LMFDB - Embedded newform 552.2.x.a.35.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.13
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28897 + 0.581846i) q^{2} +(0.880176 - 1.49174i) q^{3} +(1.32291 - 1.49997i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(-0.266561 + 2.43494i) q^{6} +(-1.41902 + 1.22959i) q^{7} +(-0.832444 + 2.70315i) q^{8} +(-1.45058 - 2.62599i) q^{9} +O(q^{10})$	\(q+(-1.28897 + 0.581846i) q^{2} +(0.880176 - 1.49174i) q^{3} +(1.32291 - 1.49997i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(-0.266561 + 2.43494i) q^{6} +(-1.41902 + 1.22959i) q^{7} +(-0.832444 + 2.70315i) q^{8} +(-1.45058 - 2.62599i) q^{9} +(0.683190 - 0.586769i) q^{10} +(-1.89865 + 2.95436i) q^{11} +(-1.07317 - 3.29368i) q^{12} +(-3.75279 - 3.25181i) q^{13} +(1.11365 - 2.41056i) q^{14} +(-0.270166 + 1.06938i) q^{15} +(-0.499820 - 3.96865i) q^{16} +(-2.10313 + 0.960465i) q^{17} +(3.39768 + 2.54082i) q^{18} +(1.65907 - 3.63286i) q^{19} +(-0.539205 + 1.15384i) q^{20} +(0.585238 + 3.19907i) q^{21} +(0.728330 - 4.91282i) q^{22} +(-3.57878 - 3.19254i) q^{23} +(3.29970 + 3.62104i) q^{24} +(-3.86512 + 2.48396i) q^{25} +(6.72930 + 2.00795i) q^{26} +(-5.19406 - 0.147447i) q^{27} +(-0.0328903 + 3.75512i) q^{28} +(-2.03808 - 4.46277i) q^{29} +(-0.273979 - 1.53560i) q^{30} +(2.96087 - 0.425709i) q^{31} +(2.95340 + 4.82467i) q^{32} +(2.73599 + 5.43266i) q^{33} +(2.15203 - 2.46171i) q^{34} +(0.646439 - 1.00588i) q^{35} +(-5.85789 - 1.29812i) q^{36} +(-2.90162 + 9.88202i) q^{37} +(-0.0247343 + 5.64799i) q^{38} +(-8.15397 + 2.73602i) q^{39} +(0.0236627 - 1.80101i) q^{40} +(2.02393 + 6.89286i) q^{41} +(-2.61572 - 3.78300i) q^{42} +(0.756804 - 5.26369i) q^{43} +(1.91971 + 6.75628i) q^{44} +(1.35745 + 1.34426i) q^{45} +(6.47053 + 2.03280i) q^{46} -6.53022 q^{47} +(-6.36012 - 2.74751i) q^{48} +(-0.494472 + 3.43913i) q^{49} +(3.53676 - 5.45067i) q^{50} +(-0.418357 + 3.98270i) q^{51} +(-9.84221 + 1.32722i) q^{52} +(-1.89278 - 2.18439i) q^{53} +(6.78080 - 2.83209i) q^{54} +(0.630059 - 2.14579i) q^{55} +(-2.14251 - 4.85940i) q^{56} +(-3.95901 - 5.67247i) q^{57} +(5.22368 + 4.56655i) q^{58} +(-10.4244 - 9.03283i) q^{59} +(1.24664 + 1.81994i) q^{60} +(8.15953 - 1.17316i) q^{61} +(-3.56879 + 2.27150i) q^{62} +(5.28729 + 1.94272i) q^{63} +(-6.61407 - 4.50045i) q^{64} +(2.87640 + 1.31361i) q^{65} +(-6.68760 - 5.41063i) q^{66} +(12.6939 - 8.15785i) q^{67} +(-1.34158 + 4.42523i) q^{68} +(-7.91240 + 2.52862i) q^{69} +(-0.247976 + 1.67268i) q^{70} +(4.04999 - 2.60277i) q^{71} +(8.30598 - 1.73515i) q^{72} +(-1.44386 + 3.16162i) q^{73} +(-2.00970 - 14.4260i) q^{74} +(0.303438 + 7.95208i) q^{75} +(-3.25438 - 7.29451i) q^{76} +(-0.938422 - 6.52687i) q^{77} +(8.91831 - 8.27101i) q^{78} +(-7.27743 - 6.30593i) q^{79} +(1.01741 + 2.33522i) q^{80} +(-4.79164 + 7.61841i) q^{81} +(-6.61938 - 7.70711i) q^{82} +(-1.16258 + 3.95938i) q^{83} +(5.57272 + 3.35424i) q^{84} +(1.11272 - 0.964175i) q^{85} +(2.08716 + 7.22511i) q^{86} +(-8.45116 - 0.887740i) q^{87} +(-6.40557 - 7.59169i) q^{88} +(-2.29892 - 0.330535i) q^{89} +(-2.53187 - 0.942895i) q^{90} +9.32367 q^{91} +(-9.52312 + 1.14463i) q^{92} +(1.97104 - 4.79155i) q^{93} +(8.41729 - 3.79958i) q^{94} +(-0.361944 + 2.51737i) q^{95} +(9.79667 - 0.159146i) q^{96} +(-5.22565 + 1.53439i) q^{97} +(-1.36368 - 4.72065i) q^{98} +(10.5123 + 0.700309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.28897	+	0.581846i	−0.911442	+	0.411428i
$2$	−1.28897	+	0.581846i	−0.911442	+	0.411428i
$3$	0.880176	−	1.49174i	0.508170	−	0.861257i
$3$	0.880176	−	1.49174i	0.508170	−	0.861257i
$4$	1.32291	−	1.49997i	0.661455	−	0.749985i
$5$	−0.611012	+	0.179409i	−0.273253	+	0.0802342i	−0.415488	−	0.909599i	$-0.636389\pi$
$5$	−0.611012	+	0.179409i	−0.273253	+	0.0802342i	0.142235	+	0.989833i	$0.454571\pi$
$6$	−0.266561	+	2.43494i	−0.108823	+	0.994061i
$7$	−1.41902	+	1.22959i	−0.536340	+	0.464741i	−0.880417	−	0.474200i	$-0.842737\pi$
$7$	−1.41902	+	1.22959i	−0.536340	+	0.464741i	0.344077	+	0.938941i	$0.388192\pi$
$8$	−0.832444	+	2.70315i	−0.294314	+	0.955709i
$9$	−1.45058	−	2.62599i	−0.483526	−	0.875330i
$10$	0.683190	−	0.586769i	0.216044	−	0.185553i
$11$	−1.89865	+	2.95436i	−0.572466	+	0.890774i	−0.999912	−	0.0132669i	$-0.995777\pi$
$11$	−1.89865	+	2.95436i	−0.572466	+	0.890774i	0.427446	+	0.904041i	$0.359413\pi$
$12$	−1.07317	−	3.29368i	−0.309798	−	0.950802i
$13$	−3.75279	−	3.25181i	−1.04084	−	0.901889i	−0.0455582	−	0.998962i	$-0.514507\pi$
$13$	−3.75279	−	3.25181i	−1.04084	−	0.901889i	−0.995277	+	0.0970726i	$0.969052\pi$
$14$	1.11365	−	2.41056i	0.297635	−	0.644249i
$15$	−0.270166	+	1.06938i	−0.0697566	+	0.276113i
$16$	−0.499820	−	3.96865i	−0.124955	−	0.992162i
$17$	−2.10313	+	0.960465i	−0.510083	+	0.232947i	−0.653794	−	0.756673i	$-0.726824\pi$
$17$	−2.10313	+	0.960465i	−0.510083	+	0.232947i	0.143711	+	0.989620i	$0.454096\pi$
$18$	3.39768	+	2.54082i	0.800841	+	0.598877i
$19$	1.65907	−	3.63286i	0.380617	−	0.833436i	−0.618256	−	0.785977i	$-0.712160\pi$
$19$	1.65907	−	3.63286i	0.380617	−	0.833436i	0.998873	−	0.0474589i	$-0.0151123\pi$
$20$	−0.539205	+	1.15384i	−0.120570	+	0.258007i
$21$	0.585238	+	3.19907i	0.127709	+	0.698093i
$22$	0.728330	−	4.91282i	0.155281	−	1.04742i
$23$	−3.57878	−	3.19254i	−0.746228	−	0.665690i
$23$	−3.57878	−	3.19254i	−0.746228	−	0.665690i
$24$	3.29970	+	3.62104i	0.673549	+	0.739142i
$25$	−3.86512	+	2.48396i	−0.773024	+	0.496792i
$26$	6.72930	+	2.00795i	1.31972	+	0.393792i
$27$	−5.19406	−	0.147447i	−0.999597	−	0.0283763i
$28$	−0.0328903	+	3.75512i	−0.00621568	+	0.709652i
$29$	−2.03808	−	4.46277i	−0.378462	−	0.828715i	−0.999007	−	0.0445451i	$-0.985816\pi$
$29$	−2.03808	−	4.46277i	−0.378462	−	0.828715i	0.620546	−	0.784170i	$-0.286911\pi$
$30$	−0.273979	−	1.53560i	−0.0500215	−	0.280361i
$31$	2.96087	−	0.425709i	0.531788	−	0.0764596i	0.128810	−	0.991669i	$-0.458884\pi$
$31$	2.96087	−	0.425709i	0.531788	−	0.0764596i	0.402978	+	0.915210i	$0.367975\pi$
$32$	2.95340	+	4.82467i	0.522092	+	0.852889i
$33$	2.73599	+	5.43266i	0.476275	+	0.945704i
$34$	2.15203	−	2.46171i	0.369070	−	0.422180i
$35$	0.646439	−	1.00588i	0.109268	−	0.170024i
$36$	−5.85789	−	1.29812i	−0.976315	−	0.216354i
$37$	−2.90162	+	9.88202i	−0.477024	+	1.62459i	0.272174	+	0.962248i	$0.412257\pi$
$37$	−2.90162	+	9.88202i	−0.477024	+	1.62459i	−0.749198	+	0.662346i	$0.769561\pi$
$38$	−0.0247343	+	5.64799i	−0.00401243	+	0.916225i
$39$	−8.15397	+	2.73602i	−1.30568	+	0.438113i
$40$	0.0236627	−	1.80101i	0.00374140	−	0.284764i
$41$	2.02393	+	6.89286i	0.316084	+	1.07648i	0.952348	+	0.305013i	$0.0986608\pi$
$41$	2.02393	+	6.89286i	0.316084	+	1.07648i	−0.636264	+	0.771471i	$0.719521\pi$
$42$	−2.61572	−	3.78300i	−0.403615	−	0.583729i
$43$	0.756804	−	5.26369i	0.115412	−	0.802705i	−0.847094	−	0.531443i	$-0.821650\pi$
$43$	0.756804	−	5.26369i	0.115412	−	0.802705i	0.962506	−	0.271262i	$-0.0874410\pi$
$44$	1.91971	+	6.75628i	0.289407	+	1.01855i
$45$	1.35745	+	1.34426i	0.202356	+	0.200391i
$46$	6.47053	+	2.03280i	0.954027	+	0.299720i
$47$	−6.53022			−0.952530			−0.476265	−	0.879302i	$-0.658010\pi$
$47$	−6.53022			−0.952530			−0.476265	+	0.879302i	$0.658010\pi$
$48$	−6.36012	−	2.74751i	−0.918005	−	0.396569i
$49$	−0.494472	+	3.43913i	−0.0706388	+	0.491304i
$50$	3.53676	−	5.45067i	0.500173	−	0.770841i
$51$	−0.418357	+	3.98270i	−0.0585817	+	0.557689i
$52$	−9.84221	+	1.32722i	−1.36487	+	0.184052i
$53$	−1.89278	−	2.18439i	−0.259994	−	0.300049i	0.610712	−	0.791853i	$-0.290883\pi$
$53$	−1.89278	−	2.18439i	−0.259994	−	0.300049i	−0.870706	+	0.491804i	$0.836338\pi$
$54$	6.78080	−	2.83209i	0.922750	−	0.385398i
$55$	0.630059	−	2.14579i	0.0849572	−	0.289338i
$56$	−2.14251	−	4.85940i	−0.286305	−	0.649364i
$57$	−3.95901	−	5.67247i	−0.524384	−	0.751337i
$58$	5.22368	+	4.56655i	0.685902	+	0.599617i
$59$	−10.4244	−	9.03283i	−1.35715	−	1.17597i	−0.966868	−	0.255277i	$-0.917833\pi$
$59$	−10.4244	−	9.03283i	−1.35715	−	1.17597i	−0.390278	−	0.920697i	$-0.627621\pi$
$60$	1.24664	+	1.81994i	0.160940	+	0.234953i
$61$	8.15953	−	1.17316i	1.04472	−	0.150208i	0.401476	−	0.915869i	$-0.368497\pi$
$61$	8.15953	−	1.17316i	1.04472	−	0.150208i	0.643244	+	0.765661i	$0.277588\pi$
$62$	−3.56879	+	2.27150i	−0.453237	+	0.288481i
$63$	5.28729	+	1.94272i	0.666136	+	0.244760i
$64$	−6.61407	−	4.50045i	−0.826759	−	0.562556i
$65$	2.87640	+	1.31361i	0.356773	+	0.162933i
$66$	−6.68760	−	5.41063i	−0.823186	−	0.666003i
$67$	12.6939	−	8.15785i	1.55080	−	0.996641i	0.565713	−	0.824602i	$-0.308601\pi$
$67$	12.6939	−	8.15785i	1.55080	−	0.996641i	0.985090	−	0.172038i	$-0.0550353\pi$
$68$	−1.34158	+	4.42523i	−0.162690	+	0.536638i
$69$	−7.91240	+	2.52862i	−0.952541	+	0.304410i
$70$	−0.247976	+	1.67268i	−0.0296388	+	0.199923i
$71$	4.04999	−	2.60277i	0.480645	−	0.308892i	−0.277789	−	0.960642i	$-0.589601\pi$
$71$	4.04999	−	2.60277i	0.480645	−	0.308892i	0.758433	+	0.651751i	$0.225965\pi$
$72$	8.30598	−	1.73515i	0.978869	−	0.204489i
$73$	−1.44386	+	3.16162i	−0.168992	+	0.370040i	−0.975112	−	0.221711i	$-0.928836\pi$
$73$	−1.44386	+	3.16162i	−0.168992	+	0.370040i	0.806121	+	0.591751i	$0.201563\pi$
$74$	−2.00970	−	14.4260i	−0.233623	−	1.67699i
$75$	0.303438	+	7.95208i	0.0350380	+	0.918227i
$76$	−3.25438	−	7.29451i	−0.373303	−	0.836738i
$77$	−0.938422	−	6.52687i	−0.106943	−	0.743805i
$78$	8.91831	−	8.27101i	1.00980	−	0.936508i
