LMFDB - Embedded newform 680.2.ba.b.21.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(21,680)] 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([0, 2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.21"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [140] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	680.21
Dual form			680.2.ba.b.421.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34753 - 0.429141i) q^{2} +(1.81913 + 1.81913i) q^{3} +(1.63168 + 1.15656i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67067 - 3.23200i) q^{6} +(-0.325706 - 0.325706i) q^{7} +(-1.70240 - 2.25872i) q^{8} +3.61847i q^{9} +(-0.649399 - 1.25630i) q^{10} +(2.26681 - 2.26681i) q^{11} +(0.864295 + 5.07217i) q^{12} +5.30047i q^{13} +(0.299124 + 0.578672i) q^{14} +2.57264i q^{15} +(1.32473 + 3.77427i) q^{16} +(-2.68145 - 3.13207i) q^{17} +(1.55284 - 4.87600i) q^{18} +3.91607 q^{19} +(0.335957 + 1.97158i) q^{20} -1.18500i q^{21} +(-4.02738 + 2.08181i) q^{22} +(6.27686 + 6.27686i) q^{23} +(1.01201 - 7.20580i) q^{24} +1.00000i q^{25} +(2.27465 - 7.14255i) q^{26} +(-1.12508 + 1.12508i) q^{27} +(-0.154747 - 0.908144i) q^{28} +(3.10847 + 3.10847i) q^{29} +(1.10403 - 3.46671i) q^{30} +(-3.97728 + 3.97728i) q^{31} +(-0.165423 - 5.65444i) q^{32} +8.24724 q^{33} +(2.26923 + 5.37127i) q^{34} -0.460617i q^{35} +(-4.18499 + 5.90417i) q^{36} +(-1.49361 - 1.49361i) q^{37} +(-5.27702 - 1.68055i) q^{38} +(-9.64225 + 9.64225i) q^{39} +(0.393375 - 2.80094i) q^{40} +(-1.90041 - 1.90041i) q^{41} +(-0.508533 + 1.59683i) q^{42} -12.1054 q^{43} +(6.32040 - 1.07699i) q^{44} +(-2.55865 + 2.55865i) q^{45} +(-5.76460 - 11.1519i) q^{46} -6.47445 q^{47} +(-4.45602 + 9.27574i) q^{48} -6.78783i q^{49} +(0.429141 - 1.34753i) q^{50} +(0.819736 - 10.5755i) q^{51} +(-6.13032 + 8.64865i) q^{52} +3.74075 q^{53} +(1.99890 - 1.03326i) q^{54} +3.20575 q^{55} +(-0.181195 + 1.29016i) q^{56} +(7.12385 + 7.12385i) q^{57} +(-2.85479 - 5.52274i) q^{58} -3.83252 q^{59} +(-2.97542 + 4.19771i) q^{60} +(-0.303730 + 0.303730i) q^{61} +(7.06631 - 3.65269i) q^{62} +(1.17856 - 1.17856i) q^{63} +(-2.20364 + 7.69051i) q^{64} +(-3.74800 + 3.74800i) q^{65} +(-11.1134 - 3.53923i) q^{66} +14.6822i q^{67} +(-0.752825 - 8.21178i) q^{68} +22.8369i q^{69} +(-0.197670 + 0.620696i) q^{70} +(9.59371 - 9.59371i) q^{71} +(8.17312 - 6.16010i) q^{72} +(5.97596 - 5.97596i) q^{73} +(1.37171 + 2.65365i) q^{74} +(-1.81913 + 1.81913i) q^{75} +(6.38976 + 4.52918i) q^{76} -1.47662 q^{77} +(17.1311 - 8.85534i) q^{78} +(-9.92269 - 9.92269i) q^{79} +(-1.73208 + 3.60554i) q^{80} +6.76207 q^{81} +(1.74532 + 3.37641i) q^{82} -1.92649 q^{83} +(1.37053 - 1.93354i) q^{84} +(0.318636 - 4.11077i) q^{85} +(16.3124 + 5.19491i) q^{86} +11.3094i q^{87} +(-8.97912 - 1.26106i) q^{88} +15.3083 q^{89} +(4.54587 - 2.34983i) q^{90} +(1.72639 - 1.72639i) q^{91} +(2.98223 + 17.5014i) q^{92} -14.4704 q^{93} +(8.72452 + 2.77845i) q^{94} +(2.76908 + 2.76908i) q^{95} +(9.98523 - 10.5871i) q^{96} +(7.40890 - 7.40890i) q^{97} +(-2.91294 + 9.14681i) q^{98} +(8.20239 + 8.20239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) $ 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Character values

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

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

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 $

$2$	−1.34753	−	0.429141i	−0.952848	−	0.303449i
$2$	−1.34753	−	0.429141i	−0.952848	−	0.303449i
$3$	1.81913	+	1.81913i	1.05028	+	1.05028i	0.998667	+	0.0516082i	$0.0164347\pi$
$3$	1.81913	+	1.81913i	1.05028	+	1.05028i	0.0516082	+	0.998667i	$0.483565\pi$
$4$	1.63168	+	1.15656i	0.815838	+	0.578281i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.67067	−	3.23200i	−0.682048	−	1.31946i
$7$	−0.325706	−	0.325706i	−0.123105	−	0.123105i	0.642870	−	0.765975i	$-0.277744\pi$
$7$	−0.325706	−	0.325706i	−0.123105	−	0.123105i	−0.765975	+	0.642870i	$0.777744\pi$
$8$	−1.70240	−	2.25872i	−0.601891	−	0.798578i
$9$			3.61847i			1.20616i
$10$	−0.649399	−	1.25630i	−0.205358	−	0.397276i
$11$	2.26681	−	2.26681i	0.683469	−	0.683469i	−0.277311	−	0.960780i	$-0.589443\pi$
$11$	2.26681	−	2.26681i	0.683469	−	0.683469i	0.960780	+	0.277311i	$0.0894434\pi$
$12$	0.864295	+	5.07217i	0.249501	+	1.46421i
$13$			5.30047i			1.47009i	0.678020	+	0.735043i	$0.262838\pi$
$13$			5.30047i			1.47009i	−0.678020	+	0.735043i	$0.737162\pi$
$14$	0.299124	+	0.578672i	0.0799444	+	0.154657i
$15$			2.57264i			0.664253i
$16$	1.32473	+	3.77427i	0.331183	+	0.943567i
$17$	−2.68145	−	3.13207i	−0.650346	−	0.759638i
$17$	−2.68145	−	3.13207i	−0.650346	−	0.759638i
$18$	1.55284	−	4.87600i	0.366007	−	1.14928i
$19$	3.91607			0.898408			0.449204	−	0.893429i	$-0.351708\pi$
$19$	3.91607			0.898408			0.449204	+	0.893429i	$0.351708\pi$
$20$	0.335957	+	1.97158i	0.0751222	+	0.440859i
$21$		−	1.18500i		−	0.258589i
$22$	−4.02738	+	2.08181i	−0.858639	+	0.443844i
$23$	6.27686	+	6.27686i	1.30882	+	1.30882i	0.922270	+	0.386546i	$0.126332\pi$
$23$	6.27686	+	6.27686i	1.30882	+	1.30882i	0.386546	+	0.922270i	$0.373668\pi$
$24$	1.01201	−	7.20580i	0.206576	−	1.47088i
$25$			1.00000i			0.200000i
$26$	2.27465	−	7.14255i	0.446096	−	1.40077i
$27$	−1.12508	+	1.12508i	−0.216522	+	0.216522i
$28$	−0.154747	−	0.908144i	−0.0292445	−	0.171623i
$29$	3.10847	+	3.10847i	0.577229	+	0.577229i	0.934139	−	0.356910i	$-0.116170\pi$
$29$	3.10847	+	3.10847i	0.577229	+	0.577229i	−0.356910	+	0.934139i	$0.616170\pi$
$30$	1.10403	−	3.46671i	0.201567	−	0.632932i
$31$	−3.97728	+	3.97728i	−0.714340	+	0.714340i	−0.967440	−	0.253100i	$-0.918550\pi$
$31$	−3.97728	+	3.97728i	−0.714340	+	0.714340i	0.253100	+	0.967440i	$0.418550\pi$
$32$	−0.165423	−	5.65444i	−0.0292429	−	0.999572i
$33$	8.24724			1.43566
$34$	2.26923	+	5.37127i	0.389170	+	0.921166i
$35$		−	0.460617i		−	0.0778585i
$36$	−4.18499	+	5.90417i	−0.697498	+	0.984029i
$37$	−1.49361	−	1.49361i	−0.245547	−	0.245547i	0.573593	−	0.819140i	$-0.305549\pi$
$37$	−1.49361	−	1.49361i	−0.245547	−	0.245547i	−0.819140	+	0.573593i	$0.805549\pi$
$38$	−5.27702	−	1.68055i	−0.856046	−	0.272621i
$39$	−9.64225	+	9.64225i	−1.54400	+	1.54400i
$40$	0.393375	−	2.80094i	0.0621980	−	0.442867i
$41$	−1.90041	−	1.90041i	−0.296795	−	0.296795i	0.542962	−	0.839757i	$-0.317303\pi$
$41$	−1.90041	−	1.90041i	−0.296795	−	0.296795i	−0.839757	+	0.542962i	$0.817303\pi$
$42$	−0.508533	+	1.59683i	−0.0784684	+	0.246396i
$43$	−12.1054			−1.84605			−0.923026	−	0.384738i	$-0.874292\pi$
$43$	−12.1054			−1.84605			−0.923026	+	0.384738i	$0.874292\pi$
$44$	6.32040	−	1.07699i	0.952836	−	0.162363i
$45$	−2.55865	+	2.55865i	−0.381421	+	0.381421i
$46$	−5.76460	−	11.1519i	−0.849944	−	1.64426i
$47$	−6.47445			−0.944396			−0.472198	−	0.881493i	$-0.656539\pi$
$47$	−6.47445			−0.944396			−0.472198	+	0.881493i	$0.656539\pi$
$48$	−4.45602	+	9.27574i	−0.643172	+	1.33884i
$49$		−	6.78783i		−	0.969690i
$50$	0.429141	−	1.34753i	0.0606897	−	0.190570i
$51$	0.819736	−	10.5755i	0.114786	−	1.48087i
$52$	−6.13032	+	8.64865i	−0.850123	+	1.19935i
$53$	3.74075			0.513831			0.256916	−	0.966434i	$-0.417294\pi$
$53$	3.74075			0.513831			0.256916	+	0.966434i	$0.417294\pi$
$54$	1.99890	−	1.03326i	0.272016	−	0.140609i
$55$	3.20575			0.432264
$56$	−0.181195	+	1.29016i	−0.0242132	+	0.172405i
$57$	7.12385	+	7.12385i	0.943576	+	0.943576i
$58$	−2.85479	−	5.52274i	−0.374852	−	0.725171i
$59$	−3.83252			−0.498952			−0.249476	−	0.968381i	$-0.580258\pi$
$59$	−3.83252			−0.498952			−0.249476	+	0.968381i	$0.580258\pi$
$60$	−2.97542	+	4.19771i	−0.384124	+	0.541922i
$61$	−0.303730	+	0.303730i	−0.0388886	+	0.0388886i	−0.726284	−	0.687395i	$-0.758754\pi$
$61$	−0.303730	+	0.303730i	−0.0388886	+	0.0388886i	0.687395	+	0.726284i	$0.258754\pi$
$62$	7.06631	−	3.65269i	0.897423	−	0.463892i
$63$	1.17856	−	1.17856i	0.148484	−	0.148484i
$64$	−2.20364	+	7.69051i	−0.275455	+	0.961314i
$65$	−3.74800	+	3.74800i	−0.464882	+	0.464882i
$66$	−11.1134	−	3.53923i	−1.36797	−	0.435649i
$67$			14.6822i			1.79372i	0.442314	+	0.896860i	$0.354158\pi$
$67$			14.6822i			1.79372i	−0.442314	+	0.896860i	$0.645842\pi$
$68$	−0.752825	−	8.21178i	−0.0912934	−	0.995824i
$69$			22.8369i			2.74924i
$70$	−0.197670	+	0.620696i	−0.0236261	+	0.0741873i
$71$	9.59371	−	9.59371i	1.13856	−	1.13856i	0.149856	−	0.988708i	$-0.452119\pi$
$71$	9.59371	−	9.59371i	1.13856	−	1.13856i	0.988708	−	0.149856i	$-0.0478811\pi$
$72$	8.17312	−	6.16010i	0.963211	−	0.725975i
$73$	5.97596	−	5.97596i	0.699433	−	0.699433i	−0.264855	−	0.964288i	$-0.585324\pi$
$73$	5.97596	−	5.97596i	0.699433	−	0.699433i	0.964288	+	0.264855i	$0.0853241\pi$
$74$	1.37171	+	2.65365i	0.159458	+	0.308480i
$75$	−1.81913	+	1.81913i	−0.210055	+	0.210055i
