LMFDB - Embedded newform 403.2.k.e.287.2

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			287.2
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.2

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	0.289847	+	0.957073i	$0.406396\pi$
$2$	−0.717286	+	2.20758i	−0.507198	+	1.56099i	−0.797044	+	0.603921i	$0.793604\pi$
$3$	0.693769	+	2.13520i	0.400548	+	1.23276i	0.924556	+	0.381046i	$0.124436\pi$
$3$	0.693769	+	2.13520i	0.400548	+	1.23276i	−0.524008	+	0.851713i	$0.675564\pi$
$4$	−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	0.761726	−	0.647900i	$-0.224352\pi$
$7$	1.00783	+	0.732228i	0.380922	+	0.276756i	−0.380803	+	0.924656i	$0.624352\pi$
$8$	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	0.382283	−	0.924045i	$-0.375138\pi$
$11$	−1.25503	−	0.911830i	−0.378405	−	0.274927i	−0.760687	+	0.649118i	$0.775138\pi$
$12$	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	−0.969295	−	0.245902i	$-0.920916\pi$
$17$	−4.26724	+	3.10033i	−1.03496	+	0.751940i	−0.0656619	+	0.997842i	$0.520916\pi$
$18$	−1.46355	−	4.50434i	−0.344962	−	1.06168i
$19$	0.367413	−	1.13078i	0.0842904	−	0.259419i	−0.900025	−	0.435839i	$-0.856452\pi$
$19$	0.367413	−	1.13078i	0.0842904	−	0.259419i	0.984315	+	0.176420i	$0.0564517\pi$
$20$	−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	−0.949246	−	0.314535i	$-0.898151\pi$
$23$	−4.52457	+	3.28729i	−0.943438	+	0.685448i	0.00580789	+	0.999983i	$0.498151\pi$
$24$	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	−0.711085	−	0.703106i	$-0.751796\pi$
$29$	1.49422	−	4.59875i	0.277470	−	0.853966i	0.988555	−	0.150860i	$-0.0482042\pi$
$30$	−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	−0.955316	−	0.295585i	$-0.904485\pi$
$41$	−0.0557628	+	0.171620i	−0.00870868	+	0.0268026i	0.946608	+	0.322388i	$0.104485\pi$
$42$	−5.25204	−	3.81583i	−0.810407	−	0.588795i
$43$	1.20261	−	3.70124i	0.183396	−	0.564434i	−0.816521	−	0.577315i	$-0.804100\pi$
$43$	1.20261	−	3.70124i	0.183396	−	0.564434i	0.999917	+	0.0128813i	$0.00410037\pi$
$44$	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	0.861431	−	0.507874i	$-0.169569\pi$
$47$	−0.918674	−	2.82739i	−0.134002	−	0.412417i	−0.995433	+	0.0954576i	$0.969569\pi$
$48$	−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	0.594371	−	0.804191i	$-0.297401\pi$
$53$	11.2323	−	8.16073i	1.54287	−	1.12096i	0.948502	−	0.316771i	$-0.102599\pi$
$54$	−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	0.987027	+	0.160556i	$0.0513288\pi$
$59$	2.17283	+	6.68727i	0.282878	+	0.870609i	−0.704149	+	0.710052i	$0.748671\pi$
$60$	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	−0.777762	−	0.628559i	$-0.783645\pi$
$71$	−3.54159	+	2.57311i	−0.420309	+	0.305372i	0.357453	+	0.933931i	$0.383645\pi$
$72$	−2.03127	+	6.25159i	−0.239387	+	0.736757i
$73$	−8.11109	−	5.89305i	−0.949332	−	0.689730i	0.00131695	−	0.999999i	$-0.499581\pi$
$73$	−8.11109	−	5.89305i	−0.949332	−	0.689730i	−0.950649	+	0.310269i	$0.899581\pi$
$74$	−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	−0.660196	+	0.751093i	$0.729527\pi$
$79$	−14.0304	+	10.1937i	−1.57854	+	1.14688i	−0.918344	+	0.395783i	$0.870473\pi$
