LMFDB - Embedded newform 153.2.n.a.106.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			106.9
Character	$\chi$	$=$	153.106
Dual form			153.2.n.a.13.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.218953 + 0.126413i) q^{2} +(1.43947 - 0.963283i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(-3.83129 - 1.02659i) q^{5} +(0.436949 - 0.0289461i) q^{6} +(2.05904 - 0.551719i) q^{7} -0.995142i q^{8} +(1.14417 - 2.77324i) q^{9} +O(q^{10})$	\(q+(0.218953 + 0.126413i) q^{2} +(1.43947 - 0.963283i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(-3.83129 - 1.02659i) q^{5} +(0.436949 - 0.0289461i) q^{6} +(2.05904 - 0.551719i) q^{7} -0.995142i q^{8} +(1.14417 - 2.77324i) q^{9} +(-0.709099 - 0.709099i) q^{10} +(1.14906 - 0.307889i) q^{11} +(-3.00860 - 1.48106i) q^{12} +(3.09696 + 5.36409i) q^{13} +(0.520578 + 0.139489i) q^{14} +(-6.50393 + 2.21286i) q^{15} +(-1.81028 + 3.13550i) q^{16} +(2.45336 + 3.31376i) q^{17} +(0.601094 - 0.462573i) q^{18} -5.66168i q^{19} +(1.98756 + 7.41767i) q^{20} +(2.43248 - 2.77762i) q^{21} +(0.290512 + 0.0778423i) q^{22} +(-0.188390 + 0.703082i) q^{23} +(-0.958603 - 1.43248i) q^{24} +(9.29474 + 5.36632i) q^{25} +1.56598i q^{26} +(-1.02441 - 5.09417i) q^{27} +(-2.91830 - 2.91830i) q^{28} +(-0.799838 - 2.98504i) q^{29} +(-1.70379 - 0.337667i) q^{30} +(0.0434097 + 0.0116316i) q^{31} +(-2.51637 + 1.45283i) q^{32} +(1.35746 - 1.55007i) q^{33} +(0.118269 + 1.03570i) q^{34} -8.45517 q^{35} +(-5.75748 + 0.766182i) q^{36} +(1.68986 - 1.68986i) q^{37} +(0.715709 - 1.23964i) q^{38} +(9.62513 + 4.73822i) q^{39} +(-1.02160 + 3.81267i) q^{40} +(-0.174405 + 0.650890i) q^{41} +(0.883726 - 0.300674i) q^{42} +(-0.442424 - 0.255434i) q^{43} +(-1.62857 - 1.62857i) q^{44} +(-7.23063 + 9.45049i) q^{45} +(-0.130127 + 0.130127i) q^{46} +(-4.74104 + 8.21172i) q^{47} +(0.414520 + 6.25728i) q^{48} +(-2.12692 + 1.22798i) q^{49} +(1.35674 + 2.34995i) q^{50} +(6.72364 + 2.40680i) q^{51} +(5.99596 - 10.3853i) q^{52} +7.10456i q^{53} +(0.419670 - 1.24488i) q^{54} -4.71845 q^{55} +(-0.549038 - 2.04904i) q^{56} +(-5.45380 - 8.14985i) q^{57} +(0.202219 - 0.754693i) q^{58} +(7.91388 - 4.56908i) q^{59} +(10.0064 + 8.76297i) q^{60} +(-5.59065 + 1.49801i) q^{61} +(0.00803432 + 0.00803432i) q^{62} +(0.825848 - 6.34148i) q^{63} +6.50650 q^{64} +(-6.35862 - 23.7307i) q^{65} +(0.493168 - 0.167793i) q^{66} +(-1.68697 - 2.92191i) q^{67} +(3.18122 - 7.32139i) q^{68} +(0.406084 + 1.19354i) q^{69} +(-1.85129 - 1.06884i) q^{70} +(2.32488 - 2.32488i) q^{71} +(-2.75977 - 1.13861i) q^{72} +(-8.24518 + 8.24518i) q^{73} +(0.583622 - 0.156381i) q^{74} +(18.5488 - 1.22879i) q^{75} +(-9.49291 + 5.48073i) q^{76} +(2.19609 - 1.26791i) q^{77} +(1.50848 + 2.25419i) q^{78} +(-0.124126 + 0.0332596i) q^{79} +(10.1546 - 10.1546i) q^{80} +(-6.38174 - 6.34613i) q^{81} +(-0.120467 + 0.120467i) q^{82} +(5.37265 + 3.10190i) q^{83} +(-7.01196 - 1.38967i) q^{84} +(-5.99764 - 15.2146i) q^{85} +(-0.0645802 - 0.111856i) q^{86} +(-4.02678 - 3.52641i) q^{87} +(-0.306394 - 1.14348i) q^{88} +8.09524 q^{89} +(-2.77783 + 1.15517i) q^{90} +(9.33624 + 9.33624i) q^{91} +(1.36122 - 0.364738i) q^{92} +(0.0736917 - 0.0250724i) q^{93} +(-2.07613 + 1.19866i) q^{94} +(-5.81223 + 21.6915i) q^{95} +(-2.22277 + 4.51528i) q^{96} +(1.05767 + 3.94729i) q^{97} -0.620928 q^{98} +(0.460869 - 3.53890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7	$ 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30} - 2 q^{31} + 12 q^{33} + 20 q^{34} - 128 q^{35} - 8 q^{37} - 24 q^{38} + 34 q^{39} - 20 q^{40} + 32 q^{41} + 20 q^{44} + 20 q^{45} - 40 q^{46} - 64 q^{47} + 62 q^{48} + 48 q^{50} + 40 q^{51} + 36 q^{52} - 46 q^{54} - 16 q^{55} + 12 q^{56} + 72 q^{57} - 10 q^{58} - 2 q^{61} - 28 q^{62} + 64 q^{63} - 8 q^{64} + 8 q^{65} - 4 q^{67} - 60 q^{68} - 24 q^{69} - 84 q^{71} + 72 q^{72} - 44 q^{73} - 14 q^{74} + 46 q^{75} - 56 q^{78} + 10 q^{79} + 204 q^{80} + 44 q^{81} - 52 q^{82} - 60 q^{84} + 22 q^{85} + 32 q^{86} + 16 q^{88} + 128 q^{89} - 66 q^{90} + 44 q^{91} + 136 q^{92} + 4 q^{95} - 2 q^{96} - 44 q^{97} + 208 q^{98} + 6 q^{99}+O(q^{100}) $ 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.218953	+	0.126413i	0.154823	+	0.0893873i	0.575410	−	0.817865i	$-0.304842\pi$
$2$	0.218953	+	0.126413i	0.154823	+	0.0893873i	−0.420587	+	0.907252i	$0.638176\pi$
$3$	1.43947	−	0.963283i	0.831081	−	0.556152i
$3$	1.43947	−	0.963283i	0.831081	−	0.556152i
$4$	−0.968040	−	1.67669i	−0.484020	−	0.838347i
$5$	−3.83129	−	1.02659i	−1.71340	−	0.459105i	−0.737149	−	0.675731i	$-0.763828\pi$
$5$	−3.83129	−	1.02659i	−1.71340	−	0.459105i	−0.976255	+	0.216626i	$0.930495\pi$
$6$	0.436949	−	0.0289461i	0.178384	−	0.0118172i
$7$	2.05904	−	0.551719i	0.778245	−	0.208530i	0.152234	−	0.988344i	$-0.451353\pi$
$7$	2.05904	−	0.551719i	0.778245	−	0.208530i	0.626011	+	0.779814i	$0.284687\pi$
$8$		−	0.995142i		−	0.351836i
$9$	1.14417	−	2.77324i	0.381391	−	0.924414i
$10$	−0.709099	−	0.709099i	−0.224237	−	0.224237i
$11$	1.14906	−	0.307889i	0.346454	−	0.0928322i	−0.0813958	−	0.996682i	$-0.525938\pi$
$11$	1.14906	−	0.307889i	0.346454	−	0.0928322i	0.427850	+	0.903850i	$0.359271\pi$
$12$	−3.00860	−	1.48106i	−0.868508	−	0.427546i
$13$	3.09696	+	5.36409i	0.858942	+	1.48773i	0.872939	+	0.487829i	$0.162211\pi$
$13$	3.09696	+	5.36409i	0.858942	+	1.48773i	−0.0139970	+	0.999902i	$0.504456\pi$
$14$	0.520578	+	0.139489i	0.139130	+	0.0372799i
$15$	−6.50393	+	2.21286i	−1.67931	+	0.571359i
$16$	−1.81028	+	3.13550i	−0.452570	+	0.783874i
$17$	2.45336	+	3.31376i	0.595027	+	0.803706i
$17$	2.45336	+	3.31376i	0.595027	+	0.803706i
$18$	0.601094	−	0.462573i	0.141679	−	0.109029i
$19$		−	5.66168i		−	1.29888i	−0.760413	−	0.649440i	$-0.775004\pi$
$19$		−	5.66168i		−	1.29888i	0.760413	−	0.649440i	$-0.224996\pi$
$20$	1.98756	+	7.41767i	0.444432	+	1.65864i
$21$	2.43248	−	2.77762i	0.530810	−	0.606127i
$22$	0.290512	+	0.0778423i	0.0619373	+	0.0165960i
$23$	−0.188390	+	0.703082i	−0.0392821	+	0.146603i	−0.982782	−	0.184771i	$-0.940846\pi$
$23$	−0.188390	+	0.703082i	−0.0392821	+	0.146603i	0.943499	+	0.331374i	$0.107512\pi$
$24$	−0.958603	−	1.43248i	−0.195674	−	0.292404i
$25$	9.29474	+	5.36632i	1.85895	+	1.07326i
$26$			1.56598i			0.307114i
$27$	−1.02441	−	5.09417i	−0.197148	−	0.980374i
$28$	−2.91830	−	2.91830i	−0.551506	−	0.551506i
$29$	−0.799838	−	2.98504i	−0.148526	−	0.554307i	−0.999573	−	0.0292175i	$-0.990698\pi$
$29$	−0.799838	−	2.98504i	−0.148526	−	0.554307i	0.851047	−	0.525090i	$-0.175968\pi$
$30$	−1.70379	−	0.337667i	−0.311069	−	0.0616492i
$31$	0.0434097	+	0.0116316i	0.00779661	+	0.00208910i	0.262715	−	0.964873i	$-0.415382\pi$
$31$	0.0434097	+	0.0116316i	0.00779661	+	0.00208910i	−0.254919	+	0.966963i	$0.582049\pi$
$32$	−2.51637	+	1.45283i	−0.444836	+	0.256826i
$33$	1.35746	−	1.55007i	0.236303	−	0.269832i
$34$	0.118269	+	1.03570i	0.0202830	+	0.177620i
$35$	−8.45517			−1.42918
$36$	−5.75748	+	0.766182i	−0.959580	+	0.127697i
$37$	1.68986	−	1.68986i	0.277812	−	0.277812i	−0.554423	−	0.832235i	$-0.687061\pi$
$37$	1.68986	−	1.68986i	0.277812	−	0.277812i	0.832235	+	0.554423i	$0.187061\pi$
$38$	0.715709	−	1.23964i	0.116103	−	0.201097i
$39$	9.62513	+	4.73822i	1.54125	+	0.758723i
$40$	−1.02160	+	3.81267i	−0.161530	+	0.602836i
$41$	−0.174405	+	0.650890i	−0.0272375	+	0.101652i	−0.978206	−	0.207635i	$-0.933424\pi$
$41$	−0.174405	+	0.650890i	−0.0272375	+	0.101652i	0.950969	+	0.309286i	$0.100090\pi$
$42$	0.883726	−	0.300674i	0.136362	−	0.0463950i
$43$	−0.442424	−	0.255434i	−0.0674691	−	0.0389533i	0.465886	−	0.884845i	$-0.345736\pi$
$43$	−0.442424	−	0.255434i	−0.0674691	−	0.0389533i	−0.533355	+	0.845891i	$0.679069\pi$
$44$	−1.62857	−	1.62857i	−0.245516	−	0.245516i
$45$	−7.23063	+	9.45049i	−1.07788	+	1.40880i
$46$	−0.130127	+	0.130127i	−0.0191862	+	0.0191862i
$47$	−4.74104	+	8.21172i	−0.691551	+	1.19780i	0.279778	+	0.960065i	$0.409739\pi$
$47$	−4.74104	+	8.21172i	−0.691551	+	1.19780i	−0.971330	+	0.237737i	$0.923594\pi$
$48$	0.414520	+	6.25728i	0.0598308	+	0.903161i
$49$	−2.12692	+	1.22798i	−0.303845	+	0.175425i
$50$	1.35674	+	2.34995i	0.191873	+	0.332333i
$51$	6.72364	+	2.40680i	0.941498	+	0.337019i
$52$	5.99596	−	10.3853i	0.831490	−	1.44018i
$53$			7.10456i			0.975886i	0.872875	+	0.487943i	$0.162253\pi$
$53$			7.10456i			0.975886i	−0.872875	+	0.487943i	$0.837747\pi$
$54$	0.419670	−	1.24488i	0.0571099	−	0.169407i
$55$	−4.71845			−0.636236
$56$	−0.549038	−	2.04904i	−0.0733683	−	0.273814i
$57$	−5.45380	−	8.14985i	−0.722374	−	1.07947i
$58$	0.202219	−	0.754693i	0.0265527	−	0.0990961i
$59$	7.91388	−	4.56908i	1.03030	−	0.594844i	0.113229	−	0.993569i	$-0.463881\pi$
$59$	7.91388	−	4.56908i	1.03030	−	0.594844i	0.917070	+	0.398725i	$0.130547\pi$
$60$	10.0064	+	8.76297i	1.29182	+	1.13129i
$61$	−5.59065	+	1.49801i	−0.715809	+	0.191800i	−0.598301	−	0.801271i	$-0.704157\pi$
$61$	−5.59065	+	1.49801i	−0.715809	+	0.191800i	−0.117508	+	0.993072i	$0.537491\pi$
$62$	0.00803432	+	0.00803432i	0.00102036	+	0.00102036i
$63$	0.825848	−	6.34148i	0.104047	−	0.798952i
$64$	6.50650			0.813312
$65$	−6.35862	−	23.7307i	−0.788689	−	2.94343i
$66$	0.493168	−	0.167793i	0.0607048	−	0.0206539i
$67$	−1.68697	−	2.92191i	−0.206096	−	0.356968i	0.744386	−	0.667750i	$-0.232742\pi$
$67$	−1.68697	−	2.92191i	−0.206096	−	0.356968i	−0.950481	+	0.310782i	$0.899409\pi$
$68$	3.18122	−	7.32139i	0.385780	−	0.887848i
$69$	0.406084	+	1.19354i	0.0488868	+	0.143685i
