LMFDB - Embedded newform 135.2.q.a.23.2

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			23.2
Character	$\chi$	$=$	135.23
Dual form			135.2.q.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849158 - 1.82102i) q^{2} +(1.18657 - 1.26176i) q^{3} +(-1.30949 + 1.56058i) q^{4} +(-1.94472 + 1.10365i) q^{5} +(-3.30529 - 1.08934i) q^{6} +(0.278616 - 3.18459i) q^{7} +(0.0721951 + 0.0193446i) q^{8} +(-0.184096 - 2.99435i) q^{9} +O(q^{10})$	\(q+(-0.849158 - 1.82102i) q^{2} +(1.18657 - 1.26176i) q^{3} +(-1.30949 + 1.56058i) q^{4} +(-1.94472 + 1.10365i) q^{5} +(-3.30529 - 1.08934i) q^{6} +(0.278616 - 3.18459i) q^{7} +(0.0721951 + 0.0193446i) q^{8} +(-0.184096 - 2.99435i) q^{9} +(3.66116 + 2.60421i) q^{10} +(-1.39635 + 0.246214i) q^{11} +(0.415290 + 3.50401i) q^{12} +(3.26894 + 1.52433i) q^{13} +(-6.03581 + 2.19686i) q^{14} +(-0.915004 + 3.76335i) q^{15} +(0.681434 + 3.86460i) q^{16} +(6.22853 - 1.66893i) q^{17} +(-5.29645 + 2.87791i) q^{18} +(-1.34486 + 0.776456i) q^{19} +(0.824244 - 4.48012i) q^{20} +(-3.68761 - 4.13030i) q^{21} +(1.63408 + 2.33371i) q^{22} +(-1.28385 + 0.112323i) q^{23} +(0.110073 - 0.0681394i) q^{24} +(2.56390 - 4.29260i) q^{25} -7.24723i q^{26} +(-3.99660 - 3.32072i) q^{27} +(4.60499 + 4.60499i) q^{28} +(9.47861 + 3.44993i) q^{29} +(7.63013 - 1.52943i) q^{30} +(-1.28914 - 1.08172i) q^{31} +(6.58134 - 4.60830i) q^{32} +(-1.34620 + 2.05401i) q^{33} +(-8.32817 - 9.92512i) q^{34} +(2.97286 + 6.50065i) q^{35} +(4.91400 + 3.63376i) q^{36} +(1.13941 + 4.25234i) q^{37} +(2.55594 + 1.78969i) q^{38} +(5.80218 - 2.31590i) q^{39} +(-0.161749 + 0.0420584i) q^{40} +(-2.01725 - 5.54236i) q^{41} +(-4.39001 + 10.2225i) q^{42} +(-1.34911 + 1.92673i) q^{43} +(1.44426 - 2.50153i) q^{44} +(3.66273 + 5.62000i) q^{45} +(1.29474 + 2.24255i) q^{46} +(-4.86633 - 0.425748i) q^{47} +(5.68478 + 3.72582i) q^{48} +(-3.17036 - 0.559020i) q^{49} +(-9.99408 - 1.02383i) q^{50} +(5.28480 - 9.83924i) q^{51} +(-6.65949 + 3.10537i) q^{52} +(0.679717 - 0.679717i) q^{53} +(-2.65337 + 10.0977i) q^{54} +(2.44378 - 2.01990i) q^{55} +(0.0817195 - 0.224523i) q^{56} +(-0.616070 + 2.61822i) q^{57} +(-1.76642 - 20.1903i) q^{58} +(-0.761756 + 4.32014i) q^{59} +(-4.67483 - 6.35599i) q^{60} +(-10.8226 + 9.08123i) q^{61} +(-0.875151 + 3.26611i) q^{62} +(-9.58707 - 0.248002i) q^{63} +(-7.18348 - 4.14738i) q^{64} +(-8.03953 + 0.643373i) q^{65} +(4.88355 + 0.707290i) q^{66} +(3.77497 - 8.09546i) q^{67} +(-5.55167 + 11.9056i) q^{68} +(-1.38166 + 1.75320i) q^{69} +(9.31342 - 10.9337i) q^{70} +(8.43086 + 4.86756i) q^{71} +(0.0446337 - 0.219739i) q^{72} +(0.308443 - 1.15112i) q^{73} +(6.77608 - 5.68580i) q^{74} +(-2.37400 - 8.32851i) q^{75} +(0.549351 - 3.11553i) q^{76} +(0.395047 + 4.51541i) q^{77} +(-9.14429 - 8.59935i) q^{78} +(-4.67487 + 12.8441i) q^{79} +(-5.59038 - 6.76352i) q^{80} +(-8.93222 + 1.10249i) q^{81} +(-8.37981 + 8.37981i) q^{82} +(-10.2981 + 4.80207i) q^{83} +(11.2745 - 0.346259i) q^{84} +(-10.2709 + 10.1197i) q^{85} +(4.65423 + 0.820666i) q^{86} +(15.6001 - 7.86618i) q^{87} +(-0.105573 - 0.00923640i) q^{88} +(4.62153 + 8.00472i) q^{89} +(7.12391 - 11.4422i) q^{90} +(5.76516 - 9.98556i) q^{91} +(1.50590 - 2.15065i) q^{92} +(-2.89453 + 0.343056i) q^{93} +(3.35698 + 9.22322i) q^{94} +(1.75844 - 2.99425i) q^{95} +(1.99464 - 13.7722i) q^{96} +(4.04993 + 2.83579i) q^{97} +(1.67415 + 6.24800i) q^{98} +(0.994312 + 4.13583i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.849158	−	1.82102i	−0.600445	−	1.28766i	−0.938092	−	0.346386i	$-0.887409\pi$
$2$	−0.849158	−	1.82102i	−0.600445	−	1.28766i	0.337647	−	0.941273i	$-0.390369\pi$
$3$	1.18657	−	1.26176i	0.685067	−	0.728480i
$3$	1.18657	−	1.26176i	0.685067	−	0.728480i
$4$	−1.30949	+	1.56058i	−0.654743	+	0.780292i
$5$	−1.94472	+	1.10365i	−0.869707	+	0.493569i
$5$	−1.94472	+	1.10365i	−0.869707	+	0.493569i
$6$	−3.30529	−	1.08934i	−1.34938	−	0.444721i
$7$	0.278616	−	3.18459i	0.105307	−	1.20366i	−0.741199	−	0.671285i	$-0.765743\pi$
$7$	0.278616	−	3.18459i	0.105307	−	1.20366i	0.846506	−	0.532379i	$-0.178702\pi$
$8$	0.0721951	+	0.0193446i	0.0255248	+	0.00683936i
$9$	−0.184096	−	2.99435i	−0.0613653	−	0.998115i
$10$	3.66116	+	2.60421i	1.15776	+	0.823525i
$11$	−1.39635	+	0.246214i	−0.421015	+	0.0742363i	−0.380142	−	0.924928i	$-0.624125\pi$
$11$	−1.39635	+	0.246214i	−0.421015	+	0.0742363i	−0.0408729	+	0.999164i	$0.513014\pi$
$12$	0.415290	+	3.50401i	0.119884	+	1.01152i
$13$	3.26894	+	1.52433i	0.906642	+	0.422774i	0.819274	−	0.573402i	$-0.194377\pi$
$13$	3.26894	+	1.52433i	0.906642	+	0.422774i	0.0873677	+	0.996176i	$0.472154\pi$
$14$	−6.03581	+	2.19686i	−1.61314	+	0.587135i
$15$	−0.915004	+	3.76335i	−0.236253	+	0.971692i
$16$	0.681434	+	3.86460i	0.170358	+	0.966150i
$17$	6.22853	−	1.66893i	1.51064	−	0.404775i	0.593993	−	0.804470i	$-0.297551\pi$
$17$	6.22853	−	1.66893i	1.51064	−	0.404775i	0.916648	+	0.399695i	$0.130884\pi$
$18$	−5.29645	+	2.87791i	−1.24839	+	0.678331i
$19$	−1.34486	+	0.776456i	−0.308532	+	0.178131i	−0.646269	−	0.763109i	$-0.723672\pi$
$19$	−1.34486	+	0.776456i	−0.308532	+	0.178131i	0.337737	+	0.941240i	$0.390338\pi$
$20$	0.824244	−	4.48012i	0.184307	−	1.00179i
$21$	−3.68761	−	4.13030i	−0.804702	−	0.901305i
$22$	1.63408	+	2.33371i	0.348388	+	0.497549i
$23$	−1.28385	+	0.112323i	−0.267702	+	0.0234209i	−0.220217	−	0.975451i	$-0.570676\pi$
$23$	−1.28385	+	0.112323i	−0.267702	+	0.0234209i	−0.0474857	+	0.998872i	$0.515121\pi$
$24$	0.110073	−	0.0681394i	0.0224686	−	0.0139089i
$25$	2.56390	−	4.29260i	0.512780	−	0.858520i
$26$		−	7.24723i		−	1.42130i
$27$	−3.99660	−	3.32072i	−0.769146	−	0.639073i
$28$	4.60499	+	4.60499i	0.870260	+	0.870260i
$29$	9.47861	+	3.44993i	1.76013	+	0.640636i	0.999959	−	0.00908143i	$-0.00289075\pi$
$29$	9.47861	+	3.44993i	1.76013	+	0.640636i	0.760175	+	0.649718i	$0.225113\pi$
$30$	7.63013	−	1.52943i	1.39306	−	0.279234i
$31$	−1.28914	−	1.08172i	−0.231537	−	0.194282i	0.519637	−	0.854387i	$-0.326067\pi$
$31$	−1.28914	−	1.08172i	−0.231537	−	0.194282i	−0.751173	+	0.660105i	$0.770512\pi$
$32$	6.58134	−	4.60830i	1.16343	−	0.814641i
$33$	−1.34620	+	2.05401i	−0.234344	+	0.357558i
$34$	−8.32817	−	9.92512i	−1.42827	−	1.70214i
$35$	2.97286	+	6.50065i	0.502505	+	1.09881i
$36$	4.91400	+	3.63376i	0.819000	+	0.605626i
$37$	1.13941	+	4.25234i	0.187318	+	0.699081i	0.994122	+	0.108262i	$0.0345285\pi$
$37$	1.13941	+	4.25234i	0.187318	+	0.699081i	−0.806804	+	0.590819i	$0.798805\pi$
$38$	2.55594	+	1.78969i	0.414629	+	0.290326i
$39$	5.80218	−	2.31590i	0.929093	−	0.370841i
$40$	−0.161749	+	0.0420584i	−0.0255748	+	0.00665002i
$41$	−2.01725	−	5.54236i	−0.315042	−	0.865571i	−0.991619	−	0.129199i	$-0.958759\pi$
$41$	−2.01725	−	5.54236i	−0.315042	−	0.865571i	0.676577	−	0.736372i	$-0.263463\pi$
$42$	−4.39001	+	10.2225i	−0.677393	+	1.57737i
$43$	−1.34911	+	1.92673i	−0.205737	+	0.293824i	−0.908739	−	0.417365i	$-0.862954\pi$
$43$	−1.34911	+	1.92673i	−0.205737	+	0.293824i	0.703002	+	0.711188i	$0.251843\pi$
$44$	1.44426	−	2.50153i	0.217731	−	0.377121i
$45$	3.66273	+	5.62000i	0.546008	+	0.837780i
$46$	1.29474	+	2.24255i	0.190899	+	0.330646i
$47$	−4.86633	−	0.425748i	−0.709826	−	0.0621018i	−0.273476	−	0.961879i	$-0.588174\pi$
$47$	−4.86633	−	0.425748i	−0.709826	−	0.0621018i	−0.436350	+	0.899777i	$0.643729\pi$
$48$	5.68478	+	3.72582i	0.820528	+	0.537776i
$49$	−3.17036	−	0.559020i	−0.452909	−	0.0798600i
$50$	−9.99408	−	1.02383i	−1.41338	−	0.144791i
$51$	5.28480	−	9.83924i	0.740020	−	1.37777i
$52$	−6.65949	+	3.10537i	−0.923505	+	0.430637i
$53$	0.679717	−	0.679717i	0.0933664	−	0.0933664i	−0.658881	−	0.752247i	$-0.728970\pi$
$53$	0.679717	−	0.679717i	0.0933664	−	0.0933664i	0.752247	+	0.658881i	$0.228970\pi$
$54$	−2.65337	+	10.0977i	−0.361078	+	1.37413i
$55$	2.44378	−	2.01990i	0.329519	−	0.272364i
$56$	0.0817195	−	0.224523i	0.0109202	−	0.0300031i
$57$	−0.616070	+	2.61822i	−0.0816004	+	0.346791i
$58$	−1.76642	−	20.1903i	−0.231943	−	2.65112i
$59$	−0.761756	+	4.32014i	−0.0991722	+	0.562434i	0.894216	+	0.447635i	$0.147734\pi$
$59$	−0.761756	+	4.32014i	−0.0991722	+	0.562434i	−0.993389	+	0.114799i	$0.963378\pi$
$60$	−4.67483	−	6.35599i	−0.603518	−	0.820555i
$61$	−10.8226	+	9.08123i	−1.38569	+	1.16273i	−0.418638	+	0.908153i	$0.637492\pi$
$61$	−10.8226	+	9.08123i	−1.38569	+	1.16273i	−0.967052	+	0.254579i	$0.918063\pi$
$62$	−0.875151	+	3.26611i	−0.111144	+	0.414796i
$63$	−9.58707	−	0.248002i	−1.20786	−	0.0312453i
$64$	−7.18348	−	4.14738i	−0.897935	−	0.518423i
$65$	−8.03953	+	0.643373i	−0.997181	+	0.0798006i
$66$	4.88355	+	0.707290i	0.601123	+	0.0870613i
$67$	3.77497	−	8.09546i	0.461187	−	0.989018i	−0.528916	−	0.848674i	$-0.677401\pi$
$67$	3.77497	−	8.09546i	0.461187	−	0.989018i	0.990103	−	0.140344i	$-0.0448208\pi$
$68$	−5.55167	+	11.9056i	−0.673239	+	1.44376i
$69$	−1.38166	+	1.75320i	−0.166332	+	0.211060i
$70$	9.31342	−	10.9337i	1.11317	−	1.30683i
$71$	8.43086	+	4.86756i	1.00056	+	0.577673i	0.908414	−	0.418072i	$-0.137294\pi$
$71$	8.43086	+	4.86756i	1.00056	+	0.577673i	0.0921455	+	0.995746i	$0.470627\pi$
$72$	0.0446337	−	0.219739i	0.00526013	−	0.0258964i
$73$	0.308443	−	1.15112i	0.0361005	−	0.134729i	−0.945524	−	0.325553i	$-0.894449\pi$
$73$	0.308443	−	1.15112i	0.0361005	−	0.134729i	0.981624	+	0.190824i	$0.0611161\pi$
$74$	6.77608	−	5.68580i	0.787703	−	0.660961i
$75$	−2.37400	−	8.32851i	−0.274126	−	0.961694i
$76$	0.549351	−	3.11553i	0.0630149	−	0.357375i
$77$	0.395047	+	4.51541i	0.0450198	+	0.514578i
