LMFDB - Embedded newform 1045.2.f.a.626.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.12
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.a.626.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53521 q^{2} +1.36588i q^{3} +0.356884 q^{4} -1.00000 q^{5} -2.09692i q^{6} +1.36858i q^{7} +2.52254 q^{8} +1.13438 q^{9} +O(q^{10})$	\(q-1.53521 q^{2} +1.36588i q^{3} +0.356884 q^{4} -1.00000 q^{5} -2.09692i q^{6} +1.36858i q^{7} +2.52254 q^{8} +1.13438 q^{9} +1.53521 q^{10} +(-3.14305 + 1.05890i) q^{11} +0.487460i q^{12} +5.07607 q^{13} -2.10106i q^{14} -1.36588i q^{15} -4.58640 q^{16} -7.63001i q^{17} -1.74151 q^{18} +(3.99075 - 1.75326i) q^{19} -0.356884 q^{20} -1.86931 q^{21} +(4.82525 - 1.62563i) q^{22} -1.64625 q^{23} +3.44547i q^{24} +1.00000 q^{25} -7.79286 q^{26} +5.64705i q^{27} +0.488423i q^{28} +1.47543 q^{29} +2.09692i q^{30} -4.43502i q^{31} +1.99604 q^{32} +(-1.44632 - 4.29302i) q^{33} +11.7137i q^{34} -1.36858i q^{35} +0.404842 q^{36} -2.89873i q^{37} +(-6.12666 + 2.69163i) q^{38} +6.93329i q^{39} -2.52254 q^{40} +4.91058 q^{41} +2.86979 q^{42} +0.286532i q^{43} +(-1.12170 + 0.377903i) q^{44} -1.13438 q^{45} +2.52735 q^{46} +4.33371 q^{47} -6.26446i q^{48} +5.12700 q^{49} -1.53521 q^{50} +10.4217 q^{51} +1.81157 q^{52} -12.4380i q^{53} -8.66944i q^{54} +(3.14305 - 1.05890i) q^{55} +3.45228i q^{56} +(2.39474 + 5.45087i) q^{57} -2.26510 q^{58} +7.90366i q^{59} -0.487460i q^{60} +15.1532i q^{61} +6.80871i q^{62} +1.55248i q^{63} +6.10845 q^{64} -5.07607 q^{65} +(2.22041 + 6.59070i) q^{66} +4.88853i q^{67} -2.72303i q^{68} -2.24858i q^{69} +2.10106i q^{70} +7.90585i q^{71} +2.86151 q^{72} -10.4311i q^{73} +4.45017i q^{74} +1.36588i q^{75} +(1.42424 - 0.625712i) q^{76} +(-1.44918 - 4.30150i) q^{77} -10.6441i q^{78} +10.1671 q^{79} +4.58640 q^{80} -4.31005 q^{81} -7.53879 q^{82} -1.19216i q^{83} -0.667127 q^{84} +7.63001i q^{85} -0.439888i q^{86} +2.01525i q^{87} +(-7.92845 + 2.67110i) q^{88} +8.37475i q^{89} +1.74151 q^{90} +6.94699i q^{91} -0.587522 q^{92} +6.05770 q^{93} -6.65317 q^{94} +(-3.99075 + 1.75326i) q^{95} +2.72635i q^{96} +13.3176i q^{97} -7.87105 q^{98} +(-3.56540 + 1.20119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.53521			−1.08556			−0.542780	−	0.839875i	$-0.682628\pi$
$2$	−1.53521			−1.08556			−0.542780	+	0.839875i	$0.682628\pi$
$3$			1.36588i			0.788590i	0.918984	+	0.394295i	$0.129011\pi$
$3$			1.36588i			0.788590i	−0.918984	+	0.394295i	$0.870989\pi$
$4$	0.356884			0.178442
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		−	2.09692i		−	0.856062i
$7$			1.36858i			0.517273i	0.965975	+	0.258637i	$0.0832732\pi$
$7$			1.36858i			0.517273i	−0.965975	+	0.258637i	$0.916727\pi$
$8$	2.52254			0.891851
$9$	1.13438			0.378126
$10$	1.53521			0.485478
$11$	−3.14305	+	1.05890i	−0.947664	+	0.319269i
$11$	−3.14305	+	1.05890i	−0.947664	+	0.319269i
$12$			0.487460i			0.140718i
$13$	5.07607			1.40785			0.703925	−	0.710275i	$-0.251429\pi$
$13$	5.07607			1.40785			0.703925	+	0.710275i	$0.251429\pi$
$14$		−	2.10106i		−	0.561531i
$15$		−	1.36588i		−	0.352668i
$16$	−4.58640			−1.14660
$17$		−	7.63001i		−	1.85055i	−0.379297	−	0.925275i	$-0.623834\pi$
$17$		−	7.63001i		−	1.85055i	0.379297	−	0.925275i	$-0.376166\pi$
$18$	−1.74151			−0.410479
$19$	3.99075	−	1.75326i	0.915540	−	0.402226i
$19$	3.99075	−	1.75326i	0.915540	−	0.402226i
$20$	−0.356884			−0.0798018
$21$	−1.86931			−0.407916
$22$	4.82525	−	1.62563i	1.02875	−	0.346586i
$23$	−1.64625			−0.343268			−0.171634	−	0.985161i	$-0.554905\pi$
$23$	−1.64625			−0.343268			−0.171634	+	0.985161i	$0.554905\pi$
$24$			3.44547i			0.703305i
$25$	1.00000			0.200000
$26$	−7.79286			−1.52831
$27$			5.64705i			1.08678i
$28$			0.488423i			0.0923033i
$29$	1.47543			0.273980			0.136990	−	0.990572i	$-0.456257\pi$
$29$	1.47543			0.273980			0.136990	+	0.990572i	$0.456257\pi$
$30$			2.09692i			0.382843i
$31$		−	4.43502i		−	0.796554i	−0.917265	−	0.398277i	$-0.869608\pi$
$31$		−	4.43502i		−	0.796554i	0.917265	−	0.398277i	$-0.130392\pi$
$32$	1.99604			0.352854
$33$	−1.44632	−	4.29302i	−0.251772	−	0.747318i
$34$			11.7137i			2.00888i
$35$		−	1.36858i		−	0.231332i
$36$	0.404842			0.0674736
$37$		−	2.89873i		−	0.476548i	−0.971198	−	0.238274i	$-0.923418\pi$
$37$		−	2.89873i		−	0.476548i	0.971198	−	0.238274i	$-0.0765816\pi$
$38$	−6.12666	+	2.69163i	−0.993875	+	0.436641i
$39$			6.93329i			1.11022i
$40$	−2.52254			−0.398848
$41$	4.91058			0.766903			0.383452	−	0.923561i	$-0.374735\pi$
$41$	4.91058			0.766903			0.383452	+	0.923561i	$0.374735\pi$
$42$	2.86979			0.442818
$43$			0.286532i			0.0436957i	0.999761	+	0.0218479i	$0.00695495\pi$
$43$			0.286532i			0.0436957i	−0.999761	+	0.0218479i	$0.993045\pi$
$44$	−1.12170	+	0.377903i	−0.169103	+	0.0569710i
$45$	−1.13438			−0.169103
$46$	2.52735			0.372638
$47$	4.33371			0.632136			0.316068	−	0.948737i	$-0.397637\pi$
$47$	4.33371			0.632136			0.316068	+	0.948737i	$0.397637\pi$
$48$		−	6.26446i		−	0.904198i
$49$	5.12700			0.732429
$50$	−1.53521			−0.217112
$51$	10.4217			1.45933
$52$	1.81157			0.251220
$53$		−	12.4380i		−	1.70848i	−0.519875	−	0.854242i	$-0.674022\pi$
$53$		−	12.4380i		−	1.70848i	0.519875	−	0.854242i	$-0.325978\pi$
$54$		−	8.66944i		−	1.17976i
$55$	3.14305	−	1.05890i	0.423808	−	0.142781i
$56$			3.45228i			0.461331i
$57$	2.39474	+	5.45087i	0.317191	+	0.721986i
$58$	−2.26510			−0.297422
$59$			7.90366i			1.02897i	0.857500	+	0.514484i	$0.172017\pi$
$59$			7.90366i			1.02897i	−0.857500	+	0.514484i	$0.827983\pi$
$60$		−	0.487460i		−	0.0629309i
$61$			15.1532i			1.94017i	0.242769	+	0.970084i	$0.421944\pi$
$61$			15.1532i			1.94017i	−0.242769	+	0.970084i	$0.578056\pi$
$62$			6.80871i			0.864707i
$63$			1.55248i			0.195594i
$64$	6.10845			0.763556
$65$	−5.07607			−0.629609
$66$	2.22041	+	6.59070i	0.273314	+	0.811259i
$67$			4.88853i			0.597229i	0.954374	+	0.298614i	$0.0965245\pi$
$67$			4.88853i			0.597229i	−0.954374	+	0.298614i	$0.903476\pi$
$68$		−	2.72303i		−	0.330216i
$69$		−	2.24858i		−	0.270697i
$70$			2.10106i			0.251124i
$71$			7.90585i			0.938251i	0.883131	+	0.469126i	$0.155431\pi$
$71$			7.90585i			0.938251i	−0.883131	+	0.469126i	$0.844569\pi$
$72$	2.86151			0.337232
$73$		−	10.4311i		−	1.22087i	−0.792067	−	0.610434i	$-0.790995\pi$
$73$		−	10.4311i		−	1.22087i	0.792067	−	0.610434i	$-0.209005\pi$
$74$			4.45017i			0.517322i
$75$			1.36588i			0.157718i
$76$	1.42424	−	0.625712i	0.163371	−	0.0717741i
$77$	−1.44918	−	4.30150i	−0.165149	−	0.490201i
$78$		−	10.6441i		−	1.20521i
$79$	10.1671			1.14389			0.571946	−	0.820291i	$-0.306189\pi$
$79$	10.1671			1.14389			0.571946	+	0.820291i	$0.306189\pi$
