LMFDB - Embedded newform 115.2.j.a.4.8

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			4.8
Character	$\chi$	$=$	115.4
Dual form			115.2.j.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49755 - 0.683908i) q^{2} +(-0.900592 - 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(1.43463 + 1.71518i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(-0.632042 + 0.0908739i) q^{7} +(-0.598154 + 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +O(q^{10})$	\(q+(1.49755 - 0.683908i) q^{2} +(-0.900592 - 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(1.43463 + 1.71518i) 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} +(3.32145 + 1.58741i) 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} +(3.96867 - 5.94488i) 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} +(1.58822 + 0.0276922i) q^{20} +(0.847934 + 1.85672i) q^{21} -6.73007i q^{22} +(-3.19949 + 3.57257i) q^{23} +6.78684 q^{24} +(-0.883674 + 4.92129i) 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} +(1.87753 - 11.6170i) 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} +(-1.06261 - 0.953694i) 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} +(-4.35217 + 1.89658i) 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} +(2.04236 + 7.97423i) 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} +(8.81420 - 2.42200i) 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} +(-1.34540 - 4.89623i) 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} +(3.79404 + 6.13628i) 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} +(15.8901 - 1.72173i) 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} +(-7.34248 + 8.18103i) 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} +(-2.81931 - 0.455656i) 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} +(-26.3644 + 3.32261i) q^{90} -2.06020 q^{91} +(0.429603 + 3.37968i) q^{92} +16.5368i q^{93} +(0.403206 + 0.882897i) q^{94} +(1.05015 + 0.0183104i) 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	0.191671	−	0.981459i	$-0.438609\pi$
$2$	1.49755	−	0.683908i	1.05893	−	0.483596i	0.867255	+	0.497863i	$0.165882\pi$
$3$	−0.900592	−	3.06714i	−0.519957	−	1.77081i	−0.629686	−	0.776850i	$-0.716816\pi$
$3$	−0.900592	−	3.06714i	−0.519957	−	1.77081i	0.109729	−	0.993962i	$-0.465002\pi$
$4$	0.465201	−	0.536871i	0.232601	−	0.268436i
$5$	1.43463	+	1.71518i	0.641586	+	0.767051i
$5$	1.43463	+	1.71518i	0.641586	+	0.767051i
$6$	−3.44632	−	3.97726i	−1.40695	−	1.62371i
$7$	−0.632042	+	0.0908739i	−0.238889	+	0.0343471i	−0.260719	−	0.965415i	$-0.583960\pi$
$7$	−0.632042	+	0.0908739i	−0.238889	+	0.0343471i	0.0218302	+	0.999762i	$0.493051\pi$
$8$	−0.598154	+	2.03713i	−0.211480	+	0.720233i
$9$	−6.07249	+	3.90255i	−2.02416	+	1.30085i
$10$	3.32145	+	1.58741i	1.05034	+	0.501983i
$11$	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	0.570144	−	0.821545i	$-0.306887\pi$
$13$	3.19357	+	0.459166i	0.885738	+	0.127350i	0.315593	+	0.948895i	$0.397796\pi$
$14$	−0.884364	+	0.568346i	−0.236356	+	0.151897i
$15$	3.96867	−	5.94488i	1.02471	−	1.53496i
$16$	0.699637	+	4.86608i	0.174909	+	1.21652i
$17$	−0.965240	+	0.836385i	−0.234105	+	0.202853i	−0.764011	−	0.645203i	$-0.776773\pi$
$17$	−0.965240	+	0.836385i	−0.234105	+	0.202853i	0.529906	+	0.848056i	$0.322227\pi$
$18$	−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	$0.210114\pi$
$20$	1.58822	+	0.0276922i	0.355137	+	0.00619216i
$21$	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
$25$	−0.883674	+	4.92129i	−0.176735	+	0.984258i
$26$	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	$0.893822\pi$
$30$	1.87753	−	11.6170i	0.342788	−	2.12096i
$31$	−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
$35$	−1.06261	−	0.953694i	−0.179614	−	0.161204i
$36$	−0.729764	+	5.07562i	−0.121627	+	0.845936i
$37$	−5.16825	−	8.04195i	−0.849655	−	1.32209i	−0.945143	−	0.326658i	$-0.894077\pi$
$37$	−5.16825	−	8.04195i	−0.849655	−	1.32209i	0.0954879	−	0.995431i	$-0.469559\pi$
$38$	0.217863	−	0.741974i	0.0353421	−	0.120364i
$39$	−1.46778	−	10.2086i	−0.235033	−	1.63469i
$40$	−4.35217	+	1.89658i	−0.688138	+	0.299876i
$41$	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	0.942215	−	0.335009i	$-0.108739\pi$
$43$	−0.206862	−	0.704508i	−0.0315462	−	0.107436i	−0.973761	+	0.227572i	$0.926921\pi$
$44$	−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	$0.0136910\pi$
$47$			0.589562i			0.0859964i	−0.999075	+	0.0429982i	$0.986309\pi$
$48$	14.2948	−	6.52824i	2.06328	−	0.942270i
$49$	−6.32523	+	1.85726i	−0.903605	+	0.265322i
$50$	2.04236	+	7.97423i	0.288834	+	1.12773i
$51$	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	0.330239	−	0.943897i	$-0.392871\pi$
$53$	6.64695	−	0.955686i	0.913028	−	0.131274i	0.582789	+	0.812624i	$0.301961\pi$
$54$	21.3007	+	6.25446i	2.89866	+	0.851124i
$55$	8.81420	−	2.42200i	1.18851	−	0.326582i
$56$	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	$0.936340\pi$
$60$	−1.34540	−	4.89623i	−0.173691	−	0.632100i
$61$	−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
$65$	3.79404	+	6.13628i	0.470593	+	0.761112i
$66$	−20.6420	+	6.06105i	−2.54086	+	0.746063i
$67$	−2.18587	+	0.998254i	−0.267047	+	0.121956i	−0.544439	−	0.838801i	$-0.683257\pi$
$67$	−2.18587	+	0.998254i	−0.267047	+	0.121956i	0.277392	+	0.960757i	$0.410530\pi$
