LMFDB - Embedded newform 315.2.be.c.311.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.15
Character	$\chi$	$=$	315.311
Dual form			315.2.be.c.236.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11687 + 1.22217i) q^{2} +(1.73076 - 0.0669518i) q^{3} +(1.98742 + 3.44231i) q^{4} -1.00000 q^{5} +(3.74561 + 1.97356i) q^{6} +(-2.50358 - 0.855621i) q^{7} +4.82720i q^{8} +(2.99103 - 0.231754i) q^{9} +O(q^{10})$	\(q+(2.11687 + 1.22217i) q^{2} +(1.73076 - 0.0669518i) q^{3} +(1.98742 + 3.44231i) q^{4} -1.00000 q^{5} +(3.74561 + 1.97356i) q^{6} +(-2.50358 - 0.855621i) q^{7} +4.82720i q^{8} +(2.99103 - 0.231754i) q^{9} +(-2.11687 - 1.22217i) q^{10} -4.38252i q^{11} +(3.67021 + 5.82475i) q^{12} +(-1.54497 - 0.891986i) q^{13} +(-4.25403 - 4.87105i) q^{14} +(-1.73076 + 0.0669518i) q^{15} +(-1.92484 + 3.33393i) q^{16} +(-3.92956 + 6.80619i) q^{17} +(6.61487 + 3.16497i) q^{18} +(-3.33955 + 1.92809i) q^{19} +(-1.98742 - 3.44231i) q^{20} +(-4.39037 - 1.31325i) q^{21} +(5.35620 - 9.27721i) q^{22} -2.26865i q^{23} +(0.323190 + 8.35471i) q^{24} +1.00000 q^{25} +(-2.18033 - 3.77644i) q^{26} +(5.16124 - 0.601365i) q^{27} +(-2.03035 - 10.3186i) q^{28} +(0.771716 - 0.445550i) q^{29} +(-3.74561 - 1.97356i) q^{30} +(6.13095 - 3.53970i) q^{31} +(0.211683 - 0.122215i) q^{32} +(-0.293417 - 7.58507i) q^{33} +(-16.6367 + 9.60521i) q^{34} +(2.50358 + 0.855621i) q^{35} +(6.74222 + 9.83549i) q^{36} +(2.58988 + 4.48580i) q^{37} -9.42586 q^{38} +(-2.73368 - 1.44037i) q^{39} -4.82720i q^{40} +(-1.78706 + 3.09527i) q^{41} +(-7.68882 - 8.14578i) q^{42} +(2.68755 + 4.65498i) q^{43} +(15.0860 - 8.70991i) q^{44} +(-2.99103 + 0.231754i) q^{45} +(2.77269 - 4.80244i) q^{46} +(0.299936 - 0.519504i) q^{47} +(-3.10822 + 5.89909i) q^{48} +(5.53583 + 4.28423i) q^{49} +(2.11687 + 1.22217i) q^{50} +(-6.34542 + 12.0430i) q^{51} -7.09101i q^{52} +(-11.9100 - 6.87623i) q^{53} +(11.6606 + 5.03492i) q^{54} +4.38252i q^{55} +(4.13026 - 12.0853i) q^{56} +(-5.65086 + 3.56065i) q^{57} +2.17816 q^{58} +(-4.46426 - 7.73233i) q^{59} +(-3.67021 - 5.82475i) q^{60} +(3.76221 + 2.17211i) q^{61} +17.3045 q^{62} +(-7.68659 - 1.97898i) q^{63} +8.29685 q^{64} +(1.54497 + 0.891986i) q^{65} +(8.64915 - 16.4152i) q^{66} +(3.24358 + 5.61805i) q^{67} -31.2387 q^{68} +(-0.151890 - 3.92648i) q^{69} +(4.25403 + 4.87105i) q^{70} +0.343987i q^{71} +(1.11873 + 14.4383i) q^{72} +(-3.38926 - 1.95679i) q^{73} +12.6611i q^{74} +(1.73076 - 0.0669518i) q^{75} +(-13.2742 - 7.66386i) q^{76} +(-3.74977 + 10.9720i) q^{77} +(-4.02645 - 6.39011i) q^{78} +(-3.43741 + 5.95376i) q^{79} +(1.92484 - 3.33393i) q^{80} +(8.89258 - 1.38637i) q^{81} +(-7.56592 + 4.36819i) q^{82} +(3.09467 + 5.36013i) q^{83} +(-4.20489 - 17.7230i) q^{84} +(3.92956 - 6.80619i) q^{85} +13.1386i q^{86} +(1.30582 - 0.822807i) q^{87} +21.1553 q^{88} +(1.69019 + 2.92749i) q^{89} +(-6.61487 - 3.16497i) q^{90} +(3.10474 + 3.55506i) q^{91} +(7.80941 - 4.50877i) q^{92} +(10.3742 - 6.53684i) q^{93} +(1.26985 - 0.733147i) q^{94} +(3.33955 - 1.92809i) q^{95} +(0.358188 - 0.225697i) q^{96} +(10.3098 - 5.95238i) q^{97} +(6.48254 + 15.8349i) q^{98} +(-1.01567 - 13.1083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.11687	+	1.22217i	1.49685	+	0.864208i	0.999993	−	0.00362365i	$-0.00115345\pi$
$2$	2.11687	+	1.22217i	1.49685	+	0.864208i	0.496859	+	0.867832i	$0.334487\pi$
$3$	1.73076	−	0.0669518i	0.999253	−	0.0386546i
$3$	1.73076	−	0.0669518i	0.999253	−	0.0386546i
$4$	1.98742	+	3.44231i	0.993711	+	1.72116i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	3.74561	+	1.97356i	1.52914	+	0.805702i
$7$	−2.50358	−	0.855621i	−0.946264	−	0.323394i
$7$	−2.50358	−	0.855621i	−0.946264	−	0.323394i
$8$			4.82720i			1.70667i
$9$	2.99103	−	0.231754i	0.997012	−	0.0772514i
$10$	−2.11687	−	1.22217i	−0.669413	−	0.386486i
$11$		−	4.38252i		−	1.32138i	−0.750659	−	0.660689i	$-0.770264\pi$
$11$		−	4.38252i		−	1.32138i	0.750659	−	0.660689i	$-0.229736\pi$
$12$	3.67021	+	5.82475i	1.05950	+	1.68146i
$13$	−1.54497	−	0.891986i	−0.428496	−	0.247393i	0.270209	−	0.962802i	$-0.412907\pi$
$13$	−1.54497	−	0.891986i	−0.428496	−	0.247393i	−0.698706	+	0.715409i	$0.746240\pi$
$14$	−4.25403	−	4.87105i	−1.13694	−	1.30184i
$15$	−1.73076	+	0.0669518i	−0.446879	+	0.0172869i
$16$	−1.92484	+	3.33393i	−0.481211	+	0.833482i
$17$	−3.92956	+	6.80619i	−0.953058	+	1.65074i	−0.214306	+	0.976767i	$0.568749\pi$
$17$	−3.92956	+	6.80619i	−0.953058	+	1.65074i	−0.738752	+	0.673978i	$0.764584\pi$
$18$	6.61487	+	3.16497i	1.55914	+	0.745991i
$19$	−3.33955	+	1.92809i	−0.766146	+	0.442335i	−0.831498	−	0.555528i	$-0.812516\pi$
$19$	−3.33955	+	1.92809i	−0.766146	+	0.442335i	0.0653519	+	0.997862i	$0.479183\pi$
$20$	−1.98742	−	3.44231i	−0.444401	−	0.769725i
$21$	−4.39037	−	1.31325i	−0.958058	−	0.286575i
$22$	5.35620	−	9.27721i	1.14195	−	1.97791i
$23$		−	2.26865i		−	0.473047i	−0.971626	−	0.236523i	$-0.923992\pi$
$23$		−	2.26865i		−	0.473047i	0.971626	−	0.236523i	$-0.0760080\pi$
$24$	0.323190	+	8.35471i	0.0659708	+	1.70540i
$25$	1.00000			0.200000
$26$	−2.18033	−	3.77644i	−0.427597	−	0.740620i
$27$	5.16124	−	0.601365i	0.993280	−	0.115733i
$28$	−2.03035	−	10.3186i	−0.383701	−	1.95003i
$29$	0.771716	−	0.445550i	0.143304	−	0.0827366i	−0.426634	−	0.904425i	$-0.640301\pi$
$29$	0.771716	−	0.445550i	0.143304	−	0.0827366i	0.569938	+	0.821688i	$0.306967\pi$
$30$	−3.74561	−	1.97356i	−0.683852	−	0.360321i
$31$	6.13095	−	3.53970i	1.10115	−	0.635750i	0.164628	−	0.986356i	$-0.447358\pi$
$31$	6.13095	−	3.53970i	1.10115	−	0.635750i	0.936523	+	0.350606i	$0.114024\pi$
$32$	0.211683	−	0.122215i	0.0374205	−	0.0216048i
$33$	−0.293417	−	7.58507i	−0.0510774	−	1.32039i
$34$	−16.6367	+	9.60521i	−2.85317	+	1.64728i
$35$	2.50358	+	0.855621i	0.423182	+	0.144626i
$36$	6.74222	+	9.83549i	1.12370	+	1.63925i
$37$	2.58988	+	4.48580i	0.425774	+	0.737461i	0.996492	−	0.0836841i	$-0.0266687\pi$
$37$	2.58988	+	4.48580i	0.425774	+	0.737461i	−0.570719	+	0.821146i	$0.693335\pi$
$38$	−9.42586			−1.52908
$39$	−2.73368	−	1.44037i	−0.437739	−	0.230644i
$40$		−	4.82720i		−	0.763248i
$41$	−1.78706	+	3.09527i	−0.279091	+	0.483400i	−0.971159	−	0.238432i	$-0.923367\pi$
$41$	−1.78706	+	3.09527i	−0.279091	+	0.483400i	0.692068	+	0.721832i	$0.256700\pi$
$42$	−7.68882	−	8.14578i	−1.18641	−	1.25692i
$43$	2.68755	+	4.65498i	0.409848	+	0.709877i	0.994872	−	0.101138i	$-0.0322485\pi$
$43$	2.68755	+	4.65498i	0.409848	+	0.709877i	−0.585025	+	0.811016i	$0.698915\pi$
$44$	15.0860	−	8.70991i	2.27430	−	1.31307i
$45$	−2.99103	+	0.231754i	−0.445877	+	0.0345479i
$46$	2.77269	−	4.80244i	0.408811	−	0.708081i
$47$	0.299936	−	0.519504i	0.0437501	−	0.0757774i	−0.843321	−	0.537410i	$-0.819403\pi$
$47$	0.299936	−	0.519504i	0.0437501	−	0.0757774i	0.887071	+	0.461633i	$0.152736\pi$
$48$	−3.10822	+	5.89909i	−0.448633	+	0.851460i
$49$	5.53583	+	4.28423i	0.790832	+	0.612033i
$50$	2.11687	+	1.22217i	0.299370	+	0.172842i
$51$	−6.34542	+	12.0430i	−0.888536	+	1.68635i
$52$		−	7.09101i		−	0.983346i
$53$	−11.9100	−	6.87623i	−1.63596	−	0.944523i	−0.982203	−	0.187820i	$-0.939858\pi$
$53$	−11.9100	−	6.87623i	−1.63596	−	0.944523i	−0.653758	−	0.756703i	$-0.726809\pi$
$54$	11.6606	+	5.03492i	1.58681	+	0.685166i
$55$			4.38252i			0.590939i
$56$	4.13026	−	12.0853i	0.551929	−	1.61497i
$57$	−5.65086	+	3.56065i	−0.748475	+	0.471619i
$58$	2.17816			0.286007
$59$	−4.46426	−	7.73233i	−0.581197	−	1.00666i	−0.995338	−	0.0964504i	$-0.969251\pi$
$59$	−4.46426	−	7.73233i	−0.581197	−	1.00666i	0.414140	−	0.910213i	$-0.364082\pi$
$60$	−3.67021	−	5.82475i	−0.473822	−	0.751971i
$61$	3.76221	+	2.17211i	0.481701	+	0.278110i	0.721125	−	0.692805i	$-0.243625\pi$
$61$	3.76221	+	2.17211i	0.481701	+	0.278110i	−0.239424	+	0.970915i	$0.576959\pi$
$62$	17.3045			2.19768
$63$	−7.68659	−	1.97898i	−0.968419	−	0.249328i
$64$	8.29685			1.03711
$65$	1.54497	+	0.891986i	0.191629	+	0.110637i
$66$	8.64915	−	16.4152i	1.06464	−	2.02057i
$67$	3.24358	+	5.61805i	0.396267	+	0.686354i	0.993262	−	0.115890i	$-0.0369722\pi$
$67$	3.24358	+	5.61805i	0.396267	+	0.686354i	−0.596995	+	0.802245i	$0.703639\pi$
$68$	−31.2387			−3.78825
$69$	−0.151890	−	3.92648i	−0.0182854	−	0.472693i
$70$	4.25403	+	4.87105i	0.508454	+	0.582202i
$71$			0.343987i			0.0408237i	0.999792	+	0.0204119i	$0.00649775\pi$
$71$			0.343987i			0.0408237i	−0.999792	+	0.0204119i	$0.993502\pi$
$72$	1.11873	+	14.4383i	0.131843	+	1.70157i
$73$	−3.38926	−	1.95679i	−0.396683	−	0.229025i	0.288369	−	0.957519i	$-0.406887\pi$
$73$	−3.38926	−	1.95679i	−0.396683	−	0.229025i	−0.685052	+	0.728494i	$0.740220\pi$
$74$			12.6611i			1.47183i
$75$	1.73076	−	0.0669518i	0.199851	−	0.00773092i
$76$	−13.2742	−	7.66386i	−1.52266	−	0.879105i
$77$	−3.74977	+	10.9720i	−0.427326	+	1.25037i
$78$	−4.02645	−	6.39011i	−0.455906	−	0.723538i
