LMFDB - Embedded newform 297.2.n.b.91.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.8
Character	$\chi$	$=$	297.91
Dual form			297.2.n.b.235.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83498 + 0.816986i) q^{2} +(1.36143 + 1.51202i) q^{4} +(-0.00498046 + 0.00221744i) q^{5} +(3.74416 - 0.795845i) q^{7} +(0.0214877 + 0.0661323i) q^{8} +O(q^{10})$	\(q+(1.83498 + 0.816986i) q^{2} +(1.36143 + 1.51202i) q^{4} +(-0.00498046 + 0.00221744i) q^{5} +(3.74416 - 0.795845i) q^{7} +(0.0214877 + 0.0661323i) q^{8} -0.0109507 q^{10} +(-2.31651 + 2.37356i) q^{11} +(0.369348 + 3.51411i) q^{13} +(7.52065 + 1.59856i) q^{14} +(0.410751 - 3.90804i) q^{16} +(-3.70012 - 2.68830i) q^{17} +(-0.211664 - 0.651435i) q^{19} +(-0.0101333 - 0.00451165i) q^{20} +(-6.18992 + 2.46287i) q^{22} +(-0.760697 + 1.31757i) q^{23} +(-3.34563 + 3.71570i) q^{25} +(-2.19323 + 6.75007i) q^{26} +(6.30072 + 4.57774i) q^{28} +(0.354669 - 0.0753873i) q^{29} +(-0.448272 - 4.26502i) q^{31} +(4.01607 - 6.95603i) q^{32} +(-4.59335 - 7.95592i) q^{34} +(-0.0168829 + 0.0122661i) q^{35} +(1.90653 - 5.86771i) q^{37} +(0.143814 - 1.36830i) q^{38} +(-0.000253663 - 0.000281721i) q^{40} +(-6.53199 - 1.38842i) q^{41} +(-3.65705 - 6.33419i) q^{43} +(-6.74261 - 0.271187i) q^{44} +(-2.47230 + 1.79623i) q^{46} +(-4.42967 + 4.91964i) q^{47} +(6.99053 - 3.11239i) q^{49} +(-9.17485 + 4.08490i) q^{50} +(-4.81055 + 5.34266i) q^{52} +(10.7752 - 7.82863i) q^{53} +(0.00627407 - 0.0169581i) q^{55} +(0.133084 + 0.230509i) q^{56} +(0.712402 + 0.151426i) q^{58} +(3.84462 + 4.26988i) q^{59} +(-1.20808 + 11.4941i) q^{61} +(2.66189 - 8.19247i) q^{62} +(6.69422 - 4.86363i) q^{64} +(-0.00963186 - 0.0166829i) q^{65} +(-6.80952 + 11.7944i) q^{67} +(-0.972694 - 9.25456i) q^{68} +(-0.0410010 + 0.00871503i) q^{70} +(2.25702 + 1.63982i) q^{71} +(-0.0206478 + 0.0635475i) q^{73} +(8.29229 - 9.20952i) q^{74} +(0.696816 - 1.20692i) q^{76} +(-6.78441 + 10.7306i) q^{77} +(3.14785 + 1.40151i) q^{79} +(0.00662012 + 0.0203746i) q^{80} +(-10.8517 - 7.88426i) q^{82} +(0.802871 - 7.63880i) q^{83} +(0.0243895 + 0.00518414i) q^{85} +(-1.53566 - 14.6109i) q^{86} +(-0.206745 - 0.102194i) q^{88} +0.897342 q^{89} +(4.17958 + 12.8634i) q^{91} +(-3.02781 + 0.643581i) q^{92} +(-12.1476 + 5.40847i) q^{94} +(0.00249870 + 0.00277509i) q^{95} +(-13.9314 - 6.20265i) q^{97} +15.3703 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.83498	+	0.816986i	1.29753	+	0.577696i	0.935122	−	0.354325i	$-0.115289\pi$
$2$	1.83498	+	0.816986i	1.29753	+	0.577696i	0.362405	+	0.932021i	$0.381956\pi$
$3$		0			0
$3$		0			0
$4$	1.36143	+	1.51202i	0.680713	+	0.756008i
$5$	−0.00498046	+	0.00221744i	−0.00222733	+	0.000991671i	−0.407850	−	0.913049i	$-0.633721\pi$
$5$	−0.00498046	+	0.00221744i	−0.00222733	+	0.000991671i	0.405623	+	0.914041i	$0.367055\pi$
$6$		0			0
$7$	3.74416	−	0.795845i	1.41516	−	0.300801i	0.564028	−	0.825755i	$-0.309251\pi$
$7$	3.74416	−	0.795845i	1.41516	−	0.300801i	0.851131	+	0.524954i	$0.175918\pi$
$8$	0.0214877	+	0.0661323i	0.00759704	+	0.0233813i
$9$		0			0
$10$	−0.0109507			−0.00346290
$11$	−2.31651	+	2.37356i	−0.698455	+	0.715654i
$11$	−2.31651	+	2.37356i	−0.698455	+	0.715654i
$12$		0			0
$13$	0.369348	+	3.51411i	0.102439	+	0.974638i	0.918164	+	0.396200i	$0.129671\pi$
$13$	0.369348	+	3.51411i	0.102439	+	0.974638i	−0.815726	+	0.578439i	$0.803662\pi$
$14$	7.52065	+	1.59856i	2.00998	+	0.427234i
$15$		0			0
$16$	0.410751	−	3.90804i	0.102688	−	0.977010i
$17$	−3.70012	−	2.68830i	−0.897412	−	0.652008i	0.0403882	−	0.999184i	$-0.487141\pi$
$17$	−3.70012	−	2.68830i	−0.897412	−	0.652008i	−0.937800	+	0.347176i	$0.887141\pi$
$18$		0			0
$19$	−0.211664	−	0.651435i	−0.0485591	−	0.149449i	0.923837	−	0.382786i	$-0.125035\pi$
$19$	−0.211664	−	0.651435i	−0.0485591	−	0.149449i	−0.972396	+	0.233337i	$0.925035\pi$
$20$	−0.0101333	−	0.00451165i	−0.00226588	−	0.00100884i
$21$		0			0
$22$	−6.18992	+	2.46287i	−1.31969	+	0.525085i
$23$	−0.760697	+	1.31757i	−0.158616	+	0.274731i	−0.934370	−	0.356304i	$-0.884037\pi$
$23$	−0.760697	+	1.31757i	−0.158616	+	0.274731i	0.775754	+	0.631036i	$0.217370\pi$
$24$		0			0
$25$	−3.34563	+	3.71570i	−0.669127	+	0.743140i
$26$	−2.19323	+	6.75007i	−0.430128	+	1.32380i
$27$		0			0
$28$	6.30072	+	4.57774i	1.19072	+	0.865112i
$29$	0.354669	−	0.0753873i	0.0658605	−	0.0139991i	−0.174864	−	0.984593i	$-0.555948\pi$
$29$	0.354669	−	0.0753873i	0.0658605	−	0.0139991i	0.240724	+	0.970594i	$0.422615\pi$
$30$		0			0
$31$	−0.448272	−	4.26502i	−0.0805120	−	0.766021i	−0.958067	−	0.286545i	$-0.907493\pi$
$31$	−0.448272	−	4.26502i	−0.0805120	−	0.766021i	0.877555	−	0.479476i	$-0.159173\pi$
$32$	4.01607	−	6.95603i	0.709947	−	1.22966i
$33$		0			0
$34$	−4.59335	−	7.95592i	−0.787753	−	1.36443i
$35$	−0.0168829	+	0.0122661i	−0.00285373	+	0.00207335i
$36$		0			0
$37$	1.90653	−	5.86771i	0.313432	−	0.964645i	−0.662963	−	0.748652i	$-0.730701\pi$
$37$	1.90653	−	5.86771i	0.313432	−	0.964645i	0.976395	−	0.215993i	$-0.0692988\pi$
$38$	0.143814	−	1.36830i	0.0233297	−	0.221967i
$39$		0			0
$40$	−0.000253663	0	0.000281721i	−4.01076e−5	0	4.45441e-5i
$41$	−6.53199	−	1.38842i	−1.02012	−	0.216834i	−0.332656	−	0.943048i	$-0.607945\pi$
$41$	−6.53199	−	1.38842i	−1.02012	−	0.216834i	−0.687469	+	0.726214i	$0.741278\pi$
$42$		0			0
$43$	−3.65705	−	6.33419i	−0.557694	−	0.965955i	−0.997688	−	0.0679544i	$-0.978353\pi$
$43$	−3.65705	−	6.33419i	−0.557694	−	0.965955i	0.439994	−	0.898001i	$-0.354981\pi$
$44$	−6.74261	−	0.271187i	−1.01649	−	0.0408830i
$45$		0			0
$46$	−2.47230	+	1.79623i	−0.364520	+	0.264839i
$47$	−4.42967	+	4.91964i	−0.646133	+	0.717604i	−0.973855	−	0.227170i	$-0.927053\pi$
$47$	−4.42967	+	4.91964i	−0.646133	+	0.717604i	0.327722	+	0.944774i	$0.393719\pi$
$48$		0			0
$49$	6.99053	−	3.11239i	0.998648	−	0.444627i
$50$	−9.17485	+	4.08490i	−1.29752	+	0.577693i
$51$		0			0
$52$	−4.81055	+	5.34266i	−0.667103	+	0.740893i
$53$	10.7752	−	7.82863i	1.48009	−	1.07535i	0.502558	−	0.864544i	$-0.332393\pi$
$53$	10.7752	−	7.82863i	1.48009	−	1.07535i	0.977529	−	0.210802i	$-0.0676075\pi$
$54$		0			0
$55$	0.00627407	−	0.0169581i	0.000845996	−	0.00228663i
$56$	0.133084	+	0.230509i	0.0177841	+	0.0308030i
$57$		0			0
$58$	0.712402	+	0.151426i	0.0935429	+	0.0198832i
$59$	3.84462	+	4.26988i	0.500526	+	0.555891i	0.939473	−	0.342622i	$-0.111315\pi$
$59$	3.84462	+	4.26988i	0.500526	+	0.555891i	−0.438947	+	0.898513i	$0.644648\pi$
$60$		0			0
$61$	−1.20808	+	11.4941i	−0.154678	+	1.47167i	0.591708	+	0.806153i	$0.298454\pi$
$61$	−1.20808	+	11.4941i	−0.154678	+	1.47167i	−0.746386	+	0.665513i	$0.768213\pi$
$62$	2.66189	−	8.19247i	0.338061	−	1.04044i
$63$		0			0
$64$	6.69422	−	4.86363i	0.836777	−	0.607954i
$65$	−0.00963186	−	0.0166829i	−0.00119468	−	0.00206925i
$66$		0			0
$67$	−6.80952	+	11.7944i	−0.831915	+	1.44092i	0.0646030	+	0.997911i	$0.479422\pi$
$67$	−6.80952	+	11.7944i	−0.831915	+	1.44092i	−0.896518	+	0.443008i	$0.853911\pi$
$68$	−0.972694	−	9.25456i	−0.117956	−	1.12228i
$69$		0			0
$70$	−0.0410010	+	0.00871503i	−0.00490056	+	0.00104165i
$71$	2.25702	+	1.63982i	0.267859	+	0.194611i	0.713605	−	0.700549i	$-0.247061\pi$
$71$	2.25702	+	1.63982i	0.267859	+	0.194611i	−0.445745	+	0.895160i	$0.647061\pi$
$72$		0			0
$73$	−0.0206478	+	0.0635475i	−0.00241665	+	0.00743768i	−0.952258	−	0.305296i	$-0.901245\pi$
$73$	−0.0206478	+	0.0635475i	−0.00241665	+	0.00743768i	0.949841	+	0.312733i	$0.101245\pi$
$74$	8.29229	−	9.20952i	0.963959	−	1.07058i
$75$		0			0
$76$	0.696816	−	1.20692i	0.0799302	−	0.138443i
$77$	−6.78441	+	10.7306i	−0.773155	+	1.22286i
$78$		0			0
$79$	3.14785	+	1.40151i	0.354161	+	0.157682i	0.576103	−	0.817377i	$-0.304573\pi$
$79$	3.14785	+	1.40151i	0.354161	+	0.157682i	−0.221942	+	0.975060i	$0.571240\pi$
$80$	0.00662012	+	0.0203746i	0.000740152	+	0.00227795i
$81$		0			0
$82$	−10.8517	−	7.88426i	−1.19838	−	0.870671i
$83$	0.802871	−	7.63880i	0.0881265	−	0.838468i	−0.857778	−	0.514021i	$-0.828155\pi$
