LMFDB - Embedded newform 115.2.j.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(4,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 4]))

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

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

chi := DirichletCharacter("115.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	115.4
Dual form			115.2.j.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49755 + 0.683908i) q^{2} +(0.900592 + 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(2.15615 + 0.592474i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(0.632042 - 0.0908739i) q^{7} +(0.598154 - 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +O(q^{10})$	\(q+(-1.49755 + 0.683908i) q^{2} +(0.900592 + 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(2.15615 + 0.592474i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(0.632042 - 0.0908739i) q^{7} +(0.598154 - 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +(-3.63413 + 0.587347i) q^{10} +(1.69819 - 3.71852i) q^{11} +(2.06561 + 0.943334i) q^{12} +(-3.19357 - 0.459166i) q^{13} +(-0.884364 + 0.568346i) q^{14} +(0.124611 + 7.14678i) q^{15} +(0.699637 + 4.86608i) q^{16} +(0.965240 - 0.836385i) q^{17} +(6.42487 - 9.99729i) q^{18} +(0.307596 - 0.354985i) q^{19} +(1.32113 - 0.881953i) q^{20} +(0.847934 + 1.85672i) q^{21} +6.73007i q^{22} +(3.19949 - 3.57257i) q^{23} +6.78684 q^{24} +(4.29795 + 2.55492i) q^{25} +(5.09656 - 1.49648i) q^{26} +(-10.1910 - 8.83052i) q^{27} +(0.245239 - 0.381599i) q^{28} +(-2.61894 - 3.02242i) q^{29} +(-5.07435 - 10.6174i) q^{30} +(-4.96368 - 1.45747i) q^{31} +(-2.07999 - 3.23653i) q^{32} +(12.9346 + 1.85971i) q^{33} +(-0.873484 + 1.91266i) q^{34} +(1.41662 + 0.178531i) q^{35} +(-0.729764 + 5.07562i) q^{36} +(5.16825 + 8.04195i) q^{37} +(-0.217863 + 0.741974i) q^{38} +(-1.46778 - 10.2086i) q^{39} +(2.49665 - 4.03796i) q^{40} +(7.36949 + 4.73608i) q^{41} +(-2.53965 - 2.20062i) q^{42} +(0.206862 + 0.704508i) q^{43} +(-1.20636 - 2.64157i) q^{44} +(-15.4054 + 4.81669i) q^{45} +(-2.34808 + 7.53826i) q^{46} -0.589562i q^{47} +(-14.2948 + 6.52824i) q^{48} +(-6.32523 + 1.85726i) q^{49} +(-8.18372 - 0.886725i) q^{50} +(3.43459 + 2.20728i) q^{51} +(-1.73217 + 1.50093i) q^{52} +(-6.64695 + 0.955686i) q^{53} +(21.3007 + 6.25446i) q^{54} +(5.86468 - 7.01154i) q^{55} +(0.192937 - 1.34191i) q^{56} +(1.36581 + 0.623742i) q^{57} +(5.98905 + 2.73511i) q^{58} +(-0.734852 + 5.11101i) q^{59} +(3.89487 + 3.25779i) q^{60} +(-2.44333 - 0.717427i) q^{61} +(8.43012 - 1.21207i) q^{62} +(-3.48343 + 3.01841i) q^{63} +(-2.94303 - 1.89137i) q^{64} +(-6.61377 - 2.88214i) q^{65} +(-20.6420 + 6.06105i) q^{66} +(2.18587 - 0.998254i) q^{67} -0.907297i q^{68} +(13.8390 + 6.59584i) q^{69} +(-2.24355 + 0.701475i) q^{70} +(-3.46453 - 7.58626i) q^{71} +(4.31771 + 14.7048i) q^{72} +(0.557471 + 0.483051i) q^{73} +(-13.2397 - 8.50861i) q^{74} +(-3.96560 + 15.4833i) q^{75} +(-0.0474869 - 0.330279i) q^{76} +(0.735411 - 2.50458i) q^{77} +(9.17984 + 14.2841i) q^{78} +(2.33484 - 16.2392i) q^{79} +(-1.37451 + 10.9065i) q^{80} +(8.91062 - 19.5115i) q^{81} +(-14.2752 - 2.05247i) q^{82} +(-5.64215 - 8.77936i) q^{83} +(1.39128 + 0.408516i) q^{84} +(2.57674 - 1.23149i) q^{85} +(-0.791605 - 0.913560i) q^{86} +(6.91157 - 10.7546i) q^{87} +(-6.55931 - 5.68368i) q^{88} +(5.75334 - 1.68933i) q^{89} +(19.7761 - 17.7491i) q^{90} -2.06020 q^{91} +(-0.429603 - 3.37968i) q^{92} -16.5368i q^{93} +(0.403206 + 0.882897i) q^{94} +(0.873542 - 0.583157i) q^{95} +(8.05365 - 9.29441i) q^{96} +(-3.48701 + 5.42589i) q^{97} +(8.20215 - 7.10721i) q^{98} +(4.19947 + 29.2080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−1.49755	+	0.683908i	−1.05893	+	0.483596i	−0.867255	−	0.497863i	$-0.834118\pi$
$2$	−1.49755	+	0.683908i	−1.05893	+	0.483596i	−0.191671	+	0.981459i	$0.561391\pi$
$3$	0.900592	+	3.06714i	0.519957	+	1.77081i	0.629686	+	0.776850i	$0.283184\pi$
$3$	0.900592	+	3.06714i	0.519957	+	1.77081i	−0.109729	+	0.993962i	$0.534998\pi$
$4$	0.465201	−	0.536871i	0.232601	−	0.268436i
$5$	2.15615	+	0.592474i	0.964259	+	0.264963i
$5$	2.15615	+	0.592474i	0.964259	+	0.264963i
$6$	−3.44632	−	3.97726i	−1.40695	−	1.62371i
$7$	0.632042	−	0.0908739i	0.238889	−	0.0343471i	−0.0218302	−	0.999762i	$-0.506949\pi$
$7$	0.632042	−	0.0908739i	0.238889	−	0.0343471i	0.260719	+	0.965415i	$0.416040\pi$
$8$	0.598154	−	2.03713i	0.211480	−	0.720233i
$9$	−6.07249	+	3.90255i	−2.02416	+	1.30085i
$10$	−3.63413	+	0.587347i	−1.14921	+	0.185735i
$11$	1.69819	−	3.71852i	0.512024	−	1.12118i	−0.460348	−	0.887738i	$-0.652275\pi$
$11$	1.69819	−	3.71852i	0.512024	−	1.12118i	0.972372	−	0.233437i	$-0.0749973\pi$
$12$	2.06561	+	0.943334i	0.596291	+	0.272317i
$13$	−3.19357	−	0.459166i	−0.885738	−	0.127350i	−0.315593	−	0.948895i	$-0.602204\pi$
$13$	−3.19357	−	0.459166i	−0.885738	−	0.127350i	−0.570144	+	0.821545i	$0.693113\pi$
$14$	−0.884364	+	0.568346i	−0.236356	+	0.151897i
$15$	0.124611	+	7.14678i	0.0321744	+	1.84529i
$16$	0.699637	+	4.86608i	0.174909	+	1.21652i
$17$	0.965240	−	0.836385i	0.234105	−	0.202853i	−0.529906	−	0.848056i	$-0.677773\pi$
$17$	0.965240	−	0.836385i	0.234105	−	0.202853i	0.764011	+	0.645203i	$0.223227\pi$
$18$	6.42487	−	9.99729i	1.51436	−	2.35638i
$19$	0.307596	−	0.354985i	0.0705674	−	0.0814391i	−0.719368	−	0.694629i	$-0.755569\pi$
$19$	0.307596	−	0.354985i	0.0705674	−	0.0814391i	0.789935	+	0.613190i	$0.210114\pi$
$20$	1.32113	−	0.881953i	0.295413	−	0.197211i
$21$	0.847934	+	1.85672i	0.185034	+	0.405169i
$22$			6.73007i			1.43486i
$23$	3.19949	−	3.57257i	0.667140	−	0.744933i
$23$	3.19949	−	3.57257i	0.667140	−	0.744933i
$24$	6.78684			1.38536
$25$	4.29795	+	2.55492i	0.859590	+	0.510985i
$26$	5.09656	−	1.49648i	0.999517	−	0.293485i
$27$	−10.1910	−	8.83052i	−1.96125	−	1.69943i
$28$	0.245239	−	0.381599i	0.0463458	−	0.0721155i
$29$	−2.61894	−	3.02242i	−0.486325	−	0.561249i	0.458555	−	0.888666i	$-0.348367\pi$
$29$	−2.61894	−	3.02242i	−0.486325	−	0.561249i	−0.944880	+	0.327417i	$0.893822\pi$
$30$	−5.07435	−	10.6174i	−0.926444	−	1.93847i
$31$	−4.96368	−	1.45747i	−0.891503	−	0.261769i	−0.196267	−	0.980551i	$-0.562882\pi$
$31$	−4.96368	−	1.45747i	−0.891503	−	0.261769i	−0.695236	+	0.718782i	$0.744700\pi$
$32$	−2.07999	−	3.23653i	−0.367694	−	0.572143i
$33$	12.9346	+	1.85971i	2.25162	+	0.323734i
$34$	−0.873484	+	1.91266i	−0.149801	+	0.328019i
$35$	1.41662	+	0.178531i	0.239452	+	0.0301772i
$36$	−0.729764	+	5.07562i	−0.121627	+	0.845936i
$37$	5.16825	+	8.04195i	0.849655	+	1.32209i	0.945143	+	0.326658i	$0.105923\pi$
$37$	5.16825	+	8.04195i	0.849655	+	1.32209i	−0.0954879	+	0.995431i	$0.530441\pi$
$38$	−0.217863	+	0.741974i	−0.0353421	+	0.120364i
$39$	−1.46778	−	10.2086i	−0.235033	−	1.63469i
$40$	2.49665	−	4.03796i	0.394756	−	0.638457i
$41$	7.36949	+	4.73608i	1.15092	+	0.739652i	0.969822	−	0.243813i	$-0.0783983\pi$
$41$	7.36949	+	4.73608i	1.15092	+	0.739652i	0.181099	+	0.983465i	$0.442035\pi$
$42$	−2.53965	−	2.20062i	−0.391876	−	0.339562i
$43$	0.206862	+	0.704508i	0.0315462	+	0.107436i	0.973761	−	0.227572i	$-0.0730789\pi$
$43$	0.206862	+	0.704508i	0.0315462	+	0.107436i	−0.942215	+	0.335009i	$0.891261\pi$
$44$	−1.20636	−	2.64157i	−0.181866	−	0.398232i
$45$	−15.4054	+	4.81669i	−2.29649	+	0.718029i
$46$	−2.34808	+	7.53826i	−0.346206	+	1.11146i
$47$		−	0.589562i		−	0.0859964i	−0.999075	−	0.0429982i	$-0.986309\pi$
$47$		−	0.589562i		−	0.0859964i	0.999075	−	0.0429982i	$-0.0136910\pi$
$48$	−14.2948	+	6.52824i	−2.06328	+	0.942270i
$49$	−6.32523	+	1.85726i	−0.903605	+	0.265322i
$50$	−8.18372	−	0.886725i	−1.15735	−	0.125402i
$51$	3.43459	+	2.20728i	0.480939	+	0.309081i
$52$	−1.73217	+	1.50093i	−0.240208	+	0.208142i
$53$	−6.64695	+	0.955686i	−0.913028	+	0.131274i	−0.582789	−	0.812624i	$-0.698039\pi$
$53$	−6.64695	+	0.955686i	−0.913028	+	0.131274i	−0.330239	+	0.943897i	$0.607129\pi$
$54$	21.3007	+	6.25446i	2.89866	+	0.851124i
$55$	5.86468	−	7.01154i	0.790793	−	0.945436i
$56$	0.192937	−	1.34191i	0.0257823	−	0.179320i
$57$	1.36581	+	0.623742i	0.180905	+	0.0826167i
$58$	5.98905	+	2.73511i	0.786401	+	0.359137i
$59$	−0.734852	+	5.11101i	−0.0956696	+	0.665396i	0.884398	+	0.466733i	$0.154569\pi$
$59$	−0.734852	+	5.11101i	−0.0956696	+	0.665396i	−0.980068	+	0.198663i	$0.936340\pi$
$60$	3.89487	+	3.25779i	0.502825	+	0.420579i
$61$	−2.44333	−	0.717427i	−0.312836	−	0.0918571i	0.121545	−	0.992586i	$-0.461215\pi$
$61$	−2.44333	−	0.717427i	−0.312836	−	0.0918571i	−0.434382	+	0.900729i	$0.643033\pi$
$62$	8.43012	−	1.21207i	1.07063	−	0.153933i
$63$	−3.48343	+	3.01841i	−0.438871	+	0.380283i
$64$	−2.94303	−	1.89137i	−0.367879	−	0.236422i
$65$	−6.61377	−	2.88214i	−0.820337	−	0.357486i
$66$	−20.6420	+	6.06105i	−2.54086	+	0.746063i
$67$	2.18587	−	0.998254i	0.267047	−	0.121956i	−0.277392	−	0.960757i	$-0.589470\pi$
$67$	2.18587	−	0.998254i	0.267047	−	0.121956i	0.544439	+	0.838801i	$0.316743\pi$
$68$		−	0.907297i		−	0.110026i
$69$	13.8390	+	6.59584i	1.66602	+	0.794046i
$70$	−2.24355	+	0.701475i	−0.268155	+	0.0838423i
$71$	−3.46453	−	7.58626i	−0.411164	−	0.900323i	−0.996015	−	0.0891826i	$-0.971575\pi$
$71$	−3.46453	−	7.58626i	−0.411164	−	0.900323i	0.584852	−	0.811140i	$-0.301153\pi$
$72$	4.31771	+	14.7048i	0.508847	+	1.73297i
$73$	0.557471	+	0.483051i	0.0652470	+	0.0565369i	0.686874	−	0.726777i	$-0.258982\pi$
