LMFDB - Embedded newform 680.2.t.a.523.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(523,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.523"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$104$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			523.12
Character	$\chi$	$=$	680.523
Dual form			680.2.t.a.667.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33036 - 0.479733i) q^{2} +2.39666i q^{3} +(1.53971 + 1.27643i) q^{4} +(-1.22372 - 1.87150i) q^{5} +(1.14976 - 3.18842i) q^{6} -2.01789 q^{7} +(-1.43602 - 2.43677i) q^{8} -2.74399 q^{9} +(0.730169 + 3.07683i) q^{10} +(2.76394 - 2.76394i) q^{11} +(-3.05918 + 3.69017i) q^{12} +(-1.51684 + 1.51684i) q^{13} +(2.68452 + 0.968049i) q^{14} +(4.48535 - 2.93284i) q^{15} +(0.741429 + 3.93068i) q^{16} +(3.88261 - 1.38756i) q^{17} +(3.65049 + 1.31638i) q^{18} +4.49749 q^{19} +(0.504668 - 4.44357i) q^{20} -4.83620i q^{21} +(-5.00298 + 2.35108i) q^{22} -4.63098i q^{23} +(5.84011 - 3.44166i) q^{24} +(-2.00502 + 4.58038i) q^{25} +(2.74563 - 1.29027i) q^{26} +0.613578i q^{27} +(-3.10697 - 2.57571i) q^{28} +(3.11178 + 3.11178i) q^{29} +(-7.37411 + 1.74997i) q^{30} +(5.38037 - 5.38037i) q^{31} +(0.899312 - 5.58491i) q^{32} +(6.62422 + 6.62422i) q^{33} +(-5.83093 - 0.0166641i) q^{34} +(2.46933 + 3.77648i) q^{35} +(-4.22495 - 3.50252i) q^{36} +2.35110i q^{37} +(-5.98328 - 2.15759i) q^{38} +(-3.63536 - 3.63536i) q^{39} +(-2.80312 + 5.66944i) q^{40} +(-4.52570 + 4.52570i) q^{41} +(-2.32008 + 6.43388i) q^{42} +(1.39646 - 1.39646i) q^{43} +(7.78365 - 0.727683i) q^{44} +(3.35787 + 5.13537i) q^{45} +(-2.22163 + 6.16086i) q^{46} +(2.29593 + 2.29593i) q^{47} +(-9.42052 + 1.77696i) q^{48} -2.92812 q^{49} +(4.86475 - 5.13168i) q^{50} +(3.32551 + 9.30531i) q^{51} +(-4.27166 + 0.399351i) q^{52} +(5.80139 + 5.80139i) q^{53} +(0.294354 - 0.816279i) q^{54} +(-8.55499 - 1.79042i) q^{55} +(2.89774 + 4.91713i) q^{56} +10.7790i q^{57} +(-2.64696 - 5.63261i) q^{58} +9.71953 q^{59} +(10.6497 + 1.20952i) q^{60} +(5.52458 + 5.52458i) q^{61} +(-9.73896 + 4.57668i) q^{62} +5.53706 q^{63} +(-3.87567 + 6.99851i) q^{64} +(4.69496 + 0.982579i) q^{65} +(-5.63474 - 11.9904i) q^{66} +(5.42568 - 5.42568i) q^{67} +(7.74924 + 2.81946i) q^{68} +11.0989 q^{69} +(-1.47340 - 6.20870i) q^{70} +(1.88486 - 1.88486i) q^{71} +(3.94043 + 6.68646i) q^{72} -5.97927i q^{73} +(1.12790 - 3.12781i) q^{74} +(-10.9776 - 4.80534i) q^{75} +(6.92484 + 5.74075i) q^{76} +(-5.57732 + 5.57732i) q^{77} +(3.09233 + 6.58034i) q^{78} +(5.52779 - 5.52779i) q^{79} +(6.44897 - 6.19764i) q^{80} -9.70250 q^{81} +(8.19193 - 3.84968i) q^{82} +(-1.58409 + 1.58409i) q^{83} +(6.17309 - 7.44636i) q^{84} +(-7.34805 - 5.56832i) q^{85} +(-2.52772 + 1.18787i) q^{86} +(-7.45789 + 7.45789i) q^{87} +(-10.7041 - 2.76599i) q^{88} -14.8352i q^{89} +(-2.00357 - 8.44277i) q^{90} +(3.06082 - 3.06082i) q^{91} +(5.91114 - 7.13037i) q^{92} +(12.8949 + 12.8949i) q^{93} +(-1.95298 - 4.15585i) q^{94} +(-5.50367 - 8.41704i) q^{95} +(13.3851 + 2.15535i) q^{96} -11.1661 q^{97} +(3.89545 + 1.40472i) q^{98} +(-7.58420 + 7.58420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) $ 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.33036	−	0.479733i	−0.940706	−	0.339222i
$2$	−1.33036	−	0.479733i	−0.940706	−	0.339222i
$3$			2.39666i			1.38371i	0.722035	+	0.691857i	$0.243207\pi$
$3$			2.39666i			1.38371i	−0.722035	+	0.691857i	$0.756793\pi$
$4$	1.53971	+	1.27643i	0.769856	+	0.638217i
$5$	−1.22372	−	1.87150i	−0.547264	−	0.836960i
$5$	−1.22372	−	1.87150i	−0.547264	−	0.836960i
$6$	1.14976	−	3.18842i	0.469387	−	1.30167i
$7$	−2.01789			−0.762691			−0.381345	−	0.924433i	$-0.624539\pi$
$7$	−2.01789			−0.762691			−0.381345	+	0.924433i	$0.624539\pi$
$8$	−1.43602	−	2.43677i	−0.507711	−	0.861527i
$9$	−2.74399			−0.914662
$10$	0.730169	+	3.07683i	0.230900	+	0.972978i
$11$	2.76394	−	2.76394i	0.833358	−	0.833358i	−0.154617	−	0.987975i	$-0.549414\pi$
$11$	2.76394	−	2.76394i	0.833358	−	0.833358i	0.987975	+	0.154617i	$0.0494142\pi$
$12$	−3.05918	+	3.69017i	−0.883110	+	1.06526i
$13$	−1.51684	+	1.51684i	−0.420697	+	0.420697i	−0.885444	−	0.464747i	$-0.846145\pi$
$13$	−1.51684	+	1.51684i	−0.420697	+	0.420697i	0.464747	+	0.885444i	$0.346145\pi$
$14$	2.68452	+	0.968049i	0.717468	+	0.258722i
$15$	4.48535	−	2.93284i	1.15811	−	0.757257i
$16$	0.741429	+	3.93068i	0.185357	+	0.982671i
$17$	3.88261	−	1.38756i	0.941672	−	0.336533i
$17$	3.88261	−	1.38756i	0.941672	−	0.336533i
$18$	3.65049	+	1.31638i	0.860428	+	0.310274i
$19$	4.49749			1.03179			0.515897	−	0.856650i	$-0.327459\pi$
$19$	4.49749			1.03179			0.515897	+	0.856650i	$0.327459\pi$
$20$	0.504668	−	4.44357i	0.112847	−	0.993612i
$21$		−	4.83620i		−	1.05535i
$22$	−5.00298	+	2.35108i	−1.06664	+	0.501251i
$23$		−	4.63098i		−	0.965625i	−0.875724	−	0.482813i	$-0.839615\pi$
$23$		−	4.63098i		−	0.965625i	0.875724	−	0.482813i	$-0.160385\pi$
$24$	5.84011	−	3.44166i	1.19211	−	0.702526i
$25$	−2.00502	+	4.58038i	−0.401003	+	0.916077i
$26$	2.74563	−	1.29027i	0.538462	−	0.253042i
$27$			0.613578i			0.118083i
$28$	−3.10697	−	2.57571i	−0.587162	−	0.486762i
$29$	3.11178	+	3.11178i	0.577843	+	0.577843i	0.934309	−	0.356465i	$-0.116018\pi$
$29$	3.11178	+	3.11178i	0.577843	+	0.577843i	−0.356465	+	0.934309i	$0.616018\pi$
$30$	−7.37411	+	1.74997i	−1.34632	+	0.319499i
$31$	5.38037	−	5.38037i	0.966343	−	0.966343i	−0.0331091	−	0.999452i	$-0.510541\pi$
$31$	5.38037	−	5.38037i	0.966343	−	0.966343i	0.999452	+	0.0331091i	$0.0105409\pi$
$32$	0.899312	−	5.58491i	0.158977	−	0.987282i
$33$	6.62422	+	6.62422i	1.15313	+	1.15313i
$34$	−5.83093	−	0.0166641i	−0.999996	−	0.00285787i
$35$	2.46933	+	3.77648i	0.417394	+	0.638342i
$36$	−4.22495	−	3.50252i	−0.704158	−	0.583753i
$37$			2.35110i			0.386518i	0.981148	+	0.193259i	$0.0619058\pi$
$37$			2.35110i			0.386518i	−0.981148	+	0.193259i	$0.938094\pi$
$38$	−5.98328	−	2.15759i	−0.970615	−	0.350008i
$39$	−3.63536	−	3.63536i	−0.582124	−	0.582124i
$40$	−2.80312	+	5.66944i	−0.443212	+	0.896417i
$41$	−4.52570	+	4.52570i	−0.706795	+	0.706795i	−0.965860	−	0.259065i	$-0.916586\pi$
$41$	−4.52570	+	4.52570i	−0.706795	+	0.706795i	0.259065	+	0.965860i	$0.416586\pi$
$42$	−2.32008	+	6.43388i	−0.357997	+	0.992770i
$43$	1.39646	−	1.39646i	0.212958	−	0.212958i	−0.592565	−	0.805523i	$-0.701884\pi$
$43$	1.39646	−	1.39646i	0.212958	−	0.212958i	0.805523	+	0.592565i	$0.201884\pi$
$44$	7.78365	−	0.727683i	1.17343	−	0.109702i
$45$	3.35787	+	5.13537i	0.500562	+	0.765535i
$46$	−2.22163	+	6.16086i	−0.327562	+	0.908370i
$47$	2.29593	+	2.29593i	0.334896	+	0.334896i	0.854442	−	0.519546i	$-0.173899\pi$
$47$	2.29593	+	2.29593i	0.334896	+	0.334896i	−0.519546	+	0.854442i	$0.673899\pi$
$48$	−9.42052	+	1.77696i	−1.35974	+	0.256481i
$49$	−2.92812			−0.418303
$50$	4.86475	−	5.13168i	0.687980	−	0.725730i
$51$	3.32551	+	9.30531i	0.465665	+	1.30300i
$52$	−4.27166	+	0.399351i	−0.592372	+	0.0553801i
$53$	5.80139	+	5.80139i	0.796882	+	0.796882i	0.982603	−	0.185721i	$-0.0594619\pi$
$53$	5.80139	+	5.80139i	0.796882	+	0.796882i	−0.185721	+	0.982603i	$0.559462\pi$
$54$	0.294354	−	0.816279i	0.0400564	−	0.111082i
$55$	−8.55499	−	1.79042i	−1.15355	−	0.241420i
$56$	2.89774	+	4.91713i	0.387226	+	0.657079i
$57$			10.7790i			1.42771i
$58$	−2.64696	−	5.63261i	−0.347563	−	0.739598i
$59$	9.71953			1.26537			0.632687	−	0.774407i	$-0.281952\pi$
$59$	9.71953			1.26537			0.632687	+	0.774407i	$0.281952\pi$
$60$	10.6497	+	1.20952i	1.37487	+	0.156148i
$61$	5.52458	+	5.52458i	0.707350	+	0.707350i	0.965977	−	0.258627i	$-0.0832702\pi$
$61$	5.52458	+	5.52458i	0.707350	+	0.707350i	−0.258627	+	0.965977i	$0.583270\pi$
$62$	−9.73896	+	4.57668i	−1.23685	+	0.581239i
$63$	5.53706			0.697604
$64$	−3.87567	+	6.99851i	−0.484459	+	0.874814i
$65$	4.69496	+	0.982579i	0.582339	+	0.121874i
$66$	−5.63474	−	11.9904i	−0.693588	−	1.47592i
$67$	5.42568	−	5.42568i	0.662852	−	0.662852i	−0.293199	−	0.956051i	$-0.594720\pi$
$67$	5.42568	−	5.42568i	0.662852	−	0.662852i	0.956051	+	0.293199i	$0.0947199\pi$
$68$	7.74924	+	2.81946i	0.939733	+	0.341909i
$69$	11.0989			1.33615
$70$	−1.47340	−	6.20870i	−0.176105	−	0.742081i
$71$	1.88486	−	1.88486i	0.223691	−	0.223691i	−0.586360	−	0.810051i	$-0.699439\pi$
$71$	1.88486	−	1.88486i	0.223691	−	0.223691i	0.810051	+	0.586360i	$0.199439\pi$
$72$	3.94043	+	6.68646i	0.464384	+	0.788007i
$73$		−	5.97927i		−	0.699821i	−0.936783	−	0.349910i	$-0.886212\pi$
$73$		−	5.97927i		−	0.699821i	0.936783	−	0.349910i	$-0.113788\pi$
$74$	1.12790	−	3.12781i	0.131116	−	0.363600i
$75$	−10.9776	−	4.80534i	−1.26759	−	0.554873i
$76$	6.92484	+	5.74075i	0.794333	+	0.658509i
$77$	−5.57732	+	5.57732i	−0.635594	+	0.635594i
$78$	3.09233	+	6.58034i	0.350138	+	0.745077i
$79$	5.52779	−	5.52779i	0.621926	−	0.621926i	−0.324098	−	0.946024i	$-0.605061\pi$
$79$	5.52779	−	5.52779i	0.621926	−	0.621926i	0.946024	+	0.324098i	$0.105061\pi$