$68$			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	0.621627	−	0.783314i	$-0.286472\pi$
$73$	−0.557471	−	0.483051i	−0.0652470	−	0.0565369i	−0.686874	+	0.726777i	$0.741018\pi$
$74$	−13.2397	−	8.50861i	−1.53908	−	0.989106i
$75$	15.8901	−	1.72173i	1.83483	−	0.198808i
$76$	−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	$-0.328750\pi$
$80$	−7.34248	+	8.18103i	−0.820914	+	0.914667i
$81$	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	$0.0123063\pi$
$83$	5.64215	+	8.77936i	0.619307	+	0.963660i	−0.379946	+	0.925009i	$0.624057\pi$
$84$	1.39128	+	0.408516i	0.151801	+	0.0445727i
$85$	−2.81931	−	0.455656i	−0.305797	−	0.0494228i
$86$	−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	$0.306147\pi$
$90$	−26.3644	+	3.32261i	−2.77906	+	0.350234i
$91$	−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
$95$	1.05015	+	0.0183104i	0.107743	+	0.00187860i
$96$	8.05365	−	9.29441i	0.821972	−	0.948607i
$97$	3.48701	−	5.42589i	0.354052	−	0.550916i	−0.617852	−	0.786295i	$-0.711997\pi$
$97$	3.48701	−	5.42589i	0.354052	−	0.550916i	0.971904	+	0.235379i	$0.0756331\pi$
$98$	−8.20215	+	7.10721i	−0.828543	+	0.717936i
$99$	4.19947	+	29.2080i	0.422063	+	2.93551i
$100$	2.23101	+	2.76381i	0.223101	+	0.276381i
$101$	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	0.297276	−	0.954792i	$-0.403922\pi$
$103$	−2.33053	−	1.06432i	−0.229634	−	0.104870i	−0.526909	+	0.849921i	$0.676649\pi$
$104$	−2.84563	+	6.23106i	−0.279037	+	0.611006i
$105$	−1.96813	+	4.11806i	−0.192070	+	0.401881i
$106$	9.30052	−	5.97708i	0.903347	−	0.580546i
$107$	0.764393	−	2.60328i	0.0738967	−	0.251669i	−0.914257	−	0.405134i	$-0.867225\pi$
$107$	0.764393	−	2.60328i	0.0738967	−	0.251669i	0.988154	+	0.153465i	$0.0490432\pi$
$108$	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	$0.888665\pi$
$110$	11.5433	−	9.65516i	1.10061	−	0.920583i
$111$	−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	0.348790	−	0.937201i	$-0.386593\pi$
$113$	13.6649	−	6.24056i	1.28549	−	0.587063i	0.936698	+	0.350138i	$0.113865\pi$
$114$	−2.47194			−0.231519
$115$	−10.7177	−	0.362380i	−0.999429	−	0.0337921i
$116$	−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
$120$	9.73660	+	11.6406i	0.888826	+	1.06264i
$121$	−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
$125$	−9.70864	+	5.54457i	−0.868367	+	0.495922i
$126$	3.15229	−	6.90255i	0.280828	−	0.614928i
$127$	8.30599	+	3.79322i	0.737038	+	0.336594i	0.748316	−	0.663343i	$-0.230863\pi$
$127$	8.30599	+	3.79322i	0.737038	+	0.336594i	−0.0112781	+	0.999936i	$0.503590\pi$
$128$	−13.3171	−	1.91471i	−1.17707	−	0.169238i
$129$	−1.97452	+	1.26895i	−0.173847	+	0.111725i
$130$	9.87841	+	6.59460i	0.866394	+	0.578385i
$131$	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
$135$	−0.525657	+	30.1478i	−0.0452414	+	2.59471i
$136$	−1.12646	−	2.46660i	−0.0965932	−	0.211510i
$137$			14.7844i			1.26311i	0.775329	+	0.631557i	$0.217584\pi$
$137$			14.7844i			1.26311i	−0.775329	+	0.631557i	$0.782416\pi$
$138$	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	$0.435577\pi$
$140$	−1.00634	+	0.126825i	−0.0850511	+	0.0107187i
$141$	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
$145$	1.42678	−	8.82800i	0.118487	−	0.733126i
$146$	−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	$0.916434\pi$
$150$	22.6187	−	13.4457i	1.84681	−	1.09784i
$151$	−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
$155$	−4.62122	−	10.6045i	−0.371186	−	0.851775i
$156$	−6.16354	−	3.96106i	−0.493478	−	0.317139i
$157$	−6.34230	−	5.49563i	−0.506171	−	0.438599i	0.363964	−	0.931413i	$-0.381423\pi$
$157$	−6.34230	−	5.49563i	−0.506171	−	0.438599i	−0.870135	+	0.492814i	$0.835968\pi$
$158$	−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	−0.642104	−	0.766617i	$-0.721938\pi$
$163$	−6.16937	+	2.81746i	−0.483222	+	0.220680i	0.158882	+	0.987298i	$0.449211\pi$
$164$	5.97096	−	1.75323i	0.466254	−	0.136904i
$165$	−15.3666	−	24.8531i	−1.19629	−	1.93481i
$166$	14.4537	+	9.28881i	1.12182	+	0.720952i
$167$	−0.990001	+	0.857841i	−0.0766086	+	0.0663817i	−0.692323	−	0.721587i	$-0.743413\pi$
$167$	−0.990001	+	0.857841i	−0.0766086	+	0.0663817i	0.615715	+	0.787969i	$0.288867\pi$
$168$	−4.28956	+	0.616746i	−0.330947	+	0.0475830i
$169$	−2.48534	−	0.729761i	−0.191180	−	0.0561355i
$170$	−4.53368	+	1.24578i	−0.347718	+	0.0955471i
$171$	−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	0.434328	−	0.900755i	$-0.356986\pi$
$173$	0.499912	+	0.228302i	0.0380076	+	0.0173575i	−0.396321	+	0.918112i	$0.629713\pi$
$174$	−2.99525	+	20.8324i	−0.227069	+	1.57930i
$175$	0.111302	−	3.19076i	0.00841364	−	0.241199i
$176$	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	$0.605695\pi$
$180$	−9.75253	+	6.02996i	−0.726911	+	0.449447i
$181$	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
$190$	1.58517	−	0.690784i	0.115000	−	0.0501147i
$191$	−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	0.531296	−	0.847186i	$-0.321705\pi$
$193$	−6.39108	−	9.94471i	−0.460040	−	0.715836i	−0.991336	+	0.131350i	$0.958069\pi$
$194$	1.51116	−	10.5103i	0.108495	−	0.754598i
$195$	15.4039	−	17.1631i	1.10310	−	1.22908i
$196$	−1.94540	+	4.25983i	−0.138957	+	0.304274i
$197$	12.5674	+	1.80693i	0.895393	+	0.128738i	0.574622	−	0.818419i	$-0.305149\pi$
