LMFDB - Embedded newform 675.2.ba.b.482.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			482.2
Character	$\chi$	$=$	675.482
Dual form			675.2.ba.b.668.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82102 + 0.849158i) q^{2} +(1.26176 + 1.18657i) q^{3} +(1.30949 - 1.56058i) q^{4} +(-3.30529 - 1.08934i) q^{6} +(-3.18459 - 0.278616i) q^{7} +(-0.0193446 + 0.0721951i) q^{8} +(0.184096 + 2.99435i) q^{9} +O(q^{10})$	\(q+(-1.82102 + 0.849158i) q^{2} +(1.26176 + 1.18657i) q^{3} +(1.30949 - 1.56058i) q^{4} +(-3.30529 - 1.08934i) q^{6} +(-3.18459 - 0.278616i) q^{7} +(-0.0193446 + 0.0721951i) q^{8} +(0.184096 + 2.99435i) q^{9} +(-1.39635 + 0.246214i) q^{11} +(3.50401 - 0.415290i) q^{12} +(-1.52433 + 3.26894i) q^{13} +(6.03581 - 2.19686i) q^{14} +(0.681434 + 3.86460i) q^{16} +(-1.66893 - 6.22853i) q^{17} +(-2.87791 - 5.29645i) q^{18} +(1.34486 - 0.776456i) q^{19} +(-3.68761 - 4.13030i) q^{21} +(2.33371 - 1.63408i) q^{22} +(-0.112323 - 1.28385i) q^{23} +(-0.110073 + 0.0681394i) q^{24} -7.24723i q^{26} +(-3.32072 + 3.99660i) q^{27} +(-4.60499 + 4.60499i) q^{28} +(-9.47861 - 3.44993i) q^{29} +(-1.28914 - 1.08172i) q^{31} +(-4.60830 - 6.58134i) q^{32} +(-2.05401 - 1.34620i) q^{33} +(8.32817 + 9.92512i) q^{34} +(4.91400 + 3.63376i) q^{36} +(4.25234 - 1.13941i) q^{37} +(-1.78969 + 2.55594i) q^{38} +(-5.80218 + 2.31590i) q^{39} +(-2.01725 - 5.54236i) q^{41} +(10.2225 + 4.39001i) q^{42} +(-1.92673 - 1.34911i) q^{43} +(-1.44426 + 2.50153i) q^{44} +(1.29474 + 2.24255i) q^{46} +(-0.425748 + 4.86633i) q^{47} +(-3.72582 + 5.68478i) q^{48} +(3.17036 + 0.559020i) q^{49} +(5.28480 - 9.83924i) q^{51} +(3.10537 + 6.65949i) q^{52} +(0.679717 + 0.679717i) q^{53} +(2.65337 - 10.0977i) q^{54} +(0.0817195 - 0.224523i) q^{56} +(2.61822 + 0.616070i) q^{57} +(20.1903 - 1.76642i) q^{58} +(0.761756 - 4.32014i) q^{59} +(-10.8226 + 9.08123i) q^{61} +(3.26611 + 0.875151i) q^{62} +(0.248002 - 9.58707i) q^{63} +(7.18348 + 4.14738i) q^{64} +(4.88355 + 0.707290i) q^{66} +(-8.09546 - 3.77497i) q^{67} +(-11.9056 - 5.55167i) q^{68} +(1.38166 - 1.75320i) q^{69} +(8.43086 + 4.86756i) q^{71} +(-0.219739 - 0.0446337i) q^{72} +(1.15112 + 0.308443i) q^{73} +(-6.77608 + 5.68580i) q^{74} +(0.549351 - 3.11553i) q^{76} +(4.51541 - 0.395047i) q^{77} +(8.59935 - 9.14429i) q^{78} +(4.67487 - 12.8441i) q^{79} +(-8.93222 + 1.10249i) q^{81} +(8.37981 + 8.37981i) q^{82} +(-4.80207 - 10.2981i) q^{83} +(-11.2745 + 0.346259i) q^{84} +(4.65423 + 0.820666i) q^{86} +(-7.86618 - 15.6001i) q^{87} +(0.00923640 - 0.105573i) q^{88} +(-4.62153 - 8.00472i) q^{89} +(5.76516 - 9.98556i) q^{91} +(-2.15065 - 1.50590i) q^{92} +(-0.343056 - 2.89453i) q^{93} +(-3.35698 - 9.22322i) q^{94} +(1.99464 - 13.7722i) q^{96} +(2.83579 - 4.04993i) q^{97} +(-6.24800 + 1.67415i) q^{98} +(-0.994312 - 4.13583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31} + 48 q^{32} + 6 q^{33} + 12 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{41} + 24 q^{42} + 12 q^{43} - 12 q^{46} + 6 q^{47} - 12 q^{48} + 144 q^{51} - 12 q^{52} + 180 q^{56} + 12 q^{57} + 12 q^{58} - 60 q^{61} + 18 q^{62} + 54 q^{63} + 72 q^{66} - 24 q^{67} + 60 q^{68} - 36 q^{71} - 180 q^{72} + 6 q^{73} - 72 q^{76} - 132 q^{77} - 78 q^{78} + 12 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{86} - 144 q^{87} + 48 q^{88} - 12 q^{91} - 258 q^{92} - 180 q^{93} - 12 q^{96} - 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.82102	+	0.849158i	−1.28766	+	0.600445i	−0.941273	−	0.337647i	$-0.890369\pi$
$2$	−1.82102	+	0.849158i	−1.28766	+	0.600445i	−0.346386	+	0.938092i	$0.612591\pi$
$3$	1.26176	+	1.18657i	0.728480	+	0.685067i
$3$	1.26176	+	1.18657i	0.728480	+	0.685067i
$4$	1.30949	−	1.56058i	0.654743	−	0.780292i
$5$		0			0
$5$		0			0
$6$	−3.30529	−	1.08934i	−1.34938	−	0.444721i
$7$	−3.18459	−	0.278616i	−1.20366	−	0.105307i	−0.532379	−	0.846506i	$-0.678702\pi$
$7$	−3.18459	−	0.278616i	−1.20366	−	0.105307i	−0.671285	+	0.741199i	$0.734257\pi$
$8$	−0.0193446	+	0.0721951i	−0.00683936	+	0.0255248i
$9$	0.184096	+	2.99435i	0.0613653	+	0.998115i
$10$		0			0
$11$	−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	$0.513014\pi$
$12$	3.50401	−	0.415290i	1.01152	−	0.119884i
$13$	−1.52433	+	3.26894i	−0.422774	+	0.906642i	0.573402	+	0.819274i	$0.305623\pi$
$13$	−1.52433	+	3.26894i	−0.422774	+	0.906642i	−0.996176	+	0.0873677i	$0.972154\pi$
$14$	6.03581	−	2.19686i	1.61314	−	0.587135i
$15$		0			0
$16$	0.681434	+	3.86460i	0.170358	+	0.966150i
$17$	−1.66893	−	6.22853i	−0.404775	−	1.51064i	−0.804470	−	0.593993i	$-0.797551\pi$
$17$	−1.66893	−	6.22853i	−0.404775	−	1.51064i	0.399695	−	0.916648i	$-0.369116\pi$
$18$	−2.87791	−	5.29645i	−0.678331	−	1.24839i
$19$	1.34486	−	0.776456i	0.308532	−	0.178131i	−0.337737	−	0.941240i	$-0.609662\pi$
$19$	1.34486	−	0.776456i	0.308532	−	0.178131i	0.646269	+	0.763109i	$0.276328\pi$
$20$		0			0
$21$	−3.68761	−	4.13030i	−0.804702	−	0.901305i
$22$	2.33371	−	1.63408i	0.497549	−	0.348388i
$23$	−0.112323	−	1.28385i	−0.0234209	−	0.267702i	−0.998872	−	0.0474857i	$-0.984879\pi$
$23$	−0.112323	−	1.28385i	−0.0234209	−	0.267702i	0.975451	−	0.220217i	$-0.0706764\pi$
$24$	−0.110073	+	0.0681394i	−0.0224686	+	0.0139089i
$25$		0			0
$26$		−	7.24723i		−	1.42130i
$27$	−3.32072	+	3.99660i	−0.639073	+	0.769146i
$28$	−4.60499	+	4.60499i	−0.870260	+	0.870260i
$29$	−9.47861	−	3.44993i	−1.76013	−	0.640636i	−0.760175	−	0.649718i	$-0.774887\pi$
$29$	−9.47861	−	3.44993i	−1.76013	−	0.640636i	−0.999959	+	0.00908143i	$0.997109\pi$
$30$		0			0
$31$	−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	$0.770512\pi$
$32$	−4.60830	−	6.58134i	−0.814641	−	1.16343i
$33$	−2.05401	−	1.34620i	−0.357558	−	0.234344i
$34$	8.32817	+	9.92512i	1.42827	+	1.70214i
$35$		0			0
$36$	4.91400	+	3.63376i	0.819000	+	0.605626i
$37$	4.25234	−	1.13941i	0.699081	−	0.187318i	0.108262	−	0.994122i	$-0.465471\pi$
$37$	4.25234	−	1.13941i	0.699081	−	0.187318i	0.590819	+	0.806804i	$0.298805\pi$
$38$	−1.78969	+	2.55594i	−0.290326	+	0.414629i
$39$	−5.80218	+	2.31590i	−0.929093	+	0.370841i
$40$		0			0
$41$	−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	$-0.263463\pi$
$42$	10.2225	+	4.39001i	1.57737	+	0.677393i
$43$	−1.92673	−	1.34911i	−0.293824	−	0.205737i	0.417365	−	0.908739i	$-0.362954\pi$
$43$	−1.92673	−	1.34911i	−0.293824	−	0.205737i	−0.711188	+	0.703002i	$0.751843\pi$
$44$	−1.44426	+	2.50153i	−0.217731	+	0.377121i
$45$		0			0
$46$	1.29474	+	2.24255i	0.190899	+	0.330646i
$47$	−0.425748	+	4.86633i	−0.0621018	+	0.709826i	0.899777	+	0.436350i	$0.143729\pi$
$47$	−0.425748	+	4.86633i	−0.0621018	+	0.709826i	−0.961879	+	0.273476i	$0.911826\pi$
$48$	−3.72582	+	5.68478i	−0.537776	+	0.820528i
$49$	3.17036	+	0.559020i	0.452909	+	0.0798600i
$50$		0			0
$51$	5.28480	−	9.83924i	0.740020	−	1.37777i
$52$	3.10537	+	6.65949i	0.430637	+	0.923505i
$53$	0.679717	+	0.679717i	0.0933664	+	0.0933664i	0.752247	−	0.658881i	$-0.228970\pi$
$53$	0.679717	+	0.679717i	0.0933664	+	0.0933664i	−0.658881	+	0.752247i	$0.728970\pi$
$54$	2.65337	−	10.0977i	0.361078	−	1.37413i
$55$		0			0
$56$	0.0817195	−	0.224523i	0.0109202	−	0.0300031i
$57$	2.61822	+	0.616070i	0.346791	+	0.0816004i
$58$	20.1903	−	1.76642i	2.65112	−	0.231943i
$59$	0.761756	−	4.32014i	0.0991722	−	0.562434i	−0.894216	−	0.447635i	$-0.852266\pi$
$59$	0.761756	−	4.32014i	0.0991722	−	0.562434i	0.993389	−	0.114799i	$-0.0366224\pi$
$60$		0			0
$61$	−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	$0.918063\pi$
$62$	3.26611	+	0.875151i	0.414796	+	0.111144i
$63$	0.248002	−	9.58707i	0.0312453	−	1.20786i
$64$	7.18348	+	4.14738i	0.897935	+	0.518423i
$65$		0			0
$66$	4.88355	+	0.707290i	0.601123	+	0.0870613i
$67$	−8.09546	−	3.77497i	−0.989018	−	0.461187i	−0.140344	−	0.990103i	$-0.544821\pi$
$67$	−8.09546	−	3.77497i	−0.989018	−	0.461187i	−0.848674	+	0.528916i	$0.822599\pi$
$68$	−11.9056	−	5.55167i	−1.44376	−	0.673239i
$69$	1.38166	−	1.75320i	0.166332	−	0.211060i
$70$		0			0
$71$	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	$0.470627\pi$
$72$	−0.219739	−	0.0446337i	−0.0258964	−	0.00526013i
$73$	1.15112	+	0.308443i	0.134729	+	0.0361005i	0.325553	−	0.945524i	$-0.394449\pi$