$76$	6.38976	+	4.52918i	0.732956	+	0.519532i
$77$	−1.47662			−0.168277
$78$	17.1311	−	8.85534i	1.93972	−	1.00267i
$79$	−9.92269	−	9.92269i	−1.11639	−	1.11639i	−0.992267	−	0.124123i	$-0.960388\pi$
$79$	−9.92269	−	9.92269i	−1.11639	−	1.11639i	−0.124123	−	0.992267i	$-0.539612\pi$
$80$	−1.73208	+	3.60554i	−0.193653	+	0.403111i
$81$	6.76207			0.751341
$82$	1.74532	+	3.37641i	0.192738	+	0.372862i
$83$	−1.92649			−0.211459			−0.105730	−	0.994395i	$-0.533718\pi$
$83$	−1.92649			−0.211459			−0.105730	+	0.994395i	$0.533718\pi$
$84$	1.37053	−	1.93354i	0.149537	−	0.210966i
$85$	0.318636	−	4.11077i	0.0345610	−	0.445876i
$86$	16.3124	+	5.19491i	1.75901	+	0.560182i
$87$			11.3094i			1.21250i
$88$	−8.97912	−	1.26106i	−0.957177	−	0.134430i
$89$	15.3083			1.62267			0.811337	−	0.584579i	$-0.198740\pi$
$89$	15.3083			1.62267			0.811337	+	0.584579i	$0.198740\pi$
$90$	4.54587	−	2.34983i	0.479177	−	0.247694i
$91$	1.72639	−	1.72639i	0.180975	−	0.180975i
$92$	2.98223	+	17.5014i	0.310919	+	1.82464i
$93$	−14.4704			−1.50051
$94$	8.72452	+	2.77845i	0.899866	+	0.286576i
$95$	2.76908	+	2.76908i	0.284102	+	0.284102i
$96$	9.98523	−	10.5871i	1.01911	−	1.08054i
$97$	7.40890	−	7.40890i	0.752259	−	0.752259i	−0.222641	−	0.974900i	$-0.571468\pi$
$97$	7.40890	−	7.40890i	0.752259	−	0.752259i	0.974900	+	0.222641i	$0.0714678\pi$
$98$	−2.91294	+	9.14681i	−0.294251	+	0.923967i
$99$	8.20239	+	8.20239i	0.824371	+	0.824371i
$100$	−1.15656	+	1.63168i	−0.115656	+	0.163168i
$101$		−	3.32862i		−	0.331210i	−0.986192	−	0.165605i	$-0.947042\pi$
$101$		−	3.32862i		−	0.331210i	0.986192	−	0.165605i	$-0.0529577\pi$
$102$	−5.64302	+	13.8991i	−0.558742	+	1.37621i
$103$	−5.95460			−0.586724			−0.293362	−	0.956001i	$-0.594774\pi$
$103$	−5.95460			−0.586724			−0.293362	+	0.956001i	$0.594774\pi$
$104$	11.9723	−	9.02355i	1.17398	−	0.884832i
$105$	0.837923	−	0.837923i	0.0817729	−	0.0817729i
$106$	−5.04077	−	1.60531i	−0.489603	−	0.155921i
$107$	0.933341	+	0.933341i	0.0902295	+	0.0902295i	0.750781	−	0.660551i	$-0.229677\pi$
$107$	0.933341	+	0.933341i	0.0902295	+	0.0902295i	−0.660551	+	0.750781i	$0.729677\pi$
$108$	−3.13700	+	0.534543i	−0.301858	+	0.0514365i
$109$	4.83341	−	4.83341i	0.462957	−	0.462957i	−0.436666	−	0.899623i	$-0.643841\pi$
$109$	4.83341	−	4.83341i	0.462957	−	0.462957i	0.899623	+	0.436666i	$0.143841\pi$
$110$	−4.31985	−	1.37572i	−0.411881	−	0.131170i
$111$		−	5.43413i		−	0.515785i
$112$	0.797827	−	1.66077i	0.0753876	−	0.156928i
$113$	−7.07240	−	7.07240i	−0.665316	−	0.665316i	0.291312	−	0.956628i	$-0.405908\pi$
$113$	−7.07240	−	7.07240i	−0.665316	−	0.665316i	−0.956628	+	0.291312i	$0.905908\pi$
$114$	−6.54246	−	12.6567i	−0.612758	−	1.18541i
$115$			8.87682i			0.827768i
$116$	1.47688	+	8.66716i	0.137125	+	0.804726i
$117$	−19.1796			−1.77316
$118$	5.16444	+	1.64469i	0.475425	+	0.151406i
$119$	−0.146769	+	1.89349i	−0.0134543	+	0.173576i
$120$	5.81087	−	4.37967i	0.530458	−	0.399808i
$121$			0.723152i			0.0657411i
$122$	0.539628	−	0.278942i	0.0488556	−	0.0252542i
$123$		−	6.91420i		−	0.623433i
$124$	−11.0896	+	1.88966i	−0.995874	+	0.169697i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−2.09391	+	1.08237i	−0.186540	+	0.0964255i
$127$			15.5317i			1.37821i	0.724661	+	0.689106i	$0.241996\pi$
$127$			15.5317i			1.37821i	−0.724661	+	0.689106i	$0.758004\pi$
$128$	6.26978	−	9.41753i	0.554176	−	0.832400i
$129$	−22.0212	−	22.0212i	−1.93886	−	1.93886i
$130$	6.65896	−	3.44212i	0.584030	−	0.301894i
$131$	−4.53628	−	4.53628i	−0.396337	−	0.396337i	0.480602	−	0.876939i	$-0.340418\pi$
$131$	−4.53628	−	4.53628i	−0.396337	−	0.396337i	−0.876939	+	0.480602i	$0.840418\pi$
$132$	13.4568	+	9.53844i	1.17127	+	0.830215i
$133$	−1.27549	−	1.27549i	−0.110599	−	0.110599i
$134$	6.30075	−	19.7848i	0.544302	−	1.70914i
$135$	−1.59111			−0.136941
$136$	−2.50956	+	11.3887i	−0.215193	+	0.976572i
$137$	12.2904			1.05004			0.525020	−	0.851090i	$-0.324058\pi$
$137$	12.2904			1.05004			0.525020	+	0.851090i	$0.324058\pi$
$138$	9.80024	−	30.7734i	0.834252	−	2.61960i
$139$	3.32565	+	3.32565i	0.282078	+	0.282078i	0.833937	−	0.551859i	$-0.186082\pi$
$139$	3.32565	+	3.32565i	0.282078	+	0.282078i	−0.551859	+	0.833937i	$0.686082\pi$
$140$	0.532732	−	0.751578i	0.0450241	−	0.0635199i
$141$	−11.7779	−	11.7779i	−0.991876	−	0.991876i
$142$	−17.0449	+	8.81076i	−1.43037	+	0.739383i
$143$	12.0152	+	12.0152i	1.00476	+	1.00476i
$144$	−13.6571	+	4.79351i	−1.13809	+	0.399459i
$145$			4.39605i			0.365072i
$146$	−10.6173	+	5.48826i	−0.878695	+	0.454211i
$147$	12.3480	−	12.3480i	1.01844	−	1.01844i
$148$	−0.709634	−	4.16453i	−0.0583316	−	0.342322i
$149$		−	24.2418i		−	1.98596i	−0.118273	−	0.992981i	$-0.537736\pi$
$149$		−	24.2418i		−	1.98596i	0.118273	−	0.992981i	$-0.462264\pi$
$150$	3.23200	−	1.67067i	0.263891	−	0.136410i
$151$		−	17.9459i		−	1.46042i	−0.683224	−	0.730209i	$-0.739423\pi$
$151$		−	17.9459i		−	1.46042i	0.683224	−	0.730209i	$-0.260577\pi$
$152$	−6.66674	−	8.84531i	−0.540744	−	0.717449i
$153$	11.3333	−	9.70274i	0.916243	−	0.784420i
$154$	1.98980	+	0.633680i	0.160342	+	0.0510634i
$155$	−5.62472			−0.451788
$156$	−26.8849	+	4.58117i	−2.15251	+	0.366787i
$157$			4.08207i			0.325785i	0.986644	+	0.162892i	$0.0520823\pi$
$157$			4.08207i			0.325785i	−0.986644	+	0.162892i	$0.947918\pi$
$158$	9.11289	+	17.6294i	0.724983	+	1.40252i
$159$	6.80491	+	6.80491i	0.539664	+	0.539664i
$160$	3.88132	−	4.11526i	0.306845	−	0.325340i
$161$		−	4.08882i		−	0.322244i
$162$	−9.11210	−	2.90188i	−0.715914	−	0.227993i
$163$	−5.59437	+	5.59437i	−0.438185	+	0.438185i	−0.891401	−	0.453216i	$-0.850277\pi$
$163$	−5.59437	+	5.59437i	−0.438185	+	0.438185i	0.453216	+	0.891401i	$0.350277\pi$
$164$	−0.902914	−	5.29881i	−0.0705058	−	0.413767i
$165$	5.83168	+	5.83168i	0.453996	+	0.453996i
$166$	2.59600	+	0.826734i	0.201489	+	0.0641670i
$167$	3.76174	−	3.76174i	0.291092	−	0.291092i	−0.546420	−	0.837512i	$-0.684010\pi$
$167$	3.76174	−	3.76174i	0.291092	−	0.291092i	0.837512	+	0.546420i	$0.184010\pi$
$168$	−2.67659	+	2.01735i	−0.206503	+	0.155642i
$169$	−15.0950			−1.16115
$170$	−2.19347	+	5.40265i	−0.168232	+	0.414365i
$171$			14.1702i			1.08362i
$172$	−19.7520	−	14.0006i	−1.50608	−	1.06754i
$173$	−7.22892	−	7.22892i	−0.549604	−	0.549604i	0.376722	−	0.926326i	$-0.377051\pi$
$173$	−7.22892	−	7.22892i	−0.549604	−	0.549604i	−0.926326	+	0.376722i	$0.877051\pi$
$174$	4.85335	−	15.2398i	0.367931	−	1.15533i
$175$	0.325706	−	0.325706i	0.0246210	−	0.0246210i
$176$	11.5585	+	5.55263i	0.871251	+	0.418545i
$177$	−6.97186	−	6.97186i	−0.524037	−	0.524037i
$178$	−20.6284	−	6.56941i	−1.54616	−	0.492398i
$179$	1.75193			0.130946			0.0654728	−	0.997854i	$-0.479144\pi$
$179$	1.75193			0.130946			0.0654728	+	0.997854i	$0.479144\pi$
$180$	−7.13411	+	1.21565i	−0.531745	+	0.0906092i
$181$	−1.20299	+	1.20299i	−0.0894172	+	0.0894172i	−0.750401	−	0.660983i	$-0.770139\pi$
$181$	−1.20299	+	1.20299i	−0.0894172	+	0.0894172i	0.660983	+	0.750401i	$0.270139\pi$
$182$	−3.06723	+	1.58550i	−0.227358	+	0.117525i
$183$	−1.10505			−0.0816875
$184$	3.49192	−	24.8634i	0.257428	−	1.83296i
$185$		−	2.11228i		−	0.155298i
$186$	19.4993	+	6.20983i	1.42976	+	0.455327i
$187$	−13.1781	−	1.02147i	−0.963680	−	0.0746972i
$188$	−10.5642	−	7.48810i	−0.770474	−	0.546126i
$189$	0.732892			0.0533100
$190$	−2.54309	−	4.91975i	−0.184495	−	0.356916i
$191$	2.42204			0.175253			0.0876263	−	0.996153i	$-0.472072\pi$
$191$	2.42204			0.175253			0.0876263	+	0.996153i	$0.472072\pi$
$192$	−17.9988	+	9.98134i	−1.29895	+	0.720341i
$193$	3.33293	+	3.33293i	0.239909	+	0.239909i	0.816813	−	0.576903i	$-0.195739\pi$
$193$	3.33293	+	3.33293i	0.239909	+	0.239909i	−0.576903	+	0.816813i	$0.695739\pi$
$194$	−13.1632	+	6.80425i	−0.945061	+	0.488517i
$195$	−13.6362			−0.976509
$196$	7.85054	−	11.0755i	0.560753	−	0.791110i
$197$	−3.32870	+	3.32870i	−0.237160	+	0.237160i	−0.815673	−	0.578513i	$-0.803633\pi$
$197$	−3.32870	+	3.32870i	−0.237160	+	0.237160i	0.578513	+	0.815673i	$0.303633\pi$
$198$	−7.53298	−	14.5729i	−0.535346	−	1.03565i
$199$	−7.14360	+	7.14360i	−0.506397	+	0.506397i	−0.913418	−	0.407022i	$-0.866567\pi$
$199$	−7.14360	+	7.14360i	−0.506397	+	0.506397i	0.407022	+	0.913418i	$0.366567\pi$
$200$	2.25872	−	1.70240i	0.159716	−	0.120378i
$201$	−26.7089	+	26.7089i	−1.88390	+	1.88390i
$202$	−1.42845	+	4.48541i	−0.100505	+	0.315593i
$203$		−	2.02489i		−	0.142120i
$204$	13.5688	−	16.3078i	0.950006	−	1.14177i
$205$		−	2.68759i		−	0.187710i
$206$	8.02400	+	2.55536i	0.559059	+	0.178041i
$207$	−22.7127	+	22.7127i	−1.57864	+	1.57864i
$208$	−20.0054	+	7.02170i	−1.38712	+	0.486868i
$209$	8.87699	−	8.87699i	0.614034	−	0.614034i
$210$	−1.48871	+	0.769539i	−0.102731	+	0.0531033i
