LMFDB - Embedded newform 441.2.g.h.67.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(67,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24,4,0,-12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			67.3
Character	$\chi$	$=$	441.67
Dual form			441.2.g.h.79.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.649936 + 1.12572i) q^{2} +(-1.52504 - 0.821126i) q^{3} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(1.65150 + 2.50450i) q^{9} +(-2.29157 + 3.96912i) q^{10} +1.17853 q^{11} +(-0.0159526 - 0.537275i) q^{12} +(1.61030 - 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} +(1.64151 - 2.84319i) q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.89275 + 0.231369i) q^{18} +(3.43318 + 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} -4.29987 q^{23} +(4.57991 + 2.46595i) q^{24} +7.43156 q^{25} +(2.09319 + 3.62551i) q^{26} +(-0.462101 - 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(6.75389 - 4.17140i) q^{30} +(0.960401 + 1.66346i) q^{31} +(-0.869378 - 1.50581i) q^{32} +(-1.79731 - 0.967725i) q^{33} +(3.18675 + 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 + 8.45637i) q^{37} -8.92540 q^{38} +(-4.74600 + 2.93127i) q^{39} -10.5886 q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 + 0.316738i) q^{44} +(5.82294 + 8.83048i) q^{45} +(2.79464 - 4.84046i) q^{46} +(-0.316609 + 0.548383i) q^{47} +(-4.83799 + 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(-7.22550 + 4.46268i) q^{51} +0.999459 q^{52} +(1.11378 - 1.92912i) q^{53} +(6.12658 + 2.84359i) q^{54} +4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} -3.53930 q^{58} +(-4.10652 - 7.11270i) q^{59} +(-0.0562464 - 1.89435i) q^{60} +(4.82958 - 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(5.67767 - 9.83402i) q^{65} +(2.25753 - 1.39432i) q^{66} +(-2.66651 - 4.61852i) q^{67} +1.52161 q^{68} +(6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(-4.95969 - 7.52136i) q^{72} +(-0.519036 + 0.898997i) q^{73} -12.6927 q^{74} +(-11.3334 - 6.10225i) q^{75} +(-1.06543 + 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +(-0.502039 + 0.869557i) q^{79} +(5.78772 - 10.0246i) q^{80} +(-3.54507 + 8.27239i) q^{81} +(-4.32432 - 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} -12.5682 q^{86} +(-0.139966 - 4.71396i) q^{87} -3.53930 q^{88} +(-6.02144 - 10.4294i) q^{89} +(-13.7252 + 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-0.0987387 - 3.32546i) q^{93} +(-0.411551 - 0.712828i) q^{94} +(12.1049 + 20.9662i) q^{95} +(0.0893807 + 3.01029i) q^{96} +(-5.46454 - 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.649936	+	1.12572i	−0.459574	+	0.796006i	−0.998938	−	0.0460668i	$-0.985331\pi$
$2$	−0.649936	+	1.12572i	−0.459574	+	0.796006i	0.539364	+	0.842073i	$0.318665\pi$
$3$	−1.52504	−	0.821126i	−0.880483	−	0.474077i
$3$	−1.52504	−	0.821126i	−0.880483	−	0.474077i
$4$	0.155166	+	0.268756i	0.0775831	+	0.134378i
$5$	3.52584			1.57680			0.788402	−	0.615160i	$-0.210909\pi$
$5$	3.52584			1.57680			0.788402	+	0.615160i	$0.210909\pi$
$6$	1.91554	−	1.18309i	0.782016	−	0.482996i
$7$		0			0
$7$		0			0
$8$	−3.00314			−1.06177
$9$	1.65150	+	2.50450i	0.550501	+	0.834834i
$10$	−2.29157	+	3.96912i	−0.724659	+	1.25515i
$11$	1.17853			0.355342			0.177671	−	0.984090i	$-0.443144\pi$
$11$	1.17853			0.355342			0.177671	+	0.984090i	$0.443144\pi$
$12$	−0.0159526	−	0.537275i	−0.00460513	−	0.155098i
$13$	1.61030	−	2.78913i	0.446618	−	0.773564i	−0.551546	−	0.834145i	$-0.685962\pi$
$13$	1.61030	−	2.78913i	0.446618	−	0.773564i	0.998163	+	0.0605803i	$0.0192951\pi$
$14$		0			0
$15$	−5.37706	−	2.89516i	−1.38835	−	0.747527i
$16$	1.64151	−	2.84319i	0.410379	−	0.710797i
$17$	2.45159	−	4.24627i	0.594597	−	1.02987i	−0.399006	−	0.916948i	$-0.630645\pi$
$17$	2.45159	−	4.24627i	0.594597	−	1.02987i	0.993604	−	0.112924i	$-0.0360218\pi$
$18$	−3.89275	+	0.231369i	−0.917529	+	0.0545342i
$19$	3.43318	+	5.94645i	0.787627	+	1.36421i	0.927417	+	0.374028i	$0.122024\pi$
$19$	3.43318	+	5.94645i	0.787627	+	1.36421i	−0.139791	+	0.990181i	$0.544643\pi$
$20$	0.547092	+	0.947591i	0.122333	+	0.211888i
$21$		0			0
$22$	−0.765972	+	1.32670i	−0.163306	+	0.282854i
$23$	−4.29987			−0.896585			−0.448293	−	0.893887i	$-0.647968\pi$
$23$	−4.29987			−0.896585			−0.448293	+	0.893887i	$0.647968\pi$
$24$	4.57991	+	2.46595i	0.934870	+	0.503361i
$25$	7.43156			1.48631
$26$	2.09319	+	3.62551i	0.410508	+	0.711020i
$27$	−0.462101	−	5.17556i	−0.0889314	−	0.996038i
$28$		0			0
$29$	1.36140	+	2.35802i	0.252806	+	0.437873i	0.964297	−	0.264822i	$-0.0853131\pi$
$29$	1.36140	+	2.35802i	0.252806	+	0.437873i	−0.711491	+	0.702695i	$0.751980\pi$
$30$	6.75389	−	4.17140i	1.23309	−	0.761590i
$31$	0.960401	+	1.66346i	0.172493	+	0.298767i	0.939291	−	0.343122i	$-0.111484\pi$
$31$	0.960401	+	1.66346i	0.172493	+	0.298767i	−0.766798	+	0.641889i	$0.778151\pi$
$32$	−0.869378	−	1.50581i	−0.153686	−	0.266192i
$33$	−1.79731	−	0.967725i	−0.312872	−	0.168459i
$34$	3.18675	+	5.51961i	0.546523	+	0.946606i
$35$		0			0
$36$	−0.416842	+	0.832466i	−0.0694737	+	0.138744i
$37$	4.88229	+	8.45637i	0.802643	+	1.39022i	0.917871	+	0.396879i	$0.129907\pi$
$37$	4.88229	+	8.45637i	0.802643	+	1.39022i	−0.115228	+	0.993339i	$0.536760\pi$
$38$	−8.92540			−1.44789
$39$	−4.74600	+	2.93127i	−0.759969	+	0.469379i
$40$	−10.5886			−1.67420
$41$	−3.32673	+	5.76206i	−0.519547	+	0.899883i	0.480194	+	0.877162i	$0.340566\pi$
$41$	−3.32673	+	5.76206i	−0.519547	+	0.899883i	−0.999742	+	0.0227205i	$0.992767\pi$
$42$		0			0
$43$	4.83441	+	8.37344i	0.737240	+	1.27694i	0.953734	+	0.300653i	$0.0972047\pi$
$43$	4.83441	+	8.37344i	0.737240	+	1.27694i	−0.216493	+	0.976284i	$0.569462\pi$
$44$	0.182869	+	0.316738i	0.0275685	+	0.0477501i
$45$	5.82294	+	8.83048i	0.868033	+	1.31637i
$46$	2.79464	−	4.84046i	0.412047	−	0.713687i
$47$	−0.316609	+	0.548383i	−0.0461822	+	0.0799899i	−0.888192	−	0.459472i	$-0.848039\pi$
$47$	−0.316609	+	0.548383i	−0.0461822	+	0.0799899i	0.842010	+	0.539461i	$0.181372\pi$
$48$	−4.83799	+	2.98809i	−0.698304	+	0.431293i
$49$		0			0
$50$	−4.83004	+	8.36587i	−0.683071	+	1.18311i
$51$	−7.22550	+	4.46268i	−1.01177	+	0.624900i
$52$	0.999459			0.138600
$53$	1.11378	−	1.92912i	0.152989	−	0.264985i	−0.779336	−	0.626606i	$-0.784443\pi$
$53$	1.11378	−	1.92912i	0.152989	−	0.264985i	0.932325	+	0.361621i	$0.117777\pi$
$54$	6.12658	+	2.84359i	0.833722	+	0.386963i
$55$	4.15533			0.560304
$56$		0			0
$57$	−0.352965	−	11.8877i	−0.0467514	−	1.57456i
$58$	−3.53930			−0.464733
$59$	−4.10652	−	7.11270i	−0.534623	−	0.925995i	−0.999181	−	0.0404521i	$-0.987120\pi$
$59$	−4.10652	−	7.11270i	−0.534623	−	0.925995i	0.464558	−	0.885543i	$-0.346213\pi$
$60$	−0.0562464	−	1.89435i	−0.00726138	−	0.244559i
$61$	4.82958	−	8.36508i	0.618364	−	1.07104i	−0.371420	−	0.928465i	$-0.621129\pi$
$61$	4.82958	−	8.36508i	0.618364	−	1.07104i	0.989784	−	0.142573i	$-0.0455376\pi$
$62$	−2.49680			−0.317093
$63$		0			0
$64$	8.82622			1.10328
$65$	5.67767	−	9.83402i	0.704229	−	1.21976i
$66$	2.25753	−	1.39432i	0.277883	−	0.171629i
$67$	−2.66651	−	4.61852i	−0.325766	−	0.564242i	0.655901	−	0.754847i	$-0.272289\pi$
$67$	−2.66651	−	4.61852i	−0.325766	−	0.564242i	−0.981667	+	0.190604i	$0.938955\pi$
$68$	1.52161			0.184523
$69$	6.55748	+	3.53074i	0.789428	+	0.425051i
$70$		0			0
$71$	−3.27719			−0.388931			−0.194466	−	0.980909i	$-0.562297\pi$
$71$	−3.27719			−0.388931			−0.194466	+	0.980909i	$0.562297\pi$
$72$	−4.95969	−	7.52136i	−0.584506	−	0.886401i
$73$	−0.519036	+	0.898997i	−0.0607486	+	0.105220i	−0.894800	−	0.446467i	$-0.852682\pi$
$73$	−0.519036	+	0.898997i	−0.0607486	+	0.105220i	0.834052	+	0.551686i	$0.186015\pi$
$74$	−12.6927			−1.47550
$75$	−11.3334	−	6.10225i	−1.30867	−	0.704627i
$76$	−1.06543	+	1.84538i	−0.122213	+	0.211679i
$77$		0			0
$78$	−0.215200	−	7.24782i	−0.0243666	−	0.820654i
$79$	−0.502039	+	0.869557i	−0.0564838	+	0.0978328i	−0.892885	−	0.450285i	$-0.851322\pi$
$79$	−0.502039	+	0.869557i	−0.0564838	+	0.0978328i	0.836401	+	0.548118i	$0.184656\pi$
$80$	5.78772	−	10.0246i	0.647087	−	1.12079i
$81$	−3.54507	+	8.27239i	−0.393896	+	0.919155i
$82$	−4.32432	−	7.48994i	−0.477541	−	0.827126i