$73$	1.15112	+	0.308443i	0.134729	+	0.0361005i	−0.190824	+	0.981624i	$0.561116\pi$
$74$	−6.77608	+	5.68580i	−0.787703	+	0.660961i
$75$		0			0
$76$	0.549351	−	3.11553i	0.0630149	−	0.357375i
$77$	4.51541	−	0.395047i	0.514578	−	0.0450198i
$78$	8.59935	−	9.14429i	0.973685	−	1.03539i
$79$	4.67487	−	12.8441i	0.525964	−	1.44507i	−0.337819	−	0.941211i	$-0.609689\pi$
$79$	4.67487	−	12.8441i	0.525964	−	1.44507i	0.863783	−	0.503864i	$-0.168089\pi$
$80$		0			0
$81$	−8.93222	+	1.10249i	−0.992469	+	0.122499i
$82$	8.37981	+	8.37981i	0.925395	+	0.925395i
$83$	−4.80207	−	10.2981i	−0.527096	−	1.13036i	−0.972043	−	0.234803i	$-0.924555\pi$
$83$	−4.80207	−	10.2981i	−0.527096	−	1.13036i	0.444947	−	0.895557i	$-0.353222\pi$
$84$	−11.2745	+	0.346259i	−1.23015	+	0.0377800i
$85$		0			0
$86$	4.65423	+	0.820666i	0.501878	+	0.0884947i
$87$	−7.86618	−	15.6001i	−0.843343	−	1.67250i
$88$	0.00923640	−	0.105573i	0.000984604	−	0.0112541i
$89$	−4.62153	−	8.00472i	−0.489881	−	0.848499i	0.510051	−	0.860144i	$-0.329626\pi$
$89$	−4.62153	−	8.00472i	−0.489881	−	0.848499i	−0.999932	+	0.0116451i	$0.996293\pi$
$90$		0			0
$91$	5.76516	−	9.98556i	0.604353	−	1.04677i
$92$	−2.15065	−	1.50590i	−0.224221	−	0.157001i
$93$	−0.343056	−	2.89453i	−0.0355733	−	0.300149i
$94$	−3.35698	−	9.22322i	−0.346246	−	0.951303i
$95$		0			0
$96$	1.99464	−	13.7722i	0.203577	−	1.40562i
$97$	2.83579	−	4.04993i	0.287931	−	0.411208i	−0.648964	−	0.760819i	$-0.724797\pi$
$97$	2.83579	−	4.04993i	0.287931	−	0.411208i	0.936895	+	0.349611i	$0.113686\pi$
$98$	−6.24800	+	1.67415i	−0.631144	+	0.169114i
$99$	−0.994312	−	4.13583i	−0.0999321	−	0.415666i
$100$		0			0
$101$	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	$0.630820\pi$
$102$	−1.26869	+	22.4051i	−0.125619	+	2.21844i
$103$	7.22389	+	10.3168i	0.711791	+	1.01654i	0.998290	+	0.0584618i	$0.0186196\pi$
$103$	7.22389	+	10.3168i	0.711791	+	1.01654i	−0.286499	+	0.958081i	$0.592492\pi$
$104$	−0.206514	−	0.173286i	−0.0202504	−	0.0169921i
$105$		0			0
$106$	−1.81497	−	0.660595i	−0.176285	−	0.0641626i
$107$	−0.811299	+	0.811299i	−0.0784313	+	0.0784313i	−0.745234	−	0.666803i	$-0.767662\pi$
$107$	−0.811299	+	0.811299i	−0.0784313	+	0.0784313i	0.666803	+	0.745234i	$0.267662\pi$
$108$	1.88860	+	10.4158i	0.181730	+	1.00226i
$109$			5.78796i			0.554386i	0.960814	+	0.277193i	$0.0894042\pi$
$109$			5.78796i			0.554386i	−0.960814	+	0.277193i	$0.910596\pi$
$110$		0			0
$111$	6.71744	+	3.60804i	0.637592	+	0.342460i
$112$	−1.09335	−	12.4970i	−0.103312	−	1.18086i
$113$	1.86154	−	1.30347i	0.175119	−	0.122620i	−0.482731	−	0.875769i	$-0.660355\pi$
$113$	1.86154	−	1.30347i	0.175119	−	0.122620i	0.657850	+	0.753149i	$0.271466\pi$
$114$	−5.29098	+	1.10140i	−0.495545	+	0.103156i
$115$		0			0
$116$	−17.7960	+	10.2745i	−1.65232	+	0.953967i
$117$	−10.0690	−	3.96258i	−0.930877	−	0.366341i
$118$	2.28130	+	8.51392i	0.210011	+	0.783770i
$119$	3.57950	+	20.3003i	0.328132	+	1.86093i
$120$		0			0
$121$	−8.44745	+	3.07462i	−0.767950	+	0.279511i
$122$	11.9968	−	25.7272i	1.08614	−	2.32923i
$123$	4.03111	−	9.38676i	0.363473	−	0.846376i
$124$	−3.37623	+	0.595320i	−0.303194	+	0.0534613i
$125$		0			0
$126$	7.68932	+	17.6689i	0.685019	+	1.57407i
$127$	−3.60755	+	13.4636i	−0.320119	+	1.19470i	0.599010	+	0.800741i	$0.295561\pi$
$127$	−3.60755	+	13.4636i	−0.320119	+	1.19470i	−0.919129	+	0.393957i	$0.871106\pi$
$128$	−0.595557	−	0.0521045i	−0.0526403	−	0.00460543i
$129$	−0.830261	−	3.98846i	−0.0731004	−	0.351164i
$130$		0			0
$131$	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	$0.211591\pi$
$132$	−4.79057	+	1.44263i	−0.416965	+	0.125564i
$133$	−4.49917	+	2.09800i	−0.390127	+	0.181919i
$134$	17.9476			1.55043
$135$		0			0
$136$	0.481955			0.0413273
$137$	−12.5374	+	5.84627i	−1.07114	+	0.499480i	−0.876503	−	0.481396i	$-0.840130\pi$
$137$	−12.5374	+	5.84627i	−1.07114	+	0.499480i	−0.194635	+	0.980876i	$0.562352\pi$
$138$	−1.02729	+	4.36587i	−0.0874491	+	0.371647i
$139$	−5.65704	+	6.74180i	−0.479824	+	0.571832i	−0.950599	−	0.310421i	$-0.899530\pi$
$139$	−5.65704	+	6.74180i	−0.479824	+	0.571832i	0.470775	+	0.882253i	$0.343974\pi$
$140$		0			0
$141$	−6.31144	+	5.63497i	−0.531519	+	0.474550i
$142$	−19.4861	−	1.70482i	−1.63524	−	0.143065i
$143$	1.32364	−	4.93990i	0.110688	−	0.413095i
$144$	−11.4465	+	2.75190i	−0.953876	+	0.229325i
$145$		0			0
$146$	−2.35814	+	0.415804i	−0.195161	+	0.0344122i
$147$	3.33693	+	4.46721i	0.275225	+	0.368450i
$148$	3.79023	−	8.12818i	0.311555	−	0.668132i
$149$	−1.25462	+	0.456644i	−0.102782	+	0.0374098i	−0.392900	−	0.919581i	$-0.628528\pi$
$149$	−1.25462	+	0.456644i	−0.102782	+	0.0374098i	0.290117	+	0.956991i	$0.406306\pi$
$150$		0			0
$151$	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	$0.758758\pi$
$152$	0.0300405	+	0.112113i	0.00243661	+	0.00909354i
$153$	18.3431	−	6.14400i	1.48295	−	0.496713i
$154$	−7.88721	+	4.55368i	−0.635569	+	0.366946i
$155$		0			0
$156$	−3.98371	+	12.0874i	−0.318952	+	0.967770i
$157$	−5.08322	+	3.55931i	−0.405685	+	0.284064i	−0.758556	−	0.651608i	$-0.774095\pi$
$157$	−5.08322	+	3.55931i	−0.405685	+	0.284064i	0.352870	+	0.935672i	$0.385206\pi$
$158$	2.39361	+	27.3591i	0.190426	+	2.17658i
$159$	0.0511095	+	1.66418i	0.00405324	+	0.131978i
$160$		0			0
$161$			4.11985i			0.324690i
$162$	15.3296	−	9.59253i	1.20441	−	0.753660i
$163$	−0.480773	+	0.480773i	−0.0376571	+	0.0376571i	−0.725685	−	0.688028i	$-0.758477\pi$
$163$	−0.480773	+	0.480773i	−0.0376571	+	0.0376571i	0.688028	+	0.725685i	$0.258477\pi$
$164$	−11.2909	−	4.10955i	−0.881670	−	0.320902i
$165$		0			0
$166$	17.4894	+	14.6753i	1.35744	+	1.13903i
$167$	12.2814	+	17.5397i	0.950365	+	1.35726i	0.933953	+	0.357396i	$0.116335\pi$
$167$	12.2814	+	17.5397i	0.950365	+	1.35726i	0.0164121	+	0.999865i	$0.494776\pi$
$168$	0.369523	−	0.186328i	0.0285093	−	0.0143755i
$169$	−0.00616029	−	0.00734155i	−0.000473868	−	0.000564734i
$170$		0			0
$171$	2.57256	+	3.88404i	0.196729	+	0.297020i
$172$	−4.62843	+	1.24018i	−0.352914	+	0.0945631i
$173$	−12.0126	+	17.1557i	−0.913298	+	1.30432i	0.0390266	+	0.999238i	$0.487574\pi$
$173$	−12.0126	+	17.1557i	−0.913298	+	1.30432i	−0.952325	+	0.305087i	$0.901315\pi$
$174$	27.5714	+	21.7285i	2.09018	+	1.64723i
$175$		0			0
$176$	−1.90304	−	5.22855i	−0.143447	−	0.394117i
$177$	6.08731	−	4.54711i	0.457550	−	0.341782i
$178$	15.2132	+	10.6524i	1.14028	+	0.798430i
$179$	−9.54123	+	16.5259i	−0.713145	+	1.23520i	0.250526	+	0.968110i	$0.419396\pi$
$179$	−9.54123	+	16.5259i	−0.713145	+	1.23520i	−0.963671	+	0.267093i	$0.913937\pi$
$180$		0			0
$181$	−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	$0.936823\pi$
$182$	−2.01919	+	23.0795i	−0.149672	+	1.71076i
$183$	−24.4311	−	1.38341i	−1.80600	−	0.102264i
$184$	0.0948609	+	0.0167265i	0.00699324	+	0.00123310i
$185$		0			0
$186$	3.08263	+	4.97971i	0.226029	+	0.365130i
$187$	3.86396	+	8.28629i	0.282561	+	0.605954i
$188$	7.03680	+	7.03680i	0.513211	+	0.513211i
$189$	11.6887	−	11.8023i	0.850225	−	0.858494i
$190$		0			0
$191$	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	$-0.000772875\pi$
$192$	4.14269	+	13.7567i	0.298973	+	0.992807i
$193$	−6.38708	+	0.558797i	−0.459752	+	0.0402231i	−0.314680	−	0.949198i	$-0.601897\pi$
$193$	−6.38708	+	0.558797i	−0.459752	+	0.0402231i	−0.145073	+	0.989421i	$0.546342\pi$
$194$	−1.72501	+	9.78304i	−0.123849	+	0.702382i
$195$		0			0
$196$	5.02394	−	4.21559i	0.358853	−	0.301113i
$197$	−12.9125	−	3.45988i	−0.919974	−	0.246506i	−0.232400	−	0.972620i	$-0.574658\pi$
$197$	−12.9125	−	3.45988i	−0.919974	−	0.246506i	−0.687574	+	0.726114i	$0.741324\pi$
$198$	5.32263	+	6.68711i	0.378263	+	0.475232i
$199$	−1.82252	−	1.05223i	−0.129195	−	0.0745909i	0.434009	−	0.900908i	$-0.357098\pi$
$199$	−1.82252	−	1.05223i	−0.129195	−	0.0745909i	−0.563205	+	0.826317i	$0.690432\pi$
$200$		0			0
$201$	−5.73528	−	14.3690i	−0.404535	−	1.01351i
$202$	−16.3046	−	7.60296i	−1.14719	−	0.534943i
$203$	29.2243	+	13.6275i	2.05115	+	0.956465i
$204$	−8.43459	−	21.1317i	−0.590539	−	1.47952i
$205$		0			0
$206$	−21.9154	−	12.6529i	−1.52692	−	0.881568i
$207$	3.82363	−	0.572685i	0.265760	−	0.0398044i
$208$	−13.6719	−	3.66337i	−0.947975	−	0.254009i