$80$	4.58640			0.512775
$81$	−4.31005			−0.478895
$82$	−7.53879			−0.832520
$83$		−	1.19216i		−	0.130856i	−0.997857	−	0.0654282i	$-0.979159\pi$
$83$		−	1.19216i		−	0.130856i	0.997857	−	0.0654282i	$-0.0208413\pi$
$84$	−0.667127			−0.0727895
$85$			7.63001i			0.827591i
$86$		−	0.439888i		−	0.0474344i
$87$			2.01525i			0.216058i
$88$	−7.92845	+	2.67110i	−0.845175	+	0.284740i
$89$			8.37475i			0.887722i	0.896096	+	0.443861i	$0.146392\pi$
$89$			8.37475i			0.887722i	−0.896096	+	0.443861i	$0.853608\pi$
$90$	1.74151			0.183572
$91$			6.94699i			0.728242i
$92$	−0.587522			−0.0612535
$93$	6.05770			0.628154
$94$	−6.65317			−0.686222
$95$	−3.99075	+	1.75326i	−0.409442	+	0.179881i
$96$			2.72635i			0.278257i
$97$			13.3176i			1.35220i	0.736809	+	0.676101i	$0.236332\pi$
$97$			13.3176i			1.35220i	−0.736809	+	0.676101i	$0.763668\pi$
$98$	−7.87105			−0.795096
$99$	−3.56540	+	1.20119i	−0.358337	+	0.120724i
$100$	0.356884			0.0356884
$101$		−	4.46305i		−	0.444090i	−0.975036	−	0.222045i	$-0.928727\pi$
$101$		−	4.46305i		−	0.444090i	0.975036	−	0.222045i	$-0.0712733\pi$
$102$	−15.9995			−1.58419
$103$			3.62575i			0.357255i	0.983917	+	0.178628i	$0.0571658\pi$
$103$			3.62575i			0.357255i	−0.983917	+	0.178628i	$0.942834\pi$
$104$	12.8046			1.25559
$105$	1.86931			0.182426
$106$			19.0949i			1.85466i
$107$	−2.68492			−0.259561			−0.129781	−	0.991543i	$-0.541427\pi$
$107$	−2.68492			−0.259561			−0.129781	+	0.991543i	$0.541427\pi$
$108$			2.01535i			0.193927i
$109$	−2.73199			−0.261677			−0.130839	−	0.991404i	$-0.541767\pi$
$109$	−2.73199			−0.261677			−0.130839	+	0.991404i	$0.541767\pi$
$110$	−4.82525	+	1.62563i	−0.460070	+	0.154998i
$111$	3.95931			0.375801
$112$		−	6.27684i		−	0.593106i
$113$			2.52242i			0.237290i	0.992937	+	0.118645i	$0.0378550\pi$
$113$			2.52242i			0.237290i	−0.992937	+	0.118645i	$0.962145\pi$
$114$	−3.67644	−	8.36826i	−0.344331	−	0.783759i
$115$	1.64625			0.153514
$116$	0.526556			0.0488895
$117$	5.75819			0.532345
$118$		−	12.1338i		−	1.11701i
$119$	10.4423			0.957240
$120$		−	3.44547i		−	0.314527i
$121$	8.75748	−	6.65631i	0.796135	−	0.605119i
$122$		−	23.2634i		−	2.10617i
$123$			6.70725i			0.604772i
$124$		−	1.58279i		−	0.142139i
$125$	−1.00000			−0.0894427
$126$		−	2.38339i		−	0.212330i
$127$	9.64064			0.855469			0.427734	−	0.903904i	$-0.359312\pi$
$127$	9.64064			0.855469			0.427734	+	0.903904i	$0.359312\pi$
$128$	−13.3699			−1.18174
$129$	−0.391368			−0.0344580
$130$	7.79286			0.683479
$131$			0.0727826i			0.00635904i	0.999995	+	0.00317952i	$0.00101207\pi$
$131$			0.0727826i			0.00635904i	−0.999995	+	0.00317952i	$0.998988\pi$
$132$	−0.516169	−	1.53211i	−0.0449268	−	0.133353i
$133$	2.39947	+	5.46164i	0.208061	+	0.473584i
$134$		−	7.50494i		−	0.648328i
$135$		−	5.64705i		−	0.486021i
$136$		−	19.2470i		−	1.65041i
$137$	20.1046			1.71765			0.858825	−	0.512268i	$-0.171195\pi$
$137$	20.1046			1.71765			0.858825	+	0.512268i	$0.171195\pi$
$138$			3.45206i			0.293859i
$139$			11.5562i			0.980182i	0.871671	+	0.490091i	$0.163037\pi$
$139$			11.5562i			0.980182i	−0.871671	+	0.490091i	$0.836963\pi$
$140$		−	0.488423i		−	0.0412793i
$141$			5.91931i			0.498496i
$142$		−	12.1372i		−	1.01853i
$143$	−15.9543	+	5.37503i	−1.33417	+	0.449482i
$144$	−5.20272			−0.433560
$145$	−1.47543			−0.122527
$146$			16.0140i			1.32533i
$147$			7.00285i			0.577586i
$148$		−	1.03451i		−	0.0850362i
$149$			5.76530i			0.472311i	0.971715	+	0.236156i	$0.0758876\pi$
$149$			5.76530i			0.472311i	−0.971715	+	0.236156i	$0.924112\pi$
$150$		−	2.09692i		−	0.171212i
$151$	10.2502			0.834152			0.417076	−	0.908872i	$-0.363055\pi$
$151$	10.2502			0.834152			0.417076	+	0.908872i	$0.363055\pi$
$152$	10.0668	−	4.42267i	0.816526	−	0.358726i
$153$		−	8.65532i		−	0.699741i
$154$	2.22480	+	6.60372i	0.179280	+	0.532143i
$155$			4.43502i			0.356230i
$156$			2.47438i			0.198109i
$157$	−12.9037			−1.02983			−0.514914	−	0.857242i	$-0.672176\pi$
$157$	−12.9037			−1.02983			−0.514914	+	0.857242i	$0.672176\pi$
$158$	−15.6087			−1.24176
$159$	16.9887			1.34729
$160$	−1.99604			−0.157801
$161$		−	2.25302i		−	0.177563i
$162$	6.61685			0.519869
$163$	−9.58063			−0.750413			−0.375207	−	0.926941i	$-0.622428\pi$
$163$	−9.58063			−0.750413			−0.375207	+	0.926941i	$0.622428\pi$
$164$	1.75251			0.136848
$165$	1.44632	+	4.29302i	0.112596	+	0.334211i
$166$			1.83022i			0.142053i
$167$	0.139417			0.0107884			0.00539421	−	0.999985i	$-0.498283\pi$
$167$	0.139417			0.0107884			0.00539421	+	0.999985i	$0.498283\pi$
$168$	−4.71539			−0.363801
$169$	12.7665			0.982039
$170$		−	11.7137i		−	0.898401i
$171$	4.52702	−	1.98886i	0.346190	−	0.152092i
$172$			0.102259i			0.00779716i
$173$	7.05380			0.536290			0.268145	−	0.963379i	$-0.413589\pi$
$173$	7.05380			0.536290			0.268145	+	0.963379i	$0.413589\pi$
$174$		−	3.09384i		−	0.234544i
$175$			1.36858i			0.103455i
$176$	14.4153	−	4.85652i	1.08659	−	0.366074i
$177$	−10.7954			−0.811434
$178$		−	12.8570i		−	0.963676i
$179$		−	23.6118i		−	1.76483i	−0.470473	−	0.882414i	$-0.655917\pi$
$179$		−	23.6118i		−	1.76483i	0.470473	−	0.882414i	$-0.344083\pi$
$180$	−0.404842			−0.0301751
$181$			7.51200i			0.558363i	0.960238	+	0.279181i	$0.0900630\pi$
$181$			7.51200i			0.558363i	−0.960238	+	0.279181i	$0.909937\pi$
$182$		−	10.6651i		−	0.790551i
$183$	−20.6974			−1.53000
$184$	−4.15274			−0.306144
$185$			2.89873i			0.213119i
$186$	−9.29987			−0.681899
$187$	8.07939	+	23.9815i	0.590823	+	1.75370i
$188$	1.54663			0.112800
$189$	−7.72842			−0.562160
$190$	6.12666	−	2.69163i	0.444474	−	0.195272i
$191$	−26.5837			−1.92353			−0.961763	−	0.273884i	$-0.911692\pi$
$191$	−26.5837			−1.92353			−0.961763	+	0.273884i	$0.911692\pi$
$192$			8.34340i			0.602133i
$193$	5.02925			0.362013			0.181007	−	0.983482i	$-0.442064\pi$
$193$	5.02925			0.362013			0.181007	+	0.983482i	$0.442064\pi$
$194$		−	20.4454i		−	1.46790i
$195$		−	6.93329i		−	0.496503i
$196$	1.82975			0.130696
$197$		−	18.5028i		−	1.31827i	−0.752023	−	0.659136i	$-0.770922\pi$
$197$		−	18.5028i		−	1.31827i	0.752023	−	0.659136i	$-0.229078\pi$
$198$	5.47366	−	1.84408i	0.388996	−	0.131053i
$199$	9.28818			0.658422			0.329211	−	0.944256i	$-0.393217\pi$
$199$	9.28818			0.658422			0.329211	+	0.944256i	$0.393217\pi$
$200$	2.52254			0.178370
$201$	−6.67713			−0.470969
$202$			6.85175i			0.482087i
$203$			2.01923i			0.141722i
$204$	3.71933			0.260405
$205$	−4.91058			−0.342969
$206$		−	5.56630i		−	0.387822i
$207$	−1.86748			−0.129799
$208$	−23.2809			−1.61424
$209$	−10.6866	+	9.73637i	−0.739207	+	0.673479i
$210$	−2.86979			−0.198034
$211$	9.20297			0.633558			0.316779	−	0.948499i	$-0.397399\pi$
