LMFDB - Embedded newform 605.2.g.l.366.2

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:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$-0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.l.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +O(q^{10})$	\(q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(-0.947822 + 0.688633i) q^{13} +(-1.49207 - 4.59211i) q^{14} +(0.874032 - 2.68999i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(5.52431 + 4.01365i) q^{17} +(-3.73017 + 11.4803i) q^{18} +(3.09726 - 2.25029i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(-10.1008 + 7.33866i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.874032 + 2.68999i) q^{26} +(4.57649 + 3.32502i) q^{27} +(-6.19453 - 4.50059i) q^{28} +(1.13003 - 3.47788i) q^{29} +(-2.11010 - 6.49422i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(1.61803 - 1.17557i) q^{35} +(5.91525 + 18.2053i) q^{36} +(-2.36610 + 7.28210i) q^{37} +(2.68085 + 1.94775i) q^{39} +(1.36407 - 4.19817i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-11.0486 + 8.02730i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(-5.52431 + 4.01365i) q^{46} +(0.874032 + 2.68999i) q^{47} +(-2.62210 + 8.06998i) q^{48} +(2.42705 + 1.76336i) q^{49} +(1.95314 + 1.41904i) q^{50} +(5.96826 - 18.3684i) q^{51} +(1.38603 + 4.26576i) q^{52} +(-9.43059 + 6.85173i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(-2.72813 - 8.39633i) q^{58} +(0.511996 - 1.57576i) q^{59} +(-8.76038 - 6.36479i) q^{60} +(-7.53495 - 5.47446i) q^{61} +(3.09017 + 9.51057i) q^{63} +(7.95136 - 5.77700i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(21.1494 - 15.3660i) q^{68} +(2.47214 + 7.60845i) q^{69} +(1.49207 - 4.59211i) q^{70} +(-9.15298 - 6.65003i) q^{71} +(17.8559 + 12.9730i) q^{72} +(0.362036 - 1.11423i) q^{73} +(5.71227 + 17.5805i) q^{74} +(2.28825 - 1.66251i) q^{75} +8.00000 q^{78} +(3.23607 - 2.35114i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-11.7188 - 8.51423i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(-6.69234 + 20.5969i) q^{84} +(2.11010 + 6.49422i) q^{85} +(11.7188 - 8.51423i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(-9.76570 + 7.09520i) q^{90} +(0.724072 + 2.22846i) q^{91} +(-3.34617 + 10.2984i) q^{92} +(5.52431 + 4.01365i) q^{94} +(-1.38603 - 4.26576i) q^{96} +(-2.95846 + 2.14944i) q^{97} +7.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * 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 $

$2$	1.95314	−	1.41904i	1.38108	−	1.00341i	0.384300	−	0.923208i	$-0.374443\pi$
$2$	1.95314	−	1.41904i	1.38108	−	1.00341i	0.996778	−	0.0802039i	$-0.0255571\pi$
$3$	−0.874032	−	2.68999i	−0.504623	−	1.55307i	−0.801404	−	0.598123i	$-0.795913\pi$
$3$	−0.874032	−	2.68999i	−0.504623	−	1.55307i	0.296781	−	0.954945i	$-0.404087\pi$
$4$	1.18305	−	3.64105i	0.591525	−	1.82053i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−5.52431	−	4.01365i	−2.25529	−	1.63857i
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	−0.763710	−	0.645560i	$-0.776624\pi$
$7$	0.618034	−	1.90211i	0.233595	−	0.718931i	0.997305	−	0.0733714i	$-0.0233759\pi$
$8$	−1.36407	−	4.19817i	−0.482271	−	1.48428i
$9$	−4.04508	+	2.93893i	−1.34836	+	0.979642i
$10$	2.41421			0.763441
$11$		0			0
$11$		0			0
$12$	−10.8284			−3.12590
$13$	−0.947822	+	0.688633i	−0.262879	+	0.190993i	−0.711415	−	0.702772i	$-0.751945\pi$
$13$	−0.947822	+	0.688633i	−0.262879	+	0.190993i	0.448537	+	0.893765i	$0.351945\pi$
$14$	−1.49207	−	4.59211i	−0.398771	−	1.22729i
$15$	0.874032	−	2.68999i	0.225674	−	0.694553i
$16$	−2.42705	−	1.76336i	−0.606763	−	0.440839i
$17$	5.52431	+	4.01365i	1.33984	+	0.973453i	0.999450	+	0.0331696i	$0.0105601\pi$
$17$	5.52431	+	4.01365i	1.33984	+	0.973453i	0.340393	+	0.940283i	$0.389440\pi$
$18$	−3.73017	+	11.4803i	−0.879208	+	2.70593i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	3.09726	−	2.25029i	0.692569	−	0.503181i
$21$	−5.65685			−1.23443
$22$		0			0
$23$	−2.82843			−0.589768			−0.294884	−	0.955533i	$-0.595281\pi$
$23$	−2.82843			−0.589768			−0.294884	+	0.955533i	$0.595281\pi$
$24$	−10.1008	+	7.33866i	−2.06182	+	1.49800i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.874032	+	2.68999i	−0.171412	+	0.527551i
$27$	4.57649	+	3.32502i	0.880746	+	0.639900i
$28$	−6.19453	−	4.50059i	−1.17066	−	0.850531i
$29$	1.13003	−	3.47788i	0.209841	−	0.645825i	−0.789638	−	0.613572i	$-0.789732\pi$
$29$	1.13003	−	3.47788i	0.209841	−	0.645825i	0.999480	−	0.0322527i	$-0.0102681\pi$
$30$	−2.11010	−	6.49422i	−0.385250	−	1.18568i
$31$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$31$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$32$	1.58579			0.280330
$33$		0			0
$34$	16.4853			2.82720
$35$	1.61803	−	1.17557i	0.273498	−	0.198708i
$36$	5.91525	+	18.2053i	0.985874	+	3.03421i
$37$	−2.36610	+	7.28210i	−0.388984	+	1.19717i	0.544564	+	0.838719i	$0.316695\pi$
$37$	−2.36610	+	7.28210i	−0.388984	+	1.19717i	−0.933549	+	0.358451i	$0.883305\pi$
$38$		0			0
$39$	2.68085	+	1.94775i	0.429279	+	0.311889i
$40$	1.36407	−	4.19817i	0.215678	−	0.663788i
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	−0.984994	−	0.172588i	$-0.944787\pi$
$41$	−1.85410	−	5.70634i	−0.289562	−	0.891180i	0.695432	−	0.718592i	$-0.255213\pi$
$42$	−11.0486	+	8.02730i	−1.70484	+	1.23864i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−5.00000			−0.745356
$46$	−5.52431	+	4.01365i	−0.814516	+	0.591780i
$47$	0.874032	+	2.68999i	0.127491	+	0.392376i	0.994347	−	0.106183i	$-0.0338628\pi$
$47$	0.874032	+	2.68999i	0.127491	+	0.392376i	−0.866856	+	0.498559i	$0.833863\pi$
$48$	−2.62210	+	8.06998i	−0.378467	+	1.16480i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	1.95314	+	1.41904i	0.276216	+	0.200682i
$51$	5.96826	−	18.3684i	0.835724	−	2.57209i
$52$	1.38603	+	4.26576i	0.192208	+	0.591554i
$53$	−9.43059	+	6.85173i	−1.29539	+	0.941157i	−0.999899	−	0.0141880i	$-0.995484\pi$
$53$	−9.43059	+	6.85173i	−1.29539	+	0.941157i	−0.295492	+	0.955345i	$0.595484\pi$
$54$	13.6569			1.85846
$55$		0			0
$56$	−8.82843			−1.17975
$57$		0			0
$58$	−2.72813	−	8.39633i	−0.358222	−	1.10249i
$59$	0.511996	−	1.57576i	0.0666562	−	0.205147i	−0.912181	−	0.409788i	$-0.865603\pi$
$59$	0.511996	−	1.57576i	0.0666562	−	0.205147i	0.978837	+	0.204641i	$0.0656027\pi$
$60$	−8.76038	−	6.36479i	−1.13096	−	0.821691i
$61$	−7.53495	−	5.47446i	−0.964751	−	0.700933i	−0.0105019	−	0.999945i	$-0.503343\pi$
$61$	−7.53495	−	5.47446i	−0.964751	−	0.700933i	−0.954249	+	0.299012i	$0.903343\pi$
$62$		0			0
$63$	3.09017	+	9.51057i	0.389325	+	1.19822i
$64$	7.95136	−	5.77700i	0.993921	−	0.722126i
$65$	−1.17157			−0.145316
$66$		0			0
$67$	12.4853			1.52532			0.762660	−	0.646800i	$-0.223893\pi$
$67$	12.4853			1.52532			0.762660	+	0.646800i	$0.223893\pi$
$68$	21.1494	−	15.3660i	2.56475	−	1.86340i
$69$	2.47214	+	7.60845i	0.297610	+	0.915950i
$70$	1.49207	−	4.59211i	0.178336	−	0.548862i
$71$	−9.15298	−	6.65003i	−1.08626	−	0.789213i	−0.107496	−	0.994206i	$-0.534283\pi$
$71$	−9.15298	−	6.65003i	−1.08626	−	0.789213i	−0.978764	+	0.204992i	$0.934283\pi$
$72$	17.8559	+	12.9730i	2.10433	+	1.52889i
$73$	0.362036	−	1.11423i	0.0423731	−	0.130411i	−0.927632	−	0.373495i	$-0.878159\pi$
$73$	0.362036	−	1.11423i	0.0423731	−	0.130411i	0.970005	+	0.243084i	$0.0781592\pi$
$74$	5.71227	+	17.5805i	0.664037	+	2.04370i
$75$	2.28825	−	1.66251i	0.264224	−	0.191970i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	3.23607	−	2.35114i	0.364086	−	0.264524i	−0.390668	−	0.920532i	$-0.627756\pi$
$79$	3.23607	−	2.35114i	0.364086	−	0.264524i	0.754754	+	0.656007i	$0.227756\pi$
$80$	−0.927051	−	2.85317i	−0.103647	−	0.318994i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−11.7188	−	8.51423i	−1.29413	−	0.940240i
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	0.288600	−	0.957450i	$-0.406810\pi$
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	−0.821407	+	0.570343i	$0.806810\pi$
$84$	−6.69234	+	20.5969i	−0.730194	+	2.24731i
$85$	2.11010	+	6.49422i	0.228872	+	0.704397i
$86$	11.7188	−	8.51423i	1.26367	−	0.918114i
