LMFDB - Embedded newform 380.2.bh.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00135 - 1.39955i) q^{3} +(-0.904597 + 2.04492i) q^{5} +(1.03769 + 3.87270i) q^{7} +(5.12098 - 6.10295i) q^{9} +O(q^{10})$	\(q+(3.00135 - 1.39955i) q^{3} +(-0.904597 + 2.04492i) q^{5} +(1.03769 + 3.87270i) q^{7} +(5.12098 - 6.10295i) q^{9} +(-1.27468 - 2.20781i) q^{11} +(0.897435 - 1.92456i) q^{13} +(0.146961 + 7.40355i) q^{15} +(-0.521800 + 5.96421i) q^{17} +(-1.63682 - 4.03991i) q^{19} +(8.53449 + 10.1710i) q^{21} +(-0.709828 + 0.497027i) q^{23} +(-3.36341 - 3.69966i) q^{25} +(4.25712 - 15.8878i) q^{27} +(0.706112 + 0.592498i) q^{29} +(-3.26351 - 1.88419i) q^{31} +(-6.91570 - 4.84242i) q^{33} +(-8.85805 - 1.38125i) q^{35} +(-4.20783 - 4.20783i) q^{37} -7.03227i q^{39} +(-0.681305 + 1.87187i) q^{41} +(4.59445 - 6.56156i) q^{43} +(7.84762 + 15.9927i) q^{45} +(-5.41236 + 0.473520i) q^{47} +(-7.85881 + 4.53728i) q^{49} +(6.78111 + 18.6309i) q^{51} +(-0.560224 - 0.800083i) q^{53} +(5.66787 - 0.609440i) q^{55} +(-10.5667 - 9.83435i) q^{57} +(-0.574552 + 0.482106i) q^{59} +(0.540706 - 3.06649i) q^{61} +(28.9488 + 13.4991i) q^{63} +(3.12375 + 3.57613i) q^{65} +(1.15605 + 13.2137i) q^{67} +(-1.43483 + 2.48519i) q^{69} +(-7.53592 + 1.32879i) q^{71} +(0.911719 + 1.95519i) q^{73} +(-15.2726 - 6.39671i) q^{75} +(7.22746 - 7.22746i) q^{77} +(10.7824 + 3.92446i) q^{79} +(-5.30841 - 30.1055i) q^{81} +(-6.50250 + 1.74234i) q^{83} +(-11.7243 - 6.46225i) q^{85} +(2.94852 + 0.790053i) q^{87} +(-8.47050 + 3.08301i) q^{89} +(8.38447 + 1.47841i) q^{91} +(-12.4319 - 1.08765i) q^{93} +(9.74195 + 0.307330i) q^{95} +(0.658909 + 0.0576470i) q^{97} +(-20.0017 - 3.52685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.00135	−	1.39955i	1.73283	−	0.808031i	0.742408	−	0.669948i	$-0.233684\pi$
$3$	3.00135	−	1.39955i	1.73283	−	0.808031i	0.990421	−	0.138083i	$-0.0440942\pi$
$4$		0			0
$5$	−0.904597	+	2.04492i	−0.404548	+	0.914517i
$5$	−0.904597	+	2.04492i	−0.404548	+	0.914517i
$6$		0			0
$7$	1.03769	+	3.87270i	0.392208	+	1.46374i	0.826483	+	0.562961i	$0.190338\pi$
$7$	1.03769	+	3.87270i	0.392208	+	1.46374i	−0.434275	+	0.900780i	$0.642995\pi$
$8$		0			0
$9$	5.12098	−	6.10295i	1.70699	−	2.03432i
$10$		0			0
$11$	−1.27468	−	2.20781i	−0.384330	−	0.665680i	0.607346	−	0.794438i	$-0.292234\pi$
$11$	−1.27468	−	2.20781i	−0.384330	−	0.665680i	−0.991676	+	0.128758i	$0.958901\pi$
$12$		0			0
$13$	0.897435	−	1.92456i	0.248904	−	0.533776i	−0.741669	−	0.670766i	$-0.765965\pi$
$13$	0.897435	−	1.92456i	0.248904	−	0.533776i	0.990572	+	0.136991i	$0.0437431\pi$
$14$		0			0
$15$	0.146961	+	7.40355i	0.0379452	+	1.91159i
$16$		0			0
$17$	−0.521800	+	5.96421i	−0.126555	+	1.44653i	0.621770	+	0.783200i	$0.286414\pi$
$17$	−0.521800	+	5.96421i	−0.126555	+	1.44653i	−0.748325	+	0.663332i	$0.769142\pi$
$18$		0			0
$19$	−1.63682	−	4.03991i	−0.375511	−	0.926818i
$19$	−1.63682	−	4.03991i	−0.375511	−	0.926818i
$20$		0			0
$21$	8.53449	+	10.1710i	1.86238	+	2.21950i
$22$		0			0
$23$	−0.709828	+	0.497027i	−0.148009	+	0.103637i	−0.645236	−	0.763984i	$-0.723241\pi$
$23$	−0.709828	+	0.497027i	−0.148009	+	0.103637i	0.497226	+	0.867621i	$0.334352\pi$
$24$		0			0
$25$	−3.36341	−	3.69966i	−0.672681	−	0.739932i
$26$		0			0
$27$	4.25712	−	15.8878i	0.819284	−	3.05761i
$28$		0			0
$29$	0.706112	+	0.592498i	0.131122	+	0.110024i	0.705990	−	0.708222i	$-0.250502\pi$
$29$	0.706112	+	0.592498i	0.131122	+	0.110024i	−0.574868	+	0.818246i	$0.694947\pi$
$30$		0			0
$31$	−3.26351	−	1.88419i	−0.586143	−	0.338410i	0.177428	−	0.984134i	$-0.443222\pi$
$31$	−3.26351	−	1.88419i	−0.586143	−	0.338410i	−0.763571	+	0.645724i	$0.776556\pi$
$32$		0			0
$33$	−6.91570	−	4.84242i	−1.20387	−	0.842958i
$34$		0			0
$35$	−8.85805	−	1.38125i	−1.49728	−	0.233473i
$36$		0			0
$37$	−4.20783	−	4.20783i	−0.691764	−	0.691764i	0.270856	−	0.962620i	$-0.412693\pi$
$37$	−4.20783	−	4.20783i	−0.691764	−	0.691764i	−0.962620	+	0.270856i	$0.912693\pi$
$38$		0			0
$39$		−	7.03227i		−	1.12606i
$40$		0			0
$41$	−0.681305	+	1.87187i	−0.106402	+	0.292337i	−0.981456	−	0.191689i	$-0.938604\pi$
$41$	−0.681305	+	1.87187i	−0.106402	+	0.292337i	0.875054	+	0.484026i	$0.160826\pi$
$42$		0			0
$43$	4.59445	−	6.56156i	0.700648	−	1.00063i	−0.298287	−	0.954476i	$-0.596415\pi$
$43$	4.59445	−	6.56156i	0.700648	−	1.00063i	0.998934	−	0.0461523i	$-0.0146960\pi$
$44$		0			0
$45$	7.84762	+	15.9927i	1.16985	+	2.38405i
$46$		0			0
$47$	−5.41236	+	0.473520i	−0.789474	+	0.0690700i	−0.474758	−	0.880116i	$-0.657465\pi$
$47$	−5.41236	+	0.473520i	−0.789474	+	0.0690700i	−0.314715	+	0.949186i	$0.601909\pi$
$48$		0			0
$49$	−7.85881	+	4.53728i	−1.12269	+	0.648183i
$50$		0			0
$51$	6.78111	+	18.6309i	0.949545	+	2.60885i
$52$		0			0
$53$	−0.560224	−	0.800083i	−0.0769527	−	0.109900i	0.778831	−	0.627234i	$-0.215813\pi$
$53$	−0.560224	−	0.800083i	−0.0769527	−	0.109900i	−0.855783	+	0.517335i	$0.826924\pi$
$54$		0			0
$55$	5.66787	−	0.609440i	0.764255	−	0.0821769i
$56$		0			0
$57$	−10.5667	−	9.83435i	−1.39959	−	1.30259i
$58$		0			0
$59$	−0.574552	+	0.482106i	−0.0748003	+	0.0627649i	−0.679421	−	0.733748i	$-0.737769\pi$
$59$	−0.574552	+	0.482106i	−0.0748003	+	0.0627649i	0.604621	+	0.796513i	$0.293325\pi$
$60$		0			0
$61$	0.540706	−	3.06649i	0.0692303	−	0.392624i	−0.930428	−	0.366475i	$-0.880564\pi$
$61$	0.540706	−	3.06649i	0.0692303	−	0.392624i	0.999658	−	0.0261491i	$-0.00832446\pi$
$62$		0			0
$63$	28.9488	+	13.4991i	3.64721	+	1.70072i
$64$		0			0
$65$	3.12375	+	3.57613i	0.387453	+	0.443565i
$66$		0			0
$67$	1.15605	+	13.2137i	0.141234	+	1.61431i	0.654486	+	0.756074i	$0.272885\pi$
$67$	1.15605	+	13.2137i	0.141234	+	1.61431i	−0.513252	+	0.858238i	$0.671559\pi$
$68$		0			0
$69$	−1.43483	+	2.48519i	−0.172733	+	0.299182i
$70$		0			0
$71$	−7.53592	+	1.32879i	−0.894349	+	0.157698i	−0.601889	−	0.798580i	$-0.705585\pi$
$71$	−7.53592	+	1.32879i	−0.894349	+	0.157698i	−0.292460	+	0.956278i	$0.594474\pi$
$72$		0			0
$73$	0.911719	+	1.95519i	0.106709	+	0.228837i	0.952411	−	0.304818i	$-0.0985957\pi$
$73$	0.911719	+	1.95519i	0.106709	+	0.228837i	−0.845702	+	0.533656i	$0.820818\pi$
$74$		0			0
$75$	−15.2726	−	6.39671i	−1.76353	−	0.738628i
$76$		0			0
$77$	7.22746	−	7.22746i	0.823645	−	0.823645i
$78$		0			0
$79$	10.7824	+	3.92446i	1.21311	+	0.441537i	0.867782	−	0.496945i	$-0.165545\pi$
$79$	10.7824	+	3.92446i	1.21311	+	0.441537i	0.345330	+	0.938481i	$0.387767\pi$
$80$		0			0
$81$	−5.30841	−	30.1055i	−0.589823	−	3.34505i
$82$		0			0
$83$	−6.50250	+	1.74234i	−0.713742	+	0.191247i	−0.597378	−	0.801960i	$-0.703791\pi$
$83$	−6.50250	+	1.74234i	−0.713742	+	0.191247i	−0.116364	+	0.993207i	$0.537124\pi$
$84$		0			0
$85$	−11.7243	−	6.46225i	−1.27168	−	0.700929i
$86$		0			0