$83$	0.802871	−	7.63880i	0.0881265	−	0.838468i	0.945904	−	0.324447i	$-0.105178\pi$
$84$		0			0
$85$	0.0243895	+	0.00518414i	0.00264541	+	0.000562299i
$86$	−1.53566	−	14.6109i	−0.165595	−	1.57553i
$87$		0			0
$88$	−0.206745	−	0.102194i	−0.0220391	−	0.0108939i
$89$	0.897342			0.0951181			0.0475590	−	0.998868i	$-0.484856\pi$
$89$	0.897342			0.0951181			0.0475590	+	0.998868i	$0.484856\pi$
$90$		0			0
$91$	4.17958	+	12.8634i	0.438139	+	1.34845i
$92$	−3.02781	+	0.643581i	−0.315671	+	0.0670980i
$93$		0			0
$94$	−12.1476	+	5.40847i	−1.25293	+	0.557842i
$95$	0.00249870	+	0.00277509i	0.000256362	+	0.000284718i
$96$		0			0
$97$	−13.9314	−	6.20265i	−1.41452	−	0.629784i	−0.449814	−	0.893122i	$-0.648510\pi$
$97$	−13.9314	−	6.20265i	−1.41452	−	0.629784i	−0.964703	+	0.263339i	$0.915176\pi$
$98$	15.3703			1.55263
$99$		0			0
$100$	−10.1730			−1.01730
$101$	10.1171	+	4.50441i	1.00669	+	0.448206i	0.842773	−	0.538269i	$-0.180921\pi$
$101$	10.1171	+	4.50441i	1.00669	+	0.448206i	0.163914	+	0.986475i	$0.447588\pi$
$102$		0			0
$103$	3.15265	+	3.50137i	0.310639	+	0.345000i	0.878167	−	0.478354i	$-0.158767\pi$
$103$	3.15265	+	3.50137i	0.310639	+	0.345000i	−0.567527	+	0.823355i	$0.692100\pi$
$104$	−0.224460	+	0.0999359i	−0.0220101	+	0.00979952i
$105$		0			0
$106$	26.1681	−	5.56221i	2.54168	−	0.540250i
$107$	4.96558	+	15.2825i	0.480041	+	1.47741i	0.839037	+	0.544075i	$0.183119\pi$
$107$	4.96558	+	15.2825i	0.480041	+	1.47741i	−0.358996	+	0.933339i	$0.616881\pi$
$108$		0			0
$109$	18.6164			1.78313			0.891564	−	0.452894i	$-0.149609\pi$
$109$	18.6164			1.78313			0.891564	+	0.452894i	$0.149609\pi$
$110$	0.0253674	−	0.0259920i	0.00241868	−	0.00247824i
$111$		0			0
$112$	−1.57228	−	14.9592i	−0.148566	−	1.41351i
$113$	4.79511	+	1.01923i	0.451086	+	0.0958812i	0.427852	−	0.903849i	$-0.359270\pi$
$113$	4.79511	+	1.01923i	0.451086	+	0.0958812i	0.0232337	+	0.999730i	$0.492604\pi$
$114$		0			0
$115$	0.000866992	−	0.00824888i	8.08475e−5	−	0.000769212i
$116$	0.596843	+	0.433632i	0.0554155	+	0.0402617i
$117$		0			0
$118$	3.56636	+	10.9761i	0.328310	+	1.01044i
$119$	−15.9933	−	7.12068i	−1.46610	−	0.652752i
$120$		0			0
$121$	−0.267531	−	10.9967i	−0.0243210	−	0.999704i
$122$	−11.6073	+	20.1044i	−1.05088	+	1.82017i
$123$		0			0
$124$	5.83850	−	6.48431i	0.524312	−	0.582308i
$125$	0.0168469	−	0.0518494i	0.00150683	−	0.00463756i
$126$		0			0
$127$	−6.99098	−	5.07925i	−0.620349	−	0.450710i	0.232694	−	0.972550i	$-0.425246\pi$
$127$	−6.99098	−	5.07925i	−0.620349	−	0.450710i	−0.853043	+	0.521840i	$0.825246\pi$
$128$	0.544047	−	0.115641i	0.0480874	−	0.0102213i
$129$		0			0
$130$	−0.00404460	−	0.0384818i	−0.000354735	−	0.00337508i
$131$	−3.05256	+	5.28719i	−0.266704	+	0.461944i	−0.968009	−	0.250917i	$-0.919268\pi$
$131$	−3.05256	+	5.28719i	−0.266704	+	0.461944i	0.701305	+	0.712861i	$0.252601\pi$
$132$		0			0
$133$	−1.31095	−	2.27062i	−0.113673	−	0.196888i
$134$	−22.1312	+	16.0793i	−1.91185	+	1.38904i
$135$		0			0
$136$	0.0982761	−	0.302463i	0.00842711	−	0.0259360i
$137$	0.0999601	−	0.951057i	0.00854017	−	0.0812543i	−0.989422	−	0.145068i	$-0.953660\pi$
$137$	0.0999601	−	0.951057i	0.00854017	−	0.0812543i	0.997962	+	0.0638141i	$0.0203265\pi$
$138$		0			0
$139$	2.80501	+	3.11528i	0.237918	+	0.264234i	0.850265	−	0.526354i	$-0.176441\pi$
$139$	2.80501	+	3.11528i	0.237918	+	0.264234i	−0.612348	+	0.790589i	$0.709775\pi$
$140$	−0.0415314	−	0.00882777i	−0.00351004	−	0.000746082i
$141$		0			0
$142$	2.80188	+	4.85300i	0.235128	+	0.407254i
$143$	−9.19653	−	7.26381i	−0.769053	−	0.607431i
$144$		0			0
$145$	−0.00159925	+	0.00116192i	−0.000132810	+	9.64924e-5i
$146$	−0.0898058	+	0.0997395i	−0.00743238	+	0.00825450i
$147$		0			0
$148$	11.4677	−	5.10574i	0.942637	−	0.419689i
$149$	19.2106	−	8.55310i	1.57379	−	0.700697i	0.580279	−	0.814418i	$-0.302944\pi$
$149$	19.2106	−	8.55310i	1.57379	−	0.700697i	0.993513	+	0.113721i	$0.0362769\pi$
$150$		0			0
$151$	−9.27670	+	10.3028i	−0.754927	+	0.838431i	−0.991078	−	0.133285i	$-0.957447\pi$
$151$	−9.27670	+	10.3028i	−0.754927	+	0.838431i	0.236151	+	0.971716i	$0.424114\pi$
$152$	0.0385327	−	0.0279957i	0.00312542	−	0.00227075i
$153$		0			0
$154$	−21.2160	+	14.1476i	−1.70963	+	1.14005i
$155$	0.0116900	+	0.0202478i	0.000938967	+	0.00162634i
$156$		0			0
$157$	7.91818	+	1.68306i	0.631939	+	0.134323i	0.512735	−	0.858547i	$-0.328632\pi$
$157$	7.91818	+	1.68306i	0.631939	+	0.134323i	0.119204	+	0.992870i	$0.461966\pi$
$158$	4.63122	+	5.14350i	0.368440	+	0.409195i
$159$		0			0
$160$	−0.00457725	+	0.0435496i	−0.000361863	+	0.00344290i
$161$	−1.79959	+	5.53857i	−0.141828	+	0.436501i
$162$		0			0
$163$	1.34265	−	0.975494i	0.105165	−	0.0764066i	−0.533960	−	0.845510i	$-0.679297\pi$
$163$	1.34265	−	0.975494i	0.105165	−	0.0764066i	0.639125	+	0.769103i	$0.279297\pi$
$164$	−6.79350	−	11.7667i	−0.530484	−	0.918824i
$165$		0			0
$166$	7.71405	−	13.3611i	0.598726	−	1.03702i
$167$	0.350251	+	3.33242i	0.0271032	+	0.257870i	0.999680	+	0.0252888i	$0.00805052\pi$
$167$	0.350251	+	3.33242i	0.0271032	+	0.257870i	−0.972577	+	0.232581i	$0.925283\pi$
$168$		0			0
$169$	0.503375	−	0.106996i	0.0387211	−	0.00823043i
$170$	0.0405188	+	0.0294386i	0.00310765	+	0.00225784i
$171$		0			0
$172$	4.59860	−	14.1530i	0.350640	−	1.07916i
$173$	1.09514	−	1.21627i	0.0832616	−	0.0924714i	−0.700074	−	0.714070i	$-0.746850\pi$
$173$	1.09514	−	1.21627i	0.0832616	−	0.0924714i	0.783336	+	0.621599i	$0.213516\pi$
$174$		0			0
$175$	−9.56946	+	16.5748i	−0.723383	+	1.25294i
$176$	8.32443	+	10.0280i	0.627478	+	0.755886i
$177$		0			0
$178$	1.64661	+	0.733116i	0.123418	+	0.0549494i
$179$	−1.11211	−	3.42274i	−0.0831233	−	0.255827i	0.900854	−	0.434123i	$-0.142942\pi$
$179$	−1.11211	−	3.42274i	−0.0831233	−	0.255827i	−0.983977	+	0.178296i	$0.942942\pi$
$180$		0			0
$181$	−18.4979	−	13.4395i	−1.37494	−	0.998952i	−0.997333	−	0.0729853i	$-0.976747\pi$
$181$	−18.4979	−	13.4395i	−1.37494	−	0.998952i	−0.377606	−	0.925966i	$-0.623253\pi$
$182$	−2.83979	+	27.0188i	−0.210499	+	2.00277i
$183$		0			0
$184$	−0.103479	−	0.0219952i	−0.00762859	−	0.00162151i
$185$	0.00351590	+	0.0334515i	0.000258494	+	0.00245940i
$186$		0			0
$187$	14.9522	−	2.55497i	1.09341	−	0.186838i
$188$	−13.4692			−0.982346
$189$		0			0
$190$	0.00231786	+	0.00713365i	0.000168155	+	0.000517529i
$191$	2.79498	−	0.594091i	0.202237	−	0.0429869i	−0.105679	−	0.994400i	$-0.533702\pi$
$191$	2.79498	−	0.594091i	0.202237	−	0.0429869i	0.307916	+	0.951413i	$0.400368\pi$
$192$		0			0
$193$	15.6199	−	6.95442i	1.12434	−	0.500590i	0.241568	−	0.970384i	$-0.422338\pi$
$193$	15.6199	−	6.95442i	1.12434	−	0.500590i	0.882776	+	0.469794i	$0.155672\pi$
$194$	−20.4963	−	22.7635i	−1.47155	−	1.63432i
$195$		0			0
$196$	14.2231	+	6.33252i	1.01593	+	0.452323i
$197$	15.4052			1.09757			0.548787	−	0.835962i	$-0.315090\pi$
$197$	15.4052			1.09757			0.548787	+	0.835962i	$0.315090\pi$
$198$		0			0
$199$	−6.44464			−0.456848			−0.228424	−	0.973562i	$-0.573357\pi$
$199$	−6.44464			−0.456848			−0.228424	+	0.973562i	$0.573357\pi$
$200$	−0.317618	−	0.141413i	−0.0224590	−	0.00999938i
$201$		0			0
$202$	14.8846	+	16.5310i	1.04728	+	1.16312i
$203$	1.26794	−	0.564524i	0.0889921	−	0.0396218i
$204$		0			0
$205$	0.0356110	−	0.00756935i	0.00248718	−	0.000528667i
$206$	2.92448	+	9.00061i	0.203758	+	0.627102i
$207$		0			0
$208$	13.8850			0.962750
$209$	2.03654	+	1.00666i	0.140870	+	0.0696323i
$210$		0			0
$211$	−0.355399	−	3.38140i	−0.0244667	−	0.232785i	−0.999921	−	0.0125825i	$-0.995995\pi$
$211$	−0.355399	−	3.38140i	−0.0244667	−	0.232785i	0.975454	−	0.220203i	$-0.0706719\pi$
$212$	26.5066	+	5.63416i	1.82048	+	0.386956i
$213$		0			0
$214$	−3.37383	+	32.0999i	−0.230631	+	2.19430i
$215$	0.0322595	+	0.0234379i	0.00220008	+	0.00159845i
$216$		0			0
$217$	−5.07270	−	15.6122i	−0.344357	−	1.05982i
$218$	34.1607	+	15.2093i	2.31366	+	1.03011i
$219$		0			0
$220$	0.0341826	−	0.0136007i	0.00230459	−	0.000916961i
$221$	8.08034	−	13.9956i	0.543542	−	0.941443i
