LMFDB - Embedded newform 93.2.f.a.70.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(4,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("93.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			70.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	93.70
Dual form			93.2.f.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.413545 + 1.27276i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.169131 + 0.122881i) q^{4} +0.827091 q^{5} +1.33826 q^{6} +(2.78716 + 2.02499i) q^{7} +(-2.39169 + 1.73767i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.413545 + 1.27276i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.169131 + 0.122881i) q^{4} +0.827091 q^{5} +1.33826 q^{6} +(2.78716 + 2.02499i) q^{7} +(-2.39169 + 1.73767i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.342040 + 1.05269i) q^{10} +(-1.37362 - 0.997993i) q^{11} +(0.0646021 - 0.198825i) q^{12} +(-0.989318 - 3.04481i) q^{13} +(-3.72995 + 2.70997i) q^{14} +(-0.255585 - 0.786610i) q^{15} +(-1.09336 - 3.36501i) q^{16} +(2.01351 - 1.46290i) q^{17} +(-0.413545 - 1.27276i) q^{18} +(0.755585 - 2.32545i) q^{19} +(0.139886 + 0.101633i) q^{20} +(1.06460 - 3.27651i) q^{21} +(1.83826 - 1.33557i) q^{22} +(-3.78716 + 2.75154i) q^{23} +(2.39169 + 1.73767i) q^{24} -4.31592 q^{25} +4.28444 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.222562 + 0.684977i) q^{28} +(2.82991 - 8.70958i) q^{29} +1.10686 q^{30} +(-4.65323 - 3.05736i) q^{31} -1.17758 q^{32} +(-0.524676 + 1.61479i) q^{33} +(1.02924 + 3.16769i) q^{34} +(2.30524 + 1.67485i) q^{35} -0.209057 q^{36} +1.85857 q^{37} +(2.64728 + 1.92336i) q^{38} +(-2.59007 + 1.88179i) q^{39} +(-1.97815 + 1.43721i) q^{40} +(-0.399552 + 1.22969i) q^{41} +(3.72995 + 2.70997i) q^{42} +(-4.00739 + 12.3335i) q^{43} +(-0.109687 - 0.337582i) q^{44} +(-0.669131 + 0.486152i) q^{45} +(-1.93589 - 5.95804i) q^{46} +(2.79864 + 8.61332i) q^{47} +(-2.86245 + 2.07969i) q^{48} +(1.50457 + 4.63059i) q^{49} +(1.78483 - 5.49314i) q^{50} +(-2.01351 - 1.46290i) q^{51} +(0.206824 - 0.636538i) q^{52} +(3.62388 - 2.63290i) q^{53} +(-1.08268 + 0.786610i) q^{54} +(-1.13611 - 0.825431i) q^{55} -10.1848 q^{56} -2.44512 q^{57} +(9.91493 + 7.20362i) q^{58} +(0.732289 + 2.25376i) q^{59} +(0.0534318 - 0.164446i) q^{60} +8.32624 q^{61} +(5.81562 - 4.65809i) q^{62} -3.44512 q^{63} +(2.67370 - 8.22880i) q^{64} +(-0.818256 - 2.51833i) q^{65} +(-1.83826 - 1.33557i) q^{66} +2.47214 q^{67} +0.520307 q^{68} +(3.78716 + 2.75154i) q^{69} +(-3.08501 + 2.24139i) q^{70} +(11.6329 - 8.45181i) q^{71} +(0.913545 - 2.81160i) q^{72} +(-5.59979 - 4.06849i) q^{73} +(-0.768602 + 2.36552i) q^{74} +(1.33369 + 4.10468i) q^{75} +(0.413545 - 0.300458i) q^{76} +(-1.80757 - 5.56314i) q^{77} +(-1.32397 - 4.07475i) q^{78} +(-14.0312 + 10.1943i) q^{79} +(-0.904307 - 2.78317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.39987 - 1.01707i) q^{82} +(1.67051 - 5.14130i) q^{83} +(0.582676 - 0.423339i) q^{84} +(1.66535 - 1.20995i) q^{85} +(-14.0404 - 10.2009i) q^{86} -9.15780 q^{87} +5.01945 q^{88} +(6.30301 + 4.57940i) q^{89} +(-0.342040 - 1.05269i) q^{90} +(3.40832 - 10.4897i) q^{91} -0.978636 q^{92} +(-1.46980 + 5.37026i) q^{93} -12.1201 q^{94} +(0.624938 - 1.92336i) q^{95} +(0.363892 + 1.11994i) q^{96} +(10.5416 + 7.65894i) q^{97} -6.51584 q^{98} +1.69789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20} + 6 q^{21} + 6 q^{22} - 17 q^{23} + 4 q^{24} - 18 q^{25} + 12 q^{26} + 2 q^{27} - 9 q^{28} - 2 q^{29} - 4 q^{30} + 17 q^{31} - q^{33} + 4 q^{34} - 3 q^{35} + 2 q^{36} + 8 q^{37} + 8 q^{38} + 3 q^{39} - 7 q^{40} - 5 q^{41} + 6 q^{42} - 19 q^{43} + 24 q^{44} - q^{45} - 17 q^{46} - 4 q^{47} - 12 q^{48} + 11 q^{49} + 12 q^{50} - 9 q^{51} - 12 q^{52} + 2 q^{54} + 8 q^{55} - 12 q^{56} + 2 q^{57} + 33 q^{58} - 29 q^{59} - 6 q^{60} + 4 q^{61} + 47 q^{62} - 6 q^{63} + 16 q^{64} + 21 q^{65} - 6 q^{66} - 16 q^{67} + 6 q^{68} + 17 q^{69} - 3 q^{70} + 37 q^{71} + q^{72} + 3 q^{73} - 2 q^{74} + 3 q^{75} - 3 q^{76} + 18 q^{77} - 27 q^{78} - 3 q^{79} - 24 q^{80} - 2 q^{81} + 35 q^{82} - 31 q^{83} - 6 q^{84} - 8 q^{85} - 44 q^{86} - 18 q^{87} - 8 q^{88} + 19 q^{89} - 11 q^{90} - 24 q^{91} + 2 q^{92} + 13 q^{93} - 94 q^{94} - 16 q^{95} + 20 q^{96} - 3 q^{97} - 34 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.413545	+	1.27276i	−0.292421	+	0.899979i	0.691655	+	0.722228i	$0.256882\pi$
$2$	−0.413545	+	1.27276i	−0.292421	+	0.899979i	−0.984076	+	0.177750i	$0.943118\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.169131	+	0.122881i	0.0845653	+	0.0614403i
$5$	0.827091			0.369886			0.184943	−	0.982749i	$-0.440790\pi$
$5$	0.827091			0.369886			0.184943	+	0.982749i	$0.440790\pi$
$6$	1.33826			0.546343
$7$	2.78716	+	2.02499i	1.05345	+	0.765376i	0.972865	−	0.231372i	$-0.0743215\pi$
$7$	2.78716	+	2.02499i	1.05345	+	0.765376i	0.0805839	+	0.996748i	$0.474322\pi$
$8$	−2.39169	+	1.73767i	−0.845591	+	0.614358i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.342040	+	1.05269i	−0.108162	+	0.332890i
$11$	−1.37362	−	0.997993i	−0.414162	−	0.300906i	0.361123	−	0.932518i	$-0.382394\pi$
$11$	−1.37362	−	0.997993i	−0.414162	−	0.300906i	−0.775285	+	0.631612i	$0.782394\pi$
$12$	0.0646021	−	0.198825i	0.0186490	−	0.0573958i
$13$	−0.989318	−	3.04481i	−0.274387	−	0.844478i	−0.989381	−	0.145346i	$-0.953570\pi$
$13$	−0.989318	−	3.04481i	−0.274387	−	0.844478i	0.714993	−	0.699131i	$-0.246430\pi$
$14$	−3.72995	+	2.70997i	−0.996872	+	0.724270i
$15$	−0.255585	−	0.786610i	−0.0659918	−	0.203102i
$16$	−1.09336	−	3.36501i	−0.273340	−	0.841253i
$17$	2.01351	−	1.46290i	0.488347	−	0.354805i	−0.316201	−	0.948692i	$-0.602408\pi$
$17$	2.01351	−	1.46290i	0.488347	−	0.354805i	0.804548	+	0.593887i	$0.202408\pi$
$18$	−0.413545	−	1.27276i	−0.0974736	−	0.299993i
$19$	0.755585	−	2.32545i	0.173343	−	0.533495i	−0.826211	−	0.563361i	$-0.809508\pi$
$19$	0.755585	−	2.32545i	0.173343	−	0.533495i	0.999554	+	0.0298658i	$0.00950800\pi$
$20$	0.139886	+	0.101633i	0.0312795	+	0.0227259i
$21$	1.06460	−	3.27651i	0.232315	−	0.714993i
$22$	1.83826	−	1.33557i	0.391919	−	0.284746i
$23$	−3.78716	+	2.75154i	−0.789678	+	0.573735i	−0.907868	−	0.419256i	$-0.862291\pi$
$23$	−3.78716	+	2.75154i	−0.789678	+	0.573735i	0.118190	+	0.992991i	$0.462291\pi$
$24$	2.39169	+	1.73767i	0.488202	+	0.354700i
$25$	−4.31592			−0.863184
$26$	4.28444			0.840248
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.222562	+	0.684977i	0.0420603	+	0.129448i
$29$	2.82991	−	8.70958i	0.525502	−	1.61733i	−0.237819	−	0.971309i	$-0.576433\pi$
$29$	2.82991	−	8.70958i	0.525502	−	1.61733i	0.763321	−	0.646019i	$-0.223567\pi$
$30$	1.10686			0.202085
$31$	−4.65323	−	3.05736i	−0.835744	−	0.549119i
$31$	−4.65323	−	3.05736i	−0.835744	−	0.549119i
$32$	−1.17758			−0.208169
$33$	−0.524676	+	1.61479i	−0.0913343	+	0.281098i
$34$	1.02924	+	3.16769i	0.176514	+	0.543254i
$35$	2.30524	+	1.67485i	0.389656	+	0.283102i
$36$	−0.209057			−0.0348428
$37$	1.85857			0.305547			0.152773	−	0.988261i	$-0.451180\pi$
$37$	1.85857			0.305547			0.152773	+	0.988261i	$0.451180\pi$
$38$	2.64728	+	1.92336i	0.429445	+	0.312010i
$39$	−2.59007	+	1.88179i	−0.414743	+	0.301328i
$40$	−1.97815	+	1.43721i	−0.312773	+	0.227243i
$41$	−0.399552	+	1.22969i	−0.0623995	+	0.192046i	−0.977396	−	0.211415i	$-0.932193\pi$
$41$	−0.399552	+	1.22969i	−0.0623995	+	0.192046i	0.914997	+	0.403461i	$0.132193\pi$
$42$	3.72995	+	2.70997i	0.575544	+	0.418158i
$43$	−4.00739	+	12.3335i	−0.611122	+	1.88084i	−0.163716	+	0.986508i	$0.552348\pi$
$43$	−4.00739	+	12.3335i	−0.611122	+	1.88084i	−0.447406	+	0.894331i	$0.647652\pi$
$44$	−0.109687	−	0.337582i	−0.0165360	−	0.0508924i
$45$	−0.669131	+	0.486152i	−0.0997481	+	0.0724712i
$46$	−1.93589	−	5.95804i	−0.285431	−	0.878466i
$47$	2.79864	+	8.61332i	0.408223	+	1.25638i	0.918174	+	0.396178i	$0.129664\pi$
$47$	2.79864	+	8.61332i	0.408223	+	1.25638i	−0.509951	+	0.860204i	$0.670336\pi$
$48$	−2.86245	+	2.07969i	−0.413159	+	0.300178i
$49$	1.50457	+	4.63059i	0.214938	+	0.661512i
$50$	1.78483	−	5.49314i	0.252413	−	0.776847i
$51$	−2.01351	−	1.46290i	−0.281947	−	0.204847i
$52$	0.206824	−	0.636538i	0.0286813	−	0.0882719i
$53$	3.62388	−	2.63290i	0.497778	−	0.361657i	−0.310389	−	0.950609i	$-0.600459\pi$
$53$	3.62388	−	2.63290i	0.497778	−	0.361657i	0.808168	+	0.588952i	$0.200459\pi$
$54$	−1.08268	+	0.786610i	−0.147334	+	0.107044i
$55$	−1.13611	−	0.825431i	−0.153193	−	0.111301i
$56$	−10.1848			−1.36100
$57$	−2.44512			−0.323865
$58$	9.91493	+	7.20362i	1.30189	+	0.945881i
$59$	0.732289	+	2.25376i	0.0953360	+	0.293414i	0.987341	−	0.158611i	$-0.0507017\pi$
$59$	0.732289	+	2.25376i	0.0953360	+	0.293414i	−0.892005	+	0.452025i	$0.850702\pi$
$60$	0.0534318	−	0.164446i	0.00689802	−	0.0212299i
$61$	8.32624			1.06607			0.533033	−	0.846095i	$-0.321052\pi$
$61$	8.32624			1.06607			0.533033	+	0.846095i	$0.321052\pi$
$62$	5.81562	−	4.65809i	0.738584	−	0.591578i
$63$	−3.44512			−0.434045
$64$	2.67370	−	8.22880i	0.334212	−	1.02860i
$65$	−0.818256	−	2.51833i	−0.101492	−	0.312361i
$66$	−1.83826	−	1.33557i	−0.226274	−	0.164398i
$67$	2.47214			0.302019			0.151010	−	0.988532i	$-0.451748\pi$
