LMFDB - Embedded newform 315.2.k.c.256.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 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("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (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			256.17
Character	$\chi$	$=$	315.256
Dual form			315.2.k.c.16.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32610 - 2.29687i) q^{2} +(-0.540247 - 1.64564i) q^{3} +(-2.51707 - 4.35969i) q^{4} +1.00000 q^{5} +(-4.49624 - 0.941405i) q^{6} +(2.58884 - 0.545800i) q^{7} -8.04712 q^{8} +(-2.41627 + 1.77810i) q^{9} +O(q^{10})$	\(q+(1.32610 - 2.29687i) q^{2} +(-0.540247 - 1.64564i) q^{3} +(-2.51707 - 4.35969i) q^{4} +1.00000 q^{5} +(-4.49624 - 0.941405i) q^{6} +(2.58884 - 0.545800i) q^{7} -8.04712 q^{8} +(-2.41627 + 1.77810i) q^{9} +(1.32610 - 2.29687i) q^{10} +5.32986 q^{11} +(-5.81465 + 6.49750i) q^{12} +(-2.30157 + 3.98643i) q^{13} +(2.17943 - 6.67001i) q^{14} +(-0.540247 - 1.64564i) q^{15} +(-5.63713 + 9.76380i) q^{16} +(-0.923899 + 1.60024i) q^{17} +(0.879863 + 7.90779i) q^{18} +(1.39618 + 2.41825i) q^{19} +(-2.51707 - 4.35969i) q^{20} +(-2.29680 - 3.96544i) q^{21} +(7.06792 - 12.2420i) q^{22} -1.70426 q^{23} +(4.34743 + 13.2427i) q^{24} +1.00000 q^{25} +(6.10421 + 10.5728i) q^{26} +(4.23150 + 3.01569i) q^{27} +(-8.89581 - 9.91273i) q^{28} +(2.11711 + 3.66695i) q^{29} +(-4.49624 - 0.941405i) q^{30} +(-1.84688 - 3.19889i) q^{31} +(6.90365 + 11.9575i) q^{32} +(-2.87944 - 8.77104i) q^{33} +(2.45036 + 4.24415i) q^{34} +(2.58884 - 0.545800i) q^{35} +(13.8339 + 6.05857i) q^{36} +(-5.06506 - 8.77294i) q^{37} +7.40587 q^{38} +(7.80365 + 1.63390i) q^{39} -8.04712 q^{40} +(-1.59776 + 2.76740i) q^{41} +(-12.1539 + 0.0168971i) q^{42} +(-4.34272 - 7.52182i) q^{43} +(-13.4156 - 23.2366i) q^{44} +(-2.41627 + 1.77810i) q^{45} +(-2.26001 + 3.91445i) q^{46} +(-5.35500 + 9.27513i) q^{47} +(19.1131 + 4.00183i) q^{48} +(6.40421 - 2.82598i) q^{49} +(1.32610 - 2.29687i) q^{50} +(3.13255 + 0.655882i) q^{51} +23.1728 q^{52} +(1.74772 - 3.02714i) q^{53} +(12.5380 - 5.72009i) q^{54} +5.32986 q^{55} +(-20.8327 + 4.39212i) q^{56} +(3.22529 - 3.60406i) q^{57} +11.2300 q^{58} +(0.965273 + 1.67190i) q^{59} +(-5.81465 + 6.49750i) q^{60} +(1.44741 - 2.50698i) q^{61} -9.79658 q^{62} +(-5.28485 + 5.92203i) q^{63} +14.0711 q^{64} +(-2.30157 + 3.98643i) q^{65} +(-23.9643 - 5.01756i) q^{66} +(-0.828267 - 1.43460i) q^{67} +9.30207 q^{68} +(0.920719 + 2.80459i) q^{69} +(2.17943 - 6.67001i) q^{70} -2.79922 q^{71} +(19.4440 - 14.3086i) q^{72} +(-1.45087 + 2.51299i) q^{73} -26.8670 q^{74} +(-0.540247 - 1.64564i) q^{75} +(7.02855 - 12.1738i) q^{76} +(13.7982 - 2.90904i) q^{77} +(14.1013 - 15.7573i) q^{78} +(-4.32536 + 7.49174i) q^{79} +(-5.63713 + 9.76380i) q^{80} +(2.67670 - 8.59275i) q^{81} +(4.23757 + 7.33969i) q^{82} +(2.26167 + 3.91732i) q^{83} +(-11.5069 + 19.9946i) q^{84} +(-0.923899 + 1.60024i) q^{85} -23.0355 q^{86} +(4.89071 - 5.46506i) q^{87} -42.8901 q^{88} +(3.12944 + 5.42035i) q^{89} +(0.879863 + 7.90779i) q^{90} +(-3.78260 + 11.5764i) q^{91} +(4.28973 + 7.43003i) q^{92} +(-4.26646 + 4.76749i) q^{93} +(14.2025 + 24.5995i) q^{94} +(1.39618 + 2.41825i) q^{95} +(15.9480 - 17.8209i) q^{96} +(-4.38018 - 7.58670i) q^{97} +(2.00170 - 18.4571i) q^{98} +(-12.8784 + 9.47705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.32610	−	2.29687i	0.937692	−	1.62413i	0.167932	−	0.985799i	$-0.446291\pi$
$2$	1.32610	−	2.29687i	0.937692	−	1.62413i	0.769761	−	0.638332i	$-0.220375\pi$
$3$	−0.540247	−	1.64564i	−0.311911	−	0.950111i
$3$	−0.540247	−	1.64564i	−0.311911	−	0.950111i
$4$	−2.51707	−	4.35969i	−1.25853	−	2.17985i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−4.49624	−	0.941405i	−1.83558	−	0.384327i
$7$	2.58884	−	0.545800i	0.978490	−	0.206293i
$7$	2.58884	−	0.545800i	0.978490	−	0.206293i
$8$	−8.04712			−2.84509
$9$	−2.41627	+	1.77810i	−0.805422	+	0.592701i
$10$	1.32610	−	2.29687i	0.419349	−	0.726333i
$11$	5.32986			1.60701			0.803507	−	0.595295i	$-0.202965\pi$
$11$	5.32986			1.60701			0.803507	+	0.595295i	$0.202965\pi$
$12$	−5.81465	+	6.49750i	−1.67854	+	1.87567i
$13$	−2.30157	+	3.98643i	−0.638340	+	1.10564i	0.347456	+	0.937696i	$0.387045\pi$
$13$	−2.30157	+	3.98643i	−0.638340	+	1.10564i	−0.985797	+	0.167942i	$0.946288\pi$
$14$	2.17943	−	6.67001i	0.582476	−	1.78264i
$15$	−0.540247	−	1.64564i	−0.139491	−	0.424903i
$16$	−5.63713	+	9.76380i	−1.40928	+	2.44095i
$17$	−0.923899	+	1.60024i	−0.224078	+	0.388115i	−0.956043	−	0.293228i	$-0.905271\pi$
$17$	−0.923899	+	1.60024i	−0.224078	+	0.388115i	0.731964	+	0.681343i	$0.238604\pi$
$18$	0.879863	+	7.90779i	0.207386	+	1.86388i
$19$	1.39618	+	2.41825i	0.320305	+	0.554785i	0.980551	−	0.196265i	$-0.0628812\pi$
$19$	1.39618	+	2.41825i	0.320305	+	0.554785i	−0.660246	+	0.751050i	$0.729548\pi$
$20$	−2.51707	−	4.35969i	−0.562834	−	0.974856i
$21$	−2.29680	−	3.96544i	−0.501204	−	0.865329i
$22$	7.06792	−	12.2420i	1.50688	−	2.61000i
$23$	−1.70426			−0.355362			−0.177681	−	0.984088i	$-0.556860\pi$
$23$	−1.70426			−0.355362			−0.177681	+	0.984088i	$0.556860\pi$
$24$	4.34743	+	13.2427i	0.887415	+	2.70315i
$25$	1.00000			0.200000
$26$	6.10421	+	10.5728i	1.19713	+	2.07350i
$27$	4.23150	+	3.01569i	0.814353	+	0.580371i
$28$	−8.89581	−	9.91273i	−1.68115	−	1.87333i
$29$	2.11711	+	3.66695i	0.393138	+	0.680935i	0.992862	−	0.119272i	$-0.0380562\pi$
$29$	2.11711	+	3.66695i	0.393138	+	0.680935i	−0.599724	+	0.800207i	$0.704723\pi$
$30$	−4.49624	−	0.941405i	−0.820897	−	0.171876i
$31$	−1.84688	−	3.19889i	−0.331710	−	0.574538i	0.651138	−	0.758960i	$-0.274292\pi$
$31$	−1.84688	−	3.19889i	−0.331710	−	0.574538i	−0.982847	+	0.184422i	$0.940959\pi$
$32$	6.90365	+	11.9575i	1.22040	+	2.11380i
$33$	−2.87944	−	8.77104i	−0.501246	−	1.52684i
$34$	2.45036	+	4.24415i	0.420233	+	0.727866i
$35$	2.58884	−	0.545800i	0.437594	−	0.0922570i
$36$	13.8339	+	6.05857i	2.30565	+	1.00976i
$37$	−5.06506	−	8.77294i	−0.832690	−	1.44226i	−0.895897	−	0.444261i	$-0.853466\pi$
$37$	−5.06506	−	8.77294i	−0.832690	−	1.44226i	0.0632070	−	0.998000i	$-0.479867\pi$
$38$	7.40587			1.20139
$39$	7.80365	+	1.63390i	1.24958	+	0.261633i
$40$	−8.04712			−1.27236
$41$	−1.59776	+	2.76740i	−0.249528	+	0.432196i	−0.963395	−	0.268086i	$-0.913609\pi$
$41$	−1.59776	+	2.76740i	−0.249528	+	0.432196i	0.713867	+	0.700282i	$0.246942\pi$
$42$	−12.1539	+	0.0168971i	−1.87538	+	0.00260727i
$43$	−4.34272	−	7.52182i	−0.662259	−	1.14707i	−0.980021	−	0.198896i	$-0.936264\pi$
$43$	−4.34272	−	7.52182i	−0.662259	−	1.14707i	0.317762	−	0.948171i	$-0.397069\pi$
$44$	−13.4156	−	23.2366i	−2.02248	−	3.50304i
$45$	−2.41627	+	1.77810i	−0.360196	+	0.265064i
$46$	−2.26001	+	3.91445i	−0.333220	+	0.577154i
$47$	−5.35500	+	9.27513i	−0.781107	+	1.35292i	0.150190	+	0.988657i	$0.452011\pi$
$47$	−5.35500	+	9.27513i	−0.781107	+	1.35292i	−0.931297	+	0.364260i	$0.881322\pi$
$48$	19.1131	+	4.00183i	2.75874	+	0.577615i
$49$	6.40421	−	2.82598i	0.914887	−	0.403711i
$50$	1.32610	−	2.29687i	0.187538	−	0.324826i
$51$	3.13255	+	0.655882i	0.438645	+	0.0918418i
$52$	23.1728			3.21349
$53$	1.74772	−	3.02714i	0.240068	−	0.415810i	−0.720666	−	0.693283i	$-0.756164\pi$
$53$	1.74772	−	3.02714i	0.240068	−	0.415810i	0.960733	+	0.277473i	$0.0894970\pi$
$54$	12.5380	−	5.72009i	1.70621	−	0.778406i
$55$	5.32986			0.718679
$56$	−20.8327	+	4.39212i	−2.78389	+	0.586921i
$57$	3.22529	−	3.60406i	0.427200	−	0.477369i
$58$	11.2300			1.47457
$59$	0.965273	+	1.67190i	0.125668	+	0.217663i	0.921994	−	0.387205i	$-0.126559\pi$
$59$	0.965273	+	1.67190i	0.125668	+	0.217663i	−0.796326	+	0.604868i	$0.793226\pi$
$60$	−5.81465	+	6.49750i	−0.750668	+	0.838823i
$61$	1.44741	−	2.50698i	0.185322	−	0.320986i	−0.758363	−	0.651832i	$-0.774001\pi$
$61$	1.44741	−	2.50698i	0.185322	−	0.320986i	0.943685	+	0.330846i	$0.107334\pi$
$62$	−9.79658			−1.24417
$63$	−5.28485	+	5.92203i	−0.665828	+	0.746105i
$64$	14.0711			1.75889
$65$	−2.30157	+	3.98643i	−0.285475	+	0.494456i
$66$	−23.9643	−	5.01756i	−2.94981	−	0.617619i
$67$	−0.828267	−	1.43460i	−0.101189	−	0.175264i	0.810986	−	0.585066i	$-0.198931\pi$
$67$	−0.828267	−	1.43460i	−0.101189	−	0.175264i	−0.912175	+	0.409801i	$0.865598\pi$
$68$	9.30207			1.12804
$69$	0.920719	+	2.80459i	0.110841	+	0.337633i
$70$	2.17943	−	6.67001i	0.260491	−	0.797219i
$71$	−2.79922			−0.332207			−0.166103	−	0.986108i	$-0.553119\pi$
$71$	−2.79922			−0.332207			−0.166103	+	0.986108i	$0.553119\pi$
$72$	19.4440	−	14.3086i	2.29150	−	1.68629i
$73$	−1.45087	+	2.51299i	−0.169812	+	0.294123i	−0.938354	−	0.345677i	$-0.887649\pi$
$73$	−1.45087	+	2.51299i	−0.169812	+	0.294123i	0.768542	+	0.639800i	$0.220983\pi$
$74$	−26.8670			−3.12323
$75$	−0.540247	−	1.64564i	−0.0623823	−	0.190022i