$79$	−3.43741	+	5.95376i	−0.386739	+	0.669851i	−0.992009	−	0.126169i	$-0.959732\pi$
$79$	−3.43741	+	5.95376i	−0.386739	+	0.669851i	0.605270	+	0.796020i	$0.293065\pi$
$80$	1.92484	−	3.33393i	0.215204	−	0.372744i
$81$	8.89258	−	1.38637i	0.988064	−	0.154041i
$82$	−7.56592	+	4.36819i	−0.835517	+	0.482386i
$83$	3.09467	+	5.36013i	0.339685	+	0.588351i	0.984373	−	0.176094i	$-0.0563463\pi$
$83$	3.09467	+	5.36013i	0.339685	+	0.588351i	−0.644689	+	0.764445i	$0.723013\pi$
$84$	−4.20489	−	17.7230i	−0.458791	−	1.93374i
$85$	3.92956	−	6.80619i	0.426220	−	0.738235i
$86$			13.1386i			1.41677i
$87$	1.30582	−	0.822807i	0.139999	−	0.0882142i
$88$	21.1553			2.25516
$89$	1.69019	+	2.92749i	0.179160	+	0.310313i	0.941593	−	0.336753i	$-0.109329\pi$
$89$	1.69019	+	2.92749i	0.179160	+	0.310313i	−0.762433	+	0.647067i	$0.775996\pi$
$90$	−6.61487	−	3.16497i	−0.697269	−	0.333617i
$91$	3.10474	+	3.55506i	0.325466	+	0.372672i
$92$	7.80941	−	4.50877i	0.814187	−	0.470071i
$93$	10.3742	−	6.53684i	1.07575	−	0.677839i
$94$	1.26985	−	0.733147i	0.130975	−	0.0756184i
$95$	3.33955	−	1.92809i	0.342631	−	0.197818i
$96$	0.358188	−	0.225697i	0.0365575	−	0.0230351i
$97$	10.3098	−	5.95238i	1.04680	−	0.604373i	0.125052	−	0.992150i	$-0.460090\pi$
$97$	10.3098	−	5.95238i	1.04680	−	0.604373i	0.921753	+	0.387777i	$0.126757\pi$
$98$	6.48254	+	15.8349i	0.654835	+	1.59957i
$99$	−1.01567	−	13.1083i	−0.102078	−	1.31743i
$100$	1.98742	+	3.44231i	0.198742	+	0.344231i
$101$	−16.8546			−1.67709			−0.838547	−	0.544829i	$-0.816595\pi$
$101$	−16.8546			−1.67709			−0.838547	+	0.544829i	$0.816595\pi$
$102$	−28.1510	+	17.7381i	−2.78736	+	1.75634i
$103$		−	13.3006i		−	1.31054i	−0.755393	−	0.655272i	$-0.772554\pi$
$103$		−	13.3006i		−	1.31054i	0.755393	−	0.655272i	$-0.227446\pi$
$104$	4.30580	−	7.45786i	0.422218	−	0.731304i
$105$	4.39037	+	1.31325i	0.428456	+	0.128160i
$106$	−16.8079	−	29.1122i	−1.63253	−	2.82762i
$107$	−16.8326	+	9.71828i	−1.62726	+	0.939502i	−0.642360	+	0.766403i	$0.722045\pi$
$107$	−16.8326	+	9.71828i	−1.62726	+	0.939502i	−0.984905	+	0.173098i	$0.944622\pi$
$108$	12.3276	+	16.5714i	1.18623	+	1.59459i
$109$	4.51255	−	7.81596i	0.432224	−	0.748633i	−0.564841	−	0.825200i	$-0.691062\pi$
$109$	4.51255	−	7.81596i	0.432224	−	0.748633i	0.997064	+	0.0765667i	$0.0243958\pi$
$110$	−5.35620	+	9.27721i	−0.510694	+	0.884548i
$111$	4.78278	+	7.59043i	0.453962	+	0.720452i
$112$	7.67158	−	6.69982i	0.724896	−	0.633073i
$113$	11.4033	+	6.58371i	1.07273	+	0.619343i	0.928927	−	0.370263i	$-0.120732\pi$
$113$	11.4033	+	6.58371i	1.07273	+	0.619343i	0.143806	+	0.989606i	$0.454066\pi$
$114$	−16.3139	+	0.631078i	−1.52793	+	0.0591059i
$115$			2.26865i			0.211553i
$116$	3.06745	+	1.77099i	0.284806	+	0.164433i
$117$	−4.82777	−	2.30991i	−0.446327	−	0.213551i
$118$		−	21.8244i		−	2.00910i
$119$	15.6615	−	13.6776i	1.43569	−	1.25383i
$120$	−0.323190	−	8.35471i	−0.0295031	−	0.762678i
$121$	−8.20646			−0.746042
$122$	5.30940	+	9.19614i	0.480690	+	0.832580i
$123$	−2.88572	+	5.47681i	−0.260197	+	0.493827i
$124$	24.3695	+	14.0698i	2.18845	+	1.26350i
$125$	−1.00000			−0.0894427
$126$	−13.8528	−	13.5836i	−1.23411	−	1.21012i
$127$	3.16484			0.280834			0.140417	−	0.990092i	$-0.455156\pi$
$127$	3.16484			0.280834			0.140417	+	0.990092i	$0.455156\pi$
$128$	17.1400	+	9.89576i	1.51497	+	0.874670i
$129$	4.96316	+	7.87669i	0.436982	+	0.693504i
$130$	2.18033	+	3.77644i	0.191227	+	0.331215i
$131$	−5.88263			−0.513967			−0.256984	−	0.966416i	$-0.582729\pi$
$131$	−5.88263			−0.513967			−0.256984	+	0.966416i	$0.582729\pi$
$132$	25.5271	−	16.0848i	2.22184	−	1.40000i
$133$	10.0106	−	1.96974i	0.868025	−	0.170798i
$134$			15.8569i			1.36983i
$135$	−5.16124	+	0.601365i	−0.444208	+	0.0517573i
$136$	−32.8549	−	18.9688i	−2.81728	−	1.62656i
$137$		−	0.497828i		−	0.0425323i	−0.999774	−	0.0212662i	$-0.993230\pi$
$137$		−	0.497828i		−	0.0425323i	0.999774	−	0.0212662i	$-0.00676974\pi$
$138$	4.47732	−	8.49748i	0.381134	−	0.723354i
$139$	9.77690	+	5.64470i	0.829266	+	0.478777i	0.853601	−	0.520927i	$-0.174414\pi$
$139$	9.77690	+	5.64470i	0.829266	+	0.478777i	−0.0243354	+	0.999704i	$0.507747\pi$
$140$	2.03035	+	10.3186i	0.171596	+	0.872080i
$141$	0.484334	−	0.919216i	0.0407883	−	0.0774119i
$142$	−0.420412	+	0.728175i	−0.0352802	+	0.0611071i
$143$	−3.90915	+	6.77084i	−0.326899	+	0.566206i
$144$	−4.98462	+	10.4180i	−0.415385	+	0.868165i
$145$	−0.771716	+	0.445550i	−0.0640875	+	0.0370009i
$146$	−4.78308	−	8.28454i	−0.395851	−	0.685633i
$147$	9.86800	+	7.04432i	0.813899	+	0.581006i
$148$	−10.2944	+	17.8304i	−0.846191	+	1.46565i
$149$		−	11.2635i		−	0.922742i	−0.887207	−	0.461371i	$-0.847358\pi$
$149$		−	11.2635i		−	0.922742i	0.887207	−	0.461371i	$-0.152642\pi$
$150$	3.74561	+	1.97356i	0.305828	+	0.161140i
$151$	−2.33427			−0.189960			−0.0949800	−	0.995479i	$-0.530279\pi$
$151$	−2.33427			−0.189960			−0.0949800	+	0.995479i	$0.530279\pi$
$152$	−9.30729	−	16.1207i	−0.754921	−	1.30756i
$153$	−10.1761	+	21.2683i	−0.822687	+	1.71944i
$154$	−21.3475	+	18.6434i	−1.72023	+	1.50233i
$155$	−6.13095	+	3.53970i	−0.492450	+	0.284316i
$156$	−0.474756	−	12.2728i	−0.0380109	−	0.982611i
$157$	−20.7939	+	12.0054i	−1.65953	+	0.958132i	−0.686602	+	0.727033i	$0.740899\pi$
$157$	−20.7939	+	12.0054i	−1.65953	+	0.958132i	−0.972930	+	0.231099i	$0.925768\pi$
$158$	−14.5531	+	8.40222i	−1.15778	+	0.668445i
$159$	−21.0737	−	11.1037i	−1.67125	−	0.880580i
$160$	−0.211683	+	0.122215i	−0.0167350	+	0.00966194i
$161$	−1.94111	+	5.67975i	−0.152981	+	0.447627i
$162$	20.5188	+	7.93352i	1.61211	+	0.623316i
$163$	6.10651	+	10.5768i	0.478299	+	0.828438i	0.999690	−	0.0248796i	$-0.00792025\pi$
$163$	6.10651	+	10.5768i	0.478299	+	0.828438i	−0.521392	+	0.853318i	$0.674587\pi$
$164$	−14.2065			−1.10934
$165$	0.293417	+	7.58507i	0.0228425	+	0.590497i
$166$			15.1289i			1.17423i
$167$	8.16312	−	14.1389i	0.631681	−	1.09410i	−0.355527	−	0.934666i	$-0.615699\pi$
$167$	8.16312	−	14.1389i	0.631681	−	1.09410i	0.987208	−	0.159438i	$-0.0509682\pi$
$168$	6.33933	−	21.1932i	0.489090	−	1.63509i
$169$	−4.90872	−	8.50215i	−0.377594	−	0.654012i
$170$	16.6367	−	9.60521i	1.27598	−	0.736686i
$171$	−9.54188	+	6.54095i	−0.729686	+	0.500199i
$172$	−10.6826	+	18.5028i	−0.814540	+	1.41083i
$173$	2.24985	−	3.89686i	0.171053	−	0.296273i	−0.767735	−	0.640767i	$-0.778616\pi$
$173$	2.24985	−	3.89686i	0.171053	−	0.296273i	0.938788	+	0.344494i	$0.111950\pi$
$174$	3.76987	−	0.145832i	0.285793	−	0.0110555i
$175$	−2.50358	−	0.855621i	−0.189253	−	0.0646788i
$176$	14.6110	+	8.43566i	1.10134	+	0.635862i
$177$	−8.24424	−	13.0839i	−0.619675	−	0.983445i
$178$			8.26282i			0.619324i
$179$	−7.40489	−	4.27521i	−0.553467	−	0.319545i	0.197052	−	0.980393i	$-0.436863\pi$
$179$	−7.40489	−	4.27521i	−0.553467	−	0.319545i	−0.750519	+	0.660849i	$0.770197\pi$
$180$	−6.74222	−	9.83549i	−0.502535	−	0.733094i
$181$		−	0.872879i		−	0.0648806i	−0.999474	−	0.0324403i	$-0.989672\pi$
$181$		−	0.872879i		−	0.0648806i	0.999474	−	0.0324403i	$-0.0103279\pi$
$182$	2.22742	+	11.3201i	0.165108	+	0.839105i
$183$	6.65689	+	3.50751i	0.492091	+	0.259282i
$184$	10.9512			0.807336
$185$	−2.58988	−	4.48580i	−0.190412	−	0.329803i
$186$	29.9500	−	1.15857i	2.19604	−	0.0849504i
$187$	29.8283	+	17.2214i	2.18126	+	1.25935i
$188$	2.38439			0.173900
$189$	−13.4361	−	2.91049i	−0.977333	−	0.211707i
$190$	9.42586			0.683824
$191$	−13.4463	−	7.76320i	−0.972937	−	0.561726i	−0.0728069	−	0.997346i	$-0.523196\pi$
$191$	−13.4463	−	7.76320i	−0.972937	−	0.561726i	−0.900130	+	0.435620i	$0.856529\pi$
$192$	14.3598	−	0.555488i	1.03633	−	0.0400889i
$193$	5.25698	+	9.10536i	0.378406	+	0.655418i	0.990830	−	0.135111i	$-0.0431391\pi$
$193$	5.25698	+	9.10536i	0.378406	+	0.655418i	−0.612425	+	0.790529i	$0.709806\pi$
$194$	29.0994			2.08922
$195$	2.73368	+	1.44037i	0.195763	+	0.103147i
$196$	−3.74565	+	27.5706i	−0.267546	+	1.96933i
$197$			6.18325i			0.440538i	0.975439	+	0.220269i	$0.0706936\pi$
$197$			6.18325i			0.440538i	−0.975439	+	0.220269i	$0.929306\pi$
$198$	13.8706	−	28.9898i	0.985737	−	2.06021i
$199$	11.5085	+	6.64441i	0.815813	+	0.471010i	0.848971	−	0.528440i	$-0.177223\pi$
$199$	11.5085	+	6.64441i	0.815813	+	0.471010i	−0.0331573	+	0.999450i	$0.510556\pi$
$200$			4.82720i			0.341335i
$201$	5.98999	+	9.50632i	0.422501	+	0.670524i
$202$	−35.6790	−	20.5993i	−2.51036	−	1.44936i
$203$	−2.31327	+	0.455175i	−0.162360	+	0.0319470i
$204$	−54.0666	+	2.09149i	−3.78542	+	0.146433i
$205$	1.78706	−	3.09527i	0.124813	−	0.216183i
$206$	16.2556	−	28.1555i	1.13258	−	1.96169i
$207$	−0.525770	−	6.78562i	−0.0365435	−	0.471633i
$208$	5.94763	−	3.43387i	0.412394	−	0.238096i
$209$	8.44990	+	14.6357i	0.584492	+	1.01237i
$210$	7.68882	+	8.14578i	0.530579	+	0.562112i
$211$	7.79496	−	13.5013i	0.536627	−	0.929466i	−0.462455	−	0.886643i	$-0.653031\pi$
