LMFDB - Embedded newform 847.2.n.h.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	847.81
Dual form			847.2.n.h.366.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0704484 + 0.670272i) q^{2} +(1.43939 + 1.59861i) q^{3} +(1.51199 + 0.321384i) q^{4} +(1.54306 + 0.687016i) q^{5} +(-1.17290 + 0.852164i) q^{6} +(1.55543 + 2.14024i) q^{7} +(-0.738465 + 2.27276i) q^{8} +(-0.170108 + 1.61847i) q^{9} +O(q^{10})$	\(q+(-0.0704484 + 0.670272i) q^{2} +(1.43939 + 1.59861i) q^{3} +(1.51199 + 0.321384i) q^{4} +(1.54306 + 0.687016i) q^{5} +(-1.17290 + 0.852164i) q^{6} +(1.55543 + 2.14024i) q^{7} +(-0.738465 + 2.27276i) q^{8} +(-0.170108 + 1.61847i) q^{9} +(-0.569194 + 0.985873i) q^{10} +(1.66258 + 2.87968i) q^{12} +(-3.21489 - 2.33575i) q^{13} +(-1.54412 + 0.891782i) q^{14} +(1.12280 + 3.45563i) q^{15} +(1.35292 + 0.602360i) q^{16} +(-0.268524 - 2.55484i) q^{17} +(-1.07283 - 0.228037i) q^{18} +(0.326881 - 0.0694807i) q^{19} +(2.11231 + 1.53468i) q^{20} +(-1.18254 + 5.56716i) q^{21} +(-2.11859 - 3.66950i) q^{23} +(-4.69619 + 2.09088i) q^{24} +(-1.43660 - 1.59551i) q^{25} +(1.79207 - 1.99030i) q^{26} +(2.38877 - 1.73554i) q^{27} +(1.66395 + 3.73593i) q^{28} +(-0.961879 - 2.96036i) q^{29} +(-2.39531 + 0.509140i) q^{30} +(-6.98764 + 3.11110i) q^{31} +(-2.88878 + 5.00351i) q^{32} +1.73135 q^{34} +(0.929739 + 4.37114i) q^{35} +(-0.777353 + 2.39245i) q^{36} +(6.78626 - 7.53690i) q^{37} +(0.0235427 + 0.223994i) q^{38} +(-0.893533 - 8.50140i) q^{39} +(-2.70092 + 2.99968i) q^{40} +(3.34791 - 10.3038i) q^{41} +(-3.64820 - 1.18482i) q^{42} +6.26797 q^{43} +(-1.37440 + 2.38053i) q^{45} +(2.60881 - 1.16152i) q^{46} +(2.31241 - 0.491518i) q^{47} +(0.984448 + 3.02982i) q^{48} +(-2.16130 + 6.65799i) q^{49} +(1.17063 - 0.850512i) q^{50} +(3.69767 - 4.10668i) q^{51} +(-4.11022 - 4.56486i) q^{52} +(-4.00761 + 1.78430i) q^{53} +(0.995001 + 1.72339i) q^{54} +(-6.01289 + 1.95462i) q^{56} +(0.581581 + 0.422544i) q^{57} +(2.05201 - 0.436168i) q^{58} +(0.0342260 + 0.00727496i) q^{59} +(0.587086 + 5.58575i) q^{60} +(3.75226 + 1.67061i) q^{61} +(-1.59301 - 4.90279i) q^{62} +(-3.72851 + 2.15334i) q^{63} +(-0.753965 - 0.547788i) q^{64} +(-3.35608 - 5.81290i) q^{65} +(-2.72981 + 4.72817i) q^{67} +(0.415078 - 3.94920i) q^{68} +(2.81661 - 8.66862i) q^{69} +(-2.99535 + 0.315239i) q^{70} +(-7.62999 + 5.54351i) q^{71} +(-3.55278 - 1.58180i) q^{72} +(-0.293170 - 0.0623152i) q^{73} +(4.57369 + 5.07960i) q^{74} +(0.482756 - 4.59311i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-1.48805 + 14.1578i) q^{79} +(1.67381 + 1.85896i) q^{80} +(10.9883 + 2.33563i) q^{81} +(6.67049 + 2.96990i) q^{82} +(-3.75728 + 2.72982i) q^{83} +(-3.57719 + 8.03746i) q^{84} +(1.34087 - 4.12676i) q^{85} +(-0.441569 + 4.20125i) q^{86} +(3.34793 - 5.79878i) q^{87} +(-6.99890 - 12.1225i) q^{89} +(-1.49878 - 1.08893i) q^{90} +(-0.00143975 - 10.5137i) q^{91} +(-2.02397 - 6.22914i) q^{92} +(-15.0314 - 6.69239i) q^{93} +(0.166545 + 1.58457i) q^{94} +(0.552132 + 0.117359i) q^{95} +(-12.1567 + 2.58399i) q^{96} +(2.67646 + 1.94456i) q^{97} +(-4.31040 - 1.91770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.0704484	+	0.670272i	−0.0498146	+	0.473954i	0.940968	+	0.338495i	$0.109918\pi$
$2$	−0.0704484	+	0.670272i	−0.0498146	+	0.473954i	−0.990783	+	0.135459i	$0.956749\pi$
$3$	1.43939	+	1.59861i	0.831033	+	0.922955i	0.998013	−	0.0630050i	$-0.0200684\pi$
$3$	1.43939	+	1.59861i	0.831033	+	0.922955i	−0.166981	+	0.985960i	$0.553402\pi$
$4$	1.51199	+	0.321384i	0.755997	+	0.160692i
$5$	1.54306	+	0.687016i	0.690079	+	0.307243i	0.721649	−	0.692259i	$-0.243384\pi$
$5$	1.54306	+	0.687016i	0.690079	+	0.307243i	−0.0315707	+	0.999502i	$0.510051\pi$
$6$	−1.17290	+	0.852164i	−0.478836	+	0.347895i
$7$	1.55543	+	2.14024i	0.587896	+	0.808936i
$7$	1.55543	+	2.14024i	0.587896	+	0.808936i
$8$	−0.738465	+	2.27276i	−0.261087	+	0.803543i
$9$	−0.170108	+	1.61847i	−0.0567027	+	0.539490i
$10$	−0.569194	+	0.985873i	−0.179995	+	0.311760i
$11$		0			0
$11$		0			0
$12$	1.66258	+	2.87968i	0.479946	+	0.831292i
$13$	−3.21489	−	2.33575i	−0.891650	−	0.647822i	0.0446577	−	0.999002i	$-0.485780\pi$
$13$	−3.21489	−	2.33575i	−0.891650	−	0.647822i	−0.936308	+	0.351181i	$0.885780\pi$
$14$	−1.54412	+	0.891782i	−0.412684	+	0.238339i
$15$	1.12280	+	3.45563i	0.289907	+	0.892241i
$16$	1.35292	+	0.602360i	0.338230	+	0.150590i
$17$	−0.268524	−	2.55484i	−0.0651267	−	0.619640i	−0.977595	−	0.210493i	$-0.932493\pi$
$17$	−0.268524	−	2.55484i	−0.0651267	−	0.619640i	0.912469	−	0.409147i	$-0.134174\pi$
$18$	−1.07283	−	0.228037i	−0.252869	−	0.0537489i
$19$	0.326881	−	0.0694807i	0.0749916	−	0.0159400i	−0.170263	−	0.985399i	$-0.554462\pi$
$19$	0.326881	−	0.0694807i	0.0749916	−	0.0159400i	0.245255	+	0.969459i	$0.421128\pi$
$20$	2.11231	+	1.53468i	0.472326	+	0.343165i
$21$	−1.18254	+	5.56716i	−0.258051	+	1.21485i
$22$		0			0
$23$	−2.11859	−	3.66950i	−0.441756	−	0.765143i	0.556064	−	0.831139i	$-0.312311\pi$
$23$	−2.11859	−	3.66950i	−0.441756	−	0.765143i	−0.997820	+	0.0659962i	$0.978977\pi$
$24$	−4.69619	+	2.09088i	−0.958606	+	0.426799i
$25$	−1.43660	−	1.59551i	−0.287320	−	0.319101i
$26$	1.79207	−	1.99030i	0.351455	−	0.390330i
$27$	2.38877	−	1.73554i	0.459719	−	0.334005i
$28$	1.66395	+	3.73593i	0.314458	+	0.706024i
$29$	−0.961879	−	2.96036i	−0.178616	−	0.549725i	0.821164	−	0.570693i	$-0.193325\pi$
$29$	−0.961879	−	2.96036i	−0.178616	−	0.549725i	−0.999780	+	0.0209678i	$0.993325\pi$
$30$	−2.39531	+	0.509140i	−0.437323	+	0.0929558i
$31$	−6.98764	+	3.11110i	−1.25502	+	0.558770i	−0.923108	−	0.384542i	$-0.874360\pi$
$31$	−6.98764	+	3.11110i	−1.25502	+	0.558770i	−0.331909	+	0.943311i	$0.607693\pi$
$32$	−2.88878	+	5.00351i	−0.510669	+	0.884504i
$33$		0			0
$34$	1.73135			0.296925
$35$	0.929739	+	4.37114i	0.157155	+	0.738857i
$36$	−0.777353	+	2.39245i	−0.129559	+	0.398741i
$37$	6.78626	−	7.53690i	1.11565	−	1.23906i	0.147404	−	0.989076i	$-0.452908\pi$
$37$	6.78626	−	7.53690i	1.11565	−	1.23906i	0.968250	−	0.249983i	$-0.0804250\pi$
$38$	0.0235427	+	0.223994i	0.00381913	+	0.0363366i
$39$	−0.893533	−	8.50140i	−0.143080	−	1.36131i
$40$	−2.70092	+	2.99968i	−0.427053	+	0.474291i
$41$	3.34791	−	10.3038i	0.522855	−	1.60918i	−0.245663	−	0.969355i	$-0.579006\pi$
$41$	3.34791	−	10.3038i	0.522855	−	1.60918i	0.768518	−	0.639828i	$-0.220994\pi$
$42$	−3.64820	−	1.18482i	−0.562930	−	0.182822i
$43$	6.26797			0.955857			0.477928	−	0.878399i	$-0.341388\pi$
$43$	6.26797			0.955857			0.477928	+	0.878399i	$0.341388\pi$
$44$		0			0
$45$	−1.37440	+	2.38053i	−0.204884	+	0.354869i
$46$	2.60881	−	1.16152i	0.384648	−	0.171257i
$47$	2.31241	−	0.491518i	0.337299	−	0.0716952i	−0.0361483	−	0.999346i	$-0.511509\pi$
$47$	2.31241	−	0.491518i	0.337299	−	0.0716952i	0.373448	+	0.927651i	$0.378176\pi$
$48$	0.984448	+	3.02982i	0.142093	+	0.437317i
$49$	−2.16130	+	6.65799i	−0.308757	+	0.951141i
$50$	1.17063	−	0.850512i	0.165552	−	0.120281i
$51$	3.69767	−	4.10668i	0.517777	−	0.575050i
$52$	−4.11022	−	4.56486i	−0.569985	−	0.633032i
$53$	−4.00761	+	1.78430i	−0.550488	+	0.245093i	−0.663080	−	0.748548i	$-0.730751\pi$
$53$	−4.00761	+	1.78430i	−0.550488	+	0.245093i	0.112593	+	0.993641i	$0.464085\pi$
$54$	0.995001	+	1.72339i	0.135402	+	0.234524i
$55$		0			0
$56$	−6.01289	+	1.95462i	−0.803507	+	0.261197i
$57$	0.581581	+	0.422544i	0.0770323	+	0.0559673i
$58$	2.05201	−	0.436168i	0.269442	−	0.0572717i
$59$	0.0342260	+	0.00727496i	0.00445584	+	0.000947119i	0.210139	−	0.977672i	$-0.432608\pi$
$59$	0.0342260	+	0.00727496i	0.00445584	+	0.000947119i	−0.205683	+	0.978619i	$0.565942\pi$
$60$	0.587086	+	5.58575i	0.0757924	+	0.721117i
$61$	3.75226	+	1.67061i	0.480428	+	0.213900i	0.632638	−	0.774448i	$-0.281972\pi$
$61$	3.75226	+	1.67061i	0.480428	+	0.213900i	−0.152210	+	0.988348i	$0.548639\pi$
$62$	−1.59301	−	4.90279i	−0.202313	−	0.622655i
$63$	−3.72851	+	2.15334i	−0.469748	+	0.271295i
$64$	−0.753965	−	0.547788i	−0.0942456	−	0.0684735i
$65$	−3.35608	−	5.81290i	−0.416270	−	0.721001i
$66$		0			0
$67$	−2.72981	+	4.72817i	−0.333499	+	0.577637i	−0.983195	−	0.182557i	$-0.941563\pi$
$67$	−2.72981	+	4.72817i	−0.333499	+	0.577637i	0.649696	+	0.760194i	$0.274896\pi$
$68$	0.415078	−	3.94920i	0.0503356	−	0.478911i
$69$	2.81661	−	8.66862i	0.339080	−	1.04358i
$70$	−2.99535	+	0.315239i	−0.358013	+	0.0376782i
$71$	−7.62999	+	5.54351i	−0.905513	+	0.657894i	−0.939876	−	0.341515i	$-0.889060\pi$
$71$	−7.62999	+	5.54351i	−0.905513	+	0.657894i	0.0343628	+	0.999409i	$0.489060\pi$
$72$	−3.55278	−	1.58180i	−0.418699	−	0.186417i
$73$	−0.293170	−	0.0623152i	−0.0343130	−	0.00729344i	0.190723	−	0.981644i	$-0.438917\pi$
$73$	−0.293170	−	0.0623152i	−0.0343130	−	0.00729344i	−0.225036	+	0.974350i	$0.572250\pi$
$74$	4.57369	+	5.07960i	0.531681	+	0.590492i
$75$	0.482756	−	4.59311i	0.0557438	−	0.530367i
$76$	0.516572			0.0592548
$77$		0			0
$78$	5.76120			0.652327
$79$	−1.48805	+	14.1578i	−0.167419	+	1.59288i	0.511905	+	0.859042i	$0.328940\pi$
$79$	−1.48805	+	14.1578i	−0.167419	+	1.59288i	−0.679323	+	0.733839i	$0.737727\pi$
$80$	1.67381	+	1.85896i	0.187138	+	0.207838i
$81$	10.9883	+	2.33563i	1.22092	+	0.259515i
$82$	6.67049	+	2.96990i	0.736633	+	0.327970i
$83$	−3.75728	+	2.72982i	−0.412415	+	0.299637i	−0.774579	−	0.632478i	$-0.782038\pi$
$83$	−3.75728	+	2.72982i	−0.412415	+	0.299637i	0.362164	+	0.932114i	$0.382038\pi$
$84$	−3.57719	+	8.03746i	−0.390303	+	0.876959i
$85$	1.34087	−	4.12676i	0.145437	−	0.447610i
