LMFDB - Embedded newform 403.2.k.e.66.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.2
Character	$\chi$	$=$	403.66
Dual form			403.2.k.e.287.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717286 - 2.20758i) q^{2} +(0.693769 - 2.13520i) q^{3} +(-2.74087 + 1.99136i) q^{4} +3.88389 q^{5} -5.21126 q^{6} +(1.00783 - 0.732228i) q^{7} +(2.60631 + 1.89360i) q^{8} +(-1.65072 - 1.19932i) q^{9} +O(q^{10})$	\(q+(-0.717286 - 2.20758i) q^{2} +(0.693769 - 2.13520i) q^{3} +(-2.74087 + 1.99136i) q^{4} +3.88389 q^{5} -5.21126 q^{6} +(1.00783 - 0.732228i) q^{7} +(2.60631 + 1.89360i) q^{8} +(-1.65072 - 1.19932i) q^{9} +(-2.78586 - 8.57400i) q^{10} +(-1.25503 + 0.911830i) q^{11} +(2.35042 + 7.23385i) q^{12} +(0.309017 - 0.951057i) q^{13} +(-2.33935 - 1.69964i) q^{14} +(2.69452 - 8.29289i) q^{15} +(0.216955 - 0.667719i) q^{16} +(-4.26724 - 3.10033i) q^{17} +(-1.46355 + 4.50434i) q^{18} +(0.367413 + 1.13078i) q^{19} +(-10.6453 + 7.73423i) q^{20} +(-0.864257 - 2.65991i) q^{21} +(2.91315 + 2.11653i) q^{22} +(-4.52457 - 3.28729i) q^{23} +(5.85139 - 4.25128i) q^{24} +10.0846 q^{25} -2.32119 q^{26} +(1.74293 - 1.26631i) q^{27} +(-1.30419 + 4.01389i) q^{28} +(1.49422 + 4.59875i) q^{29} -20.2400 q^{30} +(-0.233614 + 5.56286i) q^{31} +4.81350 q^{32} +(1.07624 + 3.31233i) q^{33} +(-3.78339 + 11.6441i) q^{34} +(3.91429 - 2.84390i) q^{35} +6.91268 q^{36} +0.987489 q^{37} +(2.23275 - 1.62219i) q^{38} +(-1.81631 - 1.31963i) q^{39} +(10.1226 + 7.35453i) q^{40} +(-0.0557628 - 0.171620i) q^{41} +(-5.25204 + 3.81583i) q^{42} +(1.20261 + 3.70124i) q^{43} +(1.62408 - 4.99841i) q^{44} +(-6.41121 - 4.65802i) q^{45} +(-4.01155 + 12.3463i) q^{46} +(-0.918674 + 2.82739i) q^{47} +(-1.27520 - 0.926485i) q^{48} +(-1.68356 + 5.18148i) q^{49} +(-7.23356 - 22.2626i) q^{50} +(-9.58030 + 6.96049i) q^{51} +(1.04692 + 3.22209i) q^{52} +(11.2323 + 8.16073i) q^{53} +(-4.04567 - 2.93935i) q^{54} +(-4.87439 + 3.54145i) q^{55} +4.01326 q^{56} +2.66935 q^{57} +(9.08031 - 6.59723i) q^{58} +(2.17283 - 6.68727i) q^{59} +(9.12879 + 28.0955i) q^{60} +3.58792 q^{61} +(12.4480 - 3.47444i) q^{62} -2.54181 q^{63} +(-3.88657 - 11.9616i) q^{64} +(1.20019 - 3.69380i) q^{65} +(6.54026 - 4.75178i) q^{66} +10.5541 q^{67} +17.8698 q^{68} +(-10.1580 + 7.38024i) q^{69} +(-9.08579 - 6.60121i) q^{70} +(-3.54159 - 2.57311i) q^{71} +(-2.03127 - 6.25159i) q^{72} +(-8.11109 + 5.89305i) q^{73} +(-0.708312 - 2.17996i) q^{74} +(6.99640 - 21.5327i) q^{75} +(-3.25883 - 2.36768i) q^{76} +(-0.597180 + 1.83793i) q^{77} +(-1.61037 + 4.95620i) q^{78} +(-14.0304 - 10.1937i) q^{79} +(0.842630 - 2.59335i) q^{80} +(-3.38620 - 10.4216i) q^{81} +(-0.338867 + 0.246201i) q^{82} +(-4.61720 - 14.2103i) q^{83} +(7.66565 + 5.56942i) q^{84} +(-16.5735 - 12.0413i) q^{85} +(7.30817 - 5.30969i) q^{86} +10.8559 q^{87} -4.99763 q^{88} +(-9.02117 + 6.55426i) q^{89} +(-5.68427 + 17.4944i) q^{90} +(-0.384955 - 1.18477i) q^{91} +18.9474 q^{92} +(11.7158 + 4.35815i) q^{93} +6.90063 q^{94} +(1.42699 + 4.39184i) q^{95} +(3.33946 - 10.2778i) q^{96} +(3.06580 - 2.22743i) q^{97} +12.6461 q^{98} +3.16527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.717286	−	2.20758i	−0.507198	−	1.56099i	−0.797044	−	0.603921i	$-0.793604\pi$
$2$	−0.717286	−	2.20758i	−0.507198	−	1.56099i	0.289847	−	0.957073i	$-0.406396\pi$
$3$	0.693769	−	2.13520i	0.400548	−	1.23276i	−0.524008	−	0.851713i	$-0.675564\pi$
$3$	0.693769	−	2.13520i	0.400548	−	1.23276i	0.924556	−	0.381046i	$-0.124436\pi$
$4$	−2.74087	+	1.99136i	−1.37044	+	0.995680i
$5$	3.88389			1.73693			0.868465	−	0.495751i	$-0.165107\pi$
$5$	3.88389			1.73693			0.868465	+	0.495751i	$0.165107\pi$
$6$	−5.21126			−2.12749
$7$	1.00783	−	0.732228i	0.380922	−	0.276756i	−0.380803	−	0.924656i	$-0.624352\pi$
$7$	1.00783	−	0.732228i	0.380922	−	0.276756i	0.761726	+	0.647900i	$0.224352\pi$
$8$	2.60631	+	1.89360i	0.921471	+	0.669488i
$9$	−1.65072	−	1.19932i	−0.550239	−	0.399772i
$10$	−2.78586	−	8.57400i	−0.880967	−	2.71134i
$11$	−1.25503	+	0.911830i	−0.378405	+	0.274927i	−0.760687	−	0.649118i	$-0.775138\pi$
$11$	−1.25503	+	0.911830i	−0.378405	+	0.274927i	0.382283	+	0.924045i	$0.375138\pi$
$12$	2.35042	+	7.23385i	0.678508	+	2.08823i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	−2.33935	−	1.69964i	−0.625218	−	0.454247i
$15$	2.69452	−	8.29289i	0.695723	−	2.14122i
$16$	0.216955	−	0.667719i	0.0542387	−	0.166930i
$17$	−4.26724	−	3.10033i	−1.03496	−	0.751940i	−0.0656619	−	0.997842i	$-0.520916\pi$
$17$	−4.26724	−	3.10033i	−1.03496	−	0.751940i	−0.969295	+	0.245902i	$0.920916\pi$
$18$	−1.46355	+	4.50434i	−0.344962	+	1.06168i
$19$	0.367413	+	1.13078i	0.0842904	+	0.259419i	0.984315	−	0.176420i	$-0.0564517\pi$
$19$	0.367413	+	1.13078i	0.0842904	+	0.259419i	−0.900025	+	0.435839i	$0.856452\pi$
$20$	−10.6453	+	7.73423i	−2.38035	+	1.72943i
$21$	−0.864257	−	2.65991i	−0.188596	−	0.580440i
$22$	2.91315	+	2.11653i	0.621085	+	0.451245i
$23$	−4.52457	−	3.28729i	−0.943438	−	0.685448i	0.00580789	−	0.999983i	$-0.498151\pi$
$23$	−4.52457	−	3.28729i	−0.943438	−	0.685448i	−0.949246	+	0.314535i	$0.898151\pi$
$24$	5.85139	−	4.25128i	1.19441	−	0.867790i
$25$	10.0846			2.01692
$26$	−2.32119			−0.455222
$27$	1.74293	−	1.26631i	0.335427	−	0.243702i
$28$	−1.30419	+	4.01389i	−0.246469	+	0.758554i
$29$	1.49422	+	4.59875i	0.277470	+	0.853966i	0.988555	+	0.150860i	$0.0482042\pi$
$29$	1.49422	+	4.59875i	0.277470	+	0.853966i	−0.711085	+	0.703106i	$0.751796\pi$
$30$	−20.2400			−3.69529
$31$	−0.233614	+	5.56286i	−0.0419583	+	0.999119i
$31$	−0.233614	+	5.56286i	−0.0419583	+	0.999119i
$32$	4.81350			0.850915
$33$	1.07624	+	3.31233i	0.187350	+	0.576603i
$34$	−3.78339	+	11.6441i	−0.648846	+	1.99694i
$35$	3.91429	−	2.84390i	0.661636	−	0.480706i
$36$	6.91268			1.15211
$37$	0.987489			0.162342			0.0811711	−	0.996700i	$-0.474134\pi$
$37$	0.987489			0.162342			0.0811711	+	0.996700i	$0.474134\pi$
$38$	2.23275	−	1.62219i	0.362200	−	0.263154i
$39$	−1.81631	−	1.31963i	−0.290842	−	0.211309i
$40$	10.1226	+	7.35453i	1.60053	+	1.16285i
$41$	−0.0557628	−	0.171620i	−0.00870868	−	0.0268026i	0.946608	−	0.322388i	$-0.104485\pi$
$41$	−0.0557628	−	0.171620i	−0.00870868	−	0.0268026i	−0.955316	+	0.295585i	$0.904485\pi$
$42$	−5.25204	+	3.81583i	−0.810407	+	0.588795i
$43$	1.20261	+	3.70124i	0.183396	+	0.564434i	0.999917	−	0.0128813i	$-0.00410037\pi$
$43$	1.20261	+	3.70124i	0.183396	+	0.564434i	−0.816521	+	0.577315i	$0.804100\pi$
$44$	1.62408	−	4.99841i	0.244840	−	0.753539i
$45$	−6.41121	−	4.65802i	−0.955727	−	0.694376i
$46$	−4.01155	+	12.3463i	−0.591470	+	1.82036i
$47$	−0.918674	+	2.82739i	−0.134002	+	0.412417i	−0.995433	−	0.0954576i	$-0.969569\pi$
$47$	−0.918674	+	2.82739i	−0.134002	+	0.412417i	0.861431	+	0.507874i	$0.169569\pi$
$48$	−1.27520	−	0.926485i	−0.184059	−	0.133727i
$49$	−1.68356	+	5.18148i	−0.240509	+	0.740211i
$50$	−7.23356	−	22.2626i	−1.02298	−	3.14841i
$51$	−9.58030	+	6.96049i	−1.34151	+	0.974664i
$52$	1.04692	+	3.22209i	0.145182	+	0.446823i
$53$	11.2323	+	8.16073i	1.54287	+	1.12096i	0.948502	+	0.316771i	$0.102599\pi$
$53$	11.2323	+	8.16073i	1.54287	+	1.12096i	0.594371	+	0.804191i	$0.297401\pi$
$54$	−4.04567	−	2.93935i	−0.550546	−	0.399995i
$55$	−4.87439	+	3.54145i	−0.657262	+	0.477529i
$56$	4.01326			0.536294
$57$	2.66935			0.353564
$58$	9.08031	−	6.59723i	1.19230	−	0.866259i
$59$	2.17283	−	6.68727i	0.282878	−	0.870609i	−0.704149	−	0.710052i	$-0.748671\pi$
$59$	2.17283	−	6.68727i	0.282878	−	0.870609i	0.987027	−	0.160556i	$-0.0513288\pi$
$60$	9.12879	+	28.0955i	1.17852	+	3.62712i
$61$	3.58792			0.459386			0.229693	−	0.973263i	$-0.426228\pi$
$61$	3.58792			0.459386			0.229693	+	0.973263i	$0.426228\pi$
$62$	12.4480	−	3.47444i	1.58090	−	0.441254i
$63$	−2.54181			−0.320238
$64$	−3.88657	−	11.9616i	−0.485821	−	1.49520i
$65$	1.20019	−	3.69380i	0.148865	−	0.458160i
$66$	6.54026	−	4.75178i	0.805050	−	0.584903i
$67$	10.5541			1.28939			0.644695	−	0.764440i	$-0.276984\pi$
$67$	10.5541			1.28939			0.644695	+	0.764440i	$0.276984\pi$
$68$	17.8698			2.16703
$69$	−10.1580	+	7.38024i	−1.22288	+	0.888477i
$70$	−9.08579	−	6.60121i	−1.08596	−	0.788996i
$71$	−3.54159	−	2.57311i	−0.420309	−	0.305372i	0.357453	−	0.933931i	$-0.383645\pi$
$71$	−3.54159	−	2.57311i	−0.420309	−	0.305372i	−0.777762	+	0.628559i	$0.783645\pi$
$72$	−2.03127	−	6.25159i	−0.239387	−	0.736757i
$73$	−8.11109	+	5.89305i	−0.949332	+	0.689730i	−0.950649	−	0.310269i	$-0.899581\pi$
$73$	−8.11109	+	5.89305i	−0.949332	+	0.689730i	0.00131695	+	0.999999i	$0.499581\pi$
$74$	−0.708312	−	2.17996i	−0.0823396	−	0.253415i
$75$	6.99640	−	21.5327i	0.807875	−	2.48638i
$76$	−3.25883	−	2.36768i	−0.373813	−	0.271591i
$77$	−0.597180	+	1.83793i	−0.0680550	+	0.209452i
