LMFDB - Embedded newform 605.2.g.m.366.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.m.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.386111 + 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.124741 - 0.0906300i) q^{6} +(0.829779 - 2.55380i) q^{7} +(-0.556333 - 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} +O(q^{10})$	\(q+(-0.386111 + 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.124741 - 0.0906300i) q^{6} +(0.829779 - 2.55380i) q^{7} +(-0.556333 - 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} -0.477260 q^{10} -0.572554 q^{12} +(3.77637 - 2.74369i) q^{13} +(0.396020 + 1.21882i) q^{14} +(-0.0998345 + 0.307259i) q^{15} +(-2.17239 - 1.57833i) q^{16} +(3.74278 + 2.71929i) q^{17} +(-0.427051 + 1.31433i) q^{18} +(-1.34127 - 4.12801i) q^{19} +(-1.43376 + 1.04169i) q^{20} +0.867517 q^{21} +2.77222 q^{23} +(0.470553 - 0.341876i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.688421 + 2.11874i) q^{26} +(1.54094 + 1.11956i) q^{27} +(3.84996 + 2.79716i) q^{28} +(-0.931196 + 2.86593i) q^{29} +(-0.0476470 - 0.146642i) q^{30} +(-1.93056 + 1.40263i) q^{31} +4.88221 q^{32} -2.20796 q^{34} +(2.17239 - 1.57833i) q^{35} +(1.58578 + 4.88053i) q^{36} +(-3.28884 + 10.1220i) q^{37} +(1.67589 + 1.21761i) q^{38} +(1.22004 + 0.886408i) q^{39} +(0.556333 - 1.71222i) q^{40} +(-0.683053 - 2.10222i) q^{41} +(-0.334958 + 0.243361i) q^{42} -7.06719 q^{43} +2.89563 q^{45} +(-1.07039 + 0.777682i) q^{46} +(1.34798 + 4.14865i) q^{47} +(0.268077 - 0.825058i) q^{48} +(-0.170221 - 0.123673i) q^{49} +(-0.386111 - 0.280526i) q^{50} +(-0.461867 + 1.42148i) q^{51} +(2.55633 + 7.86758i) q^{52} +(5.12435 - 3.72306i) q^{53} -0.909040 q^{54} -4.83428 q^{56} +(1.13446 - 0.824235i) q^{57} +(-0.444423 - 1.36779i) q^{58} +(3.63011 - 11.1723i) q^{59} +(-0.463206 - 0.336539i) q^{60} +(3.22201 + 2.34093i) q^{61} +(0.351935 - 1.08314i) q^{62} +(-2.40273 - 7.39484i) q^{63} +(2.45970 - 1.78708i) q^{64} +4.66785 q^{65} +7.31984 q^{67} +(-6.63303 + 4.81918i) q^{68} +(0.276763 + 0.851790i) q^{69} +(-0.396020 + 1.21882i) q^{70} +(-0.967351 - 0.702822i) q^{71} +(-4.21747 - 3.06417i) q^{72} +(0.315724 - 0.971700i) q^{73} +(-1.56963 - 4.83083i) q^{74} +(-0.261370 + 0.189896i) q^{75} +7.69223 q^{76} -0.719730 q^{78} +(-2.83328 + 2.05850i) q^{79} +(-0.829779 - 2.55380i) q^{80} +(2.49424 - 7.67647i) q^{81} +(0.853463 + 0.620077i) q^{82} +(-8.99290 - 6.53372i) q^{83} +(-0.475093 + 1.46219i) q^{84} +(1.42961 + 4.39990i) q^{85} +(2.72872 - 1.98253i) q^{86} -0.973547 q^{87} +2.76978 q^{89} +(-1.11803 + 0.812299i) q^{90} +(-3.87328 - 11.9207i) q^{91} +(-1.51820 + 4.67254i) q^{92} +(-0.623707 - 0.453150i) q^{93} +(-1.68428 - 1.22370i) q^{94} +(1.34127 - 4.12801i) q^{95} +(0.487413 + 1.50010i) q^{96} +(-14.9945 + 10.8941i) q^{97} +0.100418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9	$ 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21} + 10 q^{23} - 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} + 19 q^{28} + 21 q^{29} + 7 q^{30} + 15 q^{31} + 16 q^{32} + 4 q^{34} + q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} - 14 q^{39} + q^{40} + 3 q^{41} - 21 q^{42} - 38 q^{43} - 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} + 3 q^{50} + 6 q^{51} + 17 q^{52} - 2 q^{53} + 16 q^{54} + 22 q^{56} + 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} + 6 q^{61} - 5 q^{62} - 30 q^{63} + 29 q^{64} + 2 q^{65} - 38 q^{67} - 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} + 5 q^{72} - 2 q^{73} - 20 q^{74} - 5 q^{75} - 16 q^{78} - 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} - 38 q^{83} - 17 q^{84} + 13 q^{85} + 2 q^{86} + 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} - 18 q^{94} - 5 q^{95} - 17 q^{96} - 56 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.386111	+	0.280526i	−0.273022	+	0.198362i	−0.715868	−	0.698236i	$-0.753969\pi$
$2$	−0.386111	+	0.280526i	−0.273022	+	0.198362i	0.442846	+	0.896598i	$0.353969\pi$
$3$	0.0998345	+	0.307259i	0.0576395	+	0.177396i	0.975731	−	0.218972i	$-0.0702704\pi$
$3$	0.0998345	+	0.307259i	0.0576395	+	0.177396i	−0.918092	+	0.396368i	$0.870270\pi$
$4$	−0.547647	+	1.68548i	−0.273823	+	0.842742i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−0.124741	−	0.0906300i	−0.0509255	−	0.0369995i
$7$	0.829779	−	2.55380i	0.313627	−	0.965244i	−0.662689	−	0.748895i	$-0.730585\pi$
$7$	0.829779	−	2.55380i	0.313627	−	0.965244i	0.976316	−	0.216350i	$-0.0694151\pi$
$8$	−0.556333	−	1.71222i	−0.196693	−	0.605360i
$9$	2.34261	−	1.70201i	0.780870	−	0.567335i
$10$	−0.477260			−0.150923
$11$		0			0
$11$		0			0
$12$	−0.572554			−0.165282
$13$	3.77637	−	2.74369i	1.04738	−	0.760963i	0.0756644	−	0.997133i	$-0.475892\pi$
$13$	3.77637	−	2.74369i	1.04738	−	0.760963i	0.971712	+	0.236170i	$0.0758922\pi$
$14$	0.396020	+	1.21882i	0.105841	+	0.325745i
$15$	−0.0998345	+	0.307259i	−0.0257771	+	0.0793339i
$16$	−2.17239	−	1.57833i	−0.543097	−	0.394583i
$17$	3.74278	+	2.71929i	0.907756	+	0.659524i	0.940446	−	0.339942i	$-0.110407\pi$
$17$	3.74278	+	2.71929i	0.907756	+	0.659524i	−0.0326901	+	0.999466i	$0.510407\pi$
$18$	−0.427051	+	1.31433i	−0.100657	+	0.309790i
$19$	−1.34127	−	4.12801i	−0.307709	−	0.947030i	−0.978653	−	0.205522i	$-0.934111\pi$
$19$	−1.34127	−	4.12801i	−0.307709	−	0.947030i	0.670944	−	0.741508i	$-0.265889\pi$
$20$	−1.43376	+	1.04169i	−0.320598	+	0.232928i
$21$	0.867517			0.189308
$22$		0			0
$23$	2.77222			0.578048			0.289024	−	0.957322i	$-0.406669\pi$
$23$	2.77222			0.578048			0.289024	+	0.957322i	$0.406669\pi$
$24$	0.470553	−	0.341876i	0.0960511	−	0.0697852i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.688421	+	2.11874i	−0.135010	+	0.415519i
$27$	1.54094	+	1.11956i	0.296554	+	0.215459i
$28$	3.84996	+	2.79716i	0.727573	+	0.528613i
$29$	−0.931196	+	2.86593i	−0.172919	+	0.532189i	−0.999532	−	0.0305806i	$-0.990264\pi$
$29$	−0.931196	+	2.86593i	−0.172919	+	0.532189i	0.826613	+	0.562770i	$0.190264\pi$
$30$	−0.0476470	−	0.146642i	−0.00869911	−	0.0267731i
$31$	−1.93056	+	1.40263i	−0.346738	+	0.251920i	−0.747499	−	0.664262i	$-0.768746\pi$
$31$	−1.93056	+	1.40263i	−0.346738	+	0.251920i	0.400761	+	0.916183i	$0.368746\pi$
$32$	4.88221			0.863061
$33$		0			0
$34$	−2.20796			−0.378662
$35$	2.17239	−	1.57833i	0.367201	−	0.266787i
$36$	1.58578	+	4.88053i	0.264297	+	0.813422i
$37$	−3.28884	+	10.1220i	−0.540682	+	1.66405i	0.190360	+	0.981714i	$0.439035\pi$
$37$	−3.28884	+	10.1220i	−0.540682	+	1.66405i	−0.731041	+	0.682333i	$0.760965\pi$
$38$	1.67589	+	1.21761i	0.271866	+	0.197522i
$39$	1.22004	+	0.886408i	0.195362	+	0.141939i
$40$	0.556333	−	1.71222i	0.0879640	−	0.270725i
$41$	−0.683053	−	2.10222i	−0.106675	−	0.328312i	0.883445	−	0.468535i	$-0.155218\pi$
$41$	−0.683053	−	2.10222i	−0.106675	−	0.328312i	−0.990120	+	0.140223i	$0.955218\pi$
$42$	−0.334958	+	0.243361i	−0.0516852	+	0.0375515i
$43$	−7.06719			−1.07774			−0.538868	−	0.842390i	$-0.681148\pi$
$43$	−7.06719			−1.07774			−0.538868	+	0.842390i	$0.681148\pi$
$44$		0			0
$45$	2.89563			0.431654
$46$	−1.07039	+	0.777682i	−0.157820	+	0.114663i
$47$	1.34798	+	4.14865i	0.196623	+	0.605143i	0.999954	+	0.00961001i	$0.00305901\pi$
$47$	1.34798	+	4.14865i	0.196623	+	0.605143i	−0.803331	+	0.595533i	$0.796941\pi$
$48$	0.268077	−	0.825058i	0.0386936	−	0.119087i
$49$	−0.170221	−	0.123673i	−0.0243174	−	0.0176676i
$50$	−0.386111	−	0.280526i	−0.0546044	−	0.0396724i
$51$	−0.461867	+	1.42148i	−0.0646743	+	0.199047i
$52$	2.55633	+	7.86758i	0.354500	+	1.09104i
$53$	5.12435	−	3.72306i	0.703883	−	0.511401i	−0.177311	−	0.984155i	$-0.556740\pi$
$53$	5.12435	−	3.72306i	0.703883	−	0.511401i	0.881195	+	0.472754i	$0.156740\pi$
$54$	−0.909040			−0.123705
$55$		0			0
$56$	−4.83428			−0.646008
$57$	1.13446	−	0.824235i	0.150263	−	0.109173i
$58$	−0.444423	−	1.36779i	−0.0583556	−	0.179600i
$59$	3.63011	−	11.1723i	0.472600	−	1.45451i	−0.376567	−	0.926389i	$-0.622896\pi$
$59$	3.63011	−	11.1723i	0.472600	−	1.45451i	0.849167	−	0.528124i	$-0.177104\pi$
$60$	−0.463206	−	0.336539i	−0.0597996	−	0.0434470i
$61$	3.22201	+	2.34093i	0.412537	+	0.299725i	0.774628	−	0.632417i	$-0.217937\pi$
$61$	3.22201	+	2.34093i	0.412537	+	0.299725i	−0.362091	+	0.932143i	$0.617937\pi$
$62$	0.351935	−	1.08314i	0.0446958	−	0.137559i
$63$	−2.40273	−	7.39484i	−0.302715	−	0.931662i
$64$	2.45970	−	1.78708i	0.307462	−	0.223385i
$65$	4.66785			0.578975
$66$		0			0
$67$	7.31984			0.894260			0.447130	−	0.894469i	$-0.352446\pi$
$67$	7.31984			0.894260			0.447130	+	0.894469i	$0.352446\pi$
$68$	−6.63303	+	4.81918i	−0.804373	+	0.584411i
$69$	0.276763	+	0.851790i	0.0333184	+	0.102543i
$70$	−0.396020	+	1.21882i	−0.0473335	+	0.145677i
$71$	−0.967351	−	0.702822i	−0.114803	−	0.0834096i	0.528902	−	0.848683i	$-0.322604\pi$
$71$	−0.967351	−	0.702822i	−0.114803	−	0.0834096i	−0.643706	+	0.765273i	$0.722604\pi$