$80$	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	0.290913	+	0.956749i	$0.406041\pi$
$83$	−4.61720	+	14.2103i	−0.506804	+	1.55978i	−0.797717	+	0.603032i	$0.793959\pi$
$84$	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	−0.00396707	−	0.999992i	$-0.501263\pi$
$89$	−9.02117	−	6.55426i	−0.956242	−	0.694750i	−0.952275	+	0.305242i	$0.901263\pi$
$90$	−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	0.732447	−	0.680824i	$-0.238378\pi$
$97$	3.06580	+	2.22743i	0.311284	+	0.226161i	−0.421163	+	0.906985i	$0.638378\pi$
$98$	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	0.767736	−	0.640766i	$-0.221383\pi$
$101$	16.2244	−	11.7877i	1.61438	−	1.17292i	0.846649	−	0.532153i	$-0.178617\pi$
$102$	22.2377	−	16.1566i	2.20186	−	1.59974i
$103$	1.19318	−	3.67224i	0.117568	−	0.361836i	−0.874906	−	0.484293i	$-0.839077\pi$
$103$	1.19318	−	3.67224i	0.117568	−	0.361836i	0.992474	+	0.122456i	$0.0390771\pi$
$104$	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	−0.655955	−	0.754800i	$-0.727734\pi$
$107$	−1.45644	+	1.05816i	−0.140799	+	0.102296i	0.515156	+	0.857096i	$0.327734\pi$
$108$	−2.25547	−	6.94161i	−0.217032	−	0.667957i
$109$	−1.69894	−	5.22879i	−0.162729	−	0.500827i	0.836133	−	0.548527i	$-0.184811\pi$
$109$	−1.69894	−	5.22879i	−0.162729	−	0.500827i	−0.998862	+	0.0476993i	$0.984811\pi$
$110$	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	0.925002	−	0.379963i	$-0.124063\pi$
$113$	9.03005	+	6.56072i	0.849476	+	0.617180i	−0.0755255	+	0.997144i	$0.524063\pi$
$114$	−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	−0.977739	−	0.209827i	$-0.932710\pi$
$127$	−3.49425	−	10.7542i	−0.310065	−	0.954281i	0.667674	−	0.744454i	$-0.267290\pi$
$128$	−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	0.803129	−	0.595805i	$-0.203167\pi$
$131$	5.54726	+	4.03032i	0.484666	+	0.352131i	−0.318463	+	0.947935i	$0.603167\pi$
$132$	−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	0.994177	+	0.107757i	$0.0343669\pi$
$137$	2.96374	+	9.12144i	0.253209	+	0.779297i	−0.740968	+	0.671540i	$0.765633\pi$
$138$	23.5787	−	17.1309i	2.00715	−	1.45828i
$139$	−0.162813	−	0.501088i	−0.0138096	−	0.0425017i	0.943914	−	0.330191i	$-0.107113\pi$
$139$	−0.162813	−	0.501088i	−0.0138096	−	0.0425017i	−0.957724	+	0.287689i	$0.907113\pi$
$140$	−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	0.748653	−	0.662962i	$-0.230701\pi$
$151$	4.29454	+	3.12016i	0.349485	+	0.253915i	−0.399168	+	0.916878i	$0.630701\pi$
$152$	−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	−0.610310	−	0.792162i	$-0.708955\pi$
$157$	4.37374	−	13.4610i	0.349062	−	1.07430i	0.959373	−	0.282141i	$-0.0910447\pi$
$158$	−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	−0.891847	−	0.452338i	$-0.850590\pi$
$163$	−9.41250	+	6.83858i	−0.737244	+	0.535639i	0.154603	+	0.987977i	$0.450590\pi$
$164$	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	0.590331	+	0.807161i	$0.298997\pi$
$167$	−4.67412	+	14.3855i	−0.361694	+	1.11318i	−0.952025	+	0.306020i	$0.901003\pi$
$168$	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	0.815783	−	0.578358i	$-0.196306\pi$
$173$	−2.42211	−	7.45450i	−0.184150	−	0.566755i	−0.999933	+	0.0116033i	$0.996306\pi$
