LMFDB - Embedded newform 287.2.h.d.78.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, 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("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.1
Character	$\chi$	$=$	287.78
Dual form			287.2.h.d.92.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21373 + 1.60837i) q^{2} -3.42753 q^{3} +(1.69571 - 5.21887i) q^{4} +(-0.479452 + 1.47560i) q^{5} +(7.58764 - 5.51274i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.94888 + 9.07572i) q^{8} +8.74800 q^{9} +O(q^{10})$	\(q+(-2.21373 + 1.60837i) q^{2} -3.42753 q^{3} +(1.69571 - 5.21887i) q^{4} +(-0.479452 + 1.47560i) q^{5} +(7.58764 - 5.51274i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.94888 + 9.07572i) q^{8} +8.74800 q^{9} +(-1.31193 - 4.03772i) q^{10} +(0.201143 + 0.619054i) q^{11} +(-5.81212 + 17.8879i) q^{12} +(0.608537 - 0.442128i) q^{13} -2.73632 q^{14} +(1.64334 - 5.05767i) q^{15} +(-12.2462 - 8.89742i) q^{16} +(0.441807 + 1.35974i) q^{17} +(-19.3657 + 14.0700i) q^{18} +(-0.247909 - 0.180116i) q^{19} +(6.88796 + 5.00440i) q^{20} +(-2.77293 - 2.01465i) q^{21} +(-1.44094 - 1.04691i) q^{22} +(3.00510 - 2.18333i) q^{23} +(-10.1074 - 31.1073i) q^{24} +(2.09756 + 1.52397i) q^{25} +(-0.636032 + 1.95750i) q^{26} -19.7015 q^{27} +(4.43944 - 3.22544i) q^{28} +(-1.46253 + 4.50122i) q^{29} +(4.49670 + 13.8394i) q^{30} +(-1.33414 - 4.10607i) q^{31} +22.3347 q^{32} +(-0.689424 - 2.12183i) q^{33} +(-3.16501 - 2.29951i) q^{34} +(-1.25522 + 0.911972i) q^{35} +(14.8341 - 45.6547i) q^{36} +(-1.89111 + 5.82025i) q^{37} +0.838497 q^{38} +(-2.08578 + 1.51541i) q^{39} -14.8060 q^{40} +(-4.79756 + 4.24069i) q^{41} +9.37883 q^{42} +(-4.45079 + 3.23369i) q^{43} +3.57185 q^{44} +(-4.19424 + 12.9086i) q^{45} +(-3.14088 + 9.66662i) q^{46} +(-5.39339 + 3.91853i) q^{47} +(41.9744 + 30.4962i) q^{48} +(0.309017 + 0.951057i) q^{49} -7.09453 q^{50} +(-1.51431 - 4.66057i) q^{51} +(-1.27551 - 3.92560i) q^{52} +(2.11266 - 6.50211i) q^{53} +(43.6137 - 31.6872i) q^{54} -1.00992 q^{55} +(-2.94888 + 9.07572i) q^{56} +(0.849716 + 0.617355i) q^{57} +(-4.00196 - 12.3168i) q^{58} +(-2.53546 + 1.84212i) q^{59} +(-23.6087 - 17.1527i) q^{60} +(8.79725 + 6.39157i) q^{61} +(9.55752 + 6.94394i) q^{62} +(7.07728 + 5.14194i) q^{63} +(-24.9504 + 18.1275i) q^{64} +(0.360640 + 1.10994i) q^{65} +(4.93888 + 3.58831i) q^{66} +(0.0259884 - 0.0799840i) q^{67} +7.84550 q^{68} +(-10.3001 + 7.48345i) q^{69} +(1.31193 - 4.03772i) q^{70} +(2.57387 + 7.92154i) q^{71} +(25.7968 + 79.3944i) q^{72} +0.222081 q^{73} +(-5.17469 - 15.9261i) q^{74} +(-7.18946 - 5.22345i) q^{75} +(-1.36039 + 0.988379i) q^{76} +(-0.201143 + 0.619054i) q^{77} +(2.18002 - 6.70941i) q^{78} -8.14247 q^{79} +(19.0005 - 13.8047i) q^{80} +41.2834 q^{81} +(3.79992 - 17.1040i) q^{82} -9.78284 q^{83} +(-15.2163 + 11.0553i) q^{84} -2.21826 q^{85} +(4.65188 - 14.3170i) q^{86} +(5.01288 - 15.4281i) q^{87} +(-5.02521 + 3.65103i) q^{88} +(1.62047 + 1.17734i) q^{89} +(-11.4768 - 35.3219i) q^{90} +0.752193 q^{91} +(-6.29875 - 19.3856i) q^{92} +(4.57283 + 14.0737i) q^{93} +(5.63708 - 17.3491i) q^{94} +(0.384640 - 0.279457i) q^{95} -76.5528 q^{96} +(-1.18201 + 3.63784i) q^{97} +(-2.21373 - 1.60837i) q^{98} +(1.75960 + 5.41548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.21373	+	1.60837i	−1.56534	+	1.13729i	−0.633892	+	0.773421i	$0.718544\pi$
$2$	−2.21373	+	1.60837i	−1.56534	+	1.13729i	−0.931451	+	0.363867i	$0.881456\pi$
$3$	−3.42753			−1.97889			−0.989444	−	0.144915i	$-0.953709\pi$
$3$	−3.42753			−1.97889			−0.989444	+	0.144915i	$0.953709\pi$
$4$	1.69571	−	5.21887i	0.847857	−	2.60944i
$5$	−0.479452	+	1.47560i	−0.214417	+	0.659909i	0.784777	+	0.619778i	$0.212777\pi$
$5$	−0.479452	+	1.47560i	−0.214417	+	0.659909i	−0.999194	+	0.0401307i	$0.987223\pi$
$6$	7.58764	−	5.51274i	3.09764	−	2.25057i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	2.94888	+	9.07572i	1.04259	+	3.20875i
$9$	8.74800			2.91600
$10$	−1.31193	−	4.03772i	−0.414870	−	1.27684i
$11$	0.201143	+	0.619054i	0.0606468	+	0.186652i	0.976790	−	0.214200i	$-0.0687143\pi$
$11$	0.201143	+	0.619054i	0.0606468	+	0.186652i	−0.916143	+	0.400851i	$0.868714\pi$
$12$	−5.81212	+	17.8879i	−1.67782	+	5.16378i
$13$	0.608537	−	0.442128i	0.168778	−	0.122624i	−0.500190	−	0.865916i	$-0.666736\pi$
$13$	0.608537	−	0.442128i	0.168778	−	0.122624i	0.668968	+	0.743292i	$0.266736\pi$
$14$	−2.73632			−0.731312
$15$	1.64334	−	5.05767i	0.424308	−	1.30589i
$16$	−12.2462	−	8.89742i	−3.06156	−	2.22436i
$17$	0.441807	+	1.35974i	0.107154	+	0.329786i	0.990230	−	0.139444i	$-0.0445315\pi$
$17$	0.441807	+	1.35974i	0.107154	+	0.329786i	−0.883076	+	0.469230i	$0.844532\pi$
$18$	−19.3657	+	14.0700i	−4.56454	+	3.31633i
$19$	−0.247909	−	0.180116i	−0.0568742	−	0.0413215i	0.558985	−	0.829178i	$-0.311191\pi$
$19$	−0.247909	−	0.180116i	−0.0568742	−	0.0413215i	−0.615859	+	0.787856i	$0.711191\pi$
$20$	6.88796	+	5.00440i	1.54020	+	1.11902i
$21$	−2.77293	−	2.01465i	−0.605104	−	0.439634i
$22$	−1.44094	−	1.04691i	−0.307210	−	0.223201i
$23$	3.00510	−	2.18333i	0.626607	−	0.455257i	−0.228616	−	0.973517i	$-0.573420\pi$
$23$	3.00510	−	2.18333i	0.626607	−	0.455257i	0.855223	+	0.518260i	$0.173420\pi$
$24$	−10.1074	−	31.1073i	−2.06316	−	6.34976i
$25$	2.09756	+	1.52397i	0.419512	+	0.304793i
$26$	−0.636032	+	1.95750i	−0.124736	+	0.383898i
$27$	−19.7015			−3.79155
$28$	4.43944	−	3.22544i	0.838975	−	0.609551i
$29$	−1.46253	+	4.50122i	−0.271586	+	0.835855i	0.718517	+	0.695509i	$0.244821\pi$
$29$	−1.46253	+	4.50122i	−0.271586	+	0.835855i	−0.990103	+	0.140345i	$0.955179\pi$
$30$	4.49670	+	13.8394i	0.820981	+	2.52672i
$31$	−1.33414	−	4.10607i	−0.239619	−	0.737473i	−0.996475	−	0.0838905i	$-0.973265\pi$
$31$	−1.33414	−	4.10607i	−0.239619	−	0.737473i	0.756856	−	0.653582i	$-0.226735\pi$
$32$	22.3347			3.94825
$33$	−0.689424	−	2.12183i	−0.120013	−	0.369363i
$34$	−3.16501	−	2.29951i	−0.542795	−	0.394363i
$35$	−1.25522	+	0.911972i	−0.212171	+	0.154151i
$36$	14.8341	−	45.6547i	2.47235	−	7.60911i
$37$	−1.89111	+	5.82025i	−0.310897	+	0.956842i	0.666514	+	0.745493i	$0.267786\pi$
$37$	−1.89111	+	5.82025i	−0.310897	+	0.956842i	−0.977411	+	0.211350i	$0.932214\pi$
$38$	0.838497			0.136022
$39$	−2.08578	+	1.51541i	−0.333992	+	0.242660i
$40$	−14.8060			−2.34103
$41$	−4.79756	+	4.24069i	−0.749253	+	0.662284i
$41$	−4.79756	+	4.24069i	−0.749253	+	0.662284i
$42$	9.37883			1.44719
$43$	−4.45079	+	3.23369i	−0.678739	+	0.493133i	−0.872939	−	0.487829i	$-0.837789\pi$
$43$	−4.45079	+	3.23369i	−0.678739	+	0.493133i	0.194200	+	0.980962i	$0.437789\pi$
$44$	3.57185			0.538476
$45$	−4.19424	+	12.9086i	−0.625241	+	1.92429i
$46$	−3.14088	+	9.66662i	−0.463097	+	1.42527i
$47$	−5.39339	+	3.91853i	−0.786707	+	0.571576i	−0.906985	−	0.421164i	$-0.861622\pi$
$47$	−5.39339	+	3.91853i	−0.786707	+	0.571576i	0.120277	+	0.992740i	$0.461622\pi$
$48$	41.9744	+	30.4962i	6.05849	+	4.40175i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−7.09453			−1.00332
$51$	−1.51431	−	4.66057i	−0.212046	−	0.652610i
$52$	−1.27551	−	3.92560i	−0.176881	−	0.544383i
$53$	2.11266	−	6.50211i	0.290197	−	0.893133i	−0.694596	−	0.719400i	$-0.744417\pi$
$53$	2.11266	−	6.50211i	0.290197	−	0.893133i	0.984793	−	0.173733i	$-0.0555831\pi$
$54$	43.6137	−	31.6872i	5.93507	−	4.31208i
$55$	−1.00992			−0.136177
$56$	−2.94888	+	9.07572i	−0.394061	+	1.21279i
$57$	0.849716	+	0.617355i	0.112548	+	0.0817707i
$58$	−4.00196	−	12.3168i	−0.525483	−	1.61727i
$59$	−2.53546	+	1.84212i	−0.330088	+	0.239823i	−0.740468	−	0.672091i	$-0.765396\pi$
$59$	−2.53546	+	1.84212i	−0.330088	+	0.239823i	0.410380	+	0.911915i	$0.365396\pi$
$60$	−23.6087	−	17.1527i	−3.04787	−	2.21441i
$61$	8.79725	+	6.39157i	1.12637	+	0.818357i	0.985163	−	0.171623i	$-0.0549010\pi$
$61$	8.79725	+	6.39157i	1.12637	+	0.818357i	0.141209	+	0.989980i	$0.454901\pi$
$62$	9.55752	+	6.94394i	1.21381	+	0.881881i
$63$	7.07728	+	5.14194i	0.891653	+	0.647824i
$64$	−24.9504	+	18.1275i	−3.11880	+	2.26594i
$65$	0.360640	+	1.10994i	0.0447319	+	0.137671i
$66$	4.93888	+	3.58831i	0.607934	+	0.441690i
$67$	0.0259884	−	0.0799840i	0.00317499	−	0.00977160i	−0.949456	−	0.313899i	$-0.898365\pi$
$67$	0.0259884	−	0.0799840i	0.00317499	−	0.00977160i	0.952631	+	0.304127i	$0.0983648\pi$
$68$	7.84550			0.951407
$69$	−10.3001	+	7.48345i	−1.23999	+	0.900902i
$70$	1.31193	−	4.03772i	0.156806	−	0.482600i
$71$	2.57387	+	7.92154i	0.305462	+	0.940114i	0.979505	+	0.201422i	$0.0645563\pi$
$71$	2.57387	+	7.92154i	0.305462	+	0.940114i	−0.674043	+	0.738692i	$0.735444\pi$
$72$	25.7968	+	79.3944i	3.04018	+	9.35671i
$73$	0.222081			0.0259926			0.0129963	−	0.999916i	$-0.495863\pi$
$73$	0.222081			0.0259926			0.0129963	+	0.999916i	$0.495863\pi$