$222$		0			0
$223$	−7.30782	+	8.11615i	−0.489368	+	0.543498i	−0.936361	−	0.351040i	$-0.885828\pi$
$223$	−7.30782	+	8.11615i	−0.489368	+	0.543498i	0.446993	+	0.894538i	$0.352495\pi$
$224$	9.50087	−	29.2407i	0.634803	−	1.95372i
$225$		0			0
$226$	7.96623	+	5.78780i	0.529906	+	0.384999i
$227$	−3.90514	+	0.830064i	−0.259194	+	0.0550933i	−0.335676	−	0.941978i	$-0.608965\pi$
$227$	−3.90514	+	0.830064i	−0.259194	+	0.0550933i	0.0764820	+	0.997071i	$0.475631\pi$
$228$		0			0
$229$	0.733140	+	6.97536i	0.0484473	+	0.460945i	0.991672	+	0.128790i	$0.0411092\pi$
$229$	0.733140	+	6.97536i	0.0484473	+	0.460945i	−0.943225	+	0.332155i	$0.892224\pi$
$230$	0.00833013	−	0.0144282i	0.000549273	−	0.000951368i
$231$		0			0
$232$	0.0126066	+	0.0218352i	0.000827661	+	0.00143355i
$233$	10.6515	−	7.73874i	0.697800	−	0.506981i	−0.181415	−	0.983407i	$-0.558068\pi$
$233$	10.6515	−	7.73874i	0.697800	−	0.506981i	0.879215	+	0.476425i	$0.158068\pi$
$234$		0			0
$235$	0.0111527	−	0.0343246i	0.000727525	−	0.00223909i
$236$	−1.22197	+	11.6262i	−0.0795433	+	0.756804i
$237$		0			0
$238$	−23.5299	−	26.1326i	−1.52522	−	1.69393i
$239$	0.752998	+	0.160055i	0.0487074	+	0.0103531i	0.232201	−	0.972668i	$-0.425407\pi$
$239$	0.752998	+	0.160055i	0.0487074	+	0.0103531i	−0.183494	+	0.983021i	$0.558741\pi$
$240$		0			0
$241$	4.56133	+	7.90045i	0.293821	+	0.508913i	0.974710	−	0.223474i	$-0.0717397\pi$
$241$	4.56133	+	7.90045i	0.293821	+	0.508913i	−0.680889	+	0.732387i	$0.738406\pi$
$242$	8.49327	−	20.3974i	0.545968	−	1.31119i
$243$		0			0
$244$	−19.0239	+	13.8217i	−1.21788	+	0.884844i
$245$	−0.0279145	+	0.0310022i	−0.00178339	+	0.00198066i
$246$		0			0
$247$	2.21104	−	0.984417i	0.140685	−	0.0626369i
$248$	0.272423	−	0.121291i	0.0172989	−	0.00770197i
$249$		0			0
$250$	0.0732740	−	0.0813790i	0.00463426	−	0.00514686i
$251$	−14.9812	+	10.8845i	−0.945607	+	0.687024i	−0.949764	−	0.312968i	$-0.898677\pi$
$251$	−14.9812	+	10.8845i	−0.945607	+	0.687024i	0.00415685	+	0.999991i	$0.498677\pi$
$252$		0			0
$253$	−1.36515	−	4.85771i	−0.0858263	−	0.305402i
$254$	−8.67864	−	15.0318i	−0.544546	−	0.943182i
$255$		0			0
$256$	−15.0946	−	3.20845i	−0.943412	−	0.200528i
$257$	−7.54216	−	8.37642i	−0.470467	−	0.522507i	0.460475	−	0.887672i	$-0.347679\pi$
$257$	−7.54216	−	8.37642i	−0.470467	−	0.522507i	−0.930942	+	0.365166i	$0.881012\pi$
$258$		0			0
$259$	2.46858	−	23.4869i	0.153390	−	1.45941i
$260$	0.0121117	−	0.0372760i	0.000751136	−	0.00231176i
$261$		0			0
$262$	−9.92096	+	7.20800i	−0.612919	+	0.445311i
$263$	2.26891	+	3.92986i	0.139907	+	0.242326i	0.927461	−	0.373920i	$-0.121986\pi$
$263$	2.26891	+	3.92986i	0.139907	+	0.242326i	−0.787554	+	0.616245i	$0.788653\pi$
$264$		0			0
$265$	−0.0363058	+	0.0628836i	−0.00223025	+	0.00386291i
$266$	−0.550491	−	5.23758i	−0.0337528	−	0.321136i
$267$		0			0
$268$	−27.1040	+	5.76114i	−1.65564	+	0.351917i
$269$	−24.5064	−	17.8050i	−1.49418	−	1.08559i	−0.972628	−	0.232370i	$-0.925352\pi$
$269$	−24.5064	−	17.8050i	−1.49418	−	1.08559i	−0.521555	−	0.853218i	$-0.674648\pi$
$270$		0			0
$271$	−2.67794	+	8.24184i	−0.162673	+	0.500656i	−0.998857	−	0.0477926i	$-0.984781\pi$
$271$	−2.67794	+	8.24184i	−0.162673	+	0.500656i	0.836184	+	0.548449i	$0.184781\pi$
$272$	−12.0258	+	13.3560i	−0.729171	+	0.809827i
$273$		0			0
$274$	0.960425	−	1.66350i	0.0580214	−	0.100496i
$275$	−1.06922	−	16.5485i	−0.0644764	−	0.997913i
$276$		0			0
$277$	12.0132	+	5.34863i	0.721804	+	0.321368i	0.734554	−	0.678551i	$-0.237392\pi$
$277$	12.0132	+	5.34863i	0.721804	+	0.321368i	−0.0127492	+	0.999919i	$0.504058\pi$
$278$	2.60200	+	8.00812i	0.156057	+	0.480295i
$279$		0			0
$280$	−0.00117396		0.000852933i	−7.01576e−5		5.09725e-5i
$281$	1.20858	−	11.4989i	0.0720979	−	0.685966i	−0.897459	−	0.441099i	$-0.854589\pi$
$281$	1.20858	−	11.4989i	0.0720979	−	0.685966i	0.969557	−	0.244867i	$-0.0787444\pi$
$282$		0			0
$283$	14.1760	+	3.01320i	0.842676	+	0.179116i	0.608972	−	0.793192i	$-0.291582\pi$
$283$	14.1760	+	3.01320i	0.842676	+	0.179116i	0.233704	+	0.972308i	$0.424915\pi$
$284$	0.593329	+	5.64515i	0.0352076	+	0.334978i
$285$		0			0
$286$	−10.9410	−	20.8424i	−0.646956	−	1.23244i
$287$	−25.5618			−1.50886
$288$		0			0
$289$	1.21068	+	3.72610i	0.0712166	+	0.219182i
$290$	−0.00388387		0.000825541i	−0.000228068		4.84774e-5i
$291$		0			0
$292$	−0.124195	+	0.0552954i	−0.00726799	+	0.00323592i
$293$	−1.28353	−	1.42550i	−0.0749845	−	0.0832787i	0.704485	−	0.709719i	$-0.251178\pi$
$293$	−1.28353	−	1.42550i	−0.0749845	−	0.0832787i	−0.779470	+	0.626440i	$0.784511\pi$
$294$		0			0
$295$	−0.0286162	−	0.0127407i	−0.00166610	−	0.000741794i
$296$	0.429012			0.0249358
$297$		0			0
$298$	42.2388			2.44683
$299$	−4.91103	−	2.18653i	−0.284012	−	0.126450i
$300$		0			0
$301$	−18.7336	−	20.8058i	−1.07979	−	1.19922i
$302$	−25.4398	+	11.3265i	−1.46390	+	0.651769i
$303$		0			0
$304$	−2.63278	+	0.559614i	−0.151000	+	0.0320960i
$305$	−0.0194707	−	0.0599246i	−0.00111489	−	0.00343127i
$306$		0			0
$307$	−6.24046			−0.356162			−0.178081	−	0.984016i	$-0.556989\pi$
$307$	−6.24046			−0.356162			−0.178081	+	0.984016i	$0.556989\pi$
$308$	−25.4612	+	4.35071i	−1.45079	+	0.247905i
$309$		0			0
$310$	0.00490888	+	0.0467048i	0.000278805	+	0.00265266i
$311$	−16.2485	−	3.45372i	−0.921367	−	0.195843i	−0.277275	−	0.960791i	$-0.589431\pi$
$311$	−16.2485	−	3.45372i	−0.921367	−	0.195843i	−0.644092	+	0.764948i	$0.722765\pi$
$312$		0			0
$313$	0.485517	−	4.61938i	0.0274430	−	0.261103i	−0.972194	−	0.234175i	$-0.924761\pi$
$313$	0.485517	−	4.61938i	0.0274430	−	0.261103i	0.999637	−	0.0269275i	$-0.00857233\pi$
$314$	13.1547	+	9.55742i	0.742361	+	0.539357i
$315$		0			0
$316$	2.16645	+	6.66765i	0.121872	+	0.375085i
$317$	0.557636	+	0.248276i	0.0313200	+	0.0139445i	0.422337	−	0.906439i	$-0.361210\pi$
$317$	0.557636	+	0.248276i	0.0313200	+	0.0139445i	−0.391017	+	0.920383i	$0.627877\pi$
$318$		0			0
$319$	−0.642661	+	1.01646i	−0.0359821	+	0.0569110i
$320$	−0.0225554	+	0.0390672i	−0.00126089	+	0.00218392i
$321$		0			0
$322$	−7.82715	+	8.69293i	−0.436190	+	0.484438i
$323$	−0.968068	+	2.97941i	−0.0538647	+	0.165779i
$324$		0			0
$325$	−14.2931	−	10.3845i	−0.792838	−	0.576030i
$326$	3.26070	−	0.693084i	0.180594	−	0.0383864i
$327$		0			0
$328$	−0.0485381	−	0.461809i	−0.00268007	−	0.0254991i
$329$	−12.6701	+	21.9453i	−0.698525	+	1.20988i
$330$		0			0
$331$	−12.6396	−	21.8924i	−0.694735	−	1.20332i	−0.970270	−	0.242026i	$-0.922188\pi$
$331$	−12.6396	−	21.8924i	−0.694735	−	1.20332i	0.275535	−	0.961291i	$-0.411145\pi$
$332$	12.6430	−	9.18571i	0.693877	−	0.504131i
$333$		0			0
$334$	−2.07983	+	6.40107i	−0.113803	+	0.350251i
$335$	0.00776104	−	0.0738414i	0.000424031	−	0.00403438i
$336$		0			0
$337$	−18.8483	−	20.9332i	−1.02673	−	1.14030i	−0.990013	−	0.140977i	$-0.954976\pi$
$337$	−18.8483	−	20.9332i	−1.02673	−	1.14030i	−0.0367201	−	0.999326i	$-0.511691\pi$
$338$	1.01110	+	0.214915i	0.0549964	+	0.0116899i
$339$		0			0
$340$	0.0253659	+	0.0439351i	0.00137566	+	0.00238271i
$341$	11.1617	+	8.81599i	0.604440	+	0.477412i
$342$		0			0
$343$	2.01937	−	1.46716i	0.109036	−	0.0792191i
$344$	0.340313	−	0.377956i	0.0183485	−	0.0203780i
$345$		0			0
$346$	3.00323	−	1.33712i	0.161455	−	0.0718842i
$347$	25.1166	−	11.1826i	1.34833	−	0.600314i	0.399681	−	0.916654i	$-0.369121\pi$
$347$	25.1166	−	11.1826i	1.34833	−	0.600314i	0.948646	+	0.316340i	$0.102454\pi$
$348$		0			0
$349$	3.09958	−	3.44243i	0.165917	−	0.184269i	−0.654453	−	0.756103i	$-0.727101\pi$
$349$	3.09958	−	3.44243i	0.165917	−	0.184269i	0.820370	+	0.571834i	$0.193768\pi$
$350$	−31.1011	+	22.5963i	−1.66243	+	1.20782i
$351$		0			0
$352$	7.20726	+	25.6461i	0.384148	+	1.36694i
$353$	14.5846	+	25.2614i	0.776263	+	1.34453i	0.934082	+	0.357058i	$0.116220\pi$
$353$	14.5846	+	25.2614i	0.776263	+	1.34453i	−0.157820	+	0.987468i	$0.550446\pi$
$354$		0			0
$355$	−0.0148772	−	0.00316225i	−0.000789601	−	0.000167835i
$356$	1.22166	+	1.35680i	0.0647481	+	0.0719100i
