LMFDB - Embedded newform 735.2.j.g.197.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(197,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("735.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.j (of order $4$, degree $2$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.4
Character	$\chi$	$=$	735.197
Dual form			735.2.j.g.638.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929340 + 0.929340i) q^{2} +(-1.05286 - 1.37531i) q^{3} +0.272655i q^{4} +(0.980304 - 2.00973i) q^{5} +(2.25660 + 0.299670i) q^{6} +(-2.11207 - 2.11207i) q^{8} +(-0.782976 + 2.89602i) q^{9} +O(q^{10})$	\(q+(-0.929340 + 0.929340i) q^{2} +(-1.05286 - 1.37531i) q^{3} +0.272655i q^{4} +(0.980304 - 2.00973i) q^{5} +(2.25660 + 0.299670i) q^{6} +(-2.11207 - 2.11207i) q^{8} +(-0.782976 + 2.89602i) q^{9} +(0.956684 + 2.77876i) q^{10} +3.90548i q^{11} +(0.374987 - 0.287068i) q^{12} +(-1.56642 + 1.56642i) q^{13} +(-3.79613 + 0.767733i) q^{15} +3.38035 q^{16} +(1.89349 - 1.89349i) q^{17} +(-1.96374 - 3.41904i) q^{18} +1.86019i q^{19} +(0.547963 + 0.267285i) q^{20} +(-3.62951 - 3.62951i) q^{22} +(1.74459 + 1.74459i) q^{23} +(-0.681047 + 5.12847i) q^{24} +(-3.07801 - 3.94029i) q^{25} -2.91148i q^{26} +(4.80730 - 1.97227i) q^{27} +0.513153 q^{29} +(2.81441 - 4.24138i) q^{30} +8.58277 q^{31} +(1.08265 - 1.08265i) q^{32} +(5.37125 - 4.11191i) q^{33} +3.51939i q^{34} +(-0.789616 - 0.213483i) q^{36} +(4.83665 + 4.83665i) q^{37} +(-1.72875 - 1.72875i) q^{38} +(3.80355 + 0.505101i) q^{39} +(-6.31515 + 2.17421i) q^{40} +0.308469i q^{41} +(7.60892 - 7.60892i) q^{43} -1.06485 q^{44} +(5.05266 + 4.41255i) q^{45} -3.24263 q^{46} +(-3.74074 + 3.74074i) q^{47} +(-3.55903 - 4.64904i) q^{48} +(6.52238 + 0.801352i) q^{50} +(-4.59772 - 0.610565i) q^{51} +(-0.427094 - 0.427094i) q^{52} +(1.36127 + 1.36127i) q^{53} +(-2.63471 + 6.30052i) q^{54} +(7.84894 + 3.82855i) q^{55} +(2.55835 - 1.95852i) q^{57} +(-0.476893 + 0.476893i) q^{58} -0.518229 q^{59} +(-0.209327 - 1.03503i) q^{60} +5.10902 q^{61} +(-7.97631 + 7.97631i) q^{62} +8.77299i q^{64} +(1.61251 + 4.68365i) q^{65} +(-1.17035 + 8.81309i) q^{66} +(6.40207 + 6.40207i) q^{67} +(0.516270 + 0.516270i) q^{68} +(0.562551 - 4.23616i) q^{69} +15.3749i q^{71} +(7.77030 - 4.46290i) q^{72} +(-2.04880 + 2.04880i) q^{73} -8.98978 q^{74} +(-2.17843 + 8.38179i) q^{75} -0.507191 q^{76} +(-4.00420 + 3.06538i) q^{78} -5.05241i q^{79} +(3.31377 - 6.79358i) q^{80} +(-7.77390 - 4.53503i) q^{81} +(-0.286673 - 0.286673i) q^{82} +(9.16088 + 9.16088i) q^{83} +(-1.94920 - 5.66159i) q^{85} +14.1425i q^{86} +(-0.540277 - 0.705746i) q^{87} +(8.24863 - 8.24863i) q^{88} +11.3504 q^{89} +(-8.79640 + 0.594879i) q^{90} +(-0.475671 + 0.475671i) q^{92} +(-9.03644 - 11.8040i) q^{93} -6.95283i q^{94} +(3.73848 + 1.82355i) q^{95} +(-2.62885 - 0.349104i) q^{96} +(-6.81964 - 6.81964i) q^{97} +(-11.3103 - 3.05789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 12 q^{6}+O(q^{10}) $ 24 * q + 2 * q^3 - 12 * q^6	$ 24 q + 2 q^{3} - 12 q^{6} + 8 q^{10} + 10 q^{12} - 8 q^{13} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 4 q^{22} - 4 q^{25} + 20 q^{27} - 40 q^{30} + 24 q^{31} + 4 q^{33} + 4 q^{36} - 4 q^{37} + 16 q^{40} + 8 q^{43} - 40 q^{45} + 32 q^{46} + 22 q^{48} - 8 q^{51} - 36 q^{52} - 20 q^{55} - 44 q^{57} - 56 q^{58} + 50 q^{60} + 8 q^{61} - 76 q^{66} - 12 q^{67} + 34 q^{72} - 52 q^{73} - 6 q^{75} + 32 q^{76} - 60 q^{78} - 20 q^{81} - 104 q^{82} - 12 q^{85} + 46 q^{87} - 42 q^{90} + 44 q^{93} - 12 q^{96} - 60 q^{97}+O(q^{100}) $ 24 * q + 2 * q^3 - 12 * q^6 + 8 * q^10 + 10 * q^12 - 8 * q^13 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 4 * q^22 - 4 * q^25 + 20 * q^27 - 40 * q^30 + 24 * q^31 + 4 * q^33 + 4 * q^36 - 4 * q^37 + 16 * q^40 + 8 * q^43 - 40 * q^45 + 32 * q^46 + 22 * q^48 - 8 * q^51 - 36 * q^52 - 20 * q^55 - 44 * q^57 - 56 * q^58 + 50 * q^60 + 8 * q^61 - 76 * q^66 - 12 * q^67 + 34 * q^72 - 52 * q^73 - 6 * q^75 + 32 * q^76 - 60 * q^78 - 20 * q^81 - 104 * q^82 - 12 * q^85 + 46 * q^87 - 42 * q^90 + 44 * q^93 - 12 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.929340	+	0.929340i	−0.657142	+	0.657142i	−0.954703	−	0.297561i	$-0.903827\pi$
$2$	−0.929340	+	0.929340i	−0.657142	+	0.657142i	0.297561	+	0.954703i	$0.403827\pi$
$3$	−1.05286	−	1.37531i	−0.607868	−	0.794038i
$3$	−1.05286	−	1.37531i	−0.607868	−	0.794038i
$4$			0.272655i			0.136328i
$5$	0.980304	−	2.00973i	0.438405	−	0.898777i
$5$	0.980304	−	2.00973i	0.438405	−	0.898777i
$6$	2.25660	+	0.299670i	0.921252	+	0.122340i
$7$		0			0
$7$		0			0
$8$	−2.11207	−	2.11207i	−0.746729	−	0.746729i
$9$	−0.782976	+	2.89602i	−0.260992	+	0.965341i
$10$	0.956684	+	2.77876i	0.302530	+	0.878719i
$11$			3.90548i			1.17755i	0.808299	+	0.588773i	$0.200389\pi$
$11$			3.90548i			1.17755i	−0.808299	+	0.588773i	$0.799611\pi$
$12$	0.374987	−	0.287068i	0.108249	−	0.0828693i
$13$	−1.56642	+	1.56642i	−0.434448	+	0.434448i	−0.890138	−	0.455691i	$-0.849392\pi$
$13$	−1.56642	+	1.56642i	−0.434448	+	0.434448i	0.455691	+	0.890138i	$0.349392\pi$
$14$		0			0
$15$	−3.79613	+	0.767733i	−0.980156	+	0.198228i
$16$	3.38035			0.845087
$17$	1.89349	−	1.89349i	0.459239	−	0.459239i	−0.439167	−	0.898406i	$-0.644726\pi$
$17$	1.89349	−	1.89349i	0.459239	−	0.459239i	0.898406	+	0.439167i	$0.144726\pi$
$18$	−1.96374	−	3.41904i	−0.462858	−	0.805875i
$19$			1.86019i			0.426757i	0.976970	+	0.213379i	$0.0684468\pi$
$19$			1.86019i			0.426757i	−0.976970	+	0.213379i	$0.931553\pi$
$20$	0.547963	+	0.267285i	0.122528	+	0.0597668i
$21$		0			0
$22$	−3.62951	−	3.62951i	−0.773815	−	0.773815i
$23$	1.74459	+	1.74459i	0.363772	+	0.363772i	0.865200	−	0.501428i	$-0.167192\pi$
$23$	1.74459	+	1.74459i	0.363772	+	0.363772i	−0.501428	+	0.865200i	$0.667192\pi$
$24$	−0.681047	+	5.12847i	−0.139018	+	1.04684i
$25$	−3.07801	−	3.94029i	−0.615601	−	0.788058i
$26$		−	2.91148i		−	0.570988i
$27$	4.80730	−	1.97227i	0.925166	−	0.379563i
$28$		0			0
$29$	0.513153			0.0952901			0.0476450	−	0.998864i	$-0.484828\pi$
$29$	0.513153			0.0952901			0.0476450	+	0.998864i	$0.484828\pi$
$30$	2.81441	−	4.24138i	0.513838	−	0.774366i
$31$	8.58277			1.54151			0.770755	−	0.637131i	$-0.219879\pi$
$31$	8.58277			1.54151			0.770755	+	0.637131i	$0.219879\pi$
$32$	1.08265	−	1.08265i	0.191387	−	0.191387i
$33$	5.37125	−	4.11191i	0.935015	−	0.715793i
$34$			3.51939i			0.603570i
$35$		0			0
$36$	−0.789616	−	0.213483i	−0.131603	−	0.0355804i
$37$	4.83665	+	4.83665i	0.795140	+	0.795140i	0.982325	−	0.187185i	$-0.0599363\pi$
$37$	4.83665	+	4.83665i	0.795140	+	0.795140i	−0.187185	+	0.982325i	$0.559936\pi$
$38$	−1.72875	−	1.72875i	−0.280440	−	0.280440i
$39$	3.80355	+	0.505101i	0.609055	+	0.0808808i
$40$	−6.31515	+	2.17421i	−0.998513	+	0.343773i
$41$			0.308469i			0.0481748i	0.999710	+	0.0240874i	$0.00766800\pi$
$41$			0.308469i			0.0481748i	−0.999710	+	0.0240874i	$0.992332\pi$
$42$		0			0
$43$	7.60892	−	7.60892i	1.16035	−	1.16035i	0.175950	−	0.984399i	$-0.443700\pi$
$43$	7.60892	−	7.60892i	1.16035	−	1.16035i	0.984399	−	0.175950i	$-0.0562999\pi$
$44$	−1.06485			−0.160532
$45$	5.05266	+	4.41255i	0.753206	+	0.657784i
$46$	−3.24263			−0.478100
$47$	−3.74074	+	3.74074i	−0.545642	+	0.545642i	−0.925177	−	0.379535i	$-0.876084\pi$
$47$	−3.74074	+	3.74074i	−0.545642	+	0.545642i	0.379535	+	0.925177i	$0.376084\pi$
$48$	−3.55903	−	4.64904i	−0.513702	−	0.671031i
$49$		0			0
$50$	6.52238	+	0.801352i	0.922404	+	0.113328i
$51$	−4.59772	−	0.610565i	−0.643810	−	0.0854962i
$52$	−0.427094	−	0.427094i	−0.0592273	−	0.0592273i
$53$	1.36127	+	1.36127i	0.186985	+	0.186985i	0.794391	−	0.607407i	$-0.207790\pi$
$53$	1.36127	+	1.36127i	0.186985	+	0.186985i	−0.607407	+	0.794391i	$0.707790\pi$
$54$	−2.63471	+	6.30052i	−0.358539	+	0.857393i
$55$	7.84894	+	3.82855i	1.05835	+	0.516242i
$56$		0			0
$57$	2.55835	−	1.95852i	0.338861	−	0.259412i
$58$	−0.476893	+	0.476893i	−0.0626191	+	0.0626191i
$59$	−0.518229			−0.0674676			−0.0337338	−	0.999431i	$-0.510740\pi$
$59$	−0.518229			−0.0674676			−0.0337338	+	0.999431i	$0.510740\pi$
$60$	−0.209327	−	1.03503i	−0.0270240	−	0.133622i
$61$	5.10902			0.654143			0.327071	−	0.945000i	$-0.393938\pi$
$61$	5.10902			0.654143			0.327071	+	0.945000i	$0.393938\pi$
$62$	−7.97631	+	7.97631i	−1.01299	+	1.01299i
$63$		0			0
$64$			8.77299i			1.09662i
$65$	1.61251	+	4.68365i	0.200007	+	0.580936i
$66$	−1.17035	+	8.81309i	−0.144061	+	1.08482i
$67$	6.40207	+	6.40207i	0.782138	+	0.782138i	0.980191	−	0.198054i	$-0.0634620\pi$
