LMFDB - Embedded newform 882.2.l.c.227.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.4
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.495324 - 1.65972i) q^{3} -1.00000 q^{4} +(-0.995200 + 1.72374i) q^{5} +(-1.65972 + 0.495324i) q^{6} +1.00000i q^{8} +(-2.50931 + 1.64419i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.495324 - 1.65972i) q^{3} -1.00000 q^{4} +(-0.995200 + 1.72374i) q^{5} +(-1.65972 + 0.495324i) q^{6} +1.00000i q^{8} +(-2.50931 + 1.64419i) q^{9} +(1.72374 + 0.995200i) q^{10} +(-5.21285 + 3.00964i) q^{11} +(0.495324 + 1.65972i) q^{12} +(3.43197 - 1.98145i) q^{13} +(3.35386 + 0.797941i) q^{15} +1.00000 q^{16} +(0.781195 - 1.35307i) q^{17} +(1.64419 + 2.50931i) q^{18} +(4.16168 - 2.40274i) q^{19} +(0.995200 - 1.72374i) q^{20} +(3.00964 + 5.21285i) q^{22} +(5.02324 + 2.90017i) q^{23} +(1.65972 - 0.495324i) q^{24} +(0.519152 + 0.899198i) q^{25} +(-1.98145 - 3.43197i) q^{26} +(3.97181 + 3.35033i) q^{27} +(5.26041 + 3.03710i) q^{29} +(0.797941 - 3.35386i) q^{30} +1.28745i q^{31} -1.00000i q^{32} +(7.57720 + 7.16110i) q^{33} +(-1.35307 - 0.781195i) q^{34} +(2.50931 - 1.64419i) q^{36} +(-3.02623 - 5.24158i) q^{37} +(-2.40274 - 4.16168i) q^{38} +(-4.98858 - 4.71463i) q^{39} +(-1.72374 - 0.995200i) q^{40} +(2.98046 + 5.16231i) q^{41} +(-4.53614 + 7.85683i) q^{43} +(5.21285 - 3.00964i) q^{44} +(-0.336893 - 5.96169i) q^{45} +(2.90017 - 5.02324i) q^{46} +4.78762 q^{47} +(-0.495324 - 1.65972i) q^{48} +(0.899198 - 0.519152i) q^{50} +(-2.63265 - 0.626354i) q^{51} +(-3.43197 + 1.98145i) q^{52} +(7.27392 + 4.19960i) q^{53} +(3.35033 - 3.97181i) q^{54} -11.9808i q^{55} +(-6.04925 - 5.71706i) q^{57} +(3.03710 - 5.26041i) q^{58} -12.7797 q^{59} +(-3.35386 - 0.797941i) q^{60} +1.86610i q^{61} +1.28745 q^{62} -1.00000 q^{64} +7.88775i q^{65} +(7.16110 - 7.57720i) q^{66} +7.59491 q^{67} +(-0.781195 + 1.35307i) q^{68} +(2.32533 - 9.77368i) q^{69} +5.48343i q^{71} +(-1.64419 - 2.50931i) q^{72} +(9.37486 + 5.41258i) q^{73} +(-5.24158 + 3.02623i) q^{74} +(1.23526 - 1.30704i) q^{75} +(-4.16168 + 2.40274i) q^{76} +(-4.71463 + 4.98858i) q^{78} -13.8942 q^{79} +(-0.995200 + 1.72374i) q^{80} +(3.59326 - 8.25158i) q^{81} +(5.16231 - 2.98046i) q^{82} +(3.35946 - 5.81876i) q^{83} +(1.55489 + 2.69315i) q^{85} +(7.85683 + 4.53614i) q^{86} +(2.43511 - 10.2351i) q^{87} +(-3.00964 - 5.21285i) q^{88} +(2.05680 + 3.56248i) q^{89} +(-5.96169 + 0.336893i) q^{90} +(-5.02324 - 2.90017i) q^{92} +(2.13680 - 0.637705i) q^{93} -4.78762i q^{94} +9.56485i q^{95} +(-1.65972 + 0.495324i) q^{96} +(14.1120 + 8.14755i) q^{97} +(8.13222 - 16.1231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.495324	−	1.65972i	−0.285975	−	0.958237i
$3$	−0.495324	−	1.65972i	−0.285975	−	0.958237i
$4$	−1.00000			−0.500000
$5$	−0.995200	+	1.72374i	−0.445067	+	0.770879i	−0.998057	−	0.0623091i	$-0.980154\pi$
$5$	−0.995200	+	1.72374i	−0.445067	+	0.770879i	0.552990	+	0.833188i	$0.313487\pi$
$6$	−1.65972	+	0.495324i	−0.677576	+	0.202215i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.50931	+	1.64419i	−0.836436	+	0.548064i
$10$	1.72374	+	0.995200i	0.545094	+	0.314710i
$11$	−5.21285	+	3.00964i	−1.57173	+	0.907441i	−0.575778	+	0.817606i	$0.695301\pi$
$11$	−5.21285	+	3.00964i	−1.57173	+	0.907441i	−0.995957	+	0.0898353i	$0.971366\pi$
$12$	0.495324	+	1.65972i	0.142988	+	0.479118i
$13$	3.43197	−	1.98145i	0.951857	−	0.549555i	0.0581999	−	0.998305i	$-0.481464\pi$
$13$	3.43197	−	1.98145i	0.951857	−	0.549555i	0.893657	+	0.448750i	$0.148131\pi$
$14$		0			0
$15$	3.35386	+	0.797941i	0.865963	+	0.206027i
$16$	1.00000			0.250000
$17$	0.781195	−	1.35307i	0.189468	−	0.328168i	−0.755605	−	0.655027i	$-0.772657\pi$
$17$	0.781195	−	1.35307i	0.189468	−	0.328168i	0.945073	+	0.326860i	$0.105990\pi$
$18$	1.64419	+	2.50931i	0.387540	+	0.591450i
$19$	4.16168	−	2.40274i	0.954754	−	0.551227i	0.0601995	−	0.998186i	$-0.480826\pi$
$19$	4.16168	−	2.40274i	0.954754	−	0.551227i	0.894554	+	0.446959i	$0.147493\pi$
$20$	0.995200	−	1.72374i	0.222534	−	0.385439i
$21$		0			0
$22$	3.00964	+	5.21285i	0.641658	+	1.11138i
$23$	5.02324	+	2.90017i	1.04742	+	0.604728i	0.921926	−	0.387367i	$-0.126615\pi$
$23$	5.02324	+	2.90017i	1.04742	+	0.604728i	0.125493	+	0.992094i	$0.459949\pi$
$24$	1.65972	−	0.495324i	0.338788	−	0.101108i
$25$	0.519152	+	0.899198i	0.103830	+	0.179840i
$26$	−1.98145	−	3.43197i	−0.388594	−	0.673065i
$27$	3.97181	+	3.35033i	0.764376	+	0.644771i
$28$		0			0
$29$	5.26041	+	3.03710i	0.976833	+	0.563975i	0.901313	−	0.433169i	$-0.142605\pi$
$29$	5.26041	+	3.03710i	0.976833	+	0.563975i	0.0755206	+	0.997144i	$0.475938\pi$
$30$	0.797941	−	3.35386i	0.145683	−	0.612328i
$31$			1.28745i			0.231233i	0.993294	+	0.115616i	$0.0368844\pi$
$31$			1.28745i			0.231233i	−0.993294	+	0.115616i	$0.963116\pi$
$32$		−	1.00000i		−	0.176777i
$33$	7.57720	+	7.16110i	1.31902	+	1.24659i
$34$	−1.35307	−	0.781195i	−0.232050	−	0.133974i
$35$		0			0
$36$	2.50931	−	1.64419i	0.418218	−	0.274032i
$37$	−3.02623	−	5.24158i	−0.497508	−	0.861710i	0.502487	−	0.864584i	$-0.332418\pi$
$37$	−3.02623	−	5.24158i	−0.497508	−	0.861710i	−0.999996	+	0.00287465i	$0.999085\pi$
$38$	−2.40274	−	4.16168i	−0.389777	−	0.675113i
$39$	−4.98858	−	4.71463i	−0.798812	−	0.754946i
$40$	−1.72374	−	0.995200i	−0.272547	−	0.157355i
$41$	2.98046	+	5.16231i	0.465470	+	0.806218i	0.999223	−	0.0394230i	$-0.0125520\pi$
$41$	2.98046	+	5.16231i	0.465470	+	0.806218i	−0.533753	+	0.845641i	$0.679219\pi$
$42$		0			0
$43$	−4.53614	+	7.85683i	−0.691756	+	1.19816i	0.279507	+	0.960144i	$0.409829\pi$
$43$	−4.53614	+	7.85683i	−0.691756	+	1.19816i	−0.971262	+	0.238012i	$0.923504\pi$
$44$	5.21285	−	3.00964i	0.785867	−	0.453721i
$45$	−0.336893	−	5.96169i	−0.0502210	−	0.888716i
$46$	2.90017	−	5.02324i	0.427607	−	0.740637i
$47$	4.78762			0.698347			0.349173	−	0.937058i	$-0.386462\pi$
$47$	4.78762			0.698347			0.349173	+	0.937058i	$0.386462\pi$
$48$	−0.495324	−	1.65972i	−0.0714938	−	0.239559i
$49$		0			0
$50$	0.899198	−	0.519152i	0.127166	−	0.0734192i
$51$	−2.63265	−	0.626354i	−0.368645	−	0.0877070i
$52$	−3.43197	+	1.98145i	−0.475929	+	0.274778i
$53$	7.27392	+	4.19960i	0.999150	+	0.576860i	0.907997	−	0.418977i	$-0.137611\pi$
$53$	7.27392	+	4.19960i	0.999150	+	0.576860i	0.0911535	+	0.995837i	$0.470945\pi$
$54$	3.35033	−	3.97181i	0.455922	−	0.540495i
$55$		−	11.9808i		−	1.61549i
$56$		0			0
$57$	−6.04925	−	5.71706i	−0.801243	−	0.757243i
$58$	3.03710	−	5.26041i	0.398790	−	0.690725i
$59$	−12.7797			−1.66378			−0.831888	−	0.554943i	$-0.812740\pi$
$59$	−12.7797			−1.66378			−0.831888	+	0.554943i	$0.812740\pi$
$60$	−3.35386	−	0.797941i	−0.432981	−	0.103014i
$61$			1.86610i			0.238930i	0.992838	+	0.119465i	$0.0381179\pi$
$61$			1.86610i			0.238930i	−0.992838	+	0.119465i	$0.961882\pi$
$62$	1.28745			0.163506
$63$		0			0
$64$	−1.00000			−0.125000
$65$			7.88775i			0.978356i
$66$	7.16110	−	7.57720i	0.881471	−	0.932689i
$67$	7.59491			0.927866			0.463933	−	0.885870i	$-0.346438\pi$
$67$	7.59491			0.927866			0.463933	+	0.885870i	$0.346438\pi$
$68$	−0.781195	+	1.35307i	−0.0947338	+	0.164084i
$69$	2.32533	−	9.77368i	0.279936	−	1.17661i
$70$		0			0
$71$			5.48343i			0.650764i	0.945583	+	0.325382i	$0.105493\pi$
$71$			5.48343i			0.650764i	−0.945583	+	0.325382i	$0.894507\pi$
$72$	−1.64419	−	2.50931i	−0.193770	−	0.295725i
$73$	9.37486	+	5.41258i	1.09724	+	0.633494i	0.935496	−	0.353338i	$-0.114953\pi$
$73$	9.37486	+	5.41258i	1.09724	+	0.633494i	0.161748	+	0.986832i	$0.448287\pi$
$74$	−5.24158	+	3.02623i	−0.609321	+	0.351792i
$75$	1.23526	−	1.30704i	0.142636	−	0.150924i
$76$	−4.16168	+	2.40274i	−0.477377	+	0.275614i
$77$		0			0
$78$	−4.71463	+	4.98858i	−0.533827	+	0.564845i
$79$	−13.8942			−1.56322			−0.781612	−	0.623765i	$-0.785602\pi$
$79$	−13.8942			−1.56322			−0.781612	+	0.623765i	$0.785602\pi$
$80$	−0.995200	+	1.72374i	−0.111267	+	0.192720i
$81$	3.59326	−	8.25158i	0.399251	−	0.916842i
$82$	5.16231	−	2.98046i	0.570082	−	0.329137i
$83$	3.35946	−	5.81876i	0.368749	−	0.638692i	−0.620621	−	0.784111i	$-0.713119\pi$
$83$	3.35946	−	5.81876i	0.368749	−	0.638692i	0.989370	+	0.145418i	$0.0464528\pi$
$84$		0			0
$85$	1.55489	+	2.69315i	0.168652	+	0.292113i