$80$	6.44897	−	6.19764i	0.721017	−	0.692918i
$81$	−9.70250			−1.07806
$82$	8.19193	−	3.84968i	0.904647	−	0.425126i
$83$	−1.58409	+	1.58409i	−0.173876	+	0.173876i	−0.788680	−	0.614804i	$-0.789235\pi$
$83$	−1.58409	+	1.58409i	−0.173876	+	0.173876i	0.614804	+	0.788680i	$0.289235\pi$
$84$	6.17309	−	7.44636i	0.673540	−	0.812464i
$85$	−7.34805	−	5.56832i	−0.797008	−	0.603969i
$86$	−2.52772	+	1.18787i	−0.272572	+	0.128091i
$87$	−7.45789	+	7.45789i	−0.799569	+	0.799569i
$88$	−10.7041	−	2.76599i	−1.14107	−	0.294856i
$89$		−	14.8352i		−	1.57253i	−0.617890	−	0.786265i	$-0.712012\pi$
$89$		−	14.8352i		−	1.57253i	0.617890	−	0.786265i	$-0.287988\pi$
$90$	−2.00357	−	8.44277i	−0.211195	−	0.889946i
$91$	3.06082	−	3.06082i	0.320862	−	0.320862i
$92$	5.91114	−	7.13037i	0.616279	−	0.743393i
$93$	12.8949	+	12.8949i	1.33714	+	1.33714i
$94$	−1.95298	−	4.15585i	−0.201434	−	0.428643i
$95$	−5.50367	−	8.41704i	−0.564664	−	0.863570i
$96$	13.3851	+	2.15535i	1.36612	+	0.219979i
$97$	−11.1661			−1.13375			−0.566873	−	0.823805i	$-0.691847\pi$
$97$	−11.1661			−1.13375			−0.566873	+	0.823805i	$0.691847\pi$
$98$	3.89545	+	1.40472i	0.393500	+	0.141898i
$99$	−7.58420	+	7.58420i	−0.762241	+	0.762241i
$100$	−8.93371	+	4.49320i	−0.893371	+	0.449320i
$101$			2.71874i			0.270524i	0.990810	+	0.135262i	$0.0431877\pi$
$101$			2.71874i			0.270524i	−0.990810	+	0.135262i	$0.956812\pi$
$102$	0.0399382	−	13.9748i	0.00395447	−	1.38371i
$103$	−3.37830	+	3.37830i	−0.332874	+	0.332874i	−0.853677	−	0.520803i	$-0.825633\pi$
$103$	−3.37830	+	3.37830i	−0.332874	+	0.332874i	0.520803	+	0.853677i	$0.325633\pi$
$104$	5.87442	+	1.51797i	0.576034	+	0.148850i
$105$	−9.05094	+	5.91816i	−0.883282	+	0.577553i
$106$	−4.93482	−	10.5011i	−0.479312	−	1.01995i
$107$	16.5250			1.59754			0.798768	−	0.601639i	$-0.205485\pi$
$107$	16.5250			1.59754			0.798768	+	0.601639i	$0.205485\pi$
$108$	−0.783192	+	0.944733i	−0.0753627	+	0.0909070i
$109$	12.6977	−	12.6977i	1.21622	−	1.21622i	0.247279	−	0.968944i	$-0.420464\pi$
$109$	12.6977	−	12.6977i	1.21622	−	1.21622i	0.968944	−	0.247279i	$-0.0795365\pi$
$110$	10.5223	+	6.48601i	1.00326	+	0.618417i
$111$	−5.63479			−0.534830
$112$	−1.49612	−	7.93169i	−0.141370	−	0.749474i
$113$	16.9939			1.59865			0.799325	−	0.600899i	$-0.205191\pi$
$113$	16.9939			1.59865			0.799325	+	0.600899i	$0.205191\pi$
$114$	5.17102	−	14.3399i	0.484310	−	1.34305i
$115$	−8.66687	+	5.66702i	−0.808190	+	0.528452i
$116$	0.819263	+	8.76324i	0.0760667	+	0.813646i
$117$	4.16220	−	4.16220i	0.384795	−	0.384795i
$118$	−12.9305	−	4.66278i	−1.19035	−	0.429243i
$119$	−7.83469	+	2.79994i	−0.718204	+	0.256670i
$120$	−13.5877	−	6.71812i	−1.24038	−	0.613278i
$121$		−	4.27868i		−	0.388971i
$122$	−4.69935	−	10.0000i	−0.425459	−	0.905357i
$123$	−10.8466	−	10.8466i	−0.978001	−	0.978001i
$124$	15.1519	−	1.41653i	1.36068	−	0.127208i
$125$	11.0258	−	1.85272i	0.986174	−	0.165713i
$126$	−7.36628	−	2.65631i	−0.656241	−	0.236643i
$127$	−3.63347	+	3.63347i	−0.322418	+	0.322418i	−0.849694	−	0.527276i	$-0.823213\pi$
$127$	−3.63347	+	3.63347i	−0.322418	+	0.322418i	0.527276	+	0.849694i	$0.323213\pi$
$128$	8.51346	−	7.45125i	0.752490	−	0.658603i
$129$	3.34685	+	3.34685i	0.294673	+	0.294673i
$130$	−5.77462	−	3.55951i	−0.506467	−	0.312190i
$131$	−3.46937	−	3.46937i	−0.303120	−	0.303120i	0.539113	−	0.842233i	$-0.318760\pi$
$131$	−3.46937	−	3.46937i	−0.303120	−	0.303120i	−0.842233	+	0.539113i	$0.818760\pi$
$132$	1.74401	+	18.6548i	0.151797	+	1.62369i
$133$	−9.07544			−0.786940
$134$	−9.82098	+	4.61523i	−0.848404	+	0.398695i
$135$	1.14831	−	0.750848i	0.0988308	−	0.0646227i
$136$	−8.95668	−	7.46846i	−0.768029	−	0.640415i
$137$	3.90890	−	3.90890i	0.333960	−	0.333960i	−0.520128	−	0.854088i	$-0.674116\pi$
$137$	3.90890	−	3.90890i	0.333960	−	0.333960i	0.854088	+	0.520128i	$0.174116\pi$
$138$	−14.7655	−	5.32450i	−1.25692	−	0.453252i
$139$	−13.5588	+	13.5588i	−1.15005	+	1.15005i	−0.163503	+	0.986543i	$0.552279\pi$
$139$	−13.5588	+	13.5588i	−1.15005	+	1.15005i	−0.986543	+	0.163503i	$0.947721\pi$
$140$	−1.01836	+	8.96664i	−0.0860675	+	0.757819i
$141$	−5.50257	+	5.50257i	−0.463400	+	0.463400i
$142$	−3.41177	+	1.60331i	−0.286309	+	0.134547i
$143$			8.38492i			0.701182i
$144$	−2.03447	−	10.7857i	−0.169539	−	0.898812i
$145$	2.01574	−	9.63165i	0.167398	−	0.799865i
$146$	−2.86845	+	7.95458i	−0.237395	+	0.658326i
$147$		−	7.01771i		−	0.578811i
$148$	−3.00102	+	3.62001i	−0.246683	+	0.297563i
$149$	−5.04340			−0.413171			−0.206586	−	0.978429i	$-0.566235\pi$
$149$	−5.04340			−0.413171			−0.206586	+	0.978429i	$0.566235\pi$
$150$	12.2989	+	11.6592i	1.00420	+	0.951967i
$151$	1.77543			0.144482			0.0722412	−	0.997387i	$-0.476985\pi$
$151$	1.77543			0.144482			0.0722412	+	0.997387i	$0.476985\pi$
$152$	−6.45850	−	10.9593i	−0.523853	−	0.888919i
$153$	−10.6538	+	3.80744i	−0.861312	+	0.307814i
$154$	10.0955	−	4.74421i	0.813516	−	0.382300i
$155$	−16.6534	−	3.48529i	−1.33763	−	0.279945i
$156$	−0.957110	−	10.2377i	−0.0766302	−	0.819673i
$157$	9.25993	+	9.25993i	0.739023	+	0.739023i	0.972389	−	0.233366i	$-0.0749741\pi$
$157$	9.25993	+	9.25993i	0.739023	+	0.739023i	−0.233366	+	0.972389i	$0.574974\pi$
$158$	−10.0058	+	4.70209i	−0.796020	+	0.374078i
$159$	−13.9040	+	13.9040i	−1.10266	+	1.10266i
$160$	−11.5527	+	5.15131i	−0.913318	+	0.407247i
$161$			9.34480i			0.736474i
$162$	12.9078	+	4.65461i	1.01413	+	0.365701i
$163$	0.303641			0.0237830			0.0118915	−	0.999929i	$-0.496215\pi$
$163$	0.303641			0.0237830			0.0118915	+	0.999929i	$0.496215\pi$
$164$	−12.7450	+	1.19152i	−0.995219	+	0.0930417i
$165$	4.29102	−	20.5034i	0.334056	−	1.59619i
$166$	2.86735	−	1.34747i	0.222549	−	0.104584i
$167$		−	11.7741i		−	0.911104i	−0.890209	−	0.455552i	$-0.849442\pi$
$167$		−	11.7741i		−	0.911104i	0.890209	−	0.455552i	$-0.150558\pi$
$168$	−11.7847	+	6.94490i	−0.909209	+	0.535810i
$169$			8.39837i			0.646028i
$170$	7.10424	+	10.9330i	0.544870	+	0.838520i
$171$	−12.3410			−0.943743
$172$	3.93264	−	0.367658i	0.299861	−	0.0280336i
$173$	−20.8934			−1.58850			−0.794248	−	0.607593i	$-0.792135\pi$
$173$	−20.8934			−1.58850			−0.794248	+	0.607593i	$0.792135\pi$
$174$	13.4995	−	6.34388i	1.02339	−	0.480928i
$175$	4.04590	−	9.24271i	0.305841	−	0.698683i
$176$	12.9134	+	8.81490i	0.973386	+	0.664448i
$177$			23.2944i			1.75092i
$178$	−7.11694	+	19.7362i	−0.533437	+	1.47929i
$179$	−1.51184			−0.113000			−0.0565001	−	0.998403i	$-0.517994\pi$
$179$	−1.51184			−0.113000			−0.0565001	+	0.998403i	$0.517994\pi$
$180$	−1.38480	+	12.1931i	−0.103217	+	0.908820i
$181$	−13.3550	−	13.3550i	−0.992671	−	0.992671i	0.00730247	−	0.999973i	$-0.497676\pi$
$181$	−13.3550	−	13.3550i	−0.992671	−	0.992671i	−0.999973	+	0.00730247i	$0.997676\pi$
$182$	−5.54038	+	2.60362i	−0.410680	+	0.192993i
$183$	−13.2405	+	13.2405i	−0.978769	+	0.978769i
$184$	−11.2846	+	6.65019i	−0.831913	+	0.490259i
$185$	4.40008	−	2.87709i	0.323500	−	0.211528i
$186$	−10.9688	−	23.3410i	−0.804269	−	1.71145i
$187$	6.89616	−	14.5664i	0.504298	−	1.06520i
$188$	0.604468	+	6.46568i	0.0440854	+	0.471558i
$189$		−	1.23813i		−	0.0900609i
$190$	3.28392	+	13.8380i	0.238241	+	1.00391i
$191$		−	24.9476i		−	1.80514i	−0.430538	−	0.902572i	$-0.641676\pi$
$191$		−	24.9476i		−	1.80514i	0.430538	−	0.902572i	$-0.358324\pi$
$192$	−16.7731	−	9.28868i	−1.21049	−	0.670353i
$193$	−11.5711			−0.832907			−0.416454	−	0.909157i	$-0.636727\pi$
$193$	−11.5711			−0.832907			−0.416454	+	0.909157i	$0.636727\pi$
$194$	14.8549	+	5.35675i	1.06652	+	0.384592i
$195$	−2.35491	+	11.2522i	−0.168638	+	0.805790i
$196$	−4.50846	−	3.73755i	−0.322033	−	0.266968i
$197$	10.2028			0.726920			0.363460	−	0.931610i	$-0.381595\pi$
$197$	10.2028			0.726920			0.363460	+	0.931610i	$0.381595\pi$
$198$	13.7281	−	6.45132i	0.975614	−	0.458476i
$199$	13.0582	+	13.0582i	0.925674	+	0.925674i	0.997423	−	0.0717492i	$-0.0228581\pi$
$199$	13.0582	+	13.0582i	0.925674	+	0.925674i	−0.0717492	+	0.997423i	$0.522858\pi$
$200$	14.0406	−	1.69178i	0.992819	−	0.119627i
$201$	13.0035	+	13.0035i	0.917197	+	0.917197i
$202$	1.30427	−	3.61690i	0.0917680	−	0.254484i
$203$	−6.27923	−	6.27923i	−0.440716	−	0.440716i
$204$	−6.75729	+	18.5723i	−0.473105	+	1.30032i
$205$	14.0080	+	2.93165i	0.978363	+	0.204755i
$206$	6.11504	−	2.87367i	0.426055	−	0.200218i
$207$			12.7073i			0.883221i
$208$	−7.08687	−	4.83760i	−0.491386	−	0.335427i
$209$	12.4308	−	12.4308i	0.859854	−	0.859854i
$210$	14.8801	−	3.53124i	1.02683	−	0.243679i
$211$	0.000145299	0	0.000145299i	1.00028e−5	0	1.00028e-5i	−0.707102	−	0.707112i	$-0.749998\pi$
$211$	0.000145299	0	0.000145299i	1.00028e−5	0	1.00028e-5i	0.707112	+	0.707102i	$0.249998\pi$
$212$	1.52738	+	16.3376i	0.104901	+	1.12207i
$213$	4.51736	+	4.51736i	0.309525	+	0.309525i
$214$	−21.9842	−	7.92761i	−1.50281	−	0.541920i
$215$	−4.32236	−	0.904598i	−0.294782	−	0.0616930i
