LMFDB - Embedded newform 315.2.r.b.184.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.13
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36154i q^{2} +(1.72744 - 0.126307i) q^{3} +0.146205 q^{4} +(1.24734 + 1.85584i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(-1.93746 + 1.80173i) q^{7} -2.92215i q^{8} +(2.96809 - 0.436376i) q^{9} +O(q^{10})$	\(q-1.36154i q^{2} +(1.72744 - 0.126307i) q^{3} +0.146205 q^{4} +(1.24734 + 1.85584i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(-1.93746 + 1.80173i) q^{7} -2.92215i q^{8} +(2.96809 - 0.436376i) q^{9} +(2.52681 - 1.69830i) q^{10} +(-0.310611 + 0.537993i) q^{11} +(0.252560 - 0.0184667i) q^{12} +(-2.17808 - 1.25751i) q^{13} +(2.45313 + 2.63794i) q^{14} +(2.38911 + 3.04831i) q^{15} -3.68621 q^{16} +(5.28156 - 3.04931i) q^{17} +(-0.594144 - 4.04118i) q^{18} +(-0.100966 + 0.174878i) q^{19} +(0.182367 + 0.271333i) q^{20} +(-3.11928 + 3.35710i) q^{21} +(0.732500 + 0.422909i) q^{22} +(-3.46827 + 2.00240i) q^{23} +(-0.369088 - 5.04783i) q^{24} +(-1.88830 + 4.62972i) q^{25} +(-1.71216 + 2.96554i) q^{26} +(5.07208 - 1.12870i) q^{27} +(-0.283266 + 0.263422i) q^{28} +(-0.297732 - 0.515687i) q^{29} +(4.15040 - 3.25287i) q^{30} -7.03102 q^{31} -0.825359i q^{32} +(-0.468609 + 0.968583i) q^{33} +(-4.15176 - 7.19106i) q^{34} +(-5.76040 - 1.34826i) q^{35} +(0.433949 - 0.0638003i) q^{36} +(-5.67340 - 3.27554i) q^{37} +(0.238104 + 0.137469i) q^{38} +(-3.92133 - 1.89717i) q^{39} +(5.42304 - 3.64490i) q^{40} +(1.68428 - 2.91726i) q^{41} +(4.57083 + 4.24703i) q^{42} +(-7.13977 + 4.12215i) q^{43} +(-0.0454127 + 0.0786572i) q^{44} +(4.51206 + 4.96400i) q^{45} +(2.72636 + 4.72219i) q^{46} +1.54251i q^{47} +(-6.36771 + 0.465596i) q^{48} +(0.507523 - 6.98158i) q^{49} +(6.30356 + 2.57100i) q^{50} +(8.73843 - 5.93460i) q^{51} +(-0.318445 - 0.183854i) q^{52} +(-2.16836 + 1.25190i) q^{53} +(-1.53678 - 6.90585i) q^{54} +(-1.38587 + 0.0946147i) q^{55} +(5.26493 + 5.66155i) q^{56} +(-0.152324 + 0.314844i) q^{57} +(-0.702130 + 0.405375i) q^{58} +13.7660 q^{59} +(0.349298 + 0.445677i) q^{60} -6.66263 q^{61} +9.57302i q^{62} +(-4.96434 + 6.19317i) q^{63} -8.49619 q^{64} +(-0.383050 - 5.61071i) q^{65} +(1.31877 + 0.638030i) q^{66} +12.8830i q^{67} +(0.772189 - 0.445824i) q^{68} +(-5.73830 + 3.89710i) q^{69} +(-1.83571 + 7.84302i) q^{70} -8.76528 q^{71} +(-1.27516 - 8.67320i) q^{72} +(1.02561 - 0.592135i) q^{73} +(-4.45978 + 7.72457i) q^{74} +(-2.67716 + 8.23607i) q^{75} +(-0.0147617 + 0.0255680i) q^{76} +(-0.367523 - 1.60198i) q^{77} +(-2.58308 + 5.33905i) q^{78} +15.6084 q^{79} +(-4.59795 - 6.84103i) q^{80} +(8.61915 - 2.59041i) q^{81} +(-3.97197 - 2.29322i) q^{82} +(-7.36846 + 4.25418i) q^{83} +(-0.456053 + 0.490824i) q^{84} +(12.2469 + 5.99823i) q^{85} +(5.61248 + 9.72109i) q^{86} +(-0.579449 - 0.853213i) q^{87} +(1.57210 + 0.907650i) q^{88} +(-1.99854 + 3.46158i) q^{89} +(6.75870 - 6.14335i) q^{90} +(6.48565 - 1.48793i) q^{91} +(-0.507077 + 0.292761i) q^{92} +(-12.1457 + 0.888068i) q^{93} +2.10019 q^{94} +(-0.450484 + 0.0307551i) q^{95} +(-0.104249 - 1.42576i) q^{96} +(0.922012 - 0.532324i) q^{97} +(-9.50571 - 0.691014i) q^{98} +(-0.687154 + 1.73236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.36154i		−	0.962755i	−0.876513	−	0.481378i	$-0.840137\pi$
$2$		−	1.36154i		−	0.962755i	0.876513	−	0.481378i	$-0.159863\pi$
$3$	1.72744	−	0.126307i	0.997338	−	0.0729235i
$3$	1.72744	−	0.126307i	0.997338	−	0.0729235i
$4$	0.146205			0.0731024
$5$	1.24734	+	1.85584i	0.557826	+	0.829958i
$5$	1.24734	+	1.85584i	0.557826	+	0.829958i
$6$	−0.171973	−	2.35198i	−0.0702075	−	0.960192i
$7$	−1.93746	+	1.80173i	−0.732292	+	0.680991i
$7$	−1.93746	+	1.80173i	−0.732292	+	0.680991i
$8$		−	2.92215i		−	1.03313i