$78$	−9.14429	−	8.59935i	−1.03539	−	0.973685i
$79$	−4.67487	+	12.8441i	−0.525964	+	1.44507i	0.337819	+	0.941211i	$0.390311\pi$
$79$	−4.67487	+	12.8441i	−0.525964	+	1.44507i	−0.863783	+	0.503864i	$0.831911\pi$
$80$	−5.59038	−	6.76352i	−0.625023	−	0.756184i
$81$	−8.93222	+	1.10249i	−0.992469	+	0.122499i
$82$	−8.37981	+	8.37981i	−0.925395	+	0.925395i
$83$	−10.2981	+	4.80207i	−1.13036	+	0.527096i	−0.895557	−	0.444947i	$-0.853222\pi$
$83$	−10.2981	+	4.80207i	−1.13036	+	0.527096i	−0.234803	+	0.972043i	$0.575445\pi$
$84$	11.2745	−	0.346259i	1.23015	−	0.0377800i
$85$	−10.2709	+	10.1197i	−1.11403	+	1.09764i
$86$	4.65423	+	0.820666i	0.501878	+	0.0884947i
$87$	15.6001	−	7.86618i	1.67250	−	0.843343i
$88$	−0.105573	−	0.00923640i	−0.0112541	−	0.000984604i
$89$	4.62153	+	8.00472i	0.489881	+	0.848499i	0.999932	−	0.0116451i	$-0.00370684\pi$
$89$	4.62153	+	8.00472i	0.489881	+	0.848499i	−0.510051	+	0.860144i	$0.670374\pi$
$90$	7.12391	−	11.4422i	0.750926	−	1.20611i
$91$	5.76516	−	9.98556i	0.604353	−	1.04677i
$92$	1.50590	−	2.15065i	0.157001	−	0.224221i
$93$	−2.89453	+	0.343056i	−0.300149	+	0.0355733i
$94$	3.35698	+	9.22322i	0.346246	+	0.951303i
$95$	1.75844	−	2.99425i	0.180413	−	0.307204i
$96$	1.99464	−	13.7722i	0.203577	−	1.40562i
$97$	4.04993	+	2.83579i	0.411208	+	0.287931i	0.760819	−	0.648964i	$-0.224797\pi$
$97$	4.04993	+	2.83579i	0.411208	+	0.287931i	−0.349611	+	0.936895i	$0.613686\pi$
$98$	1.67415	+	6.24800i	0.169114	+	0.631144i
$99$	0.994312	+	4.13583i	0.0999321	+	0.415666i
$100$	3.34158	+	9.62228i	0.334158	+	0.962228i
$101$	5.75522	+	6.85881i	0.572666	+	0.682477i	0.972176	−	0.234252i	$-0.0752641\pi$
$101$	5.75522	+	6.85881i	0.572666	+	0.682477i	−0.399510	+	0.916729i	$0.630820\pi$
$102$	−22.4051	−	1.26869i	−2.21844	−	0.125619i
$103$	10.3168	−	7.22389i	1.01654	−	0.711791i	0.0584618	−	0.998290i	$-0.481380\pi$
$103$	10.3168	−	7.22389i	1.01654	−	0.711791i	0.958081	+	0.286499i	$0.0924915\pi$
$104$	0.206514	+	0.173286i	0.0202504	+	0.0169921i
$105$	11.7298	+	3.96245i	1.14471	+	0.386695i
$106$	−1.81497	−	0.660595i	−0.176285	−	0.0641626i
$107$	−0.811299	−	0.811299i	−0.0784313	−	0.0784313i	0.666803	−	0.745234i	$-0.267662\pi$
$107$	−0.811299	−	0.811299i	−0.0784313	−	0.0784313i	−0.745234	+	0.666803i	$0.767662\pi$
$108$	10.4158	−	1.88860i	1.00226	−	0.181730i
$109$		−	5.78796i		−	0.554386i	−0.960814	−	0.277193i	$-0.910596\pi$
$109$		−	5.78796i		−	0.554386i	0.960814	−	0.277193i	$-0.0894042\pi$
$110$	−5.75345	−	2.73496i	−0.548570	−	0.260769i
$111$	6.71744	+	3.60804i	0.637592	+	0.342460i
$112$	12.4970	−	1.09335i	1.18086	−	0.103312i
$113$	−1.30347	−	1.86154i	−0.122620	−	0.175119i	0.753149	−	0.657850i	$-0.228534\pi$
$113$	−1.30347	−	1.86154i	−0.122620	−	0.175119i	−0.875769	+	0.482731i	$0.839645\pi$
$114$	5.29098	−	1.10140i	0.495545	−	0.103156i
$115$	2.37278	−	1.63537i	0.221263	−	0.152499i
$116$	−17.7960	+	10.2745i	−1.65232	+	0.953967i
$117$	3.96258	−	10.0690i	0.366341	−	0.930877i
$118$	8.51392	−	2.28130i	0.783770	−	0.210011i
$119$	−3.57950	−	20.3003i	−0.328132	−	1.86093i
$120$	−0.138859	+	0.253995i	−0.0126761	+	0.0231865i
$121$	−8.44745	+	3.07462i	−0.767950	+	0.279511i
$122$	25.7272	+	11.9968i	2.32923	+	1.08614i
$123$	−9.38676	−	4.03111i	−0.846376	−	0.363473i
$124$	3.37623	−	0.595320i	0.303194	−	0.0534613i
$125$	−0.248533	+	11.1776i	−0.0222295	+	0.999753i
$126$	7.68932	+	17.6689i	0.685019	+	1.57407i
$127$	−13.4636	−	3.60755i	−1.19470	−	0.320119i	−0.393957	−	0.919129i	$-0.628894\pi$
$127$	−13.4636	−	3.60755i	−1.19470	−	0.320119i	−0.800741	+	0.599010i	$0.795561\pi$
$128$	−0.0521045	+	0.595557i	−0.00460543	+	0.0526403i
$129$	0.830261	+	3.98846i	0.0731004	+	0.351164i
$130$	7.99842	+	14.0938i	0.701508	+	1.23611i
$131$	0.491352	−	0.585571i	0.0429297	−	0.0511616i	−0.744152	−	0.668010i	$-0.767146\pi$
$131$	0.491352	−	0.585571i	0.0429297	−	0.0511616i	0.787082	+	0.616848i	$0.211591\pi$
$132$	−1.44263	−	4.79057i	−0.125564	−	0.416965i
$133$	2.09800	+	4.49917i	0.181919	+	0.390127i
$134$	−17.9476			−1.55043
$135$	11.4372	+	2.04702i	0.984358	+	0.176180i
$136$	0.481955			0.0413273
$137$	−5.84627	−	12.5374i	−0.499480	−	1.07114i	−0.980876	−	0.194635i	$-0.937648\pi$
$137$	−5.84627	−	12.5374i	−0.499480	−	1.07114i	0.481396	−	0.876503i	$-0.340130\pi$
$138$	4.36587	+	1.02729i	0.371647	+	0.0874491i
$139$	5.65704	−	6.74180i	0.479824	−	0.571832i	−0.470775	−	0.882253i	$-0.656026\pi$
$139$	5.65704	−	6.74180i	0.479824	−	0.571832i	0.950599	+	0.310421i	$0.100470\pi$
$140$	−14.0377	−	3.87312i	−1.18640	−	0.327338i
$141$	−6.31144	+	5.63497i	−0.531519	+	0.474550i
$142$	1.70482	−	19.4861i	0.143065	−	1.63524i
$143$	−4.93990	−	1.32364i	−0.413095	−	0.110688i
$144$	11.4465	−	2.75190i	0.953876	−	0.229325i
$145$	−22.2408	+	3.75194i	−1.84700	+	0.311581i
$146$	−2.35814	+	0.415804i	−0.195161	+	0.0344122i
$147$	−4.46721	+	3.33693i	−0.368450	+	0.275225i
$148$	−8.12818	−	3.79023i	−0.668132	−	0.311555i
$149$	1.25462	−	0.456644i	0.102782	−	0.0374098i	−0.290117	−	0.956991i	$-0.593694\pi$
$149$	1.25462	−	0.456644i	0.102782	−	0.0374098i	0.392900	+	0.919581i	$0.371472\pi$
$150$	−13.1505	+	11.3953i	−1.07374	+	0.930425i
$151$	2.35073	+	13.3316i	0.191299	+	1.08491i	0.917591	+	0.397526i	$0.130131\pi$
$151$	2.35073	+	13.3316i	0.191299	+	1.08491i	−0.726292	+	0.687387i	$0.758758\pi$
$152$	−0.112113	+	0.0300405i	−0.00909354	+	0.00243661i
$153$	−6.14400	−	18.3431i	−0.496713	−	1.48295i
$154$	7.88721	−	4.55368i	0.635569	−	0.366946i
$155$	3.70087	+	0.680878i	0.297261	+	0.0546894i
$156$	−3.98371	+	12.0874i	−0.318952	+	0.967770i
$157$	−3.55931	−	5.08322i	−0.284064	−	0.405685i	0.651608	−	0.758556i	$-0.274095\pi$
$157$	−3.55931	−	5.08322i	−0.284064	−	0.405685i	−0.935672	+	0.352870i	$0.885206\pi$
$158$	27.3591	−	2.39361i	2.17658	−	0.190426i
$159$	−0.0511095	−	1.66418i	−0.00405324	−	0.131978i
$160$	−7.71292	+	16.2254i	−0.609760	+	1.28273i
$161$			4.11985i			0.324690i
$162$	9.59253	+	15.3296i	0.753660	+	1.20441i
$163$	0.480773	+	0.480773i	0.0376571	+	0.0376571i	0.725685	−	0.688028i	$-0.241523\pi$
$163$	0.480773	+	0.480773i	0.0376571	+	0.0376571i	−0.688028	+	0.725685i	$0.741523\pi$
$164$	11.2909	+	4.10955i	0.881670	+	0.320902i
$165$	0.351077	−	5.48023i	0.0273313	−	0.426635i
$166$	17.4894	+	14.6753i	1.35744	+	1.13903i
$167$	−17.5397	+	12.2814i	−1.35726	+	0.950365i	−0.357396	+	0.933953i	$0.616335\pi$
$167$	−17.5397	+	12.2814i	−1.35726	+	0.950365i	−0.999865	+	0.0164121i	$0.994776\pi$
$168$	−0.186328	−	0.369523i	−0.0143755	−	0.0285093i
$169$	0.00616029	+	0.00734155i	0.000473868	+	0.000564734i
$170$	27.1499	+	10.1102i	2.08230	+	0.775418i
$171$	2.57256	+	3.88404i	0.196729	+	0.297020i
$172$	−1.24018	−	4.62843i	−0.0945631	−	0.352914i
$173$	17.1557	+	12.0126i	1.30432	+	0.913298i	0.999238	−	0.0390266i	$-0.0124257\pi$
$173$	17.1557	+	12.0126i	1.30432	+	0.913298i	0.305087	+	0.952325i	$0.401315\pi$
$174$	−27.5714	−	21.7285i	−2.09018	−	1.64723i
$175$	−12.9558	−	9.36097i	−0.979370	−	0.707623i
$176$	−1.90304	−	5.22855i	−0.143447	−	0.394117i
$177$	4.54711	+	6.08731i	0.341782	+	0.457550i
$178$	10.6524	−	15.2132i	0.798430	−	1.14028i
$179$	9.54123	−	16.5259i	0.713145	−	1.23520i	−0.250526	−	0.968110i	$-0.580604\pi$
$179$	9.54123	−	16.5259i	0.713145	−	1.23520i	0.963671	−	0.267093i	$-0.0860631\pi$
$180$	−13.5668	−	1.64330i	−1.01121	−	0.122484i
$181$	−4.29743	−	7.44336i	−0.319425	−	0.553261i	0.660943	−	0.750436i	$-0.270157\pi$
$181$	−4.29743	−	7.44336i	−0.319425	−	0.553261i	−0.980368	+	0.197175i	$0.936823\pi$
$182$	−23.0795	−	2.01919i	−1.71076	−	0.149672i
$183$	−1.38341	+	24.4311i	−0.102264	+	1.80600i
$184$	−0.0948609	−	0.0167265i	−0.00699324	−	0.00123310i
$185$	−6.90895	−	7.01211i	−0.507956	−	0.515541i
$186$	3.08263	+	4.97971i	0.226029	+	0.365130i
$187$	−8.28629	+	3.86396i	−0.605954	+	0.282561i
$188$	7.03680	−	7.03680i	0.513211	−	0.513211i
$189$	−11.6887	+	11.8023i	−0.850225	+	0.858494i
$190$	−6.94580	−	0.659579i	−0.503901	−	0.0478509i
$191$	3.25489	−	8.94274i	0.235516	−	0.647074i	−0.764481	−	0.644646i	$-0.777005\pi$
$191$	3.25489	−	8.94274i	0.235516	−	0.647074i	0.999997	−	0.00242805i	$-0.000772875\pi$
$192$	−13.7567	+	4.14269i	−0.992807	+	0.298973i
$193$	0.558797	+	6.38708i	0.0402231	+	0.459752i	0.989421	+	0.145073i	$0.0463416\pi$
$193$	0.558797	+	6.38708i	0.0402231	+	0.459752i	−0.949198	+	0.314680i	$0.898103\pi$
$194$	1.72501	−	9.78304i	0.123849	−	0.702382i
$195$	−8.72769	+	10.9074i	−0.625003	+	0.781095i
$196$	5.02394	−	4.21559i	0.358853	−	0.301113i
$197$	3.45988	−	12.9125i	0.246506	−	0.919974i	−0.726114	−	0.687574i	$-0.758676\pi$
$197$	3.45988	−	12.9125i	0.246506	−	0.919974i	0.972620	−	0.232400i	$-0.0746578\pi$
$198$	6.68711	−	5.32263i	0.475232	−	0.378263i
$199$	1.82252	+	1.05223i	0.129195	+	0.0745909i	0.563205	−	0.826317i	$-0.309568\pi$
$199$	1.82252	+	1.05223i	0.129195	+	0.0745909i	−0.434009	+	0.900908i	$0.642902\pi$
$200$	0.268140	−	0.260307i	0.0189604	−	0.0184065i
$201$	−5.73528	−	14.3690i	−0.404535	−	1.01351i
$202$	7.60296	−	16.3046i	0.534943	−	1.14719i
$203$	13.6275	−	29.2243i	0.956465	−	2.05115i
$204$	8.43459	+	21.1317i	0.590539	+	1.47952i
$205$	10.0398	+	8.55201i	0.701213	+	0.597298i
$206$	−21.9154	−	12.6529i	−1.52692	−	0.881568i
$207$	0.572685	+	3.82363i	0.0398044	+	0.265760i
$208$	−3.66337	+	13.6719i	−0.254009	+	0.947975i
$209$	1.68672	−	1.41533i	0.116673	−	0.0979002i
$210$	−2.74474	−	24.7250i	−0.189405	−	1.70619i
$211$	3.91408	−	22.1979i	0.269457	−	1.52816i	−0.486581	−	0.873636i	$-0.661756\pi$