$76$	7.02855	−	12.1738i	0.806230	−	1.39643i
$77$	13.7982	−	2.90904i	1.57245	−	0.331516i
$78$	14.1013	−	15.7573i	1.59665	−	1.78416i
$79$	−4.32536	+	7.49174i	−0.486641	+	0.842886i	−0.999882	−	0.0153580i	$-0.995111\pi$
$79$	−4.32536	+	7.49174i	−0.486641	+	0.842886i	0.513241	+	0.858244i	$0.328445\pi$
$80$	−5.63713	+	9.76380i	−0.630250	+	1.09163i
$81$	2.67670	−	8.59275i	0.297411	−	0.954750i
$82$	4.23757	+	7.33969i	0.467961	+	0.810533i
$83$	2.26167	+	3.91732i	0.248250	+	0.429982i	0.963040	−	0.269357i	$-0.0868111\pi$
$83$	2.26167	+	3.91732i	0.248250	+	0.429982i	−0.714790	+	0.699339i	$0.753478\pi$
$84$	−11.5069	+	19.9946i	−1.25550	+	2.18159i
$85$	−0.923899	+	1.60024i	−0.100211	+	0.173570i
$86$	−23.0355			−2.48398
$87$	4.89071	−	5.46506i	0.524340	−	0.585916i
$88$	−42.8901			−4.57210
$89$	3.12944	+	5.42035i	0.331720	+	0.574556i	0.982849	−	0.184411i	$-0.0590378\pi$
$89$	3.12944	+	5.42035i	0.331720	+	0.574556i	−0.651129	+	0.758967i	$0.725704\pi$
$90$	0.879863	+	7.90779i	0.0927457	+	0.833554i
$91$	−3.78260	+	11.5764i	−0.396525	+	1.21354i
$92$	4.28973	+	7.43003i	0.447235	+	0.774634i
$93$	−4.26646	+	4.76749i	−0.442411	+	0.494366i
$94$	14.2025	+	24.5995i	1.46488	+	2.53724i
$95$	1.39618	+	2.41825i	0.143245	+	0.248107i
$96$	15.9480	−	17.8209i	1.62769	−	1.81884i
$97$	−4.38018	−	7.58670i	−0.444740	−	0.770312i	0.553294	−	0.832986i	$-0.313371\pi$
$97$	−4.38018	−	7.58670i	−0.444740	−	0.770312i	−0.998034	+	0.0626738i	$0.980037\pi$
$98$	2.00170	−	18.4571i	0.202202	−	1.86445i
$99$	−12.8784	+	9.47705i	−1.29433	+	0.952479i
$100$	−2.51707	−	4.35969i	−0.251707	−	0.435969i
$101$	6.56659			0.653400			0.326700	−	0.945128i	$-0.394063\pi$
$101$	6.56659			0.653400			0.326700	+	0.945128i	$0.394063\pi$
$102$	5.66055	−	6.32530i	0.560478	−	0.626298i
$103$	−1.16895			−0.115180			−0.0575902	−	0.998340i	$-0.518342\pi$
$103$	−1.16895			−0.115180			−0.0575902	+	0.998340i	$0.518342\pi$
$104$	18.5210	−	32.0793i	1.81613	−	3.14564i
$105$	−2.29680	−	3.96544i	−0.224145	−	0.386987i
$106$	−4.63529	−	8.02856i	−0.450220	−	0.779803i
$107$	6.79339	+	11.7665i	0.656742	+	1.13751i	0.981454	+	0.191698i	$0.0613993\pi$
$107$	6.79339	+	11.7665i	0.656742	+	1.13751i	−0.324712	+	0.945813i	$0.605267\pi$
$108$	2.49652	−	26.0387i	0.240227	−	2.50558i
$109$	1.93478	−	3.35114i	0.185318	−	0.320981i	−0.758365	−	0.651830i	$-0.774002\pi$
$109$	1.93478	−	3.35114i	0.185318	−	0.320981i	0.943684	+	0.330849i	$0.107335\pi$
$110$	7.06792	−	12.2420i	0.673899	−	1.16723i
$111$	−11.7007	+	13.0748i	−1.11058	+	1.24101i
$112$	−9.26456	+	28.3537i	−0.875419	+	2.67917i
$113$	2.48797	−	4.30929i	0.234048	−	0.405383i	−0.724947	−	0.688804i	$-0.758136\pi$
$113$	2.48797	−	4.30929i	0.234048	−	0.405383i	0.958996	+	0.283421i	$0.0914693\pi$
$114$	−4.00100	−	12.1874i	−0.374728	−	1.14145i
$115$	−1.70426			−0.158923
$116$	10.6578	−	18.4599i	0.989555	−	1.71396i
$117$	−1.52709	−	13.7247i	−0.141179	−	1.26885i
$118$	5.12019			0.471351
$119$	−1.51842	+	4.64703i	−0.139193	+	0.425993i
$120$	4.34743	+	13.2427i	0.396864	+	1.20889i
$121$	17.4074			1.58249
$122$	−3.83881	−	6.64901i	−0.347549	−	0.601973i
$123$	5.41733	+	1.13426i	0.488465	+	0.102273i
$124$	−9.29745	+	16.1037i	−0.834936	+	1.44615i
$125$	1.00000			0.0894427
$126$	6.59389	+	19.9918i	0.587431	+	1.78101i
$127$	13.5309			1.20067			0.600337	−	0.799747i	$-0.295033\pi$
$127$	13.5309			1.20067			0.600337	+	0.799747i	$0.295033\pi$
$128$	4.85236	−	8.40454i	0.428892	−	0.742864i
$129$	−10.0321	+	11.2102i	−0.883274	+	0.987003i
$130$	6.10421	+	10.5728i	0.535375	+	0.927296i
$131$	−3.73322			−0.326173			−0.163087	−	0.986612i	$-0.552145\pi$
$131$	−3.73322			−0.326173			−0.163087	+	0.986612i	$0.552145\pi$
$132$	−30.9913	+	34.6308i	−2.69744	+	3.01422i
$133$	4.93436	+	5.49844i	0.427864	+	0.476775i
$134$	−4.39345			−0.379536
$135$	4.23150	+	3.01569i	0.364190	+	0.259550i
$136$	7.43473	−	12.8773i	0.637523	−	1.10422i
$137$	2.32875			0.198958			0.0994791	−	0.995040i	$-0.468282\pi$
$137$	2.32875			0.198958			0.0994791	+	0.995040i	$0.468282\pi$
$138$	7.66274	+	1.60440i	0.652296	+	0.136575i
$139$	−2.92543	+	5.06699i	−0.248132	+	0.429777i	−0.963007	−	0.269475i	$-0.913150\pi$
$139$	−2.92543	+	5.06699i	−0.248132	+	0.429777i	0.714876	+	0.699252i	$0.246483\pi$
$140$	−8.89581	−	9.91273i	−0.751833	−	0.837779i
$141$	18.1566	+	3.80155i	1.52906	+	0.320148i
$142$	−3.71204	+	6.42945i	−0.311508	+	0.539547i
$143$	−12.2670	+	21.2472i	−1.02582	+	1.77678i
$144$	−3.74023	−	33.6153i	−0.311686	−	2.80128i
$145$	2.11711	+	3.66695i	0.175817	+	0.304523i
$146$	3.84800	+	6.66493i	0.318463	+	0.551594i
$147$	−8.11039	−	9.01230i	−0.668934	−	0.743322i
$148$	−25.4982	+	44.1642i	−2.09594	+	3.63027i
$149$	3.03534			0.248664			0.124332	−	0.992241i	$-0.460321\pi$
$149$	3.03534			0.248664			0.124332	+	0.992241i	$0.460321\pi$
$150$	−4.49624	−	0.941405i	−0.367116	−	0.0768654i
$151$	3.27898			0.266840			0.133420	−	0.991060i	$-0.457404\pi$
$151$	3.27898			0.266840			0.133420	+	0.991060i	$0.457404\pi$
$152$	−11.2352	−	19.4600i	−0.911296	−	1.57841i
$153$	−0.613006	−	5.50940i	−0.0495586	−	0.445408i
$154$	11.6160	−	35.5502i	0.936048	−	2.86472i
$155$	−1.84688	−	3.19889i	−0.148345	−	0.256941i
$156$	−12.5190	−	38.1342i	−1.00233	−	3.05318i
$157$	−9.58292	−	16.5981i	−0.764800	−	1.32467i	−0.940352	−	0.340202i	$-0.889504\pi$
$157$	−9.58292	−	16.5981i	−0.764800	−	1.32467i	0.175552	−	0.984470i	$-0.443829\pi$
$158$	11.4717	+	19.8695i	0.912638	+	1.58074i
$159$	−5.92578	−	1.24072i	−0.469945	−	0.0983953i
$160$	6.90365	+	11.9575i	0.545781	+	0.945321i
$161$	−4.41205	+	0.930182i	−0.347718	+	0.0733086i
$162$	−16.1868	−	17.5428i	−1.27176	−	1.37830i
$163$	5.13329	+	8.89111i	0.402070	+	0.696406i	0.993976	−	0.109602i	$-0.0349575\pi$
$163$	5.13329	+	8.89111i	0.402070	+	0.696406i	−0.591906	+	0.806007i	$0.701624\pi$
$164$	16.0867			1.25616
$165$	−2.87944	−	8.77104i	−0.224164	−	0.682824i
$166$	11.9968			0.931130
$167$	7.65659	−	13.2616i	0.592485	−	1.02621i	−0.401411	−	0.915898i	$-0.631480\pi$
$167$	7.65659	−	13.2616i	0.592485	−	1.02621i	0.993897	−	0.110316i	$-0.0351864\pi$
$168$	18.4827	+	31.9104i	1.42597	+	2.46194i
$169$	−4.09444	−	7.09178i	−0.314957	−	0.545522i
$170$	2.45036	+	4.24415i	0.187934	+	0.325511i
$171$	−7.67344	−	3.36059i	−0.586803	−	0.256991i
$172$	−21.8619	+	37.8659i	−1.66695	+	2.88724i
$173$	−8.61103	+	14.9147i	−0.654684	+	1.13395i	0.327289	+	0.944924i	$0.393865\pi$
$173$	−8.61103	+	14.9147i	−0.654684	+	1.13395i	−0.981973	+	0.189022i	$0.939468\pi$
$174$	−6.06696	−	18.4805i	−0.459935	−	1.40101i
$175$	2.58884	−	0.545800i	0.195698	−	0.0412586i
$176$	−30.0451	+	52.0397i	−2.26474	+	3.92264i
$177$	2.22987	−	2.49173i	0.167607	−	0.187290i
$178$	16.5998			1.24420
$179$	−12.8188	+	22.2029i	−0.958125	+	1.65952i	−0.231076	+	0.972936i	$0.574224\pi$
$179$	−12.8188	+	22.2029i	−0.958125	+	1.65952i	−0.727049	+	0.686585i	$0.759109\pi$
$180$	13.8339	+	6.05857i	1.03112	+	0.451579i
$181$	−20.6995			−1.53858			−0.769290	−	0.638900i	$-0.779390\pi$
$181$	−20.6995			−1.53858			−0.769290	+	0.638900i	$0.779390\pi$
$182$	21.5735	+	24.0396i	1.59913	+	1.78194i
$183$	−4.90755	−	1.02752i	−0.362777	−	0.0759568i
$184$	13.7144			1.01104
$185$	−5.06506	−	8.77294i	−0.372390	−	0.644999i
$186$	5.29257	+	16.1216i	0.388070	+	1.18210i
$187$	−4.92426	+	8.52906i	−0.360097	+	0.623707i
$188$	53.9156			3.93220
$189$	12.6006	+	5.49760i	0.916562	+	0.399892i
$190$	7.40587			0.537278
$191$	11.5729	−	20.0448i	0.837385	−	1.45039i	−0.0546895	−	0.998503i	$-0.517417\pi$
$191$	11.5729	−	20.0448i	0.837385	−	1.45039i	0.892074	−	0.451889i	$-0.149250\pi$
$192$	−7.60187	−	23.1560i	−0.548617	−	1.67114i
$193$	−2.14734	−	3.71930i	−0.154569	−	0.267721i	0.778333	−	0.627852i	$-0.216066\pi$
$193$	−2.14734	−	3.71930i	−0.154569	−	0.267721i	−0.932902	+	0.360130i	$0.882732\pi$
$194$	−23.2342			−1.66812
$195$	7.80365	+	1.63390i	0.558831	+	0.117006i
$196$	−28.4402	−	20.8072i	−2.03144	−	1.48623i
$197$	−14.7455			−1.05058			−0.525288	−	0.850924i	$-0.676042\pi$
$197$	−14.7455			−1.05058			−0.525288	+	0.850924i	$0.676042\pi$
$198$	4.68955	+	42.1474i	0.333272	+	2.99529i
$199$	11.1399	−	19.2949i	0.789687	−	1.36778i	−0.136472	−	0.990644i	$-0.543576\pi$
$199$	11.1399	−	19.2949i	0.789687	−	1.36778i	0.926159	−	0.377133i	$-0.123090\pi$
$200$	−8.04712			−0.569017
$201$	−1.91337	+	2.13807i	−0.134959	+	0.150808i
$202$	8.70793	−	15.0826i	0.612688	−	1.06121i
$203$	7.48229	+	8.33763i	0.525154	+	0.585187i
$204$	−5.02541	−	15.3079i	−0.351849	−	1.07177i
$205$	−1.59776	+	2.76740i	−0.111592	+	0.193284i
$206$	−1.55015	+	2.68493i	−0.108004	+	0.187068i
$207$	4.11794	−	3.03034i	0.286217	−	0.210623i
$208$	−25.9485	−	44.9441i	−1.79920	−	3.11631i
$209$	7.44144	+	12.8889i	0.514735	+	0.891547i
