LMFDB - Embedded newform 348.2.t.a.179.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, 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:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	348.179
Dual form			348.2.t.a.35.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.927728 - 1.06739i) q^{2} +(-1.21862 - 1.23084i) q^{3} +(-0.278641 + 1.98049i) q^{4} +(-0.252365 + 0.201255i) q^{5} +(-0.183246 + 2.44263i) q^{6} +(3.46126 - 0.790009i) q^{7} +(2.37246 - 1.53994i) q^{8} +(-0.0299545 + 2.99985i) q^{9} +O(q^{10})$	\(q+(-0.927728 - 1.06739i) q^{2} +(-1.21862 - 1.23084i) q^{3} +(-0.278641 + 1.98049i) q^{4} +(-0.252365 + 0.201255i) q^{5} +(-0.183246 + 2.44263i) q^{6} +(3.46126 - 0.790009i) q^{7} +(2.37246 - 1.53994i) q^{8} +(-0.0299545 + 2.99985i) q^{9} +(0.448943 + 0.0826624i) q^{10} +(0.320018 - 0.664525i) q^{11} +(2.77724 - 2.07050i) q^{12} +(3.28982 + 1.58429i) q^{13} +(-4.05435 - 2.96159i) q^{14} +(0.555249 + 0.0653704i) q^{15} +(-3.84472 - 1.10369i) q^{16} -0.499932 q^{17} +(3.22980 - 2.75107i) q^{18} +(1.43177 - 6.27298i) q^{19} +(-0.328264 - 0.555886i) q^{20} +(-5.19032 - 3.29755i) q^{21} +(-1.00620 + 0.274914i) q^{22} +(2.29001 - 2.87158i) q^{23} +(-4.78655 - 1.04353i) q^{24} +(-1.08942 + 4.77306i) q^{25} +(-1.36100 - 4.98132i) q^{26} +(3.72885 - 3.61879i) q^{27} +(0.600163 + 7.07513i) q^{28} +(-2.28754 - 4.87516i) q^{29} +(-0.445344 - 0.653313i) q^{30} +(-3.05971 - 3.83676i) q^{31} +(2.38878 + 5.12774i) q^{32} +(-1.20791 + 0.415907i) q^{33} +(0.463801 + 0.533622i) q^{34} +(-0.714508 + 0.895964i) q^{35} +(-5.93284 - 0.895205i) q^{36} +(-1.90809 - 3.96219i) q^{37} +(-8.02401 + 4.29137i) q^{38} +(-2.05901 - 5.97990i) q^{39} +(-0.288806 + 0.866097i) q^{40} +7.55503 q^{41} +(1.29543 + 8.59932i) q^{42} +(-4.09169 + 5.13082i) q^{43} +(1.22692 + 0.818958i) q^{44} +(-0.596174 - 0.763086i) q^{45} +(-5.18960 + 0.219715i) q^{46} +(-2.12415 + 4.41085i) q^{47} +(3.32676 + 6.07723i) q^{48} +(5.04940 - 2.43166i) q^{49} +(6.10540 - 3.26527i) q^{50} +(0.609225 + 0.615338i) q^{51} +(-4.05437 + 6.07403i) q^{52} +(8.28539 - 6.60738i) q^{53} +(-7.32202 - 0.622879i) q^{54} +(0.0529771 + 0.232108i) q^{55} +(6.99513 - 7.20440i) q^{56} +(-9.46584 + 5.88207i) q^{57} +(-3.08148 + 6.96451i) q^{58} +4.97485 q^{59} +(-0.284181 + 1.08145i) q^{60} +(9.83324 - 2.24437i) q^{61} +(-1.25673 + 6.82538i) q^{62} +(2.26623 + 10.4069i) q^{63} +(3.25715 - 7.30691i) q^{64} +(-1.14908 + 0.262271i) q^{65} +(1.56454 + 0.903457i) q^{66} +(-2.56551 - 5.32735i) q^{67} +(0.139301 - 0.990112i) q^{68} +(-6.32510 + 0.680707i) q^{69} +(1.61921 - 0.0685534i) q^{70} +(11.6763 + 5.62299i) q^{71} +(4.54853 + 7.16316i) q^{72} +(2.23386 + 1.78145i) q^{73} +(-2.45901 + 5.71251i) q^{74} +(7.20248 - 4.47562i) q^{75} +(12.0247 + 4.58351i) q^{76} +(0.582685 - 2.55291i) q^{77} +(-4.47269 + 7.74549i) q^{78} +(-5.79611 + 2.79126i) q^{79} +(1.19240 - 0.495233i) q^{80} +(-8.99821 - 0.179718i) q^{81} +(-7.00902 - 8.06416i) q^{82} +(1.07201 - 4.69678i) q^{83} +(7.97701 - 9.36057i) q^{84} +(0.126165 - 0.100614i) q^{85} +(9.27255 - 0.392577i) q^{86} +(-3.21294 + 8.75654i) q^{87} +(-0.264099 - 2.06937i) q^{88} +(-2.08812 - 2.61842i) q^{89} +(-0.261423 + 1.34429i) q^{90} +(12.6385 + 2.88466i) q^{91} +(5.04906 + 5.33548i) q^{92} +(-0.993840 + 8.44156i) q^{93} +(6.67873 - 1.82477i) q^{94} +(0.901138 + 1.87123i) q^{95} +(3.40044 - 9.18896i) q^{96} +(0.496272 + 0.113271i) q^{97} +(-7.28000 - 3.13375i) q^{98} +(1.98389 + 0.979913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.927728	−	1.06739i	−0.656003	−	0.754758i
$2$	−0.927728	−	1.06739i	−0.656003	−	0.754758i
$3$	−1.21862	−	1.23084i	−0.703568	−	0.710628i
$3$	−1.21862	−	1.23084i	−0.703568	−	0.710628i
$4$	−0.278641	+	1.98049i	−0.139320	+	0.990247i
$5$	−0.252365	+	0.201255i	−0.112861	+	0.0900038i	−0.678294	−	0.734790i	$-0.737280\pi$
$5$	−0.252365	+	0.201255i	−0.112861	+	0.0900038i	0.565433	+	0.824794i	$0.308709\pi$
$6$	−0.183246	+	2.44263i	−0.0748100	+	0.997198i
$7$	3.46126	−	0.790009i	1.30823	−	0.298595i	0.489114	−	0.872220i	$-0.337320\pi$
$7$	3.46126	−	0.790009i	1.30823	−	0.298595i	0.819118	+	0.573625i	$0.194463\pi$
$8$	2.37246	−	1.53994i	0.838792	−	0.544452i
$9$	−0.0299545	+	2.99985i	−0.00998482	+	0.999950i
$10$	0.448943	+	0.0826624i	0.141968	+	0.0261402i
$11$	0.320018	−	0.664525i	0.0964891	−	0.200362i	−0.847137	−	0.531374i	$-0.821676\pi$
$11$	0.320018	−	0.664525i	0.0964891	−	0.200362i	0.943626	+	0.331012i	$0.107390\pi$
$12$	2.77724	−	2.07050i	0.801719	−	0.597701i
$13$	3.28982	+	1.58429i	0.912432	+	0.439404i	0.830363	−	0.557222i	$-0.188133\pi$
$13$	3.28982	+	1.58429i	0.912432	+	0.439404i	0.0820691	+	0.996627i	$0.473847\pi$
$14$	−4.05435	−	2.96159i	−1.08357	−	0.791520i
$15$	0.555249	+	0.0653704i	0.143365	+	0.0168786i
$16$	−3.84472	−	1.10369i	−0.961180	−	0.275923i
$17$	−0.499932			−0.121251			−0.0606256	−	0.998161i	$-0.519310\pi$
$17$	−0.499932			−0.121251			−0.0606256	+	0.998161i	$0.519310\pi$
$18$	3.22980	−	2.75107i	0.761271	−	0.648434i
$19$	1.43177	−	6.27298i	0.328470	−	1.43912i	−0.493577	−	0.869702i	$-0.664311\pi$
$19$	1.43177	−	6.27298i	0.328470	−	1.43912i	0.822047	−	0.569419i	$-0.192832\pi$
$20$	−0.328264	−	0.555886i	−0.0734021	−	0.124300i
$21$	−5.19032	−	3.29755i	−1.13262	−	0.719584i
$22$	−1.00620	+	0.274914i	−0.214522	+	0.0586119i
$23$	2.29001	−	2.87158i	0.477499	−	0.598765i	−0.483490	−	0.875350i	$-0.660631\pi$
$23$	2.29001	−	2.87158i	0.477499	−	0.598765i	0.960990	+	0.276584i	$0.0892026\pi$
$24$	−4.78655	−	1.04353i	−0.977050	−	0.213010i
$25$	−1.08942	+	4.77306i	−0.217884	+	0.954612i
$26$	−1.36100	−	4.98132i	−0.266914	−	0.976917i
$27$	3.72885	−	3.61879i	0.717618	−	0.696437i
$28$	0.600163	+	7.07513i	0.113420	+	1.33707i
$29$	−2.28754	−	4.87516i	−0.424785	−	0.905294i
$29$	−2.28754	−	4.87516i	−0.424785	−	0.905294i
$30$	−0.445344	−	0.653313i	−0.0813084	−	0.119278i
$31$	−3.05971	−	3.83676i	−0.549541	−	0.689102i	0.427045	−	0.904230i	$-0.359555\pi$
$31$	−3.05971	−	3.83676i	−0.549541	−	0.689102i	−0.976586	+	0.215128i	$0.930983\pi$
$32$	2.38878	+	5.12774i	0.422281	+	0.906465i
$33$	−1.20791	+	0.415907i	−0.210269	+	0.0724002i
$34$	0.463801	+	0.533622i	0.0795412	+	0.0915154i
$35$	−0.714508	+	0.895964i	−0.120774	+	0.151446i
$36$	−5.93284	−	0.895205i	−0.988807	−	0.149201i
$37$	−1.90809	−	3.96219i	−0.313688	−	0.651380i	0.683198	−	0.730233i	$-0.260588\pi$
$37$	−1.90809	−	3.96219i	−0.313688	−	0.651380i	−0.996886	+	0.0788531i	$0.974874\pi$
$38$	−8.02401	+	4.29137i	−1.30167	+	0.696152i
$39$	−2.05901	−	5.97990i	−0.329705	−	0.957551i
$40$	−0.288806	+	0.866097i	−0.0456643	+	0.136942i
$41$	7.55503			1.17990			0.589949	−	0.807441i	$-0.299148\pi$
$41$	7.55503			1.17990			0.589949	+	0.807441i	$0.299148\pi$
$42$	1.29543	+	8.59932i	0.199890	+	1.32690i
$43$	−4.09169	+	5.13082i	−0.623977	+	0.782442i	−0.988898	−	0.148596i	$-0.952524\pi$
$43$	−4.09169	+	5.13082i	−0.623977	+	0.782442i	0.364921	+	0.931038i	$0.381096\pi$
$44$	1.22692	+	0.818958i	0.184965	+	0.123463i
$45$	−0.596174	−	0.763086i	−0.0888724	−	0.113754i
$46$	−5.18960	+	0.219715i	−0.765164	+	0.0323951i
$47$	−2.12415	+	4.41085i	−0.309840	+	0.643389i	−0.996500	−	0.0835893i	$-0.973362\pi$
$47$	−2.12415	+	4.41085i	−0.309840	+	0.643389i	0.686661	+	0.726978i	$0.259076\pi$
$48$	3.32676	+	6.07723i	0.480176	+	0.877172i
$49$	5.04940	−	2.43166i	0.721343	−	0.347380i
$50$	6.10540	−	3.26527i	0.863434	−	0.461779i
$51$	0.609225	+	0.615338i	0.0853085	+	0.0861646i
$52$	−4.05437	+	6.07403i	−0.562239	+	0.842316i
$53$	8.28539	−	6.60738i	1.13809	−	0.907594i	0.141483	−	0.989941i	$-0.454813\pi$
$53$	8.28539	−	6.60738i	1.13809	−	0.907594i	0.996604	+	0.0823470i	$0.0262416\pi$
$54$	−7.32202	−	0.622879i	−0.996401	−	0.0847631i
$55$	0.0529771	+	0.232108i	0.00714344	+	0.0312974i
$56$	6.99513	−	7.20440i	0.934764	−	0.962729i
$57$	−9.46584	+	5.88207i	−1.25378	+	0.779099i
$58$	−3.08148	+	6.96451i	−0.404619	+	0.914486i
$59$	4.97485			0.647670			0.323835	−	0.946113i	$-0.395028\pi$
$59$	4.97485			0.647670			0.323835	+	0.946113i	$0.395028\pi$
$60$	−0.284181	+	1.08145i	−0.0366876	+	0.139615i
$61$	9.83324	−	2.24437i	1.25902	−	0.287362i	0.459593	−	0.888130i	$-0.347995\pi$
$61$	9.83324	−	2.24437i	1.25902	−	0.287362i	0.799424	+	0.600767i	$0.205138\pi$
$62$	−1.25673	+	6.82538i	−0.159605	+	0.866824i
$63$	2.26623	+	10.4069i	0.285518	+	1.31115i
$64$	3.25715	−	7.30691i	0.407144	−	0.913364i
$65$	−1.14908	+	0.262271i	−0.142526	+	0.0325307i
$66$	1.56454	+	0.903457i	0.192582	+	0.111208i
$67$	−2.56551	−	5.32735i	−0.313428	−	0.650839i	0.683433	−	0.730013i	$-0.260486\pi$
$67$	−2.56551	−	5.32735i	−0.313428	−	0.650839i	−0.996861	+	0.0791740i	$0.974772\pi$
$68$	0.139301	−	0.990112i	0.0168928	−	0.120069i
$69$	−6.32510	+	0.680707i	−0.761453	+	0.0819474i
$70$	1.61921	−	0.0685534i	0.193533	−	0.00819370i
$71$	11.6763	+	5.62299i	1.38572	+	0.667326i	0.970210	−	0.242264i	$-0.0778901\pi$
$71$	11.6763	+	5.62299i	1.38572	+	0.667326i	0.415506	+	0.909590i	$0.363604\pi$
$72$	4.54853	+	7.16316i	0.536050	+	0.844186i
$73$	2.23386	+	1.78145i	0.261454	+	0.208503i	0.745439	−	0.666573i	$-0.232240\pi$
$73$	2.23386	+	1.78145i	0.261454	+	0.208503i	−0.483985	+	0.875076i	$0.660811\pi$
$74$	−2.45901	+	5.71251i	−0.285854	+	0.664066i
$75$	7.20248	−	4.47562i	0.831670	−	0.516800i
$76$	12.0247	+	4.58351i	1.37932	+	0.525765i
$77$	0.582685	−	2.55291i	0.0664031	−	0.290931i