$87$	2.94852	+	0.790053i	0.316114	+	0.0847026i
$88$		0			0
$89$	−8.47050	+	3.08301i	−0.897871	+	0.326798i	−0.749399	−	0.662118i	$-0.769658\pi$
$89$	−8.47050	+	3.08301i	−0.897871	+	0.326798i	−0.148472	+	0.988917i	$0.547435\pi$
$90$		0			0
$91$	8.38447	+	1.47841i	0.878932	+	0.154979i
$92$		0			0
$93$	−12.4319	−	1.08765i	−1.28913	−	0.112784i
$94$		0			0
$95$	9.74195	+	0.307330i	0.999503	+	0.0315314i
$96$		0			0
$97$	0.658909	+	0.0576470i	0.0669020	+	0.00585317i	0.120558	−	0.992706i	$-0.461532\pi$
$97$	0.658909	+	0.0576470i	0.0669020	+	0.00585317i	−0.0536556	+	0.998560i	$0.517087\pi$
$98$		0			0
$99$	−20.0017	−	3.52685i	−2.01025	−	0.354462i
$100$		0			0
$101$	−15.0297	+	5.47038i	−1.49552	+	0.544323i	−0.954895	−	0.296943i	$-0.904033\pi$
$101$	−15.0297	+	5.47038i	−1.49552	+	0.544323i	−0.540620	+	0.841267i	$0.681810\pi$
$102$		0			0
$103$	14.5507	+	3.89884i	1.43372	+	0.384165i	0.890330	−	0.455315i	$-0.150473\pi$
$103$	14.5507	+	3.89884i	1.43372	+	0.384165i	0.543391	+	0.839480i	$0.317140\pi$
$104$		0			0
$105$	−28.5192	+	8.25169i	−2.78319	+	0.805283i
$106$		0			0
$107$	17.3188	−	4.64057i	1.67428	−	0.448621i	0.708017	−	0.706195i	$-0.249590\pi$
$107$	17.3188	−	4.64057i	1.67428	−	0.448621i	0.966258	+	0.257574i	$0.0829233\pi$
$108$		0			0
$109$	2.15548	+	12.2244i	0.206458	+	1.17088i	0.895129	+	0.445807i	$0.147083\pi$
$109$	2.15548	+	12.2244i	0.206458	+	1.17088i	−0.688671	+	0.725074i	$0.741806\pi$
$110$		0			0
$111$	−18.5182	−	6.74009i	−1.75767	−	0.639741i
$112$		0			0
$113$	−6.29934	+	6.29934i	−0.592592	+	0.592592i	−0.938331	−	0.345739i	$-0.887628\pi$
$113$	−6.29934	+	6.29934i	−0.592592	+	0.592592i	0.345739	+	0.938331i	$0.387628\pi$
$114$		0			0
$115$	−0.374273	−	1.90115i	−0.0349011	−	0.177283i
$116$		0			0
$117$	−7.14971	−	15.3326i	−0.660991	−	1.41750i
$118$		0			0
$119$	−23.6390	+	4.16820i	−2.16699	+	0.382098i
$120$		0			0
$121$	2.25039	−	3.89778i	0.204580	−	0.354344i
$122$		0			0
$123$	0.574945	+	6.57165i	0.0518411	+	0.592546i
$124$		0			0
$125$	10.6080	−	3.53120i	0.948812	−	0.315840i
$126$		0			0
$127$	2.61665	+	1.22016i	0.232190	+	0.108272i	0.535232	−	0.844705i	$-0.320224\pi$
$127$	2.61665	+	1.22016i	0.232190	+	0.108272i	−0.303041	+	0.952977i	$0.598002\pi$
$128$		0			0
$129$	4.60631	−	26.1237i	0.405563	−	2.30006i
$130$		0			0
$131$	5.69992	−	4.78280i	0.498004	−	0.417875i	−0.358880	−	0.933384i	$-0.616841\pi$
$131$	5.69992	−	4.78280i	0.498004	−	0.417875i	0.856884	+	0.515509i	$0.172397\pi$
$132$		0			0
$133$	13.9468	−	10.5310i	1.20934	−	0.913157i
$134$		0			0
$135$	28.6383	+	23.0775i	2.46479	+	1.98620i
$136$		0			0
$137$	6.70463	+	9.57521i	0.572815	+	0.818065i	0.996128	−	0.0879188i	$-0.0280216\pi$
$137$	6.70463	+	9.57521i	0.572815	+	0.818065i	−0.423312	+	0.905984i	$0.639133\pi$
$138$		0			0
$139$	−7.42664	−	20.4045i	−0.629919	−	1.73069i	−0.681295	−	0.732009i	$-0.738583\pi$
$139$	−7.42664	−	20.4045i	−0.629919	−	1.73069i	0.0513756	−	0.998679i	$-0.483639\pi$
$140$		0			0
$141$	−15.5817	+	8.99607i	−1.31221	+	0.757606i
$142$		0			0
$143$	−5.39299	+	0.471826i	−0.450985	+	0.0394561i
$144$		0			0
$145$	−1.85036	+	0.907971i	−0.153664	+	0.0754029i
$146$		0			0
$147$	−17.2368	+	24.6168i	−1.42167	+	2.03036i
$148$		0			0
$149$	−0.706464	+	1.94099i	−0.0578758	+	0.159012i	−0.965261	−	0.261288i	$-0.915853\pi$
$149$	−0.706464	+	1.94099i	−0.0578758	+	0.159012i	0.907385	+	0.420300i	$0.138075\pi$
$150$		0			0
$151$		−	5.99392i		−	0.487779i	−0.969803	−	0.243889i	$-0.921577\pi$
$151$		−	5.99392i		−	0.487779i	0.969803	−	0.243889i	$-0.0784234\pi$
$152$		0			0
$153$	33.7271	+	33.7271i	2.72667	+	2.72667i
$154$		0			0
$155$	6.80518	−	4.96919i	0.546605	−	0.399135i
$156$		0			0
$157$	−13.7071	−	9.59779i	−1.09394	−	0.765987i	−0.119999	−	0.992774i	$-0.538289\pi$
$157$	−13.7071	−	9.59779i	−1.09394	−	0.765987i	−0.973944	+	0.226787i	$0.927178\pi$
$158$		0			0
$159$	−2.80119	−	1.61727i	−0.222148	−	0.128257i
$160$		0			0
$161$	−2.66141	−	2.23319i	−0.209749	−	0.176000i
$162$		0			0
$163$	4.00121	−	14.9327i	0.313399	−	1.16962i	−0.612072	−	0.790802i	$-0.709664\pi$
$163$	4.00121	−	14.9327i	0.313399	−	1.16962i	0.925471	−	0.378819i	$-0.123670\pi$
$164$		0			0
$165$	16.1583	−	9.76161i	1.25792	−	0.759941i
$166$		0			0
$167$	17.7269	−	12.4125i	1.37175	−	0.960507i	0.372271	−	0.928124i	$-0.378579\pi$
$167$	17.7269	−	12.4125i	1.37175	−	0.960507i	0.999476	−	0.0323832i	$-0.0103097\pi$
$168$		0			0
$169$	5.45771	+	6.50425i	0.419824	+	0.500327i
$170$		0			0
$171$	−33.0374	−	10.6989i	−2.52643	−	0.818164i
$172$		0			0
$173$	−0.530405	+	6.06256i	−0.0403260	+	0.460928i	0.949007	+	0.315255i	$0.102090\pi$
$173$	−0.530405	+	6.06256i	−0.0403260	+	0.460928i	−0.989333	+	0.145673i	$0.953465\pi$
$174$		0			0
$175$	10.8375	−	16.8645i	0.819238	−	1.27484i
$176$		0			0
$177$	−1.04970	+	2.25108i	−0.0789001	+	0.169202i
$178$		0			0
$179$	9.63353	+	16.6858i	0.720044	+	1.24715i	0.960982	+	0.276612i	$0.0892117\pi$
$179$	9.63353	+	16.6858i	0.720044	+	1.24715i	−0.240938	+	0.970541i	$0.577455\pi$
$180$		0			0
$181$	−1.71597	+	2.04501i	−0.127547	+	0.152004i	−0.826038	−	0.563614i	$-0.809411\pi$
$181$	−1.71597	+	2.04501i	−0.127547	+	0.152004i	0.698492	+	0.715618i	$0.253855\pi$
$182$		0			0
$183$	−2.66887	−	9.96036i	−0.197289	−	0.736291i
$184$		0			0
$185$	12.4111	−	4.79829i	0.912481	−	0.352778i
$186$		0			0
$187$	13.8330	−	6.45041i	1.01157	−	0.471701i
$188$		0			0
$189$	65.9462			4.79688
$190$		0			0
$191$	8.14928			0.589662			0.294831	−	0.955549i	$-0.404737\pi$
$191$	8.14928			0.589662			0.294831	+	0.955549i	$0.404737\pi$
$192$		0			0
$193$	−10.6203	+	4.95233i	−0.764467	+	0.356477i	−0.765427	−	0.643523i	$-0.777472\pi$
$193$	−10.6203	+	4.95233i	−0.764467	+	0.356477i	0.000960024		1.00000i	$0.499694\pi$
$194$		0			0
$195$	14.3804	+	6.36137i	1.02980	+	0.455547i
$196$		0			0
$197$	−0.187646	−	0.700304i	−0.0133692	−	0.0498946i	0.958919	−	0.283680i	$-0.0915553\pi$
$197$	−0.187646	−	0.700304i	−0.0133692	−	0.0498946i	−0.972288	+	0.233785i	$0.924889\pi$
$198$		0			0
$199$	−6.24262	+	7.43967i	−0.442528	+	0.527384i	−0.940493	−	0.339813i	$-0.889636\pi$
$199$	−6.24262	+	7.43967i	−0.442528	+	0.527384i	0.497965	+	0.867197i	$0.334081\pi$
$200$		0			0
$201$	21.9630	+	38.0410i	1.54915	+	2.68321i
$202$		0			0
$203$	−1.56184	+	3.34938i	−0.109620	+	0.235081i
$204$		0			0
$205$	−3.21152	−	3.08650i	−0.224302	−	0.215571i
$206$		0			0
$207$	−0.601687	+	6.87731i	−0.0418201	+	0.478006i
$208$		0			0
$209$	−6.83293	+	8.76336i	−0.472643	+	0.606174i
$210$		0			0
$211$	10.7114	+	12.7654i	0.737405	+	0.878805i	0.996197	−	0.0871281i	$-0.0277689\pi$
$211$	10.7114	+	12.7654i	0.737405	+	0.878805i	−0.258792	+	0.965933i	$0.583325\pi$
$212$		0			0
$213$	−20.7582	+	14.5351i	−1.42233	+	0.995925i
$214$		0			0
$215$	9.26174	+	15.3309i	0.631646	+	1.04556i
