LMFDB - Embedded newform 441.2.h.h.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Character	$\chi$	$=$	441.373
Dual form			441.2.h.h.214.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71513 q^{2} +(1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 - 2.98835i) q^{9} +O(q^{10})$	\(q-2.71513 q^{2} +(1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 - 2.98835i) q^{9} +(-2.15363 - 3.73020i) q^{10} +(0.674376 - 1.16805i) q^{11} +(6.28290 - 6.86284i) q^{12} +(1.58916 - 2.75251i) q^{13} +(2.68285 + 0.593495i) q^{15} +14.1139 q^{16} +(-1.40027 - 2.42534i) q^{17} +(0.717292 + 8.11375i) q^{18} +(-0.312846 + 0.541866i) q^{19} +(4.26101 + 7.38028i) q^{20} +(-1.83102 + 3.17142i) q^{22} +(0.142434 + 0.246702i) q^{23} +(-10.7078 + 11.6962i) q^{24} +(1.24168 - 2.15065i) q^{25} +(-4.31479 + 7.47343i) q^{26} +(-4.12669 - 3.15760i) q^{27} +(2.27396 + 3.93861i) q^{29} +(-7.28430 - 1.61142i) q^{30} +7.43005 q^{31} -20.0106 q^{32} +(-0.703493 - 2.22767i) q^{33} +(3.80191 + 6.58511i) q^{34} +(-1.41918 - 16.0532i) q^{36} +(-4.01126 + 6.94770i) q^{37} +(0.849420 - 1.47124i) q^{38} +(-1.65778 - 5.24948i) q^{39} +(-7.26194 - 12.5780i) q^{40} +(5.01329 - 8.68327i) q^{41} +(-3.12937 - 5.42022i) q^{43} +(3.62271 - 6.27472i) q^{44} +(3.89601 - 2.73329i) q^{45} +(-0.386726 - 0.669829i) q^{46} +11.1477 q^{47} +(16.5073 - 18.0310i) q^{48} +(-3.37132 + 5.83930i) q^{50} +(-4.73617 - 1.04773i) q^{51} +(8.53689 - 14.7863i) q^{52} +(-1.39349 - 2.41359i) q^{53} +(11.2045 + 8.57329i) q^{54} +2.13965 q^{55} +(0.326354 + 1.03343i) q^{57} +(-6.17410 - 10.6939i) q^{58} +4.57469 q^{59} +(14.4121 + 3.18822i) q^{60} -0.385014 q^{61} -20.1736 q^{62} +26.1036 q^{64} +5.04207 q^{65} +(1.91008 + 6.04841i) q^{66} -2.53916 q^{67} +(-7.52217 - 13.0288i) q^{68} +(0.481757 + 0.106573i) q^{69} -1.45208 q^{71} +(2.41867 + 27.3591i) q^{72} +(0.234067 + 0.405416i) q^{73} +(10.8911 - 18.8639i) q^{74} +(-1.29529 - 4.10164i) q^{75} +(-1.68059 + 2.91087i) q^{76} +(4.50108 + 14.2530i) q^{78} -15.7124 q^{79} +(11.1951 + 19.3905i) q^{80} +(-8.86041 + 1.57894i) q^{81} +(-13.6117 + 23.5762i) q^{82} +(-6.99338 - 12.1129i) q^{83} +(2.22138 - 3.84754i) q^{85} +(8.49665 + 14.7166i) q^{86} +(7.69128 + 1.70145i) q^{87} +(-6.17410 + 10.6939i) q^{88} +(1.29353 - 2.24046i) q^{89} +(-10.5782 + 7.42126i) q^{90} +(0.765146 + 1.32527i) q^{92} +(8.69001 - 9.49213i) q^{93} -30.2674 q^{94} -0.992595 q^{95} +(-23.4039 + 25.5642i) q^{96} +(7.22962 + 12.5221i) q^{97} +(-3.66871 - 1.70669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.71513			−1.91989			−0.959944	−	0.280191i	$-0.909602\pi$
$2$	−2.71513			−1.91989			−0.959944	+	0.280191i	$0.909602\pi$
$3$	1.16958	−	1.27753i	0.675255	−	0.737584i
$3$	1.16958	−	1.27753i	0.675255	−	0.737584i
$4$	5.37195			2.68597
$5$	0.793197	+	1.37386i	0.354728	+	0.614407i	0.987071	−	0.160281i	$-0.0512400\pi$
$5$	0.793197	+	1.37386i	0.354728	+	0.614407i	−0.632343	+	0.774688i	$0.717907\pi$
$6$	−3.17555	+	3.46867i	−1.29641	+	1.41608i
$7$		0			0
$7$		0			0
$8$	−9.15528			−3.23688
$9$	−0.264183	−	2.98835i	−0.0880610	−	0.996115i
$10$	−2.15363	−	3.73020i	−0.681039	−	1.17959i
$11$	0.674376	−	1.16805i	0.203332	−	0.352181i	−0.746268	−	0.665646i	$-0.768156\pi$
$11$	0.674376	−	1.16805i	0.203332	−	0.352181i	0.949600	+	0.313464i	$0.101490\pi$
$12$	6.28290	−	6.86284i	1.81372	−	1.98113i
$13$	1.58916	−	2.75251i	0.440754	−	0.763409i	−0.556991	−	0.830518i	$-0.688044\pi$
$13$	1.58916	−	2.75251i	0.440754	−	0.763409i	0.997746	+	0.0671096i	$0.0213777\pi$
$14$		0			0
$15$	2.68285	+	0.593495i	0.692709	+	0.153240i
$16$	14.1139			3.52848
$17$	−1.40027	−	2.42534i	−0.339615	−	0.588230i	0.644745	−	0.764397i	$-0.276963\pi$
$17$	−1.40027	−	2.42534i	−0.339615	−	0.588230i	−0.984360	+	0.176167i	$0.943630\pi$
$18$	0.717292	+	8.11375i	0.169067	+	1.91243i
$19$	−0.312846	+	0.541866i	−0.0717719	+	0.124313i	−0.899678	−	0.436554i	$-0.856199\pi$
$19$	−0.312846	+	0.541866i	−0.0717719	+	0.124313i	0.827906	+	0.560867i	$0.189532\pi$
$20$	4.26101	+	7.38028i	0.952791	+	1.65028i
$21$		0			0
$22$	−1.83102	+	3.17142i	−0.390375	+	0.676149i
$23$	0.142434	+	0.246702i	0.0296995	+	0.0514410i	0.880493	−	0.474059i	$-0.157212\pi$
$23$	0.142434	+	0.246702i	0.0296995	+	0.0514410i	−0.850794	+	0.525500i	$0.823878\pi$
$24$	−10.7078	+	11.6962i	−2.18572	+	2.38747i
$25$	1.24168	−	2.15065i	0.248336	−	0.430130i
$26$	−4.31479	+	7.47343i	−0.846199	+	1.46566i
$27$	−4.12669	−	3.15760i	−0.794182	−	0.607679i
$28$		0			0
$29$	2.27396	+	3.93861i	0.422264	+	0.731382i	0.996161	−	0.0875454i	$-0.0279023\pi$
$29$	2.27396	+	3.93861i	0.422264	+	0.731382i	−0.573897	+	0.818928i	$0.694569\pi$
$30$	−7.28430	−	1.61142i	−1.32992	−	0.294203i
$31$	7.43005			1.33448			0.667238	−	0.744845i	$-0.267476\pi$
$31$	7.43005			1.33448			0.667238	+	0.744845i	$0.267476\pi$
$32$	−20.0106			−3.53741
$33$	−0.703493	−	2.22767i	−0.122462	−	0.387787i
$34$	3.80191	+	6.58511i	0.652023	+	1.12934i
$35$		0			0
$36$	−1.41918	−	16.0532i	−0.236529	−	2.67554i
$37$	−4.01126	+	6.94770i	−0.659447	+	1.14220i	0.321312	+	0.946973i	$0.395876\pi$
$37$	−4.01126	+	6.94770i	−0.659447	+	1.14220i	−0.980759	+	0.195222i	$0.937457\pi$
$38$	0.849420	−	1.47124i	0.137794	−	0.238666i
$39$	−1.65778	−	5.24948i	−0.265457	−	0.840589i
$40$	−7.26194	−	12.5780i	−1.14821	−	1.98876i
$41$	5.01329	−	8.68327i	0.782944	−	1.35610i	−0.147275	−	0.989096i	$-0.547050\pi$
$41$	5.01329	−	8.68327i	0.782944	−	1.35610i	0.930219	−	0.367004i	$-0.119616\pi$
$42$		0			0
$43$	−3.12937	−	5.42022i	−0.477224	−	0.826576i	0.522435	−	0.852679i	$-0.325024\pi$
$43$	−3.12937	−	5.42022i	−0.477224	−	0.826576i	−0.999659	+	0.0261027i	$0.991690\pi$
$44$	3.62271	−	6.27472i	0.546144	−	0.945950i
$45$	3.89601	−	2.73329i	0.580783	−	0.407455i
$46$	−0.386726	−	0.669829i	−0.0570197	−	0.0987609i
$47$	11.1477			1.62605			0.813026	−	0.582227i	$-0.197819\pi$
$47$	11.1477			1.62605			0.813026	+	0.582227i	$0.197819\pi$
$48$	16.5073	−	18.0310i	2.38262	−	2.60255i
$49$		0			0
$50$	−3.37132	+	5.83930i	−0.476777	+	0.825802i
$51$	−4.73617	−	1.04773i	−0.663196	−	0.146711i
$52$	8.53689	−	14.7863i	1.18385	−	2.05049i
$53$	−1.39349	−	2.41359i	−0.191410	−	0.331532i	0.754308	−	0.656521i	$-0.227973\pi$
$53$	−1.39349	−	2.41359i	−0.191410	−	0.331532i	−0.945718	+	0.324989i	$0.894639\pi$
$54$	11.2045	+	8.57329i	1.52474	+	1.16668i
$55$	2.13965			0.288510
$56$		0			0
$57$	0.326354	+	1.03343i	0.0432266	+	0.136881i
$58$	−6.17410	−	10.6939i	−0.810699	−	1.40417i
$59$	4.57469			0.595574			0.297787	−	0.954632i	$-0.403752\pi$
$59$	4.57469			0.595574			0.297787	+	0.954632i	$0.403752\pi$
$60$	14.4121	+	3.18822i	1.86060	+	0.411598i
$61$	−0.385014			−0.0492960			−0.0246480	−	0.999696i	$-0.507846\pi$
$61$	−0.385014			−0.0492960			−0.0246480	+	0.999696i	$0.507846\pi$
$62$	−20.1736			−2.56205
$63$		0			0
$64$	26.1036			3.26295
$65$	5.04207			0.625392
$66$	1.91008	+	6.04841i	0.235114	+	0.744508i
$67$	−2.53916			−0.310208			−0.155104	−	0.987898i	$-0.549571\pi$
$67$	−2.53916			−0.310208			−0.155104	+	0.987898i	$0.549571\pi$
$68$	−7.52217	−	13.0288i	−0.912197	−	1.57997i
$69$	0.481757	+	0.106573i	0.0579968	+	0.0128299i
$70$		0			0
$71$	−1.45208			−0.172330			−0.0861651	−	0.996281i	$-0.527461\pi$
$71$	−1.45208			−0.172330			−0.0861651	+	0.996281i	$0.527461\pi$
$72$	2.41867	+	27.3591i	0.285043	+	3.22431i
$73$	0.234067	+	0.405416i	0.0273955	+	0.0474503i	0.879398	−	0.476087i	$-0.157945\pi$
$73$	0.234067	+	0.405416i	0.0273955	+	0.0474503i	−0.852003	+	0.523538i	$0.824612\pi$
$74$	10.8911	−	18.8639i	1.26606	−	2.19289i
$75$	−1.29529	−	4.10164i	−0.149567	−	0.473616i
$76$	−1.68059	+	2.91087i	−0.192777	+	0.333900i
$77$		0			0
$78$	4.50108	+	14.2530i	0.509647	+	1.61384i
$79$	−15.7124			−1.76778			−0.883892	−	0.467691i	$-0.845086\pi$
$79$	−15.7124			−1.76778			−0.883892	+	0.467691i	$0.845086\pi$
$80$	11.1951	+	19.3905i	1.25165	+	2.16792i
$81$	−8.86041	+	1.57894i	−0.984491	+	0.175438i
$82$	−13.6117	+	23.5762i	−1.50317	+	2.60356i
$83$	−6.99338	−	12.1129i	−0.767623	−	1.32956i	−0.938848	−	0.344331i	$-0.888106\pi$
$83$	−6.99338	−	12.1129i	−0.767623	−	1.32956i	0.171225	−	0.985232i	$-0.445228\pi$
$84$		0			0