$70$	−1.85129	−	1.06884i	−0.221271	−	0.127751i
$71$	2.32488	−	2.32488i	0.275912	−	0.275912i	−0.555563	−	0.831475i	$-0.687497\pi$
$71$	2.32488	−	2.32488i	0.275912	−	0.275912i	0.831475	+	0.555563i	$0.187497\pi$
$72$	−2.75977	−	1.13861i	−0.325242	−	0.134187i
$73$	−8.24518	+	8.24518i	−0.965026	+	0.965026i	−0.999409	−	0.0343828i	$-0.989053\pi$
$73$	−8.24518	+	8.24518i	−0.965026	+	0.965026i	0.0343828	+	0.999409i	$0.489053\pi$
$74$	0.583622	−	0.156381i	0.0678447	−	0.0181789i
$75$	18.5488	−	1.22879i	2.14183	−	0.141888i
$76$	−9.49291	+	5.48073i	−1.08891	+	0.628683i
$77$	2.19609	−	1.26791i	0.250268	−	0.144492i
$78$	1.50848	+	2.25419i	0.170802	+	0.255237i
$79$	−0.124126	+	0.0332596i	−0.0139653	+	0.00374199i	−0.265795	−	0.964030i	$-0.585634\pi$
$79$	−0.124126	+	0.0332596i	−0.0139653	+	0.00374199i	0.251830	+	0.967772i	$0.418968\pi$
$80$	10.1546	−	10.1546i	1.13532	−	1.13532i
$81$	−6.38174	−	6.34613i	−0.709082	−	0.705126i
$82$	−0.120467	+	0.120467i	−0.0133034	+	0.0133034i
$83$	5.37265	+	3.10190i	0.589725	+	0.340478i	0.764989	−	0.644043i	$-0.222744\pi$
$83$	5.37265	+	3.10190i	0.589725	+	0.340478i	−0.175264	+	0.984522i	$0.556078\pi$
$84$	−7.01196	−	1.38967i	−0.765068	−	0.151625i
$85$	−5.99764	−	15.2146i	−0.650536	−	1.65025i
$86$	−0.0645802	−	0.111856i	−0.00696386	−	0.0120618i
$87$	−4.02678	−	3.52641i	−0.431716	−	0.378071i
$88$	−0.306394	−	1.14348i	−0.0326617	−	0.121895i
$89$	8.09524			0.858094			0.429047	−	0.903282i	$-0.358850\pi$
$89$	8.09524			0.858094			0.429047	+	0.903282i	$0.358850\pi$
$90$	−2.77783	+	1.15517i	−0.292809	+	0.121766i
$91$	9.33624	+	9.33624i	0.978704	+	0.978704i
$92$	1.36122	−	0.364738i	0.141917	−	0.0380266i
$93$	0.0736917	−	0.0250724i	0.00764147	−	0.00259989i
$94$	−2.07613	+	1.19866i	−0.214137	+	0.123632i
$95$	−5.81223	+	21.6915i	−0.596322	+	2.22550i
$96$	−2.22277	+	4.51528i	−0.226860	+	0.460839i
$97$	1.05767	+	3.94729i	0.107390	+	0.400786i	0.998605	−	0.0527947i	$-0.0168129\pi$
$97$	1.05767	+	3.94729i	0.107390	+	0.400786i	−0.891215	+	0.453581i	$0.850146\pi$
$98$	−0.620928			−0.0627232
$99$	0.460869	−	3.53890i	0.0463191	−	0.355673i
$100$		−	20.7792i		−	2.07792i
$101$	−3.57539	+	6.19276i	−0.355765	+	0.616203i	−0.987249	−	0.159186i	$-0.949113\pi$
$101$	−3.57539	+	6.19276i	−0.355765	+	0.616203i	0.631484	+	0.775389i	$0.282446\pi$
$102$	1.16791	+	1.37693i	0.115641	+	0.136336i
$103$	5.50590	+	9.53649i	0.542512	+	0.939658i	0.998759	+	0.0498052i	$0.0158601\pi$
$103$	5.50590	+	9.53649i	0.542512	+	0.939658i	−0.456247	+	0.889853i	$0.650807\pi$
$104$	5.33803	−	3.08191i	0.523437	−	0.302206i
$105$	−12.1710	+	8.14472i	−1.18777	+	0.794843i
$106$	−0.898107	+	1.55557i	−0.0872319	+	0.151090i
$107$	5.42949	−	5.42949i	0.524889	−	0.524889i	−0.394155	−	0.919044i	$-0.628963\pi$
$107$	5.42949	−	5.42949i	0.524889	−	0.524889i	0.919044	+	0.394155i	$0.128963\pi$
$108$	−7.54969	+	6.64898i	−0.726470	+	0.639799i
$109$	−7.35646	−	7.35646i	−0.704621	−	0.704621i	0.260778	−	0.965399i	$-0.416021\pi$
$109$	−7.35646	−	7.35646i	−0.704621	−	0.704621i	−0.965399	+	0.260778i	$0.916021\pi$
$110$	−1.03312	−	0.596473i	−0.0985042	−	0.0568714i
$111$	0.804698	−	4.06033i	0.0763786	−	0.385390i
$112$	−1.99753	+	7.45489i	−0.188749	+	0.704421i
$113$	3.57848	−	13.3551i	0.336635	−	1.25634i	−0.565450	−	0.824782i	$-0.691298\pi$
$113$	3.57848	−	13.3551i	0.336635	−	1.25634i	0.902085	−	0.431557i	$-0.142036\pi$
$114$	−0.163884	−	2.47387i	−0.0153491	−	0.231699i
$115$	1.44355	−	2.50031i	0.134612	−	0.233155i
$116$	−4.23072	+	4.23072i	−0.392812	+	0.392812i
$117$	18.4194	−	2.45118i	1.70287	−	0.226611i
$118$	2.31036			0.212686
$119$	6.87983	+	5.46962i	0.630673	+	0.501399i
$120$	2.20211	+	6.47234i	0.201024	+	0.590841i
$121$	−8.30074	+	4.79243i	−0.754613	+	0.435676i
$122$	−1.41346	−	0.378735i	−0.127969	−	0.0342891i
$123$	0.375939	+	1.10494i	0.0338973	+	0.0996291i
$124$	−0.0225197	−	0.0840446i	−0.00202233	−	0.00754743i
$125$	−16.0783	−	16.0783i	−1.43809	−	1.43809i
$126$	0.982467	−	1.28409i	0.0875251	−	0.114396i
$127$			10.1096i			0.897084i	0.893762	+	0.448542i	$0.148056\pi$
$127$			10.1096i			0.897084i	−0.893762	+	0.448542i	$0.851944\pi$
$128$	6.45736	+	3.72816i	0.570755	+	0.329526i
$129$	−0.882914	+	0.0584895i	−0.0777362	+	0.00514971i
$130$	1.60762	−	5.99972i	0.140998	−	0.526211i
$131$	−8.15638	−	2.18549i	−0.712626	−	0.190948i	−0.115747	−	0.993279i	$-0.536926\pi$
$131$	−8.15638	−	2.18549i	−0.712626	−	0.190948i	−0.596879	+	0.802331i	$0.703593\pi$
$132$	−3.91306	−	0.775511i	−0.340588	−	0.0674996i
$133$	−3.12366	−	11.6576i	−0.270855	−	1.01085i
$134$		−	0.853016i		−	0.0736893i
$135$	−1.30481	+	20.5689i	−0.112300	+	1.77029i
$136$	3.29766	−	2.44144i	0.282772	−	0.209352i
$137$	−1.44676	+	2.50586i	−0.123605	+	0.214090i	−0.921187	−	0.389121i	$-0.872779\pi$
$137$	−1.44676	+	2.50586i	−0.123605	+	0.214090i	0.797582	+	0.603211i	$0.206112\pi$
$138$	−0.0619654	+	0.312664i	−0.00527485	+	0.0266157i
$139$	−4.54595	−	1.21808i	−0.385582	−	0.103316i	0.0608202	−	0.998149i	$-0.480628\pi$
$139$	−4.54595	−	1.21808i	−0.385582	−	0.103316i	−0.446402	+	0.894832i	$0.647295\pi$
$140$	8.18494	+	14.1767i	0.691754	+	1.19815i
$141$	1.08561	+	16.3875i	0.0914246	+	1.38008i
$142$	0.802934	−	0.215146i	0.0673807	−	0.0180546i
$143$	5.21014	+	5.21014i	0.435694	+	0.435694i
$144$	6.62422	+	8.60789i	0.552019	+	0.717325i
$145$			12.2576i			1.01794i
$146$	−2.84761	+	0.763014i	−0.235670	+	0.0631475i
$147$	−1.87875	+	3.81646i	−0.154957	+	0.314777i
$148$	−4.46924	−	1.19753i	−0.367369	−	0.0984363i
$149$	−5.25356	−	9.09944i	−0.430389	−	0.745455i	0.566518	−	0.824049i	$-0.308290\pi$
$149$	−5.25356	−	9.09944i	−0.430389	−	0.745455i	−0.996907	+	0.0785942i	$0.974957\pi$
$150$	4.21666	+	2.07576i	0.344289	+	0.169485i
$151$	−0.878252	−	0.507059i	−0.0714711	−	0.0412639i	0.463839	−	0.885920i	$-0.346472\pi$
$151$	−0.878252	−	0.507059i	−0.0714711	−	0.0412639i	−0.535310	+	0.844656i	$0.679805\pi$
$152$	−5.63418			−0.456992
$153$	11.9969	−	3.01224i	0.969895	−	0.243525i
$154$	0.641123			0.0516631
$155$	−0.154374	−	0.0891280i	−0.0123996	−	0.00715893i
$156$	−1.37296	−	20.7252i	−0.109925	−	1.65934i
$157$	0.417298	+	0.722782i	0.0333040	+	0.0576843i	0.882197	−	0.470881i	$-0.156064\pi$
$157$	0.417298	+	0.722782i	0.0333040	+	0.0576843i	−0.848893	+	0.528565i	$0.822730\pi$
$158$	−0.0313823	−	0.00840887i	−0.00249664	−	0.000668974i
$159$	6.84370	+	10.2268i	0.542741	+	0.811040i
$160$	11.1324	−	2.98292i	0.880093	−	0.235820i
$161$			1.55161i			0.122284i
$162$	−0.595072	−	2.19624i	−0.0467533	−	0.172553i
$163$	−17.8094	−	17.8094i	−1.39494	−	1.39494i	−0.813822	−	0.581114i	$-0.802617\pi$
$163$	−17.8094	−	17.8094i	−1.39494	−	1.39494i	−0.581114	−	0.813822i	$-0.697383\pi$
$164$	1.26017	−	0.337663i	0.0984031	−	0.0263670i
$165$	−6.79209	+	4.54520i	−0.528763	+	0.353844i
$166$	0.784240	+	1.35834i	0.0608689	+	0.105428i
$167$	−2.60897	−	0.699072i	−0.201888	−	0.0540958i	0.156458	−	0.987685i	$-0.449993\pi$
$167$	−2.60897	−	0.699072i	−0.201888	−	0.0540958i	−0.358346	+	0.933589i	$0.616659\pi$
$168$	−2.76413	−	2.42066i	−0.213257	−	0.186758i
$169$	−12.6823	+	21.9664i	−0.975563	+	1.68972i
$170$	0.610113	−	4.08946i	0.0467935	−	0.313647i
$171$	−15.7012	−	6.47794i	−1.20070	−	0.495380i
$172$			0.989080i			0.0754167i
$173$	−2.66610	−	9.95002i	−0.202700	−	0.756486i	−0.990138	−	0.140093i	$-0.955260\pi$
$173$	−2.66610	−	9.95002i	−0.202700	−	0.756486i	0.787438	−	0.616393i	$-0.211407\pi$
$174$	−0.435894	−	1.28116i	−0.0330450	−	0.0971242i
$175$	22.0990	+	5.92140i	1.67052	+	0.447616i
$176$	−1.11473	+	4.16024i	−0.0840261	+	0.313590i
$177$	6.99051	−	14.2004i	0.525439	−	1.06737i
$178$	1.77248	+	1.02334i	0.132853	+	0.0767027i
$179$			9.03233i			0.675108i	0.941306	+	0.337554i	$0.109600\pi$
$179$			9.03233i			0.675108i	−0.941306	+	0.337554i	$0.890400\pi$
$180$	22.8451	+	2.97511i	1.70277	+	0.221752i
$181$	15.5693	+	15.5693i	1.15726	+	1.15726i	0.985063	+	0.172196i	$0.0550863\pi$
$181$	15.5693	+	15.5693i	1.15726	+	1.15726i	0.172196	+	0.985063i	$0.444914\pi$
$182$	0.863981	+	3.22442i	0.0640425	+	0.239010i
$183$	−6.60459	+	7.54172i	−0.488225	+	0.557500i
$184$	0.699666	+	0.187475i	0.0515801	+	0.0138208i
$185$	−8.20915	+	4.73955i	−0.603549	+	0.348459i
$186$	0.0193045	+	0.00382587i	0.00141548	+	0.000280527i
$187$	3.83933	+	3.05235i	0.280759	+	0.223210i
$188$	18.3580			1.33890
$189$	−4.91985	−	9.92393i	−0.357867	−	0.721859i
$190$	−4.01469	+	4.01469i	−0.291257	+	0.291257i
$191$	−11.6017	+	20.0948i	−0.839472	+	1.45401i	0.0508643	+	0.998706i	$0.483802\pi$
$191$	−11.6017	+	20.0948i	−0.839472	+	1.45401i	−0.890337	+	0.455303i	$0.849531\pi$
$192$	9.36594	−	6.26760i	0.675928	−	0.452325i
$193$	4.48595	−	16.7418i	0.322906	−	1.20510i	−0.593494	−	0.804838i	$-0.702252\pi$
$193$	4.48595	−	16.7418i	0.322906	−	1.20510i	0.916400	−	0.400263i	$-0.131081\pi$
$194$	−0.267407	+	0.997976i	−0.0191987	+	0.0716505i
$195$	−32.0124	−	28.0346i	−2.29246	−	2.00760i
$196$	4.11788	+	2.37746i	0.294134	+	0.169819i
$197$	−2.14303	−	2.14303i	−0.152685	−	0.152685i	0.626631	−	0.779316i	$-0.284433\pi$
$197$	−2.14303	−	2.14303i	−0.152685	−	0.152685i	−0.779316	+	0.626631i	$0.784433\pi$
$198$	0.548271	−	0.716594i	0.0389639	−	0.0509261i
$199$	2.45708	−	2.45708i	0.174178	−	0.174178i	−0.614634	−	0.788812i	$-0.710696\pi$
$199$	2.45708	−	2.45708i	0.174178	−	0.174178i	0.788812	+	0.614634i	$0.210696\pi$
$200$	5.34025	−	9.24958i	0.377613	−	0.654044i
$201$	−5.24297	−	2.58099i	−0.369810	−	0.182049i