$216$		0			0
$217$	3.91039	−	14.5938i	0.265454	−	0.990690i
$218$		0			0
$219$	5.47277	+	4.59220i	0.369816	+	0.310312i
$220$		0			0
$221$	11.0102	+	6.35672i	0.740624	+	0.427599i
$222$		0			0
$223$	−4.23243	−	2.96358i	−0.283424	−	0.198456i	0.423216	−	0.906029i	$-0.360901\pi$
$223$	−4.23243	−	2.96358i	−0.283424	−	0.198456i	−0.706640	+	0.707573i	$0.749790\pi$
$224$		0			0
$225$	−39.8028	+	1.58080i	−2.65352	+	0.105387i
$226$		0			0
$227$	1.51402	+	1.51402i	0.100489	+	0.100489i	0.755564	−	0.655075i	$-0.227363\pi$
$227$	1.51402	+	1.51402i	0.100489	+	0.100489i	−0.655075	+	0.755564i	$0.727363\pi$
$228$		0			0
$229$		−	6.86875i		−	0.453900i	−0.973906	−	0.226950i	$-0.927125\pi$
$229$		−	6.86875i		−	0.453900i	0.973906	−	0.226950i	$-0.0728753\pi$
$230$		0			0
$231$	11.5769	−	31.8073i	0.761705	−	2.09277i
$232$		0			0
$233$	1.57383	−	2.24767i	0.103105	−	0.147249i	−0.764284	−	0.644880i	$-0.776907\pi$
$233$	1.57383	−	2.24767i	0.103105	−	0.147249i	0.867389	+	0.497630i	$0.165796\pi$
$234$		0			0
$235$	3.92769	−	11.4962i	0.256215	−	0.749929i
$236$		0			0
$237$	37.8541	−	3.31181i	2.45889	−	0.215125i
$238$		0			0
$239$	4.72242	−	2.72649i	0.305468	−	0.176362i	−0.339429	−	0.940632i	$-0.610234\pi$
$239$	4.72242	−	2.72649i	0.305468	−	0.176362i	0.644897	+	0.764270i	$0.276900\pi$
$240$		0			0
$241$	0.170691	+	0.468971i	0.0109952	+	0.0302091i	0.945069	−	0.326871i	$-0.105994\pi$
$241$	0.170691	+	0.468971i	0.0109952	+	0.0302091i	−0.934074	+	0.357080i	$0.883772\pi$
$242$		0			0
$243$	−29.7635	−	42.5067i	−1.90933	−	2.72681i
$244$		0			0
$245$	−2.16933	−	20.1751i	−0.138594	−	1.28894i
$246$		0			0
$247$	−9.24396	−	0.475411i	−0.588179	−	0.0302497i
$248$		0			0
$249$	−17.0778	+	14.3299i	−1.08226	+	0.908124i
$250$		0			0
$251$	−3.65075	+	20.7044i	−0.230433	+	1.30685i	0.621588	+	0.783344i	$0.286488\pi$
$251$	−3.65075	+	20.7044i	−0.230433	+	1.30685i	−0.852022	+	0.523507i	$0.824623\pi$
$252$		0			0
$253$	2.00215	+	0.933616i	0.125874	+	0.0586959i
$254$		0			0
$255$	−44.2330	−	2.98667i	−2.76998	−	0.187032i
$256$		0			0
$257$	−1.18377	−	13.5305i	−0.0738414	−	0.844012i	−0.939315	−	0.343057i	$-0.888538\pi$
$257$	−1.18377	−	13.5305i	−0.0738414	−	0.844012i	0.865473	−	0.500955i	$-0.167018\pi$
$258$		0			0
$259$	11.9293	−	20.6621i	0.741248	−	1.28388i
$260$		0			0
$261$	7.23197	−	1.27519i	0.447648	−	0.0789323i
$262$		0			0
$263$	−11.6074	−	24.8922i	−0.715743	−	1.53492i	−0.839952	−	0.542660i	$-0.817417\pi$
$263$	−11.6074	−	24.8922i	−0.715743	−	1.53492i	0.124209	−	0.992256i	$-0.460361\pi$
$264$		0			0
$265$	2.14289	−	0.421861i	0.131636	−	0.0259147i
$266$		0			0
$267$	−21.1081	+	21.1081i	−1.29179	+	1.29179i
$268$		0			0
$269$	−23.8770	−	8.69052i	−1.45581	−	0.529870i	−0.511600	−	0.859224i	$-0.670947\pi$
$269$	−23.8770	−	8.69052i	−1.45581	−	0.529870i	−0.944207	+	0.329354i	$0.893169\pi$
$270$		0			0
$271$	0.0587048	+	0.332932i	0.00356607	+	0.0202242i	0.986539	−	0.163527i	$-0.0522871\pi$
$271$	0.0587048	+	0.332932i	0.00356607	+	0.0202242i	−0.982973	+	0.183751i	$0.941176\pi$
$272$		0			0
$273$	27.2338	−	7.29728i	1.64827	−	0.441652i
$274$		0			0
$275$	−3.88088	+	12.1416i	−0.234026	+	0.732169i
$276$		0			0
$277$	−4.89647	−	1.31201i	−0.294200	−	0.0788308i	0.108700	−	0.994075i	$-0.465331\pi$
$277$	−4.89647	−	1.31201i	−0.294200	−	0.0788308i	−0.402900	+	0.915244i	$0.631998\pi$
$278$		0			0
$279$	−28.2114	+	10.2681i	−1.68898	+	0.614737i
$280$		0			0
$281$	−14.0520	−	2.47775i	−0.838274	−	0.147810i	−0.262001	−	0.965068i	$-0.584382\pi$
$281$	−14.0520	−	2.47775i	−0.838274	−	0.147810i	−0.576273	+	0.817257i	$0.695493\pi$
$282$		0			0
$283$	9.60316	+	0.840168i	0.570849	+	0.0499428i	0.368926	−	0.929459i	$-0.379726\pi$
$283$	9.60316	+	0.840168i	0.570849	+	0.0499428i	0.201923	+	0.979401i	$0.435281\pi$
$284$		0			0
$285$	29.6691	−	12.7120i	1.75745	−	0.752991i
$286$		0			0
$287$	−7.95616	−	0.696074i	−0.469638	−	0.0410880i
$288$		0			0
$289$	−18.5577	−	3.27223i	−1.09163	−	0.192484i
$290$		0			0
$291$	2.05829	−	0.749158i	0.120659	−	0.0439164i
$292$		0			0
$293$	3.27717	+	0.878114i	0.191454	+	0.0513000i	0.353272	−	0.935521i	$-0.385069\pi$
$293$	3.27717	+	0.878114i	0.191454	+	0.0513000i	−0.161818	+	0.986821i	$0.551736\pi$
$294$		0			0
$295$	−0.466131	−	1.61103i	−0.0271392	−	0.0937975i
$296$		0			0
$297$	−40.5037	+	10.8529i	−2.35026	+	0.629751i
$298$		0			0
$299$	0.319532	+	1.81215i	0.0184790	+	0.104800i
$300$		0			0
$301$	30.1785	+	10.9841i	1.73946	+	0.633112i
$302$		0			0
$303$	−37.4534	+	37.4534i	−2.15164	+	2.15164i
$304$		0			0
$305$	5.78162	+	3.87964i	0.331055	+	0.222148i
$306$		0			0
$307$	6.77164	+	14.5218i	0.386478	+	0.828805i	0.999257	+	0.0385501i	$0.0122739\pi$
$307$	6.77164	+	14.5218i	0.386478	+	0.828805i	−0.612779	+	0.790255i	$0.709948\pi$
$308$		0			0
$309$	49.1283	−	8.66264i	2.79481	−	0.492801i
$310$		0			0
$311$	−2.57287	+	4.45633i	−0.145894	+	0.252696i	−0.929706	−	0.368302i	$-0.879939\pi$
$311$	−2.57287	+	4.45633i	−0.145894	+	0.252696i	0.783812	+	0.620998i	$0.213272\pi$
$312$		0			0
$313$	−0.784075	−	8.96202i	−0.0443185	−	0.506563i	−0.985618	−	0.168990i	$-0.945949\pi$
$313$	−0.784075	−	8.96202i	−0.0443185	−	0.506563i	0.941299	−	0.337573i	$-0.109606\pi$
$314$		0			0
$315$	−53.7915	+	46.9869i	−3.03081	+	2.64741i
$316$		0			0
$317$	27.5435	+	12.8438i	1.54700	+	0.721377i	0.993749	−	0.111638i	$-0.0356098\pi$
$317$	27.5435	+	12.8438i	1.54700	+	0.721377i	0.553250	+	0.833016i	$0.313388\pi$
$318$		0			0
$319$	0.408057	−	2.31421i	0.0228468	−	0.129571i
$320$		0			0
$321$	45.4851	−	38.1666i	2.53873	−	2.13025i
$322$		0			0
$323$	24.9489	−	7.65428i	1.38819	−	0.425895i
$324$		0			0
$325$	−10.1386	+	3.15286i	−0.562391	+	0.174889i
$326$		0			0
$327$	23.5780	+	33.6728i	1.30386	+	1.86211i
$328$		0			0
$329$	−7.45013	−	20.4691i	−0.410739	−	1.12850i
$330$		0			0
$331$	21.7021	−	12.5297i	1.19285	−	0.688694i	0.233901	−	0.972260i	$-0.424851\pi$
$331$	21.7021	−	12.5297i	1.19285	−	0.688694i	0.958953	+	0.283566i	$0.0915175\pi$
$332$		0			0
$333$	−47.2284	+	4.13195i	−2.58810	+	0.226429i
$334$		0			0
$335$	−28.0668	−	9.58906i	−1.53345	−	0.523907i
$336$		0			0
$337$	0.147212	−	0.210240i	0.00801915	−	0.0114525i	−0.815122	−	0.579289i	$-0.803330\pi$
$337$	0.147212	−	0.210240i	0.00801915	−	0.0114525i	0.823142	+	0.567836i	$0.192219\pi$
$338$		0			0
$339$	−10.0903	+	27.7228i	−0.548028	+	1.50569i
$340$		0			0
$341$			9.60694i			0.520245i
$342$		0			0
$343$	−5.88142	−	5.88142i	−0.317567	−	0.317567i
$344$		0			0
$345$	−3.78408	−	5.18221i	−0.203728	−	0.279001i
$346$		0			0
$347$	−2.80810	−	1.96625i	−0.150746	−	0.105554i	0.495770	−	0.868454i	$-0.334886\pi$
$347$	−2.80810	−	1.96625i	−0.150746	−	0.105554i	−0.646516	+	0.762900i	$0.723775\pi$
$348$		0			0
