LMFDB - Embedded newform 230.3.k.a.223.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(3,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([33, 32]))

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

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

chi := DirichletCharacter("230.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.k (of order $44$, degree $20$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			223.5
Character	$\chi$	$=$	230.223
Dual form			230.3.k.a.197.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.100889 + 1.41061i) q^{2} +(-0.738452 - 0.160640i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(4.14598 - 2.79479i) q^{5} +(0.152100 - 1.05788i) q^{6} +(2.07244 - 3.79539i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(-7.66718 - 3.50148i) q^{9} +O(q^{10})$	\(q+(0.100889 + 1.41061i) q^{2} +(-0.738452 - 0.160640i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(4.14598 - 2.79479i) q^{5} +(0.152100 - 1.05788i) q^{6} +(2.07244 - 3.79539i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(-7.66718 - 3.50148i) q^{9} +(4.36065 + 5.56639i) q^{10} +(-7.65013 - 8.82872i) q^{11} +(1.50760 + 0.107825i) q^{12} +(-5.84353 - 10.7016i) q^{13} +(5.56290 + 2.54049i) q^{14} +(-3.51056 + 1.39781i) q^{15} +(3.83797 - 1.12693i) q^{16} +(5.30253 + 7.08335i) q^{17} +(4.16570 - 11.1687i) q^{18} +(14.1529 - 2.03487i) q^{19} +(-7.41207 + 6.71276i) q^{20} +(-2.14009 + 2.46979i) q^{21} +(11.6821 - 11.6821i) q^{22} +(-0.915120 - 22.9818i) q^{23} +2.13751i q^{24} +(9.37825 - 23.1743i) q^{25} +(14.5063 - 9.32261i) q^{26} +(10.5443 + 7.89333i) q^{27} +(-3.02241 + 8.10339i) q^{28} +(41.0264 + 5.89871i) q^{29} +(-2.32594 - 4.81101i) q^{30} +(-6.13977 - 3.94579i) q^{31} +(1.97687 + 5.30019i) q^{32} +(4.23100 + 7.74851i) q^{33} +(-9.45688 + 8.19444i) q^{34} +(-2.01505 - 21.5276i) q^{35} +(16.1749 + 4.74938i) q^{36} +(10.2073 + 27.3668i) q^{37} +(4.29828 + 19.7589i) q^{38} +(2.59605 + 8.84134i) q^{39} +(-10.2169 - 9.77830i) q^{40} +(-5.77878 - 12.6538i) q^{41} +(-3.69983 - 2.76966i) q^{42} +(-68.7743 - 14.9609i) q^{43} +(17.6574 + 15.3003i) q^{44} +(-41.5739 + 6.91112i) q^{45} +(32.3260 - 3.60948i) q^{46} +(-12.8473 + 12.8473i) q^{47} +(-3.01519 + 0.215651i) q^{48} +(16.3814 + 25.4900i) q^{49} +(33.6361 + 10.8910i) q^{50} +(-2.77779 - 6.08252i) q^{51} +(14.6141 + 19.5221i) q^{52} +(-29.2815 - 15.9889i) q^{53} +(-10.0706 + 15.6702i) q^{54} +(-56.3917 - 15.2231i) q^{55} +(-11.7356 - 3.44590i) q^{56} +(-10.7781 - 0.770865i) q^{57} +(-4.18167 + 58.4674i) q^{58} +(-9.47174 + 32.2578i) q^{59} +(6.55180 - 3.76638i) q^{60} +(76.2827 + 49.0239i) q^{61} +(4.94654 - 9.05891i) q^{62} +(-29.1792 + 21.8433i) q^{63} +(-7.27706 + 3.32332i) q^{64} +(-54.1359 - 28.0372i) q^{65} +(-10.5033 + 6.75004i) q^{66} +(-6.62378 - 92.6125i) q^{67} +(-12.5133 - 12.5133i) q^{68} +(-3.01603 + 17.1180i) q^{69} +(30.1638 - 5.01434i) q^{70} +(59.9435 - 69.1785i) q^{71} +(-5.06766 + 23.2957i) q^{72} +(17.0176 - 22.7329i) q^{73} +(-37.5741 + 17.1595i) q^{74} +(-10.6481 + 15.6066i) q^{75} +(-27.4384 + 8.05665i) q^{76} +(-49.3628 + 10.7382i) q^{77} +(-12.2098 + 4.55401i) q^{78} +(-18.7850 + 63.9759i) q^{79} +(12.7626 - 15.3986i) q^{80} +(43.1593 + 49.8084i) q^{81} +(17.2665 - 9.42822i) q^{82} +(-115.056 + 42.9136i) q^{83} +(3.53364 - 5.49844i) q^{84} +(41.7807 + 14.5479i) q^{85} +(14.1655 - 98.5231i) q^{86} +(-29.3485 - 10.9464i) q^{87} +(-19.8013 + 26.4514i) q^{88} +(-47.4284 - 73.8000i) q^{89} +(-13.9432 - 57.9473i) q^{90} -52.7271 q^{91} +(8.35291 + 45.2353i) q^{92} +(3.90008 + 3.90008i) q^{93} +(-19.4187 - 16.8264i) q^{94} +(52.9904 - 47.9909i) q^{95} +(-0.608398 - 4.23150i) q^{96} +(56.6933 + 21.1455i) q^{97} +(-34.3038 + 25.6795i) q^{98} +(27.7413 + 94.4782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8}+O(q^{10}) $ 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8	$ 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8} - 16 q^{10} + 8 q^{11} + 44 q^{12} + 24 q^{13} + 24 q^{15} + 96 q^{16} + 12 q^{17} + 88 q^{18} - 24 q^{20} + 24 q^{21} + 8 q^{22} - 44 q^{23} - 128 q^{25} + 48 q^{26} - 60 q^{27} - 116 q^{28} + 120 q^{30} - 12 q^{31} + 96 q^{32} - 334 q^{33} - 224 q^{35} - 176 q^{36} + 188 q^{37} + 76 q^{38} - 16 q^{40} - 116 q^{41} + 24 q^{42} + 120 q^{43} + 204 q^{45} + 396 q^{46} - 144 q^{47} - 88 q^{48} + 170 q^{50} - 176 q^{51} + 48 q^{52} + 192 q^{53} - 312 q^{55} + 296 q^{56} + 88 q^{57} - 28 q^{58} - 72 q^{60} - 552 q^{61} - 12 q^{62} - 122 q^{63} - 392 q^{65} - 8 q^{66} - 72 q^{67} - 24 q^{68} + 100 q^{70} + 424 q^{71} - 176 q^{72} + 452 q^{73} + 604 q^{75} - 112 q^{76} + 356 q^{77} + 32 q^{78} + 16 q^{80} - 704 q^{81} + 148 q^{82} - 360 q^{83} + 428 q^{85} - 376 q^{86} - 462 q^{87} - 104 q^{88} - 510 q^{90} + 432 q^{91} - 192 q^{93} - 166 q^{95} - 1042 q^{97} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8 - 16 * q^10 + 8 * q^11 + 44 * q^12 + 24 * q^13 + 24 * q^15 + 96 * q^16 + 12 * q^17 + 88 * q^18 - 24 * q^20 + 24 * q^21 + 8 * q^22 - 44 * q^23 - 128 * q^25 + 48 * q^26 - 60 * q^27 - 116 * q^28 + 120 * q^30 - 12 * q^31 + 96 * q^32 - 334 * q^33 - 224 * q^35 - 176 * q^36 + 188 * q^37 + 76 * q^38 - 16 * q^40 - 116 * q^41 + 24 * q^42 + 120 * q^43 + 204 * q^45 + 396 * q^46 - 144 * q^47 - 88 * q^48 + 170 * q^50 - 176 * q^51 + 48 * q^52 + 192 * q^53 - 312 * q^55 + 296 * q^56 + 88 * q^57 - 28 * q^58 - 72 * q^60 - 552 * q^61 - 12 * q^62 - 122 * q^63 - 392 * q^65 - 8 * q^66 - 72 * q^67 - 24 * q^68 + 100 * q^70 + 424 * q^71 - 176 * q^72 + 452 * q^73 + 604 * q^75 - 112 * q^76 + 356 * q^77 + 32 * q^78 + 16 * q^80 - 704 * q^81 + 148 * q^82 - 360 * q^83 + 428 * q^85 - 376 * q^86 - 462 * q^87 - 104 * q^88 - 510 * q^90 + 432 * q^91 - 192 * q^93 - 166 * q^95 - 1042 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.100889	+	1.41061i	0.0504444	+	0.705305i
$2$	0.100889	+	1.41061i	0.0504444	+	0.705305i
$3$	−0.738452	−	0.160640i	−0.246151	−	0.0535468i	0.0877970	−	0.996138i	$-0.472017\pi$
$3$	−0.738452	−	0.160640i	−0.246151	−	0.0535468i	−0.333948	+	0.942592i	$0.608381\pi$
$4$	−1.97964	+	0.284630i	−0.494911	+	0.0711574i
$5$	4.14598	−	2.79479i	0.829195	−	0.558959i
$5$	4.14598	−	2.79479i	0.829195	−	0.558959i
$6$	0.152100	−	1.05788i	0.0253499	−	0.176313i
$7$	2.07244	−	3.79539i	0.296063	−	0.542198i	−0.686730	−	0.726913i	$-0.740954\pi$
$7$	2.07244	−	3.79539i	0.296063	−	0.542198i	0.982792	+	0.184715i	$0.0591362\pi$
$8$	−0.601225	−	2.76379i	−0.0751532	−	0.345474i
$9$	−7.66718	−	3.50148i	−0.851909	−	0.389054i
$10$	4.36065	+	5.56639i	0.436065	+	0.556639i
$11$	−7.65013	−	8.82872i	−0.695466	−	0.802611i	0.292667	−	0.956215i	$-0.405457\pi$
$11$	−7.65013	−	8.82872i	−0.695466	−	0.802611i	−0.988132	+	0.153604i	$0.950912\pi$
$12$	1.50760	+	0.107825i	0.125633	+	0.00898544i
$13$	−5.84353	−	10.7016i	−0.449502	−	0.823201i	0.550430	−	0.834881i	$-0.314464\pi$
$13$	−5.84353	−	10.7016i	−0.449502	−	0.823201i	−0.999932	+	0.0116801i	$0.996282\pi$
$14$	5.56290	+	2.54049i	0.397350	+	0.181464i
$15$	−3.51056	+	1.39781i	−0.234038	+	0.0931874i
$16$	3.83797	−	1.12693i	0.239873	−	0.0704331i
$17$	5.30253	+	7.08335i	0.311914	+	0.416668i	0.928914	−	0.370295i	$-0.120743\pi$
$17$	5.30253	+	7.08335i	0.311914	+	0.416668i	−0.617001	+	0.786963i	$0.711652\pi$
$18$	4.16570	−	11.1687i	0.231428	−	0.620481i
$19$	14.1529	−	2.03487i	0.744888	−	0.107099i	0.240588	−	0.970627i	$-0.422660\pi$
$19$	14.1529	−	2.03487i	0.744888	−	0.107099i	0.504300	+	0.863529i	$0.331751\pi$
$20$	−7.41207	+	6.71276i	−0.370604	+	0.335638i
$21$	−2.14009	+	2.46979i	−0.101909	+	0.117609i
$22$	11.6821	−	11.6821i	0.531003	−	0.531003i
$23$	−0.915120	−	22.9818i	−0.0397878	−	0.999208i
$23$	−0.915120	−	22.9818i	−0.0397878	−	0.999208i
$24$			2.13751i			0.0890628i
$25$	9.37825	−	23.1743i	0.375130	−	0.926972i
$26$	14.5063	−	9.32261i	0.557933	−	0.358562i
$27$	10.5443	+	7.89333i	0.390528	+	0.292346i
$28$	−3.02241	+	8.10339i	−0.107943	+	0.289407i
$29$	41.0264	+	5.89871i	1.41470	+	0.203404i	0.806902	−	0.590685i	$-0.201142\pi$
$29$	41.0264	+	5.89871i	1.41470	+	0.203404i	0.607802	+	0.794089i	$0.292051\pi$
$30$	−2.32594	−	4.81101i	−0.0775314	−	0.160367i
$31$	−6.13977	−	3.94579i	−0.198057	−	0.127284i	0.437853	−	0.899046i	$-0.355739\pi$
$31$	−6.13977	−	3.94579i	−0.198057	−	0.127284i	−0.635911	+	0.771763i	$0.719375\pi$
$32$	1.97687	+	5.30019i	0.0617771	+	0.165631i
$33$	4.23100	+	7.74851i	0.128212	+	0.234803i
$34$	−9.45688	+	8.19444i	−0.278144	+	0.241013i
$35$	−2.01505	−	21.5276i	−0.0575727	−	0.615075i
$36$	16.1749	+	4.74938i	0.449303	+	0.131927i
$37$	10.2073	+	27.3668i	0.275873	+	0.739643i	0.998812	+	0.0487314i	$0.0155178\pi$
$37$	10.2073	+	27.3668i	0.275873	+	0.739643i	−0.722939	+	0.690911i	$0.757209\pi$
$38$	4.29828	+	19.7589i	0.113113	+	0.519970i
$39$	2.59605	+	8.84134i	0.0665654	+	0.226701i
$40$	−10.2169	−	9.77830i	−0.255422	−	0.244458i
$41$	−5.77878	−	12.6538i	−0.140946	−	0.308628i	0.825974	−	0.563708i	$-0.190626\pi$
$41$	−5.77878	−	12.6538i	−0.140946	−	0.308628i	−0.966920	+	0.255080i	$0.917898\pi$
$42$	−3.69983	−	2.76966i	−0.0880912	−	0.0659442i
$43$	−68.7743	−	14.9609i	−1.59940	−	0.347929i	−0.677552	−	0.735475i	$-0.736959\pi$
$43$	−68.7743	−	14.9609i	−1.59940	−	0.347929i	−0.921850	+	0.387547i	$0.873323\pi$
$44$	17.6574	+	15.3003i	0.401305	+	0.347733i
$45$	−41.5739	+	6.91112i	−0.923864	+	0.153581i
$46$	32.3260	−	3.60948i	0.702740	−	0.0784670i
$47$	−12.8473	+	12.8473i	−0.273346	+	0.273346i	−0.830446	−	0.557099i	$-0.811914\pi$
$47$	−12.8473	+	12.8473i	−0.273346	+	0.273346i	0.557099	+	0.830446i	$0.311914\pi$
$48$	−3.01519	+	0.215651i	−0.0628165	+	0.00449272i
$49$	16.3814	+	25.4900i	0.334315	+	0.520205i
$50$	33.6361	+	10.8910i	0.672722	+	0.217820i
$51$	−2.77779	−	6.08252i	−0.0544665	−	0.119265i
$52$	14.6141	+	19.5221i	0.281040	+	0.375426i
$53$	−29.2815	−	15.9889i	−0.552481	−	0.301677i	0.178652	−	0.983912i	$-0.442826\pi$