$72$	−4.21747	−	3.06417i	−0.497034	−	0.361116i
$73$	0.315724	−	0.971700i	0.0369528	−	0.113729i	−0.930879	−	0.365329i	$-0.880957\pi$
$73$	0.315724	−	0.971700i	0.0369528	−	0.113729i	0.967831	+	0.251600i	$0.0809566\pi$
$74$	−1.56963	−	4.83083i	−0.182466	−	0.561572i
$75$	−0.261370	+	0.189896i	−0.0301804	+	0.0219274i
$76$	7.69223			0.882360
$77$		0			0
$78$	−0.719730			−0.0814934
$79$	−2.83328	+	2.05850i	−0.318769	+	0.231600i	−0.735650	−	0.677362i	$-0.763123\pi$
$79$	−2.83328	+	2.05850i	−0.318769	+	0.231600i	0.416881	+	0.908961i	$0.363123\pi$
$80$	−0.829779	−	2.55380i	−0.0927721	−	0.285523i
$81$	2.49424	−	7.67647i	0.277137	−	0.852941i
$82$	0.853463	+	0.620077i	0.0942492	+	0.0684761i
$83$	−8.99290	−	6.53372i	−0.987099	−	0.717169i	−0.0278149	−	0.999613i	$-0.508855\pi$
$83$	−8.99290	−	6.53372i	−0.987099	−	0.717169i	−0.959284	+	0.282444i	$0.908855\pi$
$84$	−0.475093	+	1.46219i	−0.0518369	+	0.159538i
$85$	1.42961	+	4.39990i	0.155063	+	0.477236i
$86$	2.72872	−	1.98253i	0.294246	−	0.213782i
$87$	−0.973547			−0.104375
$88$		0			0
$89$	2.76978			0.293596			0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978			0.293596			0.146798	+	0.989167i	$0.453103\pi$
$90$	−1.11803	+	0.812299i	−0.117851	+	0.0856239i
$91$	−3.87328	−	11.9207i	−0.406030	−	1.24963i
$92$	−1.51820	+	4.67254i	−0.158283	+	0.487146i
$93$	−0.623707	−	0.453150i	−0.0646754	−	0.0469894i
$94$	−1.68428	−	1.22370i	−0.173720	−	0.126215i
$95$	1.34127	−	4.12801i	0.137611	−	0.423525i
$96$	0.487413	+	1.50010i	0.0497464	+	0.153104i
$97$	−14.9945	+	10.8941i	−1.52246	+	1.10613i	−0.562207	+	0.826997i	$0.690048\pi$
$97$	−14.9945	+	10.8941i	−1.52246	+	1.10613i	−0.960252	+	0.279134i	$0.909952\pi$
$98$	0.100418			0.0101438
$99$		0			0
$100$	−1.77222			−0.177222
$101$	5.75580	−	4.18183i	0.572723	−	0.416108i	−0.263370	−	0.964695i	$-0.584834\pi$
$101$	5.75580	−	4.18183i	0.572723	−	0.416108i	0.836093	+	0.548587i	$0.184834\pi$
$102$	−0.220430	−	0.678415i	−0.0218259	−	0.0671731i
$103$	2.32639	−	7.15989i	0.229226	−	0.705485i	−0.768609	−	0.639719i	$-0.779051\pi$
$103$	2.32639	−	7.15989i	0.229226	−	0.705485i	0.997835	−	0.0657661i	$-0.0209491\pi$
$104$	−6.79871	−	4.93955i	−0.666669	−	0.484363i
$105$	0.701836	+	0.509914i	0.0684922	+	0.0497625i
$106$	−0.934153	+	2.87503i	−0.0907330	+	0.279247i
$107$	5.57133	+	17.1468i	0.538601	+	1.65764i	0.735737	+	0.677267i	$0.236836\pi$
$107$	5.57133	+	17.1468i	0.538601	+	1.65764i	−0.197136	+	0.980376i	$0.563164\pi$
$108$	−2.73089	+	1.98411i	−0.262780	+	0.190921i
$109$	−16.3653			−1.56751			−0.783756	−	0.621068i	$-0.786699\pi$
$109$	−16.3653			−1.56751			−0.783756	+	0.621068i	$0.786699\pi$
$110$		0			0
$111$	−3.43842			−0.326360
$112$	−5.83334	+	4.23817i	−0.551199	+	0.400469i
$113$	−0.634650	−	1.95325i	−0.0597029	−	0.183747i	0.916757	−	0.399445i	$-0.130797\pi$
$113$	−0.634650	−	1.95325i	−0.0597029	−	0.183747i	−0.976460	+	0.215699i	$0.930797\pi$
$114$	−0.206809	+	0.636493i	−0.0193694	+	0.0596130i
$115$	2.24278	+	1.62947i	0.209140	+	0.151949i
$116$	−4.32051	−	3.13903i	−0.401149	−	0.291452i
$117$	4.17678	−	12.8548i	0.386143	−	1.18843i
$118$	1.73251	+	5.33211i	0.159490	+	0.490860i
$119$	10.0502	−	7.30188i	0.921298	−	0.669362i
$120$	0.581635			0.0530958
$121$		0			0
$122$	−1.90075			−0.172086
$123$	0.577734	−	0.419748i	0.0520925	−	0.0378474i
$124$	−1.30685	−	4.02207i	−0.117359	−	0.361193i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	3.00217	+	2.18120i	0.267454	+	0.194317i
$127$	0.0617011	+	0.0448285i	0.00547509	+	0.00397788i	0.590519	−	0.807023i	$-0.298923\pi$
$127$	0.0617011	+	0.0448285i	0.00547509	+	0.00397788i	−0.585044	+	0.811001i	$0.698923\pi$
$128$	−3.46577	+	10.6665i	−0.306333	+	0.942798i
$129$	−0.705549	−	2.17146i	−0.0621201	−	0.191186i
$130$	−1.80231	+	1.30945i	−0.158073	+	0.114847i
$131$	−11.4831			−1.00328			−0.501642	−	0.865075i	$-0.667270\pi$
$131$	−11.4831			−1.00328			−0.501642	+	0.865075i	$0.667270\pi$
$132$		0			0
$133$	−11.6550			−1.01062
$134$	−2.82627	+	2.05341i	−0.244153	+	0.177387i
$135$	0.588587	+	1.81148i	0.0506575	+	0.155908i
$136$	2.57378	−	7.92127i	0.220700	−	0.679243i
$137$	14.8287	+	10.7737i	1.26690	+	0.920458i	0.999075	−	0.0430086i	$-0.0136943\pi$
$137$	14.8287	+	10.7737i	1.26690	+	0.920458i	0.267827	+	0.963467i	$0.413694\pi$
$138$	−0.345811	−	0.251246i	−0.0294374	−	0.0213875i
$139$	−7.16529	+	22.0525i	−0.607752	+	1.87047i	−0.131114	+	0.991367i	$0.541855\pi$
$139$	−7.16529	+	22.0525i	−0.607752	+	1.87047i	−0.476638	+	0.879100i	$0.658145\pi$
$140$	1.47055	+	4.52590i	0.124284	+	0.382508i
$141$	−1.14013	+	0.828356i	−0.0960167	+	0.0697602i
$142$	0.570666			0.0478892
$143$		0			0
$144$	−7.77539			−0.647949
$145$	−2.43790	+	1.77124i	−0.202457	+	0.147094i
$146$	0.150683	+	0.463754i	0.0124706	+	0.0383805i
$147$	0.0210057	−	0.0646489i	0.00173252	−	0.00533215i
$148$	−15.2594	−	11.0866i	−1.25431	−	0.911311i
$149$	−11.8639	−	8.61964i	−0.971930	−	0.706149i	−0.0160396	−	0.999871i	$-0.505106\pi$
$149$	−11.8639	−	8.61964i	−0.971930	−	0.706149i	−0.955891	+	0.293723i	$0.905106\pi$
$150$	0.0476470	−	0.146642i	0.00389036	−	0.0119733i
$151$	−2.32350	−	7.15101i	−0.189084	−	0.581941i	0.810911	−	0.585170i	$-0.198972\pi$
$151$	−2.32350	−	7.15101i	−0.189084	−	0.581941i	−0.999995	+	0.00322899i	$0.998972\pi$
$152$	−6.32185	+	4.59309i	−0.512770	+	0.372549i
$153$	13.3961			1.08301
$154$		0			0
$155$	−2.38630			−0.191672
$156$	−2.16217	+	1.57091i	−0.173113	+	0.125774i
$157$	−4.13523	−	12.7269i	−0.330028	−	1.01572i	−0.969120	−	0.246590i	$-0.920690\pi$
$157$	−4.13523	−	12.7269i	−0.330028	−	1.01572i	0.639092	−	0.769130i	$-0.279310\pi$
$158$	0.516500	−	1.58962i	0.0410905	−	0.126464i
$159$	1.65553	+	1.20281i	0.131292	+	0.0953892i
$160$	3.94979	+	2.86969i	0.312258	+	0.226869i
$161$	2.30033	−	7.07969i	0.181291	−	0.557958i
$162$	1.19040	+	3.66367i	0.0935266	+	0.287845i
$163$	0.624553	−	0.453764i	0.0489188	−	0.0355416i	−0.563057	−	0.826418i	$-0.690375\pi$
$163$	0.624553	−	0.453764i	0.0489188	−	0.0355416i	0.611976	+	0.790876i	$0.290375\pi$
$164$	3.91733			0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	6.86234	−	4.98578i	0.531024	−	0.385811i	−0.289717	−	0.957112i	$-0.593561\pi$
$167$	6.86234	−	4.98578i	0.531024	−	0.385811i	0.820741	+	0.571301i	$0.193561\pi$
$168$	−0.482628	−	1.48538i	−0.0372356	−	0.114599i
$169$	2.71589	−	8.35865i	0.208915	−	0.642973i
$170$	−1.78628	−	1.29781i	−0.137001	−	0.0995372i
$171$	−10.1680	−	7.38746i	−0.777564	−	0.564933i
$172$	3.87032	−	11.9116i	0.295109	−	0.908253i
$173$	1.56941	+	4.83014i	0.119320	+	0.367229i	0.992824	−	0.119589i	$-0.0381576\pi$
$173$	1.56941	+	4.83014i	0.119320	+	0.367229i	−0.873504	+	0.486818i	$0.838158\pi$
$174$	0.375898	−	0.273106i	0.0284967	−	0.0207041i
$175$	2.68522			0.202984
$176$		0			0
$177$	3.79521			0.285265
$178$	−1.06944	+	0.776996i	−0.0801581	+	0.0582383i
$179$	−3.49716	−	10.7632i	−0.261390	−	0.804476i	−0.992503	−	0.122219i	$-0.960999\pi$
$179$	−3.49716	−	10.7632i	−0.261390	−	0.804476i	0.731113	−	0.682256i	$-0.239001\pi$
$180$	−1.58578	+	4.88053i	−0.118197	+	0.363773i
$181$	−5.98677	−	4.34965i	−0.444993	−	0.323307i	0.342623	−	0.939473i	$-0.388685\pi$
$181$	−5.98677	−	4.34965i	−0.444993	−	0.323307i	−0.787616	+	0.616167i	$0.788685\pi$
$182$	4.83960	+	3.51617i	0.358735	+	0.260636i
$183$	−0.397604	+	1.22370i	−0.0293917	+	0.0904583i
$184$	−1.54228	−	4.74665i	−0.113698	−	0.349927i
$185$	−8.61029	+	6.25574i	−0.633041	+	0.459931i
$186$	0.367941			0.0269787
$187$		0			0
$188$	−7.73070			−0.563819
$189$	4.13776	−	3.00626i	0.300978	−	0.218673i
$190$	0.640135	+	1.97013i	0.0464403	+	0.142928i
$191$	−1.59332	+	4.90372i	−0.115288	+	0.354821i	−0.992007	−	0.126183i	$-0.959728\pi$
$191$	−1.59332	+	4.90372i	−0.115288	+	0.354821i	0.876719	+	0.481003i	$0.159728\pi$
$192$	0.794658	+	0.577353i	0.0573495	+	0.0416668i
$193$	3.26220	+	2.37013i	0.234818	+	0.170605i	0.698972	−	0.715149i	$-0.253641\pi$
$193$	3.26220	+	2.37013i	0.234818	+	0.170605i	−0.464153	+	0.885755i	$0.653641\pi$
$194$	2.73345	−	8.41270i	0.196250	−	0.603996i
$195$	0.466012	+	1.43424i	0.0333718	+	0.102708i
$196$	0.301670	−	0.219176i	0.0215479	−	0.0156555i
$197$	11.4176			0.813469			0.406734	−	0.913547i	$-0.366667\pi$
$197$	11.4176			0.813469			0.406734	+	0.913547i	$0.366667\pi$
$198$		0			0
$199$	−7.16644			−0.508015			−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644			−0.508015			−0.254008	+	0.967202i	$0.581749\pi$
$200$	1.45650	−	1.05821i	0.102990	−	0.0748266i
$201$	0.730772	+	2.24908i	0.0515447	+	0.158638i
$202$	−1.04926	+	3.22930i	−0.0738260	+	0.227213i
$203$	6.54631	+	4.75617i	0.459461	+	0.333818i
$204$	−2.14294	−	1.55694i	−0.150036	−	0.109007i
$205$	0.683053	−	2.10222i	0.0477065	−	0.146825i
$206$	1.11029	+	3.41713i	0.0773577	+	0.238083i
$207$	6.49424	−	4.71834i	0.451381	−	0.327947i
$208$	−12.5342			−0.869090