$73$	0.557471	+	0.483051i	0.0652470	+	0.0565369i	−0.621627	+	0.783314i	$0.713528\pi$
$74$	−13.2397	−	8.50861i	−1.53908	−	0.989106i
$75$	−3.96560	+	15.4833i	−0.457908	+	1.78786i
$76$	−0.0474869	−	0.330279i	−0.00544712	−	0.0378856i
$77$	0.735411	−	2.50458i	0.0838078	−	0.285423i
$78$	9.17984	+	14.2841i	1.03941	+	1.61736i
$79$	2.33484	−	16.2392i	0.262691	−	1.82705i	−0.249727	−	0.968316i	$-0.580341\pi$
$79$	2.33484	−	16.2392i	0.262691	−	1.82705i	0.512418	−	0.858736i	$-0.328750\pi$
$80$	−1.37451	+	10.9065i	−0.153675	+	1.21938i
$81$	8.91062	−	19.5115i	0.990069	−	2.16795i
$82$	−14.2752	−	2.05247i	−1.57643	−	0.226657i
$83$	−5.64215	−	8.77936i	−0.619307	−	0.963660i	−0.999253	−	0.0386517i	$-0.987694\pi$
$83$	−5.64215	−	8.77936i	−0.619307	−	0.963660i	0.379946	−	0.925009i	$-0.375943\pi$
$84$	1.39128	+	0.408516i	0.151801	+	0.0445727i
$85$	2.57674	−	1.23149i	0.279486	−	0.133574i
$86$	−0.791605	−	0.913560i	−0.0853609	−	0.0985118i
$87$	6.91157	−	10.7546i	0.740998	−	1.15302i
$88$	−6.55931	−	5.68368i	−0.699225	−	0.605882i
$89$	5.75334	−	1.68933i	0.609853	−	0.179069i	0.0377997	−	0.999285i	$-0.487965\pi$
$89$	5.75334	−	1.68933i	0.609853	−	0.179069i	0.572054	+	0.820216i	$0.306147\pi$
$90$	19.7761	−	17.7491i	2.08458	−	1.87092i
$91$	−2.06020			−0.215967
$92$	−0.429603	−	3.37968i	−0.0447892	−	0.352356i
$93$		−	16.5368i		−	1.71479i
$94$	0.403206	+	0.882897i	0.0415875	+	0.0910639i
$95$	0.873542	−	0.583157i	0.0896235	−	0.0598306i
$96$	8.05365	−	9.29441i	0.821972	−	0.948607i
$97$	−3.48701	+	5.42589i	−0.354052	+	0.550916i	−0.971904	−	0.235379i	$-0.924367\pi$
$97$	−3.48701	+	5.42589i	−0.354052	+	0.550916i	0.617852	+	0.786295i	$0.288003\pi$
$98$	8.20215	−	7.10721i	0.828543	−	0.717936i
$99$	4.19947	+	29.2080i	0.422063	+	2.93551i
$100$	3.37108	−	1.11889i	0.337108	−	0.111889i
$101$	10.7453	−	6.90556i	1.06919	−	0.687129i	0.117157	−	0.993113i	$-0.462622\pi$
$101$	10.7453	−	6.90556i	1.06919	−	0.687129i	0.952036	+	0.305985i	$0.0989857\pi$
$102$	−6.65305	−	0.956564i	−0.658750	−	0.0947139i
$103$	2.33053	+	1.06432i	0.229634	+	0.104870i	0.526909	−	0.849921i	$-0.323351\pi$
$103$	2.33053	+	1.06432i	0.229634	+	0.104870i	−0.297276	+	0.954792i	$0.596078\pi$
$104$	−2.84563	+	6.23106i	−0.279037	+	0.611006i
$105$	0.728214	+	4.50574i	0.0710664	+	0.439715i
$106$	9.30052	−	5.97708i	0.903347	−	0.580546i
$107$	−0.764393	+	2.60328i	−0.0738967	+	0.251669i	−0.988154	−	0.153465i	$-0.950957\pi$
$107$	−0.764393	+	2.60328i	−0.0738967	+	0.251669i	0.914257	+	0.405134i	$0.132775\pi$
$108$	−9.48170	+	1.36326i	−0.912377	+	0.131180i
$109$	−4.87104	−	5.62148i	−0.466561	−	0.538440i	0.472891	−	0.881121i	$-0.343210\pi$
$109$	−4.87104	−	5.62148i	−0.466561	−	0.538440i	−0.939452	+	0.342681i	$0.888665\pi$
$110$	−3.98739	+	14.5110i	−0.380183	+	1.38357i
$111$	−20.0113	+	23.0942i	−1.89939	+	2.19201i
$112$	0.884399	+	3.01199i	0.0835679	+	0.284606i
$113$	−13.6649	+	6.24056i	−1.28549	+	0.587063i	−0.936698	−	0.350138i	$-0.886135\pi$
$113$	−13.6649	+	6.24056i	−1.28549	+	0.587063i	−0.348790	+	0.937201i	$0.613407\pi$
$114$	−2.47194			−0.231519
$115$	9.01523	−	5.80738i	0.840675	−	0.541541i
$116$	−2.84098			−0.263779
$117$	21.1849	−	9.67480i	1.95854	−	0.894436i
$118$	−2.39498	−	8.15655i	−0.220476	−	0.750872i
$119$	0.534066	−	0.616345i	0.0489578	−	0.0565003i
$120$	14.6334	+	4.02103i	1.33584	+	0.367068i
$121$	−3.74006	−	4.31626i	−0.340006	−	0.392387i
$122$	4.14966	−	0.596631i	0.375693	−	0.0540164i
$123$	−7.88930	+	26.8685i	−0.711354	+	2.42265i
$124$	−3.09158	+	1.98684i	−0.277632	+	0.178423i
$125$	7.75329	+	8.05522i	0.693475	+	0.720481i
$126$	3.15229	−	6.90255i	0.280828	−	0.614928i
$127$	−8.30599	−	3.79322i	−0.737038	−	0.336594i	0.0112781	−	0.999936i	$-0.496410\pi$
$127$	−8.30599	−	3.79322i	−0.737038	−	0.336594i	−0.748316	+	0.663343i	$0.769137\pi$
$128$	13.3171	+	1.91471i	1.17707	+	0.169238i
$129$	−1.97452	+	1.26895i	−0.173847	+	0.111725i
$130$	11.8756	−	0.207062i	1.04156	−	0.0181605i
$131$	1.86945	+	13.0023i	0.163335	+	1.13602i	0.892292	+	0.451458i	$0.149096\pi$
$131$	1.86945	+	13.0023i	0.163335	+	1.13602i	−0.728958	+	0.684559i	$0.759995\pi$
$132$	7.01561	−	6.07906i	0.610630	−	0.529114i
$133$	0.162155	−	0.252318i	0.0140606	−	0.0218787i
$134$	−2.59074	+	2.98987i	−0.223806	+	0.258285i
$135$	−16.7414	−	25.0778i	−1.44087	−	2.15835i
$136$	−1.12646	−	2.46660i	−0.0965932	−	0.211510i
$137$		−	14.7844i		−	1.26311i	−0.775329	−	0.631557i	$-0.782416\pi$
$137$		−	14.7844i		−	1.26311i	0.775329	−	0.631557i	$-0.217584\pi$
$138$	−25.2355	−	0.412999i	−2.14819	−	0.0351568i
$139$	4.73976			0.402022			0.201011	−	0.979589i	$-0.435577\pi$
$139$	4.73976			0.402022			0.201011	+	0.979589i	$0.435577\pi$
$140$	0.754860	−	0.677487i	0.0637973	−	0.0572581i
$141$	1.80826	−	0.530954i	0.152283	−	0.0447144i
$142$	10.3766	+	8.99137i	0.870785	+	0.754539i
$143$	−7.13071	+	11.0956i	−0.596300	+	0.927861i
$144$	−23.2387	−	26.8189i	−1.93656	−	2.23491i
$145$	−3.85612	−	8.06844i	−0.320233	−	0.670047i
$146$	−1.16520	−	0.342134i	−0.0964328	−	0.0283152i
$147$	−11.3929	−	17.7277i	−0.939671	−	1.46216i
$148$	6.72177	+	0.966444i	0.552526	+	0.0794412i
$149$	−6.46275	+	14.1514i	−0.529449	+	1.15933i	0.436287	+	0.899807i	$0.356293\pi$
$149$	−6.46275	+	14.1514i	−0.529449	+	1.15933i	−0.965737	+	0.259524i	$0.916434\pi$
$150$	−4.65049	−	25.8992i	−0.379711	−	2.11466i
$151$	−0.120574	+	0.838607i	−0.00981214	+	0.0682449i	−0.994139	−	0.108108i	$-0.965521\pi$
$151$	−0.120574	+	0.838607i	−0.00981214	+	0.0682449i	0.984327	+	0.176353i	$0.0564299\pi$
$152$	−0.539159	−	0.838948i	−0.0437316	−	0.0680477i
$153$	−2.59737	+	8.84584i	−0.209985	+	0.715144i
$154$	0.611587	+	4.25368i	0.0492831	+	0.342772i
$155$	−9.83891	−	6.08336i	−0.790280	−	0.488628i
$156$	−6.16354	−	3.96106i	−0.493478	−	0.317139i
$157$	6.34230	+	5.49563i	0.506171	+	0.438599i	0.870135	−	0.492814i	$-0.164032\pi$
$157$	6.34230	+	5.49563i	0.506171	+	0.438599i	−0.363964	+	0.931413i	$0.618577\pi$
$158$	7.60957	+	25.9158i	0.605385	+	2.06175i
$159$	−8.91741	−	19.5264i	−0.707196	−	1.54854i
$160$	−2.56721	−	8.21078i	−0.202956	−	0.649119i
$161$	1.69756	−	2.54876i	0.133786	−	0.200871i
$162$			35.3135i			2.77449i
$163$	6.16937	−	2.81746i	0.483222	−	0.220680i	−0.158882	−	0.987298i	$-0.550789\pi$
$163$	6.16937	−	2.81746i	0.483222	−	0.220680i	0.642104	+	0.766617i	$0.278062\pi$
$164$	5.97096	−	1.75323i	0.466254	−	0.136904i
$165$	26.7870	+	11.6732i	2.08537	+	0.908759i
$166$	14.4537	+	9.28881i	1.12182	+	0.720952i
$167$	0.990001	−	0.857841i	0.0766086	−	0.0663817i	−0.615715	−	0.787969i	$-0.711133\pi$
$167$	0.990001	−	0.857841i	0.0766086	−	0.0663817i	0.692323	+	0.721587i	$0.256587\pi$
$168$	4.28956	−	0.616746i	0.330947	−	0.0475830i
$169$	−2.48534	−	0.729761i	−0.191180	−	0.0561355i
$170$	−3.01656	+	3.60647i	−0.231360	+	0.276603i
$171$	−0.482528	+	3.35605i	−0.0368998	+	0.256644i
$172$	0.474462	+	0.216680i	0.0361774	+	0.0165217i
$173$	−0.499912	−	0.228302i	−0.0380076	−	0.0173575i	0.396321	−	0.918112i	$-0.370287\pi$
$173$	−0.499912	−	0.228302i	−0.0380076	−	0.0173575i	−0.434328	+	0.900755i	$0.643014\pi$
$174$	−2.99525	+	20.8324i	−0.227069	+	1.57930i
$175$	2.94866	+	1.22425i	0.222898	+	0.0925444i
$176$	19.2827	+	5.66192i	1.45349	+	0.426783i
$177$	−16.3380	+	2.34904i	−1.22804	+	0.176565i
$178$	−7.46056	+	6.46462i	−0.559193	+	0.484543i
$179$	5.33217	+	3.42678i	0.398545	+	0.256129i	0.724527	−	0.689247i	$-0.242058\pi$
$179$	5.33217	+	3.42678i	0.398545	+	0.256129i	−0.325982	+	0.945376i	$0.605695\pi$
$180$	−4.58065	+	10.5114i	−0.341422	+	0.783475i
$181$	2.45963	−	0.722214i	0.182823	−	0.0536817i	−0.189039	−	0.981969i	$-0.560537\pi$
$181$	2.45963	−	0.722214i	0.182823	−	0.0536817i	0.371863	+	0.928288i	$0.378719\pi$
$182$	3.08525	−	1.40898i	0.228694	−	0.104441i
$183$		−	8.14013i		−	0.601736i
$184$	−5.36399	−	8.65472i	−0.395439	−	0.638034i
$185$	6.37886	+	20.4017i	0.468983	+	1.49996i
$186$	11.3097	+	24.7647i	0.829266	+	1.81584i
$187$	−1.47095	−	5.00960i	−0.107567	−	0.366338i
$188$	−0.316518	−	0.274265i	−0.0230845	−	0.0200028i
$189$	−7.24358	−	4.65516i	−0.526893	−	0.338613i
$190$	−0.909346	+	1.47073i	−0.0659709	+	0.106698i
$191$	−2.77272	−	19.2847i	−0.200627	−	1.39539i	−0.802430	−	0.596747i	$-0.796460\pi$
$191$	−2.77272	−	19.2847i	−0.200627	−	1.39539i	0.601803	−	0.798645i	$-0.294449\pi$
$192$	3.15062	−	10.7300i	0.227377	−	0.774373i
$193$	6.39108	+	9.94471i	0.460040	+	0.715836i	0.991336	−	0.131350i	$-0.0419313\pi$
$193$	6.39108	+	9.94471i	0.460040	+	0.715836i	−0.531296	+	0.847186i	$0.678295\pi$
$194$	1.51116	−	10.5103i	0.108495	−	0.754598i
$195$	2.88360	−	22.8810i	0.206499	−	1.63854i
$196$	−1.94540	+	4.25983i	−0.138957	+	0.304274i
$197$	−12.5674	−	1.80693i	−0.895393	−	0.128738i	−0.320771	−	0.947157i	$-0.603942\pi$
$197$	−12.5674	−	1.80693i	−0.895393	−	0.128738i	−0.574622	+	0.818419i	$0.694851\pi$
$198$	−26.2645	−	40.8683i	−1.86653	−	2.90438i
$199$	15.5381	+	4.56239i	1.10147	+	0.323419i	0.781434	−	0.623988i	$-0.214488\pi$
$199$	15.5381	+	4.56239i	1.10147	+	0.323419i	0.320031	+	0.947407i	$0.396307\pi$
$200$	7.77554	−	7.22723i	0.549814	−	0.511042i
$201$	5.03036	+	5.80534i	0.354814	+	0.409477i
$202$	−11.3688	+	17.6902i	−0.799905	+	1.24468i
$203$	−1.92994	−	1.67230i	−0.135455	−	0.117373i
$204$	2.78280	−	0.817104i	0.194835	−	0.0572087i
$205$	13.0837	+	14.5779i	0.913805	+	1.01817i