$210$	−12.1539	+	0.0168971i	−0.838697	+	0.00116601i
$211$	−10.6046	+	18.3677i	−0.730050	+	1.26448i	0.226812	+	0.973939i	$0.427170\pi$
$211$	−10.6046	+	18.3677i	−0.730050	+	1.26448i	−0.956861	+	0.290545i	$0.906164\pi$
$212$	−17.5965			−1.20853
$213$	1.51227	+	4.60652i	0.103619	+	0.315633i
$214$	36.0348			2.46329
$215$	−4.34272	−	7.52182i	−0.296171	−	0.512984i
$216$	−34.0514	−	24.2677i	−2.31690	−	1.65120i
$217$	−6.52724	−	7.27340i	−0.443098	−	0.493750i
$218$	−5.13141	−	8.88787i	−0.347543	−	0.601963i
$219$	4.91931	+	1.02998i	0.332416	+	0.0695999i
$220$	−13.4156	−	23.2366i	−0.904482	−	1.56661i
$221$	−4.25284	−	7.36613i	−0.286077	−	0.495499i
$222$	14.5148	+	44.2135i	0.974171	+	2.96742i
$223$	−10.5877	−	18.3384i	−0.709003	−	1.22803i	−0.965227	−	0.261412i	$-0.915812\pi$
$223$	−10.5877	−	18.3384i	−0.709003	−	1.22803i	0.256225	−	0.966617i	$-0.417521\pi$
$224$	24.3988	+	27.1880i	1.63022	+	1.81657i
$225$	−2.41627	+	1.77810i	−0.161084	+	0.118540i
$226$	−6.59857	−	11.4291i	−0.438931	−	0.760250i
$227$	−10.3583			−0.687502			−0.343751	−	0.939061i	$-0.611698\pi$
$227$	−10.3583			−0.687502			−0.343751	+	0.939061i	$0.611698\pi$
$228$	−23.8309	−	4.98961i	−1.57824	−	0.330445i
$229$	−16.4669			−1.08816			−0.544082	−	0.839032i	$-0.683122\pi$
$229$	−16.4669			−1.08816			−0.544082	+	0.839032i	$0.683122\pi$
$230$	−2.26001	+	3.91445i	−0.149021	+	0.258111i
$231$	−12.2416	−	21.1352i	−0.805441	−	1.39060i
$232$	−17.0367	−	29.5084i	−1.11851	−	1.93732i
$233$	−10.6402	−	18.4294i	−0.697063	−	1.20735i	−0.969480	−	0.245170i	$-0.921156\pi$
$233$	−10.6402	−	18.4294i	−0.697063	−	1.20735i	0.272417	−	0.962179i	$-0.412177\pi$
$234$	−33.5489	−	14.6928i	−2.19316	−	0.960498i
$235$	−5.35500	+	9.27513i	−0.349322	+	0.605043i
$236$	4.85932	−	8.41659i	0.316315	−	0.547873i
$237$	14.6655	+	3.07060i	0.952624	+	0.199457i
$238$	8.66005	+	9.65003i	0.561348	+	0.625518i
$239$	10.3537	−	17.9332i	0.669727	−	1.16000i	−0.308254	−	0.951304i	$-0.599745\pi$
$239$	10.3537	−	17.9332i	0.669727	−	1.16000i	0.977980	−	0.208696i	$-0.0669221\pi$
$240$	19.1131	+	4.00183i	1.23375	+	0.258317i
$241$	6.76249			0.435610			0.217805	−	0.975992i	$-0.430110\pi$
$241$	6.76249			0.435610			0.217805	+	0.975992i	$0.430110\pi$
$242$	23.0840	−	39.9826i	1.48389	−	2.57018i
$243$	−15.5867	+	0.237322i	−0.999884	+	0.0152242i
$244$	−14.5729			−0.932934
$245$	6.40421	−	2.82598i	0.409150	−	0.180545i
$246$	9.78916	−	10.9388i	0.624134	−	0.697430i
$247$	−12.8536			−0.817855
$248$	14.8621	+	25.7419i	0.943743	+	1.63461i
$249$	5.22465	−	5.83821i	0.331099	−	0.369982i
$250$	1.32610	−	2.29687i	0.0838698	−	0.145267i
$251$	17.1080			1.07984			0.539922	−	0.841715i	$-0.318454\pi$
$251$	17.1080			1.07984			0.539922	+	0.841715i	$0.318454\pi$
$252$	39.1205	+	8.13415i	2.46436	+	0.512403i
$253$	−9.08345			−0.571072
$254$	17.9433	−	31.0787i	1.12586	−	1.95005i
$255$	3.13255	+	0.655882i	0.196168	+	0.0410729i
$256$	1.20169	+	2.08139i	0.0751057	+	0.130087i
$257$	−20.1503			−1.25694			−0.628470	−	0.777834i	$-0.716318\pi$
$257$	−20.1503			−1.25694			−0.628470	+	0.777834i	$0.716318\pi$
$258$	12.4448	+	37.9082i	0.774782	+	2.36006i
$259$	−17.9009	−	19.9472i	−1.11231	−	1.23946i
$260$	23.1728			1.43712
$261$	−11.6357	−	5.09588i	−0.720233	−	0.315427i
$262$	−4.95061	+	8.57472i	−0.305850	+	0.529748i
$263$	17.5692			1.08336			0.541681	−	0.840584i	$-0.317788\pi$
$263$	17.5692			1.08336			0.541681	+	0.840584i	$0.317788\pi$
$264$	23.1712	+	70.5816i	1.42609	+	4.34400i
$265$	1.74772	−	3.02714i	0.107362	−	0.185956i
$266$	19.1726	−	4.04212i	1.17555	−	0.247838i
$267$	7.22928	−	8.07826i	0.442424	−	0.494381i
$268$	−4.16961	+	7.22198i	−0.254699	+	0.441152i
$269$	1.41595	−	2.45249i	0.0863318	−	0.149531i	−0.819626	−	0.572899i	$-0.805819\pi$
$269$	1.41595	−	2.45249i	0.0863318	−	0.149531i	0.905958	+	0.423368i	$0.139152\pi$
$270$	12.5380	−	5.72009i	0.763040	−	0.348114i
$271$	10.8055	+	18.7157i	0.656387	+	1.13690i	0.981544	+	0.191235i	$0.0612494\pi$
$271$	10.8055	+	18.7157i	0.656387	+	1.13690i	−0.325157	+	0.945660i	$0.605417\pi$
$272$	−10.4163	−	18.0415i	−0.631580	−	1.09393i
$273$	21.0942	−	0.0293265i	1.27668	−	0.00177492i
$274$	3.08815	−	5.34882i	0.186562	−	0.323134i
$275$	5.32986			0.321403
$276$	9.90965	−	11.0734i	0.596491	−	0.666541i
$277$	7.12385			0.428031			0.214015	−	0.976830i	$-0.431346\pi$
$277$	7.12385			0.428031			0.214015	+	0.976830i	$0.431346\pi$
$278$	7.75881	+	13.4387i	0.465343	+	0.805997i
$279$	10.1505	+	4.44543i	0.607696	+	0.266141i
$280$	−20.8327	+	4.39212i	−1.24499	+	0.262479i
$281$	0.0926995	+	0.160560i	0.00552999	+	0.00957822i	0.868777	−	0.495203i	$-0.164906\pi$
$281$	0.0926995	+	0.160560i	0.00552999	+	0.00957822i	−0.863247	+	0.504781i	$0.831573\pi$
$282$	32.8090	−	36.6620i	1.95375	−	2.18319i
$283$	−16.2828	−	28.2027i	−0.967914	−	1.67648i	−0.701573	−	0.712598i	$-0.747518\pi$
$283$	−16.2828	−	28.2027i	−0.967914	−	1.67648i	−0.266342	−	0.963879i	$-0.585815\pi$
$284$	7.04584	+	12.2038i	0.418094	+	0.724160i
$285$	3.22529	−	3.60406i	0.191050	−	0.213486i
$286$	32.5346	+	56.3516i	1.92381	+	3.33214i
$287$	−2.62590	+	8.03642i	−0.155002	+	0.474375i
$288$	−37.9427	−	16.6170i	−2.23579	−	0.979168i
$289$	6.79282	+	11.7655i	0.399578	+	0.692089i
$290$	11.2300			0.659448
$291$	−10.1186	+	11.3069i	−0.593163	+	0.662822i
$292$	14.6078			0.854857
$293$	0.0655256	−	0.113494i	0.00382805	−	0.00663037i	−0.864105	−	0.503312i	$-0.832115\pi$
$293$	0.0655256	−	0.113494i	0.00382805	−	0.00663037i	0.867933	+	0.496681i	$0.165448\pi$
$294$	−31.4552	+	6.67732i	−1.83451	+	0.389429i
$295$	0.965273	+	1.67190i	0.0562004	+	0.0973419i
$296$	40.7591	+	70.5969i	2.36908	+	4.10336i
$297$	22.5533	+	16.0732i	1.30868	+	0.932664i
$298$	4.02515	−	6.97177i	0.233171	−	0.403864i
$299$	3.92246	−	6.79391i	0.226842	−	0.392902i
$300$	−5.81465	+	6.49750i	−0.335709	+	0.375133i
$301$	−15.3480	−	17.1025i	−0.884646	−	0.985774i
$302$	4.34825	−	7.53139i	0.250214	−	0.433383i
$303$	−3.54758	−	10.8062i	−0.203803	−	0.620802i
$304$	−31.4817			−1.80560
$305$	1.44741	−	2.50698i	0.0828783	−	0.143549i
$306$	−13.4673	−	5.89800i	−0.769872	−	0.337166i
$307$	18.9900			1.08382			0.541909	−	0.840437i	$-0.317702\pi$
$307$	18.9900			1.08382			0.541909	+	0.840437i	$0.317702\pi$
$308$	−47.4134	−	52.8335i	−2.70163	−	3.01047i
$309$	0.631523	+	1.92368i	0.0359261	+	0.109434i
$310$	−9.79658			−0.556408
$311$	−0.906869	−	1.57074i	−0.0514238	−	0.0890687i	0.839168	−	0.543873i	$-0.183043\pi$
$311$	−0.906869	−	1.57074i	−0.0514238	−	0.0890687i	−0.890592	+	0.454804i	$0.849709\pi$
$312$	−62.7970	−	13.1482i	−3.55518	−	0.744369i
$313$	6.27699	−	10.8721i	0.354796	−	0.614525i	−0.632287	−	0.774734i	$-0.717884\pi$
$313$	6.27699	−	10.8721i	0.354796	−	0.614525i	0.987083	+	0.160209i	$0.0512169\pi$
$314$	−50.8315			−2.86859
$315$	−5.28485	+	5.92203i	−0.297767	+	0.333668i
$316$	43.5489			2.44982
$317$	0.262553	−	0.454755i	0.0147464	−	0.0255416i	−0.858558	−	0.512716i	$-0.828639\pi$
$317$	0.262553	−	0.454755i	0.0147464	−	0.0255416i	0.873304	+	0.487175i	$0.161973\pi$
$318$	−10.7079	+	11.9654i	−0.600471	+	0.670988i
$319$	11.2839	+	19.5443i	0.631778	+	1.09427i
$320$	14.0711			0.786599
$321$	15.6933	−	17.5363i	0.875916	−	0.978780i
$322$	−3.71430	+	11.3674i	−0.206990	+	0.633481i
$323$	−5.15971			−0.287094
$324$	−44.1991	+	9.95897i	−2.45551	+	0.553276i
$325$	−2.30157	+	3.98643i	−0.127668	+	0.221128i
$326$	27.2290			1.50807
$327$	−6.56003	−	1.37351i	−0.362770	−	0.0759554i
$328$	12.8574	−	22.2696i	0.709930	−	1.22963i
$329$	−8.80089	+	26.9346i	−0.485209	+	1.48495i
$330$	−23.9643	−	5.01756i	−1.31919	−	0.276208i
$331$	−12.6318	+	21.8790i	−0.694308	+	1.20258i	0.276105	+	0.961127i	$0.410956\pi$
$331$	−12.6318	+	21.8790i	−0.694308	+	1.20258i	−0.970413	+	0.241450i	$0.922377\pi$
$332$	11.3855	−	19.7203i	0.624863	−	1.08229i
$333$	27.8377	+	12.1916i	1.52550	+	0.668094i
$334$	−20.3068	−	35.1724i	−1.11114	−	1.92455i
$335$	−0.828267	−	1.43460i	−0.0452531	−	0.0783806i
$336$	51.6651	−	0.0718280i	2.81856	−	0.00391854i
$337$	−6.81813	+	11.8093i	−0.371407	+	0.643296i	−0.989782	−	0.142587i	$-0.954458\pi$
$337$	−6.81813	+	11.8093i	−0.371407	+	0.643296i	0.618375	+	0.785883i	$0.287791\pi$
$338$	−21.7185			−1.18133
$339$	−8.43565	−	1.76622i	−0.458162	−	0.0959281i
$340$	9.30207			0.504476
$341$	−9.84362	−	17.0497i	−0.533062	−	0.923290i
$342$	−17.8946	+	13.1684i	−0.967627	+	0.712066i
$343$	15.0371	−	10.8114i	0.811925	−	0.583762i
$344$	34.9464	+	60.5290i	1.88419	+	3.26350i
$345$	0.920719	+	2.80459i	0.0495698	+	0.150994i
$346$	22.8381	+	39.5568i	1.22779	+	2.12659i
$347$	1.12021	+	1.94026i	0.0601362	+	0.104159i	0.894526	−	0.447016i	$-0.147513\pi$
$347$	1.12021	+	1.94026i	0.0601362	+	0.104159i	−0.834390	+	0.551175i	$0.814180\pi$