$211$	3.91408	−	22.1979i	0.269457	−	1.52816i	0.756037	−	0.654528i	$-0.227133\pi$
$212$	0.170676	+	1.95084i	0.0117221	+	0.133984i
$213$	16.1455	−	4.86205i	1.10627	−	0.333142i
$214$	−0.788475	+	2.16632i	−0.0538990	+	0.148086i
$215$	0.497206	−	5.23591i	0.0339092	−	0.357086i
$216$	−0.224297	−	0.317053i	−0.0152615	−	0.0215727i
$217$	−3.80401	+	3.80401i	−0.258233	+	0.258233i
$218$	−10.5400	+	4.91489i	−0.713860	+	0.332878i
$219$	−1.08646	−	1.75507i	−0.0734160	−	0.118597i
$220$	−0.0478631	+	6.45876i	−0.00322693	+	0.435449i
$221$	22.9047	+	4.03872i	1.54074	+	0.271674i
$222$	0.866159	−	15.2964i	0.0581328	−	1.02663i
$223$	−4.15975	−	0.363931i	−0.278558	−	0.0243706i	−0.0529791	−	0.998596i	$-0.516872\pi$
$223$	−4.15975	−	0.363931i	−0.278558	−	0.0243706i	−0.225579	+	0.974225i	$0.572427\pi$
$224$	−12.8419	−	22.2428i	−0.858036	−	1.48616i
$225$	−13.3255	−	6.88695i	−0.888369	−	0.459130i
$226$	−2.28307	+	3.95439i	−0.151867	+	0.263042i
$227$	2.78887	−	3.98292i	0.185104	−	0.264356i	−0.715866	−	0.698238i	$-0.753968\pi$
$227$	2.78887	−	3.98292i	0.185104	−	0.264356i	0.900970	+	0.433882i	$0.142857\pi$
$228$	−3.27921	−	4.38995i	−0.217171	−	0.290731i
$229$	9.29671	+	25.5425i	0.614344	+	1.68790i	0.720421	+	0.693537i	$0.243949\pi$
$229$	9.29671	+	25.5425i	0.614344	+	1.68790i	−0.106077	+	0.994358i	$0.533829\pi$
$230$	−4.99290	−	2.93220i	−0.329222	−	0.193344i
$231$	6.16613	+	4.85940i	0.405701	+	0.319725i
$232$	0.617572	+	0.432429i	0.0405456	+	0.0283903i
$233$	0.477349	+	1.78149i	0.0312722	+	0.116709i	0.979798	−	0.199992i	$-0.0640915\pi$
$233$	0.477349	+	1.78149i	0.0312722	+	0.116709i	−0.948525	+	0.316701i	$0.897425\pi$
$234$	−21.7007	+	1.33418i	−1.41862	+	0.0872183i
$235$	9.93354	−	4.54277i	0.647992	−	0.296338i
$236$	−5.74443	−	6.84594i	−0.373930	−	0.445633i
$237$	10.6592	+	21.1390i	0.692387	+	1.37313i
$238$	−33.9279	+	23.7565i	−2.19922	+	1.53991i
$239$	−0.452247	−	0.379480i	−0.0292534	−	0.0245465i	0.628044	−	0.778178i	$-0.283856\pi$
$239$	−0.452247	−	0.379480i	−0.0292534	−	0.0245465i	−0.657297	+	0.753632i	$0.728300\pi$
$240$	−15.1673	−	0.971657i	−0.979048	−	0.0627202i
$241$	4.82664	+	1.75676i	0.310912	+	0.113163i	0.492763	−	0.870163i	$-0.335987\pi$
$241$	4.82664	+	1.75676i	0.310912	+	0.113163i	−0.181852	+	0.983326i	$0.558209\pi$
$242$	12.7722	+	12.7722i	0.821026	+	0.821026i
$243$	−9.20763	+	12.5785i	−0.590670	+	0.806913i
$244$		−	28.7813i		−	1.84253i
$245$	6.78244	−	2.41184i	0.433314	−	0.154087i
$246$	0.630096	+	20.5166i	0.0401735	+	1.30809i
$247$	−5.57985	+	0.488174i	−0.355037	+	0.0310618i
$248$	−0.0721443	−	0.103033i	−0.00458117	−	0.00654259i
$249$	−6.16032	+	18.6917i	−0.390394	+	1.18454i
$250$	20.5657	−	9.03894i	1.30069	−	0.571673i
$251$	−22.0874	+	12.7521i	−1.39414	+	0.804908i	−0.993771	−	0.111444i	$-0.964452\pi$
$251$	−22.0874	+	12.7521i	−1.39414	+	0.804908i	−0.400372	+	0.916353i	$0.631119\pi$
$252$	12.9412	−	14.6367i	0.815217	−	0.922024i
$253$	1.76505	−	0.472945i	0.110968	−	0.0297338i
$254$	4.86325	+	27.5809i	0.305148	+	1.73058i
$255$	0.581628	+	24.9672i	0.0364230	+	1.56351i
$256$	−14.4603	+	5.26312i	−0.903769	+	0.328945i
$257$	−14.8422	−	6.92103i	−0.925831	−	0.431722i	−0.0995836	−	0.995029i	$-0.531751\pi$
$257$	−14.8422	−	6.92103i	−0.925831	−	0.431722i	−0.826248	+	0.563307i	$0.809529\pi$
$258$	6.55806	−	4.89876i	0.408287	−	0.304983i
$259$	13.8594	−	2.44379i	0.861184	−	0.151850i
$260$	9.52361	−	13.3888i	0.590629	−	0.830341i
$261$	8.58532	−	29.0174i	0.531418	−	1.79613i
$262$	−1.48357	−	0.397523i	−0.0916555	−	0.0245590i
$263$	−1.11600	+	12.7560i	−0.0688156	+	0.786566i	0.880869	+	0.473359i	$0.156959\pi$
$263$	−1.11600	+	12.7560i	−0.0688156	+	0.786566i	−0.949685	+	0.313207i	$0.898597\pi$
$264$	−0.136924	+	0.122248i	−0.00842706	+	0.00752384i
$265$	−0.571690	+	2.07203i	−0.0351186	+	0.127284i
$266$	6.41157	−	7.64101i	0.393118	−	0.468500i
$267$	15.5838	+	3.66690i	0.953716	+	0.224411i
$268$	7.69037	+	16.4921i	0.469764	+	1.00741i
$269$	9.70363			0.591641			0.295820	−	0.955244i	$-0.404407\pi$
$269$	9.70363			0.591641			0.295820	+	0.955244i	$0.404407\pi$
$270$	−5.98431	−	22.5657i	−0.364194	−	1.37330i
$271$	18.7538			1.13921			0.569605	−	0.821918i	$-0.307096\pi$
$271$	18.7538			1.13921			0.569605	+	0.821918i	$0.307096\pi$
$272$	10.6941	+	22.9335i	0.648424	+	1.39055i
$273$	−5.75863	−	19.1229i	−0.348528	−	1.15737i
$274$	−17.8664	+	21.2924i	−1.07935	+	1.28632i
$275$	−2.52320	+	6.62524i	−0.152155	+	0.399517i
$276$	−0.926752	−	4.45199i	−0.0557839	−	0.267978i
$277$	−1.27091	+	14.5265i	−0.0763614	+	0.872815i	0.857337	+	0.514755i	$0.172117\pi$
$277$	−1.27091	+	14.5265i	−0.0763614	+	0.872815i	−0.933699	+	0.358060i	$0.883438\pi$
$278$	−17.0807	−	4.57676i	−1.02443	−	0.274496i
$279$	−3.00171	+	4.05928i	−0.179708	+	0.243023i
$280$	0.0888731	+	0.526824i	0.00531119	+	0.0314838i
$281$	−2.11529	+	0.372983i	−0.126188	+	0.0222503i	−0.236385	−	0.971659i	$-0.575963\pi$
$281$	−2.11529	+	0.372983i	−0.126188	+	0.0222503i	0.110198	+	0.993910i	$0.464852\pi$
$282$	15.6208	+	6.70830i	0.930207	+	0.399474i
$283$	13.6419	+	6.36134i	0.810930	+	0.378143i	0.783431	−	0.621479i	$-0.213468\pi$
$283$	13.6419	+	6.36134i	0.810930	+	0.378143i	0.0274989	+	0.999622i	$0.491246\pi$
$284$	−18.6363	+	6.78307i	−1.10586	+	0.402501i
$285$	−1.69152	−	5.77164i	−0.100197	−	0.341882i
$286$	1.78437	+	10.1197i	0.105512	+	0.598388i
$287$	−18.2122	+	4.87995i	−1.07503	+	0.288054i
$288$	−15.0105	−	18.8584i	−0.884499	−	1.11124i
$289$	21.2868	−	12.2900i	1.25217	−	0.722939i
$290$	25.7183	+	37.3151i	1.51023	+	2.19122i
$291$	8.38362	−	1.74518i	0.491457	−	0.102304i
$292$	1.39252	+	1.98873i	0.0814913	+	0.116382i
$293$	−28.6019	+	2.50234i	−1.67094	+	0.146188i	−0.882939	−	0.469488i	$-0.844439\pi$
$293$	−28.6019	+	2.50234i	−1.67094	+	0.146188i	−0.788000	+	0.615676i	$0.788883\pi$
$294$	9.87000	+	5.30132i	0.575630	+	0.309179i
$295$	−3.28653	−	9.24218i	−0.191349	−	0.538101i
$296$			0.329040i			0.0191251i
$297$	6.39826	+	3.65287i	0.371265	+	0.211961i
$298$	−1.89693	−	1.89693i	−0.109886	−	0.109886i
$299$	−4.36807	−	1.58985i	−0.252612	−	0.0919432i
$300$	16.1061	+	7.20125i	0.929884	+	0.415764i
$301$	5.75997	+	4.83319i	0.331999	+	0.278580i
$302$	22.2811	−	15.6014i	1.28213	−	0.897758i
$303$	15.4832	+	0.876734i	0.889485	+	0.0503671i
$304$	−3.91713	−	4.66825i	−0.224663	−	0.267742i
$305$	11.0244	−	29.6049i	0.631256	−	1.69517i
$306$	−28.1861	+	26.7646i	−1.61129	+	1.53003i
$307$	5.02015	+	18.7355i	0.286515	+	1.06929i	0.947725	+	0.319088i	$0.103377\pi$
$307$	5.02015	+	18.7355i	0.286515	+	1.06929i	−0.661210	+	0.750201i	$0.729957\pi$
$308$	−7.56398	−	5.29636i	−0.430998	−	0.301788i
$309$	3.12676	−	21.5890i	0.177875	−	1.22816i
$310$	−1.90272	−	7.31754i	−0.108067	−	0.415608i
$311$	4.20316	+	11.5481i	0.238340	+	0.654833i	0.999977	+	0.00682875i	$0.00217368\pi$
$311$	4.20316	+	11.5481i	0.238340	+	0.654833i	−0.761637	+	0.648004i	$0.775604\pi$
$312$	0.463690	−	0.0549559i	0.0262513	−	0.00311127i
$313$	7.77479	−	11.1036i	0.439457	−	0.627610i	−0.536933	−	0.843625i	$-0.680417\pi$
$313$	7.77479	−	11.1036i	0.439457	−	0.627610i	0.976390	+	0.216015i	$0.0693061\pi$
$314$	−6.23425	+	10.7980i	−0.351819	+	0.609369i
$315$	18.9179	−	10.0985i	1.06590	−	0.568986i
$316$	−13.9226	−	24.1147i	−0.783209	−	1.35656i
$317$	−9.26700	−	0.810757i	−0.520486	−	0.0455367i	−0.176114	−	0.984370i	$-0.556353\pi$
$317$	−9.26700	−	0.810757i	−0.520486	−	0.0455367i	−0.344372	+	0.938833i	$0.611908\pi$
$318$	−2.98711	+	1.50622i	−0.167509	+	0.0844646i
$319$	−14.0849	−	2.48354i	−0.788602	−	0.139052i
$320$	18.5472	+	0.137445i	1.03682	+	0.00768341i
$321$	−1.98633	+	0.0610034i	−0.110866	+	0.00340488i
$322$	7.50235	−	3.49840i	0.418090	−	0.194958i
$323$	−7.08066	+	7.08066i	−0.393978	+	0.393978i
$324$	9.97608	−	15.3832i	0.554227	−	0.854621i
$325$	14.9246	−	10.1240i	0.827868	−	0.561580i
$326$	0.467248	−	1.28375i	0.0258785	−	0.0711005i
$327$	−7.30304	−	6.86783i	−0.403859	−	0.379792i
$328$	−0.0384210	−	0.439154i	−0.00212145	−	0.0242483i
$329$	−2.71167	+	15.3787i	−0.149499	+	0.847853i
$330$	−10.2778	+	4.01426i	−0.565772	+	0.220978i
$331$	10.0079	−	8.39764i	0.550085	−	0.461576i	−0.324885	−	0.945754i	$-0.605325\pi$
$331$	10.0079	−	8.39764i	0.550085	−	0.461576i	0.874970	+	0.484177i	$0.160881\pi$
$332$	5.99114	−	22.3593i	0.328807	−	1.22712i
$333$	12.5232	−	4.19463i	0.686268	−	0.229864i
$334$	37.2587	+	21.5113i	2.03871	+	1.17705i
$335$	1.59330	+	19.9097i	0.0870511	+	1.08778i
$336$	13.4491	−	17.0657i	0.733708	−	0.931008i
$337$	6.35168	−	13.6212i	0.345998	−	0.741995i	−0.653896	−	0.756585i	$-0.726867\pi$
$337$	6.35168	−	13.6212i	0.345998	−	0.741995i	0.999894	+	0.0145899i	$0.00464428\pi$
$338$	0.00813808	−	0.0174522i	0.000442653	−	0.000949273i
$339$	−3.89549	−	0.564188i	−0.211574	−	0.0306425i
$340$	−2.34318	−	29.2802i	−0.127077	−	1.58794i
$341$	2.06643	+	1.19305i	0.111903	+	0.0646074i
$342$	4.88842	−	7.98285i	0.264335	−	0.431663i
$343$	3.12811	−	11.6743i	0.168902	−	0.630351i
$344$	−0.134671	+	0.113002i	−0.00726098	+	0.00609269i
$345$	0.752023	−	4.93436i	0.0404876	−	0.265657i
$346$	7.30726	−	41.4415i	0.392841	−	2.22791i
$347$	−0.137705	−	1.57398i	−0.00739240	−	0.0844956i	0.991602	−	0.129325i	$-0.0412811\pi$
$347$	−0.137705	−	1.57398i	−0.00739240	−	0.0844956i	−0.998995	+	0.0448295i	$0.985726\pi$
$348$	−8.15221	+	34.6458i	−0.437005	+	1.85721i
$349$	3.04560	−	8.36771i	0.163027	−	0.447913i	−0.831101	−	0.556121i	$-0.812289\pi$
$349$	3.04560	−	8.36771i	0.163027	−	0.447913i	0.994128	+	0.108208i	$0.0345112\pi$