$67$	6.40207	+	6.40207i	0.782138	+	0.782138i	−0.198054	+	0.980191i	$0.563462\pi$
$68$	0.516270	+	0.516270i	0.0626070	+	0.0626070i
$69$	0.562551	−	4.23616i	0.0677232	−	0.509974i
$70$		0			0
$71$			15.3749i			1.82467i	0.409448	+	0.912333i	$0.365721\pi$
$71$			15.3749i			1.82467i	−0.409448	+	0.912333i	$0.634279\pi$
$72$	7.77030	−	4.46290i	0.915739	−	0.525958i
$73$	−2.04880	+	2.04880i	−0.239794	+	0.239794i	−0.816765	−	0.576971i	$-0.804235\pi$
$73$	−2.04880	+	2.04880i	−0.239794	+	0.239794i	0.576971	+	0.816765i	$0.304235\pi$
$74$	−8.98978			−1.04504
$75$	−2.17843	+	8.38179i	−0.251543	+	0.967846i
$76$	−0.507191			−0.0581788
$77$		0			0
$78$	−4.00420	+	3.06538i	−0.453386	+	0.347086i
$79$		−	5.05241i		−	0.568440i	−0.958759	−	0.284220i	$-0.908265\pi$
$79$		−	5.05241i		−	0.568440i	0.958759	−	0.284220i	$-0.0917347\pi$
$80$	3.31377	−	6.79358i	0.370491	−	0.759545i
$81$	−7.77390	−	4.53503i	−0.863766	−	0.503893i
$82$	−0.286673	−	0.286673i	−0.0316577	−	0.0316577i
$83$	9.16088	+	9.16088i	1.00554	+	1.00554i	0.999985	+	0.00555287i	$0.00176754\pi$
$83$	9.16088	+	9.16088i	1.00554	+	1.00554i	0.00555287	+	0.999985i	$0.498232\pi$
$84$		0			0
$85$	−1.94920	−	5.66159i	−0.211421	−	0.614086i
$86$			14.1425i			1.52503i
$87$	−0.540277	−	0.705746i	−0.0579238	−	0.0756639i
$88$	8.24863	−	8.24863i	0.879307	−	0.879307i
$89$	11.3504			1.20314			0.601569	−	0.798821i	$-0.294542\pi$
$89$	11.3504			1.20314			0.601569	+	0.798821i	$0.294542\pi$
$90$	−8.79640	+	0.594879i	−0.927222	+	0.0627058i
$91$		0			0
$92$	−0.475671	+	0.475671i	−0.0495922	+	0.0495922i
$93$	−9.03644	−	11.8040i	−0.937036	−	1.22402i
$94$		−	6.95283i		−	0.717129i
$95$	3.73848	+	1.82355i	0.383560	+	0.187093i
$96$	−2.62885	−	0.349104i	−0.268306	−	0.0356303i
$97$	−6.81964	−	6.81964i	−0.692430	−	0.692430i	0.270336	−	0.962766i	$-0.412865\pi$
$97$	−6.81964	−	6.81964i	−0.692430	−	0.692430i	−0.962766	+	0.270336i	$0.912865\pi$
$98$		0			0
$99$	−11.3103	−	3.05789i	−1.13673	−	0.307330i
$100$	1.07434	−	0.839235i	0.107434	−	0.0839235i
$101$			4.57138i			0.454869i	0.973793	+	0.227434i	$0.0730337\pi$
$101$			4.57138i			0.454869i	−0.973793	+	0.227434i	$0.926966\pi$
$102$	4.84027	−	3.70542i	0.479258	−	0.366891i
$103$	7.16930	−	7.16930i	0.706413	−	0.706413i	−0.259366	−	0.965779i	$-0.583514\pi$
$103$	7.16930	−	7.16930i	0.706413	−	0.706413i	0.965779	+	0.259366i	$0.0835137\pi$
$104$	6.61679			0.648829
$105$		0			0
$106$	−2.53016			−0.245751
$107$	1.24996	−	1.24996i	0.120838	−	0.120838i	−0.644102	−	0.764940i	$-0.722769\pi$
$107$	1.24996	−	1.24996i	0.120838	−	0.120838i	0.764940	+	0.644102i	$0.222769\pi$
$108$	0.537749	+	1.31074i	0.0517449	+	0.126126i
$109$			5.37615i			0.514942i	0.966286	+	0.257471i	$0.0828892\pi$
$109$			5.37615i			0.514942i	−0.966286	+	0.257471i	$0.917111\pi$
$110$	−10.8524	+	3.73630i	−1.03473	+	0.356243i
$111$	1.55960	−	11.7442i	0.148031	−	1.11471i
$112$		0			0
$113$	−7.83259	−	7.83259i	−0.736828	−	0.736828i	0.235134	−	0.971963i	$-0.424447\pi$
$113$	−7.83259	−	7.83259i	−0.736828	−	0.736828i	−0.971963	+	0.235134i	$0.924447\pi$
$114$	−0.557444	+	4.19770i	−0.0522094	+	0.393151i
$115$	5.21637	−	1.79592i	0.486429	−	0.167470i
$116$			0.139914i			0.0129907i
$117$	−3.30993	−	5.76287i	−0.306003	−	0.532777i
$118$	0.481611	−	0.481611i	0.0443358	−	0.0443358i
$119$		0			0
$120$	9.63919	+	6.39618i	0.879934	+	0.583888i
$121$	−4.25274			−0.386613
$122$	−4.74801	+	4.74801i	−0.429865	+	0.429865i
$123$	0.424242	−	0.324775i	0.0382526	−	0.0292839i
$124$			2.34014i			0.210151i
$125$	−10.9363	+	2.32327i	−0.978171	+	0.207800i
$126$		0			0
$127$	8.12393	+	8.12393i	0.720883	+	0.720883i	0.968785	−	0.247902i	$-0.0797413\pi$
$127$	8.12393	+	8.12393i	0.720883	+	0.720883i	−0.247902	+	0.968785i	$0.579741\pi$
$128$	−5.98779	−	5.98779i	−0.529251	−	0.529251i
$129$	−18.4758	−	2.45353i	−1.62670	−	0.216022i
$130$	−5.85128	−	2.85414i	−0.513191	−	0.250324i
$131$		−	4.39569i		−	0.384053i	−0.981390	−	0.192027i	$-0.938494\pi$
$131$		−	4.39569i		−	0.384053i	0.981390	−	0.192027i	$-0.0615060\pi$
$132$	1.12114	+	1.46450i	0.0975823	+	0.127468i
$133$		0			0
$134$	−11.8994			−1.02795
$135$	0.748904	−	11.5948i	0.0644554	−	0.997921i
$136$	−7.99836			−0.685854
$137$	−4.70477	+	4.70477i	−0.401956	+	0.401956i	−0.878922	−	0.476966i	$-0.841737\pi$
$137$	−4.70477	+	4.70477i	−0.401956	+	0.401956i	0.476966	+	0.878922i	$0.341737\pi$
$138$	3.41403	+	4.45963i	0.290622	+	0.379629i
$139$		−	12.3455i		−	1.04713i	−0.851987	−	0.523564i	$-0.824602\pi$
$139$		−	12.3455i		−	1.04713i	0.851987	−	0.523564i	$-0.175398\pi$
$140$		0			0
$141$	9.08315	+	1.20622i	0.764939	+	0.101582i
$142$	−14.2885	−	14.2885i	−1.19907	−	1.19907i
$143$	−6.11763	−	6.11763i	−0.511582	−	0.511582i
$144$	−2.64673	+	9.78957i	−0.220561	+	0.815797i
$145$	0.503046	−	1.03130i	0.0417757	−	0.0856445i
$146$		−	3.80806i		−	0.315158i
$147$		0			0
$148$	−1.31874	+	1.31874i	−0.108400	+	0.108400i
$149$	−9.83264			−0.805521			−0.402761	−	0.915305i	$-0.631949\pi$
$149$	−9.83264			−0.805521			−0.402761	+	0.915305i	$0.631949\pi$
$150$	−5.76504	−	9.81403i	−0.470713	−	0.801312i
$151$	1.13105			0.0920437			0.0460219	−	0.998940i	$-0.485346\pi$
$151$	1.13105			0.0920437			0.0460219	+	0.998940i	$0.485346\pi$
$152$	3.92885	−	3.92885i	0.318672	−	0.318672i
$153$	4.00103	+	6.96615i	0.323464	+	0.563180i
$154$		0			0
$155$	8.41372	−	17.2490i	0.675807	−	1.38547i
$156$	−0.137718	+	1.03706i	−0.0110263	+	0.0830310i
$157$	−13.2358	−	13.2358i	−1.05633	−	1.05633i	−0.998316	−	0.0580138i	$-0.981523\pi$
$157$	−13.2358	−	13.2358i	−1.05633	−	1.05633i	−0.0580138	−	0.998316i	$-0.518477\pi$
$158$	4.69540	+	4.69540i	0.373546	+	0.373546i
$159$	0.438948	−	3.30540i	0.0348108	−	0.262135i
$160$	−1.11450	−	3.23715i	−0.0881090	−	0.255919i
$161$		0			0
$162$	11.4392	−	3.01001i	0.898747	−	0.236488i
$163$	−9.21128	+	9.21128i	−0.721483	+	0.721483i	−0.968907	−	0.247424i	$-0.920416\pi$
$163$	−9.21128	+	9.21128i	−0.721483	+	0.721483i	0.247424	+	0.968907i	$0.420416\pi$
$164$	−0.0841058			−0.00656756
$165$	−2.99836	−	14.8257i	−0.233422	−	1.15418i
$166$	−17.0271			−1.32156
$167$	2.44412	−	2.44412i	0.189132	−	0.189132i	−0.606189	−	0.795321i	$-0.707302\pi$
$167$	2.44412	−	2.44412i	0.189132	−	0.189132i	0.795321	+	0.606189i	$0.207302\pi$
$168$		0			0
$169$			8.09264i			0.622510i
$170$	7.07301	+	3.45007i	0.542475	+	0.264609i
$171$	−5.38716	−	1.45648i	−0.411966	−	0.111380i
$172$	2.07461	+	2.07461i	0.158188	+	0.158188i
$173$	−6.75619	−	6.75619i	−0.513664	−	0.513664i	0.401983	−	0.915647i	$-0.368321\pi$
$173$	−6.75619	−	6.75619i	−0.513664	−	0.513664i	−0.915647	+	0.401983i	$0.868321\pi$
$174$	1.15798	+	0.153776i	0.0877862	+	0.0116578i
$175$		0			0
$176$			13.2019i			0.995128i
$177$	0.545622	+	0.712727i	0.0410114	+	0.0535718i
$178$	−10.5484	+	10.5484i	−0.790633	+	0.790633i
$179$	10.7806			0.805780			0.402890	−	0.915248i	$-0.368006\pi$
$179$	10.7806			0.805780			0.402890	+	0.915248i	$0.368006\pi$
$180$	−1.20311	+	1.37764i	−0.0896742	+	0.102683i
$181$	−2.86639			−0.213057			−0.106529	−	0.994310i	$-0.533974\pi$
$181$	−2.86639			−0.213057			−0.106529	+	0.994310i	$0.533974\pi$
$182$		0			0
$183$	−5.37907	−	7.02650i	−0.397633	−	0.519414i
$184$		−	7.36938i		−	0.543278i
$185$	14.4617	−	4.97896i	1.06325	−	0.366060i
$186$	19.3679	+	2.57200i	1.42012	+	0.188588i
$187$	7.39498	+	7.39498i	0.540774	+	0.540774i
$188$	−1.01993	−	1.01993i	−0.0743862	−	0.0743862i
$189$		0			0
$190$	−5.16902	+	1.77961i	−0.375000	+	0.129107i
$191$			14.0064i			1.01347i	0.862102	+	0.506736i	$0.169148\pi$
$191$			14.0064i			1.01347i	−0.862102	+	0.506736i	$0.830852\pi$
$192$	12.0656	−	9.23672i	0.870761	−	0.666603i
$193$	−6.72419	+	6.72419i	−0.484018	+	0.484018i	−0.906412	−	0.422394i	$-0.861190\pi$
$193$	−6.72419	+	6.72419i	−0.484018	+	0.484018i	0.422394	+	0.906412i	$0.361190\pi$
$194$	12.6755			0.910050
$195$	4.74375	−	7.14894i	0.339707	−	0.511946i
$196$		0			0
$197$	5.29206	−	5.29206i	0.377044	−	0.377044i	−0.492991	−	0.870035i	$-0.664096\pi$
$197$	5.29206	−	5.29206i	0.377044	−	0.377044i	0.870035	+	0.492991i	$0.164096\pi$
$198$	13.3530	−	7.66933i	0.948955	−	0.545036i
$199$		−	10.3230i		−	0.731775i	−0.930659	−	0.365888i	$-0.880765\pi$
$199$		−	10.3230i		−	0.731775i	0.930659	−	0.365888i	$-0.119235\pi$
$200$	−1.82120	+	14.8231i	−0.128778	+	1.04815i
$201$	2.06438	−	15.5453i	0.145610	−	1.09648i
$202$	−4.24836	−	4.24836i	−0.298914	−	0.298914i
$203$		0			0
$204$	0.166474	−	1.25359i	0.0116555	−	0.0877691i
$205$	0.619939	+	0.302394i	0.0432984	+	0.0211201i
