LMFDB - Embedded newform 23.3.d.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	23.11
Dual form			23.3.d.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0163142 - 0.0104845i) q^{2} +(0.749667 - 5.21405i) q^{3} +(-1.66150 + 3.63819i) q^{4} +(1.45779 + 4.96477i) q^{5} +(-0.0424364 - 0.0929228i) q^{6} +(-1.27914 + 1.10838i) q^{7} +(0.0220779 + 0.153555i) q^{8} +(-17.9889 - 5.28201i) q^{9} +O(q^{10})$	\(q+(0.0163142 - 0.0104845i) q^{2} +(0.749667 - 5.21405i) q^{3} +(-1.66150 + 3.63819i) q^{4} +(1.45779 + 4.96477i) q^{5} +(-0.0424364 - 0.0929228i) q^{6} +(-1.27914 + 1.10838i) q^{7} +(0.0220779 + 0.153555i) q^{8} +(-17.9889 - 5.28201i) q^{9} +(0.0758357 + 0.0657120i) q^{10} +(5.67789 - 8.83496i) q^{11} +(17.7241 + 11.3906i) q^{12} +(-8.57997 + 9.90181i) q^{13} +(-0.00924733 + 0.0314935i) q^{14} +(26.9794 - 3.87906i) q^{15} +(-10.4748 - 12.0886i) q^{16} +(14.9751 - 6.83892i) q^{17} +(-0.348853 + 0.102432i) q^{18} +(-20.8497 - 9.52176i) q^{19} +(-20.4849 - 2.94528i) q^{20} +(4.82024 + 7.50043i) q^{21} -0.203665i q^{22} +(18.9449 + 13.0419i) q^{23} +0.817196 q^{24} +(-1.49247 + 0.959149i) q^{25} +(-0.0361597 + 0.251496i) q^{26} +(-21.3320 + 46.7105i) q^{27} +(-1.90720 - 6.49534i) q^{28} +(-5.54470 - 12.1412i) q^{29} +(0.399477 - 0.346149i) q^{30} +(1.70643 + 11.8685i) q^{31} +(-0.893031 - 0.262218i) q^{32} +(-41.8094 - 36.2281i) q^{33} +(0.172604 - 0.268578i) q^{34} +(-7.36759 - 4.73486i) q^{35} +(49.1056 - 56.6708i) q^{36} +(-5.02408 + 17.1105i) q^{37} +(-0.439977 + 0.0632592i) q^{38} +(45.1964 + 52.1594i) q^{39} +(-0.730182 + 0.333463i) q^{40} +(4.27614 - 1.25559i) q^{41} +(0.157276 + 0.0718257i) q^{42} +(60.5696 + 8.70859i) q^{43} +(22.7094 + 35.3365i) q^{44} -97.0108i q^{45} +(0.445808 + 0.0141405i) q^{46} -29.1440 q^{47} +(-70.8831 + 45.5538i) q^{48} +(-6.56573 + 45.6657i) q^{49} +(-0.0142922 + 0.0312955i) q^{50} +(-24.4321 - 83.2080i) q^{51} +(-21.7690 - 47.6674i) q^{52} +(19.2669 - 16.6948i) q^{53} +(0.141722 + 0.985697i) q^{54} +(52.1407 + 15.3099i) q^{55} +(-0.198439 - 0.171948i) q^{56} +(-65.2773 + 101.573i) q^{57} +(-0.217751 - 0.139940i) q^{58} +(-11.7572 + 13.5685i) q^{59} +(-30.7137 + 104.601i) q^{60} +(7.59459 - 1.09194i) q^{61} +(0.152274 + 0.175734i) q^{62} +(28.8649 - 13.1821i) q^{63} +(61.3729 - 18.0207i) q^{64} +(-61.6680 - 28.1628i) q^{65} +(-1.06192 - 0.152681i) q^{66} +(-50.8527 - 79.1283i) q^{67} +65.8452i q^{68} +(82.2035 - 89.0025i) q^{69} -0.169839 q^{70} +(-30.4382 + 19.5614i) q^{71} +(0.413924 - 2.87890i) q^{72} +(-3.42254 + 7.49432i) q^{73} +(0.0974305 + 0.331818i) q^{74} +(3.88220 + 8.50083i) q^{75} +(69.2839 - 60.0348i) q^{76} +(2.52970 + 17.5945i) q^{77} +(1.28421 + 0.377077i) q^{78} +(-27.2023 - 23.5709i) q^{79} +(44.7470 - 69.6277i) q^{80} +(85.6101 + 55.0183i) q^{81} +(0.0565974 - 0.0653169i) q^{82} +(4.74991 - 16.1767i) q^{83} +(-35.2968 + 5.07492i) q^{84} +(55.7842 + 64.3784i) q^{85} +(1.07945 - 0.492967i) q^{86} +(-67.4615 + 19.8085i) q^{87} +(1.48201 + 0.676812i) q^{88} +(-13.2028 - 1.89828i) q^{89} +(-1.01711 - 1.58265i) q^{90} -22.1757i q^{91} +(-78.9259 + 47.2559i) q^{92} +63.1622 q^{93} +(-0.475461 + 0.305560i) q^{94} +(16.8788 - 117.395i) q^{95} +(-2.03669 + 4.45974i) q^{96} +(27.0901 + 92.2604i) q^{97} +(0.371667 + 0.813836i) q^{98} +(-148.805 + 128.941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	0.0163142	−	0.0104845i	0.00815709	−	0.00524224i	−0.536556	−	0.843865i	$-0.680275\pi$
$2$	0.0163142	−	0.0104845i	0.00815709	−	0.00524224i	0.544713	+	0.838623i	$0.316639\pi$
$3$	0.749667	−	5.21405i	0.249889	−	1.73802i	−0.348944	−	0.937143i	$-0.613460\pi$
$3$	0.749667	−	5.21405i	0.249889	−	1.73802i	0.598833	−	0.800874i	$-0.295631\pi$
$4$	−1.66150	+	3.63819i	−0.415376	+	0.909546i
$5$	1.45779	+	4.96477i	0.291558	+	0.992954i	0.966837	+	0.255393i	$0.0822047\pi$
$5$	1.45779	+	4.96477i	0.291558	+	0.992954i	−0.675280	+	0.737562i	$0.735977\pi$
$6$	−0.0424364	−	0.0929228i	−0.00707274	−	0.0154871i
$7$	−1.27914	+	1.10838i	−0.182735	+	0.158341i	−0.741425	−	0.671036i	$-0.765850\pi$
$7$	−1.27914	+	1.10838i	−0.182735	+	0.158341i	0.558690	+	0.829377i	$0.311304\pi$
$8$	0.0220779	+	0.153555i	0.00275974	+	0.0191944i
$9$	−17.9889	−	5.28201i	−1.99877	−	0.586891i
$10$	0.0758357	+	0.0657120i	0.00758357	+	0.00657120i
$11$	5.67789	−	8.83496i	0.516172	−	0.803179i	−0.481126	−	0.876652i	$-0.659772\pi$
$11$	5.67789	−	8.83496i	0.516172	−	0.803179i	0.997297	+	0.0734731i	$0.0234083\pi$
$12$	17.7241	+	11.3906i	1.47701	+	0.949216i
$13$	−8.57997	+	9.90181i	−0.659997	+	0.761678i	−0.982777	−	0.184797i	$-0.940837\pi$
$13$	−8.57997	+	9.90181i	−0.659997	+	0.761678i	0.322779	+	0.946474i	$0.395383\pi$
$14$	−0.00924733	+	0.0314935i	−0.000660523	+	0.00224954i
$15$	26.9794	−	3.87906i	1.79863	−	0.258604i
$16$	−10.4748	−	12.0886i	−0.654676	−	0.755536i
$17$	14.9751	−	6.83892i	0.880890	−	0.402289i	0.0769751	−	0.997033i	$-0.475474\pi$
$17$	14.9751	−	6.83892i	0.880890	−	0.402289i	0.803915	+	0.594744i	$0.202747\pi$
$18$	−0.348853	+	0.102432i	−0.0193807	+	0.00569069i
$19$	−20.8497	−	9.52176i	−1.09736	−	0.501145i	−0.217342	−	0.976095i	$-0.569739\pi$
$19$	−20.8497	−	9.52176i	−1.09736	−	0.501145i	−0.880013	+	0.474950i	$0.842466\pi$
$20$	−20.4849	−	2.94528i	−1.02424	−	0.147264i
$21$	4.82024	+	7.50043i	0.229535	+	0.357164i
$22$		−	0.203665i		−	0.00925749i
$23$	18.9449	+	13.0419i	0.823691	+	0.567039i
$23$	18.9449	+	13.0419i	0.823691	+	0.567039i
$24$	0.817196			0.0340498
$25$	−1.49247	+	0.959149i	−0.0596986	+	0.0383660i
$26$	−0.0361597	+	0.251496i	−0.00139076	+	0.00967293i
$27$	−21.3320	+	46.7105i	−0.790073	+	1.73002i
$28$	−1.90720	−	6.49534i	−0.0681145	−	0.231977i
$29$	−5.54470	−	12.1412i	−0.191197	−	0.418662i	0.789620	−	0.613597i	$-0.210278\pi$
$29$	−5.54470	−	12.1412i	−0.191197	−	0.418662i	−0.980816	+	0.194934i	$0.937551\pi$
$30$	0.399477	−	0.346149i	0.0133159	−	0.0115383i
$31$	1.70643	+	11.8685i	0.0550462	+	0.382855i	0.998658	+	0.0517993i	$0.0164956\pi$
$31$	1.70643	+	11.8685i	0.0550462	+	0.382855i	−0.943611	+	0.331055i	$0.892595\pi$
$32$	−0.893031	−	0.262218i	−0.0279072	−	0.00819430i
$33$	−41.8094	−	36.2281i	−1.26695	−	1.09782i
$34$	0.172604	−	0.268578i	0.00507660	−	0.00789935i
$35$	−7.36759	−	4.73486i	−0.210503	−	0.135282i
$36$	49.1056	−	56.6708i	1.36404	−	1.57419i
$37$	−5.02408	+	17.1105i	−0.135786	+	0.462445i	−0.999109	−	0.0422072i	$-0.986561\pi$
$37$	−5.02408	+	17.1105i	−0.135786	+	0.462445i	0.863323	+	0.504652i	$0.168379\pi$
$38$	−0.439977	+	0.0632592i	−0.0115783	+	0.00166471i
$39$	45.1964	+	52.1594i	1.15888	+	1.33742i
$40$	−0.730182	+	0.333463i	−0.0182545	+	0.00833657i
$41$	4.27614	−	1.25559i	0.104296	−	0.0306241i	−0.229168	−	0.973387i	$-0.573601\pi$
$41$	4.27614	−	1.25559i	0.104296	−	0.0306241i	0.333464	+	0.942763i	$0.391782\pi$
$42$	0.157276	+	0.0718257i	0.00374467	+	0.00171014i
$43$	60.5696	+	8.70859i	1.40859	+	0.202525i	0.804294	−	0.594231i	$-0.202544\pi$
$43$	60.5696	+	8.70859i	1.40859	+	0.202525i	0.604300	+	0.796757i	$0.293453\pi$
$44$	22.7094	+	35.3365i	0.516123	+	0.803103i
$45$		−	97.0108i		−	2.15580i
$46$	0.445808	+	0.0141405i	0.00969147	+	0.000307402i
$47$	−29.1440			−0.620086			−0.310043	−	0.950723i	$-0.600343\pi$
$47$	−29.1440			−0.620086			−0.310043	+	0.950723i	$0.600343\pi$
$48$	−70.8831	+	45.5538i	−1.47673	+	0.949038i
$49$	−6.56573	+	45.6657i	−0.133995	+	0.931953i
$50$	−0.0142922	+	0.0312955i	−0.000285843	+	0.000625909i
$51$	−24.4321	−	83.2080i	−0.479060	−	1.63153i
$52$	−21.7690	−	47.6674i	−0.418634	−	0.916681i
$53$	19.2669	−	16.6948i	0.363526	−	0.314997i	−0.453876	−	0.891065i	$-0.649959\pi$
$53$	19.2669	−	16.6948i	0.363526	−	0.314997i	0.817402	+	0.576068i	$0.195414\pi$
$54$	0.141722	+	0.985697i	0.00262448	+	0.0182537i
$55$	52.1407	+	15.3099i	0.948013	+	0.278362i
$56$	−0.198439	−	0.171948i	−0.00354355	−	0.00307050i
$57$	−65.2773	+	101.573i	−1.14522	+	1.78199i
$58$	−0.217751	−	0.139940i	−0.00375434	−	0.00241277i
$59$	−11.7572	+	13.5685i	−0.199275	+	0.229975i	−0.846588	−	0.532249i	$-0.821347\pi$
$59$	−11.7572	+	13.5685i	−0.199275	+	0.229975i	0.647313	+	0.762224i	$0.275893\pi$
$60$	−30.7137	+	104.601i	−0.511895	+	1.74335i
$61$	7.59459	−	1.09194i	0.124502	−	0.0179006i	−0.0797823	−	0.996812i	$-0.525423\pi$
$61$	7.59459	−	1.09194i	0.124502	−	0.0179006i	0.204284	+	0.978912i	$0.434513\pi$
$62$	0.152274	+	0.175734i	0.00245603	+	0.00283441i
$63$	28.8649	−	13.1821i	0.458172	−	0.209240i
$64$	61.3729	−	18.0207i	0.958952	−	0.281574i
$65$	−61.6680	−	28.1628i	−0.948738	−	0.433274i
$66$	−1.06192	−	0.152681i	−0.0160897	−	0.00231335i
$67$	−50.8527	−	79.1283i	−0.758995	−	1.18102i	−0.978669	−	0.205446i	$-0.934136\pi$
$67$	−50.8527	−	79.1283i	−0.758995	−	1.18102i	0.219674	−	0.975573i	$-0.429501\pi$
$68$			65.8452i			0.968312i
$69$	82.2035	−	89.0025i	1.19136	−	1.28989i
$70$	−0.169839			−0.00242627
$71$	−30.4382	+	19.5614i	−0.428707	+	0.275513i	−0.737149	−	0.675730i	$-0.763829\pi$
$71$	−30.4382	+	19.5614i	−0.428707	+	0.275513i	0.308442	+	0.951243i	$0.400192\pi$
$72$	0.413924	−	2.87890i	0.00574894	−	0.0399848i
$73$	−3.42254	+	7.49432i	−0.0468842	+	0.102662i	−0.931625	−	0.363422i	$-0.881608\pi$
$73$	−3.42254	+	7.49432i	−0.0468842	+	0.102662i	0.884740	+	0.466084i	$0.154336\pi$
$74$	0.0974305	+	0.331818i	0.00131663	+	0.00448403i
$75$	3.88220	+	8.50083i	0.0517627	+	0.113344i
$76$	69.2839	−	60.0348i	0.911630	−	0.789932i
