LMFDB - Embedded newform 504.2.cs.b.85.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.17
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.146382 - 1.40662i) q^{2} +(1.41639 - 0.996919i) q^{3} +(-1.95714 + 0.411806i) q^{4} +(3.39378 + 1.95940i) q^{5} +(-1.60962 - 1.84638i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.865744 + 2.69267i) q^{8} +(1.01230 - 2.82405i) q^{9} +O(q^{10})$	\(q+(-0.146382 - 1.40662i) q^{2} +(1.41639 - 0.996919i) q^{3} +(-1.95714 + 0.411806i) q^{4} +(3.39378 + 1.95940i) q^{5} +(-1.60962 - 1.84638i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.865744 + 2.69267i) q^{8} +(1.01230 - 2.82405i) q^{9} +(2.25934 - 5.06056i) q^{10} +(-1.24945 + 0.721373i) q^{11} +(-2.36154 + 2.53439i) q^{12} +(1.98271 + 1.14472i) q^{13} +(-1.14498 + 0.830079i) q^{14} +(6.76026 - 0.608055i) q^{15} +(3.66083 - 1.61193i) q^{16} -0.191166 q^{17} +(-4.12054 - 1.01054i) q^{18} -4.09385i q^{19} +(-7.44900 - 2.43725i) q^{20} +(-1.57155 - 0.728168i) q^{21} +(1.19759 + 1.65191i) q^{22} +(1.62055 - 2.80688i) q^{23} +(3.91061 + 2.95079i) q^{24} +(5.17848 + 8.96938i) q^{25} +(1.31995 - 2.95648i) q^{26} +(-1.38153 - 5.00913i) q^{27} +(1.33521 + 1.48903i) q^{28} +(5.60034 - 3.23336i) q^{29} +(-1.84488 - 9.42009i) q^{30} +(-3.40118 + 5.89102i) q^{31} +(-2.80325 - 4.91343i) q^{32} +(-1.05056 + 2.26735i) q^{33} +(0.0279832 + 0.268897i) q^{34} -3.91879i q^{35} +(-0.818266 + 5.94394i) q^{36} -4.42758i q^{37} +(-5.75848 + 0.599265i) q^{38} +(3.94948 - 0.355238i) q^{39} +(-2.33788 + 10.8347i) q^{40} +(-4.51006 + 7.81166i) q^{41} +(-0.794207 + 2.31716i) q^{42} +(-10.3878 + 5.99739i) q^{43} +(2.14830 - 1.92636i) q^{44} +(8.96896 - 7.60067i) q^{45} +(-4.18542 - 1.86862i) q^{46} +(-0.676835 - 1.17231i) q^{47} +(3.57819 - 5.93267i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(11.8585 - 8.59709i) q^{50} +(-0.270765 + 0.190577i) q^{51} +(-4.35186 - 1.42389i) q^{52} -4.30001i q^{53} +(-6.84370 + 2.67653i) q^{54} -5.65383 q^{55} +(1.89905 - 2.09609i) q^{56} +(-4.08124 - 5.79847i) q^{57} +(-5.36788 - 7.40422i) q^{58} +(-8.47625 - 4.89377i) q^{59} +(-12.9804 + 3.97397i) q^{60} +(-12.0870 + 6.97843i) q^{61} +(8.78429 + 3.92183i) q^{62} +(-2.95185 + 0.535342i) q^{63} +(-6.50097 + 4.66233i) q^{64} +(4.48592 + 7.76984i) q^{65} +(3.34308 + 1.14584i) q^{66} +(6.77441 + 3.91121i) q^{67} +(0.374140 - 0.0787233i) q^{68} +(-0.502902 - 5.59118i) q^{69} +(-5.51224 + 0.573640i) q^{70} +1.95973 q^{71} +(8.48063 + 0.280903i) q^{72} -3.32315 q^{73} +(-6.22792 + 0.648117i) q^{74} +(16.2765 + 7.54160i) q^{75} +(1.68587 + 8.01225i) q^{76} +(1.24945 + 0.721373i) q^{77} +(-1.07782 - 5.50341i) q^{78} +(6.41702 + 11.1146i) q^{79} +(15.5824 + 1.70250i) q^{80} +(-6.95048 - 5.71759i) q^{81} +(11.6482 + 5.20045i) q^{82} +(-4.91508 + 2.83772i) q^{83} +(3.37562 + 0.777955i) q^{84} +(-0.648774 - 0.374570i) q^{85} +(9.95661 + 13.7337i) q^{86} +(4.70885 - 10.1628i) q^{87} +(-3.02413 - 2.73985i) q^{88} -4.44270 q^{89} +(-12.0041 - 11.5033i) q^{90} -2.28944i q^{91} +(-2.01576 + 6.16082i) q^{92} +(1.05548 + 11.7347i) q^{93} +(-1.54992 + 1.12365i) q^{94} +(8.02148 - 13.8936i) q^{95} +(-8.86878 - 4.16471i) q^{96} +(7.17699 + 12.4309i) q^{97} +(1.29136 + 0.576538i) q^{98} +(0.772363 + 4.25877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.146382	−	1.40662i	−0.103508	−	0.994629i
$2$	−0.146382	−	1.40662i	−0.103508	−	0.994629i
$3$	1.41639	−	0.996919i	0.817751	−	0.575572i
$3$	1.41639	−	0.996919i	0.817751	−	0.575572i
$4$	−1.95714	+	0.411806i	−0.978572	+	0.205903i
$5$	3.39378	+	1.95940i	1.51774	+	0.876269i	0.999782	+	0.0208644i	$0.00664183\pi$
$5$	3.39378	+	1.95940i	1.51774	+	0.876269i	0.517960	+	0.855405i	$0.326692\pi$
$6$	−1.60962	−	1.84638i	−0.657123	−	0.753783i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	0.865744	+	2.69267i	0.306087	+	0.952004i
$9$	1.01230	−	2.82405i	0.337435	−	0.941349i
$10$	2.25934	−	5.06056i	0.714465	−	1.60029i
$11$	−1.24945	+	0.721373i	−0.376725	+	0.217502i	−0.676392	−	0.736542i	$-0.736458\pi$
$11$	−1.24945	+	0.721373i	−0.376725	+	0.217502i	0.299668	+	0.954044i	$0.403124\pi$
$12$	−2.36154	+	2.53439i	−0.681717	+	0.731616i
$13$	1.98271	+	1.14472i	0.549905	+	0.317488i	0.749084	−	0.662475i	$-0.230494\pi$
$13$	1.98271	+	1.14472i	0.549905	+	0.317488i	−0.199178	+	0.979963i	$0.563827\pi$
$14$	−1.14498	+	0.830079i	−0.306008	+	0.221848i
$15$	6.76026	−	0.608055i	1.74549	−	0.156999i
$16$	3.66083	−	1.61193i	0.915208	−	0.402982i
$17$	−0.191166			−0.0463646			−0.0231823	−	0.999731i	$-0.507380\pi$
$17$	−0.191166			−0.0463646			−0.0231823	+	0.999731i	$0.507380\pi$
$18$	−4.12054	−	1.01054i	−0.971220	−	0.238186i
$19$		−	4.09385i		−	0.939193i	−0.882881	−	0.469597i	$-0.844399\pi$
$19$		−	4.09385i		−	0.939193i	0.882881	−	0.469597i	$-0.155601\pi$
$20$	−7.44900	−	2.43725i	−1.66565	−	0.544985i
$21$	−1.57155	−	0.728168i	−0.342941	−	0.158899i
$22$	1.19759	+	1.65191i	0.255328	+	0.352188i
$23$	1.62055	−	2.80688i	0.337908	−	0.585274i	−0.646131	−	0.763227i	$-0.723614\pi$
$23$	1.62055	−	2.80688i	0.337908	−	0.585274i	0.984039	+	0.177952i	$0.0569473\pi$
$24$	3.91061	+	2.95079i	0.798249	+	0.602328i
$25$	5.17848	+	8.96938i	1.03570	+	1.79388i
$26$	1.31995	−	2.95648i	0.258863	−	0.579814i
$27$	−1.38153	−	5.00913i	−0.265876	−	0.964007i
$28$	1.33521	+	1.48903i	0.252330	+	0.281401i
$29$	5.60034	−	3.23336i	1.03996	−	0.600419i	0.120135	−	0.992758i	$-0.461667\pi$
$29$	5.60034	−	3.23336i	1.03996	−	0.600419i	0.919821	+	0.392339i	$0.128334\pi$
$30$	−1.84488	−	9.42009i	−0.336827	−	1.71987i
$31$	−3.40118	+	5.89102i	−0.610871	+	1.05806i	0.380223	+	0.924895i	$0.375847\pi$
$31$	−3.40118	+	5.89102i	−0.610871	+	1.05806i	−0.991094	+	0.133164i	$0.957486\pi$
$32$	−2.80325	−	4.91343i	−0.495549	−	0.868580i
$33$	−1.05056	+	2.26735i	−0.182879	+	0.394695i
$34$	0.0279832	+	0.268897i	0.00479908	+	0.0461155i
$35$		−	3.91879i		−	0.662397i
$36$	−0.818266	+	5.94394i	−0.136378	+	0.990657i
$37$		−	4.42758i		−	0.727890i	−0.931420	−	0.363945i	$-0.881430\pi$
$37$		−	4.42758i		−	0.727890i	0.931420	−	0.363945i	$-0.118570\pi$
$38$	−5.75848	+	0.599265i	−0.934149	+	0.0972136i
$39$	3.94948	−	0.355238i	0.632423	−	0.0568836i
$40$	−2.33788	+	10.8347i	−0.369650	+	1.71311i
$41$	−4.51006	+	7.81166i	−0.704354	+	1.21998i	0.262570	+	0.964913i	$0.415430\pi$
$41$	−4.51006	+	7.81166i	−0.704354	+	1.21998i	−0.966924	+	0.255064i	$0.917904\pi$
$42$	−0.794207	+	2.31716i	−0.122549	+	0.357546i
$43$	−10.3878	+	5.99739i	−1.58412	+	0.914593i	−0.589874	+	0.807496i	$0.700822\pi$
$43$	−10.3878	+	5.99739i	−1.58412	+	0.914593i	−0.994248	+	0.107098i	$0.965844\pi$
$44$	2.14830	−	1.92636i	0.323868	−	0.290410i
$45$	8.96896	−	7.60067i	1.33701	−	1.13304i
$46$	−4.18542	−	1.86862i	−0.617107	−	0.275513i
$47$	−0.676835	−	1.17231i	−0.0987265	−	0.170999i	0.812431	−	0.583057i	$-0.198144\pi$
$47$	−0.676835	−	1.17231i	−0.0987265	−	0.170999i	−0.911158	+	0.412058i	$0.864810\pi$
$48$	3.57819	−	5.93267i	0.516467	−	0.856307i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	11.8585	−	8.59709i	1.67704	−	1.21581i
$51$	−0.270765	+	0.190577i	−0.0379147	+	0.0266861i
$52$	−4.35186	−	1.42389i	−0.603494	−	0.197458i
$53$		−	4.30001i		−	0.590652i	−0.955397	−	0.295326i	$-0.904572\pi$
$53$		−	4.30001i		−	0.590652i	0.955397	−	0.295326i	$-0.0954283\pi$
$54$	−6.84370	+	2.67653i	−0.931309	+	0.364230i
$55$	−5.65383			−0.762362
$56$	1.89905	−	2.09609i	0.253771	−	0.280102i
$57$	−4.08124	−	5.79847i	−0.540573	−	0.768027i
$58$	−5.36788	−	7.40422i	−0.704837	−	0.972222i
$59$	−8.47625	−	4.89377i	−1.10351	−	0.637114i	−0.166372	−	0.986063i	$-0.553205\pi$
$59$	−8.47625	−	4.89377i	−1.10351	−	0.637114i	−0.937142	+	0.348949i	$0.886539\pi$
$60$	−12.9804	+	3.97397i	−1.67576	+	0.513037i
$61$	−12.0870	+	6.97843i	−1.54758	+	0.893496i	−0.549256	+	0.835654i	$0.685089\pi$
$61$	−12.0870	+	6.97843i	−1.54758	+	0.893496i	−0.998326	+	0.0578421i	$0.981578\pi$
$62$	8.78429	+	3.92183i	1.11561	+	0.498072i
$63$	−2.95185	+	0.535342i	−0.371898	+	0.0674467i
$64$	−6.50097	+	4.66233i	−0.812622	+	0.582791i
$65$	4.48592	+	7.76984i	0.556410	+	0.963730i
$66$	3.34308	+	1.14584i	0.411504	+	0.141043i
$67$	6.77441	+	3.91121i	0.827626	+	0.477830i	0.853039	−	0.521847i	$-0.174757\pi$
$67$	6.77441	+	3.91121i	0.827626	+	0.477830i	−0.0254133	+	0.999677i	$0.508090\pi$
$68$	0.374140	−	0.0787233i	0.0453711	−	0.00954661i
$69$	−0.502902	−	5.59118i	−0.0605422	−	0.673099i
$70$	−5.51224	+	0.573640i	−0.658839	+	0.0685631i
$71$	1.95973			0.232578			0.116289	−	0.993215i	$-0.462900\pi$
$71$	1.95973			0.232578			0.116289	+	0.993215i	$0.462900\pi$
$72$	8.48063	+	0.280903i	0.999452	+	0.0331048i
$73$	−3.32315			−0.388946			−0.194473	−	0.980908i	$-0.562300\pi$
$73$	−3.32315			−0.388946			−0.194473	+	0.980908i	$0.562300\pi$
$74$	−6.22792	+	0.648117i	−0.723981	+	0.0753421i
$75$	16.2765	+	7.54160i	1.87945	+	0.870828i
$76$	1.68587	+	8.01225i	0.193383	+	0.919069i
$77$	1.24945	+	0.721373i	0.142389	+	0.0822081i
$78$	−1.07782	−	5.50341i	−0.122039	−	0.623138i