$78$	−4.47269	+	7.74549i	−0.506432	+	0.877004i
$79$	−5.79611	+	2.79126i	−0.652114	+	0.314041i	−0.730531	−	0.682879i	$-0.760728\pi$
$79$	−5.79611	+	2.79126i	−0.652114	+	0.314041i	0.0784176	+	0.996921i	$0.475013\pi$
$80$	1.19240	−	0.495233i	0.133314	−	0.0553688i
$81$	−8.99821	−	0.179718i	−0.999801	−	0.0199686i
$82$	−7.00902	−	8.06416i	−0.774016	−	0.890537i
$83$	1.07201	−	4.69678i	0.117668	−	0.515538i	−0.881400	−	0.472371i	$-0.843398\pi$
$83$	1.07201	−	4.69678i	0.117668	−	0.515538i	0.999068	−	0.0431670i	$-0.0137447\pi$
$84$	7.97701	−	9.36057i	0.870364	−	1.02132i
$85$	0.126165	−	0.100614i	0.0136846	−	0.0109131i
$86$	9.27255	−	0.392577i	0.999885	−	0.0423327i
$87$	−3.21294	+	8.75654i	−0.344463	+	0.938800i
$88$	−0.264099	−	2.06937i	−0.0281531	−	0.220596i
$89$	−2.08812	−	2.61842i	−0.221340	−	0.277552i	0.658746	−	0.752365i	$-0.271087\pi$
$89$	−2.08812	−	2.61842i	−0.221340	−	0.277552i	−0.880087	+	0.474813i	$0.842516\pi$
$90$	−0.261423	+	1.34429i	−0.0275564	+	0.141700i
$91$	12.6385	+	2.88466i	1.32488	+	0.302395i
$92$	5.04906	+	5.33548i	0.526400	+	0.556263i
$93$	−0.993840	+	8.44156i	−0.103056	+	0.875349i
$94$	6.67873	−	1.82477i	0.688859	−	0.188211i
$95$	0.901138	+	1.87123i	0.0924548	+	0.191984i
$96$	3.40044	−	9.18896i	0.347056	−	0.937844i
$97$	0.496272	+	0.113271i	0.0503888	+	0.0115009i	0.247641	−	0.968852i	$-0.420345\pi$
$97$	0.496272	+	0.113271i	0.0503888	+	0.0115009i	−0.197252	+	0.980353i	$0.563202\pi$
$98$	−7.28000	−	3.13375i	−0.735391	−	0.316557i
$99$	1.98389	+	0.979913i	0.199388	+	0.0984849i
$100$	−9.14946	−	3.48756i	−0.914946	−	0.348756i
$101$	−11.7409	+	14.7227i	−1.16827	+	1.46496i	−0.310760	+	0.950488i	$0.600584\pi$
$101$	−11.7409	+	14.7227i	−1.16827	+	1.46496i	−0.857507	+	0.514472i	$0.827988\pi$
$102$	0.0916107	−	1.22115i	0.00907081	−	0.120912i
$103$	−5.46701	+	11.3524i	−0.538681	+	1.11858i	0.437015	+	0.899454i	$0.356035\pi$
$103$	−5.46701	+	11.3524i	−0.538681	+	1.11858i	−0.975696	+	0.219128i	$0.929679\pi$
$104$	10.2447	−	1.30746i	1.00458	−	0.128207i
$105$	1.97350	−	0.212388i	0.192594	−	0.0207270i
$106$	−14.7392	−	2.71389i	−1.43160	−	0.263596i
$107$	−14.9982	+	7.22275i	−1.44993	+	0.698249i	−0.982583	−	0.185825i	$-0.940504\pi$
$107$	−14.9982	+	7.22275i	−1.44993	+	0.698249i	−0.467347	+	0.884074i	$0.654790\pi$
$108$	6.12799	+	8.39331i	0.589666	+	0.807647i
$109$	−1.61185	−	7.06197i	−0.154387	−	0.676414i	−0.991579	−	0.129505i	$-0.958661\pi$
$109$	−1.61185	−	7.06197i	−0.154387	−	0.676414i	0.837192	−	0.546909i	$-0.184196\pi$
$110$	0.198601	−	0.271880i	0.0189359	−	0.0259228i
$111$	−2.55161	+	7.17694i	−0.242188	+	0.681205i
$112$	−14.1795	−	0.782799i	−1.33984	−	0.0739676i
$113$	1.59193	+	6.97471i	0.149756	+	0.656125i	0.992952	+	0.118518i	$0.0378144\pi$
$113$	1.59193	+	6.97471i	0.149756	+	0.656125i	−0.843196	+	0.537607i	$0.819328\pi$
$114$	15.0602	+	4.64677i	1.41052	+	0.435210i
$115$			1.18556i			0.110554i
$116$	10.2926	−	3.17203i	0.955647	−	0.294516i
$117$	−4.85119	+	9.82152i	−0.448493	+	0.908000i
$118$	−4.61531	−	5.31010i	−0.424874	−	0.488835i
$119$	−1.73039	+	0.394951i	−0.158625	+	0.0362051i
$120$	1.41797	−	0.699963i	0.129443	−	0.0638976i
$121$	6.51921	+	8.17483i	0.592655	+	0.743166i
$122$	−11.5182	−	8.41373i	−1.04281	−	0.761743i
$123$	−9.20667	−	9.29906i	−0.830138	−	0.838468i
$124$	8.45124	−	4.99067i	0.758944	−	0.448175i
$125$	−1.38593	−	2.87791i	−0.123961	−	0.257408i
$126$	9.00579	−	12.0737i	0.802299	−	1.07561i
$127$	1.90169	+	0.915807i	0.168748	+	0.0812647i	0.516351	−	0.856377i	$-0.327290\pi$
$127$	1.90169	+	0.915807i	0.168748	+	0.0812647i	−0.347603	+	0.937642i	$0.613004\pi$
$128$	−10.8211	+	3.30218i	−0.956457	+	0.291874i
$129$	11.3014	−	1.21626i	0.995035	−	0.107086i
$130$	1.34598	+	0.983203i	0.118050	+	0.0862326i
$131$	−13.8620	−	11.0546i	−1.21113	−	0.965841i	−0.211193	−	0.977444i	$-0.567735\pi$
$131$	−13.8620	−	11.0546i	−1.21113	−	0.965841i	−0.999933	+	0.0116034i	$0.996306\pi$
$132$	−0.487131	−	2.50814i	−0.0423993	−	0.218306i
$133$		−	22.8435i		−	1.98078i
$134$	−3.30625	+	7.68073i	−0.285617	+	0.663514i
$135$	−0.212734	+	1.66371i	−0.0183092	+	0.143189i
$136$	−1.18607	+	0.769867i	−0.101705	+	0.0660155i
$137$	6.27367	−	3.02124i	0.535996	−	0.258122i	−0.146246	−	0.989248i	$-0.546719\pi$
$137$	6.27367	−	3.02124i	0.535996	−	0.258122i	0.682242	+	0.731126i	$0.261005\pi$
$138$	6.59455	+	6.11984i	0.561366	+	0.520955i
$139$	5.23403	+	4.17400i	0.443945	+	0.354034i	0.819805	−	0.572642i	$-0.194082\pi$
$139$	5.23403	+	4.17400i	0.443945	+	0.354034i	−0.375861	+	0.926676i	$0.622653\pi$
$140$	−1.57536	−	1.66473i	−0.133142	−	0.140695i
$141$	8.01760	−	2.76063i	0.675204	−	0.232487i
$142$	−4.83047	−	17.6797i	−0.405364	−	1.48365i
$143$	2.10561	−	1.67917i	0.176080	−	0.140419i
$144$	3.42608	−	11.5005i	0.285507	−	0.958377i
$145$	1.55844	+	0.769944i	0.129422	+	0.0639403i
$146$	−0.170921	−	4.03710i	−0.0141455	−	0.334113i
$147$	−9.14627	−	3.25176i	−0.754372	−	0.268201i
$148$	8.37877	−	2.67494i	0.688730	−	0.219878i
$149$	−13.8295	−	3.15649i	−1.13296	−	0.258590i	−0.385375	−	0.922760i	$-0.625928\pi$
$149$	−13.8295	−	3.15649i	−1.13296	−	0.258590i	−0.747582	+	0.664170i	$0.768785\pi$
$150$	−11.4592	−	3.53569i	−0.935637	−	0.288688i
$151$	−10.4312	−	8.31863i	−0.848881	−	0.676960i	0.0991726	−	0.995070i	$-0.468380\pi$
$151$	−10.4312	−	8.31863i	−0.848881	−	0.676960i	−0.948054	+	0.318110i	$0.896952\pi$
$152$	−6.26322	−	17.0873i	−0.508014	−	1.38596i
$153$	0.0149752	−	1.49972i	0.00121067	−	0.121245i
$154$	−3.26552	+	1.74645i	−0.263143	+	0.140733i
$155$	1.54433	+	0.352483i	0.124044	+	0.0283121i
$156$	12.4169	−	2.41161i	0.994147	−	0.193083i
$157$			6.75806i			0.539352i	0.962951	+	0.269676i	$0.0869166\pi$
$157$			6.75806i			0.539352i	−0.962951	+	0.269676i	$0.913083\pi$
$158$	8.35658	+	3.59718i	0.664814	+	0.286176i
$159$	−18.2294	−	2.14617i	−1.44568	−	0.170203i
$160$	−1.63483	−	0.813309i	−0.129244	−	0.0642977i
$161$	5.65773	−	11.7484i	0.445891	−	0.925903i
$162$	8.15606	+	9.77132i	0.640801	+	0.767707i
$163$	17.6894	+	8.51876i	1.38554	+	0.667241i	0.970173	−	0.242413i	$-0.0779390\pi$
$163$	17.6894	+	8.51876i	1.38554	+	0.667241i	0.415367	+	0.909654i	$0.363653\pi$
$164$	−2.10514	+	14.9627i	−0.164384	+	1.16839i
$165$	0.221130	−	0.348057i	0.0172150	−	0.0270962i
$166$	−6.00782	+	3.21308i	−0.466298	+	0.249384i
$167$	2.44513	+	10.7128i	0.189210	+	0.828981i	0.977034	+	0.213082i	$0.0683501\pi$
$167$	2.44513	+	10.7128i	0.189210	+	0.828981i	−0.787825	+	0.615899i	$0.788793\pi$
$168$	−17.3919	+	0.169481i	−1.34181	+	0.0130757i
$169$	0.207571	+	0.260286i	0.0159670	+	0.0200220i
$170$	−0.224441	−	0.0413256i	−0.0172138	−	0.00316953i
$171$	18.7751	+	4.48299i	1.43577	+	0.342823i
$172$	−9.02144	−	9.53322i	−0.687879	−	0.726901i
$173$			24.4511i			1.85898i	0.368845	+	0.929491i	$0.379753\pi$
$173$			24.4511i			1.85898i	−0.368845	+	0.929491i	$0.620247\pi$
$174$	12.3274	−	4.69424i	0.934536	−	0.355869i
$175$			17.3814i			1.31391i
$176$	−1.96381	+	2.20171i	−0.148028	+	0.165960i
$177$	−6.06243	−	6.12327i	−0.455680	−	0.460253i
$178$	−0.857666	+	4.65802i	−0.0642848	+	0.349134i
$179$	−14.4929	−	18.1735i	−1.08325	−	1.35835i	−0.928899	−	0.370332i	$-0.879244\pi$
$179$	−14.4929	−	18.1735i	−1.08325	−	1.35835i	−0.154348	−	0.988017i	$-0.549328\pi$
$180$	1.67741	−	0.968093i	0.125027	−	0.0721574i
$181$	3.79453	+	16.6249i	0.282045	+	1.23572i	0.895166	+	0.445733i	$0.147057\pi$
$181$	3.79453	+	16.6249i	0.282045	+	1.23572i	−0.613121	+	0.789989i	$0.710086\pi$
$182$	−8.64606	−	16.1664i	−0.640889	−	1.19833i
$183$	−14.7454	−	9.36816i	−1.09001	−	0.692514i
$184$	1.01089	−	10.3392i	0.0745237	−	0.762215i
$185$	1.27894	+	0.615907i	0.0940298	+	0.0452824i
$186$	9.93245	−	6.77066i	0.728282	−	0.496449i
$187$	−0.159987	+	0.332217i	−0.0116994	+	0.0242941i
$188$	−8.14379	−	5.43592i	−0.593947	−	0.396455i
$189$	10.0476	−	15.4714i	0.730858	−	1.12538i
$190$	1.16132	−	2.69786i	0.0842512	−	0.195723i
$191$		−	9.09714i		−	0.658246i	−0.944287	−	0.329123i	$-0.893247\pi$
$191$		−	9.09714i		−	0.658246i	0.944287	−	0.329123i	$-0.106753\pi$
$192$	−12.9629	+	4.89527i	−0.935516	+	0.353285i
$193$	12.1491	+	2.77296i	0.874512	+	0.199602i	0.636141	−	0.771573i	$-0.280530\pi$
$193$	12.1491	+	2.77296i	0.874512	+	0.199602i	0.238371	+	0.971174i	$0.423387\pi$
$194$	−0.339501	−	0.634800i	−0.0243748	−	0.0455760i
$195$	1.72310	+	1.09474i	0.123394	+	0.0783956i
$196$	3.40893	+	10.6779i	0.243495	+	0.762705i
$197$	0.531566	+	0.423910i	0.0378725	+	0.0302023i	0.642243	−	0.766501i	$-0.278004\pi$
$197$	0.531566	+	0.423910i	0.0378725	+	0.0302023i	−0.604371	+	0.796703i	$0.706575\pi$
$198$	−0.794562	−	3.02667i	−0.0564670	−	0.215096i
$199$	−13.4846	−	3.07777i	−0.955898	−	0.218177i	−0.284003	−	0.958824i	$-0.591662\pi$
$199$	−13.4846	−	3.07777i	−0.955898	−	0.218177i	−0.671895	+	0.740646i	$0.734520\pi$
$200$	4.76563	+	13.0015i	0.336981	+	0.919348i
$201$	−3.43076	+	9.64973i	−0.241987	+	0.680640i
$202$	26.6072	−	1.12648i	1.87208	−	0.0792591i
$203$	−11.7692	−	15.0670i	−0.826034	−	1.05750i
$204$	−1.38843	+	1.03511i	−0.0972095	+	0.0724720i
$205$	−1.90663	+	1.52048i	−0.133165	+	0.106195i
$206$	17.1893	−	4.69648i	1.19764	−	0.327219i
$207$	8.54571	+	6.95569i	0.593968	+	0.483454i
$208$	−10.8999	−	9.72212i	−0.755770	−	0.674108i
$209$	−3.71036	−	2.95891i	−0.256651	−	0.204672i
$210$	−2.05757	−	1.90946i	−0.141986	−	0.131765i
$211$	4.85052	−	2.33588i	0.333923	−	0.160809i	−0.259407	−	0.965768i	$-0.583527\pi$