$83$	−3.65598	−	6.33234i	−0.401296	−	0.695064i	0.592587	−	0.805506i	$-0.298107\pi$
$83$	−3.65598	−	6.33234i	−0.401296	−	0.695064i	−0.993883	+	0.110442i	$0.964773\pi$
$84$		0			0
$85$	8.64391	−	14.9717i	0.937563	−	1.62391i
$86$	−12.5682			−1.35527
$87$	−0.139966	−	4.71396i	−0.0150059	−	0.505390i
$88$	−3.53930			−0.377291
$89$	−6.02144	−	10.4294i	−0.638271	−	1.10552i	−0.985812	−	0.167853i	$-0.946317\pi$
$89$	−6.02144	−	10.4294i	−0.638271	−	1.10552i	0.347541	−	0.937665i	$-0.387017\pi$
$90$	−13.7252	+	0.815770i	−1.44676	+	0.0859897i
$91$		0			0
$92$	−0.667195	−	1.15562i	−0.0695599	−	0.120481i
$93$	−0.0987387	−	3.32546i	−0.0102387	−	0.344834i
$94$	−0.411551	−	0.712828i	−0.0424483	−	0.0735226i
$95$	12.1049	+	20.9662i	1.24193	+	2.15109i
$96$	0.0893807	+	3.01029i	0.00912238	+	0.307236i
$97$	−5.46454	−	9.46487i	−0.554840	−	0.961012i	−0.997916	−	0.0645275i	$-0.979446\pi$
$97$	−5.46454	−	9.46487i	−0.554840	−	0.961012i	0.443076	−	0.896484i	$-0.353887\pi$
$98$		0			0
$99$	1.94636	+	2.95164i	0.195616	+	0.296651i
$100$	1.15313	+	1.99728i	0.115313	+	0.199728i
$101$	−1.59509			−0.158718			−0.0793588	−	0.996846i	$-0.525287\pi$
$101$	−1.59509			−0.158718			−0.0793588	+	0.996846i	$0.525287\pi$
$102$	−0.327629	−	11.0344i	−0.0324401	−	1.09256i
$103$	2.33556			0.230129			0.115065	−	0.993358i	$-0.463292\pi$
$103$	2.33556			0.230129			0.115065	+	0.993358i	$0.463292\pi$
$104$	−4.83596	+	8.37613i	−0.474205	+	0.821347i
$105$		0			0
$106$	1.44777	+	2.50761i	0.140620	+	0.243561i
$107$	1.11181	+	1.92571i	0.107483	+	0.186166i	0.914750	−	0.404021i	$-0.132388\pi$
$107$	1.11181	+	1.92571i	0.107483	+	0.186166i	−0.807267	+	0.590186i	$0.799054\pi$
$108$	1.31926	−	0.927265i	0.126946	−	0.0892262i
$109$	0.459782	−	0.796366i	0.0440391	−	0.0762780i	−0.843166	−	0.537654i	$-0.819311\pi$
$109$	0.459782	−	0.796366i	0.0440391	−	0.0762780i	0.887205	+	0.461376i	$0.152644\pi$
$110$	−2.70070	+	4.67774i	−0.257501	+	0.446005i
$111$	−0.501947	−	16.9053i	−0.0476427	−	1.60458i
$112$		0			0
$113$	1.19327	−	2.06681i	0.112254	−	0.194429i	−0.804425	−	0.594054i	$-0.797526\pi$
$113$	1.19327	−	2.06681i	0.112254	−	0.194429i	0.916679	+	0.399625i	$0.130860\pi$
$114$	13.6116	+	7.32888i	1.27484	+	0.686412i
$115$	−15.1607			−1.41374
$116$	−0.422488	+	0.731770i	−0.0392270	+	0.0679432i
$117$	9.64479	−	0.573247i	0.891662	−	0.0529967i
$118$	10.6759			0.982796
$119$		0			0
$120$	16.1480	+	8.69456i	1.47411	+	0.793701i
$121$	−9.61106			−0.873732
$122$	6.27783	+	10.8735i	0.568368	+	0.984443i
$123$	9.80477	−	6.05572i	0.884067	−	0.546026i
$124$	−0.298044	+	0.516227i	−0.0267651	+	0.0463585i
$125$	8.57330			0.766819
$126$		0			0
$127$	−3.04170			−0.269907			−0.134954	−	0.990852i	$-0.543089\pi$
$127$	−3.04170			−0.269907			−0.134954	+	0.990852i	$0.543089\pi$
$128$	−3.99772	+	6.92426i	−0.353352	+	0.612024i
$129$	−0.497025	−	16.7395i	−0.0437606	−	1.47383i
$130$	7.38025	+	12.7830i	0.647291	+	1.12114i
$131$	−3.26176			−0.284981			−0.142490	−	0.989796i	$-0.545511\pi$
$131$	−3.26176			−0.284981			−0.142490	+	0.989796i	$0.545511\pi$
$132$	−0.0188007	−	0.633197i	−0.00163639	−	0.0551127i
$133$		0			0
$134$	6.93223			0.598854
$135$	−1.62930	−	18.2482i	−0.140227	−	1.57056i
$136$	−7.36245	+	12.7521i	−0.631325	+	1.09349i
$137$	20.9338			1.78849			0.894246	−	0.447575i	$-0.147712\pi$
$137$	20.9338			1.78849			0.894246	+	0.447575i	$0.147712\pi$
$138$	−8.23657	+	5.08715i	−0.701144	+	0.433047i
$139$	−8.31195	+	14.3967i	−0.705010	+	1.22111i	0.261677	+	0.965155i	$0.415724\pi$
$139$	−8.31195	+	14.3967i	−0.705010	+	1.22111i	−0.966688	+	0.255958i	$0.917609\pi$
$140$		0			0
$141$	0.933134	−	0.576331i	0.0785840	−	0.0485358i
$142$	2.12997	−	3.68921i	0.178743	−	0.309592i
$143$	1.89780	−	3.28708i	0.158702	−	0.274880i
$144$	9.83174	−	0.584358i	0.819311	−	0.0486965i
$145$	4.80009	+	8.31401i	0.398626	+	0.690441i
$146$	−0.674681	−	1.16858i	−0.0558370	−	0.0967124i
$147$		0			0
$148$	−1.51513	+	2.62429i	−0.124543	+	0.215715i
$149$	1.12844			0.0924456			0.0462228	−	0.998931i	$-0.485282\pi$
$149$	1.12844			0.0924456			0.0462228	+	0.998931i	$0.485282\pi$
$150$	14.2354	−	8.79224i	1.16232	−	0.717883i
$151$	−19.6295			−1.59743			−0.798714	−	0.601711i	$-0.794486\pi$
$151$	−19.6295			−1.59743			−0.798714	+	0.601711i	$0.794486\pi$
$152$	−10.3103	−	17.8580i	−0.836278	−	1.44848i
$153$	14.6836	−	0.872733i	1.18710	−	0.0705563i
$154$		0			0
$155$	3.38622	+	5.86511i	0.271988	+	0.471097i
$156$	−1.52422	−	0.820681i	−0.122035	−	0.0657071i
$157$	−4.66619	−	8.08207i	−0.372402	−	0.645020i	0.617532	−	0.786545i	$-0.288132\pi$
$157$	−4.66619	−	8.08207i	−0.372402	−	0.645020i	−0.989935	+	0.141526i	$0.954799\pi$
$158$	−0.652586	−	1.13031i	−0.0519170	−	0.0899228i
$159$	−3.28261	+	2.02744i	−0.260328	+	0.160786i
$160$	−3.06529	−	5.30924i	−0.242332	−	0.419732i
$161$		0			0
$162$	−7.00835	−	9.36729i	−0.550628	−	0.735964i
$163$	−8.45056	−	14.6368i	−0.661899	−	1.14644i	−0.980116	−	0.198425i	$-0.936417\pi$
$163$	−8.45056	−	14.6368i	−0.661899	−	1.14644i	0.318217	−	0.948018i	$-0.396916\pi$
$164$	−2.06478			−0.161232
$165$	−6.33705	−	3.41205i	−0.493338	−	0.265627i
$166$	9.50460			0.737700
$167$	2.57319	−	4.45689i	0.199119	−	0.344885i	−0.749124	−	0.662430i	$-0.769525\pi$
$167$	2.57319	−	4.45689i	0.199119	−	0.344885i	0.948243	+	0.317545i	$0.102859\pi$
$168$		0			0
$169$	1.31385	+	2.27566i	0.101066	+	0.175051i
$170$	11.2360	+	19.4613i	0.861760	+	1.49261i
$171$	−9.22298	+	18.4190i	−0.705299	+	1.40854i
$172$	−1.50027	+	2.59855i	−0.114395	+	0.198138i
$173$	−4.86834	+	8.43222i	−0.370133	+	0.641090i	−0.989586	−	0.143945i	$-0.954021\pi$
$173$	−4.86834	+	8.43222i	−0.370133	+	0.641090i	0.619453	+	0.785034i	$0.287355\pi$
$174$	5.39758	+	2.90621i	0.409190	+	0.220319i
$175$		0			0
$176$	1.93458	−	3.35079i	0.145825	−	0.252576i
$177$	0.422191	+	14.2191i	0.0317338	+	1.06878i
$178$	15.6542			1.17333
$179$	−0.687990	+	1.19163i	−0.0514228	+	0.0890668i	−0.890591	−	0.454805i	$-0.849709\pi$
$179$	−0.687990	+	1.19163i	−0.0514228	+	0.0890668i	0.839168	+	0.543872i	$0.183042\pi$
$180$	−1.46972	+	2.93514i	−0.109546	+	0.218773i
$181$	−5.66560			−0.421120			−0.210560	−	0.977581i	$-0.567529\pi$
$181$	−5.66560			−0.421120			−0.210560	+	0.977581i	$0.567529\pi$
$182$		0			0
$183$	−14.2341	+	8.79140i	−1.05221	+	0.649879i
$184$	12.9131			0.951967
$185$	17.2142	+	29.8158i	1.26561	+	2.19210i
$186$	3.80772	+	2.05018i	0.279196	+	0.150327i
$187$	2.88928	−	5.00438i	0.211285	−	0.365956i
$188$	−0.196508			−0.0143318
$189$		0			0
$190$	−31.4696			−2.28304
$191$	12.5065	−	21.6618i	0.904936	−	1.56740i	0.0839339	−	0.996471i	$-0.473252\pi$
$191$	12.5065	−	21.6618i	0.904936	−	1.56740i	0.821003	−	0.570925i	$-0.193415\pi$
$192$	−13.4604	−	7.24744i	−0.971417	−	0.523039i
$193$	−8.76688	−	15.1847i	−0.631054	−	1.09302i	−0.987337	−	0.158640i	$-0.949289\pi$
$193$	−8.76688	−	15.1847i	−0.631054	−	1.09302i	0.356282	−	0.934378i	$-0.384044\pi$
$194$	14.2064			1.01996
$195$	−16.7337	+	10.3352i	−1.19832	+	0.740119i
$196$		0			0
$197$	−19.7540			−1.40741			−0.703707	−	0.710490i	$-0.748473\pi$
$197$	−19.7540			−1.40741			−0.703707	+	0.710490i	$0.748473\pi$
$198$	−4.58774	+	0.272676i	−0.326036	+	0.0193783i
$199$	9.51110	−	16.4737i	0.674224	−	1.16779i	−0.302471	−	0.953158i	$-0.597812\pi$
$199$	9.51110	−	16.4737i	0.674224	−	1.16779i	0.976695	−	0.214631i	$-0.0688550\pi$
$200$	−22.3180			−1.57812
$201$	0.274143	+	9.23298i	0.0193366	+	0.651244i
$202$	1.03671	−	1.79563i	0.0729425	−	0.126340i
$203$		0			0
$204$	−2.32053	−	1.24944i	−0.162469	−	0.0874781i
$205$	−11.7295	+	20.3161i	−0.819225	+	1.41894i
$206$	−1.51796	+	2.62919i	−0.105761	+	0.183184i
$207$	−7.10126	−	10.7690i	−0.493572	−	0.748500i
$208$	−5.28667	−	9.15678i	−0.366565	−	0.634908i
$209$	4.04613	+	7.00810i	0.279876	+	0.484760i
$210$		0			0
$211$	3.71809	−	6.43993i	0.255964	−	0.443343i	−0.709193	−	0.705015i	$-0.750940\pi$
$211$	3.71809	−	6.43993i	0.255964	−	0.443343i	0.965157	+	0.261672i	$0.0842738\pi$
$212$	0.691283			0.0474775
$213$	4.99786	+	2.69099i	0.342447	+	0.184383i
$214$	−2.89043			−0.197585
$215$	17.0454	+	29.5234i	1.16248	+	2.01348i
$216$	1.38775	+	15.5429i	0.0944246	+	1.05756i
$217$		0			0
$218$	0.597658	+	1.03517i	0.0404785	+	0.0701108i
