LMFDB - Embedded newform 135.2.q.a.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35613 + 0.118646i) q^{2} +(0.801546 - 1.53542i) q^{3} +(-0.144600 - 0.0254969i) q^{4} +(1.16254 + 1.91010i) q^{5} +(1.26917 - 1.98714i) q^{6} +(0.495263 + 0.346787i) q^{7} +(-2.82292 - 0.756400i) q^{8} +(-1.71505 - 2.46142i) q^{9} +O(q^{10})$	\(q+(1.35613 + 0.118646i) q^{2} +(0.801546 - 1.53542i) q^{3} +(-0.144600 - 0.0254969i) q^{4} +(1.16254 + 1.91010i) q^{5} +(1.26917 - 1.98714i) q^{6} +(0.495263 + 0.346787i) q^{7} +(-2.82292 - 0.756400i) q^{8} +(-1.71505 - 2.46142i) q^{9} +(1.34993 + 2.72828i) q^{10} +(-0.461147 + 1.26699i) q^{11} +(-0.155052 + 0.201585i) q^{12} +(-0.157610 - 1.80149i) q^{13} +(0.630497 + 0.529050i) q^{14} +(3.86465 - 0.253956i) q^{15} +(-3.46256 - 1.26027i) q^{16} +(0.596735 - 0.159895i) q^{17} +(-2.03379 - 3.54150i) q^{18} +(-6.66221 + 3.84643i) q^{19} +(-0.119402 - 0.305842i) q^{20} +(0.929441 - 0.482473i) q^{21} +(-0.775699 + 1.66349i) q^{22} +(4.35606 + 6.22110i) q^{23} +(-3.42410 + 3.72809i) q^{24} +(-2.29700 + 4.44115i) q^{25} -2.46176i q^{26} +(-5.15402 + 0.660379i) q^{27} +(-0.0627730 - 0.0627730i) q^{28} +(4.15413 - 3.48573i) q^{29} +(5.27110 + 0.114128i) q^{30} +(0.651351 - 3.69400i) q^{31} +(0.751218 + 0.350299i) q^{32} +(1.57574 + 1.72361i) q^{33} +(0.828222 - 0.146038i) q^{34} +(-0.0866357 + 1.34916i) q^{35} +(0.185237 + 0.399650i) q^{36} +(-1.29170 - 4.82067i) q^{37} +(-9.49120 + 4.42582i) q^{38} +(-2.89238 - 1.20198i) q^{39} +(-1.83696 - 6.27142i) q^{40} +(7.43804 - 8.86431i) q^{41} +(1.31769 - 0.544022i) q^{42} +(-0.466380 - 1.00015i) q^{43} +(0.0989861 - 0.171449i) q^{44} +(2.70776 - 6.13743i) q^{45} +(5.16928 + 8.95346i) q^{46} +(-2.99349 + 4.27515i) q^{47} +(-4.71045 + 4.30633i) q^{48} +(-2.26912 - 6.23435i) q^{49} +(-3.64196 + 5.75025i) q^{50} +(0.232805 - 1.04440i) q^{51} +(-0.0231420 + 0.264514i) q^{52} +(0.231010 - 0.231010i) q^{53} +(-7.06788 + 0.284057i) q^{54} +(-2.95619 + 0.592089i) q^{55} +(-1.13578 - 1.35357i) q^{56} +(0.565828 + 13.3124i) q^{57} +(6.04711 - 4.23423i) q^{58} +(9.76428 - 3.55391i) q^{59} +(-0.565303 - 0.0618145i) q^{60} +(0.173537 + 0.984176i) q^{61} +(1.32160 - 4.93227i) q^{62} +(0.00418995 - 1.81381i) q^{63} +(7.35941 + 4.24896i) q^{64} +(3.25781 - 2.39536i) q^{65} +(1.93241 + 2.52439i) q^{66} +(1.61617 - 0.141397i) q^{67} +(-0.0903647 + 0.00790588i) q^{68} +(13.0436 - 1.70190i) q^{69} +(-0.277562 + 1.81936i) q^{70} +(-8.27254 - 4.77616i) q^{71} +(2.97963 + 8.24568i) q^{72} +(-2.09021 + 7.80078i) q^{73} +(-1.17975 - 6.69072i) q^{74} +(4.97789 + 7.08665i) q^{75} +(1.06143 - 0.386328i) q^{76} +(-0.667764 + 0.467574i) q^{77} +(-3.77984 - 1.97321i) q^{78} +(-5.86238 - 6.98651i) q^{79} +(-1.61812 - 8.07897i) q^{80} +(-3.11722 + 8.44292i) q^{81} +(11.1387 - 11.1387i) q^{82} +(-0.973649 + 11.1289i) q^{83} +(-0.146699 + 0.0460677i) q^{84} +(0.999144 + 0.953942i) q^{85} +(-0.513808 - 1.41168i) q^{86} +(-2.02234 - 9.17231i) q^{87} +(2.26013 - 3.22780i) q^{88} +(3.58395 + 6.20758i) q^{89} +(4.40027 - 8.00189i) q^{90} +(0.546675 - 0.946869i) q^{91} +(-0.471268 - 1.01064i) q^{92} +(-5.14976 - 3.96101i) q^{93} +(-4.56680 + 5.44250i) q^{94} +(-15.0922 - 8.25389i) q^{95} +(1.13999 - 0.872657i) q^{96} +(9.46315 - 4.41274i) q^{97} +(-2.33754 - 8.72382i) q^{98} +(3.90949 - 1.03787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.35613	+	0.118646i	0.958930	+	0.0838955i	0.555862	−	0.831275i	$-0.312388\pi$
$2$	1.35613	+	0.118646i	0.958930	+	0.0838955i	0.403068	+	0.915170i	$0.367944\pi$
$3$	0.801546	−	1.53542i	0.462773	−	0.886477i
$3$	0.801546	−	1.53542i	0.462773	−	0.886477i
$4$	−0.144600	−	0.0254969i	−0.0723000	−	0.0127484i
$5$	1.16254	+	1.91010i	0.519904	+	0.854225i
$5$	1.16254	+	1.91010i	0.519904	+	0.854225i
$6$	1.26917	−	1.98714i	0.518138	−	0.811245i
$7$	0.495263	+	0.346787i	0.187192	+	0.131073i	0.663416	−	0.748251i	$-0.269106\pi$
$7$	0.495263	+	0.346787i	0.187192	+	0.131073i	−0.476224	+	0.879324i	$0.657995\pi$
$8$	−2.82292	−	0.756400i	−0.998054	−	0.267428i
$9$	−1.71505	−	2.46142i	−0.571683	−	0.820475i
$10$	1.34993	+	2.72828i	0.426886	+	0.862759i
$11$	−0.461147	+	1.26699i	−0.139041	+	0.382012i	−0.989596	−	0.143874i	$-0.954044\pi$
$11$	−0.461147	+	1.26699i	−0.139041	+	0.382012i	0.850555	+	0.525886i	$0.176266\pi$
$12$	−0.155052	+	0.201585i	−0.0447597	+	0.0581926i
$13$	−0.157610	−	1.80149i	−0.0437132	−	0.499644i	−0.986218	−	0.165451i	$-0.947092\pi$
$13$	−0.157610	−	1.80149i	−0.0437132	−	0.499644i	0.942505	−	0.334193i	$-0.108464\pi$
$14$	0.630497	+	0.529050i	0.168507	+	0.141394i
$15$	3.86465	−	0.253956i	0.997848	−	0.0655710i
$16$	−3.46256	−	1.26027i	−0.865640	−	0.315067i
$17$	0.596735	−	0.159895i	0.144729	−	0.0387801i	−0.185727	−	0.982601i	$-0.559464\pi$
$17$	0.596735	−	0.159895i	0.144729	−	0.0387801i	0.330456	+	0.943821i	$0.392797\pi$
$18$	−2.03379	−	3.54150i	−0.479369	−	0.834739i
$19$	−6.66221	+	3.84643i	−1.52842	+	0.882432i	−0.528988	+	0.848629i	$0.677428\pi$
$19$	−6.66221	+	3.84643i	−1.52842	+	0.882432i	−0.999429	+	0.0338024i	$0.989238\pi$
$20$	−0.119402	−	0.305842i	−0.0266990	−	0.0683884i
$21$	0.929441	−	0.482473i	0.202821	−	0.105284i
$22$	−0.775699	+	1.66349i	−0.165380	+	0.354658i
$23$	4.35606	+	6.22110i	0.908302	+	1.29719i	0.954486	+	0.298257i	$0.0964051\pi$
$23$	4.35606	+	6.22110i	0.908302	+	1.29719i	−0.0461838	+	0.998933i	$0.514706\pi$
$24$	−3.42410	+	3.72809i	−0.698941	+	0.760994i
$25$	−2.29700	+	4.44115i	−0.459399	+	0.888230i
$26$		−	2.46176i		−	0.482791i
$27$	−5.15402	+	0.660379i	−0.991891	+	0.127090i
$28$	−0.0627730	−	0.0627730i	−0.0118630	−	0.0118630i
$29$	4.15413	−	3.48573i	0.771402	−	0.647283i	−0.169665	−	0.985502i	$-0.554269\pi$
$29$	4.15413	−	3.48573i	0.771402	−	0.647283i	0.941068	+	0.338218i	$0.109824\pi$
$30$	5.27110	+	0.114128i	0.962367	+	0.0208369i
$31$	0.651351	−	3.69400i	0.116986	−	0.663462i	−0.868761	−	0.495231i	$-0.835084\pi$
$31$	0.651351	−	3.69400i	0.116986	−	0.663462i	0.985748	−	0.168231i	$-0.0538054\pi$
$32$	0.751218	+	0.350299i	0.132798	+	0.0619247i
$33$	1.57574	+	1.72361i	0.274300	+	0.300041i
$34$	0.828222	−	0.146038i	0.142039	−	0.0250453i
$35$	−0.0866357	+	1.34916i	−0.0146441	+	0.228049i
$36$	0.185237	+	0.399650i	0.0308729	+	0.0666084i
$37$	−1.29170	−	4.82067i	−0.212353	−	0.792514i	−0.987081	−	0.160219i	$-0.948780\pi$
$37$	−1.29170	−	4.82067i	−0.212353	−	0.792514i	0.774728	−	0.632295i	$-0.217887\pi$
$38$	−9.49120	+	4.42582i	−1.53968	+	0.717963i
$39$	−2.89238	−	1.20198i	−0.463152	−	0.192471i
$40$	−1.83696	−	6.27142i	−0.290449	−	0.991599i
$41$	7.43804	−	8.86431i	1.16163	−	1.38437i	0.252632	−	0.967562i	$-0.418704\pi$
$41$	7.43804	−	8.86431i	1.16163	−	1.38437i	0.908994	−	0.416810i	$-0.136852\pi$
$42$	1.31769	−	0.544022i	0.203324	−	0.0839444i
$43$	−0.466380	−	1.00015i	−0.0711223	−	0.152522i	0.867532	−	0.497381i	$-0.165705\pi$
$43$	−0.466380	−	1.00015i	−0.0711223	−	0.152522i	−0.938655	+	0.344858i	$0.887927\pi$
$44$	0.0989861	−	0.171449i	0.0149227	−	0.0258469i
$45$	2.70776	−	6.13743i	0.403650	−	0.914914i
$46$	5.16928	+	8.95346i	0.762169	+	1.32012i
$47$	−2.99349	+	4.27515i	−0.436645	+	0.623594i	−0.975814	−	0.218604i	$-0.929850\pi$
$47$	−2.99349	+	4.27515i	−0.436645	+	0.623594i	0.539168	+	0.842198i	$0.318739\pi$
$48$	−4.71045	+	4.30633i	−0.679894	+	0.621565i
$49$	−2.26912	−	6.23435i	−0.324160	−	0.890621i
$50$	−3.64196	+	5.75025i	−0.515050	+	0.813208i
$51$	0.232805	−	1.04440i	0.0325992	−	0.146246i
$52$	−0.0231420	+	0.264514i	−0.00320922	+	0.0366815i
$53$	0.231010	−	0.231010i	0.0317317	−	0.0317317i	−0.691063	−	0.722795i	$-0.742857\pi$
$53$	0.231010	−	0.231010i	0.0317317	−	0.0317317i	0.722795	+	0.691063i	$0.242857\pi$
$54$	−7.06788	+	0.284057i	−0.961816	+	0.0386552i
$55$	−2.95619	+	0.592089i	−0.398612	+	0.0798373i
$56$	−1.13578	−	1.35357i	−0.151775	−	0.180878i
$57$	0.565828	+	13.3124i	0.0749457	+	1.76327i
$58$	6.04711	−	4.23423i	0.794025	−	0.555982i
$59$	9.76428	−	3.55391i	1.27120	−	0.462679i	0.383688	−	0.923463i	$-0.374654\pi$
$59$	9.76428	−	3.55391i	1.27120	−	0.462679i	0.887513	+	0.460784i	$0.152432\pi$
$60$	−0.565303	−	0.0618145i	−0.0729803	−	0.00798022i
$61$	0.173537	+	0.984176i	0.0222191	+	0.126011i	0.993900	−	0.110287i	$-0.0351770\pi$
$61$	0.173537	+	0.984176i	0.0222191	+	0.126011i	−0.971681	+	0.236298i	$0.924066\pi$
$62$	1.32160	−	4.93227i	0.167843	−	0.626398i
$63$	0.00418995	−	1.81381i	0.000527884	−	0.228518i
$64$	7.35941	+	4.24896i	0.919927	+	0.531120i
$65$	3.25781	−	2.39536i	0.404081	−	0.297108i
$66$	1.93241	+	2.52439i	0.237863	+	0.310731i
$67$	1.61617	−	0.141397i	0.197447	−	0.0172743i	0.0119966	−	0.999928i	$-0.496181\pi$
$67$	1.61617	−	0.141397i	0.197447	−	0.0172743i	0.185450	+	0.982654i	$0.440626\pi$
$68$	−0.0903647	+	0.00790588i	−0.0109583	+	0.000958729i
$69$	13.0436	−	1.70190i	1.57027	−	0.204885i
$70$	−0.277562	+	1.81936i	−0.0331750	+	0.217455i
$71$	−8.27254	−	4.77616i	−0.981770	−	0.566825i	−0.0789662	−	0.996877i	$-0.525162\pi$
$71$	−8.27254	−	4.77616i	−0.981770	−	0.566825i	−0.902804	+	0.430052i	$0.858495\pi$
$72$	2.97963	+	8.24568i	0.351152	+	0.971762i
$73$	−2.09021	+	7.80078i	−0.244641	+	0.913012i	0.728923	+	0.684596i	$0.240021\pi$
$73$	−2.09021	+	7.80078i	−0.244641	+	0.913012i	−0.973564	+	0.228416i	$0.926645\pi$
$74$	−1.17975	−	6.69072i	−0.137144	−	0.777781i
$75$	4.97789	+	7.08665i	0.574798	+	0.818296i
$76$	1.06143	−	0.386328i	0.121754	−	0.0443149i
$77$	−0.667764	+	0.467574i	−0.0760988	+	0.0532850i
$78$	−3.77984	−	1.97321i	−0.427983	−	0.223422i