$211$	4.85052	−	2.33588i	0.333923	−	0.160809i	0.593330	+	0.804959i	$0.297813\pi$
$212$	10.7772	+	18.2503i	0.740184	+	1.25343i
$213$	−7.30784	−	21.2239i	−0.500725	−	1.45424i
$214$	21.6237	+	9.30816i	1.47817	+	0.636293i
$215$		−	2.11831i		−	0.144468i
$216$	3.27382	−	14.3277i	0.222755	−	0.974874i
$217$	−13.6215	−	10.8628i	−0.924690	−	0.737415i
$218$	−6.04251	+	8.27206i	−0.409251	+	0.560255i
$219$	−0.529537	−	4.92044i	−0.0357828	−	0.332492i
$220$	−0.474450	+	0.0402462i	−0.0319874	+	0.00271340i
$221$	−1.64469	−	0.792039i	−0.110634	−	0.0532783i
$222$	10.0278	−	3.93469i	0.673022	−	0.264079i
$223$	2.90255	+	6.02721i	0.194369	+	0.403612i	0.975262	−	0.221054i	$-0.0709496\pi$
$223$	2.90255	+	6.02721i	0.194369	+	0.403612i	−0.780892	+	0.624666i	$0.785235\pi$
$224$	12.3192	+	15.8613i	0.823108	+	1.05977i
$225$	−14.2858	−	3.41107i	−0.952389	−	0.227405i
$226$	5.96785	−	8.16984i	0.396975	−	0.543450i
$227$	0.533717	+	0.669259i	0.0354240	+	0.0444203i	0.799228	−	0.601028i	$-0.205242\pi$
$227$	0.533717	+	0.669259i	0.0354240	+	0.0444203i	−0.763804	+	0.645448i	$0.776671\pi$
$228$	−9.01184	−	20.3860i	−0.596824	−	1.35010i
$229$	−16.0488	+	3.66303i	−1.06053	+	0.242060i	−0.716994	−	0.697079i	$-0.754483\pi$
$229$	−16.0488	+	3.66303i	−1.06053	+	0.242060i	−0.343538	+	0.939139i	$0.611625\pi$
$230$	1.26545	−	1.09988i	0.0834416	−	0.0725238i
$231$	−3.85230	+	2.39382i	−0.253463	+	0.157502i
$232$	−12.9346	−	8.04346i	−0.849195	−	0.528079i
$233$		−	11.1762i		−	0.732179i	−0.930580	−	0.366090i	$-0.880696\pi$
$233$		−	11.1762i		−	0.732179i	0.930580	−	0.366090i	$-0.119304\pi$
$234$	14.9840	−	3.93359i	0.979533	−	0.257147i
$235$	−0.351641	−	1.54064i	−0.0229385	−	0.100500i
$236$	−1.38620	+	9.85267i	−0.0902336	+	0.641354i
$237$	10.4988	+	3.73264i	0.681973	+	0.242461i
$238$	2.02690	+	1.48060i	0.131384	+	0.0959728i
$239$	4.35430	+	19.0774i	0.281656	+	1.23402i	0.895669	+	0.444721i	$0.146697\pi$
$239$	4.35430	+	19.0774i	0.281656	+	1.23402i	−0.614013	+	0.789296i	$0.710446\pi$
$240$	−2.06263	−	0.864155i	−0.133142	−	0.0557810i
$241$	15.3694	−	7.40151i	0.990030	−	0.476773i	0.132487	−	0.991185i	$-0.457704\pi$
$241$	15.3694	−	7.40151i	0.990030	−	0.476773i	0.857544	+	0.514411i	$0.171990\pi$
$242$	2.67767	−	14.5425i	0.172127	−	0.934830i
$243$	10.7441	+	11.2944i	0.689237	+	0.724536i
$244$	1.70503	+	20.1000i	0.109153	+	1.28677i
$245$	−0.784909	+	1.62988i	−0.0501460	+	0.104129i
$246$	−1.38443	+	18.4541i	−0.0882682	+	1.17659i
$247$	14.6485	−	18.3687i	0.932063	−	1.16877i
$248$	−13.1674	−	4.39078i	−0.836134	−	0.278815i
$249$	−7.08737	+	4.40409i	−0.449144	+	0.279098i
$250$	−1.78609	+	4.14925i	−0.112962	+	0.262421i
$251$	21.4035	+	4.88521i	1.35098	+	0.308352i	0.835943	−	0.548817i	$-0.184922\pi$
$251$	21.4035	+	4.88521i	1.35098	+	0.308352i	0.515036	+	0.857169i	$0.327779\pi$
$252$	−21.2423	+	1.58847i	−1.33814	+	0.100064i
$253$	−1.17539	−	2.44072i	−0.0738962	−	0.153447i
$254$	−0.786731	−	2.87947i	−0.0493639	−	0.180674i
$255$	−0.277587	−	0.0326807i	−0.0173832	−	0.00204655i
$256$	13.5637	+	8.48677i	0.847733	+	0.530423i
$257$	4.97743	+	1.13607i	0.310484	+	0.0708659i	0.374924	−	0.927056i	$-0.377669\pi$
$257$	4.97743	+	1.13607i	0.310484	+	0.0708659i	−0.0644399	+	0.997922i	$0.520526\pi$
$258$	−11.7829	−	10.9347i	−0.733570	−	0.680763i
$259$	−9.73455	−	12.2067i	−0.604876	−	0.758490i
$260$	−0.199245	−	2.34883i	−0.0123566	−	0.145668i
$261$	14.6933	−	6.71623i	0.909491	−	0.415724i
$262$	1.06063	+	25.0517i	0.0655259	+	1.54770i
$263$	−22.5861	+	18.0118i	−1.39272	+	1.11065i	−0.412894	+	0.910779i	$0.635482\pi$
$263$	−22.5861	+	18.0118i	−1.39272	+	1.11065i	−0.979821	+	0.199875i	$0.935947\pi$
$264$	−2.22524	+	2.84683i	−0.136954	+	0.175210i
$265$	−0.761180	+	3.33495i	−0.0467589	+	0.204864i
$266$	−24.3829	+	21.1926i	−1.49501	+	1.29940i
$267$	−0.678252	+	5.76100i	−0.0415084	+	0.352567i
$268$	11.2656	−	3.59657i	0.688158	−	0.219696i
$269$	−7.35074	+	3.53993i	−0.448182	+	0.215833i	−0.644340	−	0.764739i	$-0.722868\pi$
$269$	−7.35074	+	3.53993i	−0.448182	+	0.215833i	0.196158	+	0.980572i	$0.437154\pi$
$270$	1.97318	−	1.31640i	0.120084	−	0.0801134i
$271$	2.00199	−	8.77131i	0.121613	−	0.532819i	−0.877016	−	0.480461i	$-0.840469\pi$
$271$	2.00199	−	8.77131i	0.121613	−	0.532819i	0.998628	−	0.0523578i	$-0.0166736\pi$
$272$	1.92210	+	0.551771i	0.116544	+	0.0334560i
$273$	−11.8509	−	19.0713i	−0.717251	−	1.15425i
$274$	−9.04510	−	3.89356i	−0.546435	−	0.235219i
$275$	2.82318	+	2.25141i	0.170244	+	0.135765i
$276$	0.414294	−	12.7165i	0.0249376	−	0.765443i
$277$	7.01096	+	3.37630i	0.421248	+	0.202862i	0.632485	−	0.774573i	$-0.282035\pi$
$277$	7.01096	+	3.37630i	0.421248	+	0.202862i	−0.211237	+	0.977435i	$0.567749\pi$
$278$	−0.400474	−	9.45908i	−0.0240188	−	0.567318i
$279$	11.6014	−	9.06375i	0.694555	−	0.542633i
$280$	−0.315408	+	3.22594i	−0.0188493	+	0.192787i
$281$	2.58459	+	5.36695i	0.154183	+	0.320165i	0.963725	−	0.266897i	$-0.0859985\pi$
$281$	2.58459	+	5.36695i	0.154183	+	0.320165i	−0.809541	+	0.587063i	$0.800284\pi$
$282$	−10.3848	−	5.99679i	−0.618407	−	0.357103i
$283$	−28.7354	+	6.55866i	−1.70814	+	0.389872i	−0.961381	−	0.275222i	$-0.911249\pi$
$283$	−28.7354	+	6.55866i	−1.70814	+	0.389872i	−0.746760	+	0.665094i	$0.768392\pi$
$284$	−14.3898	+	21.5580i	−0.853876	+	1.27923i
$285$	1.20505	−	3.38947i	0.0713813	−	0.200775i
$286$	−3.74575	−	0.689693i	−0.221491	−	0.0407824i
$287$	26.1499	−	5.96854i	1.54358	−	0.352312i
$288$	−15.4540	+	7.01240i	−0.910636	+	0.413210i
$289$	−16.7501			−0.985298
$290$	−0.623981	−	2.37776i	−0.0366414	−	0.139627i
$291$	−0.465346	−	0.748867i	−0.0272791	−	0.0438994i
$292$	−4.15059	+	3.92777i	−0.242895	+	0.229856i
$293$	4.42992	+	19.4087i	0.258799	+	1.13387i	0.922538	+	0.385907i	$0.126111\pi$
$293$	4.42992	+	19.4087i	0.258799	+	1.13387i	−0.663739	+	0.747964i	$0.731032\pi$
$294$	5.01436	+	12.7794i	0.292443	+	0.745309i
$295$	−1.25548	+	1.00121i	−0.0730968	+	0.0582928i
$296$	−10.6284	−	6.46179i	−0.617764	−	0.375584i
$297$	−1.21148	−	3.63599i	−0.0702971	−	0.210982i
$298$	9.46081	+	17.6898i	0.548050	+	1.02474i
$299$	12.0831	−	5.81893i	0.698786	−	0.336518i
$300$	6.85703	+	15.5116i	0.395891	+	0.895560i
$301$	−10.1090	+	20.9915i	−0.582673	+	1.20993i
$302$	0.798130	+	18.8516i	0.0459272	+	1.08479i
$303$	32.4290	−	3.49000i	1.86300	−	0.200496i
$304$	−12.4282	+	22.5376i	−0.712805	+	1.29262i
$305$	−2.02988	+	2.54538i	−0.116230	+	0.145748i
$306$	−1.61468	+	1.37535i	−0.0923051	+	0.0786235i
$307$	0.824590			0.0470618			0.0235309	−	0.999723i	$-0.492509\pi$
$307$	0.824590			0.0470618			0.0235309	+	0.999723i	$0.492509\pi$
$308$	4.89366	+	1.86535i	0.278842	+	0.106288i
$309$	20.6352	−	7.10513i	1.17389	−	0.404197i
$310$	−1.05648	−	1.97541i	−0.0600041	−	0.112196i
$311$	9.81515	+	20.3814i	0.556566	+	1.15572i	0.969530	+	0.244974i	$0.0787795\pi$
$311$	9.81515	+	20.3814i	0.556566	+	1.15572i	−0.412963	+	0.910748i	$0.635506\pi$
$312$	−14.0936	−	11.0163i	−0.797894	−	0.623677i
$313$	12.2263	−	15.3313i	0.691072	−	0.866577i	−0.305249	−	0.952273i	$-0.598740\pi$
$313$	12.2263	−	15.3313i	0.691072	−	0.866577i	0.996321	+	0.0856951i	$0.0273111\pi$
$314$	7.21348	−	6.26964i	0.407080	−	0.353817i
$315$	−2.66636	−	2.17025i	−0.150232	−	0.122280i
$316$	−3.91305	−	12.2569i	−0.220126	−	0.689506i
$317$	−2.25457	−	2.82714i	−0.126629	−	0.158788i	0.714475	−	0.699661i	$-0.246666\pi$
$317$	−2.25457	−	2.82714i	−0.126629	−	0.158788i	−0.841104	+	0.540873i	$0.818094\pi$
$318$	14.6211	+	21.4489i	0.819910	+	1.20279i
$319$	−3.97172	−	0.0400161i	−0.222374	−	0.00224047i
$320$	0.648557	+	2.49953i	0.0362555	+	0.139728i
$321$	27.1671	+	9.65868i	1.51632	+	0.539095i
$322$	−17.7889	+	4.86032i	−0.991339	+	0.270855i
$323$	−0.715786	+	3.13606i	−0.0398274	+	0.174495i
$324$	2.86320	−	17.7708i	0.159066	−	0.987268i
$325$	−11.1459	+	13.9766i	−0.618265	+	0.775280i
$326$	−7.31811	−	26.7846i	−0.405313	−	1.48346i
$327$	−6.72796	+	10.5898i	−0.372057	+	0.585615i
$328$	17.9240	−	11.6343i	0.989689	−	0.642398i
$329$	−3.86763	+	16.9452i	−0.213229	+	0.934219i
$330$	−0.576661	+	0.0868704i	−0.0317441	+	0.00478206i
$331$	23.7698			1.30651			0.653253	−	0.757139i	$-0.273404\pi$
$331$	23.7698			1.30651			0.653253	+	0.757139i	$0.273404\pi$
$332$	9.00324	+	3.43182i	0.494117	+	0.188346i
$333$	11.9431	−	5.60530i	0.654480	−	0.307168i
$334$	9.16632	−	12.5485i	0.501559	−	0.686622i
$335$	1.71960	+	0.828115i	0.0939517	+	0.0452448i
$336$	16.3158	+	18.4067i	0.890102	+	1.00417i
$337$	−6.26978	+	13.0193i	−0.341537	+	0.709208i	−0.999020	−	0.0442607i	$-0.985907\pi$
$337$	−6.26978	+	13.0193i	−0.341537	+	0.709208i	0.657483	+	0.753469i	$0.271621\pi$
$338$	0.0852570	−	0.463035i	0.00463737	−	0.0251858i
$339$	6.64482	−	10.4589i	0.360897	−	0.568050i
$340$	0.164110	+	0.277905i	0.00890010	+	0.0150715i
$341$	−3.52879	+	0.805422i	−0.191094	+	0.0436161i
$342$	−12.6331	−	24.1994i	−0.683120	−	1.30855i
$343$	−3.87375	+	3.08922i	−0.209163	+	0.166802i
$344$	−1.80621	+	18.4736i	−0.0973845	+	0.996032i
$345$	1.45924	−	1.44474i	0.0785628	−	0.0777823i
$346$	26.0988	−	22.6840i	1.40308	−	1.21950i
$347$	−17.4812			−0.938439			−0.469219	−	0.883082i	$-0.655465\pi$
$347$	−17.4812			−0.938439			−0.469219	+	0.883082i	$0.655465\pi$
$348$	−16.4470	−	8.80313i	−0.881653	−	0.471897i
$349$	22.0072			1.17802			0.589010	−	0.808126i	$-0.299518\pi$
$349$	22.0072			1.17802			0.589010	+	0.808126i	$0.299518\pi$