$78$	−1.61037	+	4.95620i	−0.182338	+	0.561179i
$79$	−14.0304	−	10.1937i	−1.57854	−	1.14688i	−0.918344	−	0.395783i	$-0.870473\pi$
$79$	−14.0304	−	10.1937i	−1.57854	−	1.14688i	−0.660196	−	0.751093i	$-0.729527\pi$
$80$	0.842630	−	2.59335i	0.0942089	−	0.289945i
$81$	−3.38620	−	10.4216i	−0.376244	−	1.15796i
$82$	−0.338867	+	0.246201i	−0.0374216	+	0.0271884i
$83$	−4.61720	−	14.2103i	−0.506804	−	1.55978i	−0.797717	−	0.603032i	$-0.793959\pi$
$83$	−4.61720	−	14.2103i	−0.506804	−	1.55978i	0.290913	−	0.956749i	$-0.406041\pi$
$84$	7.66565	+	5.56942i	0.836391	+	0.607674i
$85$	−16.5735	−	12.0413i	−1.79765	−	1.30607i
$86$	7.30817	−	5.30969i	0.788060	−	0.572559i
$87$	10.8559			1.16387
$88$	−4.99763			−0.532749
$89$	−9.02117	+	6.55426i	−0.956242	+	0.694750i	−0.952275	−	0.305242i	$-0.901263\pi$
$89$	−9.02117	+	6.55426i	−0.956242	+	0.694750i	−0.00396707	+	0.999992i	$0.501263\pi$
$90$	−5.68427	+	17.4944i	−0.599175	+	1.84407i
$91$	−0.384955	−	1.18477i	−0.0403543	−	0.124198i
$92$	18.9474			1.97541
$93$	11.7158	+	4.35815i	1.21487	+	0.451919i
$94$	6.90063			0.711746
$95$	1.42699	+	4.39184i	0.146407	+	0.450593i
$96$	3.33946	−	10.2778i	0.340832	−	1.04897i
$97$	3.06580	−	2.22743i	0.311284	−	0.226161i	−0.421163	−	0.906985i	$-0.638378\pi$
$97$	3.06580	−	2.22743i	0.311284	−	0.226161i	0.732447	+	0.680824i	$0.238378\pi$
$98$	12.6461			1.27745
$99$	3.16527			0.318121
$100$	−27.6407	+	20.0821i	−2.76407	+	2.00821i
$101$	16.2244	+	11.7877i	1.61438	+	1.17292i	0.846649	+	0.532153i	$0.178617\pi$
$101$	16.2244	+	11.7877i	1.61438	+	1.17292i	0.767736	+	0.640766i	$0.221383\pi$
$102$	22.2377	+	16.1566i	2.20186	+	1.59974i
$103$	1.19318	+	3.67224i	0.117568	+	0.361836i	0.992474	−	0.122456i	$-0.0390771\pi$
$103$	1.19318	+	3.67224i	0.117568	+	0.361836i	−0.874906	+	0.484293i	$0.839077\pi$
$104$	2.60631	−	1.89360i	0.255570	−	0.185683i
$105$	−3.35668	−	10.3308i	−0.327578	−	1.00818i
$106$	9.95870	−	30.6497i	0.967274	−	2.97696i
$107$	−1.45644	−	1.05816i	−0.140799	−	0.102296i	0.515156	−	0.857096i	$-0.327734\pi$
$107$	−1.45644	−	1.05816i	−0.140799	−	0.102296i	−0.655955	+	0.754800i	$0.727734\pi$
$108$	−2.25547	+	6.94161i	−0.217032	+	0.667957i
$109$	−1.69894	+	5.22879i	−0.162729	+	0.500827i	−0.998862	−	0.0476993i	$-0.984811\pi$
$109$	−1.69894	+	5.22879i	−0.162729	+	0.500827i	0.836133	+	0.548527i	$0.184811\pi$
$110$	11.3144	+	8.22036i	1.07878	+	0.783781i
$111$	0.685089	−	2.10849i	0.0650258	−	0.200129i
$112$	−0.270270	−	0.831805i	−0.0255381	−	0.0785982i
$113$	9.03005	−	6.56072i	0.849476	−	0.617180i	−0.0755255	−	0.997144i	$-0.524063\pi$
$113$	9.03005	−	6.56072i	0.849476	−	0.617180i	0.925002	+	0.379963i	$0.124063\pi$
$114$	−1.91469	−	5.89279i	−0.179327	−	0.551911i
$115$	−17.5729	−	12.7675i	−1.63869	−	1.19057i
$116$	−13.2532	−	9.62904i	−1.23053	−	0.894034i
$117$	−1.65072	+	1.19932i	−0.152609	+	0.110877i
$118$	−16.3212			−1.50249
$119$	−6.57078			−0.602342
$120$	22.7262	−	16.5115i	2.07461	−	1.50729i
$121$	−2.65553	+	8.17288i	−0.241412	+	0.742989i
$122$	−2.57356	−	7.92061i	−0.232999	−	0.717098i
$123$	−0.405130			−0.0365293
$124$	−10.4374	−	15.7123i	−0.937302	−	1.41101i
$125$	19.7481			1.76633
$126$	1.82320	+	5.61125i	0.162424	+	0.499890i
$127$	−3.49425	+	10.7542i	−0.310065	+	0.954281i	0.667674	+	0.744454i	$0.267290\pi$
$127$	−3.49425	+	10.7542i	−0.310065	+	0.954281i	−0.977739	+	0.209827i	$0.932710\pi$
$128$	−15.8300	+	11.5012i	−1.39919	+	1.01657i
$129$	8.73722			0.769270
$130$	−9.01524			−0.790689
$131$	5.54726	−	4.03032i	0.484666	−	0.352131i	−0.318463	−	0.947935i	$-0.603167\pi$
$131$	5.54726	−	4.03032i	0.484666	−	0.352131i	0.803129	+	0.595805i	$0.203167\pi$
$132$	−9.54588	−	6.93549i	−0.830862	−	0.603657i
$133$	1.19828	+	0.870601i	0.103904	+	0.0754907i
$134$	−7.57032	−	23.2990i	−0.653976	−	2.01273i
$135$	6.76936	−	4.91823i	0.582614	−	0.423294i
$136$	−5.25098	−	16.1609i	−0.450268	−	1.38578i
$137$	2.96374	−	9.12144i	0.253209	−	0.779297i	−0.740968	−	0.671540i	$-0.765633\pi$
$137$	2.96374	−	9.12144i	0.253209	−	0.779297i	0.994177	−	0.107757i	$-0.0343669\pi$
$138$	23.5787	+	17.1309i	2.00715	+	1.45828i
$139$	−0.162813	+	0.501088i	−0.0138096	+	0.0425017i	−0.957724	−	0.287689i	$-0.907113\pi$
$139$	−0.162813	+	0.501088i	−0.0138096	+	0.0425017i	0.943914	+	0.330191i	$0.107113\pi$
$140$	−5.06534	+	15.5895i	−0.428099	+	1.31755i
$141$	5.39969	+	3.92311i	0.454736	+	0.330385i
$142$	−3.14002	+	9.66399i	−0.263505	+	0.810984i
$143$	0.479377	+	1.47537i	0.0400875	+	0.123377i
$144$	−1.15894	+	0.842018i	−0.0965782	+	0.0701681i
$145$	5.80340	+	17.8610i	0.481946	+	1.48328i
$146$	18.8274	+	13.6789i	1.55816	+	1.13207i
$147$	9.89549	+	7.18950i	0.816167	+	0.592980i
$148$	−2.70658	+	1.96645i	−0.222479	+	0.161641i
$149$	−10.2986			−0.843694			−0.421847	−	0.906667i	$-0.638618\pi$
$149$	−10.2986			−0.843694			−0.421847	+	0.906667i	$0.638618\pi$
$150$	−52.5536			−4.29098
$151$	4.29454	−	3.12016i	0.349485	−	0.253915i	−0.399168	−	0.916878i	$-0.630701\pi$
$151$	4.29454	−	3.12016i	0.349485	−	0.253915i	0.748653	+	0.662962i	$0.230701\pi$
$152$	−1.18365	+	3.64291i	−0.0960068	+	0.295479i
$153$	3.32573	+	10.2355i	0.268869	+	0.827494i
$154$	4.48573			0.361470
$155$	−0.907331	+	21.6056i	−0.0728786	+	1.73540i
$156$	7.60613			0.608977
$157$	4.37374	+	13.4610i	0.349062	+	1.07430i	0.959373	+	0.282141i	$0.0910447\pi$
$157$	4.37374	+	13.4610i	0.349062	+	1.07430i	−0.610310	+	0.792162i	$0.708955\pi$
$158$	−12.4395	+	38.2849i	−0.989635	+	3.04578i
$159$	25.2174	−	18.3215i	1.99987	−	1.45299i
$160$	18.6951			1.47798
$161$	−6.96703			−0.549079
$162$	−20.5777	+	14.9506i	−1.61674	+	1.17463i
$163$	−9.41250	−	6.83858i	−0.737244	−	0.535639i	0.154603	−	0.987977i	$-0.450590\pi$
$163$	−9.41250	−	6.83858i	−0.737244	−	0.535639i	−0.891847	+	0.452338i	$0.850590\pi$
$164$	0.494596	+	0.359345i	0.0386215	+	0.0280601i
$165$	4.18001	+	12.8647i	0.325413	+	1.00152i
$166$	−28.0585	+	20.3857i	−2.17776	+	1.58223i
$167$	−4.67412	−	14.3855i	−0.361694	−	1.11318i	−0.952025	−	0.306020i	$-0.901003\pi$
$167$	−4.67412	−	14.3855i	−0.361694	−	1.11318i	0.590331	−	0.807161i	$-0.298997\pi$
$168$	2.78427	−	8.56911i	0.214811	−	0.661121i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−14.6943	+	45.2244i	−1.12700	+	3.46855i
$171$	0.749670	−	2.30725i	0.0573287	−	0.176440i
$172$	−10.6667	−	7.74980i	−0.813327	−	0.590917i
$173$	−2.42211	+	7.45450i	−0.184150	+	0.566755i	−0.999933	−	0.0116033i	$-0.996306\pi$
$173$	−2.42211	+	7.45450i	−0.184150	+	0.566755i	0.815783	+	0.578358i	$0.196306\pi$
$174$	−7.78678	−	23.9652i	−0.590314	−	1.81680i
$175$	10.1635	−	7.38425i	0.768292	−	0.558197i
$176$	0.336562	+	1.03583i	0.0253693	+	0.0780786i
$177$	−12.7712	−	9.27884i	−0.959945	−	0.697441i
$178$	20.9398	+	15.2137i	1.56950	+	1.14031i
$179$	−7.34127	+	5.33375i	−0.548713	+	0.398663i	−0.827311	−	0.561745i	$-0.810130\pi$
$179$	−7.34127	+	5.33375i	−0.548713	+	0.398663i	0.278598	+	0.960408i	$0.410130\pi$
$180$	26.8481			2.00114
$181$	24.4100			1.81438			0.907191	−	0.420719i	$-0.138222\pi$
$181$	24.4100			1.81438			0.907191	+	0.420719i	$0.138222\pi$
$182$	−2.33935	+	1.69964i	−0.173404	+	0.125986i
$183$	2.48919	−	7.66093i	0.184006	−	0.566312i
$184$	−5.56764	−	17.1354i	−0.410452	−	1.26324i
$185$	3.83530			0.281977
$186$	1.21742	−	28.9895i	0.0892657	−	2.12561i
$187$	8.18246			0.598361
$188$	−3.11238	−	9.57891i	−0.226993	−	0.698614i
$189$	0.829341	−	2.55245i	0.0603257	−	0.185663i
$190$	8.67176	−	6.30040i	0.629116	−	0.457079i
$191$	9.10163			0.658571			0.329285	−	0.944230i	$-0.393192\pi$
$191$	9.10163			0.658571			0.329285	+	0.944230i	$0.393192\pi$
$192$	−28.2368			−2.03782
$193$	−20.0958	+	14.6005i	−1.44653	+	1.05096i	−0.459902	+	0.887970i	$0.652116\pi$
$193$	−20.0958	+	14.6005i	−1.44653	+	1.05096i	−0.986627	+	0.162995i	$0.947884\pi$
$194$	−7.11628	−	5.17028i	−0.510919	−	0.371205i
$195$	−7.05436	−	5.12529i	−0.505173	−	0.367030i
$196$	−5.70375	−	17.5543i	−0.407411	−	1.25388i
$197$	6.19912	−	4.50393i	0.441669	−	0.320891i	−0.344629	−	0.938739i	$-0.611995\pi$
$197$	6.19912	−	4.50393i	0.441669	−	0.320891i	0.786298	+	0.617848i	$0.211995\pi$
$198$	−2.27040	−	6.98757i	−0.161350	−	0.496585i
$199$	−7.21947	+	22.2193i	−0.511775	+	1.57508i	0.277299	+	0.960784i	$0.410561\pi$
$199$	−7.21947	+	22.2193i	−0.511775	+	1.57508i	−0.789074	+	0.614298i	$0.789439\pi$
$200$	26.2837	+	19.0962i	1.85854	+	1.35031i
$201$	7.32212	−	22.5352i	0.516462	−	1.58951i
$202$	14.3847	−	44.2717i	1.01211	−	3.11495i
$203$	4.87325	+	3.54062i	0.342035	+	0.248503i
$204$	12.3975	−	38.1556i	0.868000	−	2.67143i
$205$	−0.216577	−	0.666554i	−0.0151264	−	0.0465542i
$206$	7.25090	−	5.26809i	0.505194	−	0.367045i
$207$	3.52628	+	10.8528i	0.245094	+	0.754321i
$208$	−0.567996	−	0.412673i	−0.0393834	−	0.0286137i