$79$	−5.86238	−	6.98651i	−0.659569	−	0.786044i	0.327754	−	0.944763i	$-0.393708\pi$
$79$	−5.86238	−	6.98651i	−0.659569	−	0.786044i	−0.987324	+	0.158719i	$0.949264\pi$
$80$	−1.61812	−	8.07897i	−0.180912	−	0.903256i
$81$	−3.11722	+	8.44292i	−0.346358	+	0.938102i
$82$	11.1387	−	11.1387i	1.23006	−	1.23006i
$83$	−0.973649	+	11.1289i	−0.106872	+	1.22155i	0.733557	+	0.679628i	$0.237859\pi$
$83$	−0.973649	+	11.1289i	−0.106872	+	1.22155i	−0.840429	+	0.541922i	$0.817697\pi$
$84$	−0.146699	+	0.0460677i	−0.0160061	+	0.00502640i
$85$	0.999144	+	0.953942i	0.108372	+	0.103470i
$86$	−0.513808	−	1.41168i	−0.0554053	−	0.152225i
$87$	−2.02234	−	9.17231i	−0.216818	−	0.983375i
$88$	2.26013	−	3.22780i	0.240931	−	0.344085i
$89$	3.58395	+	6.20758i	0.379898	+	0.658002i	0.991047	−	0.133513i	$-0.0426259\pi$
$89$	3.58395	+	6.20758i	0.379898	+	0.658002i	−0.611149	+	0.791515i	$0.709293\pi$
$90$	4.40027	−	8.00189i	0.463829	−	0.843473i
$91$	0.546675	−	0.946869i	0.0573071	−	0.0992589i
$92$	−0.471268	−	1.01064i	−0.0491331	−	0.105366i
$93$	−5.14976	−	3.96101i	−0.534005	−	0.410737i
$94$	−4.56680	+	5.44250i	−0.471029	+	0.561351i
$95$	−15.0922	−	8.25389i	−1.54842	−	0.846831i
$96$	1.13999	−	0.872657i	0.116350	−	0.0890652i
$97$	9.46315	−	4.41274i	0.960838	−	0.448046i	0.122062	−	0.992523i	$-0.461049\pi$
$97$	9.46315	−	4.41274i	0.960838	−	0.448046i	0.838776	+	0.544477i	$0.183272\pi$
$98$	−2.33754	−	8.72382i	−0.236127	−	0.881238i
$99$	3.90949	−	1.03787i	0.392918	−	0.104310i
$100$	0.445381	−	0.583624i	0.0445381	−	0.0583624i
$101$	−7.45128	+	1.31386i	−0.741430	+	0.130734i	−0.531590	−	0.847002i	$-0.678405\pi$
$101$	−7.45128	+	1.31386i	−0.741430	+	0.130734i	−0.209840	+	0.977736i	$0.567294\pi$
$102$	0.439628	−	1.38873i	0.0435297	−	0.137504i
$103$	16.2593	+	7.58185i	1.60208	+	0.747062i	0.998728	−	0.0504147i	$-0.0160543\pi$
$103$	16.2593	+	7.58185i	1.60208	+	0.747062i	0.603350	+	0.797476i	$0.293832\pi$
$104$	−0.917727	+	5.20469i	−0.0899905	+	0.510362i
$105$	2.00209	+	1.21443i	0.195384	+	0.118517i
$106$	0.340688	−	0.285871i	0.0330906	−	0.0277663i
$107$	5.23935	+	5.23935i	0.506508	+	0.506508i	0.913453	−	0.406945i	$-0.133406\pi$
$107$	5.23935	+	5.23935i	0.506508	+	0.506508i	−0.406945	+	0.913453i	$0.633406\pi$
$108$	0.762108	+	0.0359205i	0.0733339	+	0.00345646i
$109$		−	2.65288i		−	0.254100i	−0.991896	−	0.127050i	$-0.959449\pi$
$109$		−	2.65288i		−	0.254100i	0.991896	−	0.127050i	$-0.0405508\pi$
$110$	−4.07922	+	0.452211i	−0.388939	+	0.0431167i
$111$	−8.43713	−	1.88069i	−0.800817	−	0.178507i
$112$	−1.27783	−	1.82494i	−0.120744	−	0.172440i
$113$	−3.27041	+	7.01342i	−0.307655	+	0.659767i	−0.997966	−	0.0637448i	$-0.979696\pi$
$113$	−3.27041	+	7.01342i	−0.307655	+	0.659767i	0.690312	+	0.723512i	$0.257473\pi$
$114$	−0.812129	+	18.1205i	−0.0760628	+	1.69714i
$115$	−6.81885	+	15.5528i	−0.635861	+	1.45031i
$116$	−0.689562	+	0.398119i	−0.0640242	+	0.0369644i
$117$	−4.16393	+	3.47759i	−0.384955	+	0.321503i
$118$	13.6633	−	3.66107i	1.25781	−	0.337029i
$119$	0.350990	+	0.127750i	0.0321752	+	0.0117108i
$120$	−11.1017	−	2.20632i	−1.01344	−	0.201409i
$121$	7.03388	+	5.90213i	0.639444	+	0.536557i
$122$	0.118570	+	1.35526i	0.0107348	+	0.122700i
$123$	−7.64853	−	18.5257i	−0.689645	−	1.67040i
$124$	−0.188371	+	0.517544i	−0.0169162	+	0.0464769i
$125$	−11.1534	+	0.775512i	−0.997591	+	0.0693639i
$126$	0.220883	−	2.45927i	0.0196779	−	0.219089i
$127$	−8.39790	−	2.25021i	−0.745193	−	0.199674i	−0.133808	−	0.991007i	$-0.542721\pi$
$127$	−8.39790	−	2.25021i	−0.745193	−	0.199674i	−0.611385	+	0.791333i	$0.709387\pi$
$128$	8.11826	+	5.68446i	0.717559	+	0.502440i
$129$	−1.90949	−	0.0855797i	−0.168121	−	0.00753488i
$130$	4.70222	−	2.86190i	0.412412	−	0.251005i
$131$	−3.98100	−	0.701958i	−0.347822	−	0.0613304i	−0.00299187	−	0.999996i	$-0.500952\pi$
$131$	−3.98100	−	0.701958i	−0.347822	−	0.0613304i	−0.344830	+	0.938665i	$0.612063\pi$
$132$	−0.183905	−	0.289410i	−0.0160069	−	0.0251899i
$133$	−4.63344	−	0.405373i	−0.401770	−	0.0351503i
$134$	2.20852			0.190787
$135$	−7.25315	−	9.07699i	−0.624252	−	0.781223i
$136$	−1.80548			−0.154819
$137$	−13.6356	−	1.19296i	−1.16497	−	0.101922i	−0.511781	−	0.859116i	$-0.671014\pi$
$137$	−13.6356	−	1.19296i	−1.16497	−	0.101922i	−0.653190	+	0.757194i	$0.726570\pi$
$138$	17.8908	−	0.760426i	1.52296	−	0.0647317i
$139$	−6.19727	−	1.09275i	−0.525645	−	0.0926854i	−0.0954725	−	0.995432i	$-0.530436\pi$
$139$	−6.19727	−	1.09275i	−0.525645	−	0.0926854i	−0.430173	+	0.902747i	$0.641547\pi$
$140$	0.0469268	−	0.192879i	0.00396604	−	0.0163013i
$141$	4.16474	+	8.02300i	0.350734	+	0.675659i
$142$	−10.6520	−	7.45860i	−0.893895	−	0.625912i
$143$	2.35515	+	0.631061i	0.196948	+	0.0527720i
$144$	2.83640	+	10.6843i	0.236367	+	0.890354i
$145$	11.4874	+	3.88252i	0.953980	+	0.322426i
$146$	−3.76013	+	10.3309i	−0.311191	+	0.854990i
$147$	−11.3912	−	1.51306i	−0.939527	−	0.124795i
$148$	0.0638670	+	0.730003i	0.00524984	+	0.0600059i
$149$	−2.60149	−	2.18291i	−0.213122	−	0.178831i	0.529977	−	0.848012i	$-0.322201\pi$
$149$	−2.60149	−	2.18291i	−0.213122	−	0.178831i	−0.743099	+	0.669181i	$0.766645\pi$
$150$	5.90987	+	10.2010i	0.482539	+	0.832911i
$151$	−21.3539	−	7.77217i	−1.73775	−	0.632490i	−0.738620	−	0.674122i	$-0.764522\pi$
$151$	−21.3539	−	7.77217i	−1.73775	−	0.632490i	−0.999133	+	0.0416312i	$0.986745\pi$
$152$	21.7164	−	5.81888i	1.76143	−	0.471974i
$153$	−1.41700	−	1.19459i	−0.114557	−	0.0965770i
$154$	−0.961052	+	0.554864i	−0.0774438	+	0.0447122i
$155$	7.81314	−	3.05027i	0.627567	−	0.245004i
$156$	0.387592	+	0.247553i	0.0310322	+	0.0198201i
$157$	−7.80411	+	16.7360i	−0.622836	+	1.33568i	0.301270	+	0.953539i	$0.402589\pi$
$157$	−7.80411	+	16.7360i	−0.622836	+	1.33568i	−0.924106	+	0.382136i	$0.875188\pi$
$158$	−7.12124	−	10.1702i	−0.566535	−	0.809096i
$159$	−0.169533	−	0.539863i	−0.0134448	−	0.0428139i
$160$	0.204215	+	1.84214i	0.0161446	+	0.145634i
$161$			4.59171i			0.361877i
$162$	−5.22908	+	11.0799i	−0.410835	+	0.870516i
$163$	−16.0458	−	16.0458i	−1.25680	−	1.25680i	−0.952611	−	0.304190i	$-0.901614\pi$
$163$	−16.0458	−	16.0458i	−1.25680	−	1.25680i	−0.304190	−	0.952611i	$-0.598386\pi$
$164$	−1.30155	+	1.09213i	−0.101634	+	0.0852811i
$165$	−1.46041	+	5.01358i	−0.113693	+	0.390307i
$166$	−2.64079	+	14.9767i	−0.204965	+	1.16241i
$167$	1.23325	+	0.575072i	0.0954315	+	0.0445004i	0.469748	−	0.882801i	$-0.344345\pi$
$167$	1.23325	+	0.575072i	0.0954315	+	0.0445004i	−0.374316	+	0.927301i	$0.622123\pi$
$168$	−2.98868	+	0.658954i	−0.230582	+	0.0508394i
$169$	9.58197	−	1.68956i	0.737075	−	0.129966i
$170$	1.24179	+	1.41222i	0.0952409	+	0.108312i
$171$	20.8937	+	9.80172i	1.59778	+	0.749556i
$172$	0.0419377	+	0.156514i	0.00319772	+	0.0119340i
$173$	16.6179	−	7.74907i	1.26344	−	0.589151i	0.328682	−	0.944441i	$-0.393395\pi$
$173$	16.6179	−	7.74907i	1.26344	−	0.589151i	0.934756	+	0.355289i	$0.115618\pi$
$174$	−1.65430	−	12.6788i	−0.125412	−	0.961178i
$175$	−2.67775	+	1.40297i	−0.202419	+	0.106054i
$176$	3.19350	−	3.80586i	0.240719	−	0.286878i
$177$	2.36977	−	17.8409i	0.178123	−	1.34101i
$178$	4.12380	+	8.84351i	0.309092	+	0.662849i
$179$	−7.37861	+	12.7801i	−0.551503	+	0.955231i	0.446663	+	0.894702i	$0.352612\pi$
$179$	−7.37861	+	12.7801i	−0.551503	+	0.955231i	−0.998166	+	0.0605291i	$0.980721\pi$
$180$	−0.548028	+	0.818432i	−0.0408476	+	0.0610023i
$181$	−2.27317	−	3.93725i	−0.168964	−	0.292653i	0.769092	−	0.639138i	$-0.220709\pi$
$181$	−2.27317	−	3.93725i	−0.168964	−	0.292653i	−0.938056	+	0.346484i	$0.887375\pi$
$182$	0.853706	−	1.21922i	0.0632809	−	0.0903745i
$183$	1.65022	+	0.522410i	0.121988	+	0.0386176i
$184$	−7.59119	−	20.8566i	−0.559630	−	1.53757i
$185$	7.70634	−	8.07150i	0.566581	−	0.593429i
$186$	−6.51379	−	5.98265i	−0.477615	−	0.438669i
$187$	−0.0725974	+	0.829792i	−0.00530885	+	0.0606804i
$188$	0.541861	−	0.541861i	0.0395193	−	0.0395193i
$189$	−2.78161	−	1.46028i	−0.202332	−	0.106220i
$190$	−19.4877	−	12.9840i	−1.41379	−	0.941957i
$191$	11.5901	+	13.8125i	0.838631	+	0.999441i	0.999921	+	0.0125340i	$0.00398981\pi$
$191$	11.5901	+	13.8125i	0.838631	+	0.999441i	−0.161291	+	0.986907i	$0.551566\pi$
$192$	12.4229	−	7.89408i	0.896543	−	0.569706i
$193$	5.09804	−	3.56969i	0.366965	−	0.256952i	−0.375520	−	0.926814i	$-0.622536\pi$
$193$	5.09804	−	3.56969i	0.366965	−	0.256952i	0.742485	+	0.669863i	$0.233647\pi$
$194$	13.3568	−	4.86149i	0.958965	−	0.349035i
$195$	−1.06661	−	6.92210i	−0.0763813	−	0.495702i
$196$	0.169158	+	0.959342i	0.0120827	+	0.0685244i
$197$	1.35510	−	5.05729i	0.0965467	−	0.360317i	−0.900703	−	0.434436i	$-0.856948\pi$
$197$	1.35510	−	5.05729i	0.0965467	−	0.360317i	0.997249	+	0.0741188i	$0.0236144\pi$
$198$	5.42492	−	0.943644i	0.385532	−	0.0670618i
$199$	13.9099	+	8.03089i	0.986047	+	0.569294i	0.904090	−	0.427342i	$-0.140550\pi$
$199$	13.9099	+	8.03089i	0.986047	+	0.569294i	0.0819565	+	0.996636i	$0.473883\pi$
$200$	9.84353	−	10.7996i	0.696043	−	0.763645i
$201$	1.07833	−	2.59484i	0.0760596	−	0.183026i
$202$	−10.2608	+	0.897704i	−0.721948	+	0.0631622i
$203$	3.26619	−	0.285755i	0.229242	−	0.0200560i
$204$	−0.0602926	+	0.145085i	−0.00422132	+	0.0101580i
$205$	25.5788	+	3.90231i	1.78650	+	0.272549i
$206$	21.1502	+	12.2111i	1.47361	+	0.850787i
$207$	7.84192	−	21.3916i	0.545051	−	1.48682i
$208$	−1.72463	+	6.43640i	−0.119581	+	0.446284i
$209$	−1.80113	−	10.2147i	−0.124587	−	0.706567i
$210$	2.57100	+	1.88447i	0.177416	+	0.130041i
$211$	−19.6727	+	7.16029i	−1.35433	+	0.492934i	−0.914295	−	0.405048i	$-0.867255\pi$
$211$	−19.6727	+	7.16029i	−1.35433	+	0.492934i	−0.440031	+	0.897983i	$0.645033\pi$