$53$	−29.2815	−	15.9889i	−0.552481	−	0.301677i	−0.731133	+	0.682235i	$0.761008\pi$
$54$	−10.0706	+	15.6702i	−0.186493	+	0.290189i
$55$	−56.3917	−	15.2231i	−1.02530	−	0.276784i
$56$	−11.7356	−	3.44590i	−0.209565	−	0.0615339i
$57$	−10.7781	−	0.770865i	−0.189089	−	0.0135239i
$58$	−4.18167	+	58.4674i	−0.0720978	+	1.00806i
$59$	−9.47174	+	32.2578i	−0.160538	+	0.546742i	0.839457	+	0.543427i	$0.182873\pi$
$59$	−9.47174	+	32.2578i	−0.160538	+	0.546742i	−0.999995	+	0.00331521i	$0.998945\pi$
$60$	6.55180	−	3.76638i	0.109197	−	0.0627730i
$61$	76.2827	+	49.0239i	1.25054	+	0.803670i	0.986960	−	0.160968i	$-0.0514617\pi$
$61$	76.2827	+	49.0239i	1.25054	+	0.803670i	0.263576	+	0.964639i	$0.415098\pi$
$62$	4.94654	−	9.05891i	0.0797829	−	0.146112i
$63$	−29.1792	+	21.8433i	−0.463163	+	0.346719i
$64$	−7.27706	+	3.32332i	−0.113704	+	0.0519269i
$65$	−54.1359	−	28.0372i	−0.832861	−	0.431342i
$66$	−10.5033	+	6.75004i	−0.159140	+	0.102273i
$67$	−6.62378	−	92.6125i	−0.0988623	−	1.38228i	−0.768624	−	0.639700i	$-0.779058\pi$
$67$	−6.62378	−	92.6125i	−0.0988623	−	1.38228i	0.669762	−	0.742576i	$-0.266396\pi$
$68$	−12.5133	−	12.5133i	−0.184018	−	0.184018i
$69$	−3.01603	+	17.1180i	−0.0437106	+	0.248086i
$70$	30.1638	−	5.01434i	0.430911	−	0.0716334i
$71$	59.9435	−	69.1785i	0.844275	−	0.974345i	−0.155634	−	0.987815i	$-0.549742\pi$
$71$	59.9435	−	69.1785i	0.844275	−	0.974345i	0.999909	+	0.0134696i	$0.00428763\pi$
$72$	−5.06766	+	23.2957i	−0.0703841	+	0.323551i
$73$	17.0176	−	22.7329i	0.233118	−	0.311410i	−0.668694	−	0.743538i	$-0.733146\pi$
$73$	17.0176	−	22.7329i	0.233118	−	0.311410i	0.901812	+	0.432128i	$0.142237\pi$
$74$	−37.5741	+	17.1595i	−0.507758	+	0.231885i
$75$	−10.6481	+	15.6066i	−0.141975	+	0.208088i
$76$	−27.4384	+	8.05665i	−0.361032	+	0.106009i
$77$	−49.3628	+	10.7382i	−0.641075	+	0.139457i
$78$	−12.2098	+	4.55401i	−0.156536	+	0.0583848i
$79$	−18.7850	+	63.9759i	−0.237785	+	0.809821i	0.750978	+	0.660327i	$0.229583\pi$
$79$	−18.7850	+	63.9759i	−0.237785	+	0.809821i	−0.988763	+	0.149494i	$0.952236\pi$
$80$	12.7626	−	15.3986i	0.159533	−	0.192482i
$81$	43.1593	+	49.8084i	0.532830	+	0.614919i
$82$	17.2665	−	9.42822i	0.210567	−	0.114978i
$83$	−115.056	+	42.9136i	−1.38621	+	0.517031i	−0.928256	−	0.371942i	$-0.878692\pi$
$83$	−115.056	+	42.9136i	−1.38621	+	0.517031i	−0.457959	+	0.888974i	$0.651419\pi$
$84$	3.53364	−	5.49844i	0.0420671	−	0.0654577i
$85$	41.7807	+	14.5479i	0.491537	+	0.171152i
$86$	14.1655	−	98.5231i	0.164715	−	1.14562i
$87$	−29.3485	−	10.9464i	−0.337339	−	0.125821i
$88$	−19.8013	+	26.4514i	−0.225014	+	0.300584i
$89$	−47.4284	−	73.8000i	−0.532903	−	0.829214i	0.465538	−	0.885028i	$-0.345861\pi$
$89$	−47.4284	−	73.8000i	−0.532903	−	0.829214i	−0.998441	+	0.0558141i	$0.982225\pi$
$90$	−13.9432	−	57.9473i	−0.154925	−	0.643859i
$91$	−52.7271			−0.579419
$92$	8.35291	+	45.2353i	0.0907925	+	0.491688i
$93$	3.90008	+	3.90008i	0.0419363	+	0.0419363i
$94$	−19.4187	−	16.8264i	−0.206581	−	0.179004i
$95$	52.9904	−	47.9909i	0.557794	−	0.505167i
$96$	−0.608398	−	4.23150i	−0.00633748	−	0.0440781i
$97$	56.6933	+	21.1455i	0.584467	+	0.217995i	0.624265	−	0.781213i	$-0.285399\pi$
$97$	56.6933	+	21.1455i	0.584467	+	0.217995i	−0.0397980	+	0.999208i	$0.512671\pi$
$98$	−34.3038	+	25.6795i	−0.350039	+	0.262036i
$99$	27.7413	+	94.4782i	0.280215	+	0.954325i
$100$	−11.9695	+	48.5462i	−0.119695	+	0.485462i
$101$	−55.3999	+	121.309i	−0.548514	+	1.20108i	0.408959	+	0.912553i	$0.365892\pi$
$101$	−55.3999	+	121.309i	−0.548514	+	1.20108i	−0.957472	+	0.288525i	$0.906835\pi$
$102$	8.29982	−	4.53204i	0.0813708	−	0.0444318i
$103$	−2.23270	+	31.2172i	−0.0216767	+	0.303080i	0.975035	+	0.222051i	$0.0712751\pi$
$103$	−2.23270	+	31.2172i	−0.0216767	+	0.303080i	−0.996712	+	0.0810288i	$0.974179\pi$
$104$	−26.0637	+	22.5844i	−0.250613	+	0.217157i
$105$	−1.97019	+	16.2208i	−0.0187637	+	0.154484i
$106$	19.5999	−	42.9179i	0.184905	−	0.404886i
$107$	0.342967	−	0.0746079i	0.00320530	−	0.000697270i	−0.210962	−	0.977494i	$-0.567660\pi$
$107$	0.342967	−	0.0746079i	0.00320530	−	0.000697270i	0.214168	+	0.976797i	$0.431296\pi$
$108$	−23.1205	−	12.6248i	−0.214079	−	0.116896i
$109$	178.813	+	25.7094i	1.64048	+	0.235866i	0.899899	−	0.436099i	$-0.143640\pi$
$109$	178.813	+	25.7094i	1.64048	+	0.235866i	0.740583	+	0.671965i	$0.234549\pi$
$110$	15.7846	−	81.0825i	0.143496	−	0.737114i
$111$	−3.14138	−	21.8488i	−0.0283007	−	0.196836i
$112$	3.67682	−	16.9021i	0.0328288	−	0.150911i
$113$	34.8019	−	2.48908i	0.307981	−	0.0220272i	0.0835066	−	0.996507i	$-0.473388\pi$
$113$	34.8019	−	2.48908i	0.307981	−	0.0220272i	0.224474	+	0.974480i	$0.427933\pi$
$114$		−	15.2815i		−	0.134048i
$115$	−68.0234	−	92.7244i	−0.591508	−	0.806299i
$116$	−82.8966			−0.714626
$117$	7.33182	+	102.512i	0.0626651	+	0.876173i
$118$	−46.4587	−	10.1065i	−0.393718	−	0.0856481i
$119$	37.8732	−	5.44535i	0.318262	−	0.0457592i
$120$	5.97389	+	8.86206i	0.0497825	+	0.0738505i
$121$	−2.20170	+	15.3132i	−0.0181959	+	0.126555i
$122$	−61.4575	+	112.551i	−0.503750	+	0.922550i
$123$	2.23465	+	10.2725i	0.0181679	+	0.0835163i
$124$	13.2776	+	6.06370i	0.107078	+	0.0489008i
$125$	−25.8854	−	122.290i	−0.207083	−	0.978323i
$126$	−33.7563	−	38.9568i	−0.267907	−	0.309181i
$127$	23.4751	+	1.67897i	0.184843	+	0.0132202i	0.163454	−	0.986551i	$-0.447737\pi$
$127$	23.4751	+	1.67897i	0.184843	+	0.0132202i	0.0213893	+	0.999771i	$0.493191\pi$
$128$	−5.42208	−	9.92980i	−0.0423600	−	0.0775766i
$129$	48.3832	+	22.0959i	0.375064	+	0.171286i
$130$	34.0879	−	79.1934i	0.262214	−	0.609180i
$131$	39.9328	−	11.7253i	0.304831	−	0.0895063i	−0.125740	−	0.992063i	$-0.540131\pi$
$131$	39.9328	−	11.7253i	0.304831	−	0.0895063i	0.430571	+	0.902557i	$0.358312\pi$
$132$	−10.5813	−	14.1350i	−0.0801616	−	0.107083i
$133$	21.6078	−	57.9327i	0.162465	−	0.435584i
$134$	129.972	−	18.6871i	0.969939	−	0.139456i
$135$	65.7765	+	3.25654i	0.487233	+	0.0241225i
$136$	16.3889	−	18.9138i	0.120506	−	0.139072i
$137$	−106.199	+	106.199i	−0.775175	+	0.775175i	−0.979006	−	0.203831i	$-0.934661\pi$
$137$	−106.199	+	106.199i	−0.775175	+	0.775175i	0.203831	+	0.979006i	$0.434661\pi$
$138$	−24.4511	−	2.52744i	−0.177182	−	0.0183148i
$139$		−	40.4953i		−	0.291333i	−0.989334	−	0.145667i	$-0.953467\pi$
$139$		−	40.4953i		−	0.291333i	0.989334	−	0.145667i	$-0.0465327\pi$
$140$	10.1165	+	42.0435i	0.0722605	+	0.300310i
$141$	11.5509	−	7.42331i	0.0819213	−	0.0526476i
$142$	103.632	+	77.5776i	0.729800	+	0.546321i
$143$	−49.7778	+	133.460i	−0.348097	+	0.933284i
$144$	−33.3724	−	4.79822i	−0.231752	−	0.0333210i
$145$	186.580	−	90.2045i	1.28676	−	0.622100i
$146$	33.7842	+	21.7118i	0.231398	+	0.148711i
$147$	−8.00219	−	21.4547i	−0.0544366	−	0.145950i
$148$	−27.9962	−	51.2712i	−0.189163	−	0.346427i
$149$	142.152	−	123.176i	0.954041	−	0.826681i	−0.0309086	−	0.999522i	$-0.509840\pi$
$149$	142.152	−	123.176i	0.954041	−	0.826681i	0.984950	+	0.172841i	$0.0552946\pi$
$150$	−23.0891	−	13.4458i	−0.153927	−	0.0896388i
$151$	264.918	+	77.7871i	1.75443	+	0.515146i	0.991359	−	0.131173i	$-0.0418744\pi$
$151$	264.918	+	77.7871i	1.75443	+	0.515146i	0.763067	+	0.646319i	$0.223693\pi$
$152$	−14.1330	−	37.8921i	−0.0929804	−	0.249290i
$153$	−15.8532	−	72.8761i	−0.103616	−	0.476314i
$154$	−20.1276	−	68.5483i	−0.130699	−	0.445119i
$155$	−36.4830	+	0.800239i	−0.235374	+	0.00516283i
$156$	−7.65576	−	16.7638i	−0.0490754	−	0.107460i
$157$	99.6643	+	74.6078i	0.634804	+	0.475209i	0.867564	−	0.497326i	$-0.165685\pi$
$157$	99.6643	+	74.6078i	0.634804	+	0.475209i	−0.232759	+	0.972534i	$0.574775\pi$
$158$	−92.1402	−	20.0439i	−0.583166	−	0.126860i
$159$	19.0545	+	16.5108i	0.119840	+	0.103842i
$160$	23.0090	+	16.4495i	0.143806	+	0.102809i
$161$	−89.1213	−	44.1551i	−0.553548	−	0.274255i
$162$	−65.9060	+	65.9060i	−0.406827	+	0.406827i
$163$	239.000	−	17.0936i	1.46626	−	0.104869i	0.684755	−	0.728773i	$-0.259909\pi$
$163$	239.000	−	17.0936i	1.46626	−	0.104869i	0.781501	+	0.623904i	$0.214454\pi$
$164$	15.0415	+	23.4051i	0.0917167	+	0.142714i
$165$	39.1971	+	20.3003i	0.237558	+	0.123032i
$166$	−72.1422	−	157.969i	−0.434592	−	0.951623i
$167$	−13.7455	−	18.3618i	−0.0823083	−	0.109951i	0.757497	−	0.652838i	$-0.226422\pi$
$167$	−13.7455	−	18.3618i	−0.0823083	−	0.109951i	−0.839806	+	0.542887i	$0.817331\pi$
$168$	8.11267	+	4.42985i	0.0482897	+	0.0263682i
$169$	10.9905	−	17.1015i	0.0650323	−	0.101192i
$170$	−16.3063	+	60.4040i	−0.0959191	+	0.355318i
$171$	−115.638	−	33.9543i	−0.676244	−	0.198563i
$172$	140.407	+	10.0421i	0.816319	+	0.0583843i
$173$	6.26285	−	87.5660i	0.0362014	−	0.506162i	−0.946711	−	0.322086i	$-0.895616\pi$
$173$	6.26285	−	87.5660i	0.0362014	−	0.506162i	0.982912	−	0.184076i	$-0.0589294\pi$
$174$	12.4802	−	42.5037i	0.0717253	−	0.244274i
$175$	−68.5196	−	83.6214i	−0.391541	−	0.477836i
$176$	−39.3103	−	25.2632i	−0.223354	−	0.143541i
$177$	12.1763	−	22.2993i	0.0687928	−	0.125985i
$178$	99.3181	−	74.3486i	0.557967	−	0.417689i
$179$	−120.750	+	55.1445i	−0.674578	+	0.308070i	−0.723091	−	0.690753i	$-0.757279\pi$
$179$	−120.750	+	55.1445i	−0.674578	+	0.308070i	0.0485125	+	0.998823i	$0.484552\pi$
$180$	80.3343	−	25.5147i	0.446302	−	0.141748i
$181$	98.8388	−	63.5198i	0.546071	−	0.350938i	−0.238338	−	0.971182i	$-0.576603\pi$
$181$	98.8388	−	63.5198i	0.546071	−	0.350938i	0.784409	+	0.620244i	$0.212966\pi$
$182$	−5.31958	−	74.3774i	−0.0292284	−	0.408667i
$183$	−48.4559	−	48.4559i	−0.264786	−	0.264786i
$184$	−62.9666	+	16.3464i	−0.342210	+	0.0888393i
$185$	118.804	+	84.9348i	0.642182	+	0.459107i
$186$	−5.10801	+	5.89496i	−0.0274624	+	0.0316933i
$187$	21.9719	−	101.003i	0.117497	−	0.540123i
$188$	21.7763	−	29.0897i	0.115831	−	0.154733i
$189$	51.8106	−	23.6611i	0.274130	−	0.125191i
$190$	73.0426	+	69.9070i	0.384435	+	0.367932i
$191$	−287.416	+	84.3931i	−1.50480	+	0.441848i	−0.927229	−	0.374494i	$-0.877816\pi$
$191$	−287.416	+	84.3931i	−1.50480	+	0.441848i	−0.577568	+	0.816342i	$0.695998\pi$
$192$	5.90762	−	1.28512i	0.0307689	−	0.00669335i
