LMFDB - Embedded newform 403.2.f.c.94.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.1
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39316 - 2.41302i) q^{2} +(-1.13229 - 1.96118i) q^{3} +(-2.88179 + 4.99141i) q^{4} -3.38130 q^{5} +(-3.15492 + 5.46447i) q^{6} +(-0.923334 + 1.59926i) q^{7} +10.4866 q^{8} +(-1.06415 + 1.84316i) q^{9} +O(q^{10})$	\(q+(-1.39316 - 2.41302i) q^{2} +(-1.13229 - 1.96118i) q^{3} +(-2.88179 + 4.99141i) q^{4} -3.38130 q^{5} +(-3.15492 + 5.46447i) q^{6} +(-0.923334 + 1.59926i) q^{7} +10.4866 q^{8} +(-1.06415 + 1.84316i) q^{9} +(4.71069 + 8.15916i) q^{10} +(-2.76077 - 4.78180i) q^{11} +13.0521 q^{12} +(-2.26284 + 2.80706i) q^{13} +5.14541 q^{14} +(3.82860 + 6.63133i) q^{15} +(-8.84587 - 15.3215i) q^{16} +(0.708645 - 1.22741i) q^{17} +5.93012 q^{18} +(1.65258 - 2.86236i) q^{19} +(9.74420 - 16.8774i) q^{20} +4.18192 q^{21} +(-7.69240 + 13.3236i) q^{22} +(0.222079 + 0.384651i) q^{23} +(-11.8738 - 20.5660i) q^{24} +6.43318 q^{25} +(9.92599 + 1.54960i) q^{26} -1.97404 q^{27} +(-5.32171 - 9.21748i) q^{28} +(3.67696 + 6.36868i) q^{29} +(10.6677 - 18.4770i) q^{30} +1.00000 q^{31} +(-14.1609 + 24.5273i) q^{32} +(-6.25198 + 10.8287i) q^{33} -3.94902 q^{34} +(3.12207 - 5.40758i) q^{35} +(-6.13331 - 10.6232i) q^{36} +(1.01200 + 1.75283i) q^{37} -9.20925 q^{38} +(8.06732 + 1.25943i) q^{39} -35.4582 q^{40} +(-2.09559 - 3.62968i) q^{41} +(-5.82608 - 10.0911i) q^{42} +(-1.85841 + 3.21886i) q^{43} +31.8239 q^{44} +(3.59820 - 6.23227i) q^{45} +(0.618782 - 1.07176i) q^{46} +1.45280 q^{47} +(-20.0321 + 34.6967i) q^{48} +(1.79491 + 3.10887i) q^{49} +(-8.96245 - 15.5234i) q^{50} -3.20956 q^{51} +(-7.49016 - 19.3841i) q^{52} -0.0993776 q^{53} +(2.75015 + 4.76340i) q^{54} +(9.33500 + 16.1687i) q^{55} +(-9.68259 + 16.7707i) q^{56} -7.48479 q^{57} +(10.2452 - 17.7452i) q^{58} +(3.70735 - 6.42133i) q^{59} -44.1329 q^{60} +(2.73433 - 4.73600i) q^{61} +(-1.39316 - 2.41302i) q^{62} +(-1.96513 - 3.40370i) q^{63} +43.5300 q^{64} +(7.65132 - 9.49150i) q^{65} +34.8400 q^{66} +(-0.171709 - 0.297409i) q^{67} +(4.08433 + 7.07427i) q^{68} +(0.502913 - 0.871072i) q^{69} -17.3982 q^{70} +(-3.05474 + 5.29096i) q^{71} +(-11.1592 + 19.3284i) q^{72} +3.63746 q^{73} +(2.81975 - 4.88396i) q^{74} +(-7.28421 - 12.6166i) q^{75} +(9.52480 + 16.4974i) q^{76} +10.1965 q^{77} +(-8.20004 - 21.2212i) q^{78} +3.33058 q^{79} +(29.9105 + 51.8065i) q^{80} +(5.42762 + 9.40092i) q^{81} +(-5.83900 + 10.1134i) q^{82} -4.45752 q^{83} +(-12.0514 + 20.8737i) q^{84} +(-2.39614 + 4.15023i) q^{85} +10.3563 q^{86} +(8.32675 - 14.4223i) q^{87} +(-28.9510 - 50.1446i) q^{88} +(-1.31514 - 2.27788i) q^{89} -20.0515 q^{90} +(-2.39987 - 6.21072i) q^{91} -2.55994 q^{92} +(-1.13229 - 1.96118i) q^{93} +(-2.02399 - 3.50565i) q^{94} +(-5.58788 + 9.67849i) q^{95} +64.1367 q^{96} +(-7.52801 + 13.0389i) q^{97} +(5.00119 - 8.66231i) q^{98} +11.7515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.39316	−	2.41302i	−0.985113	−	1.70627i	−0.641432	−	0.767180i	$-0.721659\pi$
$2$	−1.39316	−	2.41302i	−0.985113	−	1.70627i	−0.343681	−	0.939086i	$-0.611674\pi$
$3$	−1.13229	−	1.96118i	−0.653726	−	1.13229i	−0.982211	−	0.187778i	$-0.939871\pi$
$3$	−1.13229	−	1.96118i	−0.653726	−	1.13229i	0.328485	−	0.944509i	$-0.393462\pi$
$4$	−2.88179	+	4.99141i	−1.44090	+	2.49571i
$5$	−3.38130			−1.51216			−0.756081	−	0.654478i	$-0.772889\pi$
$5$	−3.38130			−1.51216			−0.756081	+	0.654478i	$0.772889\pi$
$6$	−3.15492	+	5.46447i	−1.28799	+	2.23086i
$7$	−0.923334	+	1.59926i	−0.348988	+	0.604464i	−0.986070	−	0.166332i	$-0.946808\pi$
$7$	−0.923334	+	1.59926i	−0.348988	+	0.604464i	0.637082	+	0.770796i	$0.280141\pi$
$8$	10.4866			3.70756
$9$	−1.06415	+	1.84316i	−0.354716	+	0.614386i
$10$	4.71069	+	8.15916i	1.48965	+	2.58015i
$11$	−2.76077	−	4.78180i	−0.832405	−	1.44177i	−0.896126	−	0.443799i	$-0.853630\pi$
$11$	−2.76077	−	4.78180i	−0.832405	−	1.44177i	0.0637217	−	0.997968i	$-0.479703\pi$
$12$	13.0521			3.76781
$13$	−2.26284	+	2.80706i	−0.627598	+	0.778538i
$13$	−2.26284	+	2.80706i	−0.627598	+	0.778538i
$14$	5.14541			1.37517
$15$	3.82860	+	6.63133i	0.988540	+	1.71220i
$16$	−8.84587	−	15.3215i	−2.21147	−	3.83037i
$17$	0.708645	−	1.22741i	0.171872	−	0.297690i	−0.767203	−	0.641405i	$-0.778352\pi$
$17$	0.708645	−	1.22741i	0.171872	−	0.297690i	0.939074	+	0.343715i	$0.111685\pi$
$18$	5.93012			1.39774
$19$	1.65258	−	2.86236i	0.379129	−	0.656670i	−0.611807	−	0.791007i	$-0.709557\pi$
$19$	1.65258	−	2.86236i	0.379129	−	0.656670i	0.990936	+	0.134337i	$0.0428905\pi$
$20$	9.74420	−	16.8774i	2.17887	−	3.77391i
$21$	4.18192			0.912569
$22$	−7.69240	+	13.3236i	−1.64003	+	2.84061i
$23$	0.222079	+	0.384651i	0.0463066	+	0.0802054i	0.888250	−	0.459361i	$-0.151922\pi$
$23$	0.222079	+	0.384651i	0.0463066	+	0.0802054i	−0.841943	+	0.539566i	$0.818588\pi$
$24$	−11.8738	−	20.5660i	−2.42373	−	4.19802i
$25$	6.43318			1.28664
$26$	9.92599	+	1.54960i	1.94665	+	0.303901i
$27$	−1.97404			−0.379904
$28$	−5.32171	−	9.21748i	−1.00571	−	1.74194i
$29$	3.67696	+	6.36868i	0.682794	+	1.18263i	0.974125	+	0.226012i	$0.0725687\pi$
$29$	3.67696	+	6.36868i	0.682794	+	1.18263i	−0.291331	+	0.956622i	$0.594098\pi$
$30$	10.6677	−	18.4770i	1.94765	−	3.37343i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−14.1609	+	24.5273i	−2.50331	+	4.33586i
$33$	−6.25198	+	10.8287i	−1.08833	+	1.88504i
$34$	−3.94902			−0.677252
$35$	3.12207	−	5.40758i	0.527726	−	0.914048i
$36$	−6.13331	−	10.6232i	−1.02222	−	1.77053i
$37$	1.01200	+	1.75283i	0.166372	+	0.288164i	0.937141	−	0.348950i	$-0.113462\pi$
$37$	1.01200	+	1.75283i	0.166372	+	0.288164i	−0.770770	+	0.637114i	$0.780128\pi$
$38$	−9.20925			−1.49394
$39$	8.06732	+	1.25943i	1.29181	+	0.201670i
$40$	−35.4582			−5.60643
$41$	−2.09559	−	3.62968i	−0.327277	−	0.566860i	0.654694	−	0.755894i	$-0.272798\pi$
$41$	−2.09559	−	3.62968i	−0.327277	−	0.566860i	−0.981971	+	0.189034i	$0.939464\pi$
$42$	−5.82608	−	10.0911i	−0.898984	−	1.55709i
$43$	−1.85841	+	3.21886i	−0.283405	+	0.490872i	−0.972221	−	0.234064i	$-0.924797\pi$
$43$	−1.85841	+	3.21886i	−0.283405	+	0.490872i	0.688816	+	0.724936i	$0.258131\pi$
$44$	31.8239			4.79763
$45$	3.59820	−	6.23227i	0.536388	−	0.929052i
$46$	0.618782	−	1.07176i	0.0912345	−	0.158023i
$47$	1.45280			0.211913			0.105957	−	0.994371i	$-0.466210\pi$
$47$	1.45280			0.211913			0.105957	+	0.994371i	$0.466210\pi$
$48$	−20.0321	+	34.6967i	−2.89139	+	5.00803i
$49$	1.79491	+	3.10887i	0.256415	+	0.444125i
$50$	−8.96245	−	15.5234i	−1.26748	−	2.19534i
$51$	−3.20956			−0.449428
$52$	−7.49016	−	19.3841i	−1.03870	−	2.68809i
$53$	−0.0993776			−0.0136506			−0.00682528	−	0.999977i	$-0.502173\pi$
$53$	−0.0993776			−0.0136506			−0.00682528	+	0.999977i	$0.502173\pi$
$54$	2.75015	+	4.76340i	0.374248	+	0.648217i
$55$	9.33500	+	16.1687i	1.25873	+	2.18019i
$56$	−9.68259	+	16.7707i	−1.29389	+	2.24108i
$57$	−7.48479			−0.991385
$58$	10.2452	−	17.7452i	1.34526	−	2.33006i
$59$	3.70735	−	6.42133i	0.482656	−	0.835985i	−0.517145	−	0.855898i	$-0.673005\pi$
$59$	3.70735	−	6.42133i	0.482656	−	0.835985i	0.999802	+	0.0199122i	$0.00633866\pi$
$60$	−44.1329			−5.69754
$61$	2.73433	−	4.73600i	0.350095	−	0.606383i	−0.636171	−	0.771548i	$-0.719483\pi$
$61$	2.73433	−	4.73600i	0.350095	−	0.606383i	0.986266	+	0.165166i	$0.0528159\pi$
$62$	−1.39316	−	2.41302i	−0.176932	−	0.306454i
$63$	−1.96513	−	3.40370i	−0.247583	−	0.428826i
$64$	43.5300			5.44125
$65$	7.65132	−	9.49150i	0.949030	−	1.17728i
$66$	34.8400			4.28851
$67$	−0.171709	−	0.297409i	−0.0209776	−	0.0363343i	0.855346	−	0.518057i	$-0.173345\pi$
$67$	−0.171709	−	0.297409i	−0.0209776	−	0.0363343i	−0.876324	+	0.481723i	$0.840011\pi$
$68$	4.08433	+	7.07427i	0.495298	+	0.857881i
$69$	0.502913	−	0.871072i	0.0605437	−	0.104865i
$70$	−17.3982			−2.07948
$71$	−3.05474	+	5.29096i	−0.362531	+	0.627922i	−0.988377	−	0.152025i	$-0.951421\pi$
$71$	−3.05474	+	5.29096i	−0.362531	+	0.627922i	0.625846	+	0.779947i	$0.284754\pi$
$72$	−11.1592	+	19.3284i	−1.31513	+	2.27787i
$73$	3.63746			0.425732			0.212866	−	0.977081i	$-0.431720\pi$
$73$	3.63746			0.425732			0.212866	+	0.977081i	$0.431720\pi$
$74$	2.81975	−	4.88396i	0.327790	−	0.567748i
$75$	−7.28421	−	12.6166i	−0.841108	−	1.45684i
$76$	9.52480	+	16.4974i	1.09257	+	1.89239i
$77$	10.1965			1.16200
