LMFDB - Embedded newform 343.2.g.a.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(30,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([32]))

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

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

chi := DirichletCharacter("343.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, not 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			165.1
Root			$0.826239 - 0.563320i$ of defining polynomial
Character	$\chi$	$=$	343.165
Dual form			343.2.g.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88980 + 0.284841i) q^{2} +(1.42996 - 0.974928i) q^{3} +(1.57906 + 0.487076i) q^{4} +(-0.158960 - 2.12117i) q^{5} +(2.98003 - 1.43511i) q^{6} +(-0.598393 - 0.288171i) q^{8} +(-0.00173159 + 0.00441201i) q^{9} +O(q^{10})$	\(q+(1.88980 + 0.284841i) q^{2} +(1.42996 - 0.974928i) q^{3} +(1.57906 + 0.487076i) q^{4} +(-0.158960 - 2.12117i) q^{5} +(2.98003 - 1.43511i) q^{6} +(-0.598393 - 0.288171i) q^{8} +(-0.00173159 + 0.00441201i) q^{9} +(0.303796 - 4.05387i) q^{10} +(1.70744 + 4.35048i) q^{11} +(2.73286 - 0.842974i) q^{12} +(-0.609562 + 0.764367i) q^{13} +(-2.29530 - 2.87821i) q^{15} +(-3.77944 - 2.57678i) q^{16} +(1.52786 + 1.41764i) q^{17} +(-0.00452908 + 0.00784459i) q^{18} +(-2.64558 - 4.58228i) q^{19} +(0.782166 - 3.42689i) q^{20} +(1.98752 + 8.70788i) q^{22} +(2.77064 - 2.57078i) q^{23} +(-1.13662 + 0.171318i) q^{24} +(0.470043 - 0.0708476i) q^{25} +(-1.36967 + 1.27087i) q^{26} +(1.15716 + 5.06987i) q^{27} +(-1.23460 + 5.40913i) q^{29} +(-3.51782 - 6.09304i) q^{30} +(-5.08232 + 8.80283i) q^{31} +(-5.43468 - 5.04264i) q^{32} +(6.68296 + 4.55636i) q^{33} +(2.48354 + 3.11426i) q^{34} +(-0.00488327 + 0.00612343i) q^{36} +(-1.65006 + 0.508976i) q^{37} +(-3.69439 - 9.41316i) q^{38} +(-0.126445 + 1.68729i) q^{39} +(-0.516140 + 1.31510i) q^{40} +(-3.19850 - 1.54031i) q^{41} +(9.05500 - 4.36066i) q^{43} +(0.577134 + 7.70132i) q^{44} +(0.00963390 + 0.00297166i) q^{45} +(5.96822 - 4.06907i) q^{46} +(-4.28029 - 0.645150i) q^{47} -7.91661 q^{48} +0.908468 q^{50} +(3.56687 + 0.537619i) q^{51} +(-1.33484 + 0.910080i) q^{52} +(-4.94215 - 1.52445i) q^{53} +(0.742700 + 9.91064i) q^{54} +(8.95670 - 4.31332i) q^{55} +(-8.25045 - 3.97321i) q^{57} +(-3.87389 + 9.87050i) q^{58} +(0.388615 - 5.18571i) q^{59} +(-2.22251 - 5.66286i) q^{60} +(-4.26855 + 1.31667i) q^{61} +(-12.1120 + 15.1879i) q^{62} +(-3.13007 - 3.92499i) q^{64} +(1.71825 + 1.17148i) q^{65} +(11.3316 + 10.5142i) q^{66} +(-0.241204 + 0.417777i) q^{67} +(1.72208 + 2.98273i) q^{68} +(1.45557 - 6.37728i) q^{69} +(-2.97959 - 13.0544i) q^{71} +(0.00230758 - 0.00214112i) q^{72} +(5.90021 - 0.889314i) q^{73} +(-3.26326 + 0.491857i) q^{74} +(0.603070 - 0.559567i) q^{75} +(-1.94562 - 8.52430i) q^{76} +(-0.719566 + 3.15262i) q^{78} +(-2.87907 - 4.98670i) q^{79} +(-4.86502 + 8.42646i) q^{80} +(6.58703 + 6.11187i) q^{81} +(-5.60577 - 3.82195i) q^{82} +(-1.84538 - 2.31404i) q^{83} +(2.76420 - 3.46620i) q^{85} +(18.3542 - 5.66153i) q^{86} +(3.50809 + 8.93846i) q^{87} +(0.231963 - 3.09533i) q^{88} +(4.12255 - 10.5041i) q^{89} +(0.0173597 + 0.00835998i) q^{90} +(5.62718 - 2.70991i) q^{92} +(1.31463 + 17.5426i) q^{93} +(-7.90513 - 2.43841i) q^{94} +(-9.29926 + 6.34013i) q^{95} +(-12.6876 - 1.91234i) q^{96} +1.76250 q^{97} -0.0221509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{4} - 14 q^{5} + 7 q^{6} + 6 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + q^2 - q^4 - 14 * q^5 + 7 * q^6 + 6 * q^8 + 25 * q^9	$ 12 q + q^{2} - q^{4} - 14 q^{5} + 7 q^{6} + 6 q^{8} + 25 q^{9} + 7 q^{10} + 4 q^{11} - 7 q^{12} - 7 q^{13} - 7 q^{15} - 29 q^{16} - 10 q^{18} - 7 q^{19} - 7 q^{20} + 13 q^{22} + q^{23} + 9 q^{25} + 7 q^{26} - 21 q^{27} - 11 q^{29} - 21 q^{30} - 7 q^{31} - 9 q^{32} + 49 q^{33} + 42 q^{34} - 13 q^{36} + 15 q^{37} - 21 q^{38} - 21 q^{40} - 21 q^{41} + 17 q^{43} - 18 q^{44} - 35 q^{45} + 8 q^{46} - 21 q^{47} - 46 q^{50} + 7 q^{51} + 7 q^{52} - 24 q^{53} + 21 q^{54} + 28 q^{55} + 7 q^{57} + 16 q^{58} + 7 q^{59} + 35 q^{60} - 14 q^{61} - 56 q^{62} + 14 q^{64} + 14 q^{65} + 49 q^{66} - 24 q^{67} + 28 q^{68} + 7 q^{69} - 39 q^{71} + 23 q^{72} + 21 q^{73} - 20 q^{74} + 14 q^{75} + 28 q^{76} + 8 q^{79} + 21 q^{80} + 23 q^{81} - 7 q^{82} + 7 q^{83} + 28 q^{85} - 19 q^{86} + 56 q^{87} + 16 q^{88} + 35 q^{89} + 14 q^{90} + 16 q^{92} - 7 q^{93} - 56 q^{94} - 7 q^{95} - 35 q^{96} + 28 q^{97} - 18 q^{99}+O(q^{100}) $ 12 * q + q^2 - q^4 - 14 * q^5 + 7 * q^6 + 6 * q^8 + 25 * q^9 + 7 * q^10 + 4 * q^11 - 7 * q^12 - 7 * q^13 - 7 * q^15 - 29 * q^16 - 10 * q^18 - 7 * q^19 - 7 * q^20 + 13 * q^22 + q^23 + 9 * q^25 + 7 * q^26 - 21 * q^27 - 11 * q^29 - 21 * q^30 - 7 * q^31 - 9 * q^32 + 49 * q^33 + 42 * q^34 - 13 * q^36 + 15 * q^37 - 21 * q^38 - 21 * q^40 - 21 * q^41 + 17 * q^43 - 18 * q^44 - 35 * q^45 + 8 * q^46 - 21 * q^47 - 46 * q^50 + 7 * q^51 + 7 * q^52 - 24 * q^53 + 21 * q^54 + 28 * q^55 + 7 * q^57 + 16 * q^58 + 7 * q^59 + 35 * q^60 - 14 * q^61 - 56 * q^62 + 14 * q^64 + 14 * q^65 + 49 * q^66 - 24 * q^67 + 28 * q^68 + 7 * q^69 - 39 * q^71 + 23 * q^72 + 21 * q^73 - 20 * q^74 + 14 * q^75 + 28 * q^76 + 8 * q^79 + 21 * q^80 + 23 * q^81 - 7 * q^82 + 7 * q^83 + 28 * q^85 - 19 * q^86 + 56 * q^87 + 16 * q^88 + 35 * q^89 + 14 * q^90 + 16 * q^92 - 7 * q^93 - 56 * q^94 - 7 * q^95 - 35 * q^96 + 28 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{17}{21}\right)$

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 $

$2$	1.88980	+	0.284841i	1.33629	+	0.201413i	0.778017	−	0.628244i	$-0.216226\pi$
$2$	1.88980	+	0.284841i	1.33629	+	0.201413i	0.558274	+	0.829657i	$0.311464\pi$
$3$	1.42996	−	0.974928i	0.825586	−	0.562875i	−0.0751850	−	0.997170i	$-0.523955\pi$
$3$	1.42996	−	0.974928i	0.825586	−	0.562875i	0.900771	+	0.434295i	$0.143002\pi$
$4$	1.57906	+	0.487076i	0.789531	+	0.243538i
$5$	−0.158960	−	2.12117i	−0.0710891	−	0.948618i	−0.912726	−	0.408573i	$-0.866026\pi$
$5$	−0.158960	−	2.12117i	−0.0710891	−	0.948618i	0.841636	−	0.540045i	$-0.181593\pi$
$6$	2.98003	−	1.43511i	1.21659	−	0.585880i
$7$		0			0
$7$		0			0
$8$	−0.598393	−	0.288171i	−0.211564	−	0.101884i
$9$	−0.00173159	+	0.00441201i	−0.000577196	+	0.00147067i
$10$	0.303796	−	4.05387i	0.0960686	−	1.28195i
$11$	1.70744	+	4.35048i	0.514811	+	1.31172i	0.917993	+	0.396598i	$0.129809\pi$
$11$	1.70744	+	4.35048i	0.514811	+	1.31172i	−0.403181	+	0.915120i	$0.632096\pi$
$12$	2.73286	−	0.842974i	0.788907	−	0.243346i
$13$	−0.609562	+	0.764367i	−0.169062	+	0.211997i	−0.859144	−	0.511734i	$-0.829003\pi$
$13$	−0.609562	+	0.764367i	−0.169062	+	0.211997i	0.690082	+	0.723732i	$0.257575\pi$
$14$		0			0
$15$	−2.29530	−	2.87821i	−0.592643	−	0.743151i
$16$	−3.77944	−	2.57678i	−0.944860	−	0.644195i
$17$	1.52786	+	1.41764i	0.370559	+	0.343829i	0.843368	−	0.537336i	$-0.180569\pi$
$17$	1.52786	+	1.41764i	0.370559	+	0.343829i	−0.472809	+	0.881165i	$0.656760\pi$
$18$	−0.00452908	+	0.00784459i	−0.00106751	+	0.00184899i
$19$	−2.64558	−	4.58228i	−0.606937	−	1.05125i	−0.991742	−	0.128248i	$-0.959065\pi$
$19$	−2.64558	−	4.58228i	−0.606937	−	1.05125i	0.384805	−	0.922998i	$-0.374269\pi$
$20$	0.782166	−	3.42689i	0.174898	−	0.766276i
$21$		0			0
$22$	1.98752	+	8.70788i	0.423740	+	1.85653i
$23$	2.77064	−	2.57078i	0.577719	−	0.536045i	−0.336280	−	0.941762i	$-0.609169\pi$
$23$	2.77064	−	2.57078i	0.577719	−	0.536045i	0.913999	+	0.405717i	$0.132978\pi$
$24$	−1.13662	+	0.171318i	−0.232012	+	0.0349702i
$25$	0.470043	−	0.0708476i	0.0940087	−	0.0141695i
$26$	−1.36967	+	1.27087i	−0.268615	+	0.249238i
$27$	1.15716	+	5.06987i	0.222696	+	0.975697i
$28$		0			0
$29$	−1.23460	+	5.40913i	−0.229259	+	1.00445i	0.720987	+	0.692949i	$0.243689\pi$
$29$	−1.23460	+	5.40913i	−0.229259	+	1.00445i	−0.950246	+	0.311501i	$0.899168\pi$
$30$	−3.51782	−	6.09304i	−0.642263	−	1.11243i
$31$	−5.08232	+	8.80283i	−0.912811	+	1.58103i	−0.102735	+	0.994709i	$0.532760\pi$
$31$	−5.08232	+	8.80283i	−0.912811	+	1.58103i	−0.810075	+	0.586326i	$0.800574\pi$
$32$	−5.43468	−	5.04264i	−0.960724	−	0.891422i
$33$	6.68296	+	4.55636i	1.16335	+	0.793161i
$34$	2.48354	+	3.11426i	0.425923	+	0.534091i
$35$		0			0
$36$	−0.00488327	+	0.00612343i	−0.000813879	+	0.00102057i
$37$	−1.65006	+	0.508976i	−0.271268	+	0.0836751i	−0.427405	−	0.904060i	$-0.640572\pi$
$37$	−1.65006	+	0.508976i	−0.271268	+	0.0836751i	0.156137	+	0.987735i	$0.450096\pi$
$38$	−3.69439	−	9.41316i	−0.599309	−	1.52702i
$39$	−0.126445	+	1.68729i	−0.0202474	+	0.270183i
$40$	−0.516140	+	1.31510i	−0.0816089	+	0.207936i
$41$	−3.19850	−	1.54031i	−0.499521	−	0.240557i	0.167119	−	0.985937i	$-0.446554\pi$
$41$	−3.19850	−	1.54031i	−0.499521	−	0.240557i	−0.666640	+	0.745380i	$0.732268\pi$
$42$		0			0
$43$	9.05500	−	4.36066i	1.38087	−	0.664994i	0.411688	−	0.911325i	$-0.364939\pi$
$43$	9.05500	−	4.36066i	1.38087	−	0.664994i	0.969186	+	0.246331i	$0.0792249\pi$
$44$	0.577134	+	7.70132i	0.0870063	+	1.16102i
$45$	0.00963390	+	0.00297166i	0.00143614	+	0.000442990i
$46$	5.96822	−	4.06907i	0.879967	−	0.599951i
$47$	−4.28029	−	0.645150i	−0.624345	−	0.0941048i	−0.170752	−	0.985314i	$-0.554620\pi$
$47$	−4.28029	−	0.645150i	−0.624345	−	0.0941048i	−0.453593	+	0.891209i	$0.649858\pi$
$48$	−7.91661			−1.14266
$49$		0			0
$50$	0.908468			0.128477
$51$	3.56687	+	0.537619i	0.499461	+	0.0752817i
$52$	−1.33484	+	0.910080i	−0.185109	+	0.126205i
