LMFDB - Embedded newform 1620.2.e.b.971.1

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			971.1
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41320 - 0.0535467i) q^{2} +(1.99427 + 0.151344i) q^{4} -1.00000i q^{5} -2.16432i q^{7} +(-2.81019 - 0.320666i) q^{8} +O(q^{10})$	\(q+(-1.41320 - 0.0535467i) q^{2} +(1.99427 + 0.151344i) q^{4} -1.00000i q^{5} -2.16432i q^{7} +(-2.81019 - 0.320666i) q^{8} +(-0.0535467 + 1.41320i) q^{10} +2.89264 q^{11} +6.60598 q^{13} +(-0.115892 + 3.05861i) q^{14} +(3.95419 + 0.603641i) q^{16} +5.08829i q^{17} +4.66790i q^{19} +(0.151344 - 1.99427i) q^{20} +(-4.08788 - 0.154892i) q^{22} -2.89439 q^{23} -1.00000 q^{25} +(-9.33557 - 0.353728i) q^{26} +(0.327557 - 4.31623i) q^{28} +6.92350i q^{29} +5.21794i q^{31} +(-5.55574 - 1.06480i) q^{32} +(0.272461 - 7.19076i) q^{34} -2.16432 q^{35} +4.58347 q^{37} +(0.249951 - 6.59668i) q^{38} +(-0.320666 + 2.81019i) q^{40} -4.83591i q^{41} -4.40481i q^{43} +(5.76870 + 0.437785i) q^{44} +(4.09035 + 0.154985i) q^{46} +0.0193847 q^{47} +2.31572 q^{49} +(1.41320 + 0.0535467i) q^{50} +(13.1741 + 0.999777i) q^{52} -3.21239i q^{53} -2.89264i q^{55} +(-0.694023 + 6.08215i) q^{56} +(0.370730 - 9.78429i) q^{58} +8.05302 q^{59} +0.642800 q^{61} +(0.279404 - 7.37400i) q^{62} +(7.79435 + 1.80227i) q^{64} -6.60598i q^{65} -9.46725i q^{67} +(-0.770083 + 10.1474i) q^{68} +(3.05861 + 0.115892i) q^{70} -1.17635 q^{71} +2.32539 q^{73} +(-6.47736 - 0.245430i) q^{74} +(-0.706461 + 9.30904i) q^{76} -6.26060i q^{77} +16.9721i q^{79} +(0.603641 - 3.95419i) q^{80} +(-0.258947 + 6.83410i) q^{82} -1.90123 q^{83} +5.08829 q^{85} +(-0.235863 + 6.22488i) q^{86} +(-8.12888 - 0.927573i) q^{88} -3.72649i q^{89} -14.2974i q^{91} +(-5.77218 - 0.438050i) q^{92} +(-0.0273945 - 0.00103799i) q^{94} +4.66790 q^{95} -11.5616 q^{97} +(-3.27258 - 0.123999i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * 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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.41320	−	0.0535467i	−0.999283	−	0.0378632i
$2$	−1.41320	−	0.0535467i	−0.999283	−	0.0378632i
$3$		0			0
$3$		0			0
$4$	1.99427	+	0.151344i	0.997133	+	0.0756722i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	2.16432i		−	0.818036i	−0.912526	−	0.409018i	$-0.865871\pi$
$7$		−	2.16432i		−	0.818036i	0.912526	−	0.409018i	$-0.134129\pi$
$8$	−2.81019	−	0.320666i	−0.993553	−	0.113373i
$9$		0			0
$10$	−0.0535467	+	1.41320i	−0.0169329	+	0.446893i
$11$	2.89264			0.872165			0.436083	−	0.899907i	$-0.356366\pi$
$11$	2.89264			0.872165			0.436083	+	0.899907i	$0.356366\pi$
$12$		0			0
$13$	6.60598			1.83217			0.916085	−	0.400985i	$-0.131332\pi$
$13$	6.60598			1.83217			0.916085	+	0.400985i	$0.131332\pi$
$14$	−0.115892	+	3.05861i	−0.0309735	+	0.817449i
$15$		0			0
$16$	3.95419	+	0.603641i	0.988547	+	0.150910i
$17$			5.08829i			1.23409i	0.786928	+	0.617045i	$0.211670\pi$
$17$			5.08829i			1.23409i	−0.786928	+	0.617045i	$0.788330\pi$
$18$		0			0
$19$			4.66790i			1.07089i	0.844570	+	0.535445i	$0.179856\pi$
$19$			4.66790i			1.07089i	−0.844570	+	0.535445i	$0.820144\pi$
$20$	0.151344	−	1.99427i	0.0338416	−	0.445931i
$21$		0			0
$22$	−4.08788	−	0.154892i	−0.871540	−	0.0330230i
$23$	−2.89439			−0.603522			−0.301761	−	0.953384i	$-0.597574\pi$
$23$	−2.89439			−0.603522			−0.301761	+	0.953384i	$0.597574\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−9.33557	−	0.353728i	−1.83086	−	0.0693718i
$27$		0			0
$28$	0.327557	−	4.31623i	0.0619025	−	0.815690i
$29$			6.92350i			1.28566i	0.766008	+	0.642831i	$0.222240\pi$
$29$			6.92350i			1.28566i	−0.766008	+	0.642831i	$0.777760\pi$
$30$		0			0
$31$			5.21794i			0.937171i	0.883418	+	0.468585i	$0.155236\pi$
$31$			5.21794i			0.937171i	−0.883418	+	0.468585i	$0.844764\pi$
$32$	−5.55574	−	1.06480i	−0.982125	−	0.188232i
$33$		0			0
$34$	0.272461	−	7.19076i	0.0467266	−	1.23321i
$35$	−2.16432			−0.365837
$36$		0			0
$37$	4.58347			0.753518			0.376759	−	0.926311i	$-0.377038\pi$
$37$	4.58347			0.753518			0.376759	+	0.926311i	$0.377038\pi$
$38$	0.249951	−	6.59668i	0.0405474	−	1.07012i
$39$		0			0
$40$	−0.320666	+	2.81019i	−0.0507017	+	0.444330i
$41$		−	4.83591i		−	0.755242i	−0.925960	−	0.377621i	$-0.876742\pi$
$41$		−	4.83591i		−	0.755242i	0.925960	−	0.377621i	$-0.123258\pi$
$42$		0			0
$43$		−	4.40481i		−	0.671727i	−0.941911	−	0.335864i	$-0.890972\pi$
$43$		−	4.40481i		−	0.671727i	0.941911	−	0.335864i	$-0.109028\pi$
$44$	5.76870	+	0.437785i	0.869664	+	0.0659986i
$45$		0			0
$46$	4.09035	+	0.154985i	0.603089	+	0.0228513i
$47$	0.0193847			0.00282756			0.00141378	−	0.999999i	$-0.499550\pi$
$47$	0.0193847			0.00282756			0.00141378	+	0.999999i	$0.499550\pi$
$48$		0			0
$49$	2.31572			0.330818
$50$	1.41320	+	0.0535467i	0.199857	+	0.00757265i
$51$		0			0
$52$	13.1741	+	0.999777i	1.82692	+	0.138644i
$53$		−	3.21239i		−	0.441256i	−0.975358	−	0.220628i	$-0.929189\pi$
$53$		−	3.21239i		−	0.441256i	0.975358	−	0.220628i	$-0.0708107\pi$
$54$		0			0
$55$		−	2.89264i		−	0.390044i
$56$	−0.694023	+	6.08215i	−0.0927428	+	0.812761i
$57$		0			0
$58$	0.370730	−	9.78429i	0.0486793	−	1.28474i
$59$	8.05302			1.04841			0.524207	−	0.851591i	$-0.324362\pi$
$59$	8.05302			1.04841			0.524207	+	0.851591i	$0.324362\pi$
$60$		0			0
$61$	0.642800			0.0823021			0.0411510	−	0.999153i	$-0.486898\pi$
$61$	0.642800			0.0823021			0.0411510	+	0.999153i	$0.486898\pi$
$62$	0.279404	−	7.37400i	0.0354843	−	0.936499i
$63$		0			0
$64$	7.79435	+	1.80227i	0.974293	+	0.225283i
$65$		−	6.60598i		−	0.819371i
$66$		0			0
$67$		−	9.46725i		−	1.15661i	−0.815821	−	0.578304i	$-0.803715\pi$
$67$		−	9.46725i		−	1.15661i	0.815821	−	0.578304i	$-0.196285\pi$
$68$	−0.770083	+	10.1474i	−0.0933863	+	1.23055i
$69$		0			0
$70$	3.05861	+	0.115892i	0.365574	+	0.0138518i
$71$	−1.17635			−0.139607			−0.0698035	−	0.997561i	$-0.522237\pi$
$71$	−1.17635			−0.139607			−0.0698035	+	0.997561i	$0.522237\pi$
$72$		0			0
$73$	2.32539			0.272166			0.136083	−	0.990697i	$-0.456549\pi$
$73$	2.32539			0.272166			0.136083	+	0.990697i	$0.456549\pi$
$74$	−6.47736	−	0.245430i	−0.752978	−	0.0285306i
$75$		0			0
$76$	−0.706461	+	9.30904i	−0.0810366	+	1.06782i
$77$		−	6.26060i		−	0.713462i
$78$		0			0
$79$			16.9721i			1.90951i	0.297391	+	0.954756i	$0.403884\pi$
$79$			16.9721i			1.90951i	−0.297391	+	0.954756i	$0.596116\pi$
$80$	0.603641	−	3.95419i	0.0674892	−	0.442092i
$81$		0			0
$82$	−0.258947	+	6.83410i	−0.0285959	+	0.754700i
$83$	−1.90123			−0.208687			−0.104343	−	0.994541i	$-0.533274\pi$
$83$	−1.90123			−0.208687			−0.104343	+	0.994541i	$0.533274\pi$
$84$		0			0
$85$	5.08829			0.551902
$86$	−0.235863	+	6.22488i	−0.0254338	+	0.671246i