$350$	18.5528	−	16.1253i	0.991687	−	0.861931i
$351$	18.0005	−	5.99759i	0.960795	−	0.320128i
$352$	4.17196	+	0.0535636i	0.222366	+	0.00285495i
$353$	2.17527	−	1.73472i	0.115778	−	0.0923300i	−0.563889	−	0.825850i	$-0.690696\pi$
$353$	2.17527	−	1.73472i	0.115778	−	0.0923300i	0.679667	+	0.733520i	$0.262124\pi$
$354$	−0.911624	+	12.1517i	−0.0484522	+	0.645856i
$355$	−4.07833	+	0.930853i	−0.216455	+	0.0494045i
$356$	5.76760	−	3.40591i	0.305682	−	0.180513i
$357$	2.59481	+	1.64855i	0.137332	+	0.0872505i
$358$	−5.95274	+	32.3296i	−0.314612	+	1.70867i
$359$	−3.97191	+	8.24775i	−0.209629	+	0.435300i	−0.979099	−	0.203383i	$-0.934806\pi$
$359$	−3.97191	+	8.24775i	−0.209629	+	0.435300i	0.769470	+	0.638683i	$0.220520\pi$
$360$	−2.58951	−	0.892319i	−0.136479	−	0.0470294i
$361$	−20.1819	−	9.71911i	−1.06221	−	0.511532i
$362$	14.2250	−	19.4737i	0.747649	−	1.02351i
$363$	2.11753	−	17.9861i	0.111142	−	0.944025i
$364$	−9.23466	+	24.2267i	−0.484028	+	1.26983i
$365$	−0.922274			−0.0482740
$366$	3.68026	+	24.4302i	0.192370	+	1.27699i
$367$	−2.84740	+	12.4753i	−0.148633	+	0.651204i	0.844633	+	0.535346i	$0.179819\pi$
$367$	−2.84740	+	12.4753i	−0.148633	+	0.651204i	−0.993266	+	0.115858i	$0.963038\pi$
$368$	−11.9738	+	8.51294i	−0.624176	+	0.443768i
$369$	−0.226307	+	22.6640i	−0.0117811	+	1.17984i
$370$	−0.529100	−	1.93653i	−0.0275066	−	0.100675i
$371$	23.4580	−	29.4154i	1.21788	−	1.52717i
$372$	−16.4415	−	4.32046i	−0.852455	−	0.224005i
$373$	−2.07715	+	9.10061i	−0.107551	+	0.471212i	0.892255	+	0.451531i	$0.149122\pi$
$373$	−2.07715	+	9.10061i	−0.107551	+	0.471212i	−0.999806	+	0.0196804i	$0.993735\pi$
$374$	0.503030	−	0.137438i	0.0260111	−	0.00710677i
$375$	−1.85335	+	5.21293i	−0.0957064	+	0.269194i
$376$	1.75298	+	13.7357i	0.0904033	+	0.708362i
$377$	0.198105	−	19.6625i	0.0102029	−	1.01267i
$378$	−25.8355	+	3.62852i	−1.32883	+	0.186631i
$379$	−23.8967	−	29.9655i	−1.22749	−	1.53923i	−0.751430	−	0.659813i	$-0.770635\pi$
$379$	−23.8967	−	29.9655i	−1.22749	−	1.53923i	−0.476062	−	0.879412i	$-0.657936\pi$
$380$	−3.95706	+	1.26330i	−0.202993	+	0.0648058i
$381$	−1.19022	−	3.45670i	−0.0609766	−	0.177092i
$382$	−9.71019	+	8.43967i	−0.496816	+	0.431811i
$383$	1.71540	−	2.15105i	0.0876531	−	0.109914i	−0.736071	−	0.676904i	$-0.763321\pi$
$383$	1.71540	−	2.15105i	0.0876531	−	0.109914i	0.823724	+	0.566991i	$0.191893\pi$
$384$	17.2512	+	9.29497i	0.880346	+	0.474332i
$385$	0.366735	+	0.761533i	0.0186905	+	0.0388113i
$386$	−8.31125	−	15.5404i	−0.423031	−	0.790985i
$387$	−15.2691	−	12.4281i	−0.776173	−	0.631758i
$388$	−0.362614	+	0.951302i	−0.0184089	+	0.0482950i
$389$	−13.3945			−0.679128			−0.339564	−	0.940583i	$-0.610279\pi$
$389$	−13.3945			−0.679128			−0.339564	+	0.940583i	$0.610279\pi$
$390$	−0.430064	−	2.85484i	−0.0217771	−	0.144560i
$391$	−1.14485	+	1.43559i	−0.0578974	+	0.0726011i
$392$	8.23489	−	13.5448i	0.415925	−	0.684116i
$393$	3.28598	+	30.5332i	0.165756	+	1.54019i
$394$	−0.0406720	−	0.960661i	−0.00204903	−	0.0483974i
$395$	0.900983	−	1.87091i	0.0453334	−	0.0941357i
$396$	−2.49350	+	3.65604i	−0.125303	+	0.183723i
$397$	19.6973	−	9.48574i	0.988581	−	0.476076i	0.131533	−	0.991312i	$-0.458010\pi$
$397$	19.6973	−	9.48574i	0.988581	−	0.476076i	0.857048	+	0.515236i	$0.172296\pi$
$398$	9.22486	+	17.2487i	0.462401	+	0.864597i
$399$	−28.1168	+	27.8374i	−1.40760	+	1.39362i
$400$	9.45650	−	17.1487i	0.472825	−	0.857435i
$401$	−8.64731	+	6.89600i	−0.431826	+	0.344370i	−0.815156	−	0.579242i	$-0.803349\pi$
$401$	−8.64731	+	6.89600i	−0.431826	+	0.344370i	0.383330	+	0.923612i	$0.374777\pi$
$402$	13.4828	−	5.29038i	0.672463	−	0.263860i
$403$	−3.98735	−	17.4697i	−0.198624	−	0.870230i
$404$	−25.8867	−	27.3552i	−1.28791	−	1.36097i
$405$	2.30700	−	1.76557i	0.114636	−	0.0877321i
$406$	−5.16377	+	26.5404i	−0.256274	+	1.31718i
$407$	−3.24360			−0.160779
$408$	2.39295	+	0.521696i	0.118469	+	0.0258278i
$409$	−32.4008	+	7.39528i	−1.60212	+	0.365673i	−0.927891	−	0.372851i	$-0.878380\pi$
$409$	−32.4008	+	7.39528i	−1.60212	+	0.365673i	−0.674227	+	0.738524i	$0.735523\pi$
$410$	3.39178	+	0.624517i	0.167508	+	0.0308427i
$411$	−11.3639	−	4.04018i	−0.560538	−	0.199287i
$412$	−20.9600	−	13.9906i	−1.03262	−	0.689268i
$413$	17.2192	−	3.93018i	0.847303	−	0.193391i
$414$	−0.503659	−	15.5746i	−0.0247535	−	0.765449i
$415$	0.674710	+	1.40105i	0.0331202	+	0.0687748i
$416$	−0.265174	+	20.6539i	−0.0130012	+	1.01264i
$417$	−1.24072	−	11.5288i	−0.0607586	−	0.564566i
$418$	0.283893	+	6.70547i	0.0138857	+	0.327975i
$419$	15.7047	+	7.56301i	0.767227	+	0.369477i	0.776203	−	0.630483i	$-0.217143\pi$
$419$	15.7047	+	7.56301i	0.767227	+	0.369477i	−0.00897634	+	0.999960i	$0.502857\pi$
$420$	−0.129264	+	3.96769i	−0.00630746	+	0.193603i
$421$	−17.5131	−	13.9662i	−0.853536	−	0.680672i	0.0956405	−	0.995416i	$-0.469510\pi$
$421$	−17.5131	−	13.9662i	−0.853536	−	0.680672i	−0.949177	+	0.314744i	$0.898082\pi$
$422$	−6.99326	−	3.01032i	−0.340427	−	0.146540i
$423$	−13.1683	−	6.50427i	−0.640263	−	0.316248i
$424$	9.48179	−	28.4348i	0.460477	−	1.38092i
$425$	0.544636	−	2.38621i	0.0264187	−	0.115748i
$426$	−15.8745	+	27.4903i	−0.769121	+	1.33191i
$427$	32.2623	−	15.5367i	1.56128	−	0.751873i
$428$	−10.1255	−	31.7164i	−0.489435	−	1.53307i
$429$	−4.63271	−	0.545417i	−0.223670	−	0.0263330i
$430$	−2.26106	+	1.96522i	−0.109038	+	0.0947711i
$431$	4.91082	−	21.5157i	0.236546	−	1.03638i	−0.707539	−	0.706674i	$-0.750195\pi$
$431$	4.91082	−	21.5157i	0.236546	−	1.03638i	0.944085	−	0.329702i	$-0.106948\pi$
$432$	−18.3304	+	9.79774i	−0.881923	+	0.471394i
$433$	−8.29721	+	6.61681i	−0.398739	+	0.317983i	−0.802247	−	0.596993i	$-0.796362\pi$
$433$	−8.29721	+	6.61681i	−0.398739	+	0.317983i	0.403508	+	0.914976i	$0.367791\pi$
$434$	1.04223	+	24.6172i	0.0500287	+	1.18166i
$435$	−0.951461	−	2.85646i	−0.0456190	−	0.136957i
$436$	14.4353	−	1.22451i	0.691326	−	0.0586432i
$437$	−14.7346	−	18.4766i	−0.704851	−	0.883856i
$438$	−4.76076	+	5.13005i	−0.227478	+	0.245123i
$439$	1.44167	+	0.329052i	0.0688073	+	0.0157048i	0.256786	−	0.966468i	$-0.417336\pi$
$439$	1.44167	+	0.329052i	0.0688073	+	0.0157048i	−0.187979	+	0.982173i	$0.560194\pi$
$440$	0.483119	+	0.469086i	0.0230318	+	0.0223628i
$441$	7.14337	+	15.2203i	0.340161	+	0.724775i
$442$	0.680408	+	2.49032i	0.0323637	+	0.118452i
$443$	11.7045	+	24.3046i	0.556097	+	1.15475i	0.969702	+	0.244291i	$0.0785553\pi$
$443$	11.7045	+	24.3046i	0.556097	+	1.15475i	−0.413605	+	0.910457i	$0.635730\pi$
$444$	−13.5029	−	7.05324i	−0.640820	−	0.334732i
$445$	1.05394	+	0.240555i	0.0499615	+	0.0114034i
$446$	3.74060	−	8.68977i	0.177123	−	0.411473i
$447$	12.9677	+	20.8685i	0.613351	+	0.987047i
$448$	5.50131	−	27.8643i	0.259912	−	1.31646i
$449$	7.60580	−	9.53737i	0.358940	−	0.450096i	−0.569272	−	0.822150i	$-0.692775\pi$
$449$	7.60580	−	9.53737i	0.358940	−	0.450096i	0.928211	+	0.372053i	$0.121346\pi$
$450$	9.61243	+	18.4131i	0.453134	+	0.868002i
$451$	2.41775	−	5.02051i	0.113847	−	0.236406i
$452$	−14.2569	+	1.20938i	−0.670590	+	0.0568842i
$453$	2.47272	+	22.9764i	0.116178	+	1.07953i
$454$	0.219217	−	1.19057i	0.0102883	−	0.0558764i
$455$	−3.77007	+	1.81557i	−0.176744	+	0.0851153i
$456$	−13.3993	+	28.5318i	−0.627479	+	1.33613i
$457$	−5.48242	−	24.0200i	−0.256457	−	1.12361i	−0.925009	−	0.379945i	$-0.875943\pi$
$457$	−5.48242	−	24.0200i	−0.256457	−	1.12361i	0.668553	−	0.743665i	$-0.266914\pi$
$458$	18.7988	+	13.7320i	0.878409	+	0.641654i
$459$	−1.86417	+	1.80915i	−0.0870121	+	0.0844439i
$460$	−2.34800	−	0.330345i	−0.109476	−	0.0154024i
$461$	−0.756735	−	3.31547i	−0.0352447	−	0.154417i	0.954244	−	0.299031i	$-0.0966633\pi$
$461$	−0.756735	−	3.31547i	−0.0352447	−	0.154417i	−0.989488	+	0.144614i	$0.953806\pi$
$462$	6.12902	+	1.89109i	0.285148	+	0.0879816i
$463$		−	27.5849i		−	1.28198i	−0.767550	−	0.640989i	$-0.778524\pi$
$463$		−	27.5849i		−	1.28198i	0.767550	−	0.640989i	$-0.221476\pi$
$464$	3.41425	+	21.2684i	0.158503	+	0.987359i
$465$	−1.44809	−	2.33037i	−0.0671537	−	0.108068i
$466$	−11.9294	+	10.3685i	−0.552618	+	0.480312i
$467$	−39.1575	+	8.93744i	−1.81199	+	0.413575i	−0.988181	−	0.153289i	$-0.951014\pi$
$467$	−39.1575	+	8.93744i	−1.81199	+	0.413575i	−0.823811	+	0.566864i	$0.808156\pi$
$468$	−18.0997	−	12.3444i	−0.836660	−	0.570622i
$469$	−13.0886	−	16.4125i	−0.604373	−	0.757860i
$470$	−1.31824	+	1.80463i	−0.0608057	+	0.0832416i
$471$	8.31812	−	8.23548i	0.383279	−	0.379471i
$472$	11.8026	−	7.66099i	0.543261	−	0.352626i
$473$	2.10014	+	4.36098i	0.0965645	+	0.200518i
$474$	−5.75589	−	14.6692i	−0.264377	−	0.673780i
$475$	28.3815	+	13.6678i	1.30223	+	0.627123i
$476$	−0.300040	−	3.53708i	−0.0137523	−	0.162122i
$477$	19.5730	+	25.0529i	0.896185	+	1.14709i
$478$	16.3234	−	22.3464i	0.746617	−	1.02210i
$479$	1.09334	+	0.871909i	0.0499560	+	0.0398385i	0.648150	−	0.761513i	$-0.275543\pi$
$479$	1.09334	+	0.871909i	0.0499560	+	0.0398385i	−0.598194	+	0.801352i	$0.704115\pi$
$480$	0.991168	+	3.00333i	0.0452404	+	0.137083i
$481$		−	16.0579i		−	0.732176i
$482$	−22.1589	−	9.53854i	−1.00931	−	0.434469i
$483$	−21.3550	+	7.35299i	−0.971688	+	0.334573i
$484$	−18.0067	+	10.6334i	−0.818487	+	0.483337i
$485$	−0.148038	+	0.0712914i	−0.00672206	+	0.00323717i
$486$	2.08787	−	21.9463i	0.0947078	−	0.995505i
$487$	8.93741	+	7.12735i	0.404993	+	0.322971i	0.804711	−	0.593667i	$-0.202320\pi$
$487$	8.93741	+	7.12735i	0.404993	+	0.322971i	−0.399718	+	0.916638i	$0.630892\pi$