$209$	−1.49219	−	1.08414i	−0.103217	−	0.0749917i
$210$	−20.3984	+	14.8203i	−1.40762	+	1.02270i
$211$	−15.2545			−1.05017			−0.525083	−	0.851051i	$-0.675966\pi$
$211$	−15.2545			−1.05017			−0.525083	+	0.851051i	$0.675966\pi$
$212$	−47.0372			−3.23053
$213$	−7.95116	+	5.77685i	−0.544804	+	0.395823i
$214$	−1.29130	+	3.97420i	−0.0882712	+	0.271671i
$215$	4.67079	+	14.3752i	0.318545	+	0.980382i
$216$	6.94052			0.472242
$217$	3.83784	+	5.77746i	0.260530	+	0.392199i
$218$	12.7616			0.864324
$219$	6.95563	+	21.4072i	0.470018	+	1.44657i
$220$	6.30777	−	19.4133i	0.425270	−	1.30884i
$221$	−4.26724	+	3.10033i	−0.287045	+	0.208551i
$222$	−5.14606			−0.345381
$223$	−22.8438			−1.52973			−0.764866	−	0.644189i	$-0.777195\pi$
$223$	−22.8438			−1.52973			−0.764866	+	0.644189i	$0.777195\pi$
$224$	4.85117	−	3.52458i	0.324133	−	0.235496i
$225$	−16.6469	−	12.0947i	−1.10979	−	0.806311i
$226$	−20.9604	−	15.2286i	−1.39427	−	1.01299i
$227$	−6.90128	−	21.2399i	−0.458054	−	1.40974i	−0.867512	−	0.497416i	$-0.834282\pi$
$227$	−6.90128	−	21.2399i	−0.458054	−	1.40974i	0.409458	−	0.912329i	$-0.365718\pi$
$228$	−7.31634	+	5.31563i	−0.484536	+	0.352036i
$229$	−6.51520	−	20.0517i	−0.430536	−	1.32505i	−0.897592	−	0.440827i	$-0.854685\pi$
$229$	−6.51520	−	20.0517i	−0.430536	−	1.32505i	0.467056	−	0.884228i	$-0.345315\pi$
$230$	−15.5804	+	47.9516i	−1.02734	+	3.16183i
$231$	3.51005	+	2.55020i	0.230944	+	0.167791i
$232$	−4.81376	+	14.8152i	−0.316039	+	0.972668i
$233$	6.40262	−	19.7053i	0.419450	−	1.29093i	−0.488760	−	0.872418i	$-0.662551\pi$
$233$	6.40262	−	19.7053i	0.419450	−	1.29093i	0.908210	−	0.418516i	$-0.137449\pi$
$234$	3.83162	+	2.78384i	0.250481	+	0.181985i
$235$	−3.56803	+	10.9813i	−0.232753	+	0.716339i
$236$	7.36132	+	22.6558i	0.479181	+	1.47477i
$237$	−31.4994	+	22.8856i	−2.04610	+	1.48658i
$238$	4.71313	+	14.5055i	0.305507	+	0.940253i
$239$	−0.296222	−	0.215218i	−0.0191610	−	0.0139213i	0.578164	−	0.815921i	$-0.303770\pi$
$239$	−0.296222	−	0.215218i	−0.0191610	−	0.0139213i	−0.597325	+	0.802000i	$0.703770\pi$
$240$	−4.95273	−	3.59837i	−0.319697	−	0.232274i
$241$	17.8986	−	13.0041i	1.15295	−	0.837668i	0.164080	−	0.986447i	$-0.447534\pi$
$241$	17.8986	−	13.0041i	1.15295	−	0.837668i	0.988870	+	0.148779i	$0.0475343\pi$
$242$	19.9471			1.28225
$243$	−18.1384			−1.16358
$244$	−9.83402	+	7.14483i	−0.629559	+	0.457401i
$245$	−6.53878	+	20.1243i	−0.417748	+	1.28569i
$246$	0.290594	+	0.894356i	0.0185276	+	0.0570221i
$247$	1.18897			0.0756526
$248$	−11.1427	+	14.0562i	−0.707562	+	0.892569i
$249$	−33.5451			−2.12583
$250$	−14.1651	−	43.5956i	−0.895877	−	2.75723i
$251$	−0.692247	+	2.13052i	−0.0436942	+	0.134477i	−0.970524	−	0.241005i	$-0.922523\pi$
$251$	−0.692247	+	2.13052i	−0.0436942	+	0.134477i	0.926830	+	0.375482i	$0.122523\pi$
$252$	6.96678	−	5.06166i	0.438866	−	0.318855i
$253$	8.67590			0.545449
$254$	26.2471			1.64689
$255$	−37.2089	+	27.0338i	−2.33011	+	1.69292i
$256$	16.3941	+	11.9110i	1.02463	+	0.744439i
$257$	−7.22790	−	5.25138i	−0.450864	−	0.327572i	0.339073	−	0.940760i	$-0.389887\pi$
$257$	−7.22790	−	5.25138i	−0.450864	−	0.327572i	−0.789937	+	0.613188i	$0.789887\pi$
$258$	−6.26709	−	19.2881i	−0.390172	−	1.20083i
$259$	0.995217	−	0.723067i	0.0618398	−	0.0449292i
$260$	4.06612	+	12.5142i	0.252170	+	0.776100i
$261$	3.04881	−	9.38328i	0.188717	−	0.580811i
$262$	−12.8762	−	9.35512i	−0.795495	−	0.577961i
$263$	−2.38837	+	7.35066i	−0.147273	+	0.453261i	−0.997296	−	0.0734847i	$-0.976588\pi$
$263$	−2.38837	+	7.35066i	−0.147273	+	0.453261i	0.850023	+	0.526746i	$0.176588\pi$
$264$	−3.46720	+	10.6709i	−0.213391	+	0.656751i
$265$	43.6250	+	31.6954i	2.67986	+	1.94703i
$266$	1.06241	−	3.26977i	0.0651406	−	0.200482i
$267$	7.73606	+	23.8092i	0.473439	+	1.45710i
$268$	−28.9275	+	21.0170i	−1.76703	+	1.28382i
$269$	1.69059	+	5.20309i	0.103077	+	0.317238i	0.989274	−	0.146070i	$-0.0466625\pi$
$269$	1.69059	+	5.20309i	0.103077	+	0.317238i	−0.886197	+	0.463308i	$0.846662\pi$
$270$	−15.7129	−	11.4161i	−0.956259	−	0.694763i
$271$	0.487400	+	0.354117i	0.0296074	+	0.0215111i	0.602491	−	0.798126i	$-0.294175\pi$
$271$	0.487400	+	0.354117i	0.0296074	+	0.0215111i	−0.572883	+	0.819637i	$0.694175\pi$
$272$	−2.99595	+	2.17668i	−0.181656	+	0.131981i
$273$	−2.79679			−0.169270
$274$	−22.2621			−1.34491
$275$	−12.6565	+	9.19546i	−0.763213	+	0.554507i
$276$	13.1451	−	40.4566i	0.791245	−	2.43520i
$277$	−5.96129	−	18.3470i	−0.358179	−	1.10236i	−0.954143	−	0.299351i	$-0.903230\pi$
$277$	−5.96129	−	18.3470i	−0.358179	−	1.10236i	0.595964	−	0.803011i	$-0.296770\pi$
$278$	1.22297			0.0733492
$279$	7.05726	−	8.90254i	0.422507	−	0.532981i
$280$	15.5871			0.931505
$281$	−0.836384	−	2.57412i	−0.0498945	−	0.153559i	0.923005	−	0.384788i	$-0.125725\pi$
$281$	−0.836384	−	2.57412i	−0.0498945	−	0.153559i	−0.972899	+	0.231229i	$0.925725\pi$
$282$	4.78744	−	14.7342i	0.285088	−	0.877411i
$283$	16.8187	−	12.2195i	0.999767	−	0.726374i	0.0377292	−	0.999288i	$-0.487988\pi$
$283$	16.8187	−	12.2195i	0.999767	−	0.726374i	0.962038	+	0.272914i	$0.0879876\pi$
$284$	14.8310			0.880059
$285$	10.3675			0.614115
$286$	2.91315	−	2.11653i	0.172258	−	0.125153i
$287$	−0.181864	−	0.132132i	−0.0107351	−	0.00779952i
$288$	−7.94573	−	5.77291i	−0.468207	−	0.340172i
$289$	3.34398	+	10.2917i	0.196704	+	0.605394i
$290$	35.2670	−	25.6229i	2.07095	−	1.50463i
$291$	−2.62906	−	8.09141i	−0.154118	−	0.474327i
$292$	10.4963	−	32.3042i	0.614248	−	1.89046i
$293$	−2.66717	−	1.93781i	−0.155818	−	0.113208i	0.507145	−	0.861861i	$-0.330701\pi$
$293$	−2.66717	−	1.93781i	−0.155818	−	0.113208i	−0.662962	+	0.748653i	$0.730701\pi$
$294$	8.77348	−	27.0020i	0.511680	−	1.57479i
$295$	8.43902	−	25.9726i	0.491339	−	1.51219i
$296$	2.57371	+	1.86991i	0.149594	+	0.108686i
$297$	−1.03276	+	3.17851i	−0.0599269	+	0.184436i
$298$	7.38704	+	22.7350i	0.427920	+	1.31700i
$299$	−4.52457	+	3.28729i	−0.261663	+	0.190109i
$300$	23.7031	+	72.9507i	1.36850	+	4.21181i
$301$	3.92217	+	2.84962i	0.226070	+	0.164250i
$302$	−9.96842	−	7.24248i	−0.573618	−	0.416758i
$303$	36.4250	−	26.4643i	2.09256	−	1.52034i
$304$	0.834757			0.0478766
$305$	13.9351			0.797921
$306$	20.2103	−	14.6836i	1.15534	−	0.839406i
$307$	−9.48164	+	29.1815i	−0.541146	+	1.66547i	0.188837	+	0.982009i	$0.439528\pi$
$307$	−9.48164	+	29.1815i	−0.541146	+	1.66547i	−0.729982	+	0.683466i	$0.760472\pi$
$308$	−2.02319	−	6.22673i	−0.115282	−	0.354801i
$309$	8.66876			0.493149
$310$	48.3468	−	13.4944i	2.74591	−	0.766428i
$311$	5.61147			0.318197			0.159099	−	0.987263i	$-0.449141\pi$
$311$	5.61147			0.318197			0.159099	+	0.987263i	$0.449141\pi$
$312$	−2.23503	−	6.87872i	−0.126534	−	0.389431i
$313$	3.91515	−	12.0496i	0.221298	−	0.681084i	−0.777349	−	0.629070i	$-0.783436\pi$
$313$	3.91515	−	12.0496i	0.221298	−	0.681084i	0.998646	−	0.0520140i	$-0.0165640\pi$
$314$	26.5790	−	19.3108i	1.49994	−	1.08977i
$315$	−9.87212			−0.556231
$316$	58.7547			3.30521
$317$	−9.60588	+	6.97908i	−0.539520	+	0.391984i	−0.823907	−	0.566725i	$-0.808210\pi$
$317$	−9.60588	+	6.97908i	−0.539520	+	0.391984i	0.284387	+	0.958710i	$0.408210\pi$
$318$	−58.5343	−	42.5277i	−3.28244	−	2.38483i
$319$	−6.06856	−	4.40907i	−0.339774	−	0.246860i
$320$	−15.0950	−	46.4577i	−0.843836	−	2.59706i
$321$	−3.26982	+	2.37566i	−0.182504	+	0.132597i
$322$	4.99735	+	15.3803i	0.278491	+	0.857108i
$323$	1.93796	−	5.96442i	0.107831	−	0.331869i
$324$	30.0344	+	21.8213i	1.66858	+	1.21229i
$325$	3.11632	−	9.59105i	0.172862	−	0.532016i
$326$	−8.34525	+	25.6840i	−0.462201	+	1.42251i
$327$	9.98585	+	7.25515i	0.552219	+	0.401211i
$328$	0.179644	−	0.552888i	0.00991919	−	0.0305281i
$329$	1.14443	+	3.52219i	0.0630945	+	0.194185i
$330$	25.4017	−	18.4554i	1.39832	−	1.01594i
$331$	6.26706	+	19.2880i	0.344469	+	1.06017i	0.961868	+	0.273515i	$0.0881863\pi$
$331$	6.26706	+	19.2880i	0.344469	+	1.06017i	−0.617399	+	0.786650i	$0.711814\pi$
$332$	40.9529	+	29.7540i	2.24758	+	1.63297i
$333$	−1.63007	−	1.18431i	−0.0893270	−	0.0648999i
$334$	−28.4044	+	20.6370i	−1.55422	+	1.12921i
$335$	40.9911			2.23958
$336$	−1.96358			−0.107122
$337$	−23.9184	+	17.3777i	−1.30292	+	0.946625i	−0.999980	−	0.00638593i	$-0.997967\pi$
$337$	−23.9184	+	17.3777i	−1.30292	+	0.946625i	−0.302937	+	0.953010i	$0.597967\pi$
$338$	−0.717286	+	2.20758i	−0.0390152	+	0.120076i
$339$	−7.74368	−	23.8326i	−0.420579	−	1.29441i
$340$	69.4044			3.76398
$341$	−4.77919	−	7.19455i	−0.258808	−	0.389607i
$342$	−5.63116			−0.304498
$343$	4.79197	+	14.7482i	0.258742	+	0.796327i
$344$	−3.87429	+	11.9238i	−0.208888	+	0.642891i
$345$	−39.4527	+	28.6641i	−2.12406	+	1.54322i
$346$	18.1937			0.978102
$347$	−5.91506			−0.317537			−0.158768	−	0.987316i	$-0.550752\pi$