$209$	−1.68672	+	1.41533i	−0.116673	+	0.0979002i
$210$		0			0
$211$	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	$-0.227133\pi$
$212$	1.95084	−	0.170676i	0.133984	−	0.0117221i
$213$	4.86205	+	16.1455i	0.333142	+	1.10627i
$214$	0.788475	−	2.16632i	0.0538990	−	0.148086i
$215$		0			0
$216$	−0.224297	−	0.317053i	−0.0152615	−	0.0215727i
$217$	3.80401	+	3.80401i	0.258233	+	0.258233i
$218$	−4.91489	−	10.5400i	−0.332878	−	0.713860i
$219$	1.08646	+	1.75507i	0.0734160	+	0.118597i
$220$		0			0
$221$	22.9047	+	4.03872i	1.54074	+	0.271674i
$222$	−15.2964	−	0.866159i	−1.02663	−	0.0581328i
$223$	0.363931	−	4.15975i	0.0243706	−	0.278558i	−0.974225	−	0.225579i	$-0.927573\pi$
$223$	0.363931	−	4.15975i	0.0243706	−	0.278558i	0.998596	−	0.0529791i	$-0.0168717\pi$
$224$	12.8419	+	22.2428i	0.858036	+	1.48616i
$225$		0			0
$226$	−2.28307	+	3.95439i	−0.151867	+	0.263042i
$227$	−3.98292	−	2.78887i	−0.264356	−	0.185104i	0.433882	−	0.900970i	$-0.357143\pi$
$227$	−3.98292	−	2.78887i	−0.264356	−	0.185104i	−0.698238	+	0.715866i	$0.746032\pi$
$228$	4.38995	−	3.27921i	0.290731	−	0.217171i
$229$	−9.29671	−	25.5425i	−0.614344	−	1.68790i	−0.720421	−	0.693537i	$-0.756051\pi$
$229$	−9.29671	−	25.5425i	−0.614344	−	1.68790i	0.106077	−	0.994358i	$-0.466171\pi$
$230$		0			0
$231$	6.16613	+	4.85940i	0.405701	+	0.319725i
$232$	0.432429	−	0.617572i	0.0283903	−	0.0405456i
$233$	−1.78149	+	0.477349i	−0.116709	+	0.0312722i	−0.316701	−	0.948525i	$-0.602575\pi$
$233$	−1.78149	+	0.477349i	−0.116709	+	0.0312722i	0.199992	+	0.979798i	$0.435908\pi$
$234$	21.7007	−	1.33418i	1.41862	−	0.0872183i
$235$		0			0
$236$	−5.74443	−	6.84594i	−0.373930	−	0.445633i
$237$	21.1390	−	10.6592i	1.37313	−	0.692387i
$238$	−23.7565	−	33.9279i	−1.53991	−	2.19922i
$239$	0.452247	+	0.379480i	0.0292534	+	0.0245465i	0.657297	−	0.753632i	$-0.271700\pi$
$239$	0.452247	+	0.379480i	0.0292534	+	0.0245465i	−0.628044	+	0.778178i	$0.716144\pi$
$240$		0			0
$241$	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
$243$	−12.5785	−	9.20763i	−0.806913	−	0.590670i
$244$			28.7813i			1.84253i
$245$		0			0
$246$	0.630096	+	20.5166i	0.0401735	+	1.30809i
$247$	0.488174	+	5.57985i	0.0310618	+	0.355037i
$248$	0.103033	−	0.0721443i	0.00654259	−	0.00458117i
$249$	6.16032	−	18.6917i	0.390394	−	1.18454i
$250$		0			0
$251$	−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	$0.631119\pi$
$252$	−14.6367	−	12.9412i	−0.922024	−	0.815217i
$253$	0.472945	+	1.76505i	0.0297338	+	0.110968i
$254$	−4.86325	−	27.5809i	−0.305148	−	1.73058i
$255$		0			0
$256$	−14.4603	+	5.26312i	−0.903769	+	0.328945i
$257$	−6.92103	+	14.8422i	−0.431722	+	0.925831i	0.563307	+	0.826248i	$0.309529\pi$
$257$	−6.92103	+	14.8422i	−0.431722	+	0.925831i	−0.995029	+	0.0995836i	$0.968249\pi$
$258$	4.89876	+	6.55806i	0.304983	+	0.408287i
$259$	−13.8594	+	2.44379i	−0.861184	+	0.151850i
$260$		0			0
$261$	8.58532	−	29.0174i	0.531418	−	1.79613i
$262$	−0.397523	+	1.48357i	−0.0245590	+	0.0916555i
$263$	−12.7560	−	1.11600i	−0.786566	−	0.0688156i	−0.313207	−	0.949685i	$-0.601403\pi$
$263$	−12.7560	−	1.11600i	−0.786566	−	0.0688156i	−0.473359	+	0.880869i	$0.656959\pi$
$264$	0.136924	−	0.122248i	0.00842706	−	0.00752384i
$265$		0			0
$266$	6.41157	−	7.64101i	0.393118	−	0.468500i
$267$	3.66690	−	15.5838i	0.224411	−	0.953716i
$268$	−16.4921	+	7.69037i	−1.00741	+	0.469764i
$269$	−9.70363			−0.591641			−0.295820	−	0.955244i	$-0.595593\pi$
$269$	−9.70363			−0.591641			−0.295820	+	0.955244i	$0.595593\pi$
$270$		0			0
$271$	18.7538			1.13921			0.569605	−	0.821918i	$-0.307096\pi$
$271$	18.7538			1.13921			0.569605	+	0.821918i	$0.307096\pi$
$272$	22.9335	−	10.6941i	1.39055	−	0.648424i
$273$	19.1229	−	5.75863i	1.15737	−	0.348528i
$274$	17.8664	−	21.2924i	1.07935	−	1.28632i
$275$		0			0
$276$	−0.926752	−	4.45199i	−0.0557839	−	0.267978i
$277$	14.5265	+	1.27091i	0.872815	+	0.0763614i	0.514755	−	0.857337i	$-0.327883\pi$
$277$	14.5265	+	1.27091i	0.872815	+	0.0763614i	0.358060	+	0.933699i	$0.383438\pi$
$278$	4.57676	−	17.0807i	0.274496	−	1.02443i
$279$	3.00171	−	4.05928i	0.179708	−	0.243023i
$280$		0			0
$281$	−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	$0.464852\pi$
$282$	6.70830	−	15.6208i	0.399474	−	0.930207i
$283$	−6.36134	+	13.6419i	−0.378143	+	0.810930i	0.621479	+	0.783431i	$0.286532\pi$
$283$	−6.36134	+	13.6419i	−0.378143	+	0.810930i	−0.999622	+	0.0274989i	$0.991246\pi$
$284$	18.6363	−	6.78307i	1.10586	−	0.402501i
$285$		0			0
$286$	1.78437	+	10.1197i	0.105512	+	0.598388i
$287$	4.87995	+	18.2122i	0.288054	+	1.07503i
$288$	18.8584	−	15.0105i	1.11124	−	0.884499i
$289$	−21.2868	+	12.2900i	−1.25217	+	0.722939i
$290$		0			0
$291$	8.38362	−	1.74518i	0.491457	−	0.102304i
$292$	1.98873	−	1.39252i	0.116382	−	0.0814913i
$293$	−2.50234	−	28.6019i	−0.146188	−	1.67094i	−0.615676	−	0.788000i	$-0.711117\pi$
$293$	−2.50234	−	28.6019i	−0.146188	−	1.67094i	0.469488	−	0.882939i	$-0.344439\pi$
$294$	−9.87000	−	5.30132i	−0.575630	−	0.309179i
$295$		0			0
$296$			0.329040i			0.0191251i
$297$	3.65287	−	6.39826i	0.211961	−	0.371265i
$298$	1.89693	−	1.89693i	0.109886	−	0.109886i
$299$	4.36807	+	1.58985i	0.252612	+	0.0919432i
$300$		0			0
$301$	5.75997	+	4.83319i	0.331999	+	0.278580i
$302$	−15.6014	−	22.2811i	−0.897758	−	1.28213i
$303$	−0.876734	+	15.4832i	−0.0503671	+	0.889485i
$304$	3.91713	+	4.66825i	0.224663	+	0.267742i
$305$		0			0
$306$	−28.1861	+	26.7646i	−1.61129	+	1.53003i
$307$	18.7355	−	5.02015i	1.06929	−	0.286515i	0.319088	−	0.947725i	$-0.396623\pi$
$307$	18.7355	−	5.02015i	1.06929	−	0.286515i	0.750201	+	0.661210i	$0.229957\pi$
$308$	5.29636	−	7.56398i	0.301788	−	0.430998i
$309$	−3.12676	+	21.5890i	−0.177875	+	1.22816i
$310$		0			0
$311$	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	$0.775604\pi$
$312$	−0.0549559	−	0.463690i	−0.00311127	−	0.0262513i
$313$	11.1036	+	7.77479i	0.627610	+	0.439457i	0.843625	−	0.536933i	$-0.180417\pi$
$313$	11.1036	+	7.77479i	0.627610	+	0.439457i	−0.216015	+	0.976390i	$0.569306\pi$
$314$	6.23425	−	10.7980i	0.351819	−	0.609369i
$315$		0			0
$316$	−13.9226	−	24.1147i	−0.783209	−	1.35656i
$317$	−0.810757	+	9.26700i	−0.0455367	+	0.520486i	0.938833	+	0.344372i	$0.111908\pi$
$317$	−0.810757	+	9.26700i	−0.0455367	+	0.520486i	−0.984370	+	0.176114i	$0.943647\pi$
$318$	−1.50622	−	2.98711i	−0.0844646	−	0.167509i
$319$	14.0849	+	2.48354i	0.788602	+	0.139052i
$320$		0			0
$321$	−1.98633	+	0.0610034i	−0.110866	+	0.00340488i
$322$	−3.49840	−	7.50235i	−0.194958	−	0.418090i
$323$	−7.08066	−	7.08066i	−0.393978	−	0.393978i
$324$	−9.97608	+	15.3832i	−0.554227	+	0.854621i
$325$		0			0
$326$	0.467248	−	1.28375i	0.0258785	−	0.0711005i
$327$	−6.86783	+	7.30304i	−0.379792	+	0.403859i
$328$	0.439154	−	0.0384210i	0.0242483	−	0.00212145i
$329$	2.71167	−	15.3787i	0.149499	−	0.847853i
$330$		0			0
$331$	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	$0.160881\pi$
$332$	−22.3593	−	5.99114i	−1.22712	−	0.328807i
$333$	4.19463	+	12.5232i	0.229864	+	0.686268i
$334$	−37.2587	−	21.5113i	−2.03871	−	1.17705i
$335$		0			0
$336$	13.4491	−	17.0657i	0.733708	−	0.931008i
$337$	−13.6212	−	6.35168i	−0.741995	−	0.345998i	0.0145899	−	0.999894i	$-0.495356\pi$
$337$	−13.6212	−	6.35168i	−0.741995	−	0.345998i	−0.756585	+	0.653896i	$0.773133\pi$
$338$	0.0174522	+	0.00813808i	0.000949273	+	0.000442653i
$339$	3.89549	+	0.564188i	0.211574	+	0.0306425i
$340$		0			0
$341$	2.06643	+	1.19305i	0.111903	+	0.0646074i
$342$	−7.98285	−	4.88842i	−0.431663	−	0.264335i
$343$	11.6743	+	3.12811i	0.630351	+	0.168902i
$344$	0.134671	−	0.113002i	0.00726098	−	0.00609269i
$345$		0			0
$346$	7.30726	−	41.4415i	0.392841	−	2.22791i
$347$	−1.57398	+	0.137705i	−0.0844956	+	0.00739240i	−0.129325	−	0.991602i	$-0.541281\pi$
$347$	−1.57398	+	0.137705i	−0.0844956	+	0.00739240i	0.0448295	+	0.998995i	$0.485726\pi$
$348$	−34.6458	−	8.15221i	−1.85721	−	0.437005i
$349$	−3.04560	+	8.36771i	−0.163027	+	0.447913i	−0.994128	−	0.108208i	$-0.965489\pi$
$349$	−3.04560	+	8.36771i	−0.163027	+	0.447913i	0.831101	+	0.556121i	$0.187711\pi$
$350$		0			0
$351$	−8.00278	−	16.9474i	−0.427157	−	0.904585i
$352$	8.05522	+	8.05522i	0.429345	+	0.429345i