$9$	2.96809	−	0.436376i	0.989364	−	0.145459i
$10$	2.52681	−	1.69830i	0.799046	−	0.537050i
$11$	−0.310611	+	0.537993i	−0.0936526	+	0.162211i	−0.909045	−	0.416697i	$-0.863188\pi$
$11$	−0.310611	+	0.537993i	−0.0936526	+	0.162211i	0.815393	+	0.578908i	$0.196521\pi$
$12$	0.252560	−	0.0184667i	0.0729077	−	0.00533088i
$13$	−2.17808	−	1.25751i	−0.604090	−	0.348772i	0.166559	−	0.986032i	$-0.446734\pi$
$13$	−2.17808	−	1.25751i	−0.604090	−	0.348772i	−0.770649	+	0.637260i	$0.780068\pi$
$14$	2.45313	+	2.63794i	0.655627	+	0.705018i
$15$	2.38911	+	3.04831i	0.616864	+	0.787070i
$16$	−3.68621			−0.921554
$17$	5.28156	−	3.04931i	1.28097	−	0.739566i	0.303942	−	0.952691i	$-0.401697\pi$
$17$	5.28156	−	3.04931i	1.28097	−	0.739566i	0.977025	+	0.213124i	$0.0683639\pi$
$18$	−0.594144	−	4.04118i	−0.140041	−	0.952516i
$19$	−0.100966	+	0.174878i	−0.0231631	+	0.0401198i	−0.877375	−	0.479806i	$-0.840707\pi$
$19$	−0.100966	+	0.174878i	−0.0231631	+	0.0401198i	0.854211	+	0.519926i	$0.174040\pi$
$20$	0.182367	+	0.271333i	0.0407784	+	0.0606719i
$21$	−3.11928	+	3.35710i	−0.680682	+	0.732579i
$22$	0.732500	+	0.422909i	0.156170	+	0.0901646i
$23$	−3.46827	+	2.00240i	−0.723183	+	0.417530i	−0.815923	−	0.578160i	$-0.803771\pi$
$23$	−3.46827	+	2.00240i	−0.723183	+	0.417530i	0.0927398	+	0.995690i	$0.470438\pi$
$24$	−0.369088	−	5.04783i	−0.0753398	−	1.03038i
$25$	−1.88830	+	4.62972i	−0.377660	+	0.925944i
$26$	−1.71216	+	2.96554i	−0.335782	+	0.581591i
$27$	5.07208	−	1.12870i	0.976123	−	0.217219i
$28$	−0.283266	+	0.263422i	−0.0535323	+	0.0497820i
$29$	−0.297732	−	0.515687i	−0.0552875	−	0.0957607i	0.837057	−	0.547116i	$-0.184274\pi$
$29$	−0.297732	−	0.515687i	−0.0552875	−	0.0957607i	−0.892345	+	0.451355i	$0.850941\pi$
$30$	4.15040	−	3.25287i	0.757755	−	0.593889i
$31$	−7.03102			−1.26281			−0.631404	−	0.775454i	$-0.717521\pi$
$31$	−7.03102			−1.26281			−0.631404	+	0.775454i	$0.717521\pi$
$32$		−	0.825359i		−	0.145904i
$33$	−0.468609	+	0.968583i	−0.0815743	+	0.168609i
$34$	−4.15176	−	7.19106i	−0.712021	−	1.23326i
$35$	−5.76040	−	1.34826i	−0.973685	−	0.227897i
$36$	0.433949	−	0.0638003i	0.0723249	−	0.0106334i
$37$	−5.67340	−	3.27554i	−0.932702	−	0.538496i	−0.0450367	−	0.998985i	$-0.514340\pi$
$37$	−5.67340	−	3.27554i	−0.932702	−	0.538496i	−0.887665	+	0.460490i	$0.847674\pi$
$38$	0.238104	+	0.137469i	0.0386255	+	0.0223004i
$39$	−3.92133	−	1.89717i	−0.627915	−	0.303791i
$40$	5.42304	−	3.64490i	0.857458	−	0.576310i
$41$	1.68428	−	2.91726i	0.263040	−	0.455599i	−0.704008	−	0.710192i	$-0.748608\pi$
$41$	1.68428	−	2.91726i	0.263040	−	0.455599i	0.967048	+	0.254593i	$0.0819414\pi$
$42$	4.57083	+	4.24703i	0.705294	+	0.655330i
$43$	−7.13977	+	4.12215i	−1.08880	+	0.628622i	−0.933258	−	0.359207i	$-0.883047\pi$
$43$	−7.13977	+	4.12215i	−1.08880	+	0.628622i	−0.155547	+	0.987829i	$0.549714\pi$
$44$	−0.0454127	+	0.0786572i	−0.00684623	+	0.0118580i
$45$	4.51206	+	4.96400i	0.672618	+	0.739990i
$46$	2.72636	+	4.72219i	0.401979	+	0.696249i
$47$			1.54251i			0.224998i	0.993652	+	0.112499i	$0.0358855\pi$
$47$			1.54251i			0.224998i	−0.993652	+	0.112499i	$0.964115\pi$
$48$	−6.36771	+	0.465596i	−0.919100	+	0.0672029i
$49$	0.507523	−	6.98158i	0.0725033	−	0.997368i
$50$	6.30356	+	2.57100i	0.891458	+	0.363594i
$51$	8.73843	−	5.93460i	1.22362	−	0.831010i
$52$	−0.318445	−	0.183854i	−0.0441604	−	0.0254960i
$53$	−2.16836	+	1.25190i	−0.297847	+	0.171962i	−0.641475	−	0.767144i	$-0.721677\pi$
$53$	−2.16836	+	1.25190i	−0.297847	+	0.171962i	0.343628	+	0.939106i	$0.388344\pi$
$54$	−1.53678	−	6.90585i	−0.209129	−	0.939767i
$55$	−1.38587	+	0.0946147i	−0.186870	+	0.0127578i
$56$	5.26493	+	5.66155i	0.703555	+	0.756556i
$57$	−0.152324	+	0.314844i	−0.0201758	+	0.0417021i
$58$	−0.702130	+	0.405375i	−0.0921942	+	0.0532283i