$87$		0			0
$88$	−8.12888	−	0.927573i	−0.866542	−	0.0988796i
$89$		−	3.72649i		−	0.395007i	−0.980302	−	0.197503i	$-0.936717\pi$
$89$		−	3.72649i		−	0.395007i	0.980302	−	0.197503i	$-0.0632834\pi$
$90$		0			0
$91$		−	14.2974i		−	1.49878i
$92$	−5.77218	−	0.438050i	−0.601792	−	0.0456698i
$93$		0			0
$94$	−0.0273945	−	0.00103799i	−0.00282553	−	0.000107060i
$95$	4.66790			0.478917
$96$		0			0
$97$	−11.5616			−1.17391			−0.586953	−	0.809621i	$-0.699673\pi$
$97$	−11.5616			−1.17391			−0.586953	+	0.809621i	$0.699673\pi$
$98$	−3.27258	−	0.123999i	−0.330581	−	0.0125258i
$99$		0			0
$100$	−1.99427	−	0.151344i	−0.199427	−	0.0151344i
$101$			10.9272i			1.08730i	0.839312	+	0.543650i	$0.182958\pi$
$101$			10.9272i			1.08730i	−0.839312	+	0.543650i	$0.817042\pi$
$102$		0			0
$103$		−	0.635329i		−	0.0626008i	−0.999510	−	0.0313004i	$-0.990035\pi$
$103$		−	0.635329i		−	0.0626008i	0.999510	−	0.0313004i	$-0.00996485\pi$
$104$	−18.5641	−	2.11831i	−1.82036	−	0.207718i
$105$		0			0
$106$	−0.172013	+	4.53975i	−0.0167074	+	0.440940i
$107$	18.8050			1.81795			0.908975	−	0.416850i	$-0.136866\pi$
$107$	18.8050			1.81795			0.908975	+	0.416850i	$0.136866\pi$
$108$		0			0
$109$	−3.39053			−0.324754			−0.162377	−	0.986729i	$-0.551916\pi$
$109$	−3.39053			−0.324754			−0.162377	+	0.986729i	$0.551916\pi$
$110$	−0.154892	+	4.08788i	−0.0147683	+	0.389764i
$111$		0			0
$112$	1.30647	−	8.55813i	0.123450	−	0.808667i
$113$		−	0.998205i		−	0.0939032i	−0.998897	−	0.0469516i	$-0.985049\pi$
$113$		−	0.998205i		−	0.0939032i	0.998897	−	0.0469516i	$-0.0149507\pi$
$114$		0			0
$115$			2.89439i			0.269903i
$116$	−1.04783	+	13.8073i	−0.0972888	+	1.28198i
$117$		0			0
$118$	−11.3805	−	0.431213i	−1.04766	−	0.0396963i
$119$	11.0127			1.00953
$120$		0			0
$121$	−2.63261			−0.239328
$122$	−0.908404	−	0.0344198i	−0.0822430	−	0.00311622i
$123$		0			0
$124$	−0.789706	+	10.4060i	−0.0709177	+	0.934483i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			8.78450i			0.779498i	0.920921	+	0.389749i	$0.127438\pi$
$127$			8.78450i			0.779498i	−0.920921	+	0.389749i	$0.872562\pi$
$128$	−10.9185	−	2.96432i	−0.965065	−	0.262012i
$129$		0			0
$130$	−0.353728	+	9.33557i	−0.0310240	+	0.818783i
$131$	14.1269			1.23427			0.617137	−	0.786855i	$-0.288292\pi$
$131$	14.1269			1.23427			0.617137	+	0.786855i	$0.288292\pi$
$132$		0			0
$133$	10.1028			0.876027
$134$	−0.506940	+	13.3791i	−0.0437929	+	1.15578i
$135$		0			0
$136$	1.63164	−	14.2991i	0.139912	−	1.22613i
$137$		−	15.2025i		−	1.29884i	−0.760430	−	0.649420i	$-0.775012\pi$
$137$		−	15.2025i		−	1.29884i	0.760430	−	0.649420i	$-0.224988\pi$
$138$		0			0
$139$			2.54076i			0.215504i	0.994178	+	0.107752i	$0.0343653\pi$
$139$			2.54076i			0.215504i	−0.994178	+	0.107752i	$0.965635\pi$
$140$	−4.31623	−	0.327557i	−0.364788	−	0.0276836i
$141$		0			0
$142$	1.66242	+	0.0629896i	0.139507	+	0.00528597i
$143$	19.1087			1.59795
$144$		0			0
$145$	6.92350			0.574965
$146$	−3.28624	−	0.124517i	−0.271971	−	0.0103051i
$147$		0			0
$148$	9.14066	+	0.693683i	0.751358	+	0.0570204i
$149$			6.91066i			0.566143i	0.959099	+	0.283072i	$0.0913534\pi$
$149$			6.91066i			0.566143i	−0.959099	+	0.283072i	$0.908647\pi$
$150$		0			0
$151$		−	21.3124i		−	1.73438i	−0.497976	−	0.867191i	$-0.665923\pi$
$151$		−	21.3124i		−	1.73438i	0.497976	−	0.867191i	$-0.334077\pi$
$152$	1.49684	−	13.1177i	0.121410	−	1.06399i
$153$		0			0
$154$	−0.335235	+	8.84748i	−0.0270140	+	0.712950i
$155$	5.21794			0.419115
$156$		0			0
$157$	11.6697			0.931343			0.465671	−	0.884958i	$-0.345813\pi$
$157$	11.6697			0.931343			0.465671	+	0.884958i	$0.345813\pi$
$158$	0.908800	−	23.9850i	0.0723003	−	1.90814i
$159$		0			0
$160$	−1.06480	+	5.55574i	−0.0841798	+	0.439219i
$161$			6.26438i			0.493703i
$162$		0			0
$163$		−	0.438006i		−	0.0343073i	−0.999853	−	0.0171536i	$-0.994540\pi$
$163$		−	0.438006i		−	0.0343073i	0.999853	−	0.0171536i	$-0.00546044\pi$
$164$	0.731887	−	9.64408i	0.0571508	−	0.753076i
$165$		0			0
$166$	2.68681	+	0.101804i	0.208537	+	0.00790155i
$167$	−4.16559			−0.322343			−0.161172	−	0.986926i	$-0.551527\pi$
$167$	−4.16559			−0.322343			−0.161172	+	0.986926i	$0.551527\pi$
$168$		0			0
$169$	30.6390			2.35684
$170$	−7.19076	−	0.272461i	−0.551506	−	0.0208968i
$171$		0			0
$172$	0.666643	−	8.78436i	0.0508311	−	0.669801i
$173$		−	8.95276i		−	0.680666i	−0.940305	−	0.340333i	$-0.889460\pi$
$173$		−	8.95276i		−	0.680666i	0.940305	−	0.340333i	$-0.110540\pi$
$174$		0			0
$175$			2.16432i			0.163607i
$176$	11.4381	+	1.74612i	0.862177	+	0.131619i
$177$		0			0
$178$	−0.199541	+	5.26627i	−0.0149562	+	0.394724i
$179$	10.5263			0.786776			0.393388	−	0.919373i	$-0.371303\pi$
$179$	10.5263			0.786776			0.393388	+	0.919373i	$0.371303\pi$
$180$		0			0
$181$	−9.50854			−0.706765			−0.353382	−	0.935479i	$-0.614968\pi$
$181$	−9.50854			−0.706765			−0.353382	+	0.935479i	$0.614968\pi$
$182$	−0.765581	+	20.2051i	−0.0567486	+	1.49770i
$183$		0			0
$184$	8.13379	+	0.928133i	0.599631	+	0.0684228i
$185$		−	4.58347i		−	0.336984i
$186$		0			0
$187$			14.7186i			1.07633i
$188$	0.0386583	+	0.00293377i	0.00281945	+	0.000213967i
$189$		0			0
$190$	−6.59668	−	0.249951i	−0.478573	−	0.0181333i
$191$	12.1608			0.879925			0.439963	−	0.898016i	$-0.354992\pi$
$191$	12.1608			0.879925			0.439963	+	0.898016i	$0.354992\pi$
$192$		0			0
$193$	−14.0288			−1.00981			−0.504907	−	0.863174i	$-0.668473\pi$
$193$	−14.0288			−1.00981			−0.504907	+	0.863174i	$0.668473\pi$
$194$	16.3389	+	0.619088i	1.17307	+	0.0444479i
$195$		0			0
$196$	4.61817	+	0.350472i	0.329869	+	0.0250337i
$197$			7.21555i			0.514086i	0.966400	+	0.257043i	$0.0827483\pi$
$197$			7.21555i			0.514086i	−0.966400	+	0.257043i	$0.917252\pi$
$198$		0			0
$199$			8.63093i			0.611830i	0.952059	+	0.305915i	$0.0989624\pi$
$199$			8.63093i			0.611830i	−0.952059	+	0.305915i	$0.901038\pi$
$200$	2.81019	+	0.320666i	0.198711	+	0.0226745i
$201$		0			0
$202$	0.585117	−	15.4424i	0.0411687	−	1.08652i
$203$	14.9847			1.05172
$204$		0			0
$205$	−4.83591			−0.337754
$206$	−0.0340198	+	0.897846i	−0.00237027	+	0.0625559i
$207$		0			0
$208$	26.1213	+	3.98764i	1.81119	+	0.276493i
$209$			13.5026i			0.933993i
$210$		0			0
$211$		−	18.6026i		−	1.28066i	−0.768101	−	0.640328i	$-0.778798\pi$
$211$		−	18.6026i		−	1.28066i	0.768101	−	0.640328i	$-0.221202\pi$
$212$	0.486177	−	6.40636i	0.0333908	−	0.439991i
$213$		0			0
$214$	−26.5753	−	1.00695i	−1.81665	−	0.0688335i
$215$	−4.40481			−0.300406
$216$		0			0
$217$	11.2933			0.766639
$218$	4.79150	+	0.181552i	0.324521	+	0.0122962i
$219$		0			0
$220$	0.437785	−	5.76870i	0.0295155	−	0.388926i
$221$			33.6131i			2.26106i
$222$		0			0