$79$	−7.27743	−	6.30593i	−0.818775	−	0.709472i	0.141071	−	0.989999i	$-0.454945\pi$
$79$	−7.27743	−	6.30593i	−0.818775	−	0.709472i	−0.959846	+	0.280527i	$0.909491\pi$
$80$	1.01741	+	2.33522i	0.113750	+	0.261085i
$81$	−4.79164	+	7.61841i	−0.532405	+	0.846490i
$82$	−6.61938	−	7.70711i	−0.730988	−	0.851108i
$83$	−1.16258	+	3.95938i	−0.127610	+	0.434598i	−0.998368	−	0.0571133i	$-0.981810\pi$
$83$	−1.16258	+	3.95938i	−0.127610	+	0.434598i	0.870758	+	0.491712i	$0.163629\pi$
$84$	5.57272	+	3.35424i	0.608034	+	0.365977i
$85$	1.11272	−	0.964175i	0.120691	−	0.104580i
$86$	2.08716	+	7.22511i	0.225064	+	0.779103i
$87$	−8.45116	−	0.887740i	−0.906059	−	0.0951758i
$88$	−6.40557	−	7.59169i	−0.682836	−	0.809277i
$89$	−2.29892	−	0.330535i	−0.243685	−	0.0350367i	0.0193898	−	0.999812i	$-0.493828\pi$
$89$	−2.29892	−	0.330535i	−0.243685	−	0.0350367i	−0.263075	+	0.964775i	$0.584737\pi$
$90$	−2.53187	−	0.942895i	−0.266882	−	0.0993898i
$91$	9.32367			0.977386
$92$	−9.52312	+	1.14463i	−0.992854	+	0.119336i
$93$	1.97104	−	4.79155i	0.204388	−	0.496861i
$94$	8.41729	−	3.79958i	0.868177	−	0.391897i
$95$	−0.361944	+	2.51737i	−0.0371346	+	0.258277i
$96$	9.79667	−	0.159146i	0.999868	−	0.0162428i
$97$	−5.22565	+	1.53439i	−0.530584	+	0.155794i	−0.536042	−	0.844192i	$-0.680081\pi$
$97$	−5.22565	+	1.53439i	−0.530584	+	0.155794i	0.00545759	+	0.999985i	$0.498263\pi$
$98$	−1.36368	−	4.72065i	−0.137753	−	0.476858i
$99$	10.5123	+	0.700309i	1.05652	+	0.0703837i
$100$	−1.38734	+	9.08362i	−0.138734	+	0.908362i
$101$	−4.26166	−	1.25134i	−0.424051	−	0.124513i	0.0627425	−	0.998030i	$-0.480015\pi$
$101$	−4.26166	−	1.25134i	−0.424051	−	0.124513i	−0.486793	+	0.873517i	$0.661833\pi$
$102$	−1.77807	−	5.37701i	−0.176055	−	0.532404i
$103$	−6.47732	+	10.0789i	−0.638229	+	0.993104i	0.359961	+	0.932967i	$0.382790\pi$
$103$	−6.47732	+	10.0789i	−0.638229	+	0.993104i	−0.998190	+	0.0601365i	$0.980846\pi$
$104$	11.9141	−	7.43741i	1.16828	−	0.729298i
$105$	−0.931529	−	1.84967i	−0.0909079	−	0.180509i
$106$	3.71073	+	1.71431i	0.360418	+	0.166509i
$107$	19.4694	−	2.79928i	1.88218	−	0.270617i	0.896987	−	0.442057i	$-0.145751\pi$
$107$	19.4694	−	2.79928i	1.88218	−	0.270617i	0.985195	+	0.171440i	$0.0548420\pi$
$108$	−7.09244	+	7.59587i	−0.682470	+	0.730913i
$109$	4.49147	−	2.05118i	0.430205	−	0.196468i	−0.188531	−	0.982067i	$-0.560373\pi$
$109$	4.49147	−	2.05118i	0.430205	−	0.196468i	0.618735	+	0.785599i	$0.287645\pi$
$110$	0.436387	+	3.13246i	0.0416079	+	0.298668i
$111$	12.1875	+	13.0264i	1.15678	+	1.23641i
$112$	5.58906	+	5.01702i	0.528117	+	0.474064i
$113$	−5.49021	−	8.54293i	−0.516475	−	0.803651i	0.480845	−	0.876806i	$-0.340330\pi$
$113$	−5.49021	−	8.54293i	−0.516475	−	0.803651i	−0.997321	+	0.0731540i	$0.976694\pi$
$114$	8.40357	+	5.00813i	0.787066	+	0.469054i
$115$	2.75945	+	1.30861i	0.257320	+	0.122029i
$116$	−9.39021	−	2.84678i	−0.871859	−	0.264317i
$117$	−3.09550	+	14.5718i	−0.286179	+	1.34716i
$118$	18.6926	+	5.57766i	1.72079	+	0.513465i
$119$	1.80340	−	3.94890i	0.165318	−	0.361995i
$120$	−2.66581	−	1.62050i	−0.243354	−	0.147931i
$121$	−0.553807	−	1.21267i	−0.0503461	−	0.110243i
$122$	−9.83482	+	6.25977i	−0.890403	+	0.566733i
$123$	12.0638	+	3.04776i	1.08775	+	0.274807i
$124$	3.27842	−	5.00439i	0.294410	−	0.449408i
$125$	4.00109	−	4.61750i	0.357868	−	0.413002i
$126$	−7.94554	+	0.572275i	−0.707845	+	0.0509823i
$127$	6.91534	−	10.7605i	0.613637	−	0.954838i	−0.385842	−	0.922565i	$-0.626089\pi$
$127$	6.91534	−	10.7605i	0.613637	−	0.954838i	0.999479	−	0.0322733i	$-0.0102747\pi$
$128$	11.1439	+	1.95259i	0.984994	+	0.172586i
$129$	−7.18594	−	5.76193i	−0.632687	−	0.507310i
$130$	−4.47192	−	0.0195839i	−0.392214	−	0.00171762i
$131$	−1.86721	+	1.61794i	−0.163138	+	0.141360i	−0.732604	−	0.680655i	$-0.761695\pi$
$131$	−1.86721	+	1.61794i	−0.163138	+	0.141360i	0.569466	+	0.822015i	$0.307150\pi$
$132$	11.7683	+	3.08301i	1.02430	+	0.268342i
$133$	2.11267	+	7.19509i	0.183192	+	0.623893i
$134$	−11.6155	+	17.9011i	−1.00342	+	1.54642i
$135$	3.20008	−	0.841770i	0.275419	−	0.0724480i
$136$	−0.845549	−	6.48460i	−0.0725053	−	0.556050i
$137$			3.96510i			0.338761i	0.985551	+	0.169381i	$0.0541767\pi$
$137$			3.96510i			0.338761i	−0.985551	+	0.169381i	$0.945823\pi$
$138$	8.72761	−	7.86313i	0.742944	−	0.669354i
$139$	12.2638			1.04021			0.520103	−	0.854104i	$-0.325894\pi$
$139$	12.2638			1.04021			0.520103	+	0.854104i	$0.325894\pi$
$140$	−0.653607	−	2.30033i	−0.0552399	−	0.194413i
$141$	−5.74775	+	9.74139i	−0.484048	+	0.820373i
$142$	−3.70592	+	5.71137i	−0.310994	+	0.479287i
$143$	16.7323	−	4.91303i	1.39922	−	0.410849i
$144$	−9.69660	+	7.06936i	−0.808050	+	0.589113i
$145$	2.04595	+	2.36115i	0.169907	+	0.196083i
$146$	0.0215258	−	4.91536i	0.00178149	−	0.406798i
$147$	4.69506	+	3.76466i	0.387242	+	0.310504i
$148$	10.9842	+	17.4254i	0.902892	+	1.43236i
$149$	14.2287	+	9.14424i	1.16566	+	0.749125i	0.972697	−	0.232081i	$-0.0745533\pi$
$149$	14.2287	+	9.14424i	1.16566	+	0.749125i	0.192965	+	0.981206i	$0.438190\pi$
$150$	−5.01801	−	10.0735i	−0.409719	−	0.822496i
$151$	0.626011	+	0.542441i	0.0509440	+	0.0441432i	0.679961	−	0.733249i	$-0.261997\pi$
$151$	0.626011	+	0.542441i	0.0509440	+	0.0441432i	−0.629017	+	0.777392i	$0.716542\pi$
$152$	8.43910	+	7.50888i	0.684501	+	0.609051i
$153$	5.57292	+	4.12956i	0.450544	+	0.333855i
$154$	5.00723	+	7.86695i	0.403494	+	0.633936i
$155$	−1.73275	+	0.791321i	−0.139178	+	0.0635604i
$156$	−6.68302	+	15.8502i	−0.535069	+	1.26903i
$157$	−10.9199	−	4.98695i	−0.871502	−	0.398002i	−0.0711028	−	0.997469i	$-0.522652\pi$
$157$	−10.9199	−	4.98695i	−0.871502	−	0.398002i	−0.800399	+	0.599467i	$0.795379\pi$
$158$	13.0495	+	3.89383i	1.03816	+	0.309777i
$159$	−4.92453	+	0.900895i	−0.390540	+	0.0714456i
$160$	−2.67015	−	2.41806i	−0.211094	−	0.191165i
$161$	9.00388	+	0.129849i	0.709605	+	0.0102335i
$162$	1.74356	−	12.6079i	0.136987	−	0.990573i
$163$	−14.3579	+	9.22726i	−1.12460	+	0.722735i	−0.964426	−	0.264354i	$-0.914841\pi$
$163$	−14.3579	+	9.22726i	−1.12460	+	0.722735i	−0.160172	+	0.987089i	$0.551205\pi$
$164$	13.0166	+	6.08280i	1.01642	+	0.474987i
$165$	−2.64639	−	2.82856i	−0.206021	−	0.220203i
$166$	−0.805216	−	5.77998i	−0.0624969	−	0.448613i
$167$	−5.77994	−	12.6563i	−0.447265	−	0.979374i	−0.990207	−	0.139604i	$-0.955417\pi$
$167$	−5.77994	−	12.6563i	−0.447265	−	0.979374i	0.542942	−	0.839770i	$-0.317310\pi$
$168$	−9.13474	−	1.08106i	−0.704761	−	0.0834053i
$169$	1.65906	+	11.5390i	0.127620	+	0.887615i
$170$	−0.873263	+	1.89023i	−0.0669762	+	0.144974i
$171$	−11.9465	+	0.913045i	−0.913570	+	0.0698223i
$172$	−6.89419	−	8.09857i	−0.525677	−	0.617510i
$173$	5.07788	+	3.26335i	0.386064	+	0.248108i	0.719248	−	0.694754i	$-0.244487\pi$
$173$	5.07788	+	3.26335i	0.386064	+	0.248108i	−0.333184	+	0.942862i	$0.608123\pi$
$174$	11.4099	−	3.77300i	0.864979	−	0.286031i
$175$	2.43044	−	8.27730i	0.183724	−	0.625705i
$176$	12.6738	+	6.05844i	0.955325	+	0.456672i
$177$	−22.6500	+	7.60007i	−1.70248	+	0.571257i
$178$	3.15557	−	0.911569i	0.236520	−	0.0683250i
$179$	−5.25516	−	17.8974i	−0.392789	−	1.33772i	−0.884330	−	0.466862i	$-0.845385\pi$
$179$	−5.25516	−	17.8974i	−0.392789	−	1.33772i	0.491542	−	0.870854i	$-0.336434\pi$
$180$	3.81213	−	0.257792i	0.284140	−	0.0192147i
$181$	−1.63490	−	0.235064i	−0.121521	−	0.0174722i	0.0812857	−	0.996691i	$-0.474097\pi$
$181$	−1.63490	−	0.235064i	−0.121521	−	0.0174722i	−0.202807	+	0.979219i	$0.565006\pi$
$182$	−12.0180	+	5.42494i	−0.890831	+	0.402124i
$183$	5.43177	−	13.2045i	0.401528	−	0.976104i
$184$	11.6091	−	7.01639i	0.855831	−	0.517255i
$185$		−	6.55861i		−	0.482198i
$186$	0.247324	+	7.32303i	0.0181347	+	0.536951i
$187$	1.15554	−	8.03699i	0.0845017	−	0.587723i
$188$	−8.63889	+	9.79513i	−0.630056	+	0.714384i
$189$	7.55178	−	6.17733i	0.549311	−	0.449334i
$190$	−0.998189	−	3.45543i	−0.0724162	−	0.250683i
$191$	3.59572	+	4.14968i	0.260177	+	0.300260i	0.870776	−	0.491680i	$-0.163617\pi$
$191$	3.59572	+	4.14968i	0.260177	+	0.300260i	−0.610599	+	0.791940i	$0.709071\pi$
$192$	−12.5351	+	5.90529i	−0.904640	+	0.426178i
$193$	−10.1514	−	2.98073i	−0.730716	−	0.214558i	−0.104850	−	0.994488i	$-0.533436\pi$
$193$	−10.1514	−	2.98073i	−0.730716	−	0.214558i	−0.625866	+	0.779930i	$0.715254\pi$
$194$	5.84295	−	5.01831i	0.419499	−	0.360294i
$195$	4.49130	−	3.13464i	0.321629	−	0.224476i
$196$	4.50444	+	5.29134i	0.321746	+	0.377953i
$197$	10.3049	−	11.8925i	0.734192	−	0.847302i	−0.258745	−	0.965946i	$-0.583309\pi$
$197$	10.3049	−	11.8925i	0.734192	−	0.847302i	0.992937	+	0.118643i	$0.0378545\pi$
$198$	−13.9575	+	5.21385i	−0.991918	+	0.370532i
$199$	9.71856	−	1.39732i	0.688930	−	0.0990532i	0.211046	−	0.977476i	$-0.432313\pi$
$199$	9.71856	−	1.39732i	0.688930	−	0.0990532i	0.477884	+	0.878423i	$0.341404\pi$
$200$	−3.49703	−	12.5158i	−0.247277	−	0.884999i
$201$	−0.996556	−	26.1163i	−0.0702916	−	1.84210i
$202$	6.22125	−	0.866690i	0.437726	−	0.0609801i
$203$	8.37945	+	3.82676i	0.588122	+	0.268586i
$204$	5.42048	+	5.89627i	0.379509	+	0.412821i
$205$	−2.47329	−	3.84851i	−0.172742	−	0.268791i
$206$	2.48472	−	16.7602i	0.173119	−	1.16774i
$207$	−3.19227	+	14.0289i	−0.221878	+	0.975074i
$208$	−11.0296	+	16.5188i	−0.764763	+	1.14537i
$209$	7.58279	+	11.7991i	0.524513	+	0.816157i
$210$	2.27694	+	1.84217i	0.157124	+	0.127122i
$211$	2.76183	−	6.04757i	0.190132	−	0.416332i	−0.790427	−	0.612557i	$-0.790141\pi$