$211$	9.35262	−	9.35262i	0.643861	−	0.643861i	−0.307641	−	0.951502i	$-0.599540\pi$
$211$	9.35262	−	9.35262i	0.643861	−	0.643861i	0.951502	+	0.307641i	$0.0995396\pi$
$212$	6.10369	+	4.32640i	0.419203	+	0.297139i
$213$	34.9044			2.39161
$214$	−0.857170	−	1.65824i	−0.0585949	−	0.113355i
$215$	−8.55979	−	8.55979i	−0.583773	−	0.583773i
$216$	4.45660	+	0.625902i	0.303233	+	0.0425872i
$217$	2.59084			0.175878
$218$	−8.58739	+	4.43895i	−0.581611	+	0.300644i
$219$	21.7421			1.46919
$220$	5.23075	+	3.70765i	0.352657	+	0.249970i
$221$	16.6014	−	14.2129i	1.11673	−	0.956066i
$222$	−2.33201	+	7.32266i	−0.156514	+	0.491465i
$223$		−	10.2982i		−	0.689617i	−0.938673	−	0.344808i	$-0.887944\pi$
$223$		−	10.2982i		−	0.689617i	0.938673	−	0.344808i	$-0.112056\pi$
$224$	−1.78780	+	1.89556i	−0.119453	+	0.126652i
$225$	−3.61847			−0.241232
$226$	6.49522	+	12.5653i	0.432055	+	0.835833i
$227$	10.0157	−	10.0157i	0.664764	−	0.664764i	−0.291736	−	0.956499i	$-0.594233\pi$
$227$	10.0157	−	10.0157i	0.664764	−	0.664764i	0.956499	+	0.291736i	$0.0942327\pi$
$228$	3.38464	+	19.8630i	0.224153	+	1.31546i
$229$	−11.5900			−0.765889			−0.382945	−	0.923771i	$-0.625090\pi$
$229$	−11.5900			−0.765889			−0.382945	+	0.923771i	$0.625090\pi$
$230$	3.80941	−	11.9618i	0.251185	−	0.788737i
$231$	−2.68617	−	2.68617i	−0.176737	−	0.176737i
$232$	1.72929	−	12.3131i	0.113534	−	0.808392i
$233$	7.32749	−	7.32749i	0.480040	−	0.480040i	−0.425104	−	0.905144i	$-0.639763\pi$
$233$	7.32749	−	7.32749i	0.480040	−	0.480040i	0.905144	+	0.425104i	$0.139763\pi$
$234$	25.8451	+	8.23076i	1.68955	+	0.538062i
$235$	−4.57813	−	4.57813i	−0.298644	−	0.298644i
$236$	−6.25343	−	4.43255i	−0.407064	−	0.288534i
$237$		−	36.1013i		−	2.34503i
$238$	1.01035	−	2.48856i	0.0654914	−	0.161309i
$239$	−13.6264			−0.881416			−0.440708	−	0.897651i	$-0.645273\pi$
$239$	−13.6264			−0.881416			−0.440708	+	0.897651i	$0.645273\pi$
$240$	−9.70983	+	3.40806i	−0.626767	+	0.219989i
$241$	1.38382	−	1.38382i	0.0891394	−	0.0891394i	−0.661131	−	0.750270i	$-0.729923\pi$
$241$	1.38382	−	1.38382i	0.0891394	−	0.0891394i	0.750270	+	0.661131i	$0.229923\pi$
$242$	0.310334	−	0.974469i	0.0199490	−	0.0626412i
$243$	15.6763	+	15.6763i	1.00564	+	1.00564i
$244$	−0.846871	+	0.144306i	−0.0542153	+	0.00923827i
$245$	4.79972	−	4.79972i	0.306643	−	0.306643i
$246$	−2.96717	+	9.31710i	−0.189180	+	0.594037i
$247$			20.7570i			1.32074i
$248$	15.7545	+	2.21262i	1.00041	+	0.140502i
$249$	−3.50453	−	3.50453i	−0.222091	−	0.222091i
$250$	1.25630	−	0.649399i	0.0794552	−	0.0410716i
$251$		−	12.7600i		−	0.805404i	−0.915331	−	0.402702i	$-0.868071\pi$
$251$		−	12.7600i		−	0.805404i	0.915331	−	0.402702i	$-0.131929\pi$
$252$	3.28610	−	0.559949i	0.207005	−	0.0352735i
$253$	28.4569			1.78907
$254$	6.66527	−	20.9294i	0.418216	−	1.31323i
$255$	8.05768	−	6.89840i	0.504591	−	0.431994i
$256$	−12.4902	+	9.99978i	−0.780636	+	0.624986i
$257$		−	21.6371i		−	1.34969i	−0.737961	−	0.674843i	$-0.764211\pi$
$257$		−	21.6371i		−	1.34969i	0.737961	−	0.674843i	$-0.235789\pi$
$258$	20.2241	+	39.1245i	1.25910	+	2.43579i
$259$			0.972952i			0.0604563i
$260$	−10.4503	+	1.78073i	−0.648101	+	0.110436i
$261$	−11.2479	+	11.2479i	−0.696230	+	0.696230i
$262$	4.16607	+	8.05949i	0.257381	+	0.497917i
$263$			3.42544i			0.211222i	0.994408	+	0.105611i	$0.0336798\pi$
$263$			3.42544i			0.211222i	−0.994408	+	0.105611i	$0.966320\pi$
$264$	−14.0401	−	18.6282i	−0.864111	−	1.14649i
$265$	2.64511	+	2.64511i	0.162488	+	0.162488i
$266$	1.17139	+	2.26612i	0.0718227	+	0.138945i
$267$	27.8478	+	27.8478i	1.70426	+	1.70426i
$268$	−16.9809	+	23.9566i	−1.03727	+	1.46339i
$269$	−5.48984	−	5.48984i	−0.334721	−	0.334721i	0.519655	−	0.854376i	$-0.326061\pi$
$269$	−5.48984	−	5.48984i	−0.334721	−	0.334721i	−0.854376	+	0.519655i	$0.826061\pi$
$270$	2.14407	+	0.682810i	0.130484	+	0.0415545i
$271$	18.3178			1.11273			0.556364	−	0.830938i	$-0.312196\pi$
$271$	18.3178			1.11273			0.556364	+	0.830938i	$0.312196\pi$
$272$	8.26906	−	14.2696i	0.501385	−	0.865224i
$273$	6.28107			0.380148
$274$	−16.5617	−	5.27432i	−1.00053	−	0.318633i
$275$	2.26681	+	2.26681i	0.136694	+	0.136694i
$276$	−26.4122	+	37.2624i	−1.58983	+	2.24293i
$277$	−0.272756	−	0.272756i	−0.0163883	−	0.0163883i	0.698865	−	0.715253i	$-0.253689\pi$
$277$	−0.272756	−	0.272756i	−0.0163883	−	0.0163883i	−0.715253	+	0.698865i	$0.753689\pi$
$278$	−3.05424	−	5.90858i	−0.183181	−	0.354373i
$279$	−14.3917	−	14.3917i	−0.861606	−	0.861606i
$280$	−1.04041	+	0.784157i	−0.0621761	+	0.0468623i
$281$			28.5766i			1.70474i	0.522940	+	0.852369i	$0.324835\pi$
$281$			28.5766i			1.70474i	−0.522940	+	0.852369i	$0.675165\pi$
$282$	10.8167	+	20.9254i	0.644123	+	1.24609i
$283$	−14.1646	+	14.1646i	−0.841996	+	0.841996i	−0.989118	−	0.147123i	$-0.952999\pi$
$283$	−14.1646	+	14.1646i	−0.841996	+	0.841996i	0.147123	+	0.989118i	$0.452999\pi$
$284$	26.7495	−	4.55811i	1.58729	−	0.270474i
$285$			10.0746i			0.596770i
$286$	−11.0346	−	21.3470i	−0.652489	−	1.26227i
$287$			1.23795i			0.0730739i
$288$	20.4604	−	0.598579i	1.20564	−	0.0352716i
$289$	−2.61968	+	16.7969i	−0.154099	+	0.988055i
$290$	1.88652	−	5.92381i	0.110781	−	0.347858i
$291$	26.9555			1.58016
$292$	16.6624	−	2.83926i	0.975093	−	0.166155i
$293$		−	28.8939i		−	1.68800i	−0.536342	−	0.844001i	$-0.680194\pi$
$293$		−	28.8939i		−	1.68800i	0.536342	−	0.844001i	$-0.319806\pi$
$294$	−21.9383	+	11.3402i	−1.27947	+	0.661375i
$295$	−2.71000	−	2.71000i	−0.157782	−	0.157782i
$296$	−0.830918	+	5.91636i	−0.0482961	+	0.343882i
$297$			5.10070i			0.295973i
$298$	−10.4031	+	32.6665i	−0.602637	+	1.89232i
$299$	−33.2703	+	33.2703i	−1.92407	+	1.92407i
$300$	−5.07217	+	0.864295i	−0.292842	+	0.0499001i
$301$	3.94279	+	3.94279i	0.227258	+	0.227258i
$302$	−7.70133	+	24.1827i	−0.443162	+	1.39156i
$303$	6.05519	−	6.05519i	0.347862	−	0.347862i
$304$	5.18774	+	14.7803i	0.297537	+	0.847708i
$305$	−0.429539			−0.0245953
$306$	−19.4358	+	8.21116i	−1.11107	+	0.469401i
$307$		−	20.9718i		−	1.19692i	−0.801152	−	0.598461i	$-0.795779\pi$
$307$		−	20.9718i		−	1.19692i	0.801152	−	0.598461i	$-0.204221\pi$
$308$	−2.40937	−	1.70781i	−0.137287	−	0.0973113i
$309$	−10.8322	−	10.8322i	−0.616222	−	0.616222i
$310$	7.57948	+	2.41380i	0.430485	+	0.137094i
$311$	4.09042	−	4.09042i	0.231946	−	0.231946i	−0.581558	−	0.813505i	$-0.697557\pi$
$311$	4.09042	−	4.09042i	0.231946	−	0.231946i	0.813505	+	0.581558i	$0.197557\pi$
$312$	38.1942	+	5.36414i	2.16232	+	0.303685i
$313$	11.2319	+	11.2319i	0.634865	+	0.634865i	0.949284	−	0.314419i	$-0.101810\pi$
$313$	11.2319	+	11.2319i	0.634865	+	0.634865i	−0.314419	+	0.949284i	$0.601810\pi$
$314$	1.75178	−	5.50071i	0.0988589	−	0.310423i
$315$	1.66673			0.0939097
$316$	−4.71441	−	27.6668i	−0.265206	−	1.55638i
$317$	−9.77613	+	9.77613i	−0.549082	+	0.549082i	−0.926175	−	0.377093i	$-0.876924\pi$
$317$	−9.77613	+	9.77613i	−0.549082	+	0.549082i	0.377093	+	0.926175i	$0.376924\pi$
$318$	−6.24955	−	12.0901i	−0.350458	−	0.677978i
$319$	14.0926			0.789036
$320$	−6.99622	+	3.87981i	−0.391101	+	0.216888i
$321$			3.39574i			0.189532i
$322$	−1.75468	+	5.50980i	−0.0977845	+	0.307049i
$323$	−10.5007	−	12.2654i	−0.584277	−	0.682465i
$324$	11.0335	+	7.82075i	0.612973	+	0.434486i
$325$	−5.30047			−0.294017
$326$	9.93936	−	5.13781i	0.550490	−	0.284557i
$327$	17.5852			0.972465
$328$	−1.05723	+	7.52778i	−0.0583758	+	0.415652i
$329$	2.10877	+	2.10877i	0.116260	+	0.116260i
$330$	−5.35575	−	10.3610i	−0.294825	−	0.570353i
$331$	7.37018			0.405102			0.202551	−	0.979272i	$-0.435077\pi$
$331$	7.37018			0.405102			0.202551	+	0.979272i	$0.435077\pi$
$332$	−3.14340	−	2.22810i	−0.172516	−	0.122283i
$333$	5.40458	−	5.40458i	0.296169	−	0.296169i
$334$	−6.68337	+	3.45474i	−0.365698	+	0.189035i
$335$	−10.3819	+	10.3819i	−0.567224	+	0.567224i
$336$	4.47251	−	1.56981i	0.243996	−	0.0856401i
$337$	11.8998	−	11.8998i	0.648224	−	0.648224i	−0.304339	−	0.952564i	$-0.598436\pi$
$337$	11.8998	−	11.8998i	0.648224	−	0.648224i	0.952564	+	0.304339i	$0.0984357\pi$
$338$	20.3410	+	6.47789i	1.10640	+	0.352351i
$339$		−	25.7312i		−	1.39753i
$340$	5.27427	−	6.33893i	0.286038	−	0.343777i
$341$			18.0315i			0.976458i
$342$	6.08101	−	19.0948i	0.328824	−	1.03253i
$343$	−4.49077	+	4.49077i	−0.242479	+	0.242479i
$344$	20.6082	+	27.3426i	1.11112	+	1.47422i
$345$	−16.1481	+	16.1481i	−0.869384	+	0.869384i
$346$	6.63896	+	12.8434i	0.356913	+	0.690466i
$347$	−9.99781	+	9.99781i	−0.536710	+	0.536710i	−0.922561	−	0.385851i	$-0.873908\pi$
$347$	−9.99781	+	9.99781i	−0.536710	+	0.536710i	0.385851	+	0.922561i	$0.373908\pi$
$348$	−13.0801	+	18.4533i	−0.701165	+	0.989203i
$349$	30.0473			1.60840			0.804198	−	0.594361i	$-0.202595\pi$
$349$	30.0473			1.60840			0.804198	+	0.594361i	$0.202595\pi$