$87$	−10.3431			−1.10890
$88$		0			0
$89$	−13.3137			−1.41125			−0.705625	−	0.708585i	$-0.749334\pi$
$89$	−13.3137			−1.41125			−0.705625	+	0.708585i	$0.749334\pi$
$90$	−9.76570	+	7.09520i	−1.02940	+	0.747899i
$91$	0.724072	+	2.22846i	0.0759034	+	0.233607i
$92$	−3.34617	+	10.2984i	−0.348862	+	1.07369i
$93$		0			0
$94$	5.52431	+	4.01365i	0.569789	+	0.413976i
$95$		0			0
$96$	−1.38603	−	4.26576i	−0.141461	−	0.435372i
$97$	−2.95846	+	2.14944i	−0.300386	+	0.218243i	−0.727760	−	0.685832i	$-0.759439\pi$
$97$	−2.95846	+	2.14944i	−0.300386	+	0.218243i	0.427374	+	0.904075i	$0.359439\pi$
$98$	7.24264			0.731617
$99$		0			0
$100$	3.82843			0.382843
$101$	7.53495	−	5.47446i	0.749755	−	0.544729i	−0.145996	−	0.989285i	$-0.546639\pi$
$101$	7.53495	−	5.47446i	0.749755	−	0.544729i	0.895751	+	0.444556i	$0.146639\pi$
$102$	−14.4087	−	44.3453i	−1.42667	−	4.39084i
$103$	2.11010	−	6.49422i	0.207914	−	0.639895i	−0.791667	−	0.610953i	$-0.790786\pi$
$103$	2.11010	−	6.49422i	0.207914	−	0.639895i	0.999581	−	0.0289414i	$-0.00921362\pi$
$104$	4.18389	+	3.03977i	0.410264	+	0.298074i
$105$	−4.57649	−	3.32502i	−0.446620	−	0.324488i
$106$	−8.69640	+	26.7648i	−0.844669	+	2.59962i
$107$	−2.36610	−	7.28210i	−0.228739	−	0.703987i	−0.997890	−	0.0649203i	$-0.979321\pi$
$107$	−2.36610	−	7.28210i	−0.228739	−	0.703987i	0.769151	−	0.639067i	$-0.220679\pi$
$108$	17.5208	−	12.7296i	1.68594	−	1.22490i
$109$	7.65685			0.733394			0.366697	−	0.930341i	$-0.380489\pi$
$109$	7.65685			0.733394			0.366697	+	0.930341i	$0.380489\pi$
$110$		0			0
$111$	21.6569			2.05558
$112$	−4.85410	+	3.52671i	−0.458670	+	0.333243i
$113$	6.07430	+	18.6948i	0.571422	+	1.75866i	0.648051	+	0.761597i	$0.275584\pi$
$113$	6.07430	+	18.6948i	0.571422	+	1.75866i	−0.0766284	+	0.997060i	$0.524416\pi$
$114$		0			0
$115$	−2.28825	−	1.66251i	−0.213380	−	0.155030i
$116$	−11.3262	−	8.22899i	−1.05161	−	0.764043i
$117$	1.81018	−	5.57116i	0.167351	−	0.515054i
$118$	−1.23607	−	3.80423i	−0.113789	−	0.350207i
$119$	11.0486	−	8.02730i	1.01283	−	0.735861i
$120$	−12.4853			−1.13975
$121$		0			0
$122$	−22.4853			−2.03572
$123$	−13.7295	+	9.97505i	−1.23794	+	0.899420i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	19.5314	+	14.1904i	1.74000	+	1.26418i
$127$	3.51368	+	2.55284i	0.311789	+	0.226528i	0.732664	−	0.680591i	$-0.238277\pi$
$127$	3.51368	+	2.55284i	0.311789	+	0.226528i	−0.420875	+	0.907119i	$0.638277\pi$
$128$	6.35226	−	19.5502i	0.561466	−	1.72801i
$129$	−5.24419	−	16.1400i	−0.461725	−	1.42104i
$130$	−2.28825	+	1.66251i	−0.200692	+	0.145812i
$131$	11.3137			0.988483			0.494242	−	0.869325i	$-0.335446\pi$
$131$	11.3137			0.988483			0.494242	+	0.869325i	$0.335446\pi$
$132$		0			0
$133$		0			0
$134$	24.3855	−	17.7171i	2.10659	−	1.53052i
$135$	1.74806	+	5.37999i	0.150449	+	0.463036i
$136$	9.31443	−	28.6669i	0.798706	−	2.45816i
$137$	8.87537	+	6.44833i	0.758274	+	0.550918i	0.898381	−	0.439218i	$-0.144744\pi$
$137$	8.87537	+	6.44833i	0.758274	+	0.550918i	−0.140106	+	0.990136i	$0.544744\pi$
$138$	15.6251	+	11.3523i	1.33010	+	0.966373i
$139$	1.23607	−	3.80423i	0.104842	−	0.322670i	−0.884851	−	0.465873i	$-0.845740\pi$
$139$	1.23607	−	3.80423i	0.104842	−	0.322670i	0.989693	+	0.143203i	$0.0457402\pi$
$140$	−2.36610	−	7.28210i	−0.199972	−	0.615450i
$141$	6.47214	−	4.70228i	0.545052	−	0.396004i
$142$	−27.3137			−2.29212
$143$		0			0
$144$	15.0000			1.25000
$145$	2.95846	−	2.14944i	0.245687	−	0.178502i
$146$	−0.874032	−	2.68999i	−0.0723354	−	0.222625i
$147$	2.62210	−	8.06998i	0.216267	−	0.665601i
$148$	23.7153	+	17.2302i	1.94938	+	1.41631i
$149$	0.277611	+	0.201696i	0.0227428	+	0.0165236i	0.599099	−	0.800675i	$-0.295526\pi$
$149$	0.277611	+	0.201696i	0.0227428	+	0.0165236i	−0.576356	+	0.817199i	$0.695526\pi$
$150$	2.11010	−	6.49422i	0.172289	−	0.530251i
$151$	3.70820	+	11.4127i	0.301769	+	0.928751i	0.980863	+	0.194699i	$0.0623730\pi$
$151$	3.70820	+	11.4127i	0.301769	+	0.928751i	−0.679094	+	0.734052i	$0.737627\pi$
$152$		0			0
$153$	−34.1421			−2.76023
$154$		0			0
$155$		0			0
$156$	10.2634	−	7.45682i	0.821732	−	0.597023i
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	−0.961438	−	0.275020i	$-0.911315\pi$
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	0.616167	−	0.787616i	$-0.288685\pi$
$158$	2.98413	−	9.18421i	0.237405	−	0.730657i
$159$	26.6737	+	19.3796i	2.11537	+	1.53690i
$160$	1.28293	+	0.932102i	0.101424	+	0.0736891i
$161$	−1.74806	+	5.37999i	−0.137767	+	0.424002i
$162$	−0.746033	−	2.29605i	−0.0586139	−	0.180395i
$163$	−13.3369	+	9.68981i	−1.04462	+	0.758964i	−0.971183	−	0.238335i	$-0.923398\pi$
$163$	−13.3369	+	9.68981i	−1.04462	+	0.758964i	−0.0734416	+	0.997300i	$0.523398\pi$
$164$	−22.9706			−1.79370
$165$		0			0
$166$	−14.4853			−1.12428
$167$	−18.5836	+	13.5018i	−1.43804	+	1.04480i	−0.449593	+	0.893234i	$0.648431\pi$
$167$	−18.5836	+	13.5018i	−1.43804	+	1.04480i	−0.988447	+	0.151564i	$0.951569\pi$
$168$	7.71633	+	23.7484i	0.595328	+	1.83223i
$169$	−3.59307	+	11.0583i	−0.276390	+	0.850641i
$170$	13.3369	+	9.68981i	1.02289	+	0.743174i
$171$		0			0
$172$	7.09829	−	21.8463i	0.541240	−	1.66577i
$173$	6.84230	+	21.0584i	0.520210	+	1.60104i	0.773597	+	0.633677i	$0.218455\pi$
$173$	6.84230	+	21.0584i	0.520210	+	1.60104i	−0.253387	+	0.967365i	$0.581545\pi$
$174$	−20.2016	+	14.6773i	−1.53148	+	1.11269i
$175$	2.00000			0.151186
$176$		0			0
$177$	−4.68629			−0.352243
$178$	−26.0035	+	18.8927i	−1.94905	+	1.41607i
$179$	2.98413	+	9.18421i	0.223045	+	0.686460i	0.998484	+	0.0550388i	$0.0175282\pi$
$179$	2.98413	+	9.18421i	0.223045	+	0.686460i	−0.775440	+	0.631422i	$0.782472\pi$
$180$	−5.91525	+	18.2053i	−0.440896	+	1.35694i
$181$	−17.2432	−	12.5279i	−1.28167	−	0.931190i	−0.282071	−	0.959393i	$-0.591021\pi$
$181$	−17.2432	−	12.5279i	−1.28167	−	0.931190i	−0.999602	+	0.0282032i	$0.991021\pi$
$182$	4.57649	+	3.32502i	0.339232	+	0.246467i
$183$	−8.14048	+	25.0538i	−0.601762	+	1.85203i
$184$	3.85816	+	11.8742i	0.284428	+	0.875378i
$185$	−6.19453	+	4.50059i	−0.455431	+	0.330890i
$186$		0			0
$187$		0			0
$188$	10.8284			0.789744
$189$	9.15298	−	6.65003i	0.665782	−	0.483719i
$190$		0			0
$191$	1.02399	−	3.15152i	0.0740935	−	0.228036i	−0.907150	−	0.420806i	$-0.861747\pi$
$191$	1.02399	−	3.15152i	0.0740935	−	0.228036i	0.981244	+	0.192770i	$0.0617472\pi$
$192$	−22.4899	−	16.3398i	−1.62307	−	1.17923i
$193$	−0.947822	−	0.688633i	−0.0682257	−	0.0495689i	0.553150	−	0.833082i	$-0.313426\pi$
$193$	−0.947822	−	0.688633i	−0.0682257	−	0.0495689i	−0.621375	+	0.783513i	$0.713426\pi$
$194$	−2.72813	+	8.39633i	−0.195869	+	0.602822i
$195$	1.02399	+	3.15152i	0.0733296	+	0.225685i
$196$	9.29179	−	6.75088i	0.663699	−	0.482206i
$197$	10.8284			0.771493			0.385747	−	0.922605i	$-0.373944\pi$
$197$	10.8284			0.771493			0.385747	+	0.922605i	$0.373944\pi$
$198$		0			0
$199$	10.3431			0.733206			0.366603	−	0.930377i	$-0.380521\pi$
$199$	10.3431			0.733206			0.366603	+	0.930377i	$0.380521\pi$
$200$	3.57117	−	2.59461i	0.252520	−	0.183467i
$201$	−10.9125	−	33.5853i	−0.769711	−	2.36893i
$202$	6.94833	−	21.3848i	0.488883	−	1.50463i
$203$	−5.91691	−	4.29889i	−0.415286	−	0.301723i
$204$	−59.8196	−	43.4615i	−4.18821	−	3.04291i
$205$	1.85410	−	5.70634i	0.129496	−	0.398548i
$206$	−5.09423	−	15.6784i	−0.354932	−	1.09237i
$207$	11.4412	−	8.31254i	0.795220	−	0.577761i
$208$	3.51472			0.243702
$209$		0			0
$210$	−13.6569			−0.942412
$211$	−12.9443	+	9.40456i	−0.891120	+	0.647437i	−0.936170	−	0.351548i	$-0.885655\pi$
$211$	−12.9443	+	9.40456i	−0.891120	+	0.647437i	0.0450495	+	0.998985i	$0.485655\pi$
$212$	13.7906	+	42.4432i	0.947144	+	2.91501i
$213$	−9.88854	+	30.4338i	−0.677552	+	2.08529i
$214$	−14.9549	−	10.8654i	−1.02230	−	0.742742i
$215$	4.85410	+	3.52671i	0.331047	+	0.240520i
$216$	7.71633	−	23.7484i	0.525030	−	1.61588i
$217$		0			0
$218$	14.9549	−	10.8654i	1.01287	−	0.735896i
$219$	−3.31371			−0.223920
$220$		0			0
$221$	−8.00000			−0.538138
$222$	42.2989	−	30.7319i	2.83891	−	2.06259i
$223$	−3.34617	−	10.2984i	−0.224076	−	0.689635i	−0.998384	−	0.0568262i	$-0.981902\pi$
