LMFDB - Embedded newform 345.2.m.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, 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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	345.16
Dual form			345.2.m.a.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.758566 + 0.875431i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0936713 + 0.651498i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.164852 - 1.14657i) q^{6} +(-1.51957 + 0.446185i) q^{7} +(-2.59035 - 1.66472i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.758566 + 0.875431i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0936713 + 0.651498i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.164852 - 1.14657i) q^{6} +(-1.51957 + 0.446185i) q^{7} +(-2.59035 - 1.66472i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.11144 + 0.326348i) q^{10} +(-0.942075 - 1.08721i) q^{11} +(-0.431028 - 0.497433i) q^{12} +(-2.71972 - 0.798583i) q^{13} +(0.762086 - 1.66874i) q^{14} +(0.841254 + 0.540641i) q^{15} +(2.15922 - 0.634005i) q^{16} +(0.357914 - 2.48935i) q^{17} +(0.481201 + 1.05368i) q^{18} +(0.236917 + 1.64779i) q^{19} +(0.553711 - 0.355849i) q^{20} +(1.03711 - 1.19689i) q^{21} +1.66641 q^{22} +(-3.88251 - 2.81533i) q^{23} +3.07915 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.76219 - 1.77515i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.433028 - 0.948199i) q^{28} +(0.710862 - 4.94415i) q^{29} +(-1.11144 + 0.326348i) q^{30} +(-0.239758 - 0.154083i) q^{31} +(1.47537 - 3.23061i) q^{32} +(1.38032 + 0.405297i) q^{33} +(1.90775 + 2.20166i) q^{34} +(1.03711 + 1.19689i) q^{35} +(0.631536 + 0.185436i) q^{36} +(1.36102 - 2.98021i) q^{37} +(-1.62225 - 1.04255i) q^{38} +(2.71972 - 0.798583i) q^{39} +(-0.438209 + 3.04781i) q^{40} +(-1.55665 - 3.40858i) q^{41} +(0.261079 + 1.81584i) q^{42} +(-5.20297 + 3.34375i) q^{43} +(0.620072 - 0.715601i) q^{44} -1.00000 q^{45} +(5.40977 - 1.26326i) q^{46} +3.54485 q^{47} +(-1.47369 + 1.70072i) q^{48} +(-3.77878 + 2.42847i) q^{49} +(-0.164852 - 1.14657i) q^{50} +(1.04475 + 2.28767i) q^{51} +(0.265515 - 1.84670i) q^{52} +(-10.0162 + 2.94102i) q^{53} +(-0.974476 - 0.626258i) q^{54} +(-0.597611 + 1.30859i) q^{55} +(4.67898 + 1.37387i) q^{56} +(-1.09017 - 1.25812i) q^{57} +(3.78903 + 4.37278i) q^{58} +(-6.13809 - 1.80231i) q^{59} +(-0.273425 + 0.598718i) q^{60} +(1.80318 + 1.15883i) q^{61} +(0.316761 - 0.0930093i) q^{62} +(-0.225386 + 1.56760i) q^{63} +(3.57869 + 7.83625i) q^{64} +(0.403397 + 2.80569i) q^{65} +(-1.40187 + 0.900927i) q^{66} +(-3.78136 + 4.36392i) q^{67} +1.65533 q^{68} +(4.78826 + 0.269360i) q^{69} -1.83452 q^{70} +(-5.60070 + 6.46355i) q^{71} +(-2.59035 + 1.66472i) q^{72} +(0.0961868 + 0.668994i) q^{73} +(1.57655 + 3.45216i) q^{74} +(0.142315 - 0.989821i) q^{75} +(-1.05134 + 0.308702i) q^{76} +(1.91664 + 1.23175i) q^{77} +(-1.36398 + 2.98671i) q^{78} +(7.09140 + 2.08222i) q^{79} +(-1.47369 - 1.70072i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(4.16480 + 1.22289i) q^{82} +(-6.97368 + 15.2702i) q^{83} +(0.876922 + 0.563563i) q^{84} +(-2.41307 + 0.708542i) q^{85} +(1.01957 - 7.09130i) q^{86} +(2.07500 + 4.54361i) q^{87} +(0.630403 + 4.38455i) q^{88} +(-5.70586 + 3.66694i) q^{89} +(0.758566 - 0.875431i) q^{90} +4.48911 q^{91} +(1.47050 - 2.79317i) q^{92} +0.285000 q^{93} +(-2.68900 + 3.10328i) q^{94} +(1.40047 - 0.900025i) q^{95} +(0.505439 + 3.51541i) q^{96} +(-4.51626 - 9.88923i) q^{97} +(0.740489 - 5.15022i) q^{98} +(-1.38032 + 0.405297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	−0.758566	+	0.875431i	−0.536387	+	0.619024i	−0.957657	−	0.287912i	$-0.907039\pi$
$2$	−0.758566	+	0.875431i	−0.536387	+	0.619024i	0.421270	+	0.906935i	$0.361584\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	0.0936713	+	0.651498i	0.0468357	+	0.325749i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.164852	−	1.14657i	0.0673006	−	0.468086i
$7$	−1.51957	+	0.446185i	−0.574342	+	0.168642i	−0.555989	−	0.831190i	$-0.687660\pi$
$7$	−1.51957	+	0.446185i	−0.574342	+	0.168642i	−0.0183526	+	0.999832i	$0.505842\pi$
$8$	−2.59035	−	1.66472i	−0.915827	−	0.588566i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	1.11144	+	0.326348i	0.351468	+	0.103200i
$11$	−0.942075	−	1.08721i	−0.284046	−	0.327807i	0.595739	−	0.803178i	$-0.296859\pi$
$11$	−0.942075	−	1.08721i	−0.284046	−	0.327807i	−0.879785	+	0.475371i	$0.842314\pi$
$12$	−0.431028	−	0.497433i	−0.124427	−	0.143596i
$13$	−2.71972	−	0.798583i	−0.754316	−	0.221487i	−0.118103	−	0.993001i	$-0.537681\pi$
$13$	−2.71972	−	0.798583i	−0.754316	−	0.221487i	−0.636212	+	0.771514i	$0.719500\pi$
$14$	0.762086	−	1.66874i	0.203676	−	0.445988i
$15$	0.841254	+	0.540641i	0.217211	+	0.139593i
$16$	2.15922	−	0.634005i	0.539806	−	0.158501i
$17$	0.357914	−	2.48935i	0.0868069	−	0.603755i	−0.899261	−	0.437412i	$-0.855895\pi$
$17$	0.357914	−	2.48935i	0.0868069	−	0.603755i	0.986068	−	0.166343i	$-0.0531959\pi$
$18$	0.481201	+	1.05368i	0.113420	+	0.248355i
$19$	0.236917	+	1.64779i	0.0543525	+	0.378030i	0.998783	+	0.0493189i	$0.0157051\pi$
$19$	0.236917	+	1.64779i	0.0543525	+	0.378030i	−0.944431	+	0.328711i	$0.893386\pi$
$20$	0.553711	−	0.355849i	0.123814	−	0.0795702i
$21$	1.03711	−	1.19689i	0.226317	−	0.261184i
$22$	1.66641			0.355279
$23$	−3.88251	−	2.81533i	−0.809560	−	0.587037i
$23$	−3.88251	−	2.81533i	−0.809560	−	0.587037i
$24$	3.07915			0.628530
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	2.76219	−	1.77515i	0.541711	−	0.348136i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−0.433028	−	0.948199i	−0.0818346	−	0.179193i
$29$	0.710862	−	4.94415i	0.132004	−	0.918106i	−0.810934	−	0.585138i	$-0.801041\pi$
$29$	0.710862	−	4.94415i	0.132004	−	0.918106i	0.942938	−	0.332969i	$-0.108050\pi$
$30$	−1.11144	+	0.326348i	−0.202920	+	0.0595828i
$31$	−0.239758	−	0.154083i	−0.0430617	−	0.0276741i	0.518933	−	0.854815i	$-0.326329\pi$
$31$	−0.239758	−	0.154083i	−0.0430617	−	0.0276741i	−0.561995	+	0.827141i	$0.689966\pi$
$32$	1.47537	−	3.23061i	0.260811	−	0.571096i
$33$	1.38032	+	0.405297i	0.240282	+	0.0705532i
$34$	1.90775	+	2.20166i	0.327177	+	0.377582i
$35$	1.03711	+	1.19689i	0.175304	+	0.202312i
$36$	0.631536	+	0.185436i	0.105256	+	0.0309060i
$37$	1.36102	−	2.98021i	0.223750	−	0.489944i	−0.764150	−	0.645039i	$-0.776841\pi$
$37$	1.36102	−	2.98021i	0.223750	−	0.489944i	0.987900	+	0.155095i	$0.0495684\pi$
$38$	−1.62225	−	1.04255i	−0.263163	−	0.169125i
$39$	2.71972	−	0.798583i	0.435504	−	0.127876i
$40$	−0.438209	+	3.04781i	−0.0692870	+	0.481902i
$41$	−1.55665	−	3.40858i	−0.243107	−	0.532331i	0.748266	−	0.663399i	$-0.230887\pi$
$41$	−1.55665	−	3.40858i	−0.243107	−	0.532331i	−0.991373	+	0.131068i	$0.958159\pi$
$42$	0.261079	+	1.81584i	0.0402854	+	0.280191i
$43$	−5.20297	+	3.34375i	−0.793446	+	0.509917i	−0.873471	−	0.486876i	$-0.838136\pi$
$43$	−5.20297	+	3.34375i	−0.793446	+	0.509917i	0.0800252	+	0.996793i	$0.474500\pi$
$44$	0.620072	−	0.715601i	0.0934793	−	0.107881i
$45$	−1.00000			−0.149071
$46$	5.40977	−	1.26326i	0.797627	−	0.186258i
$47$	3.54485			0.517070			0.258535	−	0.966002i	$-0.416760\pi$
$47$	3.54485			0.517070			0.258535	+	0.966002i	$0.416760\pi$
$48$	−1.47369	+	1.70072i	−0.212708	+	0.245478i
$49$	−3.77878	+	2.42847i	−0.539825	+	0.346925i
$50$	−0.164852	−	1.14657i	−0.0233136	−	0.162150i
$51$	1.04475	+	2.28767i	0.146294	+	0.320339i
$52$	0.265515	−	1.84670i	0.0368204	−	0.256091i
$53$	−10.0162	+	2.94102i	−1.37583	+	0.403980i	−0.884316	−	0.466890i	$-0.845375\pi$
$53$	−10.0162	+	2.94102i	−1.37583	+	0.403980i	−0.491514	+	0.870870i	$0.663556\pi$
$54$	−0.974476	−	0.626258i	−0.132609	−	0.0852229i
$55$	−0.597611	+	1.30859i	−0.0805819	+	0.176450i
$56$	4.67898	+	1.37387i	0.625254	+	0.183591i
$57$	−1.09017	−	1.25812i	−0.144397	−	0.166643i
$58$	3.78903	+	4.37278i	0.497524	+	0.574174i
$59$	−6.13809	−	1.80231i	−0.799111	−	0.234640i	−0.143413	−	0.989663i	$-0.545808\pi$
$59$	−6.13809	−	1.80231i	−0.799111	−	0.234640i	−0.655699	+	0.755023i	$0.727626\pi$
$60$	−0.273425	+	0.598718i	−0.0352991	+	0.0772941i
$61$	1.80318	+	1.15883i	0.230874	+	0.148374i	0.650964	−	0.759109i	$-0.274365\pi$
$61$	1.80318	+	1.15883i	0.230874	+	0.148374i	−0.420090	+	0.907483i	$0.638001\pi$
$62$	0.316761	−	0.0930093i	0.0402287	−	0.0118122i
$63$	−0.225386	+	1.56760i	−0.0283960	+	0.197499i
$64$	3.57869	+	7.83625i	0.447337	+	0.979531i
$65$	0.403397	+	2.80569i	0.0500353	+	0.348003i
$66$	−1.40187	+	0.900927i	−0.172558	+	0.110896i
$67$	−3.78136	+	4.36392i	−0.461966	+	0.533138i	−0.938160	−	0.346203i	$-0.887471\pi$
$67$	−3.78136	+	4.36392i	−0.461966	+	0.533138i	0.476193	+	0.879341i	$0.342016\pi$
$68$	1.65533			0.200738
$69$	4.78826	+	0.269360i	0.576439	+	0.0324272i
$70$	−1.83452			−0.219267
$71$	−5.60070	+	6.46355i	−0.664681	+	0.767083i	−0.983534	−	0.180721i	$-0.942157\pi$
$71$	−5.60070	+	6.46355i	−0.664681	+	0.767083i	0.318853	+	0.947804i	$0.396702\pi$
$72$	−2.59035	+	1.66472i	−0.305276	+	0.196189i
$73$	0.0961868	+	0.668994i	0.0112578	+	0.0782998i	0.994676	−	0.103054i	$-0.0328613\pi$
$73$	0.0961868	+	0.668994i	0.0112578	+	0.0782998i	−0.983418	+	0.181353i	$0.941952\pi$
$74$	1.57655	+	3.45216i	0.183270	+	0.401306i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	−1.05134	+	0.308702i	−0.120597	+	0.0354105i