$85$	2.22138	−	3.84754i	0.240942	−	0.417324i
$86$	8.49665	+	14.7166i	0.916217	+	1.58693i
$87$	7.69128	+	1.70145i	0.824592	+	0.182415i
$88$	−6.17410	+	10.6939i	−0.658162	+	1.13997i
$89$	1.29353	−	2.24046i	0.137114	−	0.237488i	−0.789289	−	0.614022i	$-0.789551\pi$
$89$	1.29353	−	2.24046i	0.137114	−	0.237488i	0.926403	+	0.376534i	$0.122884\pi$
$90$	−10.5782	+	7.42126i	−1.11504	+	0.782269i
$91$		0			0
$92$	0.765146	+	1.32527i	0.0797719	+	0.138169i
$93$	8.69001	−	9.49213i	0.901112	−	0.984288i
$94$	−30.2674			−3.12184
$95$	−0.992595			−0.101838
$96$	−23.4039	+	25.5642i	−2.38865	+	2.60913i
$97$	7.22962	+	12.5221i	0.734057	+	1.27142i	0.955136	+	0.296168i	$0.0957089\pi$
$97$	7.22962	+	12.5221i	0.734057	+	1.27142i	−0.221079	+	0.975256i	$0.570958\pi$
$98$		0			0
$99$	−3.66871	−	1.70669i	−0.368719	−	0.171529i
$100$	6.67023	−	11.5532i	0.667023	−	1.15532i
$101$	−4.91888	+	8.51975i	−0.489447	+	0.847747i	−0.999926	−	0.0121430i	$-0.996135\pi$
$101$	−4.91888	+	8.51975i	−0.489447	+	0.847747i	0.510479	+	0.859890i	$0.329468\pi$
$102$	12.8593	+	2.84471i	1.27326	+	0.281669i
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	−0.998620	−	0.0525110i	$-0.983278\pi$
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	0.453834	−	0.891086i	$-0.350056\pi$
$104$	−14.5492	+	25.2000i	−1.42667	+	2.47106i
$105$		0			0
$106$	3.78350	+	6.55322i	0.367486	+	0.636505i
$107$	0.962153	−	1.66650i	0.0930149	−	0.161106i	−0.815764	−	0.578386i	$-0.803683\pi$
$107$	0.962153	−	1.66650i	0.0930149	−	0.161106i	0.908778	+	0.417279i	$0.137016\pi$
$108$	−22.1684	−	16.9624i	−2.13315	−	1.63221i
$109$	9.30341	+	16.1140i	0.891105	+	1.54344i	0.838553	+	0.544821i	$0.183402\pi$
$109$	9.30341	+	16.1140i	0.891105	+	1.54344i	0.0525523	+	0.998618i	$0.483264\pi$
$110$	−5.80944			−0.553908
$111$	4.18445	+	13.2504i	0.397170	+	1.25767i
$112$		0			0
$113$	1.59338	−	2.75982i	0.149893	−	0.259622i	−0.781295	−	0.624162i	$-0.785440\pi$
$113$	1.59338	−	2.75982i	0.149893	−	0.259622i	0.931188	+	0.364540i	$0.118774\pi$
$114$	−0.886094	−	2.80589i	−0.0829903	−	0.262795i
$115$	−0.225956	+	0.391367i	−0.0210705	+	0.0364951i
$116$	12.2156	+	21.1580i	1.13419	+	1.96447i
$117$	−8.64528	−	4.02180i	−0.799256	−	0.371815i
$118$	−12.4209			−1.14344
$119$		0			0
$120$	−24.5623	−	5.43361i	−2.24222	−	0.496019i
$121$	4.59043	+	7.95086i	0.417312	+	0.722806i
$122$	1.04536			0.0946428
$123$	−5.22975	−	16.5604i	−0.471550	−	1.49320i
$124$	39.9138			3.58437
$125$	11.8715			1.06182
$126$		0			0
$127$	−8.37387			−0.743061			−0.371530	−	0.928421i	$-0.621167\pi$
$127$	−8.37387			−0.743061			−0.371530	+	0.928421i	$0.621167\pi$
$128$	−30.8535			−2.72709
$129$	−10.5845	−	2.34149i	−0.931918	−	0.206157i
$130$	−13.6899			−1.20068
$131$	5.98629	+	10.3686i	0.523024	+	0.905905i	0.999641	+	0.0267937i	$0.00852971\pi$
$131$	5.98629	+	10.3686i	0.523024	+	0.905905i	−0.476616	+	0.879111i	$0.658137\pi$
$132$	−3.77913	−	11.9669i	−0.328931	−	1.04158i
$133$		0			0
$134$	6.89415			0.595564
$135$	1.06480	−	8.17408i	0.0916438	−	0.703513i
$136$	12.8199	+	22.2046i	1.09929	+	1.90403i
$137$	−8.27525	+	14.3332i	−0.707003	+	1.22456i	0.258961	+	0.965888i	$0.416620\pi$
$137$	−8.27525	+	14.3332i	−0.707003	+	1.22456i	−0.965964	+	0.258677i	$0.916714\pi$
$138$	−1.30803	−	0.289361i	−0.111347	−	0.0246320i
$139$	3.95119	−	6.84367i	0.335136	−	0.580472i	−0.648375	−	0.761321i	$-0.724551\pi$
$139$	3.95119	−	6.84367i	0.335136	−	0.580472i	0.983511	+	0.180849i	$0.0578845\pi$
$140$		0			0
$141$	13.0380	−	14.2415i	1.09800	−	1.19935i
$142$	3.94259			0.330855
$143$	−2.14339	−	3.71245i	−0.179239	−	0.310451i
$144$	−3.72865	−	42.1772i	−0.310721	−	3.51477i
$145$	−3.60739	+	6.24819i	−0.299578	+	0.518884i
$146$	−0.635523	−	1.10076i	−0.0525962	−	0.0910994i
$147$		0			0
$148$	−21.5483	+	37.3227i	−1.77126	+	3.06791i
$149$	6.83427	+	11.8373i	0.559885	+	0.969749i	0.997505	+	0.0705895i	$0.0224881\pi$
$149$	6.83427	+	11.8373i	0.559885	+	0.969749i	−0.437620	+	0.899160i	$0.644179\pi$
$150$	3.51688	+	11.1365i	0.287152	+	0.909290i
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	−0.934391	−	0.356250i	$-0.884055\pi$
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	0.775717	+	0.631081i	$0.217389\pi$
$152$	2.86420	−	4.96093i	0.232317	−	0.402385i
$153$	−6.87781	+	4.82522i	−0.556038	+	0.390096i
$154$		0			0
$155$	5.89349	+	10.2078i	0.473376	+	0.819912i
$156$	−8.90548	−	28.1999i	−0.713009	−	2.25780i
$157$	−0.294352			−0.0234919			−0.0117459	−	0.999931i	$-0.503739\pi$
$157$	−0.294352			−0.0234919			−0.0117459	+	0.999931i	$0.503739\pi$
$158$	42.6613			3.39395
$159$	−4.71323	−	1.04265i	−0.373784	−	0.0826877i
$160$	−15.8723	−	27.4917i	−1.25482	−	2.17341i
$161$		0			0
$162$	24.0572	−	4.28703i	1.89011	−	0.336821i
$163$	−5.35455	+	9.27436i	−0.419401	+	0.726424i	−0.995879	−	0.0906886i	$-0.971093\pi$
$163$	−5.35455	+	9.27436i	−0.419401	+	0.726424i	0.576478	+	0.817112i	$0.304427\pi$
$164$	26.9311	−	46.6461i	2.10297	−	3.64245i
$165$	2.50249	−	2.73348i	0.194818	−	0.212801i
$166$	18.9880	+	32.8881i	1.47375	+	2.55261i
$167$	1.59872	−	2.76907i	0.123713	−	0.214277i	−0.797516	−	0.603298i	$-0.793853\pi$
$167$	1.59872	−	2.76907i	0.123713	−	0.214277i	0.921229	+	0.389020i	$0.127186\pi$
$168$		0			0
$169$	1.44913	+	2.50997i	0.111472	+	0.193074i
$170$	−6.03133	+	10.4466i	−0.462582	+	0.801215i
$171$	1.70193	+	0.791741i	0.130150	+	0.0605460i
$172$	−16.8108	−	29.1171i	−1.28181	−	2.22016i
$173$	−11.4375			−0.869577			−0.434789	−	0.900533i	$-0.643177\pi$
$173$	−11.4375			−0.869577			−0.434789	+	0.900533i	$0.643177\pi$
$174$	−20.8828	−	4.61966i	−1.58312	−	0.350216i
$175$		0			0
$176$	9.51809	−	16.4858i	0.717453	−	1.24266i
$177$	5.35045	−	5.84432i	0.402164	−	0.439286i
$178$	−3.51210	+	6.08314i	−0.263243	+	0.455951i
$179$	−0.549275	−	0.951372i	−0.0410547	−	0.0711089i	0.844768	−	0.535133i	$-0.179738\pi$
$179$	−0.549275	−	0.951372i	−0.0410547	−	0.0711089i	−0.885823	+	0.464024i	$0.846405\pi$
$180$	20.9292	−	14.6831i	1.55997	−	1.09441i
$181$	3.19013			0.237120			0.118560	−	0.992947i	$-0.462172\pi$
$181$	3.19013			0.237120			0.118560	+	0.992947i	$0.462172\pi$
$182$		0			0
$183$	−0.450303	+	0.491868i	−0.0332874	+	0.0363599i
$184$	−1.30402	−	2.25863i	−0.0961336	−	0.166508i
$185$	−12.7269			−0.935698
$186$	−23.5945	+	25.7724i	−1.73003	+	1.88972i
$187$	−3.77723			−0.276218
$188$	59.8846			4.36753
$189$		0			0
$190$	2.69503			0.195518
$191$	3.86815			0.279889			0.139945	−	0.990159i	$-0.455308\pi$
$191$	3.86815			0.279889			0.139945	+	0.990159i	$0.455308\pi$
$192$	30.5301	−	33.3482i	2.20332	−	2.40670i
$193$	−4.13585			−0.297705			−0.148853	−	0.988859i	$-0.547558\pi$
$193$	−4.13585			−0.297705			−0.148853	+	0.988859i	$0.547558\pi$
$194$	−19.6294	−	33.9991i	−1.40931	−	2.44099i
$195$	5.89709	−	6.44141i	0.422299	−	0.461279i
$196$		0			0
$197$	−0.889267			−0.0633576			−0.0316788	−	0.999498i	$-0.510085\pi$
$197$	−0.889267			−0.0633576			−0.0316788	+	0.999498i	$0.510085\pi$
$198$	9.96102	+	4.63389i	0.707899	+	0.329316i
$199$	−3.16193	−	5.47663i	−0.224143	−	0.388228i	0.731919	−	0.681392i	$-0.238625\pi$
$199$	−3.16193	−	5.47663i	−0.224143	−	0.388228i	−0.956062	+	0.293164i	$0.905292\pi$
$200$	−11.3679	+	19.6898i	−0.803833	+	1.39228i
$201$	−2.96974	+	3.24386i	−0.209469	+	0.228804i
$202$	13.3554	−	23.1323i	0.939684	−	1.62758i
$203$		0			0
$204$	−25.4424	−	5.62833i	−1.78133	−	0.394062i
$205$	15.9061			1.11093
$206$	15.0119	+	26.0014i	1.04593	+	1.81160i
$207$	0.699603	−	0.490815i	0.0486258	−	0.0341140i
$208$	22.4293	−	38.8487i	1.55519	−	2.69367i
$209$	0.421952	+	0.730843i	0.0291870	+	0.0505535i
$210$		0			0
$211$	5.71291	−	9.89505i	0.393293	−	0.681204i	−0.599589	−	0.800308i	$-0.704669\pi$
$211$	5.71291	−	9.89505i	0.393293	−	0.681204i	0.992882	+	0.119105i	$0.0380025\pi$
$212$	−7.48574	−	12.9657i	−0.514123	−	0.890487i
$213$	−1.69832	+	1.85508i	−0.116367	+	0.127108i
$214$	−2.61237	+	4.52476i	−0.178578	+	0.309307i
$215$	4.96441	−	8.59860i	0.338570	−	0.586420i
$216$	37.7810	+	28.9087i	2.57067	+	1.96699i
$217$		0			0
$218$	−25.2600	−	43.7516i	−1.71082	−	2.96323i
$219$	0.791691	+	0.175136i	0.0534975	+	0.0118346i
$220$	11.4941			0.774931
$221$	−8.90101			−0.598747