$216$	1.49515	−	0.881112i	0.101732	−	0.0599521i
$217$	−10.8570	+	10.8570i	−0.737021	+	0.737021i
$218$	−22.9841	+	10.8010i	−1.55668	+	0.731539i
$219$	14.3303			0.968351
$220$	−10.8869	−	13.6766i	−0.733993	−	0.922077i
$221$	−3.78461	+	7.99403i	−0.254580	+	0.537737i
$222$	7.49629	+	2.70319i	0.503118	+	0.181426i
$223$	17.9555	+	17.9555i	1.20239	+	1.20239i	0.973438	+	0.228950i	$0.0735293\pi$
$223$	17.9555	+	17.9555i	1.20239	+	1.20239i	0.228950	+	0.973438i	$0.426471\pi$
$224$	−1.81471	+	11.2697i	−0.121251	+	0.752991i
$225$	5.50174	−	12.5685i	0.366782	−	0.837901i
$226$	−22.6080	−	8.15252i	−1.50386	−	0.542298i
$227$		−	27.8938i		−	1.85138i	−0.378286	−	0.925689i	$-0.623487\pi$
$227$		−	27.8938i		−	1.85138i	0.378286	−	0.925689i	$-0.376513\pi$
$228$	−13.7586	+	16.5965i	−0.911188	+	1.09913i
$229$			2.18654i			0.144491i	0.997387	+	0.0722454i	$0.0230165\pi$
$229$			2.18654i			0.144491i	−0.997387	+	0.0722454i	$0.976984\pi$
$230$	14.2487	−	3.38139i	0.939532	−	0.222962i
$231$	−13.3669	−	13.3669i	−0.879480	−	0.879480i
$232$	3.11410	−	12.0513i	0.204451	−	0.791205i
$233$			3.59058i			0.235227i	0.993059	+	0.117613i	$0.0375244\pi$
$233$			3.59058i			0.235227i	−0.993059	+	0.117613i	$0.962476\pi$
$234$	−7.53397	+	3.54048i	−0.492511	+	0.231448i
$235$	1.48725	−	7.10641i	0.0970178	−	0.463571i
$236$	14.9653	+	12.4063i	0.974157	+	0.807584i
$237$	13.2483	+	13.2483i	0.860567	+	0.860567i
$238$	11.7662	+	0.0336263i	0.762688	+	0.00217967i
$239$	−29.3610			−1.89921			−0.949603	−	0.313454i	$-0.898514\pi$
$239$	−29.3610			−1.89921			−0.949603	+	0.313454i	$0.898514\pi$
$240$	14.8537	+	15.4560i	0.958799	+	0.997680i
$241$	−15.1348	−	15.1348i	−0.974915	−	0.974915i	0.0247776	−	0.999693i	$-0.492112\pi$
$241$	−15.1348	−	15.1348i	−0.974915	−	0.974915i	−0.999693	+	0.0247776i	$0.992112\pi$
$242$	−2.05262	+	5.69218i	−0.131948	+	0.365907i
$243$		−	21.4129i		−	1.37364i
$244$	1.45450	+	15.5580i	0.0931148	+	0.996000i
$245$	3.58320	+	5.47997i	0.228922	+	0.350103i
$246$	9.22637	+	19.6333i	0.588252	+	1.25177i
$247$	−6.82199	+	6.82199i	−0.434073	+	0.434073i
$248$	−20.8370	−	5.38437i	−1.32315	−	0.341908i
$249$	−3.79653	−	3.79653i	−0.240595	−	0.240595i
$250$	−15.5570	−	2.82463i	−0.983914	−	0.178645i
$251$	−4.54717			−0.287015			−0.143507	−	0.989649i	$-0.545838\pi$
$251$	−4.54717			−0.287015			−0.143507	+	0.989649i	$0.545838\pi$
$252$	8.52549	+	7.06770i	0.537055	+	0.445223i
$253$	−12.7997	−	12.7997i	−0.804712	−	0.804712i
$254$	6.57692	−	3.09073i	0.412673	−	0.193929i
$255$	13.3454	−	17.6108i	0.835720	−	1.10283i
$256$	−14.9006	+	5.82865i	−0.931285	+	0.364291i
$257$	−11.8485	−	11.8485i	−0.739087	−	0.739087i	0.233315	−	0.972401i	$-0.425043\pi$
$257$	−11.8485	−	11.8485i	−0.739087	−	0.739087i	−0.972401	+	0.233315i	$0.925043\pi$
$258$	−2.84692	−	6.05810i	−0.177241	−	0.377161i
$259$		−	4.74426i		−	0.294794i
$260$	5.97470	+	7.50570i	0.370535	+	0.465484i
$261$	−8.53869	−	8.53869i	−0.528531	−	0.528531i
$262$	2.95114	+	6.27988i	0.182322	+	0.387972i
$263$	−17.8669	−	17.8669i	−1.10172	−	1.10172i	−0.994203	−	0.107519i	$-0.965709\pi$
$263$	−17.8669	−	17.8669i	−1.10172	−	1.10172i	−0.107519	−	0.994203i	$-0.534291\pi$
$264$	6.62915	−	25.6542i	0.407996	−	1.57891i
$265$	3.75801	−	17.9566i	0.230853	−	1.10306i
$266$	12.0736	+	4.35379i	0.740279	+	0.266948i
$267$	35.5550			2.17593
$268$	15.2795	−	1.42846i	0.933345	−	0.0872572i
$269$	15.6361	+	15.6361i	0.953347	+	0.953347i	0.998959	−	0.0456123i	$-0.0145239\pi$
$269$	15.6361	+	15.6361i	0.953347	+	0.953347i	−0.0456123	+	0.998959i	$0.514524\pi$
$270$	−1.88787	+	0.448015i	−0.114892	+	0.0272653i
$271$			6.64130i			0.403430i	0.979444	+	0.201715i	$0.0646515\pi$
$271$			6.64130i			0.403430i	−0.979444	+	0.201715i	$0.935348\pi$
$272$	8.33274	+	14.2325i	0.505247	+	0.862975i
$273$	7.33576	+	7.33576i	0.443980	+	0.443980i
$274$	−7.07547	+	3.32501i	−0.427445	+	0.200871i
$275$	7.11815	+	18.2016i	0.429241	+	1.09760i
$276$	17.0891	+	14.1670i	1.02864	+	0.852753i
$277$		−	23.9005i		−	1.43604i	−0.696021	−	0.718022i	$-0.745048\pi$
$277$		−	23.9005i		−	1.43604i	0.696021	−	0.718022i	$-0.254952\pi$
$278$	24.5428	−	11.5335i	1.47198	−	0.691734i
$279$	−14.7637	+	14.7637i	−0.883877	+	0.883877i
$280$	5.65638	−	11.4403i	0.338033	−	0.683689i
$281$		−	5.28763i		−	0.315434i	−0.987484	−	0.157717i	$-0.949587\pi$
$281$		−	5.28763i		−	0.315434i	0.987484	−	0.157717i	$-0.0504134\pi$
$282$	9.96016	−	4.68063i	0.593119	−	0.278728i
$283$	27.7067			1.64699			0.823497	−	0.567321i	$-0.192020\pi$
$283$	27.7067			1.64699			0.823497	+	0.567321i	$0.192020\pi$
$284$	5.30803	−	0.496241i	0.314974	−	0.0294465i
$285$	20.1728	−	13.1904i	1.19493	−	0.781334i
$286$	4.02252	−	11.1550i	0.237857	−	0.659606i
$287$	9.13236	−	9.13236i	0.539066	−	0.539066i
$288$	−2.46770	+	15.3249i	−0.145411	+	0.903030i
$289$	13.1494	−	10.7747i	0.773492	−	0.633807i
$290$	−7.30228	+	11.8465i	−0.428805	+	0.695652i
$291$		−	26.7614i		−	1.56878i
$292$	7.63215	−	9.20636i	0.446638	−	0.538762i
$293$	−13.1072	+	13.1072i	−0.765728	+	0.765728i	−0.977351	−	0.211623i	$-0.932125\pi$
$293$	−13.1072	+	13.1072i	−0.765728	+	0.765728i	0.211623	+	0.977351i	$0.432125\pi$
$294$	−3.36663	+	9.33608i	−0.196346	+	0.544491i
$295$	−11.8940	−	18.1901i	−0.692495	−	1.05907i
$296$	5.72908	−	3.37623i	0.332996	−	0.196239i
$297$	1.69589	+	1.69589i	0.0984055	+	0.0984055i
$298$	6.70953	+	2.41948i	0.388673	+	0.140157i
$299$	7.02447	+	7.02447i	0.406236	+	0.406236i
$300$	−10.7687	−	21.4111i	−0.621730	−	1.23617i
$301$	−2.81791	+	2.81791i	−0.162421	+	0.162421i
$302$	−2.36196	−	0.851733i	−0.135916	−	0.0490117i
$303$	−6.51589			−0.374328
$304$	3.33457	+	17.6782i	0.191251	+	1.01391i
$305$	3.57870	−	17.0998i	0.204916	−	0.979131i
$306$	16.0000	+	0.0457260i	0.914658	+	0.00261398i
$307$	−16.5841	+	16.5841i	−0.946504	+	0.946504i	−0.998640	−	0.0521355i	$-0.983397\pi$
$307$	−16.5841	+	16.5841i	−0.946504	+	0.946504i	0.0521355	+	0.998640i	$0.483397\pi$
$308$	−15.7066	+	1.46838i	−0.894964	+	0.0836690i
$309$	−8.09665	−	8.09665i	−0.460602	−	0.460602i
$310$	20.4830	+	12.6259i	1.16336	+	0.717102i
$311$	−10.3746	+	10.3746i	−0.588287	+	0.588287i	−0.937167	−	0.348880i	$-0.886562\pi$
$311$	−10.3746	+	10.3746i	−0.588287	+	0.588287i	0.348880	+	0.937167i	$0.386562\pi$
$312$	−3.63807	+	14.0790i	−0.205965	+	0.797066i
$313$	31.1276			1.75944			0.879718	−	0.475496i	$-0.157731\pi$
$313$	31.1276			1.75944			0.879718	+	0.475496i	$0.157731\pi$
$314$	−7.87674	−	16.7613i	−0.444510	−	0.945896i
$315$	−6.77582	−	10.3626i	−0.381774	−	0.583867i
$316$	15.5671	−	1.45535i	0.875717	−	0.0818696i
$317$	−1.78216			−0.100096			−0.0500479	−	0.998747i	$-0.515937\pi$
$317$	−1.78216			−0.100096			−0.0500479	+	0.998747i	$0.515937\pi$
$318$	25.1675	−	11.8271i	1.41132	−	0.663230i
$319$	17.2015			0.963101
$320$	17.8404	−	1.31090i	0.997311	−	0.0732816i
$321$			39.6049i			2.21053i
$322$	4.48301	−	12.4319i	0.249828	−	0.692805i
$323$	17.4620	−	6.24053i	0.971612	−	0.347233i
$324$	−14.9391	−	12.3846i	−0.829948	−	0.688034i
$325$	−3.90643	−	9.98902i	−0.216690	−	0.554091i
$326$	−0.403951	−	0.145667i	−0.0223728	−	0.00806772i
$327$	30.4322	+	30.4322i	1.68290	+	1.68290i
$328$	17.5271	+	4.52906i	0.967771	+	0.250076i
$329$	−4.63294	−	4.63294i	−0.255422	−	0.255422i
$330$	−15.5448	+	25.2184i	−0.855711	+	1.38822i
$331$			0.416599i			0.0228984i	0.999934	+	0.0114492i	$0.00364447\pi$
$331$			0.416599i			0.0228984i	−0.999934	+	0.0114492i	$0.996356\pi$
$332$	−4.46103	+	0.417056i	−0.244831	+	0.0228889i
$333$		−	6.45138i		−	0.353533i
$334$	−5.64841	+	15.6637i	−0.309067	+	0.857081i
$335$	−16.7937	−	3.51464i	−0.917536	−	0.192025i
$336$	19.0096	−	3.58570i	1.03706	−	0.195616i
$337$	−32.8634			−1.79019			−0.895093	−	0.445880i	$-0.852891\pi$
$337$	−32.8634			−1.79019			−0.895093	+	0.445880i	$0.852891\pi$
$338$	4.02897	−	11.1728i	0.219147	−	0.607723i
$339$			40.7286i			2.21207i
$340$	−4.20629	−	17.9529i	−0.228118	−	0.973633i
$341$		−	29.7420i		−	1.61062i
$342$	16.4180	+	5.92041i	0.887785	+	0.320139i
$343$	20.0339			1.08173
$344$	−5.40820	−	1.39750i	−0.291591	−	0.0753482i
$345$	−13.5819	−	20.7715i	−0.731227	−	1.11830i
$346$	27.7957	+	10.0233i	1.49431	+	0.538854i
$347$		−	3.31469i		−	0.177942i	−0.996034	−	0.0889708i	$-0.971642\pi$
$347$		−	3.31469i		−	0.177942i	0.996034	−	0.0889708i	$-0.0283578\pi$
$348$	−21.0025	+	1.96350i	−1.12585	+	0.105254i
$349$			29.7694i			1.59352i	0.604295	+	0.796760i	$0.293455\pi$
$349$			29.7694i			1.59352i	−0.604295	+	0.796760i	$0.706545\pi$
$350$	−9.81654	+	10.3552i	−0.524716	+	0.553507i
$351$	−0.930702	−	0.930702i	−0.0496772	−	0.0496772i
$352$	−12.9507	−	17.9220i	−0.690274	−	0.955244i
$353$	17.2466	+	17.2466i	0.917947	+	0.917947i	0.996880	−	0.0789334i	$-0.0251514\pi$
$353$	17.2466	+	17.2466i	0.917947	+	0.917947i	−0.0789334	+	0.996880i	$0.525151\pi$
$354$	11.1751	−	30.9899i	0.593950	−	1.64710i