$357$		0			0
$358$	0.755619	−	7.18923i	0.0399357	−	0.379963i
$359$	5.50299	−	16.9365i	0.290437	−	0.893872i	−0.694280	−	0.719705i	$-0.744277\pi$
$359$	5.50299	−	16.9365i	0.290437	−	0.893872i	0.984716	−	0.174167i	$-0.0557231\pi$
$360$		0			0
$361$	14.9918	−	10.8921i	0.789040	−	0.573271i
$362$	−22.9634	−	39.7738i	−1.20693	−	2.09046i
$363$		0			0
$364$	−13.7595	+	23.8322i	−0.721195	+	1.24915i
$365$	−3.80773e−5	0	0.000362281i	−1.99306e−6	0	1.89627e-5i
$366$		0			0
$367$	−22.5580	+	4.79484i	−1.17752	+	0.250289i	−0.754789	−	0.655968i	$-0.772261\pi$
$367$	−22.5580	+	4.79484i	−1.17752	+	0.250289i	−0.422728	+	0.906257i	$0.638927\pi$
$368$	4.83664	+	3.51402i	0.252127	+	0.183181i
$369$		0			0
$370$	−0.0208778	+	0.0642553i	−0.00108539	+	0.00334047i
$371$	34.1136	−	37.8870i	1.77109	−	1.96700i
$372$		0			0
$373$	−1.01044	+	1.75014i	−0.0523188	+	0.0906188i	−0.890999	−	0.454006i	$-0.849995\pi$
$373$	−1.01044	+	1.75014i	−0.0523188	+	0.0906188i	0.838680	+	0.544625i	$0.183328\pi$
$374$	29.5244	+	7.52742i	1.52667	+	0.389234i
$375$		0			0
$376$	−0.420531	−	0.187232i	−0.0216872	−	0.00965577i
$377$	0.395916	+	1.21850i	0.0203907	+	0.0627561i
$378$		0			0
$379$	4.84822	+	3.52244i	0.249036	+	0.180935i	0.705300	−	0.708909i	$-0.250812\pi$
$379$	4.84822	+	3.52244i	0.249036	+	0.180935i	−0.456263	+	0.889845i	$0.650812\pi$
$380$	−0.000794185		0.00755616i	−4.07408e−5		0.000387623i
$381$		0			0
$382$	5.61409	+	1.19331i	0.287242	+	0.0610552i
$383$	−1.78867	−	17.0180i	−0.0913965	−	0.869580i	−0.940143	−	0.340780i	$-0.889309\pi$
$383$	−1.78867	−	17.0180i	−0.0913965	−	0.869580i	0.848747	−	0.528800i	$-0.177358\pi$
$384$		0			0
$385$	0.00999508	−	0.0684871i	0.000509396	−	0.00349043i
$386$	34.3439			1.74806
$387$		0			0
$388$	−9.58803	−	29.5089i	−0.486758	−	1.49809i
$389$	−21.8061	+	4.63503i	−1.10561	+	0.235005i	−0.724330	−	0.689453i	$-0.757851\pi$
$389$	−21.8061	+	4.63503i	−1.10561	+	0.235005i	−0.381283	+	0.924458i	$0.624518\pi$
$390$		0			0
$391$	6.35668	−	2.83018i	0.321471	−	0.143128i
$392$	0.356040	+	0.395422i	0.0179827	+	0.0199718i
$393$		0			0
$394$	28.2682	+	12.5858i	1.42413	+	0.634065i
$395$	−0.0187855			−0.000945201
$396$		0			0
$397$	−10.2639			−0.515129			−0.257564	−	0.966261i	$-0.582920\pi$
$397$	−10.2639			−0.515129			−0.257564	+	0.966261i	$0.582920\pi$
$398$	−11.8258	−	5.26518i	−0.592773	−	0.263919i
$399$		0			0
$400$	13.1469	+	14.6011i	0.657344	+	0.730055i
$401$	−11.0226	+	4.90756i	−0.550441	+	0.245072i	−0.663060	−	0.748566i	$-0.730743\pi$
$401$	−11.0226	+	4.90756i	−0.550441	+	0.245072i	0.112619	+	0.993638i	$0.464076\pi$
$402$		0			0
$403$	14.8222	−	3.15055i	0.738346	−	0.156940i
$404$	6.96290	+	21.4296i	0.346417	+	1.06616i
$405$		0			0
$406$	2.78786			0.138359
$407$	9.51082	+	18.1179i	0.471434	+	0.898071i
$408$		0			0
$409$	1.73071	+	16.4666i	0.0855780	+	0.814220i	0.950167	+	0.311741i	$0.100912\pi$
$409$	1.73071	+	16.4666i	0.0855780	+	0.814220i	−0.864589	+	0.502479i	$0.832421\pi$
$410$	0.0715296	+	0.0152041i	0.00353259	+	0.000750876i
$411$		0			0
$412$	−1.00203	+	9.53370i	−0.0493666	+	0.469692i
$413$	17.7930	+	12.9274i	0.875537	+	0.636115i
$414$		0			0
$415$	0.0129399	+	0.0398251i	0.000635197	+	0.00195494i
$416$	25.9276	+	11.5437i	1.27120	+	0.565977i
$417$		0			0
$418$	2.91458	+	3.51103i	0.142557	+	0.171730i
$419$	−5.94979	+	10.3053i	−0.290666	+	0.503449i	−0.973967	−	0.226688i	$-0.927210\pi$
$419$	−5.94979	+	10.3053i	−0.290666	+	0.503449i	0.683301	+	0.730137i	$0.260544\pi$
$420$		0			0
$421$	−0.332418	+	0.369187i	−0.0162011	+	0.0179931i	−0.751191	−	0.660085i	$-0.770520\pi$
$421$	−0.332418	+	0.369187i	−0.0162011	+	0.0179931i	0.734990	+	0.678078i	$0.237187\pi$
$422$	2.11041	−	6.49516i	0.102733	−	0.316179i
$423$		0			0
$424$	0.749259	+	0.544369i	0.0363873	+	0.0264369i
$425$	22.3682	−	4.75450i	1.08502	−	0.230627i
$426$		0			0
$427$	4.62428	+	43.9971i	0.223785	+	2.12917i
$428$	−16.3471	+	28.3140i	−0.790167	+	1.36861i
$429$		0			0
$430$	0.0400471	+	0.0693636i	0.00193124	+	0.00334501i
$431$	−3.57966	+	2.60077i	−0.172426	+	0.125275i	−0.670651	−	0.741773i	$-0.733985\pi$
$431$	−3.57966	+	2.60077i	−0.172426	+	0.125275i	0.498225	+	0.867048i	$0.333985\pi$
$432$		0			0
$433$	8.68600	−	26.7328i	0.417423	−	1.28469i	−0.492643	−	0.870231i	$-0.663969\pi$
$433$	8.68600	−	26.7328i	0.417423	−	1.28469i	0.910066	−	0.414463i	$-0.136031\pi$
$434$	3.44661	−	32.7924i	0.165443	−	1.57408i
$435$		0			0
$436$	25.3448	+	28.1483i	1.21380	+	1.34806i
$437$	1.01932	+	0.216663i	0.0487607	+	0.0103644i
$438$		0			0
$439$	−5.45750	−	9.45266i	−0.260472	−	0.451151i	0.705895	−	0.708316i	$-0.250545\pi$
$439$	−5.45750	−	9.45266i	−0.260472	−	0.451151i	−0.966367	+	0.257165i	$0.917212\pi$
$440$	0.00125630		5.05280e-5i	5.98915e−5		2.40883e-6i
$441$		0			0
$442$	26.2614	−	19.0800i	1.24913	−	0.907545i
$443$	−15.5140	+	17.2300i	−0.737091	+	0.818623i	−0.988810	−	0.149178i	$-0.952337\pi$
$443$	−15.5140	+	17.2300i	−0.737091	+	0.818623i	0.251719	+	0.967800i	$0.419004\pi$
$444$		0			0
$445$	−0.00446918	+	0.00198980i	−0.000211859	+	9.43258e-5i
$446$	−20.0405	+	8.92260i	−0.948945	+	0.422497i
$447$		0			0
$448$	21.1935	−	23.5378i	1.00130	−	1.11206i
$449$	−11.4567	+	8.32381i	−0.540677	+	0.392825i	−0.824336	−	0.566100i	$-0.808452\pi$
$449$	−11.4567	+	8.32381i	−0.540677	+	0.392825i	0.283659	+	0.958925i	$0.408452\pi$
$450$		0			0
$451$	18.4269	−	12.2877i	0.867690	−	0.578607i
$452$	4.98709	+	8.63788i	0.234573	+	0.406292i
$453$		0			0
$454$	−7.84401	−	1.66730i	−0.368138	−	0.0782501i
$455$	−0.0493402	−	0.0547978i	−0.00231310	−	0.00256896i
$456$		0			0
$457$	−0.181144	+	1.72347i	−0.00847357	+	0.0806206i	−0.997941	−	0.0641323i	$-0.979572\pi$
$457$	−0.181144	+	1.72347i	−0.00847357	+	0.0806206i	0.989468	+	0.144753i	$0.0462387\pi$
$458$	−4.35348	+	13.3986i	−0.203425	+	0.626076i
$459$		0			0
$460$	0.0136528	−	0.00991933i	0.000636564	−	0.000462491i
$461$	−2.96288	−	5.13186i	−0.137995	−	0.239015i	0.788742	−	0.614724i	$-0.210733\pi$
$461$	−2.96288	−	5.13186i	−0.137995	−	0.239015i	−0.926738	+	0.375709i	$0.877399\pi$
$462$		0			0
$463$	−9.62398	+	16.6692i	−0.447264	+	0.774685i	−0.998207	−	0.0598586i	$-0.980935\pi$
$463$	−9.62398	+	16.6692i	−0.447264	+	0.774685i	0.550943	+	0.834543i	$0.314268\pi$
$464$	−0.148936	−	1.41703i	−0.00691416	−	0.0657838i
$465$		0			0
$466$	25.8676	−	5.49834i	1.19830	−	0.254706i
$467$	28.3349	+	20.5865i	1.31118	+	0.952631i	0.999997	+	0.00228250i	$0.000726542\pi$
$467$	28.3349	+	20.5865i	1.31118	+	0.952631i	0.311187	+	0.950349i	$0.399273\pi$
$468$		0			0
$469$	−16.1094	+	49.5795i	−0.743861	+	2.28937i
$470$	0.0485078	−	0.0538734i	0.00223750	−	0.00248499i
$471$		0			0
$472$	−0.199765	+	0.346003i	−0.00919493	+	0.0159261i
$473$	23.5062	+	5.99304i	1.08081	+	0.275560i
$474$		0			0
$475$	3.12869	+	1.39298i	0.143554	+	0.0639144i
$476$	−11.0071	−	33.8764i	−0.504510	−	1.55272i
$477$		0			0
$478$	1.25097	+	0.908886i	0.0572182	+	0.0415715i
$479$	1.07444	−	10.2226i	0.0490924	−	0.467083i	−0.942166	−	0.335147i	$-0.891214\pi$
$479$	1.07444	−	10.2226i	0.0490924	−	0.467083i	0.991258	−	0.131936i	$-0.0421194\pi$
$480$		0			0
$481$	21.3239	+	4.53254i	0.972288	+	0.206666i
$482$	1.91539	+	18.2237i	0.0872436	+	0.830067i
$483$		0			0
$484$	16.2630	−	15.3758i	0.739229	−	0.698898i
$485$	0.0831387			0.00377513
$486$		0			0
$487$	8.56722	+	26.3672i	0.388218	+	1.19481i	0.934119	+	0.356962i	$0.116187\pi$
$487$	8.56722	+	26.3672i	0.388218	+	1.19481i	−0.545901	+	0.837849i	$0.683813\pi$
$488$	−0.786089	+	0.167088i	−0.0355846	+	0.00756373i
$489$		0			0
$490$	−0.0765510	+	0.0340827i	−0.00345822	+	0.00153970i
$491$	−1.85183	−	2.05667i	−0.0835719	−	0.0928160i	0.699908	−	0.714233i	$-0.253224\pi$
$491$	−1.85183	−	2.05667i	−0.0835719	−	0.0928160i	−0.783480	+	0.621417i	$0.786557\pi$
$492$		0			0
$493$	−1.51498	−	0.674514i	−0.0682315	−	0.0303786i
$494$	4.86146			0.218728
$495$		0			0
$496$	−16.8520			−0.756677
$497$	9.75569	+	4.34351i	0.437603	+	0.194833i
