LMFDB - Embedded newform 315.2.l.c.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
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			121.3
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35938 q^{2} +(-0.431498 + 1.67744i) q^{3} +3.56668 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01807 - 3.95772i) q^{6} +(2.33019 + 1.25307i) q^{7} -3.69640 q^{8} +(-2.62762 - 1.44762i) q^{9} +O(q^{10})$	\(q-2.35938 q^{2} +(-0.431498 + 1.67744i) q^{3} +3.56668 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01807 - 3.95772i) q^{6} +(2.33019 + 1.25307i) q^{7} -3.69640 q^{8} +(-2.62762 - 1.44762i) q^{9} +(1.17969 + 2.04328i) q^{10} +(2.53158 - 4.38482i) q^{11} +(-1.53901 + 5.98290i) q^{12} +(0.354064 - 0.613257i) q^{13} +(-5.49782 - 2.95648i) q^{14} +(1.66846 - 0.465033i) q^{15} +1.58785 q^{16} +(-1.67858 - 2.90738i) q^{17} +(6.19956 + 3.41550i) q^{18} +(1.99373 - 3.45325i) q^{19} +(-1.78334 - 3.08884i) q^{20} +(-3.10743 + 3.36807i) q^{21} +(-5.97296 + 10.3455i) q^{22} +(3.79973 + 6.58132i) q^{23} +(1.59499 - 6.20049i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.835372 + 1.44691i) q^{26} +(3.56212 - 3.78303i) q^{27} +(8.31106 + 4.46932i) q^{28} +(3.54286 + 6.13641i) q^{29} +(-3.93652 + 1.09719i) q^{30} +5.32471 q^{31} +3.64646 q^{32} +(6.26291 + 6.13862i) q^{33} +(3.96041 + 6.85962i) q^{34} +(-0.0799028 - 2.64454i) q^{35} +(-9.37188 - 5.16321i) q^{36} +(3.70507 - 6.41738i) q^{37} +(-4.70398 + 8.14753i) q^{38} +(0.875925 + 0.858541i) q^{39} +(1.84820 + 3.20117i) q^{40} +(0.911736 - 1.57917i) q^{41} +(7.33162 - 7.94655i) q^{42} +(1.09555 + 1.89755i) q^{43} +(9.02933 - 15.6393i) q^{44} +(0.0601298 + 2.99940i) q^{45} +(-8.96501 - 15.5278i) q^{46} -10.5302 q^{47} +(-0.685152 + 2.66352i) q^{48} +(3.85961 + 5.83981i) q^{49} +(1.17969 - 2.04328i) q^{50} +(5.60127 - 1.56119i) q^{51} +(1.26283 - 2.18729i) q^{52} +(4.88360 + 8.45865i) q^{53} +(-8.40439 + 8.92561i) q^{54} -5.06316 q^{55} +(-8.61332 - 4.63186i) q^{56} +(4.93233 + 4.83444i) q^{57} +(-8.35895 - 14.4781i) q^{58} +10.0174 q^{59} +(5.95085 - 1.65862i) q^{60} -0.146519 q^{61} -12.5630 q^{62} +(-4.30888 - 6.66585i) q^{63} -11.7791 q^{64} -0.708128 q^{65} +(-14.7766 - 14.4833i) q^{66} -6.82912 q^{67} +(-5.98695 - 10.3697i) q^{68} +(-12.6794 + 3.53399i) q^{69} +(0.188521 + 6.23949i) q^{70} -4.39424 q^{71} +(9.71272 + 5.35099i) q^{72} +(-1.10979 - 1.92221i) q^{73} +(-8.74168 + 15.1410i) q^{74} +(-1.23696 - 1.21241i) q^{75} +(7.11101 - 12.3166i) q^{76} +(11.3936 - 7.04523i) q^{77} +(-2.06664 - 2.02562i) q^{78} +0.556883 q^{79} +(-0.793923 - 1.37512i) q^{80} +(4.80877 + 7.60761i) q^{81} +(-2.15113 + 3.72587i) q^{82} +(-4.40286 - 7.62598i) q^{83} +(-11.0832 + 12.0128i) q^{84} +(-1.67858 + 2.90738i) q^{85} +(-2.58482 - 4.47705i) q^{86} +(-11.8222 + 3.29509i) q^{87} +(-9.35772 + 16.2080i) q^{88} +(4.50821 - 7.80845i) q^{89} +(-0.141869 - 7.07672i) q^{90} +(1.59349 - 0.985339i) q^{91} +(13.5524 + 23.4735i) q^{92} +(-2.29760 + 8.93189i) q^{93} +24.8448 q^{94} -3.98747 q^{95} +(-1.57344 + 6.11672i) q^{96} +(-1.62480 - 2.81424i) q^{97} +(-9.10629 - 13.7783i) q^{98} +(-12.9996 + 7.85687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.35938			−1.66833			−0.834167	−	0.551512i	$-0.814051\pi$
$2$	−2.35938			−1.66833			−0.834167	+	0.551512i	$0.814051\pi$
$3$	−0.431498	+	1.67744i	−0.249125	+	0.968471i
$3$	−0.431498	+	1.67744i	−0.249125	+	0.968471i
$4$	3.56668			1.78334
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.01807	−	3.95772i	0.415625	−	1.61573i
$7$	2.33019	+	1.25307i	0.880731	+	0.473618i
$7$	2.33019	+	1.25307i	0.880731	+	0.473618i
$8$	−3.69640			−1.30687
$9$	−2.62762	−	1.44762i	−0.875873	−	0.482542i
$10$	1.17969	+	2.04328i	0.373051	+	0.646143i
$11$	2.53158	−	4.38482i	0.763300	−	1.32207i	−0.177841	−	0.984059i	$-0.556911\pi$
$11$	2.53158	−	4.38482i	0.763300	−	1.32207i	0.941141	−	0.338015i	$-0.109755\pi$
$12$	−1.53901	+	5.98290i	−0.444275	+	1.72711i
$13$	0.354064	−	0.613257i	0.0981997	−	0.170087i	−0.812740	−	0.582627i	$-0.802025\pi$
$13$	0.354064	−	0.613257i	0.0981997	−	0.170087i	0.910940	+	0.412540i	$0.135358\pi$
$14$	−5.49782	−	2.95648i	−1.46935	−	0.790153i
$15$	1.66846	−	0.465033i	0.430793	−	0.120071i
$16$	1.58785			0.396962
$17$	−1.67858	−	2.90738i	−0.407115	−	0.705144i	0.587450	−	0.809260i	$-0.300132\pi$
$17$	−1.67858	−	2.90738i	−0.407115	−	0.705144i	−0.994565	+	0.104117i	$0.966798\pi$
$18$	6.19956	+	3.41550i	1.46125	+	0.805041i
$19$	1.99373	−	3.45325i	0.457394	−	0.792229i	−0.541429	−	0.840747i	$-0.682116\pi$
$19$	1.99373	−	3.45325i	0.457394	−	0.792229i	0.998822	+	0.0485175i	$0.0154497\pi$
$20$	−1.78334	−	3.08884i	−0.398767	−	0.690685i
$21$	−3.10743	+	3.36807i	−0.678097	+	0.734972i
$22$	−5.97296	+	10.3455i	−1.27344	+	2.20566i
$23$	3.79973	+	6.58132i	0.792298	+	1.37230i	0.924541	+	0.381083i	$0.124449\pi$
$23$	3.79973	+	6.58132i	0.792298	+	1.37230i	−0.132243	+	0.991217i	$0.542218\pi$
$24$	1.59499	−	6.20049i	0.325575	−	1.26567i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.835372	+	1.44691i	−0.163830	+	0.283762i
$27$	3.56212	−	3.78303i	0.685530	−	0.728044i
$28$	8.31106	+	4.46932i	1.57064	+	0.844621i
$29$	3.54286	+	6.13641i	0.657892	+	1.13950i	0.981160	+	0.193195i	$0.0618850\pi$
$29$	3.54286	+	6.13641i	0.657892	+	1.13950i	−0.323268	+	0.946307i	$0.604782\pi$
$30$	−3.93652	+	1.09719i	−0.718708	+	0.200318i
$31$	5.32471			0.956347			0.478173	−	0.878265i	$-0.341299\pi$
$31$	5.32471			0.956347			0.478173	+	0.878265i	$0.341299\pi$
$32$	3.64646			0.644608
$33$	6.26291	+	6.13862i	1.09023	+	1.06860i
$34$	3.96041	+	6.85962i	0.679204	+	1.17642i
$35$	−0.0799028	−	2.64454i	−0.0135060	−	0.447010i
$36$	−9.37188	−	5.16321i	−1.56198	−	0.860536i
$37$	3.70507	−	6.41738i	0.609110	−	1.05501i	−0.382277	−	0.924048i	$-0.624860\pi$
$37$	3.70507	−	6.41738i	0.609110	−	1.05501i	0.991387	−	0.130962i	$-0.0418067\pi$
$38$	−4.70398	+	8.14753i	−0.763086	+	1.32170i
$39$	0.875925	+	0.858541i	0.140260	+	0.137477i
$40$	1.84820	+	3.20117i	0.292226	+	0.506150i
$41$	0.911736	−	1.57917i	0.142389	−	0.246625i	−0.786007	−	0.618218i	$-0.787855\pi$
$41$	0.911736	−	1.57917i	0.142389	−	0.246625i	0.928396	+	0.371593i	$0.121188\pi$
$42$	7.33162	−	7.94655i	1.13129	−	1.22618i
$43$	1.09555	+	1.89755i	0.167070	+	0.289374i	0.937388	−	0.348286i	$-0.113236\pi$
$43$	1.09555	+	1.89755i	0.167070	+	0.289374i	−0.770318	+	0.637659i	$0.779903\pi$
$44$	9.02933	−	15.6393i	1.36122	−	2.35771i
$45$	0.0601298	+	2.99940i	0.00896362	+	0.447124i
$46$	−8.96501	−	15.5278i	−1.32182	−	2.28946i
$47$	−10.5302			−1.53599			−0.767996	−	0.640455i	$-0.778746\pi$
$47$	−10.5302			−1.53599			−0.767996	+	0.640455i	$0.778746\pi$
$48$	−0.685152	+	2.66352i	−0.0988932	+	0.384446i
$49$	3.85961	+	5.83981i	0.551373	+	0.834259i
$50$	1.17969	−	2.04328i	0.166833	−	0.288964i
$51$	5.60127	−	1.56119i	0.784334	−	0.218610i
$52$	1.26283	−	2.18729i	0.175123	−	0.303323i
$53$	4.88360	+	8.45865i	0.670814	+	1.16188i	0.977674	+	0.210130i	$0.0673886\pi$
$53$	4.88360	+	8.45865i	0.670814	+	1.16188i	−0.306859	+	0.951755i	$0.599278\pi$
$54$	−8.40439	+	8.92561i	−1.14369	+	1.21462i
$55$	−5.06316			−0.682716
$56$	−8.61332	−	4.63186i	−1.15100	−	0.618958i
$57$	4.93233	+	4.83444i	0.653303	+	0.640337i
$58$	−8.35895	−	14.4781i	−1.09758	−	1.90107i
$59$	10.0174			1.30415			0.652077	−	0.758153i	$-0.273898\pi$
$59$	10.0174			1.30415			0.652077	+	0.758153i	$0.273898\pi$
$60$	5.95085	−	1.65862i	0.768251	−	0.214127i
$61$	−0.146519			−0.0187598			−0.00937991	−	0.999956i	$-0.502986\pi$
$61$	−0.146519			−0.0187598			−0.00937991	+	0.999956i	$0.502986\pi$
$62$	−12.5630			−1.59551
$63$	−4.30888	−	6.66585i	−0.542868	−	0.839818i
$64$	−11.7791			−1.47238
$65$	−0.708128			−0.0878325
$66$	−14.7766	−	14.4833i	−1.81887	−	1.78278i
$67$	−6.82912			−0.834310			−0.417155	−	0.908835i	$-0.636973\pi$
$67$	−6.82912			−0.834310			−0.417155	+	0.908835i	$0.636973\pi$
$68$	−5.98695	−	10.3697i	−0.726024	−	1.25751i
$69$	−12.6794	+	3.53399i	−1.52642	+	0.425443i
$70$	0.188521	+	6.23949i	0.0225326	+	0.745762i
$71$	−4.39424			−0.521501			−0.260750	−	0.965406i	$-0.583970\pi$
$71$	−4.39424			−0.521501			−0.260750	+	0.965406i	$0.583970\pi$
$72$	9.71272	+	5.35099i	1.14466	+	0.630621i
$73$	−1.10979	−	1.92221i	−0.129891	−	0.224978i	0.793743	−	0.608253i	$-0.208129\pi$
$73$	−1.10979	−	1.92221i	−0.129891	−	0.224978i	−0.923634	+	0.383275i	$0.874796\pi$
$74$	−8.74168	+	15.1410i	−1.01620	+	1.76011i
$75$	−1.23696	−	1.21241i	−0.142832	−	0.139997i
$76$	7.11101	−	12.3166i	0.815689	−	1.41281i
$77$	11.3936	−	7.04523i	1.29842	−	0.802879i
$78$	−2.06664	−	2.02562i	−0.234001	−	0.229357i
$79$	0.556883			0.0626542			0.0313271	−	0.999509i	$-0.490027\pi$
$79$	0.556883			0.0626542			0.0313271	+	0.999509i	$0.490027\pi$