$174$	−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	0.278598	−	0.960408i	$-0.410130\pi$
$179$	−7.34127	−	5.33375i	−0.548713	−	0.398663i	−0.827311	+	0.561745i	$0.810130\pi$
$180$	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	−0.986627	−	0.162995i	$-0.947884\pi$
$193$	−20.0958	−	14.6005i	−1.44653	−	1.05096i	−0.459902	−	0.887970i	$-0.652116\pi$
$194$	−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	0.786298	−	0.617848i	$-0.211995\pi$
$197$	6.19912	+	4.50393i	0.441669	+	0.320891i	−0.344629	+	0.938739i	$0.611995\pi$
$198$	−2.27040	+	6.98757i	−0.161350	+	0.496585i
$199$	−7.21947	−	22.2193i	−0.511775	−	1.57508i	−0.789074	−	0.614298i	$-0.789439\pi$
$199$	−7.21947	−	22.2193i	−0.511775	−	1.57508i	0.277299	−	0.960784i	$-0.410561\pi$
$200$	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	0.409458	+	0.912329i	$0.365718\pi$
$227$	−6.90128	+	21.2399i	−0.458054	+	1.40974i	−0.867512	+	0.497416i	$0.834282\pi$
$228$	−7.31634	−	5.31563i	−0.484536	−	0.352036i
$229$	−6.51520	+	20.0517i	−0.430536	+	1.32505i	0.467056	+	0.884228i	$0.345315\pi$
$229$	−6.51520	+	20.0517i	−0.430536	+	1.32505i	−0.897592	+	0.440827i	$0.854685\pi$
$230$	−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	0.908210	+	0.418516i	$0.137449\pi$
$233$	6.40262	+	19.7053i	0.419450	+	1.29093i	−0.488760	+	0.872418i	$0.662551\pi$
$234$	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	−0.597325	−	0.802000i	$-0.703770\pi$
$239$	−0.296222	+	0.215218i	−0.0191610	+	0.0139213i	0.578164	+	0.815921i	$0.303770\pi$
$240$	−4.95273	+	3.59837i	−0.319697	+	0.232274i
$241$	17.8986	+	13.0041i	1.15295	+	0.837668i	0.988870	−	0.148779i	$-0.0475343\pi$
$241$	17.8986	+	13.0041i	1.15295	+	0.837668i	0.164080	+	0.986447i	$0.447534\pi$
$242$	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	0.926830	−	0.375482i	$-0.122523\pi$
$251$	−0.692247	−	2.13052i	−0.0436942	−	0.134477i	−0.970524	+	0.241005i	$0.922523\pi$
$252$	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	−0.789937	−	0.613188i	$-0.789887\pi$
$257$	−7.22790	+	5.25138i	−0.450864	+	0.327572i	0.339073	+	0.940760i	$0.389887\pi$
$258$	−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	0.850023	−	0.526746i	$-0.176588\pi$
$263$	−2.38837	−	7.35066i	−0.147273	−	0.453261i	−0.997296	+	0.0734847i	$0.976588\pi$
$264$	−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	−0.886197	−	0.463308i	$-0.846662\pi$
$269$	1.69059	−	5.20309i	0.103077	−	0.317238i	0.989274	+	0.146070i	$0.0466625\pi$
$270$	−15.7129	+	11.4161i	−0.956259	+	0.694763i
$271$	0.487400	−	0.354117i	0.0296074	−	0.0215111i	−0.572883	−	0.819637i	$-0.694175\pi$
$271$	0.487400	−	0.354117i	0.0296074	−	0.0215111i	0.602491	+	0.798126i	$0.294175\pi$
$272$	−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	0.595964	+	0.803011i	$0.296770\pi$
$277$	−5.96129	+	18.3470i	−0.358179	+	1.10236i	−0.954143	+	0.299351i	$0.903230\pi$
$278$	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	−0.972899	−	0.231229i	$-0.925725\pi$
$281$	−0.836384	+	2.57412i	−0.0498945	+	0.153559i	0.923005	+	0.384788i	$0.125725\pi$
$282$	4.78744	+	14.7342i	0.285088	+	0.877411i