$211$	9.20297			0.633558			0.316779	+	0.948499i	$0.397399\pi$
$212$		−	4.43891i		−	0.304866i
$213$	−10.7984			−0.739895
$214$	4.12193			0.281769
$215$		−	0.286532i		−	0.0195413i
$216$			14.2449i			0.969242i
$217$	6.06967			0.412036
$218$	4.19419			0.284067
$219$	14.2476			0.962765
$220$	1.12170	−	0.377903i	0.0756253	−	0.0254782i
$221$		−	38.7305i		−	2.60530i
$222$	−6.07839			−0.407955
$223$		−	12.4170i		−	0.831501i	−0.909479	−	0.415750i	$-0.863519\pi$
$223$		−	12.4170i		−	0.831501i	0.909479	−	0.415750i	$-0.136481\pi$
$224$			2.73173i			0.182522i
$225$	1.13438			0.0756252
$226$		−	3.87246i		−	0.257592i
$227$	−5.82492			−0.386613			−0.193307	−	0.981138i	$-0.561921\pi$
$227$	−5.82492			−0.386613			−0.193307	+	0.981138i	$0.561921\pi$
$228$	0.854646	+	1.94533i	0.0566003	+	0.128833i
$229$	7.59099			0.501627			0.250814	−	0.968035i	$-0.419302\pi$
$229$	7.59099			0.501627			0.250814	+	0.968035i	$0.419302\pi$
$230$	−2.52735			−0.166649
$231$	5.87532	−	1.97940i	0.386568	−	0.130235i
$232$	3.72181			0.244349
$233$		−	10.7500i		−	0.704253i	−0.935952	−	0.352127i	$-0.885459\pi$
$233$		−	10.7500i		−	0.704253i	0.935952	−	0.352127i	$-0.114541\pi$
$234$	−8.84005			−0.577892
$235$	−4.33371			−0.282700
$236$			2.82069i			0.183611i
$237$			13.8871i			0.902062i
$238$	−16.0311			−1.03914
$239$			12.0267i			0.777944i	0.921250	+	0.388972i	$0.127170\pi$
$239$			12.0267i			0.777944i	−0.921250	+	0.388972i	$0.872830\pi$
$240$			6.26446i			0.404369i
$241$	17.6062			1.13412			0.567058	−	0.823678i	$-0.308082\pi$
$241$	17.6062			1.13412			0.567058	+	0.823678i	$0.308082\pi$
$242$	−13.4446	+	10.2189i	−0.864253	+	0.656894i
$243$			11.0542i			0.709125i
$244$			5.40794i			0.346208i
$245$	−5.12700			−0.327552
$246$		−	10.2971i		−	0.656517i
$247$	20.2573	−	8.89969i	1.28894	−	0.566274i
$248$		−	11.1875i		−	0.710407i
$249$	1.62834			0.103192
$250$	1.53521			0.0970955
$251$	−24.7488			−1.56213			−0.781067	−	0.624448i	$-0.785324\pi$
$251$	−24.7488			−1.56213			−0.781067	+	0.624448i	$0.785324\pi$
$252$			0.554057i			0.0349023i
$253$	5.17425	−	1.74321i	0.325303	−	0.109595i
$254$	−14.8005			−0.928663
$255$	−10.4217			−0.652630
$256$	8.30872			0.519295
$257$		−	22.3043i		−	1.39130i	−0.718379	−	0.695652i	$-0.755116\pi$
$257$		−	22.3043i		−	1.39130i	0.718379	−	0.695652i	$-0.244884\pi$
$258$	0.600834			0.0374063
$259$	3.96713			0.246505
$260$	−1.81157			−0.112349
$261$	1.67369			0.103599
$262$		−	0.111737i		−	0.00690313i
$263$		−	24.8473i		−	1.53215i	−0.642752	−	0.766074i	$-0.722208\pi$
$263$		−	24.8473i		−	1.53215i	0.642752	−	0.766074i	$-0.277792\pi$
$264$	−3.64840	−	10.8293i	−0.224543	−	0.666497i
$265$			12.4380i			0.764057i
$266$	−3.68371	−	8.38479i	−0.225863	−	0.514105i
$267$	−11.4389			−0.700049
$268$			1.74464i			0.106571i
$269$			23.0947i			1.40811i	0.710147	+	0.704053i	$0.248628\pi$
$269$			23.0947i			1.40811i	−0.710147	+	0.704053i	$0.751372\pi$
$270$			8.66944i			0.527605i
$271$		−	23.0380i		−	1.39946i	−0.714409	−	0.699728i	$-0.753304\pi$
$271$		−	23.0380i		−	1.39946i	0.714409	−	0.699728i	$-0.246696\pi$
$272$			34.9943i			2.12184i
$273$	−9.48874			−0.574285
$274$	−30.8649			−1.86461
$275$	−3.14305	+	1.05890i	−0.189533	+	0.0638538i
$276$		−	0.802484i		−	0.0483039i
$277$		−	3.23655i		−	0.194465i	−0.995262	−	0.0972327i	$-0.969001\pi$
$277$		−	3.23655i		−	0.194465i	0.995262	−	0.0972327i	$-0.0309991\pi$
$278$		−	17.7412i		−	1.06405i
$279$		−	5.03099i		−	0.301198i
$280$		−	3.45228i		−	0.206313i
$281$	−21.4669			−1.28061			−0.640304	−	0.768121i	$-0.721192\pi$
$281$	−21.4669			−1.28061			−0.640304	+	0.768121i	$0.721192\pi$
$282$		−	9.08742i		−	0.541148i
$283$			10.6220i			0.631414i	0.948857	+	0.315707i	$0.102242\pi$
$283$			10.6220i			0.631414i	−0.948857	+	0.315707i	$0.897758\pi$
$284$			2.82147i			0.167424i
$285$	−2.39474	−	5.45087i	−0.141852	−	0.322882i
$286$	24.4933	−	8.25182i	1.44832	−	0.487941i
$287$			6.72050i			0.396698i
$288$	2.26427			0.133423
$289$	−41.2171			−2.42454
$290$	2.26510			0.133011
$291$	−18.1903			−1.06633
$292$		−	3.72270i		−	0.217854i
$293$	1.78302			0.104165			0.0520825	−	0.998643i	$-0.483414\pi$
$293$	1.78302			0.104165			0.0520825	+	0.998643i	$0.483414\pi$
$294$		−	10.7509i		−	0.627004i
$295$		−	7.90366i		−	0.460169i
$296$		−	7.31214i		−	0.425010i
$297$	−5.97964	−	17.7490i	−0.346974	−	1.02990i
$298$		−	8.85097i		−	0.512723i
$299$	−8.35651			−0.483269
$300$			0.487460i			0.0281435i
$301$	−0.392141			−0.0226026
$302$	−15.7363			−0.905523
$303$	6.09599			0.350205
$304$	−18.3032	+	8.04117i	−1.04976	+	0.461193i
$305$		−	15.1532i		−	0.867670i
$306$			13.2878i			0.759612i
$307$	2.89529			0.165243			0.0826215	−	0.996581i	$-0.473671\pi$
$307$	2.89529			0.165243			0.0826215	+	0.996581i	$0.473671\pi$
$308$	−0.517189	−	1.53514i	−0.0294696	−	0.0874726i
$309$	−4.95233			−0.281728
$310$		−	6.80871i		−	0.386709i
$311$	−10.8244			−0.613796			−0.306898	−	0.951742i	$-0.599291\pi$
$311$	−10.8244			−0.613796			−0.306898	+	0.951742i	$0.599291\pi$
$312$			17.4895i			0.990147i
$313$	15.0378			0.849987			0.424993	−	0.905197i	$-0.360276\pi$
$313$	15.0378			0.849987			0.424993	+	0.905197i	$0.360276\pi$
$314$	19.8100			1.11794
$315$		−	1.55248i		−	0.0874725i
$316$	3.62849			0.204119
$317$		−	2.74205i		−	0.154009i	−0.997031	−	0.0770046i	$-0.975464\pi$
$317$		−	2.74205i		−	0.154009i	0.997031	−	0.0770046i	$-0.0245356\pi$
$318$	−26.0813			−1.46257
$319$	−4.63733	+	1.56232i	−0.259641	+	0.0874732i
$320$	−6.10845			−0.341473
$321$		−	3.66727i		−	0.204687i
$322$			3.45888i			0.192756i
$323$	−13.3774	−	30.4495i	−0.744340	−	1.69425i
$324$	−1.53819			−0.0854550
$325$	5.07607			0.281570
$326$	14.7083			0.814619
$327$		−	3.73157i		−	0.206356i
$328$	12.3871			0.683963
$329$			5.93101i			0.326987i
$330$	−2.22041	−	6.59070i	−0.122230	−	0.362806i
$331$			3.49931i			0.192340i	0.995365	+	0.0961699i	$0.0306592\pi$
$331$			3.49931i			0.192340i	−0.995365	+	0.0961699i	$0.969341\pi$
$332$		−	0.425463i		−	0.0233503i
$333$		−	3.28825i		−	0.180195i
$334$	−0.214035			−0.0117115
$335$		−	4.88853i		−	0.267089i
$336$	8.57340			0.467717
$337$	−16.8603			−0.918438			−0.459219	−	0.888323i	$-0.651871\pi$
$337$	−16.8603			−0.918438			−0.459219	+	0.888323i	$0.651871\pi$
$338$	−19.5993			−1.06606
$339$	−3.44532			−0.187124
$340$			2.72303i			0.147677i
$341$	4.69622	+	13.9395i	0.254315	+	0.754865i
$342$	−6.94994	+	3.05333i	−0.375810	+	0.165105i
$343$			16.5967i			0.896139i
$344$			0.722787i			0.0389701i
$345$			2.24858i			0.121060i
$346$	−10.8291			−0.582176
$347$			22.6301i			1.21485i	0.794377	+	0.607425i	$0.207797\pi$
$347$			22.6301i			1.21485i	−0.794377	+	0.607425i	$0.792203\pi$
