LMFDB - Embedded newform 308.2.t.c.27.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(27,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 4]))

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

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

chi := DirichletCharacter("308.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.t (of order $10$, degree $4$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.13
Character	$\chi$	$=$	308.27
Dual form			308.2.t.c.251.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.765067 - 1.18940i) q^{2} +(-0.171309 - 0.124464i) q^{3} +(-0.829346 + 1.81994i) q^{4} +(-1.47093 - 0.477935i) q^{5} +(-0.0169739 + 0.298978i) q^{6} +(1.30415 - 2.30200i) q^{7} +(2.79914 - 0.405951i) q^{8} +(-0.913195 - 2.81053i) q^{9} +(0.556905 + 2.11518i) q^{10} +(2.96107 + 1.49400i) q^{11} +(0.368591 - 0.208550i) q^{12} +(-5.47516 + 1.77899i) q^{13} +(-3.73576 + 0.210019i) q^{14} +(0.192499 + 0.264952i) q^{15} +(-2.62437 - 3.01872i) q^{16} +(-3.85385 - 1.25219i) q^{17} +(-2.64419 + 3.23639i) q^{18} +(-5.40967 - 3.93036i) q^{19} +(2.08973 - 2.28064i) q^{20} +(-0.509928 + 0.232034i) q^{21} +(-0.488452 - 4.66491i) q^{22} -1.49466i q^{23} +(-0.530046 - 0.278848i) q^{24} +(-2.10986 - 1.53291i) q^{25} +(6.30479 + 5.15112i) q^{26} +(-0.389672 + 1.19929i) q^{27} +(3.10790 + 4.28263i) q^{28} +(2.07951 - 1.51086i) q^{29} +(0.167860 - 0.431665i) q^{30} +(0.257990 + 0.794012i) q^{31} +(-1.58265 + 5.43095i) q^{32} +(-0.321311 - 0.624483i) q^{33} +(1.45909 + 5.54178i) q^{34} +(-3.01853 + 2.76278i) q^{35} +(5.87235 + 0.668938i) q^{36} +(-0.977197 + 0.709976i) q^{37} +(-0.536008 + 9.44125i) q^{38} +(1.15937 + 0.376701i) q^{39} +(-4.31137 - 0.740681i) q^{40} +(5.71469 - 7.86560i) q^{41} +(0.666110 + 0.428988i) q^{42} -4.39677i q^{43} +(-5.17475 + 4.14993i) q^{44} +4.57054i q^{45} +(-1.77775 + 1.14352i) q^{46} +(9.40795 + 6.83527i) q^{47} +(0.0738583 + 0.843774i) q^{48} +(-3.59837 - 6.00431i) q^{49} +(-0.209052 + 3.68225i) q^{50} +(0.504349 + 0.694176i) q^{51} +(1.30315 - 11.4399i) q^{52} +(1.72666 + 5.31411i) q^{53} +(1.72456 - 0.454059i) q^{54} +(-3.64150 - 3.61278i) q^{55} +(2.71601 - 6.97304i) q^{56} +(0.437542 + 1.34661i) q^{57} +(-3.38798 - 1.31747i) q^{58} +(7.02258 - 5.10220i) q^{59} +(-0.641846 + 0.130600i) q^{60} +(0.140661 + 0.0457034i) q^{61} +(0.747019 - 0.914326i) q^{62} +(-7.66077 - 1.56319i) q^{63} +(7.67041 - 2.27263i) q^{64} +8.90384 q^{65} +(-0.496935 + 0.859938i) q^{66} +7.62277i q^{67} +(5.47509 - 5.97528i) q^{68} +(-0.186031 + 0.256050i) q^{69} +(5.59542 + 1.47653i) q^{70} +(-7.92415 - 2.57471i) q^{71} +(-3.69710 - 7.49635i) q^{72} +(-1.57247 - 2.16432i) q^{73} +(1.59207 + 0.619100i) q^{74} +(0.170649 + 0.525203i) q^{75} +(11.6395 - 6.58566i) q^{76} +(7.30088 - 4.86797i) q^{77} +(-0.438944 - 1.66715i) q^{78} +(13.5174 - 4.39208i) q^{79} +(2.41752 + 5.69461i) q^{80} +(-6.95631 + 5.05405i) q^{81} +(-13.7275 - 0.779350i) q^{82} +(-2.82369 + 8.69041i) q^{83} +(0.000619206 - 1.12048i) q^{84} +(5.07029 + 3.68378i) q^{85} +(-5.22953 + 3.36383i) q^{86} -0.544287 q^{87} +(8.89496 + 2.97987i) q^{88} -7.33671i q^{89} +(5.43620 - 3.49677i) q^{90} +(-3.04523 + 14.9239i) q^{91} +(2.72020 + 1.23959i) q^{92} +(0.0546294 - 0.168132i) q^{93} +(0.932171 - 16.4193i) q^{94} +(6.07881 + 8.36676i) q^{95} +(0.947079 - 0.733390i) q^{96} +(-3.19926 + 1.03950i) q^{97} +(-4.38854 + 8.87360i) q^{98} +(1.49489 - 9.68649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 10 q^{2} - 10 q^{4} + 2 q^{8} - 60 q^{9} - 32 q^{14} - 2 q^{16} + 20 q^{18} - 4 q^{21} - 70 q^{22} + 20 q^{25} - 2 q^{28} - 36 q^{29} - 52 q^{30} + 80 q^{32} - 24 q^{37} + 40 q^{42} - 58 q^{44}+ \cdots - 84 q^{98}+O(q^{100}) $ 160 * q - 10 * q^2 - 10 * q^4 + 2 * q^8 - 60 * q^9 - 32 * q^14 - 2 * q^16 + 20 * q^18 - 4 * q^21 - 70 * q^22 + 20 * q^25 - 2 * q^28 - 36 * q^29 - 52 * q^30 + 80 * q^32 - 24 * q^37 + 40 * q^42 - 58 * q^44 + 50 * q^46 - 54 * q^49 + 36 * q^50 + 40 * q^53 - 32 * q^56 + 12 * q^57 - 74 * q^58 - 52 * q^60 + 110 * q^64 - 56 * q^65 - 92 * q^70 + 142 * q^72 - 122 * q^74 - 30 * q^77 + 68 * q^78 + 36 * q^81 - 92 * q^84 + 20 * q^85 + 34 * q^86 + 2 * q^88 + 32 * q^92 + 4 * q^93 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.765067	−	1.18940i	−0.540984	−	0.841033i
$2$	−0.765067	−	1.18940i	−0.540984	−	0.841033i
$3$	−0.171309	−	0.124464i	−0.0989055	−	0.0718591i	0.537233	−	0.843434i	$-0.319469\pi$
$3$	−0.171309	−	0.124464i	−0.0989055	−	0.0718591i	−0.636139	+	0.771575i	$0.719469\pi$
$4$	−0.829346	+	1.81994i	−0.414673	+	0.909970i
$5$	−1.47093	−	0.477935i	−0.657821	−	0.213739i	−0.0389615	−	0.999241i	$-0.512405\pi$
$5$	−1.47093	−	0.477935i	−0.657821	−	0.213739i	−0.618859	+	0.785502i	$0.712405\pi$
$6$	−0.0169739	+	0.298978i	−0.00692957	+	0.122057i
$7$	1.30415	−	2.30200i	0.492924	−	0.870073i
$7$	1.30415	−	2.30200i	0.492924	−	0.870073i
$8$	2.79914	−	0.405951i	0.989647	−	0.143525i
$9$	−0.913195	−	2.81053i	−0.304398	−	0.936842i
$10$	0.556905	+	2.11518i	0.176109	+	0.668878i
$11$	2.96107	+	1.49400i	0.892797	+	0.450459i
$11$	2.96107	+	1.49400i	0.892797	+	0.450459i
$12$	0.368591	−	0.208550i	0.106403	−	0.0602031i
$13$	−5.47516	+	1.77899i	−1.51854	+	0.493403i	−0.945360	−	0.326029i	$-0.894289\pi$
$13$	−5.47516	+	1.77899i	−1.51854	+	0.493403i	−0.573177	+	0.819431i	$0.694289\pi$
$14$	−3.73576	+	0.210019i	−0.998423	+	0.0561300i
$15$	0.192499	+	0.264952i	0.0497031	+	0.0684104i
$16$	−2.62437	−	3.01872i	−0.656092	−	0.754681i
$17$	−3.85385	−	1.25219i	−0.934696	−	0.303701i	−0.198214	−	0.980159i	$-0.563514\pi$
$17$	−3.85385	−	1.25219i	−0.934696	−	0.303701i	−0.736482	+	0.676458i	$0.763514\pi$
$18$	−2.64419	+	3.23639i	−0.623240	+	0.762825i
$19$	−5.40967	−	3.93036i	−1.24106	−	0.901686i	−0.243395	−	0.969927i	$-0.578261\pi$
$19$	−5.40967	−	3.93036i	−1.24106	−	0.901686i	−0.997669	+	0.0682417i	$0.978261\pi$
$20$	2.08973	−	2.28064i	0.467277	−	0.509966i
$21$	−0.509928	+	0.232034i	−0.111276	+	0.0506340i
$22$	−0.488452	−	4.66491i	−0.104138	−	0.994563i
$23$		−	1.49466i		−	0.311658i	−0.987784	−	0.155829i	$-0.950195\pi$
$23$		−	1.49466i		−	0.311658i	0.987784	−	0.155829i	$-0.0498050\pi$
$24$	−0.530046	−	0.278848i	−0.108195	−	0.0569196i
$25$	−2.10986	−	1.53291i	−0.421973	−	0.306581i
$26$	6.30479	+	5.15112i	1.23647	+	1.01022i
$27$	−0.389672	+	1.19929i	−0.0749925	+	0.230803i
$28$	3.10790	+	4.28263i	0.587338	+	0.809342i
$29$	2.07951	−	1.51086i	0.386156	−	0.280559i	−0.377722	−	0.925919i	$-0.623293\pi$
$29$	2.07951	−	1.51086i	0.386156	−	0.280559i	0.763879	+	0.645360i	$0.223293\pi$
$30$	0.167860	−	0.431665i	0.0306468	−	0.0788108i
$31$	0.257990	+	0.794012i	0.0463364	+	0.142609i	0.971548	−	0.236843i	$-0.0761127\pi$
$31$	0.257990	+	0.794012i	0.0463364	+	0.142609i	−0.925212	+	0.379452i	$0.876113\pi$
$32$	−1.58265	+	5.43095i	−0.279776	+	0.960065i
$33$	−0.321311	−	0.624483i	−0.0559331	−	0.108708i
$34$	1.45909	+	5.54178i	0.250233	+	0.950408i
$35$	−3.01853	+	2.76278i	−0.510224	+	0.466995i
$36$	5.87235	+	0.668938i	0.978724	+	0.111490i
$37$	−0.977197	+	0.709976i	−0.160650	+	0.116719i	−0.665206	−	0.746660i	$-0.731656\pi$
$37$	−0.977197	+	0.709976i	−0.160650	+	0.116719i	0.504556	+	0.863379i	$0.331656\pi$
$38$	−0.536008	+	9.44125i	−0.0869520	+	1.53157i
$39$	1.15937	+	0.376701i	0.185647	+	0.0603204i
$40$	−4.31137	−	0.740681i	−0.681687	−	0.117112i
$41$	5.71469	−	7.86560i	0.892485	−	1.22840i	−0.0803183	−	0.996769i	$-0.525594\pi$
$41$	5.71469	−	7.86560i	0.892485	−	1.22840i	0.972804	−	0.231631i	$-0.0744063\pi$
$42$	0.666110	+	0.428988i	0.102783	+	0.0661942i
$43$		−	4.39677i		−	0.670502i	−0.942129	−	0.335251i	$-0.891179\pi$
$43$		−	4.39677i		−	0.670502i	0.942129	−	0.335251i	$-0.108821\pi$
$44$	−5.17475	+	4.14993i	−0.780123	+	0.625626i
$45$			4.57054i			0.681336i
$46$	−1.77775	+	1.14352i	−0.262115	+	0.168602i
$47$	9.40795	+	6.83527i	1.37229	+	0.997027i	0.997554	+	0.0698956i	$0.0222666\pi$
$47$	9.40795	+	6.83527i	1.37229	+	0.997027i	0.374736	+	0.927132i	$0.377733\pi$
$48$	0.0738583	+	0.843774i	0.0106605	+	0.121788i
$49$	−3.59837	−	6.00431i	−0.514052	−	0.857759i
$50$	−0.209052	+	3.68225i	−0.0295645	+	0.520749i
$51$	0.504349	+	0.694176i	0.0706229	+	0.0972041i
$52$	1.30315	−	11.4399i	0.180715	−	1.58642i
$53$	1.72666	+	5.31411i	0.237175	+	0.729949i	0.996825	+	0.0796178i	$0.0253700\pi$
$53$	1.72666	+	5.31411i	0.237175	+	0.729949i	−0.759651	+	0.650331i	$0.774630\pi$
$54$	1.72456	−	0.454059i	0.234683	−	0.0617896i
$55$	−3.64150	−	3.61278i	−0.491020	−	0.487147i
$56$	2.71601	−	6.97304i	0.362943	−	0.931811i
$57$	0.437542	+	1.34661i	0.0579538	+	0.178363i
$58$	−3.38798	−	1.31747i	−0.444863	−	0.172992i
$59$	7.02258	−	5.10220i	0.914261	−	0.664250i	−0.0278276	−	0.999613i	$-0.508859\pi$
$59$	7.02258	−	5.10220i	0.914261	−	0.664250i	0.942089	+	0.335363i	$0.108859\pi$
$60$	−0.641846	+	0.130600i	−0.0828619	+	0.0168604i
$61$	0.140661	+	0.0457034i	0.0180098	+	0.00585173i	0.318008	−	0.948088i	$-0.396986\pi$
$61$	0.140661	+	0.0457034i	0.0180098	+	0.00585173i	−0.299998	+	0.953940i	$0.596986\pi$
$62$	0.747019	−	0.914326i	0.0948715	−	0.116119i
$63$	−7.66077	−	1.56319i	−0.965166	−	0.196943i
$64$	7.67041	−	2.27263i	0.958801	−	0.284079i
$65$	8.90384			1.10438
$66$	−0.496935	+	0.859938i	−0.0611685	+	0.105851i
$67$			7.62277i			0.931269i	0.884977	+	0.465635i	$0.154174\pi$
$67$			7.62277i			0.931269i	−0.884977	+	0.465635i	$0.845826\pi$
$68$	5.47509	−	5.97528i	0.663952	−	0.724609i