$209$		0			0
$210$	−0.414031			−0.0285709
$211$	−2.81829	+	2.04760i	−0.194019	+	0.140963i	−0.680554	−	0.732698i	$-0.738261\pi$
$211$	−2.81829	+	2.04760i	−0.194019	+	0.140963i	0.486535	+	0.873661i	$0.338261\pi$
$212$	3.46882	+	10.6759i	0.238239	+	0.733226i
$213$	0.119373	−	0.367393i	0.00817932	−	0.0251734i
$214$	−6.96128	−	5.05767i	−0.475864	−	0.345735i
$215$	−5.71747	−	4.15399i	−0.389928	−	0.283300i
$216$	1.05965	−	3.26127i	0.0721001	−	0.221901i
$217$	1.98010	+	6.09412i	0.134418	+	0.413696i
$218$	6.31884	−	4.59090i	0.427966	−	0.310935i
$219$	0.330084			0.0223050
$220$		0			0
$221$	21.5950			1.45264
$222$	1.32761	−	0.964566i	0.0891035	−	0.0647374i
$223$	3.25856	+	10.0288i	0.218210	+	0.671580i	0.998910	+	0.0466747i	$0.0148624\pi$
$223$	3.25856	+	10.0288i	0.218210	+	0.671580i	−0.780701	+	0.624905i	$0.785138\pi$
$224$	4.05115	−	12.4682i	0.270679	−	0.833064i
$225$	2.34261	+	1.70201i	0.156174	+	0.113467i
$226$	0.792984	+	0.576137i	0.0527485	+	0.0383241i
$227$	0.0667531	−	0.205445i	0.00443056	−	0.0136359i	−0.948817	−	0.315827i	$-0.897718\pi$
$227$	0.0667531	−	0.205445i	0.00443056	−	0.0136359i	0.953247	+	0.302191i	$0.0977181\pi$
$228$	0.767950	+	2.36351i	0.0508587	+	0.156527i
$229$	0.0612504	−	0.0445011i	0.00404754	−	0.00294071i	−0.585760	−	0.810485i	$-0.699204\pi$
$229$	0.0612504	−	0.0445011i	0.00404754	−	0.00294071i	0.589807	+	0.807544i	$0.299204\pi$
$230$	−1.32307			−0.0872407
$231$		0			0
$232$	5.42514			0.356178
$233$	−12.2324	+	8.88735i	−0.801370	+	0.582229i	−0.911316	−	0.411708i	$-0.864932\pi$
$233$	−12.2324	+	8.88735i	−0.801370	+	0.582229i	0.109946	+	0.993938i	$0.464932\pi$
$234$	1.99341	+	6.13508i	0.130313	+	0.401063i
$235$	−1.34798	+	4.14865i	−0.0879324	+	0.270628i
$236$	16.8428	+	12.2370i	1.09637	+	0.796560i
$237$	−0.915352	−	0.665042i	−0.0594585	−	0.0431991i
$238$	−1.83212	+	5.63868i	−0.118759	+	0.365501i
$239$	−7.15826	−	22.0309i	−0.463029	−	1.42506i	−0.861444	−	0.507853i	$-0.830439\pi$
$239$	−7.15826	−	22.0309i	−0.463029	−	1.42506i	0.398414	−	0.917206i	$-0.369561\pi$
$240$	0.701836	−	0.509914i	0.0453033	−	0.0329148i
$241$	−21.3349			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$242$		0			0
$243$	8.32179			0.533843
$244$	−5.71013	+	4.14865i	−0.365553	+	0.265590i
$245$	−0.0650188	−	0.200107i	−0.00415390	−	0.0127844i
$246$	−0.105319	+	0.324139i	−0.00671490	+	0.0206664i
$247$	−16.3911	−	11.9088i	−1.04294	−	0.757741i
$248$	3.47564	+	2.52520i	0.220704	+	0.160350i
$249$	1.10974	−	3.41544i	0.0703271	−	0.216445i
$250$	−0.147481	−	0.453901i	−0.00932755	−	0.0287072i
$251$	5.03359	−	3.65712i	0.317718	−	0.230835i	−0.417483	−	0.908685i	$-0.637088\pi$
$251$	5.03359	−	3.65712i	0.317718	−	0.230835i	0.735201	+	0.677849i	$0.237088\pi$
$252$	13.7797			0.868041
$253$		0			0
$254$	−0.0363991			−0.00228388
$255$	−1.20918	+	0.878523i	−0.0757219	+	0.0550152i
$256$	0.224971	+	0.692389i	0.0140607	+	0.0432743i
$257$	−4.41595	+	13.5909i	−0.275460	+	0.847778i	0.713638	+	0.700515i	$0.247046\pi$
$257$	−4.41595	+	13.5909i	−0.275460	+	0.847778i	−0.989097	+	0.147263i	$0.952954\pi$
$258$	0.881571	+	0.640499i	0.0548842	+	0.0398757i
$259$	23.1205	+	16.7980i	1.43664	+	1.04378i
$260$	−2.55633	+	7.86758i	−0.158537	+	0.487927i
$261$	2.69640	+	8.29865i	0.166903	+	0.513674i
$262$	4.43376	−	3.22131i	0.273919	−	0.199013i
$263$	4.13132			0.254748			0.127374	−	0.991855i	$-0.459345\pi$
$263$	4.13132			0.254748			0.127374	+	0.991855i	$0.459345\pi$
$264$		0			0
$265$	6.33404			0.389097
$266$	4.50015	−	3.26955i	0.275922	−	0.200469i
$267$	0.276519	+	0.851039i	0.0169227	+	0.0520827i
$268$	−4.00869	+	12.3375i	−0.244869	+	0.753631i
$269$	1.36234	+	0.989796i	0.0830632	+	0.0603489i	0.628542	−	0.777776i	$-0.283652\pi$
$269$	1.36234	+	0.989796i	0.0830632	+	0.0603489i	−0.545479	+	0.838125i	$0.683652\pi$
$270$	−0.735429	−	0.534320i	−0.0447568	−	0.0325177i
$271$	−5.69549	+	17.5289i	−0.345976	+	1.06481i	0.615083	+	0.788463i	$0.289123\pi$
$271$	−5.69549	+	17.5289i	−0.345976	+	1.06481i	−0.961059	+	0.276343i	$0.910877\pi$
$272$	−3.83883	−	11.8147i	−0.232763	−	0.716371i
$273$	3.27606	−	2.38020i	0.198276	−	0.144056i
$274$	−8.74784			−0.528476
$275$		0			0
$276$	−1.58725			−0.0955411
$277$	2.77286	−	2.01460i	0.166605	−	0.121046i	−0.501358	−	0.865240i	$-0.667166\pi$
$277$	2.77286	−	2.01460i	0.166605	−	0.121046i	0.667964	+	0.744194i	$0.267166\pi$
$278$	−3.41970	−	10.5248i	−0.205100	−	0.631234i
$279$	−2.13525	+	6.57164i	−0.127834	+	0.393434i
$280$	−3.91102	−	2.84152i	−0.233728	−	0.169813i
$281$	18.4632	+	13.4143i	1.10142	+	0.800229i	0.981291	−	0.192529i	$-0.0616691\pi$
$281$	18.4632	+	13.4143i	1.10142	+	0.800229i	0.120129	+	0.992758i	$0.461669\pi$
$282$	0.207843	−	0.639676i	0.0123769	−	0.0380921i
$283$	−8.99211	−	27.6749i	−0.534525	−	1.64510i	−0.744673	−	0.667430i	$-0.767394\pi$
$283$	−8.99211	−	27.6749i	−0.534525	−	1.64510i	0.210147	−	0.977670i	$-0.432606\pi$
$284$	1.71436	−	1.24556i	0.101729	−	0.0739102i
$285$	1.40227			0.0830634
$286$		0			0
$287$	−5.93542			−0.350357
$288$	11.4371	−	8.30955i	0.673938	−	0.489645i
$289$	1.36057	+	4.18739i	0.0800333	+	0.246317i
$290$	0.444423	−	1.36779i	0.0260974	−	0.0803196i
$291$	−4.84428	−	3.51958i	−0.283977	−	0.206321i
$292$	1.46488	+	1.06430i	0.0857256	+	0.0622833i
$293$	6.55535	−	20.1753i	0.382968	−	1.17865i	−0.554976	−	0.831866i	$-0.687273\pi$
$293$	6.55535	−	20.1753i	0.382968	−	1.17865i	0.937944	−	0.346787i	$-0.112727\pi$
$294$	0.0100252	+	0.0308543i	0.000584680	+	0.00179946i
$295$	9.50375	−	6.90488i	0.553330	−	0.402018i
$296$	19.1608			1.11370
$297$		0			0
$298$	6.99883			0.405432
$299$	10.4689	−	7.60613i	0.605434	−	0.439874i
$300$	−0.176929	−	0.544531i	−0.0102150	−	0.0314385i
$301$	−5.86420	+	18.0481i	−0.338007	+	1.04028i
$302$	2.90318	+	2.10928i	0.167059	+	0.121376i
$303$	1.85953	+	1.35103i	0.106827	+	0.0776146i
$304$	−3.60161	+	11.0846i	−0.206566	+	0.635746i
$305$	1.23070	+	3.78770i	0.0704697	+	0.216883i
$306$	−5.17239	+	3.75796i	−0.295686	+	0.214828i
$307$	−6.87520			−0.392388			−0.196194	−	0.980565i	$-0.562858\pi$
$307$	−6.87520			−0.392388			−0.196194	+	0.980565i	$0.562858\pi$
$308$		0			0
$309$	2.43219			0.138363
$310$	0.921378	−	0.669420i	0.0523307	−	0.0380205i
$311$	7.77415	+	23.9264i	0.440831	+	1.35674i	0.886991	+	0.461786i	$0.152791\pi$
$311$	7.77415	+	23.9264i	0.440831	+	1.35674i	−0.446160	+	0.894953i	$0.647209\pi$
$312$	0.838976	−	2.58210i	0.0474977	−	0.146183i
$313$	9.36788	+	6.80616i	0.529504	+	0.384707i	0.820172	−	0.572117i	$-0.193878\pi$
$313$	9.36788	+	6.80616i	0.529504	+	0.384707i	−0.290668	+	0.956824i	$0.593878\pi$
$314$	5.16690	+	3.75398i	0.291585	+	0.211849i
$315$	2.40273	−	7.39484i	0.135378	−	0.416652i
$316$	−1.91793	−	5.90279i	−0.107892	−	0.332058i
$317$	−16.7800	+	12.1914i	−0.942460	+	0.684737i	−0.949012	−	0.315241i	$-0.897915\pi$
$317$	−16.7800	+	12.1914i	−0.942460	+	0.684737i	0.00655133	+	0.999979i	$0.497915\pi$
$318$	−0.976639			−0.0547672
$319$		0			0
$320$	3.04036			0.169961
$321$	−4.71229	+	3.42368i	−0.263015	+	0.191091i
$322$	1.09786	+	3.37885i	0.0611811	+	0.188296i
$323$	6.20515	−	19.0975i	0.345264	−	1.06261i
$324$	11.5726	+	8.40799i	0.642923	+	0.467111i
$325$	3.77637	+	2.74369i	0.209475	+	0.152193i
$326$	−0.113854	+	0.350407i	−0.00630580	+	0.0194073i
$327$	−1.63382	−	5.02839i	−0.0903506	−	0.278071i
$328$	−3.21945	+	2.33907i	−0.177764	+	0.129153i
$329$	11.7133			0.645777
$330$		0			0
$331$	−32.1415			−1.76665			−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415			−1.76665			−0.883327	+	0.468757i	$0.844702\pi$
$332$	15.9374	−	11.5792i	0.874679	−	0.635492i
$333$	9.52324	+	29.3095i	0.521871	+	1.60615i
$334$	−1.25098	+	3.85013i	−0.0684508	+	0.210670i
$335$	5.92187	+	4.30249i	0.323546	+	0.235070i
$336$	−1.88458	−	1.36923i	−0.102812	−	0.0746976i
$337$	−5.56119	+	17.1156i	−0.302937	+	0.932345i	0.677502	+	0.735521i	$0.263063\pi$
$337$	−5.56119	+	17.1156i	−0.302937	+	0.932345i	−0.980439	+	0.196824i	$0.936937\pi$
$338$	1.29619	+	3.98925i	0.0705032	+	0.216987i
$339$	0.536794	−	0.390004i	0.0291547	−	0.0211821i
$340$	−8.19888			−0.444647
$341$		0			0
$342$	5.99834			0.324353
$343$	14.7496	−	10.7162i	0.796406	−	0.578622i
$344$	3.93171	+	12.1006i	0.211983	+	0.652418i
$345$	−0.276763	+	0.851790i	−0.0149004	+	0.0458588i
$346$	−1.96095	−	1.42471i	−0.105421	−	0.0765930i
$347$	6.51244	+	4.73156i	0.349606	+	0.254004i	0.748704	−	0.662905i	$-0.230677\pi$
$347$	6.51244	+	4.73156i	0.349606	+	0.254004i	−0.399098	+	0.916908i	$0.630677\pi$
$348$	0.533160	−	1.64090i	0.0285804	−	0.0879614i
$349$	5.94220	+	18.2882i	0.318079	+	0.978946i	0.974469	+	0.224524i	$0.0720826\pi$
$349$	5.94220	+	18.2882i	0.318079	+	0.978946i	−0.656390	+	0.754422i	$0.727917\pi$
$350$	−1.03679	+	0.753275i	−0.0554190	+	0.0402642i
$351$	8.89088			0.474560
$352$		0			0
$353$	14.8497			0.790371			0.395186	−	0.918601i	$-0.370680\pi$