$349$	18.9201	+	10.9235i	1.01277	+	0.584722i	0.912001	−	0.410188i	$-0.134537\pi$
$349$	18.9201	+	10.9235i	1.01277	+	0.584722i	0.100767	+	0.994910i	$0.467870\pi$
$350$		0			0
$351$	−26.7565	−	22.4513i	−1.42815	−	1.19836i
$352$		0			0
$353$	6.84206	−	25.5349i	0.364166	−	1.35909i	−0.504382	−	0.863481i	$-0.668280\pi$
$353$	6.84206	−	25.5349i	0.364166	−	1.35909i	0.868548	−	0.495605i	$-0.165054\pi$
$354$		0			0
$355$	4.09971	−	16.6124i	0.217590	−	0.881694i
$356$		0			0
$357$	−65.1153	+	45.5942i	−3.44627	+	2.41310i
$358$		0			0
$359$	11.1261	+	13.2596i	0.587212	+	0.699812i	0.975068	−	0.221908i	$-0.0712284\pi$
$359$	11.1261	+	13.2596i	0.587212	+	0.699812i	−0.387855	+	0.921720i	$0.626784\pi$
$360$		0			0
$361$	−13.6417	+	13.2252i	−0.717983	+	0.696061i
$362$		0			0
$363$	1.29904	−	14.8481i	0.0681821	−	0.779325i
$364$		0			0
$365$	−4.82294	+	0.0957358i	−0.252444	+	0.00501104i
$366$		0			0
$367$	6.61268	−	14.1809i	0.345179	−	0.740239i	−0.654698	−	0.755890i	$-0.727204\pi$
$367$	6.61268	−	14.1809i	0.345179	−	0.740239i	0.999878	+	0.0156510i	$0.00498209\pi$
$368$		0			0
$369$	7.93497	+	13.7438i	0.413078	+	0.715472i
$370$		0			0
$371$	2.51714	−	2.99981i	0.130684	−	0.155743i
$372$		0			0
$373$	1.61789	+	6.03805i	0.0837712	+	0.312639i	0.995079	−	0.0990881i	$-0.0315926\pi$
$373$	1.61789	+	6.03805i	0.0837712	+	0.312639i	−0.911307	+	0.411727i	$0.864926\pi$
$374$		0			0
$375$	26.8963	−	25.4449i	1.38892	−	1.31397i
$376$		0			0
$377$	1.77399	−	0.827223i	0.0913649	−	0.0426041i
$378$		0			0
$379$	−14.9994			−0.770468			−0.385234	−	0.922819i	$-0.625879\pi$
$379$	−14.9994			−0.770468			−0.385234	+	0.922819i	$0.625879\pi$
$380$		0			0
$381$	9.56116			0.489833
$382$		0			0
$383$	−3.34007	+	1.55750i	−0.170670	+	0.0795846i	−0.506076	−	0.862489i	$-0.668904\pi$
$383$	−3.34007	+	1.55750i	−0.170670	+	0.0795846i	0.335406	+	0.942074i	$0.391127\pi$
$384$		0			0
$385$	8.24164	+	21.3175i	0.420033	+	1.08644i
$386$		0			0
$387$	−16.5167	−	61.6413i	−0.839593	−	3.13340i
$388$		0			0
$389$	−5.98001	+	7.12670i	−0.303199	+	0.361338i	−0.896034	−	0.443986i	$-0.853564\pi$
$389$	−5.98001	+	7.12670i	−0.303199	+	0.361338i	0.592835	+	0.805324i	$0.298009\pi$
$390$		0			0
$391$	−2.59398	−	4.49291i	−0.131183	−	0.227216i
$392$		0			0
$393$	10.4137	−	22.3322i	0.525300	−	1.12651i
$394$		0			0
$395$	−17.7789	+	18.4990i	−0.894555	+	0.930788i
$396$		0			0
$397$	−3.22827	+	36.8993i	−0.162022	+	1.85192i	0.286414	+	0.958106i	$0.407537\pi$
$397$	−3.22827	+	36.8993i	−0.162022	+	1.85192i	−0.448436	+	0.893815i	$0.648019\pi$
$398$		0			0
$399$	27.1205	−	51.1266i	1.35773	−	2.55953i
$400$		0			0
$401$	−12.0433	−	14.3526i	−0.601413	−	0.716736i	0.376343	−	0.926480i	$-0.377181\pi$
$401$	−12.0433	−	14.3526i	−0.601413	−	0.716736i	−0.977756	+	0.209744i	$0.932737\pi$
$402$		0			0
$403$	−6.55501	+	4.58987i	−0.326528	+	0.228638i
$404$		0			0
$405$	66.3653	+	16.3781i	3.29772	+	0.813832i
$406$		0			0
$407$	−3.92646	+	14.6537i	−0.194627	+	0.726359i
$408$		0			0
$409$	6.92526	+	5.81098i	0.342432	+	0.287335i	0.797743	−	0.602998i	$-0.206027\pi$
$409$	6.92526	+	5.81098i	0.342432	+	0.287335i	−0.455311	+	0.890333i	$0.650472\pi$
$410$		0			0
$411$	33.5239	+	19.3550i	1.65361	+	0.954714i
$412$		0			0
$413$	−2.46326	−	1.72479i	−0.121209	−	0.0848714i
$414$		0			0
$415$	2.31920	−	14.8732i	0.113845	−	0.730097i
$416$		0			0
$417$	−50.8471	−	50.8471i	−2.48999	−	2.48999i
$418$		0			0
$419$		−	10.7854i		−	0.526902i	−0.964673	−	0.263451i	$-0.915139\pi$
$419$		−	10.7854i		−	0.526902i	0.964673	−	0.263451i	$-0.0848608\pi$
$420$		0			0
$421$	2.97653	−	8.17794i	0.145067	−	0.398568i	−0.845785	−	0.533525i	$-0.820867\pi$
$421$	2.97653	−	8.17794i	0.145067	−	0.398568i	0.990852	+	0.134956i	$0.0430894\pi$
$422$		0			0
$423$	−24.8267	+	35.4562i	−1.20712	+	1.72394i
$424$		0			0
$425$	23.8206	−	18.1296i	1.15547	−	0.879413i
$426$		0			0
$427$	12.4367	−	1.08807i	0.601853	−	0.0526553i
$428$		0			0
$429$	−15.5259	+	8.96388i	−0.749598	+	0.432780i
$430$		0			0
$431$	−6.83809	−	18.7875i	−0.329379	−	0.904962i	−0.988269	−	0.152722i	$-0.951196\pi$
$431$	−6.83809	−	18.7875i	−0.329379	−	0.904962i	0.658890	−	0.752239i	$-0.271026\pi$
$432$		0			0
$433$	20.9033	+	29.8530i	1.00455	+	1.43464i	0.897824	+	0.440354i	$0.145147\pi$
$433$	20.9033	+	29.8530i	1.00455	+	1.43464i	0.106723	+	0.994289i	$0.465964\pi$
$434$		0			0
$435$	−4.28282	+	5.31481i	−0.205345	+	0.254826i
$436$		0			0
$437$	3.16980	+	2.05410i	0.151632	+	0.0982608i
$438$		0			0
$439$	−5.17017	+	4.33829i	−0.246759	+	0.207055i	−0.757775	−	0.652516i	$-0.773714\pi$
$439$	−5.17017	+	4.33829i	−0.246759	+	0.207055i	0.511016	+	0.859571i	$0.329269\pi$
$440$		0			0
$441$	−12.5540	+	71.1972i	−0.597809	+	3.39034i
$442$		0			0
$443$	−7.18753	−	3.35160i	−0.341490	−	0.159239i	0.244306	−	0.969698i	$-0.421440\pi$
$443$	−7.18753	−	3.35160i	−0.341490	−	0.159239i	−0.585795	+	0.810459i	$0.699218\pi$
$444$		0			0
$445$	1.35788	−	20.1104i	0.0643697	−	0.953324i
$446$		0			0
$447$	0.596176	+	6.81433i	0.0281982	+	0.322307i
$448$		0			0
$449$	−6.50902	+	11.2740i	−0.307180	+	0.532051i	−0.977744	−	0.209800i	$-0.932719\pi$
$449$	−6.50902	+	11.2740i	−0.307180	+	0.532051i	0.670565	+	0.741851i	$0.266052\pi$
$450$		0			0
$451$	5.00118	−	0.881843i	0.235496	−	0.0415243i
$452$		0			0
$453$	−8.38880	−	17.9898i	−0.394140	−	0.845237i
$454$		0			0
$455$	−10.6078	+	15.8082i	−0.497302	+	0.741101i
$456$		0			0
$457$	−0.455167	+	0.455167i	−0.0212918	+	0.0212918i	−0.717673	−	0.696381i	$-0.754793\pi$
$457$	−0.455167	+	0.455167i	−0.0212918	+	0.0212918i	0.696381	+	0.717673i	$0.254793\pi$
$458$		0			0
$459$	92.5367	+	33.6806i	4.31924	+	1.57208i
$460$		0			0
$461$	5.62718	+	31.9133i	0.262084	+	1.48635i	0.777212	+	0.629239i	$0.216633\pi$
$461$	5.62718	+	31.9133i	0.262084	+	1.48635i	−0.515128	+	0.857113i	$0.672256\pi$
$462$		0			0
$463$	−4.34816	+	1.16509i	−0.202076	+	0.0541461i	−0.358437	−	0.933554i	$-0.616690\pi$
$463$	−4.34816	+	1.16509i	−0.202076	+	0.0541461i	0.156361	+	0.987700i	$0.450024\pi$
$464$		0			0
$465$	13.4701	−	24.4384i	0.624659	−	1.13331i
$466$		0			0
$467$	26.3787	+	7.06815i	1.22066	+	0.327075i	0.810936	−	0.585135i	$-0.198958\pi$
$467$	26.3787	+	7.06815i	1.22066	+	0.327075i	0.409724	+	0.912210i	$0.365625\pi$
$468$		0			0
$469$	−49.9731	+	18.1887i	−2.30754	+	0.839877i
$470$		0			0
$471$	−54.5723	−	9.62257i	−2.51456	−	0.443384i
$472$		0			0
$473$	−20.3431	−	1.77979i	−0.935378	−	0.0818350i
$474$		0			0
$475$	−9.44101	+	19.6435i	−0.433183	+	0.901306i
$476$		0			0
$477$	−7.75176	−	0.678191i	−0.354929	−	0.0310523i
$478$		0			0
$479$	−8.18271	−	1.44283i	−0.373877	−	0.0659247i	−0.0164477	−	0.999865i	$-0.505236\pi$
$479$	−8.18271	−	1.44283i	−0.373877	−	0.0659247i	−0.357430	+	0.933940i	$0.616347\pi$
$480$		0			0