$223$		−	12.3437i		−	0.826597i	−0.910596	−	0.413299i	$-0.864377\pi$
$223$		−	12.3437i		−	0.826597i	0.910596	−	0.413299i	$-0.135623\pi$
$224$	−2.30457	+	12.0244i	−0.153980	+	0.803413i
$225$		0			0
$226$	−0.0534506	+	1.41066i	−0.00355548	+	0.0938359i
$227$	0.744049			0.0493843			0.0246921	−	0.999695i	$-0.492139\pi$
$227$	0.744049			0.0493843			0.0246921	+	0.999695i	$0.492139\pi$
$228$		0			0
$229$	−26.1566			−1.72848			−0.864238	−	0.503083i	$-0.832199\pi$
$229$	−26.1566			−1.72848			−0.864238	+	0.503083i	$0.832199\pi$
$230$	0.154985	−	4.09035i	0.0102194	−	0.269710i
$231$		0			0
$232$	2.22013	−	19.4564i	0.145759	−	1.27737i
$233$		−	25.8264i		−	1.69195i	−0.533226	−	0.845973i	$-0.679021\pi$
$233$		−	25.8264i		−	1.69195i	0.533226	−	0.845973i	$-0.320979\pi$
$234$		0			0
$235$		−	0.0193847i		−	0.00126452i
$236$	16.0599	+	1.21878i	1.04541	+	0.0793357i
$237$		0			0
$238$	−15.5631	−	0.589692i	−1.00881	−	0.0382241i
$239$	−8.23201			−0.532484			−0.266242	−	0.963906i	$-0.585782\pi$
$239$	−8.23201			−0.532484			−0.266242	+	0.963906i	$0.585782\pi$
$240$		0			0
$241$	−0.141109			−0.00908962			−0.00454481	−	0.999990i	$-0.501447\pi$
$241$	−0.141109			−0.00908962			−0.00454481	+	0.999990i	$0.501447\pi$
$242$	3.72040	+	0.140967i	0.239156	+	0.00906173i
$243$		0			0
$244$	1.28191	+	0.0972841i	0.0820661	+	0.00622797i
$245$		−	2.31572i		−	0.147946i
$246$		0			0
$247$			30.8361i			1.96205i
$248$	1.67322	−	14.6634i	0.106249	−	0.931128i
$249$		0			0
$250$	0.0535467	−	1.41320i	0.00338659	−	0.0893786i
$251$	−9.50499			−0.599950			−0.299975	−	0.953947i	$-0.596978\pi$
$251$	−9.50499			−0.599950			−0.299975	+	0.953947i	$0.596978\pi$
$252$		0			0
$253$	−8.37244			−0.526371
$254$	0.470381	−	12.4142i	0.0295143	−	0.778939i
$255$		0			0
$256$	15.2712	+	4.77383i	0.954452	+	0.298364i
$257$			25.9846i			1.62087i	0.585827	+	0.810436i	$0.300770\pi$
$257$			25.9846i			1.62087i	−0.585827	+	0.810436i	$0.699230\pi$
$258$		0			0
$259$		−	9.92010i		−	0.616405i
$260$	0.999777	−	13.1741i	0.0620036	−	0.817022i
$261$		0			0
$262$	−19.9642	−	0.756450i	−1.23339	−	0.0467336i
$263$	26.8766			1.65728			0.828640	−	0.559782i	$-0.189115\pi$
$263$	26.8766			1.65728			0.828640	+	0.559782i	$0.189115\pi$
$264$		0			0
$265$	−3.21239			−0.197336
$266$	−14.2773	−	0.540973i	−0.875398	−	0.0331692i
$267$		0			0
$268$	1.43281	−	18.8802i	0.0875231	−	1.15329i
$269$		−	16.4030i		−	1.00011i	−0.865995	−	0.500053i	$-0.833314\pi$
$269$		−	16.4030i		−	1.00011i	0.865995	−	0.500053i	$-0.166686\pi$
$270$		0			0
$271$		−	16.0484i		−	0.974873i	−0.873158	−	0.487437i	$-0.837932\pi$
$271$		−	16.0484i		−	0.974873i	0.873158	−	0.487437i	$-0.162068\pi$
$272$	−3.07150	+	20.1200i	−0.186237	+	1.21996i
$273$		0			0
$274$	−0.814046	+	21.4842i	−0.0491783	+	1.29791i
$275$	−2.89264			−0.174433
$276$		0			0
$277$	−24.3318			−1.46196			−0.730978	−	0.682401i	$-0.760936\pi$
$277$	−24.3318			−1.46196			−0.730978	+	0.682401i	$0.760936\pi$
$278$	0.136049	−	3.59060i	0.00815969	−	0.215350i
$279$		0			0
$280$	6.08215	+	0.694023i	0.363478	+	0.0414758i
$281$		−	10.4404i		−	0.622822i	−0.950275	−	0.311411i	$-0.899198\pi$
$281$		−	10.4404i		−	0.622822i	0.950275	−	0.311411i	$-0.100802\pi$
$282$		0			0
$283$		−	14.8891i		−	0.885065i	−0.896752	−	0.442533i	$-0.854080\pi$
$283$		−	14.8891i		−	0.885065i	0.896752	−	0.442533i	$-0.145920\pi$
$284$	−2.34595	−	0.178034i	−0.139207	−	0.0105644i
$285$		0			0
$286$	−27.0045	−	1.02321i	−1.59681	−	0.0605037i
$287$	−10.4664			−0.617815
$288$		0			0
$289$	−8.89065			−0.522979
$290$	−9.78429	−	0.370730i	−0.574553	−	0.0217700i
$291$		0			0
$292$	4.63745	+	0.351935i	0.271386	+	0.0205954i
$293$		−	26.1179i		−	1.52582i	−0.646503	−	0.762911i	$-0.723769\pi$
$293$		−	26.1179i		−	1.52582i	0.646503	−	0.762911i	$-0.276231\pi$
$294$		0			0
$295$		−	8.05302i		−	0.468865i
$296$	−12.8804	−	1.46976i	−0.748660	−	0.0854283i
$297$		0			0
$298$	0.370043	−	9.76614i	0.0214360	−	0.565737i
$299$	−19.1203			−1.10575
$300$		0			0
$301$	−9.53341			−0.549497
$302$	−1.14121	+	30.1187i	−0.0656693	+	1.73314i
$303$		0			0
$304$	−2.81774	+	18.4578i	−0.161608	+	1.05863i
$305$		−	0.642800i		−	0.0368066i
$306$		0			0
$307$			28.5542i			1.62967i	0.579690	+	0.814837i	$0.303174\pi$
$307$			28.5542i			1.62967i	−0.579690	+	0.814837i	$0.696826\pi$
$308$	0.947507	−	12.4853i	0.0539892	−	0.711416i
$309$		0			0
$310$	−7.37400	−	0.279404i	−0.418815	−	0.0158691i
$311$	−0.0880448			−0.00499256			−0.00249628	−	0.999997i	$-0.500795\pi$
$311$	−0.0880448			−0.00499256			−0.00249628	+	0.999997i	$0.500795\pi$
$312$		0			0
$313$	15.2161			0.860063			0.430032	−	0.902814i	$-0.358502\pi$
$313$	15.2161			0.860063			0.430032	+	0.902814i	$0.358502\pi$
$314$	−16.4916	−	0.624873i	−0.930675	−	0.0352636i
$315$		0			0
$316$	−2.56863	+	33.8469i	−0.144497	+	1.90404i
$317$		−	7.16554i		−	0.402457i	−0.979544	−	0.201228i	$-0.935507\pi$
$317$		−	7.16554i		−	0.402457i	0.979544	−	0.201228i	$-0.0644934\pi$
$318$		0			0
$319$			20.0272i			1.12131i
$320$	1.80227	−	7.79435i	0.100750	−	0.435717i
$321$		0			0
$322$	0.335437	−	8.85282i	0.0186932	−	0.493349i
$323$	−23.7516			−1.32158
$324$		0			0
$325$	−6.60598			−0.366434
$326$	−0.0234538	+	0.618990i	−0.00129898	+	0.0342827i
$327$		0			0
$328$	−1.55071	+	13.5898i	−0.0856237	+	0.750372i
$329$		−	0.0419548i		−	0.00231304i
$330$		0			0
$331$			0.819649i			0.0450520i	0.999746	+	0.0225260i	$0.00717085\pi$
$331$			0.819649i			0.0450520i	−0.999746	+	0.0225260i	$0.992829\pi$
$332$	−3.79155	−	0.287740i	−0.208088	−	0.0157918i
$333$		0			0
$334$	5.88681	+	0.223054i	0.322112	+	0.0122050i
$335$	−9.46725			−0.517251
$336$		0			0
$337$	−3.06781			−0.167114			−0.0835571	−	0.996503i	$-0.526628\pi$
$337$	−3.06781			−0.167114			−0.0835571	+	0.996503i	$0.526628\pi$
$338$	−43.2990	−	1.64062i	−2.35515	−	0.0892377i
$339$		0			0
$340$	10.1474	+	0.770083i	0.550320	+	0.0417636i
$341$			15.0937i			0.817367i
$342$		0			0
$343$		−	20.1622i		−	1.08866i
$344$	−1.41247	+	12.3784i	−0.0761554	+	0.667396i
$345$		0			0
$346$	−0.479391	+	12.6520i	−0.0257722	+	0.680178i
$347$	22.3128			1.19781			0.598906	−	0.800819i	$-0.295602\pi$
$347$	22.3128			1.19781			0.598906	+	0.800819i	$0.295602\pi$
$348$		0			0
$349$	−10.0393			−0.537392			−0.268696	−	0.963225i	$-0.586593\pi$
$349$	−10.0393			−0.537392			−0.268696	+	0.963225i	$0.586593\pi$
$350$	0.115892	−	3.05861i	0.00619469	−	0.163490i
$351$		0			0
$352$	−16.0708	−	3.08009i	−0.856575	−	0.164169i
$353$			12.7323i			0.677673i	0.940845	+	0.338836i	$0.110033\pi$
$353$			12.7323i			0.677673i	−0.940845	+	0.338836i	$0.889967\pi$
$354$		0			0
$355$			1.17635i			0.0624342i
$356$	0.563983	−	7.43161i	0.0298910	−	0.393874i