$53$	−4.94215	−	1.52445i	−0.678856	−	0.209399i	−0.0638949	−	0.997957i	$-0.520352\pi$
$53$	−4.94215	−	1.52445i	−0.678856	−	0.209399i	−0.614961	+	0.788557i	$0.710828\pi$
$54$	0.742700	+	9.91064i	0.101069	+	1.34867i
$55$	8.95670	−	4.31332i	1.20772	−	0.581608i
$56$		0			0
$57$	−8.25045	−	3.97321i	−1.09280	−	0.526264i
$58$	−3.87389	+	9.87050i	−0.508666	+	1.29606i
$59$	0.388615	−	5.18571i	0.0505934	−	0.675122i	−0.913036	−	0.407879i	$-0.866268\pi$
$59$	0.388615	−	5.18571i	0.0505934	−	0.675122i	0.963629	−	0.267243i	$-0.0861125\pi$
$60$	−2.22251	−	5.66286i	−0.286925	−	0.731072i
$61$	−4.26855	+	1.31667i	−0.546532	+	0.168583i	−0.555712	−	0.831375i	$-0.687554\pi$
$61$	−4.26855	+	1.31667i	−0.546532	+	0.168583i	0.00917985	+	0.999958i	$0.497078\pi$
$62$	−12.1120	+	15.1879i	−1.53822	+	1.92887i
$63$		0			0
$64$	−3.13007	−	3.92499i	−0.391259	−	0.490623i
$65$	1.71825	+	1.17148i	0.213123	+	0.145305i
$66$	11.3316	+	10.5142i	1.39482	+	1.29421i
$67$	−0.241204	+	0.417777i	−0.0294677	+	0.0510396i	−0.880383	−	0.474263i	$-0.842715\pi$
$67$	−0.241204	+	0.417777i	−0.0294677	+	0.0510396i	0.850915	+	0.525303i	$0.176048\pi$
$68$	1.72208	+	2.98273i	0.208833	+	0.361709i
$69$	1.45557	−	6.37728i	0.175230	−	0.767734i
$70$		0			0
$71$	−2.97959	−	13.0544i	−0.353612	−	1.54927i	−0.768770	−	0.639525i	$-0.779131\pi$
$71$	−2.97959	−	13.0544i	−0.353612	−	1.54927i	0.415158	−	0.909749i	$-0.363726\pi$
$72$	0.00230758	−	0.00214112i	0.000271951	−	0.000252334i
$73$	5.90021	−	0.889314i	0.690568	−	0.104086i	0.205623	−	0.978631i	$-0.434078\pi$
$73$	5.90021	−	0.889314i	0.690568	−	0.104086i	0.484944	+	0.874545i	$0.338840\pi$
$74$	−3.26326	+	0.491857i	−0.379346	+	0.0571772i
$75$	0.603070	−	0.559567i	0.0696366	−	0.0646133i
$76$	−1.94562	−	8.52430i	−0.223177	−	0.977804i
$77$		0			0
$78$	−0.719566	+	3.15262i	−0.0814748	+	0.356964i
$79$	−2.87907	−	4.98670i	−0.323921	−	0.561048i	0.657372	−	0.753566i	$-0.271668\pi$
$79$	−2.87907	−	4.98670i	−0.323921	−	0.561048i	−0.981293	+	0.192518i	$0.938335\pi$
$80$	−4.86502	+	8.42646i	−0.543926	+	0.942107i
$81$	6.58703	+	6.11187i	0.731892	+	0.679096i
$82$	−5.60577	−	3.82195i	−0.619054	−	0.422064i
$83$	−1.84538	−	2.31404i	−0.202557	−	0.253999i	0.670169	−	0.742208i	$-0.266222\pi$
$83$	−1.84538	−	2.31404i	−0.202557	−	0.253999i	−0.872726	+	0.488210i	$0.837650\pi$
$84$		0			0
$85$	2.76420	−	3.46620i	0.299819	−	0.375962i
$86$	18.3542	−	5.66153i	1.97919	−	0.610498i
$87$	3.50809	+	8.93846i	0.376107	+	0.958304i
$88$	0.231963	−	3.09533i	0.0247273	−	0.329963i
$89$	4.12255	−	10.5041i	0.436989	−	1.11343i	−0.527558	−	0.849519i	$-0.676892\pi$
$89$	4.12255	−	10.5041i	0.436989	−	1.11343i	0.964547	−	0.263911i	$-0.0850125\pi$
$90$	0.0173597	+	0.00835998i	0.00182987	+	0.000881220i
$91$		0			0
$92$	5.62718	−	2.70991i	0.586674	−	0.282528i
$93$	1.31463	+	17.5426i	0.136321	+	1.81908i
$94$	−7.90513	−	2.43841i	−0.815352	−	0.251503i
$95$	−9.29926	+	6.34013i	−0.954084	+	0.650484i
$96$	−12.6876	−	1.91234i	−1.29492	−	0.195178i
$97$	1.76250			0.178955			0.0894774	−	0.995989i	$-0.471480\pi$
$97$	1.76250			0.178955			0.0894774	+	0.995989i	$0.471480\pi$
$98$		0			0
$99$	−0.0221509			−0.00222625
$100$	0.776736	+	0.117074i	0.0776736	+	0.0117074i
$101$	7.96991	−	5.43379i	0.793036	−	0.540683i	−0.0976937	−	0.995217i	$-0.531147\pi$
$101$	7.96991	−	5.43379i	0.793036	−	0.540683i	0.890729	+	0.454534i	$0.150194\pi$
$102$	6.58753	+	2.03198i	0.652262	+	0.201196i
$103$	0.271760	+	3.62638i	0.0267773	+	0.357318i	0.994458	+	0.105138i	$0.0335284\pi$
$103$	0.271760	+	3.62638i	0.0267773	+	0.357318i	−0.967680	+	0.252180i	$0.918853\pi$
$104$	0.585026	−	0.281734i	0.0573665	−	0.0276262i
$105$		0			0
$106$	−8.90544	−	4.28864i	−0.864973	−	0.416549i
$107$	−1.58714	+	4.04397i	−0.153435	+	0.390945i	−0.986836	−	0.161723i	$-0.948295\pi$
$107$	−1.58714	+	4.04397i	−0.153435	+	0.390945i	0.833402	+	0.552668i	$0.186390\pi$
$108$	−0.642178	+	8.56927i	−0.0617936	+	0.824578i
$109$	0.352159	+	0.897287i	0.0337307	+	0.0859445i	0.946747	−	0.321979i	$-0.104348\pi$
$109$	0.352159	+	0.897287i	0.0337307	+	0.0859445i	−0.913016	+	0.407924i	$0.866253\pi$
$110$	18.1550	−	5.60007i	1.73101	−	0.533946i
$111$	−1.86330	+	2.33650i	−0.176856	+	0.221771i
$112$		0			0
$113$	2.34443	+	2.93983i	0.220546	+	0.276556i	0.879779	−	0.475383i	$-0.157690\pi$
$113$	2.34443	+	2.93983i	0.220546	+	0.276556i	−0.659233	+	0.751938i	$0.729119\pi$
$114$	−14.4600	−	9.85864i	−1.35430	−	0.923346i
$115$	−5.89349	−	5.46836i	−0.549571	−	0.509928i
$116$	−4.58417	+	7.94001i	−0.425629	+	0.737211i
$117$	−0.00231689	−	0.00401296i	−0.000214196	−	0.000370999i
$118$	2.21151	−	9.68926i	0.203586	−	0.891968i
$119$		0			0
$120$	0.544073	+	2.38374i	0.0496668	+	0.217605i
$121$	−7.94773	+	7.37441i	−0.722521	+	0.670401i
$122$	−8.44175	+	1.27239i	−0.764280	+	0.115197i
$123$	−6.07541	+	0.915720i	−0.547801	+	0.0825677i
$124$	−12.3129	+	11.4247i	−1.10573	+	1.02597i
$125$	−2.59164	−	11.3547i	−0.231804	−	1.01560i
$126$		0			0
$127$	−2.19982	+	9.63803i	−0.195202	+	0.855237i	0.778542	+	0.627592i	$0.215960\pi$
$127$	−2.19982	+	9.63803i	−0.195202	+	0.855237i	−0.973744	+	0.227644i	$0.926898\pi$
$128$	2.61656	+	4.53201i	0.231273	+	0.400577i
$129$	8.69693	−	15.0635i	0.765722	−	1.32627i
$130$	2.91346	+	2.70330i	0.255528	+	0.237095i
$131$	4.32209	+	2.94675i	0.377622	+	0.257459i	0.737225	−	0.675647i	$-0.236136\pi$
$131$	4.32209	+	2.94675i	0.377622	+	0.257459i	−0.359603	+	0.933105i	$0.617088\pi$
$132$	8.33351	+	10.4499i	0.725339	+	0.909547i
$133$		0			0
$134$	−0.574827	+	0.720810i	−0.0496575	+	0.0622685i
$135$	10.5701	−	3.26045i	0.909732	−	0.280615i
$136$	−0.505735	−	1.28859i	−0.0433664	−	0.110496i
$137$	1.37470	−	18.3441i	0.117449	−	1.56724i	−0.558004	−	0.829838i	$-0.688433\pi$
$137$	1.37470	−	18.3441i	0.117449	−	1.56724i	0.675453	−	0.737403i	$-0.263948\pi$
$138$	4.56726	−	11.6372i	0.388791	−	0.990622i
$139$	−6.39270	−	3.07856i	−0.542222	−	0.261120i	0.142663	−	0.989771i	$-0.454433\pi$
$139$	−6.39270	−	3.07856i	−0.542222	−	0.261120i	−0.684885	+	0.728651i	$0.740148\pi$
$140$		0			0
$141$	−6.74961	+	3.25044i	−0.568419	+	0.273736i
$142$	−1.91238	−	25.5189i	−0.160483	−	2.14150i
$143$	−4.36615	−	1.34678i	−0.365115	−	0.112623i
$144$	0.0179132	−	0.0122130i	0.00149277	−	0.00101775i
$145$	11.6700	+	1.75896i	0.969137	+	0.146074i
$146$	11.4035			0.943763
$147$		0			0
$148$	−2.85346			−0.234553
$149$	−6.94709	−	1.04711i	−0.569128	−	0.0857822i	−0.141827	−	0.989892i	$-0.545298\pi$
$149$	−6.94709	−	1.04711i	−0.569128	−	0.0857822i	−0.427301	+	0.904109i	$0.640536\pi$
$150$	1.29907	−	0.885691i	0.106069	−	0.0723164i
$151$	−1.01050	−	0.311698i	−0.0822333	−	0.0253656i	0.253366	−	0.967371i	$-0.418462\pi$
$151$	−1.01050	−	0.311698i	−0.0822333	−	0.0253656i	−0.335599	+	0.942005i	$0.608939\pi$
$152$	0.262617	+	3.50438i	0.0213011	+	0.284243i
$153$	−0.00890027	+	0.00428615i	−0.000719544	+	0.000346514i
$154$		0			0
$155$	19.4802	+	9.38118i	1.56469	+	0.753514i
$156$	−1.02150	+	2.60275i	−0.0817857	+	0.208387i
$157$	−0.356100	+	4.75182i	−0.0284199	+	0.379237i	0.964800	+	0.262985i	$0.0847070\pi$
$157$	−0.356100	+	4.75182i	−0.0284199	+	0.379237i	−0.993220	+	0.116252i	$0.962912\pi$
$158$	−4.02045	−	10.2439i	−0.319850	−	0.814964i
$159$	−8.55329	+	2.63834i	−0.678320	+	0.209234i
$160$	−9.83243	+	12.3295i	−0.777322	+	0.974731i
$161$		0			0
$162$	10.7072	+	13.4265i	0.841241	+	1.05488i
$163$	−1.17417	−	0.800535i	−0.0919680	−	0.0627027i	0.516463	−	0.856310i	$-0.327248\pi$
$163$	−1.17417	−	0.800535i	−0.0919680	−	0.0627027i	−0.608431	+	0.793607i	$0.708201\pi$
$164$	−4.30038	−	3.99017i	−0.335803	−	0.311580i
$165$	8.60252	−	14.9000i	0.669705	−	1.15996i
$166$	−2.82827	−	4.89871i	−0.219516	−	0.380214i
$167$	−2.71947	+	11.9148i	−0.210439	+	0.921992i	0.753831	+	0.657069i	$0.228204\pi$
$167$	−2.71947	+	11.9148i	−0.210439	+	0.921992i	−0.964269	+	0.264923i	$0.914653\pi$
$168$		0			0
$169$	2.68008	+	11.7422i	0.206160	+	0.903247i
$170$	6.21110	−	5.76306i	0.476370	−	0.442006i
$171$	0.0247981	−	0.00373771i	0.00189636	−	0.000285830i
$172$	16.4224	−	2.47528i	1.25219	−	0.188738i
$173$	2.70144	−	2.50657i	0.205386	−	0.190571i	−0.570772	−	0.821108i	$-0.693356\pi$
$173$	2.70144	−	2.50657i	0.205386	−	0.190571i	0.776159	+	0.630538i	$0.217166\pi$
$174$	4.08354	+	17.8912i	0.309572	+	1.35632i
$175$		0			0
$176$	4.75706	−	20.8421i	0.358577	−	1.57103i
$177$	−4.49999	−	7.79421i	−0.338240	−	0.585849i
$178$	10.7828	−	18.6763i	0.808204	−	1.39985i
$179$	10.5166	+	9.75796i	0.786046	+	0.729344i	0.967174	−	0.254116i	$-0.0817844\pi$
$179$	10.5166	+	9.75796i	0.786046	+	0.729344i	−0.181128	+	0.983460i	$0.557975\pi$
$180$	0.0137651	+	0.00938489i	0.00102599	+	0.000699508i
$181$	16.5163	+	20.7108i	1.22765	+	1.53942i	0.750964	+	0.660343i	$0.229589\pi$
$181$	16.5163	+	20.7108i	1.22765	+	1.53942i	0.476682	+	0.879076i	$0.341839\pi$
$182$		0			0
$183$	−4.82018	+	6.04431i	−0.356318	+	0.446808i
$184$	−2.39876	+	0.739918i	−0.176839	+	0.0545475i
$185$	1.34192	+	3.41916i	0.0986599	+	0.251381i
$186$	−2.51245	+	33.5264i	−0.184222	+	2.45827i
$187$	−3.55870	+	9.06743i	−0.260238	+	0.663076i
$188$	−6.44461	−	3.10356i	−0.470022	−	0.226350i
$189$		0			0
$190$	−19.3797	+	9.33276i	−1.40595	+	0.677070i
$191$	−0.672925	−	8.97956i	−0.0486912	−	0.649738i	−0.967147	−	0.254216i	$-0.918183\pi$
$191$	−0.672925	−	8.97956i	−0.0486912	−	0.649738i	0.918456	−	0.395522i	$-0.129436\pi$