$67$	2.47214			0.302019			0.151010	+	0.988532i	$0.451748\pi$
$68$	0.520307			0.0630965
$69$	3.78716	+	2.75154i	0.455921	+	0.331246i
$70$	−3.08501	+	2.24139i	−0.368729	+	0.267898i
$71$	11.6329	−	8.45181i	1.38057	−	1.00305i	0.383747	−	0.923438i	$-0.374633\pi$
$71$	11.6329	−	8.45181i	1.38057	−	1.00305i	0.996826	−	0.0796073i	$-0.0253666\pi$
$72$	0.913545	−	2.81160i	0.107662	−	0.331351i
$73$	−5.59979	−	4.06849i	−0.655406	−	0.476181i	0.209702	−	0.977765i	$-0.432751\pi$
$73$	−5.59979	−	4.06849i	−0.655406	−	0.476181i	−0.865109	+	0.501585i	$0.832751\pi$
$74$	−0.768602	+	2.36552i	−0.0893482	+	0.274986i
$75$	1.33369	+	4.10468i	0.154002	+	0.473968i
$76$	0.413545	−	0.300458i	0.0474369	−	0.0344649i
$77$	−1.80757	−	5.56314i	−0.205992	−	0.633979i
$78$	−1.32397	−	4.07475i	−0.149910	−	0.461374i
$79$	−14.0312	+	10.1943i	−1.57864	+	1.14695i	−0.660405	+	0.750910i	$0.729615\pi$
$79$	−14.0312	+	10.1943i	−1.57864	+	1.14695i	−0.918234	+	0.396039i	$0.870385\pi$
$80$	−0.904307	−	2.78317i	−0.101105	−	0.311168i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.39987	−	1.01707i	−0.154590	−	0.112316i
$83$	1.67051	−	5.14130i	0.183362	−	0.564331i	−0.816554	−	0.577269i	$-0.804118\pi$
$83$	1.67051	−	5.14130i	0.183362	−	0.564331i	0.999916	+	0.0129378i	$0.00411834\pi$
$84$	0.582676	−	0.423339i	0.0635752	−	0.0461901i
$85$	1.66535	−	1.20995i	0.180633	−	0.131237i
$86$	−14.0404	−	10.2009i	−1.51401	−	1.09999i
$87$	−9.15780			−0.981819
$88$	5.01945			0.535076
$89$	6.30301	+	4.57940i	0.668117	+	0.485416i	0.869394	−	0.494119i	$-0.164509\pi$
$89$	6.30301	+	4.57940i	0.668117	+	0.485416i	−0.201277	+	0.979534i	$0.564509\pi$
$90$	−0.342040	−	1.05269i	−0.0360541	−	0.110963i
$91$	3.40832	−	10.4897i	0.357289	−	1.09962i
$92$	−0.978636			−0.102030
$93$	−1.46980	+	5.37026i	−0.152411	+	0.556870i
$94$	−12.1201			−1.25009
$95$	0.624938	−	1.92336i	0.0641172	−	0.197333i
$96$	0.363892	+	1.11994i	0.0371396	+	0.114304i
$97$	10.5416	+	7.65894i	1.07034	+	0.777648i	0.975973	−	0.217890i	$-0.0699173\pi$
$97$	10.5416	+	7.65894i	1.07034	+	0.777648i	0.0943669	+	0.995537i	$0.469917\pi$
$98$	−6.51584			−0.658199
$99$	1.69789			0.170644
$100$	−0.729954	−	0.530343i	−0.0729954	−	0.0530343i
$101$	−14.4803	+	10.5206i	−1.44085	+	1.04684i	−0.452980	+	0.891520i	$0.649639\pi$
$101$	−14.4803	+	10.5206i	−1.44085	+	1.04684i	−0.987865	+	0.155315i	$0.950361\pi$
$102$	2.69460	−	1.95774i	0.266805	−	0.193845i
$103$	−0.651545	+	2.00525i	−0.0641986	+	0.197583i	−0.978011	−	0.208554i	$-0.933124\pi$
$103$	−0.651545	+	2.00525i	−0.0641986	+	0.197583i	0.913812	+	0.406137i	$0.133124\pi$
$104$	7.65701	+	5.56314i	0.750831	+	0.545511i
$105$	0.880523	−	2.70997i	0.0859302	−	0.264466i
$106$	1.85242	+	5.70116i	0.179923	+	0.553746i
$107$	−7.81874	+	5.68065i	−0.755867	+	0.549169i	−0.897640	−	0.440730i	$-0.854720\pi$
$107$	−7.81874	+	5.68065i	−0.755867	+	0.549169i	0.141773	+	0.989899i	$0.454720\pi$
$108$	0.0646021	+	0.198825i	0.00621634	+	0.0191319i
$109$	−1.61893	−	4.98254i	−0.155065	−	0.477241i	0.843102	−	0.537753i	$-0.180727\pi$
$109$	−1.61893	−	4.98254i	−0.155065	−	0.477241i	−0.998167	+	0.0605120i	$0.980727\pi$
$110$	1.52041	−	1.10464i	0.144965	−	0.105323i
$111$	−0.574329	−	1.76760i	−0.0545129	−	0.167773i
$112$	3.76676	−	11.5929i	0.355925	−	1.09542i
$113$	3.88256	+	2.82084i	0.365240	+	0.265363i	0.755234	−	0.655455i	$-0.227523\pi$
$113$	3.88256	+	2.82084i	0.365240	+	0.265363i	−0.389994	+	0.920817i	$0.627523\pi$
$114$	1.01117	−	3.11206i	0.0947048	−	0.291471i
$115$	−3.13233	+	2.27577i	−0.292091	+	0.212217i
$116$	1.54886	−	1.12532i	0.143808	−	0.104483i
$117$	2.59007	+	1.88179i	0.239452	+	0.173972i
$118$	−3.17133			−0.291945
$119$	8.57433			0.786007
$120$	1.97815	+	1.43721i	0.180579	+	0.131199i
$121$	−2.50835	−	7.71990i	−0.228032	−	0.701809i
$122$	−3.44328	+	10.5973i	−0.311740	+	0.959436i
$123$	1.29298			0.116584
$124$	−0.411312	−	1.08889i	−0.0369369	−	0.0977848i
$125$	−7.70511			−0.689166
$126$	1.42472	−	4.38482i	0.126924	−	0.390631i
$127$	−0.932698	−	2.87055i	−0.0827635	−	0.254720i	0.901109	−	0.433594i	$-0.142755\pi$
$127$	−0.932698	−	2.87055i	−0.0827635	−	0.254720i	−0.983872	+	0.178874i	$0.942755\pi$
$128$	7.46224	+	5.42164i	0.659575	+	0.479210i
$129$	12.9682			1.14179
$130$	3.54362			0.310796
$131$	9.48866	+	6.89392i	0.829028	+	0.602324i	0.919284	−	0.393594i	$-0.128768\pi$
$131$	9.48866	+	6.89392i	0.829028	+	0.602324i	−0.0902558	+	0.995919i	$0.528768\pi$
$132$	−0.287165	+	0.208637i	−0.0249945	+	0.0181595i
$133$	6.81497	−	4.95136i	0.590932	−	0.429338i
$134$	−1.02234	+	3.14644i	−0.0883168	+	0.271811i
$135$	0.669131	+	0.486152i	0.0575896	+	0.0418413i
$136$	−2.27366	+	6.99760i	−0.194965	+	0.600040i
$137$	1.93103	+	5.94310i	0.164979	+	0.507753i	0.999035	−	0.0439271i	$-0.0139869\pi$
$137$	1.93103	+	5.94310i	0.164979	+	0.507753i	−0.834056	+	0.551680i	$0.813987\pi$
$138$	−5.06822	+	3.68227i	−0.431435	+	0.313456i
$139$	−2.39811	−	7.38062i	−0.203405	−	0.626016i	−0.999775	−	0.0212065i	$-0.993249\pi$
$139$	−2.39811	−	7.38062i	−0.203405	−	0.626016i	0.796370	−	0.604809i	$-0.206751\pi$
$140$	0.184079	+	0.566538i	0.0155575	+	0.0478812i
$141$	7.32693	−	5.32332i	0.617038	−	0.448305i
$142$	5.94640	+	18.3011i	0.499011	+	1.53580i
$143$	−1.67975	+	5.16974i	−0.140468	+	0.432315i
$144$	2.86245	+	2.07969i	0.238537	+	0.173308i
$145$	2.34060	−	7.20362i	0.194376	−	0.598228i
$146$	7.49399	−	5.44470i	0.620207	−	0.450607i
$147$	3.93901	−	2.86186i	0.324884	−	0.236042i
$148$	0.314341	+	0.228382i	0.0258387	+	0.0187729i
$149$	−2.38452			−0.195348			−0.0976738	−	0.995218i	$-0.531140\pi$
$149$	−2.38452			−0.195348			−0.0976738	+	0.995218i	$0.531140\pi$
$150$	−5.77583			−0.471594
$151$	−11.6309	−	8.45033i	−0.946508	−	0.687678i	0.00347031	−	0.999994i	$-0.498895\pi$
$151$	−11.6309	−	8.45033i	−0.946508	−	0.687678i	−0.949978	+	0.312316i	$0.898895\pi$
$152$	2.23373	+	6.87472i	0.181180	+	0.557614i
$153$	−0.769091	+	2.36702i	−0.0621773	+	0.191362i
$154$	7.82807			0.630804
$155$	−3.84864	−	2.52872i	−0.309130	−	0.203112i
$156$	−0.669296			−0.0535865
$157$	−6.44884	+	19.8475i	−0.514673	+	1.58400i	0.269202	+	0.963084i	$0.413240\pi$
$157$	−6.44884	+	19.8475i	−0.514673	+	1.58400i	−0.783875	+	0.620918i	$0.786760\pi$
$158$	−7.17236	−	22.0742i	−0.570602	−	1.75613i
$159$	−3.62388	−	2.63290i	−0.287392	−	0.208803i
$160$	−0.973965			−0.0769987
$161$	−16.1273			−1.27101
$162$	1.08268	+	0.786610i	0.0850631	+	0.0618019i
$163$	8.09681	−	5.88267i	0.634191	−	0.460767i	−0.223659	−	0.974668i	$-0.571800\pi$
$163$	8.09681	−	5.88267i	0.634191	−	0.460767i	0.857850	+	0.513901i	$0.171800\pi$
$164$	−0.218682	+	0.158882i	−0.0170762	+	0.0124066i
$165$	−0.433955	+	1.33557i	−0.0337833	+	0.103974i
$166$	5.85282	+	4.25233i	0.454267	+	0.330044i
$167$	−5.87559	+	18.0832i	−0.454667	+	1.39932i	0.416859	+	0.908971i	$0.363131\pi$
$167$	−5.87559	+	18.0832i	−0.454667	+	1.39932i	−0.871526	+	0.490349i	$0.836869\pi$
$168$	3.14728	+	9.68633i	0.242818	+	0.747316i
$169$	2.22512	−	1.61664i	0.171163	−	0.124357i
$170$	0.851279	+	2.61997i	0.0652901	+	0.200942i
$171$	0.755585	+	2.32545i	0.0577810	+	0.177832i
$172$	−2.19332	+	1.59354i	−0.167239	+	0.121506i
$173$	−5.95282	−	18.3209i	−0.452584	−	1.39291i	−0.873948	−	0.486020i	$-0.838448\pi$
$173$	−5.95282	−	18.3209i	−0.452584	−	1.39291i	0.421363	−	0.906892i	$-0.361552\pi$
$174$	3.78716	−	11.6557i	0.287104	−	0.883616i
$175$	−12.0292	−	8.73971i	−0.909321	−	0.660660i
$176$	−1.85640	+	5.71341i	−0.139931	+	0.430664i
$177$	1.91716	−	1.39290i	0.144102	−	0.104697i
$178$	−8.43507	+	6.12844i	−0.632235	+	0.459346i
$179$	12.0462	+	8.75208i	0.900375	+	0.654161i	0.938562	−	0.345110i	$-0.112158\pi$
$179$	12.0462	+	8.75208i	0.900375	+	0.654161i	−0.0381872	+	0.999271i	$0.512158\pi$
$180$	−0.172909			−0.0128879
$181$	15.3508			1.14101			0.570507	−	0.821293i	$-0.306747\pi$
$181$	15.3508			1.14101			0.570507	+	0.821293i	$0.306747\pi$
$182$	11.9414	+	8.67597i	0.885159	+	0.643106i
$183$	−2.57295	−	7.91872i	−0.190198	−	0.585369i
$184$	4.27648	−	13.1617i	0.315266	−	0.970290i
$185$	1.53720			0.113018
$186$	−6.22723	−	4.09155i	−0.456603	−	0.300007i
$187$	−4.22575			−0.309017
$188$	−0.585074	+	1.80067i	−0.0426709	+	0.131328i
$189$	1.06460	+	3.27651i	0.0774384	+	0.238331i
$190$	2.18954	+	1.59079i	0.158846	+	0.115408i
$191$	−22.1411			−1.60207			−0.801037	−	0.598615i	$-0.795718\pi$
$191$	−22.1411			−1.60207			−0.801037	+	0.598615i	$0.795718\pi$
$192$	−8.65227			−0.624424
$193$	6.77472	+	4.92212i	0.487655	+	0.354302i	0.804282	−	0.594248i	$-0.202550\pi$
$193$	6.77472	+	4.92212i	0.487655	+	0.354302i	−0.316627	+	0.948550i	$0.602550\pi$
$194$	−14.1075	+	10.2497i	−1.01286	+	0.735883i
$195$	−2.14222	+	1.55642i	−0.153408	+	0.111457i
$196$	−0.314540	+	0.968056i	−0.0224672	+	0.0691469i
$197$	−15.9097	−	11.5591i	−1.13352	−	0.823550i	−0.147316	−	0.989089i	$-0.547064\pi$
$197$	−15.9097	−	11.5591i	−1.13352	−	0.823550i	−0.986203	+	0.165539i	$0.947064\pi$
$198$	−0.702153	+	2.16101i	−0.0498999	+	0.153576i
$199$	3.11893	+	9.59907i	0.221095	+	0.680460i	0.998665	+	0.0516632i	$0.0164522\pi$
$199$	3.11893	+	9.59907i	0.221095	+	0.680460i	−0.777570	+	0.628797i	$0.783548\pi$
