LMFDB - Embedded newform 1620.2.e.b.971.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.12
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04983 + 0.947554i) q^{2} +(0.204282 - 1.98954i) q^{4} -1.00000i q^{5} +4.17013i q^{7} +(1.67074 + 2.28224i) q^{8} +(0.947554 + 1.04983i) q^{10} +6.44191 q^{11} +1.77467 q^{13} +(-3.95142 - 4.37792i) q^{14} +(-3.91654 - 0.812853i) q^{16} +0.950682i q^{17} +2.19286i q^{19} +(-1.98954 - 0.204282i) q^{20} +(-6.76290 + 6.10406i) q^{22} +2.02013 q^{23} -1.00000 q^{25} +(-1.86310 + 1.68160i) q^{26} +(8.29663 + 0.851880i) q^{28} -6.52706i q^{29} +2.84246i q^{31} +(4.88192 - 2.85778i) q^{32} +(-0.900823 - 0.998053i) q^{34} +4.17013 q^{35} -5.83599 q^{37} +(-2.07786 - 2.30213i) q^{38} +(2.28224 - 1.67074i) q^{40} -7.11552i q^{41} +5.30982i q^{43} +(1.31596 - 12.8164i) q^{44} +(-2.12079 + 1.91418i) q^{46} -0.403992 q^{47} -10.3900 q^{49} +(1.04983 - 0.947554i) q^{50} +(0.362533 - 3.53078i) q^{52} +4.87844i q^{53} -6.44191i q^{55} +(-9.51725 + 6.96718i) q^{56} +(6.18474 + 6.85230i) q^{58} +2.68783 q^{59} +4.09304 q^{61} +(-2.69338 - 2.98409i) q^{62} +(-2.41728 + 7.62606i) q^{64} -1.77467i q^{65} +10.8959i q^{67} +(1.89142 + 0.194207i) q^{68} +(-4.37792 + 3.95142i) q^{70} -2.23126 q^{71} -1.74662 q^{73} +(6.12679 - 5.52992i) q^{74} +(4.36279 + 0.447962i) q^{76} +26.8636i q^{77} -0.247600i q^{79} +(-0.812853 + 3.91654i) q^{80} +(6.74234 + 7.47008i) q^{82} +11.6728 q^{83} +0.950682 q^{85} +(-5.03135 - 5.57441i) q^{86} +(10.7627 + 14.7020i) q^{88} +6.13881i q^{89} +7.40061i q^{91} +(0.412675 - 4.01913i) q^{92} +(0.424123 - 0.382804i) q^{94} +2.19286 q^{95} +18.1701 q^{97} +(10.9077 - 9.84505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.04983	+	0.947554i	−0.742341	+	0.670022i
$2$	−1.04983	+	0.947554i	−0.742341	+	0.670022i
$3$		0			0
$3$		0			0
$4$	0.204282	−	1.98954i	0.102141	−	0.994770i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			4.17013i			1.57616i	0.615573	+	0.788080i	$0.288925\pi$
$7$			4.17013i			1.57616i	−0.615573	+	0.788080i	$0.711075\pi$
$8$	1.67074	+	2.28224i	0.590694	+	0.806895i
$9$		0			0
$10$	0.947554	+	1.04983i	0.299643	+	0.331985i
$11$	6.44191			1.94231			0.971154	−	0.238453i	$-0.0766403\pi$
$11$	6.44191			1.94231			0.971154	+	0.238453i	$0.0766403\pi$
$12$		0			0
$13$	1.77467			0.492205			0.246103	−	0.969244i	$-0.420850\pi$
$13$	1.77467			0.492205			0.246103	+	0.969244i	$0.420850\pi$
$14$	−3.95142	−	4.37792i	−1.05606	−	1.17005i
$15$		0			0
$16$	−3.91654	−	0.812853i	−0.979135	−	0.203213i
$17$			0.950682i			0.230574i	0.993332	+	0.115287i	$0.0367788\pi$
$17$			0.950682i			0.230574i	−0.993332	+	0.115287i	$0.963221\pi$
$18$		0			0
$19$			2.19286i			0.503078i	0.967847	+	0.251539i	$0.0809366\pi$
$19$			2.19286i			0.503078i	−0.967847	+	0.251539i	$0.919063\pi$
$20$	−1.98954	−	0.204282i	−0.444875	−	0.0456788i
$21$		0			0
$22$	−6.76290	+	6.10406i	−1.44186	+	1.30139i
$23$	2.02013			0.421226			0.210613	−	0.977569i	$-0.432454\pi$
$23$	2.02013			0.421226			0.210613	+	0.977569i	$0.432454\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.86310	+	1.68160i	−0.365384	+	0.329788i
$27$		0			0
$28$	8.29663	+	0.851880i	1.56792	+	0.160990i
$29$		−	6.52706i		−	1.21204i	−0.795448	−	0.606022i	$-0.792764\pi$
$29$		−	6.52706i		−	1.21204i	0.795448	−	0.606022i	$-0.207236\pi$
$30$		0			0
$31$			2.84246i			0.510521i	0.966872	+	0.255260i	$0.0821612\pi$
$31$			2.84246i			0.510521i	−0.966872	+	0.255260i	$0.917839\pi$
$32$	4.88192	−	2.85778i	0.863009	−	0.505188i
$33$		0			0
$34$	−0.900823	−	0.998053i	−0.154490	−	0.171165i
$35$	4.17013			0.704880
$36$		0			0
$37$	−5.83599			−0.959431			−0.479715	−	0.877424i	$-0.659260\pi$
$37$	−5.83599			−0.959431			−0.479715	+	0.877424i	$0.659260\pi$
$38$	−2.07786	−	2.30213i	−0.337073	−	0.373455i
$39$		0			0
$40$	2.28224	−	1.67074i	0.360855	−	0.264167i
$41$		−	7.11552i		−	1.11126i	−0.831430	−	0.555629i	$-0.812478\pi$
$41$		−	7.11552i		−	1.11126i	0.831430	−	0.555629i	$-0.187522\pi$
$42$		0			0
$43$			5.30982i			0.809741i	0.914374	+	0.404870i	$0.132683\pi$
$43$			5.30982i			0.809741i	−0.914374	+	0.404870i	$0.867317\pi$
$44$	1.31596	−	12.8164i	0.198389	−	1.93215i
$45$		0			0
$46$	−2.12079	+	1.91418i	−0.312694	+	0.282231i
$47$	−0.403992			−0.0589283			−0.0294641	−	0.999566i	$-0.509380\pi$
$47$	−0.403992			−0.0589283			−0.0294641	+	0.999566i	$0.509380\pi$
$48$		0			0
$49$	−10.3900			−1.48428
$50$	1.04983	−	0.947554i	0.148468	−	0.134004i
$51$		0			0
$52$	0.362533	−	3.53078i	0.0502743	−	0.489631i
$53$			4.87844i			0.670106i	0.942199	+	0.335053i	$0.108754\pi$
$53$			4.87844i			0.670106i	−0.942199	+	0.335053i	$0.891246\pi$
$54$		0			0
$55$		−	6.44191i		−	0.868627i
$56$	−9.51725	+	6.96718i	−1.27180	+	0.931029i
$57$		0			0
$58$	6.18474	+	6.85230i	0.812097	+	0.899751i
$59$	2.68783			0.349926			0.174963	−	0.984575i	$-0.444019\pi$
$59$	2.68783			0.349926			0.174963	+	0.984575i	$0.444019\pi$
$60$		0			0
$61$	4.09304			0.524060			0.262030	−	0.965060i	$-0.415608\pi$
$61$	4.09304			0.524060			0.262030	+	0.965060i	$0.415608\pi$
$62$	−2.69338	−	2.98409i	−0.342060	−	0.378980i
$63$		0			0
$64$	−2.41728	+	7.62606i	−0.302160	+	0.953257i
$65$		−	1.77467i		−	0.220121i
$66$		0			0
$67$			10.8959i			1.33115i	0.746331	+	0.665575i	$0.231814\pi$
$67$			10.8959i			1.33115i	−0.746331	+	0.665575i	$0.768186\pi$
$68$	1.89142	+	0.194207i	0.229368	+	0.0235510i
$69$		0			0
$70$	−4.37792	+	3.95142i	−0.523262	+	0.472285i
$71$	−2.23126			−0.264802			−0.132401	−	0.991196i	$-0.542269\pi$
$71$	−2.23126			−0.264802			−0.132401	+	0.991196i	$0.542269\pi$
$72$		0			0
$73$	−1.74662			−0.204426			−0.102213	−	0.994763i	$-0.532592\pi$
$73$	−1.74662			−0.204426			−0.102213	+	0.994763i	$0.532592\pi$
$74$	6.12679	−	5.52992i	0.712225	−	0.642840i
$75$		0			0
$76$	4.36279	+	0.447962i	0.500447	+	0.0513848i
$77$			26.8636i			3.06139i
$78$		0			0
$79$		−	0.247600i		−	0.0278572i	−0.999903	−	0.0139286i	$-0.995566\pi$
$79$		−	0.247600i		−	0.0278572i	0.999903	−	0.0139286i	$-0.00443375\pi$
$80$	−0.812853	+	3.91654i	−0.0908797	+	0.437882i
$81$		0			0
$82$	6.74234	+	7.47008i	0.744567	+	0.824932i
$83$	11.6728			1.28126			0.640629	−	0.767851i	$-0.278674\pi$
$83$	11.6728			1.28126			0.640629	+	0.767851i	$0.278674\pi$
$84$		0			0
$85$	0.950682			0.103116
$86$	−5.03135	−	5.57441i	−0.542544	−	0.601104i
$87$		0			0
$88$	10.7627	+	14.7020i	1.14731	+	1.56724i
$89$			6.13881i			0.650713i	0.945591	+	0.325356i	$0.105484\pi$
$89$			6.13881i			0.650713i	−0.945591	+	0.325356i	$0.894516\pi$
$90$		0			0
$91$			7.40061i			0.775794i