$192$	−8.30245	−	2.56097i	−0.599178	−	0.184822i
$193$	5.67072	−	3.86623i	0.408188	−	0.278298i	−0.341770	−	0.939784i	$-0.611026\pi$
$193$	5.67072	−	3.86623i	0.408188	−	0.278298i	0.749957	+	0.661486i	$0.230074\pi$
$194$	3.33077	+	0.502033i	0.239135	+	0.0360439i
$195$	3.59914			0.257739
$196$		0			0
$197$	11.3025			0.805273			0.402636	−	0.915360i	$-0.368094\pi$
$197$	11.3025			0.805273			0.402636	+	0.915360i	$0.368094\pi$
$198$	−0.0418608	−	0.00630950i	−0.00297492	−	0.000448397i
$199$	−11.6600	+	7.94965i	−0.826555	+	0.563535i	−0.901065	−	0.433685i	$-0.857213\pi$
$199$	−11.6600	+	7.94965i	−0.826555	+	0.563535i	0.0745099	+	0.997220i	$0.476261\pi$
$200$	−0.301687	−	0.0930581i	−0.0213325	−	0.00658020i
$201$	0.0623917	+	0.832559i	0.00440077	+	0.0587242i
$202$	16.6093	−	7.99862i	1.16863	−	0.562781i
$203$		0			0
$204$	5.37044	+	2.58627i	0.376006	+	0.181075i
$205$	−2.75884	+	7.02942i	−0.192686	+	0.490956i
$206$	−0.519372	+	6.93054i	−0.0361864	+	0.482874i
$207$	0.00654471	+	0.0166756i	0.000454889	+	0.00115904i
$208$	4.27341	−	1.31817i	0.296308	−	0.0913988i
$209$	15.4179	−	19.3335i	1.06648	−	1.33732i
$210$		0			0
$211$	−10.5093	−	13.1783i	−0.723491	−	0.907229i	0.275039	−	0.961433i	$-0.411309\pi$
$211$	−10.5093	−	13.1783i	−0.723491	−	0.907229i	−0.998530	+	0.0542041i	$0.982738\pi$
$212$	−7.06144	−	4.81441i	−0.484982	−	0.330655i
$213$	−16.9878	−	15.7624i	−1.16398	−	1.08002i
$214$	−4.15126	+	7.19020i	−0.283775	+	0.491512i
$215$	−10.6891	−	18.5141i	−0.728990	−	1.26265i
$216$	0.768549	−	3.36723i	0.0522931	−	0.229111i
$217$		0			0
$218$	0.409926	+	1.79600i	0.0277637	+	0.121641i
$219$	7.57003	−	7.02396i	0.511535	−	0.474635i
$220$	16.2441	−	2.44841i	1.09518	−	0.165071i
$221$	−2.01492	+	0.303701i	−0.135538	+	0.0204291i
$222$	−4.18679	+	3.88478i	−0.280999	+	0.260729i
$223$	−3.67126	−	16.0848i	−0.245846	−	1.07712i	−0.935596	−	0.353073i	$-0.885137\pi$
$223$	−3.67126	−	16.0848i	−0.245846	−	1.07712i	0.689750	−	0.724048i	$-0.257721\pi$
$224$		0			0
$225$	−0.000501340		0.00219652i	−3.34227e−5		0.000146434i
$226$	3.59312	+	6.22347i	0.239011	+	0.413979i
$227$	−1.77433	+	3.07324i	−0.117767	+	0.203978i	−0.918882	−	0.394532i	$-0.870907\pi$
$227$	−1.77433	+	3.07324i	−0.117767	+	0.203978i	0.801116	+	0.598510i	$0.204240\pi$
$228$	−11.0927	−	10.2925i	−0.734634	−	0.681640i
$229$	11.8058	+	8.04903i	0.780147	+	0.531895i	0.886663	−	0.462416i	$-0.153017\pi$
$229$	11.8058	+	8.04903i	0.780147	+	0.531895i	−0.106516	+	0.994311i	$0.533970\pi$
$230$	−9.57991	−	12.0128i	−0.631680	−	0.792102i
$231$		0			0
$232$	2.29753	−	2.88101i	0.150840	−	0.189147i
$233$	13.5772	−	4.18802i	0.889473	−	0.274366i	0.183851	−	0.982954i	$-0.441144\pi$
$233$	13.5772	−	4.18802i	0.889473	−	0.274366i	0.705622	+	0.708588i	$0.250667\pi$
$234$	−0.00323539	−	0.00824364i	−0.000211504	−	0.000538904i
$235$	−0.688081	+	9.18180i	−0.0448854	+	0.598954i
$236$	3.13948	−	7.99927i	0.204363	−	0.520708i
$237$	−8.97862	−	4.32388i	−0.583224	−	0.280866i
$238$		0			0
$239$	−9.16287	+	4.41260i	−0.592697	+	0.285428i	−0.706090	−	0.708123i	$-0.749542\pi$
$239$	−9.16287	+	4.41260i	−0.592697	+	0.285428i	0.113393	+	0.993550i	$0.463828\pi$
$240$	1.25842	+	16.7925i	0.0812310	+	1.08395i
$241$	25.2629	+	7.79259i	1.62733	+	0.501965i	0.968224	−	0.250086i	$-0.0804589\pi$
$241$	25.2629	+	7.79259i	1.62733	+	0.501965i	0.659105	+	0.752051i	$0.270935\pi$
$242$	−17.1202	+	11.6723i	−1.10052	+	0.750325i
$243$	−0.0487057	−	0.00734120i	−0.00312447	−	0.000470938i
$244$	−7.38163			−0.472560
$245$		0			0
$246$	−11.7421			−0.748651
$247$	5.11518	+	0.770990i	0.325471	+	0.0490569i
$248$	5.57794	−	3.80297i	0.354200	−	0.241489i
$249$	−4.89484	−	1.50986i	−0.310198	−	0.0956834i
$250$	−1.66339	−	22.1964i	−0.105202	−	1.40382i
$251$	−21.9755	+	10.5828i	−1.38708	+	0.667983i	−0.970497	−	0.241114i	$-0.922487\pi$
$251$	−21.9755	+	10.5828i	−1.38708	+	0.667983i	−0.416584	+	0.909097i	$0.636773\pi$
$252$		0			0
$253$	15.9148	+	7.66417i	1.00056	+	0.481842i
$254$	−6.90252	+	17.5873i	−0.433103	+	1.10353i
$255$	0.573393	−	7.65140i	0.0359073	−	0.479150i
$256$	7.32207	+	18.6563i	0.457629	+	1.16602i
$257$	1.56696	−	0.483342i	0.0977441	−	0.0301501i	−0.245497	−	0.969397i	$-0.578951\pi$
$257$	1.56696	−	0.483342i	0.0977441	−	0.0301501i	0.343241	+	0.939247i	$0.388475\pi$
$258$	20.7262	−	25.9898i	1.29035	−	1.61805i
$259$		0			0
$260$	2.14262	+	2.68676i	0.132880	+	0.166626i
$261$	−0.0217273	−	0.0148134i	−0.00134489	−	0.000916929i
$262$	7.32852	+	6.79987i	0.452757	+	0.420098i
$263$	7.50291	−	12.9954i	0.462649	−	0.801332i	−0.536443	−	0.843937i	$-0.680232\pi$
$263$	7.50291	−	12.9954i	0.462649	−	0.801332i	0.999092	+	0.0426047i	$0.0135656\pi$
$264$	−2.68602	−	4.65233i	−0.165313	−	0.286331i
$265$	−2.44802	+	10.7255i	−0.150381	+	0.658861i
$266$		0			0
$267$	−4.34565	−	19.0396i	−0.265950	−	1.16520i
$268$	−0.584365	+	0.542211i	−0.0356958	+	0.0331208i
$269$	−7.29011	+	1.09881i	−0.444486	+	0.0669954i	−0.367472	−	0.930035i	$-0.619777\pi$
$269$	−7.29011	+	1.09881i	−0.444486	+	0.0669954i	−0.0770138	+	0.997030i	$0.524539\pi$
$270$	20.9041	−	3.15079i	1.27219	−	0.191751i
$271$	13.7781	−	12.7842i	0.836960	−	0.776586i	−0.139967	−	0.990156i	$-0.544700\pi$
$271$	13.7781	−	12.7842i	0.836960	−	0.776586i	0.976928	+	0.213570i	$0.0685092\pi$
$272$	−2.12149	−	9.29485i	−0.128634	−	0.563583i
$273$		0			0
$274$	7.82306	−	34.2751i	0.472609	−	2.07063i
$275$	1.11079	+	1.92394i	0.0669831	+	0.116018i
$276$	5.40466	−	9.36115i	0.325322	−	0.563475i
$277$	−9.24275	−	8.57602i	−0.555343	−	0.515283i	0.351817	−	0.936069i	$-0.385564\pi$
$277$	−9.24275	−	8.57602i	−0.555343	−	0.515283i	−0.907160	+	0.420786i	$0.861754\pi$
$278$	−11.2040	−	7.63877i	−0.671973	−	0.458143i
$279$	−0.0300377	−	0.0376661i	−0.00179831	−	0.00225501i
$280$		0			0
$281$	−9.38338	+	11.7664i	−0.559766	+	0.701924i	−0.978514	−	0.206178i	$-0.933897\pi$
$281$	−9.38338	+	11.7664i	−0.559766	+	0.701924i	0.418749	+	0.908102i	$0.362469\pi$
$282$	−13.6813	+	4.22011i	−0.814707	+	0.251304i
$283$	8.66864	+	22.0873i	0.515297	+	1.31296i	0.917620	+	0.397458i	$0.130107\pi$
$283$	8.66864	+	22.0873i	0.515297	+	1.31296i	−0.402323	+	0.915498i	$0.631797\pi$
$284$	1.65355	−	22.0650i	0.0981199	−	1.30932i
$285$	−7.11637	+	18.1322i	−0.421538	+	1.07406i
$286$	−7.86752	−	3.78880i	−0.465216	−	0.224036i
$287$		0			0
$288$	0.0316588	−	0.0152461i	0.00186551	−	0.000898384i
$289$	−0.945780	−	12.6206i	−0.0556341	−	0.742386i
$290$	21.5528	+	6.64817i	1.26563	+	0.390394i
$291$	2.52030	−	1.71831i	0.147742	−	0.100729i
$292$	9.74997	+	1.46957i	0.570574	+	0.0860001i
$293$	5.68397			0.332061			0.166031	−	0.986121i	$-0.446905\pi$
$293$	5.68397			0.332061			0.166031	+	0.986121i	$0.446905\pi$
$294$		0			0
$295$	−11.0616			−0.644029
$296$	1.13406	+	0.170931i	0.0659157	+	0.00993519i
$297$	−20.0806	+	13.6907i	−1.16519	+	0.794414i
$298$	−12.8303	−	3.95764i	−0.743242	−	0.229260i
$299$	0.276140	+	3.68484i	0.0159696	+	0.213100i
$300$	1.22484	−	0.589851i	0.0707160	−	0.0340551i
$301$		0			0
$302$	−1.82086	−	0.876879i	−0.104779	−	0.0504587i
$303$	6.09907	−	15.5402i	0.350382	−	0.892760i
$304$	−1.80871	+	24.1355i	−0.103736	+	1.38427i
$305$	3.47142	+	8.84504i	0.198773	+	0.506465i
$306$	−0.0180406	+	0.00556479i	−0.00103131	+	0.000318118i
$307$	−21.2853	+	26.6910i	−1.21482	+	1.52333i	−0.430991	+	0.902356i	$0.641836\pi$
$307$	−21.2853	+	26.6910i	−1.21482	+	1.52333i	−0.783828	+	0.620978i	$0.786735\pi$
$308$		0			0
$309$	3.92406	+	4.92062i	0.223232	+	0.279924i
$310$	34.1416	+	23.2773i	1.93911	+	1.32206i
$311$	−20.9147	−	19.4061i	−1.18597	−	1.10042i	−0.992866	−	0.119237i	$-0.961955\pi$
$311$	−20.9147	−	19.4061i	−1.18597	−	1.10042i	−0.193101	−	0.981179i	$-0.561854\pi$
$312$	0.561892	−	0.973225i	0.0318108	−	0.0550980i
$313$	13.5711	+	23.5059i	0.767086	+	1.32863i	0.939136	+	0.343544i	$0.111628\pi$
$313$	13.5711	+	23.5059i	0.767086	+	1.32863i	−0.172050	+	0.985088i	$0.555039\pi$
$314$	−2.02647	+	8.87856i	−0.114361	+	0.501046i
$315$		0			0
$316$	−2.11733	−	9.27664i	−0.119109	−	0.521852i
$317$	−9.00522	+	8.35562i	−0.505783	+	0.469298i	−0.891307	−	0.453399i	$-0.850211\pi$
$317$	−9.00522	+	8.35562i	−0.505783	+	0.469298i	0.385524	+	0.922698i	$0.374021\pi$
$318$	−16.9155	+	2.54960i	−0.948575	+	0.142975i
$319$	−25.6403	+	3.86465i	−1.43558	+	0.216379i
$320$	−7.82803	+	7.26335i	−0.437600	+	0.406033i
$321$	1.67303	+	7.33004i	0.0933797	+	0.409123i
$322$		0			0
$323$	2.45397	−	10.7515i	0.136542	−	0.598232i
$324$	7.42438	+	12.8594i	0.412466	+	0.714412i
$325$	−0.232367	+	0.402472i	−0.0128894	+	0.0223251i
$326$	−1.99092	−	1.84730i	−0.110267	−	0.102313i
$327$	1.37836	+	0.939752i	0.0762236	+	0.0519684i
$328$	1.47008	+	1.84343i	0.0811718	+	0.101786i
$329$		0			0
$330$	20.5012	−	25.7077i	1.12855	−	1.41516i
$331$	−16.9857	+	5.23941i	−0.933621	+	0.287984i	−0.724001	−	0.689799i	$-0.757699\pi$
$331$	−16.9857	+	5.23941i	−0.933621	+	0.287984i	−0.209620	+	0.977783i	$0.567223\pi$
$332$	−1.78686	−	4.55285i	−0.0980669	−	0.249870i
$333$	0.000611614	−	0.00816142i	3.35162e−5	−	0.000447243i
$334$	−8.53306	+	21.7419i	−0.466909	+	1.18966i
$335$	0.924520	+	0.445225i	0.0505119	+	0.0243252i
$336$		0			0
$337$	−5.50487	+	2.65100i	−0.299869	+	0.144409i	−0.577768	−	0.816201i	$-0.696076\pi$
$337$	−5.50487	+	2.65100i	−0.299869	+	0.144409i	0.277899	+	0.960610i	$0.410362\pi$
$338$	1.72015	+	22.9538i	0.0935639	+	1.24852i