$74$	−5.17469	−	15.9261i	−0.601545	−	1.85137i
$75$	−7.18946	−	5.22345i	−0.830167	−	0.603152i
$76$	−1.36039	+	0.988379i	−0.156047	+	0.113375i
$77$	−0.201143	+	0.619054i	−0.0229224	+	0.0705477i
$78$	2.18002	−	6.70941i	0.246839	−	0.759691i
$79$	−8.14247			−0.916100			−0.458050	−	0.888926i	$-0.651452\pi$
$79$	−8.14247			−0.916100			−0.458050	+	0.888926i	$0.651452\pi$
$80$	19.0005	−	13.8047i	2.12432	−	1.54341i
$81$	41.2834			4.58705
$82$	3.79992	−	17.1040i	0.419631	−	1.88882i
$83$	−9.78284			−1.07381			−0.536903	−	0.843644i	$-0.680406\pi$
$83$	−9.78284			−1.07381			−0.536903	+	0.843644i	$0.680406\pi$
$84$	−15.2163	+	11.0553i	−1.66024	+	1.20623i
$85$	−2.21826			−0.240604
$86$	4.65188	−	14.3170i	0.501626	−	1.54384i
$87$	5.01288	−	15.4281i	0.537438	−	1.65406i
$88$	−5.02521	+	3.65103i	−0.535690	+	0.389201i
$89$	1.62047	+	1.17734i	0.171770	+	0.124798i	0.670349	−	0.742046i	$-0.266145\pi$
$89$	1.62047	+	1.17734i	0.171770	+	0.124798i	−0.498579	+	0.866844i	$0.666145\pi$
$90$	−11.4768	−	35.3219i	−1.20976	−	3.72326i
$91$	0.752193			0.0788513
$92$	−6.29875	−	19.3856i	−0.656690	−	2.02108i
$93$	4.57283	+	14.0737i	0.474180	+	1.45938i
$94$	5.63708	−	17.3491i	0.581420	−	1.78943i
$95$	0.384640	−	0.279457i	0.0394632	−	0.0286717i
$96$	−76.5528			−7.81314
$97$	−1.18201	+	3.63784i	−0.120014	+	0.369366i	−0.992960	−	0.118451i	$-0.962207\pi$
$97$	−1.18201	+	3.63784i	−0.120014	+	0.369366i	0.872945	+	0.487818i	$0.162207\pi$
$98$	−2.21373	−	1.60837i	−0.223620	−	0.162470i
$99$	1.75960	+	5.41548i	0.176846	+	0.544276i
$100$	11.5103	−	8.36269i	1.15103	−	0.836269i
$101$	−5.00446	−	3.63595i	−0.497962	−	0.361791i	0.310276	−	0.950647i	$-0.399579\pi$
$101$	−5.00446	−	3.63595i	−0.497962	−	0.361791i	−0.808238	+	0.588856i	$0.799579\pi$
$102$	10.8482	+	7.88166i	1.07413	+	0.780401i
$103$	10.0540	+	7.30463i	0.990646	+	0.719747i	0.960062	−	0.279786i	$-0.0902634\pi$
$103$	10.0540	+	7.30463i	0.990646	+	0.719747i	0.0305836	+	0.999532i	$0.490263\pi$
$104$	5.80713	+	4.21913i	0.569436	+	0.413720i
$105$	4.30231	−	3.12581i	0.419863	−	0.305048i
$106$	5.78092	+	17.7918i	0.561493	+	1.72810i
$107$	−6.08542	−	4.42132i	−0.588300	−	0.427425i	0.253407	−	0.967360i	$-0.418449\pi$
$107$	−6.08542	−	4.42132i	−0.588300	−	0.427425i	−0.841707	+	0.539935i	$0.818449\pi$
$108$	−33.4080	+	102.819i	−3.21469	+	9.89380i
$109$	−13.9514			−1.33630			−0.668149	−	0.744027i	$-0.732913\pi$
$109$	−13.9514			−1.33630			−0.668149	+	0.744027i	$0.732913\pi$
$110$	2.23568	−	1.62432i	0.213164	−	0.154872i
$111$	6.48185	−	19.9491i	0.615230	−	1.89348i
$112$	−4.67765	−	14.3963i	−0.441996	−	1.36033i
$113$	−5.99349	−	18.4461i	−0.563821	−	1.73526i	−0.671430	−	0.741068i	$-0.734320\pi$
$113$	−5.99349	−	18.4461i	−0.563821	−	1.73526i	0.107609	−	0.994193i	$-0.465680\pi$
$114$	−2.87398			−0.269173
$115$	1.78093	+	5.48114i	0.166072	+	0.511118i
$116$	21.0112	+	15.2656i	1.95084	+	1.41737i
$117$	5.32348	−	3.86773i	0.492156	−	0.357572i
$118$	2.65001	−	8.15590i	0.243953	−	0.750811i
$119$	−0.441807	+	1.35974i	−0.0405004	+	0.124647i
$120$	50.7480			4.63264
$121$	8.55642	−	6.21660i	0.777856	−	0.565146i
$122$	−29.7547			−2.69387
$123$	16.4438	−	14.5351i	1.48269	−	1.31059i
$124$	−23.6914			−2.12755
$125$	−9.53055	+	6.92435i	−0.852439	+	0.619333i
$126$	−23.9373			−2.13251
$127$	−1.54023	+	4.74033i	−0.136673	+	0.420637i	−0.995847	−	0.0910479i	$-0.970978\pi$
$127$	−1.54023	+	4.74033i	−0.136673	+	0.420637i	0.859173	+	0.511685i	$0.170978\pi$
$128$	12.2741	−	37.7759i	1.08489	−	3.33894i
$129$	15.2552	−	11.0836i	1.34315	−	0.975855i
$130$	−2.58355	−	1.87706i	−0.226592	−	0.164629i
$131$	6.56403	+	20.2020i	0.573502	+	1.76506i	0.641223	+	0.767354i	$0.278427\pi$
$131$	6.56403	+	20.2020i	0.573502	+	1.76506i	−0.0677210	+	0.997704i	$0.521573\pi$
$132$	−12.2426			−1.06558
$133$	−0.0946927	−	0.291434i	−0.00821090	−	0.0252706i
$134$	0.0711125	+	0.218862i	0.00614319	+	0.0189068i
$135$	9.44590	−	29.0715i	0.812974	−	2.50208i
$136$	−11.0378	+	8.01944i	−0.946484	+	0.687661i
$137$	0.0171835			0.00146809			0.000734043	−	1.00000i	$-0.499766\pi$
$137$	0.0171835			0.00146809			0.000734043		1.00000i	$0.499766\pi$
$138$	10.7655	−	33.1327i	0.916417	−	2.82044i
$139$	−7.28588	−	5.29350i	−0.617980	−	0.448989i	0.234235	−	0.972180i	$-0.424741\pi$
$139$	−7.28588	−	5.29350i	−0.617980	−	0.448989i	−0.852215	+	0.523191i	$0.824741\pi$
$140$	2.63097	+	8.09729i	0.222357	+	0.684346i
$141$	18.4860	−	13.4309i	1.55681	−	1.13109i
$142$	−18.4386	−	13.3964i	−1.54733	−	1.12420i
$143$	0.396104	+	0.287786i	0.0331239	+	0.0240659i
$144$	−107.130	−	77.8346i	−8.92751	−	6.48622i
$145$	−5.94078	−	4.31623i	−0.493355	−	0.358444i
$146$	−0.491627	+	0.357188i	−0.0406873	+	0.0295611i
$147$	−1.05917	−	3.25978i	−0.0873586	−	0.268862i
$148$	27.1683	+	19.7390i	2.23322	+	1.62253i
$149$	−0.816075	+	2.51162i	−0.0668554	+	0.205760i	−0.978903	−	0.204324i	$-0.934500\pi$
$149$	−0.816075	+	2.51162i	−0.0668554	+	0.205760i	0.912048	+	0.410084i	$0.134500\pi$
$150$	24.3168			1.98545
$151$	−2.38987	+	1.73634i	−0.194484	+	0.141301i	−0.680766	−	0.732501i	$-0.738353\pi$
$151$	−2.38987	+	1.73634i	−0.194484	+	0.141301i	0.486282	+	0.873802i	$0.338353\pi$
$152$	0.903632	−	2.78109i	0.0732942	−	0.225576i
$153$	3.86493	+	11.8950i	0.312461	+	0.961656i
$154$	−0.550391	−	1.69393i	−0.0443518	−	0.136501i
$155$	6.69859			0.538043
$156$	4.37184	+	13.4551i	0.350027	+	1.07727i
$157$	−4.09057	−	2.97197i	−0.326463	−	0.237189i	0.412465	−	0.910973i	$-0.364668\pi$
$157$	−4.09057	−	2.97197i	−0.326463	−	0.237189i	−0.738928	+	0.673784i	$0.764668\pi$
$158$	18.0252	−	13.0961i	1.43401	−	1.04187i
$159$	−7.24122	+	22.2862i	−0.574266	+	1.76741i
$160$	−10.7084	+	32.9571i	−0.846573	+	2.60548i
$161$	3.71451			0.292744
$162$	−91.3904	+	66.3990i	−7.18030	+	5.21680i
$163$	12.1931			0.955038			0.477519	−	0.878622i	$-0.341536\pi$
$163$	12.1931			0.955038			0.477519	+	0.878622i	$0.341536\pi$
$164$	13.9963	+	32.2289i	1.09293	+	2.51665i
$165$	3.46152			0.269479
$166$	21.6566	−	15.7344i	1.68087	−	1.22123i
$167$	−8.50106			−0.657831			−0.328916	−	0.944359i	$-0.606683\pi$
$167$	−8.50106			−0.657831			−0.328916	+	0.944359i	$0.606683\pi$
$168$	10.1074	−	31.1073i	0.779802	−	2.39998i
$169$	−3.84238	+	11.8256i	−0.295568	+	0.909664i
$170$	4.91064	−	3.56779i	0.376629	−	0.273637i
$171$	−2.16871	−	1.57566i	−0.165845	−	0.120493i
$172$	9.32894	+	28.7115i	0.711325	+	2.18923i
$173$	−1.76419			−0.134129			−0.0670643	−	0.997749i	$-0.521363\pi$
$173$	−1.76419			−0.134129			−0.0670643	+	0.997749i	$0.521363\pi$
$174$	13.7169	+	42.2162i	1.03987	+	3.20040i
$175$	0.801197	+	2.46583i	0.0605648	+	0.186399i
$176$	3.04474	−	9.37074i	0.229506	−	0.706346i
$177$	8.69037	−	6.31392i	0.653208	−	0.474583i
$178$	−5.48089			−0.410810
$179$	−5.85921	+	18.0328i	−0.437938	+	1.34783i	0.452108	+	0.891963i	$0.350672\pi$
$179$	−5.85921	+	18.0328i	−0.437938	+	1.34783i	−0.890046	+	0.455871i	$0.849328\pi$
$180$	60.2559	+	43.7784i	4.49121	+	3.26305i
$181$	5.73316	+	17.6449i	0.426143	+	1.31153i	0.901896	+	0.431953i	$0.142175\pi$
$181$	5.73316	+	17.6449i	0.426143	+	1.31153i	−0.475753	+	0.879579i	$0.657825\pi$
$182$	−1.66515	+	1.20980i	−0.123429	+	0.0896766i
$183$	−30.1529	−	21.9073i	−2.22896	−	1.61944i
$184$	28.6770	+	20.8351i	2.11410	+	1.53598i
$185$	−7.68166	−	5.58106i	−0.564767	−	0.410327i
$186$	−32.7587	−	23.8006i	−2.40199	−	1.74514i
$187$	−0.752888	+	0.547005i	−0.0550566	+	0.0400010i
$188$	11.3047	+	34.7922i	0.824477	+	2.53748i
$189$	−15.9388	−	11.5802i	−1.15938	−	0.842337i
$190$	−0.402019	+	1.23729i	−0.0291655	+	0.0897622i
$191$	−9.17857			−0.664138			−0.332069	−	0.943255i	$-0.607747\pi$
$191$	−9.17857			−0.664138			−0.332069	+	0.943255i	$0.607747\pi$
$192$	85.5184	−	62.1327i	6.17176	−	4.48404i
$193$	−6.67686	+	20.5493i	−0.480611	+	1.47917i	0.357627	+	0.933865i	$0.383586\pi$
$193$	−6.67686	+	20.5493i	−0.480611	+	1.47917i	−0.838238	+	0.545305i	$0.816414\pi$
$194$	−3.23434	−	9.95429i	−0.232212	−	0.714676i
$195$	−1.23611	−	3.80435i	−0.0885195	−	0.272435i
$196$	5.48745			0.391961
$197$	4.36379	+	13.4304i	0.310907	+	0.956874i	0.977406	+	0.211369i	$0.0677920\pi$
$197$	4.36379	+	13.4304i	0.310907	+	0.956874i	−0.666499	+	0.745506i	$0.732208\pi$
$198$	−12.6054	−	9.15833i	−0.895824	−	0.650854i
$199$	−4.54786	+	3.30421i	−0.322389	+	0.234229i	−0.737194	−	0.675681i	$-0.763850\pi$
$199$	−4.54786	+	3.30421i	−0.322389	+	0.234229i	0.414805	+	0.909910i	$0.363850\pi$
$200$	−7.64564	+	23.5309i	−0.540629	+	1.66388i
$201$	−0.0890761	+	0.274148i	−0.00628294	+	0.0193369i
$202$	16.9265			1.19094
$203$	−3.82896	+	2.78190i	−0.268740	+	0.195251i
$204$	−26.8907			−1.88273
$205$	−3.95736	−	9.11249i	−0.276394	−	0.636444i
$206$	−34.0053			−2.36926
$207$	26.2886	−	19.0998i	1.82719	−	1.32753i
$208$	−11.3861			−0.789484