$78$	−8.20004	−	21.2212i	−0.928472	−	2.40283i
$79$	3.33058			0.374719			0.187360	−	0.982291i	$-0.440007\pi$
$79$	3.33058			0.374719			0.187360	+	0.982291i	$0.440007\pi$
$80$	29.9105	+	51.8065i	3.34410	+	5.79215i
$81$	5.42762	+	9.40092i	0.603069	+	1.04455i
$82$	−5.83900	+	10.1134i	−0.644810	+	1.11684i
$83$	−4.45752			−0.489276			−0.244638	−	0.969614i	$-0.578669\pi$
$83$	−4.45752			−0.489276			−0.244638	+	0.969614i	$0.578669\pi$
$84$	−12.0514	+	20.8737i	−1.31492	+	2.27750i
$85$	−2.39614	+	4.15023i	−0.259898	+	0.450156i
$86$	10.3563			1.11674
$87$	8.32675	−	14.4223i	0.892721	−	1.54624i
$88$	−28.9510	−	50.1446i	−3.08619	−	5.34543i
$89$	−1.31514	−	2.27788i	−0.139404	−	0.241455i	0.787867	−	0.615845i	$-0.211185\pi$
$89$	−1.31514	−	2.27788i	−0.139404	−	0.241455i	−0.927271	+	0.374390i	$0.877852\pi$
$90$	−20.0515			−2.11361
$91$	−2.39987	−	6.21072i	−0.251574	−	0.651060i
$92$	−2.55994			−0.266892
$93$	−1.13229	−	1.96118i	−0.117413	−	0.203365i
$94$	−2.02399	−	3.50565i	−0.208758	−	0.361580i
$95$	−5.58788	+	9.67849i	−0.573304	+	0.992992i
$96$	64.1367			6.54592
$97$	−7.52801	+	13.0389i	−0.764354	+	1.32390i	0.176234	+	0.984348i	$0.443609\pi$
$97$	−7.52801	+	13.0389i	−0.764354	+	1.32390i	−0.940588	+	0.339551i	$0.889725\pi$
$98$	5.00119	−	8.66231i	0.505196	−	0.875026i
$99$	11.7515			1.18107
$100$	−18.5391	+	32.1106i	−1.85391	+	3.21106i
$101$	5.65650	+	9.79735i	0.562843	+	0.974873i	0.997247	+	0.0741544i	$0.0236258\pi$
$101$	5.65650	+	9.79735i	0.562843	+	0.974873i	−0.434404	+	0.900718i	$0.643041\pi$
$102$	4.47143	+	7.74474i	0.442737	+	0.766843i
$103$	5.23825			0.516140			0.258070	−	0.966126i	$-0.416913\pi$
$103$	5.23825			0.516140			0.258070	+	0.966126i	$0.416913\pi$
$104$	−23.7293	+	29.4364i	−2.32685	+	2.88647i
$105$	−14.1403			−1.37995
$106$	0.138449	+	0.239801i	0.0134474	+	0.0232915i
$107$	3.36519	+	5.82868i	0.325325	+	0.563480i	0.981578	−	0.191061i	$-0.0611929\pi$
$107$	3.36519	+	5.82868i	0.325325	+	0.563480i	−0.656253	+	0.754541i	$0.727860\pi$
$108$	5.68877	−	9.85323i	0.547402	−	0.948128i
$109$	−11.8329			−1.13339			−0.566695	−	0.823928i	$-0.691778\pi$
$109$	−11.8329			−1.13339			−0.566695	+	0.823928i	$0.691778\pi$
$110$	26.0103	−	45.0512i	2.47999	−	4.29546i
$111$	2.29175	−	3.96942i	0.217523	−	0.376761i
$112$	32.6708			3.08710
$113$	−6.53134	+	11.3126i	−0.614416	+	1.06420i	0.376070	+	0.926591i	$0.377275\pi$
$113$	−6.53134	+	11.3126i	−0.614416	+	1.06420i	−0.990487	+	0.137609i	$0.956058\pi$
$114$	10.4275	+	18.0610i	0.976627	+	1.69157i
$115$	−0.750914	−	1.30062i	−0.0700231	−	0.121284i
$116$	−42.3849			−3.93534
$117$	−2.76586	−	7.15789i	−0.255704	−	0.661747i
$118$	−20.6598			−1.90188
$119$	1.30863	+	2.26662i	0.119962	+	0.207780i
$120$	40.1488	+	69.5398i	3.66507	+	6.34809i
$121$	−9.74374	+	16.8767i	−0.885795	+	1.53424i
$122$	−15.2375			−1.37953
$123$	−4.74563	+	8.21967i	−0.427899	+	0.741143i
$124$	−2.88179	+	4.99141i	−0.258793	+	0.448242i
$125$	−4.84601			−0.433440
$126$	−5.47548	+	9.48381i	−0.487794	+	0.844885i
$127$	8.33772	+	14.4414i	0.739853	+	1.28146i	0.952561	+	0.304347i	$0.0984383\pi$
$127$	8.33772	+	14.4414i	0.739853	+	1.28146i	−0.212708	+	0.977116i	$0.568228\pi$
$128$	−32.3225	−	55.9843i	−2.85693	−	4.94836i
$129$	8.41702			0.741077
$130$	−33.5627	−	5.23965i	−2.94365	−	0.459547i
$131$	−5.60345			−0.489575			−0.244788	−	0.969577i	$-0.578718\pi$
$131$	−5.60345			−0.489575			−0.244788	+	0.969577i	$0.578718\pi$
$132$	−36.0338	−	62.4124i	−3.13634	−	5.43230i
$133$	3.05177	+	5.28583i	0.264622	+	0.458339i
$134$	−0.478437	+	0.828677i	−0.0413306	+	0.0715868i
$135$	6.67481			0.574476
$136$	7.43124	−	12.8713i	0.637223	−	1.10370i
$137$	−8.33048	+	14.4288i	−0.711721	+	1.23274i	0.252489	+	0.967600i	$0.418751\pi$
$137$	−8.33048	+	14.4288i	−0.711721	+	1.23274i	−0.964211	+	0.265138i	$0.914583\pi$
$138$	−2.80256			−0.238569
$139$	7.74292	−	13.4111i	0.656746	−	1.13752i	−0.324708	−	0.945814i	$-0.605266\pi$
$139$	7.74292	−	13.4111i	0.656746	−	1.13752i	0.981453	−	0.191702i	$-0.0614008\pi$
$140$	17.9943	+	31.1671i	1.52080	+	2.63410i
$141$	−1.64499	−	2.84921i	−0.138533	−	0.239946i
$142$	17.0230			1.42854
$143$	19.6700	+	3.07078i	1.64489	+	0.256791i
$144$	37.6533			3.13777
$145$	−12.4329	−	21.5344i	−1.03250	−	1.78834i
$146$	−5.06756	−	8.77727i	−0.419394	−	0.726412i
$147$	4.06470	−	7.04027i	0.335251	−	0.580672i
$148$	−11.6655			−0.958896
$149$	7.70269	−	13.3415i	0.631029	−	1.09297i	−0.356313	−	0.934367i	$-0.615966\pi$
$149$	7.70269	−	13.3415i	0.631029	−	1.09297i	0.987342	−	0.158608i	$-0.0507005\pi$
$150$	−20.2961	+	35.1539i	−1.65717	+	2.87031i
$151$	8.01689			0.652406			0.326203	−	0.945300i	$-0.394231\pi$
$151$	8.01689			0.652406			0.326203	+	0.945300i	$0.394231\pi$
$152$	17.3299	−	30.0163i	1.40564	−	2.43464i
$153$	1.50821	+	2.61229i	0.121931	+	0.211191i
$154$	−14.2053	−	24.6043i	−1.14470	−	1.98267i
$155$	−3.38130			−0.271592
$156$	−29.5347	+	36.6379i	−2.36467	+	2.93338i
$157$	−9.90523			−0.790523			−0.395262	−	0.918569i	$-0.629346\pi$
$157$	−9.90523			−0.790523			−0.395262	+	0.918569i	$0.629346\pi$
$158$	−4.64003	−	8.03677i	−0.369141	−	0.639371i
$159$	0.112524	+	0.194897i	0.00892374	+	0.0154564i
$160$	47.8821	−	82.9343i	3.78542	−	6.55653i
$161$	−0.820211			−0.0646417
$162$	15.1231	−	26.1940i	1.18818	−	2.05799i
$163$	4.28143	−	7.41566i	0.335348	−	0.580839i	−0.648204	−	0.761467i	$-0.724480\pi$
$163$	4.28143	−	7.41566i	0.335348	−	0.580839i	0.983552	+	0.180628i	$0.0578129\pi$
$164$	24.1563			1.88629
$165$	21.1398	−	36.6152i	1.64573	−	2.85049i
$166$	6.21004	+	10.7561i	0.481993	+	0.834836i
$167$	−0.417222	−	0.722649i	−0.0322856	−	0.0559203i	0.849431	−	0.527699i	$-0.176945\pi$
$167$	−0.417222	−	0.722649i	−0.0322856	−	0.0559203i	−0.881717	+	0.471779i	$0.843612\pi$
$168$	43.8539			3.38340
$169$	−2.75915	−	12.7038i	−0.212242	−	0.977217i
$170$	13.3528			1.02411
$171$	3.51719	+	6.09194i	0.268966	+	0.465863i
$172$	−10.7111	−	18.5522i	−0.816714	−	1.41459i
$173$	−6.18514	+	10.7130i	−0.470248	+	0.814493i	−0.999421	−	0.0340209i	$-0.989169\pi$
$173$	−6.18514	+	10.7130i	−0.470248	+	0.814493i	0.529174	+	0.848514i	$0.322502\pi$
$174$	−46.4020			−3.51772
$175$	−5.93998	+	10.2883i	−0.449020	+	0.777725i
$176$	−48.8429	+	84.5983i	−3.68167	+	6.37684i
$177$	−16.7912			−1.26210
$178$	−3.66439	+	6.34691i	−0.274658	+	0.475721i
$179$	5.44950	+	9.43882i	0.407315	+	0.705490i	0.994588	−	0.103899i	$-0.0331318\pi$
$179$	5.44950	+	9.43882i	0.407315	+	0.705490i	−0.587273	+	0.809389i	$0.699798\pi$
$180$	20.7385	+	35.9202i	1.54576	+	2.67733i
$181$	−17.4373			−1.29611			−0.648053	−	0.761595i	$-0.724416\pi$
$181$	−17.4373			−1.29611			−0.648053	+	0.761595i	$0.724416\pi$
$182$	−11.6432	+	14.4435i	−0.863053	+	1.07062i
$183$	−12.3842			−0.915466
$184$	2.32884	+	4.03367i	0.171684	+	0.297366i
$185$	−3.42187	−	5.92685i	−0.251581	−	0.435751i
$186$	−3.15492	+	5.46447i	−0.231330	+	0.400675i
$187$	−7.82563			−0.572267
$188$	−4.18668	+	7.25154i	−0.305345	+	0.528873i
$189$	1.82270	−	3.15700i	0.132582	−	0.229638i
$190$	31.1392			2.25908
$191$	−9.82246	+	17.0130i	−0.710728	+	1.23102i	0.253856	+	0.967242i	$0.418301\pi$
$191$	−9.82246	+	17.0130i	−0.710728	+	1.23102i	−0.964584	+	0.263776i	$0.915032\pi$
$192$	−49.2885	−	85.3701i	−3.55709	−	6.16106i
$193$	6.22840	+	10.7879i	0.448330	+	0.776530i	0.998278	−	0.0586688i	$-0.0186856\pi$
$193$	6.22840	+	10.7879i	0.448330	+	0.776530i	−0.549947	+	0.835199i	$0.685352\pi$
$194$	41.9509			3.01190
$195$	−27.2780	−	4.25851i	−1.95342	−	0.304958i
$196$	−20.6902			−1.47787
$197$	−10.4681	−	18.1312i	−0.745818	−	1.29179i	−0.949812	−	0.312822i	$-0.898726\pi$
$197$	−10.4681	−	18.1312i	−0.745818	−	1.29179i	0.203994	−	0.978972i	$-0.434608\pi$
$198$	−16.3717	−	28.3566i	−1.16349	−	2.01522i
$199$	−1.88809	+	3.27027i	−0.133843	+	0.231824i	−0.925155	−	0.379589i	$-0.876065\pi$
$199$	−1.88809	+	3.27027i	−0.133843	+	0.231824i	0.791312	+	0.611413i	$0.209399\pi$
$200$	67.4619			4.77028
$201$	−0.388848	+	0.673504i	−0.0274272	+	0.0475053i
$202$	15.7608	−	27.2986i	1.10893	−	1.92072i
$203$	−13.5802			−0.953146
$204$	9.24927	−	16.0202i	0.647579	−	1.12164i
$205$	7.08583	+	12.2730i	0.494896	+	0.857185i
$206$	−7.29773	−	12.6400i	−0.508457	−	0.880673i
$207$	−0.945298			−0.0657028
$208$	63.0251	+	9.83915i	4.37000	+	0.682222i
$209$	−18.2496			−1.26235