$200$	10.3224	−	7.49963i	0.729901	−	0.530304i
$201$	−0.763932	−	2.35114i	−0.0538836	−	0.165837i
$202$	−7.40191	−	22.7807i	−0.520796	−	1.60285i
$203$	25.5243	−	18.5445i	1.79145	−	1.30157i
$204$	−0.160784	−	0.494841i	−0.0112571	−	0.0346458i
$205$	−0.330466	+	1.01707i	−0.0230807	+	0.0710352i
$206$	−2.28276	−	1.65852i	−0.159048	−	0.115555i
$207$	1.44657	−	4.45208i	0.100543	−	0.309441i
$208$	−9.16413	+	6.65813i	−0.635418	+	0.461658i
$209$	−3.35867	+	2.44022i	−0.232324	+	0.168793i
$210$	3.08501	+	2.24139i	0.212886	+	0.154671i
$211$	21.5136			1.48106			0.740529	−	0.672025i	$-0.234575\pi$
$211$	21.5136			1.48106			0.740529	+	0.672025i	$0.234575\pi$
$212$	0.936442			0.0643151
$213$	−11.6329	−	8.45181i	−0.797075	−	0.579109i
$214$	−3.99671	−	12.3006i	−0.273209	−	0.840852i
$215$	−3.31448	+	10.2009i	−0.226045	+	0.695696i
$216$	−2.95630			−0.201150
$217$	−6.77816	−	17.9441i	−0.460132	−	1.21813i
$218$	7.01109			0.474851
$219$	−2.13893	+	6.58295i	−0.144536	+	0.444835i
$220$	−0.0907212	−	0.279211i	−0.00611642	−	0.0188244i
$221$	−6.44624	−	4.68347i	−0.433621	−	0.315044i
$222$	2.48725			0.166933
$223$	2.02734			0.135761			0.0678804	−	0.997693i	$-0.478376\pi$
$223$	2.02734			0.135761			0.0678804	+	0.997693i	$0.478376\pi$
$224$	−3.28211	−	2.38459i	−0.219295	−	0.159327i
$225$	3.49165	−	2.53683i	0.232777	−	0.169122i
$226$	−5.19587	+	3.77502i	−0.345624	+	0.251111i
$227$	5.29833	−	16.3066i	0.351663	−	1.08231i	−0.606256	−	0.795269i	$-0.707329\pi$
$227$	5.29833	−	16.3066i	0.351663	−	1.08231i	0.957919	−	0.287038i	$-0.0926705\pi$
$228$	−0.413545	−	0.300458i	−0.0273877	−	0.0198983i
$229$	−2.48038	+	7.63383i	−0.163908	+	0.504457i	−0.998954	−	0.0457226i	$-0.985441\pi$
$229$	−2.48038	+	7.63383i	−0.163908	+	0.504457i	0.835046	+	0.550180i	$0.185441\pi$
$230$	−1.60115	−	4.92784i	−0.105577	−	0.324932i
$231$	−4.73229	+	3.43821i	−0.311362	+	0.226218i
$232$	8.36606	+	25.7481i	0.549259	+	1.69045i
$233$	−6.39823	−	19.6917i	−0.419162	−	1.29005i	−0.908475	−	0.417940i	$-0.862752\pi$
$233$	−6.39823	−	19.6917i	−0.419162	−	1.29005i	0.489313	−	0.872108i	$-0.337248\pi$
$234$	−3.46619	+	2.51833i	−0.226592	+	0.164629i
$235$	2.31473	+	7.12400i	0.150996	+	0.464718i
$236$	−0.153090	+	0.471163i	−0.00996532	+	0.0306701i
$237$	14.0312	+	10.1943i	0.911428	+	0.662191i
$238$	−3.54587	+	10.9131i	−0.229845	+	0.707390i
$239$	11.6031	−	8.43013i	0.750541	−	0.545300i	−0.145453	−	0.989365i	$-0.546464\pi$
$239$	11.6031	−	8.43013i	0.750541	−	0.545300i	0.895995	+	0.444065i	$0.146464\pi$
$240$	−2.36751	+	1.72009i	−0.152822	+	0.111032i
$241$	−2.91180	−	2.11555i	−0.187566	−	0.136274i	0.490040	−	0.871700i	$-0.336982\pi$
$241$	−2.91180	−	2.11555i	−0.187566	−	0.136274i	−0.677605	+	0.735426i	$0.736982\pi$
$242$	10.8629			0.698294
$243$	−1.00000			−0.0641500
$244$	1.40822	+	1.02313i	0.0901522	+	0.0654994i
$245$	1.24441	+	3.82992i	0.0795027	+	0.244684i
$246$	−0.534705	+	1.64565i	−0.0340915	+	0.104923i
$247$	−7.82807			−0.498088
$248$	16.4418	−	0.773479i	1.04405	−	0.0491159i
$249$	−5.40589			−0.342584
$250$	3.18641	−	9.80678i	0.201527	−	0.620235i
$251$	−2.03723	−	6.26994i	−0.128589	−	0.395755i	0.865949	−	0.500132i	$-0.166715\pi$
$251$	−2.03723	−	6.26994i	−0.128589	−	0.395755i	−0.994538	+	0.104377i	$0.966715\pi$
$252$	−0.582676	−	0.423339i	−0.0367051	−	0.0266678i
$253$	7.94813			0.499695
$254$	4.03924			0.253444
$255$	−1.66535	−	1.20995i	−0.104288	−	0.0757700i
$256$	4.01324	−	2.91579i	0.250827	−	0.182237i
$257$	4.87957	−	3.54521i	0.304379	−	0.221144i	−0.425102	−	0.905146i	$-0.639762\pi$
$257$	4.87957	−	3.54521i	0.304379	−	0.221144i	0.729481	+	0.684001i	$0.239762\pi$
$258$	−5.36294	+	16.5054i	−0.333882	+	1.02758i
$259$	5.18014	+	3.76359i	0.321878	+	0.233858i
$260$	0.171062	−	0.526475i	0.0106088	−	0.0326506i
$261$	2.82991	+	8.70958i	0.175167	+	0.539110i
$262$	−12.6983	+	9.22586i	−0.784504	+	0.569976i
$263$	−0.667976	−	2.05582i	−0.0411892	−	0.126767i	0.928347	−	0.371714i	$-0.121230\pi$
$263$	−0.667976	−	2.05582i	−0.0411892	−	0.126767i	−0.969537	+	0.244946i	$0.921230\pi$
$264$	−1.55110	−	4.77378i	−0.0954634	−	0.293806i
$265$	2.99728	−	2.17765i	0.184121	−	0.133772i
$266$	3.48361	+	10.7214i	0.213594	+	0.657374i
$267$	2.40753	−	7.40963i	0.147339	−	0.453462i
$268$	0.418114	+	0.303777i	0.0255404	+	0.0185562i
$269$	−5.29318	+	16.2907i	−0.322731	+	0.993263i	0.649724	+	0.760170i	$0.274885\pi$
$269$	−5.29318	+	16.2907i	−0.322731	+	0.993263i	−0.972455	+	0.233093i	$0.925115\pi$
$270$	−0.895472	+	0.650598i	−0.0544967	+	0.0395941i
$271$	8.53115	−	6.19824i	0.518230	−	0.376516i	−0.297707	−	0.954657i	$-0.596222\pi$
$271$	8.53115	−	6.19824i	0.518230	−	0.376516i	0.815937	+	0.578141i	$0.196222\pi$
$272$	−7.12415	−	5.17600i	−0.431965	−	0.313841i
$273$	−11.0296			−0.667540
$274$	−8.36272			−0.505210
$275$	5.92843	+	4.30726i	0.357498	+	0.259737i
$276$	0.302415	+	0.930738i	0.0182032	+	0.0560238i
$277$	−5.38335	+	16.5682i	−0.323454	+	0.995489i	0.648680	+	0.761062i	$0.275321\pi$
$277$	−5.38335	+	16.5682i	−0.323454	+	0.995489i	−0.972134	+	0.234427i	$0.924679\pi$
$278$	10.3855			0.622881
$279$	5.56161	−	0.261638i	0.332965	−	0.0156638i
$280$	−8.42376			−0.503416
$281$	−8.82956	+	27.1746i	−0.526728	+	1.62110i	0.234147	+	0.972201i	$0.424770\pi$
$281$	−8.82956	+	27.1746i	−0.526728	+	1.62110i	−0.760874	+	0.648899i	$0.775230\pi$
$282$	3.74531	+	11.5269i	0.223030	+	0.686415i
$283$	14.0073	+	10.1769i	0.832649	+	0.604955i	0.920308	−	0.391195i	$-0.127938\pi$
$283$	14.0073	+	10.1769i	0.832649	+	0.604955i	−0.0876583	+	0.996151i	$0.527938\pi$
$284$	3.00605			0.178376
$285$	−2.02234			−0.119793
$286$	−5.88519	−	4.27584i	−0.347999	−	0.252836i
$287$	−3.60374	+	2.61827i	−0.212722	+	0.154552i
$288$	0.952682	−	0.692164i	0.0561373	−	0.0407861i
$289$	−3.33915	+	10.2769i	−0.196421	+	0.604521i
$290$	8.20054	+	5.95804i	0.481553	+	0.349868i
$291$	4.02654	−	12.3924i	0.236040	−	0.726457i
$292$	−0.447158	−	1.37621i	−0.0261680	−	0.0805367i
$293$	19.7472	−	14.3472i	1.15364	−	0.838170i	0.164681	−	0.986347i	$-0.447340\pi$
$293$	19.7472	−	14.3472i	1.15364	−	0.838170i	0.988961	+	0.148177i	$0.0473404\pi$
$294$	2.01351	+	6.19693i	0.117430	+	0.361412i
$295$	0.605670	+	1.86406i	0.0352635	+	0.108530i
$296$	−4.44512	+	3.22957i	−0.258368	+	0.187715i
$297$	−0.524676	−	1.61479i	−0.0304448	−	0.0936994i
$298$	0.986108	−	3.03493i	0.0571237	−	0.175809i
$299$	12.1246	+	8.80904i	0.701184	+	0.509440i
$300$	−0.278818	+	0.858113i	−0.0160975	+	0.0495432i
$301$	−36.1445	+	26.2605i	−2.08333	+	1.51363i
$302$	15.5652	−	11.3088i	0.895675	−	0.650746i
$303$	14.4803	+	10.5206i	0.831873	+	0.604391i
$304$	−8.65130			−0.496186
$305$	6.88656			0.394323
$306$	−2.69460	−	1.95774i	−0.154040	−	0.111916i
$307$	−7.32079	−	22.5311i	−0.417820	−	1.28592i	−0.909704	−	0.415256i	$-0.863692\pi$
$307$	−7.32079	−	22.5311i	−0.417820	−	1.28592i	0.491885	−	0.870660i	$-0.336308\pi$
$308$	0.377886	−	1.16301i	0.0215320	−	0.0662688i
$309$	2.10844			0.119945
$310$	4.81005	−	3.85266i	0.273192	−	0.218817i
$311$	1.84939			0.104869			0.0524346	−	0.998624i	$-0.483302\pi$
$311$	1.84939			0.104869			0.0524346	+	0.998624i	$0.483302\pi$
$312$	2.92472	−	9.00135i	0.165579	−	0.509601i
$313$	−0.661149	−	2.03481i	−0.0373703	−	0.115014i	0.930631	−	0.365959i	$-0.119259\pi$
$313$	−0.661149	−	2.03481i	−0.0373703	−	0.115014i	−0.968001	+	0.250945i	$0.919259\pi$
$314$	−22.5942	−	16.4157i	−1.27507	−	0.926390i
$315$	−2.84943			−0.160547
$316$	−3.62580			−0.203967
$317$	−13.7499	−	9.98991i	−0.772273	−	0.561089i	0.130377	−	0.991464i	$-0.458381\pi$
$317$	−13.7499	−	9.98991i	−0.772273	−	0.561089i	−0.902650	+	0.430375i	$0.858381\pi$
$318$	4.84970	−	3.52351i	0.271958	−	0.197589i
$319$	−12.5793	+	9.13941i	−0.704307	+	0.511709i
$320$	2.21139	−	6.80597i	0.123621	−	0.380465i
$321$	7.81874	+	5.68065i	0.436400	+	0.317063i
$322$	6.66937	−	20.5262i	0.371669	−	1.14388i
$323$	−1.88052	−	5.78765i	−0.104635	−	0.322034i
$324$	0.169131	−	0.122881i	0.00939614	−	0.00682670i
$325$	4.26982	+	13.1411i	0.236847	+	0.728940i
$326$	4.13885	+	12.7381i	0.229230	+	0.705496i
$327$	−4.23840	+	3.07938i	−0.234384	+	0.170290i
$328$	−1.18119	−	3.63534i	−0.0652205	−	0.200728i
$329$	−9.64165	+	29.6740i	−0.531562	+	1.63598i
$330$	−1.52041	−	1.10464i	−0.0836958	−	0.0608085i
$331$	6.08586	−	18.7304i	0.334509	−	1.02951i	−0.632454	−	0.774598i	$-0.717952\pi$
$331$	6.08586	−	18.7304i	0.334509	−	1.02951i	0.966963	−	0.254916i	$-0.0820478\pi$
$332$	0.914301	−	0.664278i	0.0501788	−	0.0364570i
$333$	−1.50361	+	1.09244i	−0.0823975	+	0.0598653i
$334$	−20.5858	−	14.9565i	−1.12640	−	0.818381i
$335$	2.04468			0.111713
$336$	−12.1895			−0.664990
$337$	4.31592	+	3.13570i	0.235103	+	0.170812i	0.699099	−	0.715025i	$-0.253585\pi$
$337$	4.31592	+	3.13570i	0.235103	+	0.170812i	−0.463996	+	0.885837i	$0.653585\pi$
$338$	1.13741	+	3.50060i	0.0618672	+	0.190408i
$339$	1.48300	−	4.56422i	0.0805457	−	0.247894i
$340$	0.430341			0.0233385
$341$	3.34053	+	8.84354i	0.180900	+	0.478905i
$342$	−3.27222			−0.176941
$343$	2.26879	−	6.98261i	0.122503	−	0.377026i
$344$	−11.8470	−	36.4614i	−0.638749	−	1.96587i