$353$	−3.09913	−	6.64610i	−0.164950	−	0.353736i	0.806407	−	0.591361i	$-0.201409\pi$
$353$	−3.09913	−	6.64610i	−0.164950	−	0.353736i	−0.971357	+	0.237624i	$0.923631\pi$
$354$	−7.22392	+	13.4495i	−0.383947	+	0.714832i
$355$		0			0
$356$	−18.5439	−	3.26979i	−0.982823	−	0.173298i
$357$	−19.5713	+	29.8616i	−1.03582	+	1.58044i
$358$	3.34172	−	38.1961i	0.176615	−	2.01872i
$359$	5.23715	+	9.07100i	0.276406	+	0.478749i	0.970489	−	0.241146i	$-0.0775232\pi$
$359$	5.23715	+	9.07100i	0.276406	+	0.478749i	−0.694083	+	0.719895i	$0.744190\pi$
$360$		0			0
$361$	−8.29423	+	14.3660i	−0.436539	+	0.756107i
$362$	14.1463	+	9.90535i	0.743514	+	0.520614i
$363$	−14.3069	−	6.14406i	−0.750920	−	0.322479i
$364$	−8.03390	−	22.0730i	−0.421091	−	1.15694i
$365$		0			0
$366$	45.6643	−	18.2266i	2.38691	−	0.952720i
$367$	−1.15170	+	1.64480i	−0.0601185	+	0.0858581i	−0.848086	−	0.529859i	$-0.822245\pi$
$367$	−1.15170	+	1.64480i	−0.0601185	+	0.0858581i	0.787967	+	0.615717i	$0.211134\pi$
$368$	4.88505	−	1.30894i	0.254651	−	0.0682334i
$369$	16.2244	−	7.06068i	0.844607	−	0.367564i
$370$		0			0
$371$	−1.97524	−	2.35400i	−0.102550	−	0.122214i
$372$	−4.96639	−	3.25498i	−0.257495	−	0.168763i
$373$	−20.0029	−	28.5671i	−1.03571	−	1.47915i	−0.870049	−	0.492965i	$-0.835913\pi$
$373$	−20.0029	−	28.5671i	−1.03571	−	1.47915i	−0.165662	−	0.986183i	$-0.552976\pi$
$374$	−14.0727	−	11.8084i	−0.727684	−	0.610599i
$375$		0			0
$376$	−0.343089	−	0.124874i	−0.0176935	−	0.00643990i
$377$	25.7262	−	25.7262i	1.32497	−	1.32497i
$378$	−11.2633	+	31.4179i	−0.579321	+	1.61596i
$379$		−	11.2085i		−	0.575742i	−0.957669	−	0.287871i	$-0.907053\pi$
$379$		−	11.2085i		−	0.575742i	0.957669	−	0.287871i	$-0.0929474\pi$
$380$		0			0
$381$	−20.5274	+	12.7072i	−1.05165	+	0.651011i
$382$	1.66656	+	19.0489i	0.0852686	+	0.974624i
$383$	8.07127	−	5.65156i	0.412422	−	0.288781i	−0.348893	−	0.937162i	$-0.613443\pi$
$383$	8.07127	−	5.65156i	0.412422	−	0.288781i	0.761316	+	0.648381i	$0.224554\pi$
$384$	−0.689627	−	0.772415i	−0.0351924	−	0.0394171i
$385$		0			0
$386$	11.1565	−	6.44122i	0.567852	−	0.327850i
$387$	3.68500	−	6.01766i	0.187319	−	0.305895i
$388$	−2.60683	−	9.72881i	−0.132342	−	0.493905i
$389$	2.38097	+	13.5031i	0.120720	+	0.684636i	0.983758	+	0.179498i	$0.0574474\pi$
$389$	2.38097	+	13.5031i	0.120720	+	0.684636i	−0.863038	+	0.505138i	$0.831442\pi$
$390$		0			0
$391$	−7.80907	+	2.84227i	−0.394922	+	0.143740i
$392$	−0.101688	+	0.218071i	−0.00513602	+	0.0110142i
$393$	1.31479	−	0.155827i	0.0663225	−	0.00786046i
$394$	26.4519	−	4.66418i	1.33263	−	0.234978i
$395$		0			0
$396$	−7.75634	−	3.86410i	−0.389771	−	0.194178i
$397$	3.48510	−	13.0066i	0.174912	−	0.652781i	−0.821655	−	0.569986i	$-0.806949\pi$
$397$	3.48510	−	13.0066i	0.174912	−	0.652781i	0.996567	−	0.0827949i	$-0.0263846\pi$
$398$	4.21237	+	0.368535i	0.211147	+	0.0184730i
$399$	−8.16631	−	2.69141i	−0.408827	−	0.134739i
$400$		0			0
$401$	−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	$0.288812\pi$
$402$	22.6456	+	21.2961i	1.12946	+	1.06215i
$403$	5.50116	−	2.56523i	0.274032	−	0.127783i
$404$	18.2401			0.907480
$405$		0			0
$406$	−64.7901			−3.21548
$407$	−5.65721	+	2.63800i	−0.280418	+	0.130761i
$408$	0.608113	+	0.571874i	0.0301061	+	0.0283120i
$409$	−10.3591	+	12.3455i	−0.512225	+	0.610446i	−0.958724	−	0.284338i	$-0.908226\pi$
$409$	−10.3591	+	12.3455i	−0.512225	+	0.610446i	0.446499	+	0.894784i	$0.352671\pi$
$410$		0			0
$411$	−22.7562	−	7.49987i	−1.12248	−	0.369941i
$412$	25.5598	+	2.23619i	1.25924	+	0.110169i
$413$	−3.62954	+	13.5456i	−0.178598	+	0.666538i
$414$	−6.47662	+	4.28974i	−0.318308	+	0.210829i
$415$		0			0
$416$	28.5386	−	5.03213i	1.39922	−	0.246720i
$417$	−15.1375	+	1.79407i	−0.741286	+	0.0878562i
$418$	1.86972	−	4.00964i	0.0914512	−	0.196118i
$419$	2.61381	−	0.951349i	0.127693	−	0.0464764i	−0.277383	−	0.960759i	$-0.589467\pi$
$419$	2.61381	−	0.951349i	0.127693	−	0.0464764i	0.405076	+	0.914283i	$0.367245\pi$
$420$		0			0
$421$	−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	$-0.285325\pi$
$422$	11.7218	+	43.7465i	0.570611	+	2.12955i
$423$	−14.6498	−	0.378968i	−0.712300	−	0.0184261i
$424$	−0.0622212	+	0.0359234i	−0.00302173	+	0.00174460i
$425$		0			0
$426$	−22.5640	−	25.2728i	−1.09323	−	1.22447i
$427$	36.9957	−	25.9047i	1.79035	−	1.25362i
$428$	0.203716	+	2.32849i	0.00984699	+	0.112552i
$429$	7.53167	−	4.66239i	0.363632	−	0.225102i
$430$		0			0
$431$			18.9644i			0.913484i	0.889599	+	0.456742i	$0.150984\pi$
$431$			18.9644i			0.913484i	−0.889599	+	0.456742i	$0.849016\pi$
$432$	−17.7081	−	10.1098i	−0.851982	−	0.486410i
$433$	−2.72519	+	2.72519i	−0.130964	+	0.130964i	−0.769550	−	0.638586i	$-0.779520\pi$
$433$	−2.72519	+	2.72519i	−0.130964	+	0.130964i	0.638586	+	0.769550i	$0.279520\pi$
$434$	−10.1574	−	3.69699i	−0.487571	−	0.177461i
$435$		0			0
$436$	9.03260	+	7.57925i	0.432583	+	0.362980i
$437$	−1.14791	−	1.63939i	−0.0549122	−	0.0784228i
$438$	−3.46880	−	2.27346i	−0.165746	−	0.108630i
$439$	16.6256	+	19.8136i	0.793498	+	0.945654i	0.999458	−	0.0329065i	$-0.0104764\pi$
$439$	16.6256	+	19.8136i	0.793498	+	0.945654i	−0.205961	+	0.978560i	$0.566032\pi$
$440$		0			0
$441$	−1.09025	+	9.59607i	−0.0519167	+	0.456956i
$442$	−45.1396	+	12.0951i	−2.14707	+	0.575306i
$443$	−1.40321	+	2.00399i	−0.0666685	+	0.0952125i	−0.851102	−	0.525001i	$-0.824065\pi$
$443$	−1.40321	+	2.00399i	−0.0666685	+	0.0952125i	0.784433	+	0.620213i	$0.212954\pi$
$444$	14.4270	−	5.75846i	0.684677	−	0.273285i
$445$		0			0
$446$	2.86956	+	7.88405i	0.135878	+	0.373321i
$447$	−2.12487	−	0.912519i	−0.100503	−	0.0431607i
$448$	−21.7209	−	15.2092i	−1.02622	−	0.718566i
$449$	3.56778	−	6.17957i	0.168374	−	0.291632i	−0.769474	−	0.638678i	$-0.779482\pi$
$449$	3.56778	−	6.17957i	0.168374	−	0.291632i	0.937848	+	0.347046i	$0.112815\pi$
$450$		0			0
$451$	4.18140	+	7.24239i	0.196894	+	0.341031i
$452$	0.403495	−	4.61197i	0.0189788	−	0.216929i
$453$	−12.8529	+	19.6107i	−0.603880	+	0.921389i
$454$	9.62119	+	1.69648i	0.451545	+	0.0796195i
$455$		0			0
$456$	−0.0951257	+	0.177105i	−0.00445467	+	0.00829370i
$457$	−5.11535	−	10.9699i	−0.239286	−	0.513151i	0.749588	−	0.661905i	$-0.230252\pi$
$457$	−5.11535	−	10.9699i	−0.239286	−	0.513151i	−0.988874	+	0.148754i	$0.952474\pi$
$458$	38.6191	+	38.6191i	1.80455	+	1.80455i
$459$	30.4350	+	14.0132i	1.42058	+	0.654079i
$460$		0			0
$461$	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	$-0.0303681\pi$
$462$	−15.3551	−	3.61307i	−0.714382	−	0.168095i
$463$	32.0331	−	2.80254i	1.48871	−	0.130245i	0.686429	−	0.727197i	$-0.259177\pi$
$463$	32.0331	−	2.80254i	1.48871	−	0.130245i	0.802277	+	0.596952i	$0.203622\pi$
$464$	6.87357	−	38.9820i	0.319098	−	1.80969i
$465$		0			0
$466$	2.83879	−	2.38203i	0.131504	−	0.110345i
$467$	6.69128	+	1.79292i	0.309635	+	0.0829666i	0.410291	−	0.911955i	$-0.365427\pi$
$467$	6.69128	+	1.79292i	0.309635	+	0.0829666i	−0.100655	+	0.994921i	$0.532094\pi$
$468$	−19.3691	+	10.5245i	−0.895338	+	0.486497i
$469$	24.7290	+	14.2773i	1.14188	+	0.659264i
$470$		0			0
$471$	−10.6372	−	1.54060i	−0.490136	−	0.0709870i
$472$	0.297157	+	0.138567i	0.0136778	+	0.00637804i
$473$	3.02256	+	1.40944i	0.138977	+	0.0648062i
$474$	−29.4434	+	37.3610i	−1.35238	+	1.71605i
$475$		0			0
$476$	36.3677	+	20.9969i	1.66691	+	0.962391i
$477$	−1.91018	+	2.16044i	−0.0874609	+	0.0989198i
$478$	−1.14579	−	0.307014i	−0.0524072	−	0.0140425i
$479$	20.5682	−	17.2588i	0.939787	−	0.788575i	−0.0377611	−	0.999287i	$-0.512023\pi$
$479$	20.5682	−	17.2588i	0.939787	−	0.788575i	0.977548	+	0.210712i	$0.0675781\pi$
$480$		0			0
$481$	−2.75731	+	15.6375i	−0.125723	+	0.713009i
$482$	−10.2812	+	0.899488i	−0.468296	+	0.0409706i
$483$	−4.88850	+	5.19828i	−0.222434	+	0.236530i
$484$	−6.26361	+	17.2091i	−0.284710	+	0.782233i
$485$		0			0
$486$	30.7245	+	6.08616i	1.39369	+	0.276074i
$487$	−17.3982	−	17.3982i	−0.788386	−	0.788386i	0.192843	−	0.981230i	$-0.438229\pi$
$487$	−17.3982	−	17.3982i	−0.788386	−	0.788386i	−0.981230	+	0.192843i	$0.938229\pi$
$488$	−0.446262	−	0.957011i	−0.0202013	−	0.0433219i
$489$	−1.17709	+	0.0361504i	−0.0532301	+	0.00163478i
$490$		0			0