$353$	14.8497			0.790371			0.395186	+	0.918601i	$0.370680\pi$
$354$	−1.46537	+	1.06466i	−0.0778837	+	0.0565858i
$355$	−0.369495	−	1.13719i	−0.0196108	−	0.0603558i
$356$	−1.51686	+	4.66842i	−0.0803934	+	0.247426i
$357$	3.24692	+	2.35903i	0.171845	+	0.124853i
$358$	4.36964	+	3.17473i	0.230943	+	0.167790i
$359$	3.15916	−	9.72290i	0.166734	−	0.513155i	−0.832426	−	0.554137i	$-0.813048\pi$
$359$	3.15916	−	9.72290i	0.166734	−	0.513155i	0.999160	+	0.0409816i	$0.0130485\pi$
$360$	−1.61093	−	4.95794i	−0.0849035	−	0.261306i
$361$	0.129892	−	0.0943721i	0.00683642	−	0.00496695i
$362$	3.53175			0.185625
$363$		0			0
$364$	22.2134			1.16430
$365$	0.826577	−	0.600544i	0.0432650	−	0.0314339i
$366$	−0.189760	−	0.584022i	−0.00991893	−	0.0305273i
$367$	4.37055	−	13.4512i	0.228141	−	0.702145i	−0.769817	−	0.638265i	$-0.779653\pi$
$367$	4.37055	−	13.4512i	0.228141	−	0.702145i	0.997958	−	0.0638800i	$-0.0203475\pi$
$368$	−6.02234	−	4.37549i	−0.313936	−	0.228088i
$369$	−5.17812	−	3.76212i	−0.269562	−	0.195848i
$370$	1.56963	−	4.83083i	0.0816012	−	0.251143i
$371$	−5.25585	−	16.1758i	−0.272870	−	0.839808i
$372$	1.10535	−	0.803083i	0.0573096	−	0.0416379i
$373$	12.4600			0.645154			0.322577	−	0.946543i	$-0.395451\pi$
$373$	12.4600			0.645154			0.322577	+	0.946543i	$0.395451\pi$
$374$		0			0
$375$	−0.323071			−0.0166833
$376$	6.35346	−	4.61606i	0.327655	−	0.238055i
$377$	4.34668	+	13.3777i	0.223866	+	0.688987i
$378$	−0.754302	+	2.32150i	−0.0387971	+	0.119405i
$379$	−13.2169	−	9.60263i	−0.678906	−	0.493254i	0.194089	−	0.980984i	$-0.437825\pi$
$379$	−13.2169	−	9.60263i	−0.678906	−	0.493254i	−0.872995	+	0.487730i	$0.837825\pi$
$380$	6.22315	+	4.52138i	0.319241	+	0.231942i
$381$	−0.00761405	+	0.0234336i	−0.000390080	+	0.00120054i
$382$	−0.760426	−	2.34035i	−0.0389068	−	0.119743i
$383$	0.657446	−	0.477662i	0.0335939	−	0.0244074i	−0.570862	−	0.821046i	$-0.693391\pi$
$383$	0.657446	−	0.477662i	0.0335939	−	0.0244074i	0.604456	+	0.796639i	$0.293391\pi$
$384$	−3.62339			−0.184905
$385$		0			0
$386$	−1.92445			−0.0979522
$387$	−16.5557	+	12.0284i	−0.841571	+	0.611437i
$388$	−10.1502	−	31.2391i	−0.515298	−	1.58592i
$389$	−9.39230	+	28.9065i	−0.476208	+	1.46562i	0.368113	+	0.929781i	$0.380004\pi$
$389$	−9.39230	+	28.9065i	−0.476208	+	1.46562i	−0.844321	+	0.535837i	$0.819996\pi$
$390$	−0.582274	−	0.423047i	−0.0294846	−	0.0214218i
$391$	10.3758	+	7.53847i	0.524727	+	0.381237i
$392$	−0.117055	+	0.360259i	−0.00591219	+	0.0181958i
$393$	−1.14641	−	3.52829i	−0.0578287	−	0.177978i
$394$	−4.40846	+	3.20293i	−0.222095	+	0.161361i
$395$	−3.50213			−0.176211
$396$		0			0
$397$	−14.8996			−0.747789			−0.373894	−	0.927471i	$-0.621978\pi$
$397$	−14.8996			−0.747789			−0.373894	+	0.927471i	$0.621978\pi$
$398$	2.76704	−	2.01037i	0.138699	−	0.100771i
$399$	−1.16357	−	3.58112i	−0.0582516	−	0.179280i
$400$	0.829779	−	2.55380i	0.0414889	−	0.127690i
$401$	−9.84508	−	7.15287i	−0.491640	−	0.357197i	0.314175	−	0.949365i	$-0.398272\pi$
$401$	−9.84508	−	7.15287i	−0.491640	−	0.357197i	−0.805815	+	0.592168i	$0.798272\pi$
$402$	−0.913087	−	0.663396i	−0.0455406	−	0.0330872i
$403$	−3.44210	+	10.5937i	−0.171463	+	0.527710i
$404$	3.89626	+	11.9915i	0.193846	+	0.596598i
$405$	6.53000	−	4.74432i	0.324478	−	0.235747i
$406$	−3.86184			−0.191660
$407$		0			0
$408$	2.69083			0.133216
$409$	0.212050	−	0.154063i	0.0104852	−	0.00761793i	−0.582530	−	0.812809i	$-0.697937\pi$
$409$	0.212050	−	0.154063i	0.0104852	−	0.00761793i	0.593016	+	0.805191i	$0.297937\pi$
$410$	0.325994	+	1.00331i	0.0160997	+	0.0495497i
$411$	−1.82990	+	5.63184i	−0.0902621	+	0.277798i
$412$	10.7938	+	7.84218i	0.531774	+	0.386357i
$413$	−25.5197	−	18.5411i	−1.25574	−	0.912349i
$414$	−1.18388	+	3.64361i	−0.0581846	+	0.179074i
$415$	−3.43498	−	10.5718i	−0.168617	−	0.518949i
$416$	18.4370	−	13.3953i	0.903949	−	0.656758i
$417$	−7.49116			−0.366844
$418$		0			0
$419$	−1.26916			−0.0620023			−0.0310012	−	0.999519i	$-0.509870\pi$
$419$	−1.26916			−0.0620023			−0.0310012	+	0.999519i	$0.509870\pi$
$420$	−1.24381	+	0.903681i	−0.0606917	+	0.0440951i
$421$	−9.16714	−	28.2135i	−0.446779	−	1.37504i	−0.880521	−	0.474007i	$-0.842807\pi$
$421$	−9.16714	−	28.2135i	−0.446779	−	1.37504i	0.433742	−	0.901037i	$-0.357193\pi$
$422$	0.513765	−	1.58121i	0.0250097	−	0.0769720i
$423$	10.2188	+	7.42440i	0.496856	+	0.360987i
$424$	−9.22552	−	6.70273i	−0.448031	−	0.325513i
$425$	−1.42961	+	4.39990i	−0.0693464	+	0.213426i
$426$	0.0569721	+	0.175342i	0.00276031	+	0.00849535i
$427$	8.65182	−	6.28591i	0.418691	−	0.304197i
$428$	−31.9518			−1.54445
$429$		0			0
$430$	3.37289			0.162655
$431$	−25.3666	+	18.4299i	−1.22187	+	0.887739i	−0.996254	−	0.0864778i	$-0.972439\pi$
$431$	−25.3666	+	18.4299i	−1.22187	+	0.887739i	−0.225614	+	0.974217i	$0.572439\pi$
$432$	−1.58048	−	4.86423i	−0.0760411	−	0.234030i
$433$	−8.04449	+	24.7584i	−0.386594	+	1.18981i	0.548724	+	0.836003i	$0.315114\pi$
$433$	−8.04449	+	24.7584i	−0.386594	+	1.18981i	−0.935318	+	0.353809i	$0.884886\pi$
$434$	−2.47410	−	1.79754i	−0.118761	−	0.0862847i
$435$	−0.787616	−	0.572237i	−0.0377633	−	0.0274367i
$436$	8.96242	−	27.5835i	0.429222	−	1.32101i
$437$	−3.71830	−	11.4438i	−0.177870	−	0.547429i
$438$	−0.127449	+	0.0925972i	−0.00608975	+	0.00442446i
$439$	14.4191			0.688185			0.344093	−	0.938936i	$-0.388187\pi$
$439$	14.4191			0.688185			0.344093	+	0.938936i	$0.388187\pi$
$440$		0			0
$441$	−0.609255			−0.0290121
$442$	−8.33807	+	6.05796i	−0.396602	+	0.288148i
$443$	−0.102163	−	0.314427i	−0.00485393	−	0.0149389i	0.948600	−	0.316477i	$-0.102500\pi$
$443$	−0.102163	−	0.314427i	−0.00485393	−	0.0149389i	−0.953454	+	0.301538i	$0.902500\pi$
$444$	1.88304	−	5.79539i	0.0893650	−	0.275037i
$445$	2.24080	+	1.62803i	0.106224	+	0.0771762i
$446$	−4.07152	−	2.95813i	−0.192792	−	0.140072i
$447$	1.46403	−	4.50583i	0.0692464	−	0.213119i
$448$	−2.52282	−	7.76445i	−0.119192	−	0.366836i
$449$	−6.88334	+	5.00104i	−0.324845	+	0.236014i	−0.738240	−	0.674538i	$-0.764343\pi$
$449$	−6.88334	+	5.00104i	−0.324845	+	0.236014i	0.413395	+	0.910552i	$0.364343\pi$
$450$	−1.38197			−0.0651465
$451$		0			0
$452$	3.63974			0.171199
$453$	1.96525	−	1.42783i	0.0923353	−	0.0670855i
$454$	0.0318586	+	0.0980507i	0.00149520	+	0.00460175i
$455$	3.87328	−	11.9207i	0.181582	−	0.558852i
$456$	−2.04241	−	1.48390i	−0.0956444	−	0.0694898i
$457$	−0.921044	−	0.669177i	−0.0430846	−	0.0313028i	0.566035	−	0.824382i	$-0.308477\pi$
$457$	−0.921044	−	0.669177i	−0.0430846	−	0.0313028i	−0.609119	+	0.793079i	$0.708477\pi$
$458$	−0.0111658	+	0.0343647i	−0.000521743	+	0.00160576i
$459$	2.72299	+	8.38051i	0.127098	+	0.391169i
$460$	−3.97470	+	2.88779i	−0.185321	+	0.134644i
$461$	14.5073			0.675670			0.337835	−	0.941205i	$-0.390305\pi$
$461$	14.5073			0.675670			0.337835	+	0.941205i	$0.390305\pi$
$462$		0			0
$463$	−4.89739			−0.227601			−0.113801	−	0.993504i	$-0.536302\pi$
$463$	−4.89739			−0.227601			−0.113801	+	0.993504i	$0.536302\pi$
$464$	6.54631	−	4.75617i	0.303905	−	0.220800i
$465$	−0.238235	−	0.733212i	−0.0110479	−	0.0340019i
$466$	2.22993	−	6.86301i	0.103299	−	0.317923i
$467$	−26.2308	−	19.0578i	−1.21382	−	0.881889i	−0.218245	−	0.975894i	$-0.570033\pi$
$467$	−26.2308	−	19.0578i	−1.21382	−	0.881889i	−0.995572	+	0.0940049i	$0.970033\pi$
$468$	19.3792	+	14.0798i	0.895802	+	0.650838i
$469$	6.07384	−	18.6934i	0.280464	−	0.863179i
$470$	−0.643336	−	1.97998i	−0.0296749	−	0.0913299i
$471$	3.49763	−	2.54117i	0.161162	−	0.117091i
$472$	−21.1490			−0.973461
$473$		0			0
$474$	0.539990			0.0248026
$475$	3.51149	−	2.55125i	0.161118	−	0.117059i
$476$	6.80325	+	20.9383i	0.311827	+	0.959704i
$477$	5.66768	−	17.4433i	0.259505	−	0.798675i
$478$	8.94413	+	6.49829i	0.409095	+	0.297225i
$479$	−14.3482	−	10.4246i	−0.655588	−	0.476313i	0.209582	−	0.977791i	$-0.432790\pi$
$479$	−14.3482	−	10.4246i	−0.655588	−	0.476313i	−0.865170	+	0.501478i	$0.832790\pi$
$480$	−0.487413	+	1.50010i	−0.0222472	+	0.0684700i
$481$	15.3518	+	47.2480i	0.699982	+	2.15432i
$482$	8.23765	−	5.98500i	0.375215	−	0.272609i
$483$	2.40495			0.109429
$484$		0			0
$485$	−18.5342			−0.841595
$486$	−3.21314	+	2.33448i	−0.145751	+	0.105894i
$487$	−5.70454	−	17.5568i	−0.258497	−	0.795573i	−0.993120	−	0.117097i	$-0.962641\pi$
$487$	−5.70454	−	17.5568i	−0.258497	−	0.795573i	0.734623	−	0.678475i	$-0.237359\pi$
$488$	2.21567	−	6.81912i	0.100299	−	0.308687i
$489$	0.201775	+	0.146598i	0.00912458	+	0.00662940i
$490$	0.0812399	+	0.0590242i	0.00367004	+	0.00266644i
$491$	−3.53325	+	10.8742i	−0.159453	+	0.490747i	−0.998585	−	0.0531814i	$-0.983064\pi$
$491$	−3.53325	+	10.8742i	−0.159453	+	0.490747i	0.839131	+	0.543929i	$0.183064\pi$
$492$	0.391085	+	1.20363i	0.0176315	+	0.0542640i
$493$	−11.2785	+	8.19434i	−0.507960	+	0.369054i
$494$	9.66954			0.435053
$495$		0			0
$496$	6.40774			0.287716