$345$	3.13233	+	2.27577i	0.168639	+	0.122523i
$346$	25.7799			1.38594
$347$	−17.7457			−0.952641			−0.476320	−	0.879272i	$-0.658030\pi$
$347$	−17.7457			−0.952641			−0.476320	+	0.879272i	$0.658030\pi$
$348$	−1.54886	−	1.12532i	−0.0830278	−	0.0603232i
$349$	23.7898	−	17.2843i	1.27344	−	0.925206i	0.274103	−	0.961700i	$-0.411619\pi$
$349$	23.7898	−	17.2843i	1.27344	−	0.925206i	0.999334	+	0.0364945i	$0.0116191\pi$
$350$	16.0982	−	11.6960i	0.860484	−	0.625178i
$351$	0.989318	−	3.04481i	0.0528059	−	0.162520i
$352$	1.61755	+	1.17522i	0.0862155	+	0.0626392i
$353$	1.95432	−	6.01479i	0.104018	−	0.320135i	−0.885481	−	0.464676i	$-0.846171\pi$
$353$	1.95432	−	6.01479i	0.104018	−	0.320135i	0.989499	+	0.144541i	$0.0461707\pi$
$354$	0.979995	+	3.01611i	0.0520861	+	0.160305i
$355$	9.62148	−	6.99042i	0.510655	−	0.371013i
$356$	0.503312	+	1.54903i	0.0266755	+	0.0820986i
$357$	−2.64961	−	8.15467i	−0.140232	−	0.431591i
$358$	−16.1210	+	11.7126i	−0.852019	+	0.619028i
$359$	−5.09888	−	15.6927i	−0.269109	−	0.828231i	−0.990718	−	0.135931i	$-0.956597\pi$
$359$	−5.09888	−	15.6927i	−0.269109	−	0.828231i	0.721610	−	0.692300i	$-0.243403\pi$
$360$	0.755585	−	2.32545i	0.0398228	−	0.122562i
$361$	10.5345	+	7.65377i	0.554448	+	0.402830i
$362$	−6.34824	+	19.5379i	−0.333656	+	1.02689i
$363$	−6.56694	+	4.77116i	−0.344675	+	0.250421i
$364$	1.86544	−	1.35532i	0.0977755	−	0.0710380i
$365$	−4.63154	−	3.36501i	−0.242426	−	0.176133i
$366$	11.1427			0.582437
$367$	11.4747			0.598974			0.299487	−	0.954100i	$-0.403184\pi$
$367$	11.4747			0.598974			0.299487	+	0.954100i	$0.403184\pi$
$368$	13.3997	+	9.73543i	0.698506	+	0.507495i
$369$	−0.399552	−	1.22969i	−0.0207998	−	0.0640153i
$370$	−0.635704	+	1.95650i	−0.0330487	+	0.101713i
$371$	15.4320			0.801188
$372$	−0.908489	+	0.727665i	−0.0471030	+	0.0377277i
$373$	−5.96483			−0.308847			−0.154424	−	0.988005i	$-0.549352\pi$
$373$	−5.96483			−0.308847			−0.154424	+	0.988005i	$0.549352\pi$
$374$	1.74754	−	5.37838i	0.0903631	−	0.278109i
$375$	2.38101	+	7.32800i	0.122955	+	0.378416i
$376$	−21.6606	−	15.7373i	−1.11706	−	0.811590i
$377$	−29.3187			−1.50999
$378$	−4.61048			−0.237137
$379$	−5.05567	−	3.67316i	−0.259692	−	0.188677i	0.450319	−	0.892868i	$-0.351310\pi$
$379$	−5.05567	−	3.67316i	−0.259692	−	0.188677i	−0.710011	+	0.704190i	$0.751310\pi$
$380$	0.342040	−	0.248506i	0.0175463	−	0.0127481i
$381$	−2.44183	+	1.77410i	−0.125099	+	0.0908897i
$382$	9.15635	−	28.1804i	0.468480	−	1.44183i
$383$	−14.5683	−	10.5845i	−0.744406	−	0.540843i	0.149682	−	0.988734i	$-0.452175\pi$
$383$	−14.5683	−	10.5845i	−0.744406	−	0.540843i	−0.894088	+	0.447891i	$0.852175\pi$
$384$	2.85032	−	8.77239i	0.145455	−	0.447664i
$385$	−1.49503	−	4.60122i	−0.0761937	−	0.234500i
$386$	−9.06634	+	6.58708i	−0.461465	+	0.335274i
$387$	−4.00739	−	12.3335i	−0.203707	−	0.626946i
$388$	0.841777	+	2.59072i	0.0427348	+	0.131524i
$389$	7.38266	−	5.36382i	0.374316	−	0.271956i	−0.384683	−	0.923049i	$-0.625689\pi$
$389$	7.38266	−	5.36382i	0.374316	−	0.271956i	0.758998	+	0.651093i	$0.225689\pi$
$390$	−1.09504	−	3.37019i	−0.0554495	−	0.170656i
$391$	−3.60026	+	11.0805i	−0.182073	+	0.560363i
$392$	−11.6449	−	8.46050i	−0.588155	−	0.427320i
$393$	3.62435	−	11.1546i	0.182824	−	0.562675i
$394$	21.2913	−	15.4691i	1.07264	−	0.779320i
$395$	−11.6051	+	8.43161i	−0.583917	+	0.424240i
$396$	0.287165	+	0.208637i	0.0144306	+	0.0104844i
$397$	4.78534			0.240169			0.120085	−	0.992764i	$-0.461683\pi$
$397$	4.78534			0.240169			0.120085	+	0.992764i	$0.461683\pi$
$398$	−13.5071			−0.677052
$399$	−6.81497	−	4.95136i	−0.341175	−	0.247878i
$400$	4.71885	+	14.5231i	0.235942	+	0.726156i
$401$	−6.68113	+	20.5624i	−0.333640	+	1.02684i	0.633749	+	0.773539i	$0.281515\pi$
$401$	−6.68113	+	20.5624i	−0.333640	+	1.02684i	−0.967388	+	0.253298i	$0.918485\pi$
$402$	3.30836			0.165006
$403$	−4.70557	+	17.1929i	−0.234401	+	0.856439i
$404$	−3.74184			−0.186163
$405$	0.255585	−	0.786610i	0.0127001	−	0.0390870i
$406$	13.0473	+	40.1553i	0.647524	+	1.99288i
$407$	−2.55296	−	1.85484i	−0.126546	−	0.0919409i
$408$	7.35772			0.364261
$409$	−13.5031			−0.667684			−0.333842	−	0.942629i	$-0.608345\pi$
$409$	−13.5031			−0.667684			−0.333842	+	0.942629i	$0.608345\pi$
$410$	−1.15782	−	0.841208i	−0.0571808	−	0.0415443i
$411$	5.05550	−	3.67304i	0.249369	−	0.181177i
$412$	−0.356602	+	0.259087i	−0.0175685	+	0.0127643i
$413$	−2.52283	+	7.76447i	−0.124140	+	0.382065i
$414$	5.06822	+	3.68227i	0.249089	+	0.180974i
$415$	1.38166	−	4.25233i	0.0678232	−	0.208738i
$416$	1.16500	+	3.58550i	0.0571188	+	0.175794i
$417$	−6.27833	+	4.56147i	−0.307451	+	0.223376i
$418$	−1.71685	−	5.28393i	−0.0839740	−	0.258445i
$419$	10.3557	+	31.8715i	0.505908	+	1.55702i	0.799240	+	0.601013i	$0.205236\pi$
$419$	10.3557	+	31.8715i	0.505908	+	1.55702i	−0.293332	+	0.956011i	$0.594764\pi$
$420$	0.481926	−	0.350140i	0.0235156	−	0.0170851i
$421$	−2.13262	−	6.56352i	−0.103937	−	0.319887i	0.885542	−	0.464559i	$-0.153787\pi$
$421$	−2.13262	−	6.56352i	−0.103937	−	0.319887i	−0.989480	+	0.144672i	$0.953787\pi$
$422$	−8.89685	+	27.3817i	−0.433092	+	1.33292i
$423$	−7.32693	−	5.32332i	−0.356247	−	0.258829i
$424$	−4.09210	+	12.5942i	−0.198730	+	0.611628i
$425$	−8.69013	+	6.31375i	−0.421533	+	0.306262i
$426$	15.5679	−	11.3107i	0.754267	−	0.548007i
$427$	23.2066	+	16.8606i	1.12305	+	0.815941i
$428$	−2.02043			−0.0976612
$429$	5.43578			0.262442
$430$	−11.6126	−	8.43708i	−0.560012	−	0.406872i
$431$	6.13874	+	18.8931i	0.295693	+	0.910049i	0.982988	+	0.183671i	$0.0587980\pi$
$431$	6.13874	+	18.8931i	0.295693	+	0.910049i	−0.687295	+	0.726379i	$0.741202\pi$
$432$	1.09336	−	3.36501i	0.0526042	−	0.161899i
$433$	−8.92226			−0.428777			−0.214388	−	0.976749i	$-0.568776\pi$
$433$	−8.92226			−0.428777			−0.214388	+	0.976749i	$0.568776\pi$
$434$	25.6417	−	1.20628i	1.23084	−	0.0579031i
$435$	−7.57433			−0.363161
$436$	0.338448	−	1.04163i	0.0162087	−	0.0498853i
$437$	3.53704	+	10.8859i	0.169200	+	0.520743i
$438$	−7.49399	−	5.44470i	−0.358077	−	0.260158i
$439$	−25.3102			−1.20799			−0.603995	−	0.796988i	$-0.706425\pi$
$439$	−25.3102			−1.20799			−0.603995	+	0.796988i	$0.706425\pi$
$440$	4.15154			0.197917
$441$	−3.93901	−	2.86186i	−0.187572	−	0.136279i
$442$	8.62675	−	6.26770i	0.410333	−	0.298124i
$443$	−4.77882	+	3.47201i	−0.227048	+	0.164960i	−0.695494	−	0.718532i	$-0.744814\pi$
$443$	−4.77882	+	3.47201i	−0.227048	+	0.164960i	0.468445	+	0.883493i	$0.344814\pi$
$444$	0.120067	−	0.369530i	0.00569815	−	0.0175371i
$445$	5.21316	+	3.78758i	0.247127	+	0.179549i
$446$	−0.838398	+	2.58032i	−0.0396993	+	0.122182i
$447$	0.736858	+	2.26782i	0.0348522	+	0.107264i
$448$	24.1153	−	17.5208i	1.13934	−	0.827780i
$449$	−1.50605	−	4.63515i	−0.0710749	−	0.218746i	0.909209	−	0.416340i	$-0.136687\pi$
$449$	−1.50605	−	4.63515i	−0.0710749	−	0.218746i	−0.980284	+	0.197594i	$0.936687\pi$
$450$	1.78483	+	5.49314i	0.0841377	+	0.258949i
$451$	1.77606	−	1.29038i	0.0836313	−	0.0607617i
$452$	0.310032	+	0.954182i	0.0145827	+	0.0448809i
$453$	−4.44260	+	13.6729i	−0.208732	+	0.642410i
$454$	18.5633	+	13.4870i	0.871220	+	0.632978i
$455$	2.81899	−	8.67597i	0.132156	−	0.406736i
$456$	5.84799	−	4.24881i	0.273857	−	0.198969i
$457$	11.0330	−	8.01591i	0.516100	−	0.374969i	−0.299033	−	0.954243i	$-0.596664\pi$
$457$	11.0330	−	8.01591i	0.516100	−	0.374969i	0.815133	+	0.579274i	$0.196664\pi$
$458$	−8.69030	−	6.31387i	−0.406071	−	0.295028i
$459$	2.48883			0.116169
$460$	−0.809421			−0.0377394
$461$	−10.5548	−	7.66852i	−0.491587	−	0.357159i	0.314208	−	0.949354i	$-0.398261\pi$
$461$	−10.5548	−	7.66852i	−0.491587	−	0.357159i	−0.805794	+	0.592196i	$0.798261\pi$
$462$	−2.41901	−	7.44493i	−0.112542	−	0.346370i
$463$	2.83206	−	8.71619i	0.131617	−	0.405076i	−0.863431	−	0.504466i	$-0.831689\pi$
$463$	2.83206	−	8.71619i	0.131617	−	0.405076i	0.995049	+	0.0993904i	$0.0316893\pi$
$464$	−32.4019			−1.50422
$465$	−1.21566	+	4.44169i	−0.0563748	+	0.205979i
$466$	27.7089			1.28359
$467$	7.73775	−	23.8143i	0.358060	−	1.10200i	−0.596153	−	0.802871i	$-0.703305\pi$
$467$	7.73775	−	23.8143i	0.358060	−	1.10200i	0.954214	−	0.299126i	$-0.0966950\pi$
$468$	0.206824	+	0.636538i	0.00956043	+	0.0294240i
$469$	6.89025	+	5.00606i	0.318162	+	0.231158i
$470$	−10.0244			−0.462391
$471$	20.8689			0.961587
$472$	−5.66769	−	4.11782i	−0.260876	−	0.189538i
$473$	17.8134	−	12.9422i	0.819059	−	0.595081i
$474$	−18.7775	+	13.6426i	−0.862478	+	0.626627i
$475$	−3.26105	+	10.0365i	−0.149627	+	0.460505i
$476$	1.45018	+	1.05362i	0.0664690	+	0.0482925i
$477$	−1.38420	+	4.26013i	−0.0633781	+	0.195058i
$478$	5.93115	+	18.2542i	0.271285	+	0.834928i
$479$	−3.56710	+	2.59165i	−0.162985	+	0.118416i	−0.666288	−	0.745694i	$-0.732118\pi$
$479$	−3.56710	+	2.59165i	−0.162985	+	0.118416i	0.503303	+	0.864110i	$0.332118\pi$
$480$	0.300972	+	0.926296i	0.0137374	+	0.0422794i
$481$	−1.83871	−	5.65898i	−0.0838382	−	0.258027i
$482$	3.89675	−	2.83115i	0.177492	−	0.128956i
$483$	4.98361	+	15.3380i	0.226762	+	0.697902i
$484$	0.524387	−	1.61390i	0.0238358	−	0.0733590i
$485$	8.71889	+	6.33464i	0.395904	+	0.287641i
$486$	0.413545	−	1.27276i	0.0187588	−	0.0577337i