$77$	1.91664	+	1.23175i	0.218422	+	0.140371i
$78$	−1.36398	+	2.98671i	−0.154441	+	0.338178i
$79$	7.09140	+	2.08222i	0.797845	+	0.234268i	0.655150	−	0.755498i	$-0.272605\pi$
$79$	7.09140	+	2.08222i	0.797845	+	0.234268i	0.142694	+	0.989767i	$0.454423\pi$
$80$	−1.47369	−	1.70072i	−0.164763	−	0.190147i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	4.16480	+	1.22289i	0.459925	+	0.135046i
$83$	−6.97368	+	15.2702i	−0.765460	+	1.67612i	−0.0290611	+	0.999578i	$0.509252\pi$
$83$	−6.97368	+	15.2702i	−0.765460	+	1.67612i	−0.736399	+	0.676547i	$0.763476\pi$
$84$	0.876922	+	0.563563i	0.0956800	+	0.0614898i
$85$	−2.41307	+	0.708542i	−0.261734	+	0.0768522i
$86$	1.01957	−	7.09130i	0.109944	−	0.764674i
$87$	2.07500	+	4.54361i	0.222463	+	0.487126i
$88$	0.630403	+	4.38455i	0.0672012	+	0.467394i
$89$	−5.70586	+	3.66694i	−0.604820	+	0.388694i	−0.806912	−	0.590672i	$-0.798863\pi$
$89$	−5.70586	+	3.66694i	−0.604820	+	0.388694i	0.202091	+	0.979367i	$0.435226\pi$
$90$	0.758566	−	0.875431i	0.0799598	−	0.0922786i
$91$	4.48911			0.470587
$92$	1.47050	−	2.79317i	0.153310	−	0.291208i
$93$	0.285000			0.0295532
$94$	−2.68900	+	3.10328i	−0.277350	+	0.320078i
$95$	1.40047	−	0.900025i	0.143685	−	0.0923406i
$96$	0.505439	+	3.51541i	0.0515862	+	0.358790i
$97$	−4.51626	−	9.88923i	−0.458557	−	1.00410i	−0.987814	−	0.155638i	$-0.950257\pi$
$97$	−4.51626	−	9.88923i	−0.458557	−	1.00410i	0.529258	−	0.848461i	$-0.322471\pi$
$98$	0.740489	−	5.15022i	0.0748007	−	0.520250i
$99$	−1.38032	+	0.405297i	−0.138727	+	0.0407339i
$100$	−0.553711	−	0.355849i	−0.0553711	−	0.0355849i
$101$	1.55583	−	3.40679i	0.154811	−	0.338988i	−0.816296	−	0.577634i	$-0.803976\pi$
$101$	1.55583	−	3.40679i	0.154811	−	0.338988i	0.971107	+	0.238646i	$0.0767034\pi$
$102$	−2.79521	−	0.820748i	−0.276767	−	0.0812662i
$103$	−8.96519	−	10.3464i	−0.883366	−	1.01946i	−0.999656	−	0.0262434i	$-0.991645\pi$
$103$	−8.96519	−	10.3464i	−0.883366	−	1.01946i	0.116290	−	0.993215i	$-0.462900\pi$
$104$	5.71562	+	6.59618i	0.560463	+	0.646808i
$105$	−1.51957	−	0.446185i	−0.148294	−	0.0435432i
$106$	5.02328	−	10.9994i	0.487904	−	1.06836i
$107$	7.36300	+	4.73191i	0.711808	+	0.457451i	0.845779	−	0.533534i	$-0.179136\pi$
$107$	7.36300	+	4.73191i	0.711808	+	0.457451i	−0.133971	+	0.990985i	$0.542773\pi$
$108$	−0.631536	+	0.185436i	−0.0607696	+	0.0178436i
$109$	1.20499	−	8.38090i	0.115417	−	0.802745i	−0.847082	−	0.531462i	$-0.821643\pi$
$109$	1.20499	−	8.38090i	0.115417	−	0.802745i	0.962500	−	0.271283i	$-0.0874480\pi$
$110$	−0.692250	−	1.51582i	−0.0660034	−	0.144527i
$111$	0.466264	+	3.24293i	0.0442558	+	0.307806i
$112$	−2.99820	+	1.92682i	−0.283303	+	0.182068i
$113$	−5.69811	+	6.57597i	−0.536033	+	0.618615i	−0.957572	−	0.288195i	$-0.906945\pi$
$113$	−5.69811	+	6.57597i	−0.536033	+	0.618615i	0.421539	+	0.906810i	$0.361490\pi$
$114$	1.92837			0.180608
$115$	−0.948059	+	4.70119i	−0.0884070	+	0.438388i
$116$	3.28770			0.305255
$117$	−1.85623	+	2.14220i	−0.171609	+	0.198047i
$118$	6.23394	−	4.00631i	0.573880	−	0.368811i
$119$	0.566834	+	3.94242i	0.0519616	+	0.361401i
$120$	−1.27913	−	2.80090i	−0.116768	−	0.255686i
$121$	1.27094	−	8.83956i	0.115540	−	0.803597i
$122$	−2.38231	+	0.699510i	−0.215684	+	0.0633306i
$123$	3.15235	+	2.02589i	0.284238	+	0.182669i
$124$	0.0779263	−	0.170635i	0.00699799	−	0.0153235i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−1.20135	−	1.38644i	−0.107025	−	0.123513i
$127$	8.87124	+	10.2380i	0.787196	+	0.908472i	0.997607	−	0.0691407i	$-0.0220258\pi$
$127$	8.87124	+	10.2380i	0.787196	+	0.908472i	−0.210411	+	0.977613i	$0.567480\pi$
$128$	−2.75939	−	0.810229i	−0.243898	−	0.0716148i
$129$	2.56925	−	5.62588i	0.226210	−	0.495331i
$130$	−2.76219	−	1.77515i	−0.242260	−	0.155691i
$131$	−7.24054	+	2.12601i	−0.632609	+	0.185751i	−0.582288	−	0.812982i	$-0.697842\pi$
$131$	−7.24054	+	2.12601i	−0.632609	+	0.185751i	−0.0503206	+	0.998733i	$0.516024\pi$
$132$	−0.134754	+	0.937238i	−0.0117289	+	0.0815761i
$133$	−1.09523	−	2.39822i	−0.0949685	−	0.207952i
$134$	−0.951904	−	6.62064i	−0.0822320	−	0.571936i
$135$	0.841254	−	0.540641i	0.0724036	−	0.0465310i
$136$	−5.07118	+	5.85245i	−0.434850	+	0.501844i
$137$	12.7314			1.08772			0.543860	−	0.839176i	$-0.316962\pi$
$137$	12.7314			1.08772			0.543860	+	0.839176i	$0.316962\pi$
$138$	−3.86802	+	3.98747i	−0.329267	+	0.339436i
$139$	−9.35604			−0.793569			−0.396784	−	0.917912i	$-0.629874\pi$
$139$	−9.35604			−0.793569			−0.396784	+	0.917912i	$0.629874\pi$
$140$	−0.682626	+	0.787793i	−0.0576924	+	0.0665806i
$141$	−2.98212	+	1.91649i	−0.251140	+	0.161398i
$142$	−1.40990	−	9.80606i	−0.118316	−	0.822906i
$143$	1.69395	+	3.70924i	0.141656	+	0.310182i
$144$	0.320262	−	2.22747i	0.0266885	−	0.185623i
$145$	−4.79266	+	1.40725i	−0.398009	+	0.116866i
$146$	−0.658622	−	0.423271i	−0.0545080	−	0.0350302i
$147$	1.86598	−	4.08592i	0.153903	−	0.337001i
$148$	2.06909	+	0.607540i	0.170078	+	0.0499395i
$149$	−8.25663	−	9.52866i	−0.676409	−	0.780618i	0.308956	−	0.951076i	$-0.400021\pi$
$149$	−8.25663	−	9.52866i	−0.676409	−	0.780618i	−0.985365	+	0.170459i	$0.945475\pi$
$150$	0.758566	+	0.875431i	0.0619366	+	0.0714787i
$151$	14.8480	+	4.35977i	1.20831	+	0.354793i	0.823026	−	0.568004i	$-0.192284\pi$
$151$	14.8480	+	4.35977i	1.20831	+	0.354793i	0.385288	+	0.922797i	$0.374102\pi$
$152$	2.12941	−	4.66276i	0.172718	−	0.378200i
$153$	−2.11571	−	1.35968i	−0.171045	−	0.109924i
$154$	−2.53221	+	0.743524i	−0.204051	+	0.0599149i
$155$	−0.0405598	+	0.282099i	−0.00325784	+	0.0226588i
$156$	0.775035	+	1.69709i	0.0620525	+	0.135876i
$157$	−0.210145	−	1.46159i	−0.0167714	−	0.116647i	0.979716	−	0.200391i	$-0.0642213\pi$
$157$	−0.210145	−	1.46159i	−0.0167714	−	0.116647i	−0.996487	+	0.0837439i	$0.973312\pi$
$158$	−7.20213	+	4.62853i	−0.572971	+	0.368226i
$159$	6.83612	−	7.88930i	0.542140	−	0.625663i
$160$	−3.55156			−0.280775
$161$	7.15589	+	2.54576i	0.563963	+	0.200634i
$162$	1.15836			0.0910095
$163$	14.6090	−	16.8597i	1.14427	−	1.32055i	0.204450	−	0.978877i	$-0.434460\pi$
$163$	14.6090	−	16.8597i	1.14427	−	1.32055i	0.939817	−	0.341677i	$-0.110995\pi$
$164$	2.07487	−	1.33344i	0.162020	−	0.104124i
$165$	−0.204732	−	1.42395i	−0.0159384	−	0.110854i
$166$	−8.07804	−	17.6884i	−0.626978	−	1.37289i
$167$	2.18849	−	15.2213i	0.169351	−	1.17786i	−0.710880	−	0.703314i	$-0.751703\pi$
$167$	2.18849	−	15.2213i	0.169351	−	1.17786i	0.880230	−	0.474547i	$-0.157388\pi$
$168$	−4.67898	+	1.37387i	−0.360991	+	0.105996i
$169$	−4.17714	−	2.68448i	−0.321318	−	0.206499i
$170$	1.21019	−	2.64996i	0.0928176	−	0.203242i
$171$	1.59730	+	0.469011i	0.122149	+	0.0358662i
$172$	−2.66582	−	3.07651i	−0.203267	−	0.234582i
$173$	9.87812	+	11.4000i	0.751020	+	0.866723i	0.994667	−	0.103141i	$-0.0328893\pi$
$173$	9.87812	+	11.4000i	0.751020	+	0.866723i	−0.243647	+	0.969864i	$0.578344\pi$
$174$	−5.55164	−	1.63011i	−0.420869	−	0.123578i
$175$	0.657900	−	1.44060i	0.0497325	−	0.108899i
$176$	−2.72345	−	1.75025i	−0.205288	−	0.131930i
$177$	6.13809	−	1.80231i	0.461367	−	0.135470i
$178$	1.11812	−	7.77670i	0.0838067	−	0.582889i
$179$	−7.88359	−	17.2626i	−0.589247	−	1.29027i	−0.935896	−	0.352276i	$-0.885408\pi$
$179$	−7.88359	−	17.2626i	−0.589247	−	1.29027i	0.346649	−	0.937995i	$-0.387319\pi$
$180$	−0.0936713	−	0.651498i	−0.00698185	−	0.0485598i
$181$	0.902845	−	0.580223i	0.0671080	−	0.0431277i	−0.506657	−	0.862148i	$-0.669119\pi$
$181$	0.902845	−	0.580223i	0.0671080	−	0.0431277i	0.573765	+	0.819020i	$0.305482\pi$
$182$	−3.40529	+	3.92991i	−0.252417	+	0.291304i
$183$	−2.14345			−0.158448
$184$	5.37034	+	13.7560i	0.395907	+	1.01410i
$185$	−3.27628			−0.240877
$186$	−0.216191	+	0.249498i	−0.0158519	+	0.0182941i
$187$	−3.04363	+	1.95602i	−0.222572	+	0.143039i
$188$	0.332051	+	2.30947i	0.0242173	+	0.168435i
$189$	−0.657900	−	1.44060i	−0.0478552	−	0.104788i
$190$	−0.274435	+	1.90874i	−0.0199096	+	0.138475i
$191$	−3.78756	+	1.11213i	−0.274058	+	0.0804707i	−0.415874	−	0.909422i	$-0.636524\pi$
$191$	−3.78756	+	1.11213i	−0.274058	+	0.0804707i	0.141816	+	0.989893i	$0.454706\pi$
$192$	−7.24719	−	4.65748i	−0.523021	−	0.336125i
$193$	8.59566	−	18.8219i	0.618729	−	1.35483i	−0.297711	−	0.954656i	$-0.596223\pi$
$193$	8.59566	−	18.8219i	0.618729	−	1.35483i	0.916440	−	0.400172i	$-0.131050\pi$
$194$	12.0832	+	3.54795i	0.867525	+	0.254728i
$195$	−1.85623	−	2.14220i	−0.132927	−	0.153406i
$196$	−1.93611	−	2.23439i	−0.138294	−	0.159599i
$197$	16.4603	+	4.83317i	1.17275	+	0.344349i	0.809373	−	0.587294i	$-0.199807\pi$
$197$	16.4603	+	4.83317i	1.17275	+	0.344349i	0.363373	+	0.931644i	$0.381625\pi$
$198$	0.692250	−	1.51582i	0.0491961	−	0.107724i
$199$	−2.47080	−	1.58789i	−0.175151	−	0.112562i	0.450128	−	0.892964i	$-0.351378\pi$
$199$	−2.47080	−	1.58789i	−0.175151	−	0.112562i	−0.625279	+	0.780402i	$0.715015\pi$
$200$	2.95443	−	0.867498i	0.208910	−	0.0613414i
$201$	0.821768	−	5.71552i	0.0579630	−	0.403142i
$202$	1.80221	+	3.94630i	0.126803	+	0.277660i
$203$	1.12580	+	7.83014i	0.0790160	+	0.549568i
$204$	−1.39255	+	0.894940i	−0.0974983	+	0.0626583i
$205$	−2.45390	+	2.83195i	−0.171388	+	0.197792i
$206$	15.8582			1.10489
$207$	−4.17377	+	2.36213i	−0.290097	+	0.164179i
$208$	−6.37880			−0.442290
$209$	1.56831	−	1.80992i	0.108482	−	0.125195i