$86$	7.85683	+	4.53614i	0.847224	+	0.489145i
$87$	2.43511	−	10.2351i	0.261071	−	1.09732i
$88$	−3.00964	−	5.21285i	−0.320829	−	0.555692i
$89$	2.05680	+	3.56248i	0.218020	+	0.377622i	0.954203	−	0.299161i	$-0.0967068\pi$
$89$	2.05680	+	3.56248i	0.218020	+	0.377622i	−0.736183	+	0.676783i	$0.763374\pi$
$90$	−5.96169	+	0.336893i	−0.628417	+	0.0355116i
$91$		0			0
$92$	−5.02324	−	2.90017i	−0.523709	−	0.302364i
$93$	2.13680	−	0.637705i	0.221576	−	0.0661269i
$94$		−	4.78762i		−	0.493806i
$95$			9.56485i			0.981333i
$96$	−1.65972	+	0.495324i	−0.169394	+	0.0505538i
$97$	14.1120	+	8.14755i	1.43285	+	0.827258i	0.997338	−	0.0729228i	$-0.0232327\pi$
$97$	14.1120	+	8.14755i	1.43285	+	0.827258i	0.435516	+	0.900181i	$0.356566\pi$
$98$		0			0
$99$	8.13222	−	16.1231i	0.817319	−	1.62043i
$100$	−0.519152	−	0.899198i	−0.0519152	−	0.0899198i
$101$	−3.16950	−	5.48974i	−0.315377	−	0.546249i	0.664141	−	0.747608i	$-0.268798\pi$
$101$	−3.16950	−	5.48974i	−0.315377	−	0.546249i	−0.979518	+	0.201359i	$0.935464\pi$
$102$	−0.626354	+	2.63265i	−0.0620182	+	0.260672i
$103$	−11.4058	−	6.58517i	−1.12385	−	0.648856i	−0.181470	−	0.983396i	$-0.558086\pi$
$103$	−11.4058	−	6.58517i	−1.12385	−	0.648856i	−0.942381	+	0.334541i	$0.891419\pi$
$104$	1.98145	+	3.43197i	0.194297	+	0.336532i
$105$		0			0
$106$	4.19960	−	7.27392i	0.407901	−	0.706506i
$107$	−11.4530	+	6.61241i	−1.10721	+	0.639245i	−0.938104	−	0.346353i	$-0.887420\pi$
$107$	−11.4530	+	6.61241i	−1.10721	+	0.639245i	−0.169101	+	0.985599i	$0.554087\pi$
$108$	−3.97181	−	3.35033i	−0.382188	−	0.322386i
$109$	1.14786	−	1.98815i	0.109945	−	0.190430i	−0.805803	−	0.592184i	$-0.798266\pi$
$109$	1.14786	−	1.98815i	0.109945	−	0.190430i	0.915748	+	0.401754i	$0.131599\pi$
$110$	−11.9808			−1.14232
$111$	−7.20056	+	7.61895i	−0.683447	+	0.723159i
$112$		0			0
$113$	−12.0019	+	6.92933i	−1.12905	+	0.651856i	−0.943695	−	0.330816i	$-0.892676\pi$
$113$	−12.0019	+	6.92933i	−1.12905	+	0.651856i	−0.185353	+	0.982672i	$0.559343\pi$
$114$	−5.71706	+	6.04925i	−0.535452	+	0.566564i
$115$	−9.99827	+	5.77250i	−0.932343	+	0.538289i
$116$	−5.26041	−	3.03710i	−0.488417	−	0.281987i
$117$	−5.35399	+	10.6149i	−0.494976	+	0.981347i
$118$			12.7797i			1.17647i
$119$		0			0
$120$	−0.797941	+	3.35386i	−0.0728417	+	0.306164i
$121$	12.6159	−	21.8514i	1.14690	−	1.98649i
$122$	1.86610			0.168949
$123$	7.09167	−	7.50374i	0.639435	−	0.676589i
$124$		−	1.28745i		−	0.115616i
$125$	−12.0186			−1.07498
$126$		0			0
$127$	10.1548			0.901094			0.450547	−	0.892753i	$-0.351229\pi$
$127$	10.1548			0.901094			0.450547	+	0.892753i	$0.351229\pi$
$128$			1.00000i			0.0883883i
$129$	15.2870	+	3.63703i	1.34594	+	0.320223i
$130$	7.88775			0.691802
$131$	−1.93767	+	3.35615i	−0.169295	+	0.293228i	−0.938172	−	0.346169i	$-0.887482\pi$
$131$	−1.93767	+	3.35615i	−0.169295	+	0.293228i	0.768877	+	0.639397i	$0.220816\pi$
$132$	−7.57720	−	7.16110i	−0.659511	−	0.623294i
$133$		0			0
$134$		−	7.59491i		−	0.656101i
$135$	−9.72784	+	3.51211i	−0.837239	+	0.302275i
$136$	1.35307	+	0.781195i	0.116025	+	0.0669869i
$137$	3.50003	−	2.02074i	0.299028	−	0.172644i	−0.342978	−	0.939343i	$-0.611436\pi$
$137$	3.50003	−	2.02074i	0.299028	−	0.172644i	0.642006	+	0.766700i	$0.278102\pi$
$138$	−9.77368	−	2.32533i	−0.831991	−	0.197945i
$139$	−1.11021	+	0.640978i	−0.0941664	+	0.0543670i	−0.546344	−	0.837561i	$-0.683981\pi$
$139$	−1.11021	+	0.640978i	−0.0941664	+	0.0543670i	0.452177	+	0.891928i	$0.350647\pi$
$140$		0			0
$141$	−2.37142	−	7.94609i	−0.199710	−	0.669182i
$142$	5.48343			0.460159
$143$	−11.9269	+	20.6580i	−0.997378	+	1.72751i
$144$	−2.50931	+	1.64419i	−0.209109	+	0.137016i
$145$	−10.4703	+	6.04504i	−0.869513	+	0.502013i
$146$	5.41258	−	9.37486i	0.447948	−	0.775869i
$147$		0			0
$148$	3.02623	+	5.24158i	0.248754	+	0.430855i
$149$	11.9390	+	6.89299i	0.978082	+	0.564696i	0.901690	−	0.432382i	$-0.142327\pi$
$149$	11.9390	+	6.89299i	0.978082	+	0.564696i	0.0763911	+	0.997078i	$0.475660\pi$
$150$	−1.30704	−	1.23526i	−0.106719	−	0.100859i
$151$	−1.85701	−	3.21644i	−0.151122	−	0.261750i	0.780519	−	0.625133i	$-0.214955\pi$
$151$	−1.85701	−	3.21644i	−0.151122	−	0.261750i	−0.931640	+	0.363383i	$0.881622\pi$
$152$	2.40274	+	4.16168i	0.194888	+	0.337556i
$153$	0.264448	+	4.67970i	0.0213794	+	0.378332i
$154$		0			0
$155$	−2.21923	−	1.28127i	−0.178253	−	0.102914i
$156$	4.98858	+	4.71463i	0.399406	+	0.377473i
$157$			22.3696i			1.78529i	0.450761	+	0.892645i	$0.351153\pi$
$157$			22.3696i			1.78529i	−0.450761	+	0.892645i	$0.648847\pi$
$158$			13.8942i			1.10537i
$159$	3.36719	−	14.1528i	0.267036	−	1.12239i
$160$	1.72374	+	0.995200i	0.136273	+	0.0786775i
$161$		0			0
$162$	−8.25158	−	3.59326i	−0.648305	−	0.282313i
$163$	3.72381	+	6.44983i	0.291671	+	0.505190i	0.974205	−	0.225665i	$-0.0724553\pi$
$163$	3.72381	+	6.44983i	0.291671	+	0.505190i	−0.682534	+	0.730854i	$0.739122\pi$
$164$	−2.98046	−	5.16231i	−0.232735	−	0.403109i
$165$	−19.8847	+	5.93437i	−1.54802	+	0.461990i
$166$	−5.81876	−	3.35946i	−0.451624	−	0.260745i
$167$	4.77750	+	8.27487i	0.369694	+	0.640329i	0.989518	−	0.144413i	$-0.0461292\pi$
$167$	4.77750	+	8.27487i	0.369694	+	0.640329i	−0.619824	+	0.784741i	$0.712796\pi$
$168$		0			0
$169$	1.35228	−	2.34222i	0.104021	−	0.180170i
$170$	2.69315	−	1.55489i	0.206555	−	0.119255i
$171$	−6.49235	+	12.8718i	−0.496483	+	0.984333i
$172$	4.53614	−	7.85683i	0.345878	−	0.599078i
$173$	2.19043			0.166535			0.0832677	−	0.996527i	$-0.473464\pi$
$173$	2.19043			0.166535			0.0832677	+	0.996527i	$0.473464\pi$
$174$	−10.2351	−	2.43511i	−0.775923	−	0.184605i
$175$		0			0
$176$	−5.21285	+	3.00964i	−0.392934	+	0.226860i
$177$	6.33010	+	21.2107i	0.475799	+	1.59429i
$178$	3.56248	−	2.05680i	0.267019	−	0.154163i
$179$	17.5522	+	10.1338i	1.31192	+	0.757435i	0.982413	−	0.186720i	$-0.0597858\pi$
$179$	17.5522	+	10.1338i	1.31192	+	0.757435i	0.329502	+	0.944155i	$0.393119\pi$
$180$	0.336893	+	5.96169i	0.0251105	+	0.444358i
$181$		−	13.4363i		−	0.998712i	−0.866397	−	0.499356i	$-0.833570\pi$
$181$		−	13.4363i		−	0.998712i	0.866397	−	0.499356i	$-0.166430\pi$
$182$		0			0
$183$	3.09719	−	0.924324i	0.228951	−	0.0683280i
$184$	−2.90017	+	5.02324i	−0.213803	+	0.370318i
$185$	12.0468			0.885699
$186$	−0.637705	−	2.13680i	−0.0467588	−	0.156678i
$187$			9.40447i			0.687723i
$188$	−4.78762			−0.349173
$189$		0			0
$190$	9.56485			0.693907
$191$			6.61896i			0.478931i	0.970905	+	0.239466i	$0.0769722\pi$
$191$			6.61896i			0.478931i	−0.970905	+	0.239466i	$0.923028\pi$
$192$	0.495324	+	1.65972i	0.0357469	+	0.119780i
$193$	3.60343			0.259380			0.129690	−	0.991555i	$-0.458602\pi$
$193$	3.60343			0.259380			0.129690	+	0.991555i	$0.458602\pi$
$194$	8.14755	−	14.1120i	0.584960	−	1.01318i
$195$	13.0914	−	3.90699i	0.937496	−	0.279786i
$196$		0			0
$197$		−	7.20722i		−	0.513493i	−0.966479	−	0.256747i	$-0.917349\pi$
$197$		−	7.20722i		−	0.513493i	0.966479	−	0.256747i	$-0.0826506\pi$
$198$	−16.1231	−	8.13222i	−1.14582	−	0.577932i
$199$	20.4725	+	11.8198i	1.45126	+	0.837886i	0.998553	−	0.0537735i	$-0.0171249\pi$
$199$	20.4725	+	11.8198i	1.45126	+	0.837886i	0.452707	+	0.891659i	$0.350458\pi$
$200$	−0.899198	+	0.519152i	−0.0635829	+	0.0367096i
$201$	−3.76194	−	12.6054i	−0.265347	−	0.889116i
$202$	−5.48974	+	3.16950i	−0.386256	+	0.223005i
$203$		0			0
$204$	2.63265	+	0.626354i	0.184323	+	0.0438535i
$205$	−11.8646			−0.828662
$206$	−6.58517	+	11.4058i	−0.458810	+	0.794683i
$207$	−17.3733	+	0.981759i	−1.20753	+	0.0682370i
$208$	3.43197	−	1.98145i	0.237964	−	0.137389i
$209$	−14.4628	+	25.0503i	−1.00041	+	1.73277i
$210$		0			0
$211$	−8.63157	−	14.9503i	−0.594222	−	1.02922i	−0.993656	−	0.112461i	$-0.964127\pi$
$211$	−8.63157	−	14.9503i	−0.594222	−	1.02922i	0.399434	−	0.916762i	$-0.369207\pi$
$212$	−7.27392	−	4.19960i	−0.499575	−	0.288430i
$213$	9.10093	−	2.71607i	0.623586	−	0.186102i
$214$	6.61241	+	11.4530i	0.452015	+	0.782913i
$215$	−9.02875	−	15.6382i	−0.615755	−	1.06652i
$216$	−3.35033	+	3.97181i	−0.227961	+	0.270248i
$217$		0			0
$218$	−1.98815	−	1.14786i	−0.134654	−	0.0777427i
$219$	4.33974	−	18.2406i	0.293253	−	1.23258i
$220$			11.9808i			0.807745i
$221$		−	6.19159i		−	0.416492i
$222$	7.61895	+	7.20056i	0.511350	+	0.483270i
