LMFDB - Embedded newform 605.2.g.f.81.1

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:	8.0.64000000.2
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			81.1
Root			$0.437016 + 1.34500i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.f.366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95314 - 1.41904i) q^{2} +(-0.874032 + 2.68999i) q^{3} +(1.18305 + 3.64105i) q^{4} +(0.809017 - 0.587785i) q^{5} +(5.52431 - 4.01365i) q^{6} +(-0.618034 - 1.90211i) q^{7} +(1.36407 - 4.19817i) q^{8} +(-4.04508 - 2.93893i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

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	−0.996778	−	0.0802039i	$-0.974443\pi$
$2$	−1.95314	−	1.41904i	−1.38108	−	1.00341i	−0.384300	−	0.923208i	$-0.625557\pi$
$3$	−0.874032	+	2.68999i	−0.504623	+	1.55307i	0.296781	+	0.954945i	$0.404087\pi$
$3$	−0.874032	+	2.68999i	−0.504623	+	1.55307i	−0.801404	+	0.598123i	$0.795913\pi$
$4$	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	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	0.763710	−	0.645560i	$-0.223376\pi$
$8$	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	$-0.248055\pi$
$13$	0.947822	+	0.688633i	0.262879	+	0.190993i	−0.448537	+	0.893765i	$0.648055\pi$
$14$	−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	−0.340393	+	0.940283i	$0.610560\pi$
$17$	−5.52431	+	4.01365i	−1.33984	+	0.973453i	−0.999450	+	0.0331696i	$0.989440\pi$
$18$	3.73017	+	11.4803i	0.879208	+	2.70593i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	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	−0.999480	−	0.0322527i	$-0.989732\pi$
$29$	−1.13003	−	3.47788i	−0.209841	−	0.645825i	0.789638	−	0.613572i	$-0.210268\pi$
$30$	2.11010	−	6.49422i	0.385250	−	1.18568i
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$	−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	−0.933549	−	0.358451i	$-0.883305\pi$
$37$	−2.36610	−	7.28210i	−0.388984	−	1.19717i	0.544564	−	0.838719i	$-0.316695\pi$
$38$		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	−0.695432	−	0.718592i	$-0.744787\pi$
$41$	1.85410	−	5.70634i	0.289562	−	0.891180i	0.984994	−	0.172588i	$-0.0552131\pi$
$42$	−11.0486	−	8.02730i	−1.70484	−	1.23864i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		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	−0.866856	−	0.498559i	$-0.833863\pi$
$47$	0.874032	−	2.68999i	0.127491	−	0.392376i	0.994347	+	0.106183i	$0.0338628\pi$
$48$	−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	−0.295492	−	0.955345i	$-0.595484\pi$
$53$	−9.43059	−	6.85173i	−1.29539	−	0.941157i	−0.999899	+	0.0141880i	$0.995484\pi$
$54$	−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	0.978837	−	0.204641i	$-0.0656027\pi$
$59$	0.511996	+	1.57576i	0.0666562	+	0.205147i	−0.912181	+	0.409788i	$0.865603\pi$
$60$	−8.76038	+	6.36479i	−1.13096	+	0.821691i
$61$	7.53495	−	5.47446i	0.964751	−	0.700933i	0.0105019	−	0.999945i	$-0.496657\pi$
$61$	7.53495	−	5.47446i	0.964751	−	0.700933i	0.954249	+	0.299012i	$0.0966571\pi$
$62$		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	−0.978764	−	0.204992i	$-0.934283\pi$
$71$	−9.15298	+	6.65003i	−1.08626	+	0.789213i	−0.107496	+	0.994206i	$0.534283\pi$
$72$	−17.8559	+	12.9730i	−2.10433	+	1.52889i
$73$	−0.362036	−	1.11423i	−0.0423731	−	0.130411i	0.927632	−	0.373495i	$-0.121841\pi$
$73$	−0.362036	−	1.11423i	−0.0423731	−	0.130411i	−0.970005	+	0.243084i	$0.921841\pi$
$74$	−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	$-0.372244\pi$
$79$	−3.23607	−	2.35114i	−0.364086	−	0.264524i	−0.754754	+	0.656007i	$0.772244\pi$
$80$	−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	$-0.593190\pi$