$498$		0			0
$499$	−15.1282	−	16.8016i	−0.677233	−	0.752144i	0.302347	−	0.953198i	$-0.402230\pi$
$499$	−15.1282	−	16.8016i	−0.677233	−	0.752144i	−0.979580	+	0.201054i	$0.935563\pi$
$500$	0.101333	−	0.0451164i	0.00453175	−	0.00201766i
$501$		0			0
$502$	−36.3827	+	7.73339i	−1.62384	+	0.345158i
$503$	−2.92888	−	9.01417i	−0.130592	−	0.401922i	0.864286	−	0.503001i	$-0.167771\pi$
$503$	−2.92888	−	9.01417i	−0.130592	−	0.401922i	−0.994878	+	0.101078i	$0.967771\pi$
$504$		0			0
$505$	−0.0603760			−0.00268670
$506$	1.46366	−	10.0291i	0.0650676	−	0.445849i
$507$		0			0
$508$	−1.83780	−	17.4855i	−0.0815391	−	0.775793i
$509$	−21.2561	−	4.51813i	−0.942162	−	0.200263i	−0.288870	−	0.957368i	$-0.593279\pi$
$509$	−21.2561	−	4.51813i	−0.942162	−	0.200263i	−0.653292	+	0.757106i	$0.726613\pi$
$510$		0			0
$511$	−0.0267348	+	0.254365i	−0.00118268	+	0.0112524i
$512$	−25.9770	−	18.8734i	−1.14803	−	0.834093i
$513$		0			0
$514$	−6.99630	−	21.5324i	−0.308594	−	0.949753i
$515$	−0.0234657	−	0.0104476i	−0.00103402	−	0.000460377i
$516$		0			0
$517$	−1.41566	−	21.9105i	−0.0622608	−	0.963622i
$518$	23.7183	−	41.0813i	1.04212	−	1.80501i
$519$		0			0
$520$	0.000896310	0	0.000995453i	3.93058e−5	0	4.36535e-5i
$521$	−2.67902	+	8.24517i	−0.117370	+	0.361227i	−0.992434	−	0.122780i	$-0.960819\pi$
$521$	−2.67902	+	8.24517i	−0.117370	+	0.361227i	0.875064	+	0.484007i	$0.160819\pi$
$522$		0			0
$523$	30.2428	+	21.9727i	1.32242	+	0.960797i	0.999899	+	0.0142366i	$0.00453179\pi$
$523$	30.2428	+	21.9727i	1.32242	+	0.960797i	0.322525	+	0.946561i	$0.395468\pi$
$524$	−12.1502	+	2.58260i	−0.530782	+	0.112821i
$525$		0			0
$526$	0.952758	+	9.06488i	0.0415422	+	0.395248i
$527$	−9.80699	+	16.9862i	−0.427199	+	0.739931i
$528$		0			0
$529$	10.3427	+	17.9140i	0.449682	+	0.778872i
$530$	−0.117995	+	0.0857287i	−0.00512540	+	0.00372382i
$531$		0			0
$532$	1.64847	−	5.07346i	0.0714701	−	0.219962i
$533$	2.46647	−	23.4669i	0.106835	−	1.01647i
$534$		0			0
$535$	−0.0586189	−	0.0651029i	−0.00253432	−	0.00281464i
$536$	−0.926313	−	0.196894i	−0.0400106	−	0.00850452i
$537$		0			0
$538$	−30.4224	−	52.6931i	−1.31160	−	2.27176i
$539$	−8.80624	+	23.8023i	−0.379312	+	1.02524i
$540$		0			0
$541$	−9.09973	+	6.61134i	−0.391228	+	0.284244i	−0.765959	−	0.642890i	$-0.777735\pi$
$541$	−9.09973	+	6.61134i	−0.391228	+	0.284244i	0.374731	+	0.927134i	$0.377735\pi$
$542$	−11.6474	+	12.9358i	−0.500300	+	0.555639i
$543$		0			0
$544$	−33.5598	+	14.9418i	−1.43887	+	0.640624i
$545$	−0.0927182	+	0.0412808i	−0.00397161	+	0.00176828i
$546$		0			0
$547$	−2.85728	+	3.17333i	−0.122169	+	0.135682i	−0.801126	−	0.598496i	$-0.795765\pi$
$547$	−2.85728	+	3.17333i	−0.122169	+	0.135682i	0.678957	+	0.734178i	$0.262432\pi$
$548$	1.57410	−	1.14365i	0.0672423	−	0.0488544i
$549$		0			0
$550$	11.5579	−	31.2397i	0.492831	−	1.33207i
$551$	−0.124181	−	0.215087i	−0.00529028	−	0.00916303i
$552$		0			0
$553$	12.9014	+	2.74228i	0.548625	+	0.116614i
$554$	17.6743	+	19.6293i	0.750908	+	0.833967i
$555$		0			0
$556$	−0.891539	+	8.48243i	−0.0378097	+	0.359735i
$557$	−1.11629	+	3.43560i	−0.0472989	+	0.145571i	−0.971917	−	0.235325i	$-0.924384\pi$
$557$	−1.11629	+	3.43560i	−0.0472989	+	0.145571i	0.924618	+	0.380896i	$0.124384\pi$
$558$		0			0
$559$	20.9083	−	15.1908i	0.884328	−	0.642502i
$560$	0.0410018	+	0.0710173i	0.00173264	+	0.00300103i
$561$		0			0
$562$	11.6122	−	20.1128i	0.489829	−	0.848409i
$563$	2.24422	+	21.3524i	0.0945828	+	0.899895i	0.934208	+	0.356729i	$0.116108\pi$
$563$	2.24422	+	21.3524i	0.0945828	+	0.899895i	−0.839625	+	0.543166i	$0.817225\pi$
$564$		0			0
$565$	−0.0261419	+	0.00555663i	−0.00109980	+	0.000233769i
$566$	23.5509	+	17.1108i	0.989920	+	0.719219i
$567$		0			0
$568$	−0.0599470	+	0.184498i	−0.00251532	+	0.00774136i
$569$	−28.0406	+	31.1423i	−1.17552	+	1.30555i	−0.232589	+	0.972575i	$0.574720\pi$
$569$	−28.0406	+	31.1423i	−1.17552	+	1.30555i	−0.942935	+	0.332976i	$0.891947\pi$
$570$		0			0
$571$	−4.29723	+	7.44303i	−0.179834	+	0.311481i	−0.941823	−	0.336108i	$-0.890889\pi$
$571$	−4.29723	+	7.44303i	−0.179834	+	0.311481i	0.761990	+	0.647589i	$0.224223\pi$
$572$	−1.53739	−	23.7944i	−0.0642814	−	0.994896i
$573$		0			0
$574$	−46.9053	−	20.8836i	−1.95779	−	0.871664i
$575$	−2.35067	−	7.23461i	−0.0980297	−	0.301704i
$576$		0			0
$577$	18.9603	+	13.7755i	0.789327	+	0.573480i	0.907764	−	0.419482i	$-0.137788\pi$
$577$	18.9603	+	13.7755i	0.789327	+	0.573480i	−0.118437	+	0.992962i	$0.537788\pi$
$578$	−0.822590	+	7.82643i	−0.0342153	+	0.325536i
$579$		0			0
$580$	−0.00393410		0.000836220i	−0.000163355		3.47221e-5i
$581$	−3.07323	−	29.2399i	−0.127499	−	1.21307i
$582$		0			0
$583$	−6.37918	+	43.7107i	−0.264199	+	1.81031i
$584$	−0.00464622			−0.000192262
$585$		0			0
$586$	−1.19063	−	3.66439i	−0.0491846	−	0.151375i
$587$	−30.3501	+	6.45110i	−1.25268	+	0.266266i	−0.786037	−	0.618180i	$-0.787870\pi$
$587$	−30.3501	+	6.45110i	−1.25268	+	0.266266i	−0.466644	+	0.884445i	$0.654537\pi$
$588$		0			0
$589$	−2.68350	+	1.19477i	−0.110572	+	0.0492298i
$590$	−0.0421011	−	0.0467580i	−0.00173327	−	0.00192500i
$591$		0			0
$592$	−22.1481	−	9.86098i	−0.910282	−	0.405284i
$593$	6.08461			0.249865			0.124933	−	0.992165i	$-0.460129\pi$
$593$	6.08461			0.249865			0.124933	+	0.992165i	$0.460129\pi$
$594$		0			0
$595$	0.0954437			0.00391281
$596$	39.0862	+	17.4023i	1.60103	+	0.712826i
$597$		0			0
$598$	−7.22528	−	8.02448i	−0.295464	−	0.328146i
$599$	9.01795	−	4.01505i	0.368464	−	0.164051i	−0.214148	−	0.976801i	$-0.568698\pi$
$599$	9.01795	−	4.01505i	0.368464	−	0.164051i	0.582612	+	0.812751i	$0.302031\pi$
$600$		0			0
$601$	−25.6085	+	5.44325i	−1.04459	+	0.222035i	−0.698086	−	0.716014i	$-0.745965\pi$
$601$	−25.6085	+	5.44325i	−1.04459	+	0.222035i	−0.346504	+	0.938048i	$0.612631\pi$
$602$	−17.3778	−	53.4833i	−0.708265	−	2.17982i
$603$		0			0
$604$	−28.2076			−1.14775
$605$	0.0257171	+	0.0541756i	0.00104555	+	0.00220255i
$606$		0			0
$607$	−2.56764	−	24.4295i	−0.104217	−	0.991562i	−0.914243	−	0.405167i	$-0.867213\pi$
$607$	−2.56764	−	24.4295i	−0.104217	−	0.991562i	0.810025	−	0.586395i	$-0.199453\pi$
$608$	−5.38146	−	1.14387i	−0.218247	−	0.0463899i
$609$		0			0
$610$	0.0132292	−	0.125868i	0.000535636	−	0.00509624i
$611$	−18.9243	−	13.7493i	−0.765593	−	0.556236i
$612$		0			0
$613$	−0.502318	−	1.54598i	−0.0202884	−	0.0624414i	0.940400	−	0.340071i	$-0.110451\pi$
$613$	−0.502318	−	1.54598i	−0.0202884	−	0.0624414i	−0.960688	+	0.277630i	$0.910451\pi$
$614$	−11.4511	−	5.09837i	−0.462129	−	0.205753i
$615$		0			0
$616$	−0.855417	−	0.218094i	−0.0344657	−	0.00878725i
$617$	7.31858	−	12.6762i	0.294635	−	0.510323i	−0.680265	−	0.732966i	$-0.738135\pi$
$617$	7.31858	−	12.6762i	0.294635	−	0.510323i	0.974900	+	0.222644i	$0.0714686\pi$
$618$		0			0
$619$	23.7875	−	26.4187i	0.956099	−	1.06186i	−0.0419309	−	0.999121i	$-0.513351\pi$
$619$	23.7875	−	26.4187i	0.956099	−	1.06186i	0.998030	−	0.0627354i	$-0.0199824\pi$
$620$	−0.0146998	+	0.0452413i	−0.000590358	+	0.00181694i
$621$		0			0
$622$	−26.9940	−	19.6123i	−1.08236	−	0.786381i
$623$	3.35979	−	0.714146i	0.134607	−	0.0286116i
$624$		0			0
$625$	−2.61316	−	24.8626i	−0.104527	−	0.994504i
$626$	4.66488	−	8.07981i	0.186446	−	0.322934i
$627$		0			0
$628$	8.23519	+	14.2638i	0.328620	+	0.569187i
$629$	−22.8286	+	16.5859i	−0.910234	+	0.661324i
$630$		0			0
$631$	−5.15903	+	15.8779i	−0.205378	+	0.632088i	0.794320	+	0.607500i	$0.207827\pi$
$631$	−5.15903	+	15.8779i	−0.205378	+	0.632088i	−0.999698	+	0.0245881i	$0.992173\pi$
$632$	−0.0250453	+	0.238290i	−0.000996247	+	0.00947865i
$633$		0			0
$634$	0.820413	+	0.911161i	0.0325828	+	0.0361868i
$635$	0.0460812	+	0.00979487i	0.00182868	+	0.000388697i
$636$		0			0
$637$	13.5192	+	23.4159i	0.535650	+	0.927773i
$638$	−2.00971	+	1.34015i	−0.0795650	+	0.0530569i
$639$		0			0
$640$	−0.00245318	+	0.00178234i	−9.69703e−5	+	7.04531e-5i
$641$	−0.815333	+	0.905519i	−0.0322037	+	0.0357658i	−0.759031	−	0.651054i	$-0.774327\pi$