$210$	19.6997	+	34.1209i	1.35941	+	2.35457i
$211$	5.06209	+	8.76779i	0.348489	+	0.603600i	0.985981	−	0.166857i	$-0.0533617\pi$
$211$	5.06209	+	8.76779i	0.348489	+	0.603600i	−0.637493	+	0.770456i	$0.720028\pi$
$212$	0.286386	−	0.496035i	0.0196691	−	0.0340678i
$213$	13.8354			0.947983
$214$	9.37650	−	16.2406i	0.640964	−	1.11018i
$215$	6.28384	−	10.8839i	0.428554	−	0.742278i
$216$	−20.7009			−1.40851
$217$	−0.923334	+	1.59926i	−0.0626800	+	0.108565i
$218$	16.4852	+	28.5532i	1.11652	+	1.93386i
$219$	−4.11864	−	7.13370i	−0.278312	−	0.482051i
$220$	−107.606			−7.25480
$221$	1.84186	+	4.76663i	0.123897	+	0.320638i
$222$	−12.7711			−0.857139
$223$	5.63415	+	9.75863i	0.377290	+	0.653486i	0.990667	−	0.136305i	$-0.0435226\pi$
$223$	5.63415	+	9.75863i	0.377290	+	0.653486i	−0.613377	+	0.789791i	$0.710189\pi$
$224$	−26.1504	−	45.2939i	−1.74725	−	3.02632i
$225$	−6.84586	+	11.8574i	−0.456390	+	0.790491i
$226$	36.3968			2.42108
$227$	−0.0619944	+	0.107377i	−0.00411471	+	0.00712689i	−0.868075	−	0.496432i	$-0.834643\pi$
$227$	−0.0619944	+	0.107377i	−0.00411471	+	0.00712689i	0.863961	+	0.503559i	$0.167976\pi$
$228$	21.5696	−	37.3597i	1.42848	−	2.47420i
$229$	−19.7477			−1.30496			−0.652482	−	0.757804i	$-0.726272\pi$
$229$	−19.7477			−1.30496			−0.652482	+	0.757804i	$0.726272\pi$
$230$	−2.09229	+	3.62395i	−0.137961	+	0.238956i
$231$	−11.5453	−	19.9971i	−0.759627	−	1.31571i
$232$	38.5586	+	66.7855i	2.53150	+	4.38468i
$233$	−14.5007			−0.949971			−0.474986	−	0.879994i	$-0.657547\pi$
$233$	−14.5007			−0.949971			−0.474986	+	0.879994i	$0.657547\pi$
$234$	−13.4189	+	16.6462i	−0.877219	+	1.08819i
$235$	−4.91236			−0.320447
$236$	21.3676	+	37.0099i	1.39092	+	2.40914i
$237$	−3.77117	−	6.53186i	−0.244964	−	0.424290i
$238$	3.64627	−	6.31552i	0.236352	−	0.409374i
$239$	14.3544			0.928506			0.464253	−	0.885703i	$-0.346323\pi$
$239$	14.3544			0.928506			0.464253	+	0.885703i	$0.346323\pi$
$240$	67.7346	−	117.320i	4.37225	−	7.57296i
$241$	−6.64930	+	11.5169i	−0.428319	+	0.741871i	−0.996724	−	0.0808783i	$-0.974227\pi$
$241$	−6.64930	+	11.5169i	−0.428319	+	0.741871i	0.568405	+	0.822749i	$0.307561\pi$
$242$	54.2984			3.49043
$243$	9.33020	−	16.1604i	0.598532	−	1.03669i
$244$	15.7596	+	27.2963i	1.00890	+	1.74747i
$245$	−6.06912	−	10.5120i	−0.387742	−	0.671589i
$246$	26.4457			1.68612
$247$	4.29528	+	11.1159i	0.273302	+	0.707290i
$248$	10.4866			0.665897
$249$	5.04719	+	8.74199i	0.319853	+	0.554001i
$250$	6.75127	+	11.6935i	0.426988	+	0.739565i
$251$	7.69469	−	13.3276i	0.485684	−	0.841230i	−0.514180	−	0.857682i	$-0.671904\pi$
$251$	7.69469	−	13.3276i	0.485684	−	0.841230i	0.999865	+	0.0164520i	$0.00523706\pi$
$252$	22.6524			1.42697
$253$	1.22622	−	2.12387i	0.0770916	−	0.133527i
$254$	23.2316	−	40.2382i	1.45768	−	2.52477i
$255$	10.8525			0.679608
$256$	−46.5309	+	80.5939i	−2.90818	+	5.03712i
$257$	−14.1367	−	24.4854i	−0.881822	−	1.52736i	−0.849314	−	0.527889i	$-0.822984\pi$
$257$	−14.1367	−	24.4854i	−0.881822	−	1.52736i	−0.0325081	−	0.999471i	$-0.510349\pi$
$258$	−11.7263	−	20.3105i	−0.730045	−	1.26447i
$259$	−3.73765			−0.232246
$260$	25.3265	+	65.5434i	1.57068	+	4.06483i
$261$	−15.6513			−0.968792
$262$	7.80650	+	13.5213i	0.482287	+	0.835346i
$263$	−2.56045	−	4.43483i	−0.157884	−	0.273463i	0.776221	−	0.630460i	$-0.217134\pi$
$263$	−2.56045	−	4.43483i	−0.157884	−	0.273463i	−0.934105	+	0.356997i	$0.883801\pi$
$264$	−65.5617	+	113.556i	−4.03504	+	6.98890i
$265$	0.336026			0.0206419
$266$	8.50322	−	14.7280i	0.521366	−	0.903032i
$267$	−2.97822	+	5.15844i	−0.182264	+	0.315691i
$268$	1.97932			0.120906
$269$	14.1599	−	24.5257i	0.863344	−	1.49536i	−0.00533845	−	0.999986i	$-0.501699\pi$
$269$	14.1599	−	24.5257i	0.863344	−	1.49536i	0.868682	−	0.495370i	$-0.164967\pi$
$270$	−9.29908	−	16.1065i	−0.565924	−	0.980210i
$271$	−0.330870	−	0.573083i	−0.0200989	−	0.0348123i	0.855801	−	0.517305i	$-0.173065\pi$
$271$	−0.330870	−	0.573083i	−0.0200989	−	0.0348123i	−0.875900	+	0.482493i	$0.839731\pi$
$272$	−25.0743			−1.52035
$273$	−9.46299	+	11.7389i	−0.572726	+	0.710470i
$274$	46.4228			2.80450
$275$	−17.7606	−	30.7622i	−1.07100	−	1.85503i
$276$	2.89858	+	5.02049i	0.174474	+	0.302198i
$277$	4.08641	−	7.07787i	0.245529	−	0.425268i	−0.716751	−	0.697329i	$-0.754372\pi$
$277$	4.08641	−	7.07787i	0.245529	−	0.425268i	0.962280	+	0.272061i	$0.0877051\pi$
$278$	−43.1485			−2.58787
$279$	−1.06415	+	1.84316i	−0.0637089	+	0.110347i
$280$	32.7397	−	56.7069i	1.95657	−	3.38888i
$281$	19.3429			1.15390			0.576951	−	0.816779i	$-0.304243\pi$
$281$	19.3429			1.15390			0.576951	+	0.816779i	$0.304243\pi$
$282$	−4.58347	+	7.93880i	−0.272942	+	0.472749i
$283$	−4.38740	−	7.59920i	−0.260804	−	0.451726i	0.705652	−	0.708559i	$-0.250654\pi$
$283$	−4.38740	−	7.59920i	−0.260804	−	0.451726i	−0.966456	+	0.256833i	$0.917321\pi$
$284$	−17.6062	−	30.4949i	−1.04474	−	1.80954i
$285$	25.3083			1.49914
$286$	−19.9936	−	51.7422i	−1.18224	−	3.05958i
$287$	7.73974			0.456862
$288$	−30.1385	−	52.2015i	−1.77593	−	3.07600i
$289$	7.49565	+	12.9828i	0.440920	+	0.763696i
$290$	−34.6420	+	60.0018i	−2.03425	+	3.52342i
$291$	34.0955			1.99871
$292$	−10.4824	+	18.1560i	−0.613436	+	1.06250i
$293$	−15.4382	+	26.7398i	−0.901910	+	1.56215i	−0.0768982	+	0.997039i	$0.524502\pi$
$293$	−15.4382	+	26.7398i	−0.901910	+	1.56215i	−0.825012	+	0.565115i	$0.808832\pi$
$294$	−22.6511			−1.32104
$295$	−12.5357	+	21.7124i	−0.729855	+	1.26415i
$296$	10.6124	+	18.3812i	0.616832	+	1.06838i
$297$	5.44987	+	9.43946i	0.316234	+	0.547733i
$298$	−42.9243			−2.48654
$299$	−1.58227	−	0.247015i	−0.0915048	−	0.0142853i
$300$	83.9663			4.84780
$301$	−3.43187	−	5.94417i	−0.197810	−	0.342616i
$302$	−11.1688	−	19.3450i	−0.642693	−	1.11318i
$303$	12.8096	−	22.1868i	0.735891	−	1.27460i
$304$	−58.4741			−3.35372
$305$	−9.24559	+	16.0138i	−0.529401	+	0.916950i
$306$	4.20234	−	7.27867i	0.240232	−	0.416094i
$307$	18.9569			1.08193			0.540965	−	0.841045i	$-0.318059\pi$
$307$	18.9569			1.08193			0.540965	+	0.841045i	$0.318059\pi$
$308$	−29.3841	+	50.8947i	−1.67431	+	2.90000i
$309$	−5.93121	−	10.2731i	−0.337415	−	0.584419i
$310$	4.71069	+	8.15916i	0.267549	+	0.463409i
$311$	−32.1027			−1.82038			−0.910188	−	0.414195i	$-0.864063\pi$
$311$	−32.1027			−1.82038			−0.910188	+	0.414195i	$0.864063\pi$
$312$	84.5984	+	13.2071i	4.78944	+	0.747703i
$313$	27.1585			1.53509			0.767545	−	0.640995i	$-0.221478\pi$
$313$	27.1585			1.53509			0.767545	+	0.640995i	$0.221478\pi$
$314$	13.7996	+	23.9016i	0.778755	+	1.34884i
$315$	6.64469	+	11.5089i	0.374386	+	0.648455i
$316$	−9.59804	+	16.6243i	−0.539932	+	0.935189i
$317$	−18.5241			−1.04042			−0.520210	−	0.854038i	$-0.674146\pi$
$317$	−18.5241			−1.04042			−0.520210	+	0.854038i	$0.674146\pi$
$318$	0.313528	−	0.543047i	0.0175818	−	0.0304525i
$319$	20.3025	−	35.1650i	1.13672	−	1.96886i
$320$	−147.188			−8.22806
$321$	7.62072	−	13.1995i	0.425347	−	0.736723i
$322$	1.14269	+	1.97919i	0.0636794	+	0.110296i
$323$	−2.34219	−	4.05679i	−0.130323	−	0.225726i
$324$	−62.5651			−3.47584
$325$	−14.5572	+	18.0583i	−0.807490	+	1.00169i
$326$	−23.8589			−1.32142
$327$	13.3983	+	23.2065i	0.740926	+	1.28332i
$328$	−21.9756	−	38.0628i	−1.21340	−	2.10167i
$329$	−1.34142	+	2.32341i	−0.0739550	+	0.128094i
$330$	−117.805			−6.48493
$331$	−7.34563	+	12.7230i	−0.403752	+	0.699320i	−0.994175	−	0.107774i	$-0.965628\pi$
$331$	−7.34563	+	12.7230i	−0.403752	+	0.699320i	0.590423	+	0.807094i	$0.298961\pi$
$332$	12.8456	−	22.2493i	0.704997	−	1.22109i
$333$	−4.30767			−0.236059
$334$	−1.16251	+	2.01353i	−0.0636099	+	0.110176i
$335$	0.580600	+	1.00563i	0.0317216	+	0.0549433i
$336$	−36.9927	−	64.0732i	−2.01812	−	3.49548i
$337$	6.22565			0.339133			0.169567	−	0.985519i	$-0.445763\pi$
$337$	6.22565			0.339133			0.169567	+	0.985519i	$0.445763\pi$
$338$	−26.8107	+	24.3564i	−1.45831	+	1.32481i
$339$	29.5814			1.60664
$340$	−13.8103	−	23.9202i	−0.748971	−	1.29726i
$341$	−2.76077	−	4.78180i	−0.149504	−	0.258949i
$342$	9.80001	−	16.9741i	0.529924	−	0.917855i
$343$	−19.5559			−1.05592
$344$	−19.4883	+	33.7548i	−1.05074	+	1.81993i
$345$	−1.70050	+	2.94535i	−0.0915519	+	0.158572i
$346$	34.4676			1.85299
$347$	−10.6019	+	18.3630i	−0.569139	+	0.985777i	0.427513	+	0.904009i	$0.359390\pi$
$347$	−10.6019	+	18.3630i	−0.569139	+	0.985777i	−0.996651	+	0.0817677i	$0.973943\pi$