$219$	1.52974	−	0.944814i	0.103370	−	0.0638446i
$220$	0.644767	+	1.11677i	0.0434702	+	0.0752925i
$221$	−7.89559	−	13.6756i	−0.531115	−	0.919918i
$222$	19.3569	+	10.4223i	1.29915	+	0.699499i
$223$	1.64565	+	2.85034i	0.110201	+	0.190873i	0.915851	−	0.401518i	$-0.131517\pi$
$223$	1.64565	+	2.85034i	0.110201	+	0.190873i	−0.805650	+	0.592391i	$0.798184\pi$
$224$		0			0
$225$	12.2733	+	18.6124i	0.818217	+	1.24082i
$226$	1.55110	+	2.68659i	0.103178	+	0.178709i
$227$	−18.0169			−1.19583			−0.597913	−	0.801561i	$-0.704003\pi$
$227$	−18.0169			−1.19583			−0.597913	+	0.801561i	$0.704003\pi$
$228$	3.14011	−	1.93943i	0.207959	−	0.128442i
$229$	4.25491			0.281173			0.140586	−	0.990068i	$-0.455101\pi$
$229$	4.25491			0.281173			0.140586	+	0.990068i	$0.455101\pi$
$230$	9.85347	−	17.0667i	0.649718	−	1.12535i
$231$		0			0
$232$	−4.08848	−	7.08146i	−0.268422	−	0.464920i
$233$	7.35275	+	12.7353i	0.481695	+	0.834320i	0.999779	−	0.0210095i	$-0.00668801\pi$
$233$	7.35275	+	12.7353i	0.481695	+	0.834320i	−0.518084	+	0.855330i	$0.673355\pi$
$234$	−5.62318	+	11.2299i	−0.367599	+	0.734124i
$235$	−1.11631	+	1.93351i	−0.0728203	+	0.126128i
$236$	1.27439	−	2.20730i	0.0829555	−	0.143683i
$237$	1.47965	−	0.913873i	0.0961133	−	0.0593624i
$238$		0			0
$239$	7.08187	−	12.2662i	0.458088	−	0.793432i	−0.540772	−	0.841169i	$-0.681868\pi$
$239$	7.08187	−	12.2662i	0.458088	−	0.793432i	0.998860	+	0.0477377i	$0.0152011\pi$
$240$	−17.0580	+	10.5355i	−1.10109	+	0.680065i
$241$	7.93503			0.511140			0.255570	−	0.966791i	$-0.417737\pi$
$241$	7.93503			0.511140			0.255570	+	0.966791i	$0.417737\pi$
$242$	6.24657	−	10.8194i	0.401545	−	0.695496i
$243$	12.1991	−	9.70480i	0.782569	−	0.622563i
$244$	2.99755			0.191899
$245$		0			0
$246$	0.444583	+	14.9733i	0.0283456	+	0.954662i
$247$	22.1139			1.40707
$248$	−2.88422	−	4.99561i	−0.183148	−	0.317221i
$249$	0.375871	+	12.6591i	0.0238198	+	0.802238i
$250$	−5.57210	+	9.65115i	−0.352410	+	0.610392i
$251$	8.05097			0.508173			0.254087	−	0.967181i	$-0.418225\pi$
$251$	8.05097			0.508173			0.254087	+	0.967181i	$0.418225\pi$
$252$		0			0
$253$	−5.06755			−0.318594
$254$	1.97691	−	3.42411i	0.124042	−	0.214848i
$255$	−25.4760	+	15.7347i	−1.59537	+	0.985346i
$256$	3.62969	+	6.28681i	0.226856	+	0.392926i
$257$	−17.5537			−1.09497			−0.547486	−	0.836815i	$-0.684415\pi$
$257$	−17.5537			−1.09497			−0.547486	+	0.836815i	$0.684415\pi$
$258$	19.1671	+	10.3201i	1.19329	+	0.642501i
$259$		0			0
$260$	3.52393			0.218545
$261$	−3.65730	+	7.30392i	−0.226381	+	0.452101i
$262$	2.11993	−	3.67183i	0.130970	−	0.226846i
$263$	−23.3486			−1.43973			−0.719867	−	0.694112i	$-0.755797\pi$
$263$	−23.3486			−1.43973			−0.719867	+	0.694112i	$0.755797\pi$
$264$	5.39758	+	2.90621i	0.332198	+	0.178865i
$265$	3.92701	−	6.80177i	0.241234	−	0.417830i
$266$		0			0
$267$	0.619063	+	20.8497i	0.0378861	+	1.27598i
$268$	0.827504	−	1.43328i	0.0505478	−	0.0875514i
$269$	−0.269244	+	0.466344i	−0.0164161	+	0.0284335i	−0.874117	−	0.485716i	$-0.838559\pi$
$269$	−0.269244	+	0.466344i	−0.0164161	+	0.0284335i	0.857701	+	0.514149i	$0.171892\pi$
$270$	21.6014	+	10.0260i	1.31462	+	0.610165i
$271$	7.20749	+	12.4837i	0.437824	+	0.758334i	0.997521	−	0.0703635i	$-0.0224159\pi$
$271$	7.20749	+	12.4837i	0.437824	+	0.758334i	−0.559697	+	0.828697i	$0.689083\pi$
$272$	−8.04863	−	13.9406i	−0.488020	−	0.845275i
$273$		0			0
$274$	−13.6056	+	23.5656i	−0.821945	+	1.42365i
$275$	8.75835			0.528148
$276$	0.0685943	+	2.31021i	0.00412889	+	0.139059i
$277$	21.9066			1.31624			0.658121	−	0.752912i	$-0.271351\pi$
$277$	21.9066			1.31624			0.658121	+	0.752912i	$0.271351\pi$
$278$	−10.8045	−	18.7139i	−0.648009	−	1.12238i
$279$	−2.58004	+	5.15254i	−0.154463	+	0.308475i
$280$		0			0
$281$	−0.776622	−	1.34515i	−0.0463294	−	0.0802449i	0.841931	−	0.539586i	$-0.181419\pi$
$281$	−0.776622	−	1.34515i	−0.0463294	−	0.0802449i	−0.888260	+	0.459341i	$0.848086\pi$
$282$	0.0423116	+	1.42503i	0.00251962	+	0.0848592i
$283$	1.32571	+	2.29619i	0.0788051	+	0.136495i	0.902735	−	0.430198i	$-0.141556\pi$
$283$	1.32571	+	2.29619i	0.0788051	+	0.136495i	−0.823930	+	0.566692i	$0.808223\pi$
$284$	−0.508510	−	0.880765i	−0.0301745	−	0.0522638i
$285$	−1.24450	−	41.9140i	−0.0737178	−	2.48277i
$286$	2.46689	+	4.27279i	0.145870	+	0.252655i
$287$		0			0
$288$	2.33552	−	4.66421i	0.137622	−	0.274841i
$289$	−3.52056	−	6.09778i	−0.207091	−	0.358693i
$290$	−12.4790			−0.732793
$291$	0.561809	+	18.9214i	0.0329338	+	1.10919i
$292$	−0.322148			−0.0188523
$293$	−5.19314	+	8.99478i	−0.303386	+	0.525481i	−0.976901	−	0.213694i	$-0.931451\pi$
$293$	−5.19314	+	8.99478i	−0.303386	+	0.525481i	0.673514	+	0.739174i	$0.264784\pi$
$294$		0			0
$295$	−14.4789	−	25.0783i	−0.842996	−	1.46011i
$296$	−14.6622	−	25.3956i	−0.852221	−	1.47609i
$297$	−0.544602	−	6.09958i	−0.0316010	−	0.353934i
$298$	−0.733415	+	1.27031i	−0.0424856	+	0.0735872i
$299$	−6.92409	+	11.9929i	−0.400431	+	0.693566i
$300$	−0.118553	−	3.99279i	−0.00684466	−	0.230524i
$301$		0			0
$302$	12.7579	−	22.0974i	0.734137	−	1.27156i
$303$	2.43258	+	1.30977i	0.139748	+	0.0752444i
$304$	22.5425			1.29290
$305$	17.0283	−	29.4939i	0.975039	−	1.68882i
$306$	−8.56095	+	17.0969i	−0.489397	+	0.977364i
$307$	−10.6425			−0.607400			−0.303700	−	0.952768i	$-0.598222\pi$
$307$	−10.6425			−0.607400			−0.303700	+	0.952768i	$0.598222\pi$
$308$		0			0
$309$	−3.56182	−	1.91779i	−0.202625	−	0.109099i
$310$	−8.80331			−0.499994
$311$	6.85479	+	11.8728i	0.388699	+	0.673247i	0.992275	−	0.124059i	$-0.0395912\pi$
$311$	6.85479	+	11.8728i	0.388699	+	0.673247i	−0.603576	+	0.797306i	$0.706258\pi$
$312$	14.2529	−	8.80301i	0.806911	−	0.498372i
$313$	−10.6090	+	18.3752i	−0.599653	+	1.03863i	0.393219	+	0.919445i	$0.371362\pi$
$313$	−10.6090	+	18.3752i	−0.599653	+	1.03863i	−0.992872	+	0.119185i	$0.961972\pi$
$314$	12.1309			0.684586
$315$		0			0
$316$	−0.311598			−0.0175288
$317$	−1.78521	+	3.09208i	−0.100268	+	0.173669i	−0.911795	−	0.410646i	$-0.865303\pi$
$317$	−1.78521	+	3.09208i	−0.100268	+	0.173669i	0.811527	+	0.584315i	$0.198637\pi$
$318$	−0.148845	−	5.01301i	−0.00834681	−	0.281116i
$319$	1.60446	+	2.77901i	0.0898326	+	0.155595i
$320$	31.1198			1.73965
$321$	−0.114305	−	3.84973i	−0.00637989	−	0.214871i
$322$		0			0
$323$	33.6670			1.87328
$324$	−2.77333	+	0.330839i	−0.154074	+	0.0183800i
$325$	11.9671	−	20.7276i	0.663813	−	1.14976i
$326$	21.9693			1.21677
$327$	−1.35510	+	0.836952i	−0.0749374	+	0.0462835i
$328$	9.99062	−	17.3043i	0.551639	−	0.955468i
$329$		0			0
$330$	7.95969	−	4.91614i	0.438167	−	0.270625i
$331$	11.9728	−	20.7375i	0.658085	−	1.13984i	−0.323026	−	0.946390i	$-0.604700\pi$
$331$	11.9728	−	20.7375i	0.658085	−	1.13984i	0.981111	−	0.193446i	$-0.0619666\pi$
$332$	1.13457	−	1.96513i	0.0622675	−	0.107851i
$333$	−13.1159	+	26.1934i	−0.718746	+	1.43539i
$334$	3.34482	+	5.79339i	0.183020	+	0.317000i
$335$	−9.40168	−	16.2842i	−0.513669	−	0.889700i
$336$		0			0
$337$	−13.7468	+	23.8102i	−0.748838	+	1.29703i	0.199542	+	0.979889i	$0.436055\pi$
$337$	−13.7468	+	23.8102i	−0.748838	+	1.29703i	−0.948380	+	0.317137i	$0.897279\pi$
$338$	−3.41568			−0.185788
$339$	−3.51691	+	2.17215i	−0.191012	+	0.117975i
$340$	5.36497			0.290956
$341$	1.13187	+	1.96045i	0.0612940	+	0.106164i
$342$	−14.7403	−	22.3537i	−0.797066	−	1.20875i
$343$		0			0
$344$	−14.5184	−	25.1466i	−0.782779	−	1.35581i
$345$	23.1207	+	12.4488i	1.24477	+	0.670222i
$346$	−6.32822	−	10.9608i	−0.340207	−	0.589256i
$347$	2.56412	+	4.44119i	0.137649	+	0.238416i	0.926606	−	0.376033i	$-0.122712\pi$
$347$	2.56412	+	4.44119i	0.137649	+	0.238416i	−0.788957	+	0.614448i	$0.789379\pi$
$348$	1.24519	−	0.769065i	0.0667490	−	0.0412262i
$349$	−7.56980	−	13.1113i	−0.405202	−	0.701830i	0.589143	−	0.808029i	$-0.299465\pi$
$349$	−7.56980	−	13.1113i	−0.405202	−	0.701830i	−0.994345	+	0.106198i	$0.966132\pi$
$350$		0			0
$351$	−15.1794	−	7.04537i	−0.810218	−	0.376054i
$352$	−1.02459	−	1.77465i	−0.0546110	−	0.0945889i
$353$	32.9757			1.75512			0.877559	−	0.479468i	$-0.159171\pi$
$353$	32.9757			1.75512			0.877559	+	0.479468i	$0.159171\pi$
$354$	−16.2812	−	8.76626i	−0.865336	−	0.465921i
$355$	−11.5549			−0.613269