$209$	0.0616366	−	0.189698i	0.00426349	−	0.0131217i
$210$	−4.49670	+	13.8394i	−0.310302	+	0.955010i
$211$	14.4528	−	10.5006i	0.994973	−	0.722891i	0.0339688	−	0.999423i	$-0.489185\pi$
$211$	14.4528	−	10.5006i	0.994973	−	0.722891i	0.961005	+	0.276532i	$0.0891853\pi$
$212$	−30.3512	−	22.0514i	−2.08453	−	1.51450i
$213$	−8.82202	−	27.1514i	−0.604475	−	1.86038i
$214$	20.5826			1.40700
$215$	−2.63770	−	8.11799i	−0.179889	−	0.553642i
$216$	−58.0972	−	178.805i	−3.95302	−	12.1661i
$217$	1.33414	−	4.10607i	0.0905676	−	0.278738i
$218$	30.8846	−	22.4389i	2.09177	−	1.51976i
$219$	−0.761190			−0.0514365
$220$	−1.71253	+	5.27062i	−0.115459	+	0.355345i
$221$	0.870037	+	0.632119i	0.0585250	+	0.0425209i
$222$	17.7364	+	54.5871i	1.19039	+	3.66365i
$223$	15.4907	−	11.2547i	1.03734	−	0.753669i	0.0675724	−	0.997714i	$-0.478475\pi$
$223$	15.4907	−	11.2547i	1.03734	−	0.753669i	0.969764	+	0.244046i	$0.0784746\pi$
$224$	18.0691	+	13.1280i	1.20729	+	0.877150i
$225$	18.3494	+	13.3317i	1.22330	+	0.888777i
$226$	42.9361	+	31.1949i	2.85607	+	2.07505i
$227$	9.32635	+	6.77599i	0.619012	+	0.449738i	0.852576	−	0.522603i	$-0.175039\pi$
$227$	9.32635	+	6.77599i	0.619012	+	0.449738i	−0.233564	+	0.972341i	$0.575039\pi$
$228$	4.66277	−	3.38770i	0.308800	−	0.224356i
$229$	−4.93782	−	15.1971i	−0.326301	−	1.00425i	−0.970850	−	0.239687i	$-0.922955\pi$
$229$	−4.93782	−	15.1971i	−0.326301	−	1.00425i	0.644550	−	0.764562i	$-0.277045\pi$
$230$	−12.7582	−	9.26936i	−0.841250	−	0.611204i
$231$	0.689424	−	2.12183i	0.0453608	−	0.139606i
$232$	−45.1646			−2.96520
$233$	−18.7092	+	13.5930i	−1.22568	+	0.890507i	−0.996559	−	0.0828918i	$-0.973584\pi$
$233$	−18.7092	+	13.5930i	−1.22568	+	0.890507i	−0.229119	+	0.973398i	$0.573584\pi$
$234$	−5.56400	+	17.1242i	−0.363730	+	1.11945i
$235$	−3.19632	−	9.83725i	−0.208505	−	0.641711i
$236$	5.31437	+	16.3559i	0.345936	+	1.06468i
$237$	27.9086			1.81286
$238$	−1.20893	−	3.72069i	−0.0783630	−	0.241177i
$239$	4.59895	+	3.34134i	0.297482	+	0.216133i	0.726506	−	0.687160i	$-0.241143\pi$
$239$	4.59895	+	3.34134i	0.297482	+	0.216133i	−0.429025	+	0.903293i	$0.641143\pi$
$240$	−65.1250	+	47.3161i	−4.20380	+	3.05424i
$241$	−3.23454	+	9.95488i	−0.208355	+	0.641250i	0.791204	+	0.611552i	$0.209455\pi$
$241$	−3.23454	+	9.95488i	−0.208355	+	0.641250i	−0.999559	+	0.0296980i	$0.990545\pi$
$242$	−8.94301	+	27.5237i	−0.574878	+	1.76929i
$243$	−82.3960			−5.28571
$244$	48.2744	−	35.0734i	3.09045	−	2.24535i
$245$	−1.55154			−0.0991242
$246$	−13.0243	+	58.6245i	−0.830402	+	3.73776i
$247$	−0.230496			−0.0146661
$248$	33.3313	−	24.2166i	2.11654	−	1.53776i
$249$	33.5310			2.12494
$250$	9.96116	−	30.6573i	0.629999	−	1.93894i
$251$	5.90626	−	18.1776i	0.372800	−	1.14736i	−0.572152	−	0.820148i	$-0.693891\pi$
$251$	5.90626	−	18.1776i	0.372800	−	1.14736i	0.944951	−	0.327211i	$-0.106109\pi$
$252$	38.8362	−	28.2161i	2.44645	−	1.77745i
$253$	1.95606	+	1.42116i	0.122976	+	0.0893474i
$254$	−4.21456	−	12.9711i	−0.264445	−	0.813877i
$255$	7.60317			0.476129
$256$	14.5255	+	44.7049i	0.907844	+	2.79406i
$257$	−2.29728	−	7.07029i	−0.143300	−	0.441032i	0.853488	−	0.521112i	$-0.174483\pi$
$257$	−2.29728	−	7.07029i	−0.143300	−	0.441032i	−0.996788	+	0.0800795i	$0.974483\pi$
$258$	−15.9445	+	49.0721i	−0.992661	+	3.05510i
$259$	−4.95100	+	3.59711i	−0.307640	+	0.223514i
$260$	6.40417			0.397169
$261$	−12.7942	+	39.3766i	−0.791943	+	2.43735i
$262$	−47.0233	−	34.1644i	−2.90511	−	2.11069i
$263$	−6.70712	−	20.6424i	−0.413579	−	1.27286i	−0.913516	−	0.406803i	$-0.866644\pi$
$263$	−6.70712	−	20.6424i	−0.413579	−	1.27286i	0.499937	−	0.866062i	$-0.333356\pi$
$264$	17.2241	−	12.5140i	1.06007	−	0.770186i
$265$	8.58160	+	6.23489i	0.527163	+	0.383007i
$266$	0.678358	+	0.492856i	0.0415928	+	0.0302189i
$267$	−5.55422	−	4.03538i	−0.339913	−	0.246961i
$268$	−0.373358	−	0.271260i	−0.0228064	−	0.0165698i
$269$	12.9167	−	9.38453i	0.787545	−	0.572185i	−0.119689	−	0.992811i	$-0.538190\pi$
$269$	12.9167	−	9.38453i	0.787545	−	0.572185i	0.907234	+	0.420627i	$0.138190\pi$
$270$	25.8470	+	79.5489i	1.57300	+	4.84119i
$271$	10.4644	+	7.60285i	0.635669	+	0.461840i	0.858359	−	0.513049i	$-0.171484\pi$
$271$	10.4644	+	7.60285i	0.635669	+	0.461840i	−0.222691	+	0.974889i	$0.571484\pi$
$272$	6.68772	−	20.5827i	0.405503	−	1.24801i
$273$	−2.57817			−0.156038
$274$	−0.0380396	+	0.0276374i	−0.00229806	+	0.00166964i
$275$	−0.521508	+	1.60504i	−0.0314481	+	0.0967874i
$276$	21.5892	+	66.4447i	1.29952	+	3.99950i
$277$	2.00641	+	6.17511i	0.120554	+	0.371026i	0.993065	−	0.117568i	$-0.0375099\pi$
$277$	2.00641	+	6.17511i	0.120554	+	0.371026i	−0.872511	+	0.488594i	$0.837510\pi$
$278$	24.6429			1.47798
$279$	−11.6711	−	35.9199i	−0.698730	−	2.15047i
$280$	−11.9783	−	8.70274i	−0.715840	−	0.520088i
$281$	4.16275	−	3.02441i	0.248329	−	0.180421i	−0.456657	−	0.889643i	$-0.650953\pi$
$281$	4.16275	−	3.02441i	0.248329	−	0.180421i	0.704986	+	0.709221i	$0.250953\pi$
$282$	−19.3213	+	59.4648i	−1.15057	+	3.54108i
$283$	2.71969	−	8.37035i	0.161669	−	0.497566i	−0.837107	−	0.547040i	$-0.815755\pi$
$283$	2.71969	−	8.37035i	0.161669	−	0.497566i	0.998775	+	0.0494743i	$0.0157546\pi$
$284$	45.7061			2.71216
$285$	−1.31837	+	0.957850i	−0.0780934	+	0.0567381i
$286$	−1.33973			−0.0792201
$287$	−6.37392	+	0.610851i	−0.376241	+	0.0360574i
$288$	195.384			11.5131
$289$	12.0996	−	8.79086i	0.711740	−	0.517109i
$290$	20.0934			1.17992
$291$	4.05136	−	12.4688i	0.237495	−	0.730935i
$292$	0.376586	−	1.15901i	0.0220380	−	0.0678261i
$293$	1.52646	−	1.10904i	0.0891765	−	0.0647905i	−0.542304	−	0.840183i	$-0.682448\pi$
$293$	1.52646	−	1.10904i	0.0891765	−	0.0647905i	0.631480	+	0.775392i	$0.282448\pi$
$294$	7.58764	+	5.51274i	0.442520	+	0.321510i
$295$	−1.50260	−	4.62453i	−0.0874848	−	0.269251i
$296$	−58.3996			−3.39441
$297$	−3.96281	−	12.1963i	−0.229945	−	0.707699i
$298$	−2.23304	−	6.87260i	−0.129357	−	0.398119i
$299$	0.863403	−	2.65728i	0.0499319	−	0.153674i
$300$	−39.4518	+	28.6634i	−2.27775	+	1.65488i
$301$	−5.50148			−0.317100
$302$	2.49784	−	7.68757i	0.143735	−	0.442370i
$303$	17.1530	+	12.4624i	0.985412	+	0.715944i
$304$	1.43338	+	4.41150i	0.0822101	+	0.253017i
$305$	−13.6493	+	9.91678i	−0.781555	+	0.567833i
$306$	−27.6875	−	20.1161i	−1.58279	−	1.14996i
$307$	17.1296	+	12.4454i	0.977637	+	0.710295i	0.957179	−	0.289496i	$-0.0934877\pi$
$307$	17.1296	+	12.4454i	0.977637	+	0.710295i	0.0204574	+	0.999791i	$0.493488\pi$
$308$	2.88968	+	2.09948i	0.164655	+	0.119629i
$309$	−34.4603	−	25.0369i	−1.96038	−	1.42430i
$310$	−14.8289	+	10.7738i	−0.842222	+	0.611910i
$311$	2.88080	+	8.86620i	0.163355	+	0.502756i	0.998911	−	0.0466493i	$-0.0148543\pi$
$311$	2.88080	+	8.86620i	0.163355	+	0.502756i	−0.835556	+	0.549405i	$0.814854\pi$
$312$	−19.9042	−	14.4612i	−1.12685	−	0.818705i
$313$	1.34764	−	4.14761i	0.0761731	−	0.234437i	−0.905719	−	0.423879i	$-0.860668\pi$
$313$	1.34764	−	4.14761i	0.0761731	−	0.234437i	0.981892	+	0.189443i	$0.0606681\pi$
$314$	13.8354			0.780780
$315$	−10.9807	+	7.97792i	−0.618691	+	0.449505i
$316$	−13.8073	+	42.4945i	−0.776722	+	2.39051i
$317$	−6.92386	−	21.3094i	−0.388882	−	1.19686i	−0.933624	−	0.358253i	$-0.883372\pi$
$317$	−6.92386	−	21.3094i	−0.388882	−	1.19686i	0.544742	−	0.838604i	$-0.316628\pi$
$318$	−19.8143	−	60.9822i	−1.11113	−	3.41971i
$319$	−3.08067			−0.172485
$320$	−14.7865	−	45.5081i	−0.826590	−	2.54398i
$321$	20.8580	+	15.1542i	1.16418	+	0.845826i
$322$	−8.22292	+	5.97430i	−0.458245	+	0.332935i
$323$	0.135384	−	0.416669i	0.00753296	−	0.0231841i
$324$	70.0049	−	215.453i	3.88916	−	11.9696i
$325$	1.95023			0.108179
$326$	−26.9922	+	19.6110i	−1.49496	+	1.08615i
$327$	47.8188			2.64439
$328$	−52.6347	−	31.0360i	−2.90627	−	1.71368i
$329$	−6.66660			−0.367542
$330$	−7.66287	+	5.56740i	−0.421827	+	0.306475i
$331$	−16.1236			−0.886231			−0.443115	−	0.896465i	$-0.646127\pi$
$331$	−16.1236			−0.886231			−0.443115	+	0.896465i	$0.646127\pi$
$332$	−16.5889	+	51.0554i	−0.910434	+	2.80203i
$333$	−16.5434	+	50.9155i	−0.906575	+	2.79015i
$334$	18.8190	−	13.6728i	1.02973	−	0.748144i
$335$	0.105564	+	0.0766970i	0.00576759	+	0.00419040i
$336$	16.0328	+	49.3439i	0.874662	+	2.69193i
$337$	−17.7384			−0.966273			−0.483136	−	0.875545i	$-0.660502\pi$
$337$	−17.7384			−0.966273			−0.483136	+	0.875545i	$0.660502\pi$
$338$	−10.5140	−	32.3587i	−0.571885	−	1.76008i
$339$	20.5429	+	63.2246i	1.11574	+	3.43389i
$340$	−3.76154	+	11.5768i	−0.203998	+	0.627842i
$341$	2.27353	−	1.65181i	0.123118	−	0.0894508i
$342$	7.33516			0.396640
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−42.4729	−	30.8584i	−2.28999	−	1.66377i
$345$	−6.10420	−	18.7868i	−0.328639	−	1.01145i
$346$	3.90543	−	2.83746i	0.209957	−	0.152543i