$69$	−0.186031	+	0.256050i	−0.0223955	+	0.0308248i
$70$	5.59542	+	1.47653i	0.668781	+	0.176479i
$71$	−7.92415	−	2.57471i	−0.940423	−	0.305562i	−0.201605	−	0.979467i	$-0.564616\pi$
$71$	−7.92415	−	2.57471i	−0.940423	−	0.305562i	−0.738818	+	0.673905i	$0.764616\pi$
$72$	−3.69710	−	7.49635i	−0.435708	−	0.883454i
$73$	−1.57247	−	2.16432i	−0.184044	−	0.253314i	0.707019	−	0.707194i	$-0.250039\pi$
$73$	−1.57247	−	2.16432i	−0.184044	−	0.253314i	−0.891063	+	0.453880i	$0.850039\pi$
$74$	1.59207	+	0.619100i	0.185074	+	0.0719690i
$75$	0.170649	+	0.525203i	0.0197048	+	0.0606452i
$76$	11.6395	−	6.58566i	1.33514	−	0.755427i
$77$	7.30088	−	4.86797i	0.832013	−	0.554757i
$78$	−0.438944	−	1.66715i	−0.0497007	−	0.188768i
$79$	13.5174	−	4.39208i	1.52083	−	0.494148i	0.574820	−	0.818280i	$-0.305072\pi$
$79$	13.5174	−	4.39208i	1.52083	−	0.494148i	0.946012	+	0.324132i	$0.105072\pi$
$80$	2.41752	+	5.69461i	0.270287	+	0.636677i
$81$	−6.95631	+	5.05405i	−0.772923	+	0.561561i
$82$	−13.7275	−	0.779350i	−1.51595	−	0.0860648i
$83$	−2.82369	+	8.69041i	−0.309940	+	0.953897i	0.667848	+	0.744298i	$0.267216\pi$
$83$	−2.82369	+	8.69041i	−0.309940	+	0.953897i	−0.977788	+	0.209599i	$0.932784\pi$
$84$	0.000619206	−	1.12048i	6.75609e−5	−	0.122254i
$85$	5.07029	+	3.68378i	0.549950	+	0.399562i
$86$	−5.22953	+	3.36383i	−0.563914	+	0.362731i
$87$	−0.544287			−0.0583537
$88$	8.89496	+	2.97987i	0.948206	+	0.317656i
$89$		−	7.33671i		−	0.777690i	−0.921303	−	0.388845i	$-0.872874\pi$
$89$		−	7.33671i		−	0.777690i	0.921303	−	0.388845i	$-0.127126\pi$
$90$	5.43620	−	3.49677i	0.573026	−	0.368592i
$91$	−3.04523	+	14.9239i	−0.319227	+	1.56445i
$92$	2.72020	+	1.23959i	0.283600	+	0.129236i
$93$	0.0546294	−	0.168132i	0.00566481	−	0.0174345i
$94$	0.932171	−	16.4193i	0.0961461	−	1.69352i
$95$	6.07881	+	8.36676i	0.623672	+	0.858411i
$96$	0.947079	−	0.733390i	0.0966608	−	0.0748513i
$97$	−3.19926	+	1.03950i	−0.324836	+	0.105546i	−0.466896	−	0.884312i	$-0.654628\pi$
$97$	−3.19926	+	1.03950i	−0.324836	+	0.105546i	0.142059	+	0.989858i	$0.454628\pi$
$98$	−4.38854	+	8.87360i	−0.443309	+	0.896369i
$99$	1.49489	−	9.68649i	0.150242	−	0.973529i
$100$	4.53961	−	2.56852i	0.453961	−	0.256852i
$101$	16.4074	−	5.33109i	1.63260	−	0.530463i	0.657731	−	0.753253i	$-0.271516\pi$
$101$	16.4074	−	5.33109i	1.63260	−	0.530463i	0.974867	+	0.222789i	$0.0715162\pi$
$102$	0.439793	−	1.13096i	0.0435460	−	0.111982i
$103$	0.542420	−	0.394091i	0.0534462	−	0.0388309i	−0.560741	−	0.827991i	$-0.689484\pi$
$103$	0.542420	−	0.394091i	0.0534462	−	0.0388309i	0.614188	+	0.789160i	$0.289484\pi$
$104$	−14.6036	+	7.20229i	−1.43200	+	0.706243i
$105$	0.860967	−	0.0975936i	0.0840218	−	0.00952416i
$106$	4.99960	−	6.11934i	0.485604	−	0.594363i
$107$	8.13683	−	11.1994i	0.786617	−	1.08269i	−0.207904	−	0.978149i	$-0.566664\pi$
$107$	8.13683	−	11.1994i	0.786617	−	1.08269i	0.994521	−	0.104536i	$-0.0333357\pi$
$108$	−1.85946	−	1.70381i	−0.178927	−	0.163949i
$109$	−8.80549			−0.843413			−0.421707	−	0.906732i	$-0.638569\pi$
$109$	−8.80549			−0.843413			−0.421707	+	0.906732i	$0.638569\pi$
$110$	−1.51105	+	7.09522i	−0.144073	+	0.676503i
$111$	0.255769			0.0242765
$112$	−10.3717	+	2.10441i	−0.980030	+	0.198848i
$113$	−3.94014	−	2.86268i	−0.370657	−	0.269298i	0.386826	−	0.922153i	$-0.373571\pi$
$113$	−3.94014	−	2.86268i	−0.370657	−	0.269298i	−0.757483	+	0.652854i	$0.773571\pi$
$114$	1.26692	−	1.55066i	0.118657	−	0.145233i
$115$	−0.714351	+	2.19855i	−0.0666136	+	0.205015i
$116$	1.02503	+	5.03761i	0.0951717	+	0.467731i
$117$	9.99979	+	13.7635i	0.924481	+	1.27244i
$118$	−11.4413	−	4.44913i	−1.05326	−	0.409576i
$119$	−7.90855	+	7.23850i	−0.724976	+	0.663552i
$120$	0.646390	+	0.663494i	0.0590071	+	0.0605684i
$121$	6.53591	+	8.84770i	0.594174	+	0.804337i
$122$	−0.0532551	−	0.202268i	−0.00482149	−	0.0183125i
$123$	−1.95796	+	0.636180i	−0.176544	+	0.0573625i
$124$	−1.65902	−	0.188984i	−0.148984	−	0.0169713i
$125$	6.91627	+	9.51943i	0.618610	+	0.851444i
$126$	4.00174	+	10.3077i	0.356503	+	0.918279i
$127$	−16.2570	−	5.28222i	−1.44257	−	0.468721i	−0.519875	−	0.854242i	$-0.674022\pi$
$127$	−16.2570	−	5.28222i	−1.44257	−	0.468721i	−0.922699	+	0.385521i	$0.874022\pi$
$128$	−8.57144	−	7.38447i	−0.757616	−	0.652701i
$129$	−0.547238	+	0.753209i	−0.0481817	+	0.0663164i
$130$	−6.81203	−	10.5902i	−0.597454	−	0.928824i
$131$	−5.59085			−0.488475			−0.244237	−	0.969715i	$-0.578538\pi$
$131$	−5.59085			−0.488475			−0.244237	+	0.969715i	$0.578538\pi$
$132$	1.40300	−	0.0668547i	0.122115	−	0.00581896i
$133$	−16.1027	+	7.32725i	−1.39628	+	0.635353i
$134$	9.06652	−	5.83192i	0.783228	−	0.503802i
$135$	1.14636	−	1.57783i	0.0986632	−	0.135798i
$136$	−11.2958	−	1.94059i	−0.968608	−	0.166404i
$137$	−1.03230	+	3.17711i	−0.0881957	+	0.271439i	−0.985421	−	0.170135i	$-0.945580\pi$
$137$	−1.03230	+	3.17711i	−0.0881957	+	0.271439i	0.897225	+	0.441574i	$0.145580\pi$
$138$	0.446872	+	0.0253702i	0.0380402	+	0.00215966i
$139$	11.0586	−	8.03455i	0.937979	−	0.681482i	−0.00995412	−	0.999950i	$-0.503169\pi$
$139$	11.0586	−	8.03455i	0.937979	−	0.681482i	0.947933	+	0.318469i	$0.103169\pi$
$140$	−2.52469	−	7.78484i	−0.213375	−	0.657939i
$141$	−0.760927	−	2.34189i	−0.0640817	−	0.197223i
$142$	3.00014	+	11.3948i	0.251766	+	0.956231i
$143$	−18.8702	−	2.91219i	−1.57800	−	0.243530i
$144$	−6.08764	+	10.1325i	−0.507303	+	0.844379i
$145$	−3.78091	+	1.22849i	−0.313988	+	0.102021i
$146$	−1.37120	+	3.52614i	−0.113481	+	0.291826i
$147$	−0.130884	+	1.47646i	−0.0107951	+	0.121776i
$148$	−0.481678	−	2.36726i	−0.0395937	−	0.194587i
$149$	−3.16344	+	9.73606i	−0.259159	+	0.797609i	0.733823	+	0.679341i	$0.237734\pi$
$149$	−3.16344	+	9.73606i	−0.259159	+	0.797609i	−0.992982	+	0.118268i	$0.962266\pi$
$150$	0.494119	−	0.604785i	0.0403446	−	0.0493805i
$151$	5.21008	−	7.17106i	0.423990	−	0.583573i	−0.542570	−	0.840010i	$-0.682549\pi$
$151$	5.21008	−	7.17106i	0.423990	−	0.583573i	0.966561	+	0.256438i	$0.0825489\pi$
$152$	−16.7380	−	8.80557i	−1.35763	−	0.714226i
$153$			11.9748i			0.968109i
$154$	−11.3756	−	4.95935i	−0.916674	−	0.399636i
$155$		−	1.29124i		−	0.103715i
$156$	−1.64709	+	1.79756i	−0.131873	+	0.143920i
$157$	−10.3526	+	14.2492i	−0.826229	+	1.13721i	0.162385	+	0.986728i	$0.448081\pi$
$157$	−10.3526	+	14.2492i	−0.826229	+	1.13721i	−0.988613	+	0.150479i	$0.951919\pi$
$158$	−15.5657	−	12.7174i	−1.23834	−	1.01174i
$159$	0.365620	−	1.12526i	0.0289956	−	0.0892392i
$160$	4.92361	−	7.23215i	0.389246	−	0.571752i
$161$	−3.44070	−	1.94927i	−0.271165	−	0.153624i
$162$	11.3333	+	4.40715i	0.890430	+	0.346258i
$163$	15.8621	−	5.15389i	1.24241	−	0.403684i	0.387216	−	0.921989i	$-0.373437\pi$
$163$	15.8621	−	5.15389i	1.24241	−	0.403684i	0.855196	+	0.518305i	$0.173437\pi$
$164$	9.57547	+	16.9237i	0.747719	+	1.32152i
$165$	0.174165	+	1.07214i	0.0135587	+	0.0834658i
$166$	12.4967	−	3.29025i	0.969931	−	0.255373i
$167$	−2.32650	−	7.16024i	−0.180030	−	0.554076i	0.819797	−	0.572654i	$-0.194086\pi$
$167$	−2.32650	−	7.16024i	−0.180030	−	0.554076i	−0.999827	+	0.0185780i	$0.994086\pi$
$168$	−1.33317	+	0.856502i	−0.102856	+	0.0660806i
$169$	16.2954	−	11.8393i	1.25349	−	0.910715i
$170$	0.502381	−	8.84894i	0.0385308	−	0.678682i
$171$	−6.10628	+	18.7932i	−0.466959	+	1.43715i
$172$	8.00187	+	3.64645i	0.610137	+	0.278039i
$173$	1.30958	−	1.80248i	0.0995653	−	0.137040i	−0.756327	−	0.654193i	$-0.773008\pi$
$173$	1.30958	−	1.80248i	0.0995653	−	0.137040i	0.855893	+	0.517153i	$0.173008\pi$
$174$	0.416416	+	0.647375i	0.0315684	+	0.0490774i
$175$	−6.28033	+	2.85775i	−0.474748	+	0.216026i
$176$	−3.26097	−	12.8595i	−0.245805	−	0.969319i
$177$	−1.83807			−0.138158
$178$	−8.72629	+	5.61307i	−0.654063	+	0.420718i
$179$	−3.74961	+	5.16089i	−0.280259	+	0.385743i	−0.925820	−	0.377966i	$-0.876624\pi$
$179$	−3.74961	+	5.16089i	−0.280259	+	0.385743i	0.645561	+	0.763709i	$0.276624\pi$
$180$	−8.31811	−	3.79056i	−0.619996	−	0.282532i
$181$	12.1485	+	3.94730i	0.902993	+	0.293400i	0.723472	−	0.690354i	$-0.242545\pi$
$181$	12.1485	+	3.94730i	0.902993	+	0.293400i	0.179521	+	0.983754i	$0.442545\pi$
$182$	20.0803	−	7.79576i	1.48845	−	0.577860i
$183$	−0.0184081	−	0.0253366i	−0.00136077	−	0.00187293i
$184$	−0.606760	−	4.18377i	−0.0447309	−	0.308432i
$185$	1.77671	−	0.577289i	0.130627	−	0.0424431i
$186$	−0.241772	+	0.0636560i	−0.0177276	+	0.00466749i
$187$	−9.54076	−	9.46549i	−0.697689	−	0.692185i
$188$	−20.2422	+	11.4531i	−1.47632	+	0.835303i
$189$	2.25256	+	2.46108i	0.163850	+	0.179017i
$190$	5.30073	−	13.6313i	0.384556	−	0.988916i
$191$	6.38722	+	8.79125i	0.462163	+	0.636112i	0.974956	−	0.222400i	$-0.0713891\pi$
$191$	6.38722	+	8.79125i	0.462163	+	0.636112i	−0.512793	+	0.858512i	$0.671389\pi$
$192$	−1.59687	−	0.565363i	−0.115244	−	0.0408016i
$193$	5.97683	−	18.3948i	0.430221	−	1.32409i	−0.467684	−	0.883896i	$-0.654911\pi$
$193$	5.97683	−	18.3948i	0.430221	−	1.32409i	0.897905	−	0.440189i	$-0.145089\pi$
$194$	3.68404	+	3.00992i	0.264498	+	0.216099i
$195$	−1.52531	−	1.10820i	−0.109230	−	0.0793601i
$196$	13.9118	−	1.56916i	0.993699	−	0.112083i
$197$	−12.9910			−0.925568			−0.462784	−	0.886471i	$-0.653149\pi$
$197$	−12.9910			−0.925568			−0.462784	+	0.886471i	$0.653149\pi$
$198$	−12.6648	+	5.63278i	−0.900049	+	0.400304i
$199$	4.91775			0.348610			0.174305	−	0.984692i	$-0.444232\pi$
$199$	4.91775			0.348610			0.174305	+	0.984692i	$0.444232\pi$
$200$	−6.52810	−	3.43432i	−0.461606	−	0.242843i
$201$	0.948757	−	1.30585i	0.0669202	−	0.0921077i
$202$	−18.8936	−	15.4363i	−1.32935	−	1.08610i