$86$	−0.441569	+	4.20125i	−0.0476156	+	0.453032i
$87$	3.34793	−	5.79878i	0.358935	−	0.621694i
$88$		0			0
$89$	−6.99890	−	12.1225i	−0.741882	−	1.28498i	−0.951637	−	0.307224i	$-0.900600\pi$
$89$	−6.99890	−	12.1225i	−0.741882	−	1.28498i	0.209755	−	0.977754i	$-0.432733\pi$
$90$	−1.49878	−	1.08893i	−0.157985	−	0.114783i
$91$	−0.00143975	−	10.5137i	−0.000150926	−	1.10214i
$92$	−2.02397	−	6.22914i	−0.211013	−	0.649432i
$93$	−15.0314	−	6.69239i	−1.55868	−	0.693969i
$94$	0.166545	+	1.58457i	0.0171778	+	0.163436i
$95$	0.552132	+	0.117359i	0.0566476	+	0.0120408i
$96$	−12.1567	+	2.58399i	−1.24074	+	0.263727i
$97$	2.67646	+	1.94456i	0.271753	+	0.197440i	0.715313	−	0.698805i	$-0.246284\pi$
$97$	2.67646	+	1.94456i	0.271753	+	0.197440i	−0.443559	+	0.896245i	$0.646284\pi$
$98$	−4.31040	−	1.91770i	−0.435416	−	0.193717i
$99$		0			0
$100$	−1.65936	−	2.87410i	−0.165936	−	0.287410i
$101$	−8.41517	+	3.74668i	−0.837341	+	0.372808i	−0.780179	−	0.625557i	$-0.784872\pi$
$101$	−8.41517	+	3.74668i	−0.837341	+	0.372808i	−0.0571624	+	0.998365i	$0.518205\pi$
$102$	2.49210	+	2.76775i	0.246754	+	0.274048i
$103$	−11.1609	+	12.3955i	−1.09972	+	1.22136i	−0.126381	+	0.991982i	$0.540336\pi$
$103$	−11.1609	+	12.3955i	−1.09972	+	1.22136i	−0.973337	+	0.229379i	$0.926330\pi$
$104$	7.68270	−	5.58181i	0.753350	−	0.547341i
$105$	−5.64946	+	7.77806i	−0.551331	+	0.759061i
$106$	−0.913639	−	2.81189i	−0.0887404	−	0.273115i
$107$	1.31114	−	0.278692i	0.126753	−	0.0269421i	−0.144098	−	0.989563i	$-0.546028\pi$
$107$	1.31114	−	0.278692i	0.126753	−	0.0269421i	0.270851	+	0.962621i	$0.412695\pi$
$108$	4.16958	−	1.85642i	0.401218	−	0.178634i
$109$	−3.16671	+	5.48491i	−0.303316	+	0.525359i	−0.976885	−	0.213765i	$-0.931427\pi$
$109$	−3.16671	+	5.48491i	−0.303316	+	0.525359i	0.673569	+	0.739124i	$0.264760\pi$
$110$		0			0
$111$	21.8166			2.07074
$112$	0.815174	+	3.83251i	0.0770267	+	0.362138i
$113$	−4.70196	+	14.4712i	−0.442324	+	1.36133i	0.443069	+	0.896488i	$0.353890\pi$
$113$	−4.70196	+	14.4712i	−0.442324	+	1.36133i	−0.885392	+	0.464844i	$0.846110\pi$
$114$	−0.324191	+	0.360050i	−0.0303632	+	0.0337218i
$115$	−0.748108	−	7.11777i	−0.0697614	−	0.663735i
$116$	−0.502942	−	4.78518i	−0.0466970	−	0.444293i
$117$	4.32722	−	4.80587i	0.400052	−	0.444303i
$118$	−0.00728737	+	0.0224282i	−0.000670856	+	0.00206468i
$119$	5.05031	−	4.54857i	0.462961	−	0.416967i
$120$	−8.68298			−0.792644
$121$		0			0
$122$	−1.38411	+	2.39734i	−0.125311	+	0.217045i
$123$	21.2907	−	9.47921i	1.91971	−	0.854712i
$124$	−11.5651	+	2.45824i	−1.03858	+	0.220757i
$125$	−3.73042	−	11.4810i	−0.333659	−	1.02690i
$126$	−1.18065	−	2.65082i	−0.105181	−	0.236153i
$127$	4.42214	−	3.21287i	0.392402	−	0.285096i	−0.374037	−	0.927414i	$-0.622027\pi$
$127$	4.42214	−	3.21287i	0.392402	−	0.285096i	0.766439	+	0.642317i	$0.222027\pi$
$128$	−7.31160	+	8.12035i	−0.646260	+	0.717745i
$129$	9.02206	+	10.0200i	0.794348	+	0.882213i
$130$	4.13265	−	1.83998i	0.362458	−	0.161377i
$131$	2.46819	+	4.27502i	0.215646	+	0.373510i	0.953472	−	0.301481i	$-0.0974808\pi$
$131$	2.46819	+	4.27502i	0.215646	+	0.373510i	−0.737826	+	0.674991i	$0.764147\pi$
$132$		0			0
$133$	0.657145	+	0.591533i	0.0569817	+	0.0512924i
$134$	−2.97685	−	2.16281i	−0.257160	−	0.186838i
$135$	4.87837	−	1.03693i	0.419863	−	0.0892447i
$136$	6.00484	+	1.27637i	0.514911	+	0.109448i
$137$	−0.170939	−	1.62638i	−0.0146043	−	0.138951i	0.984790	−	0.173749i	$-0.0555880\pi$
$137$	−0.170939	−	1.62638i	−0.0146043	−	0.138951i	−0.999394	+	0.0347976i	$0.988921\pi$
$138$	5.61191	+	2.49858i	0.477717	+	0.212694i
$139$	2.73682	+	8.42305i	0.232134	+	0.714434i	0.997489	+	0.0708258i	$0.0225634\pi$
$139$	2.73682	+	8.42305i	0.232134	+	0.714434i	−0.765355	+	0.643608i	$0.777437\pi$
$140$	0.000945968		6.90793i	7.99489e−5		0.583827i
$141$	4.11420	+	2.98914i	0.346478	+	0.251731i
$142$	−3.17814	−	5.50470i	−0.266704	−	0.461944i
$143$		0			0
$144$	−1.20504	+	2.08720i	−0.100420	+	0.173933i
$145$	0.549574	−	5.22885i	0.0456396	−	0.434232i
$146$	0.0624215	−	0.192114i	0.00516604	−	0.0158994i
$147$	−13.7544	+	6.12839i	−1.13445	+	0.505461i
$148$	12.6830	−	9.21475i	1.04254	−	0.757448i
$149$	4.37736	+	1.94893i	0.358607	+	0.159662i	0.578129	−	0.815945i	$-0.303783\pi$
$149$	4.37736	+	1.94893i	0.358607	+	0.159662i	−0.219522	+	0.975608i	$0.570450\pi$
$150$	3.04463	+	0.647155i	0.248593	+	0.0528400i
$151$	10.7581	+	11.9481i	0.875482	+	0.972321i	0.999802	−	0.0199208i	$-0.00634140\pi$
$151$	10.7581	+	11.9481i	0.875482	+	0.972321i	−0.124319	+	0.992242i	$0.539675\pi$
$152$	−0.0834771	+	0.794231i	−0.00677089	+	0.0644207i
$153$	4.18061			0.337982
$154$		0			0
$155$	−12.9197			−1.03774
$156$	1.38120	−	13.1412i	0.110584	−	1.05214i
$157$	4.56262	+	5.06730i	0.364136	+	0.404414i	0.897174	−	0.441677i	$-0.145616\pi$
$157$	4.56262	+	5.06730i	0.364136	+	0.404414i	−0.533038	+	0.846091i	$0.678950\pi$
$158$	−9.38477	−	1.99480i	−0.746612	−	0.158697i
$159$	−8.62092	−	3.83828i	−0.683683	−	0.304395i
$160$	−7.89506	+	5.73610i	−0.624159	+	0.453478i
$161$	4.55832	−	10.2419i	0.359246	−	0.807177i
$162$	−2.33962	+	7.20060i	−0.183818	+	0.565733i
$163$	1.43407	−	13.6442i	0.112325	−	1.06870i	−0.782613	−	0.622509i	$-0.786114\pi$
$163$	1.43407	−	13.6442i	0.112325	−	1.06870i	0.894938	−	0.446191i	$-0.147220\pi$
$164$	8.37349	−	14.5033i	0.653860	−	1.13252i
$165$		0			0
$166$	−1.56503	−	2.71071i	−0.121470	−	0.210392i
$167$	−15.8236	−	11.4965i	−1.22446	−	0.889624i	−0.228000	−	0.973661i	$-0.573219\pi$
$167$	−15.8236	−	11.4965i	−1.22446	−	0.889624i	−0.996463	+	0.0840366i	$0.973219\pi$
$168$	−11.7796	−	6.79879i	−0.908813	−	0.524538i
$169$	0.862548	+	2.65465i	0.0663498	+	0.204204i
$170$	2.67159	+	1.18947i	0.204902	+	0.0912281i
$171$	0.0568473	+	0.540866i	0.00434722	+	0.0413610i
$172$	9.47714	+	2.01443i	0.722625	+	0.153599i
$173$	3.59906	−	0.765003i	0.273631	−	0.0581621i	−0.0690522	−	0.997613i	$-0.521997\pi$
$173$	3.59906	−	0.765003i	0.273631	−	0.0581621i	0.342683	+	0.939451i	$0.388664\pi$
$174$	3.65090	+	2.65254i	0.276774	+	0.201088i
$175$	1.18025	−	5.55637i	0.0892183	−	0.420022i
$176$		0			0
$177$	0.0376348	+	0.0651853i	0.00282880	+	0.00489963i
$178$	8.61840	−	3.83716i	0.645977	−	0.287607i
$179$	13.2057	+	14.6664i	0.987040	+	1.09622i	0.995357	+	0.0962539i	$0.0306861\pi$
$179$	13.2057	+	14.6664i	0.987040	+	1.09622i	−0.00831647	+	0.999965i	$0.502647\pi$
$180$	−2.84315	+	3.15764i	−0.211916	+	0.235357i
$181$	1.78990	−	1.30044i	0.133042	−	0.0966608i	−0.519274	−	0.854608i	$-0.673798\pi$
$181$	1.78990	−	1.30044i	0.133042	−	0.0966608i	0.652316	+	0.757947i	$0.273798\pi$
$182$	7.04717	+	0.739712i	0.522371	+	0.0548311i
$183$	2.73032	+	8.40305i	0.201831	+	0.621172i
$184$	9.90440	−	2.10524i	0.730162	−	0.155201i
$185$	15.6496	−	6.96765i	1.15058	−	0.512272i
$186$	5.54466	−	9.60363i	0.406554	−	0.704172i
$187$		0			0
$188$	3.65431			0.266518
$189$	7.43005	+	2.41304i	0.540456	+	0.175523i
$190$	−0.117560	+	0.361811i	−0.00852866	+	0.0262485i
$191$	5.75748	−	6.39433i	0.416597	−	0.462677i	−0.497922	−	0.867222i	$-0.665903\pi$
$191$	5.75748	−	6.39433i	0.416597	−	0.462677i	0.914518	+	0.404545i	$0.132570\pi$
$192$	−0.209554	−	1.99377i	−0.0151233	−	0.143888i
$193$	0.0267106	+	0.254135i	0.00192267	+	0.0182930i	0.995441	−	0.0953775i	$-0.0304058\pi$
$193$	0.0267106	+	0.254135i	0.00192267	+	0.0182930i	−0.993518	+	0.113671i	$0.963739\pi$
$194$	−1.49194	+	1.65697i	−0.107115	+	0.118963i
$195$	4.46182	−	13.7321i	0.319518	−	0.983374i
$196$	−5.40764	+	9.37223i	−0.386260	+	0.669445i
$197$	9.76587			0.695789			0.347895	−	0.937534i	$-0.386897\pi$
$197$	9.76587			0.695789			0.347895	+	0.937534i	$0.386897\pi$
$198$		0			0
$199$	0.176993	−	0.306561i	0.0125467	−	0.0217315i	−0.859684	−	0.510826i	$-0.829339\pi$
$199$	0.176993	−	0.306561i	0.0125467	−	0.0217315i	0.872231	+	0.489095i	$0.162673\pi$
$200$	4.68708	−	2.08682i	0.331427	−	0.147561i
$201$	−11.4877	+	2.44179i	−0.810282	+	0.172231i
$202$	−1.91846	−	5.90440i	−0.134982	−	0.415432i
$203$	4.83976	−	6.66328i	0.339685	−	0.467671i
$204$	6.91067	−	5.02090i	0.483844	−	0.351533i
$205$	12.2449	−	13.5993i	0.855222	−	0.949820i
$206$	−7.52206	−	8.35410i	−0.524087	−	0.582057i
$207$	6.29936	−	2.80465i	0.437836	−	0.194937i
$208$	−2.94253	−	5.09661i	−0.204028	−	0.353386i
$209$		0			0
$210$	−4.81542	−	4.33463i	−0.332295	−	0.299118i
$211$	12.0596	+	8.76181i	0.830217	+	0.603188i	0.919621	−	0.392808i	$-0.128496\pi$
$211$	12.0596	+	8.76181i	0.830217	+	0.603188i	−0.0894038	+	0.995995i	$0.528496\pi$
$212$	−6.63293	+	1.40987i	−0.455551	+	0.0968305i
$213$	−19.8444	−	4.21806i	−1.35972	−	0.289017i
$214$	0.0944313	+	0.898454i	0.00645519	+	0.0614171i
$215$	9.67188	+	4.30620i	0.659617	+	0.293680i
$216$	2.18045	+	6.71074i	0.148361	+	0.456608i
$217$	−17.5273	−	10.1162i	−1.18983	−	0.686731i
$218$	−3.45329	−	2.50896i	−0.233886	−	0.169928i
$219$	−0.322369	−	0.558359i	−0.0217837	−	0.0377304i
$220$		0			0
$221$	−5.10420	+	8.84073i	−0.343346	+	0.594692i
$222$	−1.53695	+	14.6231i	−0.103153	+	0.981436i
$223$	8.85465	−	27.2518i	0.592951	−	1.82492i	0.0282784	−	0.999600i	$-0.490997\pi$
$223$	8.85465	−	27.2518i	0.592951	−	1.82492i	0.564672	−	0.825315i	$-0.309003\pi$
$224$	−15.2020	+	1.59990i	−1.01573	+	0.106898i
$225$	2.82665	−	2.05368i	0.188444	−	0.136912i
$226$	−9.36836	−	4.17106i	−0.623174	−	0.277455i
$227$	−20.6055	−	4.37984i	−1.36764	−	0.290700i	−0.535156	−	0.844753i	$-0.679747\pi$