$348$	47.9919	+	83.1244i	2.57264	+	4.45594i
$349$	9.25676	+	16.0332i	0.495503	+	0.858236i	0.999987	−	0.00518521i	$-0.00165051\pi$
$349$	9.25676	+	16.0332i	0.495503	+	0.858236i	−0.504484	+	0.863421i	$0.668317\pi$
$350$	33.1014			1.76934
$351$	4.46692	−	5.54124i	0.238427	−	0.295769i
$352$	156.380			8.33507
$353$	1.08977	+	1.88753i	0.0580024	+	0.100463i	0.893569	−	0.448927i	$-0.148194\pi$
$353$	1.08977	+	1.88753i	0.0580024	+	0.100463i	−0.835566	+	0.549390i	$0.814860\pi$
$354$	23.3928	+	40.5175i	1.24331	+	2.15348i
$355$	10.3290	−	17.8903i	0.548205	−	0.949520i
$356$	15.1598			0.803468
$357$	2.96349	−	5.13292i	0.156845	−	0.271663i
$358$	15.1841	−	26.2996i	0.802503	−	1.38998i
$359$	8.14631			0.429946			0.214973	−	0.976620i	$-0.431034\pi$
$359$	8.14631			0.429946			0.214973	+	0.976620i	$0.431034\pi$
$360$	37.7327	−	65.3550i	1.98869	−	3.44451i
$361$	4.03794	+	6.99392i	0.212523	+	0.368101i
$362$	24.2930	+	42.0767i	1.27681	+	2.21150i
$363$	44.1308			2.31627
$364$	37.9162	+	5.91928i	1.98735	+	0.310255i
$365$	−12.2993			−0.643776
$366$	17.2532	+	29.8834i	0.901838	+	1.56203i
$367$	2.58850	+	4.48341i	0.135118	+	0.234032i	0.925643	−	0.378399i	$-0.123525\pi$
$367$	2.58850	+	4.48341i	0.135118	+	0.234032i	−0.790524	+	0.612431i	$0.790192\pi$
$368$	3.92896	−	6.80515i	0.204811	−	0.354743i
$369$	8.92009			0.464361
$370$	−9.53443	+	16.5141i	−0.495671	+	0.858528i
$371$	0.0917588	−	0.158931i	0.00476388	−	0.00825128i
$372$	13.0521			0.676718
$373$	3.54167	−	6.13436i	0.183381	−	0.317625i	−0.759649	−	0.650334i	$-0.774629\pi$
$373$	3.54167	−	6.13436i	0.183381	−	0.317625i	0.943030	+	0.332708i	$0.107962\pi$
$374$	10.9024	+	18.8834i	0.563747	+	0.976439i
$375$	5.48708	+	9.50390i	0.283351	+	0.490779i
$376$	15.2349			0.785680
$377$	−26.1976	−	4.08984i	−1.34925	−	0.210637i
$378$	−10.1572			−0.522432
$379$	6.33159	+	10.9666i	0.325232	+	0.563318i	0.981559	−	0.191158i	$-0.0612244\pi$
$379$	6.33159	+	10.9666i	0.325232	+	0.563318i	−0.656328	+	0.754476i	$0.727891\pi$
$380$	−32.2062	−	55.7828i	−1.65214	−	2.86160i
$381$	18.8814	−	32.7035i	0.967323	−	1.67545i
$382$	54.7371			2.80059
$383$	14.0475	−	24.3309i	0.717793	−	1.24325i	−0.244080	−	0.969755i	$-0.578486\pi$
$383$	14.0475	−	24.3309i	0.717793	−	1.24325i	0.961873	−	0.273498i	$-0.0881807\pi$
$384$	−73.1968	+	126.781i	−3.73531	+	6.46974i
$385$	−34.4773			−1.75713
$386$	17.3543	−	30.0586i	0.883312	−	1.52994i
$387$	−3.95525	−	6.85069i	−0.201057	−	0.348240i
$388$	−43.3883	−	75.1508i	−2.20271	−	3.81520i
$389$	23.6537			1.19929			0.599645	−	0.800266i	$-0.295308\pi$
$389$	23.6537			1.19929			0.599645	+	0.800266i	$0.295308\pi$
$390$	27.7268	+	71.7553i	1.40400	+	3.63347i
$391$	0.629499			0.0318351
$392$	18.8224	+	32.6014i	0.950675	+	1.64662i
$393$	6.34471	+	10.9894i	0.320048	+	0.554340i
$394$	−29.1674	+	50.5193i	−1.46943	+	2.54513i
$395$	−11.2617			−0.566637
$396$	−33.8653	+	58.6565i	−1.70180	+	2.94760i
$397$	−8.81267	+	15.2640i	−0.442295	+	0.766078i	−0.997859	−	0.0653959i	$-0.979169\pi$
$397$	−8.81267	+	15.2640i	−0.442295	+	0.766078i	0.555564	+	0.831474i	$0.312502\pi$
$398$	10.5217			0.527404
$399$	6.91097	−	11.9701i	0.345981	−	0.599257i
$400$	−56.9071	−	98.5659i	−2.84535	−	4.92830i
$401$	−10.9436	−	18.9548i	−0.546496	−	0.946559i	−0.998511	−	0.0545487i	$-0.982628\pi$
$401$	−10.9436	−	18.9548i	−0.546496	−	0.946559i	0.452015	−	0.892010i	$-0.350705\pi$
$402$	2.16691			0.108076
$403$	−2.26284	+	2.80706i	−0.112720	+	0.139830i
$404$	−65.2035			−3.24399
$405$	−18.3524	−	31.7873i	−0.911939	−	1.57952i
$406$	18.9195	+	32.7695i	0.938957	+	1.62632i
$407$	5.58780	−	9.67835i	0.276977	−	0.479738i
$408$	−33.6572			−1.66628
$409$	5.90069	−	10.2203i	0.291770	−	0.505361i	−0.682458	−	0.730925i	$-0.739089\pi$
$409$	5.90069	−	10.2203i	0.291770	−	0.505361i	0.974228	+	0.225564i	$0.0724224\pi$
$410$	19.7434	−	34.1966i	0.975057	−	1.68885i
$411$	37.7300			1.86108
$412$	−15.0956	+	26.1463i	−0.743705	+	1.28813i
$413$	6.84625	+	11.8581i	0.336882	+	0.583497i
$414$	1.31695	+	2.28103i	0.0647247	+	0.112106i
$415$	15.0722			0.739866
$416$	−36.8060	−	95.2518i	−1.80456	−	4.67010i
$417$	−35.0688			−1.71733
$418$	25.4247	+	44.0368i	1.24356	+	2.15391i
$419$	12.5695	+	21.7710i	0.614061	+	1.06358i	0.990549	+	0.137163i	$0.0437983\pi$
$419$	12.5695	+	21.7710i	0.614061	+	1.06358i	−0.376488	+	0.926421i	$0.622868\pi$
$420$	40.7494	−	70.5801i	1.98837	−	3.44396i
$421$	−15.2730			−0.744361			−0.372180	−	0.928160i	$-0.621390\pi$
$421$	−15.2730			−0.744361			−0.372180	+	0.928160i	$0.621390\pi$
$422$	14.1046	−	24.4299i	0.686601	−	1.18923i
$423$	−1.54600	+	2.67775i	−0.0751690	+	0.130196i
$424$	−1.04213			−0.0506103
$425$	4.55884	−	7.89614i	0.221136	−	0.383019i
$426$	−19.2749	−	33.3851i	−0.933871	−	1.61751i
$427$	5.04940	+	8.74582i	0.244358	+	0.423240i
$428$	−38.7911			−1.87504
$429$	−16.2497	−	42.0533i	−0.784543	−	2.03035i
$430$	−35.0176			−1.68870
$431$	0.988321	+	1.71182i	0.0476057	+	0.0824556i	0.888846	−	0.458205i	$-0.151508\pi$
$431$	0.988321	+	1.71182i	0.0476057	+	0.0824556i	−0.841241	+	0.540661i	$0.818174\pi$
$432$	17.4621	+	30.2452i	0.840145	+	1.45517i
$433$	−2.45475	+	4.25175i	−0.117968	+	0.204326i	−0.918962	−	0.394346i	$-0.870971\pi$
$433$	−2.45475	+	4.25175i	−0.117968	+	0.204326i	0.800995	+	0.598672i	$0.204305\pi$
$434$	5.14541			0.246988
$435$	−28.1552	+	48.7663i	−1.34994	+	2.33816i
$436$	34.1000	−	59.0630i	1.63310	−	2.82861i
$437$	1.46801			0.0702246
$438$	−11.4759	+	19.8768i	−0.548338	+	0.949749i
$439$	−13.4214	−	23.2466i	−0.640570	−	1.10950i	−0.985306	−	0.170800i	$-0.945365\pi$
$439$	−13.4214	−	23.2466i	−0.640570	−	1.10950i	0.344736	−	0.938700i	$-0.387968\pi$
$440$	97.8920	+	169.554i	4.66682	+	8.08316i
$441$	−7.64019			−0.363819
$442$	8.93599	−	11.0851i	0.425042	−	0.527266i
$443$	26.0142			1.23597			0.617987	−	0.786189i	$-0.287949\pi$
$443$	26.0142			1.23597			0.617987	+	0.786189i	$0.287949\pi$
$444$	13.2087	+	22.8781i	0.626856	+	1.08575i
$445$	4.44687	+	7.70220i	0.210802	+	0.365119i
$446$	15.6985	−	27.1907i	0.743347	−	1.28752i
$447$	−34.8866			−1.65008
$448$	−40.1927	+	69.6159i	−1.89893	+	3.28904i
$449$	10.9601	−	18.9835i	0.517241	−	0.895887i	−0.482559	−	0.875864i	$-0.660292\pi$
$449$	10.9601	−	18.9835i	0.517241	−	0.895887i	0.999800	−	0.0200238i	$-0.00637419\pi$
$450$	38.1495			1.79839
$451$	−11.5709	+	20.0414i	−0.544854	+	0.943714i
$452$	−37.6439	−	65.2012i	−1.77062	−	3.06680i
$453$	−9.07743	−	15.7226i	−0.426495	−	0.738710i
$454$	0.345473			0.0162138
$455$	8.11467	+	21.0003i	0.380421	+	0.984509i
$456$	−78.4897			−3.67562
$457$	13.7468	+	23.8102i	0.643049	+	1.11379i	0.984749	+	0.173984i	$0.0556640\pi$
$457$	13.7468	+	23.8102i	0.643049	+	1.11379i	−0.341700	+	0.939809i	$0.611003\pi$
$458$	27.5117	+	47.6516i	1.28554	+	2.22662i
$459$	−1.39889	+	2.42295i	−0.0652946	+	0.113094i
$460$	8.65591			0.403584
$461$	−5.62277	+	9.73892i	−0.261879	+	0.453587i	−0.966741	−	0.255757i	$-0.917675\pi$
$461$	−5.62277	+	9.73892i	−0.261879	+	0.453587i	0.704863	+	0.709344i	$0.251009\pi$
$462$	−32.1690	+	55.7183i	−1.49664	+	2.59225i
$463$	12.4456			0.578394			0.289197	−	0.957270i	$-0.406612\pi$
$463$	12.4456			0.578394			0.289197	+	0.957270i	$0.406612\pi$
$464$	65.0518	−	112.673i	3.01995	−	5.23071i
$465$	3.82860	+	6.63133i	0.177547	+	0.307521i
$466$	20.2018	+	34.9905i	0.935829	+	1.62090i
$467$	−28.3660			−1.31262			−0.656310	−	0.754491i	$-0.727884\pi$
$467$	−28.3660			−1.31262			−0.656310	+	0.754491i	$0.727884\pi$
$468$	43.6986	+	6.82200i	2.01997	+	0.315347i
$469$	0.634180			0.0292837
$470$	6.84371	+	11.8536i	0.315677	+	0.546768i
$471$	11.2156	+	19.4259i	0.516786	+	0.895099i
$472$	38.8774	−	67.3376i	1.78948	−	3.09946i
$473$	20.5226			0.943630
$474$	−10.5077	+	18.1999i	−0.482634	+	0.835947i
$475$	10.6314	−	18.4141i	0.487800	−	0.844895i
$476$	−15.0848			−0.691411
$477$	0.105753	−	0.183169i	0.00484208	−	0.00838672i
$478$	−19.9979	−	34.6374i	−0.914684	−	1.58428i
$479$	−2.02672	−	3.51038i	−0.0926032	−	0.160393i	0.816003	−	0.578048i	$-0.196185\pi$
$479$	−2.02672	−	3.51038i	−0.0926032	−	0.160393i	−0.908606	+	0.417655i	$0.862852\pi$
$480$	−216.865			−9.89850
$481$	−7.21029	−	1.12563i	−0.328761	−	0.0513245i
$482$	37.0542			1.68777
$483$	0.928714	+	1.60858i	0.0422580	+	0.0731929i
$484$	−56.1589	−	97.2700i	−2.55268	−	4.42136i