$357$		0			0
$358$	−14.8758	−	0.563651i	−0.786212	−	0.0297899i
$359$	−5.93304			−0.313134			−0.156567	−	0.987667i	$-0.550043\pi$
$359$	−5.93304			−0.313134			−0.156567	+	0.987667i	$0.550043\pi$
$360$		0			0
$361$	−2.78932			−0.146806
$362$	13.4375	+	0.509151i	0.706258	+	0.0267604i
$363$		0			0
$364$	2.16384	−	28.5129i	0.113416	−	1.49448i
$365$		−	2.32539i		−	0.121716i
$366$		0			0
$367$			26.6009i			1.38855i	0.719708	+	0.694277i	$0.244276\pi$
$367$			26.6009i			1.38855i	−0.719708	+	0.694277i	$0.755724\pi$
$368$	−11.4450	−	1.74717i	−0.596610	−	0.0910777i
$369$		0			0
$370$	−0.245430	+	6.47736i	−0.0127593	+	0.336742i
$371$	−6.95264			−0.360963
$372$		0			0
$373$	−26.4589			−1.36999			−0.684995	−	0.728548i	$-0.740195\pi$
$373$	−26.4589			−1.36999			−0.684995	+	0.728548i	$0.740195\pi$
$374$	0.788132	−	20.8003i	0.0407533	−	1.07556i
$375$		0			0
$376$	−0.0544748	−	0.00621603i	−0.00280933	−	0.000320567i
$377$			45.7365i			2.35555i
$378$		0			0
$379$			21.3357i			1.09594i	0.836497	+	0.547972i	$0.184600\pi$
$379$			21.3357i			1.09594i	−0.836497	+	0.547972i	$0.815400\pi$
$380$	9.30904	+	0.706461i	0.477544	+	0.0362407i
$381$		0			0
$382$	−17.1856	−	0.651171i	−0.879294	−	0.0333168i
$383$	−3.15352			−0.161138			−0.0805688	−	0.996749i	$-0.525674\pi$
$383$	−3.15352			−0.161138			−0.0805688	+	0.996749i	$0.525674\pi$
$384$		0			0
$385$	−6.26060			−0.319070
$386$	19.8255	+	0.751195i	1.00909	+	0.0382348i
$387$		0			0
$388$	−23.0570	−	1.74979i	−1.17054	−	0.0888321i
$389$		−	15.0051i		−	0.760786i	−0.924825	−	0.380393i	$-0.875789\pi$
$389$		−	15.0051i		−	0.760786i	0.924825	−	0.380393i	$-0.124211\pi$
$390$		0			0
$391$		−	14.7275i		−	0.744801i
$392$	−6.50763	−	0.742574i	−0.328685	−	0.0375057i
$393$		0			0
$394$	0.386369	−	10.1970i	0.0194650	−	0.513718i
$395$	16.9721			0.853960
$396$		0			0
$397$	−10.0474			−0.504266			−0.252133	−	0.967693i	$-0.581132\pi$
$397$	−10.0474			−0.504266			−0.252133	+	0.967693i	$0.581132\pi$
$398$	0.462158	−	12.1972i	0.0231659	−	0.611392i
$399$		0			0
$400$	−3.95419	−	0.603641i	−0.197709	−	0.0301821i
$401$		−	7.91146i		−	0.395080i	−0.980295	−	0.197540i	$-0.936705\pi$
$401$		−	7.91146i		−	0.395080i	0.980295	−	0.197540i	$-0.0632952\pi$
$402$		0			0
$403$			34.4696i			1.71705i
$404$	−1.65378	+	21.7918i	−0.0822784	+	1.08418i
$405$		0			0
$406$	−21.1763	−	0.802379i	−1.05096	−	0.0398214i
$407$	13.2584			0.657193
$408$		0			0
$409$	27.1649			1.34322			0.671608	−	0.740906i	$-0.265604\pi$
$409$	27.1649			1.34322			0.671608	+	0.740906i	$0.265604\pi$
$410$	6.83410	+	0.258947i	0.337512	+	0.0127885i
$411$		0			0
$412$	0.0961534	−	1.26701i	0.00473714	−	0.0624213i
$413$		−	17.4293i		−	0.857640i
$414$		0			0
$415$			1.90123i			0.0933275i
$416$	−36.7011	−	7.03404i	−1.79942	−	0.344872i
$417$		0			0
$418$	0.723019	−	19.0818i	0.0353640	−	0.933324i
$419$	−8.57054			−0.418698			−0.209349	−	0.977841i	$-0.567134\pi$
$419$	−8.57054			−0.418698			−0.209349	+	0.977841i	$0.567134\pi$
$420$		0			0
$421$	−6.83007			−0.332877			−0.166439	−	0.986052i	$-0.553227\pi$
$421$	−6.83007			−0.332877			−0.166439	+	0.986052i	$0.553227\pi$
$422$	−0.996108	+	26.2892i	−0.0484898	+	1.27974i
$423$		0			0
$424$	−1.03010	+	9.02743i	−0.0500263	+	0.438411i
$425$		−	5.08829i		−	0.246818i
$426$		0			0
$427$		−	1.39122i		−	0.0673260i
$428$	37.5022	+	2.84603i	1.81274	+	0.137568i
$429$		0			0
$430$	6.22488	+	0.235863i	0.300190	+	0.0113743i
$431$	26.5552			1.27912			0.639559	−	0.768742i	$-0.279117\pi$
$431$	26.5552			1.27912			0.639559	+	0.768742i	$0.279117\pi$
$432$		0			0
$433$	−12.4714			−0.599339			−0.299669	−	0.954043i	$-0.596876\pi$
$433$	−12.4714			−0.599339			−0.299669	+	0.954043i	$0.596876\pi$
$434$	−15.9597	−	0.604719i	−0.766089	−	0.0290274i
$435$		0			0
$436$	−6.76162	−	0.513138i	−0.323823	−	0.0245748i
$437$		−	13.5107i		−	0.646306i
$438$		0			0
$439$		−	14.8278i		−	0.707692i	−0.935304	−	0.353846i	$-0.884874\pi$
$439$		−	14.8278i		−	0.707692i	0.935304	−	0.353846i	$-0.115126\pi$
$440$	−0.927573	+	8.12888i	−0.0442203	+	0.387529i
$441$		0			0
$442$	1.79987	−	47.5020i	0.0856111	−	2.25944i
$443$	−39.5250			−1.87789			−0.938945	−	0.344067i	$-0.888195\pi$
$443$	−39.5250			−1.87789			−0.938945	+	0.344067i	$0.888195\pi$
$444$		0			0
$445$	−3.72649			−0.176652
$446$	−0.660966	+	17.4442i	−0.0312976	+	0.826005i
$447$		0			0
$448$	3.90068	−	16.8695i	0.184290	−	0.797007i
$449$		−	22.8395i		−	1.07786i	−0.842349	−	0.538932i	$-0.818828\pi$
$449$		−	22.8395i		−	1.07786i	0.842349	−	0.538932i	$-0.181172\pi$
$450$		0			0
$451$		−	13.9886i		−	0.658695i
$452$	0.151073	−	1.99069i	0.00710586	−	0.0936340i
$453$		0			0
$454$	−1.05149	−	0.0398414i	−0.0493488	−	0.00186985i
$455$	−14.2974			−0.670275
$456$		0			0
$457$	0.832481			0.0389418			0.0194709	−	0.999810i	$-0.493802\pi$
$457$	0.832481			0.0389418			0.0194709	+	0.999810i	$0.493802\pi$
$458$	36.9645	+	1.40060i	1.72724	+	0.0654457i
$459$		0			0
$460$	−0.438050	+	5.77218i	−0.0204242	+	0.269129i
$461$			35.7826i			1.66656i	0.552849	+	0.833281i	$0.313541\pi$
$461$			35.7826i			1.66656i	−0.552849	+	0.833281i	$0.686459\pi$
$462$		0			0
$463$			8.32746i			0.387010i	0.981099	+	0.193505i	$0.0619855\pi$
$463$			8.32746i			0.387010i	−0.981099	+	0.193505i	$0.938014\pi$
$464$	−4.17931	+	27.3768i	−0.194020	+	1.27094i
$465$		0			0
$466$	−1.38292	+	36.4979i	−0.0640625	+	1.69073i
$467$	−16.8607			−0.780220			−0.390110	−	0.920768i	$-0.627563\pi$
$467$	−16.8607			−0.780220			−0.390110	+	0.920768i	$0.627563\pi$
$468$		0			0
$469$	−20.4901			−0.946147
$470$	−0.00103799	+	0.0273945i	−4.78789e−5	+	0.00126361i
$471$		0			0
$472$	−22.6305	−	2.58233i	−1.04165	−	0.118861i
$473$		−	12.7415i		−	0.585857i
$474$		0			0
$475$		−	4.66790i		−	0.214178i
$476$	21.9622	+	1.66671i	1.00664	+	0.0763933i
$477$		0			0
$478$	11.6335	+	0.440797i	0.532102	+	0.0201616i
$479$	5.29381			0.241880			0.120940	−	0.992660i	$-0.461409\pi$
$479$	5.29381			0.241880			0.120940	+	0.992660i	$0.461409\pi$
$480$		0			0
$481$	30.2783			1.38057
$482$	0.199415	+	0.00755591i	0.00908310	+	0.000344162i
$483$		0			0
$484$	−5.25012	−	0.398430i	−0.238642	−	0.0181105i
$485$			11.5616i			0.524987i
$486$		0			0
$487$		−	19.8270i		−	0.898449i	−0.893419	−	0.449225i	$-0.851700\pi$
$487$		−	19.8270i		−	0.898449i	0.893419	−	0.449225i	$-0.148300\pi$
$488$	−1.80639	−	0.206124i	−0.0817714	−	0.00933079i
$489$		0			0
$490$	−0.123999	+	3.27258i	−0.00560172	+	0.147840i
$491$	−28.4478			−1.28383			−0.641916	−	0.766775i	$-0.721860\pi$
$491$	−28.4478			−1.28383			−0.641916	+	0.766775i	$0.721860\pi$
$492$		0			0
$493$	−35.2287			−1.58662
$494$	1.65117	−	43.5775i	0.0742896	−	1.96065i
$495$		0			0