$348$			0.719211i			0.0385538i
$349$			6.34613i			0.339701i	0.985470	+	0.169850i	$0.0543284\pi$
$349$			6.34613i			0.339701i	−0.985470	+	0.169850i	$0.945672\pi$
$350$		−	2.10106i		−	0.112306i
$351$			28.6649i			1.53002i
$352$	−6.27365	+	2.11360i	−0.334387	+	0.112655i
$353$	5.62040			0.299144			0.149572	−	0.988751i	$-0.452210\pi$
$353$	5.62040			0.299144			0.149572	+	0.988751i	$0.452210\pi$
$354$	16.5733			0.880861
$355$		−	7.90585i		−	0.419599i
$356$			2.98882i			0.158407i
$357$			14.2628i			0.754870i
$358$			36.2492i			1.91583i
$359$			27.7822i			1.46629i	0.680074	+	0.733144i	$0.261948\pi$
$359$			27.7822i			1.46629i	−0.680074	+	0.733144i	$0.738052\pi$
$360$	−2.86151			−0.150815
$361$	12.8521	−	13.9937i	0.676428	−	0.736508i
$362$		−	11.5325i		−	0.606137i
$363$	9.09171	+	11.9616i	0.477191	+	0.627824i
$364$			2.47927i			0.129949i
$365$			10.4311i			0.545989i
$366$	31.7750			1.66090
$367$	−7.91555			−0.413188			−0.206594	−	0.978427i	$-0.566238\pi$
$367$	−7.91555			−0.413188			−0.206594	+	0.978427i	$0.566238\pi$
$368$	7.55039			0.393591
$369$	5.57045			0.289986
$370$		−	4.45017i		−	0.231353i
$371$	17.0223			0.883753
$372$	2.16190			0.112089
$373$	6.51329			0.337246			0.168623	−	0.985681i	$-0.446068\pi$
$373$	6.51329			0.337246			0.168623	+	0.985681i	$0.446068\pi$
$374$	−12.4036	−	36.8167i	−0.641374	−	1.90375i
$375$		−	1.36588i		−	0.0705336i
$376$	10.9319			0.563771
$377$	7.48937			0.385722
$378$	11.8648			0.610259
$379$		−	20.3599i		−	1.04582i	−0.852388	−	0.522910i	$-0.824847\pi$
$379$		−	20.3599i		−	1.04582i	0.852388	−	0.522910i	$-0.175153\pi$
$380$	−1.42424	+	0.625712i	−0.0730617	+	0.0320984i
$381$			13.1679i			0.674614i
$382$	40.8116			2.08810
$383$		−	11.5783i		−	0.591621i	−0.955247	−	0.295811i	$-0.904410\pi$
$383$		−	11.5783i		−	0.591621i	0.955247	−	0.295811i	$-0.0955898\pi$
$384$		−	18.2616i		−	0.931909i
$385$	1.44918	+	4.30150i	0.0738570	+	0.219225i
$386$	−7.72098			−0.392988
$387$			0.325036i			0.0165225i
$388$			4.75286i			0.241290i
$389$	19.6836			0.998000			0.499000	−	0.866602i	$-0.333701\pi$
$389$	19.6836			0.998000			0.499000	+	0.866602i	$0.333701\pi$
$390$			10.6441i			0.538985i
$391$			12.5609i			0.635234i
$392$	12.9330			0.653217
$393$	−0.0994121			−0.00501467
$394$			28.4058i			1.43107i
$395$	−10.1671			−0.511564
$396$	−1.27244	+	0.428685i	−0.0639424	+	0.0215422i
$397$	12.7781			0.641313			0.320656	−	0.947196i	$-0.396097\pi$
$397$	12.7781			0.641313			0.320656	+	0.947196i	$0.396097\pi$
$398$	−14.2594			−0.714757
$399$	−7.45993	+	3.27739i	−0.373464	+	0.164075i
$400$	−4.58640			−0.229320
$401$		−	1.18035i		−	0.0589440i	−0.999566	−	0.0294720i	$-0.990617\pi$
$401$		−	1.18035i		−	0.0589440i	0.999566	−	0.0294720i	$-0.00938260\pi$
$402$	10.2508			0.511265
$403$		−	22.5125i		−	1.12143i
$404$		−	1.59279i		−	0.0792445i
$405$	4.31005			0.214168
$406$		−	3.09995i		−	0.153848i
$407$	3.06945	+	9.11084i	0.152147	+	0.451607i
$408$	26.2890			1.30150
$409$	28.0771			1.38833			0.694163	−	0.719818i	$-0.255775\pi$
$409$	28.0771			1.38833			0.694163	+	0.719818i	$0.255775\pi$
$410$	7.53879			0.372314
$411$			27.4604i			1.35452i
$412$			1.29397i			0.0637494i
$413$	−10.8168			−0.532258
$414$	2.86698			0.140904
$415$			1.19216i			0.0585208i
$416$	10.1321			0.496765
$417$	−15.7843			−0.772962
$418$	16.4062	−	14.9474i	0.802454	−	0.731102i
$419$	−8.72328			−0.426160			−0.213080	−	0.977035i	$-0.568350\pi$
$419$	−8.72328			−0.426160			−0.213080	+	0.977035i	$0.568350\pi$
$420$	0.667127			0.0325524
$421$			26.0458i			1.26939i	0.772761	+	0.634697i	$0.218875\pi$
$421$			26.0458i			1.26939i	−0.772761	+	0.634697i	$0.781125\pi$
$422$	−14.1285			−0.687766
$423$	4.91606			0.239027
$424$		−	31.3752i		−	1.52371i
$425$		−	7.63001i		−	0.370110i
$426$	16.5779			0.803201
$427$	−20.7383			−1.00360
$428$	−0.958206			−0.0463166
$429$	−7.34163	−	21.7917i	−0.354457	−	1.05211i
$430$			0.439888i			0.0212133i
$431$	23.5453			1.13414			0.567070	−	0.823670i	$-0.308077\pi$
$431$	23.5453			1.13414			0.567070	+	0.823670i	$0.308077\pi$
$432$		−	25.8997i		−	1.24610i
$433$			16.8788i			0.811144i	0.914063	+	0.405572i	$0.132928\pi$
$433$			16.8788i			0.811144i	−0.914063	+	0.405572i	$0.867072\pi$
$434$	−9.31824			−0.447290
$435$		−	2.01525i		−	0.0966239i
$436$	−0.975005			−0.0466943
$437$	−6.56979	+	2.88632i	−0.314276	+	0.138071i
$438$	−21.8732			−1.04514
$439$	5.05675			0.241345			0.120673	−	0.992692i	$-0.461495\pi$
$439$	5.05675			0.241345			0.120673	+	0.992692i	$0.461495\pi$
$440$	7.92845	−	2.67110i	0.377974	−	0.127340i
$441$	5.81596			0.276950
$442$			59.4596i			2.82821i
$443$	38.1004			1.81020			0.905101	−	0.425196i	$-0.139795\pi$
$443$	38.1004			1.81020			0.905101	+	0.425196i	$0.139795\pi$
$444$	1.41301			0.0670587
$445$		−	8.37475i		−	0.397001i
$446$			19.0627i			0.902644i
$447$	−7.87469			−0.372460
$448$			8.35988i			0.394967i
$449$			29.6486i			1.39920i	0.714533	+	0.699601i	$0.246639\pi$
$449$			29.6486i			1.39920i	−0.714533	+	0.699601i	$0.753361\pi$
$450$	−1.74151			−0.0820958
$451$	−15.4342	+	5.19979i	−0.726767	+	0.244848i
$452$			0.900214i			0.0423425i
$453$			14.0006i			0.657804i
$454$	8.94250			0.419692
$455$		−	6.94699i		−	0.325680i
$456$	6.04082	+	13.7500i	0.282887	+	0.643904i
$457$		−	23.8413i		−	1.11525i	−0.830093	−	0.557624i	$-0.811713\pi$
$457$		−	23.8413i		−	1.11525i	0.830093	−	0.557624i	$-0.188287\pi$
$458$	−11.6538			−0.544547
$459$	43.0871			2.01113
$460$	0.587522			0.0273934
$461$		−	6.76661i		−	0.315153i	−0.987507	−	0.157576i	$-0.949632\pi$
$461$		−	6.76661i		−	0.315153i	0.987507	−	0.157576i	$-0.0503680\pi$
$462$	−9.01988	+	3.03881i	−0.419643	+	0.141378i
$463$	−9.84317			−0.457451			−0.228726	−	0.973491i	$-0.573456\pi$
$463$	−9.84317			−0.457451			−0.228726	+	0.973491i	$0.573456\pi$
$464$	−6.76689			−0.314145
$465$	−6.05770			−0.280919
$466$			16.5035i			0.764510i
$467$	34.6881			1.60518			0.802588	−	0.596534i	$-0.203456\pi$
$467$	34.6881			1.60518			0.802588	+	0.596534i	$0.203456\pi$
$468$	2.05501			0.0949927
$469$	−6.69032			−0.308930
$470$	6.65317			0.306888
$471$		−	17.6249i		−	0.812112i
$472$			19.9373i			0.917687i
$473$	−0.303407	−	0.900584i	−0.0139507	−	0.0414089i
$474$		−	21.3196i		−	0.979243i
$475$	3.99075	−	1.75326i	0.183108	−	0.0804452i
$476$	3.72668			0.170812
$477$		−	14.1093i		−	0.646022i
$478$		−	18.4636i		−	0.844505i
$479$		−	0.978027i		−	0.0446872i	−0.999750	−	0.0223436i	$-0.992887\pi$
$479$		−	0.978027i		−	0.0446872i	0.999750	−	0.0223436i	$-0.00711278\pi$
$480$		−	2.72635i		−	0.124440i
$481$		−	14.7142i		−	0.670907i
$482$	−27.0293			−1.23115
$483$	3.07736			0.140025
$484$	3.12541	−	2.37553i	0.142064	−	0.107979i