$356$	1.86865	−	3.23659i	0.0990381	−	0.171539i
$357$		0			0
$358$	−0.894299	−	1.54897i	−0.0472651	−	0.0818656i
$359$	12.0178	+	20.8154i	0.634274	+	1.09859i	0.986669	+	0.162743i	$0.0520341\pi$
$359$	12.0178	+	20.8154i	0.634274	+	1.09859i	−0.352395	+	0.935851i	$0.614633\pi$
$360$	−17.4871	−	26.5191i	−0.921651	−	1.39768i
$361$	−14.0735	+	24.3760i	−0.740711	+	1.28295i
$362$	3.68227	−	6.37789i	0.193536	−	0.335214i
$363$	14.6573	+	7.89189i	0.769307	+	0.414217i
$364$		0			0
$365$	−1.83004	+	3.16972i	−0.0957886	+	0.165911i
$366$	−0.645424	−	21.7375i	−0.0337368	−	1.13624i
$367$	−2.65501			−0.138590			−0.0692952	−	0.997596i	$-0.522075\pi$
$367$	−2.65501			−0.138590			−0.0692952	+	0.997596i	$0.522075\pi$
$368$	−7.05830	+	12.2253i	−0.367939	+	0.637290i
$369$	−19.9252	+	1.18427i	−1.03726	+	0.0616507i
$370$	−44.7524			−2.32657
$371$		0			0
$372$	0.878416	−	0.542536i	0.0455438	−	0.0281292i
$373$	−31.9183			−1.65267			−0.826334	−	0.563181i	$-0.809577\pi$
$373$	−31.9183			−1.65267			−0.826334	+	0.563181i	$0.809577\pi$
$374$	3.75569	+	6.50505i	0.194202	+	0.336368i
$375$	−13.0746	−	7.03976i	−0.675171	−	0.363531i
$376$	0.950821	−	1.64687i	0.0490348	−	0.0849308i
$377$	8.76909			0.451631
$378$		0			0
$379$	30.2681			1.55477			0.777384	−	0.629027i	$-0.216546\pi$
$379$	30.2681			1.55477			0.777384	+	0.629027i	$0.216546\pi$
$380$	−3.75653	+	6.50651i	−0.192706	+	0.333777i
$381$	4.63872	+	2.49762i	0.237649	+	0.127957i
$382$	16.2568	+	28.1576i	0.831771	+	1.44067i
$383$	1.73305			0.0885548			0.0442774	−	0.999019i	$-0.485901\pi$
$383$	1.73305			0.0885548			0.0442774	+	0.999019i	$0.485901\pi$
$384$	11.7824	−	7.27715i	0.601267	−	0.371360i
$385$		0			0
$386$	22.7917			1.16006
$387$	−12.9873	+	25.9366i	−0.660179	+	1.31843i
$388$	1.69583	−	2.93726i	0.0860925	−	0.149117i
$389$	−11.0835			−0.561956			−0.280978	−	0.959714i	$-0.590659\pi$
$389$	−11.0835			−0.561956			−0.280978	+	0.959714i	$0.590659\pi$
$390$	−0.758762	−	25.5547i	−0.0384214	−	1.29401i
$391$	−10.5415	+	18.2584i	−0.533107	+	0.923368i
$392$		0			0
$393$	4.97431	+	2.67831i	0.250921	+	0.135103i
$394$	12.8388	−	22.2375i	0.646811	−	1.12031i
$395$	−1.77011	+	3.06592i	−0.0890639	+	0.154263i
$396$	−0.491263	+	0.981090i	−0.0246869	+	0.0493016i
$397$	−12.6696	−	21.9443i	−0.635867	−	1.10135i	−0.986331	−	0.164777i	$-0.947310\pi$
$397$	−12.6696	−	21.9443i	−0.635867	−	1.10135i	0.350464	−	0.936576i	$-0.386024\pi$
$398$	12.3632	+	21.4137i	0.619712	+	1.07337i
$399$		0			0
$400$	12.1990	−	21.1293i	0.609951	−	1.05647i
$401$	−34.8244			−1.73905			−0.869524	−	0.493890i	$-0.835575\pi$
$401$	−34.8244			−1.73905			−0.869524	+	0.493890i	$0.835575\pi$
$402$	−10.5719	−	5.69224i	−0.527281	−	0.283903i
$403$	6.18614			0.308154
$404$	−0.247505	−	0.428690i	−0.0123138	−	0.0213281i
$405$	−12.4993	+	29.1672i	−0.621097	+	1.44933i
$406$		0			0
$407$	5.75394	+	9.96612i	0.285212	+	0.494002i
$408$	21.6992	−	13.4020i	1.07427	−	0.663500i
$409$	9.12308	+	15.8016i	0.451107	+	0.781341i	0.998455	−	0.0555643i	$-0.0176958\pi$
$409$	9.12308	+	15.8016i	0.451107	+	0.781341i	−0.547348	+	0.836905i	$0.684362\pi$
$410$	−15.2469	−	26.4083i	−0.752989	−	1.30422i
$411$	−31.9249	−	17.1893i	−1.57474	−	0.847884i
$412$	0.362400	+	0.627695i	0.0178541	+	0.0309243i
$413$		0			0
$414$	16.7383	−	0.994856i	0.822643	−	0.0488945i
$415$	−12.8904	−	22.3268i	−0.632765	−	1.09598i
$416$	−5.59985			−0.274555
$417$	24.4976	−	15.1304i	1.19965	−	0.740941i
$418$	−10.5189			−0.514496
$419$	−4.20719	+	7.28708i	−0.205535	+	0.355997i	−0.950303	−	0.311326i	$-0.899227\pi$
$419$	−4.20719	+	7.28708i	−0.205535	+	0.355997i	0.744768	+	0.667323i	$0.232560\pi$
$420$		0			0
$421$	0.144291	+	0.249919i	0.00703230	+	0.0121803i	0.869520	−	0.493897i	$-0.164428\pi$
$421$	0.144291	+	0.249919i	0.00703230	+	0.0121803i	−0.862488	+	0.506078i	$0.831095\pi$
$422$	4.83304	+	8.37108i	0.235269	+	0.407498i
$423$	−1.89631	+	0.112709i	−0.0922017	+	0.00548009i
$424$	−3.34483	+	5.79341i	−0.162439	+	0.281353i
$425$	18.2191	−	31.5564i	0.883757	−	1.53071i
$426$	−6.27759	+	3.87723i	−0.304150	+	0.187852i
$427$		0			0
$428$	−0.345031	+	0.597612i	−0.0166777	+	0.0288866i
$429$	−5.59333	+	3.45461i	−0.270048	+	0.166790i
$430$	−44.3136			−2.13699
$431$	6.74795	−	11.6878i	0.325037	−	0.562981i	−0.656482	−	0.754341i	$-0.727956\pi$
$431$	6.74795	−	11.6878i	0.325037	−	0.562981i	0.981520	+	0.191360i	$0.0612898\pi$
$432$	−15.4736	−	7.18192i	−0.744476	−	0.345540i
$433$	−4.85211			−0.233177			−0.116589	−	0.993180i	$-0.537196\pi$
$433$	−4.85211			−0.233177			−0.116589	+	0.993180i	$0.537196\pi$
$434$		0			0
$435$	−0.493497	−	16.6207i	−0.0236614	−	0.796901i
$436$	0.285371			0.0136668
$437$	−14.7623	−	25.5690i	−0.706174	−	1.22313i
$438$	0.0693638	+	2.33613i	0.00331433	+	0.111625i
$439$	−1.27397	+	2.20657i	−0.0608031	+	0.105314i	−0.894825	−	0.446418i	$-0.852699\pi$
$439$	−1.27397	+	2.20657i	−0.0608031	+	0.105314i	0.834022	+	0.551732i	$0.186033\pi$
$440$	−12.4790			−0.594914
$441$		0			0
$442$	20.5265			0.976347
$443$	0.322753	−	0.559025i	0.0153345	−	0.0265601i	−0.858256	−	0.513221i	$-0.828452\pi$
$443$	0.322753	−	0.559025i	0.0153345	−	0.0265601i	0.873591	+	0.486661i	$0.161785\pi$
$444$	4.46551	−	2.75803i	0.211924	−	0.130890i
$445$	−21.2306	−	36.7725i	−1.00643	−	1.74319i
$446$	−4.27826			−0.202581
$447$	−1.72092	−	0.926593i	−0.0813968	−	0.0438264i
$448$		0			0
$449$	−5.22658			−0.246658			−0.123329	−	0.992366i	$-0.539357\pi$
$449$	−5.22658			−0.246658			−0.123329	+	0.992366i	$0.539357\pi$
$450$	−28.9292	+	1.71943i	−1.36373	+	0.0810548i
$451$	−3.92066	+	6.79079i	−0.184617	+	0.319766i
$452$	0.740624			0.0348360
$453$	29.9358	+	16.1183i	1.40651	+	0.757304i
$454$	11.7099	−	20.2821i	0.549571	−	0.951885i
$455$		0			0
$456$	1.06000	+	35.7003i	0.0496392	+	1.67182i
$457$	1.43037	−	2.47748i	0.0669101	−	0.115892i	−0.830630	−	0.556825i	$-0.812019\pi$
$457$	1.43037	−	2.47748i	0.0669101	−	0.115892i	0.897540	+	0.440934i	$0.145353\pi$
$458$	−2.76542	+	4.78985i	−0.129220	+	0.223815i
$459$	−23.1097	−	10.7261i	−1.07867	−	0.500653i
$460$	−2.35242	−	4.07452i	−0.109682	−	0.189975i
$461$	1.82624	+	3.16314i	0.0850566	+	0.147322i	0.905415	−	0.424527i	$-0.139560\pi$
$461$	1.82624	+	3.16314i	0.0850566	+	0.147322i	−0.820359	+	0.571849i	$0.806226\pi$
$462$		0			0
$463$	−15.4052	+	26.6825i	−0.715939	+	1.24004i	0.246657	+	0.969103i	$0.420668\pi$
$463$	−15.4052	+	26.6825i	−0.715939	+	1.24004i	−0.962596	+	0.270940i	$0.912666\pi$
$464$	8.93905			0.414985
$465$	−0.348137	−	11.7250i	−0.0161445	−	0.543736i
$466$	−19.1153			−0.885498
$467$	−10.2885	−	17.8202i	−0.476096	−	0.824622i	0.523529	−	0.852008i	$-0.324615\pi$
$467$	−10.2885	−	17.8202i	−0.476096	−	0.824622i	−0.999625	+	0.0273858i	$0.991282\pi$
$468$	1.65061	+	2.50315i	0.0762995	+	0.115708i
$469$		0			0
$470$	−1.45107	−	2.51332i	−0.0669327	−	0.115931i
$471$	0.479730	+	16.1570i	0.0221048	+	0.744476i
$472$	12.3324	+	21.3604i	0.567647	+	0.983193i
$473$	5.69752	+	9.86839i	0.261972	+	0.453749i
$474$	0.0670923	+	2.25963i	0.00308165	+	0.103788i
$475$	25.5139	+	44.1914i	1.17066	+	2.02764i
$476$		0			0
$477$	6.67090	−	0.396491i	0.305439	−	0.0181541i
$478$	9.20552	+	15.9444i	0.421051	+	0.729281i
$479$	25.1832			1.15065			0.575325	−	0.817925i	$-0.304876\pi$
$479$	25.1832			1.15065			0.575325	+	0.817925i	$0.304876\pi$
$480$	0.315142	+	10.6138i	0.0143842	+	0.484451i
$481$	31.4478			1.43390
$482$	−5.15726	+	8.93264i	−0.234907	+	0.406871i
$483$		0			0
$484$	−1.49131	−	2.58303i	−0.0677869	−	0.117410i
$485$	−19.2671	−	33.3716i	−0.874875	−	1.51533i
$486$	2.99631	+	20.0402i	0.135915	+	0.909044i
$487$	16.3807	−	28.3723i	0.742282	−	1.28567i	−0.209173	−	0.977879i	$-0.567077\pi$
$487$	16.3807	−	28.3723i	0.742282	−	1.28567i	0.951454	−	0.307791i	$-0.0995896\pi$
$488$	−14.5039	+	25.1215i	−0.656560	+	1.13720i
$489$	0.868801	+	29.2607i	0.0392886	+	1.32321i
$490$		0			0
$491$	1.76000	−	3.04841i	0.0794278	−	0.137573i	−0.823575	−	0.567207i	$-0.808024\pi$
$491$	1.76000	−	3.04841i	0.0794278	−	0.137573i	0.903003	+	0.429634i	$0.141357\pi$
$492$	3.14888	+	1.69545i	0.141962	+	0.0764367i
$493$	13.3504			0.601272
$494$	−14.3726	+	24.8941i	−0.646654	+	1.12004i
$495$	6.86254	+	10.4070i	0.308448	+	0.467761i