$222$	−11.3613	−	35.9766i	−0.762523	−	2.41459i
$223$	8.35953	+	14.4791i	0.559796	+	0.969595i	0.997513	+	0.0704822i	$0.0224538\pi$
$223$	8.35953	+	14.4791i	0.559796	+	0.969595i	−0.437717	+	0.899113i	$0.644213\pi$
$224$		0			0
$225$	−6.75492	−	3.14240i	−0.450328	−	0.209493i
$226$	−4.32625	+	7.49328i	−0.287778	+	0.498446i
$227$	−8.53501	+	14.7831i	−0.566489	+	0.981187i	0.430421	+	0.902628i	$0.358365\pi$
$227$	−8.53501	+	14.7831i	−0.566489	+	0.981187i	−0.996909	+	0.0785588i	$0.974968\pi$
$228$	1.75316	+	5.55150i	0.116106	+	0.367657i
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	−0.982178	−	0.187953i	$-0.939815\pi$
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	0.328317	−	0.944567i	$-0.393518\pi$
$230$	0.613500	−	1.06261i	0.0404530	−	0.0700666i
$231$		0			0
$232$	−20.8187	−	36.0591i	−1.36682	−	2.36740i
$233$	−2.96579	+	5.13691i	−0.194296	+	0.336530i	−0.946669	−	0.322207i	$-0.895575\pi$
$233$	−2.96579	+	5.13691i	−0.194296	+	0.336530i	0.752374	+	0.658736i	$0.228909\pi$
$234$	23.4731	+	10.9197i	1.53448	+	0.713844i
$235$	8.84228	+	15.3153i	0.576807	+	0.999058i
$236$	24.5750			1.59969
$237$	−18.3769	+	20.0731i	−1.19371	+	1.30389i
$238$		0			0
$239$	−10.0277	+	17.3685i	−0.648637	+	1.12347i	0.334812	+	0.942285i	$0.391327\pi$
$239$	−10.0277	+	17.3685i	−0.648637	+	1.12347i	−0.983449	+	0.181187i	$0.942006\pi$
$240$	37.8655	+	8.37654i	2.44421	+	0.540703i
$241$	−14.6444	+	25.3648i	−0.943326	+	1.63389i	−0.184256	+	0.982878i	$0.558988\pi$
$241$	−14.6444	+	25.3648i	−0.943326	+	1.63389i	−0.759069	+	0.651010i	$0.774346\pi$
$242$	−12.4636	−	21.5877i	−0.801193	−	1.38771i
$243$	−8.34578	+	13.1662i	−0.535382	+	0.844610i
$244$	−2.06827			−0.132408
$245$		0			0
$246$	14.1995	+	44.9637i	0.905324	+	2.86678i
$247$	0.994327	+	1.72223i	0.0632675	+	0.109583i
$248$	−68.0242			−4.31954
$249$	−23.6539	−	5.23267i	−1.49901	−	0.331607i
$250$	−32.2328			−2.03858
$251$	−22.7856			−1.43821			−0.719106	−	0.694901i	$-0.755448\pi$
$251$	−22.7856			−1.43821			−0.719106	+	0.694901i	$0.755448\pi$
$252$		0			0
$253$	0.384215			0.0241554
$254$	22.7362			1.42659
$255$	−2.31729	−	7.33787i	−0.145114	−	0.459515i
$256$	31.5642			1.97276
$257$	12.1444	+	21.0348i	0.757550	+	1.31211i	0.944097	+	0.329668i	$0.106937\pi$
$257$	12.1444	+	21.0348i	0.757550	+	1.31211i	−0.186547	+	0.982446i	$0.559730\pi$
$258$	28.7385	+	6.35747i	1.78918	+	0.395798i
$259$		0			0
$260$	27.0857			1.67979
$261$	11.1692	−	7.83589i	0.691356	−	0.485030i
$262$	−16.2536	−	28.1520i	−1.00415	−	1.73924i
$263$	4.30578	−	7.45782i	0.265506	−	0.459869i	−0.702190	−	0.711989i	$-0.747794\pi$
$263$	4.30578	−	7.45782i	0.265506	−	0.459869i	0.967696	+	0.252120i	$0.0811278\pi$
$264$	6.44068	+	20.3949i	0.396396	+	1.25522i
$265$	2.21062	−	3.82890i	0.135797	−	0.235208i
$266$		0			0
$267$	−1.34938	−	4.27291i	−0.0825807	−	0.261498i
$268$	−13.6402			−0.833209
$269$	7.61561	+	13.1906i	0.464332	+	0.804247i	0.999171	−	0.0407073i	$-0.0129611\pi$
$269$	7.61561	+	13.1906i	0.464332	+	0.804247i	−0.534839	+	0.844954i	$0.679628\pi$
$270$	−2.89109	+	22.1937i	−0.175946	+	1.35067i
$271$	2.33910	−	4.05144i	0.142090	−	0.246108i	−0.786193	−	0.617981i	$-0.787951\pi$
$271$	2.33910	−	4.05144i	0.142090	−	0.246108i	0.928284	+	0.371873i	$0.121284\pi$
$272$	−19.7633	−	34.2310i	−1.19832	−	2.07556i
$273$		0			0
$274$	22.4684	−	38.9164i	1.35737	−	2.35103i
$275$	−1.67472	−	2.90069i	−0.100989	−	0.174918i
$276$	2.58797	+	0.572507i	0.155778	+	0.0344608i
$277$	8.19537	−	14.1948i	0.492412	−	0.852883i	−0.507550	−	0.861622i	$-0.669449\pi$
$277$	8.19537	−	14.1948i	0.492412	−	0.852883i	0.999962	+	0.00873986i	$0.00278202\pi$
$278$	−10.7280	+	18.5815i	−0.643423	+	1.11444i
$279$	−1.96289	−	22.2035i	−0.117515	−	1.32929i
$280$		0			0
$281$	1.75702	+	3.04325i	0.104815	+	0.181545i	0.913663	−	0.406473i	$-0.133242\pi$
$281$	1.75702	+	3.04325i	0.104815	+	0.181545i	−0.808848	+	0.588018i	$0.799908\pi$
$282$	−35.4000	+	38.6676i	−2.10804	+	2.30262i
$283$	26.0708			1.54975			0.774874	−	0.632116i	$-0.217813\pi$
$283$	26.0708			1.54975			0.774874	+	0.632116i	$0.217813\pi$
$284$	−7.80050			−0.462874
$285$	−1.16092	+	1.26807i	−0.0687667	+	0.0751142i
$286$	5.81958	+	10.0798i	0.344119	+	0.596031i
$287$		0			0
$288$	5.28645	+	59.7985i	0.311507	+	3.52366i
$289$	4.57850	−	7.93019i	0.269323	−	0.466482i
$290$	9.79455	−	16.9647i	0.575156	−	0.996199i
$291$	24.4530	+	5.40944i	1.43346	+	0.317107i
$292$	1.25740	+	2.17787i	0.0735835	+	0.127450i
$293$	−9.44192	+	16.3539i	−0.551603	+	0.955404i	0.446556	+	0.894756i	$0.352650\pi$
$293$	−9.44192	+	16.3539i	−0.551603	+	0.955404i	−0.998159	+	0.0606487i	$0.980683\pi$
$294$		0			0
$295$	3.62863	+	6.28497i	0.211267	+	0.365925i
$296$	36.7242	−	63.6082i	2.13455	−	3.69715i
$297$	−6.47118	+	2.69079i	−0.375496	+	0.156136i
$298$	−18.5559	−	32.1398i	−1.07492	−	1.86181i
$299$	0.905400			0.0523606
$300$	−6.95823	−	22.0338i	−0.401733	−	1.27212i
$301$		0			0
$302$	5.29401	−	9.16950i	0.304636	−	0.527645i
$303$	5.13126	+	16.2485i	0.294783	+	0.933454i
$304$	−4.41549	+	7.64785i	−0.253246	+	0.438634i
$305$	−0.305392	−	0.528954i	−0.0174867	−	0.0302878i
$306$	18.6742	−	13.1011i	1.06753	−	0.748940i
$307$	−21.6407			−1.23510			−0.617551	−	0.786531i	$-0.711875\pi$
$307$	−21.6407			−1.23510			−0.617551	+	0.786531i	$0.711875\pi$
$308$		0			0
$309$	−18.7008	−	4.13696i	−1.06385	−	0.235343i
$310$	−16.0016	−	27.7156i	−0.908830	−	1.57414i
$311$	4.49448			0.254859			0.127429	−	0.991848i	$-0.459327\pi$
$311$	4.49448			0.254859			0.127429	+	0.991848i	$0.459327\pi$
$312$	15.1774	+	48.0604i	0.859251	+	2.72089i
$313$	8.60204			0.486216			0.243108	−	0.969999i	$-0.421833\pi$
$313$	8.60204			0.486216			0.243108	+	0.969999i	$0.421833\pi$
$314$	0.799206			0.0451018
$315$		0			0
$316$	−84.4062			−4.74822
$317$	−8.06255			−0.452838			−0.226419	−	0.974030i	$-0.572702\pi$
$317$	−8.06255			−0.452838			−0.226419	+	0.974030i	$0.572702\pi$
$318$	12.7971	+	2.83094i	0.717623	+	0.158751i
$319$	6.13402			0.343439
$320$	20.7053	+	35.8626i	1.15746	+	2.00478i
$321$	−1.00370	−	3.17828i	−0.0560208	−	0.177394i
$322$		0			0
$323$	1.75228			0.0974992
$324$	−47.5977	+	8.48198i	−2.64432	+	0.471221i
$325$	−3.94646	−	6.83546i	−0.218910	−	0.379163i
$326$	14.5383	−	25.1811i	0.805203	−	1.39465i
$327$	31.4672	+	6.96111i	1.74014	+	0.384950i
$328$	−45.8981	+	79.4978i	−2.53430	+	4.38953i
$329$		0			0
$330$	−6.79458	+	7.42175i	−0.374029	+	0.408554i
$331$	−22.9026			−1.25884			−0.629419	−	0.777066i	$-0.716707\pi$
$331$	−22.9026			−1.25884			−0.629419	+	0.777066i	$0.716707\pi$
$332$	−37.5681	−	65.0698i	−2.06182	−	3.57117i
$333$	21.8218	+	10.1516i	1.19583	+	0.556302i
$334$	−4.34075	+	7.51840i	−0.237515	+	0.411388i
$335$	−2.01405	−	3.48844i	−0.110039	−	0.190594i
$336$		0			0
$337$	−6.81891	+	11.8107i	−0.371450	+	0.643369i	−0.989789	−	0.142542i	$-0.954472\pi$
$337$	−6.81891	+	11.8107i	−0.371450	+	0.643369i	0.618339	+	0.785911i	$0.287806\pi$
$338$	−3.93458	−	6.81489i	−0.214013	−	0.370681i
$339$	−1.66218	−	5.26342i	−0.0902772	−	0.285870i
$340$	11.9331	−	20.6688i	0.647164	−	1.12092i
$341$	5.01065	−	8.67869i	0.271342	−	0.469978i
$342$	−4.62097	−	2.14968i	−0.249873	−	0.116242i
$343$		0			0
$344$	28.6502	+	49.6237i	1.54472	+	2.67553i
$345$	0.235712	+	0.746399i	0.0126903	+	0.0401848i
$346$	31.0543			1.66949
$347$	−2.82563			−0.151688			−0.0758440	−	0.997120i	$-0.524165\pi$
$347$	−2.82563			−0.151688			−0.0758440	+	0.997120i	$0.524165\pi$
$348$	41.3171	+	9.14010i	2.21483	+	0.489961i
$349$	−1.81202	−	3.13851i	−0.0969951	−	0.168000i	0.813444	−	0.581643i	$-0.197590\pi$
$349$	−1.81202	−	3.13851i	−0.0969951	−	0.168000i	−0.910440	+	0.413642i	$0.864256\pi$
$350$		0			0
$351$	−15.2493	+	6.34083i	−0.813947	+	0.338448i
$352$	−13.4947	+	23.3734i	−0.719268	+	1.24581i
$353$	1.37701	−	2.38504i	0.0732907	−	0.126943i	−0.827051	−	0.562127i	$-0.809983\pi$
$353$	1.37701	−	2.38504i	0.0732907	−	0.126943i	0.900342	+	0.435184i	$0.143317\pi$
$354$	−14.5272	+	15.8681i	−0.772110	+	0.843380i
$355$	−1.15179	−	1.99495i	−0.0611304	−	0.105881i
$356$	6.94877	−	12.0356i	0.368284	−	0.637887i
$357$		0			0
$358$	1.49135	+	2.58310i	0.0788205	+	0.136521i
$359$	8.40076	−	14.5505i	0.443375	−	0.767948i	−0.554562	−	0.832142i	$-0.687114\pi$