$641$	−0.815333	+	0.905519i	−0.0322037	+	0.0357658i	0.726828	+	0.686820i	$0.240994\pi$
$642$		0			0
$643$	−25.5140	+	11.3596i	−1.00617	+	0.447977i	−0.842592	−	0.538553i	$-0.818971\pi$
$643$	−25.5140	+	11.3596i	−1.00617	+	0.447977i	−0.163581	+	0.986530i	$0.552305\pi$
$644$	−10.8244	+	4.81934i	−0.426542	+	0.189909i
$645$		0			0
$646$	−4.21052	+	4.67625i	−0.165661	+	0.183985i
$647$	−5.14612	+	3.73887i	−0.202315	+	0.146990i	−0.684330	−	0.729173i	$-0.739905\pi$
$647$	−5.14612	+	3.73887i	−0.202315	+	0.146990i	0.482015	+	0.876163i	$0.339905\pi$
$648$		0			0
$649$	−19.0409	−	0.765822i	−0.747421	−	0.0300612i
$650$	−17.7435	−	30.7327i	−0.695958	−	1.20543i
$651$		0			0
$652$	3.30288	+	0.702049i	0.129351	+	0.0274944i
$653$	−1.59882	−	1.77567i	−0.0625667	−	0.0694874i	0.711049	−	0.703143i	$-0.248220\pi$
$653$	−1.59882	−	1.77567i	−0.0625667	−	0.0694874i	−0.773616	+	0.633655i	$0.781554\pi$
$654$		0			0
$655$	0.00347911	−	0.0331015i	0.000135940	−	0.00129338i
$656$	−8.10901	+	24.9570i	−0.316604	+	0.974406i
$657$		0			0
$658$	−41.1784	+	29.9178i	−1.60530	+	1.16632i
$659$	15.3876	+	26.6521i	0.599415	+	1.03822i	0.992907	+	0.118890i	$0.0379335\pi$
$659$	15.3876	+	26.6521i	0.599415	+	1.03822i	−0.393492	+	0.919328i	$0.628733\pi$
$660$		0			0
$661$	15.2967	−	26.4946i	0.594972	−	1.03052i	−0.398579	−	0.917134i	$-0.630497\pi$
$661$	15.2967	−	26.4946i	0.594972	−	1.03052i	0.993551	−	0.113387i	$-0.0361700\pi$
$662$	−5.30761	−	50.4986i	−0.206286	−	1.96268i
$663$		0			0
$664$	0.522423	−	0.111045i	0.0202740	−	0.00430936i
$665$	0.0115641	+	0.00840180i	0.000448436	+	0.000325808i
$666$		0			0
$667$	−0.170468	+	0.524647i	−0.00660056	+	0.0203144i
$668$	−4.56183	+	5.06642i	−0.176502	+	0.196026i
$669$		0			0
$670$	0.0745687	−	0.129157i	0.00288084	−	0.00498976i
$671$	−24.4833	−	29.4936i	−0.945168	−	1.13859i
$672$		0			0
$673$	31.0368	+	13.8185i	1.19638	+	0.532663i	0.905603	−	0.424127i	$-0.139419\pi$
$673$	31.0368	+	13.8185i	1.19638	+	0.532663i	0.290779	+	0.956790i	$0.406086\pi$
$674$	−17.4842	−	53.8108i	−0.673465	−	2.07271i
$675$		0			0
$676$	0.847087	+	0.615444i	0.0325803	+	0.0236709i
$677$	3.67398	−	34.9555i	0.141202	−	1.34345i	−0.662787	−	0.748808i	$-0.730627\pi$
$677$	3.67398	−	34.9555i	0.141202	−	1.34345i	0.803990	−	0.594643i	$-0.202707\pi$
$678$		0			0
$679$	−57.0976	−	12.1365i	−2.19121	−	0.465755i
$680$	0.000181234		0.00172433i	6.95000e−6		6.61249e-5i
$681$		0			0
$682$	13.2790	+	25.2961i	0.508478	+	0.968638i
$683$	30.2932			1.15914			0.579569	−	0.814923i	$-0.303221\pi$
$683$	30.2932			1.15914			0.579569	+	0.814923i	$0.303221\pi$
$684$		0			0
$685$	0.00161107	+	0.00495835i	6.15557e−5	+	0.000189449i
$686$	4.90415	−	1.04241i	0.187241	−	0.0397994i
$687$		0			0
$688$	−26.2564	+	11.6901i	−1.00102	+	0.445681i
$689$	31.4905	+	34.9737i	1.19969	+	1.33239i
$690$		0			0
$691$	−32.7952	−	14.6014i	−1.24759	−	0.555462i	−0.326640	−	0.945149i	$-0.605916\pi$
$691$	−32.7952	−	14.6014i	−1.24759	−	0.555462i	−0.920947	+	0.389687i	$0.872583\pi$
$692$	3.32997			0.126586
$693$		0			0
$694$	55.2244			2.09629
$695$	−0.0208782	−	0.00929556i	−0.000791954	−	0.000352601i
$696$		0			0
$697$	20.4367	+	22.6972i	0.774094	+	0.859719i
$698$	8.50008	−	3.78448i	0.321733	−	0.143245i
$699$		0			0
$700$	−38.0894	+	8.09616i	−1.43965	+	0.306006i
$701$	0.170972	+	0.526199i	0.00645754	+	0.0198743i	0.954233	−	0.299063i	$-0.0966741\pi$
$701$	0.170972	+	0.526199i	0.00645754	+	0.0198743i	−0.947776	+	0.318937i	$0.896674\pi$
$702$		0			0
$703$	−4.22598			−0.159386
$704$	−3.96314	+	27.1558i	−0.149366	+	1.02347i
$705$		0			0
$706$	6.12438	+	58.2695i	0.230494	+	2.19300i
$707$	41.4648	+	8.81361i	1.55944	+	0.331470i
$708$		0			0
$709$	1.11437	−	10.6025i	0.0418510	−	0.398186i	−0.953465	−	0.301505i	$-0.902511\pi$
$709$	1.11437	−	10.6025i	0.0418510	−	0.398186i	0.995315	−	0.0966803i	$-0.0308224\pi$
$710$	−0.0247159	−	0.0179571i	−0.000927570	−	0.000673919i
$711$		0			0
$712$	0.0192818	+	0.0593433i	0.000722616	+	0.00222398i
$713$	5.96045	+	2.65376i	0.223221	+	0.0993842i
$714$		0			0
$715$	0.0619100	+	0.0157843i	0.00231530	+	0.000590301i
$716$	3.66117	−	6.34133i	0.136824	−	0.236987i
$717$		0			0
$718$	23.9347	−	26.5822i	0.893236	−	0.992039i
$719$	14.3661	−	44.2143i	0.535765	−	1.64892i	−0.206225	−	0.978505i	$-0.566118\pi$
$719$	14.3661	−	44.2143i	0.535765	−	1.64892i	0.741990	−	0.670411i	$-0.233882\pi$
$720$		0			0
$721$	14.5906	+	10.6007i	0.543381	+	0.394789i
$722$	36.4083	−	7.73882i	1.35498	−	0.288009i
$723$		0			0
$724$	−4.86276	−	46.2660i	−0.180723	−	1.71946i
$725$	−0.906477	+	1.57006i	−0.0336657	+	0.0583107i
$726$		0			0
$727$	3.30141	+	5.71821i	0.122443	+	0.212077i	0.920730	−	0.390199i	$-0.127594\pi$
$727$	3.30141	+	5.71821i	0.122443	+	0.212077i	−0.798288	+	0.602276i	$0.794261\pi$
$728$	−0.760879	+	0.552811i	−0.0282000	+	0.0204885i
$729$		0			0
$730$	0.000226108	0	0.000695888i	8.36862e−6	0	2.57560e-5i
$731$	−3.49666	+	33.2685i	−0.129329	+	1.23048i
$732$		0			0
$733$	24.4154	+	27.1160i	0.901803	+	1.00155i	0.999980	+	0.00638498i	$0.00203242\pi$
$733$	24.4154	+	27.1160i	0.901803	+	1.00155i	−0.0981763	+	0.995169i	$0.531301\pi$
$734$	−45.3107	−	9.63109i	−1.67245	−	0.355490i
$735$		0			0
$736$	6.11002	+	10.5829i	0.225218	+	0.390090i
$737$	−12.2204	−	43.4847i	−0.450144	−	1.60178i
$738$		0			0
$739$	−8.36258	+	6.07577i	−0.307622	+	0.223501i	−0.730876	−	0.682511i	$-0.760888\pi$
$739$	−8.36258	+	6.07577i	−0.307622	+	0.223501i	0.423253	+	0.906011i	$0.360888\pi$
$740$	−0.0457926	+	0.0508578i	−0.00168337	+	0.00186957i
$741$		0			0
$742$	93.5510	−	41.6516i	3.43437	−	1.52908i
$743$	−47.5812	+	21.1845i	−1.74558	+	0.777184i	−0.752664	+	0.658405i	$0.771231\pi$
$743$	−47.5812	+	21.1845i	−1.74558	+	0.777184i	−0.992921	+	0.118779i	$0.962102\pi$
$744$		0			0
$745$	−0.0767115	+	0.0851967i	−0.00281049	+	0.00312137i
$746$	−3.28398	+	2.38595i	−0.120235	+	0.0873559i
$747$		0			0
$748$	24.2195	+	19.1296i	0.885552	+	0.699446i
$749$	30.7544	+	53.2682i	1.12374	+	1.94638i
$750$		0			0
$751$	−26.2924	−	5.58862i	−0.959423	−	0.203932i	−0.298520	−	0.954403i	$-0.596493\pi$
$751$	−26.2924	−	5.58862i	−0.959423	−	0.203932i	−0.660903	+	0.750472i	$0.729826\pi$
$752$	17.4067	+	19.3321i	0.634756	+	0.704968i
$753$		0			0
$754$	−0.269002	+	2.55939i	−0.00979649	+	0.0932074i
$755$	0.0233563	−	0.0718833i	0.000850023	−	0.00261610i
$756$		0			0
$757$	−10.2957	+	7.48027i	−0.374204	+	0.271875i	−0.758952	−	0.651146i	$-0.774288\pi$
$757$	−10.2957	+	7.48027i	−0.374204	+	0.271875i	0.384748	+	0.923022i	$0.374288\pi$
$758$	6.01860	+	10.4245i	0.218606	+	0.378636i
$759$		0			0
$760$	−0.000129832	0	0.000224875i	−4.70950e−6	0	8.15709e-6i
$761$	−0.995192	−	9.46862i	−0.0360757	−	0.343237i	−0.997640	−	0.0686582i	$-0.978128\pi$
$761$	−0.995192	−	9.46862i	−0.0360757	−	0.343237i	0.961565	−	0.274579i	$-0.0885385\pi$
$762$		0			0
$763$	69.7028	−	14.8158i	2.52341	−	0.536367i
$764$	4.70343	+	3.41724i	0.170164	+	0.123631i
$765$		0			0
$766$	10.6213	−	32.6890i	0.383764	−	1.18110i
$767$	−13.5848	+	15.0875i	−0.490519	+	0.544777i
$768$		0			0
$769$	−0.433959	+	0.751638i	−0.0156489	+	0.0271048i	−0.873744	−	0.486386i	$-0.838315\pi$
$769$	−0.433959	+	0.751638i	−0.0156489	+	0.0271048i	0.858095	+	0.513491i	$0.171648\pi$
$770$	0.0742938	−	0.117507i	0.00267736	−	0.00423465i
$771$		0			0
$772$	31.7805	+	14.1496i	1.14381	+	0.509255i
$773$	−3.78062	−	11.6355i	−0.135979	−	0.418502i	0.859762	−	0.510695i	$-0.170612\pi$
$773$	−3.78062	−	11.6355i	−0.135979	−	0.418502i	−0.995741	+	0.0921939i	$0.970612\pi$
$774$		0			0
$775$	17.3473	+	12.6036i	0.623134	+	0.452733i
$776$	0.110842	−	1.05459i	0.00397901	−	0.0378577i
$777$		0			0
$778$	−43.8005	−	9.31009i	−1.57032	−	0.333783i
$779$	0.478124	+	4.54904i	0.0171306	+	0.162986i
$780$		0			0
$781$	−9.12063	+	1.55850i	−0.326362	+	0.0557674i
$782$	13.9766			0.499802
$783$		0			0
$784$	−9.29195	−	28.5977i	−0.331855	−	1.02135i
$785$	−0.0431682	+	0.00917569i	−0.00154074	+	0.000327495i
$786$		0			0