$206$			13.3254i			0.928427i
$207$	−6.41834	+	3.68640i	−0.446105	+	0.256222i
$208$	−5.29506	+	5.29506i	−0.367146	+	0.367146i
$209$	−7.26493			−0.502526
$210$		0			0
$211$	−4.34600			−0.299191			−0.149596	−	0.988747i	$-0.547797\pi$
$211$	−4.34600			−0.299191			−0.149596	+	0.988747i	$0.547797\pi$
$212$	−0.371157	+	0.371157i	−0.0254912	+	0.0254912i
$213$	21.1453	−	16.1876i	1.44885	−	1.10916i
$214$			2.32328i			0.158816i
$215$	−7.83280	−	22.7509i	−0.534192	−	1.55160i
$216$	−14.3189	−	5.98779i	−0.974279	−	0.407418i
$217$		0			0
$218$	−4.99627	−	4.99627i	−0.338390	−	0.338390i
$219$	4.97484	+	0.660646i	0.336169	+	0.0446423i
$220$	−1.04388	+	2.14006i	−0.0703781	+	0.144283i
$221$			5.93201i			0.399030i
$222$	9.46497	+	12.3638i	0.635247	+	0.829802i
$223$	−11.5568	+	11.5568i	−0.773903	+	0.773903i	−0.978786	−	0.204883i	$-0.934318\pi$
$223$	−11.5568	+	11.5568i	−0.773903	+	0.773903i	0.204883	+	0.978786i	$0.434318\pi$
$224$		0			0
$225$	13.8212	−	5.82883i	0.921411	−	0.388588i
$226$	14.5583			0.968402
$227$	10.0622	−	10.0622i	0.667853	−	0.667853i	−0.289366	−	0.957219i	$-0.593444\pi$
$227$	10.0622	−	10.0622i	0.667853	−	0.667853i	0.957219	+	0.289366i	$0.0934443\pi$
$228$	0.534001	+	0.697547i	0.0353651	+	0.0461962i
$229$		−	17.9816i		−	1.18826i	−0.804369	−	0.594129i	$-0.797497\pi$
$229$		−	17.9816i		−	1.18826i	0.804369	−	0.594129i	$-0.202503\pi$
$230$	−3.17876	+	6.51680i	−0.209601	+	0.429705i
$231$		0			0
$232$	−1.08381	−	1.08381i	−0.0711559	−	0.0711559i
$233$	8.18223	+	8.18223i	0.536036	+	0.536036i	0.922362	−	0.386326i	$-0.126256\pi$
$233$	8.18223	+	8.18223i	0.536036	+	0.536036i	−0.386326	+	0.922362i	$0.626256\pi$
$234$	8.43171	+	2.27962i	0.551198	+	0.149023i
$235$	3.85080	+	11.1849i	0.251198	+	0.729623i
$236$		−	0.141298i		−	0.00919771i
$237$	−6.94865	+	5.31947i	−0.451363	+	0.345537i
$238$		0			0
$239$	24.0516			1.55577			0.777885	−	0.628407i	$-0.216293\pi$
$239$	24.0516			1.55577			0.777885	+	0.628407i	$0.216293\pi$
$240$	−12.8322	+	2.59521i	−0.828317	+	0.167520i
$241$	1.41457			0.0911206			0.0455603	−	0.998962i	$-0.485493\pi$
$241$	1.41457			0.0911206			0.0455603	+	0.998962i	$0.485493\pi$
$242$	3.95224	−	3.95224i	0.254060	−	0.254060i
$243$	1.94772	+	15.4663i	0.124947	+	0.992163i
$244$			1.39300i			0.0891778i
$245$		0			0
$246$	−0.0924390	+	0.696091i	−0.00589370	+	0.0443811i
$247$	−2.91385	−	2.91385i	−0.185404	−	0.185404i
$248$	−18.1274	−	18.1274i	−1.15109	−	1.15109i
$249$	2.95397	−	22.2442i	0.187200	−	1.40967i
$250$	8.00442	−	12.3226i	0.506244	−	0.779352i
$251$			10.8892i			0.687318i	0.939094	+	0.343659i	$0.111666\pi$
$251$			10.8892i			0.687318i	−0.939094	+	0.343659i	$0.888334\pi$
$252$		0			0
$253$	−6.81345	+	6.81345i	−0.428358	+	0.428358i
$254$	−15.0998			−0.947445
$255$	−5.73423	+	8.64162i	−0.359092	+	0.541159i
$256$	−6.41659			−0.401037
$257$	−14.0408	+	14.0408i	−0.875843	+	0.875843i	−0.993101	−	0.117259i	$-0.962589\pi$
$257$	−14.0408	+	14.0408i	−0.875843	+	0.875843i	0.117259	+	0.993101i	$0.462589\pi$
$258$	19.4504	−	14.8901i	1.21093	−	0.927017i
$259$		0			0
$260$	−1.27702	+	0.439660i	−0.0791977	+	0.0272666i
$261$	−0.401786	+	1.48610i	−0.0248699	+	0.0919874i
$262$	4.08509	+	4.08509i	0.252378	+	0.252378i
$263$	−18.5408	−	18.5408i	−1.14328	−	1.14328i	−0.987847	−	0.155429i	$-0.950324\pi$
$263$	−18.5408	−	18.5408i	−1.14328	−	1.14328i	−0.155429	−	0.987847i	$-0.549676\pi$
$264$	−20.0291	−	2.65981i	−1.23271	−	0.163700i
$265$	4.07024	−	1.40132i	0.250033	−	0.0860825i
$266$		0			0
$267$	−11.9504	−	15.6103i	−0.731350	−	0.955337i
$268$	−1.74556	+	1.74556i	−0.106627	+	0.106627i
$269$	0.482142			0.0293967			0.0146984	−	0.999892i	$-0.495321\pi$
$269$	0.482142			0.0293967			0.0146984	+	0.999892i	$0.495321\pi$
$270$	10.0795	+	11.4715i	0.613420	+	0.698132i
$271$	5.93166			0.360323			0.180161	−	0.983637i	$-0.442338\pi$
$271$	5.93166			0.360323			0.180161	+	0.983637i	$0.442338\pi$
$272$	6.40065	−	6.40065i	0.388097	−	0.388097i
$273$		0			0
$274$		−	8.74466i		−	0.528284i
$275$	15.3887	−	12.0211i	0.927974	−	0.724898i
$276$	1.15501	+	0.153383i	0.0695236	+	0.00923254i
$277$	−9.58848	−	9.58848i	−0.576116	−	0.576116i	0.357715	−	0.933831i	$-0.383556\pi$
$277$	−9.58848	−	9.58848i	−0.576116	−	0.576116i	−0.933831	+	0.357715i	$0.883556\pi$
$278$	11.4731	+	11.4731i	0.688112	+	0.688112i
$279$	−6.72010	+	24.8559i	−0.402322	+	1.48808i
$280$		0			0
$281$			12.2359i			0.729932i	0.931021	+	0.364966i	$0.118919\pi$
$281$			12.2359i			0.729932i	−0.931021	+	0.364966i	$0.881081\pi$
$282$	−9.56232	+	7.32035i	−0.569428	+	0.435920i
$283$	−14.4727	+	14.4727i	−0.860312	+	0.860312i	−0.991374	−	0.131063i	$-0.958161\pi$
$283$	−14.4727	+	14.4727i	−0.860312	+	0.860312i	0.131063	+	0.991374i	$0.458161\pi$
$284$	−4.19205			−0.248753
$285$	−1.42813	−	7.06152i	−0.0845952	−	0.418289i
$286$	11.3707			0.672364
$287$		0			0
$288$	2.28768	+	3.98305i	0.134803	+	0.234704i
$289$			9.82939i			0.578200i
$290$	0.490925	+	1.42593i	0.0288281	+	0.0837332i
$291$	−2.19903	+	16.5593i	−0.128909	+	0.970721i
$292$	−0.558617	−	0.558617i	−0.0326906	−	0.0326906i
$293$	−18.3002	−	18.3002i	−1.06911	−	1.06911i	−0.997427	−	0.0716843i	$-0.977163\pi$
$293$	−18.3002	−	18.3002i	−1.06911	−	1.06911i	−0.0716843	−	0.997427i	$-0.522837\pi$
$294$		0			0
$295$	−0.508022	+	1.04150i	−0.0295782	+	0.0606384i
$296$		−	20.4307i		−	1.18751i
$297$	7.70264	+	18.7748i	0.446952	+	1.08942i
$298$	9.13786	−	9.13786i	0.529342	−	0.529342i
$299$	−5.46553			−0.316080
$300$	−2.28534	−	0.593960i	−0.131944	−	0.0342923i
$301$		0			0
$302$	−1.05113	+	1.05113i	−0.0604858	+	0.0604858i
$303$	6.28708	−	4.81301i	0.361183	−	0.276500i
$304$			6.28809i			0.360647i
$305$	5.00839	−	10.2677i	0.286780	−	0.587928i
$306$	−10.1922	−	2.75560i	−0.582651	−	0.157527i
$307$	19.2900	+	19.2900i	1.10094	+	1.10094i	0.994298	+	0.106640i	$0.0340093\pi$
$307$	19.2900	+	19.2900i	1.10094	+	1.10094i	0.106640	+	0.994298i	$0.465991\pi$
$308$		0			0
$309$	−17.4083	−	2.31178i	−0.990324	−	0.131512i
$310$	8.21099	+	23.8494i	0.466353	+	1.35456i
$311$			25.3688i			1.43853i	0.694734	+	0.719266i	$0.255522\pi$
$311$			25.3688i			1.43853i	−0.694734	+	0.719266i	$0.744478\pi$
$312$	−6.96654	−	9.10016i	−0.394403	−	0.515195i
$313$	−17.3199	+	17.3199i	−0.978979	+	0.978979i	−0.999784	−	0.0208044i	$-0.993377\pi$
$313$	−17.3199	+	17.3199i	−0.978979	+	0.978979i	0.0208044	+	0.999784i	$0.493377\pi$
$314$	24.6011			1.38832
$315$		0			0
$316$	1.37757			0.0774942
$317$	8.52170	−	8.52170i	0.478626	−	0.478626i	−0.426066	−	0.904692i	$-0.640101\pi$
$317$	8.52170	−	8.52170i	0.478626	−	0.478626i	0.904692	+	0.426066i	$0.140101\pi$
$318$	2.66390	+	3.47977i	0.149384	+	0.195136i
$319$			2.00411i			0.112208i
$320$	17.6313	+	8.60020i	0.985620	+	0.480766i
$321$	−3.03512	−	0.403056i	−0.169404	−	0.0224964i
$322$		0			0
$323$	3.52225	+	3.52225i	0.195983	+	0.195983i
$324$	1.23650	−	2.11960i	0.0686945	−	0.117755i
$325$	10.9936	+	1.35070i	0.609816	+	0.0749232i
$326$		−	17.1208i		−	0.948234i
$327$	7.39389	−	5.66033i	0.408883	−	0.313017i
$328$	0.651508	−	0.651508i	0.0359735	−	0.0359735i
$329$		0			0
$330$	16.5646	+	10.9916i	0.911851	+	0.605068i
$331$	−9.74810			−0.535804			−0.267902	−	0.963446i	$-0.586330\pi$
$331$	−9.74810			−0.535804			−0.267902	+	0.963446i	$0.586330\pi$
$332$	−2.49776	+	2.49776i	−0.137083	+	0.137083i
$333$	−17.7940	+	10.2201i	−0.975107	+	0.560056i
$334$			4.54284i			0.248573i
$335$	19.1424	−	6.59044i	1.04586	−	0.360074i
$336$		0			0
$337$	10.5951	+	10.5951i	0.577152	+	0.577152i	0.934117	−	0.356966i	$-0.116189\pi$
$337$	10.5951	+	10.5951i	0.577152	+	0.577152i	−0.356966	+	0.934117i	$0.616189\pi$
$338$	−7.52081	−	7.52081i	−0.409078	−	0.409078i
$339$	−2.52566	+	19.0189i	−0.137175	+	1.03296i
$340$	1.54366	−	0.531460i	0.0837169	−	0.0288225i
$341$			33.5198i			1.81520i
$342$	6.36007	−	3.65293i	0.343913	−	0.197528i
$343$		0			0
$344$	−32.1411			−1.73293
$345$	−7.96206	−	5.28330i	−0.428663	−	0.284443i
$346$	12.5576			0.675101
$347$	15.2587	−	15.2587i	0.819131	−	0.819131i	−0.166851	−	0.985982i	$-0.553360\pi$
$347$	15.2587	−	15.2587i	0.819131	−	0.819131i	0.985982	+	0.166851i	$0.0533599\pi$
$348$	0.192425	−	0.147310i	0.0103151	−	0.00789662i
$349$		−	28.5116i		−	1.52619i	−0.646287	−	0.763094i	$-0.723679\pi$
$349$		−	28.5116i		−	1.52619i	0.646287	−	0.763094i	$-0.276321\pi$
$350$		0			0
$351$	−4.44087	+	10.6197i	−0.237036	+	0.566836i
$352$	4.22825	+	4.22825i	0.225366	+	0.225366i
$353$	8.68684	+	8.68684i	0.462354	+	0.462354i	0.899426	−	0.437072i	$-0.143985\pi$