$223$	−3.34617	−	10.2984i	−0.224076	−	0.689635i	0.774308	−	0.632809i	$-0.218098\pi$
$224$	0.980070	−	3.01635i	0.0654837	−	0.201538i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	38.3926	+	27.8938i	2.55384	+	1.85547i
$227$	−7.82237	+	24.0748i	−0.519189	+	1.59790i	0.256340	+	0.966587i	$0.417483\pi$
$227$	−7.82237	+	24.0748i	−0.519189	+	1.59790i	−0.775529	+	0.631312i	$0.782517\pi$
$228$		0			0
$229$	−1.06281	+	0.772178i	−0.0702326	+	0.0510270i	−0.622348	−	0.782741i	$-0.713821\pi$
$229$	−1.06281	+	0.772178i	−0.0702326	+	0.0510270i	0.552115	+	0.833768i	$0.313821\pi$
$230$	−6.82843			−0.450253
$231$		0			0
$232$	−16.1421			−1.05978
$233$	−4.96909	+	3.61026i	−0.325536	+	0.236516i	−0.738534	−	0.674216i	$-0.764482\pi$
$233$	−4.96909	+	3.61026i	−0.325536	+	0.236516i	0.412998	+	0.910732i	$0.364482\pi$
$234$	−4.37016	−	13.4500i	−0.285686	−	0.879252i
$235$	−0.874032	+	2.68999i	−0.0570156	+	0.175476i
$236$	−5.13171	−	3.72841i	−0.334046	−	0.242699i
$237$	−9.15298	−	6.65003i	−0.594550	−	0.431966i
$238$	10.1885	−	31.3569i	0.660420	−	2.03256i
$239$	7.20433	+	22.1727i	0.466010	+	1.43423i	0.857708	+	0.514136i	$0.171887\pi$
$239$	7.20433	+	22.1727i	0.466010	+	1.43423i	−0.391699	+	0.920093i	$0.628113\pi$
$240$	−6.86474	+	4.98752i	−0.443117	+	0.321943i
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$		0			0
$243$	14.1421			0.907218
$244$	−28.8470	+	20.9586i	−1.84674	+	1.34174i
$245$	0.927051	+	2.85317i	0.0592271	+	0.182282i
$246$	−12.6606	+	38.9653i	−0.807210	+	2.48434i
$247$		0			0
$248$		0			0
$249$	−5.24419	+	16.1400i	−0.332337	+	1.02283i
$250$	0.746033	+	2.29605i	0.0471833	+	0.145215i
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	−0.850391	−	0.526151i	$-0.823635\pi$
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	0.237614	+	0.971360i	$0.423635\pi$
$252$	38.2843			2.41168
$253$		0			0
$254$	10.4853			0.657905
$255$	15.6251	−	11.3523i	0.978483	−	0.710909i
$256$	−9.26141	−	28.5037i	−0.578838	−	1.78148i
$257$	−2.87809	+	8.85786i	−0.179531	+	0.552538i	−0.999811	−	0.0194227i	$-0.993817\pi$
$257$	−2.87809	+	8.85786i	−0.179531	+	0.552538i	0.820281	+	0.571961i	$0.193817\pi$
$258$	−33.1459	−	24.0819i	−2.06357	−	1.49927i
$259$	12.3891	+	9.00117i	0.769818	+	0.559306i
$260$	−1.38603	+	4.26576i	−0.0859578	+	0.264551i
$261$	5.65015	+	17.3894i	0.349736	+	1.07638i
$262$	22.0973	−	16.0546i	1.36517	−	0.991856i
$263$	10.9706			0.676474			0.338237	−	0.941061i	$-0.390169\pi$
$263$	10.9706			0.676474			0.338237	+	0.941061i	$0.390169\pi$
$264$		0			0
$265$	−11.6569			−0.716075
$266$		0			0
$267$	11.6366	+	35.8138i	0.712149	+	2.19177i
$268$	14.7707	−	45.4595i	0.902264	−	2.77688i
$269$	−14.0071	−	10.1767i	−0.854027	−	0.620487i	0.0722264	−	0.997388i	$-0.476990\pi$
$269$	−14.0071	−	10.1767i	−0.854027	−	0.620487i	−0.926253	+	0.376901i	$0.876990\pi$
$270$	11.0486	+	8.02730i	0.672398	+	0.488526i
$271$	−2.26006	+	6.95575i	−0.137289	+	0.422532i	−0.995939	−	0.0900304i	$-0.971304\pi$
$271$	−2.26006	+	6.95575i	−0.137289	+	0.422532i	0.858650	+	0.512562i	$0.171304\pi$
$272$	−6.33030	−	19.4827i	−0.383831	−	1.18131i
$273$	5.36169	−	3.89550i	0.324504	−	0.235766i
$274$	26.4853			1.60003
$275$		0			0
$276$	30.6274			1.84355
$277$	5.52431	−	4.01365i	0.331924	−	0.241157i	−0.409323	−	0.912390i	$-0.634235\pi$
$277$	5.52431	−	4.01365i	0.331924	−	0.241157i	0.741247	+	0.671233i	$0.234235\pi$
$278$	−2.98413	−	9.18421i	−0.178976	−	0.550833i
$279$		0			0
$280$	−7.14235	−	5.18922i	−0.426837	−	0.310115i
$281$	14.0071	+	10.1767i	0.835593	+	0.607094i	0.921136	−	0.389241i	$-0.127263\pi$
$281$	14.0071	+	10.1767i	0.835593	+	0.607094i	−0.0855434	+	0.996334i	$0.527263\pi$
$282$	5.96826	−	18.3684i	0.355405	−	1.09382i
$283$	−10.0824	−	31.0305i	−0.599338	−	1.84457i	−0.531825	−	0.846854i	$-0.678493\pi$
$283$	−10.0824	−	31.0305i	−0.599338	−	1.84457i	−0.0675133	−	0.997718i	$-0.521507\pi$
$284$	−35.0415	+	25.4592i	−2.07933	+	1.51072i
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$	−6.41464	+	4.66051i	−0.377986	+	0.274623i
$289$	9.15538	+	28.1773i	0.538551	+	1.65749i
$290$	2.72813	−	8.39633i	0.160202	−	0.493050i
$291$	8.36778	+	6.07955i	0.490528	+	0.356389i
$292$	−3.62867	−	2.63638i	−0.212352	−	0.154283i
$293$	2.83417	−	8.72268i	0.165574	−	0.509585i	−0.833504	−	0.552513i	$-0.813669\pi$
$293$	2.83417	−	8.72268i	0.165574	−	0.509585i	0.999078	+	0.0429287i	$0.0136688\pi$
$294$	−6.33030	−	19.4827i	−0.369191	−	1.13625i
$295$	1.34042	−	0.973874i	0.0780425	−	0.0567012i
$296$	33.7990			1.96453
$297$		0			0
$298$	0.828427			0.0479895
$299$	2.68085	−	1.94775i	0.155037	−	0.112641i
$300$	−3.34617	−	10.2984i	−0.193191	−	0.594581i
$301$	3.70820	−	11.4127i	0.213737	−	0.657816i
$302$	23.4377	+	17.0285i	1.34869	+	0.979878i
$303$	−21.3121	−	15.4841i	−1.22435	−	0.889539i
$304$		0			0
$305$	−2.87809	−	8.85786i	−0.164799	−	0.507200i
$306$	−66.6844	+	48.4490i	−3.81209	+	2.76965i
$307$	16.3431			0.932753			0.466376	−	0.884586i	$-0.345559\pi$
$307$	16.3431			0.932753			0.466376	+	0.884586i	$0.345559\pi$
$308$		0			0
$309$	−19.3137			−1.09872
$310$		0			0
$311$	1.44814	+	4.45693i	0.0821167	+	0.252729i	0.983683	−	0.179913i	$-0.0575815\pi$
$311$	1.44814	+	4.45693i	0.0821167	+	0.252729i	−0.901566	+	0.432642i	$0.857581\pi$
$312$	4.52012	−	13.9115i	0.255901	−	0.787584i
$313$	1.06281	+	0.772178i	0.0600737	+	0.0436461i	0.617417	−	0.786636i	$-0.288179\pi$
$313$	1.06281	+	0.772178i	0.0600737	+	0.0436461i	−0.557343	+	0.830282i	$0.688179\pi$
$314$	−27.3440	−	19.8665i	−1.54311	−	1.12113i
$315$	−3.09017	+	9.51057i	−0.174111	+	0.535860i
$316$	−4.73220	−	14.5642i	−0.266207	−	0.819300i
$317$	1.06281	−	0.772178i	0.0596935	−	0.0433699i	−0.557538	−	0.830151i	$-0.688254\pi$
$317$	1.06281	−	0.772178i	0.0596935	−	0.0433699i	0.617232	+	0.786781i	$0.288254\pi$
$318$	79.5980			4.46363
$319$		0			0
$320$	9.82843			0.549426
$321$	−17.5208	+	12.7296i	−0.977914	+	0.710496i
$322$	4.22020	+	12.9884i	0.235183	+	0.723817i
$323$		0			0
$324$	−3.09726	−	2.25029i	−0.172070	−	0.125016i
$325$	−0.947822	−	0.688633i	−0.0525757	−	0.0381985i
$326$	−12.2986	+	37.8511i	−0.681154	+	2.09638i
$327$	−6.69234	−	20.5969i	−0.370087	−	1.13901i
$328$	−21.4270	+	15.5677i	−1.18311	+	0.859580i
$329$	5.65685			0.311872
$330$		0			0
$331$	−7.31371			−0.401998			−0.200999	−	0.979591i	$-0.564419\pi$
$331$	−7.31371			−0.401998			−0.200999	+	0.979591i	$0.564419\pi$
$332$	−18.5836	+	13.5018i	−1.01991	+	0.741005i
$333$	−11.8305	−	36.4105i	−0.648307	−	1.99528i
$334$	−17.1368	+	52.7416i	−0.937684	+	2.88589i
$335$	10.1008	+	7.33866i	0.551866	+	0.400954i
$336$	13.7295	+	9.97505i	0.749004	+	0.544183i
$337$	6.33030	−	19.4827i	0.344833	−	1.06129i	−0.616840	−	0.787089i	$-0.711587\pi$
$337$	6.33030	−	19.4827i	0.344833	−	1.06129i	0.961673	−	0.274199i	$-0.0884128\pi$
$338$	8.67444	+	26.6972i	0.471827	+	1.45213i
$339$	44.9797	−	32.6797i	2.44296	−	1.77492i
$340$	26.1421			1.41776
$341$		0			0
$342$		0			0
$343$	16.1803	−	11.7557i	0.873656	−	0.634748i
$344$	−8.18440	−	25.1890i	−0.441273	−	1.35810i
$345$	−2.47214	+	7.60845i	−0.133095	+	0.409625i
$346$	43.2467	+	31.4206i	2.32496	+	1.68918i
$347$	8.87537	+	6.44833i	0.476455	+	0.346165i	0.799952	−	0.600065i	$-0.204858\pi$
$347$	8.87537	+	6.44833i	0.476455	+	0.346165i	−0.323497	+	0.946229i	$0.604858\pi$
$348$	−12.2364	+	37.6599i	−0.655943	+	2.01878i
$349$	−8.33436	−	25.6505i	−0.446128	−	1.37304i	−0.881242	−	0.472666i	$-0.843292\pi$
$349$	−8.33436	−	25.6505i	−0.446128	−	1.37304i	0.435114	−	0.900376i	$-0.356708\pi$
$350$	3.90628	−	2.83808i	0.208799	−	0.151702i
$351$	−6.62742			−0.353745
$352$		0			0
$353$	21.3137			1.13441			0.567207	−	0.823575i	$-0.308024\pi$
$353$	21.3137			1.13441			0.567207	+	0.823575i	$0.308024\pi$
$354$	−9.15298	+	6.65003i	−0.486476	+	0.353445i
$355$	−3.49613	−	10.7600i	−0.185555	−	0.571080i
$356$	−15.7508	+	48.4759i	−0.834789	+	2.56922i
$357$	−31.2502	−	22.7046i	−1.65394	−	1.20166i
$358$	18.8612	+	13.7035i	0.996845	+	0.724250i
$359$	−0.212076	+	0.652702i	−0.0111929	+	0.0344483i	−0.956497	−	0.291742i	$-0.905765\pi$