$355$	−5.83405	−	1.22097i	−0.309639	−	0.0648023i
$356$	18.9362	−	22.8420i	1.00362	−	1.21062i
$357$	−6.71052	−	18.7771i	−0.355158	−	0.993789i
$358$	2.01129	+	0.725280i	0.106300	+	0.0383322i
$359$			3.27804i			0.173008i	0.996251	+	0.0865041i	$0.0275696\pi$
$359$			3.27804i			0.173008i	−0.996251	+	0.0865041i	$0.972430\pi$
$360$	7.69171	−	15.5569i	0.405389	−	0.819919i
$361$	1.22740			0.0645998
$362$	11.3601	+	24.1738i	0.597075	+	1.27055i
$363$	10.2545			0.538224
$364$	8.61973	−	0.805848i	0.451797	−	0.0422379i
$365$	−11.1902	+	7.31696i	−0.585722	+	0.382987i
$366$	23.9666	−	11.2628i	1.25275	−	0.588714i
$367$	14.0599			0.733918			0.366959	−	0.930237i	$-0.380399\pi$
$367$	14.0599			0.733918			0.366959	+	0.930237i	$0.380399\pi$
$368$	18.2029	−	3.43354i	0.948892	−	0.178986i
$369$	12.4184	−	12.4184i	0.646479	−	0.646479i
$370$	−7.23392	+	1.71670i	−0.376073	+	0.0892469i
$371$	−11.7066	−	11.7066i	−0.607775	−	0.607775i
$372$	3.39495	+	36.3140i	0.176020	+	1.88279i
$373$	−7.78223	+	7.78223i	−0.402949	+	0.402949i	−0.879271	−	0.476322i	$-0.841970\pi$
$373$	−7.78223	+	7.78223i	−0.402949	+	0.402949i	0.476322	+	0.879271i	$0.341970\pi$
$374$	−16.1624	+	16.0703i	−0.835736	+	0.830973i
$375$	4.44035	+	26.4250i	0.229299	+	1.36458i
$376$	2.29764	−	8.89166i	0.118492	−	0.458552i
$377$	−9.44018			−0.486194
$378$	−0.593973	+	1.64716i	−0.0305507	+	0.0847208i
$379$	2.24486	−	2.24486i	0.115311	−	0.115311i	−0.647097	−	0.762408i	$-0.724017\pi$
$379$	2.24486	−	2.24486i	0.115311	−	0.115311i	0.762408	+	0.647097i	$0.224017\pi$
$380$	2.26974	−	19.9849i	0.116435	−	1.02520i
$381$	−8.70820	−	8.70820i	−0.446135	−	0.446135i
$382$	−11.9682	+	33.1893i	−0.612346	+	1.69811i
$383$	6.50132	+	6.50132i	0.332202	+	0.332202i	0.853422	−	0.521220i	$-0.174523\pi$
$383$	6.50132	+	6.50132i	0.332202	+	0.332202i	−0.521220	+	0.853422i	$0.674523\pi$
$384$	17.8581	+	20.4039i	0.911318	+	1.04123i
$385$	17.2630	+	3.61287i	0.879805	+	0.184129i
$386$	15.3937	+	5.55105i	0.783521	+	0.282541i
$387$	−3.83187	+	3.83187i	−0.194785	+	0.194785i
$388$	−17.1926	−	14.2528i	−0.872821	−	0.723576i
$389$			20.0807i			1.01813i	0.860728	+	0.509066i	$0.170009\pi$
$389$			20.0807i			1.01813i	−0.860728	+	0.509066i	$0.829991\pi$
$390$	8.53095	−	13.8398i	0.431981	−	0.700805i
$391$	−6.42576	−	17.9803i	−0.324964	−	0.909302i
$392$	4.20485	+	7.13515i	0.212377	+	0.360379i
$393$	8.31490	−	8.31490i	0.419431	−	0.419431i
$394$	−13.5734	−	4.89463i	−0.683819	−	0.246588i
$395$	−17.1097	−	3.58079i	−0.860884	−	0.180169i
$396$	−21.3582	+	1.99675i	−1.07329	+	0.100341i
$397$	−28.6090			−1.43584			−0.717922	−	0.696123i	$-0.754907\pi$
$397$	−28.6090			−1.43584			−0.717922	+	0.696123i	$0.754907\pi$
$398$	−11.1077	−	23.6366i	−0.556778	−	1.18480i
$399$		−	21.7508i		−	1.08890i
$400$	−19.4906	−	4.48505i	−0.974531	−	0.224253i
$401$	−12.7093	+	12.7093i	−0.634670	+	0.634670i	−0.949236	−	0.314566i	$-0.898141\pi$
$401$	−12.7093	+	12.7093i	−0.634670	+	0.634670i	0.314566	+	0.949236i	$0.398141\pi$
$402$	−11.0611	−	23.5376i	−0.551679	−	1.17395i
$403$			16.3224i			0.813075i
$404$	−3.47029	+	4.18607i	−0.172653	+	0.208265i
$405$	11.8731	+	18.1582i	0.589981	+	0.902289i
$406$	5.34128	+	11.3660i	0.265083	+	0.564085i
$407$	6.49828	+	6.49828i	0.322108	+	0.322108i
$408$	17.8994	−	21.4661i	0.886150	−	1.06273i
$409$			10.8762i			0.537794i	0.963169	+	0.268897i	$0.0866592\pi$
$409$			10.8762i			0.537794i	−0.963169	+	0.268897i	$0.913341\pi$
$410$	−17.2293	−	10.6203i	−0.850894	−	0.524497i
$411$	9.36831	+	9.36831i	0.462105	+	0.462105i
$412$	−9.51380	+	0.889433i	−0.468711	+	0.0438192i
$413$	−19.6129			−0.965090
$414$	6.09613	−	16.9053i	0.299608	−	0.830851i
$415$	4.90310	+	1.02614i	0.240684	+	0.0503712i
$416$	7.10732	+	9.83556i	0.348465	+	0.482228i
$417$	−32.4960	−	32.4960i	−1.59133	−	1.59133i
$418$	−22.5008	+	10.5739i	−1.10055	+	0.517188i
$419$	6.15665	+	6.15665i	0.300772	+	0.300772i	0.841316	−	0.540544i	$-0.181781\pi$
$419$	6.15665	+	6.15665i	0.300772	+	0.300772i	−0.540544	+	0.841316i	$0.681781\pi$
$420$	−21.4900	−	2.44068i	−1.04860	−	0.119093i
$421$			25.2031i			1.22832i	0.789181	+	0.614161i	$0.210505\pi$
$421$			25.2031i			1.22832i	−0.789181	+	0.614161i	$0.789495\pi$
$422$	−0.000263005	0	0.000123595i	−1.28029e−5	0	6.01653e-6i
$423$	−6.30000	−	6.30000i	−0.306317	−	0.306317i
$424$	5.80571	−	22.4676i	0.281950	−	1.09112i
$425$	−1.42914	+	20.5659i	−0.0693237	+	0.997594i
$426$	−3.84259	−	8.17685i	−0.186174	−	0.396170i
$427$	−11.1480	−	11.1480i	−0.539489	−	0.539489i
$428$	25.4438	+	21.0931i	1.22987	+	1.01958i
$429$	−20.0958			−0.970235
$430$	5.31632	+	3.27702i	0.256376	+	0.158032i
$431$	7.75680	+	7.75680i	0.373632	+	0.373632i	0.868798	−	0.495166i	$-0.164893\pi$
$431$	7.75680	+	7.75680i	0.373632	+	0.373632i	−0.495166	+	0.868798i	$0.664893\pi$
$432$	−2.41178	+	0.454925i	−0.116037	+	0.0218876i
$433$	−16.9315	+	16.9315i	−0.813678	+	0.813678i	−0.985183	−	0.171505i	$-0.945137\pi$
$433$	−16.9315	+	16.9315i	−0.813678	+	0.813678i	0.171505	+	0.985183i	$0.445137\pi$
$434$	19.6522	−	9.23524i	0.943334	−	0.443306i
$435$	23.0838	+	4.83106i	1.10678	+	0.231631i
$436$	35.7587	−	3.34304i	1.71253	−	0.160102i
$437$		−	20.8278i		−	0.996327i
$438$	−19.0644	−	6.87471i	−0.910934	−	0.328487i
$439$	14.0971	+	14.0971i	0.672817	+	0.672817i	0.958365	−	0.285548i	$-0.0921755\pi$
$439$	14.0971	+	14.0971i	0.672817	+	0.672817i	−0.285548	+	0.958365i	$0.592175\pi$
$440$	7.92233	+	23.4176i	0.377682	+	1.11639i
$441$	8.03472			0.382606
$442$	8.86988	−	8.81933i	0.421897	−	0.419493i
$443$	−17.3579	−	17.3579i	−0.824701	−	0.824701i	0.162077	−	0.986778i	$-0.448181\pi$
$443$	−17.3579	−	17.3579i	−0.824701	−	0.824701i	−0.986778	+	0.162077i	$0.948181\pi$
$444$	−8.67595	−	7.19244i	−0.411742	−	0.341338i
$445$	−27.7641	+	18.1542i	−1.31614	+	0.860589i
$446$	−15.2734	−	32.5011i	−0.723217	−	1.53897i
$447$		−	12.0873i		−	0.571711i
$448$	7.82069	−	14.1222i	0.369493	−	0.667212i
$449$	−0.0648756	−	0.0648756i	−0.00306167	−	0.00306167i	0.705574	−	0.708636i	$-0.250689\pi$
$449$	−0.0648756	−	0.0648756i	−0.00306167	−	0.00306167i	−0.708636	+	0.705574i	$0.750689\pi$
$450$	−13.3488	+	14.0813i	−0.629269	+	0.663798i
$451$			25.0175i			1.17803i
$452$	26.1657	+	21.6916i	1.23073	+	1.02029i
$453$			4.25511i			0.199922i
$454$	−13.3816	+	37.1088i	−0.628029	+	1.74160i
$455$	−9.47392	−	1.98274i	−0.444144	−	0.0929521i
$456$	26.2658	−	15.4788i	1.23001	−	0.724863i
$457$	5.56805	+	5.56805i	0.260462	+	0.260462i	0.825242	−	0.564780i	$-0.191039\pi$
$457$	5.56805	+	5.56805i	0.260462	+	0.260462i	−0.564780	+	0.825242i	$0.691039\pi$
$458$	1.04896	−	2.90889i	0.0490145	−	0.135923i
$459$	0.851376	+	2.38228i	0.0397388	+	0.111196i
$460$	−20.5781	−	2.33711i	−0.959457	−	0.108968i
$461$	−10.4510			−0.486752			−0.243376	−	0.969932i	$-0.578255\pi$
$461$	−10.4510			−0.486752			−0.243376	+	0.969932i	$0.578255\pi$
$462$	11.3703	+	24.1954i	0.528993	+	1.12567i
$463$	−2.52621	+	2.52621i	−0.117403	+	0.117403i	−0.763368	−	0.645964i	$-0.776455\pi$
$463$	−2.52621	+	2.52621i	−0.117403	+	0.117403i	0.645964	+	0.763368i	$0.276455\pi$
$464$	−9.92427	+	14.5386i	−0.460723	+	0.674938i
$465$	8.35305	−	39.9126i	0.387363	−	1.85090i
$466$	1.72252	−	4.77676i	0.0797942	−	0.221279i
$467$	1.08873	+	1.08873i	0.0503802	+	0.0503802i	0.731848	−	0.681468i	$-0.238658\pi$
$467$	1.08873	+	1.08873i	0.0503802	+	0.0503802i	−0.681468	+	0.731848i	$0.738658\pi$
$468$	11.7214	−	1.09582i	0.541820	−	0.0506541i
$469$	−10.9484	+	10.9484i	−0.505551	+	0.505551i
$470$	−5.38776	+	8.74060i	−0.248519	+	0.403174i
$471$	−22.1929	+	22.1929i	−1.02260	+	1.02260i
$472$	−13.9575	−	23.6842i	−0.642444	−	1.09016i
$473$		−	7.71946i		−	0.354941i
$474$	−11.2693	−	23.9806i	−0.517617	−	1.10146i
$475$	−9.01753	+	20.6002i	−0.413753	+	0.945203i
$476$	−15.6371	−	5.68936i	−0.716726	−	0.260771i
$477$	−15.9189	−	15.9189i	−0.728878	−	0.728878i
$478$	39.0607	+	14.0855i	1.78660	+	0.644254i
$479$	25.8994	+	25.8994i	1.18337	+	1.18337i	0.978865	+	0.204508i	$0.0655595\pi$
$479$	25.8994	+	25.8994i	1.18337	+	1.18337i	0.204508	+	0.978865i	$0.434441\pi$
$480$	−12.3459	−	27.6878i	−0.563513	−	1.26377i
$481$	−3.56625	−	3.56625i	−0.162607	−	0.162607i
$482$	12.8740	+	27.3953i	0.586396	+	1.24782i
$483$	−22.3963			−1.01907
$484$	5.46145	−	6.58794i	0.248248	−	0.299452i
$485$	13.6642	+	20.8973i	0.620459	+	0.948899i
$486$	−10.2725	+	28.4868i	−0.465968	+	1.29219i
$487$	21.8813			0.991535			0.495767	−	0.868455i	$-0.334887\pi$
$487$	21.8813			0.991535			0.495767	+	0.868455i	$0.334887\pi$
$488$	5.52869	−	21.3955i	0.250272	−	0.968530i
$489$			0.727724i			0.0329088i
$490$	−2.13802	−	9.00931i	−0.0965859	−	0.406999i
$491$			33.0713i			1.49249i	0.665674	+	0.746243i	$0.268144\pi$
$491$			33.0713i			1.49249i	−0.665674	+	0.746243i	$0.731856\pi$
$492$	−2.85566	−	30.5455i	−0.128743	−	1.37710i
$493$	16.3996	+	7.76406i	0.738602	+	0.349676i