$496$	6.30605			0.283150
$497$		0			0
$498$	−14.4949	−	7.80448i	−0.649533	−	0.349727i
$499$	15.6416			0.700216			0.350108	−	0.936709i	$-0.386145\pi$
$499$	15.6416			0.700216			0.350108	+	0.936709i	$0.386145\pi$
$500$	1.33029	+	2.30412i	0.0594922	+	0.103044i
$501$	−7.58389	+	4.68404i	−0.338823	+	0.209267i
$502$	−5.23262	+	9.06316i	−0.233543	+	0.404509i
$503$	−36.5427			−1.62936			−0.814678	−	0.579913i	$-0.803086\pi$
$503$	−36.5427			−1.62936			−0.814678	+	0.579913i	$0.803086\pi$
$504$		0			0
$505$	−5.62404			−0.250267
$506$	3.29358	−	5.70465i	0.146418	−	0.253603i
$507$	−0.135077	−	4.54931i	−0.00599898	−	0.202042i
$508$	−0.471969	−	0.817474i	−0.0209402	−	0.0362696i
$509$	−37.6458			−1.66862			−0.834311	−	0.551294i	$-0.814134\pi$
$509$	−37.6458			−1.66862			−0.834311	+	0.551294i	$0.814134\pi$
$510$	−1.15517	−	38.9054i	−0.0511518	−	1.72276i
$511$		0			0
$512$	−25.4272			−1.12373
$513$	29.1898	−	20.5165i	1.28876	−	0.905827i
$514$	11.4088	−	19.7606i	0.503221	−	0.871604i
$515$	8.23480			0.362869
$516$	4.42172	−	2.73098i	0.194655	−	0.120225i
$517$	−0.373135	+	0.646289i	−0.0164105	+	0.0284237i
$518$		0			0
$519$	14.3483	−	8.86196i	0.629822	−	0.388997i
$520$	−17.0508	+	29.5329i	−0.747728	+	1.29510i
$521$	7.17115	−	12.4208i	0.314174	−	0.544165i	−0.665088	−	0.746765i	$-0.731606\pi$
$521$	7.17115	−	12.4208i	0.314174	−	0.544165i	0.979262	+	0.202600i	$0.0649392\pi$
$522$	−5.84517	−	8.86419i	−0.255836	−	0.387975i
$523$	−5.24222	−	9.07980i	−0.229226	−	0.397032i	0.728353	−	0.685202i	$-0.240286\pi$
$523$	−5.24222	−	9.07980i	−0.229226	−	0.397032i	−0.957579	+	0.288171i	$0.906953\pi$
$524$	−0.506114	−	0.876616i	−0.0221097	−	0.0382951i
$525$		0			0
$526$	15.1751	−	26.2840i	0.661665	−	1.14604i
$527$	9.41802			0.410256
$528$	−5.70174	+	3.52156i	−0.248136	+	0.153256i
$529$	−4.51110			−0.196135
$530$	5.10461	+	8.84144i	0.221730	+	0.384047i
$531$	11.0318	−	22.0314i	0.478741	−	0.956083i
$532$		0			0
$533$	10.7141	+	18.5573i	0.464078	+	0.803807i
$534$	−23.8733	−	12.8541i	−1.03310	−	0.556250i
$535$	3.92007	+	6.78976i	0.169479	+	0.293547i
$536$	8.00788	+	13.8701i	0.345888	+	0.599095i
$537$	2.02769	−	1.25236i	0.0875014	−	0.0540435i
$538$	−0.349983	−	0.606188i	−0.0150888	−	0.0261346i
$539$		0			0
$540$	4.65150	−	3.26939i	0.200169	−	0.140692i
$541$	23.0461	+	39.9170i	0.990830	+	1.71617i	0.612430	+	0.790524i	$0.290192\pi$
$541$	23.0461	+	39.9170i	0.990830	+	1.71617i	0.378399	+	0.925643i	$0.376475\pi$
$542$	−18.7376			−0.804851
$543$	8.64027	+	4.65217i	0.370789	+	0.199644i
$544$	−8.52542			−0.365525
$545$	1.62112	−	2.80786i	0.0694411	−	0.120275i
$546$		0			0
$547$	−12.1793	−	21.0951i	−0.520747	−	0.901961i	−0.999709	−	0.0241250i	$-0.992320\pi$
$547$	−12.1793	−	21.0951i	−0.520747	−	0.901961i	0.478962	−	0.877836i	$-0.341013\pi$
$548$	3.24822	+	5.62607i	0.138757	+	0.240334i
$549$	28.9264	−	1.71927i	1.23455	−	0.0733765i
$550$	−5.69237	+	9.85947i	−0.242723	+	0.420409i
$551$	−9.34790	+	16.1910i	−0.398234	+	0.689761i
$552$	−19.6930	−	10.6033i	−0.838191	−	0.451306i
$553$		0			0
$554$	−14.2379	+	24.6608i	−0.604911	+	1.04774i
$555$	−1.76979	−	59.6054i	−0.0751233	−	2.53011i
$556$	−5.15894			−0.218788
$557$	−15.2888	+	26.4809i	−0.647806	+	1.12203i	0.335840	+	0.941919i	$0.390980\pi$
$557$	−15.2888	+	26.4809i	−0.647806	+	1.12203i	−0.983646	+	0.180114i	$0.942353\pi$
$558$	−4.12347	−	6.25323i	−0.174560	−	0.264720i
$559$	31.1394			1.31706
$560$		0			0
$561$	−8.51550	+	5.25943i	−0.359525	+	0.222053i
$562$	2.01902			0.0851672
$563$	−4.41357	−	7.64452i	−0.186010	−	0.322178i	0.757907	−	0.652363i	$-0.226222\pi$
$563$	−4.41357	−	7.64452i	−0.186010	−	0.322178i	−0.943916	+	0.330185i	$0.892889\pi$
$564$	0.299683	+	0.161358i	0.0126189	+	0.00679440i
$565$	4.20730	−	7.28725i	0.177002	−	0.306577i
$566$	−3.44650			−0.144867
$567$		0			0
$568$	9.84186			0.412955
$569$	−3.56027	+	6.16658i	−0.149254	+	0.258516i	−0.930952	−	0.365141i	$-0.881021\pi$
$569$	−3.56027	+	6.16658i	−0.149254	+	0.258516i	0.781698	+	0.623658i	$0.214354\pi$
$570$	47.9924	+	25.8405i	2.01018	+	1.08234i
$571$	−3.33181	−	5.77086i	−0.139432	−	0.241503i	0.787850	−	0.615867i	$-0.211194\pi$
$571$	−3.33181	−	5.77086i	−0.139432	−	0.241503i	−0.927282	+	0.374364i	$0.877861\pi$
$572$	1.17790			0.0492503
$573$	−36.8600	+	22.7658i	−1.53985	+	0.951056i
$574$		0			0
$575$	−31.9548			−1.33261
$576$	14.5765	+	22.1053i	0.607356	+	0.921054i
$577$	−3.95629	+	6.85250i	−0.164703	+	0.285273i	−0.936550	−	0.350535i	$-0.886000\pi$
$577$	−3.95629	+	6.85250i	−0.164703	+	0.285273i	0.771847	+	0.635808i	$0.219333\pi$
$578$	9.15254			0.380696
$579$	0.901323	+	30.3560i	0.0374577	+	1.26155i
$580$	−1.48963	+	2.58011i	−0.0618533	+	0.107133i
$581$		0			0
$582$	−21.6654	−	11.6653i	−0.898059	−	0.483540i
$583$	1.31263	−	2.27354i	0.0543634	−	0.0941602i
$584$	1.55874	−	2.69981i	0.0645010	−	0.111719i
$585$	34.0060	−	2.02118i	1.40598	−	0.0835654i
$586$	−6.75042	−	11.6921i	−0.278857	−	0.482995i
$587$	−9.13891	−	15.8291i	−0.377203	−	0.653335i	0.613451	−	0.789733i	$-0.289781\pi$
$587$	−9.13891	−	15.8291i	−0.377203	−	0.653335i	−0.990654	+	0.136398i	$0.956447\pi$
$588$		0			0
$589$	−6.59447	+	11.4220i	−0.271720	+	0.470633i
$590$	37.6415			1.54968
$591$	30.1257	+	16.2205i	1.23920	+	0.667223i
$592$	32.0574			1.31755
$593$	14.1908	+	24.5792i	0.582745	+	1.00934i	0.995152	+	0.0983450i	$0.0313549\pi$
$593$	14.1908	+	24.5792i	0.582745	+	1.00934i	−0.412407	+	0.911000i	$0.635312\pi$
$594$	7.22039	+	3.35127i	0.296256	+	0.137504i
$595$		0			0
$596$	0.175096	+	0.303275i	0.00717222	+	0.0124226i
$597$	−28.0318	+	17.3133i	−1.14727	+	0.708585i
$598$	−9.00044	−	15.5892i	−0.368055	−	0.637490i
$599$	−4.69451	−	8.13113i	−0.191813	−	0.332229i	0.754038	−	0.656830i	$-0.228103\pi$
$599$	−4.69451	−	8.13113i	−0.191813	−	0.332229i	−0.945851	+	0.324601i	$0.894770\pi$
$600$	34.0359	+	18.3259i	1.38951	+	0.748151i
$601$	−6.31432	−	10.9367i	−0.257566	−	0.446118i	0.708023	−	0.706189i	$-0.249587\pi$
$601$	−6.31432	−	10.9367i	−0.257566	−	0.446118i	−0.965589	+	0.260071i	$0.916254\pi$
$602$		0			0
$603$	7.16336	−	14.3058i	0.291714	−	0.582577i
$604$	−3.04584	−	5.27555i	−0.123934	−	0.214659i
$605$	−33.8871			−1.37771
$606$	−3.05546	+	1.88714i	−0.124120	+	0.0766600i
$607$	24.0265			0.975207			0.487604	−	0.873065i	$-0.337871\pi$
$607$	24.0265			0.975207			0.487604	+	0.873065i	$0.337871\pi$
$608$	5.96947	−	10.3394i	0.242094	−	0.419319i
$609$		0			0
$610$	22.1347	+	38.3383i	0.896206	+	1.55227i
$611$	1.01967	+	1.76613i	0.0412516	+	0.0714498i
$612$	2.51295	+	3.81089i	0.101580	+	0.154046i
$613$	14.2708	−	24.7177i	0.576390	−	0.998337i	−0.419499	−	0.907756i	$-0.637794\pi$
$613$	14.2708	−	24.7177i	0.576390	−	0.998337i	0.995889	−	0.0905814i	$-0.0288725\pi$
$614$	6.91695	−	11.9805i	0.279145	−	0.483494i
$615$	34.5701	−	21.3515i	1.39400	−	0.860976i
$616$		0			0
$617$	−6.05549	+	10.4884i	−0.243785	+	0.422248i	−0.961789	−	0.273791i	$-0.911722\pi$
$617$	−6.05549	+	10.4884i	−0.243785	+	0.422248i	0.718004	+	0.696039i	$0.245056\pi$
$618$	4.47385	−	2.76318i	0.179965	−	0.111152i
$619$	−26.5739			−1.06810			−0.534048	−	0.845454i	$-0.679330\pi$
$619$	−26.5739			−1.06810			−0.534048	+	0.845454i	$0.679330\pi$
$620$	−1.05085	+	1.82013i	−0.0422033	+	0.0730983i
$621$	1.98698	+	22.2543i	0.0797346	+	0.893033i
$622$	−17.8207			−0.714545
$623$		0			0
$624$	0.543522	+	18.3055i	0.0217583	+	0.732806i
$625$	−6.92971			−0.277188
$626$	−13.7903	−	23.8855i	−0.551170	−	0.954655i
$627$	−0.415982	−	14.0100i	−0.0166127	−	0.559506i
$628$	1.44807	−	2.50813i	0.0577843	−	0.100085i
$629$	47.8774			1.90900
$630$		0			0
$631$	3.30962			0.131754			0.0658770	−	0.997828i	$-0.479015\pi$
$631$	3.30962			0.131754			0.0658770	+	0.997828i	$0.479015\pi$
$632$	1.50769	−	2.61140i	0.0599727	−	0.103876i
$633$	−10.9582	+	6.76813i	−0.435551	+	0.269009i
$634$	−2.32055	−	4.01931i	−0.0921608	−	0.159627i
$635$	−10.7245			−0.425591
$636$	−1.05424	−	0.567631i	−0.0418032	−	0.0225080i
$637$		0			0
$638$	−4.17119			−0.165139
$639$	−5.41230	−	8.20774i	−0.214107	−	0.324693i
$640$	−14.0953	+	24.4138i	−0.557167	+	0.965041i
$641$	32.5844			1.28701			0.643503	−	0.765443i	$-0.277480\pi$
