LMFDB - Embedded newform 368.2.s.b.15.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(15,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 17]))

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

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

chi := DirichletCharacter("368.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.s (of order $22$, degree $10$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			15.5
Character	$\chi$	$=$	368.15
Dual form			368.2.s.b.319.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.106877 - 0.0488093i) q^{3} +(-1.32017 + 1.14393i) q^{5} +(-2.88624 - 1.85487i) q^{7} +(-1.95554 + 2.25682i) q^{9} +(0.293255 + 2.03963i) q^{11} +(-3.33277 + 2.14184i) q^{13} +(-0.0852617 + 0.186697i) q^{15} +(0.842757 + 2.87017i) q^{17} +(-2.26214 - 0.664224i) q^{19} +(-0.399009 - 0.0573688i) q^{21} +(0.429086 - 4.77660i) q^{23} +(-0.277311 + 1.92874i) q^{25} +(-0.198156 + 0.674859i) q^{27} +(1.50846 - 0.442925i) q^{29} +(-7.01654 - 3.20435i) q^{31} +(0.130895 + 0.203677i) q^{33} +(5.93217 - 0.852917i) q^{35} +(6.47012 + 5.60639i) q^{37} +(-0.251656 + 0.391585i) q^{39} +(-7.67520 - 8.85765i) q^{41} +(4.27491 + 9.36074i) q^{43} -5.21639i q^{45} +3.80368i q^{47} +(1.98191 + 4.33978i) q^{49} +(0.230163 + 0.265622i) q^{51} +(2.11663 - 3.29354i) q^{53} +(-2.72035 - 2.35720i) q^{55} +(-0.274192 + 0.0394228i) q^{57} +(2.94726 + 4.58603i) q^{59} +(-1.75278 - 0.800468i) q^{61} +(9.83026 - 2.88643i) q^{63} +(1.94970 - 6.64007i) q^{65} +(0.399733 - 2.78020i) q^{67} +(-0.187283 - 0.531454i) q^{69} +(-8.82677 - 1.26910i) q^{71} +(7.48818 + 2.19873i) q^{73} +(0.0645021 + 0.219674i) q^{75} +(2.93686 - 6.43082i) q^{77} +(-2.97137 + 1.90958i) q^{79} +(-1.26318 - 8.78560i) q^{81} +(6.57735 - 7.59066i) q^{83} +(-4.39586 - 2.82505i) q^{85} +(0.139602 - 0.120966i) q^{87} +(7.44478 - 3.39992i) q^{89} +13.5920 q^{91} -0.906312 q^{93} +(3.74623 - 1.71085i) q^{95} +(-0.136456 + 0.118240i) q^{97} +(-5.17655 - 3.32677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{9} + 12 q^{13} + 22 q^{17} + 66 q^{21} + 36 q^{25} + 34 q^{29} + 22 q^{33} + 12 q^{41} - 56 q^{49} - 66 q^{57} - 88 q^{61} - 154 q^{65} - 66 q^{69} - 16 q^{73} - 158 q^{77} - 248 q^{81} - 116 q^{85}+ \cdots - 22 q^{97}+O(q^{100}) $ 80 * q + 4 * q^9 + 12 * q^13 + 22 * q^17 + 66 * q^21 + 36 * q^25 + 34 * q^29 + 22 * q^33 + 12 * q^41 - 56 * q^49 - 66 * q^57 - 88 * q^61 - 154 * q^65 - 66 * q^69 - 16 * q^73 - 158 * q^77 - 248 * q^81 - 116 * q^85 - 88 * q^89 - 84 * q^93 - 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.106877	−	0.0488093i	0.0617057	−	0.0281801i	−0.384323	−	0.923199i	$-0.625565\pi$
$3$	0.106877	−	0.0488093i	0.0617057	−	0.0281801i	0.446029	+	0.895019i	$0.352838\pi$
$4$		0			0
$5$	−1.32017	+	1.14393i	−0.590398	+	0.511582i	−0.898037	−	0.439921i	$-0.855007\pi$
$5$	−1.32017	+	1.14393i	−0.590398	+	0.511582i	0.307639	+	0.951503i	$0.400461\pi$
$6$		0			0
$7$	−2.88624	−	1.85487i	−1.09090	−	0.701076i	−0.133846	−	0.991002i	$-0.542733\pi$
$7$	−2.88624	−	1.85487i	−1.09090	−	0.701076i	−0.957049	+	0.289926i	$0.906369\pi$
$8$		0			0
$9$	−1.95554	+	2.25682i	−0.651847	+	0.752272i
$10$		0			0
$11$	0.293255	+	2.03963i	0.0884197	+	0.614973i	0.985060	+	0.172213i	$0.0550916\pi$
$11$	0.293255	+	2.03963i	0.0884197	+	0.614973i	−0.896640	+	0.442760i	$0.853999\pi$
$12$		0			0
$13$	−3.33277	+	2.14184i	−0.924345	+	0.594041i	−0.913915	−	0.405905i	$-0.866956\pi$
$13$	−3.33277	+	2.14184i	−0.924345	+	0.594041i	−0.0104299	+	0.999946i	$0.503320\pi$
$14$		0			0
$15$	−0.0852617	+	0.186697i	−0.0220145	+	0.0482050i
$16$		0			0
$17$	0.842757	+	2.87017i	0.204399	+	0.696118i	0.996337	+	0.0855166i	$0.0272541\pi$
$17$	0.842757	+	2.87017i	0.204399	+	0.696118i	−0.791938	+	0.610601i	$0.790928\pi$
$18$		0			0
$19$	−2.26214	−	0.664224i	−0.518970	−	0.152383i	0.0117492	−	0.999931i	$-0.496260\pi$
$19$	−2.26214	−	0.664224i	−0.518970	−	0.152383i	−0.530719	+	0.847548i	$0.678078\pi$
$20$		0			0
$21$	−0.399009	−	0.0573688i	−0.0870708	−	0.0125189i
$22$		0			0
$23$	0.429086	−	4.77660i	0.0894706	−	0.995989i
$23$	0.429086	−	4.77660i	0.0894706	−	0.995989i
$24$		0			0
$25$	−0.277311	+	1.92874i	−0.0554621	+	0.385748i
$26$		0			0
$27$	−0.198156	+	0.674859i	−0.0381352	+	0.129877i
$28$		0			0
$29$	1.50846	−	0.442925i	0.280114	−	0.0822490i	−0.138658	−	0.990340i	$-0.544279\pi$
$29$	1.50846	−	0.442925i	0.280114	−	0.0822490i	0.418772	+	0.908091i	$0.362461\pi$
$30$		0			0
$31$	−7.01654	−	3.20435i	−1.26021	−	0.575518i	−0.330497	−	0.943807i	$-0.607216\pi$
$31$	−7.01654	−	3.20435i	−1.26021	−	0.575518i	−0.929711	+	0.368289i	$0.879944\pi$
$32$		0			0
$33$	0.130895	+	0.203677i	0.0227860	+	0.0354557i
$34$		0			0
$35$	5.93217	−	0.852917i	1.00272	−	0.144169i
$36$		0			0
$37$	6.47012	+	5.60639i	1.06368	+	0.921685i	0.997100	−	0.0760963i	$-0.0242456\pi$
$37$	6.47012	+	5.60639i	1.06368	+	0.921685i	0.0665804	+	0.997781i	$0.478791\pi$
$38$		0			0
$39$	−0.251656	+	0.391585i	−0.0402973	+	0.0627038i
$40$		0			0
$41$	−7.67520	−	8.85765i	−1.19866	−	1.38333i	−0.903889	−	0.427767i	$-0.859301\pi$
$41$	−7.67520	−	8.85765i	−1.19866	−	1.38333i	−0.294776	−	0.955567i	$-0.595245\pi$
$42$		0			0
$43$	4.27491	+	9.36074i	0.651917	+	1.42750i	0.889866	+	0.456222i	$0.150798\pi$
$43$	4.27491	+	9.36074i	0.651917	+	1.42750i	−0.237949	+	0.971278i	$0.576475\pi$
$44$		0			0
$45$		−	5.21639i		−	0.777613i
$46$		0			0
$47$			3.80368i			0.554824i	0.960751	+	0.277412i	$0.0894767\pi$
$47$			3.80368i			0.554824i	−0.960751	+	0.277412i	$0.910523\pi$
$48$		0			0
$49$	1.98191	+	4.33978i	0.283130	+	0.619969i
$50$		0			0
$51$	0.230163	+	0.265622i	0.0322292	+	0.0371945i
$52$		0			0
$53$	2.11663	−	3.29354i	0.290741	−	0.452402i	−0.664901	−	0.746931i	$-0.731526\pi$
$53$	2.11663	−	3.29354i	0.290741	−	0.452402i	0.955643	+	0.294529i	$0.0951627\pi$
$54$		0			0
$55$	−2.72035	−	2.35720i	−0.366812	−	0.317844i
$56$		0			0
$57$	−0.274192	+	0.0394228i	−0.0363176	+	0.00522168i
$58$		0			0
$59$	2.94726	+	4.58603i	0.383701	+	0.597050i	0.978355	−	0.206931i	$-0.0663477\pi$
$59$	2.94726	+	4.58603i	0.383701	+	0.597050i	−0.594655	+	0.803981i	$0.702711\pi$
$60$		0			0
$61$	−1.75278	−	0.800468i	−0.224421	−	0.102489i	0.300032	−	0.953929i	$-0.403003\pi$
$61$	−1.75278	−	0.800468i	−0.224421	−	0.102489i	−0.524452	+	0.851440i	$0.675730\pi$
$62$		0			0
$63$	9.83026	−	2.88643i	1.23850	−	0.363655i
$64$		0			0
$65$	1.94970	−	6.64007i	0.241830	−	0.823599i
$66$		0			0
$67$	0.399733	−	2.78020i	0.0488351	−	0.339656i	−0.950726	−	0.310032i	$-0.899660\pi$
$67$	0.399733	−	2.78020i	0.0488351	−	0.339656i	0.999561	−	0.0296233i	$-0.00943078\pi$
$68$		0			0
$69$	−0.187283	−	0.531454i	−0.0225462	−	0.0639795i
$70$		0			0
$71$	−8.82677	−	1.26910i	−1.04755	−	0.150614i	−0.403015	−	0.915193i	$-0.632038\pi$
$71$	−8.82677	−	1.26910i	−1.04755	−	0.150614i	−0.644530	+	0.764579i	$0.722947\pi$
$72$		0			0