$481$	−11.8745	+	4.32195i	−0.541429	+	0.197064i
$482$		0			0
$483$	−11.1133	−	2.97780i	−0.505672	−	0.135495i
$484$		0			0
$485$	−0.713931	+	1.29527i	−0.0324179	+	0.0588151i
$486$		0			0
$487$	−24.2919	+	6.50899i	−1.10077	+	0.294950i	−0.763078	−	0.646306i	$-0.776313\pi$
$487$	−24.2919	+	6.50899i	−1.10077	+	0.294950i	−0.337692	+	0.941257i	$0.609646\pi$
$488$		0			0
$489$	−8.89009	−	50.4182i	−0.402024	−	2.27999i
$490$		0			0
$491$	17.9820	+	6.54492i	0.811517	+	0.295368i	0.714250	−	0.699890i	$-0.246768\pi$
$491$	17.9820	+	6.54492i	0.811517	+	0.295368i	0.0972666	+	0.995258i	$0.468990\pi$
$492$		0			0
$493$	−3.90223	+	3.90223i	−0.175748	+	0.175748i
$494$		0			0
$495$	25.3057	−	37.7116i	1.13740	−	1.69501i
$496$		0			0
$497$	−12.9659	−	27.8055i	−0.581600	−	1.24725i
$498$		0			0
$499$	9.53409	−	1.68112i	0.426805	−	0.0752572i	0.0438801	−	0.999037i	$-0.486028\pi$
$499$	9.53409	−	1.68112i	0.426805	−	0.0752572i	0.382925	+	0.923780i	$0.374917\pi$
$500$		0			0
$501$	35.8326	−	62.0639i	1.60088	−	2.77281i
$502$		0			0
$503$	0.0770141	+	0.880275i	0.00343389	+	0.0392495i	0.997718	−	0.0675141i	$-0.0215068\pi$
$503$	0.0770141	+	0.880275i	0.00343389	+	0.0392495i	−0.994284	+	0.106764i	$0.965951\pi$
$504$		0			0
$505$	2.40937	−	35.6831i	0.107216	−	1.58788i
$506$		0			0
$507$	25.4835	+	11.8832i	1.13176	+	0.527750i
$508$		0			0
$509$	0.651754	−	3.69628i	0.0288885	−	0.163835i	−0.966951	−	0.254964i	$-0.917936\pi$
$509$	0.651754	−	3.69628i	0.0288885	−	0.163835i	0.995839	+	0.0911290i	$0.0290476\pi$
$510$		0			0
$511$	−6.62577	+	5.55968i	−0.293107	+	0.245946i
$512$		0			0
$513$	−71.1533	+	8.80701i	−3.14150	+	0.388839i
$514$		0			0
$515$	−21.1353	+	26.2281i	−0.931334	+	1.15575i
$516$		0			0
$517$	7.94446	+	11.3459i	0.349397	+	0.498991i
$518$		0			0
$519$	6.89293	+	18.9382i	0.302566	+	0.831294i
$520$		0			0
$521$	−13.8599	+	8.00204i	−0.607215	+	0.350576i	−0.771875	−	0.635775i	$-0.780681\pi$
$521$	−13.8599	+	8.00204i	−0.607215	+	0.350576i	0.164660	+	0.986350i	$0.447347\pi$
$522$		0			0
$523$	2.41618	−	0.211388i	0.105652	−	0.00924336i	−0.0342070	−	0.999415i	$-0.510891\pi$
$523$	2.41618	−	0.211388i	0.105652	−	0.00924336i	0.139859	+	0.990171i	$0.455335\pi$
$524$		0			0
$525$	8.92433	−	65.7840i	0.389490	−	2.87105i
$526$		0			0
$527$	12.9406	−	18.4811i	0.563700	−	0.805048i
$528$		0			0
$529$	−7.60964	+	20.9073i	−0.330854	+	0.909014i
$530$		0			0
$531$			5.97531i			0.259307i
$532$		0			0
$533$	2.99109	+	2.99109i	0.129559	+	0.129559i
$534$		0			0
$535$	−6.17698	+	39.6135i	−0.267054	+	1.71264i
$536$		0			0
$537$	52.2662	+	36.5972i	2.25545	+	1.57928i
$538$		0			0
$539$	20.0349	+	11.5672i	0.862965	+	0.498233i
$540$		0			0
$541$	−15.8160	−	13.2712i	−0.679983	−	0.570573i	0.236019	−	0.971749i	$-0.424157\pi$
$541$	−15.8160	−	13.2712i	−0.679983	−	0.570573i	−0.916001	+	0.401175i	$0.868602\pi$
$542$		0			0
$543$	−2.28812	+	8.53936i	−0.0981924	+	0.366459i
$544$		0			0
$545$	−26.9477	−	6.65033i	−1.15431	−	0.284869i
$546$		0			0
$547$	−13.0690	+	9.15104i	−0.558792	+	0.391270i	−0.818578	−	0.574396i	$-0.805237\pi$
$547$	−13.0690	+	9.15104i	−0.558792	+	0.391270i	0.259786	+	0.965666i	$0.416348\pi$
$548$		0			0
$549$	−15.9457	−	19.0034i	−0.680546	−	0.811043i
$550$		0			0
$551$	1.23786	−	3.82243i	0.0527347	−	0.162841i
$552$		0			0
$553$	−4.00954	+	45.8292i	−0.170503	+	1.94886i
$554$		0			0
$555$	30.5345	−	31.7713i	1.29612	−	1.34862i
$556$		0			0
$557$	−7.68259	+	16.4754i	−0.325522	+	0.698083i	−0.999160	−	0.0409777i	$-0.986953\pi$
$557$	−7.68259	+	16.4754i	−0.325522	+	0.698083i	0.673638	+	0.739061i	$0.264731\pi$
$558$		0			0
$559$	−8.50486	−	14.7309i	−0.359717	−	0.623049i
$560$		0			0
$561$	32.4898	−	38.7199i	1.37172	−	1.63475i
$562$		0			0
$563$	−7.84942	−	29.2944i	−0.330814	−	1.23461i	−0.908337	−	0.418239i	$-0.862648\pi$
$563$	−7.84942	−	29.2944i	−0.330814	−	1.23461i	0.577524	−	0.816374i	$-0.304019\pi$
$564$		0			0
$565$	−7.18329	−	18.5800i	−0.302203	−	0.781668i
$566$		0			0
$567$	111.081	−	51.7979i	4.66496	−	2.17531i
$568$		0			0
$569$	32.7041			1.37103			0.685514	−	0.728059i	$-0.259578\pi$
$569$	32.7041			1.37103			0.685514	+	0.728059i	$0.259578\pi$
$570$		0			0
$571$	−9.17647			−0.384023			−0.192012	−	0.981393i	$-0.561501\pi$
$571$	−9.17647			−0.384023			−0.192012	+	0.981393i	$0.561501\pi$
$572$		0			0
$573$	24.4588	−	11.4053i	1.02178	−	0.476465i
$574$		0			0
$575$	4.22627	+	0.954420i	0.176248	+	0.0398021i
$576$		0			0
$577$	7.75289	+	28.9342i	0.322757	+	1.20455i	0.916548	+	0.399926i	$0.130964\pi$
$577$	7.75289	+	28.9342i	0.322757	+	1.20455i	−0.593791	+	0.804620i	$0.702369\pi$
$578$		0			0
$579$	−24.9442	+	29.7273i	−1.03665	+	1.23543i
$580$		0			0
$581$	−13.4951	−	23.3742i	−0.559871	−	0.969725i
$582$		0			0
$583$	−1.05233	+	2.25672i	−0.0435828	+	0.0934637i
$584$		0			0
$585$	37.8216	−	0.750761i	1.56373	−	0.0310402i
$586$		0			0
$587$	3.68141	−	42.0787i	0.151948	−	1.73677i	−0.412194	−	0.911096i	$-0.635237\pi$
$587$	3.68141	−	42.0787i	0.151948	−	1.73677i	0.564142	−	0.825678i	$-0.309207\pi$
$588$		0			0
$589$	−2.27018	+	16.2683i	−0.0935411	+	0.670325i
$590$		0			0
$591$	−1.54330	−	1.83924i	−0.0634830	−	0.0756560i
$592$		0			0
$593$	1.26867	−	0.888329i	0.0520978	−	0.0364793i	−0.547237	−	0.836977i	$-0.684321\pi$
$593$	1.26867	−	0.888329i	0.0520978	−	0.0364793i	0.599335	+	0.800498i	$0.295432\pi$
$594$		0			0
$595$	12.8602	−	52.1105i	0.527215	−	2.13632i
$596$		0			0
$597$	−8.32409	+	31.0659i	−0.340682	+	1.27144i
$598$		0			0
$599$	17.5655	+	14.7392i	0.717706	+	0.602227i	0.926750	−	0.375679i	$-0.122591\pi$
$599$	17.5655	+	14.7392i	0.717706	+	0.602227i	−0.209044	+	0.977906i	$0.567035\pi$
$600$		0			0
$601$	−29.0465	−	16.7700i	−1.18483	−	0.684064i	−0.227706	−	0.973730i	$-0.573122\pi$
$601$	−29.0465	−	16.7700i	−1.18483	−	0.684064i	−0.957128	+	0.289666i	$0.906456\pi$
$602$		0			0
$603$	86.5627	+	60.6119i	3.52511	+	2.46831i
$604$		0			0
$605$	5.93496	+	8.12778i	0.241291	+	0.330441i
$606$		0			0
$607$	18.7998	+	18.7998i	0.763062	+	0.763062i	0.976875	−	0.213813i	$-0.0685882\pi$
$607$	18.7998	+	18.7998i	0.763062	+	0.763062i	−0.213813	+	0.976875i	$0.568588\pi$
$608$		0			0
$609$			12.2385i			0.495931i
$610$		0			0
$611$	−3.94592	+	10.8413i	−0.159635	+	0.438594i
$612$		0			0
$613$	9.88411	−	14.1160i	0.399215	−	0.570139i	−0.568341	−	0.822793i	$-0.692415\pi$
$613$	9.88411	−	14.1160i	0.399215	−	0.570139i	0.967557	+	0.252654i	$0.0813035\pi$
$614$		0			0
$615$	−13.9586	−	4.76898i	−0.562865	−	0.192304i
$616$		0			0
$617$	15.8917	−	1.39034i	0.639775	−	0.0559731i	0.237347	−	0.971425i	$-0.423722\pi$
$617$	15.8917	−	1.39034i	0.639775	−	0.0559731i	0.402428	+	0.915452i	$0.368166\pi$
$618$		0			0
$619$	−1.82508	+	1.05371i	−0.0733561	+	0.0423522i	−0.536229	−	0.844072i	$-0.680152\pi$