$359$	−0.212076	+	0.652702i	−0.0111929	+	0.0344483i	0.945304	+	0.326190i	$0.105765\pi$
$360$	6.82034	+	20.9908i	0.359463	+	1.10631i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	−51.4558			−2.70446
$363$		0			0
$364$	8.97056			0.470185
$365$	0.947822	−	0.688633i	0.0496113	−	0.0360447i
$366$	19.6529	+	60.4853i	1.02727	+	3.16162i
$367$	−2.62210	+	8.06998i	−0.136872	+	0.421250i	−0.995877	−	0.0907188i	$-0.971084\pi$
$367$	−2.62210	+	8.06998i	−0.136872	+	0.421250i	0.859004	+	0.511968i	$0.171084\pi$
$368$	6.86474	+	4.98752i	0.357849	+	0.259993i
$369$	24.2705	+	17.6336i	1.26347	+	0.917966i
$370$	−5.71227	+	17.5805i	−0.296967	+	0.913969i
$371$	7.20433	+	22.1727i	0.374030	+	1.15115i
$372$		0			0
$373$	−35.7990			−1.85360			−0.926801	−	0.375554i	$-0.877453\pi$
$373$	−35.7990			−1.85360			−0.926801	+	0.375554i	$0.877453\pi$
$374$		0			0
$375$	2.82843			0.146059
$376$	10.1008	−	7.33866i	0.520909	−	0.378463i
$377$	1.32391	+	4.07458i	0.0681850	+	0.209852i
$378$	8.44040	−	25.9769i	0.434127	−	1.33611i
$379$	−27.2290	−	19.7830i	−1.39866	−	1.01618i	−0.994852	−	0.101340i	$-0.967687\pi$
$379$	−27.2290	−	19.7830i	−1.39866	−	1.01618i	−0.403806	−	0.914845i	$-0.632313\pi$
$380$		0			0
$381$	3.79605	−	11.6830i	0.194477	−	0.598540i
$382$	−2.47214	−	7.60845i	−0.126485	−	0.389282i
$383$	4.73911	−	3.44317i	0.242157	−	0.175938i	−0.460087	−	0.887874i	$-0.652182\pi$
$383$	4.73911	−	3.44317i	0.242157	−	0.175938i	0.702244	+	0.711936i	$0.252182\pi$
$384$	−58.1421			−2.96705
$385$		0			0
$386$	−2.82843			−0.143963
$387$	−24.2705	+	17.6336i	−1.23374	+	0.896364i
$388$	4.32624	+	13.3148i	0.219631	+	0.675956i
$389$	6.37422	−	19.6178i	0.323186	−	0.994664i	−0.649067	−	0.760731i	$-0.724840\pi$
$389$	6.37422	−	19.6178i	0.323186	−	0.994664i	0.972253	−	0.233933i	$-0.0751595\pi$
$390$	6.47214	+	4.70228i	0.327729	+	0.238109i
$391$	−15.6251	−	11.3523i	−0.790196	−	0.574111i
$392$	4.09220	−	12.5945i	0.206687	−	0.636118i
$393$	−9.88854	−	30.4338i	−0.498811	−	1.53518i
$394$	21.1494	−	15.3660i	1.06549	−	0.774126i
$395$	4.00000			0.201262
$396$		0			0
$397$	−9.31371			−0.467442			−0.233721	−	0.972304i	$-0.575090\pi$
$397$	−9.31371			−0.467442			−0.233721	+	0.972304i	$0.575090\pi$
$398$	20.2016	−	14.6773i	1.01262	−	0.735708i
$399$		0			0
$400$	0.927051	−	2.85317i	0.0463525	−	0.142658i
$401$	4.29888	+	3.12332i	0.214676	+	0.155971i	0.689927	−	0.723879i	$-0.257643\pi$
$401$	4.29888	+	3.12332i	0.214676	+	0.155971i	−0.475251	+	0.879850i	$0.657643\pi$
$402$	−68.9726	−	50.1115i	−3.44004	−	2.49934i
$403$		0			0
$404$	−11.0186	−	33.9117i	−0.548195	−	1.68717i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−17.6569			−0.876295
$407$		0			0
$408$	−85.2548			−4.22074
$409$	0.832832	−	0.605088i	0.0411809	−	0.0299197i	−0.567004	−	0.823715i	$-0.691898\pi$
$409$	0.832832	−	0.605088i	0.0411809	−	0.0299197i	0.608185	+	0.793795i	$0.291898\pi$
$410$	−4.47620	−	13.7763i	−0.221064	−	0.680364i
$411$	9.58862	−	29.5107i	0.472972	−	1.45566i
$412$	−21.1494	−	15.3660i	−1.04196	−	0.757027i
$413$	−2.68085	−	1.94775i	−0.131916	−	0.0958425i
$414$	10.5505	−	32.4711i	0.518529	−	1.59587i
$415$	−1.85410	−	5.70634i	−0.0910143	−	0.280113i
$416$	−1.50304	+	1.09203i	−0.0736928	+	0.0535409i
$417$	−11.3137			−0.554035
$418$		0			0
$419$	−25.6569			−1.25342			−0.626710	−	0.779253i	$-0.715599\pi$
$419$	−25.6569			−1.25342			−0.626710	+	0.779253i	$0.715599\pi$
$420$	−17.5208	+	12.7296i	−0.854926	+	0.621140i
$421$	−1.85410	−	5.70634i	−0.0903634	−	0.278110i	0.895654	−	0.444751i	$-0.146708\pi$
$421$	−1.85410	−	5.70634i	−0.0903634	−	0.278110i	−0.986018	+	0.166641i	$0.946708\pi$
$422$	−11.9365	+	36.7369i	−0.581061	+	1.78832i
$423$	−11.4412	−	8.31254i	−0.556292	−	0.404169i
$424$	41.6287	+	30.2450i	2.02167	+	1.46883i
$425$	−2.11010	+	6.49422i	−0.102355	+	0.315016i
$426$	23.8731	+	73.4737i	1.15665	+	3.55981i
$427$	−15.0699	+	10.9489i	−0.729283	+	0.529855i
$428$	−29.3137			−1.41693
$429$		0			0
$430$	14.4853			0.698542
$431$	−9.15298	+	6.65003i	−0.440884	+	0.320321i	−0.785986	−	0.618244i	$-0.787844\pi$
$431$	−9.15298	+	6.65003i	−0.440884	+	0.320321i	0.345102	+	0.938565i	$0.387844\pi$
$432$	−5.24419	−	16.1400i	−0.252311	−	0.776534i
$433$	−2.36610	+	7.28210i	−0.113707	+	0.349955i	−0.991675	−	0.128764i	$-0.958899\pi$
$433$	−2.36610	+	7.28210i	−0.113707	+	0.349955i	0.877968	+	0.478720i	$0.158899\pi$
$434$		0			0
$435$	−8.36778	−	6.07955i	−0.401204	−	0.291492i
$436$	9.05843	−	27.8790i	0.433820	−	1.33516i
$437$		0			0
$438$	−6.47214	+	4.70228i	−0.309251	+	0.224684i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	−15.6251	+	11.3523i	−0.743211	+	0.539974i
$443$	−8.29044	−	25.5154i	−0.393891	−	1.21227i	−0.929822	−	0.368009i	$-0.880039\pi$
$443$	−8.29044	−	25.5154i	−0.393891	−	1.21227i	0.535931	−	0.844262i	$-0.319961\pi$
$444$	25.6211	−	78.8537i	1.21592	−	3.74223i
$445$	−10.7710	−	7.82560i	−0.510595	−	0.370969i
$446$	−21.1494	−	15.3660i	−1.00145	−	0.727599i
$447$	0.299920	−	0.923060i	0.0141857	−	0.0436592i
$448$	−6.07430	−	18.6948i	−0.286984	−	0.883245i
$449$	−23.1601	+	16.8268i	−1.09299	+	0.794105i	−0.979902	−	0.199480i	$-0.936075\pi$
$449$	−23.1601	+	16.8268i	−1.09299	+	0.794105i	−0.113089	+	0.993585i	$0.536075\pi$
$450$	−12.0711			−0.569036
$451$		0			0
$452$	75.2548			3.53969
$453$	27.4589	−	19.9501i	1.29013	−	0.937337i
$454$	18.8849	+	58.1216i	0.886311	+	2.72778i
$455$	−0.724072	+	2.22846i	−0.0339450	+	0.104472i
$456$		0			0
$457$	0.392601	+	0.285241i	0.0183651	+	0.0133430i	0.596930	−	0.802293i	$-0.296387\pi$
$457$	0.392601	+	0.285241i	0.0183651	+	0.0133430i	−0.578565	+	0.815636i	$0.696387\pi$
$458$	−0.980070	+	3.01635i	−0.0457957	+	0.140945i
$459$	11.9365	+	36.7369i	0.557149	+	1.71473i
$460$	−8.76038	+	6.36479i	−0.408455	+	0.296760i
$461$	−12.6274			−0.588117			−0.294059	−	0.955787i	$-0.595006\pi$
$461$	−12.6274			−0.588117			−0.294059	+	0.955787i	$0.595006\pi$
$462$		0			0
$463$	−6.14214			−0.285449			−0.142725	−	0.989762i	$-0.545586\pi$
$463$	−6.14214			−0.285449			−0.142725	+	0.989762i	$0.545586\pi$
$464$	−8.87537	+	6.44833i	−0.412029	+	0.299356i
$465$		0			0
$466$	−4.58224	+	14.1027i	−0.212268	+	0.653294i
$467$	11.9964	+	8.71593i	0.555129	+	0.403325i	0.829673	−	0.558249i	$-0.188527\pi$
$467$	11.9964	+	8.71593i	0.555129	+	0.403325i	−0.274544	+	0.961575i	$0.588527\pi$
$468$	−18.1433	−	13.1819i	−0.838676	−	0.609334i
$469$	7.71633	−	23.7484i	0.356307	−	1.09660i
$470$	2.11010	+	6.49422i	0.0973317	+	0.299556i
$471$	−32.0354	+	23.2751i	−1.47612	+	1.07246i
$472$	−7.31371			−0.336641
$473$		0			0
$474$	−27.3137			−1.25456
$475$		0			0
$476$	−16.1567	−	49.7253i	−0.740542	−	2.27916i
$477$	18.0108	−	55.4316i	0.824659	−	2.53804i
$478$	45.5349	+	33.0831i	2.08272	+	1.51318i
$479$	−29.1246	−	21.1603i	−1.33074	−	0.966837i	−0.999731	−	0.0232090i	$-0.992612\pi$
$479$	−29.1246	−	21.1603i	−1.33074	−	0.966837i	−0.331007	−	0.943628i	$-0.607388\pi$
$480$	1.38603	−	4.26576i	0.0632632	−	0.194704i
$481$	−2.77206	−	8.53151i	−0.126395	−	0.389003i
$482$	−11.7188	+	8.51423i	−0.533778	+	0.387813i
$483$	16.0000			0.728025
$484$		0			0
$485$	−3.65685			−0.166049
$486$	27.6216	−	20.0682i	1.25294	−	0.910314i
$487$	−7.56637	−	23.2869i	−0.342865	−	1.05523i	−0.962717	−	0.270511i	$-0.912807\pi$
$487$	−7.56637	−	23.2869i	−0.342865	−	1.05523i	0.619852	−	0.784719i	$-0.287193\pi$
$488$	−12.7045	+	39.1005i	−0.575107	+	1.77000i
$489$	37.7224	+	27.4069i	1.70586	+	1.23938i
$490$	5.85942	+	4.25712i	0.264702	+	0.192317i
$491$	0.212076	−	0.652702i	0.00957084	−	0.0294560i	−0.946157	−	0.323708i	$-0.895070\pi$
$491$	0.212076	−	0.652702i	0.00957084	−	0.0294560i	0.955728	+	0.294252i	$0.0950705\pi$
$492$	20.0770	+	61.7907i	0.905141	+	2.78574i
$493$	20.2016	−	14.6773i	0.909835	−	0.661034i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.3060	+	13.3001i	−0.821135	+	0.596589i
$498$	12.6606	+	38.9653i	0.567335	+	1.74608i
$499$	2.98413	−	9.18421i	0.133588	−	0.411142i	−0.861780	−	0.507283i	$-0.830650\pi$
$499$	2.98413	−	9.18421i	0.133588	−	0.411142i	0.995368	+	0.0961409i	$0.0306500\pi$
$500$	3.09726	+	2.25029i	0.138514	+	0.100636i
