LMFDB - Embedded newform 349.2.b.b.348.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(348,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.348");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			348.1
Character	$\chi$	$=$	349.348
Dual form			349.2.b.b.348.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74676i q^{2} -1.22099 q^{3} -5.54469 q^{4} +1.97385 q^{5} +3.35376i q^{6} +4.26150i q^{7} +9.73641i q^{8} -1.50918 q^{9} +O(q^{10})$	\(q-2.74676i q^{2} -1.22099 q^{3} -5.54469 q^{4} +1.97385 q^{5} +3.35376i q^{6} +4.26150i q^{7} +9.73641i q^{8} -1.50918 q^{9} -5.42170i q^{10} +1.84168i q^{11} +6.77001 q^{12} +2.52154i q^{13} +11.7053 q^{14} -2.41005 q^{15} +15.6542 q^{16} -6.77195 q^{17} +4.14537i q^{18} +3.45109 q^{19} -10.9444 q^{20} -5.20324i q^{21} +5.05866 q^{22} -6.52379 q^{23} -11.8881i q^{24} -1.10390 q^{25} +6.92606 q^{26} +5.50567 q^{27} -23.6287i q^{28} -7.41665 q^{29} +6.61984i q^{30} +4.26560 q^{31} -23.5255i q^{32} -2.24867i q^{33} +18.6009i q^{34} +8.41157i q^{35} +8.36796 q^{36} +8.41906 q^{37} -9.47931i q^{38} -3.07877i q^{39} +19.2182i q^{40} -0.301843 q^{41} -14.2921 q^{42} -2.13344i q^{43} -10.2116i q^{44} -2.97891 q^{45} +17.9193i q^{46} +1.97103i q^{47} -19.1136 q^{48} -11.1604 q^{49} +3.03216i q^{50} +8.26848 q^{51} -13.9811i q^{52} +13.5342i q^{53} -15.1227i q^{54} +3.63521i q^{55} -41.4917 q^{56} -4.21374 q^{57} +20.3718i q^{58} -2.00413i q^{59} +13.3630 q^{60} -5.31818i q^{61} -11.7166i q^{62} -6.43139i q^{63} -33.3105 q^{64} +4.97714i q^{65} -6.17657 q^{66} +10.4952 q^{67} +37.5484 q^{68} +7.96547 q^{69} +23.1046 q^{70} +10.9996i q^{71} -14.6940i q^{72} -3.20663 q^{73} -23.1251i q^{74} +1.34786 q^{75} -19.1352 q^{76} -7.84832 q^{77} -8.45664 q^{78} +4.65786i q^{79} +30.8991 q^{80} -2.19481 q^{81} +0.829090i q^{82} +3.81054 q^{83} +28.8504i q^{84} -13.3668 q^{85} -5.86005 q^{86} +9.05565 q^{87} -17.9314 q^{88} -6.10532i q^{89} +8.18235i q^{90} -10.7455 q^{91} +36.1724 q^{92} -5.20826 q^{93} +5.41393 q^{94} +6.81194 q^{95} +28.7244i q^{96} +7.67014i q^{97} +30.6548i q^{98} -2.77944i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	$ 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) $ 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	2.74676i		−	1.94225i	−0.238566	−	0.971126i	$-0.576677\pi$
$2$		−	2.74676i		−	1.94225i	0.238566	−	0.971126i	$-0.423323\pi$
$3$	−1.22099			−0.704939			−0.352469	−	0.935823i	$-0.614658\pi$
$3$	−1.22099			−0.704939			−0.352469	+	0.935823i	$0.614658\pi$
$4$	−5.54469			−2.77234
$5$	1.97385			0.882734			0.441367	−	0.897327i	$-0.354494\pi$
$5$	1.97385			0.882734			0.441367	+	0.897327i	$0.354494\pi$
$6$			3.35376i			1.36917i
$7$			4.26150i			1.61069i	0.592803	+	0.805347i	$0.298021\pi$
$7$			4.26150i			1.61069i	−0.592803	+	0.805347i	$0.701979\pi$
$8$			9.73641i			3.44234i
$9$	−1.50918			−0.503062
$10$		−	5.42170i		−	1.71449i
$11$			1.84168i			0.555288i	0.960684	+	0.277644i	$0.0895536\pi$
$11$			1.84168i			0.555288i	−0.960684	+	0.277644i	$0.910446\pi$
$12$	6.77001			1.95433
$13$			2.52154i			0.699349i	0.936871	+	0.349674i	$0.113708\pi$
$13$			2.52154i			0.699349i	−0.936871	+	0.349674i	$0.886292\pi$
$14$	11.7053			3.12838
$15$	−2.41005			−0.622273
$16$	15.6542			3.91355
$17$	−6.77195			−1.64244			−0.821220	−	0.570612i	$-0.806706\pi$
$17$	−6.77195			−1.64244			−0.821220	+	0.570612i	$0.806706\pi$
$18$			4.14537i			0.977073i
$19$	3.45109			0.791734			0.395867	−	0.918308i	$-0.370444\pi$
$19$	3.45109			0.791734			0.395867	+	0.918308i	$0.370444\pi$
$20$	−10.9444			−2.44724
$21$		−	5.20324i		−	1.13544i
$22$	5.05866			1.07851
$23$	−6.52379			−1.36030			−0.680152	−	0.733071i	$-0.738086\pi$
$23$	−6.52379			−1.36030			−0.680152	+	0.733071i	$0.738086\pi$
$24$		−	11.8881i		−	2.42664i
$25$	−1.10390			−0.220781
$26$	6.92606			1.35831
$27$	5.50567			1.05957
$28$		−	23.6287i		−	4.46540i
$29$	−7.41665			−1.37724			−0.688619	−	0.725124i	$-0.741783\pi$
$29$	−7.41665			−1.37724			−0.688619	+	0.725124i	$0.741783\pi$
$30$			6.61984i			1.20861i
$31$	4.26560			0.766125			0.383063	−	0.923722i	$-0.374869\pi$
$31$	4.26560			0.766125			0.383063	+	0.923722i	$0.374869\pi$
$32$		−	23.5255i		−	4.15876i
$33$		−	2.24867i		−	0.391444i
$34$			18.6009i			3.19003i
$35$			8.41157i			1.42181i
$36$	8.36796			1.39466
$37$	8.41906			1.38408			0.692042	−	0.721857i	$-0.256711\pi$
$37$	8.41906			1.38408			0.692042	+	0.721857i	$0.256711\pi$
$38$		−	9.47931i		−	1.53775i
$39$		−	3.07877i		−	0.492998i
$40$			19.2182i			3.03867i
$41$	−0.301843			−0.0471399			−0.0235700	−	0.999722i	$-0.507503\pi$
$41$	−0.301843			−0.0471399			−0.0235700	+	0.999722i	$0.507503\pi$
$42$	−14.2921			−2.20531
$43$		−	2.13344i		−	0.325347i	−0.986680	−	0.162673i	$-0.947988\pi$
$43$		−	2.13344i		−	0.325347i	0.986680	−	0.162673i	$-0.0520117\pi$
$44$		−	10.2116i		−	1.53945i
$45$	−2.97891			−0.444070
$46$			17.9193i			2.64205i
$47$			1.97103i			0.287504i	0.989614	+	0.143752i	$0.0459167\pi$
$47$			1.97103i			0.287504i	−0.989614	+	0.143752i	$0.954083\pi$
$48$	−19.1136			−2.75881
$49$	−11.1604			−1.59434
$50$			3.03216i			0.428812i
$51$	8.26848			1.15782
$52$		−	13.9811i		−	1.93884i
$53$			13.5342i			1.85906i	0.368748	+	0.929529i	$0.379787\pi$
$53$			13.5342i			1.85906i	−0.368748	+	0.929529i	$0.620213\pi$
$54$		−	15.1227i		−	2.05794i
$55$			3.63521i			0.490172i
$56$	−41.4917			−5.54456
$57$	−4.21374			−0.558124
$58$			20.3718i			2.67494i
$59$		−	2.00413i		−	0.260916i	−0.991454	−	0.130458i	$-0.958355\pi$
$59$		−	2.00413i		−	0.260916i	0.991454	−	0.130458i	$-0.0416447\pi$
$60$	13.3630			1.72516
$61$		−	5.31818i		−	0.680923i	−0.940258	−	0.340462i	$-0.889417\pi$
$61$		−	5.31818i		−	0.680923i	0.940258	−	0.340462i	$-0.110583\pi$
$62$		−	11.7166i		−	1.48801i
$63$		−	6.43139i		−	0.810279i
$64$	−33.3105			−4.16382
$65$			4.97714i			0.617339i
$66$	−6.17657			−0.760283
$67$	10.4952			1.28220			0.641099	−	0.767459i	$-0.278479\pi$
$67$	10.4952			1.28220			0.641099	+	0.767459i	$0.278479\pi$
$68$	37.5484			4.55341
$69$	7.96547			0.958930
$70$	23.1046			2.76152
$71$			10.9996i			1.30541i	0.757611	+	0.652706i	$0.226366\pi$
$71$			10.9996i			1.30541i	−0.757611	+	0.652706i	$0.773634\pi$
$72$		−	14.6940i		−	1.73171i
$73$	−3.20663			−0.375308			−0.187654	−	0.982235i	$-0.560088\pi$
$73$	−3.20663			−0.375308			−0.187654	+	0.982235i	$0.560088\pi$
$74$		−	23.1251i		−	2.68824i
$75$	1.34786			0.155637