$488$	19.8728	−	20.4673i	0.899598	−	0.926512i
$489$	−11.0713	−	32.1540i	−0.500661	−	1.45405i
$490$	2.46790	−	0.674283i	0.111488	−	0.0304610i
$491$	28.6863	−	22.8766i	1.29459	−	1.03240i	0.297620	−	0.954685i	$-0.403807\pi$
$491$	28.6863	−	22.8766i	1.29459	−	1.03240i	0.996975	−	0.0777204i	$-0.0247642\pi$
$492$	20.9821	−	15.6427i	0.945946	−	0.705226i
$493$	1.14361	+	2.43725i	0.0515057	+	0.109768i
$494$	−33.1963	+	1.40545i	−1.49357	+	0.0632342i
$495$	−0.697876	+	0.151971i	−0.0313672	+	0.00683058i
$496$	7.52914	+	18.1282i	0.338068	+	0.813982i
$497$	44.8567	+	10.2383i	2.01210	+	0.459249i
$498$	11.2760	+	3.47918i	0.505291	+	0.155906i
$499$	−0.634462	−	0.505967i	−0.0284024	−	0.0226502i	0.609186	−	0.793028i	$-0.291496\pi$
$499$	−0.634462	−	0.505967i	−0.0284024	−	0.0226502i	−0.637588	+	0.770377i	$0.720068\pi$
$500$	6.08586	−	1.94292i	0.272168	−	0.0868901i
$501$	10.2061	−	16.0643i	0.455976	−	0.717702i
$502$	−14.6422	−	27.3780i	−0.653515	−	1.22194i
$503$	−25.0099	−	5.70836i	−1.11514	−	0.254523i	−0.375031	−	0.927012i	$-0.622368\pi$
$503$	−25.0099	−	5.70836i	−1.11514	−	0.254523i	−0.740107	+	0.672489i	$0.765225\pi$
$504$	21.4026	+	21.2001i	0.953348	+	0.944330i
$505$		−	6.07841i		−	0.270486i
$506$	−1.51476	+	3.51893i	−0.0673393	+	0.156435i
$507$	0.0674222	−	0.572677i	0.00299433	−	0.0254335i
$508$	−2.34364	+	3.51111i	−0.103982	+	0.155780i
$509$	4.54692	−	9.44178i	0.201539	−	0.418499i	−0.775564	−	0.631269i	$-0.782534\pi$
$509$	4.54692	−	9.44178i	0.201539	−	0.418499i	0.977102	+	0.212770i	$0.0682485\pi$
$510$	0.222642	+	0.326612i	0.00985875	+	0.0144626i
$511$	9.13934	+	4.40127i	0.404301	+	0.194701i
$512$	−3.52476	−	22.3512i	−0.155774	−	0.987793i
$513$	−17.3618	−	28.5723i	−0.766541	−	1.26150i
$514$	−3.40508	−	6.36682i	−0.150192	−	0.280828i
$515$	−0.905032	−	3.96520i	−0.0398805	−	0.174728i
$516$	−0.740244	+	22.7213i	−0.0325874	+	1.00025i
$517$	2.25135	+	2.82311i	0.0990144	+	0.124160i
$518$	−3.99833	+	21.7151i	−0.175677	+	0.954107i
$519$	30.0955	−	29.7965i	1.32104	−	1.30792i
$520$	−2.32227	+	2.39175i	−0.101838	+	0.104885i
$521$		−	37.9747i		−	1.66370i	−0.554999	−	0.831851i	$-0.687281\pi$
$521$		−	37.9747i		−	1.66370i	0.554999	−	0.831851i	$-0.312719\pi$
$522$	−20.8002	−	9.45261i	−0.910400	−	0.413729i
$523$			38.7627i			1.69498i	0.530814	+	0.847488i	$0.321886\pi$
$523$			38.7627i			1.69498i	−0.530814	+	0.847488i	$0.678114\pi$
$524$	25.7560	−	24.3733i	1.12516	−	1.06475i
$525$	21.3938	−	21.1813i	0.933704	−	0.924427i
$526$	40.1793	+	7.39808i	1.75190	+	0.322572i
$527$	1.52965	+	1.91812i	0.0666325	+	0.0835545i
$528$	5.10309	−	0.265891i	0.222084	−	0.0115714i
$529$	2.11615	+	9.27148i	0.0920067	+	0.403108i
$530$	4.26585	−	2.28145i	0.185297	−	0.0990998i
$531$	−0.149019	+	14.9238i	−0.00646687	+	0.647638i
$532$	45.2415	+	6.36513i	1.96147	+	0.275963i
$533$	24.8547	+	11.9694i	1.07658	+	0.518452i
$534$	6.77846	−	4.62068i	0.293333	−	0.199956i
$535$	2.33141	−	4.84122i	0.100796	−	0.209304i
$536$	−14.2904	−	8.68818i	−0.617251	−	0.375272i
$537$	−4.70749	+	39.9849i	−0.203143	+	1.72548i
$538$	10.5980	+	4.56201i	0.456911	+	0.196682i
$539$		−	4.13363i		−	0.178048i
$540$	−3.23568	−	0.884894i	−0.139242	−	0.0380798i
$541$	−19.8375	−	4.52779i	−0.852882	−	0.194665i	−0.226336	−	0.974049i	$-0.572675\pi$
$541$	−19.8375	−	4.52779i	−0.852882	−	0.194665i	−0.626546	+	0.779385i	$0.715532\pi$
$542$	−11.2197	+	6.00049i	−0.481928	+	0.257743i
$543$	15.8386	−	24.9299i	0.679701	−	1.06984i
$544$	−1.19423	−	2.56352i	−0.0512022	−	0.109910i
$545$	1.82803	+	1.45780i	0.0783041	+	0.0624454i
$546$	−9.36211	+	30.3426i	−0.400661	+	1.29854i
$547$	16.6244	+	3.79440i	0.710807	+	0.162237i	0.562612	−	0.826721i	$-0.309797\pi$
$547$	16.6244	+	3.79440i	0.710807	+	0.162237i	0.148195	+	0.988958i	$0.452654\pi$
$548$	4.23545	+	13.2668i	0.180930	+	0.566730i
$549$	6.43823	+	29.5655i	0.274777	+	1.26182i
$550$	−0.216012	−	5.10214i	−0.00921077	−	0.217556i
$551$	−33.8570	+	7.36958i	−1.44236	+	0.313954i
$552$	−13.9578	+	11.3552i	−0.594084	+	0.483311i
$553$	−17.8567	+	14.2403i	−0.759345	+	0.605557i
$554$	−2.90044	−	10.6157i	−0.123228	−	0.451019i
$555$	−0.800455	−	2.32473i	−0.0339774	−	0.0986795i
$556$	−9.72500	+	9.20292i	−0.412432	+	0.390291i
$557$	−22.2721	−	17.7614i	−0.943701	−	0.752576i	0.0252880	−	0.999680i	$-0.491950\pi$
$557$	−22.2721	−	17.7614i	−0.943701	−	0.752576i	−0.968989	+	0.247104i	$0.920521\pi$
$558$	−20.4375	−	3.97446i	−0.865187	−	0.168252i
$559$	−21.5897	+	10.3970i	−0.913145	+	0.439747i
$560$	3.73595	−	2.65613i	0.157873	−	0.112242i
$561$	0.603871	−	0.207925i	0.0254954	−	0.00877862i
$562$	3.33083	−	7.73783i	0.140503	−	0.326401i
$563$		−	32.5999i		−	1.37392i	−0.726694	−	0.686961i	$-0.758944\pi$
$563$		−	32.5999i		−	1.37392i	0.726694	−	0.686961i	$-0.241056\pi$
$564$	3.23338	+	16.6480i	0.136150	+	0.701009i
$565$	−1.80544	−	1.43979i	−0.0759554	−	0.0605724i
$566$	33.6593	+	24.5872i	1.41480	+	1.03348i
$567$	−31.2871	+	6.48662i	−1.31393	+	0.272412i
$568$	36.3606	−	4.64044i	1.52565	−	0.194709i
$569$	17.8144	+	8.57896i	0.746818	+	0.359649i	0.768274	−	0.640121i	$-0.221116\pi$
$569$	17.8144	+	8.57896i	0.746818	+	0.359649i	−0.0214560	+	0.999770i	$0.506830\pi$
$570$	−4.73585	+	1.85825i	−0.198363	+	0.0778334i
$571$	2.32917	+	4.83657i	0.0974728	+	0.202404i	0.944003	−	0.329936i	$-0.107027\pi$
$571$	2.32917	+	4.83657i	0.0974728	+	0.202404i	−0.846531	+	0.532340i	$0.821313\pi$
$572$	2.73887	+	4.63803i	0.114518	+	0.193926i
$573$	−11.1972	+	11.0859i	−0.467768	+	0.463120i
$574$	−30.6308	−	22.3749i	−1.27850	−	0.933912i
$575$	11.2114	+	14.0587i	0.467549	+	0.586288i
$576$	21.8221	+	9.98984i	0.909253	+	0.416243i
$577$	18.0841	−	4.12758i	0.752851	−	0.171833i	0.171160	−	0.985243i	$-0.445249\pi$
$577$	18.0841	−	4.12758i	0.752851	−	0.171833i	0.581691	+	0.813410i	$0.302391\pi$
$578$	15.5395	+	17.8788i	0.646358	+	0.743662i
$579$	−11.3920	−	18.3328i	−0.473436	−	0.761886i
$580$	−1.95911	+	2.87195i	−0.0813478	+	0.119251i
$581$		−	17.1037i		−	0.709579i
$582$	−0.367618	+	1.19145i	−0.0152383	+	0.0493872i
$583$	−1.73929	−	7.62033i	−0.0720341	−	0.315602i
$584$	8.04309	+	0.786393i	0.332825	+	0.0325412i
$585$	−0.752353	−	3.45493i	−0.0311060	−	0.142844i
$586$	16.6069	−	22.7345i	0.686026	−	0.939153i
$587$	6.36740	+	27.8974i	0.262811	+	1.15145i	0.918187	+	0.396147i	$0.129653\pi$
$587$	6.36740	+	27.8974i	0.262811	+	1.15145i	−0.655376	+	0.755303i	$0.727490\pi$
$588$	8.98862	−	17.2081i	0.370685	−	0.709649i
$589$	−28.4487	+	13.7002i	−1.17221	+	0.564506i
$590$	2.23343	+	0.411233i	0.0919487	+	0.0169302i
$591$	−0.126008	−	1.17086i	−0.00518326	−	0.0481626i
$592$	2.96303	+	17.3394i	0.121780	+	0.712647i
$593$	8.21662	−	17.0620i	0.337416	−	0.700652i	−0.661362	−	0.750067i	$-0.730021\pi$
$593$	8.21662	−	17.0620i	0.337416	−	0.700652i	0.998778	+	0.0494146i	$0.0157356\pi$
$594$	−2.75710	+	4.66633i	−0.113125	+	0.191462i
$595$	0.357205	−	0.447921i	0.0146440	−	0.0183630i
$596$	10.1049	−	26.5097i	0.413912	−	1.08588i
$597$	12.6443	+	20.3481i	0.517496	+	0.832791i
$598$	−17.4209	−	7.49903i	−0.712395	−	0.306658i
$599$	−30.6401	−	6.99341i	−1.25192	−	0.285743i	−0.455364	−	0.890305i	$-0.650491\pi$
$599$	−30.6401	−	6.99341i	−1.25192	−	0.285743i	−0.796558	+	0.604562i	$0.793348\pi$
$600$	10.1954	−	21.7096i	0.416226	−	0.886292i
$601$	7.07105	+	14.6832i	0.288434	+	0.598940i	0.993960	−	0.109744i	$-0.0350033\pi$
$601$	7.07105	+	14.6832i	0.288434	+	0.598940i	−0.705526	+	0.708685i	$0.749289\pi$
$602$	31.7845	−	8.68421i	1.29544	−	0.353942i
$603$	16.0581	−	7.53658i	0.653936	−	0.306913i
$604$	19.3816	−	18.3411i	0.788624	−	0.746288i
$605$	−3.29044	−	0.751022i	−0.133775	−	0.0305334i
$606$	−33.8105	−	31.3766i	−1.37346	−	1.27459i
$607$	0.0998902	+	0.125258i	0.00405442	+	0.00508408i	0.783855	−	0.620944i	$-0.213251\pi$
$607$	0.0998902	+	0.125258i	0.00405442	+	0.00508408i	−0.779800	+	0.626029i	$0.784679\pi$
$608$	35.5864	−	7.64307i	1.44322	−	0.309968i
$609$	−4.20305	+	32.8469i	−0.170316	+	1.33102i
$610$	4.60009	−	0.194756i	0.186252	−	0.00788546i
$611$	−13.9762	+	11.1456i	−0.565416	+	0.450904i
$612$	2.96602	+	0.447541i	0.119894	+	0.0180908i
$613$	−9.18942	+	40.2615i	−0.371157	+	1.62614i	0.352378	+	0.935858i	$0.385373\pi$
$613$	−9.18942	+	40.2615i	−0.371157	+	1.62614i	−0.723535	+	0.690287i	$0.757484\pi$
$614$	−0.764995	−	0.880158i	−0.0308727	−	0.0355203i
$615$	4.19492	+	0.493875i	0.169156	+	0.0199150i
$616$	−2.54894	−	6.95398i	−0.102700	−	0.280184i
$617$	−33.5737	+	16.1682i	−1.35163	+	0.650909i	−0.962753	−	0.270382i	$-0.912850\pi$
$617$	−33.5737	+	16.1682i	−1.35163	+	0.650909i	−0.388873	+	0.921291i	$0.627136\pi$
$618$	−26.7278	−	15.4341i	−1.07515	−	0.620852i
$619$	1.49912	−	6.56809i	0.0602549	−	0.263994i	−0.935823	−	0.352469i	$-0.885342\pi$
$619$	1.49912	−	6.56809i	0.0602549	−	0.263994i	0.996078	+	0.0884750i	$0.0281993\pi$
$620$	−1.12840	+	2.96032i	−0.0453178	+	0.118889i
$621$	−1.85255	−	18.9947i	−0.0743404	−	0.762233i
$622$	12.6491	−	29.3850i	0.507181	−	1.17823i
$623$	−9.29610	−	7.41339i	−0.372440	−	0.297011i
$624$	1.31633	+	25.2636i	0.0526953	+	1.01135i
$625$	−21.1259	−	10.1737i	−0.845036	−	0.406948i
$626$	−27.7072	+	1.17305i	−1.10740	+	0.0468847i
$627$	0.879540	+	8.17265i	0.0351254	+	0.326384i
$628$	−13.3843	−	1.88307i	−0.534092	−	0.0751427i
$629$	0.953915	+	1.98082i	0.0380351	+	0.0789807i
$630$	0.157147	+	4.85945i	0.00626090	+	0.193605i