$80$	−0.793923	−	1.37512i	−0.0887633	−	0.153743i
$81$	4.80877	+	7.60761i	0.534307	+	0.845290i
$82$	−2.15113	+	3.72587i	−0.237553	+	0.411454i
$83$	−4.40286	−	7.62598i	−0.483277	−	0.837060i	0.516539	−	0.856264i	$-0.327220\pi$
$83$	−4.40286	−	7.62598i	−0.483277	−	0.837060i	−0.999816	+	0.0192036i	$0.993887\pi$
$84$	−11.0832	+	12.0128i	−1.20928	+	1.31071i
$85$	−1.67858	+	2.90738i	−0.182067	+	0.315350i
$86$	−2.58482	−	4.47705i	−0.278729	−	0.482772i
$87$	−11.8222	+	3.29509i	−1.26747	+	0.353271i
$88$	−9.35772	+	16.2080i	−0.997536	+	1.72778i
$89$	4.50821	−	7.80845i	0.477869	−	0.827694i	−0.521809	−	0.853062i	$-0.674743\pi$
$89$	4.50821	−	7.80845i	0.477869	−	0.827694i	0.999678	+	0.0253686i	$0.00807594\pi$
$90$	−0.141869	−	7.07672i	−0.0149543	−	0.745952i
$91$	1.59349	−	0.985339i	0.167044	−	0.103292i
$92$	13.5524	+	23.4735i	1.41294	+	2.44728i
$93$	−2.29760	+	8.93189i	−0.238250	+	0.926194i
$94$	24.8448			2.56255
$95$	−3.98747			−0.409105
$96$	−1.57344	+	6.11672i	−0.160588	+	0.624285i
$97$	−1.62480	−	2.81424i	−0.164974	−	0.285743i	0.771672	−	0.636020i	$-0.219421\pi$
$97$	−1.62480	−	2.81424i	−0.164974	−	0.285743i	−0.936646	+	0.350278i	$0.886087\pi$
$98$	−9.10629	−	13.7783i	−0.919874	−	1.39182i
$99$	−12.9996	+	7.85687i	−1.30651	+	0.789645i
$100$	−1.78334	+	3.08884i	−0.178334	+	0.308884i
$101$	−1.91317	+	3.31371i	−0.190368	+	0.329727i	−0.945372	−	0.325993i	$-0.894301\pi$
$101$	−1.91317	+	3.31371i	−0.190368	+	0.329727i	0.755004	+	0.655720i	$0.227635\pi$
$102$	−13.2155	+	3.68343i	−1.30853	+	0.364714i
$103$	−5.74368	−	9.94835i	−0.565942	−	0.980240i	−0.996961	−	0.0778972i	$-0.975179\pi$
$103$	−5.74368	−	9.94835i	−0.565942	−	0.980240i	0.431020	−	0.902342i	$-0.358154\pi$
$104$	−1.30876	+	2.26684i	−0.128335	+	0.222282i
$105$	4.47055	+	1.00708i	0.436281	+	0.0982812i
$106$	−11.5223	−	19.9572i	−1.11914	−	1.93841i
$107$	6.31701	−	10.9414i	0.610689	−	1.05774i	−0.380436	−	0.924807i	$-0.624226\pi$
$107$	6.31701	−	10.9414i	0.610689	−	1.05774i	0.991125	−	0.132936i	$-0.0424406\pi$
$108$	12.7049	−	13.4929i	1.22253	−	1.29835i
$109$	2.75823	+	4.77739i	0.264190	+	0.457591i	0.967351	−	0.253440i	$-0.0815619\pi$
$109$	2.75823	+	4.77739i	0.264190	+	0.457591i	−0.703161	+	0.711031i	$0.748229\pi$
$110$	11.9459			1.13900
$111$	9.16604	+	8.98413i	0.870002	+	0.852736i
$112$	3.69999	+	1.98969i	0.349616	+	0.188008i
$113$	−2.03082	+	3.51749i	−0.191044	+	0.330897i	−0.945596	−	0.325342i	$-0.894521\pi$
$113$	−2.03082	+	3.51749i	−0.191044	+	0.330897i	0.754553	+	0.656239i	$0.227854\pi$
$114$	−11.6372	−	11.4063i	−1.08993	−	1.06830i
$115$	3.79973	−	6.58132i	0.354326	−	0.613711i
$116$	12.6362	+	21.8866i	1.17325	+	2.03212i
$117$	−1.81811	+	1.09885i	−0.168084	+	0.101589i
$118$	−23.6348			−2.17576
$119$	−0.268246	−	8.87815i	−0.0245901	−	0.813858i
$120$	−6.16727	+	1.71894i	−0.562992	+	0.156917i
$121$	−7.31778	−	12.6748i	−0.665253	−	1.15225i
$122$	0.345694			0.0312976
$123$	2.25556	+	2.21079i	0.203377	+	0.199341i
$124$	18.9915			1.70549
$125$	1.00000			0.0894427
$126$	10.1663	+	15.7273i	0.905685	+	1.40110i
$127$	5.50542			0.488527			0.244264	−	0.969709i	$-0.421454\pi$
$127$	5.50542			0.488527			0.244264	+	0.969709i	$0.421454\pi$
$128$	20.4984			1.81182
$129$	−3.65576	+	1.01893i	−0.321872	+	0.0897122i
$130$	1.67074			0.146534
$131$	5.40893	+	9.36854i	0.472580	+	0.818533i	0.999508	−	0.0313773i	$-0.00998936\pi$
$131$	5.40893	+	9.36854i	0.472580	+	0.818533i	−0.526927	+	0.849910i	$0.676656\pi$
$132$	22.3378	+	21.8945i	1.94426	+	1.90567i
$133$	8.97296	−	5.54844i	0.778054	−	0.481111i
$134$	16.1125			1.39191
$135$	−5.05726	−	1.19337i	−0.435260	−	0.102709i
$136$	6.20469	+	10.7468i	0.532048	+	0.921533i
$137$	6.60966	−	11.4483i	0.564701	−	0.978091i	−0.432376	−	0.901693i	$-0.642325\pi$
$137$	6.60966	−	11.4483i	0.564701	−	0.978091i	0.997077	−	0.0763977i	$-0.0243419\pi$
$138$	29.9154	−	8.33804i	2.54657	−	0.709781i
$139$	−2.99681	+	5.19063i	−0.254186	+	0.440264i	−0.964674	−	0.263446i	$-0.915141\pi$
$139$	−2.99681	+	5.19063i	−0.254186	+	0.440264i	0.710488	+	0.703710i	$0.248474\pi$
$140$	−0.284988	−	9.43224i	−0.0240859	−	0.797170i
$141$	4.54377	−	17.6638i	0.382654	−	1.48756i
$142$	10.3677			0.870038
$143$	−1.79268	−	3.10502i	−0.149912	−	0.259654i
$144$	−4.17226	−	2.29861i	−0.347688	−	0.191550i
$145$	3.54286	−	6.13641i	0.294218	−	0.509601i
$146$	2.61842	+	4.53523i	0.216702	+	0.375339i
$147$	−11.4614	+	3.95440i	−0.945317	+	0.326153i
$148$	13.2148	−	22.8887i	1.08625	−	1.88144i
$149$	10.3226	+	17.8792i	0.845657	+	1.46472i	0.885050	+	0.465497i	$0.154124\pi$
$149$	10.3226	+	17.8792i	0.845657	+	1.46472i	−0.0393927	+	0.999224i	$0.512542\pi$
$150$	2.91846	+	2.86053i	0.238291	+	0.233562i
$151$	6.17205	−	10.6903i	0.502275	−	0.869965i	−0.497722	−	0.867337i	$-0.665830\pi$
$151$	6.17205	−	10.6903i	0.502275	−	0.869965i	0.999997	−	0.00262849i	$-0.000836677\pi$
$152$	−7.36963	+	12.7646i	−0.597756	+	1.03534i
$153$	0.201865	+	10.0694i	0.0163198	+	0.814066i
$154$	−26.8818	+	16.6224i	−2.16620	+	1.33947i
$155$	−2.66236	−	4.61134i	−0.213846	−	0.370391i
$156$	3.12414	+	3.06214i	0.250132	+	0.245167i
$157$	10.7892			0.861076			0.430538	−	0.902573i	$-0.358324\pi$
$157$	10.7892			0.861076			0.430538	+	0.902573i	$0.358324\pi$
$158$	−1.31390			−0.104528
$159$	−16.2961	+	4.54207i	−1.29237	+	0.360209i
$160$	−1.82323	−	3.15792i	−0.144139	−	0.249656i
$161$	0.607218	+	20.0971i	0.0478555	+	1.58387i
$162$	−11.3457	−	17.9493i	−0.891403	−	1.41023i
$163$	−10.3419	+	17.9128i	−0.810044	+	1.40304i	0.102789	+	0.994703i	$0.467223\pi$
$163$	−10.3419	+	17.9128i	−0.810044	+	1.40304i	−0.912833	+	0.408333i	$0.866110\pi$
$164$	3.25187	−	5.63241i	0.253929	−	0.439817i
$165$	2.18474	−	8.49315i	0.170082	−	0.661191i
$166$	10.3880	+	17.9926i	0.806268	+	1.39650i
$167$	2.96873	−	5.14199i	0.229727	−	0.397899i	−0.728000	−	0.685577i	$-0.759550\pi$
$167$	2.96873	−	5.14199i	0.229727	−	0.397899i	0.957727	+	0.287678i	$0.0928833\pi$
$168$	11.4863	−	12.4497i	0.886187	−	0.960515i
$169$	6.24928	+	10.8241i	0.480714	+	0.832620i
$170$	3.96041	−	6.85962i	0.303749	−	0.526109i
$171$	−10.2378	+	6.18764i	−0.782902	+	0.473181i
$172$	3.90748	+	6.76796i	0.297943	+	0.516052i
$173$	−10.1587			−0.772350			−0.386175	−	0.922426i	$-0.626204\pi$
$173$	−10.1587			−0.772350			−0.386175	+	0.922426i	$0.626204\pi$
$174$	27.8931	−	7.77437i	2.11457	−	0.589373i
$175$	−2.25029	+	1.39147i	−0.170106	+	0.105185i
$176$	4.01976	−	6.96243i	0.303001	−	0.524813i
$177$	−4.32248	+	16.8036i	−0.324898	+	1.26303i
$178$	−10.6366	+	18.4231i	−0.797246	+	1.38087i
$179$	−11.5302	−	19.9708i	−0.861805	−	1.49269i	−0.870185	−	0.492724i	$-0.836001\pi$
$179$	−11.5302	−	19.9708i	−0.861805	−	1.49269i	0.00838081	−	0.999965i	$-0.497332\pi$
$180$	0.214464	+	10.6979i	0.0159852	+	0.797374i
$181$	−12.1947			−0.906422			−0.453211	−	0.891403i	$-0.649722\pi$
$181$	−12.1947			−0.906422			−0.453211	+	0.891403i	$0.649722\pi$
$182$	−3.75966	+	2.32479i	−0.278685	+	0.172325i
$183$	0.0632226	−	0.245777i	0.00467355	−	0.0181683i
$184$	−14.0453	−	24.3272i	−1.03543	−	1.79342i
$185$	−7.41015			−0.544805
$186$	5.42092	−	21.0737i	0.397481	−	1.54520i
$187$	−16.9978			−1.24300
$188$	−37.5579			−2.73919
$189$	13.0408	−	4.35160i	0.948582	−	0.316532i
$190$	9.40795			0.682525
$191$	−9.11557			−0.659579			−0.329790	−	0.944054i	$-0.606978\pi$
$191$	−9.11557			−0.659579			−0.329790	+	0.944054i	$0.606978\pi$
$192$	5.08264	−	19.7587i	0.366808	−	1.42596i
$193$	−18.7089			−1.34670			−0.673348	−	0.739325i	$-0.735145\pi$
$193$	−18.7089			−1.34670			−0.673348	+	0.739325i	$0.735145\pi$
$194$	3.83353	+	6.63986i	0.275231	+	0.476714i
$195$	0.305556	−	1.18784i	0.0218813	−	0.0850632i
$196$	13.7660	+	20.8287i	0.983285	+	1.48777i
$197$	6.42671			0.457884			0.228942	−	0.973440i	$-0.426473\pi$
$197$	6.42671			0.457884			0.228942	+	0.973440i	$0.426473\pi$
$198$	30.6710	−	18.5373i	2.17969	−	1.31739i
$199$	−8.15316	−	14.1217i	−0.577962	−	1.00106i	−0.995713	−	0.0924981i	$-0.970515\pi$
$199$	−8.15316	−	14.1217i	−0.577962	−	1.00106i	0.417751	−	0.908562i	$-0.362819\pi$
$200$	1.84820	−	3.20117i	0.130687	−	0.226357i
$201$	2.94675	−	11.4555i	0.207848	−	0.808005i
$202$	4.51390	−	7.81831i	0.317597	−	0.550094i
$203$	0.566168	+	18.7385i	0.0397372	+	1.31518i
$204$	19.9779	−	5.56825i	1.39873	−	0.389856i
$205$	−1.82347			−0.127357
$206$	13.5515	+	23.4719i	0.944180	+	1.63537i
$207$	−0.456953	−	22.7938i	−0.0317605	−	1.58428i
$208$	0.562199	−	0.973758i	0.0389815	−	0.0675179i
$209$	−10.0946	−	17.4843i	−0.698257	−	1.20942i
$210$	−10.5477	−	2.37609i	−0.727862	−	0.163966i
$211$	0.919892	−	1.59330i	0.0633280	−	0.109687i	−0.832623	−	0.553840i	$-0.813162\pi$
$211$	0.919892	−	1.59330i	0.0633280	−	0.109687i	0.895951	+	0.444153i	$0.146495\pi$