$92$	0.412675	−	4.01913i	0.0430244	−	0.419023i
$93$		0			0
$94$	0.424123	−	0.382804i	0.0437449	−	0.0394833i
$95$	2.19286			0.224983
$96$		0			0
$97$	18.1701			1.84489			0.922446	−	0.386127i	$-0.126187\pi$
$97$	18.1701			1.84489			0.922446	+	0.386127i	$0.126187\pi$
$98$	10.9077	−	9.84505i	1.10184	−	0.994500i
$99$		0			0
$100$	−0.204282	+	1.98954i	−0.0204282	+	0.198954i
$101$			10.2399i			1.01891i	0.860499	+	0.509453i	$0.170152\pi$
$101$			10.2399i			1.01891i	−0.860499	+	0.509453i	$0.829848\pi$
$102$		0			0
$103$		−	9.65985i		−	0.951814i	−0.879496	−	0.475907i	$-0.842120\pi$
$103$		−	9.65985i		−	0.951814i	0.879496	−	0.475907i	$-0.157880\pi$
$104$	2.96501	+	4.05023i	0.290743	+	0.397158i
$105$		0			0
$106$	−4.62259	−	5.12153i	−0.448986	−	0.497447i
$107$	3.23356			0.312600			0.156300	−	0.987710i	$-0.450043\pi$
$107$	3.23356			0.312600			0.156300	+	0.987710i	$0.450043\pi$
$108$		0			0
$109$	2.88351			0.276190			0.138095	−	0.990419i	$-0.455902\pi$
$109$	2.88351			0.276190			0.138095	+	0.990419i	$0.455902\pi$
$110$	6.10406	+	6.76290i	0.581999	+	0.644817i
$111$		0			0
$112$	3.38970	−	16.3325i	0.320297	−	1.54327i
$113$			3.08823i			0.290516i	0.989394	+	0.145258i	$0.0464012\pi$
$113$			3.08823i			0.290516i	−0.989394	+	0.145258i	$0.953599\pi$
$114$		0			0
$115$		−	2.02013i		−	0.188378i
$116$	−12.9858	−	1.33336i	−1.20571	−	0.123799i
$117$		0			0
$118$	−2.82176	+	2.54686i	−0.259764	+	0.234458i
$119$	−3.96446			−0.363422
$120$		0			0
$121$	30.4982			2.77256
$122$	−4.29699	+	3.87838i	−0.389031	+	0.351132i
$123$		0			0
$124$	5.65518	+	0.580662i	0.507850	+	0.0521450i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	2.16321i		−	0.191954i	−0.995384	−	0.0959771i	$-0.969402\pi$
$127$		−	2.16321i		−	0.191954i	0.995384	−	0.0959771i	$-0.0305976\pi$
$128$	−4.68837	−	10.2966i	−0.414398	−	0.910096i
$129$		0			0
$130$	1.68160	+	1.86310i	0.147486	+	0.163405i
$131$	1.91441			0.167263			0.0836315	−	0.996497i	$-0.473348\pi$
$131$	1.91441			0.167263			0.0836315	+	0.996497i	$0.473348\pi$
$132$		0			0
$133$	−9.14452			−0.792931
$134$	−10.3245	−	11.4389i	−0.891901	−	0.988168i
$135$		0			0
$136$	−2.16969	+	1.58834i	−0.186049	+	0.136199i
$137$			11.6608i			0.996250i	0.867105	+	0.498125i	$0.165978\pi$
$137$			11.6608i			0.996250i	−0.867105	+	0.498125i	$0.834022\pi$
$138$		0			0
$139$			7.66107i			0.649804i	0.945748	+	0.324902i	$0.105331\pi$
$139$			7.66107i			0.649804i	−0.945748	+	0.324902i	$0.894669\pi$
$140$	0.851880	−	8.29663i	0.0719970	−	0.701194i
$141$		0			0
$142$	2.34244	−	2.11424i	0.196574	−	0.177423i
$143$	11.4323			0.956014
$144$		0			0
$145$	−6.52706			−0.542043
$146$	1.83365	−	1.65501i	0.151754	−	0.136970i
$147$		0			0
$148$	−1.19219	+	11.6109i	−0.0979970	+	0.954413i
$149$		−	3.49438i		−	0.286271i	−0.989703	−	0.143135i	$-0.954282\pi$
$149$		−	3.49438i		−	0.286271i	0.989703	−	0.143135i	$-0.0457184\pi$
$150$		0			0
$151$			7.11211i			0.578775i	0.957212	+	0.289388i	$0.0934517\pi$
$151$			7.11211i			0.578775i	−0.957212	+	0.289388i	$0.906548\pi$
$152$	−5.00465	+	3.66370i	−0.405931	+	0.297165i
$153$		0			0
$154$	−25.4547	−	28.2022i	−2.05120	−	2.27259i
$155$	2.84246			0.228312
$156$		0			0
$157$	−3.15875			−0.252096			−0.126048	−	0.992024i	$-0.540229\pi$
$157$	−3.15875			−0.252096			−0.126048	+	0.992024i	$0.540229\pi$
$158$	0.234614	+	0.259938i	0.0186649	+	0.0206795i
$159$		0			0
$160$	−2.85778	−	4.88192i	−0.225927	−	0.385949i
$161$			8.42420i			0.663920i
$162$		0			0
$163$			14.1062i			1.10488i	0.833551	+	0.552442i	$0.186304\pi$
$163$			14.1062i			1.10488i	−0.833551	+	0.552442i	$0.813696\pi$
$164$	−14.1566	−	1.45357i	−1.10545	−	0.113505i
$165$		0			0
$166$	−12.2545	+	11.0606i	−0.951131	+	0.858471i
$167$	−18.3328			−1.41863			−0.709317	−	0.704890i	$-0.750997\pi$
$167$	−18.3328			−1.41863			−0.709317	+	0.704890i	$0.750997\pi$
$168$		0			0
$169$	−9.85054			−0.757734
$170$	−0.998053	+	0.900823i	−0.0765472	+	0.0690899i
$171$		0			0
$172$	10.5641	+	1.08470i	0.805506	+	0.0827076i
$173$			7.88176i			0.599239i	0.954059	+	0.299620i	$0.0968598\pi$
$173$			7.88176i			0.599239i	−0.954059	+	0.299620i	$0.903140\pi$
$174$		0			0
$175$		−	4.17013i		−	0.315232i
$176$	−25.2300	−	5.23632i	−1.90178	−	0.394703i
$177$		0			0
$178$	−5.81686	−	6.44470i	−0.435992	−	0.483051i
$179$	−9.84108			−0.735557			−0.367778	−	0.929914i	$-0.619881\pi$
$179$	−9.84108			−0.735557			−0.367778	+	0.929914i	$0.619881\pi$
$180$		0			0
$181$	18.3215			1.36183			0.680913	−	0.732364i	$-0.261583\pi$
$181$	18.3215			1.36183			0.680913	+	0.732364i	$0.261583\pi$
$182$	−7.01248	−	7.76937i	−0.519799	−	0.575904i
$183$		0			0
$184$	3.37510	+	4.61043i	0.248816	+	0.339885i
$185$			5.83599i			0.429070i
$186$		0			0
$187$			6.12420i			0.447846i
$188$	−0.0825282	+	0.803758i	−0.00601898	+	0.0586201i
$189$		0			0
$190$	−2.30213	+	2.07786i	−0.167014	+	0.150744i
$191$	−19.0805			−1.38061			−0.690307	−	0.723516i	$-0.742525\pi$
$191$	−19.0805			−1.38061			−0.690307	+	0.723516i	$0.742525\pi$
$192$		0			0
$193$	−13.0031			−0.935983			−0.467991	−	0.883733i	$-0.655022\pi$
$193$	−13.0031			−0.935983			−0.467991	+	0.883733i	$0.655022\pi$
$194$	−19.0755	+	17.2171i	−1.36954	+	1.23612i
$195$		0			0
$196$	−2.12248	+	20.6712i	−0.151606	+	1.47652i
$197$		−	15.8462i		−	1.12899i	−0.825436	−	0.564496i	$-0.809071\pi$
$197$		−	15.8462i		−	1.12899i	0.825436	−	0.564496i	$-0.190929\pi$
$198$		0			0
$199$			1.24563i			0.0883001i	0.999025	+	0.0441500i	$0.0140580\pi$
$199$			1.24563i			0.0883001i	−0.999025	+	0.0441500i	$0.985942\pi$
$200$	−1.67074	−	2.28224i	−0.118139	−	0.161379i
$201$		0			0
$202$	−9.70284	−	10.7501i	−0.682689	−	0.756375i
$203$	27.2187			1.91038
$204$		0			0
$205$	−7.11552			−0.496970
$206$	9.15324	+	10.1412i	0.637736	+	0.706571i
$207$		0			0
$208$	−6.95057	−	1.44255i	−0.481935	−	0.100023i
$209$			14.1262i			0.977132i
$210$		0			0
$211$		−	16.3244i		−	1.12382i	−0.827198	−	0.561910i	$-0.810067\pi$
$211$		−	16.3244i		−	1.12382i	0.827198	−	0.561910i	$-0.189933\pi$
$212$	9.70586	+	0.996577i	0.666601	+	0.0684452i
$213$		0			0
$214$	−3.39469	+	3.06398i	−0.232056	+	0.209449i
$215$	5.30982			0.362127
$216$		0			0
$217$	−11.8534			−0.804662
$218$	−3.02719	+	2.73228i	−0.205027	+	0.185053i
$219$		0			0
$220$	−12.8164	−	1.31596i	−0.864084	−	0.0887222i
$221$			1.68715i			0.113490i
$222$		0			0
$223$		−	17.9257i		−	1.20040i	−0.799851	−	0.600198i	$-0.795088\pi$
$223$		−	17.9257i		−	1.20040i	0.799851	−	0.600198i	$-0.204912\pi$
$224$	11.9173	+	20.3582i	0.796257	+	1.36024i
$225$		0			0