$347$	6.41974	+	4.66422i	0.344630	+	0.250388i	0.746613	−	0.665259i	$-0.231679\pi$
$347$	6.41974	+	4.66422i	0.344630	+	0.250388i	−0.401983	+	0.915647i	$0.631679\pi$
$348$	−72.0167	−	52.3232i	−3.86050	−	2.80482i
$349$	−18.7767	−	13.6420i	−1.00509	−	0.730242i	−0.0419177	−	0.999121i	$-0.513347\pi$
$349$	−18.7767	−	13.6420i	−1.00509	−	0.730242i	−0.963174	+	0.268879i	$0.913347\pi$
$350$	−5.73960	−	4.17006i	−0.306794	−	0.222899i
$351$	−11.9891	+	8.71057i	−0.639929	+	0.464936i
$352$	4.49246	+	13.8264i	0.239449	+	0.736948i
$353$	17.0061	+	12.3556i	0.905143	+	0.657625i	0.939782	−	0.341775i	$-0.111028\pi$
$353$	17.0061	+	12.3556i	0.905143	+	0.657625i	−0.0346391	+	0.999400i	$0.511028\pi$
$354$	−9.08301	+	27.9546i	−0.482756	+	1.48577i
$355$	−12.9231			−0.685886
$356$	8.89226	−	6.46060i	0.471289	−	0.342411i
$357$	1.51431	−	4.66057i	0.0801458	−	0.246663i
$358$	−16.0327	−	49.3435i	−0.847353	−	2.60789i
$359$	8.35012	+	25.6990i	0.440702	+	1.35634i	0.887129	+	0.461522i	$0.152696\pi$
$359$	8.35012	+	25.6990i	0.440702	+	1.35634i	−0.446426	+	0.894820i	$0.647304\pi$
$360$	−129.523			−6.82645
$361$	−5.84231	−	17.9808i	−0.307490	−	0.946356i
$362$	−41.0711	−	29.8399i	−2.15865	−	1.56835i
$363$	−29.3274	+	21.3076i	−1.53929	+	1.11836i
$364$	1.27551	−	3.92560i	0.0668546	−	0.205757i
$365$	−0.106477	+	0.327703i	−0.00557327	+	0.0171528i
$366$	101.985			5.33086
$367$	9.02183	−	6.55475i	0.470936	−	0.342155i	−0.326870	−	0.945069i	$-0.605994\pi$
$367$	9.02183	−	6.55475i	0.470936	−	0.342155i	0.797806	+	0.602914i	$0.205994\pi$
$368$	−56.2273			−2.93105
$369$	−41.9690	+	37.0975i	−2.18482	+	1.93122i
$370$	25.9815			1.35071
$371$	5.53102	−	4.01852i	0.287156	−	0.208631i
$372$	81.2031			4.21019
$373$	−1.00327	+	3.08775i	−0.0519474	+	0.159878i	−0.973665	−	0.227985i	$-0.926786\pi$
$373$	−1.00327	+	3.08775i	−0.0519474	+	0.159878i	0.921717	+	0.387862i	$0.126786\pi$
$374$	0.786904	−	2.42184i	0.0406899	−	0.125230i
$375$	32.6663	−	23.7335i	1.68688	−	1.22559i
$376$	−51.4680	−	37.3937i	−2.65426	−	1.92843i
$377$	1.10011	+	3.38578i	0.0566584	+	0.174377i
$378$	53.9095			2.77280
$379$	9.74477	+	29.9913i	0.500555	+	1.54055i	0.808117	+	0.589022i	$0.200487\pi$
$379$	9.74477	+	29.9913i	0.500555	+	1.54055i	−0.307562	+	0.951528i	$0.599513\pi$
$380$	−0.806213	−	2.48127i	−0.0413579	−	0.127286i
$381$	5.27918	−	16.2477i	0.270461	−	0.832393i
$382$	20.3189	−	14.7625i	1.03960	−	0.755317i
$383$	30.3554			1.55109			0.775545	−	0.631292i	$-0.217475\pi$
$383$	30.3554			1.55109			0.775545	+	0.631292i	$0.217475\pi$
$384$	−42.0700	+	129.478i	−2.14687	+	6.60740i
$385$	−0.817038	−	0.593613i	−0.0416401	−	0.0302533i
$386$	−18.2700	−	56.2294i	−0.929920	−	2.86200i
$387$	−38.9355	+	28.2883i	−1.97920	+	1.43797i
$388$	16.9811	+	12.3375i	0.862083	+	0.626340i
$389$	−8.79362	−	6.38894i	−0.445854	−	0.323932i	0.342103	−	0.939663i	$-0.388861\pi$
$389$	−8.79362	−	6.38894i	−0.445854	−	0.323932i	−0.787957	+	0.615731i	$0.788861\pi$
$390$	8.85520	+	6.43368i	0.448401	+	0.325782i
$391$	4.29645	+	3.12155i	0.217281	+	0.157864i
$392$	−7.72027	+	5.60910i	−0.389932	+	0.283302i
$393$	−22.4985	−	69.2431i	−1.13490	−	3.49285i
$394$	−31.2612	−	22.7126i	−1.57492	−	1.14425i
$395$	3.90392	−	12.0150i	0.196428	−	0.604543i
$396$	31.2465			1.57020
$397$	31.4257	−	22.8321i	1.57721	−	1.14591i	0.657401	−	0.753541i	$-0.271656\pi$
$397$	31.4257	−	22.8321i	1.57721	−	1.14591i	0.919808	−	0.392368i	$-0.128344\pi$
$398$	4.75334	−	14.6293i	0.238263	−	0.733299i
$399$	0.324563	+	0.998901i	0.0162485	+	0.0500076i
$400$	−12.1279	−	37.3258i	−0.606394	−	1.86629i
$401$	−18.7243			−0.935045			−0.467523	−	0.883981i	$-0.654853\pi$
$401$	−18.7243			−0.935045			−0.467523	+	0.883981i	$0.654853\pi$
$402$	−0.243741	−	0.750157i	−0.0121567	−	0.0374144i
$403$	−2.62729	−	1.90884i	−0.130874	−	0.0950859i
$404$	−27.4617	+	19.9521i	−1.36627	+	0.992654i
$405$	−19.7934	+	60.9179i	−0.983543	+	3.02703i
$406$	4.00196	−	12.3168i	0.198614	−	0.611271i
$407$	−3.98343			−0.197451
$408$	37.8325	−	27.4869i	1.87299	−	1.36080i
$409$	−11.6608			−0.576591			−0.288295	−	0.957542i	$-0.593089\pi$
$409$	−11.6608			−0.576591			−0.288295	+	0.957542i	$0.593089\pi$
$410$	23.4168	+	13.8077i	1.15647	+	0.681913i
$411$	−0.0588971			−0.00290518
$412$	55.1706	−	40.0838i	2.71806	−	1.97479i
$413$	−3.13400			−0.154214
$414$	−27.4764	+	84.5636i	−1.35039	+	4.15607i
$415$	4.69040	−	14.4356i	0.230243	−	0.708614i
$416$	13.5915	−	9.87478i	0.666377	−	0.484151i
$417$	24.9726	+	18.1437i	1.22291	+	0.888499i
$418$	0.168658	+	0.519075i	0.00824931	+	0.0253888i
$419$	−25.5619			−1.24878			−0.624390	−	0.781113i	$-0.714652\pi$
$419$	−25.5619			−1.24878			−0.624390	+	0.781113i	$0.714652\pi$
$420$	−9.01773	−	27.7537i	−0.440020	−	1.35424i
$421$	10.4811	+	32.2574i	0.510817	+	1.57213i	0.790767	+	0.612117i	$0.209682\pi$
$421$	10.4811	+	32.2574i	0.510817	+	1.57213i	−0.279950	+	0.960014i	$0.590318\pi$
$422$	−15.1058	+	46.4909i	−0.735340	+	2.26314i
$423$	−47.1814	+	34.2793i	−2.29404	+	1.66672i
$424$	65.2413			3.16840
$425$	−1.14549	+	3.52544i	−0.0555642	+	0.171009i
$426$	63.1990	+	45.9167i	3.06200	+	2.22467i
$427$	3.36025	+	10.3418i	0.162614	+	0.500474i
$428$	−33.3934	+	24.2618i	−1.61413	+	1.17274i
$429$	−1.35766	−	0.986398i	−0.0655485	−	0.0476237i
$430$	18.8959	+	13.7287i	0.911240	+	0.662054i
$431$	15.3208	+	11.1312i	0.737977	+	0.536172i	0.892077	−	0.451883i	$-0.149248\pi$
$431$	15.3208	+	11.1312i	0.737977	+	0.536172i	−0.154100	+	0.988055i	$0.549248\pi$
$432$	241.269	+	175.292i	11.6081	+	8.43375i
$433$	25.3649	−	18.4287i	1.21896	−	0.885625i	0.222945	−	0.974831i	$-0.428433\pi$
$433$	25.3649	−	18.4287i	1.21896	−	0.885625i	0.996013	+	0.0892062i	$0.0284330\pi$
$434$	3.65065	+	11.2355i	0.175237	+	0.539323i
$435$	20.3622	+	14.7940i	0.976295	+	0.709320i
$436$	−23.6575	+	72.8104i	−1.13299	+	3.48699i
$437$	−1.13825			−0.0544497
$438$	1.68507	−	1.22427i	0.0805157	−	0.0584981i
$439$	6.56581	−	20.2075i	0.313369	−	0.964450i	−0.663052	−	0.748574i	$-0.730739\pi$
$439$	6.56581	−	20.2075i	0.313369	−	0.964450i	0.976421	−	0.215877i	$-0.0692610\pi$
$440$	−2.97812	−	9.16571i	−0.141976	−	0.436958i
$441$	2.70328	+	8.31984i	0.128728	+	0.396183i
$442$	−2.94271			−0.139970
$443$	0.600542	+	1.84828i	0.0285326	+	0.0878144i	0.964309	−	0.264780i	$-0.0852994\pi$
$443$	0.600542	+	1.84828i	0.0285326	+	0.0878144i	−0.935776	+	0.352595i	$0.885299\pi$
$444$	−93.1204	−	67.6560i	−4.41930	−	3.21081i
$445$	−2.51423	+	1.82669i	−0.119186	+	0.0865935i
$446$	−16.1906	+	49.8296i	−0.766648	+	2.35950i
$447$	2.79712	−	8.60866i	0.132299	−	0.407176i
$448$	−30.8404			−1.45707
$449$	16.4112	−	11.9234i	0.774493	−	0.562702i	−0.128828	−	0.991667i	$-0.541122\pi$
$449$	16.4112	−	11.9234i	0.774493	−	0.562702i	0.903321	+	0.428965i	$0.141122\pi$
$450$	−62.0629			−2.92567
$451$	−3.59021	−	2.11697i	−0.169056	−	0.0996840i
$452$	−106.431			−5.00609
$453$	8.19135	−	5.95136i	0.384863	−	0.279619i
$454$	−31.5443			−1.48045
$455$	−0.360640	+	1.10994i	−0.0169071	+	0.0520347i
$456$	−3.09723	+	9.53229i	−0.145041	+	0.446390i
$457$	−8.84181	+	6.42395i	−0.413602	+	0.300500i	−0.775059	−	0.631889i	$-0.782280\pi$
$457$	−8.84181	+	6.42395i	−0.413602	+	0.300500i	0.361456	+	0.932389i	$0.382280\pi$
$458$	35.3735	+	25.7003i	1.65289	+	1.20090i
$459$	−8.70424	−	26.7889i	−0.406279	−	1.25040i
$460$	31.6253			1.47454
$461$	−8.89225	−	27.3675i	−0.414153	−	1.27463i	−0.913006	−	0.407946i	$-0.866245\pi$
$461$	−8.89225	−	27.3675i	−0.414153	−	1.27463i	0.498852	−	0.866687i	$-0.333755\pi$
$462$	1.88649	+	5.80600i	0.0877672	+	0.270120i
$463$	−5.27700	+	16.2409i	−0.245243	+	0.754780i	0.750354	+	0.661037i	$0.229883\pi$
$463$	−5.27700	+	16.2409i	−0.245243	+	0.754780i	−0.995596	+	0.0937431i	$0.970117\pi$
$464$	57.9598	−	42.1102i	2.69071	−	1.95492i
$465$	−22.9596			−1.06473
$466$	19.5545	−	60.1824i	0.905843	−	2.78790i
$467$	17.1261	+	12.4428i	0.792501	+	0.575785i	0.908704	−	0.417440i	$-0.137073\pi$
$467$	17.1261	+	12.4428i	0.792501	+	0.575785i	−0.116204	+	0.993225i	$0.537073\pi$
$468$	−11.1581	−	34.3411i	−0.515784	−	1.58742i
$469$	0.0680385	−	0.0494328i	0.00314172	−	0.00228260i
$470$	22.8977	+	16.6362i	1.05619	+	0.767368i
$471$	14.0206	+	10.1865i	0.646034	+	0.469371i
$472$	−24.1953	−	17.5789i	−1.11368	−	0.809135i
$473$	−2.89707	−	2.10485i	−0.133208	−	0.0967809i
$474$	−61.7821	+	44.8873i	−2.83775	+	2.06174i
$475$	−0.245512	−	0.755610i	−0.0112649	−	0.0346697i
$476$	6.34715	+	4.61147i	0.290921	+	0.211366i
$477$	18.4816	−	56.8804i	0.846213	−	2.60437i
$478$	−15.5549			−0.711467
$479$	−3.57532	+	2.59762i	−0.163360	+	0.118688i	−0.666462	−	0.745539i	$-0.732192\pi$
$479$	−3.57532	+	2.59762i	−0.163360	+	0.118688i	0.503102	+	0.864227i	$0.332192\pi$
$480$	36.7034	−	112.961i	1.67527	−	5.15596i
$481$	1.42248	+	4.37795i	0.0648596	+	0.199617i