$77$	2.52970	+	17.5945i	0.0328533	+	0.228499i
$78$	1.28421	+	0.377077i	0.0164642	+	0.00483432i
$79$	−27.2023	−	23.5709i	−0.344333	−	0.298366i	0.465475	−	0.885061i	$-0.345883\pi$
$79$	−27.2023	−	23.5709i	−0.344333	−	0.298366i	−0.809808	+	0.586695i	$0.800429\pi$
$80$	44.7470	−	69.6277i	0.559337	−	0.870346i
$81$	85.6101	+	55.0183i	1.05691	+	0.679238i
$82$	0.0565974	−	0.0653169i	0.000690213	−	0.000796548i
$83$	4.74991	−	16.1767i	0.0572279	−	0.194900i	−0.925917	−	0.377726i	$-0.876706\pi$
$83$	4.74991	−	16.1767i	0.0572279	−	0.194900i	0.983145	+	0.182826i	$0.0585244\pi$
$84$	−35.2968	+	5.07492i	−0.420200	+	0.0604157i
$85$	55.7842	+	64.3784i	0.656285	+	0.757393i
$86$	1.07945	−	0.492967i	0.0125517	−	0.00573218i
$87$	−67.4615	+	19.8085i	−0.775420	+	0.227684i
$88$	1.48201	+	0.676812i	0.0168410	+	0.00769104i
$89$	−13.2028	−	1.89828i	−0.148346	−	0.0213290i	0.0677415	−	0.997703i	$-0.478421\pi$
$89$	−13.2028	−	1.89828i	−0.148346	−	0.0213290i	−0.216088	+	0.976374i	$0.569330\pi$
$90$	−1.01711	−	1.58265i	−0.0113012	−	0.0175850i
$91$		−	22.1757i		−	0.243689i
$92$	−78.9259	+	47.2559i	−0.857890	+	0.513651i
$93$	63.1622			0.679163
$94$	−0.475461	+	0.305560i	−0.00505810	+	0.00325064i
$95$	16.8788	−	117.395i	0.177672	−	1.23574i
$96$	−2.03669	+	4.45974i	−0.0212156	+	0.0464556i
$97$	27.0901	+	92.2604i	0.279279	+	0.951138i	0.972983	+	0.230878i	$0.0741597\pi$
$97$	27.0901	+	92.2604i	0.279279	+	0.951138i	−0.693703	+	0.720261i	$0.744022\pi$
$98$	0.371667	+	0.813836i	0.00379252	+	0.00830445i
$99$	−148.805	+	128.941i	−1.50308	+	1.30243i
$100$	−1.00983	−	7.02350i	−0.0100983	−	0.0702350i
$101$	−165.134	−	48.4879i	−1.63499	−	0.480078i	−0.670003	−	0.742358i	$-0.733707\pi$
$101$	−165.134	−	48.4879i	−1.63499	−	0.480078i	−0.964992	+	0.262281i	$0.915525\pi$
$102$	−1.27098	−	1.10131i	−0.0124606	−	0.0107972i
$103$	31.3940	−	48.8500i	0.304796	−	0.474271i	−0.654742	−	0.755853i	$-0.727223\pi$
$103$	31.3940	−	48.8500i	0.304796	−	0.474271i	0.959537	+	0.281581i	$0.0908589\pi$
$104$	−1.70990	−	1.09889i	−0.0164414	−	0.0105662i
$105$	−30.2111	+	34.8654i	−0.287724	+	0.332052i
$106$	0.139286	−	0.474366i	0.00131402	−	0.00447515i
$107$	175.136	−	25.1808i	1.63679	−	0.235335i	0.738345	−	0.674423i	$-0.235607\pi$
$107$	175.136	−	25.1808i	1.63679	−	0.235335i	0.898444	+	0.439088i	$0.144698\pi$
$108$	−134.498	−	155.219i	−1.24535	−	1.43722i
$109$	−132.720	+	60.6111i	−1.21761	+	0.556066i	−0.917461	−	0.397826i	$-0.869765\pi$
$109$	−132.720	+	60.6111i	−1.21761	+	0.556066i	−0.300153	+	0.953891i	$0.597038\pi$
$110$	1.01115	−	0.296900i	0.00919227	−	0.00269909i
$111$	85.4484	+	39.0230i	0.769806	+	0.351558i
$112$	26.7976	+	3.85291i	0.239264	+	0.0344010i
$113$	79.4208	+	123.581i	0.702839	+	1.09364i	0.990713	+	0.135970i	$0.0434152\pi$
$113$	79.4208	+	123.581i	0.702839	+	1.09364i	−0.287874	+	0.957668i	$0.592948\pi$
$114$			2.34149i			0.0205394i
$115$	−37.1324	+	113.069i	−0.322891	+	0.983212i
$116$	53.3845			0.460211
$117$	206.646	−	132.803i	1.76620	−	1.13507i
$118$	−0.0495500	+	0.344628i	−0.000419915	+	0.00292057i
$119$	−11.5752	+	25.3461i	−0.0972705	+	0.212993i
$120$	1.19130	+	4.05719i	0.00992749	+	0.0338099i
$121$	4.44702	+	9.73762i	0.0367522	+	0.0804762i
$122$	0.112451	−	0.0974394i	0.000921730	−	0.000798684i
$123$	−3.34101	−	23.2373i	−0.0271627	−	0.188921i
$124$	−46.0150	−	13.5112i	−0.371089	−	0.108962i
$125$	90.8255	+	78.7008i	0.726604	+	0.629606i
$126$	0.332698	−	0.517689i	0.00264046	−	0.00410864i
$127$	−121.911	−	78.3472i	−0.959927	−	0.616907i	−0.0359490	−	0.999354i	$-0.511445\pi$
$127$	−121.911	−	78.3472i	−0.959927	−	0.616907i	−0.923978	+	0.382446i	$0.875082\pi$
$128$	3.25031	−	3.75106i	0.0253931	−	0.0293052i
$129$	90.8141	−	309.284i	0.703985	−	2.39755i
$130$	−1.30133	+	0.187104i	−0.0100103	+	0.00143926i
$131$	−56.0694	−	64.7075i	−0.428010	−	0.493950i	0.500250	−	0.865881i	$-0.333241\pi$
$131$	−56.0694	−	64.7075i	−0.428010	−	0.493950i	−0.928261	+	0.371931i	$0.878696\pi$
$132$	201.271	−	91.9174i	1.52478	−	0.696344i
$133$	37.2236	−	10.9298i	0.279876	−	0.0821791i
$134$	−1.65924	−	0.757749i	−0.0123824	−	0.00565484i
$135$	−263.004	−	37.8143i	−1.94818	−	0.280106i
$136$	1.38077	+	2.14852i	0.0101527	+	0.0157980i
$137$			171.087i			1.24881i	0.781100	+	0.624406i	$0.214659\pi$
$137$			171.087i			1.24881i	−0.781100	+	0.624406i	$0.785341\pi$
$138$	0.407937	−	2.31386i	0.00295606	−	0.0167671i
$139$	−142.681			−1.02648			−0.513241	−	0.858244i	$-0.671555\pi$
$139$	−142.681			−1.02648			−0.513241	+	0.858244i	$0.671555\pi$
$140$	29.4676	−	18.9377i	0.210483	−	0.135269i
$141$	−21.8483	+	151.959i	−0.154953	+	1.07772i
$142$	−0.291482	+	0.638257i	−0.00205269	+	0.00449477i
$143$	38.7660	+	132.025i	0.271091	+	0.923252i
$144$	124.578	+	272.788i	0.865127	+	1.89436i
$145$	52.1953	−	45.2275i	0.359968	−	0.311914i
$146$	0.0227381	+	0.158147i	0.000155741	+	0.00108320i
$147$	233.181	+	68.4682i	1.58627	+	0.465770i
$148$	−53.9035	−	46.7076i	−0.364213	−	0.315592i
$149$	154.810	−	240.889i	1.03899	−	1.61671i	0.286533	−	0.958070i	$-0.407497\pi$
$149$	154.810	−	240.889i	1.03899	−	1.61671i	0.752461	−	0.658636i	$-0.228866\pi$
$150$	0.152462	+	0.0979812i	0.00101641	+	0.000653208i
$151$	−88.7318	+	102.402i	−0.587628	+	0.678159i	−0.969227	−	0.246169i	$-0.920828\pi$
$151$	−88.7318	+	102.402i	−0.587628	+	0.678159i	0.381599	+	0.924328i	$0.375374\pi$
$152$	1.00180	−	3.41181i	0.00659077	−	0.0224461i
$153$	−305.509	+	43.9256i	−1.99679	+	0.287095i
$154$	0.225739	+	0.260516i	0.00146584	+	0.00169166i
$155$	−56.4367	+	25.7738i	−0.364108	+	0.166283i
$156$	−264.860	+	77.7698i	−1.69782	+	0.498525i
$157$	−51.8358	−	23.6726i	−0.330164	−	0.150781i	0.243434	−	0.969917i	$-0.421726\pi$
$157$	−51.8358	−	23.6726i	−0.330164	−	0.150781i	−0.573599	+	0.819136i	$0.694453\pi$
$158$	−0.690912	−	0.0993381i	−0.00437286	−	0.000628722i
$159$	−72.6040	−	112.974i	−0.456629	−	0.710528i
$160$		−	4.81595i		−	0.0300997i
$161$	−38.6886	+	4.31575i	−0.240302	+	0.0268059i
$162$	1.97350			0.0121821
$163$	25.7489	−	16.5478i	0.157969	−	0.101520i	−0.459268	−	0.888298i	$-0.651888\pi$
$163$	25.7489	−	16.5478i	0.157969	−	0.101520i	0.617237	+	0.786777i	$0.288252\pi$
$164$	−2.53676	+	17.6435i	−0.0154680	+	0.107583i
$165$	118.915	−	260.387i	0.720696	−	1.57810i
$166$	−0.0921136	−	0.313710i	−0.000554901	−	0.00188982i
$167$	−91.2986	−	199.916i	−0.546698	−	1.19710i	−0.958307	−	0.285741i	$-0.907760\pi$
$167$	−91.2986	−	199.916i	−0.546698	−	1.19710i	0.411609	−	0.911361i	$-0.364967\pi$
$168$	−1.04531	+	0.905766i	−0.00622208	+	0.00539147i
$169$	−0.378787	−	2.63452i	−0.00224135	−	0.0155889i
$170$	1.58505	+	0.465412i	0.00932381	+	0.00273772i
$171$	324.770	+	281.415i	1.89924	+	1.64570i
$172$	−132.320	+	205.894i	−0.769303	+	1.19706i
$173$	−96.1879	−	61.8162i	−0.555999	−	0.357319i	0.232268	−	0.972652i	$-0.425385\pi$
$173$	−96.1879	−	61.8162i	−0.555999	−	0.357319i	−0.788267	+	0.615333i	$0.789022\pi$
$174$	−0.892897	+	1.03046i	−0.00513159	+	0.00592218i
$175$	0.845971	−	2.88111i	0.00483412	−	0.0164635i
$176$	−166.277	+	23.9070i	−0.944756	+	0.135835i
$177$	61.9331	+	71.4746i	0.349904	+	0.403811i
$178$	−0.235296	+	0.107456i	−0.00132189	+	0.000603685i
$179$	250.885	−	73.6666i	1.40159	−	0.411545i	0.508363	−	0.861143i	$-0.330251\pi$
$179$	250.885	−	73.6666i	1.40159	−	0.411545i	0.893231	+	0.449598i	$0.148433\pi$
$180$	352.943	+	161.184i	1.96080	+	0.895465i
$181$	218.993	+	31.4864i	1.20990	+	0.173958i	0.717594	−	0.696461i	$-0.245243\pi$
$181$	218.993	+	31.4864i	1.20990	+	0.173958i	0.492311	+	0.870420i	$0.336152\pi$
$182$	−0.232501	−	0.361779i	−0.00127748	−	0.00198779i
$183$		−	40.4172i		−	0.220859i
$184$	−1.58439	+	3.19702i	−0.00861081	+	0.0173751i
$185$	−92.2736			−0.498776
$186$	1.03044	−	0.662223i	0.00553999	−	0.00356034i
$187$	24.6056	−	171.135i	0.131580	−	0.915162i
$188$	48.4229	−	106.031i	0.257569	−	0.563997i
$189$	−24.4865	−	83.3934i	−0.129558	−	0.441235i
$190$	−0.955461	−	2.09217i	−0.00502874	−	0.0110114i
$191$	31.6730	−	27.4448i	0.165827	−	0.143690i	−0.567994	−	0.823033i	$-0.692280\pi$
$191$	31.6730	−	27.4448i	0.165827	−	0.143690i	0.733821	+	0.679342i	$0.237735\pi$
$192$	−47.9516	−	333.511i	−0.249748	−	1.73704i
$193$	106.253	+	31.1987i	0.550534	+	0.161651i	0.545157	−	0.838334i	$-0.316470\pi$
$193$	106.253	+	31.1987i	0.550534	+	0.161651i	0.00537736	+	0.999986i	$0.498288\pi$
$194$	1.40926	+	1.22113i	0.00726420	+	0.00629447i
$195$	−193.073	+	300.427i	−0.990117	+	1.54065i
$196$	−155.231	−	99.7611i	−0.791996	−	0.508985i
$197$	108.275	−	124.956i	0.549621	−	0.634297i	−0.411174	−	0.911557i	$-0.634881\pi$
$197$	108.275	−	124.956i	0.549621	−	0.634297i	0.960795	+	0.277260i	$0.0894265\pi$
$198$	−1.07576	+	3.66370i	−0.00543313	+	0.0185036i
$199$	−45.9417	+	6.60541i	−0.230863	+	0.0331930i	−0.256775	−	0.966471i	$-0.582660\pi$
$199$	−45.9417	+	6.60541i	−0.230863	+	0.0331930i	0.0259125	+	0.999664i	$0.491751\pi$
$200$	−0.180233	−	0.208000i	−0.000901164	−	0.00104000i
$201$	−450.701	+	205.828i	−2.24230	+	1.02402i
$202$	−3.20240	+	0.940310i	−0.0158535	+	0.00465500i
$203$	20.5496	+	9.38468i	0.101229	+	0.0462299i
$204$	343.320	+	49.3620i	1.68294	+	0.241971i
$205$	12.4674	+	19.3997i	0.0608166	+	0.0946325i
$206$		−	1.12610i		−	0.00546649i
$207$	−271.910	−	334.677i	−1.31357	−	1.61679i
$208$	209.572			1.00756
$209$	−202.507	+	130.143i	−0.968933	+	0.622695i
$210$	−0.127323	+	0.885548i	−0.000606298	+	0.00421689i