$350$	−0.578672	+	0.299124i	−0.0309313	+	0.0159889i
$351$	−5.96347	−	5.96347i	−0.318307	−	0.318307i
$352$	−13.1925	−	12.4425i	−0.703163	−	0.663190i
$353$	−17.5942			−0.936444			−0.468222	−	0.883611i	$-0.655105\pi$
$353$	−17.5942			−0.936444			−0.468222	+	0.883611i	$0.655105\pi$
$354$	6.40288	+	12.3867i	0.340309	+	0.658346i
$355$	13.5676			0.720091
$356$	24.9781	+	17.7050i	1.32384	+	0.938361i
$357$	−3.71151	+	3.17752i	−0.196434	+	0.168172i
$358$	−2.36078	−	0.751827i	−0.124771	−	0.0397353i
$359$			10.8647i			0.573415i	0.958018	+	0.286707i	$0.0925608\pi$
$359$			10.8647i			0.573415i	−0.958018	+	0.286707i	$0.907439\pi$
$360$	10.1351	+	1.42342i	0.534168	+	0.0750207i
$361$	−3.66439			−0.192862
$362$	2.13731	−	1.10481i	0.112334	−	0.0580675i
$363$	−1.31551	+	1.31551i	−0.0690462	+	0.0690462i
$364$	4.81359	−	0.820234i	0.252301	−	0.0429920i
$365$	8.45128			0.442360
$366$	1.48909	+	0.474222i	0.0778358	+	0.0247880i
$367$	−17.7524	−	17.7524i	−0.926667	−	0.926667i	0.0708220	−	0.997489i	$-0.477438\pi$
$367$	−17.7524	−	17.7524i	−0.926667	−	0.926667i	−0.997489	+	0.0708220i	$0.977438\pi$
$368$	−15.3754	+	32.0057i	−0.801498	+	1.66841i
$369$	6.87660	−	6.87660i	0.357981	−	0.357981i
$370$	−0.906466	+	2.84636i	−0.0471249	+	0.147975i
$371$	−1.21838	−	1.21838i	−0.0632553	−	0.0632553i
$372$	−23.6110	−	16.7359i	−1.22417	−	0.867714i
$373$		−	1.81988i		−	0.0942300i	−0.998889	−	0.0471150i	$-0.984997\pi$
$373$		−	1.81988i		−	0.0942300i	0.998889	−	0.0471150i	$-0.0150027\pi$
$374$	17.3196	+	7.03174i	0.895574	+	0.363602i
$375$	−2.57264			−0.132851
$376$	11.0221	+	14.6240i	0.568423	+	0.754174i
$377$	−16.4764	+	16.4764i	−0.848577	+	0.848577i
$378$	−0.987594	−	0.314514i	−0.0507963	−	0.0161769i
$379$	12.1575	+	12.1575i	0.624489	+	0.624489i	0.946676	−	0.322187i	$-0.104418\pi$
$379$	12.1575	+	12.1575i	0.624489	+	0.624489i	−0.322187	+	0.946676i	$0.604418\pi$
$380$	1.31563	+	7.72085i	0.0674904	+	0.396071i
$381$	−28.2541	+	28.2541i	−1.44750	+	1.44750i
$382$	−3.26377	−	1.03940i	−0.166989	−	0.0531801i
$383$			15.1502i			0.774141i	0.922050	+	0.387071i	$0.126513\pi$
$383$			15.1502i			0.774141i	−0.922050	+	0.387071i	$0.873487\pi$
$384$	28.5373	−	5.72615i	1.45629	−	0.292212i
$385$	−1.04413	−	1.04413i	−0.0532139	−	0.0532139i
$386$	−3.06092	−	5.92152i	−0.155797	−	0.301397i
$387$		−	43.8029i		−	2.22663i
$388$	20.6578	−	3.52007i	1.04874	−	0.178705i
$389$	−18.5850			−0.942296			−0.471148	−	0.882054i	$-0.656160\pi$
$389$	−18.5850			−0.942296			−0.471148	+	0.882054i	$0.656160\pi$
$390$	18.3752	+	5.85186i	0.930464	+	0.296320i
$391$	2.82848	−	36.4906i	0.143042	−	1.84541i
$392$	−15.3318	+	11.5556i	−0.774374	+	0.583648i
$393$		−	16.5042i		−	0.832526i
$394$	5.91400	−	3.05704i	0.297943	−	0.154011i
$395$		−	14.0328i		−	0.706067i
$396$	3.89707	+	22.8702i	0.195835	+	1.14927i
$397$	−4.14345	+	4.14345i	−0.207954	+	0.207954i	−0.803397	−	0.595443i	$-0.796976\pi$
$397$	−4.14345	+	4.14345i	−0.207954	+	0.207954i	0.595443	+	0.803397i	$0.296976\pi$
$398$	12.6918	−	6.56061i	0.636184	−	0.328854i
$399$		−	4.64055i		−	0.232318i
$400$	−3.77427	+	1.32473i	−0.188713	+	0.0662366i
$401$	−4.52926	−	4.52926i	−0.226180	−	0.226180i	0.584915	−	0.811095i	$-0.301128\pi$
$401$	−4.52926	−	4.52926i	−0.226180	−	0.226180i	−0.811095	+	0.584915i	$0.801128\pi$
$402$	47.4530	−	24.5292i	2.36674	−	1.22340i
$403$	−21.0814	−	21.0814i	−1.05014	−	1.05014i
$404$	3.84975	−	5.43123i	0.191532	−	0.270214i
$405$	4.78151	+	4.78151i	0.237595	+	0.237595i
$406$	−0.868966	+	2.72861i	−0.0431260	+	0.135419i
$407$	−6.77144			−0.335648
$408$	−25.2827	+	16.1523i	−1.25168	+	0.799658i
$409$	−2.51585			−0.124401			−0.0622003	−	0.998064i	$-0.519812\pi$
$409$	−2.51585			−0.124401			−0.0622003	+	0.998064i	$0.519812\pi$
$410$	−1.15336	+	3.62161i	−0.0569602	+	0.178859i
$411$	22.3579	+	22.3579i	1.10283	+	1.10283i
$412$	−9.71597	−	6.88686i	−0.478672	−	0.339291i
$413$	1.24827	+	1.24827i	0.0614235	+	0.0614235i
$414$	40.3529	−	20.8591i	1.98324	−	1.02517i
$415$	−1.36223	−	1.36223i	−0.0668693	−	0.0668693i
$416$	29.9712	−	0.876820i	1.46946	−	0.0429896i
$417$			12.0996i			0.592519i
$418$	−15.7715	+	8.15253i	−0.771409	+	0.398753i
$419$	8.92424	−	8.92424i	0.435978	−	0.435978i	−0.454678	−	0.890656i	$-0.650246\pi$
$419$	8.92424	−	8.92424i	0.435978	−	0.435978i	0.890656	+	0.454678i	$0.150246\pi$
$420$	2.33633	−	0.398109i	0.114001	−	0.0194257i
$421$			16.1590i			0.787541i	0.919209	+	0.393770i	$0.128829\pi$
$421$			16.1590i			0.787541i	−0.919209	+	0.393770i	$0.871171\pi$
$422$	−16.6165	+	8.58935i	−0.808881	+	0.418123i
$423$		−	23.4276i		−	1.13909i
$424$	−6.36827	−	8.44930i	−0.309270	−	0.410334i
$425$	3.13207	−	2.68145i	0.151928	−	0.130069i
$426$	−47.0348	−	14.9789i	−2.27884	−	0.725731i
$427$	0.197853			0.00957478
$428$	0.443444	+	2.60238i	0.0214347	+	0.125791i
$429$			43.7143i			2.11055i
$430$	7.86122	+	15.2079i	0.379102	+	0.733392i
$431$	20.9822	+	20.9822i	1.01068	+	1.01068i	0.999942	+	0.0107364i	$0.00341756\pi$
$431$	20.9822	+	20.9822i	1.01068	+	1.01068i	0.0107364	+	0.999942i	$0.496582\pi$
$432$	−5.73680	−	2.75593i	−0.276012	−	0.132595i
$433$		−	24.9349i		−	1.19830i	−0.800638	−	0.599148i	$-0.795506\pi$
$433$		−	24.9349i		−	1.19830i	0.800638	−	0.599148i	$-0.204494\pi$
$434$	−3.49124	−	1.11184i	−0.167585	−	0.0533699i
$435$	−7.99698	+	7.99698i	−0.383426	+	0.383426i
$436$	13.4767	−	2.29642i	0.645417	−	0.109979i
$437$	24.5806	+	24.5806i	1.17585	+	1.17585i
$438$	−29.2981	−	9.33043i	−1.39992	−	0.445825i
$439$	−20.6737	+	20.6737i	−0.986700	+	0.986700i	−0.999913	−	0.0132123i	$-0.995794\pi$
$439$	−20.6737	+	20.6737i	−0.986700	+	0.986700i	0.0132123	+	0.999913i	$0.495794\pi$
$440$	−5.45749	−	7.24090i	−0.260175	−	0.345196i
$441$	24.5616			1.16960
$442$	−28.4703	+	12.0280i	−1.35419	+	0.572114i
$443$		−	23.2913i		−	1.10660i	−0.832980	−	0.553302i	$-0.813367\pi$
$443$		−	23.2913i		−	1.10660i	0.832980	−	0.553302i	$-0.186633\pi$
$444$	6.28491	−	8.86674i	0.298268	−	0.420797i
$445$	10.8246	+	10.8246i	0.513135	+	0.513135i
$446$	−4.41937	+	13.8771i	−0.209263	+	0.657100i
$447$	44.0989	−	44.0989i	2.08581	−	2.08581i
$448$	3.22258	−	1.78711i	0.152253	−	0.0844328i
$449$	−19.8922	−	19.8922i	−0.938771	−	0.938771i	0.0594593	−	0.998231i	$-0.481062\pi$
$449$	−19.8922	−	19.8922i	−0.938771	−	0.938771i	−0.998231	+	0.0594593i	$0.981062\pi$
$450$	4.87600	+	1.55284i	0.229857	+	0.0732014i
$451$	−8.61575			−0.405700
$452$	−3.36020	−	19.7195i	−0.158050	−	0.927529i
$453$	32.6460	−	32.6460i	1.53384	−	1.53384i
$454$	−17.7946	+	9.19828i	−0.835140	+	0.431697i
$455$	2.44149			0.114459
$456$	3.96311	−	28.2184i	0.185590	−	1.32145i
$457$		−	12.5423i		−	0.586703i	−0.956005	−	0.293351i	$-0.905229\pi$
$457$		−	12.5423i		−	0.586703i	0.956005	−	0.293351i	$-0.0947706\pi$
$458$	15.6179	+	4.97375i	0.729776	+	0.232408i
$459$	6.54069	+	0.506985i	0.305293	+	0.0236640i
$460$	−10.2666	+	14.4841i	−0.478682	+	0.675324i
$461$	−8.80159			−0.409931			−0.204965	−	0.978769i	$-0.565708\pi$
$461$	−8.80159			−0.409931			−0.204965	+	0.978769i	$0.565708\pi$
$462$	2.46695	+	4.77245i	0.114773	+	0.222034i
$463$	−7.98415			−0.371055			−0.185528	−	0.982639i	$-0.559399\pi$
$463$	−7.98415			−0.371055			−0.185528	+	0.982639i	$0.559399\pi$
$464$	−7.61432	+	15.8501i	−0.353486	+	0.735823i
$465$	−10.2321	−	10.2321i	−0.474502	−	0.474502i
$466$	−13.0185	+	6.72949i	−0.603072	+	0.311738i
$467$	−38.2979			−1.77221			−0.886107	−	0.463480i	$-0.846601\pi$
$467$	−38.2979			−1.77221			−0.886107	+	0.463480i	$0.846601\pi$
$468$	−31.2949	−	22.1824i	−1.44661	−	1.02538i
$469$	4.78209	−	4.78209i	0.220816	−	0.220816i
$470$	4.20450	+	8.13383i	0.193939	+	0.375186i
$471$	−7.42582	+	7.42582i	−0.342164	+	0.342164i
$472$	6.52450	+	8.65660i	0.300315	+	0.398452i
$473$	−27.4406	+	27.4406i	−1.26172	+	1.26172i
$474$	−15.4926	+	48.6477i	−0.711597	+	2.23446i
$475$			3.91607i			0.179682i
$476$	−2.42942	+	2.91982i	−0.111352	+	0.133830i
$477$			13.5358i			0.619761i
$478$	18.3619	+	5.84763i	0.839855	+	0.267464i
$479$	−13.3009	+	13.3009i	−0.607734	+	0.607734i	−0.942353	−	0.334619i	$-0.891392\pi$
$479$	−13.3009	+	13.3009i	−0.607734	+	0.607734i	0.334619	+	0.942353i	$0.391392\pi$
$480$	14.5468	−	0.425574i	0.663969	−	0.0194247i
$481$	7.91682	−	7.91682i	0.360976	−	0.360976i
$482$	−2.45859	+	1.27088i	−0.111986	+	0.0578871i
$483$	7.43809	−	7.43809i	0.338445	−	0.338445i
$484$	−0.836369	+	1.17995i	−0.0380168	+	0.0536341i
$485$	10.4778			0.475771
$486$	−14.3970	−	27.8517i	−0.653060	−	1.26338i
$487$	−27.8703	−	27.8703i	−1.26292	−	1.26292i	−0.949669	−	0.313255i	$-0.898580\pi$
$487$	−27.8703	−	27.8703i	−1.26292	−	1.26292i	−0.313255	−	0.949669i	$-0.601420\pi$
$488$	1.20311	+	0.168970i	0.0544623	+	0.00764890i
$489$	−20.3538			−0.920430