$211$	2.76183	−	6.04757i	0.190132	−	0.416332i	0.980559	+	0.196225i	$0.0628683\pi$
$212$	−5.78050	−	0.0506301i	−0.397007	−	0.00347729i
$213$	−0.317952	−	8.33242i	−0.0217857	−	0.570928i
$214$	−23.4669	+	14.9364i	−1.60416	+	1.02103i
$215$	0.481938	+	3.35195i	0.0328679	+	0.228601i
$216$	4.72234	−	13.9176i	0.321314	−	0.946973i
$217$	−3.67809	+	4.24475i	−0.249685	+	0.288152i
$218$	−4.59591	+	5.25727i	−0.311274	+	0.356067i
$219$	3.44546	+	4.93666i	0.232823	+	0.333588i
$220$	−2.38510	−	3.78375i	−0.160804	−	0.255100i
$221$	11.0158	+	3.23454i	0.741005	+	0.217579i
$222$	−23.2887	−	9.69945i	−1.56303	−	0.650984i
$223$	−11.5484	+	10.0067i	−0.773337	+	0.670100i	−0.949326	−	0.314292i	$-0.898233\pi$
$223$	−11.5484	+	10.0067i	−0.773337	+	0.670100i	0.175989	+	0.984392i	$0.443688\pi$
$224$	−10.1233	−	3.21484i	−0.676391	−	0.214800i
$225$	12.1295	+	6.54658i	0.808635	+	0.436439i
$226$	12.0474	+	7.81716i	0.801382	+	0.519990i
$227$	−16.3412	−	2.34951i	−1.08461	−	0.155943i	−0.423248	−	0.906014i	$-0.639110\pi$
$227$	−16.3412	−	2.34951i	−1.08461	−	0.155943i	−0.661357	+	0.750071i	$0.730019\pi$
$228$	−13.7459	−	1.56576i	−0.910347	−	0.103695i
$229$		−	27.7269i		−	1.83225i	−0.400895	−	0.916124i	$-0.631301\pi$
$229$		−	27.7269i		−	1.83225i	0.400895	−	0.916124i	$-0.368699\pi$
$230$	−4.31827	−	0.0811917i	−0.284738	−	0.00535362i
$231$	−10.5624	−	4.34491i	−0.694953	−	0.285874i
$232$	13.7601	−	1.79423i	0.903397	−	0.117797i
$233$	−19.5167	−	2.80607i	−1.27858	−	0.183832i	−0.530639	−	0.847598i	$-0.678048\pi$
$233$	−19.5167	−	2.80607i	−1.27858	−	0.183832i	−0.747941	+	0.663766i	$0.768957\pi$
$234$	−4.48852	−	20.5838i	−0.293423	−	1.34560i
$235$	3.99004	−	1.17158i	0.260282	−	0.0764255i
$236$	−27.3396	+	3.68673i	−1.77965	+	0.239986i
$237$	−15.8122	+	5.30571i	−1.02711	+	0.344643i
$238$	−0.0268860	+	6.13933i	−0.00174276	+	0.397954i
$239$	22.0021	+	6.46041i	1.42320	+	0.417889i	0.900585	−	0.434680i	$-0.143138\pi$
$239$	22.0021	+	6.46041i	1.42320	+	0.417889i	0.522615	+	0.852569i	$0.324957\pi$
$240$	4.37904	+	0.537696i	0.282666	+	0.0347081i
$241$	2.42068	+	1.55568i	0.155930	+	0.100210i	0.616279	−	0.787528i	$-0.288639\pi$
$241$	2.42068	+	1.55568i	0.155930	+	0.100210i	−0.460349	+	0.887738i	$0.652276\pi$
$242$	1.41943	+	1.24087i	0.0912444	+	0.0797660i
$243$	7.14720	+	13.8534i	0.458493	+	0.888698i
$244$	9.03461	−	13.7910i	0.578381	−	0.882880i
$245$	−0.314883	−	2.19006i	−0.0201171	−	0.139918i
$246$	−17.3232	+	3.09078i	−1.10449	+	0.197061i
$247$	−18.0395	+	8.23837i	−1.14783	+	0.524195i
$248$	−1.31400	+	8.35807i	−0.0834394	+	0.530738i
$249$	4.88309	+	5.21922i	0.309453	+	0.330754i
$250$	−2.47062	+	8.27986i	−0.156256	+	0.523664i
$251$	−4.28087	−	6.66116i	−0.270206	−	0.420449i	0.679460	−	0.733712i	$-0.262214\pi$
$251$	−4.28087	−	6.66116i	−0.270206	−	0.420449i	−0.949666	+	0.313264i	$0.898578\pi$
$252$	9.90863	−	5.36073i	0.624185	−	0.337694i
$253$	16.2268	−	4.51150i	1.02017	−	0.283635i
$254$	−2.65275	+	17.8936i	−0.166448	+	1.12275i
$255$	−0.458911	−	2.50853i	−0.0287381	−	0.157090i
$256$	−15.5004	+	3.96722i	−0.968772	+	0.247951i
$257$	−14.4360	−	6.59270i	−0.900493	−	0.411241i	−0.0892897	−	0.996006i	$-0.528460\pi$
$257$	−14.4360	−	6.59270i	−0.900493	−	0.411241i	−0.811203	+	0.584764i	$0.801187\pi$
$258$	12.6150	+	3.24587i	0.785379	+	0.202079i
$259$	−8.03336	−	17.5906i	−0.499169	−	1.09303i
$260$	5.77559	−	2.57673i	0.358187	−	0.159802i
$261$	−8.76279	+	11.8256i	−0.542403	+	0.731984i
$262$	1.46539	−	3.17191i	0.0905318	−	0.195961i
$263$	7.29126	−	8.41456i	0.449598	−	0.518864i	−0.485027	−	0.874499i	$-0.661190\pi$
$263$	7.29126	−	8.41456i	0.449598	−	0.518864i	0.934625	+	0.355635i	$0.115736\pi$
$264$	−16.9629	+	2.87342i	−1.04399	+	0.176847i
$265$	1.54841	+	0.995105i	0.0951183	+	0.0611288i
$266$	−6.90961	−	8.04503i	−0.423655	−	0.493273i
$267$	−2.51653	+	3.13847i	−0.154009	+	0.192071i
$268$	4.55630	−	29.8325i	0.278321	−	1.82231i
$269$	0.200731	+	0.231656i	0.0122388	+	0.0141243i	0.761836	−	0.647770i	$-0.224298\pi$
$269$	0.200731	+	0.231656i	0.0122388	+	0.0141243i	−0.749597	+	0.661894i	$0.769753\pi$
$270$	−3.63505	+	2.94698i	−0.221222	+	0.179347i
$271$	2.02316	+	6.89026i	0.122898	+	0.418554i	0.997841	−	0.0656726i	$-0.0209193\pi$
$271$	2.02316	+	6.89026i	0.122898	+	0.418554i	−0.874943	+	0.484226i	$0.839101\pi$
$272$	4.86293	+	7.86651i	0.294859	+	0.476977i
$273$	8.20647	−	13.9085i	0.496678	−	0.841780i
$274$	−2.30708	−	5.11091i	−0.139376	−	0.308762i
$275$		−	16.1351i		−	0.972986i
$276$	−6.67454	+	15.2135i	−0.401760	+	0.915745i
$277$			17.4231i			1.04685i	0.852071	+	0.523426i	$0.175346\pi$
$277$			17.4231i			1.04685i	−0.852071	+	0.523426i	$0.824654\pi$
$278$	−15.8078	+	7.13567i	−0.948088	+	0.427969i
$279$	−5.41289	−	7.15769i	−0.324061	−	0.428520i
$280$	2.18092	+	2.58476i	0.130335	+	0.154469i
$281$	−2.51087	−	8.55124i	−0.149786	−	0.510124i	0.850077	−	0.526658i	$-0.176555\pi$
$281$	−2.51087	−	8.55124i	−0.149786	−	0.510124i	−0.999863	+	0.0165337i	$0.994737\pi$
$282$	1.74070	−	15.9007i	0.103657	−	0.946874i
$283$	−8.11873	−	9.36951i	−0.482608	−	0.556959i	0.461267	−	0.887261i	$-0.347395\pi$
$283$	−8.11873	−	9.36951i	−0.482608	−	0.556959i	−0.943875	+	0.330302i	$0.892849\pi$
$284$	1.45369	−	9.51808i	0.0862607	−	0.564794i
$285$	3.43669	+	2.75566i	0.203572	+	0.163231i
$286$	−18.7088	+	16.0684i	−1.10628	+	0.950143i
$287$	−11.3474	−	7.29252i	−0.669815	−	0.430464i
$288$	8.38539	−	14.7542i	0.494114	−	0.869397i
$289$	−7.63199	+	8.80779i	−0.448941	+	0.518105i
$290$	−4.01101	−	1.85304i	−0.235534	−	0.108814i
$291$	−2.31058	+	9.14584i	−0.135449	+	0.536139i
$292$	2.83224	+	6.34829i	0.165744	+	0.371506i
$293$	−0.452927	−	0.991772i	−0.0264603	−	0.0579399i	0.895940	−	0.444174i	$-0.146503\pi$
$293$	−0.452927	−	0.991772i	−0.0264603	−	0.0579399i	−0.922401	+	0.386234i	$0.873776\pi$
$294$	−8.24227	−	2.12075i	−0.480699	−	0.123684i
$295$	7.99003	+	3.64892i	0.465197	+	0.212448i
$296$	−24.2972	−	16.0698i	−1.41224	−	0.934036i
$297$	10.2973	−	15.0652i	0.597512	−	0.874171i
$298$	−23.6610	−	3.50776i	−1.37064	−	0.203199i
$299$	3.04889	+	23.6184i	0.176322	+	1.36589i
$300$	12.3293	+	10.0647i	0.711833	+	0.581088i
$301$	5.39825	+	8.39985i	0.311150	+	0.484159i
$302$	−1.12253	−	0.334951i	−0.0645943	−	0.0192743i
$303$	−5.61768	+	5.25589i	−0.322727	+	0.301943i
$304$	−15.2468	−	4.76850i	−0.874464	−	0.273492i
$305$	−4.77509	+	2.18071i	−0.273421	+	0.124867i
$306$	−9.58612	−	2.08031i	−0.548002	−	0.118923i
$307$	−0.399967	−	2.78183i	−0.0228273	−	0.158767i	0.975219	−	0.221240i	$-0.0710104\pi$
$307$	−0.399967	−	2.78183i	−0.0228273	−	0.158767i	−0.998047	+	0.0624727i	$0.980101\pi$
$308$	−11.0316	−	7.22685i	−0.628581	−	0.411788i
$309$	9.33392	+	18.5337i	0.530988	+	1.05434i
$310$	1.77304	−	2.02819i	0.100702	−	0.115193i
$311$	9.14613	+	5.87786i	0.518629	+	0.333303i	0.773630	−	0.633638i	$-0.218439\pi$
$311$	9.14613	+	5.87786i	0.518629	+	0.333303i	−0.255000	+	0.966941i	$0.582076\pi$
$312$	−0.608151	−	24.3190i	−0.0344298	−	1.37679i
$313$	−6.37032	−	1.87049i	−0.360072	−	0.105727i	0.0966927	−	0.995314i	$-0.469174\pi$
$313$	−6.37032	−	1.87049i	−0.360072	−	0.105727i	−0.456764	+	0.889588i	$0.650992\pi$
$314$	16.9771	+	0.0743479i	0.958073	+	0.00419569i
$315$	−3.57914	−	0.238436i	−0.201662	−	0.0134343i
$316$	−19.0861	+	2.57375i	−1.07368	+	0.144785i
$317$	4.16515	−	1.22300i	0.233938	−	0.0686904i	−0.162662	−	0.986682i	$-0.552008\pi$
$317$	4.16515	−	1.22300i	0.233938	−	0.0686904i	0.396600	+	0.917991i	$0.370190\pi$
$318$	5.82341	−	4.02655i	0.326560	−	0.225798i
$319$	17.0542	+	2.45203i	0.954854	+	0.137287i
$320$	4.84870	+	1.56320i	0.271050	+	0.0873856i
$321$	12.9607	−	31.5072i	0.723398	−	1.75856i
$322$	−11.6813	+	5.07150i	−0.650975	+	0.282624i
$323$			9.23385i			0.513785i
$324$	5.08848	+	17.2658i	0.282693	+	0.959210i
$325$	22.5823	+	3.24685i	1.25264	+	0.180103i
$326$	13.1381	−	20.2478i	0.727653	−	1.12142i
$327$	0.893449	−	8.50551i	0.0494079	−	0.470356i
$328$	−20.3173	−	0.266940i	−1.12183	−	0.0147393i
$329$	9.26652	−	8.02949i	0.510880	−	0.442680i
$330$	5.05692	+	2.10614i	0.278374	+	0.115939i
$331$	−31.7963	−	9.33623i	−1.74768	−	0.513166i	−0.757486	−	0.652852i	$-0.773572\pi$
$331$	−31.7963	−	9.33623i	−1.74768	−	0.513166i	−0.990196	+	0.139686i	$0.955391\pi$
$332$	4.40096	+	6.98173i	0.241534	+	0.383172i
$333$	30.1591	−	6.71502i	1.65271	−	0.367981i
$334$	14.8142	+	12.9506i	0.810598	+	0.708626i
$335$	−6.29251	+	7.26194i	−0.343796	+	0.396762i
$336$	12.4035	−	3.92156i	0.676664	−	0.213939i
$337$	3.72269	+	25.8919i	0.202788	+	1.41042i	0.795961	+	0.605347i	$0.206966\pi$
$337$	3.72269	+	25.8919i	0.202788	+	1.41042i	−0.593173	+	0.805075i	$0.702125\pi$
$338$	−8.85241	−	13.9082i	−0.481507	−	0.756504i
$339$	−17.5762	+	0.670679i	−0.954608	+	0.0364263i
$340$	0.0257907	−	2.94456i	0.00139870	−	0.159691i
$341$	−4.36397	+	9.55576i	−0.236322	+	0.517474i
$342$	14.8674	−	8.12791i	0.803940	−	0.439507i
$343$	−10.6329	−	16.5452i	−0.574124	−	0.893354i
$344$	13.5986	+	6.42749i	0.733185	+	0.346547i
$345$	4.38091	−	2.96457i	0.235860	−	0.159607i
$346$	−8.44403	−	1.25184i	−0.453954	−	0.0672991i
$347$	5.37378	+	8.36176i	0.288479	+	0.448883i	0.955001	−	0.296603i	$-0.0958538\pi$
$347$	5.37378	+	8.36176i	0.288479	+	0.448883i	−0.666521	+	0.745486i	$0.732217\pi$
$348$	−12.5117	+	11.5021i	−0.670698	+	0.616577i
$349$	−20.7026	−	9.45458i	−1.10819	−	0.506092i	−0.224643	−	0.974441i	$-0.572122\pi$
$349$	−20.7026	−	9.45458i	−1.10819	−	0.506092i	−0.883543	+	0.468349i	$0.844849\pi$