$226$	−2.92626	−	3.24211i	−0.194652	−	0.215662i
$227$	10.4304			0.692293			0.346146	−	0.938180i	$-0.387490\pi$
$227$	10.4304			0.692293			0.346146	+	0.938180i	$0.387490\pi$
$228$		0			0
$229$	−18.7878			−1.24153			−0.620765	−	0.783997i	$-0.713178\pi$
$229$	−18.7878			−1.24153			−0.620765	+	0.783997i	$0.713178\pi$
$230$	1.91418	+	2.12079i	0.126217	+	0.139841i
$231$		0			0
$232$	14.8963	−	10.9050i	0.977993	−	0.715948i
$233$		−	7.28693i		−	0.477382i	−0.971096	−	0.238691i	$-0.923282\pi$
$233$		−	7.28693i		−	0.477382i	0.971096	−	0.238691i	$-0.0767184\pi$
$234$		0			0
$235$			0.403992i			0.0263535i
$236$	0.549074	−	5.34754i	0.0357417	−	0.348096i
$237$		0			0
$238$	4.16201	−	3.75654i	0.269783	−	0.243501i
$239$	29.6817			1.91995			0.959973	−	0.280091i	$-0.0903647\pi$
$239$	29.6817			1.91995			0.959973	+	0.280091i	$0.0903647\pi$
$240$		0			0
$241$	−12.7503			−0.821321			−0.410661	−	0.911788i	$-0.634702\pi$
$241$	−12.7503			−0.821321			−0.410661	+	0.911788i	$0.634702\pi$
$242$	−32.0179	+	28.8987i	−2.05819	+	1.85768i
$243$		0			0
$244$	0.836133	−	8.14327i	0.0535279	−	0.521319i
$245$			10.3900i			0.663790i
$246$		0			0
$247$			3.89161i			0.247618i
$248$	−6.48718	+	4.74900i	−0.411937	+	0.301562i
$249$		0			0
$250$	−0.947554	−	1.04983i	−0.0599286	−	0.0663970i
$251$	−2.89830			−0.182939			−0.0914694	−	0.995808i	$-0.529156\pi$
$251$	−2.89830			−0.182939			−0.0914694	+	0.995808i	$0.529156\pi$
$252$		0			0
$253$	13.0135			0.818151
$254$	2.04976	+	2.27101i	0.128614	+	0.142496i
$255$		0			0
$256$	14.6785	+	6.36714i	0.917409	+	0.397946i
$257$		−	9.96613i		−	0.621670i	−0.950464	−	0.310835i	$-0.899391\pi$
$257$		−	9.96613i		−	0.621670i	0.950464	−	0.310835i	$-0.100609\pi$
$258$		0			0
$259$		−	24.3368i		−	1.51222i
$260$	−3.53078	−	0.362533i	−0.218970	−	0.0224833i
$261$		0			0
$262$	−2.00981	+	1.81401i	−0.124166	+	0.112070i
$263$	1.22162			0.0753281			0.0376640	−	0.999290i	$-0.488008\pi$
$263$	1.22162			0.0753281			0.0376640	+	0.999290i	$0.488008\pi$
$264$		0			0
$265$	4.87844			0.299680
$266$	9.60019	−	8.66493i	0.588625	−	0.531281i
$267$		0			0
$268$	21.6779	+	2.22584i	1.32419	+	0.135965i
$269$			19.0910i			1.16400i	0.813190	+	0.581998i	$0.197729\pi$
$269$			19.0910i			1.16400i	−0.813190	+	0.581998i	$0.802271\pi$
$270$		0			0
$271$		−	12.0019i		−	0.729061i	−0.931191	−	0.364531i	$-0.881229\pi$
$271$		−	12.0019i		−	0.729061i	0.931191	−	0.364531i	$-0.118771\pi$
$272$	0.772764	−	3.72338i	0.0468557	−	0.225763i
$273$		0			0
$274$	−11.0492	−	12.2418i	−0.667509	−	0.739557i
$275$	−6.44191			−0.388462
$276$		0			0
$277$	−24.0283			−1.44372			−0.721860	−	0.692039i	$-0.756712\pi$
$277$	−24.0283			−1.44372			−0.721860	+	0.692039i	$0.756712\pi$
$278$	−7.25928	−	8.04282i	−0.435383	−	0.482376i
$279$		0			0
$280$	6.96718	+	9.51725i	0.416369	+	0.568764i
$281$		−	1.54857i		−	0.0923797i	−0.998933	−	0.0461898i	$-0.985292\pi$
$281$		−	1.54857i		−	0.0923797i	0.998933	−	0.0461898i	$-0.0147079\pi$
$282$		0			0
$283$			24.5575i			1.45979i	0.683559	+	0.729895i	$0.260431\pi$
$283$			24.5575i			1.45979i	−0.683559	+	0.729895i	$0.739569\pi$
$284$	−0.455806	+	4.43919i	−0.0270471	+	0.263417i
$285$		0			0
$286$	−12.0019	+	10.8327i	−0.709689	+	0.640551i
$287$	29.6726			1.75152
$288$		0			0
$289$	16.0962			0.946836
$290$	6.85230	−	6.18474i	0.402381	−	0.363181i
$291$		0			0
$292$	−0.356802	+	3.47496i	−0.0208802	+	0.203357i
$293$		−	27.1687i		−	1.58721i	−0.608431	−	0.793607i	$-0.708201\pi$
$293$		−	27.1687i		−	1.58721i	0.608431	−	0.793607i	$-0.291799\pi$
$294$		0			0
$295$		−	2.68783i		−	0.156492i
$296$	−9.75040	−	13.3192i	−0.566730	−	0.774160i
$297$		0			0
$298$	3.31111	+	3.66850i	0.191808	+	0.212511i
$299$	3.58507			0.207330
$300$		0			0
$301$	−22.1426			−1.27628
$302$	−6.73911	−	7.46650i	−0.387792	−	0.429649i
$303$		0			0
$304$	1.78248	−	8.58844i	0.102232	−	0.492581i
$305$		−	4.09304i		−	0.234367i
$306$		0			0
$307$		−	3.96646i		−	0.226378i	−0.993573	−	0.113189i	$-0.963893\pi$
$307$		−	3.96646i		−	0.226378i	0.993573	−	0.113189i	$-0.0361065\pi$
$308$	53.4461	+	5.48773i	3.04538	+	0.312693i
$309$		0			0
$310$	−2.98409	+	2.69338i	−0.169485	+	0.152974i
$311$	−19.3841			−1.09917			−0.549586	−	0.835437i	$-0.685215\pi$
$311$	−19.3841			−1.09917			−0.549586	+	0.835437i	$0.685215\pi$
$312$		0			0
$313$	21.9702			1.24183			0.620915	−	0.783878i	$-0.286761\pi$
$313$	21.9702			1.24183			0.620915	+	0.783878i	$0.286761\pi$
$314$	3.31615	−	2.99309i	0.187141	−	0.168910i
$315$		0			0
$316$	−0.492610	−	0.0505801i	−0.0277115	−	0.00284535i
$317$		−	26.6227i		−	1.49528i	−0.664104	−	0.747640i	$-0.731187\pi$
$317$		−	26.6227i		−	1.49528i	0.664104	−	0.747640i	$-0.268813\pi$
$318$		0			0
$319$		−	42.0467i		−	2.35416i
$320$	7.62606	+	2.41728i	0.426310	+	0.135130i
$321$		0			0
$322$	−7.98238	−	8.84397i	−0.444841	−	0.492855i
$323$	−2.08472			−0.115997
$324$		0			0
$325$	−1.77467			−0.0984411
$326$	−13.3664	−	14.8091i	−0.740297	−	0.820201i
$327$		0			0
$328$	16.2394	−	11.8882i	0.896669	−	0.656414i
$329$		−	1.68470i		−	0.0928804i
$330$		0			0
$331$		−	33.2166i		−	1.82575i	−0.408238	−	0.912876i	$-0.633857\pi$
$331$		−	33.2166i		−	1.82575i	0.408238	−	0.912876i	$-0.366143\pi$
$332$	2.38454	−	23.2235i	0.130869	−	1.27456i
$333$		0			0
$334$	19.2463	−	17.3713i	1.05311	−	0.950516i
$335$	10.8959			0.595309
$336$		0			0
$337$	1.61717			0.0880927			0.0440463	−	0.999029i	$-0.485975\pi$
$337$	1.61717			0.0880927			0.0440463	+	0.999029i	$0.485975\pi$
$338$	10.3414	−	9.33392i	0.562497	−	0.507698i
$339$		0			0
$340$	0.194207	−	1.89142i	0.0105323	−	0.102577i
$341$			18.3109i			0.991588i
$342$		0			0
$343$		−	14.1366i		−	0.763302i
$344$	−12.1183	+	8.87132i	−0.653376	+	0.478309i
$345$		0			0
$346$	−7.46840	−	8.27450i	−0.401503	−	0.444840i
$347$	5.18596			0.278397			0.139198	−	0.990265i	$-0.455547\pi$
$347$	5.18596			0.278397			0.139198	+	0.990265i	$0.455547\pi$
$348$		0			0
$349$	−18.3343			−0.981414			−0.490707	−	0.871325i	$-0.663261\pi$
$349$	−18.3343			−0.981414			−0.490707	+	0.871325i	$0.663261\pi$
$350$	3.95142	+	4.37792i	0.211212	+	0.234010i
$351$		0			0
$352$	31.4489	−	18.4095i	1.67623	−	0.981231i
$353$		−	10.6975i		−	0.569368i	−0.958621	−	0.284684i	$-0.908111\pi$
$353$		−	10.6975i		−	0.569368i	0.958621	−	0.284684i	$-0.0918886\pi$
$354$		0			0
$355$			2.23126i			0.118423i
$356$	12.2134	+	1.25405i	0.647309	+	0.0664643i
$357$		0			0
$358$	10.3314	−	9.32495i	0.546034	−	0.492839i
$359$	15.1958			0.802005			0.401002	−	0.916077i	$-0.368662\pi$
$359$	15.1958			0.802005			0.401002	+	0.916077i	$0.368662\pi$
$360$		0			0