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	0.821407	+	0.570343i	$0.193190\pi$
$84$	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	0.427374	−	0.904075i	$-0.359439\pi$
$97$	−2.95846	−	2.14944i	−0.300386	−	0.218243i	−0.727760	+	0.685832i	$0.759439\pi$
$98$	−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	$-0.453361\pi$
$101$	−7.53495	−	5.47446i	−0.749755	−	0.544729i	−0.895751	+	0.444556i	$0.853361\pi$
$102$	−14.4087	+	44.3453i	−1.42667	+	4.39084i
$103$	2.11010	+	6.49422i	0.207914	+	0.639895i	0.999581	+	0.0289414i	$0.00921362\pi$
$103$	2.11010	+	6.49422i	0.207914	+	0.639895i	−0.791667	+	0.610953i	$0.790786\pi$
$104$	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	−0.769151	−	0.639067i	$-0.779321\pi$
$107$	2.36610	−	7.28210i	0.228739	−	0.703987i	0.997890	−	0.0649203i	$-0.0206793\pi$
$108$	17.5208	+	12.7296i	1.68594	+	1.22490i
$109$	−7.65685			−0.733394			−0.366697	−	0.930341i	$-0.619511\pi$
$109$	−7.65685			−0.733394			−0.366697	+	0.930341i	$0.619511\pi$
$110$		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	−0.0766284	−	0.997060i	$-0.524416\pi$
$113$	6.07430	−	18.6948i	0.571422	−	1.75866i	0.648051	−	0.761597i	$-0.275584\pi$
$114$		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	$-0.761723\pi$
$127$	−3.51368	+	2.55284i	−0.311789	+	0.226528i	0.420875	+	0.907119i	$0.361723\pi$
$128$	−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	$-0.664554\pi$
$131$	−11.3137			−0.988483			−0.494242	+	0.869325i	$0.664554\pi$
$132$		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	−0.140106	−	0.990136i	$-0.544744\pi$
$137$	8.87537	−	6.44833i	0.758274	−	0.550918i	0.898381	+	0.439218i	$0.144744\pi$
$138$	−15.6251	+	11.3523i	−1.33010	+	0.966373i
$139$	−1.23607	−	3.80423i	−0.104842	−	0.322670i	0.884851	−	0.465873i	$-0.154260\pi$
$139$	−1.23607	−	3.80423i	−0.104842	−	0.322670i	−0.989693	+	0.143203i	$0.954260\pi$
$140$	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	$-0.704474\pi$
$149$	−0.277611	+	0.201696i	−0.0227428	+	0.0165236i	0.576356	+	0.817199i	$0.304474\pi$
$150$	−2.11010	−	6.49422i	−0.172289	−	0.530251i
$151$	−3.70820	+	11.4127i	−0.301769	+	0.928751i	0.679094	+	0.734052i	$0.262373\pi$
$151$	−3.70820	+	11.4127i	−0.301769	+	0.928751i	−0.980863	+	0.194699i	$0.937627\pi$
$152$		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	0.616167	+	0.787616i	$0.288685\pi$
$157$	−4.32624	+	13.3148i	−0.345271	+	1.06264i	−0.961438	+	0.275020i	$0.911315\pi$
$158$	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	−0.0734416	−	0.997300i	$-0.523398\pi$
$163$	−13.3369	−	9.68981i	−1.04462	−	0.758964i	−0.971183	+	0.238335i	$0.923398\pi$
$164$	22.9706			1.79370
$165$		0			0
$166$	−14.4853			−1.12428
$167$	18.5836	+	13.5018i	1.43804	+	1.04480i	0.988447	+	0.151564i	$0.0484309\pi$
$167$	18.5836	+	13.5018i	1.43804	+	1.04480i	0.449593	+	0.893234i	$0.351569\pi$
$168$	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	0.253387	+	0.967365i	$0.418455\pi$
$173$	−6.84230	+	21.0584i	−0.520210	+	1.60104i	−0.773597	+	0.633677i	$0.781545\pi$
$174$	−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	−0.775440	−	0.631422i	$-0.782472\pi$
$179$	2.98413	−	9.18421i	0.223045	−	0.686460i	0.998484	−	0.0550388i	$-0.0175282\pi$
$180$	−5.91525	−	18.2053i	−0.440896	−	1.35694i
$181$	−17.2432	+	12.5279i	−1.28167	+	0.931190i	−0.999602	−	0.0282032i	$-0.991021\pi$
$181$	−17.2432	+	12.5279i	−1.28167	+	0.931190i	−0.282071	+	0.959393i	$0.591021\pi$
$182$	−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	0.981244	−	0.192770i	$-0.0617472\pi$
$191$	1.02399	+	3.15152i	0.0740935	+	0.228036i	−0.907150	+	0.420806i	$0.861747\pi$