$350$	1.68335	+	12.0834i	0.0899788	+	0.645883i
$351$	19.0127	+	17.4434i	1.01482	+	0.931061i
$352$	−19.8613	−	0.434960i	−1.05861	−	0.0231835i
$353$	15.8256	−	2.27537i	0.842309	−	0.121106i	0.292365	−	0.956307i	$-0.405558\pi$
$353$	15.8256	−	2.27537i	0.842309	−	0.121106i	0.549945	+	0.835201i	$0.314649\pi$
$354$	24.7732	−	22.9751i	1.31668	−	1.22111i
$355$	−2.00763	+	2.31693i	−0.106554	+	0.122970i
$356$	−3.53706	+	3.01105i	−0.187464	+	0.159585i
$357$	−4.30342	−	6.16594i	−0.227761	−	0.326336i
$358$	17.1873	+	20.0116i	0.908377	+	1.05765i
$359$	5.99607	+	1.76060i	0.316460	+	0.0929212i	0.436105	−	0.899896i	$-0.356357\pi$
$359$	5.99607	+	1.76060i	0.316460	+	0.0929212i	−0.119645	+	0.992817i	$0.538176\pi$
$360$	−4.76375	+	2.55036i	−0.251072	+	0.134416i
$361$	1.99718	+	2.30487i	0.105115	+	0.121309i
$362$	2.24412	−	0.648272i	0.117948	−	0.0340724i
$363$	−2.29643	−	0.241226i	−0.120532	−	0.0126611i
$364$	12.3344	−	13.9852i	0.646497	−	0.733025i
$365$	0.314994	−	2.19083i	0.0164875	−	0.114673i
$366$	0.681571	+	20.1807i	0.0356263	+	1.05486i
$367$			6.91622i			0.361024i	0.983573	+	0.180512i	$0.0577754\pi$
$367$			6.91622i			0.361024i	−0.983573	+	0.180512i	$0.942225\pi$
$368$	−10.8813	+	15.7986i	−0.567228	+	0.823561i
$369$	15.1647	−	15.3135i	0.789444	−	0.797187i
$370$	3.81610	+	8.45388i	0.198390	+	0.439496i
$371$	5.37180	+	0.772349i	0.278890	+	0.0400983i
$372$	−4.57967	−	9.29529i	−0.237445	−	0.481939i
$373$	3.44300	+	11.7258i	0.178272	+	0.607137i	0.999341	+	0.0363083i	$0.0115598\pi$
$373$	3.44300	+	11.7258i	0.178272	+	0.607137i	−0.821069	+	0.570829i	$0.806622\pi$
$374$	3.18682	+	11.0318i	0.164787	+	0.570442i
$375$	−3.36645	−	10.0328i	−0.173843	−	0.518091i
$376$	5.43604	−	17.6522i	0.280343	−	0.910342i
$377$	−6.86359	+	23.3753i	−0.353493	+	1.20389i
$378$	−6.13980	+	12.3564i	−0.315797	+	0.635544i
$379$	−15.4472	−	9.92733i	−0.793471	−	0.509933i	0.0800083	−	0.996794i	$-0.474505\pi$
$379$	−15.4472	−	9.92733i	−0.793471	−	0.509933i	−0.873479	+	0.486861i	$0.838142\pi$
$380$	3.29717	+	3.87316i	0.169141	+	0.198689i
$381$	−9.96512	−	19.7870i	−0.510529	−	1.01372i
$382$	−7.04926	−	3.25667i	−0.360672	−	0.166626i
$383$	5.06768	+	35.2465i	0.258946	+	1.80101i	0.540370	+	0.841427i	$0.318284\pi$
$383$	5.06768	+	35.2465i	0.258946	+	1.80101i	−0.281424	+	0.959584i	$0.590807\pi$
$384$	12.7214	−	14.9052i	0.649186	−	0.760630i
$385$	1.74437	+	3.81963i	0.0889011	+	0.194666i
$386$	14.8193	−	2.06449i	0.754281	−	0.105080i
$387$	−14.9202	+	5.64804i	−0.758436	+	0.287106i
$388$	−4.61152	+	9.86817i	−0.234115	+	0.500980i
$389$	−27.7131	+	17.8102i	−1.40511	+	0.903011i	−0.999937	−	0.0112286i	$-0.996426\pi$
$389$	−27.7131	+	17.8102i	−1.40511	+	0.903011i	−0.405175	+	0.914239i	$0.632789\pi$
$390$	−3.96530	+	6.65371i	−0.200791	+	0.336924i
$391$	10.5930	+	3.27701i	0.535709	+	0.165726i
$392$	−8.88486	−	4.19951i	−0.448753	−	0.212107i
$393$	0.770080	+	4.20946i	0.0388454	+	0.212339i
$394$	−6.36313	+	21.3249i	−0.320570	+	1.07433i
$395$	5.57794	+	2.54736i	0.280656	+	0.128171i
$396$	14.9572	−	14.8416i	0.751629	−	0.745821i
$397$	−31.2507	+	14.2717i	−1.56843	+	0.716276i	−0.994705	−	0.102774i	$-0.967228\pi$
$397$	−31.2507	+	14.2717i	−1.56843	+	0.716276i	−0.573721	+	0.819050i	$0.694501\pi$
$398$	−11.7139	+	7.45581i	−0.587167	+	0.373726i
$399$	12.5927	+	3.18139i	0.630425	+	0.159269i
$400$	11.7898	+	14.0978i	0.589492	+	0.704889i
$401$	6.77443	+	5.87008i	0.338299	+	0.293138i	0.807397	−	0.590008i	$-0.200876\pi$
$401$	6.77443	+	5.87008i	0.338299	+	0.293138i	−0.469098	+	0.883146i	$0.655421\pi$
$402$	16.4802	+	33.0834i	0.821958	+	1.65005i
$403$	−12.4958	−	8.03059i	−0.622462	−	0.400032i
$404$	−7.51475	+	4.73695i	−0.373873	+	0.235672i
$405$	1.56094	−	5.51460i	0.0775636	−	0.274023i
$406$	−13.0275	−	0.0570513i	−0.646543	−	0.00283141i
$407$	−23.6859	−	27.3350i	−1.17407	−	1.35494i
$408$	−10.4176	−	4.44626i	−0.515747	−	0.220122i
$409$	32.6522	−	9.58755i	1.61455	−	0.474074i	0.655002	−	0.755627i	$-0.272668\pi$
$409$	32.6522	−	9.58755i	1.61455	−	0.474074i	0.959546	+	0.281553i	$0.0908497\pi$
$410$	5.42724	+	3.52156i	0.268032	+	0.173917i
$411$	5.91490	+	3.48999i	0.291761	+	0.172148i
$412$	6.54915	+	23.0493i	0.322653	+	1.13556i
$413$	25.8992			1.27441
$414$	−4.04790	−	19.9403i	−0.198943	−	0.980011i
$415$		−	2.62780i		−	0.128994i
$416$	4.60542	−	27.7098i	0.225799	−	1.35859i
$417$	10.7943	−	18.2945i	0.528601	−	0.895884i
$418$	−16.6393	−	10.7967i	−0.813853	−	0.528082i
$419$	4.03038	+	13.7262i	0.196897	+	0.670570i	0.997454	+	0.0713133i	$0.0227190\pi$
$419$	4.03038	+	13.7262i	0.196897	+	0.670570i	−0.800557	+	0.599257i	$0.795463\pi$
$420$	−4.00678	−	1.04968i	−0.195511	−	0.0512191i
$421$	17.8416	−	15.4599i	0.869549	−	0.753468i	−0.100869	−	0.994900i	$-0.532162\pi$
$421$	17.8416	−	15.4599i	0.869549	−	0.753468i	0.970418	+	0.241431i	$0.0776169\pi$
$422$	−0.0411748	+	9.40212i	−0.00200436	+	0.457688i
$423$	9.47260	+	17.1483i	0.460573	+	0.833778i
$424$	7.48038	−	3.29810i	0.363279	−	0.160170i
$425$	5.74307	−	8.93640i	0.278580	−	0.433479i
$426$	5.25802	+	10.5553i	0.254752	+	0.511405i
$427$	−10.1360	+	11.6976i	−0.490517	+	0.566087i
$428$	21.5575	−	32.9068i	1.04202	−	1.59061i
$429$	7.39837	−	29.2845i	0.357197	−	1.41387i
$430$	−2.57153	−	4.04017i	−0.124010	−	0.194834i
$431$	−8.00903	−	17.5373i	−0.385781	−	0.844743i	−0.998516	−	0.0544548i	$-0.982658\pi$
$431$	−8.00903	−	17.5373i	−0.385781	−	0.844743i	0.612735	−	0.790289i	$-0.290069\pi$
$432$	2.01093	+	20.6871i	0.0967509	+	0.995309i
$433$	−3.05116	+	6.68110i	−0.146629	+	0.321073i	−0.968668	−	0.248358i	$-0.920109\pi$
$433$	−3.05116	+	6.68110i	−0.146629	+	0.321073i	0.822039	+	0.569431i	$0.192836\pi$
$434$	2.27118	−	7.61145i	0.109020	−	0.365361i
$435$	5.32303	−	0.973796i	0.255220	−	0.0466899i
$436$	2.86509	−	9.45060i	0.137213	−	0.452602i
$437$	−17.5355	+	7.70457i	−0.838838	+	0.368560i
$438$	−7.31349	−	4.35849i	−0.349452	−	0.208257i
$439$	1.44365	+	2.24636i	0.0689015	+	0.107213i	0.873995	−	0.485936i	$-0.161521\pi$
$439$	1.44365	+	2.24636i	0.0689015	+	0.107213i	−0.805093	+	0.593148i	$0.797885\pi$
$440$	5.27590	+	3.48939i	0.251519	+	0.166350i
$441$	9.74838	−	3.69024i	0.464208	−	0.175726i
$442$	−16.0811	+	2.24028i	−0.764901	+	0.106559i
$443$	−0.365530	+	0.166932i	−0.0173668	+	0.00793117i	−0.424080	−	0.905625i	$-0.639402\pi$
$443$	−0.365530	+	0.166932i	−0.0173668	+	0.00793117i	0.406713	+	0.913556i	$0.366675\pi$
$444$	35.6621	−	1.04810i	1.69245	−	0.0497407i
$445$	1.46397	−	0.210487i	0.0693988	−	0.00997804i
$446$	9.06319	−	19.6178i	0.429155	−	0.928930i
$447$	26.1646	−	13.1770i	1.23754	−	0.623251i
$448$	14.9192	−	1.74636i	0.704866	−	0.0825076i
$449$	18.8016	−	29.2559i	0.887304	−	1.38067i	−0.0371225	−	0.999311i	$-0.511819\pi$
$449$	18.8016	−	29.2559i	0.887304	−	1.38067i	0.924426	−	0.381361i	$-0.124544\pi$
$450$	−19.4437	−	1.38086i	−0.916587	−	0.0650944i
$451$	−24.2068	−	7.10774i	−1.13985	−	0.334691i
$452$	−20.0772	−	3.06638i	−0.944352	−	0.144230i
$453$	1.36018	−	0.456401i	0.0639069	−	0.0214436i
$454$	22.4305	−	6.47962i	1.05271	−	0.304104i
$455$	−5.69687	+	1.67275i	−0.267073	+	0.0784198i
$456$	18.6292	−	5.97980i	0.872392	−	0.280030i
$457$	−4.09863	+	28.5066i	−0.191726	+	1.33348i	0.635713	+	0.771926i	$0.280706\pi$
$457$	−4.09863	+	28.5066i	−0.191726	+	1.33348i	−0.827438	+	0.561556i	$0.810203\pi$
$458$	16.1328	+	35.7393i	0.753837	+	1.66999i
$459$	11.0654	−	4.67861i	0.516488	−	0.218379i
$460$	5.61338	−	2.40792i	0.261725	−	0.112270i
$461$	−42.1089			−1.96121			−0.980603	−	0.196004i	$-0.937203\pi$
$461$	−42.1089			−1.96121			−0.980603	+	0.196004i	$0.937203\pi$
$462$	16.1427	−	0.545194i	0.751026	−	0.0253647i
$463$	−17.9303	−	2.57799i	−0.833292	−	0.119809i	−0.287553	−	0.957765i	$-0.592842\pi$
$463$	−17.9303	−	2.57799i	−0.833292	−	0.119809i	−0.545739	+	0.837955i	$0.683751\pi$
$464$	−16.6925	+	10.3190i	−0.774929	+	0.479048i
$465$	−0.344681	+	3.28132i	−0.0159842	+	0.152167i
$466$	26.7892	−	7.73875i	1.24099	−	0.358491i
$467$	−11.3991	+	9.87735i	−0.527486	+	0.457069i	−0.877432	−	0.479700i	$-0.840745\pi$
$467$	−11.3991	+	9.87735i	−0.527486	+	0.457069i	0.349946	+	0.936770i	$0.386200\pi$
$468$	17.7622	+	23.9203i	0.821056	+	1.10572i
$469$	−7.98206	+	27.1844i	−0.368577	+	1.25526i
$470$	−4.46138	+	3.83173i	−0.205788	+	0.176744i
$471$	−17.0507	+	11.9002i	−0.785653	+	0.548334i
$472$	33.0949	−	20.6595i	1.52332	−	0.950932i
$473$	14.1139	+	12.2298i	0.648960	+	0.562327i
$474$	17.2945	−	16.0392i	0.794361	−	0.736705i
$475$	2.61138	+	18.1625i	0.119818	+	0.833354i
$476$	−3.53749	−	7.92909i	−0.162141	−	0.363429i
$477$	−2.99055	+	8.13906i	−0.136928	+	0.372662i
$478$	−32.1192	+	4.47456i	−1.46910	+	0.204662i
$479$	−16.2387	+	35.5578i	−0.741966	+	1.62468i	0.0383275	+	0.999265i	$0.487797\pi$
$479$	−16.2387	+	35.5578i	−0.741966	+	1.62468i	−0.780293	+	0.625414i	$0.784930\pi$
$480$	−5.95732	+	1.85485i	−0.271913	+	0.0846620i
$481$	43.0236	−	27.6496i	1.96171	−	1.26071i
$482$	−4.02537	−	0.596764i	−0.183350	−	0.0271819i
$483$	8.11870	−	13.3172i	0.369414	−	0.605952i
$484$	−2.55160	−	0.773557i	−0.115982	−	0.0351617i
$485$	2.91765	−	1.87506i	0.132484	−	0.0851420i
$486$	−17.2731	−	13.6981i	−0.783525	−	0.621361i
$487$	16.8988	+	7.71744i	0.765760	+	0.349711i	0.759702	−	0.650271i	$-0.225345\pi$
$487$	16.8988	+	7.71744i	0.765760	+	0.349711i	0.00605739	+	0.999982i	$0.498072\pi$
$488$	−3.62111	+	23.0330i	−0.163920	+	1.04266i