$485$	25.4545	−	44.0884i	1.15583	−	2.00195i
$486$	−51.9938			−2.35849
$487$	−12.4289	+	21.5275i	−0.563209	+	0.975506i	0.434005	+	0.900910i	$0.357100\pi$
$487$	−12.4289	+	21.5275i	−0.563209	+	0.975506i	−0.997214	+	0.0745955i	$0.976233\pi$
$488$	28.6737	−	49.6643i	1.29800	−	2.24820i
$489$	−19.3912			−0.876902
$490$	−16.9105	+	29.2899i	−0.763939	+	1.32318i
$491$	−13.9567	−	24.1736i	−0.629855	−	1.09094i	−0.987580	−	0.157114i	$-0.949781\pi$
$491$	−13.9567	−	24.1736i	−0.629855	−	1.09094i	0.357725	−	0.933827i	$-0.383552\pi$
$492$	−27.3518	−	47.3748i	−1.23312	−	2.13582i
$493$	10.4226			0.469411
$494$	20.8390	−	25.8509i	0.937592	−	1.16309i
$495$	−39.7353			−1.78597
$496$	−8.84587	−	15.3215i	−0.397191	−	0.687955i
$497$	−5.64109	−	9.77065i	−0.253037	−	0.438274i
$498$	14.0631	−	24.3580i	0.630183	−	1.09151i
$499$	−2.98653			−0.133695			−0.0668477	−	0.997763i	$-0.521294\pi$
$499$	−2.98653			−0.133695			−0.0668477	+	0.997763i	$0.521294\pi$
$500$	13.9652	−	24.1884i	0.624543	−	1.08174i
$501$	−0.944829	+	1.63649i	−0.0422119	+	0.0731131i
$502$	−42.8797			−1.91382
$503$	−4.35206	+	7.53799i	−0.194049	+	0.336102i	−0.946588	−	0.322445i	$-0.895495\pi$
$503$	−4.35206	+	7.53799i	−0.194049	+	0.336102i	0.752540	+	0.658547i	$0.228829\pi$
$504$	−20.6074	−	35.6931i	−0.917928	−	1.58990i
$505$	−19.1263	−	33.1278i	−0.851110	−	1.47417i
$506$	−6.83327			−0.303776
$507$	−21.7903	+	19.7956i	−0.967742	+	0.879152i
$508$	−96.1103			−4.26420
$509$	20.5429	+	35.5813i	0.910546	+	1.57711i	0.813294	+	0.581853i	$0.197672\pi$
$509$	20.5429	+	35.5813i	0.910546	+	1.57711i	0.0972523	+	0.995260i	$0.468995\pi$
$510$	−15.1192	−	26.1873i	−0.669491	−	1.15959i
$511$	−3.35859	+	5.81724i	−0.148575	+	0.257340i
$512$	130.010			5.74569
$513$	−3.26226	+	5.65040i	−0.144032	+	0.249471i
$514$	−39.3893	+	68.2243i	−1.73739	+	3.00925i
$515$	−17.7121			−0.780488
$516$	−24.2561	+	42.0128i	−1.06781	+	1.84951i
$517$	−4.01086	−	6.94701i	−0.176397	−	0.305529i
$518$	5.20715	+	9.01905i	0.228789	+	0.396274i
$519$	28.0134			1.22965
$520$	80.2360	−	99.5331i	3.51858	−	4.36482i
$521$	15.0651			0.660014			0.330007	−	0.943979i	$-0.392949\pi$
$521$	15.0651			0.660014			0.330007	+	0.943979i	$0.392949\pi$
$522$	21.8048	+	37.7670i	0.954370	+	1.65302i
$523$	−14.8177	−	25.6651i	−0.647934	−	1.12225i	−0.983615	−	0.180279i	$-0.942300\pi$
$523$	−14.8177	−	25.6651i	−0.647934	−	1.12225i	0.335681	−	0.941976i	$-0.391033\pi$
$524$	16.1480	−	27.9691i	0.705427	−	1.22184i
$525$	26.9030			1.17414
$526$	−7.13423	+	12.3568i	−0.311067	+	0.538784i
$527$	0.708645	−	1.22741i	0.0308690	−	0.0534667i
$528$	221.217			9.62722
$529$	11.4014	−	19.7477i	0.495711	−	0.858597i
$530$	−0.468137	−	0.810838i	−0.0203346	−	0.0352205i
$531$	7.89035	+	13.6665i	0.342412	+	0.593075i
$532$	−35.1783			−1.52517
$533$	14.9307	+	2.33091i	0.646720	+	0.100963i
$534$	16.5966			0.718204
$535$	−11.3787	−	19.7085i	−0.491945	−	0.852073i
$536$	−1.80064	−	3.11879i	−0.0777757	−	0.134711i
$537$	12.3408	−	21.3749i	0.532545	−	0.922395i
$538$	−78.9080			−3.40197
$539$	9.91067	−	17.1658i	0.426883	−	0.739383i
$540$	−19.2354	+	33.3167i	−0.827761	+	1.43372i
$541$	7.38566			0.317534			0.158767	−	0.987316i	$-0.449248\pi$
$541$	7.38566			0.317534			0.158767	+	0.987316i	$0.449248\pi$
$542$	−0.921909	+	1.59679i	−0.0395994	+	0.0685882i
$543$	19.7441	+	34.1977i	0.847298	+	1.46756i
$544$	20.0700	+	34.7623i	0.860496	+	1.49042i
$545$	40.0107			1.71387
$546$	41.5097	+	6.48028i	1.77645	+	0.277330i
$547$	36.8691			1.57641			0.788205	−	0.615413i	$-0.211011\pi$
$547$	36.8691			1.57641			0.788205	+	0.615413i	$0.211011\pi$
$548$	−48.0134	−	83.1617i	−2.05103	−	3.55249i
$549$	5.81947	+	10.0796i	0.248369	+	0.430187i
$550$	−49.4866	+	85.7133i	−2.11012	+	3.65483i
$551$	24.3059			1.03547
$552$	5.27383	−	9.13454i	0.224469	−	0.388792i
$553$	−3.07524	+	5.32647i	−0.130772	+	0.226504i
$554$	−22.7721			−0.967494
$555$	−7.74908	+	13.4218i	−0.328930	+	0.569723i
$556$	44.6269	+	77.2961i	1.89260	+	3.27809i
$557$	3.60102	+	6.23716i	0.152580	+	0.264277i	0.932175	−	0.362007i	$-0.117908\pi$
$557$	3.60102	+	6.23716i	0.152580	+	0.264277i	−0.779595	+	0.626284i	$0.784575\pi$
$558$	5.93012			0.251042
$559$	−4.83025	−	12.5004i	−0.204298	−	0.528711i
$560$	−110.470			−4.66819
$561$	8.86086	+	15.3475i	0.374106	+	0.647970i
$562$	−26.9478	−	46.6749i	−1.13672	−	1.96886i
$563$	−21.6997	+	37.5849i	−0.914532	+	1.58402i	−0.106947	+	0.994265i	$0.534108\pi$
$563$	−21.6997	+	37.5849i	−0.914532	+	1.58402i	−0.807585	+	0.589751i	$0.799226\pi$
$564$	18.9621			0.798447
$565$	22.0844	−	38.2513i	0.929098	−	1.60924i
$566$	−12.2247	+	21.1738i	−0.513843	+	0.890002i
$567$	−20.0460			−0.841854
$568$	−32.0337	+	55.4840i	−1.34410	+	2.32805i
$569$	3.99911	+	6.92666i	0.167651	+	0.290381i	0.937594	−	0.347733i	$-0.113048\pi$
$569$	3.99911	+	6.92666i	0.167651	+	0.290381i	−0.769942	+	0.638113i	$0.779715\pi$
$570$	−35.2586	−	61.0696i	−1.47682	−	2.55792i
$571$	11.8608			0.496359			0.248180	−	0.968714i	$-0.420168\pi$
$571$	11.8608			0.496359			0.248180	+	0.968714i	$0.420168\pi$
$572$	−72.0123	+	89.3315i	−3.01098	+	3.73514i
$573$	44.4874			1.85849
$574$	−10.7827	−	18.6762i	−0.450061	−	0.779529i
$575$	1.42867	+	2.47453i	0.0595797	+	0.103195i
$576$	−46.3224	+	80.2327i	−1.93010	+	3.34303i
$577$	−28.9769			−1.20632			−0.603162	−	0.797619i	$-0.706093\pi$
$577$	−28.9769			−1.20632			−0.603162	+	0.797619i	$0.706093\pi$
$578$	20.8853	−	36.1744i	0.868713	−	1.50465i
$579$	14.1047	−	24.4300i	0.586170	−	1.01528i
$580$	143.316			5.95088
$581$	4.11578	−	7.12874i	0.170751	−	0.295750i
$582$	−47.5005	−	82.2733i	−1.96896	−	3.41034i
$583$	0.274359	+	0.475204i	0.0113628	+	0.0196809i
$584$	38.1444			1.57843
$585$	9.35220	+	24.2030i	0.386666	+	1.00067i
$586$	86.0316			3.55393
$587$	−12.3620	−	21.4116i	−0.510234	−	0.883751i	−0.999930	−	0.0118575i	$-0.996226\pi$
$587$	−12.3620	−	21.4116i	−0.510234	−	0.883751i	0.489696	−	0.871893i	$-0.337108\pi$
$588$	23.4273	+	40.5772i	0.966124	+	1.67338i
$589$	1.65258	−	2.86236i	0.0680935	−	0.117941i
$590$	69.8568			2.87596
$591$	−23.7057	+	41.0595i	−0.975122	+	1.68896i
$592$	17.9040	−	31.0107i	0.735850	−	1.27453i
$593$	5.65865			0.232373			0.116186	−	0.993227i	$-0.462933\pi$
$593$	5.65865			0.232373			0.116186	+	0.993227i	$0.462933\pi$
$594$	15.1851	−	26.3014i	0.623052	−	1.07916i
$595$	−4.42487	−	7.66411i	−0.181402	−	0.314198i
$596$	44.3951	+	76.8946i	1.81849	+	3.14973i
$597$	8.55146			0.349988
$598$	1.60830	+	4.16218i	0.0657681	+	0.170204i
$599$	−34.1428			−1.39504			−0.697518	−	0.716568i	$-0.745712\pi$
$599$	−34.1428			−1.39504			−0.697518	+	0.716568i	$0.745712\pi$
$600$	−76.3862	−	132.305i	−3.11845	−	5.40132i
$601$	13.5902	+	23.5390i	0.554358	+	0.960176i	0.997953	+	0.0639486i	$0.0203694\pi$
$601$	13.5902	+	23.5390i	0.554358	+	0.960176i	−0.443595	+	0.896227i	$0.646297\pi$
$602$	−9.56228	+	16.5624i	−0.389730	+	0.675031i
$603$	0.730896			0.0297644
$604$	−23.1030	+	40.0156i	−0.940049	+	1.62821i
$605$	32.9465	−	57.0650i	1.33947	−	2.32002i
$606$	−71.3831			−2.89974
$607$	12.6169	−	21.8531i	0.512105	−	0.886992i	−0.487797	−	0.872957i	$-0.662199\pi$
$607$	12.6169	−	21.8531i	0.512105	−	0.886992i	0.999902	−	0.0140343i	$-0.00446741\pi$
$608$	46.8040	+	81.0670i	1.89815	+	3.28770i
$609$	15.3767	+	26.6333i	0.623097	+	1.07924i
$610$	51.5224			2.08608
$611$	−3.28745	+	4.07810i	−0.132996	+	0.164982i
$612$	−17.3853			−0.702761
$613$	10.6017	+	18.3627i	0.428199	+	0.741663i	0.996713	−	0.0810106i	$-0.0258148\pi$
$613$	10.6017	+	18.3627i	0.428199	+	0.741663i	−0.568514	+	0.822674i	$0.692481\pi$
$614$	−26.4101	−	45.7436i	−1.06582	−	1.84606i
$615$	16.0464	−	27.7932i	0.647053	−	1.12073i
$616$	106.926			4.30816
$617$	−13.9492	+	24.1607i	−0.561574	+	0.972674i	0.435786	+	0.900050i	$0.356471\pi$
$617$	−13.9492	+	24.1607i	−0.561574	+	0.972674i	−0.997359	+	0.0726236i	$0.976863\pi$
$618$	−16.5262	+	28.6243i	−0.664783	+	1.15144i
$619$	−12.2043			−0.490534			−0.245267	−	0.969456i	$-0.578876\pi$
$619$	−12.2043			−0.490534			−0.245267	+	0.969456i	$0.578876\pi$
$620$	9.74420	−	16.8774i	0.391336	−	0.677815i
$621$	−0.438392	−	0.759316i	−0.0175920	−	0.0304703i
$622$	44.7242	+	77.4646i	1.79328	+	3.10605i
$623$	4.85724			0.194601
$624$	−52.0661	−	134.744i	−2.08431	−	5.39408i
$625$	−15.7801			−0.631204