$193$	−24.7872	+	9.24514i	−0.128431	+	0.0479023i	−0.412858	−	0.910795i	$-0.635469\pi$
$193$	−24.7872	+	9.24514i	−0.128431	+	0.0479023i	0.284427	+	0.958698i	$0.408197\pi$
$194$	−24.1083	+	82.1054i	−0.124270	+	0.423224i
$195$	35.4729	+	29.4006i	0.181912	+	0.150772i
$196$	−39.6846	−	45.7985i	−0.202473	−	0.233666i
$197$	−96.8969	+	52.9097i	−0.491863	+	0.268577i	−0.705981	−	0.708230i	$-0.749494\pi$
$197$	−96.8969	+	52.9097i	−0.491863	+	0.268577i	0.214119	+	0.976808i	$0.431312\pi$
$198$	−130.473	+	48.6639i	−0.658955	+	0.245777i
$199$	161.161	−	250.771i	0.809852	−	1.26015i	−0.152488	−	0.988305i	$-0.548728\pi$
$199$	161.161	−	250.771i	0.809852	−	1.26015i	0.962340	−	0.271849i	$-0.0876353\pi$
$200$	−69.6873	−	11.9865i	−0.348437	−	0.0599326i
$201$	−9.98597	+	69.4540i	−0.0496815	+	0.345542i
$202$	−176.709	−	65.9090i	−0.874796	−	0.326282i
$203$	107.413	−	143.486i	0.529126	−	0.706830i
$204$	7.23031	+	11.2506i	0.0354427	+	0.0551499i
$205$	−59.3233	−	36.3117i	−0.289382	−	0.177130i
$206$	−44.2606			−0.214857
$207$	−73.4540	+	179.410i	−0.354850	+	0.866714i
$208$	−34.4873	−	34.4873i	−0.165804	−	0.165804i
$209$	−126.237	−	109.385i	−0.604002	−	0.523371i
$210$	−23.0800	−	1.14267i	−0.109905	−	0.00544130i
$211$	15.8278	+	110.085i	0.0750131	+	0.521728i	0.992335	+	0.123580i	$0.0394377\pi$
$211$	15.8278	+	110.085i	0.0750131	+	0.521728i	−0.917321	+	0.398147i	$0.869653\pi$
$212$	62.5178	+	23.3179i	0.294895	+	0.109990i
$213$	−55.3783	+	41.4557i	−0.259992	+	0.194628i
$214$	0.139844	+	0.476266i	0.000653478	+	0.00222554i
$215$	−326.949	+	130.182i	−1.52069	+	0.605499i
$216$	15.4760	−	33.8878i	0.0716483	−	0.156888i
$217$	−27.7001	+	15.1254i	−0.127650	+	0.0697023i
$218$	−18.2257	+	254.829i	−0.0836041	+	1.16894i
$219$	−16.2185	+	14.0534i	−0.0740572	+	0.0641710i
$220$	115.968	+	14.0856i	0.527129	+	0.0640254i
$221$	44.8179	−	98.1374i	0.202796	−	0.444061i
$222$	30.5032	−	6.63556i	0.137402	−	0.0298899i
$223$	−110.358	−	60.2599i	−0.494878	−	0.270224i	0.212370	−	0.977189i	$-0.431882\pi$
$223$	−110.358	−	60.2599i	−0.494878	−	0.270224i	−0.707248	+	0.706965i	$0.750064\pi$
$224$	24.2132	+	3.48133i	0.108095	+	0.0155417i
$225$	−153.049	+	144.844i	−0.680219	+	0.643750i
$226$	7.02224	+	48.8407i	0.0310719	+	0.216109i
$227$	76.0488	−	349.591i	0.335017	−	1.54005i	−0.434055	−	0.900886i	$-0.642918\pi$
$227$	76.0488	−	349.591i	0.335017	−	1.54005i	0.769072	−	0.639162i	$-0.220719\pi$
$228$	21.5562	−	1.54173i	0.0945447	−	0.00676197i
$229$			440.896i			1.92531i	0.270730	+	0.962655i	$0.412735\pi$
$229$			440.896i			1.92531i	−0.270730	+	0.962655i	$0.587265\pi$
$230$	123.935	−	105.309i	0.538849	−	0.457867i
$231$	38.1771			0.165269
$232$	−8.36334	−	116.935i	−0.0360489	−	0.504029i
$233$	321.636	+	69.9676i	1.38041	+	0.300290i	0.840673	−	0.541543i	$-0.182159\pi$
$233$	321.636	+	69.9676i	1.38041	+	0.300290i	0.539738	+	0.841833i	$0.318523\pi$
$234$	−143.865	+	20.6847i	−0.614808	+	0.0883961i
$235$	−17.3590	+	89.1700i	−0.0738682	+	0.379447i
$236$	9.56914	−	66.5548i	0.0405472	−	0.282012i
$237$	24.1489	−	44.2255i	0.101894	−	0.186605i
$238$	11.5022	+	52.8750i	0.0483288	+	0.222164i
$239$	−217.944	−	99.5318i	−0.911901	−	0.416451i	−0.0964899	−	0.995334i	$-0.530762\pi$
$239$	−217.944	−	99.5318i	−0.911901	−	0.416451i	−0.815411	+	0.578883i	$0.803489\pi$
$240$	−11.8982	+	9.32092i	−0.0495759	+	0.0388372i
$241$	171.400	+	197.806i	0.711204	+	0.820773i	0.990220	−	0.139513i	$-0.0445538\pi$
$241$	171.400	+	197.806i	0.711204	+	0.820773i	−0.279016	+	0.960286i	$0.590008\pi$
$242$	−21.8230	−	1.56081i	−0.0901779	−	0.00644965i
$243$	−80.6813	−	147.757i	−0.332022	−	0.608052i
$244$	−164.966	−	75.3375i	−0.676091	−	0.308760i
$245$	139.156	+	59.8983i	0.567986	+	0.244483i
$246$	−14.2650	+	4.18859i	−0.0579880	+	0.0170268i
$247$	−104.479	−	139.568i	−0.422992	−	0.565051i
$248$	−7.21395	+	19.3413i	−0.0290885	+	0.0779893i
$249$	91.8569	−	13.2070i	0.368903	−	0.0530403i
$250$	169.893	−	48.8520i	0.679570	−	0.195408i
$251$	49.4406	−	57.0574i	0.196974	−	0.227321i	−0.648667	−	0.761073i	$-0.724673\pi$
$251$	49.4406	−	57.0574i	0.196974	−	0.227321i	0.845641	+	0.533752i	$0.179218\pi$
$252$	51.5472	−	51.5472i	0.204552	−	0.204552i
$253$	−195.899	+	183.893i	−0.774304	+	0.726849i
$254$			33.2836i			0.131038i
$255$	−28.5161	−	17.4546i	−0.111828	−	0.0684495i
$256$	13.4601	−	8.65025i	0.0525783	−	0.0337901i
$257$	409.338	+	306.426i	1.59275	+	1.19232i	0.857423	+	0.514612i	$0.172064\pi$
$257$	409.338	+	306.426i	1.59275	+	1.19232i	0.735331	+	0.677709i	$0.237027\pi$
$258$	−26.2873	+	70.4791i	−0.101889	+	0.273175i
$259$	125.021	+	17.9754i	0.482708	+	0.0694030i
$260$	115.150	+	40.0950i	0.442885	+	0.154211i
$261$	−293.903	−	188.880i	−1.12606	−	0.723678i
$262$	20.5686	+	55.1467i	0.0785063	+	0.210483i
$263$	−4.15260	−	7.60493i	−0.0157894	−	0.0289161i	0.869665	−	0.493642i	$-0.164335\pi$
$263$	−4.15260	−	7.60493i	−0.0157894	−	0.0289161i	−0.885455	+	0.464726i	$0.846153\pi$
$264$	18.8714	−	16.3522i	0.0714828	−	0.0619402i
$265$	−166.086	+	15.5461i	−0.626740	+	0.0586646i
$266$	83.9005	+	24.6354i	0.315415	+	0.0926143i
$267$	23.1683	+	62.1167i	0.0867728	+	0.232647i
$268$	39.4730	+	181.454i	0.147287	+	0.677069i
$269$	−79.3668	−	270.299i	−0.295044	−	1.00483i	−0.964961	−	0.262392i	$-0.915489\pi$
$269$	−79.3668	−	270.299i	−0.295044	−	1.00483i	0.669918	−	0.742435i	$-0.266329\pi$
$270$	2.04240	+	93.1135i	0.00756446	+	0.344865i
$271$	52.4503	+	114.850i	0.193544	+	0.423802i	0.981378	−	0.192085i	$-0.0615250\pi$
$271$	52.4503	+	114.850i	0.193544	+	0.423802i	−0.787834	+	0.615887i	$0.788798\pi$
$272$	28.3334	+	21.2101i	0.104167	+	0.0779784i
$273$	38.9365	+	8.47011i	0.142624	+	0.0310260i
$274$	−160.520	−	139.091i	−0.585838	−	0.507632i
$275$	−276.344	+	94.4885i	−1.00489	+	0.343594i
$276$	1.09839	−	34.7459i	0.00397967	−	0.125891i
$277$	−92.5298	+	92.5298i	−0.334043	+	0.334043i	−0.854120	−	0.520077i	$-0.825903\pi$
$277$	−92.5298	+	92.5298i	−0.334043	+	0.334043i	0.520077	+	0.854120i	$0.325903\pi$
$278$	57.1231	−	4.08553i	0.205479	−	0.0146961i
$279$	33.2586	+	51.7514i	0.119207	+	0.185489i
$280$	−58.2863	+	18.5121i	−0.208165	+	0.0661147i
$281$	75.9542	+	166.316i	0.270300	+	0.591873i	0.995296	−	0.0968790i	$-0.0308860\pi$
$281$	75.9542	+	166.316i	0.270300	+	0.591873i	−0.724997	+	0.688752i	$0.758159\pi$
$282$	11.6368	+	15.5449i	0.0412651	+	0.0551237i
$283$	138.744	+	75.7601i	0.490263	+	0.267704i	0.705309	−	0.708900i	$-0.250808\pi$
$283$	138.744	+	75.7601i	0.490263	+	0.267704i	−0.215046	+	0.976604i	$0.568990\pi$
$284$	−98.9765	+	154.010i	−0.348509	+	0.542290i
$285$	−46.8402	+	26.9266i	−0.164351	+	0.0944792i
$286$	−193.281	−	56.7526i	−0.675809	−	0.198435i
$287$	−60.0020	−	4.29143i	−0.209066	−	0.0149527i
$288$	3.40152	−	47.5595i	0.0118108	−	0.165137i
$289$	59.3637	−	202.174i	0.205411	−	0.699564i
$290$	146.067	+	254.091i	0.503680	+	0.876177i
$291$	−38.4684	−	24.7222i	−0.132194	−	0.0849559i
$292$	−27.2184	+	49.8467i	−0.0932136	+	0.170708i
$293$	−300.454	+	224.917i	−1.02544	+	0.767636i	−0.972957	−	0.230986i	$-0.925805\pi$
$293$	−300.454	+	224.917i	−1.02544	+	0.767636i	−0.0524843	+	0.998622i	$0.516714\pi$
$294$	29.4569	−	13.4525i	0.100193	−	0.0457568i
$295$	50.8843	+	160.212i	0.172489	+	0.543090i
$296$	69.4991	−	44.6644i	0.234794	−	0.150893i
$297$	−10.9769	−	153.477i	−0.0369593	−	0.516758i
$298$	188.094	+	188.094i	0.631189	+	0.631189i
$299$	−240.595	+	144.088i	−0.804665	+	0.481899i
$300$	16.6374	−	33.9263i	0.0554579	−	0.113088i
$301$	−199.313	+	230.019i	−0.662169	+	0.764184i
$302$	−82.9999	+	381.544i	−0.274834	+	1.26339i
$303$	60.3973	−	80.6813i	0.199331	−	0.266275i
$304$	52.0251	−	23.7591i	0.171135	−	0.0781549i
$305$	453.278	−	9.94245i	1.48616	−	0.0325982i
$306$	101.200	−	29.7151i	0.330720	−	0.0971082i
$307$	−535.502	+	116.491i	−1.74430	+	0.379450i	−0.968008	−	0.250918i	$-0.919268\pi$
$307$	−535.502	+	116.491i	−1.74430	+	0.379450i	−0.776296	+	0.630368i	$0.782904\pi$
$308$	94.6643	−	35.3080i	0.307352	−	0.114636i
$309$	6.66349	−	22.6938i	0.0215647	−	0.0734426i
$310$	−4.80956	−	51.3826i	−0.0155147	−	0.165750i
$311$	241.485	+	278.689i	0.776480	+	0.896106i	0.996850	−	0.0793108i	$-0.0252719\pi$
$311$	241.485	+	278.689i	0.776480	+	0.896106i	−0.220370	+	0.975416i	$0.570726\pi$
$312$	22.8748	−	12.4906i	0.0733166	−	0.0400339i
$313$	387.795	−	144.640i	1.23896	−	0.462108i	0.357299	−	0.933990i	$-0.383698\pi$
$313$	387.795	−	144.640i	1.23896	−	0.462108i	0.881662	+	0.471882i	$0.156425\pi$
$314$	−95.1875	+	148.115i	−0.303145	+	0.471702i
$315$	−59.9289	+	172.112i	−0.190250	+	0.546387i
$316$	18.9782	−	131.996i	0.0600575	−	0.417709i
$317$	−562.405	−	209.766i	−1.77415	−	0.661723i	−0.999572	−	0.0292421i	$-0.990691\pi$
$317$	−562.405	−	209.766i	−1.77415	−	0.661723i	−0.774576	−	0.632481i	$-0.782037\pi$
$318$	−21.3680	+	28.5443i	−0.0671949	+	0.0897618i
$319$	−261.779	−	407.337i	−0.820625	−	1.27692i
$320$	−20.8825	+	34.1163i	−0.0652578	+	0.106613i
$321$	−0.265250			−0.000826324
$322$	53.2943	−	130.170i	0.165510	−	0.404255i
$323$	89.4597	+	89.4597i	0.276965	+	0.276965i
$324$	−99.6169	−	86.3185i	−0.307459	−	0.266415i
$325$	−302.805	+	35.0572i	−0.931706	+	0.107868i
$326$	48.2248	+	335.411i	0.147929	+	1.02887i
$327$	−127.915	−	47.7097i	−0.391176	−	0.145901i
$328$	−31.4980	+	23.5791i	−0.0960304	+	0.0718874i
$329$	22.1352	+	75.3856i	0.0672802	+	0.229135i
$330$	−24.6813	+	57.3400i	−0.0747919	+	0.173757i
$331$	8.61484	−	18.8639i	0.0260267	−	0.0569905i	−0.896172	−	0.443706i	$-0.853663\pi$
$331$	8.61484	−	18.8639i	0.0260267	−	0.0569905i	0.922199	+	0.386716i	$0.126391\pi$
$332$	215.555	−	117.702i	0.649262	−	0.354524i
$333$	17.5633	−	245.567i	0.0527426	−	0.737438i
$334$	24.5146	−	21.2420i	0.0733970	−	0.0635989i
$335$	−286.295	−	365.457i	−0.854612	−	1.09092i
$336$	−5.43032	+	11.8907i	−0.0161617	+	0.0353891i
$337$	127.316	−	27.6958i	0.377791	−	0.0821834i	−0.0196602	−	0.999807i	$-0.506258\pi$
$337$	127.316	−	27.6958i	0.377791	−	0.0821834i	0.397451	+	0.917623i	$0.369895\pi$