$489$	1.12719	+	29.5399i	0.0509734	+	1.33584i
$490$	1.68015	+	2.63972i	0.0759016	+	0.119250i
$491$	−8.03988	+	1.15596i	−0.362834	+	0.0521677i	−0.321321	−	0.946970i	$-0.604127\pi$
$491$	−8.03988	+	1.15596i	−0.362834	+	0.0521677i	−0.0415132	+	0.999138i	$0.513218\pi$
$492$	20.5308	−	14.0634i	0.925602	−	0.634027i
$493$	8.57267	+	7.42826i	0.386094	+	0.334552i
$494$	18.4590	−	21.1153i	0.830510	−	0.950021i
$495$	−6.54876	+	1.45810i	−0.294345	+	0.0655368i
$496$	−3.16939	−	11.5379i	−0.142310	−	0.518066i
$497$	−2.54668	+	8.67320i	−0.114234	+	0.389046i
$498$	−9.33096	−	3.88623i	−0.418130	−	0.174146i
$499$	9.03594	+	10.4280i	0.404504	+	0.466823i	0.921054	−	0.389434i	$-0.127329\pi$
$499$	9.03594	+	10.4280i	0.404504	+	0.466823i	−0.516550	+	0.856257i	$0.672784\pi$
$500$	−1.63304	−	12.1100i	−0.0730316	−	0.541578i
$501$	−23.9673	−	2.51761i	−1.07078	−	0.112479i
$502$	9.39370	+	6.09526i	0.419261	+	0.272045i
$503$	5.00727	−	34.8264i	0.223263	−	1.55283i	−0.502311	−	0.864687i	$-0.667517\pi$
$503$	5.00727	−	34.8264i	0.223263	−	1.55283i	0.725574	−	0.688144i	$-0.241574\pi$
$504$	−9.65284	+	12.6751i	−0.429972	+	0.564596i
$505$	2.82842			0.125863
$506$	−18.2909	+	15.2567i	−0.813130	+	0.678243i
$507$	18.6734	+	7.68147i	0.829317	+	0.341146i
$508$	−6.99203	−	24.6079i	−0.310221	−	1.09180i
$509$	−0.457104	+	3.17923i	−0.0202608	+	0.140917i	−0.997441	−	0.0714954i	$-0.977223\pi$
$509$	−0.457104	+	3.17923i	−0.0202608	+	0.140917i	0.977180	+	0.212412i	$0.0681320\pi$
$510$	2.05110	+	2.96642i	0.0908244	+	0.131355i
$511$	−1.83862	−	6.26177i	−0.0813358	−	0.277004i
$512$	17.6713	−	14.1325i	0.780966	−	0.624573i
$513$	−9.15298	+	18.6247i	−0.404114	+	0.822300i
$514$	22.4436	+	0.0982872i	0.989944	+	0.00433526i
$515$	2.14947	−	7.32042i	0.0947169	−	0.322576i
$516$	−18.1491	+	3.15618i	−0.798968	+	0.138943i
$517$	12.3986	−	19.2926i	0.545291	−	0.848489i
$518$	20.5898	+	17.9997i	0.904665	+	0.790859i
$519$	9.33751	−	4.70255i	0.409871	−	0.206419i
$520$	−5.94533	+	6.68184i	−0.260720	+	0.293018i
$521$	−9.03485	+	1.29902i	−0.395824	+	0.0569109i	−0.337353	−	0.941378i	$-0.609532\pi$
$521$	−9.03485	+	1.29902i	−0.395824	+	0.0569109i	−0.0584710	+	0.998289i	$0.518623\pi$
$522$	4.41435	−	20.3415i	0.193211	−	0.890321i
$523$	−3.24437	−	7.10418i	−0.141866	−	0.310644i	0.825340	−	0.564636i	$-0.190984\pi$
$523$	−3.24437	−	7.10418i	−0.141866	−	0.310644i	−0.967206	+	0.253992i	$0.918256\pi$
$524$	−0.0432784	+	4.94114i	−0.00189062	+	0.215855i
$525$	−10.2084	−	10.9111i	−0.445530	−	0.476198i
$526$	−4.50226	+	15.0885i	−0.196308	+	0.657892i
$527$	−5.81821	+	3.73913i	−0.253445	+	0.162879i
$528$	20.1928	−	13.5735i	0.878779	−	0.590713i
$529$	2.61538	+	22.8508i	0.113712	+	0.993514i
$530$	−2.57486	−	0.381726i	−0.111845	−	0.0165811i
$531$	−8.59864	+	40.4773i	−0.373149	+	1.75656i
$532$	13.5873	+	6.34951i	0.589083	+	0.275286i
$533$	14.8189	−	32.4489i	0.641878	−	1.40552i
$534$	1.41764	−	5.50964i	0.0613472	−	0.238425i
$535$	−11.3938	+	5.20339i	−0.492598	+	0.224962i
$536$	11.4850	+	41.1044i	0.496076	+	1.77544i
$537$	−31.3238	−	7.91356i	−1.35172	−	0.341495i
$538$	−0.393525	−	0.181804i	−0.0169661	−	0.00783812i
$539$	−9.22159	−	7.99055i	−0.397202	−	0.344178i
$540$	2.97079	−	5.91362i	0.127843	−	0.254482i
$541$	2.33565	−	3.63434i	0.100417	−	0.156253i	−0.787409	−	0.616431i	$-0.788578\pi$
$541$	2.33565	−	3.63434i	0.100417	−	0.156253i	0.887827	+	0.460178i	$0.152214\pi$
$542$	−6.61688	−	7.70420i	−0.284219	−	0.330924i
$543$	−1.78966	+	2.23196i	−0.0768016	+	0.0957824i
$544$	−10.8453	−	7.31025i	−0.464988	−	0.313424i
$545$	−2.37634	+	2.05911i	−0.101791	+	0.0882025i
$546$	−2.48533	+	22.7026i	−0.106362	+	0.971581i
$547$	11.6348	−	3.41629i	0.497469	−	0.146070i	−0.0233668	−	0.999727i	$-0.507439\pi$
$547$	11.6348	−	3.41629i	0.497469	−	0.146070i	0.520836	+	0.853657i	$0.325620\pi$
$548$	5.94753	+	5.24547i	0.254066	+	0.224075i
$549$	−14.9167	−	19.7251i	−0.636631	−	0.841845i
$550$	9.38818	+	20.7978i	0.400313	+	0.886821i
$551$	−19.5939			−0.834730
$552$	−0.248607	−	23.4934i	−0.0105814	−	0.999944i
$553$	18.0805			0.768862
$554$	−10.1376	−	22.4579i	−0.430703	−	0.954145i
$555$	−9.78374	−	5.77273i	−0.415297	−	0.245039i
$556$	16.2240	−	18.3954i	0.688049	−	0.780139i
$557$	−17.2092	+	5.05309i	−0.729179	+	0.214106i	−0.625190	−	0.780472i	$-0.714979\pi$
$557$	−17.2092	+	5.05309i	−0.729179	+	0.214106i	−0.103989	+	0.994578i	$0.533161\pi$
$558$	11.1417	+	6.07662i	0.471668	+	0.257244i
$559$	−19.9566	+	17.2925i	−0.844076	+	0.731396i
$560$	−4.31508	−	2.06273i	−0.182346	−	0.0871663i
$561$	−10.9720	−	8.79774i	−0.463239	−	0.371441i
$562$	8.21196	+	9.56139i	0.346400	+	0.403323i
$563$	−9.83583	+	15.3049i	−0.414531	+	0.645023i	−0.984243	−	0.176822i	$-0.943418\pi$
$563$	−9.83583	+	15.3049i	−0.414531	+	0.645023i	0.569712	+	0.821844i	$0.307055\pi$
$564$	7.00805	+	21.5084i	0.295092	+	0.905668i
$565$	4.88726	+	4.23484i	0.205609	+	0.178161i
$566$	15.9164	+	7.35321i	0.669018	+	0.309078i
$567$	−2.56807	−	16.7024i	−0.107849	−	0.701436i
$568$	3.66429	+	13.1144i	0.153750	+	0.550268i
$569$	3.67292	−	1.67737i	0.153977	−	0.0703188i	−0.336936	−	0.941528i	$-0.609391\pi$
$569$	3.67292	−	1.67737i	0.153977	−	0.0703188i	0.490913	+	0.871209i	$0.336663\pi$
$570$	−6.03318	−	1.55235i	−0.252702	−	0.0650206i
$571$	−7.29458	+	15.9729i	−0.305269	+	0.668445i	−0.998640	−	0.0521352i	$-0.983397\pi$
$571$	−7.29458	+	15.9729i	−0.305269	+	0.668445i	0.693371	+	0.720580i	$0.256125\pi$
$572$	14.7659	−	31.5974i	0.617392	−	1.32115i
$573$	9.35511	−	1.71143i	0.390815	−	0.0714959i
$574$	18.8696	+	2.79744i	0.787602	+	0.116763i
$575$	21.7626	+	3.44999i	0.907562	+	0.143874i
$576$	−2.22390	+	23.8967i	−0.0926625	+	0.995698i
$577$	−28.2040	+	18.1256i	−1.17415	+	0.754579i	−0.974301	−	0.225248i	$-0.927681\pi$
$577$	−28.2040	+	18.1256i	−1.17415	+	0.754579i	−0.199846	+	0.979827i	$0.564044\pi$
$578$	4.71266	−	15.7937i	0.196021	−	0.656929i
$579$	−13.3815	+	12.5197i	−0.556117	+	0.520302i
$580$	6.24827	+	0.0547272i	0.259445	+	0.00227242i
$581$	−3.21868	−	7.04794i	−0.133534	−	0.292398i
$582$	−2.34319	−	13.1332i	−0.0971285	−	0.544387i
$583$	10.0472	−	1.44457i	0.416113	−	0.0598281i
$584$	−7.34441	−	6.53486i	−0.303914	−	0.270414i
$585$	−0.722924	−	9.45889i	−0.0298892	−	0.391077i
$586$	1.16087	+	1.01483i	0.0479551	+	0.0419224i
$587$	10.3221	−	16.0616i	0.426040	−	0.662931i	−0.560180	−	0.828371i	$-0.689268\pi$
$587$	10.3221	−	16.0616i	0.426040	−	0.662931i	0.986220	+	0.165440i	$0.0529044\pi$
$588$	11.8580	−	2.06214i	0.489016	−	0.0850414i
$589$	3.36576	−	11.4627i	0.138684	−	0.472313i
$590$	−12.4220	−	0.0543999i	−0.511408	−	0.00223961i
$591$	−8.67035	−	25.8396i	−0.356650	−	1.06290i
$592$	40.6686	+	6.57629i	1.67147	+	0.270284i
$593$	−12.1992	−	41.5466i	−0.500960	−	1.70611i	−0.689708	−	0.724088i	$-0.742261\pi$
$593$	−12.1992	−	41.5466i	−0.500960	−	1.70611i	0.188748	−	0.982026i	$-0.439557\pi$
$594$	−4.50738	+	25.4101i	−0.184940	+	1.04259i
$595$	−0.393431	+	2.73637i	−0.0161291	+	0.112180i
$596$	32.5394	−	9.24564i	1.33286	−	0.378716i
$597$	6.46961	−	15.7275i	0.264784	−	0.643682i
$598$	−17.6722	−	28.6696i	−0.722671	−	1.17239i
$599$	−33.0059			−1.34858			−0.674292	−	0.738465i	$-0.735551\pi$
$599$	−33.0059			−1.34858			−0.674292	+	0.738465i	$0.735551\pi$
$600$	−21.7483	−	5.79942i	−0.887870	−	0.236761i
$601$	−1.11422	+	7.74960i	−0.0454502	+	0.316113i	0.954396	+	0.298545i	$0.0965013\pi$
$601$	−1.11422	+	7.74960i	−0.0454502	+	0.316113i	−0.999846	+	0.0175677i	$0.994408\pi$
$602$	−11.8456	−	7.68623i	−0.482792	−	0.313267i
$603$	−39.8359	−	21.5004i	−1.62224	−	0.875562i
$604$	1.64180	−	0.221396i	0.0668039	−	0.00900849i
$605$	0.555947	+	0.641597i	0.0226024	+	0.0260846i
$606$	4.18292	−	10.0433i	0.169920	−	0.407982i
$607$	8.36205	−	28.4785i	0.339405	−	1.15591i	−0.596193	−	0.802841i	$-0.703321\pi$
$607$	8.36205	−	28.4785i	0.339405	−	1.15591i	0.935598	−	0.353067i	$-0.114861\pi$
$608$	22.4273	−	2.72482i	0.909546	−	0.110506i
$609$	13.0839	−	9.13173i	0.530188	−	0.370036i
$610$	4.88613	−	5.58925i	0.197834	−	0.226302i
$611$	24.5065	+	21.2350i	0.991428	+	0.859077i
$612$	13.5667	−	2.89619i	0.548400	−	0.117071i
$613$	−46.6007	+	6.70017i	−1.88218	+	0.270617i	−0.985195	−	0.171435i	$-0.945160\pi$
$613$	−46.6007	+	6.70017i	−1.88218	+	0.270617i	−0.896989	+	0.442052i	$0.854251\pi$
$614$	2.13414	+	3.35299i	0.0861270	+	0.135316i
$615$	−7.91790	+	0.302134i	−0.319281	+	0.0121832i
$616$	18.4243	+	2.89656i	0.742336	+	0.116706i
$617$	10.6638	+	4.87000i	0.429309	+	0.196059i	0.618338	−	0.785913i	$-0.287806\pi$
$617$	10.6638	+	4.87000i	0.429309	+	0.196059i	−0.189028	+	0.981972i	$0.560534\pi$
$618$	−22.8149	−	18.4585i	−0.917752	−	0.742511i
$619$	28.8260	−	18.5253i	1.15861	−	0.744596i	0.187278	−	0.982307i	$-0.440034\pi$
$619$	28.8260	−	18.5253i	1.15861	−	0.744596i	0.971336	+	0.237711i	$0.0763972\pi$
$620$	−1.10532	+	3.64592i	−0.0443905	+	0.146424i
$621$	18.1177	+	17.1099i	0.727038	+	0.686598i
$622$	−15.2091	−	2.25477i	−0.609831	−	0.0904080i
$623$	3.66864	−	2.35769i	0.146981	−	0.0944590i
$624$	14.9338	+	30.9927i	0.597831	+	1.24070i
$625$	7.92679	−	17.3572i	0.317071	−	0.694290i
$626$	9.29952	−	1.29553i	0.371684	−	0.0517797i
$627$	24.2753	−	0.926306i	0.969463	−	0.0369931i
$628$	−21.9263	+	9.78223i	−0.874954	+	0.390353i
$629$	−3.38886	−	23.5700i	−0.135123	−	0.939799i
$630$	4.75215	−	1.77517i	0.189330	−	0.0707245i
$631$	−21.5519	−	18.6749i	−0.857969	−	0.743435i	0.110153	−	0.993915i	$-0.464866\pi$