$490$	−8.52753	+	4.40801i	−0.385234	+	0.199134i
$491$	−9.87601			−0.445698			−0.222849	−	0.974853i	$-0.571536\pi$
$491$	−9.87601			−0.445698			−0.222849	+	0.974853i	$0.571536\pi$
$492$	7.99670	−	11.2817i	0.360519	−	0.508620i
$493$	1.40074	−	18.0712i	0.0630862	−	0.813884i
$494$	8.90769	−	27.9707i	0.400776	−	1.25846i
$495$			11.5999i			0.521378i
$496$	−20.2801	−	9.74248i	−0.910604	−	0.437450i
$497$	−6.24945			−0.280326
$498$	3.21852	+	6.22640i	0.144225	+	0.279012i
$499$	10.7796	−	10.7796i	0.482563	−	0.482563i	−0.423387	−	0.905949i	$-0.639159\pi$
$499$	10.7796	−	10.7796i	0.482563	−	0.482563i	0.905949	+	0.423387i	$0.139159\pi$
$500$	−1.97158	+	0.335957i	−0.0881718	+	0.0150244i
$501$	13.6862			0.611454
$502$	−5.47584	+	17.1945i	−0.244399	+	0.767427i
$503$	13.0584	+	13.0584i	0.582245	+	0.582245i	0.935520	−	0.353274i	$-0.114932\pi$
$503$	13.0584	+	13.0584i	0.582245	+	0.582245i	−0.353274	+	0.935520i	$0.614932\pi$
$504$	−4.66841	−	0.655650i	−0.207948	−	0.0292050i
$505$	2.35369	−	2.35369i	0.104738	−	0.104738i
$506$	−38.3465	−	12.2120i	−1.70471	−	0.542891i
$507$	−27.4598	−	27.4598i	−1.21953	−	1.21953i
$508$	−17.9633	+	25.3426i	−0.796993	+	1.12440i
$509$			28.4293i			1.26011i	0.776551	+	0.630054i	$0.216967\pi$
$509$			28.4293i			1.26011i	−0.776551	+	0.630054i	$0.783033\pi$
$510$	−13.8184	+	5.83792i	−0.611887	+	0.258507i
$511$	−3.89281			−0.172208
$512$	21.1222	−	8.11496i	0.933478	−	0.358634i
$513$	−4.40591	+	4.40591i	−0.194526	+	0.194526i
$514$	−9.28537	+	29.1567i	−0.409560	+	1.28605i
$515$	−4.21054	−	4.21054i	−0.185538	−	0.185538i
$516$	−10.4626	−	61.4005i	−0.460591	−	2.70300i
$517$	−14.6763	+	14.6763i	−0.645465	+	0.645465i
$518$	0.417534	−	1.31108i	0.0183454	−	0.0576056i
$519$		−	26.3007i		−	1.15447i
$520$	14.8463	+	2.08507i	0.651053	+	0.0914365i
$521$	13.9699	+	13.9699i	0.612033	+	0.612033i	0.943475	−	0.331443i	$-0.107535\pi$
$521$	13.9699	+	13.9699i	0.612033	+	0.612033i	−0.331443	+	0.943475i	$0.607535\pi$
$522$	19.9839	−	10.3300i	0.874671	−	0.452131i
$523$		−	21.0628i		−	0.921012i	−0.887657	−	0.460506i	$-0.847668\pi$
$523$		−	21.0628i		−	0.921012i	0.887657	−	0.460506i	$-0.152332\pi$
$524$	−2.15525	−	12.6482i	−0.0941527	−	0.552541i
$525$	1.18500			0.0517177
$526$	1.47000	−	4.61588i	0.0640949	−	0.201262i
$527$	23.1219	+	1.79224i	1.00721	+	0.0780712i
$528$	10.9254	+	31.1273i	0.475466	+	1.35464i
$529$			55.7980i			2.42600i
$530$	−2.42924	−	4.69949i	−0.105519	−	0.204133i
$531$		−	13.8679i		−	0.601815i
$532$	−0.606002	−	3.55636i	−0.0262735	−	0.154188i
$533$	10.0731	−	10.0731i	0.436314	−	0.436314i
$534$	−25.5751	−	49.4763i	−1.10674	−	2.14105i
$535$			1.31994i			0.0570661i
$536$	33.1631	−	24.9951i	1.43243	−	1.07962i
$537$	3.18700	+	3.18700i	0.137529	+	0.137529i
$538$	5.04181	+	9.75364i	0.217368	+	0.420509i
$539$	−15.3867	−	15.3867i	−0.662753	−	0.662753i
$540$	−2.59617	−	1.84021i	−0.111721	−	0.0791902i
$541$	−21.9156	−	21.9156i	−0.942226	−	0.942226i	0.0561938	−	0.998420i	$-0.482104\pi$
$541$	−21.9156	−	21.9156i	−0.942226	−	0.942226i	−0.998420	+	0.0561938i	$0.982104\pi$
$542$	−24.6838	−	7.86093i	−1.06026	−	0.337656i
$543$	−4.37677			−0.187825
$544$	−17.2665	+	15.6802i	−0.740295	+	0.672282i
$545$	6.83548			0.292800
$546$	−8.46393	−	2.69547i	−0.362223	−	0.115355i
$547$	16.0160	+	16.0160i	0.684796	+	0.684796i	0.961077	−	0.276281i	$-0.0891021\pi$
$547$	16.0160	+	16.0160i	0.684796	+	0.684796i	−0.276281	+	0.961077i	$0.589102\pi$
$548$	20.0540	+	14.2146i	0.856663	+	0.607218i
$549$	−1.09904	−	1.09904i	−0.0469058	−	0.0469058i
$550$	−2.08181	−	4.02738i	−0.0887688	−	0.171728i
$551$	12.1730	+	12.1730i	0.518588	+	0.518588i
$552$	51.5821	−	38.8776i	2.19548	−	1.65474i
$553$			6.46375i			0.274867i
$554$	0.250497	+	0.484599i	0.0106426	+	0.0205886i
$555$	3.84251	−	3.84251i	0.163106	−	0.163106i
$556$	1.58006	+	9.27269i	0.0670096	+	0.393250i
$557$		−	1.47691i		−	0.0625786i	−0.999510	−	0.0312893i	$-0.990039\pi$
$557$		−	1.47691i		−	0.0625786i	0.999510	−	0.0312893i	$-0.00996132\pi$
$558$	13.2171	+	25.5693i	0.559527	+	1.08243i
$559$		−	64.1642i		−	2.71386i
$560$	1.73849	−	0.610194i	0.0734647	−	0.0257854i
$561$	−22.1145	−	25.8309i	−0.933677	−	1.09058i
$562$	12.2634	−	38.5079i	0.517301	−	1.62436i
$563$	−39.9936			−1.68553			−0.842765	−	0.538282i	$-0.819074\pi$
$563$	−39.9936			−1.68553			−0.842765	+	0.538282i	$0.819074\pi$
$564$	−5.59584	−	32.8395i	−0.235627	−	1.38279i
$565$		−	10.0019i		−	0.420782i
$566$	25.1658	−	13.0086i	1.05780	−	0.546791i
$567$	−2.20244	−	2.20244i	−0.0924940	−	0.0924940i
$568$	−38.0019	−	5.33714i	−1.59452	−	0.223941i
$569$			31.0413i			1.30132i	0.759369	+	0.650660i	$0.225508\pi$
$569$			31.0413i			1.30132i	−0.759369	+	0.650660i	$0.774492\pi$
$570$	4.32344	−	13.5759i	0.181089	−	0.568631i
$571$	−33.0089	+	33.0089i	−1.38138	+	1.38138i	−0.539203	+	0.842176i	$0.681274\pi$
$571$	−33.0089	+	33.0089i	−1.38138	+	1.38138i	−0.842176	+	0.539203i	$0.818726\pi$
$572$	5.70858	+	33.5011i	0.238688	+	1.40075i
$573$	4.40600	+	4.40600i	0.184063	+	0.184063i
$574$	0.531256	−	1.66818i	0.0221742	−	0.0696283i
$575$	−6.27686	+	6.27686i	−0.261763	+	0.261763i
$576$	−27.8279	−	7.97381i	−1.15950	−	0.332242i
$577$	45.9242			1.91185			0.955924	−	0.293615i	$-0.0948583\pi$
$577$	45.9242			1.91185			0.955924	+	0.293615i	$0.0948583\pi$
$578$	10.7384	−	21.5102i	0.446657	−	0.894705i
$579$			12.1261i			0.503942i
$580$	−5.08430	+	7.17292i	−0.211114	+	0.297839i
$581$	0.627467	+	0.627467i	0.0260317	+	0.0260317i
$582$	−36.3234	−	11.5677i	−1.50565	−	0.479497i
$583$	8.47956	−	8.47956i	0.351188	−	0.351188i
$584$	−23.6715	−	3.32452i	−0.979534	−	0.137570i
$585$	−13.5620	−	13.5620i	−0.560721	−	0.560721i
$586$	−12.3996	+	38.9355i	−0.512222	+	1.60841i
$587$	43.4983			1.79537			0.897683	−	0.440643i	$-0.145249\pi$
$587$	43.4983			1.79537			0.897683	+	0.440643i	$0.145249\pi$
$588$	34.4290	−	5.86669i	1.41983	−	0.241938i
$589$	−15.5753	+	15.5753i	−0.641769	+	0.641769i
$590$	2.48884	+	4.81478i	0.102464	+	0.198221i
$591$	−12.1107			−0.498166
$592$	3.65864	−	7.61590i	0.150369	−	0.313011i
$593$		−	17.1899i		−	0.705907i	−0.935641	−	0.352953i	$-0.885177\pi$
$593$		−	17.1899i		−	0.705907i	0.935641	−	0.352953i	$-0.114823\pi$
$594$	2.18892	−	6.87335i	0.0898125	−	0.282017i
$595$	−1.44268	+	1.23512i	−0.0591443	+	0.0506350i
$596$	28.0371	−	39.5547i	1.14844	−	1.62022i
$597$	−25.9903			−1.06371
$598$	59.1104	−	30.5551i	2.41721	−	1.24949i
$599$	−4.47248			−0.182740			−0.0913702	−	0.995817i	$-0.529125\pi$
$599$	−4.47248			−0.182740			−0.0913702	+	0.995817i	$0.529125\pi$
$600$	7.20580	+	1.01201i	0.294176	+	0.0413152i
$601$	4.23212	+	4.23212i	0.172632	+	0.172632i	0.788135	−	0.615503i	$-0.211047\pi$
$601$	4.23212	+	4.23212i	0.172632	+	0.172632i	−0.615503	+	0.788135i	$0.711047\pi$
$602$	−3.62101	−	7.00503i	−0.147581	−	0.285504i
$603$	−53.1273			−2.16351
$604$	20.7556	−	29.2819i	0.844532	−	1.19146i
$605$	−0.511346	+	0.511346i	−0.0207892	+	0.0207892i
$606$	−10.7581	+	5.56102i	−0.437017	+	0.225901i
$607$	1.12337	−	1.12337i	0.0455961	−	0.0455961i	−0.683941	−	0.729537i	$-0.739736\pi$
$607$	1.12337	−	1.12337i	0.0455961	−	0.0455961i	0.729537	+	0.683941i	$0.239736\pi$
$608$	−0.647808	−	22.1432i	−0.0262721	−	0.898024i
$609$	3.68355	−	3.68355i	0.149265	−	0.149265i
$610$	0.578817	+	0.184333i	0.0234356	+	0.00746342i
$611$		−	34.3177i		−	1.38834i
$612$	29.7141	−	2.72408i	1.20112	−	0.110114i
$613$			34.5477i			1.39537i	0.716406	+	0.697684i	$0.245786\pi$
$613$			34.5477i			1.39537i	−0.716406	+	0.697684i	$0.754214\pi$
$614$	−8.99985	+	28.2601i	−0.363204	+	1.14048i
$615$	4.88908	−	4.88908i	0.197147	−	0.197147i
$616$	2.51381	+	3.33528i	0.101284	+	0.134382i
$617$	−30.3945	+	30.3945i	−1.22364	+	1.22364i	−0.257309	+	0.966329i	$0.582836\pi$
$617$	−30.3945	+	30.3945i	−1.22364	+	1.22364i	−0.966329	+	0.257309i	$0.917164\pi$
$618$	9.94817	+	19.2452i	0.400174	+	0.774157i
$619$	−0.665957	+	0.665957i	−0.0267671	+	0.0267671i	−0.720364	−	0.693597i	$-0.756025\pi$
$619$	−0.665957	+	0.665957i	−0.0267671	+	0.0267671i	0.693597	+	0.720364i	$0.256025\pi$
$620$	−9.17772	−	6.50533i	−0.368586	−	0.261260i
$621$	−14.1240			−0.566776
$622$	−7.26733	+	3.75660i	−0.291393	+	0.150626i
$623$	−4.98599	−	4.98599i	−0.199759	−	0.199759i
$624$	−49.1658	−	23.6190i	−1.96821	−	0.945518i
$625$	−1.00000			−0.0400000
$626$	−10.3153	−	19.9554i	−0.412281	−	0.797578i
$627$	32.2968			1.28981
$628$	−4.72116	+	6.66061i	−0.188395	+	0.265787i
$629$	−0.673049	+	8.68310i	−0.0268362	+	0.346218i
$630$	−2.24597	−	0.715263i	−0.0894816	−	0.0284968i
$631$			21.2569i			0.846223i	0.906078	+	0.423111i	$0.139062\pi$
$631$			21.2569i			0.846223i	−0.906078	+	0.423111i	$0.860938\pi$
$632$	−5.52015	+	39.3050i	−0.219580	+	1.56347i
$633$	34.0273			1.35246