$202$	−1.56569	+	0.903950i	−0.110161	+	0.0636017i
$203$	−3.29380	−	5.70503i	−0.231179	−	0.400414i
$204$	−2.47328	−	13.6034i	−0.173164	−	0.952426i
$205$	1.33639	−	2.31470i	0.0933378	−	0.161666i
$206$			2.78406i			0.193975i
$207$	1.73427	+	1.32690i	0.120540	+	0.0922258i
$208$	−22.4255			−1.55493
$209$	−1.74317	−	6.50561i	−0.120578	−	0.450002i
$210$	−3.69448	+	0.244744i	−0.254943	+	0.0168890i
$211$	−2.50227	+	9.33859i	−0.172263	+	0.642895i	0.824738	+	0.565514i	$0.191322\pi$
$211$	−2.50227	+	9.33859i	−0.172263	+	0.642895i	−0.997002	+	0.0773805i	$0.975344\pi$
$212$	11.9122	−	6.87749i	0.818131	−	0.472348i
$213$	1.10709	−	5.58612i	0.0758563	−	0.382754i
$214$	1.87516	−	0.502448i	0.128183	−	0.0343467i
$215$	1.43283	+	1.43283i	0.0977181	+	0.0977181i
$216$	−5.06942	+	1.01943i	−0.344930	+	0.0693637i
$217$	0.0957998			0.00650331
$218$	−0.680771	−	2.54067i	−0.0461076	−	0.172076i
$219$	−3.92628	+	19.8112i	−0.265314	+	1.33872i
$220$	4.56765	+	7.91140i	0.307951	+	0.533386i
$221$	−10.1774	+	23.4226i	−0.684605	+	1.57558i
$222$	0.689469	−	0.787299i	0.0462742	−	0.0528401i
$223$	2.31875	+	1.33873i	0.155275	+	0.0896480i	0.575624	−	0.817714i	$-0.304759\pi$
$223$	2.31875	+	1.33873i	0.155275	+	0.0896480i	−0.420349	+	0.907362i	$0.638092\pi$
$224$	−4.37976	+	4.37976i	−0.292635	+	0.292635i
$225$	25.5169	−	19.6366i	1.70113	−	1.30911i
$226$	2.47177	−	2.47177i	0.164420	−	0.164420i
$227$	19.5602	−	5.24113i	1.29825	−	0.347866i	0.457465	−	0.889228i	$-0.348758\pi$
$227$	19.5602	−	5.24113i	1.29825	−	0.347866i	0.840790	+	0.541361i	$0.182091\pi$
$228$	−8.38530	+	17.0337i	−0.555330	+	1.12809i
$229$	−2.37683	+	1.37227i	−0.157066	+	0.0906819i	−0.576473	−	0.817116i	$-0.695571\pi$
$229$	−2.37683	+	1.37227i	−0.157066	+	0.0906819i	0.419407	+	0.907798i	$0.362238\pi$
$230$	0.632142	−	0.364967i	0.0416822	−	0.0240652i
$231$	1.93986	−	3.94059i	0.127633	−	0.259272i
$232$	−2.97053	+	0.795952i	−0.195025	+	0.0522568i
$233$	−7.71254	+	7.71254i	−0.505266	+	0.505266i	−0.913070	−	0.407804i	$-0.866295\pi$
$233$	−7.71254	+	7.71254i	−0.505266	+	0.505266i	0.407804	+	0.913070i	$0.366295\pi$
$234$	4.34285	+	1.79175i	0.283901	+	0.117130i
$235$	26.5943	−	26.5943i	1.73482	−	1.73482i
$236$	−15.3219	−	8.84610i	−0.997371	−	0.575832i
$237$	−0.146638	+	0.167445i	−0.00952519	+	0.0108767i
$238$	0.814933	+	2.06729i	0.0528243	+	0.134002i
$239$	−10.8739	−	18.8341i	−0.703371	−	1.21827i	−0.967276	−	0.253726i	$-0.918344\pi$
$239$	−10.8739	−	18.8341i	−0.703371	−	1.21827i	0.263905	−	0.964549i	$-0.414990\pi$
$240$	4.83552	−	24.3990i	0.312131	−	1.57495i
$241$	−1.51021	−	5.63618i	−0.0972812	−	0.363059i	0.900074	−	0.435737i	$-0.143512\pi$
$241$	−1.51021	−	5.63618i	−0.0972812	−	0.363059i	−0.997355	+	0.0726781i	$0.976845\pi$
$242$	−2.42330			−0.155776
$243$	−15.2995	−	2.98767i	−0.981462	−	0.191659i
$244$	7.92367	+	7.92367i	0.507261	+	0.507261i
$245$	9.40946	−	2.52126i	0.601148	−	0.161077i
$246$	−0.0573655	+	0.289454i	−0.00365749	+	0.0184549i
$247$	30.3698	−	17.5340i	1.93238	−	1.11566i
$248$	0.0115751	−	0.0431988i	0.000735019	−	0.00274313i
$249$	10.7218	−	0.710277i	0.679467	−	0.0450119i
$250$	−1.48790	−	5.55291i	−0.0941029	−	0.351197i
$251$	−0.160391			−0.0101238			−0.00506188	−	0.999987i	$-0.501611\pi$
$251$	−0.160391			−0.0101238			−0.00506188	+	0.999987i	$0.501611\pi$
$252$	−11.4322	+	4.75411i	−0.720160	+	0.299481i
$253$			0.865886i			0.0544378i
$254$	−1.27799	+	2.21354i	−0.0801879	+	0.138890i
$255$	−23.2894	−	16.1236i	−1.45844	−	1.00970i
$256$	−5.56393	−	9.63700i	−0.347745	−	0.602313i
$257$	15.7573	−	9.09748i	0.982913	−	0.567485i	0.0797648	−	0.996814i	$-0.474583\pi$
$257$	15.7573	−	9.09748i	0.982913	−	0.567485i	0.903148	+	0.429329i	$0.141250\pi$
$258$	−0.200711	−	0.0988051i	−0.0124957	−	0.00615134i
$259$	2.54717	−	4.41183i	0.158274	−	0.274138i
$260$	−33.6337	+	33.6337i	−2.08587	+	2.08587i
$261$	−9.19338	−	1.19725i	−0.569056	−	0.0741079i
$262$	−1.50959	−	1.50959i	−0.0932629	−	0.0932629i
$263$	15.2224	+	8.78864i	0.938651	+	0.541930i	0.889537	−	0.456863i	$-0.151027\pi$
$263$	15.2224	+	8.78864i	0.938651	+	0.541930i	0.0491139	+	0.998793i	$0.484360\pi$
$264$	−1.54254	−	1.35086i	−0.0949366	−	0.0831398i
$265$	7.29347	−	27.2196i	0.448034	−	1.67209i
$266$	0.789740	−	2.94735i	0.0484221	−	0.180714i
$267$	11.6529	−	7.79801i	0.713145	−	0.477230i
$268$	−3.26610	+	5.65705i	−0.199509	+	0.345559i
$269$	−12.6878	+	12.6878i	−0.773588	+	0.773588i	−0.978732	−	0.205143i	$-0.934234\pi$
$269$	−12.6878	+	12.6878i	−0.773588	+	0.773588i	0.205143	+	0.978732i	$0.434234\pi$
$270$	−2.88586	+	4.33868i	−0.175628	+	0.264044i
$271$	20.3520			1.23630			0.618148	−	0.786062i	$-0.287883\pi$
$271$	20.3520			1.23630			0.618148	+	0.786062i	$0.287883\pi$
$272$	−14.8316	+	1.69366i	−0.899296	+	0.102693i
$273$	22.4327	+	4.44583i	1.35769	+	0.269074i
$274$	−0.633545	+	0.365778i	−0.0382739	+	0.0220974i
$275$	12.3324	+	3.30447i	0.743674	+	0.199267i
$276$	1.60810	−	1.83627i	0.0967961	−	0.110531i
$277$	−6.71563	−	25.0631i	−0.403503	−	1.50589i	−0.806800	−	0.590824i	$-0.798803\pi$
$277$	−6.71563	−	25.0631i	−0.403503	−	1.50589i	0.403297	−	0.915069i	$-0.367864\pi$
$278$	−0.841369	−	0.841369i	−0.0504620	−	0.0504620i
$279$	0.0819254	−	0.107077i	0.00490474	−	0.00641054i
$280$			8.41409i			0.502838i
$281$	1.48219	+	0.855744i	0.0884202	+	0.0510494i	0.543558	−	0.839372i	$-0.317077\pi$
$281$	1.48219	+	0.855744i	0.0884202	+	0.0510494i	−0.455138	+	0.890421i	$0.650410\pi$
$282$	−1.83389	+	3.72534i	−0.109207	+	0.221840i
$283$	−0.719725	+	2.68605i	−0.0427832	+	0.159669i	−0.984013	−	0.178099i	$-0.943005\pi$
$283$	−0.719725	+	2.68605i	−0.0427832	+	0.159669i	0.941229	+	0.337768i	$0.109672\pi$
$284$	−6.14868	−	1.64753i	−0.364857	−	0.0977632i
$285$	12.5285	+	36.8232i	0.742126	+	2.18122i
$286$	0.482149	+	1.79941i	0.0285101	+	0.106401i
$287$			1.43643i			0.0847899i
$288$	1.14988	+	8.64079i	0.0677574	+	0.509163i
$289$	−4.96207	+	16.2597i	−0.291886	+	0.956453i
$290$	−1.54952	+	2.68385i	−0.0909910	+	0.157601i
$291$	5.32485	+	4.66318i	0.312148	+	0.273361i
$292$	21.8063	+	5.84298i	1.27612	+	0.341935i
$293$	3.16748	+	5.48624i	0.185046	+	0.320509i	0.943592	−	0.331110i	$-0.107423\pi$
$293$	3.16748	+	5.48624i	0.185046	+	0.320509i	−0.758546	+	0.651620i	$0.774090\pi$
$294$	−0.893809	+	0.598129i	−0.0521280	+	0.0348836i
$295$	−35.0109	+	9.38115i	−2.03841	+	0.546192i
$296$	−1.68165	−	1.68165i	−0.0977441	−	0.0977441i
$297$	−2.74555	−	5.53810i	−0.159313	−	0.321353i
$298$		−	2.65647i		−	0.153885i
$299$	−4.35483	+	1.16687i	−0.251846	+	0.0674820i
$300$	−20.0163	−	29.9112i	−1.15564	−	1.72692i
$301$	−1.05190	−	0.281855i	−0.0606304	−	0.0162459i
$302$	−0.128197	−	0.222044i	−0.00737693	−	0.0127772i
$303$	0.818696	+	12.3584i	0.0470329	+	0.709973i
$304$	17.7522	+	10.2492i	1.01816	+	0.587834i
$305$	22.9572			1.31453
$306$	3.00755	+	0.857025i	0.171930	+	0.0489929i
$307$	−6.06447			−0.346118			−0.173059	−	0.984911i	$-0.555365\pi$
$307$	−6.06447			−0.346118			−0.173059	+	0.984911i	$0.555365\pi$
$308$	−4.25181	−	2.45478i	−0.242269	−	0.139874i
$309$	17.1119	+	8.42380i	0.973464	+	0.479213i
$310$	−0.0225338	−	0.0390297i	−0.00127984	−	0.00221674i
$311$	7.29002	+	1.95336i	0.413379	+	0.110765i	0.459514	−	0.888171i	$-0.348024\pi$
$311$	7.29002	+	1.95336i	0.413379	+	0.110765i	−0.0461346	+	0.998935i	$0.514690\pi$
$312$	4.71520	−	9.57837i	0.266946	−	0.542268i
$313$	−17.3983	+	4.66185i	−0.983407	+	0.263503i	−0.714479	−	0.699657i	$-0.753336\pi$
$313$	−17.3983	+	4.66185i	−0.983407	+	0.263503i	−0.268928	+	0.963160i	$0.586670\pi$
$314$			0.211007i			0.0119078i
$315$	−9.67417	+	23.4482i	−0.545077	+	1.32116i
$316$	0.175925	+	0.175925i	0.00989658	+	0.00989658i
$317$	−20.5195	+	5.49818i	−1.15249	+	0.308809i	−0.783962	−	0.620809i	$-0.786804\pi$
$317$	−20.5195	+	5.49818i	−1.15249	+	0.308809i	−0.368527	+	0.929617i	$0.620138\pi$
$318$	0.205649	+	3.10433i	0.0115322	+	0.174082i
$319$	−1.83812	−	3.18372i	−0.102915	−	0.178254i
$320$	−24.9283	−	6.67951i	−1.39353	−	0.373396i
$321$	2.58548	−	13.0457i	0.144307	−	0.728143i
$322$	−0.196144	+	0.339731i	−0.0109307	+	0.0189325i
$323$	18.7615	−	13.8901i	1.04392	−	0.772868i
$324$	−4.46274	+	16.8435i	−0.247930	+	0.935752i
$325$			66.4771i			3.68749i
$326$	−1.64809	−	6.15075i	−0.0912791	−	0.340658i
$327$	−17.6758	−	3.50308i	−0.977473	−	0.193721i
$328$	0.647727	+	0.173558i	0.0357648	+	0.00958314i
$329$	−5.23144	+	19.5240i	−0.288418	+	1.07639i
$330$	−2.06172	+	0.136581i	−0.113494	+	0.00751853i
$331$	−3.80655	−	2.19772i	−0.209227	−	0.120797i	0.391725	−	0.920082i	$-0.371878\pi$
$331$	−3.80655	−	2.19772i	−0.209227	−	0.120797i	−0.600952	+	0.799285i	$0.705212\pi$
$332$		−	12.0111i		−	0.659193i
$333$	−2.75291	−	6.61990i	−0.150858	−	0.362768i
$334$	−0.482872	−	0.482872i	−0.0264216	−	0.0264216i
$335$	3.46364	+	12.9265i	0.189239	+	0.706250i
$336$	4.30577	+	12.6553i	0.234899	+	0.690404i
$337$	25.6582	+	6.87510i	1.39769	+	0.374511i	0.877516	−	0.479548i	$-0.159199\pi$
$337$	25.6582	+	6.87510i	1.39769	+	0.374511i	0.520177	+	0.854058i	$0.325866\pi$
$338$	−5.55367	+	3.20641i	−0.302080	+	0.174406i
$339$	−7.71359	−	22.6714i	−0.418944	−	1.23134i
$340$	−19.7042	+	24.7845i	−1.06861	+	1.34413i
$341$	0.0534616			0.00289511
$342$	−2.61894	−	3.40320i	−0.141616	−	0.184024i
$343$	−14.2532	+	14.2532i	−0.769599	+	0.769599i
$344$	−0.254193	+	0.440275i	−0.0137052	+	0.0237380i
$345$	−0.330546	−	4.98968i	−0.0177960	−	0.268635i