$641$	32.5844			1.28701			0.643503	+	0.765443i	$0.277480\pi$
$642$	4.40802	+	2.37340i	0.173971	+	0.0936707i
$643$	21.5327	−	37.2957i	0.849166	−	1.47080i	−0.0327873	−	0.999462i	$-0.510438\pi$
$643$	21.5327	−	37.2957i	0.849166	−	1.47080i	0.881953	−	0.471337i	$-0.156228\pi$
$644$		0			0
$645$	−1.75243	−	59.0208i	−0.0690019	−	2.32394i
$646$	−21.8814	+	37.8997i	−0.860912	+	1.49114i
$647$	−23.0988	+	40.0082i	−0.908106	+	1.57289i	−0.0914143	+	0.995813i	$0.529139\pi$
$647$	−23.0988	+	40.0082i	−0.908106	+	1.57289i	−0.816692	+	0.577074i	$0.804195\pi$
$648$	10.6463	−	24.8431i	0.418227	−	0.975930i
$649$	−4.83968	−	8.38256i	−0.189974	−	0.329044i
$650$	15.5556	+	26.9432i	0.610143	+	1.05680i
$651$		0			0
$652$	2.62248	−	4.54228i	0.102704	−	0.177889i
$653$	32.0005			1.25228			0.626138	−	0.779713i	$-0.284635\pi$
$653$	32.0005			1.25228			0.626138	+	0.779713i	$0.284635\pi$
$654$	−0.0614451	−	2.06943i	−0.00240269	−	0.0809213i
$655$	−11.5004			−0.449359
$656$	10.9217	+	18.9170i	0.426422	+	0.738585i
$657$	−3.10873	+	0.184770i	−0.121283	+	0.00720857i
$658$		0			0
$659$	19.2070	+	33.2674i	0.748197	+	1.29591i	0.948686	+	0.316219i	$0.102413\pi$
$659$	19.2070	+	33.2674i	0.748197	+	1.29591i	−0.200490	+	0.979696i	$0.564253\pi$
$660$	−0.0662884	−	2.23255i	−0.00258027	−	0.0869020i
$661$	−14.0130	−	24.2712i	−0.545043	−	0.944042i	−0.998604	−	0.0528170i	$-0.983180\pi$
$661$	−14.0130	−	24.2712i	−0.545043	−	0.944042i	0.453561	−	0.891225i	$-0.350153\pi$
$662$	15.5631	+	26.9561i	0.604878	+	1.04768i
$663$	0.811745	+	27.3391i	0.0315256	+	1.06176i
$664$	10.9794	+	19.0169i	0.426083	+	0.737998i
$665$		0			0
$666$	−20.9620	−	31.7889i	−0.812263	−	1.23179i
$667$	−5.85386	−	10.1392i	−0.226662	−	0.392591i
$668$	1.59709			0.0617932
$669$	−0.169189	−	5.69817i	−0.00654121	−	0.220304i
$670$	24.4420			0.944275
$671$	5.69183	−	9.85853i	0.219730	−	0.380584i
$672$		0			0
$673$	0.796281	+	1.37920i	0.0306944	+	0.0531642i	0.880965	−	0.473182i	$-0.156895\pi$
$673$	0.796281	+	1.37920i	0.0306944	+	0.0531642i	−0.850270	+	0.526347i	$0.823561\pi$
$674$	−17.8691	−	30.9503i	−0.688293	−	1.19216i
$675$	−3.43413	−	38.4625i	−0.132180	−	1.48042i
$676$	−0.407731	+	0.706211i	−0.0156820	+	0.0271619i
$677$	21.0167	−	36.4020i	0.807737	−	1.39904i	−0.106691	−	0.994292i	$-0.534025\pi$
$677$	21.0167	−	36.4020i	0.807737	−	1.39904i	0.914428	−	0.404749i	$-0.132641\pi$
$678$	−0.159469	−	5.37082i	−0.00612437	−	0.206265i
$679$		0			0
$680$	−25.9588	+	44.9620i	−0.995476	+	1.72421i
$681$	27.4766	+	14.7942i	1.05291	+	0.566914i
$682$	−2.94256			−0.112676
$683$	−17.8645	+	30.9422i	−0.683565	+	1.18397i	0.290321	+	0.956929i	$0.406238\pi$
$683$	−17.8645	+	30.9422i	−0.683565	+	1.18397i	−0.973886	+	0.227039i	$0.927095\pi$
$684$	−6.38131	+	0.379279i	−0.243996	+	0.0145021i
$685$	73.8092			2.82010
$686$		0			0
$687$	−6.48892	−	3.49382i	−0.247568	−	0.133298i
$688$	31.7430			1.21019
$689$	−3.58704	−	6.21294i	−0.136655	−	0.236694i
$690$	−29.0409	+	17.9365i	−1.10557	+	0.682831i
$691$	25.5675	−	44.2841i	0.972632	−	1.68465i	0.285094	−	0.958499i	$-0.407975\pi$
$691$	25.5675	−	44.2841i	0.972632	−	1.68465i	0.687538	−	0.726149i	$-0.258692\pi$
$692$	−3.02161			−0.114864
$693$		0			0
$694$	−6.66606			−0.253040
$695$	−29.3066	+	50.7606i	−1.11166	+	1.92546i
$696$	0.420336	+	14.1567i	0.0159328	+	0.536607i
$697$	16.3115	+	28.2524i	0.617843	+	1.07014i
$698$	19.6795			0.744881
$699$	−0.755936	−	25.4595i	−0.0285921	−	0.962965i
$700$		0			0
$701$	−24.5761			−0.928226			−0.464113	−	0.885776i	$-0.653627\pi$
$701$	−24.5761			−0.928226			−0.464113	+	0.885776i	$0.653627\pi$
$702$	17.7968	−	12.5088i	0.671696	−	0.472113i
$703$	−33.5236	+	58.0645i	−1.26437	+	2.18995i
$704$	10.4020			0.392040
$705$	3.29008	−	2.03205i	0.123912	−	0.0765315i
$706$	−21.4321	+	37.1215i	−0.806607	+	1.39708i
$707$		0			0
$708$	−3.75597	+	2.31980i	−0.141158	+	0.0871833i
$709$	−15.4488	+	26.7581i	−0.580192	+	1.00492i	0.415265	+	0.909701i	$0.363689\pi$
$709$	−15.4488	+	26.7581i	−0.580192	+	1.00492i	−0.995456	+	0.0952206i	$0.969644\pi$
$710$	7.50992	−	13.0076i	0.281842	−	0.488165i
$711$	−3.00693	+	0.178719i	−0.112769	+	0.00670250i
$712$	18.0832	+	31.3210i	0.677697	+	1.17380i
$713$	−4.12960	−	7.15268i	−0.154655	−	0.267870i
$714$		0			0
$715$	6.69133	−	11.5897i	0.250242	−	0.433431i
$716$	−0.427011			−0.0159582
$717$	−20.8722	+	12.8913i	−0.779487	+	0.481434i
$718$	−31.2431			−1.16598
$719$	3.05690	+	5.29471i	0.114003	+	0.197459i	0.917381	−	0.398011i	$-0.130299\pi$
$719$	3.05690	+	5.29471i	0.114003	+	0.197459i	−0.803378	+	0.595470i	$0.796966\pi$
$720$	34.6651	−	2.06035i	1.29189	−	0.0767848i
$721$		0			0
$722$	−18.2938	−	31.6857i	−0.680823	−	1.17922i
$723$	−12.1013	−	6.51566i	−0.450051	−	0.242320i
$724$	−0.879109	−	1.52266i	−0.0326718	−	0.0565893i
$725$	10.1174	+	17.5238i	0.375749	+	0.650816i
$726$	−18.4104	+	11.3708i	−0.683272	+	0.422009i
$727$	−22.2492	−	38.5367i	−0.825176	−	1.42925i	−0.901785	−	0.432186i	$-0.857743\pi$
$727$	−22.2492	−	38.5367i	−0.825176	−	1.42925i	0.0766087	−	0.997061i	$-0.475591\pi$
$728$		0			0
$729$	−26.5729	+	4.78327i	−0.984182	+	0.177158i
$730$	−2.37882	−	4.12023i	−0.0880440	−	0.152497i
$731$	47.4079			1.75344
$732$	−4.57139	−	2.46137i	−0.168963	−	0.0909747i
$733$	−9.83708			−0.363341			−0.181670	−	0.983359i	$-0.558150\pi$
$733$	−9.83708			−0.363341			−0.181670	+	0.983359i	$0.558150\pi$
$734$	1.72559	−	2.98881i	0.0636926	−	0.110319i
$735$		0			0
$736$	3.73821	+	6.47478i	0.137792	+	0.238663i
$737$	−3.14257	−	5.44309i	−0.115758	−	0.200499i
$738$	11.6169	−	23.1999i	0.427626	−	0.854002i
$739$	−7.42464	+	12.8598i	−0.273120	+	0.473057i	−0.969659	−	0.244461i	$-0.921389\pi$
$739$	−7.42464	+	12.8598i	−0.273120	+	0.473057i	0.696539	+	0.717519i	$0.254722\pi$
$740$	−5.34212	+	9.25282i	−0.196380	+	0.340140i
$741$	−33.7246	−	18.1583i	−1.23890	−	0.667061i
$742$		0			0
$743$	−3.04201	+	5.26892i	−0.111601	+	0.193298i	−0.916416	−	0.400228i	$-0.868931\pi$
$743$	−3.04201	+	5.26892i	−0.111601	+	0.193298i	0.804815	+	0.593525i	$0.202264\pi$
$744$	0.296526	+	9.98681i	0.0108712	+	0.366134i
$745$	3.97871			0.145769
$746$	20.7449	−	35.9311i	0.759523	−	1.31553i
$747$	9.82149	−	19.6143i	0.359350	−	0.717649i
$748$	1.79328			0.0655686
$749$		0			0
$750$	16.4225	−	10.1430i	0.599665	−	0.370371i
$751$	22.2010			0.810127			0.405063	−	0.914289i	$-0.367249\pi$
$751$	22.2010			0.810127			0.405063	+	0.914289i	$0.367249\pi$
$752$	1.03944	+	1.80036i	0.0379044	+	0.0656523i
$753$	−12.2781	−	6.61086i	−0.447438	−	0.240913i
$754$	−5.69934	+	9.87156i	−0.207558	+	0.359501i
$755$	−69.2106			−2.51883
$756$		0			0
$757$	25.0464			0.910329			0.455164	−	0.890407i	$-0.349581\pi$
$757$	25.0464			0.910329			0.455164	+	0.890407i	$0.349581\pi$
$758$	−19.6723	+	34.0735i	−0.714531	+	1.23760i
$759$	7.72822	+	4.16110i	0.280517	+	0.151038i
$760$	−36.3526	−	62.9645i	−1.31865	−	2.28396i
$761$	−6.75264			−0.244783			−0.122392	−	0.992482i	$-0.539056\pi$
$761$	−6.75264			−0.244783			−0.122392	+	0.992482i	$0.539056\pi$
$762$	−5.82649	+	3.59862i	−0.211072	+	0.130364i
$763$		0			0
$764$	7.76233			0.280831
$765$	51.7721	−	3.07712i	1.87182	−	0.111253i
$766$	−1.12637	+	1.95094i	−0.0406975	+	0.0704902i
$767$	−26.4510			−0.955089
$768$	−0.373168	−	12.5681i	−0.0134656	−	0.453512i
$769$	−21.0805	+	36.5125i	−0.760182	+	1.31667i	0.182575	+	0.983192i	$0.441557\pi$
$769$	−21.0805	+	36.5125i	−0.760182	+	1.31667i	−0.942757	+	0.333482i	$0.891776\pi$
$770$		0			0
$771$	26.7702	+	14.4138i	0.964104	+	0.519101i
$772$	2.72065	−	4.71230i	0.0979183	−	0.169600i
$773$	1.64926	−	2.85660i	0.0593197	−	0.102745i	−0.834841	−	0.550492i	$-0.814440\pi$
$773$	1.64926	−	2.85660i	0.0593197	−	0.102745i	0.894160	+	0.447747i	$0.147774\pi$
$774$	−20.7565	−	31.4771i	−0.746076	−	1.13142i
$775$	7.13728	+	12.3621i	0.256379	+	0.444061i
$776$	16.4108	+	28.4243i	0.589112	+	1.02037i
$777$		0			0
$778$	7.20356	−	12.4769i	0.258260	−	0.447320i
$779$	−45.6851			−1.63684
$780$	−5.37414	−	2.89359i	−0.192425	−	0.103607i
$781$	−3.86229			−0.138203
$782$	−13.7026	−	23.7336i	−0.490004	−	0.848713i
$783$	11.5750	−	8.13567i	0.413656	−	0.290745i
$784$		0			0
$785$	−16.4522	−	28.4961i	−0.587205	−	1.01707i
