LMFDB - Embedded newform 441.2.h.h.373.10

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			373.10
Character	$\chi$	$=$	441.373
Dual form			441.2.h.h.214.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.29987 q^{2} +(1.47364 - 0.910162i) q^{3} -0.310333 q^{4} +(-1.76292 - 3.05347i) q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(1.34321 - 2.68250i) q^{9} +(-2.29157 - 3.96912i) q^{10} +(-0.589267 + 1.02064i) q^{11} +(-0.457317 + 0.282453i) q^{12} +(1.61030 - 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} -3.28303 q^{16} +(2.45159 + 4.24627i) q^{17} +(1.74600 - 3.48690i) q^{18} +(3.43318 - 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(2.14994 + 3.72380i) q^{23} +(-4.42553 + 2.73334i) q^{24} +(-3.71578 + 6.43592i) q^{25} +(2.09319 - 3.62551i) q^{26} +(-0.462101 - 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(-6.98948 - 3.76334i) q^{30} -1.92080 q^{31} +1.73876 q^{32} +(0.0605825 + 2.04038i) q^{33} +(3.18675 + 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 - 8.45637i) q^{37} +(4.46270 - 7.72962i) q^{38} +(-0.165555 - 5.57579i) q^{39} +(5.29429 + 9.16998i) q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 - 0.316738i) q^{44} +(-10.5589 + 0.627577i) q^{45} +(2.79464 + 4.84046i) q^{46} +0.633218 q^{47} +(-4.83799 + 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(7.47754 + 4.02612i) q^{51} +(-0.499729 + 0.865557i) q^{52} +(1.11378 + 1.92912i) q^{53} +(-0.600672 - 6.72757i) q^{54} +4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} +(1.76965 + 3.06512i) q^{58} +8.21304 q^{59} +(1.66868 + 0.898462i) q^{60} -9.65916 q^{61} -2.49680 q^{62} +8.82622 q^{64} -11.3553 q^{65} +(0.0787495 + 2.65224i) q^{66} +5.33301 q^{67} +(-0.760807 - 1.31776i) q^{68} +(6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(-4.03385 + 8.05590i) q^{72} +(-0.519036 - 0.898997i) q^{73} +(6.34635 - 10.9922i) q^{74} +(0.382019 + 12.8662i) q^{75} +(-1.06543 + 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +1.00408 q^{79} +(5.78772 + 10.0246i) q^{80} +(-5.39157 - 7.20631i) q^{81} +(-4.32432 + 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(6.28411 + 10.8844i) q^{86} +(4.15239 + 2.23577i) q^{87} +(1.76965 - 3.06512i) q^{88} +(-6.02144 + 10.4294i) q^{89} +(-13.7252 + 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-2.83056 + 1.74824i) q^{93} +0.823103 q^{94} -24.2097 q^{95} +(2.56230 - 1.58255i) q^{96} +(-5.46454 - 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	1.29987			0.919148			0.459574	−	0.888139i	$-0.348002\pi$
$2$	1.29987			0.919148			0.459574	+	0.888139i	$0.348002\pi$
$3$	1.47364	−	0.910162i	0.850805	−	0.525482i
$3$	1.47364	−	0.910162i	0.850805	−	0.525482i
$4$	−0.310333			−0.155166
$5$	−1.76292	−	3.05347i	−0.788402	−	1.36555i	−0.926945	−	0.375196i	$-0.877575\pi$
$5$	−1.76292	−	3.05347i	−0.788402	−	1.36555i	0.138543	−	0.990356i	$-0.455758\pi$
$6$	1.91554	−	1.18309i	0.782016	−	0.482996i
$7$		0			0
$7$		0			0
$8$	−3.00314			−1.06177
$9$	1.34321	−	2.68250i	0.447737	−	0.894165i
$10$	−2.29157	−	3.96912i	−0.724659	−	1.25515i
$11$	−0.589267	+	1.02064i	−0.177671	+	0.307735i	−0.941082	−	0.338178i	$-0.890190\pi$
$11$	−0.589267	+	1.02064i	−0.177671	+	0.307735i	0.763412	+	0.645912i	$0.223523\pi$
$12$	−0.457317	+	0.282453i	−0.132016	+	0.0815371i
$13$	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
$16$	−3.28303			−0.820757
$17$	2.45159	+	4.24627i	0.594597	+	1.02987i	0.993604	+	0.112924i	$0.0360218\pi$
$17$	2.45159	+	4.24627i	0.594597	+	1.02987i	−0.399006	+	0.916948i	$0.630645\pi$
$18$	1.74600	−	3.48690i	0.411537	−	0.821871i
$19$	3.43318	−	5.94645i	0.787627	−	1.36421i	−0.139791	−	0.990181i	$-0.544643\pi$
$19$	3.43318	−	5.94645i	0.787627	−	1.36421i	0.927417	−	0.374028i	$-0.122024\pi$
$20$	0.547092	+	0.947591i	0.122333	+	0.211888i
$21$		0			0
$22$	−0.765972	+	1.32670i	−0.163306	+	0.282854i
$23$	2.14994	+	3.72380i	0.448293	+	0.776466i	0.998275	−	0.0587106i	$-0.0186989\pi$
$23$	2.14994	+	3.72380i	0.448293	+	0.776466i	−0.549982	+	0.835176i	$0.685366\pi$
$24$	−4.42553	+	2.73334i	−0.903358	+	0.557941i
$25$	−3.71578	+	6.43592i	−0.743156	+	1.28718i
$26$	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	$0.751980\pi$
$30$	−6.98948	−	3.76334i	−1.27610	−	0.687088i
$31$	−1.92080			−0.344986			−0.172493	−	0.985011i	$-0.555182\pi$
$31$	−1.92080			−0.344986			−0.172493	+	0.985011i	$0.555182\pi$
$32$	1.73876			0.307372
$33$	0.0605825	+	2.04038i	0.0105461	+	0.355185i
$34$	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	−0.115228	−	0.993339i	$-0.536760\pi$
$37$	4.88229	−	8.45637i	0.802643	−	1.39022i	0.917871	−	0.396879i	$-0.129907\pi$
$38$	4.46270	−	7.72962i	0.723946	−	1.25391i
$39$	−0.165555	−	5.57579i	−0.0265100	−	0.892842i
$40$	5.29429	+	9.16998i	0.837101	+	1.44990i
$41$	−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
$45$	−10.5589	+	0.627577i	−1.57403	+	0.0935537i
$46$	2.79464	+	4.84046i	0.412047	+	0.713687i
$47$	0.633218			0.0923644			0.0461822	−	0.998933i	$-0.485295\pi$
$47$	0.633218			0.0923644			0.0461822	+	0.998933i	$0.485295\pi$
$48$	−4.83799	+	2.98809i	−0.698304	+	0.431293i
$49$		0			0
$50$	−4.83004	+	8.36587i	−0.683071	+	1.18311i
$51$	7.47754	+	4.02612i	1.04707	+	0.563770i
$52$	−0.499729	+	0.865557i	−0.0693000	+	0.120031i
$53$	1.11378	+	1.92912i	0.152989	+	0.264985i	0.932325	−	0.361621i	$-0.117777\pi$
$53$	1.11378	+	1.92912i	0.152989	+	0.264985i	−0.779336	+	0.626606i	$0.784443\pi$
$54$	−0.600672	−	6.72757i	−0.0817412	−	0.915506i
$55$	4.15533			0.560304
$56$		0			0
$57$	−0.352965	−	11.8877i	−0.0467514	−	1.57456i
$58$	1.76965	+	3.06512i	0.232366	+	0.402471i
$59$	8.21304			1.06925			0.534623	−	0.845091i	$-0.320454\pi$
$59$	8.21304			1.06925			0.534623	+	0.845091i	$0.320454\pi$
$60$	1.66868	+	0.898462i	0.215425	+	0.115991i
$61$	−9.65916			−1.23673			−0.618364	−	0.785892i	$-0.712204\pi$
$61$	−9.65916			−1.23673			−0.618364	+	0.785892i	$0.712204\pi$
$62$	−2.49680			−0.317093
$63$		0			0
$64$	8.82622			1.10328
$65$	−11.3553			−1.40846
$66$	0.0787495	+	2.65224i	0.00969340	+	0.326468i
$67$	5.33301			0.651531			0.325766	−	0.945451i	$-0.394378\pi$
$67$	5.33301			0.651531			0.325766	+	0.945451i	$0.394378\pi$
$68$	−0.760807	−	1.31776i	−0.0922614	−	0.159801i
$69$	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	$0.562297\pi$
$72$	−4.03385	+	8.05590i	−0.475393	+	0.949397i
$73$	−0.519036	−	0.898997i	−0.0607486	−	0.105220i	0.834052	−	0.551686i	$-0.186015\pi$
$73$	−0.519036	−	0.898997i	−0.0607486	−	0.105220i	−0.894800	+	0.446467i	$0.852682\pi$