$491$	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	$0.367242\pi$
$492$	−9.37016	−	18.5827i	−0.422439	−	0.837774i
$493$	−5.66887	+	64.7955i	−0.255313	+	2.91824i
$494$	−5.62715	−	9.74651i	−0.253177	−	0.438516i
$495$		0			0
$496$	3.30195	−	5.71914i	0.148262	−	0.256797i
$497$	−25.4927	−	17.8502i	−1.14350	−	0.800690i
$498$	4.65413	+	39.2692i	0.208557	+	1.75969i
$499$	6.32244	+	17.3708i	0.283031	+	0.777623i	0.996997	+	0.0774416i	$0.0246751\pi$
$499$	6.32244	+	17.3708i	0.283031	+	0.777623i	−0.713965	+	0.700181i	$0.753103\pi$
$500$		0			0
$501$	−5.31584	+	36.7037i	−0.237494	+	1.63980i
$502$	29.3931	−	41.9776i	1.31188	−	1.87355i
$503$	−14.4596	+	3.87444i	−0.644723	+	0.172753i	−0.566342	−	0.824171i	$-0.691642\pi$
$503$	−14.4596	+	3.87444i	−0.644723	+	0.172753i	−0.0783811	+	0.996923i	$0.524975\pi$
$504$	0.687342	+	0.203363i	0.0306167	+	0.00905850i
$505$		0			0
$506$	−2.36005	−	2.81260i	−0.104917	−	0.125035i
$507$	0.000938441	−	0.0165729i	4.16776e−5	−	0.000736029i
$508$	16.2870	+	23.2602i	0.722619	+	1.03201i
$509$	9.33558	+	7.83348i	0.413792	+	0.347213i	0.825796	−	0.563969i	$-0.190726\pi$
$509$	9.33558	+	7.83348i	0.413792	+	0.347213i	−0.412003	+	0.911182i	$0.635171\pi$
$510$		0			0
$511$	−3.57993	−	1.30299i	−0.158367	−	0.0576407i
$512$	22.7088	−	22.7088i	1.00360	−	1.00360i
$513$	−1.36272	+	7.95326i	−0.0601657	+	0.351145i
$514$		−	32.9051i		−	1.45138i
$515$		0			0
$516$	−7.31155	−	3.92714i	−0.321873	−	0.172883i
$517$	−0.603664	−	6.89991i	−0.0265491	−	0.303458i
$518$	23.1632	−	16.2191i	1.01773	−	0.712625i
$519$	−35.5135	+	7.39270i	−1.55887	+	0.324503i
$520$		0			0
$521$	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	$0.268570\pi$
$522$	9.00624	+	60.1316i	0.394192	+	2.63189i
$523$	−9.55121	−	35.6456i	−0.417645	−	1.55867i	−0.779477	−	0.626431i	$-0.784515\pi$
$523$	−9.55121	−	35.6456i	−0.417645	−	1.55867i	0.361832	−	0.932243i	$-0.382152\pi$
$524$	−0.270414	−	1.53359i	−0.0118131	−	0.0669953i
$525$		0			0
$526$	24.1766	−	8.79955i	1.05415	−	0.383679i
$527$	−4.58603	+	9.83477i	−0.199771	+	0.428409i
$528$	3.80287	−	8.85529i	0.165499	−	0.385377i
$529$	21.0149	−	3.70550i	0.913692	−	0.161109i
$530$		0			0
$531$	13.0762	+	1.48564i	0.567460	+	0.0644715i
$532$	−2.61750	+	9.76863i	−0.113483	+	0.423524i
$533$	21.1926	+	1.85411i	0.917955	+	0.0803106i
$534$	6.55563	+	31.4923i	0.283690	+	1.36281i
$535$		0			0
$536$	0.429139	−	0.511427i	0.0185360	−	0.0220903i
$537$	−31.6479	+	9.53042i	−1.36571	+	0.411268i
$538$	17.6705	−	8.23991i	0.761831	−	0.355248i
$539$	−4.56457			−0.196610
$540$		0			0
$541$	22.0366			0.947428			0.473714	−	0.880679i	$-0.342913\pi$
$541$	22.0366			0.947428			0.473714	+	0.880679i	$0.342913\pi$
$542$	−34.1511	+	15.9249i	−1.46691	+	0.684033i
$543$	3.40975	−	14.4910i	0.146326	−	0.621867i
$544$	−33.3011	+	39.6868i	−1.42777	+	1.70156i
$545$		0			0
$546$	−29.9332	+	26.7249i	−1.28102	+	1.14372i
$547$	26.8477	+	2.34887i	1.14793	+	0.100430i	0.645199	−	0.764015i	$-0.276775\pi$
$547$	26.8477	+	2.34887i	1.14793	+	0.100430i	0.502727	+	0.864445i	$0.332330\pi$
$548$	−7.29390	+	27.2212i	−0.311580	+	1.16283i
$549$	−29.1847	−	30.7348i	−1.24557	−	1.31173i
$550$		0			0
$551$	−15.4261	+	2.72004i	−0.657175	+	0.115878i
$552$	0.0998448	+	0.133664i	0.00424968	+	0.00568913i
$553$	−18.4661	+	39.6008i	−0.785260	+	1.68400i
$554$	−27.5324	+	10.0210i	−1.16974	+	0.425750i
$555$		0			0
$556$	3.11333	+	17.6566i	0.132035	+	0.748806i
$557$	9.78211	+	36.5073i	0.414481	+	1.54687i	0.785872	+	0.618389i	$0.212214\pi$
$557$	9.78211	+	36.5073i	0.414481	+	1.54687i	−0.371391	+	0.928477i	$0.621119\pi$
$558$	−2.01923	+	9.94097i	−0.0854808	+	0.420835i
$559$	7.34714	−	4.24188i	0.310751	−	0.179412i
$560$		0			0
$561$	−4.95687	+	15.0402i	−0.209279	+	0.634998i
$562$	3.53528	−	2.47543i	0.149127	−	0.104420i
$563$	−1.46886	−	16.7892i	−0.0619052	−	0.707579i	−0.962208	−	0.272315i	$-0.912211\pi$
$563$	−1.46886	−	16.7892i	−0.0619052	−	0.707579i	0.900303	−	0.435264i	$-0.143345\pi$
$564$	0.529113	+	17.2284i	0.0222797	+	0.725448i
$565$		0			0
$566$		−	30.2441i		−	1.27125i
$567$	28.7527	−	1.02233i	1.20750	−	0.0429340i
$568$	−0.514506	+	0.514506i	−0.0215882	+	0.0215882i
$569$	4.84212	+	1.76239i	0.202992	+	0.0738831i	0.441515	−	0.897254i	$-0.354441\pi$
$569$	4.84212	+	1.76239i	0.202992	+	0.0738831i	−0.238523	+	0.971137i	$0.576663\pi$
$570$		0			0
$571$	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	$0.622777\pi$
$572$	−5.97584	−	8.53438i	−0.249862	−	0.356840i
$573$	14.7181	−	7.42146i	0.614857	−	0.310036i
$574$	−24.3515	−	29.0210i	−1.01641	−	1.21131i
$575$		0			0
$576$	−11.0963	+	22.2733i	−0.462344	+	0.928056i
$577$	18.9419	−	5.07547i	0.788562	−	0.211295i	0.158006	−	0.987438i	$-0.449493\pi$
$577$	18.9419	−	5.07547i	0.788562	−	0.211295i	0.630556	+	0.776144i	$0.282827\pi$
$578$	28.3277	−	40.4562i	1.17828	−	1.68276i
$579$	−8.72204	−	6.87366i	−0.362476	−	0.285660i
$580$		0			0
$581$	12.4234	+	34.1331i	0.515411	+	1.41608i
$582$	−13.7848	+	10.2970i	−0.571400	+	0.426826i
$583$	−1.11648	−	0.781767i	−0.0462398	−	0.0323775i
$584$	−0.0445361	+	0.0771388i	−0.00184292	+	0.00319203i
$585$		0			0
$586$	28.8443	+	49.9598i	1.19155	+	2.06382i
$587$	1.47324	−	16.8392i	0.0608071	−	0.695028i	−0.903212	−	0.429195i	$-0.858797\pi$
$587$	1.47324	−	16.8392i	0.0608071	−	0.695028i	0.964019	−	0.265833i	$-0.0856470\pi$
$588$	11.3411	+	0.642191i	0.467700	+	0.0264835i
$589$	−2.57362	−	0.453799i	−0.106044	−	0.0186985i
$590$		0			0
$591$	−12.1871	−	19.6871i	−0.501309	−	0.809819i
$592$	7.30106	+	15.6572i	0.300072	+	0.643506i
$593$	−11.2767	−	11.2767i	−0.463077	−	0.463077i	0.436586	−	0.899663i	$-0.356188\pi$
$593$	−11.2767	−	11.2767i	−0.463077	−	0.463077i	−0.899663	+	0.436586i	$0.856188\pi$
$594$	−1.21883	+	14.7532i	−0.0500092	+	0.605333i
$595$		0			0
$596$	−0.930275	+	2.55591i	−0.0381055	+	0.104694i
$597$	−1.05104	−	3.49023i	−0.0430163	−	0.142845i
$598$	−9.30438	+	0.814028i	−0.380485	+	0.0332881i
$599$	0.0318051	−	0.180376i	0.00129952	−	0.00736995i	−0.984151	−	0.177332i	$-0.943253\pi$
$599$	0.0318051	−	0.180376i	0.00129952	−	0.00736995i	0.985451	+	0.169962i	$0.0543645\pi$
$600$		0			0
$601$	−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	$0.543032\pi$
$602$	−14.5932	−	3.91023i	−0.594774	−	0.159369i
$603$	9.81324	−	24.9356i	0.399626	−	1.01545i
$604$	23.8834	+	13.7891i	0.971801	+	0.561069i
$605$		0			0
$606$	−11.5511	−	28.9397i	−0.469231	−	1.17560i
$607$	16.7479	+	7.80966i	0.679775	+	0.316984i	0.731661	−	0.681669i	$-0.238745\pi$
$607$	16.7479	+	7.80966i	0.679775	+	0.316984i	−0.0518859	+	0.998653i	$0.516523\pi$
$608$	−11.3076	−	5.27284i	−0.458586	−	0.213842i
$609$	20.7042	+	51.8715i	0.838975	+	2.10194i
$610$		0			0
$611$	−15.2588	−	8.80965i	−0.617303	−	0.356400i
$612$	14.4318	−	36.6715i	0.583373	−	1.48236i
$613$	−39.7974	−	10.6637i	−1.60740	−	0.430702i	−0.660135	−	0.751147i	$-0.729501\pi$
$613$	−39.7974	−	10.6637i	−1.60740	−	0.430702i	−0.947267	+	0.320445i	$0.896167\pi$
$614$	−29.8548	+	25.0512i	−1.20484	+	1.01098i
$615$		0			0
$616$	−0.0588284	+	0.333632i	−0.00237026	+	0.0134424i
$617$	−10.6637	+	0.932954i	−0.429305	+	0.0375593i	−0.299761	−	0.954014i	$-0.596907\pi$
$617$	−10.6637	+	0.932954i	−0.429305	+	0.0375593i	−0.129544	+	0.991574i	$0.541351\pi$
$618$	−12.6386	−	41.9692i	−0.508397	−	1.68825i
$619$	13.6868	−	37.6041i	0.550117	−	1.51143i	−0.283434	−	0.958992i	$-0.591474\pi$
$619$	13.6868	−	37.6041i	0.550117	−	1.51143i	0.833551	−	0.552443i	$-0.186304\pi$
$620$		0			0
$621$	5.50405	+	3.81441i	0.220870	+	0.153067i
$622$	−17.4602	−	17.4602i	−0.700091	−	0.700091i
$623$	12.4875	+	26.7794i	0.500299	+	1.07290i
$624$	−12.9038	−	20.8450i	−0.516567	−	0.834468i
$625$		0			0
$626$	−26.8219	−	4.72942i	−1.07202	−	0.189026i
$627$	−3.80763	−	0.215607i	−0.152062	−	0.00861051i
$628$	−1.10180	+	12.5937i	−0.0439667	+	0.502542i
$629$	−14.1937	−	24.5842i	−0.565941	−	0.980238i
$630$		0			0
$631$	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	$0.0283284\pi$
$632$	0.836848	+	0.585968i	0.0332880	+	0.0233085i
$633$	31.2780	−	23.3641i	1.24319	−	0.928641i
$634$	−6.39273	−	17.5639i	−0.253888	−	0.697551i
$635$		0			0
$636$	2.66401	+	2.09945i	0.105635	+	0.0832488i