$206$	−4.21798			−0.293880
$207$	−5.48673	+	34.1806i	−0.381354	+	2.37572i
$208$		−	15.8614i		−	1.09979i
$209$	−0.797661	−	1.74663i	−0.0551754	−	0.120817i
$210$	−4.17204	−	6.24953i	−0.287898	−	0.431258i
$211$	−16.9434	+	19.5537i	−1.16643	+	1.34613i	−0.239499	+	0.970897i	$0.576983\pi$
$211$	−16.9434	+	19.5537i	−1.16643	+	1.34613i	−0.926930	+	0.375234i	$0.877562\pi$
$212$	−2.57909	+	4.01314i	−0.177132	+	0.275624i
$213$	20.1479	−	17.4583i	1.38051	−	1.19622i
$214$	−0.635690	−	4.42132i	−0.0434548	−	0.302235i
$215$	0.0286226	+	1.64158i	0.00195205	+	0.111955i
$216$	−24.0847	+	15.4783i	−1.63875	+	1.05316i
$217$	−3.26970	−	0.470111i	−0.221961	−	0.0319132i
$218$	11.1392	+	5.08710i	0.754441	+	0.344542i
$219$	−0.979530	+	2.14487i	−0.0661905	+	0.144937i
$220$	−1.03604	−	6.41035i	−0.0698497	−	0.432186i
$221$	−3.46660	+	2.22785i	−0.233189	+	0.149861i
$222$	14.1735	−	48.2706i	0.951265	−	3.23971i
$223$	2.46883	−	0.354964i	0.165325	−	0.0237701i	−0.0591553	−	0.998249i	$-0.518841\pi$
$223$	2.46883	−	0.354964i	0.165325	−	0.0237701i	0.224480	+	0.974479i	$0.427932\pi$
$224$	−1.60876	−	1.85660i	−0.107490	−	0.124050i
$225$	−36.0700	+	1.25821i	−2.40467	+	0.0838809i
$226$	16.1959	−	18.6911i	1.07734	−	1.24331i
$227$	1.51570	+	5.16201i	0.100601	+	0.342615i	0.994377	−	0.105899i	$-0.0337719\pi$
$227$	1.51570	+	5.16201i	0.100601	+	0.342615i	−0.893776	+	0.448513i	$0.851954\pi$
$228$	0.970244	−	0.443095i	0.0642560	−	0.0293447i
$229$	9.00062			0.594778			0.297389	−	0.954756i	$-0.403884\pi$
$229$	9.00062			0.594778			0.297389	+	0.954756i	$0.403884\pi$
$230$	−9.52904	+	14.8624i	−0.628326	+	0.979999i
$231$	8.34419			0.549007
$232$	−7.72358	+	3.52724i	−0.507078	+	0.231575i
$233$	−1.45343	−	4.94991i	−0.0952171	−	0.324280i	0.898086	−	0.439821i	$-0.144958\pi$
$233$	−1.45343	−	4.94991i	−0.0952171	−	0.324280i	−0.993303	+	0.115541i	$0.963140\pi$
$234$	−25.1087	+	28.9770i	−1.64141	+	1.89428i
$235$	0.349300	−	1.27118i	0.0227858	−	0.0829228i
$236$	2.40210	+	2.77217i	0.156363	+	0.180453i
$237$	51.9106	−	7.46361i	3.37195	−	0.484814i
$238$	−0.378267	+	1.28826i	−0.0245194	+	0.0835054i
$239$	3.60018	−	2.31369i	0.232876	−	0.149660i	−0.418999	−	0.907987i	$-0.637619\pi$
$239$	3.60018	−	2.31369i	0.232876	−	0.149660i	0.651875	+	0.758326i	$0.273983\pi$
$240$	−34.6896	+	5.60652i	−2.23921	+	0.361899i
$241$	−8.85400	+	19.3876i	−0.570336	+	1.24886i	0.376282	+	0.926505i	$0.377202\pi$
$241$	−8.85400	+	19.3876i	−0.570336	+	1.24886i	−0.946618	+	0.322357i	$0.895525\pi$
$242$	8.55285	+	3.90595i	0.549798	+	0.251084i
$243$	27.8274	+	4.00097i	1.78513	+	0.256663i
$244$	−1.52181	+	0.978006i	−0.0974237	+	0.0626104i
$245$	−14.7385	+	0.256980i	−0.941609	+	0.0164179i
$246$	−6.56095	−	45.6324i	−0.418311	−	2.90942i
$247$	−1.14533	+	0.992432i	−0.0728754	+	0.0631469i
$248$	−5.93809	+	9.23985i	−0.377069	+	0.586731i
$249$	21.8462	−	25.2119i	1.38445	−	1.59774i
$250$	−17.1199	−	6.76055i	−1.08276	−	0.427575i
$251$	−6.68285	−	14.6334i	−0.421818	−	0.923653i	−0.994584	−	0.103934i	$-0.966857\pi$
$251$	−6.68285	−	14.6334i	−0.421818	−	0.923653i	0.572766	−	0.819719i	$-0.305870\pi$
$252$			3.27432i			0.206263i
$253$	−7.85133	−	17.9643i	−0.493609	−	1.12940i
$254$	15.0328			0.943245
$255$	6.09774	+	6.79413i	0.381855	+	0.425465i
$256$	−14.5391	+	4.26907i	−0.908694	+	0.266817i
$257$	−15.5654	−	13.4875i	−0.970944	−	0.841328i	0.0164089	−	0.999865i	$-0.494777\pi$
$257$	−15.5654	−	13.4875i	−0.970944	−	0.841328i	−0.987353	+	0.158538i	$0.949322\pi$
$258$	2.08910	−	3.25070i	0.130062	−	0.202380i
$259$	3.99735	+	4.61319i	0.248383	+	0.286650i
$260$	−4.62407	+	2.20997i	−0.286773	+	0.137056i
$261$	27.6987	+	8.13306i	1.71450	+	0.503424i
$262$	−11.6920	−	18.1931i	−0.722332	−	1.12397i
$263$	12.8132	+	1.84226i	0.790094	+	0.113598i	0.525536	−	0.850771i	$-0.323865\pi$
$263$	12.8132	+	1.84226i	0.790094	+	0.113598i	0.264558	+	0.964370i	$0.414774\pi$
$264$	11.5253	−	25.2370i	0.709336	−	1.55323i
$265$	−14.8980	−	1.87754i	−0.915178	−	0.115337i
$266$	−0.0702726	+	0.488757i	−0.00430869	+	0.0299676i
$267$	10.3628	+	16.1249i	0.634195	+	0.986827i
$268$	0.480937	−	1.63792i	0.0293779	−	0.100052i
$269$	1.02480	+	7.12761i	0.0624829	+	0.434578i	0.996918	+	0.0784455i	$0.0249957\pi$
$269$	1.02480	+	7.12761i	0.0624829	+	0.434578i	−0.934436	+	0.356132i	$0.884095\pi$
$270$	42.2219	+	26.1057i	2.56954	+	1.58874i
$271$	−9.71000	−	6.24024i	−0.589840	−	0.379067i	0.211409	−	0.977398i	$-0.432195\pi$
$271$	−9.71000	−	6.24024i	−0.589840	−	0.379067i	−0.801250	+	0.598330i	$0.795831\pi$
$272$	4.74524	+	4.11177i	0.287722	+	0.249313i
$273$	−1.85540	−	6.31890i	−0.112294	−	0.382437i
$274$	10.1111	+	22.1403i	0.610837	+	1.33755i
$275$	16.7993	−	11.6433i	1.01303	−	0.702114i
$276$	9.97903	−	4.36136i	0.600667	−	0.262523i
$277$		−	22.2304i		−	1.33570i	−0.744298	−	0.667848i	$-0.767216\pi$
$277$		−	22.2304i		−	1.33570i	0.744298	−	0.667848i	$-0.232784\pi$
$278$	−7.09803	+	3.24156i	−0.425711	+	0.194416i
$279$	35.8297	−	10.5206i	2.14507	−	0.629849i
$280$	1.21105	−	2.77904i	0.0723738	−	0.166079i
$281$	−20.7548	−	13.3383i	−1.23813	−	0.795697i	−0.252991	−	0.967469i	$-0.581414\pi$
$281$	−20.7548	−	13.3383i	−1.23813	−	0.795697i	−0.985137	+	0.171772i	$0.945051\pi$
$282$	−2.34484	+	2.03182i	−0.139633	+	0.120993i
$283$	0.360630	−	0.0518507i	0.0214372	−	0.00308220i	−0.131588	−	0.991305i	$-0.542008\pi$
$283$	0.360630	−	0.0518507i	0.0214372	−	0.00308220i	0.153025	+	0.988222i	$0.451098\pi$
$284$	−5.68454	−	1.66913i	−0.337316	−	0.0990448i
$285$	2.57533	+	2.15409i	0.152549	+	0.127597i
$286$	3.09022	−	21.4930i	0.182729	−	1.27091i
$287$	5.08821	+	2.32371i	0.300347	+	0.137164i
$288$	25.2615	+	11.5365i	1.48855	+	0.679796i
$289$	−2.18720	+	15.2123i	−0.128659	+	0.894844i
$290$	11.2928	+	9.44565i	0.663136	+	0.554668i
$291$	−19.7823	−	5.80861i	−1.15966	−	0.340507i
$292$	0.518673	−	0.0745739i	0.0303530	−	0.00436410i
$293$	−16.3635	+	14.1791i	−0.955967	+	0.828350i	−0.985233	−	0.171221i	$-0.945229\pi$
$293$	−16.3635	+	14.1791i	−0.955967	+	0.828350i	0.0292653	+	0.999572i	$0.490683\pi$
$294$	29.1856	+	18.7564i	1.70214	+	1.09390i
$295$	−4.61259	+	10.5847i	−0.268555	+	0.616266i
$296$	19.4739	−	5.71805i	1.13190	−	0.332355i
$297$	−50.1426	+	22.8994i	−2.90957	+	1.32876i
$298$		−	25.6124i		−	1.48369i
$299$	−11.8582	+	9.94016i	−0.685778	+	0.574855i
$300$	6.46775	+	9.33188i	0.373416	+	0.538777i
$301$	0.194767	+	0.426480i	0.0112262	+	0.0245819i
$302$	−0.392965	−	1.33832i	−0.0226126	−	0.0770115i
$303$	30.8574	+	26.7381i	1.77271	+	1.53606i
$304$	1.94259	+	1.24843i	0.111415	+	0.0716022i
$305$	−4.84313	−	2.99449i	−0.277317	−	0.171464i
$306$	−2.16004	−	15.0234i	−0.123482	−	0.858833i
$307$	−4.30546	+	14.6631i	−0.245726	+	0.836865i	0.740584	+	0.671964i	$0.234549\pi$
$307$	−4.30546	+	14.6631i	−0.245726	+	0.836865i	−0.986310	+	0.164902i	$0.947269\pi$
$308$	−1.00252	−	1.55995i	−0.0571240	−	0.0888867i
$309$	−1.16555	+	8.10656i	−0.0663057	+	0.461166i
$310$	18.8947	+	2.38123i	1.07315	+	0.135245i
$311$	−1.44379	+	3.16146i	−0.0818697	+	0.179270i	−0.946140	−	0.323758i	$-0.895054\pi$
$311$	−1.44379	+	3.16146i	−0.0818697	+	0.179270i	0.864270	+	0.503028i	$0.167781\pi$
$312$	−21.6743	−	3.11629i	−1.22706	−	0.176425i
$313$	10.0505	+	15.6389i	0.568090	+	0.883965i	0.999837	−	0.0180296i	$-0.00573930\pi$
$313$	10.0505	+	15.6389i	0.568090	+	0.883965i	−0.431748	+	0.901994i	$0.642103\pi$
$314$	−13.2564	−	3.89243i	−0.748102	−	0.219663i
$315$	−9.29911	+	4.44429i	−0.523946	+	0.250407i
$316$	−7.63218	−	8.80801i	−0.429344	−	0.495489i
$317$	−9.89235	+	15.3928i	−0.555610	+	0.864545i	−0.999503	−	0.0315344i	$-0.989961\pi$
$317$	−9.89235	+	15.3928i	−0.555610	+	0.864545i	0.443893	+	0.896080i	$0.353597\pi$
$318$	26.7085	+	23.1430i	1.49774	+	1.29780i
$319$	−15.6864	+	4.60594i	−0.878269	+	0.257883i
$320$	−5.22502	−	5.82175i	−0.292088	−	0.325446i
$321$	−8.67303			−0.484081
$322$	−0.799057	+	4.97787i	−0.0445297	+	0.277406i
$323$		−	0.599914i		−	0.0333801i
$324$	−6.32995	−	13.8606i	−0.351664	−	0.770036i
$325$	−12.5527	−	10.1328i	−0.696297	−	0.562067i
$326$	−7.31205	+	8.43856i	−0.404977	+	0.467368i
$327$	12.8550	−	20.0028i	0.710884	−	1.10616i
$328$	14.0561	−	12.1797i	0.776118	−	0.672510i
$329$	−0.0535757	−	0.372627i	−0.00295373	−	0.0205436i
$330$	−48.0983	+	0.838641i	−2.64772	+	0.0461657i
$331$	6.26264	−	4.02475i	0.344226	−	0.221220i	−0.357092	−	0.934069i	$-0.616232\pi$
$331$	6.26264	−	4.02475i	0.344226	−	0.221220i	0.701318	+	0.712849i	$0.252595\pi$
$332$	−7.33812	−	1.05506i	−0.402732	−	0.0579041i
$333$	−62.7683	−	28.6653i	−3.43968	−	1.57085i
$334$	−0.895891	+	1.96173i	−0.0490210	+	0.107341i
$335$	5.30450	−	0.857311i	0.289816	−	0.0468399i
$336$	−8.44169	+	5.42514i	−0.460532	+	0.295966i
$337$	−4.42873	+	15.0829i	−0.241248	+	0.821616i	0.746476	+	0.665412i	$0.231744\pi$
$337$	−4.42873	+	15.0829i	−0.241248	+	0.821616i	−0.987725	+	0.156204i	$0.950074\pi$
$338$	4.22101	−	0.606889i	0.229592	−	0.0330104i
$339$	−31.4472	−	36.2920i	−1.70798	−	1.97111i
$340$	0.537550	−	1.95627i	0.0291527	−	0.106093i
$341$	−13.8489	+	15.9825i	−0.749959	+	0.865499i
$342$	−1.57262	−	5.35586i	−0.0850376	−	0.289612i
$343$	−7.89489	+	3.60548i	−0.426284	+	0.194677i
$344$	1.55891			0.0840507
$345$	25.9311	+	22.4209i	1.39608	+	1.20710i
$346$	0.904780			0.0486413
$347$	31.0955	−	14.2008i	1.66929	−	0.762341i	0.669485	−	0.742825i	$-0.266515\pi$