$346$	0.674058	−	2.51562i	0.0362376	−	0.135241i
$347$	−4.11787	+	15.3681i	−0.221059	+	0.825003i	0.762886	+	0.646533i	$0.223782\pi$
$347$	−4.11787	+	15.3681i	−0.221059	+	0.825003i	−0.983945	+	0.178470i	$0.942885\pi$
$348$	−2.01463	+	10.1654i	−0.107995	+	0.544922i
$349$	−19.6887	−	11.3673i	−1.05391	−	0.608477i	−0.130171	−	0.991492i	$-0.541553\pi$
$349$	−19.6887	−	11.3673i	−1.05391	−	0.608477i	−0.923743	+	0.383014i	$0.874886\pi$
$350$	4.09010	+	4.09010i	0.218625	+	0.218625i
$351$	24.1530	−	21.2715i	1.28919	−	1.13539i
$352$	−2.44415	+	2.44415i	−0.130274	+	0.130274i
$353$	7.45918	−	12.9197i	0.397012	−	0.687645i	−0.596343	−	0.802729i	$-0.703380\pi$
$353$	7.45918	−	12.9197i	0.397012	−	0.687645i	0.993356	+	0.115084i	$0.0367137\pi$
$354$	3.32571	−	2.22553i	0.176759	−	0.118286i
$355$	−11.2940	+	6.52058i	−0.599422	+	0.346076i
$356$	−7.83651	−	13.5732i	−0.415334	−	0.719380i
$357$	15.1721	+	1.24614i	0.802994	+	0.0659529i
$358$	−1.14180	+	1.97766i	−0.0603461	+	0.104523i
$359$		−	25.3903i		−	1.34005i	−0.742339	−	0.670024i	$-0.766284\pi$
$359$		−	25.3903i		−	1.34005i	0.742339	−	0.670024i	$-0.233716\pi$
$360$	9.40457	+	7.19550i	0.495665	+	0.379236i
$361$	−13.0547			−0.687087
$362$	1.44079	+	5.37712i	0.0757265	+	0.282615i
$363$	−7.33223	+	14.8945i	−0.384842	+	0.781761i
$364$	6.61617	−	24.6919i	0.346781	−	1.29421i
$365$	40.0541	−	23.1252i	2.09653	−	1.21043i
$366$	−2.39947	+	0.816381i	−0.125422	+	0.0426729i
$367$	10.0237	−	2.68585i	0.523235	−	0.140200i	0.0124724	−	0.999922i	$-0.496030\pi$
$367$	10.0237	−	2.68585i	0.523235	−	0.140200i	0.510762	+	0.859722i	$0.329363\pi$
$368$	−1.86347	−	1.86347i	−0.0971402	−	0.0971402i
$369$	1.60553	+	1.22840i	0.0835803	+	0.0639478i
$370$	−2.39656			−0.124591
$371$	3.91972	+	14.6286i	0.203502	+	0.759478i
$372$	−0.113375	−	0.0992872i	−0.00587823	−	0.00514780i
$373$	−14.6963	−	25.4548i	−0.760946	−	1.31800i	−0.942363	−	0.334591i	$-0.891402\pi$
$373$	−14.6963	−	25.4548i	−0.760946	−	1.31800i	0.181418	−	0.983406i	$-0.441931\pi$
$374$	0.454778	+	1.15366i	0.0235160	+	0.0596544i
$375$	−38.6323	−	7.65636i	−1.99496	−	0.395373i
$376$	8.17182	+	4.71800i	0.421429	+	0.243312i
$377$	13.5349	−	13.5349i	0.697085	−	0.697085i
$378$	0.177292	−	2.79481i	0.00911893	−	0.143750i
$379$	23.3276	−	23.3276i	1.19826	−	1.19826i	0.223569	−	0.974688i	$-0.428229\pi$
$379$	23.3276	−	23.3276i	1.19826	−	1.19826i	0.974688	−	0.223569i	$-0.0717708\pi$
$380$	41.9965	−	11.2529i	2.15438	−	0.577263i
$381$	9.73842	+	14.5525i	0.498915	+	0.745549i
$382$	−5.08048	+	2.93322i	−0.259940	+	0.150076i
$383$	9.43624	−	5.44802i	0.482169	−	0.278381i	−0.239151	−	0.970982i	$-0.576869\pi$
$383$	9.43624	−	5.44802i	0.482169	−	0.278381i	0.721320	+	0.692602i	$0.243536\pi$
$384$	12.8865	−	0.853677i	0.657610	−	0.0435640i
$385$	−9.71549	+	2.60326i	−0.495147	+	0.132674i
$386$	3.09859	−	3.09859i	0.157714	−	0.157714i
$387$	−1.21459	+	0.934690i	−0.0617411	+	0.0475130i
$388$	5.59453	−	5.59453i	0.284019	−	0.284019i
$389$	−21.5125	−	12.4202i	−1.09073	−	0.629730i	−0.156956	−	0.987606i	$-0.550168\pi$
$389$	−21.5125	−	12.4202i	−1.09073	−	0.629730i	−0.933769	+	0.357875i	$0.883501\pi$
$390$	−3.46530	−	10.1850i	−0.175472	−	0.515740i
$391$	−2.79204	+	1.10063i	−0.141199	+	0.0556613i
$392$	1.22201	+	2.11658i	0.0617208	+	0.106904i
$393$	−13.8461	+	4.71094i	−0.698445	+	0.237635i
$394$	−0.198318	−	0.740131i	−0.00999110	−	0.0372873i
$395$	0.509708			0.0256462
$396$	−6.37979	+	2.65306i	−0.320596	+	0.133321i
$397$	4.48358	+	4.48358i	0.225025	+	0.225025i	0.810610	−	0.585586i	$-0.199135\pi$
$397$	4.48358	+	4.48358i	0.225025	+	0.225025i	−0.585586	+	0.810610i	$0.699135\pi$
$398$	0.848592	−	0.227379i	0.0425361	−	0.0113975i
$399$	−15.7260	−	13.7719i	−0.787286	−	0.689458i
$400$	−33.6522	+	19.4291i	−1.68261	+	0.971455i
$401$	−3.10500	+	11.5880i	−0.155056	+	0.578678i	0.844044	+	0.536274i	$0.180169\pi$
$401$	−3.10500	+	11.5880i	−0.155056	+	0.578678i	−0.999101	+	0.0424047i	$0.986498\pi$
$402$	−0.821696	−	1.22789i	−0.0409825	−	0.0612418i
$403$	0.0720452	+	0.268876i	0.00358883	+	0.0133937i
$404$	13.8445			0.688789
$405$	17.9354	+	30.8653i	0.891218	+	1.53371i
$406$		−	1.66551i		−	0.0826580i
$407$	1.42146	−	2.46204i	0.0704593	−	0.122039i
$408$	2.39511	−	6.69097i	0.118575	−	0.331252i
$409$	12.5735	+	21.7779i	0.621718	+	1.07685i	0.989166	+	0.146803i	$0.0468985\pi$
$409$	12.5735	+	21.7779i	0.621718	+	1.07685i	−0.367447	+	0.930044i	$0.619768\pi$
$410$	0.585216	−	0.337875i	0.0289018	−	0.0166864i
$411$	0.331280	+	5.00076i	0.0163408	+	0.246669i
$412$	10.6599	−	18.4634i	0.525173	−	0.909627i
$413$	13.7742	−	13.7742i	0.677782	−	0.677782i
$414$	0.211986	+	0.509762i	0.0104186	+	0.0250534i
$415$	−17.3998	−	17.3998i	−0.854122	−	0.854122i
$416$	−15.5862	−	8.99869i	−0.764176	−	0.441197i
$417$	−7.71713	+	2.62564i	−0.377910	+	0.128578i
$418$	0.440719	−	1.64478i	0.0215563	−	0.0804490i
$419$	−5.58490	+	20.8431i	−0.272840	+	1.01825i	0.684435	+	0.729074i	$0.260049\pi$
$419$	−5.58490	+	20.8431i	−0.272840	+	1.01825i	−0.957275	+	0.289179i	$0.906618\pi$
$420$	25.4382	+	12.5226i	1.24126	+	0.611041i
$421$	9.29851	−	16.1055i	0.453182	−	0.784934i	−0.545400	−	0.838176i	$-0.683622\pi$
$421$	9.29851	−	16.1055i	0.453182	−	0.784934i	0.998582	+	0.0532420i	$0.0169555\pi$
$422$	−1.72840	+	1.72840i	−0.0841370	+	0.0841370i
$423$	17.3485	+	22.5437i	0.843514	+	1.09611i
$424$	7.07004			0.343352
$425$	5.02061	+	43.9661i	0.243535	+	2.13267i
$426$	0.948557	−	1.08315i	0.0459577	−	0.0524788i
$427$	−10.6849	+	6.16893i	−0.517078	+	0.298535i
$428$	−14.3596	−	3.84763i	−0.694095	−	0.185982i
$429$	12.5187	+	2.48102i	0.604408	+	0.119785i
$430$	0.132595	+	0.494851i	0.00639429	+	0.0238638i
$431$	−7.41836	−	7.41836i	−0.357330	−	0.357330i	0.505498	−	0.862828i	$-0.331309\pi$
$431$	−7.41836	−	7.41836i	−0.357330	−	0.357330i	−0.862828	+	0.505498i	$0.831309\pi$
$432$	17.8272	+	6.00984i	0.857713	+	0.289149i
$433$		−	11.6239i		−	0.558607i	−0.960203	−	0.279303i	$-0.909897\pi$
$433$		−	11.6239i		−	0.558607i	0.960203	−	0.279303i	$-0.0901035\pi$
$434$	0.0209757	+	0.0121103i	0.00100687	+	0.000581314i
$435$	11.8076	+	17.6445i	0.566130	+	0.845991i
$436$	−5.21319	+	19.4559i	−0.249666	+	0.931767i
$437$	3.98063	+	1.06661i	0.190419	+	0.0510227i
$438$	−3.36406	+	3.84139i	−0.160741	+	0.183549i
$439$	−5.16416	−	19.2729i	−0.246472	−	0.919846i	−0.972638	−	0.232326i	$-0.925366\pi$
$439$	−5.16416	−	19.2729i	−0.246472	−	0.919846i	0.726166	−	0.687520i	$-0.241300\pi$
$440$			4.69553i			0.223850i
$441$	0.971917	+	7.30347i	0.0462817	+	0.347784i
$442$	−5.18929	+	3.84191i	−0.246829	+	0.182741i
$443$	17.7015	−	30.6600i	0.841025	−	1.45670i	−0.0480033	−	0.998847i	$-0.515286\pi$
$443$	17.7015	−	30.6600i	0.841025	−	1.45670i	0.889029	−	0.457852i	$-0.151381\pi$
$444$	−7.58691	+	2.58133i	−0.360059	+	0.122504i
$445$	−31.0152	−	8.31049i	−1.47026	−	0.393955i
$446$	0.338465	+	0.586239i	0.0160268	+	0.0277592i
$447$	−16.3277	−	8.03774i	−0.772274	−	0.380172i
$448$	13.3972	−	3.58976i	0.632956	−	0.169600i
$449$	−25.6708	−	25.6708i	−1.21148	−	1.21148i	−0.970540	−	0.240938i	$-0.922545\pi$
$449$	−25.6708	−	25.6708i	−1.21148	−	1.21148i	−0.240938	−	0.970540i	$-0.577455\pi$
$450$	8.06932	−	1.07383i	0.380392	−	0.0506210i
$451$			0.801608i			0.0377463i
$452$	−25.8565	+	6.92822i	−1.21619	+	0.325876i
$453$	−1.75266	+	0.116107i	−0.0823472	+	0.00545517i
$454$	4.94531	+	1.32509i	0.232095	+	0.0621897i
$455$	−26.1853	−	45.3543i	−1.22759	−	2.12624i
$456$	−8.11025	+	5.42731i	−0.379797	+	0.254157i
$457$	−18.2026	−	10.5093i	−0.851484	−	0.491604i	0.00966751	−	0.999953i	$-0.496923\pi$
$457$	−18.2026	−	10.5093i	−0.851484	−	0.491604i	−0.861151	+	0.508349i	$0.830256\pi$
$458$	−0.693888			−0.0324232
$459$	14.3676	−	15.8925i	0.670624	−	0.741798i
$460$	−5.58967			−0.260620
$461$	−4.21083	−	2.43113i	−0.196118	−	0.113229i	0.398725	−	0.917070i	$-0.369453\pi$
$461$	−4.21083	−	2.43113i	−0.196118	−	0.113229i	−0.594844	+	0.803842i	$0.702786\pi$
$462$	0.922879	−	0.617582i	0.0429362	−	0.0287325i
$463$	−11.4905	−	19.9022i	−0.534010	−	0.924933i	−0.999211	−	0.0397274i	$-0.987351\pi$
$463$	−11.4905	−	19.9022i	−0.534010	−	0.924933i	0.465200	−	0.885205i	$-0.345982\pi$
$464$	10.8075	+	2.89586i	0.501726	+	0.134437i
$465$	−0.308073	+	0.0204086i	−0.0142865	+	0.000946426i
$466$	−2.66365	+	0.713723i	−0.123391	+	0.0330626i
$467$			42.0080i			1.94390i	0.235193	+	0.971949i	$0.424428\pi$
$467$			42.0080i			1.94390i	−0.235193	+	0.971949i	$0.575572\pi$
$468$	−21.9406	−	28.5108i	−1.01420	−	1.31791i
$469$	−5.08560	−	5.08560i	−0.234831	−	0.234831i
$470$	9.18478	−	2.46106i	0.423662	−	0.113520i
$471$	1.29693	+	0.638449i	0.0597595	+	0.0294182i
$472$	−4.54688	−	7.87543i	−0.209287	−	0.362496i
$473$	−0.587017	−	0.157291i	−0.0269911	−	0.00723224i
$474$	−0.0532742	+	0.0181257i	−0.00244696	+	0.000832542i
$475$	30.3824	−	52.6239i	1.39404	−	2.41455i
$476$	2.51092	−	16.8302i	0.115088	−	0.771410i
$477$	19.7027	+	8.12884i	0.902123	+	0.372194i
$478$		−	5.49838i		−	0.251490i
$479$	7.49972	+	27.9894i	0.342671	+	1.27887i	0.895309	+	0.445445i	$0.146954\pi$
$479$	7.49972	+	27.9894i	0.342671	+	1.27887i	−0.552638	+	0.833421i	$0.686379\pi$
$480$	13.1514	−	15.0175i	0.600276	−	0.685451i
$481$	14.2980	+	3.83114i	0.651934	+	0.174685i
$482$	0.381820	−	1.42497i	0.0173914	−	0.0649057i
$483$	1.49464	+	2.23351i	0.0680086	+	0.101628i
$484$	16.0709	+	9.27853i	0.730495	+	0.421751i
$485$		−	16.2090i		−	0.736012i
$486$	−2.97219	−	2.58821i	−0.134821	−	0.117404i