$637$	−6.66009	+	9.51160i	−0.263883	+	0.376863i
$638$	−27.7578	+	7.43769i	−1.09894	+	0.294461i
$639$	−13.0231	+	26.1410i	−0.515185	+	1.03412i
$640$		0			0
$641$	−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	$0.877897\pi$
$642$	3.56536	−	1.79780i	0.140714	−	0.0709535i
$643$	3.68524	+	5.26307i	0.145332	+	0.207555i	0.885218	−	0.465177i	$-0.154009\pi$
$643$	3.68524	+	5.26307i	0.145332	+	0.207555i	−0.739886	+	0.672732i	$0.765121\pi$
$644$	6.42938	+	5.39489i	0.253353	+	0.212588i
$645$		0			0
$646$	18.9066	+	6.88146i	0.743872	+	0.270747i
$647$	−16.4424	+	16.4424i	−0.646419	+	0.646419i	−0.952126	−	0.305707i	$-0.901107\pi$
$647$	−16.4424	+	16.4424i	−0.646419	+	0.646419i	0.305707	+	0.952126i	$0.401107\pi$
$648$	0.0931958	−	0.666190i	0.00366108	−	0.0261704i
$649$			6.21997i			0.244155i
$650$		0			0
$651$	0.286032	+	9.31349i	0.0112105	+	0.365025i
$652$	0.120722	+	1.37985i	0.00472782	+	0.0540392i
$653$	−13.4455	+	9.41463i	−0.526163	+	0.368423i	−0.806272	−	0.591545i	$-0.798518\pi$
$653$	−13.4455	+	9.41463i	−0.526163	+	0.368423i	0.280109	+	0.959968i	$0.409629\pi$
$654$	6.30505	−	19.1309i	0.246547	−	0.748077i
$655$		0			0
$656$	20.0444	−	11.5726i	0.782602	−	0.451835i
$657$	−0.711667	+	3.50365i	−0.0277648	+	0.136690i
$658$	8.12088	+	30.3075i	0.316585	+	1.18151i
$659$	−4.40379	−	24.9751i	−0.171547	−	0.972892i	−0.942054	−	0.335461i	$-0.891108\pi$
$659$	−4.40379	−	24.9751i	−0.171547	−	0.972892i	0.770507	−	0.637431i	$-0.220003\pi$
$660$		0			0
$661$	−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	$0.611673\pi$
$662$	−11.0937	+	23.7906i	−0.431171	+	0.924649i
$663$	24.1081	+	32.2740i	0.936282	+	1.25342i
$664$	0.836365	−	0.147474i	0.0324573	−	0.00572309i
$665$		0			0
$666$	−18.2727	−	19.2432i	−0.708053	−	0.745658i
$667$	−3.36455	+	12.5567i	−0.130276	+	0.486196i
$668$	43.4545	+	3.80178i	1.68131	+	0.147095i
$669$	5.39504	−	4.81680i	0.208584	−	0.186228i
$670$		0			0
$671$	12.8762	−	15.3452i	0.497080	−	0.592396i
$672$	−10.1893	+	43.3031i	−0.393060	+	1.67045i
$673$	32.0981	−	14.9676i	1.23729	−	0.576958i	0.309798	−	0.950802i	$-0.399738\pi$
$673$	32.0981	−	14.9676i	1.23729	−	0.576958i	0.927491	+	0.373845i	$0.121961\pi$
$674$	30.1981			1.16319
$675$		0			0
$676$	−0.0195239			−0.000750920
$677$	3.02046	−	1.40846i	0.116086	−	0.0541317i	−0.363708	−	0.931513i	$-0.618489\pi$
$677$	3.02046	−	1.40846i	0.116086	−	0.0541317i	0.479794	+	0.877381i	$0.340712\pi$
$678$	−7.57286	+	2.28048i	−0.290834	+	0.0875814i
$679$	−10.1592	+	12.1073i	−0.389875	+	0.464635i
$680$		0			0
$681$	−1.71631	−	8.24492i	−0.0657692	−	0.315946i
$682$	−4.77610	−	0.417855i	−0.182886	−	0.0160005i
$683$	8.77978	−	32.7666i	0.335949	−	1.25378i	−0.566888	−	0.823795i	$-0.691853\pi$
$683$	8.77978	−	32.7666i	0.335949	−	1.25378i	0.902837	−	0.429984i	$-0.141481\pi$
$684$	9.43010	+	1.07139i	0.360569	+	0.0409657i
$685$		0			0
$686$	−23.9154	+	4.21693i	−0.913093	+	0.161003i
$687$	18.5777	−	43.2598i	0.708785	−	1.65046i
$688$	3.90084	−	8.36537i	0.148718	−	0.318927i
$689$	−3.25807	+	1.18584i	−0.124123	+	0.0451770i
$690$		0			0
$691$	−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	$-0.152119\pi$
$692$	11.0427	+	41.2118i	0.419779	+	1.56664i
$693$	2.01417	+	13.4480i	0.0765121	+	0.510846i
$694$	2.74932	−	1.58732i	0.104363	−	0.0602538i
$695$		0			0
$696$	1.27842	−	0.266123i	0.0484583	−	0.0100874i
$697$	−31.1541	+	21.8143i	−1.18005	+	0.826277i
$698$	−1.55940	−	17.8240i	−0.0590241	−	0.674648i
$699$	−2.81423	−	1.51156i	−0.106444	−	0.0571726i
$700$		0			0
$701$		−	38.4806i		−	1.45339i	−0.686958	−	0.726697i	$-0.741054\pi$
$701$		−	38.4806i		−	1.45339i	0.686958	−	0.726697i	$-0.258946\pi$
$702$	28.9643	+	24.0660i	1.09319	+	0.908313i
$703$	4.83410	−	4.83410i	0.182322	−	0.182322i
$704$	−11.0518	−	4.02252i	−0.416530	−	0.151605i
$705$		0			0
$706$	11.2872	+	9.47107i	0.424799	+	0.356448i
$707$	−16.4171	−	23.4460i	−0.617428	−	0.881778i
$708$	0.875090	−	15.4541i	0.0328879	−	0.580802i
$709$	16.1489	+	19.2455i	0.606483	+	0.722779i	0.978684	−	0.205374i	$-0.0658410\pi$
$709$	16.1489	+	19.2455i	0.606483	+	0.722779i	−0.372200	+	0.928152i	$0.621397\pi$
$710$		0			0
$711$	39.3203	+	11.6336i	1.47463	+	0.436296i
$712$	0.667304	−	0.178804i	0.0250083	−	0.00670095i
$713$	−1.24397	+	1.77657i	−0.0465870	+	0.0665332i
$714$	10.2827	−	70.9978i	0.384820	−	2.65702i
$715$		0			0
$716$	13.2959	+	36.5303i	0.496893	+	1.36520i
$717$	0.120348	+	1.01544i	0.00449449	+	0.0379222i
$718$	−17.2397	−	12.0714i	−0.643379	−	0.450499i
$719$	−1.64032	+	2.84111i	−0.0611736	+	0.105956i	−0.894990	−	0.446086i	$-0.852818\pi$
$719$	−1.64032	+	2.84111i	−0.0611736	+	0.105956i	0.833817	+	0.552041i	$0.186151\pi$
$720$		0			0
$721$	−20.1307	−	34.8674i	−0.749708	−	1.29853i
$722$	2.90497	−	33.2040i	0.108112	−	1.23573i
$723$	4.00557	+	7.94377i	0.148969	+	0.295432i
$724$	−17.2434	−	3.04048i	−0.640847	−	0.112999i
$725$		0			0
$726$	31.2706	−	0.960368i	1.16056	−	0.0356426i
$727$	−9.46148	−	20.2902i	−0.350907	−	0.752522i	0.649060	−	0.760738i	$-0.275163\pi$
$727$	−9.46148	−	20.2902i	−0.350907	−	0.752522i	−0.999966	+	0.00821575i	$0.997385\pi$
$728$	0.609384	+	0.609384i	0.0225853	+	0.0225853i
$729$	−4.94563	−	26.5432i	−0.183171	−	0.983081i
$730$		0			0
$731$	−5.18740	+	14.2523i	−0.191863	+	0.527139i
$732$	−34.1511	+	36.3152i	−1.26226	+	1.34225i
$733$	−1.50654	+	0.131805i	−0.0556452	+	0.00486833i	−0.114944	−	0.993372i	$-0.536669\pi$
$733$	−1.50654	+	0.131805i	−0.0556452	+	0.00486833i	0.0592991	+	0.998240i	$0.481113\pi$
$734$	0.700584	−	3.97321i	0.0258590	−	0.146654i
$735$		0			0
$736$	−7.93187	+	6.65563i	−0.292372	+	0.245330i
$737$	12.2335	+	3.27797i	0.450628	+	0.120745i
$738$	−23.5494	+	26.6347i	−0.866864	+	0.980438i
$739$	−32.5721	−	18.8055i	−1.19818	−	0.691771i	−0.238033	−	0.971257i	$-0.576503\pi$
$739$	−32.5721	−	18.8055i	−1.19818	−	0.691771i	−0.960150	+	0.279486i	$0.909836\pi$
$740$		0			0
$741$	−6.00493	+	7.61971i	−0.220597	+	0.279917i
$742$	5.59589	+	2.60941i	0.205432	+	0.0957943i
$743$	9.87379	+	4.60422i	0.362234	+	0.168913i	0.595210	−	0.803570i	$-0.297069\pi$
$743$	9.87379	+	4.60422i	0.362234	+	0.168913i	−0.232976	+	0.972482i	$0.574846\pi$
$744$	0.215607	+	0.0312267i	0.00790455	+	0.00114483i
$745$		0			0
$746$	60.6837	+	35.0358i	2.22179	+	1.28275i
$747$	29.9519	−	16.2749i	1.09588	−	0.595467i
$748$	17.9913	+	4.82074i	0.657826	+	0.176264i
$749$	2.80970	−	2.35762i	0.102664	−	0.0861455i
$750$		0			0
$751$	−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	$0.0568382\pi$
$752$	−19.0965	+	1.67073i	−0.696379	+	0.0609252i
$753$	−43.0004	−	10.1180i	−1.56702	−	0.368722i
$754$	−25.0024	+	68.6936i	−0.910535	+	2.50167i
$755$		0			0
$756$	−3.11242	−	33.6962i	−0.113197	−	1.22552i
$757$	1.75745	+	1.75745i	0.0638754	+	0.0638754i	0.738323	−	0.674447i	$-0.235618\pi$
$757$	1.75745	+	1.75745i	0.0638754	+	0.0638754i	−0.674447	+	0.738323i	$0.735618\pi$
$758$	9.51778	+	20.4109i	0.345701	+	0.741359i
$759$	−1.49762	+	2.78826i	−0.0543601	+	0.101208i
$760$		0			0
$761$	−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	$0.956408\pi$
$762$	26.5904	−	40.5711i	0.963269	−	1.46974i
$763$	1.61262	−	18.4323i	0.0583807	−	0.667294i
$764$	−9.69366	−	16.7899i	−0.350704	−	0.607438i
$765$		0			0
$766$	−9.89891	+	17.1454i	−0.357662	+	0.619489i
$767$	12.9611	+	9.07547i	0.467999	+	0.327696i
$768$	−24.4905	−	10.5174i	−0.883726	−	0.379513i
$769$	3.12453	+	8.58457i	0.112673	+	0.309567i	0.983194	−	0.182565i	$-0.0584399\pi$
$769$	3.12453	+	8.58457i	0.112673	+	0.309567i	−0.870521	+	0.492132i	$0.836218\pi$
$770$		0			0
$771$	−26.3440	+	10.5151i	−0.948758	+	0.378690i
$772$	−7.49174	+	10.6993i	−0.269634	+	0.385077i
$773$	−19.4510	+	5.21188i	−0.699604	+	0.187458i	−0.591053	−	0.806633i	$-0.701288\pi$
$773$	−19.4510	+	5.21188i	−0.699604	+	0.187458i	−0.108551	+	0.994091i	$0.534621\pi$
$774$	−1.60053	+	14.0875i	−0.0575300	+	0.506363i
$775$		0			0
$776$	0.237528	+	0.283074i	0.00852675	+	0.0101618i
$777$	−20.3871	−	13.3617i	−0.731382	−	0.479349i
$778$	−15.8021	−	22.5677i	−0.566533	−	0.809092i
$779$	−7.01632	−	5.88739i	−0.251386	−	0.210938i
$780$		0			0
$781$	−12.9709	−	4.72102i	−0.464135	−	0.168931i
$782$	11.8070	−	11.8070i	0.422216	−	0.422216i