$212$	−0.0392941	+	0.0275140i	−0.00269873	+	0.00188967i
$213$	−13.9642	+	8.87355i	−0.956814	+	0.608005i
$214$	6.48362	+	7.72688i	0.443211	+	0.528199i
$215$	1.36821	−	2.05355i	0.0933114	−	0.140051i
$216$	15.0489	+	2.03430i	1.02395	+	0.138417i
$217$	1.60362	−	1.60362i	0.108861	−	0.108861i
$218$	0.314754	−	3.59765i	0.0213178	−	0.243664i
$219$	10.3021	+	9.46204i	0.696151	+	0.639386i
$220$	0.442561	−	0.0102426i	0.0298374	−	0.000690558i
$221$	−0.382100	−	1.04981i	−0.0257028	−	0.0706180i
$222$	−11.2187	−	3.55150i	−0.752951	−	0.238361i
$223$	9.26122	−	13.2264i	0.620177	−	0.885705i	−0.379035	−	0.925382i	$-0.623744\pi$
$223$	9.26122	−	13.2264i	0.620177	−	0.885705i	0.999213	+	0.0396772i	$0.0126330\pi$
$224$	0.250572	+	0.434003i	0.0167420	+	0.0289980i
$225$	14.8710	−	1.96290i	0.991401	−	0.130860i
$226$	−5.26723	+	9.12310i	−0.350371	+	0.606860i
$227$	4.42259	+	9.48428i	0.293538	+	0.629494i	0.996668	−	0.0815674i	$-0.0259926\pi$
$227$	4.42259	+	9.48428i	0.293538	+	0.629494i	−0.703130	+	0.711061i	$0.748215\pi$
$228$	0.257606	−	1.93940i	0.0170604	−	0.128440i
$229$	5.43987	−	6.48298i	0.359476	−	0.428407i	−0.555749	−	0.831350i	$-0.687568\pi$
$229$	5.43987	−	6.48298i	0.359476	−	0.428407i	0.915225	+	0.402943i	$0.132013\pi$
$230$	−11.0925	+	20.2826i	−0.731421	+	1.33740i
$231$	0.182680	+	1.40008i	0.0120194	+	0.0921187i
$232$	−14.3634	+	6.69776i	−0.943003	+	0.439729i
$233$	3.39926	+	12.6862i	0.222693	+	0.831100i	0.983316	+	0.181907i	$0.0582269\pi$
$233$	3.39926	+	12.6862i	0.222693	+	0.831100i	−0.760623	+	0.649194i	$0.775106\pi$
$234$	−6.05943	+	4.22203i	−0.396118	+	0.276003i
$235$	−11.6460	−	0.747845i	−0.759703	−	0.0487841i
$236$	−1.50253	+	0.264936i	−0.0978062	+	0.0172459i
$237$	−15.4262	+	3.40122i	−1.00204	+	0.220933i
$238$	0.460832	+	0.214889i	0.0298713	+	0.0139292i
$239$	−0.262840	+	1.49064i	−0.0170017	+	0.0964214i	−0.992128	−	0.125229i	$-0.960033\pi$
$239$	−0.262840	+	1.49064i	−0.0170017	+	0.0964214i	0.975126	+	0.221651i	$0.0711445\pi$
$240$	−13.7016	−	3.99116i	−0.884436	−	0.257628i
$241$	18.7538	−	15.7363i	1.20804	−	1.01367i	0.208677	−	0.977985i	$-0.433084\pi$
$241$	18.7538	−	15.7363i	1.20804	−	1.01367i	0.999363	−	0.0356816i	$-0.0113602\pi$
$242$	8.83860	+	8.83860i	0.568167	+	0.568167i
$243$	10.4649	+	11.5536i	0.671321	+	0.741167i
$244$		−	0.146736i		−	0.00939383i
$245$	9.27031	−	11.5819i	0.592259	−	0.739943i
$246$	−8.17441	−	26.0307i	−0.521182	−	1.65966i
$247$	7.97934	+	11.3957i	0.507713	+	0.725090i
$248$	−4.63286	+	9.93519i	−0.294187	+	0.630885i
$249$	16.3071	+	10.4153i	1.03342	+	0.660040i
$250$	−15.2175	−	0.271612i	−0.962439	−	0.0171783i
$251$	−6.15607	+	3.55421i	−0.388568	+	0.224340i	−0.681539	−	0.731781i	$-0.738689\pi$
$251$	−6.15607	+	3.55421i	−0.388568	+	0.224340i	0.292972	+	0.956121i	$0.405356\pi$
$252$	−0.0468523	+	0.262170i	−0.00295142	+	0.0165151i
$253$	−9.89086	+	2.65025i	−0.621833	+	0.166620i
$254$	−11.1217	−	4.04796i	−0.697836	−	0.253992i
$255$	2.26556	−	0.769481i	0.141875	−	0.0481867i
$256$	−2.68459	−	2.25263i	−0.167787	−	0.140790i
$257$	1.19053	+	13.6078i	0.0742633	+	0.848834i	0.938394	+	0.345567i	$0.112313\pi$
$257$	1.19053	+	13.6078i	0.0742633	+	0.848834i	−0.864131	+	0.503267i	$0.832131\pi$
$258$	−2.57936	−	0.342610i	−0.160584	−	0.0213300i
$259$	1.03202	−	2.83544i	0.0641264	−	0.176186i
$260$	−0.532153	+	0.263305i	−0.0330027	+	0.0163295i
$261$	−15.7044	−	4.24688i	−0.972077	−	0.262875i
$262$	−5.31548	−	1.42428i	−0.328391	−	0.0879922i
$263$	−6.43173	−	4.50355i	−0.396598	−	0.277701i	0.358218	−	0.933638i	$-0.383385\pi$
$263$	−6.43173	−	4.50355i	−0.396598	−	0.277701i	−0.754815	+	0.655937i	$0.772273\pi$
$264$	−3.14445	−	6.05749i	−0.193527	−	0.372813i
$265$	0.709812	+	0.172695i	0.0436034	+	0.0106085i
$266$	−6.23546	−	1.09948i	−0.382320	−	0.0674134i
$267$	12.4040	−	0.527215i	0.759110	−	0.0322650i
$268$	−0.237303	−	0.0207614i	−0.0144956	−	0.00126820i
$269$	−28.0785			−1.71198			−0.855988	−	0.516995i	$-0.827051\pi$
$269$	−28.0785			−1.71198			−0.855988	+	0.516995i	$0.827051\pi$
$270$	−8.75927	−	13.1702i	−0.533072	−	0.801510i
$271$	−2.80897			−0.170633			−0.0853163	−	0.996354i	$-0.527190\pi$
$271$	−2.80897			−0.170633			−0.0853163	+	0.996354i	$0.527190\pi$
$272$	−2.26774	−	0.198402i	−0.137502	−	0.0120299i
$273$	−1.01566	−	1.59834i	−0.0614705	−	0.0967357i
$274$	−18.3502	−	3.23563i	−1.10857	−	0.195472i
$275$	−4.56764	−	4.95829i	−0.275439	−	0.298996i
$276$	−1.92950	−	0.0864767i	−0.116142	−	0.00520528i
$277$	2.39206	+	1.67494i	0.143725	+	0.100637i	0.643227	−	0.765675i	$-0.277595\pi$
$277$	2.39206	+	1.67494i	0.143725	+	0.100637i	−0.499503	+	0.866312i	$0.666484\pi$
$278$	−8.27466	−	2.21719i	−0.496281	−	0.132978i
$279$	−10.2096	+	4.73213i	−0.611232	+	0.283305i
$280$	1.26507	−	3.74304i	0.0756023	−	0.223689i
$281$	5.14517	−	14.1362i	0.306935	−	0.843297i	−0.686315	−	0.727304i	$-0.740773\pi$
$281$	5.14517	−	14.1362i	0.306935	−	0.843297i	0.993250	−	0.115992i	$-0.0370048\pi$
$282$	4.69604	+	11.3744i	0.279645	+	0.677334i
$283$	1.20465	+	13.7692i	0.0716091	+	0.818496i	0.944056	+	0.329786i	$0.106977\pi$
$283$	1.20465	+	13.7692i	0.0716091	+	0.818496i	−0.872446	+	0.488710i	$0.837468\pi$
$284$	1.07443	+	0.901556i	0.0637558	+	0.0534975i
$285$	−24.7703	+	16.5570i	−1.46727	+	0.980752i
$286$	3.11902	+	1.13523i	0.184432	+	0.0671277i
$287$	6.75781	−	1.81075i	0.398901	−	0.106885i
$288$	−0.426141	−	2.44985i	−0.0251106	−	0.144359i
$289$	−14.3919	+	8.30917i	−0.846583	+	0.488775i
$290$	15.1178	+	6.62815i	0.887750	+	0.389218i
$291$	0.809729	−	18.0670i	0.0474671	−	1.05910i
$292$	0.501140	−	1.07470i	0.0293270	−	0.0628920i
$293$	−11.1301	−	15.8954i	−0.650227	−	0.928621i	0.349739	−	0.936847i	$-0.386270\pi$
$293$	−11.1301	−	15.8954i	−0.650227	−	0.928621i	−0.999966	+	0.00822650i	$0.997381\pi$
$294$	−15.2684	−	3.40343i	−0.890471	−	0.198492i
$295$	18.1397	+	14.5192i	1.05613	+	0.845342i
$296$			14.5854i			0.847761i
$297$	1.54006	−	6.83462i	0.0893636	−	0.396585i
$298$	−3.26896	−	3.26896i	−0.189366	−	0.189366i
$299$	10.5207	−	8.82792i	0.608428	−	0.510532i
$300$	−0.539116	−	1.15165i	−0.0311259	−	0.0664905i
$301$	0.115860	−	0.657074i	0.00667805	−	0.0378731i
$302$	−28.0365	−	13.0736i	−1.61332	−	0.752304i
$303$	−3.95521	+	12.4940i	−0.227221	+	0.717761i
$304$	27.9159	−	4.92232i	1.60108	−	0.282314i
$305$	−1.67813	+	1.47562i	−0.0960897	+	0.0844936i
$306$	−1.77990	−	1.78814i	−0.101750	−	0.102221i
$307$	−1.06560	−	3.97686i	−0.0608167	−	0.226971i	0.928828	−	0.370512i	$-0.120818\pi$
$307$	−1.06560	−	3.97686i	−0.0608167	−	0.226971i	−0.989644	+	0.143541i	$0.954151\pi$
$308$	0.108480	−	0.0505852i	0.00618124	−	0.00288236i
$309$	24.6739	−	18.8877i	1.40365	−	1.07449i
$310$	10.9576	−	3.20957i	0.622347	−	0.182291i
$311$	2.34841	−	2.79872i	0.133166	−	0.158701i	−0.695341	−	0.718680i	$-0.744746\pi$
$311$	2.34841	−	2.79872i	0.133166	−	0.158701i	0.828507	+	0.559979i	$0.189191\pi$
$312$	7.25580	+	5.58090i	0.410779	+	0.315956i
$313$	8.22932	+	17.6478i	0.465148	+	0.997514i	0.989301	+	0.145890i	$0.0466044\pi$
$313$	8.22932	+	17.6478i	0.465148	+	0.997514i	−0.524152	+	0.851624i	$0.675618\pi$
$314$	−12.5691	+	21.7702i	−0.709313	+	1.22857i
$315$	3.46943	−	2.10062i	0.195481	−	0.118357i
$316$	0.669566	+	1.15972i	0.0376660	+	0.0652395i
$317$	−6.73196	+	9.61423i	−0.378104	+	0.539989i	−0.962430	−	0.271530i	$-0.912470\pi$
$317$	−6.73196	+	9.61423i	−0.378104	+	0.539989i	0.584325	+	0.811519i	$0.301359\pi$
$318$	−0.165856	−	0.752240i	−0.00930076	−	0.0421835i
$319$	2.50072	+	6.87067i	0.140013	+	0.384684i
$320$	0.439663	+	18.9968i	0.0245779	+	1.06196i
$321$	12.2442	−	3.84504i	0.683405	−	0.214609i
$322$	−0.544788	+	6.22696i	−0.0303599	+	0.347015i
$323$	−3.36055	+	3.36055i	−0.186986	+	0.186986i
$324$	0.666018	−	1.14137i	0.0370010	−	0.0634093i
$325$	8.36272	+	3.43805i	0.463880	+	0.190709i
$326$	−19.8564	−	23.6639i	−1.09974	−	1.31062i
$327$	−4.07329	−	2.12640i	−0.225253	−	0.117590i
$328$	−27.7020	+	19.3971i	−1.52959	+	1.07103i
$329$	−2.96513	+	1.07922i	−0.163473	+	0.0594993i
$330$	−2.57535	+	6.62580i	−0.141768	+	0.364738i
$331$	−2.17274	−	12.3222i	−0.119424	−	0.677290i	−0.984464	−	0.175586i	$-0.943818\pi$
$331$	−2.17274	−	12.3222i	−0.119424	−	0.677290i	0.865040	−	0.501704i	$-0.167293\pi$
$332$	0.424541	−	1.58441i	0.0232997	−	0.0869556i
$333$	−9.65040	+	11.4471i	−0.528839	+	0.627297i
$334$	1.60421	+	0.926193i	0.0877787	+	0.0506790i
$335$	2.14895	+	2.92267i	0.117409	+	0.159683i
$336$	−3.82629	+	0.499245i	−0.208741	+	0.0272361i
$337$	21.7105	−	1.89942i	1.18265	−	0.103468i	0.521183	−	0.853445i	$-0.325491\pi$
$337$	21.7105	−	1.89942i	1.18265	−	0.103468i	0.661464	+	0.749977i	$0.269935\pi$
$338$	13.1949	−	1.15440i	0.717706	−	0.0627912i
$339$	8.14719	+	10.6430i	0.442494	+	0.578051i
$340$	−0.120154	−	0.163415i	−0.00651625	−	0.00886242i
$341$	4.37989	+	2.52873i	0.237184	+	0.136938i
$342$	27.1717	+	15.7714i	1.46928	+	0.852819i
$343$	2.13356	−	7.96256i	0.115202	−	0.429938i
$344$	0.560037	+	3.17613i	0.0301952	+	0.171245i
$345$	18.4145	+	22.9361i	0.991405	+	1.23484i
$346$	23.4555	−	8.53711i	1.26098	−	0.458958i
$347$	21.9674	−	15.3818i	1.17927	−	0.825736i	0.191478	−	0.981497i	$-0.438672\pi$
$347$	21.9674	−	15.3818i	1.17927	−	0.825736i	0.987795	+	0.155761i	$0.0497829\pi$
$348$	0.0585651	+	1.37788i	0.00313942	+	0.0738621i
$349$	−6.78403	−	8.08489i	−0.363141	−	0.432774i	0.553277	−	0.832997i	$-0.313377\pi$
$349$	−6.78403	−	8.08489i	−0.363141	−	0.432774i	−0.916418	+	0.400223i	$0.868933\pi$
$350$	−3.79784	+	1.58490i	−0.203003	+	0.0847167i