$210$	1.54329	−	0.991815i	0.106497	−	0.0684417i
$211$	4.08267	+	28.3956i	0.281063	+	1.95483i	0.296743	+	0.954957i	$0.404100\pi$
$211$	4.08267	+	28.3956i	0.281063	+	1.95483i	−0.0156800	+	0.999877i	$0.504991\pi$
$212$	−2.85430	−	6.25004i	−0.196034	−	0.429255i
$213$	1.21715	−	8.46546i	0.0833977	−	0.580043i
$214$	−9.72778	+	2.85634i	−0.664978	+	0.195255i
$215$	5.20297	+	3.34375i	0.354840	+	0.228042i
$216$	1.27913	−	2.80090i	0.0870336	−	0.190577i
$217$	0.433077	+	0.127163i	0.0293991	+	0.00863237i
$218$	6.42284	+	7.41235i	0.435010	+	0.502028i
$219$	−0.442603	−	0.510791i	−0.0299083	−	0.0345161i
$220$	−0.908521	−	0.266766i	−0.0612524	−	0.0179853i
$221$	−2.96138	+	6.48451i	−0.199204	+	0.436195i
$222$	−3.19266	−	2.05180i	−0.214277	−	0.137708i
$223$	20.0951	−	5.90046i	1.34567	−	0.395124i	0.471980	−	0.881609i	$-0.343540\pi$
$223$	20.0951	−	5.90046i	1.34567	−	0.395124i	0.873689	+	0.486486i	$0.161721\pi$
$224$	−0.800472	+	5.56741i	−0.0534838	+	0.371988i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	−1.43442	−	9.97661i	−0.0954162	−	0.663634i
$227$	−9.66993	+	6.21449i	−0.641816	+	0.412470i	−0.820668	−	0.571406i	$-0.806398\pi$
$227$	−9.66993	+	6.21449i	−0.641816	+	0.412470i	0.178852	+	0.983876i	$0.442762\pi$
$228$	0.717549	−	0.828095i	0.0475208	−	0.0548419i
$229$	−23.2627			−1.53724			−0.768622	−	0.639703i	$-0.779057\pi$
$229$	−23.2627			−1.53724			−0.768622	+	0.639703i	$0.779057\pi$
$230$	−3.39640	−	4.39612i	−0.223952	−	0.289872i
$231$	−2.27832			−0.149902
$232$	−10.0720	+	11.6237i	−0.661259	+	0.763134i
$233$	7.36852	−	4.73546i	0.482728	−	0.310230i	−0.276547	−	0.961000i	$-0.589190\pi$
$233$	7.36852	−	4.73546i	0.482728	−	0.310230i	0.759275	+	0.650770i	$0.225554\pi$
$234$	−0.467280	−	3.25000i	−0.0305471	−	0.212459i
$235$	−1.47258	−	3.22451i	−0.0960608	−	0.210344i
$236$	0.599236	−	4.16778i	0.0390070	−	0.271299i
$237$	−7.09140	+	2.08222i	−0.460636	+	0.135255i
$238$	−3.88130	−	2.49436i	−0.251587	−	0.161685i
$239$	2.81195	−	6.15730i	0.181890	−	0.398283i	−0.796621	−	0.604479i	$-0.793381\pi$
$239$	2.81195	−	6.15730i	0.181890	−	0.398283i	0.978511	+	0.206196i	$0.0661086\pi$
$240$	2.15922	+	0.634005i	0.139377	+	0.0409249i
$241$	−10.8249	−	12.4926i	−0.697293	−	0.804719i	0.291091	−	0.956695i	$-0.405982\pi$
$241$	−10.8249	−	12.4926i	−0.697293	−	0.804719i	−0.988384	+	0.151976i	$0.951436\pi$
$242$	6.77434	+	7.81801i	0.435471	+	0.502561i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−0.586072	+	1.28332i	−0.0375194	+	0.0821561i
$245$	3.77878	+	2.42847i	0.241417	+	0.155149i
$246$	−4.16480	+	1.22289i	−0.265538	+	0.0779689i
$247$	0.671551	−	4.67074i	0.0427298	−	0.297192i
$248$	0.364552	+	0.798257i	0.0231491	+	0.0506894i
$249$	−2.38908	−	16.6164i	−0.151401	−	1.05302i
$250$	−0.974476	+	0.626258i	−0.0616313	+	0.0396080i
$251$	−10.1289	+	11.6894i	−0.639329	+	0.737825i	−0.979256	−	0.202627i	$-0.935052\pi$
$251$	−10.1289	+	11.6894i	−0.639329	+	0.737825i	0.339927	+	0.940452i	$0.389598\pi$
$252$	−1.04240			−0.0656650
$253$	0.596758	+	6.87337i	0.0375179	+	0.432125i
$254$	−15.6921			−0.984607
$255$	1.64694	−	1.90067i	0.103135	−	0.119025i
$256$	−11.6919	+	7.51392i	−0.730743	+	0.469620i
$257$	2.24377	+	15.6058i	0.139963	+	0.973462i	0.931863	+	0.362811i	$0.118183\pi$
$257$	2.24377	+	15.6058i	0.139963	+	0.973462i	−0.791900	+	0.610651i	$0.790908\pi$
$258$	2.97612	+	6.51680i	0.185285	+	0.405718i
$259$	−0.738429	+	5.13589i	−0.0458838	+	0.319129i
$260$	−1.79012	+	0.525626i	−0.111018	+	0.0325979i
$261$	−4.20206	−	2.70050i	−0.260101	−	0.167157i
$262$	3.63124	−	7.95132i	0.224339	−	0.491234i
$263$	13.5549	+	3.98009i	0.835833	+	0.245423i	0.671521	−	0.740986i	$-0.265641\pi$
$263$	13.5549	+	3.98009i	0.835833	+	0.245423i	0.164312	+	0.986408i	$0.447460\pi$
$264$	−2.90079	−	3.34770i	−0.178532	−	0.206036i
$265$	6.83612	+	7.88930i	0.419940	+	0.484636i
$266$	2.93028	+	0.860408i	0.179667	+	0.0527550i
$267$	2.81758	−	6.16965i	0.172433	−	0.377576i
$268$	−3.19729	−	2.05477i	−0.195306	−	0.125515i
$269$	−1.01073	+	0.296778i	−0.0616255	+	0.0180949i	−0.312400	−	0.949951i	$-0.601133\pi$
$269$	−1.01073	+	0.296778i	−0.0616255	+	0.0180949i	0.250774	+	0.968046i	$0.419315\pi$
$270$	−0.164852	+	1.14657i	−0.0100326	+	0.0697781i
$271$	3.04843	+	6.67512i	0.185179	+	0.405485i	0.979340	−	0.202223i	$-0.0648165\pi$
$271$	3.04843	+	6.67512i	0.185179	+	0.405485i	−0.794161	+	0.607708i	$0.792089\pi$
$272$	−0.805443	−	5.60198i	−0.0488371	−	0.339670i
$273$	−3.77648	+	2.42700i	−0.228563	+	0.146889i
$274$	−9.65763	+	11.1455i	−0.583439	+	0.673324i
$275$	1.43859			0.0867501
$276$	0.273035	+	3.14478i	0.0164348	+	0.189293i
$277$	−18.0390			−1.08386			−0.541928	−	0.840425i	$-0.682305\pi$
$277$	−18.0390			−1.08386			−0.541928	+	0.840425i	$0.682305\pi$
$278$	7.09717	−	8.19057i	0.425660	−	0.491238i
$279$	−0.239758	+	0.154083i	−0.0143539	+	0.00922470i
$280$	−0.694000	−	4.82687i	−0.0414744	−	0.288461i
$281$	6.04107	+	13.2281i	0.360380	+	0.789123i	0.999795	+	0.0202604i	$0.00644952\pi$
$281$	6.04107	+	13.2281i	0.360380	+	0.789123i	−0.639415	+	0.768862i	$0.720823\pi$
$282$	0.584376	−	4.06443i	0.0347991	−	0.242033i
$283$	0.376384	−	0.110516i	0.0223737	−	0.00656952i	−0.270527	−	0.962713i	$-0.587198\pi$
$283$	0.376384	−	0.110516i	0.0223737	−	0.00656952i	0.292900	+	0.956143i	$0.405380\pi$
$284$	−4.73562	−	3.04340i	−0.281007	−	0.180592i
$285$	−0.691557	+	1.51430i	−0.0409643	+	0.0896993i
$286$	−4.53216	−	1.33076i	−0.267992	−	0.0786897i
$287$	3.88628	+	4.48501i	0.229400	+	0.264742i
$288$	−2.32577	−	2.68409i	−0.137048	−	0.158161i
$289$	10.2426	+	3.00751i	0.602508	+	0.176912i
$290$	2.40360	−	5.26314i	0.141144	−	0.309062i
$291$	9.14584	+	5.87767i	0.536139	+	0.344555i
$292$	−0.426839	+	0.125331i	−0.0249788	+	0.00733445i
$293$	2.22509	−	15.4759i	0.129991	−	0.904110i	−0.815568	−	0.578661i	$-0.803575\pi$
$293$	2.22509	−	15.4759i	0.129991	−	0.904110i	0.945560	−	0.325449i	$-0.105515\pi$
$294$	2.16148	+	4.73298i	0.126060	+	0.276033i
$295$	0.910419	+	6.33211i	0.0530067	+	0.368669i
$296$	−8.48672	+	5.45408i	−0.493280	+	0.317012i
$297$	0.942075	−	1.08721i	0.0546647	−	0.0630865i
$298$	14.6049			0.846038
$299$	8.31109	+	10.7574i	0.480643	+	0.622118i
$300$	0.658198			0.0380011
$301$	6.41433	−	7.40253i	0.369716	−	0.426675i
$302$	−15.0799	+	9.69124i	−0.867749	+	0.557668i
$303$	0.533003	+	3.70712i	0.0306202	+	0.212968i
$304$	1.55627	+	3.40775i	0.0892580	+	0.195448i
$305$	0.305044	−	2.12163i	0.0174668	−	0.121484i
$306$	2.79521	−	0.820748i	0.159792	−	0.0469190i
$307$	13.2352	+	8.50576i	0.755374	+	0.485449i	0.860778	−	0.508980i	$-0.169977\pi$
$307$	13.2352	+	8.50576i	0.755374	+	0.485449i	−0.105405	+	0.994429i	$0.533614\pi$
$308$	−0.622949	+	1.36407i	−0.0354958	+	0.0777250i
$309$	13.1357	+	3.85698i	0.747262	+	0.219416i
$310$	−0.216191	−	0.249498i	−0.0122788	−	0.0141705i
$311$	−3.95490	−	4.56420i	−0.224262	−	0.258812i	0.632457	−	0.774595i	$-0.282046\pi$
$311$	−3.95490	−	4.56420i	−0.224262	−	0.258812i	−0.856719	+	0.515783i	$0.827501\pi$
$312$	−8.37445	−	2.45896i	−0.474110	−	0.139211i
$313$	−11.2117	+	24.5502i	−0.633724	+	1.38766i	0.271381	+	0.962472i	$0.412520\pi$
$313$	−11.2117	+	24.5502i	−0.633724	+	1.38766i	−0.905105	+	0.425189i	$0.860208\pi$
$314$	1.43893	+	0.924743i	0.0812034	+	0.0521863i
$315$	1.51957	−	0.446185i	0.0856178	−	0.0251397i
$316$	−0.692304	+	4.81508i	−0.0389451	+	0.270869i
$317$	−5.96291	−	13.0570i	−0.334910	−	0.733351i	0.664999	−	0.746845i	$-0.268432\pi$
$317$	−5.96291	−	13.0570i	−0.334910	−	0.733351i	−0.999909	+	0.0134932i	$0.995705\pi$
$318$	1.72090	+	11.9691i	0.0965032	+	0.671194i
$319$	−6.04503	+	3.88491i	−0.338457	+	0.217513i
$320$	5.64146	−	6.51059i	0.315367	−	0.363953i
$321$	−8.75241			−0.488512
$322$	−7.65685	+	4.33337i	−0.426700	+	0.241489i
$323$	4.18672			0.232956
$324$	0.431028	−	0.497433i	0.0239460	−	0.0276352i
$325$	2.38457	−	1.53247i	0.132272	−	0.0850061i
$326$	3.67762	+	25.5784i	0.203684	+	1.41666i
$327$	3.51735	+	7.70193i	0.194510	+	0.425918i
$328$	−1.64206	+	11.4208i	−0.0906677	+	0.630608i
$329$	−5.38663	+	1.58166i	−0.296975	+	0.0871997i
$330$	1.40187	+	0.900927i	0.0771704	+	0.0495944i
$331$	6.64549	−	14.5516i	0.365269	−	0.799828i	−0.634372	−	0.773028i	$-0.718741\pi$
$331$	6.64549	−	14.5516i	0.365269	−	0.799828i	0.999641	−	0.0267996i	$-0.00853161\pi$
$332$	−10.6018	−	3.11296i	−0.581847	−	0.170846i
$333$	−2.14551	−	2.47605i	−0.117573	−	0.135687i
$334$	11.6651	+	13.4622i	0.638286	+	0.736621i
$335$	5.54039	+	1.62681i	0.302704	+	0.0888819i
$336$	1.48052	−	3.24190i	0.0807692	−	0.176860i
$337$	17.7955	+	11.4364i	0.969380	+	0.622983i	0.926579	−	0.376101i	$-0.122735\pi$
$337$	17.7955	+	11.4364i	0.969380	+	0.622983i	0.0428016	+	0.999084i	$0.486372\pi$
$338$	5.51871	−	1.62044i	0.300178	−	0.0881403i
$339$	1.23832	−	8.61269i	0.0672562	−	0.467777i
$340$	−0.687650	−	1.50574i	−0.0372930	−	0.0816604i
$341$	0.0583488	+	0.405825i	0.00315977	+	0.0219766i
$342$	−1.62225	+	1.04255i	−0.0877211	+	0.0563749i
$343$	11.9183	−	13.7545i	0.643530	−	0.742674i
$344$	19.0439			1.02678
$345$	−1.74410	−	4.46745i	−0.0938990	−	0.240520i
$346$	−17.4731			−0.939359
$347$	−20.1696	+	23.2770i	−1.08276	+	1.24957i	−0.116177	+	0.993229i	$0.537064\pi$
$347$	−20.1696	+	23.2770i	−1.08276	+	1.24957i	−0.966585	+	0.256345i	$0.917482\pi$