$496$	−3.14977	+	20.6327i	−0.141429	+	0.926438i
$497$			2.54600i			0.114204i
$498$		0			0
$499$			5.64995i			0.252926i	0.991971	+	0.126463i	$0.0403626\pi$
$499$			5.64995i			0.252926i	−0.991971	+	0.126463i	$0.959637\pi$
$500$	−0.151344	+	1.99427i	−0.00676832	+	0.0891863i
$501$		0			0
$502$	13.4325	+	0.508961i	0.599520	+	0.0227160i
$503$	−32.7730			−1.46128			−0.730638	−	0.682765i	$-0.760777\pi$
$503$	−32.7730			−1.46128			−0.730638	+	0.682765i	$0.760777\pi$
$504$		0			0
$505$	10.9272			0.486256
$506$	11.8319	+	0.448317i	0.525994	+	0.0199301i
$507$		0			0
$508$	−1.32948	+	17.5186i	−0.0589863	+	0.777263i
$509$		−	12.5465i		−	0.556116i	−0.960564	−	0.278058i	$-0.910309\pi$
$509$		−	12.5465i		−	0.556116i	0.960564	−	0.278058i	$-0.0896907\pi$
$510$		0			0
$511$		−	5.03289i		−	0.222642i
$512$	−21.3257	−	7.56409i	−0.942471	−	0.334289i
$513$		0			0
$514$	1.39139	−	36.7214i	0.0613715	−	1.61971i
$515$	−0.635329			−0.0279959
$516$		0			0
$517$	0.0560732			0.00246610
$518$	−0.531188	+	14.0191i	−0.0233391	+	0.615963i
$519$		0			0
$520$	−2.11831	+	18.5641i	−0.0928942	+	0.814088i
$521$		−	11.7475i		−	0.514665i	−0.966323	−	0.257333i	$-0.917156\pi$
$521$		−	11.7475i		−	0.514665i	0.966323	−	0.257333i	$-0.0828436\pi$
$522$		0			0
$523$			20.5196i			0.897261i	0.893717	+	0.448630i	$0.148088\pi$
$523$			20.5196i			0.897261i	−0.893717	+	0.448630i	$0.851912\pi$
$524$	28.1728	+	2.13803i	1.23074	+	0.0934002i
$525$		0			0
$526$	−37.9819	−	1.43915i	−1.65609	−	0.0627500i
$527$	−26.5504			−1.15655
$528$		0			0
$529$	−14.6225			−0.635761
$530$	4.53975	+	0.172013i	0.197194	+	0.00747177i
$531$		0			0
$532$	20.1477	+	1.52901i	0.873515	+	0.0662908i
$533$		−	31.9459i		−	1.38373i
$534$		0			0
$535$		−	18.8050i		−	0.813012i
$536$	−3.03583	+	26.6048i	−0.131128	+	1.14915i
$537$		0			0
$538$	−0.878324	+	23.1806i	−0.0378672	+	0.999388i
$539$	6.69857			0.288528
$540$		0			0
$541$	19.0464			0.818871			0.409435	−	0.912339i	$-0.365726\pi$
$541$	19.0464			0.818871			0.409435	+	0.912339i	$0.365726\pi$
$542$	−0.859341	+	22.6796i	−0.0369118	+	0.974174i
$543$		0			0
$544$	5.41800	−	28.2692i	0.232295	−	1.21203i
$545$			3.39053i			0.145234i
$546$		0			0
$547$		−	25.0907i		−	1.07280i	−0.843964	−	0.536399i	$-0.819784\pi$
$547$		−	25.0907i		−	1.07280i	0.843964	−	0.536399i	$-0.180216\pi$
$548$	2.30082	−	30.3179i	0.0982861	−	1.29512i
$549$		0			0
$550$	4.08788	+	0.154892i	0.174308	+	0.00660460i
$551$	−32.3182			−1.37680
$552$		0			0
$553$	36.7331			1.56205
$554$	34.3857	+	1.30289i	1.46091	+	0.0553544i
$555$		0			0
$556$	−0.384530	+	5.06695i	−0.0163077	+	0.214887i
$557$		−	4.13922i		−	0.175384i	−0.996148	−	0.0876922i	$-0.972051\pi$
$557$		−	4.13922i		−	0.175384i	0.996148	−	0.0876922i	$-0.0279492\pi$
$558$		0			0
$559$		−	29.0981i		−	1.23072i
$560$	−8.55813	−	1.30647i	−0.361647	−	0.0552085i
$561$		0			0
$562$	−0.559049	+	14.7544i	−0.0235821	+	0.622376i
$563$	−29.8670			−1.25874			−0.629372	−	0.777104i	$-0.716688\pi$
$563$	−29.8670			−1.25874			−0.629372	+	0.777104i	$0.716688\pi$
$564$		0			0
$565$	−0.998205			−0.0419948
$566$	−0.797262	+	21.0413i	−0.0335114	+	0.884431i
$567$		0			0
$568$	3.30577	+	0.377215i	0.138707	+	0.0158276i
$569$			40.6588i			1.70451i	0.523130	+	0.852253i	$0.324764\pi$
$569$			40.6588i			1.70451i	−0.523130	+	0.852253i	$0.675236\pi$
$570$		0			0
$571$		−	40.1782i		−	1.68140i	−0.541498	−	0.840702i	$-0.682143\pi$
$571$		−	40.1782i		−	1.68140i	0.541498	−	0.840702i	$-0.317857\pi$
$572$	38.1079	+	2.89200i	1.59337	+	0.120921i
$573$		0			0
$574$	14.7912	+	0.560443i	0.617372	+	0.0233925i
$575$	2.89439			0.120704
$576$		0			0
$577$	33.5865			1.39822			0.699112	−	0.715013i	$-0.253579\pi$
$577$	33.5865			1.39822			0.699112	+	0.715013i	$0.253579\pi$
$578$	12.5643	+	0.476065i	0.522604	+	0.0198017i
$579$		0			0
$580$	13.8073	+	1.04783i	0.573317	+	0.0435089i
$581$			4.11486i			0.170713i
$582$		0			0
$583$		−	9.29231i		−	0.384848i
$584$	−6.53479	−	0.745674i	−0.270412	−	0.0308562i
$585$		0			0
$586$	−1.39853	+	36.9098i	−0.0577726	+	1.52473i
$587$	−37.3796			−1.54282			−0.771410	−	0.636338i	$-0.780448\pi$
$587$	−37.3796			−1.54282			−0.771410	+	0.636338i	$0.780448\pi$
$588$		0			0
$589$	−24.3569			−1.00361
$590$	−0.431213	+	11.3805i	−0.0177527	+	0.468529i
$591$		0			0
$592$	18.1239	+	2.76677i	0.744889	+	0.113714i
$593$			11.3789i			0.467275i	0.972324	+	0.233638i	$0.0750630\pi$
$593$			11.3789i			0.467275i	−0.972324	+	0.233638i	$0.924937\pi$
$594$		0			0
$595$		−	11.0127i		−	0.451475i
$596$	−1.04589	+	13.7817i	−0.0428413	+	0.564520i
$597$		0			0
$598$	27.0208	+	1.02383i	1.10496	+	0.0418674i
$599$	−2.24270			−0.0916341			−0.0458170	−	0.998950i	$-0.514589\pi$
$599$	−2.24270			−0.0916341			−0.0458170	+	0.998950i	$0.514589\pi$
$600$		0			0
$601$	17.3428			0.707427			0.353714	−	0.935354i	$-0.384919\pi$
$601$	17.3428			0.707427			0.353714	+	0.935354i	$0.384919\pi$
$602$	13.4726	+	0.510483i	0.549103	+	0.0208057i
$603$		0			0
$604$	3.22552	−	42.5027i	0.131244	−	1.72941i
$605$			2.63261i			0.107031i
$606$		0			0
$607$			17.0110i			0.690454i	0.938519	+	0.345227i	$0.112198\pi$
$607$			17.0110i			0.690454i	−0.938519	+	0.345227i	$0.887802\pi$
$608$	4.97038	−	25.9336i	0.201576	−	1.05175i
$609$		0			0
$610$	−0.0344198	+	0.908404i	−0.00139362	+	0.0367802i
$611$	0.128055			0.00518056
$612$		0			0
$613$	6.23696			0.251908			0.125954	−	0.992036i	$-0.459801\pi$
$613$	6.23696			0.251908			0.125954	+	0.992036i	$0.459801\pi$
$614$	1.52898	−	40.3528i	0.0617047	−	1.62851i
$615$		0			0
$616$	−2.00756	+	17.5935i	−0.0808870	+	0.708862i
$617$		−	8.37985i		−	0.337360i	−0.985671	−	0.168680i	$-0.946050\pi$
$617$		−	8.37985i		−	0.337360i	0.985671	−	0.168680i	$-0.0539504\pi$
$618$		0			0
$619$			36.3752i			1.46204i	0.682355	+	0.731021i	$0.260956\pi$
$619$			36.3752i			1.46204i	−0.682355	+	0.731021i	$0.739044\pi$
$620$	10.4060	+	0.789706i	0.417914	+	0.0317154i
$621$		0			0
$622$	0.124425	+	0.00471451i	0.00498898	+	0.000189034i
$623$	−8.06531			−0.323130
$624$		0			0
$625$	1.00000			0.0400000
$626$	−21.5034	−	0.814771i	−0.859447	−	0.0325648i
$627$		0			0
$628$	23.2725	+	1.76614i	0.928672	+	0.0704767i
$629$			23.3220i			0.929910i
$630$		0			0
$631$			42.3747i			1.68691i	0.537199	+	0.843455i	$0.319482\pi$
$631$			42.3747i			1.68691i	−0.537199	+	0.843455i	$0.680518\pi$
$632$	5.44238	−	47.6949i	0.216486	−	1.89720i
$633$		0			0
$634$	−0.383691	+	10.1263i	−0.0152383	+	0.402168i
$635$	8.78450			0.348602
$636$		0			0
$637$	15.2976			0.606114
$638$	1.07239	−	28.3025i	0.0424564	−	1.12051i
$639$		0			0
$640$	−2.96432	+	10.9185i	−0.117175	+	0.431590i
$641$			11.0661i			0.437083i	0.975828	+	0.218542i	$0.0701300\pi$