$192$	−22.4899	+	16.3398i	−1.62307	+	1.17923i
$193$	0.947822	−	0.688633i	0.0682257	−	0.0495689i	−0.553150	−	0.833082i	$-0.686574\pi$
$193$	0.947822	−	0.688633i	0.0682257	−	0.0495689i	0.621375	+	0.783513i	$0.286574\pi$
$194$	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	$-0.626056\pi$
$197$	−10.8284			−0.771493			−0.385747	+	0.922605i	$0.626056\pi$
$198$		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	$-0.114345\pi$
$211$	12.9443	+	9.40456i	0.891120	+	0.647437i	−0.0450495	+	0.998985i	$0.514345\pi$
$212$	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	0.774308	+	0.632809i	$0.218098\pi$
$223$	−3.34617	+	10.2984i	−0.224076	+	0.689635i	−0.998384	+	0.0568262i	$0.981902\pi$
$224$	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	0.775529	+	0.631312i	$0.217483\pi$
$227$	7.82237	+	24.0748i	0.519189	+	1.59790i	−0.256340	+	0.966587i	$0.582517\pi$
$228$		0			0
$229$	−1.06281	−	0.772178i	−0.0702326	−	0.0510270i	0.552115	−	0.833768i	$-0.313821\pi$
$229$	−1.06281	−	0.772178i	−0.0702326	−	0.0510270i	−0.622348	+	0.782741i	$0.713821\pi$
$230$	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	$-0.235518\pi$
$233$	4.96909	+	3.61026i	0.325536	+	0.236516i	−0.412998	+	0.910732i	$0.635518\pi$
$234$	−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	0.391699	+	0.920093i	$0.371887\pi$
$239$	−7.20433	+	22.1727i	−0.466010	+	1.43423i	−0.857708	+	0.514136i	$0.828113\pi$
$240$	−6.86474	−	4.98752i	−0.443117	−	0.321943i
$241$	6.00000			0.386494			0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000			0.386494			0.193247	+	0.981150i	$0.438098\pi$
$242$		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	0.237614	−	0.971360i	$-0.423635\pi$
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	−0.850391	+	0.526151i	$0.823635\pi$
$252$	−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	0.820281	−	0.571961i	$-0.193817\pi$
$257$	−2.87809	−	8.85786i	−0.179531	−	0.552538i	−0.999811	+	0.0194227i	$0.993817\pi$
$258$	−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	$-0.609831\pi$
$263$	−10.9706			−0.676474			−0.338237	+	0.941061i	$0.609831\pi$
$264$		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	−0.926253	−	0.376901i	$-0.876990\pi$
$269$	−14.0071	+	10.1767i	−0.854027	+	0.620487i	0.0722264	+	0.997388i	$0.476990\pi$
$270$	−11.0486	+	8.02730i	−0.672398	+	0.488526i
$271$	2.26006	+	6.95575i	0.137289	+	0.422532i	0.995939	−	0.0900304i	$-0.0286964\pi$
$271$	2.26006	+	6.95575i	0.137289	+	0.422532i	−0.858650	+	0.512562i	$0.828696\pi$
$272$	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	$-0.365765\pi$
$277$	−5.52431	−	4.01365i	−0.331924	−	0.241157i	−0.741247	+	0.671233i	$0.765765\pi$
$278$	−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	$-0.872737\pi$
$281$	−14.0071	+	10.1767i	−0.835593	+	0.607094i	0.0855434	+	0.996334i	$0.472737\pi$
$282$	−5.96826	−	18.3684i	−0.355405	−	1.09382i
$283$	10.0824	−	31.0305i	0.599338	−	1.84457i	0.0675133	−	0.997718i	$-0.478493\pi$
$283$	10.0824	−	31.0305i	0.599338	−	1.84457i	0.531825	−	0.846854i	$-0.321507\pi$
$284$	−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	$-0.186331\pi$
$293$	−2.83417	−	8.72268i	−0.165574	−	0.509585i	−0.999078	+	0.0429287i	$0.986331\pi$
$294$	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	$-0.654441\pi$
$307$	−16.3431			−0.932753			−0.466376	+	0.884586i	$0.654441\pi$
$308$		0			0
$309$	−19.3137			−1.09872
$310$		0			0
$311$	1.44814	−	4.45693i	0.0821167	−	0.252729i	−0.901566	−	0.432642i	$-0.857581\pi$
$311$	1.44814	−	4.45693i	0.0821167	−	0.252729i	0.983683	+	0.179913i	$0.0575815\pi$
$312$	4.52012	+	13.9115i	0.255901	+	0.787584i
$313$	1.06281	−	0.772178i	0.0600737	−	0.0436461i	−0.557343	−	0.830282i	$-0.688179\pi$