$197$	12.5674	+	1.80693i	0.895393	+	0.128738i	0.320771	+	0.947157i	$0.396058\pi$
$198$	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	$0.396307\pi$
$200$	−9.49672	−	4.74385i	−0.671520	−	0.335441i
$201$	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
$205$	2.44926	+	19.4345i	0.171064	+	1.35737i
$206$	−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
$210$	−0.130997	+	7.51301i	−0.00903964	+	0.518447i
$211$	−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
$215$	0.911586	−	1.36551i	0.0621697	−	0.0931273i
$216$	−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
$220$	2.80008	−	5.85880i	0.188781	−	0.395001i
$221$	−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	−0.224480	−	0.974479i	$-0.572068\pi$
$223$	−2.46883	+	0.354964i	−0.165325	+	0.0237701i	0.0591553	+	0.998249i	$0.481159\pi$
$224$	−1.60876	−	1.85660i	−0.107490	−	0.124050i
$225$	−13.8395	−	33.3331i	−0.922633	−	2.22221i
$226$	16.1959	−	18.6911i	1.07734	−	1.24331i
$227$	−1.51570	−	5.16201i	−0.100601	−	0.342615i	0.893776	−	0.448513i	$-0.148046\pi$
$227$	−1.51570	−	5.16201i	−0.100601	−	0.342615i	−0.994377	+	0.105899i	$0.966228\pi$
$228$	−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	$0.403884\pi$
$230$	−16.2981	+	6.78722i	−1.07466	+	0.447536i
$231$	8.34419			0.549007
$232$	7.72358	−	3.52724i	0.507078	−	0.231575i
$233$	1.45343	+	4.94991i	0.0952171	+	0.324280i	0.993303	−	0.115541i	$-0.0368602\pi$
$233$	1.45343	+	4.94991i	0.0952171	+	0.324280i	−0.898086	+	0.439821i	$0.855042\pi$
$234$	−25.1087	+	28.9770i	−1.64141	+	1.89428i
$235$	−1.01120	+	0.845803i	−0.0659636	+	0.0551741i
$236$	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	$0.273983\pi$
$240$	31.7049	+	15.1526i	2.04654	+	0.978097i
$241$	−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
$245$	−12.2599	−	8.18443i	−0.783256	−	0.522884i
$246$	−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
$250$	−10.7472	+	14.9431i	−0.679712	+	0.945084i
$251$	−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
$255$	1.14149	+	9.05757i	0.0714830	+	0.567207i
$256$	−14.5391	+	4.26907i	−0.908694	+	0.266817i
$257$	15.5654	+	13.4875i	0.970944	+	0.841328i	0.987353	−	0.158538i	$-0.0506779\pi$
$257$	15.5654	+	13.4875i	0.970944	+	0.841328i	−0.0164089	+	0.999865i	$0.505223\pi$
$258$	−2.08910	+	3.25070i	−0.130062	+	0.202380i
$259$	3.99735	+	4.61319i	0.248383	+	0.286650i
$260$	5.05938	+	0.817695i	0.313770	+	0.0507113i
$261$	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	−0.264558	−	0.964370i	$-0.585226\pi$
$263$	−12.8132	−	1.84226i	−0.790094	−	0.113598i	−0.525536	+	0.850771i	$0.676135\pi$
$264$	11.5253	−	25.2370i	0.709336	−	1.55323i
$265$	11.1751	+	10.0296i	0.686480	+	0.616116i
$266$	−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	$0.884095\pi$
$270$	19.8311	+	45.5074i	1.20689	+	2.76949i
$271$	−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	$0.232784\pi$
$277$			22.2304i			1.33570i	−0.744298	+	0.667848i	$0.767216\pi$
$278$	7.09803	−	3.24156i	0.425711	−	0.194416i
$279$	35.8297	−	10.5206i	2.14507	−	0.629849i
$280$	2.57840	−	1.59422i	0.154089	−	0.0952727i
$281$	−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	−0.153025	−	0.988222i	$-0.548902\pi$
$283$	−0.360630	+	0.0518507i	−0.0214372	+	0.00308220i	0.131588	+	0.991305i	$0.457992\pi$
$284$	−5.68454	−	1.66913i	−0.337316	−	0.0990448i
$285$	−0.889595	−	3.23744i	−0.0526951	−	0.191769i
$286$	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
$290$	−3.90087	−	14.1962i	−0.229067	−	0.833627i
$291$	−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	−0.0292653	−	0.999572i	$-0.509317\pi$
$293$	16.3635	−	14.1791i	0.955967	−	0.828350i	0.985233	+	0.171221i	$0.0547713\pi$
$294$	29.1856	+	18.7564i	1.70214	+	1.09390i
$295$	−9.82053	+	6.07200i	−0.571773	+	0.353526i
$296$	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
$305$	−2.27476	−	5.21999i	−0.130252	−	0.298896i
$306$	−2.16004	−	15.0234i	−0.123482	−	0.858833i
$307$	4.30546	−	14.6631i	0.245726	−	0.836865i	−0.740584	−	0.671964i	$-0.765451\pi$
$307$	4.30546	−	14.6631i	0.245726	−	0.836865i	0.986310	−	0.164902i	$-0.0527307\pi$
$308$	1.00252	+	1.55995i	0.0571240	+	0.0888867i
$309$	−1.16555	+	8.10656i	−0.0663057	+	0.461166i
$310$	−14.1730	−	12.7203i	−0.804973	−	0.722464i
$311$	−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	0.431748	−	0.901994i	$-0.357897\pi$
$313$	−10.0505	−	15.6389i	−0.568090	−	0.883965i	−0.999837	+	0.0180296i	$0.994261\pi$
$314$	−13.2564	−	3.89243i	−0.748102	−	0.219663i
$315$	10.1745	+	1.64440i	0.573270	+	0.0926516i
$316$	−7.63218	−	8.80801i	−0.429344	−	0.495489i
$317$	9.89235	−	15.3928i	0.555610	−	0.864545i	−0.443893	−	0.896080i	$-0.646403\pi$
$317$	9.89235	−	15.3928i	0.555610	−	0.864545i	0.999503	+	0.0315344i	$0.0100394\pi$
$318$	−26.7085	−	23.1430i	−1.49774	−	1.29780i
$319$	−15.6864	+	4.60594i	−0.878269	+	0.257883i
$320$	−0.978121	−	7.76124i	−0.0546787	−	0.433867i
$321$	−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
$325$	−5.08177	+	15.3107i	−0.281886	+	0.849288i
$326$	−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
$330$	−40.0095	−	26.7094i	−2.20245	−	1.47030i
$331$	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
$335$	−4.84810	−	2.31704i	−0.264880	−	0.126593i
$336$	−8.44169	+	5.42514i	−0.460532	+	0.295966i