$631$	−21.5519	−	18.6749i	−0.857969	−	0.743435i	−0.968122	+	0.250480i	$0.919412\pi$
$632$	23.1039	−	14.4227i	0.919026	−	0.573703i
$633$	−6.59050	−	9.44286i	−0.261949	−	0.375320i
$634$	−4.65718	+	3.99989i	−0.184960	+	0.158856i
$635$	−2.29482	+	7.81545i	−0.0910673	+	0.310147i
$636$	−5.16339	+	8.57845i	−0.204742	+	0.340158i
$637$	13.0390	−	11.2984i	0.516625	−	0.447658i
$638$	−23.4092	+	6.76234i	−0.926778	+	0.267724i
$639$	−12.7097	−	6.85970i	−0.502786	−	0.271366i
$640$	−7.15939	+	0.806271i	−0.283000	+	0.0318706i
$641$	−42.3102	−	6.08329i	−1.67115	−	0.240276i	−0.759285	−	0.650759i	$-0.774451\pi$
$641$	−42.3102	−	6.08329i	−1.67115	−	0.240276i	−0.911868	+	0.410483i	$0.865360\pi$
$642$	1.62630	+	48.1531i	0.0641848	+	1.90045i
$643$	−0.0267278			−0.00105404			−0.000527021	−	1.00000i	$-0.500168\pi$
$643$	−0.0267278			−0.00105404			−0.000527021		1.00000i	$0.500168\pi$
$644$	12.1061	−	13.3338i	0.477047	−	0.525424i
$645$	5.42443	+	2.23138i	0.213587	+	0.0878607i
$646$	−5.37268	−	11.9022i	−0.211385	−	0.468286i
$647$	2.48968	−	17.3161i	0.0978794	−	0.680766i	−0.880515	−	0.474019i	$-0.842803\pi$
$647$	2.48968	−	17.3161i	0.0978794	−	0.680766i	0.978394	−	0.206748i	$-0.0662880\pi$
$648$	−16.6050	−	19.2944i	−0.652304	−	0.757957i
$649$	46.4786	−	13.6474i	1.82445	−	0.535706i
$650$	−30.9972	+	8.95434i	−1.21581	+	0.351218i
$651$	3.09469	+	9.22288i	0.121290	+	0.361473i
$652$	−5.15359	+	33.7432i	−0.201830	+	1.32149i
$653$	−43.3013	−	12.7144i	−1.69451	−	0.497553i	−0.715029	−	0.699095i	$-0.753587\pi$
$653$	−43.3013	−	12.7144i	−1.69451	−	0.497553i	−0.979480	+	0.201542i	$0.935405\pi$
$654$	3.79727	+	11.4832i	0.148485	+	0.449030i
$655$	0.850610	−	1.32358i	0.0332361	−	0.0517164i
$656$	26.3438	−	11.4775i	1.02855	−	0.448119i
$657$	10.3968	−	0.794609i	0.405619	−	0.0310006i
$658$	−7.27238	+	15.7415i	−0.283507	+	0.613667i
$659$	9.90004	−	1.42341i	0.385651	−	0.0554482i	0.0532370	−	0.998582i	$-0.483046\pi$
$659$	9.90004	−	1.42341i	0.385651	−	0.0554482i	0.332414	+	0.943134i	$0.392137\pi$
$660$	−7.74368	+	0.227585i	−0.301423	+	0.00885874i
$661$	−18.1473	+	8.28760i	−0.705848	+	0.322350i	−0.735798	−	0.677201i	$-0.763193\pi$
$661$	−18.1473	+	8.28760i	−0.705848	+	0.322350i	0.0299495	+	0.999551i	$0.490465\pi$
$662$	46.4168	−	6.46639i	1.80404	−	0.251323i
$663$	14.5210	−	13.5858i	0.563948	−	0.527628i
$664$	−9.73502	−	6.43859i	−0.377792	−	0.249866i
$665$	−2.58173	−	4.01725i	−0.100115	−	0.155782i
$666$	−34.9672	+	26.2035i	−1.35495	+	1.01536i
$667$	−6.95372	+	22.4779i	−0.269249	+	0.870349i
$668$	−26.6304	−	8.07341i	−1.03036	−	0.312370i
$669$	4.76283	+	26.0349i	0.184142	+	1.00657i
$670$	3.88555	−	13.0217i	0.150112	−	0.503073i
$671$	−12.0262	+	26.3336i	−0.464265	+	1.01660i
$672$	−13.7060	+	12.2717i	−0.528720	+	0.473391i
$673$	−1.47097	−	3.22098i	−0.0567017	−	0.124159i	0.879160	−	0.476526i	$-0.158104\pi$
$673$	−1.47097	−	3.22098i	−0.0567017	−	0.124159i	−0.935862	+	0.352367i	$0.885377\pi$
$674$	−19.8636	−	31.2080i	−0.765116	−	1.20209i
$675$	20.4419	−	12.3319i	0.786810	−	0.474657i
$676$	19.5029	+	12.7765i	0.750113	+	0.491404i
$677$	−23.5037	+	27.1247i	−0.903321	+	1.04249i	0.0955713	+	0.995423i	$0.469532\pi$
$677$	−23.5037	+	27.1247i	−0.903321	+	1.04249i	−0.998892	+	0.0470649i	$0.985013\pi$
$678$	22.2650	−	11.0911i	0.855083	−	0.425952i
$679$	5.52864	−	8.60272i	0.212170	−	0.330142i
$680$	1.68004	+	3.81047i	0.0644265	+	0.146125i
$681$	−17.8880	+	22.3089i	−0.685471	+	0.854878i
$682$	0.0650602	−	14.8563i	0.00249129	−	0.568877i
$683$	−18.7583	+	16.2542i	−0.717768	+	0.621949i	−0.935197	−	0.354127i	$-0.884778\pi$
$683$	−18.7583	+	16.2542i	−0.717768	+	0.621949i	0.217430	+	0.976076i	$0.430233\pi$
$684$	−14.4346	+	19.1272i	−0.551919	+	0.731348i
$685$	−0.711375	−	2.42272i	−0.0271803	−	0.0925675i
$686$	23.3323	+	15.1395i	0.890831	+	0.578031i
$687$	−41.3614	−	24.4046i	−1.57804	−	0.931094i
$688$	−21.2680	−	0.372592i	−0.810835	−	0.0142049i
$689$			14.3525i			0.546787i
$690$	−3.92196	+	6.37028i	−0.149306	+	0.242512i
$691$	−0.788857			−0.0300095			−0.0150048	−	0.999887i	$-0.504776\pi$
$691$	−0.788857			−0.0300095			−0.0150048	+	0.999887i	$0.504776\pi$
$692$	11.6125	−	3.29954i	0.441441	−	0.125430i
$693$	−15.7782	+	11.9320i	−0.599365	+	0.453260i
$694$	−11.7919	−	7.65138i	−0.447615	−	0.290442i
$695$	−7.49335	+	2.20025i	−0.284239	+	0.0834601i
$696$	9.43482	−	22.1058i	0.357626	−	0.837918i
$697$	−10.8769	−	12.5526i	−0.411993	−	0.475465i
$698$	32.1863	+	0.140953i	1.21827	+	0.00533517i
$699$	−21.3641	+	26.6440i	−0.808063	+	1.00777i
$700$	−9.20046	−	14.5957i	−0.347745	−	0.551666i
$701$	32.2814	+	20.7460i	1.21925	+	0.783566i	0.982183	−	0.187926i	$-0.0601766\pi$
$701$	32.2814	+	20.7460i	1.21925	+	0.783566i	0.237070	+	0.971493i	$0.423813\pi$
$702$	−34.6563	−	11.4216i	−1.30802	−	0.431082i
$703$	31.0860	+	26.9362i	1.17243	+	1.01592i
$704$	25.8538	−	10.9956i	0.974401	−	0.414411i
$705$	1.76424	−	6.98330i	0.0664453	−	0.263006i
$706$	−19.0748	+	12.1409i	−0.717890	+	0.456930i
$707$	7.58601	−	3.46441i	0.285301	−	0.130293i
$708$	−18.5640	+	44.0285i	−0.697678	+	1.65469i
$709$	28.1651	+	12.8626i	1.05776	+	0.483064i	0.866863	−	0.498546i	$-0.166133\pi$
$709$	28.1651	+	12.8626i	1.05776	+	0.483064i	0.190899	+	0.981610i	$0.438860\pi$
$710$	1.23969	−	4.15459i	0.0465246	−	0.155919i
$711$	−6.00282	+	28.2577i	−0.225123	+	1.05975i
$712$	2.80721	−	5.93919i	0.105205	−	0.222581i
$713$	−11.9554	−	7.92918i	−0.447734	−	0.296950i
$714$	9.13463	+	5.44380i	0.341855	+	0.203729i
$715$	−9.34216	+	6.00384i	−0.349377	+	0.224531i
$716$	−33.7977	−	15.7941i	−1.26308	−	0.590253i
$717$	29.0030	−	27.1352i	1.08314	−	1.01338i
$718$	−8.75318	+	1.21942i	−0.326666	+	0.0455082i
$719$	0.991703	+	2.17153i	0.0369843	+	0.0809843i	0.927222	−	0.374511i	$-0.122189\pi$
$719$	0.991703	+	2.17153i	0.0369843	+	0.0809843i	−0.890238	+	0.455495i	$0.849462\pi$
$720$	4.65643	−	6.05912i	0.173535	−	0.225810i
$721$	−3.20146	−	22.2666i	−0.119228	−	0.829252i
$722$	−3.91540	−	1.80887i	−0.145716	−	0.0673191i
$723$	4.45130	−	2.24176i	0.165546	−	0.0833719i
$724$	−2.51542	+	2.14134i	−0.0934848	+	0.0795823i
$725$	18.9628	+	12.1866i	0.704259	+	0.452600i
$726$	3.10040	−	1.02524i	0.115067	−	0.0380502i
$727$	−11.9770	+	40.7899i	−0.444202	+	1.51281i	0.368218	+	0.929739i	$0.379968\pi$
$727$	−11.9770	+	40.7899i	−0.444202	+	1.51281i	−0.812420	+	0.583073i	$0.801850\pi$
$728$	−7.76144	+	25.2033i	−0.287658	+	0.934097i
$729$	26.9565	+	1.53170i	0.998390	+	0.0567297i
$730$	0.868708	+	3.00720i	0.0321523	+	0.111302i
$731$	3.46394	+	11.7971i	0.128118	+	0.436331i
$732$	−12.6206	−	25.6158i	−0.466471	−	0.946788i
$733$	2.61749	+	0.376339i	0.0966793	+	0.0139004i	0.190485	−	0.981690i	$-0.438994\pi$
$733$	2.61749	+	0.376339i	0.0966793	+	0.0139004i	−0.0938054	+	0.995591i	$0.529903\pi$
$734$	−4.02418	−	8.91483i	−0.148535	−	0.329052i
$735$	−3.54415	−	1.45791i	−0.130728	−	0.0537760i
$736$	4.83337	−	26.6953i	0.178160	−	0.984001i
$737$			52.9912i			1.95196i
$738$	−10.6369	+	28.5622i	−0.391548	+	1.05139i
$739$	−0.970009	+	6.74656i	−0.0356824	+	0.248176i	−0.999854	−	0.0171039i	$-0.994555\pi$
$739$	−0.970009	+	6.74656i	−0.0356824	+	0.248176i	0.964171	+	0.265280i	$0.0854645\pi$
$740$	−9.83771	−	8.67644i	−0.361642	−	0.318952i
$741$	−3.58845	+	34.1615i	−0.131825	+	1.25495i
$742$	−7.37350	+	2.13003i	−0.270690	+	0.0781957i
$743$	0.418868	+	0.483399i	0.0153668	+	0.0177342i	0.763381	−	0.645949i	$-0.223538\pi$
$743$	0.418868	+	0.483399i	0.0153668	+	0.0177342i	−0.748014	+	0.663683i	$0.768993\pi$
$744$	11.3115	+	9.31673i	0.414700	+	0.341568i
$745$	−10.3345	−	3.03447i	−0.378626	−	0.111175i
$746$	−11.2605	−	13.1109i	−0.412277	−	0.480025i
$747$	12.0837	−	2.69047i	0.442119	−	0.0984392i
$748$	−10.5266	−	12.3655i	−0.384889	−	0.452127i
$749$	−24.1856	+	27.9116i	−0.883722	+	1.01987i
$750$	10.1768	+	10.9733i	0.371605	+	0.400687i
$751$	35.8001	−	5.14727i	1.30636	−	0.187827i	0.546252	−	0.837621i	$-0.316054\pi$
$751$	35.8001	−	5.14727i	1.30636	−	0.187827i	0.760110	+	0.649794i	$0.225145\pi$
$752$	3.26394	+	25.9162i	0.119024	+	0.945065i
$753$	−13.7046	+	0.522947i	−0.499425	+	0.0190572i
$754$	−4.75381	−	34.1237i	−0.173124	−	1.24271i
$755$	−0.479819	−	0.219126i	−0.0174624	−	0.00797481i
$756$	0.724518	−	19.4995i	0.0263505	−	0.709190i
$757$	−12.3834	−	19.2689i	−0.450081	−	0.700340i	0.539870	−	0.841748i	$-0.318473\pi$
$757$	−12.3834	−	19.2689i	−0.450081	−	0.700340i	−0.989951	+	0.141408i	$0.954837\pi$
$758$	25.6873	+	3.80816i	0.933004	+	0.138319i
$759$	7.55245	−	28.1771i	0.274137	−	1.02276i
$760$	−6.50355	−	3.07396i	−0.235909	−	0.111504i
$761$	1.73199	+	2.69502i	0.0627844	+	0.0976945i	0.871226	−	0.490881i	$-0.163325\pi$
$761$	1.73199	+	2.69502i	0.0627844	+	0.0976945i	−0.808442	+	0.588576i	$0.799689\pi$
$762$	24.3578	+	19.7068i	0.882390	+	0.713901i
$763$	−3.85137	+	8.43333i	−0.139429	+	0.305307i
$764$	10.9812	+	0.0961819i	0.397286	+	0.00347974i
$765$	−4.14600	−	1.52337i	−0.149899	−	0.0550777i
$766$	−27.0401	−	42.4832i	−0.977000	−	1.53498i
$767$	9.74767	+	67.7965i	0.351968	+	2.44799i
$768$	−7.72498	+	26.6144i	−0.278751	+	0.960363i
$769$	16.7566	−	19.3381i	0.604257	−	0.697350i	−0.368381	−	0.929675i	$-0.620088\pi$
$769$	16.7566	−	19.3381i	0.604257	−	0.697350i	0.972638	+	0.232325i	$0.0746333\pi$
$770$	−4.47088	−	3.90845i	−0.161119	−	0.140851i
$771$	−22.5408	+	15.7320i	−0.811788	+	0.566575i
$772$	−17.9004	+	11.2836i	−0.644251	+	0.406106i