$485$		−	13.3176i		−	0.604723i
$486$		−	16.9705i		−	0.769798i
$487$			5.97744i			0.270864i	0.990787	+	0.135432i	$0.0432422\pi$
$487$			5.97744i			0.270864i	−0.990787	+	0.135432i	$0.956758\pi$
$488$			38.2245i			1.73034i
$489$		−	13.0860i		−	0.591768i
$490$	7.87105			0.355578
$491$		−	25.7327i		−	1.16130i	−0.814153	−	0.580651i	$-0.802798\pi$
$491$		−	25.7327i		−	1.16130i	0.814153	−	0.580651i	$-0.197202\pi$
$492$			2.39371i			0.107917i
$493$		−	11.2575i		−	0.507013i
$494$	−31.0993	+	13.6629i	−1.39923	+	0.614724i
$495$	3.56540	−	1.20119i	0.160253	−	0.0539894i
$496$			20.3408i			0.913329i
$497$	−10.8198			−0.485332
$498$	−2.49986			−0.112021
$499$	−8.01408			−0.358759			−0.179380	−	0.983780i	$-0.557409\pi$
$499$	−8.01408			−0.358759			−0.179380	+	0.983780i	$0.557409\pi$
$500$	−0.356884			−0.0159604
$501$			0.190427i			0.00850764i
$502$	37.9948			1.69579
$503$		−	22.3395i		−	0.996067i	−0.867158	−	0.498034i	$-0.834056\pi$
$503$		−	22.3395i		−	0.996067i	0.867158	−	0.498034i	$-0.165944\pi$
$504$			3.91619i			0.174441i
$505$			4.46305i			0.198603i
$506$	−7.94359	+	2.67620i	−0.353136	+	0.118972i
$507$			17.4375i			0.774426i
$508$	3.44060			0.152652
$509$			9.56976i			0.424172i	0.977251	+	0.212086i	$0.0680257\pi$
$509$			9.56976i			0.424172i	−0.977251	+	0.212086i	$0.931974\pi$
$510$	15.9995			0.708470
$511$	14.2758			0.631523
$512$	13.9841			0.618015
$513$	9.90077	+	22.5360i	0.437130	+	0.994988i
$514$			34.2419i			1.51034i
$515$		−	3.62575i		−	0.159769i
$516$	−0.139673			−0.00614876
$517$	−13.6210	+	4.58894i	−0.599053	+	0.201821i
$518$	−6.09039			−0.267597
$519$			9.63462i			0.422913i
$520$	−12.8046			−0.561518
$521$		−	26.1395i		−	1.14519i	−0.819838	−	0.572596i	$-0.805936\pi$
$521$		−	26.1395i		−	1.14519i	0.819838	−	0.572596i	$-0.194064\pi$
$522$	−2.56947			−0.112463
$523$	24.3617			1.06526			0.532631	−	0.846347i	$-0.321203\pi$
$523$	24.3617			1.06526			0.532631	+	0.846347i	$0.321203\pi$
$524$			0.0259750i			0.00113472i
$525$	−1.86931			−0.0815833
$526$			38.1459i			1.66324i
$527$	−33.8393			−1.47406
$528$	6.63341	+	19.6895i	0.288682	+	0.856876i
$529$	−20.2898			−0.882167
$530$		−	19.0949i		−	0.829431i
$531$			8.96574i			0.389080i
$532$	0.856335	+	1.94917i	0.0371268	+	0.0845074i
$533$	24.9264			1.07968
$534$	17.5612			0.759945
$535$	2.68492			0.116079
$536$			12.3315i			0.532639i
$537$	32.2508			1.39173
$538$		−	35.4553i		−	1.52859i
$539$	−16.1144	+	5.42896i	−0.694096	+	0.233842i
$540$		−	2.01535i		−	0.0867267i
$541$		−	26.3953i		−	1.13482i	−0.823435	−	0.567411i	$-0.807945\pi$
$541$		−	26.3953i		−	1.13482i	0.823435	−	0.567411i	$-0.192055\pi$
$542$			35.3682i			1.51920i
$543$	−10.2605			−0.440319
$544$		−	15.2298i		−	0.652973i
$545$	2.73199			0.117026
$546$	14.5673			0.623421
$547$	30.5737			1.30724			0.653619	−	0.756824i	$-0.273250\pi$
$547$	30.5737			1.30724			0.653619	+	0.756824i	$0.273250\pi$
$548$	7.17501			0.306501
$549$			17.1895i			0.733628i
$550$	4.82525	−	1.62563i	0.205749	−	0.0693172i
$551$	5.88805	−	2.58681i	0.250839	−	0.110202i
$552$		−	5.67213i		−	0.241422i
$553$			13.9145i			0.591705i
$554$			4.96880i			0.211104i
$555$	−3.95931			−0.168063
$556$			4.12422i			0.174906i
$557$		−	29.1432i		−	1.23484i	−0.786635	−	0.617418i	$-0.788179\pi$
$557$		−	29.1432i		−	1.23484i	0.786635	−	0.617418i	$-0.211821\pi$
$558$			7.72366i			0.326968i
$559$			1.45446i			0.0615170i
$560$			6.27684i			0.265245i
$561$	−32.7558	+	11.0355i	−1.38295	+	0.465917i
$562$	32.9563			1.39018
$563$	−9.34553			−0.393867			−0.196934	−	0.980417i	$-0.563098\pi$
$563$	−9.34553			−0.393867			−0.196934	+	0.980417i	$0.563098\pi$
$564$			2.11251i			0.0889527i
$565$		−	2.52242i		−	0.106119i
$566$		−	16.3071i		−	0.685438i
$567$		−	5.89863i		−	0.247719i
$568$			19.9428i			0.836780i
$569$	6.39268			0.267995			0.133998	−	0.990982i	$-0.457219\pi$
$569$	6.39268			0.267995			0.133998	+	0.990982i	$0.457219\pi$
$570$	3.67644	+	8.36826i	0.153989	+	0.350508i
$571$			27.3305i			1.14374i	0.820343	+	0.571872i	$0.193783\pi$
$571$			27.3305i			1.14374i	−0.820343	+	0.571872i	$0.806217\pi$
$572$	−5.69385	+	1.91826i	−0.238072	+	0.0802066i
$573$		−	36.3100i		−	1.51687i
$574$		−	10.3174i		−	0.430640i
$575$	−1.64625			−0.0686536
$576$	6.92930			0.288721
$577$	−25.2662			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$577$	−25.2662			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$578$	63.2771			2.63198
$579$			6.86934i			0.285480i
$580$	−0.526556			−0.0218641
$581$	1.63156			0.0676885
$582$	27.9260			1.15757
$583$	13.1705	+	39.0931i	0.545466	+	1.61907i
$584$		−	26.3128i		−	1.08883i
$585$	−5.75819			−0.238072
$586$	−2.73732			−0.113077
$587$	41.7299			1.72238			0.861189	−	0.508285i	$-0.169720\pi$
$587$	41.7299			1.72238			0.861189	+	0.508285i	$0.169720\pi$
$588$			2.49921i			0.103066i
$589$	−7.77576	−	17.6991i	−0.320395	−	0.729277i
$590$			12.1338i			0.499541i
$591$	25.2726			1.03958
$592$			13.2947i			0.546410i
$593$			29.5945i			1.21530i	0.794205	+	0.607650i	$0.207888\pi$
$593$			29.5945i			1.21530i	−0.794205	+	0.607650i	$0.792112\pi$
$594$	9.18003	+	27.2485i	0.376661	+	1.11802i
$595$	−10.4423			−0.428091
$596$			2.05754i			0.0842803i
$597$			12.6865i			0.519225i
$598$	12.8290			0.524618
$599$			19.5774i			0.799910i	0.916535	+	0.399955i	$0.130974\pi$
$599$			19.5774i			0.799910i	−0.916535	+	0.399955i	$0.869026\pi$
$600$			3.44547i			0.140661i
$601$	−22.5482			−0.919761			−0.459880	−	0.887981i	$-0.652108\pi$
$601$	−22.5482			−0.919761			−0.459880	+	0.887981i	$0.652108\pi$
$602$	0.602021			0.0245365
$603$			5.54544i			0.225828i
$604$	3.65815			0.148848
$605$	−8.75748	+	6.65631i	−0.356042	+	0.270618i
$606$	−9.35865			−0.380169
$607$	−39.4002			−1.59921			−0.799603	−	0.600529i	$-0.794957\pi$
$607$	−39.4002			−1.59921			−0.799603	+	0.600529i	$0.794957\pi$
$608$	7.96570	−	3.49959i	0.323052	−	0.141927i
$609$	−2.75802			−0.111761
$610$			23.2634i			0.941908i
$611$	21.9982			0.889952
$612$		−	3.08895i		−	0.124863i
$613$			11.5279i			0.465606i	0.972524	+	0.232803i	$0.0747897\pi$
$613$			11.5279i			0.465606i	−0.972524	+	0.232803i	$0.925210\pi$
$614$	−4.44489			−0.179381
$615$		−	6.70725i		−	0.270462i
$616$	−3.65560	−	10.8507i	−0.147288	−	0.437186i
$617$	10.7308			0.432007			0.216004	−	0.976393i	$-0.430698\pi$
$617$	10.7308			0.432007			0.216004	+	0.976393i	$0.430698\pi$
$618$	7.60288			0.305833
$619$	−48.4955			−1.94920			−0.974600	−	0.223955i	$-0.928103\pi$
$619$	−48.4955			−1.94920			−0.974600	+	0.223955i	$0.928103\pi$
$620$			1.58279i			0.0635664i
$621$		−	9.29649i		−	0.373055i
$622$	16.6178			0.666313
$623$	−11.4615			−0.459195
$624$		−	31.7989i		−	1.27297i