$211$	7.79496	−	13.5013i	0.536627	−	0.929466i	0.999083	−	0.0428232i	$-0.0136352\pi$
$212$		−	54.6639i		−	3.75433i
$213$	0.0230305	+	0.595358i	0.00157803	+	0.0407932i
$214$	−47.5097			−3.24770
$215$	−2.68755	−	4.65498i	−0.183290	−	0.317467i
$216$	2.90291	+	24.9143i	0.197518	+	1.69521i
$217$	−18.3780	+	3.61617i	−1.24758	+	0.245481i
$218$	19.1049	−	11.0302i	1.29395	−	0.747062i
$219$	−5.99700	−	3.15981i	−0.405240	−	0.213520i
$220$	−15.0860	+	8.70991i	−1.01710	+	0.587222i
$221$	12.1421	−	7.01022i	0.816763	−	0.471559i
$222$	0.847685	+	21.9133i	0.0568929	+	1.47073i
$223$	2.92075	−	1.68630i	0.195588	−	0.112923i	−0.399008	−	0.916947i	$-0.630645\pi$
$223$	2.92075	−	1.68630i	0.195588	−	0.112923i	0.594596	+	0.804025i	$0.297312\pi$
$224$	−0.634534	+	0.124855i	−0.0423966	+	0.00834223i
$225$	2.99103	−	0.231754i	0.199402	−	0.0154503i
$226$	16.0929	+	27.8737i	1.07048	+	1.85413i
$227$	19.3686			1.28554			0.642769	−	0.766060i	$-0.277786\pi$
$227$	19.3686			1.28554			0.642769	+	0.766060i	$0.277786\pi$
$228$	−23.4875	−	12.3755i	−1.55550	−	0.819591i
$229$		−	10.4719i		−	0.692002i	−0.938234	−	0.346001i	$-0.887539\pi$
$229$		−	10.4719i		−	0.692002i	0.938234	−	0.346001i	$-0.112461\pi$
$230$	−2.77269	+	4.80244i	−0.182826	+	0.316663i
$231$	−5.75535	+	19.2409i	−0.378674	+	1.26596i
$232$	2.15076	+	3.72523i	0.141204	+	0.244573i
$233$	−10.9648	+	6.33051i	−0.718326	+	0.414726i	−0.814136	−	0.580674i	$-0.802789\pi$
$233$	−10.9648	+	6.33051i	−0.718326	+	0.414726i	0.0958104	+	0.995400i	$0.469456\pi$
$234$	−7.39664	−	10.7902i	−0.483533	−	0.705374i
$235$	−0.299936	+	0.519504i	−0.0195656	+	0.0338887i
$236$	17.7447	−	30.7348i	1.15508	−	2.00066i
$237$	−5.55070	+	10.5347i	−0.360557	+	0.684299i
$238$	49.8698	−	9.81270i	3.23258	−	0.636063i
$239$	16.9811	+	9.80401i	1.09841	+	0.634169i	0.935804	−	0.352522i	$-0.114676\pi$
$239$	16.9811	+	9.80401i	1.09841	+	0.634169i	0.162609	+	0.986691i	$0.448009\pi$
$240$	3.10822	−	5.89909i	0.200635	−	0.380784i
$241$		−	1.75854i		−	0.113277i	−0.998395	−	0.0566386i	$-0.981962\pi$
$241$		−	1.75854i		−	0.113277i	0.998395	−	0.0566386i	$-0.0180383\pi$
$242$	−17.3720	−	10.0297i	−1.11671	−	0.644735i
$243$	15.2981	−	2.99484i	0.981372	−	0.192119i
$244$			17.2676i			1.10544i
$245$	−5.53583	−	4.28423i	−0.353671	−	0.273709i
$246$	−12.8023	+	8.06682i	−0.816246	+	0.514322i
$247$	6.87933			0.437721
$248$	17.0869	+	29.5953i	1.08502	+	1.87931i
$249$	5.71500	+	9.06989i	0.362173	+	0.574781i
$250$	−2.11687	−	1.22217i	−0.133883	−	0.0772971i
$251$	7.21616			0.455480			0.227740	−	0.973722i	$-0.426866\pi$
$251$	7.21616			0.455480			0.227740	+	0.973722i	$0.426866\pi$
$252$	−8.46423	−	30.3927i	−0.533197	−	1.91456i
$253$	−9.94241			−0.625074
$254$	6.69956	+	3.86799i	0.420368	+	0.242699i
$255$	6.34542	−	12.0430i	0.397366	−	0.754159i
$256$	15.8919	+	27.5255i	0.993241	+	1.72034i
$257$	−13.5344			−0.844254			−0.422127	−	0.906537i	$-0.638716\pi$
$257$	−13.5344			−0.844254			−0.422127	+	0.906537i	$0.638716\pi$
$258$	0.879654	+	22.7398i	0.0547649	+	1.41572i
$259$	−2.64583	−	13.4465i	−0.164404	−	0.835526i
$260$			7.09101i			0.439766i
$261$	2.20497	−	1.51151i	0.136484	−	0.0935598i
$262$	−12.4527	−	7.18960i	−0.769333	−	0.444175i
$263$			4.37208i			0.269594i	0.990873	+	0.134797i	$0.0430382\pi$
$263$			4.37208i			0.269594i	−0.990873	+	0.134797i	$0.956962\pi$
$264$	36.6147	−	1.41638i	2.25348	−	0.0871725i
$265$	11.9100	+	6.87623i	0.731624	+	0.422404i
$266$	23.5984	+	8.06496i	1.44691	+	0.494495i
$267$	3.12130	+	4.95361i	0.191021	+	0.303156i
$268$	−12.8927	+	22.3309i	−0.787549	+	1.36408i
$269$	10.5229	−	18.2262i	0.641592	−	1.11127i	−0.343486	−	0.939158i	$-0.611608\pi$
$269$	10.5229	−	18.2262i	0.641592	−	1.11127i	0.985077	−	0.172112i	$-0.0550590\pi$
$270$	−11.6606	−	5.03492i	−0.709643	−	0.306415i
$271$	2.86462	−	1.65389i	0.174013	−	0.100467i	−0.410464	−	0.911877i	$-0.634633\pi$
$271$	2.86462	−	1.65389i	0.174013	−	0.100467i	0.584477	+	0.811410i	$0.301300\pi$
$272$	−15.1276	−	26.2017i	−0.917243	−	1.58871i
$273$	5.61157	+	5.94508i	0.339628	+	0.359813i
$274$	0.608433	−	1.05384i	0.0367568	−	0.0636646i
$275$		−	4.38252i		−	0.264276i
$276$	13.2143	−	8.32643i	0.795409	−	0.501192i
$277$	−25.5694			−1.53632			−0.768159	−	0.640259i	$-0.778827\pi$
$277$	−25.5694			−1.53632			−0.768159	+	0.640259i	$0.778827\pi$
$278$	13.7976	+	23.8982i	0.827525	+	1.43332i
$279$	17.5175	−	12.0083i	1.04875	−	0.718915i
$280$	−4.13026	+	12.0853i	−0.246830	+	0.722234i
$281$	5.65129	−	3.26278i	0.337128	−	0.194641i	−0.321873	−	0.946783i	$-0.604313\pi$
$281$	5.65129	−	3.26278i	0.337128	−	0.194641i	0.659001	+	0.752142i	$0.270979\pi$
$282$	2.14871	−	1.35392i	0.127954	−	0.0806246i
$283$	−4.06423	+	2.34648i	−0.241593	+	0.139484i	−0.615909	−	0.787817i	$-0.711211\pi$
$283$	−4.06423	+	2.34648i	−0.241593	+	0.139484i	0.374315	+	0.927301i	$0.377878\pi$
$284$	−1.18411	+	0.683647i	−0.0702641	+	0.0405670i
$285$	5.65086	−	3.56065i	0.334728	−	0.210915i
$286$	−16.5503	+	9.55532i	−0.978639	+	0.565018i
$287$	7.12242	−	6.22022i	0.420423	−	0.367168i
$288$	0.604826	−	0.414608i	0.0356397	−	0.0244310i
$289$	−22.3828	−	38.7682i	−1.31664	−	2.28048i
$290$	−2.17816			−0.127906
$291$	17.4453	−	10.9924i	1.02266	−	0.644385i
$292$		−	15.5559i		−	0.910339i
$293$	5.27136	−	9.13027i	0.307956	−	0.533396i	−0.669959	−	0.742398i	$-0.733688\pi$
$293$	5.27136	−	9.13027i	0.307956	−	0.533396i	0.977915	+	0.209002i	$0.0670216\pi$
$294$	12.2799	+	26.9723i	0.716177	+	1.57306i
$295$	4.46426	+	7.73233i	0.259919	+	0.450194i
$296$	−21.6539	+	12.5019i	−1.25861	+	0.726657i
$297$	−2.63549	−	22.6192i	−0.152927	−	1.31250i
$298$	13.7660	−	23.8433i	0.797441	−	1.38121i
$299$	−2.02361	+	3.50499i	−0.117028	+	0.202699i
$300$	3.67021	+	5.82475i	0.211900	+	0.336292i
$301$	−2.74561	−	13.9536i	−0.158254	−	0.804274i
$302$	−4.94134	−	2.85288i	−0.284342	−	0.164165i
$303$	−29.1712	+	1.12844i	−1.67584	+	0.0648275i
$304$		−	14.8451i		−	0.851425i
$305$	−3.76221	−	2.17211i	−0.215423	−	0.124375i
$306$	−47.5349	+	32.5851i	−2.71739	+	1.86277i
$307$			12.9619i			0.739776i	0.929076	+	0.369888i	$0.120604\pi$
$307$			12.9619i			0.739776i	−0.929076	+	0.369888i	$0.879396\pi$
$308$	−45.2214	+	8.89806i	−2.57673	+	0.507014i
$309$	−0.890496	−	23.0200i	−0.0506585	−	1.30956i
$310$	−17.3045			−0.982832
$311$	−5.66458	−	9.81134i	−0.321209	−	0.556350i	0.659529	−	0.751679i	$-0.270756\pi$
$311$	−5.66458	−	9.81134i	−0.321209	−	0.556350i	−0.980738	+	0.195329i	$0.937422\pi$
$312$	6.95297	−	13.1960i	0.393635	−	0.747078i
$313$	−4.39353	−	2.53661i	−0.248337	−	0.143377i	0.370666	−	0.928766i	$-0.379130\pi$
$313$	−4.39353	−	2.53661i	−0.248337	−	0.143377i	−0.619003	+	0.785389i	$0.712463\pi$
$314$	−58.6906			−3.31210
$315$	7.68659	+	1.97898i	0.433090	+	0.111503i
$316$	−27.3263			−1.53722
$317$	−8.63646	−	4.98626i	−0.485072	−	0.280056i	0.237456	−	0.971398i	$-0.423687\pi$
$317$	−8.63646	−	4.98626i	−0.485072	−	0.280056i	−0.722528	+	0.691342i	$0.757020\pi$
$318$	−31.0395	−	49.2607i	−1.74061	−	2.76240i
$319$	−1.95263	−	3.38206i	−0.109326	−	0.189359i
$320$	−8.29685			−0.463808
$321$	−28.4824	+	17.9469i	−1.58973	+	1.00170i
$322$	−11.0507	+	9.65092i	−0.615832	+	0.537824i
$323$		−	30.3062i		−	1.68628i
$324$	22.4456	+	27.8558i	1.24698	+	1.54754i
$325$	−1.54497	−	0.891986i	−0.0856993	−	0.0494785i
$326$			29.8529i			1.65340i
$327$	7.28683	−	13.8296i	0.402962	−	0.764781i
$328$	−14.9415	−	8.62648i	−0.825007	−	0.476318i
$329$	−1.19541	+	1.04399i	−0.0659051	+	0.0575569i
$330$	−8.64915	+	16.4152i	−0.476120	+	0.903627i
$331$	12.5098	−	21.6676i	0.687600	−	1.19096i	−0.285011	−	0.958524i	$-0.591997\pi$
$331$	12.5098	−	21.6676i	0.687600	−	1.19096i	0.972612	−	0.232435i	$-0.0746693\pi$
$332$	−12.3008	+	21.3057i	−0.675097	+	1.16930i
$333$	8.78602	+	12.8170i	0.481471	+	0.702366i
$334$	34.5605	−	19.9535i	1.89107	−	1.09181i
$335$	−3.24358	−	5.61805i	−0.177216	−	0.306947i
$336$	12.8291	−	12.1094i	0.699883	−	0.660621i
$337$	−8.94751	+	15.4975i	−0.487402	+	0.844205i	−0.999895	−	0.0144863i	$-0.995389\pi$
$337$	−8.94751	+	15.4975i	−0.487402	+	0.844205i	0.512493	+	0.858691i	$0.328722\pi$
$338$		−	23.9973i		−	1.30528i
$339$	20.1771	+	10.6313i	1.09587	+	0.577414i
$340$	31.2387			1.69416
$341$	−15.5128	−	26.8690i	−0.840066	−	1.45504i
$342$	−28.1931	+	2.18448i	−1.52451	+	0.118123i
$343$	−10.1937	−	15.4625i	−0.550409	−	0.834895i
$344$	−22.4705	+	12.9734i	−1.21153	+	0.699477i
$345$	0.151890	+	3.92648i	0.00817749	+	0.211395i
$346$	9.52529	−	5.49943i	0.512083	−	0.295651i
$347$	22.9931	−	13.2751i	1.23433	−	0.712642i	0.266403	−	0.963862i	$-0.414165\pi$
$347$	22.9931	−	13.2751i	1.23433	−	0.712642i	0.967930	+	0.251220i	$0.0808316\pi$
$348$	5.42758	+	2.85979i	0.290949	+	0.153301i
$349$	9.98709	−	5.76605i	0.534597	−	0.308649i	−0.208290	−	0.978067i	$-0.566790\pi$