$203$	−0.765977	−	6.75742i	−0.0537610	−	0.474278i
$204$	−1.68164	+	0.342172i	−0.117738	+	0.0239568i
$205$	−12.1652	+	8.83852i	−0.849653	+	0.617309i
$206$	−0.883719	−	0.343648i	−0.0615716	−	0.0239431i
$207$	−4.20079	+	1.36492i	−0.291975	+	0.0948684i
$208$	19.7391	+	11.8593i	1.36866	+	0.822293i
$209$	−10.1465	−	19.7201i	−0.701846	−	1.36407i
$210$	−0.774775	−	0.949369i	−0.0534646	−	0.0655127i
$211$	−8.70200	+	2.82745i	−0.599070	+	0.194650i	−0.592826	−	0.805331i	$-0.701988\pi$
$211$	−8.70200	+	2.82745i	−0.599070	+	0.194650i	−0.00624466	+	0.999981i	$0.501988\pi$
$212$	−11.1034	−	1.26482i	−0.762582	−	0.0868682i
$213$	1.03702	+	1.42734i	0.0710557	+	0.0977997i
$214$	−19.5458	−	1.10967i	−1.33612	−	0.0758556i
$215$	−2.10137	+	6.46736i	−0.143312	+	0.441070i
$216$	−0.603896	+	3.51517i	−0.0410899	+	0.239177i
$217$	2.16427	+	0.441622i	0.146920	+	0.0299792i
$218$	6.73679	+	10.4733i	0.456273	+	0.709339i
$219$			0.566484i			0.0382794i
$220$	9.59511	−	3.63108i	0.646902	−	0.244807i
$221$	23.3281			1.56922
$222$	−0.195681	−	0.304212i	−0.0131332	−	0.0204174i
$223$	19.5653	+	14.2150i	1.31019	+	0.951909i	0.999999	+	0.00123550i	$0.000393271\pi$
$223$	19.5653	+	14.2150i	1.31019	+	0.951909i	0.310192	+	0.950674i	$0.399607\pi$
$224$	10.4380	+	10.7260i	0.697418	+	0.716664i
$225$	−2.38156	+	7.32967i	−0.158770	+	0.488645i
$226$	−0.390402	+	6.87655i	−0.0259692	+	0.457421i
$227$	18.1256	−	13.1690i	1.20304	−	0.874060i	0.208460	−	0.978031i	$-0.433155\pi$
$227$	18.1256	−	13.1690i	1.20304	−	0.874060i	0.994580	+	0.103971i	$0.0331548\pi$
$228$	−2.81363	−	0.320510i	−0.186337	−	0.0212263i
$229$	−1.22223	+	0.397127i	−0.0807672	+	0.0262429i	−0.349122	−	0.937077i	$-0.613520\pi$
$229$	−1.22223	+	0.397127i	−0.0807672	+	0.0262429i	0.268355	+	0.963320i	$0.413520\pi$
$230$	3.16148	−	0.832385i	0.208462	−	0.0548858i
$231$	−1.85659	−	0.0747647i	−0.122155	−	0.00491916i
$232$	5.20752	−	5.07328i	0.341891	−	0.333077i
$233$	1.75562	+	5.40325i	0.115015	+	0.353979i	0.991950	−	0.126629i	$-0.0404159\pi$
$233$	1.75562	+	5.40325i	0.115015	+	0.353979i	−0.876935	+	0.480608i	$0.840416\pi$
$234$	8.71984	−	22.4238i	0.570034	−	1.46589i
$235$	−10.5716	−	14.5506i	−0.689618	−	0.949177i
$236$	3.46156	+	17.0122i	0.225328	+	1.10740i
$237$	−2.86232	−	0.930024i	−0.185928	−	0.0604116i
$238$	14.6600	+	3.86850i	0.950269	+	0.250758i
$239$	−12.9770	+	17.8613i	−0.839411	+	1.15535i	0.146686	+	0.989183i	$0.453139\pi$
$239$	−12.9770	+	17.8613i	−0.839411	+	1.15535i	−0.986098	+	0.166167i	$0.946861\pi$
$240$	0.294628	−	1.27643i	0.0190182	−	0.0823935i
$241$		−	15.9454i		−	1.02713i	−0.858049	−	0.513567i	$-0.828324\pi$
$241$		−	15.9454i		−	1.02713i	0.858049	−	0.513567i	$-0.171676\pi$
$242$	5.52305	−	14.5429i	0.355035	−	0.934853i
$243$	5.60374			0.359480
$244$	−0.199834	+	0.218090i	−0.0127931	+	0.0139618i
$245$	2.42328	+	10.5517i	0.154818	+	0.674125i
$246$	2.25464	+	1.84208i	0.143751	+	0.117447i
$247$	36.6109	+	11.8956i	2.32950	+	0.756899i
$248$	1.04448	+	2.11782i	0.0663247	+	0.134482i
$249$	1.56536	−	1.13730i	0.0992009	−	0.0720737i
$250$	6.03100	−	15.5092i	0.381434	−	0.980889i
$251$	−0.405296	−	1.24737i	−0.0255820	−	0.0787334i	0.937450	−	0.348119i	$-0.113179\pi$
$251$	−0.405296	−	1.24737i	−0.0255820	−	0.0787334i	−0.963032	+	0.269385i	$0.913179\pi$
$252$	9.19833	−	12.6457i	0.579441	−	0.796605i
$253$	2.23303	−	4.42580i	0.140389	−	0.278248i
$254$	6.15501	+	23.3773i	0.386200	+	1.46682i
$255$	−0.410092	−	1.26213i	−0.0256809	−	0.0790378i
$256$	−2.22537	+	15.8445i	−0.139085	+	0.990280i
$257$	−7.02184	−	9.66473i	−0.438010	−	0.602869i	0.531758	−	0.846896i	$-0.321531\pi$
$257$	−7.02184	−	9.66473i	−0.438010	−	0.602869i	−0.969768	+	0.244027i	$0.921531\pi$
$258$	1.31454	+	0.0746304i	0.0818397	+	0.00464629i
$259$	0.359945	+	3.17542i	0.0223659	+	0.197311i
$260$	−7.38436	+	16.2045i	−0.457959	+	1.00496i
$261$	−6.14530	−	4.46482i	−0.380385	−	0.276366i
$262$	4.27737	+	6.64976i	0.264257	+	0.410823i
$263$		−	13.1538i		−	0.811098i	−0.914073	−	0.405549i	$-0.867080\pi$
$263$		−	13.1538i		−	0.811098i	0.914073	−	0.405549i	$-0.132920\pi$
$264$	−1.15291	−	1.61758i	−0.0709564	−	0.0995551i
$265$		−	8.64193i		−	0.530869i
$266$	21.0347	+	13.5467i	1.28972	+	0.830603i
$267$	−0.913154	+	1.25685i	−0.0558841	+	0.0769179i
$268$	−13.8730	−	6.32191i	−0.847427	−	0.386172i
$269$	−13.3688	−	4.34377i	−0.815108	−	0.264845i	−0.128348	−	0.991729i	$-0.540967\pi$
$269$	−13.3688	−	4.34377i	−0.815108	−	0.264845i	−0.686760	+	0.726885i	$0.740967\pi$
$270$	−2.75372	−	0.156337i	−0.167586	−	0.00951437i
$271$	12.5782	−	9.13857i	0.764069	−	0.555128i	−0.136087	−	0.990697i	$-0.543453\pi$
$271$	12.5782	−	9.13857i	0.764069	−	0.555128i	0.900156	+	0.435569i	$0.143453\pi$
$272$	6.33391	+	14.9199i	0.384050	+	0.904653i
$273$	2.37916	−	2.17758i	0.143993	−	0.131793i
$274$	4.56863	−	1.20287i	0.276001	−	0.0726683i
$275$	−3.95730	−	7.69119i	−0.238634	−	0.463796i
$276$	−0.311711	−	0.550919i	−0.0187628	−	0.0331614i
$277$	−7.42093	−	22.8393i	−0.445881	−	1.37228i	−0.881515	−	0.472156i	$-0.843476\pi$
$277$	−7.42093	−	22.8393i	−0.445881	−	1.37228i	0.435634	−	0.900124i	$-0.356524\pi$
$278$	−18.0169	−	7.00615i	−1.08058	−	0.420201i
$279$	1.99600	−	1.45018i	0.119497	−	0.0868198i
$280$	−7.32773	+	8.95879i	−0.437916	+	0.535390i
$281$	−0.0336367	+	0.103523i	−0.00200660	+	0.00617568i	−0.952055	−	0.305928i	$-0.901033\pi$
$281$	−0.0336367	+	0.103523i	−0.00200660	+	0.00617568i	0.950048	+	0.312103i	$0.101033\pi$
$282$	−2.20329	+	2.69675i	−0.131204	+	0.160589i
$283$	−8.06170	−	5.85717i	−0.479218	−	0.348172i	0.321805	−	0.946806i	$-0.395711\pi$
$283$	−8.06170	−	5.85717i	−0.479218	−	0.348172i	−0.801023	+	0.598634i	$0.795711\pi$
$284$	11.2577	−	12.2862i	0.668021	−	0.729049i
$285$		−	2.18989i		−	0.129718i
$286$	10.9732	+	24.6722i	0.648858	+	1.45890i
$287$	−10.6537	−	23.4132i	−0.628870	−	1.38203i
$288$	16.7091	−	0.511434i	0.984593	−	0.0301366i
$289$	−0.469113	−	0.340830i	−0.0275949	−	0.0200488i
$290$	4.35382	+	3.55714i	0.255665	+	0.208883i
$291$	0.677445	+	0.220115i	0.0397125	+	0.0129034i
$292$	5.24305	−	1.06683i	0.306827	−	0.0624316i
$293$	−3.00253	−	4.13263i	−0.175410	−	0.241431i	0.712255	−	0.701920i	$-0.247674\pi$
$293$	−3.00253	−	4.13263i	−0.175410	−	0.241431i	−0.887665	+	0.460490i	$0.847674\pi$
$294$	1.85624	−	0.973917i	0.108258	−	0.0568000i
$295$	−12.7683	+	4.14866i	−0.743396	+	0.241544i
$296$	−2.44710	+	2.38402i	−0.142235	+	0.138568i
$297$	−2.94559	+	2.96901i	−0.170920	+	0.172279i
$298$	14.0003	−	3.68614i	0.811016	−	0.213532i
$299$	2.65899	+	8.18352i	0.153773	+	0.473265i
$300$	−1.09736	−	0.125004i	−0.0633564	−	0.00721713i
$301$	−10.1214	−	5.73407i	−0.583385	−	0.330506i
$302$	−12.5153	−	0.710532i	−0.720176	−	0.0408865i
$303$	−3.47427	−	1.12886i	−0.199592	−	0.0648512i
$304$	2.33232	+	26.6450i	0.133768	+	1.52820i
$305$	−0.185059	−	0.134453i	−0.0105965	−	0.00769878i
$306$	14.2429	−	9.16155i	0.814211	−	0.523731i
$307$	−29.6754			−1.69367			−0.846833	−	0.531859i	$-0.821493\pi$
$307$	−29.6754			−1.69367			−0.846833	+	0.531859i	$0.821493\pi$
$308$	2.80446	+	17.3244i	0.159799	+	0.987150i
$309$	−0.141972			−0.00807648
$310$	−1.53580	+	0.987885i	−0.0872277	+	0.0561081i
$311$	18.9676	+	13.7808i	1.07556	+	0.781437i	0.976903	−	0.213685i	$-0.0685467\pi$
$311$	18.9676	+	13.7808i	1.07556	+	0.781437i	0.0986528	+	0.995122i	$0.468547\pi$
$312$	3.39816	+	0.583794i	0.192383	+	0.0330508i
$313$	4.41705	+	1.43519i	0.249666	+	0.0811216i	0.431177	−	0.902267i	$-0.358099\pi$
$313$	4.41705	+	1.43519i	0.249666	+	0.0811216i	−0.181510	+	0.983389i	$0.558099\pi$
$314$	24.8684	+	1.41185i	1.40340	+	0.0796755i
$315$	10.5214	+	5.96069i	0.592812	+	0.335847i
$316$	−3.21731	+	28.2435i	−0.180988	+	1.58882i
$317$	−2.53618	−	7.80557i	−0.142446	−	0.438404i	0.854228	−	0.519899i	$-0.174031\pi$
$317$	−2.53618	−	7.80557i	−0.142446	−	0.438404i	−0.996674	+	0.0814949i	$0.974031\pi$
$318$	−1.61811	+	0.426033i	−0.0907393	+	0.0238907i
$319$	8.41482	−	1.36696i	0.471139	−	0.0765348i
$320$	−12.3688	−	0.323067i	−0.691438	−	0.0180600i
$321$	−2.78783	+	0.905821i	−0.155602	+	0.0505580i
$322$	0.313908	+	5.58369i	0.0174934	+	0.311167i
$323$	15.9265	+	21.9210i	0.886174	+	1.21971i
$324$	−3.42889	−	16.8516i	−0.190494	−	0.936201i
$325$	14.2789	+	4.63949i	0.792050	+	0.257353i
$326$	−18.2656	−	14.9233i	−1.01164	−	0.826523i
$327$	1.50846	+	1.09596i	0.0834183	+	0.0606069i
$328$	12.8032	−	24.3368i	0.706938	−	1.34378i
$329$	28.0042	−	12.7428i	1.54392	−	0.702534i
$330$	1.14195	−	1.02741i	0.0628624	−	0.0565569i
$331$			7.70645i			0.423585i	0.977315	+	0.211792i	$0.0679301\pi$
$331$			7.70645i			0.423585i	−0.977315	+	0.211792i	$0.932070\pi$
$332$	−13.4742	−	12.3463i	−0.739494	−	0.677591i
$333$	2.88778	+	2.09809i	0.158249	+	0.114975i
$334$	−6.73646	+	8.24520i	−0.368603	+	0.451157i
$335$	3.64319	−	11.2126i	0.199049	−	0.612608i
$336$	2.03869	+	0.930390i	0.111219	+	0.0507569i
$337$	−0.414935	+	0.301468i	−0.0226029	+	0.0164220i	−0.599029	−	0.800727i	$-0.704447\pi$
$337$	−0.414935	+	0.301468i	−0.0226029	+	0.0164220i	0.576426	+	0.817149i	$0.304447\pi$
$338$	−26.5487	−	10.3239i	−1.44406	−	0.561546i
$339$	0.318684	+	0.980808i	0.0173085	+	0.0532702i
$340$	−10.9093	+	6.17249i	−0.591639	+	0.334750i
$341$	−0.422328	+	2.73657i	−0.0228703	+	0.148193i
$342$	27.0244	−	7.11524i	1.46131	−	0.384748i
$343$	−18.5147	+	0.452880i	−0.999701	+	0.0244532i
$344$	−1.78488	−	12.3072i	−0.0962341	−	0.663560i
$345$	0.396014	−	0.287721i	0.0213207	−	0.0154904i