$501$	52.5623	+	38.1887i	2.34831	+	1.70615i
$502$	−8.95240	+	27.5526i	−0.399565	+	1.22973i
$503$	−5.13815	−	15.8136i	−0.229099	−	0.705094i	−0.997850	−	0.0655455i	$-0.979121\pi$
$503$	−5.13815	−	15.8136i	−0.229099	−	0.705094i	0.768751	−	0.639549i	$-0.220879\pi$
$504$	35.7117	−	25.9461i	1.59073	−	1.15573i
$505$	9.31371			0.414455
$506$		0			0
$507$	32.8873			1.46058
$508$	13.4519	−	9.77335i	0.596830	−	0.433622i
$509$	−4.11416	−	12.6621i	−0.182357	−	0.561237i	0.817536	−	0.575878i	$-0.195340\pi$
$509$	−4.11416	−	12.6621i	−0.182357	−	0.561237i	−0.999893	+	0.0146406i	$0.995340\pi$
$510$	14.4087	−	44.3453i	0.638026	−	1.96364i
$511$	−1.89564	−	1.37727i	−0.0838584	−	0.0609267i
$512$	−25.2758	−	18.3640i	−1.11704	−	0.811580i
$513$		0			0
$514$	6.94833	+	21.3848i	0.306478	+	0.943242i
$515$	5.52431	−	4.01365i	0.243430	−	0.176862i
$516$	−64.9706			−2.86017
$517$		0			0
$518$	36.9706			1.62439
$519$	50.6666	−	36.8115i	2.22402	−	1.61584i
$520$	1.59810	+	4.91846i	0.0700815	+	0.215689i
$521$	7.82237	−	24.0748i	0.342704	−	1.05473i	−0.620097	−	0.784525i	$-0.712907\pi$
$521$	7.82237	−	24.0748i	0.342704	−	1.05473i	0.962801	−	0.270210i	$-0.0870931\pi$
$522$	35.7117	+	25.9461i	1.56306	+	1.13563i
$523$	−33.6535	−	24.4507i	−1.47156	−	1.06915i	−0.980157	−	0.198223i	$-0.936483\pi$
$523$	−33.6535	−	24.4507i	−1.47156	−	1.06915i	−0.491407	−	0.870930i	$-0.663517\pi$
$524$	13.3847	−	41.1938i	0.584712	−	1.79956i
$525$	−1.74806	−	5.37999i	−0.0762918	−	0.234802i
$526$	21.4270	−	15.5677i	0.934263	−	0.678782i
$527$		0			0
$528$		0			0
$529$	−15.0000			−0.652174
$530$	−22.7675	+	16.5415i	−0.988956	+	0.718518i
$531$	2.55998	+	7.87881i	0.111094	+	0.341911i
$532$		0			0
$533$	5.68693	+	4.13180i	0.246328	+	0.178968i
$534$	73.5491	+	53.4365i	3.18278	+	2.31243i
$535$	2.36610	−	7.28210i	0.102295	−	0.314833i
$536$	−17.0308	−	52.4153i	−0.735617	−	2.26400i
$537$	22.0973	−	16.0546i	0.953567	−	0.692807i
$538$	−41.7990			−1.80208
$539$		0			0
$540$	21.6569			0.931963
$541$	4.85410	−	3.52671i	0.208694	−	0.151625i	−0.478529	−	0.878072i	$-0.658830\pi$
$541$	4.85410	−	3.52671i	0.208694	−	0.151625i	0.687223	+	0.726447i	$0.258830\pi$
$542$	5.45627	+	16.7927i	0.234367	+	0.721307i
$543$	−18.6289	+	57.3337i	−0.799441	+	2.46043i
$544$	8.76038	+	6.36479i	0.375598	+	0.272888i
$545$	6.19453	+	4.50059i	0.265344	+	0.192784i
$546$	4.94427	−	15.2169i	0.211595	−	0.651223i
$547$	10.5066	+	32.3359i	0.449229	+	1.38258i	0.877779	+	0.479066i	$0.159025\pi$
$547$	10.5066	+	32.3359i	0.449229	+	1.38258i	−0.428550	+	0.903518i	$0.640975\pi$
$548$	33.9787	−	24.6870i	1.45150	−	1.05458i
$549$	46.5685			1.98750
$550$		0			0
$551$		0			0
$552$	28.5694	−	20.7569i	1.21599	−	0.883471i
$553$	−2.47214	−	7.60845i	−0.105126	−	0.323544i
$554$	5.09423	−	15.6784i	0.216433	−	0.666113i
$555$	17.5208	+	12.7296i	0.743715	+	0.540341i
$556$	−12.3891	−	9.00117i	−0.525413	−	0.381735i
$557$	−3.04625	+	9.37539i	−0.129074	+	0.397248i	−0.994621	−	0.103579i	$-0.966971\pi$
$557$	−3.04625	+	9.37539i	−0.129074	+	0.397248i	0.865548	+	0.500827i	$0.166971\pi$
$558$		0			0
$559$	−5.68693	+	4.13180i	−0.240532	+	0.174757i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	41.7990			1.76318
$563$	0.277611	−	0.201696i	0.0116999	−	0.00850047i	−0.581920	−	0.813246i	$-0.697698\pi$
$563$	0.277611	−	0.201696i	0.0116999	−	0.00850047i	0.593620	+	0.804746i	$0.297698\pi$
$564$	−9.46439	−	29.1284i	−0.398523	−	1.22653i
$565$	−6.07430	+	18.6948i	−0.255548	+	0.786495i
$566$	−63.7259	−	46.2996i	−2.67860	−	1.94612i
$567$	−1.61803	−	1.17557i	−0.0679510	−	0.0493693i
$568$	−15.4327	+	47.4968i	−0.647540	+	1.99292i
$569$	−9.78251	−	30.1075i	−0.410104	−	1.26217i	−0.916557	−	0.399903i	$-0.869044\pi$
$569$	−9.78251	−	30.1075i	−0.410104	−	1.26217i	0.506453	−	0.862267i	$-0.330956\pi$
$570$		0			0
$571$	21.9411			0.918208			0.459104	−	0.888383i	$-0.348171\pi$
$571$	21.9411			0.918208			0.459104	+	0.888383i	$0.348171\pi$
$572$		0			0
$573$	−9.37258			−0.391545
$574$	−23.4377	+	17.0285i	−0.978270	+	0.710755i
$575$	−0.874032	−	2.68999i	−0.0364497	−	0.112181i
$576$	−15.1858	+	46.7369i	−0.632740	+	1.94737i
$577$	21.8196	+	15.8529i	0.908364	+	0.659965i	0.940600	−	0.339515i	$-0.110263\pi$
$577$	21.8196	+	15.8529i	0.908364	+	0.659965i	−0.0322368	+	0.999480i	$0.510263\pi$
$578$	57.8665	+	42.0425i	2.40693	+	1.74874i
$579$	−1.02399	+	3.15152i	−0.0425557	+	0.130973i
$580$	−4.32624	−	13.3148i	−0.179637	−	0.552867i
$581$	−9.70820	+	7.05342i	−0.402764	+	0.292625i
$582$	24.9706			1.03506
$583$		0			0
$584$	−5.17157			−0.214001
$585$	4.73911	−	3.44317i	0.195938	−	0.142357i
$586$	−6.84230	−	21.0584i	−0.282653	−	0.869915i
$587$	−0.661956	+	2.03729i	−0.0273219	+	0.0840880i	−0.963788	−	0.266671i	$-0.914076\pi$
$587$	−0.661956	+	2.03729i	−0.0273219	+	0.0840880i	0.936466	+	0.350759i	$0.114076\pi$
$588$	−26.2811	−	19.0944i	−1.08382	−	0.787439i
$589$		0			0
$590$	1.23607	−	3.80423i	0.0508881	−	0.156618i
$591$	−9.46439	−	29.1284i	−0.389313	−	1.19818i
$592$	18.5836	−	13.5018i	0.763780	−	0.554919i
$593$	−3.51472			−0.144332			−0.0721661	−	0.997393i	$-0.522991\pi$
$593$	−3.51472			−0.144332			−0.0721661	+	0.997393i	$0.522991\pi$
$594$		0			0
$595$	13.6569			0.559876
$596$	1.06281	−	0.772178i	0.0435345	−	0.0316297i
$597$	−9.04024	−	27.8230i	−0.369992	−	1.13872i
$598$	2.47214	−	7.60845i	0.101093	−	0.311133i
$599$	4.57649	+	3.32502i	0.186990	+	0.135856i	0.677342	−	0.735668i	$-0.263132\pi$
$599$	4.57649	+	3.32502i	0.186990	+	0.135856i	−0.490352	+	0.871525i	$0.663132\pi$
$600$	−10.1008	−	7.33866i	−0.412364	−	0.299600i
$601$	−7.39821	+	22.7694i	−0.301779	+	0.928782i	0.679080	+	0.734064i	$0.262379\pi$
$601$	−7.39821	+	22.7694i	−0.301779	+	0.928782i	−0.980859	+	0.194717i	$0.937621\pi$
$602$	−8.95240	−	27.5526i	−0.364872	−	1.12296i
$603$	−50.5040	+	36.6933i	−2.05668	+	1.49427i
$604$	45.9411			1.86932
$605$		0			0
$606$	−63.5980			−2.58349
$607$	30.9726	−	22.5029i	1.25714	−	0.913366i	0.258526	−	0.966004i	$-0.416763\pi$
$607$	30.9726	−	22.5029i	1.25714	−	0.913366i	0.998614	+	0.0526384i	$0.0167631\pi$
$608$		0			0
$609$	−6.39242	+	19.6738i	−0.259034	+	0.797224i
$610$	−18.1910	−	13.2165i	−0.736531	−	0.535121i
$611$	−2.68085	−	1.94775i	−0.108455	−	0.0787975i
$612$	−40.3918	+	124.313i	−1.63274	+	5.02506i
$613$	7.86629	+	24.2099i	0.317716	+	0.977831i	0.974622	+	0.223858i	$0.0718650\pi$
$613$	7.86629	+	24.2099i	0.317716	+	0.977831i	−0.656905	+	0.753973i	$0.728135\pi$
$614$	31.9204	−	23.1916i	1.28820	−	0.935935i
$615$	−16.9706			−0.684319
$616$		0			0
$617$	0.343146			0.0138145			0.00690726	−	0.999976i	$-0.497801\pi$
$617$	0.343146			0.0138145			0.00690726	+	0.999976i	$0.497801\pi$
$618$	−37.7224	+	27.4069i	−1.51742	+	1.10247i
$619$	−4.43228	−	13.6411i	−0.178148	−	0.548284i	0.821615	−	0.570043i	$-0.193073\pi$
$619$	−4.43228	−	13.6411i	−0.178148	−	0.548284i	−0.999763	+	0.0217589i	$0.993073\pi$
$620$		0			0
$621$	−12.9443	−	9.40456i	−0.519436	−	0.377392i
$622$	9.15298	+	6.65003i	0.367001	+	0.266642i
$623$	−8.22832	+	25.3242i	−0.329661	+	1.01459i
$624$	−3.07198	−	9.45457i	−0.122977	−	0.378486i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	3.17157			0.126762
$627$		0			0
$628$	−53.5980			−2.13879
$629$	−42.2989	+	30.7319i	−1.68657	+	1.22536i
$630$	7.46033	+	22.9605i	0.297227	+	0.914770i
$631$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$631$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$632$	−14.2847	−	10.3784i	−0.568215	−	0.412832i
$633$	36.6119	+	26.6001i	1.45519	+	1.05726i
$634$	0.980070	−	3.01635i	0.0389235	−	0.119794i
$635$	1.34211	+	4.13058i	0.0532598	+	0.163917i
$636$	102.118	−	74.1934i	4.04926	−	2.94196i
$637$	−3.51472			−0.139258
$638$		0			0
$639$	56.5685			2.23782
$640$	16.6304	−	12.0827i	0.657376	−	0.477611i
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	0.949250	+	0.314524i	$0.101845\pi$
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	−0.583086	+	0.812410i	$0.698155\pi$
$642$	−16.1567	+	49.7253i	−0.637655	+	1.96250i
$643$	1.17780	+	0.855724i	0.0464480	+	0.0337464i	0.610767	−	0.791810i	$-0.290861\pi$