$348$	−36.1362	−	7.56606i	−1.93711	−	0.405584i
$349$	10.1506	+	17.5814i	0.543349	+	0.941108i	0.998709	+	0.0508008i	$0.0161774\pi$
$349$	10.1506	+	17.5814i	0.543349	+	0.941108i	−0.455360	+	0.890308i	$0.650489\pi$
$350$	2.17943	−	6.67001i	0.116495	−	0.356527i
$351$	−21.7610	+	9.92777i	−1.16151	+	0.529905i
$352$	36.7955	+	63.7317i	1.96121	+	3.39691i
$353$	18.9332			1.00771			0.503856	−	0.863788i	$-0.331914\pi$
$353$	18.9332			1.00771			0.503856	+	0.863788i	$0.331914\pi$
$354$	−2.76616	−	8.42599i	−0.147020	−	0.447836i
$355$	−2.79922			−0.148567
$356$	15.7540	−	27.2868i	0.834962	−	1.44620i
$357$	8.46767	−	0.0117723i	0.448157	−	0.000623054i
$358$	33.9981	+	58.8864i	1.79685	+	3.11224i
$359$	3.31533	+	5.74231i	0.174976	+	0.303068i	0.940153	−	0.340752i	$-0.110682\pi$
$359$	3.31533	+	5.74231i	0.174976	+	0.303068i	−0.765177	+	0.643820i	$0.777348\pi$
$360$	19.4440	−	14.3086i	1.02479	−	0.754130i
$361$	5.60137	−	9.70187i	0.294809	−	0.510625i
$362$	−27.4495	+	47.5440i	−1.44271	+	2.49885i
$363$	−9.40431	−	28.6464i	−0.493598	−	1.50355i
$364$	59.9908	−	12.6477i	3.14437	−	0.662921i
$365$	−1.45087	+	2.51299i	−0.0759422	+	0.131536i
$366$	−8.86798	+	9.90940i	−0.463537	+	0.517973i
$367$	8.21844			0.428999			0.214500	−	0.976724i	$-0.431188\pi$
$367$	8.21844			0.428999			0.214500	+	0.976724i	$0.431188\pi$
$368$	9.60712	−	16.6400i	0.500806	−	0.867421i
$369$	−1.06011	−	9.52777i	−0.0551872	−	0.495996i
$370$	−26.8670			−1.39675
$371$	2.87236	−	8.79069i	0.149125	−	0.456390i
$372$	31.5238	+	6.60032i	1.63443	+	0.342211i
$373$	−6.96069			−0.360411			−0.180205	−	0.983629i	$-0.557676\pi$
$373$	−6.96069			−0.360411			−0.180205	+	0.983629i	$0.557676\pi$
$374$	13.0601	+	22.6207i	0.675321	+	1.16969i
$375$	−0.540247	−	1.64564i	−0.0278982	−	0.0849805i
$376$	43.0923	−	74.6381i	2.22232	−	3.84917i
$377$	−19.4907			−1.00382
$378$	29.3370	−	21.6517i	1.50893	−	1.11364i
$379$	−22.9048			−1.17654			−0.588271	−	0.808664i	$-0.700191\pi$
$379$	−22.9048			−1.17654			−0.588271	+	0.808664i	$0.700191\pi$
$380$	7.02855	−	12.1738i	0.360557	−	0.624503i
$381$	−7.31002	−	22.2670i	−0.374504	−	1.14077i
$382$	−30.6935	−	53.1628i	−1.57042	−	2.72004i
$383$	−0.884802			−0.0452113			−0.0226056	−	0.999744i	$-0.507196\pi$
$383$	−0.884802			−0.0452113			−0.0226056	+	0.999744i	$0.507196\pi$
$384$	−16.4523	−	3.44472i	−0.839579	−	0.175788i
$385$	13.7982	−	2.90904i	0.703220	−	0.148258i
$386$	−11.3903			−0.579753
$387$	23.8678	+	10.4529i	1.21327	+	0.531351i
$388$	−22.0504	+	38.1925i	−1.11944	+	1.93893i
$389$	−7.86993			−0.399021			−0.199511	−	0.979896i	$-0.563935\pi$
$389$	−7.86993			−0.399021			−0.199511	+	0.979896i	$0.563935\pi$
$390$	14.1013	−	15.7573i	0.714045	−	0.797900i
$391$	1.57456	−	2.72722i	0.0796290	−	0.137921i
$392$	−51.5354	+	22.7410i	−2.60293	+	1.14859i
$393$	2.01686	+	6.14354i	0.101737	+	0.309901i
$394$	−19.5540	+	33.8686i	−0.985118	+	1.70627i
$395$	−4.32536	+	7.49174i	−0.217632	+	0.376950i
$396$	73.7327	+	32.2913i	3.70521	+	1.62270i
$397$	−0.143168	−	0.247974i	−0.00718539	−	0.0124455i	0.862410	−	0.506210i	$-0.168954\pi$
$397$	−0.143168	−	0.247974i	−0.00718539	−	0.0124455i	−0.869596	+	0.493764i	$0.835621\pi$
$398$	−29.5452	−	51.1738i	−1.48097	−	2.56511i
$399$	6.38268	−	11.0907i	0.319534	−	0.555230i
$400$	−5.63713	+	9.76380i	−0.281857	+	0.488190i
$401$	23.8677			1.19190			0.595948	−	0.803023i	$-0.296776\pi$
$401$	23.8677			1.19190			0.595948	+	0.803023i	$0.296776\pi$
$402$	2.37355	+	7.23004i	0.118382	+	0.360602i
$403$	17.0029			0.846975
$404$	−16.5285	−	28.6283i	−0.822326	−	1.42431i
$405$	2.67670	−	8.59275i	0.133006	−	0.426977i
$406$	29.0727	−	6.12932i	1.44285	−	0.304193i
$407$	−26.9961	−	46.7585i	−1.33814	−	2.31773i
$408$	−25.2080	−	5.27796i	−1.24798	−	0.261298i
$409$	−15.0603	−	26.0852i	−0.744684	−	1.28983i	−0.950342	−	0.311206i	$-0.899267\pi$
$409$	−15.0603	−	26.0852i	−0.744684	−	1.28983i	0.205658	−	0.978624i	$-0.434066\pi$
$410$	4.23757	+	7.33969i	0.209279	+	0.362481i
$411$	−1.25810	−	3.83228i	−0.0620574	−	0.189032i
$412$	2.94234	+	5.09628i	0.144959	+	0.251076i
$413$	3.41146	+	3.80145i	0.167867	+	0.187057i
$414$	−1.49951	−	13.4769i	−0.0736970	−	0.662353i
$415$	2.26167	+	3.91732i	0.111021	+	0.192294i
$416$	−63.5569			−3.11613
$417$	9.91891	+	2.07678i	0.485731	+	0.101700i
$418$	39.4723			1.93065
$419$	7.77995	−	13.4753i	0.380075	−	0.658310i	−0.610997	−	0.791633i	$-0.709231\pi$
$419$	7.77995	−	13.4753i	0.380075	−	0.658310i	0.991073	+	0.133323i	$0.0425647\pi$
$420$	−11.5069	+	19.9946i	−0.561478	+	0.975638i
$421$	−3.91870	−	6.78738i	−0.190986	−	0.330797i	0.754591	−	0.656195i	$-0.227835\pi$
$421$	−3.91870	−	6.78738i	−0.190986	−	0.330797i	−0.945577	+	0.325398i	$0.894502\pi$
$422$	28.1254	+	48.7147i	1.36912	+	2.37139i
$423$	−3.55303	−	31.9330i	−0.172754	−	1.55263i
$424$	−14.0641	+	24.3598i	−0.683014	+	1.18301i
$425$	−0.923899	+	1.60024i	−0.0448157	+	0.0776231i
$426$	12.5860	+	2.63520i	0.609793	+	0.127676i
$427$	2.37880	−	7.28018i	0.115118	−	0.352313i
$428$	34.1989	−	59.2342i	1.65306	−	2.86319i
$429$	41.5924	+	8.70846i	2.00810	+	0.420448i
$430$	−23.0355			−1.11087
$431$	12.7498	−	22.0832i	0.614135	−	1.06371i	−0.376401	−	0.926457i	$-0.622838\pi$
$431$	12.7498	−	22.0832i	0.614135	−	1.06371i	0.990536	−	0.137256i	$-0.0438282\pi$
$432$	−53.2981	+	24.3156i	−2.56431	+	1.16989i
$433$	−8.97110			−0.431124			−0.215562	−	0.976490i	$-0.569158\pi$
$433$	−8.97110			−0.431124			−0.215562	+	0.976490i	$0.569158\pi$
$434$	−25.3618	+	5.34697i	−1.21740	+	0.256663i
$435$	4.89071	−	5.46506i	0.234492	−	0.262030i
$436$	−19.4799			−0.932918
$437$	−2.37944	−	4.12132i	−0.113824	−	0.197149i
$438$	8.88922	−	9.93314i	0.424743	−	0.474624i
$439$	−9.51447	+	16.4795i	−0.454101	+	0.786526i	−0.998636	−	0.0522123i	$-0.983373\pi$
$439$	−9.51447	+	16.4795i	−0.454101	+	0.786526i	0.544535	+	0.838738i	$0.316706\pi$
$440$	−42.8901			−2.04470
$441$	−10.4494	+	18.2157i	−0.497590	+	0.867412i
$442$	−22.5587			−1.07301
$443$	7.87263	−	13.6358i	0.374040	−	0.647856i	−0.616143	−	0.787634i	$-0.711306\pi$
$443$	7.87263	−	13.6358i	0.374040	−	0.647856i	0.990183	+	0.139778i	$0.0446389\pi$
$444$	86.4537	+	18.1013i	4.10291	+	0.859051i
$445$	3.12944	+	5.42035i	0.148350	+	0.256949i
$446$	−56.1611			−2.65931
$447$	−1.63983	−	4.99507i	−0.0775613	−	0.236259i
$448$	36.4279	−	7.68000i	1.72106	−	0.362846i
$449$	21.6017			1.01945			0.509724	−	0.860338i	$-0.329747\pi$
$449$	21.6017			1.01945			0.509724	+	0.860338i	$0.329747\pi$
$450$	0.879863	+	7.90779i	0.0414772	+	0.372777i
$451$	−8.51584	+	14.7499i	−0.400995	+	0.694544i
$452$	−25.0495			−1.17823
$453$	−1.77146	−	5.39603i	−0.0832304	−	0.253528i
$454$	−13.7361	+	23.7915i	−0.644665	+	1.11659i
$455$	−3.78260	+	11.5764i	−0.177331	+	0.542712i
$456$	−25.9543	+	29.0023i	−1.21542	+	1.35816i
$457$	7.83093	−	13.5636i	0.366316	−	0.634477i	−0.622671	−	0.782484i	$-0.713952\pi$
$457$	7.83093	−	13.5636i	0.366316	−	0.634477i	0.988986	+	0.148007i	$0.0472857\pi$
$458$	−21.8367	+	37.8223i	−1.02036	+	1.76732i
$459$	−8.73531	+	3.98522i	−0.407730	+	0.186014i
$460$	4.28973	+	7.43003i	0.200010	+	0.346427i
$461$	3.47952	+	6.02671i	0.162057	+	0.280692i	0.935606	−	0.353045i	$-0.114854\pi$
$461$	3.47952	+	6.02671i	0.162057	+	0.280692i	−0.773549	+	0.633737i	$0.781520\pi$
$462$	−64.7785	+	0.0900590i	−3.01377	+	0.00418992i
$463$	−10.7588	+	18.6347i	−0.500002	+	0.866029i	0.499998	+	0.866027i	$0.333334\pi$
$463$	−10.7588	+	18.6347i	−0.500002	+	0.866029i	−1.00000		2.55855e-6i	$0.999999\pi$
$464$	−47.7378			−2.21617
$465$	−4.26646	+	4.76749i	−0.197852	+	0.221087i
$466$	−56.4398			−2.61452
$467$	−4.46931	−	7.74107i	−0.206815	−	0.358214i	0.743895	−	0.668297i	$-0.232976\pi$
$467$	−4.46931	−	7.74107i	−0.206815	−	0.358214i	−0.950709	+	0.310083i	$0.899643\pi$
$468$	−55.9918	+	41.2037i	−2.58822	+	1.90464i
$469$	−2.92726	−	3.26189i	−0.135168	−	0.150620i
$470$	14.2025	+	24.5995i	0.655113	+	1.13469i
$471$	−22.1374	+	24.7371i	−1.02004	+	1.13983i
$472$	−7.76767	−	13.4540i	−0.357536	−	0.619271i
$473$	−23.1461	−	40.0903i	−1.06426	−	1.84335i
$474$	26.5006	−	29.6127i	1.21721	−	1.36016i
$475$	1.39618	+	2.41825i	0.0640610	+	0.110957i
$476$	24.0816	−	5.07707i	1.10378	−	0.232707i
$477$	1.15961	+	10.4220i	0.0530949	+	0.477191i
$478$	−27.4601	−	47.5623i	−1.25600	−	2.17545i
$479$	8.39443			0.383551			0.191776	−	0.981439i	$-0.438575\pi$
$479$	8.39443			0.383551			0.191776	+	0.981439i	$0.438575\pi$
$480$	15.9480	−	17.8209i	0.727924	−	0.813409i
$481$	46.6303			2.12616
$482$	8.96772	−	15.5325i	0.408468	−	0.707488i
$483$	3.91434	+	6.75812i	0.178109	+	0.307505i
$484$	−43.8157	−	75.8910i	−1.99162	−	3.44959i
$485$	−4.38018	−	7.58670i	−0.198894	−	0.344494i
$486$	−20.1243	+	36.1152i	−0.912858	+	1.63822i