$223$	−20.6001	−	11.8934i	−1.37948	−	0.796444i	−0.387385	−	0.921918i	$-0.626622\pi$
$223$	−20.6001	−	11.8934i	−1.37948	−	0.796444i	−0.992097	+	0.125474i	$0.959955\pi$
$224$		0			0
$225$	−2.78117	−	1.40278i	−0.185411	−	0.0935186i
$226$	6.92933	+	12.0019i	0.460932	+	0.798358i
$227$	−7.20788	−	12.4844i	−0.478404	−	0.828620i	0.521289	−	0.853380i	$-0.325451\pi$
$227$	−7.20788	−	12.4844i	−0.478404	−	0.828620i	−0.999693	+	0.0247599i	$0.992118\pi$
$228$	6.04925	+	5.71706i	0.400621	+	0.378622i
$229$	6.42951	+	3.71208i	0.424874	+	0.245301i	0.697160	−	0.716915i	$-0.254447\pi$
$229$	6.42951	+	3.71208i	0.424874	+	0.245301i	−0.272287	+	0.962216i	$0.587780\pi$
$230$	5.77250	+	9.99827i	0.380628	+	0.659266i
$231$		0			0
$232$	−3.03710	+	5.26041i	−0.199395	+	0.345363i
$233$	3.91278	−	2.25905i	0.256335	−	0.147995i	−0.366327	−	0.930486i	$-0.619385\pi$
$233$	3.91278	−	2.25905i	0.256335	−	0.147995i	0.622661	+	0.782491i	$0.286051\pi$
$234$	10.6149	+	5.35399i	0.693917	+	0.350001i
$235$	−4.76465	+	8.25261i	−0.310811	+	0.538341i
$236$	12.7797			0.831888
$237$	6.88214	+	23.0605i	0.447043	+	1.49794i
$238$		0			0
$239$	−6.10620	+	3.52542i	−0.394977	+	0.228040i	−0.684315	−	0.729187i	$-0.739898\pi$
$239$	−6.10620	+	3.52542i	−0.394977	+	0.228040i	0.289337	+	0.957227i	$0.406565\pi$
$240$	3.35386	+	0.797941i	0.216491	+	0.0515068i
$241$	−6.12881	+	3.53847i	−0.394791	+	0.227933i	−0.684234	−	0.729262i	$-0.739863\pi$
$241$	−6.12881	+	3.53847i	−0.394791	+	0.227933i	0.289443	+	0.957195i	$0.406530\pi$
$242$	−21.8514	−	12.6159i	−1.40466	−	0.810981i
$243$	−15.4751	−	1.87658i	−0.992728	−	0.120383i
$244$		−	1.86610i		−	0.119465i
$245$		0			0
$246$	−7.50374	−	7.09167i	−0.478421	−	0.452149i
$247$	9.52183	−	16.4923i	0.605860	−	1.04938i
$248$	−1.28745			−0.0817532
$249$	−11.3215	−	2.69358i	−0.717472	−	0.170699i
$250$			12.0186i			0.760126i
$251$	−11.9661			−0.755291			−0.377645	−	0.925950i	$-0.623266\pi$
$251$	−11.9661			−0.755291			−0.377645	+	0.925950i	$0.623266\pi$
$252$		0			0
$253$	−34.9139			−2.19502
$254$		−	10.1548i		−	0.637169i
$255$	3.69969	−	3.91466i	0.231683	−	0.245145i
$256$	1.00000			0.0625000
$257$	−1.79537	+	3.10968i	−0.111992	+	0.193976i	−0.916573	−	0.399866i	$-0.869057\pi$
$257$	−1.79537	+	3.10968i	−0.111992	+	0.193976i	0.804581	+	0.593843i	$0.202390\pi$
$258$	3.63703	−	15.2870i	0.226432	−	0.951725i
$259$		0			0
$260$		−	7.88775i		−	0.489178i
$261$	−18.1936	+	1.02811i	−1.12615	+	0.0636385i
$262$	3.35615	+	1.93767i	0.207343	+	0.119710i
$263$	6.45370	−	3.72604i	0.397952	−	0.229758i	−0.287648	−	0.957736i	$-0.592873\pi$
$263$	6.45370	−	3.72604i	0.397952	−	0.229758i	0.685600	+	0.727979i	$0.259540\pi$
$264$	−7.16110	+	7.57720i	−0.440736	+	0.466344i
$265$	−14.4780	+	8.35889i	−0.889378	+	0.513483i
$266$		0			0
$267$	4.89392	−	5.17828i	0.299503	−	0.316905i
$268$	−7.59491			−0.463933
$269$	8.92216	−	15.4536i	0.543994	−	0.942225i	−0.454676	−	0.890657i	$-0.650245\pi$
$269$	8.92216	−	15.4536i	0.543994	−	0.942225i	0.998669	−	0.0515679i	$-0.0164219\pi$
$270$	3.51211	+	9.72784i	0.213740	+	0.592017i
$271$	21.6343	−	12.4906i	1.31419	−	0.758747i	0.331402	−	0.943490i	$-0.392478\pi$
$271$	21.6343	−	12.4906i	1.31419	−	0.758747i	0.982787	+	0.184742i	$0.0591451\pi$
$272$	0.781195	−	1.35307i	0.0473669	−	0.0820419i
$273$		0			0
$274$	−2.02074	−	3.50003i	−0.122078	−	0.211445i
$275$	−5.41253	−	3.12493i	−0.326388	−	0.188440i
$276$	−2.32533	+	9.77368i	−0.139968	+	0.588306i
$277$	10.8175	+	18.7364i	0.649960	+	1.12576i	0.983132	+	0.182898i	$0.0585477\pi$
$277$	10.8175	+	18.7364i	0.649960	+	1.12576i	−0.333172	+	0.942866i	$0.608119\pi$
$278$	0.640978	+	1.11021i	0.0384433	+	0.0665857i
$279$	−2.11682	−	3.23061i	−0.126731	−	0.193412i
$280$		0			0
$281$	0.931426	+	0.537759i	0.0555642	+	0.0320800i	0.527525	−	0.849540i	$-0.323120\pi$
$281$	0.931426	+	0.537759i	0.0555642	+	0.0320800i	−0.471961	+	0.881620i	$0.656454\pi$
$282$	−7.94609	+	2.37142i	−0.473183	+	0.141216i
$283$		−	29.3180i		−	1.74277i	−0.490596	−	0.871387i	$-0.663221\pi$
$283$		−	29.3180i		−	1.74277i	0.490596	−	0.871387i	$-0.336779\pi$
$284$		−	5.48343i		−	0.325382i
$285$	15.8749	−	4.73770i	0.940349	−	0.280637i
$286$	20.6580	+	11.9269i	1.22153	+	0.705253i
$287$		0			0
$288$	1.64419	+	2.50931i	0.0968850	+	0.147862i
$289$	7.27947	+	12.6084i	0.428204	+	0.741671i
$290$	6.04504	+	10.4703i	0.354977	+	0.614838i
$291$	6.53261	−	27.4575i	0.382949	−	1.60959i
$292$	−9.37486	−	5.41258i	−0.548622	−	0.316747i
$293$	−12.8648	−	22.2826i	−0.751572	−	1.30176i	−0.947061	−	0.321055i	$-0.895963\pi$
$293$	−12.8648	−	22.2826i	−0.751572	−	1.30176i	0.195489	−	0.980706i	$-0.437371\pi$
$294$		0			0
$295$	12.7184	−	22.0289i	0.740492	−	1.28257i
$296$	5.24158	−	3.02623i	0.304660	−	0.175896i
$297$	−30.7878	−	5.51104i	−1.78649	−	0.319783i
$298$	6.89299	−	11.9390i	0.399300	−	0.691608i
$299$	22.9862			1.32932
$300$	−1.23526	+	1.30704i	−0.0713180	+	0.0754619i
$301$		0			0
$302$	−3.21644	+	1.85701i	−0.185085	+	0.106859i
$303$	−7.54147	+	7.97966i	−0.433246	+	0.458420i
$304$	4.16168	−	2.40274i	0.238688	−	0.137807i
$305$	−3.21667	−	1.85714i	−0.184186	−	0.106340i
$306$	4.67970	−	0.264448i	0.267521	−	0.0151175i
$307$		−	15.0090i		−	0.856607i	−0.903635	−	0.428304i	$-0.859111\pi$
$307$		−	15.0090i		−	0.856607i	0.903635	−	0.428304i	$-0.140889\pi$
$308$		0			0
$309$	−5.27991	+	22.1922i	−0.300364	+	1.26247i
$310$	−1.28127	+	2.21923i	−0.0727713	+	0.126044i
$311$	−21.1923			−1.20170			−0.600852	−	0.799360i	$-0.705172\pi$
$311$	−21.1923			−1.20170			−0.600852	+	0.799360i	$0.705172\pi$
$312$	4.71463	−	4.98858i	0.266914	−	0.282423i
$313$			15.2447i			0.861679i	0.902429	+	0.430839i	$0.141782\pi$
$313$			15.2447i			0.861679i	−0.902429	+	0.430839i	$0.858218\pi$
$314$	22.3696			1.26239
$315$		0			0
$316$	13.8942			0.781612
$317$		−	15.9576i		−	0.896268i	−0.893966	−	0.448134i	$-0.852089\pi$
$317$		−	15.9576i		−	0.896268i	0.893966	−	0.448134i	$-0.147911\pi$
$318$	−14.1528	−	3.36719i	−0.793650	−	0.188823i
$319$	−36.5623			−2.04710
$320$	0.995200	−	1.72374i	0.0556334	−	0.0963599i
$321$	16.6477	+	15.7335i	0.929182	+	0.878157i
$322$		0			0
$323$		−	7.50805i		−	0.417759i
$324$	−3.59326	+	8.25158i	−0.199625	+	0.458421i
$325$	3.56343	+	2.05735i	0.197664	+	0.114121i
$326$	6.44983	−	3.72381i	0.357223	−	0.206243i
$327$	−3.86832	−	0.920339i	−0.213919	−	0.0508949i
$328$	−5.16231	+	2.98046i	−0.285041	+	0.164569i
$329$		0			0
$330$	5.93437	+	19.8847i	0.326676	+	1.09462i
$331$	5.92457			0.325644			0.162822	−	0.986655i	$-0.447940\pi$
$331$	5.92457			0.325644			0.162822	+	0.986655i	$0.447940\pi$
$332$	−3.35946	+	5.81876i	−0.184375	+	0.319346i
$333$	16.2119	+	8.17703i	0.888406	+	0.448099i
$334$	8.27487	−	4.77750i	0.452781	−	0.261413i
$335$	−7.55846	+	13.0916i	−0.412963	+	0.715273i
$336$		0			0
$337$	12.2615	+	21.2376i	0.667928	+	1.15689i	0.978483	+	0.206330i	$0.0661519\pi$
$337$	12.2615	+	21.2376i	0.667928	+	1.15689i	−0.310555	+	0.950556i	$0.600515\pi$
$338$	−2.34222	−	1.35228i	−0.127400	−	0.0735543i
$339$	17.4456	+	16.4876i	0.947513	+	0.895481i
$340$	−1.55489	−	2.69315i	−0.0843258	−	0.146057i
$341$	−3.87477	−	6.71129i	−0.209830	−	0.363437i
$342$	12.8718	+	6.49235i	0.696029	+	0.351066i
$343$		0			0
$344$	−7.85683	−	4.53614i	−0.423612	−	0.244573i
$345$	14.5331	+	13.7350i	0.782435	+	0.739469i
$346$		−	2.19043i		−	0.117758i
$347$		−	14.6076i		−	0.784177i	−0.919928	−	0.392088i	$-0.871753\pi$
$347$		−	14.6076i		−	0.784177i	0.919928	−	0.392088i	$-0.128247\pi$
$348$	−2.43511	+	10.2351i	−0.130536	+	0.548660i
$349$	15.5532	+	8.97965i	0.832545	+	0.480670i	0.854723	−	0.519084i	$-0.173727\pi$
$349$	15.5532	+	8.97965i	0.832545	+	0.480670i	−0.0221785	+	0.999754i	$0.507060\pi$
$350$		0			0
$351$	20.2696	+	3.62829i	1.08191	+	0.193664i
$352$	3.00964	+	5.21285i	0.160414	+	0.277846i
$353$	1.62784	+	2.81950i	0.0866410	+	0.150067i	0.906089	−	0.423086i	$-0.139053\pi$
$353$	1.62784	+	2.81950i	0.0866410	+	0.150067i	−0.819448	+	0.573153i	$0.805720\pi$
$354$	21.2107	−	6.33010i	1.12733	−	0.336441i
$355$	−9.45200	−	5.45711i	−0.501660	−	0.289633i
$356$	−2.05680	−	3.56248i	−0.109010	−	0.188811i
$357$		0			0
$358$	10.1338	−	17.5522i	0.535587	−	0.927664i
$359$	17.6173	−	10.1714i	0.929808	−	0.536825i	0.0430570	−	0.999073i	$-0.486290\pi$