$497$	−2.59755	+	1.88723i	−0.116516	+	0.0846539i
$498$	0.529636	+	1.63005i	0.0237336	+	0.0730444i
$499$	3.36258	−	10.3490i	0.150530	−	0.463283i	−0.847151	−	0.531353i	$-0.821684\pi$
$499$	3.36258	−	10.3490i	0.150530	−	0.463283i	0.997681	+	0.0680695i	$0.0216839\pi$
$500$	−1.43376	−	1.04169i	−0.0641196	−	0.0465856i
$501$	2.21702	+	1.61076i	0.0990493	+	0.0719635i
$502$	−0.917609	+	2.82411i	−0.0409549	+	0.126046i
$503$	13.8207	+	42.5357i	0.616234	+	1.89657i	0.380652	+	0.924718i	$0.375699\pi$
$503$	13.8207	+	42.5357i	0.616234	+	1.89657i	0.235582	+	0.971855i	$0.424301\pi$
$504$	−11.3248	+	8.22798i	−0.504449	+	0.366503i
$505$	7.11455			0.316594
$506$		0			0
$507$	2.83941			0.126103
$508$	−0.109348	+	0.0794460i	−0.00485154	+	0.00352485i
$509$	−4.26732	−	13.1335i	−0.189146	−	0.582131i	0.810849	−	0.585255i	$-0.199006\pi$
$509$	−4.26732	−	13.1335i	−0.189146	−	0.582131i	−0.999995	+	0.00312421i	$0.999006\pi$
$510$	0.220430	−	0.678415i	0.00976083	−	0.0300407i
$511$	−2.21954	−	1.61259i	−0.0981868	−	0.0713368i
$512$	−18.4281	−	13.3888i	−0.814414	−	0.591707i
$513$	2.55473	−	7.86264i	0.112794	−	0.347144i
$514$	−2.10756	−	6.48640i	−0.0929604	−	0.286103i
$515$	6.09056	−	4.42505i	0.268382	−	0.194991i
$516$	4.04635			0.178130
$517$		0			0
$518$	−13.6394			−0.599281
$519$	−1.32742	+	0.964429i	−0.0582674	+	0.0423337i
$520$	−2.59688	−	7.99237i	−0.113881	−	0.350488i
$521$	−1.12783	+	3.47109i	−0.0494110	+	0.152071i	−0.972718	−	0.231992i	$-0.925476\pi$
$521$	−1.12783	+	3.47109i	−0.0494110	+	0.152071i	0.923307	+	0.384063i	$0.125476\pi$
$522$	−3.36910	−	2.44779i	−0.147462	−	0.107137i
$523$	4.03463	+	2.93133i	0.176422	+	0.128178i	0.672492	−	0.740105i	$-0.265224\pi$
$523$	4.03463	+	2.93133i	0.176422	+	0.128178i	−0.496070	+	0.868283i	$0.665224\pi$
$524$	6.28869	−	19.3546i	0.274723	−	0.845509i
$525$	0.268077	+	0.825058i	0.0116999	+	0.0360085i
$526$	−1.59515	+	1.15894i	−0.0695518	+	0.0505323i
$527$	−11.0398			−0.480901
$528$		0			0
$529$	−15.3148			−0.665860
$530$	−2.44565	+	1.77687i	−0.106232	+	0.0771821i
$531$	−10.5114	−	32.3509i	−0.456157	−	1.40391i
$532$	6.38285	−	19.6444i	0.276732	−	0.851692i
$533$	−8.34730	−	6.06467i	−0.361562	−	0.262690i
$534$	−0.345506	−	0.251025i	−0.0149515	−	0.0108629i
$535$	−5.57133	+	17.1468i	−0.240870	+	0.741321i
$536$	−4.07227	−	12.5331i	−0.175895	−	0.541349i
$537$	2.95794	−	2.14907i	0.127644	−	0.0927391i
$538$	−0.803678			−0.0346490
$539$		0			0
$540$	−3.37556			−0.145261
$541$	−0.200308	+	0.145532i	−0.00861192	+	0.00625692i	−0.592083	−	0.805877i	$-0.701694\pi$
$541$	−0.200308	+	0.145532i	−0.00861192	+	0.00625692i	0.583471	+	0.812134i	$0.301694\pi$
$542$	−2.71823	−	8.36585i	−0.116758	−	0.359344i
$543$	0.738781	−	2.27373i	0.0317041	−	0.0975753i
$544$	18.2730	+	13.2761i	0.783449	+	0.569209i
$545$	−13.2398	−	9.61929i	−0.567132	−	0.412045i
$546$	−0.597217	+	1.83804i	−0.0255585	+	0.0786610i
$547$	−7.82185	−	24.0732i	−0.334438	−	1.02929i	−0.966998	−	0.254783i	$-0.917996\pi$
$547$	−7.82185	−	24.0732i	−0.334438	−	1.02929i	0.632560	−	0.774511i	$-0.282004\pi$
$548$	−26.2798	+	19.0934i	−1.12262	+	0.815629i
$549$	11.5322			0.492182
$550$		0			0
$551$	13.0796			0.557208
$552$	1.30448	−	0.947758i	0.0555222	−	0.0403392i
$553$	2.90599	+	8.94373i	0.123575	+	0.380326i
$554$	−0.505485	+	1.55572i	−0.0214760	+	0.0660963i
$555$	−2.78174	−	2.02105i	−0.118078	−	0.0857888i
$556$	−33.2451	−	24.1540i	−1.40990	−	1.02436i
$557$	−11.9488	+	36.7746i	−0.506287	+	1.55819i	0.292309	+	0.956324i	$0.405576\pi$
$557$	−11.9488	+	36.7746i	−0.506287	+	1.55819i	−0.798596	+	0.601867i	$0.794424\pi$
$558$	−1.01907	−	3.13638i	−0.0431407	−	0.132774i
$559$	−26.6883	+	19.3902i	−1.12879	+	0.820117i
$560$	−7.21041			−0.304695
$561$		0			0
$562$	−10.8919			−0.459447
$563$	−11.2746	+	8.19150i	−0.475169	+	0.345231i	−0.799452	−	0.600729i	$-0.794877\pi$
$563$	−11.2746	+	8.19150i	−0.475169	+	0.345231i	0.324283	+	0.945960i	$0.394877\pi$
$564$	−0.771790	−	2.37533i	−0.0324982	−	0.100019i
$565$	0.634650	−	1.95325i	0.0266999	−	0.0821739i
$566$	11.2355	+	8.16306i	0.472263	+	0.343119i
$567$	−17.5345	−	12.7395i	−0.736379	−	0.535011i
$568$	−0.665214	+	2.04732i	−0.0279118	+	0.0859036i
$569$	8.62543	+	26.5463i	0.361597	+	1.11288i	0.952085	+	0.305834i	$0.0989352\pi$
$569$	8.62543	+	26.5463i	0.361597	+	1.11288i	−0.590488	+	0.807046i	$0.701065\pi$
$570$	−0.541433	+	0.393374i	−0.0226781	+	0.0164766i
$571$	−31.4113			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$571$	−31.4113			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$572$		0			0
$573$	−1.66578			−0.0695889
$574$	2.29174	−	1.66504i	0.0956552	−	0.0694976i
$575$	0.856664	+	2.63654i	0.0357254	+	0.109951i
$576$	2.72050	−	8.37285i	0.113354	−	0.348869i
$577$	−16.7749	−	12.1877i	−0.698348	−	0.507380i	0.181045	−	0.983475i	$-0.442052\pi$
$577$	−16.7749	−	12.1877i	−0.698348	−	0.507380i	−0.879394	+	0.476095i	$0.842052\pi$
$578$	−1.70000	−	1.23512i	−0.0707108	−	0.0513744i
$579$	−0.402562	+	1.23896i	−0.0167299	+	0.0514894i
$580$	−1.65029	−	5.07906i	−0.0685245	−	0.210897i
$581$	−24.1479	+	17.5445i	−1.00182	+	0.727868i
$582$	2.85777			0.118458
$583$		0			0
$584$	−1.83941			−0.0761153
$585$	10.9349	−	7.94470i	0.452104	−	0.328473i
$586$	3.12861	+	9.62887i	0.129242	+	0.397765i
$587$	4.70840	−	14.4910i	0.194336	−	0.598106i	−0.805647	−	0.592396i	$-0.798182\pi$
$587$	4.70840	−	14.4910i	0.194336	−	0.598106i	0.999984	−	0.00571050i	$-0.00181772\pi$
$588$	0.0974610	+	0.0708095i	0.00401922	+	0.00292014i
$589$	8.37947	+	6.08804i	0.345270	+	0.250853i
$590$	−1.73251	+	5.33211i	−0.0713261	+	0.219519i
$591$	1.13987	+	3.50815i	0.0468879	+	0.144306i
$592$	23.1205	−	16.7980i	0.950248	−	0.690395i
$593$	27.5413			1.13098			0.565492	−	0.824754i	$-0.308686\pi$
$593$	27.5413			1.13098			0.565492	+	0.824754i	$0.308686\pi$
$594$		0			0
$595$	12.4227			0.509281
$596$	21.0255	−	15.2759i	0.861239	−	0.625726i
$597$	−0.715457	−	2.20195i	−0.0292817	−	0.0901199i
$598$	−1.90846	+	5.87362i	−0.0780426	+	0.240190i
$599$	21.6275	+	15.7133i	0.883676	+	0.642028i	0.934222	−	0.356693i	$-0.116096\pi$
$599$	21.6275	+	15.7133i	0.883676	+	0.642028i	−0.0505453	+	0.998722i	$0.516096\pi$
$600$	0.470553	+	0.341876i	0.0192102	+	0.0139570i
$601$	0.743741	−	2.28900i	0.0303378	−	0.0933702i	−0.934741	−	0.355330i	$-0.884369\pi$
$601$	0.743741	−	2.28900i	0.0303378	−	0.0933702i	0.965079	+	0.261959i	$0.0843686\pi$
$602$	−2.79875	−	8.61366i	−0.114068	−	0.351067i
$603$	17.1475	−	12.4584i	0.698301	−	0.507345i
$604$	13.3254			0.542202
$605$		0			0
$606$	−1.09699			−0.0445620
$607$	−8.32710	+	6.04999i	−0.337987	+	0.245562i	−0.743812	−	0.668389i	$-0.766984\pi$
$607$	−8.32710	+	6.04999i	−0.337987	+	0.245562i	0.405825	+	0.913951i	$0.366984\pi$
$608$	−6.54837	−	20.1538i	−0.265571	−	0.817344i
$609$	−0.807829	+	2.48624i	−0.0327349	+	0.100748i
$610$	−1.53774	−	1.11723i	−0.0622612	−	0.0452354i
$611$	16.4731	+	11.9684i	0.666429	+	0.484189i
$612$	−7.33634	+	22.5789i	−0.296554	+	0.912699i
$613$	8.61404	+	26.5113i	0.347918	+	1.07078i	0.960003	+	0.279989i	$0.0903310\pi$
$613$	8.61404	+	26.5113i	0.347918	+	1.07078i	−0.612085	+	0.790792i	$0.709669\pi$
$614$	2.65459	−	1.92867i	0.107131	−	0.0778350i
$615$	0.714118			0.0287960
$616$		0			0
$617$	−28.7216			−1.15629			−0.578143	−	0.815935i	$-0.696222\pi$
$617$	−28.7216			−1.15629			−0.578143	+	0.815935i	$0.696222\pi$
$618$	−0.939098	+	0.682294i	−0.0377760	+	0.0274459i
$619$	7.01370	+	21.5859i	0.281904	+	0.867612i	0.987310	+	0.158808i	$0.0507650\pi$
$619$	7.01370	+	21.5859i	0.281904	+	0.867612i	−0.705405	+	0.708804i	$0.749235\pi$
$620$	1.30685	−	4.02207i	0.0524844	−	0.161530i
$621$	4.27183	+	3.10366i	0.171423	+	0.124546i
$622$	−9.71366	−	7.05739i	−0.389482	−	0.282976i
$623$	2.29830	−	7.07345i	0.0920795	−	0.283392i
$624$	−1.25134	−	3.85124i	−0.0500939	−	0.154173i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−5.52635			−0.220877
$627$		0			0
$628$	23.7157			0.946360
$629$	−39.8340	+	28.9411i	−1.58829	+	1.15396i
$630$	1.14673	+	3.52926i	0.0456866	+	0.140609i
$631$	8.81823	−	27.1397i	0.351048	−	1.08042i	−0.607217	−	0.794536i	$-0.707714\pi$
$631$	8.81823	−	27.1397i	0.351048	−	1.08042i	0.958266	−	0.285880i	$-0.0922857\pi$
$632$	5.10085	+	3.70598i	0.202901	+	0.147416i
$633$	−0.910507	−	0.661522i	−0.0361894	−	0.0262931i
$634$	3.05895	−	9.41448i	0.121486	−	0.373897i
$635$	0.0235677	+	0.0725340i	0.000935256	+	0.00287842i
$636$	−2.93396	+	2.13165i	−0.116339	+	0.0845254i
$637$	−0.982140			−0.0389138
$638$		0			0
$639$	−3.46233			−0.136968
$640$	−9.07350	+	6.59228i	−0.358662	+	0.260583i
$641$	0.733529	+	2.25757i	0.0289727	+	0.0891687i	0.964497	−	0.264093i	$-0.0850726\pi$
$641$	0.733529	+	2.25757i	0.0289727	+	0.0891687i	−0.935525	+	0.353262i	$0.885073\pi$
$642$	0.859037	−	2.64385i	0.0339035	−	0.104344i
$643$	−9.19069	−	6.67742i	−0.362445	−	0.263332i	0.391626	−	0.920124i	$-0.371913\pi$