$643$	1.17780	+	0.855724i	0.0464480	+	0.0337464i	−0.564319	+	0.825557i	$0.690861\pi$
$644$	17.5208	+	12.7296i	0.690415	+	0.501616i
$645$	5.24419	−	16.1400i	0.206490	−	0.635510i
$646$		0			0
$647$	−21.9346	+	15.9364i	−0.862339	+	0.626526i	−0.928520	−	0.371281i	$-0.878919\pi$
$647$	−21.9346	+	15.9364i	−0.862339	+	0.626526i	0.0661810	+	0.997808i	$0.478919\pi$
$648$	−4.41421			−0.173407
$649$		0			0
$650$	−2.82843			−0.110940
$651$		0			0
$652$	19.5029	+	60.0237i	0.763792	+	2.35071i
$653$	3.60217	−	11.0863i	0.140964	−	0.433842i	−0.855506	−	0.517793i	$-0.826754\pi$
$653$	3.60217	−	11.0863i	0.140964	−	0.433842i	0.996470	+	0.0839510i	$0.0267539\pi$
$654$	−42.2989	−	30.7319i	−1.65402	−	1.20171i
$655$	9.15298	+	6.65003i	0.357637	+	0.259838i
$656$	−5.56231	+	17.1190i	−0.217172	+	0.668385i
$657$	1.81018	+	5.57116i	0.0706218	+	0.217352i
$658$	11.0486	−	8.02730i	0.430720	−	0.312937i
$659$	−45.9411			−1.78961			−0.894806	−	0.446455i	$-0.852686\pi$
$659$	−45.9411			−1.78961			−0.894806	+	0.446455i	$0.852686\pi$
$660$		0			0
$661$	44.6274			1.73581			0.867903	−	0.496734i	$-0.165468\pi$
$661$	44.6274			1.73581			0.867903	+	0.496734i	$0.165468\pi$
$662$	−14.2847	+	10.3784i	−0.555190	+	0.403369i
$663$	6.99226	+	21.5200i	0.271557	+	0.835766i
$664$	−8.18440	+	25.1890i	−0.317616	+	0.977523i
$665$		0			0
$666$	−74.7745	−	54.3269i	−2.89745	−	2.10512i
$667$	−3.19621	+	9.83692i	−0.123758	+	0.380887i
$668$	27.1753	+	83.6370i	1.05144	+	3.23601i
$669$	−24.7781	+	18.0023i	−0.957977	+	0.696011i
$670$	30.1421			1.16449
$671$		0			0
$672$	−8.97056			−0.346047
$673$	−10.1008	+	7.33866i	−0.389357	+	0.282885i	−0.765192	−	0.643802i	$-0.777356\pi$
$673$	−10.1008	+	7.33866i	−0.389357	+	0.282885i	0.375835	+	0.926687i	$0.377356\pi$
$674$	−15.2827	−	47.0353i	−0.588667	−	1.81173i
$675$	−1.74806	+	5.37999i	−0.0672830	+	0.207076i
$676$	36.0132	+	26.1651i	1.38512	+	1.00635i
$677$	18.4686	+	13.4182i	0.709805	+	0.515704i	0.883111	−	0.469164i	$-0.155445\pi$
$677$	18.4686	+	13.4182i	0.709805	+	0.515704i	−0.173305	+	0.984868i	$0.555445\pi$
$678$	41.4779	−	127.656i	1.59295	−	4.90260i
$679$	2.26006	+	6.95575i	0.0867332	+	0.266937i
$680$	24.3855	−	17.7171i	0.935141	−	0.679420i
$681$	71.5980			2.74364
$682$		0			0
$683$	−7.79899			−0.298420			−0.149210	−	0.988806i	$-0.547673\pi$
$683$	−7.79899			−0.298420			−0.149210	+	0.988806i	$0.547673\pi$
$684$		0			0
$685$	3.39009	+	10.4336i	0.129529	+	0.398648i
$686$	14.9207	−	45.9211i	0.569673	−	1.75327i
$687$	3.00609	+	2.18405i	0.114689	+	0.0833267i
$688$	−14.5623	−	10.5801i	−0.555183	−	0.403364i
$689$	4.22020	−	12.9884i	0.160777	−	0.494820i
$690$	5.96826	+	18.3684i	0.227208	+	0.699274i
$691$	31.8055	−	23.1080i	1.20994	−	0.879070i	0.214712	−	0.976677i	$-0.431119\pi$
$691$	31.8055	−	23.1080i	1.20994	−	0.879070i	0.995225	+	0.0976071i	$0.0311188\pi$
$692$	84.7696			3.22245
$693$		0			0
$694$	26.4853			1.00537
$695$	3.23607	−	2.35114i	0.122751	−	0.0891839i
$696$	14.1087	+	43.4222i	0.534791	+	1.64592i
$697$	12.6606	−	38.9653i	0.479554	−	1.47592i
$698$	−52.6773	−	38.2723i	−1.99386	−	1.44863i
$699$	14.0547	+	10.2113i	0.531598	+	0.386229i
$700$	2.36610	−	7.28210i	0.0894301	−	0.275238i
$701$	3.90209	+	12.0094i	0.147380	+	0.453588i	0.997309	−	0.0733080i	$-0.0233556\pi$
$701$	3.90209	+	12.0094i	0.147380	+	0.453588i	−0.849930	+	0.526896i	$0.823356\pi$
$702$	−12.9443	+	9.40456i	−0.488550	+	0.354952i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	41.6287	−	30.2450i	1.56671	−	1.13829i
$707$	−5.75619	−	17.7157i	−0.216484	−	0.666268i
$708$	−5.54411	+	17.0630i	−0.208361	+	0.641268i
$709$	−19.9240	−	14.4756i	−0.748261	−	0.543644i	0.147026	−	0.989133i	$-0.453030\pi$
$709$	−19.9240	−	14.4756i	−0.748261	−	0.543644i	−0.895287	+	0.445489i	$0.853030\pi$
$710$	−22.0973	−	16.0546i	−0.829295	−	0.602518i
$711$	−6.18034	+	19.0211i	−0.231781	+	0.713348i
$712$	18.1608	+	55.8932i	0.680604	+	2.09468i
$713$		0			0
$714$	−93.2548			−3.48997
$715$		0			0
$716$	36.9706			1.38165
$717$	53.3475	−	38.7592i	1.99230	−	1.44749i
$718$	0.511996	+	1.57576i	0.0191075	+	0.0588069i
$719$	5.66834	−	17.4454i	0.211394	−	0.650602i	−0.787996	−	0.615680i	$-0.788882\pi$
$719$	5.66834	−	17.4454i	0.211394	−	0.650602i	0.999390	−	0.0349227i	$-0.0111185\pi$
$720$	12.1353	+	8.81678i	0.452254	+	0.328582i
$721$	−11.0486	−	8.02730i	−0.411472	−	0.298952i
$722$	14.1746	−	43.6250i	0.527525	−	1.62356i
$723$	5.24419	+	16.1400i	0.195034	+	0.600252i
$724$	−66.0142	+	47.9621i	−2.45340	+	1.78250i
$725$	3.65685			0.135812
$726$		0			0
$727$	−19.5147			−0.723761			−0.361880	−	0.932225i	$-0.617865\pi$
$727$	−19.5147			−0.723761			−0.361880	+	0.932225i	$0.617865\pi$
$728$	8.36778	−	6.07955i	0.310131	−	0.225323i
$729$	−13.2877	−	40.8954i	−0.492138	−	1.51465i
$730$	0.874032	−	2.68999i	0.0323494	−	0.0995611i
$731$	33.1459	+	24.0819i	1.22594	+	0.890701i
$732$	81.5916	+	59.2798i	3.01571	+	2.19104i
$733$	5.39415	−	16.6015i	0.199238	−	0.613190i	−0.800663	−	0.599114i	$-0.795519\pi$
$733$	5.39415	−	16.6015i	0.199238	−	0.613190i	0.999901	−	0.0140757i	$-0.00448058\pi$
$734$	6.33030	+	19.4827i	0.233656	+	0.719118i
$735$	6.86474	−	4.98752i	0.253210	−	0.183968i
$736$	−4.48528			−0.165330
$737$		0			0
$738$	72.4264			2.66605
$739$	24.2229	−	17.5990i	0.891053	−	0.647388i	−0.0450993	−	0.998983i	$-0.514360\pi$
$739$	24.2229	−	17.5990i	0.891053	−	0.647388i	0.936152	+	0.351595i	$0.114360\pi$
$740$	9.05843	+	27.8790i	0.332995	+	1.02485i
$741$		0			0
$742$	45.5349	+	33.0831i	1.67164	+	1.21452i
$743$	−40.1256	−	29.1530i	−1.47207	−	1.06952i	−0.980009	−	0.198956i	$-0.936245\pi$
$743$	−40.1256	−	29.1530i	−1.47207	−	1.06952i	−0.492057	−	0.870563i	$-0.663755\pi$
$744$		0			0
$745$	0.106038	+	0.326351i	0.00388493	+	0.0119566i
$746$	−69.9204	+	50.8002i	−2.55997	+	1.85993i
$747$	30.0000			1.09764
$748$		0			0
$749$	−15.3137			−0.559551
$750$	5.52431	−	4.01365i	0.201719	−	0.146558i
$751$	−4.94427	−	15.2169i	−0.180419	−	0.555273i	0.819420	−	0.573193i	$-0.194295\pi$
$751$	−4.94427	−	15.2169i	−0.180419	−	0.555273i	−0.999839	+	0.0179203i	$0.994295\pi$
$752$	2.62210	−	8.06998i	0.0956180	−	0.294282i
$753$	27.4589	+	19.9501i	1.00066	+	0.727022i
$754$	8.36778	+	6.07955i	0.304737	+	0.221404i
$755$	−3.70820	+	11.4127i	−0.134955	+	0.415350i
$756$	−13.3847	−	41.1938i	−0.486796	−	1.49820i
$757$	−10.7710	+	7.82560i	−0.391479	+	0.284426i	−0.766061	−	0.642767i	$-0.777786\pi$
$757$	−10.7710	+	7.82560i	−0.391479	+	0.284426i	0.374582	+	0.927194i	$0.377786\pi$
$758$	−81.2548			−2.95131
$759$		0			0
$760$		0			0
$761$	−24.2705	+	17.6336i	−0.879805	+	0.639216i	−0.933200	−	0.359358i	$-0.882996\pi$
$761$	−24.2705	+	17.6336i	−0.879805	+	0.639216i	0.0533947	+	0.998573i	$0.482996\pi$
$762$	−9.16447	−	28.2053i	−0.331994	−	1.02177i
$763$	4.73220	−	14.5642i	0.171317	−	0.527260i
$764$	−10.2634	−	7.45682i	−0.371318	−	0.269778i
$765$	−27.6216	−	20.0682i	−0.998660	−	0.725569i
$766$	4.37016	−	13.4500i	0.157900	−	0.485967i
$767$	0.599841	+	1.84612i	0.0216590	+	0.0666595i
$768$	−68.5800	+	49.8263i	−2.47467	+	1.79795i
$769$	18.9706			0.684096			0.342048	−	0.939682i	$-0.388879\pi$
$769$	18.9706			0.684096			0.342048	+	0.939682i	$0.388879\pi$
$770$		0			0
$771$	26.3431			0.948725
$772$	−3.62867	+	2.63638i	−0.130599	+	0.0948855i
$773$	8.12229	+	24.9978i	0.292138	+	0.899109i	0.984168	+	0.177240i	$0.0567169\pi$
$773$	8.12229	+	24.9978i	0.292138	+	0.899109i	−0.692029	+	0.721869i	$0.743283\pi$
$774$	−22.3810	+	68.8816i	−0.804468	+	2.47590i
$775$		0			0
$776$	13.0593	+	9.48811i	0.468800	+	0.340603i
$777$	13.3847	−	41.1938i	0.480172	−	1.47782i
$778$	−15.3887	−	47.3617i	−0.551713	−	1.69800i
$779$		0			0
$780$	12.6863			0.454242
$781$		0			0
$782$	−46.6274			−1.66739
$783$	16.7356	−	12.1591i	0.598080	−	0.434531i
$784$	−2.78115	−	8.55951i	−0.0993269	−	0.305697i
$785$	4.32624	−	13.3148i	0.154410	−	0.475225i
$786$	−62.5005	−	45.4093i	−2.22932	−	1.61969i
$787$	−12.1114	−	8.79948i	−0.431726	−	0.313667i	0.350613	−	0.936521i	$-0.385973\pi$
$787$	−12.1114	−	8.79948i	−0.431726	−	0.313667i	−0.782339	+	0.622853i	$0.785973\pi$