$346$	−3.14578	−	0.178595i	−0.169118	−	0.00960135i
$347$	4.73236	+	1.53764i	0.254047	+	0.0825447i	0.433272	−	0.901263i	$-0.357359\pi$
$347$	4.73236	+	1.53764i	0.254047	+	0.0825447i	−0.179225	+	0.983808i	$0.557359\pi$
$348$	0.451402	−	0.990570i	0.0241977	−	0.0531001i
$349$	−8.68322	+	11.9514i	−0.464802	+	0.639745i	−0.975496	−	0.220018i	$-0.929389\pi$
$349$	−8.68322	+	11.9514i	−0.464802	+	0.639745i	0.510694	+	0.859763i	$0.329389\pi$
$350$	8.20389	+	5.28346i	0.438516	+	0.282413i
$351$		−	7.25952i		−	0.387485i
$352$	−12.8002	+	13.7170i	−0.682253	+	0.731116i
$353$		−	21.1906i		−	1.12786i	−0.825822	−	0.563931i	$-0.809289\pi$
$353$		−	21.1906i		−	1.12786i	0.825822	−	0.563931i	$-0.190711\pi$
$354$	1.40625	+	2.18620i	0.0747412	+	0.116195i
$355$	10.4253	+	7.57445i	0.553320	+	0.402010i
$356$	13.3524	+	6.08468i	0.707675	+	0.322487i
$357$	2.25574	−	0.255696i	0.119386	−	0.0135329i
$358$	9.00707	+	0.511358i	0.476038	+	0.0270261i
$359$	2.99034	+	4.11585i	0.157824	+	0.217226i	0.880605	−	0.473851i	$-0.157136\pi$
$359$	2.99034	+	4.11585i	0.157824	+	0.217226i	−0.722781	+	0.691077i	$0.757136\pi$
$360$	1.85542	+	12.7936i	0.0977891	+	0.674282i
$361$	7.94552	+	24.4538i	0.418185	+	1.28704i
$362$	−4.59952	−	17.4694i	−0.241745	−	0.918172i
$363$	−0.0184471	−	2.32918i	−0.000968222	−	0.122250i
$364$	−24.6350	−	17.9192i	−1.29123	−	0.939221i
$365$	1.27859	+	3.93510i	0.0669246	+	0.205973i
$366$	−0.0160519	+	0.0412788i	−0.000839047	+	0.00215768i
$367$	−16.5392	+	12.0164i	−0.863337	+	0.627251i	−0.928791	−	0.370604i	$-0.879151\pi$
$367$	−16.5392	+	12.0164i	−0.863337	+	0.627251i	0.0654536	+	0.997856i	$0.479151\pi$
$368$	−4.51197	+	3.92254i	−0.235203	+	0.204477i
$369$	−27.3251	−	8.87847i	−1.42249	−	0.462195i
$370$	−2.04593	−	1.67156i	−0.106363	−	0.0869002i
$371$	14.4849	+	2.95565i	0.752018	+	0.153450i
$372$	0.260684	+	0.238862i	0.0135158	+	0.0123844i
$373$	11.9716			0.619865			0.309933	−	0.950759i	$-0.399693\pi$
$373$	11.9716			0.619865			0.309933	+	0.950759i	$0.399693\pi$
$374$	−3.95895	+	18.5895i	−0.204712	+	0.961241i
$375$		−	2.49159i		−	0.128665i
$376$	29.1090	+	15.3137i	1.50118	+	0.789746i
$377$	−8.69789	+	11.9716i	−0.447964	+	0.616569i
$378$	1.20385	−	4.56209i	0.0619193	−	0.234649i
$379$	−9.15966	−	2.97615i	−0.470500	−	0.152875i	0.0641642	−	0.997939i	$-0.479562\pi$
$379$	−9.15966	−	2.97615i	−0.470500	−	0.152875i	−0.534664	+	0.845065i	$0.679562\pi$
$380$	−20.2684	+	4.12413i	−1.03975	+	0.211563i
$381$	2.12753	+	2.92830i	0.108997	+	0.150021i
$382$	5.56967	−	14.3228i	0.284969	−	0.732821i
$383$	−2.02847	−	6.24298i	−0.103650	−	0.319002i	0.885761	−	0.464141i	$-0.153637\pi$
$383$	−2.02847	−	6.24298i	−0.103650	−	0.319002i	−0.989411	+	0.145139i	$0.953637\pi$
$384$	0.549271	+	2.33186i	0.0280299	+	0.118997i
$385$	−13.0657	+	3.67111i	−0.665888	+	0.187097i
$386$	−26.4514	+	6.96439i	−1.34634	+	0.354478i
$387$	−12.3573	+	4.01511i	−0.628154	+	0.204100i
$388$	0.761462	−	6.68458i	0.0386574	−	0.339358i
$389$	−16.7020	+	12.1347i	−0.846824	+	0.615254i	−0.924269	−	0.381743i	$-0.875324\pi$
$389$	−16.7020	+	12.1347i	−0.846824	+	0.615254i	0.0774443	+	0.996997i	$0.475324\pi$
$390$	−0.151133	+	2.66205i	−0.00765291	+	0.134798i
$391$	−1.87160	+	5.76020i	−0.0946510	+	0.291306i
$392$	−12.5098	−	15.3462i	−0.631840	−	0.775098i
$393$	0.957765	+	0.695857i	0.0483129	+	0.0351014i
$394$	9.93895	+	15.4515i	0.500717	+	0.778433i
$395$	−21.9824			−1.10605
$396$	16.3891	+	10.7541i	0.823581	+	0.540412i
$397$			17.5489i			0.880756i	0.897812	+	0.440378i	$0.145156\pi$
$397$			17.5489i			0.880756i	−0.897812	+	0.440378i	$0.854844\pi$
$398$	−3.76240	−	5.84917i	−0.188592	−	0.293192i
$399$	3.67052	+	0.748973i	0.183756	+	0.0374956i
$400$	0.909647	+	10.3920i	0.0454823	+	0.519600i
$401$	10.5951	−	32.6083i	0.529093	−	1.62838i	−0.226983	−	0.973899i	$-0.572886\pi$
$401$	10.5951	−	32.6083i	0.529093	−	1.62838i	0.756076	−	0.654483i	$-0.227114\pi$
$402$	−2.27904	−	0.129388i	−0.113668	−	0.00645329i
$403$	−2.82508	−	3.88839i	−0.140727	−	0.193694i
$404$	−3.90515	+	34.2818i	−0.194289	+	1.70558i
$405$	12.6478	−	4.10951i	0.628472	−	0.204203i
$406$	−7.45125	+	6.08093i	−0.369800	+	0.301791i
$407$	−3.95426	+	0.642355i	−0.196005	+	0.0318403i
$408$	1.69355	+	1.73836i	0.0838430	+	0.0860615i
$409$	−8.77537	+	2.85129i	−0.433914	+	0.140987i	−0.517826	−	0.855486i	$-0.673259\pi$
$409$	−8.77537	+	2.85129i	−0.433914	+	0.140987i	0.0839119	+	0.996473i	$0.473259\pi$
$410$	19.8197	+	7.70721i	0.978825	+	0.380632i
$411$	0.572278	−	0.415784i	0.0282284	−	0.0205091i
$412$	0.267368	+	1.31401i	0.0131723	+	0.0647366i
$413$	−2.58672	−	22.8200i	−0.127284	−	1.12290i
$414$	4.83731	+	3.95216i	0.237741	+	0.194238i
$415$	8.30690	−	11.4335i	0.407770	−	0.561247i
$416$	−0.996321	−	32.5509i	−0.0488487	−	1.59594i
$417$	−2.89445			−0.141742
$418$	−15.6924	+	27.1554i	−0.767541	+	1.32822i
$419$	−6.34689			−0.310066			−0.155033	−	0.987909i	$-0.549548\pi$
$419$	−6.34689			−0.310066			−0.155033	+	0.987909i	$0.549548\pi$
$420$	−0.536425	+	1.64785i	−0.0261749	+	0.0804068i
$421$	−18.5855	−	13.5032i	−0.905802	−	0.658103i	0.0341479	−	0.999417i	$-0.489128\pi$
$421$	−18.5855	−	13.5032i	−0.905802	−	0.658103i	−0.939950	+	0.341313i	$0.889128\pi$
$422$	10.0206	+	8.18697i	0.487794	+	0.398536i
$423$	10.6194	−	32.6832i	0.516334	−	1.58911i
$424$	6.99044	+	14.1740i	0.339486	+	0.688351i
$425$	6.21161	+	8.54955i	0.301307	+	0.414714i
$426$	0.904287	−	2.32545i	0.0438128	−	0.112668i
$427$	0.288652	−	0.264196i	0.0139689	−	0.0127853i
$428$	13.6340	+	24.0967i	0.659023	+	1.16476i
$429$	2.87018	+	2.84754i	0.138573	+	0.137480i
$430$	9.29997	−	2.44859i	0.448484	−	0.118081i
$431$	20.5862	−	6.68888i	0.991604	−	0.322192i	0.232099	−	0.972692i	$-0.425441\pi$
$431$	20.5862	−	6.68888i	0.991604	−	0.322192i	0.759506	+	0.650500i	$0.225441\pi$
$432$	4.64296	−	1.97106i	0.223385	−	0.0948328i
$433$	−10.2182	−	14.0642i	−0.491056	−	0.675880i	0.489527	−	0.871988i	$-0.337170\pi$
$433$	−10.2182	−	14.0642i	−0.491056	−	0.675880i	−0.980582	+	0.196108i	$0.937170\pi$
$434$	−1.13055	−	2.91205i	−0.0542680	−	0.139783i
$435$	0.800609	+	0.260134i	0.0383863	+	0.0124725i
$436$	7.30280	−	16.0255i	0.349741	−	0.767481i
$437$	−5.87455	+	8.08563i	−0.281018	+	0.386788i
$438$	0.673776	−	0.433398i	0.0321942	−	0.0207085i
$439$	−28.2136			−1.34656			−0.673281	−	0.739386i	$-0.735116\pi$
$439$	−28.2136			−1.34656			−0.673281	+	0.739386i	$0.735116\pi$
$440$	−11.6597	−	8.63441i	−0.555854	−	0.411629i
$441$	−13.5893	+	15.5964i	−0.647108	+	0.742686i
$442$	−17.8475	−	27.7464i	−0.848921	−	1.31976i
$443$	−2.15954	+	2.97235i	−0.102603	+	0.141221i	−0.857231	−	0.514932i	$-0.827817\pi$
$443$	−2.15954	+	2.97235i	−0.102603	+	0.141221i	0.754628	+	0.656153i	$0.227817\pi$
$444$	−0.212121	+	0.465485i	−0.0100668	+	0.0220909i
$445$	−3.50647	+	10.7918i	−0.166223	+	0.511581i
$446$	1.93860	−	34.1465i	0.0917952	−	1.61688i
$447$	1.75371	−	1.27415i	0.0829477	−	0.0602650i
$448$	4.77180	−	20.6211i	0.225446	−	0.974256i
$449$	−7.07199	−	21.7654i	−0.333748	−	1.02717i	−0.967335	−	0.253500i	$-0.918418\pi$
$449$	−7.07199	−	21.7654i	−0.333748	−	1.02717i	0.633587	−	0.773671i	$-0.281582\pi$
$450$	10.5400	−	2.77507i	0.496859	−	0.130818i
$451$	28.6729	−	14.7529i	1.35015	−	0.694685i
$452$	8.47765	−	4.79667i	0.398755	−	0.225616i
$453$	−1.78507	+	0.580005i	−0.0838700	+	0.0272510i
$454$	−29.5306	−	11.4834i	−1.38594	−	0.538945i
$455$	11.6120	−	20.4966i	0.544378	−	0.960895i
$456$	1.77140	+	3.59175i	0.0829535	+	0.168199i
$457$	−11.3410	+	34.9039i	−0.530508	+	1.63273i	0.222653	+	0.974898i	$0.428528\pi$
$457$	−11.3410	+	34.9039i	−0.530508	+	1.63273i	−0.753161	+	0.657837i	$0.771472\pi$
$458$	1.40743	+	1.14989i	0.0657649	+	0.0537309i
$459$	3.00348	−	4.13393i	0.140190	−	0.192955i
$460$	−3.40878	−	3.12343i	−0.158935	−	0.145631i
$461$		−	27.8113i		−	1.29530i	−0.761937	−	0.647651i	$-0.775752\pi$
$461$		−	27.8113i		−	1.29530i	0.761937	−	0.647651i	$-0.224248\pi$
$462$	1.33149	+	2.26543i	0.0619467	+	0.105398i
$463$			1.22988i			0.0571574i	0.999592	+	0.0285787i	$0.00909812\pi$
$463$			1.22988i			0.0571574i	−0.999592	+	0.0285787i	$0.990902\pi$
$464$	−10.0183	−	2.31243i	−0.465086	−	0.107352i
$465$	−0.160712	+	0.221202i	−0.00745286	+	0.0102580i
$466$	5.08346	−	6.22199i	0.235487	−	0.288228i
$467$	4.73278	−	14.5660i	0.219007	−	0.674034i	−0.779838	−	0.625982i	$-0.784699\pi$
$467$	4.73278	−	14.5660i	0.219007	−	0.674034i	0.998845	−	0.0480525i	$-0.0153015\pi$
$468$	−33.3421	+	6.78429i	−1.54124	+	0.313604i
$469$	17.5476	+	9.94126i	0.810272	+	0.459045i
$470$	−9.21849	+	23.7061i	−0.425217	+	1.09348i
$471$	3.54700	−	1.15249i	0.163437	−	0.0531040i
$472$	17.5860	−	17.1326i	0.809459	−	0.788592i
$473$	6.56879	−	13.0192i	0.302033	−	0.598622i
$474$	1.08369	+	4.11598i	0.0497757	+	0.189053i
$475$	5.38881	+	16.5850i	0.247255	+	0.760974i
$476$	−6.61471	−	20.3963i	−0.303185	−	0.934864i
$477$	13.3587	−	9.70564i	0.611651	−	0.444391i
$478$	31.1725	+	1.76976i	1.42580	+	0.0809467i
$479$	4.03499	−	12.4184i	0.184363	−	0.567412i	−0.815574	−	0.578653i	$-0.803578\pi$
$479$	4.03499	−	12.4184i	0.184363	−	0.567412i	0.999937	+	0.0112417i	$0.00357843\pi$
$480$	−1.74360	+	0.626126i	−0.0795842	+	0.0285786i
$481$	4.08728	−	5.62566i	0.186364	−	0.256508i
$482$	−18.9655	+	12.1993i	−0.863854	+	0.555663i
$483$	0.346812	+	0.762170i	0.0157805	+	0.0346800i
$484$	−21.5228	+	4.55717i	−0.978310	+	0.207144i
$485$	5.20272			0.236243
$486$	−4.28724	−	6.66510i	−0.194473	−	0.302335i
$487$	−10.3282	+	14.2155i	−0.468014	+	0.644165i	−0.976146	−	0.217113i	$-0.930336\pi$