$625$	1.00000			0.0400000
$626$	−23.0862			−0.922712
$627$	−13.2987	−	14.5966i	−0.531099	−	0.582931i
$628$	−4.60514			−0.183765
$629$	−22.1173			−0.881876
$630$			2.38339i			0.0949567i
$631$	−2.68795			−0.107005			−0.0535027	−	0.998568i	$-0.517039\pi$
$631$	−2.68795			−0.107005			−0.0535027	+	0.998568i	$0.517039\pi$
$632$	25.6470			1.02018
$633$			12.5701i			0.499618i
$634$			4.20964i			0.167186i
$635$	−9.64064			−0.382577
$636$	6.06301			0.240414
$637$	26.0250			1.03115
$638$	7.11930	−	2.39850i	0.281856	−	0.0949575i
$639$			8.96822i			0.354777i
$640$	13.3699			0.528490
$641$		−	18.6329i		−	0.735954i	−0.929835	−	0.367977i	$-0.880051\pi$
$641$		−	18.6329i		−	0.735954i	0.929835	−	0.367977i	$-0.119949\pi$
$642$			5.63005i			0.222200i
$643$	−5.98825			−0.236153			−0.118077	−	0.993004i	$-0.537673\pi$
$643$	−5.98825			−0.236153			−0.118077	+	0.993004i	$0.537673\pi$
$644$		−	0.804069i		−	0.0316848i
$645$	0.391368			0.0154101
$646$	20.5372	+	46.7465i	0.808026	+	1.83922i
$647$	−18.9602			−0.745404			−0.372702	−	0.927951i	$-0.621569\pi$
$647$	−18.9602			−0.745404			−0.372702	+	0.927951i	$0.621569\pi$
$648$	−10.8723			−0.427103
$649$	−8.36915	−	24.8416i	−0.328518	−	0.975117i
$650$	−7.79286			−0.305661
$651$			8.29042i			0.324927i
$652$	−3.41918			−0.133905
$653$	−32.2566			−1.26230			−0.631149	−	0.775662i	$-0.717416\pi$
$653$	−32.2566			−1.26230			−0.631149	+	0.775662i	$0.717416\pi$
$654$			5.72875i			0.224012i
$655$		−	0.0727826i		−	0.00284385i
$656$	−22.5219			−0.879332
$657$		−	11.8328i		−	0.461642i
$658$		−	9.10537i		−	0.354964i
$659$	41.8868			1.63168			0.815840	−	0.578278i	$-0.196275\pi$
$659$	41.8868			1.63168			0.815840	+	0.578278i	$0.196275\pi$
$660$	0.516169	+	1.53211i	0.0200919	+	0.0596373i
$661$		−	13.3756i		−	0.520251i	−0.965575	−	0.260126i	$-0.916236\pi$
$661$		−	13.3756i		−	0.520251i	0.965575	−	0.260126i	$-0.0837640\pi$
$662$		−	5.37220i		−	0.208796i
$663$	52.9011			2.05451
$664$		−	3.00726i		−	0.116704i
$665$	−2.39947	−	5.46164i	−0.0930476	−	0.211793i
$666$			5.04818i			0.195613i
$667$	−2.42893			−0.0940484
$668$	0.0497558			0.00192511
$669$	16.9600			0.655713
$670$			7.50494i			0.289941i
$671$	−16.0456	−	47.6272i	−0.619435	−	1.83863i
$672$	−3.73122			−0.143935
$673$	−6.27738			−0.241975			−0.120988	−	0.992654i	$-0.538606\pi$
$673$	−6.27738			−0.241975			−0.120988	+	0.992654i	$0.538606\pi$
$674$	25.8842			0.997020
$675$			5.64705i			0.217355i
$676$	4.55617			0.175237
$677$	−32.5118			−1.24953			−0.624765	−	0.780813i	$-0.714805\pi$
$677$	−32.5118			−1.24953			−0.624765	+	0.780813i	$0.714805\pi$
$678$	5.28931			0.203135
$679$	−18.2262			−0.699458
$680$			19.2470i			0.738088i
$681$		−	7.95612i		−	0.304879i
$682$	−7.20971	−	21.4001i	−0.276074	−	0.819452i
$683$			46.7789i			1.78994i	0.446122	+	0.894972i	$0.352805\pi$
$683$			46.7789i			1.78994i	−0.446122	+	0.894972i	$0.647195\pi$
$684$	1.61562	−	0.709794i	0.0617748	−	0.0271397i
$685$	−20.1046			−0.768157
$686$		−	25.4795i		−	0.972813i
$687$			10.3684i			0.395578i
$688$		−	1.31415i		−	0.0501016i
$689$		−	63.1359i		−	2.40529i
$690$		−	3.45206i		−	0.131418i
$691$	13.5733			0.516352			0.258176	−	0.966098i	$-0.416879\pi$
$691$	13.5733			0.516352			0.258176	+	0.966098i	$0.416879\pi$
$692$	2.51739			0.0956968
$693$	−1.64392	−	4.87953i	−0.0624472	−	0.185358i
$694$		−	34.7421i		−	1.31879i
$695$		−	11.5562i		−	0.438351i
$696$			5.08354i			0.192691i
$697$		−	37.4678i		−	1.41919i
$698$		−	9.74268i		−	0.368766i
$699$	14.6831			0.555367
$700$			0.488423i			0.0184607i
$701$			40.1768i			1.51746i	0.651408	+	0.758728i	$0.274179\pi$
$701$			40.1768i			1.51746i	−0.651408	+	0.758728i	$0.725821\pi$
$702$		−	44.0067i		−	1.66093i
$703$	−5.08223	−	11.5681i	−0.191680	−	0.436299i
$704$	−19.1991	+	6.46821i	−0.723595	+	0.243780i
$705$		−	5.91931i		−	0.222934i
$706$	−8.62853			−0.324739
$707$	6.10803			0.229716
$708$	−3.85272			−0.144794
$709$	−42.8227			−1.60824			−0.804119	−	0.594468i	$-0.797363\pi$
$709$	−42.8227			−1.60824			−0.804119	+	0.594468i	$0.797363\pi$
$710$			12.1372i			0.455500i
$711$	11.5334			0.432536
$712$			21.1256i			0.791716i
$713$			7.30118i			0.273431i
$714$		−	21.8965i		−	0.819457i
$715$	15.9543	−	5.37503i	0.596658	−	0.201015i
$716$		−	8.42668i		−	0.314920i
$717$	−16.4270			−0.613479
$718$		−	42.6516i		−	1.59174i
$719$	−0.0991854			−0.00369899			−0.00184950	−	0.999998i	$-0.500589\pi$
$719$	−0.0991854			−0.00369899			−0.00184950	+	0.999998i	$0.500589\pi$
$720$	5.20272			0.193894
$721$	−4.96211			−0.184799
$722$	−19.7308	+	21.4833i	−0.734304	+	0.799525i
$723$			24.0479i			0.894352i
$724$			2.68092i			0.0996354i
$725$	1.47543			0.0547959
$726$	−13.9577	−	18.3637i	−0.518020	−	0.681541i
$727$	−3.41388			−0.126614			−0.0633070	−	0.997994i	$-0.520165\pi$
$727$	−3.41388			−0.126614			−0.0633070	+	0.997994i	$0.520165\pi$
$728$			17.5240i			0.649484i
$729$	−28.0288			−1.03810
$730$		−	16.0140i		−	0.592704i
$731$	2.18624			0.0808612
$732$	−7.38658			−0.273016
$733$		−	24.8694i		−	0.918572i	−0.888288	−	0.459286i	$-0.848105\pi$
$733$		−	24.8694i		−	0.918572i	0.888288	−	0.459286i	$-0.151895\pi$
$734$	12.1521			0.448541
$735$		−	7.00285i		−	0.258304i
$736$	−3.28599			−0.121123
$737$	−5.17644	−	15.3649i	−0.190677	−	0.565972i
$738$	−8.55184			−0.314798
$739$			44.2464i			1.62763i	0.581123	+	0.813816i	$0.302614\pi$
$739$			44.2464i			1.62763i	−0.581123	+	0.813816i	$0.697386\pi$
$740$			1.03451i			0.0380294i
$741$	12.1559	+	27.6690i	0.446558	+	1.01645i
$742$	−26.1329			−0.959367
$743$	3.56037			0.130617			0.0653087	−	0.997865i	$-0.479197\pi$
$743$	3.56037			0.130617			0.0653087	+	0.997865i	$0.479197\pi$
$744$	15.2808			0.560220
$745$		−	5.76530i		−	0.211224i
$746$	−9.99930			−0.366101
$747$		−	1.35236i		−	0.0494802i
$748$	2.88341	+	8.55862i	0.105428	+	0.312934i
$749$		−	3.67452i		−	0.134264i
$750$			2.09692i			0.0765685i
$751$		−	41.3775i		−	1.50989i	−0.655791	−	0.754943i	$-0.727665\pi$
$751$		−	41.3775i		−	1.50989i	0.655791	−	0.754943i	$-0.272335\pi$
$752$	−19.8761			−0.724808
$753$		−	33.8039i		−	1.23188i
$754$	−11.4978			−0.418725
$755$	−10.2502			−0.373044
$756$	−2.75815			−0.100313
$757$	−7.87213			−0.286117			−0.143059	−	0.989714i	$-0.545694\pi$
$757$	−7.87213			−0.286117			−0.143059	+	0.989714i	$0.545694\pi$
$758$			31.2569i			1.13530i
$759$	2.38101	+	7.06740i	0.0864253	+	0.256530i
$760$	−10.0668	+	4.42267i	−0.365161	+	0.160427i
$761$		−	26.1691i		−	0.948631i	−0.880355	−	0.474315i	$-0.842696\pi$
$761$		−	26.1691i		−	0.948631i	0.880355	−	0.474315i	$-0.157304\pi$
$762$		−	20.2156i		−	0.732335i
$763$		−	3.73894i		−	0.135359i
$764$	−9.48729			−0.343238