$634$	17.3690	−	8.97829i	0.689810	−	0.356573i
$635$	−10.9825	+	10.9825i	−0.435829	+	0.435829i
$636$	3.23311	+	18.9737i	0.128201	+	0.752356i
$637$	35.9787			1.42553
$638$	−18.9903	−	6.04773i	−0.751831	−	0.239432i
$639$	34.7146	+	34.7146i	1.37329	+	1.37329i
$640$	11.0926	−	2.22579i	0.438474	−	0.0879821i
$641$	−5.82707	+	5.82707i	−0.230155	+	0.230155i	−0.812758	−	0.582602i	$-0.802035\pi$
$641$	−5.82707	+	5.82707i	−0.230155	+	0.230155i	0.582602	+	0.812758i	$0.302035\pi$
$642$	1.45725	−	4.57586i	0.0575131	−	0.180595i
$643$	16.6867	+	16.6867i	0.658061	+	0.658061i	0.954921	−	0.296860i	$-0.0959396\pi$
$643$	16.6867	+	16.6867i	0.658061	+	0.658061i	−0.296860	+	0.954921i	$0.595940\pi$
$644$	4.72897	−	6.67162i	0.186347	−	0.262899i
$645$		−	31.1427i		−	1.22624i
$646$	8.88648	+	21.0343i	0.349634	+	0.827583i
$647$	2.62991			0.103393			0.0516963	−	0.998663i	$-0.483537\pi$
$647$	2.62991			0.103393			0.0516963	+	0.998663i	$0.483537\pi$
$648$	−11.5118	−	15.2736i	−0.452225	−	0.600005i
$649$	−8.68760	+	8.68760i	−0.341018	+	0.341018i
$650$	7.14255	+	2.27465i	0.280154	+	0.0892191i
$651$	4.71308	+	4.71308i	0.184720	+	0.184720i
$652$	−15.5984	+	2.65797i	−0.610882	+	0.104094i
$653$	−16.1557	+	16.1557i	−0.632222	+	0.632222i	−0.948625	−	0.316403i	$-0.897525\pi$
$653$	−16.1557	+	16.1557i	−0.632222	+	0.632222i	0.316403	+	0.948625i	$0.397525\pi$
$654$	−23.6966	−	7.54654i	−0.926611	−	0.295093i
$655$		−	6.41528i		−	0.250666i
$656$	4.65513	−	9.69021i	0.181752	−	0.378339i
$657$	21.6238	+	21.6238i	0.843627	+	0.843627i
$658$	−1.93667	−	3.74658i	−0.0754991	−	0.146057i
$659$			27.4618i			1.06976i	0.844928	+	0.534881i	$0.179643\pi$
$659$			27.4618i			1.06976i	−0.844928	+	0.534881i	$0.820357\pi$
$660$	2.77072	+	16.2601i	0.107850	+	0.632924i
$661$	−41.4101			−1.61067			−0.805333	−	0.592822i	$-0.798014\pi$
$661$	−41.4101			−1.61067			−0.805333	+	0.592822i	$0.798014\pi$
$662$	−9.93154	−	3.16285i	−0.386000	−	0.122928i
$663$	56.0554	+	4.34499i	2.17701	+	0.168745i
$664$	3.27966	+	4.35139i	0.127275	+	0.168867i
$665$		−	1.80381i		−	0.0699487i
$666$	−9.60215	+	4.96350i	−0.372076	+	0.192332i
$667$			39.0229i			1.51097i
$668$	10.4886	−	1.78726i	0.405817	−	0.0691510i
$669$	18.7337	−	18.7337i	0.724287	−	0.724287i
$670$	18.4452	−	9.53463i	0.712602	−	0.368355i
$671$			1.37700i			0.0531583i
$672$	−6.70052	+	0.196027i	−0.258478	+	0.00756189i
$673$	−0.329765	−	0.329765i	−0.0127115	−	0.0127115i	0.700722	−	0.713434i	$-0.252861\pi$
$673$	−0.329765	−	0.329765i	−0.0127115	−	0.0127115i	−0.713434	+	0.700722i	$0.752861\pi$
$674$	−21.1421	+	10.9287i	−0.814362	+	0.420956i
$675$	−1.12508	−	1.12508i	−0.0433045	−	0.0433045i
$676$	−24.6302	−	17.4583i	−0.947314	−	0.671473i
$677$	−21.6711	−	21.6711i	−0.832887	−	0.832887i	0.155024	−	0.987911i	$-0.450454\pi$
$677$	−21.6711	−	21.6711i	−0.832887	−	0.832887i	−0.987911	+	0.155024i	$0.950454\pi$
$678$	−11.0423	+	34.6736i	−0.424078	+	1.33163i
$679$	−4.82624			−0.185214
$680$	−9.82754	+	6.27849i	−0.376869	+	0.240769i
$681$	36.4396			1.39637
$682$	7.73804	−	24.2979i	0.296305	−	0.930416i
$683$	−14.2461	−	14.2461i	−0.545111	−	0.545111i	0.379912	−	0.925023i	$-0.375954\pi$
$683$	−14.2461	−	14.2461i	−0.545111	−	0.545111i	−0.925023	+	0.379912i	$0.875954\pi$
$684$	−16.3887	+	23.1212i	−0.626638	+	0.884060i
$685$	8.69064	+	8.69064i	0.332052	+	0.332052i
$686$	7.97863	−	4.12428i	0.304625	−	0.157466i
$687$	−21.0837	−	21.0837i	−0.804395	−	0.804395i
$688$	−16.0364	−	45.6889i	−0.611381	−	1.74187i
$689$			19.8277i			0.755376i
$690$	28.6899	−	14.8302i	1.09220	−	0.564578i
$691$	−14.8543	+	14.8543i	−0.565086	+	0.565086i	−0.930748	−	0.365662i	$-0.880843\pi$
$691$	−14.8543	+	14.8543i	−0.565086	+	0.565086i	0.365662	+	0.930748i	$0.380843\pi$
$692$	−3.43456	−	20.1559i	−0.130563	−	0.766214i
$693$		−	5.34313i		−	0.202969i
$694$	17.7628	−	9.18188i	0.674267	−	0.348539i
$695$			4.70318i			0.178402i
$696$	25.5449	−	19.2532i	0.968276	−	0.729792i
$697$	−0.856364	+	11.0481i	−0.0324371	+	0.418476i
$698$	−40.4897	−	12.8945i	−1.53256	−	0.488066i
$699$	26.6593			1.00835
$700$	0.908144	−	0.154747i	0.0343246	−	0.00584890i
$701$			4.47435i			0.168994i	0.996424	+	0.0844969i	$0.0269283\pi$
$701$			4.47435i			0.168994i	−0.996424	+	0.0844969i	$0.973072\pi$
$702$	5.47679	+	10.5951i	0.206708	+	0.399888i
$703$	−5.84907	−	5.84907i	−0.220602	−	0.220602i
$704$	12.4377	+	22.4282i	0.468763	+	0.845293i
$705$		−	16.6564i		−	0.627317i
$706$	23.7087	+	7.55039i	0.892289	+	0.284163i
$707$	−1.08415	+	1.08415i	−0.0407736	+	0.0407736i
$708$	−3.31243	−	19.4392i	−0.124489	−	0.730570i
$709$	25.5875	+	25.5875i	0.960960	+	0.960960i	0.999266	−	0.0383065i	$-0.0121963\pi$
$709$	25.5875	+	25.5875i	0.960960	+	0.960960i	−0.0383065	+	0.999266i	$0.512196\pi$
$710$	−18.2827	−	5.82240i	−0.686137	−	0.218511i
$711$	35.9050	−	35.9050i	1.34654	−	1.34654i
$712$	−26.0609	−	34.5771i	−0.976673	−	1.29583i
$713$	−49.9296			−1.86988
$714$	6.36497	−	2.68904i	0.238203	−	0.100635i
$715$			16.9920i			0.635465i
$716$	2.85859	+	2.02622i	0.106830	+	0.0757233i
$717$	−24.7881	−	24.7881i	−0.925729	−	0.925729i
$718$	4.66247	−	14.6405i	0.174002	−	0.546377i
$719$	−12.5070	+	12.5070i	−0.466433	+	0.466433i	−0.900757	−	0.434324i	$-0.856987\pi$
$719$	−12.5070	+	12.5070i	−0.466433	+	0.466433i	0.434324	+	0.900757i	$0.356987\pi$
$720$	−13.0465	−	6.26749i	−0.486216	−	0.233576i
$721$	1.93945	+	1.93945i	0.0722287	+	0.0722287i
$722$	4.93787	+	1.57254i	0.183769	+	0.0585238i
$723$	5.03469			0.187242
$724$	−3.35421	+	0.571556i	−0.124658	+	0.0212417i
$725$	−3.10847	+	3.10847i	−0.115446	+	0.115446i
$726$	2.33722	−	1.20815i	0.0867425	−	0.0448386i
$727$	43.8052			1.62464			0.812322	−	0.583209i	$-0.198203\pi$
$727$	43.8052			1.62464			0.812322	+	0.583209i	$0.198203\pi$
$728$	−6.83846	−	0.960421i	−0.253450	−	0.0355956i
$729$			36.7484i			1.36105i
$730$	−11.3884	−	3.62679i	−0.421502	−	0.134234i
$731$	32.4599	+	37.9148i	1.20057	+	1.40233i
$732$	−1.80308	−	1.27806i	−0.0666438	−	0.0472383i
$733$	−11.2247			−0.414594			−0.207297	−	0.978278i	$-0.566467\pi$
$733$	−11.2247			−0.414594			−0.207297	+	0.978278i	$0.566467\pi$
$734$	16.3036	+	31.5402i	0.601777	+	1.16417i
$735$	17.4626			0.644119
$736$	34.4538	−	36.5304i	1.26998	−	1.34653i
$737$	33.2818	+	33.2818i	1.22595	+	1.22595i
$738$	−12.2175	+	6.31539i	−0.449731	+	0.232473i
$739$	−41.8337			−1.53888			−0.769438	−	0.638721i	$-0.779464\pi$
$739$	−41.8337			−1.53888			−0.769438	+	0.638721i	$0.779464\pi$
$740$	2.44298	−	3.44655i	0.0898057	−	0.126698i
$741$	−37.7597	+	37.7597i	−1.38714	+	1.38714i
$742$	1.11895	+	2.16466i	0.0410779	+	0.0794673i
$743$	10.8139	−	10.8139i	0.396722	−	0.396722i	−0.480353	−	0.877075i	$-0.659491\pi$
$743$	10.8139	−	10.8139i	0.396722	−	0.396722i	0.877075	+	0.480353i	$0.159491\pi$
$744$	24.6344	+	32.6845i	0.903142	+	1.19827i
$745$	17.1415	−	17.1415i	0.628016	−	0.628016i
$746$	−0.780987	+	2.45235i	−0.0285940	+	0.0897868i
$747$		−	6.97094i		−	0.255053i
$748$	−20.3210	−	16.9080i	−0.743011	−	0.618218i
$749$		−	0.607989i		−	0.0222154i
$750$	3.46671	+	1.10403i	0.126586	+	0.0403133i
$751$	−3.37915	+	3.37915i	−0.123307	+	0.123307i	−0.766067	−	0.642760i	$-0.777789\pi$
$751$	−3.37915	+	3.37915i	−0.123307	+	0.123307i	0.642760	+	0.766067i	$0.277789\pi$
$752$	−8.57691	−	24.4363i	−0.312768	−	0.891100i
$753$	23.2121	−	23.2121i	0.845896	−	0.845896i
$754$	29.2731	−	15.1317i	1.06606	−	0.551065i
$755$	12.6897	−	12.6897i	0.461825	−	0.461825i
$756$	1.19584	+	0.847634i	0.0434923	+	0.0308282i
$757$	40.4904			1.47165			0.735824	−	0.677173i	$-0.236795\pi$
$757$	40.4904			1.47165			0.735824	+	0.677173i	$0.236795\pi$
$758$	−11.1653	−	21.5999i	−0.405543	−	0.784543i
$759$	51.7668	+	51.7668i	1.87902	+	1.87902i
$760$	1.54048	−	10.9687i	0.0558792	−	0.397876i
$761$	6.84788			0.248235			0.124118	−	0.992268i	$-0.460390\pi$
$761$	6.84788			0.248235			0.124118	+	0.992268i	$0.460390\pi$
$762$	50.1983	−	25.9483i	1.81849	−	0.940007i
$763$	−3.14854			−0.113985
$764$	3.95198	+	2.80124i	0.142978	+	0.101345i
$765$	14.8747	+	1.15298i	0.537797	+	0.0416860i
$766$	6.50159	−	20.4154i	0.234912	−	0.737639i
$767$		−	20.3142i		−	0.733502i
$768$	−40.9122	−	4.53035i	−1.47629	−	0.163475i
$769$	49.7298			1.79330			0.896651	−	0.442738i	$-0.145993\pi$
$769$	49.7298			1.79330			0.896651	+	0.442738i	$0.145993\pi$
$770$	0.958919	+	1.85508i	0.0345570	+	0.0668524i
$771$	39.3607	−	39.3607i	1.41754	−	1.41754i
$772$	1.58352	+	9.29299i	0.0569922	+	0.334462i
$773$	41.6759			1.49898			0.749488	−	0.662018i	$-0.230300\pi$
$773$	41.6759			1.49898			0.749488	+	0.662018i	$0.230300\pi$
$774$	−18.7976	+	59.0258i	−0.675667	+	2.12164i
$775$	−3.97728	−	3.97728i	−0.142868	−	0.142868i
$776$	−29.3476	−	4.12169i	−1.05352	−	0.147960i