$351$	2.00199	+	9.18084i	0.106858	+	0.490037i
$352$	−0.790247	+	0.790247i	−0.0421203	+	0.0421203i
$353$	1.15719	−	13.2268i	0.0615911	−	0.703989i	−0.901140	−	0.433528i	$-0.857268\pi$
$353$	1.15719	−	13.2268i	0.0615911	−	0.703989i	0.962731	−	0.270461i	$-0.0871761\pi$
$354$	5.33047	−	23.9135i	0.283311	−	1.27099i
$355$	−0.494215	−	21.3539i	−0.0262302	−	1.13335i
$356$	−0.359965	−	0.988995i	−0.0190781	−	0.0524166i
$357$	0.477485	−	0.436521i	0.0252712	−	0.0231031i
$358$	−11.5227	+	16.4561i	−0.608992	+	0.869731i
$359$	−6.52848	−	11.3077i	−0.344560	−	0.596796i	0.640714	−	0.767780i	$-0.278639\pi$
$359$	−6.52848	−	11.3077i	−0.344560	−	0.596796i	−0.985274	+	0.170984i	$0.945305\pi$
$360$	−12.2862	+	15.2773i	−0.647538	+	0.805186i
$361$	20.0901	−	34.7970i	1.05737	−	1.83142i
$362$	−2.61558	−	5.60913i	−0.137472	−	0.294809i
$363$	14.7002	−	6.06916i	0.771563	−	0.318548i
$364$	−0.103191	+	0.122979i	−0.00540870	+	0.00644584i
$365$	−17.3303	+	5.07620i	−0.907107	+	0.265700i
$366$	2.17594	+	0.904249i	0.113738	+	0.0472658i
$367$	11.4204	−	5.32542i	0.596140	−	0.277985i	−0.101038	−	0.994883i	$-0.532216\pi$
$367$	11.4204	−	5.32542i	0.596140	−	0.277985i	0.697178	+	0.716898i	$0.254439\pi$
$368$	−7.24287	−	27.0308i	−0.377561	−	1.40908i
$369$	−34.5754	−	3.10545i	−1.79992	−	0.161663i
$370$	11.4085	−	10.0317i	0.593098	−	0.521523i
$371$	0.194522	−	0.0342995i	0.0100991	−	0.00178074i
$372$	0.643662	+	0.704064i	0.0333723	+	0.0365040i
$373$	−30.1641	−	14.0658i	−1.56184	−	0.728297i	−0.566439	−	0.824104i	$-0.691679\pi$
$373$	−30.1641	−	14.0658i	−1.56184	−	0.728297i	−0.995400	+	0.0958064i	$0.969457\pi$
$374$	−0.196903	+	1.11669i	−0.0101816	+	0.0577429i
$375$	−7.74923	+	17.7468i	−0.400169	+	0.916442i
$376$	11.6841	−	9.80414i	0.602562	−	0.505610i
$377$	−6.93424	−	6.93424i	−0.357131	−	0.357131i
$378$	−3.59897	−	2.31036i	−0.185111	−	0.118832i
$379$			13.6970i			0.703566i	0.936082	+	0.351783i	$0.114424\pi$
$379$			13.6970i			0.703566i	−0.936082	+	0.351783i	$0.885576\pi$
$380$	1.97188	+	1.57832i	0.101155	+	0.0809659i
$381$	−10.1863	+	11.0907i	−0.521861	+	0.568193i
$382$	14.0789	+	20.1068i	0.720339	+	1.02875i
$383$	−1.77906	+	3.81521i	−0.0909059	+	0.194948i	−0.946504	−	0.322693i	$-0.895412\pi$
$383$	−1.77906	+	3.81521i	−0.0909059	+	0.194948i	0.855598	+	0.517641i	$0.173190\pi$
$384$	15.2352	−	7.90860i	0.777469	−	0.403584i
$385$	−1.66942	−	0.731926i	−0.0850814	−	0.0373024i
$386$	7.33715	−	4.23610i	0.373451	−	0.215612i
$387$	−1.66194	+	2.86327i	−0.0844812	+	0.145548i
$388$	−1.48088	+	0.396801i	−0.0751804	+	0.0201445i
$389$	−7.63677	−	2.77956i	−0.387200	−	0.140929i	0.141083	−	0.989998i	$-0.454942\pi$
$389$	−7.63677	−	2.77956i	−0.387200	−	0.140929i	−0.528283	+	0.849069i	$0.677164\pi$
$390$	−0.625177	−	9.51383i	−0.0316571	−	0.481752i
$391$	3.59414	+	3.01584i	0.181763	+	0.152517i
$392$	1.68988	+	19.3154i	0.0853520	+	0.975577i
$393$	−4.26876	+	5.54987i	−0.215330	+	0.279954i
$394$	2.43772	−	6.69758i	0.122810	−	0.337419i
$395$	6.52971	−	19.3199i	0.328546	−	0.972088i
$396$	−0.591774	+	0.0503963i	−0.0297378	+	0.00253251i
$397$	23.0217	+	6.16864i	1.15543	+	0.309595i	0.785137	−	0.619322i	$-0.212592\pi$
$397$	23.0217	+	6.16864i	1.15543	+	0.309595i	0.370288	+	0.928917i	$0.379259\pi$
$398$	17.9108	+	12.5413i	0.897788	+	0.628638i
$399$	−4.33633	+	6.78936i	−0.217088	+	0.339893i
$400$	13.5505	−	12.4829i	0.677527	−	0.624146i
$401$	−12.0856	−	2.13102i	−0.603527	−	0.106418i	−0.136468	−	0.990644i	$-0.543575\pi$
$401$	−12.0856	−	2.13102i	−0.603527	−	0.106418i	−0.467059	+	0.884226i	$0.654686\pi$
$402$	1.77023	−	3.39101i	0.0882909	−	0.169128i
$403$	−6.75736	−	0.591193i	−0.336608	−	0.0294494i
$404$	1.11095			0.0552721
$405$	−19.7508	+	3.86102i	−0.981423	+	0.191856i
$406$	4.46329			0.221509
$407$	6.70341	+	0.586472i	0.332276	+	0.0290703i
$408$	−1.44718	+	2.77218i	−0.0716459	+	0.137243i
$409$	−0.997728	−	0.175926i	−0.0493345	−	0.00869900i	0.148926	−	0.988848i	$-0.452418\pi$
$409$	−0.997728	−	0.175926i	−0.0493345	−	0.00869900i	−0.198261	+	0.980149i	$0.563529\pi$
$410$	34.2252	+	8.32686i	1.69026	+	0.411234i
$411$	−12.7613	+	19.9803i	−0.629468	+	0.985554i
$412$	−2.15778	−	1.51090i	−0.106306	−	0.0744365i
$413$	6.06833	+	1.62601i	0.298603	+	0.0800105i
$414$	13.1727	−	28.0794i	0.647403	−	1.38003i
$415$	−22.3892	+	11.0780i	−1.09904	+	0.543797i
$416$	0.512661	−	1.40852i	0.0251353	−	0.0690586i
$417$	−6.64522	+	8.63954i	−0.325418	+	0.423080i
$418$	−1.23063	−	14.0662i	−0.0601923	−	0.688001i
$419$	16.2085	+	13.6005i	0.791837	+	0.664430i	0.946199	−	0.323584i	$-0.104888\pi$
$419$	16.2085	+	13.6005i	0.791837	+	0.664430i	−0.154362	+	0.988014i	$0.549332\pi$
$420$	−0.258537	−	0.226654i	−0.0126153	−	0.0110596i
$421$	−13.4378	−	4.89097i	−0.654920	−	0.238371i	−0.00687840	−	0.999976i	$-0.502189\pi$
$421$	−13.4378	−	4.89097i	−0.654920	−	0.238371i	−0.648042	+	0.761605i	$0.724412\pi$
$422$	−27.5283	+	7.37620i	−1.34006	+	0.359068i
$423$	15.6569	+	0.0361679i	0.761266	+	0.00175854i
$424$	−0.826860	+	0.477388i	−0.0401558	+	0.0231840i
$425$	−0.660583	+	3.01747i	−0.0320430	+	0.146369i
$426$	−19.9902	+	10.3769i	−0.968527	+	0.502762i
$427$	−0.255353	+	0.547606i	−0.0123574	+	0.0265005i
$428$	−0.624023	−	0.891198i	−0.0301633	−	0.0430777i
$429$	2.85671	−	3.11033i	0.137923	−	0.150168i
$430$	2.09912	−	2.62256i	0.101229	−	0.126471i
$431$		−	9.05726i		−	0.436273i	−0.975918	−	0.218136i	$-0.930002\pi$
$431$		−	9.05726i		−	0.436273i	0.975918	−	0.218136i	$-0.0699978\pi$
$432$	18.6784	+	4.20885i	0.898663	+	0.202498i
$433$	−9.70288	−	9.70288i	−0.466290	−	0.466290i	0.434420	−	0.900710i	$-0.356953\pi$
$433$	−9.70288	−	9.70288i	−0.466290	−	0.466290i	−0.900710	+	0.434420i	$0.856953\pi$
$434$	2.36498	−	1.98446i	0.113523	−	0.0952570i
$435$	15.1690	−	14.5261i	0.727299	−	0.696472i
$436$	−0.0676401	+	0.383606i	−0.00323937	+	0.0183714i
$437$	−52.9501	−	24.6910i	−2.53294	−	1.18113i
$438$	12.8484	+	14.0541i	0.613918	+	0.671530i
$439$	7.70527	−	1.35865i	0.367752	−	0.0648447i	0.0132817	−	0.999912i	$-0.495772\pi$
$439$	7.70527	−	1.35865i	0.367752	−	0.0648447i	0.354471	+	0.935067i	$0.384661\pi$
$440$	8.79294	+	0.564635i	0.419187	+	0.0269179i
$441$	−11.4537	+	16.2775i	−0.545416	+	0.775117i
$442$	−0.393622	−	1.46902i	−0.0187227	−	0.0698740i
$443$	8.90936	−	4.15450i	0.423297	−	0.197386i	−0.199285	−	0.979942i	$-0.563862\pi$
$443$	8.90936	−	4.15450i	0.423297	−	0.197386i	0.622581	+	0.782555i	$0.286084\pi$
$444$	1.17206	+	0.487068i	0.0556233	+	0.0231152i
$445$	−7.69064	+	14.0623i	−0.364571	+	0.666616i
$446$	14.1287	−	16.8379i	0.669013	−	0.797299i
$447$	−5.43690	+	2.24468i	−0.257156	+	0.106170i
$448$	2.17136	+	4.65650i	0.102587	+	0.219999i
$449$	−0.516059	+	0.893841i	−0.0243543	+	0.0421830i	−0.877946	−	0.478760i	$-0.841086\pi$
$449$	−0.516059	+	0.893841i	−0.0243543	+	0.0421830i	0.853591	+	0.520943i	$0.174420\pi$
$450$	20.3999	−	0.897559i	0.961662	−	0.0423113i
$451$	7.80096	+	13.5117i	0.367333	+	0.636239i
$452$	0.651722	−	0.930755i	0.0306544	−	0.0437790i
$453$	−29.0497	+	26.5575i	−1.36487	+	1.24778i
$454$	4.87234	+	13.3867i	0.228670	+	0.628267i
$455$	2.44415	−	0.0565675i	0.114584	−	0.00265192i
$456$	8.47222	−	38.0079i	0.396748	−	1.77988i
$457$	0.333737	−	3.81463i	0.0156115	−	0.178441i	−0.984386	−	0.176026i	$-0.943676\pi$
$457$	0.333737	−	3.81463i	0.0156115	−	0.178441i	0.999997	−	0.00241489i	$-0.000768684\pi$
$458$	8.14635	−	8.14635i	0.380654	−	0.380654i
$459$	−2.96999	+	1.21817i	−0.138627	+	0.0568594i
$460$	1.38255	−	2.07508i	0.0644619	−	0.0967510i
$461$	5.22971	+	6.23252i	0.243572	+	0.290278i	0.873955	−	0.486006i	$-0.161547\pi$
$461$	5.22971	+	6.23252i	0.243572	+	0.290278i	−0.630384	+	0.776284i	$0.717102\pi$
$462$	0.0816230	+	1.92037i	0.00379745	+	0.0893437i
$463$	24.1647	−	16.9203i	1.12303	−	0.786354i	0.143901	−	0.989592i	$-0.454035\pi$
$463$	24.1647	−	16.9203i	1.12303	−	0.786354i	0.979129	+	0.203238i	$0.0651465\pi$
$464$	−18.7769	+	6.83422i	−0.871694	+	0.317271i
$465$	1.57913	−	14.4414i	0.0732305	−	0.669705i
$466$	3.10467	+	17.6075i	0.143821	+	0.815650i
$467$	−3.40841	+	12.7204i	−0.157723	+	0.588629i	0.841134	+	0.540826i	$0.181888\pi$
$467$	−3.40841	+	12.7204i	−0.157723	+	0.588629i	−0.998857	+	0.0478022i	$0.984778\pi$
$468$	0.690771	−	0.396692i	0.0319309	−	0.0183371i
$469$	0.849464	+	0.490438i	0.0392246	+	0.0226463i
$470$	−15.7048	−	2.39593i	−0.724409	−	0.110516i
$471$	19.4414	+	25.3972i	0.895814	+	1.17024i
$472$	−30.2520	+	2.64671i	−1.39246	+	0.121824i
$473$	1.48226	−	0.129681i	0.0681542	−	0.00596272i
$474$	−21.3235	+	2.78224i	−0.979422	+	0.127793i
$475$	−1.77948	−	38.4231i	−0.0816484	−	1.76297i
$476$	−0.0474959	−	0.0274218i	−0.00217697	−	0.00125688i
$477$	−0.964807	−	0.172420i	−0.0441755	−	0.00789459i
$478$	−0.533304	+	1.99032i	−0.0243928	+	0.0910350i
$479$	−1.80216	−	10.2206i	−0.0823429	−	0.466990i	−0.997898	−	0.0647982i	$-0.979360\pi$
$479$	−1.80216	−	10.2206i	−0.0823429	−	0.466990i	0.915555	−	0.402192i	$-0.131751\pi$
$480$	2.99216	+	1.16301i	0.136573	+	0.0530837i
$481$	−8.48082	+	3.08676i	−0.386692	+	0.140744i
$482$	27.2997	−	19.1155i	1.24347	−	0.870686i
$483$	7.05021	+	3.68047i	0.320796	+	0.167467i
$484$	−0.866613	−	1.03279i	−0.0393915	−	0.0469450i
$485$	19.4301	+	12.9456i	0.882275	+	0.587830i
$486$	12.8209	+	16.9099i	0.581569	+	0.767047i
$487$	−0.394954	+	0.394954i	−0.0178971	+	0.0178971i	−0.715999	−	0.698102i	$-0.754028\pi$
$487$	−0.394954	+	0.394954i	−0.0178971	+	0.0178971i	0.698102	+	0.715999i	$0.254028\pi$
$488$	0.254550	−	2.90952i	0.0115229	−	0.131708i