$211$	111.570	−	244.305i	0.528768	−	1.15784i	−0.437243	−	0.899343i	$-0.644045\pi$
$211$	111.570	−	244.305i	0.528768	−	1.15784i	0.966012	−	0.258498i	$-0.0832276\pi$
$212$	28.7269	+	97.8350i	0.135504	+	0.461486i
$213$	79.1758	+	173.371i	0.371718	+	0.813948i
$214$	2.59320	−	2.24702i	0.0121178	−	0.0105001i
$215$	45.0615	+	313.409i	0.209588	+	1.45772i
$216$	−7.64360	−	2.24436i	−0.0353871	−	0.0103906i
$217$	−15.3376	−	13.2901i	−0.0706802	−	0.0612448i
$218$	−1.52974	+	2.38032i	−0.00701715	+	0.0109189i
$219$	36.5100	+	23.4636i	0.166712	+	0.107140i
$220$	−142.332	+	164.260i	−0.646965	+	0.746637i
$221$	−60.7685	+	206.959i	−0.274971	+	0.936464i
$222$	1.80316	−	0.259255i	0.00812232	−	0.00116781i
$223$	130.495	+	150.599i	0.585177	+	0.675331i	0.968710	−	0.248197i	$-0.0798380\pi$
$223$	130.495	+	150.599i	0.585177	+	0.675331i	−0.383532	+	0.923527i	$0.625293\pi$
$224$	1.43295	−	0.654407i	0.00639711	−	0.00292146i
$225$	31.9140	−	9.37081i	0.141840	−	0.0416480i
$226$	2.59137	+	1.18344i	0.0114662	+	0.00523645i
$227$	−284.867	−	40.9577i	−1.25492	−	0.180430i	−0.517393	−	0.855748i	$-0.673097\pi$
$227$	−284.867	−	40.9577i	−1.25492	−	0.180430i	−0.737527	+	0.675318i	$0.764007\pi$
$228$	−261.085	−	406.256i	−1.14511	−	1.78182i
$229$			170.183i			0.743158i	0.928401	+	0.371579i	$0.121183\pi$
$229$			170.183i			0.743158i	−0.928401	+	0.371579i	$0.878817\pi$
$230$	0.579689	+	2.23395i	0.00252039	+	0.00971281i
$231$	93.6348			0.405346
$232$	1.74193	−	1.11947i	0.00750832	−	0.00482530i
$233$	−7.86543	+	54.7052i	−0.0337572	+	0.234786i	−0.999714	−	0.0239172i	$-0.992386\pi$
$233$	−7.86543	+	54.7052i	−0.0337572	+	0.234786i	0.965957	+	0.258704i	$0.0832953\pi$
$234$	1.97888	−	4.33314i	0.00845675	−	0.0185177i
$235$	−42.4858	−	144.694i	−0.180791	−	0.615717i
$236$	−29.8302	−	65.3191i	−0.126399	−	0.276776i
$237$	−143.293	+	124.164i	−0.604610	+	0.523898i
$238$	0.0769014	+	0.534861i	0.000323115	+	0.00224732i
$239$	363.665	+	106.782i	1.52161	+	0.446786i	0.932471	−	0.361244i	$-0.117648\pi$
$239$	363.665	+	106.782i	1.52161	+	0.446786i	0.589141	+	0.808030i	$0.299466\pi$
$240$	−329.497	−	285.511i	−1.37290	−	1.18963i
$241$	186.341	−	289.953i	0.773200	−	1.20312i	−0.201474	−	0.979494i	$-0.564573\pi$
$241$	186.341	−	289.953i	0.773200	−	1.20312i	0.974674	−	0.223629i	$-0.0717906\pi$
$242$	0.174643	+	0.112236i	0.000721667	+	0.000463787i
$243$	48.3975	−	55.8537i	0.199167	−	0.229851i
$244$	−8.64577	+	29.4448i	−0.0354335	+	0.120675i
$245$	−236.291	+	33.9735i	−0.964454	+	0.138667i
$246$	−0.298137	−	0.344068i	−0.00121194	−	0.00139865i
$247$	273.173	−	124.754i	1.10596	−	0.505076i
$248$	−1.78479	+	0.524063i	−0.00719675	+	0.00211316i
$249$	−80.7854	−	36.8934i	−0.324439	−	0.148166i
$250$	2.30688	+	0.331679i	0.00922752	+	0.00132672i
$251$	87.0098	+	135.390i	0.346653	+	0.539402i	0.970176	−	0.242403i	$-0.0779356\pi$
$251$	87.0098	+	135.390i	0.346653	+	0.539402i	−0.623523	+	0.781805i	$0.714299\pi$
$252$			126.918i			0.503642i
$253$	222.792	−	93.3270i	0.880599	−	0.368881i
$254$	−2.81030			−0.0110642
$255$	377.492	−	242.599i	1.48036	−	0.951370i
$256$	−36.3983	+	253.156i	−0.142181	+	0.988891i
$257$	−22.1590	+	48.5215i	−0.0862219	+	0.188800i	−0.947831	−	0.318772i	$-0.896730\pi$
$257$	−22.1590	+	48.5215i	−0.0862219	+	0.188800i	0.861609	+	0.507572i	$0.169457\pi$
$258$	−1.76113	−	5.99786i	−0.00682608	−	0.0232475i
$259$	−12.5384	−	27.4553i	−0.0484109	−	0.106005i
$260$	204.923	−	177.567i	0.788166	−	0.682950i
$261$	35.6130	+	247.694i	0.136448	+	0.949019i
$262$	−1.59315	−	0.467791i	−0.00608072	−	0.00178546i
$263$	179.197	+	155.275i	0.681357	+	0.590399i	0.925229	−	0.379408i	$-0.123872\pi$
$263$	179.197	+	155.275i	0.681357	+	0.590399i	−0.243873	+	0.969807i	$0.578418\pi$
$264$	4.63995	−	7.21990i	0.0175756	−	0.0273481i
$265$	110.973	+	71.3181i	0.418766	+	0.269125i
$266$	0.492678	−	0.568581i	0.00185217	−	0.00213752i
$267$	−19.7955	+	67.4171i	−0.0741403	+	0.252499i
$268$	372.375	−	53.5395i	1.38946	−	0.199774i
$269$	−250.628	−	289.241i	−0.931704	−	1.07524i	−0.997002	−	0.0773784i	$-0.975345\pi$
$269$	−250.628	−	289.241i	−0.931704	−	1.07524i	0.0652974	−	0.997866i	$-0.479200\pi$
$270$	−4.68716	+	2.14055i	−0.0173599	+	0.00792798i
$271$	−289.981	+	85.1461i	−1.07004	+	0.314192i	−0.768888	−	0.639384i	$-0.779189\pi$
$271$	−289.981	+	85.1461i	−1.07004	+	0.314192i	−0.301152	+	0.953576i	$0.597371\pi$
$272$	−239.535	−	109.392i	−0.880642	−	0.402176i
$273$	−115.625	−	16.6244i	−0.423536	−	0.0608953i
$274$	1.79376	+	2.79115i	0.00654658	+	0.0101867i
$275$			18.6318i			0.0677521i
$276$	187.226	+	446.950i	0.678356	+	1.61938i
$277$	38.6348			0.139476			0.0697379	−	0.997565i	$-0.477784\pi$
$277$	38.6348			0.139476			0.0697379	+	0.997565i	$0.477784\pi$
$278$	−2.32772	+	1.49594i	−0.00837311	+	0.00538107i
$279$	31.9927	−	222.514i	0.114669	−	0.797543i
$280$	0.564402	−	1.23587i	0.00201572	−	0.00441381i
$281$	−134.428	−	457.820i	−0.478392	−	1.62925i	−0.746158	−	0.665769i	$-0.768104\pi$
$281$	−134.428	−	457.820i	−0.478392	−	1.62925i	0.267766	−	0.963484i	$-0.413715\pi$
$282$	1.23677	+	2.70815i	0.00438571	+	0.00960336i
$283$	−221.537	+	191.963i	−0.782816	+	0.678314i	−0.951600	−	0.307339i	$-0.900561\pi$
$283$	−221.537	+	191.963i	−0.782816	+	0.678314i	0.168784	+	0.985653i	$0.446016\pi$
$284$	−20.5950	−	143.241i	−0.0725175	−	0.504371i
$285$	−599.450	−	176.014i	−2.10333	−	0.617594i
$286$	2.01665	+	1.74744i	0.00705122	+	0.00610992i
$287$	−4.07812	+	6.34567i	−0.0142095	+	0.0221104i
$288$	14.6796	+	9.43401i	0.0509709	+	0.0327570i
$289$	−11.7708	+	13.5843i	−0.0407295	+	0.0470044i
$290$	0.377336	−	1.28509i	0.00130116	−	0.00443134i
$291$	501.359	−	72.0846i	1.72288	−	0.247713i
$292$	−21.5792	−	24.9037i	−0.0739013	−	0.0852866i
$293$	−103.221	+	47.1393i	−0.352289	+	0.160885i	−0.583696	−	0.811972i	$-0.698394\pi$
$293$	−103.221	+	47.1393i	−0.352289	+	0.160885i	0.231408	+	0.972857i	$0.425667\pi$
$294$	4.52201	−	1.32778i	0.0153810	−	0.00451627i
$295$	−84.5042	−	38.5918i	−0.286455	−	0.130820i
$296$	−2.73832	−	0.393711i	−0.00925109	−	0.00133011i
$297$	291.565	+	453.684i	0.981700	+	1.52756i
$298$		−	5.55301i		−	0.0186343i
$299$	−291.685	+	75.6896i	−0.975535	+	0.253142i
$300$	−37.3779			−0.124593
$301$	−87.1296	+	55.9948i	−0.289467	+	0.186029i
$302$	−0.373955	+	2.60091i	−0.00123826	+	0.00861229i
$303$	−376.614	+	824.670i	−1.24295	+	2.72168i
$304$	103.293	+	351.783i	0.339779	+	1.15718i
$305$	16.4925	+	36.1136i	0.0540739	+	0.118405i
$306$	−4.52359	+	3.91972i	−0.0147830	+	0.0128095i
$307$	−42.5750	−	296.116i	−0.138681	−	0.964546i	−0.933724	−	0.357993i	$-0.883461\pi$
$307$	−42.5750	−	296.116i	−0.138681	−	0.964546i	0.795043	−	0.606553i	$-0.207448\pi$
$308$	−68.2150	−	20.0297i	−0.221477	−	0.0650316i
$309$	−231.171	−	200.311i	−0.748127	−	0.648255i
$310$	−0.650494	+	1.01219i	−0.00209837	+	0.00326512i
$311$	230.835	+	148.349i	0.742235	+	0.477006i	0.856307	−	0.516467i	$-0.172753\pi$
$311$	230.835	+	148.349i	0.742235	+	0.477006i	−0.114072	+	0.993472i	$0.536389\pi$
$312$	−7.01151	+	8.09172i	−0.0224728	+	0.0259350i
$313$	142.990	−	486.979i	0.456837	−	1.55584i	−0.333243	−	0.942841i	$-0.608143\pi$
$313$	142.990	−	486.979i	0.456837	−	1.55584i	0.790080	−	0.613003i	$-0.210039\pi$
$314$	−1.09385	+	0.157272i	−0.00348361	+	0.000500868i
$315$	107.525	+	124.091i	0.341350	+	0.393939i
$316$	130.952	−	59.8038i	0.414405	−	0.189253i
$317$	522.346	−	153.374i	1.64778	−	0.483831i	0.679493	−	0.733682i	$-0.262200\pi$
$317$	522.346	−	153.374i	1.64778	−	0.483831i	0.968284	+	0.249851i	$0.0803815\pi$
$318$	−2.36895	−	1.08186i	−0.00744952	−	0.00340208i
$319$	−138.749	−	19.9491i	−0.434951	−	0.0625365i
$320$	178.937	+	278.432i	0.559179	+	0.870100i
$321$		−	932.048i		−	2.90358i
$322$	−0.585925	+	0.476038i	−0.00181964	+	0.00147838i
$323$	−377.346			−1.16825
$324$	−342.408	+	220.052i	−1.05682	+	0.679174i
$325$	3.30799	−	23.0076i	0.0101784	−	0.0707925i
$326$	0.246577	−	0.539927i	0.000756370	−	0.00165622i
$327$	216.534	+	737.446i	0.662183	+	2.25519i
$328$	0.287210	+	0.628902i	0.000875640	+	0.00191738i
$329$	37.2794	−	32.3028i	0.113311	−	0.0981847i
$330$	−0.790027	−	5.49476i	−0.00239402	−	0.0166508i
$331$	−511.794	−	150.276i	−1.54620	−	0.454007i	−0.606241	−	0.795281i	$-0.707323\pi$
$331$	−511.794	−	150.276i	−1.54620	−	0.454007i	−0.939964	+	0.341275i	$0.889141\pi$
$332$	50.9619	+	44.1587i	0.153500	+	0.133008i
$333$	180.755	−	281.261i	0.542809	−	0.844627i
$334$	−3.58548	−	2.30425i	−0.0107350	−	0.00689894i
$335$	318.721	−	367.824i	0.951407	−	1.09798i
$336$	40.1785	−	136.836i	0.119579	−	0.407249i
$337$	63.6355	−	9.14941i	0.188829	−	0.0271496i	−0.0472512	−	0.998883i	$-0.515046\pi$
$337$	63.6355	−	9.14941i	0.188829	−	0.0271496i	0.236081	+	0.971733i	$0.424137\pi$
$338$	−0.0338012	−	0.0390087i	−0.000100004	−	0.000115410i
$339$	703.898	−	321.459i	2.07639	−	0.948257i
$340$	−326.906	+	95.9884i	−0.961489	+	0.282319i
$341$	114.547	+	52.3117i	0.335914	+	0.153407i
$342$	8.24884	+	1.18600i	0.0241194	+	0.00346785i
$343$	−87.0546	−	135.460i	−0.253803	−	0.394926i
$344$			9.49304i			0.0275961i
$345$	561.712	+	278.375i	1.62815	+	0.806883i
$346$	−2.21734			−0.00640849
$347$	−85.9476	+	55.2352i	−0.247688	+	0.159179i	−0.658594	−	0.752498i	$-0.728849\pi$
$347$	−85.9476	+	55.2352i	−0.247688	+	0.159179i	0.410907	+	0.911677i	$0.365212\pi$
$348$	40.0206	−	278.350i	0.115002	−	0.799855i