$487$	−10.3282	+	14.2155i	−0.468014	+	0.644165i	0.508133	+	0.861279i	$0.330336\pi$
$488$	0.412283	+	0.0708291i	0.0186632	+	0.00320628i
$489$	−3.35879	−	1.09134i	−0.151890	−	0.0493520i
$490$	10.6962	−	10.9550i	0.483207	−	0.494898i
$491$	17.3589	+	23.8925i	0.783397	+	1.07825i	0.994899	+	0.100876i	$0.0321646\pi$
$491$	17.3589	+	23.8925i	0.783397	+	1.07825i	−0.211502	+	0.977378i	$0.567835\pi$
$492$	0.466018	−	4.09099i	0.0210097	−	0.184436i
$493$	−9.90602	+	3.21866i	−0.446145	+	0.144961i
$494$	−13.8611	−	52.6459i	−0.623642	−	2.36865i
$495$	−6.82840	+	13.5337i	−0.306914	+	0.608295i
$496$	1.71984	−	2.86258i	0.0772231	−	0.128534i
$497$	−16.2613	+	14.8835i	−0.729418	+	0.667618i
$498$	−2.55032	−	0.991731i	−0.114282	−	0.0444405i
$499$	−10.1099	−	13.9151i	−0.452582	−	0.622926i	0.520368	−	0.853942i	$-0.325795\pi$
$499$	−10.1099	−	13.9151i	−0.452582	−	0.622926i	−0.972950	+	0.231017i	$0.925795\pi$
$500$	−23.0608	+	4.69230i	−1.03131	+	0.209846i
$501$	−0.492637	+	1.51618i	−0.0220094	+	0.0677380i
$502$	−1.17355	+	1.43638i	−0.0523779	+	0.0641088i
$503$	7.39146	+	5.37021i	0.329569	+	0.239446i	0.740248	−	0.672334i	$-0.234708\pi$
$503$	7.39146	+	5.37021i	0.329569	+	0.239446i	−0.410679	+	0.911780i	$0.634708\pi$
$504$	−22.0782	−	1.26568i	−0.983439	−	0.0563781i
$505$	−26.6821			−1.18734
$506$	−6.97247	+	0.730070i	−0.309964	+	0.0324556i
$507$	−4.26512			−0.189421
$508$	23.0960	−	25.2060i	1.02472	−	1.11833i
$509$	13.1595	−	18.1124i	0.583283	−	0.802820i	−0.410768	−	0.911740i	$-0.634739\pi$
$509$	13.1595	−	18.1124i	0.583283	−	0.802820i	0.994050	+	0.108920i	$0.0347393\pi$
$510$	−1.18743	+	1.45338i	−0.0525804	+	0.0643567i
$511$	−7.03299	+	0.797214i	−0.311121	+	0.0352667i
$512$	20.5480	−	9.47523i	0.908101	−	0.418750i
$513$	6.82163	−	4.95620i	0.301182	−	0.218822i
$514$	−6.12306	+	15.7459i	−0.270077	+	0.694523i
$515$	−0.986212	+	0.320440i	−0.0434577	+	0.0141203i
$516$	−0.916946	−	1.62061i	−0.0403663	−	0.0713435i
$517$	17.6457	+	34.2952i	0.776057	+	1.50830i
$518$	3.50147	−	2.85753i	0.153846	−	0.125553i
$519$	−0.448686	+	0.145787i	−0.0196951	+	0.00639933i
$520$	24.9231	−	3.61452i	1.09295	−	0.158507i
$521$	19.8593	+	27.3340i	0.870053	+	1.19753i	0.979078	+	0.203486i	$0.0652272\pi$
$521$	19.8593	+	27.3340i	0.870053	+	1.19753i	−0.109025	+	0.994039i	$0.534773\pi$
$522$	−0.608897	+	10.7251i	−0.0266507	+	0.469425i
$523$	−3.70642	+	11.4072i	−0.162070	+	0.498801i	−0.998808	−	0.0488020i	$-0.984460\pi$
$523$	−3.70642	+	11.4072i	−0.162070	+	0.498801i	0.836738	+	0.547603i	$0.184460\pi$
$524$	4.63675	−	10.1750i	0.202557	−	0.444498i
$525$	1.43157	+	0.292112i	0.0624787	+	0.0127488i
$526$	−15.6451	+	10.0635i	−0.682160	+	0.438791i
$527$		−	3.38306i		−	0.147368i
$528$	−1.04190	+	2.60882i	−0.0453429	+	0.113534i
$529$	20.7660			0.902869
$530$	−10.2787	+	6.61165i	−0.446479	+	0.287192i
$531$	−20.7528	−	15.0778i	−0.900597	−	0.654322i
$532$	0.0195535	−	35.3828i	0.000847752	−	1.53404i
$533$	−17.2961	+	53.2318i	−0.749176	+	2.30573i
$534$	2.19352	+	0.124533i	0.0949229	+	0.00538906i
$535$	−17.3213	+	12.5847i	−0.748865	+	0.544082i
$536$	3.09447	+	21.3372i	0.133661	+	0.921627i
$537$	1.28469	−	0.417420i	0.0554383	−	0.0180130i
$538$	5.06151	+	19.2241i	0.218217	+	0.828809i
$539$	−1.68457	−	23.1552i	−0.0725598	−	0.997364i
$540$	1.92083	+	3.39488i	0.0826594	+	0.146093i
$541$	6.75748	+	20.7974i	0.290527	+	0.894150i	0.984687	+	0.174330i	$0.0557758\pi$
$541$	6.75748	+	20.7974i	0.290527	+	0.894150i	−0.694160	+	0.719820i	$0.744224\pi$
$542$	−20.4925	−	7.96885i	−0.880230	−	0.342291i
$543$	−1.58986	−	2.18826i	−0.0682276	−	0.0939072i
$544$	12.8999	−	18.9483i	0.553078	−	0.812401i
$545$	12.9523	+	4.20845i	0.554815	+	0.180270i
$546$	−4.41023	−	1.16377i	−0.188740	−	0.0498050i
$547$	−11.0610	+	15.2242i	−0.472935	+	0.650939i	−0.977128	−	0.212652i	$-0.931790\pi$
$547$	−11.0610	+	15.2242i	−0.472935	+	0.650939i	0.504193	+	0.863591i	$0.331790\pi$
$548$	−4.92601	−	4.51365i	−0.210429	−	0.192814i
$549$		−	0.437067i		−	0.0186536i
$550$	−6.12031	+	10.5911i	−0.260971	+	0.451606i
$551$	−17.1877			−0.732220
$552$	−0.416784	+	0.792239i	−0.0177395	+	0.0337199i
$553$	7.51827	−	36.8451i	0.319709	−	1.56681i
$554$	−21.4875	+	26.3000i	−0.912918	+	1.11738i
$555$	−0.376219	−	0.122241i	−0.0159696	−	0.00518884i
$556$	5.45099	+	26.7894i	0.231174	+	1.13613i
$557$	−12.7413	+	9.25710i	−0.539867	+	0.392236i	−0.824035	−	0.566538i	$-0.808282\pi$
$557$	−12.7413	+	9.25710i	−0.539867	+	0.392236i	0.284169	+	0.958774i	$0.408282\pi$
$558$	−3.25191	−	1.26456i	−0.137664	−	0.0535330i
$559$	7.82181	+	24.0731i	0.330827	+	1.01818i
$560$	16.2618	+	1.86154i	0.687186	+	0.0786643i
$561$	0.456312	+	2.80901i	0.0192655	+	0.118596i
$562$	0.148865	−	0.0391946i	0.00627949	−	0.00165333i
$563$	10.8204	+	33.3016i	0.456024	+	1.40350i	0.869929	+	0.493177i	$0.164164\pi$
$563$	10.8204	+	33.3016i	0.456024	+	1.40350i	−0.413906	+	0.910320i	$0.635836\pi$
$564$	4.89318	+	0.557398i	0.206040	+	0.0234707i
$565$	4.42751	+	6.09394i	0.186267	+	0.256374i
$566$	−0.798780	+	14.0697i	−0.0335752	+	0.591394i
$567$	2.56231	+	22.6046i	0.107607	+	0.949306i
$568$	−23.2260	−	3.99017i	−0.974543	−	0.167424i
$569$	−29.5203	−	21.4478i	−1.23756	−	0.899137i	−0.240123	−	0.970742i	$-0.577188\pi$
$569$	−29.5203	−	21.4478i	−1.23756	−	0.899137i	−0.997433	+	0.0716050i	$0.977188\pi$
$570$	−2.60466	+	1.67542i	−0.109097	+	0.0701754i
$571$		−	26.4918i		−	1.10865i	−0.832301	−	0.554323i	$-0.812977\pi$
$571$		−	26.4918i		−	1.10865i	0.832301	−	0.554323i	$-0.187023\pi$
$572$	20.9499	−	31.9274i	0.875960	−	1.33495i
$573$		−	2.30100i		−	0.0961256i
$574$	−19.6968	+	30.5842i	−0.822128	+	1.27656i
$575$	−2.29118	+	3.15353i	−0.0955487	+	0.131511i
$576$	−13.3919	−	19.4825i	−0.557995	−	0.811772i
$577$	35.6604	+	11.5868i	1.48456	+	0.482363i	0.935472	−	0.353400i	$-0.114975\pi$
$577$	35.6604	+	11.5868i	1.48456	+	0.482363i	0.549090	+	0.835764i	$0.314975\pi$
$578$	−0.0464812	+	0.818720i	−0.00193336	+	0.0340543i
$579$	−3.31337	+	2.40730i	−0.137699	+	0.100044i
$580$	0.899901	−	7.89989i	0.0373664	−	0.328025i
$581$	16.3228	+	17.8337i	0.677182	+	0.739868i
$582$	−0.256485	−	0.974155i	−0.0106317	−	0.0403800i
$583$	−2.82653	+	18.3151i	−0.117063	+	0.758534i
$584$	−5.28018	−	5.41989i	−0.218495	−	0.224277i
$585$	−8.13094	−	25.0245i	−0.336173	−	1.03463i
$586$	−2.61821	+	6.73294i	−0.108157	+	0.278135i
$587$	−2.86111	+	2.07872i	−0.118091	+	0.0857980i	−0.645263	−	0.763960i	$-0.723252\pi$
$587$	−2.86111	+	2.07872i	−0.118091	+	0.0857980i	0.527172	+	0.849758i	$0.323252\pi$
$588$	−2.57852	−	1.46270i	−0.106337	−	0.0603207i
$589$	1.72511	−	5.30934i	0.0710819	−	0.218767i
$590$	14.7030	+	12.0126i	0.605312	+	0.494549i
$591$	2.22547	+	1.61690i	0.0915438	+	0.0665105i
$592$	4.70775	+	1.08665i	0.193487	+	0.0446610i
$593$			15.8993i			0.652906i	0.945213	+	0.326453i	$0.105854\pi$
$593$			15.8993i			0.652906i	−0.945213	+	0.326453i	$0.894146\pi$
$594$	5.78491	+	1.23199i	0.237358	+	0.0505493i
$595$	15.0925	−	6.86756i	0.618731	−	0.281543i
$596$	−15.0955	−	13.8318i	−0.618334	−	0.566574i
$597$	−0.842456	−	0.612080i	−0.0344794	−	0.0250508i
$598$	7.69918	−	9.42353i	0.314843	−	0.385357i
$599$	18.5992	+	6.04326i	0.759945	+	0.246921i	0.663255	−	0.748394i	$-0.269175\pi$
$599$	18.5992	+	6.04326i	0.759945	+	0.246921i	0.0966898	+	0.995315i	$0.469175\pi$
$600$	0.690877	+	1.40084i	0.0282049	+	0.0571892i
$601$	11.5747	+	15.9312i	0.472143	+	0.649849i	0.976971	−	0.213371i	$-0.0684442\pi$
$601$	11.5747	+	15.9312i	0.472143	+	0.649849i	−0.504828	+	0.863220i	$0.668444\pi$
$602$	0.923407	+	16.4253i	0.0376353	+	0.669445i
$603$	21.4240	−	6.96107i	0.872452	−	0.283477i
$604$	8.72995	+	15.4293i	0.355216	+	0.627811i
$605$	−5.38526	−	16.1381i	−0.218942	−	0.656108i
$606$	1.31538	+	4.99595i	0.0534338	+	0.202947i
$607$	−6.55959	−	20.1883i	−0.266245	−	0.819419i	−0.991404	−	0.130837i	$-0.958233\pi$
$607$	−6.55959	−	20.1883i	−0.266245	−	0.819419i	0.725158	−	0.688582i	$-0.241767\pi$
$608$	29.9072	−	23.1593i	1.21290	−	0.939232i
$609$	−0.709834	+	1.25295i	−0.0287639	+	0.0507719i
$610$	−0.0183363	+	0.322975i	−0.000742414	+	0.0130769i
$611$	−63.6699	−	20.6876i	−2.57581	−	0.836931i
$612$	−21.7935	−	9.93129i	−0.880950	−	0.401449i
$613$	30.7765	+	22.3604i	1.24305	+	0.903130i	0.997798	−	0.0663288i	$-0.0211286\pi$
$613$	30.7765	+	22.3604i	1.24305	+	0.903130i	0.245254	+	0.969459i	$0.421129\pi$
$614$	22.7037	+	35.2959i	0.916245	+	1.42443i
$615$	3.18408			0.128395
$616$	18.4601	−	16.5899i	0.743777	−	0.668428i
$617$	−9.22344			−0.371322			−0.185661	−	0.982614i	$-0.559443\pi$
$617$	−9.22344			−0.371322			−0.185661	+	0.982614i	$0.559443\pi$
$618$	0.108618	+	0.168861i	0.00436924	+	0.00679259i
$619$	−11.9077	−	8.65144i	−0.478610	−	0.347731i	0.322177	−	0.946679i	$-0.395585\pi$
$619$	−11.9077	−	8.65144i	−0.478610	−	0.347731i	−0.800787	+	0.598949i	$0.795585\pi$
$620$	2.34998	+	1.07089i	0.0943775	+	0.0430078i
$621$	1.79253	+	0.582428i	0.0719317	+	0.0233720i
$622$	1.87938	−	33.1033i	0.0753561	−	1.32732i
$623$	−16.8891	−	9.56820i	−0.676647	−	0.383342i
$624$	−1.90545	−	4.48841i	−0.0762791	−	0.179680i
$625$	−1.59421	−	4.90649i	−0.0637686	−	0.196259i
$626$	−1.67233	−	6.35166i	−0.0668396	−	0.253863i
$627$	−0.716252	+	4.64111i	−0.0286044	+	0.185348i
$628$	−17.3467	−	30.6586i	−0.692209	−	1.22341i
$629$	4.65500	−	1.51250i	0.185607	−	0.0603073i
$630$	−0.959901	−	17.0744i	−0.0382434	−	0.680262i
$631$	4.79828	+	6.60426i	0.191016	+	0.262912i	0.893774	−	0.448518i	$-0.148048\pi$