$489$	−37.4985	+	11.7756i	−1.69574	+	0.532512i
$490$	13.9459	−	14.6067i	0.630012	−	0.659865i
$491$	4.58477	+	12.5966i	0.206908	+	0.568475i	0.999128	−	0.0417610i	$-0.0132968\pi$
$491$	4.58477	+	12.5966i	0.206908	+	0.568475i	−0.792220	+	0.610236i	$0.791075\pi$
$492$	0.633630	+	2.87383i	0.0285663	+	0.129562i
$493$	1.92156	−	2.74428i	0.0865429	−	0.123596i
$494$	9.46898	+	16.4008i	0.426030	+	0.737905i
$495$	6.52738	+	6.26096i	0.293384	+	0.281409i
$496$	−6.91077	+	11.9698i	−0.310303	+	0.537460i
$497$	−2.44078	−	5.23426i	−0.109484	−	0.234789i
$498$	20.8788	+	16.0592i	0.935602	+	0.719631i
$499$	1.07489	−	1.28100i	0.0481187	−	0.0573456i	−0.741448	−	0.671010i	$-0.765861\pi$
$499$	1.07489	−	1.28100i	0.0481187	−	0.0573456i	0.789567	+	0.613664i	$0.210305\pi$
$500$	1.63256	+	0.172238i	0.0730101	+	0.00770272i
$501$	1.87148	−	1.43261i	0.0836117	−	0.0640042i
$502$	−8.77014	+	4.08958i	−0.391430	+	0.182527i
$503$	−1.14574	−	4.27597i	−0.0510861	−	0.190656i	0.935667	−	0.352884i	$-0.114799\pi$
$503$	−1.14574	−	4.27597i	−0.0510861	−	0.190656i	−0.986753	+	0.162227i	$0.948132\pi$
$504$	−1.38379	+	5.11707i	−0.0616390	+	0.227933i
$505$	−11.1720	−	12.7053i	−0.497149	−	0.565379i
$506$	−13.7277	+	2.42057i	−0.610273	+	0.107608i
$507$	5.08620	−	16.0666i	0.225886	−	0.713545i
$508$	1.15696	+	0.539501i	0.0513319	+	0.0239365i
$509$	2.24592	−	12.7373i	0.0995488	−	0.564569i	−0.893709	−	0.448646i	$-0.851906\pi$
$509$	2.24592	−	12.7373i	0.0995488	−	0.564569i	0.993258	−	0.115923i	$-0.0369826\pi$
$510$	3.16370	−	0.774716i	0.140091	−	0.0343050i
$511$	−3.74041	+	3.13858i	−0.165466	+	0.138843i
$512$	−17.3890	−	17.3890i	−0.768494	−	0.768494i
$513$	31.7971	−	24.2242i	1.40387	−	1.06952i
$514$			18.5953i			0.820202i
$515$	4.42001	+	39.8712i	0.194769	+	1.75694i
$516$	0.273929	+	0.0610607i	0.0120591	+	0.00268805i
$517$	−4.03613	−	5.76419i	−0.177509	−	0.253509i
$518$	1.73597	−	3.72279i	0.0762739	−	0.163570i
$519$	1.42194	−	31.7268i	0.0624162	−	1.39265i
$520$	−11.0084	+	4.29771i	−0.482750	+	0.188467i
$521$	30.4199	−	17.5629i	1.33272	−	0.769446i	0.347004	−	0.937864i	$-0.387199\pi$
$521$	30.4199	−	17.5629i	1.33272	−	0.769446i	0.985716	+	0.168417i	$0.0538656\pi$
$522$	−20.7933	−	7.62260i	−0.910099	−	0.333632i
$523$	−17.4537	+	4.67671i	−0.763198	+	0.204498i	−0.619364	−	0.785104i	$-0.712610\pi$
$523$	−17.4537	+	4.67671i	−0.763198	+	0.204498i	−0.143834	+	0.989602i	$0.545943\pi$
$524$	0.557755	+	0.203006i	0.0243656	+	0.00886837i
$525$	0.00780977	+	5.23602i	0.000340846	+	0.228519i
$526$	−8.18795	−	6.87050i	−0.357011	−	0.299568i
$527$	−0.201966	−	2.30848i	−0.00879779	−	0.100559i
$528$	−3.28387	−	7.95394i	−0.142912	−	0.346151i
$529$	−11.8604	+	32.5861i	−0.515668	+	1.41679i
$530$	0.942108	+	0.318413i	0.0409226	+	0.0138310i
$531$	−25.4939	−	17.9389i	−1.10634	−	0.778482i
$532$	0.659659	+	0.176755i	0.0285999	+	0.00766331i
$533$	−17.1413	−	12.0025i	−0.742471	−	0.519884i
$534$	16.8840	+	0.756708i	0.730640	+	0.0327460i
$535$	−3.91675	+	16.0987i	−0.169336	+	0.696007i
$536$	−4.66928	−	0.823320i	−0.201682	−	0.0355620i
$537$	13.7086	+	21.5731i	0.591570	+	0.930950i
$538$	−38.0781	−	3.33141i	−1.64167	−	0.143627i
$539$	8.94525			0.385299
$540$	0.817370	+	1.49747i	0.0351740	+	0.0644407i
$541$	34.9191			1.50129			0.750645	−	0.660705i	$-0.229743\pi$
$541$	34.9191			1.50129			0.750645	+	0.660705i	$0.229743\pi$
$542$	−3.80933	−	0.333273i	−0.163625	−	0.0143153i
$543$	−7.86739	+	0.334394i	−0.337622	+	0.0143502i
$544$	0.504289	+	0.0889198i	0.0216212	+	0.00381240i
$545$	5.06727	−	3.08408i	0.217058	−	0.132107i
$546$	−1.18773	−	2.28806i	−0.0508302	−	0.0979199i
$547$	−30.4652	−	21.3320i	−1.30260	−	0.912089i	−0.303430	−	0.952854i	$-0.598132\pi$
$547$	−30.4652	−	21.3320i	−1.30260	−	0.912089i	−0.999169	+	0.0407643i	$0.987021\pi$
$548$	1.94130	+	0.520169i	0.0829281	+	0.0222205i
$549$	2.12485	−	2.11506i	0.0906864	−	0.0902684i
$550$	−5.60604	−	7.26603i	−0.239042	−	0.309825i
$551$	−14.2681	+	39.2012i	−0.607841	+	1.67003i
$552$	−38.1084	−	5.06186i	−1.62200	−	0.215447i
$553$	−0.480589	−	5.49316i	−0.0204367	−	0.233593i
$554$	3.04522	+	2.55524i	0.129379	+	0.108562i
$555$	−6.21619	−	18.3022i	−0.263862	−	0.776884i
$556$	0.868263	+	0.316022i	0.0368225	+	0.0134023i
$557$	2.98290	−	0.799267i	0.126390	−	0.0338660i	−0.195070	−	0.980789i	$-0.562493\pi$
$557$	2.98290	−	0.799267i	0.126390	−	0.0338660i	0.321459	+	0.946923i	$0.395827\pi$
$558$	−14.4070	+	5.20606i	−0.609897	+	0.220390i
$559$	−1.72826	+	0.997814i	−0.0730978	+	0.0422030i
$560$	2.00028	−	4.56236i	0.0845274	−	0.192795i
$561$	1.21589	+	0.776584i	0.0513350	+	0.0327874i
$562$	8.65473	−	18.5601i	0.365078	−	0.782912i
$563$	0.209362	+	0.299000i	0.00882355	+	0.0126013i	0.823540	−	0.567259i	$-0.191996\pi$
$563$	0.209362	+	0.299000i	0.00882355	+	0.0126013i	−0.814716	+	0.579860i	$0.803107\pi$
$564$	−0.397660	−	1.26631i	−0.0167445	−	0.0533214i
$565$	−17.1984	+	1.90656i	−0.723540	+	0.0802096i
$566$			18.8158i			0.790888i
$567$	−4.47174	+	3.10046i	−0.187795	+	0.130207i
$568$	19.7401	+	19.7401i	0.828275	+	0.828275i
$569$	−27.7295	+	23.2678i	−1.16248	+	0.975439i	−0.999937	−	0.0112621i	$-0.996415\pi$
$569$	−27.7295	+	23.2678i	−1.16248	+	0.975439i	−0.162546	+	0.986701i	$0.551971\pi$
$570$	−35.5562	+	19.5146i	−1.48929	+	0.817376i
$571$	−2.67641	+	15.1787i	−0.112004	+	0.635207i	0.876186	+	0.481974i	$0.160080\pi$
$571$	−2.67641	+	15.1787i	−0.112004	+	0.635207i	−0.988190	+	0.153234i	$0.951031\pi$
$572$	−0.324465	−	0.151300i	−0.0135666	−	0.00632619i
$573$	30.4981	−	6.72432i	1.27408	−	0.280913i
$574$	9.37932	−	1.65383i	0.391485	−	0.0690294i
$575$	−37.6347	+	5.05607i	−1.56948	+	0.210853i
$576$	−2.16325	−	25.4018i	−0.0901356	−	1.05841i
$577$	8.03655	+	29.9928i	0.334566	+	1.24862i	0.904339	+	0.426815i	$0.140365\pi$
$577$	8.03655	+	29.9928i	0.334566	+	1.24862i	−0.569773	+	0.821802i	$0.692969\pi$
$578$	−20.5032	+	9.56078i	−0.852819	+	0.397676i
$579$	−1.39467	−	10.6889i	−0.0579603	−	0.444216i
$580$	−1.56209	−	0.854306i	−0.0648623	−	0.0354731i
$581$	−4.34155	+	5.17406i	−0.180118	+	0.214656i
$582$	3.24167	−	24.4051i	0.134372	−	1.01162i
$583$	0.186158	+	0.399217i	0.00770987	+	0.0165339i
$584$	11.8010	−	20.4400i	0.488330	−	0.845812i
$585$	−11.4833	−	3.91069i	−0.474776	−	0.161687i
$586$	−13.2079	−	22.8768i	−0.545615	−	0.945033i
$587$	−19.3893	+	27.6907i	−0.800280	+	1.14292i	0.186754	+	0.982407i	$0.440203\pi$
$587$	−19.3893	+	27.6907i	−0.800280	+	1.14292i	−0.987034	+	0.160512i	$0.948685\pi$
$588$	1.60858	+	0.509228i	0.0663368	+	0.0210002i
$589$	9.86926	+	27.1156i	0.406656	+	1.11728i
$590$	22.8772	+	21.8422i	0.941838	+	0.899229i
$591$	−6.67891	−	6.13430i	−0.274734	−	0.252331i
$592$	−1.60277	+	18.3198i	−0.0658735	+	0.752937i
$593$	21.3177	−	21.3177i	0.875411	−	0.875411i	−0.117644	−	0.993056i	$-0.537534\pi$
$593$	21.3177	−	21.3177i	0.875411	−	0.875411i	0.993056	+	0.117644i	$0.0375343\pi$
$594$	2.89943	−	9.08592i	0.118965	−	0.372800i
$595$	0.164025	+	0.818942i	0.00672435	+	0.0335734i
$596$	0.320517	+	0.381978i	0.0131289	+	0.0156464i
$597$	23.4802	−	14.9205i	0.960982	−	0.610654i
$598$	15.3149	−	10.7236i	0.626271	−	0.438520i
$599$	30.7669	−	11.1982i	1.25710	−	0.457548i	0.374307	−	0.927305i	$-0.377881\pi$
$599$	30.7669	−	11.1982i	1.25710	−	0.457548i	0.882796	+	0.469757i	$0.155659\pi$
$600$	−8.69187	−	23.7703i	−0.354844	−	0.970420i
$601$	7.03545	+	39.9000i	0.286982	+	1.62756i	0.698119	+	0.715982i	$0.254021\pi$
$601$	7.03545	+	39.9000i	0.286982	+	1.62756i	−0.411137	+	0.911574i	$0.634868\pi$
$602$	0.235081	−	0.877332i	0.00958117	−	0.0357574i
$603$	−3.11985	−	3.73558i	−0.127050	−	0.152125i
$604$	2.88960	+	1.66831i	0.117576	+	0.0678827i
$605$	−3.09650	+	20.2969i	−0.125891	+	0.825187i
$606$	−6.84615	+	16.4742i	−0.278106	+	0.669220i
$607$	27.2286	−	2.38219i	1.10517	−	0.0966903i	0.480069	−	0.877231i	$-0.340612\pi$
$607$	27.2286	−	2.38219i	1.10517	−	0.0966903i	0.625105	+	0.780540i	$0.285056\pi$
$608$	−6.35218	+	0.555744i	−0.257615	+	0.0225384i
$609$	2.17925	−	5.24403i	0.0883076	−	0.212499i
$610$	−2.45085	+	1.80203i	−0.0992319	+	0.0729619i
$611$	8.17344	+	4.71894i	0.330662	+	0.190908i
$612$	0.174439	+	0.208867i	0.00705130	+	0.00844294i
$613$	9.10986	−	33.9985i	0.367944	−	1.37318i	−0.495442	−	0.868641i	$-0.664994\pi$
$613$	9.10986	−	33.9985i	0.367944	−	1.37318i	0.863386	−	0.504544i	$-0.168339\pi$
$614$	−0.973249	−	5.51957i	−0.0392771	−	0.222752i
$615$	26.4943	−	36.1464i	1.06835	−	1.45756i
$616$	2.23872	−	0.814828i	0.0902006	−	0.0328303i
$617$	8.99369	−	6.29745i	0.362072	−	0.253526i	−0.378357	−	0.925660i	$-0.623511\pi$
$617$	8.99369	−	6.29745i	0.362072	−	0.253526i	0.740430	+	0.672134i	$0.234622\pi$
$618$	35.7021	−	22.6868i	1.43615	−	0.912597i
$619$	4.17573	+	4.97644i	0.167837	+	0.200020i	0.843406	−	0.537276i	$-0.180547\pi$
$619$	4.17573	+	4.97644i	0.167837	+	0.200020i	−0.675570	+	0.737296i	$0.736102\pi$
$620$	−1.20755	+	0.241859i	−0.0484965	+	0.00971328i
$621$	−26.5595	−	29.1870i	−1.06580	−	1.17123i
$622$	3.51681	−	3.51681i	0.141011	−	0.141011i
$623$	−0.377710	+	4.31725i	−0.0151327	+	0.172967i
$624$	8.50023	+	7.80711i	0.340282	+	0.312534i
$625$	−14.4476	−	20.4026i	−0.577904	−	0.816105i
$626$	9.06619	+	24.9091i	0.362358	+	0.995570i
$627$	−17.1276	−	5.42207i	−0.684011	−	0.216537i
$628$	1.55519	−	2.22104i	0.0620588	−	0.0886291i
$629$	−1.54160	−	2.67013i	−0.0614676	−	0.106465i
$630$	4.95424	−	2.43709i	0.197382	−	0.0970959i
$631$	−3.56646	+	6.17729i	−0.141979	+	0.245914i	−0.928242	−	0.371978i	$-0.878680\pi$
$631$	−3.56646	+	6.17729i	−0.141979	+	0.245914i	0.786263	+	0.617892i	$0.212013\pi$