$349$	9.98709	−	5.76605i	0.534597	−	0.308649i	0.742886	+	0.669418i	$0.233456\pi$
$350$	−4.25403	−	4.87105i	−0.227388	−	0.260368i
$351$	−8.51034	−	3.67466i	−0.454248	−	0.196139i
$352$	−0.535609	−	0.927703i	−0.0285481	−	0.0494467i
$353$	−26.6598			−1.41896			−0.709480	−	0.704725i	$-0.751070\pi$
$353$	−26.6598			−1.41896			−0.709480	+	0.704725i	$0.751070\pi$
$354$	−1.46118	−	37.7728i	−0.0776610	−	2.00760i
$355$		−	0.343987i		−	0.0182569i
$356$	−6.71823	+	11.6363i	−0.356065	+	0.616723i
$357$	26.1905	−	24.7212i	1.38615	−	1.30839i
$358$	−10.4501	−	18.1001i	−0.552306	−	0.956622i
$359$	17.8292	−	10.2937i	0.940992	−	0.543282i	0.0507207	−	0.998713i	$-0.483848\pi$
$359$	17.8292	−	10.2937i	0.940992	−	0.543282i	0.890271	+	0.455431i	$0.150515\pi$
$360$	−1.11873	−	14.4383i	−0.0589620	−	0.760967i
$361$	−2.06492	+	3.57655i	−0.108680	+	0.188239i
$362$	1.06681	−	1.84777i	0.0560703	−	0.0971166i
$363$	−14.2034	+	0.549437i	−0.745484	+	0.0288380i
$364$	−6.06721	+	17.7529i	−0.318008	+	0.930505i
$365$	3.38926	+	1.95679i	0.177402	+	0.102423i
$366$	9.80497	+	15.5608i	0.512514	+	0.813377i
$367$			18.0423i			0.941798i	0.882187	+	0.470899i	$0.156070\pi$
$367$			18.0423i			0.941798i	−0.882187	+	0.470899i	$0.843930\pi$
$368$	7.56352	+	4.36680i	0.394276	+	0.227635i
$369$	−4.62780	+	9.67222i	−0.240914	+	0.503516i
$370$		−	12.6611i		−	0.658221i
$371$	23.9342	+	27.4056i	1.24260	+	1.42283i
$372$	43.1197	+	22.7198i	2.23565	+	1.17796i
$373$	−9.54655			−0.494302			−0.247151	−	0.968977i	$-0.579494\pi$
$373$	−9.54655			−0.494302			−0.247151	+	0.968977i	$0.579494\pi$
$374$	42.0950	+	72.9107i	2.17668	+	3.77012i
$375$	−1.73076	+	0.0669518i	−0.0893759	+	0.00345737i
$376$	2.50775	+	1.44785i	0.129327	+	0.0746672i
$377$	−1.58970			−0.0818737
$378$	−24.8853	−	22.5824i	−1.27996	−	1.16151i
$379$	0.905456			0.0465101			0.0232551	−	0.999730i	$-0.492597\pi$
$379$	0.905456			0.0465101			0.0232551	+	0.999730i	$0.492597\pi$
$380$	13.2742	+	7.66386i	0.680952	+	0.393148i
$381$	5.47757	−	0.211892i	0.280625	−	0.0108555i
$382$	−18.9760	−	32.8674i	−0.970895	−	1.68164i
$383$	−6.13776			−0.313625			−0.156812	−	0.987628i	$-0.550122\pi$
$383$	−6.13776			−0.313625			−0.156812	+	0.987628i	$0.550122\pi$
$384$	30.3276	+	15.9796i	1.54765	+	0.815456i
$385$	3.74977	−	10.9720i	0.191106	−	0.559184i
$386$			25.6998i			1.30808i
$387$	9.11737	+	13.3003i	0.463462	+	0.676095i
$388$	40.9800	+	23.6598i	2.08044	+	1.20114i
$389$			8.36707i			0.424227i	0.977245	+	0.212114i	$0.0680347\pi$
$389$			8.36707i			0.424227i	−0.977245	+	0.212114i	$0.931965\pi$
$390$	4.02645	+	6.39011i	0.203887	+	0.323576i
$391$	15.4409	+	8.91480i	0.780879	+	0.450841i
$392$	−20.6809	+	26.7226i	−1.04454	+	1.34969i
$393$	−10.1814	+	0.393852i	−0.513583	+	0.0198672i
$394$	−7.55701	+	13.0891i	−0.380717	+	0.659420i
$395$	3.43741	−	5.95376i	0.172955	−	0.299566i
$396$	43.1042	−	29.5479i	2.16607	−	1.48484i
$397$	−17.1060	+	9.87616i	−0.858526	+	0.495670i	−0.863518	−	0.504317i	$-0.831744\pi$
$397$	−17.1060	+	9.87616i	−0.858526	+	0.495670i	0.00499248	+	0.999988i	$0.498411\pi$
$398$	16.2413	+	28.1307i	0.814101	+	1.41006i
$399$	17.1940	−	4.07937i	0.860774	−	0.204224i
$400$	−1.92484	+	3.33393i	−0.0962422	+	0.166696i
$401$		−	15.4433i		−	0.771200i	−0.922666	−	0.385600i	$-0.873995\pi$
$401$		−	15.4433i		−	0.771200i	0.922666	−	0.385600i	$-0.126005\pi$
$402$	1.06165	+	27.4444i	0.0529502	+	1.36880i
$403$	−12.6295			−0.629119
$404$	−33.4972	−	58.0188i	−1.66655	−	2.88654i
$405$	−8.89258	+	1.38637i	−0.441876	+	0.0688893i
$406$	−5.45320	−	1.86368i	−0.270638	−	0.0924929i
$407$	19.6591	−	11.3502i	0.974466	−	0.562608i
$408$	−58.1338	−	30.6306i	−2.87805	−	1.51644i
$409$	−4.10325	+	2.36901i	−0.202892	+	0.117140i	−0.598004	−	0.801493i	$-0.704039\pi$
$409$	−4.10325	+	2.36901i	−0.202892	+	0.117140i	0.395111	+	0.918633i	$0.370706\pi$
$410$	7.56592	−	4.36819i	0.373654	−	0.215729i
$411$	−0.0333305	−	0.861619i	−0.00164407	−	0.0425005i
$412$	45.7847	−	26.4338i	2.25565	−	1.30230i
$413$	4.56070	+	23.1782i	0.224417	+	1.14053i
$414$	7.18022	−	15.0068i	0.352889	−	0.737546i
$415$	−3.09467	−	5.36013i	−0.151912	−	0.263119i
$416$	−0.436056			−0.0213794
$417$	17.2994	+	9.11501i	0.847153	+	0.446364i
$418$			41.3090i			2.02049i
$419$	0.120202	−	0.208195i	0.00587224	−	0.0101710i	−0.863074	−	0.505077i	$-0.831464\pi$
$419$	0.120202	−	0.208195i	0.00587224	−	0.0101710i	0.868947	+	0.494906i	$0.164797\pi$
$420$	4.20489	+	17.7230i	0.205178	+	0.864795i
$421$	6.23154	+	10.7933i	0.303707	+	0.526035i	0.976973	−	0.213365i	$-0.0684424\pi$
$421$	6.23154	+	10.7933i	0.303707	+	0.526035i	−0.673266	+	0.739400i	$0.735109\pi$
$422$	33.0018	−	19.0536i	1.60650	−	0.927515i
$423$	0.776721	−	1.62337i	0.0377655	−	0.0789307i
$424$	33.1930	−	57.4919i	1.61199	−	2.79205i
$425$	−3.92956	+	6.80619i	−0.190612	+	0.330149i
$426$	−0.678878	+	1.28844i	−0.0328918	+	0.0624252i
$427$	−7.56048	−	8.65707i	−0.365877	−	0.418945i
$428$	−66.9067	−	38.6286i	−3.23406	−	1.86719i
$429$	−6.31246	+	11.9804i	−0.304768	+	0.578419i
$430$		−	13.1386i		−	0.633601i
$431$	−1.71946	−	0.992731i	−0.0828235	−	0.0478182i	0.458016	−	0.888944i	$-0.348560\pi$
$431$	−1.71946	−	0.992731i	−0.0828235	−	0.0478182i	−0.540840	+	0.841126i	$0.681893\pi$
$432$	−7.92966	+	18.3647i	−0.381516	+	0.883573i
$433$		−	31.7870i		−	1.52758i	−0.645463	−	0.763792i	$-0.723335\pi$
$433$		−	31.7870i		−	1.52758i	0.645463	−	0.763792i	$-0.276665\pi$
$434$	−43.3233	−	14.8061i	−2.07959	−	0.710717i
$435$	−1.30582	+	0.822807i	−0.0626094	+	0.0394506i
$436$	35.8733			1.71802
$437$	4.37417	+	7.57628i	0.209245	+	0.362423i
$438$	−8.83301	−	14.0183i	−0.422058	−	0.669820i
$439$	6.38185	+	3.68456i	0.304589	+	0.175855i	0.644503	−	0.764602i	$-0.277064\pi$
$439$	6.38185	+	3.68456i	0.304589	+	0.175855i	−0.339914	+	0.940457i	$0.610398\pi$
$440$	−21.1553			−1.00854
$441$	17.5507	+	11.5313i	0.835749	+	0.549111i
$442$	34.2709			1.63010
$443$	35.6305	+	20.5713i	1.69285	+	0.977370i	0.952196	+	0.305489i	$0.0988199\pi$
$443$	35.6305	+	20.5713i	1.69285	+	0.977370i	0.740659	+	0.671881i	$0.234513\pi$
$444$	−16.6233	+	31.5492i	−0.788905	+	1.49726i
$445$	−1.69019	−	2.92749i	−0.0801226	−	0.138776i
$446$	8.24379			0.390355
$447$	−0.754111	−	19.4944i	−0.0356682	−	0.922052i
$448$	−20.7718	−	7.09895i	−0.981376	−	0.335394i
$449$			26.0169i			1.22781i	0.789379	+	0.613906i	$0.210403\pi$
$449$			26.0169i			1.22781i	−0.789379	+	0.613906i	$0.789597\pi$
$450$	6.61487	+	3.16497i	0.311828	+	0.149198i
$451$	13.5651	+	7.83180i	0.638755	+	0.368785i
$452$			52.3384i			2.46179i
$453$	−4.04005	+	0.156283i	−0.189818	+	0.00734283i
$454$	41.0007	+	23.6718i	1.92426	+	1.11097i
$455$	−3.10474	−	3.55506i	−0.145553	−	0.166664i
$456$	−17.1880	−	27.2779i	−0.804900	−	1.27740i
$457$	15.3564	−	26.5981i	0.718342	−	1.24420i	−0.243315	−	0.969947i	$-0.578235\pi$
$457$	15.3564	−	26.5981i	0.718342	−	1.24420i	0.961656	−	0.274257i	$-0.0884319\pi$
$458$	12.7985	−	22.1676i	0.598033	−	1.03582i
$459$	−16.1884	+	37.4915i	−0.755608	+	1.74995i
$460$	−7.80941	+	4.50877i	−0.364116	+	0.210222i
$461$	15.7774	+	27.3273i	0.734828	+	1.27276i	0.954799	+	0.297253i	$0.0960703\pi$
$461$	15.7774	+	27.3273i	0.734828	+	1.27276i	−0.219971	+	0.975506i	$0.570596\pi$
$462$	−35.6990	+	33.6964i	−1.66087	+	1.56770i
$463$	−12.2485	+	21.2150i	−0.569234	+	0.985943i	0.427408	+	0.904059i	$0.359427\pi$
$463$	−12.2485	+	21.2150i	−0.569234	+	0.985943i	−0.996642	+	0.0818837i	$0.973906\pi$
$464$			3.43046i			0.159255i
$465$	−10.3742	+	6.53684i	−0.481091	+	0.303139i
$466$	−30.9480			−1.43364
$467$	−1.33602	−	2.31405i	−0.0618236	−	0.107082i	0.833457	−	0.552584i	$-0.186358\pi$
$467$	−1.33602	−	2.31405i	−0.0618236	−	0.107082i	−0.895281	+	0.445503i	$0.853025\pi$
$468$	−1.64337	−	21.2095i	−0.0759649	−	0.980408i
$469$	−3.31365	−	16.8405i	−0.153010	−	0.777623i
$470$	−1.26985	+	0.733147i	−0.0585737	+	0.0338176i
$471$	−35.1854	+	22.1705i	−1.62126	+	1.02156i
$472$	37.3255	−	21.5499i	1.71805	−	0.991915i
$473$	20.4005	−	11.7782i	0.938017	−	0.541564i
$474$	−24.6253	+	15.5166i	−1.13108	+	0.712699i
$475$	−3.33955	+	1.92809i	−0.153229	+	0.0884669i
$476$	78.2087	+	26.7285i	3.58469	+	1.22510i
$477$	−37.2168	−	17.8069i	−1.70404	−	0.815320i
$478$	23.9644	+	41.5076i	1.09611	+	1.89851i
$479$	−3.57167			−0.163194			−0.0815968	−	0.996665i	$-0.526002\pi$
$479$	−3.57167			−0.163194			−0.0815968	+	0.996665i	$0.526002\pi$
$480$	−0.358188	+	0.225697i	−0.0163490	+	0.0103016i
$481$		−	9.24055i		−	0.421333i
$482$	2.14924	−	3.72259i	0.0978951	−	0.169559i
$483$	−2.97931	+	9.96023i	−0.135563	+	0.453206i
$484$	−16.3097	−	28.2492i	−0.741350	−	1.28406i
$485$	−10.3098	+	5.95238i	−0.468145	+	0.270284i
$486$	36.0442	+	12.3572i	1.63500	+	0.560535i
$487$	−8.17684	+	14.1627i	−0.370528	+	0.641773i	−0.989647	−	0.143524i	$-0.954157\pi$