$631$	−33.3217	+	7.60546i	−1.32652	+	0.302769i	−0.826348	−	0.563160i	$-0.809586\pi$
$631$	−33.3217	+	7.60546i	−1.32652	+	0.302769i	−0.500168	+	0.865928i	$0.666728\pi$
$632$	−9.45268	+	15.5478i	−0.376007	+	0.618460i
$633$	−8.78602	−	3.12368i	−0.349213	−	0.124155i
$634$	−0.926032	+	5.02932i	−0.0367774	+	0.199740i
$635$	−0.664231	+	0.151606i	−0.0263592	+	0.00601632i
$636$	9.32993	−	35.5051i	0.369956	−	1.40787i
$637$	20.4641			0.810817
$638$	3.64196	+	4.27649i	0.144187	+	0.169308i
$639$	−17.2179	+	34.8586i	−0.681129	+	1.37898i
$640$	2.06628	−	3.01114i	0.0816770	−	0.119026i
$641$	−1.87562	−	8.21763i	−0.0740826	−	0.324577i	0.924284	−	0.381705i	$-0.124663\pi$
$641$	−1.87562	−	8.21763i	−0.0740826	−	0.324577i	−0.998367	+	0.0571278i	$0.981806\pi$
$642$	−14.8941	−	37.9585i	−0.587823	−	1.49810i
$643$	−30.1332	+	24.0305i	−1.18834	+	0.947669i	−0.999411	−	0.0343224i	$-0.989073\pi$
$643$	−30.1332	+	24.0305i	−1.18834	+	0.947669i	−0.188928	+	0.981991i	$0.560501\pi$
$644$	21.6912	+	14.4787i	0.854751	+	0.570540i
$645$	−2.60731	+	2.58140i	−0.102663	+	0.101643i
$646$	4.01146	−	2.14539i	0.157829	−	0.0844093i
$647$	2.43121	−	1.17081i	0.0955809	−	0.0460293i	−0.385482	−	0.922715i	$-0.625965\pi$
$647$	2.43121	−	1.17081i	0.0955809	−	0.0460293i	0.481063	+	0.876686i	$0.340251\pi$
$648$	−21.6247	+	13.4303i	−0.849497	+	0.527594i
$649$	1.59204	−	3.30591i	0.0624932	−	0.129768i
$650$	25.2588	−	1.06940i	0.990733	−	0.0419452i
$651$	3.22898	+	30.0036i	0.126554	+	1.17593i
$652$	−21.8003	+	32.6601i	−0.853767	+	1.27907i
$653$	−7.69131	+	9.64460i	−0.300984	+	0.377422i	−0.909207	−	0.416344i	$-0.863311\pi$
$653$	−7.69131	+	9.64460i	−0.300984	+	0.377422i	0.608223	+	0.793766i	$0.291883\pi$
$654$	17.5451	−	2.64306i	0.686068	−	0.103352i
$655$	5.72306			0.223618
$656$	−29.0470	−	8.33843i	−1.13409	−	0.325561i
$657$	−5.41099	+	6.64790i	−0.211103	+	0.259359i
$658$	21.6752	−	11.5923i	0.844988	−	0.451914i
$659$	−10.6820	−	22.1813i	−0.416110	−	0.864061i	−0.998684	−	0.0512834i	$-0.983669\pi$
$659$	−10.6820	−	22.1813i	−0.416110	−	0.864061i	0.582574	−	0.812777i	$-0.302045\pi$
$660$	0.627709	+	0.534930i	0.0244335	+	0.0208221i
$661$	15.6274	−	19.5962i	0.607837	−	0.762204i	−0.378739	−	0.925503i	$-0.623642\pi$
$661$	15.6274	−	19.5962i	0.607837	−	0.762204i	0.986577	+	0.163300i	$0.0522138\pi$
$662$	−22.0519	−	25.3716i	−0.857072	−	0.986097i
$663$	1.02936	+	2.98954i	0.0399772	+	0.116104i
$664$	−4.68947	−	12.7938i	−0.181987	−	0.496494i
$665$	4.59736	+	5.76491i	0.178278	+	0.223553i
$666$	−17.0630	−	7.54778i	−0.661178	−	0.292470i
$667$	−19.2379	−	4.59531i	−0.744893	−	0.177931i
$668$	−21.8980	+	1.85754i	−0.847257	+	0.0718704i
$669$	3.88147	−	10.9174i	0.150066	−	0.422093i
$670$	−0.711399	−	2.60375i	−0.0274837	−	0.100592i
$671$	1.65537	−	7.25267i	0.0639050	−	0.279986i
$672$	4.51042	−	34.4917i	0.173993	−	1.33055i
$673$	29.7939	−	37.3604i	1.14847	−	1.44014i	0.269669	−	0.962953i	$-0.413086\pi$
$673$	29.7939	−	37.3604i	1.14847	−	1.44014i	0.878803	−	0.477185i	$-0.158343\pi$
$674$	19.7134	−	5.38611i	0.759330	−	0.207465i
$675$	13.2104	+	21.7404i	0.508470	+	0.836789i
$676$	−0.573334	+	0.338568i	−0.0220513	+	0.0130218i
$677$	−7.10149	+	31.1137i	−0.272932	+	1.19579i	0.633601	+	0.773660i	$0.281576\pi$
$677$	−7.10149	+	31.1137i	−0.272932	+	1.19579i	−0.906533	+	0.422135i	$0.861281\pi$
$678$	−17.3283	+	2.61040i	−0.665490	+	0.100252i
$679$	1.80721			0.0693543
$680$	0.144383	−	0.432989i	0.00553685	−	0.0166044i
$681$	0.173359	−	1.47249i	0.00664313	−	0.0564260i
$682$	4.13345	+	3.01938i	0.158278	+	0.115618i
$683$	38.1589	+	18.3763i	1.46011	+	0.703151i	0.984317	−	0.176407i	$-0.0564473\pi$
$683$	38.1589	+	18.3763i	1.46011	+	0.703151i	0.475792	+	0.879558i	$0.342162\pi$
$684$	−14.1101	+	35.9349i	−0.539511	+	1.37400i
$685$	−0.975218	+	2.02506i	−0.0372612	+	0.0773736i
$686$	6.89119	+	1.26885i	0.263107	+	0.0484450i
$687$	24.0659	+	15.2897i	0.918170	+	0.583339i
$688$	21.3942	−	15.2106i	0.815648	−	0.579898i
$689$	37.7255	−	8.61060i	1.43723	−	0.328038i
$690$	−2.89588	−	0.217250i	−0.110244	−	0.00827055i
$691$	−26.5589	+	21.1801i	−1.01035	+	0.805727i	−0.981033	−	0.193843i	$-0.937905\pi$
$691$	−26.5589	+	21.1801i	−1.01035	+	0.805727i	−0.0293174	+	0.999570i	$0.509333\pi$
$692$	−48.4253	−	6.81307i	−1.84085	−	0.258994i
$693$	7.64089	+	1.82444i	0.290253	+	0.0693047i
$694$	16.2178	+	18.6592i	0.615618	+	0.708294i
$695$	−2.16092			−0.0819685
$696$	5.86201	+	25.7223i	0.222199	+	0.975001i
$697$	−3.77700			−0.143064
$698$	−20.4167	−	23.4903i	−0.772784	−	0.889120i
$699$	−13.7562	+	13.6195i	−0.520307	+	0.515138i
$700$	−34.4238	−	4.84317i	−1.30110	−	0.183055i
$701$	−5.26734	+	4.20056i	−0.198945	+	0.158653i	−0.717895	−	0.696151i	$-0.754894\pi$
$701$	−5.26734	+	4.20056i	−0.198945	+	0.158653i	0.518951	+	0.854804i	$0.326323\pi$
$702$	−23.1013	−	13.6494i	−0.871903	−	0.515164i
$703$	−27.5867	+	6.29648i	−1.04045	+	0.237476i
$704$	−3.81328	−	4.50280i	−0.143718	−	0.169706i
$705$	−1.46777	+	2.31026i	−0.0552796	+	0.0870096i
$706$	−3.86969	−	0.712513i	−0.145638	−	0.0268158i
$707$	−29.0074	+	60.2344i	−1.09093	+	2.26535i
$708$	13.8163	−	10.3004i	0.519250	−	0.387113i
$709$	8.88152	+	4.27712i	0.333553	+	0.160630i	0.593162	−	0.805083i	$-0.297879\pi$
$709$	8.88152	+	4.27712i	0.333553	+	0.160630i	−0.259609	+	0.965714i	$0.583594\pi$
$710$	4.77717	+	3.48959i	0.179284	+	0.130962i
$711$	−8.19975	−	17.4711i	−0.307515	−	0.655217i
$712$	−8.98621	−	2.99652i	−0.336772	−	0.112299i
$713$	−18.0243			−0.675016
$714$	−0.647629	−	4.29907i	−0.0242369	−	0.160889i
$715$	−0.193442	+	0.847526i	−0.00723433	+	0.0316957i
$716$	40.0308	−	23.6392i	1.49602	−	0.883437i
$717$	18.1751	−	28.6075i	0.678763	−	1.06837i
$718$	12.4884	−	3.41210i	0.466063	−	0.127338i
$719$	16.6797	−	20.9157i	0.622048	−	0.780023i	−0.366583	−	0.930385i	$-0.619473\pi$
$719$	16.6797	−	20.9157i	0.622048	−	0.780023i	0.988631	+	0.150362i	$0.0480440\pi$
$720$	1.44991	+	3.59184i	0.0540349	+	0.133860i
$721$	−9.95425	+	43.6124i	−0.370716	+	1.62421i
$722$	8.34928	+	30.5587i	0.310728	+	1.13728i
$723$	−27.8395	−	9.89774i	−1.03536	−	0.368101i
$724$	−33.9829	+	2.88267i	−1.26297	+	0.107134i
$725$	25.7615	−	5.60745i	0.956759	−	0.208255i
$726$	−21.1627	+	14.4260i	−0.785420	+	0.535398i
$727$	12.5844	+	15.7803i	0.466729	+	0.585260i	0.958367	−	0.285540i	$-0.0921730\pi$
$727$	12.5844	+	15.7803i	0.466729	+	0.585260i	−0.491638	+	0.870800i	$0.663602\pi$
$728$	34.4266	−	12.6189i	1.27594	−	0.467686i
$729$	0.808663	−	26.9879i	0.0299505	−	0.999551i
$730$	0.855620	+	0.984426i	0.0316679	+	0.0364352i
$731$	2.04557	−	2.56506i	0.0756580	−	0.0948721i
$732$	22.6623	−	26.5928i	0.837621	−	0.982900i
$733$	−15.6083	−	32.4109i	−0.576505	−	1.19713i	−0.961653	−	0.274271i	$-0.911564\pi$
$733$	−15.6083	−	32.4109i	−0.576505	−	1.19713i	0.385147	−	0.922855i	$-0.374151\pi$
$734$	15.9576	−	8.53437i	0.589005	−	0.315009i
$735$	2.96263	−	1.02010i	0.109278	−	0.0376268i
$736$	20.1950	+	4.88298i	0.744399	+	0.179989i
$737$	−4.36117			−0.160646
$738$	24.4012	−	20.7844i	0.898222	−	0.765086i
$739$	−5.05270	+	6.33589i	−0.185867	+	0.233069i	−0.866031	−	0.499990i	$-0.833337\pi$
$739$	−5.05270	+	6.33589i	−0.185867	+	0.233069i	0.680164	+	0.733060i	$0.261908\pi$
$740$	−1.57617	+	2.36132i	−0.0579410	+	0.0868040i
$741$	−40.4598	+	4.35428i	−1.48633	+	0.159959i
$742$	−53.1603	+	2.25068i	−1.95158	+	0.0826249i
$743$	12.8327	−	26.6475i	0.470788	−	0.977601i	−0.521454	−	0.853279i	$-0.674610\pi$
$743$	12.8327	−	26.6475i	0.470788	−	0.977601i	0.992242	−	0.124322i	$-0.0396754\pi$
$744$	10.6417	+	21.5577i	0.390143	+	0.790345i
$745$	4.12534	−	1.98666i	0.151141	−	0.0727856i
$746$	11.6409	−	6.22576i	0.426205	−	0.227941i
$747$	14.0575	+	3.35656i	0.514338	+	0.122810i
$748$	−0.613375	−	0.409423i	−0.0224272	−	0.0149700i
$749$	−46.2065	+	36.8485i	−1.68835	+	1.34641i
$750$	7.28363	−	2.85794i	0.265960	−	0.104357i
$751$	7.26063	+	31.8109i	0.264944	+	1.16080i	0.915813	+	0.401605i	$0.131548\pi$
$751$	7.26063	+	31.8109i	0.264944	+	1.16080i	−0.650869	+	0.759190i	$0.725595\pi$
$752$	13.0350	−	14.6141i	0.475338	−	0.532920i
$753$	−20.0697	−	32.2976i	−0.731381	−	1.17699i
$754$	−21.1714	+	18.0300i	−0.771016	+	0.656615i
$755$	4.30664			0.156735
$756$	27.8413	+	24.2102i	1.01258	+	0.880518i
$757$	1.76930	−	0.403831i	0.0643063	−	0.0146775i	−0.190247	−	0.981736i	$-0.560929\pi$
$757$	1.76930	−	0.403831i	0.0643063	−	0.0146775i	0.254553	+	0.967059i	$0.418072\pi$
$758$	−9.81523	+	53.3069i	−0.356505	+	1.93620i
$759$	−1.57180	+	4.42103i	−0.0570528	+	0.160473i
$760$	5.01951	+	3.05173i	0.182077	+	0.110698i
$761$	−2.24766	+	0.513013i	−0.0814775	+	0.0185967i	−0.263065	−	0.964778i	$-0.584733\pi$
$761$	−2.24766	+	0.513013i	−0.0814775	+	0.0185967i	0.181588	+	0.983375i	$0.441876\pi$
$762$	−2.58545	+	4.47730i	−0.0936610	+	0.162196i
$763$	−11.1580	−	23.1699i	−0.403948	−	0.838807i
$764$	18.0168	+	2.53483i	0.651826	+	0.0917070i
$765$	0.298046	+	0.381491i	0.0107759	+	0.0137928i
$766$	−3.88744	+	0.164584i	−0.140459	+	0.00594668i
$767$	16.3664	+	7.88163i	0.590956	+	0.284589i
$768$	−6.08307	−	27.0369i	−0.219504	−	0.975612i
$769$	4.27488	+	3.40910i	0.154156	+	0.122935i	0.697531	−	0.716555i	$-0.254282\pi$
$769$	4.27488	+	3.40910i	0.154156	+	0.122935i	−0.543374	+	0.839490i	$0.682854\pi$
$770$	0.472622	−	1.09794i	0.0170321	−	0.0395672i
$771$	−4.66725	−	7.51087i	−0.168087	−	0.270497i
$772$	−8.87706	+	23.2886i	−0.319492	+	0.838175i