$359$	8.40076	−	14.5505i	0.443375	−	0.767948i	0.997937	+	0.0641941i	$0.0204477\pi$
$360$	−35.6691	+	25.0241i	−1.87992	+	1.31888i
$361$	9.30425	+	16.1154i	0.489698	+	0.848181i
$362$	−8.66163			−0.455245
$363$	15.5264	+	3.43471i	0.814922	+	0.180276i
$364$		0			0
$365$	−0.371322	+	0.643149i	−0.0194359	+	0.0336640i
$366$	1.22263	−	1.33549i	0.0639080	−	0.0698070i
$367$	11.9670	−	20.7274i	0.624670	−	1.08196i	−0.363934	−	0.931425i	$-0.618567\pi$
$367$	11.9670	−	20.7274i	0.624670	−	1.08196i	0.988605	−	0.150536i	$-0.0480999\pi$
$368$	2.01030	+	3.48193i	0.104794	+	0.181508i
$369$	−27.2730	−	12.6875i	−1.41978	−	0.660483i
$370$	34.5551			1.79644
$371$		0			0
$372$	46.6822	−	50.9912i	2.42036	−	2.64377i
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	0.999990	−	0.00455622i	$-0.00145030\pi$
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	−0.503941	+	0.863738i	$0.668117\pi$
$374$	10.2557			0.530309
$375$	13.8847	−	15.1663i	0.717002	−	0.783184i
$376$	−102.060			−5.26334
$377$	14.4548			0.744458
$378$		0			0
$379$	10.0770			0.517622			0.258811	−	0.965928i	$-0.416669\pi$
$379$	10.0770			0.517622			0.258811	+	0.965928i	$0.416669\pi$
$380$	−5.33217			−0.273534
$381$	−9.79388	+	10.6979i	−0.501756	+	0.548070i
$382$	−10.5025			−0.537357
$383$	10.0718	+	17.4448i	0.514643	+	0.891388i	0.999856	+	0.0169915i	$0.00540883\pi$
$383$	10.0718	+	17.4448i	0.514643	+	0.891388i	−0.485213	+	0.874396i	$0.661258\pi$
$384$	−36.0855	+	39.4164i	−1.84148	+	2.01146i
$385$		0			0
$386$	11.2294			0.571561
$387$	−15.3708	+	10.7836i	−0.781340	+	0.548159i
$388$	38.8372	+	67.2679i	1.97166	+	3.41501i
$389$	−6.69736	+	11.6002i	−0.339570	+	0.588152i	−0.984352	−	0.176215i	$-0.943615\pi$
$389$	−6.69736	+	11.6002i	−0.339570	+	0.588152i	0.644782	+	0.764366i	$0.276948\pi$
$390$	−16.0114	+	17.4893i	−0.810767	+	0.885605i
$391$	0.398891	−	0.690899i	0.0201728	−	0.0349402i
$392$		0			0
$393$	20.2476	+	4.47913i	1.02136	+	0.225942i
$394$	2.41448			0.121640
$395$	−12.4630	−	21.5866i	−0.627083	−	1.08614i
$396$	−19.7081	−	9.16824i	−0.990369	−	0.460721i
$397$	9.00664	−	15.6000i	0.452031	−	0.782940i	−0.546482	−	0.837471i	$-0.684033\pi$
$397$	9.00664	−	15.6000i	0.452031	−	0.782940i	0.998512	+	0.0545313i	$0.0173665\pi$
$398$	8.58506	+	14.8698i	0.430330	+	0.745354i
$399$		0			0
$400$	17.5249	−	30.3541i	0.876247	−	1.51770i
$401$	−14.4337	−	25.0000i	−0.720787	−	1.24844i	−0.960685	−	0.277642i	$-0.910447\pi$
$401$	−14.4337	−	25.0000i	−0.720787	−	1.24844i	0.239898	−	0.970798i	$-0.422886\pi$
$402$	8.06324	−	8.80751i	0.402158	−	0.439279i
$403$	11.8075	−	20.4513i	0.588176	−	1.01875i
$404$	−26.4240	+	45.7676i	−1.31464	+	2.27703i
$405$	−9.19729	−	10.9205i	−0.457017	−	0.542646i
$406$		0			0
$407$	5.41019	+	9.37073i	0.268173	+	0.464490i
$408$	43.3610	+	9.59222i	2.14669	+	0.474886i
$409$	−10.8587			−0.536931			−0.268465	−	0.963289i	$-0.586516\pi$
$409$	−10.8587			−0.536931			−0.268465	+	0.963289i	$0.586516\pi$
$410$	−43.1872			−2.13286
$411$	8.63255	+	27.3356i	0.425812	+	1.34837i
$412$	−29.7014	−	51.4443i	−1.46328	−	2.53448i
$413$		0			0
$414$	−1.89951	+	1.33263i	−0.0933561	+	0.0654951i
$415$	11.0943	−	19.2158i	0.544595	−	0.943267i
$416$	−31.8001	+	55.0793i	−1.55913	+	2.70049i
$417$	−4.12179	−	13.0520i	−0.201845	−	0.639158i
$418$	−1.14566	−	1.98434i	−0.0560359	−	0.0970570i
$419$	−0.247572	+	0.428807i	−0.0120947	+	0.0209486i	−0.872009	−	0.489489i	$-0.837183\pi$
$419$	−0.247572	+	0.428807i	−0.0120947	+	0.0209486i	0.859915	+	0.510438i	$0.170517\pi$
$420$		0			0
$421$	9.50320	+	16.4600i	0.463158	+	0.802212i	0.999116	−	0.0420318i	$-0.0133831\pi$
$421$	9.50320	+	16.4600i	0.463158	+	0.802212i	−0.535959	+	0.844244i	$0.680050\pi$
$422$	−15.5113	+	26.8664i	−0.755079	+	1.30784i
$423$	−2.94502	−	33.3130i	−0.143192	−	1.61974i
$424$	12.7578	+	22.0971i	0.619572	+	1.07313i
$425$	−6.95473			−0.337354
$426$	4.61116	−	5.03679i	0.223411	−	0.244033i
$427$		0			0
$428$	5.16864	−	8.95234i	0.249835	−	0.432728i
$429$	−7.24963	−	1.60375i	−0.350016	−	0.0774298i
$430$	−13.4790	+	23.3464i	−0.650016	+	1.12586i
$431$	8.46073	+	14.6544i	0.407539	+	0.705878i	0.994613	−	0.103655i	$-0.0330538\pi$
$431$	8.46073	+	14.6544i	0.407539	+	0.705878i	−0.587074	+	0.809533i	$0.699720\pi$
$432$	−58.2438	−	44.5660i	−2.80226	−	2.14418i
$433$	−33.4740			−1.60866			−0.804330	−	0.594183i	$-0.797476\pi$
$433$	−33.4740			−1.60866			−0.804330	+	0.594183i	$0.797476\pi$
$434$		0			0
$435$	3.76315	+	11.9163i	0.180429	+	0.571343i
$436$	49.9774	+	86.5634i	2.39348	+	4.14564i
$437$	−0.178239			−0.00852634
$438$	−2.14955	−	0.475519i	−0.102709	−	0.0227212i
$439$	20.9315			0.999005			0.499502	−	0.866313i	$-0.333516\pi$
$439$	20.9315			0.999005			0.499502	+	0.866313i	$0.333516\pi$
$440$	−19.5891			−0.933874
$441$		0			0
$442$	24.1674			1.14953
$443$	−30.8580			−1.46611			−0.733054	−	0.680170i	$-0.761906\pi$
$443$	−30.8580			−1.46611			−0.733054	+	0.680170i	$0.761906\pi$
$444$	22.4786	+	71.1804i	1.06679	+	3.37807i
$445$	4.10409			0.194553
$446$	−22.6972	−	39.3128i	−1.07475	−	1.86151i
$447$	23.1157	+	5.11362i	1.09334	+	0.241866i
$448$		0			0
$449$	−33.2789			−1.57053			−0.785263	−	0.619162i	$-0.787472\pi$
$449$	−33.2789			−1.57053			−0.785263	+	0.619162i	$0.787472\pi$
$450$	18.3405	+	8.53203i	0.864579	+	0.402204i
$451$	−6.76168	−	11.7116i	−0.318395	−	0.551477i
$452$	8.55957	−	14.8256i	0.402608	−	0.697338i
$453$	2.03400	+	6.44083i	0.0955658	+	0.302617i
$454$	23.1737	−	40.1380i	1.08760	−	1.88377i
$455$		0			0
$456$	−2.98786	−	9.46130i	−0.139919	−	0.443066i
$457$	23.7904			1.11287			0.556434	−	0.830892i	$-0.312169\pi$
$457$	23.7904			1.11287			0.556434	+	0.830892i	$0.312169\pi$
$458$	26.8654	+	46.5323i	1.25534	+	2.17431i
$459$	−1.87975	+	14.4301i	−0.0877393	+	0.673539i
$460$	−1.21382	+	2.10240i	−0.0565947	+	0.0980249i
$461$	8.53122	+	14.7765i	0.397339	+	0.688211i	0.993397	−	0.114731i	$-0.0366005\pi$
$461$	8.53122	+	14.7765i	0.397339	+	0.688211i	−0.596058	+	0.802941i	$0.703267\pi$
$462$		0			0
$463$	18.1243	−	31.3922i	0.842306	−	1.45892i	−0.0456338	−	0.998958i	$-0.514531\pi$
$463$	18.1243	−	31.3922i	0.842306	−	1.45892i	0.887940	−	0.459959i	$-0.152136\pi$
$464$	32.0945	+	55.5893i	1.48995	+	2.58067i
$465$	19.9337	+	4.40970i	0.924404	+	0.204495i
$466$	8.05253	−	13.9474i	0.373026	−	0.646100i
$467$	4.09580	−	7.09413i	0.189531	−	0.328277i	−0.755563	−	0.655076i	$-0.772637\pi$
$467$	4.09580	−	7.09413i	0.189531	−	0.328277i	0.945094	+	0.326799i	$0.105970\pi$
$468$	−46.4420	−	21.6049i	−2.14678	−	0.998686i
$469$		0			0
$470$	−24.0080	−	41.5830i	−1.10740	−	1.91808i
$471$	−0.344268	+	0.376045i	−0.0158630	+	0.0173272i
$472$	−41.8826			−1.92780
$473$	−8.44148			−0.388140
$474$	49.8956	−	54.5012i	2.29178	−	2.50332i
$475$	0.776909	+	1.34565i	0.0356470	+	0.0617425i
$476$		0			0
$477$	−6.84451	+	4.80185i	−0.313389	+	0.219862i
$478$	27.2265	−	47.1577i	1.24531	−	2.15694i
$479$	12.7775	−	22.1312i	0.583817	−	1.01120i	−0.411205	−	0.911543i	$-0.634892\pi$
$479$	12.7775	−	22.1312i	0.583817	−	1.01120i	0.995022	−	0.0996574i	$-0.0317747\pi$
$480$	−53.6854	−	11.8762i	−2.45039	−	0.542071i
$481$	12.7491	+	22.0820i	0.581308	+	1.00685i
$482$	39.7614	−	68.8687i	1.81108	−	3.13688i
$483$		0			0
$484$	24.6596	+	42.7116i	1.12089	+	1.94144i
$485$	−11.4690	+	19.8649i	−0.520782	+	0.902020i
$486$	22.6599	−	35.7479i	1.02787	−	1.62156i
$487$	3.46140	+	5.99533i	0.156851	+	0.271674i	0.933732	−	0.357974i	$-0.116532\pi$
$487$	3.46140	+	5.99533i	0.156851	+	0.271674i	−0.776880	+	0.629648i	$0.783199\pi$
$488$	3.52491			0.159565
$489$	5.58574	+	17.6877i	0.252596	+	0.799865i
$490$		0			0
$491$	18.7262	−	32.4348i	0.845103	−	1.46376i	−0.0404294	−	0.999182i	$-0.512873\pi$
$491$	18.7262	−	32.4348i	0.845103	−	1.46376i	0.885532	−	0.464578i	$-0.153794\pi$
$492$	−28.0939	−	88.9615i	−1.26657	−	4.01070i
$493$	6.36831	−	11.0302i	0.286814	−	0.496777i
$494$	−2.69973	−	4.67607i	−0.121467	−	0.210386i
$495$	−0.565259	−	6.39402i	−0.0254065	−	0.287390i
$496$	104.867			4.70867
$497$		0			0
$498$	64.2235	+	14.2074i	2.87793	+	0.636649i
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	−0.996196	−	0.0871432i	$-0.972226\pi$