$353$	8.68684	+	8.68684i	0.462354	+	0.462354i	−0.437072	+	0.899426i	$0.643985\pi$
$354$	−1.16943	−	0.155298i	−0.0621547	−	0.00825398i
$355$	30.8994	+	15.0721i	1.63997	+	0.799944i
$356$			3.09474i			0.164021i
$357$		0			0
$358$	−10.0188	+	10.0188i	−0.529512	+	0.529512i
$359$	4.81570			0.254163			0.127081	−	0.991892i	$-0.459439\pi$
$359$	4.81570			0.254163			0.127081	+	0.991892i	$0.459439\pi$
$360$	−1.35196	−	19.9912i	−0.0712543	−	1.05363i
$361$	15.5397			0.817878
$362$	2.66385	−	2.66385i	0.140009	−	0.140009i
$363$	4.47753	+	5.84885i	0.235010	+	0.306985i
$364$		0			0
$365$	2.10908	+	6.12598i	0.110394	+	0.320648i
$366$	11.5290	+	1.53102i	0.602630	+	0.0800277i
$367$	10.1328	+	10.1328i	0.528930	+	0.528930i	0.920253	−	0.391323i	$-0.127983\pi$
$367$	10.1328	+	10.1328i	0.528930	+	0.528930i	−0.391323	+	0.920253i	$0.627983\pi$
$368$	5.89731	+	5.89731i	0.307419	+	0.307419i
$369$	−0.893334	−	0.241524i	−0.0465051	−	0.0125732i
$370$	−8.81272	+	18.0670i	−0.458151	+	0.939259i
$371$		0			0
$372$	3.21842	−	2.46384i	0.166868	−	0.127744i
$373$	−0.824685	+	0.824685i	−0.0427006	+	0.0427006i	−0.728135	−	0.685434i	$-0.759612\pi$
$373$	−0.824685	+	0.824685i	−0.0427006	+	0.0427006i	0.685434	+	0.728135i	$0.259612\pi$
$374$	−13.7449			−0.710731
$375$	14.7096	+	12.5947i	0.759600	+	0.650390i
$376$	15.8014			0.814894
$377$	−0.803814	+	0.803814i	−0.0413985	+	0.0413985i
$378$		0			0
$379$		−	24.8744i		−	1.27771i	−0.769326	−	0.638856i	$-0.779408\pi$
$379$		−	24.8744i		−	1.27771i	0.769326	−	0.638856i	$-0.220592\pi$
$380$	−0.497202	+	1.01932i	−0.0255059	+	0.0522898i
$381$	2.61960	−	19.7263i	0.134206	−	1.01061i
$382$	−13.0167	−	13.0167i	−0.665995	−	0.665995i
$383$	−1.25751	−	1.25751i	−0.0642557	−	0.0642557i	0.674249	−	0.738504i	$-0.264468\pi$
$383$	−1.25751	−	1.25751i	−0.0642557	−	0.0642557i	−0.738504	+	0.674249i	$0.764468\pi$
$384$	−1.93079	+	14.5394i	−0.0985304	+	0.741961i
$385$		0			0
$386$		−	12.4981i		−	0.636137i
$387$	16.0780	+	27.9932i	0.817291	+	1.42297i
$388$	1.85941	−	1.85941i	0.0943973	−	0.0943973i
$389$	−25.8311			−1.30969			−0.654843	−	0.755765i	$-0.727265\pi$
$389$	−25.8311			−1.30969			−0.654843	+	0.755765i	$0.727265\pi$
$390$	2.23524	+	11.0523i	0.113186	+	0.559657i
$391$	6.60672			0.334116
$392$		0			0
$393$	−6.04545	+	4.62804i	−0.304953	+	0.233454i
$394$			9.83625i			0.495543i
$395$	−10.1540	−	4.95290i	−0.510901	−	0.249207i
$396$	0.833751	−	3.08383i	0.0418976	−	0.154968i
$397$	−16.8078	−	16.8078i	−0.843557	−	0.843557i	0.145763	−	0.989320i	$-0.453436\pi$
$397$	−16.8078	−	16.8078i	−0.843557	−	0.843557i	−0.989320	+	0.145763i	$0.953436\pi$
$398$	9.59353	+	9.59353i	0.480880	+	0.480880i
$399$		0			0
$400$	−10.4047	−	13.3195i	−0.520237	−	0.665977i
$401$		−	8.01577i		−	0.400289i	−0.979766	−	0.200144i	$-0.935859\pi$
$401$		−	8.01577i		−	0.400289i	0.979766	−	0.200144i	$-0.0641411\pi$
$402$	12.5284	+	16.3654i	0.624859	+	0.816232i
$403$	−13.4442	+	13.4442i	−0.669706	+	0.669706i
$404$	−1.24641			−0.0620112
$405$	−16.7350	+	11.1777i	−0.831567	+	0.555424i
$406$		0			0
$407$	−18.8894	+	18.8894i	−0.936313	+	0.936313i
$408$	8.42115	+	11.0003i	0.416909	+	0.544594i
$409$			15.1177i			0.747521i	0.927525	+	0.373761i	$0.121932\pi$
$409$			15.1177i			0.747521i	−0.927525	+	0.373761i	$0.878068\pi$
$410$	−0.857161	+	0.295107i	−0.0423321	+	0.0145743i
$411$	11.4240	+	1.51708i	0.563504	+	0.0748319i
$412$	1.95475	+	1.95475i	0.0963036	+	0.0963036i
$413$		0			0
$414$	2.53890	−	9.39073i	0.124780	−	0.461529i
$415$	27.3913	−	9.43042i	1.34459	−	0.462921i
$416$			3.39176i			0.166295i
$417$	−16.9789	+	12.9980i	−0.831459	+	0.636516i
$418$	6.75159	−	6.75159i	0.330231	−	0.330231i
$419$	−26.4645			−1.29287			−0.646437	−	0.762967i	$-0.723742\pi$
$419$	−26.4645			−1.29287			−0.646437	+	0.762967i	$0.723742\pi$
$420$		0			0
$421$	−10.4834			−0.510929			−0.255464	−	0.966818i	$-0.582228\pi$
$421$	−10.4834			−0.510929			−0.255464	+	0.966818i	$0.582228\pi$
$422$	4.03891	−	4.03891i	0.196611	−	0.196611i
$423$	−7.90435	−	13.7622i	−0.384323	−	0.669139i
$424$		−	5.75019i		−	0.279254i
$425$	−13.2891	−	1.63272i	−0.644615	−	0.0791986i
$426$	−4.60740	+	34.6950i	−0.223229	+	1.68098i
$427$		0			0
$428$	0.340809	+	0.340809i	0.0164736	+	0.0164736i
$429$	−1.97266	+	14.8547i	−0.0952408	+	0.717190i
$430$	28.4227	+	13.8640i	1.37066	+	0.668581i
$431$			5.72268i			0.275652i	0.990456	+	0.137826i	$0.0440114\pi$
$431$			5.72268i			0.275652i	−0.990456	+	0.137826i	$0.955989\pi$
$432$	16.2504	−	6.66695i	0.781846	−	0.320764i
$433$	−0.977454	+	0.977454i	−0.0469735	+	0.0469735i	−0.730203	−	0.683230i	$-0.760575\pi$
$433$	−0.977454	+	0.977454i	−0.0469735	+	0.0469735i	0.683230	+	0.730203i	$0.260575\pi$
$434$		0			0
$435$	−1.94799	+	0.393964i	−0.0933991	+	0.0188891i
$436$	−1.46584			−0.0702008
$437$	−3.24527	+	3.24527i	−0.155242	+	0.155242i
$438$	−5.23728	+	4.00935i	−0.250247	+	0.191574i
$439$			5.67940i			0.271063i	0.990773	+	0.135531i	$0.0432742\pi$
$439$			5.67940i			0.271063i	−0.990773	+	0.135531i	$0.956726\pi$
$440$	−8.49133	−	24.6637i	−0.404808	−	1.17579i
$441$		0			0
$442$	−5.51285	−	5.51285i	−0.262220	−	0.262220i
$443$	−15.9884	−	15.9884i	−0.759634	−	0.759634i	0.216622	−	0.976256i	$-0.430496\pi$
$443$	−15.9884	−	15.9884i	−0.759634	−	0.759634i	−0.976256	+	0.216622i	$0.930496\pi$
$444$	3.20212	+	0.425234i	0.151966	+	0.0201807i
$445$	11.1268	−	22.8112i	0.527462	−	1.08135i
$446$		−	21.4805i		−	1.01713i
$447$	10.3524	+	13.5230i	0.489651	+	0.639614i
$448$		0			0
$449$	32.0075			1.51053			0.755264	−	0.655420i	$-0.227509\pi$
$449$	32.0075			1.51053			0.755264	+	0.655420i	$0.227509\pi$
$450$	−7.42760	+	18.2615i	−0.350141	+	0.860856i
$451$	−1.20472			−0.0567280
$452$	2.13560	−	2.13560i	0.100450	−	0.100450i
$453$	−1.19084	−	1.55555i	−0.0559505	−	0.0730862i
$454$			18.7024i			0.877749i
$455$		0			0
$456$	−9.53993	−	1.26688i	−0.446748	−	0.0593270i
$457$	−4.67001	−	4.67001i	−0.218454	−	0.218454i	0.589393	−	0.807847i	$-0.299367\pi$
$457$	−4.67001	−	4.67001i	−0.218454	−	0.218454i	−0.807847	+	0.589393i	$0.799367\pi$
$458$	16.7110	+	16.7110i	0.780855	+	0.780855i
$459$	5.36811	−	12.8370i	0.250562	−	0.599182i
$460$	0.489667	+	1.42227i	0.0228308	+	0.0663138i
$461$		−	28.3844i		−	1.32199i	−0.750389	−	0.660996i	$-0.770134\pi$
$461$		−	28.3844i		−	1.32199i	0.750389	−	0.660996i	$-0.229866\pi$
$462$		0			0
$463$	−3.86974	+	3.86974i	−0.179842	+	0.179842i	−0.791287	−	0.611445i	$-0.790589\pi$
$463$	−3.86974	+	3.86974i	−0.179842	+	0.179842i	0.611445	+	0.791287i	$0.290589\pi$
$464$	1.73463			0.0805284
$465$	−32.5813	+	6.58928i	−1.51092	+	0.305570i
$466$	−15.2081			−0.704504
$467$	−5.83013	+	5.83013i	−0.269786	+	0.269786i	−0.829014	−	0.559228i	$-0.811098\pi$
$467$	−5.83013	+	5.83013i	−0.269786	+	0.269786i	0.559228	+	0.829014i	$0.311098\pi$
$468$	1.57128	−	0.902469i	0.0726323	−	0.0417167i
$469$		0			0
$470$	−13.9733	−	6.81589i	−0.644540	−	0.314393i
$471$	−4.26794	+	32.1387i	−0.196656	+	1.48087i
$472$	1.09453	+	1.09453i	0.0503800	+	0.0503800i
$473$	29.7165	+	29.7165i	1.36636	+	1.36636i
$474$	1.51406	−	11.4013i	0.0695429	−	0.523677i
$475$	7.32969	−	5.72568i	0.336309	−	0.262712i
$476$		0			0
$477$	−5.00811	+	2.87642i	−0.229305	+	0.131702i
$478$	−22.3521	+	22.3521i	−1.02236	+	1.02236i
$479$	21.7317			0.992946			0.496473	−	0.868052i	$-0.334628\pi$
$479$	21.7317			0.992946			0.496473	+	0.868052i	$0.334628\pi$
$480$	−3.27868	+	4.94105i	−0.149651	+	0.225527i
$481$	−15.1525			−0.690893
$482$	−1.31462	+	1.31462i	−0.0598792	+	0.0598792i
$483$		0			0
$484$		−	1.15953i		−	0.0527060i
$485$	−20.3909	+	7.02029i	−0.925905	+	0.318775i
$486$	−16.1835	−	12.5633i	−0.734100	−	0.569885i
$487$	6.39869	+	6.39869i	0.289952	+	0.289952i	0.837061	−	0.547109i	$-0.184272\pi$
$487$	6.39869	+	6.39869i	0.289952	+	0.289952i	−0.547109	+	0.837061i	$0.684272\pi$
$488$	−10.7906	−	10.7906i	−0.488467	−	0.488467i
$489$	22.3666	+	2.97022i	1.01145	+	0.134318i
$490$		0			0
$491$		−	28.9156i		−	1.30494i	−0.757814	−	0.652471i	$-0.773732\pi$
$491$		−	28.9156i		−	1.30494i	0.757814	−	0.652471i	$-0.226268\pi$
$492$	0.0885516	+	0.115672i	0.00399221	+	0.00521489i
$493$	0.971649	−	0.971649i	0.0437609	−	0.0437609i
$494$	5.41591			0.243673
$495$	−17.2331	+	19.7330i	−0.774571	+	0.886934i
$496$	29.0127			1.30271
$497$		0			0
$498$	17.9272	+	23.4177i	0.803336	+	1.04937i
$499$		−	32.2531i		−	1.44385i	−0.691973	−	0.721924i	$-0.743258\pi$
$499$		−	32.2531i		−	1.44385i	0.691973	−	0.721924i	$-0.256742\pi$