$773$	45.4189	+	13.3362i	1.63360	+	0.479670i	0.964628	−	0.263614i	$-0.0849144\pi$
$773$	45.4189	+	13.3362i	1.63360	+	0.479670i	0.668977	+	0.743283i	$0.266733\pi$
$774$	15.9455	−	15.9614i	0.573148	−	0.573722i
$775$	−10.3867	+	9.00011i	−0.373101	+	0.323294i
$776$	0.202374	−	15.4030i	0.00726480	−	0.552936i
$777$	−33.3114	−	3.49915i	−1.19504	−	0.125531i
$778$	25.3588	−	39.0816i	0.909155	−	1.40114i
$779$	28.3987	+	4.08311i	1.01749	+	0.146293i
$780$	1.23973	−	10.8837i	0.0443893	−	0.389697i
$781$			16.9069i			0.604976i
$782$	−15.5608	+	1.93949i	−0.556452	+	0.0693558i
$783$	9.92788	+	23.4804i	0.354793	+	0.839121i
$784$	13.8958	+	0.243440i	0.496280	+	0.00869427i
$785$	7.56688	+	1.08795i	0.270074	+	0.0388307i
$786$	−3.44187	−	4.97782i	−0.122768	−	0.177553i
$787$	40.7250	−	11.9579i	1.45169	−	0.426255i	0.541590	−	0.840643i	$-0.317823\pi$
$787$	40.7250	−	11.9579i	1.45169	−	0.426255i	0.910100	+	0.414388i	$0.136004\pi$
$788$	−4.20591	−	31.1896i	−0.149829	−	1.11108i
$789$	−6.13475	−	18.2830i	−0.218403	−	0.650891i
$790$	−8.67199	−	0.0379773i	−0.308535	−	0.00135117i
$791$	18.2950	+	5.37190i	0.650496	+	0.191003i
$792$	−10.6439	+	27.8333i	−0.378215	+	0.989014i
$793$	−34.4359	−	22.1306i	−1.22285	−	0.785880i
$794$	31.9774	−	36.5789i	1.13483	−	1.29814i
$795$	2.84731	−	1.43396i	0.100984	−	0.0508574i
$796$	10.7608	−	16.4261i	0.381408	−	0.582207i
$797$	−2.21507	−	15.4061i	−0.0784618	−	0.545714i	−0.990701	−	0.136056i	$-0.956557\pi$
$797$	−2.21507	−	15.4061i	−0.0784618	−	0.545714i	0.912239	−	0.409658i	$-0.134352\pi$
$798$	−18.0828	+	3.22629i	−0.640123	+	0.114210i
$799$	13.7339	−	6.27205i	0.485869	−	0.221889i
$800$	−23.3995	−	11.3118i	−0.827299	−	0.399932i
$801$	2.46679	+	6.51642i	0.0871596	+	0.230246i
$802$	−12.1475	−	3.62470i	−0.428945	−	0.127993i
$803$	−6.59918	−	10.2685i	−0.232880	−	0.362368i
$804$	−40.4920	−	33.0547i	−1.42804	−	1.16575i
$805$	−5.52477	+	1.53604i	−0.194723	+	0.0541383i
$806$	20.7794	+	3.08056i	0.731923	+	0.108508i
$807$	0.522249	−	0.0955404i	0.0183840	−	0.00336318i
$808$	6.93014	−	10.4782i	0.243802	−	0.368623i
$809$	20.1071	+	9.18262i	0.706929	+	0.322844i	0.736234	−	0.676727i	$-0.236602\pi$
$809$	20.1071	+	9.18262i	0.706929	+	0.322844i	−0.0293051	+	0.999571i	$0.509329\pi$
$810$	1.19664	+	8.01640i	0.0420458	+	0.281668i
$811$	−3.04653	−	6.67097i	−0.106978	−	0.234250i	0.848571	−	0.529082i	$-0.177464\pi$
$811$	−3.04653	−	6.67097i	−0.106978	−	0.234250i	−0.955549	+	0.294832i	$0.904736\pi$
$812$	16.8253	−	7.50645i	0.590452	−	0.263425i
$813$	12.0592	+	3.04661i	0.422936	+	0.106849i
$814$	46.4353	+	21.4525i	1.62756	+	0.751911i
$815$	7.11739	−	8.21390i	0.249311	−	0.287720i
$816$	16.0150	−	0.330321i	0.560638	−	0.0115635i
$817$	−17.8667	−	11.4822i	−0.625076	−	0.401712i
$818$	−36.5094	+	31.3567i	−1.27652	+	1.09636i
$819$	−13.5247	−	24.4839i	−0.472592	−	0.855535i
$820$	−9.04458	−	1.38137i	−0.315850	−	0.0482397i
$821$	25.3502	+	29.2557i	0.884728	+	1.02103i	0.999618	+	0.0276523i	$0.00880314\pi$
$821$	25.3502	+	29.2557i	0.884728	+	1.02103i	−0.114890	+	0.993378i	$0.536651\pi$
$822$	−9.65479	−	1.05694i	−0.336750	−	0.0368651i
$823$	−6.54787	−	22.3000i	−0.228244	−	0.777329i	−0.991372	−	0.131081i	$-0.958155\pi$
$823$	−6.54787	−	22.3000i	−0.228244	−	0.777329i	0.763127	−	0.646248i	$-0.223663\pi$
$824$	−21.8528	−	25.8993i	−0.761279	−	0.902245i
$825$	−24.0695	−	14.2018i	−0.837991	−	0.494442i
$826$	−33.3834	+	15.0693i	−1.16156	+	0.524329i
$827$		−	37.7187i		−	1.31161i	−0.754931	−	0.655805i	$-0.772329\pi$
$827$		−	37.7187i		−	1.31161i	0.754931	−	0.655805i	$-0.227671\pi$
$828$	16.8198	+	23.3472i	0.584529	+	0.811373i
$829$		−	30.6131i		−	1.06324i	−0.846984	−	0.531618i	$-0.821584\pi$
$829$		−	30.6131i		−	1.06324i	0.846984	−	0.531618i	$-0.178416\pi$
$830$	1.52898	+	3.38717i	0.0530716	+	0.117570i
$831$	25.9907	+	15.3354i	0.901608	+	0.531979i
$832$	10.1866	+	38.3969i	0.353157	+	1.33117i
$833$	−2.26322	−	7.70783i	−0.0784161	−	0.267061i
$834$	−3.26906	+	29.8618i	−0.113198	+	1.03403i
$835$	5.80227	+	6.69618i	0.200796	+	0.231731i
$836$	27.7296	+	4.23512i	0.959047	+	0.146475i
$837$	−15.4417	+	1.77459i	−0.533744	+	0.0613387i
$838$	−13.1816	−	15.3477i	−0.455351	−	0.530177i
$839$	−37.1838	−	23.8965i	−1.28373	−	0.825000i	−0.292383	−	0.956301i	$-0.594448\pi$
$839$	−37.1838	−	23.8965i	−1.28373	−	0.825000i	−0.991343	+	0.131301i	$0.958085\pi$
$840$	5.77539	−	0.978319i	0.199270	−	0.0337552i
$841$	3.22842	−	3.72580i	0.111325	−	0.128476i
$842$	−14.0022	+	30.3085i	−0.482546	+	1.04450i
$843$	−14.9662	−	3.78103i	−0.515465	−	0.130226i
$844$	−5.41752	−	12.1431i	−0.186479	−	0.417981i
$845$	−3.08391	−	6.75281i	−0.106090	−	0.232304i
$846$	−22.1876	−	16.5921i	−0.762826	−	0.570448i
$847$	2.27695	+	1.03985i	0.0782369	+	0.0357296i
$848$	−7.72303	+	8.60360i	−0.265210	+	0.295449i
$849$	−21.1228	+	3.86421i	−0.724932	+	0.132619i
$850$	−2.20306	+	14.8604i	−0.0755645	+	0.509707i
$851$	41.9330	−	26.1021i	1.43745	−	0.894767i
$852$	−12.9190	−	10.5461i	−0.442598	−	0.361304i
$853$	−3.73389	−	5.81004i	−0.127846	−	0.198932i	0.771430	−	0.636315i	$-0.219542\pi$
$853$	−3.73389	−	5.81004i	−0.127846	−	0.198932i	−0.899276	+	0.437383i	$0.855906\pi$
$854$	6.25888	−	20.9755i	0.214174	−	0.717768i
$855$	7.13563	−	2.70119i	0.244033	−	0.0923787i
$856$	−8.64033	+	54.9591i	−0.295321	+	1.87846i
$857$	5.92312	−	2.70500i	0.202330	−	0.0924010i	−0.311673	−	0.950189i	$-0.600889\pi$
$857$	5.92312	−	2.70500i	0.202330	−	0.0924010i	0.514003	+	0.857788i	$0.328162\pi$
$858$	7.50279	+	42.0517i	0.256141	+	1.43562i
$859$	−3.13615	−	21.8124i	−0.107004	−	0.744230i	−0.970714	−	0.240240i	$-0.922774\pi$
$859$	−3.13615	−	21.8124i	−0.107004	−	0.744230i	0.863709	−	0.503990i	$-0.168135\pi$
$860$	5.66539	+	3.71144i	0.193188	+	0.126559i
$861$	−20.8662	+	10.5086i	−0.711120	+	0.358134i
$862$	20.5275	+	17.9451i	0.699168	+	0.611214i
$863$	45.8322	+	29.4546i	1.56015	+	1.00265i	0.982479	+	0.186374i	$0.0596737\pi$
$863$	45.8322	+	29.4546i	1.56015	+	1.00265i	0.577668	+	0.816272i	$0.303963\pi$
$864$	−14.6288	−	25.4951i	−0.497680	−	0.867361i
$865$	−3.68812	−	1.08293i	−0.125400	−	0.0368207i
$866$	0.0454882	−	10.3871i	0.00154575	−	0.352967i
$867$	6.42143	+	19.1374i	0.218083	+	0.649939i
$868$	1.50121	+	11.1324i	0.0509543	+	0.377860i
$869$	32.4473	−	9.52739i	1.10070	−	0.323195i
$870$	−6.29464	+	4.35238i	−0.213408	+	0.147560i
$871$	−74.1652	−	10.6633i	−2.51299	−	0.361313i
$872$	1.80577	+	13.8486i	0.0611510	+	0.468973i
$873$	11.6095	+	11.4967i	0.392922	+	0.389106i
$874$	18.1200	−	20.1340i	0.612917	−	0.681042i
$875$			11.4720i			0.387825i
$876$	11.9629	+	1.36266i	0.404188	+	0.0460399i
$877$	24.2771	+	3.49052i	0.819780	+	0.117867i	0.539429	−	0.842031i	$-0.318640\pi$
$877$	24.2771	+	3.49052i	0.819780	+	0.117867i	0.280351	+	0.959898i	$0.409549\pi$
$878$	−3.16786	−	2.05552i	−0.106910	−	0.0693704i
$879$	−1.87812	−	0.197285i	−0.0633475	−	0.00665425i
$880$	−8.83079	−	1.42798i	−0.297686	−	0.0481371i
$881$	20.7432	−	17.9741i	0.698855	−	0.605561i	−0.231233	−	0.972898i	$-0.574276\pi$
$881$	20.7432	−	17.9741i	0.698855	−	0.605561i	0.930088	+	0.367337i	$0.119731\pi$
$882$	−10.4183	+	10.4287i	−0.350801	+	0.351152i
$883$	−27.3216	−	8.02234i	−0.919445	−	0.269973i	−0.212434	−	0.977176i	$-0.568139\pi$
$883$	−27.3216	−	8.02234i	−0.919445	−	0.269973i	−0.707011	+	0.707202i	$0.749957\pi$
$884$	19.4247	−	12.2444i	0.653322	−	0.411824i
$885$	12.4759	−	8.70735i	0.419372	−	0.292694i
$886$	0.374030	−	0.427853i	0.0125658	−	0.0143740i
$887$	−8.34777	+	9.63384i	−0.280291	+	0.323473i	−0.878386	−	0.477952i	$-0.841379\pi$
$887$	−8.34777	+	9.63384i	−0.280291	+	0.323473i	0.598095	+	0.801425i	$0.295925\pi$
$888$	−45.3577	+	22.1008i	−1.52211	+	0.741656i
$889$	3.41795	+	23.7724i	0.114634	+	0.797300i
$890$	−1.76455	+	1.12312i	−0.0591478	+	0.0376470i
$891$	−13.4099	−	28.6210i	−0.449248	−	0.958839i
$892$	−0.267670	+	30.5602i	−0.00896226	+	1.02323i
$893$	−10.8341	+	23.7234i	−0.362550	+	0.793873i
$894$	−26.0585	+	32.2086i	−0.871527	+	1.07722i
$895$	6.42192	+	9.99271i	0.214661	+	0.334019i
$896$	−18.2144	+	10.9317i	−0.608499	+	0.365202i
$897$	37.9161	+	16.2402i	1.26598	+	0.542246i
$898$	−7.21237	+	48.6498i	−0.240680	+	1.62346i
$899$	−7.93433	−	12.3461i	−0.264625	−	0.411764i
$900$	25.8659	−	9.53338i	0.862198	−	0.317779i
$901$	6.07879	+	2.77609i	0.202514	+	0.0924850i
$902$	35.3375	−	4.92291i	1.17661	−	0.163915i
$903$	17.2818	−	0.659445i	0.575102	−	0.0219450i
$904$	27.6631	−	7.72936i	0.920063	−	0.257075i
$905$	1.04112	−	0.149690i	0.0346079	−	0.00497587i
$906$	−1.48768	+	1.37971i	−0.0494250	+	0.0458377i
$907$	37.5054	−	43.2835i	1.24535	−	1.43721i	0.388647	−	0.921387i	$-0.372942\pi$
$907$	37.5054	−	43.2835i	1.24535	−	1.43721i	0.856698	−	0.515818i	$-0.172512\pi$
$908$	−25.1422	+	21.4032i	−0.834372	+	0.710289i
$909$	2.89588	+	13.0062i	0.0960501	+	0.431389i
$910$	6.36983	−	5.47084i	0.211158	−	0.181356i
$911$	21.1694	+	6.21591i	0.701375	+	0.205942i	0.612928	−	0.790139i	$-0.289992\pi$
$911$	21.1694	+	6.21591i	0.701375	+	0.205942i	0.0884467	+	0.996081i	$0.471810\pi$
$912$	−20.5332	+	18.5471i	−0.679923	+	0.614157i
$913$	−9.49011	−	10.9522i	−0.314077	−	0.362464i
$914$	−11.3034	−	39.1290i	−0.373884	−	1.29427i
$915$	−0.949868	+	9.04260i	−0.0314017	+	0.298939i
$916$	−41.5896	−	36.6802i	−1.37416	−	1.21195i
$917$	0.660200	−	4.59179i	0.0218017	−	0.151634i
$918$	−11.5408	+	12.4690i	−0.380902	+	0.411537i