$74$	6.34635	−	10.9922i	0.737748	−	1.27782i
$75$	0.382019	+	12.8662i	0.0441118	+	1.48566i
$76$	−1.06543	+	1.84538i	−0.122213	+	0.211679i
$77$		0			0
$78$	−0.215200	−	7.24782i	−0.0243666	−	0.820654i
$79$	1.00408			0.112968			0.0564838	−	0.998404i	$-0.482011\pi$
$79$	1.00408			0.112968			0.0564838	+	0.998404i	$0.482011\pi$
$80$	5.78772	+	10.0246i	0.647087	+	1.12079i
$81$	−5.39157	−	7.20631i	−0.599063	−	0.800702i
$82$	−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
$86$	6.28411	+	10.8844i	0.677633	+	1.17369i
$87$	4.15239	+	2.23577i	0.445183	+	0.239699i
$88$	1.76965	−	3.06512i	0.188645	−	0.326743i
$89$	−6.02144	+	10.4294i	−0.638271	+	1.10552i	0.347541	+	0.937665i	$0.387017\pi$
$89$	−6.02144	+	10.4294i	−0.638271	+	1.10552i	−0.985812	+	0.167853i	$0.946317\pi$
$90$	−13.7252	+	0.815770i	−1.44676	+	0.0859897i
$91$		0			0
$92$	−0.667195	−	1.15562i	−0.0695599	−	0.120481i
$93$	−2.83056	+	1.74824i	−0.293516	+	0.181284i
$94$	0.823103			0.0848966
$95$	−24.2097			−2.48387
$96$	2.56230	−	1.58255i	0.261513	−	0.161518i
$97$	−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
$101$	0.797546	−	1.38139i	0.0793588	−	0.137453i	−0.823615	−	0.567150i	$-0.808046\pi$
$101$	0.797546	−	1.38139i	0.0793588	−	0.137453i	0.902973	+	0.429696i	$0.141379\pi$
$102$	9.71985	+	5.23344i	0.962409	+	0.518188i
$103$	−1.16778	−	2.02265i	−0.115065	−	0.199298i	0.802741	−	0.596328i	$-0.203374\pi$
$103$	−1.16778	−	2.02265i	−0.115065	−	0.199298i	−0.917806	+	0.397030i	$0.870041\pi$
$104$	−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	−0.807267	−	0.590186i	$-0.799054\pi$
$107$	1.11181	−	1.92571i	0.107483	−	0.186166i	0.914750	+	0.404021i	$0.132388\pi$
$108$	0.143405	+	1.60615i	0.0137992	+	0.154551i
$109$	0.459782	+	0.796366i	0.0440391	+	0.0762780i	0.887205	−	0.461376i	$-0.152644\pi$
$109$	0.459782	+	0.796366i	0.0440391	+	0.0762780i	−0.843166	+	0.537654i	$0.819311\pi$
$110$	5.40139			0.515003
$111$	−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	$0.130860\pi$
$114$	−0.458810	−	15.4524i	−0.0429715	−	1.44725i
$115$	7.58033	−	13.1295i	0.706870	−	1.22433i
$116$	−0.422488	−	0.731770i	−0.0392270	−	0.0679432i
$117$	−5.31884	−	8.06601i	−0.491727	−	0.745703i
$118$	10.6759			0.982796
$119$		0			0
$120$	16.1480	+	8.69456i	1.47411	+	0.793701i
$121$	4.80553	+	8.32342i	0.436866	+	0.756674i
$122$	−12.5557			−1.13674
$123$	0.342020	+	11.5190i	0.0308389	+	1.03864i
$124$	0.596087			0.0535302
$125$	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	$0.543089\pi$
$128$	7.99544			0.706704
$129$	14.7453	+	7.93931i	1.29826	+	0.699018i
$130$	−14.7605			−1.29458
$131$	1.63088	+	2.82476i	0.142490	+	0.246801i	0.928434	−	0.371498i	$-0.121156\pi$
$131$	1.63088	+	2.82476i	0.142490	+	0.246801i	−0.785943	+	0.618298i	$0.787822\pi$
$132$	−0.0188007	−	0.633197i	−0.00163639	−	0.0551127i
$133$		0			0
$134$	6.93223			0.598854
$135$	−14.9888	+	10.5351i	−1.29003	+	0.906719i
$136$	−7.36245	−	12.7521i	−0.631325	−	1.09349i
$137$	−10.4669	+	18.1292i	−0.894246	+	1.54888i	−0.0595120	+	0.998228i	$0.518954\pi$
$137$	−10.4669	+	18.1292i	−0.894246	+	1.54888i	−0.834734	+	0.550653i	$0.814379\pi$
$138$	8.52389	+	4.58951i	0.725602	+	0.390685i
$139$	−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
$142$	−4.25993			−0.357486
$143$	1.89780	+	3.28708i	0.158702	+	0.274880i
$144$	−4.40980	+	8.80671i	−0.367483	+	0.733893i
$145$	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
$149$	−0.564221	−	0.977260i	−0.0462228	−	0.0800602i	0.841988	−	0.539496i	$-0.181385\pi$
$149$	−0.564221	−	0.977260i	−0.0462228	−	0.0800602i	−0.888211	+	0.459435i	$0.848052\pi$
$150$	0.496576	+	16.7244i	0.0405452	+	1.36554i
$151$	9.81476	−	16.9997i	0.798714	−	1.38341i	−0.121740	−	0.992562i	$-0.538847\pi$
$151$	9.81476	−	16.9997i	0.798714	−	1.38341i	0.920454	−	0.390851i	$-0.127819\pi$
$152$	−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
$156$	0.0513771	+	1.73035i	0.00411346	+	0.138539i
$157$	9.33237			0.744804			0.372402	−	0.928071i	$-0.378534\pi$
$157$	9.33237			0.744804			0.372402	+	0.928071i	$0.378534\pi$
$158$	1.30517			0.103834
$159$	3.39712	+	1.82910i	0.269409	+	0.145057i
$160$	−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	0.318217	+	0.948018i	$0.396916\pi$
$163$	−8.45056	+	14.6368i	−0.661899	+	1.14644i	−0.980116	+	0.198425i	$0.936417\pi$
$164$	1.03239	−	1.78815i	0.0806162	−	0.139631i
$165$	6.12344	−	3.78202i	0.476709	−	0.294430i
$166$	−4.75230	−	8.23123i	−0.368850	−	0.638867i
$167$	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
$171$	−11.3398	−	17.1968i	−0.867179	−	1.31508i
$172$	−1.50027	−	2.59855i	−0.114395	−	0.198138i
$173$	9.73669			0.740266			0.370133	−	0.928979i	$-0.379312\pi$
$173$	9.73669			0.740266			0.370133	+	0.928979i	$0.379312\pi$
$174$	5.39758	+	2.90621i	0.409190	+	0.220319i
$175$		0			0
$176$	1.93458	−	3.35079i	0.145825	−	0.252576i
$177$	12.1030	−	7.47519i	0.909720	−	0.561870i
$178$	−7.82710	+	13.5569i	−0.586666	+	1.01613i
$179$	−0.687990	−	1.19163i	−0.0514228	−	0.0890668i	0.839168	−	0.543872i	$-0.183042\pi$
$179$	−0.687990	−	1.19163i	−0.0514228	−	0.0890668i	−0.890591	+	0.454805i	$0.849709\pi$
$180$	3.27677	−	0.194758i	0.244236	−	0.0145164i
$181$	−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
$184$	−6.45655	−	11.1831i	−0.475983	−	0.824427i
$185$	−34.4283			−2.53122
$186$	−3.67937	+	2.27249i	−0.269785	+	0.166627i
$187$	−5.77856			−0.422570
$188$	−0.196508			−0.0143318
$189$		0			0
$190$	−31.4696			−2.28304
$191$	−25.0129			−1.80987			−0.904936	−	0.425547i	$-0.860082\pi$
$191$	−25.0129			−1.80987			−0.904936	+	0.425547i	$0.860082\pi$
$192$	13.0066	−	8.03329i	0.938673	−	0.579753i
$193$	17.5338			1.26211			0.631054	−	0.775739i	$-0.282623\pi$
$193$	17.5338			1.26211			0.631054	+	0.775739i	$0.282623\pi$
$194$	−7.10321	−	12.3031i	−0.509981	−	0.883312i
$195$	−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	$0.748473\pi$
$198$	2.53001	+	3.83676i	0.179800	+	0.272667i
$199$	9.51110	+	16.4737i	0.674224	+	1.16779i	0.976695	+	0.214631i	$0.0688550\pi$
$199$	9.51110	+	16.4737i	0.674224	+	1.16779i	−0.302471	+	0.953158i	$0.597812\pi$
$200$	11.1590	−	19.3279i	0.789060	−	1.36669i
$201$	7.85892	−	4.85390i	0.554326	−	0.342368i
$202$	1.03671	−	1.79563i	0.0729425	−	0.126340i
$203$		0			0
$204$	−2.32053	−	1.24944i	−0.162469	−	0.0874781i
$205$	23.4590			1.63845
$206$	−1.51796	−	2.62919i	−0.105761	−	0.183184i
$207$	12.8769	−	0.765349i	0.895006	−	0.0531955i
$208$	−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	$0.0842738\pi$
$212$	−0.345642	−	0.598669i	−0.0237388	−	0.0411168i