$349$	−180.657	+	395.584i	−0.517642	+	1.13348i	0.452683	+	0.891672i	$0.350467\pi$
$349$	−180.657	+	395.584i	−0.517642	+	1.13348i	−0.970325	+	0.241806i	$0.922260\pi$
$350$	−0.0164057	−	0.0558725i	−4.68733e−5	−	0.000159636i
$351$	−279.491	−	611.999i	−0.796270	−	1.74359i
$352$	−7.38722	+	6.40106i	−0.0209864	+	0.0181848i
$353$	54.3124	+	377.751i	0.153859	+	1.07012i	0.909672	+	0.415328i	$0.136333\pi$
$353$	54.3124	+	377.751i	0.153859	+	1.07012i	−0.755812	+	0.654788i	$0.772758\pi$
$354$	1.75976	+	0.516712i	0.00497108	+	0.00145964i
$355$	−141.491	−	122.602i	−0.398565	−	0.345358i
$356$	28.8428	−	44.8803i	0.0810192	−	0.126068i
$357$	123.479	+	79.3548i	0.345878	+	0.222282i
$358$	3.32063	−	3.83221i	0.00927550	−	0.0107045i
$359$	−139.521	+	475.167i	−0.388639	+	1.32358i	0.500417	+	0.865785i	$0.333180\pi$
$359$	−139.521	+	475.167i	−0.388639	+	1.32358i	−0.889056	+	0.457799i	$0.848638\pi$
$360$	14.8965	−	2.14179i	0.0413792	−	0.00594943i
$361$	107.643	+	124.227i	0.298181	+	0.344119i
$362$	3.90280	−	1.78235i	0.0107812	−	0.00492362i
$363$	54.1062	−	15.8870i	0.149053	−	0.0437659i
$364$	80.6794	+	36.8450i	0.221647	+	0.101223i
$365$	−42.1969	−	6.06701i	−0.115608	−	0.0166219i
$366$	−0.423753	−	0.659373i	−0.00115780	−	0.00180157i
$367$			216.687i			0.590427i	0.955431	+	0.295213i	$0.0953908\pi$
$367$			216.687i			0.590427i	−0.955431	+	0.295213i	$0.904609\pi$
$368$	−40.7861	−	365.628i	−0.110832	−	0.993555i
$369$	−83.5550			−0.226436
$370$	−1.50537	+	0.967440i	−0.00406856	+	0.00261470i
$371$	−6.14079	+	42.7102i	−0.0165520	+	0.115122i
$372$	−104.944	+	229.796i	−0.282108	+	0.617731i
$373$	−83.4102	−	284.069i	−0.223620	−	0.761580i	−0.992506	−	0.122194i	$-0.961007\pi$
$373$	−83.4102	−	284.069i	−0.223620	−	0.761580i	0.768886	−	0.639386i	$-0.220811\pi$
$374$	−1.39285	−	3.04991i	−0.00372419	−	0.00815484i
$375$	478.439	−	414.570i	1.27584	−	1.10552i
$376$	−0.643440	−	4.47522i	−0.00171128	−	0.0119022i
$377$	167.793	+	49.2685i	0.445075	+	0.130686i
$378$	−1.27381	−	1.10377i	−0.00336988	−	0.00292001i
$379$	−325.242	+	506.087i	−0.858159	+	1.33532i	0.0827182	+	0.996573i	$0.473640\pi$
$379$	−325.242	+	506.087i	−0.858159	+	1.33532i	−0.940877	+	0.338748i	$0.889997\pi$
$380$	399.060	+	256.460i	1.05016	+	0.674896i
$381$	−499.899	+	576.914i	−1.31207	+	1.51421i
$382$	0.228974	−	0.779815i	0.000599409	−	0.00204140i
$383$	−98.3196	+	14.1362i	−0.256709	+	0.0369092i	−0.269468	−	0.963009i	$-0.586848\pi$
$383$	−98.3196	+	14.1362i	−0.256709	+	0.0369092i	0.0127587	+	0.999919i	$0.495939\pi$
$384$	−17.1216	−	19.7593i	−0.0445874	−	0.0514566i
$385$	−83.6647	+	38.2084i	−0.217311	+	0.0992425i
$386$	2.06053	−	0.605027i	0.00533817	−	0.00156743i
$387$	−1043.58	−	476.587i	−2.69659	−	1.23149i
$388$	−380.671	−	54.7322i	−0.981110	−	0.141062i
$389$	−165.821	−	258.023i	−0.426275	−	0.663297i	0.559984	−	0.828504i	$-0.310807\pi$
$389$	−165.821	−	258.023i	−0.426275	−	0.663297i	−0.986259	+	0.165206i	$0.947171\pi$
$390$			6.92549i			0.0177577i
$391$	372.895	+	65.7418i	0.953695	+	0.168138i
$392$	−7.15716			−0.0182581
$393$	−379.421	+	243.839i	−0.965449	+	0.620456i
$394$	0.456320	−	3.17377i	0.00115817	−	0.00805526i
$395$	77.3690	−	169.415i	0.195871	−	0.428898i
$396$	−221.869	−	755.617i	−0.560275	−	1.90812i
$397$	182.439	+	399.487i	0.459545	+	1.00626i	0.987591	+	0.157048i	$0.0501977\pi$
$397$	182.439	+	399.487i	0.459545	+	1.00626i	−0.528046	+	0.849216i	$0.677075\pi$
$398$	−0.680246	+	0.589436i	−0.00170916	+	0.00148100i
$399$	−29.0834	−	202.279i	−0.0728907	−	0.506966i
$400$	27.2281	+	7.99488i	0.0680701	+	0.0199872i
$401$	198.848	+	172.303i	0.495881	+	0.429684i	0.866557	−	0.499079i	$-0.166328\pi$
$401$	198.848	+	172.303i	0.495881	+	0.429684i	−0.370675	+	0.928763i	$0.620874\pi$
$402$	−5.19482	+	8.08329i	−0.0129224	+	0.0201077i
$403$	−132.161	−	84.9345i	−0.327942	−	0.210756i
$404$	450.779	−	520.227i	1.11579	−	1.28769i
$405$	−148.352	+	505.239i	−0.366300	+	1.24750i
$406$	0.433643	−	0.0623484i	0.00106809	−	0.000153568i
$407$	122.644	+	141.539i	0.301337	+	0.347761i
$408$	12.2376	−	5.58873i	0.0299942	−	0.0136979i
$409$	−286.555	+	84.1402i	−0.700624	+	0.205722i	−0.612596	−	0.790396i	$-0.709875\pi$
$409$	−286.555	+	84.1402i	−0.700624	+	0.205722i	−0.0880279	+	0.996118i	$0.528056\pi$
$410$	0.406791	+	0.185775i	0.000992172	+	0.000453110i
$411$	892.058	+	128.259i	2.17046	+	0.312065i
$412$	125.564	+	195.381i	0.304767	+	0.474227i
$413$		−	30.3876i		−	0.0735777i
$414$	−7.94490	−	2.60914i	−0.0191906	−	0.00630226i
$415$	87.2381			0.210212
$416$	10.2586	−	6.59281i	0.0246601	−	0.0158481i
$417$	−106.963	+	743.946i	−0.256507	+	1.78404i
$418$	−1.93925	+	4.24636i	−0.00463935	+	0.0101588i
$419$	−153.881	−	524.069i	−0.367257	−	1.25076i	−0.911314	−	0.411713i	$-0.864931\pi$
$419$	−153.881	−	524.069i	−0.367257	−	1.25076i	0.544057	−	0.839048i	$-0.316888\pi$
$420$	−76.6511	−	167.842i	−0.182503	−	0.399625i
$421$	−3.11956	+	2.70311i	−0.00740988	+	0.00642070i	−0.658558	−	0.752530i	$-0.728833\pi$
$421$	−3.11956	+	2.70311i	−0.00740988	+	0.00642070i	0.651148	+	0.758951i	$0.274288\pi$
$422$	−0.741232	−	5.15538i	−0.00175647	−	0.0122165i
$423$	524.269	+	153.939i	1.23941	+	0.363923i
$424$	2.98895	+	2.58994i	0.00704941	+	0.00610835i
$425$	−15.7903	+	24.5702i	−0.0371537	+	0.0578123i
$426$	3.10939	+	1.99828i	0.00729904	+	0.00469081i
$427$	−8.50428	+	9.81447i	−0.0199164	+	0.0229847i
$428$	−199.377	+	679.017i	−0.465835	+	1.58649i
$429$	717.447	−	103.153i	1.67237	−	0.240451i
$430$	4.02108	+	4.64057i	0.00935134	+	0.0107920i
$431$	−351.142	+	160.361i	−0.814715	+	0.372068i	−0.778788	−	0.627287i	$-0.784165\pi$
$431$	−351.142	+	160.361i	−0.814715	+	0.372068i	−0.0359262	+	0.999354i	$0.511438\pi$
$432$	788.112	−	231.411i	1.82433	−	0.535673i
$433$	325.906	+	148.836i	0.752671	+	0.343733i	0.754530	−	0.656265i	$-0.227865\pi$
$433$	325.906	+	148.836i	0.752671	+	0.343733i	−0.00185982	+	0.999998i	$0.500592\pi$
$434$	−0.389560	−	0.0560103i	−0.000897605	−	0.000129056i
$435$	−196.689	−	306.055i	−0.452159	−	0.703574i
$436$		−	583.565i		−	1.33845i
$437$	−270.814	−	452.309i	−0.619712	−	1.03503i
$438$	0.841634			0.00192154
$439$	33.7815	−	21.7100i	0.0769510	−	0.0494534i	−0.501600	−	0.865100i	$-0.667255\pi$
$439$	33.7815	−	21.7100i	0.0769510	−	0.0494534i	0.578551	+	0.815647i	$0.303619\pi$
$440$	−1.19976	+	8.34449i	−0.00272672	+	0.0189648i
$441$	359.317	−	786.795i	0.814778	−	1.78412i
$442$	1.17847	+	4.01348i	0.00266621	+	0.00908028i
$443$	−117.483	−	257.251i	−0.265198	−	0.580702i	0.729449	−	0.684035i	$-0.239777\pi$
$443$	−117.483	−	257.251i	−0.265198	−	0.580702i	−0.994647	+	0.103333i	$0.967049\pi$
$444$	−283.946	+	246.040i	−0.639517	+	0.554145i
$445$	−9.82240	−	68.3163i	−0.0220728	−	0.153520i
$446$	3.70786	+	1.08873i	0.00831359	+	0.00244109i
$447$	−1139.95	−	987.775i	−2.55023	−	2.20979i
$448$	−58.5309	+	91.0758i	−0.130649	+	0.203294i
$449$	−57.9118	−	37.2176i	−0.128979	−	0.0828901i	0.474560	−	0.880223i	$-0.342607\pi$
$449$	−57.9118	−	37.2176i	−0.128979	−	0.0828901i	−0.603540	+	0.797333i	$0.706243\pi$
$450$	0.422403	−	0.487479i	0.000938673	−	0.00108329i
$451$	13.1864	−	44.9086i	0.0292380	−	0.0995756i
$452$	−581.569	+	83.6170i	−1.28666	+	0.184993i
$453$	467.410	+	539.420i	1.03181	+	1.19077i
$454$	−5.07679	+	2.31849i	−0.0111823	+	0.00510681i
$455$	110.097	−	32.3275i	0.241972	−	0.0710495i
$456$	−17.0383	−	7.78114i	−0.0373647	−	0.0170639i
$457$	507.639	+	72.9875i	1.11081	+	0.159710i	0.673203	−	0.739457i	$-0.264918\pi$
$457$	507.639	+	72.9875i	1.11081	+	0.159710i	0.437605	+	0.899167i	$0.355827\pi$
$458$	1.78428	+	2.77640i	0.00389581	+	0.00606200i
$459$			845.383i			1.84179i
$460$	−349.672	−	322.960i	−0.760156	−	0.702087i
$461$	727.834			1.57882			0.789408	−	0.613869i	$-0.210388\pi$
$461$	727.834			1.57882			0.789408	+	0.613869i	$0.210388\pi$
$462$	1.52757	−	0.981713i	0.00330644	−	0.00212492i
$463$	62.2753	−	433.134i	0.134504	−	0.935495i	−0.805078	−	0.593170i	$-0.797876\pi$
$463$	62.2753	−	433.134i	0.134504	−	0.935495i	0.939581	−	0.342325i	$-0.111215\pi$
$464$	−88.6902	+	194.204i	−0.191143	+	0.418544i
$465$	92.0771	+	313.586i	0.198015	+	0.674378i
$466$	0.445238	+	0.974936i	0.000955447	+	0.00209214i
$467$	−478.320	+	414.467i	−1.02424	+	0.887510i	−0.993706	−	0.112024i	$-0.964267\pi$
$467$	−478.320	+	414.467i	−1.02424	+	0.887510i	−0.0305354	+	0.999534i	$0.509721\pi$
$468$	139.820	+	972.468i	0.298760	+	2.07792i
$469$	152.752	+	44.8521i	0.325698	+	0.0956335i
$470$	−2.21016	−	1.91511i	−0.00470246	−	0.00407471i
$471$	−162.290	+	252.528i	−0.344565	+	0.536153i
$472$	−2.34309	−	1.50582i	−0.00496418	−	0.00319029i
$473$	420.847	−	485.684i	0.889741	−	1.02682i
$474$	−1.03591	+	3.52798i	−0.00218546	+	0.00744299i
$475$	40.2503	−	5.78712i	0.0847375	−	0.0121834i
$476$	−72.9817	−	84.2254i	−0.153323	−	0.176944i
$477$	−434.772	+	198.554i	−0.911472	+	0.416255i
$478$	7.05245	−	2.07079i	0.0147541	−	0.00433219i
$479$	650.202	+	296.937i	1.35741	+	0.619911i	0.955289	−	0.295674i	$-0.0955442\pi$
$479$	650.202	+	296.937i	1.35741	+	0.619911i	0.402126	+	0.915584i	$0.368271\pi$
$480$	−25.1106	−	3.61036i	−0.0523138	−	0.00752159i
$481$	−126.318	−	196.555i	−0.262615	−	0.408638i
$482$		−	6.68403i		−	0.0138673i
$483$	−6.50109	+	204.960i	−0.0134598	+	0.424348i
$484$	−42.8160			−0.0884628
$485$	−418.560	+	268.992i	−0.863011	+	0.554623i
$486$	0.203968	−	1.41863i	0.000419687	−	0.00291899i