$283$	16.8187	+	12.2195i	0.999767	+	0.726374i	0.962038	−	0.272914i	$-0.0879876\pi$
$283$	16.8187	+	12.2195i	0.999767	+	0.726374i	0.0377292	+	0.999288i	$0.487988\pi$
$284$	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	−0.662962	−	0.748653i	$-0.730701\pi$
$293$	−2.66717	+	1.93781i	−0.155818	+	0.113208i	0.507145	+	0.861861i	$0.330701\pi$
$294$	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	−0.729982	−	0.683466i	$-0.760472\pi$
$307$	−9.48164	−	29.1815i	−0.541146	−	1.66547i	0.188837	−	0.982009i	$-0.439528\pi$
$308$	−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	0.998646	+	0.0520140i	$0.0165640\pi$
$313$	3.91515	+	12.0496i	0.221298	+	0.681084i	−0.777349	+	0.629070i	$0.783436\pi$
$314$	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	0.284387	−	0.958710i	$-0.408210\pi$
$317$	−9.60588	−	6.97908i	−0.539520	−	0.391984i	−0.823907	+	0.566725i	$0.808210\pi$
$318$	−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	−0.617399	−	0.786650i	$-0.711814\pi$
$331$	6.26706	−	19.2880i	0.344469	−	1.06017i	0.961868	−	0.273515i	$-0.0881863\pi$
$332$	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	−0.302937	−	0.953010i	$-0.597967\pi$
$337$	−23.9184	−	17.3777i	−1.30292	−	0.946625i	−0.999980	+	0.00638593i	$0.997967\pi$
$338$	−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	−0.118139	−	0.992997i	$-0.537693\pi$
$349$	14.7537	−	10.7192i	0.789750	−	0.573787i	0.907889	+	0.419210i	$0.137693\pi$
$350$	−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	−0.719078	−	0.694930i	$-0.755436\pi$
$353$	5.09422	−	15.6784i	0.271138	−	0.834476i	0.990216	−	0.139547i	$-0.0445645\pi$
$354$	−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	0.872502	+	0.488611i	$0.162496\pi$
$359$	8.59887	+	26.4646i	0.453831	+	1.39675i	−0.418671	+	0.908138i	$0.637504\pi$
$360$	−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	−0.960923	−	0.276814i	$-0.910721\pi$
$379$	−29.6133	−	21.5153i	−1.52113	−	1.10517i	−0.560208	−	0.828352i	$-0.689279\pi$
$380$	−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	0.376316	−	0.926491i	$-0.377191\pi$
$383$	−7.60391	−	5.52456i	−0.388542	−	0.282292i	−0.764858	+	0.644199i	$0.777191\pi$
$384$	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	−0.910946	−	0.412527i	$-0.864646\pi$
$389$	−15.7806	+	11.4653i	−0.800107	+	0.581312i	0.110839	+	0.993838i	$0.464646\pi$
$390$	−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	−0.954385	−	0.298579i	$-0.903487\pi$
$401$	−0.135585	+	0.417287i	−0.00677079	+	0.0208383i	0.947614	+	0.319418i	$0.103487\pi$
$402$	−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	0.980270	−	0.197663i	$-0.0633351\pi$
$419$	1.45398	+	4.47490i	0.0710317	+	0.218613i	−0.909238	+	0.416276i	$0.863335\pi$
$420$	29.7726	−	21.6310i	1.45275	−	1.05549i
$421$	2.21740	+	6.82446i	0.108070	+	0.332604i	0.990439	−	0.137954i	$-0.0440526\pi$
$421$	2.21740	+	6.82446i	0.108070	+	0.332604i	−0.882369	+	0.470558i	$0.844053\pi$
$422$	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	0.872890	+	0.487918i	$0.162243\pi$
$431$	9.41486	+	28.9760i	0.453498	+	1.39572i	−0.419392	+	0.907805i	$0.637757\pi$
$432$	−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	−0.0970232	−	0.995282i	$-0.530932\pi$