$73$	7.48818	+	2.19873i	0.876425	+	0.257342i	0.688846	−	0.724908i	$-0.258118\pi$
$73$	7.48818	+	2.19873i	0.876425	+	0.257342i	0.187579	+	0.982249i	$0.439936\pi$
$74$		0			0
$75$	0.0645021	+	0.219674i	0.00744806	+	0.0253658i
$76$		0			0
$77$	2.93686	−	6.43082i	0.334686	−	0.732860i
$78$		0			0
$79$	−2.97137	+	1.90958i	−0.334305	+	0.214845i	−0.697014	−	0.717058i	$-0.745488\pi$
$79$	−2.97137	+	1.90958i	−0.334305	+	0.214845i	0.362709	+	0.931903i	$0.381852\pi$
$80$		0			0
$81$	−1.26318	−	8.78560i	−0.140353	−	0.976178i
$82$		0			0
$83$	6.57735	−	7.59066i	0.721958	−	0.833184i	−0.269583	−	0.962977i	$-0.586886\pi$
$83$	6.57735	−	7.59066i	0.721958	−	0.833184i	0.991541	+	0.129793i	$0.0414314\pi$
$84$		0			0
$85$	−4.39586	−	2.82505i	−0.476798	−	0.306420i
$86$		0			0
$87$	0.139602	−	0.120966i	0.0149669	−	0.0129689i
$88$		0			0
$89$	7.44478	−	3.39992i	0.789145	−	0.360390i	0.0202741	−	0.999794i	$-0.493546\pi$
$89$	7.44478	−	3.39992i	0.789145	−	0.360390i	0.768871	+	0.639404i	$0.220819\pi$
$90$		0			0
$91$	13.5920			1.42483
$92$		0			0
$93$	−0.906312			−0.0939802
$94$		0			0
$95$	3.74623	−	1.71085i	0.384355	−	0.175529i
$96$		0			0
$97$	−0.136456	+	0.118240i	−0.0138550	+	0.0120054i	−0.661761	−	0.749715i	$-0.730191\pi$
$97$	−0.136456	+	0.118240i	−0.0138550	+	0.0120054i	0.647906	+	0.761721i	$0.275645\pi$
$98$		0			0
$99$	−5.17655	−	3.32677i	−0.520263	−	0.334353i
$100$		0			0
$101$	0.0767173	−	0.0885364i	0.00763365	−	0.00880970i	−0.751920	−	0.659254i	$-0.770872\pi$
$101$	0.0767173	−	0.0885364i	0.00763365	−	0.00880970i	0.759554	+	0.650445i	$0.225417\pi$
$102$		0			0
$103$	2.11055	+	14.6792i	0.207959	+	1.44638i	0.779805	+	0.626023i	$0.215318\pi$
$103$	2.11055	+	14.6792i	0.207959	+	1.44638i	−0.571846	+	0.820361i	$0.693773\pi$
$104$		0			0
$105$	0.592385	−	0.380703i	0.0578108	−	0.0371528i
$106$		0			0
$107$	−6.90224	+	15.1138i	−0.667265	+	1.46111i	0.208329	+	0.978059i	$0.433198\pi$
$107$	−6.90224	+	15.1138i	−0.667265	+	1.46111i	−0.875594	+	0.483048i	$0.839530\pi$
$108$		0			0
$109$	3.28732	+	11.1956i	0.314868	+	1.07234i	0.953140	+	0.302531i	$0.0978315\pi$
$109$	3.28732	+	11.1956i	0.314868	+	1.07234i	−0.638271	+	0.769811i	$0.720350\pi$
$110$		0			0
$111$	0.965154	+	0.283395i	0.0916083	+	0.0268986i
$112$		0			0
$113$	−2.47103	−	0.355281i	−0.232455	−	0.0334220i	0.0251028	−	0.999685i	$-0.492009\pi$
$113$	−2.47103	−	0.355281i	−0.232455	−	0.0334220i	−0.257558	+	0.966263i	$0.582918\pi$
$114$		0			0
$115$	4.89764	+	6.79676i	0.456707	+	0.633801i
$116$		0			0
$117$	1.68363	−	11.7099i	0.155652	−	1.08258i
$118$		0			0
$119$	2.89140	−	9.84719i	0.265054	−	0.902691i
$120$		0			0
$121$	6.48032	−	1.90279i	0.589120	−	0.172981i
$122$		0			0
$123$	−1.25264	−	0.572062i	−0.112947	−	0.0515811i
$124$		0			0
$125$	−6.56230	−	10.2111i	−0.586950	−	0.913312i
$126$		0			0
$127$	−5.88243	+	0.845766i	−0.521981	+	0.0750496i	−0.398269	−	0.917269i	$-0.630389\pi$
$127$	−5.88243	+	0.845766i	−0.521981	+	0.0750496i	−0.123712	+	0.992318i	$0.539480\pi$
$128$		0			0
$129$	0.913782	+	0.791797i	0.0804540	+	0.0697138i
$130$		0			0
$131$	1.89584	−	2.94999i	0.165641	−	0.257742i	−0.748504	−	0.663130i	$-0.769227\pi$
$131$	1.89584	−	2.94999i	0.165641	−	0.257742i	0.914144	+	0.405389i	$0.132864\pi$
$132$		0			0
$133$	5.29702	+	6.11309i	0.459310	+	0.530072i
$134$		0			0
$135$	−0.510393	−	1.11761i	−0.0439277	−	0.0961882i
$136$		0			0
$137$			14.5442i			1.24260i	0.783573	+	0.621299i	$0.213395\pi$
$137$			14.5442i			1.24260i	−0.783573	+	0.621299i	$0.786605\pi$
$138$		0			0
$139$			4.46279i			0.378529i	0.981926	+	0.189265i	$0.0606104\pi$
$139$			4.46279i			0.378529i	−0.981926	+	0.189265i	$0.939390\pi$
$140$		0			0
$141$	0.185655	+	0.406528i	0.0156350	+	0.0342358i
$142$		0			0
$143$	−5.34593	−	6.16953i	−0.447049	−	0.515922i
$144$		0			0
$145$	−1.48475	+	2.31032i	−0.123302	+	0.191861i
$146$		0			0
$147$	0.423643	+	0.367089i	0.0349415	+	0.0302770i
$148$		0			0
$149$	−5.20979	+	0.749055i	−0.426803	+	0.0613650i	−0.352369	−	0.935861i	$-0.614624\pi$
$149$	−5.20979	+	0.749055i	−0.426803	+	0.0613650i	−0.0744334	+	0.997226i	$0.523715\pi$
$150$		0			0
$151$	−8.90169	−	13.8513i	−0.724409	−	1.12720i	−0.986753	−	0.162229i	$-0.948132\pi$
$151$	−8.90169	−	13.8513i	−0.724409	−	1.12720i	0.262344	−	0.964974i	$-0.415505\pi$
$152$		0			0
$153$	−8.12549	−	3.71079i	−0.656907	−	0.299999i
$154$		0			0
$155$	12.9286	−	3.79617i	1.03845	−	0.304916i
$156$		0			0
$157$	−2.26692	+	7.72043i	−0.180920	+	0.616158i	0.818228	+	0.574894i	$0.194957\pi$
$157$	−2.26692	+	7.72043i	−0.180920	+	0.616158i	−0.999148	+	0.0412639i	$0.986862\pi$
$158$		0			0
$159$	0.0654646	−	0.455316i	0.00519168	−	0.0361089i
$160$		0			0
$161$	−10.0984	+	12.9905i	−0.795867	+	1.02379i
$162$		0			0
$163$	−22.2514	−	3.19928i	−1.74287	−	0.250587i	−0.803942	−	0.594707i	$-0.797268\pi$
$163$	−22.2514	−	3.19928i	−1.74287	−	0.250587i	−0.938925	+	0.344121i	$0.888177\pi$
$164$		0			0
$165$	−0.405797	−	0.119153i	−0.0315913	−	0.00927603i
$166$		0			0
$167$	−5.02153	−	17.1018i	−0.388578	−	1.32337i	−0.889125	−	0.457665i	$-0.848686\pi$
$167$	−5.02153	−	17.1018i	−0.388578	−	1.32337i	0.500547	−	0.865710i	$-0.333132\pi$
$168$		0			0
$169$	1.11949	−	2.45135i	0.0861148	−	0.188565i
$170$		0			0
$171$	5.92274	−	3.80631i	0.452923	−	0.291076i
$172$		0			0
$173$	3.18949	+	22.1834i	0.242493	+	1.68657i	0.639527	+	0.768769i	$0.279130\pi$
$173$	3.18949	+	22.1834i	0.242493	+	1.68657i	−0.397034	+	0.917804i	$0.629961\pi$
$174$		0			0
$175$	4.37795	−	5.05242i	0.330942	−	0.381927i
$176$		0			0
$177$	0.538836	+	0.346289i	0.0405014	+	0.0260287i
$178$		0			0
$179$	−17.7381	+	15.3701i	−1.32581	+	1.14882i	−0.348423	+	0.937337i	$0.613283\pi$
$179$	−17.7381	+	15.3701i	−1.32581	+	1.14882i	−0.977382	+	0.211480i	$0.932172\pi$
$180$		0			0
$181$	−21.7001	+	9.91012i	−1.61296	+	0.736614i	−0.998624	−	0.0524324i	$-0.983303\pi$
$181$	−21.7001	+	9.91012i	−1.61296	+	0.736614i	−0.614334	+	0.789046i	$0.710575\pi$
$182$		0			0
$183$	−0.226403			−0.0167362
$184$		0			0
$185$	−14.9550			−1.09951
$186$		0			0
$187$	−5.60695	+	2.56061i	−0.410021	+	0.187250i
$188$		0			0
$189$	1.82370	−	1.58025i	0.132655	−	0.114946i
$190$		0			0
$191$	17.3800	+	11.1694i	1.25757	+	0.808192i	0.987950	−	0.154775i	$-0.0494653\pi$
$191$	17.3800	+	11.1694i	1.25757	+	0.808192i	0.269621	+	0.962967i	$0.413102\pi$
$192$		0			0
$193$	0.929480	−	1.07268i	0.0669055	−	0.0772130i	−0.721310	−	0.692612i	$-0.756460\pi$
$193$	0.929480	−	1.07268i	0.0669055	−	0.0772130i	0.788216	+	0.615399i	$0.211005\pi$
$194$		0			0
$195$	−0.115718	−	0.804837i	−0.00828674	−	0.0576355i
$196$		0			0
$197$	10.5825	−	6.80094i	0.753970	−	0.484547i	−0.106333	−	0.994331i	$-0.533911\pi$
$197$	10.5825	−	6.80094i	0.753970	−	0.484547i	0.860303	+	0.509784i	$0.170275\pi$
$198$		0			0
$199$	−4.46040	+	9.76691i	−0.316189	+	0.692358i	−0.999279	−	0.0379768i	$-0.987909\pi$
$199$	−4.46040	+	9.76691i	−0.316189	+	0.692358i	0.683089	+	0.730335i	$0.260636\pi$