$361$	14.1913			0.746913
$362$	−19.2344	+	17.3606i	−1.01094	+	0.912454i
$363$		0			0
$364$	14.7238	+	1.51181i	0.771737	+	0.0792403i
$365$			1.74662i			0.0914221i
$366$		0			0
$367$			24.5582i			1.28193i	0.767571	+	0.640964i	$0.221465\pi$
$367$			24.5582i			1.28193i	−0.767571	+	0.640964i	$0.778535\pi$
$368$	−7.91192	−	1.64207i	−0.412437	−	0.0855987i
$369$		0			0
$370$	−5.52992	−	6.12679i	−0.287487	−	0.318517i
$371$	−20.3437			−1.05619
$372$		0			0
$373$	18.6090			0.963538			0.481769	−	0.876298i	$-0.339994\pi$
$373$	18.6090			0.963538			0.481769	+	0.876298i	$0.339994\pi$
$374$	−5.80302	−	6.42937i	−0.300067	−	0.332455i
$375$		0			0
$376$	−0.674964	−	0.922009i	−0.0348086	−	0.0475490i
$377$		−	11.5834i		−	0.596575i
$378$		0			0
$379$			27.9052i			1.43339i	0.697386	+	0.716696i	$0.254347\pi$
$379$			27.9052i			1.43339i	−0.697386	+	0.716696i	$0.745653\pi$
$380$	0.447962	−	4.36279i	0.0229800	−	0.223806i
$381$		0			0
$382$	20.0312	−	18.0798i	1.02489	−	0.925042i
$383$	7.40233			0.378241			0.189121	−	0.981954i	$-0.439436\pi$
$383$	7.40233			0.378241			0.189121	+	0.981954i	$0.439436\pi$
$384$		0			0
$385$	26.8636			1.36909
$386$	13.6510	−	12.3211i	0.694818	−	0.627129i
$387$		0			0
$388$	3.71181	−	36.1501i	0.188439	−	1.83524i
$389$			17.9397i			0.909579i	0.890599	+	0.454789i	$0.150285\pi$
$389$			17.9397i			0.909579i	−0.890599	+	0.454789i	$0.849715\pi$
$390$		0			0
$391$			1.92050i			0.0971239i
$392$	−17.3589	−	23.7124i	−0.876756	−	1.19766i
$393$		0			0
$394$	15.0151	+	16.6358i	0.756450	+	0.838097i
$395$	−0.247600			−0.0124581
$396$		0			0
$397$	−27.9101			−1.40077			−0.700383	−	0.713768i	$-0.746987\pi$
$397$	−27.9101			−1.40077			−0.700383	+	0.713768i	$0.746987\pi$
$398$	−1.18030	−	1.30769i	−0.0591630	−	0.0655488i
$399$		0			0
$400$	3.91654	+	0.812853i	0.195827	+	0.0406426i
$401$			3.99705i			0.199603i	0.995007	+	0.0998015i	$0.0318208\pi$
$401$			3.99705i			0.199603i	−0.995007	+	0.0998015i	$0.968179\pi$
$402$		0			0
$403$			5.04443i			0.251281i
$404$	20.3726	+	2.09182i	1.01358	+	0.104072i
$405$		0			0
$406$	−28.5749	+	25.7912i	−1.41815	+	1.27999i
$407$	−37.5949			−1.86351
$408$		0			0
$409$	22.1291			1.09421			0.547107	−	0.837063i	$-0.315729\pi$
$409$	22.1291			1.09421			0.547107	+	0.837063i	$0.315729\pi$
$410$	7.47008	−	6.74234i	0.368921	−	0.332981i
$411$		0			0
$412$	−19.2187	−	1.97333i	−0.946836	−	0.0972190i
$413$			11.2086i			0.551539i
$414$		0			0
$415$		−	11.6728i		−	0.572996i
$416$	8.66380	−	5.07161i	0.424778	−	0.248656i
$417$		0			0
$418$	−13.3854	−	14.8301i	−0.654700	−	0.725365i
$419$	−31.6137			−1.54443			−0.772215	−	0.635362i	$-0.780851\pi$
$419$	−31.6137			−1.54443			−0.772215	+	0.635362i	$0.780851\pi$
$420$		0			0
$421$	30.0566			1.46487			0.732435	−	0.680837i	$-0.238384\pi$
$421$	30.0566			1.46487			0.732435	+	0.680837i	$0.238384\pi$
$422$	15.4683	+	17.1379i	0.752984	+	0.834258i
$423$		0			0
$424$	−11.1338	+	8.15059i	−0.540705	+	0.395828i
$425$		−	0.950682i		−	0.0461148i
$426$		0			0
$427$			17.0685i			0.826002i
$428$	0.660558	−	6.43331i	0.0319293	−	0.310966i
$429$		0			0
$430$	−5.57441	+	5.03135i	−0.268822	+	0.242633i
$431$	−25.0832			−1.20822			−0.604108	−	0.796902i	$-0.706471\pi$
$431$	−25.0832			−1.20822			−0.604108	+	0.796902i	$0.706471\pi$
$432$		0			0
$433$	29.4297			1.41430			0.707151	−	0.707062i	$-0.249980\pi$
$433$	29.4297			1.41430			0.707151	+	0.707062i	$0.249980\pi$
$434$	12.4441	−	11.2318i	0.597334	−	0.539141i
$435$		0			0
$436$	0.589048	−	5.73685i	0.0282103	−	0.274745i
$437$			4.42987i			0.211909i
$438$		0			0
$439$			28.6552i			1.36764i	0.729651	+	0.683819i	$0.239682\pi$
$439$			28.6552i			1.36764i	−0.729651	+	0.683819i	$0.760318\pi$
$440$	14.7020	−	10.7627i	0.700891	−	0.513093i
$441$		0			0
$442$	−1.59866	−	1.77122i	−0.0760407	−	0.0842482i
$443$	29.8579			1.41859			0.709297	−	0.704910i	$-0.249013\pi$
$443$	29.8579			1.41859			0.709297	+	0.704910i	$0.249013\pi$
$444$		0			0
$445$	6.13881			0.291008
$446$	16.9856	+	18.8190i	0.804292	+	0.891104i
$447$		0			0
$448$	−31.8016	−	10.0804i	−1.50249	−	0.476252i
$449$		−	14.7017i		−	0.693815i	−0.937899	−	0.346908i	$-0.887232\pi$
$449$		−	14.7017i		−	0.693815i	0.937899	−	0.346908i	$-0.112768\pi$
$450$		0			0
$451$		−	45.8375i		−	2.15841i
$452$	6.14415	+	0.630868i	0.288997	+	0.0296735i
$453$		0			0
$454$	−10.9502	+	9.88341i	−0.513918	+	0.463852i
$455$	7.40061			0.346946
$456$		0			0
$457$	−8.83336			−0.413207			−0.206604	−	0.978425i	$-0.566241\pi$
$457$	−8.83336			−0.413207			−0.206604	+	0.978425i	$0.566241\pi$
$458$	19.7239	−	17.8024i	0.921639	−	0.831853i
$459$		0			0
$460$	−4.01913	−	0.412675i	−0.187393	−	0.0192411i
$461$		−	0.913372i		−	0.0425400i	−0.999774	−	0.0212700i	$-0.993229\pi$
$461$		−	0.913372i		−	0.0425400i	0.999774	−	0.0212700i	$-0.00677096\pi$
$462$		0			0
$463$		−	7.87134i		−	0.365812i	−0.983130	−	0.182906i	$-0.941450\pi$
$463$		−	7.87134i		−	0.365812i	0.983130	−	0.182906i	$-0.0585505\pi$
$464$	−5.30554	+	25.5635i	−0.246303	+	1.18675i
$465$		0			0
$466$	6.90476	+	7.65003i	0.319857	+	0.354381i
$467$	−28.6765			−1.32699			−0.663495	−	0.748181i	$-0.730928\pi$
$467$	−28.6765			−1.32699			−0.663495	+	0.748181i	$0.730928\pi$
$468$		0			0
$469$	−45.4375			−2.09811
$470$	−0.382804	−	0.424123i	−0.0176575	−	0.0195633i
$471$		0			0
$472$	4.49066	+	6.13429i	0.206699	+	0.282353i
$473$			34.2054i			1.57277i
$474$		0			0
$475$		−	2.19286i		−	0.100616i
$476$	−0.809867	+	7.88746i	−0.0371202	+	0.361521i
$477$		0			0
$478$	−31.1607	+	28.1250i	−1.42526	+	1.28641i
$479$	26.3817			1.20541			0.602706	−	0.797963i	$-0.294089\pi$
$479$	26.3817			1.20541			0.602706	+	0.797963i	$0.294089\pi$
$480$		0			0
$481$	−10.3570			−0.472237
$482$	13.3857	−	12.0816i	0.609701	−	0.550304i
$483$		0			0
$484$	6.23022	−	60.6773i	0.283192	−	2.75806i
$485$		−	18.1701i		−	0.825060i
$486$		0			0
$487$		−	7.87222i		−	0.356724i	−0.983965	−	0.178362i	$-0.942920\pi$
$487$		−	7.87222i		−	0.356724i	0.983965	−	0.178362i	$-0.0570799\pi$
$488$	6.83839	+	9.34132i	0.309559	+	0.422862i
$489$		0			0
$490$	−9.84505	−	10.9077i	−0.444754	−	0.492759i
$491$	−19.4940			−0.879751			−0.439876	−	0.898059i	$-0.644977\pi$
$491$	−19.4940			−0.879751			−0.439876	+	0.898059i	$0.644977\pi$
$492$		0			0
$493$	6.20516			0.279466
$494$	−3.68752	−	4.08553i	−0.165909	−	0.183817i
$495$		0			0
$496$	2.31050	−	11.1326i	0.103745	−	0.499868i
$497$		−	9.30465i		−	0.417371i
$498$		0			0
$499$		−	0.846463i		−	0.0378929i	−0.999821	−	0.0189464i	$-0.993969\pi$
$499$		−	0.846463i		−	0.0378929i	0.999821	−	0.0189464i	$-0.00603120\pi$