$494$	12.3484	−	5.80296i	0.555582	−	0.261088i
$495$	23.4748	+	4.91288i	1.05511	+	0.220818i
$496$	25.1377	+	17.1594i	1.12872	+	0.770478i
$497$	−3.80343	+	3.80343i	−0.170607	+	0.170607i
$498$	3.22942	+	6.87206i	0.144714	+	0.307944i
$499$	−16.4666	−	16.4666i	−0.737145	−	0.737145i	0.234880	−	0.972024i	$-0.424530\pi$
$499$	−16.4666	−	16.4666i	−0.737145	−	0.737145i	−0.972024	+	0.234880i	$0.924530\pi$
$500$	19.3414	+	11.2210i	0.864973	+	0.501818i
$501$	28.2184			1.26071
$502$	6.04937	+	2.18143i	0.269997	+	0.0973619i
$503$		−	35.9499i		−	1.60293i	−0.598043	−	0.801464i	$-0.704055\pi$
$503$		−	35.9499i		−	1.60293i	0.598043	−	0.801464i	$-0.295945\pi$
$504$	−7.95135	−	13.4925i	−0.354181	−	0.601005i
$505$	5.08811	−	3.32697i	0.226418	−	0.148048i
$506$	10.8878	+	23.1687i	0.484021	+	1.02997i
$507$	−20.1280			−0.893918
$508$	−10.2324	+	0.956613i	−0.453989	+	0.0424428i
$509$	−4.17769			−0.185173			−0.0925865	−	0.995705i	$-0.529513\pi$
$509$	−4.17769			−0.185173			−0.0925865	+	0.995705i	$0.529513\pi$
$510$	−26.2026	+	17.0265i	−1.16027	+	0.753944i
$511$			12.0655i			0.533747i
$512$	22.6193	−	0.605907i	0.999641	−	0.0267775i
$513$			2.75956i			0.121837i
$514$	10.0786	+	21.4468i	0.444549	+	0.945978i
$515$	10.4566	+	2.18839i	0.460772	+	0.0964320i
$516$	0.881151	+	9.42521i	0.0387905	+	0.414922i
$517$	12.6916			0.558176
$518$	−2.27598	+	6.31157i	−0.100001	+	0.277314i
$519$		−	50.0744i		−	2.19802i
$520$	−4.34776	−	12.8515i	−0.190662	−	0.563578i
$521$	20.7871	−	20.7871i	0.910698	−	0.910698i	−0.0856295	−	0.996327i	$-0.527290\pi$
$521$	20.7871	−	20.7871i	0.910698	−	0.910698i	0.996327	+	0.0856295i	$0.0272901\pi$
$522$	7.26323	+	15.4558i	0.317903	+	0.676483i
$523$	−3.64859	−	3.64859i	−0.159542	−	0.159542i	0.622822	−	0.782364i	$-0.285986\pi$
$523$	−3.64859	−	3.64859i	−0.159542	−	0.159542i	−0.782364	+	0.622822i	$0.785986\pi$
$524$	−0.913408	−	9.77025i	−0.0399024	−	0.426815i
$525$	22.1516	+	9.69666i	0.966777	+	0.423197i
$526$	15.1981	+	32.3408i	0.662668	+	1.41013i
$527$	13.4243	−	28.3555i	0.584772	−	1.23518i
$528$	−21.1263	+	30.9491i	−0.919405	+	1.34689i
$529$	1.55405			0.0675676
$530$	−13.6139	+	22.0859i	−0.591349	+	0.959348i
$531$	−26.6703			−1.15739
$532$	−13.9736	−	11.5842i	−0.605831	−	0.502239i
$533$		−	13.7295i		−	0.594693i
$534$	−47.3009	−	17.0569i	−2.04691	−	0.738124i
$535$	−20.2220	−	30.9266i	−0.874275	−	1.33707i
$536$	−21.0125	−	5.42972i	−0.907603	−	0.234528i
$537$		−	3.62337i		−	0.156360i
$538$	−13.3004	−	28.3027i	−0.573423	−	1.22022i
$539$	−8.09313	+	8.09313i	−0.348596	+	0.348596i
$540$	2.72648	+	0.309653i	0.117329	+	0.0133253i
$541$	−26.0336	+	26.0336i	−1.11927	+	1.11927i	−0.127426	+	0.991848i	$0.540671\pi$
$541$	−26.0336	+	26.0336i	−1.11927	+	1.11927i	−0.991848	+	0.127426i	$0.959329\pi$
$542$	3.18605	−	8.83532i	0.136853	−	0.379509i
$543$	32.0075	−	32.0075i	1.37357	−	1.37357i
$544$	−4.25772	−	22.9319i	−0.182548	−	0.983197i
$545$	−39.3023	−	8.22532i	−1.68353	−	0.352334i
$546$	−6.23999	−	13.2784i	−0.267047	−	0.568263i
$547$	10.1608			0.434443			0.217221	−	0.976122i	$-0.430301\pi$
$547$	10.1608			0.434443			0.217221	+	0.976122i	$0.430301\pi$
$548$	11.0080	−	1.02913i	0.470240	−	0.0439621i
$549$	−15.1594	−	15.1594i	−0.646986	−	0.646986i
$550$	−0.737781	−	27.6295i	−0.0314591	−	1.17813i
$551$	13.9952	+	13.9952i	0.596216	+	0.596216i
$552$	−15.9383	−	27.0454i	−0.678377	−	1.15113i
$553$	−11.1545	+	11.1545i	−0.474337	+	0.474337i
$554$	−11.4659	+	31.7963i	−0.487138	+	1.35090i
$555$	6.89540	+	10.5455i	0.292694	+	0.447631i
$556$	−38.1837	+	3.56974i	−1.61935	+	0.151391i
$557$	−0.876037	−	0.876037i	−0.0371189	−	0.0371189i	0.688304	−	0.725423i	$-0.258356\pi$
$557$	−0.876037	−	0.876037i	−0.0371189	−	0.0371189i	−0.725423	+	0.688304i	$0.758356\pi$
$558$	26.7236	−	12.5584i	1.13130	−	0.531638i
$559$			4.23643i			0.179182i
$560$	−13.0133	+	12.5062i	−0.549913	+	0.528482i
$561$	34.9108	+	16.5278i	1.47393	+	0.697803i
$562$	−2.53665	+	7.03446i	−0.107002	+	0.296731i
$563$	−10.7493	+	10.7493i	−0.453031	+	0.453031i	−0.896359	−	0.443328i	$-0.853798\pi$
$563$	−10.7493	+	10.7493i	−0.453031	+	0.453031i	0.443328	+	0.896359i	$0.353798\pi$
$564$	−15.4960	+	1.44871i	−0.652501	+	0.0610015i
$565$	−20.7958	−	31.8040i	−0.874884	−	1.33801i
$566$	−36.8599	−	13.2918i	−1.54934	−	0.558697i
$567$	19.5786			0.822223
$568$	−7.29966	−	1.88626i	−0.306287	−	0.0791457i
$569$	−35.2352			−1.47714			−0.738569	−	0.674178i	$-0.764498\pi$
$569$	−35.2352			−1.47714			−0.738569	+	0.674178i	$0.764498\pi$
$570$	−33.1650	+	7.87045i	−1.38913	+	0.329657i
$571$	−6.07542	+	6.07542i	−0.254248	+	0.254248i	−0.822710	−	0.568461i	$-0.807539\pi$
$571$	−6.07542	+	6.07542i	−0.254248	+	0.254248i	0.568461	+	0.822710i	$0.307539\pi$
$572$	−10.7028	+	12.9104i	−0.447507	+	0.539809i
$573$	59.7909			2.49780
$574$	−16.5304	+	7.76823i	−0.689966	+	0.324239i
$575$	21.2116	+	9.28518i	0.884587	+	0.387219i
$576$	10.6348	−	19.2038i	0.443117	−	0.800159i
$577$	10.2795	−	10.2795i	0.427940	−	0.427940i	−0.459986	−	0.887926i	$-0.652146\pi$
$577$	10.2795	−	10.2795i	0.427940	−	0.427940i	0.887926	+	0.459986i	$0.152146\pi$
$578$	−22.6624	+	8.02606i	−0.942630	+	0.333840i
$579$		−	27.7321i		−	1.15250i
$580$	15.3978	−	12.2570i	0.639360	−	0.508944i
$581$	3.19652	−	3.19652i	0.132614	−	0.132614i
$582$	−12.8383	+	35.6022i	−0.532165	+	1.47576i
$583$	32.0693			1.32818
$584$	−14.5701	+	8.58637i	−0.602915	+	0.355307i
$585$	−12.8829	−	2.69618i	−0.532643	−	0.111473i
$586$	23.7252	−	11.1493i	0.980077	−	0.460573i
$587$	2.36561	+	2.36561i	0.0976393	+	0.0976393i	0.754239	−	0.656600i	$-0.228006\pi$
$587$	2.36561	+	2.36561i	0.0976393	+	0.0976393i	−0.656600	+	0.754239i	$0.728006\pi$
$588$	8.95765	−	10.8053i	0.369407	−	0.445601i
$589$	24.1981	−	24.1981i	0.997067	−	0.997067i
$590$	7.09689	+	29.9053i	0.292174	+	1.23118i
$591$			24.4527i			1.00585i
$592$	−9.24142	+	1.74317i	−0.379820	+	0.0716440i
$593$	−16.2960	+	16.2960i	−0.669197	+	0.669197i	−0.957530	−	0.288333i	$-0.906899\pi$
$593$	−16.2960	+	16.2960i	−0.669197	+	0.669197i	0.288333	+	0.957530i	$0.406899\pi$
$594$	−1.44257	−	3.06972i	−0.0591893	−	0.125952i
$595$	14.8276	+	11.2363i	0.607871	+	0.460642i
$596$	−7.76538	−	6.43757i	−0.318083	−	0.263693i
$597$	−31.2962	+	31.2962i	−1.28087	+	1.28087i
$598$	−5.97520	−	12.7149i	−0.244344	−	0.519952i
$599$	−43.5609			−1.77985			−0.889925	−	0.456108i	$-0.849243\pi$
$599$	−43.5609			−1.77985			−0.889925	+	0.456108i	$0.849243\pi$
$600$	4.05462	+	33.6505i	0.165529	+	1.37378i
$601$	−5.89439	+	5.89439i	−0.240437	+	0.240437i	−0.817031	−	0.576594i	$-0.804382\pi$
$601$	−5.89439	+	5.89439i	−0.240437	+	0.240437i	0.576594	+	0.817031i	$0.304382\pi$
$602$	5.10067	−	2.39699i	0.207888	−	0.0976939i
$603$	−14.8880	+	14.8880i	−0.606286	+	0.606286i
$604$	2.73365	+	2.26622i	0.111231	+	0.0922112i
$605$	−8.00754	+	5.23591i	−0.325553	+	0.212870i
$606$	8.66848	+	3.12589i	0.352133	+	0.126981i
$607$		−	31.7380i		−	1.28820i	−0.764940	−	0.644102i	$-0.777231\pi$
$607$		−	31.7380i		−	1.28820i	0.764940	−	0.644102i	$-0.222769\pi$
$608$	4.04464	−	25.1181i	0.164032	−	1.01867i
$609$	15.0492	−	15.0492i	0.609824	−	0.609824i
$610$	−12.9643	+	21.0320i	−0.524909	+	0.851562i
$611$	−6.96514			−0.281779
$612$	−21.2638	−	7.73655i	−0.859538	−	0.312732i
$613$	0.808133	−	0.808133i	0.0326402	−	0.0326402i	−0.690598	−	0.723239i	$-0.742653\pi$
$613$	0.808133	−	0.808133i	0.0326402	−	0.0326402i	0.723239	+	0.690598i	$0.242653\pi$
$614$	30.0188	−	14.1069i	1.21146	−	0.569307i
$615$	−7.02617	+	33.5725i	−0.283322	+	1.35377i
$616$	21.5998	+	5.58147i	0.870280	+	0.224884i
$617$	21.4101			0.861937			0.430969	−	0.902367i	$-0.358172\pi$
$617$	21.4101			0.861937			0.430969	+	0.902367i	$0.358172\pi$
$618$	6.88722	+	14.6557i	0.277045	+	0.589538i
$619$	23.0357	+	23.0357i	0.925885	+	0.925885i	0.997437	−	0.0715521i	$-0.0227952\pi$
$619$	23.0357	+	23.0357i	0.925885	+	0.925885i	−0.0715521	+	0.997437i	$0.522795\pi$
$620$	−21.1927	−	26.6233i	−0.851121	−	1.06922i
$621$	2.84146			0.114024
$622$	18.7789	−	8.82487i	0.752965	−	0.353845i
$623$			29.9358i			1.19935i
$624$	11.5941	−	16.9848i	0.464135	−	0.679937i
$625$	−16.9598	−	18.3675i	−0.678393	−	0.734699i
$626$	−41.4109	−	14.9329i	−1.65511	−	0.596840i
$627$	29.7923	+	29.7923i	1.18979	+	1.18979i
$628$	2.43793	+	26.0773i	0.0972842	+	1.04060i
$629$	3.26229	+	9.12840i	0.130076	+	0.363973i
$630$	4.04299	+	17.0366i	0.161077	+	0.678753i
$631$	−25.2827			−1.00649			−0.503245	−	0.864144i	$-0.667861\pi$
$631$	−25.2827			−1.00649			−0.503245	+	0.864144i	$0.667861\pi$
$632$	−21.4080	−	5.53191i	−0.851564	−	0.220048i
$633$	0.000348233	0	0.000348233i	1.38410e−5	0	1.38410e-5i
$634$	2.37091	+	0.854959i	0.0941607	+	0.0339547i
$635$	11.2464	+	2.35368i	0.446299	+	0.0934031i
$636$	−39.1556	+	3.66061i	−1.55262	+	0.145153i
$637$	4.44150	−	4.44150i	0.175979	−	0.175979i