$443$	17.2498	−	12.5327i	0.819565	−	0.595448i	0.916588	+	0.399834i	$0.130932\pi$
$444$	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	−0.999999	−	0.00105082i	$-0.999666\pi$
$449$	−4.05994	−	12.4952i	−0.191601	−	0.589686i	0.808399	−	0.588635i	$-0.200334\pi$
$450$	−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	−0.780781	−	0.624805i	$-0.785178\pi$
$457$	−9.14596	+	6.64493i	−0.427830	+	0.310837i	0.352951	+	0.935642i	$0.385178\pi$
$458$	−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	0.324096	−	0.946024i	$-0.394940\pi$
$461$	−10.2089	−	7.41720i	−0.475476	−	0.345453i	−0.799571	+	0.600571i	$0.794940\pi$
$462$	3.11206	+	9.57793i	0.144786	+	0.445606i
$463$	2.67160	−	8.22234i	0.124160	−	0.382124i	−0.869587	−	0.493779i	$-0.835615\pi$
$463$	2.67160	−	8.22234i	0.124160	−	0.382124i	0.993747	+	0.111655i	$0.0356151\pi$
$464$	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	0.205138	−	0.978733i	$-0.434236\pi$
$467$	13.2787	−	40.8675i	0.614463	−	1.89112i	0.409325	−	0.912389i	$-0.365764\pi$
$468$	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	−0.315875	+	0.948801i	$0.602298\pi$
$479$	−28.7988	+	20.9235i	−1.31585	+	0.956020i	−0.999974	+	0.00721931i	$0.997702\pi$
$480$	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	−0.511818	−	0.859094i	$-0.671028\pi$
$487$	3.24552	−	2.35801i	0.147068	−	0.106851i	0.658886	+	0.752242i	$0.271028\pi$
$488$	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	−0.992334	−	0.123586i	$-0.960561\pi$
$499$	−5.85623	−	18.0236i	−0.262161	−	0.806848i	0.730173	−	0.683262i	$-0.239439\pi$
$500$	−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	0.809964	−	0.586480i	$-0.199487\pi$
$503$	11.2695	+	8.18775i	0.502481	+	0.365074i	−0.307483	+	0.951554i	$0.599487\pi$
$504$	−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	0.942693	−	0.333662i	$-0.108285\pi$
$509$	−0.362860	−	1.11677i	−0.0160835	−	0.0494999i	−0.958776	+	0.284162i	$0.908285\pi$
$510$	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	0.783258	−	0.621697i	$-0.213557\pi$
$523$	9.92588	+	7.21157i	0.434028	+	0.315340i	−0.349229	+	0.937037i	$0.613557\pi$
$524$	−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	−0.955758	−	0.294153i	$-0.904963\pi$
$541$	−22.5930	+	16.4148i	−0.971348	+	0.705726i	−0.0155896	+	0.999878i	$0.504963\pi$
$542$	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	0.663914	−	0.747809i	$-0.268894\pi$
$547$	3.69217	+	2.68252i	0.157866	+	0.114696i	−0.506048	+	0.862505i	$0.668894\pi$
$548$	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	0.857516	−	0.514457i	$-0.172006\pi$
$569$	15.1048	+	10.9743i	0.633226	+	0.460065i	−0.224291	+	0.974522i	$0.572006\pi$
$570$	−7.43643	+	22.8870i	−0.311478	+	0.958630i
$571$	3.23810	+	9.96583i	0.135510	+	0.417057i	0.995669	−	0.0929690i	$-0.0296357\pi$
$571$	3.23810	+	9.96583i	0.135510	+	0.417057i	−0.860159	+	0.510026i	$0.829636\pi$
$572$	−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	−0.432451	−	0.901657i	$-0.642351\pi$
$577$	10.7467	−	33.0749i	0.447390	−	1.37693i	0.879841	−	0.475268i	$-0.157649\pi$
$578$	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	−0.973323	−	0.229441i	$-0.926310\pi$