$347$	31.0955	−	14.2008i	1.66929	−	0.762341i	0.999810	−	0.0195162i	$-0.00621258\pi$
$348$	−2.55857	−	8.71368i	−0.137154	−	0.467102i
$349$	10.5863	−	12.2173i	0.566673	−	0.653976i	−0.398012	−	0.917380i	$-0.630300\pi$
$349$	10.5863	−	12.2173i	0.566673	−	0.653976i	0.964686	+	0.263404i	$0.0848453\pi$
$350$	−5.25303	+	0.183239i	−0.280786	+	0.00979455i
$351$	28.4909	+	32.8802i	1.52073	+	1.75502i
$352$	−15.5673	+	2.23824i	−0.829741	+	0.119299i
$353$	9.41658	−	32.0699i	0.501194	−	1.70691i	−0.187856	−	0.982197i	$-0.560154\pi$
$353$	9.41658	−	32.0699i	0.501194	−	1.70691i	0.689050	−	0.724714i	$-0.258028\pi$
$354$	22.8604	−	14.6915i	1.21501	−	0.780842i
$355$	−2.97537	−	18.4097i	−0.157916	−	0.977087i
$356$	1.76951	−	3.87468i	0.0937838	−	0.205358i
$357$	2.37139	+	1.08298i	0.125507	+	0.0573172i
$358$	−10.3288	−	1.48505i	−0.545893	−	0.0784876i
$359$	−8.75079	+	5.62379i	−0.461849	+	0.296812i	−0.750798	−	0.660532i	$-0.770331\pi$
$359$	−8.75079	+	5.62379i	−0.461849	+	0.296812i	0.288949	+	0.957345i	$0.406694\pi$
$360$	0.597423	+	34.2638i	0.0314869	+	1.80586i
$361$	2.67258	+	18.5882i	0.140662	+	0.978328i
$362$	−3.18949	+	2.76371i	−0.167636	+	0.145258i
$363$	9.87029	−	15.3585i	0.518056	−	0.806110i
$364$	−0.958406	+	1.10606i	−0.0502341	+	0.0579733i
$365$	0.915794	+	1.37182i	0.0479349	+	0.0718042i
$366$	5.56710	+	12.1902i	0.290997	+	0.637195i
$367$			22.9608i			1.19854i	0.800546	+	0.599271i	$0.204543\pi$
$367$			22.9608i			1.19854i	−0.800546	+	0.599271i	$0.795457\pi$
$368$	19.6229	+	13.0695i	1.02291	+	0.681294i
$369$	−63.2340			−3.29183
$370$	−23.5055	−	26.1900i	−1.22199	−	1.36155i
$371$	−4.11430	+	1.20807i	−0.213604	+	0.0627197i
$372$	−8.87816	−	7.69297i	−0.460311	−	0.398862i
$373$	6.33121	−	9.85156i	0.327818	−	0.510094i	−0.637751	−	0.770243i	$-0.720135\pi$
$373$	6.33121	−	9.85156i	0.327818	−	0.510094i	0.965569	+	0.260148i	$0.0837714\pi$
$374$	5.62893	+	6.49613i	0.291065	+	0.335907i
$375$	−17.7239	+	31.0348i	−0.915258	+	1.60263i
$376$	−1.20101	−	0.352649i	−0.0619374	−	0.0181865i
$377$	6.97598	+	10.8548i	0.359281	+	0.559053i
$378$	14.0313	+	2.01740i	0.721693	+	0.103764i
$379$	−6.40153	+	14.0174i	−0.328825	+	0.720026i	−0.999769	−	0.0214819i	$-0.993162\pi$
$379$	−6.40153	+	14.0174i	−0.328825	+	0.720026i	0.670945	+	0.741508i	$0.265889\pi$
$380$	0.0932929	−	0.740265i	0.00478582	−	0.0379748i
$381$	4.15401	−	28.8918i	0.212816	−	1.48017i
$382$	17.3412	+	26.9835i	0.887255	+	1.38060i
$383$	6.55633	−	22.3288i	0.335013	−	1.14095i	−0.603976	−	0.797003i	$-0.706418\pi$
$383$	6.55633	−	22.3288i	0.335013	−	1.14095i	0.938989	−	0.343947i	$-0.111764\pi$
$384$	6.12059	+	42.5697i	0.312340	+	2.17237i
$385$	3.06955	−	4.96453i	0.156439	−	0.253016i
$386$	−16.3722	−	10.5218i	−0.833324	−	0.535545i
$387$	−4.00555	−	3.47083i	−0.203613	−	0.176432i
$388$	1.29084	+	4.39621i	0.0655326	+	0.223184i
$389$	3.51058	+	7.68709i	0.177993	+	0.389751i	0.977509	−	0.210894i	$-0.0676376\pi$
$389$	3.51058	+	7.68709i	0.177993	+	0.389751i	−0.799516	+	0.600645i	$0.794910\pi$
$390$	11.3301	+	36.2375i	0.573723	+	1.83496i
$391$	0.100230	−	6.12439i	0.00506887	−	0.309724i
$392$			13.9962i			0.706916i
$393$	−38.1962	+	17.4436i	−1.92675	+	0.879915i
$394$	20.0561	−	5.88901i	1.01041	−	0.296684i
$395$	14.6556	−	33.6308i	0.737402	−	1.69215i
$396$	17.6345	+	11.3330i	0.886167	+	0.569505i
$397$	1.67657	−	1.45276i	0.0841449	−	0.0729120i	−0.611773	−	0.791034i	$-0.709543\pi$
$397$	1.67657	−	1.45276i	0.0841449	−	0.0729120i	0.695918	+	0.718122i	$0.254998\pi$
$398$	−26.3893	+	3.79421i	−1.32278	+	0.190186i
$399$	0.919927	+	0.270115i	0.0460540	+	0.0135227i
$400$	−9.42547	+	22.7017i	−0.471274	+	1.13508i
$401$	−3.19654	+	22.2324i	−0.159628	+	1.11023i	0.739693	+	0.672944i	$0.234971\pi$
$401$	−3.19654	+	22.2324i	−0.159628	+	1.11023i	−0.899321	+	0.437290i	$0.855938\pi$
$402$	−11.5035	−	5.25349i	−0.573744	−	0.262020i
$403$	15.1826	+	6.93368i	0.756301	+	0.345391i
$404$	1.29131	−	8.98129i	0.0642453	−	0.446836i
$405$	30.7727	−	36.7904i	1.52911	−	1.82813i
$406$	4.03388	+	1.18445i	0.200198	+	0.0587834i
$407$	38.6808	−	5.56146i	1.91734	−	0.275671i
$408$	6.55093	−	5.67641i	0.324319	−	0.281024i
$409$	8.68745	+	5.58309i	0.429567	+	0.276066i	0.737506	−	0.675340i	$-0.236003\pi$
$409$	8.68745	+	5.58309i	0.429567	+	0.276066i	−0.307940	+	0.951406i	$0.599639\pi$
$410$	−29.5634	−	12.8831i	−1.46003	−	0.636252i
$411$	45.3457	−	13.3147i	2.23674	−	0.656765i
$412$	1.65557	−	0.756072i	0.0815639	−	0.0372490i
$413$			3.29715i			0.162242i
$414$	−15.1597	−	54.9395i	−0.745060	−	2.70013i
$415$	−6.96377	−	22.2724i	−0.341838	−	1.09331i
$416$	5.15650	+	11.2912i	0.252818	+	0.553594i
$417$	4.26859	+	14.5375i	0.209034	+	0.711904i
$418$	2.38907	+	2.07014i	0.116853	+	0.101254i
$419$	22.7196	+	14.6010i	1.10993	+	0.713306i	0.961277	−	0.275584i	$-0.0888711\pi$
$419$	22.7196	+	14.6010i	1.10993	+	0.713306i	0.148649	+	0.988890i	$0.452507\pi$
$420$	2.75776	+	1.70512i	0.134565	+	0.0832012i
$421$	2.92388	+	20.3360i	0.142501	+	0.991116i	0.928087	+	0.372364i	$0.121453\pi$
$421$	2.92388	+	20.3360i	0.142501	+	0.991116i	−0.785586	+	0.618753i	$0.787638\pi$
$422$	12.0006	−	40.8703i	0.584180	−	1.98953i
$423$	2.30080	+	3.58011i	0.111868	+	0.174071i
$424$	−2.02905	+	14.1123i	−0.0985391	+	0.685355i
$425$	6.28545	−	1.12862i	0.304889	−	0.0547463i
$426$	−18.2327	+	39.9240i	−0.883376	+	1.93432i
$427$	−1.60948	−	0.231409i	−0.0778883	−	0.0111986i
$428$	1.04203	+	1.62143i	0.0503685	+	0.0783749i
$429$	−40.4536	−	11.8782i	−1.95312	−	0.573487i
$430$	−1.16556	−	2.43878i	−0.0562081	−	0.117608i
$431$	14.4502	+	16.6765i	0.696044	+	0.803277i	0.988212	−	0.153090i	$-0.0489223\pi$
$431$	14.4502	+	16.6765i	0.696044	+	0.803277i	−0.292169	+	0.956367i	$0.594377\pi$
$432$	35.8401	−	55.7682i	1.72436	−	2.68315i
$433$	−1.98896	−	1.72344i	−0.0955833	−	0.0828234i	0.605758	−	0.795649i	$-0.292870\pi$
$433$	−1.98896	−	1.72344i	−0.0955833	−	0.0828234i	−0.701342	+	0.712825i	$0.747415\pi$
$434$	5.21804	−	1.53216i	0.250474	−	0.0735458i
$435$	21.2742	−	19.0936i	1.02002	−	0.915469i
$436$	−5.28402			−0.253059
$437$	−0.284058	−	2.23468i	−0.0135883	−	0.106899i
$438$		−	3.88196i		−	0.185487i
$439$	−11.0401	−	24.1745i	−0.526917	−	1.15379i	−0.966754	−	0.255710i	$-0.917691\pi$
$439$	−11.0401	−	24.1745i	−0.526917	−	1.15379i	0.439837	−	0.898078i	$-0.355036\pi$
$440$	−10.7754	−	16.1411i	−0.513698	−	0.769496i
$441$	31.1619	−	35.9627i	1.48390	−	1.71251i
$442$	3.66776	−	5.70715i	0.174458	−	0.271461i
$443$	−12.2165	+	10.5857i	−0.580424	+	0.502940i	−0.894865	−	0.446337i	$-0.852728\pi$
$443$	−12.2165	+	10.5857i	−0.580424	+	0.502940i	0.314441	+	0.949277i	$0.398183\pi$
$444$	3.08936	+	21.4869i	0.146614	+	1.01973i
$445$	13.4059	−	0.233746i	0.635503	−	0.0110806i
$446$	−3.45443	+	2.22003i	−0.163572	+	0.105121i
$447$	−49.2247	−	7.07744i	−2.32825	−	0.334752i
$448$	−2.03199	−	0.927981i	−0.0960027	−	0.0438430i
$449$	11.5794	−	25.3553i	0.546465	−	1.19659i	−0.411948	−	0.911207i	$-0.635151\pi$
$449$	11.5794	−	25.3553i	0.546465	−	1.19659i	0.958413	−	0.285384i	$-0.0921212\pi$
$450$	53.1561	−	26.5528i	2.50580	−	1.25171i
$451$	30.1260	−	19.3608i	1.41858	−	0.911665i
$452$	−3.00657	+	10.2394i	−0.141417	+	0.481622i
$453$	−2.68071	+	0.385428i	−0.125951	+	0.0181090i
$454$	−5.80018	−	6.69376i	−0.272216	−	0.314154i
$455$	−4.44209	−	1.22061i	−0.208248	−	0.0572232i
$456$	2.08760	−	2.40922i	0.0977610	−	0.112822i
$457$	8.91353	+	30.3567i	0.416958	+	1.42003i	0.853853	+	0.520515i	$0.174260\pi$
$457$	8.91353	+	30.3567i	0.416958	+	1.42003i	−0.436895	+	0.899512i	$0.643922\pi$
$458$	−13.4789	+	6.15559i	−0.629826	+	0.287632i
$459$	−17.2224			−0.803875
$460$	1.07609	−	7.54162i	0.0501728	−	0.351630i
$461$	−21.3245			−0.993183			−0.496591	−	0.867984i	$-0.665415\pi$
$461$	−21.3245			−0.993183			−0.496591	+	0.867984i	$0.665415\pi$
$462$	−12.4958	+	5.70665i	−0.581359	+	0.265498i
$463$	6.47788	+	22.0616i	0.301053	+	1.02529i	0.961588	+	0.274496i	$0.0885112\pi$
$463$	6.47788	+	22.0616i	0.301053	+	1.02529i	−0.660535	+	0.750795i	$0.729671\pi$
$464$	12.8750	−	14.8586i	0.597708	−	0.689792i
$465$	9.79766	−	35.6559i	0.454356	−	1.65350i
$466$	5.56186	+	6.41873i	0.257648	+	0.297342i
$467$	−39.2327	+	5.64081i	−1.81547	+	0.261026i	−0.964481	−	0.264153i	$-0.914907\pi$
$467$	−39.2327	+	5.64081i	−1.81547	+	0.261026i	−0.850992	+	0.525179i	$0.823998\pi$
$468$	4.66111	−	15.8743i	0.215460	−	0.733788i
$469$	1.29085	−	0.829577i	0.0596058	−	0.0383063i
$470$	0.346277	+	2.14255i	0.0159726	+	0.0988283i
$471$	−11.1440	+	24.4020i	−0.513490	+	1.12439i
$472$	9.97222	+	4.55416i	0.459008	+	0.209622i
$473$	2.97102	+	0.427168i	0.136608	+	0.0196412i
$474$	−72.6342	+	46.6792i	−3.33620	+	2.14404i
$475$	2.22899	−	0.739822i	0.102273	−	0.0339453i
$476$	−0.0824496	−	0.573449i	−0.00377907	−	0.0262840i
$477$	36.6339	−	31.7435i	1.67735	−	1.45343i
$478$	−3.80909	+	5.92706i	−0.174224	+	0.271097i
$479$	3.78663	−	4.37000i	0.173015	−	0.199670i	−0.662619	−	0.748957i	$-0.730555\pi$
$479$	3.78663	−	4.37000i	0.173015	−	0.199670i	0.835634	+	0.549286i	$0.185100\pi$
$480$	22.8716	−	15.2685i	1.04394	−	0.696910i
$481$	−12.8126	−	28.0556i	−0.584203	−	1.27923i
$482$		−	35.0891i		−	1.59827i
$483$	9.34621	+	2.91124i	0.425267	+	0.132466i
$484$	−4.05716			−0.184416
$485$	−10.7332	+	9.63306i	−0.487370	+	0.437415i
$486$	−44.4092	+	13.0397i	−2.01444	+	0.591493i