$347$	−5.91506			−0.317537			−0.158768	+	0.987316i	$0.550752\pi$
$348$	−29.7546	+	21.6180i	−1.59501	+	1.15885i
$349$	14.7537	+	10.7192i	0.789750	+	0.573787i	0.907889	−	0.419210i	$-0.137693\pi$
$349$	14.7537	+	10.7192i	0.789750	+	0.573787i	−0.118139	+	0.992997i	$0.537693\pi$
$350$	−23.5915	−	17.1402i	−1.26102	−	0.916183i
$351$	−0.665741	−	2.04894i	−0.0355346	−	0.109364i
$352$	−6.04107	+	4.38909i	−0.321990	+	0.233939i
$353$	5.09422	+	15.6784i	0.271138	+	0.834476i	0.990216	+	0.139547i	$0.0445645\pi$
$353$	5.09422	+	15.6784i	0.271138	+	0.834476i	−0.719078	+	0.694930i	$0.755436\pi$
$354$	−11.3232	+	34.8491i	−0.601819	+	1.85221i
$355$	−13.7551	−	9.99370i	−0.730047	−	0.530410i
$356$	11.6740	−	35.9288i	0.618719	−	1.90422i
$357$	−4.55860	+	14.0299i	−0.241267	+	0.742543i
$358$	17.0405	+	12.3806i	0.900616	+	0.654336i
$359$	8.59887	−	26.4646i	0.453831	−	1.39675i	−0.418671	−	0.908138i	$-0.637504\pi$
$359$	8.59887	−	26.4646i	0.453831	−	1.39675i	0.872502	−	0.488611i	$-0.162496\pi$
$360$	−7.88922	−	24.2805i	−0.415798	−	1.27970i
$361$	14.2276	−	10.3370i	0.748824	−	0.544052i
$362$	−17.5090	−	53.8870i	−0.920250	−	2.83224i
$363$	15.6084	+	11.3402i	0.819230	+	0.595205i
$364$	3.41442	+	2.48072i	0.178964	+	0.130025i
$365$	−31.5026	+	22.8880i	−1.64892	+	1.19801i
$366$	−18.6976			−0.977337
$367$	26.7543			1.39656			0.698280	−	0.715824i	$-0.253949\pi$
$367$	26.7543			1.39656			0.698280	+	0.715824i	$0.253949\pi$
$368$	−3.17661	+	2.30795i	−0.165592	+	0.120310i
$369$	−0.113778	+	0.350174i	−0.00592306	+	0.0182293i
$370$	−2.75101	−	8.46673i	−0.143018	−	0.440164i
$371$	17.2957			0.897948
$372$	−40.7900	+	11.3851i	−2.11486	+	0.590292i
$373$	−33.4961			−1.73436			−0.867181	−	0.497994i	$-0.834070\pi$
$373$	−33.4961			−1.73436			−0.867181	+	0.497994i	$0.834070\pi$
$374$	−5.86916	−	18.0634i	−0.303487	−	0.934038i
$375$	13.7006	−	42.1662i	0.707498	−	2.17746i
$376$	−7.74828	+	5.62946i	−0.399587	+	0.290317i
$377$	4.83541			0.249036
$378$	−6.22961			−0.320416
$379$	−29.6133	+	21.5153i	−1.52113	+	1.10517i	−0.560208	+	0.828352i	$0.689279\pi$
$379$	−29.6133	+	21.5153i	−1.52113	+	1.10517i	−0.960923	+	0.276814i	$0.910721\pi$
$380$	−12.6569	−	9.19580i	−0.649287	−	0.471735i
$381$	20.5382	+	14.9219i	1.05220	+	0.764470i
$382$	−6.52847	−	20.0926i	−0.334026	−	1.02802i
$383$	−7.60391	+	5.52456i	−0.388542	+	0.282292i	−0.764858	−	0.644199i	$-0.777191\pi$
$383$	−7.60391	+	5.52456i	−0.388542	+	0.282292i	0.376316	+	0.926491i	$0.377191\pi$
$384$	13.5750	+	41.7795i	0.692745	+	2.13205i
$385$	−2.31938	+	7.13833i	−0.118207	+	0.363803i
$386$	46.6461	+	33.8904i	2.37423	+	1.72498i
$387$	2.45380	−	7.55201i	0.124734	−	0.383890i
$388$	−3.96734	+	12.2102i	−0.201411	+	0.619879i
$389$	−15.7806	−	11.4653i	−0.800107	−	0.581312i	0.110839	−	0.993838i	$-0.464646\pi$
$389$	−15.7806	−	11.4653i	−0.800107	−	0.581312i	−0.910946	+	0.412527i	$0.864646\pi$
$390$	−6.25449	+	19.2493i	−0.316708	+	0.974728i
$391$	9.11572	+	28.0553i	0.461002	+	1.41882i
$392$	−14.1995	+	10.3166i	−0.717185	+	0.521065i
$393$	−4.75703	−	14.6406i	−0.239960	−	0.738522i
$394$	−14.3893	−	10.4544i	−0.724923	−	0.526688i
$395$	−54.4925	−	39.5911i	−2.74181	−	1.99204i
$396$	−8.67559	+	6.30318i	−0.435965	+	0.316747i
$397$	9.36246			0.469888			0.234944	−	0.972009i	$-0.424509\pi$
$397$	9.36246			0.469888			0.234944	+	0.972009i	$0.424509\pi$
$398$	54.2292			2.71826
$399$	2.69024	−	1.95457i	0.134680	−	0.0978510i
$400$	2.18791	−	6.73369i	0.109395	−	0.336685i
$401$	−0.135585	−	0.417287i	−0.00677079	−	0.0208383i	0.947614	−	0.319418i	$-0.103487\pi$
$401$	−0.135585	−	0.417287i	−0.00677079	−	0.0208383i	−0.954385	+	0.298579i	$0.903487\pi$
$402$	−55.0002			−2.74316
$403$	5.21840	+	1.94120i	0.259947	+	0.0966980i
$404$	−67.9424			−3.38026
$405$	−13.1516	−	40.4766i	−0.653510	−	2.01130i
$406$	4.32069	−	13.2977i	0.214432	−	0.659955i
$407$	−1.23932	+	0.900422i	−0.0614310	+	0.0446322i
$408$	−38.1496			−1.88869
$409$	15.6919			0.775915			0.387957	−	0.921677i	$-0.373181\pi$
$409$	15.6919			0.775915			0.387957	+	0.921677i	$0.373181\pi$
$410$	−1.31612	+	0.956220i	−0.0649987	+	0.0472243i
$411$	−17.4200	−	12.6563i	−0.859263	−	0.624291i
$412$	−10.5831	−	7.68908i	−0.521392	−	0.378814i
$413$	−2.70678	−	8.33061i	−0.133192	−	0.409923i
$414$	21.4290	−	15.5691i	1.05318	−	0.765179i
$415$	−17.9327	−	55.1912i	−0.880282	−	2.70923i
$416$	1.48745	−	4.57791i	0.0729284	−	0.224451i
$417$	0.956969	+	0.695278i	0.0468630	+	0.0340479i
$418$	−1.32300	+	4.07178i	−0.0647100	+	0.199157i
$419$	1.45398	−	4.47490i	0.0710317	−	0.218613i	−0.909238	−	0.416276i	$-0.863335\pi$
$419$	1.45398	−	4.47490i	0.0710317	−	0.218613i	0.980270	+	0.197663i	$0.0633351\pi$
$420$	29.7726	+	21.6310i	1.45275	+	1.05549i
$421$	2.21740	−	6.82446i	0.108070	−	0.332604i	−0.882369	−	0.470558i	$-0.844053\pi$
$421$	2.21740	−	6.82446i	0.108070	−	0.332604i	0.990439	+	0.137954i	$0.0440526\pi$
$422$	10.9419	+	33.6756i	0.532642	+	1.63930i
$423$	4.90740	−	3.56544i	0.238606	−	0.173358i
$424$	13.8217	+	42.5388i	0.671242	+	2.06587i
$425$	−43.0335	−	31.2656i	−2.08743	−	1.51661i
$426$	18.4561	+	13.4092i	0.894202	+	0.649675i
$427$	3.61600	−	2.62718i	0.174990	−	0.127138i
$428$	6.09908			0.294810
$429$	3.48279			0.168151
$430$	28.3841	−	20.6223i	1.36880	−	0.994495i
$431$	9.41486	−	28.9760i	0.453498	−	1.39572i	−0.419392	−	0.907805i	$-0.637757\pi$
$431$	9.41486	−	28.9760i	0.453498	−	1.39572i	0.872890	−	0.487918i	$-0.162243\pi$
$432$	−0.467404	−	1.43852i	−0.0224880	−	0.0692109i
$433$	−20.8162			−1.00036			−0.500182	−	0.865920i	$-0.666734\pi$
$433$	−20.8162			−1.00036			−0.500182	+	0.865920i	$0.666734\pi$
$434$	10.0014	−	12.6164i	0.480080	−	0.605608i
$435$	42.1631			2.02157
$436$	−5.75584	−	17.7146i	−0.275655	−	0.848377i
$437$	2.05482	−	6.32410i	0.0982955	−	0.302523i
$438$	42.2690	−	30.7102i	2.01969	−	1.46739i
$439$	−11.1604			−0.532659			−0.266329	−	0.963882i	$-0.585811\pi$
$439$	−11.1604			−0.532659			−0.266329	+	0.963882i	$0.585811\pi$
$440$	−19.4103			−0.925348
$441$	8.99332	−	6.53403i	0.428253	−	0.311144i
$442$	9.90505	+	7.19644i	0.471135	+	0.342300i
$443$	17.2498	+	12.5327i	0.819565	+	0.595448i	0.916588	−	0.399834i	$-0.130932\pi$
$443$	17.2498	+	12.5327i	0.819565	+	0.595448i	−0.0970232	+	0.995282i	$0.530932\pi$
$444$	2.32102	+	7.14335i	0.110151	+	0.339008i
$445$	−35.0373	+	25.4561i	−1.66093	+	1.20673i
$446$	16.3855	+	50.4294i	0.775876	+	2.38790i
$447$	−7.14485	+	21.9896i	−0.337940	+	1.04007i
$448$	−12.6756	−	9.20938i	−0.598867	−	0.435102i
$449$	−4.05994	+	12.4952i	−0.191601	+	0.589686i	0.808399	+	0.588635i	$0.200334\pi$
$449$	−4.05994	+	12.4952i	−0.191601	+	0.589686i	−0.999999	+	0.00105082i	$0.999666\pi$
$450$	−14.7593	+	45.4246i	−0.695762	+	2.14134i
$451$	0.226472	+	0.164542i	0.0106642	+	0.00774796i
$452$	−11.6855	+	35.9642i	−0.549638	+	1.69161i
$453$	−3.68276	−	11.3344i	−0.173031	−	0.532536i
$454$	−41.9387	+	30.4702i	−1.96828	+	1.43004i
$455$	−1.49513	−	4.60152i	−0.0700925	−	0.215723i
$456$	6.95716	+	5.05467i	0.325799	+	0.236707i
$457$	−9.14596	−	6.64493i	−0.427830	−	0.310837i	0.352951	−	0.935642i	$-0.385178\pi$
$457$	−9.14596	−	6.64493i	−0.427830	−	0.310837i	−0.780781	+	0.624805i	$0.785178\pi$
$458$	−39.5925	+	28.7656i	−1.85004	+	1.34413i
$459$	−11.3635			−0.530402
$460$	73.5898			3.43114
$461$	−10.2089	+	7.41720i	−0.475476	+	0.345453i	−0.799571	−	0.600571i	$-0.794940\pi$
$461$	−10.2089	+	7.41720i	−0.475476	+	0.345453i	0.324096	+	0.946024i	$0.394940\pi$
$462$	3.11206	−	9.57793i	0.144786	−	0.445606i
$463$	2.67160	+	8.22234i	0.124160	+	0.382124i	0.993747	−	0.111655i	$-0.0356151\pi$
$463$	2.67160	+	8.22234i	0.124160	+	0.382124i	−0.869587	+	0.493779i	$0.835615\pi$
$464$	3.39485			0.157602
$465$	45.5027	+	16.9266i	2.11014	+	0.784952i
$466$	−48.0934			−2.22788
$467$	13.2787	+	40.8675i	0.614463	+	1.89112i	0.409325	+	0.912389i	$0.365764\pi$
$467$	13.2787	+	40.8675i	0.614463	+	1.89112i	0.205138	+	0.978733i	$0.434236\pi$
$468$	2.13613	−	6.57435i	0.0987429	−	0.303899i
$469$	10.6367	−	7.72802i	0.491158	−	0.356847i
$470$	26.8013			1.23625
$471$	31.7763			1.46417
$472$	18.3261	−	13.3147i	0.843526	−	0.612857i
$473$	−4.88420	−	3.54858i	−0.224576	−	0.163164i
$474$	73.1158	+	53.1218i	3.35832	+	2.43996i
$475$	3.70523	+	11.4035i	0.170007	+	0.523229i
$476$	18.0097	−	13.0848i	0.825471	−	0.599740i
$477$	−8.75403	−	26.9421i	−0.400819	−	1.23360i
$478$	−0.262634	+	0.808305i	−0.0120126	+	0.0369710i
$479$	−28.7988	−	20.9235i	−1.31585	−	0.956020i	−0.999974	−	0.00721931i	$-0.997702\pi$
$479$	−28.7988	−	20.9235i	−1.31585	−	0.956020i	−0.315875	−	0.948801i	$-0.602298\pi$
$480$	12.9701	−	39.9178i	0.592001	−	1.82199i
$481$	0.305151	−	0.939158i	0.0139137	−	0.0428219i
$482$	−41.5460	−	30.1849i	−1.89237	−	1.37489i