$641$			11.0661i			0.437083i	−0.975828	+	0.218542i	$0.929870\pi$
$642$		0			0
$643$			12.1887i			0.480676i	0.970689	+	0.240338i	$0.0772583\pi$
$643$			12.1887i			0.480676i	−0.970689	+	0.240338i	$0.922742\pi$
$644$	−0.948079	+	12.4928i	−0.0373595	+	0.492287i
$645$		0			0
$646$	33.5658	+	1.27182i	1.32063	+	0.0500391i
$647$	−13.5692			−0.533460			−0.266730	−	0.963771i	$-0.585943\pi$
$647$	−13.5692			−0.533460			−0.266730	+	0.963771i	$0.585943\pi$
$648$		0			0
$649$	23.2945			0.914390
$650$	9.33557	+	0.353728i	0.366171	+	0.0138744i
$651$		0			0
$652$	0.0662897	−	0.873501i	0.00259611	−	0.0342089i
$653$			11.4694i			0.448833i	0.974493	+	0.224416i	$0.0720475\pi$
$653$			11.4694i			0.448833i	−0.974493	+	0.224416i	$0.927952\pi$
$654$		0			0
$655$		−	14.1269i		−	0.551985i
$656$	2.91915	−	19.1221i	0.113974	−	0.746592i
$657$		0			0
$658$	−0.00224654	+	0.0592905i	−8.75792e−5	+	0.00231138i
$659$	16.9310			0.659536			0.329768	−	0.944062i	$-0.393029\pi$
$659$	16.9310			0.659536			0.329768	+	0.944062i	$0.393029\pi$
$660$		0			0
$661$	−13.8511			−0.538746			−0.269373	−	0.963036i	$-0.586816\pi$
$661$	−13.8511			−0.538746			−0.269373	+	0.963036i	$0.586816\pi$
$662$	0.0438895	−	1.15833i	0.00170581	−	0.0450197i
$663$		0			0
$664$	5.34281	+	0.609658i	0.207341	+	0.0236593i
$665$		−	10.1028i		−	0.391771i
$666$		0			0
$667$		−	20.0393i		−	0.775925i
$668$	−8.30730	−	0.630439i	−0.321419	−	0.0243924i
$669$		0			0
$670$	13.3791	+	0.506940i	0.516880	+	0.0195848i
$671$	1.85939			0.0717810
$672$		0			0
$673$	−15.3757			−0.592690			−0.296345	−	0.955081i	$-0.595768\pi$
$673$	−15.3757			−0.592690			−0.296345	+	0.955081i	$0.595768\pi$
$674$	4.33542	+	0.164271i	0.166994	+	0.00632748i
$675$		0			0
$676$	61.1022	+	4.63703i	2.35009	+	0.178347i
$677$			39.7283i			1.52688i	0.645877	+	0.763441i	$0.276492\pi$
$677$			39.7283i			1.52688i	−0.645877	+	0.763441i	$0.723508\pi$
$678$		0			0
$679$			25.0231i			0.960298i
$680$	−14.2991	−	1.63164i	−0.548344	−	0.0625705i
$681$		0			0
$682$	0.808215	−	21.3303i	0.0309482	−	0.816781i
$683$	21.6572			0.828690			0.414345	−	0.910120i	$-0.364011\pi$
$683$	21.6572			0.828690			0.414345	+	0.910120i	$0.364011\pi$
$684$		0			0
$685$	−15.2025			−0.580859
$686$	−1.07962	+	28.4932i	−0.0412200	+	1.08788i
$687$		0			0
$688$	2.65893	−	17.4175i	0.101371	−	0.664034i
$689$		−	21.2210i		−	0.808456i
$690$		0			0
$691$		−	17.7558i		−	0.675463i	−0.941242	−	0.337732i	$-0.890340\pi$
$691$		−	17.7558i		−	0.675463i	0.941242	−	0.337732i	$-0.109660\pi$
$692$	1.35495	−	17.8542i	0.0515075	−	0.678714i
$693$		0			0
$694$	−31.5324	−	1.19477i	−1.19695	−	0.0453530i
$695$	2.54076			0.0963765
$696$		0			0
$697$	24.6065			0.932037
$698$	14.1875	+	0.537572i	0.537006	+	0.0203474i
$699$		0			0
$700$	−0.327557	+	4.31623i	−0.0123805	+	0.163138i
$701$			38.3642i			1.44900i	0.689277	+	0.724498i	$0.257928\pi$
$701$			38.3642i			1.44900i	−0.689277	+	0.724498i	$0.742072\pi$
$702$		0			0
$703$			21.3952i			0.806936i
$704$	22.5463	+	5.21331i	0.849745	+	0.196484i
$705$		0			0
$706$	0.681773	−	17.9933i	0.0256589	−	0.677187i
$707$	23.6500			0.889451
$708$		0			0
$709$	3.93701			0.147858			0.0739288	−	0.997264i	$-0.476446\pi$
$709$	3.93701			0.147858			0.0739288	+	0.997264i	$0.476446\pi$
$710$	0.0629896	−	1.66242i	0.00236396	−	0.0623894i
$711$		0			0
$712$	−1.19496	+	10.4721i	−0.0447829	+	0.392460i
$713$		−	15.1028i		−	0.565603i
$714$		0			0
$715$		−	19.1087i		−	0.714627i
$716$	20.9923	+	1.59310i	0.784520	+	0.0595370i
$717$		0			0
$718$	8.38457	+	0.317695i	0.312909	+	0.0118563i
$719$	−25.9983			−0.969573			−0.484787	−	0.874632i	$-0.661103\pi$
$719$	−25.9983			−0.969573			−0.484787	+	0.874632i	$0.661103\pi$
$720$		0			0
$721$	−1.37505			−0.0512097
$722$	3.94187	+	0.149359i	0.146701	+	0.00555857i
$723$		0			0
$724$	−18.9626	−	1.43906i	−0.704738	−	0.0534824i
$725$		−	6.92350i		−	0.257132i
$726$		0			0
$727$			26.8216i			0.994758i	0.867533	+	0.497379i	$0.165704\pi$
$727$			26.8216i			0.994758i	−0.867533	+	0.497379i	$0.834296\pi$
$728$	−4.58470	+	40.1786i	−0.169920	+	1.48912i
$729$		0			0
$730$	−0.124517	+	3.28624i	−0.00460858	+	0.121629i
$731$	22.4129			0.828972
$732$		0			0
$733$	16.0019			0.591044			0.295522	−	0.955336i	$-0.404506\pi$
$733$	16.0019			0.591044			0.295522	+	0.955336i	$0.404506\pi$
$734$	1.42439	−	37.5923i	0.0525751	−	1.38756i
$735$		0			0
$736$	16.0805	+	3.08195i	0.592734	+	0.113602i
$737$		−	27.3854i		−	1.00875i
$738$		0			0
$739$			2.17451i			0.0799905i	0.999200	+	0.0399952i	$0.0127343\pi$
$739$			2.17451i			0.0799905i	−0.999200	+	0.0399952i	$0.987266\pi$
$740$	0.693683	−	9.14066i	0.0255003	−	0.336018i
$741$		0			0
$742$	9.82547	+	0.372291i	0.360704	+	0.0136672i
$743$	18.3321			0.672539			0.336269	−	0.941766i	$-0.390835\pi$
$743$	18.3321			0.672539			0.336269	+	0.941766i	$0.390835\pi$
$744$		0			0
$745$	6.91066			0.253187
$746$	37.3917	+	1.41679i	1.36901	+	0.0518722i
$747$		0			0
$748$	−2.22758	+	29.3528i	−0.0814483	+	1.07324i
$749$		−	40.7001i		−	1.48715i
$750$		0			0
$751$		−	27.6393i		−	1.00857i	−0.863537	−	0.504286i	$-0.831756\pi$
$751$		−	27.6393i		−	1.00857i	0.863537	−	0.504286i	$-0.168244\pi$
$752$	0.0766510	+	0.0117014i	0.00279517	+	0.000426707i
$753$		0			0
$754$	2.44904	−	64.6348i	0.0891887	−	2.35386i
$755$	−21.3124			−0.775639
$756$		0			0
$757$	−47.4098			−1.72314			−0.861570	−	0.507640i	$-0.830518\pi$
$757$	−47.4098			−1.72314			−0.861570	+	0.507640i	$0.830518\pi$
$758$	1.14246	−	30.1517i	0.0414959	−	1.09516i
$759$		0			0
$760$	−13.1177	−	1.49684i	−0.475829	−	0.0542960i
$761$		−	22.7384i		−	0.824265i	−0.911124	−	0.412132i	$-0.864784\pi$
$761$		−	22.7384i		−	0.824265i	0.911124	−	0.412132i	$-0.135216\pi$
$762$		0			0
$763$			7.33819i			0.265660i
$764$	24.2519	+	1.84047i	0.877402	+	0.0665858i
$765$		0			0
$766$	4.45656	+	0.168861i	0.161022	+	0.00610119i
$767$	53.1981			1.92087
$768$		0			0
$769$	34.9614			1.26074			0.630371	−	0.776294i	$-0.282903\pi$
$769$	34.9614			1.26074			0.630371	+	0.776294i	$0.282903\pi$
$770$	8.84748	+	0.335235i	0.318841	+	0.0120810i
$771$		0			0
$772$	−27.9771	−	2.12318i	−1.00692	−	0.0764148i
$773$			5.74824i			0.206750i	0.994642	+	0.103375i	$0.0329642\pi$
$773$			5.74824i			0.206750i	−0.994642	+	0.103375i	$0.967036\pi$
$774$		0			0
$775$		−	5.21794i		−	0.187434i
$776$	32.4904	+	3.70743i	1.16634	+	0.133089i
$777$		0			0
$778$	−0.803471	+	21.2051i	−0.0288058	+	0.760241i
$779$	22.5735			0.808781
$780$		0			0
$781$	−3.40276			−0.121760
$782$	−0.788608	+	20.8129i	−0.0282006	+	0.744267i
$783$		0			0
$784$	9.15681	+	1.39787i	0.327029	+	0.0499238i
$785$		−	11.6697i		−	0.416509i
$786$		0			0