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	0.422630	−	0.906302i	$-0.361107\pi$
$500$	63.7733			2.85203
$501$	−1.66775	−	5.28106i	−0.0745096	−	0.235941i
$502$	61.8658			2.76121
$503$	−5.79692			−0.258472			−0.129236	−	0.991614i	$-0.541252\pi$
$503$	−5.79692			−0.258472			−0.129236	+	0.991614i	$0.541252\pi$
$504$		0			0
$505$	−15.6066			−0.694483
$506$	−1.04320			−0.0463757
$507$	4.90143	+	1.08429i	0.217680	+	0.0481548i
$508$	−44.9840			−1.99584
$509$	−12.5697	−	21.7714i	−0.557144	−	0.965002i	−0.997733	−	0.0672931i	$-0.978564\pi$
$509$	−12.5697	−	21.7714i	−0.557144	−	0.965002i	0.440589	−	0.897709i	$-0.354770\pi$
$510$	6.29174	+	19.9233i	0.278603	+	0.882218i
$511$		0			0
$512$	−23.9940			−1.06039
$513$	3.00201	−	1.24827i	0.132542	−	0.0551125i
$514$	−32.9738	−	57.1123i	−1.45441	−	2.51911i
$515$	8.77113	−	15.1920i	0.386502	−	0.669441i
$516$	−56.8596	−	12.5784i	−2.50311	−	0.553732i
$517$	7.51771	−	13.0211i	0.330629	−	0.572665i
$518$		0			0
$519$	−13.3770	+	14.6118i	−0.587186	+	0.641386i
$520$	−46.1616			−2.02432
$521$	−3.64828	−	6.31900i	−0.159834	−	0.276841i	0.774975	−	0.631992i	$-0.217763\pi$
$521$	−3.64828	−	6.31900i	−0.159834	−	0.276841i	−0.934809	+	0.355152i	$0.884429\pi$
$522$	−30.3259	+	21.2755i	−1.32733	+	0.931203i
$523$	−8.38637	+	14.5256i	−0.366710	+	0.635161i	−0.989049	−	0.147587i	$-0.952849\pi$
$523$	−8.38637	+	14.5256i	−0.366710	+	0.635161i	0.622339	+	0.782748i	$0.286183\pi$
$524$	32.1580	+	55.6993i	1.40483	+	2.43324i
$525$		0			0
$526$	−11.6908	+	20.2490i	−0.509741	+	0.882898i
$527$	−10.4041	−	18.0204i	−0.453208	−	0.784979i
$528$	−9.92904	−	31.4411i	−0.432106	−	1.36830i
$529$	11.4594	−	19.8483i	0.498236	−	0.862970i
$530$	−6.00212	+	10.3960i	−0.260716	+	0.451573i
$531$	−1.20855	−	13.6707i	−0.0524468	−	0.593260i
$532$		0			0
$533$	−15.9339	−	27.5982i	−0.690172	−	1.19541i
$534$	3.66374	+	11.6015i	0.158546	+	0.502047i
$535$	3.05271			0.131980
$536$	23.2467			1.00411
$537$	−1.85783	−	0.410985i	−0.0801712	−	0.0177353i
$538$	−20.6774	−	35.8143i	−0.891466	−	1.54406i
$539$		0			0
$540$	5.72007	−	43.9107i	0.246153	−	1.88962i
$541$	2.64908	−	4.58834i	0.113893	−	0.197268i	−0.803444	−	0.595381i	$-0.797001\pi$
$541$	2.64908	−	4.58834i	0.113893	−	0.197268i	0.917337	+	0.398112i	$0.130335\pi$
$542$	−6.35097	+	11.0002i	−0.272798	+	0.472499i
$543$	3.73110	−	4.07550i	0.160117	−	0.174896i
$544$	28.0202	+	48.5324i	1.20136	+	2.08081i
$545$	−14.7589	+	25.5631i	−0.632200	+	1.09500i
$546$		0			0
$547$	16.4325	+	28.4619i	0.702603	+	1.21694i	0.967550	+	0.252681i	$0.0813123\pi$
$547$	16.4325	+	28.4619i	0.702603	+	1.21694i	−0.264947	+	0.964263i	$0.585354\pi$
$548$	−44.4542	+	76.9970i	−1.89899	+	3.28915i
$549$	0.101714	+	1.15055i	0.00434105	+	0.0491045i
$550$	4.54708	+	7.87577i	0.193888	+	0.335824i
$551$	−2.84560			−0.121227
$552$	−4.41062	−	0.975709i	−0.187729	−	0.0415290i
$553$		0			0
$554$	−22.2515	+	38.5408i	−0.945376	+	1.63744i
$555$	−14.8850	+	16.2590i	−0.631835	+	0.690156i
$556$	21.2256	−	36.7638i	0.900166	−	1.55913i
$557$	9.40798	+	16.2951i	0.398629	+	0.690446i	0.993557	−	0.113333i	$-0.0361527\pi$
$557$	9.40798	+	16.2951i	0.398629	+	0.690446i	−0.594928	+	0.803779i	$0.702819\pi$
$558$	5.32951	+	60.2856i	0.225616	+	2.55209i
$559$	−19.8923			−0.841354
$560$		0			0
$561$	−4.41776	+	4.82554i	−0.186518	+	0.203734i
$562$	−4.77054	−	8.26282i	−0.201233	−	0.348546i
$563$	27.6650			1.16594			0.582970	−	0.812494i	$-0.301891\pi$
$563$	27.6650			1.16594			0.582970	+	0.812494i	$0.301891\pi$
$564$	70.0396	−	76.5046i	2.94920	−	3.22142i
$565$	5.05547			0.212685
$566$	−70.7856			−2.97534
$567$		0			0
$568$	13.2942			0.557812
$569$	−40.1831			−1.68456			−0.842282	−	0.539037i	$-0.818788\pi$
$569$	−40.1831			−1.68456			−0.842282	+	0.539037i	$0.818788\pi$
$570$	3.15204	−	3.44299i	0.132024	−	0.144211i
$571$	−6.81129			−0.285044			−0.142522	−	0.989792i	$-0.545521\pi$
$571$	−6.81129			−0.285044			−0.142522	+	0.989792i	$0.545521\pi$
$572$	−11.5142	−	19.9431i	−0.481431	−	0.833863i
$573$	4.52409	−	4.94169i	0.188997	−	0.206442i
$574$		0			0
$575$	0.707427			0.0295017
$576$	−6.89612	−	78.0065i	−0.287338	−	3.25027i
$577$	18.2111	+	31.5425i	0.758138	+	1.31313i	0.943799	+	0.330519i	$0.107224\pi$
$577$	18.2111	+	31.5425i	0.758138	+	1.31313i	−0.185661	+	0.982614i	$0.559443\pi$
$578$	−12.4312	+	21.5315i	−0.517071	+	0.895593i
$579$	−4.83720	+	5.28369i	−0.201027	+	0.219583i
$580$	−19.3787	+	33.5649i	−0.804658	+	1.39371i
$581$		0			0
$582$	−66.3930	−	14.6873i	−2.75208	−	0.608810i
$583$	−3.75894			−0.155679
$584$	−2.14295	−	3.71170i	−0.0886759	−	0.153591i
$585$	−1.33203	−	15.0674i	−0.0550726	−	0.622962i
$586$	25.6361	−	44.4030i	1.05902	−	1.83427i
$587$	5.57943	+	9.66385i	0.230288	+	0.398870i	0.957893	−	0.287126i	$-0.0927000\pi$
$587$	5.57943	+	9.66385i	0.230288	+	0.398870i	−0.727605	+	0.685996i	$0.759367\pi$
$588$		0			0
$589$	−2.32446	+	4.02609i	−0.0957779	+	0.165892i
$590$	−9.85220	−	17.0645i	−0.405609	−	0.702535i
$591$	−1.04007	+	1.13607i	−0.0427826	+	0.0467316i
$592$	−56.6145	+	98.0593i	−2.32684	+	4.03021i
$593$	−9.90427	+	17.1547i	−0.406720	+	0.704459i	−0.994520	−	0.104547i	$-0.966661\pi$
$593$	−9.90427	+	17.1547i	−0.406720	+	0.704459i	0.587800	+	0.809006i	$0.299994\pi$
$594$	17.5701	−	7.30586i	0.720911	−	0.299763i
$595$		0			0
$596$	36.7133	+	63.5893i	1.50384	+	2.60472i
$597$	−10.6947	−	2.36586i	−0.437705	−	0.0968281i
$598$	−2.45828			−0.100527
$599$	−18.1320			−0.740853			−0.370427	−	0.928862i	$-0.620789\pi$
$599$	−18.1320			−0.740853			−0.370427	+	0.928862i	$0.620789\pi$
$600$	11.8587	+	37.5516i	0.484131	+	1.53304i
$601$	−12.3285	−	21.3536i	−0.502889	−	0.871030i	−0.999994	−	0.00333942i	$-0.998937\pi$
$601$	−12.3285	−	21.3536i	−0.502889	−	0.871030i	0.497105	−	0.867690i	$-0.334396\pi$
$602$		0			0
$603$	0.670802	+	7.58788i	0.0273172	+	0.309003i
$604$	−10.4743	+	18.1420i	−0.426194	+	0.738189i
$605$	−7.28223	+	12.6132i	−0.296065	+	0.512799i
$606$	−13.9321	−	44.1169i	−0.565951	−	1.79213i
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	0.635725	−	0.771916i	$-0.280701\pi$
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	−0.986361	+	0.164596i	$0.947368\pi$
$608$	6.26024	−	10.8431i	0.253886	−	0.439744i
$609$		0			0
$610$	0.829179	+	1.43618i	0.0335725	+	0.0581492i
$611$	17.7154	−	30.6840i	0.716689	−	1.24134i
$612$	−36.9472	+	25.9208i	−1.49350	+	1.04779i
$613$	−9.77828	−	16.9365i	−0.394941	−	0.684058i	0.598153	−	0.801382i	$-0.295902\pi$
$613$	−9.77828	−	16.9365i	−0.394941	−	0.684058i	−0.993094	+	0.117324i	$0.962568\pi$
$614$	58.7575			2.37126
$615$	18.6034	−	20.3206i	0.750161	−	0.819404i
$616$		0			0
$617$	10.8723	−	18.8314i	0.437702	−	0.758122i	−0.559810	−	0.828621i	$-0.689126\pi$
$617$	10.8723	−	18.8314i	0.437702	−	0.758122i	0.997512	+	0.0704988i	$0.0224591\pi$
$618$	50.7752	+	11.2324i	2.04248	+	0.451833i
$619$	−16.9024	+	29.2758i	−0.679366	+	1.17670i	0.295807	+	0.955248i	$0.404412\pi$
$619$	−16.9024	+	29.2758i	−0.679366	+	1.17670i	−0.975172	+	0.221448i	$0.928922\pi$
$620$	31.6595	+	54.8359i	1.27148	+	2.20226i
$621$	0.191206	−	1.46781i	0.00767284	−	0.0589013i
$622$	−12.2031			−0.489300
$623$		0			0
$624$	−23.3977	−	74.0906i	−0.936658	−	2.96600i
$625$	3.20808	+	5.55655i	0.128323	+	0.222262i
$626$	−23.3557			−0.933481
$627$	1.42718	+	0.315718i	0.0569961	+	0.0126086i
$628$	−1.58125			−0.0630986
$629$	22.4674			0.895832
$630$		0			0
$631$	−23.6410			−0.941134			−0.470567	−	0.882364i	$-0.655951\pi$
$631$	−23.6410			−0.941134			−0.470567	+	0.882364i	$0.655951\pi$
$632$	143.852			5.72211
$633$	−5.95957	−	18.8715i	−0.236872	−	0.750073i
$634$	21.8909			0.869399
$635$	−6.64213	−	11.5045i	−0.263585	−	0.456542i
$636$	−25.3192	−	5.60107i	−1.00397	−	0.222097i
$637$		0			0
$638$	−16.6547			−0.659365
$639$	0.383615	+	4.33932i	0.0151756	+	0.171661i
$640$	−24.4729	−	42.3883i	−0.967375	−	1.67554i
$641$	−7.95901	+	13.7854i	−0.314362	+	0.544491i	−0.979302	−	0.202406i	$-0.935124\pi$
$641$	−7.95901	+	13.7854i	−0.314362	+	0.544491i	0.664940	+	0.746897i	$0.268457\pi$
$642$	2.72517	+	8.62945i	0.107554	+	0.340577i
$643$	−13.2527	+	22.9544i	−0.522636	+	0.905231i	0.477017	+	0.878894i	$0.341718\pi$