$213$	−4.82939	+	2.98278i	−0.330904	+	0.204376i
$214$	1.44521	−	2.50318i	0.0987927	−	0.171114i
$215$	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
$219$	−1.58310	−	0.852388i	−0.106976	−	0.0575990i
$220$	−1.28953			−0.0869403
$221$	15.7912			1.06223
$222$	−0.652467	−	21.9747i	−0.0437907	−	1.47485i
$223$	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
$227$	9.00847	−	15.6031i	0.597913	−	1.03562i	−0.395215	−	0.918589i	$-0.629330\pi$
$227$	9.00847	−	15.6031i	0.597913	−	1.03562i	0.993129	−	0.117028i	$-0.0373366\pi$
$228$	0.109537	+	3.68913i	0.00725424	+	0.244318i
$229$	−2.12746	−	3.68486i	−0.140586	−	0.243503i	0.787131	−	0.616785i	$-0.211565\pi$
$229$	−2.12746	−	3.68486i	−0.140586	−	0.243503i	−0.927718	+	0.373283i	$0.878232\pi$
$230$	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	−0.518084	−	0.855330i	$-0.673355\pi$
$233$	7.35275	−	12.7353i	0.481695	−	0.834320i	0.999779	+	0.0210095i	$0.00668801\pi$
$234$	−6.91382	−	10.4848i	−0.451970	−	0.685412i
$235$	−1.11631	−	1.93351i	−0.0728203	−	0.126128i
$236$	−2.54877			−0.165911
$237$	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	$0.0152011\pi$
$240$	17.6530	+	9.50489i	1.13950	+	0.613538i
$241$	−3.96752	+	6.87194i	−0.255570	+	0.442661i	−0.965050	−	0.262065i	$-0.915597\pi$
$241$	−3.96752	+	6.87194i	−0.255570	+	0.442661i	0.709480	+	0.704726i	$0.248930\pi$
$242$	6.24657	+	10.8194i	0.401545	+	0.695496i
$243$	−14.5041	−	5.71229i	−0.930440	−	0.366443i
$244$	2.99755			0.191899
$245$		0			0
$246$	0.444583	+	14.9733i	0.0283456	+	0.954662i
$247$	−11.0569	−	19.1512i	−0.703536	−	1.21856i
$248$	5.76843			0.366296
$249$	−11.1510	−	6.00403i	−0.706668	−	0.380490i
$250$	11.1442			0.704821
$251$	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
$254$	−3.95382			−0.248085
$255$	−0.888679	−	29.9302i	−0.0556513	−	1.87430i
$256$	−7.25938			−0.453712
$257$	8.77687	+	15.2020i	0.547486	+	0.948273i	0.998446	+	0.0557293i	$0.0177484\pi$
$257$	8.77687	+	15.2020i	0.547486	+	0.948273i	−0.450960	+	0.892544i	$0.648918\pi$
$258$	19.1671	+	10.3201i	1.19329	+	0.642501i
$259$		0			0
$260$	3.52393			0.218545
$261$	8.15403	−	0.484642i	0.504722	−	0.0299986i
$262$	2.11993	+	3.67183i	0.130970	+	0.226846i
$263$	11.6743	−	20.2205i	0.719867	−	1.24685i	−0.241185	−	0.970479i	$-0.577536\pi$
$263$	11.6743	−	20.2205i	0.719867	−	1.24685i	0.961052	−	0.276367i	$-0.0891306\pi$
$264$	−0.181938	−	6.12755i	−0.0111975	−	0.377125i
$265$	3.92701	−	6.80177i	0.241234	−	0.417830i
$266$		0			0
$267$	0.619063	+	20.8497i	0.0378861	+	1.27598i
$268$	−1.65501			−0.101096
$269$	−0.269244	−	0.466344i	−0.0164161	−	0.0284335i	0.857701	−	0.514149i	$-0.171892\pi$
$269$	−0.269244	−	0.466344i	−0.0164161	−	0.0284335i	−0.874117	+	0.485716i	$0.838559\pi$
$270$	−19.4835	+	13.6943i	−1.18573	+	0.833409i
$271$	7.20749	−	12.4837i	0.437824	−	0.758334i	−0.559697	−	0.828697i	$-0.689083\pi$
$271$	7.20749	−	12.4837i	0.437824	−	0.758334i	0.997521	+	0.0703635i	$0.0224159\pi$
$272$	−8.04863	−	13.9406i	−0.488020	−	0.845275i
$273$		0			0
$274$	−13.6056	+	23.5656i	−0.821945	+	1.42365i
$275$	−4.37918	−	7.58495i	−0.264074	−	0.457390i
$276$	−2.03500	−	1.09570i	−0.122493	−	0.0659535i
$277$	−10.9533	+	18.9717i	−0.658121	+	1.13990i	0.322980	+	0.946406i	$0.395315\pi$
$277$	−10.9533	+	18.9717i	−0.658121	+	1.13990i	−0.981101	+	0.193494i	$0.938018\pi$
$278$	−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	$0.848086\pi$
$282$	1.21295	−	0.749157i	0.0722304	−	0.0446116i
$283$	−2.65142			−0.157610			−0.0788051	−	0.996890i	$-0.525110\pi$
$283$	−2.65142			−0.157610			−0.0788051	+	0.996890i	$0.525110\pi$
$284$	1.01702			0.0603490
$285$	−35.6763	+	22.0348i	−2.11328	+	1.30523i
$286$	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
$290$	6.23951	−	10.8071i	0.366396	−	0.634617i
$291$	−16.6673	−	8.97416i	−0.977055	−	0.526074i
$292$	0.161074	+	0.278988i	0.00942613	+	0.0163265i
$293$	−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
$297$	5.55469	+	2.57815i	0.322316	+	0.149600i
$298$	−0.733415	−	1.27031i	−0.0424856	−	0.0735872i
$299$	13.8482			0.800861
$300$	−0.118553	−	3.99279i	−0.00684466	−	0.230524i
$301$		0			0
$302$	12.7579	−	22.0974i	0.734137	−	1.27156i
$303$	−0.0819956	−	2.76156i	−0.00471053	−	0.158648i
$304$	−11.2712	+	19.5224i	−0.646450	+	1.11968i
$305$	17.0283	+	29.4939i	0.975039	+	1.68882i
$306$	19.0868	−	1.13444i	1.09112	−	0.0648517i
$307$	−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
$310$	4.40165	+	7.62389i	0.249997	+	0.433008i
$311$	−13.7096			−0.777399			−0.388699	−	0.921365i	$-0.627075\pi$
$311$	−13.7096			−0.777399			−0.388699	+	0.921365i	$0.627075\pi$
$312$	0.497184	+	16.7449i	0.0281475	+	0.947992i
$313$	21.2179			1.19931			0.599653	−	0.800260i	$-0.295305\pi$
$313$	21.2179			1.19931			0.599653	+	0.800260i	$0.295305\pi$
$314$	12.1309			0.684586
$315$		0			0
$316$	−0.311598			−0.0175288
$317$	3.57043			0.200535			0.100268	−	0.994961i	$-0.468030\pi$
$317$	3.57043			0.200535			0.100268	+	0.994961i	$0.468030\pi$
$318$	4.41582	+	2.37760i	0.247627	+	0.133329i
$319$	−3.20892			−0.179665
$320$	−15.5599	−	26.9506i	−0.869826	−	1.50658i
$321$	−0.114305	−	3.84973i	−0.00637989	−	0.214871i
$322$		0			0
$323$	33.6670			1.87328
$324$	1.67318	+	2.23635i	0.0929544	+	0.124242i
$325$	11.9671	+	20.7276i	0.663813	+	1.14976i
$326$	−10.9846	+	19.0260i	−0.608383	+	1.05375i
$327$	1.40237	+	0.755078i	0.0775514	+	0.0417559i
$328$	9.99062	−	17.3043i	0.551639	−	0.955468i
$329$		0			0
$330$	7.95969	−	4.91614i	0.438167	−	0.270625i
$331$	−23.9456			−1.31617			−0.658085	−	0.752944i	$-0.728633\pi$
$331$	−23.9456			−1.31617			−0.658085	+	0.752944i	$0.728633\pi$
$332$	1.13457	+	1.96513i	0.0622675	+	0.107851i
$333$	−16.1262	−	24.4554i	−0.883712	−	1.34015i
$334$	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	$0.897279\pi$
$338$	1.70784	+	2.95806i	0.0928942	+	0.160897i
$339$	−0.122680	−	4.13180i	−0.00666309	−	0.224409i
$340$	−2.68249	+	4.64620i	−0.145478	+	0.251976i
$341$	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
$345$	−0.779333	−	26.2475i	−0.0419579	−	1.41312i
$346$	12.6564			0.680415
$347$	−5.12824			−0.275299			−0.137649	−	0.990481i	$-0.543955\pi$
$347$	−5.12824			−0.275299			−0.137649	+	0.990481i	$0.543955\pi$
$348$	−1.28862	−	0.693831i	−0.0690774	−	0.0371933i
$349$	−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
$353$	−16.4878	+	28.5578i	−0.877559	+	1.51998i	−0.0235477	+	0.999723i	$0.507496\pi$
$353$	−16.4878	+	28.5578i	−0.877559	+	1.51998i	−0.854011	+	0.520254i	$0.825837\pi$