$787$	44.9091	−	19.9948i	1.60084	−	0.712738i	0.604367	−	0.796706i	$-0.293426\pi$
$787$	44.9091	−	19.9948i	1.60084	−	0.712738i	0.996468	+	0.0839680i	$0.0267593\pi$
$788$	20.9730	+	23.2929i	0.747133	+	0.829775i
$789$		0			0
$790$	−0.0344710	−	0.0153475i	−0.00122642	−	0.000546039i
$791$	18.7648			0.667199
$792$		0			0
$793$	−40.8377			−1.45019
$794$	−18.8340	−	8.38543i	−0.668393	−	0.297588i
$795$		0			0
$796$	−8.77389	−	9.74439i	−0.310982	−	0.345381i
$797$	24.5558	−	10.9330i	0.869813	−	0.387266i	0.0772178	−	0.997014i	$-0.475396\pi$
$797$	24.5558	−	10.9330i	0.869813	−	0.387266i	0.792595	+	0.609749i	$0.208730\pi$
$798$		0			0
$799$	29.6158	−	6.29503i	1.04773	−	0.222702i
$800$	12.4103	+	38.1949i	0.438769	+	1.35039i
$801$		0			0
$802$	−24.2356			−0.855789
$803$	−0.103003	−	0.196218i	−0.00363488	−	0.00692437i
$804$		0			0
$805$	−0.00331868	−	0.0315751i	−0.000116968	−	0.00111288i
$806$	29.7724	+	6.32832i	1.04869	+	0.222905i
$807$		0			0
$808$	−0.0804946	+	0.765855i	−0.00283179	+	0.0269427i
$809$	6.63615	+	4.82145i	0.233315	+	0.169513i	0.698300	−	0.715806i	$-0.253940\pi$
$809$	6.63615	+	4.82145i	0.233315	+	0.169513i	−0.464985	+	0.885319i	$0.653940\pi$
$810$		0			0
$811$	3.68853	+	11.3521i	0.129522	+	0.398627i	0.994698	−	0.102841i	$-0.0327934\pi$
$811$	3.68853	+	11.3521i	0.129522	+	0.398627i	−0.865176	+	0.501468i	$0.832793\pi$
$812$	2.57978	+	1.14859i	0.0905325	+	0.0403076i
$813$		0			0
$814$	2.65011	+	41.0162i	0.0928862	+	1.43762i
$815$	−0.00452392	+	0.00783566i	−0.000158466	+	0.000274471i
$816$		0			0
$817$	−3.35225	+	3.72305i	−0.117280	+	0.130253i
$818$	−10.2771	+	31.6298i	−0.359332	+	1.10591i
$819$		0			0
$820$	0.0599267	+	0.0435393i	0.00209273	+	0.00152046i
$821$	−48.0311	+	10.2093i	−1.67630	+	0.356308i	−0.945332	−	0.326108i	$-0.894263\pi$
$821$	−48.0311	+	10.2093i	−1.67630	+	0.356308i	−0.730964	+	0.682416i	$0.760929\pi$
$822$		0			0
$823$	−3.50760	−	33.3725i	−0.122267	−	1.16329i	−0.867831	−	0.496859i	$-0.834486\pi$
$823$	−3.50760	−	33.3725i	−0.122267	−	1.16329i	0.745564	−	0.666434i	$-0.232180\pi$
$824$	−0.163810	+	0.283728i	−0.00570661	+	0.00988413i
$825$		0			0
$826$	22.0883	+	38.2581i	0.768552	+	1.33117i
$827$	6.95202	−	5.05094i	0.241745	−	0.175638i	−0.460315	−	0.887756i	$-0.652264\pi$
$827$	6.95202	−	5.05094i	0.241745	−	0.175638i	0.702061	+	0.712117i	$0.252264\pi$
$828$		0			0
$829$	−6.54721	+	20.1502i	−0.227394	+	0.699846i	0.770646	+	0.637264i	$0.219934\pi$
$829$	−6.54721	+	20.1502i	−0.227394	+	0.699846i	−0.998040	+	0.0625828i	$0.980066\pi$
$830$	−0.00879197	+	0.0836500i	−0.000305174	+	0.00290353i
$831$		0			0
$832$	19.5638	+	21.7278i	0.678254	+	0.753277i
$833$	−34.2329	−	7.27642i	−1.18610	−	0.252113i
$834$		0			0
$835$	−0.00913385	−	0.0158203i	−0.000316090	−	0.000547484i
$836$	1.25051	+	4.44978i	0.0432498	+	0.153899i
$837$		0			0
$838$	−19.3371	+	14.0492i	−0.667987	+	0.485321i
$839$	29.3758	−	32.6251i	1.01417	−	1.12635i	0.0222107	−	0.999753i	$-0.492930\pi$
$839$	29.3758	−	32.6251i	1.01417	−	1.12635i	0.991955	−	0.126592i	$-0.0404038\pi$
$840$		0			0
$841$	−26.3727	+	11.7419i	−0.909404	+	0.404893i
$842$	−0.911601	+	0.405871i	−0.0314158	+	0.0139872i
$843$		0			0
$844$	4.62888	−	5.14089i	0.159333	−	0.176957i
$845$	−0.00226978	+	0.00164909i	−7.80828e−5	+	5.67305e-5i
$846$		0			0
$847$	−9.75339	−	40.9606i	−0.335130	−	1.40742i
$848$	−26.1687	−	45.3255i	−0.898636	−	1.55648i
$849$		0			0
$850$	44.9295	+	9.55006i	1.54107	+	0.327564i
$851$	6.28080	+	6.97553i	0.215303	+	0.239118i
$852$		0			0
$853$	−4.46737	+	42.5042i	−0.152960	+	1.45532i	0.601449	+	0.798912i	$0.294590\pi$
$853$	−4.46737	+	42.5042i	−0.152960	+	1.45532i	−0.754408	+	0.656405i	$0.772076\pi$
$854$	−27.4595	+	84.5118i	−0.939646	+	2.89193i
$855$		0			0
$856$	−0.903967	+	0.656771i	−0.0308970	+	0.0224480i
$857$	−26.9988	−	46.7632i	−0.922260	−	1.59740i	−0.795909	−	0.605416i	$-0.793007\pi$
$857$	−26.9988	−	46.7632i	−0.922260	−	1.59740i	−0.126351	−	0.991986i	$-0.540327\pi$
$858$		0			0
$859$	13.0444	−	22.5935i	0.445068	−	0.770880i	−0.552989	−	0.833188i	$-0.686513\pi$
$859$	13.0444	−	22.5935i	0.445068	−	0.770880i	0.998057	+	0.0623086i	$0.0198463\pi$
$860$	0.00848042	+	0.0806858i	0.000289180	+	0.00275136i
$861$		0			0
$862$	−8.69340	+	1.84784i	−0.296098	+	0.0629376i
$863$	13.8707	+	10.0777i	0.472165	+	0.343048i	0.798285	−	0.602280i	$-0.205741\pi$
$863$	13.8707	+	10.0777i	0.472165	+	0.343048i	−0.326119	+	0.945329i	$0.605741\pi$
$864$		0			0
$865$	−0.00275727	+	0.00848599i	−9.37498e−5	+	0.000288532i
$866$	37.7789	−	41.9578i	1.28378	−	1.42578i
$867$		0			0
$868$	16.6997	−	28.9248i	0.566826	−	0.981772i
$869$	−10.6186	+	4.22497i	−0.360211	+	0.143322i
$870$		0			0
$871$	−43.9620	−	19.5731i	−1.48960	−	0.663210i
$872$	0.400023	+	1.23115i	0.0135465	+	0.0416918i
$873$		0			0
$874$	1.69342	+	1.23034i	0.0572809	+	0.0416170i
$875$	0.0218133	−	0.207540i	0.000737426	−	0.00701614i
$876$		0			0
$877$	3.95002	+	0.839602i	0.133383	+	0.0283514i	0.274119	−	0.961696i	$-0.411614\pi$
$877$	3.95002	+	0.839602i	0.133383	+	0.0283514i	−0.140737	+	0.990047i	$0.544947\pi$
$878$	−2.29171	−	21.8041i	−0.0773414	−	0.735854i
$879$		0			0
$880$	−0.0636959	−	0.0314849i	−0.00214719	−	0.00106136i
$881$	−34.7957			−1.17230			−0.586149	−	0.810203i	$-0.699357\pi$
$881$	−34.7957			−1.17230			−0.586149	+	0.810203i	$0.699357\pi$
$882$		0			0
$883$	−11.9715	−	36.8445i	−0.402874	−	1.23992i	−0.922658	−	0.385620i	$-0.873988\pi$
$883$	−11.9715	−	36.8445i	−0.402874	−	1.23992i	0.519784	−	0.854298i	$-0.326012\pi$
$884$	32.1623	−	6.83630i	1.08173	−	0.229930i
$885$		0			0
$886$	−42.5445	+	18.9420i	−1.42931	+	0.636370i
$887$	28.4451	+	31.5915i	0.955095	+	1.06074i	0.998097	+	0.0616650i	$0.0196411\pi$
$887$	28.4451	+	31.5915i	0.955095	+	1.06074i	−0.0430023	+	0.999075i	$0.513692\pi$
$888$		0			0
$889$	−30.2176	−	13.4538i	−1.01347	−	0.451225i
$890$	−0.00982649			−0.000329385
$891$		0			0
$892$	−22.2208			−0.744008
$893$	4.14243	+	1.84433i	0.138621	+	0.0617181i
$894$		0			0
$895$	0.0131286	+	0.0145807i	0.000438839	+	0.000487380i
$896$	1.94497	−	0.865955i	0.0649768	−	0.0289295i
$897$		0			0
$898$	−27.8233	+	5.91403i	−0.928476	+	0.197354i
$899$	−0.480517	−	1.47888i	−0.0160261	−	0.0493234i
$900$		0			0
$901$	−60.9152			−2.02938
$902$	43.8519	−	7.49324i	1.46011	−	0.249498i
$903$		0			0
$904$	0.0356316	+	0.339012i	0.00118509	+	0.0112754i
$905$	0.121929	+	0.0259169i	0.00405307	+	0.000861507i
$906$		0			0
$907$	4.18300	−	39.7985i	0.138894	−	1.32149i	−0.673850	−	0.738868i	$-0.735361\pi$
$907$	4.18300	−	39.7985i	0.138894	−	1.32149i	0.812744	−	0.582621i	$-0.197973\pi$
$908$	−6.57163	−	4.77457i	−0.218087	−	0.158450i
$909$		0			0
$910$	−0.0457692	−	0.140863i	−0.00151723	−	0.00466957i
$911$	−13.0755	−	5.82161i	−0.433212	−	0.192878i	0.178532	−	0.983934i	$-0.442865\pi$
$911$	−13.0755	−	5.82161i	−0.433212	−	0.192878i	−0.611744	+	0.791056i	$0.709532\pi$
$912$		0			0
$913$	16.2713	+	19.6011i	0.538500	+	0.648700i
$914$	−1.74045	+	3.01454i	−0.0575689	+	0.0997123i
$915$		0			0
$916$	−9.54875	+	10.6050i	−0.315499	+	0.350398i
$917$	−7.22149	+	22.2255i	−0.238475	+	0.733949i
$918$		0			0
$919$	−20.3984	−	14.8203i	−0.672880	−	0.488876i	0.198108	−	0.980180i	$-0.436520\pi$
$919$	−20.3984	−	14.8203i	−0.672880	−	0.488876i	−0.870988	+	0.491305i	$0.836520\pi$
$920$	0.000564147	0	0.000119913i	1.85994e−5	0	3.95342e-6i
$921$		0			0
$922$	−1.24417	−	11.8375i	−0.0409746	−	0.389847i
$923$	−4.92889	+	8.53708i	−0.162236	+	0.281002i
$924$		0			0
$925$	15.4241	+	26.7153i	0.507141	+	0.878394i
$926$	−31.2783	+	22.7250i	−1.02787	+	0.746791i
$927$		0			0
$928$	0.899980	−	2.76985i	0.0295433	−	0.0909249i
$929$	2.10213	−	20.0004i	0.0689685	−	0.656192i	−0.904359	−	0.426772i	$-0.859651\pi$
$929$	2.10213	−	20.0004i	0.0689685	−	0.656192i	0.973328	−	0.229420i	$-0.0736828\pi$
$930$		0			0
$931$	−3.50716	−	3.89510i	−0.114943	−	0.127657i
$932$	26.2023	+	5.56946i	0.858283	+	0.182434i
$933$		0			0