$787$			53.0039i			1.88939i	0.327957	+	0.944693i	$0.393640\pi$
$787$			53.0039i			1.88939i	−0.327957	+	0.944693i	$0.606360\pi$
$788$	−1.09203	+	14.3897i	−0.0389020	+	0.512612i
$789$		0			0
$790$	−23.9850	−	0.908800i	−0.853347	−	0.0323337i
$791$	−2.16043			−0.0768162
$792$		0			0
$793$	4.24632			0.150791
$794$	14.1990	+	0.538006i	0.503904	+	0.0190931i
$795$		0			0
$796$	−1.30624	+	17.2124i	−0.0462985	+	0.610076i
$797$			13.8783i			0.491596i	0.969321	+	0.245798i	$0.0790500\pi$
$797$			13.8783i			0.491596i	−0.969321	+	0.245798i	$0.920950\pi$
$798$		0			0
$799$			0.0986351i			0.00348946i
$800$	5.55574	+	1.06480i	0.196425	+	0.0376463i
$801$		0			0
$802$	−0.423633	+	11.1805i	−0.0149590	+	0.394796i
$803$	6.72653			0.237374
$804$		0			0
$805$	6.26438			0.220791
$806$	1.84573	−	48.7125i	0.0650132	−	1.71582i
$807$		0			0
$808$	3.50399	−	30.7076i	0.123270	−	1.08029i
$809$			46.1210i			1.62153i	0.585372	+	0.810765i	$0.300948\pi$
$809$			46.1210i			1.62153i	−0.585372	+	0.810765i	$0.699052\pi$
$810$		0			0
$811$		−	31.7719i		−	1.11566i	−0.829954	−	0.557832i	$-0.811633\pi$
$811$		−	31.7719i		−	1.11566i	0.829954	−	0.557832i	$-0.188367\pi$
$812$	29.8834	+	2.26784i	1.04870	+	0.0795857i
$813$		0			0
$814$	−18.7367	−	0.709941i	−0.656721	−	0.0248834i
$815$	−0.438006			−0.0153427
$816$		0			0
$817$	20.5612			0.719346
$818$	−38.3894	−	1.45459i	−1.34225	−	0.0508585i
$819$		0			0
$820$	−9.64408	−	0.731887i	−0.336786	−	0.0255586i
$821$		−	13.5902i		−	0.474302i	−0.971473	−	0.237151i	$-0.923786\pi$
$821$		−	13.5902i		−	0.474302i	0.971473	−	0.237151i	$-0.0762136\pi$
$822$		0			0
$823$			29.6476i			1.03345i	0.856151	+	0.516725i	$0.172849\pi$
$823$			29.6476i			1.03345i	−0.856151	+	0.516725i	$0.827151\pi$
$824$	−0.203728	+	1.78540i	−0.00709721	+	0.0621972i
$825$		0			0
$826$	−0.933281	+	24.6311i	−0.0324730	+	0.857025i
$827$	−24.1020			−0.838110			−0.419055	−	0.907961i	$-0.637639\pi$
$827$	−24.1020			−0.838110			−0.419055	+	0.907961i	$0.637639\pi$
$828$		0			0
$829$	42.6555			1.48149			0.740743	−	0.671789i	$-0.234474\pi$
$829$	42.6555			1.48149			0.740743	+	0.671789i	$0.234474\pi$
$830$	0.101804	−	2.68681i	0.00353368	−	0.0932606i
$831$		0			0
$832$	51.4893	+	11.9057i	1.78507	+	0.412757i
$833$			11.7831i			0.408259i
$834$		0			0
$835$			4.16559i			0.144156i
$836$	−2.04354	+	26.9277i	−0.0706773	+	0.931315i
$837$		0			0
$838$	12.1119	+	0.458924i	0.418398	+	0.0158533i
$839$	−19.1361			−0.660653			−0.330327	−	0.943867i	$-0.607159\pi$
$839$	−19.1361			−0.660653			−0.330327	+	0.943867i	$0.607159\pi$
$840$		0			0
$841$	−18.9348			−0.652926
$842$	9.65226	+	0.365728i	0.332639	+	0.0126038i
$843$		0			0
$844$	2.81540	−	37.0985i	0.0969100	−	1.27698i
$845$		−	30.6390i		−	1.05401i
$846$		0			0
$847$			5.69781i			0.195779i
$848$	1.93913	−	12.7024i	0.0665901	−	0.436202i
$849$		0			0
$850$	−0.272461	+	7.19076i	−0.00934533	+	0.246641i
$851$	−13.2664			−0.454765
$852$		0			0
$853$	28.9762			0.992127			0.496064	−	0.868286i	$-0.334778\pi$
$853$	28.9762			0.992127			0.496064	+	0.868286i	$0.334778\pi$
$854$	−0.0744954	+	1.96608i	−0.00254918	+	0.0672777i
$855$		0			0
$856$	−52.8457	−	6.03013i	−1.80623	−	0.206106i
$857$			16.2549i			0.555256i	0.960689	+	0.277628i	$0.0895482\pi$
$857$			16.2549i			0.555256i	−0.960689	+	0.277628i	$0.910452\pi$
$858$		0			0
$859$		−	45.5262i		−	1.55333i	−0.629912	−	0.776666i	$-0.716909\pi$
$859$		−	45.5262i		−	1.55333i	0.629912	−	0.776666i	$-0.283091\pi$
$860$	−8.78436	−	0.666643i	−0.299544	−	0.0227323i
$861$		0			0
$862$	−37.5278	−	1.42194i	−1.27820	−	0.0484315i
$863$	14.4497			0.491875			0.245937	−	0.969286i	$-0.420904\pi$
$863$	14.4497			0.491875			0.245937	+	0.969286i	$0.420904\pi$
$864$		0			0
$865$	−8.95276			−0.304403
$866$	17.6246	+	0.667804i	0.598909	+	0.0226929i
$867$		0			0
$868$	22.5218	+	1.70918i	0.764441	+	0.0580132i
$869$			49.0943i			1.66541i
$870$		0			0
$871$		−	62.5405i		−	2.11910i
$872$	9.52804	+	1.08723i	0.322660	+	0.0368182i
$873$		0			0
$874$	−0.723455	+	19.0934i	−0.0244712	+	0.645843i
$875$	2.16432			0.0731673
$876$		0			0
$877$	−23.9076			−0.807302			−0.403651	−	0.914913i	$-0.632259\pi$
$877$	−23.9076			−0.807302			−0.403651	+	0.914913i	$0.632259\pi$
$878$	−0.793979	+	20.9546i	−0.0267955	+	0.707184i
$879$		0			0
$880$	1.74612	−	11.4381i	0.0588617	−	0.385577i
$881$		−	51.7852i		−	1.74469i	−0.488893	−	0.872344i	$-0.662599\pi$
$881$		−	51.7852i		−	1.74469i	0.488893	−	0.872344i	$-0.337401\pi$
$882$		0			0
$883$			17.1884i			0.578436i	0.957263	+	0.289218i	$0.0933953\pi$
$883$			17.1884i			0.578436i	−0.957263	+	0.289218i	$0.906605\pi$
$884$	−5.08715	+	67.0335i	−0.171099	+	2.25458i
$885$		0			0
$886$	55.8567	+	2.11643i	1.87654	+	0.0711030i
$887$	−17.8475			−0.599262			−0.299631	−	0.954055i	$-0.596863\pi$
$887$	−17.8475			−0.599262			−0.299631	+	0.954055i	$0.596863\pi$
$888$		0			0
$889$	19.0125			0.637657
$890$	5.26627	+	0.199541i	0.176526	+	0.00668863i
$891$		0			0
$892$	1.86815	−	24.6167i	0.0625504	−	0.824227i
$893$			0.0904861i			0.00302800i
$894$		0			0
$895$		−	10.5263i		−	0.351857i
$896$	−6.41574	+	23.6310i	−0.214335	+	0.789457i
$897$		0			0
$898$	−1.22298	+	32.2768i	−0.0408114	+	1.07709i
$899$	−36.1264			−1.20488
$900$		0			0
$901$	16.3456			0.544550
$902$	−0.749041	+	19.7686i	−0.0249403	+	0.658223i
$903$		0			0
$904$	−0.320090	+	2.80515i	−0.0106461	+	0.0932978i
$905$			9.50854i			0.316075i
$906$		0			0
$907$		−	2.35986i		−	0.0783580i	−0.999232	−	0.0391790i	$-0.987526\pi$
$907$		−	2.35986i		−	0.0783580i	0.999232	−	0.0391790i	$-0.0124743\pi$
$908$	1.48383	+	0.112608i	0.0492427	+	0.00373701i
$909$		0			0
$910$	20.2051	+	0.765581i	0.669794	+	0.0253788i
$911$	−37.3791			−1.23842			−0.619212	−	0.785224i	$-0.712548\pi$
$911$	−37.3791			−1.23842			−0.619212	+	0.785224i	$0.712548\pi$
$912$		0			0
$913$	−5.49957			−0.182009
$914$	−1.17646	−	0.0445766i	−0.0389139	−	0.00147446i
$915$		0			0
$916$	−52.1632	−	3.95865i	−1.72352	−	0.130798i
$917$		−	30.5752i		−	1.00968i
$918$		0			0
$919$			4.73062i			0.156049i	0.996951	+	0.0780243i	$0.0248612\pi$
$919$			4.73062i			0.156049i	−0.996951	+	0.0780243i	$0.975139\pi$
$920$	0.928133	−	8.13379i	0.0305996	−	0.268163i
$921$		0			0
$922$	1.91604	−	50.5680i	0.0631014	−	1.66537i
$923$	−7.77094			−0.255784
$924$		0			0
$925$	−4.58347			−0.150704
$926$	0.445908	−	11.7684i	0.0146534	−	0.386732i
$927$		0			0
$928$	7.37214	−	38.4651i	0.242002	−	1.26268i
$929$		−	29.4058i		−	0.964772i	−0.875959	−	0.482386i	$-0.839770\pi$
$929$		−	29.4058i		−	0.964772i	0.875959	−	0.482386i	$-0.160230\pi$
$930$		0			0
$931$			10.8096i			0.354270i
$932$	3.90868	−	51.5048i	0.128033	−	1.68709i
$933$		0			0