$79$	6.41702	+	11.1146i	0.721971	+	1.25049i	0.960209	+	0.279284i	$0.0900971\pi$
$79$	6.41702	+	11.1146i	0.721971	+	1.25049i	−0.238237	+	0.971207i	$0.576570\pi$
$80$	15.5824	+	1.70250i	1.74217	+	0.190345i
$81$	−6.95048	−	5.71759i	−0.772275	−	0.635288i
$82$	11.6482	+	5.20045i	1.28633	+	0.574294i
$83$	−4.91508	+	2.83772i	−0.539500	+	0.311480i	−0.744876	−	0.667203i	$-0.767491\pi$
$83$	−4.91508	+	2.83772i	−0.539500	+	0.311480i	0.205376	+	0.978683i	$0.434158\pi$
$84$	3.37562	+	0.777955i	0.368310	+	0.0848819i
$85$	−0.648774	−	0.374570i	−0.0703695	−	0.0406278i
$86$	9.95661	+	13.7337i	1.07365	+	1.48095i
$87$	4.70885	−	10.1628i	0.504842	−	1.08956i
$88$	−3.02413	−	2.73985i	−0.322373	−	0.292069i
$89$	−4.44270			−0.470925			−0.235463	−	0.971883i	$-0.575661\pi$
$89$	−4.44270			−0.470925			−0.235463	+	0.971883i	$0.575661\pi$
$90$	−12.0041	−	11.5033i	−1.26535	−	1.21255i
$91$		−	2.28944i		−	0.239998i
$92$	−2.01576	+	6.16082i	−0.210158	+	0.642310i
$93$	1.05548	+	11.7347i	0.109448	+	1.21683i
$94$	−1.54992	+	1.12365i	−0.159862	+	0.115896i
$95$	8.02148	−	13.8936i	0.822986	−	1.42545i
$96$	−8.86878	−	4.16471i	−0.905166	−	0.425059i
$97$	7.17699	+	12.4309i	0.728713	+	1.26217i	0.957427	+	0.288674i	$0.0932144\pi$
$97$	7.17699	+	12.4309i	0.728713	+	1.26217i	−0.228715	+	0.973493i	$0.573452\pi$
$98$	1.29136	+	0.576538i	0.130447	+	0.0582392i
$99$	0.772363	+	4.25877i	0.0776254	+	0.428022i
$100$	−13.8287	−	15.4219i	−1.38287	−	1.54219i
$101$	14.3370	−	8.27747i	1.42658	−	0.823639i	0.429735	−	0.902955i	$-0.358607\pi$
$101$	14.3370	−	8.27747i	1.42658	−	0.823639i	0.996850	+	0.0793157i	$0.0252735\pi$
$102$	0.307704	+	0.352966i	0.0304672	+	0.0349488i
$103$	7.07555	−	12.2552i	0.697175	−	1.20754i	−0.272267	−	0.962222i	$-0.587774\pi$
$103$	7.07555	−	12.2552i	0.697175	−	1.20754i	0.969442	−	0.245320i	$-0.0788931\pi$
$104$	−1.36583	+	6.32983i	−0.133931	+	0.620691i
$105$	−3.90672	−	5.55053i	−0.381257	−	0.541676i
$106$	−6.04847	+	0.629443i	−0.587480	+	0.0611369i
$107$		−	9.28596i		−	0.897708i	−0.893605	−	0.448854i	$-0.851832\pi$
$107$		−	9.28596i		−	0.897708i	0.893605	−	0.448854i	$-0.148168\pi$
$108$	4.76665	+	9.23467i	0.458671	+	0.888606i
$109$			4.41970i			0.423331i	0.977342	+	0.211665i	$0.0678887\pi$
$109$			4.41970i			0.423331i	−0.977342	+	0.211665i	$0.932111\pi$
$110$	0.827617	+	7.95277i	0.0789102	+	0.758267i
$111$	−4.41394	−	6.27117i	−0.418953	−	0.595233i
$112$	−3.22639	−	2.36441i	−0.304865	−	0.223416i
$113$	−1.14401	+	1.98149i	−0.107620	+	0.186403i	−0.914806	−	0.403895i	$-0.867656\pi$
$113$	−1.14401	+	1.98149i	−0.107620	+	0.186403i	0.807186	+	0.590298i	$0.200990\pi$
$114$	−7.55882	+	6.58953i	−0.707948	+	0.617166i
$115$	10.9996	−	6.35061i	1.02572	−	0.592197i
$116$	−9.62915	+	8.63440i	−0.894044	+	0.801684i
$117$	5.23985	−	4.44047i	0.484424	−	0.410521i
$118$	−5.64289	+	12.6392i	−0.519470	+	1.16353i
$119$	0.0955830	+	0.165555i	0.00876208	+	0.0151764i
$120$	7.48995	+	17.6767i	0.683736	+	1.61366i
$121$	−4.45924	+	7.72363i	−0.405386	+	0.702148i
$122$	11.5853	+	15.9803i	1.04888	+	1.44679i
$123$	1.39960	+	15.5605i	0.126197	+	1.40304i
$124$	4.23065	−	12.9302i	0.379924	−	1.16117i
$125$			20.9928i			1.87765i
$126$	1.18512	+	4.07376i	0.105579	+	0.362919i
$127$	−8.81726			−0.782405			−0.391203	−	0.920305i	$-0.627941\pi$
$127$	−8.81726			−0.782405			−0.391203	+	0.920305i	$0.627941\pi$
$128$	7.50974	+	8.46190i	0.663773	+	0.747934i
$129$	−8.73421	+	18.8504i	−0.769004	+	1.65969i
$130$	10.2725	−	7.44734i	0.900961	−	0.653175i
$131$	3.17376	+	1.83237i	0.277293	+	0.160095i	0.632197	−	0.774807i	$-0.282153\pi$
$131$	3.17376	+	1.83237i	0.277293	+	0.160095i	−0.354904	+	0.934903i	$0.615487\pi$
$132$	1.12239	−	4.87016i	0.0976916	−	0.423893i
$133$	−3.54538	+	2.04692i	−0.307423	+	0.177491i
$134$	4.50992	−	10.1015i	0.389598	−	0.872639i
$135$	5.12627	−	19.7068i	0.441199	−	1.69609i
$136$	−0.165501	−	0.514747i	−0.0141916	−	0.0441392i
$137$	−5.39199	−	9.33920i	−0.460669	−	0.797902i	0.538326	−	0.842737i	$-0.319057\pi$
$137$	−5.39199	−	9.33920i	−0.460669	−	0.797902i	−0.998994	+	0.0448353i	$0.985724\pi$
$138$	−7.79104	+	1.52584i	−0.663217	+	0.129888i
$139$	6.85738	+	3.95911i	0.581635	+	0.335807i	0.761783	−	0.647832i	$-0.224324\pi$
$139$	6.85738	+	3.95911i	0.581635	+	0.335807i	−0.180148	+	0.983640i	$0.557658\pi$
$140$	1.61378	+	7.66965i	0.136390	+	0.648204i
$141$	−2.12736	−	0.985698i	−0.179156	−	0.0830108i
$142$	−0.286869	−	2.75660i	−0.0240735	−	0.231328i
$143$	−3.30308			−0.276217
$144$	−0.846286	−	11.9701i	−0.0705238	−	0.997510i
$145$	25.3417			2.10451
$146$	0.486449	+	4.67440i	0.0402588	+	0.386857i
$147$	0.155164	+	1.72509i	0.0127977	+	0.142283i
$148$	1.82331	+	8.66542i	0.149875	+	0.712293i
$149$	−13.2024	−	7.62240i	−1.08158	−	0.624452i	−0.150259	−	0.988647i	$-0.548011\pi$
$149$	−13.2024	−	7.62240i	−1.08158	−	0.624452i	−0.931323	+	0.364195i	$0.881344\pi$
$150$	8.22556	−	23.9987i	0.671614	−	1.95949i
$151$	0.795684	+	1.37817i	0.0647519	+	0.112154i	0.896584	−	0.442874i	$-0.146041\pi$
$151$	0.795684	+	1.37817i	0.0647519	+	0.112154i	−0.831832	+	0.555027i	$0.812708\pi$
$152$	11.0234	−	3.54422i	0.894115	−	0.287475i
$153$	−0.193518	+	0.539862i	−0.0156450	+	0.0436452i
$154$	0.831799	−	1.86310i	0.0670282	−	0.150133i
$155$	−23.0857	+	13.3285i	−1.85429	+	1.07057i
$156$	−7.58342	+	2.32167i	−0.607159	+	0.185883i
$157$	14.9150	+	8.61121i	1.19035	+	0.687249i	0.958386	−	0.285475i	$-0.0921515\pi$
$157$	14.9150	+	8.61121i	1.19035	+	0.687249i	0.231964	+	0.972724i	$0.425485\pi$
$158$	14.6947	−	10.6533i	1.16904	−	0.847528i
$159$	−4.28677	−	6.09048i	−0.339963	−	0.483007i
$160$	0.113778	−	22.1678i	0.00899495	−	1.75252i
$161$	−3.24110			−0.255435
$162$	−7.02504	+	10.6136i	−0.551939	+	0.833884i
$163$		−	10.3227i		−	0.808533i	−0.914641	−	0.404267i	$-0.867527\pi$
$163$		−	10.3227i		−	0.808533i	0.914641	−	0.404267i	$-0.132473\pi$
$164$	5.60996	−	17.1458i	0.438064	−	1.33886i
$165$	−8.00801	+	5.63641i	−0.623422	+	0.438794i
$166$	4.71106	+	6.49824i	0.365650	+	0.504361i
$167$	−10.4721	+	18.1382i	−0.810353	+	1.40357i	0.102264	+	0.994757i	$0.467391\pi$
$167$	−10.4721	+	18.1382i	−0.810353	+	1.40357i	−0.912617	+	0.408816i	$0.865942\pi$
$168$	0.600156	−	4.86208i	0.0463031	−	0.375118i
$169$	−3.87924	−	6.71903i	−0.298403	−	0.516849i
$170$	−0.431908	+	0.967408i	−0.0331258	+	0.0741968i
$171$	−11.5612	−	4.14422i	−0.884109	−	0.316917i
$172$	17.8606	−	16.0155i	1.36186	−	1.22117i
$173$	−3.03485	+	1.75217i	−0.230735	+	0.133215i	−0.610911	−	0.791699i	$-0.709197\pi$
$173$	−3.03485	+	1.75217i	−0.230735	+	0.133215i	0.380176	+	0.924914i	$0.375863\pi$
$174$	−14.9844	−	5.13591i	−1.13597	−	0.389352i
$175$	5.17848	−	8.96938i	0.391456	−	0.678022i
$176$	−3.41124	+	4.65486i	−0.257132	+	0.350873i
$177$	−16.8843	+	1.51867i	−1.26910	+	0.114150i
$178$	0.650330	+	6.24918i	0.0487443	+	0.468396i
$179$		−	15.0170i		−	1.12242i	−0.827672	−	0.561212i	$-0.810335\pi$
$179$		−	15.0170i		−	1.12242i	0.827672	−	0.561212i	$-0.189665\pi$
$180$	−14.4236	+	18.5691i	−1.07507	+	1.38406i
$181$			7.61200i			0.565795i	0.959150	+	0.282898i	$0.0912957\pi$
$181$			7.61200i			0.565795i	−0.959150	+	0.282898i	$0.908704\pi$
$182$	−3.22036	+	0.335132i	−0.238709	+	0.0248416i
$183$	−10.1629	+	21.9339i	−0.751266	+	1.62140i
$184$	8.96098	+	1.93358i	0.660612	+	0.142545i
$185$	8.67540	−	15.0262i	0.637828	−	1.10475i
$186$	16.3517	−	3.20240i	1.19896	−	0.234811i
$187$	0.238853	−	0.137902i	0.0174667	−	0.0100844i
$188$	1.80743	+	2.01566i	0.131820	+	0.147007i
$189$	−3.64727	+	3.70101i	−0.265300	+	0.269209i
$190$	−20.7172	−	9.24938i	−1.50298	−	0.671020i
$191$	7.16402	+	12.4084i	0.518370	+	0.897843i	0.999772	+	0.0213435i	$0.00679438\pi$
$191$	7.16402	+	12.4084i	0.518370	+	0.897843i	−0.481402	+	0.876500i	$0.659872\pi$
$192$	−4.55993	+	13.0846i	−0.329085	+	0.944300i
$193$	−12.3726	+	21.4299i	−0.890598	+	1.54256i	−0.0514386	+	0.998676i	$0.516381\pi$
$193$	−12.3726	+	21.4299i	−0.890598	+	1.54256i	−0.839160	+	0.543885i	$0.816953\pi$
$194$	16.4350	−	11.9149i	1.17996	−	0.855442i
$195$	14.0997	+	6.53300i	1.00970	+	0.467838i
$196$	0.621938	−	1.90084i	0.0444241	−	0.135774i
$197$			5.73696i			0.408741i	0.978894	+	0.204371i	$0.0655148\pi$
$197$			5.73696i			0.408741i	−0.978894	+	0.204371i	$0.934485\pi$
$198$	5.87740	−	1.70982i	0.417688	−	0.121512i
$199$	23.0892			1.63675			0.818377	−	0.574682i	$-0.194874\pi$
$199$	23.0892			1.63675			0.818377	+	0.574682i	$0.194874\pi$
$200$	−19.6684	+	21.7091i	−1.39076	+	1.53507i
$201$	13.4943	−	1.21376i	0.951817	−	0.0856117i
$202$	−13.7419	−	18.9550i	−0.966877	−	1.33367i
$203$	−5.60034	−	3.23336i	−0.393066	−	0.226937i
$204$	0.451446	−	0.484490i	0.0316075	−	0.0339211i
$205$	−30.6123	+	17.6740i	−2.13806	+	1.23441i
$206$	−18.2741	−	8.15865i	−1.27322	−	0.568440i
$207$	−6.28626	−	7.41793i	−0.436925	−	0.515581i
$208$	9.10358	+	0.994634i	0.631220	+	0.0689655i
$209$	2.95319	+	5.11508i	0.204277	+	0.353817i
$210$	−7.23560	+	6.30776i	−0.499304	+	0.435277i
$211$	−19.0057	−	10.9730i	−1.30841	−	0.755410i	−0.326578	−	0.945170i	$-0.605896\pi$