$212$	17.4182	+	30.1693i	1.19629	+	2.07204i
$213$	1.89611	−	7.37109i	0.129919	−	0.505058i
$214$	−14.9042	+	25.8149i	−1.01883	+	1.76467i
$215$	1.09555	−	1.89755i	0.0747160	−	0.129412i
$216$	−13.1670	+	13.9836i	−0.895901	+	0.951462i
$217$	12.4076	+	6.67226i	0.842284	+	0.452943i
$218$	−6.50771	−	11.2717i	−0.440758	−	0.763415i
$219$	3.70327	−	1.03218i	0.250244	−	0.0697481i
$220$	−18.0587			−1.21751
$221$	−2.37730			−0.159914
$222$	−21.6262	−	21.1970i	−1.45145	−	1.42265i
$223$	6.24964	+	10.8247i	0.418507	+	0.724875i	0.995789	−	0.0916695i	$-0.0292203\pi$
$223$	6.24964	+	10.8247i	0.418507	+	0.724875i	−0.577283	+	0.816544i	$0.695887\pi$
$224$	8.49695	+	4.56928i	0.567726	+	0.305298i
$225$	2.56749	−	1.55177i	0.171166	−	0.103452i
$226$	4.79148	−	8.29909i	0.318725	−	0.552047i
$227$	−13.5432	+	23.4575i	−0.898894	+	1.55693i	−0.0699844	+	0.997548i	$0.522295\pi$
$227$	−13.5432	+	23.4575i	−0.898894	+	1.55693i	−0.828910	+	0.559382i	$0.811038\pi$
$228$	17.5920	+	17.2429i	1.16506	+	1.14194i
$229$	−6.76954	−	11.7252i	−0.447344	−	0.774822i	0.550868	−	0.834592i	$-0.314297\pi$
$229$	−6.76954	−	11.7252i	−0.447344	−	0.774822i	−0.998212	+	0.0597699i	$0.980963\pi$
$230$	−8.96501	+	15.5278i	−0.591135	+	1.02388i
$231$	6.90166	+	22.1521i	0.454096	+	1.45750i
$232$	−13.0958	−	22.6826i	−0.859781	−	1.48919i
$233$	0.0292898	−	0.0507314i	0.00191884	−	0.00332353i	−0.865064	−	0.501661i	$-0.832723\pi$
$233$	0.0292898	−	0.0507314i	0.00191884	−	0.00332353i	0.866983	+	0.498337i	$0.166056\pi$
$234$	4.28962	−	2.59261i	0.280421	−	0.169485i
$235$	5.26511	+	9.11944i	0.343458	+	0.594887i
$236$	35.7288			2.32575
$237$	−0.240294	+	0.934139i	−0.0156088	+	0.0606788i
$238$	0.632895	+	20.9469i	0.0410245	+	1.35779i
$239$	7.50537	−	12.9997i	0.485482	−	0.840880i	−0.514379	−	0.857563i	$-0.671977\pi$
$239$	7.50537	−	12.9997i	0.485482	−	0.840880i	0.999861	+	0.0166834i	$0.00531075\pi$
$240$	2.64925	−	0.738400i	0.171008	−	0.0476635i
$241$	−5.28071	+	9.14645i	−0.340160	+	0.589175i	−0.984462	−	0.175596i	$-0.943815\pi$
$241$	−5.28071	+	9.14645i	−0.340160	+	0.589175i	0.644302	+	0.764771i	$0.277148\pi$
$242$	17.2654	+	29.9046i	1.10986	+	1.92234i
$243$	−14.8363	+	4.78375i	−0.951749	+	0.306878i
$244$	−0.522586			−0.0334551
$245$	3.12762	−	6.26243i	0.199816	−	0.400092i
$246$	−5.32172	−	5.21611i	−0.339301	−	0.332567i
$247$	−1.41182	−	2.44534i	−0.0898319	−	0.155593i
$248$	−19.6822			−1.24982
$249$	14.6920	−	4.09495i	0.931065	−	0.259507i
$250$	−2.35938			−0.149220
$251$	−19.7244			−1.24499			−0.622496	−	0.782623i	$-0.713881\pi$
$251$	−19.7244			−1.24499			−0.622496	+	0.782623i	$0.713881\pi$
$252$	−15.3684	−	23.7750i	−0.968118	−	1.49768i
$253$	38.4772			2.41904
$254$	−12.9894			−0.815027
$255$	−4.15266	−	4.07025i	−0.260050	−	0.254889i
$256$	−24.8054			−1.55034
$257$	−10.0646	−	17.4323i	−0.627810	−	1.08740i	−0.987990	−	0.154516i	$-0.950618\pi$
$257$	−10.0646	−	17.4323i	−0.627810	−	1.08740i	0.360180	−	0.932883i	$-0.382715\pi$
$258$	8.62533	−	2.40406i	0.536990	−	0.149670i
$259$	16.6750	−	10.3110i	1.03613	−	0.640694i
$260$	−2.52567			−0.156635
$261$	−0.426062	−	21.2529i	−0.0263726	−	1.31552i
$262$	−12.7617	−	22.1040i	−0.788422	−	1.36559i
$263$	10.4638	−	18.1238i	0.645224	−	1.11756i	−0.339025	−	0.940777i	$-0.610097\pi$
$263$	10.4638	−	18.1238i	0.645224	−	1.11756i	0.984250	−	0.176784i	$-0.0565694\pi$
$264$	−23.1502	−	22.6908i	−1.42480	−	1.39652i
$265$	4.88360	−	8.45865i	0.299997	−	0.519611i
$266$	−21.1706	+	13.0909i	−1.29806	+	0.802654i
$267$	11.1529	+	10.9316i	0.682548	+	0.669002i
$268$	−24.3573			−1.48786
$269$	3.71801	+	6.43978i	0.226691	+	0.392640i	0.956825	−	0.290663i	$-0.0938759\pi$
$269$	3.71801	+	6.43978i	0.226691	+	0.392640i	−0.730134	+	0.683303i	$0.760543\pi$
$270$	11.9320	+	2.81561i	0.726159	+	0.171353i
$271$	−10.4314	+	18.0677i	−0.633661	+	1.09753i	0.353136	+	0.935572i	$0.385115\pi$
$271$	−10.4314	+	18.0677i	−0.633661	+	1.09753i	−0.986797	+	0.161961i	$0.948218\pi$
$272$	−2.66532	−	4.61648i	−0.161609	−	0.279915i
$273$	0.965259	+	3.09817i	0.0584201	+	0.187509i
$274$	−15.5947	+	27.0108i	−0.942110	+	1.63178i
$275$	2.53158	+	4.38482i	0.152660	+	0.264415i
$276$	−45.2232	+	12.6046i	−2.72212	+	0.758709i
$277$	−6.33723	+	10.9764i	−0.380767	+	0.659508i	−0.991172	−	0.132581i	$-0.957673\pi$
$277$	−6.33723	+	10.9764i	−0.380767	+	0.659508i	0.610405	+	0.792090i	$0.291007\pi$
$278$	7.07063	−	12.2467i	0.424068	−	0.734507i
$279$	−13.9913	−	7.70819i	−0.837638	−	0.461477i
$280$	0.295352	+	9.77528i	0.0176507	+	0.584185i
$281$	1.39225	+	2.41145i	0.0830548	+	0.143855i	0.904561	−	0.426345i	$-0.140199\pi$
$281$	1.39225	+	2.41145i	0.0830548	+	0.143855i	−0.821506	+	0.570200i	$0.806866\pi$
$282$	−10.7205	+	41.6757i	−0.638396	+	2.48175i
$283$	8.41619			0.500291			0.250145	−	0.968208i	$-0.419522\pi$
$283$	8.41619			0.500291			0.250145	+	0.968208i	$0.419522\pi$
$284$	−15.6729			−0.930013
$285$	1.72058	−	6.68874i	0.101919	−	0.396207i
$286$	4.22962	+	7.32592i	0.250103	+	0.433191i
$287$	4.10334	−	2.53731i	0.242213	−	0.149773i
$288$	−9.58150	−	5.27870i	−0.564595	−	0.311050i
$289$	2.86475	−	4.96190i	0.168515	−	0.291876i
$290$	−8.35895	+	14.4781i	−0.490854	+	0.850185i
$291$	5.42182	−	1.51117i	0.317833	−	0.0885865i
$292$	−3.95827	−	6.85592i	−0.231640	−	0.401212i
$293$	4.58606	−	7.94328i	0.267920	−	0.464051i	−0.700404	−	0.713746i	$-0.746997\pi$
$293$	4.58606	−	7.94328i	0.267920	−	0.464051i	0.968325	+	0.249695i	$0.0803303\pi$
$294$	27.0417	−	9.32994i	1.57710	−	0.544133i
$295$	−5.00870	−	8.67532i	−0.291618	−	0.505096i
$296$	−13.6954	+	23.7212i	−0.796030	+	1.37876i
$297$	−7.57014	−	25.1963i	−0.439264	−	1.46204i
$298$	−24.3548	−	42.1838i	−1.41084	−	2.44364i
$299$	5.38139			0.311214
$300$	−4.41183	−	4.32427i	−0.254717	−	0.249662i
$301$	0.175075	+	5.79447i	0.0100912	+	0.333988i
$302$	−14.5622	+	25.2225i	−0.837962	+	1.45139i
$303$	−4.73303	−	4.63909i	−0.271905	−	0.266509i
$304$	3.16574	−	5.48323i	0.181568	−	0.314485i
$305$	0.0732594	+	0.126889i	0.00419482	+	0.00726565i
$306$	−0.476276	−	23.7577i	−0.0272269	−	1.35813i
$307$	23.0042			1.31292			0.656459	−	0.754361i	$-0.272053\pi$
$307$	23.0042			1.31292			0.656459	+	0.754361i	$0.272053\pi$
$308$	40.6373	−	25.1281i	2.31552	−	1.43181i
$309$	19.1662	−	5.34200i	1.09032	−	0.303896i
$310$	6.28151	+	10.8799i	0.356766	+	0.617937i
$311$	−22.6924			−1.28677			−0.643384	−	0.765544i	$-0.722470\pi$
$311$	−22.6924			−1.28677			−0.643384	+	0.765544i	$0.722470\pi$
$312$	−3.23776	−	3.17351i	−0.183302	−	0.179664i
$313$	−21.7495			−1.22936			−0.614678	−	0.788778i	$-0.710714\pi$
$313$	−21.7495			−1.22936			−0.614678	+	0.788778i	$0.710714\pi$
$314$	−25.4559			−1.43656
$315$	−3.61835	+	7.06453i	−0.203871	+	0.398041i
$316$	1.98622			0.111734
$317$	−4.98755			−0.280129			−0.140064	−	0.990142i	$-0.544731\pi$
$317$	−4.98755			−0.280129			−0.140064	+	0.990142i	$0.544731\pi$
$318$	38.4488	−	10.7165i	2.15610	−	0.600950i
$319$	35.8761			2.00868
$320$	5.88954	+	10.2010i	0.329235	+	0.570252i
$321$	15.6278	+	15.3176i	0.872256	+	0.854945i
$322$	−1.43266	−	47.4167i	−0.0798389	−	2.64243i
$323$	−13.3865			−0.744847
$324$	17.1513	+	27.1339i	0.952851	+	1.50744i
$325$	0.354064	+	0.613257i	0.0196399	+	0.0340174i
$326$	24.4006	−	42.2631i	1.35142	−	2.34073i
$327$	−9.20397	+	2.56533i	−0.508981	+	0.141863i
$328$	−3.37014	+	5.83725i	−0.186085	+	0.322308i
$329$	−24.5375	−	13.1952i	−1.35279	−	0.727472i
$330$	−5.15464	+	20.0386i	−0.283754	+	1.10309i
$331$	12.8387			0.705677			0.352839	−	0.935684i	$-0.385216\pi$
$331$	12.8387			0.705677			0.352839	+	0.935684i	$0.385216\pi$
$332$	−15.7036	−	27.1994i	−0.861847	−	1.49276i
$333$	−19.0255	+	11.4989i	−1.04259	+	0.630134i
$334$	−7.00436	+	12.1319i	−0.383262	+	0.663829i
$335$	3.41456	+	5.91419i	0.186557	+	0.323127i
$336$	−4.93413	+	5.34797i	−0.269179	+	0.291756i
$337$	−10.1938	+	17.6562i	−0.555292	+	0.961795i	0.442588	+	0.896725i	$0.354060\pi$
$337$	−10.1938	+	17.6562i	−0.555292	+	0.961795i	−0.997881	+	0.0650697i	$0.979273\pi$
$338$	−14.7444	−	25.5381i	−0.801991	−	1.38909i
$339$	−5.02408	−	4.92437i	−0.272871	−	0.267455i
$340$	−5.98695	+	10.3697i	−0.324688	+	0.562376i
$341$	13.4799	−	23.3479i	0.729979	−	1.26436i
$342$	24.1548	−	14.5990i	1.30614	−	0.789424i
$343$	1.67592	+	18.4443i	0.0904911	+	0.995897i
$344$	−4.04959	−	7.01410i	−0.218339	−	0.378175i
$345$	9.40021	+	9.21365i	0.506090	+	0.496046i
$346$	23.9682			1.28854
$347$	−6.00512			−0.322372			−0.161186	−	0.986924i	$-0.551532\pi$
$347$	−6.00512			−0.322372			−0.161186	+	0.986924i	$0.551532\pi$
$348$	−42.1660	+	11.7525i	−2.26034	+	0.630001i
$349$	7.12279	+	12.3370i	0.381274	+	0.660386i	0.991245	−	0.132038i	$-0.0421521\pi$
$349$	7.12279	+	12.3370i	0.381274	+	0.660386i	−0.609971	+	0.792424i	$0.708819\pi$
$350$	5.30930	−	3.28301i	0.283794	−	0.175484i