$337$	4.42873	−	15.0829i	0.241248	−	0.821616i	−0.746476	−	0.665412i	$-0.768256\pi$
$337$	4.42873	−	15.0829i	0.241248	−	0.821616i	0.987725	−	0.156204i	$-0.0499259\pi$
$338$	−4.22101	+	0.606889i	−0.229592	+	0.0330104i
$339$	−31.4472	−	36.2920i	−1.70798	−	1.97111i
$340$	−1.55618	+	1.30164i	−0.0843955	+	0.0705911i
$341$	−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
$345$	8.54079	+	33.1989i	0.459821	+	1.78737i
$346$	0.904780			0.0486413
$347$	−31.0955	+	14.2008i	−1.66929	+	0.762341i	−0.669485	+	0.742825i	$0.733485\pi$
$347$	−31.0955	+	14.2008i	−1.66929	+	0.762341i	−0.999810	+	0.0195162i	$0.993787\pi$
$348$	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	$0.0848453\pi$
$350$	−2.01551	−	4.85445i	−0.107733	−	0.259481i
$351$	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	$0.439846\pi$
$353$	−9.41658	+	32.0699i	−0.501194	+	1.70691i	−0.689050	+	0.724714i	$0.741972\pi$
$354$	22.8604	−	14.6915i	1.21501	−	0.780842i
$355$	8.04147	−	16.8258i	0.426797	−	0.893018i
$356$	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	$0.406694\pi$
$360$	19.0270	−	28.5015i	1.00281	−	1.50216i
$361$	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
$365$	0.0287548	−	1.64916i	0.00150509	−	0.0863211i
$366$	5.56710	+	12.1902i	0.290997	+	0.637195i
$367$		−	22.9608i		−	1.19854i	−0.800546	−	0.599271i	$-0.795457\pi$
$367$		−	22.9608i		−	1.19854i	0.800546	−	0.599271i	$-0.204543\pi$
$368$	−19.6229	−	13.0695i	−1.02291	−	0.681294i
$369$	−63.2340			−3.29183
$370$	−4.40022	−	34.9151i	−0.228757	−	1.81515i
$371$	−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	−0.965569	−	0.260148i	$-0.916229\pi$
$373$	−6.33121	+	9.85156i	−0.327818	+	0.510094i	0.637751	+	0.770243i	$0.279865\pi$
$374$	5.62893	+	6.49613i	0.291065	+	0.335907i
$375$	25.7495	+	24.7843i	1.32970	+	1.27986i
$376$	−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	$0.265889\pi$
$380$	0.498361	−	0.555276i	0.0255654	−	0.0284851i
$381$	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	$0.293582\pi$
$383$	−6.55633	+	22.3288i	−0.335013	+	1.14095i	−0.938989	+	0.343947i	$0.888236\pi$
$384$	6.12059	+	42.5697i	0.312340	+	2.17237i
$385$	−5.35084	+	2.33178i	−0.272704	+	0.118839i
$386$	−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
$395$	31.2028	−	19.2926i	1.56998	−	0.970714i
$396$	17.6345	+	11.3330i	0.886167	+	0.569505i
$397$	−1.67657	+	1.45276i	−0.0841449	+	0.0729120i	−0.695918	−	0.718122i	$-0.745002\pi$
$397$	−1.67657	+	1.45276i	−0.0841449	+	0.0729120i	0.611773	+	0.791034i	$0.290457\pi$
$398$	26.3893	−	3.79421i	1.32278	−	0.190186i
$399$	0.919927	+	0.270115i	0.0460540	+	0.0135227i
$400$	−24.5657	−	0.856913i	−1.22828	−	0.0428457i
$401$	−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
$405$	46.2492	−	12.7085i	2.29814	−	0.631492i
$406$	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	$0.599639\pi$
$410$	16.9593	+	27.4291i	0.837560	+	1.35463i
$411$	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	$0.452507\pi$
$420$	1.29529	+	2.97236i	0.0632037	+	0.145036i
$421$	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
$425$	−3.26314	−	5.48932i	−0.158285	−	0.266271i
$426$	−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
$430$	0.431260	−	2.66836i	0.0207972	−	0.128680i
$431$	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	0.701342	−	0.712825i	$-0.252585\pi$
$433$	1.98896	+	1.72344i	0.0955833	+	0.0828234i	−0.605758	+	0.795649i	$0.707130\pi$
$434$	5.21804	−	1.53216i	0.250474	−	0.0735458i
$435$	−28.3616	+	3.57431i	−1.35984	+	0.171375i
$436$	−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	$-0.355036\pi$
$440$	−0.338334	+	19.4044i	−0.0161295	+	0.925067i
$441$	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	−0.314441	−	0.949277i	$-0.601817\pi$
$443$	12.2165	−	10.5857i	0.580424	−	0.502940i	0.894865	+	0.446337i	$0.147272\pi$
$444$	3.08936	+	21.4869i	0.146614	+	1.01973i
$445$	11.1514	+	7.44444i	0.528628	+	0.352900i
$446$	−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	$-0.0921212\pi$
$450$	−43.5221	−	40.4530i	−2.05165	−	1.90697i
$451$	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
$455$	−2.95562	−	3.53360i	−0.138562	−	0.165658i
$456$	2.08760	−	2.40922i	0.0977610	−	0.112822i
$457$	−8.91353	−	30.3567i	−0.416958	−	1.42003i	−0.853853	−	0.520515i	$-0.825740\pi$
$457$	−8.91353	−	30.3567i	−0.416958	−	1.42003i	0.436895	−	0.899512i	$-0.356078\pi$
$458$	13.4789	−	6.15559i	0.629826	−	0.287632i
$459$	−17.2224			−0.803875
$460$	−5.18043	+	5.58543i	−0.241539	+	0.260422i
$461$	−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	$-0.911489\pi$
$463$	−6.47788	−	22.0616i	−0.301053	−	1.02529i	0.660535	−	0.750795i	$-0.270329\pi$
$464$	12.8750	−	14.8586i	0.597708	−	0.689792i
$465$	−28.3636	+	23.7243i	−1.31533	+	1.10019i
$466$	5.56186	+	6.41873i	0.257648	+	0.297342i
$467$	39.2327	−	5.64081i	1.81547	−	0.261026i	0.850992	−	0.525179i	$-0.176002\pi$
$467$	39.2327	−	5.64081i	1.81547	−	0.261026i	0.964481	+	0.264153i	$0.0850925\pi$
$468$	−4.66111	+	15.8743i	−0.215460	+	0.733788i
$469$	1.29085	−	0.829577i	0.0596058	−	0.0383063i
$470$	−0.935875	+	1.95820i	−0.0431687	+	0.0903250i
$471$	−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
$475$	1.47517	+	1.82746i	0.0676854	+	0.0838497i
$476$	−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	$0.185100\pi$