$487$	−12.2109	−	10.5808i	−0.553327	−	0.479460i	0.332740	−	0.943019i	$-0.392027\pi$
$487$	−12.2109	−	10.5808i	−0.553327	−	0.479460i	−0.886066	+	0.463558i	$0.846572\pi$
$488$	−2.92298	+	4.54824i	−0.132317	+	0.205889i
$489$	14.1976	+	16.3849i	0.642038	+	0.740951i
$490$	21.8959	−	10.4646i	0.989156	−	0.472743i
$491$	−24.1929	−	7.10367i	−1.09181	−	0.320584i	−0.314216	−	0.949351i	$-0.601742\pi$
$491$	−24.1929	−	7.10367i	−1.09181	−	0.320584i	−0.777594	+	0.628767i	$0.783560\pi$
$492$	10.7548	+	16.7348i	0.484864	+	0.754463i
$493$	−5.05581	−	0.726916i	−0.227702	−	0.0327387i
$494$	1.03645	−	2.26951i	0.0466322	−	0.102110i
$495$	−8.25028	+	65.4647i	−0.370823	+	2.94242i
$496$	3.61938	−	25.1734i	0.162515	−	1.13032i
$497$	−2.87912	−	4.47999i	−0.129146	−	0.200955i
$498$	−15.4732	+	52.6968i	−0.693370	+	2.36140i
$499$	1.49388	+	10.3902i	0.0668752	+	0.465128i	0.995550	+	0.0942329i	$0.0300398\pi$
$499$	1.49388	+	10.3902i	0.0668752	+	0.465128i	−0.928675	+	0.370895i	$0.879051\pi$
$500$	7.93145	−	0.415215i	0.354705	−	0.0185690i
$501$	3.52270	+	2.26390i	0.157383	+	0.101144i
$502$	20.0158	+	17.3438i	0.893349	+	0.774091i
$503$	−10.6465	−	36.2588i	−0.474705	−	1.61670i	−0.754265	−	0.656570i	$-0.772007\pi$
$503$	−10.6465	−	36.2588i	−0.474705	−	1.61670i	0.279560	−	0.960128i	$-0.409811\pi$
$504$	4.06525	+	8.90166i	0.181081	+	0.396511i
$505$	27.2597	−	8.52311i	1.21304	−	0.379274i
$506$	24.0436	+	21.5328i	1.06887	+	0.957249i
$507$		−	8.28009i		−	0.367732i
$508$	−5.90043	+	2.69464i	−0.261789	+	0.119555i
$509$	24.3006	−	7.13531i	1.07711	−	0.316267i	0.305386	−	0.952229i	$-0.401215\pi$
$509$	24.3006	−	7.13531i	1.07711	−	0.316267i	0.771721	+	0.635962i	$0.219396\pi$
$510$	−13.7782	−	6.00425i	−0.610110	−	0.265873i
$511$	0.396242	+	0.254649i	0.0175287	+	0.0112650i
$512$	−1.48238	+	1.28449i	−0.0655124	+	0.0567668i
$513$	−6.26940	+	0.901404i	−0.276801	+	0.0397979i
$514$	32.5342	+	9.55290i	1.43502	+	0.421360i
$515$	4.39439	+	3.67560i	0.193640	+	0.161966i
$516$	−0.237289	+	1.65038i	−0.0104461	+	0.0726540i
$517$	−2.19230	−	1.00119i	−0.0964170	−	0.0440322i
$518$	−9.14122	−	4.17466i	−0.401642	−	0.183424i
$519$	0.250017	−	1.73890i	0.0109745	−	0.0763294i
$520$	−9.82734	+	11.7491i	−0.430957	+	0.515233i
$521$	13.3860	+	3.93048i	0.586451	+	0.172198i	0.561480	−	0.827491i	$-0.310232\pi$
$521$	13.3860	+	3.93048i	0.586451	+	0.172198i	0.0249715	+	0.999688i	$0.492050\pi$
$522$	−47.0423	+	6.76367i	−2.05899	+	0.296038i
$523$	−7.42978	+	6.43794i	−0.324881	+	0.281511i	−0.801996	−	0.597330i	$-0.796228\pi$
$523$	−7.42978	+	6.43794i	−0.324881	+	0.281511i	0.477114	+	0.878841i	$0.341683\pi$
$524$	7.85023	+	5.04504i	0.342939	+	0.220394i
$525$	−1.09939	+	10.1465i	−0.0479815	+	0.442829i
$526$	−20.4483	+	6.00416i	−0.891587	+	0.261794i
$527$	−6.01014	+	2.74474i	−0.261806	+	0.119563i
$528$			64.2418i			2.79577i
$529$	−2.52653	−	22.8608i	−0.109849	−	0.993948i
$530$	23.5946	−	7.37716i	1.02488	−	0.320443i
$531$	−15.4836	−	33.9043i	−0.671931	−	1.47132i
$532$	−0.0600274	−	0.204435i	−0.00260252	−	0.00886337i
$533$	−21.3603	−	18.5088i	−0.925219	−	0.801707i
$534$	−26.5468	−	17.0606i	−1.14879	−	0.738283i
$535$	−3.19052	+	5.16018i	−0.137938	+	0.223094i
$536$	−0.726082	−	5.05001i	−0.0313620	−	0.218127i
$537$	−5.70828	+	19.4406i	−0.246330	+	0.838924i
$538$	−6.40931	−	9.97307i	−0.276325	−	0.429970i
$539$	−3.83521	+	26.6745i	−0.165194	+	1.14895i
$540$	−21.2516	−	2.67827i	−0.914525	−	0.115254i
$541$	1.53156	−	3.35365i	0.0658468	−	0.144184i	−0.873847	−	0.486201i	$-0.838382\pi$
$541$	1.53156	−	3.35365i	0.0658468	−	0.144184i	0.939694	+	0.342016i	$0.111110\pi$
$542$	18.8089	+	2.70432i	0.807913	+	0.116160i
$543$	4.43025	+	6.89361i	0.190120	+	0.295833i
$544$	−4.71468	−	1.38435i	−0.202140	−	0.0593537i
$545$	−7.17210	−	15.0067i	−0.307219	−	0.642816i
$546$	7.10009	+	8.19394i	0.303856	+	0.350668i
$547$	8.90580	−	13.8577i	0.380785	−	0.592512i	−0.596970	−	0.802263i	$-0.703629\pi$
$547$	8.90580	−	13.8577i	0.380785	−	0.592512i	0.977755	+	0.209751i	$0.0672654\pi$
$548$	−7.93730	−	6.87771i	−0.339065	−	0.293801i
$549$	17.6369	−	5.17866i	0.752725	−	0.221020i
$550$	−17.1948	+	28.9255i	−0.733190	+	1.23339i
$551$	−1.87849			−0.0800263
$552$	21.7144	−	24.2465i	0.924227	−	1.03200i
$553$		−	10.4760i		−	0.445486i
$554$	15.2035	+	33.2911i	0.645937	+	1.41440i
$555$	−56.8300	+	37.9384i	−2.41230	+	1.61040i
$556$	2.20495	−	2.54464i	0.0935105	−	0.107917i
$557$	−17.0009	+	26.4538i	−0.720349	+	1.12089i	0.267210	+	0.963638i	$0.413898\pi$
$557$	−17.0009	+	26.4538i	−0.720349	+	1.12089i	−0.987559	+	0.157247i	$0.949738\pi$
$558$	−46.4617	+	40.2593i	−1.96688	+	1.70431i
$559$	−0.337143	−	2.34488i	−0.0142596	−	0.0991779i
$560$	0.122371	+	7.01828i	0.00517110	+	0.296576i
$561$	14.0404	−	9.02322i	0.592786	−	0.380961i
$562$	40.2035	+	5.78039i	1.69588	+	0.243831i
$563$	36.1260	+	16.4982i	1.52253	+	0.695315i	0.988649	−	0.150246i	$-0.0480066\pi$
$563$	36.1260	+	16.4982i	1.52253	+	0.695315i	0.533879	+	0.845561i	$0.320734\pi$
$564$	0.556153	−	1.21781i	0.0234183	−	0.0512789i
$565$	−33.1610	+	5.35946i	−1.39509	+	0.225474i
$566$	−0.504599	+	0.324286i	−0.0212099	+	0.0136308i
$567$	3.85879	−	13.1418i	0.162054	−	0.551906i
$568$	−17.5265	+	2.51993i	−0.735395	+	0.105734i
$569$	9.99749	+	11.5377i	0.419116	+	0.483686i	0.925568	−	0.378583i	$-0.123588\pi$
$569$	9.99749	+	11.5377i	0.419116	+	0.483686i	−0.506451	+	0.862269i	$0.669043\pi$
$570$	−5.32987	−	1.46456i	−0.223244	−	0.0613438i
$571$	17.3423	−	20.0140i	0.725751	−	0.837561i	−0.266235	−	0.963908i	$-0.585780\pi$
$571$	17.3423	−	20.0140i	0.725751	−	0.837561i	0.991986	+	0.126347i	$0.0403253\pi$
$572$	2.63969	+	8.98996i	0.110371	+	0.375889i
$573$	56.6517	−	25.8720i	2.36666	−	1.08082i
$574$	−9.20904			−0.384378
$575$	22.8789	−	7.18027i	0.954116	−	0.299438i
$576$	25.2527			1.05220
$577$	−4.78684	+	2.18608i	−0.199279	+	0.0910076i	−0.512555	−	0.858655i	$-0.671301\pi$
$577$	−4.78684	+	2.18608i	−0.199279	+	0.0910076i	0.313276	+	0.949662i	$0.398574\pi$
$578$	−7.12839	−	24.2771i	−0.296502	−	1.00979i
$579$	−24.7460	+	28.5584i	−1.02841	+	1.18685i
$580$	−6.12558	−	1.68321i	−0.254351	−	0.0698915i
$581$	−4.36389	−	5.03620i	−0.181045	−	0.208937i
$582$	33.5975	−	4.83060i	1.39266	−	0.200235i
$583$	−7.73404	+	26.3397i	−0.320311	+	1.09088i
$584$	1.31749	−	0.846700i	0.0545182	−	0.0350367i
$585$	51.4098	−	8.30882i	2.12553	−	0.343527i
$586$	14.8080	−	32.4250i	0.611713	−	1.33946i
$587$	22.8678	+	10.4434i	0.943856	+	0.431045i	0.827062	−	0.562111i	$-0.190011\pi$
$587$	22.8678	+	10.4434i	0.943856	+	0.431045i	0.116795	+	0.993156i	$0.462738\pi$
$588$	−14.8175	−	2.13043i	−0.611063	−	0.0878576i
$589$	−2.04419	+	1.31372i	−0.0842292	+	0.0541308i
$590$	−0.331383	−	19.0057i	−0.0136428	−	0.782452i
$591$	−5.77606	−	40.1734i	−0.237595	−	1.65251i
$592$	−35.5169	+	30.7756i	−1.45974	+	1.26487i
$593$	3.35907	−	5.22681i	0.137940	−	0.214640i	−0.765410	−	0.643543i	$-0.777464\pi$
$593$	3.35907	−	5.22681i	0.137940	−	0.214640i	0.903350	+	0.428904i	$0.141100\pi$
$594$	59.4300	−	68.5859i	2.43844	−	2.81411i
$595$	1.51669	−	1.01251i	0.0621784	−	0.0415089i
$596$	4.59102	+	10.0529i	0.188056	+	0.411784i
$597$			51.7662i			2.11865i
$598$	10.9601	−	22.9958i	0.448191	−	0.940368i
$599$	−21.7863			−0.890164			−0.445082	−	0.895490i	$-0.646825\pi$
$599$	−21.7863			−0.890164			−0.445082	+	0.895490i	$0.646825\pi$
$600$	29.1695	+	17.3399i	1.19084	+	0.707897i
$601$	−14.7064	+	4.31819i	−0.599886	+	0.176143i	−0.567556	−	0.823335i	$-0.692111\pi$
$601$	−14.7064	+	4.31819i	−0.599886	+	0.176143i	−0.0323303	+	0.999477i	$0.510293\pi$
$602$	−0.583346	−	0.505472i	−0.0237754	−	0.0206015i
$603$	−9.37795	+	14.5924i	−0.381900	+	0.594247i
$604$	0.394133	+	0.454854i	0.0160370	+	0.0185077i
$605$	−5.50685	−	11.5224i	−0.223885	−	0.468452i
$606$	−64.4968	−	18.9380i	−2.62000	−	0.769302i
$607$	−18.2962	−	28.4695i	−0.742621	−	1.15554i	−0.982775	−	0.184806i	$-0.940834\pi$
$607$	−18.2962	−	28.4695i	−0.742621	−	1.15554i	0.240154	−	0.970735i	$-0.422802\pi$
$608$	−1.78872	−	0.257179i	−0.0725420	−	0.0104300i
$609$	3.39109	−	7.42544i	0.137414	−	0.300894i
$610$	9.30077	+	1.17214i	0.376577	+	0.0474587i
$611$	−0.270707	+	1.88281i	−0.0109516	+	0.0761702i
$612$	3.54077	+	5.50955i	0.143127	+	0.222710i
$613$	−0.962165	+	3.27683i	−0.0388615	+	0.132350i	−0.976639	−	0.214887i	$-0.931062\pi$
$613$	−0.962165	+	3.27683i	−0.0388615	+	0.132350i	0.937778	+	0.347237i	$0.112880\pi$
$614$	−3.58054	−	24.9032i	−0.144499	−	1.00501i
$615$	−32.9294	+	53.2582i	−1.32784	+	2.14758i
$616$	−4.66226	−	2.99625i	−0.187848	−	0.120722i
$617$	−22.5722	−	19.5589i	−0.908721	−	0.787412i	0.0689350	−	0.997621i	$-0.478040\pi$
$617$	−22.5722	−	19.5589i	−0.908721	−	0.787412i	−0.977656	+	0.210210i	$0.932585\pi$
$618$	−3.79868	−	12.9371i	−0.152805	−	0.520407i
$619$	1.80206	+	3.94596i	0.0724310	+	0.158602i	0.942384	−	0.334533i	$-0.108578\pi$
$619$	1.80206	+	3.94596i	0.0724310	+	0.158602i	−0.869953	+	0.493134i	$0.835851\pi$
$620$	−7.84306	+	2.45224i	−0.314985	+	0.0984841i
$621$	−64.1535	+	8.15478i	−2.57439	+	0.327240i
$622$		−	5.72185i		−	0.229425i
$623$	3.48284	−	1.59056i	0.139537	−	0.0637244i
$624$	48.6492	−	14.2847i	1.94753	−	0.571845i
$625$	11.9447	+	21.9619i	0.477789	+	0.878475i
$626$	−25.7467	−	16.5464i	−1.02905	−	0.661328i
$627$	4.63879	−	4.01954i	0.185256	−	0.160525i
$628$	5.90089	−	0.848420i	0.235471	−	0.0338557i