$76$	−19.1352			−2.19496
$77$	−7.84832			−0.894400
$78$	−8.45664			−0.957526
$79$			4.65786i			0.524050i	0.965061	+	0.262025i	$0.0843903\pi$
$79$			4.65786i			0.524050i	−0.965061	+	0.262025i	$0.915610\pi$
$80$	30.8991			3.45462
$81$	−2.19481			−0.243867
$82$			0.829090i			0.0915577i
$83$	3.81054			0.418262			0.209131	−	0.977888i	$-0.432937\pi$
$83$	3.81054			0.418262			0.209131	+	0.977888i	$0.432937\pi$
$84$			28.8504i			3.14783i
$85$	−13.3668			−1.44984
$86$	−5.86005			−0.631905
$87$	9.05565			0.970868
$88$	−17.9314			−1.91149
$89$		−	6.10532i		−	0.647163i	−0.946200	−	0.323581i	$-0.895113\pi$
$89$		−	6.10532i		−	0.647163i	0.946200	−	0.323581i	$-0.104887\pi$
$90$			8.18235i			0.862495i
$91$	−10.7455			−1.12644
$92$	36.1724			3.77123
$93$	−5.20826			−0.540071
$94$	5.41393			0.558405
$95$	6.81194			0.698891
$96$			28.7244i			2.93167i
$97$			7.67014i			0.778785i	0.921072	+	0.389393i	$0.127315\pi$
$97$			7.67014i			0.778785i	−0.921072	+	0.389393i	$0.872685\pi$
$98$			30.6548i			3.09660i
$99$		−	2.77944i		−	0.279344i
$100$	6.12081			0.612081
$101$		−	6.37394i		−	0.634230i	−0.948387	−	0.317115i	$-0.897286\pi$
$101$		−	6.37394i		−	0.634230i	0.948387	−	0.317115i	$-0.102714\pi$
$102$		−	22.7115i		−	2.24878i
$103$			5.96570i			0.587818i	0.955833	+	0.293909i	$0.0949563\pi$
$103$			5.96570i			0.587818i	−0.955833	+	0.293909i	$0.905044\pi$
$104$	−24.5507			−2.40740
$105$		−	10.2704i		−	1.00229i
$106$	37.1751			3.61076
$107$			6.23766i			0.603018i	0.953463	+	0.301509i	$0.0974903\pi$
$107$			6.23766i			0.603018i	−0.953463	+	0.301509i	$0.902510\pi$
$108$	−30.5272			−2.93748
$109$	−7.35851			−0.704818			−0.352409	−	0.935846i	$-0.614637\pi$
$109$	−7.35851			−0.704818			−0.352409	+	0.935846i	$0.614637\pi$
$110$	9.98505			0.952037
$111$	−10.2796			−0.975694
$112$			66.7103i			6.30353i
$113$		−	13.1628i		−	1.23825i	−0.785291	−	0.619127i	$-0.787487\pi$
$113$		−	13.1628i		−	1.23825i	0.785291	−	0.619127i	$-0.212513\pi$
$114$			11.5741i			1.08402i
$115$	−12.8770			−1.20079
$116$	41.1230			3.81818
$117$		−	3.80547i		−	0.351816i
$118$	−5.50487			−0.506764
$119$		−	28.8587i		−	2.64547i
$120$		−	23.4653i		−	2.14208i
$121$	7.60821			0.691655
$122$	−14.6078			−1.32252
$123$	0.368547			0.0332308
$124$	−23.6515			−2.12396
$125$	−12.0482			−1.07762
$126$	−17.6655			−1.57377
$127$		−	8.84002i		−	0.784425i	−0.919875	−	0.392213i	$-0.871710\pi$
$127$		−	8.84002i		−	0.784425i	0.919875	−	0.392213i	$-0.128290\pi$
$128$			44.4450i			3.92842i
$129$			2.60491i			0.229349i
$130$	13.6710			1.19903
$131$		−	17.7246i		−	1.54860i	−0.632816	−	0.774302i	$-0.718101\pi$
$131$		−	17.7246i		−	1.54860i	0.632816	−	0.774302i	$-0.281899\pi$
$132$			12.4682i			1.08522i
$133$			14.7068i			1.27524i
$134$		−	28.8279i		−	2.49035i
$135$	10.8674			0.935315
$136$		−	65.9345i		−	5.65384i
$137$			1.95991i			0.167446i	0.996489	+	0.0837231i	$0.0266811\pi$
$137$			1.95991i			0.167446i	−0.996489	+	0.0837231i	$0.973319\pi$
$138$		−	21.8792i		−	1.86249i
$139$	6.82871			0.579204			0.289602	−	0.957147i	$-0.406477\pi$
$139$	6.82871			0.579204			0.289602	+	0.957147i	$0.406477\pi$
$140$		−	46.6395i		−	3.94176i
$141$		−	2.40660i		−	0.202672i
$142$	30.2133			2.53544
$143$	−4.64387			−0.388340
$144$	−23.6251			−1.96876
$145$	−14.6394			−1.21573
$146$			8.80785i			0.728943i
$147$	13.6267			1.12391
$148$	−46.6810			−3.83716
$149$			7.76870i			0.636436i	0.948018	+	0.318218i	$0.103084\pi$
$149$			7.76870i			0.636436i	−0.948018	+	0.318218i	$0.896916\pi$
$150$		−	3.70224i		−	0.302286i
$151$	0.00989886			0.000805558			0.000402779	−	1.00000i	$-0.499872\pi$
$151$	0.00989886			0.000805558			0.000402779		1.00000i	$0.499872\pi$
$152$			33.6012i			2.72542i
$153$	10.2201			0.826248
$154$			21.5575i			1.73715i
$155$	8.41968			0.676285
$156$			17.0708i			1.36676i
$157$	−4.30171			−0.343314			−0.171657	−	0.985157i	$-0.554912\pi$
$157$	−4.30171			−0.343314			−0.171657	+	0.985157i	$0.554912\pi$
$158$	12.7940			1.01784
$159$		−	16.5251i		−	1.31052i
$160$		−	46.4359i		−	3.67108i
$161$		−	27.8011i		−	2.19103i
$162$			6.02861i			0.473652i
$163$			0.357851i			0.0280291i	0.999902	+	0.0140145i	$0.00446111\pi$
$163$			0.357851i			0.0280291i	−0.999902	+	0.0140145i	$0.995539\pi$
$164$	1.67363			0.130688
$165$		−	4.43855i		−	0.345541i
$166$		−	10.4666i		−	0.812370i
$167$			9.63951i			0.745928i	0.927846	+	0.372964i	$0.121658\pi$
$167$			9.63951i			0.745928i	−0.927846	+	0.372964i	$0.878342\pi$
$168$	50.6609			3.90857
$169$	6.64185			0.510911
$170$			36.7155i			2.81595i
$171$	−5.20833			−0.398291
$172$			11.8293i			0.901973i
$173$			18.6810i			1.42029i	0.704056	+	0.710144i	$0.251370\pi$
$173$			18.6810i			1.42029i	−0.704056	+	0.710144i	$0.748630\pi$
$174$		−	24.8737i		−	1.88567i
$175$		−	4.70429i		−	0.355611i
$176$			28.8301i			2.17315i
$177$			2.44702i			0.183930i
$178$	−16.7698			−1.25695
$179$			10.6981i			0.799613i	0.916600	+	0.399806i	$0.130923\pi$
$179$			10.6981i			0.799613i	−0.916600	+	0.399806i	$0.869077\pi$
$180$	16.5171			1.23111
$181$	−5.66559			−0.421120			−0.210560	−	0.977581i	$-0.567529\pi$
$181$	−5.66559			−0.421120			−0.210560	+	0.977581i	$0.567529\pi$
$182$			29.5154i			2.18783i
$183$			6.49344i			0.480009i
$184$		−	63.5183i		−	4.68263i
$185$	16.6180			1.22178
$186$			14.3058i			1.04895i
$187$		−	12.4718i		−	0.912027i
$188$		−	10.9287i		−	0.797059i
$189$			23.4624i			1.70664i
$190$		−	18.7108i		−	1.35742i
$191$	−16.6777			−1.20676			−0.603379	−	0.797455i	$-0.706179\pi$
$191$	−16.6777			−1.20676			−0.603379	+	0.797455i	$0.706179\pi$
$192$	40.6718			2.93523
$193$		−	18.2718i		−	1.31523i	−0.753353	−	0.657616i	$-0.771565\pi$
$193$		−	18.2718i		−	1.31523i	0.753353	−	0.657616i	$-0.228435\pi$
$194$	21.0680			1.51260
$195$		−	6.07704i		−	0.435186i
$196$	61.8807			4.42005
$197$			13.6551i			0.972887i	0.873712	+	0.486443i	$0.161706\pi$
$197$			13.6551i			0.972887i	−0.873712	+	0.486443i	$0.838294\pi$
$198$	−7.63445			−0.542557
$199$			18.0500i			1.27953i	0.768570	+	0.639765i	$0.220968\pi$
$199$			18.0500i			1.27953i	−0.768570	+	0.639765i	$0.779032\pi$
$200$		−	10.7481i		−	0.760003i
$201$	−12.8146			−0.903870
$202$	−17.5077			−1.23184
$203$		−	31.6060i		−	2.21831i
$204$	−45.8462			−3.20987
$205$	−0.595794			−0.0416120
$206$	16.3864			1.14169
$207$	9.84560			0.684317
$208$			39.4727i			2.73694i
$209$			6.35581i			0.439641i
$210$	−28.2104			−1.94670