$619$	−1.82508	+	1.05371i	−0.0733561	+	0.0423522i	0.462873	+	0.886424i	$0.346818\pi$
$620$		0			0
$621$	4.87484	+	13.3935i	0.195621	+	0.537463i
$622$		0			0
$623$	−20.7293	−	29.6045i	−0.830501	−	1.18608i
$624$		0			0
$625$	−2.37499	+	24.8869i	−0.0949996	+	0.995477i
$626$		0			0
$627$	−8.24322	+	35.8649i	−0.329202	+	1.43231i
$628$		0			0
$629$	27.2920	−	22.9007i	1.08820	−	0.913112i
$630$		0			0
$631$	−3.94005	+	22.3452i	−0.156851	+	0.889547i	0.800223	+	0.599703i	$0.204715\pi$
$631$	−3.94005	+	22.3452i	−0.156851	+	0.889547i	−0.957074	+	0.289844i	$0.906397\pi$
$632$		0			0
$633$	50.0145	+	23.3221i	1.98790	+	0.926972i
$634$		0			0
$635$	−4.86216	+	4.24709i	−0.192949	+	0.168541i
$636$		0			0
$637$	1.67949	+	19.1966i	0.0665437	+	0.760598i
$638$		0			0
$639$	−30.4818	+	52.7960i	−1.20584	+	2.08858i
$640$		0			0
$641$	−7.71213	+	1.35986i	−0.304611	+	0.0537111i	−0.323864	−	0.946104i	$-0.604982\pi$
$641$	−7.71213	+	1.35986i	−0.304611	+	0.0537111i	0.0192534	+	0.999815i	$0.493871\pi$
$642$		0			0
$643$	−13.6483	−	29.2688i	−0.538234	−	1.15425i	−0.967918	−	0.251268i	$-0.919153\pi$
$643$	−13.6483	−	29.2688i	−0.538234	−	1.15425i	0.429683	−	0.902980i	$-0.358625\pi$
$644$		0			0
$645$	49.2541	+	33.0510i	1.93938	+	1.30138i
$646$		0			0
$647$	−33.1073	+	33.1073i	−1.30158	+	1.30158i	−0.374257	+	0.927325i	$0.622102\pi$
$647$	−33.1073	+	33.1073i	−1.30158	+	1.30158i	−0.927325	+	0.374257i	$0.877898\pi$
$648$		0			0
$649$	1.79677	+	0.653970i	0.0705293	+	0.0256706i
$650$		0			0
$651$	−8.68829	−	49.2738i	−0.340521	−	1.93119i
$652$		0			0
$653$	15.8108	−	4.23650i	0.618726	−	0.165787i	0.0641775	−	0.997938i	$-0.479558\pi$
$653$	15.8108	−	4.23650i	0.618726	−	0.165787i	0.554549	+	0.832151i	$0.312891\pi$
$654$		0			0
$655$	4.62432	+	15.9824i	0.180687	+	0.624484i
$656$		0			0
$657$	16.6013	+	4.44831i	0.647678	+	0.173545i
$658$		0			0
$659$	−19.2998	+	7.02457i	−0.751815	+	0.273638i	−0.689369	−	0.724410i	$-0.742112\pi$
$659$	−19.2998	+	7.02457i	−0.751815	+	0.273638i	−0.0624458	+	0.998048i	$0.519890\pi$
$660$		0			0
$661$	−22.9631	−	4.04901i	−0.893161	−	0.157488i	−0.291813	−	0.956475i	$-0.594258\pi$
$661$	−22.9631	−	4.04901i	−0.893161	−	0.157488i	−0.601348	+	0.798987i	$0.705370\pi$
$662$		0			0
$663$	41.9419	+	3.66944i	1.62889	+	0.142509i
$664$		0			0
$665$	8.91888	+	38.0465i	0.345859	+	1.47538i
$666$		0			0
$667$	−0.795706	−	0.0696153i	−0.0308099	−	0.00269551i
$668$		0			0
$669$	−16.8507	−	2.97123i	−0.651484	−	0.114874i
$670$		0			0
$671$	−7.45946	+	2.71502i	−0.287969	+	0.104812i
$672$		0			0
$673$	−31.2452	−	8.37213i	−1.20441	−	0.322722i	−0.399846	−	0.916582i	$-0.630937\pi$
$673$	−31.2452	−	8.37213i	−1.20441	−	0.322722i	−0.804568	+	0.593860i	$0.797603\pi$
$674$		0			0
$675$	−73.0979	+	37.6872i	−2.81354	+	1.45058i
$676$		0			0
$677$	31.8193	−	8.52597i	1.22292	−	0.327679i	0.411099	−	0.911591i	$-0.365145\pi$
$677$	31.8193	−	8.52597i	1.22292	−	0.327679i	0.811817	+	0.583911i	$0.198478\pi$
$678$		0			0
$679$	0.460491	+	2.61157i	0.0176720	+	0.100223i
$680$		0			0
$681$	6.66303	+	2.42515i	0.255328	+	0.0929318i
$682$		0			0
$683$	28.8207	−	28.8207i	1.10279	−	1.10279i	0.108722	−	0.994072i	$-0.465324\pi$
$683$	28.8207	−	28.8207i	1.10279	−	1.10279i	0.994072	−	0.108722i	$-0.0346760\pi$
$684$		0			0
$685$	−25.6455	+	5.04874i	−0.979865	+	0.192902i
$686$		0			0
$687$	−9.61316	−	20.6155i	−0.366765	−	0.786530i
$688$		0			0
$689$	−2.04257	+	0.360160i	−0.0778157	+	0.0137210i
$690$		0			0
$691$	6.02517	−	10.4359i	0.229208	−	0.397000i	−0.728365	−	0.685189i	$-0.759720\pi$
$691$	6.02517	−	10.4359i	0.229208	−	0.397000i	0.957574	+	0.288189i	$0.0930530\pi$
$692$		0			0
$693$	−7.09712	−	81.1205i	−0.269597	−	3.08151i
$694$		0			0
$695$	48.4438	+	3.27099i	1.83758	+	0.124076i
$696$		0			0
$697$	−10.8087	−	5.04019i	−0.409409	−	0.190911i
$698$		0			0
$699$	1.57789	−	8.94869i	0.0596815	−	0.338470i
$700$		0			0
$701$	−9.32359	+	7.82342i	−0.352147	+	0.295487i	−0.801652	−	0.597791i	$-0.796045\pi$
$701$	−9.32359	+	7.82342i	−0.352147	+	0.295487i	0.449504	+	0.893278i	$0.351601\pi$
$702$		0			0
$703$	−10.1118	+	23.8867i	−0.381374	+	0.900904i
$704$		0			0
$705$	−4.30113	−	40.0011i	−0.161990	−	1.50653i
$706$		0			0
$707$	−36.7813	−	52.5291i	−1.38330	−	1.97556i
$708$		0			0
$709$	−6.66194	−	18.3035i	−0.250195	−	0.687404i	−0.999678	−	0.0253806i	$-0.991920\pi$
$709$	−6.66194	−	18.3035i	−0.250195	−	0.687404i	0.749483	−	0.662023i	$-0.230302\pi$
$710$		0			0
$711$	79.1671	−	45.7071i	2.96900	−	1.71415i
$712$		0			0
$713$	3.25302	−	0.284603i	0.121827	−	0.0106585i
$714$		0			0
$715$	3.91364	−	11.4551i	0.146362	−	0.428395i
$716$		0			0
$717$	10.3578	−	14.7924i	0.386818	−	0.552433i
$718$		0			0
$719$	−13.4929	+	37.0714i	−0.503200	+	1.38253i	0.384934	+	0.922944i	$0.374224\pi$
$719$	−13.4929	+	37.0714i	−0.503200	+	1.38253i	−0.888134	+	0.459586i	$0.847998\pi$
$720$		0			0
$721$			60.3962i			2.24927i
$722$		0			0
$723$	1.16865	+	1.16865i	0.0434627	+	0.0434627i
$724$		0			0
$725$	−0.182899	−	4.60519i	−0.00679269	−	0.171032i
$726$		0			0
$727$	−33.8514	−	23.7030i	−1.25548	−	0.879097i	−0.259247	−	0.965811i	$-0.583474\pi$
$727$	−33.8514	−	23.7030i	−1.25548	−	0.879097i	−0.996233	+	0.0867140i	$0.972363\pi$
$728$		0			0
$729$	−69.3981	−	40.0670i	−2.57030	−	1.48396i
$730$		0			0
$731$	36.7371	+	30.8261i	1.35877	+	1.14014i
$732$		0			0
$733$	−10.2512	+	38.2581i	−0.378638	+	1.41309i	0.469319	+	0.883029i	$0.344499\pi$
$733$	−10.2512	+	38.2581i	−0.378638	+	1.41309i	−0.847956	+	0.530066i	$0.822167\pi$
$734$		0			0
$735$	−34.7469	−	57.5163i	−1.28166	−	2.12152i
$736$		0			0
$737$	27.6998	−	19.3956i	1.02033	−	0.714446i
$738$		0			0
$739$	−11.7618	−	14.0172i	−0.432666	−	0.515632i	0.505023	−	0.863106i	$-0.331484\pi$
$739$	−11.7618	−	14.0172i	−0.432666	−	0.515632i	−0.937690	+	0.347474i	$0.887039\pi$
$740$		0			0
$741$	−28.4097	+	11.5105i	−1.04366	+	0.422850i
$742$		0			0
$743$	−1.21406	+	13.8768i	−0.0445397	+	0.509091i	0.940856	+	0.338808i	$0.110024\pi$
$743$	−1.21406	+	13.8768i	−0.0445397	+	0.509091i	−0.985395	+	0.170283i	$0.945532\pi$
$744$		0			0
$745$	−3.33011	−	3.20048i	−0.122006	−	0.117257i
$746$		0			0
$747$	−22.6658	+	48.6069i	−0.829297	+	1.77843i
$748$		0			0
$749$	35.9430	+	62.2552i	1.31333	+	2.27475i
$750$		0			0
$751$	5.19311	−	6.18891i	0.189499	−	0.225837i	−0.662927	−	0.748684i	$-0.730686\pi$
$751$	5.19311	−	6.18891i	0.189499	−	0.225837i	0.852426	+	0.522848i	$0.175130\pi$
$752$		0			0
$753$	18.0197	+	67.2505i	0.656675	+	2.45075i
$754$		0			0
$755$	12.2571	+	5.42209i	0.446082	+	0.197330i
$756$		0			0
$757$	13.4789	−	6.28533i	0.489900	−	0.228444i	−0.161940	−	0.986801i	$-0.551775\pi$
$757$	13.4789	−	6.28533i	0.489900	−	0.228444i	0.651840	+	0.758357i	$0.273997\pi$
$758$		0			0
$759$	7.31578			0.265546