$211$	−19.0057	−	10.9730i	−1.30841	−	0.755410i	−0.981830	+	0.189760i	$0.939229\pi$
$212$	1.77077	+	8.41575i	0.121617	+	0.577996i
$213$	2.77574	−	1.95370i	0.190191	−	0.133865i
$214$	−13.0618	+	1.35930i	−0.892886	+	0.0929195i
$215$	−47.0051			−3.20572
$216$	12.2919	−	8.05663i	0.836357	−	0.548185i
$217$	6.80237			0.461775
$218$	6.21683	−	0.646964i	0.421057	−	0.0438179i
$219$	−4.70687	+	3.31292i	−0.318061	+	0.223866i
$220$	11.0654	−	2.32828i	0.746026	−	0.156973i
$221$	−0.379027	−	0.218831i	−0.0254961	−	0.0147202i
$222$	−8.17502	+	7.12671i	−0.548671	+	0.478314i
$223$	−4.90061	−	8.48811i	−0.328169	−	0.568406i	0.653979	−	0.756512i	$-0.273098\pi$
$223$	−4.90061	−	8.48811i	−0.328169	−	0.568406i	−0.982149	+	0.188107i	$0.939765\pi$
$224$	−2.85353	+	4.88440i	−0.190660	+	0.326353i
$225$	30.5721	−	5.54451i	2.03814	−	0.369634i
$226$	2.95466	+	1.31914i	0.196541	+	0.0877477i
$227$	13.3952	−	7.73372i	0.889070	−	0.513305i	0.0154319	−	0.999881i	$-0.495088\pi$
$227$	13.3952	−	7.73372i	0.889070	−	0.513305i	0.873638	+	0.486576i	$0.161754\pi$
$228$	10.3754	+	9.66777i	0.687129	+	0.640264i
$229$	−22.7840	−	13.1543i	−1.50561	−	0.869264i	−0.999979	−	0.00651329i	$-0.997927\pi$
$229$	−22.7840	−	13.1543i	−1.50561	−	0.869264i	−0.505630	−	0.862750i	$-0.668740\pi$
$230$	−10.5430	−	14.5426i	−0.695185	−	0.958909i
$231$	2.48886	−	0.223862i	0.163755	−	0.0147290i
$232$	13.5548	+	12.2806i	0.889918	+	0.806262i
$233$	17.5072			1.14693			0.573466	−	0.819229i	$-0.305598\pi$
$233$	17.5072			1.14693			0.573466	+	0.819229i	$0.305598\pi$
$234$	−7.01306	−	6.72046i	−0.458458	−	0.439330i
$235$		−	5.30475i		−	0.346044i
$236$	18.6045	+	6.08724i	1.21105	+	0.396245i
$237$	20.1693	+	9.34533i	1.31014	+	0.607045i
$238$	0.218880	−	0.158683i	0.0141879	−	0.0102859i
$239$	5.64314	−	9.77421i	0.365025	−	0.632241i	−0.623755	−	0.781620i	$-0.714394\pi$
$239$	5.64314	−	9.77421i	0.365025	−	0.632241i	0.988780	+	0.149378i	$0.0477272\pi$
$240$	23.7680	−	13.1230i	1.53422	−	0.847089i
$241$	−12.8157	−	22.1974i	−0.825531	−	1.42986i	−0.901513	−	0.432752i	$-0.857542\pi$
$241$	−12.8157	−	22.1974i	−0.825531	−	1.42986i	0.0759819	−	0.997109i	$-0.475791\pi$
$242$	11.5169	+	5.14185i	0.740337	+	0.330531i
$243$	−15.5445	−	1.16925i	−0.997183	−	0.0750077i
$244$	20.7822	−	18.6353i	1.33045	−	1.19300i
$245$	−3.39378	+	1.95940i	−0.216820	+	0.125181i
$246$	21.6828	−	4.24647i	1.38244	−	0.270745i
$247$	4.68631	−	8.11692i	0.298183	−	0.516467i
$248$	−18.8072	−	4.05816i	−1.19426	−	0.257693i
$249$	−4.13267	+	8.91924i	−0.261897	+	0.565234i
$250$	29.5288	−	3.07296i	1.86757	−	0.194351i
$251$		−	5.80061i		−	0.366132i	−0.983101	−	0.183066i	$-0.941398\pi$
$251$		−	5.80061i		−	0.366132i	0.983101	−	0.183066i	$-0.0586021\pi$
$252$	5.55674	−	2.26333i	0.350042	−	0.142576i
$253$			4.67609i			0.293983i
$254$	1.29069	+	12.4025i	0.0809848	+	0.778203i
$255$	−1.29233	+	0.116239i	−0.0809290	+	0.00727920i
$256$	10.8034	−	11.8020i	0.675211	−	0.737625i
$257$	5.91102	−	10.2382i	0.368719	−	0.638641i	−0.620646	−	0.784091i	$-0.713130\pi$
$257$	5.91102	−	10.2382i	0.368719	−	0.638641i	0.989366	+	0.145450i	$0.0464630\pi$
$258$	27.7938	+	9.52634i	1.73037	+	0.593084i
$259$	−3.83440	+	2.21379i	−0.238258	+	0.137558i
$260$	−11.9793	−	13.3594i	−0.742922	−	0.828513i
$261$	−3.46190	−	19.0887i	−0.214286	−	1.18156i
$262$	2.11287	−	4.73250i	0.130533	−	0.292375i
$263$	3.80505	+	6.59055i	0.234630	+	0.406390i	0.959165	−	0.282847i	$-0.0912789\pi$
$263$	3.80505	+	6.59055i	0.234630	+	0.406390i	−0.724535	+	0.689238i	$0.757946\pi$
$264$	−7.01475	−	0.865873i	−0.431728	−	0.0532908i
$265$	8.42543	−	14.5933i	0.517570	−	0.896458i
$266$	3.39822	+	4.68736i	0.208358	+	0.287400i
$267$	−6.29258	+	4.42901i	−0.385100	+	0.271051i
$268$	−14.8692	−	4.86505i	−0.908278	−	0.297180i
$269$		−	7.26443i		−	0.442920i	−0.975169	−	0.221460i	$-0.928918\pi$
$269$		−	7.26443i		−	0.442920i	0.975169	−	0.221460i	$-0.0710823\pi$
$270$	−28.4704	−	4.32598i	−1.73265	−	0.263270i
$271$	−1.66899			−0.101384			−0.0506919	−	0.998714i	$-0.516143\pi$
$271$	−1.66899			−0.101384			−0.0506919	+	0.998714i	$0.516143\pi$
$272$	−0.699826	+	0.308146i	−0.0424332	+	0.0186841i
$273$	−2.28239	−	3.24273i	−0.138136	−	0.196259i
$274$	−12.3474	+	8.95155i	−0.745933	+	0.540783i
$275$	−12.9405	−	7.47122i	−0.780344	−	0.450532i
$276$	3.28673	+	10.7357i	0.197838	+	0.646210i
$277$	−0.723610	+	0.417776i	−0.0434775	+	0.0251017i	−0.521581	−	0.853202i	$-0.674658\pi$
$277$	−0.723610	+	0.417776i	−0.0434775	+	0.0251017i	0.478104	+	0.878303i	$0.341324\pi$
$278$	4.56516	−	10.2252i	0.273800	−	0.613270i
$279$	13.1935	+	15.5686i	0.789874	+	0.932068i
$280$	10.5520	−	3.39267i	0.630605	−	0.202751i
$281$	−11.5851	−	20.0659i	−0.691107	−	1.19703i	−0.971476	−	0.237140i	$-0.923790\pi$
$281$	−11.5851	−	20.0659i	−0.691107	−	1.19703i	0.280369	−	0.959892i	$-0.409543\pi$
$282$	−1.07509	+	3.13667i	−0.0640209	+	0.186786i
$283$	1.90459	+	1.09961i	0.113216	+	0.0653652i	0.555539	−	0.831491i	$-0.312512\pi$
$283$	1.90459	+	1.09961i	0.113216	+	0.0653652i	−0.442323	+	0.896856i	$0.645845\pi$
$284$	−3.83548	+	0.807030i	−0.227594	+	0.0478884i
$285$	−2.48928	−	27.6755i	−0.147453	−	1.63935i
$286$	0.483510	+	4.64617i	0.0285906	+	0.274734i
$287$	9.02013			0.532441
$288$	−16.7135	+	2.94261i	−0.984852	+	0.173395i
$289$	−16.9635			−0.997850
$290$	−3.70956	−	35.6461i	−0.217833	−	2.09321i
$291$	22.5580	+	10.4521i	1.32237	+	0.612713i
$292$	6.50389	−	1.36850i	0.380611	−	0.0800851i
$293$	13.9656	+	8.06302i	0.815876	+	0.471046i	0.848992	−	0.528405i	$-0.177210\pi$
$293$	13.9656	+	8.06302i	0.815876	+	0.471046i	−0.0331161	+	0.999452i	$0.510543\pi$
$294$	2.40382	−	0.470777i	0.140194	−	0.0274563i
$295$	−19.1777	−	33.2167i	−1.11657	−	1.93395i
$296$	11.9220	−	3.83315i	0.692954	−	0.222798i
$297$	5.33961	+	5.26208i	0.309836	+	0.305337i
$298$	−8.78922	+	19.6865i	−0.509146	+	1.14041i
$299$	6.42617	−	3.71015i	0.371635	−	0.214564i
$300$	−34.9611	−	8.05724i	−2.01848	−	0.465185i
$301$	10.3878	+	5.99739i	0.598742	+	0.345684i
$302$	1.82208	−	1.32096i	0.104849	−	0.0760128i
$303$	12.0548	−	26.0169i	0.692529	−	1.49463i
$304$	−6.59899	−	14.9869i	−0.378478	−	0.859557i
$305$	−54.6941			−3.13177
$306$	0.787706	+	0.193180i	0.0450302	+	0.0110434i
$307$			5.24769i			0.299501i	0.988724	+	0.149751i	$0.0478471\pi$
$307$			5.24769i			0.299501i	−0.988724	+	0.149751i	$0.952153\pi$
$308$	−2.74243	−	0.897298i	−0.156264	−	0.0511283i
$309$	−2.19574	−	24.4119i	−0.124911	−	1.38874i
$310$	22.1275	+	30.5217i	1.25676	+	1.73352i
$311$	−13.9733	+	24.2024i	−0.792352	+	1.37239i	0.132155	+	0.991229i	$0.457810\pi$
$311$	−13.9733	+	24.2024i	−0.792352	+	1.37239i	−0.924507	+	0.381165i	$0.875523\pi$
$312$	4.37578	+	10.3271i	0.247730	+	0.584658i
$313$	−5.19499	−	8.99799i	−0.293638	−	0.508596i	0.681029	−	0.732257i	$-0.261533\pi$
$313$	−5.19499	−	8.99799i	−0.293638	−	0.508596i	−0.974667	+	0.223660i	$0.928199\pi$
$314$	9.92938	−	22.2403i	0.560347	−	1.25509i
$315$	−11.0669	−	3.96701i	−0.623547	−	0.223516i
$316$	−17.1361	−	19.1103i	−0.963981	−	1.07504i
$317$	28.8706	−	16.6684i	1.62153	−	0.936192i	0.635022	−	0.772494i	$-0.280991\pi$
$317$	28.8706	−	16.6684i	1.62153	−	0.936192i	0.986510	−	0.163698i	$-0.0523424\pi$
$318$	−7.93947	+	6.92137i	−0.445224	+	0.388131i
$319$	−4.66491	+	8.07986i	−0.261185	+	0.452385i
$320$	−31.1982	+	3.08491i	−1.74403	+	0.172452i
$321$	−9.25735	−	13.1525i	−0.516695	−	0.734102i
$322$	0.474438	+	4.55899i	0.0264394	+	0.254063i
$323$			0.782605i			0.0435453i
$324$	15.9576	+	8.32790i	0.886535	+	0.462661i
$325$			23.7116i			1.31528i
$326$	−14.5200	+	1.51105i	−0.804190	+	0.0836893i
$327$	4.40609	+	6.26001i	0.243657	+	0.346179i
$328$	−24.9388	−	5.38123i	−1.37702	−	0.297129i
$329$	−0.676835	+	1.17231i	−0.0373151	+	0.0646317i
$330$	9.10049	+	10.4391i	0.500966	+	0.574655i
$331$	25.3966	−	14.6627i	1.39592	−	0.805937i	0.401962	−	0.915656i	$-0.368328\pi$
$331$	25.3966	−	14.6627i	1.39592	−	0.805937i	0.993963	+	0.109719i	$0.0349951\pi$
$332$	8.45093	−	7.57789i	0.463805	−	0.415891i
$333$	−12.5037	−	4.48206i	−0.685199	−	0.245616i
$334$	27.0464	+	12.0751i	1.47991	+	0.660720i
$335$	15.3272	+	26.5475i	0.837415	+	1.45045i
$336$	−6.92694	−	0.132471i	−0.377895	−	0.00722688i
$337$	−4.44641	+	7.70141i	−0.242212	+	0.419523i	−0.961344	−	0.275350i	$-0.911206\pi$
$337$	−4.44641	+	7.70141i	−0.242212	+	0.419523i	0.719132	+	0.694873i	$0.244539\pi$
$338$	−8.88326	+	6.44014i	−0.483186	+	0.350298i
$339$	0.355019	+	3.94705i	0.0192820	+	0.214374i
$340$	1.42400	+	0.465919i	0.0772270	+	0.0252680i
$341$		−	9.81409i		−	0.531463i
$342$	−4.13698	+	16.8688i	−0.223702	+	0.912163i
$343$	1.00000			0.0539949
$344$	−25.1422	−	22.7787i	−1.35557	−	1.22815i
$345$	9.24861	−	19.9606i	0.497929	−	1.07464i
$346$	2.90888	+	4.01239i	0.156382	+	0.215707i
$347$	−1.67870	−	0.969195i	−0.0901171	−	0.0520291i	0.454264	−	0.890867i	$-0.349902\pi$
$347$	−1.67870	−	0.969195i	−0.0901171	−	0.0520291i	−0.544381	+	0.838838i	$0.683236\pi$
$348$	−5.03081	+	21.8291i	−0.269680	+	1.17016i
$349$	−4.06686	+	2.34801i	−0.217694	+	0.125686i	−0.604882	−	0.796315i	$-0.706780\pi$