$643$	−13.2527	+	22.9544i	−0.522636	+	0.905231i	−0.999653	+	0.0263376i	$0.991616\pi$
$644$		0			0
$645$	−5.17875	−	16.3989i	−0.203913	−	0.645707i
$646$	−4.75766			−0.187188
$647$	−0.00801958	−	0.0138903i	−0.000315282	−	0.000546085i	0.865868	−	0.500273i	$-0.166767\pi$
$647$	−0.00801958	−	0.0138903i	−0.000315282	−	0.000546085i	−0.866183	+	0.499727i	$0.833434\pi$
$648$	81.1196	−	14.4556i	3.18668	−	0.567871i
$649$	3.08506	−	5.34348i	0.121099	−	0.209750i
$650$	10.7152	+	18.5592i	0.420283	+	0.727951i
$651$		0			0
$652$	−28.7644	+	49.8214i	−1.12650	+	1.95115i
$653$	16.6440	+	28.8282i	0.651328	+	1.12813i	0.982801	+	0.184669i	$0.0591212\pi$
$653$	16.6440	+	28.8282i	0.651328	+	1.12813i	−0.331473	+	0.943465i	$0.607545\pi$
$654$	−85.4376	−	18.9003i	−3.34087	−	0.739062i
$655$	−9.49661	+	16.4486i	−0.371063	+	0.642700i
$656$	70.7571	−	122.555i	2.76260	−	4.78497i
$657$	1.14969	−	0.806577i	0.0448535	−	0.0314676i
$658$		0			0
$659$	19.4156	+	33.6288i	0.756324	+	1.30999i	0.944713	+	0.327897i	$0.106340\pi$
$659$	19.4156	+	33.6288i	0.756324	+	1.30999i	−0.188389	+	0.982094i	$0.560327\pi$
$660$	13.4432	−	14.6841i	0.523276	−	0.571577i
$661$	5.30644			0.206397			0.103198	−	0.994661i	$-0.467092\pi$
$661$	5.30644			0.206397			0.103198	+	0.994661i	$0.467092\pi$
$662$	62.1835			2.41683
$663$	−10.4104	+	11.3713i	−0.404307	+	0.441626i
$664$	64.0264	+	110.897i	2.48471	+	4.30364i
$665$		0			0
$666$	−59.2492	−	27.5628i	−2.29586	−	1.06804i
$667$	−0.647777	+	1.12198i	−0.0250820	+	0.0434433i
$668$	8.58826	−	14.8753i	0.332290	−	0.575543i
$669$	28.2747	+	6.25487i	1.09316	+	0.241827i
$670$	5.46842	+	9.47158i	0.211263	+	0.365919i
$671$	−0.259644	+	0.449717i	−0.0100235	+	0.0173611i
$672$		0			0
$673$	−3.03565	−	5.25789i	−0.117016	−	0.202677i	0.801568	−	0.597903i	$-0.203999\pi$
$673$	−3.03565	−	5.25789i	−0.117016	−	0.202677i	−0.918584	+	0.395227i	$0.870666\pi$
$674$	18.5142	−	32.0676i	0.713142	−	1.23520i
$675$	−11.9149	+	4.95435i	−0.458605	+	0.190693i
$676$	7.78465	+	13.4834i	0.299410	+	0.518593i
$677$	−34.7850			−1.33690			−0.668449	−	0.743758i	$-0.733041\pi$
$677$	−34.7850			−1.33690			−0.668449	+	0.743758i	$0.733041\pi$
$678$	4.51304	+	14.2909i	0.173322	+	0.548838i
$679$		0			0
$680$	−20.3373	+	35.2253i	−0.779901	+	1.35083i
$681$	8.90352	+	28.1937i	0.341184	+	1.08038i
$682$	−13.6046	+	23.5638i	−0.520946	+	0.902305i
$683$	−9.71206	−	16.8218i	−0.371622	−	0.643667i	0.618194	−	0.786026i	$-0.287865\pi$
$683$	−9.71206	−	16.8218i	−0.371622	−	0.643667i	−0.989815	+	0.142358i	$0.954531\pi$
$684$	9.14268	+	4.25319i	0.349579	+	0.162625i
$685$	−26.2556			−1.00318
$686$		0			0
$687$	−33.4672	−	7.40354i	−1.27685	−	0.282463i
$688$	−44.1676	−	76.5006i	−1.68387	−	2.91656i
$689$	−8.85791			−0.337459
$690$	−0.639988	−	2.02657i	−0.0243639	−	0.0771503i
$691$	−6.63675			−0.252474			−0.126237	−	0.992000i	$-0.540290\pi$
$691$	−6.63675			−0.252474			−0.126237	+	0.992000i	$0.540290\pi$
$692$	−61.4416			−2.33566
$693$		0			0
$694$	7.67197			0.291224
$695$	12.5363			0.475529
$696$	−70.4158	−	15.5773i	−2.66911	−	0.590454i
$697$	−28.0798			−1.06360
$698$	4.91987	+	8.52147i	0.186220	+	0.322542i
$699$	3.09385	+	9.79690i	0.117020	+	0.370553i
$700$		0			0
$701$	−13.9153			−0.525574			−0.262787	−	0.964854i	$-0.584642\pi$
$701$	−13.9153			−0.525574			−0.262787	+	0.964854i	$0.584642\pi$
$702$	41.4038	−	17.2162i	1.56269	−	0.649783i
$703$	−2.50982	−	4.34713i	−0.0946595	−	0.163955i
$704$	17.6036	−	30.4904i	0.663462	−	1.14915i
$705$	29.9075	+	6.61608i	1.12638	+	0.249176i
$706$	−3.73876	+	6.47571i	−0.140710	+	0.243717i
$707$		0			0
$708$	28.7423	−	31.3954i	1.08020	−	1.17991i
$709$	34.1556			1.28274			0.641370	−	0.767231i	$-0.278366\pi$
$709$	34.1556			1.28274			0.641370	+	0.767231i	$0.278366\pi$
$710$	3.12725	+	5.41655i	0.117364	+	0.203280i
$711$	4.15095	+	46.9541i	0.155673	+	1.76092i
$712$	−11.8426	+	20.5120i	−0.443821	+	0.768721i
$713$	1.05829	+	1.83301i	0.0396332	+	0.0686467i
$714$		0			0
$715$	3.40025	−	5.88941i	0.127162	−	0.220251i
$716$	−2.95068	−	5.11072i	−0.110272	−	0.190997i
$717$	10.4606	+	33.1244i	0.390660	+	1.23705i
$718$	−22.8092	+	39.5066i	−0.851231	+	1.47437i
$719$	22.1450	−	38.3563i	0.825870	−	1.43045i	−0.0753825	−	0.997155i	$-0.524018\pi$
$719$	22.1450	−	38.3563i	0.825870	−	1.43045i	0.901253	−	0.433294i	$-0.142649\pi$
$720$	54.9879	−	38.5775i	2.04928	−	1.43770i
$721$		0			0
$722$	−25.2623	−	43.7556i	−0.940165	−	1.62841i
$723$	15.2766	+	48.3747i	0.568144	+	1.79907i
$724$	17.1372			0.636899
$725$	11.2941			0.419453
$726$	−42.1561	−	9.32569i	−1.56456	−	0.346109i
$727$	14.1247	+	24.4647i	0.523857	+	0.907346i	0.999614	+	0.0277700i	$0.00884060\pi$
$727$	14.1247	+	24.4647i	0.523857	+	0.907346i	−0.475758	+	0.879576i	$0.657826\pi$
$728$		0			0
$729$	7.05919	+	26.0608i	0.261451	+	0.965217i
$730$	1.00819	−	1.74623i	0.0373147	−	0.0646310i
$731$	−8.76391	+	15.1795i	−0.324145	+	0.561435i
$732$	−2.41900	+	2.64229i	−0.0894090	+	0.0976618i
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	0.999061	−	0.0433249i	$-0.0137951\pi$
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	−0.537051	+	0.843550i	$0.680462\pi$
$734$	−32.4919	+	56.2776i	−1.19930	+	2.07724i
$735$		0			0
$736$	−2.85018	−	4.93666i	−0.105059	−	0.181968i
$737$	−1.71235	+	2.96587i	−0.0630752	+	0.109249i
$738$	74.0499	+	34.4482i	2.72582	+	1.26805i
$739$	−16.0115	−	27.7327i	−0.588992	−	1.02016i	−0.994365	−	0.106013i	$-0.966192\pi$
$739$	−16.0115	−	27.7327i	−0.588992	−	1.02016i	0.405373	−	0.914151i	$-0.367142\pi$
$740$	−68.3680			−2.51326
$741$	3.36314	+	0.743987i	0.123548	+	0.0273311i
$742$		0			0
$743$	19.4031	−	33.6072i	0.711833	−	1.23293i	−0.252336	−	0.967640i	$-0.581199\pi$
$743$	19.4031	−	33.6072i	0.711833	−	1.23293i	0.964169	−	0.265290i	$-0.0854678\pi$
$744$	−79.5595	+	86.9032i	−2.91679	+	3.18602i
$745$	−10.8418	+	18.7786i	−0.397214	+	0.687995i
$746$	−26.0118	−	45.0537i	−0.952359	−	1.64953i
$747$	−34.3500	+	24.0987i	−1.25680	+	0.881724i
$748$	−20.2911			−0.741915
$749$		0			0
$750$	−37.6987	+	41.1785i	−1.37656	+	1.50363i
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	0.597311	−	0.802010i	$-0.296236\pi$
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	−0.993216	+	0.116282i	$0.962903\pi$
$752$	157.337			5.73749
$753$	−26.6494	+	29.1093i	−0.971160	+	1.06080i
$754$	−39.2466			−1.42928
$755$	−6.18635			−0.225144
$756$		0			0
$757$	33.5242			1.21846			0.609229	−	0.792995i	$-0.291479\pi$
$757$	33.5242			1.21846			0.609229	+	0.792995i	$0.291479\pi$
$758$	−27.3605			−0.993778
$759$	0.449369	−	0.490848i	0.0163111	−	0.0178166i
$760$	9.08748			0.329638
$761$	6.66048	+	11.5363i	0.241442	+	0.418190i	0.961125	−	0.276113i	$-0.0890462\pi$
$761$	6.66048	+	11.5363i	0.241442	+	0.418190i	−0.719683	+	0.694303i	$0.755713\pi$
$762$	26.5917	−	29.0462i	0.963315	−	1.05223i
$763$		0			0
$764$	20.7795			0.751775
$765$	−12.0846	−	5.62179i	−0.436920	−	0.203256i
$766$	−27.3462	−	47.3649i	−0.988057	−	1.71137i
$767$	7.26992	−	12.5919i	0.262502	−	0.454666i
$768$	36.9167	−	40.3243i	1.33212	−	1.45508i
$769$	27.3568	−	47.3833i	0.986510	−	1.70869i	0.351488	−	0.936192i	$-0.385676\pi$
$769$	27.3568	−	47.3833i	0.986510	−	1.70869i	0.635022	−	0.772494i	$-0.280991\pi$
$770$		0			0
$771$	41.0765	+	9.08686i	1.47933	+	0.327255i
$772$	−22.2176			−0.799628
$773$	−1.18021	−	2.04418i	−0.0424491	−	0.0735240i	0.844020	−	0.536311i	$-0.180183\pi$
$773$	−1.18021	−	2.04418i	−0.0424491	−	0.0735240i	−0.886469	+	0.462787i	$0.846849\pi$
$774$	41.7337	−	29.2788i	1.50009	−	1.05240i
$775$	9.22573	−	15.9794i	0.331398	−	0.573998i
$776$	−66.1892	−	114.643i	−2.37606	−	4.11545i
$777$		0			0
$778$	18.1842	−	31.4960i	0.651936	−	1.12919i
$779$	3.13678	+	5.43306i	0.112387	+	0.194660i
$780$	31.6788	−	34.6029i	1.13428	−	1.23898i
$781$	−0.979248	+	1.69611i	−0.0350403	+	0.0606915i
$782$	−1.08304	+	1.87588i	−0.0387295	+	0.0670814i
$783$	3.05261	−	23.4337i	0.109092	−	0.837452i
$784$		0			0
$785$	−0.233479	−	0.404398i	−0.00833323	−	0.0144336i
$786$	−54.9749	−	12.1614i	−1.96089	−	0.433784i
$787$	−1.66794			−0.0594557			−0.0297278	−	0.999558i	$-0.509464\pi$
$787$	−1.66794			−0.0594557			−0.0297278	+	0.999558i	$0.509464\pi$