$339$	6.21856	+	1.91817i	0.337746	+	0.104181i
$340$	6.05314	−	4.12696i	0.328278	−	0.223816i
$341$	−46.9742	−	7.08022i	−2.54380	−	0.383416i
$342$	0.0479281			0.00259166
$343$		0			0
$344$	−6.67506			−0.359895
$345$	−13.7587	−	2.07379i	−0.740744	−	0.111649i
$346$	5.81915	−	3.96743i	0.312839	−	0.213290i
$347$	19.0606	+	5.87941i	1.02323	+	0.315623i	0.760563	−	0.649264i	$-0.224923\pi$
$347$	19.0606	+	5.87941i	1.02323	+	0.315623i	0.262663	+	0.964888i	$0.415399\pi$
$348$	1.18578	+	15.8231i	0.0635643	+	0.848207i
$349$	−18.1531	+	8.74208i	−0.971714	+	0.467953i	−0.851247	−	0.524765i	$-0.824153\pi$
$349$	−18.1531	+	8.74208i	−0.971714	+	0.467953i	−0.120466	+	0.992717i	$0.538439\pi$
$350$		0			0
$351$	−4.58060	−	2.20590i	−0.244494	−	0.117742i
$352$	12.6585	−	32.2534i	0.674702	−	1.71911i
$353$	1.38418	−	18.4706i	0.0736725	−	0.983092i	−0.830803	−	0.556566i	$-0.812118\pi$
$353$	1.38418	−	18.4706i	0.0736725	−	0.983092i	0.904476	−	0.426525i	$-0.140262\pi$
$354$	−6.28396	−	16.0113i	−0.333989	−	0.850990i
$355$	−27.2171	+	8.39535i	−1.44453	+	0.445579i
$356$	11.6260	−	14.5786i	0.616179	−	0.772664i
$357$		0			0
$358$	17.0948	+	21.4361i	0.903486	+	1.13294i
$359$	−13.0287	−	8.88283i	−0.687629	−	0.468818i	0.168418	−	0.985716i	$-0.446134\pi$
$359$	−13.0287	−	8.88283i	−0.687629	−	0.468818i	−0.856047	+	0.516898i	$0.827087\pi$
$360$	−0.00490851	−	0.00455443i	−0.000258701	−	0.000240040i
$361$	−4.49817	+	7.79106i	−0.236746	+	0.410056i
$362$	25.3132	+	43.8437i	1.33043	+	2.30437i
$363$	−4.17538	+	18.2936i	−0.219151	+	0.960162i
$364$		0			0
$365$	−2.82429	−	12.3740i	−0.147830	−	0.647685i
$366$	−10.8308	+	10.0496i	−0.566137	+	0.525299i
$367$	−14.2250	+	2.14407i	−0.742539	+	0.111920i	−0.509408	−	0.860525i	$-0.670135\pi$
$367$	−14.2250	+	2.14407i	−0.742539	+	0.111920i	−0.233132	+	0.972445i	$0.574897\pi$
$368$	−17.0958	+	2.57678i	−0.891181	+	0.134324i
$369$	0.0123344	−	0.0114446i	0.000642101	−	0.000595783i
$370$	1.56204	+	6.84376i	0.0812067	+	0.355790i
$371$		0			0
$372$	−6.46867	+	28.3411i	−0.335385	+	1.46942i
$373$	1.97264	+	3.41671i	0.102139	+	0.176911i	0.912566	−	0.408930i	$-0.134098\pi$
$373$	1.97264	+	3.41671i	0.102139	+	0.176911i	−0.810426	+	0.585840i	$0.800765\pi$
$374$	−9.30802	+	16.1220i	−0.481306	+	0.833647i
$375$	−14.7760	−	13.7101i	−0.763029	−	0.707987i
$376$	2.37538	+	1.61951i	0.122501	+	0.0835198i
$377$	−3.38199	−	4.24088i	−0.174181	−	0.218417i
$378$		0			0
$379$	−16.6555	+	20.8853i	−0.855536	+	1.07281i	0.141030	+	0.990005i	$0.454959\pi$
$379$	−16.6555	+	20.8853i	−0.855536	+	1.07281i	−0.996566	+	0.0828026i	$0.973613\pi$
$380$	−17.7722	+	5.48201i	−0.911697	+	0.281221i
$381$	6.25074	+	15.9266i	0.320235	+	0.815946i
$382$	1.28606	−	17.1613i	0.0658005	−	0.878046i
$383$	0.249371	−	0.635386i	0.0127422	−	0.0324667i	−0.924361	−	0.381519i	$-0.875401\pi$
$383$	0.249371	−	0.635386i	0.0127422	−	0.0324667i	0.937103	+	0.349052i	$0.113496\pi$
$384$	8.15995	+	3.92962i	0.416411	+	0.200533i
$385$		0			0
$386$	11.8178	−	5.69115i	0.601510	−	0.289672i
$387$	0.00355975	+	0.0475016i	0.000180952	+	0.00241464i
$388$	2.78310	+	0.858472i	0.141290	+	0.0435823i
$389$	26.3250	−	17.9481i	1.33473	−	0.910004i	0.335247	−	0.942130i	$-0.391180\pi$
$389$	26.3250	−	17.9481i	1.33473	−	0.910004i	0.999484	+	0.0321261i	$0.0102278\pi$
$390$	6.80165	+	1.02518i	0.344415	+	0.0519122i
$391$	7.87759			0.398387
$392$		0			0
$393$	9.05326			0.456677
$394$	21.3595	+	3.21943i	1.07608	+	0.162193i
$395$	−10.1200	+	6.89970i	−0.509192	+	0.347162i
$396$	−0.0349777	−	0.0107892i	−0.00175770	−	0.000542177i
$397$	0.586137	+	7.82146i	0.0294174	+	0.392548i	0.992406	+	0.123006i	$0.0392533\pi$
$397$	0.586137	+	7.82146i	0.0294174	+	0.392548i	−0.962989	+	0.269542i	$0.913128\pi$
$398$	−24.2994	+	11.7020i	−1.21802	+	0.586568i
$399$		0			0
$400$	−1.95906	−	0.943434i	−0.0979530	−	0.0471717i
$401$	7.22540	−	18.4100i	0.360819	−	0.919353i	−0.629049	−	0.777366i	$-0.716556\pi$
$401$	7.22540	−	18.4100i	0.360819	−	0.919353i	0.989868	−	0.141987i	$-0.0453492\pi$
$402$	−0.119240	+	1.59114i	−0.00594713	+	0.0793589i
$403$	−3.63060	−	9.25062i	−0.180853	−	0.460806i
$404$	15.2317	−	4.69834i	0.757803	−	0.233751i
$405$	11.9173	−	14.9438i	0.592173	−	0.742562i
$406$		0			0
$407$	−5.03166	−	6.30950i	−0.249410	−	0.312750i
$408$	−1.97946	−	1.34957i	−0.0979979	−	0.0668139i
$409$	6.65845	+	6.17814i	0.329239	+	0.305489i	0.827420	−	0.561584i	$-0.189808\pi$
$409$	6.65845	+	6.17814i	0.329239	+	0.305489i	−0.498181	+	0.867073i	$0.665998\pi$
$410$	−7.21593	+	12.4984i	−0.356369	+	0.617250i
$411$	−15.9184	−	27.5715i	−0.785197	−	1.36000i
$412$	−1.33720	+	5.85865i	−0.0658790	+	0.288635i
$413$		0			0
$414$	0.00761827	+	0.0333778i	0.000374418	+	0.00164043i
$415$	−4.61514	+	4.28222i	−0.226548	+	0.210206i
$416$	7.16720	−	1.08028i	0.351401	−	0.0529652i
$417$	−12.1427	+	1.83021i	−0.594629	+	0.0896259i
$418$	34.6438	−	32.1447i	1.69448	−	1.57225i
$419$	1.37067	+	6.00531i	0.0669617	+	0.293378i	0.997310	−	0.0732985i	$-0.0233526\pi$
$419$	1.37067	+	6.00531i	0.0669617	+	0.293378i	−0.930348	+	0.366677i	$0.880495\pi$
$420$		0			0
$421$	−2.18693	+	9.58155i	−0.106584	+	0.466976i	0.893264	+	0.449533i	$0.148410\pi$
$421$	−2.18693	+	9.58155i	−0.106584	+	0.466976i	−0.999848	+	0.0174428i	$0.994447\pi$
$422$	−16.1068	−	27.8978i	−0.784066	−	1.35804i
$423$	0.0102581	−	0.0177676i	0.000498766	−	0.000863889i
$424$	2.51804	+	2.33640i	0.122287	+	0.113466i
$425$	0.818595	+	0.558109i	0.0397077	+	0.0270722i
$426$	−27.6138	−	34.6265i	−1.33789	−	1.67766i
$427$		0			0
$428$	−4.47591	+	5.61262i	−0.216351	+	0.271296i
$429$	−7.55641	+	2.33084i	−0.364827	+	0.112534i
$430$	−14.9267	−	38.0326i	−0.719828	−	1.83409i
$431$	−0.176207	+	2.35131i	−0.00848757	+	0.113259i	−0.999838	−	0.0179801i	$-0.994276\pi$
$431$	−0.176207	+	2.35131i	−0.00848757	+	0.113259i	0.991351	+	0.131239i	$0.0418955\pi$
$432$	8.69050	−	22.1430i	0.418122	−	1.06536i
$433$	22.9471	+	11.0507i	1.10277	+	0.531064i	0.894527	−	0.447014i	$-0.147512\pi$
$433$	22.9471	+	11.0507i	1.10277	+	0.531064i	0.208239	+	0.978078i	$0.433227\pi$
$434$		0			0
$435$	18.4024	−	8.86212i	0.882327	−	0.424906i
$436$	0.119034	+	1.58840i	0.00570070	+	0.0760706i
$437$	−19.1100	−	5.89465i	−0.914154	−	0.281979i
$438$	16.3066	−	11.1176i	0.779157	−	0.531220i
$439$	37.8011	+	5.69759i	1.80415	+	0.271931i	0.963122	−	0.269066i	$-0.0867150\pi$
$439$	37.8011	+	5.69759i	1.80415	+	0.271931i	0.841024	+	0.540997i	$0.181953\pi$
$440$	−6.60260			−0.314767
$441$		0			0
$442$	−3.89430			−0.185233
$443$	−13.5709	−	2.04548i	−0.644772	−	0.0971837i	−0.181487	−	0.983393i	$-0.558091\pi$
$443$	−13.5709	−	2.04548i	−0.644772	−	0.0971837i	−0.463285	+	0.886210i	$0.653329\pi$
$444$	−4.08032	+	2.78192i	−0.193643	+	0.132024i
$445$	−22.9363	−	7.07491i	−1.08728	−	0.335383i
$446$	−2.35632	−	31.4429i	−0.111575	−	1.48886i
$447$	−10.9549	+	5.27560i	−0.518148	+	0.249527i
$448$		0			0
$449$	4.90891	+	2.36401i	0.231666	+	0.111564i	0.546116	−	0.837710i	$-0.316106\pi$
$449$	4.90891	+	2.36401i	0.231666	+	0.111564i	−0.314450	+	0.949274i	$0.601820\pi$
$450$	−0.00157309	+	0.00400817i	−7.41563e−5	+	0.000188947i
$451$	1.23987	−	16.5450i	0.0583834	−	0.779072i
$452$	2.27009	+	5.78409i	0.106776	+	0.272061i
$453$	−1.74885	+	0.539450i	−0.0821684	+	0.0253456i
$454$	−4.22852	+	5.30240i	−0.198454	+	0.248854i
$455$		0			0
$456$	3.79205	+	4.75508i	0.177579	+	0.222677i
$457$	19.0403	+	12.9815i	0.890668	+	0.607247i	0.919825	−	0.392328i	$-0.128330\pi$
$457$	19.0403	+	12.9815i	0.890668	+	0.607247i	−0.0291578	+	0.999575i	$0.509283\pi$
$458$	20.0178	+	18.5738i	0.935372	+	0.867898i
$459$	−5.41928	+	9.38647i	−0.252950	+	0.438123i
$460$	−6.64269	−	11.5055i	−0.309717	−	0.536445i
$461$	7.37198	−	32.2988i	0.343347	−	1.50430i	−0.448610	−	0.893727i	$-0.648081\pi$
$461$	7.37198	−	32.2988i	0.343347	−	1.50430i	0.791958	−	0.610576i	$-0.209062\pi$
$462$		0			0
$463$	−0.375043	−	1.64317i	−0.0174297	−	0.0763645i	0.965465	−	0.260532i	$-0.0838981\pi$
$463$	−0.375043	−	1.64317i	−0.0174297	−	0.0763645i	−0.982895	+	0.184168i	$0.941041\pi$
$464$	18.6042	−	17.2622i	0.863679	−	0.801377i
$465$	37.0018	−	5.57713i	1.71592	−	0.258633i
$466$	26.8511	−	4.04716i	1.24386	−	0.187481i
$467$	−14.6255	+	13.5705i	−0.676787	+	0.627967i	−0.941759	−	0.336289i	$-0.890828\pi$
$467$	−14.6255	+	13.5705i	−0.676787	+	0.627967i	0.264971	+	0.964256i	$0.414637\pi$
$468$	−0.00170389	−	0.00746522i	−7.87622e−5	−	0.000345080i
$469$		0			0
$470$	−3.91569	+	17.1558i	−0.180617	+	0.791336i
$471$	4.12348	+	7.14207i	0.190000	+	0.329089i
$472$	−1.72691	+	2.99110i	−0.0794877	+	0.137677i
$473$	34.4318	+	31.9480i	1.58317	+	1.46897i
$474$	−15.7362	−	10.7287i	−0.722786	−	0.492787i
$475$	−1.56818	−	1.96644i	−0.0719530	−	0.0902263i
$476$		0			0
$477$	0.0152837	−	0.0191651i	0.000699791	−	0.000877510i
$478$	−18.5729	+	5.72897i	−0.849504	+	0.262037i
$479$	−1.07099	−	2.72883i	−0.0489347	−	0.124684i	0.904316	−	0.426863i	$-0.140381\pi$
$479$	−1.07099	−	2.72883i	−0.0489347	−	0.124684i	−0.953251	+	0.302179i	$0.902286\pi$
$480$	−2.03960	+	27.2165i	−0.0930944	+	1.24226i
$481$	0.616769	−	1.57150i	0.0281223	−	0.0716544i
$482$	45.5222	+	21.9224i	2.07348	+	0.998536i
$483$		0			0
$484$	−16.1419	+	7.77351i	−0.733721	+	0.353341i
$485$	−0.280167	−	3.73857i	−0.0127217	−	0.169760i
$486$	−0.0899529	−	0.0277468i	−0.00408034	−	0.00125862i