$349$	−4.06686	+	2.34801i	−0.217694	+	0.125686i	0.387188	+	0.922001i	$0.373446\pi$
$350$	−13.3745	−	5.97118i	−0.714898	−	0.319173i
$351$	2.99487	−	11.5131i	0.159854	−	0.614525i
$352$	7.04695	+	4.11693i	0.375603	+	0.219433i
$353$	−0.492796	−	0.853548i	−0.0262289	−	0.0454298i	0.852613	−	0.522543i	$-0.175017\pi$
$353$	−0.492796	−	0.853548i	−0.0262289	−	0.0454298i	−0.878842	+	0.477113i	$0.841683\pi$
$354$	4.60775	+	23.5275i	0.244899	+	1.25047i
$355$	6.65090	+	3.83990i	0.352993	+	0.203801i
$356$	8.69501	−	1.82953i	0.460834	−	0.0969650i
$357$	0.300427	+	0.139201i	0.0159003	+	0.00736729i
$358$	−21.1232	+	2.19821i	−1.11639	+	0.116179i
$359$	−12.6911			−0.669810			−0.334905	−	0.942252i	$-0.608704\pi$
$359$	−12.6911			−0.669810			−0.334905	+	0.942252i	$0.608704\pi$
$360$	28.2310	+	17.5702i	1.48790	+	0.926033i
$361$	2.24041			0.117916
$362$	10.7072	−	1.11426i	0.562756	−	0.0585641i
$363$	1.38383	+	15.3852i	0.0726320	+	0.807511i
$364$	0.942805	+	4.48076i	0.0494164	+	0.234856i
$365$	−11.2780	−	6.51138i	−0.590319	−	0.340821i
$366$	32.3403	+	11.0846i	1.69045	+	0.579403i
$367$	16.8384	+	29.1650i	0.878957	+	1.52240i	0.852486	+	0.522749i	$0.175094\pi$
$367$	16.8384	+	29.1650i	0.878957	+	1.52240i	0.0264711	+	0.999650i	$0.491573\pi$
$368$	1.40808	−	12.8877i	0.0734012	−	0.671819i
$369$	17.4949	+	20.6444i	0.910750	+	1.07471i
$370$	−22.4061	−	10.0034i	−1.16484	−	0.520052i
$371$	−3.72392	+	2.15001i	−0.193336	+	0.111623i
$372$	−6.89814	−	22.5318i	−0.357652	−	1.16822i
$373$	13.6218	+	7.86453i	0.705308	+	0.407210i	0.809321	−	0.587366i	$-0.199835\pi$
$373$	13.6218	+	7.86453i	0.705308	+	0.407210i	−0.104013	+	0.994576i	$0.533168\pi$
$374$	−0.228939	−	0.315789i	−0.0118382	−	0.0163291i
$375$	20.9281	+	29.7339i	1.08072	+	1.53545i
$376$	2.57069	−	2.83742i	0.132573	−	0.146329i
$377$	14.8051			0.762503
$378$	5.73979	+	4.58855i	0.295223	+	0.236010i
$379$			13.5218i			0.694568i	0.937760	+	0.347284i	$0.112896\pi$
$379$			13.5218i			0.694568i	−0.937760	+	0.347284i	$0.887104\pi$
$380$	−9.97772	+	30.4951i	−0.511846	+	1.56436i
$381$	−12.4887	+	8.79010i	−0.639813	+	0.450330i
$382$	16.4053	−	11.8934i	0.839366	−	0.608519i
$383$	−9.02183	+	15.6263i	−0.460994	+	0.798465i	−0.999011	−	0.0444689i	$-0.985840\pi$
$383$	−9.02183	+	15.6263i	−0.460994	+	0.798465i	0.538017	+	0.842934i	$0.319174\pi$
$384$	19.0725	+	4.49873i	0.973291	+	0.229575i
$385$	2.82691	+	4.89636i	0.144073	+	0.249541i
$386$	31.9549	+	14.2665i	1.62646	+	0.726148i
$387$	6.42131	+	35.4068i	0.326413	+	1.79983i
$388$	−19.1655	−	21.3736i	−0.972982	−	1.08508i
$389$	15.0035	−	8.66229i	0.760709	−	0.439195i	−0.0688415	−	0.997628i	$-0.521930\pi$
$389$	15.0035	−	8.66229i	0.760709	−	0.439195i	0.829550	+	0.558432i	$0.188597\pi$
$390$	7.12550	−	20.7892i	0.360814	−	1.05270i
$391$	−0.309794	+	0.536579i	−0.0156670	+	0.0271360i
$392$	−2.76480	−	0.596580i	−0.139643	−	0.0301318i
$393$	6.32201	−	0.568636i	0.318903	−	0.0286839i
$394$	8.06970	−	0.839786i	0.406546	−	0.0423078i
$395$			50.2940i			2.53056i
$396$	−3.26541	−	8.01696i	−0.164093	−	0.402867i
$397$		−	16.9374i		−	0.850064i	−0.905178	−	0.425032i	$-0.860263\pi$
$397$		−	16.9374i		−	0.850064i	0.905178	−	0.425032i	$-0.139737\pi$
$398$	−3.37984	−	32.4777i	−0.169416	−	1.62796i
$399$	−2.98101	+	6.43369i	−0.149237	+	0.322087i
$400$	33.4155	+	24.4881i	1.67078	+	1.22440i
$401$	6.96012	−	12.0553i	0.347572	−	0.602012i	−0.638246	−	0.769833i	$-0.720340\pi$
$401$	6.96012	−	12.0553i	0.347572	−	0.602012i	0.985818	+	0.167821i	$0.0536730\pi$
$402$	−3.68261	−	18.8037i	−0.183672	−	0.937843i
$403$	−13.4871	+	7.78680i	−0.671842	+	0.387888i
$404$	−24.6509	+	22.1043i	−1.22643	+	1.09973i
$405$	−12.3853	−	33.0230i	−0.615432	−	1.64092i
$406$	−3.72831	+	8.35083i	−0.185033	+	0.414445i
$407$	3.19394	+	5.53207i	0.158318	+	0.274214i
$408$	−0.747575	−	0.564091i	−0.0370105	−	0.0279267i
$409$	−1.89753	+	3.28663i	−0.0938270	+	0.162513i	−0.909118	−	0.416538i	$-0.863243\pi$
$409$	−1.89753	+	3.28663i	−0.0938270	+	0.162513i	0.815291	+	0.579051i	$0.196577\pi$
$410$	29.3417	+	40.4726i	1.44908	+	1.99880i
$411$	−16.9476	−	7.85254i	−0.835962	−	0.387337i
$412$	−8.80110	+	26.8990i	−0.433599	+	1.32522i
$413$			9.78753i			0.481613i
$414$	−9.51399	+	9.92821i	−0.467587	+	0.487945i
$415$	−22.2409			−1.09176
$416$	0.0664715	−	12.9509i	0.00325903	−	0.634968i
$417$	13.6596	−	1.22862i	0.668914	−	0.0601658i
$418$	6.76266	−	4.90277i	0.330773	−	0.239802i
$419$	−7.82969	−	4.52048i	−0.382506	−	0.220840i	0.296402	−	0.955063i	$-0.404213\pi$
$419$	−7.82969	−	4.52048i	−0.382506	−	0.220840i	−0.678908	+	0.734224i	$0.737546\pi$
$420$	9.93176	+	9.25438i	0.484620	+	0.451567i
$421$	12.7840	−	7.38086i	0.623055	−	0.359721i	−0.155002	−	0.987914i	$-0.549539\pi$
$421$	12.7840	−	7.38086i	0.623055	−	0.359721i	0.778057	+	0.628193i	$0.216205\pi$
$422$	−12.6527	+	28.3400i	−0.615922	+	1.37957i
$423$	−3.99583	+	0.724676i	−0.194284	+	0.0352350i
$424$	11.5785	−	3.72271i	0.562303	−	0.180791i
$425$	−0.989948	−	1.71464i	−0.0480195	−	0.0831723i
$426$	−3.15442	−	3.61842i	−0.152832	−	0.175313i
$427$	12.0870	+	6.97843i	0.584931	+	0.337710i
$428$	3.82402	+	18.1740i	0.184841	+	0.878472i
$429$	−4.67844	+	3.29290i	−0.225877	+	0.158983i
$430$	6.88068	+	66.1182i	0.331816	+	3.18850i
$431$	−1.12944			−0.0544032			−0.0272016	−	0.999630i	$-0.508660\pi$
$431$	−1.12944			−0.0544032			−0.0272016	+	0.999630i	$0.508660\pi$
$432$	−13.1319	−	16.1106i	−0.631809	−	0.775124i
$433$	−1.96374			−0.0943711			−0.0471856	−	0.998886i	$-0.515025\pi$
$433$	−1.96374			−0.0943711			−0.0471856	+	0.998886i	$0.515025\pi$
$434$	−0.995742	−	9.56833i	−0.0477972	−	0.459294i
$435$	35.8937	−	25.2636i	1.72097	−	1.21130i
$436$	−1.82006	−	8.65000i	−0.0871651	−	0.414260i
$437$	−11.4909	−	6.63429i	−0.549686	−	0.317361i
$438$	5.34900	+	6.13582i	0.255585	+	0.293181i
$439$	6.78329	+	11.7490i	0.323749	+	0.560750i	0.981258	−	0.192697i	$-0.0617234\pi$
$439$	6.78329	+	11.7490i	0.323749	+	0.560750i	−0.657509	+	0.753446i	$0.728390\pi$
$440$	−4.89477	−	15.2239i	−0.233349	−	0.725771i
$441$	1.93954	+	2.28870i	0.0923592	+	0.108986i
$442$	−0.252329	+	0.565179i	−0.0120021	+	0.0268828i
$443$	−22.4035	+	12.9347i	−1.06442	+	0.614545i	−0.926652	−	0.375919i	$-0.877327\pi$
$443$	−22.4035	+	12.9347i	−1.06442	+	0.614545i	−0.137771	+	0.990464i	$0.543994\pi$
$444$	11.2212	+	10.4559i	0.532536	+	0.496215i
$445$	−15.0775	−	8.70501i	−0.714743	−	0.412657i
$446$	−11.2222	+	8.13579i	−0.531385	+	0.385241i
$447$	−26.2986	+	2.36544i	−1.24388	+	0.111882i
$448$	7.28818	+	3.29884i	0.344334	+	0.155856i
$449$	2.72639			0.128666			0.0643332	−	0.997928i	$-0.479508\pi$
$449$	2.72639			0.128666			0.0643332	+	0.997928i	$0.479508\pi$
$450$	−12.2742	−	42.1917i	−0.578612	−	1.98894i
$451$		−	13.0138i		−	0.612794i
$452$	1.42301	−	4.34918i	0.0669329	−	0.204568i
$453$	2.50092	+	1.15878i	0.117503	+	0.0544444i
$454$	−12.8392	−	17.7098i	−0.602573	−	0.831164i
$455$	4.48592	−	7.76984i	0.210303	−	0.364256i
$456$	12.0801	−	16.0094i	0.565702	−	0.749710i
$457$	−14.9623	−	25.9154i	−0.699906	−	1.21227i	−0.968499	−	0.249019i	$-0.919892\pi$
$457$	−14.9623	−	25.9154i	−0.699906	−	1.21227i	0.268592	−	0.963254i	$-0.413442\pi$
$458$	−15.1680	+	33.9739i	−0.708753	+	1.58750i
$459$	0.264102	+	0.957575i	0.0123272	+	0.0446958i
$460$	−18.9125	+	16.9587i	−0.881802	+	0.790706i
$461$	21.8593	−	12.6205i	1.01809	−	0.587795i	0.104540	−	0.994521i	$-0.466663\pi$
$461$	21.8593	−	12.6205i	1.01809	−	0.587795i	0.913550	+	0.406726i	$0.133330\pi$
$462$	−0.679212	−	3.46811i	−0.0315998	−	0.161351i
$463$	−14.6517	+	25.3775i	−0.680922	+	1.17939i	0.293777	+	0.955874i	$0.405088\pi$
$463$	−14.6517	+	25.3775i	−0.680922	+	1.17939i	−0.974700	+	0.223518i	$0.928246\pi$
$464$	15.2899	−	20.8641i	0.709818	−	0.968592i
$465$	−19.4108	+	41.8930i	−0.900155	+	1.94274i
$466$	−2.56273	−	24.6259i	−0.118716	−	1.14077i
$467$			7.82286i			0.361999i	0.983483	+	0.180999i	$0.0579332\pi$
$467$			7.82286i			0.361999i	−0.983483	+	0.180999i	$0.942067\pi$
$468$	−8.42653	+	10.8484i	−0.389517	+	0.501469i
$469$		−	7.82241i		−	0.361205i
$470$	−7.46176	+	0.776519i	−0.344185	+	0.0358181i
$471$	29.7102	−	2.67229i	1.36897	−	0.123133i
$472$	5.83905	−	27.0605i	0.268764	−	1.24556i
$473$	8.65271	−	14.9869i	0.397852	−	0.689100i
$474$	10.1929	−	29.7385i	0.468175	−	1.36594i
$475$	36.7193	−	21.1999i	1.68480	−	0.972718i
$476$	−0.255246	−	0.284653i	−0.0116992	−	0.0130470i
$477$	−12.1434	−	4.35292i	−0.556010	−	0.199307i
$478$	−14.5746	−	6.50698i	−0.666628	−	0.297622i
$479$	−9.36243	−	16.2162i	−0.427780	−	0.740938i	0.568895	−	0.822410i	$-0.307371\pi$
$479$	−9.36243	−	16.2162i	−0.427780	−	0.740938i	−0.996676	+	0.0814726i	$0.974038\pi$
$480$	−21.9383	−	31.5116i	−1.00134	−	1.43830i
$481$	5.06834	−	8.77862i	0.231096	−	0.400271i
$482$	−29.3473	+	21.2761i	−1.33673	+	0.969098i
$483$	−4.59065	+	3.23112i	−0.208882	+	0.147021i
$484$	5.54674	−	16.9526i	0.252125	−	0.770573i
$485$			56.2503i			2.55419i
$486$	0.630743	+	22.0364i	0.0286111	+	0.999591i