$313$	1.06281	−	0.772178i	0.0600737	−	0.0436461i	0.617417	+	0.786636i	$0.288179\pi$
$314$	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	0.617232	−	0.786781i	$-0.288254\pi$
$317$	1.06281	+	0.772178i	0.0596935	+	0.0433699i	−0.557538	+	0.830151i	$0.688254\pi$
$318$	−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	−0.961673	−	0.274199i	$-0.911587\pi$
$337$	−6.33030	−	19.4827i	−0.344833	−	1.06129i	0.616840	−	0.787089i	$-0.288413\pi$
$338$	−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	$-0.795142\pi$
$347$	−8.87537	+	6.44833i	−0.476455	+	0.346165i	0.323497	+	0.946229i	$0.395142\pi$
$348$	12.2364	+	37.6599i	0.655943	+	2.01878i
$349$	8.33436	−	25.6505i	0.446128	−	1.37304i	−0.435114	−	0.900376i	$-0.643292\pi$
$349$	8.33436	−	25.6505i	0.446128	−	1.37304i	0.881242	−	0.472666i	$-0.156708\pi$
$350$	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	$-0.0942349\pi$
$359$	0.212076	+	0.652702i	0.0111929	+	0.0344483i	−0.945304	+	0.326190i	$0.894235\pi$
$360$	−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	0.859004	−	0.511968i	$-0.171084\pi$
$367$	−2.62210	−	8.06998i	−0.136872	−	0.421250i	−0.995877	+	0.0907188i	$0.971084\pi$
$368$	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	$-0.122547\pi$
$373$	35.7990			1.85360			0.926801	+	0.375554i	$0.122547\pi$
$374$		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	−0.403806	+	0.914845i	$0.632313\pi$
$379$	−27.2290	+	19.7830i	−1.39866	+	1.01618i	−0.994852	+	0.101340i	$0.967687\pi$
$380$		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	0.702244	−	0.711936i	$-0.252182\pi$
$383$	4.73911	+	3.44317i	0.242157	+	0.175938i	−0.460087	+	0.887874i	$0.652182\pi$
$384$	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	0.972253	+	0.233933i	$0.0751595\pi$
$389$	6.37422	+	19.6178i	0.323186	+	0.994664i	−0.649067	+	0.760731i	$0.724840\pi$
$390$	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	−0.475251	−	0.879850i	$-0.657643\pi$
$401$	4.29888	−	3.12332i	0.214676	−	0.155971i	0.689927	+	0.723879i	$0.257643\pi$
$402$	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	$-0.308102\pi$
$409$	−0.832832	−	0.605088i	−0.0411809	−	0.0299197i	−0.608185	+	0.793795i	$0.708102\pi$
$410$	−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	−0.986018	−	0.166641i	$-0.946708\pi$
$421$	−1.85410	+	5.70634i	−0.0903634	+	0.278110i	0.895654	+	0.444751i	$0.146708\pi$
$422$	−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	$-0.212156\pi$
$431$	9.15298	+	6.65003i	0.440884	+	0.320321i	−0.345102	+	0.938565i	$0.612156\pi$
$432$	−5.24419	+	16.1400i	−0.252311	+	0.776534i
$433$	−2.36610	−	7.28210i	−0.113707	−	0.349955i	0.877968	−	0.478720i	$-0.158899\pi$
$433$	−2.36610	−	7.28210i	−0.113707	−	0.349955i	−0.991675	+	0.128764i	$0.958899\pi$
$434$		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	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		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	0.535931	+	0.844262i	$0.319961\pi$
$443$	−8.29044	+	25.5154i	−0.393891	+	1.21227i	−0.929822	+	0.368009i	$0.880039\pi$
$444$	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	−0.113089	−	0.993585i	$-0.536075\pi$
$449$	−23.1601	−	16.8268i	−1.09299	−	0.794105i	−0.979902	+	0.199480i	$0.936075\pi$
$450$	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	$-0.703613\pi$
$457$	−0.392601	+	0.285241i	−0.0183651	+	0.0133430i	0.578565	+	0.815636i	$0.303613\pi$
$458$	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	$-0.404994\pi$
$461$	12.6274			0.588117			0.294059	+	0.955787i	$0.404994\pi$
$462$		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	−0.274544	−	0.961575i	$-0.588527\pi$