$200$		0			0
$201$	−0.0929772	−	0.316651i	−0.00655811	−	0.0223349i
$202$		0			0
$203$	−5.17535	−	1.51962i	−0.363238	−	0.106656i
$204$		0			0
$205$	20.2651	+	2.91368i	1.41538	+	0.203501i
$206$		0			0
$207$	9.94080	+	10.3092i	0.690934	+	0.716539i
$208$		0			0
$209$	0.691390	−	4.80872i	0.0478244	−	0.332626i
$210$		0			0
$211$	3.22656	−	10.9887i	0.222126	−	0.756491i	−0.770729	−	0.637163i	$-0.780108\pi$
$211$	3.22656	−	10.9887i	0.222126	−	0.756491i	0.992855	−	0.119328i	$-0.0380740\pi$
$212$		0			0
$213$	−1.00533	+	0.295191i	−0.0688838	+	0.0202261i
$214$		0			0
$215$	−16.3517	−	7.46755i	−1.11517	−	0.509283i
$216$		0			0
$217$	14.3078	+	22.2633i	0.971274	+	1.51133i
$218$		0			0
$219$	0.907636	−	0.130498i	0.0613323	−	0.00881826i
$220$		0			0
$221$	−8.95617	−	7.76057i	−0.602457	−	0.522032i
$222$		0			0
$223$	−13.6521	+	21.2431i	−0.914212	+	1.42254i	−0.00788217	+	0.999969i	$0.502509\pi$
$223$	−13.6521	+	21.2431i	−0.914212	+	1.42254i	−0.906329	+	0.422572i	$0.861127\pi$
$224$		0			0
$225$	−3.81051	−	4.39757i	−0.254034	−	0.293171i
$226$		0			0
$227$	−2.36847	−	5.18623i	−0.157201	−	0.344222i	0.814600	−	0.580022i	$-0.196956\pi$
$227$	−2.36847	−	5.18623i	−0.157201	−	0.344222i	−0.971802	+	0.235800i	$0.924229\pi$
$228$		0			0
$229$			13.6778i			0.903852i	0.892055	+	0.451926i	$0.149263\pi$
$229$			13.6778i			0.903852i	−0.892055	+	0.451926i	$0.850737\pi$
$230$		0			0
$231$		−	0.830655i		−	0.0546531i
$232$		0			0
$233$	−2.23268	−	4.88888i	−0.146268	−	0.320281i	0.822291	−	0.569067i	$-0.192696\pi$
$233$	−2.23268	−	4.88888i	−0.146268	−	0.320281i	−0.968558	+	0.248786i	$0.919968\pi$
$234$		0			0
$235$	−4.35115	−	5.02150i	−0.283838	−	0.327567i
$236$		0			0
$237$	−0.224367	+	0.349122i	−0.0145742	+	0.0226779i
$238$		0			0
$239$	19.9940	+	17.3249i	1.29330	+	1.12065i	0.985586	+	0.169175i	$0.0541103\pi$
$239$	19.9940	+	17.3249i	1.29330	+	1.12065i	0.307716	+	0.951478i	$0.400435\pi$
$240$		0			0
$241$	−20.8629	+	2.99963i	−1.34390	+	0.193223i	−0.776445	−	0.630185i	$-0.782979\pi$
$241$	−20.8629	+	2.99963i	−1.34390	+	0.193223i	−0.567450	+	0.823408i	$0.692070\pi$
$242$		0			0
$243$	−1.70460	−	2.65241i	−0.109350	−	0.170152i
$244$		0			0
$245$	−7.58088	−	3.46207i	−0.484324	−	0.221184i
$246$		0			0
$247$	8.96186	−	2.63144i	0.570229	−	0.167434i
$248$		0			0
$249$	0.332475	−	1.13231i	0.0210698	−	0.0717570i
$250$		0			0
$251$	3.92078	−	27.2696i	0.247478	−	1.72124i	−0.365215	−	0.930923i	$-0.619004\pi$
$251$	3.92078	−	27.2696i	0.247478	−	1.72124i	0.612692	−	0.790321i	$-0.290086\pi$
$252$		0			0
$253$	9.86834	−	0.525584i	0.620417	−	0.0330432i
$254$		0			0
$255$	−0.607707	−	0.0873751i	−0.0380561	−	0.00547164i
$256$		0			0
$257$	6.46197	+	1.89741i	0.403087	+	0.118357i	0.476991	−	0.878908i	$-0.341728\pi$
$257$	6.46197	+	1.89741i	0.403087	+	0.118357i	−0.0739038	+	0.997265i	$0.523546\pi$
$258$		0			0
$259$	−8.27516	−	28.1826i	−0.514194	−	1.75118i
$260$		0			0
$261$	−1.95026	+	4.27048i	−0.120718	+	0.264336i
$262$		0			0
$263$	1.97785	−	1.27109i	0.121960	−	0.0783787i	−0.478239	−	0.878230i	$-0.658725\pi$
$263$	1.97785	−	1.27109i	0.121960	−	0.0783787i	0.600198	+	0.799851i	$0.295088\pi$
$264$		0			0
$265$	0.973280	+	6.76931i	0.0597881	+	0.415835i
$266$		0			0
$267$	0.629731	−	0.726749i	0.0385389	−	0.0444763i
$268$		0			0
$269$	−7.41974	−	4.76838i	−0.452390	−	0.290733i	0.294536	−	0.955640i	$-0.404835\pi$
$269$	−7.41974	−	4.76838i	−0.452390	−	0.290733i	−0.746926	+	0.664907i	$0.768471\pi$
$270$		0			0
$271$	−6.14891	+	5.32806i	−0.373520	+	0.323657i	−0.821310	−	0.570482i	$-0.806757\pi$
$271$	−6.14891	+	5.32806i	−0.373520	+	0.323657i	0.447790	+	0.894139i	$0.352211\pi$
$272$		0			0
$273$	1.45268	−	0.663417i	0.0879202	−	0.0401518i
$274$		0			0
$275$	−4.01524			−0.242128
$276$		0			0
$277$	0.0850459			0.00510991			0.00255496	−	0.999997i	$-0.499187\pi$
$277$	0.0850459			0.00510991			0.00255496	+	0.999997i	$0.499187\pi$
$278$		0			0
$279$	20.9528	−	9.56881i	1.25441	−	0.572870i
$280$		0			0
$281$	13.7750	−	11.9361i	0.821748	−	0.712049i	−0.138752	−	0.990327i	$-0.544309\pi$
$281$	13.7750	−	11.9361i	0.821748	−	0.712049i	0.960501	+	0.278278i	$0.0897637\pi$
$282$		0			0
$283$	−16.5423	−	10.6311i	−0.983341	−	0.631955i	−0.0529781	−	0.998596i	$-0.516871\pi$
$283$	−16.5423	−	10.6311i	−0.983341	−	0.631955i	−0.930362	+	0.366641i	$0.880508\pi$
$284$		0			0
$285$	0.316882	−	0.365702i	0.0187705	−	0.0216623i
$286$		0			0
$287$	5.72264	+	39.8018i	0.337797	+	2.34943i
$288$		0			0
$289$	6.77368	−	4.35318i	0.398452	−	0.256070i
$290$		0			0
$291$	−0.00881286	+	0.0192975i	−0.000516619	+	0.00113124i
$292$		0			0
$293$	−2.95593	−	10.0670i	−0.172687	−	0.588118i	−0.999665	−	0.0258837i	$-0.991760\pi$
$293$	−2.95593	−	10.0670i	−0.172687	−	0.588118i	0.826978	−	0.562234i	$-0.190058\pi$
$294$		0			0
$295$	−9.13699	−	2.68286i	−0.531976	−	0.156202i
$296$		0			0
$297$	−1.43458	−	0.206261i	−0.0832425	−	0.0119685i
$298$		0			0
$299$	8.80068	+	16.8384i	0.508956	+	0.973787i
$300$		0			0
$301$	5.02458	−	34.9467i	0.289612	−	2.01430i
$302$		0			0
$303$	0.00387794	−	0.0132071i	0.000222782	−	0.000758726i
$304$		0			0
$305$	3.22965	−	0.948310i	0.184929	−	0.0543001i
$306$		0			0
$307$	3.16545	+	1.44561i	0.180662	+	0.0825056i	0.503693	−	0.863883i	$-0.331974\pi$
$307$	3.16545	+	1.44561i	0.180662	+	0.0825056i	−0.323031	+	0.946389i	$0.604702\pi$
$308$		0			0
$309$	0.942051	+	1.46586i	0.0535914	+	0.0833899i
$310$		0			0
$311$	23.9759	−	3.44721i	1.35955	−	0.195473i	0.576328	−	0.817219i	$-0.304485\pi$
$311$	23.9759	−	3.44721i	1.35955	−	0.195473i	0.783219	+	0.621745i	$0.213576\pi$
$312$		0			0
$313$	0.954438	+	0.827025i	0.0539480	+	0.0467462i	0.681417	−	0.731895i	$-0.261364\pi$
$313$	0.954438	+	0.827025i	0.0539480	+	0.0467462i	−0.627469	+	0.778641i	$0.715909\pi$
$314$		0			0
$315$	−9.67573	+	15.0557i	−0.545166	+	0.848294i
$316$		0			0
$317$	15.7072	+	18.1271i	0.882205	+	1.01812i	0.999686	+	0.0250439i	$0.00797257\pi$
$317$	15.7072	+	18.1271i	0.882205	+	1.01812i	−0.117481	+	0.993075i	$0.537482\pi$
$318$		0			0
$319$	1.34577	+	2.94682i	0.0753486	+	0.164990i
$320$		0			0
$321$			1.95222i			0.108962i
$322$		0			0
$323$		−	7.05250i		−	0.392411i
$324$		0			0
$325$	−3.20684	−	7.02200i	−0.177884	−	0.389511i
$326$		0			0
$327$	0.897789	+	1.03610i	0.0496478	+	0.0572966i
$328$		0			0
$329$	7.05534	−	10.9783i	0.388974	−	0.605255i
$330$		0			0
$331$	23.1969	+	20.1002i	1.27501	+	1.10481i	0.989208	+	0.146520i	$0.0468071\pi$
$331$	23.1969	+	20.1002i	1.27501	+	1.10481i	0.285807	+	0.958287i	$0.407738\pi$
$332$		0			0
$333$	−25.3052	+	3.63833i	−1.38671	+	0.199380i
$334$		0			0
$335$	2.65265	+	4.12760i	0.144930	+	0.225515i
$336$		0			0
$337$	2.98910	+	1.36508i	0.162827	+	0.0743605i	0.495161	−	0.868801i	$-0.335109\pi$
$337$	2.98910	+	1.36508i	0.162827	+	0.0743605i	−0.332334	+	0.943162i	$0.607836\pi$
$338$		0			0
$339$	−0.281438	+	0.0826378i	−0.0152856	+	0.00448827i
$340$		0			0