$359$	17.6173	−	10.1714i	0.929808	−	0.536825i	0.886751	+	0.462248i	$0.152957\pi$
$360$	5.96169	−	0.336893i	0.314209	−	0.0177558i
$361$	2.04636	−	3.54441i	0.107703	−	0.186548i
$362$	−13.4363			−0.706196
$363$	−42.5160	−	10.1153i	−2.23151	−	0.530915i
$364$		0			0
$365$	−18.6597	+	10.7732i	−0.976695	+	0.563895i
$366$	−0.924324	−	3.09719i	−0.0483152	−	0.161893i
$367$	3.04871	−	1.76018i	0.159142	−	0.0918804i	−0.418314	−	0.908302i	$-0.637379\pi$
$367$	3.04871	−	1.76018i	0.159142	−	0.0918804i	0.577456	+	0.816422i	$0.304046\pi$
$368$	5.02324	+	2.90017i	0.261855	+	0.151182i
$369$	−15.9667	−	8.05338i	−0.831195	−	0.419242i
$370$		−	12.0468i		−	0.626283i
$371$		0			0
$372$	−2.13680	+	0.637705i	−0.110788	+	0.0330635i
$373$	2.92210	−	5.06122i	0.151300	−	0.262060i	−0.780405	−	0.625274i	$-0.784987\pi$
$373$	2.92210	−	5.06122i	0.151300	−	0.262060i	0.931706	+	0.363214i	$0.118321\pi$
$374$	9.40447			0.486294
$375$	5.95312	+	19.9475i	0.307418	+	1.03009i
$376$			4.78762i			0.246903i
$377$	24.0714			1.23974
$378$		0			0
$379$	−1.11033			−0.0570337			−0.0285168	−	0.999593i	$-0.509078\pi$
$379$	−1.11033			−0.0570337			−0.0285168	+	0.999593i	$0.509078\pi$
$380$		−	9.56485i		−	0.490666i
$381$	−5.02992	−	16.8541i	−0.257691	−	0.863461i
$382$	6.61896			0.338655
$383$	−4.01664	+	6.95702i	−0.205241	+	0.355487i	−0.950209	−	0.311612i	$-0.899131\pi$
$383$	−4.01664	+	6.95702i	−0.205241	+	0.355487i	0.744969	+	0.667099i	$0.232464\pi$
$384$	1.65972	−	0.495324i	0.0846970	−	0.0252769i
$385$		0			0
$386$		−	3.60343i		−	0.183410i
$387$	−1.53556	−	27.1735i	−0.0780571	−	1.38131i
$388$	−14.1120	−	8.14755i	−0.716427	−	0.413629i
$389$	−19.4971	+	11.2566i	−0.988541	+	0.570734i	−0.904838	−	0.425756i	$-0.860008\pi$
$389$	−19.4971	+	11.2566i	−0.988541	+	0.570734i	−0.0837030	+	0.996491i	$0.526675\pi$
$390$	−3.90699	−	13.0914i	−0.197838	−	0.662910i
$391$	7.84827	−	4.53120i	0.396904	−	0.229153i
$392$		0			0
$393$	6.53002	+	1.55360i	0.329396	+	0.0783690i
$394$	−7.20722			−0.363095
$395$	13.8275	−	23.9500i	0.695739	−	1.20506i
$396$	−8.13222	+	16.1231i	−0.408660	+	0.810214i
$397$	−25.9311	+	14.9713i	−1.30144	+	0.751388i	−0.980651	−	0.195762i	$-0.937282\pi$
$397$	−25.9311	+	14.9713i	−1.30144	+	0.751388i	−0.320791	+	0.947150i	$0.603949\pi$
$398$	11.8198	−	20.4725i	0.592475	−	1.02620i
$399$		0			0
$400$	0.519152	+	0.899198i	0.0259576	+	0.0449599i
$401$	−23.9666	−	13.8371i	−1.19684	−	0.690994i	−0.236988	−	0.971513i	$-0.576160\pi$
$401$	−23.9666	−	13.8371i	−1.19684	−	0.690994i	−0.959848	+	0.280519i	$0.909493\pi$
$402$	−12.6054	+	3.76194i	−0.628700	+	0.187629i
$403$	2.55102	+	4.41849i	0.127075	+	0.220101i
$404$	3.16950	+	5.48974i	0.157689	+	0.273125i
$405$	10.6475	+	14.4058i	0.529081	+	0.715830i
$406$		0			0
$407$	31.5505	+	18.2157i	1.56390	+	0.902919i
$408$	0.626354	−	2.63265i	0.0310091	−	0.130336i
$409$		−	36.7599i		−	1.81766i	−0.417167	−	0.908830i	$-0.636977\pi$
$409$		−	36.7599i		−	1.81766i	0.417167	−	0.908830i	$-0.363023\pi$
$410$			11.8646i			0.585952i
$411$	−5.08751	−	4.80813i	−0.250948	−	0.237168i
$412$	11.4058	+	6.58517i	0.561926	+	0.324428i
$413$		0			0
$414$	0.981759	+	17.3733i	0.0482508	+	0.853852i
$415$	6.68668	+	11.5817i	0.328236	+	0.568522i
$416$	−1.98145	−	3.43197i	−0.0971485	−	0.168266i
$417$	1.61375	+	1.52513i	0.0790258	+	0.0746861i
$418$	25.0503	+	14.4628i	1.22525	+	0.707399i
$419$	−7.82990	−	13.5618i	−0.382516	−	0.662537i	0.608905	−	0.793243i	$-0.291609\pi$
$419$	−7.82990	−	13.5618i	−0.382516	−	0.662537i	−0.991421	+	0.130706i	$0.958276\pi$
$420$		0			0
$421$	−12.8725	+	22.2959i	−0.627368	+	1.08663i	0.360710	+	0.932678i	$0.382535\pi$
$421$	−12.8725	+	22.2959i	−0.627368	+	1.08663i	−0.988078	+	0.153955i	$0.950799\pi$
$422$	−14.9503	+	8.63157i	−0.727770	+	0.420178i
$423$	−12.0136	+	7.87178i	−0.584123	+	0.382739i
$424$	−4.19960	+	7.27392i	−0.203951	+	0.353253i
$425$	1.62224			0.0786900
$426$	−2.71607	−	9.10093i	−0.131594	−	0.440942i
$427$		0			0
$428$	11.4530	−	6.61241i	0.553603	−	0.319623i
$429$	40.1941	+	9.56286i	1.94059	+	0.461699i
$430$	−15.6382	+	9.02875i	−0.754143	+	0.435405i
$431$	18.4735	+	10.6657i	0.889837	+	0.513748i	0.873889	−	0.486125i	$-0.161590\pi$
$431$	18.4735	+	10.6657i	0.889837	+	0.513748i	0.0159481	+	0.999873i	$0.494923\pi$
$432$	3.97181	+	3.35033i	0.191094	+	0.161193i
$433$		−	32.5613i		−	1.56480i	−0.622778	−	0.782399i	$-0.713996\pi$
$433$		−	32.5613i		−	1.56480i	0.622778	−	0.782399i	$-0.286004\pi$
$434$		0			0
$435$	15.2192	+	14.3835i	0.729707	+	0.689636i
$436$	−1.14786	+	1.98815i	−0.0549724	+	0.0952150i
$437$	27.8735			1.33337
$438$	−18.2406	−	4.33974i	−0.871568	−	0.207361i
$439$			6.71910i			0.320685i	0.987061	+	0.160343i	$0.0512599\pi$
$439$			6.71910i			0.320685i	−0.987061	+	0.160343i	$0.948740\pi$
$440$	11.9808			0.571162
$441$		0			0
$442$	−6.19159			−0.294504
$443$			1.61352i			0.0766608i	0.999265	+	0.0383304i	$0.0122039\pi$
$443$			1.61352i			0.0766608i	−0.999265	+	0.0383304i	$0.987796\pi$
$444$	7.20056	−	7.61895i	0.341724	−	0.361579i
$445$	−8.18770			−0.388134
$446$	−11.8934	+	20.6001i	−0.563171	+	0.975441i
$447$	5.52672	−	23.2296i	0.261405	−	1.09872i
$448$		0			0
$449$			7.27512i			0.343334i	0.985155	+	0.171667i	$0.0549154\pi$
$449$			7.27512i			0.343334i	−0.985155	+	0.171667i	$0.945085\pi$
$450$	−1.40278	+	2.78117i	−0.0661276	+	0.131106i
$451$	−31.0734	−	17.9403i	−1.46319	−	0.844774i
$452$	12.0019	−	6.92933i	0.564524	−	0.325928i
$453$	−4.41855	+	4.67529i	−0.207602	+	0.219664i
$454$	−12.4844	+	7.20788i	−0.585923	+	0.338283i
$455$		0			0
$456$	5.71706	−	6.04925i	0.267726	−	0.283282i
$457$	−0.276261			−0.0129230			−0.00646148	−	0.999979i	$-0.502057\pi$
$457$	−0.276261			−0.0129230			−0.00646148	+	0.999979i	$0.502057\pi$
$458$	3.71208	−	6.42951i	0.173454	−	0.300431i
$459$	7.63599	−	2.75688i	0.356417	−	0.128680i
$460$	9.99827	−	5.77250i	0.466172	−	0.269144i
$461$	8.30512	−	14.3849i	0.386808	−	0.669971i	−0.605210	−	0.796066i	$-0.706911\pi$
$461$	8.30512	−	14.3849i	0.386808	−	0.669971i	0.992018	+	0.126094i	$0.0402442\pi$
$462$		0			0
$463$	−3.19859	−	5.54011i	−0.148651	−	0.257471i	0.782078	−	0.623180i	$-0.214160\pi$
$463$	−3.19859	−	5.54011i	−0.148651	−	0.257471i	−0.930729	+	0.365709i	$0.880826\pi$
$464$	5.26041	+	3.03710i	0.244208	+	0.140994i
$465$	−1.02731	+	4.31793i	−0.0476403	+	0.200239i
$466$	−2.25905	−	3.91278i	−0.104648	−	0.181256i
$467$	−3.39599	−	5.88203i	−0.157148	−	0.272188i	0.776691	−	0.629881i	$-0.216897\pi$
$467$	−3.39599	−	5.88203i	−0.157148	−	0.272188i	−0.933839	+	0.357694i	$0.883563\pi$
$468$	5.35399	−	10.6149i	0.247488	−	0.490673i
$469$		0			0
$470$	8.25261	+	4.76465i	0.380664	+	0.219777i
$471$	37.1272	−	11.0802i	1.71073	−	0.510549i
$472$		−	12.7797i		−	0.588234i
$473$		−	54.6087i		−	2.51091i
$474$	23.0605	−	6.88214i	1.05920	−	0.316107i
$475$	4.32109	+	2.49478i	0.198265	+	0.114468i
$476$		0			0
$477$	−25.1575	+	1.42164i	−1.15188	+	0.0650924i
$478$	3.52542	+	6.10620i	0.161249	+	0.279291i
$479$	12.4257	+	21.5219i	0.567743	+	0.983360i	0.996789	+	0.0800774i	$0.0255167\pi$
$479$	12.4257	+	21.5219i	0.567743	+	0.983360i	−0.429045	+	0.903283i	$0.641150\pi$
$480$	0.797941	−	3.35386i	0.0364208	−	0.153082i
$481$	−20.7718	−	11.9926i	−0.947114	−	0.546817i
$482$	3.53847	+	6.12881i	0.161173	+	0.279160i
$483$		0			0
$484$	−12.6159	+	21.8514i	−0.573450	+	0.993244i
$485$	−28.0885	+	16.2169i	−1.27543	+	0.736371i
$486$	−1.87658	+	15.4751i	−0.0851235	+	0.701964i
$487$	−6.65840	+	11.5327i	−0.301721	+	0.522596i	−0.976526	−	0.215400i	$-0.930894\pi$
$487$	−6.65840	+	11.5327i	−0.301721	+	0.522596i	0.674805	+	0.737996i	$0.264228\pi$
$488$	−1.86610			−0.0844744
$489$	8.86039	−	9.37522i	0.400681	−	0.423962i
$490$		0			0
$491$	24.2581	−	14.0054i	1.09475	−	0.632057i	0.159916	−	0.987131i	$-0.448878\pi$
$491$	24.2581	−	14.0054i	1.09475	−	0.632057i	0.934838	+	0.355074i	$0.115544\pi$
$492$	−7.09167	+	7.50374i	−0.319717	+	0.338295i
$493$	8.21881	−	4.74513i	0.370157	−	0.213710i
$494$	−16.4923	−	9.52183i	−0.742023	−	0.428407i
$495$	19.6987	+	30.0635i	0.885392	+	1.35125i
$496$			1.28745i			0.0578082i
$497$		0			0
$498$	−2.69358	+	11.3215i	−0.120702	+	0.507329i