$467$	11.9964	−	8.71593i	0.555129	−	0.403325i	0.829673	+	0.558249i	$0.188527\pi$
$468$	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	0.331007	−	0.943628i	$-0.392612\pi$
$479$	29.1246	−	21.1603i	1.33074	−	0.966837i	0.999731	−	0.0232090i	$-0.00738832\pi$
$480$	−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	0.619852	+	0.784719i	$0.287193\pi$
$487$	−7.56637	+	23.2869i	−0.342865	+	1.05523i	−0.962717	+	0.270511i	$0.912807\pi$
$488$	−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	$-0.104930\pi$
$491$	−0.212076	−	0.652702i	−0.00957084	−	0.0294560i	−0.955728	+	0.294252i	$0.904930\pi$
$492$	−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	0.995368	−	0.0961409i	$-0.0306500\pi$
$499$	2.98413	+	9.18421i	0.133588	+	0.411142i	−0.861780	+	0.507283i	$0.830650\pi$
$500$	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	−0.768751	−	0.639549i	$-0.779121\pi$
$503$	5.13815	−	15.8136i	0.229099	−	0.705094i	0.997850	−	0.0655455i	$-0.0208787\pi$
$504$	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	−0.999893	−	0.0146406i	$-0.995340\pi$
$509$	−4.11416	+	12.6621i	−0.182357	+	0.561237i	0.817536	+	0.575878i	$0.195340\pi$
$510$	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	0.962801	+	0.270210i	$0.0870931\pi$
$521$	7.82237	+	24.0748i	0.342704	+	1.05473i	−0.620097	+	0.784525i	$0.712907\pi$
$522$	35.7117	−	25.9461i	1.56306	−	1.13563i
$523$	33.6535	−	24.4507i	1.47156	−	1.06915i	0.491407	−	0.870930i	$-0.336483\pi$
$523$	33.6535	−	24.4507i	1.47156	−	1.06915i	0.980157	−	0.198223i	$-0.0635171\pi$
$524$	−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	$-0.341170\pi$
$541$	−4.85410	−	3.52671i	−0.208694	−	0.151625i	−0.687223	+	0.726447i	$0.741170\pi$
$542$	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	0.428550	+	0.903518i	$0.359025\pi$
$547$	−10.5066	+	32.3359i	−0.449229	+	1.38258i	−0.877779	+	0.479066i	$0.840975\pi$
$548$	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	$-0.0330294\pi$
$557$	3.04625	+	9.37539i	0.129074	+	0.397248i	−0.865548	+	0.500827i	$0.833029\pi$
$558$		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	$-0.302302\pi$
$563$	−0.277611	−	0.201696i	−0.0116999	−	0.00850047i	−0.593620	+	0.804746i	$0.702302\pi$
$564$	−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	−0.506453	−	0.862267i	$-0.669044\pi$
$569$	9.78251	−	30.1075i	0.410104	−	1.26217i	0.916557	−	0.399903i	$-0.130956\pi$
$570$		0			0
$571$	−21.9411			−0.918208			−0.459104	−	0.888383i	$-0.651829\pi$
$571$	−21.9411			−0.918208			−0.459104	+	0.888383i	$0.651829\pi$
$572$		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	−0.0322368	−	0.999480i	$-0.510263\pi$
$577$	21.8196	−	15.8529i	0.908364	−	0.659965i	0.940600	+	0.339515i	$0.110263\pi$
$578$	−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	0.936466	−	0.350759i	$-0.114076\pi$
$587$	−0.661956	−	2.03729i	−0.0273219	−	0.0840880i	−0.963788	+	0.266671i	$0.914076\pi$
$588$	−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	$-0.477009\pi$
$593$	3.51472			0.144332			0.0721661	+	0.997393i	$0.477009\pi$
$594$		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	−0.490352	−	0.871525i	$-0.663132\pi$
$599$	4.57649	−	3.32502i	0.186990	−	0.135856i	0.677342	+	0.735668i	$0.263132\pi$
$600$	10.1008	−	7.33866i	0.412364	−	0.299600i
$601$	7.39821	+	22.7694i	0.301779	+	0.928782i	0.980859	+	0.194717i	$0.0623790\pi$
$601$	7.39821	+	22.7694i	0.301779	+	0.928782i	−0.679080	+	0.734064i	$0.737621\pi$
$602$	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	$-0.583237\pi$
$607$	−30.9726	−	22.5029i	−1.25714	−	0.913366i	−0.998614	+	0.0526384i	$0.983237\pi$