$341$	4.47806	−	15.2509i	0.242501	−	0.825881i
$342$		0			0
$343$	−1.08838	+	7.56986i	−0.0587671	+	0.408734i
$344$		0			0
$345$	0.855192	+	0.487370i	0.0460420	+	0.0262391i
$346$		0			0
$347$	−16.8716	−	2.42577i	−0.905713	−	0.130222i	−0.326310	−	0.945263i	$-0.605805\pi$
$347$	−16.8716	−	2.42577i	−0.905713	−	0.130222i	−0.579403	+	0.815041i	$0.696714\pi$
$348$		0			0
$349$	−13.3777	−	3.92804i	−0.716090	−	0.210263i	−0.0966630	−	0.995317i	$-0.530817\pi$
$349$	−13.3777	−	3.92804i	−0.716090	−	0.210263i	−0.619427	+	0.785054i	$0.712635\pi$
$350$		0			0
$351$	−0.785032	−	2.67357i	−0.0419019	−	0.142705i
$352$		0			0
$353$	12.7876	−	28.0010i	0.680616	−	1.49034i	−0.181373	−	0.983414i	$-0.558054\pi$
$353$	12.7876	−	28.0010i	0.680616	−	1.49034i	0.861989	−	0.506927i	$-0.169219\pi$
$354$		0			0
$355$	13.1046	−	8.42181i	0.695520	−	0.446983i
$356$		0			0
$357$	−0.171609	−	1.19357i	−0.00908254	−	0.0631704i
$358$		0			0
$359$	13.3442	−	15.4001i	0.704282	−	0.812784i	−0.285043	−	0.958515i	$-0.592008\pi$
$359$	13.3442	−	15.4001i	0.704282	−	0.812784i	0.989324	+	0.145731i	$0.0465533\pi$
$360$		0			0
$361$	−11.3077	−	7.26704i	−0.595144	−	0.382476i
$362$		0			0
$363$	0.599726	−	0.519665i	0.0314774	−	0.0272753i
$364$		0			0
$365$	−12.4009	+	5.66328i	−0.649091	+	0.296430i
$366$		0			0
$367$	12.9167			0.674247			0.337124	−	0.941460i	$-0.390546\pi$
$367$	12.9167			0.674247			0.337124	+	0.941460i	$0.390546\pi$
$368$		0			0
$369$	34.9993			1.82199
$370$		0			0
$371$	−12.2182	+	5.57986i	−0.634337	+	0.289692i
$372$		0			0
$373$	16.0991	−	13.9499i	0.833579	−	0.722300i	−0.129483	−	0.991582i	$-0.541332\pi$
$373$	16.0991	−	13.9499i	0.833579	−	0.722300i	0.963062	+	0.269281i	$0.0867862\pi$
$374$		0			0
$375$	−1.19976	−	0.771039i	−0.0619553	−	0.0398163i
$376$		0			0
$377$	−4.07869	+	4.70706i	−0.210063	+	0.242426i
$378$		0			0
$379$	3.11878	+	21.6916i	0.160201	+	1.11422i	0.898253	+	0.439479i	$0.144837\pi$
$379$	3.11878	+	21.6916i	0.160201	+	1.11422i	−0.738051	+	0.674744i	$0.764254\pi$
$380$		0			0
$381$	−0.587418	+	0.377511i	−0.0300943	+	0.0193405i
$382$		0			0
$383$	4.48093	−	9.81186i	0.228965	−	0.501363i	−0.759926	−	0.650010i	$-0.774765\pi$
$383$	4.48093	−	9.81186i	0.228965	−	0.501363i	0.988890	+	0.148647i	$0.0474920\pi$
$384$		0			0
$385$	3.47928	+	11.8493i	0.177320	+	0.603898i
$386$		0			0
$387$	−29.4852	−	8.65764i	−1.49882	−	0.440093i
$388$		0			0
$389$	26.1130	+	3.75449i	1.32398	+	0.190360i	0.767795	−	0.640696i	$-0.221354\pi$
$389$	26.1130	+	3.75449i	1.32398	+	0.190360i	0.556189	+	0.831056i	$0.312263\pi$
$390$		0			0
$391$	14.0713	−	2.79397i	0.711614	−	0.141297i
$392$		0			0
$393$	0.0586359	−	0.407822i	0.00295779	−	0.0205719i
$394$		0			0
$395$	1.73827	−	5.92002i	0.0874620	−	0.297868i
$396$		0			0
$397$	33.1789	−	9.74221i	1.66520	−	0.488947i	0.692580	−	0.721341i	$-0.256474\pi$
$397$	33.1789	−	9.74221i	1.66520	−	0.488947i	0.972622	+	0.232394i	$0.0746558\pi$
$398$		0			0
$399$	0.864507	+	0.394807i	0.0432795	+	0.0197651i
$400$		0			0
$401$	−7.97618	−	12.4112i	−0.398311	−	0.619784i	0.582941	−	0.812515i	$-0.301902\pi$
$401$	−7.97618	−	12.4112i	−0.398311	−	0.619784i	−0.981252	+	0.192731i	$0.938266\pi$
$402$		0			0
$403$	30.2478	−	4.34897i	1.50675	−	0.216638i
$404$		0			0
$405$	11.7177	+	10.1535i	0.582260	+	0.504531i
$406$		0			0
$407$	−9.53759	+	14.8408i	−0.472761	+	0.735630i
$408$		0			0
$409$	−22.8572	−	26.3786i	−1.13022	−	1.30434i	−0.946988	−	0.321268i	$-0.895891\pi$
$409$	−22.8572	−	26.3786i	−1.13022	−	1.30434i	−0.183228	−	0.983071i	$-0.558655\pi$
$410$		0			0
$411$	0.709894	+	1.55445i	0.0350165	+	0.0766754i
$412$		0			0
$413$		−	18.7032i		−	0.920322i
$414$		0			0
$415$			17.5450i			0.861250i
$416$		0			0
$417$	0.217826	+	0.476972i	0.0106670	+	0.0233574i
$418$		0			0
$419$	−25.0836	−	28.9481i	−1.22542	−	1.41421i	−0.879472	−	0.475950i	$-0.842104\pi$
$419$	−25.0836	−	28.9481i	−1.22542	−	1.41421i	−0.345944	−	0.938255i	$-0.612441\pi$
$420$		0			0
$421$	−6.85029	+	10.6593i	−0.333863	+	0.519501i	−0.967080	−	0.254474i	$-0.918098\pi$
$421$	−6.85029	+	10.6593i	−0.333863	+	0.519501i	0.633217	+	0.773974i	$0.281734\pi$
$422$		0			0
$423$	−8.58420	−	7.43826i	−0.417378	−	0.361660i
$424$		0			0
$425$	−5.76951	+	0.829530i	−0.279862	+	0.0402381i
$426$		0			0
$427$	3.57417	+	5.56152i	0.172966	+	0.269141i
$428$		0			0
$429$	−0.872490	−	0.398453i	−0.0421242	−	0.0192375i
$430$		0			0
$431$	19.3748	−	5.68896i	0.933252	−	0.274028i	0.220455	−	0.975397i	$-0.429246\pi$
$431$	19.3748	−	5.68896i	0.933252	−	0.274028i	0.712798	+	0.701370i	$0.247428\pi$
$432$		0			0
$433$	−5.17013	+	17.6078i	−0.248460	+	0.846178i	0.736945	+	0.675953i	$0.236268\pi$
$433$	−5.17013	+	17.6078i	−0.248460	+	0.846178i	−0.985405	+	0.170225i	$0.945550\pi$
$434$		0			0
$435$	−0.0459214	+	0.319390i	−0.00220176	+	0.0153136i
$436$		0			0
$437$	−4.14338	+	10.5203i	−0.198205	+	0.503255i
$438$		0			0
$439$	−17.7035	−	2.54538i	−0.844941	−	0.121484i	−0.293769	−	0.955876i	$-0.594910\pi$
$439$	−17.7035	−	2.54538i	−0.844941	−	0.121484i	−0.551171	+	0.834392i	$0.685819\pi$
$440$		0			0
$441$	−13.6698	−	4.01381i	−0.650943	−	0.191134i
$442$		0			0
$443$	3.42704	+	11.6714i	0.162824	+	0.554527i	0.999971	+	0.00754993i	$0.00240324\pi$
$443$	3.42704	+	11.6714i	0.162824	+	0.554527i	−0.837148	+	0.546977i	$0.815779\pi$
$444$		0			0
$445$	−5.93909	+	13.0048i	−0.281540	+	0.616486i
$446$		0			0
$447$	−0.520248	+	0.334343i	−0.0246069	+	0.0158139i
$448$		0			0
$449$	3.57335	+	24.8532i	0.168637	+	1.17290i	0.881705	+	0.471801i	$0.156396\pi$
$449$	3.57335	+	24.8532i	0.168637	+	1.17290i	−0.713068	+	0.701095i	$0.752695\pi$
$450$		0			0
$451$	15.8156	−	18.2521i	0.744726	−	0.859460i
$452$		0			0
$453$	−1.62746	−	1.04591i	−0.0764648	−	0.0491410i
$454$		0			0
$455$	−17.9438	+	15.5484i	−0.841217	+	0.728919i
$456$		0			0
$457$	12.6576	−	5.78055i	0.592100	−	0.270403i	−0.0967481	−	0.995309i	$-0.530844\pi$
$457$	12.6576	−	5.78055i	0.592100	−	0.270403i	0.688848	+	0.724906i	$0.258117\pi$
$458$		0			0
$459$	−2.10396			−0.0982043
$460$		0			0
$461$	−36.7453			−1.71140			−0.855701	−	0.517471i	$-0.826874\pi$
$461$	−36.7453			−1.71140			−0.855701	+	0.517471i	$0.826874\pi$
$462$		0			0
$463$	−10.6743	+	4.87477i	−0.496075	+	0.226550i	−0.647710	−	0.761887i	$-0.724273\pi$
$463$	−10.6743	+	4.87477i	−0.496075	+	0.226550i	0.151635	+	0.988436i	$0.451546\pi$
$464$		0			0
$465$	1.19649	−	1.03676i	0.0554857	−	0.0480786i
$466$		0			0
$467$	10.2099	+	6.56148i	0.472456	+	0.303629i	0.755116	−	0.655591i	$-0.227580\pi$
$467$	10.2099	+	6.56148i	0.472456	+	0.303629i	−0.282660	+	0.959220i	$0.591217\pi$
$468$		0			0
$469$	−6.31064	+	7.28287i	−0.291398	+	0.336292i
$470$		0			0
$471$	0.134546	+	0.935787i	0.00619955	+	0.0431188i
$472$		0			0
$473$	−17.8388	+	11.4643i	−0.820231	+	0.527130i
$474$		0			0
$475$	1.90843	−	4.17888i	0.0875647	−	0.191740i
$476$		0			0
$477$	3.29375	+	11.2175i	0.150811	+	0.513614i
$478$		0			0