$338$	25.2324	+	13.7779i	0.0746520	+	0.0407631i
$339$	−26.0994	−	3.75252i	−0.0769893	−	0.0110694i
$340$	−86.8516	−	16.9077i	−0.255446	−	0.0497285i
$341$	12.1338	+	84.3921i	0.0355829	+	0.247484i
$342$	36.2297	−	166.545i	0.105935	−	0.486974i
$343$	342.047	−	24.4637i	0.997222	−	0.0713227i
$344$			199.072i			0.578699i
$345$	35.3368	+	79.3999i	0.102425	+	0.230145i
$346$	124.153			0.358825
$347$	−12.2255	−	170.934i	−0.0352319	−	0.492606i	−0.984180	−	0.177173i	$-0.943305\pi$
$347$	−12.2255	−	170.934i	−0.0352319	−	0.492606i	0.948948	−	0.315433i	$-0.102150\pi$
$348$	61.2152	+	13.3166i	0.175906	+	0.0382660i
$349$	132.278	−	19.0187i	0.379020	−	0.0544948i	0.0498277	−	0.998758i	$-0.484133\pi$
$349$	132.278	−	19.0187i	0.379020	−	0.0544948i	0.329192	+	0.944263i	$0.393224\pi$
$350$	111.044	−	105.091i	0.317269	−	0.300260i
$351$	22.8558	−	158.965i	0.0651162	−	0.452893i
$352$	31.6706	−	58.0003i	0.0899732	−	0.164774i
$353$	−3.93589	−	18.0930i	−0.0111498	−	0.0512549i	0.971236	−	0.238120i	$-0.0765310\pi$
$353$	−3.93589	−	18.0930i	−0.0111498	−	0.0512549i	−0.982386	+	0.186865i	$0.940167\pi$
$354$	32.6841	+	14.9263i	0.0923279	+	0.0421647i
$355$	55.1847	−	454.342i	0.155450	−	1.27984i
$356$	114.897	+	132.598i	0.322744	+	0.372467i
$357$	−28.8423	−	2.06284i	−0.0807908	−	0.00577827i
$358$	−89.9696	−	164.767i	−0.251312	−	0.460243i
$359$	319.721	+	146.012i	0.890589	+	0.406718i	0.807530	−	0.589826i	$-0.200804\pi$
$359$	319.721	+	146.012i	0.890589	+	0.406718i	0.0830588	+	0.996545i	$0.473531\pi$
$360$	44.0962	+	110.746i	0.122489	+	0.307629i
$361$	−150.214	+	44.1069i	−0.416106	+	0.122180i
$362$	99.5735	+	133.015i	0.275065	+	0.367444i
$363$	4.08577	−	10.9544i	0.0112556	−	0.0301773i
$364$	104.381	−	15.0077i	0.286761	−	0.0412299i
$365$	7.02094	−	141.811i	0.0192355	−	0.388523i
$366$	63.4637	−	73.2410i	0.173398	−	0.200112i
$367$	407.468	−	407.468i	1.11027	−	1.11027i	0.117153	−	0.993114i	$-0.462623\pi$
$367$	407.468	−	407.468i	1.11027	−	1.11027i	0.993114	−	0.117153i	$-0.0373768\pi$
$368$	−29.4111	−	87.1722i	−0.0799214	−	0.236881i
$369$			117.253i			0.317759i
$370$	−107.824	+	176.155i	−0.291416	+	0.476094i
$371$	−121.368	+	77.9986i	−0.327138	+	0.210239i
$372$	−8.83084	−	6.61068i	−0.0237388	−	0.0177706i
$373$	245.466	−	658.119i	0.658085	−	1.76439i	0.0134410	−	0.999910i	$-0.495721\pi$
$373$	245.466	−	658.119i	0.658085	−	1.76439i	0.644644	−	0.764483i	$-0.277006\pi$
$374$	144.693	+	20.8037i	0.386879	+	0.0556248i
$375$	−0.529638	+	94.4639i	−0.00141237	+	0.251904i
$376$	43.2313	+	27.7831i	0.114977	+	0.0738911i
$377$	−176.613	−	473.518i	−0.468470	−	1.25602i
$378$	38.6037	+	70.6974i	0.102126	+	0.187030i
$379$	−345.202	+	299.119i	−0.910823	+	0.789232i	−0.978021	−	0.208507i	$-0.933139\pi$
$379$	−345.202	+	299.119i	−0.910823	+	0.789232i	0.0671982	+	0.997740i	$0.478594\pi$
$380$	−91.2424	+	110.087i	−0.240112	+	0.289704i
$381$	−17.0655	−	5.01089i	−0.0447914	−	0.0131519i
$382$	−148.043	−	396.918i	−0.387547	−	1.03905i
$383$	−61.4807	−	282.622i	−0.160524	−	0.737917i	−0.985074	−	0.172129i	$-0.944935\pi$
$383$	−61.4807	−	282.622i	−0.160524	−	0.737917i	0.824550	−	0.565789i	$-0.191428\pi$
$384$	2.40882	+	8.20369i	0.00627297	+	0.0213638i
$385$	−174.646	+	182.479i	−0.453626	+	0.473972i
$386$	−15.5420	−	34.0323i	−0.0402644	−	0.0881667i
$387$	474.919	+	355.520i	1.22718	+	0.918657i
$388$	−118.251	−	25.7239i	−0.304771	−	0.0662988i
$389$	−238.393	−	206.568i	−0.612835	−	0.531024i	0.292203	−	0.956356i	$-0.405612\pi$
$389$	−238.393	−	206.568i	−0.612835	−	0.531024i	−0.905037	+	0.425332i	$0.860157\pi$
$390$	−37.8939	+	53.0046i	−0.0971639	+	0.135909i
$391$	157.936	−	128.344i	0.403927	−	0.328245i
$392$	60.6001	−	60.6001i	0.154592	−	0.154592i
$393$	−31.3720	+	2.24377i	−0.0798271	+	0.00570934i
$394$	−84.4108	−	131.346i	−0.214241	−	0.333365i
$395$	100.917	+	317.743i	0.255487	+	0.804412i
$396$	−81.8091	−	179.137i	−0.206589	−	0.452366i
$397$	22.1057	+	29.5297i	0.0556818	+	0.0743822i	0.827518	−	0.561440i	$-0.189752\pi$
$397$	22.1057	+	29.5297i	0.0556818	+	0.0743822i	−0.771836	+	0.635822i	$0.780661\pi$
$398$	369.999	+	202.035i	0.929646	+	0.507625i
$399$	−25.2627	+	39.3095i	−0.0633150	+	0.0985200i
$400$	9.87763	−	99.5110i	0.0246941	−	0.248777i
$401$	0.133320	+	0.0391464i	0.000332470	+	9.76219e-5i	0.281899	−	0.959444i	$-0.409036\pi$
$401$	0.133320	+	0.0391464i	0.000332470	+	9.76219e-5i	−0.281566	+	0.959542i	$0.590854\pi$
$402$	−98.9800	−	7.07919i	−0.246219	−	0.0176099i
$403$	−6.34844	+	88.7628i	−0.0157530	+	0.220255i
$404$	75.1439	−	255.917i	0.186000	−	0.633457i
$405$	318.142	+	85.8834i	0.785535	+	0.212058i
$406$	213.240	+	137.041i	0.525222	+	0.337540i
$407$	163.527	−	299.477i	0.401785	−	0.735815i
$408$	−15.1407	+	11.3342i	−0.0371096	+	0.0277799i
$409$	−114.154	+	52.1324i	−0.279105	+	0.127463i	−0.550050	−	0.835132i	$-0.685391\pi$
$409$	−114.154	+	52.1324i	−0.279105	+	0.127463i	0.270945	+	0.962595i	$0.412664\pi$
$410$	45.2366	−	87.3455i	0.110333	−	0.213038i
$411$	95.4828	−	61.3630i	0.232318	−	0.149302i
$412$	−4.46540	−	62.4344i	−0.0108383	−	0.151540i
$413$	102.801	+	102.801i	0.248913	+	0.248913i
$414$	−260.488	−	85.5145i	−0.629198	−	0.206557i
$415$	−357.084	+	499.476i	−0.860443	+	1.20356i
$416$	45.1687	−	52.1275i	0.108579	−	0.125306i
$417$	−6.50519	+	29.9039i	−0.0156000	+	0.0717119i
$418$	141.563	−	189.106i	0.338668	−	0.452407i
$419$	388.955	−	177.630i	0.928294	−	0.423938i	0.106881	−	0.994272i	$-0.465914\pi$
$419$	388.955	−	177.630i	0.928294	−	0.423938i	0.821413	+	0.570334i	$0.193186\pi$
$420$	−0.716650	−	32.6722i	−0.00170631	−	0.0777910i
$421$	−609.428	+	178.944i	−1.44757	+	0.425045i	−0.908738	−	0.417367i	$-0.862953\pi$
$421$	−609.428	+	178.944i	−1.44757	+	0.425045i	−0.538834	+	0.842412i	$0.681135\pi$
$422$	−153.690	+	33.4331i	−0.364193	+	0.0792254i
$423$	143.487	−	53.5179i	0.339213	−	0.126520i
$424$	−26.5852	+	90.5408i	−0.0627009	+	0.213540i
$425$	213.880	−	56.4530i	0.503248	−	0.132831i
$426$	−64.0649	−	73.9348i	−0.150387	−	0.173556i
$427$	344.156	−	187.923i	0.805985	−	0.440101i
$428$	−0.657717	+	0.245316i	−0.00153672	+	0.000573167i
$429$	58.1976	−	90.5572i	0.135659	−	0.211089i
$430$	−216.622	−	448.064i	−0.503772	−	1.04201i
$431$	0.885767	−	6.16064i	0.00205514	−	0.0142938i	−0.988768	−	0.149458i	$-0.952247\pi$
$431$	0.885767	−	6.16064i	0.00205514	−	0.0142938i	0.990823	+	0.135164i	$0.0431562\pi$
$432$	49.3638	+	18.4117i	0.114268	+	0.0426198i
$433$	263.144	−	351.519i	0.607722	−	0.811822i	−0.386141	−	0.922440i	$-0.626192\pi$
$433$	263.144	−	351.519i	0.607722	−	0.811822i	0.993863	+	0.110618i	$0.0352830\pi$
$434$	−24.1307	−	37.5481i	−0.0556006	−	0.0865163i
$435$	−152.271	+	36.6394i	−0.350049	+	0.0842285i
$436$	−361.303			−0.828676
$437$	−59.7166	−	323.396i	−0.136651	−	0.740036i
$438$	−21.4602	−	21.4602i	−0.0489959	−	0.0489959i
$439$	320.223	+	277.475i	0.729438	+	0.632062i	0.938276	−	0.345889i	$-0.112423\pi$
$439$	320.223	+	277.475i	0.729438	+	0.632062i	−0.208838	+	0.977950i	$0.566968\pi$
$440$	−8.16937	+	165.007i	−0.0185668	+	0.375016i
$441$	−36.3466	−	252.796i	−0.0824185	−	0.573234i
$442$	142.955	+	53.3196i	0.323428	+	0.120632i
$443$	32.9524	−	24.6678i	0.0743846	−	0.0556836i	−0.561438	−	0.827519i	$-0.689752\pi$
$443$	32.9524	−	24.6678i	0.0743846	−	0.0556836i	0.635823	+	0.771835i	$0.280661\pi$
$444$	12.4376	+	42.3586i	0.0280127	+	0.0954023i
$445$	−402.893	−	173.421i	−0.905378	−	0.389709i
$446$	73.8694	−	161.751i	0.165626	−	0.362671i
$447$	−124.760	+	68.1239i	−0.279104	+	0.152402i
$448$	−2.46796	+	34.5066i	−0.00550884	+	0.0770237i
$449$	−70.8240	+	61.3693i	−0.157737	+	0.136680i	−0.730154	−	0.683283i	$-0.760552\pi$
$449$	−70.8240	+	61.3693i	−0.157737	+	0.136680i	0.572417	+	0.819963i	$0.306006\pi$
$450$	−219.759	−	201.280i	−0.488354	−	0.447288i
$451$	−67.5080	+	147.822i	−0.149685	+	0.327765i
$452$	−68.1868	+	14.8331i	−0.150856	+	0.0328167i
$453$	−183.134	−	99.9987i	−0.404269	−	0.220748i
$454$	500.809	+	72.0055i	1.10310	+	0.158602i
$455$	−218.605	+	147.361i	−0.480451	+	0.323871i
$456$	4.34956	+	30.2519i	0.00953851	+	0.0663418i
$457$	1.12076	−	5.15203i	0.00245242	−	0.0112736i	−0.975904	−	0.218199i	$-0.929982\pi$
$457$	1.12076	−	5.15203i	0.00245242	−	0.0112736i	0.978357	+	0.206925i	$0.0663456\pi$
$458$	−621.933	+	44.4815i	−1.35793	+	0.0971212i
$459$			116.543i			0.253907i
$460$	161.054	+	164.200i	0.350118	+	0.356956i
$461$	−130.979			−0.284120			−0.142060	−	0.989858i	$-0.545373\pi$
$461$	−130.979			−0.284120			−0.142060	+	0.989858i	$0.545373\pi$
$462$	3.85164	+	53.8530i	0.00833688	+	0.116565i
$463$	−85.8087	−	18.6665i	−0.185332	−	0.0403165i	0.118941	−	0.992901i	$-0.462050\pi$
$463$	−85.8087	−	18.6665i	−0.185332	−	0.0403165i	−0.304273	+	0.952585i	$0.598414\pi$
$464$	164.106	−	23.5948i	0.353676	−	0.0508509i
$465$	27.0695	+	5.26971i	0.0582141	+	0.0113327i
$466$	−66.2476	+	460.762i	−0.142162	+	0.988760i
$467$	−53.5052	+	97.9874i	−0.114572	+	0.209823i	−0.928672	−	0.370901i	$-0.879049\pi$
$467$	−53.5052	+	97.9874i	−0.114572	+	0.209823i	0.814100	+	0.580724i	$0.197231\pi$
$468$	−43.6924	−	200.851i	−0.0933599	−	0.429168i
$469$	−365.228	−	166.794i	−0.778737	−	0.355637i
$470$	−127.535	−	15.4905i	−0.271352	−	0.0329586i
$471$	−61.6123	−	71.1044i	−0.130812	−	0.150965i
$472$	94.8483	+	6.78369i	0.200950	+	0.0143722i
$473$	394.046	+	721.641i	0.833078	+	1.52567i
$474$	64.8213	+	29.6029i	0.136754	+	0.0624534i
$475$	85.5723	−	347.066i	0.180152	−	0.730666i
$476$	−73.4255	+	21.5597i	−0.154255	+	0.0452935i
$477$	168.522	+	225.119i	0.353295	+	0.471947i
$478$	118.412	−	317.476i	0.247725	−	0.664176i
$479$	305.470	−	43.9199i	0.637724	−	0.0916908i	0.184134	−	0.982901i	$-0.441052\pi$
$479$	305.470	−	43.9199i	0.637724	−	0.0916908i	0.453590	+	0.891210i	$0.350143\pi$
$480$	−14.3486	−	15.8434i	−0.0298929	−	0.0330070i
$481$	233.222	−	269.153i	0.484870	−	0.559570i
$482$	−261.735	+	261.735i	−0.543019	+	0.543019i
$483$	58.7187	+	46.9229i	0.121571	+	0.0971489i