$227$	−20.6055	−	4.37984i	−1.36764	−	0.290700i	−0.832481	+	0.554053i	$0.813080\pi$
$228$	0.743549	+	0.825794i	0.0492427	+	0.0546896i
$229$	0.754459	−	7.17820i	0.0498560	−	0.474348i	−0.940899	−	0.338687i	$-0.890017\pi$
$229$	0.754459	−	7.17820i	0.0498560	−	0.474348i	0.990755	−	0.135662i	$-0.0433160\pi$
$230$	4.82354			0.318055
$231$		0			0
$232$	7.43851			0.488362
$233$	2.68471	−	25.5433i	0.175881	−	1.67340i	−0.449653	−	0.893203i	$-0.648452\pi$
$233$	2.68471	−	25.5433i	0.175881	−	1.67340i	0.625535	−	0.780196i	$-0.284881\pi$
$234$	2.91639	+	3.23898i	0.190651	+	0.211739i
$235$	3.90587	+	0.830219i	0.254791	+	0.0541575i
$236$	0.0494114	+	0.0219994i	0.00321641	+	0.00143204i
$237$	−24.7747	+	17.9999i	−1.60929	+	1.16922i
$238$	2.69300	+	3.70552i	0.174561	+	0.240193i
$239$	2.68081	−	8.25068i	0.173407	−	0.533692i	−0.826150	−	0.563450i	$-0.809474\pi$
$239$	2.68081	−	8.25068i	0.173407	−	0.533692i	0.999557	+	0.0297580i	$0.00947366\pi$
$240$	−0.562469	+	5.35153i	−0.0363072	+	0.345440i
$241$	−11.0355	+	19.1141i	−0.710862	+	1.23125i	0.253672	+	0.967290i	$0.418362\pi$
$241$	−11.0355	+	19.1141i	−0.710862	+	1.23125i	−0.964534	+	0.263959i	$0.914972\pi$
$242$		0			0
$243$	7.65366	+	13.2565i	0.490983	+	0.850407i
$244$	5.13649	+	3.73188i	0.328830	+	0.238909i
$245$	−7.90916	+	8.78885i	−0.505298	+	0.561499i
$246$	4.85376	+	14.9383i	0.309464	+	0.952433i
$247$	−1.21318	−	0.540141i	−0.0771925	−	0.0343683i
$248$	−1.91066	−	18.1787i	−0.121327	−	1.15435i
$249$	−9.77210	−	2.07712i	−0.619282	−	0.131632i
$250$	7.95823	−	1.69157i	0.503322	−	0.106984i
$251$	−13.9429	−	10.1301i	−0.880065	−	0.639405i	0.0532037	−	0.998584i	$-0.483057\pi$
$251$	−13.9429	−	10.1301i	−0.880065	−	0.639405i	−0.933269	+	0.359179i	$0.883057\pi$
$252$	−6.32953	+	2.05755i	−0.398723	+	0.129613i
$253$		0			0
$254$	1.84197	+	3.19038i	0.115575	+	0.200182i
$255$	8.52709	−	3.79650i	0.533987	−	0.237746i
$256$	−6.17495	−	6.85798i	−0.385934	−	0.428624i
$257$	−3.83726	+	4.26171i	−0.239362	+	0.265838i	−0.850842	−	0.525421i	$-0.823908\pi$
$257$	−3.83726	+	4.26171i	−0.239362	+	0.265838i	0.611480	+	0.791260i	$0.290574\pi$
$258$	−7.35173	+	5.34134i	−0.457698	+	0.332537i
$259$	26.6863	+	2.80115i	1.65821	+	0.174055i
$260$	−3.20619	−	9.86765i	−0.198840	−	0.611966i
$261$	4.95487	−	1.05319i	0.306699	−	0.0651909i
$262$	−3.03931	+	1.35319i	−0.187769	+	0.0836002i
$263$	11.2982	−	19.5691i	0.696679	−	1.20668i	−0.272933	−	0.962033i	$-0.587994\pi$
$263$	11.2982	−	19.5691i	0.696679	−	1.20668i	0.969612	−	0.244650i	$-0.0786729\pi$
$264$		0			0
$265$	−7.40984			−0.455183
$266$	−0.442783	+	0.398793i	−0.0271488	+	0.0244516i
$267$	9.30487	−	28.6374i	0.569449	−	1.75258i
$268$	−5.64701	+	6.27164i	−0.344946	+	0.383101i
$269$	1.69966	+	16.1712i	0.103630	+	0.985977i	0.915549	+	0.402207i	$0.131757\pi$
$269$	1.69966	+	16.1712i	0.103630	+	0.985977i	−0.811919	+	0.583771i	$0.801577\pi$
$270$	0.351351	+	3.34288i	0.0213826	+	0.203441i
$271$	−4.72825	+	5.25126i	−0.287221	+	0.318991i	−0.869438	−	0.494042i	$-0.835519\pi$
$271$	−4.72825	+	5.25126i	−0.287221	+	0.318991i	0.582217	+	0.813034i	$0.302185\pi$
$272$	1.17564	−	3.61825i	0.0712836	−	0.219388i
$273$	16.8053	−	15.1357i	1.01710	−	0.916054i
$274$	1.10216			0.0665839
$275$		0			0
$276$	7.04465	−	12.2017i	0.424038	−	0.734455i
$277$	−10.8619	+	4.83605i	−0.652631	+	0.290570i	−0.706219	−	0.707993i	$-0.749601\pi$
$277$	−10.8619	+	4.83605i	−0.652631	+	0.290570i	0.0535882	+	0.998563i	$0.482934\pi$
$278$	−5.83854	+	1.24102i	−0.350172	+	0.0744315i
$279$	−3.84656	−	11.8385i	−0.230288	−	0.708753i
$280$	−10.6211	−	1.11486i	−0.634734	−	0.0666254i
$281$	8.40665	−	6.10779i	0.501499	−	0.364360i	−0.308091	−	0.951357i	$-0.599690\pi$
$281$	8.40665	−	6.10779i	0.501499	−	0.364360i	0.809589	+	0.586997i	$0.199690\pi$
$282$	−2.29338	+	2.54705i	−0.136569	+	0.151675i
$283$	13.5836	+	15.0861i	0.807462	+	0.896777i	0.996362	−	0.0852192i	$-0.0271591\pi$
$283$	13.5836	+	15.0861i	0.807462	+	0.896777i	−0.188901	+	0.981996i	$0.560492\pi$
$284$	−13.3181	+	5.92960i	−0.790284	+	0.351857i
$285$	0.607123	+	1.05157i	0.0359628	+	0.0622895i
$286$		0			0
$287$	27.2601	−	8.86146i	1.60911	−	0.523076i
$288$	−7.60663	−	5.52654i	−0.448225	−	0.325654i
$289$	10.1734	−	2.16242i	0.598436	−	0.127201i
$290$	3.46603	+	0.736728i	0.203533	+	0.0432622i
$291$	0.743885	+	7.07759i	0.0436073	+	0.414896i
$292$	−0.423244	−	0.188440i	−0.0247685	−	0.0110276i
$293$	−7.37798	−	22.7071i	−0.431026	−	1.32656i	−0.897105	−	0.441818i	$-0.854334\pi$
$293$	−7.37798	−	22.7071i	−0.431026	−	1.32656i	0.466079	−	0.884743i	$-0.345666\pi$
$294$	−3.13871	−	9.65095i	−0.183053	−	0.562855i
$295$	0.0478148	+	0.0347395i	0.00278389	+	0.00202261i
$296$	12.1182	+	20.9893i	0.704354	+	1.21998i
$297$		0			0
$298$	−1.61469	+	2.79672i	−0.0935364	+	0.162010i
$299$	−1.76003	+	16.7455i	−0.101785	+	0.968419i
$300$	2.20608	−	6.78961i	0.127368	−	0.391998i
$301$	9.74937	+	13.4150i	0.561945	+	0.773228i
$302$	−8.76636	+	6.36913i	−0.504447	+	0.366502i
$303$	−18.1022	−	8.05961i	−1.03994	−	0.463013i
$304$	0.484097	+	0.102898i	0.0277648	+	0.00590160i
$305$	4.64224	+	5.15573i	0.265814	+	0.295216i
$306$	−0.294517	+	2.80214i	−0.0168364	+	0.160188i
$307$	−8.73868			−0.498743			−0.249372	−	0.968408i	$-0.580224\pi$
$307$	−8.73868			−0.498743			−0.249372	+	0.968408i	$0.580224\pi$
$308$		0			0
$309$	−35.8804			−2.04116
$310$	0.910176	−	8.65974i	0.0516945	−	0.491840i
$311$	1.75188	+	1.94566i	0.0993403	+	0.110329i	0.790765	−	0.612120i	$-0.209683\pi$
$311$	1.75188	+	1.94566i	0.0993403	+	0.110329i	−0.691424	+	0.722449i	$0.743017\pi$
$312$	19.9815	+	4.24720i	1.13123	+	0.240450i
$313$	−20.7864	−	9.25471i	−1.17492	−	0.523107i	−0.275971	−	0.961166i	$-0.588999\pi$
$313$	−20.7864	−	9.25471i	−1.17492	−	0.523107i	−0.898946	+	0.438059i	$0.855666\pi$
$314$	−3.71790	+	2.70121i	−0.209813	+	0.152438i
$315$	−7.23270	+	0.761189i	−0.407517	+	0.0428882i
$316$	−6.80003	+	20.9283i	−0.382531	+	1.17731i
$317$	−0.469138	+	4.46355i	−0.0263494	+	0.250698i	0.973416	+	0.229044i	$0.0735599\pi$
$317$	−0.469138	+	4.46355i	−0.0263494	+	0.250698i	−0.999766	+	0.0216541i	$0.993107\pi$
$318$	3.18002	−	5.50796i	0.178327	−	0.308871i
$319$		0			0
$320$	−0.787077	−	1.36326i	−0.0439989	−	0.0762084i
$321$	2.33276	+	1.69485i	0.130202	+	0.0945973i
$322$	6.54375	+	3.77684i	0.364669	+	0.210475i
$323$	−0.265287	−	0.816471i	−0.0147610	−	0.0454297i
$324$	15.8636	+	7.06292i	0.881310	+	0.392385i
$325$	0.891801	+	8.48492i	0.0494682	+	0.470659i
$326$	9.04433	+	1.92243i	0.500919	+	0.106474i
$327$	−13.3263	+	2.83260i	−0.736948	+	0.156643i
$328$	20.9458	+	15.2180i	1.15654	+	0.840273i
$329$	4.64875	+	4.18460i	0.256294	+	0.230705i
$330$		0			0
$331$	6.90068	+	11.9523i	0.379296	+	0.656960i	0.990960	−	0.134158i	$-0.0428330\pi$
$331$	6.90068	+	11.9523i	0.379296	+	0.656960i	−0.611664	+	0.791118i	$0.709500\pi$
$332$	−6.55830	+	2.91994i	−0.359934	+	0.160253i
$333$	11.0438	+	12.2654i	0.605199	+	0.672142i
$334$	8.82051	−	9.79617i	0.482637	−	0.536023i
$335$	−7.46059	+	5.42044i	−0.407616	+	0.296150i
$336$	−4.95332	+	6.81962i	−0.270226	+	0.372041i
$337$	3.47803	+	10.7043i	0.189460	+	0.583099i	0.999997	−	0.00258955i	$-0.000824281\pi$
$337$	3.47803	+	10.7043i	0.189460	+	0.583099i	−0.810536	+	0.585688i	$0.800824\pi$
$338$	−1.84010	+	0.391126i	−0.100088	+	0.0212744i
$339$	−29.9016	+	13.3131i	−1.62403	+	0.723066i
$340$	3.35366	−	5.80870i	0.181877	−	0.315021i
$341$		0			0
$342$	−0.366532			−0.0198198
$343$	−17.6115	+	5.73031i	−0.950929	+	0.309408i
$344$	−4.62868	+	14.2456i	−0.249562	+	0.768072i
$345$	10.3017	−	11.4412i	0.554624	−	0.615972i
$346$	0.259212	+	2.46624i	0.0139353	+	0.132586i
$347$	−1.61381	−	15.3544i	−0.0866340	−	0.824267i	−0.948425	−	0.317003i	$-0.897323\pi$
$347$	−1.61381	−	15.3544i	−0.0866340	−	0.824267i	0.861791	−	0.507264i	$-0.169343\pi$
$348$	6.92568	−	7.69175i	0.371255	−	0.412321i
$349$	3.05996	−	9.41759i	0.163796	−	0.504112i	−0.835150	−	0.550023i	$-0.814619\pi$
$349$	3.05996	−	9.41759i	0.163796	−	0.504112i	0.998946	+	0.0459108i	$0.0146190\pi$
$350$	3.64113	+	1.18252i	0.194627	+	0.0632086i
$351$	−11.7334			−0.626285
$352$		0			0
$353$	−4.91732	+	8.51704i	−0.261722	+	0.453316i	−0.966700	−	0.255913i	$-0.917624\pi$
$353$	−4.91732	+	8.51704i	−0.261722	+	0.453316i	0.704977	+	0.709230i	$0.250957\pi$
$354$	−0.0463432	+	0.0206333i	−0.00246311	+	0.00109665i
$355$	−15.5820	+	3.31206i	−0.827009	+	0.175786i
$356$	−6.68633	−	20.5784i	−0.354375	−	1.09065i
$357$	14.5407	+	1.52628i	0.769578	+	0.0807793i
$358$	−10.7608	+	7.81819i	−0.568726	+	0.413204i
$359$	−2.04711	+	2.27354i	−0.108042	+	0.119993i	−0.794740	−	0.606950i	$-0.792393\pi$
$359$	−2.04711	+	2.27354i	−0.108042	+	0.119993i	0.686698	+	0.726943i	$0.259060\pi$
$360$	−4.39544	−	4.88163i	−0.231660	−	0.257284i
$361$	−17.2553	+	7.68257i	−0.908176	+	0.404346i
$362$	0.745552	+	1.29133i	0.0391853	+	0.0678710i
$363$		0			0
$364$	3.37677	−	15.8972i	0.176991	−	0.833239i
$365$	−0.409568	−	0.297569i	−0.0214378	−	0.0155755i
$366$	−5.82468	+	1.23807i	−0.304461	+	0.0647151i
$367$	7.51215	+	1.59676i	0.392131	+	0.0833500i	0.399758	−	0.916621i	$-0.369094\pi$
$367$	7.51215	+	1.59676i	0.392131	+	0.0833500i	−0.00762652	+	0.999971i	$0.502428\pi$
$368$	−0.655923	−	6.24069i	−0.0341924	−	0.325319i
$369$	16.1069	+	7.17124i	0.838491	+	0.373320i
$370$	3.56773	+	10.9803i	0.185478	+	0.570841i
$371$	−10.0524	−	5.80192i	−0.521894	−	0.301220i
$372$	−20.5765	−	14.9497i	−1.06684	−	0.775106i