$638$	−22.8842	−	8.25214i	−0.905995	−	0.326705i
$639$	−5.17202	+	5.17202i	−0.204602	+	0.204602i
$640$	−24.3631	−	6.81468i	−0.963036	−	0.269374i
$641$	19.9818	+	19.9818i	0.789234	+	0.789234i	0.981369	−	0.192135i	$-0.0615411\pi$
$641$	19.9818	+	19.9818i	0.789234	+	0.789234i	−0.192135	+	0.981369i	$0.561541\pi$
$642$	18.9998	−	52.6888i	0.749862	−	2.07946i
$643$			11.8285i			0.466469i	0.972421	+	0.233234i	$0.0749309\pi$
$643$			11.8285i			0.466469i	−0.972421	+	0.233234i	$0.925069\pi$
$644$	−11.9280	+	14.3883i	−0.470030	+	0.566979i
$645$	2.16801	−	10.3592i	0.0853655	−	0.407894i
$646$	−26.2245	−	0.0749465i	−1.03179	−	0.00294873i
$647$	4.32648	+	4.32648i	0.170092	+	0.170092i	0.787020	−	0.616928i	$-0.211623\pi$
$647$	4.32648	+	4.32648i	0.170092	+	0.170092i	−0.616928	+	0.787020i	$0.711623\pi$
$648$	13.9330	+	23.6427i	0.547340	+	0.928774i
$649$	26.8641	−	26.8641i	1.05451	−	1.05451i
$650$	0.404893	+	15.1630i	0.0158812	+	0.594743i
$651$	−26.0205	−	26.0205i	−1.01983	−	1.01983i
$652$	0.467520	+	0.387578i	0.0183095	+	0.0151787i
$653$		−	10.0400i		−	0.392896i	−0.980514	−	0.196448i	$-0.937059\pi$
$653$		−	10.0400i		−	0.392896i	0.980514	−	0.196448i	$-0.0629408\pi$
$654$	−25.8864	−	55.0851i	−1.01224	−	2.15400i
$655$	−2.24738	+	10.7385i	−0.0878125	+	0.419586i
$656$	−21.1446	−	14.4336i	−0.825557	−	0.563537i
$657$			16.4070i			0.640100i
$658$	3.94090	+	8.38604i	0.153632	+	0.326922i
$659$		−	40.5131i		−	1.57817i	−0.614286	−	0.789084i	$-0.710556\pi$
$659$		−	40.5131i		−	1.57817i	0.614286	−	0.789084i	$-0.289444\pi$
$660$	32.7782	−	26.0921i	1.27589	−	1.01564i
$661$	2.08022			0.0809114			0.0404557	−	0.999181i	$-0.487119\pi$
$661$	2.08022			0.0809114			0.0404557	+	0.999181i	$0.487119\pi$
$662$	0.199856	−	0.554226i	0.00776763	−	0.0215406i
$663$	−19.1590	−	9.07042i	−0.744073	−	0.352266i
$664$	6.13485	+	1.58527i	0.238078	+	0.0615203i
$665$	11.1058	+	16.9847i	0.430664	+	0.658637i
$666$	−3.09494	+	8.58266i	−0.119926	+	0.332571i
$667$	14.4106	−	14.4106i	0.557980	−	0.557980i
$668$	15.0288	−	18.1287i	0.581482	−	0.701419i
$669$	−43.0332	+	43.0332i	−1.66376	+	1.66376i
$670$	20.6555	+	12.7322i	0.797993	+	0.491888i
$671$	30.5392			1.17895
$672$	−27.0097	−	4.34925i	−1.04192	−	0.167776i
$673$	18.2171			0.702217			0.351108	−	0.936335i	$-0.385805\pi$
$673$	18.2171			0.702217			0.351108	+	0.936335i	$0.385805\pi$
$674$	43.7202	+	15.7657i	1.68404	+	0.607271i
$675$	−2.81042	−	1.23023i	−0.108173	−	0.0473517i
$676$	−10.7200	+	12.9311i	−0.412306	+	0.497349i
$677$		−	34.8924i		−	1.34102i	−0.741899	−	0.670512i	$-0.766075\pi$
$677$		−	34.8924i		−	1.34102i	0.741899	−	0.670512i	$-0.233925\pi$
$678$	19.5388	−	54.1836i	0.750385	−	2.08091i
$679$	22.5320			0.864697
$680$	−3.01673	+	25.9017i	−0.115686	+	0.993286i
$681$	66.8520			2.56178
$682$	−14.2682	+	39.5675i	−0.546358	+	1.51512i
$683$		−	23.4250i		−	0.896333i	−0.893950	−	0.448166i	$-0.852077\pi$
$683$		−	23.4250i		−	0.896333i	0.893950	−	0.448166i	$-0.147923\pi$
$684$	−19.0017	−	15.7525i	−0.726547	−	0.602313i
$685$	−12.0989	−	2.53210i	−0.462275	−	0.0967466i
$686$	−26.6522	−	9.61090i	−1.01759	−	0.366946i
$687$	−5.24040			−0.199934
$688$	6.52443	+	4.45367i	0.248742	+	0.169795i
$689$	−17.5996			−0.670492
$690$	8.10406	+	34.1493i	0.308516	+	1.30004i
$691$	−26.1398	+	26.1398i	−0.994406	+	0.994406i	−0.999984	−	0.00557833i	$-0.998224\pi$
$691$	−26.1398	+	26.1398i	−0.994406	+	0.994406i	0.00557833	+	0.999984i	$0.498224\pi$
$692$	−32.1698	−	26.6691i	−1.22291	−	1.01381i
$693$	15.3041	−	15.3041i	0.581354	−	0.581354i
$694$	−1.59016	+	4.40972i	−0.0603618	+	0.167391i
$695$	41.9676	+	8.78312i	1.59192	+	0.333163i
$696$	28.8828	+	7.46344i	1.09480	+	0.282901i
$697$	−11.2918	+	23.8512i	−0.427709	+	0.903428i
$698$	14.2814	−	39.6040i	0.540558	−	1.49903i
$699$	−8.60541			−0.325486
$700$	18.0272	−	9.06679i	0.681366	−	0.342692i
$701$			2.91892i			0.110246i	0.998480	+	0.0551230i	$0.0175551\pi$
$701$			2.91892i			0.110246i	−0.998480	+	0.0551230i	$0.982445\pi$
$702$	0.791680	+	1.68466i	0.0298800	+	0.0635833i
$703$			10.5740i			0.398807i
$704$	8.63132	+	30.0555i	0.325305	+	1.13276i
$705$	17.0317	+	3.56445i	0.641449	+	0.134245i
$706$	−14.6705	−	31.2180i	−0.552130	−	1.17491i
$707$		−	5.48611i		−	0.206327i
$708$	−29.7338	+	35.8667i	−1.11746	+	1.34795i
$709$	−22.4889	−	22.4889i	−0.844588	−	0.844588i	0.144863	−	0.989452i	$-0.453726\pi$
$709$	−22.4889	−	22.4889i	−0.844588	−	0.844588i	−0.989452	+	0.144863i	$0.953726\pi$
$710$	7.17564	+	4.42311i	0.269297	+	0.165996i
$711$	−15.1682	+	15.1682i	−0.568852	+	0.568852i
$712$	−36.1500	+	21.3037i	−1.35478	+	0.798390i
$713$	−24.9164	−	24.9164i	−0.933125	−	0.933125i
$714$	−0.0805909	+	28.1995i	−0.00301604	+	1.05534i
$715$	15.6924	−	10.2608i	0.586861	−	0.383732i
$716$	−2.32780	−	1.92977i	−0.0869939	−	0.0721187i
$717$		−	70.3684i		−	2.62796i
$718$	1.57258	−	4.36097i	0.0586883	−	0.162750i
$719$	5.05850	+	5.05850i	0.188650	+	0.188650i	0.795112	−	0.606462i	$-0.207412\pi$
$719$	5.05850	+	5.05850i	0.188650	+	0.188650i	−0.606462	+	0.795112i	$0.707412\pi$
$720$	−17.6959	+	17.0063i	−0.659487	+	0.633786i
$721$	6.81705	−	6.81705i	0.253880	−	0.253880i
$722$	−1.63288	−	0.588822i	−0.0607694	−	0.0219137i
$723$	36.2729	−	36.2729i	1.34900	−	1.34900i
$724$	−3.51608	−	37.6097i	−0.130674	−	1.39775i
$725$	−20.4923	+	8.01398i	−0.761066	+	0.297632i
$726$	−13.6422	−	4.91944i	−0.506311	−	0.182578i
$727$	−28.5861	−	28.5861i	−1.06020	−	1.06020i	−0.998068	−	0.0621329i	$-0.980210\pi$
$727$	−28.5861	−	28.5861i	−1.06020	−	1.06020i	−0.0621329	−	0.998068i	$-0.519790\pi$
$728$	−11.8539	−	3.06310i	−0.439336	−	0.113526i
$729$	22.2119			0.822663
$730$	18.3972	−	4.36588i	0.680910	−	0.161588i
$731$	3.48425	−	7.35959i	0.128869	−	0.272204i
$732$	−37.2873	+	3.48594i	−1.37818	+	0.128844i
$733$	−15.0238	−	15.0238i	−0.554915	−	0.554915i	0.372940	−	0.927855i	$-0.378350\pi$
$733$	−15.0238	−	15.0238i	−0.554915	−	0.554915i	−0.927855	+	0.372940i	$0.878350\pi$
$734$	−18.7047	−	6.74498i	−0.690402	−	0.248962i
$735$	−13.1336	+	8.58772i	−0.484441	+	0.316763i
$736$	−25.8636	−	4.16469i	−0.953345	−	0.153513i
$737$		−	29.9925i		−	1.10479i
$738$	−22.4785	+	10.5635i	−0.827446	+	0.388846i
$739$	19.8141			0.728874			0.364437	−	0.931228i	$-0.381261\pi$
$739$	19.8141			0.728874			0.364437	+	0.931228i	$0.381261\pi$
$740$	10.4473	+	1.18652i	0.384049	+	0.0436175i
$741$	−16.3500	−	16.3500i	−0.600632	−	0.600632i
$742$	9.95792	+	21.1900i	0.365567	+	0.777908i
$743$	4.96981			0.182325			0.0911623	−	0.995836i	$-0.470942\pi$
$743$	4.96981			0.182325			0.0911623	+	0.995836i	$0.470942\pi$
$744$	12.9045	−	49.9393i	0.473103	−	1.83086i
$745$	6.17171	+	9.43872i	0.226114	+	0.345808i
$746$	14.0866	−	6.61977i	0.515745	−	0.242367i
$747$	4.34672	−	4.34672i	0.159038	−	0.159038i
$748$	29.2112	−	13.6256i	1.06807	−	0.498201i
$749$	−33.3457			−1.21843
$750$	6.76969	−	37.2850i	0.247194	−	1.36145i
$751$	33.8398	−	33.8398i	1.23483	−	1.23483i	0.272748	−	0.962086i	$-0.412067\pi$
$751$	33.8398	−	33.8398i	1.23483	−	1.23483i	0.962086	−	0.272748i	$-0.0879325\pi$
$752$	−7.32231	+	10.7269i	−0.267017	+	0.391168i
$753$		−	10.8980i		−	0.397146i
$754$	12.5588	+	4.52876i	0.457365	+	0.164928i
$755$	−2.17263	−	3.32272i	−0.0790701	−	0.120926i
$756$	1.58040	−	1.90637i	0.0574784	−	0.0693339i
$757$	−6.22750	+	6.22750i	−0.226342	+	0.226342i	−0.811163	−	0.584821i	$-0.801165\pi$
$757$	−6.22750	+	6.22750i	−0.226342	+	0.226342i	0.584821	+	0.811163i	$0.301165\pi$
$758$	−4.06340	+	1.90954i	−0.147589	+	0.0693575i
$759$	30.6766	−	30.6766i	1.11349	−	1.11349i
$760$	−12.6070	+	25.4982i	−0.457303	+	0.924918i
$761$	−25.8950			−0.938694			−0.469347	−	0.883014i	$-0.655511\pi$
$761$	−25.8950			−0.938694			−0.469347	+	0.883014i	$0.655511\pi$
$762$	7.40743	+	15.7627i	0.268343	+	0.571021i
$763$	−25.6227	+	25.6227i	−0.927602	+	0.927602i
$764$	31.8440	−	38.4121i	1.15207	−	1.38970i
$765$	20.1629	+	15.2794i	0.728993	+	0.552428i
$766$	−5.53020	−	11.7680i	−0.199814	−	0.425195i
$767$	−14.7430	+	14.7430i	−0.532339	+	0.532339i
$768$	−13.9693	−	35.7116i	−0.504074	−	1.28863i
$769$			19.9884i			0.720800i	0.932798	+	0.360400i	$0.117360\pi$
$769$			19.9884i			0.720800i	−0.932798	+	0.360400i	$0.882640\pi$
$770$	−21.2328	−	13.0881i	−0.765178	−	0.471661i
$771$	28.3968	−	28.3968i	1.02268	−	1.02268i
$772$	−17.8162	−	14.7698i	−0.641219	−	0.531576i
$773$	29.1722	+	29.1722i	1.04925	+	1.04925i	0.998723	+	0.0505291i	$0.0160908\pi$
$773$	29.1722	+	29.1722i	1.04925	+	1.04925i	0.0505291	+	0.998723i	$0.483909\pi$
$774$	6.93604	−	3.25949i	0.249311	−	0.117160i
$775$	13.8564	+	35.4319i	0.497737	+	1.27275i
$776$	16.0348	+	27.2092i	0.575615	+	0.976753i
$777$	11.3704			0.407910
$778$	9.63337	−	26.7145i	0.345373	−	0.957763i
$779$	−20.3543	+	20.3543i	−0.729267	+	0.729267i
$780$	−17.9886	+	14.3193i	−0.644096	+	0.512714i
$781$		−	10.4192i		−	0.372830i
$782$	−0.0771710	+	27.0029i	−0.00275963	+	0.965621i