$765$			8.65532i			0.312934i
$766$			17.7751i			0.642241i
$767$			40.1195i			1.44863i
$768$			11.3487i			0.409511i
$769$		−	38.2230i		−	1.37836i	−0.724591	−	0.689179i	$-0.757971\pi$
$769$		−	38.2230i		−	1.37836i	0.724591	−	0.689179i	$-0.242029\pi$
$770$	−2.22480	−	6.60372i	−0.0801762	−	0.237982i
$771$	30.4649			1.09717
$772$	1.79486			0.0645985
$773$			15.4769i			0.556666i	0.960485	+	0.278333i	$0.0897819\pi$
$773$			15.4769i			0.556666i	−0.960485	+	0.278333i	$0.910218\pi$
$774$		−	0.499000i		−	0.0179362i
$775$		−	4.43502i		−	0.159311i
$776$			33.5942i			1.20596i
$777$			5.41861i			0.194392i
$778$	−30.2186			−1.08339
$779$	19.5969	−	8.60953i	0.702131	−	0.308468i
$780$		−	2.47438i		−	0.0885972i
$781$	−8.37146	−	24.8484i	−0.299555	−	0.889147i
$782$		−	19.2837i		−	0.689585i
$783$			8.33181i			0.297755i
$784$	−23.5145			−0.839803
$785$	12.9037			0.460553
$786$	0.152619			0.00544373
$787$	17.2563			0.615120			0.307560	−	0.951529i	$-0.400488\pi$
$787$	17.2563			0.615120			0.307560	+	0.951529i	$0.400488\pi$
$788$		−	6.60337i		−	0.235235i
$789$	33.9383			1.20824
$790$	15.6087			0.555334
$791$	−3.45213			−0.122744
$792$	−8.99386	+	3.03004i	−0.319583	+	0.107668i
$793$			76.9187i			2.73146i
$794$	−19.6171			−0.696184
$795$	−16.9887			−0.602528
$796$	3.31481			0.117490
$797$			32.2919i			1.14384i	0.820311	+	0.571918i	$0.193801\pi$
$797$			32.2919i			1.14384i	−0.820311	+	0.571918i	$0.806199\pi$
$798$	11.4526	−	5.03149i	0.405418	−	0.178113i
$799$		−	33.0662i		−	1.16980i
$800$	1.99604			0.0705707
$801$			9.50014i			0.335671i
$802$			1.81210i			0.0639873i
$803$	11.0455	+	32.7855i	0.389785	+	1.15697i
$804$	−2.38296			−0.0840407
$805$			2.25302i			0.0794087i
$806$			34.5615i			1.21738i
$807$	−31.5445			−1.11042
$808$		−	11.2582i		−	0.396062i
$809$			38.1733i			1.34210i	0.741411	+	0.671052i	$0.234157\pi$
$809$			38.1733i			1.34210i	−0.741411	+	0.671052i	$0.765843\pi$
$810$	−6.61685			−0.232493
$811$	32.4910			1.14091			0.570456	−	0.821328i	$-0.306766\pi$
$811$	32.4910			1.14091			0.570456	+	0.821328i	$0.306766\pi$
$812$			0.720632i			0.0252892i
$813$	31.4670			1.10360
$814$	−4.71226	−	13.9871i	−0.165165	−	0.490247i
$815$	9.58063			0.335595
$816$	−47.7980			−1.67326
$817$	0.502366	+	1.14348i	0.0175756	+	0.0400052i
$818$	−43.1044			−1.50711
$819$			7.88052i			0.275367i
$820$	−1.75251			−0.0612002
$821$			13.1261i			0.458103i	0.973414	+	0.229051i	$0.0735624\pi$
$821$			13.1261i			0.458103i	−0.973414	+	0.229051i	$0.926438\pi$
$822$		−	42.1576i		−	1.47042i
$823$	−45.8794			−1.59926			−0.799628	−	0.600496i	$-0.794970\pi$
$823$	−45.8794			−1.59926			−0.799628	+	0.600496i	$0.794970\pi$
$824$			9.14607i			0.318619i
$825$	−1.44632	−	4.29302i	−0.0503544	−	0.149464i
$826$	16.6060			0.577798
$827$	52.1371			1.81298			0.906492	−	0.422222i	$-0.138750\pi$
$827$	52.1371			1.81298			0.906492	+	0.422222i	$0.138750\pi$
$828$	−0.666473			−0.0231615
$829$		−	41.5563i		−	1.44331i	−0.692253	−	0.721655i	$-0.743382\pi$
$829$		−	41.5563i		−	1.44331i	0.692253	−	0.721655i	$-0.256618\pi$
$830$		−	1.83022i		−	0.0635278i
$831$	4.42073			0.153353
$832$	31.0069			1.07497
$833$		−	39.1191i		−	1.35540i
$834$	24.2323			0.839097
$835$	−0.139417			−0.00482473
$836$	−3.81387	+	3.47476i	−0.131906	+	0.120177i
$837$	25.0448			0.865676
$838$	13.3921			0.462623
$839$			38.8216i			1.34027i	0.742239	+	0.670135i	$0.233764\pi$
$839$			38.8216i			1.34027i	−0.742239	+	0.670135i	$0.766236\pi$
$840$	4.71539			0.162697
$841$	−26.8231			−0.924935
$842$		−	39.9859i		−	1.37800i
$843$		−	29.3212i		−	1.00988i
$844$	3.28439			0.113054
$845$	−12.7665			−0.439181
$846$	−7.54721			−0.259479
$847$	9.10967	+	11.9853i	0.313012	+	0.411819i
$848$			57.0455i			1.95895i
$849$	−14.5084			−0.497927
$850$			11.7137i			0.401777i
$851$			4.77204i			0.163584i
$852$	−3.85379			−0.132029
$853$		−	12.5417i		−	0.429421i	−0.976678	−	0.214710i	$-0.931119\pi$
$853$		−	12.5417i		−	0.429421i	0.976678	−	0.214710i	$-0.0688808\pi$
$854$	31.8378			1.08947
$855$	−4.52702	+	1.98886i	−0.154821	+	0.0680177i
$856$	−6.77281			−0.231490
$857$	−51.3725			−1.75485			−0.877426	−	0.479711i	$-0.840741\pi$
$857$	−51.3725			−1.75485			−0.877426	+	0.479711i	$0.840741\pi$
$858$	11.2710	+	33.4549i	0.384785	+	1.14213i
$859$	4.52524			0.154399			0.0771996	−	0.997016i	$-0.475402\pi$
$859$	4.52524			0.154399			0.0771996	+	0.997016i	$0.475402\pi$
$860$		−	0.102259i		−	0.00348700i
$861$	−9.17938			−0.312832
$862$	−36.1472			−1.23118
$863$			15.4305i			0.525260i	0.964897	+	0.262630i	$0.0845899\pi$
$863$			15.4305i			0.525260i	−0.964897	+	0.262630i	$0.915410\pi$
$864$			11.2718i			0.383473i
$865$	−7.05380			−0.239836
$866$		−	25.9126i		−	0.880546i
$867$		−	56.2975i		−	1.91196i
$868$	2.16617			0.0735246
$869$	−31.9558	+	10.7659i	−1.08403	+	0.365209i
$870$			3.09384i			0.104891i
$871$			24.8145i			0.840808i
$872$	−6.89154			−0.233377
$873$			15.1073i			0.511303i
$874$	10.0860	−	4.43112i	0.341165	−	0.149885i
$875$		−	1.36858i		−	0.0462663i
$876$	5.08475			0.171798
$877$	−33.4336			−1.12897			−0.564486	−	0.825443i	$-0.690925\pi$
$877$	−33.4336			−1.12897			−0.564486	+	0.825443i	$0.690925\pi$
$878$	−7.76320			−0.261995
$879$			2.43538i			0.0821435i
$880$	−14.4153	+	4.85652i	−0.485939	+	0.163713i
$881$	−35.8636			−1.20828			−0.604138	−	0.796880i	$-0.706482\pi$
$881$	−35.8636			−1.20828			−0.604138	+	0.796880i	$0.706482\pi$
$882$	−8.92874			−0.300646
$883$	37.6858			1.26823			0.634114	−	0.773240i	$-0.281365\pi$
$883$	37.6858			1.26823			0.634114	+	0.773240i	$0.281365\pi$
$884$		−	13.8223i		−	0.464895i
$885$	10.7954			0.362884
$886$	−58.4922			−1.96508
$887$	−18.4545			−0.619641			−0.309820	−	0.950795i	$-0.600269\pi$
$887$	−18.4545			−0.619641			−0.309820	+	0.950795i	$0.600269\pi$
$888$	9.98749			0.335158
$889$			13.1940i			0.442511i
$890$			12.8570i			0.430969i
$891$	13.5467	−	4.56389i	0.453831	−	0.152896i
$892$		−	4.43142i		−	0.148375i
$893$	17.2947	−	7.59813i	0.578746	−	0.254262i
$894$	12.0893			0.404328
$895$			23.6118i			0.789255i
$896$		−	18.2977i		−	0.611283i
$897$		−	11.4140i		−	0.381101i
$898$		−	45.5169i		−	1.51892i
$899$		−	6.54355i		−	0.218239i
$900$	0.404842			0.0134947
$901$	−94.9018			−3.16164
$902$	23.6948	−	7.98279i	0.788949	−	0.265798i
$903$		−	0.535617i		−	0.0178242i
$904$			6.36291i			0.211627i
$905$		−	7.51200i		−	0.249707i
$906$		−	21.4939i		−	0.714086i
$907$		−	42.7474i		−	1.41941i	−0.704501	−	0.709703i	$-0.748829\pi$
$907$		−	42.7474i		−	1.41941i	0.704501	−	0.709703i	$-0.251171\pi$
$908$	−2.07882			−0.0689881
$909$		−	5.06279i		−	0.167922i
$910$			10.6651i			0.353545i
$911$		−	35.2749i		−	1.16871i	−0.811498	−	0.584355i	$-0.801347\pi$