$483$	−4.83351	+	14.8760i	−0.219932	+	0.676882i
$484$	−8.99668	−	27.6889i	−0.408940	−	1.25859i
$485$	11.9072	−	8.65110i	0.540679	−	0.392826i
$486$	13.0104	+	40.0420i	0.590165	+	1.81634i
$487$	3.24552	+	2.35801i	0.147068	+	0.106851i	0.658886	−	0.752242i	$-0.271028\pi$
$487$	3.24552	+	2.35801i	0.147068	+	0.106851i	−0.511818	+	0.859094i	$0.671028\pi$
$488$	9.35124	+	6.79407i	0.423311	+	0.307553i
$489$	−21.1318	+	15.3532i	−0.955615	+	0.694295i
$490$	49.1162			2.21884
$491$	−5.50408			−0.248396			−0.124198	−	0.992257i	$-0.539636\pi$
$491$	−5.50408			−0.248396			−0.124198	+	0.992257i	$0.539636\pi$
$492$	1.11041	−	0.806760i	0.0500611	−	0.0363715i
$493$	7.88142	−	24.2565i	0.354961	−	1.09246i
$494$	−0.852835	−	2.62476i	−0.0383708	−	0.118093i
$495$	12.2936			0.552554
$496$	3.66374	+	1.36288i	0.164507	+	0.0611951i
$497$	−5.45341			−0.244619
$498$	24.0614	+	74.0534i	1.07822	+	3.31841i
$499$	−5.85623	+	18.0236i	−0.262161	+	0.806848i	0.730173	+	0.683262i	$0.239439\pi$
$499$	−5.85623	+	18.0236i	−0.262161	+	0.806848i	−0.992334	+	0.123586i	$0.960561\pi$
$500$	−54.1271	+	39.3256i	−2.42064	+	1.75870i
$501$	−33.9586			−1.51716
$502$	5.19982			0.232079
$503$	11.2695	−	8.18775i	0.502481	−	0.365074i	−0.307483	−	0.951554i	$-0.599487\pi$
$503$	11.2695	−	8.18775i	0.502481	−	0.365074i	0.809964	+	0.586480i	$0.199487\pi$
$504$	−6.62476	−	4.81317i	−0.295090	−	0.214395i
$505$	63.0137	+	45.7821i	2.80407	+	2.03728i
$506$	−6.22310	−	19.1527i	−0.276651	−	0.851443i
$507$	−1.81631	+	1.31963i	−0.0806652	+	0.0586067i
$508$	−11.8382	−	36.4342i	−0.525234	−	1.61651i
$509$	−0.362860	+	1.11677i	−0.0160835	+	0.0494999i	−0.958776	−	0.284162i	$-0.908285\pi$
$509$	−0.362860	+	1.11677i	−0.0160835	+	0.0494999i	0.942693	+	0.333662i	$0.108285\pi$
$510$	86.3687	+	62.7505i	3.82447	+	2.77864i
$511$	−3.85951	+	11.8783i	−0.170735	+	0.525467i
$512$	2.44219	−	7.51629i	0.107931	−	0.332176i
$513$	2.07230	+	1.50562i	0.0914944	+	0.0664746i
$514$	−6.40836	+	19.7229i	−0.282661	+	0.869940i
$515$	4.63419	+	14.2626i	0.204207	+	0.628484i
$516$	−23.9476	+	17.3990i	−1.05423	+	0.765946i
$517$	−1.42514	−	4.38612i	−0.0626774	−	0.192901i
$518$	−2.31008	−	1.67837i	−0.101499	−	0.0737435i
$519$	14.2365	+	10.3434i	0.624912	+	0.454025i
$520$	10.1226	−	7.35453i	0.443907	−	0.322517i
$521$	−19.1804			−0.840308			−0.420154	−	0.907453i	$-0.638024\pi$
$521$	−19.1804			−0.840308			−0.420154	+	0.907453i	$0.638024\pi$
$522$	−22.9012			−1.00236
$523$	9.92588	−	7.21157i	0.434028	−	0.315340i	−0.349229	−	0.937037i	$-0.613557\pi$
$523$	9.92588	−	7.21157i	0.434028	−	0.315340i	0.783258	+	0.621697i	$0.213557\pi$
$524$	−7.17851	+	22.0932i	−0.313595	+	0.965145i
$525$	−8.71570	−	26.8242i	−0.380385	−	1.17070i
$526$	17.9403			0.782234
$527$	18.2436	−	23.0138i	0.794703	−	1.00250i
$528$	2.44520			0.106414
$529$	2.55805	+	7.87286i	0.111219	+	0.342298i
$530$	38.6785	−	119.040i	1.68009	−	5.17078i
$531$	−11.6069	+	8.43289i	−0.503696	+	0.365956i
$532$	−5.01801			−0.217558
$533$	−0.180452			−0.00781625
$534$	47.0116	−	34.1559i	2.03439	−	1.47807i
$535$	−5.65664	−	4.10979i	−0.244558	−	0.177682i
$536$	27.5073	+	19.9852i	1.18814	+	0.863231i
$537$	6.29548	+	19.3755i	0.271670	+	0.836114i
$538$	10.2736	−	7.46420i	0.442926	−	0.321805i
$539$	−2.61171	−	8.03801i	−0.112494	−	0.346222i
$540$	−8.75999	+	26.9605i	−0.376970	+	1.16019i
$541$	−22.5930	−	16.4148i	−0.971348	−	0.705726i	−0.0155896	−	0.999878i	$-0.504963\pi$
$541$	−22.5930	−	16.4148i	−0.971348	−	0.705726i	−0.955758	+	0.294153i	$0.904963\pi$
$542$	0.432135	−	1.32998i	0.0185618	−	0.0571274i
$543$	16.9349	−	52.1203i	0.726746	−	2.23670i
$544$	−20.5403	−	14.9234i	−0.880660	−	0.639837i
$545$	−6.59849	+	20.3081i	−0.282648	+	0.869902i
$546$	2.00610	+	6.17414i	0.0858532	+	0.264229i
$547$	3.69217	−	2.68252i	0.157866	−	0.114696i	−0.506048	−	0.862505i	$-0.668894\pi$
$547$	3.69217	−	2.68252i	0.157866	−	0.114696i	0.663914	+	0.747809i	$0.268894\pi$
$548$	10.0408	+	30.9026i	0.428924	+	1.32009i
$549$	−5.92264	−	4.30305i	−0.252772	−	0.183650i
$550$	29.3780	+	21.3444i	1.25268	+	0.910127i
$551$	−4.65118	+	3.37928i	−0.198147	+	0.143962i
$552$	−40.4502			−1.72168
$553$	−21.6043			−0.918707
$554$	−36.2264	+	26.3200i	−1.53911	+	1.11823i
$555$	2.66081	−	8.18914i	0.112945	−	0.347610i
$556$	−0.551596	−	1.69764i	−0.0233929	−	0.0719959i
$557$	−31.1325			−1.31913			−0.659564	−	0.751649i	$-0.729259\pi$
$557$	−31.1325			−1.31913			−0.659564	+	0.751649i	$0.729259\pi$
$558$	−24.7151	−	9.19380i	−1.04627	−	0.389205i
$559$	3.89171			0.164602
$560$	−1.04970	−	3.23064i	−0.0443579	−	0.136520i
$561$	5.67674	−	17.4712i	0.239672	−	0.737635i
$562$	−5.08266	+	3.69277i	−0.214399	+	0.155770i
$563$	−23.5013			−0.990462			−0.495231	−	0.868761i	$-0.664917\pi$
$563$	−23.5013			−0.990462			−0.495231	+	0.868761i	$0.664917\pi$
$564$	−22.6122			−0.952144
$565$	35.0718	−	25.4811i	1.47548	−	1.07200i
$566$	−39.0393	−	28.3637i	−1.64094	−	1.19222i
$567$	−11.0437	−	8.02374i	−0.463793	−	0.336965i
$568$	−4.35804	−	13.4127i	−0.182859	−	0.562784i
$569$	15.1048	−	10.9743i	0.633226	−	0.460065i	−0.224291	−	0.974522i	$-0.572006\pi$
$569$	15.1048	−	10.9743i	0.633226	−	0.460065i	0.857516	+	0.514457i	$0.172006\pi$
$570$	−7.43643	−	22.8870i	−0.311478	−	0.958630i
$571$	3.23810	−	9.96583i	0.135510	−	0.417057i	−0.860159	−	0.510026i	$-0.829636\pi$
$571$	3.23810	−	9.96583i	0.135510	−	0.417057i	0.995669	+	0.0929690i	$0.0296357\pi$
$572$	−4.25191	−	3.08919i	−0.177781	−	0.129166i
$573$	6.31443	−	19.4338i	0.263789	−	0.811859i
$574$	−0.161243	+	0.496256i	−0.00673017	+	0.0207133i
$575$	−45.6286	−	33.1511i	−1.90284	−	1.38250i
$576$	−7.93015	+	24.4065i	−0.330423	+	1.01694i
$577$	10.7467	+	33.0749i	0.447390	+	1.37693i	0.879841	+	0.475268i	$0.157649\pi$
$577$	10.7467	+	33.0749i	0.447390	+	1.37693i	−0.432451	+	0.901657i	$0.642351\pi$
$578$	20.3211	−	14.7642i	0.845248	−	0.614109i
$579$	17.2331	+	53.0380i	0.716183	+	2.20418i
$580$	−51.4741	−	37.3981i	−2.13735	−	1.55287i
$581$	−15.0585	−	10.9406i	−0.624732	−	0.453895i
$582$	−15.9766	+	11.6077i	−0.662253	+	0.481155i
$583$	−21.5380			−0.892013
$584$	−32.2991			−1.33655
$585$	−6.41121	+	4.65802i	−0.265071	+	0.192585i
$586$	−2.36475	+	7.27794i	−0.0976868	+	0.300649i
$587$	−1.23627	−	3.80485i	−0.0510263	−	0.157043i	0.922296	−	0.386483i	$-0.126310\pi$
$587$	−1.23627	−	3.80485i	−0.0510263	−	0.157043i	−0.973323	+	0.229441i	$0.926310\pi$
$588$	−41.4391			−1.70892
$589$	−6.37622	+	1.77970i	−0.262727	+	0.0733314i
$590$	−63.3899			−2.60972
$591$	−5.31603	−	16.3611i	−0.218672	−	0.673004i
$592$	0.214241	−	0.659365i	0.00880524	−	0.0270997i
$593$	−26.1645	+	19.0096i	−1.07445	+	0.780633i	−0.976707	−	0.214579i	$-0.931162\pi$
$593$	−26.1645	+	19.0096i	−1.07445	+	0.780633i	−0.0977419	+	0.995212i	$0.531162\pi$
$594$	7.75761			0.318298
$595$	−25.5202			−1.04623
$596$	28.2271	−	20.5082i	1.15623	−	0.840049i
$597$	42.4339	+	30.8301i	1.73671	+	1.26179i
$598$	10.5024	+	7.63041i	0.429474	+	0.312031i
$599$	7.71260	+	23.7369i	0.315128	+	0.969865i	0.975702	+	0.219103i	$0.0703132\pi$
$599$	7.71260	+	23.7369i	0.315128	+	0.969865i	−0.660574	+	0.750761i	$0.729687\pi$
$600$	59.0091	−	42.8726i	2.40904	−	1.75027i
$601$	−5.22269	−	16.0738i	−0.213038	−	0.655663i	−0.999287	−	0.0377535i	$-0.987980\pi$
$601$	−5.22269	−	16.0738i	−0.213038	−	0.655663i	0.786249	−	0.617909i	$-0.212020\pi$
$602$	3.47745	−	10.7025i	0.141730	−	0.436201i
$603$	−17.4219	−	12.6577i	−0.709473	−	0.515463i
$604$	−5.55741	+	17.1039i	−0.226128	+	0.695949i
$605$	−10.3138	+	31.7426i	−0.419315	+	1.29052i
$606$	−84.5493	−	61.4287i	−3.43458	−	2.49537i
$607$	3.12048	−	9.60384i	0.126656	−	0.389808i	−0.867543	−	0.497362i	$-0.834302\pi$
$607$	3.12048	−	9.60384i	0.126656	−	0.389808i	0.994199	+	0.107554i	$0.0343020\pi$
$608$	1.76854	+	5.44302i	0.0717240	+	0.220744i
$609$	10.9409	−	7.94900i	0.443346	−	0.322110i
$610$	−9.99544	−	30.7628i	−0.404704	−	1.24555i
$611$	2.40512	+	1.74742i	0.0973007	+	0.0706931i
$612$	−29.4980	−	21.4316i	−1.19239	−	0.866320i
$613$	3.41928	−	2.48425i	0.138104	−	0.100338i	−0.516589	−	0.856234i	$-0.672798\pi$
$613$	3.41928	−	2.48425i	0.138104	−	0.100338i	0.654692	+	0.755896i	$0.272798\pi$
$614$	71.2214			2.87426
$615$	−1.57348			−0.0634489
$616$	−5.03674	+	3.65941i	−0.202936	+	0.147442i
$617$	−3.77969	+	11.6327i	−0.152165	+	0.468314i	−0.997863	−	0.0653474i	$-0.979184\pi$
$617$	−3.77969	+	11.6327i	−0.152165	+	0.468314i	0.845698	+	0.533662i	$0.179184\pi$
$618$	−6.21798	−	19.1370i	−0.250124	−	0.769802i
$619$	−2.76594			−0.111172			−0.0555862	−	0.998454i	$-0.517703\pi$
$619$	−2.76594			−0.111172			−0.0555862	+	0.998454i	$0.517703\pi$
$620$	−40.5376	−	61.0249i	−1.62803	−	2.45082i
$621$	−12.0488			−0.483500