$351$	−1.05875	−	3.52393i	−0.0565120	−	0.188093i
$352$	9.23129	−	15.9891i	0.492029	−	0.852220i
$353$	−11.9130	+	20.6340i	−0.634067	+	1.09824i	0.352645	+	0.935757i	$0.385282\pi$
$353$	−11.9130	+	20.6340i	−0.634067	+	1.09824i	−0.986712	+	0.162480i	$0.948051\pi$
$354$	10.1984	−	39.6461i	0.542038	−	2.10716i
$355$	2.19712	+	3.80553i	0.116611	+	0.201976i
$356$	16.0793	−	27.8502i	0.852203	−	1.47606i
$357$	15.0083	+	3.38093i	0.794324	+	0.178938i
$358$	27.2040	+	47.1188i	1.43778	+	2.49031i
$359$	−10.5275	+	18.2342i	−0.555620	+	0.962362i	0.442235	+	0.896899i	$0.354186\pi$
$359$	−10.5275	+	18.2342i	−0.555620	+	0.962362i	−0.997855	+	0.0654627i	$0.979148\pi$
$360$	−0.222263	−	11.0870i	−0.0117143	−	0.584334i
$361$	1.55006	+	2.68478i	0.0815819	+	0.141304i
$362$	28.7719			1.51222
$363$	24.4188	−	6.80601i	1.28165	−	0.357223i
$364$	5.68348	−	3.51439i	0.297896	−	0.184204i
$365$	−1.10979	+	1.92221i	−0.0580891	+	0.100613i
$366$	−0.149166	+	0.579881i	−0.00779704	+	0.0303109i
$367$	5.02172	−	8.69787i	0.262131	−	0.454025i	−0.704677	−	0.709529i	$-0.748908\pi$
$367$	5.02172	−	8.69787i	0.262131	−	0.454025i	0.966808	+	0.255504i	$0.0822413\pi$
$368$	6.03338	+	10.4501i	0.314512	+	0.544751i
$369$	−4.68175	+	2.82961i	−0.243722	+	0.147304i
$370$	17.4834			0.908917
$371$	0.780427	+	25.8298i	0.0405177	+	1.34102i
$372$	−8.19481	+	31.8572i	−0.424881	+	1.65172i
$373$	7.05229	+	12.2149i	0.365154	+	0.632465i	0.988801	−	0.149241i	$-0.0476830\pi$
$373$	7.05229	+	12.2149i	0.365154	+	0.632465i	−0.623647	+	0.781706i	$0.714350\pi$
$374$	40.1043			2.07374
$375$	−0.431498	+	1.67744i	−0.0222825	+	0.0866227i
$376$	38.9239			2.00735
$377$	5.01759			0.258419
$378$	−30.7683	+	10.2671i	−1.58255	+	0.528081i
$379$	8.80817			0.452445			0.226223	−	0.974076i	$-0.427362\pi$
$379$	8.80817			0.452445			0.226223	+	0.974076i	$0.427362\pi$
$380$	−14.2220			−0.729574
$381$	−2.37558	+	9.23502i	−0.121705	+	0.473125i
$382$	21.5071			1.10040
$383$	−18.9384	−	32.8023i	−0.967708	−	1.67612i	−0.702156	−	0.712023i	$-0.747779\pi$
$383$	−18.9384	−	32.8023i	−0.967708	−	1.67612i	−0.265552	−	0.964097i	$-0.585554\pi$
$384$	−8.84502	+	34.3849i	−0.451371	+	1.75470i
$385$	−11.7981	−	6.34451i	−0.601289	−	0.323346i
$386$	44.1414			2.24674
$387$	−0.131751	−	6.57199i	−0.00669726	−	0.334073i
$388$	−5.79515	−	10.0375i	−0.294204	−	0.509576i
$389$	−4.40532	+	7.63024i	−0.223359	+	0.386868i	−0.955826	−	0.293934i	$-0.905035\pi$
$389$	−4.40532	+	7.63024i	−0.223359	+	0.386868i	0.732467	+	0.680802i	$0.238369\pi$
$390$	−0.720922	+	2.80258i	−0.0365053	+	0.141914i
$391$	12.7563	−	22.0945i	0.645113	−	1.11737i
$392$	−14.2666	−	21.5863i	−0.720574	−	1.09027i
$393$	−18.0491	+	5.03066i	−0.910457	+	0.253763i
$394$	−15.1631			−0.763904
$395$	−0.278441	−	0.482275i	−0.0140099	−	0.0242659i
$396$	−46.3654	+	28.0229i	−2.32995	+	1.40821i
$397$	−13.8876	+	24.0541i	−0.697000	+	1.20724i	0.272502	+	0.962155i	$0.412149\pi$
$397$	−13.8876	+	24.0541i	−0.697000	+	1.20724i	−0.969502	+	0.245084i	$0.921184\pi$
$398$	19.2364	+	33.3184i	0.964234	+	1.67010i
$399$	5.43537	+	17.4458i	0.272109	+	0.873380i
$400$	−0.793923	+	1.37512i	−0.0396962	+	0.0687558i
$401$	9.00513	+	15.5973i	0.449695	+	0.778894i	0.998366	−	0.0571442i	$-0.0181995\pi$
$401$	9.00513	+	15.5973i	0.449695	+	0.778894i	−0.548671	+	0.836038i	$0.684866\pi$
$402$	−6.95251	+	27.0278i	−0.346760	+	1.34802i
$403$	1.88529	−	3.26542i	0.0939130	−	0.162662i
$404$	−6.82367	+	11.8189i	−0.339490	+	0.588015i
$405$	4.18400	−	7.96832i	0.207905	−	0.395949i
$406$	−1.33581	−	44.2112i	−0.0662950	−	2.19417i
$407$	−18.7594	−	32.4922i	−0.929868	−	1.61058i
$408$	−20.7045	+	5.77076i	−1.02503	+	0.285695i
$409$	−33.8068			−1.67164			−0.835819	−	0.549006i	$-0.815006\pi$
$409$	−33.8068			−1.67164			−0.835819	+	0.549006i	$0.815006\pi$
$410$	4.30227			0.212474
$411$	16.3517	+	16.0272i	0.806572	+	0.790564i
$412$	−20.4859	−	35.4826i	−1.00927	−	1.74810i
$413$	23.3425	+	12.5525i	1.14861	+	0.617670i
$414$	1.07813	+	53.7792i	0.0529871	+	2.64311i
$415$	−4.40286	+	7.62598i	−0.216128	+	0.374345i
$416$	1.29108	−	2.23621i	0.0633004	−	0.109639i
$417$	−7.41387	−	7.26673i	−0.363059	−	0.355853i
$418$	23.8170	+	41.2522i	1.16493	+	2.01771i
$419$	−10.9847	+	19.0260i	−0.536636	+	0.929481i	0.462446	+	0.886647i	$0.346972\pi$
$419$	−10.9847	+	19.0260i	−0.536636	+	0.929481i	−0.999082	+	0.0428336i	$0.986361\pi$
$420$	15.9450	+	3.59194i	0.778037	+	0.175269i
$421$	−16.1133	−	27.9091i	−0.785316	−	1.36021i	−0.928810	−	0.370557i	$-0.879167\pi$
$421$	−16.1133	−	27.9091i	−0.785316	−	1.36021i	0.143493	−	0.989651i	$-0.454166\pi$
$422$	−2.17038	+	3.75920i	−0.105652	+	0.182995i
$423$	27.6694	+	15.2438i	1.34533	+	0.741180i
$424$	−18.0517	−	31.2665i	−0.876669	−	1.51844i
$425$	3.35716			0.162846
$426$	−4.47364	+	17.3912i	−0.216748	+	0.842606i
$427$	−0.341417	−	0.183599i	−0.0165223	−	0.00888498i
$428$	22.5308	−	39.0244i	1.08907	−	1.88632i
$429$	5.98202	−	1.66731i	0.288815	−	0.0804985i
$430$	−2.58482	+	4.47705i	−0.124651	+	0.215902i
$431$	−2.06161	−	3.57080i	−0.0993040	−	0.172000i	0.812093	−	0.583528i	$-0.198328\pi$
$431$	−2.06161	−	3.57080i	−0.0993040	−	0.172000i	−0.911397	+	0.411529i	$0.864995\pi$
$432$	5.65610	−	6.00687i	0.272129	−	0.289006i
$433$	25.8911			1.24425			0.622123	−	0.782919i	$-0.286270\pi$
$433$	25.8911			1.24425			0.622123	+	0.782919i	$0.286270\pi$
$434$	−29.2743	−	15.7424i	−1.40521	−	0.755660i
$435$	8.76473	+	8.59078i	0.420237	+	0.411896i
$436$	9.83772	+	17.0394i	0.471141	+	0.816041i
$437$	30.3026			1.44957
$438$	−8.73743	+	2.43530i	−0.417491	+	0.116363i
$439$	−5.01652			−0.239425			−0.119713	−	0.992809i	$-0.538197\pi$
$439$	−5.01652			−0.239425			−0.119713	+	0.992809i	$0.538197\pi$
$440$	18.7154			0.892223
$441$	−1.68772	−	20.9321i	−0.0803678	−	0.996765i
$442$	5.60895			0.266790
$443$	8.69659			0.413187			0.206594	−	0.978427i	$-0.433762\pi$
$443$	8.69659			0.413187			0.206594	+	0.978427i	$0.433762\pi$
$444$	32.6923	+	32.0435i	1.55151	+	1.52072i
$445$	−9.01642			−0.427419
$446$	−14.7453	−	25.5396i	−0.698209	−	1.20933i
$447$	−34.4455	+	9.60065i	−1.62921	+	0.454095i
$448$	−27.4475	−	14.7601i	−1.29677	−	0.697347i
$449$	−1.51265			−0.0713865			−0.0356932	−	0.999363i	$-0.511364\pi$
$449$	−1.51265			−0.0713865			−0.0356932	+	0.999363i	$0.511364\pi$
$450$	−6.05769	+	3.66122i	−0.285562	+	0.172592i
$451$	−4.61626	−	7.99560i	−0.217371	−	0.376498i
$452$	−7.24329	+	12.5458i	−0.340696	+	0.590102i
$453$	15.2691	+	14.9661i	0.717407	+	0.703169i
$454$	31.9536	−	55.3452i	1.49966	−	2.59748i
$455$	−1.65008	−	0.887337i	−0.0773567	−	0.0415990i
$456$	−18.2318	−	17.8700i	−0.853784	−	0.836839i
$457$	5.63562			0.263623			0.131812	−	0.991275i	$-0.457921\pi$
$457$	5.63562			0.263623			0.131812	+	0.991275i	$0.457921\pi$
$458$	15.9719	+	27.6642i	0.746319	+	1.29266i
$459$	−16.9780	−	4.00633i	−0.792465	−	0.186999i
$460$	13.5524	−	23.4735i	0.631885	−	1.09446i
$461$	10.1602	+	17.5980i	0.473208	+	0.819620i	0.999530	−	0.0306652i	$-0.00976255\pi$
$461$	10.1602	+	17.5980i	0.473208	+	0.819620i	−0.526322	+	0.850286i	$0.676429\pi$
$462$	−16.2836	−	52.2652i	−0.757584	−	2.43160i
$463$	3.53941	−	6.13043i	0.164490	−	0.284905i	−0.771984	−	0.635642i	$-0.780735\pi$
$463$	3.53941	−	6.13043i	0.164490	−	0.284905i	0.936474	+	0.350737i	$0.114069\pi$
$464$	5.62551	+	9.74367i	0.261158	+	0.452339i
$465$	8.88405	−	2.47617i	0.411988	−	0.114829i
$466$	−0.0691058	+	0.119695i	−0.00320127	+	0.00554475i
$467$	7.40898	−	12.8327i	0.342847	−	0.593828i	−0.642113	−	0.766610i	$-0.721942\pi$
$467$	7.40898	−	12.8327i	0.342847	−	0.593828i	0.984960	+	0.172782i	$0.0552755\pi$
$468$	−6.48462	+	3.91926i	−0.299752	+	0.181168i
$469$	−15.9132	−	8.55740i	−0.734802	−	0.395144i
$470$	−12.4224	−	21.5162i	−0.573003	−	0.992470i
$471$	−4.65554	+	18.0983i	−0.214516	+	0.833927i
$472$	−37.0282			−1.70436
$473$	11.0939			0.510098
$474$	0.566945	−	2.20399i	0.0260406	−	0.101233i
$475$	1.99373	+	3.45325i	0.0914788	+	0.158446i
$476$	−0.956748	−	31.6655i	−0.0438525	−	1.45139i
$477$	−0.587300	−	29.2957i	−0.0268906	−	1.34136i
$478$	−17.7080	+	30.6712i	−0.809947	+	1.40287i
$479$	−0.736217	+	1.27517i	−0.0336386	+	0.0582638i	−0.882355	−	0.470585i	$-0.844043\pi$
$479$	−0.736217	+	1.27517i	−0.0336386	+	0.0582638i	0.848716	+	0.528849i	$0.177376\pi$
$480$	6.08395	−	1.69572i	0.277693	−	0.0773987i
$481$	−2.62367	−	4.54432i	−0.119629	−	0.207203i
$482$	12.4592	−	21.5800i	0.567501	−	0.982941i
$483$	−33.9737	−	7.65328i	−1.54586	−	0.348236i
$484$	−26.1002	−	45.2068i	−1.18637	−	2.05486i
$485$	−1.62480	+	2.81424i	−0.0737785	+	0.127788i
$486$	35.0045	−	11.2867i	1.58784	−	0.511975i
$487$	1.81203	+	3.13852i	0.0821108	+	0.142220i	0.904156	−	0.427202i	$-0.140501\pi$
$487$	1.81203	+	3.13852i	0.0821108	+	0.142220i	−0.822046	+	0.569422i	$0.807167\pi$