$487$	−0.820187	+	0.595901i	−0.0371662	+	0.0270028i	−0.606213	−	0.795302i	$-0.707312\pi$
$487$	−0.820187	+	0.595901i	−0.0371662	+	0.0270028i	0.569047	+	0.822305i	$0.307312\pi$
$488$	−19.9138	+	14.4682i	−0.901456	+	0.654946i
$489$	−8.09681	−	5.88267i	−0.366150	−	0.266024i
$490$	−5.38919			−0.243459
$491$	22.5885			1.01940			0.509701	−	0.860351i	$-0.329756\pi$
$491$	22.5885			1.01940			0.509701	+	0.860351i	$0.329756\pi$
$492$	0.218682	+	0.158882i	0.00985894	+	0.00716294i
$493$	−7.04317	−	21.6767i	−0.317209	−	0.976268i
$494$	3.23726	−	9.96327i	0.145651	−	0.448269i
$495$	1.40431			0.0631189
$496$	−5.20042	+	19.0010i	−0.233506	+	0.853168i
$497$	49.5377			2.22207
$498$	2.23558	−	6.88041i	0.100179	−	0.308318i
$499$	2.32876	+	7.16719i	0.104250	+	0.320847i	0.989554	−	0.144165i	$-0.0460497\pi$
$499$	2.32876	+	7.16719i	0.104250	+	0.320847i	−0.885304	+	0.465013i	$0.846050\pi$
$500$	−1.30317	−	0.946809i	−0.0582796	−	0.0423426i
$501$	19.0138			0.849474
$502$	8.82262			0.393773
$503$	0.934977	+	0.679301i	0.0416886	+	0.0302885i	0.608434	−	0.793604i	$-0.291798\pi$
$503$	0.934977	+	0.679301i	0.0416886	+	0.0302885i	−0.566746	+	0.823893i	$0.691798\pi$
$504$	8.23968	−	5.98648i	0.367025	−	0.266659i
$505$	−11.9765	+	8.70147i	−0.532949	+	0.387210i
$506$	−3.28692	+	10.1161i	−0.146121	+	0.449715i
$507$	−2.22512	−	1.61664i	−0.0988210	−	0.0717977i
$508$	0.194987	−	0.600108i	0.00865115	−	0.0266255i
$509$	−11.7805	−	36.2567i	−0.522162	−	1.60705i	−0.769860	−	0.638212i	$-0.779674\pi$
$509$	−11.7805	−	36.2567i	−0.522162	−	1.60705i	0.247698	−	0.968837i	$-0.420326\pi$
$510$	2.22868	−	1.61923i	0.0986874	−	0.0717006i
$511$	−7.36889	−	22.6791i	−0.325980	−	1.00326i
$512$	7.75210	+	23.8585i	0.342597	+	1.05441i
$513$	1.97815	−	1.43721i	0.0873374	−	0.0634543i
$514$	2.49429	+	7.67664i	0.110018	+	0.338602i
$515$	−0.538887	+	1.65852i	−0.0237462	+	0.0730833i
$516$	2.19332	+	1.59354i	0.0965555	+	0.0701516i
$517$	4.75177	−	14.6244i	0.208983	−	0.643182i
$518$	−6.93237	+	5.03667i	−0.304591	+	0.221298i
$519$	−15.5847	+	11.3229i	−0.684092	+	0.497022i
$520$	6.33304	+	4.60122i	0.277722	+	0.201777i
$521$	43.3680			1.89999			0.949994	−	0.312268i	$-0.101089\pi$
$521$	43.3680			1.89999			0.949994	+	0.312268i	$0.101089\pi$
$522$	−12.2555			−0.536410
$523$	−21.7470	−	15.8001i	−0.950929	−	0.690890i	9.75283e−5	−	1.00000i	$-0.499969\pi$
$523$	−21.7470	−	15.8001i	−0.950929	−	0.690890i	−0.951026	+	0.309110i	$0.899969\pi$
$524$	0.757695	+	2.33195i	0.0331001	+	0.101871i
$525$	−4.59474	+	14.1412i	−0.200531	+	0.617170i
$526$	2.89281			0.126132
$527$	−13.8419	+	0.651172i	−0.602963	+	0.0283655i
$528$	6.00743			0.261440
$529$	−0.335726	+	1.03326i	−0.0145968	+	0.0449243i
$530$	1.53212	+	4.71538i	0.0665510	+	0.204823i
$531$	−1.91716	−	1.39290i	−0.0831976	−	0.0604466i
$532$	1.76105			0.0763510
$533$	4.13946			0.179300
$534$	8.43507	+	6.12844i	0.365021	+	0.265203i
$535$	−6.46681	+	4.69841i	−0.279585	+	0.203130i
$536$	−5.91259	+	4.29575i	−0.255385	+	0.185548i
$537$	4.60124	−	14.1612i	0.198558	−	0.611099i
$538$	−18.5452	−	13.4739i	−0.799542	−	0.580901i
$539$	2.55459	−	7.86221i	0.110034	−	0.338649i
$540$	0.0534318	+	0.164446i	0.00229934	+	0.00707664i
$541$	−9.04541	+	6.57187i	−0.388892	+	0.282547i	−0.765002	−	0.644028i	$-0.777262\pi$
$541$	−9.04541	+	6.57187i	−0.388892	+	0.282547i	0.376109	+	0.926575i	$0.377262\pi$
$542$	4.36087	+	13.4214i	0.187315	+	0.576497i
$543$	−4.74365	−	14.5994i	−0.203569	−	0.626522i
$544$	−2.37106	+	1.72268i	−0.101658	+	0.0738592i
$545$	−1.33900	−	4.12102i	−0.0573564	−	0.176525i
$546$	4.56123	−	14.0380i	0.195203	−	0.600772i
$547$	−25.0612	−	18.2080i	−1.07154	−	0.778519i	−0.0953507	−	0.995444i	$-0.530397\pi$
$547$	−25.0612	−	18.2080i	−1.07154	−	0.778519i	−0.976188	+	0.216925i	$0.930397\pi$
$548$	−0.403695	+	1.24245i	−0.0172450	+	0.0530746i
$549$	−6.73607	+	4.89404i	−0.287488	+	0.208873i
$550$	−7.93379	+	5.76424i	−0.338298	+	0.245788i
$551$	−18.1155	−	13.1617i	−0.771745	−	0.560706i
$552$	−13.8390			−0.589026
$553$	−59.7508			−2.54086
$554$	−18.8612	−	13.7034i	−0.801334	−	0.582203i
$555$	−0.475022	−	1.46197i	−0.0201636	−	0.0620571i
$556$	0.501341	−	1.54297i	0.0212616	−	0.0654365i
$557$	−13.9437			−0.590815			−0.295408	−	0.955371i	$-0.595455\pi$
$557$	−13.9437			−0.590815			−0.295408	+	0.955371i	$0.595455\pi$
$558$	−1.96698	+	7.18681i	−0.0832688	+	0.304242i
$559$	41.5177			1.75601
$560$	3.11545	−	9.58837i	0.131652	−	0.405182i
$561$	1.30583	+	4.01893i	0.0551321	+	0.169679i
$562$	−30.9354	−	22.4759i	−1.30493	−	0.948087i
$563$	12.5438			0.528657			0.264328	−	0.964433i	$-0.414850\pi$
$563$	12.5438			0.528657			0.264328	+	0.964433i	$0.414850\pi$
$564$	1.89334			0.0797240
$565$	3.21123	+	2.33309i	0.135097	+	0.0981540i
$566$	−18.7455	+	13.6194i	−0.787931	+	0.572465i
$567$	2.78716	−	2.02499i	0.117050	−	0.0850417i
$568$	−13.1359	+	40.4283i	−0.551172	+	1.69633i
$569$	−19.1359	−	13.9031i	−0.802220	−	0.582847i	0.109344	−	0.994004i	$-0.465125\pi$
$569$	−19.1359	−	13.9031i	−0.802220	−	0.582847i	−0.911565	+	0.411157i	$0.865125\pi$
$570$	0.836330	−	2.57396i	0.0350300	−	0.107811i
$571$	−7.98404	−	24.5723i	−0.334122	−	1.02832i	−0.967153	−	0.254194i	$-0.918190\pi$
$571$	−7.98404	−	24.5723i	−0.334122	−	1.02832i	0.633032	−	0.774126i	$-0.281810\pi$
$572$	−0.919357	+	0.667952i	−0.0384403	+	0.0279285i
$573$	6.84198	+	21.0574i	0.285828	+	0.879687i
$574$	−1.84212	−	5.66948i	−0.0768888	−	0.236639i
$575$	16.3451	−	11.8754i	0.681638	−	0.495239i
$576$	2.67370	+	8.22880i	0.111404	+	0.342867i
$577$	0.447822	−	1.37825i	0.0186431	−	0.0573775i	−0.941302	−	0.337565i	$-0.890397\pi$
$577$	0.447822	−	1.37825i	0.0186431	−	0.0573775i	0.959945	+	0.280188i	$0.0903967\pi$
$578$	−11.6991	−	8.49989i	−0.486618	−	0.353549i
$579$	2.58771	−	7.96416i	0.107542	−	0.330979i
$580$	1.28105	−	0.930738i	0.0531927	−	0.0386468i
$581$	15.0671	−	10.9469i	0.625088	−	0.454153i
$582$	14.1075	+	10.2497i	0.584773	+	0.424862i
$583$	−7.60545			−0.314986
$584$	20.4627			0.846751
$585$	2.14222	+	1.55642i	0.0885700	+	0.0643498i
$586$	10.0942	+	31.0667i	0.416986	+	1.28335i
$587$	1.57890	−	4.85935i	0.0651681	−	0.200567i	−0.913171	−	0.407578i	$-0.866374\pi$
$587$	1.57890	−	4.85935i	0.0651681	−	0.200567i	0.978339	+	0.207011i	$0.0663736\pi$
$588$	1.01787			0.0419764
$589$	−10.6257	+	8.51076i	−0.437823	+	0.350680i
$590$	−2.62298			−0.107986
$591$	−6.07697	+	18.7030i	−0.249973	+	0.769338i
$592$	−2.03208	−	6.25410i	−0.0835180	−	0.257042i
$593$	30.7150	+	22.3158i	1.26131	+	0.916398i	0.998821	−	0.0485359i	$-0.0154555\pi$
$593$	30.7150	+	22.3158i	1.26131	+	0.916398i	0.262492	+	0.964934i	$0.415456\pi$
$594$	2.27222			0.0932301
$595$	7.09175			0.290733
$596$	−0.403296	−	0.293011i	−0.0165196	−	0.0120022i
$597$	8.16545	−	5.93255i	0.334190	−	0.242803i
$598$	−16.2259	+	11.7888i	−0.663526	+	0.482080i
$599$	1.05219	−	3.23830i	0.0429912	−	0.132313i	−0.927257	−	0.374425i	$-0.877840\pi$
$599$	1.05219	−	3.23830i	0.0429912	−	0.132313i	0.970248	+	0.242112i	$0.0778401\pi$
$600$	−10.3224	−	7.49963i	−0.421408	−	0.306171i
$601$	5.87928	−	18.0946i	0.239821	−	0.738093i	−0.756624	−	0.653850i	$-0.773153\pi$
$601$	5.87928	−	18.0946i	0.239821	−	0.738093i	0.996445	−	0.0842428i	$-0.0268471\pi$
$602$	−18.4760	−	56.8632i	−0.753025	−	2.31757i
$603$	−2.00000	+	1.45309i	−0.0814463	+	0.0591742i
$604$	−0.928757	−	2.85842i	−0.0377906	−	0.116307i
$605$	−2.07463	−	6.38506i	−0.0843457	−	0.259589i
$606$	−19.3784	+	14.0793i	−0.787196	+	0.571931i
$607$	−3.86301	−	11.8891i	−0.156795	−	0.482565i	0.841543	−	0.540189i	$-0.181647\pi$
$607$	−3.86301	−	11.8891i	−0.156795	−	0.482565i	−0.998338	+	0.0576244i	$0.981647\pi$
$608$	−0.889762	+	2.73840i	−0.0360846	+	0.111057i
$609$	−25.5243	−	18.5445i	−1.03430	−	0.751460i
$610$	−2.84790	+	8.76495i	−0.115308	+	0.354882i
$611$	23.4572	−	17.0426i	0.948975	−	0.689471i
$612$	−0.420937	+	0.305829i	−0.0170154	+	0.0123624i
$613$	26.2984	+	19.1069i	1.06218	+	0.771722i	0.974491	−	0.224426i	$-0.0720507\pi$
$613$	26.2984	+	19.1069i	1.06218	+	0.771722i	0.0876925	+	0.996148i	$0.472051\pi$
$614$	31.7042			1.27948
$615$	1.06941			0.0431227
$616$	13.9900	+	10.1644i	0.563675	+	0.409534i
$617$	2.78792	+	8.58032i	0.112237	+	0.345431i	0.991361	−	0.131163i	$-0.0418712\pi$
$617$	2.78792	+	8.58032i	0.112237	+	0.345431i	−0.879124	+	0.476594i	$0.841871\pi$
$618$	−0.871937	+	2.68355i	−0.0350745	+	0.107948i
$619$	11.0942			0.445913			0.222957	−	0.974828i	$-0.428429\pi$
$619$	11.0942			0.445913			0.222957	+	0.974828i	$0.428429\pi$
$620$	−0.340193	−	0.900607i	−0.0136625	−	0.0361692i
$621$	−4.68119			−0.187850
$622$	−0.764806	+	2.35383i	−0.0306659	+	0.0943801i
$623$	8.29425	+	25.5271i	0.332302	+	1.02272i
$624$	9.16413	+	6.65813i	0.366859	+	0.266539i
$625$	15.2068			0.608271
$626$	2.86324			0.114438
$627$	3.35867	+	2.44022i	0.134132	+	0.0974529i
$628$	−3.52957	+	2.56438i	−0.140845	+	0.102330i
$629$	3.74224	−	2.71889i	0.149213	−	0.108409i
$630$	1.17837	−	3.62665i	0.0469474	−	0.144489i
$631$	−2.67837	−	1.94595i	−0.106624	−	0.0774670i	0.533196	−	0.845992i	$-0.320991\pi$
$631$	−2.67837	−	1.94595i	−0.106624	−	0.0774670i	−0.639820	+	0.768525i	$0.720991\pi$