$934$	23.8275	+	0.902834i	0.779660	+	0.0295416i
$935$	14.7186			0.481350
$936$		0			0
$937$	20.2810			0.662551			0.331276	−	0.943534i	$-0.392521\pi$
$937$	20.2810			0.662551			0.331276	+	0.943534i	$0.392521\pi$
$938$	28.9567	+	1.09718i	0.945469	+	0.0358242i
$939$		0			0
$940$	0.00293377	−	0.0386583i	9.56891e−5	−	0.00126090i
$941$		−	8.19696i		−	0.267213i	−0.991034	−	0.133607i	$-0.957344\pi$
$941$		−	8.19696i		−	0.267213i	0.991034	−	0.133607i	$-0.0426559\pi$
$942$		0			0
$943$			13.9970i			0.455805i
$944$	31.8432	+	4.86114i	1.03641	+	0.158217i
$945$		0			0
$946$	−0.682268	+	18.0064i	−0.0221824	+	0.585437i
$947$	−42.0880			−1.36768			−0.683839	−	0.729633i	$-0.739691\pi$
$947$	−42.0880			−1.36768			−0.683839	+	0.729633i	$0.739691\pi$
$948$		0			0
$949$	15.3615			0.498655
$950$	−0.249951	+	6.59668i	−0.00810947	+	0.214025i
$951$		0			0
$952$	−30.9477	−	3.53139i	−1.00302	−	0.114453i
$953$			17.5687i			0.569106i	0.958660	+	0.284553i	$0.0918452\pi$
$953$			17.5687i			0.569106i	−0.958660	+	0.284553i	$0.908155\pi$
$954$		0			0
$955$		−	12.1608i		−	0.393515i
$956$	−16.4168	−	1.24587i	−0.530957	−	0.0402942i
$957$		0			0
$958$	−7.48121	−	0.283466i	−0.241707	−	0.00915838i
$959$	−32.9031			−1.06250
$960$		0			0
$961$	3.77305			0.121711
$962$	−42.7893	−	1.62130i	−1.37958	−	0.0522730i
$963$		0			0
$964$	−0.281408	−	0.0213560i	−0.00906356	−	0.000687831i
$965$			14.0288i			0.451603i
$966$		0			0
$967$		−	23.2633i		−	0.748096i	−0.927409	−	0.374048i	$-0.877970\pi$
$967$		−	23.2633i		−	0.748096i	0.927409	−	0.374048i	$-0.122030\pi$
$968$	7.39813	+	0.844188i	0.237785	+	0.0271332i
$969$		0			0
$970$	0.619088	−	16.3389i	0.0198777	−	0.524611i
$971$	−25.2618			−0.810688			−0.405344	−	0.914164i	$-0.632848\pi$
$971$	−25.2618			−0.810688			−0.405344	+	0.914164i	$0.632848\pi$
$972$		0			0
$973$	5.49901			0.176290
$974$	−1.06167	+	28.0196i	−0.0340182	+	0.897805i
$975$		0			0
$976$	2.54175	+	0.388020i	0.0813595	+	0.0124202i
$977$			24.9191i			0.797232i	0.917118	+	0.398616i	$0.130509\pi$
$977$			24.9191i			0.797232i	−0.917118	+	0.398616i	$0.869491\pi$
$978$		0			0
$979$		−	10.7794i		−	0.344511i
$980$	0.350472	−	4.61817i	0.0111954	−	0.147522i
$981$		0			0
$982$	40.2024	+	1.52329i	1.28291	+	0.0486100i
$983$	15.9928			0.510092			0.255046	−	0.966929i	$-0.417909\pi$
$983$	15.9928			0.510092			0.255046	+	0.966929i	$0.417909\pi$
$984$		0			0
$985$	7.21555			0.229906
$986$	49.7852	+	1.88638i	1.58548	+	0.0600747i
$987$		0			0
$988$	−4.66686	+	61.4953i	−0.148473	+	1.95643i
$989$			12.7492i			0.405402i
$990$		0			0
$991$		−	29.4708i		−	0.936171i	−0.883683	−	0.468085i	$-0.844944\pi$
$991$		−	29.4708i		−	0.936171i	0.883683	−	0.468085i	$-0.155056\pi$
$992$	5.55607	−	28.9895i	0.176405	−	0.920418i
$993$		0			0
$994$	0.136330	−	3.59800i	0.00432411	−	0.114122i
$995$	8.63093			0.273619
$996$		0			0
$997$	38.7038			1.22576			0.612881	−	0.790175i	$-0.290011\pi$
$997$	38.7038			1.22576			0.612881	+	0.790175i	$0.290011\pi$
$998$	0.302536	−	7.98451i	0.00957661	−	0.252745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.1		48
3.2	odd	2	inner	1620.2.e.b.971.48		48
4.3	odd	2	inner	1620.2.e.b.971.47		48
9.2	odd	6		180.2.q.a.131.9	yes	48
9.4	even	3		180.2.q.a.11.17	yes	48
9.5	odd	6		540.2.q.a.251.8		48
9.7	even	3		540.2.q.a.71.16		48
12.11	even	2	inner	1620.2.e.b.971.2		48
36.7	odd	6		540.2.q.a.71.8		48
36.11	even	6		180.2.q.a.131.17	yes	48
36.23	even	6		540.2.q.a.251.16		48
36.31	odd	6		180.2.q.a.11.9	✓	48
45.2	even	12		900.2.o.b.599.21		48
45.4	even	6		900.2.r.f.551.8		48
45.13	odd	12		900.2.o.b.299.5		48
45.22	odd	12		900.2.o.c.299.20		48
45.29	odd	6		900.2.r.f.851.16		48
45.38	even	12		900.2.o.c.599.4		48
180.47	odd	12		900.2.o.b.599.5		48
180.67	even	12		900.2.o.c.299.4		48
180.83	odd	12		900.2.o.c.599.20		48
180.103	even	12		900.2.o.b.299.21		48
180.119	even	6		900.2.r.f.851.8		48
180.139	odd	6		900.2.r.f.551.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.9	✓	48	36.31	odd	6
180.2.q.a.11.17	yes	48	9.4	even	3
180.2.q.a.131.9	yes	48	9.2	odd	6
180.2.q.a.131.17	yes	48	36.11	even	6
540.2.q.a.71.8		48	36.7	odd	6
540.2.q.a.71.16		48	9.7	even	3
540.2.q.a.251.8		48	9.5	odd	6
540.2.q.a.251.16		48	36.23	even	6
900.2.o.b.299.5		48	45.13	odd	12
900.2.o.b.299.21		48	180.103	even	12
900.2.o.b.599.5		48	180.47	odd	12
900.2.o.b.599.21		48	45.2	even	12
900.2.o.c.299.4		48	180.67	even	12
900.2.o.c.299.20		48	45.22	odd	12
900.2.o.c.599.4		48	45.38	even	12
900.2.o.c.599.20		48	180.83	odd	12
900.2.r.f.551.8		48	45.4	even	6
900.2.r.f.551.16		48	180.139	odd	6
900.2.r.f.851.8		48	180.119	even	6
900.2.r.f.851.16		48	45.29	odd	6
1620.2.e.b.971.1		48	1.1	even	1	trivial
1620.2.e.b.971.2		48	12.11	even	2	inner
1620.2.e.b.971.47		48	4.3	odd	2	inner
1620.2.e.b.971.48		48	3.2	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)

\(f(q)\)	\(=\)	\(q+(-1.41320 - 0.0535467i) q^{2} +(1.99427 + 0.151344i) q^{4} -1.00000i q^{5} -2.16432i q^{7} +(-2.81019 - 0.320666i) q^{8} +O(q^{10})\)	\(q+(-1.41320 - 0.0535467i) q^{2} +(1.99427 + 0.151344i) q^{4} -1.00000i q^{5} -2.16432i q^{7} +(-2.81019 - 0.320666i) q^{8} +(-0.0535467 + 1.41320i) q^{10} +2.89264 q^{11} +6.60598 q^{13} +(-0.115892 + 3.05861i) q^{14} +(3.95419 + 0.603641i) q^{16} +5.08829i q^{17} +4.66790i q^{19} +(0.151344 - 1.99427i) q^{20} +(-4.08788 - 0.154892i) q^{22} -2.89439 q^{23} -1.00000 q^{25} +(-9.33557 - 0.353728i) q^{26} +(0.327557 - 4.31623i) q^{28} +6.92350i q^{29} +5.21794i q^{31} +(-5.55574 - 1.06480i) q^{32} +(0.272461 - 7.19076i) q^{34} -2.16432 q^{35} +4.58347 q^{37} +(0.249951 - 6.59668i) q^{38} +(-0.320666 + 2.81019i) q^{40} -4.83591i q^{41} -4.40481i q^{43} +(5.76870 + 0.437785i) q^{44} +(4.09035 + 0.154985i) q^{46} +0.0193847 q^{47} +2.31572 q^{49} +(1.41320 + 0.0535467i) q^{50} +(13.1741 + 0.999777i) q^{52} -3.21239i q^{53} -2.89264i q^{55} +(-0.694023 + 6.08215i) q^{56} +(0.370730 - 9.78429i) q^{58} +8.05302 q^{59} +0.642800 q^{61} +(0.279404 - 7.37400i) q^{62} +(7.79435 + 1.80227i) q^{64} -6.60598i q^{65} -9.46725i q^{67} +(-0.770083 + 10.1474i) q^{68} +(3.05861 + 0.115892i) q^{70} -1.17635 q^{71} +2.32539 q^{73} +(-6.47736 - 0.245430i) q^{74} +(-0.706461 + 9.30904i) q^{76} -6.26060i q^{77} +16.9721i q^{79} +(0.603641 - 3.95419i) q^{80} +(-0.258947 + 6.83410i) q^{82} -1.90123 q^{83} +5.08829 q^{85} +(-0.235863 + 6.22488i) q^{86} +(-8.12888 - 0.927573i) q^{88} -3.72649i q^{89} -14.2974i q^{91} +(-5.77218 - 0.438050i) q^{92} +(-0.0273945 - 0.00103799i) q^{94} +4.66790 q^{95} -11.5616 q^{97} +(-3.27258 - 0.123999i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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