$480$	27.4956	+	0.479412i	1.25500	+	0.0218821i
$481$	−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
$485$	14.3089	−	1.80330i	0.649736	−	0.0818838i
$486$	−44.4092	+	13.0397i	−2.01444	+	0.591493i
$487$	12.2109	+	10.5808i	0.553327	+	0.479460i	0.886066	−	0.463558i	$-0.153428\pi$
$487$	12.2109	+	10.5808i	0.553327	+	0.479460i	−0.332740	+	0.943019i	$0.607973\pi$
$488$	2.92298	−	4.54824i	0.132317	−	0.205889i
$489$	14.1976	+	16.3849i	0.642038	+	0.740951i
$490$	−23.9572	−	3.87195i	−1.08228	−	0.174917i
$491$	−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
$495$	−44.0722	+	49.1054i	−1.98090	+	2.20713i
$496$	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	$0.879051\pi$
$500$	−1.53975	+	7.79163i	−0.0688598	+	0.348452i
$501$	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	$0.227993\pi$
$503$	10.6465	+	36.2588i	0.474705	+	1.61670i	−0.279560	+	0.960128i	$0.590189\pi$
$504$	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	$0.219396\pi$
$510$	7.90398	+	12.7835i	0.349994	+	0.566062i
$511$	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
$515$	−1.51795	−	5.52418i	−0.0668890	−	0.243424i
$516$	−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
$520$	−14.7698	+	4.05850i	−0.647699	+	0.177977i
$521$	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	−0.477114	−	0.878841i	$-0.658317\pi$
$523$	7.42978	−	6.43794i	0.324881	−	0.281511i	0.801996	+	0.597330i	$0.203772\pi$
$524$	7.85023	+	5.04504i	0.342939	+	0.220394i
$525$	−9.88674	+	2.53220i	−0.431493	+	0.110514i
$526$	−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
$535$	5.56172	−	2.42368i	0.240454	−	0.104785i
$536$	−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
$540$	15.9410	+	14.3070i	0.685990	+	0.615677i
$541$	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
$545$	2.65370	−	16.4194i	0.113672	−	0.703331i
$546$	7.10009	+	8.19394i	0.303856	+	0.350668i
$547$	−8.90580	+	13.8577i	−0.380785	+	0.592512i	−0.977755	−	0.209751i	$-0.932735\pi$
$547$	−8.90580	+	13.8577i	−0.380785	+	0.592512i	0.596970	+	0.802263i	$0.296371\pi$
$548$	7.93730	+	6.87771i	0.339065	+	0.293801i
$549$	17.6369	−	5.17866i	0.752725	−	0.221020i
$550$	33.1206	+	5.94719i	1.41227	+	0.253589i
$551$	−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
$555$	−68.3195	−	1.19122i	−2.90000	−	0.0505644i
$556$	2.20495	−	2.54464i	0.0935105	−	0.107917i
$557$	17.0009	−	26.4538i	0.720349	−	1.12089i	−0.267210	−	0.963638i	$-0.586102\pi$
$557$	17.0009	−	26.4538i	0.720349	−	1.12089i	0.987559	−	0.157247i	$-0.0502619\pi$
$558$	46.4617	−	40.2593i	1.96688	−	1.70431i
$559$	−0.337143	−	2.34488i	−0.0142596	−	0.0991779i
$560$	3.89731	−	5.83799i	0.164691	−	0.246700i
$561$	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	−0.533879	−	0.845561i	$-0.679266\pi$
$563$	−36.1260	−	16.4982i	−1.52253	−	0.695315i	−0.988649	+	0.150246i	$0.951993\pi$
$564$	0.556153	−	1.21781i	0.0234183	−	0.0512789i
$565$	30.3078	+	14.4849i	1.27506	+	0.609384i
$566$	−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	$0.669043\pi$
$570$	−3.54632	−	4.23982i	−0.148539	−	0.177587i
$571$	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
$575$	−14.7544	−	18.9026i	−0.615299	−	0.788294i
$576$	25.2527			1.05220
$577$	4.78684	−	2.18608i	0.199279	−	0.0910076i	−0.313276	−	0.949662i	$-0.601426\pi$
$577$	4.78684	−	2.18608i	0.199279	−	0.0910076i	0.512555	+	0.858655i	$0.328699\pi$
$578$	7.12839	+	24.2771i	0.296502	+	1.00979i
$579$	−24.7460	+	28.5584i	−1.02841	+	1.18685i
$580$	−4.07576	−	4.87280i	−0.169237	−	0.202332i
$581$	−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
$585$	−46.9864	−	22.4561i	−1.94265	−	0.928444i
$586$	14.8080	−	32.4250i	0.611713	−	1.33946i
$587$	−22.8678	−	10.4434i	−0.943856	−	0.431045i	−0.116795	−	0.993156i	$-0.537262\pi$
$587$	−22.8678	−	10.4434i	−0.943856	−	0.431045i	−0.827062	+	0.562111i	$0.809989\pi$
$588$	14.8175	+	2.13043i	0.611063	+	0.0878576i
$589$	−2.04419	+	1.31372i	−0.0842292	+	0.0541308i
$590$	−10.5540	+	15.8095i	−0.434503	+	0.650865i
$591$	−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	−0.903350	−	0.428904i	$-0.858900\pi$
$593$	−3.35907	+	5.22681i	−0.137940	+	0.214640i	0.765410	+	0.643543i	$0.222536\pi$
$594$	59.4300	−	68.5859i	2.43844	−	2.81411i
$595$	1.82333	+	0.0317915i	0.0747492	+	0.00130333i
$596$	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	$0.646825\pi$
$600$	−5.99735	+	33.4000i	−0.244841	+	1.36355i
$601$	−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
$605$	2.03755	−	12.6071i	0.0828383	−	0.512552i
$606$	−64.4968	−	18.9380i	−2.62000	−	0.769302i
$607$	18.2962	+	28.4695i	0.742621	+	1.15554i	0.982775	+	0.184806i	$0.0591658\pi$
$607$	18.2962	+	28.4695i	0.742621	+	1.15554i	−0.240154	+	0.970735i	$0.577198\pi$
$608$	1.78872	+	0.257179i	0.0725420	+	0.0104300i
$609$	3.39109	−	7.42544i	0.137414	−	0.300894i
$610$	−6.97656	−	6.26146i	−0.282472	−	0.253519i
$611$	−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	−0.937778	−	0.347237i	$-0.887120\pi$
$613$	0.962165	−	3.27683i	0.0388615	−	0.132350i	0.976639	+	0.214887i	$0.0689382\pi$
$614$	−3.58054	−	24.9032i	−0.144499	−	1.00501i
$615$	57.4025	−	25.0148i	2.31469	−	1.00869i
$616$	−4.66226	−	2.99625i	−0.187848	−	0.120722i
$617$	22.5722	+	19.5589i	0.908721	+	0.787412i	0.977656	−	0.210210i	$-0.0674146\pi$