$211$		−	12.2024i		−	0.840046i	−0.907513	−	0.420023i	$-0.862022\pi$
$211$		−	12.2024i		−	0.840046i	0.907513	−	0.420023i	$-0.137978\pi$
$212$		−	75.0427i		−	5.15395i
$213$		−	13.4304i		−	0.920236i
$214$	17.1334			1.17121
$215$		−	4.21110i		−	0.287195i
$216$			53.6054i			3.64739i
$217$			18.1779i			1.23399i
$218$			20.2121i			1.36893i
$219$	3.91526			0.264569
$220$		−	20.1561i		−	1.35892i
$221$		−	17.0757i		−	1.14864i
$222$			28.2355i			1.89504i
$223$	4.43404			0.296925			0.148463	−	0.988918i	$-0.452568\pi$
$223$	4.43404			0.296925			0.148463	+	0.988918i	$0.452568\pi$
$224$	100.254			6.69850
$225$	1.66600			0.111066
$226$	−36.1551			−2.40500
$227$	25.9124			1.71986			0.859932	−	0.510408i	$-0.170506\pi$
$227$	25.9124			1.71986			0.859932	+	0.510408i	$0.170506\pi$
$228$	23.3639			1.54731
$229$			0.713480i			0.0471481i	0.999722	+	0.0235741i	$0.00750455\pi$
$229$			0.713480i			0.0471481i	−0.999722	+	0.0235741i	$0.992495\pi$
$230$			35.3700i			2.33223i
$231$	9.58272			0.630497
$232$		−	72.2116i		−	4.74092i
$233$	−14.6631			−0.960609			−0.480305	−	0.877102i	$-0.659474\pi$
$233$	−14.6631			−0.960609			−0.480305	+	0.877102i	$0.659474\pi$
$234$	−10.4527			−0.683315
$235$			3.89052i			0.253789i
$236$			11.1123i			0.723348i
$237$		−	5.68720i		−	0.369423i
$238$	−79.2678			−5.13817
$239$	−11.5453			−0.746806			−0.373403	−	0.927669i	$-0.621809\pi$
$239$	−11.5453			−0.746806			−0.373403	+	0.927669i	$0.621809\pi$
$240$	−37.7275			−2.43530
$241$	14.9696			0.964276			0.482138	−	0.876095i	$-0.339860\pi$
$241$	14.9696			0.964276			0.482138	+	0.876095i	$0.339860\pi$
$242$		−	20.8979i		−	1.34337i
$243$	−13.8372			−0.887655
$244$			29.4877i			1.88775i
$245$	−22.0289			−1.40738
$246$		−	1.01231i		−	0.0645425i
$247$			8.70205i			0.553698i
$248$			41.5317i			2.63726i
$249$	−4.65263			−0.294849
$250$			33.0935i			2.09302i
$251$			18.2787i			1.15374i	0.816836	+	0.576871i	$0.195726\pi$
$251$			18.2787i			1.15374i	−0.816836	+	0.576871i	$0.804274\pi$
$252$			35.6600i			2.24637i
$253$		−	12.0147i		−	0.755361i
$254$	−24.2814			−1.52355
$255$	16.3208			1.02205
$256$	55.4587			3.46617
$257$	−0.570406			−0.0355809			−0.0177905	−	0.999842i	$-0.505663\pi$
$257$	−0.570406			−0.0355809			−0.0177905	+	0.999842i	$0.505663\pi$
$258$	7.15506			0.445454
$259$			35.8778i			2.22934i
$260$		−	27.5967i		−	1.71148i
$261$	11.1931			0.692835
$262$	−48.6852			−3.00778
$263$	24.1266			1.48771			0.743856	−	0.668340i	$-0.232995\pi$
$263$	24.1266			1.48771			0.743856	+	0.668340i	$0.232995\pi$
$264$	21.8940			1.34748
$265$			26.7144i			1.64105i
$266$	40.3961			2.47684
$267$			7.45453i			0.456210i
$268$	−58.1928			−3.55469
$269$	−3.52185			−0.214731			−0.107366	−	0.994220i	$-0.534242\pi$
$269$	−3.52185			−0.214731			−0.107366	+	0.994220i	$0.534242\pi$
$270$		−	29.8501i		−	1.81662i
$271$	−0.0228321			−0.00138695			−0.000693474	−	1.00000i	$-0.500221\pi$
$271$	−0.0228321			−0.00138695			−0.000693474		1.00000i	$0.500221\pi$
$272$	−106.010			−6.42777
$273$	13.1202			0.794069
$274$	5.38339			0.325223
$275$		−	2.03304i		−	0.122597i
$276$	−44.1661			−2.65849
$277$			26.7037i			1.60447i	0.597009	+	0.802235i	$0.296356\pi$
$277$			26.7037i			1.60447i	−0.597009	+	0.802235i	$0.703644\pi$
$278$		−	18.7568i		−	1.12496i
$279$	−6.43759			−0.385408
$280$	−81.8985			−4.89437
$281$	29.0773			1.73461			0.867304	−	0.497779i	$-0.165851\pi$
$281$	29.0773			1.73461			0.867304	+	0.497779i	$0.165851\pi$
$282$	−6.61036			−0.393641
$283$	14.1673			0.842159			0.421080	−	0.907024i	$-0.361651\pi$
$283$	14.1673			0.842159			0.421080	+	0.907024i	$0.361651\pi$
$284$		−	60.9894i		−	3.61905i
$285$	−8.31731			−0.492675
$286$			12.7556i			0.754254i
$287$		−	1.28630i		−	0.0759280i
$288$			35.5043i			2.09211i
$289$	28.8593			1.69761
$290$			40.2109i			2.36126i
$291$		−	9.36516i		−	0.548996i
$292$	17.7798			1.04048
$293$	9.61452			0.561686			0.280843	−	0.959754i	$-0.409386\pi$
$293$	9.61452			0.561686			0.280843	+	0.959754i	$0.409386\pi$
$294$		−	37.4292i		−	2.18292i
$295$		−	3.95586i		−	0.230319i
$296$			81.9714i			4.76449i
$297$			10.1397i			0.588365i
$298$	21.3387			1.23612
$299$		−	16.4500i		−	0.951327i
$300$	−7.47344			−0.431479
$301$	9.09165			0.524034
$302$		−	0.0271898i		−	0.00156460i
$303$			7.78251i			0.447093i
$304$	54.0241			3.09849
$305$		−	10.4973i		−	0.601074i
$306$		−	28.0722i		−	1.60478i
$307$	−6.99412			−0.399175			−0.199588	−	0.979880i	$-0.563960\pi$
$307$	−6.99412			−0.399175			−0.199588	+	0.979880i	$0.563960\pi$
$308$	43.5165			2.47958
$309$		−	7.28406i		−	0.414376i
$310$		−	23.1268i		−	1.31352i
$311$			16.5128i			0.936357i	0.883634	+	0.468178i	$0.155090\pi$
$311$			16.5128i			0.936357i	−0.883634	+	0.468178i	$0.844910\pi$
$312$	29.9762			1.69707
$313$	25.3223			1.43130			0.715651	−	0.698458i	$-0.246130\pi$
$313$	25.3223			1.43130			0.715651	+	0.698458i	$0.246130\pi$
$314$			11.8158i			0.666802i
$315$		−	12.6946i		−	0.715260i
$316$		−	25.8264i		−	1.45285i
$317$		−	20.0258i		−	1.12476i	−0.826878	−	0.562382i	$-0.809885\pi$
$317$		−	20.0258i		−	1.12476i	0.826878	−	0.562382i	$-0.190115\pi$
$318$	−45.3904			−2.54536
$319$		−	13.6591i		−	0.764764i
$320$	−65.7501			−3.67554
$321$		−	7.61612i		−	0.425090i
$322$	−76.3629			−4.25554
$323$	−23.3706			−1.30038
$324$	12.1695			0.676084
$325$		−	2.78354i		−	0.154403i
$326$	0.982931			0.0544395
$327$	8.98467			0.496853
$328$		−	2.93887i		−	0.162272i
$329$	−8.39952			−0.463081
$330$	−12.1916			−0.671128
$331$		−	16.6632i		−	0.915892i	−0.888980	−	0.457946i	$-0.848585\pi$
$331$		−	16.6632i		−	0.915892i	0.888980	−	0.457946i	$-0.151415\pi$
$332$	−21.1283			−1.15957
$333$	−12.7059			−0.696280
$334$	26.4774			1.44878
$335$	20.7161			1.13184
$336$		−	81.4526i		−	4.44360i
$337$	10.0821			0.549209			0.274605	−	0.961557i	$-0.411453\pi$
$337$	10.0821			0.549209			0.274605	+	0.961557i	$0.411453\pi$
$338$		−	18.2436i		−	0.992319i
$339$			16.0717i			0.872892i
$340$	74.1150			4.01945
$341$			7.85589i			0.425420i
$342$			14.3060i			0.773582i
$343$		−	17.7294i		−	0.957295i
$344$	20.7721			1.11995
$345$	15.7227			0.846480
$346$	51.3122			2.75856
$347$			19.2269i			1.03215i	0.856542	+	0.516077i	$0.172608\pi$
$347$			19.2269i			1.03215i	−0.856542	+	0.516077i	$0.827392\pi$
$348$	−50.2108			−2.69158
$349$	−18.6813	+	0.0914728i	−0.999988	+	0.00489642i
$349$	−18.6813	+	0.0914728i	−0.999988	+	0.00489642i
$350$	−12.9215			−0.690686
$351$			13.8827i			0.741006i