$500$	1.98954	+	0.204282i	0.0889749	+	0.00913575i
$501$		0			0
$502$	3.04272	−	2.74629i	0.135803	−	0.122573i
$503$	18.5253			0.826002			0.413001	−	0.910731i	$-0.364481\pi$
$503$	18.5253			0.826002			0.413001	+	0.910731i	$0.364481\pi$
$504$		0			0
$505$	10.2399			0.455668
$506$	−13.6619	+	12.3310i	−0.607347	+	0.548179i
$507$		0			0
$508$	−4.30380	−	0.441905i	−0.190950	−	0.0196064i
$509$		−	27.3040i		−	1.21023i	−0.796138	−	0.605115i	$-0.793127\pi$
$509$		−	27.3040i		−	1.21023i	0.796138	−	0.605115i	$-0.206873\pi$
$510$		0			0
$511$		−	7.28361i		−	0.322208i
$512$	−21.4432	+	7.22431i	−0.947663	+	0.319272i
$513$		0			0
$514$	9.44345	+	10.4627i	0.416533	+	0.461491i
$515$	−9.65985			−0.425664
$516$		0			0
$517$	−2.60248			−0.114457
$518$	23.0605	+	25.5495i	1.01322	+	1.12258i
$519$		0			0
$520$	4.05023	−	2.96501i	0.177615	−	0.130024i
$521$		−	25.9868i		−	1.13850i	−0.822163	−	0.569252i	$-0.807233\pi$
$521$		−	25.9868i		−	1.13850i	0.822163	−	0.569252i	$-0.192767\pi$
$522$		0			0
$523$			30.1683i			1.31917i	0.751631	+	0.659584i	$0.229268\pi$
$523$			30.1683i			1.31917i	−0.751631	+	0.659584i	$0.770732\pi$
$524$	0.391079	−	3.80880i	0.0170844	−	0.166388i
$525$		0			0
$526$	−1.28249	+	1.15755i	−0.0559191	+	0.0504715i
$527$	−2.70227			−0.117713
$528$		0			0
$529$	−18.9191			−0.822568
$530$	−5.12153	+	4.62259i	−0.222465	+	0.200793i
$531$		0			0
$532$	−1.86806	+	18.1934i	−0.0809906	+	0.788784i
$533$		−	12.6277i		−	0.546967i
$534$		0			0
$535$		−	3.23356i		−	0.139799i
$536$	−24.8672	+	18.2042i	−1.07410	+	0.786304i
$537$		0			0
$538$	−18.0897	−	20.0423i	−0.779904	−	0.864083i
$539$	−66.9311			−2.88293
$540$		0			0
$541$	−34.2068			−1.47067			−0.735333	−	0.677706i	$-0.762974\pi$
$541$	−34.2068			−1.47067			−0.735333	+	0.677706i	$0.762974\pi$
$542$	11.3724	+	12.5999i	0.488487	+	0.541212i
$543$		0			0
$544$	2.71684	+	4.64115i	0.116483	+	0.198988i
$545$		−	2.88351i		−	0.123516i
$546$		0			0
$547$		−	16.0152i		−	0.684761i	−0.939561	−	0.342380i	$-0.888767\pi$
$547$		−	16.0152i		−	0.684761i	0.939561	−	0.342380i	$-0.111233\pi$
$548$	23.1996	+	2.38209i	0.991039	+	0.101758i
$549$		0			0
$550$	6.76290	−	6.10406i	0.288371	−	0.260278i
$551$	14.3130			0.609753
$552$		0			0
$553$	1.03252			0.0439073
$554$	25.2256	−	22.7681i	1.07173	−	0.967324i
$555$		0			0
$556$	15.2420	+	1.56502i	0.646405	+	0.0663715i
$557$		−	16.0344i		−	0.679401i	−0.940534	−	0.339701i	$-0.889674\pi$
$557$		−	16.0344i		−	0.679401i	0.940534	−	0.339701i	$-0.110326\pi$
$558$		0			0
$559$			9.42320i			0.398559i
$560$	−16.3325	−	3.38970i	−0.690172	−	0.143241i
$561$		0			0
$562$	1.46735	+	1.62573i	0.0618964	+	0.0685772i
$563$	4.47364			0.188541			0.0942707	−	0.995547i	$-0.469948\pi$
$563$	4.47364			0.188541			0.0942707	+	0.995547i	$0.469948\pi$
$564$		0			0
$565$	3.08823			0.129923
$566$	−23.2695	−	25.7812i	−0.978092	−	1.08366i
$567$		0			0
$568$	−3.72785	−	5.09229i	−0.156417	−	0.213668i
$569$		−	41.0451i		−	1.72070i	−0.509705	−	0.860349i	$-0.670245\pi$
$569$		−	41.0451i		−	1.72070i	0.509705	−	0.860349i	$-0.329755\pi$
$570$		0			0
$571$		−	45.2501i		−	1.89366i	−0.321741	−	0.946828i	$-0.604268\pi$
$571$		−	45.2501i		−	1.89366i	0.321741	−	0.946828i	$-0.395732\pi$
$572$	2.33540	−	22.7450i	0.0976481	−	0.951014i
$573$		0			0
$574$	−31.1512	+	28.1164i	−1.30023	+	1.17356i
$575$	−2.02013			−0.0842452
$576$		0			0
$577$	−27.1400			−1.12985			−0.564927	−	0.825141i	$-0.691096\pi$
$577$	−27.1400			−1.12985			−0.564927	+	0.825141i	$0.691096\pi$
$578$	−16.8983	+	15.2520i	−0.702875	+	0.634401i
$579$		0			0
$580$	−1.33336	+	12.9858i	−0.0553647	+	0.539208i
$581$			48.6771i			2.01947i
$582$		0			0
$583$			31.4265i			1.30155i
$584$	−2.91814	−	3.98621i	−0.120753	−	0.164950i
$585$		0			0
$586$	25.7438	+	28.5225i	1.06347	+	1.17825i
$587$	17.5383			0.723883			0.361941	−	0.932201i	$-0.382114\pi$
$587$	17.5383			0.723883			0.361941	+	0.932201i	$0.382114\pi$
$588$		0			0
$589$	−6.23313			−0.256831
$590$	2.54686	+	2.82176i	0.104853	+	0.116170i
$591$		0			0
$592$	22.8569	+	4.74380i	0.939412	+	0.194969i
$593$			15.6793i			0.643872i	0.946761	+	0.321936i	$0.104334\pi$
$593$			15.6793i			0.643872i	−0.946761	+	0.321936i	$0.895666\pi$
$594$		0			0
$595$			3.96446i			0.162527i
$596$	−6.95221	−	0.713837i	−0.284773	−	0.0292399i
$597$		0			0
$598$	−3.76371	+	3.39705i	−0.153909	+	0.138916i
$599$	−7.21949			−0.294980			−0.147490	−	0.989064i	$-0.547119\pi$
$599$	−7.21949			−0.294980			−0.147490	+	0.989064i	$0.547119\pi$
$600$		0			0
$601$	45.9916			1.87604			0.938019	−	0.346583i	$-0.112658\pi$
$601$	45.9916			1.87604			0.938019	+	0.346583i	$0.112658\pi$
$602$	23.2460	−	20.9814i	0.947436	−	0.855136i
$603$		0			0
$604$	14.1498	+	1.45287i	0.575748	+	0.0591166i
$605$		−	30.4982i		−	1.23993i
$606$		0			0
$607$		−	2.14863i		−	0.0872103i	−0.999049	−	0.0436052i	$-0.986116\pi$
$607$		−	2.14863i		−	0.0872103i	0.999049	−	0.0436052i	$-0.0138844\pi$
$608$	6.26672	+	10.7054i	0.254149	+	0.434161i
$609$		0			0
$610$	3.87838	+	4.29699i	0.157031	+	0.173980i
$611$	−0.716953			−0.0290048
$612$		0			0
$613$	−44.8432			−1.81120			−0.905601	−	0.424131i	$-0.860579\pi$
$613$	−44.8432			−1.81120			−0.905601	+	0.424131i	$0.860579\pi$
$614$	3.75844	+	4.16411i	0.151678	+	0.168050i
$615$		0			0
$616$	−61.3092	+	44.8819i	−2.47022	+	1.80835i
$617$		−	34.4459i		−	1.38674i	−0.720581	−	0.693371i	$-0.756125\pi$
$617$		−	34.4459i		−	1.38674i	0.720581	−	0.693371i	$-0.243875\pi$
$618$		0			0
$619$			12.7731i			0.513396i	0.966492	+	0.256698i	$0.0826345\pi$
$619$			12.7731i			0.513396i	−0.966492	+	0.256698i	$0.917365\pi$
$620$	0.580662	−	5.65518i	0.0233199	−	0.227118i
$621$		0			0
$622$	20.3500	−	18.3675i	0.815961	−	0.736469i
$623$	−25.5996			−1.02563
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.0650	+	20.8180i	−0.921862	+	0.832054i
$627$		0			0
$628$	−0.645275	+	6.28446i	−0.0257493	+	0.250777i
$629$		−	5.54817i		−	0.221220i
$630$		0			0
$631$		−	12.9765i		−	0.516586i	−0.966067	−	0.258293i	$-0.916840\pi$
$631$		−	12.9765i		−	0.516586i	0.966067	−	0.258293i	$-0.0831600\pi$
$632$	0.565083	−	0.413674i	0.0224778	−	0.0164551i
$633$		0			0
$634$	25.2265	+	27.9493i	1.00187	+	1.11001i
$635$	−2.16321			−0.0858445
$636$		0			0
$637$	−18.4388			−0.730570
$638$	39.8415	+	44.1419i	1.57734	+	1.74759i
$639$		0			0
$640$	−10.2966	+	4.68837i	−0.407007	+	0.185324i
$641$		−	30.5564i		−	1.20691i	−0.797398	−	0.603453i	$-0.793791\pi$
$641$		−	30.5564i		−	1.20691i	0.797398	−	0.603453i	$-0.206209\pi$
$642$		0			0
$643$			6.17425i			0.243489i	0.992561	+	0.121744i	$0.0388488\pi$