$773$	−5.47793	+	24.0004i	−0.197027	+	0.863233i	0.775667	+	0.631143i	$0.217414\pi$
$773$	−5.47793	+	24.0004i	−0.197027	+	0.863233i	−0.972694	+	0.232091i	$0.925443\pi$
$774$	0.899918	+	27.8280i	0.0323469	+	1.00026i
$775$	21.6464	−	10.4244i	0.777562	−	0.374454i
$776$	1.35182	−	0.495500i	0.0485274	−	0.0177874i
$777$	−3.16193	+	26.8570i	−0.113433	+	0.963491i
$778$	12.4264	+	14.2971i	0.445510	+	0.512577i
$779$	10.8170	−	47.3926i	0.387561	−	1.69802i
$780$	−2.64824	+	3.10756i	−0.0948223	+	0.111269i
$781$	7.47323	−	5.95970i	0.267413	−	0.213255i
$782$	2.59444	−	0.109842i	0.0927771	−	0.00392795i
$783$	−26.1721	−	9.90063i	−0.935314	−	0.353819i
$784$	−22.0973	+	3.77608i	−0.789190	+	0.134860i
$785$	−1.36009	−	1.70550i	−0.0485437	−	0.0608719i
$786$	29.5423	−	31.8339i	1.05374	−	1.13548i
$787$	36.7634	+	8.39101i	1.31047	+	0.299107i	0.820007	−	0.572353i	$-0.193969\pi$
$787$	36.7634	+	8.39101i	1.31047	+	0.299107i	0.490466	+	0.871460i	$0.336826\pi$
$788$	−0.987667	+	0.934645i	−0.0351842	+	0.0332954i
$789$	49.6934	+	5.85049i	1.76913	+	0.208283i
$790$	−2.83286	+	0.773997i	−0.100789	+	0.0275376i
$791$	11.0202	+	22.8836i	0.391832	+	0.813647i
$792$	6.21571	−	0.730271i	0.220866	−	0.0259490i
$793$	35.9053	+	8.19516i	1.27504	+	0.291019i
$794$	−28.3988	−	12.2245i	−1.00783	−	0.433833i
$795$	5.03238	−	3.12712i	0.178480	−	0.110908i
$796$	9.85287	−	25.8486i	0.349226	−	0.916179i
$797$	5.58545	−	7.00393i	0.197847	−	0.248092i	−0.673005	−	0.739638i	$-0.734997\pi$
$797$	5.58545	−	7.00393i	0.197847	−	0.248092i	0.870852	+	0.491546i	$0.163568\pi$
$798$	55.7981	+	4.18599i	1.97523	+	0.148182i
$799$	1.06193	−	2.20513i	0.0375685	−	0.0780117i
$800$	−27.0774	+	5.81555i	−0.957331	+	0.205611i
$801$	7.91742	−	6.18562i	0.279748	−	0.218558i
$802$	15.3831	+	2.83243i	0.543195	+	0.100017i
$803$	1.89869	−	0.914363i	0.0670034	−	0.0322672i
$804$	−18.1553	−	9.48341i	−0.640288	−	0.334454i
$805$	0.936604	+	4.10353i	0.0330109	+	0.144630i
$806$	−14.9478	+	20.4632i	−0.526515	+	0.720787i
$807$	13.3148	+	4.73380i	0.468704	+	0.166638i
$808$	−5.18286	+	53.0094i	−0.182332	+	1.86486i
$809$	−5.02237	−	22.0044i	−0.176577	−	0.773635i	−0.983195	−	0.182561i	$-0.941561\pi$
$809$	−5.02237	−	22.0044i	−0.176577	−	0.773635i	0.806617	−	0.591074i	$-0.201296\pi$
$810$	−4.02483	−	0.824497i	−0.141418	−	0.0289699i
$811$			27.8239i			0.977029i	0.872556	+	0.488515i	$0.162461\pi$
$811$			27.8239i			0.977029i	−0.872556	+	0.488515i	$0.837539\pi$
$812$	33.1195	−	19.1105i	1.16227	−	0.670647i
$813$	−13.2358	+	8.22471i	−0.464199	+	0.288453i
$814$	3.00918	+	3.46218i	0.105472	+	0.121349i
$815$	−6.17862	+	1.41023i	−0.216428	+	0.0493982i
$816$	−1.66315	−	3.03820i	−0.0582220	−	0.106358i
$817$	26.3272	+	33.0132i	0.921071	+	1.15499i
$818$	37.9528	+	27.7235i	1.32699	+	0.969329i
$819$	−9.03213	+	37.8273i	−0.315608	+	1.32179i
$820$	−2.48005	−	4.19973i	−0.0866070	−	0.146661i
$821$	−12.6171	−	26.1997i	−0.440341	−	0.914377i	−0.996523	−	0.0833166i	$-0.973449\pi$
$821$	−12.6171	−	26.1997i	−0.440341	−	0.914377i	0.556182	−	0.831060i	$-0.312266\pi$
$822$	6.23013	+	15.8779i	0.217301	+	0.553804i
$823$	−5.11301	−	2.46229i	−0.178228	−	0.0858302i	0.342642	−	0.939466i	$-0.388678\pi$
$823$	−5.11301	−	2.46229i	−0.178228	−	0.0858302i	−0.520870	+	0.853636i	$0.674392\pi$
$824$	4.51172	+	35.3519i	0.157173	+	1.23154i
$825$	−0.669235	−	6.21850i	−0.0232998	−	0.216501i
$826$	−20.1698	−	14.7335i	−0.701797	−	0.512644i
$827$	0.639941	+	0.510336i	0.0222529	+	0.0177461i	0.634553	−	0.772879i	$-0.281184\pi$
$827$	0.639941	+	0.510336i	0.0222529	+	0.0177461i	−0.612300	+	0.790625i	$0.709756\pi$
$828$	−16.1569	+	14.9866i	−0.561491	+	0.520820i
$829$			5.04869i			0.175348i	0.996149	+	0.0876741i	$0.0279434\pi$
$829$			5.04869i			0.175348i	−0.996149	+	0.0876741i	$0.972057\pi$
$830$	0.869518	−	2.01997i	0.0301814	−	0.0701143i
$831$	−4.38796	−	12.7438i	−0.152217	−	0.442078i
$832$	22.2918	−	18.8782i	0.772827	−	0.654482i
$833$	−2.52436	+	1.21567i	−0.0874637	+	0.0421203i
$834$	−11.1546	+	12.0199i	−0.386253	+	0.416215i
$835$	−2.77306	−	2.21144i	−0.0959658	−	0.0765302i
$836$	6.89397	−	6.52388i	0.238433	−	0.225633i
$837$	−25.2937	−	3.23423i	−0.874277	−	0.111791i
$838$	−6.49706	−	23.7795i	−0.224437	−	0.821449i
$839$	−26.6586	+	21.2595i	−0.920356	+	0.733959i	−0.964227	−	0.265078i	$-0.914602\pi$
$839$	−26.6586	+	21.2595i	−0.920356	+	0.733959i	0.0438713	+	0.999037i	$0.486031\pi$
$840$	4.35499	−	3.54296i	0.150262	−	0.122244i
$841$	−18.5344	+	22.3042i	−0.639116	+	0.769110i
$842$	1.33999	+	31.6502i	0.0461791	+	1.09074i
$843$	3.45626	−	9.72147i	0.119040	−	0.334825i
$844$	3.27466	+	10.2573i	0.112718	+	0.353071i
$845$	−0.104768	−	0.0239125i	−0.00360412	−	0.000822616i
$846$	5.27399	+	20.0899i	0.181323	+	0.690704i
$847$	29.0228	+	23.1449i	0.997236	+	0.795269i
$848$	−39.1475	+	16.2590i	−1.34433	+	0.558336i
$849$	43.0900	+	27.3763i	1.47885	+	0.939551i
$850$	−3.05228	+	1.63241i	−0.104692	+	0.0559913i
$851$	−15.7473	−	3.59421i	−0.539809	−	0.123208i
$852$	44.0701	−	8.55929i	1.50982	−	0.293237i
$853$			19.1447i			0.655503i	0.944764	+	0.327751i	$0.106291\pi$
$853$			19.1447i			0.655503i	−0.944764	+	0.327751i	$0.893709\pi$
$854$	−46.5143	−	20.0226i	−1.59169	−	0.685159i
$855$	−5.64041	+	2.64723i	−0.192898	+	0.0905332i
$856$	−24.4600	+	40.2320i	−0.836026	+	1.37510i
$857$	14.5555	−	30.2248i	0.497206	−	1.03246i	−0.489809	−	0.871830i	$-0.662934\pi$
$857$	14.5555	−	30.2248i	0.497206	−	1.03246i	0.987015	−	0.160629i	$-0.0513521\pi$
$858$	3.71573	+	5.45091i	0.126853	+	0.186091i
$859$	6.35465	+	3.06024i	0.216818	+	0.104414i	0.539140	−	0.842216i	$-0.318749\pi$
$859$	6.35465	+	3.06024i	0.216818	+	0.104414i	−0.322323	+	0.946630i	$0.604464\pi$
$860$	4.19530	+	0.590247i	0.143059	+	0.0201273i
$861$	−39.2130	−	24.9131i	−1.33638	−	0.849036i
$862$	−27.5216	+	14.7190i	−0.937388	+	0.501331i
$863$	2.00702	+	8.79335i	0.0683199	+	0.299329i	0.997532	−	0.0702188i	$-0.0223697\pi$
$863$	2.00702	+	8.79335i	0.0683199	+	0.299329i	−0.929212	+	0.369548i	$0.879513\pi$
$864$	27.4637	+	10.4761i	0.934332	+	0.356403i
$865$	−4.92089	−	6.17060i	−0.167315	−	0.209807i
$866$	14.7603	+	2.71776i	0.501574	+	0.0923532i
$867$	20.4119	+	20.6167i	0.693224	+	0.700181i
$868$	25.3092	−	23.9505i	0.859052	−	0.812935i
$869$			4.74492i			0.160960i
$870$	−2.16626	+	3.66560i	−0.0734432	+	0.124276i
$871$		−	21.5906i		−	0.731568i
$872$	−14.6991	−	14.2721i	−0.497774	−	0.483314i
$873$	−0.354661	+	1.48535i	−0.0120035	+	0.0502714i
$874$	−6.05203	+	32.8688i	−0.204713	+	1.11180i
$875$	−7.07063	−	8.86629i	−0.239031	−	0.299735i
$876$	9.89245	+	0.322289i	0.334235	+	0.0108891i
$877$	−7.07577	−	31.0010i	−0.238932	−	1.04683i	−0.941975	−	0.335682i	$-0.891033\pi$
$877$	−7.07577	−	31.0010i	−0.238932	−	1.04683i	0.703043	−	0.711147i	$-0.251824\pi$
$878$	−0.986253	−	1.84410i	−0.0332844	−	0.0622353i
$879$	18.4908	−	29.1043i	0.623678	−	0.981664i
$880$	0.0524937	−	0.950861i	0.00176956	−	0.0320535i
$881$	14.7482	+	7.10235i	0.496879	+	0.239284i	0.665502	−	0.746396i	$-0.268218\pi$
$881$	14.7482	+	7.10235i	0.496879	+	0.239284i	−0.168623	+	0.985681i	$0.553932\pi$
$882$	9.61886	−	21.7450i	0.323884	−	0.732194i
$883$	21.5873	−	44.8264i	0.726470	−	1.50853i	−0.129542	−	0.991574i	$-0.541351\pi$
$883$	21.5873	−	44.8264i	0.726470	−	1.50853i	0.856012	−	0.516956i	$-0.172935\pi$
$884$	2.02691	−	3.03660i	0.0681722	−	0.102132i
$885$	2.76228	+	0.325208i	0.0928531	+	0.0109317i
$886$	15.0839	−	35.0414i	0.506754	−	1.17724i
$887$			11.7555i			0.394711i	0.980332	+	0.197355i	$0.0632352\pi$
$887$			11.7555i			0.394711i	−0.980332	+	0.197355i	$0.936765\pi$
$888$	4.99849	+	20.9564i	0.167738	+	0.703249i
$889$	7.30574	+	1.66749i	0.245027	+	0.0559257i
$890$	−0.721003	−	1.34813i	−0.0241681	−	0.0451895i
$891$	−2.99902	+	5.92202i	−0.100471	+	0.198395i
$892$	−12.7456	+	4.06906i	−0.426755	+	0.136242i
$893$	24.6279	+	19.6401i	0.824141	+	0.657231i
$894$	10.2443	−	33.2019i	0.342622	−	1.11044i
$895$	7.31499	+	1.66960i	0.244513	+	0.0558085i
$896$	−34.8458	+	19.9784i	−1.16411	+	0.667433i
$897$	−21.8869	−	7.78142i	−0.730782	−	0.259814i
$898$	−17.2362	+	0.729738i	−0.575180	+	0.0243517i
$899$	−11.7056	+	23.6933i	−0.390404	+	0.790216i
$900$	10.7362	−	27.3426i	0.357874	−	0.911419i
$901$	−4.14213	+	3.30324i	−0.137994	+	0.110047i
$902$	−7.60185	+	2.07699i	−0.253114	+	0.0691561i
$903$	38.1563	−	13.1380i	1.26976	−	0.437206i
$904$	14.5174	+	14.0957i	0.482843	+	0.468817i
$905$	−4.30345	−	3.43189i	−0.143052	−	0.114080i
$906$	22.2308	−	23.9552i	0.738568	−	0.795859i
$907$	−20.2470	+	9.75046i	−0.672292	+	0.323759i	−0.738700	−	0.674034i	$-0.764560\pi$
$907$	−20.2470	+	9.75046i	−0.672292	+	0.323759i	0.0664086	+	0.997793i	$0.478846\pi$
$908$	−1.47418	+	0.870540i	−0.0489224	+	0.0288899i
$909$	−43.8141	−	35.6621i	−1.45322	−	1.18284i
$910$	5.43553	+	2.33978i	0.180186	+	0.0775630i
$911$			12.6274i			0.418365i	0.977877	+	0.209183i	$0.0670803\pi$
$911$			12.6274i			0.418365i	−0.977877	+	0.209183i	$0.932920\pi$
$912$	42.8855	−	12.1675i	1.42008	−	0.402907i
$913$	−2.77806	−	2.21543i	−0.0919405	−	0.0733201i
$914$	−20.5525	+	28.1359i	−0.679817	+	0.930654i
$915$	5.60661	−	0.603383i	0.185349	−	0.0199472i
$916$	−2.78277	−	32.8052i	−0.0919452	−	1.08391i
$917$	−56.7130	−	27.3116i	−1.87283	−	0.901907i
$918$	3.66051	+	0.311397i	0.120815	+	0.0102776i
$919$	−3.41521	−	7.09176i	−0.112658	−	0.233936i	0.837015	−	0.547180i	$-0.184299\pi$