$632$	11.2645	+	24.1567i	0.448076	+	0.960902i
$633$	−4.77453	+	35.9453i	−0.189770	+	1.42870i
$634$	−10.2701	+	12.2394i	−0.407878	+	0.486090i
$635$	−5.46477	−	18.6568i	−0.216863	−	0.740374i
$636$	0.0107496	+	0.0823868i	0.000426251	+	0.00326685i
$637$	−10.8735	+	5.07039i	−0.430823	+	0.200896i
$638$	2.57613	+	9.61423i	0.101990	+	0.380631i
$639$	2.43166	+	28.5536i	0.0961951	+	1.12956i
$640$	−1.42012	+	22.1151i	−0.0561350	+	0.874178i
$641$	22.7641	−	4.01393i	0.899128	−	0.158541i	0.295065	−	0.955477i	$-0.404659\pi$
$641$	22.7641	−	4.01393i	0.899128	−	0.158541i	0.604063	+	0.796937i	$0.293548\pi$
$642$	17.0610	−	3.76165i	0.673342	−	0.148461i
$643$	19.3507	+	9.02340i	0.763119	+	0.355848i	0.764899	−	0.644150i	$-0.222789\pi$
$643$	19.3507	+	9.02340i	0.763119	+	0.355848i	−0.00178012	+	0.999998i	$0.500567\pi$
$644$	0.117074	−	0.663961i	0.00461337	−	0.0261637i
$645$	−2.05639	−	3.74681i	−0.0809702	−	0.147530i
$646$	−4.95607	+	4.15863i	−0.194994	+	0.163619i
$647$	10.9929	+	10.9929i	0.432177	+	0.432177i	0.889368	−	0.457192i	$-0.151145\pi$
$647$	10.9929	+	10.9929i	0.432177	+	0.432177i	−0.457192	+	0.889368i	$0.651145\pi$
$648$	15.1859	−	21.4759i	0.596559	−	0.843651i
$649$			14.0101i			0.549945i
$650$	10.9330	+	5.65465i	0.428829	+	0.221794i
$651$	−1.17686	−	3.74761i	−0.0461248	−	0.146880i
$652$	1.91110	+	2.72933i	0.0748445	+	0.106889i
$653$	−11.2306	+	24.0841i	−0.439488	+	0.942484i	0.554417	+	0.832239i	$0.312941\pi$
$653$	−11.2306	+	24.0841i	−0.439488	+	0.942484i	−0.993904	+	0.110245i	$0.964836\pi$
$654$	−5.27163	−	3.36696i	−0.206137	−	0.131659i
$655$	−3.28727	−	8.42019i	−0.128444	−	0.329004i
$656$	−36.9261	+	21.3193i	−1.44172	+	0.832378i
$657$	22.7858	−	8.23381i	0.888960	−	0.321231i
$658$	−4.14915	+	1.11176i	−0.161751	+	0.0433410i
$659$	−8.34013	−	3.03556i	−0.324885	−	0.118249i	0.174428	−	0.984670i	$-0.444192\pi$
$659$	−8.34013	−	3.03556i	−0.324885	−	0.118249i	−0.499314	+	0.866421i	$0.666414\pi$
$660$	0.339006	−	0.687728i	0.0131958	−	0.0267698i
$661$	−25.3280	−	21.2527i	−0.985145	−	0.826635i	−0.000287075	−	1.00000i	$-0.500091\pi$
$661$	−25.3280	−	21.2527i	−0.985145	−	0.826635i	−0.984858	+	0.173365i	$0.944536\pi$
$662$	−1.48454	−	16.9683i	−0.0576981	−	0.659492i
$663$	−1.91818	−	0.254787i	−0.0744958	−	0.00989510i
$664$	11.1664	−	30.6794i	0.433340	−	1.19059i
$665$	−4.61226	−	9.32162i	−0.178856	−	0.361477i
$666$	−14.4454	+	14.3788i	−0.559747	+	0.557167i
$667$	39.7807	+	10.6592i	1.54032	+	0.412726i
$668$	−0.163665	−	0.114599i	−0.00633238	−	0.00443398i
$669$	−12.8848	−	24.8215i	−0.498156	−	0.959653i
$670$	2.56749	+	4.21850i	0.0991908	+	0.162975i
$671$	−1.32697	−	0.233980i	−0.0512270	−	0.00903270i
$672$	0.867223	−	0.0368602i	0.0334538	−	0.00142191i
$673$	−33.5092	−	2.93167i	−1.29168	−	0.113008i	−0.579484	−	0.814984i	$-0.696746\pi$
$673$	−33.5092	−	2.93167i	−1.29168	−	0.113008i	−0.712201	+	0.701976i	$0.752301\pi$
$674$	29.6677			1.14276
$675$	8.90592	−	24.4066i	0.342789	−	0.939412i
$676$	−1.42863			−0.0549473
$677$	26.5016	+	2.31859i	1.01854	+	0.0891106i	0.584176	−	0.811627i	$-0.301418\pi$
$677$	26.5016	+	2.31859i	1.01854	+	0.0891106i	0.434363	+	0.900738i	$0.356973\pi$
$678$	9.78590	+	15.4000i	0.375825	+	0.591434i
$679$	6.21703	+	1.09623i	0.238588	+	0.0420695i
$680$	−2.09895	−	3.44866i	−0.0804909	−	0.132250i
$681$	18.1073	+	0.811537i	0.693873	+	0.0310982i
$682$	5.63968	+	3.94895i	0.215955	+	0.151213i
$683$	12.7453	+	3.41509i	0.487684	+	0.130675i	0.494278	−	0.869304i	$-0.335432\pi$
$683$	12.7453	+	3.41509i	0.487684	+	0.130675i	−0.00659412	+	0.999978i	$0.502099\pi$
$684$	−2.77132	−	1.95005i	−0.105964	−	0.0745621i
$685$	−13.5733	−	27.4324i	−0.518609	−	1.04814i
$686$	3.83812	−	10.5451i	0.146540	−	0.402615i
$687$	−5.59381	−	13.5489i	−0.213417	−	0.516923i
$688$	0.354404	+	4.05086i	0.0135115	+	0.154438i
$689$	−0.452572	−	0.379753i	−0.0172416	−	0.0144674i
$690$	22.2512	+	33.2892i	0.847091	+	1.26730i
$691$	−17.4857	−	6.36426i	−0.665186	−	0.242108i	−0.0127124	−	0.999919i	$-0.504047\pi$
$691$	−17.4857	−	6.36426i	−0.665186	−	0.242108i	−0.652474	+	0.757811i	$0.726269\pi$
$692$	−2.60053	+	0.696810i	−0.0988573	+	0.0264887i
$693$	2.29615	+	0.841740i	0.0872234	+	0.0319751i
$694$	31.6157	−	18.2533i	1.20012	−	0.692887i
$695$	−5.11732	−	13.1078i	−0.194111	−	0.497207i
$696$	−1.22902	+	27.4224i	−0.0465861	+	1.03944i
$697$	3.02118	−	6.47894i	0.114435	−	0.245407i
$698$	−8.24080	−	11.7691i	−0.311919	−	0.445466i
$699$	22.2033	+	4.94927i	0.839808	+	0.187199i
$700$	0.422974	−	0.134595i	0.0159869	−	0.00508721i
$701$		−	35.6956i		−	1.34820i	−0.738639	−	0.674102i	$-0.764531\pi$
$701$		−	35.6956i		−	1.34820i	0.738639	−	0.674102i	$-0.235469\pi$
$702$	1.62569	+	12.6879i	0.0613579	+	0.478876i
$703$	27.1479	+	27.1479i	1.02390	+	1.02390i
$704$	−8.77716	+	7.36491i	−0.330802	+	0.277576i
$705$	−10.4831	+	17.2822i	−0.394816	+	0.650884i
$706$	3.13861	−	17.7999i	0.118123	−	0.669909i
$707$	−4.14598	−	1.93330i	−0.155925	−	0.0727092i
$708$	−0.797556	+	2.51937i	−0.0299740	+	0.0946839i
$709$	−17.3058	+	3.05148i	−0.649933	+	0.114601i	−0.488888	−	0.872346i	$-0.662597\pi$
$709$	−17.3058	+	3.05148i	−0.649933	+	0.114601i	−0.161045	+	0.986947i	$0.551486\pi$
$710$	1.86334	−	29.0173i	0.0699298	−	1.08900i
$711$	−7.14251	+	26.4120i	−0.267865	+	0.990528i
$712$	−5.42180	−	20.2344i	−0.203190	−	0.758317i
$713$	25.8181	−	12.0392i	0.966894	−	0.450870i
$714$	0.699324	−	0.535328i	0.0261715	−	0.0200341i
$715$	1.53257	+	5.23222i	0.0573148	+	0.195674i
$716$	1.39280	−	1.65987i	0.0520514	−	0.0620324i
$717$	2.07808	+	1.59839i	0.0776074	+	0.0596928i
$718$	−7.51187	−	16.1093i	−0.280341	−	0.601192i
$719$	13.2107	−	22.8817i	0.492677	−	0.853342i	−0.507287	−	0.861777i	$-0.669352\pi$
$719$	13.2107	−	22.8817i	0.492677	−	0.853342i	0.999964	+	0.00843523i	$0.00268505\pi$
$720$	−17.1106	+	17.8387i	−0.637675	+	0.664809i
$721$	5.42336	+	9.39353i	0.201976	+	0.349833i
$722$	31.3733	−	44.8057i	1.16759	−	1.66750i
$723$	−9.12987	−	41.4085i	−0.339543	−	1.54000i
$724$	0.228313	+	0.627285i	0.00848519	+	0.0233129i
$725$	5.93861	+	26.4558i	0.220555	+	0.982544i
$726$	20.6555	−	6.48645i	0.766599	−	0.240735i
$727$	−0.914614	+	10.4541i	−0.0339212	+	0.387721i	0.960189	+	0.279350i	$0.0901189\pi$
$727$	−0.914614	+	10.4541i	−0.0339212	+	0.387721i	−0.994111	+	0.108371i	$0.965437\pi$
$728$	−2.25943	+	2.25943i	−0.0837402	+	0.0837402i
$729$	26.1278	−	6.80721i	0.967696	−	0.252119i
$730$	−24.1044	+	4.82783i	−0.892143	+	0.178686i
$731$	−0.438224	−	0.522256i	−0.0162083	−	0.0193163i
$732$	−0.225302	−	0.117616i	−0.00832742	−	0.00434721i
$733$	−13.8177	+	9.67529i	−0.510370	+	0.357365i	−0.800219	−	0.599707i	$-0.795284\pi$
$733$	−13.8177	+	9.67529i	−0.510370	+	0.357365i	0.289849	+	0.957072i	$0.406395\pi$
$734$	16.1194	−	5.86698i	0.594978	−	0.216554i
$735$	−10.3526	−	23.5173i	−0.381861	−	0.867449i
$736$	1.09311	+	6.19933i	0.0402925	+	0.228510i
$737$	−0.566144	+	2.11288i	−0.0208542	+	0.0778288i
$738$	−46.5204	−	8.31364i	−1.71244	−	0.306029i
$739$	−31.2734	−	18.0557i	−1.15041	−	0.664190i	−0.201424	−	0.979504i	$-0.564557\pi$
$739$	−31.2734	−	18.0557i	−1.15041	−	0.664190i	−0.948988	+	0.315314i	$0.897890\pi$
$740$	−1.32013	+	0.970651i	−0.0485291	+	0.0356819i
$741$	23.8930	−	3.11750i	0.877731	−	0.114524i
$742$	0.267867	−	0.0234353i	0.00983370	−	0.000860337i
$743$	21.5696	−	1.88710i	0.791313	−	0.0692309i	0.315670	−	0.948869i	$-0.397771\pi$
$743$	21.5696	−	1.88710i	0.791313	−	0.0692309i	0.475643	+	0.879638i	$0.342215\pi$
$744$	11.5413	+	15.0769i	0.423124	+	0.552746i
$745$	1.14524	−	7.50683i	0.0419585	−	0.275029i
$746$	−39.2377	−	22.6539i	−1.43659	−	0.829417i
$747$	29.0627	−	16.6900i	1.06335	−	0.610654i
$748$	0.0316547	−	0.118137i	0.00115741	−	0.00431951i
$749$	0.777919	+	4.41180i	0.0284245	+	0.161204i
$750$	−12.6146	+	23.1476i	−0.460619	+	0.845231i
$751$	−14.1719	+	5.15816i	−0.517141	+	0.188224i	−0.587388	−	0.809306i	$-0.699844\pi$
$751$	−14.1719	+	5.15816i	−0.517141	+	0.188224i	0.0702468	+	0.997530i	$0.477621\pi$
$752$	15.7530	−	11.0304i	0.574452	−	0.402236i
$753$	0.522841	+	12.3010i	0.0190534	+	0.448275i
$754$	−8.58102	−	10.2265i	−0.312502	−	0.372426i
$755$	−9.97909	−	49.8236i	−0.363176	−	1.81327i
$756$	0.364987	+	0.282079i	0.0132745	+	0.0102591i
$757$	−20.5414	+	20.5414i	−0.746590	+	0.746590i	−0.973837	−	0.227247i	$-0.927027\pi$
$757$	−20.5414	+	20.5414i	−0.746590	+	0.746590i	0.227247	+	0.973837i	$0.427027\pi$
$758$	−1.62509	+	18.5749i	−0.0590260	+	0.674670i
$759$	−3.85873	+	17.3109i	−0.140063	+	0.628348i
$760$	36.3608	+	34.7158i	1.31895	+	1.25928i
$761$	9.96854	+	27.3884i	0.361359	+	0.992827i	0.978549	+	0.206013i	$0.0660488\pi$
$761$	9.96854	+	27.3884i	0.361359	+	0.992827i	−0.617190	+	0.786814i	$0.711729\pi$
$762$	−15.1299	+	13.8319i	−0.548097	+	0.501075i
$763$	0.919983	−	1.31387i	0.0333056	−	0.0475654i
$764$	−1.32375	−	2.29281i	−0.0478917	−	0.0829508i
$765$	0.634476	−	4.09537i	0.0229395	−	0.148069i
$766$	−2.86530	+	4.96285i	−0.103528	+	0.179315i
$767$	−7.94128	−	17.0301i	−0.286743	−	0.614922i
$768$	−5.61057	+	2.31638i	−0.202454	+	0.0835853i
$769$	10.6700	−	12.7160i	0.384770	−	0.458552i	−0.538543	−	0.842598i	$-0.681025\pi$
$769$	10.6700	−	12.7160i	0.384770	−	0.458552i	0.923314	+	0.384046i	$0.125470\pi$
$770$	−2.17711	−	1.19066i	−0.0784576	−	0.0429083i
$771$	21.8481	+	9.07934i	0.786839	+	0.326984i
$772$	−0.828193	+	0.386193i	−0.0298073	+	0.0138994i
$773$	7.98684	+	29.8073i	0.287267	+	1.07209i	0.947167	+	0.320741i	$0.103932\pi$