$608$		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	0.656905	+	0.753973i	$0.271865\pi$
$613$	−7.86629	+	24.2099i	−0.317716	+	0.977831i	−0.974622	+	0.223858i	$0.928135\pi$
$614$	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	−0.999763	−	0.0217589i	$-0.993073\pi$
$619$	−4.43228	+	13.6411i	−0.178148	+	0.548284i	0.821615	+	0.570043i	$0.193073\pi$
$620$		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	$-0.100000\pi$
$631$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$632$	−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	−0.583086	−	0.812410i	$-0.698155\pi$
$641$	9.27051	−	28.5317i	0.366163	−	1.12693i	0.949250	−	0.314524i	$-0.101845\pi$
$642$	−16.1567	−	49.7253i	−0.637655	−	1.96250i
$643$	1.17780	−	0.855724i	0.0464480	−	0.0337464i	−0.564319	−	0.825557i	$-0.690861\pi$
$643$	1.17780	−	0.855724i	0.0464480	−	0.0337464i	0.610767	+	0.791810i	$0.290861\pi$
$644$	−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	0.0661810	−	0.997808i	$-0.478919\pi$
$647$	−21.9346	−	15.9364i	−0.862339	−	0.626526i	−0.928520	+	0.371281i	$0.878919\pi$
$648$	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	0.996470	−	0.0839510i	$-0.0267539\pi$
$653$	3.60217	+	11.0863i	0.140964	+	0.433842i	−0.855506	+	0.517793i	$0.826754\pi$
$654$	−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	$-0.147314\pi$
$659$	45.9411			1.78961			0.894806	+	0.446455i	$0.147314\pi$
$660$		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	$-0.222644\pi$
$673$	10.1008	+	7.33866i	0.389357	+	0.282885i	−0.375835	+	0.926687i	$0.622644\pi$
$674$	−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	$-0.844555\pi$
$677$	−18.4686	+	13.4182i	−0.709805	+	0.515704i	0.173305	+	0.984868i	$0.444555\pi$
$678$	−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	0.995225	−	0.0976071i	$-0.0311188\pi$
$691$	31.8055	+	23.1080i	1.20994	+	0.879070i	0.214712	+	0.976677i	$0.431119\pi$
$692$	−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	$-0.976644\pi$
$701$	−3.90209	+	12.0094i	−0.147380	+	0.453588i	0.849930	+	0.526896i	$0.176644\pi$
$702$	−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	−0.895287	−	0.445489i	$-0.853030\pi$
$709$	−19.9240	+	14.4756i	−0.748261	+	0.543644i	0.147026	+	0.989133i	$0.453030\pi$
$710$	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	0.999390	+	0.0349227i	$0.0111185\pi$
$719$	5.66834	+	17.4454i	0.211394	+	0.650602i	−0.787996	+	0.615680i	$0.788882\pi$
$720$	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	−0.999901	−	0.0140757i	$-0.995519\pi$
$733$	−5.39415	−	16.6015i	−0.199238	−	0.613190i	0.800663	−	0.599114i	$-0.204481\pi$
$734$	−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	$-0.485640\pi$
$739$	−24.2229	−	17.5990i	−0.891053	−	0.647388i	−0.936152	+	0.351595i	$0.885640\pi$
$740$	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	0.492057	−	0.870563i	$-0.336245\pi$
$743$	40.1256	−	29.1530i	1.47207	−	1.06952i	0.980009	−	0.198956i	$-0.0637550\pi$
$744$		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	−0.999839	−	0.0179203i	$-0.994295\pi$
$751$	−4.94427	+	15.2169i	−0.180419	+	0.555273i	0.819420	+	0.573193i	$0.194295\pi$
$752$	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	0.374582	−	0.927194i	$-0.377786\pi$
$757$	−10.7710	−	7.82560i	−0.391479	−	0.284426i	−0.766061	+	0.642767i	$0.777786\pi$
$758$	81.2548			2.95131
$759$		0			0
$760$		0			0
$761$	24.2705	+	17.6336i	0.879805	+	0.639216i	0.933200	−	0.359358i	$-0.117004\pi$
$761$	24.2705	+	17.6336i	0.879805	+	0.639216i	−0.0533947	+	0.998573i	$0.517004\pi$
$762$	−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	$-0.611121\pi$