$487$	−69.3463	+	151.847i	−0.142395	+	0.311801i	−0.967370	−	0.253368i	$-0.918462\pi$
$487$	−69.3463	+	151.847i	−0.142395	+	0.311801i	0.824975	+	0.565169i	$0.191189\pi$
$488$	0.335345	+	1.14208i	0.000687183	+	0.00234033i
$489$	−66.9780	−	146.661i	−0.136969	−	0.299921i
$490$	−3.49870	+	3.03164i	−0.00714020	+	0.00618702i
$491$	1.98457	+	13.8030i	0.00404190	+	0.0281121i	0.991743	−	0.128244i	$-0.0409342\pi$
$491$	1.98457	+	13.8030i	0.00404190	+	0.0281121i	−0.987701	+	0.156357i	$0.950025\pi$
$492$	90.0926	+	26.4536i	0.183115	+	0.0537674i
$493$	−166.065	−	143.896i	−0.336847	−	0.291879i
$494$	3.14861	−	4.89933i	0.00637370	−	0.00991767i
$495$	−857.087	−	550.816i	−1.73149	−	1.11276i
$496$	125.599	−	144.949i	0.253223	−	0.292235i
$497$	17.2532	−	58.7591i	0.0347147	−	0.118228i
$498$	−1.70476	+	0.245107i	−0.00342320	+	0.000492182i
$499$	−49.9814	−	57.6816i	−0.100163	−	0.115594i	0.703455	−	0.710740i	$-0.251640\pi$
$499$	−49.9814	−	57.6816i	−0.100163	−	0.115594i	−0.803618	+	0.595146i	$0.797094\pi$
$500$	−437.235	+	199.679i	−0.874470	+	0.399357i
$501$	−1110.82	+	326.165i	−2.21720	+	0.651028i
$502$	2.83899	+	1.29652i	0.00565535	+	0.00258271i
$503$	−452.217	−	65.0189i	−0.899039	−	0.129262i	−0.322727	−	0.946492i	$-0.604600\pi$
$503$	−452.217	−	65.0189i	−0.899039	−	0.129262i	−0.576312	+	0.817230i	$0.695509\pi$
$504$	2.66146	+	4.14132i	0.00528068	+	0.00821690i
$505$		−	890.540i		−	1.76345i
$506$	2.65618	−	3.85841i	0.00524936	−	0.00762531i
$507$	−14.0205			−0.0276539
$508$	487.597	−	313.360i	0.959837	−	0.616849i
$509$	49.8255	−	346.544i	0.0978890	−	0.680833i	−0.880498	−	0.474050i	$-0.842792\pi$
$509$	49.8255	−	346.544i	0.0978890	−	0.680833i	0.978387	−	0.206783i	$-0.0662994\pi$
$510$	3.61494	−	7.91562i	0.00708812	−	0.0155208i
$511$	−3.92866	−	13.3798i	−0.00768819	−	0.0261836i
$512$	10.3078	+	22.5710i	0.0201325	+	0.0440840i
$513$	889.532	−	770.784i	1.73398	−	1.50250i
$514$	0.147217	+	1.02391i	0.000286414	+	0.00199205i
$515$	288.295	+	84.6509i	0.559795	+	0.164371i
$516$	974.346	+	844.276i	1.88827	+	1.63619i
$517$	−165.477	+	257.487i	−0.320071	+	0.498040i
$518$	−0.492409	−	0.316452i	−0.000950597	−	0.000610911i
$519$	−394.422	+	455.187i	−0.759965	+	0.877046i
$520$	2.96305	−	10.0912i	0.00569817	−	0.0194062i
$521$	−466.725	+	67.1049i	−0.895825	+	0.128800i	−0.574822	−	0.818278i	$-0.694929\pi$
$521$	−466.725	+	67.1049i	−0.895825	+	0.128800i	−0.321002	+	0.947078i	$0.604020\pi$
$522$	3.17794	+	3.66754i	0.00608801	+	0.00702594i
$523$	263.703	−	120.429i	0.504211	−	0.230266i	−0.147036	−	0.989131i	$-0.546973\pi$
$523$	263.703	−	120.429i	0.504211	−	0.230266i	0.651247	+	0.758865i	$0.274246\pi$
$524$	328.577	−	96.4790i	0.627056	−	0.184120i
$525$	−14.3881	−	6.57081i	−0.0274059	−	0.0125158i
$526$	4.55142	+	0.654396i	0.00865290	+	0.00124410i
$527$	106.722	+	166.062i	0.202508	+	0.315108i
$528$			884.899i			1.67595i
$529$	188.818	+	494.155i	0.356933	+	0.934130i
$530$	2.55817			0.00482673
$531$	283.168	−	181.981i	0.533274	−	0.342714i
$532$	−22.0824	+	153.586i	−0.0415082	+	0.288696i
$533$	−24.2565	+	53.1144i	−0.0455094	+	0.0996517i
$534$	0.383887	+	1.30740i	0.000718890	+	0.00244831i
$535$	380.329	+	832.804i	0.710895	+	1.55664i
$536$	11.0278	−	9.55568i	0.0205743	−	0.0178278i
$537$	−196.021	−	1363.35i	−0.365029	−	2.53883i
$538$	−7.12134	−	2.09101i	−0.0132367	−	0.00388664i
$539$	366.175	+	317.293i	0.679360	+	0.588669i
$540$	574.558	−	894.030i	1.06400	−	1.65561i
$541$	821.244	+	527.782i	1.51801	+	0.975567i	0.992158	+	0.124992i	$0.0398905\pi$
$541$	821.244	+	527.782i	1.51801	+	0.975567i	0.525854	+	0.850575i	$0.323746\pi$
$542$	−3.83809	+	4.42939i	−0.00708134	+	0.00817230i
$543$	328.343	−	1118.24i	0.604684	−	2.05937i
$544$	−15.1666	+	2.18062i	−0.0278797	+	0.00400849i
$545$	−494.398	−	570.566i	−0.907152	−	1.04691i
$546$	−2.06063	+	0.941058i	−0.00377405	+	0.00172355i
$547$	506.188	−	148.630i	0.925390	−	0.271719i	0.215884	−	0.976419i	$-0.430737\pi$
$547$	506.188	−	148.630i	0.925390	−	0.271719i	0.709505	+	0.704700i	$0.248918\pi$
$548$	−622.448	−	284.262i	−1.13585	−	0.518727i
$549$	−142.386	−	20.4720i	−0.259355	−	0.0372896i
$550$	0.195345	+	0.303963i	0.000355173	+	0.000552659i
$551$			305.936i			0.555238i
$552$	15.4817	+	10.6578i	0.0280465	+	0.0193076i
$553$	60.9212			0.110165
$554$	0.630295	−	0.405066i	0.00113772	−	0.000731166i
$555$	−69.1745	+	481.119i	−0.124639	+	0.866881i
$556$	237.065	−	519.100i	0.426376	−	0.933633i
$557$	58.5874	+	199.530i	0.105184	+	0.358223i	0.995219	−	0.0976687i	$-0.0311386\pi$
$557$	58.5874	+	199.530i	0.105184	+	0.358223i	−0.890035	+	0.455892i	$0.849320\pi$
$558$	−1.81101	−	3.96557i	−0.00324554	−	0.00710675i
$559$	−605.916	+	525.029i	−1.08393	+	0.939229i
$560$	19.9364	+	138.661i	0.0356007	+	0.247608i
$561$	−873.863	−	256.589i	−1.55769	−	0.457378i
$562$	−6.99309	−	6.05955i	−0.0124432	−	0.0107821i
$563$	77.3741	−	120.396i	0.137432	−	0.213848i	−0.765715	−	0.643180i	$-0.777615\pi$
$563$	77.3741	−	120.396i	0.137432	−	0.213848i	0.903147	+	0.429332i	$0.141251\pi$
$564$	−516.552	−	331.968i	−0.915873	−	0.588596i
$565$	−497.773	+	574.461i	−0.881015	+	1.01675i
$566$	−1.60156	+	5.45441i	−0.00282961	+	0.00963677i
$567$	−170.489	+	24.5126i	−0.300686	+	0.0432321i
$568$	−3.67577	−	4.24207i	−0.00647143	−	0.00746843i
$569$	932.058	−	425.657i	1.63806	−	0.748079i	0.638299	−	0.769788i	$-0.279638\pi$
$569$	932.058	−	425.657i	1.63806	−	0.748079i	0.999764	+	0.0217098i	$0.00691098\pi$
$570$	−11.6249	+	3.41339i	−0.0203946	+	0.00598841i
$571$	518.291	+	236.696i	0.907690	+	0.414528i	0.813861	−	0.581060i	$-0.197362\pi$
$571$	518.291	+	236.696i	0.907690	+	0.414528i	0.0938295	+	0.995588i	$0.470089\pi$
$572$	−544.742	−	78.3220i	−0.952345	−	0.136927i
$573$	−119.354	−	185.719i	−0.208298	−	0.324117i
$574$			0.146281i			0.000254846i
$575$	−40.7837	−	1.29361i	−0.0709282	−	0.00224976i
$576$	−1199.22			−2.08197
$577$	621.126	−	399.173i	1.07647	−	0.691808i	0.122734	−	0.992440i	$-0.460834\pi$
$577$	621.126	−	399.173i	1.07647	−	0.691808i	0.953740	+	0.300631i	$0.0971974\pi$
$578$	−0.0496074	+	0.345027i	−8.58260e−5	+	0.000596933i
$579$	242.326	−	530.620i	0.418525	−	0.916443i
$580$	77.8233	+	265.042i	0.134178	+	0.456969i
$581$	11.8542	+	25.9571i	0.0204031	+	0.0446765i
$582$	7.42349	−	6.43249i	0.0127551	−	0.0110524i
$583$	−38.1032	−	265.014i	−0.0653571	−	0.454569i
$584$	−1.22636	−	0.360090i	−0.00209992	−	0.000616593i
$585$	960.582	+	832.349i	1.64202	+	1.42282i
$586$	−1.18973	+	1.85125i	−0.00203025	+	0.00315914i
$587$	548.439	+	352.460i	0.934309	+	0.600444i	0.916776	−	0.399403i	$-0.130782\pi$
$587$	548.439	+	352.460i	0.934309	+	0.600444i	0.0175330	+	0.999846i	$0.494419\pi$
$588$	−636.531	+	734.596i	−1.08254	+	1.24931i
$589$	77.4303	−	263.703i	0.131461	−	0.447714i
$590$	−1.78323	+	0.256390i	−0.00302243	+	0.000434559i
$591$	−570.359	−	658.229i	−0.965074	−	1.11375i
$592$	259.468	−	118.495i	0.438290	−	0.200160i
$593$	−901.640	+	264.745i	−1.52047	+	0.446451i	−0.932119	−	0.362152i	$-0.882042\pi$
$593$	−901.640	+	264.745i	−1.52047	+	0.446451i	−0.588354	+	0.808604i	$0.700224\pi$
$594$	9.51328	+	4.34457i	0.0160156	+	0.00731409i
$595$	−142.712	−	20.5189i	−0.239852	−	0.0344855i
$596$	619.182	+	963.467i	1.03890	+	1.61655i
$597$			244.494i			0.409538i
$598$	−3.96503	+	4.29298i	−0.00663049	+	0.00717889i
$599$	−880.647			−1.47020			−0.735098	−	0.677961i	$-0.762864\pi$
$599$	−880.647			−1.47020			−0.735098	+	0.677961i	$0.762864\pi$
$600$	−1.21964	+	0.783813i	−0.00203273	+	0.00130635i
$601$	−55.0740	+	383.048i	−0.0916373	+	0.637351i	0.891301	+	0.453413i	$0.149794\pi$
$601$	−55.0740	+	383.048i	−0.0916373	+	0.637351i	−0.982938	+	0.183938i	$0.941115\pi$
$602$	−0.834371	+	1.82702i	−0.00138600	+	0.00303491i
$603$	496.826	+	1692.03i	0.823924	+	2.80603i
$604$	−225.129	−	492.964i	−0.372730	−	0.816166i
$605$	−41.8622	+	36.2738i	−0.0691938	+	0.0599567i
$606$	2.50209	+	17.4024i	0.00412886	+	0.0287168i
$607$	−108.784	−	31.9420i	−0.179216	−	0.0526227i	0.190893	−	0.981611i	$-0.438862\pi$
$607$	−108.784	−	31.9420i	−0.179216	−	0.0526227i	−0.370109	+	0.928988i	$0.620680\pi$
$608$	16.1227	+	13.9704i	0.0265176	+	0.0229776i
$609$	64.3375	−	100.111i	0.105645	−	0.164386i
$610$	0.647694	+	0.416248i	0.00106179	+	0.000682374i
$611$	250.055	−	288.579i	0.409255	−	0.472306i
$612$	347.795	−	1184.48i	0.568293	−	1.93543i
$613$	−629.830	+	90.5558i	−1.02745	+	0.147726i	−0.635373	−	0.772205i	$-0.719154\pi$
$613$	−629.830	+	90.5558i	−1.02745	+	0.147726i	−0.392081	+	0.919931i	$0.628245\pi$
$614$	−3.79919	−	4.38450i	−0.00618761	−	0.00714089i
$615$	110.497	−	50.4624i	0.179670	−	0.0820527i
$616$	−2.64587	+	0.776898i	−0.00429524	+	0.00126120i
$617$	586.764	+	267.966i	0.950995	+	0.434305i	0.829637	−	0.558304i	$-0.188548\pi$
$617$	586.764	+	267.966i	0.950995	+	0.434305i	0.121358	+	0.992609i	$0.461275\pi$
$618$	−5.87152	−	0.844197i	−0.00950084	−	0.00136602i
$619$	−317.931	−	494.710i	−0.513620	−	0.799208i	0.483477	−	0.875357i	$-0.339374\pi$
$619$	−317.931	−	494.710i	−0.513620	−	0.799208i	−0.997096	+	0.0761493i	$0.975737\pi$
$620$		−	248.151i		−	0.400243i
$621$	−1013.33	+	606.715i	−1.63176	+	0.976998i
$622$	5.32125			0.00855506
$623$	18.9923	−	12.2056i	0.0304853	−	0.0195917i
$624$	157.110	−	1092.72i	0.251778	−	1.75116i
$625$	−276.752	+	606.001i	−0.442802	+	0.969602i
$626$	−2.77296	−	9.44384i	−0.00442965	−	0.0150860i
$627$	526.761	+	1153.45i	0.840129	+	1.83963i