$354$	15.7324	−	9.71680i	0.836168	−	0.516442i
$355$	5.77743	+	10.0068i	0.306634	+	0.531106i
$356$	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	−0.352395	−	0.935851i	$-0.614633\pi$
$359$	12.0178	−	20.8154i	0.634274	−	1.09859i	0.986669	−	0.162743i	$-0.0520341\pi$
$360$	31.7098	−	1.88470i	1.67125	−	0.0993324i
$361$	−14.0735	−	24.3760i	−0.740711	−	1.28295i
$362$	−7.36455			−0.387072
$363$	14.6573	+	7.89189i	0.769307	+	0.414217i
$364$		0			0
$365$	−1.83004	+	3.16972i	−0.0957886	+	0.165911i
$366$	−18.5025	+	11.4277i	−0.967141	+	0.597335i
$367$	1.32751	−	2.29931i	0.0692952	−	0.120023i	−0.829296	−	0.558810i	$-0.811258\pi$
$367$	1.32751	−	2.29931i	0.0692952	−	0.120023i	0.898591	+	0.438787i	$0.144592\pi$
$368$	−7.05830	−	12.2253i	−0.367939	−	0.637290i
$369$	10.9882	+	16.6636i	0.572023	+	0.867472i
$370$	−44.7524			−2.32657
$371$		0			0
$372$	0.878416	−	0.542536i	0.0455438	−	0.0281292i
$373$	15.9592	+	27.6421i	0.826334	+	1.43125i	0.900896	+	0.434036i	$0.142911\pi$
$373$	15.9592	+	27.6421i	0.826334	+	1.43125i	−0.0745621	+	0.997216i	$0.523756\pi$
$374$	−7.51139			−0.388405
$375$	12.6339	−	7.80309i	0.652413	−	0.402950i
$376$	−1.90164			−0.0980697
$377$	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	$0.216546\pi$
$380$	7.51307			0.385412
$381$	−4.48236	+	2.76844i	−0.229638	+	0.141831i
$382$	−32.5136			−1.66354
$383$	−0.866526	−	1.50087i	−0.0442774	−	0.0766907i	0.843037	−	0.537855i	$-0.180765\pi$
$383$	−0.866526	−	1.50087i	−0.0442774	−	0.0766907i	−0.887315	+	0.461164i	$0.847432\pi$
$384$	11.7824	−	7.27715i	0.601267	−	0.371360i
$385$		0			0
$386$	22.7917			1.16006
$387$	28.9553	−	1.72099i	1.47188	−	0.0874826i
$388$	1.69583	+	2.93726i	0.0860925	+	0.149117i
$389$	5.54175	−	9.59859i	0.280978	−	0.486668i	−0.690648	−	0.723191i	$-0.742675\pi$
$389$	5.54175	−	9.59859i	0.280978	−	0.486668i	0.971626	+	0.236523i	$0.0760079\pi$
$390$	−21.7516	+	13.4344i	−1.10144	+	0.680279i
$391$	−10.5415	+	18.2584i	−0.533107	+	0.923368i
$392$		0			0
$393$	4.97431	+	2.67831i	0.250921	+	0.135103i
$394$	−25.6777			−1.29362
$395$	−1.77011	−	3.06592i	−0.0890639	−	0.154263i
$396$	−0.604017	−	0.915991i	−0.0303530	−	0.0460303i
$397$	−12.6696	+	21.9443i	−0.635867	+	1.10135i	0.350464	+	0.936576i	$0.386024\pi$
$397$	−12.6696	+	21.9443i	−0.635867	+	1.10135i	−0.986331	+	0.164777i	$0.947310\pi$
$398$	12.3632	+	21.4137i	0.619712	+	1.07337i
$399$		0			0
$400$	12.1990	−	21.1293i	0.609951	−	1.05647i
$401$	17.4122	+	30.1588i	0.869524	+	1.50606i	0.862483	+	0.506085i	$0.168908\pi$
$401$	17.4122	+	30.1588i	0.869524	+	1.50606i	0.00704089	+	0.999975i	$0.497759\pi$
$402$	10.2156	−	6.30945i	0.509507	−	0.314687i
$403$	−3.09307	+	5.35736i	−0.154077	+	0.266869i
$404$	−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
$408$	−22.4561	−	12.0910i	−1.11174	−	0.598594i
$409$	−18.2462			−0.902215			−0.451107	−	0.892470i	$-0.648971\pi$
$409$	−18.2462			−0.902215			−0.451107	+	0.892470i	$0.648971\pi$
$410$	30.4937			1.50598
$411$	1.07610	+	36.2424i	0.0530801	+	1.78771i
$412$	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
$416$	2.79992	−	4.84961i	0.137278	−	0.237772i
$417$	0.854551	+	28.7808i	0.0418475	+	1.40940i
$418$	5.25945	+	9.10963i	0.257248	+	0.445567i
$419$	−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
$423$	0.850546	−	1.69861i	0.0413549	−	0.0825890i
$424$	−3.34483	−	5.79341i	−0.162439	−	0.281353i
$425$	−36.4382			−1.76751
$426$	−6.27759	+	3.87723i	−0.304150	+	0.187852i
$427$		0			0
$428$	−0.345031	+	0.597612i	−0.0166777	+	0.0288866i
$429$	5.78844	+	3.11666i	0.279469	+	0.150474i
$430$	22.1568	−	38.3767i	1.06849	−	1.85069i
$431$	6.74795	+	11.6878i	0.325037	+	0.562981i	0.981520	−	0.191360i	$-0.0612898\pi$
$431$	6.74795	+	11.6878i	0.325037	+	0.562981i	−0.656482	+	0.754341i	$0.727956\pi$
$432$	1.51709	+	16.9915i	0.0729911	+	0.817505i
$433$	−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
$436$	−0.142685	−	0.247138i	−0.00683339	−	0.0118358i
$437$	29.5245			1.41235
$438$	−2.05783	−	1.10800i	−0.0983270	−	0.0529421i
$439$	2.54793			0.121606			0.0608031	−	0.998150i	$-0.480634\pi$
$439$	2.54793			0.121606			0.0608031	+	0.998150i	$0.480634\pi$
$440$	−12.4790			−0.594914
$441$		0			0
$442$	20.5265			0.976347
$443$	−0.645506			−0.0306689			−0.0153345	−	0.999882i	$-0.504881\pi$
$443$	−0.645506			−0.0306689			−0.0153345	+	0.999882i	$0.504881\pi$
$444$	0.155771	+	5.24626i	0.00739255	+	0.248976i
$445$	42.4613			2.01286
$446$	2.13913	+	3.70508i	0.101291	+	0.175441i
$447$	−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	$0.539357\pi$
$450$	15.9537	+	24.1937i	0.752063	+	1.14050i
$451$	−3.92066	−	6.79079i	−0.184617	−	0.319766i
$452$	−0.370312	+	0.641399i	−0.0174180	+	0.0301689i
$453$	−1.00905	−	33.9844i	−0.0474095	−	1.59672i
$454$	11.7099	−	20.2821i	0.549571	−	0.951885i
$455$		0			0
$456$	1.06000	+	35.7003i	0.0496392	+	1.67182i
$457$	−2.86075			−0.133820			−0.0669101	−	0.997759i	$-0.521314\pi$
$457$	−2.86075			−0.133820			−0.0669101	+	0.997759i	$0.521314\pi$
$458$	−2.76542	−	4.78985i	−0.129220	−	0.223815i
$459$	20.8440	−	14.6506i	0.972913	−	0.683829i
$460$	−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	$0.912666\pi$
$464$	−4.46953	−	7.74145i	−0.207493	−	0.359388i
$465$	10.3283	+	5.56103i	0.478962	+	0.257887i
$466$	9.55764	−	16.5543i	0.442749	−	0.766864i
$467$	−10.2885	+	17.8202i	−0.476096	+	0.824622i	−0.999625	−	0.0273858i	$-0.991282\pi$
$467$	−10.2885	+	17.8202i	−0.476096	+	0.824622i	0.523529	+	0.852008i	$0.324615\pi$
$468$	1.65061	+	2.50315i	0.0762995	+	0.115708i
$469$		0			0
$470$	−1.45107	−	2.51332i	−0.0669327	−	0.115931i
$471$	13.7525	−	8.49397i	0.633683	−	0.391381i
$472$	−24.6649			−1.13529
$473$	−11.3950			−0.523944
$474$	1.92335	−	1.18792i	0.0883424	−	0.0545629i
$475$	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
$479$	−12.5916	+	21.8093i	−0.575325	+	0.996492i	0.420682	+	0.907208i	$0.361791\pi$
$479$	−12.5916	+	21.8093i	−0.575325	+	0.996492i	−0.996006	+	0.0892833i	$0.971542\pi$
$480$	−9.34939	−	5.03398i	−0.426739	−	0.229769i
$481$	−15.7239	−	27.2346i	−0.716949	−	1.24179i
$482$	−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
$486$	−18.8535	−	7.42524i	−0.855213	−	0.336816i
$487$	16.3807	+	28.3723i	0.742282	+	1.28567i	0.951454	+	0.307791i	$0.0995896\pi$
$487$	16.3807	+	28.3723i	0.742282	+	1.28567i	−0.209173	+	0.977879i	$0.567077\pi$
$488$	29.0078			1.31312
$489$	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	$0.141357\pi$
$492$	−0.106140	−	3.57473i	−0.00478516	−	0.161161i
$493$	−6.67520	+	11.5618i	−0.300636	+	0.520716i