$350$	−6.04499	+	31.5419i	−0.323118	+	1.68598i
$351$	−8.00278	−	16.9474i	−0.427157	−	0.904585i
$352$	−8.05522	+	8.05522i	−0.429345	+	0.429345i
$353$	−6.64610	+	3.09913i	−0.353736	+	0.164950i	−0.591361	−	0.806407i	$-0.701409\pi$
$353$	−6.64610	+	3.09913i	−0.353736	+	0.164950i	0.237624	+	0.971357i	$0.423631\pi$
$354$	7.22392	−	13.4495i	0.383947	−	0.714832i
$355$	−21.7678	−	0.161312i	−1.15531	−	0.00856154i
$356$	−18.5439	−	3.26979i	−0.982823	−	0.173298i
$357$	−29.8616	−	19.5713i	−1.58044	−	1.03582i
$358$	−38.1961	−	3.34172i	−2.01872	−	0.176615i
$359$	−5.23715	−	9.07100i	−0.276406	−	0.478749i	0.694083	−	0.719895i	$-0.255810\pi$
$359$	−5.23715	−	9.07100i	−0.276406	−	0.478749i	−0.970489	+	0.241146i	$0.922477\pi$
$360$	0.155715	+	0.476591i	0.00820690	+	0.0251185i
$361$	−8.29423	+	14.3660i	−0.436539	+	0.756107i
$362$	−9.90535	+	14.1463i	−0.520614	+	0.743514i
$363$	−6.14406	+	14.3069i	−0.322479	+	0.750920i
$364$	8.03390	+	22.0730i	0.421091	+	1.15694i
$365$	0.670606	+	2.57903i	0.0351011	+	0.134993i
$366$	45.6643	−	18.2266i	2.38691	−	0.952720i
$367$	−1.64480	−	1.15170i	−0.0858581	−	0.0601185i	0.529859	−	0.848086i	$-0.322245\pi$
$367$	−1.64480	−	1.15170i	−0.0858581	−	0.0601185i	−0.615717	+	0.787967i	$0.711134\pi$
$368$	−1.30894	−	4.88505i	−0.0682334	−	0.254651i
$369$	−16.2244	+	7.06068i	−0.844607	+	0.367564i
$370$	−6.90244	+	18.5358i	−0.358841	+	0.963628i
$371$	−1.97524	−	2.35400i	−0.102550	−	0.122214i
$372$	3.25498	−	4.96639i	0.168763	−	0.257495i
$373$	−28.5671	+	20.0029i	−1.47915	+	1.03571i	−0.492965	+	0.870049i	$0.664087\pi$
$373$	−28.5671	+	20.0029i	−1.47915	+	1.03571i	−0.986183	+	0.165662i	$0.947024\pi$
$374$	14.0727	+	11.8084i	0.727684	+	0.610599i
$375$	13.8086	+	13.5766i	0.713071	+	0.701092i
$376$	−0.343089	−	0.124874i	−0.0176935	−	0.00643990i
$377$	25.7262	+	25.7262i	1.32497	+	1.32497i
$378$	31.4179	+	11.2633i	1.61596	+	0.579321i
$379$			11.2085i			0.575742i	0.957669	+	0.287871i	$0.0929474\pi$
$379$			11.2085i			0.575742i	−0.957669	+	0.287871i	$0.907053\pi$
$380$	2.37012	+	6.66513i	0.121585	+	0.341914i
$381$	−20.5274	+	12.7072i	−1.05165	+	0.651011i
$382$	−19.0489	+	1.66656i	−0.974624	+	0.0852686i
$383$	−5.65156	−	8.07127i	−0.288781	−	0.412422i	0.648381	−	0.761316i	$-0.275446\pi$
$383$	−5.65156	−	8.07127i	−0.288781	−	0.412422i	−0.937162	+	0.348893i	$0.886557\pi$
$384$	0.689627	+	0.772415i	0.0351924	+	0.0394171i
$385$	−5.75170	−	8.34522i	−0.293134	−	0.425312i
$386$	11.1565	−	6.44122i	0.567852	−	0.327850i
$387$	6.01766	+	3.68500i	0.305895	+	0.187319i
$388$	−9.72881	+	2.60683i	−0.493905	+	0.132342i
$389$	−2.38097	−	13.5031i	−0.120720	−	0.684636i	−0.983758	−	0.179498i	$-0.942553\pi$
$389$	−2.38097	−	13.5031i	−0.120720	−	0.684636i	0.863038	−	0.505138i	$-0.168558\pi$
$390$	27.2738	+	6.63124i	1.38106	+	0.335786i
$391$	−7.80907	+	2.84227i	−0.394922	+	0.143740i
$392$	−0.218071	−	0.101688i	−0.0110142	−	0.00513602i
$393$	−0.155827	−	1.31479i	−0.00786046	−	0.0663225i
$394$	−26.4519	+	4.66418i	−1.33263	+	0.234978i
$395$	−5.08410	−	30.1377i	−0.255809	−	1.51639i
$396$	−7.75634	−	3.86410i	−0.389771	−	0.194178i
$397$	13.0066	+	3.48510i	0.652781	+	0.174912i	0.569986	−	0.821655i	$-0.306949\pi$
$397$	13.0066	+	3.48510i	0.652781	+	0.174912i	0.0827949	+	0.996567i	$0.473615\pi$
$398$	0.368535	−	4.21237i	0.0184730	−	0.211147i
$399$	8.16631	+	2.69141i	0.408827	+	0.134739i
$400$	18.3363	+	6.98333i	0.916816	+	0.349166i
$401$	−5.34628	+	6.37145i	−0.266981	+	0.318175i	−0.882834	−	0.469686i	$-0.844367\pi$
$401$	−5.34628	+	6.37145i	−0.266981	+	0.318175i	0.615853	+	0.787861i	$0.288812\pi$
$402$	−21.2961	+	22.6456i	−1.06215	+	1.12946i
$403$	−2.56523	−	5.50116i	−0.127783	−	0.274032i
$404$	−18.2401			−0.907480
$405$	16.1539	−	12.0021i	0.802695	−	0.596390i
$406$	−64.7901			−3.21548
$407$	−2.63800	−	5.65721i	−0.130761	−	0.280418i
$408$	0.571874	−	0.608113i	0.0283120	−	0.0301061i
$409$	10.3591	−	12.3455i	0.512225	−	0.610446i	−0.446499	−	0.894784i	$-0.647329\pi$
$409$	10.3591	−	12.3455i	0.512225	−	0.610446i	0.958724	+	0.284338i	$0.0917737\pi$
$410$	7.04801	−	25.5448i	0.348076	−	1.26157i
$411$	−22.7562	−	7.49987i	−1.12248	−	0.369941i
$412$	−2.23619	+	25.5598i	−0.110169	+	1.25924i
$413$	13.5456	+	3.62954i	0.666538	+	0.178598i
$414$	6.47662	−	4.28974i	0.318308	−	0.210829i
$415$	14.7271	−	20.7042i	0.722924	−	1.01633i
$416$	28.5386	−	5.03213i	1.39922	−	0.246720i
$417$	−1.79407	−	15.1375i	−0.0878562	−	0.741286i
$418$	−4.00964	−	1.86972i	−0.196118	−	0.0914512i
$419$	−2.61381	+	0.951349i	−0.127693	+	0.0464764i	−0.405076	−	0.914283i	$-0.632755\pi$
$419$	−2.61381	+	0.951349i	−0.127693	+	0.0464764i	0.277383	+	0.960759i	$0.410533\pi$
$420$	−21.5437	+	13.1166i	−1.05123	+	0.640023i
$421$	−4.70858	−	26.7037i	−0.229482	−	1.30146i	−0.853929	−	0.520390i	$-0.825787\pi$
$421$	−4.70858	−	26.7037i	−0.229482	−	1.30146i	0.624447	−	0.781067i	$-0.285325\pi$
$422$	−43.7465	+	11.7218i	−2.12955	+	0.570611i
$423$	−0.378968	+	14.6498i	−0.0184261	+	0.712300i
$424$	0.0622212	−	0.0359234i	0.00302173	−	0.00174460i
$425$	8.80528	−	31.0156i	0.427119	−	1.50448i
$426$	−22.5640	−	25.2728i	−1.09323	−	1.22447i
$427$	25.9047	+	36.9957i	1.25362	+	1.79035i
$428$	2.32849	−	0.203716i	0.112552	−	0.00984699i
$429$	−7.53167	+	4.66239i	−0.363632	+	0.225102i
$430$	−9.95692	+	3.54069i	−0.480165	+	0.170747i
$431$			18.9644i			0.913484i	0.889599	+	0.456742i	$0.150984\pi$
$431$			18.9644i			0.913484i	−0.889599	+	0.456742i	$0.849016\pi$
$432$	10.1098	−	17.7081i	0.486410	−	0.851982i
$433$	2.72519	+	2.72519i	0.130964	+	0.130964i	0.769550	−	0.638586i	$-0.220480\pi$
$433$	2.72519	+	2.72519i	0.130964	+	0.130964i	−0.638586	+	0.769550i	$0.720480\pi$
$434$	10.1574	+	3.69699i	0.487571	+	0.177461i
$435$	−21.6563	+	32.5146i	−1.03834	+	1.55896i
$436$	9.03260	+	7.57925i	0.432583	+	0.362980i
$437$	1.63939	−	1.14791i	0.0784228	−	0.0549122i
$438$	−2.27346	+	3.46880i	−0.108630	+	0.165746i
$439$	−16.6256	−	19.8136i	−0.793498	−	0.945654i	0.205961	−	0.978560i	$-0.433968\pi$
$439$	−16.6256	−	19.8136i	−0.793498	−	0.945654i	−0.999458	+	0.0329065i	$0.989524\pi$
$440$	0.215503	−	0.0985532i	0.0102737	−	0.00469834i
$441$	−1.09025	+	9.59607i	−0.0519167	+	0.456956i
$442$	−12.0951	−	45.1396i	−0.575306	−	2.14707i
$443$	2.00399	+	1.40321i	0.0952125	+	0.0666685i	0.620213	−	0.784433i	$-0.287046\pi$
$443$	2.00399	+	1.40321i	0.0952125	+	0.0666685i	−0.525001	+	0.851102i	$0.675935\pi$
$444$	−14.4270	+	5.75846i	−0.684677	+	0.273285i
$445$	−17.8220	−	10.4664i	−0.844846	−	0.496155i
$446$	2.86956	+	7.88405i	0.135878	+	0.373321i
$447$	0.912519	−	2.12487i	0.0431607	−	0.100503i
$448$	−15.2092	+	21.7209i	−0.718566	+	1.02622i
$449$	−3.56778	+	6.17957i	−0.168374	+	0.291632i	−0.937848	−	0.347046i	$-0.887185\pi$
$449$	−3.56778	+	6.17957i	−0.168374	+	0.291632i	0.769474	+	0.638678i	$0.220518\pi$
$450$	−1.22583	+	30.1142i	−0.0577861	+	1.41960i
$451$	4.18140	+	7.24239i	0.196894	+	0.341031i
$452$	4.61197	+	0.403495i	0.216929	+	0.0189788i
$453$	19.6107	+	12.8529i	0.921389	+	0.603880i
$454$	−9.62119	−	1.69648i	−0.451545	−	0.0796195i
$455$	−0.191059	+	25.7819i	−0.00895696	+	1.20867i
$456$	−0.0951257	+	0.177105i	−0.00445467	+	0.00829370i
$457$	10.9699	−	5.11535i	0.513151	−	0.239286i	−0.148754	−	0.988874i	$-0.547526\pi$
$457$	10.9699	−	5.11535i	0.513151	−	0.239286i	0.661905	+	0.749588i	$0.269748\pi$
$458$	38.6191	−	38.6191i	1.80455	−	1.80455i
$459$	−30.4350	−	14.0132i	−1.42058	−	0.654079i
$460$	−0.554990	+	5.84441i	−0.0258765	+	0.272497i
$461$	6.31509	−	17.3506i	0.294123	−	0.808097i	−0.701329	−	0.712837i	$-0.747410\pi$
$461$	6.31509	−	17.3506i	0.294123	−	0.808097i	0.995452	−	0.0952594i	$-0.0303681\pi$
$462$	3.61307	−	15.3551i	0.168095	−	0.714382i
$463$	−2.80254	−	32.0331i	−0.130245	−	1.48871i	−0.727197	−	0.686429i	$-0.759177\pi$
$463$	−2.80254	−	32.0331i	−0.130245	−	1.48871i	0.596952	−	0.802277i	$-0.296378\pi$
$464$	−6.87357	+	38.9820i	−0.319098	+	1.80969i
$465$	5.25045	−	3.86171i	0.243484	−	0.179082i
$466$	2.83879	−	2.38203i	0.131504	−	0.110345i
$467$	−1.79292	+	6.69128i	−0.0829666	+	0.309635i	−0.994921	−	0.100655i	$-0.967906\pi$
$467$	−1.79292	+	6.69128i	−0.0829666	+	0.309635i	0.911955	+	0.410291i	$0.134573\pi$
$468$	10.5245	+	19.3691i	0.486497	+	0.895338i
$469$	−24.7290	−	14.2773i	−1.14188	−	0.659264i
$470$	−16.7076	−	14.2317i	−0.770666	−	0.656458i
$471$	−10.6372	−	1.54060i	−0.490136	−	0.0709870i
$472$	−0.138567	+	0.297157i	−0.00637804	+	0.0136778i
$473$	1.40944	−	3.02256i	0.0648062	−	0.138977i
$474$	29.4434	−	37.3610i	1.35238	−	1.71605i
$475$	−0.115073	+	7.76370i	−0.00527993	+	0.356223i
$476$	36.3677	+	20.9969i	1.66691	+	0.962391i
$477$	−2.16044	−	1.91018i	−0.0989198	−	0.0874609i
$478$	−0.307014	+	1.14579i	−0.0140425	+	0.0524072i
$479$	−20.5682	+	17.2588i	−0.939787	+	0.788575i	−0.977548	−	0.210712i	$-0.932422\pi$
$479$	−20.5682	+	17.2588i	−0.939787	+	0.788575i	0.0377611	+	0.999287i	$0.487977\pi$
$480$	11.3207	+	28.9845i	0.516716	+	1.32295i
$481$	−2.75731	+	15.6375i	−0.125723	+	0.713009i
$482$	−0.899488	−	10.2812i	−0.0409706	−	0.468296i
$483$	5.19828	+	4.88850i	0.236530	+	0.222434i
$484$	6.26361	−	17.2091i	0.284710	−	0.782233i
$485$	−11.0057	−	1.04511i	−0.499744	−	0.0474561i
$486$	30.7245	+	6.08616i	1.39369	+	0.276074i
$487$	17.3982	−	17.3982i	0.788386	−	0.788386i	−0.192843	−	0.981230i	$-0.561771\pi$
$487$	17.3982	−	17.3982i	0.788386	−	0.788386i	0.981230	+	0.192843i	$0.0617709\pi$
$488$	−0.957011	+	0.446262i	−0.0433219	+	0.0202013i