$479$	15.0197	+	4.41019i	0.686269	+	0.201507i	0.606235	−	0.795285i	$-0.292679\pi$
$479$	15.0197	+	4.41019i	0.686269	+	0.201507i	0.0800338	+	0.996792i	$0.474497\pi$
$480$		0			0
$481$	−33.5715	−	4.82685i	−1.53073	−	0.220085i
$482$		0			0
$483$	−0.445237	+	1.88129i	−0.0202590	+	0.0856016i
$484$		0			0
$485$	0.0448866	−	0.312193i	0.00203819	−	0.0141759i
$486$		0			0
$487$	0.234925	−	0.800081i	0.0106455	−	0.0362551i	−0.953999	−	0.299810i	$-0.903077\pi$
$487$	0.234925	−	0.800081i	0.0106455	−	0.0362551i	0.964644	+	0.263555i	$0.0848949\pi$
$488$		0			0
$489$	−2.53433	+	0.744147i	−0.114606	+	0.0336515i
$490$		0			0
$491$	−25.1086	−	11.4667i	−1.13314	−	0.517486i	−0.241573	−	0.970383i	$-0.577663\pi$
$491$	−25.1086	−	11.4667i	−1.13314	−	0.517486i	−0.891563	+	0.452897i	$0.850391\pi$
$492$		0			0
$493$	2.54254	+	3.95626i	0.114510	+	0.178181i
$494$		0			0
$495$	10.6395	−	1.52973i	0.478211	−	0.0687563i
$496$		0			0
$497$	23.1221	+	20.0355i	1.03717	+	0.898713i
$498$		0			0
$499$	−20.0953	+	31.2689i	−0.899588	+	1.39979i	0.0169575	+	0.999856i	$0.494602\pi$
$499$	−20.0953	+	31.2689i	−0.899588	+	1.39979i	−0.916546	+	0.399930i	$0.869034\pi$
$500$		0			0
$501$	−1.37141	−	1.58270i	−0.0612703	−	0.0707096i
$502$		0			0
$503$	3.39112	+	7.42551i	0.151202	+	0.331087i	0.970043	−	0.242934i	$-0.0781099\pi$
$503$	3.39112	+	7.42551i	0.151202	+	0.331087i	−0.818840	+	0.574021i	$0.805383\pi$
$504$		0			0
$505$			0.204642i			0.00910647i
$506$		0			0
$507$		−	0.316635i		−	0.0140623i
$508$		0			0
$509$	7.92945	+	17.3631i	0.351467	+	0.769604i	0.999965	+	0.00838826i	$0.00267010\pi$
$509$	7.92945	+	17.3631i	0.351467	+	0.769604i	−0.648498	+	0.761216i	$0.724603\pi$
$510$		0			0
$511$	−17.5343	−	20.2357i	−0.775672	−	0.895173i
$512$		0			0
$513$	0.896515	−	1.39500i	0.0395821	−	0.0615909i
$514$		0			0
$515$	−19.5783	−	16.9647i	−0.862723	−	0.747553i
$516$		0			0
$517$	−7.75811	+	1.11545i	−0.341201	+	0.0490574i
$518$		0			0
$519$	1.42364	+	2.21523i	0.0624909	+	0.0972377i
$520$		0			0
$521$	13.5591	+	6.19221i	0.594033	+	0.271286i	0.689662	−	0.724131i	$-0.257759\pi$
$521$	13.5591	+	6.19221i	0.594033	+	0.271286i	−0.0956292	+	0.995417i	$0.530486\pi$
$522$		0			0
$523$	27.5519	−	8.08998i	1.20476	−	0.353750i	0.383090	−	0.923711i	$-0.374860\pi$
$523$	27.5519	−	8.08998i	1.20476	−	0.353750i	0.821672	+	0.569961i	$0.193042\pi$
$524$		0			0
$525$	0.221299	−	0.753674i	0.00965827	−	0.0328930i
$526$		0			0
$527$	3.28377	−	22.8392i	0.143043	−	0.994889i
$528$		0			0
$529$	−22.6318	−	4.09914i	−0.983990	−	0.178223i
$530$		0			0
$531$	−16.1133	−	2.31674i	−0.699258	−	0.100538i
$532$		0			0
$533$	44.5514	+	13.0815i	1.92974	+	0.566622i
$534$		0			0
$535$	−8.17705	−	27.8485i	−0.353525	−	1.20399i
$536$		0			0
$537$	−1.14559	+	2.50850i	−0.0494361	+	0.108250i
$538$		0			0
$539$	−8.27036	+	5.31504i	−0.356229	+	0.228935i
$540$		0			0
$541$	−2.99096	−	20.8026i	−0.128592	−	0.894374i	−0.947342	−	0.320224i	$-0.896242\pi$
$541$	−2.99096	−	20.8026i	−0.128592	−	0.894374i	0.818750	−	0.574150i	$-0.194667\pi$
$542$		0			0
$543$	−1.83555	+	2.11834i	−0.0787710	+	0.0909065i
$544$		0			0
$545$	−17.1468	−	11.0196i	−0.734489	−	0.472027i
$546$		0			0
$547$	19.7118	−	17.0804i	0.842818	−	0.730306i	−0.122196	−	0.992506i	$-0.538994\pi$
$547$	19.7118	−	17.0804i	0.842818	−	0.730306i	0.965013	+	0.262200i	$0.0844481\pi$
$548$		0			0
$549$	5.23414	−	2.39035i	0.223388	−	0.102018i
$550$		0			0
$551$	−3.70655			−0.157904
$552$		0			0
$553$	12.1181			0.515314
$554$		0			0
$555$	−1.59835	+	0.729942i	−0.0678462	+	0.0309843i
$556$		0			0
$557$	−7.58689	+	6.57408i	−0.321467	+	0.278553i	−0.800612	−	0.599183i	$-0.795492\pi$
$557$	−7.58689	+	6.57408i	−0.321467	+	0.278553i	0.479145	+	0.877736i	$0.340947\pi$
$558$		0			0
$559$	−34.2965	−	22.0410i	−1.45059	−	0.932237i
$560$		0			0
$561$	−0.474275	+	0.547342i	−0.0200239	+	0.0231088i
$562$		0			0
$563$	3.73863	+	26.0027i	0.157564	+	1.09588i	0.903104	+	0.429423i	$0.141283\pi$
$563$	3.73863	+	26.0027i	0.157564	+	1.09588i	−0.745539	+	0.666462i	$0.767808\pi$
$564$		0			0
$565$	3.66860	−	2.35766i	0.154339	−	0.0991876i
$566$		0			0
$567$	−12.6503	+	27.7004i	−0.531264	+	1.16331i
$568$		0			0
$569$	12.9112	+	43.9715i	0.541266	+	1.84338i	0.537303	+	0.843389i	$0.319443\pi$
$569$	12.9112	+	43.9715i	0.541266	+	1.84338i	0.00396223	+	0.999992i	$0.498739\pi$
$570$		0			0
$571$	11.4841	+	3.37204i	0.480595	+	0.141115i	0.513052	−	0.858358i	$-0.328515\pi$
$571$	11.4841	+	3.37204i	0.480595	+	0.141115i	−0.0324565	+	0.999473i	$0.510333\pi$
$572$		0			0
$573$	2.40270	+	0.345456i	0.100374	+	0.0144316i
$574$		0			0
$575$	9.09381	+	2.15219i	0.379238	+	0.0897527i
$576$		0			0
$577$	−3.29784	+	22.9369i	−0.137291	+	0.954878i	0.798418	+	0.602104i	$0.205671\pi$
$577$	−3.29784	+	22.9369i	−0.137291	+	0.954878i	−0.935709	+	0.352774i	$0.885238\pi$
$578$		0			0
$579$	0.0469838	−	0.160012i	0.00195258	−	0.00664988i
$580$		0			0
$581$	−33.0635	+	9.70832i	−1.37171	+	0.402769i
$582$		0			0
$583$	7.33833	+	3.35130i	0.303922	+	0.138797i
$584$		0			0
$585$	11.1727	+	17.3850i	0.461934	+	0.718783i
$586$		0			0
$587$	−11.2753	+	1.62114i	−0.465381	+	0.0669117i	−0.371017	−	0.928626i	$-0.620991\pi$
$587$	−11.2753	+	1.62114i	−0.465381	+	0.0669117i	−0.0943641	+	0.995538i	$0.530082\pi$
$588$		0			0
$589$	13.7440	+	11.9092i	0.566311	+	0.490712i
$590$		0			0
$591$	0.799078	−	1.24339i	0.0328697	−	0.0511462i
$592$		0			0
$593$	−3.92550	−	4.53027i	−0.161201	−	0.186036i	0.669403	−	0.742900i	$-0.266550\pi$
$593$	−3.92550	−	4.53027i	−0.161201	−	0.186036i	−0.830604	+	0.556864i	$0.812005\pi$
$594$		0			0
$595$	7.44740	+	16.3075i	0.305314	+	0.668543i
$596$		0			0
$597$			1.26157i			0.0516327i
$598$		0			0
$599$		−	8.44243i		−	0.344948i	−0.985014	−	0.172474i	$-0.944824\pi$
$599$		−	8.44243i		−	0.344948i	0.985014	−	0.172474i	$-0.0551761\pi$
$600$		0			0
$601$	−7.27392	−	15.9277i	−0.296709	−	0.649703i	0.701293	−	0.712873i	$-0.252606\pi$
$601$	−7.27392	−	15.9277i	−0.296709	−	0.649703i	−0.998003	+	0.0631699i	$0.979879\pi$
$602$		0			0
$603$	5.49271	+	6.33892i	0.223680	+	0.258141i
$604$		0			0
$605$	−6.37844	+	9.92505i	−0.259321	+	0.403511i
$606$		0			0
$607$	−5.93429	−	5.14209i	−0.240865	−	0.208711i	0.526060	−	0.850448i	$-0.323669\pi$
$607$	−5.93429	−	5.14209i	−0.240865	−	0.208711i	−0.766925	+	0.641737i	$0.778214\pi$
$608$		0			0
$609$	−0.627300	+	0.0901921i	−0.0254195	+	0.00365477i
$610$		0			0
$611$	−8.14689	−	12.6768i	−0.329588	−	0.512849i
$612$		0			0
$613$	−41.3412	−	18.8799i	−1.66975	−	0.762551i	−0.999797	−	0.0201509i	$-0.993585\pi$
$613$	−41.3412	−	18.8799i	−1.66975	−	0.762551i	−0.669957	−	0.742400i	$-0.733687\pi$
$614$		0			0
$615$	2.30810	−	0.677719i	0.0930715	−	0.0273283i
$616$		0			0
$617$	8.52953	−	29.0489i	0.343386	−	1.16947i	−0.589040	−	0.808104i	$-0.700494\pi$
$617$	8.52953	−	29.0489i	0.343386	−	1.16947i	0.932426	−	0.361362i	$-0.117688\pi$
$618$		0			0