$783$	−1.90932	+	1.90932i	−0.0682335	+	0.0682335i
$784$	−2.17099	−	11.5095i	−0.0775355	−	0.411054i
$785$	5.99838	−	28.6615i	0.214091	−	1.02297i
$786$	−15.0507	+	7.07288i	−0.536842	+	0.252281i
$787$	−23.0062			−0.820084			−0.410042	−	0.912067i	$-0.634486\pi$
$787$	−23.0062			−0.820084			−0.410042	+	0.912067i	$0.634486\pi$
$788$	15.7094	+	13.0232i	0.559624	+	0.463933i
$789$	42.8210	−	42.8210i	1.52447	−	1.52447i
$790$	21.0443	+	12.9718i	0.748722	+	0.461517i
$791$	−34.2918			−1.21928
$792$	29.3720	+	7.58985i	1.04369	+	0.269693i
$793$	−16.7598			−0.595160
$794$	38.0602	+	13.7247i	1.35071	+	0.487071i
$795$	43.0358	+	9.00669i	1.52632	+	0.319434i
$796$	3.43794	+	36.7739i	0.121855	+	1.30342i
$797$	12.5824	−	12.5824i	0.445691	−	0.445691i	−0.448228	−	0.893919i	$-0.647945\pi$
$797$	12.5824	−	12.5824i	0.445691	−	0.445691i	0.893919	+	0.448228i	$0.147945\pi$
$798$	−10.4346	+	28.9363i	−0.369379	+	1.02433i
$799$	12.1000	+	5.72847i	0.428066	+	0.202659i
$800$	23.7779	+	15.3170i	0.840676	+	0.541539i
$801$			40.7076i			1.43833i
$802$	23.0049	−	10.8108i	0.812332	−	0.381744i
$803$	−16.5263	−	16.5263i	−0.583201	−	0.583201i
$804$	3.42354	+	36.6198i	0.120739	+	1.29148i
$805$	17.4888	−	11.4354i	0.616399	−	0.403046i
$806$	7.83037	−	21.7146i	0.275813	−	0.764864i
$807$	−37.4743	+	37.4743i	−1.31916	+	1.31916i
$808$	6.62493	−	3.90417i	0.233064	−	0.137348i
$809$	−10.7696	−	10.7696i	−0.378637	−	0.378637i	0.491973	−	0.870610i	$-0.336276\pi$
$809$	−10.7696	−	10.7696i	−0.378637	−	0.378637i	−0.870610	+	0.491973i	$0.836276\pi$
$810$	−7.08446	−	29.8529i	−0.248922	−	1.04892i
$811$	12.4159	+	12.4159i	0.435982	+	0.435982i	0.890657	−	0.454675i	$-0.150245\pi$
$811$	12.4159	+	12.4159i	0.435982	+	0.435982i	−0.454675	+	0.890657i	$0.650245\pi$
$812$	−1.65318	−	17.6832i	−0.0580154	−	0.620560i
$813$	−15.9170			−0.558232
$814$	−5.52761	−	11.7625i	−0.193743	−	0.412275i
$815$	−0.371572	−	0.568263i	−0.0130156	−	0.0199054i
$816$	−34.1106	+	19.9708i	−1.19411	+	0.699117i
$817$	6.28057	−	6.28057i	0.219729	−	0.219729i
$818$	5.21768	−	14.4693i	0.182432	−	0.505906i
$819$	−8.39886	+	8.39886i	−0.293480	+	0.293480i
$820$	17.8263	+	22.3942i	0.622520	+	0.782040i
$821$	−7.29757	+	7.29757i	−0.254687	+	0.254687i	−0.822889	−	0.568202i	$-0.807639\pi$
$821$	−7.29757	+	7.29757i	−0.254687	+	0.254687i	0.568202	+	0.822889i	$0.307639\pi$
$822$	−7.96893	−	16.9575i	−0.277948	−	0.591461i
$823$			51.2262i			1.78563i	0.450422	+	0.892816i	$0.351274\pi$
$823$			51.2262i			1.78563i	−0.450422	+	0.892816i	$0.648726\pi$
$824$	13.0835	+	3.38082i	0.455784	+	0.117776i
$825$	−43.6231	+	17.0598i	−1.51876	+	0.593946i
$826$	26.0923	+	9.40897i	0.907866	+	0.327380i
$827$			8.46846i			0.294477i	0.989101	+	0.147239i	$0.0470385\pi$
$827$			8.46846i			0.294477i	−0.989101	+	0.147239i	$0.952961\pi$
$828$	−16.2201	+	19.5656i	−0.563687	+	0.679953i
$829$	42.0554			1.46065			0.730323	−	0.683102i	$-0.239370\pi$
$829$	42.0554			1.46065			0.730323	+	0.683102i	$0.239370\pi$
$830$	−6.03062	−	3.71731i	−0.209326	−	0.129030i
$831$	57.2815			1.98707
$832$	−4.73686	−	16.4944i	−0.164221	−	0.571842i
$833$	−11.3688	+	4.06294i	−0.393904	+	0.140773i
$834$	27.6419	+	58.8207i	0.957161	+	2.03679i
$835$	−22.0351	+	14.4082i	−0.762557	+	0.498615i
$836$	35.0069	−	3.27275i	1.21074	−	0.113190i
$837$	3.30127	+	3.30127i	0.114109	+	0.114109i
$838$	−5.23701	−	11.1441i	−0.180910	−	0.384967i
$839$	−8.45607	+	8.45607i	−0.291936	+	0.291936i	−0.837845	−	0.545909i	$-0.816185\pi$
$839$	−8.45607	+	8.45607i	−0.291936	+	0.291936i	0.545909	+	0.837845i	$0.316185\pi$
$840$	27.4185	+	13.5564i	0.946030	+	0.467741i
$841$		−	9.63363i		−	0.332194i
$842$	12.0907	−	33.5291i	0.416674	−	1.15549i
$843$	12.6727			0.436470
$844$	0.000409184	0	3.82541e-5i	1.40847e−5	0	1.31676e-6i
$845$	15.7175	−	10.2773i	0.540700	−	0.353548i
$846$	5.35895	+	11.4036i	0.184245	+	0.392063i
$847$			8.63391i			0.296665i
$848$	−18.5021	+	27.1048i	−0.635365	+	0.930781i
$849$			66.4036i			2.27897i
$850$	11.7674	−	26.6745i	0.403620	−	0.914927i
$851$	10.8879			0.373232
$852$	1.18932	+	12.7216i	0.0407455	+	0.435834i
$853$	−47.3315			−1.62060			−0.810299	−	0.586017i	$-0.800695\pi$
$853$	−47.3315			−1.62060			−0.810299	+	0.586017i	$0.800695\pi$
$854$	9.48278	+	20.1789i	0.324494	+	0.690508i
$855$	15.1020	+	23.0963i	0.516477	+	0.789875i
$856$	−23.7303	−	40.2677i	−0.811086	−	1.37632i
$857$		−	12.9330i		−	0.441781i	−0.975299	−	0.220891i	$-0.929104\pi$
$857$		−	12.9330i		−	0.441781i	0.975299	−	0.220891i	$-0.0708964\pi$
$858$	26.7347	+	9.64062i	0.912706	+	0.329125i
$859$	−16.4770			−0.562189			−0.281094	−	0.959680i	$-0.590697\pi$
$859$	−16.4770			−0.562189			−0.281094	+	0.959680i	$0.590697\pi$
$860$	−5.50053	−	6.91002i	−0.187566	−	0.235630i
$861$	21.8872	+	21.8872i	0.745913	+	0.745913i
$862$	−6.59814	−	14.0405i	−0.224734	−	0.478222i
$863$	6.60967	−	6.60967i	0.224996	−	0.224996i	−0.585602	−	0.810598i	$-0.699142\pi$
$863$	6.60967	−	6.60967i	0.224996	−	0.224996i	0.810598	+	0.585602i	$0.199142\pi$
$864$	3.42678	+	0.551798i	0.116581	+	0.0187725i
$865$	25.5677	+	39.1020i	0.869328	+	1.32951i
$866$	30.6476	−	14.4024i	1.04145	−	0.489414i
$867$	25.8233	+	31.5146i	0.877007	+	1.07029i
$868$	−30.5749	+	2.85841i	−1.03778	+	0.0970206i
$869$		−	30.5569i		−	1.03657i
$870$	−28.3921	−	17.5011i	−0.962583	−	0.593343i
$871$			16.4598i			0.557720i
$872$	−49.1757	−	12.7072i	−1.66530	−	0.430320i
$873$	30.6396			1.03699
$874$	−9.99176	+	27.7084i	−0.337976	+	0.937251i
$875$	−22.2488	+	3.73860i	−0.752146	+	0.126388i
$876$	22.0645	+	18.2917i	0.745491	+	0.618019i
$877$	−4.31990			−0.145873			−0.0729364	−	0.997337i	$-0.523237\pi$
$877$	−4.31990			−0.145873			−0.0729364	+	0.997337i	$0.523237\pi$
$878$	−11.9913	−	25.5170i	−0.404688	−	0.861158i
$879$	−31.4134	−	31.4134i	−1.05955	−	1.05955i
$880$	0.694648	−	34.9544i	0.0234166	−	1.17831i
$881$	9.41805	+	9.41805i	0.317302	+	0.317302i	0.847730	−	0.530428i	$-0.177969\pi$
$881$	9.41805	+	9.41805i	0.317302	+	0.317302i	−0.530428	+	0.847730i	$0.677969\pi$
$882$	−10.6891	−	3.85452i	−0.359919	−	0.129788i
$883$	16.3017	+	16.3017i	0.548597	+	0.548597i	0.926035	−	0.377438i	$-0.123195\pi$
$883$	16.3017	+	16.3017i	0.548597	+	0.548597i	−0.377438	+	0.926035i	$0.623195\pi$
$884$	−16.0311	+	7.47770i	−0.539183	+	0.251502i
$885$	43.5955	−	28.5059i	1.46545	−	0.958214i
$886$	14.7651	+	31.4195i	0.496044	+	1.05556i
$887$			39.0956i			1.31270i	0.754456	+	0.656350i	$0.227901\pi$
$887$			39.0956i			1.31270i	−0.754456	+	0.656350i	$0.772099\pi$
$888$	8.09168	+	13.7307i	0.271539	+	0.460771i
$889$	7.33195	−	7.33195i	0.245906	−	0.245906i
$890$	45.6454	−	10.8322i	1.53004	−	0.363096i
$891$	−26.8171	+	26.8171i	−0.898406	+	0.898406i
$892$	4.72728	+	50.5653i	0.158281	+	1.69305i
$893$	10.3259	+	10.3259i	0.345544	+	0.345544i
$894$	−5.79869	+	16.0805i	−0.193937	+	0.537812i
$895$	1.85007	+	2.82941i	0.0618410	+	0.0945766i
$896$	−17.1792	+	15.0358i	−0.573917	+	0.502311i
$897$	−16.8353	+	16.8353i	−0.562113	+	0.562113i
$898$	0.0551849	+	0.117431i	0.00184154	+	0.00391871i
$899$	33.4851			1.11679
$900$	24.5140	−	12.3293i	0.817132	−	0.410976i
$901$	30.5743	+	14.4748i	1.01858	+	0.482225i
$902$	12.0017	−	33.2822i	0.399613	−	1.10818i
$903$	−6.75357	−	6.75357i	−0.224745	−	0.224745i
$904$	−24.4036	−	41.4101i	−0.811652	−	1.37728i
$905$	−8.65109	+	41.3367i	−0.287572	+	1.37408i
$906$	2.04131	−	5.66082i	0.0678181	−	0.188068i
$907$		−	13.5619i		−	0.450316i	−0.974322	−	0.225158i	$-0.927710\pi$
$907$		−	13.5619i		−	0.450316i	0.974322	−	0.225158i	$-0.0722898\pi$
$908$	35.6046	−	42.9484i	1.18158	−	1.42529i
$909$		−	7.46018i		−	0.247439i
$910$	11.6525	+	7.18271i	0.386278	+	0.238104i
$911$	−31.3006	−	31.3006i	−1.03703	−	1.03703i	−0.999287	−	0.0377475i	$-0.987982\pi$
$911$	−31.3006	−	31.3006i	−1.03703	−	1.03703i	−0.0377475	−	0.999287i	$-0.512018\pi$
$912$	−42.3687	+	7.99183i	−1.40297	+	0.264636i
$913$			8.75664i			0.289802i
$914$	−4.73633	−	10.0787i	−0.156664	−	0.333373i
$915$	40.9824	+	8.57694i	1.35484	+	0.283545i
$916$	−2.79098	+	3.36665i	−0.0922165	+	0.111237i
$917$	7.00081	+	7.00081i	0.231187	+	0.231187i
$918$	0.0102247	−	3.57773i	0.000337466	−	0.118083i
$919$	−3.78384			−0.124817			−0.0624086	−	0.998051i	$-0.519878\pi$
$919$	−3.78384			−0.124817			−0.0624086	+	0.998051i	$0.519878\pi$
$920$	26.2550	+	12.9812i	0.865603	+	0.427976i
$921$	−39.7465	−	39.7465i	−1.30969	−	1.30969i
$922$	13.9036	+	5.01369i	0.457891	+	0.165117i
$923$			5.71807i			0.188212i
$924$	−3.51922	−	37.6433i	−0.115774	−	1.23837i
$925$	−10.7689	−	4.71399i	−0.354080	−	0.154995i
$926$	4.57268	−	2.14886i	0.150268	−	0.0706161i
$927$	9.27002	−	9.27002i	0.304467	−	0.304467i
$928$	20.1775	−	14.5806i	0.662359	−	0.478630i
$929$	−14.2491	−	14.2491i	−0.467499	−	0.467499i	0.433604	−	0.901103i	$-0.357242\pi$
$929$	−14.2491	−	14.2491i	−0.467499	−	0.467499i	−0.901103	+	0.433604i	$0.857242\pi$