$488$	0.541592			0.0245167
$489$	−25.5851	−	25.0773i	−1.15700	−	1.13404i
$490$	−7.37925	+	14.7755i	−0.333361	+	0.667487i
$491$	−15.8605	+	27.4713i	−0.715776	+	1.23976i	0.246883	+	0.969045i	$0.420594\pi$
$491$	−15.8605	+	27.4713i	−0.715776	+	1.23976i	−0.962659	+	0.270716i	$0.912740\pi$
$492$	8.04486	+	7.88520i	0.362690	+	0.355492i
$493$	11.8939	−	20.6009i	0.535675	−	0.927817i
$494$	3.33102	+	5.76949i	0.149870	+	0.259582i
$495$	13.3040	+	7.32955i	0.597973	+	0.329439i
$496$	8.45483			0.379633
$497$	−10.2394	−	5.50631i	−0.459302	−	0.246992i
$498$	−34.6639	+	9.66155i	−1.55333	+	0.432944i
$499$	−17.0737	−	29.5725i	−0.764323	−	1.32385i	−0.940604	−	0.339506i	$-0.889740\pi$
$499$	−17.0737	−	29.5725i	−0.764323	−	1.32385i	0.176281	−	0.984340i	$-0.443593\pi$
$500$	3.56668			0.159507
$501$	7.34438	+	7.19862i	0.328123	+	0.321611i
$502$	46.5373			2.07706
$503$	24.5601			1.09508			0.547540	−	0.836780i	$-0.315565\pi$
$503$	24.5601			1.09508			0.547540	+	0.836780i	$0.315565\pi$
$504$	15.9273	+	24.6396i	0.709460	+	1.09754i
$505$	3.82634			0.170270
$506$	−90.7825			−4.03577
$507$	−20.8533	+	5.81224i	−0.926127	+	0.258130i
$508$	19.6361			0.871210
$509$	19.2295	+	33.3064i	0.852331	+	1.47628i	0.879099	+	0.476639i	$0.158145\pi$
$509$	19.2295	+	33.3064i	0.852331	+	1.47628i	−0.0267686	+	0.999642i	$0.508522\pi$
$510$	9.79771	+	9.60326i	0.433850	+	0.425239i
$511$	−0.177351	−	5.86978i	−0.00784553	−	0.259664i
$512$	17.5286			0.774663
$513$	−5.96183	−	19.8432i	−0.263221	−	0.876100i
$514$	23.7461	+	41.1295i	1.04740	+	1.81415i
$515$	−5.74368	+	9.94835i	−0.253097	+	0.438377i
$516$	−13.0389	+	3.63421i	−0.574007	+	0.159987i
$517$	−26.6581	+	46.1732i	−1.17242	+	2.03069i
$518$	−39.3427	+	24.3276i	−1.72862	+	1.06889i
$519$	4.38345	−	17.0406i	0.192412	−	0.747998i
$520$	2.61752			0.114786
$521$	−12.6742	−	21.9523i	−0.555267	−	0.961750i	−0.997883	−	0.0650387i	$-0.979283\pi$
$521$	−12.6742	−	21.9523i	−0.555267	−	0.961750i	0.442616	−	0.896711i	$-0.354050\pi$
$522$	1.00524	+	50.1436i	0.0439983	+	2.19473i
$523$	−17.3852	+	30.1121i	−0.760203	+	1.31671i	0.182543	+	0.983198i	$0.441567\pi$
$523$	−17.3852	+	30.1121i	−0.760203	+	1.31671i	−0.942746	+	0.333512i	$0.891766\pi$
$524$	19.2919	+	33.4146i	0.842771	+	1.45972i
$525$	−1.36311	−	4.37515i	−0.0594912	−	0.190947i
$526$	−24.6880	+	42.7610i	−1.07645	+	1.86447i
$527$	−8.93795	−	15.4810i	−0.389343	−	0.674362i
$528$	9.94454	+	9.74718i	0.432781	+	0.424192i
$529$	−17.3759	+	30.0959i	−0.755472	+	1.30852i
$530$	−11.5223	+	19.9572i	−0.500496	+	0.866884i
$531$	−26.3219	−	14.5014i	−1.14227	−	0.629308i
$532$	32.0037	−	19.7895i	1.38754	−	0.857984i
$533$	−0.645626	−	1.11826i	−0.0279652	−	0.0484371i
$534$	−26.3140	−	25.7918i	−1.13872	−	1.11612i
$535$	−12.6340			−0.546216
$536$	25.2431			1.09034
$537$	38.4751	−	10.7238i	1.66032	−	0.462766i
$538$	−8.77220	−	15.1939i	−0.378196	−	0.655055i
$539$	35.3775	−	2.13976i	1.52381	−	0.0921658i
$540$	−18.0376	−	4.25637i	−0.776216	−	0.183165i
$541$	−1.85952	+	3.22079i	−0.0799472	+	0.138473i	−0.903227	−	0.429163i	$-0.858808\pi$
$541$	−1.85952	+	3.22079i	−0.0799472	+	0.138473i	0.823280	+	0.567636i	$0.192142\pi$
$542$	24.6116	−	42.6285i	1.05716	−	1.83105i
$543$	5.26197	−	20.4558i	0.225813	−	0.877844i
$544$	−6.12086	−	10.6016i	−0.262430	−	0.454542i
$545$	2.75823	−	4.77739i	0.118150	−	0.204641i
$546$	−2.27741	−	7.30975i	−0.0974643	−	0.312829i
$547$	13.1159	+	22.7174i	0.560795	+	0.971325i	0.997427	+	0.0716849i	$0.0228376\pi$
$547$	13.1159	+	22.7174i	0.560795	+	0.971325i	−0.436633	+	0.899640i	$0.643829\pi$
$548$	23.5745	−	40.8323i	1.00705	−	1.74427i
$549$	0.384996	+	0.212104i	0.0164312	+	0.00905239i
$550$	−5.97296	−	10.3455i	−0.254688	−	0.441132i
$551$	28.2540			1.20366
$552$	46.8679	−	13.0630i	1.99483	−	0.556000i
$553$	1.29765	+	0.697816i	0.0551815	+	0.0296741i
$554$	14.9519	−	25.8975i	0.635247	−	1.10028i
$555$	3.19746	−	12.4301i	0.135725	−	0.527628i
$556$	−10.6887	+	18.5133i	−0.453301	+	0.785140i
$557$	20.4595	+	35.4370i	0.866899	+	1.50151i	0.865149	+	0.501515i	$0.167224\pi$
$557$	20.4595	+	35.4370i	0.866899	+	1.50151i	0.00174970	+	0.999998i	$0.499443\pi$
$558$	33.0109	+	18.1866i	1.39746	+	0.769898i
$559$	1.55158			0.0656249
$560$	−0.126873	−	4.19913i	−0.00536138	−	0.177446i
$561$	7.33452	−	28.5128i	0.309664	−	1.20381i
$562$	−3.28485	−	5.68953i	−0.138563	−	0.239998i
$563$	−3.87663			−0.163381			−0.0816903	−	0.996658i	$-0.526032\pi$
$563$	−3.87663			−0.163381			−0.0816903	+	0.996658i	$0.526032\pi$
$564$	16.2062	−	63.0012i	0.682403	−	2.65283i
$565$	4.06164			0.170875
$566$	−19.8570			−0.834652
$567$	1.67245	+	23.7530i	0.0702363	+	0.997530i
$568$	16.2429			0.681535
$569$	−14.3317			−0.600818			−0.300409	−	0.953810i	$-0.597123\pi$
$569$	−14.3317			−0.600818			−0.300409	+	0.953810i	$0.597123\pi$
$570$	−4.05951	+	15.7813i	−0.170034	+	0.661006i
$571$	3.46705			0.145092			0.0725458	−	0.997365i	$-0.476888\pi$
$571$	3.46705			0.145092			0.0725458	+	0.997365i	$0.476888\pi$
$572$	−6.39392	−	11.0746i	−0.267343	−	0.463052i
$573$	3.93335	−	15.2908i	0.164318	−	0.638784i
$574$	−9.68135	+	5.98648i	−0.404092	+	0.249871i
$575$	−7.59946			−0.316919
$576$	30.9509	+	17.0517i	1.28962	+	0.710487i
$577$	8.30443	+	14.3837i	0.345718	+	0.598801i	0.985484	−	0.169769i	$-0.0543020\pi$
$577$	8.30443	+	14.3837i	0.345718	+	0.598801i	−0.639766	+	0.768570i	$0.720969\pi$
$578$	−6.75904	+	11.7070i	−0.281139	+	0.486947i
$579$	8.07285	−	31.3831i	0.335496	−	1.30424i
$580$	12.6362	−	21.8866i	0.524691	−	0.908792i
$581$	−0.703602	−	23.2871i	−0.0291903	−	0.966113i
$582$	−12.7921	+	3.56543i	−0.530251	+	0.147792i
$583$	49.4529			2.04813
$584$	4.10222	+	7.10526i	0.169751	+	0.294018i
$585$	1.86069	+	1.02510i	0.0769301	+	0.0423828i
$586$	−10.8203	+	18.7412i	−0.446981	+	0.774193i
$587$	−15.2235	−	26.3678i	−0.628340	−	1.08832i	−0.987885	−	0.155190i	$-0.950401\pi$
$587$	−15.2235	−	26.3678i	−0.628340	−	1.08832i	0.359544	−	0.933128i	$-0.382932\pi$
$588$	−40.8790	+	14.1041i	−1.68582	+	0.581643i
$589$	10.6161	−	18.3876i	0.437427	−	0.757646i
$590$	11.8174	+	20.4684i	0.486516	+	0.842670i
$591$	−2.77311	+	10.7804i	−0.114071	+	0.443448i
$592$	5.88309	−	10.1898i	0.241793	−	0.418798i
$593$	−3.59542	+	6.22745i	−0.147646	+	0.255731i	−0.930357	−	0.366655i	$-0.880503\pi$
$593$	−3.59542	+	6.22745i	−0.147646	+	0.255731i	0.782711	+	0.622385i	$0.213836\pi$
$594$	17.8608	+	59.4477i	0.732839	+	2.43917i
$595$	−7.55458	+	4.67138i	−0.309708	+	0.191508i
$596$	36.8173	+	63.7694i	1.50809	+	2.61209i
$597$	27.2064	−	7.58297i	1.11348	−	0.310350i
$598$	−12.6967			−0.519209
$599$	−14.5406			−0.594113			−0.297056	−	0.954860i	$-0.596005\pi$
$599$	−14.5406			−0.594113			−0.297056	+	0.954860i	$0.596005\pi$
$600$	4.57229	+	4.48154i	0.186663	+	0.182958i
$601$	−1.63381	−	2.82984i	−0.0666445	−	0.115432i	0.830778	−	0.556604i	$-0.187896\pi$
$601$	−1.63381	−	2.82984i	−0.0666445	−	0.115432i	−0.897422	+	0.441173i	$0.854563\pi$
$602$	−0.413069	−	13.6714i	−0.0168354	−	0.557203i
$603$	17.9443	+	9.88601i	0.730750	+	0.402589i
$604$	22.0137	−	38.1289i	0.895726	−	1.55144i
$605$	−7.31778	+	12.6748i	−0.297510	+	0.515303i
$606$	11.1670	+	10.9454i	0.453629	+	0.444626i
$607$	20.0573	+	34.7403i	0.814101	+	1.41006i	0.909972	+	0.414670i	$0.136103\pi$
$607$	20.0573	+	34.7403i	0.814101	+	1.41006i	−0.0958707	+	0.995394i	$0.530564\pi$
$608$	7.27006	−	12.5921i	0.294840	−	0.510678i
$609$	−31.6770	−	7.13590i	−1.28362	−	0.289161i
$610$	−0.172847	−	0.299380i	−0.00699837	−	0.0121215i
$611$	−3.72837	+	6.45773i	−0.150834	+	0.261252i
$612$	0.719988	+	35.9145i	0.0291038	+	1.45176i
$613$	−11.5120	−	19.9393i	−0.464964	−	0.805342i	0.534236	−	0.845336i	$-0.320599\pi$
$613$	−11.5120	−	19.9393i	−0.464964	−	0.805342i	−0.999200	+	0.0399939i	$0.987266\pi$
$614$	−54.2757			−2.19039
$615$	0.786825	−	3.05877i	0.0317278	−	0.123341i
$616$	−42.1152	+	26.0420i	−1.69687	+	1.04926i
$617$	−14.3350	+	24.8289i	−0.577105	+	0.999576i	0.418704	+	0.908123i	$0.362484\pi$
$617$	−14.3350	+	24.8289i	−0.577105	+	0.999576i	−0.995809	+	0.0914531i	$0.970849\pi$
$618$	−45.2203	+	12.6038i	−1.81903	+	0.506999i
$619$	22.7277	−	39.3655i	0.913502	−	1.58223i	0.104423	−	0.994533i	$-0.466700\pi$
$619$	22.7277	−	39.3655i	0.913502	−	1.58223i	0.809079	−	0.587700i	$-0.199966\pi$
$620$	−9.49577	−	16.4472i	−0.381359	−	0.660534i
$621$	38.4324	+	9.06896i	1.54224	+	0.363925i
$622$	53.5400			2.14676
$623$	20.2896	−	12.5461i	0.812884	−	0.502648i
$624$	1.39083	+	1.36323i	0.0556779	+	0.0545729i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	51.3154			2.05098
$627$	33.6847	−	9.38862i	1.34524	−	0.374945i
$628$	38.4818			1.53559
$629$	−24.8770			−0.991912
$630$	8.53708	−	16.6679i	0.340125	−	0.664065i