$911$		−	35.2749i		−	1.16871i	0.811498	−	0.584355i	$-0.198653\pi$
$912$	−10.9833	−	24.9999i	−0.363692	−	0.827829i
$913$	1.26237	+	3.74701i	0.0417784	+	0.124008i
$914$			36.6015i			1.21067i
$915$	20.6974			0.684235
$916$	2.70911			0.0895114
$917$	−0.0996085			−0.00328936
$918$	−66.1480			−2.18321
$919$		−	21.0274i		−	0.693631i	−0.937933	−	0.346816i	$-0.887263\pi$
$919$		−	21.0274i		−	0.693631i	0.937933	−	0.346816i	$-0.112737\pi$
$920$	4.15274			0.136912
$921$			3.95461i			0.130309i
$922$			10.3882i			0.342117i
$923$			40.1306i			1.32092i
$924$	2.09681	−	0.706417i	0.0689800	−	0.0232394i
$925$		−	2.89873i		−	0.0953096i
$926$	15.1114			0.496591
$927$			4.11297i			0.135088i
$928$	2.94501			0.0966747
$929$	21.0218			0.689703			0.344851	−	0.938657i	$-0.387929\pi$
$929$	21.0218			0.689703			0.344851	+	0.938657i	$0.387929\pi$
$930$	9.29987			0.304955
$931$	20.4606	−	8.98898i	0.670568	−	0.294602i
$932$		−	3.83649i		−	0.125669i
$933$		−	14.7848i		−	0.484033i
$934$	−53.2537			−1.74252
$935$	−8.07939	−	23.9815i	−0.264224	−	0.784279i
$936$	14.5252			0.474772
$937$		−	56.6117i		−	1.84942i	−0.380668	−	0.924712i	$-0.624306\pi$
$937$		−	56.6117i		−	1.84942i	0.380668	−	0.924712i	$-0.375694\pi$
$938$	10.2711			0.335363
$939$			20.5398i			0.670291i
$940$	−1.54663			−0.0504456
$941$	−49.2191			−1.60450			−0.802248	−	0.596990i	$-0.796363\pi$
$941$	−49.2191			−1.60450			−0.802248	+	0.596990i	$0.796363\pi$
$942$			27.0580i			0.881597i
$943$	−8.08406			−0.263253
$944$		−	36.2494i		−	1.17982i
$945$	7.72842			0.251406
$946$	0.465796	+	1.38259i	0.0151443	+	0.0449519i
$947$	16.7651			0.544794			0.272397	−	0.962185i	$-0.412184\pi$
$947$	16.7651			0.544794			0.272397	+	0.962185i	$0.412184\pi$
$948$			4.95608i			0.160966i
$949$		−	52.9491i		−	1.71880i
$950$	−6.12666	+	2.69163i	−0.198775	+	0.0873282i
$951$	3.74531			0.121450
$952$	26.3410			0.853715
$953$	−29.7768			−0.964566			−0.482283	−	0.876016i	$-0.660192\pi$
$953$	−29.7768			−0.964566			−0.482283	+	0.876016i	$0.660192\pi$
$954$			21.6609i			0.701297i
$955$	26.5837			0.860227
$956$			4.29215i			0.138818i
$957$	−2.13394	−	6.33403i	−0.0689805	−	0.204750i
$958$			1.50148i			0.0485107i
$959$			27.5147i			0.888495i
$960$		−	8.34340i		−	0.269282i
$961$	11.3306			0.365502
$962$			22.5894i			0.728311i
$963$	−3.04572			−0.0981468
$964$	6.28338			0.202374
$965$	−5.02925			−0.161897
$966$	−4.72440			−0.152005
$967$		−	33.4592i		−	1.07597i	−0.842953	−	0.537987i	$-0.819185\pi$
$967$		−	33.4592i		−	1.07597i	0.842953	−	0.537987i	$-0.180815\pi$
$968$	22.0911	−	16.7908i	0.710033	−	0.539676i
$969$	41.5902	−	18.2719i	1.33607	−	0.586979i
$970$			20.4454i			0.656464i
$971$			14.0261i			0.450120i	0.974345	+	0.225060i	$0.0722578\pi$
$971$			14.0261i			0.450120i	−0.974345	+	0.225060i	$0.927742\pi$
$972$			3.94506i			0.126538i
$973$	−15.8155			−0.507022
$974$		−	9.17665i		−	0.294039i
$975$			6.93329i			0.222043i
$976$		−	69.4987i		−	2.22460i
$977$			32.1209i			1.02764i	0.857898	+	0.513820i	$0.171770\pi$
$977$			32.1209i			1.02764i	−0.857898	+	0.513820i	$0.828230\pi$
$978$			20.0898i			0.642400i
$979$	−8.86799	−	26.3222i	−0.283422	−	0.841262i
$980$	−1.82975			−0.0584491
$981$	−3.09911			−0.0989470
$982$			39.5053i			1.26066i
$983$		−	54.4277i		−	1.73598i	−0.496586	−	0.867988i	$-0.665413\pi$
$983$		−	54.4277i		−	1.73598i	0.496586	−	0.867988i	$-0.334587\pi$
$984$			16.9193i			0.539366i
$985$			18.5028i			0.589550i
$986$			17.2827i			0.550394i
$987$	−8.10103			−0.257859
$988$	7.22952	−	3.17616i	0.230002	−	0.101047i
$989$		−	0.471705i		−	0.0149993i
$990$	−5.47366	+	1.84408i	−0.173964	+	0.0586087i
$991$			19.5871i			0.622206i	0.950376	+	0.311103i	$0.100698\pi$
$991$			19.5871i			0.622206i	−0.950376	+	0.311103i	$0.899302\pi$
$992$		−	8.85249i		−	0.281067i
$993$	−4.77964			−0.151677
$994$	16.6106			0.526858
$995$	−9.28818			−0.294455
$996$	0.581130			0.0184138
$997$			9.41064i			0.298038i	0.988834	+	0.149019i	$0.0476116\pi$
$997$			9.41064i			0.298038i	−0.988834	+	0.149019i	$0.952388\pi$
$998$	12.3033			0.389455
$999$	16.3693			0.517901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.a.626.12	yes	40
11.10	odd	2	inner	1045.2.f.a.626.30	yes	40
19.18	odd	2	inner	1045.2.f.a.626.29	yes	40
209.208	even	2	inner	1045.2.f.a.626.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.a.626.11	✓	40	209.208	even	2	inner
1045.2.f.a.626.12	yes	40	1.1	even	1	trivial
1045.2.f.a.626.29	yes	40	19.18	odd	2	inner
1045.2.f.a.626.30	yes	40	11.10	odd	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.53521 q^{2} +1.36588i q^{3} +0.356884 q^{4} -1.00000 q^{5} -2.09692i q^{6} +1.36858i q^{7} +2.52254 q^{8} +1.13438 q^{9} +O(q^{10})\)	\(q-1.53521 q^{2} +1.36588i q^{3} +0.356884 q^{4} -1.00000 q^{5} -2.09692i q^{6} +1.36858i q^{7} +2.52254 q^{8} +1.13438 q^{9} +1.53521 q^{10} +(-3.14305 + 1.05890i) q^{11} +0.487460i q^{12} +5.07607 q^{13} -2.10106i q^{14} -1.36588i q^{15} -4.58640 q^{16} -7.63001i q^{17} -1.74151 q^{18} +(3.99075 - 1.75326i) q^{19} -0.356884 q^{20} -1.86931 q^{21} +(4.82525 - 1.62563i) q^{22} -1.64625 q^{23} +3.44547i q^{24} +1.00000 q^{25} -7.79286 q^{26} +5.64705i q^{27} +0.488423i q^{28} +1.47543 q^{29} +2.09692i q^{30} -4.43502i q^{31} +1.99604 q^{32} +(-1.44632 - 4.29302i) q^{33} +11.7137i q^{34} -1.36858i q^{35} +0.404842 q^{36} -2.89873i q^{37} +(-6.12666 + 2.69163i) q^{38} +6.93329i q^{39} -2.52254 q^{40} +4.91058 q^{41} +2.86979 q^{42} +0.286532i q^{43} +(-1.12170 + 0.377903i) q^{44} -1.13438 q^{45} +2.52735 q^{46} +4.33371 q^{47} -6.26446i q^{48} +5.12700 q^{49} -1.53521 q^{50} +10.4217 q^{51} +1.81157 q^{52} -12.4380i q^{53} -8.66944i q^{54} +(3.14305 - 1.05890i) q^{55} +3.45228i q^{56} +(2.39474 + 5.45087i) q^{57} -2.26510 q^{58} +7.90366i q^{59} -0.487460i q^{60} +15.1532i q^{61} +6.80871i q^{62} +1.55248i q^{63} +6.10845 q^{64} -5.07607 q^{65} +(2.22041 + 6.59070i) q^{66} +4.88853i q^{67} -2.72303i q^{68} -2.24858i q^{69} +2.10106i q^{70} +7.90585i q^{71} +2.86151 q^{72} -10.4311i q^{73} +4.45017i q^{74} +1.36588i q^{75} +(1.42424 - 0.625712i) q^{76} +(-1.44918 - 4.30150i) q^{77} -10.6441i q^{78} +10.1671 q^{79} +4.58640 q^{80} -4.31005 q^{81} -7.53879 q^{82} -1.19216i q^{83} -0.667127 q^{84} +7.63001i q^{85} -0.439888i q^{86} +2.01525i q^{87} +(-7.92845 + 2.67110i) q^{88} +8.37475i q^{89} +1.74151 q^{90} +6.94699i q^{91} -0.587522 q^{92} +6.05770 q^{93} -6.65317 q^{94} +(-3.99075 + 1.75326i) q^{95} +2.72635i q^{96} +13.3176i q^{97} -7.87105 q^{98} +(-3.56540 + 1.20119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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