$487$	−9.71049			−0.440024			−0.220012	−	0.975497i	$-0.570610\pi$
$487$	−9.71049			−0.440024			−0.220012	+	0.975497i	$0.570610\pi$
$488$	−29.2549	−	26.5048i	−1.32431	−	1.19982i
$489$	−10.2909	−	14.6209i	−0.465369	−	0.661179i
$490$	3.25291	+	4.48692i	0.146951	+	0.202699i
$491$	1.37669	+	0.794834i	0.0621293	+	0.0358704i	0.530743	−	0.847533i	$-0.321913\pi$
$491$	1.37669	+	0.794834i	0.0621293	+	0.0358704i	−0.468614	+	0.883403i	$0.655246\pi$
$492$	−9.14713	−	29.8778i	−0.412384	−	1.34700i
$493$	−1.07059	+	0.618108i	−0.0482171	+	0.0278382i
$494$	−12.1034	−	5.40367i	−0.544557	−	0.243123i
$495$	−5.72339	+	15.9667i	−0.257247	+	0.717648i
$496$	−2.95525	+	27.0485i	−0.132695	+	1.21451i
$497$	−0.979867	−	1.69718i	−0.0439530	−	0.0761289i
$498$	13.1509	+	4.50747i	0.589306	+	0.201985i
$499$	2.86396	+	1.65351i	0.128209	+	0.0740213i	0.562733	−	0.826639i	$-0.309750\pi$
$499$	2.86396	+	1.65351i	0.128209	+	0.0740213i	−0.434524	+	0.900660i	$0.643083\pi$
$500$	−8.64496	−	41.0859i	−0.386614	−	1.83742i
$501$	3.24977	+	36.1305i	0.145189	+	1.61419i
$502$	−8.15924	+	0.849104i	−0.364165	+	0.0378974i
$503$	15.0686			0.671874			0.335937	−	0.941884i	$-0.390947\pi$
$503$	15.0686			0.671874			0.335937	+	0.941884i	$0.390947\pi$
$504$	−3.99705	−	7.48489i	−0.178043	−	0.333404i
$505$	64.8754			2.88692
$506$	6.57747	−	0.684494i	0.292404	−	0.0304295i
$507$	−12.1928	−	5.64947i	−0.541503	−	0.250902i
$508$	17.2567	−	3.63100i	0.765640	−	0.161100i
$509$	11.6835	+	6.74546i	0.517861	+	0.298987i	0.736059	−	0.676917i	$-0.236685\pi$
$509$	11.6835	+	6.74546i	0.517861	+	0.298987i	−0.218198	+	0.975904i	$0.570018\pi$
$510$	0.352678	+	1.80080i	0.0156169	+	0.0797408i
$511$	1.66158	+	2.87794i	0.0735038	+	0.127312i
$512$	−18.1823	−	13.4686i	−0.803552	−	0.595234i
$513$	−20.5066	+	5.65578i	−0.905389	+	0.249709i
$514$	−15.2665	−	6.81586i	−0.673376	−	0.300635i
$515$	48.0257	−	27.7276i	2.11626	−	1.22183i
$516$	9.33140	−	40.4898i	0.410792	−	1.78246i
$517$	1.69135	+	0.976501i	0.0743854	+	0.0429465i
$518$	3.67524	+	5.06948i	0.161481	+	0.222740i
$519$	−2.55175	+	5.50725i	−0.112009	+	0.241742i
$520$	−17.0380	+	18.8058i	−0.747165	+	0.824689i
$521$	30.1383			1.32038			0.660191	−	0.751097i	$-0.270475\pi$
$521$	30.1383			1.32038			0.660191	+	0.751097i	$0.270475\pi$
$522$	−26.3438	+	7.66381i	−1.15304	+	0.335436i
$523$			8.32807i			0.364161i	0.983284	+	0.182080i	$0.0582831\pi$
$523$			8.32807i			0.364161i	−0.983284	+	0.182080i	$0.941717\pi$
$524$	−6.96610	−	2.27924i	−0.304315	−	0.0995693i
$525$	−1.60702	−	17.8666i	−0.0701363	−	0.779764i
$526$	8.71338	−	6.31699i	0.379922	−	0.275434i
$527$	0.650191	−	1.12616i	0.0283228	−	0.0490564i
$528$	−0.191122	+	9.99381i	−0.00831751	+	0.434925i
$529$	6.24763	+	10.8212i	0.271636	+	0.470487i
$530$	−21.7605	−	9.71517i	−0.945215	−	0.422000i
$531$	−22.4008	+	18.9833i	−0.972111	+	0.823807i
$532$	6.09588	−	5.46614i	0.264290	−	0.236987i
$533$	−17.8843	+	10.3255i	−0.774656	+	0.447248i
$534$	7.15104	+	8.20293i	0.309456	+	0.354975i
$535$	18.1949	−	31.5145i	0.786634	−	1.36249i
$536$	−4.66670	+	21.6274i	−0.201571	+	0.934160i
$537$	−14.9707	−	21.2699i	−0.646035	−	0.917863i
$538$	−10.2183	+	1.06338i	−0.440541	+	0.0458456i
$539$		−	1.44275i		−	0.0621435i
$540$	−1.91745	+	40.6801i	−0.0825140	+	1.75059i
$541$		−	33.7750i		−	1.45210i	−0.687642	−	0.726050i	$-0.741354\pi$
$541$		−	33.7750i		−	1.45210i	0.687642	−	0.726050i	$-0.258646\pi$
$542$	0.244309	+	2.34763i	0.0104940	+	0.100839i
$543$	7.58855	+	10.7815i	0.325656	+	0.462680i
$544$	0.535885	+	0.939281i	0.0229759	+	0.0402713i
$545$	−8.65996	+	14.9995i	−0.370952	+	0.642507i
$546$	−4.22718	+	3.68512i	−0.180907	+	0.157709i
$547$	38.9535	−	22.4898i	1.66553	−	0.961595i	0.695530	−	0.718497i	$-0.255169\pi$
$547$	38.9535	−	22.4898i	1.66553	−	0.961595i	0.970002	−	0.243099i	$-0.0781639\pi$
$548$	14.3988	+	16.0577i	0.615088	+	0.685951i
$549$	7.47169	+	41.1985i	0.318884	+	1.75831i
$550$	−8.61490	+	19.2960i	−0.367340	+	0.822786i
$551$	−13.2369	−	22.9269i	−0.563909	−	0.976720i
$552$	14.6198	−	6.19468i	0.622262	−	0.263663i
$553$	6.41702	−	11.1146i	0.272879	−	0.472641i
$554$	0.693575	+	0.956687i	0.0294672	+	0.0406457i
$555$	−2.69221	−	29.9316i	−0.114278	−	1.27053i
$556$	−15.0513	−	4.92464i	−0.638316	−	0.208851i
$557$		−	2.86522i		−	0.121403i	−0.998156	−	0.0607016i	$-0.980666\pi$
$557$		−	2.86522i		−	0.121403i	0.998156	−	0.0607016i	$-0.0193338\pi$
$558$	19.9678	−	20.8372i	0.845304	−	0.882107i
$559$	−27.4613			−1.16149
$560$	−6.31682	−	14.3460i	−0.266934	−	0.606231i
$561$	0.200832	−	0.433440i	0.00847911	−	0.0182999i
$562$	−26.5292	+	19.2330i	−1.11907	+	0.811296i
$563$	−15.0821	−	8.70766i	−0.635635	−	0.366984i	0.147296	−	0.989092i	$-0.452943\pi$
$563$	−15.0821	−	8.70766i	−0.635635	−	0.366984i	−0.782931	+	0.622108i	$0.786276\pi$
$564$	4.56947	+	1.05309i	0.192409	+	0.0443433i
$565$	−7.76506	+	4.48316i	−0.326678	+	0.188608i
$566$	1.26794	−	2.83999i	0.0532954	−	0.119374i
$567$	−1.47634	+	8.87809i	−0.0620004	+	0.372845i
$568$	1.69663	+	5.27692i	0.0711889	+	0.221415i
$569$	−2.60365	−	4.50966i	−0.109151	−	0.189055i	0.806276	−	0.591540i	$-0.201480\pi$
$569$	−2.60365	−	4.50966i	−0.109151	−	0.189055i	−0.915426	+	0.402485i	$0.868146\pi$
$570$	−38.5644	+	7.55266i	−1.61529	+	0.316346i
$571$	−19.2826	−	11.1328i	−0.806953	−	0.465894i	0.0389438	−	0.999241i	$-0.487601\pi$
$571$	−19.2826	−	11.1328i	−0.806953	−	0.465894i	−0.845897	+	0.533347i	$0.820934\pi$
$572$	6.46460	−	1.36023i	0.270299	−	0.0568740i
$573$	22.5172	+	10.4332i	0.940671	+	0.435854i
$574$	−1.32038	−	12.6879i	−0.0551117	−	0.529581i
$575$	33.5679			1.39988
$576$	6.58567	+	23.0788i	0.274403	+	0.961615i
$577$	24.9296			1.03783			0.518917	−	0.854824i	$-0.326335\pi$
$577$	24.9296			1.03783			0.518917	+	0.854824i	$0.326335\pi$
$578$	2.48314	+	23.8611i	0.103285	+	0.992491i
$579$	3.83955	+	42.6876i	0.159566	+	1.77403i
$580$	−49.5974	+	10.4359i	−2.05942	+	0.433326i
$581$	4.91508	+	2.83772i	0.203912	+	0.117728i
$582$	11.4000	−	33.2605i	0.472546	−	1.37869i
$583$	3.10191	+	5.37267i	0.128468	+	0.222513i
$584$	−2.87700	−	8.94816i	−0.119051	−	0.370278i
$585$	26.4835	−	4.80300i	1.09496	−	0.198580i
$586$	9.29728	−	20.8245i	0.384067	−	0.860251i
$587$	0.175097	−	0.101092i	0.00722702	−	0.00417252i	−0.496382	−	0.868104i	$-0.665339\pi$
$587$	0.175097	−	0.101092i	0.00722702	−	0.00417252i	0.503609	+	0.863932i	$0.332005\pi$
$588$	−1.01408	−	3.31235i	−0.0418199	−	0.136599i
$589$	24.1170	+	13.9239i	0.993722	+	0.573726i
$590$	−43.9159	+	31.8380i	−1.80799	+	1.31075i
$591$	5.71928	+	8.12575i	0.235260	+	0.334249i
$592$	−7.13695	−	16.2086i	−0.293327	−	0.666171i
$593$	38.5038			1.58116			0.790580	−	0.612358i	$-0.209779\pi$
$593$	38.5038			1.58116			0.790580	+	0.612358i	$0.209779\pi$
$594$	6.62011	−	8.28106i	0.271626	−	0.339776i
$595$			0.749140i			0.0307118i
$596$	28.9779	+	9.48132i	1.18698	+	0.388370i
$597$	32.7033	−	23.0181i	1.33846	−	0.942069i
$598$	−6.15944	−	8.49607i	−0.251878	−	0.347430i
$599$	13.5530	−	23.4744i	0.553760	−	0.959140i	−0.444239	−	0.895908i	$-0.646526\pi$
$599$	13.5530	−	23.4744i	0.553760	−	0.959140i	0.997999	−	0.0632315i	$-0.0201406\pi$
$600$	−6.21579	+	50.3563i	−0.253759	+	2.05579i
$601$	−0.361170	−	0.625566i	−0.0147324	−	0.0255173i	0.858565	−	0.512704i	$-0.171356\pi$
$601$	−0.361170	−	0.625566i	−0.0147324	−	0.0255173i	−0.873298	+	0.487187i	$0.838023\pi$
$602$	6.91545	−	15.4895i	0.281853	−	0.631307i
$603$	17.9032	−	15.1719i	0.729074	−	0.617848i
$604$	−2.12481	−	2.36960i	−0.0864572	−	0.0964178i
$605$	−30.2673	+	17.4749i	−1.23054	+	0.710454i
$606$	−38.3605	−	13.1480i	−1.55829	−	0.534103i
$607$	−4.48806	+	7.77356i	−0.182165	+	0.315519i	−0.942618	−	0.333875i	$-0.891644\pi$
$607$	−4.48806	+	7.77356i	−0.182165	+	0.315519i	0.760453	+	0.649393i	$0.224977\pi$
$608$	−20.1148	+	11.4761i	−0.815765	+	0.465416i
$609$	−11.1556	+	1.00340i	−0.452049	+	0.0406598i
$610$	8.00621	+	76.9336i	0.324162	+	3.11495i
$611$		−	3.09914i		−	0.125378i
$612$	0.156425	−	1.13628i	0.00632309	−	0.0459314i
$613$			19.5210i			0.788446i	0.919015	+	0.394223i	$0.128986\pi$
$613$			19.5210i			0.788446i	−0.919015	+	0.394223i	$0.871014\pi$
$614$	7.38149	−	0.768166i	0.297893	−	0.0310006i
$615$	−25.7393	+	55.5512i	−1.03791	+	2.24004i
$616$	−0.860714	+	3.98890i	−0.0346791	+	0.160717i
$617$	−0.779033	+	1.34932i	−0.0313627	+	0.0543217i	−0.881281	−	0.472593i	$-0.843318\pi$
$617$	−0.779033	+	1.34932i	−0.0313627	+	0.0543217i	0.849918	+	0.526915i	$0.176651\pi$
$618$	−34.0168	+	6.66202i	−1.36835	+	0.267986i
$619$	18.4399	−	10.6463i	0.741162	−	0.427910i	−0.0813298	−	0.996687i	$-0.525917\pi$
$619$	18.4399	−	10.6463i	0.741162	−	0.427910i	0.822492	+	0.568777i	$0.192583\pi$
$620$	39.6933	−	35.5927i	1.59412	−	1.42944i
$621$	−16.2988	−	4.23976i	−0.654050	−	0.170136i
$622$	36.0890	+	16.1123i	1.44704	+	0.646043i
$623$	2.22135	+	3.84749i	0.0889965	+	0.154146i
$624$	13.8858	−	7.66675i	0.555875	−	0.306915i
$625$	−15.2408	+	26.3979i	−0.609633	+	1.05592i
$626$	−11.8963	+	8.62451i	−0.475471	+	0.344705i
$627$	9.28218	+	4.30084i	0.370695	+	0.171759i