$643$	−9.19069	−	6.67742i	−0.362445	−	0.263332i	−0.754071	+	0.656793i	$0.771913\pi$
$644$	10.6729	+	7.75434i	0.420573	+	0.305564i
$645$	0.705549	−	2.17146i	0.0277810	−	0.0855010i
$646$	2.96147	+	9.11447i	0.116518	+	0.358604i
$647$	39.1742	−	28.4617i	1.54010	−	1.11895i	0.589821	−	0.807534i	$-0.299198\pi$
$647$	39.1742	−	28.4617i	1.54010	−	1.11895i	0.950275	−	0.311411i	$-0.100802\pi$
$648$	−14.5314			−0.570848
$649$		0			0
$650$	−2.22778			−0.0873806
$651$	−1.67479	+	1.21681i	−0.0656402	+	0.0476904i
$652$	0.422778	+	1.30118i	0.0165573	+	0.0509580i
$653$	9.19474	−	28.2985i	0.359818	−	1.10741i	−0.593345	−	0.804949i	$-0.702193\pi$
$653$	9.19474	−	28.2985i	0.359818	−	1.10741i	0.953163	−	0.302458i	$-0.0978071\pi$
$654$	2.04143	+	1.48319i	0.0798264	+	0.0579972i
$655$	−9.29003	−	6.74960i	−0.362991	−	0.263729i
$656$	−1.83415	+	5.64492i	−0.0716114	+	0.220397i
$657$	−0.914220	−	2.81368i	−0.0356671	−	0.109772i
$658$	−4.52265	+	3.28590i	−0.176311	+	0.128098i
$659$	−28.4931			−1.10993			−0.554966	−	0.831873i	$-0.687269\pi$
$659$	−28.4931			−1.10993			−0.554966	+	0.831873i	$0.687269\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$	12.4102	−	9.01653i	0.482336	−	0.350437i
$663$	2.15592	+	6.63525i	0.0837291	+	0.257692i
$664$	−6.18410	+	19.0327i	−0.239990	+	0.738613i
$665$	−9.42913	−	6.85066i	−0.365646	−	0.265657i
$666$	−11.8991	−	8.64522i	−0.461082	−	0.334996i
$667$	−2.58148	+	7.94499i	−0.0999555	+	0.307631i
$668$	4.64531	+	14.2968i	0.179733	+	0.553160i
$669$	−2.75613	+	2.00245i	−0.106558	+	0.0774190i
$670$	−3.49346			−0.134964
$671$		0			0
$672$	4.23540			0.163384
$673$	−10.5471	+	7.66291i	−0.406560	+	0.295383i	−0.772208	−	0.635370i	$-0.780848\pi$
$673$	−10.5471	+	7.66291i	−0.406560	+	0.295383i	0.365647	+	0.930753i	$0.380848\pi$
$674$	−2.65413	−	8.16858i	−0.102233	−	0.314642i
$675$	−0.588587	+	1.81148i	−0.0226547	+	0.0697240i
$676$	12.6010	+	9.15518i	0.484655	+	0.352122i
$677$	30.0197	+	21.8106i	1.15375	+	0.838250i	0.988975	−	0.148081i	$-0.0473096\pi$
$677$	30.0197	+	21.8106i	1.15375	+	0.838250i	0.164777	+	0.986331i	$0.447310\pi$
$678$	−0.0978560	+	0.301170i	−0.00375814	+	0.0115664i
$679$	15.3793	+	47.3326i	0.590203	+	1.81646i
$680$	6.73823	−	4.89561i	0.258400	−	0.187738i
$681$	0.0697890			0.00267432
$682$		0			0
$683$	−32.8992			−1.25885			−0.629426	−	0.777061i	$-0.716710\pi$
$683$	−32.8992			−1.25885			−0.629426	+	0.777061i	$0.716710\pi$
$684$	18.0199	−	13.0922i	0.689008	−	0.500594i
$685$	5.66406	+	17.4322i	0.216413	+	0.666050i
$686$	−2.68882	+	8.27532i	−0.102659	+	0.315953i
$687$	0.0197882	+	0.0143770i	0.000754969	+	0.000548517i
$688$	15.3527	+	11.1544i	0.585315	+	0.425256i
$689$	9.13650	−	28.1193i	0.348073	−	1.07126i
$690$	−0.132088	−	0.406525i	−0.00502851	−	0.0154762i
$691$	−29.6908	+	21.5716i	−1.12949	+	0.820623i	−0.985621	−	0.168973i	$-0.945955\pi$
$691$	−29.6908	+	21.5716i	−1.12949	+	0.820623i	−0.143871	+	0.989597i	$0.545955\pi$
$692$	−9.00061			−0.342152
$693$		0			0
$694$	−3.84185			−0.145835
$695$	−18.7590	+	13.6292i	−0.711568	+	0.516984i
$696$	0.541616	+	1.66692i	0.0205299	+	0.0631846i
$697$	3.16002	−	9.72555i	0.119694	−	0.368382i
$698$	−7.42468	−	5.39434i	−0.281028	−	0.204179i
$699$	−3.95193	−	2.87124i	−0.149476	−	0.108600i
$700$	−1.47055	+	4.52590i	−0.0555817	+	0.171063i
$701$	−11.2018	−	34.4755i	−0.423085	−	1.30212i	−0.904816	−	0.425802i	$-0.859992\pi$
$701$	−11.2018	−	34.4755i	−0.423085	−	1.30212i	0.481731	−	0.876319i	$-0.340008\pi$
$702$	−3.43287	+	2.49413i	−0.129565	+	0.0941347i
$703$	46.1949			1.74227
$704$		0			0
$705$	−1.40928			−0.0530767
$706$	−5.73365	+	4.16574i	−0.215789	+	0.156780i
$707$	−5.90350	−	18.1691i	−0.222024	−	0.683320i
$708$	−2.07843	+	6.39676i	−0.0781123	+	0.240405i
$709$	15.0487	+	10.9336i	0.565167	+	0.410618i	0.833347	−	0.552751i	$-0.186422\pi$
$709$	15.0487	+	10.9336i	0.565167	+	0.410618i	−0.268179	+	0.963369i	$0.586422\pi$
$710$	0.461678	+	0.335429i	0.0173265	+	0.0125884i
$711$	−3.13370	+	9.64453i	−0.117523	+	0.361698i
$712$	−1.54092	−	4.74246i	−0.0577484	−	0.177731i
$713$	−5.35193	+	3.88841i	−0.200432	+	0.145622i
$714$	−1.91544			−0.0716836
$715$		0			0
$716$	20.0563			0.749540
$717$	6.05454	−	4.39888i	0.226111	−	0.164279i
$718$	1.50774	+	4.64035i	0.0562684	+	0.173176i
$719$	−11.5659	+	35.5961i	−0.431335	+	1.32751i	0.465462	+	0.885068i	$0.345888\pi$
$719$	−11.5659	+	35.5961i	−0.431335	+	1.32751i	−0.896796	+	0.442444i	$0.854112\pi$
$720$	−6.29042	−	4.57026i	−0.234430	−	0.170324i
$721$	−16.3545	−	11.8822i	−0.609074	−	0.442518i
$722$	−0.0236789	+	0.0728763i	−0.000881239	+	0.00271217i
$723$	−2.12996	−	6.55534i	−0.0792140	−	0.243796i
$724$	10.6099	−	7.70854i	0.394314	−	0.286486i
$725$	−3.01341			−0.111915
$726$		0			0
$727$	14.6011			0.541526			0.270763	−	0.962646i	$-0.412724\pi$
$727$	14.6011			0.541526			0.270763	+	0.962646i	$0.412724\pi$
$728$	−18.2560	+	13.2638i	−0.676614	+	0.491589i
$729$	−6.65191	−	20.4725i	−0.246367	−	0.758240i
$730$	−0.150683	+	0.463754i	−0.00557702	+	0.0171643i
$731$	−26.4509	−	19.2177i	−0.978321	−	0.710792i
$732$	−1.84478	−	1.34031i	−0.0681849	−	0.0495392i
$733$	12.9283	−	39.7893i	0.477518	−	1.46965i	−0.365013	−	0.931002i	$-0.618936\pi$
$733$	12.9283	−	39.7893i	0.477518	−	1.46965i	0.842531	−	0.538647i	$-0.181064\pi$
$734$	2.08589	+	6.41970i	0.0769915	+	0.236955i
$735$	0.0549936	−	0.0399552i	0.00202847	−	0.00147377i
$736$	13.5346			0.498891
$737$		0			0
$738$	3.05470			0.112445
$739$	9.65149	−	7.01222i	0.355036	−	0.257949i	−0.395943	−	0.918275i	$-0.629582\pi$
$739$	9.65149	−	7.01222i	0.355036	−	0.257949i	0.750979	+	0.660327i	$0.229582\pi$
$740$	−5.82856	−	17.9385i	−0.214262	−	0.659431i
$741$	2.02270	−	6.22523i	0.0743057	−	0.228689i
$742$	6.56710	+	4.77127i	0.241086	+	0.175159i
$743$	−37.7651	−	27.4380i	−1.38547	−	1.00660i	−0.996345	−	0.0854162i	$-0.972778\pi$
$743$	−37.7651	−	27.4380i	−1.38547	−	1.00660i	−0.389123	−	0.921186i	$-0.627222\pi$
$744$	−0.428902	+	1.32002i	−0.0157243	+	0.0483944i
$745$	−4.53161	−	13.9469i	−0.166026	−	0.510974i
$746$	−4.81095	+	3.49536i	−0.176141	+	0.127974i
$747$	−32.1873			−1.17767
$748$		0			0
$749$	48.4124			1.76895
$750$	0.124741	−	0.0906300i	0.00455491	−	0.00330934i
$751$	4.45106	+	13.6989i	0.162421	+	0.499882i	0.998837	−	0.0482140i	$-0.0153529\pi$
$751$	4.45106	+	13.6989i	0.162421	+	0.499882i	−0.836416	+	0.548096i	$0.815353\pi$
$752$	3.61962	−	11.1400i	0.131994	−	0.406235i
$753$	1.62621	+	1.18151i	0.0592623	+	0.0430566i
$754$	−5.43111	−	3.94593i	−0.197789	−	0.143702i
$755$	2.32350	−	7.15101i	0.0845610	−	0.260252i
$756$	2.80097	+	8.62050i	0.101870	+	0.313525i
$757$	12.9941	−	9.44076i	0.472278	−	0.343130i	−0.326050	−	0.945352i	$-0.605718\pi$
$757$	12.9941	−	9.44076i	0.472278	−	0.343130i	0.798328	+	0.602222i	$0.205718\pi$
$758$	7.79698			0.283199
$759$		0			0
$760$	−7.81423			−0.283452
$761$	31.4578	−	22.8555i	1.14035	−	0.828510i	0.153178	−	0.988199i	$-0.451049\pi$
$761$	31.4578	−	22.8555i	1.14035	−	0.828510i	0.987167	+	0.159689i	$0.0510491\pi$
$762$	−0.00363388	−	0.0111839i	−0.000131642	−	0.000405151i
$763$	−13.5796	+	41.7937i	−0.491614	+	1.51303i
$764$	−7.39257	−	5.37102i	−0.267454	−	0.194317i
$765$	10.8377	+	7.87403i	0.391837	+	0.284686i
$766$	−0.119850	+	0.368862i	−0.00433037	+	0.0133275i
$767$	−16.9448	−	52.1507i	−0.611841	−	1.88305i
$768$	−0.190283	+	0.138249i	−0.00686624	+	0.00498862i
$769$	43.0017			1.55068			0.775341	−	0.631543i	$-0.217578\pi$
$769$	43.0017			1.55068			0.775341	+	0.631543i	$0.217578\pi$
$770$		0			0
$771$	−4.61679			−0.166270
$772$	−5.78134	+	4.20039i	−0.208075	+	0.151175i
$773$	−2.42721	−	7.47019i	−0.0873007	−	0.268684i	0.897870	−	0.440261i	$-0.145114\pi$
$773$	−2.42721	−	7.47019i	−0.0873007	−	0.268684i	−0.985171	+	0.171576i	$0.945114\pi$
$774$	3.01805	−	9.28860i	0.108482	−	0.333872i
$775$	−1.93056	−	1.40263i	−0.0693477	−	0.0503840i
$776$	26.9950	+	19.6130i	0.969065	+	0.704067i
$777$	−2.85312	+	8.78101i	−0.102355	+	0.315017i
$778$	−4.48257	−	13.7959i	−0.160708	−	0.494608i
$779$	−7.76182	+	5.63929i	−0.278096	+	0.202049i
$780$	−2.67259			−0.0956942
$781$		0			0
$782$	−6.12096			−0.218885
$783$	−4.64349	+	3.37369i	−0.165945	+	0.120566i
$784$	0.174590	+	0.537332i	0.00623535	+	0.0191904i
$785$	4.13523	−	12.7269i	0.147593	−	0.454244i
$786$	1.43242	+	1.04071i	0.0510927	+	0.0371210i
$787$	9.24293	+	6.71538i	0.329475	+	0.239377i	0.740208	−	0.672378i	$-0.234727\pi$
$787$	9.24293	+	6.71538i	0.329475	+	0.239377i	−0.410733	+	0.911756i	$0.634727\pi$
$788$	−6.25280	+	19.2441i	−0.222747	+	0.685544i
$789$	0.412448	+	1.26938i	0.0146835	+	0.0451912i
$790$	1.35221	−	0.982441i	0.0481096	−	0.0349537i
$791$	−5.51483			−0.196085
$792$		0			0
$793$	18.5903			0.660161
$794$	5.75290	−	4.17973i	0.204163	−	0.148333i
$795$	0.632355	+	1.94619i	0.0224273	+	0.0690242i