$617$	22.5722	+	19.5589i	0.908721	+	0.787412i	−0.0689350	+	0.997621i	$0.521960\pi$
$618$	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
$625$	−23.4382	−	8.69764i	−0.937530	−	0.347906i
$626$	−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
$630$	16.3615	−	4.49587i	0.651857	−	0.179120i
$631$	−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
$635$	5.40998	+	19.6881i	0.214688	+	0.781300i
$636$	−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
$640$	−15.8210	−	25.5881i	−0.625381	−	1.01146i
$641$	−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	$-0.884345\pi$
$643$		−	18.0240i		−	0.710797i	0.934715	−	0.355399i	$-0.115655\pi$
$644$	−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	0.857204	−	0.514977i	$-0.172200\pi$
$647$	−3.62058	−	12.3305i	−0.142340	−	0.484764i	−0.999543	+	0.0302132i	$0.990381\pi$
$648$	34.4175	+	29.8230i	1.35205	+	1.17156i
$649$	17.7575	+	11.4120i	0.697041	+	0.447961i
$650$	2.86094	+	26.4041i	0.112215	+	1.03565i
$651$	−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	$-0.985549\pi$
$653$	−15.9779	−	24.8621i	−0.625265	−	0.972931i	0.373705	−	0.927548i	$-0.378087\pi$
$654$	−5.57095	+	38.7468i	−0.217841	+	1.51512i
$655$	−19.6193	+	21.8599i	−0.766590	+	0.854139i
$656$	−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	$0.704984\pi$
$660$	−20.4915	−	3.31182i	−0.797629	−	0.128912i
$661$	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
$665$	−0.665402	+	0.0838582i	−0.0258032	+	0.00325188i
$666$	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
$670$	−8.84491	−	0.154220i	−0.341709	−	0.00595802i
$671$	−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	−0.577220	−	0.816589i	$-0.695863\pi$
$673$	3.86306	−	3.34736i	0.148910	−	0.129031i	0.726130	+	0.687557i	$0.241317\pi$
$674$	−3.68305	−	25.6162i	−0.141866	−	0.986698i
$675$	−52.4631	+	42.3494i	−2.01930	+	1.63003i
$676$	−1.54797	+	0.994820i	−0.0595373	+	0.0382623i
$677$	−12.8777	−	1.85153i	−0.494930	−	0.0711601i	−0.109669	−	0.993968i	$-0.534979\pi$
$677$	−12.8777	−	1.85153i	−0.494930	−	0.0711601i	−0.385260	+	0.922808i	$0.625888\pi$
$678$	−71.9140	−	32.8420i	−2.76184	−	1.26129i
$679$	−1.71086	+	3.74627i	−0.0656569	+	0.143769i
$680$	2.61461	−	5.47074i	0.100266	−	0.209793i
$681$	−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	−0.996000	−	0.0893487i	$-0.971521\pi$
$683$	−50.3472	+	7.23884i	−1.92648	+	0.276986i	−0.930483	+	0.366335i	$0.880612\pi$
$684$	1.57729	+	1.82030i	0.0603094	+	0.0696007i
$685$	−25.3578	+	21.2101i	−0.968873	+	0.810396i
$686$	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
$690$	35.4953	+	43.8759i	1.35128	+	1.67033i
$691$	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
$695$	6.79981	+	8.12954i	0.257931	+	0.308371i
$696$	−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
$700$	−1.66125	−	1.54410i	−0.0627894	−	0.0583616i
$701$	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
$705$	3.50487	+	2.33977i	0.132001	+	0.0881210i
$706$	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	$0.00843798\pi$
$710$	0.535232	−	30.6970i	0.0200869	−	1.15204i
$711$	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
$715$	29.2609	−	3.68764i	1.09429	−	0.137910i
$716$	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	$0.851917\pi$
$720$	12.6602	−	78.3337i	0.471819	−	2.91932i
$721$	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
$725$	17.1885	−	10.2177i	0.638365	−	0.379477i
$726$	−4.27746	+	29.7504i	−0.158752	+	1.10414i
$727$	24.7010	+	38.4355i	0.916110	+	1.42550i	0.904931	+	0.425558i	$0.139922\pi$
$727$	24.7010	+	38.4355i	0.916110	+	1.42550i	0.0111793	+	0.999938i	$0.496441\pi$
$728$	1.23232	−	4.19688i	0.0456727	−	0.155547i
$729$	3.63167	+	25.2588i	0.134506	+	0.935512i
$730$	−1.08481	−	2.48937i	−0.0401507	−	0.0921356i
$731$	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	$-0.730637\pi$
$733$	−13.8089	−	47.0288i	−0.510043	−	1.73705i	0.152768	−	0.988262i	$-0.451181\pi$
$734$	−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	$0.772342\pi$
$740$	−7.98562	−	12.9155i	−0.293557	−	0.474784i
$741$	−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	−0.0494736	−	0.998775i	$-0.515754\pi$
$743$	5.02759	−	0.722859i	0.184444	−	0.0265191i	0.233918	+	0.972256i	$0.424845\pi$
$744$	−33.6877	−	9.89159i	−1.23505	−	0.362643i
$745$	−33.5439	+	9.21732i	−1.22895	+	0.337696i
$746$	−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
$750$	55.5113	+	19.5055i	2.02699	+	0.712238i
$751$	−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
$755$	−1.61134	+	0.996286i	−0.0586427	+	0.0362586i
$756$	−5.86894	+	1.72328i	−0.213451	+	0.0626750i
$757$	−25.8760	+	11.8172i	−0.940481	+	0.429503i	−0.825840	−	0.563904i	$-0.809299\pi$
$757$	−25.8760	+	11.8172i	−0.940481	+	0.429503i	−0.114640	+	0.993407i	$0.536572\pi$
$758$			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
$765$	18.8985	−	8.23555i	0.683275	−	0.297757i
$766$	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	$-0.0308549\pi$
$770$	−6.41842	+	7.15144i	−0.231304	+	0.257720i
$771$	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	0.685718	−	0.727867i	$-0.259488\pi$
$773$	−7.26298	−	11.3014i	−0.261231	−	0.406484i	−0.946949	+	0.321384i	$0.895852\pi$
$774$	8.37223	+	2.45831i	0.300934	+	0.0883621i