$760$		0			0
$761$	−52.4394			−1.90093			−0.950463	−	0.310838i	$-0.899390\pi$
$761$	−52.4394			−1.90093			−0.950463	+	0.310838i	$0.899390\pi$
$762$		0			0
$763$	−45.1045	+	21.0326i	−1.63289	+	0.761430i
$764$		0			0
$765$	−99.4787	+	38.4598i	−3.59666	+	1.39052i
$766$		0			0
$767$	0.412217	+	1.53842i	0.0148843	+	0.0555490i
$768$		0			0
$769$	26.0151	−	31.0036i	0.938128	−	1.11802i	−0.0547041	−	0.998503i	$-0.517422\pi$
$769$	26.0151	−	31.0036i	0.938128	−	1.11802i	0.992832	−	0.119515i	$-0.0381340\pi$
$770$		0			0
$771$	−22.4896	−	38.9531i	−0.809942	−	1.40286i
$772$		0			0
$773$	−22.4341	+	48.1102i	−0.806900	+	1.73040i	−0.133598	+	0.991036i	$0.542653\pi$
$773$	−22.4341	+	48.1102i	−0.806900	+	1.73040i	−0.673302	+	0.739368i	$0.735125\pi$
$774$		0			0
$775$	4.00565	+	18.4112i	0.143887	+	0.661348i
$776$		0			0
$777$	6.88620	−	78.7096i	0.247041	−	2.82369i
$778$		0			0
$779$	8.67735	−	0.311497i	0.310898	−	0.0111606i
$780$		0			0
$781$	12.5396	+	14.9441i	0.448702	+	0.534742i
$782$		0			0
$783$	12.4195	−	8.69622i	0.443836	−	0.310778i
$784$		0			0
$785$	32.0261	−	19.3477i	1.14306	−	0.690550i
$786$		0			0
$787$	1.73835	−	6.48762i	0.0619655	−	0.231259i	−0.927997	−	0.372587i	$-0.878471\pi$
$787$	1.73835	−	6.48762i	0.0619655	−	0.231259i	0.989963	+	0.141329i	$0.0451374\pi$
$788$		0			0
$789$	−69.6757	−	58.4649i	−2.48052	−	2.08140i
$790$		0			0
$791$	−30.9322	−	17.8587i	−1.09982	−	0.634982i
$792$		0			0
$793$	−5.41639	−	3.79260i	−0.192342	−	0.134679i
$794$		0			0
$795$	5.84113	−	4.26523i	0.207163	−	0.151272i
$796$		0			0
$797$	−30.9335	−	30.9335i	−1.09572	−	1.09572i	−0.994905	−	0.100816i	$-0.967855\pi$
$797$	−30.9335	−	30.9335i	−1.09572	−	1.09572i	−0.100816	−	0.994905i	$-0.532145\pi$
$798$		0			0
$799$		−	32.5275i		−	1.15074i
$800$		0			0
$801$	−24.5618	+	67.4830i	−0.867849	+	2.38440i
$802$		0			0
$803$	3.15453	−	4.50514i	0.111321	−	0.158983i
$804$		0			0
$805$	6.97421	−	3.42224i	0.245809	−	0.120618i
$806$		0			0
$807$	−83.8260	+	7.33382i	−2.95081	+	0.258163i
$808$		0			0
$809$	37.8992	−	21.8811i	1.33246	−	0.769299i	0.346788	−	0.937944i	$-0.387272\pi$
$809$	37.8992	−	21.8811i	1.33246	−	0.769299i	0.985677	+	0.168645i	$0.0539391\pi$
$810$		0			0
$811$	9.03265	+	24.8170i	0.317179	+	0.871442i	0.991157	+	0.132691i	$0.0423619\pi$
$811$	9.03265	+	24.8170i	0.317179	+	0.871442i	−0.673978	+	0.738751i	$0.735416\pi$
$812$		0			0
$813$	0.642149	+	0.917083i	0.0225211	+	0.0321635i
$814$		0			0
$815$	26.9168	+	21.6903i	0.942853	+	0.759777i
$816$		0			0
$817$	−34.0284	−	7.82110i	−1.19050	−	0.273626i
$818$		0			0
$819$	51.9594	−	43.5991i	1.81561	−	1.52348i
$820$		0			0
$821$	3.52497	−	19.9911i	0.123022	−	0.697694i	−0.859441	−	0.511236i	$-0.829188\pi$
$821$	3.52497	−	19.9911i	0.123022	−	0.697694i	0.982463	−	0.186458i	$-0.0597009\pi$
$822$		0			0
$823$	−41.3414	−	19.2778i	−1.44107	−	0.671982i	−0.464184	−	0.885739i	$-0.653652\pi$
$823$	−41.3414	−	19.2778i	−1.44107	−	0.671982i	−0.976887	+	0.213757i	$0.931430\pi$
$824$		0			0
$825$	5.34498	+	41.8728i	0.186088	+	1.45782i
$826$		0			0
$827$	−0.260850	−	2.98153i	−0.00907066	−	0.103678i	0.990310	−	0.138877i	$-0.0443492\pi$
$827$	−0.260850	−	2.98153i	−0.00907066	−	0.103678i	−0.999380	+	0.0351986i	$0.988794\pi$
$828$		0			0
$829$	19.7092	−	34.1374i	0.684529	−	1.18564i	−0.289055	−	0.957312i	$-0.593341\pi$
$829$	19.7092	−	34.1374i	0.684529	−	1.18564i	0.973585	−	0.228327i	$-0.0733255\pi$
$830$		0			0
$831$	−16.5322	+	2.91508i	−0.573497	+	0.101123i
$832$		0			0
$833$	−22.9606	−	49.2391i	−0.795536	−	1.70603i
$834$		0			0
$835$	9.34688	+	47.4784i	0.323462	+	1.64306i
$836$		0			0
$837$	−43.8287	+	43.8287i	−1.51494	+	1.51494i
$838$		0			0
$839$	−32.6520	−	11.8844i	−1.12727	−	0.410294i	−0.289971	−	0.957035i	$-0.593646\pi$
$839$	−32.6520	−	11.8844i	−1.12727	−	0.410294i	−0.837301	+	0.546742i	$0.815868\pi$
$840$		0			0
$841$	−4.88826	−	27.7227i	−0.168561	−	0.955955i
$842$		0			0
$843$	−45.6428	+	12.2299i	−1.57202	+	0.421221i
$844$		0			0
$845$	−18.2377	+	5.27687i	−0.627396	+	0.181530i
$846$		0			0
$847$	17.4301	+	4.67039i	0.598906	+	0.160476i
$848$		0			0
$849$	29.9983	−	10.9185i	1.02954	−	0.374721i
$850$		0			0
$851$	5.07825	+	0.895432i	0.174080	+	0.0306950i
$852$		0			0
$853$	43.8529	+	3.83664i	1.50150	+	0.131364i	0.808037	−	0.589132i	$-0.200530\pi$
$853$	43.8529	+	3.83664i	1.50150	+	0.131364i	0.693459	+	0.720496i	$0.256086\pi$
$854$		0			0
$855$	51.7639	−	57.8807i	1.77029	−	1.97948i
$856$		0			0
$857$	3.44315	+	0.301236i	0.117616	+	0.0102900i	0.145812	−	0.989312i	$-0.453421\pi$
$857$	3.44315	+	0.301236i	0.117616	+	0.0102900i	−0.0281959	+	0.999602i	$0.508976\pi$
$858$		0			0
$859$	−43.4355	−	7.65885i	−1.48200	−	0.261317i	−0.626624	−	0.779322i	$-0.715564\pi$
$859$	−43.4355	−	7.65885i	−1.48200	−	0.261317i	−0.855377	+	0.518005i	$0.826675\pi$
$860$		0			0
$861$	−24.8534	+	9.04590i	−0.847002	+	0.308283i
$862$		0			0
$863$	9.15517	+	2.45312i	0.311646	+	0.0835052i	0.411252	−	0.911522i	$-0.365092\pi$
$863$	9.15517	+	2.45312i	0.311646	+	0.0835052i	−0.0996063	+	0.995027i	$0.531758\pi$
$864$		0			0
$865$	−11.9177	−	6.56881i	−0.405212	−	0.223346i
$866$		0			0
$867$	−60.2779	+	16.1514i	−2.04714	+	0.548531i
$868$		0			0
$869$	−5.07960	−	28.8079i	−0.172314	−	0.977240i
$870$		0			0
$871$	26.4680	+	9.63357i	0.896834	+	0.326421i
$872$		0			0
$873$	3.72607	−	3.72607i	0.126109	−	0.126109i
$874$		0			0
$875$	24.6831	+	37.4175i	0.834440	+	1.26494i
$876$		0			0
$877$	−7.82178	−	16.7739i	−0.264123	−	0.566413i	0.728861	−	0.684661i	$-0.240050\pi$
$877$	−7.82178	−	16.7739i	−0.264123	−	0.566413i	−0.992984	+	0.118248i	$0.962272\pi$
$878$		0			0
$879$	11.0649	−	1.95104i	0.373209	−	0.0658069i
$880$		0			0
$881$	−3.48677	+	6.03926i	−0.117472	+	0.203468i	−0.918765	−	0.394804i	$-0.870812\pi$
$881$	−3.48677	+	6.03926i	−0.117472	+	0.203468i	0.801293	+	0.598272i	$0.204146\pi$
$882$		0			0
$883$	2.48966	+	28.4570i	0.0837838	+	0.957653i	0.915464	+	0.402399i	$0.131824\pi$
$883$	2.48966	+	28.4570i	0.0837838	+	0.957653i	−0.831681	+	0.555254i	$0.812621\pi$
$884$		0			0
$885$	−3.65373	−	4.18287i	−0.122819	−	0.140606i
$886$		0			0
$887$	−2.51914	−	1.17469i	−0.0845843	−	0.0394423i	0.379866	−	0.925042i	$-0.375970\pi$
$887$	−2.51914	−	1.17469i	−0.0845843	−	0.0394423i	−0.464450	+	0.885599i	$0.653748\pi$
$888$		0			0
$889$	−2.01006	+	11.3996i	−0.0674154	+	0.382332i
$890$		0			0
$891$	−59.7006	+	50.0948i	−2.00005	+	1.67824i
$892$		0			0
$893$	10.7720	+	21.0903i	0.360471	+	0.705762i
$894$		0			0
$895$	−42.8355	+	4.60591i	−1.43183	+	0.153959i
$896$		0			0
$897$	3.49523	+	4.99170i	0.116702	+	0.166668i
$898$		0			0
$899$	−1.18802	−	3.26407i	−0.0396228	−	0.108863i
$900$		0			0
$901$	5.06419	−	2.92381i	0.168713	−	0.0974062i
$902$		0			0