$622$	−4.02503	−	12.3878i	−0.161389	−	0.496704i
$623$	−4.29255	+	13.2111i	−0.171977	+	0.529292i
$624$	−1.27520	+	0.926485i	−0.0510488	+	0.0370891i
$625$	26.2765			1.05106
$626$	−29.4087			−1.17541
$627$	−3.35010	+	2.43399i	−0.133790	+	0.0972042i
$628$	−38.7935	−	28.1851i	−1.54803	−	1.12471i
$629$	−4.21385	−	3.06154i	−0.168017	−	0.122072i
$630$	7.08113	+	21.7935i	0.282119	+	0.868273i
$631$	27.8520	−	20.2357i	1.10877	−	0.805570i	0.126302	−	0.991992i	$-0.459689\pi$
$631$	27.8520	−	20.2357i	1.10877	−	0.805570i	0.982470	+	0.186422i	$0.0596893\pi$
$632$	−17.2649	−	53.1358i	−0.686759	−	2.11363i
$633$	−10.5831	+	32.5715i	−0.420642	+	1.29460i
$634$	22.2970	+	16.1997i	0.885528	+	0.643374i
$635$	−13.5713	+	41.7681i	−0.538560	+	1.65752i
$636$	−32.6329	+	100.434i	−1.29398	+	3.98246i
$637$	4.40763	+	3.20233i	0.174637	+	0.126881i
$638$	−5.38047	+	16.5594i	−0.213015	+	0.655593i
$639$	2.76018	+	8.49497i	0.109191	+	0.336056i
$640$	−61.4821	+	44.6694i	−2.43030	+	1.76571i
$641$	−0.948276	−	2.91849i	−0.0374546	−	0.115274i	0.930581	−	0.366086i	$-0.119302\pi$
$641$	−0.948276	−	2.91849i	−0.0374546	−	0.115274i	−0.968036	+	0.250812i	$0.919302\pi$
$642$	7.58986	+	5.51435i	0.299548	+	0.217634i
$643$	−32.8291	−	23.8518i	−1.29465	−	0.940622i	−0.294766	−	0.955569i	$-0.595242\pi$
$643$	−32.8291	−	23.8518i	−1.29465	−	0.940622i	−0.999888	+	0.0149478i	$0.995242\pi$
$644$	19.0957	−	13.8739i	0.752477	−	0.546706i
$645$	33.9344			1.33617
$646$	−14.5570			−0.572737
$647$	−1.16525	+	0.846601i	−0.0458106	+	0.0332833i	−0.610455	−	0.792051i	$-0.709013\pi$
$647$	−1.16525	+	0.846601i	−0.0458106	+	0.0332833i	0.564644	+	0.825334i	$0.309013\pi$
$648$	10.9089	−	33.5742i	0.428543	−	1.31892i
$649$	3.37070	+	10.3739i	0.132312	+	0.407213i
$650$	−23.4083			−0.918148
$651$	14.9986	−	4.18635i	0.587842	−	0.164076i
$652$	39.4165			1.54367
$653$	−12.9919	−	39.9850i	−0.508412	−	1.56473i	−0.794957	−	0.606666i	$-0.792507\pi$
$653$	−12.9919	−	39.9850i	−0.508412	−	1.56473i	0.286545	−	0.958067i	$-0.407493\pi$
$654$	8.85360	−	27.2486i	0.346203	−	1.06550i
$655$	21.5450	−	15.6533i	0.841831	−	0.611626i
$656$	−0.126692			−0.00494649
$657$	20.4568			0.798095
$658$	6.95464	−	5.05284i	0.271120	−	0.196980i
$659$	32.4068	+	23.5449i	1.26239	+	0.917181i	0.998872	−	0.0474737i	$-0.0151170\pi$
$659$	32.4068	+	23.5449i	1.26239	+	0.917181i	0.263518	+	0.964654i	$0.415117\pi$
$660$	−37.0752	−	26.9367i	−1.44315	−	1.04851i
$661$	7.59869	+	23.3864i	0.295555	+	0.909625i	0.983034	+	0.183421i	$0.0587171\pi$
$661$	7.59869	+	23.3864i	0.295555	+	0.909625i	−0.687480	+	0.726204i	$0.741283\pi$
$662$	38.0845	−	27.6700i	1.48020	−	1.07543i
$663$	3.65935	+	11.2623i	0.142117	+	0.437392i
$664$	14.8747	−	45.7796i	0.577250	−	1.77659i
$665$	4.65399	+	3.38132i	0.180474	+	0.131122i
$666$	−1.44524	+	4.44799i	−0.0560019	+	0.172356i
$667$	8.35671	−	25.7193i	0.323573	−	0.995855i
$668$	41.4578	+	30.1209i	1.60405	+	1.16541i
$669$	−15.8483	+	48.7760i	−0.612731	+	1.88579i
$670$	−29.4023	−	90.4910i	−1.13591	−	3.49597i
$671$	−4.50293	+	3.27157i	−0.173834	+	0.126298i
$672$	−4.16010	−	12.8035i	−0.160479	−	0.493905i
$673$	31.7995	+	23.1037i	1.22578	+	0.890580i	0.996567	−	0.0827961i	$-0.0263850\pi$
$673$	31.7995	+	23.1037i	1.22578	+	0.890580i	0.229212	+	0.973376i	$0.426385\pi$
$674$	55.5190	+	40.3369i	2.13851	+	1.55372i
$675$	17.5768	−	12.7703i	0.676532	−	0.491529i
$676$	3.38790			0.130304
$677$	−14.9379			−0.574112			−0.287056	−	0.957914i	$-0.592677\pi$
$677$	−14.9379			−0.574112			−0.287056	+	0.957914i	$0.592677\pi$
$678$	−47.0579	+	34.1896i	−1.80725	+	1.31304i
$679$	1.45880	−	4.48973i	0.0559836	−	0.172300i
$680$	−20.3942	−	62.7670i	−0.782084	−	2.40701i
$681$	−50.1395			−1.92135
$682$	−12.4545	+	15.7110i	−0.476907	+	0.601605i
$683$	23.6260			0.904025			0.452012	−	0.892012i	$-0.350706\pi$
$683$	23.6260			0.904025			0.452012	+	0.892012i	$0.350706\pi$
$684$	2.53981	+	7.81673i	0.0971121	+	0.298880i
$685$	11.5108	−	35.4267i	0.439806	−	1.35358i
$686$	29.1205	−	21.1573i	1.11183	−	0.807790i
$687$	−47.3345			−1.80592
$688$	2.73230			0.104168
$689$	11.2323	−	8.16073i	0.427916	−	0.310899i
$690$	91.5771	+	66.5346i	3.48628	+	2.53293i
$691$	6.40036	+	4.65013i	0.243481	+	0.176899i	0.702833	−	0.711355i	$-0.251918\pi$
$691$	6.40036	+	4.65013i	0.243481	+	0.176899i	−0.459352	+	0.888254i	$0.651918\pi$
$692$	−8.20589	−	25.2551i	−0.311941	−	0.960056i
$693$	3.19004	−	2.31770i	0.121180	−	0.0880421i
$694$	4.24279	+	13.0580i	0.161054	+	0.495673i
$695$	−0.632350	+	1.94617i	−0.0239864	+	0.0738225i
$696$	28.2939	+	20.5567i	1.07248	+	0.779200i
$697$	−0.294126	+	0.905226i	−0.0111408	+	0.0342879i
$698$	13.0809	−	40.2588i	0.495119	−	1.52382i
$699$	−37.6327	−	27.3418i	−1.42340	−	1.03416i
$700$	−13.1523	+	40.4786i	−0.497109	+	1.52995i
$701$	3.83527	+	11.8037i	0.144856	+	0.445821i	0.996992	−	0.0774988i	$-0.0246934\pi$
$701$	3.83527	+	11.8037i	0.144856	+	0.445821i	−0.852136	+	0.523320i	$0.824693\pi$
$702$	−4.04567	+	2.93935i	−0.152694	+	0.110939i
$703$	0.362817	+	1.11663i	0.0136839	+	0.0421147i
$704$	15.7847	+	11.4683i	0.594908	+	0.432226i
$705$	20.9718	+	15.2369i	0.789845	+	0.573856i
$706$	30.9573	−	22.4918i	1.16509	−	0.846489i
$707$	24.9826			0.939568
$708$	53.4818			2.00997
$709$	18.2545	−	13.2627i	0.685564	−	0.498091i	−0.189635	−	0.981855i	$-0.560730\pi$
$709$	18.2545	−	13.2627i	0.685564	−	0.498091i	0.875199	+	0.483763i	$0.160730\pi$
$710$	−12.1955	+	37.5339i	−0.457689	+	1.40862i
$711$	10.9348	+	33.6537i	0.410085	+	1.26211i
$712$	−35.9231			−1.34628
$713$	19.3437	−	24.4016i	0.724429	−	0.913847i
$714$	34.2420			1.28148
$715$	1.86185	+	5.73018i	0.0696292	+	0.214297i
$716$	9.50008	−	29.2382i	0.355035	−	1.09268i
$717$	−0.665042	+	0.483182i	−0.0248365	+	0.0180447i
$718$	−64.5906			−2.41050
$719$	−45.1964			−1.68554			−0.842771	−	0.538273i	$-0.819077\pi$
$719$	−45.1964			−1.68554			−0.842771	+	0.538273i	$0.819077\pi$
$720$	−4.50119	+	3.27031i	−0.167749	+	0.121877i
$721$	3.89144	+	2.82730i	0.144925	+	0.105294i
$722$	−33.0250	−	23.9941i	−1.22906	−	0.892967i
$723$	−15.3489	−	47.2390i	−0.570831	−	1.75684i
$724$	−66.9047	+	48.6091i	−2.48649	+	1.80654i
$725$	15.0687	+	46.3766i	0.559637	+	1.72238i
$726$	13.8386	−	42.5910i	0.513600	−	1.58070i
$727$	30.2494	+	21.9775i	1.12189	+	0.815100i	0.984494	−	0.175417i	$-0.0561273\pi$
$727$	30.2494	+	21.9775i	1.12189	+	0.815100i	0.137394	+	0.990516i	$0.456127\pi$
$728$	1.24016	−	3.81683i	0.0459636	−	0.141461i
$729$	−2.42527	+	7.46420i	−0.0898247	+	0.276452i
$730$	73.1234	+	53.1273i	2.70642	+	1.96633i
$731$	6.34326	−	19.5225i	0.234614	−	0.722067i
$732$	8.43312	+	25.9545i	0.311697	+	0.959305i
$733$	−13.1268	+	9.53721i	−0.484851	+	0.352265i	−0.803201	−	0.595708i	$-0.796871\pi$
$733$	−13.1268	+	9.53721i	−0.484851	+	0.352265i	0.318350	+	0.947973i	$0.396871\pi$
$734$	−19.1904	−	59.0621i	−0.708332	−	2.18002i
$735$	38.4330	+	27.9232i	1.41762	+	1.02996i
$736$	−21.7790	−	15.8234i	−0.802785	−	0.583258i
$737$	−13.2457	+	9.62355i	−0.487911	+	0.354488i
$738$	0.854648			0.0314600
$739$	25.0208			0.920406			0.460203	−	0.887814i	$-0.347777\pi$
$739$	25.0208			0.920406			0.460203	+	0.887814i	$0.347777\pi$
$740$	−10.5121	+	7.63746i	−0.386431	+	0.280759i
$741$	0.824874	−	2.53870i	0.0303025	−	0.0932615i
$742$	−12.4060	−	38.1816i	−0.455437	−	1.40169i
$743$	−3.45326			−0.126688			−0.0633440	−	0.997992i	$-0.520177\pi$
$743$	−3.45326			−0.126688			−0.0633440	+	0.997992i	$0.520177\pi$
$744$	22.2823	+	33.5436i	0.816910	+	1.22977i
$745$	−39.9987			−1.46544
$746$	24.0263	+	73.9452i	0.879664	+	2.70733i
$747$	−9.42094	+	28.9947i	−0.344694	+	1.06086i
$748$	−22.4271	+	16.2942i	−0.820015	+	0.595776i
$749$	−2.24265			−0.0819447
$750$	−102.913			−3.75784
$751$	−24.9622	+	18.1361i	−0.910883	+	0.661795i	−0.941238	−	0.337744i	$-0.890336\pi$
$751$	−24.9622	+	18.1361i	−0.910883	+	0.661795i	0.0303554	+	0.999539i	$0.490336\pi$
$752$	1.68859	+	1.22683i	0.0615765	+	0.0447379i
$753$	4.06882	+	2.95617i	0.148276	+	0.107729i
$754$	−3.46837	−	10.6745i	−0.126311	−	0.388744i
$755$	16.6795	−	12.1184i	0.607030	−	0.441033i
$756$	2.80973	+	8.64745i	0.102189	+	0.314505i
$757$	14.7200	−	45.3036i	0.535008	−	1.64659i	−0.208622	−	0.977996i	$-0.566898\pi$
$757$	14.7200	−	45.3036i	0.535008	−	1.64659i	0.743631	−	0.668591i	$-0.233102\pi$
$758$	68.7379	+	49.9410i	2.49667	+	1.81394i
$759$	6.01907	−	18.5248i	0.218478	−	0.672407i
$760$	−4.59718	+	14.1487i	−0.166757	+	0.513226i
$761$	27.8257	+	20.2165i	1.00868	+	0.732849i	0.963932	−	0.266149i	$-0.0857514\pi$
$761$	27.8257	+	20.2165i	1.00868	+	0.732849i	0.0447483	+	0.998998i	$0.485751\pi$
$762$	18.2094	−	56.0429i	0.659658	−	2.03022i
$763$	2.11644	+	6.51372i	0.0766202	+	0.235813i
$764$	−24.9464	+	18.1246i	−0.902529	+	0.655726i