$59$	13.7660			1.79217			0.896087	−	0.443878i	$-0.146398\pi$
$59$	13.7660			1.79217			0.896087	+	0.443878i	$0.146398\pi$
$60$	0.349298	+	0.445677i	0.0450942	+	0.0575366i
$61$	−6.66263			−0.853063			−0.426531	−	0.904473i	$-0.640265\pi$
$61$	−6.66263			−0.853063			−0.426531	+	0.904473i	$0.640265\pi$
$62$			9.57302i			1.21577i
$63$	−4.96434	+	6.19317i	−0.625448	+	0.780266i
$64$	−8.49619			−1.06202
$65$	−0.383050	−	5.61071i	−0.0475115	−	0.695923i
$66$	1.31877	+	0.638030i	0.162329	+	0.0785361i
$67$			12.8830i			1.57390i	0.617014	+	0.786952i	$0.288342\pi$
$67$			12.8830i			1.57390i	−0.617014	+	0.786952i	$0.711658\pi$
$68$	0.772189	−	0.445824i	0.0936417	−	0.0540641i
$69$	−5.73830	+	3.89710i	−0.690810	+	0.469156i
$70$	−1.83571	+	7.84302i	−0.219409	+	0.937421i
$71$	−8.76528			−1.04025			−0.520124	−	0.854091i	$-0.674114\pi$
$71$	−8.76528			−1.04025			−0.520124	+	0.854091i	$0.674114\pi$
$72$	−1.27516	−	8.67320i	−0.150278	−	1.02215i
$73$	1.02561	−	0.592135i	0.120038	−	0.0693042i	−0.438779	−	0.898595i	$-0.644589\pi$
$73$	1.02561	−	0.592135i	0.120038	−	0.0693042i	0.558817	+	0.829291i	$0.311255\pi$
$74$	−4.45978	+	7.72457i	−0.518439	+	0.897963i
$75$	−2.67716	+	8.23607i	−0.309132	+	0.951019i
$76$	−0.0147617	+	0.0255680i	−0.00169328	+	0.00293285i
$77$	−0.367523	−	1.60198i	−0.0418832	−	0.182562i
$78$	−2.58308	+	5.33905i	−0.292476	+	0.604529i
$79$	15.6084			1.75608			0.878039	−	0.478588i	$-0.158851\pi$
$79$	15.6084			1.75608			0.878039	+	0.478588i	$0.158851\pi$
$80$	−4.59795	−	6.84103i	−0.514067	−	0.764851i
$81$	8.61915	−	2.59041i	0.957684	−	0.287823i
$82$	−3.97197	−	2.29322i	−0.438630	−	0.253243i
$83$	−7.36846	+	4.25418i	−0.808793	+	0.466957i	−0.846537	−	0.532330i	$-0.821316\pi$
$83$	−7.36846	+	4.25418i	−0.808793	+	0.466957i	0.0377433	+	0.999287i	$0.487983\pi$
$84$	−0.456053	+	0.490824i	−0.0497595	+	0.0535533i
$85$	12.2469	+	5.99823i	1.32837	+	0.650599i
$86$	5.61248	+	9.72109i	0.605209	+	1.04825i
$87$	−0.579449	−	0.853213i	−0.0621235	−	0.0914740i
$88$	1.57210	+	0.907650i	0.167586	+	0.0967558i
$89$	−1.99854	+	3.46158i	−0.211845	+	0.366927i	−0.952292	−	0.305188i	$-0.901281\pi$
$89$	−1.99854	+	3.46158i	−0.211845	+	0.366927i	0.740447	+	0.672115i	$0.234614\pi$
$90$	6.75870	−	6.14335i	0.712429	−	0.647566i
$91$	6.48565	−	1.48793i	0.679881	−	0.155977i
$92$	−0.507077	+	0.292761i	−0.0528664	+	0.0305224i
$93$	−12.1457	+	0.888068i	−1.25945	+	0.0920884i
$94$	2.10019			0.216618
$95$	−0.450484	+	0.0307551i	−0.0462187	+	0.00315540i
$96$	−0.104249	−	1.42576i	−0.0106399	−	0.145516i
$97$	0.922012	−	0.532324i	0.0936162	−	0.0540493i	−0.452461	−	0.891784i	$-0.649454\pi$
$97$	0.922012	−	0.532324i	0.0936162	−	0.0540493i	0.546077	+	0.837735i	$0.316121\pi$
$98$	−9.50571	−	0.691014i	−0.960221	−	0.0698029i
$99$	−0.687154	+	1.73236i	−0.0690616	+	0.174108i
$100$	−0.276079	+	0.676887i	−0.0276079	+	0.0676887i
$101$	5.46104	−	9.45880i	0.543394	−	0.941186i	−0.455312	−	0.890332i	$-0.650472\pi$
$101$	5.46104	−	9.45880i	0.543394	−	0.941186i	0.998706	−	0.0508541i	$-0.0161943\pi$
$102$	−8.08020	−	11.8977i	−0.800059	−	1.17805i
$103$	9.80565	−	5.66129i	0.966179	−	0.557824i	0.0681100	−	0.997678i	$-0.478303\pi$
$103$	9.80565	−	5.66129i	0.966179	−	0.557824i	0.898069	+	0.439854i	$0.144970\pi$
$104$	−3.67464	+	6.36466i	−0.360328	+	0.624107i
$105$	−10.1210	−	1.60145i	−0.987712	−	0.156286i
$106$	1.70452	+	2.95231i	0.165557	+	0.286754i
$107$	14.3799	+	8.30225i	1.39016	+	0.802609i	0.993333	−	0.115284i	$-0.0367780\pi$
$107$	14.3799	+	8.30225i	1.39016	+	0.802609i	0.396827	+	0.917893i	$0.370111\pi$
$108$	0.741563	−	0.165022i	0.0713569	−	0.0158792i
$109$	2.59019	+	4.48634i	0.248095	+	0.429713i	0.962997	−	0.269511i	$-0.0868622\pi$
$109$	2.59019	+	4.48634i	0.248095	+	0.429713i	−0.714902	+	0.699224i	$0.753529\pi$
$110$	0.128822	+	1.88692i	0.0122827	+	0.179910i