$499$	−5.94998	+	10.3057i	−0.266357	+	0.461345i	−0.967918	−	0.251265i	$-0.919153\pi$
$499$	−5.94998	+	10.3057i	−0.266357	+	0.461345i	0.701561	+	0.712609i	$0.252487\pi$
$500$	12.0186			0.537490
$501$	11.3675	−	12.0280i	0.507863	−	0.537372i
$502$			11.9661i			0.534071i
$503$	−5.08019			−0.226514			−0.113257	−	0.993566i	$-0.536128\pi$
$503$	−5.08019			−0.226514			−0.113257	+	0.993566i	$0.536128\pi$
$504$		0			0
$505$	12.6172			0.561456
$506$			34.9139i			1.55211i
$507$	−4.55723	−	1.08424i	−0.202394	−	0.0481529i
$508$	−10.1548			−0.450547
$509$	−0.500521	+	0.866928i	−0.0221852	+	0.0384259i	−0.876905	−	0.480664i	$-0.840396\pi$
$509$	−0.500521	+	0.866928i	−0.0221852	+	0.0384259i	0.854720	+	0.519090i	$0.173729\pi$
$510$	−3.91466	−	3.69969i	−0.173344	−	0.163825i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	24.5794	+	4.39973i	1.08521	+	0.194253i
$514$	3.10968	+	1.79537i	0.137162	+	0.0791905i
$515$	22.7022	−	13.1071i	1.00038	−	0.577569i
$516$	−15.2870	−	3.63703i	−0.672971	−	0.160111i
$517$	−24.9572	+	14.4090i	−1.09762	+	0.633709i
$518$		0			0
$519$	−1.08497	−	3.63549i	−0.0476250	−	0.159580i
$520$	−7.88775			−0.345901
$521$	11.9375	−	20.6763i	0.522991	−	0.905846i	−0.476651	−	0.879092i	$-0.658150\pi$
$521$	11.9375	−	20.6763i	0.522991	−	0.905846i	0.999642	−	0.0267539i	$-0.00851706\pi$
$522$	1.02811	+	18.1936i	0.0449992	+	0.796310i
$523$	6.96630	−	4.02199i	0.304615	−	0.175870i	−0.339899	−	0.940462i	$-0.610393\pi$
$523$	6.96630	−	4.02199i	0.304615	−	0.175870i	0.644514	+	0.764592i	$0.277060\pi$
$524$	1.93767	−	3.35615i	0.0846476	−	0.146614i
$525$		0			0
$526$	−3.72604	−	6.45370i	−0.162463	−	0.281395i
$527$	1.74201	+	1.00575i	0.0758832	+	0.0438112i
$528$	7.57720	+	7.16110i	0.329755	+	0.311647i
$529$	5.32199	+	9.21796i	0.231391	+	0.400781i
$530$	8.35889	+	14.4780i	0.363087	+	0.628885i
$531$	32.0682	−	21.0123i	1.39164	−	0.911857i
$532$		0			0
$533$	20.4577	+	11.8113i	0.886122	+	0.511603i
$534$	−5.17828	−	4.89392i	−0.224086	−	0.211780i
$535$		−	26.3227i		−	1.13803i
$536$			7.59491i			0.328050i
$537$	8.12516	−	34.1512i	0.350626	−	1.47373i
$538$	−15.4536	−	8.92216i	−0.666254	−	0.384662i
$539$		0			0
$540$	9.72784	−	3.51211i	0.418619	−	0.151137i
$541$	−0.0629344	−	0.109006i	−0.00270576	−	0.00468652i	0.864669	−	0.502341i	$-0.167528\pi$
$541$	−0.0629344	−	0.109006i	−0.00270576	−	0.00468652i	−0.867375	+	0.497655i	$0.834195\pi$
$542$	−12.4906	−	21.6343i	−0.536515	−	0.929272i
$543$	−22.3004	+	6.65532i	−0.957003	+	0.285607i
$544$	−1.35307	−	0.781195i	−0.0580124	−	0.0334935i
$545$	2.28470	+	3.95721i	0.0978656	+	0.169508i
$546$		0			0
$547$	6.59217	−	11.4180i	0.281861	−	0.488197i	−0.689982	−	0.723826i	$-0.742382\pi$
$547$	6.59217	−	11.4180i	0.281861	−	0.488197i	0.971843	+	0.235629i	$0.0757150\pi$
$548$	−3.50003	+	2.02074i	−0.149514	+	0.0863219i
$549$	−3.06823	−	4.68262i	−0.130949	−	0.199849i
$550$	−3.12493	+	5.41253i	−0.133247	+	0.230791i
$551$	29.1895			1.24351
$552$	9.77368	+	2.32533i	0.415995	+	0.0989724i
$553$		0			0
$554$	18.7364	−	10.8175i	0.796035	−	0.459591i
$555$	−5.96707	−	19.9943i	−0.253288	−	0.848709i
$556$	1.11021	−	0.640978i	0.0470832	−	0.0271835i
$557$	−23.6292	−	13.6423i	−1.00120	−	0.578043i	−0.0925969	−	0.995704i	$-0.529517\pi$
$557$	−23.6292	−	13.6423i	−1.00120	−	0.578043i	−0.908603	+	0.417661i	$0.862850\pi$
$558$	−3.23061	+	2.11682i	−0.136763	+	0.0896120i
$559$			35.9526i			1.52063i
$560$		0			0
$561$	15.6087	−	4.65826i	0.659002	−	0.196672i
$562$	0.537759	−	0.931426i	0.0226840	−	0.0392898i
$563$	−6.92687			−0.291933			−0.145966	−	0.989290i	$-0.546629\pi$
$563$	−6.92687			−0.291933			−0.145966	+	0.989290i	$0.546629\pi$
$564$	2.37142	+	7.94609i	0.0998550	+	0.334591i
$565$		−	27.5843i		−	1.16048i
$566$	−29.3180			−1.23233
$567$		0			0
$568$	−5.48343			−0.230080
$569$		−	17.8781i		−	0.749490i	−0.927128	−	0.374745i	$-0.877730\pi$
$569$		−	17.8781i		−	0.749490i	0.927128	−	0.374745i	$-0.122270\pi$
$570$	−4.73770	−	15.8749i	−0.198440	−	0.664927i
$571$	−27.2242			−1.13930			−0.569649	−	0.821888i	$-0.692921\pi$
$571$	−27.2242			−1.13930			−0.569649	+	0.821888i	$0.692921\pi$
$572$	11.9269	−	20.6580i	0.498689	−	0.863755i
$573$	10.9856	−	3.27853i	0.458930	−	0.136963i
$574$		0			0
$575$			6.02252i			0.251157i
$576$	2.50931	−	1.64419i	0.104555	−	0.0685080i
$577$	−2.21846	−	1.28083i	−0.0923555	−	0.0533215i	0.453111	−	0.891454i	$-0.350314\pi$
$577$	−2.21846	−	1.28083i	−0.0923555	−	0.0533215i	−0.545466	+	0.838133i	$0.683647\pi$
$578$	12.6084	−	7.27947i	0.524441	−	0.302786i
$579$	−1.78486	−	5.98066i	−0.0741764	−	0.248548i
$580$	10.4703	−	6.04504i	0.434756	−	0.251007i
$581$		0			0
$582$	−27.4575	−	6.53261i	−1.13815	−	0.270786i
$583$	−50.5572			−2.09387
$584$	−5.41258	+	9.37486i	−0.223974	+	0.387934i
$585$	−12.9690	−	19.7928i	−0.536202	−	0.818332i
$586$	−22.2826	+	12.8648i	−0.920484	+	0.531441i
$587$	−1.52947	+	2.64912i	−0.0631280	+	0.109341i	−0.895862	−	0.444332i	$-0.853441\pi$
$587$	−1.52947	+	2.64912i	−0.0631280	+	0.109341i	0.832734	+	0.553673i	$0.186774\pi$
$588$		0			0
$589$	3.09342	+	5.35795i	0.127462	+	0.220771i
$590$	−22.0289	−	12.7184i	−0.906914	−	0.523607i
$591$	−11.9619	+	3.56991i	−0.492048	+	0.146846i
$592$	−3.02623	−	5.24158i	−0.124377	−	0.215427i
$593$	9.14720	+	15.8434i	0.375631	+	0.650611i	0.990421	−	0.138079i	$-0.0440928\pi$
$593$	9.14720	+	15.8434i	0.375631	+	0.650611i	−0.614791	+	0.788690i	$0.710759\pi$
$594$	−5.51104	+	30.7878i	−0.226121	+	1.26324i
$595$		0			0
$596$	−11.9390	−	6.89299i	−0.489041	−	0.282348i
$597$	9.47701	−	39.8332i	0.387868	−	1.63027i
$598$		−	22.9862i		−	0.939974i
$599$			39.5874i			1.61750i	0.588154	+	0.808749i	$0.299855\pi$
$599$			39.5874i			1.61750i	−0.588154	+	0.808749i	$0.700145\pi$
$600$	1.30704	+	1.23526i	0.0533596	+	0.0504294i
$601$	20.8019	+	12.0100i	0.848526	+	0.489897i	0.860153	−	0.510036i	$-0.170368\pi$
$601$	20.8019	+	12.0100i	0.848526	+	0.489897i	−0.0116274	+	0.999932i	$0.503701\pi$
$602$		0			0
$603$	−19.0580	+	12.4875i	−0.776101	+	0.508530i
$604$	1.85701	+	3.21644i	0.0755608	+	0.130875i
$605$	25.1107	+	43.4930i	1.02089	+	1.76824i
$606$	7.97966	+	7.54147i	0.324152	+	0.306351i
$607$	18.5544	+	10.7124i	0.753099	+	0.434802i	0.826813	−	0.562477i	$-0.190152\pi$
$607$	18.5544	+	10.7124i	0.753099	+	0.434802i	−0.0737135	+	0.997279i	$0.523485\pi$
$608$	−2.40274	−	4.16168i	−0.0974442	−	0.168778i
$609$		0			0
$610$	−1.85714	+	3.21667i	−0.0751936	+	0.130239i
$611$	16.4310	−	9.48643i	0.664726	−	0.383780i
$612$	−0.264448	−	4.67970i	−0.0106897	−	0.189166i
$613$	2.17810	−	3.77258i	0.0879726	−	0.152373i	−0.818681	−	0.574248i	$-0.805295\pi$
$613$	2.17810	−	3.77258i	0.0879726	−	0.152373i	0.906654	+	0.421875i	$0.138628\pi$
$614$	−15.0090			−0.605713
$615$	5.87683	+	19.6919i	0.236977	+	0.794054i
$616$		0			0
$617$	28.4809	−	16.4434i	1.14660	−	0.661988i	0.198541	−	0.980093i	$-0.436380\pi$
$617$	28.4809	−	16.4434i	1.14660	−	0.661988i	0.948056	+	0.318105i	$0.103046\pi$
$618$	22.1922	+	5.27991i	0.892703	+	0.212389i
$619$	3.59040	−	2.07292i	0.144310	−	0.0833176i	−0.426106	−	0.904673i	$-0.640115\pi$
$619$	3.59040	−	2.07292i	0.144310	−	0.0833176i	0.570417	+	0.821355i	$0.306782\pi$
$620$	2.21923	+	1.28127i	0.0891263	+	0.0514571i
$621$	10.2349	+	28.3485i	0.410711	+	1.13758i
$622$			21.1923i			0.849733i
$623$		0			0
$624$	−4.98858	−	4.71463i	−0.199703	−	0.188736i
$625$	9.36520	−	16.2210i	0.374608	−	0.648840i
$626$	15.2447			0.609299
$627$	48.7402	+	11.5961i	1.94649	+	0.463104i
$628$		−	22.3696i		−	0.892645i
$629$	−9.45629			−0.377047
$630$		0			0
$631$	−18.7414			−0.746084			−0.373042	−	0.927815i	$-0.621685\pi$
$631$	−18.7414			−0.746084			−0.373042	+	0.927815i	$0.621685\pi$
$632$		−	13.8942i		−	0.552683i
$633$	−20.5378	+	21.7312i	−0.816306	+	0.863738i
$634$	−15.9576			−0.633757
$635$	−10.1061	+	17.5042i	−0.401047	+	0.694634i
$636$	−3.36719	+	14.1528i	−0.133518	+	0.561195i
$637$		0			0
$638$			36.5623i			1.44752i
$639$	−9.01582	−	13.7596i	−0.356660	−	0.544322i
$640$	−1.72374	−	0.995200i	−0.0681367	−	0.0393388i
$641$	−5.81323	+	3.35627i	−0.229609	+	0.132565i	−0.610392	−	0.792100i	$-0.708988\pi$
$641$	−5.81323	+	3.35627i	−0.229609	+	0.132565i	0.380783	+	0.924665i	$0.375655\pi$
$642$	15.7335	−	16.6477i	0.620951	−	0.657031i