$500$	−0.633453	−	2.98184i	−0.0283289	−	0.133352i
$501$	−5.93475	−	0.788119i	−0.265145	−	0.0352106i
$502$	−10.1197	−	10.1197i	−0.451666	−	0.451666i
$503$	−7.21038	−	7.21038i	−0.321495	−	0.321495i	0.527845	−	0.849340i	$-0.323000\pi$
$503$	−7.21038	−	7.21038i	−0.321495	−	0.321495i	−0.849340	+	0.527845i	$0.823000\pi$
$504$		0			0
$505$	9.18722	+	4.48134i	0.408826	+	0.199417i
$506$		−	12.6640i		−	0.562984i
$507$	11.1299	−	8.52040i	0.494297	−	0.378404i
$508$	−2.21503	+	2.21503i	−0.0982763	+	0.0982763i
$509$	23.8747			1.05823			0.529113	−	0.848551i	$-0.322525\pi$
$509$	23.8747			1.05823			0.529113	+	0.848551i	$0.322525\pi$
$510$	−2.70195	−	13.3601i	−0.119645	−	0.591593i
$511$		0			0
$512$	17.9388	−	17.9388i	0.792789	−	0.792789i
$513$	3.66879	+	8.94250i	0.161981	+	0.394821i
$514$		−	26.0974i		−	1.15111i
$515$	−7.38025	−	21.4364i	−0.325213	−	0.944603i
$516$	0.668969	−	5.03752i	0.0294497	−	0.221764i
$517$	−14.6093	−	14.6093i	−0.642518	−	0.642518i
$518$		0			0
$519$	−2.17857	+	16.4052i	−0.0956285	+	0.720109i
$520$	6.48647	−	13.2979i	0.284450	−	0.583153i
$521$		−	21.1485i		−	0.926533i	−0.886219	−	0.463267i	$-0.846677\pi$
$521$		−	21.1485i		−	0.926533i	0.886219	−	0.463267i	$-0.153323\pi$
$522$	−1.00770	−	1.75449i	−0.0441057	−	0.0767919i
$523$	−11.7408	+	11.7408i	−0.513391	+	0.513391i	−0.915564	−	0.402173i	$-0.868255\pi$
$523$	−11.7408	+	11.7408i	−0.513391	+	0.513391i	0.402173	+	0.915564i	$0.368255\pi$
$524$	1.19851			0.0523571
$525$		0			0
$526$	34.4614			1.50259
$527$	16.2514	−	16.2514i	0.707921	−	0.707921i
$528$	18.1567	−	13.8997i	0.790169	−	0.604907i
$529$		−	16.9128i		−	0.735340i
$530$	−2.48033	+	5.08493i	−0.107739	+	0.220875i
$531$	0.405761	−	1.50080i	0.0176085	−	0.0651293i
$532$		0			0
$533$	−0.483193	−	0.483193i	−0.0209294	−	0.0209294i
$534$	25.6133	+	3.40137i	1.10839	+	0.147192i
$535$	−1.28674	−	3.73742i	−0.0556305	−	0.161583i
$536$		−	27.0432i		−	1.16809i
$537$	−11.3505	−	14.8267i	−0.489808	−	0.639820i
$538$	−0.448074	+	0.448074i	−0.0193178	+	0.0193178i
$539$		0			0
$540$	3.16138	+	0.204193i	0.136044	+	0.00878705i
$541$	40.5929			1.74523			0.872613	−	0.488412i	$-0.162424\pi$
$541$	40.5929			1.74523			0.872613	+	0.488412i	$0.162424\pi$
$542$	−5.51253	+	5.51253i	−0.236783	+	0.236783i
$543$	3.01791	+	3.94219i	0.129511	+	0.169175i
$544$		−	4.09996i		−	0.175784i
$545$	10.8046	+	5.27026i	0.462818	+	0.225753i
$546$		0			0
$547$	−7.28811	−	7.28811i	−0.311617	−	0.311617i	0.533919	−	0.845536i	$-0.320719\pi$
$547$	−7.28811	−	7.28811i	−0.311617	−	0.311617i	−0.845536	+	0.533919i	$0.820719\pi$
$548$	−1.28278	−	1.28278i	−0.0547977	−	0.0547977i
$549$	−4.00024	+	14.7958i	−0.170726	+	0.631471i
$550$	−3.12966	+	25.4730i	−0.133449	+	1.08617i
$551$			0.954562i			0.0406657i
$552$	−10.1352	+	7.75892i	−0.431383	+	0.330241i
$553$		0			0
$554$	17.8219			0.757181
$555$	−22.0738	−	14.6473i	−0.936980	−	0.621742i
$556$	3.36605			0.142752
$557$	−23.2752	+	23.2752i	−0.986201	+	0.986201i	−0.999906	−	0.0137054i	$-0.995637\pi$
$557$	−23.2752	+	23.2752i	−0.986201	+	0.986201i	0.0137054	+	0.999906i	$0.495637\pi$
$558$	−16.8543	−	29.3448i	−0.713500	−	1.24227i
$559$			23.8376i			1.00822i
$560$		0			0
$561$	2.38455	−	17.9563i	0.100676	−	0.758115i
$562$	−11.3713	−	11.3713i	−0.479669	−	0.479669i
$563$	9.97289	+	9.97289i	0.420307	+	0.420307i	0.885309	−	0.465002i	$-0.153946\pi$
$563$	9.97289	+	9.97289i	0.420307	+	0.420307i	−0.465002	+	0.885309i	$0.653946\pi$
$564$	−0.328882	+	2.47657i	−0.0138484	+	0.104282i
$565$	−23.4197	+	8.06305i	−0.985274	+	0.339215i
$566$		−	26.9001i		−	1.13069i
$567$		0			0
$568$	32.4729	−	32.4729i	1.36253	−	1.36253i
$569$	45.4260			1.90436			0.952178	−	0.305543i	$-0.0988381\pi$
$569$	45.4260			1.90436			0.952178	+	0.305543i	$0.0988381\pi$
$570$	7.88977	+	5.23534i	0.330466	+	0.219284i
$571$	22.0102			0.921097			0.460548	−	0.887635i	$-0.347653\pi$
$571$	22.0102			0.921097			0.460548	+	0.887635i	$0.347653\pi$
$572$	1.66800	−	1.66800i	0.0697428	−	0.0697428i
$573$	19.2633	−	14.7468i	0.804734	−	0.616057i
$574$		0			0
$575$	1.50433	−	12.2440i	0.0627347	−	0.510612i
$576$	−25.4068	−	6.86904i	−1.05862	−	0.286210i
$577$	−28.0618	−	28.0618i	−1.16823	−	1.16823i	−0.982625	−	0.185602i	$-0.940576\pi$
$577$	−28.0618	−	28.0618i	−1.16823	−	1.16823i	−0.185602	−	0.982625i	$-0.559424\pi$
$578$	−9.13485	−	9.13485i	−0.379959	−	0.379959i
$579$	16.3275	+	2.16825i	0.678547	+	0.0901093i
$580$	0.281189	+	0.137158i	0.0116757	+	0.00569518i
$581$		0			0
$582$	−13.3455	−	17.4328i	−0.553191	−	0.722614i
$583$	−5.31640	+	5.31640i	−0.220183	+	0.220183i
$584$	8.65442			0.358122
$585$	−14.8265	+	1.00268i	−0.613002	+	0.0414558i
$586$	34.0143			1.40512
$587$	2.66817	−	2.66817i	0.110127	−	0.110127i	−0.649896	−	0.760023i	$-0.725188\pi$
$587$	2.66817	−	2.66817i	0.110127	−	0.110127i	0.760023	+	0.649896i	$0.225188\pi$
$588$		0			0
$589$			15.9656i			0.657851i
$590$	−0.495781	−	1.44003i	−0.0204110	−	0.0592851i
$591$	−12.8500	−	1.70645i	−0.528580	−	0.0701940i
$592$	16.3496	+	16.3496i	0.671963	+	0.671963i
$593$	−8.53960	−	8.53960i	−0.350679	−	0.350679i	0.509683	−	0.860362i	$-0.329763\pi$
$593$	−8.53960	−	8.53960i	−0.350679	−	0.350679i	−0.860362	+	0.509683i	$0.829763\pi$
$594$	−24.6065	−	10.2898i	−1.00962	−	0.422196i
$595$		0			0
$596$		−	2.68092i		−	0.109815i
$597$	−14.1973	+	10.8686i	−0.581057	+	0.444823i
$598$	5.07933	−	5.07933i	0.207709	−	0.207709i
$599$	32.7277			1.33722			0.668610	−	0.743614i	$-0.266890\pi$
$599$	32.7277			1.33722			0.668610	+	0.743614i	$0.266890\pi$
$600$	22.3039	−	13.1019i	0.910553	−	0.534884i
$601$	−46.3697			−1.89146			−0.945729	−	0.324956i	$-0.894651\pi$
$601$	−46.3697			−1.89146			−0.945729	+	0.324956i	$0.894651\pi$
$602$		0			0
$603$	−23.5532	+	13.5279i	−0.959161	+	0.550898i
$604$			0.308388i			0.0125481i
$605$	−4.16898	+	8.54684i	−0.169493	+	0.347479i
$606$	−1.36990	+	10.3158i	−0.0556486	+	0.419049i
$607$	11.4745	+	11.4745i	0.465736	+	0.465736i	0.900530	−	0.434794i	$-0.143179\pi$
$607$	11.4745	+	11.4745i	0.465736	+	0.465736i	−0.434794	+	0.900530i	$0.643179\pi$
$608$	2.01393	+	2.01393i	0.0816756	+	0.0816756i
$609$		0			0
$610$	4.88771	+	14.1967i	0.197898	+	0.574808i
$611$		−	11.7191i		−	0.474106i
$612$	−1.89936	+	1.09090i	−0.0767770	+	0.0440971i
$613$	9.74729	−	9.74729i	0.393689	−	0.393689i	−0.482311	−	0.876000i	$-0.660202\pi$
$613$	9.74729	−	9.74729i	0.393689	−	0.393689i	0.876000	+	0.482311i	$0.160202\pi$
$614$	−35.8539			−1.44695
$615$	−0.236822	−	1.17099i	−0.00954959	−	0.0472188i
$616$		0			0
$617$	−10.5782	+	10.5782i	−0.425862	+	0.425862i	−0.887216	−	0.461354i	$-0.847364\pi$
$617$	−10.5782	+	10.5782i	−0.425862	+	0.425862i	0.461354	+	0.887216i	$0.347364\pi$
$618$	18.3267	−	14.0298i	0.737206	−	0.564362i
$619$		−	28.9289i		−	1.16275i	−0.813636	−	0.581375i	$-0.802515\pi$
$619$		−	28.9289i		−	1.16275i	0.813636	−	0.581375i	$-0.197485\pi$
$620$	4.70304	+	2.29405i	0.188879	+	0.0921312i
$621$	11.8276	+	4.94597i	0.474623	+	0.198475i
$622$	−23.5762	−	23.5762i	−0.945321	−	0.945321i
$623$		0			0
$624$	12.8573	+	1.70742i	0.514704	+	0.0683514i
$625$	−6.05175	+	24.2565i	−0.242070	+	0.970259i
$626$		−	32.1922i		−	1.28666i
$627$	7.64895	+	9.99156i	0.305470	+	0.399024i
$628$	3.60880	−	3.60880i	0.144007	−	0.144007i
$629$	18.3163			0.730318
$630$		0			0
$631$	−4.13783			−0.164724			−0.0823622	−	0.996602i	$-0.526246\pi$
$631$	−4.13783			−0.164724			−0.0823622	+	0.996602i	$0.526246\pi$
$632$	−10.6710	+	10.6710i	−0.424471	+	0.424471i
$633$	4.57573	+	5.97712i	0.181869	+	0.237569i
$634$			15.8391i			0.629051i
$635$	24.2908	−	8.36296i	0.963952	−	0.331874i
$636$	0.901234	+	0.119681i	0.0357362	+	0.00474568i
$637$		0			0
$638$	−1.86249	−	1.86249i	−0.0737369	−	0.0737369i
$639$	−44.5261	−	12.0382i	−1.76143	−	0.476223i
$640$	−17.9037	+	6.16397i	−0.707706	+	0.243652i
$641$		−	0.616587i		−	0.0243537i	−0.999926	−	0.0121769i	$-0.996124\pi$
$641$		−	0.616587i		−	0.0243537i	0.999926	−	0.0121769i	$-0.00387611\pi$
$642$	3.19523	−	2.44608i	0.126106	−	0.0965392i
$643$	−12.1411	+	12.1411i	−0.478799	+	0.478799i	−0.904747	−	0.425949i	$-0.859940\pi$
$643$	−12.1411	+	12.1411i	−0.478799	+	0.478799i	0.425949	+	0.904747i	$0.359940\pi$
$644$		0			0
$645$	−23.0428	+	34.7261i	−0.907310	+	1.36734i
$646$	−6.54674			−0.257578
$647$	−20.6057	+	20.6057i	−0.810094	+	0.810094i	−0.984648	−	0.174553i	$-0.944152\pi$
$647$	−20.6057	+	20.6057i	−0.810094	+	0.810094i	0.174553	+	0.984648i	$0.444152\pi$
$648$	6.84071	+	25.9973i	0.268728	+	1.02127i
$649$		−	2.02393i		−	0.0794462i