$775$	11.5589	−	23.1398i	0.415208	−	0.831205i
$776$	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
$780$	−2.04846	−	16.2542i	−0.0733467	−	0.581995i
$781$	−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
$785$	0.327140	−	18.7624i	0.0116761	−	0.669658i
$786$	45.2709	−	52.2454i	1.61476	−	1.86353i
$787$	18.6624	−	29.0393i	0.665243	−	1.03514i	−0.330575	−	0.943780i	$-0.607243\pi$
$787$	18.6624	−	29.0393i	0.665243	−	1.03514i	0.995818	−	0.0913591i	$-0.0291211\pi$
$788$	6.81648	−	5.90651i	0.242827	−	0.210411i
$789$	5.88899	+	40.9588i	0.209654	+	1.45817i
$790$	33.5333	−	50.2314i	1.19306	−	1.78715i
$791$	−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
$795$	20.6981	−	43.3081i	0.734085	−	1.53598i
$796$	9.67775	−	6.21951i	0.343019	−	0.220445i
$797$	−0.249259	+	0.848898i	−0.00882921	+	0.0300695i	−0.963790	−	0.266663i	$-0.914079\pi$
$797$	−0.249259	+	0.848898i	−0.00882921	+	0.0300695i	0.954961	+	0.296733i	$0.0958970\pi$
$798$	1.56237	−	0.224635i	0.0553073	−	0.00795199i
$799$	−0.493100	−	0.569068i	−0.0174446	−	0.0201322i
$800$	−17.7659	+	7.37621i	−0.628121	+	0.260788i
$801$	−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
$805$	6.80695	−	0.744918i	0.239913	−	0.0262549i
$806$	−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	$0.178302\pi$
$810$	60.5690	−	50.6618i	2.12818	−	1.78008i
$811$	−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
$815$	−13.6832	−	6.53956i	−0.479302	−	0.229071i
$816$	−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
$820$	11.5732	+	7.72603i	0.404155	+	0.269805i
$821$	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	$-0.634308\pi$
$823$	16.9387	−	26.3572i	0.590447	−	0.918754i	0.999979	−	0.00645833i	$-0.00205576\pi$
$824$	3.56217	−	4.11096i	0.124094	−	0.143212i
$825$	20.5821	−	62.0115i	0.716578	−	2.15896i
$826$	−2.25494	−	4.93764i	−0.0784596	−	0.171802i
$827$		−	8.94280i		−	0.310972i	−0.987838	−	0.155486i	$-0.950306\pi$
$827$		−	8.94280i		−	0.310972i	0.987838	−	0.155486i	$-0.0496943\pi$
$828$	−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	$0.466283\pi$
$830$	4.80370	+	38.1166i	0.166739	+	1.32305i
$831$	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
$835$	−2.89163	−	0.467344i	−0.100069	−	0.0161731i
$836$	−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	$0.182549\pi$
$840$	−7.21176	−	6.47256i	−0.248830	−	0.223325i
$841$	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
$845$	−2.31387	−	5.30974i	−0.0795996	−	0.182660i
$846$	−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	$0.792037\pi$
$853$	−51.7952	+	23.6541i	−1.77343	+	0.809900i	−0.979373	+	0.202062i	$0.935236\pi$
$854$	2.56854	−	0.754191i	0.0878936	−	0.0258079i
$855$	−6.44848	+	3.98707i	−0.220533	+	0.136355i
$856$	4.84599	+	3.11433i	0.165633	+	0.106446i
$857$	31.7900	−	27.5462i	1.08593	−	0.940961i	0.0874524	−	0.996169i	$-0.472127\pi$
$857$	31.7900	−	27.5462i	1.08593	−	0.940961i	0.998475	+	0.0552073i	$0.0175820\pi$
$858$	−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	$0.409186\pi$
$860$	−0.309034	−	1.12464i	−0.0105380	−	0.0383500i
$861$	−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	0.496054	−	0.868291i	$-0.334782\pi$
$863$	4.83808	+	2.20948i	0.164690	+	0.0752115i	−0.331364	+	0.943503i	$0.607509\pi$
$864$	−7.38313	+	51.3508i	−0.251179	+	1.74699i
$865$	0.325610	+	1.18497i	0.0110711	+	0.0402901i
$866$	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
$870$	−40.0284	+	24.7494i	−1.35709	+	0.839085i
$871$	−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	$0.295770\pi$
$877$	15.6402	+	53.2658i	0.528133	+	1.79866i	−0.0703508	+	0.997522i	$0.522412\pi$
$878$	−33.0663	−	28.6521i	−1.11593	−	0.966962i
$879$	−58.2260	−	37.4196i	−1.96391	−	1.26213i
$880$	17.9524	+	41.1961i	0.605175	+	1.38872i
$881$	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	0.994383	−	0.105846i	$-0.0337550\pi$
$883$	14.4125	+	22.4263i	0.485020	+	0.754706i	−0.509362	+	0.860552i	$0.670119\pi$
$884$	−0.416600	+	2.89752i	−0.0140118	+	0.0974541i
$885$	27.4679	+	24.6525i	0.923325	+	0.828685i
$886$	11.0552	−	24.2075i	0.371407	−	0.813267i
$887$	−29.5701	−	4.25154i	−0.992868	−	0.142753i	−0.373312	−	0.927706i	$-0.621778\pi$
$887$	−29.5701	−	4.25154i	−0.992868	−	0.142753i	−0.619556	+	0.784953i	$0.712687\pi$
$888$	−35.0761	−	54.5794i	−1.17708	−	1.83157i
$889$	−5.59444	−	1.64268i	−0.187631	−	0.0550936i
$890$	21.7911	+	3.52187i	0.730440	+	0.118053i
$891$	−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
$895$	1.77215	+	14.0618i	0.0592366	+	0.470033i
$896$	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
$900$	−24.3337	−	8.07657i	−0.811124	−	0.269219i
$901$	−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
$905$	4.76739	+	3.18260i	0.158473	+	0.105793i
$906$	3.75090	−	2.41056i	0.124615	−	0.0800853i
$907$	4.23567	+	0.608997i	0.140643	+	0.0202214i	0.212277	−	0.977210i	$-0.431912\pi$
$907$	4.23567	+	0.608997i	0.140643	+	0.0202214i	−0.0716337	+	0.997431i	$0.522821\pi$
$908$	−3.47644	−	1.58764i	−0.115370	−	0.0526876i
$909$	−38.3012	+	83.8679i	−1.27037	+	2.78172i
$910$	−6.84284	−	3.27038i	−0.226838	−	0.108412i
$911$	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
$915$	−13.9618	+	11.6781i	−0.461562	+	0.386065i
$916$	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	$0.650384\pi$