$643$	−7.11267	+	4.10650i	−0.280496	+	0.161945i	−0.633648	−	0.773621i	$-0.718443\pi$
$643$	−7.11267	+	4.10650i	−0.280496	+	0.161945i	0.353152	+	0.935566i	$0.385110\pi$
$644$		0			0
$645$	−21.4829	+	22.7311i	−0.845888	+	0.895038i
$646$	−7.50805			−0.295400
$647$	−8.40246	+	14.5535i	−0.330335	+	0.572157i	−0.982577	−	0.185854i	$-0.940495\pi$
$647$	−8.40246	+	14.5535i	−0.330335	+	0.572157i	0.652243	+	0.758010i	$0.273828\pi$
$648$	8.25158	+	3.59326i	0.324152	+	0.141157i
$649$	66.6188	−	38.4624i	2.61502	−	1.50978i
$650$	2.05735	−	3.56343i	0.0806958	−	0.139769i
$651$		0			0
$652$	−3.72381	−	6.44983i	−0.145836	−	0.252595i
$653$	−20.2758	−	11.7062i	−0.793452	−	0.458100i	0.0477241	−	0.998861i	$-0.484803\pi$
$653$	−20.2758	−	11.7062i	−0.793452	−	0.458100i	−0.841177	+	0.540761i	$0.818137\pi$
$654$	−0.920339	+	3.86832i	−0.0359881	+	0.151263i
$655$	−3.85674	−	6.68008i	−0.150695	−	0.261012i
$656$	2.98046	+	5.16231i	0.116368	+	0.201554i
$657$	−32.4237	+	1.83225i	−1.26497	+	0.0714830i
$658$		0			0
$659$	−14.5941	−	8.42589i	−0.568504	−	0.328226i	0.188047	−	0.982160i	$-0.439784\pi$
$659$	−14.5941	−	8.42589i	−0.568504	−	0.328226i	−0.756552	+	0.653934i	$0.773117\pi$
$660$	19.8847	−	5.93437i	0.774011	−	0.230995i
$661$			38.3082i			1.49002i	0.667054	+	0.745009i	$0.267555\pi$
$661$			38.3082i			1.49002i	−0.667054	+	0.745009i	$0.732445\pi$
$662$		−	5.92457i		−	0.230265i
$663$	−10.2763	+	3.06684i	−0.399098	+	0.119106i
$664$	5.81876	+	3.35946i	0.225812	+	0.130372i
$665$		0			0
$666$	8.17703	−	16.2119i	0.316854	−	0.628198i
$667$	17.6162	+	30.5122i	0.682102	+	1.18144i
$668$	−4.77750	−	8.27487i	−0.184847	−	0.320164i
$669$	−9.53604	+	40.0813i	−0.368684	+	1.54963i
$670$	13.0916	+	7.55846i	0.505774	+	0.292009i
$671$	−5.61629	−	9.72771i	−0.216815	−	0.375534i
$672$		0			0
$673$	−3.52300	+	6.10201i	−0.135802	+	0.235215i	−0.925903	−	0.377760i	$-0.876694\pi$
$673$	−3.52300	+	6.10201i	−0.135802	+	0.235215i	0.790102	+	0.612976i	$0.210028\pi$
$674$	21.2376	−	12.2615i	0.818041	−	0.472296i
$675$	−0.950634	+	5.31078i	−0.0365899	+	0.204412i
$676$	−1.35228	+	2.34222i	−0.0520107	+	0.0900852i
$677$	−43.9101			−1.68760			−0.843801	−	0.536657i	$-0.819687\pi$
$677$	−43.9101			−1.68760			−0.843801	+	0.536657i	$0.819687\pi$
$678$	16.4876	−	17.4456i	0.633201	−	0.669993i
$679$		0			0
$680$	−2.69315	+	1.55489i	−0.103278	+	0.0596274i
$681$	−17.1503	+	18.1469i	−0.657203	+	0.695389i
$682$	−6.71129	+	3.87477i	−0.256989	+	0.148372i
$683$	−9.86301	−	5.69441i	−0.377397	−	0.217891i	0.299288	−	0.954163i	$-0.403251\pi$
$683$	−9.86301	−	5.69441i	−0.377397	−	0.217891i	−0.676685	+	0.736272i	$0.736584\pi$
$684$	6.49235	−	12.8718i	0.248241	−	0.492167i
$685$			8.04418i			0.307352i
$686$		0			0
$687$	2.97630	−	12.5098i	0.113553	−	0.477280i
$688$	−4.53614	+	7.85683i	−0.172939	+	0.299539i
$689$	33.2852			1.26806
$690$	13.7350	−	14.5331i	0.522883	−	0.553265i
$691$		−	2.09395i		−	0.0796577i	−0.999207	−	0.0398288i	$-0.987319\pi$
$691$		−	2.09395i		−	0.0796577i	0.999207	−	0.0398288i	$-0.0126813\pi$
$692$	−2.19043			−0.0832677
$693$		0			0
$694$	−14.6076			−0.554497
$695$		−	2.55160i		−	0.0967879i
$696$	10.2351	+	2.43511i	0.387961	+	0.0923027i
$697$	9.31329			0.352766
$698$	8.97965	−	15.5532i	0.339885	−	0.588698i
$699$	−5.68747	−	5.37514i	−0.215120	−	0.203307i
$700$		0			0
$701$		−	7.35719i		−	0.277877i	−0.990301	−	0.138939i	$-0.955631\pi$
$701$		−	7.35719i		−	0.277877i	0.990301	−	0.138939i	$-0.0443690\pi$
$702$	3.62829	−	20.2696i	0.136941	−	0.765029i
$703$	−25.1883	−	14.5425i	−0.949996	−	0.548481i
$704$	5.21285	−	3.00964i	0.196467	−	0.113430i
$705$	16.0570	+	3.82024i	0.604742	+	0.143879i
$706$	2.81950	−	1.62784i	0.106113	−	0.0612645i
$707$		0			0
$708$	−6.33010	−	21.2107i	−0.237900	−	0.797146i
$709$	22.9874			0.863311			0.431656	−	0.902039i	$-0.357930\pi$
$709$	22.9874			0.863311			0.431656	+	0.902039i	$0.357930\pi$
$710$	−5.45711	+	9.45200i	−0.204802	+	0.354727i
$711$	34.8649	−	22.8448i	1.30754	−	0.856747i
$712$	−3.56248	+	2.05680i	−0.133509	+	0.0770817i
$713$	−3.73383	+	6.46718i	−0.139833	+	0.242198i
$714$		0			0
$715$	−23.7393	−	41.1177i	−0.887800	−	1.53772i
$716$	−17.5522	−	10.1338i	−0.655958	−	0.378717i
$717$	8.87574	+	8.38833i	0.331470	+	0.313268i
$718$	−10.1714	−	17.6173i	−0.379592	−	0.657473i
$719$	0.334921	+	0.580100i	0.0124905	+	0.0216341i	0.872203	−	0.489144i	$-0.162691\pi$
$719$	0.334921	+	0.580100i	0.0124905	+	0.0216341i	−0.859713	+	0.510778i	$0.829357\pi$
$720$	−0.336893	−	5.96169i	−0.0125553	−	0.222179i
$721$		0			0
$722$	−3.54441	−	2.04636i	−0.131909	−	0.0761578i
$723$	8.90859	+	8.41939i	0.331314	+	0.313120i
$724$			13.4363i			0.499356i
$725$			6.30686i			0.234231i
$726$	−10.1153	+	42.5160i	−0.375414	+	1.57792i
$727$	10.8032	+	6.23723i	0.400669	+	0.231326i	0.686772	−	0.726873i	$-0.259027\pi$
$727$	10.8032	+	6.23723i	0.400669	+	0.231326i	−0.286104	+	0.958199i	$0.592360\pi$
$728$		0			0
$729$	4.55059	+	26.6138i	0.168540	+	0.985695i
$730$	10.7732	+	18.6597i	0.398734	+	0.690627i
$731$	7.08723	+	12.2754i	0.262131	+	0.454024i
$732$	−3.09719	+	0.924324i	−0.114476	+	0.0341640i
$733$	−18.5364	−	10.7020i	−0.684659	−	0.395288i	0.116949	−	0.993138i	$-0.462689\pi$
$733$	−18.5364	−	10.7020i	−0.684659	−	0.395288i	−0.801608	+	0.597850i	$0.796022\pi$
$734$	−1.76018	−	3.04871i	−0.0649693	−	0.112530i
$735$		0			0
$736$	2.90017	−	5.02324i	0.106902	−	0.185159i
$737$	−39.5912	+	22.8580i	−1.45836	+	0.841984i
$738$	−8.05338	+	15.9667i	−0.296449	+	0.587744i
$739$	11.6420	−	20.1646i	0.428258	−	0.741765i	−0.568460	−	0.822711i	$-0.692461\pi$
$739$	11.6420	−	20.1646i	0.428258	−	0.741765i	0.996719	+	0.0809456i	$0.0257940\pi$
$740$	−12.0468			−0.442849
$741$	−32.0889	−	7.63450i	−1.17882	−	0.280460i
$742$		0			0
$743$	−5.94043	+	3.42971i	−0.217933	+	0.125824i	−0.604993	−	0.796231i	$-0.706824\pi$
$743$	−5.94043	+	3.42971i	−0.217933	+	0.125824i	0.387060	+	0.922055i	$0.373491\pi$
$744$	0.637705	+	2.13680i	0.0233794	+	0.0783389i
$745$	−23.7634	+	13.7198i	−0.870624	+	0.502655i
$746$	−5.06122	−	2.92210i	−0.185304	−	0.106986i
$747$	1.13724	+	20.1247i	0.0416094	+	0.736323i
$748$		−	9.40447i		−	0.343862i
$749$		0			0
$750$	19.9475	−	5.95312i	0.728381	−	0.217377i
$751$	−22.5956	+	39.1367i	−0.824524	+	1.42812i	0.0777577	+	0.996972i	$0.475224\pi$
$751$	−22.5956	+	39.1367i	−0.824524	+	1.42812i	−0.902282	+	0.431146i	$0.858109\pi$
$752$	4.78762			0.174587
$753$	5.92707	+	19.8602i	0.215995	+	0.723747i
$754$		−	24.0714i		−	0.876629i
$755$	7.39240			0.269037
$756$		0			0
$757$	−17.8760			−0.649716			−0.324858	−	0.945763i	$-0.605316\pi$
$757$	−17.8760			−0.649716			−0.324858	+	0.945763i	$0.605316\pi$
$758$			1.11033i			0.0403289i
$759$	17.2937	+	57.9472i	0.627721	+	2.10335i
$760$	−9.56485			−0.346954
$761$	−5.70198	+	9.87613i	−0.206697	+	0.358009i	−0.950672	−	0.310198i	$-0.899605\pi$
$761$	−5.70198	+	9.87613i	−0.206697	+	0.358009i	0.743975	+	0.668207i	$0.232938\pi$
$762$	−16.8541	+	5.02992i	−0.610559	+	0.182215i
$763$		0			0
$764$		−	6.61896i		−	0.239466i
$765$	−8.32976	−	4.20140i	−0.301163	−	0.151902i
$766$	6.95702	+	4.01664i	0.251367	+	0.145127i
$767$	−43.8596	+	25.3223i	−1.58368	+	0.914337i
$768$	−0.495324	−	1.65972i	−0.0178735	−	0.0598898i
$769$	−0.332429	+	0.191928i	−0.0119877	+	0.00692109i	−0.505982	−	0.862544i	$-0.668870\pi$
$769$	−0.332429	+	0.191928i	−0.0119877	+	0.00692109i	0.493994	+	0.869465i	$0.335536\pi$
$770$		0			0
$771$	6.05047	+	1.43951i	0.217902	+	0.0518427i
$772$	−3.60343			−0.129690
$773$	13.9330	−	24.1326i	0.501134	−	0.867990i	−0.498865	−	0.866680i	$-0.666250\pi$
$773$	13.9330	−	24.1326i	0.501134	−	0.867990i	0.999999	−	0.00131020i	$-0.000417050\pi$
$774$	−27.1735	+	1.53556i	−0.976732	+	0.0551947i
$775$	−1.15767	+	0.668383i	−0.0415849	+	0.0240090i
$776$	−8.14755	+	14.1120i	−0.292480	+	0.506590i
$777$		0			0
$778$	11.2566	+	19.4971i	0.403570	+	0.699004i
$779$	24.8074	+	14.3226i	0.888819	+	0.513160i
$780$	−13.0914	+	3.90699i	−0.468748	+	0.139893i
$781$	−16.5032	−	28.5843i	−0.590530	−	1.02283i
$782$	−4.53120	−	7.84827i	−0.162035	−	0.280653i
$783$	10.7181	+	29.6869i	0.383033	+	1.06092i
$784$		0			0
$785$	−38.5593	−	22.2622i	−1.37624	−	0.794574i