$765$	12.9168	+	39.7537i	0.467007	+	1.43730i
$766$	17.6501	+	12.8235i	0.637724	+	0.463333i
$767$	−5.68853	−	4.13296i	−0.205401	−	0.149233i
$768$	36.8062	−	26.7412i	1.32813	−	0.964942i
$769$	−24.2298			−0.873749			−0.436874	−	0.899522i	$-0.643915\pi$
$769$	−24.2298			−0.873749			−0.436874	+	0.899522i	$0.643915\pi$
$770$	17.4221			0.627848
$771$	−16.2272	+	11.7898i	−0.584410	+	0.424599i
$772$	26.0053	−	80.0360i	0.935950	−	2.88056i
$773$	−11.3409	−	34.9037i	−0.407904	−	1.25540i	−0.918446	−	0.395546i	$-0.870556\pi$
$773$	−11.3409	−	34.9037i	−0.407904	−	1.25540i	0.510543	−	0.859852i	$-0.329444\pi$
$774$	−18.4317			−0.662515
$775$	−2.35591	+	56.0994i	−0.0846267	+	2.01515i
$776$	12.2083			0.438252
$777$	−0.853444	−	2.62663i	−0.0306171	−	0.0942298i
$778$	−13.9913	+	43.0607i	−0.501612	+	1.54380i
$779$	0.173577	−	0.126111i	0.00621904	−	0.00451840i
$780$	29.5414			1.05775
$781$	6.79102			0.243002
$782$	55.3957	−	40.2473i	1.98095	−	1.43924i
$783$	8.42779	+	6.12315i	0.301185	+	0.218823i
$784$	3.09451	+	2.24829i	0.110518	+	0.0802962i
$785$	16.9871	+	52.2810i	0.606297	+	1.86599i
$786$	−28.9082	+	21.0030i	−1.03112	+	0.749153i
$787$	6.08443	+	18.7259i	0.216886	+	0.667508i	0.999014	+	0.0443899i	$0.0141344\pi$
$787$	6.08443	+	18.7259i	0.216886	+	0.667508i	−0.782128	+	0.623118i	$0.785866\pi$
$788$	−8.02206	+	24.6894i	−0.285774	+	0.879522i
$789$	14.0382	+	10.1993i	0.499771	+	0.363105i
$790$	−48.3138	+	148.695i	−1.71893	+	5.29031i
$791$	4.29678	−	13.2241i	0.152776	−	0.470196i
$792$	8.24968	+	5.99374i	0.293139	+	0.212978i
$793$	1.10873	−	3.41231i	0.0393721	−	0.121175i
$794$	−6.71556	−	20.6684i	−0.238326	−	0.733493i
$795$	97.9417	−	71.1588i	3.47363	−	2.52374i
$796$	−24.4589	−	75.2767i	−0.866922	−	2.66811i
$797$	27.7618	+	20.1701i	0.983374	+	0.714463i	0.958460	−	0.285226i	$-0.0920688\pi$
$797$	27.7618	+	20.1701i	0.983374	+	0.714463i	0.0249141	+	0.999690i	$0.492069\pi$
$798$	−6.24454	−	4.53693i	−0.221054	−	0.160605i
$799$	12.6860	−	9.21694i	0.448799	−	0.326072i
$800$	48.5423			1.71623
$801$	22.7520			0.803904
$802$	−0.823942	+	0.598629i	−0.0290944	+	0.0211383i
$803$	4.80617	−	14.7919i	0.169606	−	0.521994i
$804$	24.8066	+	76.3469i	0.874862	+	2.69255i
$805$	−27.0592			−0.953711
$806$	0.542261	−	12.9124i	0.0191003	−	0.454821i
$807$	12.2825			0.432365
$808$	19.9646	+	61.4448i	0.702353	+	2.16162i
$809$	−0.524786	+	1.61513i	−0.0184505	+	0.0567848i	−0.959858	−	0.280487i	$-0.909504\pi$
$809$	−0.524786	+	1.61513i	−0.0184505	+	0.0567848i	0.941407	+	0.337272i	$0.109504\pi$
$810$	−79.9217	+	58.0665i	−2.80816	+	2.04025i
$811$	34.6681			1.21736			0.608681	−	0.793415i	$-0.291699\pi$
$811$	34.6681			1.21736			0.608681	+	0.793415i	$0.291699\pi$
$812$	−20.4076			−0.716167
$813$	1.09425	−	0.795021i	0.0383771	−	0.0278826i
$814$	2.87670	+	2.09005i	0.100828	+	0.0732561i
$815$	−36.5571	−	26.5603i	−1.28054	−	0.930367i
$816$	2.56916	+	7.90706i	0.0899386	+	0.276802i
$817$	−3.74344	+	2.71977i	−0.130967	+	0.0951527i
$818$	−11.2556	−	34.6411i	−0.393542	−	1.21120i
$819$	−0.785463	+	2.41741i	−0.0274463	+	0.0844710i
$820$	1.92096	+	1.39566i	0.0670828	+	0.0487385i
$821$	0.670481	−	2.06353i	0.0234000	−	0.0720176i	−0.938675	−	0.344804i	$-0.887945\pi$
$821$	0.670481	−	2.06353i	0.0234000	−	0.0720176i	0.962075	+	0.272787i	$0.0879453\pi$
$822$	−15.4448	+	47.5341i	−0.538699	+	1.65794i
$823$	25.4301	+	18.4760i	0.886436	+	0.644033i	0.934946	−	0.354789i	$-0.115447\pi$
$823$	25.4301	+	18.4760i	0.886436	+	0.644033i	−0.0485103	+	0.998823i	$0.515447\pi$
$824$	−3.84393	+	11.8304i	−0.133910	+	0.412132i
$825$	10.8535	+	33.4036i	0.377870	+	1.16296i
$826$	−16.4489	+	11.9509i	−0.572332	+	0.415824i
$827$	0.711237	+	2.18896i	0.0247321	+	0.0761177i	0.962661	−	0.270711i	$-0.0872586\pi$
$827$	0.711237	+	2.18896i	0.0247321	+	0.0761177i	−0.937929	+	0.346828i	$0.887259\pi$
$828$	−31.2769	−	22.7240i	−1.08695	−	0.789713i
$829$	1.92151	+	1.39606i	0.0667367	+	0.0484871i	0.620653	−	0.784085i	$-0.286867\pi$
$829$	1.92151	+	1.39606i	0.0667367	+	0.0484871i	−0.553917	+	0.832572i	$0.686867\pi$
$830$	−108.976	+	79.1758i	−3.78261	+	2.74823i
$831$	−43.3102			−1.50241
$832$	−12.5772			−0.436036
$833$	23.2484	−	16.8910i	0.805511	−	0.585238i
$834$	0.848462	−	2.61130i	0.0293798	−	0.0904218i
$835$	−18.1538	−	55.8716i	−0.628238	−	1.93352i
$836$	6.24883			0.216120
$837$	6.63716	+	9.99152i	0.229414	+	0.345357i
$838$	−10.9216			−0.377281
$839$	−5.82280	−	17.9207i	−0.201026	−	0.618693i	−0.999853	−	0.0171330i	$-0.994546\pi$
$839$	−5.82280	−	17.9207i	−0.201026	−	0.618693i	0.798828	−	0.601560i	$-0.205454\pi$
$840$	10.8138	−	33.2815i	0.373112	−	1.14832i
$841$	4.54572	−	3.30266i	0.156749	−	0.113885i
$842$	−16.6561			−0.574005
$843$	−6.07653			−0.209287
$844$	41.8107	−	30.3773i	1.43918	−	1.04563i
$845$	−3.14214	−	2.28289i	−0.108093	−	0.0785340i
$846$	−11.3910	−	8.27604i	−0.391630	−	0.284536i
$847$	3.30810	+	10.1813i	0.113668	+	0.349834i
$848$	7.88597	−	5.72949i	0.270805	−	0.196752i
$849$	−14.4228	−	44.3888i	−0.494989	−	1.52342i
$850$	−38.1541	+	117.426i	−1.30867	+	4.02768i
$851$	−4.46796	−	3.24616i	−0.153160	−	0.111277i
$852$	10.2893	−	31.6672i	0.352506	−	1.08490i
$853$	−10.3371	+	31.8144i	−0.353936	+	1.08930i	0.602687	+	0.797977i	$0.294097\pi$
$853$	−10.3371	+	31.8144i	−0.353936	+	1.08930i	−0.956624	+	0.291326i	$0.905903\pi$
$854$	−8.39340	−	6.09816i	−0.287216	−	0.208675i
$855$	2.91164	−	8.96110i	0.0995759	−	0.306463i
$856$	−1.79219	−	5.51581i	−0.0612559	−	0.188526i
$857$	−7.41861	+	5.38993i	−0.253415	+	0.184117i	−0.707239	−	0.706975i	$-0.750059\pi$
$857$	−7.41861	+	5.38993i	−0.253415	+	0.184117i	0.453824	+	0.891091i	$0.350059\pi$
$858$	−2.49816	−	7.68854i	−0.0852857	−	0.262482i
$859$	−34.3731	−	24.9735i	−1.17280	−	0.852086i	−0.181455	−	0.983399i	$-0.558081\pi$
$859$	−34.3731	−	24.9735i	−1.17280	−	0.852086i	−0.991341	+	0.131313i	$0.958081\pi$
$860$	−41.4283	−	30.0994i	−1.41269	−	1.02638i
$861$	−0.408301	+	0.296648i	−0.0139148	+	0.0101097i
$862$	−70.7199			−2.40873
$863$	1.91329			0.0651290			0.0325645	−	0.999470i	$-0.489633\pi$
$863$	1.91329			0.0651290			0.0325645	+	0.999470i	$0.489633\pi$
$864$	8.38961	−	6.09541i	0.285420	−	0.207370i
$865$	−9.40723	+	28.9525i	−0.319855	+	0.984414i
$866$	14.9312	+	45.9535i	0.507383	+	1.56156i
$867$	24.2948			0.825094
$868$	−22.0240	−	8.19273i	−0.747544	−	0.278080i
$869$	26.9034			0.912634
$870$	−30.2430	−	93.0784i	−1.02533	−	3.15565i
$871$	3.26140	−	10.0376i	0.110508	−	0.340110i
$872$	−14.3292	+	10.4108i	−0.485248	+	0.352553i
$873$	−7.73216			−0.261694
$874$	−15.4348			−0.522091
$875$	19.9027	−	14.4601i	0.672834	−	0.488842i
$876$	−61.6940	−	44.8233i	−2.08445	−	1.51444i
$877$	−3.66850	−	2.66532i	−0.123876	−	0.0900015i	0.524122	−	0.851643i	$-0.324394\pi$
$877$	−3.66850	−	2.66532i	−0.123876	−	0.0900015i	−0.647998	+	0.761642i	$0.724394\pi$
$878$	8.00523	+	24.6376i	0.270163	+	0.831477i
$879$	−5.98801	+	4.35055i	−0.201971	+	0.146740i
$880$	1.30717	+	4.02305i	0.0440647	+	0.135617i
$881$	−0.409295	+	1.25968i	−0.0137895	+	0.0424397i	−0.957715	−	0.287720i	$-0.907103\pi$
$881$	−0.409295	+	1.25968i	−0.0137895	+	0.0424397i	0.943925	+	0.330160i	$0.107103\pi$
$882$	−20.8752	−	15.1667i	−0.702904	−	0.510689i
$883$	7.51315	−	23.1231i	0.252838	−	0.778155i	−0.741410	−	0.671052i	$-0.765843\pi$
$883$	7.51315	−	23.1231i	0.252838	−	0.778155i	0.994248	−	0.107102i	$-0.0341573\pi$
$884$	5.52207	−	16.9952i	0.185727	−	0.571610i
$885$	−49.6021	−	36.0380i	−1.66736	−	1.21141i
$886$	15.2939	−	47.0699i	0.513810	−	1.58135i
$887$	−6.27750	−	19.3202i	−0.210778	−	0.648707i	−0.999426	−	0.0338632i	$-0.989219\pi$
$887$	−6.27750	−	19.3202i	−0.210778	−	0.648707i	0.788649	−	0.614844i	$-0.210781\pi$
$888$	5.77818	−	4.19810i	0.193903	−	0.140879i
$889$	4.35293	+	13.3969i	0.145993	+	0.449319i
$890$	81.3280	+	59.0882i	2.72612	+	1.98064i
$891$	13.7525	+	9.99180i	0.460727	+	0.334738i
$892$	62.6118	−	45.4902i	2.09640	−	1.52312i
$893$	−3.53469			−0.118284
$894$	53.6686			1.79495
$895$	−28.5127	+	20.7157i	−0.953075	+	0.692450i
$896$	−7.53242	+	23.1824i	−0.251640	+	0.774470i
$897$	3.88002	+	11.9415i	0.129550	+	0.398715i
$898$	30.4963			1.01768
$899$	−25.9313	+	7.23783i	−0.864856	+	0.241395i
$900$	69.7117			2.32372
$901$	−22.6298	−	69.6475i	−0.753910	−	2.32030i
$902$	0.200793	−	0.617978i	0.00668569	−	0.0205764i
$903$	8.80560	−	6.39764i	0.293032	−	0.212900i
$904$	35.9585			1.19596
$905$	94.8059			3.15145
$906$	−22.3799	+	16.2600i	−0.743524	+	0.540202i
$907$	8.78659	+	6.38383i	0.291754	+	0.211972i	0.724028	−	0.689771i	$-0.242289\pi$
$907$	8.78659	+	6.38383i	0.291754	+	0.211972i	−0.432274	+	0.901742i	$0.642289\pi$
$908$	61.2119	+	44.4730i	2.03139	+	1.47589i