$632$	15.8441	−	48.7633i	0.630246	−	1.93970i
$633$	−6.64807	−	20.4606i	−0.264237	−	0.813238i
$634$	18.4010	−	13.3691i	0.730797	−	0.530955i
$635$	−0.771426	−	2.37420i	−0.0306131	−	0.0942174i
$636$	−0.289376	−	0.890609i	−0.0114745	−	0.0353149i
$637$	12.6107	−	9.16224i	0.499656	−	0.363021i
$638$	−6.43018	−	19.7900i	−0.254573	−	0.783495i
$639$	−4.44338	+	13.6753i	−0.175777	+	0.540987i
$640$	6.17195	+	4.48419i	0.243968	+	0.177253i
$641$	−3.55055	+	10.9275i	−0.140238	+	0.431609i	−0.996368	−	0.0851522i	$-0.972862\pi$
$641$	−3.55055	+	10.9275i	−0.140238	+	0.431609i	0.856130	+	0.516761i	$0.172862\pi$
$642$	−10.4635	+	7.60219i	−0.412962	+	0.300035i
$643$	−14.0869	+	10.2347i	−0.555532	+	0.403618i	−0.829821	−	0.558030i	$-0.811558\pi$
$643$	−14.0869	+	10.2347i	−0.555532	+	0.403618i	0.274289	+	0.961647i	$0.411558\pi$
$644$	−2.72762	−	1.98173i	−0.107483	−	0.0780912i
$645$	10.7259			0.422331
$646$	8.14399			0.320421
$647$	−9.00244	−	6.54065i	−0.353922	−	0.257140i	0.396590	−	0.917996i	$-0.370193\pi$
$647$	−9.00244	−	6.54065i	−0.353922	−	0.257140i	−0.750513	+	0.660856i	$0.770193\pi$
$648$	0.913545	+	2.81160i	0.0358875	+	0.110450i
$649$	1.24334	−	3.82662i	0.0488055	−	0.150208i
$650$	−18.4913			−0.725289
$651$	−14.9713	+	11.9915i	−0.586772	+	0.469982i
$652$	2.09228			0.0819402
$653$	−5.15097	+	15.8531i	−0.201573	+	0.620378i	0.798264	+	0.602308i	$0.205752\pi$
$653$	−5.15097	+	15.8531i	−0.201573	+	0.620378i	−0.999837	+	0.0180700i	$0.994248\pi$
$654$	−2.16655	−	6.66794i	−0.0847186	−	0.260737i
$655$	7.84799	+	5.70190i	0.306646	+	0.222792i
$656$	4.57479			0.178615
$657$	6.92173			0.270042
$658$	−33.7806	−	24.5431i	−1.31691	−	0.956788i
$659$	−8.10121	+	5.88587i	−0.315578	+	0.229281i	−0.734286	−	0.678840i	$-0.762483\pi$
$659$	−8.10121	+	5.88587i	−0.315578	+	0.229281i	0.418708	+	0.908121i	$0.362483\pi$
$660$	−0.237511	+	0.172562i	−0.00924511	+	0.00671697i
$661$	3.49694	−	10.7625i	0.136015	−	0.418612i	−0.859731	−	0.510746i	$-0.829369\pi$
$661$	3.49694	−	10.7625i	0.136015	−	0.418612i	0.995747	+	0.0921349i	$0.0293691\pi$
$662$	21.3225	+	15.4917i	0.828723	+	0.602103i
$663$	−2.46224	+	7.57801i	−0.0956256	+	0.294305i
$664$	4.93852	+	15.1992i	0.191652	+	0.589844i
$665$	5.63660	−	4.09523i	0.218578	−	0.158806i
$666$	−0.768602	−	2.36552i	−0.0297827	−	0.0916619i
$667$	13.2474	+	40.7712i	0.512940	+	1.57867i
$668$	−3.21582	+	2.33643i	−0.124424	+	0.0903991i
$669$	−0.626483	−	1.92812i	−0.0242212	−	0.0745453i
$670$	−0.845569	+	2.60239i	−0.0326672	+	0.100539i
$671$	−11.4371	−	8.30952i	−0.441524	−	0.320786i
$672$	−1.25365	+	3.85835i	−0.0483607	+	0.148839i
$673$	17.7486	−	12.8951i	0.684159	−	0.497070i	−0.190576	−	0.981672i	$-0.561036\pi$
$673$	17.7486	−	12.8951i	0.684159	−	0.497070i	0.874735	+	0.484602i	$0.161036\pi$
$674$	−5.77583	+	4.19639i	−0.222477	+	0.161639i
$675$	−3.49165	−	2.53683i	−0.134394	−	0.0976428i
$676$	0.574990			0.0221150
$677$	−3.08201			−0.118451			−0.0592256	−	0.998245i	$-0.518863\pi$
$677$	−3.08201			−0.118451			−0.0592256	+	0.998245i	$0.518863\pi$
$678$	5.19587	+	3.77502i	0.199546	+	0.144979i
$679$	13.8719	+	42.6935i	0.532356	+	1.63842i
$680$	−1.88052	+	5.78765i	−0.0721148	+	0.221946i
$681$	−17.1458			−0.657027
$682$	−12.6372	+	0.594498i	−0.483903	+	0.0227645i
$683$	22.3303			0.854445			0.427223	−	0.904146i	$-0.359492\pi$
$683$	22.3303			0.854445			0.427223	+	0.904146i	$0.359492\pi$
$684$	−0.157960	+	0.486152i	−0.00603976	+	0.0185885i
$685$	1.59714	+	4.91548i	0.0610235	+	0.187811i
$686$	7.94896	+	5.77526i	0.303493	+	0.220500i
$687$	8.02668			0.306237
$688$	45.8838			1.74930
$689$	−11.6019	−	8.42924i	−0.441995	−	0.321128i
$690$	−4.19187	+	3.04558i	−0.159582	+	0.115943i
$691$	−8.36129	+	6.07484i	−0.318079	+	0.231098i	−0.735355	−	0.677682i	$-0.762985\pi$
$691$	−8.36129	+	6.07484i	−0.318079	+	0.231098i	0.417277	+	0.908780i	$0.362985\pi$
$692$	1.24448	−	3.83011i	0.0473080	−	0.145599i
$693$	4.73229	+	3.43821i	0.179765	+	0.130607i
$694$	7.33866	−	22.5861i	0.278572	−	0.857356i
$695$	−1.98345	−	6.10444i	−0.0752367	−	0.231555i
$696$	21.9026	−	15.9132i	0.830217	−	0.603188i
$697$	0.994416	+	3.06050i	0.0376662	+	0.115925i
$698$	12.1606	+	37.4265i	0.460286	+	1.41662i
$699$	−16.7508	+	12.1702i	−0.633573	+	0.460318i
$700$	−0.960562	−	2.95631i	−0.0363058	−	0.111738i
$701$	5.15172	−	15.8554i	0.194578	−	0.598849i	−0.805403	−	0.592727i	$-0.798051\pi$
$701$	5.15172	−	15.8554i	0.194578	−	0.598849i	0.999981	−	0.00612191i	$-0.00194868\pi$
$702$	3.46619	+	2.51833i	0.130823	+	0.0950483i
$703$	1.40431	−	4.32201i	0.0529644	−	0.163008i
$704$	−11.8849	+	8.63490i	−0.447930	+	0.325440i
$705$	6.06003	−	4.40287i	0.228234	−	0.165822i
$706$	6.84720	+	4.97478i	0.257698	+	0.187228i
$707$	−61.6631			−2.31908
$708$	0.495410			0.0186187
$709$	−2.17427	−	1.57970i	−0.0816563	−	0.0593268i	0.546208	−	0.837650i	$-0.316071\pi$
$709$	−2.17427	−	1.57970i	−0.0816563	−	0.0593268i	−0.627864	+	0.778323i	$0.716071\pi$
$710$	4.91822	+	15.1367i	0.184577	+	0.568071i
$711$	5.35946	−	16.4947i	0.200995	−	0.618600i
$712$	−23.0323			−0.863173
$713$	26.0350	−	1.22478i	0.975018	−	0.0458683i
$714$	11.4747			0.429430
$715$	−1.38931	+	4.27584i	−0.0519571	+	0.159907i
$716$	0.961921	+	2.96049i	0.0359487	+	0.110639i
$717$	−11.6031	−	8.43013i	−0.433325	−	0.314829i
$718$	22.0817			0.824084
$719$	35.8508			1.33701			0.668505	−	0.743708i	$-0.266935\pi$
$719$	35.8508			1.33701			0.668505	+	0.743708i	$0.266935\pi$
$720$	2.36751	+	1.72009i	0.0882317	+	0.0641041i
$721$	−5.87658	+	4.26958i	−0.218855	+	0.159008i
$722$	−14.0979	+	10.2427i	−0.524670	+	0.381195i
$723$	−1.11221	+	3.42303i	−0.0413635	+	0.127304i
$724$	2.59628	+	1.88631i	0.0964901	+	0.0701042i
$725$	−12.2137	+	37.5899i	−0.453605	+	1.39605i
$726$	−3.35682	−	10.3312i	−0.124583	−	0.383428i
$727$	−39.3390	+	28.5814i	−1.45900	+	1.06003i	−0.475381	+	0.879780i	$0.657690\pi$
$727$	−39.3390	+	28.5814i	−1.45900	+	1.06003i	−0.983621	+	0.180247i	$0.942310\pi$
$728$	10.0760	+	31.0108i	0.373442	+	1.14934i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	6.19821	−	4.50326i	0.229406	−	0.166673i
$731$	9.97372	+	30.6959i	0.368891	+	1.13533i
$732$	0.537893	−	1.65546i	0.0198811	−	0.0611877i
$733$	0.557312	+	0.404911i	0.0205848	+	0.0149557i	0.598030	−	0.801474i	$-0.295950\pi$
$733$	0.557312	+	0.404911i	0.0205848	+	0.0149557i	−0.577445	+	0.816429i	$0.695950\pi$
$734$	−4.74531	+	14.6046i	−0.175152	+	0.539064i
$735$	3.25792	−	2.36702i	0.120170	−	0.0873088i
$736$	4.45969	−	3.24015i	0.164386	−	0.119434i
$737$	−3.39577	−	2.46717i	−0.125085	−	0.0908795i
$738$	1.73034			0.0636947
$739$	−49.7931			−1.83167			−0.915834	−	0.401557i	$-0.868469\pi$
$739$	−49.7931			−1.83167			−0.915834	+	0.401557i	$0.868469\pi$
$740$	0.259988	+	0.188893i	0.00955736	+	0.00694383i
$741$	2.41901	+	7.44493i	0.0888644	+	0.273496i
$742$	−6.38182	+	19.6412i	−0.234284	+	0.721052i
$743$	−50.3858			−1.84848			−0.924239	−	0.381815i	$-0.875299\pi$
$743$	−50.3858			−1.84848			−0.924239	+	0.381815i	$0.875299\pi$
$744$	−5.81641	−	15.3980i	−0.213240	−	0.564519i
$745$	−1.97222			−0.0722564
$746$	2.46673	−	7.59181i	0.0903133	−	0.277956i
$747$	1.67051	+	5.14130i	0.0611208	+	0.188110i
$748$	−0.714704	−	0.519263i	−0.0261322	−	0.0189861i
$749$	−33.2954			−1.21659
$750$	−10.3115			−0.376521
$751$	27.2865	+	19.8248i	0.995699	+	0.723417i	0.961162	−	0.275986i	$-0.0890043\pi$
$751$	27.2865	+	19.8248i	0.995699	+	0.723417i	0.0345370	+	0.999403i	$0.489004\pi$
$752$	25.9240	−	18.8349i	0.945351	−	0.686838i
$753$	−5.33353	+	3.87503i	−0.194365	+	0.141214i
$754$	12.1246	−	37.3157i	0.441552	−	1.35896i
$755$	−9.61980	−	6.98919i	−0.350100	−	0.254363i
$756$	−0.222562	+	0.684977i	−0.00809452	+	0.0249124i
$757$	−3.55026	−	10.9266i	−0.129036	−	0.397133i	0.865579	−	0.500773i	$-0.166951\pi$
$757$	−3.55026	−	10.9266i	−0.129036	−	0.397133i	−0.994615	+	0.103640i	$0.966951\pi$
$758$	6.76580	−	4.91564i	0.245745	−	0.178544i
$759$	−2.45611	−	7.55913i	−0.0891511	−	0.274379i
$760$	1.84750	+	5.68602i	0.0670159	+	0.206254i
$761$	10.3928	−	7.55079i	0.376738	−	0.273716i	−0.383262	−	0.923640i	$-0.625199\pi$
$761$	10.3928	−	7.55079i	0.376738	−	0.273716i	0.759999	+	0.649924i	$0.225199\pi$
$762$	−1.24819	−	3.84154i	−0.0452173	−	0.139164i
$763$	5.57740	−	17.1655i	0.201916	−	0.621432i
$764$	−3.74474	−	2.72071i	−0.135480	−	0.0984319i
$765$	−0.636108	+	1.95774i	−0.0229985	+	0.0707822i
$766$	19.4962	−	14.1648i	0.704427	−	0.511796i
$767$	6.13778	−	4.45936i	0.221623	−	0.161018i
$768$	−4.01324	−	2.91579i	−0.144815	−	0.105214i
$769$	26.5320			0.956769			0.478384	−	0.878151i	$-0.341223\pi$
$769$	26.5320			0.956769			0.478384	+	0.878151i	$0.341223\pi$
$770$	6.47452			0.233326
$771$	−4.87957	−	3.54521i	−0.175733	−	0.127678i
$772$	0.540979	+	1.66496i	0.0194703	+	0.0599233i
$773$	13.3618	−	41.1234i	0.480591	−	1.47911i	−0.357676	−	0.933846i	$-0.616431\pi$
$773$	13.3618	−	41.1234i	0.480591	−	1.47911i	0.838267	−	0.545261i	$-0.183569\pi$
$774$	17.3548			0.623806
$775$	20.0830	+	13.1953i	0.721401	+	0.473991i
$776$	−38.5210			−1.38282
$777$	1.97864	−	6.08961i	0.0709832	−	0.218464i