$487$	−24.6705	+	16.8200i	−1.11793	+	0.762189i	−0.973808	−	0.227372i	$-0.926987\pi$
$487$	−24.6705	+	16.8200i	−1.11793	+	0.762189i	−0.144118	+	0.989561i	$0.546034\pi$
$488$	2.93370	+	0.442184i	0.132802	+	0.0200167i
$489$	−2.45947			−0.111221
$490$		0			0
$491$	−0.0655631			−0.00295882			−0.00147941	−	0.999999i	$-0.500471\pi$
$491$	−0.0655631			−0.00295882			−0.00147941	+	0.999999i	$0.500471\pi$
$492$	−10.0395	−	1.51321i	−0.452614	−	0.0682206i
$493$	−9.55450	+	6.51415i	−0.430313	+	0.293382i
$494$	9.44706	+	2.91403i	0.425043	+	0.131109i
$495$	0.00352111	+	0.0469860i	0.000158262	+	0.00211186i
$496$	41.8913	−	20.1738i	1.88097	−	0.905829i
$497$		0			0
$498$	−8.82020	−	4.24758i	−0.395242	−	0.190339i
$499$	1.69704	−	4.32398i	0.0759698	−	0.193568i	−0.887844	−	0.460145i	$-0.847797\pi$
$499$	1.69704	−	4.32398i	0.0759698	−	0.193568i	0.963814	+	0.266577i	$0.0858927\pi$
$500$	1.43825	−	19.1922i	0.0643207	−	0.858300i
$501$	7.72731	+	19.6889i	0.345231	+	0.879634i
$502$	−44.5437	+	13.7399i	−1.98808	+	0.613243i
$503$	13.7881	−	17.2898i	0.614782	−	0.770913i	−0.372817	−	0.927905i	$-0.621608\pi$
$503$	13.7881	−	17.2898i	0.614782	−	0.770913i	0.987600	+	0.156992i	$0.0501797\pi$
$504$		0			0
$505$	−12.7929	−	16.0418i	−0.569277	−	0.713851i
$506$	27.8927	+	19.0169i	1.23998	+	0.845406i
$507$	15.2802	+	14.1780i	0.678618	+	0.629665i
$508$	−8.16811	+	14.1476i	−0.362401	+	0.627697i
$509$	5.35918	+	9.28237i	0.237542	+	0.411434i	0.960008	−	0.279972i	$-0.0903251\pi$
$509$	5.35918	+	9.28237i	0.237542	+	0.411434i	−0.722467	+	0.691406i	$0.756992\pi$
$510$	3.26304	−	14.2963i	0.144490	−	0.633051i
$511$		0			0
$512$	6.19419	+	27.1385i	0.273747	+	1.19937i
$513$	20.1702	−	18.7152i	0.890535	−	0.826295i
$514$	3.09891	−	0.467086i	0.136687	−	0.0206023i
$515$	7.64898	−	1.15290i	0.337054	−	0.0508028i
$516$	21.0701	−	19.5502i	0.927558	−	0.860648i
$517$	−4.50161	−	19.7229i	−0.197981	−	0.867410i
$518$		0			0
$519$	1.41921	−	6.21799i	0.0622966	−	0.272939i
$520$	−0.690602	−	1.19616i	−0.0302849	−	0.0524550i
$521$	1.95478	−	3.38578i	0.0856405	−	0.148334i	−0.820023	−	0.572330i	$-0.806040\pi$
$521$	1.95478	−	3.38578i	0.0856405	−	0.148334i	0.905664	+	0.423996i	$0.139373\pi$
$522$	−0.0368408	−	0.0341833i	−0.00161248	−	0.00149616i
$523$	−30.2781	−	20.6433i	−1.32397	−	0.902668i	−0.324899	−	0.945749i	$-0.605330\pi$
$523$	−30.2781	−	20.6433i	−1.32397	−	0.902668i	−0.999072	+	0.0430809i	$0.986283\pi$
$524$	5.38955	+	6.75829i	0.235444	+	0.295237i
$525$		0			0
$526$	17.8806	−	22.4216i	0.779633	−	0.977628i
$527$	−20.2443	+	6.24454i	−0.881856	+	0.272017i
$528$	−13.5171	−	34.4410i	−0.588257	−	1.49885i
$529$	−0.651245	+	8.69026i	−0.0283150	+	0.377837i
$530$	−7.68133	+	19.5717i	−0.333656	+	0.850141i
$531$	0.0222065	+	0.0106941i	0.000963679	+	0.000464084i
$532$		0			0
$533$	3.12705	−	1.50591i	0.135447	−	0.0652281i
$534$	−2.78916	−	37.2188i	−0.120699	−	1.61061i
$535$	8.83025	+	2.72377i	0.381765	+	0.117759i
$536$	0.264726	−	0.180487i	0.0114344	−	0.00779585i
$537$	24.5516	+	3.70055i	1.05948	+	0.159691i
$538$	−14.0898			−0.607456
$539$		0			0
$540$	18.2790			0.786602
$541$	33.6346	+	5.06960i	1.44607	+	0.217959i	0.824704	−	0.565565i	$-0.191342\pi$
$541$	33.6346	+	5.06960i	1.44607	+	0.217959i	0.621361	+	0.783524i	$0.286580\pi$
$542$	29.6793	−	20.2350i	1.27484	−	0.869169i
$543$	43.8091	+	13.5133i	1.88003	+	0.579912i
$544$	−1.15473	−	15.4089i	−0.0495088	−	0.660650i
$545$	1.84732	−	0.889624i	0.0791306	−	0.0381073i
$546$		0			0
$547$	−23.6873	−	11.4072i	−1.01280	−	0.487736i	−0.147534	−	0.989057i	$-0.547133\pi$
$547$	−23.6873	−	11.4072i	−1.01280	−	0.487736i	−0.865262	+	0.501321i	$0.832848\pi$
$548$	11.1057	−	28.2969i	0.474412	−	1.20878i
$549$	0.00158219	−	0.0211128i	6.75261e−5	−	0.000901073i
$550$	1.55115	+	3.95227i	0.0661413	+	0.168525i
$551$	28.0523	−	8.65300i	1.19507	−	0.368630i
$552$	−2.70875	+	3.39667i	−0.115292	+	0.144572i
$553$		0			0
$554$	−15.0241	−	18.8397i	−0.638315	−	0.800421i
$555$	5.25232	+	3.58097i	0.222949	+	0.152004i
$556$	−8.59498	−	7.97498i	−0.364508	−	0.338214i
$557$	1.50611	−	2.60866i	0.0638159	−	0.110532i	−0.832352	−	0.554247i	$-0.813006\pi$
$557$	1.50611	−	2.60866i	0.0638159	−	0.110532i	0.896168	+	0.443715i	$0.146340\pi$
$558$	−0.0460364	−	0.0797374i	−0.00194888	−	0.00337555i
$559$	−2.18644	+	9.57943i	−0.0924767	+	0.405167i
$560$		0			0
$561$	3.75130	+	16.4355i	0.158380	+	0.693908i
$562$	−21.0843	+	19.5633i	−0.889386	+	0.825230i
$563$	0.416553	−	0.0627853i	0.0175556	−	0.00264608i	−0.140259	−	0.990115i	$-0.544793\pi$
$563$	0.416553	−	0.0627853i	0.0175556	−	0.00264608i	0.157814	+	0.987469i	$0.449555\pi$
$564$	−12.2413	+	1.84507i	−0.515450	+	0.0776916i
$565$	5.86321	−	5.44027i	0.246667	−	0.228874i
$566$	10.0906	+	44.2098i	0.424140	+	1.85828i
$567$		0			0
$568$	−1.97894	+	8.67030i	−0.0830345	+	0.363798i
$569$	16.7939	+	29.0879i	0.704037	+	1.21943i	0.967038	+	0.254633i	$0.0819546\pi$
$569$	16.7939	+	29.0879i	0.704037	+	1.21943i	−0.263001	+	0.964796i	$0.584712\pi$
$570$	−18.6133	+	32.2392i	−0.779627	+	1.35035i
$571$	−10.2326	−	9.49444i	−0.428220	−	0.397330i	0.436403	−	0.899751i	$-0.356252\pi$
$571$	−10.2326	−	9.49444i	−0.428220	−	0.397330i	−0.864623	+	0.502421i	$0.832443\pi$
$572$	−6.23843	−	4.25329i	−0.260842	−	0.177839i
$573$	−9.71668	−	12.1843i	−0.405920	−	0.509008i
$574$		0			0
$575$	1.12019	−	1.40467i	0.0467151	−	0.0585789i
$576$	0.0227371	−	0.00701346i	0.000947379	−	0.000292228i
$577$	−13.5909	−	34.6290i	−0.565795	−	1.44162i	−0.871928	−	0.489634i	$-0.837131\pi$
$577$	−13.5909	−	34.6290i	−0.565795	−	1.44162i	0.306133	−	0.951989i	$-0.400965\pi$
$578$	1.80752	−	24.1197i	0.0751831	−	1.00325i
$579$	4.33959	−	11.0571i	0.180347	−	0.459517i
$580$	17.5708	+	8.46167i	0.729589	+	0.351352i
$581$		0			0
$582$	5.25230	−	2.52938i	0.217715	−	0.104846i
$583$	−1.80632	−	24.1036i	−0.0748099	−	0.998269i
$584$	−3.78692	−	1.16811i	−0.156704	−	0.0483367i
$585$	−0.00814390	+	0.00555242i	−0.000336709	+	0.000229564i
$586$	10.7416	+	1.61903i	0.443730	+	0.0668816i
$587$	35.8868			1.48120			0.740602	−	0.671943i	$-0.234540\pi$
$587$	35.8868			1.48120			0.740602	+	0.671943i	$0.234540\pi$
$588$		0			0
$589$	53.7827			2.21608
$590$	−20.9041	−	3.15079i	−0.860610	−	0.129716i
$591$	16.1621	−	11.0192i	0.664822	−	0.453268i
$592$	7.54782	+	2.32819i	0.310214	+	0.0956882i
$593$	−1.94432	−	25.9452i	−0.0798437	−	1.06544i	−0.882907	−	0.469547i	$-0.844417\pi$
$593$	−1.94432	−	25.9452i	−0.0798437	−	1.06544i	0.803064	−	0.595893i	$-0.203202\pi$
$594$	−41.8479	+	20.1529i	−1.71704	+	0.826883i
$595$		0			0
$596$	−10.4599	−	5.03721i	−0.428453	−	0.206332i
$597$	−8.92295	+	22.7353i	−0.365192	+	0.930494i
$598$	−0.527744	+	7.04226i	−0.0215811	+	0.287979i
$599$	−10.7046	−	27.2750i	−0.437380	−	1.11443i	−0.964371	−	0.264555i	$-0.914775\pi$
$599$	−10.7046	−	27.2750i	−0.437380	−	1.11443i	0.526991	−	0.849871i	$-0.323320\pi$
$600$	−0.522124	+	0.161054i	−0.0213156	+	0.00657500i
$601$	0.155428	−	0.194901i	0.00634005	−	0.00795017i	−0.778651	−	0.627457i	$-0.784096\pi$
$601$	0.155428	−	0.194901i	0.00634005	−	0.00795017i	0.784991	+	0.619507i	$0.212667\pi$
$602$		0			0
$603$	−0.00142557	−	0.00178761i	−5.80538e−5	−	7.27971e-5i
$604$	−1.44382	−	0.984381i	−0.0587483	−	0.0400539i
$605$	16.9058	+	15.6863i	0.687318	+	0.637738i
$606$	15.9525	−	27.6306i	0.648026	−	1.12241i
$607$	2.15676	+	3.73563i	0.0875404	+	0.151624i	0.906471	−	0.422268i	$-0.138766\pi$
$607$	2.15676	+	3.73563i	0.0875404	+	0.151624i	−0.818931	+	0.573893i	$0.805433\pi$
$608$	−8.72892	+	38.2439i	−0.354005	+	1.55100i
$609$		0			0
$610$	4.04086	+	17.7042i	0.163610	+	0.716820i
$611$	3.10223	−	2.87845i	0.125503	−	0.116450i
$612$	−0.0161418	+	0.00243298i	−0.000652492	+	9.83474e-5i
$613$	20.1726	−	3.04053i	0.814764	−	0.122806i	0.271576	−	0.962417i	$-0.412455\pi$
$613$	20.1726	−	3.04053i	0.814764	−	0.122806i	0.543188	+	0.839611i	$0.317217\pi$
$614$	−47.8277	+	44.3777i	−1.93017	+	1.79094i
$615$	2.90815	+	12.7414i	0.117268	+	0.513784i
$616$		0			0
$617$	−7.00176	+	30.6767i	−0.281880	+	1.23500i	0.613500	+	0.789695i	$0.289761\pi$
$617$	−7.00176	+	30.6767i	−0.281880	+	1.23500i	−0.895380	+	0.445303i	$0.853096\pi$
$618$	6.01410	+	10.4167i	0.241922	+	0.419022i
$619$	8.05856	−	13.9578i	0.323901	−	0.561013i	−0.657388	−	0.753552i	$-0.728339\pi$
$619$	8.05856	−	13.9578i	0.323901	−	0.561013i	0.981289	+	0.192539i	$0.0616722\pi$
$620$	26.1911	+	24.3018i	1.05186	+	0.975984i
$621$	16.2396	+	11.0720i	0.651673	+	0.444303i
$622$	−33.9970	−	42.6309i	−1.36316	−	1.70934i
$623$		0			0
$624$	4.82567	−	6.05119i	0.193181	−	0.242242i
$625$	−21.4022	+	6.60171i	−0.856089	+	0.264069i
$626$	18.9513	+	48.2871i	0.757446	+	1.92994i
$627$	3.19823	−	42.6774i	0.127725	−	1.70437i
$628$	−2.87681	+	7.32998i	−0.114797	+	0.292498i
$629$	−3.24260	−	1.56155i	−0.129291	−	0.0622632i
$630$		0			0
$631$	36.5783	−	17.6152i	1.45616	−	0.701249i	0.472507	−	0.881327i	$-0.343349\pi$
$631$	36.5783	−	17.6152i	1.45616	−	0.701249i	0.983652	+	0.180077i	$0.0576348\pi$
$632$	0.285795	+	3.81367i	0.0113683	+	0.151700i
$633$	−27.8757	−	8.59852i	−1.10796	−	0.341760i
$634$	−19.3981	+	13.2254i	−0.770396	+	0.525247i
$635$	20.7936	+	3.13413i	0.825170	+	0.124374i
$636$	−14.7913			−0.586511
$637$		0			0
$638$	−49.5558			−1.96193
$639$	0.0627557	+	0.00945889i	0.00248258	+	0.000374188i
$640$	9.19726	−	6.27058i	0.363553	−	0.247867i
$641$	−24.9036	−	7.68173i	−0.983631	−	0.303410i	−0.239098	−	0.970995i	$-0.576852\pi$