$909$	−12.6447	−	38.9163i	−0.419397	−	1.29077i
$910$	−9.08579	+	6.60121i	−0.301191	+	0.218828i
$911$	17.5305	+	53.9534i	0.580812	+	1.78756i	0.615474	+	0.788158i	$0.288965\pi$
$911$	17.5305	+	53.9534i	0.580812	+	1.78756i	−0.0346612	+	0.999399i	$0.511035\pi$
$912$	0.579128	−	1.78237i	0.0191769	−	0.0590203i
$913$	18.7521	+	13.6242i	0.620603	+	0.450894i
$914$	−8.10894	+	24.9567i	−0.268220	+	0.825496i
$915$	9.66773	−	29.7542i	0.319605	−	0.983644i
$916$	57.7875	+	41.9851i	1.90935	+	1.38723i
$917$	2.63956	−	8.12372i	0.0871659	−	0.268269i
$918$	8.15087	+	25.0858i	0.269019	+	0.827955i
$919$	0.427874	−	0.310869i	0.0141143	−	0.0102546i	−0.580706	−	0.814114i	$-0.697223\pi$
$919$	0.427874	−	0.310869i	0.0141143	−	0.0102546i	0.594820	+	0.803859i	$0.297223\pi$
$920$	−21.6241	−	66.5522i	−0.712926	−	2.19416i
$921$	55.7303	+	40.4904i	1.83637	+	1.33420i
$922$	23.6967	+	17.2167i	0.780411	+	0.567001i
$923$	−3.54159	+	2.57311i	−0.116573	+	0.0846951i
$924$	−14.6990			−0.483560
$925$	9.95845			0.327432
$926$	16.2352	−	11.7955i	0.533520	−	0.387625i
$927$	2.43457	−	7.49284i	0.0799618	−	0.246097i
$928$	7.19245	+	22.1361i	0.236104	+	0.726652i
$929$	−7.72931			−0.253590			−0.126795	−	0.991929i	$-0.540469\pi$
$929$	−7.72931			−0.253590			−0.126795	+	0.991929i	$0.540469\pi$
$930$	4.72833	−	112.592i	0.155048	−	3.69204i
$931$	−6.47769			−0.212298
$932$	21.6915	+	66.7595i	0.710528	+	2.18678i
$933$	3.89306	−	11.9816i	0.127453	−	0.392260i
$934$	80.6936	−	58.6273i	2.64038	−	1.91835i
$935$	31.7798			1.03931
$936$	−6.57331			−0.214855
$937$	22.6513	−	16.4571i	0.739986	−	0.537631i	−0.152721	−	0.988269i	$-0.548804\pi$
$937$	22.6513	−	16.4571i	0.739986	−	0.537631i	0.892707	+	0.450638i	$0.148804\pi$
$938$	−24.6898	−	17.9382i	−0.806150	−	0.585702i
$939$	−23.0121	−	16.7193i	−0.750972	−	0.545613i
$940$	−12.0881	−	37.2035i	−0.394272	−	1.21344i
$941$	−21.7069	+	15.7710i	−0.707626	+	0.514120i	−0.882407	−	0.470487i	$-0.844078\pi$
$941$	−21.7069	+	15.7710i	−0.707626	+	0.514120i	0.174781	+	0.984607i	$0.444078\pi$
$942$	−22.7927	−	70.1487i	−0.742626	−	2.28557i
$943$	−0.311863	+	0.959816i	−0.0101557	+	0.0312559i
$944$	−3.99381	−	2.90167i	−0.129987	−	0.0944414i
$945$	3.22107	−	9.91344i	0.104781	−	0.322484i
$946$	−4.33040	+	13.3276i	−0.140794	+	0.433318i
$947$	−6.21184	−	4.51317i	−0.201858	−	0.146658i	0.482264	−	0.876026i	$-0.339814\pi$
$947$	−6.21184	−	4.51317i	−0.201858	−	0.146658i	−0.684122	+	0.729368i	$0.739814\pi$
$948$	40.7622	−	125.453i	1.32389	−	4.07453i
$949$	3.09816	+	9.53516i	0.100571	+	0.309524i
$950$	22.5164	−	16.3592i	0.730530	−	0.530761i
$951$	8.23748	+	25.3524i	0.267119	+	0.822107i
$952$	−17.1255	−	12.4424i	−0.555041	−	0.403261i
$953$	−12.0154	−	8.72972i	−0.389218	−	0.282783i	0.375917	−	0.926653i	$-0.377328\pi$
$953$	−12.0154	−	8.72972i	−0.389218	−	0.282783i	−0.765135	+	0.643870i	$0.777328\pi$
$954$	−53.1977	+	38.6504i	−1.72234	+	1.25135i
$955$	35.3497			1.14389
$956$	1.24048			0.0401200
$957$	−13.6244	+	9.89873i	−0.440415	+	0.319980i
$958$	−25.5334	+	78.5837i	−0.824946	+	2.53892i
$959$	−3.69205	−	11.3630i	−0.119222	−	0.366929i
$960$	−109.669			−3.53955
$961$	−30.8908	−	2.59912i	−0.996479	−	0.0838427i
$962$	−2.29215			−0.0739017
$963$	1.13509	+	3.49346i	0.0365778	+	0.112575i
$964$	−23.1619	+	71.2851i	−0.745996	+	2.29594i
$965$	−78.0500	+	56.7067i	−2.51252	+	1.82545i
$966$	36.3070			1.16816
$967$	20.1829			0.649039			0.324520	−	0.945879i	$-0.394797\pi$
$967$	20.1829			0.649039			0.324520	+	0.945879i	$0.394797\pi$
$968$	−22.3973	+	16.2726i	−0.719876	+	0.523021i
$969$	−11.3907	−	8.27585i	−0.365923	−	0.265859i
$970$	−27.6389	−	20.0808i	−0.887431	−	0.644756i
$971$	16.4865	+	50.7404i	0.529078	+	1.62834i	0.756107	+	0.654448i	$0.227099\pi$
$971$	16.4865	+	50.7404i	0.529078	+	1.62834i	−0.227028	+	0.973888i	$0.572901\pi$
$972$	49.7150	−	36.1201i	1.59461	−	1.15855i
$973$	0.202823	+	0.624226i	0.00650222	+	0.0200118i
$974$	2.87752	−	8.85609i	0.0922017	−	0.283768i
$975$	−18.3168	−	13.3079i	−0.586607	−	0.426195i
$976$	0.778417	−	2.39572i	0.0249165	−	0.0766851i
$977$	15.2263	−	46.8616i	0.487131	−	1.49923i	−0.341740	−	0.939795i	$-0.611016\pi$
$977$	15.2263	−	46.8616i	0.487131	−	1.49923i	0.828871	−	0.559440i	$-0.188984\pi$
$978$	49.0509	+	35.6376i	1.56848	+	1.13956i
$979$	5.34543	−	16.4515i	0.170841	−	0.525793i
$980$	−22.1528	−	68.1792i	−0.707644	−	2.17790i
$981$	9.07544	−	6.59370i	0.289757	−	0.210521i
$982$	3.94800	+	12.1507i	0.125986	+	0.387744i
$983$	−4.21456	−	3.06206i	−0.134423	−	0.0976644i	0.518542	−	0.855052i	$-0.326475\pi$
$983$	−4.21456	−	3.06206i	−0.134423	−	0.0976644i	−0.652965	+	0.757388i	$0.726475\pi$
$984$	−1.05590	−	0.767153i	−0.0336607	−	0.0244560i
$985$	24.0767	−	17.4928i	0.767148	−	0.557366i
$986$	−59.2014			−1.88536
$987$	8.31456			0.264655
$988$	−3.25883	+	2.36768i	−0.103677	+	0.0753258i
$989$	6.72578	−	20.6998i	0.213867	−	0.658216i
$990$	−8.81799	−	27.1390i	−0.280254	−	0.862534i
$991$	−27.3511			−0.868836			−0.434418	−	0.900711i	$-0.643046\pi$
$991$	−27.3511			−0.868836			−0.434418	+	0.900711i	$0.643046\pi$
$992$	−1.12450	+	26.7768i	−0.0357029	+	0.850165i
$993$	45.5317			1.44490
$994$	3.91165	+	12.0388i	0.124070	+	0.381849i
$995$	−28.0397	+	86.2972i	−0.888917	+	2.73581i
$996$	91.9428	−	66.8003i	2.91332	−	2.11665i
$997$	42.8236			1.35624			0.678119	−	0.734952i	$-0.262795\pi$
$997$	42.8236			1.35624			0.678119	+	0.734952i	$0.262795\pi$
$998$	43.9892			1.39245
$999$	1.72113	−	1.25047i	0.0544540	−	0.0395632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.66.2	✓	68
31.8	even	5	inner	403.2.k.e.287.2	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.2	✓	68	1.1	even	1	trivial
403.2.k.e.287.2	yes	68	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.717286 - 2.20758i) q^{2} +(0.693769 - 2.13520i) q^{3} +(-2.74087 + 1.99136i) q^{4} +3.88389 q^{5} -5.21126 q^{6} +(1.00783 - 0.732228i) q^{7} +(2.60631 + 1.89360i) q^{8} +(-1.65072 - 1.19932i) q^{9} +O(q^{10})\)	\(q+(-0.717286 - 2.20758i) q^{2} +(0.693769 - 2.13520i) q^{3} +(-2.74087 + 1.99136i) q^{4} +3.88389 q^{5} -5.21126 q^{6} +(1.00783 - 0.732228i) q^{7} +(2.60631 + 1.89360i) q^{8} +(-1.65072 - 1.19932i) q^{9} +(-2.78586 - 8.57400i) q^{10} +(-1.25503 + 0.911830i) q^{11} +(2.35042 + 7.23385i) q^{12} +(0.309017 - 0.951057i) q^{13} +(-2.33935 - 1.69964i) q^{14} +(2.69452 - 8.29289i) q^{15} +(0.216955 - 0.667719i) q^{16} +(-4.26724 - 3.10033i) q^{17} +(-1.46355 + 4.50434i) q^{18} +(0.367413 + 1.13078i) q^{19} +(-10.6453 + 7.73423i) q^{20} +(-0.864257 - 2.65991i) q^{21} +(2.91315 + 2.11653i) q^{22} +(-4.52457 - 3.28729i) q^{23} +(5.85139 - 4.25128i) q^{24} +10.0846 q^{25} -2.32119 q^{26} +(1.74293 - 1.26631i) q^{27} +(-1.30419 + 4.01389i) q^{28} +(1.49422 + 4.59875i) q^{29} -20.2400 q^{30} +(-0.233614 + 5.56286i) q^{31} +4.81350 q^{32} +(1.07624 + 3.31233i) q^{33} +(-3.78339 + 11.6441i) q^{34} +(3.91429 - 2.84390i) q^{35} +6.91268 q^{36} +0.987489 q^{37} +(2.23275 - 1.62219i) q^{38} +(-1.81631 - 1.31963i) q^{39} +(10.1226 + 7.35453i) q^{40} +(-0.0557628 - 0.171620i) q^{41} +(-5.25204 + 3.81583i) q^{42} +(1.20261 + 3.70124i) q^{43} +(1.62408 - 4.99841i) q^{44} +(-6.41121 - 4.65802i) q^{45} +(-4.01155 + 12.3463i) q^{46} +(-0.918674 + 2.82739i) q^{47} +(-1.27520 - 0.926485i) q^{48} +(-1.68356 + 5.18148i) q^{49} +(-7.23356 - 22.2626i) q^{50} +(-9.58030 + 6.96049i) q^{51} +(1.04692 + 3.22209i) q^{52} +(11.2323 + 8.16073i) q^{53} +(-4.04567 - 2.93935i) q^{54} +(-4.87439 + 3.54145i) q^{55} +4.01326 q^{56} +2.66935 q^{57} +(9.08031 - 6.59723i) q^{58} +(2.17283 - 6.68727i) q^{59} +(9.12879 + 28.0955i) q^{60} +3.58792 q^{61} +(12.4480 - 3.47444i) q^{62} -2.54181 q^{63} +(-3.88657 - 11.9616i) q^{64} +(1.20019 - 3.69380i) q^{65} +(6.54026 - 4.75178i) q^{66} +10.5541 q^{67} +17.8698 q^{68} +(-10.1580 + 7.38024i) q^{69} +(-9.08579 - 6.60121i) q^{70} +(-3.54159 - 2.57311i) q^{71} +(-2.03127 - 6.25159i) q^{72} +(-8.11109 + 5.89305i) q^{73} +(-0.708312 - 2.17996i) q^{74} +(6.99640 - 21.5327i) q^{75} +(-3.25883 - 2.36768i) q^{76} +(-0.597180 + 1.83793i) q^{77} +(-1.61037 + 4.95620i) q^{78} +(-14.0304 - 10.1937i) q^{79} +(0.842630 - 2.59335i) q^{80} +(-3.38620 - 10.4216i) q^{81} +(-0.338867 + 0.246201i) q^{82} +(-4.61720 - 14.2103i) q^{83} +(7.66565 + 5.56942i) q^{84} +(-16.5735 - 12.0413i) q^{85} +(7.30817 - 5.30969i) q^{86} +10.8559 q^{87} -4.99763 q^{88} +(-9.02117 + 6.55426i) q^{89} +(-5.68427 + 17.4944i) q^{90} +(-0.384955 - 1.18477i) q^{91} +18.9474 q^{92} +(11.7158 + 4.35815i) q^{93} +6.90063 q^{94} +(1.42699 + 4.39184i) q^{95} +(3.33946 - 10.2778i) q^{96} +(3.06580 - 2.22743i) q^{97} +12.6461 q^{98} +3.16527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more