$643$			6.17425i			0.243489i	−0.992561	+	0.121744i	$0.961151\pi$
$644$	16.7603	+	1.72091i	0.660447	+	0.0678133i
$645$		0			0
$646$	2.18860	−	1.97538i	0.0861091	−	0.0777204i
$647$	−9.68580			−0.380788			−0.190394	−	0.981708i	$-0.560977\pi$
$647$	−9.68580			−0.380788			−0.190394	+	0.981708i	$0.560977\pi$
$648$		0			0
$649$	17.3148			0.679663
$650$	1.86310	−	1.68160i	0.0730769	−	0.0659577i
$651$		0			0
$652$	28.0649	+	2.88164i	1.09911	+	0.112854i
$653$		−	16.3465i		−	0.639688i	−0.947470	−	0.319844i	$-0.896369\pi$
$653$		−	16.3465i		−	0.639688i	0.947470	−	0.319844i	$-0.103631\pi$
$654$		0			0
$655$		−	1.91441i		−	0.0748023i
$656$	−5.78387	+	27.8682i	−0.225822	+	1.08807i
$657$		0			0
$658$	1.59634	+	1.76864i	0.0622319	+	0.0689490i
$659$	−23.0858			−0.899295			−0.449648	−	0.893206i	$-0.648450\pi$
$659$	−23.0858			−0.899295			−0.449648	+	0.893206i	$0.648450\pi$
$660$		0			0
$661$	18.4701			0.718403			0.359202	−	0.933260i	$-0.383049\pi$
$661$	18.4701			0.718403			0.359202	+	0.933260i	$0.383049\pi$
$662$	31.4746	+	34.8718i	1.22329	+	1.35533i
$663$		0			0
$664$	19.5022	+	26.6402i	0.756832	+	1.03384i
$665$			9.14452i			0.354609i
$666$		0			0
$667$		−	13.1855i		−	0.510545i
$668$	−3.74505	+	36.4738i	−0.144900	+	1.41121i
$669$		0			0
$670$	−11.4389	+	10.3245i	−0.441922	+	0.398870i
$671$	26.3670			1.01789
$672$		0			0
$673$	−30.3154			−1.16857			−0.584286	−	0.811548i	$-0.698625\pi$
$673$	−30.3154			−1.16857			−0.584286	+	0.811548i	$0.698625\pi$
$674$	−1.69775	+	1.53235i	−0.0653948	+	0.0590240i
$675$		0			0
$676$	−2.01228	+	19.5980i	−0.0773956	+	0.753771i
$677$			42.3891i			1.62915i	0.580061	+	0.814573i	$0.303029\pi$
$677$			42.3891i			1.62915i	−0.580061	+	0.814573i	$0.696971\pi$
$678$		0			0
$679$			75.7715i			2.90784i
$680$	1.58834	+	2.16969i	0.0609100	+	0.0832037i
$681$		0			0
$682$	−17.3505	−	19.2233i	−0.664386	−	0.736097i
$683$	20.7847			0.795303			0.397652	−	0.917536i	$-0.369825\pi$
$683$	20.7847			0.795303			0.397652	+	0.917536i	$0.369825\pi$
$684$		0			0
$685$	11.6608			0.445536
$686$	13.3952	+	14.8410i	0.511429	+	0.566631i
$687$		0			0
$688$	4.31611	−	20.7961i	0.164550	−	0.792845i
$689$			8.65764i			0.329830i
$690$		0			0
$691$		−	42.6767i		−	1.62350i	−0.584007	−	0.811748i	$-0.698516\pi$
$691$		−	42.6767i		−	1.62350i	0.584007	−	0.811748i	$-0.301484\pi$
$692$	15.6811	+	1.61010i	0.596105	+	0.0612068i
$693$		0			0
$694$	−5.44437	+	4.91398i	−0.206665	+	0.186532i
$695$	7.66107			0.290601
$696$		0			0
$697$	6.76460			0.256227
$698$	19.2479	−	17.3728i	0.728544	−	0.657569i
$699$		0			0
$700$	−8.29663	−	0.851880i	−0.313583	−	0.0321981i
$701$		−	26.5424i		−	1.00249i	−0.865305	−	0.501247i	$-0.832875\pi$
$701$		−	26.5424i		−	1.00249i	0.865305	−	0.501247i	$-0.167125\pi$
$702$		0			0
$703$		−	12.7975i		−	0.482668i
$704$	−15.5719	+	49.1264i	−0.586888	+	1.85152i
$705$		0			0
$706$	10.1364	+	11.2305i	0.381489	+	0.422665i
$707$	−42.7016			−1.60596
$708$		0			0
$709$	46.2540			1.73711			0.868553	−	0.495596i	$-0.165050\pi$
$709$	46.2540			1.73711			0.868553	+	0.495596i	$0.165050\pi$
$710$	−2.11424	−	2.34244i	−0.0793461	−	0.0879104i
$711$		0			0
$712$	−14.0103	+	10.2563i	−0.525057	+	0.384372i
$713$			5.74213i			0.215045i
$714$		0			0
$715$		−	11.4323i		−	0.427543i
$716$	−2.01035	+	19.5792i	−0.0751304	+	0.731710i
$717$		0			0
$718$	−15.9530	+	14.3989i	−0.595361	+	0.537361i
$719$	44.9992			1.67819			0.839094	−	0.543986i	$-0.183086\pi$
$719$	44.9992			1.67819			0.839094	+	0.543986i	$0.183086\pi$
$720$		0			0
$721$	40.2828			1.50021
$722$	−14.8985	+	13.4471i	−0.554464	+	0.500448i
$723$		0			0
$724$	3.74275	−	36.4514i	0.139098	−	1.35470i
$725$			6.52706i			0.242409i
$726$		0			0
$727$			35.6578i			1.32247i	0.750177	+	0.661237i	$0.229968\pi$
$727$			35.6578i			1.32247i	−0.750177	+	0.661237i	$0.770032\pi$
$728$	−16.8900	+	12.3645i	−0.625985	+	0.458257i
$729$		0			0
$730$	−1.65501	−	1.83365i	−0.0612548	−	0.0678664i
$731$	−5.04795			−0.186705
$732$		0			0
$733$	−47.1392			−1.74113			−0.870563	−	0.492057i	$-0.836245\pi$
$733$	−47.1392			−1.74113			−0.870563	+	0.492057i	$0.836245\pi$
$734$	−23.2702	−	25.7819i	−0.858920	−	0.951628i
$735$		0			0
$736$	9.86211	−	5.77308i	0.363522	−	0.212798i
$737$			70.1906i			2.58551i
$738$		0			0
$739$		−	40.9282i		−	1.50557i	−0.658268	−	0.752784i	$-0.728711\pi$
$739$		−	40.9282i		−	1.50557i	0.658268	−	0.752784i	$-0.271289\pi$
$740$	11.6109	+	1.19219i	0.426826	+	0.0438256i
$741$		0			0
$742$	21.3574	−	19.2768i	0.784056	−	0.707673i
$743$	−33.8553			−1.24203			−0.621014	−	0.783799i	$-0.713279\pi$
$743$	−33.8553			−1.24203			−0.621014	+	0.783799i	$0.713279\pi$
$744$		0			0
$745$	−3.49438			−0.128024
$746$	−19.5363	+	17.6331i	−0.715274	+	0.645592i
$747$		0			0
$748$	12.1843	+	1.25106i	0.445504	+	0.0457434i
$749$			13.4844i			0.492708i
$750$		0			0
$751$			6.85461i			0.250128i	0.992149	+	0.125064i	$0.0399137\pi$
$751$			6.85461i			0.250128i	−0.992149	+	0.125064i	$0.960086\pi$
$752$	1.58225	+	0.328386i	0.0576987	+	0.0119750i
$753$		0			0
$754$	10.9759	+	12.1606i	0.399718	+	0.442862i
$755$	7.11211			0.258836
$756$		0			0
$757$	40.8568			1.48497			0.742483	−	0.669865i	$-0.233648\pi$
$757$	40.8568			1.48497			0.742483	+	0.669865i	$0.233648\pi$
$758$	−26.4417	−	29.2957i	−0.960404	−	1.06407i
$759$		0			0
$760$	3.66370	+	5.00465i	0.132896	+	0.181538i
$761$		−	27.9013i		−	1.01142i	−0.862703	−	0.505710i	$-0.831231\pi$
$761$		−	27.9013i		−	1.01142i	0.862703	−	0.505710i	$-0.168769\pi$
$762$		0			0
$763$			12.0246i			0.435319i
$764$	−3.89779	+	37.9614i	−0.141017	+	1.37339i
$765$		0			0
$766$	−7.77118	+	7.01411i	−0.280784	+	0.253430i
$767$	4.77002			0.172235
$768$		0			0
$769$	6.12340			0.220816			0.110408	−	0.993886i	$-0.464784\pi$
$769$	6.12340			0.220816			0.110408	+	0.993886i	$0.464784\pi$
$770$	−28.2022	+	25.4547i	−1.01634	+	0.917323i
$771$		0			0
$772$	−2.65629	+	25.8702i	−0.0956020	+	0.931087i
$773$		−	14.8193i		−	0.533012i	−0.963833	−	0.266506i	$-0.914131\pi$
$773$		−	14.8193i		−	0.533012i	0.963833	−	0.266506i	$-0.0858692\pi$
$774$		0			0
$775$		−	2.84246i		−	0.102104i
$776$	30.3574	+	41.4685i	1.08977	+	1.48863i
$777$		0			0
$778$	−16.9988	−	18.8336i	−0.609438	−	0.675218i
$779$	15.6034			0.559049
$780$		0			0
$781$	−14.3736			−0.514328
$782$	−1.81978	−	2.01620i	−0.0650751	−	0.0720991i
$783$		0			0
$784$	40.6927	+	8.44551i	1.45331	+	0.301625i
$785$			3.15875i			0.112741i
$786$		0			0
$787$			15.7271i			0.560609i	0.959911	+	0.280305i	$0.0904355\pi$
$787$			15.7271i			0.560609i	−0.959911	+	0.280305i	$0.909564\pi$