$494$	−14.3726	−	24.8941i	−0.646654	−	1.12004i
$495$	5.58148	−	11.1466i	0.250869	−	0.501005i
$496$	6.30605			0.283150
$497$		0			0
$498$	−14.4949	−	7.80448i	−0.649533	−	0.349727i
$499$	−7.82082	−	13.5461i	−0.350108	−	0.606405i	0.636160	−	0.771557i	$-0.280522\pi$
$499$	−7.82082	−	13.5461i	−0.350108	−	0.606405i	−0.986268	+	0.165152i	$0.947188\pi$
$500$	−2.66057			−0.118984
$501$	−0.264549	−	8.90986i	−0.0118192	−	0.398063i
$502$	10.4652			0.467086
$503$	−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
$506$	−6.58716			−0.292835
$507$	4.00736	+	2.15768i	0.177973	+	0.0958257i
$508$	0.943938			0.0418805
$509$	18.8229	+	32.6023i	0.834311	+	1.44507i	0.894590	+	0.446888i	$0.147468\pi$
$509$	18.8229	+	32.6023i	0.834311	+	1.44507i	−0.0602789	+	0.998182i	$0.519199\pi$
$510$	−1.15517	−	38.9054i	−0.0511518	−	1.72276i
$511$		0			0
$512$	−25.4272			−1.12373
$513$	−32.3627	−	15.0208i	−1.42885	−	0.663185i
$514$	11.4088	+	19.7606i	0.503221	+	0.871604i
$515$	−4.11740	+	7.13155i	−0.181434	+	0.314254i
$516$	−4.57596	−	2.46383i	−0.201445	−	0.108464i
$517$	−0.373135	+	0.646289i	−0.0164105	+	0.0284237i
$518$		0			0
$519$	14.3483	−	8.86196i	0.629822	−	0.388997i
$520$	34.1017			1.49546
$521$	7.17115	+	12.4208i	0.314174	+	0.544165i	0.979262	−	0.202600i	$-0.0649392\pi$
$521$	7.17115	+	12.4208i	0.314174	+	0.544165i	−0.665088	+	0.746765i	$0.731606\pi$
$522$	10.5992	−	0.629973i	0.463914	−	0.0275732i
$523$	−5.24222	+	9.07980i	−0.229226	+	0.397032i	−0.957579	−	0.288171i	$-0.906953\pi$
$523$	−5.24222	+	9.07980i	−0.229226	+	0.397032i	0.728353	+	0.685202i	$0.240286\pi$
$524$	−0.506114	−	0.876616i	−0.0221097	−	0.0382951i
$525$		0			0
$526$	15.1751	−	26.2840i	0.661665	−	1.14604i
$527$	−4.70901	−	8.15625i	−0.205128	−	0.355292i
$528$	−0.198894	−	6.69863i	−0.00865576	−	0.291521i
$529$	2.25555	−	3.90673i	0.0980674	−	0.169858i
$530$	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
$534$	0.804703	+	27.1019i	0.0348229	+	1.17281i
$535$	−7.84014			−0.338959
$536$	−16.0158			−0.691776
$537$	−2.09843	−	1.12985i	−0.0905538	−	0.0487567i
$538$	−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	0.378399	−	0.925643i	$-0.376475\pi$
$541$	23.0461	−	39.9170i	0.990830	−	1.71617i	0.612430	−	0.790524i	$-0.290192\pi$
$542$	9.36882	−	16.2273i	0.402425	−	0.697021i
$543$	−8.34903	+	5.15661i	−0.358291	+	0.221291i
$544$	4.26271	+	7.38323i	0.182762	+	0.316554i
$545$	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
$549$	−12.9743	+	25.9107i	−0.553729	+	1.10584i
$550$	−5.69237	−	9.85947i	−0.242723	−	0.420409i
$551$	18.6958			0.796468
$552$	−19.6930	−	10.6033i	−0.838191	−	0.451306i
$553$		0			0
$554$	−14.2379	+	24.6608i	−0.604911	+	1.04774i
$555$	−50.7349	+	31.3354i	−2.15357	+	1.33011i
$556$	2.57947	−	4.46777i	0.109394	−	0.189476i
$557$	−15.2888	−	26.4809i	−0.647806	−	1.12203i	−0.983646	−	0.180114i	$-0.942353\pi$
$557$	−15.2888	−	26.4809i	−0.647806	−	1.12203i	0.335840	−	0.941919i	$-0.390980\pi$
$558$	−3.35372	+	6.69765i	−0.141974	+	0.283534i
$559$	31.1394			1.31706
$560$		0			0
$561$	−8.51550	+	5.25943i	−0.359525	+	0.222053i
$562$	−1.00951	−	1.74852i	−0.0425836	−	0.0737570i
$563$	8.82714			0.372019			0.186010	−	0.982548i	$-0.440444\pi$
$563$	8.82714			0.372019			0.186010	+	0.982548i	$0.440444\pi$
$564$	−0.289582	+	0.178854i	−0.0121936	+	0.00753113i
$565$	−8.41459			−0.354005
$566$	−3.44650			−0.144867
$567$		0			0
$568$	9.84186			0.412955
$569$	7.12055			0.298509			0.149254	−	0.988799i	$-0.452313\pi$
$569$	7.12055			0.298509			0.149254	+	0.988799i	$0.452313\pi$
$570$	−46.3747	+	28.6424i	−1.94242	+	1.19970i
$571$	6.66361			0.278863			0.139432	−	0.990232i	$-0.455472\pi$
$571$	6.66361			0.278863			0.139432	+	0.990232i	$0.455472\pi$
$572$	−0.588948	−	1.02009i	−0.0246252	−	0.0426520i
$573$	−36.8600	+	22.7658i	−1.53985	+	0.951056i
$574$		0			0
$575$	−31.9548			−1.33261
$576$	11.8555	−	23.6763i	0.493978	−	0.986512i
$577$	−3.95629	−	6.85250i	−0.164703	−	0.285273i	0.771847	−	0.635808i	$-0.219333\pi$
$577$	−3.95629	−	6.85250i	−0.164703	−	0.285273i	−0.936550	+	0.350535i	$0.886000\pi$
$578$	−4.57627	+	7.92633i	−0.190348	+	0.329692i
$579$	25.8384	−	15.9586i	1.07381	−	0.663215i
$580$	−1.48963	+	2.58011i	−0.0618533	+	0.107133i
$581$		0			0
$582$	−21.6654	−	11.6653i	−0.898059	−	0.483540i
$583$	−2.62525			−0.108727
$584$	1.55874	+	2.69981i	0.0645010	+	0.111719i
$585$	−15.2526	+	30.4607i	−0.630618	+	1.25939i
$586$	−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
$590$	−18.8208	−	32.5985i	−0.774839	−	1.34206i
$591$	−29.1102	+	17.9793i	−1.19743	+	0.739571i
$592$	−16.0287	+	27.7625i	−0.658775	+	1.14103i
$593$	14.1908	−	24.5792i	0.582745	−	1.00934i	−0.412407	−	0.911000i	$-0.635312\pi$
$593$	14.1908	−	24.5792i	0.582745	−	1.00934i	0.995152	−	0.0983450i	$-0.0313549\pi$
$594$	7.22039	+	3.35127i	0.296256	+	0.137504i
$595$		0			0
$596$	0.175096	+	0.303275i	0.00717222	+	0.0124226i
$597$	29.0096	+	15.6196i	1.18729	+	0.639268i
$598$	18.0009			0.736111
$599$	9.38902			0.383625			0.191813	−	0.981432i	$-0.438563\pi$
$599$	9.38902			0.383625			0.191813	+	0.981432i	$0.438563\pi$
$600$	−1.14726	−	38.6389i	−0.0468365	−	1.57743i
$601$	−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
$605$	16.9435	−	29.3471i	0.688853	−	1.19313i
$606$	−0.106584	−	3.58968i	−0.00432967	−	0.145821i
$607$	−12.0133	−	20.8076i	−0.487604	−	0.844554i	0.512295	−	0.858810i	$-0.328796\pi$
$607$	−12.0133	−	20.8076i	−0.487604	−	0.844554i	−0.999898	+	0.0142555i	$0.995462\pi$
$608$	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
$612$	−4.55680	+	0.270837i	−0.184198	+	0.0109480i
$613$	14.2708	+	24.7177i	0.576390	+	0.998337i	0.995889	+	0.0905814i	$0.0288725\pi$
$613$	14.2708	+	24.7177i	0.576390	+	0.998337i	−0.419499	+	0.907756i	$0.637794\pi$
$614$	−13.8339			−0.558291
$615$	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	$0.245056\pi$
$618$	−4.62991	−	2.49288i	−0.186242	−	0.100278i
$619$	13.2870	−	23.0137i	0.534048	−	0.924998i	−0.465161	−	0.885226i	$-0.654003\pi$
$619$	13.2870	−	23.0137i	0.534048	−	0.924998i	0.999209	−	0.0397721i	$-0.0126632\pi$
$620$	−1.05085	−	1.82013i	−0.0422033	−	0.0730983i
$621$	18.2793	−	12.8479i	0.733522	−	0.515569i
$622$	−17.8207			−0.714545
$623$		0			0
$624$	0.543522	+	18.3055i	0.0217583	+	0.732806i
$625$	3.46486	+	6.00131i	0.138594	+	0.240052i
$626$	27.5806			1.10234
$627$	12.3410	+	6.64476i	0.492853	+	0.265366i
$628$	−2.89614			−0.115569
$629$	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	$0.479015\pi$
$632$	−3.01538			−0.119945
$633$	−0.382257	−	12.8742i	−0.0151933	−	0.511703i