$587$	−1.23627	+	3.80485i	−0.0510263	+	0.157043i	0.922296	+	0.386483i	$0.126310\pi$
$588$	−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	−0.0977419	−	0.995212i	$-0.531162\pi$
$593$	−26.1645	−	19.0096i	−1.07445	−	0.780633i	−0.976707	+	0.214579i	$0.931162\pi$
$594$	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	−0.660574	−	0.750761i	$-0.729687\pi$
$599$	7.71260	−	23.7369i	0.315128	−	0.969865i	0.975702	−	0.219103i	$-0.0703132\pi$
$600$	59.0091	+	42.8726i	2.40904	+	1.75027i
$601$	−5.22269	+	16.0738i	−0.213038	+	0.655663i	0.786249	+	0.617909i	$0.212020\pi$
$601$	−5.22269	+	16.0738i	−0.213038	+	0.655663i	−0.999287	+	0.0377535i	$0.987980\pi$
$602$	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	0.994199	−	0.107554i	$-0.0343020\pi$
$607$	3.12048	+	9.60384i	0.126656	+	0.389808i	−0.867543	+	0.497362i	$0.834302\pi$
$608$	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	0.654692	−	0.755896i	$-0.272798\pi$
$613$	3.41928	+	2.48425i	0.138104	+	0.100338i	−0.516589	+	0.856234i	$0.672798\pi$
$614$	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	0.845698	−	0.533662i	$-0.179184\pi$
$617$	−3.77969	−	11.6327i	−0.152165	−	0.468314i	−0.997863	+	0.0653474i	$0.979184\pi$
$618$	−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	0.982470	−	0.186422i	$-0.0596893\pi$
$631$	27.8520	+	20.2357i	1.10877	+	0.805570i	0.126302	+	0.991992i	$0.459689\pi$
$632$	−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	−0.968036	−	0.250812i	$-0.919302\pi$
$641$	−0.948276	+	2.91849i	−0.0374546	+	0.115274i	0.930581	+	0.366086i	$0.119302\pi$
$642$	7.58986	−	5.51435i	0.299548	−	0.217634i
$643$	−32.8291	+	23.8518i	−1.29465	+	0.940622i	−0.999888	−	0.0149478i	$-0.995242\pi$
$643$	−32.8291	+	23.8518i	−1.29465	+	0.940622i	−0.294766	+	0.955569i	$0.595242\pi$
$644$	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	0.564644	−	0.825334i	$-0.309013\pi$
$647$	−1.16525	−	0.846601i	−0.0458106	−	0.0332833i	−0.610455	+	0.792051i	$0.709013\pi$
$648$	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	0.286545	+	0.958067i	$0.407493\pi$
$653$	−12.9919	+	39.9850i	−0.508412	+	1.56473i	−0.794957	+	0.606666i	$0.792507\pi$
$654$	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	0.263518	−	0.964654i	$-0.415117\pi$
$659$	32.4068	−	23.5449i	1.26239	−	0.917181i	0.998872	+	0.0474737i	$0.0151170\pi$
$660$	−37.0752	+	26.9367i	−1.44315	+	1.04851i
$661$	7.59869	−	23.3864i	0.295555	−	0.909625i	−0.687480	−	0.726204i	$-0.741283\pi$
$661$	7.59869	−	23.3864i	0.295555	−	0.909625i	0.983034	−	0.183421i	$-0.0587171\pi$
$662$	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	0.229212	−	0.973376i	$-0.426385\pi$
$673$	31.7995	−	23.1037i	1.22578	−	0.890580i	0.996567	+	0.0827961i	$0.0263850\pi$
$674$	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	−0.459352	−	0.888254i	$-0.651918\pi$
$691$	6.40036	−	4.65013i	0.243481	−	0.176899i	0.702833	+	0.711355i	$0.251918\pi$
$692$	−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	−0.852136	−	0.523320i	$-0.824693\pi$
$701$	3.83527	−	11.8037i	0.144856	−	0.445821i	0.996992	+	0.0774988i	$0.0246934\pi$