$631$	−24.1172			−0.960091			−0.480045	−	0.877244i	$-0.659380\pi$
$631$	−24.1172			−0.960091			−0.480045	+	0.877244i	$0.659380\pi$
$632$	−2.05846			−0.0818811
$633$	2.27574	+	2.23057i	0.0904524	+	0.0886572i
$634$	11.7675			0.467348
$635$	−2.75271	−	4.76783i	−0.109238	−	0.189206i
$636$	−58.1232	+	16.2001i	−2.30473	+	0.642376i
$637$	4.94785	−	0.299264i	0.196041	−	0.0118573i
$638$	−84.6454			−3.35114
$639$	11.5464	+	6.36122i	0.456768	+	0.251646i
$640$	−10.2492	−	17.7521i	−0.405135	−	0.701715i
$641$	−12.0033	+	20.7904i	−0.474103	+	0.821170i	−0.999560	−	0.0296499i	$-0.990561\pi$
$641$	−12.0033	+	20.7904i	−0.474103	+	0.821170i	0.525458	+	0.850820i	$0.323894\pi$
$642$	−36.8718	−	36.1401i	−1.45522	−	1.42633i
$643$	−7.48115	+	12.9577i	−0.295028	+	0.511003i	−0.974991	−	0.222243i	$-0.928662\pi$
$643$	−7.48115	+	12.9577i	−0.295028	+	0.511003i	0.679964	+	0.733246i	$0.261996\pi$
$644$	2.16575	+	71.6799i	0.0853425	+	2.82458i
$645$	2.71030	+	2.65651i	0.106718	+	0.104600i
$646$	31.5840			1.24265
$647$	−23.7006	−	41.0507i	−0.931768	−	1.61387i	−0.780298	−	0.625407i	$-0.784933\pi$
$647$	−23.7006	−	41.0507i	−0.931768	−	1.61387i	−0.151469	−	0.988462i	$-0.548401\pi$
$648$	−17.7751	−	28.1207i	−0.698272	−	1.10469i
$649$	25.3598	−	43.9245i	0.995460	−	1.72419i
$650$	−0.835372	−	1.44691i	−0.0327660	−	0.0567524i
$651$	−16.5462	+	17.9340i	−0.648496	+	0.702888i
$652$	−36.8864	+	63.8891i	−1.44458	+	2.50209i
$653$	10.2916	+	17.8256i	0.402742	+	0.697570i	0.994056	−	0.108872i	$-0.0347237\pi$
$653$	10.2916	+	17.8256i	0.402742	+	0.697570i	−0.591313	+	0.806442i	$0.701390\pi$
$654$	21.7157	−	6.05260i	0.849150	−	0.236675i
$655$	5.40893	−	9.36854i	0.211344	−	0.366059i
$656$	1.44770	−	2.50749i	0.0565231	−	0.0979008i
$657$	0.133463	+	6.65740i	0.00520688	+	0.259730i
$658$	57.8932	+	31.1324i	2.25691	+	1.21367i
$659$	−0.224450	−	0.388759i	−0.00874333	−	0.0151439i	0.861621	−	0.507553i	$-0.169450\pi$
$659$	−0.224450	−	0.388759i	−0.00874333	−	0.0151439i	−0.870364	+	0.492409i	$0.836116\pi$
$660$	7.79227	−	30.2923i	0.303314	−	1.17913i
$661$	23.9281			0.930695			0.465347	−	0.885128i	$-0.345929\pi$
$661$	23.9281			0.930695			0.465347	+	0.885128i	$0.345929\pi$
$662$	−30.2913			−1.17731
$663$	1.02580	−	3.98777i	0.0398387	−	0.154872i
$664$	16.2747	+	28.1886i	0.631582	+	1.09393i
$665$	−9.29157	−	4.99659i	−0.360312	−	0.193760i
$666$	44.8883	−	27.1302i	1.73939	−	1.05127i
$667$	−26.9238	+	46.6334i	−1.04249	+	1.80565i
$668$	10.5885	−	18.3398i	0.409682	−	0.709589i
$669$	−20.8545	+	5.81257i	−0.806281	+	0.224727i
$670$	−8.05625	−	13.9538i	−0.311240	−	0.539084i
$671$	−0.370924	+	0.642459i	−0.0143194	+	0.0248019i
$672$	−11.3311	+	12.2815i	−0.437107	+	0.473769i
$673$	−4.07241	−	7.05362i	−0.156980	−	0.271897i	0.776798	−	0.629749i	$-0.216842\pi$
$673$	−4.07241	−	7.05362i	−0.156980	−	0.271897i	−0.933778	+	0.357852i	$0.883509\pi$
$674$	24.0511	−	41.6577i	0.926413	−	1.60460i
$675$	1.49514	+	4.97640i	0.0575480	+	0.191542i
$676$	22.2892	+	38.6060i	0.857276	+	1.48485i
$677$	24.5607			0.943945			0.471972	−	0.881613i	$-0.343542\pi$
$677$	24.5607			0.943945			0.471972	+	0.881613i	$0.343542\pi$
$678$	11.8537	+	11.6185i	0.455240	+	0.446205i
$679$	−0.259652	−	8.59372i	−0.00996454	−	0.329797i
$680$	6.20469	−	10.7468i	0.237939	−	0.412122i
$681$	−33.5048	−	32.8398i	−1.28390	−	1.25842i
$682$	−31.8043	+	55.0867i	−1.21785	+	2.10938i
$683$	−22.8015	−	39.4933i	−0.872473	−	1.51117i	−0.859430	−	0.511253i	$-0.829181\pi$
$683$	−22.8015	−	39.4933i	−0.872473	−	1.51117i	−0.0130435	−	0.999915i	$-0.504152\pi$
$684$	−36.5149	+	22.0693i	−1.39618	+	0.843842i
$685$	−13.2193			−0.505084
$686$	−3.95413	−	43.5171i	−0.150969	−	1.66149i
$687$	22.5894	−	6.29611i	0.861838	−	0.240212i
$688$	1.73957	+	3.01302i	0.0663204	+	0.114870i
$689$	6.91643			0.263495
$690$	−22.1787	−	21.7385i	−0.844328	−	0.827571i
$691$	−24.5848			−0.935251			−0.467625	−	0.883927i	$-0.654890\pi$
$691$	−24.5848			−0.935251			−0.467625	+	0.883927i	$0.654890\pi$
$692$	−36.2327			−1.37736
$693$	−40.1368	+	2.01856i	−1.52467	+	0.0766787i
$694$	14.1684			0.537824
$695$	5.99363			0.227351
$696$	43.6995	−	12.1799i	1.65643	−	0.461680i
$697$	−6.12168			−0.231875
$698$	−16.8054	−	29.1078i	−0.636093	−	1.10174i
$699$	0.0724605	+	0.0710224i	0.00274071	+	0.00268632i
$700$	−8.02607	+	4.96293i	−0.303357	+	0.187581i
$701$	−13.0612			−0.493316			−0.246658	−	0.969103i	$-0.579332\pi$
$701$	−13.0612			−0.493316			−0.246658	+	0.969103i	$0.579332\pi$
$702$	2.49800	+	8.31429i	0.0942809	+	0.313803i
$703$	−14.7739	−	25.5891i	−0.557207	−	0.965110i
$704$	−29.8197	+	51.6491i	−1.12387	+	1.94660i
$705$	−17.5692	+	4.89690i	−0.661695	+	0.184428i
$706$	28.1074	−	48.6835i	1.05784	−	1.83223i
$707$	−8.61039	+	5.32424i	−0.323827	+	0.200239i
$708$	−15.4169	+	59.9330i	−0.579403	+	2.25242i
$709$	−24.1747			−0.907900			−0.453950	−	0.891027i	$-0.649985\pi$
$709$	−24.1747			−0.907900			−0.453950	+	0.891027i	$0.649985\pi$
$710$	−5.18385	−	8.97869i	−0.194546	−	0.336964i
$711$	−1.46328	−	0.806158i	−0.0548772	−	0.0302333i
$712$	−16.6641	+	28.8631i	−0.624514	+	1.08169i
$713$	20.2325	+	35.0436i	0.757712	+	1.31239i
$714$	−35.4103	−	7.97691i	−1.32520	−	0.298528i
$715$	−1.79268	+	3.10502i	−0.0670425	+	0.116121i
$716$	−41.1244	−	71.2295i	−1.53689	−	2.66197i
$717$	18.5677	+	18.1992i	0.693422	+	0.679660i
$718$	24.8384	−	43.0213i	0.926960	−	1.60554i
$719$	10.7109	−	18.5518i	0.399449	−	0.691867i	−0.594209	−	0.804311i	$-0.702535\pi$
$719$	10.7109	−	18.5518i	0.399449	−	0.691867i	0.993658	+	0.112444i	$0.0358680\pi$
$720$	0.0954768	+	4.76258i	0.00355821	+	0.177491i
$721$	−0.917872	−	30.3788i	−0.0341833	−	1.13137i
$722$	−3.65717	−	6.33441i	−0.136106	−	0.235742i
$723$	−13.0640	−	12.8048i	−0.485856	−	0.476214i
$724$	−43.4945			−1.61646
$725$	−7.08571			−0.263157
$726$	−57.6132	+	16.0580i	−2.13823	+	0.595968i
$727$	0.144033	+	0.249472i	0.00534188	+	0.00925240i	0.868684	−	0.495367i	$-0.164966\pi$
$727$	0.144033	+	0.249472i	0.00534188	+	0.00925240i	−0.863342	+	0.504619i	$0.831633\pi$
$728$	−5.89019	+	3.64220i	−0.218305	+	0.134989i
$729$	−1.62263	−	26.9512i	−0.0600976	−	0.998193i
$730$	2.61842	−	4.53523i	0.0969120	−	0.167857i
$731$	3.67794	−	6.37038i	0.136033	−	0.235617i
$732$	0.225495	−	0.876607i	0.00833452	−	0.0324003i
$733$	−14.2466	−	24.6758i	−0.526209	−	0.911421i	−0.999534	−	0.0305332i	$-0.990279\pi$
$733$	−14.2466	−	24.6758i	−0.526209	−	0.911421i	0.473324	−	0.880888i	$-0.343054\pi$
$734$	−11.8481	+	20.5216i	−0.437323	+	0.757465i
$735$	9.15529	+	7.94863i	0.337698	+	0.293189i
$736$	13.8555	+	23.9985i	0.510722	+	0.884596i
$737$	−17.2885	+	29.9445i	−0.636829	+	1.10302i
$738$	11.0460	−	6.67614i	0.406610	−	0.245752i
$739$	7.15454	+	12.3920i	0.263184	+	0.455848i	0.967086	−	0.254449i	$-0.0818940\pi$
$739$	7.15454	+	12.3920i	0.263184	+	0.455848i	−0.703902	+	0.710297i	$0.748561\pi$
$740$	−26.4296			−0.971572
$741$	4.71111	−	1.31308i	0.173067	−	0.0482373i
$742$	−1.84132	−	60.9424i	−0.0675971	−	2.23726i
$743$	−5.27412	+	9.13504i	−0.193489	+	0.335132i	−0.946404	−	0.322985i	$-0.895314\pi$
$743$	−5.27412	+	9.13504i	−0.193489	+	0.335132i	0.752915	+	0.658117i	$0.228647\pi$
$744$	8.49285	−	33.0158i	0.311363	−	1.21042i
$745$	10.3226	−	17.8792i	0.378189	−	0.655043i
$746$	−16.6390	−	28.8197i	−0.609199	−	1.05516i
$747$	0.529486	+	26.4119i	0.0193729	+	0.966360i
$748$	−60.6257			−2.21670
$749$	28.4302	−	17.5799i	1.03882	−	0.642354i
$750$	1.01807	−	3.95772i	0.0371746	−	0.144516i
$751$	8.85194	+	15.3320i	0.323012	+	0.559473i	0.981108	−	0.193461i	$-0.0619712\pi$
$751$	8.85194	+	15.3320i	0.323012	+	0.559473i	−0.658096	+	0.752934i	$0.728638\pi$
$752$	−16.7204			−0.609729
$753$	8.51103	−	33.0865i	0.310159	−	1.20574i
$754$	−11.8384			−0.431130
$755$	−12.3441			−0.449248
$756$	46.5125	−	15.5208i	1.69164	−	0.564484i
$757$	−28.3306			−1.02969			−0.514847	−	0.857282i	$-0.672151\pi$
$757$	−28.3306			−1.02969			−0.514847	+	0.857282i	$0.672151\pi$
$758$	−20.7818			−0.754830
$759$	−16.6028	+	64.5433i	−0.602645	+	2.34277i
$760$	14.7393			0.534649
$761$	9.64761	+	16.7102i	0.349726	+	0.605742i	0.986201	−	0.165555i	$-0.0529415\pi$
$761$	9.64761	+	16.7102i	0.349726	+	0.605742i	−0.636475	+	0.771297i	$0.719608\pi$
$762$	5.60489	−	21.7889i	0.203044	−	0.789330i
$763$	0.440780	+	14.5885i	0.0159573	+	0.528140i
$764$	−32.5123			−1.17625
$765$	8.61946	−	5.20954i	0.311637	−	0.188351i
$766$	44.6830	+	77.3931i	1.61446	+	2.79633i
$767$	3.54680	−	6.14323i	0.128067	−	0.221819i
$768$	10.7035	−	41.6096i	0.386229	−	1.50146i
$769$	−12.1188	+	20.9903i	−0.437015	+	0.756931i	−0.997458	−	0.0712616i	$-0.977297\pi$
$769$	−12.1188	+	20.9903i	−0.437015	+	0.756931i	0.560443	+	0.828193i	$0.310631\pi$
$770$	27.8363	+	14.9691i	1.00315	+	0.539450i
$771$	33.5845	−	9.36070i	1.20952	−	0.337117i