$634$	4.64110			0.184322
$635$	5.36227	+	9.28773i	0.212795	+	0.368572i
$636$	−1.05424	−	0.567631i	−0.0418032	−	0.0225080i
$637$		0			0
$638$	−4.17119			−0.165139
$639$	−4.40196	+	8.79106i	−0.174139	+	0.347769i
$640$	−14.0953	−	24.4138i	−0.557167	−	0.965041i
$641$	−16.2922	+	28.2189i	−0.643503	+	1.11458i	0.341142	+	0.940012i	$0.389186\pi$
$641$	−16.2922	+	28.2189i	−0.643503	+	1.11458i	−0.984645	+	0.174568i	$0.944147\pi$
$642$	−0.148582	−	5.00416i	−0.00586407	−	0.197498i
$643$	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
$646$	43.7628			1.72182
$647$	−23.0988	−	40.0082i	−0.908106	−	1.57289i	−0.816692	−	0.577074i	$-0.804195\pi$
$647$	−23.0988	−	40.0082i	−0.908106	−	1.57289i	−0.0914143	−	0.995813i	$-0.529139\pi$
$648$	16.1916	+	21.6415i	0.636067	+	0.850160i
$649$	−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
$653$	−16.0002	−	27.7132i	−0.626138	−	1.08450i	−0.988320	−	0.152395i	$-0.951301\pi$
$653$	−16.0002	−	27.7132i	−0.626138	−	1.08450i	0.362182	−	0.932107i	$-0.382032\pi$
$654$	1.82291	+	0.981504i	0.0712812	+	0.0383799i
$655$	5.75022	−	9.95967i	0.224680	−	0.389156i
$656$	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	$0.564253\pi$
$660$	−1.90030	+	1.17368i	−0.0739692	+	0.0456856i
$661$	28.0260			1.09009			0.545043	−	0.838408i	$-0.316513\pi$
$661$	28.0260			1.09009			0.545043	+	0.838408i	$0.316513\pi$
$662$	−31.1262			−1.20976
$663$	23.2705	−	14.3725i	0.903750	−	0.558183i
$664$	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
$668$	−0.798544	+	1.38312i	−0.0308966	+	0.0535145i
$669$	5.01936	+	2.70256i	0.194060	+	0.104487i
$670$	−12.2210	−	21.1674i	−0.472138	−	0.817766i
$671$	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
$675$	35.0266	+	16.2572i	1.34817	+	0.625740i
$676$	−0.407731	−	0.706211i	−0.0156820	−	0.0271619i
$677$	−42.0334			−1.61547			−0.807737	−	0.589543i	$-0.799308\pi$
$677$	−42.0334			−1.61547			−0.807737	+	0.589543i	$0.799308\pi$
$678$	−0.159469	−	5.37082i	−0.00612437	−	0.206265i
$679$		0			0
$680$	−25.9588	+	44.9620i	−0.995476	+	1.72421i
$681$	−0.926160	−	31.1925i	−0.0354905	−	1.19530i
$682$	1.47128	−	2.54833i	0.0563382	−	0.0975807i
$683$	−17.8645	−	30.9422i	−0.683565	−	1.18397i	−0.973886	−	0.227039i	$-0.927095\pi$
$683$	−17.8645	−	30.9422i	−0.683565	−	1.18397i	0.290321	−	0.956929i	$-0.406238\pi$
$684$	3.51912	+	5.33674i	0.134557	+	0.204055i
$685$	73.8092			2.82010
$686$		0			0
$687$	−6.48892	−	3.49382i	−0.247568	−	0.133298i
$688$	−15.8715	−	27.4902i	−0.605095	−	1.04806i
$689$	7.17408			0.273311
$690$	−1.01303	−	34.1184i	−0.0385655	−	1.29886i
$691$	−51.1349			−1.94526			−0.972632	−	0.232351i	$-0.925358\pi$
$691$	−51.1349			−1.94526			−0.972632	+	0.232351i	$0.925358\pi$
$692$	−3.02161			−0.114864
$693$		0			0
$694$	−6.66606			−0.253040
$695$	58.6132			2.22333
$696$	−12.4702	−	6.71432i	−0.472682	−	0.254505i
$697$	−32.6230			−1.23569
$698$	−9.83977	−	17.0430i	−0.372441	−	0.645086i
$699$	−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	$0.653627\pi$
$702$	−19.7313	−	9.15807i	−0.744710	−	0.345649i
$703$	−33.5236	−	58.0645i	−1.26437	−	2.18995i
$704$	−5.20100	+	9.00840i	−0.196020	+	0.339517i
$705$	−3.40485	−	1.83327i	−0.128234	−	0.0690449i
$706$	−21.4321	+	37.1215i	−0.806607	+	1.39708i
$707$		0			0
$708$	−3.75597	+	2.31980i	−0.141158	+	0.0871833i
$709$	30.8976			1.16038			0.580192	−	0.814480i	$-0.302978\pi$
$709$	30.8976			1.16038			0.580192	+	0.814480i	$0.302978\pi$
$710$	7.50992	+	13.0076i	0.281842	+	0.488165i
$711$	1.34869	−	2.69343i	0.0505797	−	0.101012i
$712$	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
$716$	0.213506	+	0.369803i	0.00797908	+	0.0138202i
$717$	−0.728086	−	24.5215i	−0.0271909	−	0.915772i
$718$	15.6216	−	27.0573i	0.582992	−	1.00977i
$719$	3.05690	−	5.29471i	0.114003	−	0.197459i	−0.803378	−	0.595470i	$-0.796966\pi$
$719$	3.05690	−	5.29471i	0.114003	−	0.197459i	0.917381	+	0.398011i	$0.130299\pi$
$720$	34.6651	−	2.06035i	1.29189	−	0.0767848i
$721$		0			0
$722$	−18.2938	−	31.6857i	−0.680823	−	1.17922i
$723$	0.407900	+	13.7378i	0.0151700	+	0.510915i
$724$	1.75822			0.0653437
$725$	−20.2347			−0.751498
$726$	19.0526	+	10.2584i	0.707107	+	0.380727i
$727$	−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
$731$	−23.7039	+	41.0564i	−0.876722	+	1.51853i
$732$	4.41730	−	2.72826i	0.163268	−	0.100839i
$733$	4.91854	+	8.51916i	0.181670	+	0.314662i	0.942449	−	0.334349i	$-0.108516\pi$
$733$	4.91854	+	8.51916i	0.181670	+	0.314662i	−0.760779	+	0.649011i	$0.775183\pi$
$734$	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
$738$	14.2833	+	21.6605i	0.525774	+	0.797335i
$739$	−7.42464	−	12.8598i	−0.273120	−	0.473057i	0.696539	−	0.717519i	$-0.254722\pi$
$739$	−7.42464	−	12.8598i	−0.273120	−	0.473057i	−0.969659	+	0.244461i	$0.921389\pi$
$740$	10.6842			0.392760
$741$	−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	$0.202264\pi$
$744$	8.50057	−	5.25021i	0.311646	−	0.192482i
$745$	−1.98935	+	3.44566i	−0.0728843	+	0.126239i
$746$	20.7449	+	35.9311i	0.759523	+	1.31553i
$747$	−21.8972	+	1.30148i	−0.801177	+	0.0476187i
$748$	1.79328			0.0655686
$749$		0			0
$750$	16.4225	−	10.1430i	0.599665	−	0.370371i
$751$	−11.1005	−	19.2266i	−0.405063	−	0.701590i	0.589266	−	0.807939i	$-0.299417\pi$
$751$	−11.1005	−	19.2266i	−0.405063	−	0.701590i	−0.994329	+	0.106349i	$0.966084\pi$
$752$	−2.07887			−0.0758087
$753$	11.8642	−	7.32769i	0.432356	−	0.267036i
$754$	11.3987			0.415116
$755$	−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	$0.349581\pi$
$758$	39.3446			1.42906
$759$	−7.46773	+	4.61229i	−0.271061	+	0.167415i
$760$	72.7051			2.63729
$761$	3.37632	+	5.84796i	0.122392	+	0.211988i	0.920710	−	0.390247i	$-0.127610\pi$
$761$	3.37632	+	5.84796i	0.122392	+	0.211988i	−0.798319	+	0.602235i	$0.794277\pi$
$762$	−5.82649	+	3.59862i	−0.211072	+	0.130364i
$763$		0			0
$764$	7.76233			0.280831
$765$	−28.5509	−	43.2974i	−1.03226	−	1.56542i
$766$	−1.12637	−	1.95094i	−0.0406975	−	0.0704902i
$767$	13.2255	−	22.9072i	0.477544	−	0.827131i
$768$	−10.6977	+	6.60722i	−0.386020	+	0.238417i
$769$	−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
$772$	−5.44130			−0.195837
$773$	1.64926	+	2.85660i	0.0593197	+	0.102745i	0.894160	−	0.447747i	$-0.147774\pi$
$773$	1.64926	+	2.85660i	0.0593197	+	0.102745i	−0.834841	+	0.550492i	$0.814440\pi$
$774$	37.6382	−	2.23706i	1.35288	−	0.0804095i
$775$	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
$779$	22.8425	+	39.5644i	0.818419	+	1.41754i
$780$	5.19300	−	3.20735i	0.185939	−	0.114842i