$650$	−11.4721	+	8.96155i	−0.449971	+	0.351501i
$651$		0			0
$652$	−2.51151	−	2.51151i	−0.0983581	−	0.0983581i
$653$	10.6984	+	10.6984i	0.418660	+	0.418660i	0.884742	−	0.466082i	$-0.154335\pi$
$653$	10.6984	+	10.6984i	0.418660	+	0.418660i	−0.466082	+	0.884742i	$0.654335\pi$
$654$	−1.61107	+	12.1318i	−0.0629979	+	0.474391i
$655$	−8.83413	−	4.30911i	−0.345178	−	0.168371i
$656$			1.04273i			0.0407119i
$657$	−4.32921	−	7.53753i	−0.168899	−	0.294067i
$658$		0			0
$659$	−6.05597			−0.235907			−0.117954	−	0.993019i	$-0.537633\pi$
$659$	−6.05597			−0.235907			−0.117954	+	0.993019i	$0.537633\pi$
$660$	4.04230	−	0.817520i	0.157346	−	0.0318219i
$661$	21.5585			0.838529			0.419264	−	0.907864i	$-0.362288\pi$
$661$	21.5585			0.838529			0.419264	+	0.907864i	$0.362288\pi$
$662$	9.05929	−	9.05929i	0.352099	−	0.352099i
$663$	8.15838	−	6.24557i	0.316845	−	0.242558i
$664$		−	38.6968i		−	1.50173i
$665$		0			0
$666$	7.03878	−	26.0346i	0.272747	−	1.00882i
$667$	0.895240	+	0.895240i	0.0346638	+	0.0346638i
$668$	0.666404	+	0.666404i	0.0257839	+	0.0257839i
$669$	28.0620	+	3.72656i	1.08494	+	0.144077i
$670$	−11.6650	+	23.9145i	−0.450660	+	0.923900i
$671$			19.9531i			0.770282i
$672$		0			0
$673$	14.8200	−	14.8200i	0.571271	−	0.571271i	−0.361213	−	0.932483i	$-0.617637\pi$
$673$	14.8200	−	14.8200i	0.571271	−	0.571271i	0.932483	+	0.361213i	$0.117637\pi$
$674$	−19.6929			−0.758542
$675$	−22.5682	−	12.8715i	−0.868651	−	0.495425i
$676$	−2.20650			−0.0848654
$677$	0.150664	−	0.150664i	0.00579050	−	0.00579050i	−0.704206	−	0.709996i	$-0.748697\pi$
$677$	0.150664	−	0.150664i	0.00579050	−	0.00579050i	0.709996	+	0.704206i	$0.248697\pi$
$678$	−15.3278	−	20.0222i	−0.588661	−	0.768948i
$679$		0			0
$680$	−7.84083	+	16.0745i	−0.300682	+	0.616430i
$681$	−24.4328	−	3.24461i	−0.936267	−	0.124334i
$682$	−31.1513	−	31.1513i	−1.19284	−	1.19284i
$683$	−27.2871	−	27.2871i	−1.04411	−	1.04411i	−0.998981	−	0.0451289i	$-0.985630\pi$
$683$	−27.2871	−	27.2871i	−1.04411	−	1.04411i	−0.0451289	−	0.998981i	$-0.514370\pi$
$684$	0.397118	−	1.46884i	0.0151842	−	0.0561624i
$685$	4.84320	+	14.0674i	0.185049	+	0.537488i
$686$		0			0
$687$	−24.7304	+	18.9321i	−0.943522	+	0.722305i
$688$	25.7208	−	25.7208i	0.980596	−	0.980596i
$689$	−4.26465			−0.162470
$690$	12.3094	−	2.48947i	0.468612	−	0.0947727i
$691$	−21.5273			−0.818937			−0.409469	−	0.912324i	$-0.634286\pi$
$691$	−21.5273			−0.818937			−0.409469	+	0.912324i	$0.634286\pi$
$692$	1.84211	−	1.84211i	0.0700266	−	0.0700266i
$693$		0			0
$694$			28.3611i			1.07657i
$695$	−24.8110	−	12.1023i	−0.941134	−	0.459066i
$696$	−0.349481	+	2.63169i	−0.0132470	+	0.0997538i
$697$	0.584083	+	0.584083i	0.0221237	+	0.0221237i
$698$	26.4969	+	26.4969i	1.00292	+	1.00292i
$699$	2.63840	−	19.8679i	0.0997934	−	0.751472i
$700$		0			0
$701$			5.55742i			0.209901i	0.994477	+	0.104951i	$0.0334684\pi$
$701$			5.55742i			0.209901i	−0.994477	+	0.104951i	$0.966532\pi$
$702$	−5.74221	−	13.9964i	−0.216726	−	0.528259i
$703$	−8.99709	+	8.99709i	−0.339332	+	0.339332i
$704$	−34.2627			−1.29132
$705$	11.3284	−	17.0722i	0.426653	−	0.642976i
$706$	−16.1461			−0.607665
$707$		0			0
$708$	−0.194329	+	0.148767i	−0.00730333	+	0.00559100i
$709$		−	38.9725i		−	1.46364i	−0.681496	−	0.731822i	$-0.738670\pi$
$709$		−	38.9725i		−	1.46364i	0.681496	−	0.731822i	$-0.261330\pi$
$710$	−42.7231	+	14.7089i	−1.60337	+	0.552016i
$711$	14.6319	+	3.95592i	0.548739	+	0.148358i
$712$	−23.9728	−	23.9728i	−0.898419	−	0.898419i
$713$	14.9734	+	14.9734i	0.560758	+	0.560758i
$714$		0			0
$715$	−18.2919	+	6.29763i	−0.684078	+	0.235518i
$716$			2.93939i			0.109850i
$717$	−25.3230	−	33.0785i	−0.945704	−	1.23534i
$718$	−4.47542	+	4.47542i	−0.167021	+	0.167021i
$719$	12.7528			0.475599			0.237799	−	0.971314i	$-0.423574\pi$
$719$	12.7528			0.475599			0.237799	+	0.971314i	$0.423574\pi$
$720$	17.0798	+	14.9160i	0.636525	+	0.555885i
$721$		0			0
$722$	−14.4417	+	14.4417i	−0.537463	+	0.537463i
$723$	−1.48934	−	1.94548i	−0.0553893	−	0.0723532i
$724$		−	0.781537i		−	0.0290456i
$725$	−1.57949	−	2.02197i	−0.0586607	−	0.0750941i
$726$	−9.59672	−	1.27442i	−0.356168	−	0.0472981i
$727$	7.96907	+	7.96907i	0.295557	+	0.295557i	0.839271	−	0.543714i	$-0.182982\pi$
$727$	7.96907	+	7.96907i	0.295557	+	0.295557i	−0.543714	+	0.839271i	$0.682982\pi$
$728$		0			0
$729$	19.2203	−	18.9626i	0.711864	−	0.702317i
$730$	−7.65317	−	3.73306i	−0.283256	−	0.138167i
$731$		−	28.8148i		−	1.06575i
$732$	1.91581	−	1.46663i	0.0708105	−	0.0542083i
$733$	3.83455	−	3.83455i	0.141633	−	0.141633i	−0.632735	−	0.774368i	$-0.718068\pi$
$733$	3.83455	−	3.83455i	0.141633	−	0.141633i	0.774368	+	0.632735i	$0.218068\pi$
$734$	−18.8337			−0.695165
$735$		0			0
$736$	3.77754			0.139242
$737$	−25.0031	+	25.0031i	−0.921002	+	0.921002i
$738$	1.05467	−	0.605753i	0.0388229	−	0.0222981i
$739$			14.8832i			0.547486i	0.961803	+	0.273743i	$0.0882617\pi$
$739$			14.8832i			0.547486i	−0.961803	+	0.273743i	$0.911738\pi$
$740$	1.35754	+	3.94307i	0.0499041	+	0.144950i
$741$	−0.939584	+	7.07532i	−0.0345165	+	0.259918i
$742$		0			0
$743$	22.4301	+	22.4301i	0.822879	+	0.822879i	0.986520	−	0.163641i	$-0.0523239\pi$
$743$	22.4301	+	22.4301i	0.822879	+	0.822879i	−0.163641	+	0.986520i	$0.552324\pi$
$744$	−5.84527	+	44.0165i	−0.214298	+	1.61372i
$745$	−9.63898	+	19.7609i	−0.353145	+	0.723984i
$746$		−	1.53282i		−	0.0561207i
$747$	−33.7029	+	19.3574i	−1.23312	+	0.708249i
$748$	−2.01628	+	2.01628i	−0.0737225	+	0.0737225i
$749$		0			0
$750$	−25.3750	+	1.96541i	−0.926565	+	0.0717667i
$751$	−42.4130			−1.54767			−0.773836	−	0.633385i	$-0.781665\pi$
$751$	−42.4130			−1.54767			−0.773836	+	0.633385i	$0.781665\pi$
$752$	−12.6450	+	12.6450i	−0.461115	+	0.461115i
$753$	14.9760	−	11.4648i	0.545757	−	0.417799i
$754$		−	1.49403i		−	0.0544095i
$755$	1.10878	−	2.27311i	0.0403525	−	0.0827268i
$756$		0			0
$757$	13.4589	+	13.4589i	0.489171	+	0.489171i	0.908045	−	0.418873i	$-0.137575\pi$
$757$	13.4589	+	13.4589i	0.489171	+	0.489171i	−0.418873	+	0.908045i	$0.637575\pi$
$758$	23.1168	+	23.1168i	0.839639	+	0.839639i
$759$	16.5442	+	2.19703i	0.600517	+	0.0797471i
$760$	−4.04445	−	11.7474i	−0.146708	−	0.426123i
$761$			33.8362i			1.22656i	0.789866	+	0.613280i	$0.210150\pi$
$761$			33.8362i			1.22656i	−0.789866	+	0.613280i	$0.789850\pi$
$762$	15.8979	+	20.7669i	0.575922	+	0.752307i
$763$		0			0
$764$	−3.81893			−0.138164
$765$	17.9223	−	1.21204i	0.647982	−	0.0438214i
$766$	2.33731			0.0844503
$767$	0.811765	−	0.811765i	0.0293112	−	0.0293112i
$768$	6.75576	+	8.82482i	0.243778	+	0.318438i
$769$		−	3.27472i		−	0.118090i	−0.998255	−	0.0590448i	$-0.981195\pi$
$769$		−	3.27472i		−	0.118090i	0.998255	−	0.0590448i	$-0.0188055\pi$
$770$		0			0
$771$	34.0935	+	4.52753i	1.22785	+	0.163055i
$772$	−1.83339	−	1.83339i	−0.0659850	−	0.0659850i
$773$	−1.35034	−	1.35034i	−0.0485682	−	0.0485682i	0.682406	−	0.730974i	$-0.260934\pi$
$773$	−1.35034	−	1.35034i	−0.0485682	−	0.0485682i	−0.730974	+	0.682406i	$0.760934\pi$
$774$	−40.9571	−	11.0733i	−1.47217	−	0.398021i
$775$	−26.4178	−	33.8186i	−0.948956	−	1.21480i
$776$			28.8071i			1.03411i
$777$		0			0
$778$	24.0058	−	24.0058i	0.860651	−	0.860651i
$779$	−0.573812			−0.0205589
$780$	1.94920	+	1.29341i	0.0697924	+	0.0463114i
$781$	−60.0464			−2.14863
$782$	−6.13989	+	6.13989i	−0.219562	+	0.219562i
$783$	2.46688	−	1.01207i	0.0881591	−	0.0361686i
$784$		0			0
$785$	−39.5754	+	13.6252i	−1.41251	+	0.486304i
$786$	1.31726	−	9.91930i	0.0469850	−	0.353810i
$787$	15.8766	+	15.8766i	0.565941	+	0.565941i	0.930989	−	0.365048i	$-0.118947\pi$
$787$	15.8766	+	15.8766i	0.565941	+	0.565941i	−0.365048	+	0.930989i	$0.618947\pi$
$788$	1.44291	+	1.44291i	0.0514015	+	0.0514015i
$789$	−5.97858	+	45.0203i	−0.212843	+	1.60277i
$790$	14.0394	−	4.83356i	0.499500	−	0.171970i
$791$		0			0
$792$	17.4297	+	30.3467i	0.619339	+	1.07832i
$793$	−8.00288	+	8.00288i	−0.284191	+	0.284191i
$794$	31.2402			1.10867
$795$	−6.21264	−	4.12246i	−0.220340	−	0.146209i
$796$	2.81461			0.0997612
$797$	13.6812	−	13.6812i	0.484611	−	0.484611i	−0.421989	−	0.906601i	$-0.638668\pi$
$797$	13.6812	−	13.6812i	0.484611	−	0.484611i	0.906601	+	0.421989i	$0.138668\pi$
$798$		0			0
$799$			14.1661i			0.501160i
$800$	−7.59833	−	0.933546i	−0.268642	−	0.0330058i
$801$	−8.88708	+	32.8710i	−0.314010	+	1.16144i
$802$	7.44938	+	7.44938i	0.263047	+	0.263047i
$803$	−8.00154	−	8.00154i	−0.282368	−	0.282368i
$804$	4.23852	+	0.562864i	0.149481	+	0.0198507i
$805$		0			0