$626$	−37.8362	−	65.5342i	−1.51224	−	2.61927i
$627$	20.6638	+	35.7908i	0.825233	+	1.42935i
$628$	28.5448	−	49.4411i	1.13906	−	1.97291i
$629$	2.86859			0.114378
$630$	18.5142	−	32.0676i	0.737625	−	1.27760i
$631$	−8.33492	+	14.4365i	−0.331808	+	0.574708i	−0.982866	−	0.184320i	$-0.940992\pi$
$631$	−8.33492	+	14.4365i	−0.331808	+	0.574708i	0.651059	+	0.759027i	$0.274325\pi$
$632$	34.9263			1.38929
$633$	11.4635	−	19.8553i	0.455632	−	0.789178i
$634$	25.8071	+	44.6992i	1.02493	+	1.77523i
$635$	−28.1923	−	48.8305i	−1.11878	−	1.93778i
$636$	−1.29708			−0.0514327
$637$	−12.7884	−	1.99645i	−0.506694	−	0.0791024i
$638$	−113.139			−4.47920
$639$	−6.50139	−	11.2607i	−0.257191	−	0.445468i
$640$	109.292	+	189.300i	4.32015	+	7.48272i
$641$	20.6710	−	35.8032i	0.816454	−	1.41414i	−0.0918243	−	0.995775i	$-0.529270\pi$
$641$	20.6710	−	35.8032i	0.816454	−	1.41414i	0.908279	−	0.418365i	$-0.137397\pi$
$642$	−42.4676			−1.67606
$643$	−10.4849	+	18.1603i	−0.413483	+	0.716174i	−0.995268	−	0.0971690i	$-0.969021\pi$
$643$	−10.4849	+	18.1603i	−0.413483	+	0.716174i	0.581785	+	0.813343i	$0.302355\pi$
$644$	2.36368	−	4.09401i	0.0931419	−	0.161327i
$645$	−28.4604			−1.12063
$646$	−6.52609	+	11.3035i	−0.256765	+	0.444731i
$647$	−0.181203	−	0.313852i	−0.00712381	−	0.0123388i	0.862442	−	0.506157i	$-0.168934\pi$
$647$	−0.181203	−	0.313852i	−0.00712381	−	0.0123388i	−0.869565	+	0.493818i	$0.835601\pi$
$648$	56.9170	+	98.5832i	2.23591	+	3.87271i
$649$	−40.9407			−1.60706
$650$	63.8557	+	9.96883i	2.50463	+	0.391010i
$651$	4.18192			0.163902
$652$	24.6764	+	42.7408i	0.966402	+	1.67386i
$653$	19.9374	+	34.5326i	0.780210	+	1.35136i	0.931819	+	0.362924i	$0.118221\pi$
$653$	19.9374	+	34.5326i	0.780210	+	1.35136i	−0.151608	+	0.988441i	$0.548445\pi$
$654$	37.3319	−	64.6607i	1.45979	−	2.52844i
$655$	18.9469			0.740318
$656$	−37.0747	+	64.2153i	−1.44752	+	2.50719i
$657$	−3.87079	+	6.70441i	−0.151014	+	0.261564i
$658$	7.47527			0.291416
$659$	−18.4757	+	32.0009i	−0.719711	+	1.24658i	0.241403	+	0.970425i	$0.422392\pi$
$659$	−18.4757	+	32.0009i	−0.719711	+	1.24658i	−0.961114	+	0.276151i	$0.910941\pi$
$660$	121.841	+	211.035i	4.74266	+	8.21452i
$661$	3.43669	+	5.95251i	0.133672	+	0.231526i	0.925089	−	0.379750i	$-0.123990\pi$
$661$	3.43669	+	5.95251i	0.133672	+	0.231526i	−0.791418	+	0.611276i	$0.790657\pi$
$662$	40.9346			1.59097
$663$	7.26270	−	9.00941i	0.282060	−	0.349897i
$664$	−46.7440			−1.81402
$665$	−10.3190	−	17.8730i	−0.400152	−	0.693083i
$666$	6.00127	+	10.3945i	0.232544	+	0.402779i
$667$	−1.63315	+	2.82869i	−0.0632357	+	0.109527i
$668$	4.80938			0.186081
$669$	12.7589	−	22.0991i	0.493289	−	0.854402i
$670$	1.61774	−	2.80200i	0.0624986	−	0.108251i
$671$	−30.1955			−1.16568
$672$	−59.2196	+	102.571i	−2.28445	+	3.95678i
$673$	−12.9512	−	22.4322i	−0.499233	−	0.864696i	0.500767	−	0.865582i	$-0.333051\pi$
$673$	−12.9512	−	22.4322i	−0.499233	−	0.864696i	−1.00000		0.000885998i	$0.999718\pi$
$674$	−8.67334	−	15.0227i	−0.334084	−	0.578651i
$675$	−12.6993			−0.488798
$676$	71.3613	+	22.8377i	2.74466	+	0.878374i
$677$	−15.0970			−0.580226			−0.290113	−	0.956992i	$-0.593693\pi$
$677$	−15.0970			−0.580226			−0.290113	+	0.956992i	$0.593693\pi$
$678$	−41.2116	−	71.3806i	−1.58272	−	2.74136i
$679$	−13.9017	−	24.0785i	−0.533500	−	0.924049i
$680$	−25.1272	+	43.5217i	−0.963586	+	1.66898i
$681$	0.280782			0.0107596
$682$	−7.69240	+	13.3236i	−0.294557	+	0.510188i
$683$	14.3814	−	24.9092i	0.550288	−	0.953126i	−0.447966	−	0.894051i	$-0.647851\pi$
$683$	14.3814	−	24.9092i	0.550288	−	0.953126i	0.998254	−	0.0590753i	$-0.0188152\pi$
$684$	−40.5432			−1.55021
$685$	28.1679	−	48.7882i	1.07624	−	1.86410i
$686$	27.2445	+	47.1888i	1.04020	+	1.80168i
$687$	22.3600	+	38.7287i	0.853089	+	1.47759i
$688$	65.7570			2.50696
$689$	0.224875	−	0.278959i	0.00856707	−	0.0106275i
$690$	9.47628			0.360756
$691$	2.67913	+	4.64039i	0.101919	+	0.176529i	0.912475	−	0.409132i	$-0.134168\pi$
$691$	2.67913	+	4.64039i	0.101919	+	0.176529i	−0.810556	+	0.585661i	$0.800835\pi$
$692$	−35.6486	−	61.7452i	−1.35516	−	2.34720i
$693$	−10.8505	+	18.7937i	−0.412178	+	0.713914i
$694$	59.0805			2.24266
$695$	−26.1811	+	45.3470i	−0.993106	+	1.72011i
$696$	87.3189	−	151.241i	3.30981	−	5.73276i
$697$	−5.94013			−0.224998
$698$	25.7923	−	44.6736i	0.976253	−	1.69092i
$699$	16.4189	+	28.4384i	0.621021	+	1.07564i
$700$	−34.2355	−	59.2977i	−1.29398	−	2.24124i
$701$	−35.8839			−1.35532			−0.677658	−	0.735377i	$-0.737005\pi$
$701$	−35.8839			−1.35532			−0.677658	+	0.735377i	$0.737005\pi$
$702$	−19.5943	−	3.05896i	−0.739539	−	0.115453i
$703$	6.68965			0.252305
$704$	−120.176	−	208.152i	−4.52932	−	7.84501i
$705$	5.56220	+	9.63402i	0.209485	+	0.362838i
$706$	3.03644	−	5.25926i	0.114278	−	0.197935i
$707$	−20.8914			−0.785701
$708$	48.3886	−	83.8116i	1.81856	−	3.14983i
$709$	−25.7469	+	44.5950i	−0.966946	+	1.67480i	−0.262652	+	0.964891i	$0.584597\pi$
$709$	−25.7469	+	44.5950i	−0.966946	+	1.67480i	−0.704294	+	0.709909i	$0.748736\pi$
$710$	−57.5597			−2.16018
$711$	−3.54423	+	6.13879i	−0.132919	+	0.230222i
$712$	−13.7912	−	23.8871i	−0.516849	−	0.895209i
$713$	0.222079	+	0.384651i	0.00831691	+	0.0144053i
$714$	−16.5145			−0.618039
$715$	−66.5100	−	10.3832i	−2.48733	−	0.388310i
$716$	−62.8173			−2.34759
$717$	−16.2533	−	28.1515i	−0.606989	−	1.05134i
$718$	−11.3491	−	19.6573i	−0.423546	−	0.733602i
$719$	−4.01880	+	6.96076i	−0.149876	+	0.259593i	−0.931181	−	0.364556i	$-0.881221\pi$
$719$	−4.01880	+	6.96076i	−0.149876	+	0.259593i	0.781306	+	0.624149i	$0.214554\pi$
$720$	−127.317			−4.74482
$721$	−4.83666	+	8.37734i	−0.180127	+	0.311988i
$722$	11.2510	−	19.4873i	0.418719	−	0.725242i
$723$	30.1157			1.12001
$724$	50.2507	−	87.0368i	1.86755	−	3.23470i
$725$	23.6545	+	40.9709i	0.878508	+	1.52162i
$726$	−61.4814	−	106.489i	−2.28179	−	3.95217i
$727$	45.0580			1.67111			0.835554	−	0.549409i	$-0.185147\pi$
$727$	45.0580			1.67111			0.835554	+	0.549409i	$0.185147\pi$
$728$	−25.1663	−	65.1290i	−0.932726	−	2.41384i
$729$	−9.69211			−0.358967
$730$	17.1349	+	29.6786i	0.634192	+	1.09845i
$731$	2.63390	+	4.56206i	0.0974185	+	0.168734i
$732$	35.6887	−	61.8146i	1.31909	−	2.28473i
$733$	−50.3366			−1.85922			−0.929612	−	0.368540i	$-0.879858\pi$
$733$	−50.3366			−1.85922			−0.929612	+	0.368540i	$0.879858\pi$
$734$	7.21238	−	12.4922i	0.266214	−	0.461096i
$735$	−13.7440	+	23.8053i	−0.506954	+	0.878070i
$736$	−12.5793			−0.463679
$737$	−0.948100	+	1.64216i	−0.0349237	+	0.0604896i
$738$	−12.4271	−	21.5244i	−0.457449	−	0.792324i
$739$	11.7905	+	20.4217i	0.433720	+	0.751225i	0.997190	−	0.0749114i	$-0.0238674\pi$
$739$	11.7905	+	20.4217i	0.433720	+	0.751225i	−0.563470	+	0.826136i	$0.690534\pi$
$740$	39.4445			1.45001
$741$	16.9369	−	21.0103i	0.622191	−	0.771831i
$742$	−0.511339			−0.0187718
$743$	24.3238	+	42.1300i	0.892353	+	1.54560i	0.837047	+	0.547131i	$0.184280\pi$
$743$	24.3238	+	42.1300i	0.892353	+	1.54560i	0.0553058	+	0.998469i	$0.482387\pi$
$744$	−11.8738	−	20.5660i	−0.435314	−	0.753986i
$745$	−26.0451	+	45.1114i	−0.954219	+	1.65276i
$746$	−19.7365			−0.722604
$747$	4.74346	−	8.21592i	0.173554	−	0.300605i
$748$	22.5518	−	39.0609i	0.824577	−	1.42821i
$749$	−12.4288			−0.454138
$750$	15.2888	−	26.4809i	0.558266	−	0.966946i
$751$	−25.1521	−	43.5648i	−0.917815	−	1.58970i	−0.802727	−	0.596346i	$-0.796619\pi$
$751$	−25.1521	−	43.5648i	−0.917815	−	1.58970i	−0.115087	−	0.993355i	$-0.536715\pi$
$752$	−12.8513	−	22.2591i	−0.468639	−	0.811706i
$753$	−34.8504			−1.27002
$754$	26.6286	+	68.9133i	0.969756	+	2.50967i
$755$	−27.1075			−0.986543
$756$	10.5053	+	18.1957i	0.382073	+	0.661770i
$757$	9.62335	+	16.6681i	0.349767	+	0.605814i	0.986208	−	0.165512i	$-0.0529275\pi$
$757$	9.62335	+	16.6681i	0.349767	+	0.605814i	−0.636441	+	0.771325i	$0.719594\pi$
$758$	17.6418	−	30.5565i	0.640780	−	1.10986i
$759$	−5.55372			−0.201587
$760$	−58.5976	+	101.494i	−2.12556	+	3.68157i
$761$	11.4956	−	19.9109i	0.416715	−	0.721771i	−0.578892	−	0.815404i	$-0.696515\pi$
$761$	11.4956	−	19.9109i	0.416715	−	0.721771i	0.995607	+	0.0936332i	$0.0298481\pi$
$762$	−105.219			−3.81169
$763$	10.9258	−	18.9240i	0.395539	−	0.685093i
$764$	−56.6126	−	98.0559i	−2.04817	−	3.54754i
$765$	−5.09969	−	8.83293i	−0.184380	−	0.319355i
$766$	−78.2816			−2.82843