$773$	7.98684	+	29.8073i	0.287267	+	1.07209i	−0.659900	+	0.751353i	$0.729402\pi$
$774$	−2.59353	+	3.68579i	−0.0932224	+	0.132483i
$775$	14.9094	+	11.3779i	0.535563	+	0.408704i
$776$	−30.0516	+	5.29890i	−1.07879	+	0.190219i
$777$	−3.52640	−	3.85732i	−0.126509	−	0.138381i
$778$	−10.0267	−	4.67552i	−0.359474	−	0.167625i
$779$	−15.4578	+	87.6658i	−0.553835	+	3.14095i
$780$	−0.0222608	+	1.02813i	−0.000797065	+	0.0368130i
$781$	9.86620	−	8.27872i	0.353040	−	0.296236i
$782$	4.51630	+	4.51630i	0.161503	+	0.161503i
$783$	−19.1085	+	20.7088i	−0.682884	+	0.740072i
$784$			24.4465i			0.873089i
$785$	−41.0400	+	4.54958i	−1.46478	+	0.162381i
$786$	−6.44747	+	7.01989i	−0.229974	+	0.250391i
$787$	−31.1666	−	44.5105i	−1.11097	−	1.58663i	−0.759601	−	0.650389i	$-0.774606\pi$
$787$	−31.1666	−	44.5105i	−1.11097	−	1.58663i	−0.351367	−	0.936238i	$-0.614283\pi$
$788$	−0.324892	+	0.696734i	−0.0115738	+	0.0248201i
$789$	−12.0702	+	6.26563i	−0.429710	+	0.223062i
$790$	11.1474	−	25.4256i	0.396606	−	0.904601i
$791$	−4.05188	+	2.33935i	−0.144068	+	0.0831778i
$792$	−11.8212	−	0.0273074i	−0.420049	−	0.000970325i
$793$	1.74563	−	0.467741i	0.0619892	−	0.0166100i
$794$	30.4885	+	11.0969i	1.08200	+	0.393815i
$795$	0.834106	−	0.951439i	0.0295827	−	0.0337441i
$796$	−1.80661	−	1.51592i	−0.0640335	−	0.0537305i
$797$	2.76406	+	31.5934i	0.0979081	+	1.11909i	0.873157	+	0.487439i	$0.162069\pi$
$797$	2.76406	+	31.5934i	0.0979081	+	1.11909i	−0.775249	+	0.631656i	$0.782376\pi$
$798$	−6.68617	+	8.69278i	−0.236688	+	0.307721i
$799$	−1.10275	+	3.02977i	−0.0390124	+	0.107186i
$800$	−3.28128	+	2.53164i	−0.116011	+	0.0895069i
$801$	9.13285	−	19.4679i	0.322693	−	0.687865i
$802$	−16.1368	−	4.32385i	−0.569812	−	0.152681i
$803$	−8.91961	−	6.24558i	−0.314766	−	0.220402i
$804$	−0.222087	+	0.347720i	−0.00783240	+	0.0122631i
$805$	−8.77064	+	5.33805i	−0.309124	+	0.188141i
$806$	−9.09373	−	1.60347i	−0.320313	−	0.0564798i
$807$	−22.5062	+	43.1124i	−0.792256	+	1.51763i
$808$	22.0282	+	1.92722i	0.774950	+	0.0677993i
$809$	−16.9032			−0.594286			−0.297143	−	0.954833i	$-0.596034\pi$
$809$	−16.9032			−0.594286			−0.297143	+	0.954833i	$0.596034\pi$
$810$	−27.2427	+	2.89271i	−0.957212	+	0.101639i
$811$	3.82992			0.134487			0.0672434	−	0.997737i	$-0.478580\pi$
$811$	3.82992			0.134487			0.0672434	+	0.997737i	$0.478580\pi$
$812$	−0.479577	−	0.0419575i	−0.0168298	−	0.00147242i
$813$	−2.25152	+	4.31295i	−0.0789641	+	0.151262i
$814$	9.02112	+	1.59067i	0.316190	+	0.0557528i
$815$	11.9952	−	49.3030i	0.420175	−	1.72701i
$816$	−2.12233	+	3.32291i	−0.0742964	+	0.116325i
$817$	6.95415	+	4.86935i	0.243295	+	0.170357i
$818$	−1.33218	−	0.356956i	−0.0465785	−	0.0124807i
$819$	−3.26822	+	0.278326i	−0.114201	+	0.00972551i
$820$	−3.59919	−	1.21645i	−0.125689	−	0.0424803i
$821$	8.11493	−	22.2956i	0.283213	−	0.778122i	−0.713761	−	0.700389i	$-0.753010\pi$
$821$	8.11493	−	22.2956i	0.283213	−	0.778122i	0.996974	−	0.0777325i	$-0.0247680\pi$
$822$	−19.6766	+	25.5818i	−0.686299	+	0.892267i
$823$	−0.888066	−	10.1506i	−0.0309561	−	0.353829i	−0.995838	−	0.0911443i	$-0.970948\pi$
$823$	−0.888066	−	10.1506i	−0.0309561	−	0.353829i	0.964882	−	0.262685i	$-0.0846080\pi$
$824$	−40.1639	−	33.7015i	−1.39918	−	1.17405i
$825$	−11.2743	+	3.03896i	−0.392519	+	0.105803i
$826$	8.03654	+	2.92506i	0.279627	+	0.101776i
$827$	−27.0882	+	7.25827i	−0.941950	+	0.252395i	−0.696943	−	0.717127i	$-0.745457\pi$
$827$	−27.0882	+	7.25827i	−0.941950	+	0.252395i	−0.245007	+	0.969521i	$0.578790\pi$
$828$	−1.67936	+	2.89328i	−0.0583618	+	0.100548i
$829$	27.7547	−	16.0242i	0.963962	−	0.556544i	0.0665716	−	0.997782i	$-0.478794\pi$
$829$	27.7547	−	16.0242i	0.963962	−	0.556544i	0.897390	+	0.441238i	$0.145461\pi$
$830$	−31.6770	+	12.3668i	−1.09953	+	0.429258i
$831$	4.48908	−	2.33028i	0.155725	−	0.0808366i
$832$	6.49455	−	13.9276i	0.225158	−	0.482853i
$833$	−2.35090	−	3.35743i	−0.0814539	−	0.116328i
$834$	−10.0368	+	10.9279i	−0.347547	+	0.378403i
$835$	0.335251	+	3.02417i	0.0116019	+	0.104656i
$836$			1.52297i			0.0526731i
$837$	−0.917638	+	19.4691i	−0.0317182	+	0.672949i
$838$	20.3672	+	20.3672i	0.703573	+	0.703573i
$839$	11.5345	−	9.67859i	0.398215	−	0.334142i	−0.421588	−	0.906787i	$-0.638527\pi$
$839$	11.5345	−	9.67859i	0.398215	−	0.334142i	0.819803	+	0.572645i	$0.194083\pi$
$840$	−4.73314	−	4.94263i	−0.163309	−	0.170537i
$841$	0.0706876	−	0.400889i	0.00243750	−	0.0138238i
$842$	−17.6432	−	8.22715i	−0.608024	−	0.283526i
$843$	−17.5810	−	19.2308i	−0.605522	−	0.662345i
$844$	3.02724	−	0.533784i	0.104202	−	0.0183736i
$845$	14.3667	+	16.3384i	0.494228	+	0.562057i
$846$	21.2286	+	1.90668i	0.729853	+	0.0655531i
$847$	1.43684	+	5.36236i	0.0493704	+	0.184253i
$848$	−1.09102	+	0.508751i	−0.0374658	+	0.0174706i
$849$	22.1072	+	9.18702i	0.758717	+	0.315298i
$850$	−1.25385	+	4.01371i	−0.0430066	+	0.137669i
$851$	24.3632	−	29.0349i	0.835160	−	0.995304i
$852$	2.24548	−	0.927070i	0.0769288	−	0.0317609i
$853$	10.9551	+	23.4934i	0.375097	+	0.804398i	0.999724	+	0.0234754i	$0.00747313\pi$
$853$	10.9551	+	23.4934i	0.375097	+	0.804398i	−0.624627	+	0.780923i	$0.714749\pi$
$854$	−0.411263	+	0.712329i	−0.0140731	+	0.0243754i
$855$	5.56748	+	51.3041i	0.190404	+	1.75456i
$856$	−10.8272	−	18.7533i	−0.370068	−	0.640976i
$857$	−9.96651	+	14.2337i	−0.340450	+	0.486212i	−0.952471	−	0.304629i	$-0.901468\pi$
$857$	−9.96651	+	14.2337i	−0.340450	+	0.486212i	0.612022	+	0.790841i	$0.290357\pi$
$858$	4.24310	−	3.87908i	0.144857	−	0.132430i
$859$	−8.27669	−	22.7400i	−0.282397	−	0.775879i	−0.997075	−	0.0764258i	$-0.975649\pi$
$859$	−8.27669	−	22.7400i	−0.282397	−	0.775879i	0.714678	−	0.699453i	$-0.246573\pi$
$860$	−0.250203	+	0.262059i	−0.00853185	+	0.00893613i
$861$	2.63643	−	11.8275i	0.0898493	−	0.403080i
$862$	1.07461	−	12.2828i	0.0366013	−	0.418355i
$863$	−34.9760	+	34.9760i	−1.19060	+	1.19060i	−0.213699	+	0.976900i	$0.568551\pi$
$863$	−34.9760	+	34.9760i	−1.19060	+	1.19060i	−0.976900	+	0.213699i	$0.931449\pi$
$864$	−4.10312	−	1.30936i	−0.139591	−	0.0445453i
$865$	34.1206	+	22.7334i	1.16013	+	0.772958i
$866$	−12.0072	−	14.3096i	−0.408020	−	0.486259i
$867$	1.22232	+	28.7578i	0.0415121	+	0.976668i
$868$	−0.272771	+	0.190996i	−0.00925844	+	0.00648283i
$869$	11.5553	−	4.20577i	0.391985	−	0.142671i
$870$	22.2947	−	17.8995i	0.755860	−	0.606851i
$871$	−0.509449	−	2.88923i	−0.0172620	−	0.0978979i
$872$	−2.00664	+	7.48887i	−0.0679533	+	0.253605i
$873$	−27.0914	−	15.7248i	−0.916905	−	0.532203i
$874$	−68.8777	−	39.7666i	−2.32982	−	1.34512i
$875$	−5.79281	−	3.48377i	−0.195833	−	0.117773i
$876$	−1.24843	−	1.63088i	−0.0421805	−	0.0551024i
$877$	−0.729539	+	0.0638264i	−0.0246348	+	0.00215526i	−0.0994665	−	0.995041i	$-0.531714\pi$
$877$	−0.729539	+	0.0638264i	−0.0246348	+	0.00215526i	0.0748317	+	0.997196i	$0.476158\pi$
$878$	10.6106	−	0.928303i	0.358089	−	0.0313287i
$879$	−33.3275	+	4.34849i	−1.12411	+	0.146671i
$880$	10.9822	+	1.67544i	0.370209	+	0.0564792i
$881$	23.4491	+	13.5383i	0.790020	+	0.456118i	0.839970	−	0.542634i	$-0.182573\pi$
$881$	23.4491	+	13.5383i	0.790020	+	0.456118i	−0.0499497	+	0.998752i	$0.515906\pi$
$882$	−17.4640	+	20.7154i	−0.588044	+	0.697525i
$883$	−4.83571	+	18.0471i	−0.162735	+	0.607334i	0.835584	+	0.549363i	$0.185130\pi$
$883$	−4.83571	+	18.0471i	−0.162735	+	0.607334i	−0.998318	+	0.0579709i	$0.981537\pi$
$884$	0.0284848	+	0.161545i	0.000958046	+	0.00543335i
$885$	36.8330	−	16.2143i	1.23813	−	0.545037i
$886$	12.5752	−	4.57699i	0.422471	−	0.153767i
$887$	−10.1719	+	7.12245i	−0.341539	+	0.239148i	−0.731744	−	0.681580i	$-0.761293\pi$
$887$	−10.1719	+	7.12245i	−0.341539	+	0.239148i	0.390204	+	0.920728i	$0.372404\pi$
$888$	22.3948	+	11.6909i	0.751520	+	0.392321i
$889$	−3.37883	−	4.02673i	−0.113322	−	0.135052i
$890$	−12.0980	+	18.1578i	−0.405524	+	0.608652i
$891$	−9.25960	−	7.84291i	−0.310208	−	0.262747i
$892$	−1.67640	+	1.67640i	−0.0561302	+	0.0561302i
$893$	3.49921	−	39.9962i	0.117097	−	1.33842i
$894$	−7.63947	+	2.39902i	−0.255502	+	0.0802351i
$895$	−32.9893	+	0.763505i	−1.10271	+	0.0255212i
$896$	2.04937	+	5.63061i	0.0684648	+	0.188105i
$897$	−5.12176	−	23.2297i	−0.171011	−	0.775618i
$898$	−0.805895	+	1.15094i	−0.0268931	+	0.0384073i
$899$	−10.1705	−	17.6158i	−0.339204	−	0.587519i
$900$	−2.20040	−	0.0953294i	−0.0733465	−	0.00317765i
$901$	0.100914	−	0.174789i	0.00336195	−	0.00582307i
$902$	8.97602	+	19.2491i	0.298869	+	0.640926i
$903$	−0.916020	−	0.704569i	−0.0304832	−	0.0234466i
$904$	14.5371	−	17.3246i	0.483496	−	0.576208i
$905$	4.87790	−	8.91921i	0.162147	−	0.296485i
$906$	−42.5461	+	32.5688i	−1.41350	+	1.08203i
$907$	−0.322094	+	0.150195i	−0.0106950	+	0.00498714i	−0.427958	−	0.903798i	$-0.640767\pi$
$907$	−0.322094	+	0.150195i	−0.0106950	+	0.00498714i	0.417263	+	0.908786i	$0.362989\pi$
$908$	−0.397687	−	1.48419i	−0.0131977	−	0.0492545i
$909$	16.0133	+	16.0874i	0.531127	+	0.533587i
$910$	3.32130	+	0.213276i	0.110100	+	0.00707003i
$911$	39.6436	−	6.99023i	1.31345	−	0.231597i	0.527324	−	0.849664i	$-0.323195\pi$
$911$	39.6436	−	6.99023i	1.31345	−	0.231597i	0.786125	+	0.618067i	$0.212084\pi$
$912$	14.8180	−	46.8081i	0.490673	−	1.54997i
$913$	−13.6512	−	6.36564i	−0.451787	−	0.210672i
$914$	0.905182	−	5.13354i	0.0299407	−	0.169802i
$915$	0.920595	+	3.75942i	0.0304339	+	0.124283i
$916$	−0.951900	+	0.798739i	−0.0314517	+	0.0263911i
$917$	−1.72821	−	1.72821i	−0.0570707	−	0.0570707i
$918$	−4.17223	+	1.29962i	−0.137704	+	0.0428939i
$919$		−	40.7569i		−	1.34445i	−0.740349	−	0.672223i	$-0.765340\pi$
$919$		−	40.7569i		−	1.34445i	0.740349	−	0.672223i	$-0.234660\pi$