$348$	−2.76579	+	1.77746i	−0.148262	+	0.0952820i
$349$	2.75619	+	19.1697i	0.147535	+	1.02613i	0.920237	+	0.391361i	$0.127996\pi$
$349$	2.75619	+	19.1697i	0.147535	+	1.02613i	−0.772702	+	0.634769i	$0.781095\pi$
$350$	0.762086	+	1.66874i	0.0407352	+	0.0891977i
$351$	0.403397	−	2.80569i	0.0215318	−	0.149757i
$352$	−4.90227	+	1.43944i	−0.261292	+	0.0767222i
$353$	−10.0291	−	6.44530i	−0.533794	−	0.343049i	0.245813	−	0.969317i	$-0.420945\pi$
$353$	−10.0291	−	6.44530i	−0.533794	−	0.343049i	−0.779607	+	0.626268i	$0.784581\pi$
$354$	−3.07835	+	6.74064i	−0.163612	+	0.358261i
$355$	8.20607	+	2.40952i	0.435533	+	0.127884i
$356$	−2.92348	−	3.37387i	−0.154944	−	0.178815i
$357$	−2.60828	−	3.01012i	−0.138045	−	0.159313i
$358$	21.0925	+	6.19331i	1.11477	+	0.327327i
$359$	0.0704316	−	0.154224i	0.00371724	−	0.00813962i	−0.907764	−	0.419481i	$-0.862212\pi$
$359$	0.0704316	−	0.154224i	0.00371724	−	0.00813962i	0.911482	+	0.411341i	$0.134939\pi$
$360$	2.59035	+	1.66472i	0.136523	+	0.0877383i
$361$	15.5713	−	4.57214i	0.819541	−	0.240639i
$362$	−0.176922	+	1.23052i	−0.00929879	+	0.0646745i
$363$	3.70985	+	8.12344i	0.194717	+	0.426370i
$364$	0.420501	+	2.92465i	0.0220402	+	0.153293i
$365$	0.568581	−	0.365405i	0.0297609	−	0.0191262i
$366$	1.62594	−	1.87644i	0.0849895	−	0.0980831i
$367$	−11.2096			−0.585137			−0.292568	−	0.956245i	$-0.594510\pi$
$367$	−11.2096			−0.585137			−0.292568	+	0.956245i	$0.594510\pi$
$368$	−10.1682	−	3.61739i	−0.530051	−	0.188570i
$369$	−3.74721			−0.195072
$370$	2.48528	−	2.86816i	0.129203	−	0.149109i
$371$	13.9080	−	8.93814i	0.722068	−	0.464045i
$372$	0.0266964	+	0.185677i	0.00138414	+	0.00962692i
$373$	−9.90189	−	21.6821i	−0.512700	−	1.12266i	−0.972130	−	0.234443i	$-0.924673\pi$
$373$	−9.90189	−	21.6821i	−0.512700	−	1.12266i	0.459430	−	0.888214i	$-0.348054\pi$
$374$	0.596430	−	4.14826i	0.0308407	−	0.214502i
$375$	−0.959493	+	0.281733i	−0.0495480	+	0.0145486i
$376$	−9.18241	−	5.90118i	−0.473547	−	0.304330i
$377$	−5.88166	+	12.8790i	−0.302921	+	0.663305i
$378$	1.76021	+	0.516843i	0.0905352	+	0.0265835i
$379$	4.83977	+	5.58539i	0.248602	+	0.286902i	0.866311	−	0.499504i	$-0.166485\pi$
$379$	4.83977	+	5.58539i	0.248602	+	0.286902i	−0.617709	+	0.786407i	$0.711939\pi$
$380$	0.717549	+	0.828095i	0.0368095	+	0.0424804i
$381$	−12.9980	−	3.81656i	−0.665909	−	0.195529i
$382$	1.89952	−	4.15937i	0.0971879	−	0.212812i
$383$	−13.9336	−	8.95457i	−0.711972	−	0.457557i	0.133864	−	0.991000i	$-0.457262\pi$
$383$	−13.9336	−	8.95457i	−0.711972	−	0.457557i	−0.845836	+	0.533443i	$0.820898\pi$
$384$	2.75939	−	0.810229i	0.140814	−	0.0413468i
$385$	0.324238	−	2.25513i	0.0165247	−	0.114932i
$386$	9.95689	+	21.8025i	0.506792	+	1.10972i
$387$	0.880187	+	6.12183i	0.0447424	+	0.311190i
$388$	6.01977	−	3.86867i	0.305608	−	0.196402i
$389$	16.5039	−	19.0466i	0.836783	−	0.965699i	−0.162998	−	0.986626i	$-0.552116\pi$
$389$	16.5039	−	19.0466i	0.836783	−	0.965699i	0.999781	+	0.0209272i	$0.00666182\pi$
$390$	3.28343			0.166263
$391$	−8.39794	+	8.65728i	−0.424702	+	0.437817i
$392$	13.8311			0.698575
$393$	4.94172	−	5.70305i	0.249277	−	0.287681i
$394$	−16.7173	+	10.7436i	−0.842206	+	0.541253i
$395$	−1.05182	−	7.31555i	−0.0529227	−	0.368085i
$396$	−0.393346	−	0.861308i	−0.0197664	−	0.0432824i
$397$	2.93963	−	20.4456i	0.147536	−	1.02613i	−0.772701	−	0.634771i	$-0.781095\pi$
$397$	2.93963	−	20.4456i	0.147536	−	1.02613i	0.920236	−	0.391363i	$-0.127996\pi$
$398$	3.26435	−	0.958501i	0.163627	−	0.0480453i
$399$	2.21794	+	1.42538i	0.111036	+	0.0713585i
$400$	−0.934842	+	2.04702i	−0.0467421	+	0.102351i
$401$	−20.7454	−	6.09141i	−1.03598	−	0.304191i	−0.280839	−	0.959755i	$-0.590613\pi$
$401$	−20.7454	−	6.09141i	−1.03598	−	0.304191i	−0.755139	+	0.655564i	$0.772431\pi$
$402$	4.38018	+	5.05500i	0.218464	+	0.252120i
$403$	0.529026	+	0.610529i	0.0263527	+	0.0304126i
$404$	2.36526	+	0.694502i	0.117676	+	0.0345527i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−7.70875	−	4.95411i	−0.382579	−	0.245868i
$407$	−4.52230	+	1.32787i	−0.224162	+	0.0658200i
$408$	1.10207	−	7.66509i	0.0545607	−	0.379478i
$409$	−13.6704	−	29.9341i	−0.675960	−	1.48015i	−0.866868	−	0.498538i	$-0.833870\pi$
$409$	−13.6704	−	29.9341i	−0.675960	−	1.48015i	0.190908	−	0.981608i	$-0.438857\pi$
$410$	−0.617735	−	4.29644i	−0.0305078	−	0.212186i
$411$	−10.7104	+	6.88313i	−0.528303	+	0.339520i
$412$	5.90087	−	6.80996i	0.290715	−	0.335503i
$413$	10.1314			0.498533
$414$	1.09820	−	5.44568i	0.0539734	−	0.267640i
$415$	16.7873			0.824054
$416$	−6.59251	+	7.60816i	−0.323224	+	0.373021i
$417$	7.87080	−	5.05826i	0.385435	−	0.247704i
$418$	0.394800	+	2.74589i	0.0193103	+	0.134306i
$419$	13.7662	+	30.1438i	0.672525	+	1.47262i	0.870374	+	0.492391i	$0.163877\pi$
$419$	13.7662	+	30.1438i	0.672525	+	1.47262i	−0.197850	+	0.980232i	$0.563396\pi$
$420$	0.148349	−	1.03179i	0.00723868	−	0.0503461i
$421$	−5.85478	+	1.71912i	−0.285344	+	0.0837847i	−0.421273	−	0.906934i	$-0.638416\pi$
$421$	−5.85478	+	1.71912i	−0.285344	+	0.0837847i	0.135928	+	0.990719i	$0.456598\pi$
$422$	−27.9554	−	17.9658i	−1.36085	−	0.874563i
$423$	1.47258	−	3.22451i	0.0715995	−	0.156781i
$424$	30.8414	+	9.05585i	1.49779	+	0.439791i
$425$	1.64694	+	1.90067i	0.0798883	+	0.0921960i
$426$	6.48764	+	7.48713i	0.314327	+	0.362753i
$427$	−3.25711	−	0.956372i	−0.157622	−	0.0462821i
$428$	−2.39313	+	5.24023i	−0.115676	+	0.253296i
$429$	−3.43041	−	2.20459i	−0.165622	−	0.106439i
$430$	−6.87402	+	2.01839i	−0.331495	+	0.0973356i
$431$	3.15176	−	21.9210i	0.151815	−	1.05590i	−0.761361	−	0.648329i	$-0.775468\pi$
$431$	3.15176	−	21.9210i	0.151815	−	1.05590i	0.913175	−	0.407567i	$-0.133623\pi$
$432$	0.934842	+	2.04702i	0.0449776	+	0.0984872i
$433$	−2.21340	−	15.3945i	−0.106369	−	0.739814i	−0.971289	−	0.237904i	$-0.923540\pi$
$433$	−2.21340	−	15.3945i	−0.106369	−	0.739814i	0.864920	−	0.501911i	$-0.167369\pi$
$434$	−0.439839	+	0.282668i	−0.0211130	+	0.0135685i
$435$	3.27103	−	3.77497i	0.156834	−	0.180996i
$436$	5.57302			0.266899
$437$	3.71925	−	7.06458i	0.177916	−	0.337945i
$438$	0.782906			0.0374087
$439$	−4.38950	+	5.06575i	−0.209499	+	0.241775i	−0.850768	−	0.525541i	$-0.823863\pi$
$439$	−4.38950	+	5.06575i	−0.209499	+	0.241775i	0.641269	+	0.767316i	$0.278408\pi$
$440$	3.72645	−	2.39484i	0.177651	−	0.114170i
$441$	0.639256	+	4.44612i	0.0304407	+	0.211720i
$442$	−3.43035	−	7.51141i	−0.163165	−	0.357281i
$443$	3.79439	−	26.3905i	0.180277	−	1.25385i	−0.675832	−	0.737056i	$-0.736215\pi$
$443$	3.79439	−	26.3905i	0.180277	−	1.25385i	0.856108	−	0.516796i	$-0.172876\pi$
$444$	−2.06909	+	0.607540i	−0.0981947	+	0.0288326i
$445$	5.70586	+	3.66694i	0.270484	+	0.173829i
$446$	−10.0780	+	22.0678i	−0.477208	+	1.04494i
$447$	12.0975	+	3.55215i	0.572192	+	0.168011i
$448$	−8.93447	−	10.3109i	−0.422114	−	0.487146i
$449$	13.1558	+	15.1826i	0.620860	+	0.716510i	0.975870	−	0.218352i	$-0.0700681\pi$
$449$	13.1558	+	15.1826i	0.620860	+	0.716510i	−0.355010	+	0.934862i	$0.615523\pi$
$450$	−1.11144	−	0.326348i	−0.0523938	−	0.0153842i
$451$	−2.23937	+	4.90354i	−0.105448	+	0.230899i
$452$	−4.81798	−	3.09633i	−0.226619	−	0.145639i
$453$	−14.8480	+	4.35977i	−0.697620	+	0.204840i
$454$	1.89492	−	13.1795i	0.0889330	−	0.618543i
$455$	−1.86484	−	4.08344i	−0.0874253	−	0.191435i
$456$	0.729504	+	5.07381i	0.0341621	+	0.237603i
$457$	28.6565	−	18.4164i	1.34049	−	0.861483i	0.343514	−	0.939148i	$-0.388383\pi$
$457$	28.6565	−	18.4164i	1.34049	−	0.861483i	0.996980	+	0.0776646i	$0.0247463\pi$
$458$	17.6463	−	20.3649i	0.824558	−	0.951590i
$459$	2.51495			0.117388
$460$	−3.15162	−	0.177292i	−0.146945	−	0.00826630i
$461$	−25.6751			−1.19581			−0.597905	−	0.801567i	$-0.704000\pi$
$461$	−25.6751			−1.19581			−0.597905	+	0.801567i	$0.704000\pi$
$462$	1.72825	−	1.99451i	0.0804056	−	0.0927930i
$463$	5.17073	−	3.32303i	0.240304	−	0.154434i	−0.414946	−	0.909846i	$-0.636200\pi$
$463$	5.17073	−	3.32303i	0.240304	−	0.154434i	0.655250	+	0.755412i	$0.272563\pi$
$464$	−1.59971	−	11.1262i	−0.0742646	−	0.516522i
$465$	−0.118393	−	0.259245i	−0.00549036	−	0.0120222i
$466$	−1.44393	+	10.0428i	−0.0668890	+	0.465223i
$467$	−37.0090	+	10.8668i	−1.71257	+	0.502857i	−0.983397	−	0.181468i	$-0.941915\pi$
$467$	−37.0090	+	10.8668i	−1.71257	+	0.502857i	−0.729177	+	0.684325i	$0.760097\pi$
$468$	−1.56952	−	1.00867i	−0.0725510	−	0.0466257i
$469$	3.79891	−	8.31844i	0.175417	−	0.384110i
$470$	3.93989	+	1.15686i	0.181734	+	0.0533618i
$471$	0.966979	+	1.11595i	0.0445560	+	0.0514204i
$472$	12.8995	+	14.8868i	0.593746	+	0.685220i
$473$	8.53695	+	2.50668i	0.392529	+	0.115257i
$474$	3.55645	−	7.78754i	0.163353	−	0.357693i
$475$	−1.40047	−	0.900025i	−0.0642578	−	0.0412960i
$476$	−2.51538	+	0.738584i	−0.115292	+	0.0338529i
$477$	−1.48563	+	10.3328i	−0.0680224	+	0.473106i
$478$	3.25725	+	7.13238i	0.148983	+	0.326228i
$479$	−5.14835	−	35.8075i	−0.235234	−	1.63609i	−0.674887	−	0.737921i	$-0.735808\pi$
$479$	−5.14835	−	35.8075i	−0.235234	−	1.63609i	0.439654	−	0.898167i	$-0.355101\pi$
$480$	2.98776	−	1.92012i	0.136372	−	0.0876409i
$481$	−6.08153	+	7.01846i	−0.277294	+	0.320014i
$482$	19.1478			0.872159
$483$	−7.39626	+	1.72714i	−0.336541	+	0.0785875i
$484$	5.87801			0.267182
$485$	−7.11944	+	8.21627i	−0.323277	+	0.373082i
$486$	−0.974476	+	0.626258i	−0.0442031	+	0.0284076i