$487$	−16.5245	+	28.6212i	−0.748795	+	1.29695i	0.199605	+	0.979876i	$0.436034\pi$
$487$	−16.5245	+	28.6212i	−0.748795	+	1.29695i	−0.948401	+	0.317075i	$0.897299\pi$
$488$	−11.6475	+	20.1740i	−0.527256	+	0.913234i
$489$	11.8583	−	13.2509i	0.536253	−	0.599228i
$490$	2.00170	−	18.4571i	0.0904277	−	0.833808i
$491$	−11.6636	+	20.2020i	−0.526371	+	0.911702i	0.473156	+	0.880978i	$0.343115\pi$
$491$	−11.6636	+	20.2020i	−0.526371	+	0.911702i	−0.999528	+	0.0307237i	$0.990219\pi$
$492$	−8.69078	−	26.4729i	−0.391810	−	1.19349i
$493$	−7.82399			−0.352375
$494$	−17.0451	+	29.5230i	−0.766896	+	1.32830i
$495$	−12.8784	+	9.47705i	−0.578840	+	0.425962i
$496$	41.6444			1.86989
$497$	−7.24675	+	1.52782i	−0.325061	+	0.0685319i
$498$	−6.48121	−	19.7424i	−0.290430	−	0.884677i
$499$	−7.78357			−0.348440			−0.174220	−	0.984707i	$-0.555740\pi$
$499$	−7.78357			−0.348440			−0.174220	+	0.984707i	$0.555740\pi$
$500$	−2.51707	−	4.35969i	−0.112567	−	0.194971i
$501$	−25.9603	−	5.43547i	−1.15982	−	0.242839i
$502$	22.6868	−	39.2947i	1.01256	−	1.75381i
$503$	−39.0069			−1.73923			−0.869615	−	0.493731i	$-0.835633\pi$
$503$	−39.0069			−1.73923			−0.869615	+	0.493731i	$0.835633\pi$
$504$	42.5278	−	47.6553i	1.89434	−	2.12273i
$505$	6.56659			0.292209
$506$	−12.0455	+	20.8635i	−0.535490	+	0.927495i
$507$	−9.45852	+	10.5693i	−0.420068	+	0.469399i
$508$	−34.0582	−	58.9905i	−1.51109	−	2.61728i
$509$	−15.1895			−0.673262			−0.336631	−	0.941637i	$-0.609288\pi$
$509$	−15.1895			−0.673262			−0.336631	+	0.941637i	$0.609288\pi$
$510$	5.66055	−	6.32530i	0.250653	−	0.280089i
$511$	−2.38450	+	7.29762i	−0.105484	+	0.322828i
$512$	25.7837			1.13949
$513$	−1.38478	+	14.4433i	−0.0611394	+	0.637686i
$514$	−26.7212	+	46.2825i	−1.17862	+	2.04143i
$515$	−1.16895			−0.0515103
$516$	74.1244	+	15.5199i	3.26314	+	0.683224i
$517$	−28.5414	+	49.4352i	−1.25525	+	2.17416i
$518$	−69.5545	+	14.6640i	−3.05605	+	0.644300i
$519$	29.1964	+	6.11302i	1.28158	+	0.268332i
$520$	18.5210	−	32.0793i	0.812200	−	1.40677i
$521$	6.23269	−	10.7953i	0.273059	−	0.472952i	−0.696584	−	0.717475i	$-0.745298\pi$
$521$	6.23269	−	10.7953i	0.273059	−	0.472952i	0.969644	+	0.244522i	$0.0786312\pi$
$522$	−27.1347	+	19.9681i	−1.18765	+	0.873979i
$523$	18.6955	+	32.3816i	0.817499	+	1.41595i	0.907519	+	0.420010i	$0.137973\pi$
$523$	18.6955	+	32.3816i	0.817499	+	1.41595i	−0.0900202	+	0.995940i	$0.528693\pi$
$524$	9.39677	+	16.2757i	0.410500	+	0.711007i
$525$	−2.29680	−	3.96544i	−0.100241	−	0.173066i
$526$	23.2985	−	40.3541i	1.01586	−	1.75952i
$527$	6.82533			0.297316
$528$	101.870	+	21.3292i	4.43334	+	0.928236i
$529$	−20.0955			−0.873718
$530$	−4.63529	−	8.02856i	−0.201344	−	0.348739i
$531$	−5.30517	−	2.32341i	−0.230225	−	0.100827i
$532$	11.5513	−	35.3522i	0.500814	−	1.53271i
$533$	−7.35471	−	12.7387i	−0.318568	−	0.551776i
$534$	−8.96796	−	27.3172i	−0.388082	−	1.18213i
$535$	6.79339	+	11.7665i	0.293704	+	0.508710i
$536$	6.66517	+	11.5444i	0.287891	+	0.498642i
$537$	43.4633	+	9.10017i	1.87558	+	0.392701i
$538$	−3.75537	−	6.50449i	−0.161905	−	0.280428i
$539$	34.1335	−	15.0621i	1.47024	−	0.648769i
$540$	2.49652	−	26.0387i	0.107433	−	1.12053i
$541$	−11.9362	−	20.6741i	−0.513177	−	0.888849i	−0.999883	−	0.0152833i	$-0.995135\pi$
$541$	−11.9362	−	20.6741i	−0.513177	−	0.888849i	0.486706	−	0.873566i	$-0.338198\pi$
$542$	57.3165			2.46196
$543$	11.1828	+	34.0639i	0.479901	+	1.46182i
$544$	−25.5131			−1.09386
$545$	1.93478	−	3.35114i	0.0828769	−	0.143547i
$546$	27.9056	−	48.4895i	1.19425	−	2.07516i
$547$	17.3201	+	29.9993i	0.740554	+	1.28268i	0.952243	+	0.305340i	$0.0987701\pi$
$547$	17.3201	+	29.9993i	0.740554	+	1.28268i	−0.211690	+	0.977337i	$0.567897\pi$
$548$	−5.86162	−	10.1526i	−0.250396	−	0.433698i
$549$	0.960353	+	8.63118i	0.0409869	+	0.368370i
$550$	7.06792	−	12.2420i	0.301377	−	0.522000i
$551$	−5.91173	+	10.2394i	−0.251848	+	0.436214i
$552$	−7.40913	−	22.5689i	−0.315354	−	0.960597i
$553$	−7.10868	+	21.7557i	−0.302292	+	0.925147i
$554$	9.44692	−	16.3625i	0.401361	−	0.695178i
$555$	−11.7007	+	13.0748i	−0.496668	+	0.554995i
$556$	29.4540			1.24913
$557$	−22.8043	+	39.4982i	−0.966249	+	1.67359i	−0.260029	+	0.965601i	$0.583732\pi$
$557$	−22.8043	+	39.4982i	−0.966249	+	1.67359i	−0.706221	+	0.707992i	$0.749601\pi$
$558$	23.6711	−	17.4193i	1.00208	−	0.737419i
$559$	39.9803			1.69099
$560$	−9.26456	+	28.3537i	−0.391499	+	1.19816i
$561$	16.6961	+	3.49576i	0.704909	+	0.147591i
$562$	0.491714			0.0207417
$563$	−1.95050	−	3.37837i	−0.0822039	−	0.142381i	0.821992	−	0.569498i	$-0.192863\pi$
$563$	−1.95050	−	3.37837i	−0.0822039	−	0.142381i	−0.904196	+	0.427117i	$0.859529\pi$
$564$	−29.1277	−	88.7257i	−1.22650	−	3.73603i
$565$	2.48797	−	4.30929i	0.104670	−	0.181293i
$566$	−86.3705			−3.63042
$567$	2.23962	−	23.7062i	0.0940554	−	0.995567i
$568$	22.5257			0.945158
$569$	−13.4476	+	23.2920i	−0.563754	+	0.976450i	0.433411	+	0.901196i	$0.357310\pi$
$569$	−13.4476	+	23.2920i	−0.563754	+	0.976450i	−0.997164	+	0.0752535i	$0.976023\pi$
$570$	−4.00100	−	12.1874i	−0.167583	−	0.510474i
$571$	15.7018	+	27.1963i	0.657099	+	1.13813i	0.981363	+	0.192162i	$0.0615499\pi$
$571$	15.7018	+	27.1963i	0.657099	+	1.13813i	−0.324265	+	0.945966i	$0.605117\pi$
$572$	123.508			5.16413
$573$	−39.2388	−	8.21566i	−1.63922	−	0.343214i
$574$	14.9764	+	16.6884i	0.625103	+	0.696562i
$575$	−1.70426			−0.0710724
$576$	−33.9996	+	25.0199i	−1.41665	+	1.04250i
$577$	19.5367	−	33.8386i	0.813324	−	1.40872i	−0.0972010	−	0.995265i	$-0.530989\pi$
$577$	19.5367	−	33.8386i	0.813324	−	1.40872i	0.910525	−	0.413454i	$-0.135678\pi$
$578$	36.0318			1.49872
$579$	−4.96055	+	5.54309i	−0.206153	+	0.230363i
$580$	10.6578	−	18.4599i	0.442543	−	0.766506i
$581$	7.99318	+	8.90692i	0.331613	+	0.369521i
$582$	12.5522	+	38.2351i	0.520305	+	1.58490i
$583$	9.31511	−	16.1342i	0.385792	−	0.668212i
$584$	11.6754	−	20.2223i	0.483130	−	0.836806i
$585$	−1.52709	−	13.7247i	−0.0631373	−	0.567447i
$586$	−0.173787	−	0.301007i	−0.00717906	−	0.0124345i
$587$	15.0916	+	26.1394i	0.622897	+	1.07889i	0.988944	+	0.148293i	$0.0473777\pi$
$587$	15.0916	+	26.1394i	0.622897	+	1.07889i	−0.366047	+	0.930596i	$0.619289\pi$
$588$	−18.8764	+	58.0434i	−0.778450	+	2.39367i
$589$	5.15715	−	8.93244i	0.212497	−	0.368055i
$590$	5.12019			0.210795
$591$	7.96623	+	24.2659i	0.327687	+	0.998164i
$592$	114.210			4.69398
$593$	17.4563	+	30.2353i	0.716846	+	1.24161i	0.962243	+	0.272191i	$0.0877483\pi$
$593$	17.4563	+	30.2353i	0.716846	+	1.24161i	−0.245397	+	0.969423i	$0.578918\pi$
$594$	66.8260	−	30.4873i	2.74190	−	1.25091i
$595$	−1.51842	+	4.64703i	−0.0622491	+	0.190510i
$596$	−7.64015	−	13.2331i	−0.312953	−	0.542050i
$597$	−37.7707	−	7.90829i	−1.54585	−	0.323665i
$598$	−10.4031	−	18.0188i	−0.425416	−	0.736842i
$599$	−15.1124	−	26.1754i	−0.617475	−	1.06950i	−0.989945	−	0.141453i	$-0.954823\pi$
$599$	−15.1124	−	26.1754i	−0.617475	−	1.06950i	0.372470	−	0.928044i	$-0.378511\pi$
$600$	4.34743	+	13.2427i	0.177483	+	0.540630i
$601$	2.96737	+	5.13964i	0.121042	+	0.209650i	0.920179	−	0.391499i	$-0.128043\pi$
$601$	2.96737	+	5.13964i	0.121042	+	0.209650i	−0.799137	+	0.601149i	$0.794710\pi$
$602$	−59.6353	+	12.5728i	−2.43055	+	0.512428i
$603$	4.55218	+	1.99363i	0.185379	+	0.0811871i
$604$	−8.25342	−	14.2954i	−0.335827	−	0.581670i
$605$	17.4074			0.707713
$606$	−29.5249	−	6.18182i	−1.19937	−	0.251119i
$607$	−9.34192			−0.379177			−0.189588	−	0.981864i	$-0.560715\pi$
$607$	−9.34192			−0.379177			−0.189588	+	0.981864i	$0.560715\pi$
$608$	−19.2774	+	33.3895i	−0.781803	+	1.35412i
$609$	9.67846	−	16.8175i	0.392191	−	0.681481i
$610$	−3.83881	−	6.64901i	−0.155429	−	0.269211i
$611$	−24.6498	−	42.6947i	−0.997225	−	1.72724i
$612$	−22.4763	+	16.5400i	−0.908550	+	0.668592i
$613$	8.04187	−	13.9289i	0.324808	−	0.562584i	−0.656665	−	0.754182i	$-0.728034\pi$
$613$	8.04187	−	13.9289i	0.324808	−	0.562584i	0.981473	+	0.191598i	$0.0613670\pi$
$614$	25.1826	−	43.6175i	1.01629	−	1.76026i
$615$	5.41733	+	1.13426i	0.218448	+	0.0457378i
$616$	−111.036	+	23.4094i	−4.47375	+	0.943191i
$617$	−19.2709	+	33.3781i	−0.775816	+	1.34375i	0.158519	+	0.987356i	$0.449328\pi$
$617$	−19.2709	+	33.3781i	−0.775816	+	1.34375i	−0.934335	+	0.356397i	$0.884005\pi$
$618$	5.25590	+	1.10046i	0.211423	+	0.0442669i
$619$	−20.8325			−0.837328			−0.418664	−	0.908141i	$-0.637502\pi$
$619$	−20.8325			−0.837328			−0.418664	+	0.908141i	$0.637502\pi$
$620$	−9.29745	+	16.1037i	−0.373395	+	0.646738i
$621$	−7.21156	−	5.13952i	−0.289390	−	0.206242i
$622$	−4.81039			−0.192879
$623$	11.0600	+	12.3244i	0.443111	+	0.493766i
$624$	−59.9433	+	66.9828i	−2.39965	+	2.68146i
$625$	1.00000			0.0400000
$626$	−16.6478	−	28.8348i	−0.665379	−	1.15247i
$627$	17.1904	−	19.2091i	0.686517	−	0.767139i