$641$	−24.9036	−	7.68173i	−0.983631	−	0.303410i	−0.744533	+	0.667585i	$0.767328\pi$
$642$	1.07380	+	14.3289i	0.0423795	+	0.565515i
$643$	16.3705	−	7.88362i	0.645589	−	0.310899i	−0.0822861	−	0.996609i	$-0.526222\pi$
$643$	16.3705	−	7.88362i	0.645589	−	0.310899i	0.727876	+	0.685709i	$0.240508\pi$
$644$		0			0
$645$	−33.3348	−	16.0532i	−1.31256	−	0.632094i
$646$	7.70000	−	19.6193i	0.302952	−	0.771910i
$647$	−0.408618	+	5.45263i	−0.0160644	+	0.214365i	0.983395	+	0.181480i	$0.0580886\pi$
$647$	−0.408618	+	5.45263i	−0.0160644	+	0.214365i	−0.999459	+	0.0328853i	$0.989530\pi$
$648$	−2.18037	−	5.55549i	−0.0856530	−	0.218240i
$649$	23.2238	−	7.16360i	0.911615	−	0.281196i
$650$	−0.553768	+	0.694403i	−0.0217206	+	0.0272367i
$651$		0			0
$652$	−1.46416	−	1.83600i	−0.0573411	−	0.0719035i
$653$	−26.4814	−	18.0547i	−1.03630	−	0.706536i	−0.0793648	−	0.996846i	$-0.525289\pi$
$653$	−26.4814	−	18.0547i	−1.03630	−	0.706536i	−0.956933	+	0.290310i	$0.906242\pi$
$654$	2.33715	+	2.16856i	0.0913898	+	0.0847973i
$655$	5.56353	−	9.63631i	0.217385	−	0.376522i
$656$	8.11948	+	14.0634i	0.317012	+	0.549082i
$657$	−0.00629307	+	0.0275717i	−0.000245516	+	0.00107568i
$658$		0			0
$659$	9.45761	+	41.4365i	0.368416	+	1.61414i	0.731132	+	0.682236i	$0.238993\pi$
$659$	9.45761	+	41.4365i	0.368416	+	1.61414i	−0.362716	+	0.931900i	$0.618150\pi$
$660$	20.8413	−	19.3379i	0.811248	−	0.752729i
$661$	−11.5496	+	1.74082i	−0.449228	+	0.0677102i	−0.369760	−	0.929127i	$-0.620560\pi$
$661$	−11.5496	+	1.74082i	−0.449228	+	0.0677102i	−0.0794677	+	0.996837i	$0.525322\pi$
$662$	−33.5920	+	5.06319i	−1.30559	+	0.196786i
$663$	−2.58516	+	2.39868i	−0.100399	+	0.0931571i
$664$	0.437426	+	1.91649i	0.0169754	+	0.0743742i
$665$		0			0
$666$	0.00348054	−	0.0152492i	0.000134868	−	0.000590896i
$667$	10.4851	+	18.1606i	0.405983	+	0.703183i
$668$	−10.0976	+	17.4896i	−0.390688	+	0.676692i
$669$	−20.9313	−	19.4214i	−0.809251	−	0.750876i
$670$	1.62034	+	1.10473i	0.0625991	+	0.0426794i
$671$	−13.0164	−	16.3221i	−0.502494	−	0.630107i
$672$		0			0
$673$	−3.92924	+	4.92711i	−0.151461	+	0.189926i	−0.851773	−	0.523911i	$-0.824473\pi$
$673$	−3.92924	+	4.92711i	−0.151461	+	0.189926i	0.700312	+	0.713837i	$0.253044\pi$
$674$	−11.1582	+	3.44185i	−0.429798	+	0.132575i
$675$	0.903106	+	2.30108i	0.0347605	+	0.0885684i
$676$	−1.48733	+	19.8471i	−0.0572051	+	0.763349i
$677$	−0.167889	+	0.427773i	−0.00645249	+	0.0164407i	−0.934064	−	0.357106i	$-0.883763\pi$
$677$	−0.167889	+	0.427773i	−0.00645249	+	0.0164407i	0.927611	+	0.373547i	$0.121859\pi$
$678$	11.2055	+	5.39626i	0.430343	+	0.207242i
$679$		0			0
$680$	−2.65293	+	1.27759i	−0.101735	+	0.0489932i
$681$	0.458964	+	6.12444i	0.0175875	+	0.234689i
$682$	−86.7551	−	26.7604i	−3.32202	−	1.02471i
$683$	−37.3541	+	25.4676i	−1.42931	+	0.974490i	−0.431953	+	0.901896i	$0.642175\pi$
$683$	−37.3541	+	25.4676i	−1.42931	+	0.974490i	−0.997362	+	0.0725939i	$0.976872\pi$
$684$	0.0409783	+	0.00617649i	0.00156685	+	0.000236164i
$685$	−39.1295			−1.49506
$686$		0			0
$687$	24.7290			0.943469
$688$	−45.4593	−	6.85189i	−1.73312	−	0.261226i
$689$	4.17779	−	2.84837i	0.159161	−	0.108514i
$690$	−25.4105	−	7.83810i	−0.967361	−	0.298391i
$691$	0.920717	+	12.2861i	0.0350257	+	0.467386i	0.986947	+	0.161044i	$0.0514860\pi$
$691$	0.920717	+	12.2861i	0.0350257	+	0.467386i	−0.951922	+	0.306342i	$0.900895\pi$
$692$	5.48663	−	2.64222i	0.208570	−	0.100442i
$693$		0			0
$694$	34.3460	+	16.5402i	1.30376	+	0.627856i
$695$	−5.51398	+	14.0494i	−0.209157	+	0.532924i
$696$	0.476589	−	6.35964i	0.0180651	−	0.241062i
$697$	−2.70322	−	6.88770i	−0.102392	−	0.260890i
$698$	−36.7958	+	11.3500i	−1.39274	+	0.429604i
$699$	15.3318	−	19.2255i	0.579903	−	0.727175i
$700$		0			0
$701$	−11.1294	−	13.9558i	−0.420350	−	0.527102i	0.525896	−	0.850549i	$-0.323730\pi$
$701$	−11.1294	−	13.9558i	−0.420350	−	0.527102i	−0.946247	+	0.323446i	$0.895159\pi$
$702$	−8.02809	−	5.47346i	−0.303001	−	0.206582i
$703$	6.69763	+	6.21449i	0.252606	+	0.234384i
$704$	11.7312	−	20.3190i	0.442135	−	0.765800i
$705$	7.96766	+	13.8004i	0.300080	+	0.519753i
$706$	7.87702	−	34.5115i	0.296456	−	1.29886i
$707$		0			0
$708$	−3.30939	−	14.4994i	−0.124374	−	0.544920i
$709$	−26.9928	+	25.0457i	−1.01374	+	0.940611i	−0.998242	−	0.0592688i	$-0.981123\pi$
$709$	−26.9928	+	25.0457i	−1.01374	+	0.940611i	−0.0154957	+	0.999880i	$0.504933\pi$
$710$	−53.8261	+	8.11298i	−2.02006	+	0.304475i
$711$	0.0269867	−	0.00406760i	0.00101208	−	0.000152547i
$712$	−5.49387	+	5.09757i	−0.205891	+	0.191039i
$713$	8.54886	+	37.4550i	0.320157	+	1.40270i
$714$		0			0
$715$	−2.16271	+	9.47544i	−0.0808807	+	0.354361i
$716$	11.8535	+	20.5308i	0.442985	+	0.767272i
$717$	−8.80053	+	15.2430i	−0.328662	+	0.569259i
$718$	−22.0915	−	20.4979i	−0.824446	−	0.764974i
$719$	−15.9480	−	10.8732i	−0.594760	−	0.405501i	0.228188	−	0.973617i	$-0.426720\pi$
$719$	−15.9480	−	10.8732i	−0.594760	−	0.405501i	−0.822948	+	0.568116i	$0.807672\pi$
$720$	−0.0287534	−	0.0360557i	−0.00107158	−	0.00134372i
$721$		0			0
$722$	−10.7199	+	13.4423i	−0.398952	+	0.500270i
$723$	43.7221	−	13.4865i	1.62604	−	0.501568i
$724$	15.9925	+	40.7483i	0.594357	+	1.51440i
$725$	−0.197091	+	2.62999i	−0.00731977	+	0.0976755i
$726$	−13.1014	+	33.3818i	−0.486239	+	1.23892i
$727$	−22.2549	−	10.7174i	−0.825390	−	0.397487i	−0.0270055	−	0.999635i	$-0.508597\pi$
$727$	−22.2549	−	10.7174i	−0.825390	−	0.397487i	−0.798384	+	0.602149i	$0.794311\pi$
$728$		0			0
$729$	−24.3645	+	11.7333i	−0.902388	+	0.434567i
$730$	−1.81271	−	24.1889i	−0.0670912	−	0.895270i
$731$	20.0166	+	6.17430i	0.740340	+	0.228365i
$732$	−10.5554	+	7.19655i	−0.390139	+	0.265992i
$733$	−29.1082	−	4.38736i	−1.07514	−	0.162051i	−0.412474	−	0.910969i	$-0.635335\pi$
$733$	−29.1082	−	4.38736i	−1.07514	−	0.162051i	−0.662662	+	0.748919i	$0.730573\pi$
$734$	−27.4931			−1.01479
$735$		0			0
$736$	−28.0211			−1.03287
$737$	−2.22937	−	0.336023i	−0.0821198	−	0.0123776i
$738$	0.0265694	−	0.0181147i	0.000978032	−	0.000666811i
$739$	14.5910	+	4.50072i	0.536737	+	0.165562i	0.551261	−	0.834333i	$-0.314147\pi$
$739$	14.5910	+	4.50072i	0.536737	+	0.165562i	−0.0145234	+	0.999895i	$0.504623\pi$
$740$	0.453586	+	6.05268i	0.0166741	+	0.222501i
$741$	8.06615	−	3.88445i	0.296317	−	0.142699i
$742$		0			0
$743$	0.634609	+	0.305612i	0.0232815	+	0.0112118i	0.445488	−	0.895288i	$-0.353030\pi$
$743$	0.634609	+	0.305612i	0.0232815	+	0.0112118i	−0.422207	+	0.906500i	$0.638744\pi$
$744$	4.26859	−	10.8762i	0.156494	−	0.398740i
$745$	−1.11678	+	14.9024i	−0.0409158	+	0.545983i
$746$	2.75467	+	7.01879i	0.100856	+	0.256976i
$747$	0.0134050	−	0.00413490i	0.000490464	−	0.000151288i
$748$	−10.0359	+	12.5847i	−0.366951	+	0.460141i
$749$		0			0
$750$	−24.0184	−	30.1182i	−0.877030	−	1.09976i
$751$	24.6888	+	16.8325i	0.900906	+	0.614227i	0.922693	−	0.385536i	$-0.125983\pi$
$751$	24.6888	+	16.8325i	0.900906	+	0.614227i	−0.0217874	+	0.999763i	$0.506936\pi$
$752$	14.5147	+	13.4677i	0.529297	+	0.491116i
$753$	−21.1065	+	36.5575i	−0.769164	+	1.33223i
$754$	−5.18331	−	8.97775i	−0.188765	−	0.326951i
$755$	−0.500537	+	2.19299i	−0.0182164	+	0.0798112i
$756$		0			0
$757$	−7.55547	−	33.1027i	−0.274608	−	1.20314i	−0.904506	−	0.426460i	$-0.859760\pi$
$757$	−7.55547	−	33.1027i	−0.274608	−	1.20314i	0.629898	−	0.776678i	$-0.283097\pi$
$758$	−37.4246	+	34.7249i	−1.35932	+	1.26127i
$759$	30.2295	−	4.55636i	1.09726	−	0.165386i
$760$	7.39165	−	1.11411i	0.268124	−	0.0404131i
$761$	12.4213	−	11.5252i	0.450270	−	0.417790i	−0.422165	−	0.906519i	$-0.638730\pi$
$761$	12.4213	−	11.5252i	0.450270	−	0.417790i	0.872436	+	0.488729i	$0.162539\pi$
$762$	7.27608	+	31.8786i	0.263585	+	1.15484i
$763$		0			0
$764$	3.31114	−	14.5071i	0.119793	−	0.524847i
$765$	0.0105064	+	0.0181977i	0.000379861	+	0.000657939i
$766$	0.652245	−	1.12972i	0.0235666	−	0.0408185i
$767$	3.72690	+	3.45806i	0.134570	+	0.124863i
$768$	28.6588	+	19.5393i	1.03414	+	0.705062i
$769$	22.9209	+	28.7419i	0.826549	+	1.03646i	0.998679	+	0.0513857i	$0.0163638\pi$
$769$	22.9209	+	28.7419i	0.826549	+	1.03646i	−0.172130	+	0.985074i	$0.555065\pi$
$770$		0			0
$771$	1.76946	−	2.21883i	0.0637255	−	0.0799092i
$772$	10.8376	−	3.34295i	0.390053	−	0.120315i
$773$	17.6630	+	45.0045i	0.635292	+	1.61870i	0.777515	+	0.628864i	$0.216480\pi$
$773$	17.6630	+	45.0045i	0.635292	+	1.61870i	−0.142223	+	0.989835i	$0.545425\pi$
$774$	−0.00680321	+	0.0907825i	−0.000244536	+	0.00326311i
$775$	−1.76525	+	4.49778i	−0.0634096	+	0.161565i
$776$	−1.05467	−	0.507901i	−0.0378603	−	0.0182326i
$777$		0			0
$778$	54.8614	−	26.4198i	1.96687	−	0.947197i
$779$	1.40373	+	18.7314i	0.0502937	+	0.671123i
$780$	5.68326	+	1.75305i	0.203493	+	0.0627694i
$781$	51.7055	−	35.2522i	1.85017	−	1.26142i
$782$	14.8871	+	2.24386i	0.532360	+	0.0802404i
$783$	−28.8522			−1.03109
$784$		0			0
$785$	10.1361			0.361771
$786$	17.1089	+	2.57874i	0.610253	+	0.0919808i
$787$	20.5124	−	13.9851i	0.731189	−	0.498516i	−0.139579	−	0.990211i	$-0.544575\pi$
$787$	20.5124	−	13.9851i	0.731189	−	0.498516i	0.870768	+	0.491695i	$0.163622\pi$
$788$	17.8474	+	5.50520i	0.635788	+	0.196115i
$789$	−1.94076	−	25.8977i	−0.0690930	−	0.921982i
$790$	−21.0901	+	10.1565i	−0.750352	+	0.361350i
$791$		0			0
$792$	0.0132550	+	0.00638325i	0.000470994	+	0.000226819i
$793$	1.59552	−	4.06533i	0.0566587	−	0.144364i