$487$	14.3249	+	14.3249i	0.649122	+	0.649122i	0.952781	−	0.303658i	$-0.0982082\pi$
$487$	14.3249	+	14.3249i	0.649122	+	0.649122i	−0.303658	+	0.952781i	$0.598208\pi$
$488$	1.49073	+	5.56349i	0.0674822	+	0.251847i
$489$	−42.7915	−	8.48066i	−1.93510	−	0.383509i
$490$	2.37895	+	0.637438i	0.107470	+	0.0287965i
$491$	24.6487	−	14.2310i	1.11238	−	0.642234i	0.172937	−	0.984933i	$-0.444674\pi$
$491$	24.6487	−	14.2310i	1.11238	−	0.642234i	0.939445	+	0.342699i	$0.111341\pi$
$492$	1.48872	−	1.69996i	0.0671168	−	0.0766402i
$493$	7.92941	−	9.97384i	0.357123	−	0.449199i
$494$	8.86609			0.398904
$495$	−5.39872	+	13.0854i	−0.242654	+	0.588145i
$496$	−0.115055	+	0.115055i	−0.00516610	+	0.00516610i
$497$	3.50434	−	6.06970i	0.157191	−	0.272263i
$498$	2.43736	+	1.19986i	0.109221	+	0.0537668i
$499$	1.30751	−	4.87968i	0.0585320	−	0.218445i	−0.930465	−	0.366381i	$-0.880597\pi$
$499$	1.30751	−	4.87968i	0.0585320	−	0.218445i	0.988997	+	0.147937i	$0.0472632\pi$
$500$	−11.3940	+	42.5229i	−0.509554	+	1.90168i
$501$	−4.42895	+	1.50688i	−0.197871	+	0.0673226i
$502$	−0.0351181	−	0.0202754i	−0.00156740	−	0.000904936i
$503$	13.3944	+	13.3944i	0.597227	+	0.597227i	0.939574	−	0.342346i	$-0.111222\pi$
$503$	13.3944	+	13.3944i	0.597227	+	0.597227i	−0.342346	+	0.939574i	$0.611222\pi$
$504$	−6.31067	−	0.821836i	−0.281100	−	0.0366075i
$505$	20.0558	−	20.0558i	0.892470	−	0.892470i
$506$	−0.109459	+	0.189589i	−0.00486605	+	0.00842824i
$507$	2.90401	+	43.8368i	0.128972	+	1.94686i
$508$	16.9507	−	9.78651i	0.752067	−	0.434206i
$509$	−10.9921	−	19.0388i	−0.487214	−	0.843880i	0.512677	−	0.858581i	$-0.328654\pi$
$509$	−10.9921	−	19.0388i	−0.487214	−	0.843880i	−0.999892	+	0.0147010i	$0.995320\pi$
$510$	−3.06107	−	6.47438i	−0.135546	−	0.286691i
$511$	−12.4282	+	21.5262i	−0.549789	+	0.952263i
$512$		−	17.7260i		−	0.783388i
$513$	−28.8416	+	5.79989i	−1.27339	+	0.256071i
$514$	4.60015			0.202904
$515$	−11.3046	−	42.1893i	−0.498140	−	1.85908i
$516$	0.952764	+	1.42376i	0.0419431	+	0.0626773i
$517$	−2.91943	+	10.8955i	−0.128396	+	0.479182i
$518$	1.11542	−	0.643990i	0.0490089	−	0.0282953i
$519$	−13.4225	−	11.7546i	−0.589181	−	0.515969i
$520$	−23.6154	+	6.32772i	−1.03560	+	0.277489i
$521$	2.16814	+	2.16814i	0.0949880	+	0.0949880i	0.753004	−	0.658016i	$-0.228604\pi$
$521$	2.16814	+	2.16814i	0.0949880	+	0.0949880i	−0.658016	+	0.753004i	$0.728604\pi$
$522$	−1.86157	−	1.42430i	−0.0814789	−	0.0623400i
$523$	−8.39511			−0.367093			−0.183546	−	0.983011i	$-0.558758\pi$
$523$	−8.39511			−0.367093			−0.183546	+	0.983011i	$0.558758\pi$
$524$	4.23129	+	15.7914i	0.184845	+	0.689850i
$525$	37.5149	−	12.7639i	1.63728	−	0.557060i
$526$	2.22199	+	3.84860i	0.0968835	+	0.167807i
$527$	0.0679552	+	0.172386i	0.00296018	+	0.00750925i
$528$	2.40286	+	7.06236i	0.104571	+	0.307350i
$529$	19.4598	+	11.2351i	0.846076	+	0.488482i
$530$	5.03784	−	5.03784i	0.218830	−	0.218830i
$531$	−3.61633	−	27.1749i	−0.156935	−	1.17929i
$532$	−16.5225	+	16.5225i	−0.716340	+	0.716340i
$533$	−4.03156	+	1.08025i	−0.174626	+	0.0467909i
$534$	3.53721	−	0.234326i	0.153070	−	0.0101403i
$535$	−26.3758	+	15.2281i	−1.14033	+	0.658367i
$536$	−2.90771	+	1.67877i	−0.125594	+	0.0725118i
$537$	8.70069	+	13.0018i	0.375463	+	0.561069i
$538$	−4.38193	+	1.17414i	−0.188919	+	0.0506206i
$539$	−2.06587	+	2.06587i	−0.0889834	+	0.0889834i
$540$	35.7508	−	17.7237i	1.53847	−	0.762707i
$541$	−9.57793	+	9.57793i	−0.411787	+	0.411787i	−0.882361	−	0.470574i	$-0.844047\pi$
$541$	−9.57793	+	9.57793i	−0.411787	+	0.411787i	0.470574	+	0.882361i	$0.344047\pi$
$542$	4.45614	+	2.57275i	0.191408	+	0.110509i
$543$	37.4093	+	7.41397i	1.60539	+	0.318164i
$544$	−10.9879	−	4.77435i	−0.471102	−	0.204699i
$545$	20.6326	+	35.7368i	0.883805	+	1.53080i
$546$	4.34971	+	3.80921i	0.186150	+	0.163019i
$547$	8.93403	+	33.3422i	0.381991	+	1.42561i	0.842855	+	0.538141i	$0.180873\pi$
$547$	8.93403	+	33.3422i	0.381991	+	1.42561i	−0.460864	+	0.887471i	$0.652460\pi$
$548$	5.60208			0.239309
$549$	−2.24232	+	17.2182i	−0.0956998	+	0.734855i
$550$	2.28250	+	2.28250i	0.0973263	+	0.0973263i
$551$	−16.9003	+	4.52843i	−0.719978	+	0.192918i
$552$	1.18774	−	0.404111i	0.0505537	−	0.0172001i
$553$	−0.237232	+	0.136966i	−0.0100881	+	0.00582437i
$554$	1.69788	−	6.33658i	0.0721361	−	0.269216i
$555$	−7.25133	+	14.7302i	−0.307802	+	0.625262i
$556$	2.35831	+	8.80131i	0.100014	+	0.373259i
$557$	−1.00975			−0.0427845			−0.0213923	−	0.999771i	$-0.506810\pi$
$557$	−1.00975			−0.0427845			−0.0213923	+	0.999771i	$0.506810\pi$
$558$	0.0314738	−	0.0130885i	0.00133239	−	0.000554079i
$559$		−	3.16427i		−	0.133835i
$560$	15.3062	−	26.5112i	0.646806	−	1.12030i
$561$	8.46689	+	0.695417i	0.357472	+	0.0293605i
$562$	0.216354	+	0.374736i	0.00912634	+	0.0158073i
$563$	18.4533	−	10.6540i	0.777716	−	0.449014i	−0.0579043	−	0.998322i	$-0.518442\pi$
$563$	18.4533	−	10.6540i	0.777716	−	0.449014i	0.835620	+	0.549308i	$0.185109\pi$
$564$	26.4259	−	17.6840i	1.11273	−	0.744630i
$565$	−27.4204	+	47.4935i	−1.15358	+	1.99807i
$566$	−0.497137	+	0.497137i	−0.0208962	+	0.0208962i
$567$	−16.6416	−	9.54602i	−0.698880	−	0.400895i
$568$	−2.31358	−	2.31358i	−0.0970758	−	0.0970758i
$569$	−15.8917	−	9.17509i	−0.666215	−	0.384640i	0.128426	−	0.991719i	$-0.459008\pi$
$569$	−15.8917	−	9.17509i	−0.666215	−	0.384640i	−0.794641	+	0.607079i	$0.792341\pi$
$570$	−1.91176	+	9.64633i	−0.0800749	+	0.404040i
$571$	−4.26965	+	15.9345i	−0.178679	+	0.666840i	0.817216	+	0.576331i	$0.195516\pi$
$571$	−4.26965	+	15.9345i	−0.178679	+	0.666840i	−0.995896	+	0.0905089i	$0.971151\pi$
$572$	3.69219	−	13.7794i	0.154378	−	0.576147i
$573$	2.65658	+	40.1017i	0.110980	+	1.67527i
$574$	−0.181583	+	0.314512i	−0.00757914	+	0.0131275i
$575$	−5.52400	+	5.52400i	−0.230367	+	0.230367i
$576$	7.44455	−	18.0441i	0.310190	−	0.751837i
$577$	−12.1380			−0.505314			−0.252657	−	0.967556i	$-0.581304\pi$
$577$	−12.1380			−0.505314			−0.252657	+	0.967556i	$0.581304\pi$
$578$	−3.14190	+	2.93285i	−0.130686	+	0.121990i
$579$	−9.66969	−	28.4206i	−0.401858	−	1.18112i
$580$	20.5523	−	11.8659i	0.853388	−	0.492704i
$581$	12.7739	+	3.42276i	0.529951	+	0.142000i
$582$	0.576408	+	1.69415i	0.0238929	+	0.0702247i
$583$	2.18742	+	8.16356i	0.0905936	+	0.338100i
$584$	8.20513	+	8.20513i	0.339531	+	0.339531i
$585$	−73.0863	−	9.51799i	−3.02175	−	0.393521i
$586$			1.60164i			0.0661631i
$587$	−36.4005	−	21.0158i	−1.50241	−	0.867416i	−0.999996	−	0.00278844i	$-0.999112\pi$
$587$	−36.4005	−	21.0158i	−1.50241	−	0.867416i	−0.502413	−	0.864628i	$-0.667554\pi$
$588$	8.21775	−	0.544393i	0.338894	−	0.0224504i
$589$	0.0658544	−	0.245772i	0.00271348	−	0.0101269i
$590$	−8.85166	−	2.37179i	−0.364417	−	0.0976452i
$591$	−5.14919	−	1.02049i	−0.211809	−	0.0419775i
$592$	2.23944	+	8.35769i	0.0920403	+	0.343499i
$593$			45.7907i			1.88040i	0.340627	+	0.940198i	$0.389361\pi$
$593$			45.7907i			1.88040i	−0.340627	+	0.940198i	$0.610639\pi$
$594$	0.0989389	−	1.55966i	0.00405951	−	0.0639935i
$595$	−20.7436	−	28.0184i	−0.850403	−	1.14864i
$596$	−10.1713	+	17.6172i	−0.416633	+	0.721630i
$597$	1.17004	−	5.90376i	0.0478865	−	0.241625i
$598$	−1.10101	−	0.295016i	−0.0450238	−	0.0120641i
$599$	19.4601	+	33.7059i	0.795119	+	1.37719i	0.922764	+	0.385367i	$0.125925\pi$
$599$	19.4601	+	33.7059i	0.795119	+	1.37719i	−0.127644	+	0.991820i	$0.540742\pi$
$600$	−1.22282	−	18.4587i	−0.0499212	−	0.753574i
$601$	30.8860	−	8.27589i	1.25987	−	0.337581i	0.433727	−	0.901044i	$-0.357198\pi$
$601$	30.8860	−	8.27589i	1.25987	−	0.337581i	0.826141	+	0.563464i	$0.190532\pi$
$602$	−0.194687	−	0.194687i	−0.00793483	−	0.00793483i
$603$	−10.0333	+	1.33520i	−0.408589	+	0.0543734i
$604$			1.96341i			0.0798901i
$605$	36.7224	−	9.83973i	1.49298	−	0.400042i
$606$	−1.38301	+	2.80941i	−0.0561808	+	0.114125i
$607$	−21.8683	−	5.85959i	−0.887606	−	0.237833i	−0.213920	−	0.976851i	$-0.568623\pi$
$607$	−21.8683	−	5.85959i	−0.887606	−	0.237833i	−0.673686	+	0.739018i	$0.735290\pi$
$608$	8.22544	+	14.2469i	0.333586	+	0.577788i
$609$	−10.2369	−	5.03938i	−0.414820	−	0.204206i
$610$	5.02656	+	2.90209i	0.203519	+	0.117502i
$611$	−58.7312			−2.37601
$612$	−16.6641	−	17.1992i	−0.673607	−	0.695237i
$613$	10.3407			0.417657			0.208829	−	0.977952i	$-0.433035\pi$
$613$	10.3407			0.417657			0.208829	+	0.977952i	$0.433035\pi$
$614$	−1.32784	−	0.766627i	−0.0535871	−	0.0309386i
$615$	−0.306009	−	4.61928i	−0.0123395	−	0.186267i
$616$	−1.26175	−	2.18542i	−0.0508375	−	0.0880532i
$617$	−18.8884	−	5.06113i	−0.760418	−	0.203753i	−0.142283	−	0.989826i	$-0.545444\pi$
$617$	−18.8884	−	5.06113i	−0.760418	−	0.203753i	−0.618134	+	0.786073i	$0.712111\pi$
$618$	2.68184	+	4.00759i	0.107879	+	0.161209i
$619$	2.42533	−	0.649866i	0.0974824	−	0.0261203i	−0.209748	−	0.977755i	$-0.567264\pi$
$619$	2.42533	−	0.649866i	0.0974824	−	0.0261203i	0.307231	+	0.951635i	$0.400598\pi$
$620$			0.345118i			0.0138603i
$621$	3.77461	+	0.239447i	0.151470	+	0.00960868i
$622$	1.34925	+	1.34925i	0.0540998	+	0.0540998i
$623$	16.6684	−	4.46629i	0.667807	−	0.178938i
$624$	−32.2809	+	21.6021i	−1.29227	+	0.864775i
$625$	18.2632	+	31.6328i	0.730529	+	1.26531i
$626$	−4.39872	−	1.17863i	−0.175808	−	0.0471077i
$627$	−8.77599	−	7.68549i	−0.350479	−	0.306929i
$628$	0.807922	−	1.39936i	0.0322396	−	0.0558406i
$629$	9.74565	+	1.45397i	0.388585	+	0.0579735i
$630$	−5.08235	+	3.91113i	−0.202486	+	0.155823i
$631$		−	36.9651i		−	1.47156i	−0.677223	−	0.735778i	$-0.736817\pi$