$628$	−48.2417	+	83.5571i	−1.92505	+	3.33429i
$629$	18.7184			0.746352
$630$	6.59389	+	19.9918i	0.262707	+	0.796492i
$631$	−13.3824			−0.532745			−0.266372	−	0.963870i	$-0.585825\pi$
$631$	−13.3824			−0.532745			−0.266372	+	0.963870i	$0.585825\pi$
$632$	34.8067	−	60.2869i	1.38454	−	2.39809i
$633$	35.9557	+	7.52826i	1.42911	+	0.299222i
$634$	−0.696341	−	1.20610i	−0.0276552	−	0.0479003i
$635$	13.5309			0.536957
$636$	9.50646	+	28.9576i	0.376956	+	1.14824i
$637$	−3.47415	+	32.0341i	−0.137651	+	1.26924i
$638$	59.8543			2.36965
$639$	6.76368	−	4.97731i	0.267567	−	0.196899i
$640$	4.85236	−	8.40454i	0.191807	−	0.332219i
$641$	−18.1564			−0.717135			−0.358568	−	0.933504i	$-0.616735\pi$
$641$	−18.1564			−0.717135			−0.358568	+	0.933504i	$0.616735\pi$
$642$	−19.4677	−	59.3003i	−0.768328	−	2.34040i
$643$	−5.12873	+	8.88322i	−0.202257	+	0.350320i	−0.949255	−	0.314506i	$-0.898161\pi$
$643$	−5.12873	+	8.88322i	−0.202257	+	0.350320i	0.746998	+	0.664826i	$0.231494\pi$
$644$	15.1607	+	16.8938i	0.597417	+	0.665711i
$645$	−10.0321	+	11.2102i	−0.395012	+	0.441401i
$646$	−6.84228	+	11.8512i	−0.269206	+	0.466278i
$647$	−15.5836	+	26.9916i	−0.612654	+	1.06115i	0.378137	+	0.925750i	$0.376565\pi$
$647$	−15.5836	+	26.9916i	−0.612654	+	1.06115i	−0.990791	+	0.135399i	$0.956768\pi$
$648$	−21.5397	+	69.1469i	−0.846159	+	2.71635i
$649$	5.14477	+	8.91101i	0.201950	+	0.349788i
$650$	6.10421	+	10.5728i	0.239427	+	0.414699i
$651$	−8.44308	+	14.6709i	−0.330911	+	0.574998i
$652$	25.8417	−	44.7591i	1.01204	−	1.75290i
$653$	8.94425			0.350016			0.175008	−	0.984567i	$-0.444005\pi$
$653$	8.94425			0.350016			0.175008	+	0.984567i	$0.444005\pi$
$654$	−11.8540	+	13.2461i	−0.463529	+	0.517964i
$655$	−3.73322			−0.145869
$656$	−18.0136	−	31.2004i	−0.703312	−	1.21817i
$657$	−0.962653	−	8.65186i	−0.0375567	−	0.337541i
$658$	50.1944	+	55.9324i	1.95678	+	2.18047i
$659$	−9.44019	−	16.3509i	−0.367737	−	0.636940i	0.621474	−	0.783435i	$-0.286534\pi$
$659$	−9.44019	−	16.3509i	−0.367737	−	0.636940i	−0.989211	+	0.146495i	$0.953201\pi$
$660$	−30.9913	+	34.6308i	−1.20633	+	1.34800i
$661$	1.73774	+	3.00986i	0.0675904	+	0.117070i	0.897840	−	0.440322i	$-0.145136\pi$
$661$	1.73774	+	3.00986i	0.0675904	+	0.117070i	−0.830250	+	0.557392i	$0.811802\pi$
$662$	33.5021	+	58.0273i	1.30210	+	2.25529i
$663$	−9.82442	+	10.9782i	−0.381549	+	0.426357i
$664$	−18.1999	−	31.5232i	−0.706294	−	1.22334i
$665$	4.93436	+	5.49844i	0.191346	+	0.213220i
$666$	64.9179	−	47.7724i	2.51552	−	1.85114i
$667$	−3.60810	−	6.24942i	−0.139706	−	0.241978i
$668$	−77.0887			−2.98265
$669$	−24.4584	+	27.3307i	−0.945618	+	1.05667i
$670$	−4.39345			−0.169734
$671$	7.71449	−	13.3619i	0.297814	−	0.515830i
$672$	31.5603	−	54.8399i	1.21746	−	2.11550i
$673$	−2.80825	−	4.86403i	−0.108250	−	0.187495i	0.806811	−	0.590809i	$-0.201191\pi$
$673$	−2.80825	−	4.86403i	−0.108250	−	0.187495i	−0.915061	+	0.403314i	$0.867858\pi$
$674$	18.0830	+	31.3207i	0.696531	+	1.20643i
$675$	4.23150	+	3.01569i	0.162871	+	0.116074i
$676$	−20.6120	+	35.7010i	−0.792769	+	1.37312i
$677$	−8.41767	+	14.5798i	−0.323517	+	0.560348i	−0.981211	−	0.192937i	$-0.938199\pi$
$677$	−8.41767	+	14.5798i	−0.323517	+	0.560348i	0.657694	+	0.753285i	$0.271532\pi$
$678$	−15.2433	+	17.0334i	−0.585415	+	0.654164i
$679$	−15.4804	−	17.2501i	−0.594084	−	0.661996i
$680$	7.43473	−	12.8773i	0.285109	−	0.493823i
$681$	5.59601	+	17.0460i	0.214440	+	0.653203i
$682$	−52.2144			−1.99939
$683$	19.4914	−	33.7601i	0.745819	−	1.29180i	−0.203992	−	0.978972i	$-0.565392\pi$
$683$	19.4914	−	33.7601i	0.745819	−	1.29180i	0.949811	−	0.312824i	$-0.101275\pi$
$684$	4.66343	+	41.9127i	0.178311	+	1.60257i
$685$	2.32875			0.0889769
$686$	−4.89181	−	48.8751i	−0.186770	−	1.86606i
$687$	8.89619	+	27.0986i	0.339411	+	1.03388i
$688$	97.9220			3.73324
$689$	8.04500	+	13.9343i	0.306490	+	0.530856i
$690$	7.66274	+	1.60440i	0.291716	+	0.0610783i
$691$	4.61930	−	8.00086i	0.175726	−	0.304367i	−0.764686	−	0.644403i	$-0.777106\pi$
$691$	4.61930	−	8.00086i	0.175726	−	0.304367i	0.940412	+	0.340036i	$0.110439\pi$
$692$	86.6982			3.29577
$693$	−28.1675	+	31.5636i	−1.06999	+	1.19900i
$694$	5.94204			0.225557
$695$	−2.92543	+	5.06699i	−0.110968	+	0.192202i
$696$	−39.3562	+	43.9780i	−1.49179	+	1.66698i
$697$	−2.95234	−	5.11360i	−0.111828	−	0.193691i
$698$	53.8427			2.03798
$699$	−24.5798	+	27.4664i	−0.929694	+	1.03887i
$700$	−8.89581	−	9.91273i	−0.336230	−	0.374666i
$701$	−11.0745			−0.418277			−0.209138	−	0.977886i	$-0.567066\pi$
$701$	−11.0745			−0.418277			−0.209138	+	0.977886i	$0.567066\pi$
$702$	−6.05437	+	63.1472i	−0.228507	+	2.38334i
$703$	14.1434	−	24.4972i	0.533430	−	0.923928i
$704$	74.9971			2.82656
$705$	18.1566	+	3.80155i	0.683816	+	0.143175i
$706$	25.1072	−	43.4870i	0.944923	−	1.63666i
$707$	16.9999	−	3.58404i	0.639345	−	0.134792i
$708$	−16.4759	−	3.44966i	−0.619202	−	0.129646i
$709$	23.3900	−	40.5126i	0.878428	−	1.52148i	0.0253632	−	0.999678i	$-0.491926\pi$
$709$	23.3900	−	40.5126i	0.878428	−	1.52148i	0.853065	−	0.521804i	$-0.174741\pi$
$710$	−3.71204	+	6.42945i	−0.139311	+	0.241293i
$711$	−2.86987	−	25.7930i	−0.107628	−	0.967312i
$712$	−25.1830	−	43.6182i	−0.943772	−	1.63466i
$713$	3.14756	+	5.45173i	0.117877	+	0.204169i
$714$	11.2019	−	19.4647i	0.419221	−	0.728449i
$715$	−12.2670	+	21.2472i	−0.458762	+	0.794598i
$716$	129.064			4.82333
$717$	−35.1051	−	7.35017i	−1.31102	−	0.274497i
$718$	17.5858			0.656296
$719$	−13.6176	−	23.5865i	−0.507853	−	0.879626i	−0.999959	−	0.00909117i	$-0.997106\pi$
$719$	−13.6176	−	23.5865i	−0.507853	−	0.879626i	0.492106	−	0.870535i	$-0.336227\pi$
$720$	−3.74023	−	33.6153i	−0.139390	−	1.25277i
$721$	−3.02624	+	0.638015i	−0.112703	+	0.0237609i
$722$	−14.8559	−	25.7312i	−0.552881	−	0.957618i
$723$	−3.65341	−	11.1286i	−0.135872	−	0.413878i
$724$	52.1020	+	90.2433i	1.93636	+	3.35387i
$725$	2.11711	+	3.66695i	0.0786276	+	0.136187i
$726$	−78.2680	−	16.3874i	−2.90480	−	0.608195i
$727$	−11.4509	−	19.8335i	−0.424691	−	0.735586i	0.571701	−	0.820462i	$-0.306284\pi$
$727$	−11.4509	−	19.8335i	−0.424691	−	0.735586i	−0.996391	+	0.0848765i	$0.972950\pi$
$728$	30.4391	−	93.1571i	1.12815	−	3.45263i
$729$	8.81118	+	25.5218i	0.326340	+	0.945252i
$730$	3.84800	+	6.66493i	0.142421	+	0.246680i
$731$	16.0490			0.593592
$732$	7.87296	+	23.9818i	0.290993	+	0.886391i
$733$	−5.03877			−0.186111			−0.0930556	−	0.995661i	$-0.529663\pi$
$733$	−5.03877			−0.186111			−0.0930556	+	0.995661i	$0.529663\pi$
$734$	10.8985	−	18.8767i	0.402269	−	0.696751i
$735$	−8.11039	−	9.01230i	−0.299156	−	0.332424i
$736$	−11.7656	−	20.3786i	−0.433685	−	0.751165i
$737$	−4.41455	−	7.64622i	−0.162612	−	0.281652i
$738$	−23.2898	−	10.1998i	−0.857311	−	0.375460i
$739$	−0.624198	+	1.08114i	−0.0229615	+	0.0397705i	−0.877278	−	0.479983i	$-0.840643\pi$
$739$	−0.624198	+	1.08114i	−0.0229615	+	0.0397705i	0.854316	+	0.519753i	$0.173976\pi$
$740$	−25.4982	+	44.1642i	−0.937332	+	1.62351i
$741$	6.94411	+	21.1524i	0.255098	+	0.777053i
$742$	−16.3820	−	18.2547i	−0.601403	−	0.670153i
$743$	16.1691	−	28.0058i	0.593189	−	1.02743i	−0.400611	−	0.916248i	$-0.631202\pi$
$743$	16.1691	−	28.0058i	0.593189	−	1.02743i	0.993800	−	0.111185i	$-0.0354645\pi$
$744$	34.3327	−	38.3646i	1.25870	−	1.40651i
$745$	3.03534			0.111206
$746$	−9.23055	+	15.9878i	−0.337954	+	0.585354i
$747$	−12.4302	−	5.44382i	−0.454797	−	0.199179i
$748$	49.5788			1.81278
$749$	24.0092	+	26.7538i	0.877276	+	0.977562i
$750$	−4.49624	−	0.941405i	−0.164179	−	0.0343752i
$751$	18.4981			0.675006			0.337503	−	0.941324i	$-0.390418\pi$
$751$	18.4981			0.675006			0.337503	+	0.941324i	$0.390418\pi$
$752$	−60.3737	−	104.570i	−2.20160	−	3.81329i
$753$	−9.24251	−	28.1535i	−0.336816	−	1.02597i
$754$	−25.8466	+	44.7676i	−0.941278	+	1.63034i
$755$	3.27898			0.119334
$756$	−7.74885	−	68.7728i	−0.281823	−	2.50124i
$757$	−35.5818			−1.29324			−0.646620	−	0.762812i	$-0.723818\pi$
$757$	−35.5818			−1.29324			−0.646620	+	0.762812i	$0.723818\pi$
$758$	−30.3740	+	52.6093i	−1.10323	+	1.91086i
$759$	4.90730	+	14.9481i	0.178124	+	0.542582i
$760$	−11.2352	−	19.4600i	−0.407544	−	0.705887i
$761$	35.9725			1.30400			0.652001	−	0.758218i	$-0.273930\pi$
$761$	35.9725			1.30400			0.652001	+	0.758218i	$0.273930\pi$
$762$	−60.8382	−	12.7381i	−2.20393	−	0.461451i
$763$	3.17979	−	9.73157i	0.115116	−	0.352306i
$764$	−116.519			−4.21551
$765$	−0.613006	−	5.50940i	−0.0221633	−	0.199193i
$766$	−1.17333	+	2.03227i	−0.0423943	+	0.0734291i
$767$	−8.88657			−0.320876
$768$	2.77601	−	3.10202i	0.100171	−	0.111934i
$769$	22.7889	−	39.4715i	0.821788	−	1.42338i	−0.0825609	−	0.996586i	$-0.526310\pi$
$769$	22.7889	−	39.4715i	0.821788	−	1.42338i	0.904349	−	0.426793i	$-0.140357\pi$
$770$	11.6160	−	35.5502i	0.418613	−	1.28114i