$484$		−	30.9413i		−	0.0639283i
$485$	294.146	−	70.7773i	0.606487	−	0.145933i
$486$	200.287	−	128.717i	0.412114	−	0.264849i
$487$	701.308	+	524.993i	1.44006	+	1.07801i	0.981955	+	0.189115i	$0.0605618\pi$
$487$	701.308	+	524.993i	1.44006	+	1.07801i	0.458103	+	0.888899i	$0.348529\pi$
$488$	89.6286	−	240.304i	0.183665	−	0.492425i
$489$	−179.236	−	25.7702i	−0.366536	−	0.0526999i
$490$	−70.4538	+	202.339i	−0.143783	+	0.412936i
$491$	259.092	+	166.508i	0.527681	+	0.339120i	0.777204	−	0.629249i	$-0.216637\pi$
$491$	259.092	+	166.508i	0.527681	+	0.339120i	−0.249523	+	0.968369i	$0.580274\pi$
$492$	−7.34766	−	19.6998i	−0.0149343	−	0.0400403i
$493$	175.761	+	321.883i	0.356514	+	0.652906i
$494$	186.335	−	161.460i	0.377196	−	0.326842i
$495$	379.062	+	314.173i	0.765781	+	0.634693i
$496$	−28.0109	−	8.22475i	−0.0564736	−	0.0165821i
$497$	−138.330	−	370.877i	−0.278330	−	0.746231i
$498$	27.8973	+	128.242i	0.0560187	+	0.257514i
$499$	140.165	+	477.357i	0.280891	+	0.956627i	0.972217	+	0.234083i	$0.0752088\pi$
$499$	140.165	+	477.357i	0.280891	+	0.956627i	−0.691326	+	0.722543i	$0.742973\pi$
$500$	86.0514	+	234.724i	0.172103	+	0.469447i
$501$	7.20074	+	15.7674i	0.0143727	+	0.0314719i
$502$	85.4738	+	63.9849i	0.170267	+	0.127460i
$503$	−297.616	−	64.7423i	−0.591681	−	0.128712i	−0.0932516	−	0.995643i	$-0.529726\pi$
$503$	−297.616	−	64.7423i	−0.591681	−	0.128712i	−0.498430	+	0.866930i	$0.666090\pi$
$504$	77.9136	+	67.5125i	0.154590	+	0.133953i
$505$	109.347	+	657.775i	0.216528	+	1.30252i
$506$	−279.165	−	257.784i	−0.551710	−	0.509455i
$507$	−10.8631	+	10.8631i	−0.0214263	+	0.0214263i
$508$	−46.9501	+	3.35794i	−0.0924215	+	0.00661012i
$509$	−410.298	−	638.437i	−0.806087	−	1.25430i	−0.963751	−	0.266803i	$-0.914033\pi$
$509$	−410.298	−	638.437i	−0.806087	−	1.25430i	0.157664	−	0.987493i	$-0.449604\pi$
$510$	21.7447	−	41.9860i	0.0426367	−	0.0823255i
$511$	−51.0121	−	111.701i	−0.0998281	−	0.218593i
$512$	13.5601	+	18.1142i	0.0264846	+	0.0353793i
$513$	165.293	+	90.2570i	0.322209	+	0.175940i
$514$	−390.951	+	608.331i	−0.760604	+	1.18352i
$515$	77.9890	+	135.666i	0.151435	+	0.263429i
$516$	−102.071	−	29.9706i	−0.197811	−	0.0580826i
$517$	211.708	+	15.1417i	0.409494	+	0.0292876i
$518$	−12.7430	+	178.170i	−0.0246003	+	0.343958i
$519$	−18.6915	+	63.6573i	−0.0360144	+	0.122654i
$520$	−44.9410	+	166.477i	−0.0864250	+	0.320148i
$521$	481.704	+	309.572i	0.924576	+	0.594189i	0.913982	−	0.405755i	$-0.132991\pi$
$521$	481.704	+	309.572i	0.924576	+	0.594189i	0.0105941	+	0.999944i	$0.496628\pi$
$522$	236.784	−	433.638i	0.453610	−	0.830725i
$523$	−151.875	+	113.692i	−0.290391	+	0.217384i	−0.734534	−	0.678572i	$-0.762599\pi$
$523$	−151.875	+	113.692i	−0.290391	+	0.217384i	0.444143	+	0.895956i	$0.353508\pi$
$524$	−75.7153	+	34.5780i	−0.144495	+	0.0659886i
$525$	37.1655	+	72.7574i	0.0707914	+	0.138586i
$526$	10.3086	−	6.62496i	0.0195982	−	0.0125950i
$527$	−4.60690	−	64.4129i	−0.00874174	−	0.122226i
$528$	24.9705	+	24.9705i	0.0472926	+	0.0472926i
$529$	−527.325	+	42.0622i	−0.996834	+	0.0795126i
$530$	−38.6858	−	232.714i	−0.0729920	−	0.439084i
$531$	185.572	−	214.161i	0.349476	−	0.403317i
$532$	−26.2863	+	120.836i	−0.0494104	+	0.227136i
$533$	−101.647	+	135.785i	−0.190708	+	0.254756i
$534$	−85.2851	+	38.9484i	−0.159710	+	0.0729371i
$535$	1.21342	−	1.26785i	0.00226807	−	0.00236980i
$536$	−251.979	+	73.9877i	−0.470110	+	0.138037i
$537$	98.0262	−	21.3243i	0.182544	−	0.0397100i
$538$	373.279	−	139.226i	0.693826	−	0.258784i
$539$	99.7241	−	339.629i	0.185017	−	0.630109i
$540$	−131.141	+	12.2752i	−0.242853	+	0.0227318i
$541$	−539.036	−	622.081i	−0.996370	−	1.14987i	−0.988701	−	0.149902i	$-0.952104\pi$
$541$	−539.036	−	622.081i	−0.996370	−	1.14987i	−0.00766951	−	0.999971i	$-0.502441\pi$
$542$	−156.717	+	85.5741i	−0.289146	+	0.157886i
$543$	−83.1916	+	31.0289i	−0.153207	+	0.0571434i
$544$	−27.0607	+	42.1073i	−0.0497439	+	0.0774031i
$545$	813.205	−	393.154i	1.49212	−	0.721383i
$546$	−8.01977	+	55.7787i	−0.0146882	+	0.102159i
$547$	−436.432	−	162.781i	−0.797864	−	0.297588i	−0.0827270	−	0.996572i	$-0.526363\pi$
$547$	−436.432	−	162.781i	−0.797864	−	0.297588i	−0.715137	+	0.698984i	$0.753636\pi$
$548$	180.009	−	240.463i	0.328483	−	0.438802i
$549$	−413.217	−	642.978i	−0.752671	−	1.17118i
$550$	−161.166	−	380.281i	−0.293030	−	0.691420i
$551$	592.645			1.07558
$552$	49.1237	−	1.95607i	0.0889923	−	0.00354361i
$553$	203.882	+	203.882i	0.368684	+	0.368684i
$554$	−139.859	−	121.188i	−0.252453	−	0.218751i
$555$	−74.0869	−	81.8050i	−0.133490	−	0.147396i
$556$	11.5262	+	80.1663i	0.0207305	+	0.144184i
$557$	−386.034	−	143.983i	−0.693060	−	0.258498i	−0.0218456	−	0.999761i	$-0.506954\pi$
$557$	−386.034	−	143.983i	−0.693060	−	0.258498i	−0.671214	+	0.741263i	$0.734227\pi$
$558$	−69.6457	+	52.1361i	−0.124813	+	0.0934339i
$559$	241.778	+	823.421i	0.432519	+	1.47302i
$560$	−31.9938	−	80.3516i	−0.0571318	−	0.143485i
$561$	−32.4504	+	71.0564i	−0.0578438	+	0.126660i
$562$	−226.945	+	123.921i	−0.403816	+	0.220500i
$563$	15.2372	−	213.043i	0.0270642	−	0.378407i	−0.965811	−	0.259248i	$-0.916525\pi$
$563$	15.2372	−	213.043i	0.0270642	−	0.378407i	0.992875	−	0.119160i	$-0.0380200\pi$
$564$	−20.7538	+	17.9832i	−0.0367974	+	0.0318852i
$565$	137.331	−	107.584i	0.243064	−	0.190414i
$566$	−92.8703	+	203.358i	−0.164082	+	0.359289i
$567$	278.487	−	60.5812i	0.491159	−	0.106845i
$568$	−227.234	−	124.079i	−0.400060	−	0.218450i
$569$	−331.493	−	47.6615i	−0.582589	−	0.0837636i	−0.155282	−	0.987870i	$-0.549629\pi$
$569$	−331.493	−	47.6615i	−0.582589	−	0.0837636i	−0.427307	+	0.904107i	$0.640538\pi$
$570$	−42.7086	−	63.3566i	−0.0749273	−	0.111152i
$571$	93.4822	+	650.183i	0.163717	+	1.13867i	0.891551	+	0.452921i	$0.149618\pi$
$571$	93.4822	+	650.183i	0.163717	+	1.13867i	−0.727834	+	0.685753i	$0.759473\pi$
$572$	60.5558	−	278.370i	0.105867	−	0.486662i
$573$	225.800	−	16.1496i	0.394067	−	0.0281842i
$574$		−	85.0724i		−	0.148210i
$575$	−541.169	−	194.322i	−0.941164	−	0.337951i
$576$	67.4311			0.117068
$577$	78.6157	+	1099.19i	0.136249	+	1.90501i	0.364173	+	0.931331i	$0.381352\pi$
$577$	78.6157	+	1099.19i	0.136249	+	1.90501i	−0.227924	+	0.973679i	$0.573194\pi$
$578$	291.178	+	63.3419i	0.503768	+	0.109588i
$579$	19.7893	−	2.84527i	0.0341784	−	0.00491411i
$580$	−343.687	+	231.679i	−0.592565	+	0.399447i
$581$	−75.5723	+	525.617i	−0.130073	+	0.904676i
$582$	30.9923	−	56.7582i	0.0532514	−	0.0975226i
$583$	82.8456	+	380.835i	0.142102	+	0.653233i
$584$	−73.0604	−	33.3656i	−0.125103	−	0.0571328i
$585$	316.898	+	404.523i	0.541706	+	0.691491i
$586$	−347.583	−	401.132i	−0.593145	−	0.684526i
$587$	−1024.03	−	73.2399i	−1.74451	−	0.124770i	−0.837651	−	0.546206i	$-0.816072\pi$
$587$	−1024.03	−	73.2399i	−1.74451	−	0.124770i	−0.906858	+	0.421436i	$0.861526\pi$
$588$	21.9481	+	40.1950i	0.0373267	+	0.0683588i
$589$	−94.9246	−	43.3506i	−0.161162	−	0.0736003i
$590$	−220.862	+	87.9414i	−0.374343	+	0.149053i
$591$	80.0532	−	23.5057i	0.135454	−	0.0397728i
$592$	70.0157	+	93.5301i	0.118270	+	0.157990i
$593$	−267.290	+	716.632i	−0.450742	+	1.20849i	0.490705	+	0.871326i	$0.336739\pi$
$593$	−267.290	+	716.632i	−0.450742	+	1.20849i	−0.941447	+	0.337160i	$0.890534\pi$
$594$	215.389	−	30.9683i	0.362608	−	0.0521351i
$595$	141.803	−	128.424i	0.238324	−	0.215839i
$596$	−246.351	+	284.304i	−0.413341	+	0.477021i
$597$	−159.293	+	159.293i	−0.266823	+	0.266823i
$598$	−227.525	−	324.849i	−0.380477	−	0.543225i
$599$			337.779i			0.563904i	0.959428	+	0.281952i	$0.0909819\pi$
$599$			337.779i			0.563904i	−0.959428	+	0.281952i	$0.909018\pi$
$600$	49.5353	+	20.0461i	0.0825588	+	0.0334101i
$601$	−472.421	+	303.607i	−0.786059	+	0.505169i	−0.871039	−	0.491213i	$-0.836553\pi$
$601$	−472.421	+	303.607i	−0.786059	+	0.505169i	0.0849807	+	0.996383i	$0.472917\pi$
$602$	−344.576	−	257.946i	−0.572386	−	0.428482i
$603$	−273.496	+	733.270i	−0.453558	+	1.21604i
$604$	−546.584	−	78.5870i	−0.904941	−	0.130111i
$605$	33.6690	+	69.6414i	0.0556512	+	0.115110i
$606$	119.903	+	77.0572i	0.197860	+	0.127157i
$607$	−12.3996	−	33.2447i	−0.0204277	−	0.0547689i	0.926336	−	0.376699i	$-0.122941\pi$
$607$	−12.3996	−	33.2447i	−0.0204277	−	0.0547689i	−0.946763	+	0.321930i	$0.895668\pi$
$608$	38.7636	+	70.9902i	0.0637559	+	0.116760i
$609$	−102.369	+	88.7031i	−0.168093	+	0.145654i
$610$	59.7556	+	638.395i	0.0979600	+	1.04655i
$611$	212.560	+	62.4133i	0.347889	+	0.102149i
$612$	52.1264	+	139.756i	0.0851739	+	0.228360i
$613$	−45.6947	−	210.055i	−0.0745427	−	0.342667i	0.924737	−	0.380606i	$-0.124285\pi$
$613$	−45.6947	−	210.055i	−0.0745427	−	0.342667i	−0.999280	+	0.0379385i	$0.987921\pi$
$614$	−218.350	−	743.631i	−0.355619	−	1.21113i
$615$	37.9743	+	36.3442i	0.0617469	+	0.0590962i
$616$	59.3563	+	129.972i	0.0963577	+	0.210994i
$617$	37.0139	+	27.7083i	0.0599902	+	0.0449081i	0.628852	−	0.777525i	$-0.283525\pi$
$617$	37.0139	+	27.7083i	0.0599902	+	0.0449081i	−0.568862	+	0.822433i	$0.692616\pi$
$618$	32.6843	+	7.11004i	0.0528873	+	0.0115049i
$619$	602.364	+	521.951i	0.973124	+	0.843217i	0.987650	−	0.156678i	$-0.0500783\pi$
$619$	602.364	+	521.951i	0.973124	+	0.843217i	−0.0145255	+	0.999894i	$0.504624\pi$
$620$	71.9956	−	11.9683i	0.116122	−	0.0193038i
$621$	171.754	−	249.549i	0.276576	−	0.401851i
$622$	−368.758	+	368.758i	−0.592859	+	0.592859i
$623$	−378.392	+	27.0631i	−0.607371	+	0.0434400i
$624$	19.9272	+	31.0073i	0.0319345	+	0.0496911i
$625$	−449.097	−	434.669i	−0.718555	−	0.695470i
$626$	243.155	+	532.434i	0.388426	+	0.850534i
$627$	75.6481	+	101.054i	0.120651	+	0.161171i
$628$	−218.535	−	119.329i	−0.347986	−	0.190015i
$629$	−139.724	+	217.415i	−0.222137	+	0.345652i
$630$	−248.829	−	67.1722i	−0.394966	−	0.106622i
$631$	−13.6147	−	3.99764i	−0.0215764	−	0.00633540i	0.270927	−	0.962600i	$-0.412670\pi$
$631$	−13.6147	−	3.99764i	−0.0215764	−	0.00633540i	−0.292503	+	0.956265i	$0.594488\pi$
$632$	188.110	+	13.4539i	0.297642	+	0.0212878i
$633$	5.99598	−	83.8348i	0.00947233	−	0.132440i