$619$	−1.27237	+	8.84949i	−0.0511407	+	0.355691i	0.948143	+	0.317844i	$0.102959\pi$
$619$	−1.27237	+	8.84949i	−0.0511407	+	0.355691i	−0.999284	+	0.0378468i	$0.987950\pi$
$620$		0			0
$621$	3.13850	+	1.23609i	0.125944	+	0.0496024i
$622$		0			0
$623$	−27.7938	−	3.99615i	−1.11354	−	0.160102i
$624$		0			0
$625$	10.9960	+	3.22872i	0.439840	+	0.129149i
$626$		0			0
$627$	−0.160816	−	0.547690i	−0.00642238	−	0.0218726i
$628$		0			0
$629$	−10.6385	+	23.2952i	−0.424186	+	0.928839i
$630$		0			0
$631$	−13.2886	+	8.54007i	−0.529011	+	0.339975i	−0.777728	−	0.628601i	$-0.783628\pi$
$631$	−13.2886	+	8.54007i	−0.529011	+	0.339975i	0.248716	+	0.968576i	$0.419991\pi$
$632$		0			0
$633$	−0.191502	−	1.33193i	−0.00761152	−	0.0529393i
$634$		0			0
$635$	6.79830	−	7.84566i	0.269782	−	0.311346i
$636$		0			0
$637$	−15.9004	−	10.2186i	−0.629996	−	0.404874i
$638$		0			0
$639$	20.1252	−	17.4386i	0.796142	−	0.689861i
$640$		0			0
$641$	12.0461	−	5.50126i	0.475791	−	0.217287i	−0.163061	−	0.986616i	$-0.552137\pi$
$641$	12.0461	−	5.50126i	0.475791	−	0.217287i	0.638852	+	0.769329i	$0.279409\pi$
$642$		0			0
$643$	34.1878			1.34824			0.674119	−	0.738623i	$-0.264524\pi$
$643$	34.1878			1.34824			0.674119	+	0.738623i	$0.264524\pi$
$644$		0			0
$645$	−2.11211			−0.0831642
$646$		0			0
$647$	−18.0980	+	8.26507i	−0.711505	+	0.324933i	−0.738080	−	0.674713i	$-0.764267\pi$
$647$	−18.0980	+	8.26507i	−0.711505	+	0.324933i	0.0265749	+	0.999647i	$0.491540\pi$
$648$		0			0
$649$	−8.48951	+	7.35621i	−0.333243	+	0.288756i
$650$		0			0
$651$	2.61583	+	1.68109i	0.102523	+	0.0658872i
$652$		0			0
$653$	−23.0306	+	26.5787i	−0.901257	+	1.04011i	0.0977351	+	0.995212i	$0.468840\pi$
$653$	−23.0306	+	26.5787i	−0.901257	+	1.04011i	−0.998992	+	0.0448932i	$0.985705\pi$
$654$		0			0
$655$	0.871756	+	6.06320i	0.0340623	+	0.236909i
$656$		0			0
$657$	−19.6056	+	12.5997i	−0.764886	+	0.491562i
$658$		0			0
$659$	−14.8013	+	32.4104i	−0.576578	+	1.26253i	0.366642	+	0.930362i	$0.380507\pi$
$659$	−14.8013	+	32.4104i	−0.576578	+	1.26253i	−0.943220	+	0.332168i	$0.892220\pi$
$660$		0			0
$661$	−2.85669	−	9.72901i	−0.111113	−	0.378415i	0.885096	−	0.465408i	$-0.154092\pi$
$661$	−2.85669	−	9.72901i	−0.111113	−	0.378415i	−0.996209	+	0.0869932i	$0.972274\pi$
$662$		0			0
$663$	−1.33600	−	0.392285i	−0.0518860	−	0.0152351i
$664$		0			0
$665$	−13.9859	−	2.01087i	−0.542351	−	0.0779783i
$666$		0			0
$667$	−1.46841	−	7.39537i	−0.0568572	−	0.286350i
$668$		0			0
$669$	−0.422241	+	2.93675i	−0.0163248	+	0.113541i
$670$		0			0
$671$	1.11865	−	3.80977i	0.0431850	−	0.147075i
$672$		0			0
$673$	32.3571	−	9.50091i	1.24728	−	0.366233i	0.409531	−	0.912296i	$-0.365692\pi$
$673$	32.3571	−	9.50091i	1.24728	−	0.366233i	0.837744	+	0.546063i	$0.183874\pi$
$674$		0			0
$675$	−1.24667	−	0.569337i	−0.0479845	−	0.0219138i
$676$		0			0
$677$	−10.6410	−	16.5578i	−0.408969	−	0.636368i	0.574275	−	0.818662i	$-0.305284\pi$
$677$	−10.6410	−	16.5578i	−0.408969	−	0.636368i	−0.983244	+	0.182295i	$0.941648\pi$
$678$		0			0
$679$	0.613164	−	0.0881596i	0.0235311	−	0.00338326i
$680$		0			0
$681$	−0.506273	−	0.438688i	−0.0194004	−	0.0168106i
$682$		0			0
$683$	15.7767	−	24.5490i	0.603678	−	0.939342i	−0.396099	−	0.918208i	$-0.629636\pi$
$683$	15.7767	−	24.5490i	0.603678	−	0.939342i	0.999777	−	0.0211335i	$-0.00672751\pi$
$684$		0			0
$685$	−16.6376	−	19.2009i	−0.635692	−	0.733627i
$686$		0			0
$687$	0.667602	+	1.46184i	0.0254706	+	0.0557728i
$688$		0			0
$689$			15.5101i			0.590888i
$690$		0			0
$691$		−	3.82254i		−	0.145416i	−0.997353	−	0.0727082i	$-0.976836\pi$
$691$		−	3.82254i		−	0.145416i	0.997353	−	0.0727082i	$-0.0231642\pi$
$692$		0			0
$693$	8.77002	+	19.2037i	0.333146	+	0.729487i
$694$		0			0
$695$	−5.10514	−	5.89164i	−0.193649	−	0.223483i
$696$		0			0
$697$	18.9546	−	29.4940i	0.717958	−	1.11716i
$698$		0			0
$699$	−0.477245	−	0.413536i	−0.0180511	−	0.0156414i
$700$		0			0
$701$	41.0831	−	5.90686i	1.55169	−	0.223099i	0.687469	−	0.726214i	$-0.258722\pi$
$701$	41.0831	−	5.90686i	1.55169	−	0.223099i	0.864220	+	0.503115i	$0.167813\pi$
$702$		0			0
$703$	−10.9124	−	16.9800i	−0.411569	−	0.640414i
$704$		0			0
$705$	−0.710136	−	0.324308i	−0.0267453	−	0.0122142i
$706$		0			0
$707$	−0.385648	+	0.113236i	−0.0145038	+	0.00425870i
$708$		0			0
$709$	8.92143	−	30.3836i	0.335051	−	1.14108i	−0.603909	−	0.797054i	$-0.706391\pi$
$709$	8.92143	−	30.3836i	0.335051	−	1.14108i	0.938960	−	0.344027i	$-0.111791\pi$
$710$		0			0
$711$	1.50106	−	10.4401i	0.0562941	−	0.391534i
$712$		0			0
$713$	−18.3166	+	32.1403i	−0.685961	+	1.20366i
$714$		0			0
$715$	14.1151	+	2.02944i	0.527873	+	0.0758967i
$716$		0			0
$717$	2.98252	+	0.875747i	0.111384	+	0.0327054i
$718$		0			0
$719$	5.56102	+	18.9391i	0.207391	+	0.706309i	0.995833	+	0.0911993i	$0.0290700\pi$
$719$	5.56102	+	18.9391i	0.207391	+	0.706309i	−0.788442	+	0.615110i	$0.789112\pi$
$720$		0			0
$721$	21.1365	−	46.2824i	0.787164	−	1.72365i
$722$		0			0
$723$	−2.08336	+	1.33889i	−0.0774810	+	0.0497940i
$724$		0			0
$725$	0.435973	+	3.03226i	0.0161916	+	0.112615i
$726$		0			0
$727$	7.98857	−	9.21930i	0.296280	−	0.341925i	−0.588019	−	0.808847i	$-0.700092\pi$
$727$	7.98857	−	9.21930i	0.296280	−	0.341925i	0.884298	+	0.466922i	$0.154637\pi$
$728$		0			0
$729$	22.0891	+	14.1958i	0.818115	+	0.525771i
$730$		0			0
$731$	−23.2642	+	20.1585i	−0.860457	+	0.745590i
$732$		0			0
$733$	−0.521302	+	0.238070i	−0.0192547	+	0.00879333i	−0.425019	−	0.905184i	$-0.639733\pi$
$733$	−0.521302	+	0.238070i	−0.0192547	+	0.00879333i	0.405764	+	0.913978i	$0.367005\pi$
$734$		0			0
$735$	−0.979206			−0.0361185
$736$		0			0
$737$	5.78782			0.213197
$738$		0			0
$739$	28.6453	−	13.0819i	1.05373	−	0.481224i	0.188229	−	0.982125i	$-0.439725\pi$
$739$	28.6453	−	13.0819i	1.05373	−	0.481224i	0.865505	+	0.500901i	$0.166998\pi$
$740$		0			0
$741$	0.829382	−	0.718663i	0.0304681	−	0.0264008i
$742$		0			0
$743$	20.6339	+	13.2606i	0.756983	+	0.486483i	0.861323	−	0.508058i	$-0.169637\pi$
$743$	20.6339	+	13.2606i	0.756983	+	0.486483i	−0.104340	+	0.994542i	$0.533273\pi$
$744$		0			0
$745$	6.02094	−	6.94853i	0.220590	−	0.254575i
$746$		0			0
$747$	4.26845	+	29.6877i	0.156174	+	1.08622i
$748$		0			0
$749$	47.9557	−	30.8193i	1.75226	−	1.12611i
$750$		0			0
$751$	−2.51237	+	5.50132i	−0.0916777	+	0.200746i	−0.949916	−	0.312505i	$-0.898832\pi$
$751$	−2.51237	+	5.50132i	−0.0916777	+	0.200746i	0.858238	+	0.513251i	$0.171559\pi$
$752$		0			0
$753$	−0.911969	−	3.10588i	−0.0332340	−	0.113185i
$754$		0			0
$755$	27.5967	+	8.10312i	1.00435	+	0.294903i
$756$		0			0
$757$	29.1174	+	4.18645i	1.05829	+	0.152159i	0.649418	−	0.760432i	$-0.275013\pi$
$757$	29.1174	+	4.18645i	1.05829	+	0.152159i	0.408873	+	0.912591i	$0.365922\pi$
$758$		0			0
$759$	1.02905	−	0.537840i	0.0373521	−	0.0195223i
$760$		0			0
$761$	1.70128	−	11.8326i	0.0616712	−	0.428933i	−0.935472	−	0.353401i	$-0.885025\pi$