$769$	−18.9706			−0.684096			−0.342048	+	0.939682i	$0.611121\pi$
$770$		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	−0.692029	−	0.721869i	$-0.743283\pi$
$773$	8.12229	−	24.9978i	0.292138	−	0.899109i	0.984168	−	0.177240i	$-0.0567169\pi$
$774$	−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	$-0.614027\pi$
$787$	12.1114	−	8.79948i	0.431726	−	0.313667i	0.782339	+	0.622853i	$0.214027\pi$
$788$	−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	−0.947212	−	0.320609i	$-0.896113\pi$
$797$	−26.3961	+	19.1779i	−0.934999	+	0.679317i	0.0122126	+	0.999925i	$0.496113\pi$
$798$		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	$-0.638226\pi$
$809$	8.87537	−	6.44833i	0.312041	−	0.226711i	0.732772	+	0.680474i	$0.238226\pi$
$810$	−0.746033	−	2.29605i	−0.0262129	−	0.0806751i
$811$	16.6687	−	51.3011i	0.585318	−	1.80142i	−0.0126712	−	0.999920i	$-0.504033\pi$
$811$	16.6687	−	51.3011i	0.585318	−	1.80142i	0.597989	−	0.801504i	$-0.295967\pi$
$812$	−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	−0.881870	−	0.471493i	$-0.843715\pi$
$821$	−12.7666	−	39.2917i	−0.445559	−	1.37129i	0.436311	−	0.899796i	$-0.356285\pi$
$822$	23.1490	−	71.2452i	0.807414	−	2.48496i
$823$	−15.7877	−	11.4705i	−0.550326	−	0.399835i	0.277580	−	0.960703i	$-0.410468\pi$
$823$	−15.7877	−	11.4705i	−0.550326	−	0.399835i	−0.827906	+	0.560867i	$0.810468\pi$
$824$	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	$-0.426644\pi$
$827$	−18.0284	−	13.0984i	−0.626907	−	0.455475i	−0.855327	+	0.518088i	$0.826644\pi$
$828$	−16.7308	+	51.4922i	−0.581437	+	1.78948i
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	0.999993	+	0.00375172i	$0.00119421\pi$
$829$	5.56231	+	17.1190i	0.193187	+	0.594568i	−0.806806	+	0.590816i	$0.798806\pi$
$830$	−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	−0.706517	−	0.707696i	$-0.749735\pi$
$839$	8.14048	−	25.0538i	0.281041	−	0.864954i	0.987558	−	0.157258i	$-0.0502654\pi$
$840$	−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	$-0.614428\pi$
$853$	12.5517	−	9.11932i	0.429761	−	0.312240i	0.781553	+	0.623838i	$0.214428\pi$
$854$	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	$-0.360957\pi$
$857$	24.7696			0.846112			0.423056	+	0.906104i	$0.360957\pi$
$858$		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	−0.454290	−	0.890854i	$-0.650107\pi$
$863$	7.41996	−	5.39092i	0.252578	−	0.183509i	0.706869	+	0.707345i	$0.250107\pi$
$864$	−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	0.265285	+	0.964170i	$0.414534\pi$
$877$	−15.2827	+	47.0353i	−0.516060	+	1.58827i	−0.781345	+	0.624099i	$0.785466\pi$
$878$	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	−0.548788	−	0.835961i	$-0.684911\pi$
$883$	11.4866	−	35.3523i	0.386556	−	1.18970i	0.935345	−	0.353737i	$-0.115089\pi$
$884$	−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	0.927212	+	0.374537i	$0.122198\pi$
$887$	11.8305	+	36.4105i	0.397229	+	1.22255i	−0.529983	+	0.848008i	$0.677802\pi$
$888$	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	−0.153311	−	0.988178i	$-0.548993\pi$
$907$	22.2599	−	16.1727i	0.739127	−	0.537007i	0.892438	+	0.451171i	$0.148993\pi$
$908$	−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	0.712991	−	0.701174i	$-0.247340\pi$
$911$	8.04254	+	5.84325i	0.266461	+	0.193595i	−0.446529	+	0.894769i	$0.647340\pi$
$912$		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	$-0.523020\pi$
$919$	25.8885	−	18.8091i	0.853984	−	0.620456i	0.926242	+	0.376930i	$0.123020\pi$
$920$	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	−0.656069	−	0.754701i	$-0.727782\pi$
$929$	−4.29888	+	3.12332i	−0.141042	+	0.102473i	0.515027	+	0.857174i	$0.327782\pi$