$806$		−	24.9885i		−	0.880184i
$807$	−0.507627	−	0.663096i	−0.0178693	−	0.0233421i
$808$	9.65506	−	9.65506i	0.339664	−	0.339664i
$809$	46.2731			1.62688			0.813438	−	0.581652i	$-0.197593\pi$
$809$	46.2731			1.62688			0.813438	+	0.581652i	$0.197593\pi$
$810$	5.16458	−	25.9403i	0.181465	−	0.911451i
$811$	29.6188			1.04006			0.520028	−	0.854149i	$-0.325922\pi$
$811$	29.6188			1.04006			0.520028	+	0.854149i	$0.325922\pi$
$812$		0			0
$813$	−6.24520	−	8.15790i	−0.219029	−	0.286110i
$814$		−	35.1094i		−	1.23058i
$815$	9.48230	+	27.5420i	0.332151	+	0.964755i
$816$	−15.5419	−	2.06392i	−0.544075	−	0.0722517i
$817$	14.1540	+	14.1540i	0.495187	+	0.495187i
$818$	−14.0495	−	14.0495i	−0.491228	−	0.491228i
$819$		0			0
$820$	−0.0824493	+	0.169030i	−0.00287925	+	0.00590277i
$821$		−	54.5990i		−	1.90552i	−0.303728	−	0.952759i	$-0.598231\pi$
$821$		−	54.5990i		−	1.90552i	0.303728	−	0.952759i	$-0.401769\pi$
$822$	−12.0267	+	9.20690i	−0.419478	+	0.321127i
$823$	24.8304	−	24.8304i	0.865532	−	0.865532i	−0.126442	−	0.991974i	$-0.540356\pi$
$823$	24.8304	−	24.8304i	0.865532	−	0.865532i	0.991974	+	0.126442i	$0.0403557\pi$
$824$	−30.2841			−1.05500
$825$	−32.7349	−	8.50779i	−1.13968	−	0.296203i
$826$		0			0
$827$	15.5901	−	15.5901i	0.542122	−	0.542122i	−0.382028	−	0.924151i	$-0.624774\pi$
$827$	15.5901	−	15.5901i	0.542122	−	0.542122i	0.924151	+	0.382028i	$0.124774\pi$
$828$	−1.00512	−	1.74999i	−0.0349302	−	0.0608165i
$829$		−	13.9384i		−	0.484099i	−0.970264	−	0.242050i	$-0.922180\pi$
$829$		−	13.9384i		−	0.484099i	0.970264	−	0.242050i	$-0.0778197\pi$
$830$	−16.6918	+	34.2199i	−0.579380	+	1.18779i
$831$	−3.09185	+	23.2825i	−0.107255	+	0.807661i
$832$	−13.7422	−	13.7422i	−0.476426	−	0.476426i
$833$		0			0
$834$	3.69956	−	27.8587i	0.128105	−	0.964668i
$835$	−2.51604	−	7.30801i	−0.0870710	−	0.252904i
$836$		−	1.98082i		−	0.0685082i
$837$	41.2600	−	16.9275i	1.42615	−	0.585100i
$838$	24.5945	−	24.5945i	0.849602	−	0.849602i
$839$	−8.40213			−0.290074			−0.145037	−	0.989426i	$-0.546330\pi$
$839$	−8.40213			−0.290074			−0.145037	+	0.989426i	$0.546330\pi$
$840$		0			0
$841$	−28.7367			−0.990920
$842$	9.74262	−	9.74262i	0.335753	−	0.335753i
$843$	16.8282	−	12.8827i	0.579593	−	0.443702i
$844$		−	1.18496i		−	0.0407881i
$845$	16.2640	+	7.93325i	0.559498	+	0.272912i
$846$	20.1355	+	5.44390i	0.692274	+	0.187165i
$847$		0			0
$848$	4.60156	+	4.60156i	0.158018	+	0.158018i
$849$	35.1422	+	4.66679i	1.20608	+	0.160164i
$850$	13.8674	−	10.8327i	0.475648	−	0.371559i
$851$			16.8759i			0.578499i
$852$	4.41364	+	5.76539i	0.151209	+	0.197519i
$853$	1.24579	−	1.24579i	0.0426549	−	0.0426549i	−0.685458	−	0.728113i	$-0.740398\pi$
$853$	1.24579	−	1.24579i	0.0426549	−	0.0426549i	0.728113	+	0.685458i	$0.240398\pi$
$854$		0			0
$855$	−8.20819	+	9.39892i	−0.280714	+	0.321436i
$856$	−5.28001			−0.180467
$857$	6.07380	−	6.07380i	0.207477	−	0.207477i	−0.595717	−	0.803194i	$-0.703132\pi$
$857$	6.07380	−	6.07380i	0.207477	−	0.207477i	0.803194	+	0.595717i	$0.203132\pi$
$858$	−11.9718	−	15.6383i	−0.408709	−	0.533882i
$859$			19.6568i			0.670682i	0.942097	+	0.335341i	$0.108851\pi$
$859$			19.6568i			0.670682i	−0.942097	+	0.335341i	$0.891149\pi$
$860$	6.20316	−	2.13565i	0.211526	−	0.0728252i
$861$		0			0
$862$	−5.31831	−	5.31831i	−0.181142	−	0.181142i
$863$	19.3016	+	19.3016i	0.657035	+	0.657035i	0.954677	−	0.297642i	$-0.0962003\pi$
$863$	19.3016	+	19.3016i	0.657035	+	0.657035i	−0.297642	+	0.954677i	$0.596200\pi$
$864$	3.06934	−	7.33987i	0.104421	−	0.249708i
$865$	−20.2012	+	6.95498i	−0.686862	+	0.236476i
$866$		−	1.81677i		−	0.0617365i
$867$	13.5185	−	10.3490i	0.459112	−	0.351469i
$868$		0			0
$869$	19.7321			0.669364
$870$	1.44422	−	2.17647i	0.0489637	−	0.0737894i
$871$	−20.0567			−0.679596
$872$	11.3548	−	11.3548i	0.384522	−	0.384522i
$873$	25.0895	−	14.4102i	0.849149	−	0.487712i
$874$		−	6.03191i		−	0.204032i
$875$		0			0
$876$	−0.180129	+	1.35642i	−0.00608598	+	0.0458291i
$877$	2.65855	+	2.65855i	0.0897730	+	0.0897730i	0.750567	−	0.660794i	$-0.229780\pi$
$877$	2.65855	+	2.65855i	0.0897730	+	0.0897730i	−0.660794	+	0.750567i	$0.729780\pi$
$878$	−5.27809	−	5.27809i	−0.178127	−	0.178127i
$879$	−5.90100	+	44.4362i	−0.199036	+	1.49879i
$880$	26.5322	+	12.9418i	0.894399	+	0.436270i
$881$			23.1988i			0.781586i	0.920479	+	0.390793i	$0.127799\pi$
$881$			23.1988i			0.781586i	−0.920479	+	0.390793i	$0.872201\pi$
$882$		0			0
$883$	−12.7408	+	12.7408i	−0.428761	+	0.428761i	−0.888206	−	0.459445i	$-0.848048\pi$
$883$	−12.7408	+	12.7408i	−0.428761	+	0.428761i	0.459445	+	0.888206i	$0.348048\pi$
$884$	−1.61740			−0.0543989
$885$	1.96726	−	0.397861i	0.0661288	−	0.0133740i
$886$	29.7174			0.998375
$887$	29.8372	−	29.8372i	1.00183	−	1.00183i	0.00183631	−	0.999998i	$-0.499415\pi$
$887$	29.8372	−	29.8372i	1.00183	−	1.00183i	0.999998	−	0.00183631i	$-0.000584516\pi$
$888$	−28.0986	+	21.5106i	−0.942927	+	0.721849i
$889$		0			0
$890$	10.8587	+	31.5399i	0.363985	+	1.05722i
$891$	17.7115	−	30.3608i	0.593356	−	1.01712i
$892$	−3.15103	−	3.15103i	−0.105504	−	0.105504i
$893$	−6.95848	−	6.95848i	−0.232857	−	0.232857i
$894$	−22.1883	−	2.94655i	−0.742088	−	0.0985473i
$895$	10.5683	−	21.6661i	0.353258	−	0.724217i
$896$		0			0
$897$	5.75443	+	7.51681i	0.192135	+	0.250979i
$898$	−29.7459	+	29.7459i	−0.992632	+	0.992632i
$899$	4.40427			0.146891
$900$	1.58926	+	3.76842i	0.0529754	+	0.125614i
$901$	5.15510			0.171741
$902$	1.11959	−	1.11959i	0.0372784	−	0.0372784i
$903$		0			0
$904$			33.0860i			1.10042i
$905$	−2.80994	+	5.76066i	−0.0934054	+	0.191491i
$906$	2.55233	+	0.338942i	0.0847955	+	0.0112606i
$907$	19.5239	+	19.5239i	0.648281	+	0.648281i	0.952577	−	0.304296i	$-0.0984213\pi$
$907$	19.5239	+	19.5239i	0.648281	+	0.648281i	−0.304296	+	0.952577i	$0.598421\pi$
$908$	2.74352	+	2.74352i	0.0910469	+	0.0910469i
$909$	−13.2388	−	3.57928i	−0.439104	−	0.118717i
$910$		0			0
$911$		−	34.8909i		−	1.15599i	−0.816042	−	0.577993i	$-0.803836\pi$
$911$		−	34.8909i		−	1.15599i	0.816042	−	0.577993i	$-0.196164\pi$
$912$	8.64810	−	6.62048i	0.286367	−	0.219226i
$913$	−35.7776	+	35.7776i	−1.18407	+	1.18407i
$914$	8.68004			0.287110
$915$	−19.3945	+	3.92236i	−0.641162	+	0.129669i
$916$	4.90279			0.161993
$917$		0			0
$918$	6.94117	+	16.9188i	0.229093	+	0.558403i
$919$			43.7641i			1.44364i	0.692078	+	0.721822i	$0.256695\pi$
$919$			43.7641i			1.44364i	−0.692078	+	0.721822i	$0.743305\pi$
$920$	−14.8104	−	7.22424i	−0.488286	−	0.238176i
$921$	6.22015	−	46.8394i	0.204961	−	1.54341i
$922$	26.3787	+	26.3787i	0.868737	+	0.868737i
$923$	−24.0836	−	24.0836i	−0.792722	−	0.792722i
$924$		0			0
$925$	4.17055	−	33.9450i	0.137127	−	1.11611i
$926$		−	7.19262i		−	0.236364i
$927$	15.1491	+	26.3759i	0.497561	+	0.866297i
$928$	0.555563	−	0.555563i	0.0182372	−	0.0182372i
$929$	−45.4522			−1.49124			−0.745619	−	0.666373i	$-0.767846\pi$
$929$	−45.4522			−1.49124			−0.745619	+	0.666373i	$0.767846\pi$
$930$	24.1554	−	36.4028i	0.792087	−	1.19369i
$931$		0			0
$932$	−2.23093	+	2.23093i	−0.0730765	+	0.0730765i
$933$	34.8901	−	26.7098i	1.14225	−	0.874439i
$934$		−	10.8363i		−	0.354576i
$935$	22.1112	−	7.61256i	0.723114	−	0.248957i
$936$	−5.18079	+	19.1624i	−0.169339	+	0.626342i
$937$	−28.5393	−	28.5393i	−0.932338	−	0.932338i	0.0655135	−	0.997852i	$-0.479131\pi$
$937$	−28.5393	−	28.5393i	−0.932338	−	0.932338i	−0.997852	+	0.0655135i	$0.979131\pi$
$938$		0			0
$939$	42.0557	+	5.58489i	1.37244	+	0.182256i
$940$	−3.04963	+	1.04994i	−0.0994679	+	0.0342453i
$941$		−	1.56805i		−	0.0511169i	−0.999673	−	0.0255585i	$-0.991864\pi$
$941$		−	1.56805i		−	0.0511169i	0.999673	−	0.0255585i	$-0.00813640\pi$
$942$	−25.9014	−	33.8342i	−0.843915	−	1.10238i
$943$	−0.538152	+	0.538152i	−0.0175246	+	0.0175246i
$944$	−1.75179			−0.0570160
$945$		0			0
$946$	−55.2334			−1.79579
$947$	−28.6990	+	28.6990i	−0.932594	+	0.932594i	−0.997867	−	0.0652736i	$-0.979208\pi$
$947$	−28.6990	+	28.6990i	−0.932594	+	0.932594i	0.0652736	+	0.997867i	$0.479208\pi$
$948$	−1.45038	−	1.89459i	−0.0471063	−	0.0615333i
$949$		−	6.41858i		−	0.208356i
$950$	−1.49067	+	12.1329i	−0.0483637	+	0.393642i
$951$	−20.6921	−	2.74786i	−0.670989	−	0.0891055i
$952$		0			0
$953$	31.1034	+	31.1034i	1.00754	+	1.00754i	0.999971	+	0.00756809i	$0.00240902\pi$
$953$	31.1034	+	31.1034i	1.00754	+	1.00754i	0.00756809	+	0.999971i	$0.497591\pi$
$954$	1.98106	−	7.32741i	0.0641391	−	0.237234i
$955$	28.1491	+	13.7306i	0.910885	+	0.444311i
$956$			6.55781i			0.212095i