$628$	172.251	−	149.256i	0.274285	−	0.237669i
$629$	41.7806	+	290.591i	0.0664239	+	0.461988i
$630$	3.05521	+	0.897091i	0.00484954	+	0.00142395i
$631$	−152.639	−	132.262i	−0.241899	−	0.209607i	0.525470	−	0.850812i	$-0.323889\pi$
$631$	−152.639	−	132.262i	−0.241899	−	0.209607i	−0.767370	+	0.641205i	$0.778435\pi$
$632$	3.01887	−	4.69745i	0.00477669	−	0.00743267i
$633$	−1190.18	−	764.880i	−1.88021	−	1.20834i
$634$	6.91358	−	7.97870i	0.0109047	−	0.0125847i
$635$	211.256	−	719.472i	0.332687	−	1.13303i
$636$	531.652	−	76.4401i	0.835931	−	0.120189i
$637$	−395.839	−	456.823i	−0.621411	−	0.717147i
$638$	−2.47274	+	1.12926i	−0.00387576	+	0.00177000i
$639$	650.873	−	191.114i	1.01858	−	0.299082i
$640$	23.3614	+	10.6688i	0.0365022	+	0.0166700i
$641$	−599.513	−	86.1970i	−0.935278	−	0.134473i	−0.342209	−	0.939624i	$-0.611175\pi$
$641$	−599.513	−	86.1970i	−0.935278	−	0.134473i	−0.593069	+	0.805151i	$0.702084\pi$
$642$	−9.77204	−	15.2056i	−0.0152212	−	0.0236847i
$643$			137.308i			0.213542i	0.994284	+	0.106771i	$0.0340512\pi$
$643$			137.308i			0.213542i	−0.994284	+	0.106771i	$0.965949\pi$
$644$	48.5798	−	147.927i	0.0754345	−	0.229700i
$645$	1667.91			2.58591
$646$	−6.15609	+	3.95628i	−0.00952955	+	0.00612427i
$647$	87.8540	−	611.038i	0.135787	−	0.944417i	−0.802029	−	0.597285i	$-0.796246\pi$
$647$	87.8540	−	611.038i	0.135787	−	0.944417i	0.937816	−	0.347133i	$-0.112845\pi$
$648$	−6.55825	+	14.3606i	−0.0101208	+	0.0221614i
$649$	53.1215	+	180.915i	0.0818513	+	0.278760i
$650$	−0.187255	−	0.410032i	−0.000288085	−	0.000630819i
$651$	−80.7935	+	70.0079i	−0.124107	+	0.107539i
$652$	17.4221	+	121.173i	0.0267210	+	0.185849i
$653$	−229.382	−	67.3525i	−0.351274	−	0.103143i	0.101335	−	0.994852i	$-0.467688\pi$
$653$	−229.382	−	67.3525i	−0.351274	−	0.103143i	−0.452609	+	0.891709i	$0.649507\pi$
$654$	11.2643	+	9.76058i	0.0172237	+	0.0149244i
$655$	239.521	−	372.701i	0.365680	−	0.569010i
$656$	−59.9700	−	38.5404i	−0.0914177	−	0.0587506i
$657$	101.153	−	116.737i	0.153962	−	0.177681i
$658$	0.269505	−	0.917848i	0.000409581	−	0.00139491i
$659$	−70.0696	+	10.0745i	−0.106327	+	0.0152875i	−0.195273	−	0.980749i	$-0.562559\pi$
$659$	−70.0696	+	10.0745i	−0.106327	+	0.0152875i	0.0889458	+	0.996036i	$0.471650\pi$
$660$	749.759	+	865.268i	1.13600	+	1.31101i
$661$	−892.523	+	407.602i	−1.35026	+	0.616644i	−0.953532	−	0.301292i	$-0.902582\pi$
$661$	−892.523	+	407.602i	−1.35026	+	0.616644i	−0.396730	+	0.917935i	$0.629855\pi$
$662$	−9.92506	+	2.91426i	−0.0149925	+	0.00440220i
$663$	1033.54	+	472.000i	1.55888	+	0.711916i
$664$	2.58889	+	0.372226i	0.00389893	+	0.000560581i
$665$	108.528	+	168.873i	0.163200	+	0.253945i
$666$		−	6.48367i		−	0.00973523i
$667$	53.3006	−	302.327i	0.0799110	−	0.453264i
$668$	879.024			1.31590
$669$	883.057	−	567.506i	1.31997	−	0.848290i
$670$	1.34323	−	9.34237i	0.00200482	−	0.0139438i
$671$	33.4740	−	73.2979i	0.0498868	−	0.109237i
$672$	−2.33788	−	7.96208i	−0.00347898	−	0.0118483i
$673$	−119.102	−	260.796i	−0.176971	−	0.387513i	0.800271	−	0.599638i	$-0.204689\pi$
$673$	−119.102	−	260.796i	−0.176971	−	0.387513i	−0.977242	+	0.212125i	$0.931961\pi$
$674$	0.942234	−	0.816451i	0.00139797	−	0.00121135i
$675$	−12.9651	−	90.1743i	−0.0192076	−	0.133592i
$676$	10.2142	+	2.99917i	0.0151098	+	0.00443665i
$677$	516.916	+	447.910i	0.763539	+	0.661610i	0.946934	−	0.321429i	$-0.104163\pi$
$677$	516.916	+	447.910i	0.763539	+	0.661610i	−0.183395	+	0.983039i	$0.558709\pi$
$678$	8.11317	−	12.6243i	0.0119663	−	0.0186200i
$679$	−136.912	−	87.9880i	−0.201638	−	0.129585i
$680$	−8.65404	+	9.98730i	−0.0127265	+	0.0146872i
$681$	−427.111	+	1454.61i	−0.627182	+	2.13598i
$682$	2.41719	−	0.347540i	0.00354427	−	0.000509590i
$683$	−534.990	−	617.411i	−0.783294	−	0.903969i	0.214049	−	0.976823i	$-0.431335\pi$
$683$	−534.990	−	617.411i	−0.783294	−	0.903969i	−0.997343	+	0.0728537i	$0.976789\pi$
$684$	−1563.44	+	714.001i	−2.28574	+	1.04386i
$685$	−849.409	+	249.409i	−1.24001	+	0.364101i
$686$	−2.84045	−	1.29719i	−0.00414059	−	0.00189095i
$687$	887.343	+	127.581i	1.29162	+	0.185707i
$688$	−529.181	−	823.421i	−0.769158	−	1.19683i
$689$			334.018i			0.484787i
$690$	12.0825	−	1.34781i	0.0175109	−	0.00195335i
$691$	−48.0139			−0.0694847			−0.0347424	−	0.999396i	$-0.511061\pi$
$691$	−48.0139			−0.0694847			−0.0347424	+	0.999396i	$0.511061\pi$
$692$	384.715	−	247.242i	0.555947	−	0.357285i
$693$	47.4277	−	329.867i	0.0684382	−	0.475998i
$694$	−0.823052	+	1.80223i	−0.00118595	+	0.00259688i
$695$	−207.999	−	708.379i	−0.299279	−	1.01925i
$696$	−4.53111	−	9.92174i	−0.00651021	−	0.0142554i
$697$	55.4489	−	48.0467i	0.0795536	−	0.0689336i
$698$	1.20022	+	8.34771i	0.00171951	+	0.0119595i
$699$	279.340	+	82.0215i	0.399627	+	0.117341i
$700$	9.07644	+	7.86478i	0.0129663	+	0.0112354i
$701$	196.695	−	306.063i	0.280592	−	0.436610i	−0.672139	−	0.740425i	$-0.734624\pi$
$701$	196.695	−	306.063i	0.280592	−	0.436610i	0.952731	+	0.303815i	$0.0982606\pi$
$702$	−10.9762	−	7.05395i	−0.0156356	−	0.0100484i
$703$	267.673	−	308.911i	0.380758	−	0.439418i
$704$	189.256	−	644.547i	0.268830	−	0.915550i
$705$	−786.290	+	113.051i	−1.11530	+	0.160357i
$706$	4.84658	+	5.59326i	0.00686485	+	0.00792246i
$707$	264.974	−	121.009i	0.374786	−	0.171159i
$708$	−362.940	+	106.569i	−0.512627	+	0.150521i
$709$	−729.077	−	332.958i	−1.02832	−	0.469617i	−0.171471	−	0.985189i	$-0.554852\pi$
$709$	−729.077	−	332.958i	−1.02832	−	0.469617i	−0.856846	+	0.515573i	$0.827579\pi$
$710$	−3.59372	−	0.516699i	−0.00506158	−	0.000727745i
$711$	364.837	+	567.697i	0.513132	+	0.798449i
$712$		−	2.06927i		−	0.00290628i
$713$	−122.460	+	247.102i	−0.171753	+	0.346567i
$714$	2.84644			0.00398662
$715$	−598.961	+	384.929i	−0.837708	+	0.538362i
$716$	−148.834	+	1035.16i	−0.207869	+	1.44576i
$717$	829.394	−	1816.12i	1.15676	−	2.53294i
$718$	2.70570	+	9.21476i	0.00376838	+	0.0128339i
$719$	248.977	+	545.184i	0.346282	+	0.758253i	0.999999	+	0.00151302i	$0.000481608\pi$
$719$	248.977	+	545.184i	0.346282	+	0.758253i	−0.653717	+	0.756740i	$0.726791\pi$
$720$	−1172.72	+	1016.17i	−1.62878	+	1.41135i
$721$	13.9871	+	97.2826i	0.0193996	+	0.134927i
$722$	3.05857	+	0.898076i	0.00423624	+	0.00124387i
$723$	−1372.13	−	1188.96i	−1.89783	−	1.64448i
$724$	−478.411	+	744.422i	−0.660788	+	1.02821i
$725$	19.9205	+	12.8021i	0.0274766	+	0.0176581i
$726$	0.716131	−	0.826459i	0.000986406	−	0.00113837i
$727$	−208.961	+	711.655i	−0.287429	+	0.978892i	0.681555	+	0.731767i	$0.261304\pi$
$727$	−208.961	+	711.655i	−0.287429	+	0.978892i	−0.968984	+	0.247125i	$0.920514\pi$
$728$	3.40520	−	0.489593i	0.00467747	−	0.000672518i
$729$	344.835	+	397.960i	0.473024	+	0.545899i
$730$	−0.752018	+	0.343435i	−0.00103016	+	0.000470459i
$731$	966.595	−	283.818i	1.32229	−	0.388260i
$732$	147.045	+	67.1533i	0.200881	+	0.0917395i
$733$	282.005	+	40.5462i	0.384727	+	0.0553154i	0.331965	−	0.943292i	$-0.392288\pi$
$733$	282.005	+	40.5462i	0.384727	+	0.0553154i	0.0527620	+	0.998607i	$0.483198\pi$
$734$	2.27185	+	3.53506i	0.00309516	+	0.00481616i
$735$			1257.50i			1.71089i
$736$	−13.4986	−	16.6145i	−0.0183404	−	0.0225741i
$737$	−987.831			−1.34034
$738$	−1.36313	+	0.876031i	−0.00184706	+	0.00118703i
$739$	−169.682	+	1180.17i	−0.229611	+	1.59698i	0.470140	+	0.882592i	$0.344203\pi$
$739$	−169.682	+	1180.17i	−0.229611	+	1.59698i	−0.699751	+	0.714387i	$0.746706\pi$
$740$	153.313	−	335.708i	0.207180	−	0.453660i
$741$	−445.684	−	1517.86i	−0.601463	−	2.04839i
$742$	0.347612	+	0.761164i	0.000468480	+	0.00102583i
$743$	286.882	−	248.584i	0.386112	−	0.334568i	−0.440078	−	0.897960i	$-0.645049\pi$
$743$	286.882	−	248.584i	0.386112	−	0.334568i	0.826190	+	0.563391i	$0.190504\pi$
$744$	1.39449	+	9.69888i	0.00187431	+	0.0130361i
$745$	1421.64	+	417.431i	1.90824	+	0.560311i
$746$	−4.33909	−	3.75984i	−0.00581647	−	0.00504000i
$747$	−170.891	+	265.912i	−0.228770	+	0.355973i
$748$	581.740	+	373.862i	0.777727	+	0.499815i
$749$	−196.115	+	226.328i	−0.261835	+	0.302174i
$750$	3.45879	−	11.7795i	0.00461171	−	0.0157061i
$751$	123.290	−	17.7264i	0.164167	−	0.0236037i	−0.0597410	−	0.998214i	$-0.519027\pi$
$751$	123.290	−	17.7264i	0.164167	−	0.0236037i	0.223908	+	0.974610i	$0.428118\pi$
$752$	305.279	+	352.310i	0.405955	+	0.468498i
$753$	771.159	−	352.176i	1.02411	−	0.467698i
$754$	3.25396	−	0.955450i	0.00431560	−	0.00126717i
$755$	−637.755	−	291.253i	−0.844708	−	0.385765i
$756$	344.085	+	49.4720i	0.455139	+	0.0654391i
$757$	−355.687	−	553.459i	−0.469863	−	0.731122i	0.522744	−	0.852490i	$-0.324908\pi$
$757$	−355.687	−	553.459i	−0.469863	−	0.731122i	−0.992608	+	0.121368i	$0.961272\pi$
$758$			11.6664i			0.0153910i
$759$	−319.592	−	1231.61i	−0.421070	−	1.62268i
$760$	18.3993			0.0242095
$761$	−208.447	+	133.961i	−0.273912	+	0.176032i	−0.670384	−	0.742014i	$-0.733871\pi$
$761$	−208.447	+	133.961i	−0.273912	+	0.176032i	0.396472	+	0.918047i	$0.370234\pi$
$762$	−2.10679	+	14.6531i	−0.00276482	+	0.0192297i
$763$	102.587	−	224.635i	0.134453	−	0.294410i
$764$	47.2245	+	160.832i	0.0618122	+	0.210513i
$765$	−663.448	−	1452.75i	−0.867253	−	1.89902i
$766$	−1.45579	+	1.26145i	−0.00190051	+	0.00164680i
$767$	−33.4767	−	232.835i	−0.0436462	−	0.303566i
$768$	1292.68	+	379.566i	1.68318	+	0.494226i
$769$	299.861	+	259.831i	0.389936	+	0.337882i	0.827662	−	0.561227i	$-0.189670\pi$
$769$	299.861	+	259.831i	0.389936	+	0.337882i	−0.437726	+	0.899109i	$0.644216\pi$