$628$	−32.7370	−	10.7113i	−1.30635	−	0.427426i
$629$			0.846404i			0.0337483i
$630$	−3.96008	+	16.1475i	−0.157774	+	0.643333i
$631$	−19.5682			−0.779000			−0.389500	−	0.921027i	$-0.627352\pi$
$631$	−19.5682			−0.779000			−0.389500	+	0.921027i	$0.627352\pi$
$632$	−24.3725	+	26.9013i	−0.969486	+	1.07008i
$633$	−37.8586	+	3.40521i	−1.50475	+	0.135345i
$634$	−27.6722	−	38.1699i	−1.09900	−	1.51592i
$635$	−29.9238	−	17.2765i	−1.18749	−	0.685598i
$636$	10.8979	+	10.1546i	0.432131	+	0.402658i
$637$	−1.98271	+	1.14472i	−0.0785579	+	0.0453554i
$638$	12.0481	+	5.37900i	0.476990	+	0.212957i
$639$	1.98385	−	5.53438i	0.0784798	−	0.218937i
$640$	8.90614	+	43.4324i	0.352046	+	1.71681i
$641$	17.1538	+	29.7113i	0.677536	+	1.17353i	0.975721	+	0.219018i	$0.0702854\pi$
$641$	17.1538	+	29.7113i	0.677536	+	1.17353i	−0.298185	+	0.954508i	$0.596381\pi$
$642$	−17.1455	+	14.9468i	−0.676677	+	0.589905i
$643$	2.29660	+	1.32594i	0.0905689	+	0.0522900i	0.544600	−	0.838696i	$-0.316681\pi$
$643$	2.29660	+	1.32594i	0.0905689	+	0.0522900i	−0.454032	+	0.890986i	$0.650015\pi$
$644$	6.34331	−	1.33471i	0.249961	−	0.0525948i
$645$	−66.5774	+	46.8603i	−2.62148	+	1.84512i
$646$	1.10083	−	0.114559i	0.0433114	−	0.00450726i
$647$	−6.46511			−0.254170			−0.127085	−	0.991892i	$-0.540562\pi$
$647$	−6.46511			−0.254170			−0.127085	+	0.991892i	$0.540562\pi$
$648$	9.37826	−	23.6653i	0.368413	−	0.929662i
$649$	14.1209			0.554295
$650$	33.3532	−	3.47095i	1.30822	−	0.136142i
$651$	9.63479	−	6.78141i	0.377617	−	0.265784i
$652$	4.25094	+	20.2029i	0.166480	+	0.791208i
$653$	−22.9691	−	13.2612i	−0.898849	−	0.518951i	−0.0220224	−	0.999757i	$-0.507011\pi$
$653$	−22.9691	−	13.2612i	−0.898849	−	0.518951i	−0.876827	+	0.480807i	$0.840344\pi$
$654$	8.16047	−	7.11403i	0.319100	−	0.278181i
$655$	7.18070	+	12.4373i	0.280573	+	0.485967i
$656$	−3.91875	+	35.8671i	−0.153001	+	1.40037i
$657$	−3.36404	+	9.38474i	−0.131244	+	0.366134i
$658$	1.74807	+	0.780442i	0.0681469	+	0.0304248i
$659$	16.3461	−	9.43744i	0.636755	−	0.367630i	−0.146609	−	0.989195i	$-0.546836\pi$
$659$	16.3461	−	9.43744i	0.636755	−	0.367630i	0.783363	+	0.621564i	$0.213502\pi$
$660$	13.3517	−	14.3290i	0.519715	−	0.557756i
$661$	−13.1578	−	7.59667i	−0.511780	−	0.295476i	0.221785	−	0.975096i	$-0.428812\pi$
$661$	−13.1578	−	7.59667i	−0.511780	−	0.295476i	−0.733565	+	0.679619i	$0.762145\pi$
$662$	−24.3425	−	33.5770i	−0.946097	−	1.30501i
$663$	−0.755006	+	0.0679094i	−0.0293220	+	0.00263738i
$664$	−11.8963	−	10.7780i	−0.461664	−	0.418266i
$665$	−16.0430			−0.622119
$666$	−4.47423	+	18.2440i	−0.173373	+	0.706941i
$667$		−	20.9593i		−	0.811546i
$668$	13.0260	−	39.8115i	0.503989	−	1.54035i
$669$	−15.4031	−	7.13693i	−0.595519	−	0.275930i
$670$	35.0986	−	25.4456i	1.35598	−	0.983049i
$671$	10.0681	−	17.4385i	0.388675	−	0.673205i
$672$	0.827641	+	9.76294i	0.0319270	+	0.376614i
$673$	−12.3880	−	21.4567i	−0.477524	−	0.827096i	0.522144	−	0.852857i	$-0.325132\pi$
$673$	−12.3880	−	21.4567i	−0.477524	−	0.827096i	−0.999668	+	0.0257612i	$0.991799\pi$
$674$	11.4838	+	5.12706i	0.442340	+	0.197487i
$675$	37.7746	−	38.3311i	1.45394	−	1.47537i
$676$	10.3592	+	11.5526i	0.398429	+	0.444332i
$677$	16.0524	−	9.26787i	0.616945	−	0.356193i	−0.158734	−	0.987321i	$-0.550741\pi$
$677$	16.0524	−	9.26787i	0.616945	−	0.356193i	0.775679	+	0.631128i	$0.217408\pi$
$678$	5.50002	−	1.07715i	0.211227	−	0.0413678i
$679$	7.17699	−	12.4309i	0.275428	−	0.477054i
$680$	0.446922	−	2.07122i	0.0171387	−	0.0794276i
$681$	11.2629	−	24.3079i	0.431595	−	0.931479i
$682$	−13.8047	+	1.43660i	−0.528608	+	0.0550104i
$683$			21.7574i			0.832525i	0.909245	+	0.416262i	$0.136660\pi$
$683$			21.7574i			0.832525i	−0.909245	+	0.416262i	$0.863340\pi$
$684$	24.3336	+	3.34986i	0.930418	+	0.128085i
$685$		−	42.2602i		−	1.61468i
$686$	−0.146382	−	1.40662i	−0.00558888	−	0.0537049i
$687$	−45.3848	+	4.08216i	−1.73154	+	0.155744i
$688$	−28.3606	+	38.6998i	−1.08124	+	1.47542i
$689$	4.92231	−	8.52569i	0.187525	−	0.324803i
$690$	−29.4308	−	10.0874i	−1.12041	−	0.384020i
$691$	−12.5101	+	7.22273i	−0.475908	+	0.274766i	−0.718710	−	0.695310i	$-0.755267\pi$
$691$	−12.5101	+	7.22273i	−0.475908	+	0.274766i	0.242802	+	0.970076i	$0.421934\pi$
$692$	5.21809	−	4.67902i	0.198362	−	0.177870i
$693$	3.30202	−	2.79827i	0.125433	−	0.106297i
$694$	−1.11756	+	2.50315i	−0.0424219	+	0.0950185i
$695$	15.5149	+	26.8727i	0.588515	+	1.01934i
$696$	31.4417	+	3.88104i	1.19179	+	0.147110i
$697$	0.862171	−	1.49332i	0.0326571	−	0.0565637i
$698$	3.89806	+	5.37682i	0.147544	+	0.203516i
$699$	24.7969	−	17.4532i	0.937905	−	0.660141i
$700$	−6.44138	+	19.6869i	−0.243461	+	0.744095i
$701$		−	26.1331i		−	0.987035i	−0.869736	−	0.493518i	$-0.835711\pi$
$701$		−	26.1331i		−	0.987035i	0.869736	−	0.493518i	$-0.164289\pi$
$702$	−16.6330	−	2.52732i	−0.627770	−	0.0953876i
$703$	−18.1259			−0.683630
$704$	4.75939	−	10.5150i	0.179376	−	0.396299i
$705$	−5.28841	−	7.51358i	−0.199173	−	0.282978i
$706$	−1.12848	+	0.818120i	−0.0424709	+	0.0307903i
$707$	−14.3370	−	8.27747i	−0.539198	−	0.311306i
$708$	32.4197	−	9.92534i	1.21841	−	0.373017i
$709$	1.62003	−	0.935322i	0.0608413	−	0.0351268i	−0.469271	−	0.883054i	$-0.655483\pi$
$709$	1.62003	−	0.935322i	0.0608413	−	0.0351268i	0.530112	+	0.847928i	$0.322150\pi$
$710$	4.42770	−	9.91736i	0.166168	−	0.372192i
$711$	37.8841	−	6.87060i	1.42077	−	0.257668i
$712$	−3.84624	−	11.9627i	−0.144144	−	0.448323i
$713$	11.0236	+	19.0934i	0.412836	+	0.715054i
$714$	0.151825	−	0.442962i	0.00568192	−	0.0165775i
$715$	−11.2099	−	6.47204i	−0.419227	−	0.242041i
$716$	6.18409	+	29.3904i	0.231110	+	1.09837i
$717$	−1.75122	−	19.4698i	−0.0654006	−	0.727114i
$718$	1.85774	+	17.8515i	0.0693303	+	0.666212i
$719$	33.6876			1.25634			0.628168	−	0.778077i	$-0.283805\pi$
$719$	33.6876			1.25634			0.628168	+	0.778077i	$0.283805\pi$
$720$	20.5821	−	42.2821i	0.767050	−	1.57576i
$721$	−14.1511			−0.527015
$722$	−0.327954	−	3.15139i	−0.0122052	−	0.117283i
$723$	−40.2810	−	18.6639i	−1.49807	−	0.694119i
$724$	−3.13467	−	14.8978i	−0.116499	−	0.553672i
$725$	58.0024	+	33.4877i	2.15415	+	1.24370i
$726$	21.4385	−	4.19862i	0.795656	−	0.155825i
$727$	−1.40284	−	2.42979i	−0.0520284	−	0.0901158i	0.838838	−	0.544381i	$-0.183235\pi$
$727$	−1.40284	−	2.42979i	−0.0520284	−	0.0901158i	−0.890867	+	0.454265i	$0.849902\pi$
$728$	6.16471	−	1.98207i	0.228479	−	0.0734603i
$729$	−23.1827	+	13.8405i	−0.858620	+	0.512612i
$730$	−7.50812	+	16.8170i	−0.277888	+	0.622426i
$731$	1.98579	−	1.14650i	0.0734471	−	0.0424047i
$732$	10.8578	−	47.1130i	0.401316	−	1.74135i
$733$	9.91594	+	5.72497i	0.366254	+	0.211457i	0.671820	−	0.740714i	$-0.265513\pi$
$733$	9.91594	+	5.72497i	0.366254	+	0.211457i	−0.305567	+	0.952171i	$0.598846\pi$
$734$	38.5591	−	27.9544i	1.42324	−	1.03182i
$735$	−2.85354	+	6.15858i	−0.105254	+	0.227163i
$736$	−18.3342	−	0.0941020i	−0.675808	−	0.00346865i
$737$	−11.2858			−0.415716
$738$	26.4778	−	27.6306i	0.974663	−	1.01710i
$739$		−	5.32862i		−	0.196017i	−0.995186	−	0.0980083i	$-0.968753\pi$
$739$		−	5.32862i		−	0.196017i	0.995186	−	0.0980083i	$-0.0312472\pi$
$740$	−10.7911	+	32.9811i	−0.396689	+	1.21241i
$741$	−1.45429	−	16.1686i	−0.0534247	−	0.593967i
$742$	3.56935	+	4.92341i	0.131035	+	0.180744i
$743$	13.3860	−	23.1853i	0.491086	−	0.850585i	−0.508862	−	0.860848i	$-0.669934\pi$
$743$	13.3860	−	23.1853i	0.491086	−	0.850585i	0.999947	+	0.0102631i	$0.00326691\pi$
$744$	−30.6839	+	13.0013i	−1.12492	+	0.476650i
$745$	−29.8706	−	51.7375i	−1.09438	−	1.89551i
$746$	9.06841	−	20.3118i	0.332018	−	0.743669i
$747$	3.03830	+	16.7530i	0.111166	+	0.612962i
$748$	−0.410682	+	0.368255i	−0.0150160	+	0.0134648i
$749$	−8.04188	+	4.64298i	−0.293844	+	0.169651i
$750$	38.7607	−	33.7903i	1.41534	−	1.23385i
$751$	0.0609412	−	0.105553i	0.00222378	−	0.00385170i	−0.864911	−	0.501925i	$-0.832625\pi$
$751$	0.0609412	−	0.105553i	0.00222378	−	0.00385170i	0.867135	+	0.498073i	$0.165959\pi$
$752$	−4.36746	−	3.20063i	−0.159265	−	0.116715i
$753$	−5.78274	−	8.21591i	−0.210735	−	0.299405i
$754$	−2.16720	−	20.8252i	−0.0789248	−	0.758408i
$755$			6.23625i			0.226960i
$756$	5.61413	−	8.74537i	0.204184	−	0.318066i
$757$		−	13.5109i		−	0.491064i	−0.969389	−	0.245532i	$-0.921037\pi$
$757$		−	13.5109i		−	0.491064i	0.969389	−	0.245532i	$-0.0789626\pi$
$758$	19.0200	−	1.97934i	0.690837	−	0.0718930i
$759$	4.66168	+	6.62315i	0.169208	+	0.240405i
$760$	44.3555	+	9.57091i	1.60894	+	0.347173i
$761$	25.0346	−	43.3613i	0.907505	−	1.57184i	0.0899861	−	0.995943i	$-0.471318\pi$
$761$	25.0346	−	43.3613i	0.907505	−	1.57184i	0.817519	−	0.575902i	$-0.195349\pi$
$762$	14.1924	+	16.2800i	0.514137	+	0.589764i
$763$	3.82758	−	2.20985i	0.138568	−	0.0800020i
$764$	−19.1309	−	21.3349i	−0.692131	−	0.771871i
$765$	−1.71456	+	1.45299i	−0.0619901	+	0.0525330i
$766$	23.3008	+	10.4029i	0.841893	+	0.375871i
$767$	−11.2040	−	19.4059i	−0.404552	−	0.700705i
$768$	3.53612	−	27.4863i	0.127599	−	0.991826i
$769$	−18.3939	+	31.8592i	−0.663302	+	1.14887i	0.316441	+	0.948612i	$0.397512\pi$