$634$	239.158	−	814.497i	0.377221	−	1.28470i
$635$	102.019	−	58.6470i	0.160661	−	0.0923575i
$636$	−42.4206	−	27.2621i	−0.0666991	−	0.0428649i
$637$	177.059	−	324.260i	0.277958	−	0.509042i
$638$	548.182	−	410.364i	0.859220	−	0.643204i
$639$	−701.825	+	320.513i	−1.09832	+	0.501585i
$640$	−50.2316	−	26.0151i	−0.0784869	−	0.0406486i
$641$	220.331	−	141.598i	0.343730	−	0.220902i	−0.357373	−	0.933962i	$-0.616328\pi$
$641$	220.331	−	141.598i	0.343730	−	0.220902i	0.701103	+	0.713060i	$0.252691\pi$
$642$	−0.0267608	−	0.374164i	−4.16834e−5	−	0.000582810i
$643$	−698.203	−	698.203i	−1.08585	−	1.08585i	−0.995951	−	0.0899019i	$-0.971345\pi$
$643$	−698.203	−	698.203i	−1.08585	−	1.08585i	−0.0899019	−	0.995951i	$-0.528655\pi$
$644$	188.996	+	62.0447i	0.293472	+	0.0963428i
$645$	262.349	−	43.6121i	0.406743	−	0.0676157i
$646$	−117.167	+	135.218i	−0.181374	+	0.209316i
$647$	−126.168	+	579.986i	−0.195005	+	0.896423i	0.770785	+	0.637096i	$0.219864\pi$
$647$	−126.168	+	579.986i	−0.195005	+	0.896423i	−0.965790	+	0.259327i	$0.916499\pi$
$648$	111.712	−	149.229i	0.172394	−	0.230292i
$649$	357.255	−	163.153i	0.550470	−	0.251391i
$650$	−80.0017	−	423.602i	−0.123080	−	0.651696i
$651$	22.8850	−	6.71963i	0.0351535	−	0.0103220i
$652$	−468.269	+	101.866i	−0.718204	+	0.156236i
$653$	−1062.66	+	396.352i	−1.62735	+	0.606971i	−0.986944	−	0.161062i	$-0.948508\pi$
$653$	−1062.66	+	396.352i	−1.62735	+	0.606971i	−0.640409	+	0.768034i	$0.721235\pi$
$654$	54.3946	−	185.251i	0.0831722	−	0.283258i
$655$	132.791	−	160.217i	0.202734	−	0.244606i
$656$	−36.4387	−	42.0525i	−0.0555468	−	0.0641044i
$657$	−210.076	+	114.710i	−0.319751	+	0.174597i
$658$	−104.106	+	38.8297i	−0.158217	+	0.0590117i
$659$	471.586	−	733.801i	0.715608	−	1.11351i	−0.272857	−	0.962055i	$-0.587969\pi$
$659$	471.586	−	733.801i	0.715608	−	1.11351i	0.988465	−	0.151453i	$-0.0483951\pi$
$660$	−83.3744	−	29.0308i	−0.126325	−	0.0439860i
$661$	133.797	−	930.581i	0.202416	−	1.40784i	−0.594669	−	0.803971i	$-0.702717\pi$
$661$	133.797	−	930.581i	0.202416	−	1.40784i	0.797085	−	0.603867i	$-0.206374\pi$
$662$	27.4787	+	10.2490i	0.0415086	+	0.0154819i
$663$	−48.8607	+	65.2702i	−0.0736964	+	0.0984468i
$664$	187.779	+	292.189i	0.282799	+	0.440044i
$665$	−72.3247	−	300.577i	−0.108759	−	0.451996i
$666$	348.171			0.522779
$667$	98.0188	−	948.259i	0.146955	−	1.42168i
$668$	32.4375	+	32.4375i	0.0485591	+	0.0485591i
$669$	71.8138	+	62.2270i	0.107345	+	0.0930150i
$670$	486.634	−	440.721i	0.726319	−	0.657793i
$671$	−150.754	−	1048.52i	−0.224671	−	1.56262i
$672$	−17.3210	−	6.46042i	−0.0257754	−	0.00961372i
$673$	−386.891	+	289.623i	−0.574875	+	0.430346i	−0.846754	−	0.531985i	$-0.821446\pi$
$673$	−386.891	+	289.623i	−0.574875	+	0.430346i	0.271878	+	0.962332i	$0.412355\pi$
$674$	51.9127	+	176.798i	0.0770218	+	0.262312i
$675$	281.809	−	170.330i	0.417495	−	0.252341i
$676$	−16.8896	+	36.9831i	−0.0249846	+	0.0547087i
$677$	206.073	−	112.525i	0.304392	−	0.166211i	−0.319792	−	0.947488i	$-0.603613\pi$
$677$	206.073	−	112.525i	0.304392	−	0.166211i	0.624184	+	0.781277i	$0.285431\pi$
$678$	2.66021	−	37.1946i	0.00392362	−	0.0548593i
$679$	197.749	−	171.350i	0.291235	−	0.252357i
$680$	15.0878	−	124.220i	0.0221879	−	0.182676i
$681$	−112.317	+	245.940i	−0.164929	+	0.361145i
$682$	−117.820	+	25.6302i	−0.172757	+	0.0375810i
$683$	727.077	+	397.014i	1.06453	+	0.581280i	0.913329	−	0.407222i	$-0.133503\pi$
$683$	727.077	+	397.014i	1.06453	+	0.581280i	0.151206	+	0.988502i	$0.451684\pi$
$684$	238.586	+	34.3034i	0.348809	+	0.0501512i
$685$	−143.494	+	737.103i	−0.209481	+	1.07606i
$686$	69.0174	+	480.027i	0.100609	+	0.699748i
$687$	70.8258	−	325.581i	0.103094	−	0.473917i
$688$	−280.814	+	20.0842i	−0.408159	+	0.0291921i
$689$			406.791i			0.590408i
$690$	−108.437	+	57.8570i	−0.157155	+	0.0838507i
$691$	−187.689			−0.271620			−0.135810	−	0.990735i	$-0.543364\pi$
$691$	−187.689			−0.271620			−0.135810	+	0.990735i	$0.543364\pi$
$692$	12.5257	+	175.132i	0.0181007	+	0.253081i
$693$	416.073	+	90.5112i	0.600394	+	0.130608i
$694$	239.888	−	34.4907i	0.345660	−	0.0496984i
$695$	−113.176	−	167.893i	−0.162843	−	0.241572i
$696$	−12.6085	+	87.6943i	−0.0181157	+	0.125998i
$697$	58.9889	−	108.030i	0.0846325	−	0.154993i
$698$	40.1733	+	184.674i	0.0575549	+	0.264575i
$699$	−226.273	−	103.336i	−0.323710	−	0.147833i
$700$	159.445	+	146.038i	0.227779	+	0.208625i
$701$	−323.075	−	372.848i	−0.460877	−	0.531881i	0.476974	−	0.878917i	$-0.341733\pi$
$701$	−323.075	−	372.848i	−0.460877	−	0.531881i	−0.937852	+	0.347036i	$0.887188\pi$
$702$	226.544	+	16.2028i	0.322713	+	0.0230809i
$703$	200.150	+	366.548i	0.284709	+	0.521405i
$704$	85.0110	+	38.8232i	0.120754	+	0.0551466i
$705$	27.1431	−	63.0593i	0.0385009	−	0.0894458i
$706$	25.1251	−	7.37739i	0.0355879	−	0.0104496i
$707$	345.601	+	461.669i	0.488828	+	0.652997i
$708$	−17.7578	+	47.6104i	−0.0250816	+	0.0672463i
$709$	−628.385	+	90.3482i	−0.886298	+	0.127430i	−0.570404	−	0.821364i	$-0.693213\pi$
$709$	−628.385	+	90.3482i	−0.886298	+	0.127430i	−0.315894	+	0.948795i	$0.602304\pi$
$710$	646.467	+	32.0061i	0.910518	+	0.0450790i
$711$	368.039	−	424.739i	0.517635	−	0.597383i
$712$	−175.453	+	175.453i	−0.246422	+	0.246422i
$713$	−85.0627	+	144.714i	−0.119303	+	0.202965i
$714$		−	40.8934i		−	0.0572736i
$715$	166.614	+	692.439i	0.233027	+	0.968446i
$716$	223.345	−	143.535i	0.311935	−	0.200468i
$717$	144.953	+	108.510i	0.202165	+	0.151339i
$718$	−173.710	+	465.733i	−0.241935	+	0.648654i
$719$	1203.49	+	173.036i	1.67384	+	0.240662i	0.912907	−	0.408167i	$-0.133832\pi$
$719$	1203.49	+	173.036i	1.67384	+	0.240662i	0.760934	+	0.648829i	$0.224741\pi$
$720$	−151.771	+	73.3756i	−0.210793	+	0.101911i
$721$	113.854	+	73.1697i	0.157912	+	0.101484i
$722$	−77.3725	−	207.444i	−0.107164	−	0.287318i
$723$	−94.7951	−	173.604i	−0.131114	−	0.240117i
$724$	−177.586	+	153.879i	−0.245284	+	0.212540i
$725$	521.455	−	895.439i	0.719248	−	1.23509i
$726$	15.8645	+	4.65825i	0.0218520	+	0.00641633i
$727$	219.752	+	589.179i	0.302273	+	0.810425i	0.995931	+	0.0901206i	$0.0287252\pi$
$727$	219.752	+	589.179i	0.302273	+	0.810425i	−0.693658	+	0.720305i	$0.744002\pi$
$728$	31.7009	+	145.727i	0.0435452	+	0.200174i
$729$	−131.267	−	447.055i	−0.180065	−	0.613244i
$730$	200.748	−	4.40332i	0.274998	−	0.00603195i
$731$	−258.704	−	566.483i	−0.353905	−	0.774943i
$732$	109.717	+	82.1334i	0.149887	+	0.112204i
$733$	−1318.17	−	286.751i	−1.79832	−	0.391201i	−0.815949	−	0.578124i	$-0.803785\pi$
$733$	−1318.17	−	286.751i	−1.79832	−	0.391201i	−0.982375	+	0.186922i	$0.940149\pi$
$734$	615.887	+	533.669i	0.839084	+	0.727070i
$735$	−93.1383	−	66.5862i	−0.126719	−	0.0905934i
$736$	119.999	−	50.2823i	0.163042	−	0.0683183i
$737$	−766.977	+	766.977i	−1.04067	+	1.04067i
$738$	−165.398	+	11.8295i	−0.224117	+	0.0160291i
$739$	166.313	+	258.788i	0.225051	+	0.350186i	0.935356	−	0.353708i	$-0.115079\pi$
$739$	166.313	+	258.788i	0.225051	+	0.350186i	−0.710305	+	0.703894i	$0.751443\pi$
$740$	−259.364	−	134.326i	−0.350492	−	0.181521i
$741$	54.7326	+	119.848i	0.0738632	+	0.161738i
$742$	−122.270	−	163.334i	−0.164785	−	0.220127i
$743$	−1158.59	−	632.636i	−1.55934	−	0.851461i	−0.999742	−	0.0226938i	$-0.992776\pi$
$743$	−1158.59	−	632.636i	−1.55934	−	0.851461i	−0.559593	−	0.828768i	$-0.689042\pi$
$744$	8.43416	−	13.1238i	0.0113362	−	0.0176395i
$745$	245.109	−	907.969i	0.329006	−	1.21875i
$746$	953.114	+	279.859i	1.27763	+	0.375147i
$747$	1032.41	+	73.8398i	1.38208	+	0.0988484i
$748$	−14.7480	+	206.204i	−0.0197166	+	0.275674i
$749$	0.427612	−	1.45631i	0.000570911	−	0.00194434i
$750$	−133.305	+	8.78324i	−0.177740	+	0.0117110i
$751$	−880.467	−	565.842i	−1.17239	−	0.753451i	−0.198420	−	0.980117i	$-0.563581\pi$
$751$	−880.467	−	565.842i	−1.17239	−	0.753451i	−0.973973	+	0.226666i	$0.927217\pi$
$752$	−34.8295	+	63.7855i	−0.0463158	+	0.0848211i
$753$	−45.6752	+	34.1921i	−0.0606577	+	0.0454078i
$754$	650.132	−	296.905i	0.862244	−	0.393773i
$755$	1315.74	−	417.889i	1.74271	−	0.553496i
$756$	−95.8317	+	61.5873i	−0.126762	+	0.0814647i
$757$	86.7711	+	1213.22i	0.114625	+	1.60267i	0.651262	+	0.758853i	$0.274240\pi$
$757$	86.7711	+	1213.22i	0.114625	+	1.60267i	−0.536637	+	0.843813i	$0.680306\pi$
$758$	−456.767	−	456.767i	−0.602596	−	0.602596i
$759$	174.203	−	104.327i	0.229516	−	0.137453i
$760$	−164.496	−	117.601i	−0.216442	−	0.154738i
$761$	687.321	−	793.211i	0.903182	−	1.04233i	−0.0957170	−	0.995409i	$-0.530514\pi$
$761$	687.321	−	793.211i	0.903182	−	1.04233i	0.998899	−	0.0469186i	$-0.0149401\pi$
$762$	5.34669	−	24.5783i	0.00701665	−	0.0322550i
$763$	468.155	−	625.382i	0.613571	−	0.819635i
$764$	544.961	−	248.875i	0.713300	−	0.325753i
$765$	−269.401	−	257.836i	−0.352158	−	0.337041i
$766$	392.467	−	115.239i	0.512359	−	0.150442i
$767$	400.559	−	87.1362i	0.522241	−	0.113607i
$768$	−11.3292	+	4.22557i	−0.0147516	+	0.00550204i
$769$	306.944	−	1045.36i	0.399147	−	1.35937i	−0.477667	−	0.878541i	$-0.658517\pi$
$769$	306.944	−	1045.36i	0.399147	−	1.35937i	0.876814	−	0.480829i	$-0.159664\pi$
$770$	−275.027	−	227.947i	−0.357178	−	0.296035i
$771$	−253.052	−	292.038i	−0.328213	−	0.378778i
$772$	46.4383	−	25.3573i	0.0601533	−	0.0328462i
$773$	314.398	−	117.264i	0.406725	−	0.151700i	−0.137771	−	0.990464i	$-0.543994\pi$
$773$	314.398	−	117.264i	0.406725	−	0.151700i	0.544496	+	0.838764i	$0.316721\pi$
$774$	−453.586	+	705.794i	−0.586029	+	0.911879i
$775$	−149.021	+	105.280i	−0.192286	+	0.135846i
$776$	24.3562	−	169.401i	0.0313869	−	0.218301i
$777$	−89.4348	−	33.3575i	−0.115103	−	0.0429311i
$778$	267.336	−	357.120i	0.343620	−	0.459023i
$779$	−107.535	−	167.328i	−0.138042	−	0.214798i
$780$	−78.5920	−	48.1060i	−0.100759	−	0.0616743i
$781$	−1069.33			−1.36918
$782$	196.977	+	209.837i	0.251889	+	0.268334i
$783$	386.033	+	386.033i	0.493017	+	0.493017i
$784$	91.5970	+	79.3692i	0.116833	+	0.101236i
$785$	621.719	+	30.7808i	0.791999	+	0.0392112i