$796$	3.92468	−	12.0789i	0.139107	−	0.428126i
$797$	3.46665	+	2.51867i	0.122795	+	0.0892159i	0.647488	−	0.762076i	$-0.275820\pi$
$797$	3.46665	+	2.51867i	0.122795	+	0.0892159i	−0.524693	+	0.851292i	$0.675820\pi$
$798$	1.45387	+	1.05630i	0.0514663	+	0.0373925i
$799$	−6.23618	+	19.1930i	−0.220620	+	0.679000i
$800$	1.50869	+	4.64326i	0.0533401	+	0.164164i
$801$	6.48851	−	4.71418i	0.229260	−	0.166567i
$802$	5.80787			0.205083
$803$		0			0
$804$	−4.19100			−0.147805
$805$	6.02234	−	4.37549i	0.212260	−	0.154216i
$806$	−1.64278	−	5.05595i	−0.0578644	−	0.178088i
$807$	−0.168115	+	0.517406i	−0.00591794	+	0.0182136i
$808$	−10.3623	−	7.52868i	−0.364546	−	0.264858i
$809$	16.0577	+	11.6666i	0.564559	+	0.410176i	0.833125	−	0.553085i	$-0.186550\pi$
$809$	16.0577	+	11.6666i	0.564559	+	0.410176i	−0.268566	+	0.963261i	$0.586550\pi$
$810$	−1.19040	+	3.66367i	−0.0418264	+	0.128728i
$811$	−0.969807	−	2.98476i	−0.0340545	−	0.104809i	0.932584	−	0.360952i	$-0.117548\pi$
$811$	−0.969807	−	2.98476i	−0.0340545	−	0.104809i	−0.966639	+	0.256143i	$0.917548\pi$
$812$	−11.6015	+	8.42900i	−0.407133	+	0.295800i
$813$	−5.95452			−0.208834
$814$		0			0
$815$	0.771990			0.0270416
$816$	3.24692	−	2.35903i	0.113665	−	0.0825824i
$817$	9.47901	+	29.1734i	0.331629	+	1.02065i
$818$	−0.0386560	+	0.118971i	−0.00135158	+	0.00415972i
$819$	−29.3627	−	21.3333i	−1.02602	−	0.745445i
$820$	3.16919	+	2.30255i	0.110673	+	0.0804085i
$821$	7.26186	−	22.3497i	0.253441	−	0.780010i	−0.740692	−	0.671845i	$-0.765502\pi$
$821$	7.26186	−	22.3497i	0.253441	−	0.780010i	0.994133	−	0.108166i	$-0.0344977\pi$
$822$	−0.873336	−	2.68785i	−0.0304611	−	0.0937496i
$823$	10.2392	−	7.43922i	0.356916	−	0.259315i	−0.394848	−	0.918746i	$-0.629203\pi$
$823$	10.2392	−	7.43922i	0.356916	−	0.259315i	0.751765	+	0.659431i	$0.229203\pi$
$824$	−13.5535			−0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−24.4514	+	17.7650i	−0.850258	+	0.617748i	−0.925217	−	0.379438i	$-0.876117\pi$
$827$	−24.4514	+	17.7650i	−0.850258	+	0.617748i	0.0749595	+	0.997187i	$0.476117\pi$
$828$	4.39614	+	13.5299i	0.152776	+	0.470197i
$829$	0.618546	−	1.90369i	0.0214830	−	0.0661178i	−0.939740	−	0.341889i	$-0.888933\pi$
$829$	0.618546	−	1.90369i	0.0214830	−	0.0661178i	0.961223	+	0.275771i	$0.0889333\pi$
$830$	4.29195	+	3.11828i	0.148976	+	0.108237i
$831$	0.895832	+	0.650860i	0.0310761	+	0.0225781i
$832$	4.38554	−	13.4973i	0.152041	−	0.467935i
$833$	−0.300798	−	0.925761i	−0.0104220	−	0.0320757i
$834$	2.89242	−	2.10147i	0.100156	−	0.0727679i
$835$	8.48232			0.293543
$836$		0			0
$837$	−4.54520			−0.157105
$838$	0.490036	−	0.356032i	0.0169280	−	0.0122989i
$839$	10.9313	+	33.6430i	0.377390	+	1.16149i	0.941852	+	0.336027i	$0.109083\pi$
$839$	10.9313	+	33.6430i	0.377390	+	1.16149i	−0.564463	+	0.825459i	$0.690917\pi$
$840$	0.482628	−	1.48538i	0.0166523	−	0.0512504i
$841$	16.1151	+	11.7083i	0.555692	+	0.403734i
$842$	11.4542	+	8.32195i	0.394737	+	0.286793i
$843$	−2.27840	+	7.01218i	−0.0784721	+	0.241512i
$844$	−1.90778	−	5.87154i	−0.0656685	−	0.202107i
$845$	7.11029	−	5.16593i	0.244601	−	0.177713i
$846$	−6.02834			−0.207259
$847$		0			0
$848$	−17.0083			−0.584067
$849$	7.60562	−	5.52581i	0.261024	−	0.189645i
$850$	−0.682297	−	2.09989i	−0.0234026	−	0.0720258i
$851$	−9.11739	+	28.0605i	−0.312540	+	0.961900i
$852$	0.553861	+	0.402403i	0.0189750	+	0.0137861i
$853$	14.7268	+	10.6997i	0.504237	+	0.366350i	0.810633	−	0.585554i	$-0.199123\pi$
$853$	14.7268	+	10.6997i	0.504237	+	0.366350i	−0.306396	+	0.951904i	$0.599123\pi$
$854$	−1.57720	+	4.85413i	−0.0539707	+	0.166105i
$855$	−3.88382	−	11.9532i	−0.132824	−	0.408789i
$856$	26.2595	−	19.0787i	0.897532	−	0.652095i
$857$	−29.2837			−1.00031			−0.500156	−	0.865935i	$-0.666724\pi$
$857$	−29.2837			−1.00031			−0.500156	+	0.865935i	$0.666724\pi$
$858$		0			0
$859$	8.44030			0.287979			0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030			0.287979			0.143990	+	0.989579i	$0.454007\pi$
$860$	10.1326	−	7.36179i	0.345520	−	0.251035i
$861$	−0.592560	−	1.82371i	−0.0201944	−	0.0621519i
$862$	4.62426	−	14.2320i	0.157503	−	0.484745i
$863$	15.6534	+	11.3729i	0.532848	+	0.387137i	0.821422	−	0.570321i	$-0.193181\pi$
$863$	15.6534	+	11.3729i	0.532848	+	0.387137i	−0.288574	+	0.957458i	$0.593181\pi$
$864$	7.52319	+	5.46592i	0.255944	+	0.185954i
$865$	−1.56941	+	4.83014i	−0.0533615	+	0.164230i
$866$	−3.83931	−	11.8162i	−0.130465	−	0.401531i
$867$	−1.15078	+	0.836091i	−0.0390826	+	0.0283952i
$868$	−11.3559			−0.385446
$869$		0			0
$870$	0.464635			0.0157526
$871$	27.6424	−	20.0834i	0.936627	−	0.680499i
$872$	9.10456	+	28.0210i	0.308319	+	0.948910i
$873$	−16.5844	+	51.0414i	−0.561295	+	1.72749i
$874$	4.64595	+	3.37548i	0.157152	+	0.114177i
$875$	2.17239	+	1.57833i	0.0734401	+	0.0533574i
$876$	−0.180769	+	0.556351i	−0.00610763	+	0.0187973i
$877$	5.41211	+	16.6568i	0.182754	+	0.562459i	0.999902	−	0.0139682i	$-0.00444635\pi$
$877$	5.41211	+	16.6568i	0.182754	+	0.562459i	−0.817148	+	0.576427i	$0.804446\pi$
$878$	−5.56737	+	4.04493i	−0.187890	+	0.136510i
$879$	6.85349			0.231163
$880$		0			0
$881$	−20.0575			−0.675754			−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575			−0.675754			−0.337877	+	0.941190i	$0.609709\pi$
$882$	0.235240	−	0.170912i	0.00792095	−	0.00575491i
$883$	8.31193	+	25.5815i	0.279719	+	0.860886i	0.987932	+	0.154887i	$0.0495014\pi$
$883$	8.31193	+	25.5815i	0.279719	+	0.860886i	−0.708213	+	0.705998i	$0.750499\pi$
$884$	−11.8264	+	36.3980i	−0.397766	+	1.22420i
$885$	3.07039	+	2.23077i	0.103210	+	0.0749864i
$886$	0.127651	+	0.0927442i	0.00428853	+	0.00311580i
$887$	2.10307	−	6.47258i	0.0706142	−	0.217328i	−0.909521	−	0.415657i	$-0.863552\pi$
$887$	2.10307	−	6.47258i	0.0706142	−	0.217328i	0.980135	+	0.198329i	$0.0635515\pi$
$888$	1.91290	+	5.88731i	0.0641928	+	0.197565i
$889$	0.165681	−	0.120374i	0.00555676	−	0.00403722i
$890$	−1.32190			−0.0443103
$891$		0			0
$892$	−18.6880			−0.625720
$893$	15.3177	−	11.1289i	0.512586	−	0.372415i
$894$	0.698725	+	2.15045i	0.0233688	+	0.0719219i
$895$	3.49716	−	10.7632i	0.116897	−	0.359772i
$896$	24.3643	+	17.7017i	0.813955	+	0.591373i
$897$	3.38221	+	2.45732i	0.112929	+	0.0820475i
$898$	1.25481	−	3.86192i	0.0418737	−	0.128874i
$899$	−2.22211	−	6.83896i	−0.0741117	−	0.228092i
$900$	−4.15163	+	3.01633i	−0.138388	+	0.100544i
$901$	29.3033			0.976235
$902$		0			0
$903$	−6.13090			−0.204024
$904$	−2.99131	+	2.17332i	−0.0994896	+	0.0722834i
$905$	−2.28674	−	7.03787i	−0.0760139	−	0.233947i
$906$	−0.358259	+	1.10261i	−0.0119023	+	0.0366316i
$907$	17.2574	+	12.5382i	0.573023	+	0.416325i	0.836202	−	0.548422i	$-0.184771\pi$
$907$	17.2574	+	12.5382i	0.573023	+	0.416325i	−0.263179	+	0.964747i	$0.584771\pi$
$908$	0.309717	+	0.225023i	0.0102783	+	0.00746764i
$909$	6.36608	−	19.5928i	0.211150	−	0.649852i
$910$	1.84856	+	5.68929i	0.0612792	+	0.188598i
$911$	22.3198	−	16.2163i	0.739489	−	0.537270i	−0.153062	−	0.988217i	$-0.548913\pi$
$911$	22.3198	−	16.2163i	0.739489	−	0.537270i	0.892551	+	0.450946i	$0.148913\pi$
$912$	−3.76541			−0.124685
$913$		0			0
$914$	0.543347			0.0179723
$915$	−1.04094	+	0.756287i	−0.0344124	+	0.0250021i
$916$	0.0414622	+	0.127608i	0.00136995	+	0.00421627i
$917$	−9.52843	+	29.3255i	−0.314657	+	0.968414i
$918$	−3.40233	−	2.47194i	−0.112294	−	0.0815862i
$919$	4.86129	+	3.53194i	0.160359	+	0.116508i	0.665071	−	0.746780i	$-0.268401\pi$
$919$	4.86129	+	3.53194i	0.160359	+	0.116508i	−0.504712	+	0.863288i	$0.668401\pi$
$920$	1.54228	−	4.74665i	0.0508474	−	0.156492i
$921$	−0.686382	−	2.11247i	−0.0226170	−	0.0696081i
$922$	−5.60142	+	4.06967i	−0.184473	+	0.134027i
$923$	−5.58140			−0.183714
$924$		0			0
$925$	−10.6429			−0.349937
$926$	1.89094	−	1.37385i	0.0621401	−	0.0451474i
$927$	−6.73635	−	20.7324i	−0.221251	−	0.680940i
$928$	−4.54630	+	13.9921i	−0.149239	+	0.459312i
$929$	−7.76445	−	5.64121i	−0.254743	−	0.185082i	0.453083	−	0.891468i	$-0.350324\pi$
$929$	−7.76445	−	5.64121i	−0.254743	−	0.185082i	−0.707826	+	0.706386i	$0.750324\pi$
$930$	0.297671	+	0.216270i	0.00976100	+	0.00709178i
$931$	−0.282210	+	0.868554i	−0.00924907	+	0.0284657i
$932$	−8.28045	−	25.4846i	−0.271235	−	0.834776i
$933$	−6.57546	+	4.77735i	−0.215271	+	0.156403i
$934$	15.4742			0.506332
$935$		0			0
$936$	−24.3339			−0.795378
$937$	31.2214	−	22.6837i	1.01996	−	0.741043i	0.0536837	−	0.998558i	$-0.482904\pi$
$937$	31.2214	−	22.6837i	1.01996	−	0.741043i	0.966274	+	0.257515i	$0.0829037\pi$
$938$	2.89880	+	8.92160i	0.0946492	+	0.291300i
$939$	−1.15602	+	3.55785i	−0.0377252	+	0.116106i
$940$	−6.25427	−	4.54399i	−0.203992	−	0.148209i
$941$	23.6108	+	17.1543i	0.769691	+	0.559213i	0.901867	−	0.432013i	$-0.142196\pi$
$941$	23.6108	+	17.1543i	0.769691	+	0.559213i	−0.132176	+	0.991226i	$0.542196\pi$
$942$	−0.637607	+	1.96235i	−0.0207744	+	0.0639369i
$943$	−1.89357	−	5.82782i	−0.0616633	−	0.189780i