$352$	43.3265			2.30931
$353$	−8.72859			−0.464576			−0.232288	−	0.972647i	$-0.574621\pi$
$353$	−8.72859			−0.464576			−0.232288	+	0.972647i	$0.574621\pi$
$354$	6.72139			0.357238
$355$			21.7116i			1.15233i
$356$			33.8521i			1.79416i
$357$			35.2361i			1.86489i
$358$	29.3851			1.55305
$359$		−	16.5631i		−	0.874165i	−0.899421	−	0.437082i	$-0.856012\pi$
$359$		−	16.5631i		−	0.874165i	0.899421	−	0.437082i	$-0.143988\pi$
$360$		−	29.0039i		−	1.52864i
$361$	−7.08998			−0.373157
$362$			15.5620i			0.817921i
$363$	−9.28954			−0.487574
$364$	59.5806			3.12287
$365$	−6.32942			−0.331297
$366$	17.8359			0.932299
$367$			37.7596i			1.97104i	0.169574	+	0.985518i	$0.445761\pi$
$367$			37.7596i			1.97104i	−0.169574	+	0.985518i	$0.554239\pi$
$368$	−102.125			−5.32362
$369$	0.455537			0.0237143
$370$		−	45.6456i		−	2.37300i
$371$	−57.6757			−2.99438
$372$	28.8782			1.49726
$373$		−	15.8701i		−	0.821724i	−0.911698	−	0.410862i	$-0.865228\pi$
$373$		−	15.8701i		−	0.821724i	0.911698	−	0.410862i	$-0.134772\pi$
$374$	−34.2570			−1.77139
$375$	14.7107			0.759659
$376$	−19.1907			−0.989686
$377$		−	18.7014i		−	0.963169i
$378$	64.4455			3.31472
$379$			6.87685i			0.353240i	0.984279	+	0.176620i	$0.0565164\pi$
$379$			6.87685i			0.353240i	−0.984279	+	0.176620i	$0.943484\pi$
$380$	−37.7701			−1.93757
$381$			10.7936i			0.552972i
$382$			45.8097i			2.34383i
$383$			35.6435i			1.82130i	0.413183	+	0.910648i	$0.364417\pi$
$383$			35.6435i			1.82130i	−0.413183	+	0.910648i	$0.635583\pi$
$384$		−	54.2669i		−	2.76929i
$385$	−15.4914			−0.789517
$386$	−50.1882			−2.55451
$387$			3.21976i			0.163669i
$388$		−	42.5286i		−	2.15906i
$389$		−	30.1665i		−	1.52950i	−0.644325	−	0.764752i	$-0.722861\pi$
$389$		−	30.1665i		−	1.52950i	0.644325	−	0.764752i	$-0.277139\pi$
$390$	−16.6922			−0.845241
$391$	44.1788			2.23422
$392$		−	108.662i		−	5.48825i
$393$			21.6415i			1.09167i
$394$	37.5073			1.88959
$395$			9.19393i			0.462597i
$396$			15.4111i			0.774438i
$397$	−11.6763			−0.586018			−0.293009	−	0.956110i	$-0.594657\pi$
$397$	−11.6763			−0.586018			−0.293009	+	0.956110i	$0.594657\pi$
$398$	49.5790			2.48517
$399$		−	17.9569i		−	0.898967i
$400$	−17.2807			−0.864037
$401$		−	27.8877i		−	1.39264i	−0.717729	−	0.696322i	$-0.754818\pi$
$401$		−	27.8877i		−	1.39264i	0.717729	−	0.696322i	$-0.245182\pi$
$402$			35.1986i			1.75554i
$403$			10.7559i			0.535789i
$404$			35.3415i			1.75830i
$405$	−4.33222			−0.215270
$406$	−86.8142			−4.30852
$407$			15.5052i			0.768566i
$408$			80.5053i			3.98561i
$409$	−27.4052			−1.35510			−0.677550	−	0.735477i	$-0.736958\pi$
$409$	−27.4052			−1.35510			−0.677550	+	0.735477i	$0.736958\pi$
$410$			1.63650i			0.0808211i
$411$		−	2.39302i		−	0.118039i
$412$		−	33.0780i		−	1.62964i
$413$	8.54060			0.420256
$414$		−	27.0435i		−	1.32912i
$415$	7.52145			0.369214
$416$	59.3205			2.90843
$417$	−8.33779			−0.408303
$418$	17.4579			0.853893
$419$	−9.85071			−0.481239			−0.240619	−	0.970620i	$-0.577351\pi$
$419$	−9.85071			−0.481239			−0.240619	+	0.970620i	$0.577351\pi$
$420$			56.9464i			2.77870i
$421$		−	15.8178i		−	0.770912i	−0.922726	−	0.385456i	$-0.874044\pi$
$421$		−	15.8178i		−	0.770912i	0.922726	−	0.385456i	$-0.125956\pi$
$422$	−33.5170			−1.63158
$423$		−	2.97464i		−	0.144632i
$424$	−131.774			−6.39951
$425$	7.47559			0.362619
$426$	−36.8901			−1.78733
$427$	22.6634			1.09676
$428$		−	34.5859i		−	1.67177i
$429$	5.67012			0.273756
$430$	−11.5669			−0.557804
$431$		−	11.9706i		−	0.576603i	−0.957540	−	0.288302i	$-0.906909\pi$
$431$		−	11.9706i		−	0.576603i	0.957540	−	0.288302i	$-0.0930906\pi$
$432$	86.1868			4.14667
$433$			24.6837i			1.18622i	0.805120	+	0.593112i	$0.202101\pi$
$433$			24.6837i			1.18622i	−0.805120	+	0.593112i	$0.797899\pi$
$434$	49.9302			2.39673
$435$	17.8745			0.857018
$436$	40.8007			1.95400
$437$	−22.5142			−1.07700
$438$		−	10.7543i		−	0.513860i
$439$		−	24.4252i		−	1.16575i	−0.812561	−	0.582876i	$-0.801927\pi$
$439$		−	24.4252i		−	1.16575i	0.812561	−	0.582876i	$-0.198073\pi$
$440$	−35.3939			−1.68734
$441$	16.8430			0.802050
$442$	−46.9029			−2.23094
$443$	14.6682			0.696905			0.348452	−	0.937326i	$-0.386707\pi$
$443$	14.6682			0.696905			0.348452	+	0.937326i	$0.386707\pi$
$444$	56.9971			2.70496
$445$		−	12.0510i		−	0.571272i
$446$		−	12.1792i		−	0.576704i
$447$		−	9.48549i		−	0.448648i
$448$		−	141.953i		−	6.70664i
$449$	−1.03260			−0.0487312			−0.0243656	−	0.999703i	$-0.507757\pi$
$449$	−1.03260			−0.0487312			−0.0243656	+	0.999703i	$0.507757\pi$
$450$		−	4.57609i		−	0.215719i
$451$		−	0.555899i		−	0.0261763i
$452$			72.9837i			3.43286i
$453$	−0.0120864			−0.000567869
$454$		−	71.1751i		−	3.34041i
$455$	−21.2101			−0.994344
$456$		−	41.0267i		−	1.92125i
$457$	−9.48028			−0.443469			−0.221734	−	0.975107i	$-0.571172\pi$
$457$	−9.48028			−0.443469			−0.221734	+	0.975107i	$0.571172\pi$
$458$	1.95976			0.0915735
$459$	−37.2841			−1.74027
$460$	71.3989			3.32899
$461$		−	36.3897i		−	1.69484i	−0.530927	−	0.847418i	$-0.678156\pi$
$461$		−	36.3897i		−	1.69484i	0.530927	−	0.847418i	$-0.321844\pi$
$462$		−	26.3214i		−	1.22458i
$463$		−	3.25083i		−	0.151079i	−0.997143	−	0.0755395i	$-0.975932\pi$
$463$		−	3.25083i		−	0.151079i	0.997143	−	0.0755395i	$-0.0240679\pi$
$464$	−116.102			−5.38989
$465$	−10.2803			−0.476739
$466$			40.2759i			1.86575i
$467$	−16.9559			−0.784627			−0.392313	−	0.919832i	$-0.628325\pi$
$467$	−16.9559			−0.784627			−0.392313	+	0.919832i	$0.628325\pi$
$468$			21.1001i			0.975354i
$469$			44.7254i			2.06523i
$470$	10.6863			0.492923
$471$	5.25234			0.242015
$472$	19.5131			0.898161
$473$	3.92912			0.180661
$474$	−15.6214			−0.717513
$475$	−3.80967			−0.174800
$476$			160.012i			7.33415i
$477$		−	20.4255i		−	0.935221i
$478$			31.7123i			1.45049i
$479$	37.3839			1.70811			0.854057	−	0.520179i	$-0.174135\pi$
$479$	37.3839			1.70811			0.854057	+	0.520179i	$0.174135\pi$
$480$			56.6977i			2.58789i
$481$			21.2290i			0.967958i
$482$		−	41.1179i		−	1.87287i
$483$			33.9448i			1.54454i
$484$	−42.1851			−1.91751
$485$			15.1397i			0.687460i
$486$			38.0074i			1.72405i
$487$			19.1564i			0.868058i	0.900899	+	0.434029i	$0.142908\pi$
$487$			19.1564i			0.868058i	−0.900899	+	0.434029i	$0.857092\pi$
$488$	51.7800			2.34397
$489$		−	0.436932i		−	0.0197588i
$490$			60.5081i			2.73348i
$491$	2.32731			0.105030			0.0525149	−	0.998620i	$-0.483276\pi$