$373$	−3.34422	−	5.79236i	−0.173157	−	0.299917i	0.766365	−	0.642406i	$-0.222064\pi$
$373$	−3.34422	−	5.79236i	−0.173157	−	0.299917i	−0.939522	+	0.342488i	$0.888730\pi$
$374$		0			0
$375$	12.9841	−	22.4892i	0.670498	−	1.16134i
$376$	−0.590531	+	5.61852i	−0.0304543	+	0.289753i
$377$	−3.82234	+	11.7639i	−0.196860	+	0.605874i
$378$	−2.14083	+	4.81016i	−0.110112	+	0.247408i
$379$	10.9294	−	7.94069i	0.561407	−	0.407886i	−0.270567	−	0.962701i	$-0.587211\pi$
$379$	10.9294	−	7.94069i	0.561407	−	0.407886i	0.831973	+	0.554815i	$0.187211\pi$
$380$	0.797103	+	0.354893i	0.0408905	+	0.0182056i
$381$	11.5013	+	2.44468i	0.589230	+	0.125245i
$382$	3.88033	+	4.30955i	0.198535	+	0.220496i
$383$	−0.0523905	+	0.498463i	−0.00267703	+	0.0254702i	−0.995779	−	0.0917848i	$-0.970743\pi$
$383$	−0.0523905	+	0.498463i	−0.00267703	+	0.0254702i	0.993102	+	0.117255i	$0.0374095\pi$
$384$	−23.5055			−1.19951
$385$		0			0
$386$	−0.172221			−0.00876582
$387$	−1.06623	+	10.1445i	−0.0541996	+	0.515675i
$388$	3.42184	+	3.80034i	0.173718	+	0.192933i
$389$	18.2978	+	3.88932i	0.927735	+	0.197196i	0.646913	−	0.762564i	$-0.276060\pi$
$389$	18.2978	+	3.88932i	0.927735	+	0.197196i	0.280822	+	0.959760i	$0.409393\pi$
$390$	8.88990	+	3.95804i	0.450157	+	0.200423i
$391$	−8.80609	+	6.39800i	−0.445343	+	0.323561i
$392$	−13.5360	−	9.82880i	−0.683670	−	0.496429i
$393$	−3.28139	+	10.0991i	−0.165524	+	0.509431i
$394$	−0.687990	+	6.54579i	−0.0346604	+	0.329772i
$395$	−12.0228	+	20.8241i	−0.604934	+	1.04778i
$396$		0			0
$397$	−2.36033	−	4.08821i	−0.118461	−	0.205181i	0.800697	−	0.599070i	$-0.204463\pi$
$397$	−2.36033	−	4.08821i	−0.118461	−	0.205181i	−0.919158	+	0.393889i	$0.871130\pi$
$398$	0.193010	+	0.140230i	0.00967473	+	0.00702910i
$399$	0.000260453		1.90196i	1.30390e−5		0.0952172i
$400$	−0.982539	−	3.02394i	−0.0491270	−	0.151197i
$401$	15.4459	+	6.87696i	0.771332	+	0.343419i	0.754381	−	0.656437i	$-0.227937\pi$
$401$	15.4459	+	6.87696i	0.771332	+	0.343419i	0.0169511	+	0.999856i	$0.494604\pi$
$402$	−0.827373	−	7.87192i	−0.0412656	−	0.392616i
$403$	29.7312	+	6.31957i	1.48102	+	0.314800i
$404$	−13.9278	+	2.96045i	−0.692935	+	0.147288i
$405$	15.3510	+	11.1532i	0.762798	+	0.554205i
$406$	4.12526	+	3.71337i	0.204733	+	0.184292i
$407$		0			0
$408$	6.60290	+	11.4366i	0.326892	+	0.566194i
$409$	23.2897	−	10.3692i	1.15160	−	0.512726i	0.260028	−	0.965601i	$-0.416268\pi$
$409$	23.2897	−	10.3692i	1.15160	−	0.512726i	0.891574	+	0.452875i	$0.149602\pi$
$410$	8.25263	+	9.16547i	0.407568	+	0.452650i
$411$	2.35389	−	2.61426i	0.116109	−	0.128952i
$412$	−20.8589	+	15.1549i	−1.02765	+	0.746629i
$413$	0.0376658	+	0.0845676i	0.00185341	+	0.00416130i
$414$	1.43610	+	4.41987i	0.0705805	+	0.217225i
$415$	−7.67315	+	1.63098i	−0.376660	+	0.0800616i
$416$	20.9741	−	9.33826i	1.02834	−	0.457846i
$417$	−9.52579	+	16.4992i	−0.466480	+	0.807967i
$418$		0			0
$419$	−22.6624			−1.10713			−0.553565	−	0.832806i	$-0.686733\pi$
$419$	−22.6624			−1.10713			−0.553565	+	0.832806i	$0.686733\pi$
$420$	−11.0417	+	9.94473i	−0.538780	+	0.485253i
$421$	−5.80566	+	17.8680i	−0.282951	+	0.870833i	0.704055	+	0.710146i	$0.251371\pi$
$421$	−5.80566	+	17.8680i	−0.282951	+	0.870833i	−0.987005	+	0.160687i	$0.948629\pi$
$422$	−6.72238	+	7.46596i	−0.327240	+	0.363437i
$423$	0.402147	+	3.82617i	0.0195531	+	0.186035i
$424$	−1.09582	−	10.4260i	−0.0532175	−	0.506331i
$425$	−3.69050	+	4.09871i	−0.179016	+	0.198817i
$426$	4.22526	−	13.0040i	0.204714	−	0.630046i
$427$	2.26084	+	10.6293i	0.109410	+	0.514387i
$428$	2.07200			0.100154
$429$		0			0
$430$	−3.56769	+	6.17942i	−0.172049	+	0.297998i
$431$	−31.3307	+	13.9493i	−1.50915	+	0.671916i	−0.983849	−	0.179001i	$-0.942714\pi$
$431$	−31.3307	+	13.9493i	−1.50915	+	0.671916i	−0.525300	+	0.850917i	$0.676047\pi$
$432$	4.27724	−	0.909156i	0.205789	−	0.0437418i
$433$	0.984720	+	3.03066i	0.0473226	+	0.145644i	0.971926	−	0.235288i	$-0.0756033\pi$
$433$	0.984720	+	3.03066i	0.0473226	+	0.145644i	−0.924603	+	0.380932i	$0.875603\pi$
$434$	8.01536	−	11.0354i	0.384749	−	0.529715i
$435$	9.14992	−	6.64780i	0.438705	−	0.318738i
$436$	−6.55081	+	7.27542i	−0.313727	+	0.348429i
$437$	−0.947484	−	1.05229i	−0.0453243	−	0.0503378i
$438$	0.396963	−	0.176739i	0.0189676	−	0.00844493i
$439$	6.18390	+	10.7108i	0.295141	+	0.511200i	0.975018	−	0.222127i	$-0.0713000\pi$
$439$	6.18390	+	10.7108i	0.295141	+	0.511200i	−0.679877	+	0.733327i	$0.737967\pi$
$440$		0			0
$441$	−10.4081	−	4.63057i	−0.495624	−	0.220503i
$442$	−5.56611	−	4.04402i	−0.264753	−	0.192354i
$443$	4.99147	−	1.06097i	0.237152	−	0.0504082i	−0.0878024	−	0.996138i	$-0.527984\pi$
$443$	4.99147	−	1.06097i	0.237152	−	0.0504082i	0.324954	+	0.945730i	$0.394651\pi$
$444$	32.9866	+	7.01151i	1.56547	+	0.332752i
$445$	−2.47143	−	23.5141i	−0.117157	−	1.11467i
$446$	17.6423	+	7.85487i	0.835388	+	0.371939i
$447$	3.18517	+	9.80293i	0.150653	+	0.463663i
$448$	−0.000337653	−	2.46571i	−1.59526e−5	−	0.116494i
$449$	0.989674	+	0.719040i	0.0467056	+	0.0339336i	0.610893	−	0.791713i	$-0.290810\pi$
$449$	0.989674	+	0.719040i	0.0467056	+	0.0339336i	−0.564188	+	0.825647i	$0.690810\pi$
$450$	1.17739	+	2.03931i	0.0555029	+	0.0961338i
$451$		0			0
$452$	−11.7601	+	20.3692i	−0.553150	+	0.958085i
$453$	−3.61516	+	34.3959i	−0.169855	+	1.61606i
$454$	4.38731	−	13.5028i	0.205907	−	0.633716i
$455$	7.22089	−	16.2244i	0.338521	−	0.760610i
$456$	−1.38982	+	1.00976i	−0.0650842	+	0.0472865i
$457$	−4.69013	−	2.08818i	−0.219395	−	0.0976810i	0.294096	−	0.955776i	$-0.404981\pi$
$457$	−4.69013	−	2.08818i	−0.219395	−	0.0976810i	−0.513491	+	0.858095i	$0.671648\pi$
$458$	4.75819	+	1.01139i	0.222336	+	0.0472589i
$459$	−5.07548	−	5.63689i	−0.236903	−	0.263107i
$460$	1.15640	−	11.0025i	0.0539176	−	0.512992i
$461$	−22.7757			−1.06077			−0.530386	−	0.847757i	$-0.677953\pi$
$461$	−22.7757			−1.06077			−0.530386	+	0.847757i	$0.677953\pi$
$462$		0			0
$463$	29.8445			1.38699			0.693496	−	0.720460i	$-0.256069\pi$
$463$	29.8445			1.38699			0.693496	+	0.720460i	$0.256069\pi$
$464$	0.481854	−	4.58453i	0.0223695	−	0.212832i
$465$	−18.5966	−	20.6536i	−0.862395	−	0.957786i
$466$	16.9319	+	3.59898i	0.784353	+	0.166719i
$467$	1.41599	+	0.630440i	0.0655243	+	0.0291733i	0.439237	−	0.898371i	$-0.355249\pi$
$467$	1.41599	+	0.630440i	0.0655243	+	0.0291733i	−0.373713	+	0.927544i	$0.621915\pi$
$468$	8.08727	−	5.87574i	0.373834	−	0.271606i
$469$	−14.3654	+	1.51186i	−0.663335	+	0.0698111i
$470$	−0.831635	+	2.55951i	−0.0383605	+	0.118061i
$471$	−1.53322	+	14.5876i	−0.0706472	+	0.672163i
$472$	−0.0418089	+	0.0724152i	−0.00192441	+	0.00333318i
$473$		0			0
$474$	−10.3195	−	17.8738i	−0.473989	−	0.820973i
$475$	−0.580454	−	0.421724i	−0.0266331	−	0.0193500i
$476$	9.09788	−	5.25432i	0.417001	−	0.240832i
$477$	−2.20611	−	6.78972i	−0.101011	−	0.310880i
$478$	5.34134	+	2.37812i	0.244307	+	0.108773i
$479$	−1.22774	−	11.6811i	−0.0560967	−	0.533724i	−0.986098	−	0.166167i	$-0.946861\pi$
$479$	−1.22774	−	11.6811i	−0.0560967	−	0.533724i	0.930001	−	0.367557i	$-0.119806\pi$
$480$	−20.5338	−	4.36460i	−0.937237	−	0.199216i
$481$	−39.4214	+	8.37928i	−1.79746	+	0.382062i
$482$	−12.0342	−	8.74338i	−0.548144	−	0.398250i
$483$	22.9340	−	7.45518i	1.04353	−	0.339222i
$484$		0			0
$485$	2.79400	+	4.83936i	0.126869	+	0.219744i
$486$	−9.42467	+	4.19613i	−0.427512	+	0.190340i
$487$	4.91404	+	5.45759i	0.222676	+	0.247307i	0.844123	−	0.536149i	$-0.180122\pi$
$487$	4.91404	+	5.45759i	0.222676	+	0.247307i	−0.621447	+	0.783456i	$0.713455\pi$
$488$	−6.56782	+	7.29431i	−0.297311	+	0.330198i
$489$	23.8759	−	17.3469i	1.07971	−	0.784453i
$490$	−5.33373	−	5.92045i	−0.240954	−	0.267459i
$491$	4.00526	+	12.3269i	0.180755	+	0.556306i	0.999849	−	0.0173525i	$-0.00552375\pi$
$491$	4.00526	+	12.3269i	0.180755	+	0.556306i	−0.819095	+	0.573658i	$0.805524\pi$
$492$	35.2378	−	7.49003i	1.58864	−	0.337677i
$493$	−7.30496	+	3.25238i	−0.328999	+	0.146480i
$494$	0.447507	−	0.775106i	0.0201343	−	0.0348737i
$495$		0			0
$496$	−11.3277			−0.508630
$497$	−23.7324	−	7.70752i	−1.06454	−	0.345730i
$498$	2.08067	−	6.40363i	0.0932369	−	0.286954i
$499$	2.92647	−	3.25017i	0.131007	−	0.145498i	−0.674072	−	0.738666i	$-0.735456\pi$
$499$	2.92647	−	3.25017i	0.131007	−	0.145498i	0.805079	+	0.593168i	$0.202123\pi$
$500$	−1.95054	−	18.5582i	−0.0872309	−	0.829947i
$501$	−4.39793	−	41.8435i	−0.196485	−	1.86943i
$502$	7.77216	−	8.63185i	0.346888	−	0.385259i
$503$	−9.89177	+	30.4437i	−0.441052	+	1.35742i	0.445703	+	0.895181i	$0.352954\pi$
$503$	−9.89177	+	30.4437i	−0.441052	+	1.35742i	−0.886756	+	0.462238i	$0.847046\pi$
$504$	−2.14065	−	10.0642i	−0.0953521	−	0.448294i
$505$	−15.5592			−0.692374
$506$		0			0
$507$	−3.00219	+	5.19995i	−0.133332	+	0.230938i
$508$	7.71881	−	3.43664i	0.342467	−	0.152476i
$509$	21.1494	−	4.49543i	0.937429	−	0.199257i	0.286227	−	0.958162i	$-0.407599\pi$
$509$	21.1494	−	4.49543i	0.937429	−	0.199257i	0.651201	+	0.758905i	$0.274265\pi$
$510$	1.94397	+	5.98293i	0.0860805	+	0.264928i
$511$	−0.322635	−	0.724382i	−0.0142725	−	0.0320448i
$512$	−12.6486	+	9.18971i	−0.558992	+	0.406132i
$513$	0.660257	−	0.733289i	0.0291510	−	0.0323755i
$514$	−2.58618	−	2.87224i	−0.114071	−	0.126689i
$515$	−25.7379	+	11.4592i	−1.13415	+	0.504955i
$516$	10.4210	+	18.0497i	0.458760	+	0.794596i
$517$		0			0
$518$	−3.75755	+	17.6898i	−0.165097	+	0.777244i
$519$	6.40339	+	4.65233i	0.281078	+	0.204215i
$520$	15.6897	−	3.33494i	0.688038	−	0.146247i