$629$	11.7148	+	3.43977i	0.467098	+	0.137152i
$630$	10.8864	−	13.0153i	0.433724	−	0.518541i
$631$	−0.273871	+	1.90481i	−0.0109026	+	0.0758293i	−0.994546	−	0.104296i	$-0.966741\pi$
$631$	−0.273871	+	1.90481i	−0.0109026	+	0.0758293i	0.983644	+	0.180125i	$0.0576502\pi$
$632$	−31.6847	−	14.4699i	−1.26035	−	0.575583i
$633$	−75.2328	−	34.3577i	−2.99024	−	1.36560i
$634$	4.28702	−	29.8169i	0.170259	−	1.18418i
$635$	−15.6616	−	13.0998i	−0.621510	−	0.519851i
$636$	−14.6315	−	4.29621i	−0.580179	−	0.170356i
$637$	21.0529	−	3.02695i	0.834145	−	0.119932i
$638$	20.3411	−	17.6257i	0.805311	−	0.697806i
$639$	50.6441	+	32.5470i	2.00345	+	1.28754i
$640$	27.5792	+	12.0184i	1.09016	+	0.475070i
$641$	−24.5825	+	7.21809i	−0.970952	+	0.285097i	−0.728485	−	0.685062i	$-0.759775\pi$
$641$	−24.5825	+	7.21809i	−0.970952	+	0.285097i	−0.242468	+	0.970159i	$0.577957\pi$
$642$	12.9883	−	5.93155i	0.512607	−	0.234100i
$643$			18.0240i			0.710797i	0.934715	+	0.355399i	$0.115655\pi$
$643$			18.0240i			0.710797i	−0.934715	+	0.355399i	$0.884345\pi$
$644$	−0.578651	−	2.09706i	−0.0228020	−	0.0826356i
$645$	−5.00918	+	1.56619i	−0.197236	+	0.0616686i
$646$	0.410286	+	0.898401i	0.0161425	+	0.0353471i
$647$	3.62058	+	12.3305i	0.142340	+	0.484764i	0.999543	−	0.0302132i	$-0.00961862\pi$
$647$	3.62058	+	12.3305i	0.142340	+	0.484764i	−0.857204	+	0.514977i	$0.827800\pi$
$648$	−34.4175	−	29.8230i	−1.35205	−	1.17156i
$649$	17.7575	+	11.4120i	0.697041	+	0.447961i
$650$	25.7281	+	6.58951i	1.00914	+	0.258462i
$651$	−1.50277	−	10.4520i	−0.0588981	−	0.409645i
$652$	1.35739	−	4.62284i	0.0531594	−	0.181044i
$653$	15.9779	+	24.8621i	0.625265	+	0.972931i	0.998970	+	0.0453834i	$0.0144509\pi$
$653$	15.9779	+	24.8621i	0.625265	+	0.972931i	−0.373705	+	0.927548i	$0.621913\pi$
$654$	−5.57095	+	38.7468i	−0.217841	+	1.51512i
$655$	−3.67272	+	29.1425i	−0.143505	+	1.13869i
$656$	−17.8902	+	39.1741i	−0.698495	+	1.52949i
$657$	−5.27037	−	0.757765i	−0.205617	−	0.0295632i
$658$	0.335075	+	0.521387i	0.0130626	+	0.0203258i
$659$	−17.2790	−	5.07358i	−0.673096	−	0.197639i	−0.0727146	−	0.997353i	$-0.523166\pi$
$659$	−17.2790	−	5.07358i	−0.673096	−	0.197639i	−0.600381	+	0.799714i	$0.704984\pi$
$660$	18.7284	−	8.95078i	0.729001	−	0.348409i
$661$	23.3762	+	26.9776i	0.909230	+	1.04931i	0.998578	+	0.0533064i	$0.0169760\pi$
$661$	23.3762	+	26.9776i	0.909230	+	1.04931i	−0.0893487	+	0.996000i	$0.528479\pi$
$662$	−6.62604	+	10.3103i	−0.257529	+	0.400722i
$663$	−9.95511	−	8.62616i	−0.386625	−	0.335012i
$664$	−21.2596	+	6.24237i	−0.825031	+	0.242251i
$665$	0.499121	−	0.447962i	0.0193551	−	0.0173712i
$666$	113.603			4.40203
$667$	−19.1771	−	0.313848i	−0.742540	−	0.0121522i
$668$		−	0.930571i		−	0.0360049i
$669$	3.31213	+	7.25255i	0.128054	+	0.280400i
$670$	−7.35743	+	4.91166i	−0.284242	+	0.189754i
$671$	−6.81701	+	7.86724i	−0.263168	+	0.303712i
$672$	4.24562	−	6.60632i	0.163778	−	0.254844i
$673$	−3.86306	+	3.34736i	−0.148910	+	0.129031i	−0.726130	−	0.687557i	$-0.758683\pi$
$673$	−3.86306	+	3.34736i	−0.148910	+	0.129031i	0.577220	+	0.816589i	$0.304137\pi$
$674$	−3.68305	−	25.6162i	−0.141866	−	0.986698i
$675$	−21.2389	−	63.9903i	−0.817486	−	2.46299i
$676$	−1.54797	+	0.994820i	−0.0595373	+	0.0382623i
$677$	12.8777	+	1.85153i	0.494930	+	0.0711601i	0.385260	−	0.922808i	$-0.374112\pi$
$677$	12.8777	+	1.85153i	0.494930	+	0.0711601i	0.109669	+	0.993968i	$0.465021\pi$
$678$	71.9140	+	32.8420i	2.76184	+	1.26129i
$679$	−1.71086	+	3.74627i	−0.0656569	+	0.143769i
$680$	−0.967415	−	5.98576i	−0.0370987	−	0.229543i
$681$	−14.4676	+	9.29773i	−0.554398	+	0.356290i
$682$	9.80885	−	33.4059i	0.375600	−	1.27918i
$683$	50.3472	−	7.23884i	1.92648	−	0.276986i	0.930483	−	0.366335i	$-0.119388\pi$
$683$	50.3472	−	7.23884i	1.92648	−	0.276986i	0.996000	+	0.0893487i	$0.0284785\pi$
$684$	1.57729	+	1.82030i	0.0603094	+	0.0696007i
$685$	8.75936	−	31.8773i	0.334678	−	1.21797i
$686$	9.35718	−	10.7988i	0.357259	−	0.412298i
$687$	8.10589	+	27.6061i	0.309259	+	1.05324i
$688$	−3.28347	+	1.49951i	−0.125181	+	0.0571682i
$689$	21.6663			0.825421
$690$	−54.1668	−	15.8419i	−2.06210	−	0.603090i
$691$	34.5692			1.31507			0.657536	−	0.753423i	$-0.271599\pi$
$691$	34.5692			1.31507			0.657536	+	0.753423i	$0.271599\pi$
$692$	−0.355128	+	0.162182i	−0.0135000	+	0.00616522i
$693$	5.30848	+	18.0790i	0.201652	+	0.686765i
$694$	−36.8550	+	42.5329i	−1.39900	+	1.61453i
$695$	10.2196	+	2.80819i	0.387653	+	0.106521i
$696$	−17.7743	−	20.5127i	−0.673734	−	0.777531i
$697$	11.0745	−	1.59227i	0.419477	−	0.0603117i
$698$	−7.49806	+	25.5360i	−0.283806	+	0.966553i
$699$	13.8731	−	8.91571i	0.524729	−	0.337223i
$700$	2.02898	−	1.01353i	0.0766883	−	0.0383077i
$701$	14.0335	−	30.7290i	0.530037	−	1.16062i	−0.435461	−	0.900207i	$-0.643415\pi$
$701$	14.0335	−	30.7290i	0.530037	−	1.16062i	0.965498	−	0.260411i	$-0.0838580\pi$
$702$	−65.1536	−	29.7546i	−2.45906	−	1.12302i
$703$	4.44450	+	0.639023i	0.167628	+	0.0241012i
$704$	−12.0309	+	7.73181i	−0.453433	+	0.291404i
$705$	4.21346	−	0.0734659i	0.158688	−	0.00276688i
$706$	7.83108	+	54.4664i	0.294727	+	2.04987i
$707$	6.16391	−	5.34106i	0.231818	−	0.200871i
$708$	−6.33931	+	9.86415i	−0.238246	+	0.370718i
$709$	22.1310	−	25.5406i	0.831148	−	0.959196i	−0.168501	−	0.985702i	$-0.553893\pi$
$709$	22.1310	−	25.5406i	0.831148	−	0.959196i	0.999649	+	0.0265056i	$0.00843798\pi$
$710$	17.0463	+	25.5346i	0.639737	+	0.958296i
$711$	49.1960	+	107.724i	1.84499	+	4.03998i
$712$		−	12.7308i		−	0.477106i
$713$	−21.0881	+	13.0699i	−0.789757	+	0.489473i
$714$	−4.29193			−0.160621
$715$	−21.9487	+	19.6990i	−0.820836	+	0.736701i
$716$	4.32027	−	1.26855i	0.161456	−	0.0474078i
$717$	10.3387	+	8.95854i	0.386106	+	0.334563i
$718$	9.25859	−	14.4066i	0.345527	−	0.537651i
$719$	−8.64717	−	9.97936i	−0.322485	−	0.372167i	0.571240	−	0.820783i	$-0.306463\pi$
$719$	−8.64717	−	9.97936i	−0.322485	−	0.372167i	−0.893725	+	0.448616i	$0.851917\pi$
$720$	−34.2166	−	71.5938i	−1.27518	−	2.66814i
$721$	1.56971	+	0.460908i	0.0584591	+	0.0171651i
$722$	−16.7150	−	26.0090i	−0.622066	−	0.967954i
$723$	−67.4381	−	9.69613i	−2.50805	−	0.360603i
$724$	0.756490	−	1.65648i	0.0281147	−	0.0615626i
$725$	−3.53402	−	19.6814i	−0.131250	−	0.730949i
$726$	−4.27746	+	29.7504i	−0.158752	+	1.10414i
$727$	−24.7010	−	38.4355i	−0.916110	−	1.42550i	−0.904931	−	0.425558i	$-0.860078\pi$
$727$	−24.7010	−	38.4355i	−0.916110	−	1.42550i	−0.0111793	−	0.999938i	$-0.503559\pi$
$728$	−1.23232	+	4.19688i	−0.0456727	+	0.155547i
$729$	3.63167	+	25.2588i	0.134506	+	0.935512i
$730$	−2.30964	−	1.42804i	−0.0854837	−	0.0528543i
$731$	0.788912	+	0.507003i	0.0291789	+	0.0187522i
$732$	−4.37020	−	3.78680i	−0.161527	−	0.139964i
$733$	13.8089	+	47.0288i	0.510043	+	1.73705i	0.662811	+	0.748786i	$0.269363\pi$
$733$	13.8089	+	47.0288i	0.510043	+	1.73705i	−0.152768	+	0.988262i	$0.548819\pi$
$734$	−15.7030	−	34.3849i	−0.579610	−	1.26917i
$735$	−14.0616	−	44.9736i	−0.518669	−	1.65888i
$736$	−18.2176	−	2.92433i	−0.671511	−	0.107792i
$737$		−	9.82343i		−	0.361851i
$738$	94.6960	−	43.2462i	3.48581	−	1.59191i
$739$	−47.4263	+	13.9256i	−1.74461	+	0.512262i	−0.989649	−	0.143512i	$-0.954160\pi$
$739$	−47.4263	+	13.9256i	−1.74461	+	0.512262i	−0.754957	+	0.655774i	$0.772342\pi$
$740$	13.9205	+	6.06627i	0.511729	+	0.223001i
$741$	−4.07540	−	2.61910i	−0.149713	−	0.0962150i
$742$	5.33516	−	4.62294i	0.195860	−	0.169713i
$743$	−5.02759	+	0.722859i	−0.184444	+	0.0265191i	−0.233918	−	0.972256i	$-0.575155\pi$
$743$	−5.02759	+	0.722859i	−0.184444	+	0.0265191i	0.0494736	+	0.998775i	$0.484246\pi$
$744$	−33.6877	−	9.89159i	−1.23505	−	0.362643i
$745$	−22.3190	+	26.6836i	−0.817705	+	0.977612i
$746$	−2.74374	+	19.0832i	−0.100456	+	0.698684i
$747$	68.5239	+	31.2938i	2.50716	+	1.14498i
$748$	−3.37380	−	1.54076i	−0.123358	−	0.0563359i
$749$	−0.246558	+	1.71485i	−0.00900902	+	0.0626591i
$750$	5.31744	−	58.5977i	0.194166	−	2.13969i
$751$	−16.5964	−	4.87313i	−0.605610	−	0.177823i	−0.0354699	−	0.999371i	$-0.511293\pi$
$751$	−16.5964	−	4.87313i	−0.605610	−	0.177823i	−0.570140	+	0.821548i	$0.693111\pi$
$752$	2.86885	−	0.412479i	0.104616	−	0.0150416i
$753$	38.8641	−	33.6760i	1.41629	−	1.22722i
$754$	−17.8706	−	11.4847i	−0.650808	−	0.418249i
$755$	−0.756828	+	1.73673i	−0.0275438	+	0.0632059i
$756$	−5.86894	+	1.72328i	−0.213451	+	0.0626750i
$757$	25.8760	−	11.8172i	0.940481	−	0.429503i	0.114640	−	0.993407i	$-0.463428\pi$
$757$	25.8760	−	11.8172i	0.940481	−	0.429503i	0.825840	+	0.563904i	$0.190701\pi$
$758$		−	25.3698i		−	0.921473i
$759$	48.0280	−	40.2596i	1.74331	−	1.46133i
$760$	−0.665452	−	2.12833i	−0.0241385	−	0.0772028i
$761$	−10.4443	−	22.8699i	−0.378606	−	0.829032i	−0.998999	−	0.0447407i	$-0.985754\pi$
$761$	−10.4443	−	22.8699i	−0.378606	−	0.829032i	0.620392	−	0.784292i	$-0.286973\pi$
$762$	13.5385	+	46.1078i	0.490447	+	1.67031i
$763$	−3.58954	−	3.11036i	−0.129950	−	0.112602i
$764$	−11.6433	−	7.48267i	−0.421239	−	0.270714i
$765$	−10.8413	+	17.5341i	−0.391966	+	0.633945i
$766$	5.45242	+	37.9224i	0.197004	+	1.37019i
$767$	4.69361	−	15.9850i	0.169476	−	0.577183i
$768$	−26.1876	−	40.7487i	−0.944964	−	1.47039i
$769$	1.87415	−	13.0350i	0.0675835	−	0.470054i	−0.927722	−	0.373272i	$-0.878236\pi$
$769$	1.87415	−	13.0350i	0.0675835	−	0.470054i	0.995306	−	0.0967819i	$-0.0308549\pi$