$786$	−6.24802	+	3.85896i	−0.222860	+	0.137645i
$787$	3.36455	+	5.82757i	0.119933	+	0.207731i	0.919741	−	0.392526i	$-0.128399\pi$
$787$	3.36455	+	5.82757i	0.119933	+	0.207731i	−0.799808	+	0.600256i	$0.795065\pi$
$788$	−3.06515	−	5.30900i	−0.109192	−	0.189125i
$789$	35.6075	+	19.1721i	1.26766	+	0.682545i
$790$	−2.30092	−	3.98530i	−0.0818629	−	0.141791i
$791$		0			0
$792$	−5.84517	−	8.86419i	−0.207699	−	0.314975i
$793$	−15.5542	−	26.9406i	−0.552345	−	0.956689i
$794$	32.9376			1.16891
$795$	−11.5740	+	7.14842i	−0.410486	+	0.253528i
$796$	5.90321			0.209234
$797$	−8.86302	+	15.3512i	−0.313944	+	0.543767i	−0.979213	−	0.202837i	$-0.934984\pi$
$797$	−8.86302	+	15.3512i	−0.313944	+	0.543767i	0.665268	+	0.746604i	$0.268317\pi$
$798$		0			0
$799$	1.55239	+	2.68882i	0.0549196	+	0.0951235i
$800$	−6.46084	−	11.1905i	−0.228425	−	0.395644i
$801$	16.1761	−	32.3050i	0.571555	−	1.14144i
$802$	22.6336	−	39.2026i	0.799222	−	1.38429i
$803$	−0.611702	+	1.05950i	−0.0215865	+	0.0373889i
$804$	−2.43888	+	1.50632i	−0.0860126	+	0.0531240i
$805$		0			0
$806$	−4.02060	+	6.96388i	−0.141620	+	0.245292i
$807$	0.793535	−	0.490111i	0.0279338	−	0.0172527i
$808$	4.79028			0.168521
$809$	−19.5428	+	33.8492i	−0.687089	+	1.19007i	0.285686	+	0.958323i	$0.407779\pi$
$809$	−19.5428	+	33.8492i	−0.687089	+	1.19007i	−0.972775	+	0.231751i	$0.925555\pi$
$810$	−24.7103	−	33.0276i	−0.868233	−	1.16047i
$811$	−13.9559			−0.490058			−0.245029	−	0.969516i	$-0.578797\pi$
$811$	−13.9559			−0.490058			−0.245029	+	0.969516i	$0.578797\pi$
$812$		0			0
$813$	−0.741002	−	24.9565i	−0.0259881	−	0.875263i
$814$	−14.9588			−0.524305
$815$	−29.7953	−	51.6070i	−1.04369	−	1.80772i
$816$	0.827479	+	27.8690i	0.0289676	+	0.975610i
$817$	−33.1948	+	57.4951i	−1.16134	+	2.01150i
$818$	−23.7177			−0.829269
$819$		0			0
$820$	−7.28010			−0.254232
$821$	22.4983	−	38.9682i	0.785196	−	1.36000i	−0.143685	−	0.989623i	$-0.545895\pi$
$821$	22.4983	−	38.9682i	0.785196	−	1.36000i	0.928882	−	0.370376i	$-0.120771\pi$
$822$	40.0995	−	24.7666i	1.39863	−	0.863835i
$823$	27.6232	+	47.8449i	0.962886	+	1.66777i	0.715191	+	0.698929i	$0.246340\pi$
$823$	27.6232	+	47.8449i	0.962886	+	1.66777i	0.247694	+	0.968838i	$0.420327\pi$
$824$	−7.01400			−0.244344
$825$	−13.3569	−	7.19171i	−0.465026	−	0.250383i
$826$		0			0
$827$	−13.8901			−0.483005			−0.241502	−	0.970400i	$-0.577640\pi$
$827$	−13.8901			−0.483005			−0.241502	+	0.970400i	$0.577640\pi$
$828$	1.79237	−	3.57950i	0.0622891	−	0.124396i
$829$	−19.4896	+	33.7570i	−0.676903	+	1.17243i	0.299006	+	0.954251i	$0.403345\pi$
$829$	−19.4896	+	33.7570i	−0.676903	+	1.17243i	−0.975909	+	0.218179i	$0.929988\pi$
$830$	33.5117			1.16321
$831$	−33.4085	−	17.9881i	−1.15893	−	0.624001i
$832$	14.2129	−	24.6174i	0.492743	−	0.853456i
$833$		0			0
$834$	1.11081	+	37.4113i	0.0384641	+	1.29545i
$835$	9.07266	−	15.7143i	0.313972	−	0.543816i
$836$	−1.25564	+	2.17484i	−0.0434274	+	0.0752184i
$837$	8.16556	−	5.73930i	0.282243	−	0.198379i
$838$	−5.46882	−	9.47227i	−0.188917	−	0.327214i
$839$	19.4708	+	33.7244i	0.672206	+	1.16429i	0.977277	+	0.211965i	$0.0679862\pi$
$839$	19.4708	+	33.7244i	0.672206	+	1.16429i	−0.305072	+	0.952329i	$0.598680\pi$
$840$		0			0
$841$	10.7932	−	18.6943i	0.372178	−	0.644631i
$842$	−0.375119			−0.0129275
$843$	0.0798445	+	2.68911i	0.00274999	+	0.0926180i
$844$	2.30769			0.0794340
$845$	4.63243	+	8.02361i	0.159361	+	0.276021i
$846$	1.10560	−	2.20797i	0.0380113	−	0.0759116i
$847$		0			0
$848$	−3.65657	−	6.33336i	−0.125567	−	0.217488i
$849$	−0.136296	−	4.59036i	−0.00467766	−	0.157541i
$850$	23.6825	+	41.0193i	0.812304	+	1.40695i
$851$	−20.9932	−	36.3613i	−0.719638	−	1.24645i
$852$	0.0522798	+	1.76075i	0.00179108	+	0.0603224i
$853$	3.83890	+	6.64916i	0.131441	+	0.227663i	0.924232	−	0.381830i	$-0.124706\pi$
$853$	3.83890	+	6.64916i	0.131441	+	0.227663i	−0.792791	+	0.609493i	$0.791373\pi$
$854$		0			0
$855$	−32.5188	+	64.9425i	−1.11212	+	2.22099i
$856$	−3.33892	−	5.78318i	−0.114122	−	0.197665i
$857$	15.9639			0.545316			0.272658	−	0.962111i	$-0.412097\pi$
$857$	15.9639			0.545316			0.272658	+	0.962111i	$0.412097\pi$
$858$	−0.253621	−	8.54181i	−0.00865848	−	0.291612i
$859$	−48.3291			−1.64897			−0.824483	−	0.565887i	$-0.808534\pi$
$859$	−48.3291			−1.64897			−0.824483	+	0.565887i	$0.808534\pi$
$860$	−5.28973	+	9.16208i	−0.180378	+	0.312424i
$861$		0			0
$862$	8.77148	+	15.1926i	0.298758	+	0.517463i
$863$	17.1526	+	29.7092i	0.583881	+	1.01131i	0.995014	+	0.0997366i	$0.0318000\pi$
$863$	17.1526	+	29.7092i	0.583881	+	1.01131i	−0.411133	+	0.911576i	$0.634867\pi$
$864$	−7.39166	+	5.19536i	−0.251469	+	0.176750i
$865$	−17.1650	+	29.7307i	−0.583628	+	1.01087i
$866$	3.15356	−	5.46212i	0.107162	−	0.185611i
$867$	0.361948	+	12.1902i	0.0122924	+	0.414001i
$868$		0			0
$869$	−0.591670	+	1.02480i	−0.0200710	+	0.0347640i
$870$	19.0310	+	10.2468i	0.645212	+	0.347400i
$871$	−17.1755			−0.581970
$872$	−1.38079	+	2.39159i	−0.0467594	+	0.0809896i
$873$	14.6801	−	29.3172i	0.496845	−	0.992238i
$874$	38.3781			1.29816
$875$		0			0
$876$	0.491288	+	0.264524i	0.0165991	+	0.00893743i
$877$	14.1815			0.478876			0.239438	−	0.970912i	$-0.423037\pi$
$877$	14.1815			0.478876			0.239438	+	0.970912i	$0.423037\pi$
$878$	−1.65599	−	2.86826i	−0.0558870	−	0.0967992i
$879$	15.3056	−	9.45319i	0.516245	−	0.318848i
$880$	6.82103	−	11.8144i	0.229937	−	0.398262i
$881$	46.2822			1.55929			0.779643	−	0.626224i	$-0.215400\pi$
$881$	46.2822			1.55929			0.779643	+	0.626224i	$0.215400\pi$
$882$		0			0
$883$	−4.37483			−0.147225			−0.0736124	−	0.997287i	$-0.523453\pi$
$883$	−4.37483			−0.147225			−0.0736124	+	0.997287i	$0.523453\pi$
$884$	2.45026	−	4.24397i	0.0824111	−	0.142740i
$885$	1.48858	+	50.1344i	0.0500380	+	1.68525i
$886$	0.419538	+	0.726661i	0.0140946	+	0.0244126i
$887$	19.1442			0.642798			0.321399	−	0.946944i	$-0.395847\pi$
$887$	19.1442			0.642798			0.321399	+	0.946944i	$0.395847\pi$
$888$	1.50742	+	50.7689i	0.0505856	+	1.70369i
$889$		0			0
$890$	55.1942			1.85011
$891$	−4.17798	+	9.74930i	−0.139968	+	0.326614i
$892$	−0.510697	+	0.884554i	−0.0170994	+	0.0296171i
$893$	−4.34791			−0.145497
$894$	2.16158	−	1.33505i	0.0722939	−	0.0446509i
$895$	−2.42574	+	4.20151i	−0.0810836	+	0.140441i
$896$		0			0
$897$	20.4072	−	12.6041i	0.681377	−	0.420838i
$898$	3.39694	−	5.88368i	0.113358	−	0.196341i
$899$	−2.61499	+	4.52929i	−0.0872147	+	0.151060i
$900$	−3.09779	+	6.18652i	−0.103260	+	0.206217i
$901$	−5.46105	−	9.45881i	−0.181934	−	0.315119i
$902$	−5.09636	−	8.82715i	−0.169690	−	0.293912i
$903$		0			0
$904$	−3.58357	+	6.20692i	−0.119188	+	0.206439i
$905$	−19.9760			−0.664024
$906$	−37.6011	+	23.2236i	−1.24921	+	0.771552i
$907$	39.8450			1.32303			0.661515	−	0.749932i	$-0.269914\pi$
$907$	39.8450			1.32303			0.661515	+	0.749932i	$0.269914\pi$
$908$	−2.79562	−	4.84216i	−0.0927760	−	0.160693i
$909$	−2.63430	−	3.99491i	−0.0873743	−	0.132503i
$910$		0			0
$911$	14.3727	+	24.8942i	0.476189	+	0.824783i	0.999628	−	0.0272803i	$-0.00868466\pi$
$911$	14.3727	+	24.8942i	0.476189	+	0.824783i	−0.523439	+	0.852063i	$0.675351\pi$
$912$	−34.3782	−	18.5102i	−1.13838	−	0.612935i
$913$	−4.30870	−	7.46288i	−0.142597	−	0.246985i
$914$	1.85930	+	3.22041i	0.0615003	+	0.106522i
$915$	−50.1871	+	30.9971i	−1.65914	+	1.02473i
$916$	0.660219	+	1.14353i	0.0218142	+	0.0377834i
$917$		0			0
$918$	27.0945	−	19.0438i	0.894252	−	0.628540i
$919$	8.01347	+	13.8797i	0.264340	+	0.457850i	0.967390	−	0.253290i	$-0.0815126\pi$
$919$	8.01347	+	13.8797i	0.264340	+	0.457850i	−0.703051	+	0.711140i	$0.748179\pi$
$920$	45.5296			1.50107
$921$	16.2303	+	8.73884i	0.534806	+	0.287955i
$922$	−4.74776			−0.156359
$923$	−5.27727	+	9.14050i	−0.173704	+	0.300863i
$924$		0			0
$925$	36.2830	+	62.8440i	1.19298	+	2.06630i
$926$	−20.0247	−	34.6839i	−0.658054	−	1.13978i
$927$	3.85718	+	5.84941i	0.126686	+	0.192120i
$928$	2.36715	−	4.10002i	0.0777055	−	0.134590i
$929$	7.00796	−	12.1381i	0.229924	−	0.398239i	−0.727862	−	0.685724i	$-0.759486\pi$
$929$	7.00796	−	12.1381i	0.229924	−	0.398239i	0.957785	+	0.287485i	$0.0928190\pi$
$930$	13.4254	+	7.22863i	0.440237	+	0.237036i
$931$		0			0
$932$	−2.28180	+	3.95219i	−0.0747428	+	0.129458i