$631$		−	36.9651i		−	1.47156i	0.677223	−	0.735778i	$-0.263183\pi$
$632$	0.0330980	+	0.123523i	0.00131657	+	0.00491349i
$633$	5.39375	+	15.8530i	0.214382	+	0.630102i
$634$	−5.18785	−	1.39008i	−0.206036	−	0.0552072i
$635$	10.3784	−	38.7328i	0.411856	−	1.53707i
$636$	10.5223	−	21.3748i	0.417236	−	0.847565i
$637$	−13.1740	−	7.60599i	−0.521971	−	0.301360i
$638$		−	0.929449i		−	0.0367972i
$639$	−3.78739	−	9.10751i	−0.149827	−	0.360287i
$640$	−20.9127	−	20.9127i	−0.826647	−	0.826647i
$641$	7.91284	+	29.5311i	0.312538	+	1.16641i	0.926260	+	0.376886i	$0.123005\pi$
$641$	7.91284	+	29.5311i	0.312538	+	1.16641i	−0.613721	+	0.789523i	$0.710328\pi$
$642$	2.21525	−	2.52957i	0.0874289	−	0.0998343i
$643$	32.6957	+	8.76080i	1.28939	+	0.345492i	0.837430	−	0.546544i	$-0.184057\pi$
$643$	32.6957	+	8.76080i	1.28939	+	0.345492i	0.451964	+	0.892036i	$0.350724\pi$
$644$	2.60158	−	1.50202i	0.102517	−	0.0591880i
$645$	3.44274	+	0.682300i	0.135558	+	0.0268656i
$646$	5.86378	−	0.669601i	0.230707	−	0.0263451i
$647$	−45.5491			−1.79072			−0.895360	−	0.445343i	$-0.853082\pi$
$647$	−45.5491			−1.79072			−0.895360	+	0.445343i	$0.853082\pi$
$648$	−6.31530	+	6.35074i	−0.248088	+	0.249480i
$649$	7.68675	−	7.68675i	0.301731	−	0.301731i
$650$	−8.40356	+	14.5554i	−0.329615	+	0.570909i
$651$	0.137901	−	0.0922823i	0.00540478	−	0.00361683i
$652$	−12.6207	+	47.1010i	−0.494264	+	1.84462i
$653$	−1.28148	+	4.78256i	−0.0501483	+	0.187156i	−0.986456	−	0.164024i	$-0.947553\pi$
$653$	−1.28148	+	4.78256i	−0.0501483	+	0.187156i	0.936308	+	0.351180i	$0.114219\pi$
$654$	−3.42734	−	3.00146i	−0.134020	−	0.117366i
$655$	29.0058	+	16.7465i	1.13335	+	0.654340i
$656$	−1.72514	−	1.72514i	−0.0673554	−	0.0673554i
$657$	13.4320	+	32.2998i	0.524032	+	1.26014i
$658$	−3.61352	+	3.61352i	−0.140870	+	0.140870i
$659$	−10.5183	+	18.2183i	−0.409736	+	0.709683i	−0.994860	−	0.101260i	$-0.967712\pi$
$659$	−10.5183	+	18.2183i	−0.409736	+	0.709683i	0.585124	+	0.810944i	$0.301046\pi$
$660$	14.1959	+	6.98832i	0.552576	+	0.272020i
$661$	26.7663	−	15.4535i	1.04109	−	0.601073i	0.120948	−	0.992659i	$-0.461407\pi$
$661$	26.7663	−	15.4535i	1.04109	−	0.601073i	0.920142	+	0.391586i	$0.128073\pi$
$662$	−0.555639	−	0.962394i	−0.0215955	−	0.0374045i
$663$	7.91255	+	43.5200i	0.307298	+	1.69018i
$664$	3.08683	−	5.34655i	0.119792	−	0.207486i
$665$			47.8705i			1.85634i
$666$	0.234081	−	1.79745i	0.00907046	−	0.0696498i
$667$	2.24941			0.0870973
$668$	1.35346	+	5.05118i	0.0523669	+	0.195436i
$669$	4.62735	−	0.306544i	0.178904	−	0.0118517i
$670$	−0.875698	+	3.26815i	−0.0338312	+	0.126260i
$671$	−5.96276	+	3.44260i	−0.230190	+	0.132900i
$672$	−2.08560	+	10.5235i	−0.0804539	+	0.405953i
$673$	16.5067	−	4.42294i	0.636285	−	0.170492i	0.0737647	−	0.997276i	$-0.476499\pi$
$673$	16.5067	−	4.42294i	0.636285	−	0.170492i	0.562520	+	0.826784i	$0.309832\pi$
$674$	4.74885	+	4.74885i	0.182919	+	0.182919i
$675$	17.8153	−	52.8463i	0.685712	−	2.03406i
$676$	49.1080			1.88877
$677$	−9.19256	−	34.3071i	−0.353299	−	1.31853i	−0.882612	−	0.470103i	$-0.844217\pi$
$677$	−9.19256	−	34.3071i	−0.353299	−	1.31853i	0.529313	−	0.848427i	$-0.322450\pi$
$678$	1.17704	−	5.93907i	0.0452038	−	0.228089i
$679$	4.35559	+	7.54410i	0.167152	+	0.289516i
$680$	−15.1407	+	5.96850i	−0.580618	+	0.228882i
$681$	23.1077	−	26.3865i	0.885488	−	1.01113i
$682$	0.0117056	+	0.00675823i	0.000448230	+	0.000258786i
$683$	−21.8027	+	21.8027i	−0.834259	+	0.834259i	−0.988096	−	0.153837i	$-0.950837\pi$
$683$	−21.8027	+	21.8027i	−0.834259	+	0.834259i	0.153837	+	0.988096i	$0.450837\pi$
$684$	4.33788	+	32.5970i	0.165863	+	1.24638i
$685$	8.11544	−	8.11544i	0.310075	−	0.310075i
$686$	−4.92257	+	1.31900i	−0.187944	+	0.0503596i
$687$	−2.09951	+	4.26490i	−0.0801013	+	0.162716i
$688$	1.60182	−	0.924814i	0.0610690	−	0.0352582i
$689$	−38.1095	+	22.0025i	−1.45186	+	0.838230i
$690$	0.558385	−	1.13429i	0.0212574	−	0.0431818i
$691$	35.1659	−	9.42266i	1.33777	−	0.358455i	0.482165	−	0.876080i	$-0.339851\pi$
$691$	35.1659	−	9.42266i	1.33777	−	0.358455i	0.855607	+	0.517625i	$0.173184\pi$
$692$	−14.1023	+	14.1023i	−0.536087	+	0.536087i
$693$	−1.00353	−	7.54101i	−0.0381208	−	0.286459i
$694$	−2.84435	+	2.84435i	−0.107970	+	0.107970i
$695$	16.1664	+	9.33365i	0.613225	+	0.354046i
$696$	−3.50928	+	4.00722i	−0.133019	+	0.151893i
$697$	−2.58477	+	1.01893i	−0.0979053	+	0.0385946i
$698$	−2.87394	−	4.97782i	−0.108780	−	0.188413i
$699$	−3.67265	+	18.5314i	−0.138912	+	0.700921i
$700$	−11.4643	−	42.7853i	−0.433310	−	1.61713i
$701$	29.3060			1.10687			0.553435	−	0.832892i	$-0.313317\pi$
$701$	29.3060			1.10687			0.553435	+	0.832892i	$0.313317\pi$
$702$	7.97738	−	1.60421i	0.301087	−	0.0605470i
$703$	−9.56747	−	9.56747i	−0.360844	−	0.360844i
$704$	7.47635	−	2.00328i	0.281776	−	0.0755015i
$705$	12.6640	−	63.8997i	0.476953	−	2.40660i
$706$	3.26643	−	1.88587i	0.122934	−	0.0709757i
$707$	−3.94522	+	14.7238i	−0.148375	+	0.553744i
$708$	−30.5768	+	2.02559i	−1.14915	+	0.0761263i
$709$	3.53383	+	13.1884i	0.132716	+	0.495302i	0.999997	−	0.00251670i	$-0.000801091\pi$
$709$	3.53383	+	13.1884i	0.132716	+	0.495302i	−0.867281	+	0.497819i	$0.834134\pi$
$710$	−3.29714			−0.123739
$711$	−0.0497851	+	0.382287i	−0.00186709	+	0.0143369i
$712$		−	8.05591i		−	0.301908i
$713$	−0.0163559	+	0.0283293i	−0.000612534	+	0.00106094i
$714$	3.16446	+	2.19080i	0.118427	+	0.0819886i
$715$	−14.6129	−	25.3102i	−0.546490	−	0.946548i
$716$	15.1445	−	8.74366i	0.565975	−	0.326766i
$717$	−33.7952	−	16.6366i	−1.26210	−	0.621304i
$718$	3.20966	−	5.55929i	0.119783	−	0.207471i
$719$	1.37014	−	1.37014i	0.0510976	−	0.0510976i	−0.681096	−	0.732194i	$-0.738497\pi$
$719$	1.37014	−	1.37014i	0.0510976	−	0.0510976i	0.732194	+	0.681096i	$0.238497\pi$
$720$	−16.5425	−	39.7797i	−0.616503	−	1.48250i
$721$	16.5983	+	16.5983i	0.618154	+	0.618154i
$722$	−2.85836	−	1.65028i	−0.106377	−	0.0614169i
$723$	−7.60315	−	6.65838i	−0.282764	−	0.247628i
$724$	11.0333	−	41.1767i	0.410048	−	1.53032i
$725$	8.58438	−	32.0373i	0.318816	−	1.18984i
$726$	−3.48828	+	2.33432i	−0.129462	+	0.0866349i
$727$	3.06673	−	5.31173i	0.113739	−	0.197001i	−0.803536	−	0.595256i	$-0.797051\pi$
$727$	3.06673	−	5.31173i	0.113739	−	0.197001i	0.917275	+	0.398255i	$0.130384\pi$
$728$	9.29088	−	9.29088i	0.344343	−	0.344343i
$729$	−24.9012	+	10.4371i	−0.922265	+	0.386557i
$730$	11.6933			0.432789
$731$	−0.238978	−	2.09276i	−0.00883892	−	0.0774036i
$732$	19.0387	+	3.77318i	0.703689	+	0.139461i
$733$	−5.68407	+	3.28170i	−0.209946	+	0.121212i	−0.601286	−	0.799034i	$-0.705345\pi$
$733$	−5.68407	+	3.28170i	−0.209946	+	0.121212i	0.391340	+	0.920246i	$0.372012\pi$
$734$	2.53426	+	0.679052i	0.0935411	+	0.0250643i
$735$	11.1160	−	12.6933i	0.410019	−	0.468198i
$736$	−0.547397	−	2.04291i	−0.0201773	−	0.0753027i
$737$	−2.83805	−	2.83805i	−0.104541	−	0.104541i
$738$	0.196250	+	0.471921i	0.00722406	+	0.0173716i
$739$			30.7767i			1.13214i	0.824358	+	0.566069i	$0.191536\pi$
$739$			30.7767i			1.13214i	−0.824358	+	0.566069i	$0.808464\pi$
$740$	15.8936	+	9.17615i	0.584259	+	0.337322i
$741$	26.8263	−	54.4944i	0.985489	−	2.00190i
$742$	−0.991005	+	3.69848i	−0.0363809	+	0.135775i
$743$	−41.3290	−	11.0741i	−1.51622	−	0.406269i	−0.597722	−	0.801704i	$-0.703927\pi$
$743$	−41.3290	−	11.0741i	−1.51622	−	0.406269i	−0.918494	+	0.395435i	$0.870594\pi$
$744$	−0.0249506	−	0.0733336i	−0.000914735	−	0.00268854i
$745$	10.7865	+	40.2558i	0.395187	+	1.47486i
$746$		−	7.43120i		−	0.272076i
$747$	14.7496	−	11.3506i	0.539658	−	0.415295i
$748$	1.40123	−	9.39217i	0.0512341	−	0.343412i
$749$	8.18400	−	14.1751i	0.299037	−	0.517947i
$750$	−7.49081	−	6.56000i	−0.273526	−	0.239537i
$751$	15.0661	+	4.03694i	0.549768	+	0.147310i	0.523002	−	0.852332i	$-0.324812\pi$
$751$	15.0661	+	4.03694i	0.549768	+	0.147310i	0.0267667	+	0.999642i	$0.491479\pi$
$752$	−17.1652	−	29.7310i	−0.625951	−	1.08418i
$753$	−0.230878	+	0.154502i	−0.00841367	+	0.00563035i
$754$	4.67451	−	1.25253i	0.170236	−	0.0456145i
$755$	2.84429	+	2.84429i	0.103514	+	0.103514i
$756$	−11.8768	+	17.8558i	−0.431954	+	0.649411i
$757$		−	35.5119i		−	1.29070i	−0.763887	−	0.645350i	$-0.776711\pi$
$757$		−	35.5119i		−	1.29070i	0.763887	−	0.645350i	$-0.223289\pi$
$758$	8.05656	−	2.15875i	0.292627	−	0.0784092i
$759$	0.834093	+	1.24642i	0.0302757	+	0.0452422i
$760$	21.5861	+	5.78399i	0.783012	+	0.209807i
$761$	−4.19687	−	7.26919i	−0.152136	−	0.263508i	0.779876	−	0.625934i	$-0.215282\pi$
$761$	−4.19687	−	7.26919i	−0.152136	−	0.263508i	−0.932013	+	0.362426i	$0.881949\pi$
$762$	0.292634	+	4.41739i	0.0106010	+	0.160025i
$763$	−19.2060	−	11.0886i	−0.695302	−	0.401433i
$764$	44.9238			1.62528
$765$	−49.0560	−	0.775174i	−1.77362	−	0.0280265i
$766$	2.75480			0.0995348
$767$	49.0179	+	28.3005i	1.76994	+	1.02187i
$768$	−17.2923	−	8.51258i	−0.623982	−	0.307171i
$769$	6.89301	+	11.9390i	0.248568	+	0.430533i	0.963129	−	0.269041i	$-0.0867066\pi$
$769$	6.89301	+	11.9390i	0.248568	+	0.430533i	−0.714560	+	0.699574i	$0.753373\pi$
$770$	−2.45632	−	0.658170i	−0.0885198	−	0.0237188i
$771$	13.9188	−	28.2743i	0.501272	−	1.01827i
$772$	−32.4135	+	8.68516i	−1.16659	+	0.312586i
$773$		−	26.6931i		−	0.960083i	−0.877246	−	0.480041i	$-0.840622\pi$
$773$		−	26.6931i		−	0.960083i	0.877246	−	0.480041i	$-0.159378\pi$
$774$	−0.384095	+	0.0511138i	−0.0138060	+	0.00183725i
$775$	0.341063	+	0.341063i	0.0122513	+	0.0122513i
$776$	3.92811	−	1.05253i	0.141011	−	0.0377838i