$487$	0.781525	+	5.43563i	0.0354143	+	0.246312i	0.999837	−	0.0180531i	$-0.00574679\pi$
$487$	0.781525	+	5.43563i	0.0354143	+	0.246312i	−0.964423	+	0.264365i	$0.914838\pi$
$488$	−2.74174	−	6.00357i	−0.124113	−	0.271769i
$489$	−3.17484	+	22.0815i	−0.143571	+	0.998561i
$490$	−4.99241	+	1.46590i	−0.225534	+	0.0662228i
$491$	−26.4710	−	17.0119i	−1.19462	−	0.767734i	−0.216601	−	0.976260i	$-0.569497\pi$
$491$	−26.4710	−	17.0119i	−1.19462	−	0.767734i	−0.978017	+	0.208526i	$0.933133\pi$
$492$	−1.02458	+	2.24352i	−0.0461917	+	0.101146i
$493$	−12.0533	−	3.53916i	−0.542853	−	0.159396i
$494$	3.57950	+	4.13096i	0.161049	+	0.185861i
$495$	0.942075	+	1.08721i	0.0423431	+	0.0488666i
$496$	−0.615379	−	0.180692i	−0.0276313	−	0.00811330i
$497$	5.62669	−	12.3207i	0.252392	−	0.552661i
$498$	16.3588	+	10.5131i	0.733054	+	0.471105i
$499$	−30.7593	+	9.03173i	−1.37697	+	0.404316i	−0.884715	−	0.466133i	$-0.845647\pi$
$499$	−30.7593	+	9.03173i	−1.37697	+	0.404316i	−0.492259	+	0.870449i	$0.663829\pi$
$500$	−0.0936713	+	0.651498i	−0.00418911	+	0.0291359i
$501$	6.38818	+	13.9882i	0.285403	+	0.624945i
$502$	−2.54980	−	17.7343i	−0.113803	−	0.791520i
$503$	−16.4429	+	10.5672i	−0.733151	+	0.471167i	−0.853189	−	0.521602i	$-0.825335\pi$
$503$	−16.4429	+	10.5672i	−0.733151	+	0.471167i	0.120038	+	0.992769i	$0.461698\pi$
$504$	3.19343	−	3.68542i	0.142247	−	0.164162i
$505$	−3.74524			−0.166661
$506$	−6.46984	−	4.69148i	−0.287620	−	0.208562i
$507$	4.96537			0.220520
$508$	−5.83903	+	6.73861i	−0.259065	+	0.298977i
$509$	18.7796	−	12.0689i	0.832391	−	0.534945i	−0.0536457	−	0.998560i	$-0.517084\pi$
$509$	18.7796	−	12.0689i	0.832391	−	0.534945i	0.886037	+	0.463615i	$0.153448\pi$
$510$	0.414594	+	2.88356i	0.0183585	+	0.127686i
$511$	−0.444657	−	0.973663i	−0.0196705	−	0.0430723i
$512$	3.10971	−	21.6285i	0.137431	−	0.955853i
$513$	−1.59730	+	0.469011i	−0.0705227	+	0.0207073i
$514$	−15.3638	−	9.87375i	−0.677670	−	0.435512i
$515$	−5.68712	+	12.4531i	−0.250605	+	0.548747i
$516$	3.90592	+	1.14688i	0.171948	+	0.0504886i
$517$	−3.33952	−	3.85401i	−0.146872	−	0.169499i
$518$	−3.93597	−	4.54235i	−0.172937	−	0.199580i
$519$	−14.4733	−	4.24974i	−0.635307	−	0.186543i
$520$	3.62574	−	7.93926i	0.158999	−	0.348160i
$521$	−25.4078	−	16.3286i	−1.11313	−	0.715368i	−0.151161	−	0.988509i	$-0.548301\pi$
$521$	−25.4078	−	16.3286i	−1.11313	−	0.715368i	−0.961974	+	0.273141i	$0.911937\pi$
$522$	5.55164	−	1.63011i	0.242989	−	0.0713479i
$523$	5.97672	−	41.5690i	0.261344	−	1.81769i	−0.261438	−	0.965220i	$-0.584197\pi$
$523$	5.97672	−	41.5690i	0.261344	−	1.81769i	0.522782	−	0.852467i	$-0.324894\pi$
$524$	−2.06333	−	4.51805i	−0.0901368	−	0.197372i
$525$	0.225386	+	1.56760i	0.00983667	+	0.0684155i
$526$	−13.7666	+	8.84726i	−0.600252	+	0.385759i
$527$	−0.469378	+	0.541691i	−0.0204464	+	0.0235964i
$528$	3.23737			0.140888
$529$	7.14784	+	21.8611i	0.310776	+	0.950483i
$530$	−12.0922			−0.525251
$531$	−4.18929	+	4.83470i	−0.181800	+	0.209808i
$532$	1.45984	−	0.938185i	0.0632923	−	0.0406755i
$533$	1.51161	+	10.5135i	0.0654753	+	0.455390i
$534$	3.26378	+	7.14668i	0.141238	+	0.309267i
$535$	1.24560	−	8.66333i	0.0538519	−	0.374548i
$536$	17.0597	−	5.00919i	0.736868	−	0.216364i
$537$	15.9650	+	10.2601i	0.688940	+	0.442755i
$538$	0.506899	−	1.10995i	0.0218540	−	0.0478535i
$539$	6.20016	+	1.82053i	0.267060	+	0.0784158i
$540$	0.431028	+	0.497433i	0.0185485	+	0.0214061i
$541$	8.84983	+	10.2133i	0.380484	+	0.439102i	0.913398	−	0.407067i	$-0.133449\pi$
$541$	8.84983	+	10.2133i	0.380484	+	0.439102i	−0.532914	+	0.846169i	$0.678903\pi$
$542$	−8.15604	−	2.39483i	−0.350332	−	0.102867i
$543$	−0.445829	+	0.976230i	−0.0191324	+	0.0418940i
$544$	−7.51405	−	4.82899i	−0.322162	−	0.207041i
$545$	−8.12411	+	2.38545i	−0.347999	+	0.102182i
$546$	0.740039	−	5.14709i	0.0316708	−	0.220275i
$547$	11.7800	+	25.7945i	0.503675	+	1.10289i	0.975257	+	0.221072i	$0.0709557\pi$
$547$	11.7800	+	25.7945i	0.503675	+	1.10289i	−0.471582	+	0.881822i	$0.656317\pi$
$548$	1.19257	+	8.29451i	0.0509441	+	0.354324i
$549$	1.80318	−	1.15883i	0.0769579	−	0.0494578i
$550$	−1.09126	+	1.25939i	−0.0465316	+	0.0537004i
$551$	8.31536			0.354246
$552$	−11.9549	−	8.66884i	−0.508833	−	0.368970i
$553$	−11.7049			−0.497743
$554$	13.6837	−	15.7919i	0.581366	−	0.670932i
$555$	2.75618	−	1.77129i	0.116993	−	0.0751872i
$556$	−0.876392	−	6.09544i	−0.0371673	−	0.258504i
$557$	2.56735	+	5.62171i	0.108782	+	0.238200i	0.956192	−	0.292739i	$-0.0945667\pi$
$557$	2.56735	+	5.62171i	0.108782	+	0.238200i	−0.847410	+	0.530939i	$0.821839\pi$
$558$	0.0469829	−	0.326773i	0.00198894	−	0.0138334i
$559$	16.8209	−	4.93906i	0.711448	−	0.208900i
$560$	2.99820	+	1.92682i	0.126697	+	0.0814232i
$561$	1.50296	−	3.29102i	0.0634550	−	0.138947i
$562$	−16.1628	−	4.74584i	−0.681789	−	0.200191i
$563$	4.74702	+	5.47836i	0.200063	+	0.230885i	0.846912	−	0.531733i	$-0.178459\pi$
$563$	4.74702	+	5.47836i	0.200063	+	0.230885i	−0.646849	+	0.762618i	$0.723914\pi$
$564$	−1.52793	−	1.76333i	−0.0643375	−	0.0742494i
$565$	8.34879	+	2.45143i	0.351236	+	0.103132i
$566$	−0.188763	+	0.413333i	−0.00793429	+	0.0173737i
$567$	1.33231	+	0.856222i	0.0559516	+	0.0359579i
$568$	25.2678	−	7.41929i	1.06021	−	0.311306i
$569$	−2.92274	+	20.3281i	−0.122527	+	0.852197i	0.832149	+	0.554552i	$0.187110\pi$
$569$	−2.92274	+	20.3281i	−0.122527	+	0.852197i	−0.954677	+	0.297645i	$0.903799\pi$
$570$	−0.801073	−	1.75411i	−0.0335533	−	0.0734714i
$571$	−3.03775	−	21.1280i	−0.127126	−	0.884179i	−0.949172	−	0.314758i	$-0.898077\pi$
$571$	−3.03775	−	21.1280i	−0.127126	−	0.884179i	0.822046	−	0.569421i	$-0.192832\pi$
$572$	−2.25789	+	1.45106i	−0.0944071	+	0.0606718i
$573$	2.58503	−	2.98329i	0.107991	−	0.124629i
$574$	−6.87432			−0.286928
$575$	4.67019	−	1.09056i	0.194760	−	0.0454795i
$576$	8.61475			0.358948
$577$	−7.29132	+	8.41463i	−0.303542	+	0.350306i	−0.886943	−	0.461878i	$-0.847176\pi$
$577$	−7.29132	+	8.41463i	−0.303542	+	0.350306i	0.583402	+	0.812184i	$0.301721\pi$
$578$	−10.4026	+	6.68533i	−0.432690	+	0.278073i
$579$	2.94474	+	20.4811i	0.122379	+	0.851167i
$580$	−1.36576	−	2.99059i	−0.0567100	−	0.124178i
$581$	3.78362	−	26.3156i	0.156971	−	1.09176i
$582$	−12.0832	+	3.54795i	−0.500866	+	0.147067i
$583$	12.6335	+	8.11907i	0.523227	+	0.336257i
$584$	0.864528	−	1.89305i	0.0357744	−	0.0783351i
$585$	2.71972	+	0.798583i	0.112447	+	0.0330173i
$586$	11.8602	+	13.6874i	0.489940	+	0.565420i
$587$	−17.3102	−	19.9770i	−0.714467	−	0.824539i	0.276163	−	0.961111i	$-0.410937\pi$
$587$	−17.3102	−	19.9770i	−0.714467	−	0.824539i	−0.990630	+	0.136572i	$0.956392\pi$
$588$	2.83676	+	0.832948i	0.116986	+	0.0343502i
$589$	0.197094	−	0.431576i	0.00812112	−	0.0177828i
$590$	−6.23394	−	4.00631i	−0.256647	−	0.164937i
$591$	−16.4603	+	4.83317i	−0.677085	+	0.198810i
$592$	1.04927	−	7.29783i	0.0431247	−	0.299939i
$593$	4.22213	+	9.24517i	0.173382	+	0.379654i	0.976296	−	0.216442i	$-0.0694452\pi$
$593$	4.22213	+	9.24517i	0.173382	+	0.379654i	−0.802913	+	0.596096i	$0.796718\pi$
$594$	0.237154	+	1.64944i	0.00973056	+	0.0676775i
$595$	3.35068	−	2.15335i	0.137364	−	0.0882788i
$596$	5.43449	−	6.27174i	0.222606	−	0.256901i
$597$	2.93705			0.120205
$598$	−15.7219	−	0.884424i	−0.642916	−	0.0361668i
$599$	−4.34301			−0.177451			−0.0887253	−	0.996056i	$-0.528279\pi$
$599$	−4.34301			−0.177451			−0.0887253	+	0.996056i	$0.528279\pi$
$600$	−2.01642	+	2.32707i	−0.0823199	+	0.0950022i
$601$	7.31137	−	4.69873i	0.298237	−	0.191665i	−0.382961	−	0.923765i	$-0.625096\pi$
$601$	7.31137	−	4.69873i	0.298237	−	0.191665i	0.681198	+	0.732099i	$0.261459\pi$
$602$	1.61472	+	11.2306i	0.0658110	+	0.457725i
$603$	2.39873	+	5.25248i	0.0976838	+	0.213898i
$604$	−1.44955	+	10.0818i	−0.0589813	+	0.410224i
$605$	−8.56872	+	2.51600i	−0.348368	+	0.102290i
$606$	−3.64965	−	2.34549i	−0.148257	−	0.0952788i
$607$	−5.29654	+	11.5978i	−0.214980	+	0.470741i	−0.986143	−	0.165897i	$-0.946948\pi$
$607$	−5.29654	+	11.5978i	−0.214980	+	0.470741i	0.771163	+	0.636638i	$0.219675\pi$
$608$	5.67292	+	1.66572i	0.230067	+	0.0675538i
$609$	−5.18038	−	5.97848i	−0.209920	−	0.242260i
$610$	1.62594	+	1.87644i	0.0658326	+	0.0759748i
$611$	−9.64102	−	2.83086i	−0.390034	−	0.114524i
$612$	0.687650	−	1.50574i	0.0277966	−	0.0608660i
$613$	16.1306	+	10.3665i	0.651510	+	0.418700i	0.824218	−	0.566273i	$-0.191615\pi$
$613$	16.1306	+	10.3665i	0.651510	+	0.418700i	−0.172708	+	0.984973i	$0.555252\pi$
$614$	−17.4860	+	5.13435i	−0.705677	+	0.207205i
$615$	0.533283	−	3.70907i	0.0215041	−	0.149564i
$616$	−2.91426	−	6.38133i	−0.117419	−	0.257111i
$617$	3.05657	+	21.2589i	0.123053	+	0.855853i	0.954065	+	0.299599i	$0.0968528\pi$
$617$	3.05657	+	21.2589i	0.123053	+	0.855853i	−0.831012	+	0.556254i	$0.812238\pi$
$618$	−13.3408	+	8.57360i	−0.536645	+	0.344881i
$619$	1.33625	−	1.54211i	0.0537083	−	0.0619826i	−0.728260	−	0.685301i	$-0.759671\pi$
$619$	1.33625	−	1.54211i	0.0537083	−	0.0619826i	0.781968	+	0.623319i	$0.214216\pi$
$620$	−0.187587			−0.00753366
$621$	2.23413	−	4.24366i	0.0896527	−	0.170292i
$622$	6.99569			0.280502
$623$	7.03430	−	8.11802i	0.281823	−	0.325241i
$624$	5.36618	−	3.44864i	0.214819	−	0.138056i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−12.9872	−	28.4380i	−0.519074	−	1.13661i