$111$	−10.2142	−	4.94171i	−0.969487	−	0.469046i
$112$	7.14190	−	6.64157i	0.674846	−	0.627569i
$113$	−5.18922	−	2.99600i	−0.488160	−	0.281840i	0.235651	−	0.971838i	$-0.424278\pi$
$113$	−5.18922	−	2.99600i	−0.488160	−	0.281840i	−0.723811	+	0.689998i	$0.757611\pi$
$114$	0.428673	+	0.207395i	0.0401489	+	0.0194244i
$115$	−8.04224	−	3.93888i	−0.749943	−	0.367303i
$116$	−0.0435299	−	0.0753959i	−0.00404165	−	0.00700034i
$117$	−7.01349	−	2.78196i	−0.648397	−	0.257192i
$118$		−	18.7429i		−	1.72543i
$119$	−4.73879	+	15.4239i	−0.434404	+	1.41390i
$120$	8.90760	−	6.98132i	0.813149	−	0.637304i
$121$	5.30704	+	9.19207i	0.482458	+	0.835642i
$122$			9.07145i			0.821290i
$123$	2.54102	−	5.25212i	0.229116	−	0.473568i
$124$	−1.02797			−0.0923142
$125$	−10.9474	+	2.27043i	−0.979163	+	0.203074i
$126$	8.43226	+	6.75915i	0.751205	+	0.602153i
$127$		−	6.32526i		−	0.561276i	−0.959814	−	0.280638i	$-0.909454\pi$
$127$		−	6.32526i		−	0.561276i	0.959814	−	0.280638i	$-0.0905460\pi$
$128$			9.91720i			0.876565i
$129$	−11.8129	+	8.02257i	−1.04006	+	0.706347i
$130$	−7.63922	+	0.521538i	−0.670004	+	0.0457419i
$131$	−8.76378	−	15.1793i	−0.765695	−	1.32622i	−0.939878	−	0.341509i	$-0.889062\pi$
$131$	−8.76378	−	15.1793i	−0.765695	−	1.32622i	0.174184	−	0.984713i	$-0.444271\pi$
$132$	−0.0685128	+	0.141611i	−0.00596327	+	0.0123257i
$133$	−0.119466	−	0.520733i	−0.0103590	−	0.0451533i
$134$	17.5407			1.51529
$135$	8.42129	+	8.00511i	0.724790	+	0.688970i
$136$	−8.91053	−	15.4335i	−0.764072	−	1.32341i
$137$	12.1792	+	7.03166i	1.04054	+	0.600755i	0.919986	−	0.391952i	$-0.128200\pi$
$137$	12.1792	+	7.03166i	1.04054	+	0.600755i	0.120552	+	0.992707i	$0.461533\pi$
$138$	5.30606	+	7.81293i	0.451682	+	0.665081i
$139$	6.68525	−	11.5792i	0.567036	−	0.982135i	−0.429821	−	0.902914i	$-0.641423\pi$
$139$	6.68525	−	11.5792i	0.567036	−	0.982135i	0.996857	−	0.0792208i	$-0.0252432\pi$
$140$	−0.842198	−	0.197122i	−0.0711787	−	0.0166598i
$141$	0.194830	+	2.66459i	0.0164076	+	0.224399i
$142$			11.9343i			1.00150i
$143$	1.35307	−	0.781194i	0.113149	−	0.0653268i
$144$	−10.9410	+	1.60858i	−0.911752	+	0.134048i
$145$	0.585662	−	1.19578i	0.0486366	−	0.0993041i
$146$	−0.806216	−	1.39641i	−0.0667229	−	0.115568i
$147$	−0.00510830	−	12.1244i	−0.000421325	−	1.00000i
$148$	−0.829478	−	0.478900i	−0.0681827	−	0.0393653i
$149$	−10.4794	−	18.1508i	−0.858502	−	1.48697i	−0.873358	−	0.487080i	$-0.838062\pi$
$149$	−10.4794	−	18.1508i	−0.858502	−	1.48697i	0.0148555	−	0.999890i	$-0.495271\pi$
$150$	11.2137	+	3.64506i	0.915599	+	0.297618i
$151$	2.62070	−	4.53919i	0.213270	−	0.369394i	−0.739466	−	0.673194i	$-0.764922\pi$
$151$	2.62070	−	4.53919i	0.213270	−	0.369394i	0.952736	+	0.303800i	$0.0982553\pi$
$152$	0.511019	+	0.295037i	0.0414491	+	0.0239307i
$153$	14.3455	−	11.3554i	1.15977	−	0.918028i
$154$	−2.18116	+	0.500398i	−0.175763	+	0.0403233i
$155$	−8.77005	−	13.0485i	−0.704427	−	1.04808i
$156$	−0.573317	−	0.277376i	−0.0459021	−	0.0222078i
$157$			9.80911i			0.782853i	0.920209	+	0.391426i	$0.128018\pi$
$157$			9.80911i			0.782853i	−0.920209	+	0.391426i	$0.871982\pi$
$158$		−	21.2514i		−	1.69067i
$159$	−3.58758	+	2.43646i	−0.284514	+	0.193224i
$160$	1.53174	−	1.02950i	0.121094	−	0.0813892i
$161$	3.11184	−	10.1285i	0.245247	−	0.798235i
$162$	−3.52695	−	11.7353i	−0.277103	−	0.922015i
$163$	−1.19707	−	0.691129i	−0.0937618	−	0.0541334i	0.452386	−	0.891822i	$-0.350573\pi$
$163$	−1.19707	−	0.691129i	−0.0937618	−	0.0541334i	−0.546148	+	0.837689i	$0.683906\pi$
$164$	0.246250	−	0.426517i	0.0192289	−	0.0333054i
$165$	−2.38205	+	0.338486i	−0.185442	+	0.0263511i
$166$	5.79224	+	10.0325i	0.449565	+	0.778670i
$167$	5.10891	+	2.94963i	0.395339	+	0.228249i	0.684471	−	0.729040i	$-0.260033\pi$