$631$	4.79828	+	6.60426i	0.191016	+	0.262912i	−0.702757	+	0.711430i	$0.748048\pi$
$632$	36.0543	−	17.7815i	1.43416	−	0.707310i
$633$	1.84265	+	0.598713i	0.0732388	+	0.0237967i
$634$	−7.34360	+	8.98832i	−0.291651	+	0.356972i
$635$	21.3884	+	15.5396i	0.848772	+	0.616669i
$636$	1.74469	+	1.59864i	0.0691814	+	0.0633902i
$637$	30.3833	+	26.4731i	1.20383	+	1.04890i
$638$	−8.06375	−	8.96277i	−0.319247	−	0.354840i
$639$			24.6222i			0.974040i
$640$	9.07871	+	14.9586i	0.358868	+	0.591292i
$641$	25.4019	+	18.4556i	1.00332	+	0.728951i	0.962797	−	0.270227i	$-0.0870988\pi$
$641$	25.4019	+	18.4556i	1.00332	+	0.728951i	0.0405191	+	0.999179i	$0.487099\pi$
$642$	3.21026	+	2.62283i	0.126699	+	0.103515i
$643$	8.52755	−	26.2451i	0.336294	−	1.03501i	−0.629788	−	0.776767i	$-0.716858\pi$
$643$	8.52755	−	26.2451i	0.336294	−	1.03501i	0.966081	−	0.258238i	$-0.0831419\pi$
$644$	6.40109	−	4.64526i	0.252238	−	0.183049i
$645$	1.16494	−	0.846375i	0.0458693	−	0.0333260i
$646$	13.8880	−	35.7140i	0.546414	−	1.40515i
$647$	5.94191	+	18.2873i	0.233601	+	0.718949i	0.997304	+	0.0733814i	$0.0233790\pi$
$647$	5.94191	+	18.2873i	0.233601	+	0.718949i	−0.763703	+	0.645567i	$0.776621\pi$
$648$	−17.4200	+	16.9709i	−0.684322	+	0.666681i
$649$	28.4171	−	4.61625i	1.11547	−	0.181203i
$650$	−5.40608	−	20.5328i	−0.212044	−	0.805364i
$651$	−0.315794	−	0.345027i	−0.0123770	−	0.0135227i
$652$	−3.77535	+	33.1424i	−0.147854	+	1.29796i
$653$	4.62724	−	3.36189i	0.181078	−	0.131561i	−0.493554	−	0.869715i	$-0.664302\pi$
$653$	4.62724	−	3.36189i	0.181078	−	0.131561i	0.674632	+	0.738154i	$0.264302\pi$
$654$	0.149464	−	2.63265i	0.00584449	−	0.102945i
$655$	8.22376	+	2.67206i	0.321329	+	0.104406i
$656$	−38.7415	+	3.39117i	−1.51260	+	0.132403i
$657$	−4.64690	+	6.39591i	−0.181293	+	0.249528i
$658$	−36.5814	−	23.5591i	−1.42609	−	0.918429i
$659$			9.18568i			0.357823i	0.983865	+	0.178912i	$0.0572576\pi$
$659$			9.18568i			0.357823i	−0.983865	+	0.178912i	$0.942742\pi$
$660$	−2.09567	−	0.572204i	−0.0815738	−	0.0222730i
$661$		−	0.696054i		−	0.0270734i	−0.999908	−	0.0135367i	$-0.995691\pi$
$661$		−	0.696054i		−	0.0270734i	0.999908	−	0.0135367i	$-0.00430899\pi$
$662$	9.16606	−	5.89595i	0.356249	−	0.229153i
$663$	−3.99632	−	2.90350i	−0.155204	−	0.112763i
$664$	−4.37602	+	25.4720i	−0.169822	+	0.988505i
$665$	27.1879	−	3.08185i	1.05430	−	0.119509i
$666$	0.286130	−	5.03990i	0.0110873	−	0.195292i
$667$	−2.25822	−	3.10817i	−0.0874385	−	0.120349i
$668$	14.9607	+	1.70422i	0.578846	+	0.0659382i
$669$	−1.58247	−	4.87034i	−0.0611818	−	0.188298i
$670$	−16.1235	+	4.24516i	−0.622906	+	0.164005i
$671$	0.348226	+	0.345479i	0.0134431	+	0.0133371i
$672$	−0.453126	−	3.13662i	−0.0174797	−	0.120998i
$673$	9.72940	+	29.9440i	0.375041	+	1.15426i	0.943451	+	0.331512i	$0.107559\pi$
$673$	9.72940	+	29.9440i	0.375041	+	1.15426i	−0.568410	+	0.822745i	$0.692441\pi$
$674$	0.676018	+	0.262881i	0.0260392	+	0.0101258i
$675$	2.66055	−	1.93300i	0.102405	−	0.0744014i
$676$	8.03230	+	39.4755i	0.308935	+	1.51829i
$677$	21.6788	+	7.04387i	0.833184	+	0.270718i	0.694386	−	0.719603i	$-0.255676\pi$
$677$	21.6788	+	7.04387i	0.833184	+	0.270718i	0.138798	+	0.990321i	$0.455676\pi$
$678$	0.922759	−	1.12943i	0.0354384	−	0.0433754i
$679$	−1.77940	+	8.72036i	−0.0682870	+	0.334657i
$680$	15.6879	+	8.25314i	0.601603	+	0.316493i
$681$	−4.74416			−0.181797
$682$	3.57798	−	1.59134i	0.137008	−	0.0609355i
$683$			12.1202i			0.463765i	0.972744	+	0.231883i	$0.0744886\pi$
$683$			12.1202i			0.463765i	−0.972744	+	0.231883i	$0.925511\pi$
$684$	−29.1383	−	26.6991i	−1.11413	−	1.02087i
$685$	3.03690	−	4.17993i	0.116034	−	0.159707i
$686$	14.7037	+	21.6749i	0.561388	+	0.827553i
$687$	0.258807	+	0.0840916i	0.00987411	+	0.00320829i
$688$	−13.2726	+	11.5388i	−0.506015	+	0.439911i
$689$	−18.9075	−	26.0239i	−0.720318	−	0.991432i
$690$	−0.645193	−	0.250893i	−0.0245621	−	0.00955135i
$691$	6.24084	+	19.2073i	0.237413	+	0.730682i	0.996792	+	0.0800334i	$0.0255027\pi$
$691$	6.24084	+	19.2073i	0.237413	+	0.730682i	−0.759379	+	0.650648i	$0.774497\pi$
$692$	2.19431	+	3.87823i	0.0834152	+	0.147428i
$693$	−20.3487	−	16.0739i	−0.772983	−	0.610597i
$694$	−1.79171	−	6.80507i	−0.0680122	−	0.258317i
$695$	−20.1065	+	6.53299i	−0.762682	+	0.247810i
$696$	−1.52354	+	0.220954i	−0.0577495	+	0.00837524i
$697$	−31.8728	+	23.1570i	−1.20727	+	0.877132i
$698$	20.8583	+	1.18419i	0.789497	+	0.0448221i
$699$	0.371753	−	1.14414i	0.0140610	−	0.0432753i
$700$	0.00762620	−	13.7999i	0.000288243	−	0.521587i
$701$	−5.66180	−	4.11354i	−0.213843	−	0.155366i	0.475708	−	0.879603i	$-0.342192\pi$
$701$	−5.66180	−	4.11354i	−0.213843	−	0.155366i	−0.689551	+	0.724237i	$0.742192\pi$
$702$	−8.63448	+	5.55402i	−0.325887	+	0.209623i
$703$	8.07677			0.304621
$704$	26.1080	+	4.73017i	0.983981	+	0.178275i
$705$			3.80844i			0.143434i
$706$	−25.2041	+	16.2122i	−0.948568	+	0.610155i
$707$	9.12563	−	44.7223i	0.343205	−	1.68196i
$708$	1.52440	−	3.34518i	0.0572904	−	0.125720i
$709$	8.31805	−	25.6003i	0.312391	−	0.961440i	−0.664424	−	0.747356i	$-0.731323\pi$
$709$	8.31805	−	25.6003i	0.312391	−	0.961440i	0.976815	−	0.214084i	$-0.0686768\pi$
$710$	1.03298	−	18.1949i	0.0387669	−	0.682841i
$711$	−24.6881	−	33.9803i	−0.925877	−	1.27436i
$712$	−2.97835	−	20.5365i	−0.111618	−	0.769638i
$713$	1.18678	−	0.385608i	0.0444452	−	0.0144411i
$714$	−2.02991	−	2.48735i	−0.0759677	−	0.0930868i
$715$	26.3649	+	13.3024i	0.985992	+	0.497480i
$716$	−6.28280	−	11.1042i	−0.234799	−	0.414985i
$717$	4.44616	−	1.44464i	0.166045	−	0.0539512i
$718$	2.60758	−	6.70561i	0.0973141	−	0.250251i
$719$	39.7752	−	28.8984i	1.48337	−	1.07773i	0.506912	−	0.861998i	$-0.330787\pi$
$719$	39.7752	−	28.8984i	1.48337	−	1.07773i	0.976453	−	0.215730i	$-0.0692131\pi$
$720$	13.7972	−	11.9948i	0.514191	−	0.447019i
$721$	−0.199797	−	1.76260i	−0.00744083	−	0.0656427i
$722$	23.0065	−	28.1592i	0.856213	−	1.04798i
$723$	−1.98462	+	2.73160i	−0.0738089	+	0.101589i
$724$	−17.2592	+	18.8359i	−0.641433	+	0.700032i
$725$	−6.70349			−0.248962
$726$	−2.75621	+	1.80392i	−0.102293	+	0.0669497i
$727$	6.38105			0.236660			0.118330	−	0.992974i	$-0.462246\pi$
$727$	6.38105			0.236660			0.118330	+	0.992974i	$0.462246\pi$
$728$	−2.46567	+	43.0103i	−0.0913838	+	1.59407i
$729$	19.9089	+	14.4647i	0.737368	+	0.535729i
$730$	3.70221	−	4.53138i	0.137025	−	0.167714i
$731$	−5.50561	+	16.9445i	−0.203632	+	0.626715i
$732$	0.0613777	−	0.0124889i	0.00226859	−	0.000461601i
$733$	−29.1652	−	40.1425i	−1.07724	−	1.48270i	−0.862520	−	0.506022i	$-0.831115\pi$
$733$	−29.1652	−	40.1425i	−1.07724	−	1.48270i	−0.214722	−	0.976675i	$-0.568885\pi$
$734$	26.9459	+	10.4783i	0.994590	+	0.386762i
$735$	0.898174	−	2.10922i	0.0331296	−	0.0777997i
$736$	8.11743	+	2.36553i	0.299213	+	0.0871945i
$737$	−11.3884	+	22.5716i	−0.419498	+	0.831435i
$738$	10.3455	+	39.2931i	0.380822	+	1.44640i
$739$	37.3107	−	12.1230i	1.37250	−	0.445951i	0.472300	−	0.881438i	$-0.343424\pi$
$739$	37.3107	−	12.1230i	1.37250	−	0.445951i	0.900195	+	0.435487i	$0.143424\pi$
$740$	−0.422878	+	3.71229i	−0.0155453	+	0.136466i
$741$	−4.79122	−	6.59455i	−0.176010	−	0.242257i
$742$	−7.56645	−	19.4896i	−0.277773	−	0.715486i
$743$	30.1625	+	9.80040i	1.10656	+	0.359542i	0.804622	−	0.593787i	$-0.202368\pi$
$743$	30.1625	+	9.80040i	1.10656	+	0.359542i	0.301934	+	0.953329i	$0.402368\pi$
$744$	0.0846622	−	0.492803i	0.00310387	−	0.0180670i
$745$	9.30640	−	12.8092i	0.340960	−	0.469292i
$746$	−9.15906	−	14.2390i	−0.335337	−	0.521327i
$747$	27.0032			0.987995
$748$	25.1392	−	9.51344i	0.919181	−	0.347846i
$749$	−15.1693	−	33.3367i	−0.554272	−	1.21809i
$750$	−2.96350	+	1.90623i	−0.108212	+	0.0696058i
$751$	2.76888	−	3.81103i	0.101038	−	0.139067i	−0.755504	−	0.655143i	$-0.772608\pi$
$751$	2.76888	−	3.81103i	0.101038	−	0.139067i	0.856542	+	0.516077i	$0.172608\pi$
$752$	−4.05614	−	46.3383i	−0.147912	−	1.68978i
$753$	−0.0858214	+	0.264131i	−0.00312751	+	0.00962547i
$754$	20.8935	+	1.18619i	0.760896	+	0.0431984i
$755$	−11.0910	+	8.05806i	−0.403642	+	0.293263i
$756$	−6.34717	+	2.05844i	−0.230845	+	0.0748649i
$757$	−11.7230	−	36.0798i	−0.426081	−	1.31134i	−0.901955	−	0.431830i	$-0.857868\pi$
$757$	−11.7230	−	36.0798i	−0.426081	−	1.31134i	0.475874	−	0.879513i	$-0.342132\pi$
$758$	3.46791	+	13.1715i	0.125960	+	0.478409i
$759$	−0.933390	+	0.480251i	−0.0338799	+	0.0174320i
$760$	20.4119	+	20.9521i	0.740419	+	0.760011i
$761$	4.58592	−	1.49006i	0.166239	−	0.0540145i	−0.224715	−	0.974425i	$-0.572145\pi$
$761$	4.58592	−	1.49006i	0.166239	−	0.0540145i	0.390954	+	0.920410i	$0.372145\pi$
$762$	1.85521	−	4.77083i	0.0672073	−	0.172829i
$763$	−11.4837	+	20.2702i	−0.415738	+	0.733831i
$764$	−21.2968	+	4.33337i	−0.770490	+	0.156776i
$765$	5.72319	−	17.6142i	0.206923	−	0.636842i
$766$	−5.87349	+	7.18896i	−0.212218	+	0.259748i
$767$	−29.3730	+	40.4285i	−1.06060	+	1.45979i
$768$	2.35329	−	2.43733i	0.0849170	−	0.0879497i
$769$		−	15.1547i		−	0.546493i	−0.961944	−	0.273246i	$-0.911903\pi$
$769$		−	15.1547i		−	0.546493i	0.961944	−	0.273246i	$-0.0880975\pi$
$770$	14.3625	+	12.7317i	0.517590	+	0.458818i
$771$			2.52962i			0.0911021i
$772$	28.5206	+	26.1331i	1.02648	+	0.940551i
$773$	−3.36352	+	4.62949i	−0.120977	+	0.166511i	−0.865210	−	0.501409i	$-0.832815\pi$
$773$	−3.36352	+	4.62949i	−0.120977	+	0.166511i	0.744233	+	0.667920i	$0.232815\pi$
$774$	14.2297	+	11.6259i	0.511476	+	0.417884i
$775$	0.672822	−	2.07073i	0.0241685	−	0.0743829i
