372242\pi$
$968$		0			0
$969$	−5.70905	−	4.14787i	−0.183401	−	0.133249i
$970$		0			0
$971$	2.33261	−	7.17904i	0.0748571	−	0.230386i	−0.906626	−	0.421935i	$-0.861351\pi$
$971$	2.33261	−	7.17904i	0.0748571	−	0.230386i	0.981483	+	0.191549i	$0.0613510\pi$
$972$		0			0
$973$	16.6727	−	12.1134i	0.534503	−	0.388339i
$974$		0			0
$975$	1.83427			0.0587435
$976$		0			0
$977$	−7.09717	−	21.8429i	−0.227059	−	0.698815i	−0.998076	−	0.0620007i	$-0.980252\pi$
$977$	−7.09717	−	21.8429i	−0.227059	−	0.698815i	0.771017	−	0.636814i	$-0.219748\pi$
$978$		0			0
$979$	−44.9955	−	32.6911i	−1.43806	−	1.04481i
$980$		0			0
$981$	24.0551			0.768019
$982$		0			0
$983$	17.3237			0.552542			0.276271	−	0.961080i	$-0.410901\pi$
$983$	17.3237			0.552542			0.276271	+	0.961080i	$0.410901\pi$
$984$		0			0
$985$	23.2709			0.741472
$986$		0			0
$987$	2.01914			0.0642699
$988$		0			0
$989$	−3.21157	−	2.33334i	−0.102122	−	0.0741959i
$990$		0			0
$991$	−2.05433	−	6.32258i	−0.0652580	−	0.200843i	0.913111	−	0.407711i	$-0.133673\pi$
$991$	−2.05433	−	6.32258i	−0.0652580	−	0.200843i	−0.978369	+	0.206868i	$0.933673\pi$
$992$		0			0
$993$	−11.2588			−0.357289
$994$		0			0
$995$	−1.72007	+	1.24970i	−0.0545298	+	0.0396182i
$996$		0			0
$997$	−9.16291	+	28.2005i	−0.290192	+	0.893120i	0.694602	+	0.719394i	$0.255581\pi$
$997$	−9.16291	+	28.2005i	−0.290192	+	0.893120i	−0.984794	+	0.173726i	$0.944419\pi$
$998$		0			0
$999$	−13.1731	−	9.57078i	−0.416777	−	0.302806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.221.4	yes	32
41.18	even	5	inner	820.2.u.b.141.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.141.4	✓	32	41.18	even	5	inner
820.2.u.b.221.4	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.355750 q^{3} +(0.809017 + 0.587785i) q^{5} +(0.307592 + 0.946670i) q^{7} -2.87344 q^{9} +(3.39225 - 2.46462i) q^{11} +(-1.59331 + 4.90370i) q^{13} +(-0.287808 - 0.209105i) q^{15} +(2.28447 - 1.65977i) q^{17} +(2.17078 + 6.68097i) q^{19} +(-0.109426 - 0.336778i) q^{21} +(-0.101413 + 0.312117i) q^{23} +(0.309017 + 0.951057i) q^{25} +2.08948 q^{27} +(3.80723 + 2.76611i) q^{29} +(-2.25881 + 1.64112i) q^{31} +(-1.20679 + 0.876788i) q^{33} +(-0.307592 + 0.946670i) q^{35} +(-6.30447 - 4.58047i) q^{37} +(0.566819 - 1.74449i) q^{39} +(6.39530 + 0.316543i) q^{41} +(-3.73793 + 11.5042i) q^{43} +(-2.32466 - 1.68897i) q^{45} +(-1.76202 + 5.42294i) q^{47} +(4.86155 - 3.53212i) q^{49} +(-0.812702 + 0.590462i) q^{51} +(8.16912 + 5.93522i) q^{53} +4.19306 q^{55} +(-0.772254 - 2.37675i) q^{57} +(-1.06083 + 3.26489i) q^{59} +(-4.03007 - 12.4033i) q^{61} +(-0.883847 - 2.72020i) q^{63} +(-4.17133 + 3.03065i) q^{65} +(7.67956 + 5.57953i) q^{67} +(0.0360776 - 0.111035i) q^{69} +(-11.8629 + 8.61891i) q^{71} +6.31718 q^{73} +(-0.109933 - 0.338338i) q^{75} +(3.37661 + 2.45325i) q^{77} +8.58590 q^{79} +7.87699 q^{81} +3.73133 q^{83} +2.82376 q^{85} +(-1.35442 - 0.984045i) q^{87} +(-4.09886 - 12.6150i) q^{89} -5.13227 q^{91} +(0.803571 - 0.583829i) q^{93} +(-2.17078 + 6.68097i) q^{95} +(9.84725 + 7.15445i) q^{97} +(-9.74745 + 7.08193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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