$786$	1.55360	−	6.53002i	0.0554152	−	0.232918i
$787$		−	31.6313i		−	1.12753i	−0.825934	−	0.563767i	$-0.809352\pi$
$787$		−	31.6313i		−	1.12753i	0.825934	−	0.563767i	$-0.190648\pi$
$788$			7.20722i			0.256747i
$789$	−9.38084	−	8.86570i	−0.333967	−	0.315627i
$790$	−23.9500	−	13.8275i	−0.852103	−	0.491962i
$791$		0			0
$792$	16.1231	+	8.13222i	0.572908	+	0.288966i
$793$	3.69758	+	6.40440i	0.131305	+	0.227427i
$794$	14.9713	+	25.9311i	0.531312	+	0.920259i
$795$	21.0447	+	19.8890i	0.746378	+	0.705391i
$796$	−20.4725	−	11.8198i	−0.725630	−	0.418943i
$797$	−7.27060	−	12.5931i	−0.257538	−	0.446069i	0.708044	−	0.706169i	$-0.249578\pi$
$797$	−7.27060	−	12.5931i	−0.257538	−	0.446069i	−0.965582	+	0.260100i	$0.916245\pi$
$798$		0			0
$799$	3.74007	−	6.47799i	0.132314	−	0.229175i
$800$	0.899198	−	0.519152i	0.0317915	−	0.0183548i
$801$	−11.0185	−	5.55758i	−0.389321	−	0.196368i
$802$	−13.8371	+	23.9666i	−0.488606	+	0.846291i
$803$	−65.1597			−2.29944
$804$	3.76194	+	12.6054i	0.132673	+	0.444558i
$805$		0			0
$806$	4.41849	−	2.55102i	0.155635	−	0.0898558i
$807$	−30.0680	−	7.15369i	−1.05844	−	0.251822i
$808$	5.48974	−	3.16950i	0.193128	−	0.111503i
$809$	32.7025	+	18.8808i	1.14976	+	0.663814i	0.948829	−	0.315791i	$-0.102270\pi$
$809$	32.7025	+	18.8808i	1.14976	+	0.663814i	0.200932	+	0.979605i	$0.435603\pi$
$810$	14.4058	−	10.6475i	0.506168	−	0.374116i
$811$		−	9.24256i		−	0.324550i	−0.986746	−	0.162275i	$-0.948117\pi$
$811$		−	9.24256i		−	0.324550i	0.986746	−	0.162275i	$-0.0518832\pi$
$812$		0			0
$813$	−31.4467	−	29.7199i	−1.10289	−	1.04232i
$814$	18.2157	−	31.5505i	0.638460	−	1.10585i
$815$	−14.8238			−0.519253
$816$	−2.63265	−	0.626354i	−0.0921614	−	0.0219268i
$817$			43.5968i			1.52526i
$818$	−36.7599			−1.28528
$819$		0			0
$820$	11.8646			0.414331
$821$			2.26566i			0.0790719i	0.999218	+	0.0395360i	$0.0125880\pi$
$821$			2.26566i			0.0790719i	−0.999218	+	0.0395360i	$0.987412\pi$
$822$	−4.80813	+	5.08751i	−0.167703	+	0.177447i
$823$	6.81784			0.237655			0.118828	−	0.992915i	$-0.462086\pi$
$823$	6.81784			0.237655			0.118828	+	0.992915i	$0.462086\pi$
$824$	6.58517	−	11.4058i	0.229405	−	0.397341i
$825$	−2.50553	+	10.5311i	−0.0872314	+	0.366646i
$826$		0			0
$827$			15.7635i			0.548151i	0.961708	+	0.274076i	$0.0883719\pi$
$827$			15.7635i			0.548151i	−0.961708	+	0.274076i	$0.911628\pi$
$828$	17.3733	−	0.981759i	0.603764	−	0.0341185i
$829$	18.1323	+	10.4687i	0.629759	+	0.363592i	0.780659	−	0.624957i	$-0.214884\pi$
$829$	18.1323	+	10.4687i	0.629759	+	0.363592i	−0.150900	+	0.988549i	$0.548217\pi$
$830$	11.5817	−	6.68668i	0.402006	−	0.232098i
$831$	25.7390	−	27.2346i	0.892876	−	0.944756i
$832$	−3.43197	+	1.98145i	−0.118982	+	0.0686944i
$833$		0			0
$834$	1.52513	−	1.61375i	0.0528111	−	0.0558796i
$835$	−19.0183			−0.658154
$836$	14.4628	−	25.0503i	0.500207	−	0.866383i
$837$	−4.31338	+	5.11351i	−0.149092	+	0.176749i
$838$	−13.5618	+	7.82990i	−0.468484	+	0.270479i
$839$	7.96961	−	13.8038i	0.275142	−	0.476559i	−0.695029	−	0.718981i	$-0.744609\pi$
$839$	7.96961	−	13.8038i	0.275142	−	0.476559i	0.970171	+	0.242422i	$0.0779419\pi$
$840$		0			0
$841$	3.94792	+	6.83801i	0.136135	+	0.235793i
$842$	22.2959	+	12.8725i	0.768366	+	0.443616i
$843$	0.431169	−	1.81227i	0.0148503	−	0.0624178i
$844$	8.63157	+	14.9503i	0.297111	+	0.514611i
$845$	2.69158	+	4.66195i	0.0925931	+	0.160376i
$846$	7.87178	+	12.0136i	0.270637	+	0.413037i
$847$		0			0
$848$	7.27392	+	4.19960i	0.249788	+	0.144215i
$849$	−48.6595	+	14.5219i	−1.66999	+	0.498390i
$850$		−	1.62224i		−	0.0556423i
$851$		−	35.1063i		−	1.20343i
$852$	−9.10093	+	2.71607i	−0.311793	+	0.0930512i
$853$	−7.10530	−	4.10225i	−0.243281	−	0.140458i	0.373403	−	0.927669i	$-0.378191\pi$
$853$	−7.10530	−	4.10225i	−0.243281	−	0.140458i	−0.616684	+	0.787211i	$0.711524\pi$
$854$		0			0
$855$	−15.7265	−	24.0012i	−0.537834	−	0.820822i
$856$	−6.61241	−	11.4530i	−0.226007	−	0.391456i
$857$	1.91332	+	3.31396i	0.0653576	+	0.113203i	0.896853	−	0.442330i	$-0.145848\pi$
$857$	1.91332	+	3.31396i	0.0653576	+	0.113203i	−0.831495	+	0.555532i	$0.812515\pi$
$858$	9.56286	−	40.1941i	0.326471	−	1.37220i
$859$	−22.2863	−	12.8670i	−0.760399	−	0.439017i	0.0690397	−	0.997614i	$-0.478006\pi$
$859$	−22.2863	−	12.8670i	−0.760399	−	0.439017i	−0.829439	+	0.558597i	$0.811340\pi$
$860$	9.02875	+	15.6382i	0.307878	+	0.533260i
$861$		0			0
$862$	10.6657	−	18.4735i	0.363275	−	0.629210i
$863$	33.7506	−	19.4859i	1.14888	−	0.663308i	0.200268	−	0.979741i	$-0.435819\pi$
$863$	33.7506	−	19.4859i	1.14888	−	0.663308i	0.948615	+	0.316434i	$0.102485\pi$
$864$	3.35033	−	3.97181i	0.113981	−	0.135124i
$865$	−2.17992	+	3.77573i	−0.0741194	+	0.128379i
$866$	−32.5613			−1.10648
$867$	17.3207	−	18.3271i	0.588241	−	0.622421i
$868$		0			0
$869$	72.4286	−	41.8167i	2.45697	−	1.41853i
$870$	14.3835	−	15.2192i	0.487646	−	0.515981i
$871$	26.0655	−	15.0489i	0.883196	−	0.509914i
$872$	1.98815	+	1.14786i	0.0673272	+	0.0388714i
$873$	−48.8074	+	2.75809i	−1.65188	+	0.0933472i
$874$		−	27.8735i		−	0.942835i
$875$		0			0
$876$	−4.33974	+	18.2406i	−0.146626	+	0.616292i
$877$	−29.4947	+	51.0863i	−0.995966	+	1.72506i	−0.420269	+	0.907399i	$0.638064\pi$
$877$	−29.4947	+	51.0863i	−0.995966	+	1.72506i	−0.575696	+	0.817664i	$0.695269\pi$
$878$	6.71910			0.226759
$879$	−30.6104	+	32.3890i	−1.03246	+	1.09246i
$880$		−	11.9808i		−	0.403872i
$881$	18.1949			0.613002			0.306501	−	0.951870i	$-0.400842\pi$
$881$	18.1949			0.613002			0.306501	+	0.951870i	$0.400842\pi$
$882$		0			0
$883$	−11.8187			−0.397731			−0.198865	−	0.980027i	$-0.563726\pi$
$883$	−11.8187			−0.397731			−0.198865	+	0.980027i	$0.563726\pi$
$884$			6.19159i			0.208246i
$885$	−42.8614	−	10.1975i	−1.44077	−	0.342784i
$886$	1.61352			0.0542074
$887$	13.5323	−	23.4386i	0.454370	−	0.786993i	−0.544281	−	0.838903i	$-0.683198\pi$
$887$	13.5323	−	23.4386i	0.454370	−	0.786993i	0.998652	+	0.0519101i	$0.0165309\pi$
$888$	−7.61895	−	7.20056i	−0.255675	−	0.241635i
$889$		0			0
$890$			8.18770i			0.274452i
$891$	6.10316	+	53.8287i	0.204464	+	1.80333i
$892$	20.6001	+	11.8934i	0.689741	+	0.398222i
$893$	19.9245	−	11.5034i	0.666749	−	0.384948i
$894$	−23.2296	−	5.52672i	−0.776914	−	0.184841i
$895$	−34.9360	+	20.1703i	−1.16778	+	0.674219i
$896$		0			0
$897$	−11.3856	−	38.1505i	−0.380154	−	1.27381i
$898$	7.27512			0.242774
$899$	−3.91011	+	6.77252i	−0.130410	+	0.225876i
$900$	2.78117	+	1.40278i	0.0927056	+	0.0467593i
$901$	11.3647	−	6.56142i	0.378613	−	0.218592i
$902$	−17.9403	+	31.0734i	−0.597345	+	1.03463i
$903$		0			0
$904$	−6.92933	−	12.0019i	−0.230466	−	0.399179i
$905$	23.1606	+	13.3718i	0.769886	+	0.444494i
$906$	4.67529	+	4.41855i	0.155326	+	0.146797i
$907$	4.22543	+	7.31866i	0.140303	+	0.243012i	0.927611	−	0.373548i	$-0.121859\pi$
$907$	4.22543	+	7.31866i	0.140303	+	0.243012i	−0.787308	+	0.616560i	$0.788526\pi$
$908$	7.20788	+	12.4844i	0.239202	+	0.414310i
$909$	16.9794	+	8.56417i	0.563172	+	0.284056i
$910$		0			0
$911$	−26.1362	−	15.0897i	−0.865931	−	0.499945i	6.31533e−5	−	1.00000i	$-0.499980\pi$
$911$	−26.1362	−	15.0897i	−0.865931	−	0.499945i	−0.865994	+	0.500055i	$0.833313\pi$
$912$	−6.04925	−	5.71706i	−0.200311	−	0.189311i
$913$			40.4431i			1.33847i
$914$			0.276261i			0.00913791i
$915$	−1.48904	+	6.25864i	−0.0492261	+	0.206904i
$916$	−6.42951	−	3.71208i	−0.212437	−	0.122651i
$917$		0			0
$918$	−2.75688	−	7.63599i	−0.0909905	−	0.252025i
$919$	1.66175	+	2.87824i	0.0548161	+	0.0949443i	0.892131	−	0.451776i	$-0.149209\pi$
$919$	1.66175	+	2.87824i	0.0548161	+	0.0949443i	−0.837315	+	0.546720i	$0.815876\pi$
$920$	−5.77250	−	9.99827i	−0.190314	−	0.329633i
$921$	−24.9106	+	7.43430i	−0.820833	+	0.244969i
$922$	−14.3849	−	8.30512i	−0.473741	−	0.273515i
$923$	10.8651	+	18.8190i	0.357630	+	0.619434i
$924$		0			0
$925$	3.14214	−	5.44235i	0.103313	−	0.178943i
$926$	−5.54011	+	3.19859i	−0.182059	+	0.105112i
$927$	39.4481	−	2.22920i	1.29564	−	0.0732164i
$928$	3.03710	−	5.26041i	0.0996976	−	0.172681i
$929$	44.0556			1.44542			0.722709	−	0.691152i	$-0.242897\pi$
$929$	44.0556			1.44542			0.722709	+	0.691152i	$0.242897\pi$
$930$	4.31793	+	1.02731i	0.141590	+	0.0336868i
$931$		0			0
$932$	−3.91278	+	2.25905i	−0.128167	+	0.0739975i