$627$	−0.340826	+	2.37050i	−0.0136113	+	0.0946685i
$628$	0.932537	−	0.273818i	0.0372123	−	0.0109265i
$629$	−6.93165	−	4.45470i	−0.276383	−	0.177621i
$630$	−0.762086	+	1.66874i	−0.0303622	+	0.0664840i
$631$	−0.578363	−	0.169823i	−0.0230243	−	0.00676054i	0.270200	−	0.962804i	$-0.412910\pi$
$631$	−0.578363	−	0.169823i	−0.0230243	−	0.00676054i	−0.293224	+	0.956044i	$0.594728\pi$
$632$	−14.9029	−	17.1989i	−0.592805	−	0.684134i
$633$	−18.7864	−	21.6806i	−0.746692	−	0.861728i
$634$	15.9537	+	4.68444i	0.633603	+	0.186043i
$635$	5.62753	−	12.3226i	0.223322	−	0.489006i
$636$	5.78022	+	3.71472i	0.229201	+	0.147298i
$637$	12.2166	−	3.58711i	0.484038	−	0.142126i
$638$	1.18458	−	8.23897i	0.0468981	−	0.326184i
$639$	3.55284	+	7.77964i	0.140548	+	0.307758i
$640$	0.409281	+	2.84661i	0.0161782	+	0.112522i
$641$	35.4395	−	22.7756i	1.39978	−	0.899581i	0.399919	−	0.916550i	$-0.369038\pi$
$641$	35.4395	−	22.7756i	1.39978	−	0.899581i	0.999856	+	0.0169695i	$0.00540183\pi$
$642$	6.63928	−	7.66214i	0.262032	−	0.302401i
$643$	−17.0063			−0.670664			−0.335332	−	0.942100i	$-0.608848\pi$
$643$	−17.0063			−0.670664			−0.335332	+	0.942100i	$0.608848\pi$
$644$	−0.988256	+	4.90052i	−0.0389427	+	0.193107i
$645$	−6.18478			−0.243526
$646$	−3.17591	+	3.66519i	−0.124954	+	0.144205i
$647$	34.9156	−	22.4389i	1.37267	−	0.882164i	0.373704	−	0.927548i	$-0.378088\pi$
$647$	34.9156	−	22.4389i	1.37267	−	0.882164i	0.998970	+	0.0453845i	$0.0144513\pi$
$648$	0.438209	+	3.04781i	0.0172145	+	0.119729i
$649$	3.82305	+	8.37131i	0.150068	+	0.328603i
$650$	−0.467280	+	3.25000i	−0.0183282	+	0.127476i
$651$	−0.433077	+	0.127163i	−0.0169736	+	0.00498390i
$652$	12.3525	+	7.93848i	0.483762	+	0.310895i
$653$	−8.87077	+	19.4243i	−0.347140	+	0.760131i	0.652856	+	0.757482i	$0.273570\pi$
$653$	−8.87077	+	19.4243i	−0.347140	+	0.760131i	−0.999996	+	0.00264899i	$0.999157\pi$
$654$	−9.41066	−	2.76322i	−0.367986	−	0.108050i
$655$	4.94172	+	5.70305i	0.193089	+	0.222837i
$656$	−5.52220	−	6.37296i	−0.215606	−	0.248822i
$657$	0.648496	+	0.190416i	0.0253002	+	0.00742882i
$658$	2.70148	−	5.91542i	0.105315	−	0.230607i
$659$	−33.0912	−	21.2664i	−1.28905	−	0.828422i	−0.297074	−	0.954854i	$-0.596011\pi$
$659$	−33.0912	−	21.2664i	−1.28905	−	0.828422i	−0.991975	+	0.126433i	$0.959647\pi$
$660$	0.908521	−	0.266766i	0.0353641	−	0.0103838i
$661$	−2.25609	+	15.6915i	−0.0877517	+	0.610327i	0.897730	+	0.440546i	$0.145215\pi$
$661$	−2.25609	+	15.6915i	−0.0877517	+	0.610327i	−0.985482	+	0.169781i	$0.945694\pi$
$662$	7.69788	+	16.8560i	0.299187	+	0.655127i
$663$	−1.01452	−	7.05616i	−0.0394008	−	0.274039i
$664$	43.4849	−	27.9460i	1.68754	−	1.08452i
$665$	−1.72652	+	1.99251i	−0.0669517	+	0.0772664i
$666$	3.79512			0.147058
$667$	−16.6794	+	17.1944i	−0.645827	+	0.665771i
$668$	10.1217			0.391619
$669$	−13.7151	+	15.8280i	−0.530255	+	0.611947i
$670$	−5.62691	+	3.61620i	−0.217387	+	0.139706i
$671$	−0.438833	−	3.05215i	−0.0169410	−	0.117827i
$672$	−2.33657	−	5.11637i	−0.0901351	−	0.197368i
$673$	−6.85264	+	47.6611i	−0.264150	+	1.83720i	0.236597	+	0.971608i	$0.423968\pi$
$673$	−6.85264	+	47.6611i	−0.264150	+	1.83720i	−0.500747	+	0.865594i	$0.666941\pi$
$674$	−23.5108	+	6.90341i	−0.905604	+	0.265909i
$675$	−0.841254	−	0.540641i	−0.0323799	−	0.0208093i
$676$	1.35766	−	2.97286i	0.0522176	−	0.114341i
$677$	−19.6727	−	5.77643i	−0.756083	−	0.222006i	−0.119099	−	0.992882i	$-0.538000\pi$
$677$	−19.6727	−	5.77643i	−0.756083	−	0.222006i	−0.636985	+	0.770876i	$0.719819\pi$
$678$	6.60047	+	7.61735i	0.253490	+	0.292543i
$679$	11.2752	+	13.0122i	0.432701	+	0.499364i
$680$	7.43022	+	2.18171i	0.284936	+	0.0836648i
$681$	4.77506	−	10.4559i	0.182981	−	0.400672i
$682$	−0.399533	−	0.256764i	−0.0152989	−	0.00983202i
$683$	6.19768	−	1.81980i	0.237148	−	0.0696328i	−0.160999	−	0.986955i	$-0.551472\pi$
$683$	6.19768	−	1.81980i	0.237148	−	0.0696328i	0.398147	+	0.917322i	$0.369653\pi$
$684$	−0.155938	+	1.08457i	−0.00596245	+	0.0414697i
$685$	−5.28883	−	11.5809i	−0.202076	−	0.442484i
$686$	3.00028	+	20.8674i	0.114551	+	0.796721i
$687$	19.5699	−	12.5768i	0.746636	−	0.479834i
$688$	−9.11443	+	10.5186i	−0.347484	+	0.401018i
$689$	29.5899			1.12729
$690$	5.23396	+	1.86202i	0.199253	+	0.0708858i
$691$	14.6052			0.555607			0.277803	−	0.960638i	$-0.410394\pi$
$691$	14.6052			0.555607			0.277803	+	0.960638i	$0.410394\pi$
$692$	−6.50176	+	7.50343i	−0.247160	+	0.285238i
$693$	1.91664	−	1.23175i	0.0728072	−	0.0467903i
$694$	−5.07742	−	35.3142i	−0.192736	−	1.34051i
$695$	3.88664	+	8.51055i	0.147429	+	0.322824i
$696$	2.18885	−	15.2238i	0.0829683	−	0.577057i
$697$	−9.04228	+	2.65505i	−0.342501	+	0.100567i
$698$	−18.8725	−	12.1286i	−0.714335	−	0.459075i
$699$	−3.63861	+	7.96744i	−0.137625	+	0.301356i
$700$	1.00017	+	0.293678i	0.0378030	+	0.0111000i
$701$	15.1662	+	17.5027i	0.572819	+	0.661068i	0.966045	−	0.258373i	$-0.0831865\pi$
$701$	15.1662	+	17.5027i	0.572819	+	0.661068i	−0.393226	+	0.919442i	$0.628641\pi$
$702$	2.15019	+	2.48145i	0.0811536	+	0.0936562i
$703$	5.23322	+	1.53661i	0.197375	+	0.0579544i
$704$	5.14827	−	11.2731i	0.194033	−	0.424872i
$705$	2.98212	+	1.91649i	0.112313	+	0.0721793i
$706$	13.2501	−	3.89059i	0.498676	−	0.146424i
$707$	−0.844126	+	5.87103i	−0.0317466	+	0.220803i
$708$	1.74916	+	3.83013i	0.0657375	+	0.143945i
$709$	−5.66727	−	39.4167i	−0.212839	−	1.48033i	−0.763614	−	0.645673i	$-0.776577\pi$
$709$	−5.66727	−	39.4167i	−0.212839	−	1.48033i	0.550775	−	0.834654i	$-0.314332\pi$
$710$	−8.33421	+	5.35607i	−0.312777	+	0.201010i
$711$	4.83993	−	5.58558i	0.181512	−	0.209475i
$712$	20.8846			0.782683
$713$	0.497068	+	1.27323i	0.0186153	+	0.0476827i
$714$	4.61371			0.172664
$715$	2.67035	−	3.08175i	0.0998655	−	0.115251i
$716$	10.5081	−	6.75316i	0.392707	−	0.252377i
$717$	0.963330	+	6.70011i	0.0359762	+	0.250220i
$718$	0.0815853	+	0.178647i	0.00304474	+	0.00666704i
$719$	−3.39727	+	23.6285i	−0.126697	+	0.881194i	0.823004	+	0.568035i	$0.192296\pi$
$719$	−3.39727	+	23.6285i	−0.126697	+	0.881194i	−0.949701	+	0.313159i	$0.898613\pi$
$720$	−2.15922	+	0.634005i	−0.0804695	+	0.0236280i
$721$	18.2396	+	11.7219i	0.679277	+	0.436545i
$722$	−7.80924	+	17.0999i	−0.290630	+	0.636391i
$723$	15.8605	+	4.65706i	0.589858	+	0.173198i
$724$	0.462585	+	0.533852i	0.0171918	+	0.0198405i
$725$	3.27103	+	3.77497i	0.121483	+	0.140199i
$726$	−9.92568	−	2.91444i	−0.368376	−	0.108165i
$727$	−6.48615	+	14.2027i	−0.240558	+	0.526749i	−0.990948	−	0.134247i	$-0.957139\pi$
$727$	−6.48615	+	14.2027i	−0.240558	+	0.526749i	0.750390	+	0.660996i	$0.229866\pi$
$728$	−11.6284	−	7.47310i	−0.430976	−	0.276972i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.111419	+	0.774937i	−0.00412381	+	0.0286817i
$731$	6.46153	+	14.1488i	0.238988	+	0.523311i
$732$	−0.200779	−	1.39645i	−0.00742102	−	0.0516143i
$733$	−32.4597	+	20.8606i	−1.19893	+	0.770503i	−0.978770	−	0.204962i	$-0.934293\pi$
$733$	−32.4597	+	20.8606i	−1.19893	+	0.770503i	−0.220156	+	0.975465i	$0.570657\pi$
$734$	8.50322	−	9.81324i	0.313860	−	0.362213i
$735$	−4.49184			−0.165684
$736$	−14.8234	+	8.38923i	−0.546397	+	0.309231i
$737$	8.30683			0.305986
$738$	2.84250	−	3.28042i	0.104634	−	0.120754i
$739$	−30.4335	+	19.5584i	−1.11951	+	0.719468i	−0.963346	−	0.268262i	$-0.913551\pi$
$739$	−30.4335	+	19.5584i	−1.11951	+	0.719468i	−0.156168	+	0.987730i	$0.549914\pi$
$740$	−0.306894	−	2.13449i	−0.0112816	−	0.0784655i
$741$	1.96025	+	4.29234i	0.0720115	+	0.157683i
$742$	−2.72542	+	18.9557i	−0.100053	+	0.695885i
$743$	21.9579	−	6.44743i	0.805558	−	0.236533i	0.147072	−	0.989126i	$-0.453015\pi$
$743$	21.9579	−	6.44743i	0.805558	−	0.236533i	0.658486	+	0.752593i	$0.271197\pi$
$744$	−0.738251	−	0.474445i	−0.0270656	−	0.0173940i
$745$	−5.23764	+	11.4688i	−0.191892	+	0.420186i
$746$	26.4924	+	7.77888i	0.969957	+	0.284805i
$747$	10.9933	+	12.6870i	0.402224	+	0.464192i
$748$	−1.55945	−	1.79970i	−0.0570190	−	0.0658034i
$749$	−13.2999	−	3.90519i	−0.485966	−	0.142693i
$750$	0.481201	−	1.05368i	0.0175710	−	0.0384751i
$751$	1.70573	+	1.09620i	0.0622428	+	0.0400010i	0.571392	−	0.820677i	$-0.306404\pi$
$751$	1.70573	+	1.09620i	0.0622428	+	0.0400010i	−0.509149	+	0.860678i	$0.670040\pi$
$752$	7.65413	−	2.24745i	0.279117	−	0.0819563i
$753$	2.20122	−	15.3098i	0.0802168	−	0.557920i
$754$	−6.81309	−	14.9186i	−0.248118	−	0.543303i
$755$	−2.20230	−	15.3173i	−0.0801499	−	0.557455i
$756$	0.876922	−	0.563563i	0.0318933	−	0.0204966i
$757$	−16.1532	+	18.6417i	−0.587097	+	0.677546i	−0.969115	−	0.246609i	$-0.920684\pi$
$757$	−16.1532	+	18.6417i	−0.587097	+	0.677546i	0.382018	+	0.924155i	$0.375229\pi$
$758$	−8.56091			−0.310946
$759$	−4.21805	−	5.45961i	−0.153105	−	0.198171i
$760$	−5.12599			−0.185939
$761$	−3.63469	+	4.19466i	−0.131758	+	0.152056i	−0.817794	−	0.575510i	$-0.804803\pi$
$761$	−3.63469	+	4.19466i	−0.131758	+	0.152056i	0.686037	+	0.727567i	$0.259349\pi$
$762$	13.2010	−	8.48377i	0.478222	−	0.307334i
$763$	1.90837	+	13.2730i	0.0690875	+	0.480514i
$764$	−1.07933	−	2.36341i	−0.0390490	−	0.0855053i
$765$	−0.357914	+	2.48935i	−0.0129404	+	0.0900025i
$766$	18.4086	−	5.40526i	0.665131	−	0.195300i
$767$	15.2546	+	9.80354i	0.550812	+	0.353985i
$768$	5.77351	−	12.6422i	0.208334	−	0.456187i
$769$	11.9867	+	3.51960i	0.432250	+	0.126920i	0.490617	−	0.871375i	$-0.336771\pi$