$769$	−18.3939	+	31.8592i	−0.663302	+	1.14887i	−0.979743	+	0.200260i	$0.935821\pi$
$770$	6.47349	−	4.69312i	0.233288	−	0.169128i
$771$	−1.83435	−	20.3940i	−0.0660626	−	0.734474i
$772$	15.3900	−	47.0366i	0.553897	−	1.69288i
$773$			4.81937i			0.173341i	0.996237	+	0.0866704i	$0.0276227\pi$
$773$			4.81937i			0.173341i	−0.996237	+	0.0866704i	$0.972377\pi$
$774$	48.8638	−	14.2152i	1.75637	−	0.510956i
$775$	−70.4518			−2.53070
$776$	−27.2589	+	30.0873i	−0.978539	+	1.08007i
$777$	−3.22402	+	6.95817i	−0.115661	+	0.249623i
$778$	−14.3808	−	19.8362i	−0.515575	−	0.711163i
$779$	31.9798	+	18.4635i	1.14579	+	0.661524i
$780$	−30.2855	−	6.97969i	−1.08439	−	0.249913i
$781$	−2.44860	+	1.41370i	−0.0876177	+	0.0505861i
$782$	0.800110	+	0.357217i	0.0286119	+	0.0127740i
$783$	−23.9333	−	23.5858i	−0.855307	−	0.842888i
$784$	−0.434444	+	3.97634i	−0.0155159	+	0.142012i
$785$	33.7455	+	58.4490i	1.20443	+	2.08613i
$786$	−1.72528	−	8.80941i	−0.0615387	−	0.314221i
$787$	−23.4255	−	13.5247i	−0.835028	−	0.482104i	0.0205430	−	0.999789i	$-0.493461\pi$
$787$	−23.4255	−	13.5247i	−0.835028	−	0.482104i	−0.855571	+	0.517685i	$0.826794\pi$
$788$	−2.36251	−	11.2281i	−0.0841611	−	0.399983i
$789$	11.9597	+	5.54143i	0.425775	+	0.197280i
$790$	70.7444	−	7.36212i	2.51697	−	0.261932i
$791$	2.28803			0.0813530
$792$	−10.7988	+	5.76672i	−0.383719	+	0.204912i
$793$	−31.9534			−1.13470
$794$	−23.8245	+	2.47933i	−0.845498	+	0.0879881i
$795$	−2.61464	−	29.0692i	−0.0927319	−	1.03098i
$796$	−45.1890	+	9.50829i	−1.60168	+	0.337013i
$797$	5.65465	+	3.26471i	0.200298	+	0.115642i	0.596794	−	0.802394i	$-0.296441\pi$
$797$	5.65465	+	3.26471i	0.200298	+	0.115642i	−0.396496	+	0.918036i	$0.629774\pi$
$798$	9.48611	+	3.25136i	0.335805	+	0.115097i
$799$	0.129388	+	0.224106i	0.00457741	+	0.00792831i
$800$	29.5539	−	50.5875i	1.04489	−	1.78854i
$801$	−4.49736	+	12.5464i	−0.158907	+	0.443305i
$802$	−17.9760	−	8.02555i	−0.634754	−	0.283392i
$803$	4.15213	−	2.39723i	0.146525	−	0.0845965i
$804$	−25.9105	+	7.93255i	−0.913794	+	0.279759i
$805$	−10.9996	−	6.35061i	−0.387684	−	0.223829i
$806$	12.9273	+	17.8314i	0.455345	+	0.628084i
$807$	−7.24205	−	10.2893i	−0.254932	−	0.362199i
$808$	34.7007	+	31.4387i	1.22077	+	1.10601i
$809$	−45.8787			−1.61301			−0.806504	−	0.591229i	$-0.798643\pi$
$809$	−45.8787			−1.61301			−0.806504	+	0.591229i	$0.798643\pi$
$810$	−44.6377	+	22.2554i	−1.56841	+	0.781975i
$811$			38.7088i			1.35925i	0.733560	+	0.679624i	$0.237857\pi$
$811$			38.7088i			1.35925i	−0.733560	+	0.679624i	$0.762143\pi$
$812$	12.2922	+	4.02189i	0.431371	+	0.141141i
$813$	−2.36393	+	1.66385i	−0.0829067	+	0.0583536i
$814$	7.31397	−	5.30244i	0.256354	−	0.185851i
$815$	20.2262	−	35.0328i	0.708493	−	1.22715i
$816$	−0.684029	+	1.13412i	−0.0239458	+	0.0397023i
$817$	24.5524	+	42.5260i	0.858980	+	1.48780i
$818$	4.90079	+	2.18800i	0.171352	+	0.0765017i
$819$	−6.46548	−	2.31761i	−0.225922	−	0.0809838i
$820$	52.6344	−	47.1969i	1.83807	−	1.64819i
$821$	−2.32727	+	1.34365i	−0.0812224	+	0.0468938i	−0.540061	−	0.841626i	$-0.681599\pi$
$821$	−2.32727	+	1.34365i	−0.0812224	+	0.0468938i	0.458839	+	0.888520i	$0.348266\pi$
$822$	−8.56471	+	24.9882i	−0.298729	+	0.871564i
$823$	13.4743	−	23.3382i	0.469685	−	0.813518i	−0.529714	−	0.848176i	$-0.677701\pi$
$823$	13.4743	−	23.3382i	0.469685	−	0.813518i	0.999399	+	0.0346578i	$0.0110341\pi$
$824$	39.1249	+	8.44227i	1.36298	+	0.294100i
$825$	−25.7770	+	2.31853i	−0.897441	+	0.0807207i
$826$	13.7673	−	1.43272i	0.479026	−	0.0498506i
$827$			36.3338i			1.26345i	0.775192	+	0.631725i	$0.217653\pi$
$827$			36.3338i			1.26345i	−0.775192	+	0.631725i	$0.782347\pi$
$828$	15.3579	+	11.9292i	0.533723	+	0.414570i
$829$			23.1359i			0.803541i	0.915740	+	0.401771i	$0.131605\pi$
$829$			23.1359i			0.803541i	−0.915740	+	0.401771i	$0.868395\pi$
$830$	3.25566	+	31.2844i	0.113006	+	1.08590i
$831$	−0.608422	+	1.31311i	−0.0211059	+	0.0455514i
$832$	−18.2266	+	1.80227i	−0.631894	+	0.0624824i
$833$	0.0955830	−	0.165555i	0.00331175	−	0.00573613i
$834$	−3.72772	−	19.0340i	−0.129080	−	0.659094i
$835$	−71.0797	+	41.0379i	−2.45982	+	1.42018i
$836$	−7.88625	−	8.79481i	−0.272751	−	0.304175i
$837$	34.2077	+	8.89834i	1.18239	+	0.307571i
$838$	−5.21246	+	11.6751i	−0.180061	+	0.403310i
$839$	−3.70019	−	6.40891i	−0.127745	−	0.221260i	0.795058	−	0.606534i	$-0.207440\pi$
$839$	−3.70019	−	6.40891i	−0.127745	−	0.221260i	−0.922802	+	0.385273i	$0.874107\pi$
$840$	11.5635	−	15.3249i	0.398980	−	0.528758i
$841$	6.40917	−	11.1010i	0.221006	−	0.382793i
$842$	−12.2534	−	16.9018i	−0.422280	−	0.582475i
$843$	−36.4130	−	16.8717i	−1.25413	−	0.581093i
$844$	41.7157	+	13.6490i	1.43591	+	0.469818i
$845$		−	30.4039i		−	1.04592i
$846$	1.60426	+	5.51452i	0.0551555	+	0.189593i
$847$	8.91848			0.306443
$848$	−6.93131	−	15.7416i	−0.238022	−	0.540570i
$849$	3.79386	−	0.341240i	0.130205	−	0.0117113i
$850$	−2.26693	+	1.64347i	−0.0777552	+	0.0563706i
$851$	−12.4277	−	7.17513i	−0.426015	−	0.245960i
$852$	−4.62798	+	4.96673i	−0.158552	+	0.170157i
$853$	40.1176	−	23.1619i	1.37360	−	0.793048i	0.382221	−	0.924071i	$-0.375159\pi$
$853$	40.1176	−	23.1619i	1.37360	−	0.793048i	0.991379	+	0.131023i	$0.0418261\pi$
$854$	8.04667	−	18.0233i	0.275351	−	0.616744i
$855$	−31.1160	−	36.7176i	−1.06415	−	1.25571i
$856$	25.0041	−	8.03927i	0.854621	−	0.274776i
$857$	19.6244	+	33.9905i	0.670357	+	1.16109i	0.977803	+	0.209526i	$0.0671922\pi$
$857$	19.6244	+	33.9905i	0.670357	+	1.16109i	−0.307446	+	0.951565i	$0.599474\pi$
$858$	5.31669	+	6.09875i	0.181509	+	0.208208i
$859$	38.3982	+	22.1692i	1.31013	+	0.756404i	0.982117	−	0.188270i	$-0.0602879\pi$
$859$	38.3982	+	22.1692i	1.31013	+	0.756404i	0.328012	+	0.944673i	$0.393621\pi$
$860$	91.9957	−	19.3570i	3.13703	−	0.660068i
$861$	12.7760	−	8.99234i	0.435405	−	0.306458i
$862$	0.165329	+	1.58869i	0.00563114	+	0.0541109i
$863$	15.4430			0.525685			0.262843	−	0.964839i	$-0.415340\pi$
$863$	15.4430			0.525685			0.262843	+	0.964839i	$0.415340\pi$
$864$	−20.7392	+	20.8299i	−0.705563	+	0.708647i
$865$	−13.7328			−0.466929
$866$	0.287455	+	2.76223i	0.00976812	+	0.0938642i
$867$	−24.0268	+	16.9112i	−0.815994	+	0.574334i
$868$	−13.3132	+	2.80126i	−0.451880	+	0.0950809i
$869$	−16.0356	−	9.25813i	−0.543969	−	0.314061i
$870$	−40.7904	−	46.7905i	−1.38293	−	1.58635i
$871$	8.95447	+	15.5096i	0.303411	+	0.525522i
$872$	−11.9008	+	3.82633i	−0.403013	+	0.129576i
$873$	42.3708	−	7.68429i	1.43403	−	0.260074i
$874$	−7.64985	+	17.1345i	−0.258760	+	0.579582i
$875$	18.1803	−	10.4964i	0.614606	−	0.354843i
$876$	7.84775	−	8.42217i	0.265151	−	0.284559i
$877$	−31.5552	−	18.2184i	−1.06554	−	0.615192i	−0.138583	−	0.990351i	$-0.544255\pi$
$877$	−31.5552	−	18.2184i	−1.06554	−	0.615192i	−0.926961	+	0.375159i	$0.877588\pi$
$878$	15.5334	−	11.2613i	0.524227	−	0.380052i
$879$	27.8188	−	2.50218i	0.938305	−	0.0843963i
$880$	−20.6977	+	9.11356i	−0.697719	+	0.307218i
$881$	33.1305			1.11619			0.558097	−	0.829776i	$-0.311532\pi$
$881$	33.1305			1.11619			0.558097	+	0.829776i	$0.311532\pi$
$882$	2.93542	−	3.06322i	0.0988407	−	0.103144i
$883$		−	9.93261i		−	0.334259i	−0.985935	−	0.167129i	$-0.946550\pi$
$883$		−	9.93261i		−	0.334259i	0.985935	−	0.167129i	$-0.0534498\pi$
$884$	0.831927	+	0.272199i	0.0279807	+	0.00915504i
$885$	−60.2773	−	27.9291i	−2.02620	−	0.938827i
$886$	21.4736	+	29.6198i	0.721420	+	0.995096i
$887$	−20.5053	+	35.5163i	−0.688502	+	1.19252i	0.283821	+	0.958877i	$0.408398\pi$
$887$	−20.5053	+	35.5163i	−0.688502	+	1.19252i	−0.972323	+	0.233642i	$0.924935\pi$
$888$	13.0649	−	17.3145i	0.438428	−	0.581038i
$889$	4.40863	+	7.63597i	0.147861	+	0.256102i
$890$	−10.0375	+	22.4826i	−0.336459	+	0.753617i
$891$	12.8088	+	2.12998i	0.429112	+	0.0713571i
$892$	13.0867	+	14.5944i	0.438174	+	0.488655i
$893$	−4.79927	+	2.77086i	−0.160601	+	0.0927233i
$894$	7.17691	+	36.6458i	0.240032	+	1.22562i
$895$	29.4243	−	50.9643i	0.983545	−	1.70355i
$896$	3.57335	−	10.7346i	0.119377	−	0.358617i
$897$	5.40323	−	11.6614i	0.180408	−	0.389362i
$898$	−0.399094	−	3.83499i	−0.0133179	−	0.127975i
$899$			43.9889i			1.46711i
$900$	−57.5509	+	23.4412i	−1.91836	+	0.781374i
$901$			0.822016i			0.0273853i
$902$	−18.3054	+	1.90498i	−0.609502	+	0.0634288i
$903$	20.6920	−	1.86116i	0.688588	−	0.0619354i
$904$	−6.32593	−	1.36499i	−0.210397	−	0.0453990i
$905$	−14.9149	+	25.8334i	−0.495789	+	0.858732i
$906$	1.26388	−	3.68746i	0.0419895	−	0.122508i
$907$	0.160634	−	0.0927423i	0.00533378	−	0.00307946i	−0.497331	−	0.867561i	$-0.665686\pi$
$907$	0.160634	−	0.0927423i	0.00533378	−	0.00307946i	0.502665	+	0.864482i	$0.332353\pi$
$908$	−23.0315	+	20.6522i	−0.764328	+	0.685368i
$909$	−8.86256	−	48.8677i	−0.293952	−	1.62084i
$910$	−11.5858	−	5.17261i	−0.384067	−	0.171470i
$911$	14.9984	+	25.9781i	0.496921	+	0.860692i	0.999994	−	0.00355194i	$-0.00113062\pi$
$911$	14.9984	+	25.9781i	0.496921	+	0.860692i	−0.503073	+	0.864244i	$0.667797\pi$
$912$	−24.2874	−	14.6486i	−0.804238	−	0.485063i
$913$	4.09411	−	7.09121i	0.135495	−	0.234685i