$772$	−66.7287			−2.40162
$773$	1.44049	+	2.49500i	0.0518108	+	0.0897389i	0.890768	−	0.454459i	$-0.150167\pi$
$773$	1.44049	+	2.49500i	0.0518108	+	0.0897389i	−0.838957	+	0.544198i	$0.816834\pi$
$774$	0.310850	+	15.5058i	0.0111733	+	0.557346i
$775$	−2.66236	+	4.61134i	−0.0956347	+	0.165644i
$776$	6.00591	+	10.4025i	0.215600	+	0.373430i
$777$	10.1009	+	32.4205i	0.362367	+	1.16308i
$778$	10.3938	−	18.0026i	0.372637	−	0.645426i
$779$	−3.63552	−	6.29690i	−0.130256	−	0.225610i
$780$	1.08982	−	4.23666i	0.0390218	−	0.151697i
$781$	−11.1244	+	19.2680i	−0.398061	+	0.689462i
$782$	−30.0969	+	52.1294i	−1.07626	+	1.86414i
$783$	35.8343	+	8.45587i	1.28061	+	0.302188i
$784$	6.12847	+	9.27273i	0.218874	+	0.331169i
$785$	−5.39462	−	9.34376i	−0.192542	−	0.333493i
$786$	42.5847	−	11.8692i	1.51895	−	0.423362i
$787$	−11.2773			−0.401993			−0.200997	−	0.979592i	$-0.564418\pi$
$787$	−11.2773			−0.401993			−0.200997	+	0.979592i	$0.564418\pi$
$788$	22.9220			0.816563
$789$	25.8865	+	25.3728i	0.921584	+	0.903294i
$790$	0.656950	+	1.13787i	0.0233732	+	0.0404836i
$791$	−9.13988	+	5.65166i	−0.324977	+	0.200950i
$792$	48.0517	−	29.0421i	1.70744	−	1.03197i
$793$	−0.0518771	+	0.0898537i	−0.00184221	+	0.00319080i
$794$	32.7662	−	56.7527i	1.16283	−	2.01408i
$795$	12.0816	+	11.8418i	0.428491	+	0.419987i
$796$	−29.0797	−	50.3675i	−1.03070	−	1.78523i
$797$	9.92304	−	17.1872i	0.351492	−	0.608802i	−0.635019	−	0.772496i	$-0.719008\pi$
$797$	9.92304	−	17.1872i	0.351492	−	0.608802i	0.986511	+	0.163694i	$0.0523411\pi$
$798$	−12.8241	−	41.1612i	−0.453969	−	1.45709i
$799$	17.6758	+	30.6154i	0.625325	+	1.08309i
$800$	−1.82323	+	3.15792i	−0.0644608	+	0.111649i
$801$	−23.1496	+	13.9914i	−0.817949	+	0.494363i
$802$	−21.2465	−	36.8001i	−0.750241	−	1.29946i
$803$	−11.2381			−0.396583
$804$	10.5101	−	40.8579i	0.370663	−	1.44095i
$805$	17.1010	−	10.5744i	0.602731	−	0.372699i
$806$	−4.44812	+	7.70436i	−0.156678	+	0.271375i
$807$	−12.4067	+	3.45799i	−0.436735	+	0.121727i
$808$	7.07184	−	12.2488i	0.248786	−	0.430911i
$809$	11.2804	+	19.5383i	0.396599	+	0.686929i	0.993304	−	0.115532i	$-0.0368572\pi$
$809$	11.2804	+	19.5383i	0.396599	+	0.686929i	−0.596705	+	0.802461i	$0.703524\pi$
$810$	−9.87166	+	18.8003i	−0.346855	+	0.660575i
$811$	32.9253			1.15616			0.578081	−	0.815979i	$-0.303802\pi$
$811$	32.9253			1.15616			0.578081	+	0.815979i	$0.303802\pi$
$812$	2.01934	+	66.8342i	0.0708650	+	2.34542i
$813$	−25.8064	−	25.2942i	−0.905068	−	0.887106i
$814$	44.2605	+	76.6615i	1.55133	+	2.68698i
$815$	20.6839			0.724525
$816$	8.89395	−	2.47892i	0.311351	−	0.0867797i
$817$	8.73695			0.305667
$818$	79.7631			2.78885
$819$	−5.61350	+	0.282314i	−0.196151	+	0.00986484i
$820$	−6.50374			−0.227121
$821$	−12.0729			−0.421348			−0.210674	−	0.977556i	$-0.567566\pi$
$821$	−12.0729			−0.421348			−0.210674	+	0.977556i	$0.567566\pi$
$822$	−38.5800	−	37.8143i	−1.34563	−	1.31893i
$823$	−30.6007			−1.06667			−0.533337	−	0.845903i	$-0.679062\pi$
$823$	−30.6007			−1.06667			−0.533337	+	0.845903i	$0.679062\pi$
$824$	21.2309	+	36.7730i	0.739614	+	1.28105i
$825$	−8.44765	+	2.35453i	−0.294110	+	0.0819743i
$826$	−55.0738	−	29.6162i	−1.91626	−	1.03048i
$827$	42.8152			1.48883			0.744416	−	0.667716i	$-0.232728\pi$
$827$	42.8152			1.48883			0.744416	+	0.667716i	$0.232728\pi$
$828$	−1.62981	−	81.2981i	−0.0566397	−	2.82531i
$829$	17.7651	+	30.7701i	0.617009	+	1.06869i	0.990028	+	0.140868i	$0.0449892\pi$
$829$	17.7651	+	30.7701i	0.617009	+	1.06869i	−0.373019	+	0.927824i	$0.621677\pi$
$830$	10.3880	−	17.9926i	0.360574	−	0.624532i
$831$	−15.6778	−	15.3666i	−0.543856	−	0.533062i
$832$	−4.17055	+	7.22360i	−0.144588	+	0.250433i
$833$	10.4999	−	21.0239i	0.363800	−	0.728436i
$834$	17.4921	+	17.1450i	0.605703	+	0.593682i
$835$	−5.93746			−0.205474
$836$	−36.0042	−	62.3610i	−1.24523	−	2.15680i
$837$	18.9673	−	20.1436i	0.655604	−	0.696263i
$838$	25.9170	−	44.8896i	0.895289	−	1.55069i
$839$	8.69365	+	15.0578i	0.300138	+	0.519855i	0.976167	−	0.217021i	$-0.0696339\pi$
$839$	8.69365	+	15.0578i	0.300138	+	0.519855i	−0.676029	+	0.736875i	$0.736301\pi$
$840$	−16.5249	−	3.72258i	−0.570163	−	0.128441i
$841$	−10.6037	+	18.3661i	−0.365644	+	0.633314i
$842$	38.0175	+	65.8483i	1.31017	+	2.26928i
$843$	−4.64582	+	1.29488i	−0.160011	+	0.0445982i
$844$	3.28096	−	5.68279i	0.112935	−	0.195610i
$845$	6.24928	−	10.8241i	0.214982	−	0.372359i
$846$	−65.2827	−	35.9660i	−2.24447	−	1.23654i
$847$	−1.16942	−	38.7044i	−0.0401818	−	1.32990i
$848$	7.75441	+	13.4310i	0.266288	+	0.461224i
$849$	−3.63157	+	14.1177i	−0.124635	+	0.484517i
$850$	−7.92081			−0.271682
$851$	56.3131			1.93039
$852$	6.76281	−	26.2903i	0.231690	−	0.900691i
$853$	−21.6322	−	37.4681i	−0.740673	−	1.28288i	−0.952189	−	0.305509i	$-0.901173\pi$
$853$	−21.6322	−	37.4681i	−0.740673	−	1.28288i	0.211516	−	0.977375i	$-0.432160\pi$
$854$	0.805534	+	0.433180i	0.0275648	+	0.0148231i
$855$	10.4775	+	5.77236i	0.358324	+	0.197410i
$856$	−23.3502	+	40.4437i	−0.798092	+	1.38234i
$857$	−1.70768	+	2.95779i	−0.0583333	+	0.101036i	−0.893717	−	0.448630i	$-0.851912\pi$
$857$	−1.70768	+	2.95779i	−0.0583333	+	0.101036i	0.835384	+	0.549667i	$0.185245\pi$
$858$	−14.1139	+	3.93382i	−0.481840	+	0.134298i
$859$	−14.4876	−	25.0932i	−0.494309	−	0.856169i	0.505669	−	0.862727i	$-0.331246\pi$
$859$	−14.4876	−	25.0932i	−0.494309	−	0.856169i	−0.999978	+	0.00655862i	$0.997912\pi$
$860$	3.90748	−	6.76796i	0.133244	−	0.230785i
$861$	2.48560	+	7.97796i	0.0847090	+	0.271888i
$862$	4.86411	+	8.42489i	0.165672	+	0.286953i
$863$	2.94473	−	5.10043i	0.100240	−	0.173621i	−0.811544	−	0.584292i	$-0.801372\pi$
$863$	2.94473	−	5.10043i	0.100240	−	0.173621i	0.911783	+	0.410671i	$0.134706\pi$
$864$	12.9891	−	13.7947i	0.441898	−	0.469304i
$865$	5.07934	+	8.79767i	0.172703	+	0.299130i
$866$	−61.0870			−2.07582
$867$	7.08716	+	6.94650i	0.240693	+	0.235916i
$868$	44.2540	+	23.7978i	1.50208	+	0.807751i
$869$	1.40979	−	2.44183i	0.0478240	−	0.0828335i
$870$	−20.6793	−	20.2689i	−0.701095	−	0.687181i
$871$	−2.41795	+	4.18801i	−0.0819290	+	0.141905i
$872$	−10.1955	−	17.6591i	−0.345263	−	0.598014i
$873$	0.195398	+	9.74685i	0.00661322	+	0.329881i
$874$	−71.4953			−2.41837
$875$	2.33019	+	1.25307i	0.0787749	+	0.0423616i
$876$	13.2084	−	3.68145i	0.446270	−	0.124385i
$877$	15.2759	+	26.4586i	0.515829	+	0.893442i	0.999831	+	0.0183755i	$0.00584943\pi$
$877$	15.2759	+	26.4586i	0.515829	+	0.893442i	−0.484002	+	0.875067i	$0.660817\pi$
$878$	11.8359			0.399441
$879$	11.3455	+	11.1203i	0.382675	+	0.375080i
$880$	−8.03952			−0.271012
$881$	0.318761			0.0107393			0.00536967	−	0.999986i	$-0.498291\pi$
$881$	0.318761			0.0107393			0.00536967	+	0.999986i	$0.498291\pi$
$882$	3.98199	+	49.3867i	0.134080	+	1.66294i
$883$	−3.99156			−0.134327			−0.0671634	−	0.997742i	$-0.521395\pi$
$883$	−3.99156			−0.134327			−0.0671634	+	0.997742i	$0.521395\pi$
$884$	−8.47905			−0.285181
$885$	16.7136	−	4.65841i	0.561821	−	0.156591i
$886$	−20.5186			−0.689335
$887$	−19.3609	−	33.5340i	−0.650075	−	1.12596i	−0.983104	−	0.183046i	$-0.941404\pi$
$887$	−19.3609	−	33.5340i	−0.650075	−	1.12596i	0.333030	−	0.942916i	$-0.391929\pi$
$888$	−33.8813	−	33.2089i	−1.13698	−	1.11442i
$889$	12.8287	+	6.89870i	0.430261	+	0.231375i
$890$	21.2732			0.713078
$891$	45.5318	−	1.82631i	1.52537	−	0.0611838i
$892$	22.2905	+	38.6082i	0.746340	+	1.29270i
$893$	−20.9945	+	36.3635i	−0.702553	+	1.21686i
$894$	81.2700	−	22.6516i	2.71807	−	0.757583i
$895$	−11.5302	+	19.9708i	−0.385411	+	0.667551i
$896$	47.7653	+	25.6860i	1.59573	+	0.858110i
$897$	−2.32206	+	9.02696i	−0.0775312	+	0.301401i
$898$	3.56892			0.119097
$899$	18.8647	+	32.6746i	0.629173	+	1.08976i
$900$	9.15741	−	5.53468i	0.305247	−	0.184489i
$901$	16.3950	−	28.3970i	0.546197	−	0.946041i
$902$	10.8915	+	18.8647i	0.362648	+	0.628125i
$903$	−9.79543	−	2.20662i	−0.325972	−	0.0734318i
$904$	7.50672	−	13.0020i	0.249670	−	0.432441i
$905$	6.09733	+	10.5609i	0.202682	+	0.351056i
$906$	−36.0257	−	35.3107i	−1.19687	−	1.17312i
$907$	0.854723	−	1.48042i	0.0283806	−	0.0491566i	−0.851486	−	0.524377i	$-0.824298\pi$
$907$	0.854723	−	1.48042i	0.0283806	−	0.0491566i	0.879867	+	0.475220i	$0.157632\pi$
$908$	−48.3043	+	83.6655i	−1.60303	+	2.77654i
$909$	9.82410	−	5.93761i	0.325845	−	0.196938i
$910$	3.89316	+	2.09357i	0.129057	+	0.0694011i
$911$	16.6788	+	28.8885i	0.552592	+	0.957118i	0.998086	+	0.0618333i	$0.0196947\pi$
$911$	16.6788	+	28.8885i	0.552592	+	0.957118i	−0.445494	+	0.895285i	$0.646972\pi$
$912$	7.83178	+	7.67635i	0.259336	+	0.254189i
$913$	−44.5848			−1.47554
$914$	−13.2966			−0.439812
$915$	−0.244460	+	0.0681360i	−0.00808161	+	0.00225251i
$916$	−24.1448	−	41.8200i	−0.797766	−	1.38177i
$917$	0.864377	+	28.6083i	0.0285442	+	0.944729i