$489$	1.17709	−	0.0361504i	0.0532301	−	0.00163478i
$490$	−10.1514	−	10.3030i	−0.458593	−	0.465440i
$491$	24.3399	+	4.29178i	1.09844	+	0.193685i	0.693357	−	0.720594i	$-0.256131\pi$
$491$	24.3399	+	4.29178i	1.09844	+	0.193685i	0.405085	+	0.914279i	$0.367242\pi$
$492$	18.5827	−	9.37016i	0.837774	−	0.422439i
$493$	64.7955	+	5.66887i	2.91824	+	0.255313i
$494$	5.62715	+	9.74651i	0.253177	+	0.438516i
$495$	−6.49818	−	6.94566i	−0.292071	−	0.312184i
$496$	3.30195	−	5.71914i	0.148262	−	0.256797i
$497$	17.8502	−	25.4927i	0.800690	−	1.14350i
$498$	39.2692	−	4.65413i	1.75969	−	0.208557i
$499$	−6.32244	−	17.3708i	−0.283031	−	0.777623i	−0.996997	−	0.0774416i	$-0.975325\pi$
$499$	−6.32244	−	17.3708i	−0.283031	−	0.777623i	0.713965	−	0.700181i	$-0.246897\pi$
$500$	−17.1181	−	15.0247i	−0.765545	−	0.671927i
$501$	−5.31584	+	36.7037i	−0.237494	+	1.63980i
$502$	41.9776	+	29.3931i	1.87355	+	1.31188i
$503$	3.87444	+	14.4596i	0.172753	+	0.644723i	0.996923	+	0.0783811i	$0.0249751\pi$
$503$	3.87444	+	14.4596i	0.172753	+	0.644723i	−0.824171	+	0.566342i	$0.808358\pi$
$504$	−0.687342	−	0.203363i	−0.0306167	−	0.00905850i
$505$	−18.7621	−	6.98671i	−0.834901	−	0.310905i
$506$	−2.36005	−	2.81260i	−0.104917	−	0.125035i
$507$	0.0165729		0.000938441i	0.000736029		4.16776e-5i
$508$	23.2602	−	16.2870i	1.03201	−	0.722619i
$509$	−9.33558	−	7.83348i	−0.413792	−	0.347213i	0.412003	−	0.911182i	$-0.364829\pi$
$509$	−9.33558	−	7.83348i	−0.413792	−	0.347213i	−0.825796	+	0.563969i	$0.809274\pi$
$510$	44.9720	−	22.2602i	1.99139	−	0.985700i
$511$	−3.57993	−	1.30299i	−0.158367	−	0.0576407i
$512$	22.7088	+	22.7088i	1.00360	+	1.00360i
$513$	7.95326	+	1.36272i	0.351145	+	0.0601657i
$514$			32.9051i			1.45138i
$515$	−12.0906	+	25.4346i	−0.532776	+	1.12078i
$516$	−7.31155	−	3.92714i	−0.321873	−	0.172883i
$517$	6.89991	−	0.603664i	0.303458	−	0.0265491i
$518$	−16.2191	−	23.1632i	−0.712625	−	1.01773i
$519$	35.5135	−	7.39270i	1.55887	−	0.324503i
$520$	−0.592861	−	0.109073i	−0.0259987	−	0.00478318i
$521$	7.98838	−	4.61209i	0.349977	−	0.202059i	−0.314698	−	0.949192i	$-0.601903\pi$
$521$	7.98838	−	4.61209i	0.349977	−	0.202059i	0.664675	+	0.747132i	$0.268570\pi$
$522$	−60.1316	+	9.00624i	−2.63189	+	0.394192i
$523$	−35.6456	+	9.55121i	−1.55867	+	0.417645i	−0.932243	−	0.361832i	$-0.882152\pi$
$523$	−35.6456	+	9.55121i	−1.55867	+	0.417645i	−0.626431	+	0.779477i	$0.715485\pi$
$524$	0.270414	+	1.53359i	0.0118131	+	0.0669953i
$525$	−27.1844	+	5.23976i	−1.18642	+	0.228682i
$526$	24.1766	−	8.79955i	1.05415	−	0.383679i
$527$	−9.83477	−	4.58603i	−0.428409	−	0.199771i
$528$	−8.85529	−	3.80287i	−0.385377	−	0.165499i
$529$	−21.0149	+	3.70550i	−0.913692	+	0.161109i
$530$	4.25868	−	0.718422i	0.184985	−	0.0312063i
$531$	13.0762	+	1.48564i	0.567460	+	0.0644715i
$532$	−9.76863	−	2.61750i	−0.423524	−	0.113483i
$533$	1.85411	−	21.1926i	0.0803106	−	0.917955i
$534$	−6.55563	−	31.4923i	−0.283690	−	1.36281i
$535$	2.47315	+	0.682360i	0.106923	+	0.0295010i
$536$	0.429139	−	0.511427i	0.0185360	−	0.0220903i
$537$	−9.53042	−	31.6479i	−0.411268	−	1.36571i
$538$	−8.23991	−	17.6705i	−0.355248	−	0.761831i
$539$	4.56457			0.196610
$540$	−18.1714	+	15.1682i	−0.781973	+	0.652735i
$541$	22.0366			0.947428			0.473714	−	0.880679i	$-0.342913\pi$
$541$	22.0366			0.947428			0.473714	+	0.880679i	$0.342913\pi$
$542$	−15.9249	−	34.1511i	−0.684033	−	1.46691i
$543$	−14.4910	−	3.40975i	−0.621867	−	0.146326i
$544$	33.3011	−	39.6868i	1.42777	−	1.70156i
$545$	6.38790	+	11.2560i	0.273628	+	0.482153i
$546$	−29.9332	+	26.7249i	−1.28102	+	1.14372i
$547$	−2.34887	+	26.8477i	−0.100430	+	1.14793i	0.764015	+	0.645199i	$0.223225\pi$
$547$	−2.34887	+	26.8477i	−0.100430	+	1.14793i	−0.864445	+	0.502727i	$0.832330\pi$
$548$	27.2212	+	7.29390i	1.16283	+	0.311580i
$549$	29.1847	+	30.7348i	1.24557	+	1.31173i
$550$	14.2073	−	1.03106i	0.605802	−	0.0439646i
$551$	−15.4261	+	2.72004i	−0.657175	+	0.115878i
$552$	−0.133664	+	0.0998448i	−0.00568913	+	0.00424968i
$553$	39.6008	+	18.4661i	1.68400	+	0.785260i
$554$	27.5324	−	10.0210i	1.16974	−	0.425750i
$555$	−17.0456	+	0.397089i	−0.723545	+	0.0168555i
$556$	3.11333	+	17.6566i	0.132035	+	0.748806i
$557$	−36.5073	+	9.78211i	−1.54687	+	0.414481i	−0.928477	−	0.371391i	$-0.878881\pi$
$557$	−36.5073	+	9.78211i	−1.54687	+	0.414481i	−0.618389	+	0.785872i	$0.712214\pi$
$558$	9.94097	+	2.01923i	0.420835	+	0.0854808i
$559$	−7.34714	+	4.24188i	−0.310751	+	0.179412i
$560$	−23.0966	+	15.9187i	−0.976011	+	0.672687i
$561$	−4.95687	+	15.0402i	−0.209279	+	0.634998i
$562$	2.47543	+	3.53528i	0.104420	+	0.149127i
$563$	−16.7892	+	1.46886i	−0.707579	+	0.0619052i	−0.435264	−	0.900303i	$-0.643345\pi$
$563$	−16.7892	+	1.46886i	−0.707579	+	0.0619052i	−0.272315	+	0.962208i	$0.587789\pi$
$564$	−0.529113	−	17.2284i	−0.0222797	−	0.725448i
$565$	4.58938	+	2.18161i	0.193077	+	0.0917812i
$566$		−	30.2441i		−	1.27125i
$567$	1.02233	+	28.7527i	0.0429340	+	1.20750i
$568$	0.514506	+	0.514506i	0.0215882	+	0.0215882i
$569$	−4.84212	−	1.76239i	−0.202992	−	0.0738831i	0.238523	−	0.971137i	$-0.423337\pi$
$569$	−4.84212	−	1.76239i	−0.202992	−	0.0738831i	−0.441515	+	0.897254i	$0.645559\pi$
$570$	−9.07392	+	7.98132i	−0.380065	+	0.334301i
$571$	11.2525	+	9.44196i	0.470902	+	0.395134i	0.847124	−	0.531396i	$-0.178332\pi$
$571$	11.2525	+	9.44196i	0.470902	+	0.395134i	−0.376221	+	0.926530i	$0.622777\pi$
$572$	8.53438	−	5.97584i	0.356840	−	0.249862i
$573$	−7.42146	−	14.7181i	−0.310036	−	0.614857i
$574$	24.3515	+	29.0210i	1.01641	+	1.21131i
$575$	−2.80952	+	5.79906i	−0.117165	+	0.241837i
$576$	−11.0963	+	22.2733i	−0.462344	+	0.928056i
$577$	5.07547	+	18.9419i	0.211295	+	0.788562i	0.987438	+	0.158006i	$0.0505065\pi$
$577$	5.07547	+	18.9419i	0.211295	+	0.788562i	−0.776144	+	0.630556i	$0.782827\pi$
$578$	−40.4562	−	28.3277i	−1.68276	−	1.17828i
$579$	8.72204	+	6.87366i	0.362476	+	0.285660i
$580$	23.2688	−	39.6218i	0.966185	−	1.64520i
$581$	12.4234	+	34.1331i	0.515411	+	1.41608i
$582$	−10.2970	−	13.7848i	−0.426826	−	0.571400i
$583$	−0.781767	+	1.11648i	−0.0323775	+	0.0462398i
$584$	0.0445361	−	0.0771388i	0.00184292	−	0.00319203i
$585$	3.40652	+	23.9547i	0.140842	+	0.990404i
$586$	28.8443	+	49.9598i	1.19155	+	2.06382i
$587$	16.8392	+	1.47324i	0.695028	+	0.0608071i	0.429195	−	0.903212i	$-0.358797\pi$
$587$	16.8392	+	1.47324i	0.695028	+	0.0608071i	0.265833	+	0.964019i	$0.414353\pi$
$588$	0.642191	−	11.3411i	0.0264835	−	0.467700i
$589$	2.57362	+	0.453799i	0.106044	+	0.0186985i
$590$	−14.0395	+	13.8329i	−0.577996	+	0.569492i
$591$	−12.1871	−	19.6871i	−0.501309	−	0.809819i
$592$	−15.6572	+	7.30106i	−0.643506	+	0.300072i
$593$	−11.2767	+	11.2767i	−0.463077	+	0.463077i	−0.899663	−	0.436586i	$-0.856188\pi$
$593$	−11.2767	+	11.2767i	−0.463077	+	0.463077i	0.436586	+	0.899663i	$0.356188\pi$
$594$	1.21883	−	14.7532i	0.0500092	−	0.605333i
$595$	29.3657	+	35.5280i	1.20387	+	1.45651i
$596$	−0.930275	+	2.55591i	−0.0381055	+	0.104694i
$597$	3.49023	−	1.05104i	0.142845	−	0.0430163i
$598$	0.814028	+	9.30438i	0.0332881	+	0.380485i
$599$	−0.0318051	+	0.180376i	−0.00129952	+	0.00736995i	−0.985451	−	0.169962i	$-0.945636\pi$
$599$	−0.0318051	+	0.180376i	−0.00129952	+	0.00736995i	0.984151	+	0.177332i	$0.0567466\pi$
$600$	−0.0102791	−	0.647202i	−0.000419643	−	0.0264219i
$601$	−27.8004	+	23.3273i	−1.13400	+	0.951541i	−0.999226	−	0.0393353i	$-0.987476\pi$
$601$	−27.8004	+	23.3273i	−1.13400	+	0.951541i	−0.134776	+	0.990876i	$0.543032\pi$
$602$	3.91023	−	14.5932i	0.159369	−	0.594774i
$603$	−24.9356	−	9.81324i	−1.01545	−	0.399626i
$604$	−23.8834	−	13.7891i	−0.971801	−	0.561069i
$605$	13.0346	−	15.3023i	0.529933	−	0.622129i
$606$	−11.5511	−	28.9397i	−0.469231	−	1.17560i
$607$	−7.80966	+	16.7479i	−0.316984	+	0.679775i	−0.998653	−	0.0518859i	$-0.983477\pi$
$607$	−7.80966	+	16.7479i	−0.316984	+	0.679775i	0.681669	+	0.731661i	$0.261255\pi$
$608$	−5.27284	+	11.3076i	−0.213842	+	0.458586i
$609$	−20.7042	−	51.8715i	−0.838975	−	2.10194i
$610$	−63.2726	+	5.06347i	−2.56183	+	0.205014i
$611$	−15.2588	−	8.80965i	−0.617303	−	0.356400i
$612$	36.6715	+	14.4318i	1.48236	+	0.583373i
$613$	−10.6637	+	39.7974i	−0.430702	+	1.60740i	0.320445	+	0.947267i	$0.396167\pi$
$613$	−10.6637	+	39.7974i	−0.430702	+	1.60740i	−0.751147	+	0.660135i	$0.770499\pi$
$614$	29.8548	−	25.0512i	1.20484	−	1.01098i
$615$	22.7036	−	2.52034i	0.915498	−	0.101630i
$616$	−0.0588284	+	0.333632i	−0.00237026	+	0.0134424i
$617$	−0.932954	−	10.6637i	−0.0375593	−	0.429305i	−0.991574	−	0.129544i	$-0.958649\pi$
$617$	−0.932954	−	10.6637i	−0.0375593	−	0.429305i	0.954014	−	0.299761i	$-0.0969069\pi$
$618$	−41.9692	+	12.6386i	−1.68825	+	0.508397i
$619$	−13.6868	+	37.6041i	−0.550117	+	1.51143i	0.283434	+	0.958992i	$0.408526\pi$
$619$	−13.6868	+	37.6041i	−0.550117	+	1.51143i	−0.833551	+	0.552443i	$0.813696\pi$
$620$	−5.90880	+	4.88391i	−0.237303	+	0.196143i
$621$	5.50405	+	3.81441i	0.220870	+	0.153067i
$622$	17.4602	−	17.4602i	0.700091	−	0.700091i
$623$	26.7794	−	12.4875i	1.07290	−	0.500299i
$624$	12.9038	+	20.8450i	0.516567	+	0.834468i
$625$	−11.8528	−	22.0116i	−0.474114	−	0.880464i
$626$	−26.8219	−	4.72942i	−1.07202	−	0.189026i
$627$	0.215607	−	3.80763i	0.00861051	−	0.152062i
$628$	12.5937	+	1.10180i	0.502542	+	0.0439667i
$629$	14.1937	+	24.5842i	0.565941	+	0.980238i
$630$	−34.4539	−	25.8748i	−1.37268	−	1.03087i
$631$	10.5767	−	18.3193i	0.421050	−	0.729280i	−0.574992	−	0.818159i	$-0.694995\pi$