$914$	−34.2629	+	24.8398i	−1.13332	+	0.821626i
$915$	−77.4680	+	54.5256i	−2.56101	+	1.80256i
$916$	50.0086	+	16.3624i	1.65233	+	0.540628i
$917$		−	3.66475i		−	0.121021i
$918$	1.30828	−	0.511662i	0.0431797	−	0.0168874i
$919$	18.8837			0.622917			0.311459	−	0.950260i	$-0.399182\pi$
$919$	18.8837			0.622917			0.311459	+	0.950260i	$0.399182\pi$
$920$	26.6229	+	24.1203i	0.877732	+	0.795221i
$921$	5.23152	+	7.43276i	0.172384	+	0.244918i
$922$	−20.9520	−	28.9003i	−0.690017	−	0.951780i
$923$	3.88559	+	2.24334i	0.127896	+	0.0738406i
$924$	−4.77888	+	1.46306i	−0.157213	+	0.0481311i
$925$	39.7127	−	22.9281i	1.30575	−	0.753872i
$926$	37.8412	+	16.8945i	1.24354	+	0.555189i
$927$	−27.4467	−	32.3877i	−0.901467	−	1.06375i
$928$	−31.5860	−	18.4530i	−1.03686	−	0.605749i
$929$	−15.6043	−	27.0275i	−0.511962	−	0.886743i	−0.999904	−	0.0138675i	$-0.995586\pi$
$929$	−15.6043	−	27.0275i	−0.511962	−	0.886743i	0.487942	−	0.872876i	$-0.337748\pi$
$930$	61.7688	+	21.1712i	2.02548	+	0.694232i
$931$	3.54538	+	2.04692i	0.116195	+	0.0670852i
$932$	−34.2640	+	7.20956i	−1.12236	+	0.236157i
$933$	4.33629	+	48.2102i	0.141964	+	1.57833i
$934$	11.0038	−	1.14512i	0.360054	−	0.0374696i
$935$	1.08082			0.0353466
$936$	16.4931	+	10.2649i	0.539094	+	0.335518i
$937$	−17.0049			−0.555525			−0.277762	−	0.960650i	$-0.589593\pi$
$937$	−17.0049			−0.555525			−0.277762	+	0.960650i	$0.589593\pi$
$938$	−11.0031	+	1.14506i	−0.359265	+	0.0373875i
$939$	−16.3284	−	7.56565i	−0.532857	−	0.246896i
$940$	2.18453	+	10.3822i	0.0712515	+	0.338629i
$941$	−1.27289	−	0.734903i	−0.0414950	−	0.0239572i	0.479109	−	0.877755i	$-0.340960\pi$
$941$	−1.27289	−	0.734903i	−0.0414950	−	0.0239572i	−0.520604	+	0.853798i	$0.674293\pi$
$942$	−8.10792	−	41.3996i	−0.264170	−	1.34887i
$943$	14.6176	+	25.3184i	0.476014	+	0.824480i
$944$	−38.9185	−	4.25214i	−1.26669	−	0.138395i
$945$	−19.6297	+	5.41394i	−0.638556	+	0.176115i
$946$	−22.3475	−	9.97724i	−0.726579	−	0.324388i
$947$	22.6117	−	13.0549i	0.734780	−	0.424226i	−0.0853880	−	0.996348i	$-0.527213\pi$
$947$	22.6117	−	13.0549i	0.734780	−	0.424226i	0.820168	+	0.572122i	$0.193880\pi$
$948$	−43.3228	−	9.98431i	−1.40706	−	0.324275i
$949$	−6.58886	−	3.80408i	−0.213883	−	0.123486i
$950$	−35.1952	−	48.5467i	−1.14188	−	1.57506i
$951$	24.2748	−	52.3906i	0.787165	−	1.69888i
$952$	−0.363034	+	0.400702i	−0.0117660	+	0.0129868i
$953$	1.46141			0.0473396			0.0236698	−	0.999720i	$-0.492465\pi$
$953$	1.46141			0.0473396			0.0236698	+	0.999720i	$0.492465\pi$
$954$	−4.34532	+	17.7184i	−0.140685	+	0.573653i
$955$			56.1486i			1.81693i
$956$	−7.01937	+	21.4534i	−0.227023	+	0.693854i
$957$	1.44765	+	16.0948i	0.0467959	+	0.520269i
$958$	−21.4395	+	15.5431i	−0.692679	+	0.502175i
$959$	−5.39199	+	9.33920i	−0.174116	+	0.301578i
$960$	−41.1133	+	35.4715i	−1.32693	+	1.14484i
$961$	−7.63610	−	13.2261i	−0.246326	−	0.426649i
$962$	−13.0901	−	5.84419i	−0.422041	−	0.188424i
$963$	−26.2240	−	9.40022i	−0.845056	−	0.302918i
$964$	34.2232	+	38.1660i	1.10225	+	1.22924i
$965$	−83.9796	+	48.4856i	−2.70340	+	1.56081i
$966$	5.21693	+	5.98432i	0.167852	+	0.192542i
$967$	−8.31206	+	14.3969i	−0.267298	+	0.462973i	−0.968163	−	0.250320i	$-0.919464\pi$
$967$	−8.31206	+	14.3969i	−0.267298	+	0.462973i	0.700865	+	0.713294i	$0.252797\pi$
$968$	−24.6578	−	5.32059i	−0.792531	−	0.171010i
$969$	0.780193	+	1.10847i	0.0250634	+	0.0356092i
$970$	79.1226	−	8.23401i	2.54047	−	0.264378i
$971$		−	18.2019i		−	0.584127i	−0.956399	−	0.292064i	$-0.905658\pi$
$971$		−	18.2019i		−	0.584127i	0.956399	−	0.292064i	$-0.0943419\pi$
$972$	30.9044	−	4.11294i	0.991260	−	0.131923i
$973$		−	7.91822i		−	0.253846i
$974$	1.42144	+	13.6589i	0.0455458	+	0.437661i
$975$	23.6386	+	33.5848i	0.757039	+	1.07557i
$976$	−32.9997	+	45.0302i	−1.05630	+	1.44138i
$977$	−5.60317	+	9.70498i	−0.179261	+	0.310490i	−0.941628	−	0.336656i	$-0.890704\pi$
$977$	−5.60317	+	9.70498i	−0.179261	+	0.310490i	0.762366	+	0.647146i	$0.224037\pi$
$978$	−19.0596	+	16.6155i	−0.609459	+	0.531306i
$979$	5.55095	−	3.20484i	0.177409	−	0.102427i
$980$	5.83522	−	5.23240i	0.186399	−	0.167143i
$981$	12.4815	+	4.47409i	0.398502	+	0.142847i
$982$	0.916505	−	2.05283i	0.0292468	−	0.0655084i
$983$	12.3959	+	21.4703i	0.395367	+	0.684796i	0.993148	−	0.116864i	$-0.0372841\pi$
$983$	12.3959	+	21.4703i	0.395367	+	0.684796i	−0.597781	+	0.801659i	$0.703951\pi$
$984$	−40.6877	+	17.2401i	−1.29708	+	0.549593i
$985$	−11.2410	+	19.4699i	−0.358167	+	0.620364i
$986$	1.02616	+	1.41544i	0.0326795	+	0.0450767i
$987$	0.210040	+	2.33520i	0.00668566	+	0.0743301i
$988$	−5.82918	+	17.8158i	−0.185451	+	0.566797i
$989$			38.8763i			1.23619i
$990$	23.2968	+	5.71340i	0.740421	+	0.181584i
$991$	6.64478			0.211078			0.105539	−	0.994415i	$-0.466343\pi$
$991$	6.64478			0.211078			0.105539	+	0.994415i	$0.466343\pi$
$992$	38.4795	+	0.197500i	1.22173	+	0.00627062i
$993$	21.3539	−	46.0865i	0.677645	−	1.46251i
$994$	−2.24385	+	1.62673i	−0.0711705	+	0.0515969i
$995$	78.3597	+	45.2410i	2.48417	+	1.43424i
$996$	4.41524	−	19.1581i	0.139902	−	0.607048i
$997$	0.722586	−	0.417185i	0.0228845	−	0.0132124i	−0.488514	−	0.872556i	$-0.662461\pi$
$997$	0.722586	−	0.417185i	0.0228845	−	0.0132124i	0.511399	+	0.859344i	$0.329128\pi$
$998$	1.90662	−	4.27054i	0.0603531	−	0.135182i
$999$	−22.1783	+	6.11685i	−0.701692	+	0.193528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.17	yes	72
8.5	even	2	inner	504.2.cs.b.85.7	✓	72
9.7	even	3	inner	504.2.cs.b.421.7	yes	72
72.61	even	6	inner	504.2.cs.b.421.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.7	✓	72	8.5	even	2	inner
504.2.cs.b.85.17	yes	72	1.1	even	1	trivial
504.2.cs.b.421.7	yes	72	9.7	even	3	inner
504.2.cs.b.421.17	yes	72	72.61	even	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.146382 - 1.40662i) q^{2} +(1.41639 - 0.996919i) q^{3} +(-1.95714 + 0.411806i) q^{4} +(3.39378 + 1.95940i) q^{5} +(-1.60962 - 1.84638i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.865744 + 2.69267i) q^{8} +(1.01230 - 2.82405i) q^{9} +O(q^{10})\)	\(q+(-0.146382 - 1.40662i) q^{2} +(1.41639 - 0.996919i) q^{3} +(-1.95714 + 0.411806i) q^{4} +(3.39378 + 1.95940i) q^{5} +(-1.60962 - 1.84638i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.865744 + 2.69267i) q^{8} +(1.01230 - 2.82405i) q^{9} +(2.25934 - 5.06056i) q^{10} +(-1.24945 + 0.721373i) q^{11} +(-2.36154 + 2.53439i) q^{12} +(1.98271 + 1.14472i) q^{13} +(-1.14498 + 0.830079i) q^{14} +(6.76026 - 0.608055i) q^{15} +(3.66083 - 1.61193i) q^{16} -0.191166 q^{17} +(-4.12054 - 1.01054i) q^{18} -4.09385i q^{19} +(-7.44900 - 2.43725i) q^{20} +(-1.57155 - 0.728168i) q^{21} +(1.19759 + 1.65191i) q^{22} +(1.62055 - 2.80688i) q^{23} +(3.91061 + 2.95079i) q^{24} +(5.17848 + 8.96938i) q^{25} +(1.31995 - 2.95648i) q^{26} +(-1.38153 - 5.00913i) q^{27} +(1.33521 + 1.48903i) q^{28} +(5.60034 - 3.23336i) q^{29} +(-1.84488 - 9.42009i) q^{30} +(-3.40118 + 5.89102i) q^{31} +(-2.80325 - 4.91343i) q^{32} +(-1.05056 + 2.26735i) q^{33} +(0.0279832 + 0.268897i) q^{34} -3.91879i q^{35} +(-0.818266 + 5.94394i) q^{36} -4.42758i q^{37} +(-5.75848 + 0.599265i) q^{38} +(3.94948 - 0.355238i) q^{39} +(-2.33788 + 10.8347i) q^{40} +(-4.51006 + 7.81166i) q^{41} +(-0.794207 + 2.31716i) q^{42} +(-10.3878 + 5.99739i) q^{43} +(2.14830 - 1.92636i) q^{44} +(8.96896 - 7.60067i) q^{45} +(-4.18542 - 1.86862i) q^{46} +(-0.676835 - 1.17231i) q^{47} +(3.57819 - 5.93267i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(11.8585 - 8.59709i) q^{50} +(-0.270765 + 0.190577i) q^{51} +(-4.35186 - 1.42389i) q^{52} -4.30001i q^{53} +(-6.84370 + 2.67653i) q^{54} -5.65383 q^{55} +(1.89905 - 2.09609i) q^{56} +(-4.08124 - 5.79847i) q^{57} +(-5.36788 - 7.40422i) q^{58} +(-8.47625 - 4.89377i) q^{59} +(-12.9804 + 3.97397i) q^{60} +(-12.0870 + 6.97843i) q^{61} +(8.78429 + 3.92183i) q^{62} +(-2.95185 + 0.535342i) q^{63} +(-6.50097 + 4.66233i) q^{64} +(4.48592 + 7.76984i) q^{65} +(3.34308 + 1.14584i) q^{66} +(6.77441 + 3.91121i) q^{67} +(0.374140 - 0.0787233i) q^{68} +(-0.502902 - 5.59118i) q^{69} +(-5.51224 + 0.573640i) q^{70} +1.95973 q^{71} +(8.48063 + 0.280903i) q^{72} -3.32315 q^{73} +(-6.22792 + 0.648117i) q^{74} +(16.2765 + 7.54160i) q^{75} +(1.68587 + 8.01225i) q^{76} +(1.24945 + 0.721373i) q^{77} +(-1.07782 - 5.50341i) q^{78} +(6.41702 + 11.1146i) q^{79} +(15.5824 + 1.70250i) q^{80} +(-6.95048 - 5.71759i) q^{81} +(11.6482 + 5.20045i) q^{82} +(-4.91508 + 2.83772i) q^{83} +(3.37562 + 0.777955i) q^{84} +(-0.648774 - 0.374570i) q^{85} +(9.95661 + 13.7337i) q^{86} +(4.70885 - 10.1628i) q^{87} +(-3.02413 - 2.73985i) q^{88} -4.44270 q^{89} +(-12.0041 - 11.5033i) q^{90} -2.28944i q^{91} +(-2.01576 + 6.16082i) q^{92} +(1.05548 + 11.7347i) q^{93} +(-1.54992 + 1.12365i) q^{94} +(8.02148 - 13.8936i) q^{95} +(-8.86878 - 4.16471i) q^{96} +(7.17699 + 12.4309i) q^{97} +(1.29136 + 0.576538i) q^{98} +(0.772363 + 4.25877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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