$770$	−1.20153	+	9.53392i	−0.0433000	+	0.343579i
$771$	27.3499	−	59.8880i	0.984984	−	2.15681i
$772$	8.31216	+	1.19511i	0.299161	+	0.0430129i
$773$	7.26298	+	11.3014i	0.261231	+	0.406484i	0.946949	−	0.321384i	$-0.104148\pi$
$773$	7.26298	+	11.3014i	0.261231	+	0.406484i	−0.685718	+	0.727867i	$0.740512\pi$
$774$	8.37223	+	2.45831i	0.300934	+	0.0883621i
$775$	−17.6099	−	18.9459i	−0.632566	−	0.680558i
$776$	8.96746	+	10.3490i	0.321913	+	0.371508i
$777$	−10.5493	+	16.4150i	−0.378454	+	0.588885i
$778$	−10.5145	−	9.11089i	−0.376964	−	0.326641i
$779$	3.94806	−	1.15926i	0.141454	−	0.0415347i
$780$	−10.9427	−	12.1924i	−0.391810	−	0.436557i
$781$	−34.0931			−1.21995
$782$	4.03842	+	9.24013i	0.144414	+	0.330426i
$783$			53.9280i			1.92723i
$784$	−13.4629	−	29.4797i	−0.480819	−	1.05285i
$785$	10.4189	+	15.6071i	0.371867	+	0.557040i
$786$	45.2709	−	52.2454i	1.61476	−	1.86353i
$787$	−18.6624	+	29.0393i	−0.665243	+	1.03514i	0.330575	+	0.943780i	$0.392757\pi$
$787$	−18.6624	+	29.0393i	−0.665243	+	1.03514i	−0.995818	+	0.0913591i	$0.970879\pi$
$788$	−6.81648	+	5.90651i	−0.242827	+	0.210411i
$789$	5.88899	+	40.9588i	0.209654	+	1.45817i
$790$	1.05290	+	60.3868i	0.0374606	+	2.14847i
$791$	−8.06970	+	5.18608i	−0.286925	+	0.184396i
$792$	62.0122	+	8.91601i	2.20351	+	0.316817i
$793$	7.47353	+	3.41305i	0.265393	+	0.121201i
$794$	−1.51720	+	3.32220i	−0.0538434	+	0.117901i
$795$	−7.65836	−	47.3851i	−0.271614	−	1.68058i
$796$	9.67775	−	6.21951i	0.343019	−	0.220445i
$797$	0.249259	−	0.848898i	0.00882921	−	0.0300695i	−0.954961	−	0.296733i	$-0.904103\pi$
$797$	0.249259	−	0.848898i	0.00882921	−	0.0300695i	0.963790	+	0.266663i	$0.0859211\pi$
$798$	−1.56237	+	0.224635i	−0.0553073	+	0.00795199i
$799$	−0.493100	−	0.569068i	−0.0174446	−	0.0201322i
$800$	−0.670606	−	19.2247i	−0.0237095	−	0.679694i
$801$	−28.3444	+	32.7112i	−1.00150	+	1.15579i
$802$	−10.4179	−	35.4803i	−0.367870	−	1.25285i
$803$	2.74293	−	1.25265i	0.0967958	−	0.0442052i
$804$	5.45685			0.192448
$805$	5.17026	−	4.48975i	0.182228	−	0.158243i
$806$	−27.4787			−0.967897
$807$	−20.9384	+	9.56225i	−0.737067	+	0.336607i
$808$	−7.64017	−	26.0200i	−0.268780	−	0.915382i
$809$	5.70849	−	6.58795i	0.200700	−	0.231620i	−0.646474	−	0.762936i	$-0.723757\pi$
$809$	5.70849	−	6.58795i	0.200700	−	0.231620i	0.847174	+	0.531316i	$0.178302\pi$
$810$	−20.9224	+	76.1412i	−0.735137	+	2.67533i
$811$	−2.71573	−	3.13412i	−0.0953622	−	0.110054i	0.706063	−	0.708150i	$-0.250470\pi$
$811$	−2.71573	−	3.13412i	−0.0953622	−	0.110054i	−0.801425	+	0.598096i	$0.795924\pi$
$812$	−1.79562	+	0.258171i	−0.0630139	+	0.00906003i
$813$	10.3949	−	35.4018i	0.364565	−	1.24159i
$814$	−54.1229	+	34.7827i	−1.89701	+	1.21913i
$815$	14.9713	−	2.41966i	0.524423	−	0.0847570i
$816$	−8.33783	+	18.2573i	−0.291883	+	0.639134i
$817$	0.313720	+	0.143271i	0.0109757	+	0.00501242i
$818$	−16.8282	−	2.41953i	−0.588384	−	0.0845969i
$819$	12.5105	−	8.04003i	0.437153	−	0.280941i
$820$	13.9130	−	0.242587i	0.485864	−	0.00847151i
$821$	2.10104	+	14.6130i	0.0733267	+	0.509999i	0.993074	+	0.117488i	$0.0374842\pi$
$821$	2.10104	+	14.6130i	0.0733267	+	0.509999i	−0.919748	+	0.392510i	$0.871607\pi$
$822$	−58.8013	+	50.9517i	−2.05093	+	1.77714i
$823$	−16.9387	+	26.3572i	−0.590447	+	0.918754i	0.409532	+	0.912296i	$0.365692\pi$
$823$	−16.9387	+	26.3572i	−0.590447	+	0.918754i	−0.999979	+	0.00645833i	$0.997944\pi$
$824$	3.56217	−	4.11096i	0.124094	−	0.143212i
$825$	50.8407	+	41.0398i	1.77005	+	1.42882i
$826$	−2.25494	−	4.93764i	−0.0784596	−	0.171802i
$827$			8.94280i			0.310972i	0.987838	+	0.155486i	$0.0496943\pi$
$827$			8.94280i			0.310972i	−0.987838	+	0.155486i	$0.950306\pi$
$828$	15.7981	+	18.8465i	0.549023	+	0.654962i
$829$	6.08831			0.211456			0.105728	−	0.994395i	$-0.466283\pi$
$829$	6.08831			0.211456			0.105728	+	0.994395i	$0.466283\pi$
$830$	25.6609	+	28.5915i	0.890702	+	0.992425i
$831$	68.1837	−	20.0205i	2.36527	−	0.694505i
$832$	8.53033	+	7.39157i	0.295736	+	0.256257i
$833$	−4.55199	+	7.08303i	−0.157717	+	0.245412i
$834$	−16.3347	−	18.8513i	−0.565626	−	0.652767i
$835$	2.64284	−	1.26308i	0.0914591	−	0.0437107i
$836$	−1.30879	−	0.384295i	−0.0452654	−	0.0132911i
$837$	37.7144	+	58.6848i	1.30360	+	2.02844i
$838$	−44.0095	−	6.32761i	−1.52028	−	0.218584i
$839$	−3.47954	+	7.61913i	−0.120127	+	0.263042i	−0.960137	−	0.279529i	$-0.909822\pi$
$839$	−3.47954	+	7.61913i	−0.120127	+	0.263042i	0.840010	+	0.542571i	$0.182549\pi$
$840$	9.61434	+	1.21166i	0.331726	+	0.0418063i
$841$	1.85097	−	12.8737i	0.0638264	−	0.443922i
$842$	−18.2866	−	28.4545i	−0.630198	−	0.980607i
$843$	22.2188	−	75.6702i	0.765255	−	2.60622i
$844$	2.61573	+	18.1928i	0.0900371	+	0.626222i
$845$	−4.92639	−	3.04597i	−0.169473	−	0.104785i
$846$	−5.89402	−	3.78785i	−0.202640	−	0.130229i
$847$	−2.75611	−	2.38818i	−0.0947010	−	0.0820589i
$848$	−9.30090	−	31.6760i	−0.319394	−	1.08776i
$849$	0.483813	+	1.05940i	0.0166044	+	0.0363586i
$850$	−8.64090	+	5.98884i	−0.296380	+	0.205415i
$851$	45.2662	+	7.26621i	1.55171	+	0.249082i
$852$		−	18.9385i		−	0.648821i
$853$	51.7952	−	23.6541i	1.77343	−	0.809900i	0.794061	−	0.607838i	$-0.207963\pi$
$853$	51.7952	−	23.6541i	1.77343	−	0.809900i	0.979373	−	0.202062i	$-0.0647641\pi$
$854$	2.56854	−	0.754191i	0.0878936	−	0.0258079i
$855$	−3.02878	+	6.95026i	−0.103582	+	0.237694i
$856$	4.84599	+	3.11433i	0.165633	+	0.106446i
$857$	−31.7900	+	27.5462i	−1.08593	+	0.940961i	−0.998475	−	0.0552073i	$-0.982418\pi$
$857$	−31.7900	+	27.5462i	−1.08593	+	0.940961i	−0.0874524	+	0.996169i	$0.527873\pi$
$858$	68.7048	−	9.87827i	2.34554	−	0.337238i
$859$	30.3932	+	8.92424i	1.03700	+	0.304491i	0.755554	−	0.655086i	$-0.227368\pi$
$859$	30.3932	+	8.92424i	1.03700	+	0.304491i	0.281447	+	0.959577i	$0.409186\pi$
$860$	0.894634	+	0.748300i	0.0305068	+	0.0255168i
$861$	−2.54472	+	17.6989i	−0.0867239	+	0.603178i
$862$	−33.0451	−	15.0912i	−1.12552	−	0.514008i
$863$	−4.83808	−	2.20948i	−0.164690	−	0.0752115i	0.331364	−	0.943503i	$-0.392491\pi$
$863$	−4.83808	−	2.20948i	−0.164690	−	0.0752115i	−0.496054	+	0.868291i	$0.665218\pi$
$864$	−7.38313	+	51.3508i	−0.251179	+	1.74699i
$865$	−0.942620	−	0.788438i	−0.0320501	−	0.0268077i
$866$	4.15724	+	1.22068i	0.141269	+	0.0414802i
$867$	−48.6281	+	6.99166i	−1.65150	+	0.237449i
$868$	−1.77346	+	1.53671i	−0.0601950	+	0.0521593i
$869$	−56.4208	−	36.2594i	−1.91394	−	1.23002i
$870$	−18.8009	+	43.1432i	−0.637410	+	1.46269i
$871$	−7.43910	+	2.18432i	−0.252064	+	0.0740128i
$872$	−14.3653	+	6.56041i	−0.486470	+	0.222163i
$873$		−	46.5569i		−	1.57571i
$874$	1.95370	+	3.15227i	0.0660850	+	0.106627i
$875$	5.63241	+	4.38666i	0.190410	+	0.148296i
$876$	0.695841	+	1.52368i	0.0235103	+	0.0514803i
$877$	−15.6402	−	53.2658i	−0.528133	−	1.79866i	−0.598484	−	0.801135i	$-0.704230\pi$
$877$	−15.6402	−	53.2658i	−0.528133	−	1.79866i	0.0703508	−	0.997522i	$-0.477588\pi$
$878$	33.0663	+	28.6521i	1.11593	+	0.966962i
$879$	−58.2260	−	37.4196i	−1.96391	−	1.26213i
$880$	38.2219	+	23.6325i	1.28846	+	0.796650i
$881$	4.81175	+	33.4665i	0.162112	+	1.12751i	0.894643	+	0.446781i	$0.147430\pi$
$881$	4.81175	+	33.4665i	0.162112	+	1.12751i	−0.732531	+	0.680733i	$0.761661\pi$
$882$	−22.0713	+	75.1678i	−0.743178	+	2.53103i
$883$	−14.4125	−	22.4263i	−0.485020	−	0.754706i	0.509362	−	0.860552i	$-0.329881\pi$
$883$	−14.4125	−	22.4263i	−0.485020	−	0.754706i	−0.994383	+	0.105846i	$0.966245\pi$
$884$	−0.416600	+	2.89752i	−0.0140118	+	0.0974541i
$885$	−36.6188	−	4.61493i	−1.23093	−	0.155129i
$886$	11.0552	−	24.2075i	0.371407	−	0.813267i
$887$	29.5701	+	4.25154i	0.992868	+	0.142753i	0.619556	−	0.784953i	$-0.287313\pi$
$887$	29.5701	+	4.25154i	0.992868	+	0.142753i	0.373312	+	0.927706i	$0.378222\pi$
$888$	35.0761	+	54.5794i	1.17708	+	1.83157i
$889$	−5.59444	−	1.64268i	−0.187631	−	0.0550936i
$890$	−19.9162	+	9.51848i	−0.667593	+	0.319060i
$891$	−57.4221	−	66.2686i	−1.92371	−	2.22008i
$892$	0.957932	−	1.49057i	0.0320739	−	0.0499080i
$893$	−0.209285	−	0.181347i	−0.00700347	−	0.00606854i
$894$	78.5567	−	23.0663i	2.62733	−	0.771454i
$895$	9.46666	+	10.5478i	0.316436	+	0.352574i
$896$	8.59095			0.287003
$897$	−41.1672	−	27.4187i	−1.37453	−	0.915483i
$898$			45.8901i			1.53137i
$899$	8.59450	+	18.8193i	0.286643	+	0.627660i
$900$	−16.1043	+	19.9503i	−0.536810	+	0.665008i
$901$	−5.61657	+	6.48187i	−0.187115	+	0.215942i
$902$	−31.8742	+	49.5972i	−1.06129	+	1.65140i
$903$	−1.13267	+	0.981461i	−0.0376928	+	0.0326610i
$904$	4.53908	+	31.5700i	0.150968	+	1.05000i
$905$	5.73123	−	0.0999296i	0.190512	−	0.00332177i
$906$	3.75090	−	2.41056i	0.124615	−	0.0800853i
$907$	−4.23567	−	0.608997i	−0.140643	−	0.0202214i	0.0716337	−	0.997431i	$-0.477179\pi$
$907$	−4.23567	−	0.608997i	−0.140643	−	0.0202214i	−0.212277	+	0.977210i	$0.568088\pi$
$908$	3.47644	+	1.58764i	0.115370	+	0.0526876i
$909$	−38.3012	+	83.8679i	−1.27037	+	2.78172i
$910$	7.48703	−	1.21005i	0.248193	−	0.0401128i
$911$	10.3673	−	6.66263i	0.343483	−	0.220743i	−0.357514	−	0.933908i	$-0.616375\pi$
$911$	10.3673	−	6.66263i	0.343483	−	0.220743i	0.700996	+	0.713165i	$0.252739\pi$
$912$	−2.07961	+	7.08251i	−0.0688629	+	0.234525i
$913$	−42.2277	+	6.07142i	−1.39753	+	0.200935i
$914$	−34.1096	−	39.3646i	−1.12825	−	1.30207i
$915$	4.82282	−	17.5513i	0.159438	−	0.580229i
$916$	4.18710	−	4.83217i	0.138346	−	0.159659i
$917$	2.36314	+	8.04812i	0.0780378	+	0.265772i