$761$	1.70128	−	11.8326i	0.0616712	−	0.428933i	0.997143	−	0.0755323i	$-0.0240656\pi$
$762$		0			0
$763$	11.2784	−	38.4107i	0.408305	−	1.39056i
$764$		0			0
$765$	14.9719	−	4.39615i	0.541310	−	0.158943i
$766$		0			0
$767$	−19.6451	−	8.97162i	−0.709344	−	0.323946i
$768$		0			0
$769$	−21.4693	−	33.4068i	−0.774201	−	1.20468i	−0.974377	−	0.224921i	$-0.927788\pi$
$769$	−21.4693	−	33.4068i	−0.774201	−	1.20468i	0.200176	−	0.979760i	$-0.435849\pi$
$770$		0			0
$771$	0.783250	−	0.112614i	0.0282081	−	0.00405571i
$772$		0			0
$773$	0.683625	+	0.592365i	0.0245883	+	0.0213059i	0.667068	−	0.744997i	$-0.267549\pi$
$773$	0.683625	+	0.592365i	0.0245883	+	0.0213059i	−0.642480	+	0.766303i	$0.722094\pi$
$774$		0			0
$775$	8.12611	−	12.6445i	0.291898	−	0.454203i
$776$		0			0
$777$	−2.26000	−	2.60818i	−0.0810771	−	0.0935680i
$778$		0			0
$779$	11.4789	+	25.1353i	0.411274	+	0.900565i
$780$		0			0
$781$		−	18.3756i		−	0.657529i
$782$		0			0
$783$			1.10577i			0.0395169i
$784$		0			0
$785$	−5.83894	−	12.7855i	−0.208401	−	0.456334i
$786$		0			0
$787$	35.4591	+	40.9219i	1.26398	+	1.45871i	0.829977	+	0.557798i	$0.188354\pi$
$787$	35.4591	+	40.9219i	1.26398	+	1.45871i	0.434003	+	0.900912i	$0.357101\pi$
$788$		0			0
$789$	0.149347	−	0.232388i	0.00531689	−	0.00827324i
$790$		0			0
$791$	6.47298	+	5.60887i	0.230153	+	0.199428i
$792$		0			0
$793$	7.55610	−	1.08640i	0.268325	−	0.0385793i
$794$		0			0
$795$	0.434427	+	0.675981i	0.0154075	+	0.0239746i
$796$		0			0
$797$	12.3929	+	5.65963i	0.438978	+	0.200474i	0.622629	−	0.782517i	$-0.286065\pi$
$797$	12.3929	+	5.65963i	0.438978	+	0.200474i	−0.183652	+	0.982991i	$0.558792\pi$
$798$		0			0
$799$	−10.9172	+	3.20558i	−0.386223	+	0.113405i
$800$		0			0
$801$	−6.88559	+	23.4502i	−0.243290	+	0.828571i
$802$		0			0
$803$	−2.28865	+	15.9179i	−0.0807648	+	0.561731i
$804$		0			0
$805$	−1.52863	−	28.7016i	−0.0538773	−	1.01160i
$806$		0			0
$807$	−1.02574	−	0.147480i	−0.0361079	−	0.00519153i
$808$		0			0
$809$	−14.6083	−	4.28939i	−0.513601	−	0.150807i	0.0146541	−	0.999893i	$-0.495335\pi$
$809$	−14.6083	−	4.28939i	−0.513601	−	0.150807i	−0.528255	+	0.849086i	$0.677153\pi$
$810$		0			0
$811$	−2.78682	−	9.49103i	−0.0978585	−	0.333275i	0.895983	−	0.444089i	$-0.146473\pi$
$811$	−2.78682	−	9.49103i	−0.0978585	−	0.333275i	−0.993841	+	0.110814i	$0.964654\pi$
$812$		0			0
$813$	−0.397121	+	0.869574i	−0.0139276	+	0.0304973i
$814$		0			0
$815$	33.0354	−	21.2306i	1.15718	−	0.743675i
$816$		0			0
$817$	−3.45280	−	24.0148i	−0.120798	−	0.840171i
$818$		0			0
$819$	−26.5798	+	30.6747i	−0.928772	+	1.07186i
$820$		0			0
$821$	2.23257	+	1.43479i	0.0779173	+	0.0500744i	0.579019	−	0.815314i	$-0.303436\pi$
$821$	2.23257	+	1.43479i	0.0779173	+	0.0500744i	−0.501102	+	0.865388i	$0.667072\pi$
$822$		0			0
$823$	−25.7224	+	22.2886i	−0.896628	+	0.776933i	−0.975511	−	0.219951i	$-0.929410\pi$
$823$	−25.7224	+	22.2886i	−0.896628	+	0.776933i	0.0788827	+	0.996884i	$0.474865\pi$
$824$		0			0
$825$	−0.429139	+	0.195981i	−0.0149407	+	0.00682318i
$826$		0			0
$827$	−10.0459			−0.349329			−0.174664	−	0.984628i	$-0.555884\pi$
$827$	−10.0459			−0.349329			−0.174664	+	0.984628i	$0.555884\pi$
$828$		0			0
$829$	−17.5669			−0.610125			−0.305062	−	0.952332i	$-0.598677\pi$
$829$	−17.5669			−0.610125			−0.305062	+	0.952332i	$0.598677\pi$
$830$		0			0
$831$	0.00908949	−	0.00415103i	0.000315311	−	0.000143998i
$832$		0			0
$833$	−10.7856	+	9.34580i	−0.373700	+	0.323813i
$834$		0			0
$835$	26.1926	+	16.8329i	0.906431	+	0.582528i
$836$		0			0
$837$	3.55286	−	4.10021i	0.122805	−	0.141724i
$838$		0			0
$839$	−6.36234	−	44.2510i	−0.219652	−	1.52772i	−0.739324	−	0.673350i	$-0.764855\pi$
$839$	−6.36234	−	44.2510i	−0.219652	−	1.52772i	0.519672	−	0.854366i	$-0.326054\pi$
$840$		0			0
$841$	−22.3171	+	14.3423i	−0.769554	+	0.494563i
$842$		0			0
$843$	0.889645	−	1.94805i	0.0306410	−	0.0670944i
$844$		0			0
$845$	1.32626	+	4.51681i	0.0456246	+	0.155383i
$846$		0			0
$847$	−22.2332	−	6.52825i	−0.763941	−	0.224313i
$848$		0			0
$849$	−2.28690	−	0.328807i	−0.0784862	−	0.0112846i
$850$		0			0
$851$	29.5557	−	28.4995i	1.01316	−	0.976951i
$852$		0			0
$853$	2.14980	−	14.9522i	0.0736079	−	0.511954i	−0.919346	−	0.393451i	$-0.871281\pi$
$853$	2.14980	−	14.9522i	0.0736079	−	0.511954i	0.992954	−	0.118504i	$-0.0378097\pi$
$854$		0			0
$855$	−3.46485	+	11.8002i	−0.118495	+	0.403558i
$856$		0			0
$857$	12.4399	−	3.65269i	0.424939	−	0.124773i	−0.0622685	−	0.998059i	$-0.519834\pi$
$857$	12.4399	−	3.65269i	0.424939	−	0.124773i	0.487208	+	0.873286i	$0.338015\pi$
$858$		0			0
$859$	−17.0018	−	7.76444i	−0.580093	−	0.264919i	0.103685	−	0.994610i	$-0.466937\pi$
$859$	−17.0018	−	7.76444i	−0.580093	−	0.264919i	−0.683777	+	0.729691i	$0.739664\pi$
$860$		0			0
$861$	2.55432	+	3.97460i	0.0870509	+	0.135454i
$862$		0			0
$863$	−15.3396	+	2.20550i	−0.522166	+	0.0750762i	−0.398358	−	0.917230i	$-0.630420\pi$
$863$	−15.3396	+	2.20550i	−0.522166	+	0.0750762i	−0.123808	+	0.992306i	$0.539511\pi$
$864$		0			0
$865$	−29.5870	−	25.6373i	−1.00599	−	0.871694i
$866$		0			0
$867$	0.511478	−	0.795876i	0.0173707	−	0.0270294i
$868$		0			0
$869$	−4.76622	−	5.50051i	−0.161683	−	0.186592i
$870$		0			0
$871$	4.62254	+	10.1219i	0.156629	+	0.342969i
$872$		0			0
$873$		−	0.539179i		−	0.0182484i
$874$		0			0
$875$			41.6440i			1.40782i
$876$		0			0
$877$	10.0439	+	21.9931i	0.339160	+	0.742656i	0.999969	−	0.00789806i	$-0.00251406\pi$
$877$	10.0439	+	21.9931i	0.339160	+	0.742656i	−0.660809	+	0.750554i	$0.729787\pi$
$878$		0			0
$879$	−0.807283	−	0.931654i	−0.0272290	−	0.0314239i
$880$		0			0
$881$	−14.5573	+	22.6517i	−0.490449	+	0.763154i	−0.994962	−	0.100250i	$-0.968036\pi$
$881$	−14.5573	+	22.6517i	−0.490449	+	0.763154i	0.504513	+	0.863404i	$0.331672\pi$
$882$		0			0
$883$	17.6976	+	15.3351i	0.595573	+	0.516067i	0.899668	−	0.436575i	$-0.143809\pi$
$883$	17.6976	+	15.3351i	0.595573	+	0.516067i	−0.304095	+	0.952642i	$0.598354\pi$
$884$		0			0
$885$	−1.10749	+	0.159233i	−0.0372277	+	0.00535254i
$886$		0			0
$887$	6.33778	+	9.86178i	0.212802	+	0.331126i	0.931202	−	0.364504i	$-0.118762\pi$
$887$	6.33778	+	9.86178i	0.212802	+	0.331126i	−0.718400	+	0.695630i	$0.755125\pi$
$888$		0			0
$889$	18.5469	+	8.47008i	0.622042	+	0.284077i
$890$		0			0
$891$	17.5490	−	5.15284i	0.587913	−	0.172627i
$892$		0			0
$893$	2.52649	−	8.60445i	0.0845459	−	0.287937i
$894$		0			0
$895$	5.83486	−	40.5823i	0.195038	−	1.35652i
$896$		0			0
$897$	1.76246	+	1.37009i	0.0588469	+	0.0457458i
$898$		0			0
$899$	−12.0035	−	1.72584i	−0.400338	−	0.0575600i
$900$		0			0
$901$	11.2368	+	3.29943i	0.374353	+	0.109920i
$902$		0			0
$903$	−1.16871	−	3.98026i	−0.0388923	−	0.132455i
$904$		0			0
$905$	17.3113	−	37.9065i	0.575448	−	1.26006i
$906$		0			0
$907$	7.47865	−	4.80624i	0.248325	−	0.159588i	−0.410558	−	0.911835i	$-0.634666\pi$
$907$	7.47865	−	4.80624i	0.248325	−	0.159588i	0.658882	+	0.752246i	$0.271030\pi$
$908$		0			0