$919$	−3.41521	−	7.09176i	−0.112658	−	0.233936i	−0.949673	+	0.313244i	$0.898584\pi$
$920$	1.82570	+	2.81270i	0.0601914	+	0.0927319i
$921$	−1.00486	−	1.01494i	−0.0331112	−	0.0334434i
$922$	−2.83686	+	3.88359i	−0.0934269	+	0.127899i
$923$	29.5043	+	36.9973i	0.971147	+	1.21778i
$924$	−3.66754	−	8.29648i	−0.120653	−	0.272934i
$925$	20.9905	−	4.79094i	0.690163	−	0.157525i
$926$	−29.4438	+	25.5913i	−0.967584	+	0.840981i
$927$	−33.8916	−	16.7403i	−1.11315	−	0.549823i
$928$	19.5341	−	23.3756i	0.641239	−	0.767341i
$929$		−	27.6787i		−	0.908109i	−0.890974	−	0.454054i	$-0.849977\pi$
$929$		−	27.6787i		−	0.908109i	0.890974	−	0.454054i	$-0.150023\pi$
$930$	−1.14398	+	3.70763i	−0.0375125	+	0.121578i
$931$	−8.02421	−	35.1564i	−0.262983	−	1.15220i
$932$	22.1345	+	3.11415i	0.725039	+	0.102007i
$933$	13.1254	−	36.9180i	0.429706	−	1.20864i
$934$	45.8672	+	33.5048i	1.50082	+	1.09631i
$935$	−0.0264850	−	0.116038i	−0.000866151	−	0.00379486i
$936$	3.61531	+	30.7717i	0.118170	+	1.00581i
$937$	14.2963	−	6.88472i	0.467038	−	0.224914i	−0.185538	−	0.982637i	$-0.559403\pi$
$937$	14.2963	−	6.88472i	0.467038	−	0.224914i	0.652576	+	0.757723i	$0.273688\pi$
$938$	−5.37594	+	29.1970i	−0.175531	+	0.953315i
$939$	−33.7696	+	3.63428i	−1.10203	+	0.118600i
$940$	3.14921	−	0.267139i	0.102716	−	0.00871310i
$941$	−21.6635	+	44.9847i	−0.706210	+	1.46646i	0.170459	+	0.985365i	$0.445475\pi$
$941$	−21.6635	+	44.9847i	−0.706210	+	1.46646i	−0.876668	+	0.481095i	$0.840239\pi$
$942$	−16.5074	−	1.23839i	−0.537841	−	0.0403489i
$943$	17.3011	−	21.6949i	0.563400	−	0.706482i
$944$	−19.1269	−	5.49071i	−0.622528	−	0.178707i
$945$	0.578017	+	5.92657i	0.0188029	+	0.192791i
$946$	2.70651	−	6.28747i	0.0879962	−	0.204423i
$947$	−4.35848	−	0.994794i	−0.141631	−	0.0323265i	0.151117	−	0.988516i	$-0.451713\pi$
$947$	−4.35848	−	0.994794i	−0.141631	−	0.0323265i	−0.292749	+	0.956189i	$0.594570\pi$
$948$	−10.3179	+	19.7528i	−0.335109	+	0.641542i
$949$	4.52668	+	9.39975i	0.146942	+	0.305129i
$950$	−11.7415	−	42.9742i	−0.380943	−	1.39427i
$951$	−0.732317	+	6.22022i	−0.0237470	+	0.201704i
$952$	−3.49709	+	3.60171i	−0.113341	+	0.116732i
$953$	43.8211	+	10.0019i	1.41951	+	0.323993i	0.862307	−	0.506386i	$-0.169019\pi$
$953$	43.8211	+	10.0019i	1.41951	+	0.323993i	0.557199	+	0.830379i	$0.311876\pi$
$954$	8.58277	−	44.1342i	0.277877	−	1.42890i
$955$	1.83084	+	2.29580i	0.0592446	+	0.0742903i
$956$	−38.9960	+	3.30792i	−1.26122	+	0.106986i
$957$	4.79074	+	4.93733i	0.154863	+	0.159601i
$958$	−0.0836553	−	1.97591i	−0.00270278	−	0.0638389i
$959$	19.3280	−	15.4135i	0.624133	−	0.497729i
$960$	2.28619	−	3.84423i	0.0737863	−	0.124072i
$961$	1.53927	−	6.74400i	0.0496540	−	0.217548i
$962$	−17.1400	+	14.8973i	−0.552616	+	0.480310i
$963$	−21.2179	−	45.2087i	−0.683737	−	1.45683i
$964$	10.3761	+	32.5014i	0.334192	+	1.04680i
$965$	−3.62408	+	1.74527i	−0.116663	+	0.0561821i
$966$	27.6602	+	15.9726i	0.889951	+	0.513909i
$967$	5.18627	−	22.7225i	0.166779	−	0.730707i	−0.820492	−	0.571658i	$-0.806300\pi$
$967$	5.18627	−	22.7225i	0.166779	−	0.730707i	0.987271	−	0.159048i	$-0.0508426\pi$
$968$	28.0553	+	9.35526i	0.901733	+	0.300689i
$969$	4.73227	−	2.94063i	0.152023	−	0.0944668i
$970$	0.213435	+	0.0918752i	0.00685298	+	0.00294994i
$971$	15.1012	+	12.0428i	0.484619	+	0.386471i	0.835099	−	0.550099i	$-0.185410\pi$
$971$	15.1012	+	12.0428i	0.484619	+	0.386471i	−0.350480	+	0.936570i	$0.613982\pi$
$972$	−25.3622	+	18.1316i	−0.813494	+	0.581573i
$973$	21.4138	+	10.3123i	0.686495	+	0.330599i
$974$	−0.683833	−	16.1519i	−0.0219114	−	0.517541i
$975$	30.7856	−	3.31314i	0.985927	−	0.106105i
$976$	−40.2831	−	2.22389i	−1.28943	−	0.0711850i
$977$	19.1705	+	39.8080i	0.613319	+	1.27357i	0.944037	+	0.329841i	$0.106995\pi$
$977$	19.1705	+	39.8080i	0.613319	+	1.27357i	−0.330717	+	0.943730i	$0.607291\pi$
$978$	−24.0497	+	41.6475i	−0.769023	+	1.33174i
$979$	−2.40824	+	0.549666i	−0.0769678	+	0.0175674i
$980$	−3.00926	−	2.00866i	−0.0961274	−	0.0641643i
$981$	21.2331	−	4.62377i	0.677922	−	0.147626i
$982$	−51.0313	−	9.39622i	−1.62847	−	0.299846i
$983$	55.1181	−	12.5803i	1.75799	−	0.401251i	0.782742	−	0.622347i	$-0.213821\pi$
$983$	55.1181	−	12.5803i	1.75799	−	0.401251i	0.975252	+	0.221096i	$0.0709635\pi$
$984$	−36.1625	−	7.88392i	−1.15282	−	0.251330i
$985$	−0.219462			−0.00699266
$986$	1.54053	−	3.48178i	0.0490605	−	0.110883i
$987$	25.5700	−	15.8892i	0.813903	−	0.505759i
$988$	32.2974	+	34.1296i	1.02752	+	1.08581i
$989$	5.36354	+	23.4992i	0.170551	+	0.747231i
$990$	0.809652	+	0.603918i	0.0257324	+	0.0191938i
$991$	43.7862	−	34.9184i	1.39092	−	1.10922i	0.410593	−	0.911819i	$-0.365322\pi$
$991$	43.7862	−	34.9184i	1.39092	−	1.10922i	0.980323	−	0.197400i	$-0.0632496\pi$
$992$	12.3649	−	24.8546i	0.392586	−	0.789134i
$993$	−28.9662	−	29.2569i	−0.919216	−	0.928441i
$994$	−30.6866	−	57.3779i	−0.973321	−	1.81992i
$995$	4.02246	−	1.93711i	0.127521	−	0.0614106i
$996$	−6.74745	−	15.2637i	−0.213801	−	0.483647i
$997$	22.5347	−	46.7938i	0.713682	−	1.48198i	−0.155684	−	0.987807i	$-0.549758\pi$
$997$	22.5347	−	46.7938i	0.713682	−	1.48198i	0.869366	−	0.494169i	$-0.164527\pi$
$998$	0.0485450	+	1.14662i	0.00153666	+	0.0362956i
$999$	−21.4533	−	7.86943i	−0.678753	−	0.248978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.179.16	yes	336
3.2	odd	2	inner	348.2.t.a.179.41	yes	336
4.3	odd	2	inner	348.2.t.a.179.18	yes	336
12.11	even	2	inner	348.2.t.a.179.39	yes	336
29.6	even	14	inner	348.2.t.a.35.39	yes	336
87.35	odd	14	inner	348.2.t.a.35.18	yes	336
116.35	odd	14	inner	348.2.t.a.35.41	yes	336
348.35	even	14	inner	348.2.t.a.35.16	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.16	✓	336	348.35	even	14	inner
348.2.t.a.35.18	yes	336	87.35	odd	14	inner
348.2.t.a.35.39	yes	336	29.6	even	14	inner
348.2.t.a.35.41	yes	336	116.35	odd	14	inner
348.2.t.a.179.16	yes	336	1.1	even	1	trivial
348.2.t.a.179.18	yes	336	4.3	odd	2	inner
348.2.t.a.179.39	yes	336	12.11	even	2	inner
348.2.t.a.179.41	yes	336	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927728 - 1.06739i) q^{2} +(-1.21862 - 1.23084i) q^{3} +(-0.278641 + 1.98049i) q^{4} +(-0.252365 + 0.201255i) q^{5} +(-0.183246 + 2.44263i) q^{6} +(3.46126 - 0.790009i) q^{7} +(2.37246 - 1.53994i) q^{8} +(-0.0299545 + 2.99985i) q^{9} +O(q^{10})\)	\(q+(-0.927728 - 1.06739i) q^{2} +(-1.21862 - 1.23084i) q^{3} +(-0.278641 + 1.98049i) q^{4} +(-0.252365 + 0.201255i) q^{5} +(-0.183246 + 2.44263i) q^{6} +(3.46126 - 0.790009i) q^{7} +(2.37246 - 1.53994i) q^{8} +(-0.0299545 + 2.99985i) q^{9} +(0.448943 + 0.0826624i) q^{10} +(0.320018 - 0.664525i) q^{11} +(2.77724 - 2.07050i) q^{12} +(3.28982 + 1.58429i) q^{13} +(-4.05435 - 2.96159i) q^{14} +(0.555249 + 0.0653704i) q^{15} +(-3.84472 - 1.10369i) q^{16} -0.499932 q^{17} +(3.22980 - 2.75107i) q^{18} +(1.43177 - 6.27298i) q^{19} +(-0.328264 - 0.555886i) q^{20} +(-5.19032 - 3.29755i) q^{21} +(-1.00620 + 0.274914i) q^{22} +(2.29001 - 2.87158i) q^{23} +(-4.78655 - 1.04353i) q^{24} +(-1.08942 + 4.77306i) q^{25} +(-1.36100 - 4.98132i) q^{26} +(3.72885 - 3.61879i) q^{27} +(0.600163 + 7.07513i) q^{28} +(-2.28754 - 4.87516i) q^{29} +(-0.445344 - 0.653313i) q^{30} +(-3.05971 - 3.83676i) q^{31} +(2.38878 + 5.12774i) q^{32} +(-1.20791 + 0.415907i) q^{33} +(0.463801 + 0.533622i) q^{34} +(-0.714508 + 0.895964i) q^{35} +(-5.93284 - 0.895205i) q^{36} +(-1.90809 - 3.96219i) q^{37} +(-8.02401 + 4.29137i) q^{38} +(-2.05901 - 5.97990i) q^{39} +(-0.288806 + 0.866097i) q^{40} +7.55503 q^{41} +(1.29543 + 8.59932i) q^{42} +(-4.09169 + 5.13082i) q^{43} +(1.22692 + 0.818958i) q^{44} +(-0.596174 - 0.763086i) q^{45} +(-5.18960 + 0.219715i) q^{46} +(-2.12415 + 4.41085i) q^{47} +(3.32676 + 6.07723i) q^{48} +(5.04940 - 2.43166i) q^{49} +(6.10540 - 3.26527i) q^{50} +(0.609225 + 0.615338i) q^{51} +(-4.05437 + 6.07403i) q^{52} +(8.28539 - 6.60738i) q^{53} +(-7.32202 - 0.622879i) q^{54} +(0.0529771 + 0.232108i) q^{55} +(6.99513 - 7.20440i) q^{56} +(-9.46584 + 5.88207i) q^{57} +(-3.08148 + 6.96451i) q^{58} +4.97485 q^{59} +(-0.284181 + 1.08145i) q^{60} +(9.83324 - 2.24437i) q^{61} +(-1.25673 + 6.82538i) q^{62} +(2.26623 + 10.4069i) q^{63} +(3.25715 - 7.30691i) q^{64} +(-1.14908 + 0.262271i) q^{65} +(1.56454 + 0.903457i) q^{66} +(-2.56551 - 5.32735i) q^{67} +(0.139301 - 0.990112i) q^{68} +(-6.32510 + 0.680707i) q^{69} +(1.61921 - 0.0685534i) q^{70} +(11.6763 + 5.62299i) q^{71} +(4.54853 + 7.16316i) q^{72} +(2.23386 + 1.78145i) q^{73} +(-2.45901 + 5.71251i) q^{74} +(7.20248 - 4.47562i) q^{75} +(12.0247 + 4.58351i) q^{76} +(0.582685 - 2.55291i) q^{77} +(-4.47269 + 7.74549i) q^{78} +(-5.79611 + 2.79126i) q^{79} +(1.19240 - 0.495233i) q^{80} +(-8.99821 - 0.179718i) q^{81} +(-7.00902 - 8.06416i) q^{82} +(1.07201 - 4.69678i) q^{83} +(7.97701 - 9.36057i) q^{84} +(0.126165 - 0.100614i) q^{85} +(9.27255 - 0.392577i) q^{86} +(-3.21294 + 8.75654i) q^{87} +(-0.264099 - 2.06937i) q^{88} +(-2.08812 - 2.61842i) q^{89} +(-0.261423 + 1.34429i) q^{90} +(12.6385 + 2.88466i) q^{91} +(5.04906 + 5.33548i) q^{92} +(-0.993840 + 8.44156i) q^{93} +(6.67873 - 1.82477i) q^{94} +(0.901138 + 1.87123i) q^{95} +(3.40044 - 9.18896i) q^{96} +(0.496272 + 0.113271i) q^{97} +(-7.28000 - 3.13375i) q^{98} +(1.98389 + 0.979913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

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