$918$	25.7914	−	11.7786i	0.851244	−	0.388750i
$919$	−27.5906			−0.910129			−0.455064	−	0.890459i	$-0.650384\pi$
$919$	−27.5906			−0.910129			−0.455064	+	0.890459i	$0.650384\pi$
$920$	−6.43786	−	21.8389i	−0.212250	−	0.720006i
$921$	−48.8511			−1.60970
$922$	31.9345	−	14.5840i	1.05171	−	0.480299i
$923$	7.58086	+	25.8180i	0.249527	+	0.849811i
$924$	3.88173	−	4.47975i	0.127699	−	0.147373i
$925$	1.66628	+	47.7684i	0.0547871	+	1.57061i
$926$	−24.7891	−	28.6081i	−0.814619	−	0.940121i
$927$	−18.3057	+	2.63196i	−0.601237	+	0.0864449i
$928$	−4.33478	+	14.7629i	−0.142296	+	0.484616i
$929$	11.3678	−	7.30566i	0.372966	−	0.239691i	−0.340707	−	0.940169i	$-0.610666\pi$
$929$	11.3678	−	7.30566i	0.372966	−	0.239691i	0.713673	+	0.700479i	$0.247030\pi$
$930$	9.71287	+	60.0971i	0.318497	+	1.97066i
$931$	−1.28632	+	2.81665i	−0.0421574	+	0.0923118i
$932$	−3.33360	−	1.52240i	−0.109196	−	0.0498680i
$933$	−10.9969	−	1.58111i	−0.360022	−	0.0517633i
$934$	54.8951	−	35.2789i	1.79622	−	1.15436i
$935$	−0.203529	−	11.6729i	−0.00665612	−	0.381746i
$936$	−7.03698	−	48.9433i	−0.230011	−	1.59976i
$937$	36.8543	−	31.9344i	1.20398	−	1.04325i	0.206073	−	0.978537i	$-0.433931\pi$
$937$	36.8543	−	31.9344i	1.20398	−	1.04325i	0.997904	−	0.0647155i	$-0.0206140\pi$
$938$	−1.36575	+	2.12515i	−0.0445934	+	0.0693887i
$939$	−38.9153	+	44.9106i	−1.26995	+	1.46560i
$940$	−0.519966	−	0.778885i	−0.0169594	−	0.0254044i
$941$	−18.6918	−	40.9292i	−0.609334	−	1.33425i	−0.923029	−	0.384731i	$-0.874294\pi$
$941$	−18.6918	−	40.9292i	−0.609334	−	1.33425i	0.313695	−	0.949524i	$-0.398433\pi$
$942$		−	44.1647i		−	1.43896i
$943$	40.4986	−	11.1750i	1.31882	−	0.363907i
$944$	−25.3847			−0.826202
$945$	−12.8602	−	14.3289i	−0.418341	−	0.466118i
$946$	−4.74139	+	1.39220i	−0.154156	+	0.0452642i
$947$	−3.88956	−	3.37033i	−0.126394	−	0.109521i	0.589370	−	0.807863i	$-0.299376\pi$
$947$	−3.88956	−	3.37033i	−0.126394	−	0.109521i	−0.715764	+	0.698342i	$0.753921\pi$
$948$	20.1419	−	31.3414i	0.654177	−	1.01792i
$949$	−1.55852	−	1.79863i	−0.0505918	−	0.0583860i
$950$	−2.83205	+	2.63234i	−0.0918840	+	0.0854045i
$951$	−56.1207	−	16.4785i	−1.81984	−	0.534353i
$952$	−0.936119	−	1.45663i	−0.0303398	−	0.0472097i
$953$	12.3212	+	1.77151i	0.399121	+	0.0573850i	0.338953	−	0.940803i	$-0.389927\pi$
$953$	12.3212	+	1.77151i	0.399121	+	0.0573850i	0.0601682	+	0.998188i	$0.480836\pi$
$954$	−33.1515	+	72.5916i	−1.07332	+	2.35024i
$955$	5.44729	−	43.2234i	0.176270	−	1.39868i
$956$	0.432653	−	3.00917i	0.0139930	−	0.0973234i
$957$	−28.2541	−	43.9642i	−0.913324	−	1.42116i
$958$	−2.68198	+	9.13400i	−0.0866509	+	0.295106i
$959$	−1.34351	−	9.34434i	−0.0433843	−	0.301744i
$960$	13.1505	−	21.2689i	0.424430	−	0.686450i
$961$	−3.56499	−	2.29108i	−0.115000	−	0.0739058i
$962$	38.3749	+	33.2521i	1.23726	+	1.07209i
$963$	−5.51768	−	18.7915i	−0.177805	−	0.605548i
$964$	6.28972	+	13.7726i	0.202578	+	0.443585i
$965$	7.88812	+	25.2288i	0.253928	+	0.812144i
$966$	−15.9874	+	2.03222i	−0.514387	+	0.0653855i
$967$		−	14.8332i		−	0.477004i	−0.971142	−	0.238502i	$-0.923344\pi$
$967$		−	14.8332i		−	0.477004i	0.971142	−	0.238502i	$-0.0766563\pi$
$968$	−11.0299	+	5.03719i	−0.354515	+	0.161901i
$969$	1.84002	−	0.540278i	0.0591099	−	0.0173562i
$970$	9.48538	−	21.7665i	0.304557	−	0.698880i
$971$	40.8875	+	26.2768i	1.31214	+	0.843263i	0.994479	−	0.104940i	$-0.0334651\pi$
$971$	40.8875	+	26.2768i	1.31214	+	0.843263i	0.317664	+	0.948203i	$0.397101\pi$
$972$	15.0933	−	13.0785i	0.484119	−	0.419492i
$973$	2.99573	−	0.430721i	0.0960386	−	0.0138083i
$974$	25.5226	+	7.49412i	0.817798	+	0.240127i
$975$	19.7739	−	47.6263i	0.633270	−	1.52526i
$976$	1.78161	−	12.3914i	0.0570280	−	0.396639i
$977$	27.7315	+	12.6646i	0.887210	+	0.405175i	0.806273	−	0.591544i	$-0.201481\pi$
$977$	27.7315	+	12.6646i	0.887210	+	0.405175i	0.0809371	+	0.996719i	$0.474209\pi$
$978$	−32.4674	−	14.8274i	−1.03819	−	0.474126i
$979$	3.48845	−	24.2627i	0.111491	−	0.775440i
$980$	−6.71841	+	8.03223i	−0.214612	+	0.256580i
$981$	51.5174	+	15.1269i	1.64483	+	0.482964i
$982$	41.0883	−	5.90761i	1.31118	−	0.188519i
$983$	14.2083	−	12.3116i	0.453176	−	0.392679i	−0.398147	−	0.917322i	$-0.630347\pi$
$983$	14.2083	−	12.3116i	0.453176	−	0.392679i	0.851323	+	0.524643i	$0.175801\pi$
$984$	50.0155	+	32.1430i	1.59444	+	1.02468i
$985$	−26.0267	−	11.3419i	−0.829280	−	0.361383i
$986$	8.06847	−	2.36912i	0.256952	−	0.0754480i
$987$	1.09465	−	0.499909i	0.0348431	−	0.0159123i
$988$			1.07657i			0.0342504i
$989$	3.17876	+	1.51504i	0.101079	+	0.0481754i
$990$	−32.4166	−	103.679i	−1.03027	−	3.29514i
$991$	−17.6204	−	38.5833i	−0.559730	−	1.22564i	−0.952088	−	0.305826i	$-0.901068\pi$
$991$	−17.6204	−	38.5833i	−0.559730	−	1.22564i	0.392357	−	0.919813i	$-0.371660\pi$
$992$	5.60727	+	19.0966i	0.178031	+	0.606318i
$993$	17.9845	+	15.5837i	0.570722	+	0.494534i
$994$	7.37552	+	4.73996i	0.233937	+	0.150342i
$995$	30.7993	+	19.0431i	0.976404	+	0.603707i
$996$	−3.37264	−	23.4572i	−0.106866	−	0.743270i
$997$	8.99299	−	30.6273i	0.284811	−	0.969977i	−0.685491	−	0.728081i	$-0.740413\pi$
$997$	8.99299	−	30.6273i	0.284811	−	0.969977i	0.970302	−	0.241896i	$-0.0777692\pi$
$998$	−9.34307	−	14.5381i	−0.295750	−	0.460196i
$999$	18.3452	−	127.594i	0.580416	−	4.03688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.4.3	✓	100
5.2	odd	4		575.2.k.g.326.3		100
5.3	odd	4		575.2.k.g.326.8		100
5.4	even	2	inner	115.2.j.a.4.8	yes	100
23.6	even	11	inner	115.2.j.a.29.8	yes	100
115.29	even	22	inner	115.2.j.a.29.3	yes	100
115.52	odd	44		575.2.k.g.351.3		100
115.98	odd	44		575.2.k.g.351.8		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.4.3	✓	100	1.1	even	1	trivial
115.2.j.a.4.8	yes	100	5.4	even	2	inner
115.2.j.a.29.3	yes	100	115.29	even	22	inner
115.2.j.a.29.8	yes	100	23.6	even	11	inner
575.2.k.g.326.3		100	5.2	odd	4
575.2.k.g.326.8		100	5.3	odd	4
575.2.k.g.351.3		100	115.52	odd	44
575.2.k.g.351.8		100	115.98	odd	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49755 + 0.683908i) q^{2} +(0.900592 + 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(2.15615 + 0.592474i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(0.632042 - 0.0908739i) q^{7} +(0.598154 - 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +O(q^{10})\)	\(q+(-1.49755 + 0.683908i) q^{2} +(0.900592 + 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(2.15615 + 0.592474i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(0.632042 - 0.0908739i) q^{7} +(0.598154 - 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +(-3.63413 + 0.587347i) q^{10} +(1.69819 - 3.71852i) q^{11} +(2.06561 + 0.943334i) q^{12} +(-3.19357 - 0.459166i) q^{13} +(-0.884364 + 0.568346i) q^{14} +(0.124611 + 7.14678i) q^{15} +(0.699637 + 4.86608i) q^{16} +(0.965240 - 0.836385i) q^{17} +(6.42487 - 9.99729i) q^{18} +(0.307596 - 0.354985i) q^{19} +(1.32113 - 0.881953i) q^{20} +(0.847934 + 1.85672i) q^{21} +6.73007i q^{22} +(3.19949 - 3.57257i) q^{23} +6.78684 q^{24} +(4.29795 + 2.55492i) q^{25} +(5.09656 - 1.49648i) q^{26} +(-10.1910 - 8.83052i) q^{27} +(0.245239 - 0.381599i) q^{28} +(-2.61894 - 3.02242i) q^{29} +(-5.07435 - 10.6174i) q^{30} +(-4.96368 - 1.45747i) q^{31} +(-2.07999 - 3.23653i) q^{32} +(12.9346 + 1.85971i) q^{33} +(-0.873484 + 1.91266i) q^{34} +(1.41662 + 0.178531i) q^{35} +(-0.729764 + 5.07562i) q^{36} +(5.16825 + 8.04195i) q^{37} +(-0.217863 + 0.741974i) q^{38} +(-1.46778 - 10.2086i) q^{39} +(2.49665 - 4.03796i) q^{40} +(7.36949 + 4.73608i) q^{41} +(-2.53965 - 2.20062i) q^{42} +(0.206862 + 0.704508i) q^{43} +(-1.20636 - 2.64157i) q^{44} +(-15.4054 + 4.81669i) q^{45} +(-2.34808 + 7.53826i) q^{46} -0.589562i q^{47} +(-14.2948 + 6.52824i) q^{48} +(-6.32523 + 1.85726i) q^{49} +(-8.18372 - 0.886725i) q^{50} +(3.43459 + 2.20728i) q^{51} +(-1.73217 + 1.50093i) q^{52} +(-6.64695 + 0.955686i) q^{53} +(21.3007 + 6.25446i) q^{54} +(5.86468 - 7.01154i) q^{55} +(0.192937 - 1.34191i) q^{56} +(1.36581 + 0.623742i) q^{57} +(5.98905 + 2.73511i) q^{58} +(-0.734852 + 5.11101i) q^{59} +(3.89487 + 3.25779i) q^{60} +(-2.44333 - 0.717427i) q^{61} +(8.43012 - 1.21207i) q^{62} +(-3.48343 + 3.01841i) q^{63} +(-2.94303 - 1.89137i) q^{64} +(-6.61377 - 2.88214i) q^{65} +(-20.6420 + 6.06105i) q^{66} +(2.18587 - 0.998254i) q^{67} -0.907297i q^{68} +(13.8390 + 6.59584i) q^{69} +(-2.24355 + 0.701475i) q^{70} +(-3.46453 - 7.58626i) q^{71} +(4.31771 + 14.7048i) q^{72} +(0.557471 + 0.483051i) q^{73} +(-13.2397 - 8.50861i) q^{74} +(-3.96560 + 15.4833i) q^{75} +(-0.0474869 - 0.330279i) q^{76} +(0.735411 - 2.50458i) q^{77} +(9.17984 + 14.2841i) q^{78} +(2.33484 - 16.2392i) q^{79} +(-1.37451 + 10.9065i) q^{80} +(8.91062 - 19.5115i) q^{81} +(-14.2752 - 2.05247i) q^{82} +(-5.64215 - 8.77936i) q^{83} +(1.39128 + 0.408516i) q^{84} +(2.57674 - 1.23149i) q^{85} +(-0.791605 - 0.913560i) q^{86} +(6.91157 - 10.7546i) q^{87} +(-6.55931 - 5.68368i) q^{88} +(5.75334 - 1.68933i) q^{89} +(19.7761 - 17.7491i) q^{90} -2.06020 q^{91} +(-0.429603 - 3.37968i) q^{92} -16.5368i q^{93} +(0.403206 + 0.882897i) q^{94} +(0.873542 - 0.583157i) q^{95} +(8.05365 - 9.29441i) q^{96} +(-3.48701 + 5.42589i) q^{97} +(8.20215 - 7.10721i) q^{98} +(4.19947 + 29.2080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

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