$631$	10.5767	−	18.3193i	0.421050	−	0.729280i	0.996042	+	0.0888788i	$0.0283284\pi$
$632$	−0.585968	+	0.836848i	−0.0233085	+	0.0332880i
$633$	−23.3641	−	31.2780i	−0.928641	−	1.24319i
$634$	6.39273	+	17.5639i	0.253888	+	0.697551i
$635$	30.1644	−	7.84342i	1.19704	−	0.311257i
$636$	2.66401	+	2.09945i	0.105635	+	0.0832488i
$637$	−9.51160	−	6.66009i	−0.376863	−	0.263883i
$638$	7.43769	+	27.7578i	0.294461	+	1.09894i
$639$	13.0231	−	26.1410i	0.515185	−	1.03412i
$640$	−0.555960	−	1.21570i	−0.0219762	−	0.0480547i
$641$	−10.0696	−	12.0004i	−0.397724	−	0.473989i	0.529601	−	0.848247i	$-0.322342\pi$
$641$	−10.0696	−	12.0004i	−0.397724	−	0.473989i	−0.927324	+	0.374258i	$0.877897\pi$
$642$	1.79780	+	3.56536i	0.0709535	+	0.140714i
$643$	5.26307	−	3.68524i	0.207555	−	0.145332i	−0.465177	−	0.885218i	$-0.654009\pi$
$643$	5.26307	−	3.68524i	0.207555	−	0.145332i	0.672732	+	0.739886i	$0.265121\pi$
$644$	−6.42938	−	5.39489i	−0.253353	−	0.212588i
$645$	−6.01651	−	6.84013i	−0.236900	−	0.269330i
$646$	18.9066	+	6.88146i	0.743872	+	0.270747i
$647$	−16.4424	−	16.4424i	−0.646419	−	0.646419i	0.305707	−	0.952126i	$-0.401107\pi$
$647$	−16.4424	−	16.4424i	−0.646419	−	0.646419i	−0.952126	+	0.305707i	$0.901107\pi$
$648$	−0.666190	−	0.0931958i	−0.0261704	−	0.00366108i
$649$		−	6.21997i		−	0.244155i
$650$	−31.1094	−	18.5812i	−1.22021	−	0.728813i
$651$	0.286032	+	9.31349i	0.0112105	+	0.365025i
$652$	−1.37985	+	0.120722i	−0.0540392	+	0.00472782i
$653$	9.41463	+	13.4455i	0.368423	+	0.526163i	0.959968	−	0.280109i	$-0.0903707\pi$
$653$	9.41463	+	13.4455i	0.368423	+	0.526163i	−0.591545	+	0.806272i	$0.701482\pi$
$654$	−6.30505	+	19.1309i	−0.246547	+	0.748077i
$655$	−0.309277	+	1.68106i	−0.0120845	+	0.0656843i
$656$	20.0444	−	11.5726i	0.782602	−	0.451835i
$657$	−3.50365	−	0.711667i	−0.136690	−	0.0277648i
$658$	30.3075	−	8.12088i	1.18151	−	0.316585i
$659$	4.40379	+	24.9751i	0.171547	+	0.972892i	0.942054	+	0.335461i	$0.108892\pi$
$659$	4.40379	+	24.9751i	0.171547	+	0.972892i	−0.770507	+	0.637431i	$0.779997\pi$
$660$	8.09263	+	7.72417i	0.315005	+	0.300663i
$661$	−31.1241	+	11.3282i	−1.21059	+	0.440618i	−0.866907	−	0.498469i	$-0.833896\pi$
$661$	−31.1241	+	11.3282i	−1.21059	+	0.440618i	−0.343680	+	0.939087i	$0.611673\pi$
$662$	−23.7906	−	11.0937i	−0.924649	−	0.431171i
$663$	32.2740	−	24.1081i	1.25342	−	0.936282i
$664$	−0.836365	+	0.147474i	−0.0324573	+	0.00572309i
$665$	−9.04555	−	6.43418i	−0.350771	−	0.249507i
$666$	−18.2727	−	19.2432i	−0.708053	−	0.745658i
$667$	−12.5567	−	3.36455i	−0.486196	−	0.130276i
$668$	3.80178	−	43.4545i	0.147095	−	1.68131i
$669$	−5.39504	+	4.81680i	−0.208584	+	0.186228i
$670$	34.9031	−	19.8079i	1.34842	−	0.765246i
$671$	12.8762	−	15.3452i	0.497080	−	0.592396i
$672$	−43.3031	−	10.1893i	−1.67045	−	0.393060i
$673$	−14.9676	−	32.0981i	−0.576958	−	1.23729i	−0.950802	−	0.309798i	$-0.899738\pi$
$673$	−14.9676	−	32.0981i	−0.576958	−	1.23729i	0.373845	−	0.927491i	$-0.378039\pi$
$674$	−30.1981			−1.16319
$675$	−24.5014	+	8.64182i	−0.943060	+	0.332624i
$676$	−0.0195239			−0.000750920
$677$	1.40846	+	3.02046i	0.0541317	+	0.116086i	0.931513	−	0.363708i	$-0.118489\pi$
$677$	1.40846	+	3.02046i	0.0541317	+	0.116086i	−0.877381	+	0.479794i	$0.840712\pi$
$678$	2.28048	+	7.57286i	0.0875814	+	0.290834i
$679$	10.1592	−	12.1073i	0.389875	−	0.464635i
$680$	−0.937268	+	0.531911i	−0.0359426	+	0.0203978i
$681$	−1.71631	−	8.24492i	−0.0657692	−	0.315946i
$682$	0.417855	−	4.77610i	0.0160005	−	0.182886i
$683$	−32.7666	−	8.77978i	−1.25378	−	0.335949i	−0.429984	−	0.902837i	$-0.641481\pi$
$683$	−32.7666	−	8.77978i	−1.25378	−	0.335949i	−0.823795	+	0.566888i	$0.808147\pi$
$684$	−9.43010	−	1.07139i	−0.360569	−	0.0409657i
$685$	25.2063	+	17.9294i	0.963082	+	0.685049i
$686$	−23.9154	+	4.21693i	−0.913093	+	0.161003i
$687$	43.2598	+	18.5777i	1.65046	+	0.708785i
$688$	−8.36537	−	3.90084i	−0.318927	−	0.148718i
$689$	3.25807	−	1.18584i	0.124123	−	0.0451770i
$690$	−9.62418	+	2.82060i	−0.366386	+	0.107378i
$691$	−2.72721	−	15.4668i	−0.103748	−	0.588385i	−0.991713	−	0.128473i	$-0.958992\pi$
$691$	−2.72721	−	15.4668i	−0.103748	−	0.588385i	0.887965	−	0.459911i	$-0.152119\pi$
$692$	−41.2118	+	11.0427i	−1.56664	+	0.419779i
$693$	13.4480	−	2.01417i	0.510846	−	0.0765121i
$694$	−2.74932	+	1.58732i	−0.104363	+	0.0602538i
$695$	−3.56078	+	19.3544i	−0.135068	+	0.734153i
$696$	1.27842	−	0.266123i	0.0484583	−	0.0100874i
$697$	−21.8143	−	31.1541i	−0.826277	−	1.18005i
$698$	−17.8240	+	1.55940i	−0.674648	+	0.0590241i
$699$	2.81423	+	1.51156i	0.106444	+	0.0571726i
$700$	31.5741	−	7.96064i	1.19339	−	0.300884i
$701$		−	38.4806i		−	1.45339i	−0.686958	−	0.726697i	$-0.741054\pi$
$701$		−	38.4806i		−	1.45339i	0.686958	−	0.726697i	$-0.258946\pi$
$702$	−24.0660	+	28.9643i	−0.908313	+	1.09319i
$703$	−4.83410	−	4.83410i	−0.182322	−	0.182322i
$704$	11.0518	+	4.02252i	0.416530	+	0.151605i
$705$	6.05495	−	17.9241i	0.228042	−	0.675061i
$706$	11.2872	+	9.47107i	0.424799	+	0.356448i
$707$	23.4460	−	16.4171i	0.881778	−	0.617428i
$708$	−15.4541	−	0.875090i	−0.580802	−	0.0328879i
$709$	−16.1489	−	19.2455i	−0.606483	−	0.722779i	0.372200	−	0.928152i	$-0.378603\pi$
$709$	−16.1489	−	19.2455i	−0.606483	−	0.722779i	−0.978684	+	0.205374i	$0.934159\pi$
$710$	18.1905	+	39.7767i	0.682679	+	1.49279i
$711$	39.3203	+	11.6336i	1.47463	+	0.436296i
$712$	0.178804	+	0.667304i	0.00670095	+	0.0250083i
$713$	1.77657	+	1.24397i	0.0665332	+	0.0465870i
$714$	−10.2827	+	70.9978i	−0.384820	+	2.65702i
$715$	11.0676	−	2.87782i	0.413904	−	0.107624i
$716$	13.2959	+	36.5303i	0.496893	+	1.36520i
$717$	−1.01544	+	0.120348i	−0.0379222	+	0.00449449i
$718$	−12.0714	+	17.2397i	−0.450499	+	0.643379i
$719$	1.64032	−	2.84111i	0.0611736	−	0.105956i	−0.833817	−	0.552041i	$-0.813849\pi$
$719$	1.64032	−	2.84111i	0.0611736	−	0.105956i	0.894990	+	0.446086i	$0.147182\pi$
$720$	−19.2231	+	17.9847i	−0.716404	+	0.670249i
$721$	−20.1307	−	34.8674i	−0.749708	−	1.29853i
$722$	33.2040	+	2.90497i	1.23573	+	0.108112i
$723$	7.94377	−	4.00557i	0.295432	−	0.148969i
$724$	17.2434	+	3.04048i	0.640847	+	0.112999i
$725$	39.1114	−	31.8426i	1.45256	−	1.18261i
$726$	31.2706	−	0.960368i	1.16056	−	0.0356426i
$727$	20.2902	−	9.46148i	0.752522	−	0.350907i	−0.00821575	−	0.999966i	$-0.502615\pi$
$727$	20.2902	−	9.46148i	0.752522	−	0.350907i	0.760738	+	0.649060i	$0.224837\pi$
$728$	0.609384	−	0.609384i	0.0225853	−	0.0225853i
$729$	4.94563	+	26.5432i	0.183171	+	0.983081i
$730$	4.12703	−	3.41119i	0.152748	−	0.126254i
$731$	−5.18740	+	14.2523i	−0.191863	+	0.527139i
$732$	−36.3152	−	34.1511i	−1.34225	−	1.26226i
$733$	0.131805	+	1.50654i	0.00486833	+	0.0556452i	0.998240	−	0.0592991i	$-0.0188866\pi$
$733$	0.131805	+	1.50654i	0.00486833	+	0.0556452i	−0.993372	+	0.114944i	$0.963331\pi$
$734$	−0.700584	+	3.97321i	−0.0258590	+	0.146654i
$735$	5.00468	−	11.4197i	0.184600	−	0.421221i
$736$	−7.93187	+	6.65563i	−0.292372	+	0.245330i
$737$	−3.27797	+	12.2335i	−0.120745	+	0.450628i
$738$	26.6347	+	23.5494i	0.980438	+	0.866864i
$739$	32.5721	+	18.8055i	1.19818	+	0.691771i	0.960150	−	0.279486i	$-0.0901639\pi$
$739$	32.5721	+	18.8055i	1.19818	+	0.691771i	0.238033	+	0.971257i	$0.423497\pi$
$740$	19.9902	−	1.59974i	0.734853	−	0.0588075i
$741$	−6.00493	+	7.61971i	−0.220597	+	0.279917i
$742$	−2.60941	+	5.59589i	−0.0957943	+	0.205432i
$743$	4.60422	−	9.87379i	0.168913	−	0.362234i	−0.803570	−	0.595210i	$-0.797069\pi$
$743$	4.60422	−	9.87379i	0.168913	−	0.362234i	0.972482	+	0.232976i	$0.0748464\pi$
$744$	−0.215607	−	0.0312267i	−0.00790455	−	0.00114483i
$745$	−1.93591	+	2.27271i	−0.0709263	+	0.0832657i
$746$	60.6837	+	35.0358i	2.22179	+	1.28275i
$747$	16.2749	+	29.9519i	0.595467	+	1.09588i
$748$	4.82074	−	17.9913i	0.176264	−	0.657826i
$749$	−2.80970	+	2.35762i	−0.102664	+	0.0861455i
$750$	12.9976	−	36.6744i	0.474607	−	1.33916i
$751$	−0.0383497	+	0.217492i	−0.00139940	+	0.00793639i	−0.985499	−	0.169679i	$-0.945727\pi$
$751$	−0.0383497	+	0.217492i	−0.00139940	+	0.00793639i	0.984100	+	0.177615i	$0.0568382\pi$
$752$	−1.67073	−	19.0965i	−0.0609252	−	0.696379i
$753$	−10.1180	+	43.0004i	−0.368722	+	1.56702i
$754$	25.0024	−	68.6936i	0.910535	−	2.50167i
$755$	−19.2850	−	23.3319i	−0.701853	−	0.849136i
$756$	−3.11242	−	33.6962i	−0.113197	−	1.22552i
$757$	−1.75745	+	1.75745i	−0.0638754	+	0.0638754i	−0.738323	−	0.674447i	$-0.764382\pi$
$757$	−1.75745	+	1.75745i	−0.0638754	+	0.0638754i	0.674447	+	0.738323i	$0.264382\pi$
$758$	20.4109	−	9.51778i	0.741359	−	0.345701i
$759$	1.49762	−	2.78826i	0.0543601	−	0.101208i
$760$	0.184874	−	0.182154i	0.00670608	−	0.00660742i
$761$	−51.7197	−	9.11958i	−1.87484	−	0.330585i	−0.884201	−	0.467106i	$-0.845297\pi$
$761$	−51.7197	−	9.11958i	−1.87484	−	0.330585i	−0.990637	+	0.136521i	$0.956408\pi$
$762$	40.5711	+	26.5904i	1.46974	+	0.963269i
$763$	−18.4323	−	1.61262i	−0.667294	−	0.0583807i
$764$	9.69366	+	16.7899i	0.350704	+	0.607438i
$765$	32.1928	+	28.8915i	1.16393	+	1.04457i
$766$	−9.89891	+	17.1454i	−0.357662	+	0.619489i
$767$	−9.07547	+	12.9611i	−0.327696	+	0.467999i
$768$	−10.5174	+	24.4905i	−0.379513	+	0.883726i
$769$	−3.12453	−	8.58457i	−0.112673	−	0.309567i	0.870521	−	0.492132i	$-0.163782\pi$
$769$	−3.12453	−	8.58457i	−0.112673	−	0.309567i	−0.983194	+	0.182565i	$0.941560\pi$
$770$	−10.3128	+	17.5604i	−0.371646	+	0.632832i
$771$	−26.3440	+	10.5151i	−0.948758	+	0.378690i
$772$	−10.6993	−	7.49174i	−0.385077	−	0.269634i
$773$	5.21188	+	19.4510i	0.187458	+	0.699604i	0.994091	+	0.108551i	$0.0346210\pi$