$702$	−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	0.875199	−	0.483763i	$-0.160730\pi$
$709$	18.2545	+	13.2627i	0.685564	+	0.498091i	−0.189635	+	0.981855i	$0.560730\pi$
$710$	−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	0.137394	−	0.990516i	$-0.456127\pi$
$727$	30.2494	−	21.9775i	1.12189	−	0.815100i	0.984494	+	0.175417i	$0.0561273\pi$
$728$	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	0.318350	−	0.947973i	$-0.396871\pi$
$733$	−13.1268	−	9.53721i	−0.484851	−	0.352265i	−0.803201	+	0.595708i	$0.796871\pi$
$734$	−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	0.0303554	−	0.999539i	$-0.490336\pi$
$751$	−24.9622	−	18.1361i	−0.910883	−	0.661795i	−0.941238	+	0.337744i	$0.890336\pi$
$752$	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	0.743631	+	0.668591i	$0.233102\pi$
$757$	14.7200	+	45.3036i	0.535008	+	1.64659i	−0.208622	+	0.977996i	$0.566898\pi$
$758$	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	0.0447483	−	0.998998i	$-0.485751\pi$
$761$	27.8257	−	20.2165i	1.00868	−	0.732849i	0.963932	+	0.266149i	$0.0857514\pi$
$762$	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	0.510543	+	0.859852i	$0.329444\pi$
$773$	−11.3409	+	34.9037i	−0.407904	+	1.25540i	−0.918446	+	0.395546i	$0.870556\pi$
$774$	−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	−0.782128	−	0.623118i	$-0.785866\pi$
$787$	6.08443	−	18.7259i	0.216886	−	0.667508i	0.999014	−	0.0443899i	$-0.0141344\pi$
$788$	−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	0.0249141	−	0.999690i	$-0.492069\pi$
$797$	27.7618	−	20.1701i	0.983374	−	0.714463i	0.958460	+	0.285226i	$0.0920688\pi$
$798$	−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	0.941407	−	0.337272i	$-0.109504\pi$
$809$	−0.524786	−	1.61513i	−0.0184505	−	0.0567848i	−0.959858	+	0.280487i	$0.909504\pi$
$810$	−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	0.962075	−	0.272787i	$-0.0879453\pi$
$821$	0.670481	+	2.06353i	0.0234000	+	0.0720176i	−0.938675	+	0.344804i	$0.887945\pi$
$822$	−15.4448	−	47.5341i	−0.538699	−	1.65794i
$823$	25.4301	−	18.4760i	0.886436	−	0.644033i	−0.0485103	−	0.998823i	$-0.515447\pi$
$823$	25.4301	−	18.4760i	0.886436	−	0.644033i	0.934946	+	0.354789i	$0.115447\pi$
$824$	−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	−0.937929	−	0.346828i	$-0.887259\pi$
$827$	0.711237	−	2.18896i	0.0247321	−	0.0761177i	0.962661	+	0.270711i	$0.0872586\pi$
$828$	−31.2769	+	22.7240i	−1.08695	+	0.789713i
$829$	1.92151	−	1.39606i	0.0667367	−	0.0484871i	−0.553917	−	0.832572i	$-0.686867\pi$
$829$	1.92151	−	1.39606i	0.0667367	−	0.0484871i	0.620653	+	0.784085i	$0.286867\pi$
$830$	−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	0.798828	+	0.601560i	$0.205454\pi$
$839$	−5.82280	+	17.9207i	−0.201026	+	0.618693i	−0.999853	+	0.0171330i	$0.994546\pi$
$840$	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	−0.956624	−	0.291326i	$-0.905903\pi$
$853$	−10.3371	−	31.8144i	−0.353936	−	1.08930i	0.602687	−	0.797977i	$-0.294097\pi$
$854$	−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	0.453824	−	0.891091i	$-0.350059\pi$
$857$	−7.41861	−	5.38993i	−0.253415	−	0.184117i	−0.707239	+	0.706975i	$0.750059\pi$