$778$	3.77380	+	11.6145i	0.135297	+	0.416402i
$779$	2.55770	+	1.85828i	0.0916391	+	0.0665797i
$780$	−0.553568			−0.0198209
$781$	−24.4140			−0.873603
$782$	−12.6139	−	9.16455i	−0.451073	−	0.327724i
$783$	7.40881	−	5.38282i	0.264769	−	0.192366i
$784$	13.9369	−	10.1258i	0.497748	−	0.361635i
$785$	−5.33378	+	16.4157i	−0.190371	+	0.585901i
$786$	12.6983	+	9.22586i	0.452934	+	0.329076i
$787$	3.63853	−	11.1982i	0.129699	−	0.399174i	−0.865028	−	0.501723i	$-0.832700\pi$
$787$	3.63853	−	11.1982i	0.129699	−	0.399174i	0.994728	+	0.102549i	$0.0326998\pi$
$788$	−1.27043	−	3.90999i	−0.0452573	−	0.139288i
$789$	−1.74878	+	1.27057i	−0.0622583	+	0.0452333i
$790$	−5.93219	−	18.2574i	−0.211058	−	0.649569i
$791$	5.10914	+	15.7243i	0.181660	+	0.559092i
$792$	−4.06082	+	2.95036i	−0.144295	+	0.104837i
$793$	−8.23730	−	25.3518i	−0.292515	−	0.900268i
$794$	−1.97896	+	6.09060i	−0.0702305	+	0.216147i
$795$	−2.99728	−	2.17765i	−0.106303	−	0.0772333i
$796$	−0.652033	+	2.00675i	−0.0231107	+	0.0711274i
$797$	0.640375	−	0.465259i	0.0226832	−	0.0164803i	−0.576386	−	0.817178i	$-0.695537\pi$
$797$	0.640375	−	0.465259i	0.0226832	−	0.0164803i	0.599069	+	0.800697i	$0.295537\pi$
$798$	9.12020	−	6.62622i	0.322852	−	0.234566i
$799$	18.2355	+	13.2488i	0.645125	+	0.468710i
$800$	5.08234			0.179688
$801$	−7.79094			−0.275279
$802$	−23.4081	−	17.0070i	−0.826569	−	0.600537i
$803$	3.63166	+	11.1771i	0.128159	+	0.394432i
$804$	0.159705	−	0.491522i	0.00563237	−	0.0173347i
$805$	−13.3387			−0.470129
$806$	−19.9365	−	13.0991i	−0.702233	−	0.461396i
$807$	17.1291			0.602972
$808$	16.3512	−	50.3239i	0.575235	−	1.77039i
$809$	0.0222775	+	0.0685632i	0.000783236	+	0.00241055i	0.951447	−	0.307811i	$-0.0995966\pi$
$809$	0.0222775	+	0.0685632i	0.000783236	+	0.00241055i	−0.950664	+	0.310222i	$0.899597\pi$
$810$	0.895472	+	0.650598i	0.0314637	+	0.0228597i
$811$	−3.27538			−0.115014			−0.0575070	−	0.998345i	$-0.518315\pi$
$811$	−3.27538			−0.115014			−0.0575070	+	0.998345i	$0.518315\pi$
$812$	6.59569			0.231463
$813$	−8.53115	−	6.19824i	−0.299200	−	0.217382i
$814$	3.41653	−	2.48226i	0.119749	−	0.0870031i
$815$	6.69679	−	4.86551i	0.234578	−	0.170431i
$816$	−2.72118	+	8.37494i	−0.0952604	+	0.293181i
$817$	25.6530	+	18.6380i	0.897485	+	0.652061i
$818$	5.58414	−	17.1862i	0.195245	−	0.600902i
$819$	3.40832	+	10.4897i	0.119096	+	0.366541i
$820$	−0.180870	+	0.131410i	−0.00631625	+	0.00458902i
$821$	−15.6393	−	48.1327i	−0.545814	−	1.67984i	−0.719047	−	0.694961i	$-0.755422\pi$
$821$	−15.6393	−	48.1327i	−0.545814	−	1.67984i	0.173234	−	0.984881i	$-0.444578\pi$
$822$	2.58422	+	7.95342i	0.0901351	+	0.277407i
$823$	−20.4583	+	14.8639i	−0.713133	+	0.518122i	−0.884183	−	0.467141i	$-0.845284\pi$
$823$	−20.4583	+	14.8639i	−0.713133	+	0.518122i	0.171050	+	0.985262i	$0.445284\pi$
$824$	−1.92616	−	5.92811i	−0.0671009	−	0.206515i
$825$	2.26446	−	6.96929i	0.0788383	−	0.242639i
$826$	−8.83902	−	6.42192i	−0.307549	−	0.223447i
$827$	−10.8397	+	33.3612i	−0.376933	+	1.16008i	0.565232	+	0.824932i	$0.308787\pi$
$827$	−10.8397	+	33.3612i	−0.376933	+	1.16008i	−0.942165	+	0.335149i	$0.891213\pi$
$828$	0.791733	−	0.575228i	0.0275146	−	0.0199905i
$829$	−0.975613	+	0.708824i	−0.0338844	+	0.0246185i	−0.604599	−	0.796530i	$-0.706666\pi$
$829$	−0.975613	+	0.708824i	−0.0338844	+	0.0246185i	0.570714	+	0.821149i	$0.306666\pi$
$830$	4.84082	+	3.51706i	0.168027	+	0.122079i
$831$	17.4209			0.604323
$832$	−27.7002			−0.960333
$833$	9.80353	+	7.12268i	0.339672	+	0.246786i
$834$	−3.20930	−	9.87720i	−0.111129	−	0.342019i
$835$	−4.85965	+	14.9565i	−0.168175	+	0.517589i
$836$	−0.867909			−0.0300173
$837$	−1.96747	−	5.20856i	−0.0680056	−	0.180034i
$838$	−44.8473			−1.54923
$839$	0.0440323	−	0.135518i	0.00152016	−	0.00467858i	−0.950294	−	0.311355i	$-0.899217\pi$
$839$	0.0440323	−	0.135518i	0.00152016	−	0.00467858i	0.951814	+	0.306677i	$0.0992171\pi$
$840$	2.60309	+	8.01147i	0.0898150	+	0.276422i
$841$	−44.3869	−	32.2490i	−1.53058	−	1.11203i
$842$	9.23574			0.318285
$843$	28.5731			0.984109
$844$	3.63861	+	2.64360i	0.125246	+	0.0909966i
$845$	1.84038	−	1.33711i	0.0633108	−	0.0459980i
$846$	9.80534	−	7.12400i	0.337115	−	0.244928i
$847$	8.64157	−	26.5960i	0.296928	−	0.913850i
$848$	−12.8219	−	9.31569i	−0.440307	−	0.319902i
$849$	5.35032	−	16.4666i	0.183623	−	0.565132i
$850$	−4.44214	−	13.6715i	−0.152364	−	0.468928i
$851$	−7.03870	+	5.11392i	−0.241284	+	0.175303i
$852$	−0.928919	−	2.85892i	−0.0318243	−	0.0979450i
$853$	8.57520	+	26.3918i	0.293609	+	0.903637i	0.983685	+	0.179899i	$0.0575772\pi$
$853$	8.57520	+	26.3918i	0.293609	+	0.903637i	−0.690076	+	0.723737i	$0.742423\pi$
$854$	−31.0565	+	22.5639i	−1.06273	+	0.772119i
$855$	0.624938	+	1.92336i	0.0213724	+	0.0657775i
$856$	8.82896	−	27.1727i	0.301768	−	0.928745i
$857$	28.3922	+	20.6282i	0.969860	+	0.704644i	0.955420	−	0.295251i	$-0.0954034\pi$
$857$	28.3922	+	20.6282i	0.969860	+	0.704644i	0.0144402	+	0.999896i	$0.495403\pi$
$858$	−2.24794	+	6.91846i	−0.0767435	+	0.236192i
$859$	19.8055	−	14.3896i	0.675756	−	0.490966i	−0.196191	−	0.980566i	$-0.562857\pi$
$859$	19.8055	−	14.3896i	0.675756	−	0.490966i	0.871947	+	0.489600i	$0.162857\pi$
$860$	−1.81407	+	1.31800i	−0.0618594	+	0.0449435i
$861$	3.60374	+	2.61827i	0.122815	+	0.0892304i
$862$	−26.5851			−0.905492
$863$	−57.0030			−1.94040			−0.970201	−	0.242300i	$-0.922098\pi$
$863$	−57.0030			−1.94040			−0.970201	+	0.242300i	$0.922098\pi$
$864$	−0.952682	−	0.692164i	−0.0324109	−	0.0235479i
$865$	−4.92352	−	15.1530i	−0.167405	−	0.515219i
$866$	3.68976	−	11.3559i	0.125383	−	0.385890i
$867$	10.8057			0.366982
$868$	1.05859	−	3.86781i	0.0359309	−	0.131282i
$869$	29.4474			0.998936
$870$	3.13233	−	9.64032i	0.106196	−	0.326837i
$871$	−2.44573	−	7.52718i	−0.0828703	−	0.255049i
$872$	12.5300	+	9.10356i	0.424318	+	0.308285i
$873$	−13.0302			−0.441004
$874$	−15.3179			−0.518135
$875$	−21.4754	−	15.6028i	−0.726002	−	0.527471i
$876$	−1.17068	+	0.850546i	−0.0395535	+	0.0287373i
$877$	27.8490	−	20.2335i	0.940395	−	0.683237i	−0.00812057	−	0.999967i	$-0.502585\pi$
$877$	27.8490	−	20.2335i	0.940395	−	0.683237i	0.948516	+	0.316730i	$0.102585\pi$
$878$	10.4669	−	32.2138i	0.353241	−	1.08716i
$879$	−19.7472	−	14.3472i	−0.666056	−	0.483918i
$880$	−1.53541	+	4.72551i	−0.0517587	+	0.159297i
$881$	14.3571	+	44.1865i	0.483702	+	1.48868i	0.833852	+	0.551987i	$0.186130\pi$
$881$	14.3571	+	44.1865i	0.483702	+	1.48868i	−0.350151	+	0.936693i	$0.613870\pi$
$882$	5.27143	−	3.82992i	0.177498	−	0.128960i
$883$	8.36048	+	25.7309i	0.281352	+	0.865914i	0.987468	+	0.157817i	$0.0504457\pi$
$883$	8.36048	+	25.7309i	0.281352	+	0.865914i	−0.706116	+	0.708096i	$0.749554\pi$
$884$	−0.514749	−	1.58423i	−0.0173129	−	0.0532836i
$885$	1.58566	−	1.15205i	0.0533015	−	0.0387258i
$886$	−2.44279	−	7.51813i	−0.0820671	−	0.252577i
$887$	−1.16116	+	3.57367i	−0.0389878	+	0.119992i	−0.968656	−	0.248405i	$-0.920093\pi$
$887$	−1.16116	+	3.57367i	−0.0389878	+	0.119992i	0.929668	+	0.368398i	$0.120093\pi$
$888$	4.44512	+	3.22957i	0.149169	+	0.108377i
$889$	3.21326	−	9.88940i	0.107769	−	0.331680i
$890$	−6.97657	+	5.06877i	−0.233855	+	0.169906i
$891$	−1.37362	+	0.997993i	−0.0460180	+	0.0334340i
$892$	0.342885	+	0.249121i	0.0114807	+	0.00834118i
$893$	22.1445			0.741036
$894$	−3.19111			−0.106727
$895$	9.96330	+	7.23876i	0.333036	+	0.241965i
$896$	9.81972	+	30.2220i	0.328054	+	1.00965i
$897$	4.63119	−	14.2533i	0.154631	−	0.475905i
$898$	6.52226			0.217651
$899$	−39.7966	+	31.8756i	−1.32729	+	1.06311i
$900$	0.902273			0.0300758
$901$	3.44504	−	10.6027i	0.114771	−	0.353228i
$902$	0.907868	+	2.79413i	0.0302287	+	0.0930343i
$903$	36.1445	+	26.2605i	1.20281	+	0.873895i
$904$	−14.1876			−0.471871
$905$	12.6965			0.422045
$906$	−15.5652	−	11.3088i	−0.517118	−	0.375708i
$907$	−13.6440	+	9.91292i	−0.453040	+	0.329153i	−0.790795	−	0.612081i	$-0.790333\pi$
$907$	−13.6440	+	9.91292i	−0.453040	+	0.329153i	0.337755	+	0.941234i	$0.390333\pi$
$908$	2.89987	−	2.10688i	0.0962357	−	0.0699193i
$909$	5.53099	−	17.0226i	0.183451	−	0.564605i
$910$	9.87666	+	7.17582i	0.327408	+	0.237876i
$911$	−4.82214	+	14.8410i	−0.159765	+	0.491705i	−0.998612	−	0.0526612i	$-0.983230\pi$
$911$	−4.82214	+	14.8410i	−0.159765	+	0.491705i	0.838848	+	0.544366i	$0.183230\pi$
$912$	2.67340	+	8.22787i	0.0885250	+	0.272452i
$913$	−7.42563	+	5.39504i	−0.245752	+	0.178550i
$914$	5.63972	+	17.3573i	0.186545	+	0.574128i
$915$	−2.12806	−	6.54950i	−0.0703516	−	0.216520i
$916$	−1.35756	+	0.986323i	−0.0448550	+	0.0325890i
$917$	12.4863	+	38.4290i	0.412335	+	1.26904i
$918$	−1.02924	+	3.16769i	−0.0339701	+	0.104549i
$919$	8.30432	+	6.03344i	0.273934	+	0.199025i	0.716267	−	0.697826i	$-0.245849\pi$
$919$	8.30432	+	6.03344i	0.273934	+	0.199025i	−0.442333	+	0.896851i	$0.645849\pi$
$920$	3.53704	−	10.8859i	0.116613	−	0.358897i
$921$	−19.1661	+	13.9250i	−0.631544	+	0.458843i
$922$	14.1251	−	10.2625i	0.465185	−	0.337977i
$923$	−37.2428	−	27.0585i	−1.22586	−	0.890640i
$924$	−1.22286			−0.0402293
$925$	−8.02143			−0.263743
$926$	9.92245	+	7.20908i	0.326072	+	0.236905i
$927$	−0.651545	−	2.00525i	−0.0213995	−	0.0658610i