$786$	−6.33018	−	44.0274i	−0.00805366	−	0.0560144i
$787$	726.442	+	270.949i	0.923052	+	0.344280i	0.765652	−	0.643255i	$-0.222416\pi$
$787$	726.442	+	270.949i	0.923052	+	0.344280i	0.157399	+	0.987535i	$0.449689\pi$
$788$	176.762	−	132.322i	0.224317	−	0.167921i
$789$	1.84484	+	6.28295i	0.00233820	+	0.00796318i
$790$	−438.030	+	174.411i	−0.554468	+	0.220774i
$791$	62.6777	−	137.245i	0.0792385	−	0.173508i
$792$	244.439	−	133.474i	0.308635	−	0.168527i
$793$	78.8753	−	1102.82i	0.0994644	−	1.39069i
$794$	−39.4247	+	34.1617i	−0.0496533	+	0.0430248i
$795$	125.144	+	15.2001i	0.157414	+	0.0191196i
$796$	−247.664	+	542.308i	−0.311135	+	0.681291i
$797$	−764.919	+	166.398i	−0.959748	+	0.208780i	−0.665041	−	0.746807i	$-0.731586\pi$
$797$	−764.919	+	166.398i	−0.959748	+	0.208780i	−0.294707	+	0.955588i	$0.595222\pi$
$798$	−57.9991	−	31.6699i	−0.0726805	−	0.0396866i
$799$	−159.125	−	22.8787i	−0.199155	−	0.0286342i
$800$	141.368	+	3.89394i	0.176710	+	0.00486742i
$801$	105.233	+	731.908i	0.131376	+	0.913743i
$802$	−0.0417698	+	0.192013i	−5.20820e−5	+	0.000239417i
$803$	−330.889	+	23.6657i	−0.412066	+	0.0294716i
$804$		−	140.336i		−	0.174548i
$805$	−492.899	+	66.0097i	−0.612297	+	0.0819996i
$806$	−125.850			−0.156142
$807$	15.1877	+	212.352i	0.0188200	+	0.263138i
$808$	368.580	+	80.1796i	0.456163	+	0.0992322i
$809$	1215.54	−	174.768i	1.50252	−	0.216030i	0.658599	−	0.752494i	$-0.271149\pi$
$809$	1215.54	−	174.768i	1.50252	−	0.216030i	0.843924	+	0.536463i	$0.180240\pi$
$810$	−89.0510	+	457.439i	−0.109940	+	0.564739i
$811$	−15.1870	+	105.628i	−0.0187263	+	0.130244i	−0.997040	−	0.0768844i	$-0.975503\pi$
$811$	−15.1870	+	105.628i	−0.0187263	+	0.130244i	0.978314	+	0.207129i	$0.0664118\pi$
$812$	−171.798	+	314.625i	−0.211574	+	0.387469i
$813$	−20.2825	−	93.2371i	−0.0249477	−	0.114683i
$814$	438.943	+	200.458i	0.539242	+	0.246263i
$815$	943.114	−	738.825i	1.15720	−	0.906534i
$816$	−17.5157	−	20.2142i	−0.0214653	−	0.0247723i
$817$	−1003.80	−	71.7929i	−1.22864	−	0.0878739i
$818$	−85.0553	−	155.767i	−0.103980	−	0.190424i
$819$	404.268	+	184.623i	0.493612	+	0.225425i
$820$	127.774	+	54.9990i	0.155822	+	0.0670719i
$821$	−760.216	+	223.219i	−0.925963	+	0.271887i	−0.709746	−	0.704458i	$-0.751190\pi$
$821$	−760.216	+	223.219i	−0.925963	+	0.271887i	−0.216217	+	0.976345i	$0.569372\pi$
$822$	96.1925	+	128.498i	0.117022	+	0.156324i
$823$	−41.7687	+	111.986i	−0.0507518	+	0.136071i	−0.959852	−	0.280506i	$-0.909498\pi$
$823$	−41.7687	+	111.986i	−0.0507518	+	0.136071i	0.909100	+	0.416577i	$0.136770\pi$
$824$	87.6202	−	12.5979i	0.106335	−	0.0152887i
$825$	219.246	−	25.3832i	0.265752	−	0.0307675i
$826$	−134.641	+	155.384i	−0.163003	+	0.188116i
$827$	285.524	−	285.524i	0.345252	−	0.345252i	−0.513085	−	0.858338i	$-0.671498\pi$
$827$	285.524	−	285.524i	0.345252	−	0.345252i	0.858338	+	0.513085i	$0.171498\pi$
$828$	94.3473	−	376.075i	0.113946	−	0.454196i
$829$		−	199.988i		−	0.241240i	−0.992699	−	0.120620i	$-0.961512\pi$
$829$		−	199.988i		−	0.241240i	0.992699	−	0.120620i	$-0.0384883\pi$
$830$	−740.592	−	453.315i	−0.892279	−	0.546162i
$831$	83.1929	−	53.4648i	0.100112	−	0.0643380i
$832$	78.0886	+	58.4564i	0.0938564	+	0.0702601i
$833$	−93.6917	+	251.197i	−0.112475	+	0.301557i
$834$	−42.8390	−	6.15932i	−0.0513657	−	0.00738527i
$835$	−108.306	−	37.7119i	−0.129708	−	0.0451639i
$836$	281.037	+	180.612i	0.336169	+	0.216043i
$837$	−33.5939	−	90.0687i	−0.0401361	−	0.107609i
$838$	289.808	+	530.743i	0.345833	+	0.633345i
$839$	−959.083	+	831.050i	−1.14313	+	0.990524i	−0.143127	+	0.989704i	$0.545716\pi$
$839$	−959.083	+	831.050i	−1.14313	+	0.990524i	−1.00000		0.000820093i	$0.999739\pi$
$840$	46.0155	−	4.30718i	0.0547803	−	0.00512759i
$841$	841.439	+	247.069i	1.00052	+	0.293780i
$842$	−313.905	−	841.612i	−0.372809	−	0.999539i
$843$	−29.3714	−	135.018i	−0.0348415	−	0.160164i
$844$	−62.6667	−	213.423i	−0.0742496	−	0.252871i
$845$	−2.22896	−	101.618i	−0.00263782	−	0.120259i
$846$	89.9691	+	197.005i	0.106346	+	0.232866i
$847$	53.5565	+	40.0919i	0.0632308	+	0.0473340i
$848$	−130.400	−	28.3668i	−0.153773	−	0.0334514i
$849$	−90.2859	−	78.2332i	−0.106344	−	0.0921475i
$850$	101.211	+	296.006i	0.119072	+	0.348243i
$851$	619.597	−	259.626i	0.728081	−	0.305083i
$852$	97.8297	−	97.8297i	0.114824	−	0.114824i
$853$	−119.362	+	8.53697i	−0.139933	+	0.0100082i	−0.141130	−	0.989991i	$-0.545073\pi$
$853$	−119.362	+	8.53697i	−0.139933	+	0.0100082i	0.00119717	+	0.999999i	$0.499619\pi$
$854$	299.808	+	466.510i	0.351063	+	0.546265i
$855$	−574.326	+	182.410i	−0.671727	+	0.213345i
$856$	−0.412401	−	0.903032i	−0.000481777	−	0.00105494i
$857$	277.350	+	370.496i	0.323628	+	0.432317i	0.932620	−	0.360860i	$-0.117517\pi$
$857$	277.350	+	370.496i	0.323628	+	0.432317i	−0.608992	+	0.793177i	$0.708426\pi$
$858$	133.612	+	72.9579i	0.155725	+	0.0850325i
$859$	−809.982	+	1260.36i	−0.942936	+	1.46724i	−0.0597514	+	0.998213i	$0.519031\pi$
$859$	−809.982	+	1260.36i	−0.942936	+	1.46724i	−0.883185	+	0.469025i	$0.844606\pi$
$860$	610.189	−	350.774i	0.709522	−	0.407877i
$861$	43.6193	+	12.8078i	0.0506612	+	0.0148755i
$862$	8.77963	+	0.627932i	0.0101852	+	0.000728459i
$863$	8.80790	−	123.150i	0.0102061	−	0.142700i	−0.989794	−	0.142507i	$-0.954484\pi$
$863$	8.80790	−	123.150i	0.0102061	−	0.142700i	1.00000		0.000193791i	$-6.16857e-5\pi$
$864$	−20.9915	+	71.4906i	−0.0242958	+	0.0827438i
$865$	−218.763	−	380.550i	−0.252906	−	0.439942i
$866$	522.404	+	335.729i	0.603238	+	0.387678i
$867$	−76.3146	+	139.760i	−0.0880214	+	0.161199i
$868$	50.5312	−	37.8272i	0.0582156	−	0.0435797i
$869$	708.532	−	323.576i	0.815342	−	0.372354i
$870$	−67.0464	−	211.099i	−0.0770648	−	0.242642i
$871$	−952.397	+	612.069i	−1.09345	+	0.702719i
$872$	−36.4514	−	509.657i	−0.0418021	−	0.584469i
$873$	−360.637	−	360.637i	−0.413101	−	0.413101i
$874$	450.161	−	116.864i	0.515058	−	0.133712i
$875$	−517.785	−	155.194i	−0.591755	−	0.177365i
$876$	28.1069	−	32.4371i	0.0320855	−	0.0370286i
$877$	−170.059	+	781.749i	−0.193910	+	0.891390i	0.772626	+	0.634861i	$0.218943\pi$
$877$	−170.059	+	781.749i	−0.193910	+	0.891390i	−0.966536	+	0.256529i	$0.917421\pi$
$878$	−359.102	+	479.704i	−0.409000	+	0.546360i
$879$	258.002	−	117.826i	0.293518	−	0.134045i
$880$	−233.585	+	5.12359i	−0.265438	+	0.00582226i
$881$	311.485	−	91.4602i	0.353558	−	0.103814i	−0.100130	−	0.994974i	$-0.531926\pi$
$881$	311.485	−	91.4602i	0.353558	−	0.103814i	0.453689	+	0.891160i	$0.350108\pi$
$882$	352.930	−	76.7751i	0.400147	−	0.0870467i
$883$	−612.432	+	228.425i	−0.693581	+	0.258692i	−0.671436	−	0.741063i	$-0.734322\pi$
$883$	−612.432	+	228.425i	−0.693581	+	0.258692i	−0.0221447	+	0.999755i	$0.507049\pi$
$884$	−60.7905	+	207.034i	−0.0687676	+	0.234201i
$885$	−11.8391	−	126.483i	−0.0133776	−	0.142918i
$886$	38.1212	+	43.9942i	0.0430262	+	0.0496549i
$887$	−473.020	+	258.288i	−0.533281	+	0.291193i	−0.723238	−	0.690599i	$-0.757347\pi$
$887$	−473.020	+	258.288i	−0.533281	+	0.291193i	0.189957	+	0.981792i	$0.439165\pi$
$888$	−58.4967	+	21.8181i	−0.0658747	+	0.0245700i
$889$	55.0230	−	85.6174i	0.0618931	−	0.0963075i
$890$	203.982	−	585.821i	0.229193	−	0.658226i
$891$	109.571	−	762.082i	0.122975	−	0.855310i
$892$	235.621	+	87.8820i	0.264149	+	0.0985225i
$893$	−155.683	+	207.968i	−0.174337	+	0.232887i
$894$	−108.683	−	169.114i	−0.121569	−	0.189166i
$895$	−346.507	+	566.098i	−0.387159	+	0.632511i
$896$	−48.9244			−0.0546031
$897$	200.814	−	67.7528i	0.223873	−	0.0755327i
$898$	−93.7135	−	93.7135i	−0.104358	−	0.104358i
$899$	−228.618	−	198.099i	−0.254302	−	0.220354i
$900$	261.756	−	330.301i	0.290840	−	0.367002i
$901$	−42.0110	−	292.193i	−0.0466271	−	0.324298i
$902$	−215.330	−	80.3139i	−0.238725	−	0.0890398i
$903$	184.134	−	137.841i	0.203913	−	0.152647i
$904$	−27.8030	−	94.6885i	−0.0307556	−	0.104744i
$905$	232.258	−	539.586i	0.256639	−	0.596227i
$906$	122.583	−	268.419i	0.135301	−	0.296269i
$907$	−769.661	+	420.267i	−0.848579	+	0.463359i	−0.843818	−	0.536630i	$-0.819697\pi$
$907$	−769.661	+	420.267i	−0.848579	+	0.463359i	−0.00476070	+	0.999989i	$0.501515\pi$
$908$	−51.0456	+	713.711i	−0.0562176	+	0.786025i
$909$	849.522	−	736.115i	0.934568	−	0.809808i
$910$	−229.924	−	293.500i	−0.252664	−	0.322527i
$911$	−149.299	+	326.918i	−0.163884	+	0.358857i	−0.973702	−	0.227825i	$-0.926839\pi$
$911$	−149.299	+	326.918i	−0.163884	+	0.358857i	0.809818	+	0.586681i	$0.199566\pi$
$912$	−42.2348	+	9.18761i	−0.0463100	+	0.0100741i
$913$	1259.06	+	687.501i	1.37904	+	0.753013i
$914$	7.38058	+	1.06117i	0.00807503	+	0.00116101i
$915$	−336.321	−	65.4728i	−0.367564	−	0.0715549i
$916$	−125.492	−	872.817i	−0.137000	−	0.952857i
$917$	38.2561	−	175.860i	0.0417188	−	0.191778i
$918$	−164.397	+	11.7579i	−0.179082	+	0.0128082i
$919$		−	1.67503i		−	0.00182267i	−1.00000		0.000911333i	$-0.999710\pi$
$919$		−	1.67503i		−	0.00182267i	1.00000		0.000911333i	$-0.000290086\pi$
$920$	−215.373	+	243.751i	−0.234101	+	0.264946i
$921$	414.156			0.449680
$922$	−13.2143	−	184.761i	−0.0143322	−	0.200391i
$923$	−1090.60	−	237.246i	−1.18159	−	0.257038i
$924$	−75.5770	+	10.8663i	−0.0817932	+	0.0117601i
$925$	729.933	+	20.1058i	0.789116	+	0.0217360i
$926$	17.6741	−	122.926i	0.0190865	−	0.132749i
$927$	126.425	−	231.530i	0.136381	−	0.249763i
$928$	49.8396	+	229.109i	0.0537064	+	0.246884i
$929$	−1645.17	−	751.324i	−1.77090	−	0.808745i	−0.980597	−	0.196034i	$-0.937194\pi$
$929$	−1645.17	−	751.324i	−1.77090	−	0.808745i	−0.790307	−	0.612711i	$-0.790079\pi$
$930$	−4.70250	+	38.7162i	−0.00505645	+	0.0416303i
$931$	283.713	+	327.423i	0.304740	+	0.351689i
$932$	−656.639	−	46.9638i	−0.704548	−	0.0503903i
$933$	−133.557	−	244.591i	−0.143148	−	0.262155i
$934$	−143.620	−	65.5891i	−0.153769	−	0.0702239i
$935$	−191.188	−	480.163i	−0.204479	−	0.513544i
$936$	278.914	−	81.8966i	0.297985	−	0.0874963i
$937$	−456.039	−	609.197i	−0.486702	−	0.650157i	0.488216	−	0.872723i	$-0.337648\pi$
$937$	−456.039	−	609.197i	−0.486702	−	0.650157i	−0.974918	+	0.222565i	$0.928557\pi$