$773$	5.21188	+	19.4510i	0.187458	+	0.699604i	−0.806633	+	0.591053i	$0.798712\pi$
$774$	1.60053	−	14.0875i	0.0575300	−	0.506363i
$775$	−7.94862	+	2.76035i	−0.285523	+	0.0991548i
$776$	0.237528	+	0.283074i	0.00852675	+	0.0101618i
$777$	13.3617	−	20.3871i	0.479349	−	0.731382i
$778$	−22.5677	+	15.8021i	−0.809092	+	0.566533i
$779$	7.01632	+	5.88739i	0.251386	+	0.210938i
$780$	−5.59312	−	27.9034i	−0.200266	−	0.999101i
$781$	−12.9709	−	4.72102i	−0.464135	−	0.168931i
$782$	11.8070	+	11.8070i	0.422216	+	0.422216i
$783$	−26.4260	−	45.2638i	−0.944387	−	1.61760i
$784$		−	12.6331i		−	0.451183i
$785$	12.5320	+	5.95722i	0.447286	+	0.212622i
$786$	−2.26195	+	1.40023i	−0.0806810	+	0.0499446i
$787$	−55.3008	+	4.83819i	−1.97126	+	0.172463i	−0.998289	−	0.0584659i	$-0.981379\pi$
$787$	−55.3008	+	4.83819i	−1.97126	+	0.172463i	−0.972971	+	0.230929i	$0.925824\pi$
$788$	15.6203	+	22.3081i	0.556450	+	0.794693i
$789$	14.7708	+	16.5440i	0.525854	+	0.588981i
$790$	−50.5642	+	34.8499i	−1.79899	+	1.23990i
$791$	−6.29143	+	3.63236i	−0.223698	+	0.129152i
$792$	−0.00822152	+	0.317821i	−0.000292139	+	0.0112933i
$793$	−49.2212	+	13.1888i	−1.74790	+	0.468348i
$794$	−4.69817	−	26.6447i	−0.166732	−	0.945584i
$795$	1.93607	+	3.17996i	0.0686652	+	0.112781i
$796$	−4.02867	+	1.46632i	−0.142792	+	0.0519722i
$797$	−0.291013	−	0.135702i	−0.0103082	−	0.00480680i	0.417457	−	0.908697i	$-0.362921\pi$
$797$	−0.291013	−	0.135702i	−0.0103082	−	0.00480680i	−0.427766	+	0.903890i	$0.640699\pi$
$798$	−2.03336	−	17.1565i	−0.0719803	−	0.607333i
$799$	−31.0206	+	5.46977i	−1.09743	+	0.193507i
$800$	−2.90771	−	40.0663i	−0.102803	−	1.41656i
$801$	23.1181	−	15.3121i	0.816838	−	0.541026i
$802$	16.1424	+	4.32535i	0.570008	+	0.152733i
$803$	−0.147271	+	1.68331i	−0.00519708	+	0.0594028i
$804$	29.9343	+	9.86557i	1.05570	+	0.347932i
$805$	−4.54689	−	8.01197i	−0.160257	−	0.282385i
$806$	−7.83946	+	9.34270i	−0.276133	+	0.329083i
$807$	11.5140	−	12.2437i	0.405314	−	0.430998i
$808$	0.282818	+	0.606505i	0.00994950	+	0.0213368i
$809$	30.0007			1.05477			0.527384	−	0.849627i	$-0.323173\pi$
$809$	30.0007			1.05477			0.527384	+	0.849627i	$0.323173\pi$
$810$	−35.5734	−	19.2250i	−1.24992	−	0.675498i
$811$	21.6188			0.759140			0.379570	−	0.925163i	$-0.376072\pi$
$811$	21.6188			0.759140			0.379570	+	0.925163i	$0.376072\pi$
$812$	27.7620	+	59.5358i	0.974255	+	2.08930i
$813$	22.2527	−	23.6628i	0.780436	−	0.829892i
$814$	−8.06185	+	9.60773i	−0.282568	+	0.336751i
$815$	−1.46558	−	0.404364i	−0.0513370	−	0.0141643i
$816$	41.6260	+	13.7189i	1.45720	+	0.480257i
$817$	0.318346	−	3.63871i	0.0111375	−	0.127302i
$818$	−31.2780	−	8.38092i	−1.09361	−	0.293032i
$819$	−30.9616	−	15.4246i	−1.08188	−	0.538979i
$820$	−26.4932	+	4.46929i	−0.925181	+	0.156074i
$821$	−12.6915	+	2.23786i	−0.442937	+	0.0781018i	−0.390669	−	0.920531i	$-0.627756\pi$
$821$	−12.6915	+	2.23786i	−0.442937	+	0.0781018i	−0.0522685	+	0.998633i	$0.516645\pi$
$822$	5.66616	+	47.8082i	0.197630	+	1.66750i
$823$	−28.3477	−	13.2188i	−0.988140	−	0.460777i	−0.139772	−	0.990184i	$-0.544637\pi$
$823$	−28.3477	−	13.2188i	−0.988140	−	0.460777i	−0.848368	+	0.529407i	$0.822415\pi$
$824$	0.884565	−	0.321955i	0.0308153	−	0.0112158i
$825$	5.36553	+	11.0450i	0.186804	+	0.384538i
$826$	−4.89290	−	27.7490i	−0.170246	−	0.965511i
$827$	54.9503	−	14.7239i	1.91081	−	0.512000i	0.917309	−	0.398177i	$-0.130357\pi$
$827$	54.9503	−	14.7239i	1.91081	−	0.512000i	0.993501	−	0.113823i	$-0.0363097\pi$
$828$	−6.71702	−	4.11326i	−0.233432	−	0.142946i
$829$	−13.5565	+	7.82684i	−0.470836	+	0.271837i	−0.716590	−	0.697495i	$-0.754298\pi$
$829$	−13.5565	+	7.82684i	−0.470836	+	0.271837i	0.245753	+	0.969332i	$0.420965\pi$
$830$	−50.2085	−	9.23725i	−1.74276	−	0.320630i
$831$	16.8210	+	18.8403i	0.583515	+	0.653564i
$832$	−17.1604	−	24.5076i	−0.594930	−	0.849648i
$833$	−20.6797	+	1.80924i	−0.716508	+	0.0626863i
$834$	−26.0423	+	16.1212i	−0.901770	+	0.558230i
$835$	20.5554	−	43.2417i	0.711349	−	1.49644i
$836$			4.48562i			0.155138i
$837$	1.56010	+	8.60408i	0.0539249	+	0.297400i
$838$	3.95197	+	3.95197i	0.136518	+	0.136518i
$839$	−17.8822	−	6.50860i	−0.617363	−	0.224702i	0.0143589	−	0.999897i	$-0.495429\pi$
$839$	−17.8822	−	6.50860i	−0.617363	−	0.224702i	−0.631722	+	0.775195i	$0.717651\pi$
$840$	0.770182	+	0.512978i	0.0265738	+	0.0176994i
$841$	55.7268	+	46.7603i	1.92161	+	1.61242i
$842$	−44.6297	+	31.2501i	−1.53804	+	1.07695i
$843$	−2.03933	+	3.11157i	−0.0702383	+	0.107168i
$844$	29.5162	+	35.1760i	1.01599	+	1.21081i
$845$	−0.0200826	−	0.00747846i	−0.000690862	−	0.000257267i
$846$	26.9995	−	11.7499i	0.928263	−	0.403970i
$847$	7.43782	+	27.7583i	0.255567	+	0.953788i
$848$	3.09002	+	2.16365i	0.106112	+	0.0743002i
$849$	24.2137	−	9.66472i	0.831011	−	0.331692i
$850$	−63.9572	+	10.3025i	−2.19371	+	0.353372i
$851$	−1.94047	−	5.33141i	−0.0665186	−	0.182758i
$852$	−13.5547	+	31.5633i	−0.464377	+	1.08134i
$853$	4.62155	−	6.60026i	0.158239	−	0.225988i	−0.732202	−	0.681088i	$-0.761507\pi$
$853$	4.62155	−	6.60026i	0.158239	−	0.225988i	0.890441	+	0.455099i	$0.150396\pi$
$854$	45.3730	−	78.5883i	1.55263	−	2.68923i
$855$	−9.28955	−	4.71416i	−0.317696	−	0.161221i
$856$	−0.0428776	−	0.0742662i	−0.00146553	−	0.00253837i
$857$	51.6637	+	4.51999i	1.76480	+	0.154400i	0.922850	−	0.385158i	$-0.125853\pi$
$857$	51.6637	+	4.51999i	1.76480	+	0.154400i	0.841948	+	0.539558i	$0.181409\pi$
$858$	14.8859	+	9.75625i	0.508196	+	0.333073i
$859$	40.2472	+	7.09666i	1.37322	+	0.242135i	0.811092	−	0.584918i	$-0.198873\pi$
$859$	40.2472	+	7.09666i	1.37322	+	0.242135i	0.562124	+	0.827053i	$0.309984\pi$
$860$	7.51999	+	7.63228i	0.256430	+	0.260259i
$861$	−15.4527	+	28.7699i	−0.526628	+	0.980476i
$862$	34.5347	−	16.1038i	1.17626	−	0.548497i
$863$	29.8445	−	29.8445i	1.01592	−	1.01592i	0.0160467	−	0.999871i	$-0.494892\pi$
$863$	29.8445	−	29.8445i	1.01592	−	1.01592i	0.999871	−	0.0160467i	$-0.00510806\pi$
$864$	−41.6059	−	3.43724i	−1.41546	−	0.116937i
$865$	−46.6208	−	4.42715i	−1.58516	−	0.150528i
$866$	2.64852	−	7.27674i	0.0900003	−	0.247274i
$867$	9.75133	−	41.4419i	0.331173	−	1.40744i
$868$	−0.955182	−	10.9178i	−0.0324210	−	0.370573i
$869$	3.36535	−	19.0859i	0.114162	−	0.647444i
$870$	77.5994	+	11.8266i	2.63087	+	0.400958i
$871$	24.6804	−	20.7093i	0.836262	−	0.701707i
$872$	0.111966	−	0.417863i	0.00379165	−	0.0141506i
$873$	7.74576	−	12.6489i	0.262154	−	0.428102i
$874$	−3.48248	−	2.01061i	−0.117797	−	0.0680100i
$875$	35.5268	+	3.90573i	1.20103	+	0.132038i
$876$	4.16164	+	0.602735i	0.140609	+	0.0203645i
$877$	−5.46684	+	11.7237i	−0.184602	+	0.395880i	−0.976729	−	0.214476i	$-0.931196\pi$
$877$	−5.46684	+	11.7237i	−0.184602	+	0.395880i	0.792127	+	0.610356i	$0.208974\pi$
$878$	−21.9634	+	47.1006i	−0.741227	+	1.58957i
$879$	−30.7808	+	39.0580i	−1.03821	+	1.31739i
$880$	9.47139	+	8.06780i	0.319281	+	0.271965i
$881$	30.4813	+	17.5984i	1.02694	+	0.592905i	0.916107	−	0.400934i	$-0.131314\pi$
$881$	30.4813	+	17.5984i	1.02694	+	0.592905i	0.110834	+	0.993839i	$0.464648\pi$
$882$	18.4005	−	6.16321i	0.619576	−	0.207526i
$883$	10.2619	−	38.2981i	0.345342	−	1.28883i	−0.546870	−	0.837217i	$-0.684181\pi$
$883$	10.2619	−	38.2981i	0.345342	−	1.28883i	0.892212	−	0.451617i	$-0.149152\pi$
$884$	−36.2962	+	30.4561i	−1.22077	+	1.02435i
$885$	−15.5612	−	6.81969i	−0.523082	−	0.229242i
$886$	0.853574	−	4.84086i	0.0286764	−	0.162632i
$887$	1.07122	+	12.2441i	0.0359682	+	0.411118i	0.992740	+	0.120279i	$0.0383789\pi$
$887$	1.07122	+	12.2441i	0.0359682	+	0.411118i	−0.956772	+	0.290839i	$0.906066\pi$
$888$	0.415171	+	0.390429i	0.0139322	+	0.0131020i
$889$	−15.2398	+	41.8709i	−0.511125	+	1.40430i
$890$	−3.92587	+	41.3420i	−0.131595	+	1.38579i
$891$	12.2010	−	3.73870i	0.408750	−	0.125251i
$892$	6.01508	−	6.01508i	0.201400	−	0.201400i
$893$	6.87510	−	3.20591i	0.230067	−	0.107282i
$894$	−4.64432	+	0.142634i	−0.155329	+	0.00477041i
$895$	−0.316198	+	42.6685i	−0.0105693	+	1.42625i
$896$	1.88209	+	0.331863i	0.0628762	+	0.0110868i
$897$	−7.18903	+	3.62500i	−0.240035	+	0.121035i
$898$	14.2827	+	1.24958i	0.476621	+	0.0416990i
$899$	−8.48742	−	14.7006i	−0.283071	−	0.490294i
$900$	28.1973	−	11.7773i	0.939909	−	0.392575i
$901$	3.09924	−	5.36804i	0.103251	−	0.178835i
$902$	9.63791	−	13.7644i	0.320907	−	0.458303i
$903$	12.9330	−	1.53280i	0.430382	−	0.0510083i
$904$	−0.0580931	−	0.159610i	−0.00193215	−	0.00530854i
$905$	16.5722	+	9.73242i	0.550879	+	0.323516i
$906$	6.75284	−	46.6256i	0.224348	−	1.54903i
$907$	−31.6422	−	22.1561i	−1.05066	−	0.735681i	−0.0852357	−	0.996361i	$-0.527164\pi$
$907$	−31.6422	−	22.1561i	−1.05066	−	0.735681i	−0.965425	+	0.260680i	$0.916053\pi$
$908$	2.56370	+	9.56785i	0.0850793	+	0.317520i
$909$	19.4781	−	18.4958i	0.646049	−	0.613467i
$910$	47.1117	−	21.5450i	1.56174	−	0.714209i
$911$	−22.6169	−	26.9538i	−0.749333	−	0.893020i	0.247791	−	0.968814i	$-0.420295\pi$
$911$	−22.6169	−	26.9538i	−0.749333	−	0.893020i	−0.997124	+	0.0757937i	$0.975851\pi$
$912$	−10.5382	−	0.596724i	−0.348954	−	0.0197595i
$913$	13.1974	−	9.24090i	0.436769	−	0.305829i
$914$	−18.6304	−	15.6327i	−0.616238	−	0.517085i
$915$	−24.2731	−	49.0385i	−0.802443	−	1.62116i
$916$	−52.0351	−	18.9392i	−1.71929	−	0.625770i
$917$	−1.72791	−	1.72791i	−0.0570605	−	0.0570605i
$918$	0.325794	+	67.3223i	0.0107528	+	2.22197i
$919$			21.8380i			0.720370i	0.932881	+	0.360185i	$0.117286\pi$
$919$			21.8380i			0.720370i	−0.932881	+	0.360185i	$0.882714\pi$
$920$	0.202939	−	0.0721651i	0.00669069	−	0.00237921i