$930$		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	$-0.292430\pi$
$937$	1.17780	+	0.855724i	0.0384771	+	0.0279553i	−0.568380	+	0.822766i	$0.692430\pi$
$938$	−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	$-0.665240\pi$
$941$	5.40932	−	3.93010i	0.176339	−	0.128118i	0.672454	+	0.740139i	$0.265240\pi$
$942$	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	0.749518	+	0.661984i	$0.230285\pi$
$953$	16.4309	+	50.5692i	0.532250	+	1.63810i	−0.217268	+	0.976112i	$0.569715\pi$
$954$	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	$-0.577380\pi$
$967$	−14.9706			−0.481421			−0.240710	+	0.970597i	$0.577380\pi$
$968$		0			0
$969$		0			0
$970$	7.14235	+	5.18922i	0.229327	+	0.166616i
$971$	−2.68421	+	8.26115i	−0.0861405	+	0.265113i	−0.984844	−	0.173444i	$-0.944510\pi$
$971$	−2.68421	+	8.26115i	−0.0861405	+	0.265113i	0.898703	+	0.438557i	$0.144510\pi$
$972$	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	0.0844379	−	0.996429i	$-0.473091\pi$
$977$	−26.1662	−	19.0108i	−0.837129	−	0.608210i	−0.921567	+	0.388219i	$0.873091\pi$
$978$	−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	−0.999123	−	0.0418829i	$-0.986664\pi$
$983$	−6.75445	−	20.7881i	−0.215434	−	0.663036i	0.783689	−	0.621153i	$-0.213336\pi$
$984$	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	−0.920297	−	0.391220i	$-0.872053\pi$
$997$	−12.8106	−	39.4269i	−0.405715	−	1.24866i	0.514583	−	0.857441i	$-0.327947\pi$
$998$	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.f.81.1		8
11.2	odd	10		605.2.g.l.511.1		8
11.3	even	5	inner	605.2.g.f.366.1		8
11.4	even	5	inner	605.2.g.f.251.2		8
11.5	even	5		55.2.a.b.1.2	✓	2
11.6	odd	10		605.2.a.d.1.1		2
11.7	odd	10		605.2.g.l.251.1		8
11.8	odd	10		605.2.g.l.366.2		8
11.9	even	5	inner	605.2.g.f.511.2		8
11.10	odd	2		605.2.g.l.81.2		8
33.5	odd	10		495.2.a.b.1.1		2
33.17	even	10		5445.2.a.y.1.2		2
44.27	odd	10		880.2.a.m.1.2		2
44.39	even	10		9680.2.a.bn.1.2		2
55.27	odd	20		275.2.b.d.199.4		4
55.38	odd	20		275.2.b.d.199.1		4
55.39	odd	10		3025.2.a.o.1.2		2
55.49	even	10		275.2.a.c.1.1		2
77.27	odd	10		2695.2.a.f.1.2		2
88.5	even	10		3520.2.a.bn.1.2		2
88.27	odd	10		3520.2.a.bo.1.1		2
132.71	even	10		7920.2.a.ch.1.2		2
143.38	even	10		9295.2.a.g.1.1		2
165.38	even	20		2475.2.c.l.199.4		4
165.104	odd	10		2475.2.a.x.1.2		2
165.137	even	20		2475.2.c.l.199.1		4
220.27	even	20		4400.2.b.q.4049.2		4
220.159	odd	10		4400.2.a.bn.1.1		2
220.203	even	20		4400.2.b.q.4049.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.2	✓	2	11.5	even	5
275.2.a.c.1.1		2	55.49	even	10
275.2.b.d.199.1		4	55.38	odd	20
275.2.b.d.199.4		4	55.27	odd	20
495.2.a.b.1.1		2	33.5	odd	10
605.2.a.d.1.1		2	11.6	odd	10
605.2.g.f.81.1		8	1.1	even	1	trivial
605.2.g.f.251.2		8	11.4	even	5	inner
605.2.g.f.366.1		8	11.3	even	5	inner
605.2.g.f.511.2		8	11.9	even	5	inner
605.2.g.l.81.2		8	11.10	odd	2
605.2.g.l.251.1		8	11.7	odd	10
605.2.g.l.366.2		8	11.8	odd	10
605.2.g.l.511.1		8	11.2	odd	10
880.2.a.m.1.2		2	44.27	odd	10
2475.2.a.x.1.2		2	165.104	odd	10
2475.2.c.l.199.1		4	165.137	even	20
2475.2.c.l.199.4		4	165.38	even	20
2695.2.a.f.1.2		2	77.27	odd	10
3025.2.a.o.1.2		2	55.39	odd	10
3520.2.a.bn.1.2		2	88.5	even	10
3520.2.a.bo.1.1		2	88.27	odd	10
4400.2.a.bn.1.1		2	220.159	odd	10
4400.2.b.q.4049.2		4	220.27	even	20
4400.2.b.q.4049.3		4	220.203	even	20
5445.2.a.y.1.2		2	33.17	even	10
7920.2.a.ch.1.2		2	132.71	even	10
9295.2.a.g.1.1		2	143.38	even	10
9680.2.a.bn.1.2		2	44.39	even	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

L-functions

Modular forms

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Database

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