$521$	−1.43929	−	0.305931i	−0.0630565	−	0.0134031i	0.176275	−	0.984341i	$-0.443595\pi$
$521$	−1.43929	−	0.305931i	−0.0630565	−	0.0134031i	−0.239332	+	0.970938i	$0.576928\pi$
$522$	0.356861	+	3.39531i	0.0156194	+	0.148609i
$523$	−31.5426	−	14.0437i	−1.37926	−	0.614087i	−0.422874	−	0.906189i	$-0.638979\pi$
$523$	−31.5426	−	14.0437i	−1.37926	−	0.614087i	−0.956387	+	0.292102i	$0.905645\pi$
$524$	2.35796	+	7.25704i	0.103008	+	0.317025i
$525$	10.5813	−	6.11103i	0.461805	−	0.266707i
$526$	12.3207	+	8.95150i	0.537207	+	0.390304i
$527$	9.82471	+	17.0169i	0.427971	+	0.741267i
$528$		0			0
$529$	2.52319	−	4.37030i	0.109704	−	0.190013i
$530$	0.522012	−	4.96661i	0.0226747	−	0.215736i
$531$	−0.0175964	+	0.0541562i	−0.000763619	+	0.00235018i
$532$	0.803490	+	1.10559i	0.0348357	+	0.0479334i
$533$	−34.8303	+	25.3057i	−1.50867	+	1.09611i
$534$	18.5394	+	8.25425i	0.802276	+	0.357196i
$535$	2.21464	+	0.470736i	0.0957472	+	0.0203517i
$536$	−8.73013	−	9.69579i	−0.377084	−	0.418794i
$537$	−4.43765	+	42.2214i	−0.191499	+	1.82199i
$538$	−10.9589			−0.472470
$539$		0			0
$540$	7.70932			0.331756
$541$	−0.639481	+	6.08425i	−0.0274934	+	0.261582i	0.972137	+	0.234412i	$0.0753164\pi$
$541$	−0.639481	+	6.08425i	−0.0274934	+	0.261582i	−0.999631	+	0.0271706i	$0.991350\pi$
$542$	−3.18667	−	3.53916i	−0.136879	−	0.152020i
$543$	4.65525	+	0.989504i	0.199776	+	0.0424637i
$544$	13.5589	+	6.03680i	0.581332	+	0.258826i
$545$	−8.65466	+	6.28798i	−0.370725	+	0.269347i
$546$	8.96112	+	12.3304i	0.383501	+	0.527691i
$547$	7.75042	−	23.8533i	0.331384	−	1.01990i	−0.637092	−	0.770788i	$-0.719863\pi$
$547$	7.75042	−	23.8533i	0.331384	−	1.01990i	0.968476	−	0.249107i	$-0.0801372\pi$
$548$	0.264233	−	2.51401i	0.0112875	−	0.107393i
$549$	−3.34213	+	5.78874i	−0.142639	+	0.247057i
$550$		0			0
$551$	−0.520108	−	0.900853i	−0.0221573	−	0.0383776i
$552$	17.6217	+	12.8029i	0.750031	+	0.544930i
$553$	−32.6158	+	18.8367i	−1.38696	+	0.801018i
$554$	−2.47626	−	7.62115i	−0.105206	−	0.323792i
$555$	33.6644	+	14.9884i	1.42897	+	0.636220i
$556$	1.43101	+	13.6152i	0.0606884	+	0.577412i
$557$	−30.0257	−	6.38216i	−1.27223	−	0.270421i	−0.478174	−	0.878265i	$-0.658701\pi$
$557$	−30.0257	−	6.38216i	−1.27223	−	0.270421i	−0.794056	+	0.607844i	$0.792035\pi$
$558$	8.20600	−	1.74424i	0.347388	−	0.0738395i
$559$	−20.1508	−	14.6404i	−0.852290	−	0.619225i
$560$	−1.37513	+	6.47384i	−0.0581099	+	0.273570i
$561$		0			0
$562$	3.50164	+	6.06502i	0.147708	+	0.255838i
$563$	15.9619	−	7.10670i	0.672714	−	0.299512i	−0.0418067	−	0.999126i	$-0.513311\pi$
$563$	15.9619	−	7.10670i	0.672714	−	0.299512i	0.714521	+	0.699614i	$0.246645\pi$
$564$	5.25998	+	5.84180i	0.221485	+	0.245984i
$565$	−17.1973	+	19.0996i	−0.723498	+	0.803525i
$566$	−11.0688	+	8.04192i	−0.465254	+	0.338027i
$567$	12.0927	+	27.1505i	0.507844	+	1.14022i
$568$	−6.96460	−	21.4348i	−0.292228	−	0.899386i
$569$	22.8347	−	4.85366i	0.957279	−	0.203476i	0.297320	−	0.954778i	$-0.403907\pi$
$569$	22.8347	−	4.85366i	0.957279	−	0.203476i	0.659959	+	0.751302i	$0.270574\pi$
$570$	−0.747607	+	0.332856i	−0.0313138	+	0.0139418i
$571$	7.38432	−	12.7900i	0.309024	−	0.535245i	−0.669125	−	0.743150i	$-0.733331\pi$
$571$	7.38432	−	12.7900i	0.309024	−	0.535245i	0.978149	+	0.207905i	$0.0666643\pi$
$572$		0			0
$573$	18.5093			0.773236
$574$	4.01916	+	18.8959i	0.167757	+	0.788702i
$575$	−2.81115	+	8.65182i	−0.117233	+	0.360806i
$576$	1.01483	−	1.12709i	0.0422847	−	0.0469619i
$577$	3.78757	+	36.0363i	0.157678	+	1.50021i	0.731845	+	0.681471i	$0.238660\pi$
$577$	3.78757	+	36.0363i	0.157678	+	1.50021i	−0.574166	+	0.818739i	$0.694674\pi$
$578$	0.732712	+	6.97129i	0.0304768	+	0.289967i
$579$	−0.367814	+	0.408499i	−0.0152858	+	0.0169766i
$580$	2.51142	−	7.72936i	0.104281	−	0.320944i
$581$	−11.6867	−	3.79546i	−0.484844	−	0.157462i
$582$	−4.79632			−0.198814
$583$		0			0
$584$	0.358123	−	0.620288i	0.0148193	−	0.0256677i
$585$	9.97889	−	4.44289i	0.412576	−	0.183691i
$586$	15.7397	−	3.34557i	0.650200	−	0.138204i
$587$	−5.62163	−	17.3016i	−0.232030	−	0.714113i	−0.997502	−	0.0706443i	$-0.977494\pi$
$587$	−5.62163	−	17.3016i	−0.232030	−	0.714113i	0.765472	−	0.643469i	$-0.222506\pi$
$588$	−22.7662	+	4.84562i	−0.938862	+	0.199830i
$589$	−2.06796	+	1.50246i	−0.0852090	+	0.0619080i
$590$	−0.0266534	+	0.0296016i	−0.00109730	+	0.00121868i
$591$	14.0569	+	15.6118i	0.578224	+	0.642182i
$592$	13.7212	−	6.10907i	0.563938	−	0.251081i
$593$	−21.2413	−	36.7910i	−0.872276	−	1.51083i	−0.859637	−	0.510906i	$-0.829310\pi$
$593$	−21.2413	−	36.7910i	−0.872276	−	1.51083i	−0.0126393	−	0.999920i	$-0.504023\pi$
$594$		0			0
$595$	10.9179	−	3.54909i	0.447590	−	0.145499i
$596$	5.99218	+	4.35358i	0.245449	+	0.178329i
$597$	0.744832	−	0.158319i	0.0304839	−	0.00647956i
$598$	−11.1001	−	2.35939i	−0.453915	−	0.0964827i
$599$	1.83846	+	17.4918i	0.0751174	+	0.714694i	0.965663	+	0.259799i	$0.0836565\pi$
$599$	1.83846	+	17.4918i	0.0751174	+	0.714694i	−0.890545	+	0.454895i	$0.849677\pi$
$600$	10.0826	+	4.48904i	0.411618	+	0.183264i
$601$	−9.48505	−	29.1920i	−0.386903	−	1.19077i	−0.935090	−	0.354410i	$-0.884682\pi$
$601$	−9.48505	−	29.1920i	−0.386903	−	1.19077i	0.548187	−	0.836356i	$-0.315318\pi$
$602$	−9.67853	+	5.58967i	−0.394467	+	0.227818i
$603$	−7.18803	−	5.22241i	−0.292719	−	0.212673i
$604$	12.4263	+	21.5229i	0.505617	+	0.875755i
$605$		0			0
$606$	6.67740	−	11.5656i	0.271251	−	0.469820i
$607$	3.70780	−	35.2773i	0.150495	−	1.43186i	−0.615054	−	0.788485i	$-0.710866\pi$
$607$	3.70780	−	35.2773i	0.150495	−	1.43186i	0.765549	−	0.643378i	$-0.222468\pi$
$608$	−0.596639	+	1.83627i	−0.0241969	+	0.0744705i
$609$	17.6183	−	1.85419i	0.713928	−	0.0751357i
$610$	−3.78278	+	2.74835i	−0.153160	+	0.111277i
$611$	−8.58220	−	3.82104i	−0.347199	−	0.154583i
$612$	6.32105	+	1.34358i	0.255513	+	0.0543110i
$613$	−9.19525	−	10.2124i	−0.371393	−	0.412473i	0.528258	−	0.849084i	$-0.322845\pi$
$613$	−9.19525	−	10.2124i	−0.371393	−	0.412473i	−0.899651	+	0.436611i	$0.856179\pi$
$614$	0.615627	−	5.85730i	0.0248447	−	0.236381i
$615$	39.3652			1.58736
$616$		0			0
$617$	2.42135			0.0974798			0.0487399	−	0.998812i	$-0.484479\pi$
$617$	2.42135			0.0974798			0.0487399	+	0.998812i	$0.484479\pi$
$618$	2.52772	−	24.0496i	0.101680	−	0.967417i
$619$	−9.30906	−	10.3388i	−0.374163	−	0.415550i	0.526427	−	0.850220i	$-0.323531\pi$
$619$	−9.30906	−	10.3388i	−0.374163	−	0.415550i	−0.900589	+	0.434671i	$0.856865\pi$
$620$	−19.5346	−	4.15220i	−0.784527	−	0.166756i
$621$	−11.4294	−	5.08869i	−0.458645	−	0.204202i
$622$	−1.42754	+	1.03717i	−0.0572392	+	0.0415867i
$623$	15.0587	−	33.8350i	0.603316	−	1.35557i
$624$	3.91202	−	12.0400i	0.156606	−	0.481984i
$625$	1.00930	−	9.60282i	0.0403719	−	0.384113i
$626$	7.66754	−	13.2806i	0.306457	−	0.530798i
$627$		0			0
$628$	5.27010	+	9.12808i	0.210300	+	0.364250i
$629$	−21.0779	−	15.3140i	−0.840429	−	0.610607i
$630$	−0.000671209	−	4.90150i	−2.67416e−5	−	0.195281i
$631$	11.9862	+	36.8898i	0.477164	+	1.46856i	0.843017	+	0.537888i	$0.180778\pi$
$631$	11.9862	+	36.8898i	0.477164	+	1.46856i	−0.365852	+	0.930673i	$0.619222\pi$
$632$	−31.0785	−	13.8371i	−1.23624	−	0.550408i
$633$	3.35180	+	31.8902i	0.133222	+	1.26752i
$634$	−2.95874	−	0.628900i	−0.117507	−	0.0249768i
$635$	9.03094	−	1.91958i	0.358382	−	0.0761764i
$636$	−11.8012	−	8.57408i	−0.467948	−	0.339984i
$637$	22.4997	−	16.3564i	0.891473	−	0.648066i
$638$		0			0
$639$	−7.67408	−	13.2919i	−0.303582	−	0.525819i
$640$	−16.8611	+	7.50703i	−0.666492	+	0.296742i
$641$	−16.9244	−	18.7964i	−0.668472	−	0.742413i	0.309557	−	0.950881i	$-0.399819\pi$
$641$	−16.9244	−	18.7964i	−0.668472	−	0.742413i	−0.978029	+	0.208467i	$0.933152\pi$
$642$	−1.30035	+	1.44419i	−0.0513207	+	0.0569974i
$643$	0.0725695	−	0.0527248i	0.00286186	−	0.00207926i	−0.586353	−	0.810055i	$-0.699437\pi$
$643$	0.0725695	−	0.0527248i	0.00286186	−	0.00207926i	0.589215	+	0.807976i	$0.299437\pi$
$644$	10.1837	−	14.0208i	0.401296	−	0.552495i
$645$	7.03770	+	21.6598i	0.277109	+	0.852854i
$646$	0.565947	−	0.120296i	0.0222669	−	0.00473297i
$647$	−3.96464	+	1.76517i	−0.155866	+	0.0693960i	−0.483187	−	0.875517i	$-0.660521\pi$
$647$	−3.96464	+	1.76517i	−0.155866	+	0.0693960i	0.327321	+	0.944913i	$0.393854\pi$
$648$	−13.4228	+	23.2490i	−0.527298	+	0.913306i
$649$		0			0
$650$	−5.75003			−0.225535
$651$	−9.05682	−	42.5803i	−0.354965	−	1.66885i
$652$	6.55334	−	20.1691i	0.256649	−	0.789884i
$653$	−14.2020	+	15.7729i	−0.555768	+	0.617243i	−0.953914	−	0.300079i	$-0.902987\pi$
$653$	−14.2020	+	15.7729i	−0.555768	+	0.617243i	0.398146	+	0.917322i	$0.369654\pi$
$654$	−0.959794	−	9.13183i	−0.0375309	−	0.357083i
$655$	0.871557	+	8.29231i	0.0340546	+	0.324007i
$656$	10.7361	−	11.9236i	0.419172	−	0.465538i
$657$	0.150726	−	0.463886i	0.00588037	−	0.0180979i
$658$	−3.13232	+	2.82113i	−0.122110	+	0.109979i
$659$	25.4606			0.991805			0.495902	−	0.868378i	$-0.334837\pi$
$659$	25.4606			0.991805			0.495902	+	0.868378i	$0.334837\pi$
$660$		0			0
$661$	−4.77124	+	8.26403i	−0.185580	+	0.321433i	−0.943772	−	0.330598i	$-0.892750\pi$
$661$	−4.77124	+	8.26403i	−0.185580	+	0.321433i	0.758192	+	0.652031i	$0.226083\pi$
$662$	−8.49746	+	3.78331i	−0.330263	+	0.147043i
$663$	−21.4798	+	4.56567i	−0.834206	+	0.177316i
$664$	−3.42962	−	10.5553i	−0.133095	−	0.409624i
$665$	0.607623	+	1.36424i	0.0235626	+	0.0529030i
$666$	−8.99920	+	6.53830i	−0.348712	+	0.253354i
$667$	−8.82521	+	9.80139i	−0.341713	+	0.379511i