$771$	10.8861	+	33.1601i	0.392054	+	1.19423i
$772$	−10.8100	+	18.7235i	−0.389061	+	0.673873i
$773$	20.8811	−	36.1671i	0.751040	−	1.30084i	−0.196279	−	0.980548i	$-0.562886\pi$
$773$	20.8811	−	36.1671i	0.751040	−	1.30084i	0.947319	−	0.320291i	$-0.103781\pi$
$774$	55.6599	−	40.9595i	2.00065	−	1.47226i
$775$	−1.84688	−	3.19889i	−0.0663419	−	0.114908i
$776$	35.2479	+	61.0511i	1.26532	+	2.19161i
$777$	−23.1551	+	40.2349i	−0.830684	+	1.44342i
$778$	−10.4363	+	18.0762i	−0.374159	+	0.648063i
$779$	−8.92303			−0.319701
$780$	−12.5190	−	38.1342i	−0.448254	−	1.36542i
$781$	−14.9195			−0.533861
$782$	−4.17604	−	7.23312i	−0.149335	−	0.258656i
$783$	−2.09983	+	21.9012i	−0.0750417	+	0.782687i
$784$	−8.50907	+	78.4598i	−0.303895	+	2.80213i
$785$	−9.58292	−	16.5981i	−0.342029	−	0.592412i
$786$	16.7855	+	3.51447i	0.598717	+	0.125357i
$787$	11.9536	+	20.7042i	0.426099	+	0.738025i	0.996522	−	0.0833257i	$-0.0265542\pi$
$787$	11.9536	+	20.7042i	0.426099	+	0.738025i	−0.570423	+	0.821351i	$0.693221\pi$
$788$	37.1155	+	64.2860i	1.32219	+	2.29009i
$789$	−9.49169	−	28.9126i	−0.337913	−	1.02931i
$790$	11.4717	+	19.8695i	0.408144	+	0.706927i
$791$	4.08895	−	12.5140i	0.145386	−	0.444946i
$792$	103.634	−	76.2630i	3.68247	−	2.70989i
$793$	6.66262	+	11.5400i	0.236597	+	0.409797i
$794$	−0.759418			−0.0269508
$795$	−5.92578	−	1.24072i	−0.210166	−	0.0440037i
$796$	−112.160			−3.97539
$797$	−18.7732	+	32.5161i	−0.664980	+	1.15178i	0.314310	+	0.949320i	$0.398227\pi$
$797$	−18.7732	+	32.5161i	−0.664980	+	1.15178i	−0.979291	+	0.202459i	$0.935107\pi$
$798$	−17.0098	−	29.3675i	−0.602141	−	1.03960i
$799$	−9.89496	−	17.1386i	−0.350059	−	0.606319i
$800$	6.90365	+	11.9575i	0.244081	+	0.422760i
$801$	−17.1995	−	7.53254i	−0.607714	−	0.266149i
$802$	31.6509	−	54.8209i	1.11763	−	1.93579i
$803$	−7.73296	+	13.3939i	−0.272890	+	0.472660i
$804$	14.1374	+	2.96003i	0.498588	+	0.104392i
$805$	−4.41205	+	0.930182i	−0.155504	+	0.0327846i
$806$	22.5475	−	39.0534i	0.794202	−	1.37560i
$807$	−4.80088	−	1.00519i	−0.168999	−	0.0353844i
$808$	−52.8421			−1.85898
$809$	−6.33279	+	10.9687i	−0.222649	+	0.385639i	−0.955612	−	0.294630i	$-0.904804\pi$
$809$	−6.33279	+	10.9687i	−0.222649	+	0.385639i	0.732963	+	0.680269i	$0.238137\pi$
$810$	−16.1868	−	17.5428i	−0.568748	−	0.616392i
$811$	−11.6090			−0.407649			−0.203824	−	0.979007i	$-0.565337\pi$
$811$	−11.6090			−0.407649			−0.203824	+	0.979007i	$0.565337\pi$
$812$	17.5160	−	53.6068i	0.614692	−	1.88123i
$813$	24.9616	−	27.8930i	0.875442	−	0.978251i
$814$	−143.198			−5.01907
$815$	5.13329	+	8.89111i	0.179811	+	0.311442i
$816$	−24.0625	+	26.8883i	−0.842357	+	0.941280i
$817$	12.1264	−	21.0036i	0.424250	−	0.734823i
$818$	−79.8857			−2.79314
$819$	−11.4443	−	34.6977i	−0.399897	−	1.21243i
$820$	16.0867			0.561771
$821$	−11.3993	+	19.7441i	−0.397838	+	0.689075i	−0.993459	−	0.114190i	$-0.963573\pi$
$821$	−11.3993	+	19.7441i	−0.397838	+	0.689075i	0.595621	+	0.803266i	$0.296906\pi$
$822$	−10.4706	−	2.19229i	−0.365204	−	0.0764650i
$823$	1.30273	+	2.25639i	0.0454103	+	0.0786529i	0.887837	−	0.460158i	$-0.152207\pi$
$823$	1.30273	+	2.25639i	0.0454103	+	0.0786529i	−0.842427	+	0.538811i	$0.818874\pi$
$824$	9.40671			0.327698
$825$	−2.87944	−	8.77104i	−0.100249	−	0.305368i
$826$	13.2554	−	2.79460i	0.461213	−	0.0972364i
$827$	24.3866			0.848004			0.424002	−	0.905661i	$-0.360625\pi$
$827$	24.3866			0.848004			0.424002	+	0.905661i	$0.360625\pi$
$828$	−23.5765	−	10.3254i	−0.819340	−	0.358831i
$829$	3.13403	−	5.42830i	0.108849	−	0.188533i	−0.806455	−	0.591295i	$-0.798617\pi$
$829$	3.13403	−	5.42830i	0.108849	−	0.188533i	0.915304	+	0.402763i	$0.131950\pi$
$830$	11.9968			0.416414
$831$	−3.84864	−	11.7233i	−0.133508	−	0.406677i
$832$	−32.3856	+	56.0935i	−1.12277	+	1.94469i
$833$	−1.39460	+	12.8592i	−0.0483199	+	0.445544i
$834$	17.9235	−	20.0284i	0.620641	−	0.693527i
$835$	7.65659	−	13.2616i	0.264967	−	0.458937i
$836$	37.4612	−	64.8847i	1.29562	−	2.24408i
$837$	1.83180	−	19.1057i	0.0633163	−	0.660391i
$838$	−20.6339	−	35.7390i	−0.712787	−	1.23458i
$839$	0.469775	+	0.813675i	0.0162185	+	0.0280912i	0.874021	−	0.485889i	$-0.161504\pi$
$839$	0.469775	+	0.813675i	0.0162185	+	0.0280912i	−0.857802	+	0.513980i	$0.828171\pi$
$840$	18.4827	+	31.9104i	0.637712	+	1.10101i
$841$	5.53567	−	9.58806i	0.190885	−	0.330623i
$842$	−20.7863			−0.716343
$843$	0.214144	−	0.239292i	0.00737551	−	0.00824166i
$844$	106.770			3.67517
$845$	−4.09444	−	7.09178i	−0.140853	−	0.243965i
$846$	−78.0574	−	34.1854i	−2.68367	−	1.17532i
$847$	45.0651	−	9.50097i	1.54846	−	0.326457i
$848$	19.7043	+	34.1288i	0.676647	+	1.17199i
$849$	−37.6148	+	42.0321i	−1.29094	+	1.44254i
$850$	2.45036	+	4.24415i	0.0840467	+	0.145573i
$851$	8.63216	+	14.9513i	0.295906	+	0.512525i
$852$	16.2765	−	18.1880i	0.557624	−	0.623109i
$853$	−20.8291	−	36.0771i	−0.713175	−	1.23526i	−0.963659	−	0.267134i	$-0.913923\pi$
$853$	−20.8291	−	36.0771i	−0.713175	−	1.23526i	0.250484	−	0.968121i	$-0.419410\pi$
$854$	−13.5671	−	15.1180i	−0.464256	−	0.517328i
$855$	−7.67344	−	3.36059i	−0.262426	−	0.114930i
$856$	−54.6673	−	94.6865i	−1.86849	−	3.23632i
$857$	−11.5649			−0.395049			−0.197525	−	0.980298i	$-0.563290\pi$
$857$	−11.5649			−0.395049			−0.197525	+	0.980298i	$0.563290\pi$
$858$	75.1578	−	83.9840i	2.56584	−	2.86717i
$859$	49.4858			1.68843			0.844217	−	0.536002i	$-0.180066\pi$
$859$	49.4858			1.68843			0.844217	+	0.536002i	$0.180066\pi$
$860$	−21.8619	+	37.8659i	−0.745483	+	1.29122i
$861$	14.6437	−	0.0203586i	0.499056	−	0.000693818i
$862$	−33.8149	−	58.5691i	−1.15174	−	1.99487i
$863$	19.1330	+	33.1392i	0.651293	+	1.12807i	0.982809	+	0.184623i	$0.0591066\pi$
$863$	19.1330	+	33.1392i	0.651293	+	1.12807i	−0.331516	+	0.943450i	$0.607560\pi$
$864$	−6.84728	+	71.4173i	−0.232949	+	2.42967i
$865$	−8.61103	+	14.9147i	−0.292784	+	0.507116i
$866$	−11.8966	+	20.6054i	−0.404261	+	0.700201i
$867$	15.6920	−	17.5348i	0.532928	−	0.595514i
$868$	−15.2803	+	46.7644i	−0.518646	+	1.58729i
$869$	−23.0536	+	39.9299i	−0.782038	+	1.35453i
$870$	−6.06696	−	18.4805i	−0.205689	−	0.626549i
$871$	7.62526			0.258372
$872$	−15.5694	+	26.9670i	−0.527247	+	0.913218i
$873$	24.0736	+	10.5431i	0.814769	+	0.356829i
$874$	−12.6215			−0.426929
$875$	2.58884	−	0.545800i	0.0875188	−	0.0184514i
$876$	−7.89181	−	24.0392i	−0.266640	−	0.812209i
$877$	31.7635			1.07258			0.536288	−	0.844035i	$-0.319826\pi$
$877$	31.7635			1.07258			0.536288	+	0.844035i	$0.319826\pi$
$878$	25.2342	+	43.7070i	0.851614	+	1.47504i
$879$	−0.222170	−	0.0465171i	−0.00749360	−	0.00156898i
$880$	−30.0451	+	52.0397i	−1.01282	+	1.75426i
$881$	28.5661			0.962416			0.481208	−	0.876606i	$-0.340198\pi$
$881$	28.5661			0.962416			0.481208	+	0.876606i	$0.340198\pi$
$882$	27.9821	+	48.1566i	0.942205	+	1.62152i
$883$	47.4172			1.59572			0.797858	−	0.602845i	$-0.205966\pi$
$883$	47.4172			1.59572			0.797858	+	0.602845i	$0.205966\pi$
$884$	−21.4094	+	37.0821i	−0.720075	+	1.24721i
$885$	2.22987	−	2.49173i	0.0749561	−	0.0837587i
$886$	−20.8798	−	36.1648i	−0.701469	−	1.21498i
$887$	−43.5533			−1.46238			−0.731188	−	0.682176i	$-0.761034\pi$
$887$	−43.5533			−1.46238			−0.731188	+	0.682176i	$0.761034\pi$
$888$	94.1571	−	105.215i	3.15971	−	3.53077i
$889$	35.0294	−	7.38516i	1.17485	−	0.247690i
$890$	16.5998			0.556425
$891$	14.2664	−	45.7982i	0.477943	−	1.53430i
$892$	−53.2998	+	92.3179i	−1.78461	+	3.09103i
$893$	−29.9061			−1.00077
$894$	−13.6476	−	2.85748i	−0.456444	−	0.0955684i
$895$	−12.8188	+	22.2029i	−0.428486	+	0.742160i
$896$	7.97481	−	24.4064i	0.266420	−	0.815362i
$897$	−13.2994	−	2.78458i	−0.444055	−	0.0929745i
$898$	28.6460	−	49.6163i	0.955929	−	1.65572i
$899$	7.82011	−	13.5448i	0.260815	−	0.451745i
$900$	13.8339	+	6.05857i	0.461130	+	0.201952i
$901$	3.22943	+	5.59354i	0.107588	+	0.186348i
$902$	22.5857	+	39.1195i	0.752021	+	1.30254i
$903$	−19.8529	+	34.4969i	−0.660664	+	1.14799i
$904$	−20.0210	+	34.6773i	−0.665888	+	1.15335i
$905$	−20.6995			−0.688074
$906$	−14.7431	−	3.08685i	−0.489806	−	0.102554i
$907$	26.3289			0.874236			0.437118	−	0.899404i	$-0.355999\pi$
$907$	26.3289			0.874236			0.437118	+	0.899404i	$0.355999\pi$
$908$	26.0724	+	45.1588i	0.865244	+	1.49865i
$909$	−15.8666	+	11.6761i	−0.526263	+	0.387271i
$910$	21.5735	+	24.0396i	0.715153	+	0.796906i
$911$	2.76965	+	4.79718i	0.0917627	+	0.158938i	0.908253	−	0.418422i	$-0.137417\pi$
$911$	2.76965	+	4.79718i	0.0917627	+	0.158938i	−0.816490	+	0.577359i	$0.804083\pi$
$912$	17.0079	+	51.8076i	0.563188	+	1.71552i
$913$	12.0544	+	20.8788i	0.398942	+	0.690987i
$914$	−20.7692	−	35.9732i	−0.686983	−	1.18989i
$915$	−4.90755	−	1.02752i	−0.162239	−	0.0339689i
$916$	41.4484	+	71.7907i	1.36949	+	2.37203i