$781$	1.93114	−	3.34484i	0.0691017	−	0.119688i
$782$	−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
$786$	6.46597	+	3.48146i	0.230634	+	0.124180i
$787$	−6.72910			−0.239867			−0.119933	−	0.992782i	$-0.538268\pi$
$787$	−6.72910			−0.239867			−0.119933	+	0.992782i	$0.538268\pi$
$788$	6.13031			0.218383
$789$	−1.20023	−	40.4231i	−0.0427294	−	1.43910i
$790$	−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
$794$	−16.4688	+	28.5248i	−0.584456	+	1.01231i
$795$	−0.403735	−	13.5976i	−0.0143190	−	0.482256i
$796$	−2.95160	−	5.11233i	−0.104617	−	0.181202i
$797$	−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
$801$	19.8889	+	30.1614i	0.702738	+	1.06570i
$802$	22.6336	+	39.2026i	0.799222	+	1.38429i
$803$	1.22340			0.0431730
$804$	−2.43888	+	1.50632i	−0.0860126	+	0.0531240i
$805$		0			0
$806$	−4.02060	+	6.96388i	−0.141620	+	0.245292i
$807$	−0.821216	−	0.442166i	−0.0289082	−	0.0155650i
$808$	−2.39514	+	4.14850i	−0.0842607	+	0.145944i
$809$	−19.5428	−	33.8492i	−0.687089	−	1.19007i	−0.972775	−	0.231751i	$-0.925555\pi$
$809$	−19.5428	−	33.8492i	−0.687089	−	1.19007i	0.285686	−	0.958323i	$-0.407779\pi$
$810$	−16.2475	+	37.9136i	−0.570881	+	1.33215i
$811$	−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
$814$	7.47939	+	12.9547i	0.262152	+	0.454061i
$815$	59.5907			2.08737
$816$	−24.5490	−	13.2179i	−0.859387	−	0.462718i
$817$	66.3896			2.32268
$818$	−23.7177			−0.829269
$819$		0			0
$820$	−7.28010			−0.254232
$821$	−44.9966			−1.57039			−0.785196	−	0.619247i	$-0.787438\pi$
$821$	−44.9966			−1.57039			−0.785196	+	0.619247i	$0.787438\pi$
$822$	1.39879	+	47.1105i	0.0487885	+	1.64317i
$823$	−55.2465			−1.92577			−0.962886	−	0.269909i	$-0.913006\pi$
$823$	−55.2465			−1.92577			−0.962886	+	0.269909i	$0.913006\pi$
$824$	3.50700	+	6.07430i	0.122172	+	0.211608i
$825$	−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	$0.577640\pi$
$828$	−3.99612	+	0.237513i	−0.138875	+	0.00825414i
$829$	−19.4896	−	33.7570i	−0.676903	−	1.17243i	−0.975909	−	0.218179i	$-0.929988\pi$
$829$	−19.4896	−	33.7570i	−0.676903	−	1.17243i	0.299006	−	0.954251i	$-0.403345\pi$
$830$	−16.7559	+	29.0220i	−0.581605	+	1.00737i
$831$	1.12611	+	37.9267i	0.0390643	+	1.31566i
$832$	14.2129	−	24.6174i	0.492743	−	0.853456i
$833$		0			0
$834$	1.11081	+	37.4113i	0.0384641	+	1.29545i
$835$	−18.1453			−0.627944
$836$	−1.25564	−	2.17484i	−0.0434274	−	0.0752184i
$837$	0.887605	+	9.94123i	0.0306801	+	0.343619i
$838$	−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
$842$	0.187560	+	0.324863i	0.00646373	+	0.0111955i
$843$	−2.36876	−	1.27541i	−0.0815845	−	0.0439274i
$844$	−1.15385	+	1.99852i	−0.0397170	+	0.0687918i
$845$	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
$849$	−3.90722	+	2.41322i	−0.134096	+	0.0828214i
$850$	−47.3650			−1.62461
$851$	41.9864			1.43928
$852$	1.49872	−	0.925653i	0.0513452	−	0.0317123i
$853$	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
$857$	−7.98194	+	13.8251i	−0.272658	+	0.472258i	−0.969542	−	0.244927i	$-0.921236\pi$
$857$	−7.98194	+	13.8251i	−0.272658	+	0.472258i	0.696884	+	0.717184i	$0.254569\pi$
$858$	7.52423	+	4.05126i	0.256873	+	0.138308i
$859$	24.1645	+	41.8542i	0.824483	+	1.42805i	0.902314	+	0.431080i	$0.141867\pi$
$859$	24.1645	+	41.8542i	0.824483	+	1.42805i	−0.0778308	+	0.996967i	$0.524799\pi$
$860$	−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	−0.411133	−	0.911576i	$-0.634867\pi$
$863$	17.1526	−	29.7092i	0.583881	−	1.01131i	0.995014	−	0.0997366i	$-0.0318000\pi$
$864$	−0.803481	−	8.99904i	−0.0273350	−	0.306154i
$865$	−17.1650	−	29.7307i	−0.583628	−	1.01087i
$866$	−6.30712			−0.214325
$867$	0.361948	+	12.1902i	0.0122924	+	0.414001i
$868$		0			0
$869$	−0.591670	+	1.02480i	−0.0200710	+	0.0347640i
$870$	−0.641483	−	21.6048i	−0.0217483	−	0.732470i
$871$	8.58776	−	14.8744i	0.290985	−	0.504001i
$872$	−1.38079	−	2.39159i	−0.0467594	−	0.0809896i
$873$	−32.7295	+	1.94531i	−1.10773	+	0.0658387i
$874$	38.3781			1.29816
$875$		0			0
$876$	0.491288	+	0.264524i	0.0165991	+	0.00893743i
$877$	−7.09076	−	12.2816i	−0.239438	−	0.414719i	0.721115	−	0.692815i	$-0.243630\pi$
$877$	−7.09076	−	12.2816i	−0.239438	−	0.414719i	−0.960553	+	0.278097i	$0.910296\pi$
$878$	3.31198			0.111774
$879$	0.533906	+	17.9816i	0.0180082	+	0.606505i
$880$	−13.6421			−0.459874
$881$	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	$0.523453\pi$
$884$	−4.90052			−0.164822
$885$	−44.1620	−	23.7781i	−1.48449	−	0.799291i
$886$	−0.839076			−0.0281893
$887$	−9.57208	−	16.5793i	−0.321399	−	0.556679i	0.659378	−	0.751812i	$-0.270820\pi$
$887$	−9.57208	−	16.5793i	−0.321399	−	0.556679i	−0.980777	+	0.195132i	$0.937486\pi$
$888$	1.50742	+	50.7689i	0.0505856	+	1.70369i
$889$		0			0
$890$	55.1942			1.85011
$891$	10.5321	−	1.25641i	0.352840	−	0.0420914i
$892$	−0.510697	−	0.884554i	−0.0170994	−	0.0296171i
$893$	2.17396	−	3.76540i	0.0727486	−	0.126004i
$894$	−2.23698	−	1.20445i	−0.0748157	−	0.0402829i
$895$	−2.42574	+	4.20151i	−0.0810836	+	0.140441i
$896$		0			0
$897$	20.4072	−	12.6041i	0.681377	−	0.420838i
$898$	−6.79389			−0.226715
$899$	−2.61499	−	4.52929i	−0.0872147	−	0.151060i
$900$	−3.80879	−	5.77602i	−0.126960	−	0.192534i
$901$	−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
$905$	9.98800	+	17.2997i	0.332012	+	0.575062i
$906$	−1.31164	−	44.1753i	−0.0435764	−	1.46763i
$907$	−19.9225	+	34.5068i	−0.661515	+	1.14578i	0.318702	+	0.947855i	$0.396753\pi$
$907$	−19.9225	+	34.5068i	−0.661515	+	1.14578i	−0.980218	+	0.197923i	$0.936580\pi$
$908$	−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	$0.675351\pi$
$912$	1.15880	+	39.0275i	0.0383715	+	1.29233i
$913$	8.61739			0.285194
$914$	−3.71861			−0.123001
$915$	51.9378	+	27.9648i	1.71701	+	0.924488i
$916$	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	−0.703051	−	0.711140i	$-0.748179\pi$
$919$	8.01347	−	13.8797i	0.264340	−	0.457850i	0.967390	+	0.253290i	$0.0815126\pi$
$920$	−22.7648	+	39.4298i	−0.750533	+	1.29996i
$921$	−15.6832	+	9.68641i	−0.516779	+	0.319178i
$922$	2.37388	+	4.11168i	0.0781796	+	0.135411i
$923$	−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
$927$	−6.99433	+	0.415714i	−0.229724	+	0.0136538i
$928$	2.36715	+	4.10002i	0.0777055	+	0.134590i
$929$	−14.0159			−0.459847			−0.229924	−	0.973209i	$-0.573848\pi$
$929$	−14.0159			−0.459847			−0.229924	+	0.973209i	$0.573848\pi$
$930$	13.4254	+	7.22863i	0.440237	+	0.237036i
$931$		0			0
$932$	−2.28180	+	3.95219i	−0.0747428	+	0.129458i
$933$	−20.2029	+	12.4779i	−0.661414	+	0.408509i
$934$	−13.3738	+	23.1640i	−0.437603	+	0.757950i