$769$	11.9867	+	3.51960i	0.432250	+	0.126920i	−0.0583674	+	0.998295i	$0.518589\pi$
$770$	1.72825	+	1.99451i	0.0622819	+	0.0718771i
$771$	−10.3247	−	11.9153i	−0.371835	−	0.429121i
$772$	13.0676	+	3.83699i	0.470313	+	0.138096i
$773$	−16.3911	+	35.8914i	−0.589546	+	1.29093i	0.346170	+	0.938172i	$0.387482\pi$
$773$	−16.3911	+	35.8914i	−0.589546	+	1.29093i	−0.935716	+	0.352754i	$0.885245\pi$
$774$	−6.02692	−	3.87327i	−0.216633	−	0.139222i
$775$	0.273456	−	0.0802939i	0.00982282	−	0.00288424i
$776$	−4.76407	+	33.1349i	−0.171020	+	1.18947i
$777$	−2.15547	−	4.71981i	−0.0773269	−	0.169322i
$778$	4.15464	+	28.8961i	0.148951	+	1.03598i
$779$	5.24784	−	3.37258i	0.188023	−	0.120835i
$780$	1.22177	−	1.40999i	0.0437463	−	0.0504859i
$781$	12.3035			0.440255
$782$	−1.20847	−	13.9189i	−0.0432147	−	0.497740i
$783$	4.99500			0.178507
$784$	−6.61956	+	7.63938i	−0.236413	+	0.272835i
$785$	−1.24221	+	0.798320i	−0.0443364	+	0.0284932i
$786$	1.24401	+	8.65227i	0.0443723	+	0.308616i
$787$	−18.8550	−	41.2868i	−0.672110	−	1.47171i	−0.870792	−	0.491651i	$-0.836394\pi$
$787$	−18.8550	−	41.2868i	−0.672110	−	1.47171i	0.198683	−	0.980064i	$-0.436334\pi$
$788$	−1.60695	+	11.1766i	−0.0572452	+	0.398149i
$789$	−13.5549	+	3.98009i	−0.482568	+	0.141695i
$790$	7.20213	+	4.62853i	0.256240	+	0.164676i
$791$	5.72455	−	12.5350i	0.203542	−	0.445694i
$792$	4.25020	+	1.24797i	0.151024	+	0.0443448i
$793$	−3.97873	−	4.59170i	−0.141289	−	0.163056i
$794$	15.6688	+	18.0827i	0.556064	+	0.641733i
$795$	−10.0162	−	2.94102i	−0.355238	−	0.104307i
$796$	0.803064	−	1.75846i	0.0284638	−	0.0623271i
$797$	24.2014	+	15.5533i	0.857257	+	0.550925i	0.893830	−	0.448405i	$-0.148008\pi$
$797$	24.2014	+	15.5533i	0.857257	+	0.550925i	−0.0365735	+	0.999331i	$0.511644\pi$
$798$	−2.93028	+	0.860408i	−0.103731	+	0.0304581i
$799$	1.26875	−	8.82437i	0.0448852	−	0.312184i
$800$	1.47537	+	3.23061i	0.0521622	+	0.114219i
$801$	0.965261	+	6.71354i	0.0341058	+	0.237211i
$802$	21.0694	−	13.5405i	0.743986	−	0.478131i
$803$	0.636723	−	0.734818i	0.0224695	−	0.0259312i
$804$	3.80063			0.134038
$805$	−0.656961	−	7.56677i	−0.0231548	−	0.266694i
$806$	−0.935777			−0.0329613
$807$	0.689833	−	0.796110i	0.0242833	−	0.0280244i
$808$	−9.70148	+	6.23476i	−0.341297	+	0.219338i
$809$	−0.113261	−	0.787746i	−0.00398204	−	0.0276957i	0.987734	−	0.156149i	$-0.0499079\pi$
$809$	−0.113261	−	0.787746i	−0.00398204	−	0.0276957i	−0.991716	+	0.128453i	$0.958999\pi$
$810$	−0.481201	−	1.05368i	−0.0169077	−	0.0370226i
$811$	−6.54278	+	45.5060i	−0.229748	+	1.59793i	0.469420	+	0.882975i	$0.344463\pi$
$811$	−6.54278	+	45.5060i	−0.229748	+	1.59793i	−0.699168	+	0.714958i	$0.746446\pi$
$812$	−4.99587	+	1.46692i	−0.175321	+	0.0514788i
$813$	−6.17334	−	3.96737i	−0.216509	−	0.139142i
$814$	2.26801	−	4.96624i	0.0794936	−	0.174067i
$815$	−21.4049	−	6.28506i	−0.749782	−	0.220156i
$816$	3.70624	+	4.27723i	0.129744	+	0.149733i
$817$	−6.74248	−	7.78123i	−0.235889	−	0.272231i
$818$	36.5752	+	10.7394i	1.27882	+	0.375496i
$819$	1.86484	−	4.08344i	0.0651629	−	0.142687i
$820$	−2.07487	−	1.33344i	−0.0724576	−	0.0465657i
$821$	27.8767	−	8.18534i	0.972903	−	0.285670i	0.243611	−	0.969873i	$-0.421668\pi$
$821$	27.8767	−	8.18534i	0.972903	−	0.285670i	0.729292	+	0.684203i	$0.239850\pi$
$822$	2.09880	−	14.5975i	0.0732042	−	0.509146i
$823$	1.69366	+	3.70859i	0.0590371	+	0.129273i	0.936851	−	0.349728i	$-0.113726\pi$
$823$	1.69366	+	3.70859i	0.0590371	+	0.129273i	−0.877814	+	0.479002i	$0.840999\pi$
$824$	5.99918	+	41.7252i	0.208991	+	1.45357i
$825$	−1.21022	+	0.777759i	−0.0421344	+	0.0270781i
$826$	−7.68532	+	8.86933i	−0.267407	+	0.308604i
$827$	−35.8416			−1.24634			−0.623168	−	0.782088i	$-0.714155\pi$
$827$	−35.8416			−1.24634			−0.623168	+	0.782088i	$0.714155\pi$
$828$	−1.92989	−	2.49794i	−0.0670682	−	0.0868094i
$829$	−36.7969			−1.27801			−0.639005	−	0.769203i	$-0.720654\pi$
$829$	−36.7969			−1.27801			−0.639005	+	0.769203i	$0.720654\pi$
$830$	−12.7342	+	14.6961i	−0.442012	+	0.510109i
$831$	15.1753	−	9.75260i	0.526427	−	0.338314i
$832$	−3.47517	−	24.1703i	−0.120480	−	0.837955i
$833$	4.69283	+	10.2759i	0.162597	+	0.356038i
$834$	−1.54236	+	10.7274i	−0.0534076	+	0.371458i
$835$	−14.7549	+	4.33244i	−0.510615	+	0.149930i
$836$	1.32607	+	0.852212i	0.0458630	+	0.0294744i
$837$	0.118393	−	0.259245i	0.00409227	−	0.00896083i
$838$	−36.8315	−	10.8147i	−1.27232	−	0.373587i
$839$	−7.56592	−	8.73153i	−0.261204	−	0.301446i	0.609965	−	0.792428i	$-0.291183\pi$
$839$	−7.56592	−	8.73153i	−0.261204	−	0.301446i	−0.871170	+	0.490982i	$0.836638\pi$
$840$	3.19343	+	3.68542i	0.110184	+	0.127159i
$841$	3.88596	+	1.14102i	0.133999	+	0.0393456i
$842$	2.93626	−	6.42952i	0.101190	−	0.221576i
$843$	−12.2337	−	7.86214i	−0.421352	−	0.270786i
$844$	−18.1173	+	5.31971i	−0.623622	+	0.183112i
$845$	−0.706646	+	4.91483i	−0.0243094	+	0.169075i
$846$	1.70579	+	3.73515i	0.0586461	+	0.128417i
$847$	2.01281	+	13.9994i	0.0691608	+	0.481024i
$848$	−19.7626	+	12.7006i	−0.678650	+	0.436142i
$849$	−0.256885	+	0.296461i	−0.00881627	+	0.0101745i
$850$	−2.91322			−0.0999225
$851$	−13.6744	+	7.73900i	−0.468754	+	0.265290i
$852$	5.62924			0.192855
$853$	−31.1938	+	35.9995i	−1.06805	+	1.23260i	−0.0966127	+	0.995322i	$0.530801\pi$
$853$	−31.1938	+	35.9995i	−1.06805	+	1.23260i	−0.971442	+	0.237278i	$0.923745\pi$
$854$	3.30797	−	2.12590i	0.113196	−	0.0727468i
$855$	−0.236917	−	1.64779i	−0.00810239	−	0.0563533i
$856$	−11.1955	−	24.5146i	−0.382653	−	0.837892i
$857$	4.22917	−	29.4145i	0.144466	−	1.00478i	−0.780616	−	0.625011i	$-0.785094\pi$
$857$	4.22917	−	29.4145i	0.144466	−	1.00478i	0.925081	−	0.379769i	$-0.123996\pi$
$858$	4.53216	−	1.33076i	0.154725	−	0.0454315i
$859$	−1.78453	−	1.14685i	−0.0608875	−	0.0391300i	0.509843	−	0.860267i	$-0.329704\pi$
$859$	−1.78453	−	1.14685i	−0.0608875	−	0.0391300i	−0.570730	+	0.821137i	$0.693340\pi$
$860$	−1.69108	+	3.70294i	−0.0576652	+	0.126269i
$861$	−5.69413	−	1.67195i	−0.194055	−	0.0569798i
$862$	16.7995	+	19.3876i	0.572192	+	0.660345i
$863$	−16.4989	−	19.0407i	−0.561629	−	0.648154i	0.401924	−	0.915673i	$-0.368342\pi$
$863$	−16.4989	−	19.0407i	−0.561629	−	0.648154i	−0.963553	+	0.267519i	$0.913796\pi$
$864$	3.40769	+	1.00059i	0.115932	+	0.0340407i
$865$	6.26625	−	13.7212i	0.213059	−	0.466534i
$866$	15.1559	+	9.74009i	0.515017	+	0.330982i
$867$	−10.2426	+	3.00751i	−0.347858	+	0.102140i
$868$	−0.0422795	+	0.294060i	−0.00143506	+	0.00998105i
$869$	−4.41681	−	9.67147i	−0.149830	−	0.328082i
$870$	0.823435	+	5.72712i	0.0279171	+	0.194168i
$871$	13.7692	−	8.84893i	0.466552	−	0.299834i
$872$	−17.0732	+	19.7035i	−0.578171	+	0.667245i
$873$	−10.8717			−0.367951
$874$	3.36326	+	8.61489i	0.113764	+	0.291403i
$875$	−1.58372			−0.0535394
$876$	0.291320	−	0.336202i	0.00984280	−	0.0113592i
$877$	−8.44943	+	5.43012i	−0.285317	+	0.183362i	−0.675469	−	0.737388i	$-0.736059\pi$
$877$	−8.44943	+	5.43012i	−0.285317	+	0.183362i	0.390152	+	0.920750i	$0.372422\pi$
$878$	−1.10499	−	7.68541i	−0.0372918	−	0.259370i
$879$	6.49502	+	14.2221i	0.219072	+	0.479700i
$880$	−0.460726	+	3.20442i	−0.0155311	+	0.108021i
$881$	16.7432	−	4.91626i	0.564094	−	0.165633i	0.0127617	−	0.999919i	$-0.495938\pi$
$881$	16.7432	−	4.91626i	0.564094	−	0.165633i	0.551333	+	0.834286i	$0.314120\pi$
$882$	−4.37719	−	2.81305i	−0.147388	−	0.0947203i
$883$	−5.88833	+	12.8936i	−0.198158	+	0.433905i	−0.982460	−	0.186474i	$-0.940294\pi$
$883$	−5.88833	+	12.8936i	−0.198158	+	0.433905i	0.784302	+	0.620379i	$0.213021\pi$
$884$	−4.50204	−	1.32192i	−0.151420	−	0.0444610i
$885$	−4.18929	−	4.83470i	−0.140821	−	0.162517i
$886$	20.2248	+	23.3407i	0.679466	+	0.784145i
$887$	29.7241	+	8.72780i	0.998039	+	0.293051i	0.739651	−	0.672991i	$-0.234991\pi$
$887$	29.7241	+	8.72780i	0.998039	+	0.293051i	0.258388	+	0.966041i	$0.416809\pi$
$888$	4.19078	−	9.17653i	0.140633	−	0.307944i
$889$	−18.0485	−	11.5990i	−0.605326	−	0.389019i
$890$	−7.53842	+	2.21348i	−0.252689	+	0.0741960i
$891$	−0.204732	+	1.42395i	−0.00685879	+	0.0477040i
$892$	5.72647	+	12.5392i	0.191737	+	0.419844i
$893$	0.839835	+	5.84118i	0.0281040	+	0.195468i
$894$	−12.2864	+	7.89599i	−0.410919	+	0.264082i
$895$	−12.4277	+	14.3423i	−0.415412	+	0.479411i
$896$	4.55458			0.152158
$897$	−12.8076	−	4.55641i	−0.427635	−	0.152134i
$898$	−23.2708			−0.776558
$899$	−0.932244	+	1.07587i	−0.0310921	+	0.0358822i
$900$	−0.553711	+	0.355849i	−0.0184570	+	0.0118616i
$901$	3.73628	+	25.9864i	0.124474	+	0.865733i
$902$	−2.59400	−	5.68008i	−0.0863709	−	0.189126i
$903$	−1.39397	+	9.69525i	−0.0463883	+	0.322638i
$904$	25.7072	−	7.54832i	0.855009	−	0.251053i
$905$	−0.902845	−	0.580223i	−0.0300116	−	0.0192873i
$906$	7.44651	−	16.3056i	0.247394	−	0.541717i
$907$	−44.2475	−	12.9922i	−1.46921	−	0.431400i	−0.553370	−	0.832935i	$-0.686659\pi$
$907$	−44.2475	−	12.9922i	−1.46921	−	0.431400i	−0.915844	+	0.401535i	$0.868477\pi$
$908$	−4.95452	−	5.71783i	−0.164422	−	0.189753i
$909$	−2.45261	−	2.83046i	−0.0813480	−	0.0938806i
$910$	4.98938	+	1.46501i	0.165396	+	0.0485647i
$911$	−2.20447	+	4.82711i	−0.0730372	+	0.159929i	−0.942629	−	0.333842i	$-0.891655\pi$
$911$	−2.20447	+	4.82711i	−0.0730372	+	0.159929i	0.869592	+	0.493771i	$0.164382\pi$
$912$	−3.15158	−	2.02540i	−0.104359	−	0.0670676i