$920$	31.0133	−	38.7466i	1.02248	−	1.27744i
$921$	−6.96028	−	1.55149i	−0.229349	−	0.0511235i
$922$	6.35271	+	9.07260i	0.209215	+	0.298790i
$923$	−7.30037	+	15.6557i	−0.240294	+	0.515313i
$924$	0.00928229	−	0.207110i	0.000305365	−	0.00681341i
$925$	24.3763	+	5.33646i	0.801489	+	0.175462i
$926$	34.7781	−	20.0791i	1.14288	−	0.659841i
$927$	−9.22338	−	53.0243i	−0.302935	−	1.74155i
$928$	4.34170	−	1.16336i	0.142523	−	0.0381890i
$929$	−23.3744	−	8.50760i	−0.766891	−	0.279125i	−0.0711955	−	0.997462i	$-0.522681\pi$
$929$	−23.3744	−	8.50760i	−0.766891	−	0.279125i	−0.695695	+	0.718337i	$0.744904\pi$
$930$	3.85493	−	19.3971i	0.126408	−	0.636056i
$931$	39.0973	+	32.8065i	1.28136	+	1.07519i
$932$	−0.168074	−	1.92109i	−0.00550545	−	0.0629275i
$933$	−2.41487	−	5.84910i	−0.0790592	−	0.191491i
$934$	−6.13148	+	16.8461i	−0.200628	+	0.551221i
$935$	−1.66939	+	0.825999i	−0.0545948	+	0.0270130i
$936$	14.3849	−	6.66737i	0.470185	−	0.217930i
$937$	−23.0665	−	6.18064i	−0.753549	−	0.201913i	−0.138457	−	0.990368i	$-0.544214\pi$
$937$	−23.0665	−	6.18064i	−0.753549	−	0.201913i	−0.615092	+	0.788456i	$0.710881\pi$
$938$	1.09380	+	0.765884i	0.0357137	+	0.0250070i
$939$	33.6931	+	1.51006i	1.09953	+	0.0492790i
$940$	1.66495	+	0.405076i	0.0543046	+	0.0132121i
$941$	−53.8645	−	9.49777i	−1.75593	−	0.309618i	−0.799304	−	0.600926i	$-0.794798\pi$
$941$	−53.8645	−	9.49777i	−1.75593	−	0.309618i	−0.956629	+	0.291308i	$0.905910\pi$
$942$	23.3518	+	36.7487i	0.760844	+	1.19734i
$943$	87.5463	+	7.65931i	2.85090	+	0.249421i
$944$	−38.2883			−1.24618
$945$	−0.444434	−	7.01080i	−0.0144574	−	0.228061i
$946$	2.02552			0.0658553
$947$	−4.89270	−	0.428056i	−0.158992	−	0.0139100i	0.00738203	−	0.999973i	$-0.497650\pi$
$947$	−4.89270	−	0.428056i	−0.158992	−	0.0139100i	−0.166374	+	0.986063i	$0.553206\pi$
$948$	2.31735	−	0.0984962i	0.0752641	−	0.00319901i
$949$	14.3825	+	2.53602i	0.466875	+	0.0823226i
$950$	2.14554	−	52.3179i	0.0696105	−	1.69742i
$951$	9.36594	+	18.0427i	0.303711	+	0.585073i
$952$	−0.894188	−	0.626117i	−0.0289808	−	0.0202926i
$953$	−12.3494	−	3.30900i	−0.400035	−	0.107189i	0.0531917	−	0.998584i	$-0.483061\pi$
$953$	−12.3494	−	3.30900i	−0.400035	−	0.107189i	−0.453227	+	0.891395i	$0.649727\pi$
$954$	−1.28795	−	0.348295i	−0.0416989	−	0.0112765i
$955$	−12.9094	+	38.1960i	−0.417740	+	1.23599i
$956$	0.0760133	−	0.208845i	0.00245844	−	0.00675452i
$957$	12.5538	+	1.66750i	0.405808	+	0.0539025i
$958$	−1.23134	−	14.0743i	−0.0397827	−	0.454719i
$959$	−6.33952	−	5.31949i	−0.204714	−	0.171775i
$960$	29.5206	+	14.5518i	0.952773	+	0.469656i
$961$	15.9091	+	5.79044i	0.513197	+	0.186789i
$962$	−11.8673	+	3.17984i	−0.382618	+	0.102522i
$963$	3.91053	−	21.8820i	0.126015	−	0.705138i
$964$	−3.11303	+	1.79731i	−0.100264	+	0.0578874i
$965$	12.7452	+	5.58789i	0.410281	+	0.179880i
$966$	9.12434	+	5.82768i	0.293571	+	0.187502i
$967$	15.9653	−	34.2378i	0.513411	−	1.10101i	−0.463250	−	0.886227i	$-0.653317\pi$
$967$	15.9653	−	34.2378i	0.513411	−	1.10101i	0.976661	−	0.214786i	$-0.0689053\pi$
$968$	−15.3917	−	21.9817i	−0.494709	−	0.706518i
$969$	2.46623	+	7.85351i	0.0792268	+	0.252291i
$970$	24.8138	+	19.8613i	0.796724	+	0.637707i
$971$			17.4880i			0.561217i	0.959822	+	0.280608i	$0.0905362\pi$
$971$			17.4880i			0.561217i	−0.959822	+	0.280608i	$0.909464\pi$
$972$	−1.21864	−	1.93748i	−0.0390878	−	0.0621446i
$973$	−2.69033	−	2.69033i	−0.0862479	−	0.0862479i
$974$	−0.582470	+	0.488750i	−0.0186635	+	0.0156606i
$975$	11.9820	−	10.0846i	0.383730	−	0.322964i
$976$	0.639444	−	3.62647i	0.0204681	−	0.116080i
$977$	55.0455	+	25.6682i	1.76106	+	0.821197i	0.980607	+	0.195986i	$0.0627907\pi$
$977$	55.0455	+	25.6682i	1.76106	+	0.821197i	0.780456	+	0.625211i	$0.214987\pi$
$978$	−52.2500	+	11.5202i	−1.67077	+	0.368377i
$979$	−9.51767	+	1.67822i	−0.304186	+	0.0536362i
$980$	−1.63579	+	1.43838i	−0.0522534	+	0.0459475i
$981$	−6.52986	+	4.54981i	−0.208482	+	0.145264i
$982$	4.72302	+	17.6266i	0.150718	+	0.562486i
$983$	−22.0353	+	10.2752i	−0.702816	+	0.327729i	−0.740965	−	0.671543i	$-0.765632\pi$
$983$	−22.0353	+	10.2752i	−0.702816	+	0.327729i	0.0381489	+	0.999272i	$0.487854\pi$
$984$	7.57839	+	58.0819i	0.241590	+	1.85158i
$985$	11.2353	−	3.29093i	0.357987	−	0.104858i
$986$	2.93149	−	3.49362i	0.0933577	−	0.111259i
$987$	−0.719630	+	5.41777i	−0.0229061	+	0.172450i
$988$	−0.863258	−	1.85126i	−0.0274639	−	0.0588965i
$989$	4.19049	−	7.25813i	0.133250	−	0.230795i
$990$	8.10915	+	9.26514i	0.257726	+	0.294465i
$991$	−7.89179	−	13.6690i	−0.250691	−	0.434209i	0.713025	−	0.701138i	$-0.247324\pi$
$991$	−7.89179	−	13.6690i	−0.250691	−	0.434209i	−0.963716	+	0.266929i	$0.913991\pi$
$992$	1.78331	−	2.54683i	0.0566202	−	0.0808620i
$993$	−20.6613	−	6.54074i	−0.655668	−	0.207564i
$994$	−2.68899	−	7.38794i	−0.0852896	−	0.234331i
$995$	0.831000	+	35.9056i	0.0263445	+	1.13828i
$996$	−2.09245	−	1.92182i	−0.0663017	−	0.0608953i
$997$	0.356003	−	4.06914i	0.0112747	−	0.128871i	−0.988471	−	0.151409i	$-0.951619\pi$
$997$	0.356003	−	4.06914i	0.0112747	−	0.128871i	0.999746	+	0.0225378i	$0.00717461\pi$
$998$	1.60968	−	1.60968i	0.0509535	−	0.0509535i
$999$	9.84089	+	23.9928i	0.311352	+	0.759099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.12	yes	192
3.2	odd	2		405.2.r.a.368.5		192
5.2	odd	4	inner	135.2.q.a.32.5	✓	192
5.3	odd	4		675.2.ba.b.32.12		192
5.4	even	2		675.2.ba.b.518.5		192
15.2	even	4		405.2.r.a.287.12		192
27.11	odd	18	inner	135.2.q.a.38.5	yes	192
27.16	even	9		405.2.r.a.278.12		192
135.38	even	36		675.2.ba.b.632.5		192
135.92	even	36	inner	135.2.q.a.92.12	yes	192
135.97	odd	36		405.2.r.a.197.5		192
135.119	odd	18		675.2.ba.b.443.12		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.5	✓	192	5.2	odd	4	inner
135.2.q.a.38.5	yes	192	27.11	odd	18	inner
135.2.q.a.92.12	yes	192	135.92	even	36	inner
135.2.q.a.113.12	yes	192	1.1	even	1	trivial
405.2.r.a.197.5		192	135.97	odd	36
405.2.r.a.278.12		192	27.16	even	9
405.2.r.a.287.12		192	15.2	even	4
405.2.r.a.368.5		192	3.2	odd	2
675.2.ba.b.32.12		192	5.3	odd	4
675.2.ba.b.443.12		192	135.119	odd	18
675.2.ba.b.518.5		192	5.4	even	2
675.2.ba.b.632.5		192	135.38	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35613 + 0.118646i) q^{2} +(0.801546 - 1.53542i) q^{3} +(-0.144600 - 0.0254969i) q^{4} +(1.16254 + 1.91010i) q^{5} +(1.26917 - 1.98714i) q^{6} +(0.495263 + 0.346787i) q^{7} +(-2.82292 - 0.756400i) q^{8} +(-1.71505 - 2.46142i) q^{9} +O(q^{10})\)	\(q+(1.35613 + 0.118646i) q^{2} +(0.801546 - 1.53542i) q^{3} +(-0.144600 - 0.0254969i) q^{4} +(1.16254 + 1.91010i) q^{5} +(1.26917 - 1.98714i) q^{6} +(0.495263 + 0.346787i) q^{7} +(-2.82292 - 0.756400i) q^{8} +(-1.71505 - 2.46142i) q^{9} +(1.34993 + 2.72828i) q^{10} +(-0.461147 + 1.26699i) q^{11} +(-0.155052 + 0.201585i) q^{12} +(-0.157610 - 1.80149i) q^{13} +(0.630497 + 0.529050i) q^{14} +(3.86465 - 0.253956i) q^{15} +(-3.46256 - 1.26027i) q^{16} +(0.596735 - 0.159895i) q^{17} +(-2.03379 - 3.54150i) q^{18} +(-6.66221 + 3.84643i) q^{19} +(-0.119402 - 0.305842i) q^{20} +(0.929441 - 0.482473i) q^{21} +(-0.775699 + 1.66349i) q^{22} +(4.35606 + 6.22110i) q^{23} +(-3.42410 + 3.72809i) q^{24} +(-2.29700 + 4.44115i) q^{25} -2.46176i q^{26} +(-5.15402 + 0.660379i) q^{27} +(-0.0627730 - 0.0627730i) q^{28} +(4.15413 - 3.48573i) q^{29} +(5.27110 + 0.114128i) q^{30} +(0.651351 - 3.69400i) q^{31} +(0.751218 + 0.350299i) q^{32} +(1.57574 + 1.72361i) q^{33} +(0.828222 - 0.146038i) q^{34} +(-0.0866357 + 1.34916i) q^{35} +(0.185237 + 0.399650i) q^{36} +(-1.29170 - 4.82067i) q^{37} +(-9.49120 + 4.42582i) q^{38} +(-2.89238 - 1.20198i) q^{39} +(-1.83696 - 6.27142i) q^{40} +(7.43804 - 8.86431i) q^{41} +(1.31769 - 0.544022i) q^{42} +(-0.466380 - 1.00015i) q^{43} +(0.0989861 - 0.171449i) q^{44} +(2.70776 - 6.13743i) q^{45} +(5.16928 + 8.95346i) q^{46} +(-2.99349 + 4.27515i) q^{47} +(-4.71045 + 4.30633i) q^{48} +(-2.26912 - 6.23435i) q^{49} +(-3.64196 + 5.75025i) q^{50} +(0.232805 - 1.04440i) q^{51} +(-0.0231420 + 0.264514i) q^{52} +(0.231010 - 0.231010i) q^{53} +(-7.06788 + 0.284057i) q^{54} +(-2.95619 + 0.592089i) q^{55} +(-1.13578 - 1.35357i) q^{56} +(0.565828 + 13.3124i) q^{57} +(6.04711 - 4.23423i) q^{58} +(9.76428 - 3.55391i) q^{59} +(-0.565303 - 0.0618145i) q^{60} +(0.173537 + 0.984176i) q^{61} +(1.32160 - 4.93227i) q^{62} +(0.00418995 - 1.81381i) q^{63} +(7.35941 + 4.24896i) q^{64} +(3.25781 - 2.39536i) q^{65} +(1.93241 + 2.52439i) q^{66} +(1.61617 - 0.141397i) q^{67} +(-0.0903647 + 0.00790588i) q^{68} +(13.0436 - 1.70190i) q^{69} +(-0.277562 + 1.81936i) q^{70} +(-8.27254 - 4.77616i) q^{71} +(2.97963 + 8.24568i) q^{72} +(-2.09021 + 7.80078i) q^{73} +(-1.17975 - 6.69072i) q^{74} +(4.97789 + 7.08665i) q^{75} +(1.06143 - 0.386328i) q^{76} +(-0.667764 + 0.467574i) q^{77} +(-3.77984 - 1.97321i) q^{78} +(-5.86238 - 6.98651i) q^{79} +(-1.61812 - 8.07897i) q^{80} +(-3.11722 + 8.44292i) q^{81} +(11.1387 - 11.1387i) q^{82} +(-0.973649 + 11.1289i) q^{83} +(-0.146699 + 0.0460677i) q^{84} +(0.999144 + 0.953942i) q^{85} +(-0.513808 - 1.41168i) q^{86} +(-2.02234 - 9.17231i) q^{87} +(2.26013 - 3.22780i) q^{88} +(3.58395 + 6.20758i) q^{89} +(4.40027 - 8.00189i) q^{90} +(0.546675 - 0.946869i) q^{91} +(-0.471268 - 1.01064i) q^{92} +(-5.14976 - 3.96101i) q^{93} +(-4.56680 + 5.44250i) q^{94} +(-15.0922 - 8.25389i) q^{95} +(1.13999 - 0.872657i) q^{96} +(9.46315 - 4.41274i) q^{97} +(-2.33754 - 8.72382i) q^{98} +(3.90949 - 1.03787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more