$788$	12.8106	−	39.4269i	0.456357	−	1.40452i
$789$	−9.58862	−	29.5107i	−0.341364	−	1.05061i
$790$	7.81256	−	5.67616i	0.277958	−	0.201949i
$791$	39.3137			1.39783
$792$		0			0
$793$	10.9117			0.387485
$794$	−18.1910	+	13.2165i	−0.645574	+	0.469037i
$795$	10.1885	+	31.3569i	0.361348	+	1.11211i
$796$	12.2364	−	37.6599i	0.433709	−	1.33482i
$797$	−26.3961	−	19.1779i	−0.934999	−	0.679317i	0.0122126	−	0.999925i	$-0.496113\pi$
$797$	−26.3961	−	19.1779i	−0.934999	−	0.679317i	−0.947212	+	0.320609i	$0.896113\pi$
$798$		0			0
$799$	−5.96826	+	18.3684i	−0.211142	+	0.649828i
$800$	0.490035	+	1.50817i	0.0173254	+	0.0533220i
$801$	53.8551	−	39.1280i	1.90288	−	1.38252i
$802$	12.8284			0.452988
$803$		0			0
$804$	−135.196			−4.76799
$805$	−4.57649	+	3.32502i	−0.161300	+	0.117191i
$806$		0			0
$807$	−15.1327	+	46.5738i	−0.532698	+	1.63947i
$808$	−33.2609	−	24.1654i	−1.17011	−	0.850137i
$809$	−8.87537	−	6.44833i	−0.312041	−	0.226711i	0.420731	−	0.907186i	$-0.361774\pi$
$809$	−8.87537	−	6.44833i	−0.312041	−	0.226711i	−0.732772	+	0.680474i	$0.761774\pi$
$810$	0.746033	−	2.29605i	0.0262129	−	0.0806751i
$811$	−16.6687	−	51.3011i	−0.585318	−	1.80142i	−0.597989	−	0.801504i	$-0.704033\pi$
$811$	−16.6687	−	51.3011i	−0.585318	−	1.80142i	0.0126712	−	0.999920i	$-0.495967\pi$
$812$	−22.6525	+	16.4580i	−0.794946	+	0.577562i
$813$	20.6863			0.725500
$814$		0			0
$815$	−16.4853			−0.577454
$816$	−46.8754	+	34.0569i	−1.64097	+	1.19223i
$817$		0			0
$818$	0.767994	−	2.36364i	0.0268523	−	0.0826428i
$819$	−9.47822	−	6.88633i	−0.331196	−	0.240628i
$820$	−18.5836	−	13.5018i	−0.648967	−	0.471502i
$821$	12.7666	−	39.2917i	0.445559	−	1.37129i	−0.436311	−	0.899796i	$-0.643715\pi$
$821$	12.7666	−	39.2917i	0.445559	−	1.37129i	0.881870	−	0.471493i	$-0.156285\pi$
$822$	−23.1490	−	71.2452i	−0.807414	−	2.48496i
$823$	−15.7877	+	11.4705i	−0.550326	+	0.399835i	−0.827906	−	0.560867i	$-0.810468\pi$
$823$	−15.7877	+	11.4705i	−0.550326	+	0.399835i	0.277580	+	0.960703i	$0.410468\pi$
$824$	−30.1421			−1.05005
$825$		0			0
$826$	−8.00000			−0.278356
$827$	18.0284	−	13.0984i	0.626907	−	0.455475i	−0.228420	−	0.973563i	$-0.573356\pi$
$827$	18.0284	−	13.0984i	0.626907	−	0.455475i	0.855327	+	0.518088i	$0.173356\pi$
$828$	−16.7308	−	51.4922i	−0.581437	−	1.78948i
$829$	5.56231	−	17.1190i	0.193187	−	0.594568i	−0.806806	−	0.590816i	$-0.798806\pi$
$829$	5.56231	−	17.1190i	0.193187	−	0.594568i	0.999993	−	0.00375172i	$-0.00119421\pi$
$830$	−11.7188	−	8.51423i	−0.406767	−	0.295533i
$831$	−15.6251	−	11.3523i	−0.542029	−	0.393807i
$832$	−3.55824	+	10.9511i	−0.123360	+	0.379663i
$833$	6.33030	+	19.4827i	0.219332	+	0.675034i
$834$	−22.0973	+	16.0546i	−0.765165	+	0.555925i
$835$	−22.9706			−0.794929
$836$		0			0
$837$		0			0
$838$	−50.1114	+	36.4081i	−1.73107	+	1.25770i
$839$	8.14048	+	25.0538i	0.281041	+	0.864954i	0.987558	+	0.157258i	$0.0502654\pi$
$839$	8.14048	+	25.0538i	0.281041	+	0.864954i	−0.706517	+	0.707696i	$0.749735\pi$
$840$	−7.71633	+	23.7484i	−0.266239	+	0.819398i
$841$	12.6428	+	9.18557i	0.435960	+	0.316744i
$842$	−11.7188	−	8.51423i	−0.403858	−	0.293420i
$843$	15.1327	−	46.5738i	0.521199	−	1.60409i
$844$	18.9288	+	58.2568i	0.651556	+	2.00528i
$845$	−9.40678	+	6.83442i	−0.323603	+	0.235111i
$846$	−34.1421			−1.17383
$847$		0			0
$848$	34.9706			1.20089
$849$	−74.6595	+	54.2433i	−2.56231	+	1.86163i
$850$	5.09423	+	15.6784i	0.174731	+	0.537766i
$851$	6.69234	−	20.5969i	0.229410	−	0.706052i
$852$	99.1124	+	72.0094i	3.39553	+	2.46700i
$853$	−12.5517	−	9.11932i	−0.429761	−	0.312240i	0.351792	−	0.936078i	$-0.385572\pi$
$853$	−12.5517	−	9.11932i	−0.429761	−	0.312240i	−0.781553	+	0.623838i	$0.785572\pi$
$854$	−13.8967	+	42.7695i	−0.475534	+	1.46354i
$855$		0			0
$856$	−27.3440	+	19.8665i	−0.934597	+	0.679025i
$857$	−24.7696			−0.846112			−0.423056	−	0.906104i	$-0.639043\pi$
$857$	−24.7696			−0.846112			−0.423056	+	0.906104i	$0.639043\pi$
$858$		0			0
$859$	24.2843			0.828569			0.414284	−	0.910148i	$-0.364032\pi$
$859$	24.2843			0.828569			0.414284	+	0.910148i	$0.364032\pi$
$860$	18.5836	−	13.5018i	0.633695	−	0.460406i
$861$	10.4884	+	32.2799i	0.357443	+	1.10010i
$862$	−8.44040	+	25.9769i	−0.287481	+	0.884776i
$863$	7.41996	+	5.39092i	0.252578	+	0.183509i	0.706869	−	0.707345i	$-0.250107\pi$
$863$	7.41996	+	5.39092i	0.252578	+	0.183509i	−0.454290	+	0.890854i	$0.650107\pi$
$864$	7.25734	+	5.27276i	0.246900	+	0.179383i
$865$	−6.84230	+	21.0584i	−0.232645	+	0.716008i
$866$	5.71227	+	17.5805i	0.194111	+	0.597411i
$867$	67.7948	−	49.2558i	2.30243	−	1.67282i
$868$		0			0
$869$		0			0
$870$	−24.9706			−0.846581
$871$	−11.8338	+	8.59778i	−0.400974	+	0.291325i
$872$	−10.4445	−	32.1447i	−0.353694	−	1.08856i
$873$	5.65015	−	17.3894i	0.191229	−	0.588541i
$874$		0			0
$875$	1.61803	+	1.17557i	0.0546995	+	0.0397415i
$876$	−3.92028	+	12.0654i	−0.132454	+	0.407651i
$877$	15.2827	+	47.0353i	0.516060	+	1.58827i	0.781345	+	0.624099i	$0.214534\pi$
$877$	15.2827	+	47.0353i	0.516060	+	1.58827i	−0.265285	+	0.964170i	$0.585466\pi$
$878$	31.2502	−	22.7046i	1.05464	−	0.766244i
$879$	−25.9411			−0.874972
$880$		0			0
$881$	−7.37258			−0.248389			−0.124194	−	0.992258i	$-0.539635\pi$
$881$	−7.37258			−0.248389			−0.124194	+	0.992258i	$0.539635\pi$
$882$	−29.2971	+	21.2856i	−0.986485	+	0.716723i
$883$	11.4866	+	35.3523i	0.386556	+	1.18970i	0.935345	+	0.353737i	$0.115089\pi$
$883$	11.4866	+	35.3523i	0.386556	+	1.18970i	−0.548788	+	0.835961i	$0.684911\pi$
$884$	−9.46439	+	29.1284i	−0.318322	+	0.979694i
$885$	−3.79129	−	2.75453i	−0.127443	−	0.0925926i
$886$	−52.3997	−	38.0706i	−1.76040	−	1.27901i
$887$	−11.8305	+	36.4105i	−0.397229	+	1.22255i	0.529983	+	0.848008i	$0.322198\pi$
$887$	−11.8305	+	36.4105i	−0.397229	+	1.22255i	−0.927212	+	0.374537i	$0.877802\pi$
$888$	−29.5414	−	90.9191i	−0.991344	−	3.05104i
$889$	7.02736	−	5.10567i	0.235690	−	0.171239i
$890$	−32.1421			−1.07741
$891$		0			0
$892$	−41.4558			−1.38804
$893$		0			0
$894$	−0.724072	−	2.22846i	−0.0242166	−	0.0745310i
$895$	−2.98413	+	9.18421i	−0.0997485	+	0.306994i
$896$	−33.2609	−	24.1654i	−1.11117	−	0.807311i
$897$	−7.58258	−	5.50907i	−0.253175	−	0.183942i
$898$	−21.3570	+	65.7301i	−0.712692	+	2.19344i
$899$		0			0
$900$	−15.4863	+	11.2515i	−0.516210	+	0.375049i
$901$	−79.5980			−2.65179
$902$		0			0
$903$	−33.9411			−1.12949
$904$	70.1980	−	51.0019i	2.33475	−	1.69630i
$905$	−6.58630	−	20.2705i	−0.218936	−	0.673816i
$906$	25.3212	−	77.9306i	0.841241	−	2.58907i
$907$	22.2599	+	16.1727i	0.739127	+	0.537007i	0.892438	−	0.451171i	$-0.148993\pi$
$907$	22.2599	+	16.1727i	0.739127	+	0.537007i	−0.153311	+	0.988178i	$0.548993\pi$
$908$	78.4032	+	56.9633i	2.60190	+	1.89039i
$909$	−14.3905	+	44.2893i	−0.477302	+	1.46898i
$910$	1.74806	+	5.37999i	0.0579478	+	0.178345i
$911$	8.04254	−	5.84325i	0.266461	−	0.193595i	−0.446529	−	0.894769i	$-0.647340\pi$
$911$	8.04254	−	5.84325i	0.266461	−	0.193595i	0.712991	+	0.701174i	$0.247340\pi$
$912$		0			0
$913$		0			0
$914$	1.17157			0.0387522
$915$	−21.3121	+	15.4841i	−0.704555	+	0.511889i
$916$	1.55418	+	4.78328i	0.0513516	+	0.158044i
$917$	6.99226	−	21.5200i	0.230905	−	0.710651i
$918$	75.4447	+	54.8138i	2.49005	+	1.80913i
$919$	−25.8885	−	18.8091i	−0.853984	−	0.620456i	0.0722574	−	0.997386i	$-0.476980\pi$
$919$	−25.8885	−	18.8091i	−0.853984	−	0.620456i	−0.926242	+	0.376930i	$0.876980\pi$
$920$	−3.85816	+	11.8742i	−0.127200	+	0.391481i
$921$	−14.2844	−	43.9630i	−0.470688	−	1.44863i
$922$	−24.6631	+	17.9188i	−0.812236	+	0.590124i
$923$	13.2548			0.436288
$924$		0			0
$925$	−7.65685			−0.251756
$926$	−11.9964	+	8.71593i	−0.394228	+	0.286423i
$927$	10.5505	+	32.4711i	0.346524	+	1.06649i
$928$	1.79199	−	5.51517i	0.0588248	−	0.181044i
$929$	−4.29888	−	3.12332i	−0.141042	−	0.102473i	0.515027	−	0.857174i	$-0.327782\pi$
$929$	−4.29888	−	3.12332i	−0.141042	−	0.102473i	−0.656069	+	0.754701i	$0.727782\pi$
$930$		0			0
$931$		0			0
$932$	7.26645	+	22.3638i	0.238020	+	0.732551i
$933$	10.7234	−	7.79100i	0.351068	−	0.255066i
$934$	35.7990			1.17138
$935$		0			0
$936$	−25.8579			−0.845191