$668$	−20.2303	−	22.4680i	−0.782735	−	0.869315i
$669$	56.3102	−	25.0709i	2.17708	−	0.969297i
$670$	−3.10758	−	5.38249i	−0.120056	−	0.207944i
$671$		0			0
$672$	−24.4393	−	21.9992i	−0.942765	−	0.848636i
$673$	13.3808	+	9.72172i	0.515792	+	0.374745i	0.815016	−	0.579438i	$-0.196728\pi$
$673$	13.3808	+	9.72172i	0.515792	+	0.374745i	−0.299224	+	0.954183i	$0.596728\pi$
$674$	−7.41979	+	1.57713i	−0.285800	+	0.0607486i
$675$	−6.20078	−	1.31802i	−0.238668	−	0.0507305i
$676$	0.451005	+	4.29102i	0.0173463	+	0.165039i
$677$	2.22323	+	0.989847i	0.0854458	+	0.0380429i	0.449015	−	0.893524i	$-0.351775\pi$
$677$	2.22323	+	0.989847i	0.0854458	+	0.0380429i	−0.363569	+	0.931567i	$0.618442\pi$
$678$	−6.81685	−	20.9801i	−0.261800	−	0.805736i
$679$	0.00119862	+	8.75291i	4.59987e−5	+	0.335906i
$680$	8.38896	+	6.09494i	0.321702	+	0.233730i
$681$	−22.6578	−	39.2444i	−0.868248	−	1.50385i
$682$		0			0
$683$	2.64045	−	4.57339i	0.101034	−	0.174996i	−0.811077	−	0.584939i	$-0.801118\pi$
$683$	2.64045	−	4.57339i	0.101034	−	0.174996i	0.912111	+	0.409944i	$0.134452\pi$
$684$	−0.0878730	+	0.836056i	−0.00335991	+	0.0319674i
$685$	0.853578	−	2.62704i	0.0326136	−	0.100374i
$686$	−2.60017	−	12.2082i	−0.0992748	−	0.466110i
$687$	12.5611	−	9.12615i	0.479234	−	0.348184i
$688$	8.48008	+	3.77557i	0.323300	+	0.143942i
$689$	17.0517	+	3.62446i	0.649619	+	0.138081i
$690$	6.94296	+	7.71094i	0.264314	+	0.293551i
$691$	2.20535	−	20.9825i	0.0838953	−	0.798211i	−0.868980	−	0.494848i	$-0.835224\pi$
$691$	2.20535	−	20.9825i	0.0838953	−	0.798211i	0.952875	−	0.303363i	$-0.0981095\pi$
$692$	5.68761			0.216211
$693$		0			0
$694$	10.4053			0.394980
$695$	−1.56369	+	14.8775i	−0.0593142	+	0.564337i
$696$	10.7069	+	11.8912i	0.405845	+	0.450736i
$697$	−27.2236	−	5.78655i	−1.03117	−	0.219181i
$698$	6.09678	+	2.71446i	0.230766	+	0.102744i
$699$	44.6981	−	32.4750i	1.69064	−	1.22832i
$700$	3.57026	−	8.02188i	0.134943	−	0.303199i
$701$	−8.68131	+	26.7183i	−0.327888	+	1.00914i	0.642231	+	0.766511i	$0.278009\pi$
$701$	−8.68131	+	26.7183i	−0.327888	+	1.00914i	−0.970120	+	0.242626i	$0.921991\pi$
$702$	0.826602	−	7.86459i	0.0311981	−	0.296830i
$703$	1.69463	−	2.93518i	0.0639141	−	0.110703i
$704$		0			0
$705$	4.29489	+	7.43896i	0.161755	+	0.280167i
$706$	−5.36232	−	3.89595i	−0.201813	−	0.146626i
$707$	−21.1080	−	12.1829i	−0.793848	−	0.458183i
$708$	0.0359540	+	0.110655i	0.00135123	+	0.00415867i
$709$	−4.65867	−	2.07418i	−0.174960	−	0.0778973i	0.317387	−	0.948296i	$-0.397194\pi$
$709$	−4.65867	−	2.07418i	−0.174960	−	0.0778973i	−0.492348	+	0.870399i	$0.663861\pi$
$710$	−1.12225	−	10.6775i	−0.0421174	−	0.400721i
$711$	−22.6609	−	4.81672i	−0.849850	−	0.180641i
$712$	32.7199	−	6.95483i	1.22623	−	0.260643i
$713$	26.2201	+	19.0500i	0.981950	+	0.713428i
$714$	−2.04740	+	9.63873i	−0.0766219	+	0.360720i
$715$		0			0
$716$	15.2534	+	26.4196i	0.570046	+	0.987348i
$717$	17.0483	−	7.59040i	0.636681	−	0.283469i
$718$	−1.37968	−	1.53229i	−0.0514890	−	0.0571844i
$719$	16.0856	−	17.8649i	0.599891	−	0.666247i	−0.364353	−	0.931261i	$-0.618710\pi$
$719$	16.0856	−	17.8649i	0.599891	−	0.666247i	0.964245	+	0.265014i	$0.0853765\pi$
$720$	−3.29339	+	2.39279i	−0.122738	+	0.0891741i
$721$	−43.8893	−	4.60688i	−1.63452	−	0.171569i
$722$	−3.93380	−	12.1070i	−0.146401	−	0.450576i
$723$	−46.4404	+	9.87122i	−1.72714	+	0.367114i
$724$	3.12426	−	1.39101i	0.116112	−	0.0516964i
$725$	−3.34144	+	5.78754i	−0.124098	+	0.214944i
$726$		0			0
$727$	14.6738			0.544221			0.272111	−	0.962266i	$-0.412278\pi$
$727$	14.6738			0.544221			0.272111	+	0.962266i	$0.412278\pi$
$728$	23.8963	+	7.76076i	0.885656	+	0.287633i
$729$	0.238931	−	0.735355i	0.00884931	−	0.0272354i
$730$	0.228305	−	0.253559i	0.00844997	−	0.00938464i
$731$	−1.68310	−	16.0137i	−0.0622519	−	0.592287i
$732$	1.42761	+	13.5828i	0.0527662	+	0.502036i
$733$	−32.4697	+	36.0612i	−1.19929	+	1.33195i	−0.269889	+	0.962891i	$0.586987\pi$
$733$	−32.4697	+	36.0612i	−1.19929	+	1.33195i	−0.929405	+	0.369060i	$0.879680\pi$
$734$	−1.59948	+	4.92270i	−0.0590379	+	0.181700i
$735$	−25.4343	+	0.00696591i	−0.938157	+	0.000256941i
$736$	24.4805			0.902363
$737$		0			0
$738$	−5.94139	+	10.2908i	−0.218706	+	0.378809i
$739$	10.3080	−	4.58943i	0.379187	−	0.168825i	−0.208287	−	0.978068i	$-0.566789\pi$
$739$	10.3080	−	4.58943i	0.379187	−	0.168825i	0.587475	+	0.809243i	$0.300122\pi$
$740$	25.9014	−	5.50551i	0.952154	−	0.202387i
$741$	−0.882762	−	2.71686i	−0.0324291	−	0.0998064i
$742$	4.59704	−	6.32910i	0.168763	−	0.232349i
$743$	2.80142	−	2.03535i	0.102774	−	0.0746698i	−0.535211	−	0.844718i	$-0.679768\pi$
$743$	2.80142	−	2.03535i	0.102774	−	0.0746698i	0.637985	+	0.770048i	$0.279768\pi$
$744$	26.3103	−	29.2206i	0.964584	−	1.07128i
$745$	5.41560	+	6.01463i	0.198412	+	0.220359i
$746$	4.11805	−	1.83348i	0.150773	−	0.0671283i
$747$	−3.77899	−	6.54540i	−0.138266	−	0.239484i
$748$		0			0
$749$	2.63585	+	2.37268i	0.0963119	+	0.0866957i
$750$	14.1592	+	10.2872i	0.517019	+	0.375636i
$751$	−2.09396	+	0.445084i	−0.0764095	+	0.0162413i	−0.245958	−	0.969281i	$-0.579102\pi$
$751$	−2.09396	+	0.445084i	−0.0764095	+	0.0162413i	0.169548	+	0.985522i	$0.445769\pi$
$752$	3.42458	+	0.727917i	0.124882	+	0.0265444i
$753$	−3.87522	−	36.8702i	−0.141221	−	1.34363i
$754$	−7.61576	−	3.39076i	−0.277350	−	0.123484i
$755$	8.39191	+	25.8276i	0.305413	+	0.939964i
$756$	10.4587	+	6.03640i	0.380378	+	0.219542i
$757$	29.7684	+	21.6280i	1.08195	+	0.786084i	0.978022	−	0.208501i	$-0.0668585\pi$
$757$	29.7684	+	21.6280i	1.08195	+	0.786084i	0.103929	+	0.994585i	$0.466858\pi$
$758$	4.55246	+	7.88509i	0.165353	+	0.286399i
$759$		0			0
$760$	−0.674460	+	1.16820i	−0.0244652	+	0.0423750i
$761$	3.07299	−	29.2376i	0.111396	−	1.05986i	−0.785876	−	0.618384i	$-0.787788\pi$
$761$	3.07299	−	29.2376i	0.111396	−	1.05986i	0.897272	−	0.441478i	$-0.145546\pi$
$762$	−2.44885	+	7.53678i	−0.0887124	+	0.273029i
$763$	−16.6646	+	1.75383i	−0.603300	+	0.0634930i
$764$	10.7603	−	7.81782i	0.389294	−	0.282839i
$765$	6.45094	+	2.87214i	0.233234	+	0.103843i
$766$	−0.330415	−	0.0702318i	−0.0119384	−	0.00253758i
$767$	−0.0930402	−	0.103332i	−0.00335949	−	0.00373109i
$768$	2.07503	−	19.7426i	0.0748763	−	0.712400i
$769$	1.47798			0.0532972			0.0266486	−	0.999645i	$-0.491516\pi$
$769$	1.47798			0.0532972			0.0266486	+	0.999645i	$0.491516\pi$
$770$		0			0
$771$	−12.3361			−0.444274
$772$	−0.0412885	+	0.392834i	−0.00148601	+	0.0141384i
$773$	12.5539	+	13.9425i	0.451532	+	0.501477i	0.925333	−	0.379155i	$-0.123785\pi$
$773$	12.5539	+	13.9425i	0.451532	+	0.501477i	−0.473801	+	0.880632i	$0.657118\pi$
$774$	−6.72447	−	1.42933i	−0.241706	−	0.0513762i
$775$	15.0022	+	6.67942i	0.538896	+	0.239932i
$776$	−6.39600	+	4.64697i	−0.229603	+	0.166816i
$777$	33.9341	+	46.6929i	1.21738	+	1.67510i
$778$	−3.89595	+	11.9905i	−0.139677	+	0.429881i
$779$	0.378452	−	3.60073i	0.0135595	−	0.129010i
$780$	11.1595	−	19.3288i	0.399575	−	0.692084i
$781$		0			0
$782$	−3.66802	−	6.35320i	−0.131168	−	0.227190i
$783$	−7.43554	−	5.40224i	−0.265725	−	0.193060i
$784$	−6.93457	+	7.70586i	−0.247663	+	0.275209i
$785$	3.55909	+	10.9538i	0.127029	+	0.390956i
$786$	−6.53796	−	2.91089i	−0.233201	−	0.103828i
$787$	−1.98145	−	18.8523i	−0.0706312	−	0.672011i	−0.971357	−	0.237623i	$-0.923632\pi$
$787$	−1.98145	−	18.8523i	−0.0706312	−	0.672011i	0.900726	−	0.434387i	$-0.143035\pi$
$788$	14.7659	+	3.13860i	0.526015	+	0.111808i
$789$	47.5458	−	10.1062i	1.69268	−	0.359790i
$790$	−13.1108	−	9.52558i	−0.466463	−	0.338905i
$791$	−38.2854	+	12.4455i	−1.36127	+	0.442510i
$792$		0			0
$793$	−8.16096	−	14.1352i	−0.289804	−	0.501956i
$794$	2.90649	−	1.29405i	0.103148	−	0.0459242i
$795$	−10.6657	−	11.8454i	−0.378272	−	0.420114i
$796$	0.366136	−	0.406635i	0.0129774	−	0.0144128i
$797$	32.1770	−	23.3779i	1.13977	−	0.828089i	0.152680	−	0.988276i	$-0.451210\pi$
$797$	32.1770	−	23.3779i	1.13977	−	0.828089i	0.987087	+	0.160187i	$0.0512097\pi$
$798$	−1.27485	−	0.133816i	−0.0451292	−	0.00473702i
$799$	−1.87669	−	5.77585i	−0.0663924	−	0.204335i
$800$	12.1332	−	2.57898i	0.428972	−	0.0911808i
$801$	20.8104	−	9.26538i	0.735299	−	0.327376i
$802$	−5.69757	+	9.86849i	−0.201188	+	0.348468i
$803$		0			0
$804$	−18.1541			−0.640247
$805$	14.0701	−	12.6723i	0.495907	−	0.446640i
$806$	−6.33035	+	19.4828i	−0.222977	+	0.686253i
$807$	−23.4049	+	25.9938i	−0.823893	+	0.915026i
$808$	−2.30099	−	21.8925i	−0.0809486	−	0.770175i
$809$	5.85801	+	55.7352i	0.205957	+	1.95955i	0.273621	+	0.961838i	$0.411779\pi$
$809$	5.85801	+	55.7352i	0.205957	+	1.95955i	−0.0676640	+	0.997708i	$0.521555\pi$
$810$	−8.55710	+	9.50363i	−0.300666	+	0.333923i
$811$	6.48875	−	19.9703i	0.227851	−	0.701253i	−0.770139	−	0.637876i	$-0.779813\pi$
$811$	6.48875	−	19.9703i	0.227851	−	0.701253i	0.997990	−	0.0633764i	$-0.0201869\pi$
$812$	9.45916	−	8.51941i	0.331951	−	0.298973i
$813$	−15.2005			−0.533105
$814$		0			0
$815$	11.5867	−	20.0687i	0.405863	−	0.702976i
$816$	7.47635	−	3.32869i	0.261725	−	0.116527i
$817$	2.04888	−	0.435503i	0.0716813	−	0.0152363i
$818$	5.30949	+	16.3409i	0.185642	+	0.571347i
$819$	17.0164	+	1.78614i	0.594602	+	0.0624128i
$820$	22.8848	−	16.6268i	0.799173	−	0.580633i
$821$	−21.6995	+	24.0997i	−0.757317	+	0.841085i	−0.991364	−	0.131140i	$-0.958136\pi$
$821$	−21.6995	+	24.0997i	−0.757317	+	0.841085i	0.234047	+	0.972225i	$0.424803\pi$
$822$	1.58644	+	1.76192i	0.0553334	+	0.0614539i