$794$	−1.12019	+	14.9479i	−0.0397542	+	0.530483i
$795$	6.95601	+	17.7236i	0.246704	+	0.628592i
$796$	−22.2839	+	6.87368i	−0.789833	+	0.243631i
$797$	−6.80816	+	8.53717i	−0.241157	+	0.302402i	−0.887650	−	0.460518i	$-0.847664\pi$
$797$	−6.80816	+	8.53717i	−0.241157	+	0.302402i	0.646493	+	0.762920i	$0.276235\pi$
$798$		0			0
$799$	−5.62507	−	7.05362i	−0.199001	−	0.249539i
$800$	−2.91179	−	1.98523i	−0.102947	−	0.0701884i
$801$	0.0392056	+	0.0363774i	0.00138526	+	0.00128533i
$802$	18.8985	−	32.7332i	0.667329	−	1.15585i
$803$	13.9432	+	24.1503i	0.492044	+	0.852245i
$804$	−0.306999	+	1.34505i	−0.0108270	+	0.0474364i
$805$		0			0
$806$	−4.22615	−	18.5160i	−0.148860	−	0.652197i
$807$	−9.35328	+	8.67858i	−0.329251	+	0.305500i
$808$	−6.33500	+	0.954847i	−0.222864	+	0.0335914i
$809$	38.4191	−	5.79074i	1.35074	−	0.203592i	0.566508	−	0.824056i	$-0.308294\pi$
$809$	38.4191	−	5.79074i	1.35074	−	0.203592i	0.784234	+	0.620465i	$0.213056\pi$
$810$	26.7778	−	24.8462i	0.940878	−	0.873007i
$811$	−12.0968	−	52.9994i	−0.424775	−	1.86106i	−0.503246	−	0.864143i	$-0.667861\pi$
$811$	−12.0968	−	52.9994i	−0.424775	−	1.86106i	0.0784712	−	0.996916i	$-0.474996\pi$
$812$		0			0
$813$	7.23841	−	31.7135i	0.253862	−	1.11224i
$814$	−7.71162	−	13.3569i	−0.270292	−	0.468160i
$815$	−1.51143	+	2.61787i	−0.0529430	+	0.0916999i
$816$	−12.0954	−	11.2229i	−0.423425	−	0.392881i
$817$	−43.9374	−	29.9560i	−1.53718	−	1.04803i
$818$	10.8233	+	13.5721i	0.378430	+	0.474536i
$819$		0			0
$820$	−7.78025	+	9.75612i	−0.271698	+	0.340699i
$821$	7.63451	−	2.35493i	0.266446	−	0.0821877i	−0.158653	−	0.987334i	$-0.550715\pi$
$821$	7.63451	−	2.35493i	0.266446	−	0.0821877i	0.425100	+	0.905147i	$0.360239\pi$
$822$	−22.2291	−	56.6388i	−0.775329	−	1.97551i
$823$	−3.10405	+	41.4207i	−0.108201	+	1.44384i	0.633832	+	0.773471i	$0.281481\pi$
$823$	−3.10405	+	41.4207i	−0.108201	+	1.44384i	−0.742032	+	0.670364i	$0.766138\pi$
$824$	0.882398	−	2.24831i	0.0307398	−	0.0783237i
$825$	3.46409	+	1.66822i	0.120604	+	0.0580799i
$826$		0			0
$827$	5.90952	−	2.84587i	0.205494	−	0.0989607i	−0.328306	−	0.944571i	$-0.606478\pi$
$827$	5.90952	−	2.84587i	0.205494	−	0.0989607i	0.533800	+	0.845611i	$0.320763\pi$
$828$	0.00221219	+	0.0295196i	7.68790e−5	+	0.00102588i
$829$	−24.0043	−	7.40434i	−0.833704	−	0.257163i	−0.151621	−	0.988439i	$-0.548449\pi$
$829$	−24.0043	−	7.40434i	−0.833704	−	0.257163i	−0.682083	+	0.731275i	$0.738926\pi$
$830$	−9.94144	+	6.77796i	−0.345072	+	0.235266i
$831$	−21.5777	−	3.25232i	−0.748523	−	0.112822i
$832$	4.90810			0.170158
$833$		0			0
$834$	−23.4685			−0.812648
$835$	25.7056	+	3.87449i	0.889578	+	0.134082i
$836$	33.7627	−	23.0190i	1.16771	−	0.796130i
$837$	−50.5102	−	15.5803i	−1.74589	−	0.538536i
$838$	0.879735	+	11.7393i	0.0303899	+	0.405526i
$839$	35.7622	−	17.2222i	1.23465	−	0.594575i	0.301293	−	0.953532i	$-0.402582\pi$
$839$	35.7622	−	17.2222i	1.23465	−	0.594575i	0.933354	+	0.358957i	$0.116867\pi$
$840$		0			0
$841$	−1.60633	−	0.773570i	−0.0553908	−	0.0266748i
$842$	−6.86207	+	17.4843i	−0.236483	+	0.602548i
$843$	−1.94645	+	25.9736i	−0.0670393	+	0.894577i
$844$	−10.1760	−	25.9281i	−0.350274	−	0.892483i
$845$	24.4812	−	7.55146i	0.842180	−	0.259778i
$846$	0.0244467	−	0.0306552i	0.000840495	−	0.00105395i
$847$		0			0
$848$	14.7504	+	18.4964i	0.506530	+	0.635169i
$849$	33.9293	+	23.1326i	1.16445	+	0.793910i
$850$	1.38801	+	1.28788i	0.0476083	+	0.0441740i
$851$	−3.26326	+	5.65213i	−0.111863	+	0.193753i
$852$	−19.1473	−	33.1641i	−0.655976	−	1.13618i
$853$	−2.88141	+	12.6243i	−0.0986575	+	0.432247i	−1.00000		0.000860998i	$-0.999726\pi$
$853$	−2.88141	+	12.6243i	−0.0986575	+	0.432247i	0.901342	+	0.433108i	$0.142583\pi$
$854$		0			0
$855$	−0.0118702	−	0.0520070i	−0.000405954	−	0.00177860i
$856$	2.11509	−	1.96251i	0.0722922	−	0.0670773i
$857$	48.5429	−	7.31667i	1.65820	−	0.249933i	0.747876	−	0.663839i	$-0.231074\pi$
$857$	48.5429	−	7.31667i	1.65820	−	0.249933i	0.910320	+	0.413906i	$0.135836\pi$
$858$	−14.9440	+	2.25245i	−0.510181	+	0.0768973i
$859$	37.4965	−	34.7917i	1.27936	−	1.18708i	0.307496	−	0.951549i	$-0.400509\pi$
$859$	37.4965	−	34.7917i	1.27936	−	1.18708i	0.971868	−	0.235527i	$-0.0756817\pi$
$860$	−7.86099	−	34.4413i	−0.268058	−	1.17444i
$861$		0			0
$862$	−1.00275	+	4.39332i	−0.0341537	+	0.149637i
$863$	−3.62081	−	6.27142i	−0.123254	−	0.213482i	0.797795	−	0.602928i	$-0.206000\pi$
$863$	−3.62081	−	6.27142i	−0.123254	−	0.213482i	−0.921049	+	0.389447i	$0.872666\pi$
$864$	19.2767	−	33.3883i	0.655807	−	1.13589i
$865$	−5.74628	−	5.33177i	−0.195380	−	0.181286i
$866$	40.2177	+	27.4199i	1.36665	+	0.931768i
$867$	−13.6566	−	17.1248i	−0.463801	−	0.581588i
$868$		0			0
$869$	16.7787	−	21.0398i	0.569178	−	0.713726i
$870$	37.3011	−	11.5059i	1.26463	−	0.390086i
$871$	−0.172306	−	0.439029i	−0.00583837	−	0.0148759i
$872$	0.0478424	−	0.638412i	0.00162015	−	0.0216194i
$873$	−0.00305192	+	0.00777617i	−0.000103292	+	0.000263183i
$874$	−34.4350	−	16.5830i	−1.16478	−	0.560929i
$875$		0			0
$876$	15.3748	−	7.40409i	0.519465	−	0.250161i
$877$	0.654738	+	8.73688i	0.0221089	+	0.295023i	0.997288	+	0.0736037i	$0.0234500\pi$
$877$	0.654738	+	8.73688i	0.0221089	+	0.295023i	−0.975179	+	0.221420i	$0.928931\pi$
$878$	69.8135	+	21.5346i	2.35609	+	0.726758i
$879$	8.12784	−	5.54146i	0.274145	−	0.186909i
$880$	−44.9658	−	6.77750i	−1.51580	−	0.228470i
$881$	12.2501			0.412715			0.206358	−	0.978477i	$-0.433839\pi$
$881$	12.2501			0.412715			0.206358	+	0.978477i	$0.433839\pi$
$882$		0			0
$883$	−26.9923			−0.908362			−0.454181	−	0.890910i	$-0.650068\pi$
$883$	−26.9923			−0.908362			−0.454181	+	0.890910i	$0.650068\pi$
$884$	−3.32961	−	0.501858i	−0.111987	−	0.0168793i
$885$	−15.8176	+	10.7842i	−0.531701	+	0.362508i
$886$	−25.0636	−	7.73110i	−0.842028	−	0.259731i
$887$	4.25752	+	56.8127i	0.142954	+	1.90758i	0.362503	+	0.931983i	$0.381922\pi$
$887$	4.25752	+	56.8127i	0.142954	+	1.90758i	−0.219549	+	0.975601i	$0.570459\pi$
$888$	1.78830	−	0.861198i	0.0600113	−	0.0288999i
$889$		0			0
$890$	−41.3298	−	19.9034i	−1.38538	−	0.667162i
$891$	−15.3426	+	39.0923i	−0.513997	+	1.30964i
$892$	2.03740	−	27.1872i	0.0682171	−	0.910294i
$893$	8.36759	+	21.3203i	0.280011	+	0.713456i
$894$	−22.2053	+	6.84941i	−0.742655	+	0.229079i
$895$	19.0266	−	23.8586i	0.635989	−	0.797506i
$896$		0			0
$897$	3.98732	+	4.99994i	0.133133	+	0.166943i
$898$	8.60349	+	5.86576i	0.287102	+	0.195743i
$899$	−41.3410	−	38.3588i	−1.37880	−	1.27934i
$900$	−0.00186152	+	0.00322425i	−6.20506e−5	+	0.000107475i
$901$	−5.38976	−	9.33534i	−0.179559	−	0.311005i
$902$	7.05581	−	30.9135i	0.234933	−	1.02931i
$903$		0			0
$904$	−0.555720	−	2.43477i	−0.0184830	−	0.0809792i
$905$	41.3057	−	38.3261i	1.37305	−	1.27400i
$906$	−3.45864	+	0.521306i	−0.114906	+	0.0173192i
$907$	36.5201	−	5.50452i	1.21263	−	0.182774i	0.488578	−	0.872520i	$-0.337516\pi$
$907$	36.5201	−	5.50452i	1.21263	−	0.182774i	0.724052	+	0.689746i	$0.242278\pi$
$908$	−4.29869	+	3.98860i	−0.142657	+	0.132366i
$909$	0.0101734	+	0.0445724i	0.000337429	+	0.00147837i
$910$		0			0
$911$	−0.123056	+	0.539145i	−0.00407704	+	0.0178627i	−0.976926	−	0.213580i	$-0.931488\pi$
$911$	−0.123056	+	0.539145i	−0.00407704	+	0.0178627i	0.972848	+	0.231443i	$0.0743447\pi$
$912$	20.9440	+	36.2761i	0.693526	+	1.20122i
$913$	6.91629	−	11.9794i	0.228896	−	0.396459i
$914$	32.2847	+	29.9558i	1.06788	+	0.990850i
$915$	13.5873	+	9.26363i	0.449181	+	0.306246i
$916$	14.7215	+	18.4602i	0.486414	+	0.609943i
$917$		0			0
$918$	−12.9150	+	16.1949i	−0.426259	+	0.534512i
$919$	−10.2984	+	3.17663i	−0.339712	+	0.104787i	−0.459917	−	0.887962i	$-0.652121\pi$
$919$	−10.2984	+	3.17663i	−0.339712	+	0.104787i	0.120205	+	0.992749i	$0.461645\pi$
$920$	1.95080	+	4.97056i	0.0643160	+	0.163875i
$921$	−4.41534	+	58.9186i	−0.145490	+	1.94143i
$922$	23.1316	−	58.9383i	0.761798	−	1.94103i
$923$	11.7946	+	5.67998i	0.388224	+	0.186959i
$924$		0			0
$925$	−0.739540	+	0.356144i	−0.0243159	+	0.0117099i
$926$	−0.240713	−	3.21209i	−0.00791031	−	0.105556i
$927$	−0.0164702	−	0.00508039i	−0.000540953	−	0.000166862i
$928$	33.9859	−	23.1712i	1.11564	−	0.760633i
$929$	−12.5141	−	1.88619i	−0.410573	−	0.0618839i	−0.0594915	−	0.998229i	$-0.518948\pi$
$929$	−12.5141	−	1.88619i	−0.410573	−	0.0618839i	−0.351082	+	0.936345i	$0.614186\pi$
$930$	71.5147			2.34506
$931$		0			0
$932$	23.4792			0.769086
$933$	−48.8267	−	7.35944i	−1.59851	−	0.240937i
$934$	−31.5047	+	21.4795i	−1.03087	+	0.702832i
$935$	19.7993	+	6.10727i	0.647506	+	0.199729i
$936$	0.000229989		0.00306899i	7.51742e−6		0.000100313i
$937$	−10.8546	+	5.22729i	−0.354604	+	0.170768i	−0.602701	−	0.797967i	$-0.705909\pi$
$937$	−10.8546	+	5.22729i	−0.354604	+	0.170768i	0.248098	+	0.968735i	$0.420195\pi$
$938$		0			0
$939$	42.3227	+	20.3815i	1.38115	+	0.665127i
$940$	−5.55876	+	14.1635i	−0.181307	+	0.461962i
$941$	1.57083	−	20.9613i	0.0512076	−	0.683318i	−0.911244	−	0.411866i	$-0.864877\pi$
$941$	1.57083	−	20.9613i	0.0512076	−	0.683318i	0.962452	−	0.271452i	$-0.0875037\pi$
$942$	5.75819	+	14.6716i	0.187612	+	0.478027i
$943$	−12.8217	+	3.95497i	−0.417532	+	0.128792i
$944$	−14.8312	+	18.5977i	−0.482714	+	0.605304i
$945$		0			0
$946$	55.9690	+	70.1829i	1.81971	+	2.28184i
$947$	−30.0540	−	20.4905i	−0.976624	−	0.665851i	−0.0339003	−	0.999425i	$-0.510793\pi$
$947$	−30.0540	−	20.4905i	−0.976624	−	0.665851i	−0.942724	+	0.333574i	$0.891745\pi$