$788$	−31.5266	−	3.23708i	−1.12309	−	0.115316i
$789$		0			0
$790$	0.259938	−	0.234614i	0.00924816	−	0.00834720i
$791$	−12.8783			−0.457900
$792$		0			0
$793$	7.26380			0.257945
$794$	29.3008	−	26.4463i	1.03985	−	0.938544i
$795$		0			0
$796$	2.47822	+	0.254459i	0.0878383	+	0.00901904i
$797$		−	43.3678i		−	1.53617i	−0.640350	−	0.768083i	$-0.721211\pi$
$797$		−	43.3678i		−	1.53617i	0.640350	−	0.768083i	$-0.278789\pi$
$798$		0			0
$799$		−	0.384068i		−	0.0135873i
$800$	−4.88192	+	2.85778i	−0.172602	+	0.101038i
$801$		0			0
$802$	−3.78742	−	4.19622i	−0.133738	−	0.148174i
$803$	−11.2515			−0.397058
$804$		0			0
$805$	8.42420			0.296914
$806$	−4.77987	−	5.29579i	−0.168364	−	0.186536i
$807$		0			0
$808$	−23.3699	+	17.1081i	−0.822150	+	0.601862i
$809$		−	0.395982i		−	0.0139220i	−0.999976	−	0.00696100i	$-0.997784\pi$
$809$		−	0.395982i		−	0.0139220i	0.999976	−	0.00696100i	$-0.00221577\pi$
$810$		0			0
$811$			45.9241i			1.61261i	0.591498	+	0.806307i	$0.298537\pi$
$811$			45.9241i			1.61261i	−0.591498	+	0.806307i	$0.701463\pi$
$812$	5.56027	−	54.1526i	0.195127	−	1.90038i
$813$		0			0
$814$	39.4682	−	35.6232i	1.38336	−	1.24859i
$815$	14.1062			0.494119
$816$		0			0
$817$	−11.6437			−0.407362
$818$	−23.2318	+	20.9685i	−0.812279	+	0.733147i
$819$		0			0
$820$	−1.45357	+	14.1566i	−0.0507609	+	0.494370i
$821$		−	34.0437i		−	1.18813i	−0.804415	−	0.594067i	$-0.797521\pi$
$821$		−	34.0437i		−	1.18813i	0.804415	−	0.594067i	$-0.202479\pi$
$822$		0			0
$823$		−	10.5134i		−	0.366475i	−0.983069	−	0.183238i	$-0.941342\pi$
$823$		−	10.5134i		−	0.366475i	0.983069	−	0.183238i	$-0.0586578\pi$
$824$	22.0462	−	16.1391i	0.768014	−	0.562231i
$825$		0			0
$826$	−10.6207	−	11.7671i	−0.369543	−	0.409430i
$827$	−40.8826			−1.42163			−0.710813	−	0.703381i	$-0.751673\pi$
$827$	−40.8826			−1.42163			−0.710813	+	0.703381i	$0.751673\pi$
$828$		0			0
$829$	24.0184			0.834194			0.417097	−	0.908862i	$-0.363048\pi$
$829$	24.0184			0.834194			0.417097	+	0.908862i	$0.363048\pi$
$830$	11.0606	+	12.2545i	0.383920	+	0.425359i
$831$		0			0
$832$	−4.28988	+	13.5337i	−0.148725	+	0.469198i
$833$		−	9.87754i		−	0.342237i
$834$		0			0
$835$			18.3328i			0.634432i
$836$	28.1047	+	2.88573i	0.972021	+	0.0998050i
$837$		0			0
$838$	33.1890	−	29.9557i	1.14649	−	1.03480i
$839$	−34.1904			−1.18038			−0.590192	−	0.807263i	$-0.700948\pi$
$839$	−34.1904			−1.18038			−0.590192	+	0.807263i	$0.700948\pi$
$840$		0			0
$841$	−13.6025			−0.469052
$842$	−31.5543	+	28.4803i	−1.08743	+	0.981495i
$843$		0			0
$844$	−32.4781	−	3.33478i	−1.11794	−	0.114788i
$845$			9.85054i			0.338869i
$846$		0			0
$847$			127.181i			4.37000i
$848$	3.96546	−	19.1066i	0.136174	−	0.656124i
$849$		0			0
$850$	0.900823	+	0.998053i	0.0308980	+	0.0342329i
$851$	−11.7895			−0.404137
$852$		0			0
$853$	−24.7483			−0.847366			−0.423683	−	0.905811i	$-0.639263\pi$
$853$	−24.7483			−0.847366			−0.423683	+	0.905811i	$0.639263\pi$
$854$	−16.1733	−	17.9190i	−0.553440	−	0.613176i
$855$		0			0
$856$	5.40243	+	7.37979i	0.184651	+	0.252236i
$857$			10.6711i			0.364518i	0.983251	+	0.182259i	$0.0583410\pi$
$857$			10.6711i			0.364518i	−0.983251	+	0.182259i	$0.941659\pi$
$858$		0			0
$859$			23.8104i			0.812401i	0.913784	+	0.406200i	$0.133146\pi$
$859$			23.8104i			0.812401i	−0.913784	+	0.406200i	$0.866854\pi$
$860$	1.08470	−	10.5641i	0.0369880	−	0.360233i
$861$		0			0
$862$	26.3331	−	23.7677i	0.896909	−	0.809532i
$863$	−53.1072			−1.80779			−0.903896	−	0.427753i	$-0.859305\pi$
$863$	−53.1072			−1.80779			−0.903896	+	0.427753i	$0.859305\pi$
$864$		0			0
$865$	7.88176			0.267988
$866$	−30.8962	+	27.8863i	−1.04989	+	0.947614i
$867$		0			0
$868$	−2.42143	+	23.5828i	−0.0821888	+	0.800454i
$869$		−	1.59502i		−	0.0541072i
$870$		0			0
$871$			19.3367i			0.655200i
$872$	4.81758	+	6.58087i	0.163144	+	0.222856i
$873$		0			0
$874$	−4.19754	−	4.65061i	−0.141984	−	0.157309i
$875$	−4.17013			−0.140976
$876$		0			0
$877$	−41.4276			−1.39891			−0.699456	−	0.714676i	$-0.746574\pi$
$877$	−41.4276			−1.39891			−0.699456	+	0.714676i	$0.746574\pi$
$878$	−27.1524	−	30.0831i	−0.916348	−	1.01525i
$879$		0			0
$880$	−5.23632	+	25.2300i	−0.176516	+	0.850502i
$881$		−	18.8579i		−	0.635340i	−0.948201	−	0.317670i	$-0.897100\pi$
$881$		−	18.8579i		−	0.635340i	0.948201	−	0.317670i	$-0.102900\pi$
$882$		0			0
$883$		−	36.0305i		−	1.21252i	−0.795266	−	0.606261i	$-0.792669\pi$
$883$		−	36.0305i		−	1.21252i	0.795266	−	0.606261i	$-0.207331\pi$
$884$	3.35665	+	0.344653i	0.112896	+	0.0115919i
$885$		0			0
$886$	−31.3457	+	28.2920i	−1.05308	+	0.950489i
$887$	−19.3362			−0.649245			−0.324623	−	0.945844i	$-0.605237\pi$
$887$	−19.3362			−0.649245			−0.324623	+	0.945844i	$0.605237\pi$
$888$		0			0
$889$	9.02088			0.302551
$890$	−6.44470	+	5.81686i	−0.216027	+	0.194981i
$891$		0			0
$892$	−35.6640	−	3.66190i	−1.19412	−	0.122609i
$893$		−	0.885900i		−	0.0296455i
$894$		0			0
$895$			9.84108i			0.328951i
$896$	42.9380	−	19.5511i	1.43446	−	0.653157i
$897$		0			0
$898$	13.9306	+	15.4343i	0.464872	+	0.515048i
$899$	18.5529			0.618774
$900$		0			0
$901$	−4.63785			−0.154509
$902$	43.4336	+	48.1216i	1.44618	+	1.60227i
$903$		0			0
$904$	−7.04809	+	5.15961i	−0.234416	+	0.171606i
$905$		−	18.3215i		−	0.609027i
$906$		0			0
$907$		−	17.1102i		−	0.568134i	−0.958804	−	0.284067i	$-0.908316\pi$
$907$		−	17.1102i		−	0.568134i	0.958804	−	0.284067i	$-0.0916838\pi$
$908$	2.13075	−	20.7518i	0.0707114	−	0.688672i
$909$		0			0
$910$	−7.76937	+	7.01248i	−0.257552	+	0.232461i
$911$	−11.3283			−0.375324			−0.187662	−	0.982234i	$-0.560091\pi$
$911$	−11.3283			−0.375324			−0.187662	+	0.982234i	$0.560091\pi$
$912$		0			0
$913$	75.1952			2.48860
$914$	9.27352	−	8.37009i	0.306741	−	0.276858i
$915$		0			0
$916$	−3.83799	+	37.3790i	−0.126811	+	1.23504i
$917$			7.98334i			0.263633i
$918$		0			0
$919$			33.3567i			1.10034i	0.835054	+	0.550169i	$0.185437\pi$
$919$			33.3567i			1.10034i	−0.835054	+	0.550169i	$0.814563\pi$
$920$	4.61043	−	3.37510i	0.152001	−	0.111274i
$921$		0			0
$922$	0.865470	+	0.958885i	0.0285027	+	0.0315792i
$923$	−3.95976			−0.130337
$924$		0			0
$925$	5.83599			0.191886
$926$	7.45853	+	8.26357i	0.245102	+	0.271558i
$927$		0			0
$928$	−18.6529	−	31.8646i	−0.612311	−	1.04601i
$929$			10.4925i			0.344248i	0.985075	+	0.172124i	$0.0550630\pi$
$929$			10.4925i			0.344248i	−0.985075	+	0.172124i	$0.944937\pi$
$930$		0			0
$931$		−	22.7838i		−	0.746708i
$932$	−14.4976	−	1.48859i	−0.474886	−	0.0487602i
$933$		0			0
$934$	30.1054	−	27.1725i	0.985079	−	0.889113i