$934$	35.1751	+	60.9251i	1.15097	+	1.99353i
$935$	−0.0688033	+	0.0458806i	−0.00225011	+	0.00150046i
$936$		0			0
$937$	32.0366	−	23.2760i	1.04659	−	0.760393i	0.0750295	−	0.997181i	$-0.476095\pi$
$937$	32.0366	−	23.2760i	1.04659	−	0.760393i	0.971561	+	0.236789i	$0.0760949\pi$
$938$	−70.0661	+	77.8163i	−2.28774	+	2.54079i
$939$		0			0
$940$	0.0670830	−	0.0298673i	0.00218801	−	0.000974163i
$941$	−36.0821	+	16.0648i	−1.17624	+	0.523697i	−0.899361	−	0.437207i	$-0.855968\pi$
$941$	−36.0821	+	16.0648i	−1.17624	+	0.523697i	−0.276882	+	0.960904i	$0.589301\pi$
$942$		0			0
$943$	6.79819	−	7.55016i	0.221380	−	0.245867i
$944$	18.2660	−	13.2710i	0.594509	−	0.431936i
$945$		0			0
$946$	38.2371	+	30.2013i	1.24320	+	0.981929i
$947$	−25.7180	−	44.5449i	−0.835723	−	1.44751i	−0.893440	−	0.449182i	$-0.851716\pi$
$947$	−25.7180	−	44.5449i	−0.835723	−	1.44751i	0.0577176	−	0.998333i	$-0.481618\pi$
$948$		0			0
$949$	−0.230939	−	0.0490877i	−0.00749660	−	0.00159345i
$950$	4.60304	+	5.11219i	0.149342	+	0.165861i
$951$		0			0
$952$	0.127248	−	1.21068i	0.00412412	−	0.0392384i
$953$	−0.255695	+	0.786947i	−0.00828276	+	0.0254917i	−0.955112	−	0.296243i	$-0.904266\pi$
$953$	−0.255695	+	0.786947i	−0.00828276	+	0.0254917i	0.946830	+	0.321735i	$0.104266\pi$
$954$		0			0
$955$	−0.0126029	+	0.00915655i	−0.000407820	+	0.000296299i
$956$	0.783145	+	1.35645i	0.0253287	+	0.0438706i
$957$		0			0
$958$	10.3233	−	17.8805i	0.333531	−	0.577693i
$959$	−0.382628	−	3.64046i	−0.0123557	−	0.117557i
$960$		0			0
$961$	12.3331	−	2.62148i	0.397842	−	0.0845639i
$962$	35.4260	+	25.7385i	1.14218	+	0.829842i
$963$		0			0
$964$	−5.73570	+	17.6527i	−0.184734	+	0.568554i
$965$	−0.0623732	+	0.0692724i	−0.00200786	+	0.00222996i
$966$		0			0
$967$	12.5837	−	21.7957i	0.404666	−	0.700902i	−0.589616	−	0.807683i	$-0.700721\pi$
$967$	12.5837	−	21.7957i	0.404666	−	0.700902i	0.994283	+	0.106781i	$0.0340544\pi$
$968$	0.721491	−	0.253987i	0.0231896	−	0.00816345i
$969$		0			0
$970$	0.152558	+	0.0679231i	0.00489834	+	0.00218088i
$971$	16.3754	+	50.3983i	0.525512	+	1.61736i	0.763301	+	0.646043i	$0.223577\pi$
$971$	16.3754	+	50.3983i	0.525512	+	1.61736i	−0.237789	+	0.971317i	$0.576423\pi$
$972$		0			0
$973$	12.9817	+	9.43173i	0.416173	+	0.302367i
$974$	−5.82094	+	55.3826i	−0.186515	+	1.77457i
$975$		0			0
$976$	44.4231	+	9.44242i	1.42195	+	0.302244i
$977$	4.03624	+	38.4022i	0.129131	+	1.22860i	0.846685	+	0.532094i	$0.178595\pi$
$977$	4.03624	+	38.4022i	0.129131	+	1.22860i	−0.717555	+	0.696502i	$0.754739\pi$
$978$		0			0
$979$	−2.07871	+	2.12989i	−0.0664357	+	0.0680716i
$980$	−0.0848794			−0.00271137
$981$		0			0
$982$	−1.71780	−	5.28686i	−0.0548173	−	0.168710i
$983$	29.3885	−	6.24671i	0.937347	−	0.199239i	0.286182	−	0.958175i	$-0.407614\pi$
$983$	29.3885	−	6.24671i	0.937347	−	0.199239i	0.651165	+	0.758936i	$0.274281\pi$
$984$		0			0
$985$	−0.0767249	+	0.0341601i	−0.00244466	+	0.00108843i
$986$	−2.22890	−	2.47544i	−0.0709826	−	0.0788341i
$987$		0			0
$988$	4.49862	+	2.00291i	0.143120	+	0.0637211i
$989$	11.1276			0.353838
$990$		0			0
$991$	34.2415			1.08772			0.543858	−	0.839177i	$-0.316963\pi$
$991$	34.2415			1.08772			0.543858	+	0.839177i	$0.316963\pi$
$992$	−31.4679	−	14.0104i	−0.999108	−	0.444832i
$993$		0			0
$994$	14.3529	+	15.9405i	0.455247	+	0.505603i
$995$	0.0320972	−	0.0142906i	0.00101755	−	0.000453043i
$996$		0			0
$997$	36.4736	−	7.75270i	1.15513	−	0.245530i	0.409767	−	0.912190i	$-0.365610\pi$
$997$	36.4736	−	7.75270i	1.15513	−	0.245530i	0.745362	+	0.666660i	$0.232277\pi$
$998$	−14.0333	−	43.1902i	−0.444218	−	1.36716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.91.8		72
3.2	odd	2		99.2.m.b.58.2	yes	72
9.2	odd	6		99.2.m.b.25.8	yes	72
9.4	even	3		891.2.f.e.487.2		36
9.5	odd	6		891.2.f.f.487.8		36
9.7	even	3	inner	297.2.n.b.289.2		72
11.4	even	5	inner	297.2.n.b.37.2		72
33.2	even	10		1089.2.e.o.364.3		36
33.20	odd	10		1089.2.e.p.364.16		36
33.26	odd	10		99.2.m.b.4.8	✓	72
99.2	even	30		1089.2.e.o.727.3		36
99.4	even	15		891.2.f.e.730.2		36
99.13	odd	30		9801.2.a.cn.1.3		18
99.20	odd	30		1089.2.e.p.727.16		36
99.31	even	15		9801.2.a.cp.1.16		18
99.59	odd	30		891.2.f.f.730.8		36
99.68	even	30		9801.2.a.co.1.16		18
99.70	even	15	inner	297.2.n.b.235.8		72
99.86	odd	30		9801.2.a.cm.1.3		18
99.92	odd	30		99.2.m.b.70.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.8	✓	72	33.26	odd	10
99.2.m.b.25.8	yes	72	9.2	odd	6
99.2.m.b.58.2	yes	72	3.2	odd	2
99.2.m.b.70.2	yes	72	99.92	odd	30
297.2.n.b.37.2		72	11.4	even	5	inner
297.2.n.b.91.8		72	1.1	even	1	trivial
297.2.n.b.235.8		72	99.70	even	15	inner
297.2.n.b.289.2		72	9.7	even	3	inner
891.2.f.e.487.2		36	9.4	even	3
891.2.f.e.730.2		36	99.4	even	15
891.2.f.f.487.8		36	9.5	odd	6
891.2.f.f.730.8		36	99.59	odd	30
1089.2.e.o.364.3		36	33.2	even	10
1089.2.e.o.727.3		36	99.2	even	30
1089.2.e.p.364.16		36	33.20	odd	10
1089.2.e.p.727.16		36	99.20	odd	30
9801.2.a.cm.1.3		18	99.86	odd	30
9801.2.a.cn.1.3		18	99.13	odd	30
9801.2.a.co.1.16		18	99.68	even	30
9801.2.a.cp.1.16		18	99.31	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.83498 + 0.816986i) q^{2} +(1.36143 + 1.51202i) q^{4} +(-0.00498046 + 0.00221744i) q^{5} +(3.74416 - 0.795845i) q^{7} +(0.0214877 + 0.0661323i) q^{8} +O(q^{10})\)	\(q+(1.83498 + 0.816986i) q^{2} +(1.36143 + 1.51202i) q^{4} +(-0.00498046 + 0.00221744i) q^{5} +(3.74416 - 0.795845i) q^{7} +(0.0214877 + 0.0661323i) q^{8} -0.0109507 q^{10} +(-2.31651 + 2.37356i) q^{11} +(0.369348 + 3.51411i) q^{13} +(7.52065 + 1.59856i) q^{14} +(0.410751 - 3.90804i) q^{16} +(-3.70012 - 2.68830i) q^{17} +(-0.211664 - 0.651435i) q^{19} +(-0.0101333 - 0.00451165i) q^{20} +(-6.18992 + 2.46287i) q^{22} +(-0.760697 + 1.31757i) q^{23} +(-3.34563 + 3.71570i) q^{25} +(-2.19323 + 6.75007i) q^{26} +(6.30072 + 4.57774i) q^{28} +(0.354669 - 0.0753873i) q^{29} +(-0.448272 - 4.26502i) q^{31} +(4.01607 - 6.95603i) q^{32} +(-4.59335 - 7.95592i) q^{34} +(-0.0168829 + 0.0122661i) q^{35} +(1.90653 - 5.86771i) q^{37} +(0.143814 - 1.36830i) q^{38} +(-0.000253663 - 0.000281721i) q^{40} +(-6.53199 - 1.38842i) q^{41} +(-3.65705 - 6.33419i) q^{43} +(-6.74261 - 0.271187i) q^{44} +(-2.47230 + 1.79623i) q^{46} +(-4.42967 + 4.91964i) q^{47} +(6.99053 - 3.11239i) q^{49} +(-9.17485 + 4.08490i) q^{50} +(-4.81055 + 5.34266i) q^{52} +(10.7752 - 7.82863i) q^{53} +(0.00627407 - 0.0169581i) q^{55} +(0.133084 + 0.230509i) q^{56} +(0.712402 + 0.151426i) q^{58} +(3.84462 + 4.26988i) q^{59} +(-1.20808 + 11.4941i) q^{61} +(2.66189 - 8.19247i) q^{62} +(6.69422 - 4.86363i) q^{64} +(-0.00963186 - 0.0166829i) q^{65} +(-6.80952 + 11.7944i) q^{67} +(-0.972694 - 9.25456i) q^{68} +(-0.0410010 + 0.00871503i) q^{70} +(2.25702 + 1.63982i) q^{71} +(-0.0206478 + 0.0635475i) q^{73} +(8.29229 - 9.20952i) q^{74} +(0.696816 - 1.20692i) q^{76} +(-6.78441 + 10.7306i) q^{77} +(3.14785 + 1.40151i) q^{79} +(0.00662012 + 0.0203746i) q^{80} +(-10.8517 - 7.88426i) q^{82} +(0.802871 - 7.63880i) q^{83} +(0.0243895 + 0.00518414i) q^{85} +(-1.53566 - 14.6109i) q^{86} +(-0.206745 - 0.102194i) q^{88} +0.897342 q^{89} +(4.17958 + 12.8634i) q^{91} +(-3.02781 + 0.643581i) q^{92} +(-12.1476 + 5.40847i) q^{94} +(0.00249870 + 0.00277509i) q^{95} +(-13.9314 - 6.20265i) q^{97} +15.3703 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28} + 23 q^{29} + 3 q^{31} - 18 q^{32} + 8 q^{34} - 18 q^{35} - 42 q^{37} + q^{38} - 25 q^{40} - 10 q^{41} - 8 q^{43} - 38 q^{44} - 18 q^{46} + 34 q^{47} + q^{49} - 27 q^{52} - 4 q^{53} + 18 q^{55} - 114 q^{56} + q^{58} + 16 q^{59} - 3 q^{61} - 184 q^{62} + 26 q^{64} - 84 q^{65} + 10 q^{67} + 23 q^{68} - 46 q^{70} + 48 q^{71} - 40 q^{73} - 68 q^{74} + 16 q^{76} + 26 q^{77} + 19 q^{79} + 56 q^{80} + 94 q^{82} - 7 q^{83} + 25 q^{85} + 77 q^{86} + 18 q^{88} + 56 q^{89} + 20 q^{91} - 50 q^{92} - 63 q^{94} + 77 q^{95} - 33 q^{97} + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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