$776$	−8.53321	+	4.20847i	−0.306324	+	0.151075i
$777$	0.333562	−	0.588780i	0.0119665	−	0.0211224i
$778$	27.2112	+	10.5815i	0.975567	+	0.379365i
$779$	−61.8292	+	20.0895i	−2.21526	+	0.719782i
$780$	3.28188	−	1.85689i	0.117510	−	0.0664874i
$781$	−19.6174	−	19.4626i	−0.701964	−	0.696427i
$782$	8.28309	−	2.18085i	0.296203	−	0.0779871i
$783$	1.00162	+	3.08268i	0.0357950	+	0.110166i
$784$	−8.68190	+	26.6200i	−0.310068	+	0.950714i
$785$	22.0382	−	16.0117i	0.786576	−	0.571481i
$786$	0.0948986	−	1.67154i	0.00338492	−	0.0596220i
$787$	1.79508	−	5.52470i	0.0639878	−	0.196934i	−0.913952	−	0.405823i	$-0.866985\pi$
$787$	1.79508	−	5.52470i	0.0639878	−	0.196934i	0.977939	+	0.208889i	$0.0669848\pi$
$788$	10.7740	−	23.6428i	0.383808	−	0.842239i
$789$	−1.63717	+	2.25337i	−0.0582848	+	0.0802221i
$790$	16.8180	+	26.1458i	0.598357	+	0.930228i
$791$	−11.7284	+	5.33681i	−0.417015	+	0.189755i
$792$	0.252178	−	27.7207i	0.00896077	−	0.985013i
$793$	−0.851447			−0.0302358
$794$	20.8727	−	13.4261i	0.740745	−	0.476475i
$795$	−1.07561	+	1.48044i	−0.0381478	+	0.0525059i
$796$	−4.07851	+	8.95001i	−0.144559	+	0.317225i
$797$	−11.5649	−	3.75768i	−0.409651	−	0.133104i	0.0969397	−	0.995290i	$-0.469095\pi$
$797$	−11.5649	−	3.75768i	−0.409651	−	0.133104i	−0.506591	+	0.862186i	$0.669095\pi$
$798$	−1.91736	−	4.93873i	−0.0678740	−	0.174829i
$799$	−27.6977	−	38.1227i	−0.979876	−	1.34868i
$800$	11.6643	−	9.03251i	0.412396	−	0.319348i
$801$	−20.6200	+	6.69985i	−0.728573	+	0.236728i
$802$	−46.8903	+	12.3457i	−1.65575	+	0.435943i
$803$	−1.42270	−	8.75798i	−0.0502060	−	0.309062i
$804$	1.58973	+	2.80968i	0.0560653	+	0.0990899i
$805$	4.12942	+	4.51167i	0.145543	+	0.159016i
$806$	−2.46347	+	6.33502i	−0.0867722	+	0.223142i
$807$	1.74955	+	2.40805i	0.0615872	+	0.0847675i
$808$	43.7625	−	21.5831i	1.53956	−	0.759291i
$809$	−0.0494770	+	0.152275i	−0.00173952	+	0.00535369i	−0.951923	−	0.306339i	$-0.900896\pi$
$809$	−0.0494770	+	0.152275i	−0.00173952	+	0.00535369i	0.950183	+	0.311693i	$0.100896\pi$
$810$	−14.5642	−	11.8992i	−0.511735	−	0.418096i
$811$	−4.55142	−	3.30680i	−0.159822	−	0.116117i	0.505000	−	0.863119i	$-0.331493\pi$
$811$	−4.55142	−	3.30680i	−0.159822	−	0.116117i	−0.664822	+	0.747002i	$0.731493\pi$
$812$	12.9334	+	4.21021i	0.453872	+	0.147749i
$813$	−3.29218			−0.115462
$814$	3.78929	+	4.21175i	0.132814	+	0.147622i
$815$	−25.7952			−0.903568
$816$	0.771928	−	3.34426i	0.0270229	−	0.117073i
$817$	−17.2809	+	23.7851i	−0.604582	+	0.832136i
$818$	10.1051	+	8.25600i	0.353315	+	0.288664i
$819$	44.7248	−	5.06971i	1.56281	−	0.177150i
$820$	−5.99644	−	29.4701i	−0.209405	−	1.02914i
$821$	23.4975	−	17.0719i	0.820067	−	0.595814i	−0.0966647	−	0.995317i	$-0.530817\pi$
$821$	23.4975	−	17.0719i	0.820067	−	0.595814i	0.916732	+	0.399503i	$0.130817\pi$
$822$	−0.932364	−	0.362565i	−0.0325199	−	0.0126459i
$823$	−19.4674	+	6.32534i	−0.678590	+	0.220487i	−0.627978	−	0.778231i	$-0.716117\pi$
$823$	−19.4674	+	6.32534i	−0.678590	+	0.220487i	−0.0506123	+	0.998718i	$0.516117\pi$
$824$	1.35833	−	1.32331i	0.0473196	−	0.0460998i
$825$	−0.279351	+	1.81011i	−0.00972574	+	0.0630201i
$826$	−25.1631	+	20.5355i	−0.875536	+	0.714520i
$827$	21.4752	−	6.97772i	0.746766	−	0.242639i	0.0891772	−	0.996016i	$-0.471576\pi$
$827$	21.4752	−	6.97772i	0.746766	−	0.242639i	0.657589	+	0.753377i	$0.271576\pi$
$828$	0.999835	−	8.77717i	0.0347467	−	0.305028i
$829$	−10.5131	−	14.4700i	−0.365133	−	0.502563i	0.586437	−	0.809995i	$-0.300530\pi$
$829$	−10.5131	−	14.4700i	−0.365133	−	0.502563i	−0.951570	+	0.307432i	$0.900530\pi$
$830$	−19.9543	−	1.13287i	−0.692624	−	0.0393223i
$831$	−1.57138	+	4.83622i	−0.0545107	+	0.167767i
$832$	−37.9537	+	26.0886i	−1.31581	+	0.904459i
$833$	6.34902	+	27.6456i	0.219980	+	0.957862i
$834$	2.21445	+	3.44266i	0.0766801	+	0.119210i
$835$			11.6441i			0.402962i
$836$	44.3044	−	2.11116i	1.53230	−	0.0730161i
$837$	−1.05278			−0.0363894
$838$	4.85579	+	7.54899i	0.167741	+	0.260776i
$839$	−10.5724	−	7.68128i	−0.364999	−	0.265187i	0.390135	−	0.920758i	$-0.372428\pi$
$839$	−10.5724	−	7.68128i	−0.364999	−	0.265187i	−0.755134	+	0.655570i	$0.772428\pi$
$840$	2.37035	−	0.622689i	0.0817849	−	0.0214848i
$841$	−6.91980	+	21.2969i	−0.238614	+	0.734378i
$842$	−1.84151	+	32.4364i	−0.0634627	+	1.11783i
$843$	0.0186472	−	0.0135480i	0.000642242	−	0.000466616i
$844$	2.07118	−	18.1821i	0.0712929	−	0.625852i
$845$	−29.6278	+	9.62667i	−1.01923	+	0.331167i
$846$	−46.9980	+	12.3741i	−1.61582	+	0.425430i
$847$	28.8912	−	3.50688i	0.992714	−	0.120498i
$848$	11.5104	−	19.1585i	0.395270	−	0.657905i
$849$	0.652041	+	2.00678i	0.0223780	+	0.0688724i
$850$	5.41654	−	13.9291i	0.185786	−	0.477763i
$851$	1.06117	+	1.46058i	0.0363765	+	0.0500680i
$852$	−3.45773	+	0.703562i	−0.118460	+	0.0241036i
$853$	−21.4356	−	6.96485i	−0.733941	−	0.238472i	−0.0818842	−	0.996642i	$-0.526094\pi$
$853$	−21.4356	−	6.96485i	−0.733941	−	0.238472i	−0.652057	+	0.758170i	$0.726094\pi$
$854$	−0.535073	−	0.141196i	−0.0183098	−	0.00483161i
$855$	17.9639	−	24.7251i	0.614351	−	0.845581i
$856$	18.2297	−	34.6518i	0.623080	−	1.18438i
$857$			37.1469i			1.26891i	0.772958	+	0.634457i	$0.218776\pi$
$857$			37.1469i			1.26891i	−0.772958	+	0.634457i	$0.781224\pi$
$858$	1.19098	−	5.59234i	0.0406595	−	0.190919i
$859$	10.4690			0.357199			0.178600	−	0.983922i	$-0.442843\pi$
$859$	10.4690			0.357199			0.178600	+	0.983922i	$0.442843\pi$
$860$	−10.0274	−	9.18805i	−0.341933	−	0.313310i
$861$	−1.08900	+	5.33690i	−0.0371130	+	0.181881i
$862$	−23.7056	−	19.3678i	−0.807416	−	0.659671i
$863$	5.25298	+	1.70680i	0.178814	+	0.0581001i	0.397055	−	0.917795i	$-0.370032\pi$
$863$	5.25298	+	1.70680i	0.178814	+	0.0581001i	−0.218242	+	0.975895i	$0.570032\pi$
$864$	−5.89656	−	4.01435i	−0.200605	−	0.136571i
$865$	−2.78777	+	2.02543i	−0.0947869	+	0.0688667i
$866$	−8.91030	+	22.9136i	−0.302784	+	0.778634i
$867$	0.0379425	+	0.116775i	0.00128859	+	0.00396588i
$868$	−2.59866	+	3.57259i	−0.0882041	+	0.121262i
$869$	46.5879	+	7.18981i	1.58039	+	0.243898i
$870$	−0.303116	−	1.15126i	−0.0102766	−	0.0390315i
$871$	−13.5608	−	41.7359i	−0.459491	−	1.41417i
$872$	−24.6478	+	3.57460i	−0.834681	+	0.121051i
$873$	5.84311	+	8.04234i	0.197759	+	0.272192i
$874$	14.1115	+	0.801151i	0.477328	+	0.0270993i
$875$	30.9336	−	3.50643i	1.04575	−	0.118539i
$876$	−1.03097	−	0.469811i	−0.0348331	−	0.0158734i
$877$	−30.3915	−	22.0807i	−1.02625	−	0.745614i	−0.0586947	−	0.998276i	$-0.518694\pi$
$877$	−30.3915	−	22.0807i	−1.02625	−	0.745614i	−0.967555	+	0.252662i	$0.918694\pi$
$878$	21.5853	+	33.5573i	0.728469	+	1.13250i
$879$			1.08166i			0.0364836i
$880$	−1.34932	+	20.4739i	−0.0454855	+	0.690177i
$881$			41.7388i			1.40622i	0.711083	+	0.703109i	$0.248205\pi$
$881$			41.7388i			1.40622i	−0.711083	+	0.703109i	$0.751795\pi$
$882$	28.9471	+	4.23078i	0.974698	+	0.142458i
$883$	12.8719	−	17.7167i	0.433174	−	0.596213i	−0.535504	−	0.844533i	$-0.679878\pi$
$883$	12.8719	−	17.7167i	0.433174	−	0.596213i	0.968678	+	0.248319i	$0.0798783\pi$
$884$	−19.3471	+	42.4558i	−0.650712	+	1.42794i
$885$	2.70368	+	0.878478i	0.0908832	+	0.0295297i
$886$	5.18751	+	0.294510i	0.174278	+	0.00989427i
$887$	−27.1246	+	19.7072i	−0.910754	+	0.661702i	−0.941205	−	0.337835i	$-0.890306\pi$
$887$	−27.1246	+	19.7072i	−0.910754	+	0.661702i	0.0304514	+	0.999536i	$0.490306\pi$
$888$	0.715935	−	0.103830i	0.0240252	−	0.00348430i
$889$	−33.3612	+	30.5347i	−1.11890	+	1.02410i
$890$	15.5185	−	4.08585i	0.520180	−	0.136958i
$891$	−28.1489	+	4.57268i	−0.943024	+	0.153191i
$892$	−42.0970	+	23.8185i	−1.40951	+	0.797504i
$893$	−24.0288	−	73.9532i	−0.804095	−	2.47475i
$894$	−2.85718	−	1.11106i	−0.0955582	−	0.0371594i
$895$	7.98199	−	5.79926i	0.266809	−	0.193848i
$896$	−28.1775	+	10.1009i	−0.941344	+	0.337449i
$897$	0.563041	−	1.73286i	0.0187994	−	0.0578585i
$898$	−20.4772	+	25.0634i	−0.683332	+	0.836376i
$899$	1.73613	+	1.26137i	0.0579032	+	0.0420692i
$900$	−11.3644	−	10.4131i	−0.378815	−	0.347104i
$901$		−	22.6419i		−	0.754311i
$902$	−39.4837	−	22.8166i	−1.31466	−	0.759709i
$903$	1.02020	+	2.24204i	0.0339502	+	0.0746104i
$904$	−12.1911	−	6.41355i	−0.405471	−	0.213311i
$905$	−15.9831	−	11.6124i	−0.531297	−	0.386010i
$906$	2.05556	+	1.67942i	0.0682913	+	0.0557951i
$907$	−50.9129	−	16.5426i	−1.69053	−	0.549288i	−0.703626	−	0.710570i	$-0.748437\pi$
$907$	−50.9129	−	16.5426i	−1.69053	−	0.549288i	−0.986908	+	0.161282i	$0.948437\pi$
$908$	8.93446	+	43.9093i	0.296500	+	1.45718i
$909$	−29.9663	−	41.2451i	−0.993920	−	1.36801i
$910$	−33.2626	+	1.86998i	−1.10264	+	0.0619891i
$911$	21.6108	−	7.02178i	0.715999	−	0.232642i	0.0717111	−	0.997425i	$-0.477154\pi$
$911$	21.6108	−	7.02178i	0.715999	−	0.232642i	0.644287	+	0.764783i	$0.277154\pi$
$912$	2.91678	−	4.85483i	0.0965844	−	0.160759i
$913$	−21.3446	+	21.5144i	−0.706404	+	0.712021i
$914$	50.1913	−	13.2149i	1.66018	−	0.437108i
$915$	0.0149678	+	0.0460663i	0.000494821	+	0.00152290i
$916$	0.290905	−	2.55374i	0.00961177	−	0.0843780i
$917$	−7.29133	+	12.8701i	−0.240781	+	0.425009i
$918$	−7.21476	−	0.409604i	−0.238123	−	0.0135189i
$919$	26.3208	+	8.55214i	0.868243	+	0.282109i	0.709067	−	0.705141i	$-0.249116\pi$
$919$	26.3208	+	8.55214i	0.868243	+	0.282109i	0.159176	+	0.987250i	$0.449116\pi$
$920$	−1.10707	+	6.44404i	−0.0364989	+	0.212454i
$921$	5.08368	+	3.69351i	0.167513	+	0.121705i
$922$	−33.0788	+	21.2775i	−1.08939	+	0.700737i
$923$	47.9664			1.57883
$924$	1.67583	−	3.31689i	0.0551307	−	0.109118i
$925$	3.15008			0.103574