$777$	−0.583254	−	8.80436i	−0.0209241	−	0.315855i
$778$	−3.14015	−	5.43890i	−0.112580	−	0.194994i
$779$	3.68513	+	0.987428i	0.132034	+	0.0353783i
$780$	−16.0161	+	80.8136i	−0.573467	+	2.89359i
$781$	1.95562	−	3.38723i	0.0699775	−	0.121205i
$782$	−0.750460	−	0.111962i	−0.0268364	−	0.00400376i
$783$	−14.3869	+	7.13241i	−0.514147	+	0.254892i
$784$		−	8.89193i		−	0.317569i
$785$	−0.856788	−	3.19758i	−0.0305801	−	0.114126i
$786$	−3.62718	−	0.718854i	−0.129377	−	0.0256407i
$787$	−37.8357	−	10.1380i	−1.34870	−	0.361382i	−0.489043	−	0.872260i	$-0.662654\pi$
$787$	−37.8357	−	10.1380i	−1.34870	−	0.361382i	−0.859654	+	0.510878i	$0.829321\pi$
$788$	−1.51867	+	5.66775i	−0.0541004	+	0.201905i
$789$	30.3781	−	2.01243i	1.08149	−	0.0716444i
$790$	0.111602	+	0.0644336i	0.00397063	+	0.00229244i
$791$		−	29.4730i		−	1.04794i
$792$	−3.52170	−	0.458630i	−0.125138	−	0.0162967i
$793$	−25.3495	−	25.3495i	−0.900186	−	0.900186i
$794$	0.414913	+	1.54848i	0.0147247	+	0.0549534i
$795$	−15.7214	−	46.2076i	−0.557581	−	1.63881i
$796$	−6.49832	−	1.74122i	−0.230327	−	0.0617159i
$797$	−24.2216	+	13.9843i	−0.857972	+	0.495350i	−0.863333	−	0.504635i	$-0.831627\pi$
$797$	−24.2216	+	13.9843i	−0.857972	+	0.495350i	0.00536065	+	0.999986i	$0.498294\pi$
$798$	−1.70232	−	5.00338i	−0.0602615	−	0.177118i
$799$	−38.8431	+	4.43561i	−1.37417	+	0.156920i
$800$	−31.1853			−1.10257
$801$	9.26234	−	22.4501i	0.327269	−	0.793234i
$802$	−2.14473	+	2.14473i	−0.0757329	+	0.0757329i
$803$	−6.93560	+	12.0128i	−0.244752	+	0.423923i
$804$	0.747874	+	11.2894i	0.0263755	+	0.398145i
$805$	1.59287	−	5.94468i	0.0561413	−	0.209522i
$806$	−0.0182149	+	0.0679788i	−0.000641591	+	0.00239445i
$807$	−6.04182	+	30.4857i	−0.212682	+	1.07315i
$808$	6.16267	+	3.55802i	0.216802	+	0.125171i
$809$	−22.5970	−	22.5970i	−0.794469	−	0.794469i	0.187748	−	0.982217i	$-0.439881\pi$
$809$	−22.5970	−	22.5970i	−0.794469	−	0.794469i	−0.982217	+	0.187748i	$0.939881\pi$
$810$	0.0252523	+	9.02532i	0.000887274	+	0.317117i
$811$	−24.4577	+	24.4577i	−0.858827	+	0.858827i	−0.991200	−	0.132373i	$-0.957740\pi$
$811$	−24.4577	+	24.4577i	−0.858827	+	0.858827i	0.132373	+	0.991200i	$0.457740\pi$
$812$	−6.37706	+	11.0454i	−0.223791	+	0.387617i
$813$	29.2962	−	19.6047i	1.02746	−	0.687568i
$814$	0.622468	−	0.359382i	0.0218175	−	0.0125963i
$815$	49.9498	+	86.5156i	1.74967	+	3.03051i
$816$	−19.7182	+	16.7250i	−0.690275	+	0.585491i
$817$	−1.44619	+	2.50487i	−0.0505956	+	0.0876342i
$818$			6.35779i			0.222295i
$819$	36.5739	−	15.2094i	1.27800	−	0.531459i
$820$	−5.17473			−0.180709
$821$	−8.48084	−	31.6509i	−0.295983	−	1.10462i	−0.940433	−	0.339978i	$-0.889580\pi$
$821$	−8.48084	−	31.6509i	−0.295983	−	1.10462i	0.644450	−	0.764646i	$-0.277086\pi$
$822$	−0.559625	+	1.13681i	−0.0195192	+	0.0396508i
$823$	−2.43706	+	9.09521i	−0.0849504	+	0.317039i	−0.995305	−	0.0967903i	$-0.969142\pi$
$823$	−2.43706	+	9.09521i	−0.0849504	+	0.317039i	0.910354	+	0.413830i	$0.135809\pi$
$824$	9.49016	−	5.47915i	0.330605	−	0.190875i
$825$	20.9354	−	7.12294i	0.728876	−	0.247989i
$826$	4.75713	−	1.27467i	0.165522	−	0.0443514i
$827$	35.7044	+	35.7044i	1.24156	+	1.24156i	0.959352	+	0.282213i	$0.0910685\pi$
$827$	35.7044	+	35.7044i	1.24156	+	1.24156i	0.282213	+	0.959352i	$0.408932\pi$
$828$	0.545964	−	4.19232i	0.0189736	−	0.145693i
$829$	17.1199			0.594599			0.297300	−	0.954784i	$-0.403914\pi$
$829$	17.1199			0.594599			0.297300	+	0.954784i	$0.403914\pi$
$830$	−1.61019	−	6.00930i	−0.0558904	−	0.208586i
$831$	−33.8098	−	29.6086i	−1.17285	−	1.02711i
$832$	20.1504	+	34.9015i	0.698588	+	1.20999i
$833$	−9.28731	−	4.03544i	−0.321786	−	0.139820i
$834$	−2.02161	−	0.400653i	−0.0700025	−	0.0138735i
$835$	9.27806	+	5.35669i	0.321081	+	0.185376i
$836$	−9.22045	+	9.22045i	−0.318896	+	0.318896i
$837$	0.0147840	−	0.233052i	0.000511008	−	0.00805546i
$838$	−3.85767	+	3.85767i	−0.133261	+	0.133261i
$839$	−45.5353	+	12.2012i	−1.57205	+	0.421231i	−0.936455	−	0.350788i	$-0.885914\pi$
$839$	−45.5353	+	12.2012i	−1.57205	+	0.421231i	−0.635600	+	0.772019i	$0.719247\pi$
$840$	8.10515	+	12.1119i	0.279654	+	0.417899i
$841$	16.8440	−	9.72491i	0.580829	−	0.335342i
$842$	4.07188	−	2.35090i	0.140326	−	0.0810174i
$843$	2.95790	−	0.195949i	0.101875	−	0.00674884i
$844$	18.0802	−	4.84459i	0.622348	−	0.166758i
$845$	71.1401	−	71.1401i	2.44729	−	2.44729i
$846$	0.948710	+	7.12908i	0.0326173	+	0.245103i
$847$	−14.4475	+	14.4475i	−0.496422	+	0.496422i
$848$	−22.2763	−	12.8612i	−0.764972	−	0.441657i
$849$	1.55140	+	4.55980i	0.0532439	+	0.156492i
$850$	−4.45860	+	10.2612i	−0.152929	+	0.351956i
$851$	0.869759	+	1.50647i	0.0298149	+	0.0516410i
$852$	−10.4379	+	3.55134i	−0.357597	+	0.121667i
$853$	6.50876	+	24.2910i	0.222856	+	0.831709i	0.983252	+	0.182250i	$0.0583379\pi$
$853$	6.50876	+	24.2910i	0.222856	+	0.831709i	−0.760397	+	0.649459i	$0.774995\pi$
$854$	−3.11933			−0.106741
$855$	53.5057	+	40.9376i	1.82986	+	1.40003i
$856$	−5.40311	−	5.40311i	−0.184675	−	0.184675i
$857$	−3.09913	+	0.830409i	−0.105864	+	0.0283662i	−0.311362	−	0.950291i	$-0.600785\pi$
$857$	−3.09913	+	0.830409i	−0.105864	+	0.0283662i	0.205498	+	0.978658i	$0.434119\pi$
$858$	2.42738	+	2.12575i	0.0828693	+	0.0725719i
$859$	−39.2004	+	22.6324i	−1.33750	+	0.772206i	−0.986436	−	0.164145i	$-0.947514\pi$
$859$	−39.2004	+	22.6324i	−1.33750	+	0.772206i	−0.351064	+	0.936351i	$0.614180\pi$
$860$	1.01538	−	3.78945i	0.0346242	−	0.129219i
$861$	1.38369	+	2.06771i	0.0471560	+	0.0704673i
$862$	−0.686500	−	2.56205i	−0.0233823	−	0.0872638i
$863$	35.5005			1.20845			0.604226	−	0.796813i	$-0.293483\pi$
$863$	35.5005			1.20845			0.604226	+	0.796813i	$0.293483\pi$
$864$	9.97875	+	11.3305i	0.339484	+	0.385472i
$865$			40.8584i			1.38923i
$866$	1.46940	−	2.54508i	0.0499324	−	0.0864854i
$867$	8.51993	+	28.1853i	0.289352	+	0.957223i
$868$	−0.0927380	−	0.160627i	−0.00314773	−	0.00545203i
$869$	−0.132388	+	0.0764344i	−0.00449097	+	0.00259286i
$870$	0.354811	+	5.35596i	0.0120292	+	0.181584i
$871$	10.4489	−	18.0981i	0.354048	−	0.613230i
$872$	−7.32072	+	7.32072i	−0.247911	+	0.247911i
$873$	12.1569	+	1.58319i	0.411450	+	0.0535830i
$874$	0.736739	+	0.736739i	0.0249206	+	0.0249206i
$875$	−41.9767	−	24.2352i	−1.41907	−	0.819301i
$876$	37.0181	−	12.5948i	1.25072	−	0.425540i
$877$	−9.44642	+	35.2545i	−0.318983	+	1.19046i	0.601241	+	0.799068i	$0.294673\pi$
$877$	−9.44642	+	35.2545i	−0.318983	+	1.19046i	−0.920224	+	0.391392i	$0.871994\pi$
$878$	1.30563	−	4.87269i	0.0440630	−	0.164445i
$879$	9.84431	+	4.84612i	0.332040	+	0.163455i
$880$	8.54172	−	14.7947i	0.287941	−	0.498729i
$881$	−4.47095	+	4.47095i	−0.150630	+	0.150630i	−0.778399	−	0.627769i	$-0.783968\pi$
$881$	−4.47095	+	4.47095i	−0.150630	+	0.150630i	0.627769	+	0.778399i	$0.283968\pi$
$882$	−0.710448	+	1.72198i	−0.0239220	+	0.0579822i
$883$	−58.5316			−1.96974			−0.984872	−	0.173282i	$-0.944563\pi$
$883$	−58.5316			−1.96974			−0.984872	+	0.173282i	$0.944563\pi$
$884$	49.1247	−	5.60968i	1.65224	−	0.188674i
$885$	−41.3606	+	47.2293i	−1.39032	+	1.58760i
$886$	7.75162	−	4.47540i	0.260421	−	0.150354i
$887$	−29.6505	−	7.94483i	−0.995566	−	0.266761i	−0.275979	−	0.961164i	$-0.589002\pi$
$887$	−29.6505	−	7.94483i	−0.995566	−	0.266761i	−0.719587	+	0.694402i	$0.755669\pi$
$888$	−4.04061	−	0.800789i	−0.135594	−	0.0268727i
$889$	5.57766	+	20.8161i	0.187069	+	0.698151i
$890$	−5.74033	−	5.74033i	−0.192416	−	0.192416i
$891$	−9.28691	−	5.32721i	−0.311123	−	0.178468i
$892$		−	5.18377i		−	0.173566i
$893$	46.4921	+	26.8422i	1.55580	+	0.898241i
$894$	−2.55893	−	3.82392i	−0.0855835	−	0.127891i
$895$	9.27250	−	34.6055i	0.309946	−	1.15673i
$896$	15.3529	+	4.11379i	0.512903	+	0.137432i
$897$	−5.14464	+	5.87462i	−0.171774	+	0.196148i
$898$	−2.37559	−	8.86582i	−0.0792744	−	0.295856i
$899$		−	0.138883i		−	0.00463200i
$900$	−57.6259	−	23.7750i	−1.92086	−	0.792501i
$901$	−23.5428	+	17.4300i	−0.784325	+	0.580678i
$902$	−0.101334	+	0.175515i	−0.00337404	+	0.00584401i
$903$	−1.78569	+	0.607552i	−0.0594239	+	0.0202181i
$904$	−13.2902	−	3.56110i	−0.442025	−	0.118440i
$905$	−43.6672	−	75.6339i	−1.45155	−	2.51415i
$906$	−0.398429	−	0.196137i	−0.0132369	−	0.00651621i
$907$	29.6201	−	7.93668i	0.983519	−	0.263533i	0.268993	−	0.963142i	$-0.413309\pi$
$907$	29.6201	−	7.93668i	0.983519	−	0.263533i	0.714526	+	0.699609i	$0.246642\pi$
$908$	−27.7228	−	27.7228i	−0.920014	−	0.920014i
$909$	13.0832	+	17.0010i	0.433941	+	0.563888i
$910$		−	13.2406i		−	0.438923i
$911$	−0.179844	+	0.0481892i	−0.00595851	+	0.00159658i	−0.261797	−	0.965123i	$-0.584315\pi$
$911$	−0.179844	+	0.0481892i	−0.00595851	+	0.00159658i	0.255839	+	0.966720i	$0.417648\pi$
$912$	35.4267	−	2.34688i	1.17310	−	0.0777129i
$913$	7.12854	+	1.91009i	0.235920	+	0.0632146i
$914$	−2.65702	−	4.60209i	−0.0878864	−	0.152224i
$915$	33.0463	−	22.1143i	1.09248	−	0.731076i
$916$	4.60174	+	2.65682i	0.152046	+	0.0877836i
$917$	−18.0001			−0.594416
$918$	5.15486	−	1.66346i	0.170136	−	0.0549024i
$919$	46.3030			1.52740			0.763698	−	0.645573i	$-0.223382\pi$
$919$	46.3030			1.52740			0.763698	+	0.645573i	$0.223382\pi$
$920$	−2.48816	−	1.43654i	−0.0820322	−	0.0473613i
$921$	−8.72965	+	5.84181i	−0.287652	+	0.192494i
$922$	−0.614651	−	1.06461i	−0.0202425	−	0.0350610i
$923$	19.6709	+	5.27080i	0.647476	+	0.173491i
$924$	−8.48502	+	0.562099i	−0.279137	+	0.0184917i
$925$	24.7752	−	6.63850i	0.814604	−	0.218272i
$926$		−	5.81020i		−	0.190935i
$927$	32.7467	−	4.35780i	1.07554	−	0.143129i