$920$	7.14904	−	21.6165i	0.235697	−	0.712675i
$921$	−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
$925$	44.1438	−	18.3280i	1.45144	−	0.602621i
$926$	−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	$0.247030\pi$
$930$	−26.2507	+	54.9263i	−0.860796	+	1.80111i
$931$	−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
$935$	−6.48209	+	9.70987i	−0.211987	+	0.317547i
$936$	−7.03698	−	48.9433i	−0.230011	−	1.59976i
$937$	−36.8543	+	31.9344i	−1.20398	+	1.04325i	−0.206073	+	0.978537i	$0.566069\pi$
$937$	−36.8543	+	31.9344i	−1.20398	+	1.04325i	−0.997904	+	0.0647155i	$0.979386\pi$
$938$	1.36575	−	2.12515i	0.0445934	−	0.0693887i
$939$	−38.9153	+	44.9106i	−1.26995	+	1.46560i
$940$	−0.0163263	+	0.936354i	−0.000532504	+	0.0305405i
$941$	−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
$945$	−2.40741	−	19.1025i	−0.0783132	−	0.621403i
$946$	−4.74139	+	1.39220i	−0.154156	+	0.0452642i
$947$	3.88956	+	3.37033i	0.126394	+	0.109521i	0.715764	−	0.698342i	$-0.246079\pi$
$947$	3.88956	+	3.37033i	0.126394	+	0.109521i	−0.589370	+	0.807863i	$0.700624\pi$
$948$	−20.1419	+	31.3414i	−0.654177	+	1.01792i
$949$	−1.55852	−	1.79863i	−0.0505918	−	0.0583860i
$950$	3.45895	+	1.72783i	0.112223	+	0.0560583i
$951$	−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	−0.0601682	−	0.998188i	$-0.519164\pi$
$953$	−12.3212	−	1.77151i	−0.399121	−	0.0573850i	−0.338953	+	0.940803i	$0.610073\pi$
$954$	−33.1515	+	72.5916i	−1.07332	+	2.35024i
$955$	29.0989	−	32.4221i	0.941617	−	1.04915i
$956$	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
$960$	−22.9239	+	9.98975i	−0.739866	+	0.322418i
$961$	−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	$0.0766563\pi$
$967$			14.8332i			0.477004i	−0.971142	+	0.238502i	$0.923344\pi$
$968$	11.0299	−	5.03719i	0.354515	−	0.161901i
$969$	1.84002	−	0.540278i	0.0591099	−	0.0173562i
$970$	20.1950	−	12.4865i	0.648424	−	0.400918i
$971$	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
$975$	51.5367	+	1.79773i	1.65050	+	0.0575736i
$976$	1.78161	−	12.3914i	0.0570280	−	0.396639i
$977$	−27.7315	−	12.6646i	−0.887210	−	0.405175i	−0.0809371	−	0.996719i	$-0.525791\pi$
$977$	−27.7315	−	12.6646i	−0.887210	−	0.405175i	−0.806273	+	0.591544i	$0.798519\pi$
$978$	32.4674	+	14.8274i	1.03819	+	0.474126i
$979$	3.48845	−	24.2627i	0.111491	−	0.775440i
$980$	−10.0973	+	2.77457i	−0.322546	+	0.0886305i
$981$	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	−0.851323	−	0.524643i	$-0.824199\pi$
$983$	−14.2083	+	12.3116i	−0.453176	+	0.392679i	0.398147	+	0.917322i	$0.369653\pi$
$984$	50.0155	+	32.1430i	1.59444	+	1.02468i
$985$	14.9304	+	24.1477i	0.475723	+	0.769409i
$986$	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
$995$	14.4661	+	33.1959i	0.458606	+	1.05238i
$996$	−3.37264	−	23.4572i	−0.106866	−	0.743270i
$997$	−8.99299	+	30.6273i	−0.284811	+	0.969977i	0.685491	+	0.728081i	$0.259587\pi$
$997$	−8.99299	+	30.6273i	−0.284811	+	0.969977i	−0.970302	+	0.241896i	$0.922231\pi$
$998$	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.4.8	yes	100
5.2	odd	4		575.2.k.g.326.8		100
5.3	odd	4		575.2.k.g.326.3		100
5.4	even	2	inner	115.2.j.a.4.3	✓	100
23.6	even	11	inner	115.2.j.a.29.3	yes	100
115.29	even	22	inner	115.2.j.a.29.8	yes	100
115.52	odd	44		575.2.k.g.351.8		100
115.98	odd	44		575.2.k.g.351.3		100

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

\(f(q)\)	\(=\)	\(q+(1.49755 - 0.683908i) q^{2} +(-0.900592 - 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(1.43463 + 1.71518i) q^{5} +(-3.44632 - 3.97726i) q^{6} +(-0.632042 + 0.0908739i) q^{7} +(-0.598154 + 2.03713i) q^{8} +(-6.07249 + 3.90255i) q^{9} +O(q^{10})\)	\(q+(1.49755 - 0.683908i) q^{2} +(-0.900592 - 3.06714i) q^{3} +(0.465201 - 0.536871i) q^{4} +(1.43463 + 1.71518i) 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} +(3.32145 + 1.58741i) 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} +(3.96867 - 5.94488i) 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} +(1.58822 + 0.0276922i) q^{20} +(0.847934 + 1.85672i) q^{21} -6.73007i q^{22} +(-3.19949 + 3.57257i) q^{23} +6.78684 q^{24} +(-0.883674 + 4.92129i) 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} +(1.87753 - 11.6170i) 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} +(-1.06261 - 0.953694i) 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} +(-4.35217 + 1.89658i) 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} +(2.04236 + 7.97423i) 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} +(8.81420 - 2.42200i) 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} +(-1.34540 - 4.89623i) 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} +(3.79404 + 6.13628i) 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} +(15.8901 - 1.72173i) 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} +(-7.34248 + 8.18103i) 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} +(-2.81931 - 0.455656i) 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} +(-26.3644 + 3.32261i) q^{90} -2.06020 q^{91} +(0.429603 + 3.37968i) q^{92} +16.5368i q^{93} +(0.403206 + 0.882897i) q^{94} +(1.05015 + 0.0183104i) 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

Introduction

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