$487$	−8.17684	+	14.1627i	−0.370528	+	0.641773i	0.619119	+	0.785297i	$0.287490\pi$
$488$	−10.4852	+	18.1609i	−0.474644	+	0.822107i
$489$	11.2770	+	17.8970i	0.509964	+	0.809330i
$490$	−6.48254	−	15.8349i	−0.292851	−	0.715348i
$491$	−36.3236	−	20.9714i	−1.63926	−	0.946427i	−0.981089	−	0.193559i	$-0.937997\pi$
$491$	−36.3236	−	20.9714i	−1.63926	−	0.946427i	−0.658172	−	0.752868i	$-0.728670\pi$
$492$	−24.5880	+	0.951152i	−1.10851	+	0.0428812i
$493$			7.00326i			0.315411i
$494$	14.5626	+	8.40774i	0.655204	+	0.378282i
$495$	1.01567	+	13.1083i	0.0456509	+	0.589173i
$496$			27.2535i			1.22372i
$497$	0.294322	−	0.861199i	0.0132022	−	0.0386301i
$498$	1.01291	+	26.1845i	0.0453895	+	1.17336i
$499$	−31.0823			−1.39144			−0.695718	−	0.718315i	$-0.744914\pi$
$499$	−31.0823			−1.39144			−0.695718	+	0.718315i	$0.744914\pi$
$500$	−1.98742	−	3.44231i	−0.0888802	−	0.153945i
$501$	13.1817	−	25.0176i	0.588917	−	1.11770i
$502$	15.2757	+	8.81941i	0.681787	+	0.393630i
$503$	16.2335			0.723815			0.361908	−	0.932214i	$-0.382126\pi$
$503$	16.2335			0.723815			0.361908	+	0.932214i	$0.382126\pi$
$504$	9.55292	−	37.1047i	0.425521	−	1.65278i
$505$	16.8546			0.750020
$506$	−21.0468	−	12.1514i	−0.935643	−	0.540194i
$507$	−9.06503	−	14.3865i	−0.402592	−	0.638927i
$508$	6.28988	+	10.8944i	0.279068	+	0.483360i
$509$	−12.7227			−0.563925			−0.281962	−	0.959425i	$-0.590985\pi$
$509$	−12.7227			−0.563925			−0.281962	+	0.959425i	$0.590985\pi$
$510$	28.1510	−	17.7381i	1.24655	−	0.785458i
$511$	6.81102	+	7.79891i	0.301302	+	0.345003i
$512$			38.1074i			1.68413i
$513$	−16.0767	+	11.9596i	−0.709805	+	0.528031i
$514$	−28.6506	−	16.5414i	−1.26372	−	0.729611i
$515$			13.3006i			0.586093i
$516$	−17.2502	+	32.7391i	−0.759397	+	1.44126i
$517$	−2.27673	−	1.31447i	−0.100131	−	0.0578105i
$518$	10.8331	−	31.6982i	0.475981	−	1.39274i
$519$	3.63305	−	6.89515i	0.159473	−	0.302663i
$520$	−4.30580	+	7.45786i	−0.188822	+	0.327049i
$521$	−3.53054	+	6.11507i	−0.154676	+	0.267906i	−0.932941	−	0.360030i	$-0.882767\pi$
$521$	−3.53054	+	6.11507i	−0.154676	+	0.267906i	0.778265	+	0.627936i	$0.216100\pi$
$522$	6.51496	−	0.504798i	0.285152	−	0.0220944i
$523$	22.9186	−	13.2321i	1.00216	−	0.578598i	0.0932737	−	0.995641i	$-0.470267\pi$
$523$	22.9186	−	13.2321i	1.00216	−	0.578598i	0.908887	+	0.417043i	$0.136934\pi$
$524$	−11.6913	−	20.2498i	−0.510735	−	0.884619i
$525$	−4.39037	−	1.31325i	−0.191612	−	0.0573150i
$526$	−5.34345	+	9.25512i	−0.232985	+	0.403542i
$527$			55.6379i			2.42362i
$528$	25.8528	+	13.6218i	1.12510	+	0.592814i
$529$	17.8532			0.776227
$530$	16.8079	+	29.1122i	0.730089	+	1.26455i
$531$	−15.1448	−	22.0931i	−0.657227	−	0.958757i
$532$	26.6757	+	30.5448i	1.15654	+	1.32428i
$533$	5.52188	−	3.18806i	0.239179	−	0.138090i
$534$	0.553210	+	14.3009i	0.0239397	+	0.618861i
$535$	16.8326	−	9.71828i	0.727735	−	0.420158i
$536$	−27.1195	+	15.6574i	−1.17138	+	0.676299i
$537$	−13.1023	−	6.90358i	−0.565406	−	0.297912i
$538$	44.5511	−	25.7216i	1.92074	−	1.10894i
$539$	18.7757	−	24.2609i	0.808727	−	1.04499i
$540$	−12.3276	−	16.5714i	−0.530497	−	0.713121i
$541$	16.1875	+	28.0376i	0.695955	+	1.20543i	0.969858	+	0.243672i	$0.0783520\pi$
$541$	16.1875	+	28.0376i	0.695955	+	1.20543i	−0.273903	+	0.961757i	$0.588315\pi$
$542$	8.08537			0.347296
$543$	−0.0584408	−	1.51074i	−0.00250793	−	0.0648321i
$544$			1.92100i			0.0823623i
$545$	−4.51255	+	7.81596i	−0.193296	+	0.334799i
$546$	4.61303	+	19.4433i	0.197420	+	0.832095i
$547$	−2.71649	−	4.70510i	−0.116149	−	0.201176i	0.802090	−	0.597204i	$-0.203722\pi$
$547$	−2.71649	−	4.70510i	−0.116149	−	0.201176i	−0.918238	+	0.396028i	$0.870388\pi$
$548$	1.71368	−	0.989394i	0.0732048	−	0.0422648i
$549$	11.7563	+	5.62495i	0.501746	+	0.240067i
$550$	5.35620	−	9.27721i	0.228389	−	0.395582i
$551$	−1.71812	+	2.97588i	−0.0731946	+	0.126777i
$552$	18.9539	−	0.733205i	0.806733	−	0.0312073i
$553$	13.7000	−	11.9646i	0.582583	−	0.508787i
$554$	−54.1271	−	31.2503i	−2.29964	−	1.32770i
$555$	−4.78278	−	7.59043i	−0.203018	−	0.322196i
$556$			44.8735i			1.90306i
$557$	−22.1583	−	12.7931i	−0.938878	−	0.542061i	−0.0492696	−	0.998786i	$-0.515689\pi$
$557$	−22.1583	−	12.7931i	−0.938878	−	0.542061i	−0.889608	+	0.456724i	$0.849023\pi$
$558$	51.7585	−	4.01040i	2.19111	−	0.169774i
$559$		−	9.58904i		−	0.405573i
$560$	−7.67158	+	6.69982i	−0.324183	+	0.283119i
$561$	52.7784	+	27.8089i	2.22831	+	1.17409i
$562$	15.9507			0.672841
$563$	−7.35414	−	12.7377i	−0.309940	−	0.536832i	0.668409	−	0.743794i	$-0.266976\pi$
$563$	−7.35414	−	12.7377i	−0.309940	−	0.536832i	−0.978349	+	0.206962i	$0.933642\pi$
$564$	4.12680	−	0.159639i	0.173770	−	0.00672203i
$565$	−11.4033	−	6.58371i	−0.479741	−	0.276979i
$566$	−11.4713			−0.482173
$567$	−23.4495	−	4.13779i	−0.984786	−	0.173771i
$568$	−1.66050			−0.0696728
$569$	0.121208	+	0.0699796i	0.00508131	+	0.00293370i	0.502539	−	0.864555i	$-0.332400\pi$
$569$	0.121208	+	0.0699796i	0.00508131	+	0.00293370i	−0.497457	+	0.867489i	$0.665733\pi$
$570$	16.3139	−	0.631078i	0.683313	−	0.0264329i
$571$	−16.5670	−	28.6949i	−0.693307	−	1.20084i	−0.970748	−	0.240101i	$-0.922820\pi$
$571$	−16.5670	−	28.6949i	−0.693307	−	1.20084i	0.277441	−	0.960743i	$-0.410514\pi$
$572$	−31.0765			−1.29937
$573$	−23.7920	−	12.5360i	−0.993924	−	0.523697i
$574$	22.6794	−	4.46255i	0.946620	−	0.186263i
$575$		−	2.26865i		−	0.0946093i
$576$	24.8162	−	1.92283i	1.03401	−	0.0801179i
$577$	26.9549	+	15.5624i	1.12215	+	0.647871i	0.941948	−	0.335759i	$-0.108993\pi$
$577$	26.9549	+	15.5624i	1.12215	+	0.647871i	0.180198	+	0.983630i	$0.442326\pi$
$578$		−	109.423i		−	4.55139i
$579$	9.70817	+	15.4072i	0.403458	+	0.640301i
$580$	−3.06745	−	1.77099i	−0.127369	−	0.0735365i
$581$	−3.16152	−	16.0674i	−0.131162	−	0.666588i
$582$	50.3640	−	1.94826i	2.08765	−	0.0807578i
$583$	−30.1352	+	52.1957i	−1.24807	+	2.16173i
$584$	9.44583	−	16.3607i	0.390871	−	0.677009i
$585$	4.82777	+	2.30991i	0.199604	+	0.0955030i
$586$	22.3176	−	12.8851i	0.921930	−	0.532277i
$587$	−9.74979	−	16.8871i	−0.402417	−	0.697007i	0.591600	−	0.806232i	$-0.298496\pi$
$587$	−9.74979	−	16.8871i	−0.402417	−	0.697007i	−0.994017	+	0.109225i	$0.965163\pi$
$588$	−4.63690	+	47.9688i	−0.191223	+	1.97820i
$589$	−13.6498	+	23.6421i	−0.562428	+	0.974154i
$590$			21.8244i			0.898498i
$591$	0.413979	+	10.7017i	0.0170288	+	0.440209i
$592$	−19.9404			−0.819547
$593$	16.3836	+	28.3772i	0.672794	+	1.16531i	0.977108	+	0.212742i	$0.0682393\pi$
$593$	16.3836	+	28.3772i	0.672794	+	1.16531i	−0.304314	+	0.952572i	$0.598427\pi$
$594$	22.0656	−	51.1029i	0.905364	−	2.09678i
$595$	−15.6615	+	13.6776i	−0.642058	+	0.560728i
$596$	38.7725	−	22.3853i	1.58818	−	0.916938i
$597$	20.3632	+	10.7294i	0.833410	+	0.439123i
$598$	−8.56742	+	4.94640i	−0.350348	+	0.202273i
$599$	−1.10893	+	0.640239i	−0.0453095	+	0.0261594i	−0.522484	−	0.852649i	$-0.674994\pi$
$599$	−1.10893	+	0.640239i	−0.0453095	+	0.0261594i	0.477174	+	0.878809i	$0.341661\pi$
$600$	0.323190	+	8.35471i	0.0131942	+	0.341080i
$601$	16.8456	−	9.72583i	0.687148	−	0.396725i	−0.115395	−	0.993320i	$-0.536813\pi$
$601$	16.8456	−	9.72583i	0.687148	−	0.396725i	0.802543	+	0.596595i	$0.203480\pi$
$602$	11.2417	−	32.8936i	0.458177	−	1.34064i
$603$	11.0037	+	16.0521i	0.448105	+	0.653691i
$604$	−4.63917	−	8.03529i	−0.188765	−	0.326951i
$605$	8.20646			0.333640
$606$	−63.1307	−	33.2635i	−2.56451	−	1.35124i
$607$		−	22.7241i		−	0.922342i	−0.887311	−	0.461171i	$-0.847429\pi$
$607$		−	22.7241i		−	0.922342i	0.887311	−	0.461171i	$-0.152571\pi$
$608$	−0.471284	+	0.816287i	−0.0191131	+	0.0331048i
$609$	−3.97324	+	0.942675i	−0.161004	+	0.0381991i
$610$	−5.30940	−	9.19614i	−0.214971	−	0.372341i
$611$	−0.926781	+	0.535077i	−0.0374935	+	0.0216469i
$612$	−93.4362	+	7.23971i	−3.77693	+	0.292648i
$613$	−22.1377	+	38.3437i	−0.894134	+	1.54869i	−0.0592614	+	0.998242i	$0.518875\pi$
$613$	−22.1377	+	38.3437i	−0.894134	+	1.54869i	−0.834873	+	0.550443i	$0.814459\pi$
$614$	−15.8417	+	27.4387i	−0.639321	+	1.10734i
$615$	2.88572	−	5.47681i	0.116364	−	0.220846i
$616$	−52.9640	−	18.1009i	−2.13398	−	0.729307i
$617$	−5.53420	−	3.19517i	−0.222798	−	0.128633i	0.384447	−	0.923147i	$-0.374392\pi$
$617$	−5.53420	−	3.19517i	−0.222798	−	0.128633i	−0.607245	+	0.794514i	$0.707726\pi$
$618$	26.2494	−	49.8187i	1.05591	−	2.00400i
$619$			16.7760i			0.674285i	0.941454	+	0.337143i	$0.109460\pi$
$619$			16.7760i			0.674285i	−0.941454	+	0.337143i	$0.890540\pi$
$620$	−24.3695	−	14.0698i	−0.978705	−	0.565055i
$621$	−1.36429	−	11.7090i	−0.0547470	−	0.469868i
$622$		−	27.6924i		−	1.11036i
$623$	−1.72670	−	8.77537i	−0.0691787	−	0.351578i
$624$	10.0640	−	6.34139i	0.402882	−	0.253859i
$625$	1.00000			0.0400000
$626$	−6.20035	−	10.7393i	−0.247816	−	0.429230i
$627$	15.6046	+	24.7650i	0.623188	+	0.989019i
$628$	−82.6524	−	47.7194i	−3.29819	−	1.90421i
$629$	−40.7083			−1.62315