$909$	0.0497866	+	0.346273i	0.00165132	+	0.0114852i
$910$		0			0
$911$	−4.09127	+	4.72158i	−0.135550	+	0.156433i	−0.819466	−	0.573128i	$-0.805730\pi$
$911$	−4.09127	+	4.72158i	−0.135550	+	0.156433i	0.683916	+	0.729561i	$0.260275\pi$
$912$		0			0
$913$	17.4110	+	11.1894i	0.576221	+	0.370314i
$914$		0			0
$915$	0.298890	−	0.258990i	0.00988100	−	0.00856194i
$916$		0			0
$917$	−10.9437	+	4.99782i	−0.361393	+	0.165043i
$918$		0			0
$919$	44.4385			1.46589			0.732945	−	0.680288i	$-0.238145\pi$
$919$	44.4385			1.46589			0.732945	+	0.680288i	$0.238145\pi$
$920$		0			0
$921$	0.408875			0.0134729
$922$		0			0
$923$	32.1358	−	14.6759i	1.05776	−	0.483065i
$924$		0			0
$925$	−12.6075	+	10.9244i	−0.414532	+	0.359194i
$926$		0			0
$927$	−37.2555	−	23.9427i	−1.22363	−	0.786380i
$928$		0			0
$929$	31.2517	−	36.0664i	1.02534	−	1.18330i	0.0424483	−	0.999099i	$-0.486484\pi$
$929$	31.2517	−	36.0664i	1.02534	−	1.18330i	0.982888	−	0.184203i	$-0.0589703\pi$
$930$		0			0
$931$	−1.60077	−	11.1336i	−0.0524632	−	0.364890i
$932$		0			0
$933$	2.39422	−	1.53867i	0.0783834	−	0.0503739i
$934$		0			0
$935$	4.47296	−	9.79441i	0.146281	−	0.320311i
$936$		0			0
$937$	−6.33560	−	21.5771i	−0.206975	−	0.704892i	−0.995905	−	0.0904086i	$-0.971183\pi$
$937$	−6.33560	−	21.5771i	−0.206975	−	0.704892i	0.788930	−	0.614483i	$-0.210635\pi$
$938$		0			0
$939$	0.142374	+	0.0418049i	0.00464621	+	0.00136425i
$940$		0			0
$941$	3.89577	+	0.560127i	0.126998	+	0.0182596i	0.205521	−	0.978653i	$-0.434111\pi$
$941$	3.89577	+	0.560127i	0.126998	+	0.0182596i	−0.0785225	+	0.996912i	$0.525020\pi$
$942$		0			0
$943$	−45.6028	+	32.8607i	−1.48503	+	1.07009i
$944$		0			0
$945$	−0.599899	+	4.17239i	−0.0195147	+	0.135728i
$946$		0			0
$947$	−14.6947	+	50.0455i	−0.477513	+	1.62626i	0.270602	+	0.962691i	$0.412777\pi$
$947$	−14.6947	+	50.0455i	−0.477513	+	1.62626i	−0.748115	+	0.663569i	$0.769041\pi$
$948$		0			0
$949$	−29.6657	+	8.71065i	−0.962990	+	0.282760i
$950$		0			0
$951$	2.56352	+	1.17072i	0.0831278	+	0.0379632i
$952$		0			0
$953$	27.2605	+	42.4182i	0.883054	+	1.37406i	0.927014	+	0.375026i	$0.122366\pi$
$953$	27.2605	+	42.4182i	0.883054	+	1.37406i	−0.0439598	+	0.999033i	$0.513997\pi$
$954$		0			0
$955$	−35.7216	+	5.13599i	−1.15592	+	0.166197i
$956$		0			0
$957$	0.287665	+	0.249263i	0.00929887	+	0.00805752i
$958$		0			0
$959$	26.9777	−	41.9781i	0.871156	−	1.35555i
$960$		0			0
$961$	18.6634	+	21.5387i	0.602044	+	0.694796i
$962$		0			0
$963$	−20.6114	−	45.1328i	−0.664194	−	1.45438i
$964$		0			0
$965$			2.47938i			0.0798140i
$966$		0			0
$967$		−	3.03743i		−	0.0976771i	−0.998807	−	0.0488385i	$-0.984448\pi$
$967$		−	3.03743i		−	0.0976771i	0.998807	−	0.0488385i	$-0.0155520\pi$
$968$		0			0
$969$	−0.344227	−	0.753753i	−0.0110582	−	0.0242140i
$970$		0			0
$971$	0.183013	+	0.211208i	0.00587316	+	0.00677798i	0.758679	−	0.651465i	$-0.225845\pi$
$971$	0.183013	+	0.211208i	0.00587316	+	0.00677798i	−0.752805	+	0.658243i	$0.771300\pi$
$972$		0			0
$973$	8.27791	−	12.8807i	0.265378	−	0.412936i
$974$		0			0
$975$	−0.685478	−	0.593970i	−0.0219529	−	0.0190223i
$976$		0			0
$977$	−31.1017	+	4.47175i	−0.995033	+	0.143064i	−0.620547	−	0.784169i	$-0.713090\pi$
$977$	−31.1017	+	4.47175i	−0.995033	+	0.143064i	−0.374485	+	0.927233i	$0.622180\pi$
$978$		0			0
$979$	9.11780	+	14.1876i	0.291406	+	0.453437i
$980$		0			0
$981$	−31.6949	−	14.4746i	−1.01194	−	0.462137i
$982$		0			0
$983$	−18.0776	+	5.30806i	−0.576585	+	0.169301i	−0.557007	−	0.830508i	$-0.688050\pi$
$983$	−18.0776	+	5.30806i	−0.576585	+	0.169301i	−0.0195781	+	0.999808i	$0.506232\pi$
$984$		0			0
$985$	−6.19083	+	21.0840i	−0.197256	+	0.671793i
$986$		0			0
$987$	0.218213	−	1.51770i	0.00694578	−	0.0483090i
$988$		0			0
$989$	46.5468	−	16.4029i	1.48010	−	0.521583i
$990$		0			0
$991$	19.6292	+	2.82225i	0.623541	+	0.0896516i	0.446841	−	0.894613i	$-0.352549\pi$
$991$	19.6292	+	2.82225i	0.623541	+	0.0896516i	0.176699	+	0.984265i	$0.443458\pi$
$992$		0			0
$993$	3.46030	+	1.01604i	0.109809	+	0.0322429i
$994$		0			0
$995$	−5.28421	−	17.9964i	−0.167521	−	0.570523i
$996$		0			0
$997$	−18.6659	+	40.8727i	−0.591156	+	1.29445i	0.343586	+	0.939121i	$0.388358\pi$
$997$	−18.6659	+	40.8727i	−0.591156	+	1.29445i	−0.934741	+	0.355329i	$0.884369\pi$
$998$		0			0
$999$	−5.06562	+	3.25547i	−0.160269	+	0.102999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.s.b.15.5	yes	80
4.3	odd	2	inner	368.2.s.b.15.4	✓	80
23.20	odd	22	inner	368.2.s.b.319.4	yes	80
92.43	even	22	inner	368.2.s.b.319.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.s.b.15.4	✓	80	4.3	odd	2	inner
368.2.s.b.15.5	yes	80	1.1	even	1	trivial
368.2.s.b.319.4	yes	80	23.20	odd	22	inner
368.2.s.b.319.5	yes	80	92.43	even	22	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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.106877 - 0.0488093i) q^{3} +(-1.32017 + 1.14393i) q^{5} +(-2.88624 - 1.85487i) q^{7} +(-1.95554 + 2.25682i) q^{9} +(0.293255 + 2.03963i) q^{11} +(-3.33277 + 2.14184i) q^{13} +(-0.0852617 + 0.186697i) q^{15} +(0.842757 + 2.87017i) q^{17} +(-2.26214 - 0.664224i) q^{19} +(-0.399009 - 0.0573688i) q^{21} +(0.429086 - 4.77660i) q^{23} +(-0.277311 + 1.92874i) q^{25} +(-0.198156 + 0.674859i) q^{27} +(1.50846 - 0.442925i) q^{29} +(-7.01654 - 3.20435i) q^{31} +(0.130895 + 0.203677i) q^{33} +(5.93217 - 0.852917i) q^{35} +(6.47012 + 5.60639i) q^{37} +(-0.251656 + 0.391585i) q^{39} +(-7.67520 - 8.85765i) q^{41} +(4.27491 + 9.36074i) q^{43} -5.21639i q^{45} +3.80368i q^{47} +(1.98191 + 4.33978i) q^{49} +(0.230163 + 0.265622i) q^{51} +(2.11663 - 3.29354i) q^{53} +(-2.72035 - 2.35720i) q^{55} +(-0.274192 + 0.0394228i) q^{57} +(2.94726 + 4.58603i) q^{59} +(-1.75278 - 0.800468i) q^{61} +(9.83026 - 2.88643i) q^{63} +(1.94970 - 6.64007i) q^{65} +(0.399733 - 2.78020i) q^{67} +(-0.187283 - 0.531454i) q^{69} +(-8.82677 - 1.26910i) q^{71} +(7.48818 + 2.19873i) q^{73} +(0.0645021 + 0.219674i) q^{75} +(2.93686 - 6.43082i) q^{77} +(-2.97137 + 1.90958i) q^{79} +(-1.26318 - 8.78560i) q^{81} +(6.57735 - 7.59066i) q^{83} +(-4.39586 - 2.82505i) q^{85} +(0.139602 - 0.120966i) q^{87} +(7.44478 - 3.39992i) q^{89} +13.5920 q^{91} -0.906312 q^{93} +(3.74623 - 1.71085i) q^{95} +(-0.136456 + 0.118240i) q^{97} +(-5.17655 - 3.32677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{9} + 12 q^{13} + 22 q^{17} + 66 q^{21} + 36 q^{25} + 34 q^{29} + 22 q^{33} + 12 q^{41} - 56 q^{49} - 66 q^{57} - 88 q^{61} - 154 q^{65} - 66 q^{69} - 16 q^{73} - 158 q^{77} - 248 q^{81} - 116 q^{85}+ \cdots - 22 q^{97}+O(q^{100}) \) 80 * q + 4 * q^9 + 12 * q^13 + 22 * q^17 + 66 * q^21 + 36 * q^25 + 34 * q^29 + 22 * q^33 + 12 * q^41 - 56 * q^49 - 66 * q^57 - 88 * q^61 - 154 * q^65 - 66 * q^69 - 16 * q^73 - 158 * q^77 - 248 * q^81 - 116 * q^85 - 88 * q^89 - 84 * q^93 - 22 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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