$930$	−30.2600	+	49.0909i	−0.992263	+	1.60975i
$931$	−13.1692			−0.431602
$932$	−4.58314	+	5.52846i	−0.150126	+	0.181091i
$933$	−24.8643	−	24.8643i	−0.814021	−	0.814021i
$934$	−0.926099	−	1.97069i	−0.0303029	−	0.0644831i
$935$	−35.7000	+	4.91906i	−1.16752	+	0.160870i
$936$	−16.1193	−	4.16530i	−0.526877	−	0.136147i
$937$	16.8975	+	16.8975i	0.552017	+	0.552017i	0.927023	−	0.375006i	$-0.122359\pi$
$937$	16.8975	+	16.8975i	0.552017	+	0.552017i	−0.375006	+	0.927023i	$0.622359\pi$
$938$	19.8177	−	9.31302i	0.647070	−	0.304081i
$939$			74.6023i			2.43455i
$940$	11.3608	−	9.04345i	0.370549	−	0.294965i
$941$	−22.4153	−	22.4153i	−0.730717	−	0.730717i	0.240045	−	0.970762i	$-0.422838\pi$
$941$	−22.4153	−	22.4153i	−0.730717	−	0.730717i	−0.970762	+	0.240045i	$0.922838\pi$
$942$	40.1712	−	18.8779i	1.30885	−	0.615075i
$943$	20.9584	+	20.9584i	0.682499	+	0.682499i
$944$	7.20634	+	38.2044i	0.234546	+	1.24345i
$945$	−2.31716	+	1.51513i	−0.0753773	+	0.0492871i
$946$	−3.70328	+	10.2697i	−0.120404	+	0.333895i
$947$	19.7448			0.641619			0.320809	−	0.947144i	$-0.396045\pi$
$947$	19.7448			0.641619			0.320809	+	0.947144i	$0.396045\pi$
$948$	3.48797	+	37.3090i	0.113284	+	1.21174i
$949$	9.06962	+	9.06962i	0.294412	+	0.294412i
$950$	21.8792	−	23.0797i	0.709854	−	0.748804i
$951$		−	4.27122i		−	0.138504i
$952$	18.0736	+	15.0705i	0.585769	+	0.488439i
$953$	−8.63995	−	8.63995i	−0.279875	−	0.279875i	0.553184	−	0.833059i	$-0.313413\pi$
$953$	−8.63995	−	8.63995i	−0.279875	−	0.279875i	−0.833059	+	0.553184i	$0.813413\pi$
$954$	13.5411	+	28.8147i	0.438408	+	0.932912i
$955$	−46.6894	+	30.5289i	−1.51083	+	0.987892i
$956$	−45.2075	−	37.4774i	−1.46212	−	1.21211i
$957$			41.2262i			1.33266i
$958$	−22.0307	−	46.8803i	−0.711780	−	1.51463i
$959$	−7.88773	+	7.88773i	−0.254708	+	0.254708i
$960$	3.14179	+	42.7575i	0.101401	+	1.37999i
$961$		−	26.8967i		−	0.867636i
$962$	3.03355	+	6.45524i	0.0978054	+	0.208125i
$963$	−45.3445			−1.46121
$964$	−3.98465	−	42.6217i	−0.128337	−	1.37275i
$965$	14.1598	+	21.6553i	0.455821	+	0.697110i
$966$	29.7952	+	10.7443i	0.958644	+	0.345691i
$967$	−0.498262	+	0.498262i	−0.0160230	+	0.0160230i	−0.715073	−	0.699050i	$-0.753607\pi$
$967$	−0.498262	+	0.498262i	−0.0160230	+	0.0160230i	0.699050	+	0.715073i	$0.253607\pi$
$968$	−10.4261	+	6.14428i	−0.335109	+	0.197485i
$969$	14.9564	+	41.8505i	0.480470	+	1.34443i
$970$	−8.15313	−	34.3561i	−0.261781	−	1.10311i
$971$			53.5426i			1.71826i	0.511755	+	0.859131i	$0.328995\pi$
$971$			53.5426i			1.71826i	−0.511755	+	0.859131i	$0.671005\pi$
$972$	27.3321	−	32.9697i	0.876678	−	1.05750i
$973$	27.3603	−	27.3603i	0.877130	−	0.877130i
$974$	−29.1099	−	10.4972i	−0.932743	−	0.336351i
$975$	23.9403	−	9.36239i	0.766703	−	0.299837i
$976$	−17.6193	+	25.8115i	−0.563980	+	0.826205i
$977$	−21.6684	−	21.6684i	−0.693234	−	0.693234i	0.269708	−	0.962942i	$-0.413073\pi$
$977$	−21.6684	−	21.6684i	−0.693234	−	0.693234i	−0.962942	+	0.269708i	$0.913073\pi$
$978$	0.349113	−	0.968135i	0.0111634	−	0.0309575i
$979$	−41.0036	−	41.0036i	−1.31048	−	1.31048i
$980$	−1.47773	+	13.0113i	−0.0472043	+	0.415631i
$981$	−34.8424	+	34.8424i	−1.11243	+	1.11243i
$982$	15.8654	−	43.9967i	0.506285	−	1.40399i
$983$	−31.3779			−1.00080			−0.500399	−	0.865795i	$-0.666814\pi$
$983$	−31.3779			−1.00080			−0.500399	+	0.865795i	$0.666814\pi$
$984$	−10.8546	+	42.0065i	−0.346033	+	1.33912i
$985$	−12.4854	−	19.0946i	−0.397818	−	0.608403i
$986$	−18.0927	−	18.1964i	−0.576190	−	0.579492i
$987$	11.1036	−	11.1036i	0.353431	−	0.353431i
$988$	−19.2117	+	1.79608i	−0.611206	+	0.0571409i
$989$	−6.46698	−	6.46698i	−0.205638	−	0.205638i
$990$	−28.8730	−	17.7975i	−0.917644	−	0.565642i
$991$	40.7200	−	40.7200i	1.29351	−	1.29351i	0.360913	−	0.932600i	$-0.382465\pi$
$991$	40.7200	−	40.7200i	1.29351	−	1.29351i	0.932600	−	0.360913i	$-0.117535\pi$
$992$	−25.2103	−	34.8875i	−0.800426	−	1.10768i
$993$	−0.998447			−0.0316847
$994$	6.88457	−	3.23530i	0.218365	−	0.102618i
$995$	8.45884	−	40.4181i	0.268163	−	1.28134i
$996$	−0.999541	−	10.6916i	−0.0316717	−	0.338775i
$997$	−27.8923			−0.883359			−0.441679	−	0.897173i	$-0.645617\pi$
$997$	−27.8923			−0.883359			−0.441679	+	0.897173i	$0.645617\pi$
$998$	14.0069	+	29.8060i	0.443381	+	0.943493i
$999$	−1.44258			−0.0456413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.t.a.523.12	✓	208
5.2	odd	4		680.2.bl.a.387.64	yes	208
8.3	odd	2	inner	680.2.t.a.523.41	yes	208
17.4	even	4		680.2.bl.a.123.93	yes	208
40.27	even	4		680.2.bl.a.387.93	yes	208
85.72	odd	4	inner	680.2.t.a.667.41	yes	208
136.123	odd	4		680.2.bl.a.123.64	yes	208
680.667	even	4	inner	680.2.t.a.667.12	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.t.a.523.12	✓	208	1.1	even	1	trivial
680.2.t.a.523.41	yes	208	8.3	odd	2	inner
680.2.t.a.667.12	yes	208	680.667	even	4	inner
680.2.t.a.667.41	yes	208	85.72	odd	4	inner
680.2.bl.a.123.64	yes	208	136.123	odd	4
680.2.bl.a.123.93	yes	208	17.4	even	4
680.2.bl.a.387.64	yes	208	5.2	odd	4
680.2.bl.a.387.93	yes	208	40.27	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33036 - 0.479733i) q^{2} +2.39666i q^{3} +(1.53971 + 1.27643i) q^{4} +(-1.22372 - 1.87150i) q^{5} +(1.14976 - 3.18842i) q^{6} -2.01789 q^{7} +(-1.43602 - 2.43677i) q^{8} -2.74399 q^{9} +(0.730169 + 3.07683i) q^{10} +(2.76394 - 2.76394i) q^{11} +(-3.05918 + 3.69017i) q^{12} +(-1.51684 + 1.51684i) q^{13} +(2.68452 + 0.968049i) q^{14} +(4.48535 - 2.93284i) q^{15} +(0.741429 + 3.93068i) q^{16} +(3.88261 - 1.38756i) q^{17} +(3.65049 + 1.31638i) q^{18} +4.49749 q^{19} +(0.504668 - 4.44357i) q^{20} -4.83620i q^{21} +(-5.00298 + 2.35108i) q^{22} -4.63098i q^{23} +(5.84011 - 3.44166i) q^{24} +(-2.00502 + 4.58038i) q^{25} +(2.74563 - 1.29027i) q^{26} +0.613578i q^{27} +(-3.10697 - 2.57571i) q^{28} +(3.11178 + 3.11178i) q^{29} +(-7.37411 + 1.74997i) q^{30} +(5.38037 - 5.38037i) q^{31} +(0.899312 - 5.58491i) q^{32} +(6.62422 + 6.62422i) q^{33} +(-5.83093 - 0.0166641i) q^{34} +(2.46933 + 3.77648i) q^{35} +(-4.22495 - 3.50252i) q^{36} +2.35110i q^{37} +(-5.98328 - 2.15759i) q^{38} +(-3.63536 - 3.63536i) q^{39} +(-2.80312 + 5.66944i) q^{40} +(-4.52570 + 4.52570i) q^{41} +(-2.32008 + 6.43388i) q^{42} +(1.39646 - 1.39646i) q^{43} +(7.78365 - 0.727683i) q^{44} +(3.35787 + 5.13537i) q^{45} +(-2.22163 + 6.16086i) q^{46} +(2.29593 + 2.29593i) q^{47} +(-9.42052 + 1.77696i) q^{48} -2.92812 q^{49} +(4.86475 - 5.13168i) q^{50} +(3.32551 + 9.30531i) q^{51} +(-4.27166 + 0.399351i) q^{52} +(5.80139 + 5.80139i) q^{53} +(0.294354 - 0.816279i) q^{54} +(-8.55499 - 1.79042i) q^{55} +(2.89774 + 4.91713i) q^{56} +10.7790i q^{57} +(-2.64696 - 5.63261i) q^{58} +9.71953 q^{59} +(10.6497 + 1.20952i) q^{60} +(5.52458 + 5.52458i) q^{61} +(-9.73896 + 4.57668i) q^{62} +5.53706 q^{63} +(-3.87567 + 6.99851i) q^{64} +(4.69496 + 0.982579i) q^{65} +(-5.63474 - 11.9904i) q^{66} +(5.42568 - 5.42568i) q^{67} +(7.74924 + 2.81946i) q^{68} +11.0989 q^{69} +(-1.47340 - 6.20870i) q^{70} +(1.88486 - 1.88486i) q^{71} +(3.94043 + 6.68646i) q^{72} -5.97927i q^{73} +(1.12790 - 3.12781i) q^{74} +(-10.9776 - 4.80534i) q^{75} +(6.92484 + 5.74075i) q^{76} +(-5.57732 + 5.57732i) q^{77} +(3.09233 + 6.58034i) q^{78} +(5.52779 - 5.52779i) q^{79} +(6.44897 - 6.19764i) q^{80} -9.70250 q^{81} +(8.19193 - 3.84968i) q^{82} +(-1.58409 + 1.58409i) q^{83} +(6.17309 - 7.44636i) q^{84} +(-7.34805 - 5.56832i) q^{85} +(-2.52772 + 1.18787i) q^{86} +(-7.45789 + 7.45789i) q^{87} +(-10.7041 - 2.76599i) q^{88} -14.8352i q^{89} +(-2.00357 - 8.44277i) q^{90} +(3.06082 - 3.06082i) q^{91} +(5.91114 - 7.13037i) q^{92} +(12.8949 + 12.8949i) q^{93} +(-1.95298 - 4.15585i) q^{94} +(-5.50367 - 8.41704i) q^{95} +(13.3851 + 2.15535i) q^{96} -11.1661 q^{97} +(3.89545 + 1.40472i) q^{98} +(-7.58420 + 7.58420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 8 q^{6} - 192 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{12} - 16 q^{14} - 16 q^{16} - 12 q^{18} - 10 q^{20} + 4 q^{22} + 16 q^{24} + 12 q^{28} - 24 q^{30} + 20 q^{32} - 8 q^{33} - 4 q^{34} - 8 q^{35} - 12 q^{38}+ \cdots + 24 q^{99}+O(q^{100}) \) 208 * q - 8 * q^6 - 192 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^12 - 16 * q^14 - 16 * q^16 - 12 * q^18 - 10 * q^20 + 4 * q^22 + 16 * q^24 + 12 * q^28 - 24 * q^30 + 20 * q^32 - 8 * q^33 - 4 * q^34 - 8 * q^35 - 12 * q^38 - 42 * q^40 - 8 * q^41 - 32 * q^42 + 8 * q^44 - 16 * q^46 + 160 * q^49 + 16 * q^50 - 8 * q^51 - 20 * q^52 + 36 * q^54 + 4 * q^56 - 56 * q^58 - 64 * q^59 + 32 * q^60 - 48 * q^65 - 8 * q^67 - 56 * q^68 - 28 * q^70 - 56 * q^72 + 8 * q^74 + 8 * q^75 - 12 * q^78 + 6 * q^80 + 128 * q^81 + 44 * q^82 + 8 * q^86 - 82 * q^90 + 24 * q^91 + 64 * q^94 - 48 * q^96 - 16 * q^97 - 40 * q^98 + 24 * q^99

Introduction

L-functions

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