$630$	13.8528	+	13.5836i	0.551911	+	0.541183i
$631$	−12.0000			−0.477713			−0.238857	−	0.971055i	$-0.576773\pi$
$631$	−12.0000			−0.477713			−0.238857	+	0.971055i	$0.576773\pi$
$632$	−28.7400	−	16.5931i	−1.14322	−	0.660037i
$633$	12.5872	−	23.8893i	0.500298	−	0.949514i
$634$	−12.1882	−	21.1105i	−0.484054	−	0.838406i
$635$	−3.16484			−0.125593
$636$	−3.65984	−	94.6098i	−0.145122	−	3.75152i
$637$	−4.73119	−	11.5569i	−0.187456	−	0.457900i
$638$		−	9.54583i		−	0.377923i
$639$	0.0797205	+	1.02888i	0.00315369	+	0.0407017i
$640$	−17.1400	−	9.89576i	−0.677517	−	0.391164i
$641$		−	1.92735i		−	0.0761256i	−0.999275	−	0.0380628i	$-0.987881\pi$
$641$		−	1.92735i		−	0.0761256i	0.999275	−	0.0380628i	$-0.0121187\pi$
$642$	−82.2278	+	3.18086i	−3.24527	+	0.125539i
$643$	−0.105313	−	0.0608025i	−0.00415314	−	0.00239782i	0.497922	−	0.867222i	$-0.334097\pi$
$643$	−0.105313	−	0.0608025i	−0.00415314	−	0.00239782i	−0.502075	+	0.864824i	$0.667430\pi$
$644$	−23.4093	+	4.60616i	−0.922455	+	0.181508i
$645$	−4.96316	−	7.87669i	−0.195424	−	0.310145i
$646$	37.0395	−	64.1542i	1.45730	−	2.52411i
$647$	−18.1842	+	31.4959i	−0.714894	+	1.23823i	0.248107	+	0.968733i	$0.420192\pi$
$647$	−18.1842	+	31.4959i	−0.714894	+	1.23823i	−0.963000	+	0.269500i	$0.913142\pi$
$648$	6.69229	+	42.9263i	0.262898	+	1.68630i
$649$	−33.8871	+	19.5647i	−1.33018	+	0.767982i
$650$	−2.18033	−	3.77644i	−0.0855194	−	0.148124i
$651$	−31.5657	+	7.48914i	−1.23716	+	0.293523i
$652$	−24.2724	+	42.0411i	−0.950581	+	1.64645i
$653$			37.1210i			1.45266i	0.687348	+	0.726328i	$0.258775\pi$
$653$			37.1210i			1.45266i	−0.687348	+	0.726328i	$0.741225\pi$
$654$	32.3275	−	20.3698i	1.26410	−	0.796521i
$655$	5.88263			0.229853
$656$	−6.87960	−	11.9158i	−0.268603	−	0.465235i
$657$	−10.5909	−	5.06736i	−0.413190	−	0.197696i
$658$	−3.80646	+	0.748985i	−0.148391	+	0.0291985i
$659$	−34.3197	+	19.8145i	−1.33691	+	0.771863i	−0.986347	−	0.164677i	$-0.947342\pi$
$659$	−34.3197	+	19.8145i	−1.33691	+	0.771863i	−0.350559	+	0.936541i	$0.614008\pi$
$660$	−25.5271	+	16.0848i	−0.993639	+	0.626099i
$661$	−16.1215	+	9.30777i	−0.627055	+	0.362030i	−0.779611	−	0.626264i	$-0.784583\pi$
$661$	−16.1215	+	9.30777i	−0.627055	+	0.362030i	0.152556	+	0.988295i	$0.451250\pi$
$662$	52.9632	−	30.5783i	2.05847	−	1.18846i
$663$	20.5456	−	12.9459i	0.797925	−	0.502778i
$664$	−25.8745	+	14.9386i	−1.00412	+	0.579731i
$665$	−10.0106	+	1.96974i	−0.388193	+	0.0763833i
$666$	2.93427	+	37.8699i	0.113701	+	1.46743i
$667$	−1.01080	−	1.75075i	−0.0391383	−	0.0677895i
$668$	64.8942			2.51083
$669$	4.94221	−	3.11412i	0.191077	−	0.120399i
$670$		−	15.8569i		−	0.612606i
$671$	9.51931	−	16.4879i	0.367489	−	0.636510i
$672$	−1.08986	+	0.258577i	−0.0420424	+	0.00997482i
$673$	17.5049	+	30.3194i	0.674765	+	1.16873i	0.976538	+	0.215347i	$0.0690883\pi$
$673$	17.5049	+	30.3194i	0.674765	+	1.16873i	−0.301773	+	0.953380i	$0.597578\pi$
$674$	−37.8814	+	21.8708i	−1.45914	+	0.842433i
$675$	5.16124	−	0.601365i	0.198656	−	0.0231466i
$676$	19.5114	−	33.7947i	0.750438	−	1.29980i
$677$	21.1000	−	36.5463i	0.810940	−	1.40459i	−0.101267	−	0.994859i	$-0.532290\pi$
$677$	21.1000	−	36.5463i	0.810940	−	1.40459i	0.912207	−	0.409730i	$-0.134377\pi$
$678$	29.7190	+	47.1651i	1.14135	+	1.81136i
$679$	−30.9045	+	6.08097i	−1.18600	+	0.233366i
$680$	32.8549	+	18.9688i	1.25993	+	0.727419i
$681$	33.5223	−	1.29676i	1.28458	−	0.0496920i
$682$		−	75.8375i		−	2.90397i
$683$	7.07680	+	4.08579i	0.270786	+	0.156339i	0.629245	−	0.777207i	$-0.283364\pi$
$683$	7.07680	+	4.08579i	0.270786	+	0.156339i	−0.358459	+	0.933546i	$0.616698\pi$
$684$	−41.4797	−	19.8465i	−1.58602	−	0.758851i
$685$			0.497828i			0.0190210i
$686$	−2.68089	−	45.1905i	−0.102357	−	1.72538i
$687$	−0.701111	−	18.1243i	−0.0267491	−	0.691484i
$688$	−20.6925			−0.788893
$689$	12.2670	+	21.2471i	0.467336	+	0.809449i
$690$	−4.47732	+	8.49748i	−0.170449	+	0.323494i
$691$	−32.7072	−	18.8835i	−1.24424	−	0.718364i	−0.274287	−	0.961648i	$-0.588442\pi$
$691$	−32.7072	−	18.8835i	−1.24424	−	0.718364i	−0.969955	+	0.243284i	$0.921775\pi$
$692$	17.8856			0.679910
$693$	−8.67290	+	33.6866i	−0.329456	+	1.27965i
$694$	64.8977			2.46348
$695$	−9.77690	−	5.64470i	−0.370859	−	0.214116i
$696$	3.97186	+	6.30347i	0.150553	+	0.238932i
$697$	−14.0447	−	24.3261i	−0.531980	−	0.921416i
$698$	28.1885			1.06695
$699$	−18.5535	+	11.6907i	−0.701758	+	0.442182i
$700$	−2.03035	−	10.3186i	−0.0767401	−	0.390006i
$701$			35.4760i			1.33991i	0.742402	+	0.669954i	$0.233686\pi$
$701$			35.4760i			1.33991i	−0.742402	+	0.669954i	$0.766314\pi$
$702$	−13.5242	−	18.1799i	−0.510438	−	0.686156i
$703$	−17.2981	−	9.98705i	−0.652410	−	0.376669i
$704$		−	36.3611i		−	1.37041i
$705$	−0.484334	+	0.919216i	−0.0182411	+	0.0346197i
$706$	−56.4354	−	32.5830i	−2.12397	−	1.22628i
$707$	42.1968	+	14.4211i	1.58698	+	0.542363i
$708$	28.6541	−	54.3825i	1.07689	−	2.04382i
$709$	−0.191901	+	0.332383i	−0.00720701	+	0.0124829i	−0.869606	−	0.493746i	$-0.835627\pi$
$709$	−0.191901	+	0.332383i	−0.00720701	+	0.0124829i	0.862399	+	0.506228i	$0.168961\pi$
$710$	0.420412	−	0.728175i	0.0157778	−	0.0273279i
$711$	−8.90159	+	18.6045i	−0.333836	+	0.697725i
$712$	−14.1316	+	8.15888i	−0.529604	+	0.305767i
$713$	−8.03036	−	13.9090i	−0.300739	−	0.520896i
$714$	85.6554	−	20.3223i	3.20557	−	0.760541i
$715$	3.90915	−	6.77084i	0.146194	−	0.253215i
$716$		−	33.9866i		−	1.27014i
$717$	30.0465	+	15.8314i	1.12211	+	0.591236i
$718$	50.3229			1.87803
$719$	20.4550	+	35.4291i	0.762842	+	1.32128i	0.941380	+	0.337349i	$0.109530\pi$
$719$	20.4550	+	35.4291i	0.762842	+	1.32128i	−0.178537	+	0.983933i	$0.557137\pi$
$720$	4.98462	−	10.4180i	0.185766	−	0.388255i
$721$	−11.3802	+	33.2990i	−0.423822	+	1.24012i
$722$	−8.74233	+	5.04739i	−0.325356	+	0.187844i
$723$	−0.117737	−	3.04360i	−0.00437869	−	0.113193i
$724$	3.00472	−	1.73478i	0.111670	−	0.0644725i
$725$	0.771716	−	0.445550i	0.0286608	−	0.0165473i
$726$	−30.7382	−	16.1959i	−1.14080	−	0.601087i
$727$	−0.765637	+	0.442041i	−0.0283959	+	0.0163944i	−0.514131	−	0.857712i	$-0.671885\pi$
$727$	−0.765637	+	0.442041i	−0.0283959	+	0.0163944i	0.485735	+	0.874106i	$0.338552\pi$
$728$	−17.1610	+	14.9872i	−0.636030	+	0.555464i
$729$	26.2767	−	6.20758i	0.973212	−	0.229910i
$730$	4.78308	+	8.28454i	0.177030	+	0.306625i
$731$	−42.2436			−1.56243
$732$	1.15610	+	29.8860i	0.0427305	+	1.10462i
$733$		−	41.5621i		−	1.53513i	−0.640970	−	0.767566i	$-0.721468\pi$
$733$		−	41.5621i		−	1.53513i	0.640970	−	0.767566i	$-0.278532\pi$
$734$	−22.0508	+	38.1931i	−0.813909	+	1.40973i
$735$	−9.86800	−	7.04432i	−0.363987	−	0.259834i
$736$	−0.277263	−	0.480234i	−0.0102201	−	0.0177017i
$737$	24.6212	−	14.2151i	0.906934	−	0.523619i
$738$	−21.6176	+	14.8188i	−0.795755	+	0.545489i
$739$	−7.43979	+	12.8861i	−0.273677	+	0.474023i	−0.969800	−	0.243900i	$-0.921573\pi$
$739$	−7.43979	+	12.8861i	−0.273677	+	0.474023i	0.696123	+	0.717922i	$0.254907\pi$
$740$	10.2944	−	17.8304i	0.378428	−	0.655457i
$741$	11.9064	−	0.460583i	0.437394	−	0.0169199i
$742$	17.1710	+	87.2658i	0.630367	+	3.20363i
$743$	2.00964	+	1.16027i	0.0737265	+	0.0425660i	0.536410	−	0.843957i	$-0.319780\pi$
$743$	2.00964	+	1.16027i	0.0737265	+	0.0425660i	−0.462684	+	0.886523i	$0.653113\pi$
$744$	31.5547	+	50.0783i	1.15685	+	1.83596i
$745$			11.2635i			0.412663i
$746$	−20.2088	−	11.6675i	−0.739896	−	0.427179i
$747$	10.4985	+	15.3151i	0.384121	+	0.560352i
$748$			136.904i			5.00572i
$749$	50.4568	−	9.92821i	1.84365	−	0.362769i
$750$	−3.74561	−	1.97356i	−0.136770	−	0.0720642i
$751$	32.8916			1.20023			0.600116	−	0.799913i	$-0.295121\pi$
$751$	32.8916			1.20023			0.600116	+	0.799913i	$0.295121\pi$
$752$	1.15466	+	1.99993i	0.0421061	+	0.0729298i
$753$	12.4894	−	0.483135i	0.455140	−	0.0176064i
$754$	−3.36518	−	1.94289i	−0.122553	−	0.0707559i
$755$	2.33427			0.0849527
$756$	−16.6844	−	52.0357i	−0.606805	−	1.89252i
$757$	−18.8340			−0.684535			−0.342268	−	0.939603i	$-0.611195\pi$
$757$	−18.8340			−0.684535			−0.342268	+	0.939603i	$0.611195\pi$
$758$	1.91673	+	1.10663i	0.0696188	+	0.0401944i
$759$	−17.2079	+	0.665661i	−0.624607	+	0.0241620i
$760$	9.30729	+	16.1207i	0.337611	+	0.584760i
$761$	−9.50593			−0.344590			−0.172295	−	0.985045i	$-0.555118\pi$
$761$	−9.50593			−0.344590			−0.172295	+	0.985045i	$0.555118\pi$
$762$	11.8543	+	6.24600i	0.429435	+	0.226269i
$763$	−17.9850	+	15.7069i	−0.651101	+	0.568626i
$764$		−	61.7150i		−	2.23277i
$765$	10.1761	−	21.2683i	0.367917	−	0.768955i
$766$	−12.9928	−	7.50142i	−0.469450	−	0.271037i
$767$			15.9282i			0.575136i
$768$	29.3478	+	46.5759i	1.05900	+	1.68066i
$769$	−14.2817	−	8.24557i	−0.515013	−	0.297343i	0.219879	−	0.975527i	$-0.429434\pi$
$769$	−14.2817	−	8.24557i	−0.515013	−	0.297343i	−0.734892	+	0.678184i	$0.762767\pi$