$919$			40.3168i			1.32993i	0.746875	+	0.664964i	$0.231553\pi$
$919$			40.3168i			1.32993i	−0.746875	+	0.664964i	$0.768447\pi$
$920$	−5.83447	+	6.36987i	−0.192357	+	0.210008i
$921$	−4.50181	−	1.85185i	−0.148340	−	0.0610207i
$922$	54.2773	−	24.5009i	1.78753	−	0.806894i
$923$	−23.6624	−	3.40214i	−0.778858	−	0.111983i
$924$	−20.4903	+	10.0953i	−0.674081	+	0.332111i
$925$	−13.3314	−	45.4027i	−0.438335	−	1.49283i
$926$	24.6117	−	7.10972i	0.808790	−	0.233640i
$927$	35.8630	+	2.38913i	1.17789	+	0.0784692i
$928$	15.5121	−	23.0134i	0.509210	−	0.755452i
$929$	−14.3735	+	48.9515i	−0.471578	+	1.60605i	0.289358	+	0.957221i	$0.406558\pi$
$929$	−14.3735	+	48.9515i	−0.471578	+	1.60605i	−0.760936	+	0.648827i	$0.775260\pi$
$930$	−1.46494	−	4.43008i	−0.0480372	−	0.145268i
$931$	11.6735	+	7.50211i	0.382584	+	0.245872i
$932$	−30.0278	+	25.5623i	−0.983594	+	0.837319i
$933$	16.8184	−	8.47009i	0.550611	−	0.277298i
$934$	8.94601	−	19.3642i	0.292722	−	0.633615i
$935$	0.735858	+	5.11801i	0.0240651	+	0.167377i
$936$	−36.8129	−	20.4978i	−1.20327	−	0.669992i
$937$	−14.0341	−	30.7303i	−0.458473	−	1.00392i	−0.987833	−	0.155519i	$-0.950295\pi$
$937$	−14.0341	−	30.7303i	−0.458473	−	1.00392i	0.529360	−	0.848397i	$-0.322432\pi$
$938$	−5.52848	−	39.6843i	−0.180511	−	1.29574i
$939$	−8.39730	+	7.85650i	−0.274036	+	0.256387i
$940$	3.52113	−	7.53484i	0.114846	−	0.245759i
$941$	−30.9989	+	19.9218i	−1.01054	+	0.649432i	−0.937532	−	0.347899i	$-0.886895\pi$
$941$	−30.9989	+	19.9218i	−1.01054	+	0.649432i	−0.0730046	+	0.997332i	$0.523259\pi$
$942$	15.0537	−	25.2600i	0.490478	−	0.823014i
$943$	14.7625	−	31.1295i	0.480734	−	1.01372i
$944$	−30.6378	+	45.8857i	−0.997175	+	1.49345i
$945$	−3.50596	+	5.12928i	−0.114049	+	0.166855i
$946$	−25.3084	−	7.55175i	−0.822846	−	0.245529i
$947$	−14.9411	−	6.82339i	−0.485522	−	0.221730i	0.157587	−	0.987505i	$-0.449629\pi$
$947$	−14.9411	−	6.82339i	−0.485522	−	0.221730i	−0.643109	+	0.765775i	$0.722356\pi$
$948$	−12.9598	+	30.7368i	−0.420913	+	0.998286i
$949$	15.6995	−	7.16972i	0.509627	−	0.232739i
$950$	−13.9338	−	21.8916i	−0.452072	−	0.710258i
$951$	1.84167	−	7.28978i	0.0597203	−	0.236387i
$952$	9.17325	+	8.16211i	0.297307	+	0.264536i
$953$	−14.6296	−	12.6766i	−0.473898	−	0.410635i	0.384893	−	0.922961i	$-0.374238\pi$
$953$	−14.6296	−	12.6766i	−0.473898	−	0.410635i	−0.858791	+	0.512326i	$0.828784\pi$
$954$	−0.880939	−	12.2311i	−0.0285215	−	0.395996i
$955$	−2.94151	−	1.89040i	−0.0951852	−	0.0611718i
$956$	38.7973	−	24.4560i	1.25479	−	0.790964i
$957$	18.6685	−	23.2823i	0.603468	−	0.752609i
$958$	0.242095	−	55.2816i	0.00782173	−	1.78607i
$959$	−4.87544	−	5.62656i	−0.157436	−	0.181691i
$960$	6.59960	−	5.85710i	0.213001	−	0.189037i
$961$	−21.1587	+	6.21277i	−0.682540	+	0.200412i
$962$	−39.3685	+	60.6727i	−1.26929	+	1.95617i
$963$	−35.5928	−	47.0660i	−1.14696	−	1.51668i
$964$	5.53582	−	1.57293i	0.178297	−	0.0506607i
$965$	6.73741			0.216885
$966$	−2.71626	+	21.8893i	−0.0873942	+	0.704277i
$967$			2.33875i			0.0752091i	0.999293	+	0.0376045i	$0.0119727\pi$
$967$			2.33875i			0.0752091i	−0.999293	+	0.0376045i	$0.988027\pi$
$968$	3.73904	−	0.487546i	0.120177	−	0.0156703i
$969$	13.7745	+	8.12742i	0.442501	+	0.261090i
$970$	−2.66978	+	4.11452i	−0.0857214	+	0.132109i
$971$	−2.12050	−	7.22174i	−0.0680499	−	0.231757i	0.918445	−	0.395549i	$-0.129446\pi$
$971$	−2.12050	−	7.22174i	−0.0680499	−	0.231757i	−0.986495	+	0.163792i	$0.947627\pi$
$972$	30.2348	+	7.60626i	0.969783	+	0.243971i
$973$	−17.4027	+	15.0795i	−0.557903	+	0.483426i
$974$	−26.2725	−	0.115055i	−0.841827	−	0.00368662i
$975$	24.7199	−	30.8292i	0.791670	−	0.987324i
$976$	−8.73417	−	31.7959i	−0.279574	−	1.01776i
$977$	8.87146	−	13.8043i	0.283823	−	0.441637i	−0.669844	−	0.742502i	$-0.733639\pi$
$977$	8.87146	−	13.8043i	0.283823	−	0.441637i	0.953667	+	0.300865i	$0.0972753\pi$
$978$	−18.6406	−	37.4203i	−0.596060	−	1.19657i
$979$	5.34138	−	6.16428i	0.170711	−	0.197011i
$980$	−3.70158	−	2.42493i	−0.118243	−	0.0774617i
$981$	−11.9016	−	8.81914i	−0.379989	−	0.281574i
$982$	9.69060	−	6.16797i	0.309240	−	0.196828i
$983$	−11.3352	−	24.8207i	−0.361538	−	0.791657i	−0.999762	−	0.0218069i	$-0.993058\pi$
$983$	−11.3352	−	24.8207i	−0.361538	−	0.791657i	0.638224	−	0.769850i	$-0.279669\pi$
$984$	−18.2810	+	30.0731i	−0.582777	+	0.958697i
$985$	−4.16278	+	9.11521i	−0.132637	+	0.290435i
$986$	−15.3721	−	4.58686i	−0.489546	−	0.146075i
$987$	−3.82173	−	20.8906i	−0.121647	−	0.664955i
$988$	−11.5073	+	37.9574i	−0.366097	+	1.20758i
$989$	−19.5130	+	16.4215i	−0.620477	+	0.522173i
$990$	7.59279	−	5.68983i	0.241315	−	0.180835i
$991$	17.2203	+	26.7953i	0.547020	+	0.851180i	0.999169	−	0.0407628i	$-0.0129788\pi$
$991$	17.2203	+	26.7953i	0.547020	+	0.851180i	−0.452149	+	0.891942i	$0.649342\pi$
$992$	10.7985	+	13.0279i	0.342854	+	0.413637i
$993$	−41.9136	+	39.2143i	−1.33009	+	1.24443i
$994$	−1.76386	−	12.6613i	−0.0559463	−	0.401592i
$995$	−5.68746	+	2.59738i	−0.180305	+	0.0823424i
$996$	14.2886	−	0.419937i	0.452750	−	0.0133062i
$997$	−24.3768	+	3.50485i	−0.772021	+	0.111000i	−0.517057	−	0.855951i	$-0.672973\pi$
$997$	−24.3768	+	3.50485i	−0.772021	+	0.111000i	−0.254963	+	0.966951i	$0.582063\pi$
$998$	−17.7146	−	8.18393i	−0.560746	−	0.259058i
$999$	16.5283	−	50.9000i	0.522932	−	1.61040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.13	✓	920
3.2	odd	2	inner	552.2.x.a.35.80	yes	920
8.3	odd	2	inner	552.2.x.a.35.73	yes	920
23.2	even	11	inner	552.2.x.a.347.20	yes	920
24.11	even	2	inner	552.2.x.a.35.20	yes	920
69.2	odd	22	inner	552.2.x.a.347.73	yes	920
184.163	odd	22	inner	552.2.x.a.347.80	yes	920
552.347	even	22	inner	552.2.x.a.347.13	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.13	✓	920	1.1	even	1	trivial
552.2.x.a.35.20	yes	920	24.11	even	2	inner
552.2.x.a.35.73	yes	920	8.3	odd	2	inner
552.2.x.a.35.80	yes	920	3.2	odd	2	inner
552.2.x.a.347.13	yes	920	552.347	even	22	inner
552.2.x.a.347.20	yes	920	23.2	even	11	inner
552.2.x.a.347.73	yes	920	69.2	odd	22	inner
552.2.x.a.347.80	yes	920	184.163	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28897 + 0.581846i) q^{2} +(0.880176 - 1.49174i) q^{3} +(1.32291 - 1.49997i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(-0.266561 + 2.43494i) q^{6} +(-1.41902 + 1.22959i) q^{7} +(-0.832444 + 2.70315i) q^{8} +(-1.45058 - 2.62599i) q^{9} +O(q^{10})\)	\(q+(-1.28897 + 0.581846i) q^{2} +(0.880176 - 1.49174i) q^{3} +(1.32291 - 1.49997i) q^{4} +(-0.611012 + 0.179409i) q^{5} +(-0.266561 + 2.43494i) q^{6} +(-1.41902 + 1.22959i) q^{7} +(-0.832444 + 2.70315i) q^{8} +(-1.45058 - 2.62599i) q^{9} +(0.683190 - 0.586769i) q^{10} +(-1.89865 + 2.95436i) q^{11} +(-1.07317 - 3.29368i) q^{12} +(-3.75279 - 3.25181i) q^{13} +(1.11365 - 2.41056i) q^{14} +(-0.270166 + 1.06938i) q^{15} +(-0.499820 - 3.96865i) q^{16} +(-2.10313 + 0.960465i) q^{17} +(3.39768 + 2.54082i) q^{18} +(1.65907 - 3.63286i) q^{19} +(-0.539205 + 1.15384i) q^{20} +(0.585238 + 3.19907i) q^{21} +(0.728330 - 4.91282i) q^{22} +(-3.57878 - 3.19254i) q^{23} +(3.29970 + 3.62104i) q^{24} +(-3.86512 + 2.48396i) q^{25} +(6.72930 + 2.00795i) q^{26} +(-5.19406 - 0.147447i) q^{27} +(-0.0328903 + 3.75512i) q^{28} +(-2.03808 - 4.46277i) q^{29} +(-0.273979 - 1.53560i) q^{30} +(2.96087 - 0.425709i) q^{31} +(2.95340 + 4.82467i) q^{32} +(2.73599 + 5.43266i) q^{33} +(2.15203 - 2.46171i) q^{34} +(0.646439 - 1.00588i) q^{35} +(-5.85789 - 1.29812i) q^{36} +(-2.90162 + 9.88202i) q^{37} +(-0.0247343 + 5.64799i) q^{38} +(-8.15397 + 2.73602i) q^{39} +(0.0236627 - 1.80101i) q^{40} +(2.02393 + 6.89286i) q^{41} +(-2.61572 - 3.78300i) q^{42} +(0.756804 - 5.26369i) q^{43} +(1.91971 + 6.75628i) q^{44} +(1.35745 + 1.34426i) q^{45} +(6.47053 + 2.03280i) q^{46} -6.53022 q^{47} +(-6.36012 - 2.74751i) q^{48} +(-0.494472 + 3.43913i) q^{49} +(3.53676 - 5.45067i) q^{50} +(-0.418357 + 3.98270i) q^{51} +(-9.84221 + 1.32722i) q^{52} +(-1.89278 - 2.18439i) q^{53} +(6.78080 - 2.83209i) q^{54} +(0.630059 - 2.14579i) q^{55} +(-2.14251 - 4.85940i) q^{56} +(-3.95901 - 5.67247i) q^{57} +(5.22368 + 4.56655i) q^{58} +(-10.4244 - 9.03283i) q^{59} +(1.24664 + 1.81994i) q^{60} +(8.15953 - 1.17316i) q^{61} +(-3.56879 + 2.27150i) q^{62} +(5.28729 + 1.94272i) q^{63} +(-6.61407 - 4.50045i) q^{64} +(2.87640 + 1.31361i) q^{65} +(-6.68760 - 5.41063i) q^{66} +(12.6939 - 8.15785i) q^{67} +(-1.34158 + 4.42523i) q^{68} +(-7.91240 + 2.52862i) q^{69} +(-0.247976 + 1.67268i) q^{70} +(4.04999 - 2.60277i) q^{71} +(8.30598 - 1.73515i) q^{72} +(-1.44386 + 3.16162i) q^{73} +(-2.00970 - 14.4260i) q^{74} +(0.303438 + 7.95208i) q^{75} +(-3.25438 - 7.29451i) q^{76} +(-0.938422 - 6.52687i) q^{77} +(8.91831 - 8.27101i) q^{78} +(-7.27743 - 6.30593i) q^{79} +(1.01741 + 2.33522i) q^{80} +(-4.79164 + 7.61841i) q^{81} +(-6.61938 - 7.70711i) q^{82} +(-1.16258 + 3.95938i) q^{83} +(5.57272 + 3.35424i) q^{84} +(1.11272 - 0.964175i) q^{85} +(2.08716 + 7.22511i) q^{86} +(-8.45116 - 0.887740i) q^{87} +(-6.40557 - 7.59169i) q^{88} +(-2.29892 - 0.330535i) q^{89} +(-2.53187 - 0.942895i) q^{90} +9.32367 q^{91} +(-9.52312 + 1.14463i) q^{92} +(1.97104 - 4.79155i) q^{93} +(8.41729 - 3.79958i) q^{94} +(-0.361944 + 2.51737i) q^{95} +(9.79667 - 0.159146i) q^{96} +(-5.22565 + 1.53439i) q^{97} +(-1.36368 - 4.72065i) q^{98} +(10.5123 + 0.700309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

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