$938$	198.434	−	532.021i	0.211550	−	0.567187i
$939$	−309.603	+	44.5142i	−0.329716	+	0.0474059i
$940$	8.98422	−	181.466i	0.00955768	−	0.193049i
$941$	373.218	−	430.716i	0.396618	−	0.457722i	−0.521955	−	0.852973i	$-0.674797\pi$
$941$	373.218	−	430.716i	0.396618	−	0.457722i	0.918573	+	0.395251i	$0.129342\pi$
$942$	94.0846	−	94.0846i	0.0998775	−	0.0998775i
$943$	−285.518	+	144.386i	−0.302776	+	0.153114i
$944$			134.478i			0.142456i
$945$	148.677	−	242.898i	0.157331	−	0.257035i
$946$	−978.200	+	628.651i	−1.03404	+	0.664536i
$947$	−32.8301	−	24.5763i	−0.0346675	−	0.0259518i	0.581803	−	0.813329i	$-0.302347\pi$
$947$	−32.8301	−	24.5763i	−0.0346675	−	0.0259518i	−0.616471	+	0.787378i	$0.711438\pi$
$948$	−35.2184	+	94.4242i	−0.0371502	+	0.0996036i
$949$	−342.722	−	49.2760i	−0.361140	−	0.0519241i
$950$	498.209	+	85.6940i	0.524430	+	0.0902042i
$951$	381.612	+	245.247i	0.401275	+	0.257884i
$952$	−37.8201	−	101.400i	−0.0397270	−	0.106512i
$953$	352.441	+	645.448i	0.369823	+	0.677280i	0.994629	−	0.103500i	$-0.0330041\pi$
$953$	352.441	+	645.448i	0.369823	+	0.677280i	−0.624807	+	0.780779i	$0.714822\pi$
$954$	−300.553	+	260.430i	−0.315045	+	0.272988i
$955$	−955.760	+	1153.16i	−1.00080	+	1.20750i
$956$	459.781	+	135.004i	0.480943	+	0.141218i
$957$	127.877	+	342.851i	0.133623	+	0.358256i
$958$	92.7724	+	426.468i	0.0968396	+	0.445165i
$959$	182.975	+	623.157i	0.190798	+	0.649799i
$960$	20.9012	−	21.8387i	0.0217721	−	0.0227486i
$961$	−377.086	−	825.704i	−0.392389	−	0.859213i
$962$	403.199	+	301.831i	0.419126	+	0.313754i
$963$	−2.89083	−	0.628861i	−0.00300190	−	0.000653023i
$964$	−395.613	−	342.800i	−0.410386	−	0.355602i
$965$	−76.9288	+	107.605i	−0.0797190	+	0.111508i
$966$	−60.2659	+	87.5632i	−0.0623870	+	0.0906452i
$967$	861.956	−	861.956i	0.891371	−	0.891371i	−0.103281	−	0.994652i	$-0.532934\pi$
$967$	861.956	−	861.956i	0.891371	−	0.891371i	0.994652	+	0.103281i	$0.0329341\pi$
$968$	43.6461	−	3.12163i	0.0450889	−	0.00322482i
$969$	−51.6909	−	80.4326i	−0.0533446	−	0.0830058i
$970$	129.515	+	407.785i	0.133521	+	0.420397i
$971$	87.5489	+	191.705i	0.0901637	+	0.197431i	0.949342	−	0.314246i	$-0.101752\pi$
$971$	87.5489	+	191.705i	0.0901637	+	0.197431i	−0.859178	+	0.511677i	$0.829024\pi$
$972$	201.776	+	269.541i	0.207589	+	0.277306i
$973$	−153.695	−	83.9240i	−0.157960	−	0.0862528i
$974$	−669.806	+	1042.24i	−0.687686	+	1.07006i
$975$	229.238	+	22.7546i	0.235116	+	0.0233380i
$976$	348.017	+	102.187i	0.356575	+	0.104700i
$977$	490.908	+	35.1104i	0.502465	+	0.0359370i	0.320272	−	0.947326i	$-0.396226\pi$
$977$	490.908	+	35.1104i	0.502465	+	0.0359370i	0.182193	+	0.983263i	$0.441680\pi$
$978$	18.2689	−	255.432i	0.0186798	−	0.261178i
$979$	−288.726	+	983.312i	−0.294920	+	1.00440i
$980$	−292.529	−	78.9691i	−0.298499	−	0.0805808i
$981$	−1280.97	−	823.228i	−1.30578	−	0.839172i
$982$	−208.738	+	382.276i	−0.212565	+	0.389283i
$983$	−1142.02	+	854.906i	−1.16177	+	0.869691i	−0.993248	−	0.116007i	$-0.962991\pi$
$983$	−1142.02	+	854.906i	−1.16177	+	0.869691i	−0.168523	+	0.985698i	$0.553900\pi$
$984$	27.0475	−	12.3522i	0.0274873	−	0.0125530i
$985$	−253.861	+	490.170i	−0.257727	+	0.497634i
$986$	−436.319	+	280.405i	−0.442514	+	0.284386i
$987$	−4.23582	−	59.2245i	−0.00429161	−	0.0600045i
$988$	246.556	+	246.556i	0.249551	+	0.249551i
$989$	−280.892	+	1594.25i	−0.284016	+	1.61198i
$990$	−404.933	+	566.405i	−0.409023	+	0.572126i
$991$	345.353	−	398.559i	0.348489	−	0.402178i	−0.554261	−	0.832343i	$-0.686999\pi$
$991$	345.353	−	398.559i	0.348489	−	0.402178i	0.902750	+	0.430165i	$0.141545\pi$
$992$	8.77592	−	40.3423i	0.00884670	−	0.0406676i
$993$	−9.39195	+	12.5462i	−0.00945816	+	0.0126346i
$994$	509.207	−	232.547i	0.512281	−	0.233951i
$995$	−32.6847	−	1490.10i	−0.0328489	−	1.49759i
$996$	−178.085	+	52.2904i	−0.178800	+	0.0525004i
$997$	1726.17	−	375.504i	1.73136	−	0.376634i	0.767087	−	0.641543i	$-0.221706\pi$
$997$	1726.17	−	375.504i	1.73136	−	0.376634i	0.964273	+	0.264909i	$0.0853419\pi$
$998$	−659.223	+	245.878i	−0.660544	+	0.246370i
$999$	−108.387	+	369.132i	−0.108495	+	0.369501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.k.a.223.5	yes	240
5.2	odd	4	inner	230.3.k.a.177.5	yes	240
23.13	even	11	inner	230.3.k.a.13.5	✓	240
115.82	odd	44	inner	230.3.k.a.197.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.k.a.13.5	✓	240	23.13	even	11	inner
230.3.k.a.177.5	yes	240	5.2	odd	4	inner
230.3.k.a.197.5	yes	240	115.82	odd	44	inner
230.3.k.a.223.5	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.k (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.100889 + 1.41061i) q^{2} +(-0.738452 - 0.160640i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(4.14598 - 2.79479i) q^{5} +(0.152100 - 1.05788i) q^{6} +(2.07244 - 3.79539i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(-7.66718 - 3.50148i) q^{9} +O(q^{10})\)	\(q+(0.100889 + 1.41061i) q^{2} +(-0.738452 - 0.160640i) q^{3} +(-1.97964 + 0.284630i) q^{4} +(4.14598 - 2.79479i) q^{5} +(0.152100 - 1.05788i) q^{6} +(2.07244 - 3.79539i) q^{7} +(-0.601225 - 2.76379i) q^{8} +(-7.66718 - 3.50148i) q^{9} +(4.36065 + 5.56639i) q^{10} +(-7.65013 - 8.82872i) q^{11} +(1.50760 + 0.107825i) q^{12} +(-5.84353 - 10.7016i) q^{13} +(5.56290 + 2.54049i) q^{14} +(-3.51056 + 1.39781i) q^{15} +(3.83797 - 1.12693i) q^{16} +(5.30253 + 7.08335i) q^{17} +(4.16570 - 11.1687i) q^{18} +(14.1529 - 2.03487i) q^{19} +(-7.41207 + 6.71276i) q^{20} +(-2.14009 + 2.46979i) q^{21} +(11.6821 - 11.6821i) q^{22} +(-0.915120 - 22.9818i) q^{23} +2.13751i q^{24} +(9.37825 - 23.1743i) q^{25} +(14.5063 - 9.32261i) q^{26} +(10.5443 + 7.89333i) q^{27} +(-3.02241 + 8.10339i) q^{28} +(41.0264 + 5.89871i) q^{29} +(-2.32594 - 4.81101i) q^{30} +(-6.13977 - 3.94579i) q^{31} +(1.97687 + 5.30019i) q^{32} +(4.23100 + 7.74851i) q^{33} +(-9.45688 + 8.19444i) q^{34} +(-2.01505 - 21.5276i) q^{35} +(16.1749 + 4.74938i) q^{36} +(10.2073 + 27.3668i) q^{37} +(4.29828 + 19.7589i) q^{38} +(2.59605 + 8.84134i) q^{39} +(-10.2169 - 9.77830i) q^{40} +(-5.77878 - 12.6538i) q^{41} +(-3.69983 - 2.76966i) q^{42} +(-68.7743 - 14.9609i) q^{43} +(17.6574 + 15.3003i) q^{44} +(-41.5739 + 6.91112i) q^{45} +(32.3260 - 3.60948i) q^{46} +(-12.8473 + 12.8473i) q^{47} +(-3.01519 + 0.215651i) q^{48} +(16.3814 + 25.4900i) q^{49} +(33.6361 + 10.8910i) q^{50} +(-2.77779 - 6.08252i) q^{51} +(14.6141 + 19.5221i) q^{52} +(-29.2815 - 15.9889i) q^{53} +(-10.0706 + 15.6702i) q^{54} +(-56.3917 - 15.2231i) q^{55} +(-11.7356 - 3.44590i) q^{56} +(-10.7781 - 0.770865i) q^{57} +(-4.18167 + 58.4674i) q^{58} +(-9.47174 + 32.2578i) q^{59} +(6.55180 - 3.76638i) q^{60} +(76.2827 + 49.0239i) q^{61} +(4.94654 - 9.05891i) q^{62} +(-29.1792 + 21.8433i) q^{63} +(-7.27706 + 3.32332i) q^{64} +(-54.1359 - 28.0372i) q^{65} +(-10.5033 + 6.75004i) q^{66} +(-6.62378 - 92.6125i) q^{67} +(-12.5133 - 12.5133i) q^{68} +(-3.01603 + 17.1180i) q^{69} +(30.1638 - 5.01434i) q^{70} +(59.9435 - 69.1785i) q^{71} +(-5.06766 + 23.2957i) q^{72} +(17.0176 - 22.7329i) q^{73} +(-37.5741 + 17.1595i) q^{74} +(-10.6481 + 15.6066i) q^{75} +(-27.4384 + 8.05665i) q^{76} +(-49.3628 + 10.7382i) q^{77} +(-12.2098 + 4.55401i) q^{78} +(-18.7850 + 63.9759i) q^{79} +(12.7626 - 15.3986i) q^{80} +(43.1593 + 49.8084i) q^{81} +(17.2665 - 9.42822i) q^{82} +(-115.056 + 42.9136i) q^{83} +(3.53364 - 5.49844i) q^{84} +(41.7807 + 14.5479i) q^{85} +(14.1655 - 98.5231i) q^{86} +(-29.3485 - 10.9464i) q^{87} +(-19.8013 + 26.4514i) q^{88} +(-47.4284 - 73.8000i) q^{89} +(-13.9432 - 57.9473i) q^{90} -52.7271 q^{91} +(8.35291 + 45.2353i) q^{92} +(3.90008 + 3.90008i) q^{93} +(-19.4187 - 16.8264i) q^{94} +(52.9904 - 47.9909i) q^{95} +(-0.608398 - 4.23150i) q^{96} +(56.6933 + 21.1455i) q^{97} +(-34.3038 + 25.6795i) q^{98} +(27.7413 + 94.4782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8}+O(q^{10}) \) 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8	\( 240 q - 24 q^{2} - 4 q^{5} - 74 q^{7} + 48 q^{8} - 16 q^{10} + 8 q^{11} + 44 q^{12} + 24 q^{13} + 24 q^{15} + 96 q^{16} + 12 q^{17} + 88 q^{18} - 24 q^{20} + 24 q^{21} + 8 q^{22} - 44 q^{23} - 128 q^{25} + 48 q^{26} - 60 q^{27} - 116 q^{28} + 120 q^{30} - 12 q^{31} + 96 q^{32} - 334 q^{33} - 224 q^{35} - 176 q^{36} + 188 q^{37} + 76 q^{38} - 16 q^{40} - 116 q^{41} + 24 q^{42} + 120 q^{43} + 204 q^{45} + 396 q^{46} - 144 q^{47} - 88 q^{48} + 170 q^{50} - 176 q^{51} + 48 q^{52} + 192 q^{53} - 312 q^{55} + 296 q^{56} + 88 q^{57} - 28 q^{58} - 72 q^{60} - 552 q^{61} - 12 q^{62} - 122 q^{63} - 392 q^{65} - 8 q^{66} - 72 q^{67} - 24 q^{68} + 100 q^{70} + 424 q^{71} - 176 q^{72} + 452 q^{73} + 604 q^{75} - 112 q^{76} + 356 q^{77} + 32 q^{78} + 16 q^{80} - 704 q^{81} + 148 q^{82} - 360 q^{83} + 428 q^{85} - 376 q^{86} - 462 q^{87} - 104 q^{88} - 510 q^{90} + 432 q^{91} - 192 q^{93} - 166 q^{95} - 1042 q^{97} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 - 4 * q^5 - 74 * q^7 + 48 * q^8 - 16 * q^10 + 8 * q^11 + 44 * q^12 + 24 * q^13 + 24 * q^15 + 96 * q^16 + 12 * q^17 + 88 * q^18 - 24 * q^20 + 24 * q^21 + 8 * q^22 - 44 * q^23 - 128 * q^25 + 48 * q^26 - 60 * q^27 - 116 * q^28 + 120 * q^30 - 12 * q^31 + 96 * q^32 - 334 * q^33 - 224 * q^35 - 176 * q^36 + 188 * q^37 + 76 * q^38 - 16 * q^40 - 116 * q^41 + 24 * q^42 + 120 * q^43 + 204 * q^45 + 396 * q^46 - 144 * q^47 - 88 * q^48 + 170 * q^50 - 176 * q^51 + 48 * q^52 + 192 * q^53 - 312 * q^55 + 296 * q^56 + 88 * q^57 - 28 * q^58 - 72 * q^60 - 552 * q^61 - 12 * q^62 - 122 * q^63 - 392 * q^65 - 8 * q^66 - 72 * q^67 - 24 * q^68 + 100 * q^70 + 424 * q^71 - 176 * q^72 + 452 * q^73 + 604 * q^75 - 112 * q^76 + 356 * q^77 + 32 * q^78 + 16 * q^80 - 704 * q^81 + 148 * q^82 - 360 * q^83 + 428 * q^85 - 376 * q^86 - 462 * q^87 - 104 * q^88 - 510 * q^90 + 432 * q^91 - 192 * q^93 - 166 * q^95 - 1042 * q^97 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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