$167$	5.10891	+	2.94963i	0.395339	+	0.228249i	−0.289132	+	0.957289i	$0.593367\pi$
$168$	9.80993	+	9.11499i	0.756853	+	0.703236i
$169$	−3.33732	−	5.78040i	−0.256717	−	0.444646i
$170$	8.16683	−	16.6747i	0.626368	−	1.27889i
$171$	−0.223363	+	0.563113i	−0.0170810	+	0.0430623i
$172$	−1.04387	+	0.602678i	−0.0795942	+	0.0459537i
$173$		−	18.2772i		−	1.38959i	−0.719207	−	0.694796i	$-0.755495\pi$
$173$		−	18.2772i		−	1.38959i	0.719207	−	0.694796i	$-0.244505\pi$
$174$	−1.16168	+	0.788944i	−0.0880671	+	0.0598097i
$175$	−4.68301	−	12.3721i	−0.354002	−	0.935245i
$176$	1.14498	−	1.98316i	0.0863059	−	0.149486i
$177$	23.7799	−	1.73874i	1.78740	−	0.130692i
$178$	4.71308	+	2.72110i	0.353260	+	0.203955i
$179$	9.23806	+	16.0008i	0.690485	+	1.19596i	0.971679	+	0.236305i	$0.0759363\pi$
$179$	9.23806	+	16.0008i	0.690485	+	1.19596i	−0.281194	+	0.959651i	$0.590730\pi$
$180$	0.659684	+	0.725761i	0.0491700	+	0.0540950i
$181$	20.4831			1.52250			0.761248	−	0.648461i	$-0.224587\pi$
$181$	20.4831			1.52250			0.761248	+	0.648461i	$0.224587\pi$
$182$	−2.02587	−	8.83048i	−0.150168	−	0.654559i
$183$	−11.5093	+	0.841539i	−0.850791	+	0.0622083i
$184$	5.85132	+	10.1348i	0.431365	+	0.747146i
$185$	−0.997759	−	14.6146i	−0.0733567	−	1.07449i
$186$	1.20914	+	16.5368i	0.0886586	+	1.21254i
$187$			3.78859i			0.277049i
$188$			0.225522i			0.0164479i
$189$	−7.79335	+	11.3254i	−0.566883	+	0.823799i
$190$	0.0418743	+	0.613353i	0.00303788	+	0.0444973i
$191$	−5.83264			−0.422035			−0.211017	−	0.977482i	$-0.567678\pi$
$191$	−5.83264			−0.422035			−0.211017	+	0.977482i	$0.567678\pi$
$192$	−14.6767	+	1.07313i	−1.05920	+	0.0774465i
$193$			7.24230i			0.521312i	0.965432	+	0.260656i	$0.0839389\pi$
$193$			7.24230i			0.521312i	−0.965432	+	0.260656i	$0.916061\pi$
$194$	−0.724781	−	1.25536i	−0.0520363	−	0.0901295i
$195$	−1.37037	−	9.64378i	−0.0981342	−	0.690606i
$196$	0.0742023	−	1.02074i	0.00530016	−	0.0729100i
$197$		−	15.2073i		−	1.08348i	−0.840547	−	0.541739i	$-0.817766\pi$
$197$		−	15.2073i		−	1.08348i	0.840547	−	0.541739i	$-0.182234\pi$
$198$	2.35868	+	0.935588i	0.167624	+	0.0664894i
$199$	−0.772275	−	1.33762i	−0.0547451	−	0.0948213i	0.837354	−	0.546661i	$-0.184101\pi$
$199$	−0.772275	−	1.33762i	−0.0547451	−	0.0948213i	−0.892099	+	0.451840i	$0.850768\pi$
$200$	13.5287	+	5.51789i	0.956625	+	0.390174i
$201$	1.62721	+	22.2545i	0.114775	+	1.56971i
$202$	−12.8786	−	7.43544i	−0.906132	−	0.523155i
$203$	1.50598	+	0.462691i	0.105699	+	0.0324746i
$204$	1.27760	−	0.867666i	0.0894498	−	0.0607488i
$205$	7.51484	−	0.513046i	0.524859	−	0.0358327i
$206$	−7.70809	−	13.3508i	−0.537048	−	0.930194i
$207$	−9.42033	+	7.45679i	−0.654758	+	0.518283i
$208$	8.02886	+	4.63547i	0.556702	+	0.321412i
$209$	−0.0627221	−	0.108638i	−0.00433858	−	0.00751464i
$210$	−2.18045	+	13.7802i	−0.150465	+	0.950925i
$211$	−8.98538	+	15.5631i	−0.618579	+	1.07141i	0.371166	+	0.928566i	$0.378958\pi$
$211$	−8.98538	+	15.5631i	−0.618579	+	1.07141i	−0.989745	+	0.142844i	$0.954375\pi$
$212$	−0.317024	+	0.183034i	−0.0217733	+	0.0125708i
$213$	−15.1415	+	1.10712i	−1.03748	+	0.0758585i
$214$	11.3039	−	19.5789i	0.772716	−	1.33838i
$215$	−16.5558	−	8.10858i	−1.12909	−	0.553000i
$216$	−3.29824	−	14.8214i	−0.224417	−	1.00847i
$217$	13.6223	−	12.6680i	0.924744	−	0.859960i
$218$	6.10833	−	3.52665i	0.413709	−	0.238855i
$219$	1.69688	−	1.15242i	0.114665	−	0.0778732i
$220$	−0.202620	+	0.0138331i	−0.0136607	+	0.000932629i
$221$	−15.3382			−1.03176
$222$	−6.72834	+	13.9070i	−0.451576	+	0.933379i
$223$	−24.1381	+	13.9362i	−1.61641	+	0.933235i	−0.628571	+	0.777752i	$0.716360\pi$
$223$	−24.1381	+	13.9362i	−1.61641	+	0.933235i	−0.987839	+	0.155483i	$0.950307\pi$
$224$	1.48708	+	1.59910i	0.0993595	+	0.106845i
$225$	−3.58435	+	14.5655i	−0.238957	+	0.971030i
$226$	−4.07917	+	7.06533i	−0.271342	+	0.469979i