$491$	2.32731			0.105030			0.0525149	+	0.998620i	$0.483276\pi$
$492$	−2.04348			−0.0921271
$493$	50.2252			2.26203
$494$	23.9024			1.07542
$495$		−	5.48620i		−	0.246587i
$496$	66.7746			2.99827
$497$	−46.8748			−2.10262
$498$			12.7797i			0.572671i
$499$			32.0857i			1.43636i	0.695860	+	0.718178i	$0.255024\pi$
$499$			32.0857i			1.43636i	−0.695860	+	0.718178i	$0.744976\pi$
$500$	66.8036			2.98755
$501$		−	11.7697i		−	0.525833i
$502$	50.2072			2.24086
$503$		−	5.48715i		−	0.244660i	−0.992489	−	0.122330i	$-0.960963\pi$
$503$		−	5.48715i		−	0.244660i	0.992489	−	0.122330i	$-0.0390366\pi$
$504$	62.6186			2.78926
$505$		−	12.5812i		−	0.559857i
$506$	−33.0016			−1.46710
$507$	−8.10963			−0.360161
$508$			49.0152i			2.17470i
$509$			15.3716i			0.681334i	0.940184	+	0.340667i	$0.110653\pi$
$509$			15.3716i			0.681334i	−0.940184	+	0.340667i	$0.889347\pi$
$510$		−	44.8292i		−	1.98507i
$511$		−	13.6651i		−	0.604506i
$512$		−	63.4417i		−	2.80375i
$513$	19.0006			0.838895
$514$			1.56677i			0.0691071i
$515$			11.7754i			0.518887i
$516$		−	14.4434i		−	0.635836i
$517$	−3.63000			−0.159647
$518$	98.5476			4.32994
$519$		−	22.8093i		−	1.00122i
$520$	−48.4595			−2.12509
$521$		−	23.7667i		−	1.04124i	−0.853789	−	0.520619i	$-0.825701\pi$
$521$		−	23.7667i		−	1.04124i	0.853789	−	0.520619i	$-0.174299\pi$
$522$		−	30.7448i		−	1.34566i
$523$		−	7.39982i		−	0.323572i	−0.986826	−	0.161786i	$-0.948275\pi$
$523$		−	7.39982i		−	0.323572i	0.986826	−	0.161786i	$-0.0517254\pi$
$524$			98.2773i			4.29326i
$525$			5.74388i			0.250684i
$526$		−	66.2700i		−	2.88951i
$527$	−28.8865			−1.25831
$528$		−	35.2012i		−	1.53194i
$529$	19.5598			0.850426
$530$	73.3781			3.18734
$531$			3.02461i			0.131257i
$532$		−	81.5447i		−	3.53541i
$533$		−	0.761108i		−	0.0329673i
$534$	20.4758			0.886075
$535$			12.3122i			0.532304i
$536$			102.186i			4.41376i
$537$		−	13.0623i		−	0.563678i
$538$			9.67368i			0.417062i
$539$		−	20.5538i		−	0.885316i
$540$	−60.2562			−2.59302
$541$	37.1939			1.59909			0.799545	−	0.600607i	$-0.205074\pi$
$541$	37.1939			1.59909			0.799545	+	0.600607i	$0.205074\pi$
$542$			0.0627142i			0.00269380i
$543$	6.91762			0.296863
$544$			159.314i			6.83052i
$545$	−14.5246			−0.622167
$546$		−	36.0380i		−	1.54228i
$547$	−11.7001			−0.500259			−0.250130	−	0.968212i	$-0.580473\pi$
$547$	−11.7001			−0.500259			−0.250130	+	0.968212i	$0.580473\pi$
$548$		−	10.8671i		−	0.464218i
$549$			8.02612i			0.342546i
$550$	−5.58428			−0.238114
$551$	−25.5955			−1.09041
$552$			77.5551i			3.30097i
$553$	−19.8495			−0.844085
$554$	73.3486			3.11629
$555$	−20.2904			−0.861278
$556$	−37.8631			−1.60575
$557$			27.1110i			1.14873i	0.818599	+	0.574365i	$0.194751\pi$
$557$			27.1110i			1.14873i	−0.818599	+	0.574365i	$0.805249\pi$
$558$			17.6825i			0.748560i
$559$	5.37955			0.227531
$560$			131.676i			5.56434i
$561$			15.2279i			0.642923i
$562$		−	79.8684i		−	3.36905i
$563$	1.35627			0.0571600			0.0285800	−	0.999592i	$-0.490901\pi$
$563$	1.35627			0.0571600			0.0285800	+	0.999592i	$0.490901\pi$
$564$			13.3439i			0.561878i
$565$		−	25.9815i		−	1.09305i
$566$		−	38.9142i		−	1.63569i
$567$		−	9.35316i		−	0.392796i
$568$	−107.097			−4.49368
$569$		−	12.0985i		−	0.507197i	−0.967310	−	0.253599i	$-0.918386\pi$
$569$		−	12.0985i		−	0.507197i	0.967310	−	0.253599i	$-0.0816142\pi$
$570$			22.8457i			0.956899i
$571$		−	14.0368i		−	0.587421i	−0.955894	−	0.293711i	$-0.905110\pi$
$571$		−	14.0368i		−	0.587421i	0.955894	−	0.293711i	$-0.0948902\pi$
$572$	25.7488			1.07661
$573$	20.3633			0.850690
$574$	−3.53316			−0.147471
$575$	7.20164			0.300329
$576$	50.2717			2.09466
$577$	−36.3649			−1.51389			−0.756946	−	0.653478i	$-0.773309\pi$
$577$	−36.3649			−1.51389			−0.756946	+	0.653478i	$0.773309\pi$
$578$		−	79.2696i		−	3.29718i
$579$			22.3097i			0.927158i
$580$	81.1708			3.37043
$581$			16.2386i			0.673692i
$582$	−25.7239			−1.06629
$583$	−24.9256			−1.03231
$584$		−	31.2211i		−	1.29194i
$585$		−	7.51143i		−	0.310559i
$586$		−	26.4088i		−	1.09094i
$587$	−3.36674			−0.138960			−0.0694802	−	0.997583i	$-0.522134\pi$
$587$	−3.36674			−0.138960			−0.0694802	+	0.997583i	$0.522134\pi$
$588$	−75.5557			−3.11586
$589$	14.7210			0.606568
$590$	−10.8658			−0.447338
$591$		−	16.6727i		−	0.685825i
$592$	131.794			5.41668
$593$		−	11.9668i		−	0.491419i	−0.969343	−	0.245710i	$-0.920979\pi$
$593$		−	11.9668i		−	0.491419i	0.969343	−	0.245710i	$-0.0790209\pi$
$594$	27.8513			1.14275
$595$		−	56.9627i		−	2.33524i
$596$		−	43.0750i		−	1.76442i
$597$		−	22.0389i		−	0.901991i
$598$	−45.1841			−1.84772
$599$			24.5084i			1.00139i	0.865625	+	0.500694i	$0.166922\pi$
$599$			24.5084i			1.00139i	−0.865625	+	0.500694i	$0.833078\pi$
$600$			13.1233i			0.535756i
$601$			27.0838i			1.10477i	0.833589	+	0.552385i	$0.186282\pi$
$601$			27.0838i			1.10477i	−0.833589	+	0.552385i	$0.813718\pi$
$602$		−	24.9726i		−	1.01781i
$603$	−15.8393			−0.645024
$604$	−0.0548861			−0.00223329
$605$	15.0175			0.610547
$606$	21.3767			0.868368
$607$	8.49002			0.344599			0.172300	−	0.985045i	$-0.444880\pi$
$607$	8.49002			0.344599			0.172300	+	0.985045i	$0.444880\pi$
$608$		−	81.1887i		−	3.29263i
$609$			38.5906i			1.56377i
$610$	−28.8336			−1.16744
$611$	−4.97002			−0.201065
$612$	−56.6674			−2.29065
$613$	−9.36842			−0.378387			−0.189194	−	0.981940i	$-0.560587\pi$
$613$	−9.36842			−0.378387			−0.189194	+	0.981940i	$0.560587\pi$
$614$			19.2112i			0.775299i
$615$	0.727458			0.0293339
$616$		−	76.4145i		−	3.07883i
$617$	35.0748			1.41206			0.706028	−	0.708183i	$-0.250485\pi$
$617$	35.0748			1.41206			0.706028	+	0.708183i	$0.250485\pi$
$618$	−20.0076			−0.804822
$619$		−	38.5004i		−	1.54746i	−0.633515	−	0.773731i	$-0.718388\pi$
$619$		−	38.5004i		−	1.54746i	0.633515	−	0.773731i	$-0.281612\pi$
$620$	−46.6845			−1.87489
$621$	−35.9178			−1.44133
$622$	45.3568			1.81864
$623$	26.0178			1.04238
$624$		−	48.1957i		−	1.92937i
$625$	−18.2619			−0.730475
$626$		−	69.5544i		−	2.77995i
$627$		−	7.76038i		−	0.309920i
$628$	23.8517			0.951785
$629$	−57.0134			−2.27327
$630$	−34.8691			−1.38922
$631$	15.4035			0.613205			0.306603	−	0.951838i	$-0.400808\pi$
$631$	15.4035			0.613205			0.306603	+	0.951838i	$0.400808\pi$
$632$	−45.3508			−1.80396
$633$			14.8990i			0.592181i
$634$	−55.0062			−2.18457
$635$		−	17.4489i		−	0.692439i
$636$			91.6263i			3.63322i
$637$		−	28.1413i		−	1.11500i
$638$	−37.5183			−1.48536