$788$	−4.77709			−0.170177
$789$	−4.49168	−	14.2233i	−0.159908	−	0.506362i
$790$	33.8388	+	58.6105i	1.20393	+	2.08527i
$791$		0			0
$792$	33.5880	+	15.6252i	1.19350	+	0.555218i
$793$	−0.611849	+	1.05975i	−0.0217274	+	0.0376330i
$794$	−24.4542	+	42.3560i	−0.867848	+	1.50316i
$795$	−2.30607	−	7.30234i	−0.0817877	−	0.258987i
$796$	−16.9857	−	29.4201i	−0.602043	−	1.04277i
$797$	−14.3148	+	24.7939i	−0.507055	+	0.878244i	0.492912	+	0.870079i	$0.335932\pi$
$797$	−14.3148	+	24.7939i	−0.507055	+	0.878244i	−0.999967	+	0.00816511i	$0.997401\pi$
$798$		0			0
$799$	−15.6097	−	27.0368i	−0.552232	−	0.956493i
$800$	−24.8467	+	43.0358i	−0.878464	+	1.52154i
$801$	−7.03699	−	3.27362i	−0.248640	−	0.115668i
$802$	39.1895	+	67.8783i	1.38383	+	2.39687i
$803$	0.631397			0.0222815
$804$	−15.9533	+	17.4258i	−0.562629	+	0.614562i
$805$		0			0
$806$	−32.0591	+	55.5279i	−1.12923	+	1.95589i
$807$	25.7585	+	5.69824i	0.906742	+	0.200588i
$808$	45.0337	−	78.0007i	1.58428	−	2.74406i
$809$	1.42846	+	2.47416i	0.0502219	+	0.0869868i	0.890043	−	0.455876i	$-0.150674\pi$
$809$	1.42846	+	2.47416i	0.0502219	+	0.0869868i	−0.839822	+	0.542862i	$0.817340\pi$
$810$	24.9719	+	29.6507i	0.877422	+	1.04182i
$811$	26.2917			0.923225			0.461613	−	0.887082i	$-0.347271\pi$
$811$	26.2917			0.923225			0.461613	+	0.887082i	$0.347271\pi$
$812$		0			0
$813$	−2.44010	−	7.72675i	−0.0855779	−	0.270989i
$814$	−14.6894	−	25.4428i	−0.514863	−	0.891769i
$815$	−16.9889			−0.595094
$816$	−66.8459	−	14.7875i	−2.34007	−	0.517666i
$817$	3.91605			0.137005
$818$	29.4829			1.03085
$819$		0			0
$820$	85.4467			2.98393
$821$	−2.65849			−0.0927821			−0.0463910	−	0.998923i	$-0.514772\pi$
$821$	−2.65849			−0.0927821			−0.0463910	+	0.998923i	$0.514772\pi$
$822$	−23.4385	−	74.2199i	−0.817512	−	2.58872i
$823$	−12.2154			−0.425801			−0.212901	−	0.977074i	$-0.568291\pi$
$823$	−12.2154			−0.425801			−0.212901	+	0.977074i	$0.568291\pi$
$824$	50.6193	+	87.6752i	1.76341	+	3.05431i
$825$	−5.66444	−	1.25308i	−0.197211	−	0.0436265i
$826$		0			0
$827$	9.15812			0.318459			0.159230	−	0.987242i	$-0.449099\pi$
$827$	9.15812			0.318459			0.159230	+	0.987242i	$0.449099\pi$
$828$	3.75823	−	2.63663i	0.130607	−	0.0916293i
$829$	−9.17156	−	15.8856i	−0.318541	−	0.551730i	0.661642	−	0.749819i	$-0.269860\pi$
$829$	−9.17156	−	15.8856i	−0.318541	−	0.551730i	−0.980184	+	0.198089i	$0.936526\pi$
$830$	−30.1224	+	52.1735i	−1.04556	+	1.81097i
$831$	−8.54922	−	27.0718i	−0.296569	−	0.939109i
$832$	41.4828	−	71.8503i	1.43816	−	2.49096i
$833$		0			0
$834$	11.1912	+	35.4378i	0.387520	+	1.22711i
$835$	5.07241			0.175538
$836$	2.26670	+	3.92605i	0.0783956	+	0.135785i
$837$	−30.6615	−	23.4611i	−1.05982	−	0.810934i
$838$	0.672190	−	1.16427i	0.0232204	−	0.0402190i
$839$	−9.47055	−	16.4035i	−0.326960	−	0.566311i	0.654947	−	0.755675i	$-0.272691\pi$
$839$	−9.47055	−	16.4035i	−0.326960	−	0.566311i	−0.981907	+	0.189364i	$0.939357\pi$
$840$		0			0
$841$	4.15821	−	7.20224i	0.143387	−	0.248353i
$842$	−25.8024	−	44.6911i	−0.889211	−	1.54016i
$843$	5.94282	+	1.31466i	0.204682	+	0.0452793i
$844$	30.6895	−	53.1557i	1.05637	−	1.82969i
$845$	−2.29889	+	3.98179i	−0.0790842	+	0.136978i
$846$	7.99612	+	90.4493i	0.274912	+	3.10971i
$847$		0			0
$848$	−19.6676	−	34.0652i	−0.675387	−	1.16980i
$849$	30.4918	−	33.3063i	1.04647	−	1.14307i
$850$	18.8830			0.647682
$851$	−2.28535			−0.0783408
$852$	−9.12328	+	9.96540i	−0.312558	+	0.341409i
$853$	−9.97922	−	17.2845i	−0.341682	−	0.591811i	0.643063	−	0.765813i	$-0.277663\pi$
$853$	−9.97922	−	17.2845i	−0.341682	−	0.591811i	−0.984745	+	0.174002i	$0.944330\pi$
$854$		0			0
$855$	0.262227	+	2.96622i	0.00896796	+	0.101442i
$856$	−8.80878	+	15.2573i	−0.301078	+	0.521482i
$857$	8.20001	−	14.2028i	0.280107	−	0.485159i	−0.691304	−	0.722564i	$-0.742963\pi$
$857$	8.20001	−	14.2028i	0.280107	−	0.485159i	0.971411	+	0.237405i	$0.0762967\pi$
$858$	19.6837	+	4.35439i	0.671991	+	0.148657i
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	−0.996023	−	0.0890968i	$-0.971602\pi$
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	0.420851	−	0.907130i	$-0.361731\pi$
$860$	26.6685	−	46.1912i	0.909389	−	1.57511i
$861$		0			0
$862$	−22.9720	−	39.7887i	−0.782429	−	1.35521i
$863$	14.3415	−	24.8403i	0.488191	−	0.845572i	−0.511716	−	0.859154i	$-0.670990\pi$
$863$	14.3415	−	24.8403i	0.488191	−	0.845572i	0.999908	+	0.0135822i	$0.00432348\pi$
$864$	82.5775	+	63.1853i	2.80934	+	2.14961i
$865$	−9.07219	−	15.7135i	−0.308464	−	0.534275i
$866$	90.8865			3.08845
$867$	−4.77618	−	15.1241i	−0.162208	−	0.513643i
$868$		0			0
$869$	−10.5961	+	18.3529i	−0.359447	+	0.622581i
$870$	−10.2174	−	32.3543i	−0.346404	−	1.09691i
$871$	−4.03513	+	6.98906i	−0.136725	+	0.236815i
$872$	−85.1753	−	147.528i	−2.88440	−	4.99593i
$873$	35.5103	−	24.9127i	1.20184	−	0.843168i
$874$	0.483944			0.0163696
$875$		0			0
$876$	4.25292	+	0.940823i	0.143693	+	0.0317875i
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	0.999998	−	0.00175202i	$-0.000557684\pi$
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	−0.501517	+	0.865148i	$0.667224\pi$
$878$	−56.8317			−1.91798
$879$	9.84959	+	31.1895i	0.332218	+	1.05200i
$880$	30.1988			1.01800
$881$	57.5032			1.93733			0.968666	−	0.248366i	$-0.0798934\pi$
$881$	57.5032			1.93733			0.968666	+	0.248366i	$0.0798934\pi$
$882$		0			0
$883$	19.8715			0.668730			0.334365	−	0.942444i	$-0.391478\pi$
$883$	19.8715			0.668730			0.334365	+	0.942444i	$0.391478\pi$
$884$	−47.8158			−1.60822
$885$	12.2732	+	2.71505i	0.412559	+	0.0912656i
$886$	83.7836			2.81477
$887$	−18.5475	−	32.1253i	−0.622766	−	1.07866i	−0.988968	−	0.148127i	$-0.952676\pi$
$887$	−18.5475	−	32.1253i	−0.622766	−	1.07866i	0.366203	−	0.930535i	$-0.380658\pi$
$888$	−38.3098	−	121.311i	−1.28559	−	4.07093i
$889$		0			0
$890$	−11.1432			−0.373519
$891$	−4.13097	+	11.4142i	−0.138393	+	0.382391i
$892$	44.9070	+	77.7812i	1.50360	+	2.60431i
$893$	−3.48750	+	6.04053i	−0.116705	+	0.202139i
$894$	−62.7623	−	13.8842i	−2.09909	−	0.464356i
$895$	0.871366	−	1.50925i	0.0291266	−	0.0504487i
$896$		0			0
$897$	1.05893	−	1.15668i	0.0353568	−	0.0386204i
$898$	90.3565			3.01524
$899$	16.8956	+	29.2641i	0.563501	+	0.976012i
$900$	−36.2870	−	16.8808i	−1.20957	−	0.562693i
$901$	−3.90251	+	6.75935i	−0.130012	+	0.225187i
$902$	18.3589	+	31.7985i	0.611284	+	1.05877i
$903$		0			0
$904$	−14.5879	+	25.2669i	−0.485185	+	0.840366i
$905$	2.53040	+	4.38278i	0.0841133	+	0.145689i
$906$	−5.52259	−	17.4877i	−0.183476	−	0.580990i
$907$	−12.2044	+	21.1386i	−0.405240	+	0.701896i	−0.994349	−	0.106157i	$-0.966145\pi$
$907$	−12.2044	+	21.1386i	−0.405240	+	0.701896i	0.589110	+	0.808053i	$0.299479\pi$
$908$	−45.8496	+	79.4139i	−1.52157	+	2.63544i
$909$	26.7594	+	12.4485i	0.887555	+	0.412892i
$910$		0			0
$911$	−12.5493	−	21.7360i	−0.415776	−	0.720146i	0.579733	−	0.814806i	$-0.303157\pi$
$911$	−12.5493	−	21.7360i	−0.415776	−	0.720146i	−0.995510	+	0.0946604i	$0.969823\pi$
$912$	4.60613	+	14.5857i	0.152524	+	0.482980i
$913$	−18.8647			−0.624330
$914$	−64.5941			−2.13658
$915$	−1.03294	−	0.228504i	−0.0341478	−	0.00755411i
$916$	−53.1538	−	92.0652i	−1.75625	−	3.04192i
$917$		0			0
$918$	5.10378	−	39.1796i	0.168450	−	1.29312i
$919$	14.2988	−	24.7662i	0.471674	−	0.816963i	−0.527801	−	0.849368i	$-0.676983\pi$
$919$	14.2988	−	24.7662i	0.471674	−	0.816963i	0.999475	+	0.0324050i	$0.0103167\pi$
$920$	2.06869	−	3.58307i	0.0682026	−	0.118130i
$921$	−25.3105	+	27.6468i	−0.834009	+	0.910992i
$922$	−23.1634	−	40.1202i	−0.762846	−	1.32129i
$923$	−2.30759	+	3.99686i	−0.0759553	+	0.131558i
$924$		0			0
$925$	9.96139	+	17.2536i	0.327528	+	0.567296i
$926$	−49.2098	+	85.2339i	−1.61713	+	2.80096i
$927$	−27.1571	+	19.0524i	−0.891957	+	0.625764i
$928$	−45.5033	−	78.8140i	−1.49372	−	2.58720i
$929$	−45.4570			−1.49140			−0.745698	−	0.666284i	$-0.767884\pi$
$929$	−45.4570			−1.49140			−0.745698	+	0.666284i	$0.767884\pi$
$930$	−54.1227	−	11.9729i	−1.77475	−	0.392607i
$931$		0			0
$932$	−15.9321	+	27.5952i	−0.521873	+	0.903910i
$933$	5.25664	−	5.74185i	0.172095	−	0.187980i
$934$	−11.1206	+	19.2615i	−0.363878	+	0.630256i
$935$	−2.99609	−	5.18937i	−0.0979825	−	0.169711i