$482$	−8.85073	−	27.2397i	−0.403140	−	1.24074i
$483$	−12.7316			−0.579308
$484$	−17.9344	−	55.1964i	−0.815201	−	2.50893i
$485$	−4.80128	−	3.48834i	−0.218015	−	0.158397i
$486$	182.403	−	132.523i	8.27395	−	6.01138i
$487$	−3.03941	+	9.35435i	−0.137729	+	0.423886i	−0.996005	−	0.0893029i	$-0.971536\pi$
$487$	−3.03941	+	9.35435i	−0.137729	+	0.423886i	0.858276	+	0.513189i	$0.171536\pi$
$488$	−32.0661	+	98.6893i	−1.45156	+	4.46746i
$489$	−41.7923			−1.88991
$490$	3.43469	−	2.49545i	0.155163	−	0.112733i
$491$	16.6029			0.749277			0.374638	−	0.927171i	$-0.377767\pi$
$491$	16.6029			0.749277			0.374638	+	0.927171i	$0.377767\pi$
$492$	−47.9728	−	110.466i	−2.16278	−	4.98017i
$493$	−6.76665			−0.304755
$494$	0.510256	−	0.370723i	0.0229575	−	0.0166796i
$495$	−8.83473			−0.397092
$496$	−20.1952	+	62.1544i	−0.906791	+	2.79082i
$497$	−2.57387	+	7.92154i	−0.115454	+	0.355330i
$498$	−74.2286	+	53.9302i	−3.32626	+	2.41667i
$499$	−1.79305	−	1.30273i	−0.0802679	−	0.0583181i	0.546928	−	0.837180i	$-0.315797\pi$
$499$	−1.79305	−	1.30273i	−0.0802679	−	0.0583181i	−0.627196	+	0.778862i	$0.715797\pi$
$500$	19.9762	+	61.4805i	0.893364	+	2.74949i
$501$	29.1377			1.30177
$502$	16.1614	+	49.7397i	0.721319	+	2.21999i
$503$	9.49101	+	29.2103i	0.423183	+	1.30242i	0.904723	+	0.426000i	$0.140078\pi$
$503$	9.49101	+	29.2103i	0.423183	+	1.30242i	−0.481540	+	0.876424i	$0.659922\pi$
$504$	−25.7968	+	79.3944i	−1.14908	+	3.53651i
$505$	7.76461	−	5.64132i	0.345521	−	0.251036i
$506$	−6.61593			−0.294114
$507$	13.1699	−	40.5328i	0.584896	−	1.80012i
$508$	22.1274	+	16.0765i	0.981745	+	0.713280i
$509$	−5.43966	−	16.7415i	−0.241109	−	0.742056i	−0.996252	−	0.0864965i	$-0.972433\pi$
$509$	−5.43966	−	16.7415i	−0.241109	−	0.742056i	0.755144	−	0.655559i	$-0.227567\pi$
$510$	−16.8314	+	12.2287i	−0.745306	+	0.541496i
$511$	0.179667	+	0.130536i	0.00794801	+	0.00577457i
$512$	−39.7894	−	28.9087i	−1.75846	−	1.27760i
$513$	4.88416	+	3.54855i	0.215641	+	0.156672i
$514$	16.4572	+	11.9568i	0.725895	+	0.527394i
$515$	−15.5991	+	11.3334i	−0.687379	+	0.499410i
$516$	−31.9753	−	98.4098i	−1.40763	−	4.33225i
$517$	−3.51062	−	2.55062i	−0.154397	−	0.112176i
$518$	5.17469	−	15.9261i	0.227363	−	0.699751i
$519$	6.04681			0.265426
$520$	−9.00999	+	6.54614i	−0.395114	+	0.287067i
$521$	0.482190	−	1.48403i	0.0211251	−	0.0650164i	−0.939938	−	0.341345i	$-0.889118\pi$
$521$	0.482190	−	1.48403i	0.0211251	−	0.0650164i	0.961063	+	0.276328i	$0.0891177\pi$
$522$	−35.0091	−	107.747i	−1.53231	−	4.71596i
$523$	6.02666	+	18.5482i	0.263528	+	0.811054i	0.992029	+	0.126010i	$0.0402172\pi$
$523$	6.02666	+	18.5482i	0.263528	+	0.811054i	−0.728501	+	0.685044i	$0.759783\pi$
$524$	116.563			5.09206
$525$	−2.74613	−	8.45172i	−0.119851	−	0.368863i
$526$	48.0483	+	34.9092i	2.09501	+	1.52211i
$527$	4.99377	−	3.62819i	0.217532	−	0.158046i
$528$	−10.4359	+	32.1185i	−0.454166	+	1.39778i
$529$	−2.84370	+	8.75202i	−0.123639	+	0.380523i
$530$	−29.0253			−1.26078
$531$	−22.1802	+	16.1148i	−0.962537	+	0.699324i
$532$	−1.68153			−0.0729036
$533$	−1.04457	+	4.70175i	−0.0452452	+	0.203655i
$534$	18.7859			0.812947
$535$	9.44177	−	6.85985i	0.408203	−	0.296577i
$536$	0.802549			0.0346648
$537$	20.0826	−	61.8080i	0.866630	−	2.66721i
$538$	−13.5003	+	41.5496i	−0.582039	+	1.79133i
$539$	−0.526599	+	0.382596i	−0.0226822	+	0.0164796i
$540$	−135.703	−	98.5939i	−5.83972	−	4.24281i
$541$	−0.294270	−	0.905669i	−0.0126516	−	0.0389378i	0.944531	−	0.328421i	$-0.106517\pi$
$541$	−0.294270	−	0.905669i	−0.0126516	−	0.0389378i	−0.957183	+	0.289483i	$0.906517\pi$
$542$	−35.3936			−1.52029
$543$	−19.6506	−	60.4784i	−0.843288	−	2.59537i
$544$	9.86761	+	30.3694i	0.423070	+	1.30208i
$545$	6.68901	−	20.5867i	0.286526	−	0.881836i
$546$	5.70737	−	4.14665i	0.244253	−	0.177460i
$547$	28.7959			1.23122			0.615612	−	0.788050i	$-0.288909\pi$
$547$	28.7959			1.23122			0.615612	+	0.788050i	$0.288909\pi$
$548$	0.0291383	−	0.0896786i	0.00124473	−	0.00383088i
$549$	76.9583	+	55.9135i	3.28450	+	2.38633i
$550$	−1.42701	−	4.39190i	−0.0608481	−	0.187271i
$551$	1.17332	−	0.852465i	0.0499850	−	0.0363162i
$552$	−98.2915	−	71.4129i	−4.18356	−	3.03954i
$553$	−6.58740	−	4.78603i	−0.280125	−	0.203523i
$554$	−14.3735	−	10.4430i	−0.610672	−	0.443679i
$555$	26.3292	+	19.1293i	1.11761	+	0.811992i
$556$	−39.9809	+	29.0478i	−1.69557	+	1.23190i
$557$	−11.4815	−	35.3365i	−0.486488	−	1.49726i	−0.829814	−	0.558041i	$-0.811553\pi$
$557$	−11.4815	−	35.3365i	−0.486488	−	1.49726i	0.343325	−	0.939217i	$-0.388447\pi$
$558$	83.6091	+	60.7456i	3.53946	+	2.57156i
$559$	−1.27877	+	3.93564i	−0.0540861	+	0.166460i
$560$	23.4859			0.992462
$561$	2.58055	−	1.87488i	0.108951	−	0.0791574i
$562$	−4.35082	+	13.3905i	−0.183528	+	0.564842i
$563$	−8.52836	−	26.2476i	−0.359427	−	1.10620i	−0.953398	−	0.301717i	$-0.902440\pi$
$563$	−8.52836	−	26.2476i	−0.359427	−	1.10620i	0.593970	−	0.804487i	$-0.297560\pi$
$564$	−38.7471	−	119.251i	−1.63155	−	5.02139i
$565$	30.0926			1.26601
$566$	7.44195	+	22.9040i	0.312808	+	0.962725i
$567$	33.3990	+	24.2658i	1.40263	+	1.01907i
$568$	−64.3037	+	46.7194i	−2.69812	+	1.96030i
$569$	8.52950	−	26.2511i	0.357575	−	1.10050i	−0.596926	−	0.802296i	$-0.703611\pi$
$569$	8.52950	−	26.2511i	0.357575	−	1.10050i	0.954501	−	0.298207i	$-0.0963886\pi$
$570$	1.37793	−	4.24084i	0.0577153	−	0.177629i
$571$	17.5092			0.732739			0.366370	−	0.930469i	$-0.380601\pi$
$571$	17.5092			0.732739			0.366370	+	0.930469i	$0.380601\pi$
$572$	2.17360	−	1.57921i	0.0908828	−	0.0660302i
$573$	31.4599			1.31426
$574$	13.1277	−	11.6039i	0.547938	−	0.484336i
$575$	9.63071			0.401628
$576$	−218.266	+	158.580i	−9.09442	+	6.60748i
$577$	−9.01683			−0.375376			−0.187688	−	0.982229i	$-0.560099\pi$
$577$	−9.01683			−0.375376			−0.187688	+	0.982229i	$0.560099\pi$
$578$	−12.6463	+	38.9212i	−0.526015	+	1.61891i
$579$	22.8852	−	70.4334i	0.951076	−	2.92711i
$580$	−32.5997	+	23.6851i	−1.35363	+	0.983470i
$581$	−7.91448	−	5.75021i	−0.328348	−	0.238559i
$582$	11.0858	+	34.1187i	0.459522	+	1.41426i
$583$	4.45010			0.184304
$584$	0.654890	+	2.01554i	0.0270995	+	0.0834038i
$585$	3.15488	+	9.70972i	0.130438	+	0.401448i
$586$	−1.59542	+	4.91021i	−0.0659063	+	0.202839i
$587$	19.0571	−	13.8458i	0.786571	−	0.571477i	−0.120373	−	0.992729i	$-0.538409\pi$
$587$	19.0571	−	13.8458i	0.786571	−	0.571477i	0.906944	+	0.421252i	$0.138409\pi$
$588$	−18.8084			−0.775646
$589$	−0.408825	+	1.25823i	−0.0168453	+	0.0518446i
$590$	10.7643	+	7.82072i	0.443159	+	0.321974i
$591$	−14.9571	−	46.0331i	−0.615251	−	1.89355i
$592$	74.9442	−	54.4501i	3.08019	−	2.23789i
$593$	28.5198	+	20.7208i	1.17117	+	0.850903i	0.991148	−	0.132760i	$-0.0423841\pi$
$593$	28.5198	+	20.7208i	1.17117	+	0.850903i	0.180019	+	0.983663i	$0.442384\pi$
$594$	28.3887	+	20.6256i	1.16480	+	0.846278i
$595$	−1.79461	−	1.30386i	−0.0735719	−	0.0534531i
$596$	11.7240	+	8.51798i	0.480234	+	0.348910i
$597$	15.5879	−	11.3253i	0.637972	−	0.463514i
$598$	2.36255	+	7.27117i	0.0966117	+	0.297340i
$599$	−22.4225	−	16.2909i	−0.916158	−	0.665628i	0.0264068	−	0.999651i	$-0.491593\pi$
$599$	−22.4225	−	16.2909i	−0.916158	−	0.665628i	−0.942565	+	0.334024i	$0.891593\pi$
$600$	26.2057	−	80.6529i	1.06984	−	3.29264i
$601$	−0.0232831			−0.000949737			−0.000474868	−	1.00000i	$-0.500151\pi$
$601$	−0.0232831			−0.000949737			−0.000474868		1.00000i	$0.500151\pi$
$602$	12.1788	−	8.84841i	0.496370	−	0.360634i
$603$	0.227346	−	0.699700i	0.00925825	−	0.0284940i
$604$	5.00920	+	15.4167i	0.203822	+	0.627298i
$605$	5.07083	+	15.6064i	0.206159	+	0.634491i
$606$	−58.0161			−2.35674
$607$	7.07001	+	21.7593i	0.286963	+	0.883181i	0.985803	+	0.167903i	$0.0536997\pi$
$607$	7.07001	+	21.7593i	0.286963	+	0.883181i	−0.698841	+	0.715277i	$0.746300\pi$
$608$	−5.53696	−	4.02284i	−0.224553	−	0.163148i
$609$	13.1239	−	9.53507i	0.531807	−	0.386381i
$610$	14.2660	−	43.9061i	0.577612	−	1.77771i
$611$	−1.54959	+	4.76914i	−0.0626896	+	0.192939i
$612$	68.6324			2.77430
$613$	−22.1930	+	16.1242i	−0.896367	+	0.651248i	−0.937530	−	0.347904i	$-0.886894\pi$
$613$	−22.1930	+	16.1242i	−0.896367	+	0.651248i	0.0411636	+	0.999152i	$0.486894\pi$
$614$	−57.9370			−2.33815
$615$	13.5640	+	31.2334i	0.546953	+	1.25945i
$616$	−6.21151			−0.250269
$617$	3.91158	−	2.84193i	0.157474	−	0.114412i	−0.506258	−	0.862382i	$-0.668972\pi$
$617$	3.91158	−	2.84193i	0.157474	−	0.114412i	0.663732	+	0.747970i	$0.268972\pi$
$618$	116.554			4.68850
$619$	6.23719	−	19.1961i	0.250694	−	0.771556i	−0.743954	−	0.668231i	$-0.767052\pi$
$619$	6.23719	−	19.1961i	0.250694	−	0.771556i	0.994648	−	0.103325i	$-0.0329482\pi$
$620$	11.3589	−	34.9591i	0.456184	−	1.40399i
$621$	−59.2049	+	43.0149i	−2.37581	+	1.72613i
$622$	−20.6374	−	14.9940i	−0.827486	−	0.601204i