$639$		−	16.6004i		−	0.656703i
$640$			87.7279i			3.46775i
$641$	6.79173			0.268257			0.134129	−	0.990964i	$-0.457177\pi$
$641$	6.79173			0.268257			0.134129	+	0.990964i	$0.457177\pi$
$642$	−20.9197			−0.825633
$643$			18.0463i			0.711677i	0.934547	+	0.355839i	$0.115805\pi$
$643$			18.0463i			0.711677i	−0.934547	+	0.355839i	$0.884195\pi$
$644$			154.148i			6.07430i
$645$			5.14171i			0.202454i
$646$			64.1935i			2.52566i
$647$	37.3001			1.46642			0.733209	−	0.680003i	$-0.238021\pi$
$647$	37.3001			1.46642			0.733209	+	0.680003i	$0.238021\pi$
$648$		−	21.3695i		−	0.839475i
$649$	3.69097			0.144883
$650$	−7.64571			−0.299889
$651$		−	22.1950i		−	0.869890i
$652$		−	1.98417i		−	0.0777062i
$653$	21.8941			0.856784			0.428392	−	0.903593i	$-0.359080\pi$
$653$	21.8941			0.856784			0.428392	+	0.903593i	$0.359080\pi$
$654$		−	24.6787i		−	0.965014i
$655$		−	34.9857i		−	1.36700i
$656$	−4.72511			−0.184485
$657$	4.83940			0.188803
$658$			23.0715i			0.899419i
$659$		−	17.6142i		−	0.686151i	−0.939308	−	0.343076i	$-0.888531\pi$
$659$		−	17.6142i		−	0.686151i	0.939308	−	0.343076i	$-0.111469\pi$
$660$			24.6104i			0.957959i
$661$	−12.5959			−0.489922			−0.244961	−	0.969533i	$-0.578775\pi$
$661$	−12.5959			−0.489922			−0.244961	+	0.969533i	$0.578775\pi$
$662$	−45.7698			−1.77889
$663$			20.8493i			0.809719i
$664$			37.1010i			1.43980i
$665$			29.0291i			1.12570i
$666$			34.9001i			1.35235i
$667$	48.3847			1.87346
$668$		−	53.4481i		−	2.06797i
$669$	−5.41392			−0.209314
$670$		−	56.9020i		−	2.19832i
$671$	9.79440			0.378109
$672$	−122.409			−4.72203
$673$	20.6513			0.796049			0.398024	−	0.917375i	$-0.369696\pi$
$673$	20.6513			0.796049			0.398024	+	0.917375i	$0.369696\pi$
$674$		−	27.6932i		−	1.06670i
$675$	−6.07773			−0.233932
$676$	−36.8270			−1.41642
$677$		−	19.9022i		−	0.764902i	−0.923976	−	0.382451i	$-0.875080\pi$
$677$		−	19.9022i		−	0.764902i	0.923976	−	0.382451i	$-0.124920\pi$
$678$	44.1450			1.69538
$679$	−32.6863			−1.25438
$680$		−	130.145i		−	4.99083i
$681$	−31.6387			−1.21240
$682$	21.5782			0.826274
$683$	−8.05828			−0.308342			−0.154171	−	0.988044i	$-0.549271\pi$
$683$	−8.05828			−0.308342			−0.154171	+	0.988044i	$0.549271\pi$
$684$	28.8786			1.10420
$685$			3.86857i			0.147810i
$686$	−48.6983			−1.85931
$687$		−	0.871152i		−	0.0332365i
$688$		−	33.3973i		−	1.27326i
$689$	−34.1269			−1.30013
$690$		−	43.1864i		−	1.64408i
$691$			31.9451i			1.21525i	0.794224	+	0.607625i	$0.207877\pi$
$691$			31.9451i			1.21525i	−0.794224	+	0.607625i	$0.792123\pi$
$692$		−	103.580i		−	3.93753i
$693$	11.8446			0.449938
$694$	52.8117			2.00471
$695$	13.4789			0.511283
$696$			88.1696i			3.34206i
$697$	2.04407			0.0774245
$698$	0.251254	+	51.3131i	0.00951009	+	1.94223i
$699$	17.9034			0.677170
$700$			26.0838i			0.985875i
$701$	−36.3188			−1.37174			−0.685871	−	0.727723i	$-0.740579\pi$
$701$	−36.3188			−1.37174			−0.685871	+	0.727723i	$0.740579\pi$
$702$	38.1326			1.43922
$703$	29.0549			1.09583
$704$		−	61.3474i		−	2.31212i
$705$		−	4.75028i		−	0.178906i
$706$			23.9753i			0.902324i
$707$	27.1625			1.02155
$708$		−	13.5680i		−	0.509916i
$709$		−	8.58122i		−	0.322274i	−0.986932	−	0.161137i	$-0.948484\pi$
$709$		−	8.58122i		−	0.322274i	0.986932	−	0.161137i	$-0.0515162\pi$
$710$	59.6365			2.23812
$711$		−	7.02957i		−	0.263630i
$712$	59.4439			2.22775
$713$	−27.8279			−1.04216
$714$	96.7851			3.62209
$715$	−9.16632			−0.342801
$716$		−	59.3176i		−	2.21680i
$717$	14.0967			0.526453
$718$	−45.4947			−1.69785
$719$		−	7.69573i		−	0.287002i	−0.989650	−	0.143501i	$-0.954164\pi$
$719$		−	7.69573i		−	0.287002i	0.989650	−	0.143501i	$-0.0458360\pi$
$720$	−46.6324			−1.73789
$721$	−25.4228			−0.946796
$722$			19.4745i			0.724765i
$723$	−18.2777			−0.679756
$724$	31.4139			1.16749
$725$	8.18728			0.304068
$726$			25.5161i			0.946992i
$727$	−43.6660			−1.61948			−0.809741	−	0.586788i	$-0.800392\pi$
$727$	−43.6660			−1.61948			−0.809741	+	0.586788i	$0.800392\pi$
$728$		−	104.623i		−	3.87758i
$729$	23.4795			0.869609
$730$			17.3854i			0.643462i
$731$			14.4476i			0.534362i
$732$		−	36.0041i		−	1.33075i
$733$		−	43.0212i		−	1.58903i	−0.607247	−	0.794513i	$-0.707726\pi$
$733$		−	43.0212i		−	1.58903i	0.607247	−	0.794513i	$-0.292274\pi$
$734$	103.717			3.82825
$735$	26.8971			0.992113
$736$			153.475i			5.65718i
$737$			19.3289i			0.711989i
$738$		−	1.25125i		−	0.0460592i
$739$	6.04822			0.222488			0.111244	−	0.993793i	$-0.464517\pi$
$739$	6.04822			0.222488			0.111244	+	0.993793i	$0.464517\pi$
$740$	−92.1415			−3.38719
$741$		−	10.6251i		−	0.390323i
$742$			158.421i			5.81583i
$743$	28.9247			1.06115			0.530573	−	0.847639i	$-0.321977\pi$
$743$	28.9247			1.06115			0.530573	+	0.847639i	$0.321977\pi$
$744$		−	50.7097i		−	1.85911i
$745$			15.3343i			0.561804i
$746$	−43.5914			−1.59600
$747$	−5.75082			−0.210411
$748$			69.1522i			2.52845i
$749$	−26.5818			−0.971277
$750$		−	40.4069i		−	1.47545i
$751$		−	29.5079i		−	1.07676i	−0.842703	−	0.538379i	$-0.819037\pi$
$751$		−	29.5079i		−	1.07676i	0.842703	−	0.538379i	$-0.180963\pi$
$752$			30.8548i			1.12516i
$753$		−	22.3181i		−	0.813317i
$754$	−51.3682			−1.87072
$755$	0.0195389			0.000711094
$756$		−	130.092i		−	4.73139i
$757$			43.7652i			1.59067i	0.606168	+	0.795337i	$0.292706\pi$
$757$			43.7652i			1.59067i	−0.606168	+	0.795337i	$0.707294\pi$
$758$	18.8890			0.686081
$759$			14.6699i			0.532483i
$760$			66.3239i			2.40582i
$761$		−	21.0710i		−	0.763823i	−0.924199	−	0.381911i	$-0.875266\pi$
$761$		−	21.0710i		−	0.763823i	0.924199	−	0.381911i	$-0.124734\pi$
$762$	29.6474			1.07401
$763$		−	31.3583i		−	1.13525i
$764$	92.4728			3.34555
$765$	20.1730			0.729357
$766$	97.9040			3.53742
$767$	5.05349			0.182471
$768$	−67.7144			−2.44343
$769$		−	33.8386i		−	1.22025i	−0.792305	−	0.610125i	$-0.791119\pi$
$769$		−	33.8386i		−	1.22025i	0.792305	−	0.610125i	$-0.208881\pi$
$770$			42.5513i			1.53344i
$771$	0.696459			0.0250824
$772$			101.311i			3.64628i
$773$	16.6788			0.599896			0.299948	−	0.953956i	$-0.403031\pi$
$773$	16.6788			0.599896			0.299948	+	0.953956i	$0.403031\pi$
$774$	8.84390			0.317887
$775$	−4.70882			−0.169146
$776$	−74.6797			−2.68084
$777$		−	43.8064i		−	1.57155i
$778$	−82.8602			−2.97068
$779$	−1.04169			−0.0373223
$780$			33.6953i			1.20649i
$781$	−20.2578			−0.724880
$782$		−	121.348i		−	4.33941i
$783$	−40.8336			−1.45927
$784$	−174.706			−6.23952