$928$	6.34943	+	6.34943i	0.208430	+	0.208430i
$929$	−6.50445	+	1.74286i	−0.213404	+	0.0571814i	−0.363937	−	0.931424i	$-0.618568\pi$
$929$	−6.50445	+	1.74286i	−0.213404	+	0.0571814i	0.150533	+	0.988605i	$0.451901\pi$
$930$	−0.0700335	−	0.0344758i	−0.00229649	−	0.00113051i
$931$	6.95241	+	12.0419i	0.227856	+	0.394658i
$932$	20.3976	+	5.46553i	0.668146	+	0.179029i
$933$	12.3754	−	4.21055i	0.405154	−	0.137847i
$934$	−5.31035	+	9.19779i	−0.173760	+	0.300961i
$935$	−11.5761	−	15.6358i	−0.378577	−	0.511346i
$936$	−2.43927	−	18.3299i	−0.0797300	−	0.599131i
$937$		−	21.6108i		−	0.705993i	−0.935625	−	0.352996i	$-0.885163\pi$
$937$		−	21.6108i		−	0.705993i	0.935625	−	0.352996i	$-0.114837\pi$
$938$	−0.470625	−	1.75640i	−0.0153664	−	0.0573483i
$939$	−20.5537	+	23.4700i	−0.670743	+	0.765916i
$940$	−70.3349	−	18.8462i	−2.29407	−	0.614695i
$941$	−10.0946	+	37.6735i	−0.329074	+	1.22812i	0.581078	+	0.813848i	$0.302631\pi$
$941$	−10.0946	+	37.6735i	−0.329074	+	1.22812i	−0.910152	+	0.414274i	$0.864035\pi$
$942$	0.203260	+	0.303740i	0.00662256	+	0.00989637i
$943$	−0.424772	−	0.245242i	−0.0138325	−	0.00798619i
$944$			33.0853i			1.07683i
$945$	8.66157	+	43.0721i	0.281761	+	1.40113i
$946$	−0.108646	−	0.108646i	−0.00353238	−	0.00353238i
$947$	8.08099	+	30.1587i	0.262597	+	0.980025i	0.963705	+	0.266970i	$0.0860225\pi$
$947$	8.08099	+	30.1587i	0.262597	+	0.980025i	−0.701108	+	0.713055i	$0.747311\pi$
$948$	0.422706	+	0.0837741i	0.0137289	+	0.00272086i
$949$	−69.7629	−	18.6929i	−2.26460	−	0.606798i
$950$	13.3047	−	7.68145i	0.431660	−	0.249219i
$951$	−24.2410	+	27.6806i	−0.786067	+	0.897604i
$952$	5.44304	−	6.84641i	0.176410	−	0.221893i
$953$	−12.7689			−0.413626			−0.206813	−	0.978380i	$-0.566309\pi$
$953$	−12.7689			−0.413626			−0.206813	+	0.978380i	$0.566309\pi$
$954$	3.28638	+	4.27050i	0.106400	+	0.138263i
$955$	65.0787	−	65.0787i	2.10590	−	2.10590i
$956$	−21.0526	+	36.4643i	−0.680891	+	1.17934i
$957$	−5.71275	−	2.81225i	−0.184667	−	0.0909072i
$958$	−1.89612	+	7.07642i	−0.0612609	+	0.228629i
$959$	−1.59641	+	5.95787i	−0.0515507	+	0.192390i
$960$	−42.3178	+	14.3980i	−1.36580	+	0.464693i
$961$	−26.8450	−	15.4990i	−0.865969	−	0.499967i
$962$	2.64630	+	2.64630i	0.0853200	+	0.0853200i
$963$	−8.84502	−	21.2696i	−0.285027	−	0.685402i
$964$	−7.98821	+	7.98821i	−0.257283	+	0.257283i
$965$	−34.3740	+	59.5374i	−1.10654	+	1.91658i
$966$	0.0449132	+	0.677976i	0.00144506	+	0.0218135i
$967$	2.47812	−	1.43074i	0.0796909	−	0.0460095i	−0.459625	−	0.888113i	$-0.652016\pi$
$967$	2.47812	−	1.43074i	0.0796909	−	0.0460095i	0.539316	+	0.842104i	$0.318683\pi$
$968$	4.76915	+	8.26041i	0.153286	+	0.265500i
$969$	13.6265	−	38.0671i	0.437747	−	1.22289i
$970$	2.04902	−	3.54901i	0.0657902	−	0.113952i
$971$			12.2706i			0.393782i	0.980425	+	0.196891i	$0.0630845\pi$
$971$			12.2706i			0.393782i	−0.980425	+	0.196891i	$0.936915\pi$
$972$	9.80109	+	28.5447i	0.314370	+	0.915572i
$973$	−10.0323			−0.321622
$974$	1.32563	+	4.94733i	0.0424760	+	0.158523i
$975$	64.0363	+	95.6921i	2.05080	+	3.06460i
$976$	5.42363	−	20.2413i	0.173606	−	0.647908i
$977$	23.1580	−	13.3703i	0.740890	−	0.427753i	−0.0815031	−	0.996673i	$-0.525972\pi$
$977$	23.1580	−	13.3703i	0.740890	−	0.427753i	0.822393	+	0.568920i	$0.192639\pi$
$978$	−8.29729	−	7.26627i	−0.265318	−	0.232350i
$979$	9.30191	−	2.49244i	0.297290	−	0.0796587i
$980$	−13.3361	−	13.3361i	−0.426006	−	0.426006i
$981$	−28.8183	+	11.9842i	−0.920097	+	0.382626i
$982$	7.19590			0.229630
$983$	−6.54950	−	24.4431i	−0.208897	−	0.779613i	−0.988226	−	0.152999i	$-0.951107\pi$
$983$	−6.54950	−	24.4431i	−0.208897	−	0.779613i	0.779330	−	0.626614i	$-0.215560\pi$
$984$	1.09957	−	0.374112i	0.0350531	−	0.0119263i
$985$	6.01056	+	10.4106i	0.191512	+	0.331709i
$986$	2.99699	−	1.18143i	0.0954437	−	0.0376243i
$987$	11.2766	+	33.1436i	0.358938	+	1.05497i
$988$	−58.7983	−	33.9472i	−1.87062	−	1.08001i
$989$	0.262939	−	0.262939i	0.00836098	−	0.00836098i
$990$	−2.83623	+	2.18263i	−0.0901413	+	0.0693684i
$991$	17.5471	−	17.5471i	0.557403	−	0.557403i	−0.371165	−	0.928567i	$-0.621041\pi$
$991$	17.5471	−	17.5471i	0.557403	−	0.557403i	0.928567	+	0.371165i	$0.121041\pi$
$992$	−0.126134	+	0.0337974i	−0.00400474	+	0.00107307i
$993$	−7.59646	+	0.503235i	−0.241066	+	0.0159697i
$994$	1.53458	−	0.885987i	0.0486738	−	0.0281018i
$995$	−11.9362	+	6.89136i	−0.378402	+	0.218471i
$996$	−11.5700	−	17.2896i	−0.366611	−	0.547842i
$997$	−7.60277	+	2.03716i	−0.240782	+	0.0645174i	−0.377192	−	0.926135i	$-0.623110\pi$
$997$	−7.60277	+	2.03716i	−0.240782	+	0.0645174i	0.136410	+	0.990653i	$0.456444\pi$
$998$	0.903137	−	0.903137i	0.0285883	−	0.0285883i
$999$	−10.3396	−	6.87734i	−0.327130	−	0.217589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.n.a.106.9	yes	64
3.2	odd	2		459.2.o.a.208.8		64
9.4	even	3	inner	153.2.n.a.4.8	✓	64
9.5	odd	6		459.2.o.a.361.9		64
17.13	even	4	inner	153.2.n.a.115.8	yes	64
51.47	odd	4		459.2.o.a.370.9		64
153.13	even	12	inner	153.2.n.a.13.9	yes	64
153.149	odd	12		459.2.o.a.64.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.8	✓	64	9.4	even	3	inner
153.2.n.a.13.9	yes	64	153.13	even	12	inner
153.2.n.a.106.9	yes	64	1.1	even	1	trivial
153.2.n.a.115.8	yes	64	17.13	even	4	inner
459.2.o.a.64.8		64	153.149	odd	12
459.2.o.a.208.8		64	3.2	odd	2
459.2.o.a.361.9		64	9.5	odd	6
459.2.o.a.370.9		64	51.47	odd	4

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.218953 + 0.126413i) q^{2} +(1.43947 - 0.963283i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(-3.83129 - 1.02659i) q^{5} +(0.436949 - 0.0289461i) q^{6} +(2.05904 - 0.551719i) q^{7} -0.995142i q^{8} +(1.14417 - 2.77324i) q^{9} +O(q^{10})\)	\(q+(0.218953 + 0.126413i) q^{2} +(1.43947 - 0.963283i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(-3.83129 - 1.02659i) q^{5} +(0.436949 - 0.0289461i) q^{6} +(2.05904 - 0.551719i) q^{7} -0.995142i q^{8} +(1.14417 - 2.77324i) q^{9} +(-0.709099 - 0.709099i) q^{10} +(1.14906 - 0.307889i) q^{11} +(-3.00860 - 1.48106i) q^{12} +(3.09696 + 5.36409i) q^{13} +(0.520578 + 0.139489i) q^{14} +(-6.50393 + 2.21286i) q^{15} +(-1.81028 + 3.13550i) q^{16} +(2.45336 + 3.31376i) q^{17} +(0.601094 - 0.462573i) q^{18} -5.66168i q^{19} +(1.98756 + 7.41767i) q^{20} +(2.43248 - 2.77762i) q^{21} +(0.290512 + 0.0778423i) q^{22} +(-0.188390 + 0.703082i) q^{23} +(-0.958603 - 1.43248i) q^{24} +(9.29474 + 5.36632i) q^{25} +1.56598i q^{26} +(-1.02441 - 5.09417i) q^{27} +(-2.91830 - 2.91830i) q^{28} +(-0.799838 - 2.98504i) q^{29} +(-1.70379 - 0.337667i) q^{30} +(0.0434097 + 0.0116316i) q^{31} +(-2.51637 + 1.45283i) q^{32} +(1.35746 - 1.55007i) q^{33} +(0.118269 + 1.03570i) q^{34} -8.45517 q^{35} +(-5.75748 + 0.766182i) q^{36} +(1.68986 - 1.68986i) q^{37} +(0.715709 - 1.23964i) q^{38} +(9.62513 + 4.73822i) q^{39} +(-1.02160 + 3.81267i) q^{40} +(-0.174405 + 0.650890i) q^{41} +(0.883726 - 0.300674i) q^{42} +(-0.442424 - 0.255434i) q^{43} +(-1.62857 - 1.62857i) q^{44} +(-7.23063 + 9.45049i) q^{45} +(-0.130127 + 0.130127i) q^{46} +(-4.74104 + 8.21172i) q^{47} +(0.414520 + 6.25728i) q^{48} +(-2.12692 + 1.22798i) q^{49} +(1.35674 + 2.34995i) q^{50} +(6.72364 + 2.40680i) q^{51} +(5.99596 - 10.3853i) q^{52} +7.10456i q^{53} +(0.419670 - 1.24488i) q^{54} -4.71845 q^{55} +(-0.549038 - 2.04904i) q^{56} +(-5.45380 - 8.14985i) q^{57} +(0.202219 - 0.754693i) q^{58} +(7.91388 - 4.56908i) q^{59} +(10.0064 + 8.76297i) q^{60} +(-5.59065 + 1.49801i) q^{61} +(0.00803432 + 0.00803432i) q^{62} +(0.825848 - 6.34148i) q^{63} +6.50650 q^{64} +(-6.35862 - 23.7307i) q^{65} +(0.493168 - 0.167793i) q^{66} +(-1.68697 - 2.92191i) q^{67} +(3.18122 - 7.32139i) q^{68} +(0.406084 + 1.19354i) q^{69} +(-1.85129 - 1.06884i) q^{70} +(2.32488 - 2.32488i) q^{71} +(-2.75977 - 1.13861i) q^{72} +(-8.24518 + 8.24518i) q^{73} +(0.583622 - 0.156381i) q^{74} +(18.5488 - 1.22879i) q^{75} +(-9.49291 + 5.48073i) q^{76} +(2.19609 - 1.26791i) q^{77} +(1.50848 + 2.25419i) q^{78} +(-0.124126 + 0.0332596i) q^{79} +(10.1546 - 10.1546i) q^{80} +(-6.38174 - 6.34613i) q^{81} +(-0.120467 + 0.120467i) q^{82} +(5.37265 + 3.10190i) q^{83} +(-7.01196 - 1.38967i) q^{84} +(-5.99764 - 15.2146i) q^{85} +(-0.0645802 - 0.111856i) q^{86} +(-4.02678 - 3.52641i) q^{87} +(-0.306394 - 1.14348i) q^{88} +8.09524 q^{89} +(-2.77783 + 1.15517i) q^{90} +(9.33624 + 9.33624i) q^{91} +(1.36122 - 0.364738i) q^{92} +(0.0736917 - 0.0250724i) q^{93} +(-2.07613 + 1.19866i) q^{94} +(-5.81223 + 21.6915i) q^{95} +(-2.22277 + 4.51528i) q^{96} +(1.05767 + 3.94729i) q^{97} -0.620928 q^{98} +(0.460869 - 3.53890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7	\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30} - 2 q^{31} + 12 q^{33} + 20 q^{34} - 128 q^{35} - 8 q^{37} - 24 q^{38} + 34 q^{39} - 20 q^{40} + 32 q^{41} + 20 q^{44} + 20 q^{45} - 40 q^{46} - 64 q^{47} + 62 q^{48} + 48 q^{50} + 40 q^{51} + 36 q^{52} - 46 q^{54} - 16 q^{55} + 12 q^{56} + 72 q^{57} - 10 q^{58} - 2 q^{61} - 28 q^{62} + 64 q^{63} - 8 q^{64} + 8 q^{65} - 4 q^{67} - 60 q^{68} - 24 q^{69} - 84 q^{71} + 72 q^{72} - 44 q^{73} - 14 q^{74} + 46 q^{75} - 56 q^{78} + 10 q^{79} + 204 q^{80} + 44 q^{81} - 52 q^{82} - 60 q^{84} + 22 q^{85} + 32 q^{86} + 16 q^{88} + 128 q^{89} - 66 q^{90} + 44 q^{91} + 136 q^{92} + 4 q^{95} - 2 q^{96} - 44 q^{97} + 208 q^{98} + 6 q^{99}+O(q^{100}) \) 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more