$917$	−9.66472	+	2.03759i	−0.319157	+	0.0672872i
$918$	−2.43035	+	25.3487i	−0.0802136	+	0.836630i
$919$	7.73926	+	13.4048i	0.255295	+	0.442183i	0.964975	−	0.262340i	$-0.0844942\pi$
$919$	7.73926	+	13.4048i	0.255295	+	0.442183i	−0.709681	+	0.704523i	$0.751161\pi$
$920$	13.7144			0.452149
$921$	−10.2593	−	31.2507i	−0.338055	−	1.02975i
$922$	18.4567			0.607840
$923$	6.44261	−	11.1589i	0.212061	−	0.367301i
$924$	−61.3300	+	106.569i	−2.01761	+	3.50585i
$925$	−5.06506	−	8.77294i	−0.166538	−	0.288452i
$926$	28.5343	+	49.4229i	0.937697	+	1.62414i
$927$	2.82451	−	2.07852i	0.0927689	−	0.0682676i
$928$	−29.2316	+	50.6306i	−0.959574	+	1.66203i
$929$	25.2011	−	43.6495i	0.826820	−	1.43209i	−0.0737009	−	0.997280i	$-0.523481\pi$
$929$	25.2011	−	43.6495i	0.826820	−	1.43209i	0.900521	−	0.434813i	$-0.143186\pi$
$930$	5.29257	+	16.1216i	0.173550	+	0.528650i
$931$	15.7753	+	11.5414i	0.517016	+	0.378254i
$932$	−53.5643	+	92.7760i	−1.75456	+	3.03898i
$933$	−2.09495	+	2.34097i	−0.0685855	+	0.0766399i
$934$	−23.7069			−0.775715
$935$	−4.92426	+	8.52906i	−0.161040	+	0.278930i
$936$	12.2887	+	110.445i	0.401667	+	3.60999i
$937$	−42.3109			−1.38224			−0.691118	−	0.722742i	$-0.742882\pi$
$937$	−42.3109			−1.38224			−0.691118	+	0.722742i	$0.742882\pi$
$938$	−11.3740	+	2.39794i	−0.371373	+	0.0782956i
$939$	−21.2826	−	4.45607i	−0.694532	−	0.145418i
$940$	53.9156			1.75853
$941$	−25.1327	−	43.5311i	−0.819303	−	1.41907i	−0.906197	−	0.422856i	$-0.861028\pi$
$941$	−25.1327	−	43.5311i	−0.819303	−	1.41907i	0.0868941	−	0.996218i	$-0.472306\pi$
$942$	27.4616	+	83.6504i	0.894746	+	2.72548i
$943$	2.72299	−	4.71636i	0.0886728	−	0.153586i
$944$	−21.7655			−0.708406
$945$	12.6006	+	5.49760i	0.409899	+	0.178837i
$946$	−122.776			−3.99179
$947$	22.3264	−	38.6705i	0.725511	−	1.25662i	−0.233252	−	0.972416i	$-0.574937\pi$
$947$	22.3264	−	38.6705i	0.725511	−	1.25662i	0.958763	−	0.284206i	$-0.0917299\pi$
$948$	−23.5271	−	71.6658i	−0.764126	−	2.32760i
$949$	−6.67858	−	11.5676i	−0.216796	−	0.375501i
$950$	7.40587			0.240278
$951$	−0.890206	−	0.186388i	−0.0288669	−	0.00604404i
$952$	12.2189	−	37.3952i	0.396017	−	1.21199i
$953$	21.3886			0.692845			0.346423	−	0.938079i	$-0.387396\pi$
$953$	21.3886			0.692845			0.346423	+	0.938079i	$0.387396\pi$
$954$	25.4757	+	11.1571i	0.824807	+	0.361225i
$955$	11.5729	−	20.0448i	0.374490	−	0.648635i
$956$	−104.244			−3.37150
$957$	26.0668	−	29.1280i	0.842621	−	0.941576i
$958$	11.1318	−	19.2809i	0.359653	−	0.622938i
$959$	6.02876	−	1.27103i	0.194679	−	0.0410437i
$960$	−7.60187	−	23.1560i	−0.245349	−	0.747356i
$961$	8.67806	−	15.0308i	0.279937	−	0.484866i
$962$	61.8363	−	107.104i	1.99368	−	3.45316i
$963$	−37.3367	−	16.3517i	−1.20316	−	0.526925i
$964$	−17.0217	−	29.4824i	−0.548230	−	0.949563i
$965$	−2.14734	−	3.71930i	−0.0691254	−	0.119729i
$966$	20.7133	−	0.0287969i	0.666440	−	0.000926525i
$967$	20.8575	−	36.1262i	0.670731	−	1.16174i	−0.306966	−	0.951721i	$-0.599314\pi$
$967$	20.8575	−	36.1262i	0.670731	−	1.16174i	0.977697	−	0.210020i	$-0.0673530\pi$
$968$	−140.080			−4.50233
$969$	2.78752	+	8.49103i	0.0895479	+	0.272771i
$970$	−23.2342			−0.746005
$971$	5.27744	+	9.14080i	0.169361	+	0.293342i	0.938195	−	0.346106i	$-0.112496\pi$
$971$	5.27744	+	9.14080i	0.169361	+	0.293342i	−0.768834	+	0.639448i	$0.779163\pi$
$972$	40.2673	+	67.3556i	1.29157	+	2.16043i
$973$	−4.80791	+	14.7143i	−0.154135	+	0.471720i
$974$	43.8261	+	75.9090i	1.40428	+	2.43228i
$975$	7.80365	+	1.63390i	0.249917	+	0.0523266i
$976$	16.3185	+	28.2644i	0.522341	+	0.904721i
$977$	−1.90301	−	3.29611i	−0.0608827	−	0.105452i	0.833978	−	0.551798i	$-0.186058\pi$
$977$	−1.90301	−	3.29611i	−0.0608827	−	0.105452i	−0.894860	+	0.446346i	$0.852725\pi$
$978$	−14.7103	−	44.8091i	−0.470385	−	1.43284i
$979$	16.6795	+	28.8897i	0.533078	+	0.923319i
$980$	−28.4402	−	20.8072i	−0.908489	−	0.664661i
$981$	1.28372	+	11.5375i	0.0409861	+	0.368364i
$982$	30.9342	+	53.5796i	0.987149	+	1.70979i
$983$	−2.76263			−0.0881142			−0.0440571	−	0.999029i	$-0.514028\pi$
$983$	−2.76263			−0.0881142			−0.0440571	+	0.999029i	$0.514028\pi$
$984$	−43.5939	−	9.12753i	−1.38972	−	0.290975i
$985$	−14.7455			−0.469832
$986$	−10.3754	+	17.9707i	−0.330419	+	0.572303i
$987$	49.0793	−	0.0682331i	1.56221	−	0.00217188i
$988$	32.3534	+	56.0377i	1.02930	+	1.78280i
$989$	7.40111	+	12.8191i	0.235342	+	0.407624i
$990$	4.68955	+	42.1474i	0.149044	+	1.33953i
$991$	11.8370	−	20.5022i	0.376013	−	0.651274i	−0.614465	−	0.788944i	$-0.710628\pi$
$991$	11.8370	−	20.5022i	0.376013	−	0.651274i	0.990478	+	0.137670i	$0.0439614\pi$
$992$	25.5004	−	44.1680i	0.809639	−	1.40234i
$993$	42.8292	+	8.96742i	1.35914	+	0.284572i
$994$	−6.10071	+	18.6709i	−0.193503	+	0.592204i
$995$	11.1399	−	19.2949i	0.353159	−	0.611689i
$996$	−38.6036	−	8.08267i	−1.22320	−	0.256109i
$997$	30.4035			0.962889			0.481445	−	0.876477i	$-0.340112\pi$
$997$	30.4035			0.962889			0.481445	+	0.876477i	$0.340112\pi$
$998$	−10.3218	+	17.8778i	−0.326730	+	0.565913i
$999$	5.02370	−	52.3973i	0.158943	−	1.65778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.256.17	yes	36
3.2	odd	2		945.2.k.c.361.2		36
7.2	even	3		315.2.l.c.121.2	yes	36
9.2	odd	6		945.2.l.c.46.17		36
9.7	even	3		315.2.l.c.151.2	yes	36
21.2	odd	6		945.2.l.c.226.17		36
63.2	odd	6		945.2.k.c.856.2		36
63.16	even	3	inner	315.2.k.c.16.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.17	✓	36	63.16	even	3	inner
315.2.k.c.256.17	yes	36	1.1	even	1	trivial
315.2.l.c.121.2	yes	36	7.2	even	3
315.2.l.c.151.2	yes	36	9.7	even	3
945.2.k.c.361.2		36	3.2	odd	2
945.2.k.c.856.2		36	63.2	odd	6
945.2.l.c.46.17		36	9.2	odd	6
945.2.l.c.226.17		36	21.2	odd	6

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

\(f(q)\)	\(=\)	\(q+(1.32610 - 2.29687i) q^{2} +(-0.540247 - 1.64564i) q^{3} +(-2.51707 - 4.35969i) q^{4} +1.00000 q^{5} +(-4.49624 - 0.941405i) q^{6} +(2.58884 - 0.545800i) q^{7} -8.04712 q^{8} +(-2.41627 + 1.77810i) q^{9} +O(q^{10})\)	\(q+(1.32610 - 2.29687i) q^{2} +(-0.540247 - 1.64564i) q^{3} +(-2.51707 - 4.35969i) q^{4} +1.00000 q^{5} +(-4.49624 - 0.941405i) q^{6} +(2.58884 - 0.545800i) q^{7} -8.04712 q^{8} +(-2.41627 + 1.77810i) q^{9} +(1.32610 - 2.29687i) q^{10} +5.32986 q^{11} +(-5.81465 + 6.49750i) q^{12} +(-2.30157 + 3.98643i) q^{13} +(2.17943 - 6.67001i) q^{14} +(-0.540247 - 1.64564i) q^{15} +(-5.63713 + 9.76380i) q^{16} +(-0.923899 + 1.60024i) q^{17} +(0.879863 + 7.90779i) q^{18} +(1.39618 + 2.41825i) q^{19} +(-2.51707 - 4.35969i) q^{20} +(-2.29680 - 3.96544i) q^{21} +(7.06792 - 12.2420i) q^{22} -1.70426 q^{23} +(4.34743 + 13.2427i) q^{24} +1.00000 q^{25} +(6.10421 + 10.5728i) q^{26} +(4.23150 + 3.01569i) q^{27} +(-8.89581 - 9.91273i) q^{28} +(2.11711 + 3.66695i) q^{29} +(-4.49624 - 0.941405i) q^{30} +(-1.84688 - 3.19889i) q^{31} +(6.90365 + 11.9575i) q^{32} +(-2.87944 - 8.77104i) q^{33} +(2.45036 + 4.24415i) q^{34} +(2.58884 - 0.545800i) q^{35} +(13.8339 + 6.05857i) q^{36} +(-5.06506 - 8.77294i) q^{37} +7.40587 q^{38} +(7.80365 + 1.63390i) q^{39} -8.04712 q^{40} +(-1.59776 + 2.76740i) q^{41} +(-12.1539 + 0.0168971i) q^{42} +(-4.34272 - 7.52182i) q^{43} +(-13.4156 - 23.2366i) q^{44} +(-2.41627 + 1.77810i) q^{45} +(-2.26001 + 3.91445i) q^{46} +(-5.35500 + 9.27513i) q^{47} +(19.1131 + 4.00183i) q^{48} +(6.40421 - 2.82598i) q^{49} +(1.32610 - 2.29687i) q^{50} +(3.13255 + 0.655882i) q^{51} +23.1728 q^{52} +(1.74772 - 3.02714i) q^{53} +(12.5380 - 5.72009i) q^{54} +5.32986 q^{55} +(-20.8327 + 4.39212i) q^{56} +(3.22529 - 3.60406i) q^{57} +11.2300 q^{58} +(0.965273 + 1.67190i) q^{59} +(-5.81465 + 6.49750i) q^{60} +(1.44741 - 2.50698i) q^{61} -9.79658 q^{62} +(-5.28485 + 5.92203i) q^{63} +14.0711 q^{64} +(-2.30157 + 3.98643i) q^{65} +(-23.9643 - 5.01756i) q^{66} +(-0.828267 - 1.43460i) q^{67} +9.30207 q^{68} +(0.920719 + 2.80459i) q^{69} +(2.17943 - 6.67001i) q^{70} -2.79922 q^{71} +(19.4440 - 14.3086i) q^{72} +(-1.45087 + 2.51299i) q^{73} -26.8670 q^{74} +(-0.540247 - 1.64564i) q^{75} +(7.02855 - 12.1738i) q^{76} +(13.7982 - 2.90904i) q^{77} +(14.1013 - 15.7573i) q^{78} +(-4.32536 + 7.49174i) q^{79} +(-5.63713 + 9.76380i) q^{80} +(2.67670 - 8.59275i) q^{81} +(4.23757 + 7.33969i) q^{82} +(2.26167 + 3.91732i) q^{83} +(-11.5069 + 19.9946i) q^{84} +(-0.923899 + 1.60024i) q^{85} -23.0355 q^{86} +(4.89071 - 5.46506i) q^{87} -42.8901 q^{88} +(3.12944 + 5.42035i) q^{89} +(0.879863 + 7.90779i) q^{90} +(-3.78260 + 11.5764i) q^{91} +(4.28973 + 7.43003i) q^{92} +(-4.26646 + 4.76749i) q^{93} +(14.2025 + 24.5995i) q^{94} +(1.39618 + 2.41825i) q^{95} +(15.9480 - 17.8209i) q^{96} +(-4.38018 - 7.58670i) q^{97} +(2.00170 - 18.4571i) q^{98} +(-12.8784 + 9.47705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more