$936$	79.1499	+	36.8207i	2.58710	+	1.20352i
$937$	27.0083			0.882322			0.441161	−	0.897428i	$-0.354567\pi$
$937$	27.0083			0.882322			0.441161	+	0.897428i	$0.354567\pi$
$938$		0			0
$939$	10.0607	−	10.9894i	0.328320	−	0.358625i
$940$	47.5002	+	82.2728i	1.54929	+	2.68344i
$941$	12.7131			0.414436			0.207218	−	0.978295i	$-0.433559\pi$
$941$	12.7131			0.414436			0.207218	+	0.978295i	$0.433559\pi$
$942$	0.934732	−	1.02101i	0.0304552	−	0.0332664i
$943$	2.85624			0.0930121
$944$	64.5667			2.10147
$945$		0			0
$946$	22.9197			0.745185
$947$	47.5447			1.54500			0.772498	−	0.635017i	$-0.219007\pi$
$947$	47.5447			1.54500			0.772498	+	0.635017i	$0.219007\pi$
$948$	−98.7195	+	107.832i	−3.20626	+	3.50221i
$949$	1.48788			0.0482987
$950$	−2.10941	−	3.65361i	−0.0684384	−	0.118539i
$951$	−9.42977	+	10.3002i	−0.305781	+	0.334006i
$952$		0			0
$953$	38.2355			1.23857			0.619285	−	0.785166i	$-0.287423\pi$
$953$	38.2355			1.23857			0.619285	+	0.785166i	$0.287423\pi$
$954$	18.5838	−	13.0377i	0.601671	−	0.422110i
$955$	3.06820	+	5.31428i	0.0992847	+	0.171966i
$956$	−53.8682	+	93.3024i	−1.74222	+	3.01762i
$957$	7.17420	−	7.83641i	0.231909	−	0.253315i
$958$	−34.6925	+	60.0891i	−1.12086	+	1.94139i
$959$		0			0
$960$	70.0320	+	15.4923i	2.26027	+	0.500013i
$961$	24.2056			0.780826
$962$	−34.6154	−	59.9557i	−1.11605	−	1.93305i
$963$	−5.23426	−	2.43499i	−0.168672	−	0.0784663i
$964$	−78.6687	+	136.258i	−2.53375	+	4.38858i
$965$	−3.28054	−	5.68207i	−0.105604	−	0.182912i
$966$		0			0
$967$	−20.4093	+	35.3499i	−0.656317	+	1.13678i	0.325244	+	0.945630i	$0.394553\pi$
$967$	−20.4093	+	35.3499i	−0.656317	+	1.13678i	−0.981562	+	0.191145i	$0.938780\pi$
$968$	−42.0267	−	72.7924i	−1.35079	−	2.33964i
$969$	2.04942	−	2.23859i	0.0658369	−	0.0719139i
$970$	31.1399	−	53.9359i	0.999843	−	1.73178i
$971$	−22.4735	+	38.9253i	−0.721210	+	1.24917i	0.239305	+	0.970944i	$0.423080\pi$
$971$	−22.4735	+	38.9253i	−0.721210	+	1.24917i	−0.960515	+	0.278228i	$0.910253\pi$
$972$	−44.8331	+	70.7279i	−1.43802	+	2.26860i
$973$		0			0
$974$	−9.39817	−	16.2781i	−0.301137	−	0.521584i
$975$	−13.3482	−	2.95287i	−0.427485	−	0.0945674i
$976$	−5.43405			−0.173940
$977$	53.5104			1.71195			0.855974	−	0.517018i	$-0.172958\pi$
$977$	53.5104			1.71195			0.855974	+	0.517018i	$0.172958\pi$
$978$	−15.1660	−	48.0244i	−0.484956	−	1.53565i
$979$	−1.74465	−	3.02182i	−0.0557593	−	0.0965779i
$980$		0			0
$981$	45.6963	−	32.0588i	1.45897	−	1.02356i
$982$	−50.8442	+	88.0647i	−1.62250	+	2.81026i
$983$	−5.80278	+	10.0507i	−0.185080	+	0.320568i	−0.943603	−	0.331078i	$-0.892588\pi$
$983$	−5.80278	+	10.0507i	−0.185080	+	0.320568i	0.758524	+	0.651646i	$0.225921\pi$
$984$	47.8798	+	151.615i	1.52635	+	4.83331i
$985$	−0.705363	−	1.22172i	−0.0224747	−	0.0389274i
$986$	−17.2908	+	29.9485i	−0.550651	+	0.953756i
$987$		0			0
$988$	5.34147	+	9.25170i	0.169935	+	0.294336i
$989$	0.891454	−	1.54404i	0.0283466	−	0.0490977i
$990$	1.53475	+	17.3606i	0.0487777	+	0.551756i
$991$	−13.0046	−	22.5246i	−0.413104	−	0.715517i	0.582123	−	0.813100i	$-0.302222\pi$
$991$	−13.0046	−	22.5246i	−0.413104	−	0.715517i	−0.995227	+	0.0975835i	$0.968889\pi$
$992$	−148.680			−4.72058
$993$	−26.7863	+	29.2588i	−0.850037	+	0.928500i
$994$		0			0
$995$	5.01607	−	8.68808i	0.159020	−	0.275431i
$996$	−127.068	−	28.1096i	−4.02629	−	0.890688i
$997$	23.4499	−	40.6164i	0.742666	−	1.28633i	−0.208612	−	0.977999i	$-0.566895\pi$
$997$	23.4499	−	40.6164i	0.742666	−	1.28633i	0.951277	−	0.308336i	$-0.0997721\pi$
$998$	34.7876	+	60.2539i	1.10118	+	1.90731i
$999$	38.4913	−	16.0051i	1.21781	−	0.506379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.h.373.2		24
3.2	odd	2		1323.2.h.h.226.12		24
7.2	even	3		441.2.f.h.148.12	yes	24
7.3	odd	6		441.2.g.h.67.12		24
7.4	even	3		441.2.g.h.67.11		24
7.5	odd	6		441.2.f.h.148.11	✓	24
7.6	odd	2	inner	441.2.h.h.373.1		24
9.2	odd	6		1323.2.g.h.667.1		24
9.7	even	3		441.2.g.h.79.11		24
21.2	odd	6		1323.2.f.h.442.2		24
21.5	even	6		1323.2.f.h.442.1		24
21.11	odd	6		1323.2.g.h.361.1		24
21.17	even	6		1323.2.g.h.361.2		24
21.20	even	2		1323.2.h.h.226.11		24
63.2	odd	6		1323.2.f.h.883.2		24
63.5	even	6		3969.2.a.bi.1.11		12
63.11	odd	6		1323.2.h.h.802.12		24
63.16	even	3		441.2.f.h.295.12	yes	24
63.20	even	6		1323.2.g.h.667.2		24
63.23	odd	6		3969.2.a.bi.1.12		12
63.25	even	3	inner	441.2.h.h.214.2		24
63.34	odd	6		441.2.g.h.79.12		24
63.38	even	6		1323.2.h.h.802.11		24
63.40	odd	6		3969.2.a.bh.1.2		12
63.47	even	6		1323.2.f.h.883.1		24
63.52	odd	6	inner	441.2.h.h.214.1		24
63.58	even	3		3969.2.a.bh.1.1		12
63.61	odd	6		441.2.f.h.295.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.11	✓	24	7.5	odd	6
441.2.f.h.148.12	yes	24	7.2	even	3
441.2.f.h.295.11	yes	24	63.61	odd	6
441.2.f.h.295.12	yes	24	63.16	even	3
441.2.g.h.67.11		24	7.4	even	3
441.2.g.h.67.12		24	7.3	odd	6
441.2.g.h.79.11		24	9.7	even	3
441.2.g.h.79.12		24	63.34	odd	6
441.2.h.h.214.1		24	63.52	odd	6	inner
441.2.h.h.214.2		24	63.25	even	3	inner
441.2.h.h.373.1		24	7.6	odd	2	inner
441.2.h.h.373.2		24	1.1	even	1	trivial
1323.2.f.h.442.1		24	21.5	even	6
1323.2.f.h.442.2		24	21.2	odd	6
1323.2.f.h.883.1		24	63.47	even	6
1323.2.f.h.883.2		24	63.2	odd	6
1323.2.g.h.361.1		24	21.11	odd	6
1323.2.g.h.361.2		24	21.17	even	6
1323.2.g.h.667.1		24	9.2	odd	6
1323.2.g.h.667.2		24	63.20	even	6
1323.2.h.h.226.11		24	21.20	even	2
1323.2.h.h.226.12		24	3.2	odd	2
1323.2.h.h.802.11		24	63.38	even	6
1323.2.h.h.802.12		24	63.11	odd	6
3969.2.a.bh.1.1		12	63.58	even	3
3969.2.a.bh.1.2		12	63.40	odd	6
3969.2.a.bi.1.11		12	63.5	even	6
3969.2.a.bi.1.12		12	63.23	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.71513 q^{2} +(1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 - 2.98835i) q^{9} +O(q^{10})\)	\(q-2.71513 q^{2} +(1.16958 - 1.27753i) q^{3} +5.37195 q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 + 3.46867i) q^{6} -9.15528 q^{8} +(-0.264183 - 2.98835i) q^{9} +(-2.15363 - 3.73020i) q^{10} +(0.674376 - 1.16805i) q^{11} +(6.28290 - 6.86284i) q^{12} +(1.58916 - 2.75251i) q^{13} +(2.68285 + 0.593495i) q^{15} +14.1139 q^{16} +(-1.40027 - 2.42534i) q^{17} +(0.717292 + 8.11375i) q^{18} +(-0.312846 + 0.541866i) q^{19} +(4.26101 + 7.38028i) q^{20} +(-1.83102 + 3.17142i) q^{22} +(0.142434 + 0.246702i) q^{23} +(-10.7078 + 11.6962i) q^{24} +(1.24168 - 2.15065i) q^{25} +(-4.31479 + 7.47343i) q^{26} +(-4.12669 - 3.15760i) q^{27} +(2.27396 + 3.93861i) q^{29} +(-7.28430 - 1.61142i) q^{30} +7.43005 q^{31} -20.0106 q^{32} +(-0.703493 - 2.22767i) q^{33} +(3.80191 + 6.58511i) q^{34} +(-1.41918 - 16.0532i) q^{36} +(-4.01126 + 6.94770i) q^{37} +(0.849420 - 1.47124i) q^{38} +(-1.65778 - 5.24948i) q^{39} +(-7.26194 - 12.5780i) q^{40} +(5.01329 - 8.68327i) q^{41} +(-3.12937 - 5.42022i) q^{43} +(3.62271 - 6.27472i) q^{44} +(3.89601 - 2.73329i) q^{45} +(-0.386726 - 0.669829i) q^{46} +11.1477 q^{47} +(16.5073 - 18.0310i) q^{48} +(-3.37132 + 5.83930i) q^{50} +(-4.73617 - 1.04773i) q^{51} +(8.53689 - 14.7863i) q^{52} +(-1.39349 - 2.41359i) q^{53} +(11.2045 + 8.57329i) q^{54} +2.13965 q^{55} +(0.326354 + 1.03343i) q^{57} +(-6.17410 - 10.6939i) q^{58} +4.57469 q^{59} +(14.4121 + 3.18822i) q^{60} -0.385014 q^{61} -20.1736 q^{62} +26.1036 q^{64} +5.04207 q^{65} +(1.91008 + 6.04841i) q^{66} -2.53916 q^{67} +(-7.52217 - 13.0288i) q^{68} +(0.481757 + 0.106573i) q^{69} -1.45208 q^{71} +(2.41867 + 27.3591i) q^{72} +(0.234067 + 0.405416i) q^{73} +(10.8911 - 18.8639i) q^{74} +(-1.29529 - 4.10164i) q^{75} +(-1.68059 + 2.91087i) q^{76} +(4.50108 + 14.2530i) q^{78} -15.7124 q^{79} +(11.1951 + 19.3905i) q^{80} +(-8.86041 + 1.57894i) q^{81} +(-13.6117 + 23.5762i) q^{82} +(-6.99338 - 12.1129i) q^{83} +(2.22138 - 3.84754i) q^{85} +(8.49665 + 14.7166i) q^{86} +(7.69128 + 1.70145i) q^{87} +(-6.17410 + 10.6939i) q^{88} +(1.29353 - 2.24046i) q^{89} +(-10.5782 + 7.42126i) q^{90} +(0.765146 + 1.32527i) q^{92} +(8.69001 - 9.49213i) q^{93} -30.2674 q^{94} -0.992595 q^{95} +(-23.4039 + 25.5642i) q^{96} +(7.22962 + 12.5221i) q^{97} +(-3.66871 - 1.70669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

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