$770$	21.3475	−	18.6434i	0.769309	−	0.671860i
$771$	−23.4248	+	0.906154i	−0.843623	+	0.0326343i
$772$	−20.8957	+	36.1924i	−0.752051	+	1.30259i
$773$	19.5007	−	33.7762i	0.701392	−	1.21485i	−0.266585	−	0.963811i	$-0.585895\pi$
$773$	19.5007	−	33.7762i	0.701392	−	1.21485i	0.967978	−	0.251036i	$-0.0807712\pi$
$774$	3.04493	+	39.2981i	0.109448	+	1.41254i
$775$	6.13095	−	3.53970i	0.220230	−	0.127150i
$776$	28.7334	+	49.7677i	1.03147	+	1.78655i
$777$	−5.47955	−	23.0955i	−0.196578	−	0.828547i
$778$	−10.2260	+	17.7120i	−0.366620	+	0.635005i
$779$		−	13.7824i		−	0.493807i
$780$	0.474756	+	12.2728i	0.0169990	+	0.439437i
$781$	1.50753			0.0539436
$782$	21.7909	+	37.7429i	0.779240	+	1.34968i
$783$	3.71507	−	2.76367i	0.132766	−	0.0987657i
$784$	−24.9389	+	10.2096i	−0.890675	+	0.364627i
$785$	20.7939	−	12.0054i	0.742166	−	0.428490i
$786$	−22.0340	−	11.6097i	−0.785928	−	0.414104i
$787$	32.8889	−	18.9884i	1.17236	−	0.676864i	0.218128	−	0.975920i	$-0.430005\pi$
$787$	32.8889	−	18.9884i	1.17236	−	0.676864i	0.954236	+	0.299056i	$0.0966717\pi$
$788$	−21.2847	+	12.2887i	−0.758236	+	0.437767i
$789$	0.292718	+	7.56701i	0.0104211	+	0.269393i
$790$	14.5531	−	8.40222i	0.517775	−	0.298938i
$791$	−22.9160	−	26.2397i	−0.814798	−	0.932978i
$792$	63.2763	−	4.90283i	2.24842	−	0.174215i
$793$	−3.87499	−	6.71167i	−0.137605	−	0.238338i
$794$	−48.2816			−1.71345
$795$	21.0737	+	11.1037i	0.747405	+	0.393807i
$796$			52.8210i			1.87219i
$797$	−18.9269	+	32.7823i	−0.670425	+	1.16121i	0.307359	+	0.951594i	$0.400555\pi$
$797$	−18.9269	+	32.7823i	−0.670425	+	1.16121i	−0.977784	+	0.209616i	$0.932779\pi$
$798$	41.3830	+	12.3785i	1.46494	+	0.438195i
$799$	2.35723	+	4.08284i	0.0833927	+	0.144440i
$800$	0.211683	−	0.122215i	0.00748411	−	0.00432095i
$801$	5.73387	+	8.36452i	0.202596	+	0.295546i
$802$	18.8744	−	32.6914i	0.666477	−	1.15437i
$803$	−8.57567	+	14.8535i	−0.302629	+	0.524169i
$804$	−20.8191	+	39.5125i	−0.734233	+	1.39350i
$805$	1.94111	−	5.67975i	0.0684150	−	0.200185i
$806$	−26.7349	−	15.4354i	−0.941698	−	0.543689i
$807$	16.9923	−	32.2496i	0.598157	−	1.13524i
$808$		−	81.3606i		−	2.86225i
$809$	45.8364	+	26.4637i	1.61152	+	0.930413i	0.989018	+	0.147798i	$0.0472185\pi$
$809$	45.8364	+	26.4637i	1.61152	+	0.930413i	0.622506	+	0.782615i	$0.286115\pi$
$810$	−20.5188	−	7.93352i	−0.720957	−	0.278755i
$811$			16.7360i			0.587682i	0.955854	+	0.293841i	$0.0949335\pi$
$811$			16.7360i			0.587682i	−0.955854	+	0.293841i	$0.905066\pi$
$812$	−6.16431	−	7.05840i	−0.216325	−	0.247701i
$813$	4.84723	−	3.05427i	0.170000	−	0.107118i
$814$	55.4877			1.94484
$815$	−6.10651	−	10.5768i	−0.213902	−	0.370489i
$816$	−27.9364	−	44.3360i	−0.977969	−	1.55207i
$817$	−17.9504	−	10.3637i	−0.628007	−	0.362580i
$818$	−11.5814			−0.404933
$819$	10.1103	+	9.91378i	0.353282	+	0.346416i
$820$	14.2065			0.496114
$821$	−11.0487	−	6.37895i	−0.385601	−	0.222627i	0.294651	−	0.955605i	$-0.404797\pi$
$821$	−11.0487	−	6.37895i	−0.385601	−	0.222627i	−0.680252	+	0.732978i	$0.738130\pi$
$822$	0.982493	−	1.86467i	0.0342684	−	0.0650378i
$823$	18.1983	+	31.5204i	0.634353	+	1.09873i	0.986652	+	0.162844i	$0.0520668\pi$
$823$	18.1983	+	31.5204i	0.634353	+	1.09873i	−0.352299	+	0.935888i	$0.614600\pi$
$824$	64.2045			2.23667
$825$	−0.293417	−	7.58507i	−0.0102155	−	0.264078i
$826$	−18.6734	+	54.6392i	−0.649732	+	1.90114i
$827$		−	14.5352i		−	0.505439i	−0.967540	−	0.252720i	$-0.918675\pi$
$827$		−	14.5352i		−	0.505439i	0.967540	−	0.252720i	$-0.0813250\pi$
$828$	22.3133	−	15.2957i	0.775441	−	0.531564i
$829$	2.33693	+	1.34923i	0.0811651	+	0.0468607i	0.540033	−	0.841644i	$-0.318412\pi$
$829$	2.33693	+	1.34923i	0.0811651	+	0.0468607i	−0.458868	+	0.888504i	$0.651745\pi$
$830$		−	15.1289i		−	0.525133i
$831$	−44.2545	+	1.71192i	−1.53517	+	0.0593858i
$832$	−12.8183	−	7.40067i	−0.444396	−	0.256572i
$833$	−50.9126	+	20.8428i	−1.76402	+	0.722159i
$834$	25.4803	+	40.4381i	0.882311	+	1.40026i
$835$	−8.16312	+	14.1389i	−0.282496	+	0.489298i
$836$	−33.5870	+	58.1744i	−1.16163	+	2.01200i
$837$	29.5146	−	21.9562i	1.02017	−	0.758917i
$838$	0.508902	−	0.293815i	0.0175797	−	0.0101497i
$839$	10.6019	+	18.3631i	0.366019	+	0.633964i	0.988939	−	0.148322i	$-0.0473871\pi$
$839$	10.6019	+	18.3631i	0.366019	+	0.633964i	−0.622920	+	0.782286i	$0.714054\pi$
$840$	−6.33933	+	21.1932i	−0.218728	+	0.731236i
$841$	−14.1030	+	24.4271i	−0.486309	+	0.842312i
$842$			30.4641i			1.04986i
$843$	9.56257	−	6.02544i	0.329352	−	0.207527i
$844$	61.9675			2.13301
$845$	4.90872	+	8.50215i	0.168865	+	0.292483i
$846$	3.62825	−	2.48716i	0.124742	−	0.0855104i
$847$	20.5455	+	7.02162i	0.705953	+	0.241266i
$848$	45.8497	−	26.4713i	1.57449	−	0.909029i
$849$	−6.87709	+	4.33330i	−0.236021	+	0.148718i
$850$	−16.6367	+	9.60521i	−0.570634	+	0.329456i
$851$	10.1767	−	5.87553i	0.348854	−	0.201411i
$852$	−2.00364	+	1.26250i	−0.0686435	+	0.0432527i
$853$	4.49048	−	2.59258i	0.153751	−	0.0887682i	−0.421151	−	0.906991i	$-0.638374\pi$
$853$	4.49048	−	2.59258i	0.153751	−	0.0887682i	0.574902	+	0.818222i	$0.305040\pi$
$854$	−5.42409	−	27.5661i	−0.185608	−	0.943293i
$855$	9.54188	−	6.54095i	0.326325	−	0.223696i
$856$	−46.9121	−	81.2542i	−1.60342	−	2.77721i
$857$	−50.7818			−1.73467			−0.867337	−	0.497722i	$-0.834170\pi$
$857$	−50.7818			−1.73467			−0.867337	+	0.497722i	$0.834170\pi$
$858$	−28.0048	+	17.6460i	−0.956068	+	0.602424i
$859$		−	35.1165i		−	1.19816i	−0.800689	−	0.599080i	$-0.795533\pi$
$859$		−	35.1165i		−	1.19816i	0.800689	−	0.599080i	$-0.204467\pi$
$860$	10.6826	−	18.5028i	0.364273	−	0.630940i
$861$	11.9107	−	11.2425i	0.405916	−	0.383145i
$862$	−2.42658	−	4.20296i	−0.0826497	−	0.143153i
$863$	45.8409	−	26.4663i	1.56044	−	0.900922i	0.563230	−	0.826300i	$-0.309558\pi$
$863$	45.8409	−	26.4663i	1.56044	−	0.900922i	0.997212	−	0.0746216i	$-0.0237749\pi$
$864$	1.01905	−	0.758079i	0.0346687	−	0.0257904i
$865$	−2.24985	+	3.89686i	−0.0764973	+	0.132497i
$866$	38.8492	−	67.2888i	1.32015	−	2.28657i
$867$	−41.3348	−	65.5998i	−1.40380	−	2.22788i
$868$	−48.9727	−	56.0759i	−1.66224	−	1.90334i
$869$	26.0925	+	15.0645i	0.885127	+	0.511028i
$870$	−3.76987	+	0.145832i	−0.127810	+	0.00494416i
$871$		−	11.5729i		−	0.392134i
$872$	37.7292	+	21.7830i	1.27767	+	0.737665i
$873$	29.4576	−	20.1931i	0.996988	−	0.683434i
$874$			21.3840i			0.723324i
$875$	2.50358	+	0.855621i	0.0846365	+	0.0289253i
$876$	−1.04149	−	26.9234i	−0.0351888	−	0.909658i
$877$	−19.3060			−0.651918			−0.325959	−	0.945384i	$-0.605687\pi$
$877$	−19.3060			−0.651918			−0.325959	+	0.945384i	$0.605687\pi$
$878$	9.00636	+	15.5995i	0.303950	+	0.526457i
$879$	8.51216	−	16.1552i	0.287108	−	0.544901i
$880$	−14.6110	−	8.43566i	−0.492536	−	0.284366i
$881$	0.474565			0.0159885			0.00799424	−	0.999968i	$-0.497455\pi$
$881$	0.474565			0.0159885			0.00799424	+	0.999968i	$0.497455\pi$
$882$	23.0593	+	45.8604i	0.776447	+	1.54420i
$883$	−43.6911			−1.47032			−0.735162	−	0.677892i	$-0.762894\pi$
$883$	−43.6911			−1.47032			−0.735162	+	0.677892i	$0.762894\pi$
$884$	48.2628	+	27.8645i	1.62325	+	0.937186i
$885$	8.24424	+	13.0839i	0.277127	+	0.439810i
$886$	50.2833	+	87.0933i	1.68930	+	2.92596i
$887$	−27.8601			−0.935452			−0.467726	−	0.883874i	$-0.654927\pi$
$887$	−27.8601			−0.935452			−0.467726	+	0.883874i	$0.654927\pi$
$888$	−36.6406	+	23.0875i	−1.22958	+	0.774765i
$889$	−7.92344	−	2.70791i	−0.265744	−	0.0908202i
$890$		−	8.26282i		−	0.276970i
$891$	−6.07579	−	38.9719i	−0.203547	−	1.30561i
$892$	11.6095	+	6.70276i	0.388716	+	0.224425i
$893$			2.31321i			0.0774088i
$894$	22.2292	−	42.1887i	0.743455	−	1.41100i
$895$	7.40489	+	4.27521i	0.247518	+	0.142905i
$896$	−34.4443	−	39.4401i	−1.15070	−	1.31760i
$897$	−3.26770	+	6.20177i	−0.109105	+	0.207071i
$898$	−31.7971	+	55.0743i	−1.06108	+	1.83785i
$899$	3.15423	−	5.46329i	0.105200	−	0.182211i
$900$	6.74222	+	9.83549i	0.224741	+	0.327850i
$901$	93.6019	−	54.0411i	3.11833	−	1.80037i
$902$	19.1437	+	33.1578i	0.637414	+	1.10403i
$903$	−5.68620	−	23.9665i	−0.189225	−	0.797556i
$904$	−31.7809	+	55.0461i	−1.05702	+	1.83081i
$905$			0.872879i			0.0290155i
$906$	−8.74326	−	4.60681i	−0.290475	−	0.153051i
$907$	−4.26124			−0.141492			−0.0707461	−	0.997494i	$-0.522538\pi$
$907$	−4.26124			−0.141492			−0.0707461	+	0.997494i	$0.522538\pi$
$908$	38.4935	+	66.6727i	1.27745	+	2.21261i
$909$	−50.4127	+	3.90613i	−1.67208	+	0.129558i
$910$	−2.22742	−	11.3201i	−0.0738384	−	0.375259i
$911$	3.52078	−	2.03273i	0.116649	−	0.0673472i	−0.440540	−	0.897733i	$-0.645213\pi$
$911$	3.52078	−	2.03273i	0.116649	−	0.0673472i	0.557189	+	0.830386i	$0.311880\pi$
$912$	−0.993906	−	25.6933i	−0.0329115	−	0.850789i
$913$	23.4909	−	13.5625i	0.777435	−	0.448852i
$914$	65.0149	−	37.5364i	2.15050	−	1.24159i
$915$	−6.65689	−	3.50751i	−0.220070	−	0.115955i
$916$	36.0475	−	20.8120i	1.19104	−	0.687649i