$948$	−12.0717	−	11.2009i	−0.392072	−	0.363790i
$949$	−2.91678	+	5.05202i	−0.0946828	+	0.163995i
$950$	−2.40342	−	4.16285i	−0.0779774	−	0.135061i
$951$	−4.73094	+	20.7276i	−0.153411	+	0.672139i
$952$		0			0
$953$	−10.6329	−	46.5859i	−0.344435	−	1.50907i	−0.789602	−	0.613619i	$-0.789713\pi$
$953$	−10.6329	−	46.5859i	−0.344435	−	1.50907i	0.445168	−	0.895447i	$-0.353144\pi$
$954$	0.0343421	−	0.0318648i	0.00111187	−	0.00103166i
$955$	−18.9402	+	2.85478i	−0.612892	+	0.0923786i
$956$	−16.6180	+	2.50476i	−0.537465	+	0.0810098i
$957$	−32.8967	+	30.5237i	−1.06340	+	0.986691i
$958$	−1.24667	−	5.46201i	−0.0402780	−	0.176470i
$959$		0			0
$960$	−4.11250	+	18.0180i	−0.132730	+	0.581529i
$961$	−36.1599	−	62.6307i	−1.16645	−	2.02035i
$962$	1.61320	−	2.79414i	0.0520117	−	0.0900868i
$963$	−0.0150938	−	0.0140050i	−0.000486389	−	0.000451303i
$964$	36.0962	+	24.6100i	1.16258	+	0.792633i
$965$	−9.10237	−	11.4140i	−0.293016	−	0.367430i
$966$		0			0
$967$	8.21453	−	10.3007i	0.264162	−	0.331248i	−0.632006	−	0.774963i	$-0.717768\pi$
$967$	8.21453	−	10.3007i	0.264162	−	0.331248i	0.896168	+	0.443715i	$0.146340\pi$
$968$	6.88095	−	2.12249i	0.221162	−	0.0682195i
$969$	−6.97291	−	17.7667i	−0.224002	−	0.570748i
$970$	0.535440	−	7.14495i	0.0171919	−	0.229410i
$971$	−4.58860	+	11.6916i	−0.147255	+	0.375200i	−0.985402	−	0.170245i	$-0.945544\pi$
$971$	−4.58860	+	11.6916i	−0.147255	+	0.375200i	0.838147	+	0.545445i	$0.183639\pi$
$972$	−0.0733336	−	0.0353156i	−0.00235217	−	0.00113275i
$973$		0			0
$974$	−51.4133	+	24.7593i	−1.64739	+	0.793340i
$975$	0.0601059	+	0.802058i	0.00192493	+	0.0256864i
$976$	19.5255	+	6.02282i	0.624996	+	0.192786i
$977$	−48.7010	+	33.2038i	−1.55808	+	1.06228i	−0.591376	+	0.806396i	$0.701415\pi$
$977$	−48.7010	+	33.2038i	−1.55808	+	1.06228i	−0.966707	+	0.255887i	$0.917633\pi$
$978$	−4.64791	−	0.700560i	−0.148624	−	0.0224014i
$979$	52.7367			1.68547
$980$		0			0
$981$	−0.00456864			−0.000145865
$982$	−0.123901	−	0.0186751i	−0.00395384	−	0.000595946i
$983$	−25.0082	+	17.0503i	−0.797638	+	0.543821i	−0.892169	−	0.451701i	$-0.850817\pi$
$983$	−25.0082	+	17.0503i	−0.797638	+	0.543821i	0.0945308	+	0.995522i	$0.469865\pi$
$984$	3.89936	+	1.20279i	0.124307	+	0.0383437i
$985$	−1.79665	−	23.9747i	−0.0572461	−	0.763896i
$986$	−19.9116	+	9.58891i	−0.634114	+	0.305373i
$987$		0			0
$988$	7.70166	+	3.70893i	0.245023	+	0.117997i
$989$	13.8779	−	35.3602i	0.441291	−	1.12439i
$990$	−0.00672936	+	0.0897970i	−0.000213873	+	0.00285394i
$991$	−7.99810	−	20.3788i	−0.254068	−	0.647355i	0.745754	−	0.666221i	$-0.232089\pi$
$991$	−7.99810	−	20.3788i	−0.254068	−	0.647355i	−0.999822	+	0.0188666i	$0.993994\pi$
$992$	72.0103	−	22.2122i	2.28633	−	0.705239i
$993$	−19.1808	+	24.0520i	−0.608685	+	0.763267i
$994$		0			0
$995$	18.7161	+	23.4692i	0.593339	+	0.744023i
$996$	−6.99384	−	4.76832i	−0.221608	−	0.151090i
$997$	15.4363	+	14.3228i	0.488873	+	0.453608i	0.885681	−	0.464294i	$-0.153692\pi$
$997$	15.4363	+	14.3228i	0.488873	+	0.453608i	−0.396808	+	0.917902i	$0.629882\pi$
$998$	4.43871	−	7.68807i	0.140505	−	0.243362i
$999$	−4.48983	−	7.77661i	−0.142052	−	0.246041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.a.165.1		12
7.2	even	3		343.2.g.c.226.1		12
7.3	odd	6		49.2.e.b.43.1	yes	12
7.4	even	3		343.2.e.b.295.1		12
7.5	odd	6		343.2.g.b.226.1		12
7.6	odd	2		343.2.g.d.165.1		12
21.17	even	6		441.2.u.b.190.2		12
28.3	even	6		784.2.u.b.337.1		12
49.3	odd	42		49.2.e.b.8.1	✓	12
49.5	odd	42		343.2.g.d.79.1		12
49.8	even	7		343.2.g.c.214.1		12
49.17	odd	42		2401.2.a.c.1.1		6
49.32	even	21		2401.2.a.d.1.1		6
49.41	odd	14		343.2.g.b.214.1		12
49.44	even	21	inner	343.2.g.a.79.1		12
49.46	even	21		343.2.e.b.50.1		12
147.101	even	42		441.2.u.b.253.2		12
196.3	even	42		784.2.u.b.449.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.8.1	✓	12	49.3	odd	42
49.2.e.b.43.1	yes	12	7.3	odd	6
343.2.e.b.50.1		12	49.46	even	21
343.2.e.b.295.1		12	7.4	even	3
343.2.g.a.79.1		12	49.44	even	21	inner
343.2.g.a.165.1		12	1.1	even	1	trivial
343.2.g.b.214.1		12	49.41	odd	14
343.2.g.b.226.1		12	7.5	odd	6
343.2.g.c.214.1		12	49.8	even	7
343.2.g.c.226.1		12	7.2	even	3
343.2.g.d.79.1		12	49.5	odd	42
343.2.g.d.165.1		12	7.6	odd	2
441.2.u.b.190.2		12	21.17	even	6
441.2.u.b.253.2		12	147.101	even	42
784.2.u.b.337.1		12	28.3	even	6
784.2.u.b.449.1		12	196.3	even	42
2401.2.a.c.1.1		6	49.17	odd	42
2401.2.a.d.1.1		6	49.32	even	21

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.88980 + 0.284841i) q^{2} +(1.42996 - 0.974928i) q^{3} +(1.57906 + 0.487076i) q^{4} +(-0.158960 - 2.12117i) q^{5} +(2.98003 - 1.43511i) q^{6} +(-0.598393 - 0.288171i) q^{8} +(-0.00173159 + 0.00441201i) q^{9} +O(q^{10})\)	\(q+(1.88980 + 0.284841i) q^{2} +(1.42996 - 0.974928i) q^{3} +(1.57906 + 0.487076i) q^{4} +(-0.158960 - 2.12117i) q^{5} +(2.98003 - 1.43511i) q^{6} +(-0.598393 - 0.288171i) q^{8} +(-0.00173159 + 0.00441201i) q^{9} +(0.303796 - 4.05387i) q^{10} +(1.70744 + 4.35048i) q^{11} +(2.73286 - 0.842974i) q^{12} +(-0.609562 + 0.764367i) q^{13} +(-2.29530 - 2.87821i) q^{15} +(-3.77944 - 2.57678i) q^{16} +(1.52786 + 1.41764i) q^{17} +(-0.00452908 + 0.00784459i) q^{18} +(-2.64558 - 4.58228i) q^{19} +(0.782166 - 3.42689i) q^{20} +(1.98752 + 8.70788i) q^{22} +(2.77064 - 2.57078i) q^{23} +(-1.13662 + 0.171318i) q^{24} +(0.470043 - 0.0708476i) q^{25} +(-1.36967 + 1.27087i) q^{26} +(1.15716 + 5.06987i) q^{27} +(-1.23460 + 5.40913i) q^{29} +(-3.51782 - 6.09304i) q^{30} +(-5.08232 + 8.80283i) q^{31} +(-5.43468 - 5.04264i) q^{32} +(6.68296 + 4.55636i) q^{33} +(2.48354 + 3.11426i) q^{34} +(-0.00488327 + 0.00612343i) q^{36} +(-1.65006 + 0.508976i) q^{37} +(-3.69439 - 9.41316i) q^{38} +(-0.126445 + 1.68729i) q^{39} +(-0.516140 + 1.31510i) q^{40} +(-3.19850 - 1.54031i) q^{41} +(9.05500 - 4.36066i) q^{43} +(0.577134 + 7.70132i) q^{44} +(0.00963390 + 0.00297166i) q^{45} +(5.96822 - 4.06907i) q^{46} +(-4.28029 - 0.645150i) q^{47} -7.91661 q^{48} +0.908468 q^{50} +(3.56687 + 0.537619i) q^{51} +(-1.33484 + 0.910080i) q^{52} +(-4.94215 - 1.52445i) q^{53} +(0.742700 + 9.91064i) q^{54} +(8.95670 - 4.31332i) q^{55} +(-8.25045 - 3.97321i) q^{57} +(-3.87389 + 9.87050i) q^{58} +(0.388615 - 5.18571i) q^{59} +(-2.22251 - 5.66286i) q^{60} +(-4.26855 + 1.31667i) q^{61} +(-12.1120 + 15.1879i) q^{62} +(-3.13007 - 3.92499i) q^{64} +(1.71825 + 1.17148i) q^{65} +(11.3316 + 10.5142i) q^{66} +(-0.241204 + 0.417777i) q^{67} +(1.72208 + 2.98273i) q^{68} +(1.45557 - 6.37728i) q^{69} +(-2.97959 - 13.0544i) q^{71} +(0.00230758 - 0.00214112i) q^{72} +(5.90021 - 0.889314i) q^{73} +(-3.26326 + 0.491857i) q^{74} +(0.603070 - 0.559567i) q^{75} +(-1.94562 - 8.52430i) q^{76} +(-0.719566 + 3.15262i) q^{78} +(-2.87907 - 4.98670i) q^{79} +(-4.86502 + 8.42646i) q^{80} +(6.58703 + 6.11187i) q^{81} +(-5.60577 - 3.82195i) q^{82} +(-1.84538 - 2.31404i) q^{83} +(2.76420 - 3.46620i) q^{85} +(18.3542 - 5.66153i) q^{86} +(3.50809 + 8.93846i) q^{87} +(0.231963 - 3.09533i) q^{88} +(4.12255 - 10.5041i) q^{89} +(0.0173597 + 0.00835998i) q^{90} +(5.62718 - 2.70991i) q^{92} +(1.31463 + 17.5426i) q^{93} +(-7.90513 - 2.43841i) q^{94} +(-9.29926 + 6.34013i) q^{95} +(-12.6876 - 1.91234i) q^{96} +1.76250 q^{97} -0.0221509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{4} - 14 q^{5} + 7 q^{6} + 6 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + q^2 - q^4 - 14 * q^5 + 7 * q^6 + 6 * q^8 + 25 * q^9	\( 12 q + q^{2} - q^{4} - 14 q^{5} + 7 q^{6} + 6 q^{8} + 25 q^{9} + 7 q^{10} + 4 q^{11} - 7 q^{12} - 7 q^{13} - 7 q^{15} - 29 q^{16} - 10 q^{18} - 7 q^{19} - 7 q^{20} + 13 q^{22} + q^{23} + 9 q^{25} + 7 q^{26} - 21 q^{27} - 11 q^{29} - 21 q^{30} - 7 q^{31} - 9 q^{32} + 49 q^{33} + 42 q^{34} - 13 q^{36} + 15 q^{37} - 21 q^{38} - 21 q^{40} - 21 q^{41} + 17 q^{43} - 18 q^{44} - 35 q^{45} + 8 q^{46} - 21 q^{47} - 46 q^{50} + 7 q^{51} + 7 q^{52} - 24 q^{53} + 21 q^{54} + 28 q^{55} + 7 q^{57} + 16 q^{58} + 7 q^{59} + 35 q^{60} - 14 q^{61} - 56 q^{62} + 14 q^{64} + 14 q^{65} + 49 q^{66} - 24 q^{67} + 28 q^{68} + 7 q^{69} - 39 q^{71} + 23 q^{72} + 21 q^{73} - 20 q^{74} + 14 q^{75} + 28 q^{76} + 8 q^{79} + 21 q^{80} + 23 q^{81} - 7 q^{82} + 7 q^{83} + 28 q^{85} - 19 q^{86} + 56 q^{87} + 16 q^{88} + 35 q^{89} + 14 q^{90} + 16 q^{92} - 7 q^{93} - 56 q^{94} - 7 q^{95} - 35 q^{96} + 28 q^{97} - 18 q^{99}+O(q^{100}) \) 12 * q + q^2 - q^4 - 14 * q^5 + 7 * q^6 + 6 * q^8 + 25 * q^9 + 7 * q^10 + 4 * q^11 - 7 * q^12 - 7 * q^13 - 7 * q^15 - 29 * q^16 - 10 * q^18 - 7 * q^19 - 7 * q^20 + 13 * q^22 + q^23 + 9 * q^25 + 7 * q^26 - 21 * q^27 - 11 * q^29 - 21 * q^30 - 7 * q^31 - 9 * q^32 + 49 * q^33 + 42 * q^34 - 13 * q^36 + 15 * q^37 - 21 * q^38 - 21 * q^40 - 21 * q^41 + 17 * q^43 - 18 * q^44 - 35 * q^45 + 8 * q^46 - 21 * q^47 - 46 * q^50 + 7 * q^51 + 7 * q^52 - 24 * q^53 + 21 * q^54 + 28 * q^55 + 7 * q^57 + 16 * q^58 + 7 * q^59 + 35 * q^60 - 14 * q^61 - 56 * q^62 + 14 * q^64 + 14 * q^65 + 49 * q^66 - 24 * q^67 + 28 * q^68 + 7 * q^69 - 39 * q^71 + 23 * q^72 + 21 * q^73 - 20 * q^74 + 14 * q^75 + 28 * q^76 + 8 * q^79 + 21 * q^80 + 23 * q^81 - 7 * q^82 + 7 * q^83 + 28 * q^85 - 19 * q^86 + 56 * q^87 + 16 * q^88 + 35 * q^89 + 14 * q^90 + 16 * q^92 - 7 * q^93 - 56 * q^94 - 7 * q^95 - 35 * q^96 + 28 * q^97 - 18 * q^99

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