$227$	−10.8139	−	6.24340i	−0.717742	−	0.414389i	0.0961788	−	0.995364i	$-0.469338\pi$
$227$	−10.8139	−	6.24340i	−0.717742	−	0.414389i	−0.813921	+	0.580975i	$0.802671\pi$
$228$	−0.0222705	+	0.0460316i	−0.00147490	+	0.00304852i
$229$	8.26639	+	14.3178i	0.546258	+	0.946147i	0.998527	+	0.0542651i	$0.0172816\pi$
$229$	8.26639	+	14.3178i	0.546258	+	0.946147i	−0.452268	+	0.891882i	$0.649385\pi$
$230$	−5.36295	+	10.9498i	−0.353622	+	0.722012i
$231$	−0.837216	−	2.72090i	−0.0550848	−	0.179022i
$232$	−1.50691	+	0.870017i	−0.0989338	+	0.0571194i
$233$	10.0137	+	5.78138i	0.656016	+	0.378751i	0.790757	−	0.612130i	$-0.209687\pi$
$233$	10.0137	+	5.78138i	0.656016	+	0.378751i	−0.134741	+	0.990881i	$0.543020\pi$
$234$	−3.78775	+	9.54915i	−0.247613	+	0.624248i
$235$	−2.86265	+	1.92403i	−0.186739	+	0.125510i
$236$	2.01265			0.131012
$237$	26.9625	−	1.97145i	1.75140	−	0.128059i
$238$	21.0003	+	6.45205i	1.36124	+	0.418225i
$239$	−3.97892	+	6.89170i	−0.257375	+	0.445787i	−0.965538	−	0.260262i	$-0.916191\pi$
$239$	−3.97892	+	6.89170i	−0.257375	+	0.445787i	0.708163	+	0.706049i	$0.249524\pi$
$240$	−8.80675	−	11.2367i	−0.568474	−	0.725327i
$241$	−0.806135	+	1.39627i	−0.0519277	+	0.0899414i	−0.890821	−	0.454355i	$-0.849870\pi$
$241$	−0.806135	+	1.39627i	−0.0519277	+	0.0899414i	0.838893	+	0.544296i	$0.183203\pi$
$242$	12.5154	−	7.22576i	0.804519	−	0.464489i
$243$	14.5619	−	5.56344i	0.934145	−	0.356895i
$244$	−0.974108			−0.0623609
$245$	13.5898	−	7.76650i	0.868218	−	0.496183i
$246$	−7.15098	−	3.45970i	−0.455930	−	0.220583i
$247$	0.439823	−	0.253932i	0.0279853	−	0.0161573i
$248$			20.5457i			1.30465i
$249$	−12.1912	+	8.27953i	−0.772588	+	0.524694i
$250$	3.09129	+	14.9053i	0.195510	+	0.942695i
$251$	14.8246			0.935719			0.467860	−	0.883803i	$-0.345025\pi$
$251$	14.8246			0.935719			0.467860	+	0.883803i	$0.345025\pi$
$252$	−0.725809	+	0.905471i	−0.0457217	+	0.0570393i
$253$		−	2.48787i		−	0.156411i
$254$	−8.61210			−0.540371
$255$	21.9134	+	8.81470i	1.37227	+	0.551998i
$256$	−3.48971			−0.218107
$257$	−19.4961	+	11.2561i	−1.21613	+	0.702133i	−0.964088	−	0.265583i	$-0.914436\pi$
$257$	−19.4961	+	11.2561i	−1.21613	+	0.702133i	−0.252043	+	0.967716i	$0.581102\pi$
$258$	10.9231	+	16.0837i	0.680040	+	1.00133i
$259$	16.8937	−	3.87571i	1.04972	−	0.240825i
$260$	−0.0560037	−	0.820313i	−0.00347320	−	0.0508736i
$261$	−1.10873	−	1.40068i	−0.0686287	−	0.0867002i
$262$	−20.6673	+	11.9322i	−1.27683	+	0.737177i
$263$	11.2541	+	6.49755i	0.693956	+	0.400656i	0.805093	−	0.593149i	$-0.202116\pi$
$263$	11.2541	+	6.49755i	0.693956	+	0.400656i	−0.111136	+	0.993805i	$0.535449\pi$
$264$	2.83034	+	1.36934i	0.174196	+	0.0842772i
$265$	−5.02800	−	2.46259i	−0.308868	−	0.151275i
$266$	−0.708999	+	0.162657i	−0.0434715	+	0.00997317i
$267$	−3.01514	+	6.23210i	−0.184524	+	0.381398i
$268$			1.88355i			0.115056i
$269$	3.97205	+	6.87979i	0.242180	+	0.419468i	0.961335	−	0.275382i	$-0.0888042\pi$
$269$	3.97205	+	6.87979i	0.242180	+	0.419468i	−0.719155	+	0.694850i	$0.755471\pi$
$270$	10.8993	−	11.4659i	0.663310	−	0.697795i
$271$	2.85337	−	4.94217i	0.173330	−	0.300216i	−0.766252	−	0.642540i	$-0.777881\pi$
$271$	2.85337	−	4.94217i	0.173330	−	0.300216i	0.939582	+	0.342324i	$0.111214\pi$
$272$	−19.4690	+	11.2404i	−1.18048	+	0.681550i
$273$	11.0156	−	3.38949i	0.666696	−	0.205141i
$274$	9.57389	−	16.5825i	0.578380	−	1.00178i
$275$	−1.90423	−	2.45393i	−0.114830	−	0.147978i
$276$	−0.838967	+	0.569774i	−0.0504999	+	0.0342964i
$277$	−10.7146	−	6.18608i	−0.643778	−	0.371686i	0.142290	−	0.989825i	$-0.454553\pi$
$277$	−10.7146	−	6.18608i	−0.643778	−	0.371686i	−0.786068	+	0.618139i	$0.787887\pi$
$278$	−15.7656	−	9.10225i	−0.945555	−	0.545917i
$279$	−20.8687	+	3.06817i	−1.24938	+	0.183686i