$933$	10.4970	+	35.1732i	0.343658	+	1.15152i
$934$	−5.88203	+	3.39599i	−0.192466	+	0.111120i
$935$	−16.2108	−	9.35934i	−0.530151	−	0.306083i
$936$	−10.6149	−	5.35399i	−0.346958	−	0.175001i
$937$			5.51314i			0.180107i	0.995937	+	0.0900533i	$0.0287037\pi$
$937$			5.51314i			0.180107i	−0.995937	+	0.0900533i	$0.971296\pi$
$938$		0			0
$939$	25.3018	−	7.55104i	0.825692	−	0.246419i
$940$	4.76465	−	8.25261i	0.155406	−	0.269170i
$941$	−34.5536			−1.12642			−0.563208	−	0.826315i	$-0.690433\pi$
$941$	−34.5536			−1.12642			−0.563208	+	0.826315i	$0.690433\pi$
$942$	−11.0802	−	37.1272i	−0.361013	−	1.20967i
$943$			34.5754i			1.12593i
$944$	−12.7797			−0.415944
$945$		0			0
$946$	−54.6087			−1.77548
$947$			24.2906i			0.789338i	0.918823	+	0.394669i	$0.129141\pi$
$947$			24.2906i			0.789338i	−0.918823	+	0.394669i	$0.870859\pi$
$948$	−6.88214	−	23.0605i	−0.223522	−	0.748969i
$949$	42.8990			1.39256
$950$	2.49478	−	4.32109i	0.0809414	−	0.140195i
$951$	−26.4851	+	7.90418i	−0.858837	+	0.256311i
$952$		0			0
$953$		−	27.3395i		−	0.885613i	−0.896617	−	0.442807i	$-0.853983\pi$
$953$		−	27.3395i		−	0.885613i	0.896617	−	0.442807i	$-0.146017\pi$
$954$	1.42164	+	25.1575i	0.0460273	+	0.814503i
$955$	−11.4094	−	6.58719i	−0.369198	−	0.213157i
$956$	6.10620	−	3.52542i	0.197489	−	0.114020i
$957$	18.1102	+	60.6830i	0.585419	+	1.96160i
$958$	21.5219	−	12.4257i	0.695341	−	0.401455i
$959$		0			0
$960$	−3.35386	−	0.797941i	−0.108245	−	0.0257534i
$961$	29.3425			0.946531
$962$	−11.9926	+	20.7718i	−0.386658	+	0.669711i
$963$	17.8671	−	35.4235i	0.575759	−	1.14151i
$964$	6.12881	−	3.53847i	0.197396	−	0.113966i
$965$	−3.58613	+	6.21136i	−0.115442	+	0.199951i
$966$		0			0
$967$	18.5829	+	32.1865i	0.597586	+	1.03505i	0.993176	+	0.116622i	$0.0372066\pi$
$967$	18.5829	+	32.1865i	0.597586	+	1.03505i	−0.395590	+	0.918427i	$0.629460\pi$
$968$	21.8514	+	12.6159i	0.702330	+	0.405490i
$969$	−12.4612	+	3.71892i	−0.400312	+	0.119469i
$970$	16.2169	+	28.0885i	0.520693	+	0.901867i
$971$	−22.2733	−	38.5785i	−0.714785	−	1.23804i	−0.963042	−	0.269350i	$-0.913191\pi$
$971$	−22.2733	−	38.5785i	−0.714785	−	1.23804i	0.248257	−	0.968694i	$-0.420142\pi$
$972$	15.4751	+	1.87658i	0.496364	+	0.0601914i
$973$		0			0
$974$	11.5327	+	6.65840i	0.369531	+	0.213349i
$975$	1.64956	−	6.93333i	0.0528281	−	0.222044i
$976$			1.86610i			0.0597324i
$977$		−	54.4124i		−	1.74081i	−0.492340	−	0.870403i	$-0.663858\pi$
$977$		−	54.4124i		−	1.74081i	0.492340	−	0.870403i	$-0.336142\pi$
$978$	−9.37522	−	8.86039i	−0.299786	−	0.283324i
$979$	−21.4436	−	12.3804i	−0.685339	−	0.395681i
$980$		0			0
$981$	0.388570	+	6.87617i	0.0124061	+	0.219539i
$982$	−14.0054	−	24.2581i	−0.446931	−	0.774108i
$983$	11.9161	+	20.6392i	0.380064	+	0.658289i	0.991071	−	0.133335i	$-0.0425688\pi$
$983$	11.9161	+	20.6392i	0.380064	+	0.658289i	−0.611007	+	0.791625i	$0.709235\pi$
$984$	7.50374	+	7.09167i	0.239210	+	0.226074i
$985$	12.4234	+	7.17263i	0.395841	+	0.228539i
$986$	−4.74513	−	8.21881i	−0.151116	−	0.261740i
$987$		0			0
$988$	−9.52183	+	16.4923i	−0.302930	+	0.524690i
$989$	−45.5723	+	26.3112i	−1.44912	+	0.836647i
$990$	30.0635	−	19.6987i	0.955481	−	0.626067i
$991$	−7.45815	+	12.9179i	−0.236916	+	0.410351i	−0.959828	−	0.280590i	$-0.909470\pi$
$991$	−7.45815	+	12.9179i	−0.236916	+	0.410351i	0.722912	+	0.690940i	$0.242803\pi$
$992$	1.28745			0.0408766
$993$	−2.93458	−	9.83310i	−0.0931261	−	0.312044i
$994$		0			0
$995$	−40.7486	+	23.5262i	−1.29182	+	0.745831i
$996$	11.3215	+	2.69358i	0.358736	+	0.0853494i
$997$	−18.0939	+	10.4465i	−0.573040	+	0.330845i	−0.758362	−	0.651833i	$-0.774000\pi$
$997$	−18.0939	+	10.4465i	−0.573040	+	0.330845i	0.185323	+	0.982678i	$0.440667\pi$
$998$	10.3057	+	5.94998i	0.326220	+	0.188343i
$999$	5.54140	−	30.9574i	0.175322	−	0.979449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.4		48
3.2	odd	2		2646.2.l.c.521.14		48
7.2	even	3		882.2.t.c.803.12		48
7.3	odd	6		882.2.m.c.587.22	yes	48
7.4	even	3		882.2.m.c.587.15	yes	48
7.5	odd	6		882.2.t.c.803.1		48
7.6	odd	2	inner	882.2.l.c.227.9		48
9.4	even	3		2646.2.t.c.2285.20		48
9.5	odd	6		882.2.t.c.815.1		48
21.2	odd	6		2646.2.t.c.1979.19		48
21.5	even	6		2646.2.t.c.1979.20		48
21.11	odd	6		2646.2.m.c.1763.8		48
21.17	even	6		2646.2.m.c.1763.7		48
21.20	even	2		2646.2.l.c.521.13		48
63.4	even	3		2646.2.m.c.881.7		48
63.5	even	6	inner	882.2.l.c.509.16		48
63.13	odd	6		2646.2.t.c.2285.19		48
63.23	odd	6	inner	882.2.l.c.509.21		48
63.31	odd	6		2646.2.m.c.881.8		48
63.32	odd	6		882.2.m.c.293.22	yes	48
63.40	odd	6		2646.2.l.c.1097.14		48
63.41	even	6		882.2.t.c.815.12		48
63.58	even	3		2646.2.l.c.1097.13		48
63.59	even	6		882.2.m.c.293.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.4		48	1.1	even	1	trivial
882.2.l.c.227.9		48	7.6	odd	2	inner
882.2.l.c.509.16		48	63.5	even	6	inner
882.2.l.c.509.21		48	63.23	odd	6	inner
882.2.m.c.293.15	✓	48	63.59	even	6
882.2.m.c.293.22	yes	48	63.32	odd	6
882.2.m.c.587.15	yes	48	7.4	even	3
882.2.m.c.587.22	yes	48	7.3	odd	6
882.2.t.c.803.1		48	7.5	odd	6
882.2.t.c.803.12		48	7.2	even	3
882.2.t.c.815.1		48	9.5	odd	6
882.2.t.c.815.12		48	63.41	even	6
2646.2.l.c.521.13		48	21.20	even	2
2646.2.l.c.521.14		48	3.2	odd	2
2646.2.l.c.1097.13		48	63.58	even	3
2646.2.l.c.1097.14		48	63.40	odd	6
2646.2.m.c.881.7		48	63.4	even	3
2646.2.m.c.881.8		48	63.31	odd	6
2646.2.m.c.1763.7		48	21.17	even	6
2646.2.m.c.1763.8		48	21.11	odd	6
2646.2.t.c.1979.19		48	21.2	odd	6
2646.2.t.c.1979.20		48	21.5	even	6
2646.2.t.c.2285.19		48	63.13	odd	6
2646.2.t.c.2285.20		48	9.4	even	3

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.495324 - 1.65972i) q^{3} -1.00000 q^{4} +(-0.995200 + 1.72374i) q^{5} +(-1.65972 + 0.495324i) q^{6} +1.00000i q^{8} +(-2.50931 + 1.64419i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.495324 - 1.65972i) q^{3} -1.00000 q^{4} +(-0.995200 + 1.72374i) q^{5} +(-1.65972 + 0.495324i) q^{6} +1.00000i q^{8} +(-2.50931 + 1.64419i) q^{9} +(1.72374 + 0.995200i) q^{10} +(-5.21285 + 3.00964i) q^{11} +(0.495324 + 1.65972i) q^{12} +(3.43197 - 1.98145i) q^{13} +(3.35386 + 0.797941i) q^{15} +1.00000 q^{16} +(0.781195 - 1.35307i) q^{17} +(1.64419 + 2.50931i) q^{18} +(4.16168 - 2.40274i) q^{19} +(0.995200 - 1.72374i) q^{20} +(3.00964 + 5.21285i) q^{22} +(5.02324 + 2.90017i) q^{23} +(1.65972 - 0.495324i) q^{24} +(0.519152 + 0.899198i) q^{25} +(-1.98145 - 3.43197i) q^{26} +(3.97181 + 3.35033i) q^{27} +(5.26041 + 3.03710i) q^{29} +(0.797941 - 3.35386i) q^{30} +1.28745i q^{31} -1.00000i q^{32} +(7.57720 + 7.16110i) q^{33} +(-1.35307 - 0.781195i) q^{34} +(2.50931 - 1.64419i) q^{36} +(-3.02623 - 5.24158i) q^{37} +(-2.40274 - 4.16168i) q^{38} +(-4.98858 - 4.71463i) q^{39} +(-1.72374 - 0.995200i) q^{40} +(2.98046 + 5.16231i) q^{41} +(-4.53614 + 7.85683i) q^{43} +(5.21285 - 3.00964i) q^{44} +(-0.336893 - 5.96169i) q^{45} +(2.90017 - 5.02324i) q^{46} +4.78762 q^{47} +(-0.495324 - 1.65972i) q^{48} +(0.899198 - 0.519152i) q^{50} +(-2.63265 - 0.626354i) q^{51} +(-3.43197 + 1.98145i) q^{52} +(7.27392 + 4.19960i) q^{53} +(3.35033 - 3.97181i) q^{54} -11.9808i q^{55} +(-6.04925 - 5.71706i) q^{57} +(3.03710 - 5.26041i) q^{58} -12.7797 q^{59} +(-3.35386 - 0.797941i) q^{60} +1.86610i q^{61} +1.28745 q^{62} -1.00000 q^{64} +7.88775i q^{65} +(7.16110 - 7.57720i) q^{66} +7.59491 q^{67} +(-0.781195 + 1.35307i) q^{68} +(2.32533 - 9.77368i) q^{69} +5.48343i q^{71} +(-1.64419 - 2.50931i) q^{72} +(9.37486 + 5.41258i) q^{73} +(-5.24158 + 3.02623i) q^{74} +(1.23526 - 1.30704i) q^{75} +(-4.16168 + 2.40274i) q^{76} +(-4.71463 + 4.98858i) q^{78} -13.8942 q^{79} +(-0.995200 + 1.72374i) q^{80} +(3.59326 - 8.25158i) q^{81} +(5.16231 - 2.98046i) q^{82} +(3.35946 - 5.81876i) q^{83} +(1.55489 + 2.69315i) q^{85} +(7.85683 + 4.53614i) q^{86} +(2.43511 - 10.2351i) q^{87} +(-3.00964 - 5.21285i) q^{88} +(2.05680 + 3.56248i) q^{89} +(-5.96169 + 0.336893i) q^{90} +(-5.02324 - 2.90017i) q^{92} +(2.13680 - 0.637705i) q^{93} -4.78762i q^{94} +9.56485i q^{95} +(-1.65972 + 0.495324i) q^{96} +(14.1120 + 8.14755i) q^{97} +(8.13222 - 16.1231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

L-functions

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