$623$	0.618965	+	1.90498i	0.0247983	+	0.0763214i
$624$	39.0262			1.56230
$625$	−1.64216	−	5.05404i	−0.0656863	−	0.202162i
$626$	3.68757	+	11.3492i	0.147385	+	0.453605i
$627$	−0.211262	+	0.650197i	−0.00843698	+	0.0259664i
$628$	−22.4468	+	16.3086i	−0.895725	+	0.650782i
$629$	−8.74954			−0.348867
$630$	11.4768	−	35.3219i	0.457246	−	1.40726i
$631$	−30.9847	−	22.5117i	−1.23348	−	0.896178i	−0.236337	−	0.971671i	$-0.575947\pi$
$631$	−30.9847	−	22.5117i	−1.23348	−	0.896178i	−0.997146	+	0.0754934i	$0.975947\pi$
$632$	−24.0112	−	73.8988i	−0.955113	−	2.93954i
$633$	−49.5376	+	35.9911i	−1.96894	+	1.43052i
$634$	49.6010	+	36.0372i	1.96991	+	1.43122i
$635$	−6.25638	−	4.54552i	−0.248277	−	0.180384i
$636$	104.030	+	75.5821i	4.12505	+	2.99702i
$637$	0.608537	+	0.442128i	0.0241111	+	0.0175178i
$638$	6.81978	−	4.95486i	0.269998	−	0.196165i
$639$	22.5162	+	69.2976i	0.890726	+	2.74137i
$640$	49.8572	+	36.2234i	1.97078	+	1.43186i
$641$	−5.90081	+	18.1608i	−0.233068	+	0.717309i	0.764304	+	0.644856i	$0.223083\pi$
$641$	−5.90081	+	18.1608i	−0.233068	+	0.717309i	−0.997372	+	0.0724531i	$0.976917\pi$
$642$	−70.5475			−2.78429
$643$	−35.3068	+	25.6519i	−1.39236	+	1.01161i	−0.396762	+	0.917921i	$0.629866\pi$
$643$	−35.3068	+	25.6519i	−1.39236	+	1.01161i	−0.995601	+	0.0936899i	$0.970134\pi$
$644$	6.29875	−	19.3856i	0.248206	−	0.763898i
$645$	9.04079	+	27.8247i	0.355981	+	1.09560i
$646$	0.370454	+	1.14014i	0.0145753	+	0.0448582i
$647$	−6.35321			−0.249770			−0.124885	−	0.992171i	$-0.539856\pi$
$647$	−6.35321			−0.249770			−0.124885	+	0.992171i	$0.539856\pi$
$648$	121.740	+	374.677i	4.78239	+	14.7187i
$649$	−1.65036	−	1.19906i	−0.0647823	−	0.0470671i
$650$	−4.31729	+	3.13669i	−0.169338	+	0.123031i
$651$	−4.57283	+	14.0737i	−0.179223	+	0.551592i
$652$	20.6760	−	63.6343i	0.809736	−	2.49211i
$653$	17.7123			0.693136			0.346568	−	0.938025i	$-0.387347\pi$
$653$	17.7123			0.693136			0.346568	+	0.938025i	$0.387347\pi$
$654$	−105.858	+	76.9103i	−4.13937	+	3.00743i
$655$	−32.9573			−1.28775
$656$	96.4833	−	9.24657i	3.76704	−	0.361018i
$657$	1.94276			0.0757944
$658$	14.7581	−	10.7224i	0.575329	−	0.418001i
$659$	44.6279			1.73846			0.869229	−	0.494410i	$-0.164616\pi$
$659$	44.6279			1.73846			0.869229	+	0.494410i	$0.164616\pi$
$660$	5.86975	−	18.0652i	0.228480	−	0.703188i
$661$	−8.25791	+	25.4152i	−0.321195	+	0.988538i	0.651933	+	0.758276i	$0.273958\pi$
$661$	−8.25791	+	25.4152i	−0.321195	+	0.988538i	−0.973129	+	0.230261i	$0.926042\pi$
$662$	35.6932	−	25.9326i	1.38726	−	1.00790i
$663$	−2.98208	−	2.16661i	−0.115814	−	0.0841441i
$664$	−28.8484	−	88.7863i	−1.11954	−	3.44558i
$665$	0.475441			0.0184368
$666$	−45.2682	−	139.321i	−1.75411	−	5.39858i
$667$	5.43260	+	16.7198i	0.210351	+	0.647394i
$668$	−14.4154	+	44.3659i	−0.557747	+	1.71657i
$669$	−53.0950	+	38.5758i	−2.05277	+	1.49143i
$670$	−0.357048			−0.0137940
$671$	−2.18723	+	6.73159i	−0.0844369	+	0.259870i
$672$	−61.9325	−	44.9966i	−2.38910	−	1.73578i
$673$	−5.37693	−	16.5485i	−0.207265	−	0.637898i	−0.999613	−	0.0278272i	$-0.991141\pi$
$673$	−5.37693	−	16.5485i	−0.207265	−	0.637898i	0.792347	−	0.610070i	$-0.208859\pi$
$674$	39.2680	−	28.5299i	1.51255	−	1.09893i
$675$	−41.3250	−	30.0244i	−1.59060	−	1.15564i
$676$	55.2009	+	40.1058i	2.12311	+	1.54253i
$677$	−18.0919	−	13.1446i	−0.695330	−	0.505187i	0.183078	−	0.983098i	$-0.441394\pi$
$677$	−18.0919	−	13.1446i	−0.695330	−	0.505187i	−0.878408	+	0.477912i	$0.841394\pi$
$678$	−147.165	−	106.922i	−5.65183	−	4.10630i
$679$	−3.09453	+	2.24831i	−0.118757	+	0.0862821i
$680$	−6.54139	−	20.1323i	−0.250851	−	0.772040i
$681$	−31.9664	−	23.2250i	−1.22496	−	0.889982i
$682$	−2.37625	+	7.31334i	−0.0909913	+	0.280042i
$683$	−8.63129			−0.330267			−0.165134	−	0.986271i	$-0.552806\pi$
$683$	−8.63129			−0.330267			−0.165134	+	0.986271i	$0.552806\pi$
$684$	−11.9007	+	8.64633i	−0.455033	+	0.330601i
$685$	−0.00823867	+	0.0253560i	−0.000314783	+	0.000968803i
$686$	−0.845569	−	2.60240i	−0.0322840	−	0.0993599i
$687$	16.9246	+	52.0884i	0.645712	+	1.98730i
$688$	83.2770			3.17491
$689$	−1.58913	−	4.89084i	−0.0605410	−	0.186326i
$690$	43.7291	+	31.7711i	1.66474	+	1.20950i
$691$	0.0341064	−	0.0247797i	0.00129747	−	0.000942666i	−0.587136	−	0.809488i	$-0.699745\pi$
$691$	0.0341064	−	0.0247797i	0.00129747	−	0.000942666i	0.588434	+	0.808545i	$0.299745\pi$
$692$	−2.99156	+	9.20707i	−0.113722	+	0.350000i
$693$	−1.75960	+	5.41548i	−0.0668415	+	0.205717i
$694$	−21.7134			−0.824228
$695$	11.3043	−	8.21307i	0.428797	−	0.311540i
$696$	154.803			5.86780
$697$	−7.88584	−	4.64988i	−0.298697	−	0.176127i
$698$	63.5079			2.40381
$699$	64.1263	−	46.5905i	2.42548	−	1.76221i
$700$	14.2275			0.537747
$701$	6.70920	−	20.6488i	0.253403	−	0.779895i	−0.740737	−	0.671795i	$-0.765524\pi$
$701$	6.70920	−	20.6488i	0.253403	−	0.779895i	0.994140	−	0.108099i	$-0.0344765\pi$
$702$	12.5307	−	38.5657i	0.472943	−	1.45557i
$703$	1.51714	−	1.10227i	0.0572202	−	0.0415729i
$704$	−16.2405	−	11.7994i	−0.612087	−	0.444708i
$705$	10.9555	+	33.7175i	0.412607	+	1.26987i
$706$	−57.5193			−2.16477
$707$	−1.91153	−	5.88310i	−0.0718906	−	0.221257i
$708$	−18.2152	−	56.0605i	−0.684568	−	2.10688i
$709$	5.97127	−	18.3777i	0.224256	−	0.690188i	−0.774111	−	0.633050i	$-0.781803\pi$
$709$	5.97127	−	18.3777i	0.224256	−	0.690188i	0.998366	−	0.0571377i	$-0.0181974\pi$
$710$	28.6082	−	20.7851i	1.07365	−	0.780050i
$711$	−71.2303			−2.67135
$712$	−5.90665	+	18.1788i	−0.221361	+	0.681279i
$713$	−12.9742	−	9.42629i	−0.485887	−	0.353017i
$714$	4.14364	+	12.7528i	0.155072	+	0.477262i
$715$	−0.614571	+	0.446512i	−0.0229836	+	0.0166986i
$716$	84.1753	+	61.1570i	3.14578	+	2.28554i
$717$	−15.7631	−	11.4525i	−0.588683	−	0.427703i
$718$	−59.8184	−	43.4606i	−2.23240	−	1.62194i
$719$	−20.6522	−	15.0047i	−0.770197	−	0.559581i	0.131824	−	0.991273i	$-0.457917\pi$
$719$	−20.6522	−	15.0047i	−0.770197	−	0.559581i	−0.902021	+	0.431692i	$0.857917\pi$
$720$	166.217	−	120.763i	6.19452	−	4.50059i
$721$	3.84027	+	11.8191i	0.143019	+	0.440168i
$722$	41.8530	+	30.4080i	1.55761	+	1.13167i
$723$	11.0865	−	34.1207i	0.412311	−	1.26896i
$724$	101.808			3.78367
$725$	−9.92746	+	7.21272i	−0.368696	+	0.267874i
$726$	30.6525	−	94.3386i	1.13762	−	3.50123i
$727$	2.12197	+	6.53074i	0.0786994	+	0.242212i	0.982664	−	0.185395i	$-0.0593566\pi$
$727$	2.12197	+	6.53074i	0.0786994	+	0.242212i	−0.903965	+	0.427607i	$0.859357\pi$
$728$	2.21813	+	6.82669i	0.0822093	+	0.253014i
$729$	158.565			5.87278
$730$	−0.291355	−	0.896700i	−0.0107835	−	0.0331884i
$731$	−6.36338	−	4.62326i	−0.235358	−	0.170998i
$732$	−165.462	+	120.215i	−6.11566	+	4.44329i
$733$	−8.46267	+	26.0454i	−0.312576	+	0.962010i	0.664165	+	0.747586i	$0.268787\pi$
$733$	−8.46267	+	26.0454i	−0.312576	+	0.962010i	−0.976741	+	0.214424i	$0.931213\pi$
$734$	−9.42945	+	29.0209i	−0.348047	+	1.07118i
$735$	5.31795			0.196156
$736$	67.1179	−	48.7640i	2.47400	−	1.79747i
$737$	0.0547418			0.00201644
$738$	33.2416	−	149.626i	1.22364	−	5.50779i
$739$	13.9292			0.512396			0.256198	−	0.966624i	$-0.417530\pi$
$739$	13.9292			0.512396			0.256198	+	0.966624i	$0.417530\pi$
$740$	−42.1527	+	30.6258i	−1.54957	+	1.12583i
$741$	0.790034			0.0290226
$742$	−5.78092	+	17.7918i	−0.212224	+	0.653159i
$743$	−11.1489	+	34.3129i	−0.409015	+	1.25882i	0.508481	+	0.861073i	$0.330207\pi$
$743$	−11.1489	+	34.3129i	−0.409015	+	1.25882i	−0.917496	+	0.397745i	$0.869793\pi$
$744$	−114.244	+	83.0034i	−4.18840	+	3.04305i
$745$	−3.31488	−	2.40840i	−0.121448	−	0.0882370i
$746$	−2.74527	−	8.44907i	−0.100511	−	0.309342i
$747$	−85.5802			−3.13122
$748$	1.57807	+	4.85679i	0.0576998	+	0.177582i
$749$	−2.32442	−	7.15384i	−0.0849326	−	0.261396i
$750$	−34.1422	+	105.079i	−1.24670	+	3.83694i
$751$	−35.8094	+	26.0171i	−1.30670	+	0.949376i	−0.999997	−	0.00242737i	$-0.999227\pi$
$751$	−35.8094	+	26.0171i	−1.30670	+	0.949376i	−0.306708	+	0.951804i	$0.599227\pi$
$752$	100.914			3.67994
$753$	−20.2439	+	62.3043i	−0.737729	+	2.27050i
$754$	−7.88093	−	5.72583i	−0.287007	−	0.208522i
$755$	−1.41632	−	4.35898i	−0.0515451	−	0.158639i
$756$	−87.4634	+	63.5459i	−3.18101	+	2.31114i
$757$	−31.4769	−	22.8693i	−1.14405	−	0.831200i	−0.156370	−	0.987699i	$-0.549979\pi$
$757$	−31.4769	−	22.8693i	−1.14405	−	0.831200i	−0.987678	+	0.156499i	$0.949979\pi$
$758$	−69.8094	−	50.7195i	−2.53559	−	1.84221i
$759$	−6.70445	−	4.87107i	−0.243356	−	0.176809i
$760$	3.67054	+	2.66680i	0.133144	+	0.0967350i
$761$	20.7282	−	15.0599i	0.751396	−	0.545921i	−0.144863	−	0.989452i	$-0.546274\pi$
$761$	20.7282	−	15.0599i	0.751396	−	0.545921i	0.896259	+	0.443531i	$0.146274\pi$
$762$	14.4455	+	44.4588i	0.523307	+	1.61057i
$763$	−11.2869	−	8.20041i	−0.408613	−	0.296875i