$933$	−0.704740	−	23.7352i	−0.0230721	−	0.777056i
$934$	26.7475			0.875205
$935$	10.1871	−	17.6447i	0.333155	−	0.577042i
$936$	−28.9646	+	1.72154i	−0.946739	+	0.0562703i
$937$	−51.5307			−1.68344			−0.841718	−	0.539918i	$-0.818455\pi$
$937$	−51.5307			−1.68344			−0.841718	+	0.539918i	$0.818455\pi$
$938$		0			0
$939$	31.2675	−	19.3117i	1.02038	−	0.630214i
$940$	−0.692857			−0.0225985
$941$	−23.1564	−	40.1081i	−0.754877	−	1.30749i	−0.945435	−	0.325809i	$-0.894363\pi$
$941$	−23.1564	−	40.1081i	−0.754877	−	1.30749i	0.190558	−	0.981676i	$-0.438970\pi$
$942$	−18.5001	−	9.96099i	−0.602766	−	0.324547i
$943$	14.3045	−	24.7761i	0.465819	−	0.806821i
$944$	−26.9636			−0.877592
$945$		0			0
$946$	−14.8121			−0.481582
$947$	−10.0041	+	17.3277i	−0.325091	+	0.563073i	−0.981531	−	0.191305i	$-0.938728\pi$
$947$	−10.0041	+	17.3277i	−0.325091	+	0.563073i	0.656440	+	0.754378i	$0.272061\pi$
$948$	0.475200	+	0.255861i	0.0154338	+	0.00830998i
$949$	1.67161	+	2.89531i	0.0542628	+	0.0939859i
$950$	−66.3297			−2.15202
$951$	5.26152	−	3.24967i	0.170616	−	0.105378i
$952$		0			0
$953$	30.0109			0.972148			0.486074	−	0.873918i	$-0.338429\pi$
$953$	30.0109			0.972148			0.486074	+	0.873918i	$0.338429\pi$
$954$	−3.88932	+	7.76727i	−0.125921	+	0.251475i
$955$	44.0958	−	76.3762i	1.42691	−	2.47148i
$956$	4.39547			0.142160
$957$	−0.164954	−	5.55557i	−0.00533222	−	0.179586i
$958$	−16.3675	+	28.3493i	−0.528809	+	0.915924i
$959$		0			0
$960$	−47.4591	−	25.5533i	−1.53173	−	0.824730i
$961$	13.6553	−	23.6516i	0.440492	−	0.762955i
$962$	−20.4391	+	35.4015i	−0.658982	+	1.14139i
$963$	−2.98679	+	5.96486i	−0.0962481	+	0.192215i
$964$	1.23125	+	2.13259i	0.0396559	+	0.0686860i
$965$	−30.9106	−	53.5388i	−0.995049	−	1.72348i
$966$		0			0
$967$	16.5721	−	28.7037i	0.532923	−	0.923050i	−0.466338	−	0.884607i	$-0.654427\pi$
$967$	16.5721	−	28.7037i	0.532923	−	0.923050i	0.999261	−	0.0384431i	$-0.0122398\pi$
$968$	28.8633			0.927702
$969$	−51.3436	−	27.6448i	−1.64939	−	0.888080i
$970$	50.0896			1.60828
$971$	20.8234	+	36.0672i	0.668256	+	1.15745i	0.978392	+	0.206761i	$0.0662921\pi$
$971$	20.8234	+	36.0672i	0.668256	+	1.15745i	−0.310136	+	0.950692i	$0.600375\pi$
$972$	4.50110	+	1.77271i	0.144373	+	0.0568597i
$973$		0			0
$974$	21.2928	+	36.8803i	0.682267	+	1.18172i
$975$	−35.2702	+	21.7839i	−1.12955	+	0.697644i
$976$	−15.8556	−	27.4628i	−0.507527	−	0.879062i
$977$	−18.7590	−	32.4916i	−0.600154	−	1.03950i	−0.992797	−	0.119807i	$-0.961772\pi$
$977$	−18.7590	−	32.4916i	−0.600154	−	1.03950i	0.392643	−	0.919691i	$-0.371561\pi$
$978$	−33.5041	−	18.0396i	−1.07134	−	0.576842i
$979$	−7.09647	−	12.2914i	−0.226804	−	0.392836i
$980$		0			0
$981$	2.75383	−	0.163676i	0.0879231	−	0.00522578i
$982$	2.28778	+	3.96255i	0.0730059	+	0.126450i
$983$	−48.0758			−1.53338			−0.766690	−	0.642017i	$-0.778098\pi$
$983$	−48.0758			−1.53338			−0.766690	+	0.642017i	$0.778098\pi$
$984$	−29.4451	+	18.1862i	−0.938675	+	0.579753i
$985$	−69.6495			−2.21922
$986$	−8.67690	+	15.0288i	−0.276329	+	0.478616i
$987$		0			0
$988$	3.43133	+	5.94323i	0.109165	+	0.189079i
$989$	−20.7873	−	36.0047i	−0.660999	−	1.14488i
$990$	−16.1756	+	0.961413i	−0.514095	+	0.0305557i
$991$	17.0643	−	29.5562i	0.542065	−	0.938884i	−0.456720	−	0.889610i	$-0.650976\pi$
$991$	17.0643	−	29.5562i	0.542065	−	0.938884i	0.998785	−	0.0492737i	$-0.0156907\pi$
$992$	1.66990	−	2.89236i	0.0530195	−	0.0918324i
$993$	−35.2871	+	21.7944i	−1.11980	+	0.691624i
$994$		0			0
$995$	33.5346	−	58.0837i	1.06312	−	1.84138i
$996$	−3.34388	+	2.06528i	−0.105955	+	0.0654410i
$997$	44.0827			1.39611			0.698056	−	0.716043i	$-0.254049\pi$
$997$	44.0827			1.39611			0.698056	+	0.716043i	$0.254049\pi$
$998$	−10.1661	+	17.6081i	−0.321801	+	0.557376i
$999$	41.5104	−	29.1763i	1.31333	−	0.923097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.h.67.3		24
3.2	odd	2		1323.2.g.h.361.10		24
7.2	even	3		441.2.h.h.373.10		24
7.3	odd	6		441.2.f.h.148.3	✓	24
7.4	even	3		441.2.f.h.148.4	yes	24
7.5	odd	6		441.2.h.h.373.9		24
7.6	odd	2	inner	441.2.g.h.67.4		24
9.2	odd	6		1323.2.h.h.802.3		24
9.7	even	3		441.2.h.h.214.10		24
21.2	odd	6		1323.2.h.h.226.3		24
21.5	even	6		1323.2.h.h.226.4		24
21.11	odd	6		1323.2.f.h.442.10		24
21.17	even	6		1323.2.f.h.442.9		24
21.20	even	2		1323.2.g.h.361.9		24
63.2	odd	6		1323.2.g.h.667.10		24
63.4	even	3		3969.2.a.bh.1.10		12
63.11	odd	6		1323.2.f.h.883.10		24
63.16	even	3	inner	441.2.g.h.79.3		24
63.20	even	6		1323.2.h.h.802.4		24
63.25	even	3		441.2.f.h.295.4	yes	24
63.31	odd	6		3969.2.a.bh.1.9		12
63.32	odd	6		3969.2.a.bi.1.3		12
63.34	odd	6		441.2.h.h.214.9		24
63.38	even	6		1323.2.f.h.883.9		24
63.47	even	6		1323.2.g.h.667.9		24
63.52	odd	6		441.2.f.h.295.3	yes	24
63.59	even	6		3969.2.a.bi.1.4		12
63.61	odd	6	inner	441.2.g.h.79.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.3	✓	24	7.3	odd	6
441.2.f.h.148.4	yes	24	7.4	even	3
441.2.f.h.295.3	yes	24	63.52	odd	6
441.2.f.h.295.4	yes	24	63.25	even	3
441.2.g.h.67.3		24	1.1	even	1	trivial
441.2.g.h.67.4		24	7.6	odd	2	inner
441.2.g.h.79.3		24	63.16	even	3	inner
441.2.g.h.79.4		24	63.61	odd	6	inner
441.2.h.h.214.9		24	63.34	odd	6
441.2.h.h.214.10		24	9.7	even	3
441.2.h.h.373.9		24	7.5	odd	6
441.2.h.h.373.10		24	7.2	even	3
1323.2.f.h.442.9		24	21.17	even	6
1323.2.f.h.442.10		24	21.11	odd	6
1323.2.f.h.883.9		24	63.38	even	6
1323.2.f.h.883.10		24	63.11	odd	6
1323.2.g.h.361.9		24	21.20	even	2
1323.2.g.h.361.10		24	3.2	odd	2
1323.2.g.h.667.9		24	63.47	even	6
1323.2.g.h.667.10		24	63.2	odd	6
1323.2.h.h.226.3		24	21.2	odd	6
1323.2.h.h.226.4		24	21.5	even	6
1323.2.h.h.802.3		24	9.2	odd	6
1323.2.h.h.802.4		24	63.20	even	6
3969.2.a.bh.1.9		12	63.31	odd	6
3969.2.a.bh.1.10		12	63.4	even	3
3969.2.a.bi.1.3		12	63.32	odd	6
3969.2.a.bi.1.4		12	63.59	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.649936 + 1.12572i) q^{2} +(-1.52504 - 0.821126i) q^{3} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(1.65150 + 2.50450i) q^{9} +(-2.29157 + 3.96912i) q^{10} +1.17853 q^{11} +(-0.0159526 - 0.537275i) q^{12} +(1.61030 - 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} +(1.64151 - 2.84319i) q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.89275 + 0.231369i) q^{18} +(3.43318 + 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} -4.29987 q^{23} +(4.57991 + 2.46595i) q^{24} +7.43156 q^{25} +(2.09319 + 3.62551i) q^{26} +(-0.462101 - 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(6.75389 - 4.17140i) q^{30} +(0.960401 + 1.66346i) q^{31} +(-0.869378 - 1.50581i) q^{32} +(-1.79731 - 0.967725i) q^{33} +(3.18675 + 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 + 8.45637i) q^{37} -8.92540 q^{38} +(-4.74600 + 2.93127i) q^{39} -10.5886 q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 + 0.316738i) q^{44} +(5.82294 + 8.83048i) q^{45} +(2.79464 - 4.84046i) q^{46} +(-0.316609 + 0.548383i) q^{47} +(-4.83799 + 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(-7.22550 + 4.46268i) q^{51} +0.999459 q^{52} +(1.11378 - 1.92912i) q^{53} +(6.12658 + 2.84359i) q^{54} +4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} -3.53930 q^{58} +(-4.10652 - 7.11270i) q^{59} +(-0.0562464 - 1.89435i) q^{60} +(4.82958 - 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(5.67767 - 9.83402i) q^{65} +(2.25753 - 1.39432i) q^{66} +(-2.66651 - 4.61852i) q^{67} +1.52161 q^{68} +(6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(-4.95969 - 7.52136i) q^{72} +(-0.519036 + 0.898997i) q^{73} -12.6927 q^{74} +(-11.3334 - 6.10225i) q^{75} +(-1.06543 + 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +(-0.502039 + 0.869557i) q^{79} +(5.78772 - 10.0246i) q^{80} +(-3.54507 + 8.27239i) q^{81} +(-4.32432 - 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} -12.5682 q^{86} +(-0.139966 - 4.71396i) q^{87} -3.53930 q^{88} +(-6.02144 - 10.4294i) q^{89} +(-13.7252 + 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-0.0987387 - 3.32546i) q^{93} +(-0.411551 - 0.712828i) q^{94} +(12.1049 + 20.9662i) q^{95} +(0.0893807 + 3.01029i) q^{96} +(-5.46454 - 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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