$928$	−3.33245	+	10.2562i	−0.109393	+	0.336677i
$929$	50.9829			1.67270			0.836348	−	0.548199i	$-0.184687\pi$
$929$	50.9829			1.67270			0.836348	+	0.548199i	$0.184687\pi$
$930$	−5.15049	−	3.38409i	−0.168891	−	0.110969i
$931$	11.9050			0.390172
$932$	1.33759	−	4.11669i	0.0438144	−	0.134847i
$933$	−0.571493	−	1.75887i	−0.0187098	−	0.0575829i
$934$	27.1101	+	19.6966i	0.887069	+	0.644493i
$935$	−3.49508			−0.114301
$936$	−9.46458			−0.309359
$937$	38.9611	+	28.3069i	1.27280	+	0.924745i	0.999310	−	0.0371295i	$-0.0118214\pi$
$937$	38.9611	+	28.3069i	1.27280	+	0.924745i	0.273492	+	0.961874i	$0.411821\pi$
$938$	−9.22095	+	6.69942i	−0.301075	+	0.218744i
$939$	−1.73091	+	1.25758i	−0.0564861	+	0.0410395i
$940$	−0.483910	+	1.48932i	−0.0157834	+	0.0485763i
$941$	−10.1463	−	7.37174i	−0.330761	−	0.240312i	0.409993	−	0.912089i	$-0.365531\pi$
$941$	−10.1463	−	7.37174i	−0.330761	−	0.240312i	−0.740753	+	0.671777i	$0.765531\pi$
$942$	−8.63023	+	26.5611i	−0.281188	+	0.865408i
$943$	−1.87038	−	5.75643i	−0.0609079	−	0.187455i
$944$	6.78326	−	4.92832i	0.220776	−	0.160403i
$945$	0.880523	+	2.70997i	0.0286434	+	0.0881553i
$946$	9.10566	+	28.0243i	0.296051	+	0.911150i
$947$	−21.3350	+	15.5008i	−0.693293	+	0.503707i	−0.877741	−	0.479135i	$-0.840950\pi$
$947$	−21.3350	+	15.5008i	−0.693293	+	0.503707i	0.184448	+	0.982842i	$0.440950\pi$
$948$	1.12043	+	3.44834i	0.0363899	+	0.111997i
$949$	−6.84779	+	21.0753i	−0.222289	+	0.684134i
$950$	−11.4254	−	8.30107i	−0.370690	−	0.269322i
$951$	−5.25201	+	16.1640i	−0.170308	+	0.524154i
$952$	−20.5072	+	14.8993i	−0.664641	+	0.482890i
$953$	−13.6589	+	9.92375i	−0.442454	+	0.321462i	−0.786609	−	0.617451i	$-0.788165\pi$
$953$	−13.6589	+	9.92375i	−0.442454	+	0.321462i	0.344155	+	0.938913i	$0.388165\pi$
$954$	−4.84970	−	3.52351i	−0.157015	−	0.114078i
$955$	−18.3127			−0.592585
$956$	2.99834			0.0969731
$957$	12.5793	+	9.13941i	0.406632	+	0.295435i
$958$	−1.82340	−	5.61184i	−0.0589113	−	0.181310i
$959$	−6.65264	+	20.4747i	−0.214825	+	0.661163i
$960$	−7.15622			−0.230966
$961$	12.3050	+	28.4532i	0.396937	+	0.917846i
$962$	7.96293			0.256735
$963$	2.98649	−	9.19148i	0.0962384	−	0.296191i
$964$	−0.232515	−	0.715607i	−0.00748880	−	0.0230482i
$965$	5.60331	+	4.07104i	0.180377	+	0.131051i
$966$	−21.5825			−0.694407
$967$	28.7320			0.923957			0.461979	−	0.886891i	$-0.347140\pi$
$967$	28.7320			0.923957			0.461979	+	0.886891i	$0.347140\pi$
$968$	19.4138	+	14.1050i	0.623983	+	0.453350i
$969$	−4.92327	+	3.57697i	−0.158158	+	0.114909i
$970$	−11.6681	+	8.47741i	−0.374642	+	0.272193i
$971$	7.92029	−	24.3762i	0.254174	−	0.782268i	−0.739817	−	0.672808i	$-0.765088\pi$
$971$	7.92029	−	24.3762i	0.254174	−	0.782268i	0.993991	−	0.109460i	$-0.0349121\pi$
$972$	−0.169131	−	0.122881i	−0.00542487	−	0.00394140i
$973$	8.26178	−	25.4272i	0.264861	−	0.815157i
$974$	−0.419255	−	1.29034i	−0.0134338	−	0.0413450i
$975$	11.1785	−	8.12168i	0.357999	−	0.260102i
$976$	−9.10356	−	28.0179i	−0.291398	−	0.896830i
$977$	−11.1253	−	34.2403i	−0.355931	−	1.09544i	−0.955467	−	0.295097i	$-0.904648\pi$
$977$	−11.1253	−	34.2403i	−0.355931	−	1.09544i	0.599536	−	0.800348i	$-0.295352\pi$
$978$	10.8356	−	7.87255i	0.346486	−	0.251737i
$979$	−4.08772	−	12.5807i	−0.130644	−	0.402081i
$980$	−0.260154	+	0.800670i	−0.00831030	+	0.0255765i
$981$	4.23840	+	3.07938i	0.135322	+	0.0983170i
$982$	−9.34135	+	28.7497i	−0.298095	+	0.917441i
$983$	29.4642	−	21.4070i	0.939764	−	0.682778i	−0.00860016	−	0.999963i	$-0.502738\pi$
$983$	29.4642	−	21.4070i	0.939764	−	0.682778i	0.948364	+	0.317185i	$0.102738\pi$
$984$	−3.09240	+	2.24676i	−0.0985822	+	0.0716242i
$985$	−13.1588	−	9.56041i	−0.419273	−	0.304620i
$986$	30.5019			0.971379
$987$	31.2010			0.993140
$988$	−1.32397	−	0.961917i	−0.0421210	−	0.0306027i
$989$	−18.7594	−	57.7354i	−0.596513	−	1.83588i
$990$	−0.580745	+	1.78735i	−0.0184573	+	0.0568057i
$991$	−29.9219			−0.950501			−0.475250	−	0.879851i	$-0.657642\pi$
$991$	−29.9219			−0.950501			−0.475250	+	0.879851i	$0.657642\pi$
$992$	5.47954	+	3.60029i	0.173976	+	0.114309i
$993$	−19.6943			−0.624979
$994$	−20.4861	+	63.0497i	−0.649780	+	1.99982i
$995$	2.57964	+	7.93930i	0.0817799	+	0.251693i
$996$	−0.914301	−	0.664278i	−0.0289707	−	0.0210485i
$997$	12.8338			0.406449			0.203225	−	0.979132i	$-0.434858\pi$
$997$	12.8338			0.406449			0.203225	+	0.979132i	$0.434858\pi$
$998$	−10.0852			−0.319240
$999$	1.50361	+	1.09244i	0.0475722	+	0.0345632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.f.a.70.1	yes	8
3.2	odd	2		279.2.i.b.163.2		8
31.2	even	5		2883.2.a.k.1.2		4
31.4	even	5	inner	93.2.f.a.4.1	✓	8
31.29	odd	10		2883.2.a.l.1.2		4
93.2	odd	10		8649.2.a.w.1.3		4
93.29	even	10		8649.2.a.x.1.3		4
93.35	odd	10		279.2.i.b.190.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.a.4.1	✓	8	31.4	even	5	inner
93.2.f.a.70.1	yes	8	1.1	even	1	trivial
279.2.i.b.163.2		8	3.2	odd	2
279.2.i.b.190.2		8	93.35	odd	10
2883.2.a.k.1.2		4	31.2	even	5
2883.2.a.l.1.2		4	31.29	odd	10
8649.2.a.w.1.3		4	93.2	odd	10
8649.2.a.x.1.3		4	93.29	even	10

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.413545 + 1.27276i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.169131 + 0.122881i) q^{4} +0.827091 q^{5} +1.33826 q^{6} +(2.78716 + 2.02499i) q^{7} +(-2.39169 + 1.73767i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.413545 + 1.27276i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.169131 + 0.122881i) q^{4} +0.827091 q^{5} +1.33826 q^{6} +(2.78716 + 2.02499i) q^{7} +(-2.39169 + 1.73767i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.342040 + 1.05269i) q^{10} +(-1.37362 - 0.997993i) q^{11} +(0.0646021 - 0.198825i) q^{12} +(-0.989318 - 3.04481i) q^{13} +(-3.72995 + 2.70997i) q^{14} +(-0.255585 - 0.786610i) q^{15} +(-1.09336 - 3.36501i) q^{16} +(2.01351 - 1.46290i) q^{17} +(-0.413545 - 1.27276i) q^{18} +(0.755585 - 2.32545i) q^{19} +(0.139886 + 0.101633i) q^{20} +(1.06460 - 3.27651i) q^{21} +(1.83826 - 1.33557i) q^{22} +(-3.78716 + 2.75154i) q^{23} +(2.39169 + 1.73767i) q^{24} -4.31592 q^{25} +4.28444 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.222562 + 0.684977i) q^{28} +(2.82991 - 8.70958i) q^{29} +1.10686 q^{30} +(-4.65323 - 3.05736i) q^{31} -1.17758 q^{32} +(-0.524676 + 1.61479i) q^{33} +(1.02924 + 3.16769i) q^{34} +(2.30524 + 1.67485i) q^{35} -0.209057 q^{36} +1.85857 q^{37} +(2.64728 + 1.92336i) q^{38} +(-2.59007 + 1.88179i) q^{39} +(-1.97815 + 1.43721i) q^{40} +(-0.399552 + 1.22969i) q^{41} +(3.72995 + 2.70997i) q^{42} +(-4.00739 + 12.3335i) q^{43} +(-0.109687 - 0.337582i) q^{44} +(-0.669131 + 0.486152i) q^{45} +(-1.93589 - 5.95804i) q^{46} +(2.79864 + 8.61332i) q^{47} +(-2.86245 + 2.07969i) q^{48} +(1.50457 + 4.63059i) q^{49} +(1.78483 - 5.49314i) q^{50} +(-2.01351 - 1.46290i) q^{51} +(0.206824 - 0.636538i) q^{52} +(3.62388 - 2.63290i) q^{53} +(-1.08268 + 0.786610i) q^{54} +(-1.13611 - 0.825431i) q^{55} -10.1848 q^{56} -2.44512 q^{57} +(9.91493 + 7.20362i) q^{58} +(0.732289 + 2.25376i) q^{59} +(0.0534318 - 0.164446i) q^{60} +8.32624 q^{61} +(5.81562 - 4.65809i) q^{62} -3.44512 q^{63} +(2.67370 - 8.22880i) q^{64} +(-0.818256 - 2.51833i) q^{65} +(-1.83826 - 1.33557i) q^{66} +2.47214 q^{67} +0.520307 q^{68} +(3.78716 + 2.75154i) q^{69} +(-3.08501 + 2.24139i) q^{70} +(11.6329 - 8.45181i) q^{71} +(0.913545 - 2.81160i) q^{72} +(-5.59979 - 4.06849i) q^{73} +(-0.768602 + 2.36552i) q^{74} +(1.33369 + 4.10468i) q^{75} +(0.413545 - 0.300458i) q^{76} +(-1.80757 - 5.56314i) q^{77} +(-1.32397 - 4.07475i) q^{78} +(-14.0312 + 10.1943i) q^{79} +(-0.904307 - 2.78317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.39987 - 1.01707i) q^{82} +(1.67051 - 5.14130i) q^{83} +(0.582676 - 0.423339i) q^{84} +(1.66535 - 1.20995i) q^{85} +(-14.0404 - 10.2009i) q^{86} -9.15780 q^{87} +5.01945 q^{88} +(6.30301 + 4.57940i) q^{89} +(-0.342040 - 1.05269i) q^{90} +(3.40832 - 10.4897i) q^{91} -0.978636 q^{92} +(-1.46980 + 5.37026i) q^{93} -12.1201 q^{94} +(0.624938 - 1.92336i) q^{95} +(0.363892 + 1.11994i) q^{96} +(10.5416 + 7.65894i) q^{97} -6.51584 q^{98} +1.69789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20} + 6 q^{21} + 6 q^{22} - 17 q^{23} + 4 q^{24} - 18 q^{25} + 12 q^{26} + 2 q^{27} - 9 q^{28} - 2 q^{29} - 4 q^{30} + 17 q^{31} - q^{33} + 4 q^{34} - 3 q^{35} + 2 q^{36} + 8 q^{37} + 8 q^{38} + 3 q^{39} - 7 q^{40} - 5 q^{41} + 6 q^{42} - 19 q^{43} + 24 q^{44} - q^{45} - 17 q^{46} - 4 q^{47} - 12 q^{48} + 11 q^{49} + 12 q^{50} - 9 q^{51} - 12 q^{52} + 2 q^{54} + 8 q^{55} - 12 q^{56} + 2 q^{57} + 33 q^{58} - 29 q^{59} - 6 q^{60} + 4 q^{61} + 47 q^{62} - 6 q^{63} + 16 q^{64} + 21 q^{65} - 6 q^{66} - 16 q^{67} + 6 q^{68} + 17 q^{69} - 3 q^{70} + 37 q^{71} + q^{72} + 3 q^{73} - 2 q^{74} + 3 q^{75} - 3 q^{76} + 18 q^{77} - 27 q^{78} - 3 q^{79} - 24 q^{80} - 2 q^{81} + 35 q^{82} - 31 q^{83} - 6 q^{84} - 8 q^{85} - 44 q^{86} - 18 q^{87} - 8 q^{88} + 19 q^{89} - 11 q^{90} - 24 q^{91} + 2 q^{92} + 13 q^{93} - 94 q^{94} - 16 q^{95} + 20 q^{96} - 3 q^{97} - 34 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

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