$764$	−15.5642	+	47.9018i	−0.563095	+	1.73303i
$765$	−19.4054			−0.701602
$766$	−67.1987	+	48.8227i	−2.42799	+	1.76404i
$767$	−0.728468	+	2.24199i	−0.0263034	+	0.0809537i
$768$	−49.7867	−	153.228i	−1.79652	−	5.52913i
$769$	11.5066	+	35.4138i	0.414940	+	1.27705i	0.912305	+	0.409512i	$0.134301\pi$
$769$	11.5066	+	35.4138i	0.414940	+	1.27705i	−0.497365	+	0.867542i	$0.665699\pi$
$770$	2.76345			0.0995879
$771$	7.87399	+	24.2337i	0.283575	+	0.872754i
$772$	95.9220	+	69.6914i	3.45231	+	2.50825i
$773$	14.5438	−	10.5667i	0.523105	−	0.380058i	−0.294668	−	0.955600i	$-0.595209\pi$
$773$	14.5438	−	10.5667i	0.523105	−	0.380058i	0.817772	+	0.575542i	$0.195209\pi$
$774$	40.6947	−	125.245i	1.46274	−	4.50185i
$775$	3.45907	−	10.6459i	0.124254	−	0.382413i
$776$	−36.5016			−1.31033
$777$	16.9697	−	12.3292i	0.608785	−	0.442308i
$778$	29.7425			1.06632
$779$	1.95317	−	0.187184i	0.0699797	−	0.00670658i
$780$	−21.9505			−0.785954
$781$	−4.38615	+	3.18672i	−0.156949	+	0.114030i
$782$	−14.5318			−0.519655
$783$	28.8140	−	88.6805i	1.02973	−	3.16918i
$784$	4.67765	−	14.3963i	0.167059	−	0.514155i
$785$	6.34668	−	4.61113i	0.226523	−	0.164578i
$786$	161.174	+	117.100i	5.74889	+	4.17681i
$787$	−2.68035	−	8.24928i	−0.0955443	−	0.294055i	0.891851	−	0.452330i	$-0.149407\pi$
$787$	−2.68035	−	8.24928i	−0.0955443	−	0.294055i	−0.987395	+	0.158274i	$0.949407\pi$
$788$	77.4912			2.76051
$789$	22.9889	+	70.7525i	0.818426	+	2.51886i
$790$	10.6824	+	32.8770i	0.380062	+	1.16971i
$791$	5.99349	−	18.4461i	0.213104	−	0.655867i
$792$	−43.9605	+	31.9392i	−1.56207	+	1.13491i
$793$	8.17935			0.290457
$794$	−32.8455	+	101.088i	−1.16564	+	3.58748i
$795$	−29.4137	−	21.3703i	−1.04320	−	0.757927i
$796$	9.53240	+	29.3377i	0.337867	+	1.03985i
$797$	−11.9470	+	8.67998i	−0.423183	+	0.307461i	−0.778917	−	0.627127i	$-0.784231\pi$
$797$	−11.9470	+	8.67998i	−0.423183	+	0.307461i	0.355734	+	0.934587i	$0.384231\pi$
$798$	−2.32510	−	1.68928i	−0.0823075	−	0.0597999i
$799$	−7.71103	−	5.60239i	−0.272797	−	0.198198i
$800$	46.8483	+	34.0373i	1.65634	+	1.20340i
$801$	14.1759	+	10.2994i	0.500880	+	0.363911i
$802$	41.4505	−	30.1155i	1.46367	−	1.06342i
$803$	0.0446700	+	0.137480i	0.00157637	+	0.00485157i
$804$	1.27970	+	0.929754i	0.0451314	+	0.0327899i
$805$	−1.78093	+	5.48114i	−0.0627695	+	0.193185i
$806$	8.88621			0.313004
$807$	−44.2724	+	32.1658i	−1.55846	+	1.13229i
$808$	18.2413	−	56.1411i	0.641728	−	1.97504i
$809$	0.824018	+	2.53607i	0.0289709	+	0.0891633i	0.964496	−	0.264096i	$-0.0850735\pi$
$809$	0.824018	+	2.53607i	0.0289709	+	0.0891633i	−0.935526	+	0.353259i	$0.885073\pi$
$810$	−54.1611	−	166.691i	−1.90303	−	5.85692i
$811$	−10.1132			−0.355124			−0.177562	−	0.984110i	$-0.556821\pi$
$811$	−10.1132			−0.355124			−0.177562	+	0.984110i	$0.556821\pi$
$812$	8.02558	+	24.7002i	0.281643	+	0.866807i
$813$	−35.8672	−	26.0590i	−1.25792	−	0.913930i
$814$	8.81824	−	6.40682i	0.309079	−	0.224559i
$815$	−5.84601	+	17.9922i	−0.204777	+	0.630238i
$816$	−22.9224	+	70.5479i	−0.802445	+	2.46967i
$817$	1.68583			0.0589797
$818$	25.8139	−	18.7549i	0.902563	−	0.655750i
$819$	6.58018			0.229930
$820$	−54.2675	+	5.20078i	−1.89510	+	0.181619i
$821$	17.3753			0.606403			0.303201	−	0.952927i	$-0.401945\pi$
$821$	17.3753			0.606403			0.303201	+	0.952927i	$0.401945\pi$
$822$	0.130382	−	0.0947282i	0.00454760	−	0.00330403i
$823$	−49.4972			−1.72536			−0.862682	−	0.505747i	$-0.831217\pi$
$823$	−49.4972			−1.72536			−0.862682	+	0.505747i	$0.831217\pi$
$824$	−36.6468	+	112.787i	−1.27665	+	3.92914i
$825$	1.78749	−	5.50132i	0.0622324	−	0.191532i
$826$	6.93782	−	5.04062i	0.241398	−	0.175386i
$827$	26.1305	+	18.9849i	0.908645	+	0.660169i	0.940672	−	0.339318i	$-0.110196\pi$
$827$	26.1305	+	18.9849i	0.908645	+	0.660169i	−0.0320267	+	0.999487i	$0.510196\pi$
$828$	−55.1014	−	169.585i	−1.91491	−	5.89348i
$829$	38.3870			1.33324			0.666619	−	0.745399i	$-0.267741\pi$
$829$	38.3870			1.33324			0.666619	+	0.745399i	$0.267741\pi$
$830$	12.8344	+	39.5003i	0.445490	+	1.37108i
$831$	−6.87705	−	21.1654i	−0.238562	−	0.734219i
$832$	−7.16856	+	22.0625i	−0.248525	+	0.764881i
$833$	−1.15667	+	0.840367i	−0.0400761	+	0.0291170i
$834$	−84.4643			−2.92476
$835$	4.07585	−	12.5442i	0.141051	−	0.434109i
$836$	−0.885492	−	0.643348i	−0.0306254	−	0.0222506i
$837$	26.2846	+	80.8956i	0.908528	+	2.79616i
$838$	56.5871	−	41.1130i	1.95477	−	1.42022i
$839$	−20.0379	−	14.5584i	−0.691787	−	0.502612i	0.185460	−	0.982652i	$-0.440622\pi$
$839$	−20.0379	−	14.5584i	−0.691787	−	0.502612i	−0.877247	+	0.480039i	$0.840622\pi$
$840$	41.0560	+	29.8290i	1.41657	+	1.02920i
$841$	5.33956	+	3.87941i	0.184123	+	0.133773i
$842$	−75.0841	−	54.5518i	−2.58757	−	1.87998i
$843$	−14.2680	+	10.3663i	−0.491414	+	0.357034i
$844$	−30.2934	−	93.2335i	−1.04274	−	3.20923i
$845$	−15.6077	−	11.3396i	−0.536920	−	0.390096i
$846$	49.3131	−	151.770i	1.69542	−	5.21797i
$847$	10.5763			0.363406
$848$	−83.7242	+	60.8292i	−2.87510	+	2.08888i
$849$	−9.32184	+	28.6897i	−0.319925	+	0.984627i
$850$	−3.13442	−	9.64674i	−0.107510	−	0.330880i
$851$	7.02456	+	21.6194i	0.240799	+	0.741102i
$852$	−156.659			−5.36706
$853$	16.2797	+	50.1039i	0.557408	+	1.71552i	0.689499	+	0.724287i	$0.257831\pi$
$853$	16.2797	+	50.1039i	0.557408	+	1.71552i	−0.132091	+	0.991238i	$0.542169\pi$
$854$	−24.0721	−	17.4894i	−0.823730	−	0.598475i
$855$	3.36483	−	2.44469i	0.115075	−	0.0836067i
$856$	22.1815	−	68.2675i	0.758147	−	2.33334i
$857$	5.60416	−	17.2478i	0.191434	−	0.589175i	−0.808565	−	0.588406i	$-0.799756\pi$
$857$	5.60416	−	17.2478i	0.191434	−	0.589175i	1.00000		0.000768095i	$-0.000244492\pi$
$858$	4.59198			0.156768
$859$	−17.2890	+	12.5612i	−0.589894	+	0.428583i	−0.842277	−	0.539044i	$-0.818786\pi$
$859$	−17.2890	+	12.5612i	−0.589894	+	0.428583i	0.252384	+	0.967627i	$0.418786\pi$
$860$	−46.8395			−1.59722
$861$	21.8468	−	2.09371i	0.744538	−	0.0713536i
$862$	−51.8192			−1.76497
$863$	−4.25175	+	3.08907i	−0.144731	+	0.105153i	−0.657795	−	0.753197i	$-0.728511\pi$
$863$	−4.25175	+	3.08907i	−0.144731	+	0.105153i	0.513064	+	0.858351i	$0.328511\pi$
$864$	−440.025			−14.9700
$865$	0.845843	−	2.60324i	0.0287595	−	0.0885127i
$866$	−26.5109	+	81.5921i	−0.900877	+	2.77261i
$867$	−41.4717	+	30.1310i	−1.40845	+	1.02330i
$868$	−19.1668	−	13.9255i	−0.650562	−	0.472661i
$869$	−1.63780	−	5.04063i	−0.0555586	−	0.170992i
$870$	−68.8708			−2.33494
$871$	−0.0195483	−	0.0601634i	−0.000662368	−	0.00203856i
$872$	−41.1409	−	126.619i	−1.39321	−	4.28785i
$873$	−10.3402	+	31.8238i	−0.349962	+	1.07707i
$874$	2.51977	−	1.83072i	0.0852324	−	0.0619250i
$875$	−11.7804			−0.398251
$876$	−1.29076	+	3.97255i	−0.0436108	+	0.134220i
$877$	−0.549478	−	0.399219i	−0.0185546	−	0.0134807i	0.578469	−	0.815704i	$-0.303650\pi$
$877$	−0.549478	−	0.399219i	−0.0185546	−	0.0134807i	−0.597024	+	0.802223i	$0.703650\pi$
$878$	17.9662	+	55.2941i	0.606328	+	1.86609i
$879$	−5.23198	+	3.80126i	−0.176470	+	0.128213i
$880$	12.3677	+	8.98564i	0.416914	+	0.302906i
$881$	−42.7760	−	31.0786i	−1.44116	−	1.04706i	−0.987799	−	0.155737i	$-0.950225\pi$
$881$	−42.7760	−	31.0786i	−1.44116	−	1.04706i	−0.453361	−	0.891327i	$-0.649775\pi$
$882$	−19.3657	−	14.0700i	−0.652077	−	0.473762i
$883$	6.51581	+	4.73401i	0.219275	+	0.159312i	0.692000	−	0.721897i	$-0.256730\pi$
$883$	6.51581	+	4.73401i	0.219275	+	0.159312i	−0.472726	+	0.881210i	$0.656730\pi$
$884$	4.77428	−	3.46872i	0.160576	−	0.116666i
$885$	5.15022	+	15.8507i	0.173123	+	0.532817i
$886$	−4.30215	−	3.12570i	−0.144534	−	0.105010i
$887$	−8.00887	+	24.6488i	−0.268912	+	0.827625i	0.721855	+	0.692044i	$0.243290\pi$
$887$	−8.00887	+	24.6488i	−0.268912	+	0.827625i	−0.990766	+	0.135580i	$0.956710\pi$
$888$	200.167			6.71715
$889$	−4.03237	+	2.92969i	−0.135241	+	0.0982586i
$890$	2.62782	−	8.08760i	0.0880848	−	0.271097i
$891$	8.30387	+	25.5567i	0.278190	+	0.856181i
$892$	−32.4689	−	99.9289i	−1.08714	−	3.34587i
$893$	2.04286			0.0683618
$894$	7.65383	+	23.5561i	0.255982	+	0.787832i
$895$	−23.8000	−	17.2917i	−0.795546	−	0.577998i
$896$	32.1341	−	23.3468i	1.07352	−	0.779960i
$897$	−2.95934	+	9.10792i	−0.0988096	+	0.304105i
$898$	−17.1527	+	52.7906i	−0.572393	+	1.76164i
$899$	20.4336			0.681497
$900$	100.692	−	73.1568i	3.35639	−	2.43856i
$901$	9.77458			0.325639
$902$	11.3526	−	1.08799i	0.378001	−	0.0362261i
$903$	18.8565			0.627506
$904$	149.737	−	108.791i	4.98019	−	3.61832i
$905$	−28.7855			−0.956864
$906$	−8.56144	+	26.3494i	−0.284435	+	0.875401i
$907$	2.17467	−	6.69296i	0.0722089	−	0.222236i	−0.908438	−	0.418019i	$-0.862725\pi$
$907$	2.17467	−	6.69296i	0.0722089	−	0.222236i	0.980647	+	0.195783i	$0.0627247\pi$
$908$	51.1779	−	37.1829i	1.69840	−	1.23396i
$909$	−43.7790	−	31.8073i	−1.45206	−	1.05498i
$910$	−0.986828	−	3.03714i	−0.0327130	−	0.100680i