$944$	−25.5197	+	18.5411i	−0.830594	+	0.603462i
$945$	5.11455			0.166376
$946$		0			0
$947$	46.7623			1.51957			0.759785	−	0.650174i	$-0.225304\pi$
$947$	46.7623			1.51957			0.759785	+	0.650174i	$0.225304\pi$
$948$	1.62221	−	1.17860i	0.0526869	−	0.0382793i
$949$	−1.47375	−	4.53575i	−0.0478401	−	0.147237i
$950$	−0.640135	+	1.97013i	−0.0207687	+	0.0639195i
$951$	−5.42114	−	3.93869i	−0.175793	−	0.127721i
$952$	−18.0936	−	13.1458i	−0.586418	−	0.426058i
$953$	−1.90119	+	5.85126i	−0.0615855	+	0.189541i	−0.977116	−	0.212709i	$-0.931772\pi$
$953$	−1.90119	+	5.85126i	−0.0615855	+	0.189541i	0.915530	+	0.402249i	$0.131772\pi$
$954$	2.70496	+	8.32501i	0.0875763	+	0.269532i
$955$	−4.17135	+	3.03067i	−0.134982	+	0.0980701i
$956$	41.0529			1.32774
$957$		0			0
$958$	8.46440			0.273472
$959$	39.8183	−	28.9297i	1.28580	−	0.934189i
$960$	0.303532	+	0.934176i	0.00979646	+	0.0301504i
$961$	−7.81985	+	24.0670i	−0.252253	+	0.776356i
$962$	−19.1818	−	13.9364i	−0.618446	−	0.449328i
$963$	42.2354	+	30.6858i	1.36102	+	0.988836i
$964$	11.6840	−	35.9596i	0.376316	−	1.15818i
$965$	1.24605	+	3.83494i	0.0401117	+	0.123451i
$966$	−0.928579	+	0.674652i	−0.0298765	+	0.0217066i
$967$	3.39625			0.109216			0.0546080	−	0.998508i	$-0.482609\pi$
$967$	3.39625			0.109216			0.0546080	+	0.998508i	$0.482609\pi$
$968$		0			0
$969$	6.48736			0.208404
$970$	7.15627	−	5.19933i	0.229774	−	0.166940i
$971$	−2.90322	−	8.93518i	−0.0931686	−	0.286744i	0.893603	−	0.448857i	$-0.148169\pi$
$971$	−2.90322	−	8.93518i	−0.0931686	−	0.286744i	−0.986772	+	0.162114i	$0.948169\pi$
$972$	−4.55740	+	14.0262i	−0.146179	+	0.449892i
$973$	50.3719	+	36.5974i	1.61485	+	1.17326i
$974$	7.12772	+	5.17859i	0.228387	+	0.165933i
$975$	−0.466012	+	1.43424i	−0.0149243	+	0.0459324i
$976$	−3.30470	−	10.1708i	−0.105781	−	0.325560i
$977$	13.3935	−	9.73092i	0.428495	−	0.311320i	−0.352552	−	0.935792i	$-0.614686\pi$
$977$	13.3935	−	9.73092i	0.428495	−	0.311320i	0.781047	+	0.624472i	$0.214686\pi$
$978$	−0.119032			−0.00380623
$979$		0			0
$980$	0.372885			0.0119114
$981$	−38.3376	+	27.8539i	−1.22402	+	0.889305i
$982$	−1.68628	−	5.18984i	−0.0538114	−	0.165614i
$983$	15.7036	−	48.3308i	0.500868	−	1.54151i	−0.306741	−	0.951793i	$-0.599238\pi$
$983$	15.7036	−	48.3308i	0.500868	−	1.54151i	0.807608	−	0.589719i	$-0.200762\pi$
$984$	−1.04011	−	0.755685i	−0.0331576	−	0.0240904i
$985$	9.23701	+	6.71108i	0.294316	+	0.213833i
$986$	2.05604	−	6.32785i	0.0654778	−	0.201520i
$987$	1.16939	+	3.59902i	0.0372222	+	0.114558i
$988$	29.0487	−	21.1051i	0.924162	−	0.671443i
$989$	−19.5918			−0.622983
$990$		0			0
$991$	11.3642			0.360996			0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642			0.360996			0.180498	+	0.983575i	$0.442229\pi$
$992$	−9.42539	+	6.84794i	−0.299256	+	0.217422i
$993$	−3.20883	−	9.87575i	−0.101829	−	0.313397i
$994$	0.473526	−	1.45736i	0.0150193	−	0.0462248i
$995$	−5.79777	−	4.21233i	−0.183802	−	0.133540i
$996$	5.14892	+	3.74091i	0.163150	+	0.118535i
$997$	−9.01231	+	27.7370i	−0.285423	+	0.878441i	0.700849	+	0.713310i	$0.252805\pi$
$997$	−9.01231	+	27.7370i	−0.285423	+	0.878441i	−0.986272	+	0.165131i	$0.947195\pi$
$998$	1.60483	+	4.93915i	0.0507999	+	0.156346i
$999$	−16.4001	+	11.9154i	−0.518875	+	0.376985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.m.366.1		8
11.2	odd	10		605.2.a.k.1.2		4
11.3	even	5		55.2.g.b.16.2	✓	8
11.4	even	5	inner	605.2.g.m.81.1		8
11.5	even	5		55.2.g.b.31.2	yes	8
11.6	odd	10		605.2.g.k.251.1		8
11.7	odd	10		605.2.g.e.81.2		8
11.8	odd	10		605.2.g.k.511.1		8
11.9	even	5		605.2.a.j.1.3		4
11.10	odd	2		605.2.g.e.366.2		8
33.2	even	10		5445.2.a.bi.1.3		4
33.5	odd	10		495.2.n.e.361.1		8
33.14	odd	10		495.2.n.e.181.1		8
33.20	odd	10		5445.2.a.bp.1.2		4
44.3	odd	10		880.2.bo.h.401.1		8
44.27	odd	10		880.2.bo.h.801.1		8
44.31	odd	10		9680.2.a.cn.1.3		4
44.35	even	10		9680.2.a.cm.1.3		4
55.3	odd	20		275.2.z.a.49.3		16
55.9	even	10		3025.2.a.bd.1.2		4
55.14	even	10		275.2.h.a.126.1		8
55.24	odd	10		3025.2.a.w.1.3		4
55.27	odd	20		275.2.z.a.174.3		16
55.38	odd	20		275.2.z.a.174.2		16
55.47	odd	20		275.2.z.a.49.2		16
55.49	even	10		275.2.h.a.251.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	11.3	even	5
55.2.g.b.31.2	yes	8	11.5	even	5
275.2.h.a.126.1		8	55.14	even	10
275.2.h.a.251.1		8	55.49	even	10
275.2.z.a.49.2		16	55.47	odd	20
275.2.z.a.49.3		16	55.3	odd	20
275.2.z.a.174.2		16	55.38	odd	20
275.2.z.a.174.3		16	55.27	odd	20
495.2.n.e.181.1		8	33.14	odd	10
495.2.n.e.361.1		8	33.5	odd	10
605.2.a.j.1.3		4	11.9	even	5
605.2.a.k.1.2		4	11.2	odd	10
605.2.g.e.81.2		8	11.7	odd	10
605.2.g.e.366.2		8	11.10	odd	2
605.2.g.k.251.1		8	11.6	odd	10
605.2.g.k.511.1		8	11.8	odd	10
605.2.g.m.81.1		8	11.4	even	5	inner
605.2.g.m.366.1		8	1.1	even	1	trivial
880.2.bo.h.401.1		8	44.3	odd	10
880.2.bo.h.801.1		8	44.27	odd	10
3025.2.a.w.1.3		4	55.24	odd	10
3025.2.a.bd.1.2		4	55.9	even	10
5445.2.a.bi.1.3		4	33.2	even	10
5445.2.a.bp.1.2		4	33.20	odd	10
9680.2.a.cm.1.3		4	44.35	even	10
9680.2.a.cn.1.3		4	44.31	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.386111 + 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.124741 - 0.0906300i) q^{6} +(0.829779 - 2.55380i) q^{7} +(-0.556333 - 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} +O(q^{10})\)	\(q+(-0.386111 + 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.124741 - 0.0906300i) q^{6} +(0.829779 - 2.55380i) q^{7} +(-0.556333 - 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} -0.477260 q^{10} -0.572554 q^{12} +(3.77637 - 2.74369i) q^{13} +(0.396020 + 1.21882i) q^{14} +(-0.0998345 + 0.307259i) q^{15} +(-2.17239 - 1.57833i) q^{16} +(3.74278 + 2.71929i) q^{17} +(-0.427051 + 1.31433i) q^{18} +(-1.34127 - 4.12801i) q^{19} +(-1.43376 + 1.04169i) q^{20} +0.867517 q^{21} +2.77222 q^{23} +(0.470553 - 0.341876i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.688421 + 2.11874i) q^{26} +(1.54094 + 1.11956i) q^{27} +(3.84996 + 2.79716i) q^{28} +(-0.931196 + 2.86593i) q^{29} +(-0.0476470 - 0.146642i) q^{30} +(-1.93056 + 1.40263i) q^{31} +4.88221 q^{32} -2.20796 q^{34} +(2.17239 - 1.57833i) q^{35} +(1.58578 + 4.88053i) q^{36} +(-3.28884 + 10.1220i) q^{37} +(1.67589 + 1.21761i) q^{38} +(1.22004 + 0.886408i) q^{39} +(0.556333 - 1.71222i) q^{40} +(-0.683053 - 2.10222i) q^{41} +(-0.334958 + 0.243361i) q^{42} -7.06719 q^{43} +2.89563 q^{45} +(-1.07039 + 0.777682i) q^{46} +(1.34798 + 4.14865i) q^{47} +(0.268077 - 0.825058i) q^{48} +(-0.170221 - 0.123673i) q^{49} +(-0.386111 - 0.280526i) q^{50} +(-0.461867 + 1.42148i) q^{51} +(2.55633 + 7.86758i) q^{52} +(5.12435 - 3.72306i) q^{53} -0.909040 q^{54} -4.83428 q^{56} +(1.13446 - 0.824235i) q^{57} +(-0.444423 - 1.36779i) q^{58} +(3.63011 - 11.1723i) q^{59} +(-0.463206 - 0.336539i) q^{60} +(3.22201 + 2.34093i) q^{61} +(0.351935 - 1.08314i) q^{62} +(-2.40273 - 7.39484i) q^{63} +(2.45970 - 1.78708i) q^{64} +4.66785 q^{65} +7.31984 q^{67} +(-6.63303 + 4.81918i) q^{68} +(0.276763 + 0.851790i) q^{69} +(-0.396020 + 1.21882i) q^{70} +(-0.967351 - 0.702822i) q^{71} +(-4.21747 - 3.06417i) q^{72} +(0.315724 - 0.971700i) q^{73} +(-1.56963 - 4.83083i) q^{74} +(-0.261370 + 0.189896i) q^{75} +7.69223 q^{76} -0.719730 q^{78} +(-2.83328 + 2.05850i) q^{79} +(-0.829779 - 2.55380i) q^{80} +(2.49424 - 7.67647i) q^{81} +(0.853463 + 0.620077i) q^{82} +(-8.99290 - 6.53372i) q^{83} +(-0.475093 + 1.46219i) q^{84} +(1.42961 + 4.39990i) q^{85} +(2.72872 - 1.98253i) q^{86} -0.973547 q^{87} +2.76978 q^{89} +(-1.11803 + 0.812299i) q^{90} +(-3.87328 - 11.9207i) q^{91} +(-1.51820 + 4.67254i) q^{92} +(-0.623707 - 0.453150i) q^{93} +(-1.68428 - 1.22370i) q^{94} +(1.34127 - 4.12801i) q^{95} +(0.487413 + 1.50010i) q^{96} +(-14.9945 + 10.8941i) q^{97} +0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9	\( 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21} + 10 q^{23} - 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} + 19 q^{28} + 21 q^{29} + 7 q^{30} + 15 q^{31} + 16 q^{32} + 4 q^{34} + q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} - 14 q^{39} + q^{40} + 3 q^{41} - 21 q^{42} - 38 q^{43} - 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} + 3 q^{50} + 6 q^{51} + 17 q^{52} - 2 q^{53} + 16 q^{54} + 22 q^{56} + 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} + 6 q^{61} - 5 q^{62} - 30 q^{63} + 29 q^{64} + 2 q^{65} - 38 q^{67} - 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} + 5 q^{72} - 2 q^{73} - 20 q^{74} - 5 q^{75} - 16 q^{78} - 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} - 38 q^{83} - 17 q^{84} + 13 q^{85} + 2 q^{86} + 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} - 18 q^{94} - 5 q^{95} - 17 q^{96} - 56 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

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