$903$	105.949	−	9.26934i	3.52576	−	0.308464i
$904$		0			0
$905$	−2.62962	−	5.35893i	−0.0874116	−	0.178137i
$906$		0			0
$907$	−3.95189	+	5.64389i	−0.131220	+	0.187402i	−0.879385	−	0.476110i	$-0.842046\pi$
$907$	−3.95189	+	5.64389i	−0.131220	+	0.187402i	0.748165	+	0.663513i	$0.230935\pi$
$908$		0			0
$909$	−43.5816	+	119.739i	−1.44551	+	3.97151i
$910$		0			0
$911$		−	40.7176i		−	1.34903i	−0.738260	−	0.674516i	$-0.764352\pi$
$911$		−	40.7176i		−	1.34903i	0.738260	−	0.674516i	$-0.235648\pi$
$912$		0			0
$913$	12.1354	+	12.1354i	0.401622	+	0.401622i
$914$		0			0
$915$	22.7824	+	3.55249i	0.753163	+	0.117442i
$916$		0			0
$917$	24.4370	+	17.1110i	0.806982	+	0.565055i
$918$		0			0
$919$	49.4990	+	28.5782i	1.63282	+	0.942709i	0.983218	+	0.182434i	$0.0583977\pi$
$919$	49.4990	+	28.5782i	1.63282	+	0.942709i	0.649602	+	0.760275i	$0.274936\pi$
$920$		0			0
$921$	40.6481	+	34.1078i	1.33940	+	1.12389i
$922$		0			0
$923$	−4.20568	+	15.6958i	−0.138431	+	0.516633i
$924$		0			0
$925$	−1.41490	+	29.7202i	−0.0465217	+	0.977195i
$926$		0			0
$927$	98.3082	−	68.8361i	3.22886	−	2.26088i
$928$		0			0
$929$	−13.8701	−	16.5297i	−0.455063	−	0.542323i	0.488915	−	0.872331i	$-0.337393\pi$
$929$	−13.8701	−	16.5297i	−0.455063	−	0.542323i	−0.943978	+	0.330009i	$0.892948\pi$
$930$		0			0
$931$	31.1936	+	24.3221i	1.02233	+	0.797126i
$932$		0			0
$933$	−1.48520	+	16.9759i	−0.0486231	+	0.555765i
$934$		0			0
$935$	0.677331	+	34.1223i	0.0221511	+	1.11592i
$936$		0			0
$937$	−5.98285	+	12.8303i	−0.195451	+	0.419147i	−0.979470	−	0.201591i	$-0.935389\pi$
$937$	−5.98285	+	12.8303i	−0.195451	+	0.419147i	0.784019	+	0.620737i	$0.213167\pi$
$938$		0			0
$939$	−14.8961	−	25.8008i	−0.486115	−	0.841976i
$940$		0			0
$941$	21.0833	−	25.1261i	0.687296	−	0.819087i	−0.303730	−	0.952758i	$-0.598232\pi$
$941$	21.0833	−	25.1261i	0.687296	−	0.819087i	0.991026	+	0.133671i	$0.0426765\pi$
$942$		0			0
$943$	−0.446761	−	1.66733i	−0.0145485	−	0.0542959i
$944$		0			0
$945$	−59.6547	+	134.855i	−1.94057	+	4.38682i
$946$		0			0
$947$	−0.803162	+	0.374520i	−0.0260992	+	0.0121703i	−0.435624	−	0.900129i	$-0.643472\pi$
$947$	−0.803162	+	0.374520i	−0.0260992	+	0.0121703i	0.409525	+	0.912299i	$0.365695\pi$
$948$		0			0
$949$	4.58108			0.148708
$950$		0			0
$951$	100.643			3.26358
$952$		0			0
$953$	2.43056	−	1.13339i	0.0787334	−	0.0367140i	−0.382853	−	0.923809i	$-0.625058\pi$
$953$	2.43056	−	1.13339i	0.0787334	−	0.0367140i	0.461586	+	0.887095i	$0.347281\pi$
$954$		0			0
$955$	−7.37182	+	16.6646i	−0.238547	+	0.539255i
$956$		0			0
$957$	−2.01413	−	7.51683i	−0.0651075	−	0.242985i
$958$		0			0
$959$	−30.1246	+	35.9011i	−0.972773	+	1.15931i
$960$		0			0
$961$	−8.39968	−	14.5487i	−0.270957	−	0.469312i
$962$		0			0
$963$	60.3683	−	129.460i	1.94534	−	4.17180i
$964$		0			0
$965$	−0.520024	−	26.1976i	−0.0167402	−	0.843330i
$966$		0			0
$967$	−2.29815	+	26.2680i	−0.0739035	+	0.844721i	0.865276	+	0.501295i	$0.167143\pi$
$967$	−2.29815	+	26.2680i	−0.0739035	+	0.844721i	−0.939180	+	0.343426i	$0.888413\pi$
$968$		0			0
$969$	64.1678	−	57.8904i	2.06137	−	1.85971i
$970$		0			0
$971$	9.31522	+	11.1014i	0.298940	+	0.356262i	0.894516	−	0.447036i	$-0.147521\pi$
$971$	9.31522	+	11.1014i	0.298940	+	0.356262i	−0.595576	+	0.803299i	$0.703076\pi$
$972$		0			0
$973$	71.3140	−	49.9346i	2.28622	−	1.60083i
$974$		0			0
$975$	−26.0170	+	23.6524i	−0.833211	+	0.757482i
$976$		0			0
$977$	13.7645	−	51.3699i	0.440367	−	1.64347i	−0.287522	−	0.957774i	$-0.592831\pi$
$977$	13.7645	−	51.3699i	0.440367	−	1.64347i	0.727888	−	0.685696i	$-0.240502\pi$
$978$		0			0
$979$	17.6039	+	14.7714i	0.562622	+	0.472096i
$980$		0			0
$981$	85.6428	+	49.4459i	2.73436	+	1.57869i
$982$		0			0
$983$	−16.9445	−	11.8646i	−0.540445	−	0.378423i	0.271247	−	0.962510i	$-0.412564\pi$
$983$	−16.9445	−	11.8646i	−0.540445	−	0.378423i	−0.811691	+	0.584086i	$0.801453\pi$
$984$		0			0
$985$	1.60181	+	0.249772i	0.0510379	+	0.00795840i
$986$		0			0
$987$	−51.0079	−	51.0079i	−1.62360	−	1.62360i
$988$		0			0
$989$			6.94115i			0.220716i
$990$		0			0
$991$	6.81710	−	18.7298i	0.216552	−	0.594972i	−0.783085	−	0.621915i	$-0.786355\pi$
$991$	6.81710	−	18.7298i	0.216552	−	0.594972i	0.999637	+	0.0269427i	$0.00857716\pi$
$992$		0			0
$993$	47.5995	−	67.9791i	1.51052	−	2.15725i
$994$		0			0
$995$	−9.56648	−	19.4956i	−0.303278	−	0.618052i
$996$		0			0
$997$	−36.8458	+	3.22359i	−1.16692	+	0.102092i	−0.654101	−	0.756407i	$-0.726953\pi$
$997$	−36.8458	+	3.22359i	−1.16692	+	0.102092i	−0.512815	+	0.858499i	$0.671397\pi$
$998$		0			0
$999$	−84.7665	+	48.9399i	−2.68189	+	1.54839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.13.10	✓	120
5.2	odd	4	inner	380.2.bh.a.317.1	yes	120
19.3	odd	18	inner	380.2.bh.a.193.1	yes	120
95.22	even	36	inner	380.2.bh.a.117.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.10	✓	120	1.1	even	1	trivial
380.2.bh.a.117.10	yes	120	95.22	even	36	inner
380.2.bh.a.193.1	yes	120	19.3	odd	18	inner
380.2.bh.a.317.1	yes	120	5.2	odd	4	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.00135 - 1.39955i) q^{3} +(-0.904597 + 2.04492i) q^{5} +(1.03769 + 3.87270i) q^{7} +(5.12098 - 6.10295i) q^{9} +O(q^{10})\)	\(q+(3.00135 - 1.39955i) q^{3} +(-0.904597 + 2.04492i) q^{5} +(1.03769 + 3.87270i) q^{7} +(5.12098 - 6.10295i) q^{9} +(-1.27468 - 2.20781i) q^{11} +(0.897435 - 1.92456i) q^{13} +(0.146961 + 7.40355i) q^{15} +(-0.521800 + 5.96421i) q^{17} +(-1.63682 - 4.03991i) q^{19} +(8.53449 + 10.1710i) q^{21} +(-0.709828 + 0.497027i) q^{23} +(-3.36341 - 3.69966i) q^{25} +(4.25712 - 15.8878i) q^{27} +(0.706112 + 0.592498i) q^{29} +(-3.26351 - 1.88419i) q^{31} +(-6.91570 - 4.84242i) q^{33} +(-8.85805 - 1.38125i) q^{35} +(-4.20783 - 4.20783i) q^{37} -7.03227i q^{39} +(-0.681305 + 1.87187i) q^{41} +(4.59445 - 6.56156i) q^{43} +(7.84762 + 15.9927i) q^{45} +(-5.41236 + 0.473520i) q^{47} +(-7.85881 + 4.53728i) q^{49} +(6.78111 + 18.6309i) q^{51} +(-0.560224 - 0.800083i) q^{53} +(5.66787 - 0.609440i) q^{55} +(-10.5667 - 9.83435i) q^{57} +(-0.574552 + 0.482106i) q^{59} +(0.540706 - 3.06649i) q^{61} +(28.9488 + 13.4991i) q^{63} +(3.12375 + 3.57613i) q^{65} +(1.15605 + 13.2137i) q^{67} +(-1.43483 + 2.48519i) q^{69} +(-7.53592 + 1.32879i) q^{71} +(0.911719 + 1.95519i) q^{73} +(-15.2726 - 6.39671i) q^{75} +(7.22746 - 7.22746i) q^{77} +(10.7824 + 3.92446i) q^{79} +(-5.30841 - 30.1055i) q^{81} +(-6.50250 + 1.74234i) q^{83} +(-11.7243 - 6.46225i) q^{85} +(2.94852 + 0.790053i) q^{87} +(-8.47050 + 3.08301i) q^{89} +(8.38447 + 1.47841i) q^{91} +(-12.4319 - 1.08765i) q^{93} +(9.74195 + 0.307330i) q^{95} +(0.658909 + 0.0576470i) q^{97} +(-20.0017 - 3.52685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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