$911$	17.2990			0.573143			0.286572	−	0.958059i	$-0.407484\pi$
$911$	17.2990			0.573143			0.286572	+	0.958059i	$0.407484\pi$
$912$	−4.91297	−	15.1206i	−0.162685	−	0.500692i
$913$	−1.96775	−	6.05610i	−0.0651229	−	0.200428i
$914$	9.24130	−	28.4418i	0.305675	−	0.940771i
$915$	46.7833	−	33.9901i	1.54661	−	1.12368i
$916$	−87.6847			−2.89718
$917$	−6.56403	+	20.2020i	−0.216764	+	0.667129i
$918$	62.3553	+	45.3038i	2.05803	+	1.49525i
$919$	−5.86327	−	18.0453i	−0.193411	−	0.595259i	−0.999991	−	0.00413437i	$-0.998684\pi$
$919$	−5.86327	−	18.0453i	−0.193411	−	0.595259i	0.806580	−	0.591125i	$-0.201316\pi$
$920$	−44.4935	+	32.3264i	−1.46691	+	1.06577i
$921$	−58.7122	−	42.6569i	−1.93463	−	1.40559i
$922$	63.7021	+	46.2823i	2.09792	+	1.52423i
$923$	5.06863	+	3.68258i	0.166836	+	0.121213i
$924$	−9.90449	−	7.19603i	−0.325834	−	0.236732i
$925$	−12.8366	+	9.32632i	−0.422064	+	0.306648i
$926$	−14.4396	−	44.4404i	−0.474513	−	1.46040i
$927$	87.9520	+	63.9009i	2.88872	+	2.09878i
$928$	−32.6652	+	100.533i	−1.07229	+	3.30016i
$929$	43.8818			1.43972			0.719858	−	0.694121i	$-0.244207\pi$
$929$	43.8818			1.43972			0.719858	+	0.694121i	$0.244207\pi$
$930$	50.8264	−	36.9276i	1.66666	−	1.21090i
$931$	0.0946927	−	0.291434i	0.00310343	−	0.00955137i
$932$	39.2147	+	120.691i	1.28452	+	3.95335i
$933$	−9.87405	−	30.3892i	−0.323262	−	0.994898i
$934$	−57.9252			−1.89537
$935$	−0.446188	−	1.37322i	−0.0145919	−	0.0449092i
$936$	50.8008	+	36.9089i	1.66048	+	1.20641i
$937$	42.7055	−	31.0274i	1.39513	−	1.01362i	0.399848	−	0.916581i	$-0.369063\pi$
$937$	42.7055	−	31.0274i	1.39513	−	1.01362i	0.995281	−	0.0970391i	$-0.0309372\pi$
$938$	−0.0711125	+	0.218862i	−0.00232191	+	0.00714609i
$939$	−4.61908	+	14.2161i	−0.150738	+	0.463924i
$940$	−56.7594			−1.85129
$941$	42.9733	−	31.2219i	1.40089	−	1.01781i	0.406321	−	0.913730i	$-0.366811\pi$
$941$	42.9733	−	31.2219i	1.40089	−	1.01781i	0.994569	−	0.104076i	$-0.0331885\pi$
$942$	−47.4215			−1.54508
$943$	−5.15832	+	23.2184i	−0.167978	+	0.756094i
$944$	47.4399			1.54404
$945$	24.7297	−	17.9672i	0.804457	−	0.584472i
$946$	9.79871			0.318583
$947$	−3.15518	+	9.71065i	−0.102530	+	0.315554i	−0.989143	−	0.146958i	$-0.953052\pi$
$947$	−3.15518	+	9.71065i	−0.102530	+	0.315554i	0.886613	+	0.462512i	$0.153052\pi$
$948$	47.3251	−	145.652i	1.53705	−	4.73054i
$949$	0.135144	−	0.0981882i	0.00438698	−	0.00318732i
$950$	1.75880	+	1.27784i	0.0570629	+	0.0414586i
$951$	23.7318	+	73.0388i	0.769555	+	2.36845i
$952$	−13.6435			−0.442188
$953$	5.79901	+	17.8475i	0.187848	+	0.578138i	0.999986	−	0.00532828i	$-0.00169605\pi$
$953$	5.79901	+	17.8475i	0.187848	+	0.578138i	−0.812137	+	0.583466i	$0.801696\pi$
$954$	50.5715	+	155.643i	1.63731	+	5.03913i
$955$	4.40068	−	13.5439i	0.142403	−	0.438271i
$956$	25.2365	−	18.3354i	0.816208	−	0.593010i
$957$	10.5591			0.341328
$958$	3.73686	−	11.5009i	0.120732	−	0.371576i
$959$	0.0139018	+	0.0101002i	0.000448911	+	0.000326153i
$960$	50.6812	+	155.981i	1.63573	+	5.03425i
$961$	9.99963	−	7.26515i	0.322569	−	0.234360i
$962$	−10.1903	−	7.40372i	−0.328550	−	0.238706i
$963$	−53.2352	−	38.6777i	−1.71548	−	1.24637i
$964$	46.4684	+	33.7613i	1.49665	+	1.08738i
$965$	−27.1213	−	19.7048i	−0.873065	−	0.634319i
$966$	28.1843	−	20.4771i	0.906816	−	0.658841i
$967$	−9.05634	−	27.8726i	−0.291232	−	0.896321i	−0.984461	−	0.175603i	$-0.943812\pi$
$967$	−9.05634	−	27.8726i	−0.291232	−	0.896321i	0.693229	−	0.720718i	$-0.256188\pi$
$968$	81.6520	+	59.3236i	2.62439	+	1.90673i
$969$	−0.464033	+	1.42815i	−0.0149069	+	0.0458787i
$970$	16.2393			0.521412
$971$	12.7497	−	9.26320i	0.409158	−	0.297270i	−0.364103	−	0.931359i	$-0.618624\pi$
$971$	12.7497	−	9.26320i	0.409158	−	0.297270i	0.773261	+	0.634088i	$0.218624\pi$
$972$	−139.720	+	430.015i	−4.48153	+	13.7927i
$973$	−2.78296	−	8.56506i	−0.0892175	−	0.274583i
$974$	−8.31681	−	25.5965i	−0.266488	−	0.820165i
$975$	−6.68449			−0.214075
$976$	−50.8647	−	156.546i	−1.62814	−	5.01090i
$977$	33.1699	+	24.0993i	1.06120	+	0.771005i	0.974310	−	0.225213i	$-0.0723077\pi$
$977$	33.1699	+	24.0993i	1.06120	+	0.771005i	0.0868883	+	0.996218i	$0.472308\pi$
$978$	92.5168	−	67.2174i	2.95836	−	2.14938i
$979$	−0.402892	+	1.23997i	−0.0128765	+	0.0396297i
$980$	−2.63097	+	8.09729i	−0.0840432	+	0.258658i
$981$	−122.047			−3.89665
$982$	−36.7542	+	26.7035i	−1.17287	+	0.852143i
$983$	55.5244			1.77095			0.885476	−	0.464684i	$-0.153832\pi$
$983$	55.5244			1.77095			0.885476	+	0.464684i	$0.153832\pi$
$984$	180.407	+	106.377i	5.75117	+	3.39118i
$985$	−21.9101			−0.698114
$986$	14.9795	−	10.8833i	0.477046	−	0.346594i
$987$	22.8500			0.727324
$988$	−0.390856	+	1.20293i	−0.0124348	+	0.0382703i
$989$	−6.31486	+	19.4351i	−0.200801	+	0.618001i
$990$	19.5577	−	14.2095i	0.621585	−	0.451608i
$991$	−34.7218	−	25.2269i	−1.10298	−	0.801358i	−0.121432	−	0.992600i	$-0.538749\pi$
$991$	−34.7218	−	25.2269i	−1.10298	−	0.801358i	−0.981543	+	0.191241i	$0.938749\pi$
$992$	−29.7977	−	91.7078i	−0.946077	−	2.91172i
$993$	55.2640			1.75375
$994$	−7.04292	−	21.6759i	−0.223388	−	0.687517i
$995$	−2.69522	−	8.29504i	−0.0854442	−	0.262970i
$996$	56.8590	−	174.994i	1.80165	−	5.54490i
$997$	−15.3288	+	11.1370i	−0.485468	+	0.352713i	−0.803439	−	0.595387i	$-0.796999\pi$
$997$	−15.3288	+	11.1370i	−0.485468	+	0.352713i	0.317971	+	0.948100i	$0.396999\pi$
$998$	6.06459			0.191971
$999$	37.2577	−	114.667i	1.17878	−	3.62791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.d.78.1	✓	40
41.10	even	5	inner	287.2.h.d.92.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.d.78.1	✓	40	1.1	even	1	trivial
287.2.h.d.92.1	yes	40	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21373 + 1.60837i) q^{2} -3.42753 q^{3} +(1.69571 - 5.21887i) q^{4} +(-0.479452 + 1.47560i) q^{5} +(7.58764 - 5.51274i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.94888 + 9.07572i) q^{8} +8.74800 q^{9} +O(q^{10})\)	\(q+(-2.21373 + 1.60837i) q^{2} -3.42753 q^{3} +(1.69571 - 5.21887i) q^{4} +(-0.479452 + 1.47560i) q^{5} +(7.58764 - 5.51274i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.94888 + 9.07572i) q^{8} +8.74800 q^{9} +(-1.31193 - 4.03772i) q^{10} +(0.201143 + 0.619054i) q^{11} +(-5.81212 + 17.8879i) q^{12} +(0.608537 - 0.442128i) q^{13} -2.73632 q^{14} +(1.64334 - 5.05767i) q^{15} +(-12.2462 - 8.89742i) q^{16} +(0.441807 + 1.35974i) q^{17} +(-19.3657 + 14.0700i) q^{18} +(-0.247909 - 0.180116i) q^{19} +(6.88796 + 5.00440i) q^{20} +(-2.77293 - 2.01465i) q^{21} +(-1.44094 - 1.04691i) q^{22} +(3.00510 - 2.18333i) q^{23} +(-10.1074 - 31.1073i) q^{24} +(2.09756 + 1.52397i) q^{25} +(-0.636032 + 1.95750i) q^{26} -19.7015 q^{27} +(4.43944 - 3.22544i) q^{28} +(-1.46253 + 4.50122i) q^{29} +(4.49670 + 13.8394i) q^{30} +(-1.33414 - 4.10607i) q^{31} +22.3347 q^{32} +(-0.689424 - 2.12183i) q^{33} +(-3.16501 - 2.29951i) q^{34} +(-1.25522 + 0.911972i) q^{35} +(14.8341 - 45.6547i) q^{36} +(-1.89111 + 5.82025i) q^{37} +0.838497 q^{38} +(-2.08578 + 1.51541i) q^{39} -14.8060 q^{40} +(-4.79756 + 4.24069i) q^{41} +9.37883 q^{42} +(-4.45079 + 3.23369i) q^{43} +3.57185 q^{44} +(-4.19424 + 12.9086i) q^{45} +(-3.14088 + 9.66662i) q^{46} +(-5.39339 + 3.91853i) q^{47} +(41.9744 + 30.4962i) q^{48} +(0.309017 + 0.951057i) q^{49} -7.09453 q^{50} +(-1.51431 - 4.66057i) q^{51} +(-1.27551 - 3.92560i) q^{52} +(2.11266 - 6.50211i) q^{53} +(43.6137 - 31.6872i) q^{54} -1.00992 q^{55} +(-2.94888 + 9.07572i) q^{56} +(0.849716 + 0.617355i) q^{57} +(-4.00196 - 12.3168i) q^{58} +(-2.53546 + 1.84212i) q^{59} +(-23.6087 - 17.1527i) q^{60} +(8.79725 + 6.39157i) q^{61} +(9.55752 + 6.94394i) q^{62} +(7.07728 + 5.14194i) q^{63} +(-24.9504 + 18.1275i) q^{64} +(0.360640 + 1.10994i) q^{65} +(4.93888 + 3.58831i) q^{66} +(0.0259884 - 0.0799840i) q^{67} +7.84550 q^{68} +(-10.3001 + 7.48345i) q^{69} +(1.31193 - 4.03772i) q^{70} +(2.57387 + 7.92154i) q^{71} +(25.7968 + 79.3944i) q^{72} +0.222081 q^{73} +(-5.17469 - 15.9261i) q^{74} +(-7.18946 - 5.22345i) q^{75} +(-1.36039 + 0.988379i) q^{76} +(-0.201143 + 0.619054i) q^{77} +(2.18002 - 6.70941i) q^{78} -8.14247 q^{79} +(19.0005 - 13.8047i) q^{80} +41.2834 q^{81} +(3.79992 - 17.1040i) q^{82} -9.78284 q^{83} +(-15.2163 + 11.0553i) q^{84} -2.21826 q^{85} +(4.65188 - 14.3170i) q^{86} +(5.01288 - 15.4281i) q^{87} +(-5.02521 + 3.65103i) q^{88} +(1.62047 + 1.17734i) q^{89} +(-11.4768 - 35.3219i) q^{90} +0.752193 q^{91} +(-6.29875 - 19.3856i) q^{92} +(4.57283 + 14.0737i) q^{93} +(5.63708 - 17.3491i) q^{94} +(0.384640 - 0.279457i) q^{95} -76.5528 q^{96} +(-1.18201 + 3.63784i) q^{97} +(-2.21373 - 1.60837i) q^{98} +(1.75960 + 5.41548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

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