$783$	45.2638	−	26.4260i	1.61760	−	0.944387i
$784$			12.6331i			0.451183i
$785$		0			0
$786$	−2.26195	+	1.40023i	−0.0806810	+	0.0499446i
$787$	4.83819	+	55.3008i	0.172463	+	1.97126i	0.230929	+	0.972971i	$0.425824\pi$
$787$	4.83819	+	55.3008i	0.172463	+	1.97126i	−0.0584659	+	0.998289i	$0.518621\pi$
$788$	−22.3081	+	15.6203i	−0.794693	+	0.556450i
$789$	−14.7708	−	16.5440i	−0.525854	−	0.588981i
$790$		0			0
$791$	−6.29143	+	3.63236i	−0.223698	+	0.129152i
$792$	0.317821	+	0.00822152i	0.0112933	+	0.000292139i
$793$	−13.1888	−	49.2212i	−0.468348	−	1.74790i
$794$	4.69817	+	26.6447i	0.166732	+	0.945584i
$795$		0			0
$796$	−4.02867	+	1.46632i	−0.142792	+	0.0519722i
$797$	−0.135702	+	0.291013i	−0.00480680	+	0.0103082i	−0.908697	−	0.417457i	$-0.862921\pi$
$797$	−0.135702	+	0.291013i	−0.00480680	+	0.0103082i	0.903890	+	0.427766i	$0.140699\pi$
$798$	17.1565	−	2.03336i	0.607333	−	0.0719803i
$799$	31.0206	−	5.46977i	1.09743	−	0.193507i
$800$		0			0
$801$	23.1181	−	15.3121i	0.816838	−	0.541026i
$802$	4.32535	−	16.1424i	0.152733	−	0.570008i
$803$	−1.68331	−	0.147271i	−0.0594028	−	0.00519708i
$804$	−29.9343	−	9.86557i	−1.05570	−	0.347932i
$805$		0			0
$806$	−7.83946	+	9.34270i	−0.276133	+	0.329083i
$807$	−12.2437	−	11.5140i	−0.430998	−	0.405314i
$808$	−0.606505	+	0.282818i	−0.0213368	+	0.00994950i
$809$	−30.0007			−1.05477			−0.527384	−	0.849627i	$-0.676827\pi$
$809$	−30.0007			−1.05477			−0.527384	+	0.849627i	$0.676827\pi$
$810$		0			0
$811$	21.6188			0.759140			0.379570	−	0.925163i	$-0.376072\pi$
$811$	21.6188			0.759140			0.379570	+	0.925163i	$0.376072\pi$
$812$	59.5358	−	27.7620i	2.08930	−	0.974255i
$813$	23.6628	+	22.2527i	0.829892	+	0.780436i
$814$	8.06185	−	9.60773i	0.282568	−	0.336751i
$815$		0			0
$816$	41.6260	+	13.7189i	1.45720	+	0.480257i
$817$	−3.63871	−	0.318346i	−0.127302	−	0.0111375i
$818$	8.38092	−	31.2780i	0.293032	−	1.09361i
$819$	30.9616	+	15.4246i	1.08188	+	0.538979i
$820$		0			0
$821$	−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	$0.516645\pi$
$822$	47.8082	−	5.66616i	1.66750	−	0.197630i
$823$	13.2188	−	28.3477i	0.460777	−	0.988140i	−0.529407	−	0.848368i	$-0.677585\pi$
$823$	13.2188	−	28.3477i	0.460777	−	0.988140i	0.990184	−	0.139772i	$-0.0446368\pi$
$824$	−0.884565	+	0.321955i	−0.0308153	+	0.0112158i
$825$		0			0
$826$	−4.89290	−	27.7490i	−0.170246	−	0.965511i
$827$	−14.7239	−	54.9503i	−0.512000	−	1.91081i	−0.398177	−	0.917309i	$-0.630357\pi$
$827$	−14.7239	−	54.9503i	−0.512000	−	1.91081i	−0.113823	−	0.993501i	$-0.536310\pi$
$828$	4.11326	−	6.71702i	0.142946	−	0.233432i
$829$	13.5565	−	7.82684i	0.470836	−	0.271837i	−0.245753	−	0.969332i	$-0.579035\pi$
$829$	13.5565	−	7.82684i	0.470836	−	0.271837i	0.716590	+	0.697495i	$0.245702\pi$
$830$		0			0
$831$	16.8210	+	18.8403i	0.583515	+	0.653564i
$832$	−24.5076	+	17.1604i	−0.849648	+	0.594930i
$833$	−1.80924	−	20.6797i	−0.0626863	−	0.716508i
$834$	26.0423	−	16.1212i	0.901770	−	0.558230i
$835$		0			0
$836$			4.48562i			0.155138i
$837$	8.60408	−	1.56010i	0.297400	−	0.0539249i
$838$	−3.95197	+	3.95197i	−0.136518	+	0.136518i
$839$	17.8822	+	6.50860i	0.617363	+	0.224702i	0.631722	−	0.775195i	$-0.282349\pi$
$839$	17.8822	+	6.50860i	0.617363	+	0.224702i	−0.0143589	+	0.999897i	$0.504571\pi$
$840$		0			0
$841$	55.7268	+	46.7603i	1.92161	+	1.61242i
$842$	31.2501	+	44.6297i	1.07695	+	1.53804i
$843$	−3.11157	−	2.03933i	−0.107168	−	0.0702383i
$844$	−29.5162	−	35.1760i	−1.01599	−	1.21081i
$845$		0			0
$846$	26.9995	−	11.7499i	0.928263	−	0.403970i
$847$	27.7583	−	7.43782i	0.953788	−	0.255567i
$848$	−2.16365	+	3.09002i	−0.0743002	+	0.106112i
$849$	−24.2137	+	9.66472i	−0.831011	+	0.331692i
$850$		0			0
$851$	−1.94047	−	5.33141i	−0.0665186	−	0.182758i
$852$	31.5633	+	13.5547i	1.08134	+	0.464377i
$853$	6.60026	+	4.62155i	0.225988	+	0.158239i	0.681088	−	0.732202i	$-0.261507\pi$
$853$	6.60026	+	4.62155i	0.225988	+	0.158239i	−0.455099	+	0.890441i	$0.650396\pi$
$854$	−45.3730	+	78.5883i	−1.55263	+	2.68923i
$855$		0			0
$856$	−0.0428776	−	0.0742662i	−0.00146553	−	0.00253837i
$857$	4.51999	−	51.6637i	0.154400	−	1.76480i	−0.385158	−	0.922850i	$-0.625853\pi$
$857$	4.51999	−	51.6637i	0.154400	−	1.76480i	0.539558	−	0.841948i	$-0.318591\pi$
$858$	−9.75625	+	14.8859i	−0.333073	+	0.508196i
$859$	−40.2472	−	7.09666i	−1.37322	−	0.242135i	−0.562124	−	0.827053i	$-0.690016\pi$
$859$	−40.2472	−	7.09666i	−1.37322	−	0.242135i	−0.811092	+	0.584918i	$0.801127\pi$
$860$		0			0
$861$	−15.4527	+	28.7699i	−0.526628	+	0.980476i
$862$	−16.1038	−	34.5347i	−0.548497	−	1.17626i
$863$	29.8445	+	29.8445i	1.01592	+	1.01592i	0.999871	+	0.0160467i	$0.00510806\pi$
$863$	29.8445	+	29.8445i	1.01592	+	1.01592i	0.0160467	+	0.999871i	$0.494892\pi$
$864$	41.6059	+	3.43724i	1.41546	+	0.116937i
$865$		0			0
$866$	2.64852	−	7.27674i	0.0900003	−	0.247274i
$867$	−41.4419	−	9.75133i	−1.40744	−	0.331173i
$868$	10.9178	−	0.955182i	0.370573	−	0.0324210i
$869$	−3.36535	+	19.0859i	−0.114162	+	0.647444i
$870$		0			0
$871$	24.6804	−	20.7093i	0.836262	−	0.701707i
$872$	−0.417863	−	0.111966i	−0.0141506	−	0.00379165i
$873$	12.6489	+	7.74576i	0.428102	+	0.262154i
$874$	3.48248	+	2.01061i	0.117797	+	0.0680100i
$875$		0			0
$876$	4.16164	+	0.602735i	0.140609	+	0.0203645i
$877$	11.7237	+	5.46684i	0.395880	+	0.184602i	0.610356	−	0.792127i	$-0.291026\pi$
$877$	11.7237	+	5.46684i	0.395880	+	0.184602i	−0.214476	+	0.976729i	$0.568804\pi$
$878$	−47.1006	−	21.9634i	−1.58957	−	0.741227i
$879$	30.7808	−	39.0580i	1.03821	−	1.31739i
$880$		0			0
$881$	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	$0.464648\pi$
$882$	−6.16321	−	18.4005i	−0.207526	−	0.619576i
$883$	38.2981	+	10.2619i	1.28883	+	0.345342i	0.837217	−	0.546870i	$-0.184181\pi$
$883$	38.2981	+	10.2619i	1.28883	+	0.345342i	0.451617	+	0.892212i	$0.350848\pi$
$884$	36.2962	−	30.4561i	1.22077	−	1.02435i
$885$		0			0
$886$	0.853574	−	4.84086i	0.0286764	−	0.162632i
$887$	12.2441	−	1.07122i	0.411118	−	0.0359682i	0.120279	−	0.992740i	$-0.461621\pi$
$887$	12.2441	−	1.07122i	0.411118	−	0.0359682i	0.290839	+	0.956772i	$0.406066\pi$
$888$	−0.390429	+	0.415171i	−0.0131020	+	0.0139322i
$889$	15.2398	−	41.8709i	0.511125	−	1.40430i
$890$		0			0
$891$	12.2010	−	3.73870i	0.408750	−	0.125251i
$892$	−6.01508	−	6.01508i	−0.201400	−	0.201400i
$893$	3.20591	+	6.87510i	0.107282	+	0.230067i
$894$	4.64432	−	0.142634i	0.155329	−	0.00477041i
$895$		0			0
$896$	1.88209	+	0.331863i	0.0628762	+	0.0110868i
$897$	3.62500	+	7.18903i	0.121035	+	0.240035i
$898$	−1.24958	+	14.2827i	−0.0416990	+	0.476621i
$899$	8.48742	+	14.7006i	0.283071	+	0.490294i
$900$		0			0
$901$	3.09924	−	5.36804i	0.103251	−	0.178835i
$902$	−13.7644	−	9.63791i	−0.458303	−	0.320907i
$903$	1.53280	+	12.9330i	0.0510083	+	0.430382i
$904$	0.0580931	+	0.159610i	0.00193215	+	0.00530854i
$905$		0			0
$906$	6.75284	−	46.6256i	0.224348	−	1.54903i
$907$	−22.1561	+	31.6422i	−0.735681	+	1.05066i	0.260680	+	0.965425i	$0.416053\pi$
$907$	−22.1561	+	31.6422i	−0.735681	+	1.05066i	−0.996361	+	0.0852357i	$0.972836\pi$
$908$	−9.56785	+	2.56370i	−0.317520	+	0.0850793i
$909$	−19.4781	+	18.4958i	−0.646049	+	0.613467i
$910$		0			0
$911$	−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	$0.975851\pi$
$912$	−0.596724	+	10.5382i	−0.0197595	+	0.348954i
$913$	9.24090	+	13.1974i	0.305829	+	0.436769i
$914$	18.6304	+	15.6327i	0.616238	+	0.517085i
$915$		0			0
$916$	−52.0351	−	18.9392i	−1.71929	−	0.625770i
$917$	−1.72791	+	1.72791i	−0.0570605	+	0.0570605i
$918$	−67.3223	+	0.325794i	−2.22197	+	0.0107528i
$919$		−	21.8380i		−	0.720370i	−0.932881	−	0.360185i	$-0.882714\pi$
$919$		−	21.8380i		−	0.720370i	0.932881	−	0.360185i	$-0.117286\pi$
$920$		0			0
$921$	29.5965	+	15.8967i	0.975237	+	0.523814i
$922$	3.23343	+	36.9583i	0.106488	+	1.21716i
$923$	−28.7632	+	20.1402i	−0.946753	+	0.662924i
$924$	15.6580	−	3.25945i	0.515109	−	0.107228i
$925$		0			0
$926$	−55.9533	+	32.3047i	−1.83874	+	1.06160i
$927$	−29.5621	+	23.5301i	−0.970947	+	0.772830i
$928$	20.9751	+	78.2803i	0.688543	+	2.56968i
$929$	−2.34106	−	13.2768i	−0.0768076	−	0.435598i	−0.998826	−	0.0484506i	$-0.984572\pi$