$770$	−0.964325	+	1.50052i	−0.00125237	+	0.00194873i
$771$	236.382	+	151.913i	0.306591	+	0.197034i
$772$	−290.047	+	334.732i	−0.375708	+	0.433590i
$773$	−414.810	+	1412.71i	−0.536624	+	1.82757i	0.0242984	+	0.999705i	$0.492265\pi$
$773$	−414.810	+	1412.71i	−0.536624	+	1.82757i	−0.560922	+	0.827868i	$0.689553\pi$
$774$	−22.0219	+	3.16627i	−0.0284521	+	0.00409079i
$775$	−13.9304	−	16.0766i	−0.0179748	−	0.0207440i
$776$	−13.5690	+	6.19674i	−0.0174858	+	0.00798549i
$777$	−152.553	+	44.7936i	−0.196336	+	0.0576495i
$778$	−5.41047	−	2.47088i	−0.00695433	−	0.00317593i
$779$	−101.112	−	14.5377i	−0.129797	−	0.0186620i
$780$	−772.219	−	1201.60i	−0.990024	−	1.54051i
$781$			379.988i			0.486540i
$782$	6.77274	−	2.83709i	0.00866079	−	0.00362799i
$783$	685.401			0.875352
$784$	620.808	−	398.969i	0.791847	−	0.508889i
$785$	41.9635	−	291.863i	0.0534567	−	0.371800i
$786$	−3.63342	+	7.95608i	−0.00462267	+	0.0101222i
$787$	−217.506	−	740.756i	−0.276373	−	0.941240i	−0.974335	−	0.225105i	$-0.927728\pi$
$787$	−217.506	−	740.756i	−0.276373	−	0.941240i	0.697961	−	0.716135i	$-0.254091\pi$
$788$	274.715	+	601.542i	0.348623	+	0.763378i
$789$	943.949	−	817.937i	1.19639	−	1.03668i
$790$	−0.514012	−	3.57503i	−0.000650648	−	0.00452536i
$791$	−238.566	−	70.0493i	−0.301600	−	0.0885578i
$792$	−23.0848	−	20.0031i	−0.0291475	−	0.0252564i
$793$	−54.3492	+	84.5690i	−0.0685362	+	0.106644i
$794$	7.16476	+	4.60451i	0.00902363	+	0.00579913i
$795$	455.049	−	525.154i	0.572389	−	0.660572i
$796$	52.3005	−	178.119i	0.0657042	−	0.223768i
$797$	1344.77	−	193.349i	1.68729	−	0.242596i	0.769214	−	0.638991i	$-0.220648\pi$
$797$	1344.77	−	193.349i	1.68729	−	0.242596i	0.918080	+	0.396395i	$0.129739\pi$
$798$	−2.59526	−	2.99510i	−0.00325221	−	0.00375325i
$799$	−436.436	+	199.314i	−0.546228	+	0.249454i
$800$	1.58432	−	0.465200i	0.00198041	−	0.000581499i
$801$	227.477	+	103.885i	0.283992	+	0.129695i
$802$	5.05056	+	0.726160i	0.00629745	+	0.000905437i
$803$	46.7793	+	72.7900i	0.0582556	+	0.0906475i
$804$		−	1981.72i		−	2.46483i
$805$	−77.8265	−	185.789i	−0.0966789	−	0.230794i
$806$	−3.04659			−0.00377988
$807$	−1696.00	+	1089.96i	−2.10162	+	1.35063i
$808$	3.79974	−	26.4278i	0.00470265	−	0.0327076i
$809$	−66.6154	+	145.867i	−0.0823429	+	0.180306i	−0.946325	−	0.323217i	$-0.895236\pi$
$809$	−66.6154	+	145.867i	−0.0823429	+	0.180306i	0.863982	+	0.503523i	$0.167963\pi$
$810$	2.87694	+	9.79795i	0.00355178	+	0.0120962i
$811$	258.329	+	565.661i	0.318531	+	0.697486i	0.999390	−	0.0349290i	$-0.0111205\pi$
$811$	258.329	+	565.661i	0.318531	+	0.697486i	−0.680859	+	0.732415i	$0.738393\pi$
$812$	−68.2864	+	59.1705i	−0.0840966	+	0.0728701i
$813$	226.567	+	1575.81i	0.278680	+	1.93826i
$814$	3.48480	+	1.02323i	0.00428108	+	0.00125704i
$815$	119.692	+	103.714i	0.146862	+	0.127257i
$816$	−749.946	+	1166.94i	−0.919051	+	1.43007i
$817$	−1179.94	−	758.301i	−1.44423	−	0.928153i
$818$	−3.79274	+	4.37706i	−0.00463661	+	0.00535093i
$819$	−117.132	+	398.917i	−0.143019	+	0.487078i
$820$	−91.2942	+	13.1261i	−0.111334	+	0.0160075i
$821$	104.237	+	120.296i	0.126964	+	0.146524i	0.815672	−	0.578514i	$-0.196367\pi$
$821$	104.237	+	120.296i	0.126964	+	0.146524i	−0.688708	+	0.725039i	$0.741822\pi$
$822$	15.8979	−	7.26033i	0.0193405	−	0.00883252i
$823$	1104.12	−	324.198i	1.34158	−	0.393923i	0.469345	−	0.883015i	$-0.344490\pi$
$823$	1104.12	−	324.198i	1.34158	−	0.393923i	0.872232	+	0.489092i	$0.162672\pi$
$824$	8.19428	+	3.74220i	0.00994451	+	0.00454151i
$825$	97.1472	+	13.9677i	0.117754	+	0.0169305i
$826$	−0.318598	−	0.495748i	−0.000385712	−	0.000600180i
$827$			166.246i			0.201022i	0.994936	+	0.100511i	$0.0320478\pi$
$827$			166.246i			0.201022i	−0.994936	+	0.100511i	$0.967952\pi$
$828$	1669.39	−	433.193i	2.01618	−	0.523180i
$829$	279.862			0.337590			0.168795	−	0.985651i	$-0.446012\pi$
$829$	279.862			0.337590			0.168795	+	0.985651i	$0.446012\pi$
$830$	1.42322	−	0.914646i	0.00171472	−	0.00110198i
$831$	28.9632	−	201.444i	0.0348535	−	0.242411i
$832$	−348.140	+	762.320i	−0.418437	+	0.916250i
$833$	213.981	+	728.752i	0.256880	+	0.874853i
$834$	6.05487	+	13.2583i	0.00726004	+	0.0158973i
$835$	859.443	−	744.712i	1.02927	−	0.891870i
$836$	−137.019	−	952.991i	−0.163899	−	1.13994i
$837$	−590.785	−	173.470i	−0.705836	−	0.207252i
$838$	−8.00503	−	6.93639i	−0.00955254	−	0.00827732i
$839$	133.359	−	207.511i	0.158950	−	0.247331i	−0.752639	−	0.658433i	$-0.771220\pi$
$839$	133.359	−	207.511i	0.158950	−	0.247331i	0.911589	+	0.411102i	$0.134856\pi$
$840$	−6.02076	−	3.86931i	−0.00716758	−	0.00460632i
$841$	434.073	−	500.947i	0.516139	−	0.595656i
$842$	−0.0225523	+	0.0768060i	−2.67842e−5	+	9.12186e-5i
$843$	−2487.87	+	357.702i	−2.95121	+	0.424321i
$844$	703.451	+	811.826i	0.833473	+	0.961879i
$845$	12.5276	−	5.72117i	0.0148256	−	0.00677062i
$846$	10.1670	−	2.98530i	0.0120177	−	0.00352872i
$847$	−16.4814	−	7.52680i	−0.0194585	−	0.00888642i
$848$	−403.634	−	58.0338i	−0.475983	−	0.0684361i
$849$	834.825	+	1299.01i	0.983304	+	1.53005i
$850$			0.566396i			0.000666349i
$851$	−318.334	+	258.632i	−0.374070	+	0.303916i
$852$	−762.306			−0.894726
$853$	−916.145	+	588.771i	−1.07403	+	0.690235i	−0.953170	−	0.302435i	$-0.902201\pi$
$853$	−916.145	+	588.771i	−1.07403	+	0.690235i	−0.120857	+	0.992670i	$0.538564\pi$
$854$	−0.0358408	+	0.249278i	−4.19681e−5	+	0.000291895i
$855$	−923.713	+	2022.65i	−1.08037	+	2.36567i
$856$	7.73329	+	26.3372i	0.00903422	+	0.0307677i
$857$	−578.869	−	1267.55i	−0.675460	−	1.47905i	−0.867383	−	0.497641i	$-0.834200\pi$
$857$	−578.869	−	1267.55i	−0.675460	−	1.47905i	0.191924	−	0.981410i	$-0.438527\pi$
$858$	10.6230	−	9.20492i	0.0123812	−	0.0107283i
$859$	−74.4572	−	517.861i	−0.0866790	−	0.602865i	−0.986146	−	0.165878i	$-0.946954\pi$
$859$	−74.4572	−	517.861i	−0.0866790	−	0.602865i	0.899467	−	0.436988i	$-0.143955\pi$
$860$	−1215.11	−	356.789i	−1.41292	−	0.414871i
$861$	30.0294	+	26.0207i	0.0348774	+	0.0302214i
$862$	−4.04729	+	6.29770i	−0.00469523	+	0.00730592i
$863$	11.5328	+	7.41168i	0.0133636	+	0.00858827i	0.547306	−	0.836933i	$-0.315654\pi$
$863$	11.5328	+	7.41168i	0.0133636	+	0.00858827i	−0.533942	+	0.845521i	$0.679290\pi$
$864$	31.2984	−	36.1203i	0.0362250	−	0.0418059i
$865$	166.682	−	567.666i	0.192696	−	0.656261i
$866$	6.87737	−	0.988816i	0.00794153	−	0.00114182i
$867$	62.0049	+	71.5574i	0.0715166	+	0.0825345i
$868$	73.8354	−	33.7195i	0.0850638	−	0.0388474i
$869$	−362.700	+	106.498i	−0.417376	+	0.122553i
$870$	−6.41765	−	2.93084i	−0.00737660	−	0.00336878i
$871$	1219.83	+	175.385i	1.40049	+	0.201360i
$872$	−12.2373	−	19.0417i	−0.0140336	−	0.0218368i
$873$		−	1802.75i		−	2.06501i
$874$	−9.16034	−	4.53970i	−0.0104809	−	0.00519417i
$875$	−203.409			−0.232468
$876$	−146.026	+	93.8454i	−0.166697	+	0.107129i
$877$	150.639	−	1047.72i	0.171766	−	1.19466i	−0.703385	−	0.710809i	$-0.748329\pi$
$877$	150.639	−	1047.72i	0.171766	−	1.19466i	0.875151	−	0.483850i	$-0.160762\pi$
$878$	0.323498	−	0.708363i	0.000368449	−	0.000806791i
$879$	168.406	+	573.537i	0.191588	+	0.652487i
$880$	−361.090	−	790.676i	−0.410329	−	0.898495i
$881$	−247.308	+	214.294i	−0.280713	+	0.243240i	−0.783825	−	0.620982i	$-0.786734\pi$
$881$	−247.308	+	214.294i	−0.280713	+	0.243240i	0.503111	+	0.864222i	$0.332189\pi$
$882$	−2.38717	−	16.6032i	−0.00270655	−	0.0188244i
$883$	−688.211	−	202.077i	−0.779401	−	0.228853i	−0.132252	−	0.991216i	$-0.542221\pi$
$883$	−688.211	−	202.077i	−0.779401	−	0.228853i	−0.647149	+	0.762363i	$0.724039\pi$
$884$	−651.987	−	564.950i	−0.737541	−	0.639083i
$885$	−264.570	+	411.678i	−0.298949	+	0.465173i
$886$	−4.61378	−	2.96510i	−0.00520742	−	0.00334661i
$887$	42.0565	−	48.5358i	0.0474143	−	0.0547190i	−0.731547	−	0.681791i	$-0.761201\pi$
$887$	42.0565	−	48.5358i	0.0474143	−	0.0547190i	0.778961	+	0.627072i	$0.215747\pi$
$888$	−4.10566	+	13.9826i	−0.00462349	+	0.0157462i
$889$	242.780	−	34.9065i	0.273093	−	0.0392649i
$890$	−0.876505	−	1.01154i	−0.000984838	−	0.00113656i
$891$	972.169	−	443.975i	1.09110	−	0.498288i
$892$	−764.723	+	224.543i	−0.857313	+	0.251730i
$893$	607.646	+	277.503i	0.680455	+	0.310753i
$894$	−28.9537	−	4.16291i	−0.0323867	−	0.00465650i
$895$	731.475	+	1138.20i	0.817291	+	1.27173i
$896$			8.40073i			0.00937582i
$897$	175.983	+	1577.60i	0.196190	+	1.75875i
$898$	−1.33499			−0.00148663
$899$	134.636	−	86.5254i	0.149762	−	0.0962463i
$900$	−18.9326	+	131.679i	−0.0210362	+	0.146310i
$901$	174.349	−	381.772i	0.193507	−	0.423720i
$902$	−0.255719	−	0.870899i	−0.000283502	−	0.000965519i
$903$	226.641	+	496.276i	0.250987	+	0.549585i
$904$	−17.2231	+	14.9239i	−0.0190521	+	0.0165087i
$905$	162.922	+	1133.15i	0.180025	+	1.25210i
$906$	13.2809	+	3.89964i	0.0146589	+	0.00430423i
$907$	177.493	+	153.798i	0.195692	+	0.169568i	0.747195	−	0.664605i	$-0.231400\pi$
$907$	177.493	+	153.798i	0.195692	+	0.169568i	−0.551503	+	0.834173i	$0.685946\pi$
$908$	622.319	−	968.347i	0.685373	−	1.06646i
$909$	2714.47	+	1744.49i	2.98622	+	1.91913i
$910$	1.45721	−	1.68171i	0.00160133	−	0.00184803i
$911$	108.391	−	369.147i	0.118981	−	0.405211i	−0.878368	−	0.477985i	$-0.841367\pi$
$911$	108.391	−	369.147i	0.118981	−	0.405211i	0.997348	+	0.0727746i	$0.0231854\pi$
$912$	1911.65	−	274.853i	2.09610	−	0.301374i
$913$	−115.951	−	133.815i	−0.127000	−	0.146566i
$914$	9.04695	−	4.13160i	0.00989820	−	0.00452035i
$915$	200.662	−	58.9197i	0.219303	−	0.0643931i