$935$	6.12420			0.200283
$936$		0			0
$937$	29.4458			0.961952			0.480976	−	0.876734i	$-0.340282\pi$
$937$	29.4458			0.961952			0.480976	+	0.876734i	$0.340282\pi$
$938$	47.7016	−	43.0545i	1.55751	−	1.40578i
$939$		0			0
$940$	0.803758	+	0.0825282i	0.0262157	+	0.00269177i
$941$		−	36.0415i		−	1.17492i	−0.809254	−	0.587459i	$-0.800128\pi$
$941$		−	36.0415i		−	1.17492i	0.809254	−	0.587459i	$-0.199872\pi$
$942$		0			0
$943$		−	14.3743i		−	0.468091i
$944$	−10.5270	−	2.18481i	−0.342624	−	0.0711095i
$945$		0			0
$946$	−32.4115	−	35.9098i	−1.05379	−	1.16753i
$947$	−12.1726			−0.395557			−0.197778	−	0.980247i	$-0.563373\pi$
$947$	−12.1726			−0.395557			−0.197778	+	0.980247i	$0.563373\pi$
$948$		0			0
$949$	−3.09967			−0.100620
$950$	2.07786	+	2.30213i	0.0674146	+	0.0746911i
$951$		0			0
$952$	−6.62357	−	9.04787i	−0.214671	−	0.293243i
$953$		−	25.0300i		−	0.810801i	−0.914139	−	0.405400i	$-0.867132\pi$
$953$		−	25.0300i		−	0.810801i	0.914139	−	0.405400i	$-0.132868\pi$
$954$		0			0
$955$			19.0805i			0.617430i
$956$	6.06342	−	59.0528i	0.196105	−	1.90991i
$957$		0			0
$958$	−27.6963	+	24.9981i	−0.894827	+	0.807653i
$959$	−48.6270			−1.57025
$960$		0			0
$961$	22.9204			0.739369
$962$	10.8730	−	9.81379i	0.350561	−	0.316409i
$963$		0			0
$964$	−2.60466	+	25.3673i	−0.0838905	+	0.817026i
$965$			13.0031i			0.418584i
$966$		0			0
$967$		−	2.75536i		−	0.0886063i	−0.999018	−	0.0443032i	$-0.985893\pi$
$967$		−	2.75536i		−	0.0886063i	0.999018	−	0.0443032i	$-0.0141068\pi$
$968$	50.9544	+	69.6043i	1.63774	+	2.23717i
$969$		0			0
$970$	17.2171	+	19.0755i	0.552809	+	0.612476i
$971$	33.6700			1.08052			0.540261	−	0.841497i	$-0.318325\pi$
$971$	33.6700			1.08052			0.540261	+	0.841497i	$0.318325\pi$
$972$		0			0
$973$	−31.9476			−1.02419
$974$	7.45936	+	8.26448i	0.239013	+	0.264811i
$975$		0			0
$976$	−16.0305	−	3.32704i	−0.513125	−	0.106496i
$977$			56.0751i			1.79400i	0.442030	+	0.897000i	$0.354258\pi$
$977$			56.0751i			1.79400i	−0.442030	+	0.897000i	$0.645742\pi$
$978$		0			0
$979$			39.5457i			1.26388i
$980$	20.6712	+	2.12248i	0.660318	+	0.0678001i
$981$		0			0
$982$	20.4654	−	18.4716i	0.653076	−	0.589453i
$983$	−15.0532			−0.480124			−0.240062	−	0.970758i	$-0.577168\pi$
$983$	−15.0532			−0.480124			−0.240062	+	0.970758i	$0.577168\pi$
$984$		0			0
$985$	−15.8462			−0.504901
$986$	−6.51435	+	5.87972i	−0.207459	+	0.187249i
$987$		0			0
$988$	7.74252	+	0.794985i	0.246322	+	0.0252919i
$989$			10.7265i			0.341084i
$990$		0			0
$991$		−	32.4096i		−	1.02953i	−0.857333	−	0.514763i	$-0.827880\pi$
$991$		−	32.4096i		−	1.02953i	0.857333	−	0.514763i	$-0.172120\pi$
$992$	8.12311	+	13.8766i	0.257909	+	0.440584i
$993$		0			0
$994$	8.81666	+	9.76829i	0.279648	+	0.309831i
$995$	1.24563			0.0394890
$996$		0			0
$997$	−44.1499			−1.39824			−0.699120	−	0.715004i	$-0.746425\pi$
$997$	−44.1499			−1.39824			−0.699120	+	0.715004i	$0.746425\pi$
$998$	0.802069	+	0.888641i	0.0253891	+	0.0281294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.12		48
3.2	odd	2	inner	1620.2.e.b.971.37		48
4.3	odd	2	inner	1620.2.e.b.971.38		48
9.2	odd	6		180.2.q.a.131.3	yes	48
9.4	even	3		180.2.q.a.11.10	yes	48
9.5	odd	6		540.2.q.a.251.15		48
9.7	even	3		540.2.q.a.71.22		48
12.11	even	2	inner	1620.2.e.b.971.11		48
36.7	odd	6		540.2.q.a.71.15		48
36.11	even	6		180.2.q.a.131.10	yes	48
36.23	even	6		540.2.q.a.251.22		48
36.31	odd	6		180.2.q.a.11.3	✓	48
45.2	even	12		900.2.o.b.599.15		48
45.4	even	6		900.2.r.f.551.15		48
45.13	odd	12		900.2.o.b.299.2		48
45.22	odd	12		900.2.o.c.299.23		48
45.29	odd	6		900.2.r.f.851.22		48
45.38	even	12		900.2.o.c.599.10		48
180.47	odd	12		900.2.o.b.599.2		48
180.67	even	12		900.2.o.c.299.10		48
180.83	odd	12		900.2.o.c.599.23		48
180.103	even	12		900.2.o.b.299.15		48
180.119	even	6		900.2.r.f.851.15		48
180.139	odd	6		900.2.r.f.551.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.3	✓	48	36.31	odd	6
180.2.q.a.11.10	yes	48	9.4	even	3
180.2.q.a.131.3	yes	48	9.2	odd	6
180.2.q.a.131.10	yes	48	36.11	even	6
540.2.q.a.71.15		48	36.7	odd	6
540.2.q.a.71.22		48	9.7	even	3
540.2.q.a.251.15		48	9.5	odd	6
540.2.q.a.251.22		48	36.23	even	6
900.2.o.b.299.2		48	45.13	odd	12
900.2.o.b.299.15		48	180.103	even	12
900.2.o.b.599.2		48	180.47	odd	12
900.2.o.b.599.15		48	45.2	even	12
900.2.o.c.299.10		48	180.67	even	12
900.2.o.c.299.23		48	45.22	odd	12
900.2.o.c.599.10		48	45.38	even	12
900.2.o.c.599.23		48	180.83	odd	12
900.2.r.f.551.15		48	45.4	even	6
900.2.r.f.551.22		48	180.139	odd	6
900.2.r.f.851.15		48	180.119	even	6
900.2.r.f.851.22		48	45.29	odd	6
1620.2.e.b.971.11		48	12.11	even	2	inner
1620.2.e.b.971.12		48	1.1	even	1	trivial
1620.2.e.b.971.37		48	3.2	odd	2	inner
1620.2.e.b.971.38		48	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04983 + 0.947554i) q^{2} +(0.204282 - 1.98954i) q^{4} -1.00000i q^{5} +4.17013i q^{7} +(1.67074 + 2.28224i) q^{8} +(0.947554 + 1.04983i) q^{10} +6.44191 q^{11} +1.77467 q^{13} +(-3.95142 - 4.37792i) q^{14} +(-3.91654 - 0.812853i) q^{16} +0.950682i q^{17} +2.19286i q^{19} +(-1.98954 - 0.204282i) q^{20} +(-6.76290 + 6.10406i) q^{22} +2.02013 q^{23} -1.00000 q^{25} +(-1.86310 + 1.68160i) q^{26} +(8.29663 + 0.851880i) q^{28} -6.52706i q^{29} +2.84246i q^{31} +(4.88192 - 2.85778i) q^{32} +(-0.900823 - 0.998053i) q^{34} +4.17013 q^{35} -5.83599 q^{37} +(-2.07786 - 2.30213i) q^{38} +(2.28224 - 1.67074i) q^{40} -7.11552i q^{41} +5.30982i q^{43} +(1.31596 - 12.8164i) q^{44} +(-2.12079 + 1.91418i) q^{46} -0.403992 q^{47} -10.3900 q^{49} +(1.04983 - 0.947554i) q^{50} +(0.362533 - 3.53078i) q^{52} +4.87844i q^{53} -6.44191i q^{55} +(-9.51725 + 6.96718i) q^{56} +(6.18474 + 6.85230i) q^{58} +2.68783 q^{59} +4.09304 q^{61} +(-2.69338 - 2.98409i) q^{62} +(-2.41728 + 7.62606i) q^{64} -1.77467i q^{65} +10.8959i q^{67} +(1.89142 + 0.194207i) q^{68} +(-4.37792 + 3.95142i) q^{70} -2.23126 q^{71} -1.74662 q^{73} +(6.12679 - 5.52992i) q^{74} +(4.36279 + 0.447962i) q^{76} +26.8636i q^{77} -0.247600i q^{79} +(-0.812853 + 3.91654i) q^{80} +(6.74234 + 7.47008i) q^{82} +11.6728 q^{83} +0.950682 q^{85} +(-5.03135 - 5.57441i) q^{86} +(10.7627 + 14.7020i) q^{88} +6.13881i q^{89} +7.40061i q^{91} +(0.412675 - 4.01913i) q^{92} +(0.424123 - 0.382804i) q^{94} +2.19286 q^{95} +18.1701 q^{97} +(10.9077 - 9.84505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

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Representations

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Database

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