$913$	23.1717	−	6.80383i	0.766871	−	0.225174i
$914$	−5.61553	+	39.0568i	−0.185745	+	1.29189i
$915$	0.890420	+	1.94975i	0.0294364	+	0.0644566i
$916$	−2.17905	−	15.1556i	−0.0719979	−	0.500756i
$917$	10.0539	−	6.46123i	0.332008	−	0.213369i
$918$	−1.90775	+	2.20166i	−0.0629652	+	0.0726657i
$919$	−10.9840			−0.362329			−0.181164	−	0.983453i	$-0.557987\pi$
$919$	−10.9840			−0.362329			−0.181164	+	0.983453i	$0.557987\pi$
$920$	10.2820	−	10.5995i	0.338986	−	0.349454i
$921$	−15.7327			−0.518411
$922$	19.4763	−	22.4768i	0.641416	−	0.740234i
$923$	20.3940	−	13.1065i	0.671278	−	0.431404i
$924$	−0.213413	−	1.48432i	−0.00702077	−	0.0488305i
$925$	1.36102	+	2.98021i	0.0447500	+	0.0979887i
$926$	−1.01326	+	7.04736i	−0.0332977	+	0.231591i
$927$	−13.1357	+	3.85698i	−0.431432	+	0.126680i
$928$	−14.9238	−	9.59097i	−0.489899	−	0.314839i
$929$	−3.58998	+	7.86097i	−0.117784	+	0.257910i	−0.959337	−	0.282264i	$-0.908914\pi$
$929$	−3.58998	+	7.86097i	−0.117784	+	0.257910i	0.841553	+	0.540174i	$0.181642\pi$
$930$	0.316761	+	0.0930093i	0.0103870	+	0.00304990i
$931$	−4.89688	−	5.65130i	−0.160489	−	0.185214i
$932$	3.77536	+	4.35700i	0.123666	+	0.142718i
$933$	5.79466	+	1.70147i	0.189709	+	0.0557035i
$934$	18.5606	−	40.6421i	0.607322	−	1.32985i
$935$	3.04363	+	1.95602i	0.0995374	+	0.0639688i
$936$	8.37445	−	2.45896i	0.273727	−	0.0803736i
$937$	3.90118	−	27.1333i	0.127446	−	0.886406i	−0.821329	−	0.570455i	$-0.806767\pi$
$937$	3.90118	−	27.1333i	0.127446	−	0.886406i	0.948775	−	0.315952i	$-0.102324\pi$
$938$	4.40051	+	9.63577i	0.143682	+	0.314619i
$939$	−3.84096	−	26.7145i	−0.125345	−	0.871794i
$940$	1.96282	−	1.26143i	0.0640203	−	0.0411433i
$941$	28.4193	−	32.7976i	0.926442	−	1.06917i	−0.0709846	−	0.997477i	$-0.522614\pi$
$941$	28.4193	−	32.7976i	0.926442	−	1.06917i	0.997427	−	0.0716938i	$-0.0228404\pi$
$942$	−1.71046			−0.0557297
$943$	−3.55257	+	17.6163i	−0.115688	+	0.573667i
$944$	−14.3962			−0.468556
$945$	−1.03711	+	1.19689i	−0.0337373	+	0.0389349i
$946$	−8.67026	+	5.57204i	−0.281895	+	0.181163i
$947$	−2.51474	−	17.4904i	−0.0817180	−	0.568361i	−0.989009	−	0.147857i	$-0.952762\pi$
$947$	−2.51474	−	17.4904i	−0.0817180	−	0.568361i	0.907291	−	0.420504i	$-0.138147\pi$
$948$	−2.02083	−	4.42499i	−0.0656334	−	0.143717i
$949$	0.272646	−	1.89629i	0.00885045	−	0.0615562i
$950$	1.85026	−	0.543284i	0.0600302	−	0.0176265i
$951$	12.0754	+	7.76041i	0.391573	+	0.251649i
$952$	5.09471	−	11.1559i	0.165121	−	0.361564i
$953$	−24.6002	−	7.22327i	−0.796878	−	0.233985i	−0.142146	−	0.989846i	$-0.545400\pi$
$953$	−24.6002	−	7.22327i	−0.796878	−	0.233985i	−0.654732	+	0.755861i	$0.727218\pi$
$954$	−7.91870	−	9.13867i	−0.256377	−	0.295875i
$955$	2.58503	+	2.98329i	0.0836498	+	0.0965370i
$956$	4.27487	+	1.25522i	0.138259	+	0.0405966i
$957$	2.98506	−	6.53638i	0.0964934	−	0.211291i
$958$	35.2524	+	22.6553i	1.13895	+	0.731961i
$959$	−19.3462	+	5.68057i	−0.624723	+	0.183435i
$960$	−1.22601	+	8.52706i	−0.0395692	+	0.275210i
$961$	−12.8441	−	28.1247i	−0.414327	−	0.907249i
$962$	−1.53094	−	10.6479i	−0.0493595	−	0.343303i
$963$	7.36300	−	4.73191i	0.237269	−	0.152484i
$964$	7.12493	−	8.22260i	0.229478	−	0.264832i
$965$	−20.6917			−0.666091
$966$	4.09856	−	7.78506i	0.131869	−	0.250480i
$967$	−39.1155			−1.25787			−0.628935	−	0.777458i	$-0.716509\pi$
$967$	−39.1155			−1.25787			−0.628935	+	0.777458i	$0.716509\pi$
$968$	−18.0075	+	20.7818i	−0.578784	+	0.667953i
$969$	−3.52210	+	2.26351i	−0.113146	+	0.0727146i
$970$	−1.79222	−	12.4652i	−0.0575447	−	0.400232i
$971$	12.6346	+	27.6660i	0.405465	+	0.887844i	0.996687	+	0.0813354i	$0.0259185\pi$
$971$	12.6346	+	27.6660i	0.405465	+	0.887844i	−0.591222	+	0.806509i	$0.701354\pi$
$972$	−0.0936713	+	0.651498i	−0.00300451	+	0.0208968i
$973$	14.2171	−	4.17452i	0.455779	−	0.133829i
$974$	−5.35136	−	3.43911i	−0.171469	−	0.110196i
$975$	−1.17751	+	2.57839i	−0.0377105	+	0.0825746i
$976$	4.62818	+	1.35896i	0.148144	+	0.0434991i
$977$	25.5938	+	29.5369i	0.818819	+	0.944968i	0.999254	−	0.0386193i	$-0.0122960\pi$
$977$	25.5938	+	29.5369i	0.818819	+	0.944968i	−0.180435	+	0.983587i	$0.557751\pi$
$978$	−16.9225	−	19.5296i	−0.541123	−	0.624489i
$979$	9.36209	+	2.74896i	0.299214	+	0.0878571i
$980$	−1.22818	+	2.68935i	−0.0392329	+	0.0859080i
$981$	−7.12297	−	4.57765i	−0.227419	−	0.146153i
$982$	34.9727	−	10.2689i	1.11602	−	0.327694i
$983$	6.77381	−	47.1129i	0.216051	−	1.50267i	−0.536369	−	0.843984i	$-0.680204\pi$
$983$	6.77381	−	47.1129i	0.216051	−	1.50267i	0.752420	−	0.658684i	$-0.228887\pi$
$984$	−4.79316	−	10.4955i	−0.152800	−	0.334586i
$985$	−2.44144	−	16.9806i	−0.0777907	−	0.541046i
$986$	12.2415	−	7.86714i	0.389849	−	0.250541i
$987$	3.67642	−	4.24281i	0.117022	−	0.135050i
$988$	3.10588			0.0988113
$989$	29.6144	+	1.66593i	0.941682	+	0.0529736i
$990$	−1.66641			−0.0529618
$991$	34.3071	−	39.5926i	1.08980	−	1.25770i	0.125729	−	0.992065i	$-0.459873\pi$
$991$	34.3071	−	39.5926i	1.08980	−	1.25770i	0.964074	−	0.265635i	$-0.0855814\pi$
$992$	−0.851512	+	0.547234i	−0.0270355	+	0.0173747i
$993$	2.27664	+	15.8344i	0.0722471	+	0.502490i
$994$	6.51775	+	14.2719i	0.206730	+	0.452676i
$995$	−0.417986	+	2.90715i	−0.0132510	+	0.0921630i
$996$	10.6018	−	3.11296i	0.335930	−	0.0986378i
$997$	29.4598	+	18.9327i	0.933002	+	0.599604i	0.916402	−	0.400259i	$-0.131080\pi$
$997$	29.4598	+	18.9327i	0.933002	+	0.599604i	0.0165993	+	0.999862i	$0.494716\pi$
$998$	15.4263	−	33.7788i	0.488310	−	1.06925i
$999$	3.14357	+	0.923035i	0.0994581	+	0.0292035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.16.2	✓	30
23.6	even	11		7935.2.a.bp.1.11		15
23.13	even	11	inner	345.2.m.a.151.2	yes	30
23.17	odd	22		7935.2.a.bq.1.11		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.16.2	✓	30	1.1	even	1	trivial
345.2.m.a.151.2	yes	30	23.13	even	11	inner
7935.2.a.bp.1.11		15	23.6	even	11
7935.2.a.bq.1.11		15	23.17	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.758566 + 0.875431i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0936713 + 0.651498i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.164852 - 1.14657i) q^{6} +(-1.51957 + 0.446185i) q^{7} +(-2.59035 - 1.66472i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.758566 + 0.875431i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(0.0936713 + 0.651498i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.164852 - 1.14657i) q^{6} +(-1.51957 + 0.446185i) q^{7} +(-2.59035 - 1.66472i) q^{8} +(0.415415 - 0.909632i) q^{9} +(1.11144 + 0.326348i) q^{10} +(-0.942075 - 1.08721i) q^{11} +(-0.431028 - 0.497433i) q^{12} +(-2.71972 - 0.798583i) q^{13} +(0.762086 - 1.66874i) q^{14} +(0.841254 + 0.540641i) q^{15} +(2.15922 - 0.634005i) q^{16} +(0.357914 - 2.48935i) q^{17} +(0.481201 + 1.05368i) q^{18} +(0.236917 + 1.64779i) q^{19} +(0.553711 - 0.355849i) q^{20} +(1.03711 - 1.19689i) q^{21} +1.66641 q^{22} +(-3.88251 - 2.81533i) q^{23} +3.07915 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.76219 - 1.77515i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.433028 - 0.948199i) q^{28} +(0.710862 - 4.94415i) q^{29} +(-1.11144 + 0.326348i) q^{30} +(-0.239758 - 0.154083i) q^{31} +(1.47537 - 3.23061i) q^{32} +(1.38032 + 0.405297i) q^{33} +(1.90775 + 2.20166i) q^{34} +(1.03711 + 1.19689i) q^{35} +(0.631536 + 0.185436i) q^{36} +(1.36102 - 2.98021i) q^{37} +(-1.62225 - 1.04255i) q^{38} +(2.71972 - 0.798583i) q^{39} +(-0.438209 + 3.04781i) q^{40} +(-1.55665 - 3.40858i) q^{41} +(0.261079 + 1.81584i) q^{42} +(-5.20297 + 3.34375i) q^{43} +(0.620072 - 0.715601i) q^{44} -1.00000 q^{45} +(5.40977 - 1.26326i) q^{46} +3.54485 q^{47} +(-1.47369 + 1.70072i) q^{48} +(-3.77878 + 2.42847i) q^{49} +(-0.164852 - 1.14657i) q^{50} +(1.04475 + 2.28767i) q^{51} +(0.265515 - 1.84670i) q^{52} +(-10.0162 + 2.94102i) q^{53} +(-0.974476 - 0.626258i) q^{54} +(-0.597611 + 1.30859i) q^{55} +(4.67898 + 1.37387i) q^{56} +(-1.09017 - 1.25812i) q^{57} +(3.78903 + 4.37278i) q^{58} +(-6.13809 - 1.80231i) q^{59} +(-0.273425 + 0.598718i) q^{60} +(1.80318 + 1.15883i) q^{61} +(0.316761 - 0.0930093i) q^{62} +(-0.225386 + 1.56760i) q^{63} +(3.57869 + 7.83625i) q^{64} +(0.403397 + 2.80569i) q^{65} +(-1.40187 + 0.900927i) q^{66} +(-3.78136 + 4.36392i) q^{67} +1.65533 q^{68} +(4.78826 + 0.269360i) q^{69} -1.83452 q^{70} +(-5.60070 + 6.46355i) q^{71} +(-2.59035 + 1.66472i) q^{72} +(0.0961868 + 0.668994i) q^{73} +(1.57655 + 3.45216i) q^{74} +(0.142315 - 0.989821i) q^{75} +(-1.05134 + 0.308702i) q^{76} +(1.91664 + 1.23175i) q^{77} +(-1.36398 + 2.98671i) q^{78} +(7.09140 + 2.08222i) q^{79} +(-1.47369 - 1.70072i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(4.16480 + 1.22289i) q^{82} +(-6.97368 + 15.2702i) q^{83} +(0.876922 + 0.563563i) q^{84} +(-2.41307 + 0.708542i) q^{85} +(1.01957 - 7.09130i) q^{86} +(2.07500 + 4.54361i) q^{87} +(0.630403 + 4.38455i) q^{88} +(-5.70586 + 3.66694i) q^{89} +(0.758566 - 0.875431i) q^{90} +4.48911 q^{91} +(1.47050 - 2.79317i) q^{92} +0.285000 q^{93} +(-2.68900 + 3.10328i) q^{94} +(1.40047 - 0.900025i) q^{95} +(0.505439 + 3.51541i) q^{96} +(-4.51626 - 9.88923i) q^{97} +(0.740489 - 5.15022i) q^{98} +(-1.38032 + 0.405297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

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