$280$	−3.93981	+	16.8327i	−0.235449	+	1.00595i
$281$	−9.64532	−	16.7062i	−0.575391	−	0.996607i	−0.995999	−	0.0893643i	$-0.971516\pi$
$281$	−9.64532	−	16.7062i	−0.575391	−	0.996607i	0.420608	−	0.907243i	$-0.361817\pi$
$282$	3.62795	−	0.265269i	0.216041	−	0.0157965i
$283$			4.64421i			0.276070i	0.990427	+	0.138035i	$0.0440786\pi$
$283$			4.64421i			0.276070i	−0.990427	+	0.138035i	$0.955921\pi$
$284$	−1.28153			−0.0760446
$285$	−0.774300	+	0.110027i	−0.0458656	+	0.00651743i
$286$	−1.06363	−	1.84226i	−0.0628937	−	0.108935i
$287$	1.99289	+	8.68670i	0.117636	+	0.512760i
$288$	−0.360167	−	2.44974i	−0.0212231	−	0.144352i
$289$	10.0966	−	17.4878i	0.593917	−	1.02869i
$290$	−1.62810	−	0.797403i	−0.0956056	−	0.0468251i
$291$	1.52548	−	1.03601i	0.0894255	−	0.0607322i
$292$	0.149949	−	0.0865729i	0.00877508	−	0.00506630i
$293$	26.2767	+	15.1708i	1.53510	+	0.886289i	0.999115	+	0.0420610i	$0.0133924\pi$
$293$	26.2767	+	15.1708i	1.53510	+	0.886289i	0.535983	+	0.844229i	$0.319941\pi$
$294$	−16.5078	+	0.00695516i	−0.962755	+	0.000405633i
$295$	17.1708	+	25.5474i	0.999722	+	1.48743i
$296$	−9.57161	+	16.5785i	−0.556339	+	0.963607i
$297$	−0.968207	+	3.07934i	−0.0561811	+	0.178681i
$298$	−24.7130	+	14.2681i	−1.43159	+	0.826527i
$299$	10.0722			0.582491
$300$	−0.391413	+	1.20415i	−0.0225982	+	0.0695218i
$301$	6.40603	−	20.8505i	0.369237	−	1.20180i
$302$	−6.18030	−	3.56820i	−0.355636	−	0.205327i
$303$	8.23890	−	17.0293i	0.473313	−	0.978306i
$304$	0.372182	−	0.644638i	0.0213461	−	0.0369725i
$305$	−8.31055	−	12.3648i	−0.475861	−	0.708006i
$306$	−15.4608	−	19.5320i	−0.883837	−	1.11657i
$307$		−	5.12962i		−	0.292763i	−0.989228	−	0.146381i	$-0.953237\pi$
$307$		−	5.12962i		−	0.292763i	0.989228	−	0.146381i	$-0.0467627\pi$
$308$	−0.0537337	−	0.234217i	−0.00306176	−	0.0133457i
$309$	16.2236	−	11.0181i	0.922928	−	0.626796i
$310$	−17.7660	+	11.9408i	−1.00904	+	0.678191i
$311$	−8.28028			−0.469532			−0.234766	−	0.972052i	$-0.575432\pi$
$311$	−8.28028			−0.469532			−0.234766	+	0.972052i	$0.575432\pi$
$312$	−5.54382	+	11.4587i	−0.313857	+	0.648721i
$313$		−	20.2883i		−	1.14676i	−0.819289	−	0.573381i	$-0.805631\pi$
$313$		−	20.2883i		−	1.14676i	0.819289	−	0.573381i	$-0.194369\pi$
$314$	13.3555			0.753695
$315$	−17.6857	−	1.48805i	−0.996479	−	0.0838424i
$316$	2.28202			0.128374
$317$		−	23.7480i		−	1.33382i	−0.745138	−	0.666911i	$-0.767616\pi$
$317$		−	23.7480i		−	1.33382i	0.745138	−	0.666911i	$-0.232384\pi$
$318$	3.31735	+	4.88464i	0.186028	+	0.273917i
$319$	0.369915			0.0207113
$320$	−10.5976	−	15.7676i	−0.592425	−	0.881435i
$321$	25.8891	+	12.5253i	1.44499	+	0.699097i
$322$	−13.7903	−	4.23690i	−0.768505	−	0.236113i
$323$			1.23150i			0.0685228i
$324$	1.26016	−	0.378730i	0.0700089	−	0.0210406i
$325$	9.93481	−	7.70933i	0.551084	−	0.427637i
$326$	−0.941000	+	1.62986i	−0.0521172	+	0.0902696i
$327$	5.04105	+	7.42271i	0.278771	+	0.410477i
$328$	−8.52466	−	4.92171i	−0.470695	−	0.271756i
$329$	−2.77918	−	2.98855i	−0.153221	−	0.164764i
$330$	0.460863	+	3.24326i	0.0253697	+	0.178536i
$331$	−27.4155			−1.50689			−0.753447	−	0.657509i	$-0.771610\pi$
$331$	−27.4155			−1.50689			−0.753447	+	0.657509i	$0.771610\pi$
$332$	−1.07730	+	0.621981i	−0.0591247	+	0.0341357i
$333$	−18.2686	−	7.24637i	−1.00111	−	0.397099i
$334$	4.01605	−	6.95599i	0.219748	−	0.380615i
$335$	−23.9088	+	16.0694i	−1.30627	+	0.877965i
$336$	11.4983	−	12.3750i	0.627285	−	0.675111i
$337$	4.77272	+	2.75553i	0.259986	+	0.150103i	0.624328	−	0.781162i	$-0.285373\pi$
$337$	4.77272	+	2.75553i	0.259986	+	0.150103i	−0.364342	+	0.931265i	$0.618706\pi$
$338$	−7.87026	+	4.54390i	−0.428086	+	0.247155i
$339$	−9.34247	−	4.51996i	−0.507413	−	0.245491i
$340$	1.79056	+	0.876969i	0.0971067	+	0.0475603i
$341$	2.18391	−	3.78264i	0.118265	−	0.204841i