$926$	1.46282	−	0.940941i	0.0480713	−	0.0309212i
$927$	−1.60294	−	1.16460i	−0.0526474	−	0.0382506i
$928$	4.91423	+	13.6849i	0.161318	+	0.449229i
$929$	−25.0385	−	8.13551i	−0.821488	−	0.266918i	−0.132032	−	0.991245i	$-0.542150\pi$
$929$	−25.0385	−	8.13551i	−0.821488	−	0.266918i	−0.689456	+	0.724328i	$0.742150\pi$
$930$	0.386053	+	0.0219174i	0.0126592	+	0.000718700i
$931$	−4.13310	+	46.6242i	−0.135457	+	1.52805i
$932$	−11.2896	−	1.28604i	−0.369804	−	0.0421255i
$933$	−1.53413	−	4.72156i	−0.0502251	−	0.154577i
$934$	−20.9457	+	5.51479i	−0.685364	+	0.180449i
$935$	9.50992	+	18.4830i	0.311008	+	0.604457i
$936$	33.5782	+	34.4667i	1.09754	+	1.12658i
$937$	56.9498	−	18.5041i	1.86047	−	0.604503i	0.865928	−	0.500169i	$-0.166729\pi$
$937$	56.9498	−	18.5041i	1.86047	−	0.604503i	0.994542	−	0.104335i	$-0.0332713\pi$
$938$	−1.60093	−	28.4768i	−0.0522721	−	0.929801i
$939$	−0.578054	−	0.795623i	−0.0188641	−	0.0259642i
$940$	35.2488	−	7.17226i	1.14969	−	0.233933i
$941$	−22.0307	−	7.15820i	−0.718179	−	0.233351i	−0.0729456	−	0.997336i	$-0.523240\pi$
$941$	−22.0307	−	7.15820i	−0.718179	−	0.233351i	−0.645234	+	0.763985i	$0.723240\pi$
$942$	−4.08447	−	3.33707i	−0.133079	−	0.108728i
$943$	−11.7564	−	8.54153i	−0.382842	−	0.278151i
$944$	−33.8320	−	7.80915i	−1.10114	−	0.254166i
$945$	−2.13713	−	4.69666i	−0.0695209	−	0.152782i
$946$	−20.5106	+	2.14761i	−0.666856	+	0.0698249i
$947$		−	24.1558i		−	0.784959i	−0.919761	−	0.392479i	$-0.871617\pi$
$947$		−	24.1558i		−	0.784959i	0.919761	−	0.392479i	$-0.128383\pi$
$948$	4.06644	−	4.43794i	0.132072	−	0.144138i
$949$	12.4598	+	9.05260i	0.404463	+	0.293860i
$950$	15.6035	−	19.0981i	0.506243	−	0.619625i
$951$	−0.537037	+	1.65283i	−0.0174146	+	0.0535967i
$952$	−19.1987	+	23.4721i	−0.622233	+	0.760734i
$953$	2.60705	−	1.89413i	0.0844505	−	0.0613569i	−0.544759	−	0.838593i	$-0.683379\pi$
$953$	2.60705	−	1.89413i	0.0844505	−	0.0613569i	0.629209	+	0.777236i	$0.283379\pi$
$954$	−21.7642	−	8.46334i	−0.704641	−	0.274011i
$955$	−5.19352	−	15.9840i	−0.168058	−	0.517230i
$956$	−21.7441	−	38.4305i	−0.703253	−	1.24293i
$957$	−1.61167	−	0.813166i	−0.0520980	−	0.0262859i
$958$	−17.8575	+	4.70170i	−0.576949	+	0.151905i
$959$	5.96740	+	6.51979i	0.192697	+	0.210535i
$960$	2.07869	+	1.59481i	0.0670893	+	0.0514723i
$961$	24.5156	−	17.8116i	0.790827	−	0.574569i
$962$	−9.81820	−	0.557409i	−0.316551	−	0.0179716i
$963$	−38.9067	−	12.6415i	−1.25375	−	0.407368i
$964$	29.0197	+	13.2243i	0.934662	+	0.425925i
$965$	−17.5830	+	24.2009i	−0.566017	+	0.779056i
$966$	0.641191	−	0.995610i	0.0206300	−	0.0320332i
$967$		−	58.0609i		−	1.86711i	−0.358432	−	0.933556i	$-0.616689\pi$
$967$		−	58.0609i		−	1.86711i	0.358432	−	0.933556i	$-0.383311\pi$
$968$	21.8867	+	22.1127i	0.703465	+	0.710730i
$969$		−	5.73754i		−	0.184316i
$970$	−3.98042	−	6.18811i	−0.127804	−	0.198688i
$971$	−41.8686	−	30.4193i	−1.34363	−	0.976201i	−0.999302	−	0.0373504i	$-0.988108\pi$
$971$	−41.8686	−	30.4193i	−1.34363	−	0.976201i	−0.344324	−	0.938851i	$-0.611892\pi$
$972$	−4.64744	+	10.1985i	−0.149067	+	0.327117i
$973$	−4.07337	−	35.9352i	−0.130586	−	1.15203i
$974$	24.8096	+	1.40852i	0.794952	+	0.0451318i
$975$	−1.86866	−	2.57199i	−0.0598450	−	0.0823696i
$976$	−0.231180	−	0.544558i	−0.00739988	−	0.0174309i
$977$	−5.35233	−	16.4728i	−0.171236	−	0.527011i	0.828205	−	0.560425i	$-0.189362\pi$
$977$	−5.35233	−	16.4728i	−0.171236	−	0.527011i	−0.999442	+	0.0334139i	$0.989362\pi$
$978$	1.27166	+	4.82989i	0.0406633	+	0.154443i
$979$	10.9611	−	21.7246i	0.350317	−	0.694320i
$980$	−21.2132	−	4.34080i	−0.677632	−	0.138662i
$981$	8.04114	+	24.7481i	0.256734	+	0.790145i
$982$	15.1370	−	38.9261i	0.483042	−	1.24218i
$983$	17.4046	−	12.6452i	0.555122	−	0.403319i	−0.274549	−	0.961573i	$-0.588528\pi$
$983$	17.4046	−	12.6452i	0.555122	−	0.403319i	0.829670	+	0.558254i	$0.188528\pi$
$984$	−5.22236	+	2.57560i	−0.166483	+	0.0821071i
$985$	19.1088	+	6.20883i	0.608858	+	0.197830i
$986$	11.4070	+	9.31973i	0.363274	+	0.296801i
$987$	−6.38340	−	1.30254i	−0.203186	−	0.0414602i
$988$	−52.0124	+	56.7641i	−1.65473	+	1.80591i
$989$	−6.57169			−0.208968
$990$	21.3212	−	2.23249i	0.677632	−	0.0709532i
$991$			26.1485i			0.830633i	0.909677	+	0.415317i	$0.136329\pi$
$991$			26.1485i			0.830633i	−0.909677	+	0.415317i	$0.863671\pi$
$992$	−4.72055	+	0.144487i	−0.149878	+	0.00458747i
$993$	0.959173	−	1.32019i	0.0304384	−	0.0418949i
$994$	30.1434	+	7.95428i	0.956092	+	0.252294i
$995$	−7.23367	−	2.35036i	−0.229323	−	0.0745115i
$996$	0.771596	+	3.79209i	0.0244490	+	0.120157i
$997$	−1.38044	−	1.90001i	−0.0437189	−	0.0601739i	0.786598	−	0.617466i	$-0.211841\pi$
$997$	−1.38044	−	1.90001i	−0.0437189	−	0.0601739i	−0.830317	+	0.557292i	$0.811841\pi$
$998$	−8.81587	+	22.6707i	−0.279062	+	0.717629i
$999$	−0.470678	−	1.44860i	−0.0148916	−	0.0458316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.t.c.27.13	✓	160
4.3	odd	2	inner	308.2.t.c.27.20	yes	160
7.6	odd	2	inner	308.2.t.c.27.14	yes	160
11.9	even	5	inner	308.2.t.c.251.19	yes	160
28.27	even	2	inner	308.2.t.c.27.19	yes	160
44.31	odd	10	inner	308.2.t.c.251.14	yes	160
77.20	odd	10	inner	308.2.t.c.251.20	yes	160
308.251	even	10	inner	308.2.t.c.251.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.t.c.27.13	✓	160	1.1	even	1	trivial
308.2.t.c.27.14	yes	160	7.6	odd	2	inner
308.2.t.c.27.19	yes	160	28.27	even	2	inner
308.2.t.c.27.20	yes	160	4.3	odd	2	inner
308.2.t.c.251.13	yes	160	308.251	even	10	inner
308.2.t.c.251.14	yes	160	44.31	odd	10	inner
308.2.t.c.251.19	yes	160	11.9	even	5	inner
308.2.t.c.251.20	yes	160	77.20	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.765067 - 1.18940i) q^{2} +(-0.171309 - 0.124464i) q^{3} +(-0.829346 + 1.81994i) q^{4} +(-1.47093 - 0.477935i) q^{5} +(-0.0169739 + 0.298978i) q^{6} +(1.30415 - 2.30200i) q^{7} +(2.79914 - 0.405951i) q^{8} +(-0.913195 - 2.81053i) q^{9} +(0.556905 + 2.11518i) q^{10} +(2.96107 + 1.49400i) q^{11} +(0.368591 - 0.208550i) q^{12} +(-5.47516 + 1.77899i) q^{13} +(-3.73576 + 0.210019i) q^{14} +(0.192499 + 0.264952i) q^{15} +(-2.62437 - 3.01872i) q^{16} +(-3.85385 - 1.25219i) q^{17} +(-2.64419 + 3.23639i) q^{18} +(-5.40967 - 3.93036i) q^{19} +(2.08973 - 2.28064i) q^{20} +(-0.509928 + 0.232034i) q^{21} +(-0.488452 - 4.66491i) q^{22} -1.49466i q^{23} +(-0.530046 - 0.278848i) q^{24} +(-2.10986 - 1.53291i) q^{25} +(6.30479 + 5.15112i) q^{26} +(-0.389672 + 1.19929i) q^{27} +(3.10790 + 4.28263i) q^{28} +(2.07951 - 1.51086i) q^{29} +(0.167860 - 0.431665i) q^{30} +(0.257990 + 0.794012i) q^{31} +(-1.58265 + 5.43095i) q^{32} +(-0.321311 - 0.624483i) q^{33} +(1.45909 + 5.54178i) q^{34} +(-3.01853 + 2.76278i) q^{35} +(5.87235 + 0.668938i) q^{36} +(-0.977197 + 0.709976i) q^{37} +(-0.536008 + 9.44125i) q^{38} +(1.15937 + 0.376701i) q^{39} +(-4.31137 - 0.740681i) q^{40} +(5.71469 - 7.86560i) q^{41} +(0.666110 + 0.428988i) q^{42} -4.39677i q^{43} +(-5.17475 + 4.14993i) q^{44} +4.57054i q^{45} +(-1.77775 + 1.14352i) q^{46} +(9.40795 + 6.83527i) q^{47} +(0.0738583 + 0.843774i) q^{48} +(-3.59837 - 6.00431i) q^{49} +(-0.209052 + 3.68225i) q^{50} +(0.504349 + 0.694176i) q^{51} +(1.30315 - 11.4399i) q^{52} +(1.72666 + 5.31411i) q^{53} +(1.72456 - 0.454059i) q^{54} +(-3.64150 - 3.61278i) q^{55} +(2.71601 - 6.97304i) q^{56} +(0.437542 + 1.34661i) q^{57} +(-3.38798 - 1.31747i) q^{58} +(7.02258 - 5.10220i) q^{59} +(-0.641846 + 0.130600i) q^{60} +(0.140661 + 0.0457034i) q^{61} +(0.747019 - 0.914326i) q^{62} +(-7.66077 - 1.56319i) q^{63} +(7.67041 - 2.27263i) q^{64} +8.90384 q^{65} +(-0.496935 + 0.859938i) q^{66} +7.62277i q^{67} +(5.47509 - 5.97528i) q^{68} +(-0.186031 + 0.256050i) q^{69} +(5.59542 + 1.47653i) q^{70} +(-7.92415 - 2.57471i) q^{71} +(-3.69710 - 7.49635i) q^{72} +(-1.57247 - 2.16432i) q^{73} +(1.59207 + 0.619100i) q^{74} +(0.170649 + 0.525203i) q^{75} +(11.6395 - 6.58566i) q^{76} +(7.30088 - 4.86797i) q^{77} +(-0.438944 - 1.66715i) q^{78} +(13.5174 - 4.39208i) q^{79} +(2.41752 + 5.69461i) q^{80} +(-6.95631 + 5.05405i) q^{81} +(-13.7275 - 0.779350i) q^{82} +(-2.82369 + 8.69041i) q^{83} +(0.000619206 - 1.12048i) q^{84} +(5.07029 + 3.68378i) q^{85} +(-5.22953 + 3.36383i) q^{86} -0.544287 q^{87} +(8.89496 + 2.97987i) q^{88} -7.33671i q^{89} +(5.43620 - 3.49677i) q^{90} +(-3.04523 + 14.9239i) q^{91} +(2.72020 + 1.23959i) q^{92} +(0.0546294 - 0.168132i) q^{93} +(0.932171 - 16.4193i) q^{94} +(6.07881 + 8.36676i) q^{95} +(0.947079 - 0.733390i) q^{96} +(-3.19926 + 1.03950i) q^{97} +(-4.38854 + 8.87360i) q^{98} +(1.49489 - 9.68649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 10 q^{2} - 10 q^{4} + 2 q^{8} - 60 q^{9} - 32 q^{14} - 2 q^{16} + 20 q^{18} - 4 q^{21} - 70 q^{22} + 20 q^{25} - 2 q^{28} - 36 q^{29} - 52 q^{30} + 80 q^{32} - 24 q^{37} + 40 q^{42} - 58 q^{44}+ \cdots - 84 q^{98}+O(q^{100}) \) 160 * q - 10 * q^2 - 10 * q^4 + 2 * q^8 - 60 * q^9 - 32 * q^14 - 2 * q^16 + 20 * q^18 - 4 * q^21 - 70 * q^22 + 20 * q^25 - 2 * q^28 - 36 * q^29 - 52 * q^30 + 80 * q^32 - 24 * q^37 + 40 * q^42 - 58 * q^44 + 50 * q^46 - 54 * q^49 + 36 * q^50 + 40 * q^53 - 32 * q^56 + 12 * q^57 - 74 * q^58 - 52 * q^60 + 110 * q^64 - 56 * q^65 - 92 * q^70 + 142 * q^72 - 122 * q^74 - 30 * q^77 + 68 * q^78 + 36 * q^81 - 92 * q^84 + 20 * q^85 + 34 * q^86 + 2 * q^88 + 32 * q^92 + 4 * q^93 - 84 * q^98

Introduction

L-functions

Modular forms

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Database

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