$929$	−2.34106	−	13.2768i	−0.0768076	−	0.435598i	0.922018	−	0.387147i	$-0.126539\pi$
$930$		0			0
$931$	4.69775	−	1.70984i	0.153963	−	0.0560378i
$932$	−1.58789	+	3.40525i	−0.0520131	+	0.111543i
$933$	−8.39924	+	19.5583i	−0.274979	+	0.640311i
$934$	−13.7075	+	2.41699i	−0.448522	+	0.0790865i
$935$		0			0
$936$	0.480860	−	0.650276i	0.0157174	−	0.0212549i
$937$	−2.47270	+	9.22824i	−0.0807796	+	0.301473i	−0.994482	−	0.104911i	$-0.966544\pi$
$937$	−2.47270	+	9.22824i	−0.0807796	+	0.301473i	0.913702	+	0.406385i	$0.133211\pi$
$938$	−57.1558	−	5.00048i	−1.86620	−	0.163271i
$939$	4.78471	+	22.9851i	0.156143	+	0.750091i
$940$		0			0
$941$	−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	$0.437542\pi$
$942$	20.6788	−	6.22719i	0.673752	−	0.202893i
$943$	−6.88900	+	3.21239i	−0.224337	+	0.104610i
$944$	17.2147			0.560290
$945$		0			0
$946$	−6.70099			−0.217868
$947$	−8.23615	+	3.84058i	−0.267639	+	0.124802i	−0.551805	−	0.833973i	$-0.686061\pi$
$947$	−8.23615	+	3.84058i	−0.267639	+	0.124802i	0.284167	+	0.958775i	$0.408283\pi$
$948$	11.0468	−	46.9473i	0.358782	−	1.52478i
$949$	−2.76298	+	3.29279i	−0.0896901	+	0.106888i
$950$		0			0
$951$	−12.0189	+	10.7307i	−0.389741	+	0.347968i
$952$	−1.53483	−	0.134280i	−0.0497441	−	0.00435205i
$953$	−4.45291	+	16.6185i	−0.144244	+	0.538326i	0.855544	+	0.517730i	$0.173223\pi$
$953$	−4.45291	+	16.6185i	−0.144244	+	0.538326i	−0.999788	+	0.0205956i	$0.993444\pi$
$954$	1.64392	−	5.55626i	0.0532239	−	0.179890i
$955$		0			0
$956$	1.18442	−	0.208845i	0.0383069	−	0.00675454i
$957$	14.8249	+	19.8464i	0.479220	+	0.641542i
$958$	−22.7998	+	48.8944i	−0.736629	+	1.57971i
$959$	41.5553	−	15.1249i	1.34189	−	0.488408i
$960$		0			0
$961$	−4.89132	−	27.7401i	−0.157785	−	0.894841i
$962$	−8.25757	−	30.8177i	−0.266235	−	0.993602i
$963$	−2.57867	−	2.27995i	−0.0830964	−	0.0734705i
$964$	9.06199	−	5.23194i	0.291867	−	0.168509i
$965$		0			0
$966$	4.48792	−	13.6173i	0.144396	−	0.438129i
$967$	−19.9012	+	13.9349i	−0.639978	+	0.448117i	−0.847992	−	0.530008i	$-0.822189\pi$
$967$	−19.9012	+	13.9349i	−0.639978	+	0.448117i	0.208014	+	0.978126i	$0.433300\pi$
$968$	−0.0585599	−	0.669342i	−0.00188219	−	0.0215135i
$969$	−0.532410	−	17.3358i	−0.0171035	−	0.556907i
$970$		0			0
$971$		−	9.34984i		−	0.300051i	−0.988682	−	0.150025i	$-0.952064\pi$
$971$		−	9.34984i		−	0.300051i	0.988682	−	0.150025i	$-0.0479355\pi$
$972$	−30.8407	+	7.57261i	−0.989216	+	0.242891i
$973$	19.8938	−	19.8938i	0.637765	−	0.637765i
$974$	46.4563	+	16.9087i	1.48856	+	0.541790i
$975$		0			0
$976$	−42.4702	−	35.6367i	−1.35944	−	1.14070i
$977$	−1.12227	−	1.60277i	−0.0359048	−	0.0512773i	0.800798	−	0.598934i	$-0.204409\pi$
$977$	−1.12227	−	1.60277i	−0.0359048	−	0.0512773i	−0.836703	+	0.547657i	$0.815520\pi$
$978$	2.11282	−	1.06537i	0.0675605	−	0.0340668i
$979$	8.42414	+	10.0395i	0.269237	+	0.320864i
$980$		0			0
$981$	−17.3312	+	1.06554i	−0.553341	+	0.0340200i
$982$	−47.9679	+	12.8530i	−1.53072	+	0.410154i
$983$	−20.8651	+	29.7984i	−0.665493	+	0.950423i	0.334475	+	0.942405i	$0.391441\pi$
$983$	−20.8651	+	29.7984i	−0.665493	+	0.950423i	−0.999968	+	0.00801795i	$0.997448\pi$
$984$	0.599699	+	0.472610i	0.0191177	+	0.0150663i
$985$		0			0
$986$	−44.6985	−	122.808i	−1.42349	−	3.91100i
$987$	21.6694	−	16.1866i	0.689743	−	0.515226i
$988$	9.34709	+	6.54490i	0.297370	+	0.208221i
$989$	−1.51565	+	2.62518i	−0.0481948	+	0.0834758i
$990$		0			0
$991$	−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	$-0.363868\pi$
$992$	−1.17840	+	13.4692i	−0.0374142	+	0.427646i
$993$	22.5920	+	1.27927i	0.716937	+	0.0405965i
$994$	61.5804	+	10.8583i	1.95321	+	0.344404i
$995$		0			0
$996$	−21.1032	−	34.0903i	−0.668680	−	1.08019i
$997$	−16.9724	−	36.3975i	−0.537523	−	1.15272i	−0.968191	−	0.250211i	$-0.919500\pi$
$997$	−16.9724	−	36.3975i	−0.537523	−	1.15272i	0.430668	−	0.902510i	$-0.358278\pi$
$998$	−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	675.2.ba.b.482.2		192
5.2	odd	4		135.2.q.a.23.2	✓	192
5.3	odd	4	inner	675.2.ba.b.293.15		192
5.4	even	2		135.2.q.a.77.15	yes	192
15.2	even	4		405.2.r.a.98.15		192
15.14	odd	2		405.2.r.a.17.2		192
27.20	odd	18	inner	675.2.ba.b.182.15		192
135.7	odd	36		405.2.r.a.143.2		192
135.34	even	18		405.2.r.a.62.15		192
135.47	even	36		135.2.q.a.128.15	yes	192
135.74	odd	18		135.2.q.a.47.2	yes	192
135.128	even	36	inner	675.2.ba.b.668.2		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.2	✓	192	5.2	odd	4
135.2.q.a.47.2	yes	192	135.74	odd	18
135.2.q.a.77.15	yes	192	5.4	even	2
135.2.q.a.128.15	yes	192	135.47	even	36
405.2.r.a.17.2		192	15.14	odd	2
405.2.r.a.62.15		192	135.34	even	18
405.2.r.a.98.15		192	15.2	even	4
405.2.r.a.143.2		192	135.7	odd	36
675.2.ba.b.182.15		192	27.20	odd	18	inner
675.2.ba.b.293.15		192	5.3	odd	4	inner
675.2.ba.b.482.2		192	1.1	even	1	trivial
675.2.ba.b.668.2		192	135.128	even	36	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82102 + 0.849158i) q^{2} +(1.26176 + 1.18657i) q^{3} +(1.30949 - 1.56058i) q^{4} +(-3.30529 - 1.08934i) q^{6} +(-3.18459 - 0.278616i) q^{7} +(-0.0193446 + 0.0721951i) q^{8} +(0.184096 + 2.99435i) q^{9} +O(q^{10})\)	\(q+(-1.82102 + 0.849158i) q^{2} +(1.26176 + 1.18657i) q^{3} +(1.30949 - 1.56058i) q^{4} +(-3.30529 - 1.08934i) q^{6} +(-3.18459 - 0.278616i) q^{7} +(-0.0193446 + 0.0721951i) q^{8} +(0.184096 + 2.99435i) q^{9} +(-1.39635 + 0.246214i) q^{11} +(3.50401 - 0.415290i) q^{12} +(-1.52433 + 3.26894i) q^{13} +(6.03581 - 2.19686i) q^{14} +(0.681434 + 3.86460i) q^{16} +(-1.66893 - 6.22853i) q^{17} +(-2.87791 - 5.29645i) q^{18} +(1.34486 - 0.776456i) q^{19} +(-3.68761 - 4.13030i) q^{21} +(2.33371 - 1.63408i) q^{22} +(-0.112323 - 1.28385i) q^{23} +(-0.110073 + 0.0681394i) q^{24} -7.24723i q^{26} +(-3.32072 + 3.99660i) q^{27} +(-4.60499 + 4.60499i) q^{28} +(-9.47861 - 3.44993i) q^{29} +(-1.28914 - 1.08172i) q^{31} +(-4.60830 - 6.58134i) q^{32} +(-2.05401 - 1.34620i) q^{33} +(8.32817 + 9.92512i) q^{34} +(4.91400 + 3.63376i) q^{36} +(4.25234 - 1.13941i) q^{37} +(-1.78969 + 2.55594i) q^{38} +(-5.80218 + 2.31590i) q^{39} +(-2.01725 - 5.54236i) q^{41} +(10.2225 + 4.39001i) q^{42} +(-1.92673 - 1.34911i) q^{43} +(-1.44426 + 2.50153i) q^{44} +(1.29474 + 2.24255i) q^{46} +(-0.425748 + 4.86633i) q^{47} +(-3.72582 + 5.68478i) q^{48} +(3.17036 + 0.559020i) q^{49} +(5.28480 - 9.83924i) q^{51} +(3.10537 + 6.65949i) q^{52} +(0.679717 + 0.679717i) q^{53} +(2.65337 - 10.0977i) q^{54} +(0.0817195 - 0.224523i) q^{56} +(2.61822 + 0.616070i) q^{57} +(20.1903 - 1.76642i) q^{58} +(0.761756 - 4.32014i) q^{59} +(-10.8226 + 9.08123i) q^{61} +(3.26611 + 0.875151i) q^{62} +(0.248002 - 9.58707i) q^{63} +(7.18348 + 4.14738i) q^{64} +(4.88355 + 0.707290i) q^{66} +(-8.09546 - 3.77497i) q^{67} +(-11.9056 - 5.55167i) q^{68} +(1.38166 - 1.75320i) q^{69} +(8.43086 + 4.86756i) q^{71} +(-0.219739 - 0.0446337i) q^{72} +(1.15112 + 0.308443i) q^{73} +(-6.77608 + 5.68580i) q^{74} +(0.549351 - 3.11553i) q^{76} +(4.51541 - 0.395047i) q^{77} +(8.59935 - 9.14429i) q^{78} +(4.67487 - 12.8441i) q^{79} +(-8.93222 + 1.10249i) q^{81} +(8.37981 + 8.37981i) q^{82} +(-4.80207 - 10.2981i) q^{83} +(-11.2745 + 0.346259i) q^{84} +(4.65423 + 0.820666i) q^{86} +(-7.86618 - 15.6001i) q^{87} +(0.00923640 - 0.105573i) q^{88} +(-4.62153 - 8.00472i) q^{89} +(5.76516 - 9.98556i) q^{91} +(-2.15065 - 1.50590i) q^{92} +(-0.343056 - 2.89453i) q^{93} +(-3.35698 - 9.22322i) q^{94} +(1.99464 - 13.7722i) q^{96} +(2.83579 - 4.04993i) q^{97} +(-6.24800 + 1.67415i) q^{98} +(-0.994312 - 4.13583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31} + 48 q^{32} + 6 q^{33} + 12 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{41} + 24 q^{42} + 12 q^{43} - 12 q^{46} + 6 q^{47} - 12 q^{48} + 144 q^{51} - 12 q^{52} + 180 q^{56} + 12 q^{57} + 12 q^{58} - 60 q^{61} + 18 q^{62} + 54 q^{63} + 72 q^{66} - 24 q^{67} + 60 q^{68} - 36 q^{71} - 180 q^{72} + 6 q^{73} - 72 q^{76} - 132 q^{77} - 78 q^{78} + 12 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{86} - 144 q^{87} + 48 q^{88} - 12 q^{91} - 258 q^{92} - 180 q^{93} - 12 q^{96} - 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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