$957$	2.75627	−	2.11004i	0.0890977	−	0.0682079i
$958$	−20.1961	+	20.1961i	−0.652507	+	0.652507i
$959$		0			0
$960$	−6.73532	−	33.3034i	−0.217381	−	1.07486i
$961$	42.6639			1.37625
$962$	14.0818	−	14.0818i	0.454015	−	0.454015i
$963$	2.64123	+	4.59860i	0.0851123	+	0.148188i
$964$			0.385691i			0.0124223i
$965$	6.92203	+	20.1055i	0.222828	+	0.647220i
$966$		0			0
$967$	−4.87814	−	4.87814i	−0.156870	−	0.156870i	0.624308	−	0.781178i	$-0.285381\pi$
$967$	−4.87814	−	4.87814i	−0.156870	−	0.156870i	−0.781178	+	0.624308i	$0.785381\pi$
$968$	8.98208	+	8.98208i	0.288695	+	0.288695i
$969$	1.13577	−	8.55264i	0.0364861	−	0.274750i
$970$	12.4259	−	25.4744i	0.398971	−	0.817932i
$971$		−	27.3732i		−	0.878449i	−0.898377	−	0.439224i	$-0.855253\pi$
$971$		−	27.3732i		−	0.878449i	0.898377	−	0.439224i	$-0.144747\pi$
$972$	−4.21697	+	0.531058i	−0.135259	+	0.0170337i
$973$		0			0
$974$	−11.8931			−0.381080
$975$	−9.71710	−	16.5418i	−0.311196	−	0.529761i
$976$	17.2703			0.552807
$977$	−0.221692	+	0.221692i	−0.00709254	+	0.00709254i	−0.710644	−	0.703552i	$-0.751596\pi$
$977$	−0.221692	+	0.221692i	−0.00709254	+	0.00709254i	0.703552	+	0.710644i	$0.251596\pi$
$978$	−23.5465	+	18.0258i	−0.752934	+	0.576402i
$979$			44.3287i			1.41675i
$980$		0			0
$981$	−15.5695	−	4.20940i	−0.497094	−	0.134396i
$982$	26.8724	+	26.8724i	0.857533	+	0.857533i
$983$	38.4867	+	38.4867i	1.22754	+	1.22754i	0.964893	+	0.262642i	$0.0845937\pi$
$983$	38.4867	+	38.4867i	1.22754	+	1.22754i	0.262642	+	0.964893i	$0.415406\pi$
$984$	−1.58197	−	0.210082i	−0.0504315	−	0.00669717i
$985$	−5.44777	−	15.8234i	−0.173580	−	0.504177i
$986$			1.80598i			0.0575143i
$987$		0			0
$988$	0.794476	−	0.794476i	0.0252756	−	0.0252756i
$989$	26.5489			0.844205
$990$	−2.32329	−	34.3541i	−0.0738389	−	1.09185i
$991$	5.75813			0.182913			0.0914565	−	0.995809i	$-0.470848\pi$
$991$	5.75813			0.182913			0.0914565	+	0.995809i	$0.470848\pi$
$992$	9.29210	−	9.29210i	0.295024	−	0.295024i
$993$	10.2634	+	13.4067i	0.325698	+	0.425448i
$994$		0			0
$995$	−20.7463	−	10.1196i	−0.657703	−	0.320814i
$996$	6.06500	+	0.805416i	0.192177	+	0.0255206i
$997$	25.5371	+	25.5371i	0.808769	+	0.808769i	0.984448	−	0.175679i	$-0.0562119\pi$
$997$	25.5371	+	25.5371i	0.808769	+	0.808769i	−0.175679	+	0.984448i	$0.556212\pi$
$998$	29.9741	+	29.9741i	0.948813	+	0.948813i
$999$	32.7904	+	13.7121i	1.03744	+	0.433831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.g.197.4		24
3.2	odd	2	inner	735.2.j.g.197.9		24
5.3	odd	4	inner	735.2.j.g.638.9		24
7.2	even	3		105.2.x.a.32.9	yes	48
7.3	odd	6		735.2.y.i.422.4		48
7.4	even	3		105.2.x.a.2.4	✓	48
7.5	odd	6		735.2.y.i.557.9		48
7.6	odd	2		735.2.j.e.197.4		24
15.8	even	4	inner	735.2.j.g.638.4		24
21.2	odd	6		105.2.x.a.32.4	yes	48
21.5	even	6		735.2.y.i.557.4		48
21.11	odd	6		105.2.x.a.2.9	yes	48
21.17	even	6		735.2.y.i.422.9		48
21.20	even	2		735.2.j.e.197.9		24
35.2	odd	12		525.2.bf.f.368.4		48
35.3	even	12		735.2.y.i.128.4		48
35.4	even	6		525.2.bf.f.107.9		48
35.9	even	6		525.2.bf.f.32.4		48
35.13	even	4		735.2.j.e.638.9		24
35.18	odd	12		105.2.x.a.23.4	yes	48
35.23	odd	12		105.2.x.a.53.9	yes	48
35.32	odd	12		525.2.bf.f.443.9		48
35.33	even	12		735.2.y.i.263.9		48
105.2	even	12		525.2.bf.f.368.9		48
105.23	even	12		105.2.x.a.53.4	yes	48
105.32	even	12		525.2.bf.f.443.4		48
105.38	odd	12		735.2.y.i.128.9		48
105.44	odd	6		525.2.bf.f.32.9		48
105.53	even	12		105.2.x.a.23.9	yes	48
105.68	odd	12		735.2.y.i.263.4		48
105.74	odd	6		525.2.bf.f.107.4		48
105.83	odd	4		735.2.j.e.638.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.x.a.2.4	✓	48	7.4	even	3
105.2.x.a.2.9	yes	48	21.11	odd	6
105.2.x.a.23.4	yes	48	35.18	odd	12
105.2.x.a.23.9	yes	48	105.53	even	12
105.2.x.a.32.4	yes	48	21.2	odd	6
105.2.x.a.32.9	yes	48	7.2	even	3
105.2.x.a.53.4	yes	48	105.23	even	12
105.2.x.a.53.9	yes	48	35.23	odd	12
525.2.bf.f.32.4		48	35.9	even	6
525.2.bf.f.32.9		48	105.44	odd	6
525.2.bf.f.107.4		48	105.74	odd	6
525.2.bf.f.107.9		48	35.4	even	6
525.2.bf.f.368.4		48	35.2	odd	12
525.2.bf.f.368.9		48	105.2	even	12
525.2.bf.f.443.4		48	105.32	even	12
525.2.bf.f.443.9		48	35.32	odd	12
735.2.j.e.197.4		24	7.6	odd	2
735.2.j.e.197.9		24	21.20	even	2
735.2.j.e.638.4		24	105.83	odd	4
735.2.j.e.638.9		24	35.13	even	4
735.2.j.g.197.4		24	1.1	even	1	trivial
735.2.j.g.197.9		24	3.2	odd	2	inner
735.2.j.g.638.4		24	15.8	even	4	inner
735.2.j.g.638.9		24	5.3	odd	4	inner
735.2.y.i.128.4		48	35.3	even	12
735.2.y.i.128.9		48	105.38	odd	12
735.2.y.i.263.4		48	105.68	odd	12
735.2.y.i.263.9		48	35.33	even	12
735.2.y.i.422.4		48	7.3	odd	6
735.2.y.i.422.9		48	21.17	even	6
735.2.y.i.557.4		48	21.5	even	6
735.2.y.i.557.9		48	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929340 + 0.929340i) q^{2} +(-1.05286 - 1.37531i) q^{3} +0.272655i q^{4} +(0.980304 - 2.00973i) q^{5} +(2.25660 + 0.299670i) q^{6} +(-2.11207 - 2.11207i) q^{8} +(-0.782976 + 2.89602i) q^{9} +O(q^{10})\)	\(q+(-0.929340 + 0.929340i) q^{2} +(-1.05286 - 1.37531i) q^{3} +0.272655i q^{4} +(0.980304 - 2.00973i) q^{5} +(2.25660 + 0.299670i) q^{6} +(-2.11207 - 2.11207i) q^{8} +(-0.782976 + 2.89602i) q^{9} +(0.956684 + 2.77876i) q^{10} +3.90548i q^{11} +(0.374987 - 0.287068i) q^{12} +(-1.56642 + 1.56642i) q^{13} +(-3.79613 + 0.767733i) q^{15} +3.38035 q^{16} +(1.89349 - 1.89349i) q^{17} +(-1.96374 - 3.41904i) q^{18} +1.86019i q^{19} +(0.547963 + 0.267285i) q^{20} +(-3.62951 - 3.62951i) q^{22} +(1.74459 + 1.74459i) q^{23} +(-0.681047 + 5.12847i) q^{24} +(-3.07801 - 3.94029i) q^{25} -2.91148i q^{26} +(4.80730 - 1.97227i) q^{27} +0.513153 q^{29} +(2.81441 - 4.24138i) q^{30} +8.58277 q^{31} +(1.08265 - 1.08265i) q^{32} +(5.37125 - 4.11191i) q^{33} +3.51939i q^{34} +(-0.789616 - 0.213483i) q^{36} +(4.83665 + 4.83665i) q^{37} +(-1.72875 - 1.72875i) q^{38} +(3.80355 + 0.505101i) q^{39} +(-6.31515 + 2.17421i) q^{40} +0.308469i q^{41} +(7.60892 - 7.60892i) q^{43} -1.06485 q^{44} +(5.05266 + 4.41255i) q^{45} -3.24263 q^{46} +(-3.74074 + 3.74074i) q^{47} +(-3.55903 - 4.64904i) q^{48} +(6.52238 + 0.801352i) q^{50} +(-4.59772 - 0.610565i) q^{51} +(-0.427094 - 0.427094i) q^{52} +(1.36127 + 1.36127i) q^{53} +(-2.63471 + 6.30052i) q^{54} +(7.84894 + 3.82855i) q^{55} +(2.55835 - 1.95852i) q^{57} +(-0.476893 + 0.476893i) q^{58} -0.518229 q^{59} +(-0.209327 - 1.03503i) q^{60} +5.10902 q^{61} +(-7.97631 + 7.97631i) q^{62} +8.77299i q^{64} +(1.61251 + 4.68365i) q^{65} +(-1.17035 + 8.81309i) q^{66} +(6.40207 + 6.40207i) q^{67} +(0.516270 + 0.516270i) q^{68} +(0.562551 - 4.23616i) q^{69} +15.3749i q^{71} +(7.77030 - 4.46290i) q^{72} +(-2.04880 + 2.04880i) q^{73} -8.98978 q^{74} +(-2.17843 + 8.38179i) q^{75} -0.507191 q^{76} +(-4.00420 + 3.06538i) q^{78} -5.05241i q^{79} +(3.31377 - 6.79358i) q^{80} +(-7.77390 - 4.53503i) q^{81} +(-0.286673 - 0.286673i) q^{82} +(9.16088 + 9.16088i) q^{83} +(-1.94920 - 5.66159i) q^{85} +14.1425i q^{86} +(-0.540277 - 0.705746i) q^{87} +(8.24863 - 8.24863i) q^{88} +11.3504 q^{89} +(-8.79640 + 0.594879i) q^{90} +(-0.475671 + 0.475671i) q^{92} +(-9.03644 - 11.8040i) q^{93} -6.95283i q^{94} +(3.73848 + 1.82355i) q^{95} +(-2.62885 - 0.349104i) q^{96} +(-6.81964 - 6.81964i) q^{97} +(-11.3103 - 3.05789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 12 q^{6}+O(q^{10}) \) 24 * q + 2 * q^3 - 12 * q^6	\( 24 q + 2 q^{3} - 12 q^{6} + 8 q^{10} + 10 q^{12} - 8 q^{13} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 4 q^{22} - 4 q^{25} + 20 q^{27} - 40 q^{30} + 24 q^{31} + 4 q^{33} + 4 q^{36} - 4 q^{37} + 16 q^{40} + 8 q^{43} - 40 q^{45} + 32 q^{46} + 22 q^{48} - 8 q^{51} - 36 q^{52} - 20 q^{55} - 44 q^{57} - 56 q^{58} + 50 q^{60} + 8 q^{61} - 76 q^{66} - 12 q^{67} + 34 q^{72} - 52 q^{73} - 6 q^{75} + 32 q^{76} - 60 q^{78} - 20 q^{81} - 104 q^{82} - 12 q^{85} + 46 q^{87} - 42 q^{90} + 44 q^{93} - 12 q^{96} - 60 q^{97}+O(q^{100}) \) 24 * q + 2 * q^3 - 12 * q^6 + 8 * q^10 + 10 * q^12 - 8 * q^13 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 4 * q^22 - 4 * q^25 + 20 * q^27 - 40 * q^30 + 24 * q^31 + 4 * q^33 + 4 * q^36 - 4 * q^37 + 16 * q^40 + 8 * q^43 - 40 * q^45 + 32 * q^46 + 22 * q^48 - 8 * q^51 - 36 * q^52 - 20 * q^55 - 44 * q^57 - 56 * q^58 + 50 * q^60 + 8 * q^61 - 76 * q^66 - 12 * q^67 + 34 * q^72 - 52 * q^73 - 6 * q^75 + 32 * q^76 - 60 * q^78 - 20 * q^81 - 104 * q^82 - 12 * q^85 + 46 * q^87 - 42 * q^90 + 44 * q^93 - 12 * q^96 - 60 * q^97

Introduction

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