$785$	−8.49095			−0.303055
$786$	59.4441			2.12030
$787$		−	26.3824i		−	0.940429i	−0.882552	−	0.470215i	$-0.844176\pi$
$787$		−	26.3824i		−	0.940429i	0.882552	−	0.470215i	$-0.155824\pi$
$788$		−	75.7134i		−	2.69718i
$789$	−29.4583			−1.04874
$790$	25.2535			0.898480
$791$	56.0933			1.99445
$792$	27.0618			0.961598
$793$	13.4100			0.476203
$794$			32.0721i			1.13820i
$795$		−	32.6180i		−	1.15684i
$796$		−	100.082i		−	3.54730i
$797$			40.4939i			1.43437i	0.696884	+	0.717183i	$0.254569\pi$
$797$			40.4939i			1.43437i	−0.696884	+	0.717183i	$0.745431\pi$
$798$	−49.3232			−1.74602
$799$		−	13.3477i		−	0.472207i
$800$			25.9699i			0.918175i
$801$			9.21406i			0.325563i
$802$	−76.6008			−2.70487
$803$		−	5.90560i		−	0.208404i
$804$	71.0528			2.50584
$805$		−	54.8753i		−	1.93410i
$806$	29.5438			1.04064
$807$	4.30015			0.151372
$808$	62.0592			2.18324
$809$	−0.458673			−0.0161261			−0.00806305	−	0.999967i	$-0.502567\pi$
$809$	−0.458673			−0.0161261			−0.00806305	+	0.999967i	$0.502567\pi$
$810$			11.8996i			0.418109i
$811$			31.3540i			1.10099i	0.834839	+	0.550494i	$0.185561\pi$
$811$			31.3540i			1.10099i	−0.834839	+	0.550494i	$0.814439\pi$
$812$			175.246i			6.14992i
$813$	0.0278777			0.000977713
$814$	42.5891			1.49275
$815$			0.706346i			0.0247422i
$816$	129.436			4.53118
$817$		−	7.36270i		−	0.257588i
$818$			75.2755i			2.63194i
$819$	16.2170			0.566667
$820$	3.30349			0.115363
$821$	5.04126			0.175941			0.0879706	−	0.996123i	$-0.471962\pi$
$821$	5.04126			0.175941			0.0879706	+	0.996123i	$0.471962\pi$
$822$	−6.57306			−0.229262
$823$	−29.4187			−1.02547			−0.512736	−	0.858546i	$-0.671368\pi$
$823$	−29.4187			−1.02547			−0.512736	+	0.858546i	$0.671368\pi$
$824$	−58.0845			−2.02347
$825$			2.48232i			0.0864234i
$826$		−	23.4590i		−	0.816242i
$827$			6.40953i			0.222881i	0.993771	+	0.111441i	$0.0355465\pi$
$827$			6.40953i			0.222881i	−0.993771	+	0.111441i	$0.964454\pi$
$828$	−54.5908			−1.89716
$829$			23.9181i			0.830709i	0.909660	+	0.415354i	$0.136342\pi$
$829$			23.9181i			0.830709i	−0.909660	+	0.415354i	$0.863658\pi$
$830$		−	20.6596i		−	0.717106i
$831$		−	32.6049i		−	1.13105i
$832$		−	83.9937i		−	2.91196i
$833$	75.5774			2.61860
$834$			22.9019i			0.793028i
$835$			19.0270i			0.658455i
$836$		−	35.2410i		−	1.21884i
$837$	23.4850			0.811760
$838$			27.0575i			0.934687i
$839$			44.7934i			1.54644i	0.634138	+	0.773220i	$0.281355\pi$
$839$			44.7934i			1.54644i	−0.634138	+	0.773220i	$0.718645\pi$
$840$	99.9972			3.45023
$841$	26.0067			0.896783
$842$	−43.4477			−1.49731
$843$	−35.5031			−1.22279
$844$			67.6584i			2.32890i
$845$	13.1100			0.450999
$846$	−8.17063			−0.280912
$847$			32.4223i			1.11404i
$848$			211.866i			7.27552i
$849$	−17.2981			−0.593670
$850$		−	20.5336i		−	0.704298i
$851$	−54.9241			−1.88277
$852$			74.4674i			2.55121i
$853$	−34.3475			−1.17604			−0.588018	−	0.808848i	$-0.700091\pi$
$853$	−34.3475			−1.17604			−0.588018	+	0.808848i	$0.700091\pi$
$854$		−	62.2509i		−	2.13018i
$855$	−10.2805			−0.351585
$856$	−60.7324			−2.07579
$857$			23.9746i			0.818957i	0.912320	+	0.409478i	$0.134289\pi$
$857$			23.9746i			0.818957i	−0.912320	+	0.409478i	$0.865711\pi$
$858$		−	15.5745i		−	0.531703i
$859$			40.2404i			1.37299i	0.727137	+	0.686493i	$0.240851\pi$
$859$			40.2404i			1.37299i	−0.727137	+	0.686493i	$0.759149\pi$
$860$			23.3492i			0.796202i
$861$			1.57056i			0.0535246i
$862$	−32.8804			−1.11991
$863$			1.25026i			0.0425595i	0.999774	+	0.0212797i	$0.00677406\pi$
$863$			1.25026i			0.0425595i	−0.999774	+	0.0212797i	$0.993226\pi$
$864$		−	129.524i		−	4.40648i
$865$			36.8735i			1.25374i
$866$	67.8002			2.30395
$867$	−35.2369			−1.19671
$868$		−	100.791i		−	3.42106i
$869$	−8.57830			−0.290999
$870$		−	49.0970i		−	1.66455i
$871$			26.4641i			0.896703i
$872$		−	71.6455i		−	2.42622i
$873$		−	11.5757i		−	0.391777i
$874$			61.8410i			2.09180i
$875$		−	51.3434i		−	1.73572i
$876$	−21.7089			−0.733477
$877$		−	11.1759i		−	0.377385i	−0.982036	−	0.188692i	$-0.939575\pi$
$877$		−	11.1759i		−	0.377385i	0.982036	−	0.188692i	$-0.0604249\pi$
$878$	−67.0902			−2.26418
$879$	−11.7392			−0.395954
$880$			56.9063i			1.91831i
$881$			55.2517i			1.86148i	0.365684	+	0.930739i	$0.380835\pi$
$881$			55.2517i			1.86148i	−0.365684	+	0.930739i	$0.619165\pi$
$882$		−	46.2638i		−	1.55778i
$883$	−9.46038			−0.318367			−0.159184	−	0.987249i	$-0.550886\pi$
$883$	−9.46038			−0.318367			−0.159184	+	0.987249i	$0.550886\pi$
$884$			94.6796i			3.18442i
$885$			4.83007i			0.162361i
$886$		−	40.2899i		−	1.35357i
$887$			18.5086i			0.621458i	0.950499	+	0.310729i	$0.100573\pi$
$887$			18.5086i			0.621458i	−0.950499	+	0.310729i	$0.899427\pi$
$888$		−	100.086i		−	3.35867i
$889$	37.6717			1.26347
$890$	−33.1012			−1.10956
$891$		−	4.04214i		−	0.135417i
$892$	−24.5854			−0.823179
$893$			6.80219i			0.227627i
$894$	−26.0544			−0.871389
$895$			21.1165i			0.705845i
$896$	−189.402			−6.32748
$897$			20.0852i			0.670627i
$898$			2.83629i			0.0946482i
$899$	−31.6365			−1.05514
$900$	−9.23743			−0.307914
$901$		−	91.6526i		−	3.05339i
$902$	−1.52692			−0.0508409
$903$	−11.1008			−0.369412
$904$	128.159			4.26249
$905$	−11.1830			−0.371737
$906$			0.0331985i			0.00110295i
$907$		−	3.06940i		−	0.101918i	−0.998701	−	0.0509589i	$-0.983772\pi$
$907$		−	3.06940i		−	0.101918i	0.998701	−	0.0509589i	$-0.0162278\pi$
$908$	−143.676			−4.76806
$909$			9.61945i			0.319057i
$910$			58.2590i			1.93127i
$911$		−	2.37809i		−	0.0787896i	−0.999224	−	0.0393948i	$-0.987457\pi$
$911$		−	2.37809i		−	0.0787896i	0.999224	−	0.0393948i	$-0.0125430\pi$
$912$	−65.9628			−2.18425
$913$			7.01781i			0.232256i
$914$			26.0400i			0.861328i
$915$			12.8171i			0.423720i
$916$		−	3.95603i		−	0.130711i
$917$	75.5332			2.49433
$918$			102.410i			3.38005i
$919$			26.8132i			0.884486i	0.896895	+	0.442243i	$0.145817\pi$
$919$			26.8132i			0.884486i	−0.896895	+	0.442243i	$0.854183\pi$
$920$		−	125.376i		−	4.13352i
$921$	8.53974			0.281394
$922$	−99.9537			−3.29180
$923$	−27.7359			−0.912939
$924$	−53.1332			−1.74795
$925$	−9.29383			−0.305579
$926$	−8.92926			−0.293434
$927$		−	9.00335i		−	0.295709i
$928$			174.481i			5.72760i
$929$	−45.5694			−1.49508			−0.747541	−	0.664216i	$-0.768766\pi$
$929$	−45.5694			−1.49508			−0.747541	+	0.664216i	$0.768766\pi$
$930$			28.2376i			0.925948i
$931$	−38.5154			−1.26229
$932$	81.3021			2.66314
$933$		−	20.1620i		−	0.660074i