$777$	−1.76993	+	1.76993i	−0.0634958	+	0.0634958i
$778$	25.0438	+	7.97558i	0.897865	+	0.285938i
$779$	−7.44216	−	7.44216i	−0.266643	−	0.266643i
$780$	−22.2499	−	15.7711i	−0.796673	−	0.564696i
$781$		−	43.4942i		−	1.55635i
$782$	−19.4711	+	47.9584i	−0.696285	+	1.71499i
$783$	−6.99459			−0.249966
$784$	25.6191	−	8.99206i	0.914967	−	0.321145i
$785$	−2.88646	+	2.88646i	−0.103022	+	0.103022i
$786$	−7.08263	+	22.2399i	−0.252629	+	0.793271i
$787$	34.0259	+	34.0259i	1.21289	+	1.21289i	0.970071	+	0.242821i	$0.0780729\pi$
$787$	34.0259	+	34.0259i	1.21289	+	1.21289i	0.242821	+	0.970071i	$0.421927\pi$
$788$	−9.28120	+	1.58151i	−0.330629	+	0.0563390i
$789$	−6.23132	+	6.23132i	−0.221841	+	0.221841i
$790$	−6.02205	+	18.9096i	−0.214255	+	0.672774i
$791$			4.60704i			0.163807i
$792$	4.56312	−	32.4907i	0.162143	−	1.15451i
$793$	−1.60991	−	1.60991i	−0.0571696	−	0.0571696i
$794$	7.36156	−	3.80530i	0.261252	−	0.135045i
$795$			9.62359i			0.341314i
$796$	−19.9181	+	3.39403i	−0.705977	+	0.120298i
$797$	−8.55745			−0.303121			−0.151560	−	0.988448i	$-0.548430\pi$
$797$	−8.55745			−0.303121			−0.151560	+	0.988448i	$0.548430\pi$
$798$	−1.99145	+	6.25328i	−0.0704966	+	0.221364i
$799$	17.3609	+	20.2784i	0.614184	+	0.717399i
$800$	5.65444	−	0.165423i	0.199914	−	0.00584859i
$801$			55.3926i			1.95720i
$802$	4.15962	+	8.04700i	0.146881	+	0.284149i
$803$		−	27.0927i		−	0.956081i
$804$	−74.4708	+	12.6898i	−2.62638	+	0.447534i
$805$	2.89123	−	2.89123i	0.101902	−	0.101902i
$806$	19.3610	+	37.4548i	0.681961	+	1.31929i
$807$		−	19.9735i		−	0.703099i
$808$	−7.51842	+	5.66666i	−0.264497	+	0.199352i
$809$	5.34694	+	5.34694i	0.187988	+	0.187988i	0.794826	−	0.606838i	$-0.207562\pi$
$809$	5.34694	+	5.34694i	0.187988	+	0.187988i	−0.606838	+	0.794826i	$0.707562\pi$
$810$	−4.39128	−	8.49517i	−0.154294	−	0.298490i
$811$	2.55381	+	2.55381i	0.0896765	+	0.0896765i	0.750522	−	0.660846i	$-0.229802\pi$
$811$	2.55381	+	2.55381i	0.0896765	+	0.0896765i	−0.660846	+	0.750522i	$0.729802\pi$
$812$	2.34192	−	3.30397i	0.0821851	−	0.115947i
$813$	33.3225	+	33.3225i	1.16867	+	1.16867i
$814$	9.12472	+	2.90590i	0.319821	+	0.101852i
$815$	−7.91164			−0.277133
$816$	41.0008	−	10.9159i	1.43532	−	0.382131i
$817$	−47.4055			−1.65851
$818$	3.39018	+	1.07965i	0.118535	+	0.0377492i
$819$	6.24691	+	6.24691i	0.218285	+	0.218285i
$820$	3.10836	−	4.38528i	0.108549	−	0.153141i
$821$	−10.3459	−	10.3459i	−0.361073	−	0.361073i	0.503135	−	0.864208i	$-0.332180\pi$
$821$	−10.3459	−	10.3459i	−0.361073	−	0.361073i	−0.864208	+	0.503135i	$0.832180\pi$
$822$	−20.5332	−	39.7226i	−0.716178	−	1.38548i
$823$	36.9418	+	36.9418i	1.28771	+	1.28771i	0.936175	+	0.351534i	$0.114340\pi$
$823$	36.9418	+	36.9418i	1.28771	+	1.28771i	0.351534	+	0.936175i	$0.385660\pi$
$824$	10.1371	+	13.4498i	0.353144	+	0.468545i
$825$			8.24724i			0.287132i
$826$	−1.14640	−	2.21777i	−0.0398884	−	0.0771662i
$827$	−9.66429	+	9.66429i	−0.336060	+	0.336060i	−0.854882	−	0.518822i	$-0.826371\pi$
$827$	−9.66429	+	9.66429i	−0.336060	+	0.336060i	0.518822	+	0.854882i	$0.326371\pi$
$828$	−63.3283	+	10.7911i	−2.20081	+	0.375017i
$829$		−	35.6343i		−	1.23763i	−0.785536	−	0.618815i	$-0.787613\pi$
$829$		−	35.6343i		−	1.23763i	0.785536	−	0.618815i	$-0.212387\pi$
$830$	1.25106	+	2.42024i	0.0434249	+	0.0840077i
$831$		−	0.992359i		−	0.0344246i
$832$	−40.7634	−	11.6803i	−1.41321	−	0.404942i
$833$	−21.2599	+	18.2012i	−0.736613	+	0.630635i
$834$	5.19243	−	16.3045i	0.179799	−	0.564580i
$835$	5.31990			0.184103
$836$	24.7511	−	4.21758i	0.856036	−	0.145868i
$837$		−	8.94953i		−	0.309341i
$838$	−15.8554	+	8.19593i	−0.547717	+	0.283124i
$839$	−11.5245	−	11.5245i	−0.397870	−	0.397870i	0.479611	−	0.877481i	$-0.340778\pi$
$839$	−11.5245	−	11.5245i	−0.397870	−	0.397870i	−0.877481	+	0.479611i	$0.840778\pi$
$840$	−3.31912	−	0.466150i	−0.114520	−	0.0160837i
$841$		−	9.67477i		−	0.333613i
$842$	6.93449	−	21.7747i	0.238978	−	0.750406i
$843$	−51.9846	+	51.9846i	−1.79045	+	1.79045i
$844$	26.0773	−	4.44357i	0.897619	−	0.152954i
$845$	−10.6738	−	10.6738i	−0.367189	−	0.367189i
$846$	−10.0538	+	31.5694i	−0.345655	+	1.08538i
$847$	0.235535	−	0.235535i	0.00809306	−	0.00809306i
$848$	4.95549	+	14.1186i	0.170172	+	0.484834i
$849$	−51.5344			−1.76866
$850$	−5.37127	+	2.26923i	−0.184233	+	0.0778340i
$851$		−	18.7503i		−	0.642753i
$852$	56.9527	+	40.3691i	1.95117	+	1.38302i
$853$	−14.5505	−	14.5505i	−0.498200	−	0.498200i	0.412677	−	0.910877i	$-0.364594\pi$
$853$	−14.5505	−	14.5505i	−0.498200	−	0.498200i	−0.910877	+	0.412677i	$0.864594\pi$
$854$	−0.266613	−	0.0849068i	−0.00912330	−	0.00290545i
$855$	−10.0198	+	10.0198i	−0.342671	+	0.342671i
$856$	0.519233	−	3.69708i	0.0177470	−	0.126364i
$857$	−35.6324	−	35.6324i	−1.21718	−	1.21718i	−0.968615	−	0.248564i	$-0.920041\pi$
$857$	−35.6324	−	35.6324i	−1.21718	−	1.21718i	−0.248564	−	0.968615i	$-0.579959\pi$
$858$	18.7596	−	58.9063i	0.640442	−	2.01103i
$859$	−56.5983			−1.93111			−0.965555	−	0.260200i	$-0.916211\pi$
$859$	−56.5983			−1.93111			−0.965555	+	0.260200i	$0.916211\pi$
$860$	−4.06688	−	23.8667i	−0.138679	−	0.813848i
$861$	−2.25199	+	2.25199i	−0.0767478	+	0.0767478i
$862$	−19.2699	−	37.2785i	−0.656334	−	1.26971i
$863$	−35.8242			−1.21947			−0.609736	−	0.792605i	$-0.708724\pi$
$863$	−35.8242			−1.21947			−0.609736	+	0.792605i	$0.708724\pi$
$864$	6.54783	+	6.17560i	0.222762	+	0.210098i
$865$		−	10.2232i		−	0.347600i
$866$	−10.7006	+	33.6006i	−0.363621	+	1.14179i
$867$	−35.3214	+	25.7903i	−1.19958	+	0.875884i
$868$	4.22741	+	2.99647i	0.143488	+	0.101707i
$869$	−44.9857			−1.52604
$870$	14.2080	−	7.34434i	0.481697	−	0.248997i
$871$	−77.8228			−2.63692
$872$	−19.1458	−	2.68891i	−0.648357	−	0.0910578i
$873$	26.8089	+	26.8089i	0.907343	+	0.907343i
$874$	−22.5746	−	43.6717i	−0.763597	−	1.47722i
$875$	0.460617			0.0155717
$876$	35.4761	+	25.1461i	1.19862	+	0.849607i
$877$	6.44380	−	6.44380i	0.217592	−	0.217592i	−0.589891	−	0.807483i	$-0.700829\pi$
$877$	6.44380	−	6.44380i	0.217592	−	0.217592i	0.807483	+	0.589891i	$0.200829\pi$
$878$	36.7303	−	18.9865i	1.23959	−	0.640762i
$879$	52.5618	−	52.5618i	1.77287	−	1.77287i
$880$	4.24676	+	12.0994i	0.143158	+	0.407869i
$881$	16.8558	−	16.8558i	0.567885	−	0.567885i	−0.363650	−	0.931535i	$-0.618470\pi$
$881$	16.8558	−	16.8558i	0.567885	−	0.567885i	0.931535	+	0.363650i	$0.118470\pi$
$882$	−33.0975	−	10.5404i	−1.11445	−	0.354913i
$883$			21.4178i			0.720767i	0.932804	+	0.360384i	$0.117354\pi$
$883$			21.4178i			0.720767i	−0.932804	+	0.360384i	$0.882646\pi$
$884$	43.5263	−	3.99033i	1.46395	−	0.134209i
$885$		−	9.85970i		−	0.331430i
$886$	−9.99527	+	31.3858i	−0.335798	+	1.05443i
$887$	−14.4142	+	14.4142i	−0.483981	+	0.483981i	−0.906401	−	0.422419i	$-0.861181\pi$
$887$	−14.4142	+	14.4142i	−0.483981	+	0.483981i	0.422419	+	0.906401i	$0.361181\pi$
$888$	−12.2742	+	9.25109i	−0.411895	+	0.310446i
$889$	5.05875	−	5.05875i	0.169665	−	0.169665i
$890$	−9.94118	−	19.2317i	−0.333229	−	0.644649i
$891$	15.3283	−	15.3283i	0.513518	−	0.513518i
$892$	11.9105	−	16.8033i	0.398792	−	0.562615i
$893$	−25.3544			−0.848453
$894$	−78.3493	+	40.5000i	−2.62039	+	1.35452i
$895$	1.23880	+	1.23880i	0.0414086	+	0.0414086i
$896$	−5.10944	+	1.02524i	−0.170695	+	0.0342508i
$897$	−121.046			−4.04161
$898$	18.2688	+	35.3419i	0.609637	+	1.17938i
$899$	−24.7265			−0.824676
$900$	−5.90417	−	4.18499i	−0.196806	−	0.139500i
$901$	−10.0306	−	11.7163i	−0.334168	−	0.390326i
$902$	11.6100	+	3.69737i	0.386570	+	0.123109i
$903$			14.3449i			0.477368i
$904$	−3.93449	+	28.0147i	−0.130859	+	0.931754i
$905$	−1.70128			−0.0565524
$906$	−58.0012	+	29.9817i	−1.92696	+	0.996075i
$907$	−17.1433	+	17.1433i	−0.569233	+	0.569233i	−0.931914	−	0.362680i	$-0.881862\pi$
$907$	−17.1433	+	17.1433i	−0.569233	+	0.569233i	0.362680	+	0.931914i	$0.381862\pi$
$908$	27.9261	−	4.75859i	0.926759	−	0.157919i
$909$	12.0445			0.399491
$910$	−3.28998	−	1.04774i	−0.109062	−	0.0347324i
$911$	11.2270	+	11.2270i	0.371966	+	0.371966i	0.868193	−	0.496227i	$-0.165282\pi$
$911$	11.2270	+	11.2270i	0.371966	+	0.371966i	−0.496227	+	0.868193i	$0.665282\pi$
$912$	−17.4501	+	36.3245i	−0.577831	+	1.20282i
$913$	−4.36698	+	4.36698i	−0.144526	+	0.144526i
$914$	−5.38241	+	16.9011i	−0.178034	+	0.559039i
$915$	−0.781387	−	0.781387i	−0.0258319	−	0.0258319i
$916$	−18.9111	−	13.4046i	−0.624841	−	0.442899i
$917$			2.95499i			0.0975822i
$918$	−8.59621	−	3.49006i	−0.283717	−	0.115189i
$919$	−28.9408			−0.954668			−0.477334	−	0.878722i	$-0.658397\pi$
$919$	−28.9408			−0.954668			−0.477334	+	0.878722i	$0.658397\pi$
$920$	20.0503	−	15.1119i	0.661038	−	0.498226i
$921$	38.1504	−	38.1504i	1.25710	−	1.25710i
$922$	11.8604	+	3.77712i	0.390602	+	0.124393i