$767$	9.63590	+	24.9372i	0.347932	+	0.900429i
$768$	210.746			7.60462
$769$	−10.5807	−	18.3262i	−0.381548	−	0.660861i	0.609736	−	0.792605i	$-0.291276\pi$
$769$	−10.5807	−	18.3262i	−0.381548	−	0.660861i	−0.991284	+	0.131744i	$0.957942\pi$
$770$	48.0324	+	83.1946i	1.73097	+	2.99812i
$771$	−32.0136	+	55.4491i	−1.15294	+	1.99695i
$772$	−71.7958			−2.58399
$773$	−8.13825	+	14.0959i	−0.292713	+	0.506993i	−0.974450	−	0.224604i	$-0.927891\pi$
$773$	−8.13825	+	14.0959i	−0.292713	+	0.506993i	0.681738	+	0.731597i	$0.261225\pi$
$774$	−11.0206	+	19.0882i	−0.396127	+	0.686112i
$775$	6.43318			0.231087
$776$	−78.9429	+	136.733i	−2.83389	+	4.90843i
$777$	4.23209	+	7.33020i	0.151826	+	0.262970i
$778$	−32.9534	−	57.0770i	−1.18144	−	2.04631i
$779$	−13.8526			−0.496320
$780$	99.8656	−	123.884i	3.57576	−	4.43575i
$781$	33.7338			1.20709
$782$	−0.876993	−	1.51900i	−0.0313612	−	0.0543192i
$783$	−7.25846	−	12.5720i	−0.259396	−	0.449287i
$784$	31.7550	−	55.0013i	1.13411	−	1.96433i
$785$	33.4925			1.19540
$786$	17.6784	−	30.6199i	0.630568	−	1.09218i
$787$	5.40644	−	9.36423i	0.192719	−	0.333799i	−0.753432	−	0.657526i	$-0.771603\pi$
$787$	5.40644	−	9.36423i	0.192719	−	0.333799i	0.946150	+	0.323728i	$0.104936\pi$
$788$	120.667			4.29858
$789$	−5.79832	+	10.0430i	−0.206426	+	0.357540i
$790$	15.6893	+	27.1747i	0.558201	+	0.966833i
$791$	−12.0612	−	20.8906i	−0.428847	−	0.742785i
$792$	123.233			4.37888
$793$	7.10689	+	18.3922i	0.252373	+	0.653127i
$794$	49.1098			1.74284
$795$	−0.380477	−	0.659006i	−0.0134941	−	0.0233725i
$796$	−10.8822	−	18.8485i	−0.385709	−	0.668067i
$797$	−7.95433	+	13.7773i	−0.281757	+	0.488017i	−0.971818	−	0.235734i	$-0.924251\pi$
$797$	−7.95433	+	13.7773i	−0.281757	+	0.488017i	0.690061	+	0.723752i	$0.257584\pi$
$798$	−38.5123			−1.36332
$799$	1.02952	−	1.78318i	0.0364218	−	0.0630845i
$800$	−91.0994	+	157.789i	−3.22085	+	5.57868i
$801$	5.59800			0.197796
$802$	−30.4923	+	52.8142i	−1.07672	+	1.86494i
$803$	−10.0422	−	17.3936i	−0.354381	−	0.613806i
$804$	−2.24116	−	3.88180i	−0.0790396	−	0.136901i
$805$	2.77338			0.0977487
$806$	9.92599	+	1.54960i	0.349628	+	0.0545822i
$807$	−64.1323			−2.25756
$808$	59.3172	+	102.740i	2.08677	+	3.61440i
$809$	3.44883	+	5.97355i	0.121254	+	0.210019i	0.920263	−	0.391301i	$-0.127975\pi$
$809$	3.44883	+	5.97355i	0.121254	+	0.210019i	−0.799008	+	0.601320i	$0.794642\pi$
$810$	−51.1357	+	88.5696i	−1.79673	+	3.11202i
$811$	−53.4737			−1.87772			−0.938859	−	0.344303i	$-0.888115\pi$
$811$	−53.4737			−1.87772			−0.938859	+	0.344303i	$0.888115\pi$
$812$	39.1354	−	67.7846i	1.37338	−	2.37877i
$813$	−0.749279	+	1.29779i	−0.0262784	+	0.0455155i
$814$	−31.1388			−1.09141
$815$	−14.4768	+	25.0745i	−0.507100	+	0.878323i
$816$	28.3913	+	49.1752i	0.993895	+	1.72148i
$817$	6.14235	+	10.6389i	0.214894	+	0.372207i
$818$	−32.8824			−1.14971
$819$	14.0012	+	2.18579i	0.489240	+	0.0763776i
$820$	−81.6796			−2.85237
$821$	−16.9571	−	29.3706i	−0.591807	−	1.02504i	−0.993989	−	0.109480i	$-0.965081\pi$
$821$	−16.9571	−	29.3706i	−0.591807	−	1.02504i	0.402182	−	0.915560i	$-0.368252\pi$
$822$	−52.5639	−	91.0434i	−1.83338	−	3.17550i
$823$	11.3619	−	19.6793i	0.396049	−	0.685977i	−0.597185	−	0.802103i	$-0.703714\pi$
$823$	11.3619	−	19.6793i	0.396049	−	0.685977i	0.993235	+	0.116126i	$0.0370476\pi$
$824$	54.9312			1.91362
$825$	−40.2201	+	69.6632i	−1.40028	+	2.42536i
$826$	19.0759	−	33.0404i	0.663734	−	1.14962i
$827$	−0.680968			−0.0236796			−0.0118398	−	0.999930i	$-0.503769\pi$
$827$	−0.680968			−0.0236796			−0.0118398	+	0.999930i	$0.503769\pi$
$828$	2.72415	−	4.71837i	0.0946708	−	0.163975i
$829$	18.8565	+	32.6605i	0.654914	+	1.13435i	0.981915	+	0.189321i	$0.0606287\pi$
$829$	18.8565	+	32.6605i	0.654914	+	1.13435i	−0.327001	+	0.945024i	$0.606038\pi$
$830$	−20.9980	−	36.3696i	−0.728851	−	1.26241i
$831$	−18.5080			−0.642034
$832$	−98.5012	+	122.191i	−3.41492	+	4.23622i
$833$	5.08781			0.176282
$834$	48.8565	+	84.6219i	1.69176	+	2.93022i
$835$	1.41075	+	2.44349i	0.0488210	+	0.0845605i
$836$	52.5916	−	91.0914i	1.81892	−	3.15046i
$837$	−1.97404			−0.0682327
$838$	35.0227	−	60.6611i	1.20984	−	2.09550i
$839$	−9.04752	+	15.6708i	−0.312355	+	0.541015i	−0.978872	−	0.204475i	$-0.934451\pi$
$839$	−9.04752	+	15.6708i	−0.312355	+	0.541015i	0.666517	+	0.745490i	$0.267785\pi$
$840$	−148.283			−5.11625
$841$	−12.5400	+	21.7200i	−0.432415	+	0.748966i
$842$	21.2777	+	36.8541i	0.733279	+	1.27008i
$843$	−21.9017	−	37.9349i	−0.754336	−	1.30655i
$844$	−58.3515			−2.00854
$845$	9.32951	+	42.9554i	0.320945	+	1.47771i
$846$	8.61529			0.296200
$847$	−17.9935	−	31.1656i	−0.618263	−	1.07086i
$848$	0.879081	+	1.52261i	0.0301878	+	0.0522868i
$849$	−9.93560	+	17.2090i	−0.340989	+	0.590610i
$850$	−25.4048			−0.871377
$851$	−0.449486	+	0.778533i	−0.0154082	+	0.0266878i
$852$	−39.8706	+	69.0580i	−1.36595	+	2.36589i
$853$	24.8050			0.849306			0.424653	−	0.905356i	$-0.360396\pi$
$853$	24.8050			0.849306			0.424653	+	0.905356i	$0.360396\pi$
$854$	14.0693	−	24.3687i	0.481440	−	0.833879i
$855$	−11.8927	−	20.5987i	−0.406720	−	0.704460i
$856$	35.2893	+	61.1228i	1.20616	+	2.08913i
$857$	−8.50765			−0.290616			−0.145308	−	0.989386i	$-0.546417\pi$
$857$	−8.50765			−0.290616			−0.145308	+	0.989386i	$0.546417\pi$
$858$	−78.8372	+	97.7980i	−2.69146	+	3.33877i
$859$	41.8477			1.42783			0.713913	−	0.700234i	$-0.246921\pi$
$859$	41.8477			1.42783			0.713913	+	0.700234i	$0.246921\pi$
$860$	36.2174	+	62.7304i	1.23500	+	2.13909i
$861$	−8.76360	−	15.1790i	−0.298663	−	0.517299i
$862$	2.75378	−	4.76969i	0.0937941	−	0.162456i
$863$	−22.0840			−0.751748			−0.375874	−	0.926671i	$-0.622658\pi$
$863$	−22.0840			−0.751748			−0.375874	+	0.926671i	$0.622658\pi$
$864$	27.9541	−	48.4179i	0.951018	−	1.64721i
$865$	20.9138	−	36.2238i	0.711091	−	1.23165i
$866$	13.6794			0.464846
$867$	16.9744	−	29.4006i	0.576482	−	0.998497i
$868$	−5.32171	−	9.21748i	−0.180631	−	0.312862i
$869$	−9.19498	−	15.9262i	−0.311918	−	0.540258i
$870$	156.899			5.31937
$871$	1.22339	+	0.190990i	0.0414531	+	0.00647145i
$872$	−124.087			−4.20210
$873$	−16.0218	−	27.7506i	−0.542257	−	0.939217i
$874$	−2.04518	−	3.54235i	−0.0691792	−	0.119822i
$875$	4.47449	−	7.75004i	0.151265	−	0.261999i
$876$	47.4763			1.60408
$877$	−17.8512	+	30.9191i	−0.602791	+	1.04406i	0.389605	+	0.920982i	$0.372611\pi$
$877$	−17.8512	+	30.9191i	−0.602791	+	1.04406i	−0.992396	+	0.123083i	$0.960722\pi$
$878$	−37.3964	+	64.7725i	−1.26207	+	2.18597i
$879$	69.9220			2.35841
$880$	165.152	−	286.052i	5.56728	−	9.64282i
$881$	−15.1142	−	26.1786i	−0.509211	−	0.881979i	−0.999943	−	0.0106685i	$-0.996604\pi$
$881$	−15.1142	−	26.1786i	−0.509211	−	0.881979i	0.490732	−	0.871310i	$-0.336729\pi$
$882$	10.6440	+	18.4360i	0.358403	+	0.620771i
$883$	45.1062			1.51794			0.758972	−	0.651123i	$-0.225702\pi$
$883$	45.1062			1.51794			0.758972	+	0.651123i	$0.225702\pi$
$884$	−29.1001	−	4.54295i	−0.978741	−	0.152796i
$885$	56.7759			1.90850
$886$	−36.2420	−	62.7730i	−1.21757	−	2.10890i
$887$	−13.9863	−	24.2249i	−0.469612	−	0.813392i	0.529784	−	0.848133i	$-0.322273\pi$
$887$	−13.9863	−	24.2249i	−0.469612	−	0.813392i	−0.999396	+	0.0347401i	$0.988940\pi$
$888$	24.0325	−	41.6255i	0.806478	−	1.39686i
$889$	−30.7940			−1.03280
$890$	12.3904	−	21.4608i	0.415327	−	0.719368i
$891$	29.9689	−	51.9076i	1.00399	−	1.73897i
$892$	−64.9457			−2.17454
$893$	2.40088	−	4.15844i	0.0803423	−	0.139157i
$894$	48.6027	+	84.1823i	1.62552	+	2.81548i
$895$	−18.4264	−	31.9155i	−0.615927	−	1.06682i
$896$	119.378			3.98814
$897$	1.30714	+	3.38280i	0.0436441	+	0.112948i
$898$	−61.0769			−2.03816
$899$	3.67696	+	6.36868i	0.122633	+	0.212407i
$900$	−39.4567	−	68.3410i	−1.31522	−	2.27803i
$901$	−0.0704234	+	0.121977i	−0.00234614	+	0.00406364i
$902$	64.4806			2.14697
$903$	−7.77172	+	13.4610i	−0.258627	+	0.447954i
$904$	−68.4912	+	118.630i	−2.27798	+	3.94558i
$905$	58.9608			1.95992
$906$	−25.2926	+	43.8081i	−0.840291	+	1.45543i
$907$	−20.6319	−	35.7355i	−0.685071	−	1.18658i	−0.973414	−	0.229051i	$-0.926438\pi$
$907$	−20.6319	−	35.7355i	−0.685071	−	1.18658i	0.288343	−	0.957527i	$-0.406896\pi$
$908$	−0.357310	−	0.618879i	−0.0118577	−	0.0205382i
$909$	−24.0774			−0.798598
$910$	39.3692	−	48.8377i	1.30508	−	1.61895i
$911$	53.8135			1.78292			0.891460	−	0.453100i	$-0.149682\pi$