$921$	29.5965	+	15.8967i	0.975237	+	0.523814i
$922$	−36.9583	+	3.23343i	−1.21716	+	0.106488i
$923$	20.1402	+	28.7632i	0.662924	+	0.946753i
$924$	−15.6580	+	3.25945i	−0.515109	+	0.107228i
$925$	21.1749	+	6.01154i	0.696228	+	0.197658i
$926$	−55.9533	+	32.3047i	−1.83874	+	1.06160i
$927$	−23.5301	−	29.5621i	−0.772830	−	0.970947i
$928$	78.2803	−	20.9751i	2.56968	−	0.688543i
$929$	2.34106	+	13.2768i	0.0768076	+	0.435598i	0.998826	+	0.0484506i	$0.0154284\pi$
$929$	2.34106	+	13.2768i	0.0768076	+	0.435598i	−0.922018	+	0.387147i	$0.873461\pi$
$930$	−11.4907	−	6.28200i	−0.376796	−	0.205995i
$931$	4.69775	−	1.70984i	0.153963	−	0.0560378i
$932$	−3.40525	−	1.58789i	−0.111543	−	0.0520131i
$933$	19.5583	+	8.39924i	0.640311	+	0.274979i
$934$	13.7075	−	2.41699i	0.448522	−	0.0790865i
$935$	11.8501	−	16.6595i	0.387539	−	0.544825i
$936$	0.480860	−	0.650276i	0.0157174	−	0.0212549i
$937$	−9.22824	−	2.47270i	−0.301473	−	0.0807796i	0.104911	−	0.994482i	$-0.466544\pi$
$937$	−9.22824	−	2.47270i	−0.301473	−	0.0807796i	−0.406385	+	0.913702i	$0.633211\pi$
$938$	−5.00048	+	57.1558i	−0.163271	+	1.86620i
$939$	−4.78471	−	22.9851i	−0.156143	−	0.750091i
$940$	−5.91844	+	21.4508i	−0.193038	+	0.699649i
$941$	−24.6880	+	29.4220i	−0.804805	+	0.959129i	−0.999765	−	0.0216818i	$-0.993098\pi$
$941$	−24.6880	+	29.4220i	−0.804805	+	0.959129i	0.194960	+	0.980811i	$0.437542\pi$
$942$	6.22719	+	20.6788i	0.202893	+	0.673752i
$943$	3.21239	+	6.88900i	0.104610	+	0.224337i
$944$	−17.2147			−0.560290
$945$	9.70553	−	35.8525i	0.315721	−	1.16628i
$946$	−6.70099			−0.217868
$947$	−3.84058	−	8.23615i	−0.124802	−	0.267639i	0.833973	−	0.551805i	$-0.186061\pi$
$947$	−3.84058	−	8.23615i	−0.124802	−	0.267639i	−0.958775	+	0.284167i	$0.908283\pi$
$948$	−46.9473	−	11.0468i	−1.52478	−	0.358782i
$949$	2.76298	−	3.29279i	0.0896901	−	0.106888i
$950$	14.2356	−	6.38306i	0.461864	−	0.207094i
$951$	−12.0189	+	10.7307i	−0.389741	+	0.347968i
$952$	0.134280	−	1.53483i	0.00435205	−	0.0497441i
$953$	16.6185	+	4.45291i	0.538326	+	0.144244i	0.517730	−	0.855544i	$-0.326777\pi$
$953$	16.6185	+	4.45291i	0.538326	+	0.144244i	0.0205956	+	0.999788i	$0.493444\pi$
$954$	−1.64392	+	5.55626i	−0.0532239	+	0.179890i
$955$	3.53982	+	20.9834i	0.114546	+	0.679008i
$956$	1.18442	−	0.208845i	0.0383069	−	0.00675454i
$957$	−19.8464	+	14.8249i	−0.641542	+	0.479220i
$958$	48.8944	+	22.7998i	1.57971	+	0.736629i
$959$	−41.5553	+	15.1249i	−1.34189	+	0.488408i
$960$	22.1810	−	23.2390i	0.715887	−	0.750037i
$961$	−4.89132	−	27.7401i	−0.157785	−	0.894841i
$962$	30.8177	−	8.25757i	0.993602	−	0.266235i
$963$	−2.27995	+	2.57867i	−0.0734705	+	0.0830964i
$964$	−9.06199	+	5.23194i	−0.291867	+	0.168509i
$965$	−8.13583	−	11.8044i	−0.261902	−	0.379997i
$966$	4.48792	−	13.6173i	0.144396	−	0.438129i
$967$	−13.9349	−	19.9012i	−0.448117	−	0.639978i	0.530008	−	0.847992i	$-0.322189\pi$
$967$	−13.9349	−	19.9012i	−0.448117	−	0.639978i	−0.978126	+	0.208014i	$0.933300\pi$
$968$	−0.669342	+	0.0585599i	−0.0215135	+	0.00188219i
$969$	0.532410	+	17.3358i	0.0171035	+	0.556907i
$970$	7.44241	+	20.9291i	0.238961	+	0.671994i
$971$		−	9.34984i		−	0.300051i	−0.988682	−	0.150025i	$-0.952064\pi$
$971$		−	9.34984i		−	0.300051i	0.988682	−	0.150025i	$-0.0479355\pi$
$972$	−7.57261	−	30.8407i	−0.242891	−	0.989216i
$973$	−19.8938	−	19.8938i	−0.637765	−	0.637765i
$974$	−46.4563	−	16.9087i	−1.48856	−	0.541790i
$975$	4.93497	−	30.8442i	0.158045	−	0.987805i
$976$	−42.4702	−	35.6367i	−1.35944	−	1.14070i
$977$	1.60277	−	1.12227i	0.0512773	−	0.0359048i	−0.547657	−	0.836703i	$-0.684480\pi$
$977$	1.60277	−	1.12227i	0.0512773	−	0.0359048i	0.598934	+	0.800798i	$0.295591\pi$
$978$	−1.06537	−	2.11282i	−0.0340668	−	0.0675605i
$979$	−8.42414	−	10.0395i	−0.269237	−	0.320864i
$980$	−5.11763	+	13.7428i	−0.163477	+	0.438999i
$981$	−17.3312	+	1.06554i	−0.553341	+	0.0340200i
$982$	−12.8530	−	47.9679i	−0.410154	−	1.53072i
$983$	29.7984	+	20.8651i	0.950423	+	0.665493i	0.942405	−	0.334475i	$-0.108559\pi$
$983$	29.7984	+	20.8651i	0.950423	+	0.665493i	0.00801795	+	0.999968i	$0.497448\pi$
$984$	−0.599699	−	0.472610i	−0.0191177	−	0.0150663i
$985$	7.52236	+	28.9297i	0.239682	+	0.921776i
$986$	−44.6985	−	122.808i	−1.42349	−	3.91100i
$987$	16.1866	+	21.6694i	0.515226	+	0.689743i
$988$	6.54490	−	9.34709i	0.208221	−	0.297370i
$989$	1.51565	−	2.62518i	0.0481948	−	0.0834758i
$990$	−7.13024	+	17.7313i	−0.226614	+	0.563538i
$991$	−18.2789	−	31.6600i	−0.580649	−	1.00571i	−0.995403	−	0.0957794i	$-0.969466\pi$
$991$	−18.2789	−	31.6600i	−0.580649	−	1.00571i	0.414754	−	0.909934i	$-0.363868\pi$
$992$	−13.4692	−	1.17840i	−0.427646	−	0.0374142i
$993$	1.27927	−	22.5920i	0.0405965	−	0.716937i
$994$	−61.5804	−	10.8583i	−1.95321	−	0.344404i
$995$	−4.70561	−	0.0348712i	−0.149178	−	0.00110549i
$996$	−21.1032	−	34.0903i	−0.668680	−	1.08019i
$997$	36.3975	−	16.9724i	1.15272	−	0.537523i	0.250211	−	0.968191i	$-0.419500\pi$
$997$	36.3975	−	16.9724i	1.15272	−	0.537523i	0.902510	+	0.430668i	$0.141722\pi$
$998$	−26.2639	+	26.2639i	−0.831368	+	0.831368i
$999$	9.56707	−	20.7786i	0.302689	−	0.657405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.23.2	✓	192
3.2	odd	2		405.2.r.a.98.15		192
5.2	odd	4	inner	135.2.q.a.77.15	yes	192
5.3	odd	4		675.2.ba.b.482.2		192
5.4	even	2		675.2.ba.b.293.15		192
15.2	even	4		405.2.r.a.17.2		192
27.7	even	9		405.2.r.a.143.2		192
27.20	odd	18	inner	135.2.q.a.128.15	yes	192
135.7	odd	36		405.2.r.a.62.15		192
135.47	even	36	inner	135.2.q.a.47.2	yes	192
135.74	odd	18		675.2.ba.b.668.2		192
135.128	even	36		675.2.ba.b.182.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.2	✓	192	1.1	even	1	trivial
135.2.q.a.47.2	yes	192	135.47	even	36	inner
135.2.q.a.77.15	yes	192	5.2	odd	4	inner
135.2.q.a.128.15	yes	192	27.20	odd	18	inner
405.2.r.a.17.2		192	15.2	even	4
405.2.r.a.62.15		192	135.7	odd	36
405.2.r.a.98.15		192	3.2	odd	2
405.2.r.a.143.2		192	27.7	even	9
675.2.ba.b.182.15		192	135.128	even	36
675.2.ba.b.293.15		192	5.4	even	2
675.2.ba.b.482.2		192	5.3	odd	4
675.2.ba.b.668.2		192	135.74	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.849158 - 1.82102i) q^{2} +(1.18657 - 1.26176i) q^{3} +(-1.30949 + 1.56058i) q^{4} +(-1.94472 + 1.10365i) q^{5} +(-3.30529 - 1.08934i) q^{6} +(0.278616 - 3.18459i) q^{7} +(0.0721951 + 0.0193446i) q^{8} +(-0.184096 - 2.99435i) q^{9} +O(q^{10})\)	\(q+(-0.849158 - 1.82102i) q^{2} +(1.18657 - 1.26176i) q^{3} +(-1.30949 + 1.56058i) q^{4} +(-1.94472 + 1.10365i) q^{5} +(-3.30529 - 1.08934i) q^{6} +(0.278616 - 3.18459i) q^{7} +(0.0721951 + 0.0193446i) q^{8} +(-0.184096 - 2.99435i) q^{9} +(3.66116 + 2.60421i) q^{10} +(-1.39635 + 0.246214i) q^{11} +(0.415290 + 3.50401i) q^{12} +(3.26894 + 1.52433i) q^{13} +(-6.03581 + 2.19686i) q^{14} +(-0.915004 + 3.76335i) q^{15} +(0.681434 + 3.86460i) q^{16} +(6.22853 - 1.66893i) q^{17} +(-5.29645 + 2.87791i) q^{18} +(-1.34486 + 0.776456i) q^{19} +(0.824244 - 4.48012i) q^{20} +(-3.68761 - 4.13030i) q^{21} +(1.63408 + 2.33371i) q^{22} +(-1.28385 + 0.112323i) q^{23} +(0.110073 - 0.0681394i) q^{24} +(2.56390 - 4.29260i) q^{25} -7.24723i q^{26} +(-3.99660 - 3.32072i) q^{27} +(4.60499 + 4.60499i) q^{28} +(9.47861 + 3.44993i) q^{29} +(7.63013 - 1.52943i) q^{30} +(-1.28914 - 1.08172i) q^{31} +(6.58134 - 4.60830i) q^{32} +(-1.34620 + 2.05401i) q^{33} +(-8.32817 - 9.92512i) q^{34} +(2.97286 + 6.50065i) q^{35} +(4.91400 + 3.63376i) q^{36} +(1.13941 + 4.25234i) q^{37} +(2.55594 + 1.78969i) q^{38} +(5.80218 - 2.31590i) q^{39} +(-0.161749 + 0.0420584i) q^{40} +(-2.01725 - 5.54236i) q^{41} +(-4.39001 + 10.2225i) q^{42} +(-1.34911 + 1.92673i) q^{43} +(1.44426 - 2.50153i) q^{44} +(3.66273 + 5.62000i) q^{45} +(1.29474 + 2.24255i) q^{46} +(-4.86633 - 0.425748i) q^{47} +(5.68478 + 3.72582i) q^{48} +(-3.17036 - 0.559020i) q^{49} +(-9.99408 - 1.02383i) q^{50} +(5.28480 - 9.83924i) q^{51} +(-6.65949 + 3.10537i) q^{52} +(0.679717 - 0.679717i) q^{53} +(-2.65337 + 10.0977i) q^{54} +(2.44378 - 2.01990i) q^{55} +(0.0817195 - 0.224523i) q^{56} +(-0.616070 + 2.61822i) q^{57} +(-1.76642 - 20.1903i) q^{58} +(-0.761756 + 4.32014i) q^{59} +(-4.67483 - 6.35599i) q^{60} +(-10.8226 + 9.08123i) q^{61} +(-0.875151 + 3.26611i) q^{62} +(-9.58707 - 0.248002i) q^{63} +(-7.18348 - 4.14738i) q^{64} +(-8.03953 + 0.643373i) q^{65} +(4.88355 + 0.707290i) q^{66} +(3.77497 - 8.09546i) q^{67} +(-5.55167 + 11.9056i) q^{68} +(-1.38166 + 1.75320i) q^{69} +(9.31342 - 10.9337i) q^{70} +(8.43086 + 4.86756i) q^{71} +(0.0446337 - 0.219739i) q^{72} +(0.308443 - 1.15112i) q^{73} +(6.77608 - 5.68580i) q^{74} +(-2.37400 - 8.32851i) q^{75} +(0.549351 - 3.11553i) q^{76} +(0.395047 + 4.51541i) q^{77} +(-9.14429 - 8.59935i) q^{78} +(-4.67487 + 12.8441i) q^{79} +(-5.59038 - 6.76352i) q^{80} +(-8.93222 + 1.10249i) q^{81} +(-8.37981 + 8.37981i) q^{82} +(-10.2981 + 4.80207i) q^{83} +(11.2745 - 0.346259i) q^{84} +(-10.2709 + 10.1197i) q^{85} +(4.65423 + 0.820666i) q^{86} +(15.6001 - 7.86618i) q^{87} +(-0.105573 - 0.00923640i) q^{88} +(4.62153 + 8.00472i) q^{89} +(7.12391 - 11.4422i) q^{90} +(5.76516 - 9.98556i) q^{91} +(1.50590 - 2.15065i) q^{92} +(-2.89453 + 0.343056i) q^{93} +(3.35698 + 9.22322i) q^{94} +(1.75844 - 2.99425i) q^{95} +(1.99464 - 13.7722i) q^{96} +(4.04993 + 2.83579i) q^{97} +(1.67415 + 6.24800i) q^{98} +(0.994312 + 4.13583i) 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

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