$923$	50.8512	+	50.8512i	1.67379	+	1.67379i
$924$	−1.27624	−	7.48969i	−0.0419852	−	0.246393i
$925$	1.49361	−	1.49361i	0.0491095	−	0.0491095i
$926$	10.7589	+	3.42633i	0.353559	+	0.112596i
$927$		−	21.5466i		−	0.707682i
$928$	17.0625	−	18.0909i	0.560103	−	0.593862i
$929$	−17.0447	−	17.0447i	−0.559220	−	0.559220i	0.369866	−	0.929085i	$-0.379404\pi$
$929$	−17.0447	−	17.0447i	−0.559220	−	0.559220i	−0.929085	+	0.369866i	$0.879404\pi$
$930$	9.39705	+	18.1791i	0.308141	+	0.596115i
$931$		−	26.5816i		−	0.871178i
$932$	20.4308	−	3.48140i	0.669233	−	0.114037i
$933$	14.8820			0.487215
$934$	51.6076	+	16.4352i	1.68865	+	0.537776i
$935$	−8.59606	−	10.0406i	−0.281121	−	0.328364i
$936$	32.6515	+	43.3214i	1.06725	+	1.41600i
$937$			21.2476i			0.694130i	0.937841	+	0.347065i	$0.112822\pi$
$937$			21.2476i			0.694130i	−0.937841	+	0.347065i	$0.887178\pi$
$938$	−8.49620	+	4.39182i	−0.277411	+	0.143398i
$939$			40.8646i			1.33357i
$940$	−2.17513	−	12.7649i	−0.0709451	−	0.416345i
$941$	22.1360	−	22.1360i	0.721615	−	0.721615i	−0.247319	−	0.968934i	$-0.579550\pi$
$941$	22.1360	−	22.1360i	0.721615	−	0.721615i	0.968934	+	0.247319i	$0.0795497\pi$
$942$	13.1932	−	6.81979i	0.429859	−	0.222201i
$943$		−	23.8573i		−	0.776900i
$944$	−5.07706	−	14.4650i	−0.165244	−	0.470794i
$945$	0.518233	+	0.518233i	0.0168581	+	0.0168581i
$946$	48.7529	−	25.2011i	1.58509	−	0.819359i
$947$	9.14076	+	9.14076i	0.297035	+	0.297035i	0.839851	−	0.542816i	$-0.182642\pi$
$947$	9.14076	+	9.14076i	0.297035	+	0.297035i	−0.542816	+	0.839851i	$0.682642\pi$
$948$	41.7534	−	58.9057i	1.35609	−	1.91317i
$949$	31.6754	+	31.6754i	1.02823	+	1.02823i
$950$	1.68055	−	5.27702i	0.0545242	−	0.171209i
$951$	−35.5681			−1.15337
$952$	4.52673	−	2.89198i	0.146712	−	0.0937296i
$953$	−36.2813			−1.17527			−0.587633	−	0.809128i	$-0.699940\pi$
$953$	−36.2813			−1.17527			−0.587633	+	0.809128i	$0.699940\pi$
$954$	5.80877	−	18.2399i	0.188066	−	0.590538i
$955$	1.71264	+	1.71264i	0.0554197	+	0.0554197i
$956$	−22.2338	−	15.7597i	−0.719092	−	0.509706i
$957$	25.6364	+	25.6364i	0.828706	+	0.828706i
$958$	23.6313	−	12.2154i	0.763494	−	0.394662i
$959$	−4.00306	−	4.00306i	−0.129265	−	0.129265i
$960$	−19.7849	−	5.66917i	−0.638555	−	0.182972i
$961$		−	0.637448i		−	0.0205628i
$962$	−14.0656	+	7.27072i	−0.453493	+	0.234418i
$963$	−3.37727	+	3.37727i	−0.108831	+	0.108831i
$964$	3.85841	−	0.657471i	0.124271	−	0.0211757i
$965$			4.71347i			0.151732i
$966$	−13.2150	+	6.83106i	−0.425187	+	0.219786i
$967$		−	15.8587i		−	0.509982i	−0.966943	−	0.254991i	$-0.917928\pi$
$967$		−	15.8587i		−	0.509982i	0.966943	−	0.254991i	$-0.0820724\pi$
$968$	1.63340	−	1.23110i	0.0524994	−	0.0395689i
$969$	3.21015	−	41.4146i	0.103125	−	1.33043i
$970$	−14.1191	−	4.49644i	−0.453337	−	0.144372i
$971$	8.65169			0.277646			0.138823	−	0.990317i	$-0.455668\pi$
$971$	8.65169			0.277646			0.138823	+	0.990317i	$0.455668\pi$
$972$	7.44806	+	43.7094i	0.238897	+	1.40198i
$973$		−	2.16636i		−	0.0694504i
$974$	25.5958	+	49.5164i	0.820142	+	1.58661i
$975$	−9.64225	−	9.64225i	−0.308799	−	0.308799i
$976$	−1.54872	−	0.743997i	−0.0495732	−	0.0238148i
$977$		−	38.9102i		−	1.24485i	−0.782681	−	0.622423i	$-0.786148\pi$
$977$		−	38.9102i		−	1.24485i	0.782681	−	0.622423i	$-0.213852\pi$
$978$	27.4273	+	8.73465i	0.877030	+	0.279303i
$979$	34.7009	−	34.7009i	1.10905	−	1.10905i
$980$	13.3828	−	2.28042i	0.427497	−	0.0728452i
$981$	17.4896	+	17.4896i	0.558399	+	0.558399i
$982$	13.3082	+	4.23820i	0.424682	+	0.135246i
$983$	−6.74947	+	6.74947i	−0.215275	+	0.215275i	−0.806504	−	0.591229i	$-0.798643\pi$
$983$	−6.74947	+	6.74947i	−0.215275	+	0.215275i	0.591229	+	0.806504i	$0.298643\pi$
$984$	−15.6173	+	11.7708i	−0.497860	+	0.375238i
$985$	−4.70749			−0.149993
$986$	−9.64262	+	23.7503i	−0.307084	+	0.756364i
$987$			7.67224i			0.244210i
$988$	−24.0068	+	33.8687i	−0.763757	+	1.07751i
$989$	−75.9837	−	75.9837i	−2.41614	−	2.41614i
$990$	4.97801	−	15.6313i	0.158211	−	0.496794i
$991$	−10.6626	+	10.6626i	−0.338708	+	0.338708i	−0.855881	−	0.517173i	$-0.826984\pi$
$991$	−10.6626	+	10.6626i	−0.338708	+	0.338708i	0.517173	+	0.855881i	$0.326984\pi$
$992$	23.1472	+	21.8313i	0.734924	+	0.693145i
$993$	13.4073	+	13.4073i	0.425469	+	0.425469i
$994$	8.42132	+	2.68190i	0.267108	+	0.0850646i
$995$	−10.1026			−0.320273
$996$	−1.66505	−	9.77146i	−0.0527592	−	0.309621i
$997$	31.3237	−	31.3237i	0.992030	−	0.992030i	−0.00793802	−	0.999968i	$-0.502527\pi$
$997$	31.3237	−	31.3237i	0.992030	−	0.992030i	0.999968	+	0.00793802i	$0.00252678\pi$
$998$	−19.1519	+	9.89990i	−0.606242	+	0.313376i
$999$	3.36086			0.106333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.ba.b.21.5	✓	140
8.5	even	2	inner	680.2.ba.b.21.66	yes	140
17.13	even	4	inner	680.2.ba.b.421.66	yes	140
136.13	even	4	inner	680.2.ba.b.421.5	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.ba.b.21.5	✓	140	1.1	even	1	trivial
680.2.ba.b.21.66	yes	140	8.5	even	2	inner
680.2.ba.b.421.5	yes	140	136.13	even	4	inner
680.2.ba.b.421.66	yes	140	17.13	even	4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.34753 - 0.429141i) q^{2} +(1.81913 + 1.81913i) q^{3} +(1.63168 + 1.15656i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67067 - 3.23200i) q^{6} +(-0.325706 - 0.325706i) q^{7} +(-1.70240 - 2.25872i) q^{8} +3.61847i q^{9} +(-0.649399 - 1.25630i) q^{10} +(2.26681 - 2.26681i) q^{11} +(0.864295 + 5.07217i) q^{12} +5.30047i q^{13} +(0.299124 + 0.578672i) q^{14} +2.57264i q^{15} +(1.32473 + 3.77427i) q^{16} +(-2.68145 - 3.13207i) q^{17} +(1.55284 - 4.87600i) q^{18} +3.91607 q^{19} +(0.335957 + 1.97158i) q^{20} -1.18500i q^{21} +(-4.02738 + 2.08181i) q^{22} +(6.27686 + 6.27686i) q^{23} +(1.01201 - 7.20580i) q^{24} +1.00000i q^{25} +(2.27465 - 7.14255i) q^{26} +(-1.12508 + 1.12508i) q^{27} +(-0.154747 - 0.908144i) q^{28} +(3.10847 + 3.10847i) q^{29} +(1.10403 - 3.46671i) q^{30} +(-3.97728 + 3.97728i) q^{31} +(-0.165423 - 5.65444i) q^{32} +8.24724 q^{33} +(2.26923 + 5.37127i) q^{34} -0.460617i q^{35} +(-4.18499 + 5.90417i) q^{36} +(-1.49361 - 1.49361i) q^{37} +(-5.27702 - 1.68055i) q^{38} +(-9.64225 + 9.64225i) q^{39} +(0.393375 - 2.80094i) q^{40} +(-1.90041 - 1.90041i) q^{41} +(-0.508533 + 1.59683i) q^{42} -12.1054 q^{43} +(6.32040 - 1.07699i) q^{44} +(-2.55865 + 2.55865i) q^{45} +(-5.76460 - 11.1519i) q^{46} -6.47445 q^{47} +(-4.45602 + 9.27574i) q^{48} -6.78783i q^{49} +(0.429141 - 1.34753i) q^{50} +(0.819736 - 10.5755i) q^{51} +(-6.13032 + 8.64865i) q^{52} +3.74075 q^{53} +(1.99890 - 1.03326i) q^{54} +3.20575 q^{55} +(-0.181195 + 1.29016i) q^{56} +(7.12385 + 7.12385i) q^{57} +(-2.85479 - 5.52274i) q^{58} -3.83252 q^{59} +(-2.97542 + 4.19771i) q^{60} +(-0.303730 + 0.303730i) q^{61} +(7.06631 - 3.65269i) q^{62} +(1.17856 - 1.17856i) q^{63} +(-2.20364 + 7.69051i) q^{64} +(-3.74800 + 3.74800i) q^{65} +(-11.1134 - 3.53923i) q^{66} +14.6822i q^{67} +(-0.752825 - 8.21178i) q^{68} +22.8369i q^{69} +(-0.197670 + 0.620696i) q^{70} +(9.59371 - 9.59371i) q^{71} +(8.17312 - 6.16010i) q^{72} +(5.97596 - 5.97596i) q^{73} +(1.37171 + 2.65365i) q^{74} +(-1.81913 + 1.81913i) q^{75} +(6.38976 + 4.52918i) q^{76} -1.47662 q^{77} +(17.1311 - 8.85534i) q^{78} +(-9.92269 - 9.92269i) q^{79} +(-1.73208 + 3.60554i) q^{80} +6.76207 q^{81} +(1.74532 + 3.37641i) q^{82} -1.92649 q^{83} +(1.37053 - 1.93354i) q^{84} +(0.318636 - 4.11077i) q^{85} +(16.3124 + 5.19491i) q^{86} +11.3094i q^{87} +(-8.97912 - 1.26106i) q^{88} +15.3083 q^{89} +(4.54587 - 2.34983i) q^{90} +(1.72639 - 1.72639i) q^{91} +(2.98223 + 17.5014i) q^{92} -14.4704 q^{93} +(8.72452 + 2.77845i) q^{94} +(2.76908 + 2.76908i) q^{95} +(9.98523 - 10.5871i) q^{96} +(7.40890 - 7.40890i) q^{97} +(-2.91294 + 9.14681i) q^{98} +(8.20239 + 8.20239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 8 q^{4} - 4 q^{6} - 12 q^{7} + 20 q^{12} + 28 q^{14} - 24 q^{16} - 16 q^{17} - 8 q^{20} + 40 q^{22} + 4 q^{23} + 48 q^{24} - 20 q^{28} + 28 q^{31} - 8 q^{34} - 56 q^{38} + 24 q^{40} + 44 q^{41}+ \cdots + 176 q^{98}+O(q^{100}) \) 140 * q - 8 * q^4 - 4 * q^6 - 12 * q^7 + 20 * q^12 + 28 * q^14 - 24 * q^16 - 16 * q^17 - 8 * q^20 + 40 * q^22 + 4 * q^23 + 48 * q^24 - 20 * q^28 + 28 * q^31 - 8 * q^34 - 56 * q^38 + 24 * q^40 + 44 * q^41 + 28 * q^44 - 40 * q^46 - 120 * q^47 + 32 * q^48 - 48 * q^52 - 4 * q^54 + 16 * q^55 + 16 * q^56 - 16 * q^57 - 52 * q^58 - 72 * q^62 + 44 * q^63 - 104 * q^64 + 8 * q^68 + 12 * q^71 - 104 * q^72 + 36 * q^73 + 20 * q^74 + 28 * q^78 - 44 * q^79 - 76 * q^81 - 44 * q^82 + 48 * q^84 + 120 * q^86 + 28 * q^88 + 24 * q^89 + 28 * q^90 - 72 * q^92 + 8 * q^95 - 116 * q^96 + 12 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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