$917$	14.7276	+	5.03330i	0.486349	+	0.166214i
$918$	−80.0898	+	59.5795i	−2.64336	+	1.96642i
$919$	11.2988	+	19.5700i	0.372712	+	0.645556i	0.989982	−	0.141196i	$-0.0450947\pi$
$919$	11.2988	+	19.5700i	0.372712	+	0.645556i	−0.617270	+	0.786751i	$0.711761\pi$
$920$	−10.9512			−0.361052
$921$	0.867824	+	22.4339i	0.0285958	+	0.739223i
$922$			77.1310i			2.54018i
$923$	0.306832	−	0.531448i	0.0100995	−	0.0174928i
$924$	−77.6715	+	18.4280i	−2.55520	+	0.606237i
$925$	2.58988	+	4.48580i	0.0851547	+	0.147492i
$926$	−51.8568	+	29.9395i	−1.70412	+	0.983874i
$927$	−3.08246	−	39.7824i	−0.101241	−	1.30663i
$928$	0.108906	−	0.188631i	0.00357501	−	0.00619210i
$929$	−2.45508	+	4.25233i	−0.0805486	+	0.139514i	−0.903486	−	0.428618i	$-0.859001\pi$
$929$	−2.45508	+	4.25233i	−0.0805486	+	0.139514i	0.822937	+	0.568132i	$0.192334\pi$
$930$	−29.9500	+	1.15857i	−0.982098	+	0.0379910i
$931$	−26.7476	−	3.63383i	−0.876617	−	0.119094i
$932$	−43.5832	−	25.1628i	−1.42762	−	0.824234i
$933$	−10.4609	−	16.6018i	−0.342474	−	0.543518i
$934$		−	6.53140i		−	0.213714i
$935$	−29.8283	−	17.2214i	−0.975488	−	0.563198i
$936$	11.1504	−	23.3046i	0.364462	−	0.761735i
$937$			53.9957i			1.76396i	0.471284	+	0.881982i	$0.343791\pi$
$937$			53.9957i			1.76396i	−0.471284	+	0.881982i	$0.656209\pi$
$938$	13.5675	−	39.6990i	0.442994	−	1.29622i
$939$	−7.77396	−	4.09609i	−0.253694	−	0.133671i
$940$	−2.38439			−0.0777703
$941$	3.63741	+	6.30018i	0.118576	+	0.205380i	0.919204	−	0.393783i	$-0.128834\pi$
$941$	3.63741	+	6.30018i	0.118576	+	0.205380i	−0.800627	+	0.599162i	$0.795500\pi$
$942$	−101.579	+	3.92944i	−3.30962	+	0.128028i
$943$	7.02209	+	4.05421i	0.228671	+	0.132023i
$944$	34.3720			1.11871
$945$	13.4361	+	2.91049i	0.437077	+	0.0946784i
$946$	57.5803			1.87210
$947$	−21.1860	−	12.2317i	−0.688453	−	0.397478i	0.114579	−	0.993414i	$-0.463448\pi$
$947$	−21.1860	−	12.2317i	−0.688453	−	0.397478i	−0.803032	+	0.595936i	$0.796781\pi$
$948$	−47.2952	+	1.82954i	−1.53608	+	0.0594208i
$949$	3.49086	+	6.04635i	0.113318	+	0.196273i
$950$	−9.42586			−0.305815
$951$	−15.2814	−	8.05178i	−0.495535	−	0.261097i
$952$	66.0247	+	75.6012i	2.13987	+	2.45025i
$953$			24.1698i			0.782938i	0.920191	+	0.391469i	$0.128033\pi$
$953$			24.1698i			0.782938i	−0.920191	+	0.391469i	$0.871967\pi$
$954$	−57.0199	−	83.1802i	−1.84609	−	2.69306i
$955$	13.4463	+	7.76320i	0.435111	+	0.251211i
$956$			77.9388i			2.52072i
$957$	−3.60597	−	5.72279i	−0.116564	−	0.184991i
$958$	−7.56075	−	4.36520i	−0.244277	−	0.141033i
$959$	−0.425952	+	1.24635i	−0.0137547	+	0.0402468i
$960$	−14.3598	+	0.555488i	−0.463461	+	0.0179283i
$961$	9.55901	−	16.5567i	0.308355	−	0.534087i
$962$	11.2936	−	19.5610i	0.364119	−	0.630673i
$963$	−48.0945	+	32.9687i	−1.54982	+	1.06240i
$964$	6.05343	−	3.49495i	0.194968	−	0.112565i
$965$	−5.25698	−	9.10536i	−0.169228	−	0.293112i
$966$	−18.4799	+	17.4432i	−0.594582	+	0.561227i
$967$	−1.86561	+	3.23133i	−0.0599939	+	0.103913i	−0.894462	−	0.447143i	$-0.852441\pi$
$967$	−1.86561	+	3.23133i	−0.0599939	+	0.103913i	0.834469	+	0.551056i	$0.185775\pi$
$968$		−	39.6143i		−	1.27325i
$969$	−2.02905	−	52.4526i	−0.0651826	−	1.68502i
$970$	−29.0994			−0.934326
$971$	20.5327	+	35.5637i	0.658926	+	1.14129i	0.980894	+	0.194543i	$0.0623224\pi$
$971$	20.5327	+	35.5637i	0.658926	+	1.14129i	−0.321968	+	0.946751i	$0.604344\pi$
$972$	40.7129	+	46.7087i	1.30587	+	1.49818i
$973$	−19.6475	−	22.4973i	−0.629871	−	0.721229i
$974$	−34.6186	+	19.9871i	−1.10925	+	0.640426i
$975$	−2.73368	−	1.44037i	−0.0875478	−	0.0461288i
$976$	−14.4833	+	8.36194i	−0.463600	+	0.267659i
$977$	−41.6944	+	24.0723i	−1.33392	+	0.770141i	−0.985899	−	0.167344i	$-0.946481\pi$
$977$	−41.6944	+	24.0723i	−1.33392	+	0.770141i	−0.348025	+	0.937485i	$0.613148\pi$
$978$	1.99870	+	51.6681i	0.0639115	+	1.65216i
$979$	12.8298	−	7.40728i	0.410042	−	0.236738i
$980$	3.74565	−	27.5706i	0.119650	−	0.880711i
$981$	11.6858	−	24.4236i	0.373099	−	0.779786i
$982$	−51.2615	−	88.7875i	−1.63582	−	2.83332i
$983$	−5.64986			−0.180203			−0.0901013	−	0.995933i	$-0.528719\pi$
$983$	−5.64986			−0.180203			−0.0901013	+	0.995933i	$0.528719\pi$
$984$	−26.4377	−	13.9300i	−0.842802	−	0.444072i
$985$		−	6.18325i		−	0.197015i
$986$	−8.55921	+	14.8250i	−0.272581	+	0.472124i
$987$	−1.99907	+	1.88692i	−0.0636310	+	0.0600615i
$988$	13.6721	+	23.6808i	0.434968	+	0.753387i
$989$	10.5605	−	6.09712i	0.335805	−	0.193877i
$990$	−13.8706	+	28.9898i	−0.440835	+	0.921356i
$991$	−12.8768	+	22.3033i	−0.409046	+	0.708489i	−0.994783	−	0.102013i	$-0.967472\pi$
$991$	−12.8768	+	22.3033i	−0.409046	+	0.708489i	0.585737	+	0.810501i	$0.300805\pi$
$992$	0.865210	−	1.49859i	0.0274704	−	0.0475802i
$993$	20.2007	−	38.3389i	0.641051	−	1.21665i
$994$	1.67558	−	1.46333i	0.0531461	−	0.0464141i
$995$	−11.5085	−	6.64441i	−0.364843	−	0.210642i
$996$	−19.8633	+	37.6985i	−0.629393	+	1.19452i
$997$		−	29.7079i		−	0.940860i	−0.882437	−	0.470430i	$-0.844099\pi$
$997$		−	29.7079i		−	0.940860i	0.882437	−	0.470430i	$-0.155901\pi$
$998$	−65.7972	−	37.9880i	−2.08277	−	1.20249i
$999$	16.0646	+	21.5948i	0.508261	+	0.683230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.311.15	yes	32
3.2	odd	2		945.2.be.c.206.2		32
7.5	odd	6		315.2.t.c.131.2	yes	32
9.2	odd	6		315.2.t.c.101.15	✓	32
9.7	even	3		945.2.t.c.521.2		32
21.5	even	6		945.2.t.c.341.15		32
63.47	even	6	inner	315.2.be.c.236.15	yes	32
63.61	odd	6		945.2.be.c.656.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.15	✓	32	9.2	odd	6
315.2.t.c.131.2	yes	32	7.5	odd	6
315.2.be.c.236.15	yes	32	63.47	even	6	inner
315.2.be.c.311.15	yes	32	1.1	even	1	trivial
945.2.t.c.341.15		32	21.5	even	6
945.2.t.c.521.2		32	9.7	even	3
945.2.be.c.206.2		32	3.2	odd	2
945.2.be.c.656.2		32	63.61	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11687 + 1.22217i) q^{2} +(1.73076 - 0.0669518i) q^{3} +(1.98742 + 3.44231i) q^{4} -1.00000 q^{5} +(3.74561 + 1.97356i) q^{6} +(-2.50358 - 0.855621i) q^{7} +4.82720i q^{8} +(2.99103 - 0.231754i) q^{9} +O(q^{10})\)	\(q+(2.11687 + 1.22217i) q^{2} +(1.73076 - 0.0669518i) q^{3} +(1.98742 + 3.44231i) q^{4} -1.00000 q^{5} +(3.74561 + 1.97356i) q^{6} +(-2.50358 - 0.855621i) q^{7} +4.82720i q^{8} +(2.99103 - 0.231754i) q^{9} +(-2.11687 - 1.22217i) q^{10} -4.38252i q^{11} +(3.67021 + 5.82475i) q^{12} +(-1.54497 - 0.891986i) q^{13} +(-4.25403 - 4.87105i) q^{14} +(-1.73076 + 0.0669518i) q^{15} +(-1.92484 + 3.33393i) q^{16} +(-3.92956 + 6.80619i) q^{17} +(6.61487 + 3.16497i) q^{18} +(-3.33955 + 1.92809i) q^{19} +(-1.98742 - 3.44231i) q^{20} +(-4.39037 - 1.31325i) q^{21} +(5.35620 - 9.27721i) q^{22} -2.26865i q^{23} +(0.323190 + 8.35471i) q^{24} +1.00000 q^{25} +(-2.18033 - 3.77644i) q^{26} +(5.16124 - 0.601365i) q^{27} +(-2.03035 - 10.3186i) q^{28} +(0.771716 - 0.445550i) q^{29} +(-3.74561 - 1.97356i) q^{30} +(6.13095 - 3.53970i) q^{31} +(0.211683 - 0.122215i) q^{32} +(-0.293417 - 7.58507i) q^{33} +(-16.6367 + 9.60521i) q^{34} +(2.50358 + 0.855621i) q^{35} +(6.74222 + 9.83549i) q^{36} +(2.58988 + 4.48580i) q^{37} -9.42586 q^{38} +(-2.73368 - 1.44037i) q^{39} -4.82720i q^{40} +(-1.78706 + 3.09527i) q^{41} +(-7.68882 - 8.14578i) q^{42} +(2.68755 + 4.65498i) q^{43} +(15.0860 - 8.70991i) q^{44} +(-2.99103 + 0.231754i) q^{45} +(2.77269 - 4.80244i) q^{46} +(0.299936 - 0.519504i) q^{47} +(-3.10822 + 5.89909i) q^{48} +(5.53583 + 4.28423i) q^{49} +(2.11687 + 1.22217i) q^{50} +(-6.34542 + 12.0430i) q^{51} -7.09101i q^{52} +(-11.9100 - 6.87623i) q^{53} +(11.6606 + 5.03492i) q^{54} +4.38252i q^{55} +(4.13026 - 12.0853i) q^{56} +(-5.65086 + 3.56065i) q^{57} +2.17816 q^{58} +(-4.46426 - 7.73233i) q^{59} +(-3.67021 - 5.82475i) q^{60} +(3.76221 + 2.17211i) q^{61} +17.3045 q^{62} +(-7.68659 - 1.97898i) q^{63} +8.29685 q^{64} +(1.54497 + 0.891986i) q^{65} +(8.64915 - 16.4152i) q^{66} +(3.24358 + 5.61805i) q^{67} -31.2387 q^{68} +(-0.151890 - 3.92648i) q^{69} +(4.25403 + 4.87105i) q^{70} +0.343987i q^{71} +(1.11873 + 14.4383i) q^{72} +(-3.38926 - 1.95679i) q^{73} +12.6611i q^{74} +(1.73076 - 0.0669518i) q^{75} +(-13.2742 - 7.66386i) q^{76} +(-3.74977 + 10.9720i) q^{77} +(-4.02645 - 6.39011i) q^{78} +(-3.43741 + 5.95376i) q^{79} +(1.92484 - 3.33393i) q^{80} +(8.89258 - 1.38637i) q^{81} +(-7.56592 + 4.36819i) q^{82} +(3.09467 + 5.36013i) q^{83} +(-4.20489 - 17.7230i) q^{84} +(3.92956 - 6.80619i) q^{85} +13.1386i q^{86} +(1.30582 - 0.822807i) q^{87} +21.1553 q^{88} +(1.69019 + 2.92749i) q^{89} +(-6.61487 - 3.16497i) q^{90} +(3.10474 + 3.55506i) q^{91} +(7.80941 - 4.50877i) q^{92} +(10.3742 - 6.53684i) q^{93} +(1.26985 - 0.733147i) q^{94} +(3.33955 - 1.92809i) q^{95} +(0.358188 - 0.225697i) q^{96} +(10.3098 - 5.95238i) q^{97} +(6.48254 + 15.8349i) q^{98} +(-1.01567 - 13.1083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more