$937$	−1.17780	+	0.855724i	−0.0384771	+	0.0279553i	−0.606858	−	0.794811i	$-0.707570\pi$
$937$	−1.17780	+	0.855724i	−0.0384771	+	0.0279553i	0.568380	+	0.822766i	$0.307570\pi$
$938$	−18.6289	−	57.3337i	−0.608254	−	1.87201i
$939$	1.14822	−	3.53387i	0.0374709	−	0.115323i
$940$	8.76038	+	6.36479i	0.285732	+	0.207597i
$941$	−5.40932	−	3.93010i	−0.176339	−	0.128118i	0.496115	−	0.868257i	$-0.334760\pi$
$941$	−5.40932	−	3.93010i	−0.176339	−	0.128118i	−0.672454	+	0.740139i	$0.734760\pi$
$942$	−29.5414	+	90.9191i	−0.962511	+	2.96230i
$943$	5.24419	+	16.1400i	0.170774	+	0.525590i
$944$	−4.02127	+	2.92162i	−0.130881	+	0.0950907i
$945$	11.3137			0.368035
$946$		0			0
$947$	41.1716			1.33790			0.668948	−	0.743309i	$-0.266745\pi$
$947$	41.1716			1.33790			0.668948	+	0.743309i	$0.266745\pi$
$948$	−35.0415	+	25.4592i	−1.13810	+	0.826875i
$949$	0.424151	+	1.30540i	0.0137685	+	0.0423752i
$950$		0			0
$951$	−3.00609	−	2.18405i	−0.0974791	−	0.0708227i
$952$	−48.7710	−	35.4342i	−1.58068	−	1.14843i
$953$	−16.4309	+	50.5692i	−0.532250	+	1.63810i	0.217268	+	0.976112i	$0.430285\pi$
$953$	−16.4309	+	50.5692i	−0.532250	+	1.63810i	−0.749518	+	0.661984i	$0.769715\pi$
$954$	−43.4820	−	133.824i	−1.40778	−	4.33271i
$955$	2.68085	−	1.94775i	0.0867502	−	0.0630277i
$956$	89.2548			2.88671
$957$		0			0
$958$	−86.9117			−2.80799
$959$	17.7507	−	12.8967i	0.573201	−	0.416455i
$960$	−8.59036	−	26.4384i	−0.277253	−	0.853296i
$961$	−9.57953	+	29.4828i	−0.309017	+	0.951057i
$962$	−17.5208	−	12.7296i	−0.564892	−	0.410418i
$963$	30.9726	+	22.5029i	0.998079	+	0.725147i
$964$	−7.09829	+	21.8463i	−0.228621	+	0.703622i
$965$	−0.362036	−	1.11423i	−0.0116543	−	0.0358684i
$966$	31.2502	−	22.7046i	1.00546	−	0.730509i
$967$	14.9706			0.481421			0.240710	−	0.970597i	$-0.422620\pi$
$967$	14.9706			0.481421			0.240710	+	0.970597i	$0.422620\pi$
$968$		0			0
$969$		0			0
$970$	−7.14235	+	5.18922i	−0.229327	+	0.166616i
$971$	−2.68421	−	8.26115i	−0.0861405	−	0.265113i	0.898703	−	0.438557i	$-0.144510\pi$
$971$	−2.68421	−	8.26115i	−0.0861405	−	0.265113i	−0.984844	+	0.173444i	$0.944510\pi$
$972$	16.7308	−	51.4922i	0.536642	−	1.65161i
$973$	−6.47214	−	4.70228i	−0.207487	−	0.150748i
$974$	−47.8232	−	34.7456i	−1.53235	−	1.11332i
$975$	−1.02399	+	3.15152i	−0.0327940	+	0.100930i
$976$	8.63428	+	26.5736i	0.276377	+	0.850600i
$977$	−26.1662	+	19.0108i	−0.837129	+	0.608210i	−0.921567	−	0.388219i	$-0.873091\pi$
$977$	−26.1662	+	19.0108i	−0.837129	+	0.608210i	0.0844379	+	0.996429i	$0.473091\pi$
$978$	112.569			3.59955
$979$		0			0
$980$	11.4853			0.366884
$981$	−30.9726	+	22.5029i	−0.988880	+	0.718463i
$982$	−0.511996	−	1.57576i	−0.0163385	−	0.0502846i
$983$	−6.75445	+	20.7881i	−0.215434	+	0.663036i	0.783689	+	0.621153i	$0.213336\pi$
$983$	−6.75445	+	20.7881i	−0.215434	+	0.663036i	−0.999123	+	0.0418829i	$0.986664\pi$
$984$	60.6048	+	44.0320i	1.93201	+	1.40369i
$985$	8.76038	+	6.36479i	0.279129	+	0.202799i
$986$	18.6289	−	57.3337i	0.593264	−	1.82588i
$987$	−4.94427	−	15.2169i	−0.157378	−	0.484359i
$988$		0			0
$989$	−16.9706			−0.539633
$990$		0			0
$991$	−57.9411			−1.84056			−0.920280	−	0.391260i	$-0.872039\pi$
$991$	−57.9411			−1.84056			−0.920280	+	0.391260i	$0.872039\pi$
$992$		0			0
$993$	6.39242	+	19.6738i	0.202857	+	0.624330i
$994$	−16.8808	+	51.9538i	−0.535426	+	1.64787i
$995$	8.36778	+	6.07955i	0.265276	+	0.192735i
$996$	52.5623	+	38.1887i	1.66550	+	1.21006i
$997$	12.8106	−	39.4269i	0.405715	−	1.24866i	−0.514583	−	0.857441i	$-0.672053\pi$
$997$	12.8106	−	39.4269i	0.405715	−	1.24866i	0.920297	−	0.391220i	$-0.127947\pi$
$998$	−7.20433	−	22.1727i	−0.228049	−	0.701863i
$999$	−35.0415	+	25.4592i	−1.10866	+	0.805492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.l.366.2		8
11.2	odd	10		55.2.a.b.1.2	✓	2
11.3	even	5	inner	605.2.g.l.511.1		8
11.4	even	5	inner	605.2.g.l.81.2		8
11.5	even	5	inner	605.2.g.l.251.1		8
11.6	odd	10		605.2.g.f.251.2		8
11.7	odd	10		605.2.g.f.81.1		8
11.8	odd	10		605.2.g.f.511.2		8
11.9	even	5		605.2.a.d.1.1		2
11.10	odd	2		605.2.g.f.366.1		8
33.2	even	10		495.2.a.b.1.1		2
33.20	odd	10		5445.2.a.y.1.2		2
44.31	odd	10		9680.2.a.bn.1.2		2
44.35	even	10		880.2.a.m.1.2		2
55.2	even	20		275.2.b.d.199.4		4
55.9	even	10		3025.2.a.o.1.2		2
55.13	even	20		275.2.b.d.199.1		4
55.24	odd	10		275.2.a.c.1.1		2
77.13	even	10		2695.2.a.f.1.2		2
88.13	odd	10		3520.2.a.bn.1.2		2
88.35	even	10		3520.2.a.bo.1.1		2
132.35	odd	10		7920.2.a.ch.1.2		2
143.90	odd	10		9295.2.a.g.1.1		2
165.2	odd	20		2475.2.c.l.199.1		4
165.68	odd	20		2475.2.c.l.199.4		4
165.134	even	10		2475.2.a.x.1.2		2
220.79	even	10		4400.2.a.bn.1.1		2
220.123	odd	20		4400.2.b.q.4049.3		4
220.167	odd	20		4400.2.b.q.4049.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.2	✓	2	11.2	odd	10
275.2.a.c.1.1		2	55.24	odd	10
275.2.b.d.199.1		4	55.13	even	20
275.2.b.d.199.4		4	55.2	even	20
495.2.a.b.1.1		2	33.2	even	10
605.2.a.d.1.1		2	11.9	even	5
605.2.g.f.81.1		8	11.7	odd	10
605.2.g.f.251.2		8	11.6	odd	10
605.2.g.f.366.1		8	11.10	odd	2
605.2.g.f.511.2		8	11.8	odd	10
605.2.g.l.81.2		8	11.4	even	5	inner
605.2.g.l.251.1		8	11.5	even	5	inner
605.2.g.l.366.2		8	1.1	even	1	trivial
605.2.g.l.511.1		8	11.3	even	5	inner
880.2.a.m.1.2		2	44.35	even	10
2475.2.a.x.1.2		2	165.134	even	10
2475.2.c.l.199.1		4	165.2	odd	20
2475.2.c.l.199.4		4	165.68	odd	20
2695.2.a.f.1.2		2	77.13	even	10
3025.2.a.o.1.2		2	55.9	even	10
3520.2.a.bn.1.2		2	88.13	odd	10
3520.2.a.bo.1.1		2	88.35	even	10
4400.2.a.bn.1.1		2	220.79	even	10
4400.2.b.q.4049.2		4	220.167	odd	20
4400.2.b.q.4049.3		4	220.123	odd	20
5445.2.a.y.1.2		2	33.20	odd	10
7920.2.a.ch.1.2		2	132.35	odd	10
9295.2.a.g.1.1		2	143.90	odd	10
9680.2.a.bn.1.2		2	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)

\(f(q)\)	\(=\)	\(q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +O(q^{10})\)	\(q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(-0.947822 + 0.688633i) q^{13} +(-1.49207 - 4.59211i) q^{14} +(0.874032 - 2.68999i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(5.52431 + 4.01365i) q^{17} +(-3.73017 + 11.4803i) q^{18} +(3.09726 - 2.25029i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(-10.1008 + 7.33866i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.874032 + 2.68999i) q^{26} +(4.57649 + 3.32502i) q^{27} +(-6.19453 - 4.50059i) q^{28} +(1.13003 - 3.47788i) q^{29} +(-2.11010 - 6.49422i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(1.61803 - 1.17557i) q^{35} +(5.91525 + 18.2053i) q^{36} +(-2.36610 + 7.28210i) q^{37} +(2.68085 + 1.94775i) q^{39} +(1.36407 - 4.19817i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-11.0486 + 8.02730i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(-5.52431 + 4.01365i) q^{46} +(0.874032 + 2.68999i) q^{47} +(-2.62210 + 8.06998i) q^{48} +(2.42705 + 1.76336i) q^{49} +(1.95314 + 1.41904i) q^{50} +(5.96826 - 18.3684i) q^{51} +(1.38603 + 4.26576i) q^{52} +(-9.43059 + 6.85173i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(-2.72813 - 8.39633i) q^{58} +(0.511996 - 1.57576i) q^{59} +(-8.76038 - 6.36479i) q^{60} +(-7.53495 - 5.47446i) q^{61} +(3.09017 + 9.51057i) q^{63} +(7.95136 - 5.77700i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(21.1494 - 15.3660i) q^{68} +(2.47214 + 7.60845i) q^{69} +(1.49207 - 4.59211i) q^{70} +(-9.15298 - 6.65003i) q^{71} +(17.8559 + 12.9730i) q^{72} +(0.362036 - 1.11423i) q^{73} +(5.71227 + 17.5805i) q^{74} +(2.28825 - 1.66251i) q^{75} +8.00000 q^{78} +(3.23607 - 2.35114i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-11.7188 - 8.51423i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(-6.69234 + 20.5969i) q^{84} +(2.11010 + 6.49422i) q^{85} +(11.7188 - 8.51423i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(-9.76570 + 7.09520i) q^{90} +(0.724072 + 2.22846i) q^{91} +(-3.34617 + 10.2984i) q^{92} +(5.52431 + 4.01365i) q^{94} +(-1.38603 - 4.26576i) q^{96} +(-2.95846 + 2.14944i) q^{97} +7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Introduction

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