$916$	−619.158	−	282.760i	−0.675936	−	0.308690i
$917$	143.441	+	20.6238i	0.156425	+	0.0224905i
$918$	8.86341	+	13.7917i	0.00965513	+	0.0150237i
$919$		−	670.787i		−	0.729910i	−0.931025	−	0.364955i	$-0.881084\pi$
$919$		−	670.787i		−	0.729910i	0.931025	−	0.364955i	$-0.118916\pi$
$920$	−18.1822	−	3.20554i	−0.0197633	−	0.00348429i
$921$	−1575.88			−1.71105
$922$	11.8740	−	7.63096i	0.0128785	−	0.00827653i
$923$	67.4650	−	469.230i	0.0730932	−	0.508375i
$924$	−155.575	+	340.661i	−0.168371	+	0.368681i
$925$	−8.91321	−	30.3556i	−0.00963590	−	0.0328169i
$926$	−3.52522	−	7.71915i	−0.00380693	−	0.00833602i
$927$	−822.769	+	712.933i	−0.887561	+	0.769076i
$928$	1.76795	+	12.2964i	0.00190512	+	0.0132504i
$929$	−641.045	−	188.228i	−0.690037	−	0.202613i	−0.0821306	−	0.996622i	$-0.526172\pi$
$929$	−641.045	−	188.228i	−0.690037	−	0.202613i	−0.607907	+	0.794008i	$0.707991\pi$
$930$	4.78995	+	4.15051i	0.00515048	+	0.00446292i
$931$	571.712	−	889.601i	0.614083	−	0.955532i
$932$	−185.959	−	119.509i	−0.199527	−	0.128228i
$933$	946.548	−	1092.37i	1.01452	−	1.17082i
$934$	−3.45793	+	11.7766i	−0.00370228	+	0.0126088i
$935$	885.518	−	127.318i	0.947078	−	0.136169i
$936$	24.9549	+	28.7995i	0.0266612	+	0.0307687i
$937$	1011.21	−	461.803i	1.07920	−	0.492853i	0.205168	−	0.978727i	$-0.434226\pi$
$937$	1011.21	−	461.803i	1.07920	−	0.492853i	0.874029	+	0.485874i	$0.161499\pi$
$938$	2.96228	−	0.869803i	0.00315808	−	0.000927296i
$939$	−2431.94	−	1110.63i	−2.58992	−	1.18278i
$940$	597.012	+	85.8374i	0.635119	+	0.0913164i
$941$	−428.237	−	666.349i	−0.455087	−	0.708129i	0.535572	−	0.844489i	$-0.320096\pi$
$941$	−428.237	−	666.349i	−0.455087	−	0.708129i	−0.990659	+	0.136360i	$0.956460\pi$
$942$			5.82131i			0.00617974i
$943$	97.3862	+	31.9820i	0.103273	+	0.0339152i
$944$	287.179			0.304215
$945$	378.333	−	243.140i	0.400352	−	0.257291i
$946$	1.77363	−	12.3359i	0.00187488	−	0.0130401i
$947$	−547.383	+	1198.60i	−0.578018	+	1.26568i	0.364399	+	0.931243i	$0.381274\pi$
$947$	−547.383	+	1198.60i	−0.578018	+	1.26568i	−0.942417	+	0.334440i	$0.891453\pi$
$948$	−213.650	−	727.624i	−0.225369	−	0.767536i
$949$	−44.8421	−	98.1904i	−0.0472519	−	0.103467i
$950$	0.595976	−	0.516416i	0.000627343	−	0.000543596i
$951$	−408.117	−	2838.52i	−0.429145	−	2.98477i
$952$	−4.14759	−	1.21784i	−0.00435671	−	0.00127925i
$953$	−259.977	−	225.271i	−0.272799	−	0.236381i	0.507707	−	0.861530i	$-0.330493\pi$
$953$	−259.977	−	225.271i	−0.272799	−	0.236381i	−0.780506	+	0.625148i	$0.785039\pi$
$954$	−5.01121	+	7.79760i	−0.00525284	+	0.00817358i
$955$	182.430	+	117.241i	0.191026	+	0.122765i
$956$	−992.723	+	1145.66i	−1.03841	+	1.19839i
$957$	−208.032	+	708.491i	−0.217379	+	0.740325i
$958$	13.7207	−	1.97274i	0.0143223	−	0.00205923i
$959$	−189.630	−	218.845i	−0.197738	−	0.228201i
$960$	1585.90	−	724.257i	1.65198	−	0.754435i
$961$	784.124	−	230.239i	0.815945	−	0.239583i
$962$	−4.12155	−	1.88225i	−0.00428435	−	0.00195660i
$963$	−3283.52	−	472.098i	−3.40967	−	0.490237i
$964$	745.295	+	1159.70i	0.773128	+	1.20301i
$965$			573.003i			0.593786i
$966$	2.04284	+	3.41191i	0.00211474	+	0.00353200i
$967$	−442.377			−0.457473			−0.228737	−	0.973488i	$-0.573459\pi$
$967$	−442.377			−0.457473			−0.228737	+	0.973488i	$0.573459\pi$
$968$	−1.39708	+	0.897849i	−0.00144327	+	0.000927530i
$969$	−282.884	+	1967.50i	−0.291934	+	2.03045i
$970$	−4.00822	+	8.77677i	−0.00413218	+	0.00904822i
$971$	330.289	+	1124.86i	0.340153	+	1.15846i	0.935009	+	0.354623i	$0.115391\pi$
$971$	330.289	+	1124.86i	0.340153	+	1.15846i	−0.594856	+	0.803832i	$0.702791\pi$
$972$	122.793	+	268.880i	0.126331	+	0.276626i
$973$	182.509	−	158.145i	0.187574	−	0.162534i
$974$	0.460712	+	3.20432i	0.000473010	+	0.00328986i
$975$	−117.483	−	34.4961i	−0.120495	−	0.0353806i
$976$	−92.7520	−	80.3700i	−0.0950327	−	0.0823463i
$977$	−68.7437	+	106.967i	−0.0703620	+	0.109485i	−0.874652	−	0.484752i	$-0.838910\pi$
$977$	−68.7437	+	106.967i	−0.0703620	+	0.109485i	0.804290	+	0.594238i	$0.202546\pi$
$978$	−2.63036	−	1.69043i	−0.00268953	−	0.00172845i
$979$	−91.7354	+	105.868i	−0.0937032	+	0.108139i
$980$	268.997	−	916.118i	0.274486	−	0.934815i
$981$	2707.63	−	389.299i	2.76007	−	0.396839i
$982$	0.177094	+	0.204378i	0.000180340	+	0.000208124i
$983$	−373.072	+	170.376i	−0.379524	+	0.173323i	−0.596037	−	0.802957i	$-0.703259\pi$
$983$	−373.072	+	170.376i	−0.379524	+	0.173323i	0.216513	+	0.976280i	$0.430532\pi$
$984$	3.49444	−	1.02606i	0.00355126	−	0.00104274i
$985$	778.223	+	355.402i	0.790074	+	0.360815i
$986$	−4.21790	−	0.606442i	−0.00427779	−	0.000615053i
$987$	−140.481	−	218.593i	−0.142332	−	0.221472i
$988$			1201.13i			1.21572i
$989$	1033.91	+	954.926i	1.04541	+	0.965547i
$990$	−19.7577			−0.0199573
$991$	273.939	−	176.050i	0.276427	−	0.177649i	−0.395081	−	0.918646i	$-0.629283\pi$
$991$	273.939	−	176.050i	0.276427	−	0.177649i	0.671508	+	0.740997i	$0.265647\pi$
$992$	1.58823	−	11.0464i	0.00160104	−	0.0111355i
$993$	−1167.22	+	2555.86i	−1.17545	+	2.57388i
$994$	−0.334586	−	1.13950i	−0.000336606	−	0.00114637i
$995$	−99.7676	−	218.461i	−0.100269	−	0.219558i
$996$	268.450	−	232.614i	0.269529	−	0.233548i
$997$	240.375	+	1671.85i	0.241099	+	1.67688i	0.646635	+	0.762800i	$0.276176\pi$
$997$	240.375	+	1671.85i	0.241099	+	1.67688i	−0.405536	+	0.914079i	$0.632915\pi$
$998$	−1.42017	−	0.416999i	−0.00142301	−	0.000417834i
$999$	−692.064	−	599.677i	−0.692757	−	0.600277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.11.2	✓	30
3.2	odd	2		207.3.j.a.172.2		30
4.3	odd	2		368.3.p.a.241.1		30
23.5	odd	22		529.3.b.b.528.15		30
23.18	even	11		529.3.b.b.528.16		30
23.21	odd	22	inner	23.3.d.a.21.2	yes	30
69.44	even	22		207.3.j.a.136.2		30
92.67	even	22		368.3.p.a.113.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.11.2	✓	30	1.1	even	1	trivial
23.3.d.a.21.2	yes	30	23.21	odd	22	inner
207.3.j.a.136.2		30	69.44	even	22
207.3.j.a.172.2		30	3.2	odd	2
368.3.p.a.113.1		30	92.67	even	22
368.3.p.a.241.1		30	4.3	odd	2
529.3.b.b.528.15		30	23.5	odd	22
529.3.b.b.528.16		30	23.18	even	11

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0163142 - 0.0104845i) q^{2} +(0.749667 - 5.21405i) q^{3} +(-1.66150 + 3.63819i) q^{4} +(1.45779 + 4.96477i) q^{5} +(-0.0424364 - 0.0929228i) q^{6} +(-1.27914 + 1.10838i) q^{7} +(0.0220779 + 0.153555i) q^{8} +(-17.9889 - 5.28201i) q^{9} +O(q^{10})\)	\(q+(0.0163142 - 0.0104845i) q^{2} +(0.749667 - 5.21405i) q^{3} +(-1.66150 + 3.63819i) q^{4} +(1.45779 + 4.96477i) q^{5} +(-0.0424364 - 0.0929228i) q^{6} +(-1.27914 + 1.10838i) q^{7} +(0.0220779 + 0.153555i) q^{8} +(-17.9889 - 5.28201i) q^{9} +(0.0758357 + 0.0657120i) q^{10} +(5.67789 - 8.83496i) q^{11} +(17.7241 + 11.3906i) q^{12} +(-8.57997 + 9.90181i) q^{13} +(-0.00924733 + 0.0314935i) q^{14} +(26.9794 - 3.87906i) q^{15} +(-10.4748 - 12.0886i) q^{16} +(14.9751 - 6.83892i) q^{17} +(-0.348853 + 0.102432i) q^{18} +(-20.8497 - 9.52176i) q^{19} +(-20.4849 - 2.94528i) q^{20} +(4.82024 + 7.50043i) q^{21} -0.203665i q^{22} +(18.9449 + 13.0419i) q^{23} +0.817196 q^{24} +(-1.49247 + 0.959149i) q^{25} +(-0.0361597 + 0.251496i) q^{26} +(-21.3320 + 46.7105i) q^{27} +(-1.90720 - 6.49534i) q^{28} +(-5.54470 - 12.1412i) q^{29} +(0.399477 - 0.346149i) q^{30} +(1.70643 + 11.8685i) q^{31} +(-0.893031 - 0.262218i) q^{32} +(-41.8094 - 36.2281i) q^{33} +(0.172604 - 0.268578i) q^{34} +(-7.36759 - 4.73486i) q^{35} +(49.1056 - 56.6708i) q^{36} +(-5.02408 + 17.1105i) q^{37} +(-0.439977 + 0.0632592i) q^{38} +(45.1964 + 52.1594i) q^{39} +(-0.730182 + 0.333463i) q^{40} +(4.27614 - 1.25559i) q^{41} +(0.157276 + 0.0718257i) q^{42} +(60.5696 + 8.70859i) q^{43} +(22.7094 + 35.3365i) q^{44} -97.0108i q^{45} +(0.445808 + 0.0141405i) q^{46} -29.1440 q^{47} +(-70.8831 + 45.5538i) q^{48} +(-6.56573 + 45.6657i) q^{49} +(-0.0142922 + 0.0312955i) q^{50} +(-24.4321 - 83.2080i) q^{51} +(-21.7690 - 47.6674i) q^{52} +(19.2669 - 16.6948i) q^{53} +(0.141722 + 0.985697i) q^{54} +(52.1407 + 15.3099i) q^{55} +(-0.198439 - 0.171948i) q^{56} +(-65.2773 + 101.573i) q^{57} +(-0.217751 - 0.139940i) q^{58} +(-11.7572 + 13.5685i) q^{59} +(-30.7137 + 104.601i) q^{60} +(7.59459 - 1.09194i) q^{61} +(0.152274 + 0.175734i) q^{62} +(28.8649 - 13.1821i) q^{63} +(61.3729 - 18.0207i) q^{64} +(-61.6680 - 28.1628i) q^{65} +(-1.06192 - 0.152681i) q^{66} +(-50.8527 - 79.1283i) q^{67} +65.8452i q^{68} +(82.2035 - 89.0025i) q^{69} -0.169839 q^{70} +(-30.4382 + 19.5614i) q^{71} +(0.413924 - 2.87890i) q^{72} +(-3.42254 + 7.49432i) q^{73} +(0.0974305 + 0.331818i) q^{74} +(3.88220 + 8.50083i) q^{75} +(69.2839 - 60.0348i) q^{76} +(2.52970 + 17.5945i) q^{77} +(1.28421 + 0.377077i) q^{78} +(-27.2023 - 23.5709i) q^{79} +(44.7470 - 69.6277i) q^{80} +(85.6101 + 55.0183i) q^{81} +(0.0565974 - 0.0653169i) q^{82} +(4.74991 - 16.1767i) q^{83} +(-35.2968 + 5.07492i) q^{84} +(55.7842 + 64.3784i) q^{85} +(1.07945 - 0.492967i) q^{86} +(-67.4615 + 19.8085i) q^{87} +(1.48201 + 0.676812i) q^{88} +(-13.2028 - 1.89828i) q^{89} +(-1.01711 - 1.58265i) q^{90} -22.1757i q^{91} +(-78.9259 + 47.2559i) q^{92} +63.1622 q^{93} +(-0.475461 + 0.305560i) q^{94} +(16.8788 - 117.395i) q^{95} +(-2.03669 + 4.45974i) q^{96} +(27.0901 + 92.2604i) q^{97} +(0.371667 + 0.813836i) q^{98} +(-148.805 + 128.941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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