$934$			46.5739i			1.52394i
$935$		−	24.6175i		−	0.805077i
$936$	37.0516			1.21107
$937$	21.8393			0.713458			0.356729	−	0.934208i	$-0.383892\pi$
$937$	21.8393			0.713458			0.356729	+	0.934208i	$0.383892\pi$
$938$	122.850			4.01119
$939$	−30.9183			−1.00898
$940$		−	21.5717i		−	0.703591i
$941$	2.69627			0.0878958			0.0439479	−	0.999034i	$-0.486006\pi$
$941$	2.69627			0.0878958			0.0439479	+	0.999034i	$0.486006\pi$
$942$		−	14.4269i		−	0.470055i
$943$	1.96916			0.0641246
$944$		−	31.3731i		−	1.02111i
$945$			46.3113i			1.50651i
$946$		−	10.7924i		−	0.350890i
$947$	−20.7233			−0.673416			−0.336708	−	0.941609i	$-0.609313\pi$
$947$	−20.7233			−0.673416			−0.336708	+	0.941609i	$0.609313\pi$
$948$			31.5337i			1.02417i
$949$		−	8.08564i		−	0.262471i
$950$			10.4643i			0.339505i
$951$			24.4513i			0.792889i
$952$	280.980			9.10660
$953$	16.8179			0.544784			0.272392	−	0.962186i	$-0.412185\pi$
$953$	16.8179			0.544784			0.272392	+	0.962186i	$0.412185\pi$
$954$	−56.1040			−1.81644
$955$	−32.9194			−1.06525
$956$	64.0154			2.07040
$957$			16.6776i			0.539111i
$958$		−	102.685i		−	3.31759i
$959$	−8.35214			−0.269705
$960$	80.2802			2.59103
$961$	−12.8046			−0.413052
$962$	58.3109			1.88002
$963$		−	9.41379i		−	0.303355i
$964$	−83.0017			−2.67331
$965$		−	36.0658i		−	1.16100i
$966$	93.2383			2.99989
$967$	−56.9340			−1.83087			−0.915437	−	0.402460i	$-0.868155\pi$
$967$	−56.9340			−1.83087			−0.915437	+	0.402460i	$0.868155\pi$
$968$			74.0766i			2.38091i
$969$	28.5353			0.916685
$970$	41.5852			1.33522
$971$	−33.8980			−1.08784			−0.543920	−	0.839137i	$-0.683060\pi$
$971$	−33.8980			−1.08784			−0.543920	+	0.839137i	$0.683060\pi$
$972$	76.7228			2.46088
$973$			29.1005i			0.932921i
$974$	52.6179			1.68599
$975$			3.39867i			0.108845i
$976$		−	83.2519i		−	2.66483i
$977$	52.5455			1.68108			0.840540	−	0.541749i	$-0.182238\pi$
$977$	52.5455			1.68108			0.840540	+	0.541749i	$0.182238\pi$
$978$	−1.20015			−0.0383765
$979$	11.2441			0.359362
$980$	122.143			3.90173
$981$	11.1054			0.354567
$982$		−	6.39255i		−	0.203994i
$983$	33.2600			1.06083			0.530415	−	0.847738i	$-0.322036\pi$
$983$	33.2600			1.06083			0.530415	+	0.847738i	$0.322036\pi$
$984$			3.58832i			0.114392i
$985$			26.9532i			0.858800i
$986$		−	137.957i		−	4.39343i
$987$	10.2557			0.326443
$988$		−	48.2502i		−	1.53504i
$989$			13.9181i			0.442570i
$990$	−15.0693			−0.478933
$991$	−29.5036			−0.937214			−0.468607	−	0.883407i	$-0.655244\pi$
$991$	−29.5036			−0.937214			−0.468607	+	0.883407i	$0.655244\pi$
$992$		−	100.351i		−	3.18613i
$993$			20.3456i			0.645648i
$994$			128.754i			4.08382i
$995$			35.6281i			1.12949i
$996$	25.7974			0.817422
$997$			17.0548i			0.540132i	0.962842	+	0.270066i	$0.0870455\pi$
$997$			17.0548i			0.540132i	−0.962842	+	0.270066i	$0.912955\pi$
$998$	88.1318			2.78976
$999$	46.3525			1.46653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.b.b.348.1	✓	26
349.348	even	2	inner	349.2.b.b.348.26	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.b.b.348.1	✓	26	1.1	even	1	trivial
349.2.b.b.348.26	yes	26	349.348	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.74676i q^{2} -1.22099 q^{3} -5.54469 q^{4} +1.97385 q^{5} +3.35376i q^{6} +4.26150i q^{7} +9.73641i q^{8} -1.50918 q^{9} +O(q^{10})\)	\(q-2.74676i q^{2} -1.22099 q^{3} -5.54469 q^{4} +1.97385 q^{5} +3.35376i q^{6} +4.26150i q^{7} +9.73641i q^{8} -1.50918 q^{9} -5.42170i q^{10} +1.84168i q^{11} +6.77001 q^{12} +2.52154i q^{13} +11.7053 q^{14} -2.41005 q^{15} +15.6542 q^{16} -6.77195 q^{17} +4.14537i q^{18} +3.45109 q^{19} -10.9444 q^{20} -5.20324i q^{21} +5.05866 q^{22} -6.52379 q^{23} -11.8881i q^{24} -1.10390 q^{25} +6.92606 q^{26} +5.50567 q^{27} -23.6287i q^{28} -7.41665 q^{29} +6.61984i q^{30} +4.26560 q^{31} -23.5255i q^{32} -2.24867i q^{33} +18.6009i q^{34} +8.41157i q^{35} +8.36796 q^{36} +8.41906 q^{37} -9.47931i q^{38} -3.07877i q^{39} +19.2182i q^{40} -0.301843 q^{41} -14.2921 q^{42} -2.13344i q^{43} -10.2116i q^{44} -2.97891 q^{45} +17.9193i q^{46} +1.97103i q^{47} -19.1136 q^{48} -11.1604 q^{49} +3.03216i q^{50} +8.26848 q^{51} -13.9811i q^{52} +13.5342i q^{53} -15.1227i q^{54} +3.63521i q^{55} -41.4917 q^{56} -4.21374 q^{57} +20.3718i q^{58} -2.00413i q^{59} +13.3630 q^{60} -5.31818i q^{61} -11.7166i q^{62} -6.43139i q^{63} -33.3105 q^{64} +4.97714i q^{65} -6.17657 q^{66} +10.4952 q^{67} +37.5484 q^{68} +7.96547 q^{69} +23.1046 q^{70} +10.9996i q^{71} -14.6940i q^{72} -3.20663 q^{73} -23.1251i q^{74} +1.34786 q^{75} -19.1352 q^{76} -7.84832 q^{77} -8.45664 q^{78} +4.65786i q^{79} +30.8991 q^{80} -2.19481 q^{81} +0.829090i q^{82} +3.81054 q^{83} +28.8504i q^{84} -13.3668 q^{85} -5.86005 q^{86} +9.05565 q^{87} -17.9314 q^{88} -6.10532i q^{89} +8.18235i q^{90} -10.7455 q^{91} +36.1724 q^{92} -5.20826 q^{93} +5.41393 q^{94} +6.81194 q^{95} +28.7244i q^{96} +7.67014i q^{97} +30.6548i q^{98} -2.77944i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9}+O(q^{10}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9	\( 26 q - 2 q^{3} - 36 q^{4} - 12 q^{5} + 32 q^{9} + 12 q^{12} + 4 q^{14} + 12 q^{15} + 20 q^{16} - 14 q^{17} - 4 q^{19} - 2 q^{20} - 12 q^{22} - 18 q^{23} + 18 q^{25} + 22 q^{26} + 4 q^{27} - 18 q^{29} + 10 q^{31} - 54 q^{36} + 30 q^{37} - 16 q^{41} - 44 q^{45} - 74 q^{48} - 22 q^{49} + 32 q^{51} - 38 q^{56} - 16 q^{57} - 78 q^{60} - 96 q^{64} + 104 q^{66} + 72 q^{67} + 36 q^{68} - 40 q^{69} + 86 q^{70} + 72 q^{73} - 38 q^{75} + 96 q^{76} - 28 q^{77} - 30 q^{78} + 30 q^{80} - 6 q^{81} - 8 q^{83} - 22 q^{85} + 60 q^{86} + 32 q^{87} + 110 q^{88} - 12 q^{91} + 14 q^{92} + 84 q^{93} + 22 q^{94} - 10 q^{95}+O(q^{100}) \) 26 * q - 2 * q^3 - 36 * q^4 - 12 * q^5 + 32 * q^9 + 12 * q^12 + 4 * q^14 + 12 * q^15 + 20 * q^16 - 14 * q^17 - 4 * q^19 - 2 * q^20 - 12 * q^22 - 18 * q^23 + 18 * q^25 + 22 * q^26 + 4 * q^27 - 18 * q^29 + 10 * q^31 - 54 * q^36 + 30 * q^37 - 16 * q^41 - 44 * q^45 - 74 * q^48 - 22 * q^49 + 32 * q^51 - 38 * q^56 - 16 * q^57 - 78 * q^60 - 96 * q^64 + 104 * q^66 + 72 * q^67 + 36 * q^68 - 40 * q^69 + 86 * q^70 + 72 * q^73 - 38 * q^75 + 96 * q^76 - 28 * q^77 - 30 * q^78 + 30 * q^80 - 6 * q^81 - 8 * q^83 - 22 * q^85 + 60 * q^86 + 32 * q^87 + 110 * q^88 - 12 * q^91 + 14 * q^92 + 84 * q^93 + 22 * q^94 - 10 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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