$918$	40.0576	+	9.45245i	1.32210	+	0.311977i
$919$	10.6608	−	18.4650i	0.351667	−	0.609105i	−0.634875	−	0.772615i	$-0.718948\pi$
$919$	10.6608	−	18.4650i	0.351667	−	0.609105i	0.986542	+	0.163510i	$0.0522816\pi$
$920$	−14.0453	+	24.3272i	−0.463060	+	0.802043i
$921$	−9.92626	+	38.5882i	−0.327081	+	1.27152i
$922$	−23.9718	−	41.5204i	−0.789469	−	1.36740i
$923$	−1.55584	+	2.69480i	−0.0512112	+	0.0887004i
$924$	24.6160	+	79.0093i	0.809807	+	2.59922i
$925$	3.70507	+	6.41738i	0.121822	+	0.211002i
$926$	−8.35081	+	14.4640i	−0.274425	+	0.475317i
$927$	0.690732	+	34.4552i	0.0226866	+	1.13166i
$928$	12.9189	+	22.3761i	0.424083	+	0.734533i
$929$	9.39777			0.308331			0.154165	−	0.988045i	$-0.450731\pi$
$929$	9.39777			0.308331			0.154165	+	0.988045i	$0.450731\pi$
$930$	−20.9609	+	5.84222i	−0.687334	+	0.191574i
$931$	27.8613	−	1.68515i	0.913119	−	0.0552287i
$932$	0.104467	−	0.180943i	0.00342194	−	0.00592698i
$933$	9.79172	−	38.0652i	0.320567	−	1.24620i
$934$	−17.4806	+	30.2773i	−0.571983	+	0.990704i
$935$	8.49890	+	14.7205i	0.277944	+	0.481413i
$936$	6.72046	−	4.06180i	0.219665	−	0.132764i
$937$	−30.3633			−0.991926			−0.495963	−	0.868344i	$-0.665185\pi$
$937$	−30.3633			−0.991926			−0.495963	+	0.868344i	$0.665185\pi$
$938$	37.5453	+	20.1902i	1.22590	+	0.659232i
$939$	9.38487	−	36.4835i	0.306264	−	1.19060i
$940$	18.7790	+	32.5261i	0.612502	+	1.06089i
$941$	8.46005			0.275790			0.137895	−	0.990447i	$-0.455966\pi$
$941$	8.46005			0.275790			0.137895	+	0.990447i	$0.455966\pi$
$942$	10.9842	−	42.7009i	0.357884	−	1.39127i
$943$	13.8574			0.451259
$944$	15.9061			0.517699
$945$	−10.2890	−	9.11790i	−0.334702	−	0.296605i
$946$	−26.1747			−0.851014
$947$	23.7389			0.771410			0.385705	−	0.922622i	$-0.373958\pi$
$947$	23.7389			0.771410			0.385705	+	0.922622i	$0.373958\pi$
$948$	−0.857051	+	3.33177i	−0.0278357	+	0.108211i
$949$	−1.57175			−0.0510211
$950$	−4.70398	−	8.14753i	−0.152617	−	0.264341i
$951$	2.15212	−	8.36632i	0.0697872	−	0.271297i
$952$	0.991544	+	32.8171i	0.0321361	+	1.06361i
$953$	18.8696			0.611248			0.305624	−	0.952152i	$-0.401135\pi$
$953$	18.8696			0.611248			0.305624	+	0.952152i	$0.401135\pi$
$954$	1.38566	+	69.1198i	0.0448625	+	2.23784i
$955$	4.55778	+	7.89431i	0.147486	+	0.255454i
$956$	26.7693	−	46.3657i	0.865780	−	1.49957i
$957$	−15.4805	+	60.1800i	−0.500412	+	1.94534i
$958$	1.73702	−	3.00860i	0.0561205	−	0.0972035i
$959$	29.7473	−	18.3943i	0.960591	−	0.593982i
$960$	−19.6529	+	5.47765i	−0.634293	+	0.176790i
$961$	−2.64743			−0.0854010
$962$	6.19023	+	10.7218i	0.199581	+	0.345684i
$963$	−32.4377	+	19.6051i	−1.04529	+	0.631766i
$964$	−18.8346	+	32.6225i	−0.606621	+	1.05070i
$965$	9.35445	+	16.2024i	0.301131	+	0.521573i
$966$	80.1570	+	18.0570i	2.57901	+	0.580975i
$967$	26.7460	−	46.3254i	0.860093	−	1.48972i	−0.0117455	−	0.999931i	$-0.503739\pi$
$967$	26.7460	−	46.3254i	0.860093	−	1.48972i	0.871838	−	0.489794i	$-0.162928\pi$
$968$	27.0494	+	46.8510i	0.869401	+	1.50585i
$969$	5.77627	−	22.4551i	0.185560	−	0.721363i
$970$	3.83353	−	6.63986i	0.123087	−	0.213193i
$971$	2.52332	−	4.37052i	0.0809772	−	0.140257i	−0.822693	−	0.568486i	$-0.807529\pi$
$971$	2.52332	−	4.37052i	0.0809772	−	0.140257i	0.903670	+	0.428230i	$0.140863\pi$
$972$	−52.9163	+	17.0621i	−1.69729	+	0.547268i
$973$	−13.4874	+	8.33995i	−0.432386	+	0.267367i
$974$	−4.27526	−	7.40497i	−0.136988	−	0.237271i
$975$	−1.18148	+	0.329303i	−0.0378377	+	0.0105461i
$976$	−0.232649			−0.00744693
$977$	−26.7167			−0.854743			−0.427372	−	0.904076i	$-0.640560\pi$
$977$	−26.7167			−0.854743			−0.427372	+	0.904076i	$0.640560\pi$
$978$	60.3650	+	59.1670i	1.93026	+	1.89195i
$979$	−22.8258	−	39.5354i	−0.729515	−	1.26356i
$980$	11.1552	−	22.3361i	0.356341	−	0.713500i
$981$	−0.331703	−	16.5461i	−0.0105905	−	0.528275i
$982$	37.4211	−	64.8152i	1.19415	−	2.06834i
$983$	3.46008	−	5.99304i	0.110359	−	0.191148i	−0.805556	−	0.592520i	$-0.798133\pi$
$983$	3.46008	−	5.99304i	0.110359	−	0.191148i	0.915915	+	0.401372i	$0.131466\pi$
$984$	−8.33744	−	8.17197i	−0.265788	−	0.260513i
$985$	−3.21336	−	5.56570i	−0.102386	−	0.177338i
$986$	−28.0623	+	48.6053i	−0.893686	+	1.54791i
$987$	32.7220	−	35.4665i	1.04155	−	1.12891i
$988$	−5.03550	−	8.72175i	−0.160201	−	0.277476i
$989$	−8.32560	+	14.4204i	−0.264739	+	0.458541i
$990$	−31.3893	−	17.2932i	−0.997618	−	0.549614i
$991$	−0.137335	−	0.237872i	−0.00436260	−	0.00755624i	0.863836	−	0.503773i	$-0.168055\pi$
$991$	−0.137335	−	0.237872i	−0.00436260	−	0.00755624i	−0.868198	+	0.496217i	$0.834722\pi$
$992$	19.4163			0.616469
$993$	−5.53986	+	21.5361i	−0.175802	+	0.683428i
$994$	24.1587	+	12.9915i	0.766269	+	0.412065i
$995$	−8.15316	+	14.1217i	−0.258473	+	0.447688i
$996$	52.4015	−	14.6054i	1.66041	−	0.462789i
$997$	−6.22792	+	10.7871i	−0.197240	+	0.341630i	−0.947633	−	0.319363i	$-0.896531\pi$
$997$	−6.22792	+	10.7871i	−0.197240	+	0.341630i	0.750392	+	0.660993i	$0.229865\pi$
$998$	40.2833	+	69.7728i	1.27515	+	2.20862i
$999$	−11.0792	−	36.8759i	−0.350531	−	1.16670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.3	yes	36
3.2	odd	2		945.2.l.c.226.16		36
7.4	even	3		315.2.k.c.256.16	yes	36
9.2	odd	6		945.2.k.c.856.3		36
9.7	even	3		315.2.k.c.16.16	✓	36
21.11	odd	6		945.2.k.c.361.3		36
63.11	odd	6		945.2.l.c.46.16		36
63.25	even	3	inner	315.2.l.c.151.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.16	✓	36	9.7	even	3
315.2.k.c.256.16	yes	36	7.4	even	3
315.2.l.c.121.3	yes	36	1.1	even	1	trivial
315.2.l.c.151.3	yes	36	63.25	even	3	inner
945.2.k.c.361.3		36	21.11	odd	6
945.2.k.c.856.3		36	9.2	odd	6
945.2.l.c.46.16		36	63.11	odd	6
945.2.l.c.226.16		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.35938 q^{2} +(-0.431498 + 1.67744i) q^{3} +3.56668 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01807 - 3.95772i) q^{6} +(2.33019 + 1.25307i) q^{7} -3.69640 q^{8} +(-2.62762 - 1.44762i) q^{9} +O(q^{10})\)	\(q-2.35938 q^{2} +(-0.431498 + 1.67744i) q^{3} +3.56668 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.01807 - 3.95772i) q^{6} +(2.33019 + 1.25307i) q^{7} -3.69640 q^{8} +(-2.62762 - 1.44762i) q^{9} +(1.17969 + 2.04328i) q^{10} +(2.53158 - 4.38482i) q^{11} +(-1.53901 + 5.98290i) q^{12} +(0.354064 - 0.613257i) q^{13} +(-5.49782 - 2.95648i) q^{14} +(1.66846 - 0.465033i) q^{15} +1.58785 q^{16} +(-1.67858 - 2.90738i) q^{17} +(6.19956 + 3.41550i) q^{18} +(1.99373 - 3.45325i) q^{19} +(-1.78334 - 3.08884i) q^{20} +(-3.10743 + 3.36807i) q^{21} +(-5.97296 + 10.3455i) q^{22} +(3.79973 + 6.58132i) q^{23} +(1.59499 - 6.20049i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.835372 + 1.44691i) q^{26} +(3.56212 - 3.78303i) q^{27} +(8.31106 + 4.46932i) q^{28} +(3.54286 + 6.13641i) q^{29} +(-3.93652 + 1.09719i) q^{30} +5.32471 q^{31} +3.64646 q^{32} +(6.26291 + 6.13862i) q^{33} +(3.96041 + 6.85962i) q^{34} +(-0.0799028 - 2.64454i) q^{35} +(-9.37188 - 5.16321i) q^{36} +(3.70507 - 6.41738i) q^{37} +(-4.70398 + 8.14753i) q^{38} +(0.875925 + 0.858541i) q^{39} +(1.84820 + 3.20117i) q^{40} +(0.911736 - 1.57917i) q^{41} +(7.33162 - 7.94655i) q^{42} +(1.09555 + 1.89755i) q^{43} +(9.02933 - 15.6393i) q^{44} +(0.0601298 + 2.99940i) q^{45} +(-8.96501 - 15.5278i) q^{46} -10.5302 q^{47} +(-0.685152 + 2.66352i) q^{48} +(3.85961 + 5.83981i) q^{49} +(1.17969 - 2.04328i) q^{50} +(5.60127 - 1.56119i) q^{51} +(1.26283 - 2.18729i) q^{52} +(4.88360 + 8.45865i) q^{53} +(-8.40439 + 8.92561i) q^{54} -5.06316 q^{55} +(-8.61332 - 4.63186i) q^{56} +(4.93233 + 4.83444i) q^{57} +(-8.35895 - 14.4781i) q^{58} +10.0174 q^{59} +(5.95085 - 1.65862i) q^{60} -0.146519 q^{61} -12.5630 q^{62} +(-4.30888 - 6.66585i) q^{63} -11.7791 q^{64} -0.708128 q^{65} +(-14.7766 - 14.4833i) q^{66} -6.82912 q^{67} +(-5.98695 - 10.3697i) q^{68} +(-12.6794 + 3.53399i) q^{69} +(0.188521 + 6.23949i) q^{70} -4.39424 q^{71} +(9.71272 + 5.35099i) q^{72} +(-1.10979 - 1.92221i) q^{73} +(-8.74168 + 15.1410i) q^{74} +(-1.23696 - 1.21241i) q^{75} +(7.11101 - 12.3166i) q^{76} +(11.3936 - 7.04523i) q^{77} +(-2.06664 - 2.02562i) q^{78} +0.556883 q^{79} +(-0.793923 - 1.37512i) q^{80} +(4.80877 + 7.60761i) q^{81} +(-2.15113 + 3.72587i) q^{82} +(-4.40286 - 7.62598i) q^{83} +(-11.0832 + 12.0128i) q^{84} +(-1.67858 + 2.90738i) q^{85} +(-2.58482 - 4.47705i) q^{86} +(-11.8222 + 3.29509i) q^{87} +(-9.35772 + 16.2080i) q^{88} +(4.50821 - 7.80845i) q^{89} +(-0.141869 - 7.07672i) q^{90} +(1.59349 - 0.985339i) q^{91} +(13.5524 + 23.4735i) q^{92} +(-2.29760 + 8.93189i) q^{93} +24.8448 q^{94} -3.98747 q^{95} +(-1.57344 + 6.11672i) q^{96} +(-1.62480 - 2.81424i) q^{97} +(-9.10629 - 13.7783i) q^{98} +(-12.9996 + 7.85687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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