$935$	10.1871	+	17.6447i	0.333155	+	0.577042i
$936$	15.9732	+	24.2233i	0.522101	+	0.791765i
$937$	−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
$940$	0.346429	+	0.600032i	0.0112993	+	0.0195709i
$941$	46.3128			1.50975			0.754877	−	0.655866i	$-0.227697\pi$
$941$	46.3128			1.50975			0.754877	+	0.655866i	$0.227697\pi$
$942$	17.8765	−	11.0411i	0.582449	−	0.359738i
$943$	−28.6090			−0.931637
$944$	−26.9636			−0.877592
$945$		0			0
$946$	−14.8121			−0.481582
$947$	20.0083			0.650181			0.325091	−	0.945683i	$-0.394605\pi$
$947$	20.0083			0.650181			0.325091	+	0.945683i	$0.394605\pi$
$948$	−0.459182	+	0.283605i	−0.0149135	+	0.00921105i
$949$	−3.34322			−0.108526
$950$	33.1648	+	57.4432i	1.07601	+	1.86370i
$951$	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	$0.338429\pi$
$954$	8.67131	−	0.515387i	0.280744	−	0.0166863i
$955$	44.0958	+	76.3762i	1.42691	+	2.47148i
$956$	−2.19773	+	3.80659i	−0.0710798	+	0.123114i
$957$	−4.72879	+	2.92064i	−0.152860	+	0.0944108i
$958$	−16.3675	+	28.3493i	−0.528809	+	0.915924i
$959$		0			0
$960$	−47.4591	−	25.5533i	−1.53173	−	0.824730i
$961$	−27.3105			−0.880985
$962$	−20.4391	−	35.4015i	−0.658982	−	1.14139i
$963$	−3.67232	−	5.56907i	−0.118339	−	0.179461i
$964$	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	$-0.0122398\pi$
$968$	−14.4317	−	24.9964i	−0.463851	−	0.803414i
$969$	49.6129	−	30.6424i	1.59380	−	0.984376i
$970$	−25.0448	+	43.3788i	−0.804140	+	1.39281i
$971$	20.8234	−	36.0672i	0.668256	−	1.15745i	−0.310136	−	0.950692i	$-0.600375\pi$
$971$	20.8234	−	36.0672i	0.668256	−	1.15745i	0.978392	−	0.206761i	$-0.0662921\pi$
$972$	4.50110	+	1.77271i	0.144373	+	0.0568597i
$973$		0			0
$974$	21.2928	+	36.8803i	0.682267	+	1.18172i
$975$	36.5005	+	19.6529i	1.16895	+	0.629397i
$976$	31.7113			1.01505
$977$	37.5181			1.20031			0.600154	−	0.799884i	$-0.295106\pi$
$977$	37.5181			1.20031			0.600154	+	0.799884i	$0.295106\pi$
$978$	1.12933	+	38.0352i	0.0361120	+	1.21623i
$979$	−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
$983$	24.0379	−	41.6349i	0.766690	−	1.32795i	−0.172658	−	0.984982i	$-0.555236\pi$
$983$	24.0379	−	41.6349i	0.766690	−	1.32795i	0.939348	−	0.342964i	$-0.111431\pi$
$984$	−1.02713	−	34.5933i	−0.0327438	−	1.10279i
$985$	34.8247	+	60.3182i	1.10961	+	1.92190i
$986$	−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
$990$	7.25521	−	14.4892i	0.230586	−	0.460498i
$991$	17.0643	+	29.5562i	0.542065	+	0.938884i	0.998785	+	0.0492737i	$0.0156907\pi$
$991$	17.0643	+	29.5562i	0.542065	+	0.938884i	−0.456720	+	0.889610i	$0.650976\pi$
$992$	−3.33981			−0.106039
$993$	−35.2871	+	21.7944i	−1.11980	+	0.691624i
$994$		0			0
$995$	33.5346	−	58.0837i	1.06312	−	1.84138i
$996$	3.46053	+	1.86325i	0.109651	+	0.0590393i
$997$	−22.0413	+	38.1767i	−0.698056	+	1.20907i	0.271084	+	0.962556i	$0.412618\pi$
$997$	−22.0413	+	38.1767i	−0.698056	+	1.20907i	−0.969140	+	0.246512i	$0.920715\pi$
$998$	−10.1661	−	17.6081i	−0.321801	−	0.557376i
$999$	−46.0226	−	21.3609i	−1.45609	−	0.675829i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.3	✓	24	7.5	odd	6
441.2.f.h.148.4	yes	24	7.2	even	3
441.2.f.h.295.3	yes	24	63.61	odd	6
441.2.f.h.295.4	yes	24	63.16	even	3
441.2.g.h.67.3		24	7.4	even	3
441.2.g.h.67.4		24	7.3	odd	6
441.2.g.h.79.3		24	9.7	even	3
441.2.g.h.79.4		24	63.34	odd	6
441.2.h.h.214.9		24	63.52	odd	6	inner
441.2.h.h.214.10		24	63.25	even	3	inner
441.2.h.h.373.9		24	7.6	odd	2	inner
441.2.h.h.373.10		24	1.1	even	1	trivial
1323.2.f.h.442.9		24	21.5	even	6
1323.2.f.h.442.10		24	21.2	odd	6
1323.2.f.h.883.9		24	63.47	even	6
1323.2.f.h.883.10		24	63.2	odd	6
1323.2.g.h.361.9		24	21.17	even	6
1323.2.g.h.361.10		24	21.11	odd	6
1323.2.g.h.667.9		24	63.20	even	6
1323.2.g.h.667.10		24	9.2	odd	6
1323.2.h.h.226.3		24	3.2	odd	2
1323.2.h.h.226.4		24	21.20	even	2
1323.2.h.h.802.3		24	63.11	odd	6
1323.2.h.h.802.4		24	63.38	even	6
3969.2.a.bh.1.9		12	63.40	odd	6
3969.2.a.bh.1.10		12	63.58	even	3
3969.2.a.bi.1.3		12	63.23	odd	6
3969.2.a.bi.1.4		12	63.5	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 $\F_{q}$

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+1.29987 q^{2} +(1.47364 - 0.910162i) q^{3} -0.310333 q^{4} +(-1.76292 - 3.05347i) q^{5} +(1.91554 - 1.18309i) q^{6} -3.00314 q^{8} +(1.34321 - 2.68250i) q^{9} +(-2.29157 - 3.96912i) q^{10} +(-0.589267 + 1.02064i) q^{11} +(-0.457317 + 0.282453i) q^{12} +(1.61030 - 2.78913i) q^{13} +(-5.37706 - 2.89516i) q^{15} -3.28303 q^{16} +(2.45159 + 4.24627i) q^{17} +(1.74600 - 3.48690i) q^{18} +(3.43318 - 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(2.14994 + 3.72380i) q^{23} +(-4.42553 + 2.73334i) q^{24} +(-3.71578 + 6.43592i) q^{25} +(2.09319 - 3.62551i) q^{26} +(-0.462101 - 5.17556i) q^{27} +(1.36140 + 2.35802i) q^{29} +(-6.98948 - 3.76334i) q^{30} -1.92080 q^{31} +1.73876 q^{32} +(0.0605825 + 2.04038i) q^{33} +(3.18675 + 5.51961i) q^{34} +(-0.416842 + 0.832466i) q^{36} +(4.88229 - 8.45637i) q^{37} +(4.46270 - 7.72962i) q^{38} +(-0.165555 - 5.57579i) q^{39} +(5.29429 + 9.16998i) q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(0.182869 - 0.316738i) q^{44} +(-10.5589 + 0.627577i) q^{45} +(2.79464 + 4.84046i) q^{46} +0.633218 q^{47} +(-4.83799 + 2.98809i) q^{48} +(-4.83004 + 8.36587i) q^{50} +(7.47754 + 4.02612i) q^{51} +(-0.499729 + 0.865557i) q^{52} +(1.11378 + 1.92912i) q^{53} +(-0.600672 - 6.72757i) q^{54} +4.15533 q^{55} +(-0.352965 - 11.8877i) q^{57} +(1.76965 + 3.06512i) q^{58} +8.21304 q^{59} +(1.66868 + 0.898462i) q^{60} -9.65916 q^{61} -2.49680 q^{62} +8.82622 q^{64} -11.3553 q^{65} +(0.0787495 + 2.65224i) q^{66} +5.33301 q^{67} +(-0.760807 - 1.31776i) q^{68} +(6.55748 + 3.53074i) q^{69} -3.27719 q^{71} +(-4.03385 + 8.05590i) q^{72} +(-0.519036 - 0.898997i) q^{73} +(6.34635 - 10.9922i) q^{74} +(0.382019 + 12.8662i) q^{75} +(-1.06543 + 1.84538i) q^{76} +(-0.215200 - 7.24782i) q^{78} +1.00408 q^{79} +(5.78772 + 10.0246i) q^{80} +(-5.39157 - 7.20631i) q^{81} +(-4.32432 + 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(6.28411 + 10.8844i) q^{86} +(4.15239 + 2.23577i) q^{87} +(1.76965 - 3.06512i) q^{88} +(-6.02144 + 10.4294i) q^{89} +(-13.7252 + 0.815770i) q^{90} +(-0.667195 - 1.15562i) q^{92} +(-2.83056 + 1.74824i) q^{93} +0.823103 q^{94} -24.2097 q^{95} +(2.56230 - 1.58255i) q^{96} +(-5.46454 - 9.46487i) q^{97} +(1.94636 + 2.95164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 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

Introduction

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