$823$	1.60289	−	0.713653i	0.0558732	−	0.0248764i	−0.378610	−	0.925556i	$-0.623598\pi$
$823$	1.60289	−	0.713653i	0.0558732	−	0.0248764i	0.434483	+	0.900680i	$0.356931\pi$
$824$	−19.9300	−	34.5197i	−0.694294	−	1.20255i
$825$		0			0
$826$	−0.0593368	+	0.0192887i	−0.00206459	+	0.000671139i
$827$	9.42529	+	6.84787i	0.327749	+	0.238124i	0.739475	−	0.673184i	$-0.235074\pi$
$827$	9.42529	+	6.84787i	0.327749	+	0.238124i	−0.411726	+	0.911308i	$0.635074\pi$
$828$	10.4260	−	2.21611i	0.362327	−	0.0770150i
$829$	−19.2097	−	4.08315i	−0.667180	−	0.141814i	−0.138143	−	0.990412i	$-0.544113\pi$
$829$	−19.2097	−	4.08315i	−0.667180	−	0.141814i	−0.529037	+	0.848599i	$0.677447\pi$
$830$	−0.552638	−	5.25800i	−0.0191823	−	0.182508i
$831$	−23.3655	−	10.4030i	−0.810541	−	0.360876i
$832$	1.14442	+	3.52215i	0.0396755	+	0.122109i
$833$	17.5905	+	3.73393i	0.609473	+	0.129373i
$834$	−10.3878	−	7.54721i	−0.359702	−	0.261339i
$835$	−16.5185	−	28.6108i	−0.571645	−	0.990119i
$836$		0			0
$837$	−11.2924	+	19.5590i	−0.390323	+	0.676060i
$838$	1.59653	−	15.1900i	0.0551512	−	0.524729i
$839$	−13.6927	+	42.1417i	−0.472723	+	1.45489i	0.376281	+	0.926506i	$0.377203\pi$
$839$	−13.6927	+	42.1417i	−0.472723	+	1.45489i	−0.849004	+	0.528386i	$0.822797\pi$
$840$	−13.5057	−	18.5837i	−0.465992	−	0.641199i
$841$	15.6230	−	11.3508i	0.538723	−	0.391405i
$842$	−11.5674	−	5.15014i	−0.398639	−	0.177486i
$843$	21.8644	+	4.64742i	0.753050	+	0.160066i
$844$	15.4181	+	17.1236i	0.530714	+	0.589417i
$845$	−0.492821	+	4.68888i	−0.0169535	+	0.161302i
$846$	−2.59291			−0.0891460
$847$		0			0
$848$	−6.49678			−0.223100
$849$	−4.56464	+	43.4297i	−0.156658	+	1.49050i
$850$	−2.48726	−	2.76239i	−0.0853125	−	0.0947491i
$851$	−42.0339	−	8.93458i	−1.44090	−	0.306274i
$852$	−28.6490	−	12.7554i	−0.981500	−	0.436992i
$853$	15.9849	−	11.6137i	0.547313	−	0.397646i	−0.279481	−	0.960151i	$-0.590162\pi$
$853$	15.9849	−	11.6137i	0.547313	−	0.397646i	0.826794	+	0.562505i	$0.190162\pi$
$854$	−7.28378	+	0.766565i	−0.249246	+	0.0262313i
$855$	−0.283865	+	0.873645i	−0.00970796	+	0.0298780i
$856$	−0.334832	+	3.18571i	−0.0114443	+	0.108885i
$857$	−1.69370	+	2.93357i	−0.0578556	+	0.100209i	−0.893503	−	0.449058i	$-0.851760\pi$
$857$	−1.69370	+	2.93357i	−0.0578556	+	0.100209i	0.835647	+	0.549267i	$0.185093\pi$
$858$		0			0
$859$	−8.04855	−	13.9405i	−0.274613	−	0.475643i	0.695425	−	0.718599i	$-0.255216\pi$
$859$	−8.04855	−	13.9405i	−0.274613	−	0.475643i	−0.970037	+	0.242956i	$0.921883\pi$
$860$	13.2399	+	9.61933i	0.451476	+	0.328017i
$861$	53.4039	+	30.8230i	1.82000	+	1.05045i
$862$	−7.14266	−	21.9828i	−0.243280	−	0.748738i
$863$	−41.1863	−	18.3373i	−1.40200	−	0.624210i	−0.440183	−	0.897908i	$-0.645087\pi$
$863$	−41.1863	−	18.3373i	−1.40200	−	0.624210i	−0.961816	+	0.273698i	$0.911753\pi$
$864$	1.78318	+	16.9658i	0.0606651	+	0.577190i
$865$	6.07914	+	1.29216i	0.206697	+	0.0439348i
$866$	−2.10074	+	0.446525i	−0.0713859	+	0.0151735i
$867$	18.1004	+	13.1507i	0.614721	+	0.446621i
$868$	−23.2499	−	20.9286i	−0.789154	−	0.710362i
$869$		0			0
$870$	3.81124	+	6.60126i	0.129213	+	0.223804i
$871$	19.8199	−	8.82437i	0.671570	−	0.299002i
$872$	−10.1274	−	11.2476i	−0.342956	−	0.380892i
$873$	−3.60250	+	4.00098i	−0.121926	+	0.135413i
$874$	0.772068	−	0.560940i	0.0261156	−	0.0189741i
$875$	18.7699	−	25.8419i	0.634537	−	0.873617i
$876$	−0.307972	−	0.947840i	−0.0104054	−	0.0320245i
$877$	−54.9264	+	11.6750i	−1.85473	+	0.394236i	−0.993486	−	0.113951i	$-0.963649\pi$
$877$	−54.9264	+	11.6750i	−1.85473	+	0.394236i	−0.861247	+	0.508187i	$0.830316\pi$
$878$	−7.61481	+	3.39033i	−0.256987	+	0.114418i
$879$	25.6799	−	44.4788i	0.866160	−	1.50023i
$880$		0			0
$881$	20.4943			0.690469			0.345235	−	0.938516i	$-0.387799\pi$
$881$	20.4943			0.690469			0.345235	+	0.938516i	$0.387799\pi$
$882$	3.83697	−	6.65004i	0.129198	−	0.223918i
$883$	5.60013	−	17.2354i	0.188459	−	0.580018i	−0.811531	−	0.584309i	$-0.801366\pi$
$883$	5.60013	−	17.2354i	0.188459	−	0.580018i	0.999991	+	0.00429039i	$0.00136568\pi$
$884$	−10.5588	+	11.7267i	−0.355131	+	0.394412i
$885$	0.0132895	+	0.126441i	0.000446720	+	0.00425026i
$886$	0.359497	+	3.42039i	0.0120775	+	0.114910i
$887$	10.0850	−	11.2005i	0.338621	−	0.376076i	−0.549651	−	0.835394i	$-0.685239\pi$
$887$	10.0850	−	11.2005i	0.338621	−	0.376076i	0.888272	+	0.459318i	$0.151906\pi$
$888$	−16.1108	+	49.5840i	−0.540643	+	1.66393i
$889$	13.7547	+	4.46707i	0.461316	+	0.149821i
$890$	15.9349			0.534140
$891$		0			0
$892$	22.1465	−	38.3588i	0.741518	−	1.28435i
$893$	0.721731	−	0.321335i	0.0241518	−	0.0107531i
$894$	−6.79502	+	1.44433i	−0.227259	+	0.0483055i
$895$	10.3012	+	31.7037i	0.344330	+	1.05974i
$896$	−28.7522	−	3.01800i	−0.960544	−	0.100824i
$897$	−29.3028	+	21.2898i	−0.978394	+	0.710845i
$898$	−0.551674	+	0.612696i	−0.0184096	+	0.0204459i
$899$	15.9312	+	17.6934i	0.531336	+	0.590109i
$900$	4.93390	−	2.19672i	0.164463	−	0.0732239i
$901$	5.63475	+	9.75967i	0.187721	+	0.325142i
$902$		0			0
$903$	−7.41213	+	34.8948i	−0.246660	+	1.16123i
$904$	−29.4173	−	21.3729i	−0.978403	−	0.710852i
$905$	3.65535	−	0.776968i	0.121508	−	0.0258273i
$906$	−22.7999	−	4.84628i	−0.757477	−	0.161007i
$907$	−1.70142	−	16.1879i	−0.0564947	−	0.537511i	−0.985767	−	0.168116i	$-0.946232\pi$
$907$	−1.70142	−	16.1879i	−0.0564947	−	0.537511i	0.929273	−	0.369395i	$-0.120435\pi$
$908$	−29.7478	−	13.2446i	−0.987216	−	0.439537i
$909$	−4.63239	−	14.2570i	−0.153647	−	0.472876i
$910$	10.3660	+	5.98294i	0.343631	+	0.198333i
$911$	6.68078	+	4.85387i	0.221344	+	0.160816i	0.692931	−	0.721003i	$-0.256319\pi$
$911$	6.68078	+	4.85387i	0.221344	+	0.160816i	−0.471587	+	0.881819i	$0.656319\pi$
$912$	0.532311	+	0.921990i	0.0176266	+	0.0305301i
$913$		0			0
$914$	1.73006	−	2.99655i	0.0572253	−	0.0991172i
$915$	−1.55998	+	14.8422i	−0.0515713	+	0.490669i
$916$	3.44769	−	10.6109i	0.113915	−	0.350594i
$917$	−5.31051	+	11.9320i	−0.175369	+	0.394030i
$918$	4.13581	−	3.00484i	0.136502	−	0.0991745i
$919$	34.1998	+	15.2267i	1.12815	+	0.502283i	0.884015	−	0.467459i	$-0.154831\pi$
$919$	34.1998	+	15.2267i	1.12815	+	0.502283i	0.244131	+	0.969742i	$0.421497\pi$
$920$	16.7294	+	3.55595i	0.551553	+	0.117236i
$921$	−12.5784	−	13.9697i	−0.414472	−	0.460318i
$922$	1.60451	−	15.2659i	0.0528418	−	0.502757i
$923$	37.4779			1.23360
$924$		0			0
$925$	−21.7743			−0.715935
$926$	−2.10250	+	20.0040i	−0.0690924	+	0.657371i
$927$	−18.1631	−	20.1722i	−0.596555	−	0.662541i
$928$	17.5909	+	3.73905i	0.577448	+	0.122740i
$929$	49.5267	+	22.0507i	1.62492	+	0.723460i	0.998432	−	0.0559731i	$-0.0178261\pi$
$929$	49.5267	+	22.0507i	1.62492	+	0.723460i	0.626485	+	0.779433i	$0.284493\pi$
$930$	15.1536	−	11.0097i	0.496906	−	0.361024i
$931$	−0.243885	+	2.32654i	−0.00799300	+	0.0762492i
$932$	12.2685	−	37.7585i	0.401868	−	1.23682i
$933$	−0.588704	+	5.60114i	−0.0192733	+	0.183373i
$934$	−0.522321	+	0.904686i	−0.0170909	+	0.0296022i
$935$		0			0
$936$	7.72709	+	13.3837i	0.252568	+	0.437460i
$937$	18.9834	+	13.7922i	0.620160	+	0.450572i	0.852977	−	0.521948i	$-0.174794\pi$
$937$	18.9834	+	13.7922i	0.620160	+	0.450572i	−0.232818	+	0.972520i	$0.574794\pi$
$938$	−0.00133314	−	9.73527i	−4.35286e−5	−	0.317868i
$939$	−15.1251	−	46.5504i	−0.493590	−	1.51912i
$940$	5.63884	+	2.51057i	0.183919	+	0.0818858i
$941$	4.48558	+	42.6775i	0.146226	+	1.39125i	0.783875	+	0.620919i	$0.213240\pi$
$941$	4.48558	+	42.6775i	0.146226	+	1.39125i	−0.637649	+	0.770327i	$0.720093\pi$
$942$	−9.66968	−	2.05535i	−0.315055	−	0.0669670i
$943$	−44.9026	+	9.54434i	−1.46223	+	0.310807i
$944$	0.0419229	+	0.0304588i	0.00136448	+	0.000991349i
$945$	9.80723	+	8.82804i	0.319029	+	0.287176i
$946$		0			0
$947$	−26.8719	−	46.5435i	−0.873219	−	1.51246i	−0.858648	−	0.512566i	$-0.828695\pi$
$947$	−26.8719	−	46.5435i	−0.873219	−	1.51246i	−0.0145710	−	0.999894i	$-0.504638\pi$
$948$	−43.2440	+	19.2535i	−1.40450	+	0.625324i
$949$	0.796956	+	0.885110i	0.0258703	+	0.0287319i
$950$	0.323562	−	0.359352i	0.0104977	−	0.0116589i
$951$	−7.81072	+	5.67482i	−0.253280	+	0.184019i
$952$	6.60835	+	14.8371i	0.214178	+	0.480874i
$953$	−2.95509	−	9.09484i	−0.0957249	−	0.294611i	0.891717	−	0.452593i	$-0.149501\pi$
$953$	−2.95509	−	9.09484i	−0.0957249	−	0.294611i	−0.987442	+	0.157982i	$0.949501\pi$
$954$	4.70638	−	1.00037i	0.152375	−	0.0323882i
$955$	13.2772	−	5.91137i	0.429639	−	0.191288i
$956$	6.70500	−	11.6134i	0.216855	−	0.375604i
$957$		0			0
$958$	7.91603			0.255755
$959$	3.21497	−	2.89557i	0.103817	−	0.0935027i
$960$	1.04640	−	3.22048i	0.0337724	−	0.103941i
$961$	18.4051	−	20.4410i	0.593714	−	0.659386i
$962$	−2.83922	−	27.0134i	−0.0915402	−	0.870946i
$963$	0.228018	+	2.16945i	0.00734778	+	0.0699095i
$964$	−22.8287	+	25.3538i	−0.735262	+	0.816591i
$965$	−0.133378	+	0.410496i	−0.00429360	+	0.0132143i
$966$	3.38133	+	15.8972i	0.108793	+	0.511485i
$967$	−34.7245			−1.11666			−0.558332	−	0.829618i	$-0.688558\pi$
$967$	−34.7245			−1.11666			−0.558332	+	0.829618i	$0.688558\pi$
$968$		0			0
$969$	0.923362	−	1.59931i	0.0296627	−	0.0513773i
$970$	−3.44052	+	1.53182i	−0.110468	+	0.0491837i
$971$	8.01862	−	1.70441i	0.257330	−	0.0546972i	−0.0774402	−	0.996997i	$-0.524675\pi$
$971$	8.01862	−	1.70441i	0.257330	−	0.0546972i	0.334770	+	0.942300i	$0.391341\pi$
$972$	7.31185	+	22.5036i	0.234528	+	0.721802i
$973$	−13.7705	+	18.9589i	−0.441461	+	0.607794i
$974$	−4.00426	+	2.90926i	−0.128305	+	0.0932188i
$975$	−12.2804	+	13.6388i	−0.393287	+	0.436790i