$858$	−2.49816	+	7.68854i	−0.0852857	+	0.262482i
$859$	−34.3731	+	24.9735i	−1.17280	+	0.852086i	−0.991341	−	0.131313i	$-0.958081\pi$
$859$	−34.3731	+	24.9735i	−1.17280	+	0.852086i	−0.181455	+	0.983399i	$0.558081\pi$
$860$	−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	−0.647998	−	0.761642i	$-0.724394\pi$
$877$	−3.66850	+	2.66532i	−0.123876	+	0.0900015i	0.524122	+	0.851643i	$0.324394\pi$
$878$	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	0.943925	−	0.330160i	$-0.107103\pi$
$881$	−0.409295	−	1.25968i	−0.0137895	−	0.0424397i	−0.957715	+	0.287720i	$0.907103\pi$
$882$	−20.8752	+	15.1667i	−0.702904	+	0.510689i
$883$	7.51315	+	23.1231i	0.252838	+	0.778155i	0.994248	+	0.107102i	$0.0341573\pi$
$883$	7.51315	+	23.1231i	0.252838	+	0.778155i	−0.741410	+	0.671052i	$0.765843\pi$
$884$	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	0.788649	+	0.614844i	$0.210781\pi$
$887$	−6.27750	+	19.3202i	−0.210778	+	0.648707i	−0.999426	+	0.0338632i	$0.989219\pi$
$888$	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	−0.432274	−	0.901742i	$-0.642289\pi$
$907$	8.78659	−	6.38383i	0.291754	−	0.211972i	0.724028	+	0.689771i	$0.242289\pi$
$908$	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	−0.0346612	−	0.999399i	$-0.511035\pi$
$911$	17.5305	−	53.9534i	0.580812	−	1.78756i	0.615474	−	0.788158i	$-0.288965\pi$
$912$	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	0.594820	−	0.803859i	$-0.297223\pi$
$919$	0.427874	+	0.310869i	0.0141143	+	0.0102546i	−0.580706	+	0.814114i	$0.697223\pi$
$920$	−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	0.892707	−	0.450638i	$-0.148804\pi$
$937$	22.6513	+	16.4571i	0.739986	+	0.537631i	−0.152721	+	0.988269i	$0.548804\pi$
$938$	−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	0.174781	−	0.984607i	$-0.444078\pi$
$941$	−21.7069	−	15.7710i	−0.707626	−	0.514120i	−0.882407	+	0.470487i	$0.844078\pi$
$942$	−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	−0.684122	−	0.729368i	$-0.739814\pi$
$947$	−6.21184	+	4.51317i	−0.201858	+	0.146658i	0.482264	+	0.876026i	$0.339814\pi$
$948$	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	−0.765135	−	0.643870i	$-0.777328\pi$
$953$	−12.0154	+	8.72972i	−0.389218	+	0.282783i	0.375917	+	0.926653i	$0.377328\pi$
$954$	−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	−0.227028	−	0.973888i	$-0.572901\pi$
$971$	16.4865	−	50.7404i	0.529078	−	1.62834i	0.756107	−	0.654448i	$-0.227099\pi$
$972$	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	0.828871	+	0.559440i	$0.188984\pi$
$977$	15.2263	+	46.8616i	0.487131	+	1.49923i	−0.341740	+	0.939795i	$0.611016\pi$
$978$	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	−0.652965	−	0.757388i	$-0.726475\pi$
$983$	−4.21456	+	3.06206i	−0.134423	+	0.0976644i	0.518542	+	0.855052i	$0.326475\pi$
$984$	−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.287.2	yes	68
31.4	even	5	inner	403.2.k.e.66.2	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.2	✓	68	31.4	even	5	inner
403.2.k.e.287.2	yes	68	1.1	even	1	trivial

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

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