$911$	53.8135			1.78292			0.891460	+	0.453100i	$0.149682\pi$
$912$	66.2095	+	114.678i	2.19242	+	3.79737i
$913$	12.3062	+	21.3150i	0.407276	+	0.705423i
$914$	38.3030	−	66.3428i	1.26695	−	2.19442i
$915$	41.8747			1.38433
$916$	56.9087	−	98.5688i	1.88032	−	3.25680i
$917$	5.17385	−	8.96138i	0.170856	−	0.295931i
$918$	7.79552			0.257290
$919$	−24.1939	+	41.9050i	−0.798082	+	1.38232i	0.122782	+	0.992434i	$0.460819\pi$
$919$	−24.1939	+	41.9050i	−0.798082	+	1.38232i	−0.920864	+	0.389885i	$0.872515\pi$
$920$	−7.87450	−	13.6390i	−0.259615	−	0.449666i
$921$	−21.4647	−	37.1779i	−0.707286	−	1.22505i
$922$	31.3337			1.03192
$923$	−7.93967	−	20.5474i	−0.261337	−	0.676326i
$924$	133.085			4.37817
$925$	6.51037	+	11.2763i	0.214060	+	0.370762i
$926$	−17.3387	−	30.0314i	−0.569783	−	0.986894i
$927$	−5.57428	+	9.65493i	−0.183083	+	0.317110i
$928$	−208.276			−6.83699
$929$	−25.2123	+	43.6689i	−0.827187	+	1.43273i	0.0730488	+	0.997328i	$0.476727\pi$
$929$	−25.2123	+	43.6689i	−0.827187	+	1.43273i	−0.900236	+	0.435402i	$0.856606\pi$
$930$	10.6677	−	18.4770i	0.349808	−	0.605885i
$931$	11.8649			0.388858
$932$	41.7879	−	72.3788i	1.36881	−	2.37085i
$933$	36.3495	+	62.9591i	1.19003	+	2.06119i
$934$	39.5183	+	68.4477i	1.29308	+	2.23968i
$935$	26.4608			0.865360
$936$	−29.0043	−	75.0616i	−0.948037	−	2.45347i
$937$	14.8403			0.484810			0.242405	−	0.970175i	$-0.422064\pi$
$937$	14.8403			0.484810			0.242405	+	0.970175i	$0.422064\pi$
$938$	−0.883514	−	1.53029i	−0.0288477	−	0.0499658i
$939$	−30.7512	−	53.2627i	−1.00353	−	1.73816i
$940$	14.1564	−	24.5196i	0.461731	−	0.799741i
$941$	−10.6321			−0.346597			−0.173299	−	0.984869i	$-0.555443\pi$
$941$	−10.6321			−0.346597			−0.173299	+	0.984869i	$0.555443\pi$
$942$	31.2502	−	54.1269i	1.01819	−	1.76355i
$943$	0.930773	−	1.61215i	0.0303102	−	0.0524987i
$944$	−131.179			−4.26951
$945$	−6.16308	+	10.6748i	−0.200485	+	0.347250i
$946$	−28.5913	−	49.5215i	−0.929582	−	1.61008i
$947$	−21.9241	−	37.9737i	−0.712438	−	1.23398i	−0.963939	−	0.266122i	$-0.914257\pi$
$947$	−21.9241	−	37.9737i	−0.712438	−	1.23398i	0.251501	−	0.967857i	$-0.419076\pi$
$948$	43.4709			1.41187
$949$	−8.23097	+	10.2106i	−0.267188	+	0.331449i
$950$	−59.2448			−1.92215
$951$	20.9747	+	36.3292i	0.680150	+	1.17805i
$952$	13.7230	+	23.7690i	0.444766	+	0.770357i
$953$	23.9749	−	41.5258i	0.776624	−	1.34515i	−0.157254	−	0.987558i	$-0.550264\pi$
$953$	23.9749	−	41.5258i	0.776624	−	1.34515i	0.933877	−	0.357593i	$-0.116403\pi$
$954$	−0.589321			−0.0190800
$955$	33.2127	−	57.5260i	1.07474	−	1.86150i
$956$	−41.3663	+	71.6485i	−1.33788	+	2.31728i
$957$	−91.9530			−2.97242
$958$	−5.64709	+	9.78105i	−0.182449	+	0.316011i
$959$	−15.3836	−	26.6452i	−0.496764	−	0.860420i
$960$	166.659	+	288.662i	5.37890	+	9.31652i
$961$	1.00000			0.0322581
$962$	7.32891	+	18.9668i	0.236294	+	0.611514i
$963$	−14.3242			−0.461592
$964$	−38.3238	−	66.3788i	−1.23433	−	2.13792i
$965$	−21.0601	−	36.4771i	−0.677948	−	1.17424i
$966$	2.58770	−	4.48202i	0.0832578	−	0.144207i
$967$	−18.3122			−0.588881			−0.294440	−	0.955670i	$-0.595133\pi$
$967$	−18.3122			−0.588881			−0.294440	+	0.955670i	$0.595133\pi$
$968$	−102.178	+	176.978i	−3.28413	+	5.68829i
$969$	−5.30406	+	9.18690i	−0.170391	+	0.295126i
$970$	−141.849			−4.55448
$971$	−12.0359	+	20.8467i	−0.386249	+	0.669003i	−0.991942	−	0.126696i	$-0.959563\pi$
$971$	−12.0359	+	20.8467i	−0.386249	+	0.669003i	0.605693	+	0.795699i	$0.292896\pi$
$972$	53.7754	+	93.1417i	1.72485	+	2.98752i
$973$	14.2986	+	24.7659i	0.458392	+	0.793958i
$974$	69.2620			2.21930
$975$	51.8985	+	8.10214i	1.66208	+	0.259476i
$976$	−96.7501			−3.09690
$977$	15.4023	+	26.6775i	0.492763	+	0.853490i	0.999965	−	0.00833705i	$-0.00265380\pi$
$977$	15.4023	+	26.6775i	0.492763	+	0.853490i	−0.507203	+	0.861827i	$0.669320\pi$
$978$	27.0151	+	46.7915i	0.863848	+	1.49623i
$979$	−7.26159	+	12.5774i	−0.232081	+	0.401977i
$980$	69.9598			2.23478
$981$	12.5920	−	21.8100i	0.402031	−	0.696339i
$982$	−38.8877	+	67.3555i	−1.24096	+	2.14940i
$983$	−13.2509			−0.422637			−0.211319	−	0.977417i	$-0.567776\pi$
$983$	−13.2509			−0.422637			−0.211319	+	0.977417i	$0.567776\pi$
$984$	−49.7653	+	86.1960i	−1.58646	+	2.74783i
$985$	35.3956	+	61.3070i	1.12780	+	1.95340i
$986$	−14.5204	−	25.1501i	−0.462423	−	0.800941i
$987$	6.07550			0.193385
$988$	−67.8623	−	10.5943i	−2.15899	−	0.337050i
$989$	−1.65085			−0.0524941
$990$	55.3576	+	95.8822i	1.75938	+	3.04734i
$991$	−5.03224	−	8.71610i	−0.159854	−	0.276876i	0.774962	−	0.632008i	$-0.217769\pi$
$991$	−5.03224	−	8.71610i	−0.159854	−	0.276876i	−0.934816	+	0.355132i	$0.884436\pi$
$992$	−14.1609	+	24.5273i	−0.449608	+	0.778744i
$993$	33.2695			1.05577
$994$	−15.7179	+	27.2242i	−0.498541	+	0.863498i
$995$	6.38421	−	11.0578i	0.202393	−	0.350555i
$996$	−58.1798			−1.84350
$997$	6.14988	−	10.6519i	0.194769	−	0.337349i	−0.752056	−	0.659099i	$-0.770938\pi$
$997$	6.14988	−	10.6519i	0.194769	−	0.337349i	0.946825	+	0.321750i	$0.104271\pi$
$998$	4.16072	+	7.20657i	0.131705	+	0.228120i
$999$	−1.99772	−	3.46016i	−0.0632052	−	0.109475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.1	✓	36
13.3	even	3		5239.2.a.p.1.18		18
13.9	even	3	inner	403.2.f.c.373.1	yes	36
13.10	even	6		5239.2.a.o.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.1	✓	36	1.1	even	1	trivial
403.2.f.c.373.1	yes	36	13.9	even	3	inner
5239.2.a.o.1.1		18	13.10	even	6
5239.2.a.p.1.18		18	13.3	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39316 - 2.41302i) q^{2} +(-1.13229 - 1.96118i) q^{3} +(-2.88179 + 4.99141i) q^{4} -3.38130 q^{5} +(-3.15492 + 5.46447i) q^{6} +(-0.923334 + 1.59926i) q^{7} +10.4866 q^{8} +(-1.06415 + 1.84316i) q^{9} +O(q^{10})\)	\(q+(-1.39316 - 2.41302i) q^{2} +(-1.13229 - 1.96118i) q^{3} +(-2.88179 + 4.99141i) q^{4} -3.38130 q^{5} +(-3.15492 + 5.46447i) q^{6} +(-0.923334 + 1.59926i) q^{7} +10.4866 q^{8} +(-1.06415 + 1.84316i) q^{9} +(4.71069 + 8.15916i) q^{10} +(-2.76077 - 4.78180i) q^{11} +13.0521 q^{12} +(-2.26284 + 2.80706i) q^{13} +5.14541 q^{14} +(3.82860 + 6.63133i) q^{15} +(-8.84587 - 15.3215i) q^{16} +(0.708645 - 1.22741i) q^{17} +5.93012 q^{18} +(1.65258 - 2.86236i) q^{19} +(9.74420 - 16.8774i) q^{20} +4.18192 q^{21} +(-7.69240 + 13.3236i) q^{22} +(0.222079 + 0.384651i) q^{23} +(-11.8738 - 20.5660i) q^{24} +6.43318 q^{25} +(9.92599 + 1.54960i) q^{26} -1.97404 q^{27} +(-5.32171 - 9.21748i) q^{28} +(3.67696 + 6.36868i) q^{29} +(10.6677 - 18.4770i) q^{30} +1.00000 q^{31} +(-14.1609 + 24.5273i) q^{32} +(-6.25198 + 10.8287i) q^{33} -3.94902 q^{34} +(3.12207 - 5.40758i) q^{35} +(-6.13331 - 10.6232i) q^{36} +(1.01200 + 1.75283i) q^{37} -9.20925 q^{38} +(8.06732 + 1.25943i) q^{39} -35.4582 q^{40} +(-2.09559 - 3.62968i) q^{41} +(-5.82608 - 10.0911i) q^{42} +(-1.85841 + 3.21886i) q^{43} +31.8239 q^{44} +(3.59820 - 6.23227i) q^{45} +(0.618782 - 1.07176i) q^{46} +1.45280 q^{47} +(-20.0321 + 34.6967i) q^{48} +(1.79491 + 3.10887i) q^{49} +(-8.96245 - 15.5234i) q^{50} -3.20956 q^{51} +(-7.49016 - 19.3841i) q^{52} -0.0993776 q^{53} +(2.75015 + 4.76340i) q^{54} +(9.33500 + 16.1687i) q^{55} +(-9.68259 + 16.7707i) q^{56} -7.48479 q^{57} +(10.2452 - 17.7452i) q^{58} +(3.70735 - 6.42133i) q^{59} -44.1329 q^{60} +(2.73433 - 4.73600i) q^{61} +(-1.39316 - 2.41302i) q^{62} +(-1.96513 - 3.40370i) q^{63} +43.5300 q^{64} +(7.65132 - 9.49150i) q^{65} +34.8400 q^{66} +(-0.171709 - 0.297409i) q^{67} +(4.08433 + 7.07427i) q^{68} +(0.502913 - 0.871072i) q^{69} -17.3982 q^{70} +(-3.05474 + 5.29096i) q^{71} +(-11.1592 + 19.3284i) q^{72} +3.63746 q^{73} +(2.81975 - 4.88396i) q^{74} +(-7.28421 - 12.6166i) q^{75} +(9.52480 + 16.4974i) q^{76} +10.1965 q^{77} +(-8.20004 - 21.2212i) q^{78} +3.33058 q^{79} +(29.9105 + 51.8065i) q^{80} +(5.42762 + 9.40092i) q^{81} +(-5.83900 + 10.1134i) q^{82} -4.45752 q^{83} +(-12.0514 + 20.8737i) q^{84} +(-2.39614 + 4.15023i) q^{85} +10.3563 q^{86} +(8.32675 - 14.4223i) q^{87} +(-28.9510 - 50.1446i) q^{88} +(-1.31514 - 2.27788i) q^{89} -20.0515 q^{90} +(-2.39987 - 6.21072i) q^{91} -2.55994 q^{92} +(-1.13229 - 1.96118i) q^{93} +(-2.02399 - 3.50565i) q^{94} +(-5.58788 + 9.67849i) q^{95} +64.1367 q^{96} +(-7.52801 + 13.0389i) q^{97} +(5.00119 - 8.66231i) q^{98} +11.7515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more