$976$	4.07021	+	4.52042i	0.130284	+	0.144695i
$977$	1.72700	−	0.768911i	0.0552517	−	0.0245996i	−0.378925	−	0.925427i	$-0.623706\pi$
$977$	1.72700	−	0.768911i	0.0552517	−	0.0245996i	0.434176	+	0.900828i	$0.357039\pi$
$978$	9.94511	+	17.2254i	0.318010	+	0.550809i
$979$		0			0
$980$	−14.7832	+	10.7468i	−0.472232	+	0.343294i
$981$	−8.33847	−	6.05825i	−0.266227	−	0.193425i
$982$	−8.54455	+	1.81620i	−0.272668	+	0.0579573i
$983$	39.3534	+	8.36482i	1.25518	+	0.266796i	0.787064	−	0.616871i	$-0.211600\pi$
$983$	39.3534	+	8.36482i	1.25518	+	0.266796i	0.468114	+	0.883668i	$0.344933\pi$
$984$	5.82158	+	55.3887i	0.185585	+	1.76573i
$985$	15.0694	+	6.70931i	0.480150	+	0.213776i
$986$	−1.66535	−	5.12543i	−0.0530357	−	0.163227i
$987$	0.00184249	+	13.4548i	5.86471e−5	+	0.428271i
$988$	−1.66072	−	1.20658i	−0.0528346	−	0.0383866i
$989$	−13.2792	−	23.0003i	−0.422255	−	0.731367i
$990$		0			0
$991$	−12.7333	+	22.0548i	−0.404487	+	0.700592i	−0.994262	−	0.106976i	$-0.965883\pi$
$991$	−12.7333	+	22.0548i	−0.404487	+	0.700592i	0.589774	+	0.807568i	$0.299217\pi$
$992$	4.61933	−	43.9500i	0.146664	−	1.39541i
$993$	−9.17428	+	28.2355i	−0.291137	+	0.896028i
$994$	6.83804	−	15.3642i	0.216890	−	0.487322i
$995$	0.483724	−	0.351446i	0.0153351	−	0.0111416i
$996$	−14.1078	−	6.28120i	−0.447023	−	0.199027i
$997$	−16.1326	−	3.42909i	−0.510925	−	0.108600i	−0.0547668	−	0.998499i	$-0.517442\pi$
$997$	−16.1326	−	3.42909i	−0.510925	−	0.108600i	−0.456158	+	0.889899i	$0.650775\pi$
$998$	1.97234	+	2.19050i	0.0624332	+	0.0693391i
$999$	3.13019	−	29.7818i	0.0990349	−	0.942254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.h.81.2		40
7.2	even	3	inner	847.2.n.h.807.4		40
11.2	odd	10		77.2.m.b.60.2	yes	40
11.3	even	5	inner	847.2.n.h.487.4		40
11.4	even	5		847.2.n.j.130.2		40
11.5	even	5		847.2.e.h.606.4		20
11.6	odd	10		847.2.e.i.606.7		20
11.7	odd	10		77.2.m.b.53.4	yes	40
11.8	odd	10		847.2.n.i.487.2		40
11.9	even	5		847.2.n.j.753.4		40
11.10	odd	2		847.2.n.i.81.4		40
33.2	even	10		693.2.by.b.676.4		40
33.29	even	10		693.2.by.b.361.2		40
77.2	odd	30		77.2.m.b.16.4	yes	40
77.9	even	15		847.2.n.j.632.2		40
77.13	even	10		539.2.q.h.214.2		40
77.16	even	15		847.2.e.h.485.4		20
77.17	even	30		5929.2.a.bx.1.4		10
77.18	odd	30		539.2.f.h.295.2		20
77.24	even	30		539.2.f.g.148.2		20
77.30	odd	30		847.2.n.i.366.4		40
77.37	even	15		847.2.n.j.9.4		40
77.38	odd	30		5929.2.a.bz.1.7		10
77.39	odd	30		5929.2.a.bw.1.4		10
77.40	even	30		539.2.q.h.471.2		40
77.46	odd	30		539.2.f.h.148.2		20
77.51	odd	30		77.2.m.b.9.2	✓	40
77.58	even	15	inner	847.2.n.h.366.2		40
77.60	even	15		5929.2.a.by.1.7		10
77.62	even	10		539.2.q.h.361.4		40
77.65	odd	6		847.2.n.i.807.2		40
77.68	even	30		539.2.q.h.324.4		40
77.72	odd	30		847.2.e.i.485.7		20
77.73	even	30		539.2.f.g.295.2		20
231.2	even	30		693.2.by.b.478.2		40
231.128	even	30		693.2.by.b.163.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.2	✓	40	77.51	odd	30
77.2.m.b.16.4	yes	40	77.2	odd	30
77.2.m.b.53.4	yes	40	11.7	odd	10
77.2.m.b.60.2	yes	40	11.2	odd	10
539.2.f.g.148.2		20	77.24	even	30
539.2.f.g.295.2		20	77.73	even	30
539.2.f.h.148.2		20	77.46	odd	30
539.2.f.h.295.2		20	77.18	odd	30
539.2.q.h.214.2		40	77.13	even	10
539.2.q.h.324.4		40	77.68	even	30
539.2.q.h.361.4		40	77.62	even	10
539.2.q.h.471.2		40	77.40	even	30
693.2.by.b.163.4		40	231.128	even	30
693.2.by.b.361.2		40	33.29	even	10
693.2.by.b.478.2		40	231.2	even	30
693.2.by.b.676.4		40	33.2	even	10
847.2.e.h.485.4		20	77.16	even	15
847.2.e.h.606.4		20	11.5	even	5
847.2.e.i.485.7		20	77.72	odd	30
847.2.e.i.606.7		20	11.6	odd	10
847.2.n.h.81.2		40	1.1	even	1	trivial
847.2.n.h.366.2		40	77.58	even	15	inner
847.2.n.h.487.4		40	11.3	even	5	inner
847.2.n.h.807.4		40	7.2	even	3	inner
847.2.n.i.81.4		40	11.10	odd	2
847.2.n.i.366.4		40	77.30	odd	30
847.2.n.i.487.2		40	11.8	odd	10
847.2.n.i.807.2		40	77.65	odd	6
847.2.n.j.9.4		40	77.37	even	15
847.2.n.j.130.2		40	11.4	even	5
847.2.n.j.632.2		40	77.9	even	15
847.2.n.j.753.4		40	11.9	even	5
5929.2.a.bw.1.4		10	77.39	odd	30
5929.2.a.bx.1.4		10	77.17	even	30
5929.2.a.by.1.7		10	77.60	even	15
5929.2.a.bz.1.7		10	77.38	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0704484 + 0.670272i) q^{2} +(1.43939 + 1.59861i) q^{3} +(1.51199 + 0.321384i) q^{4} +(1.54306 + 0.687016i) q^{5} +(-1.17290 + 0.852164i) q^{6} +(1.55543 + 2.14024i) q^{7} +(-0.738465 + 2.27276i) q^{8} +(-0.170108 + 1.61847i) q^{9} +O(q^{10})\)	\(q+(-0.0704484 + 0.670272i) q^{2} +(1.43939 + 1.59861i) q^{3} +(1.51199 + 0.321384i) q^{4} +(1.54306 + 0.687016i) q^{5} +(-1.17290 + 0.852164i) q^{6} +(1.55543 + 2.14024i) q^{7} +(-0.738465 + 2.27276i) q^{8} +(-0.170108 + 1.61847i) q^{9} +(-0.569194 + 0.985873i) q^{10} +(1.66258 + 2.87968i) q^{12} +(-3.21489 - 2.33575i) q^{13} +(-1.54412 + 0.891782i) q^{14} +(1.12280 + 3.45563i) q^{15} +(1.35292 + 0.602360i) q^{16} +(-0.268524 - 2.55484i) q^{17} +(-1.07283 - 0.228037i) q^{18} +(0.326881 - 0.0694807i) q^{19} +(2.11231 + 1.53468i) q^{20} +(-1.18254 + 5.56716i) q^{21} +(-2.11859 - 3.66950i) q^{23} +(-4.69619 + 2.09088i) q^{24} +(-1.43660 - 1.59551i) q^{25} +(1.79207 - 1.99030i) q^{26} +(2.38877 - 1.73554i) q^{27} +(1.66395 + 3.73593i) q^{28} +(-0.961879 - 2.96036i) q^{29} +(-2.39531 + 0.509140i) q^{30} +(-6.98764 + 3.11110i) q^{31} +(-2.88878 + 5.00351i) q^{32} +1.73135 q^{34} +(0.929739 + 4.37114i) q^{35} +(-0.777353 + 2.39245i) q^{36} +(6.78626 - 7.53690i) q^{37} +(0.0235427 + 0.223994i) q^{38} +(-0.893533 - 8.50140i) q^{39} +(-2.70092 + 2.99968i) q^{40} +(3.34791 - 10.3038i) q^{41} +(-3.64820 - 1.18482i) q^{42} +6.26797 q^{43} +(-1.37440 + 2.38053i) q^{45} +(2.60881 - 1.16152i) q^{46} +(2.31241 - 0.491518i) q^{47} +(0.984448 + 3.02982i) q^{48} +(-2.16130 + 6.65799i) q^{49} +(1.17063 - 0.850512i) q^{50} +(3.69767 - 4.10668i) q^{51} +(-4.11022 - 4.56486i) q^{52} +(-4.00761 + 1.78430i) q^{53} +(0.995001 + 1.72339i) q^{54} +(-6.01289 + 1.95462i) q^{56} +(0.581581 + 0.422544i) q^{57} +(2.05201 - 0.436168i) q^{58} +(0.0342260 + 0.00727496i) q^{59} +(0.587086 + 5.58575i) q^{60} +(3.75226 + 1.67061i) q^{61} +(-1.59301 - 4.90279i) q^{62} +(-3.72851 + 2.15334i) q^{63} +(-0.753965 - 0.547788i) q^{64} +(-3.35608 - 5.81290i) q^{65} +(-2.72981 + 4.72817i) q^{67} +(0.415078 - 3.94920i) q^{68} +(2.81661 - 8.66862i) q^{69} +(-2.99535 + 0.315239i) q^{70} +(-7.62999 + 5.54351i) q^{71} +(-3.55278 - 1.58180i) q^{72} +(-0.293170 - 0.0623152i) q^{73} +(4.57369 + 5.07960i) q^{74} +(0.482756 - 4.59311i) q^{75} +0.516572 q^{76} +5.76120 q^{78} +(-1.48805 + 14.1578i) q^{79} +(1.67381 + 1.85896i) q^{80} +(10.9883 + 2.33563i) q^{81} +(6.67049 + 2.96990i) q^{82} +(-3.75728 + 2.72982i) q^{83} +(-3.57719 + 8.03746i) q^{84} +(1.34087 - 4.12676i) q^{85} +(-0.441569 + 4.20125i) q^{86} +(3.34793 - 5.79878i) q^{87} +(-6.99890 - 12.1225i) q^{89} +(-1.49878 - 1.08893i) q^{90} +(-0.00143975 - 10.5137i) q^{91} +(-2.02397 - 6.22914i) q^{92} +(-15.0314 - 6.69239i) q^{93} +(0.166545 + 1.58457i) q^{94} +(0.552132 + 0.117359i) q^{95} +(-12.1567 + 2.58399i) q^{96} +(2.67646 + 1.94456i) q^{97} +(-4.31040 - 1.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9	\( 40 q - 2 q^{2} + q^{3} + 12 q^{4} - 6 q^{5} - 34 q^{6} - 13 q^{7} - 32 q^{8} + 2 q^{9} - 14 q^{10} - 18 q^{12} + 4 q^{13} + 22 q^{14} + 16 q^{15} + 20 q^{16} + 12 q^{17} + 41 q^{18} + 24 q^{19} + 40 q^{20} + 2 q^{21} - 14 q^{23} + 7 q^{24} - 29 q^{25} - 5 q^{26} + 4 q^{27} + 24 q^{28} + 30 q^{29} - 6 q^{30} + 3 q^{31} + 30 q^{32} + 48 q^{34} - 6 q^{35} - 46 q^{36} - 11 q^{37} + 12 q^{38} + 32 q^{39} + 20 q^{40} - 10 q^{41} + 45 q^{42} + 72 q^{43} - 16 q^{45} + 17 q^{46} + 3 q^{47} - 62 q^{48} + 35 q^{49} - 6 q^{50} - 28 q^{51} - 2 q^{52} - 42 q^{53} - 34 q^{54} + 24 q^{56} + 36 q^{57} + 8 q^{58} - 9 q^{59} + 27 q^{60} + 20 q^{61} - 128 q^{62} + 36 q^{63} - 36 q^{64} + 40 q^{65} - 38 q^{67} + 33 q^{68} + 106 q^{69} - 18 q^{70} - 50 q^{71} - 42 q^{72} + 14 q^{73} + q^{74} - 16 q^{75} + 96 q^{76} - 100 q^{78} - 11 q^{79} - 18 q^{80} + 12 q^{81} - 24 q^{82} - 104 q^{83} + 44 q^{84} - 32 q^{85} + 2 q^{86} - 48 q^{87} - 10 q^{89} - 42 q^{90} - 14 q^{91} + 80 q^{92} - 13 q^{93} + 18 q^{94} + 8 q^{95} - 7 q^{96} + 46 q^{97} - 116 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + q^3 + 12 * q^4 - 6 * q^5 - 34 * q^6 - 13 * q^7 - 32 * q^8 + 2 * q^9 - 14 * q^10 - 18 * q^12 + 4 * q^13 + 22 * q^14 + 16 * q^15 + 20 * q^16 + 12 * q^17 + 41 * q^18 + 24 * q^19 + 40 * q^20 + 2 * q^21 - 14 * q^23 + 7 * q^24 - 29 * q^25 - 5 * q^26 + 4 * q^27 + 24 * q^28 + 30 * q^29 - 6 * q^30 + 3 * q^31 + 30 * q^32 + 48 * q^34 - 6 * q^35 - 46 * q^36 - 11 * q^37 + 12 * q^38 + 32 * q^39 + 20 * q^40 - 10 * q^41 + 45 * q^42 + 72 * q^43 - 16 * q^45 + 17 * q^46 + 3 * q^47 - 62 * q^48 + 35 * q^49 - 6 * q^50 - 28 * q^51 - 2 * q^52 - 42 * q^53 - 34 * q^54 + 24 * q^56 + 36 * q^57 + 8 * q^58 - 9 * q^59 + 27 * q^60 + 20 * q^61 - 128 * q^62 + 36 * q^63 - 36 * q^64 + 40 * q^65 - 38 * q^67 + 33 * q^68 + 106 * q^69 - 18 * q^70 - 50 * q^71 - 42 * q^72 + 14 * q^73 + q^74 - 16 * q^75 + 96 * q^76 - 100 * q^78 - 11 * q^79 - 18 * q^80 + 12 * q^81 - 24 * q^82 - 104 * q^83 + 44 * q^84 - 32 * q^85 + 2 * q^86 - 48 * q^87 - 10 * q^89 - 42 * q^90 - 14 * q^91 + 80 * q^92 - 13 * q^93 + 18 * q^94 + 8 * q^95 - 7 * q^96 + 46 * q^97 - 116 * q^98

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