$342$	0.766702	+	0.304119i	0.0414585	+	0.0164448i
$343$	11.5956	+	14.4410i	0.626105	+	0.779739i
$344$	12.0455	+	20.8635i	0.649451	+	1.12488i
$345$	−14.3900	−	5.78839i	−0.774731	−	0.311636i
$346$	−24.8852			−1.33784
$347$			0.380384i			0.0204201i	0.999948	+	0.0102100i	$0.00325001\pi$
$347$			0.380384i			0.0204201i	−0.999948	+	0.0102100i	$0.996750\pi$
$348$	−0.0847182	−	0.124744i	−0.00454137	−	0.00668697i
$349$	0.417229	+	0.722662i	0.0223338	+	0.0386832i	0.876976	−	0.480534i	$-0.159557\pi$
$349$	0.417229	+	0.722662i	0.0223338	+	0.0386832i	−0.854643	+	0.519217i	$0.826224\pi$
$350$	−16.8452	+	6.37611i	−0.900412	+	0.340817i
$351$	−12.4668	−	3.91981i	−0.665426	−	0.209224i
$352$	0.444038	+	0.256365i	0.0236673	+	0.0136643i
$353$	12.7249	+	7.34675i	0.677280	+	0.391028i	0.798829	−	0.601558i	$-0.205453\pi$
$353$	12.7249	+	7.34675i	0.677280	+	0.391028i	−0.121549	+	0.992585i	$0.538786\pi$
$354$	−2.36737	−	32.3773i	−0.125824	−	1.72083i
$355$	−10.9333	−	16.2670i	−0.580277	−	0.863362i
$356$	−0.292196	+	0.506099i	−0.0154864	+	0.0268232i
$357$	−6.23782	+	27.2424i	−0.330140	+	1.44182i
$358$	21.7857	−	12.5780i	1.15141	−	0.664768i
$359$	−9.92659	+	17.1934i	−0.523905	+	0.907430i	0.475708	+	0.879603i	$0.342192\pi$
$359$	−9.92659	+	17.1934i	−0.523905	+	0.907430i	−0.999613	+	0.0278269i	$0.991141\pi$
$360$	14.5055	−	13.1849i	0.764510	−	0.694905i
$361$	9.47961	+	16.4192i	0.498927	+	0.864167i
$362$		−	27.8886i		−	1.46579i
$363$	10.3286	+	15.2084i	0.542112	+	0.798235i
$364$	0.948232	−	0.217542i	0.0497009	−	0.0114023i
$365$	2.37819	+	1.16477i	0.124480	+	0.0609671i
$366$	1.14579	+	15.6704i	0.0598914	+	0.819104i
$367$	16.3540	+	9.44197i	0.853670	+	0.492867i	0.861888	−	0.507099i	$-0.169282\pi$
$367$	16.3540	+	9.44197i	0.853670	+	0.492867i	−0.00821719	+	0.999966i	$0.502616\pi$
$368$	12.7848	−	7.38129i	0.666452	−	0.384776i
$369$	3.72608	−	9.39367i	0.193972	−	0.489015i
$370$	−19.8984	+	1.35849i	−1.03447	+	0.0706245i
$371$	1.94552	−	6.33231i	0.101006	−	0.328757i
$372$	−1.77575	+	0.129840i	−0.0920684	+	0.00673188i
$373$	4.68819	−	2.70673i	0.242745	−	0.140149i	−0.373692	−	0.927553i	$-0.621908\pi$
$373$	4.68819	−	2.70673i	0.242745	−	0.140149i	0.616438	+	0.787404i	$0.288575\pi$
$374$	5.15833			0.266731
$375$	−18.6242	+	5.30477i	−0.961748	+	0.273937i
$376$	4.50743			0.232453
$377$			1.49761i			0.0771308i
$378$	15.4199	+	10.6110i	0.793116	+	0.545769i
$379$	−36.1233			−1.85553			−0.927765	−	0.373164i	$-0.878273\pi$
$379$	−36.1233			−1.85553			−0.927765	+	0.373164i	$0.878273\pi$
$380$	−0.0658629	+	0.00449654i	−0.00337870	+	0.000230668i
$381$	−0.798926	−	10.9265i	−0.0409302	−	0.559781i
$382$			7.94138i			0.406316i
$383$	30.1481	−	17.4060i	1.54050	−	0.889405i	0.541688	−	0.840580i	$-0.317785\pi$
$383$	30.1481	−	17.4060i	1.54050	−	0.889405i	0.998807	−	0.0488258i	$-0.0155479\pi$
$384$	1.25261	+	17.1314i	0.0639222	+	0.874231i
$385$	2.51460	−	2.68027i	0.128156	−	0.136599i
$386$	9.86069			0.501896
$387$	−19.3927	+	15.3505i	−0.985786	+	0.780312i
$388$	0.134803	−	0.0778283i	0.00684356	−	0.00395113i
$389$	13.9113	−	24.0952i	0.705333	−	1.22167i	−0.261238	−	0.965274i	$-0.584131\pi$
$389$	13.9113	−	24.0952i	0.705333	−	1.22167i	0.966571	−	0.256399i	$-0.0825360\pi$
$390$	−13.1304	+	1.86581i	−0.664884	+	0.0944792i
$391$	−12.2119	+	21.1516i	−0.617583	+	1.06968i
$392$	−20.4012	−	1.48306i	−1.03042	−	0.0749057i
$393$	−17.0562	−	25.1144i	−0.860369	−	1.26685i
$394$	−20.7054			−1.04312
$395$	19.4689	+	28.9667i	0.979586	+	1.45747i
$396$	−0.100465	+	0.253279i	−0.00504856	+	0.0127277i
$397$	22.6589	+	13.0821i	1.13722	+	0.656572i	0.945740	−	0.324925i	$-0.105339\pi$
$397$	22.6589	+	13.0821i	1.13722	+	0.656572i	0.191476	+	0.981497i	$0.438672\pi$
$398$	−1.82122	+	1.05148i	−0.0912897	+	0.0527062i
$399$	−0.272142	−	0.884445i	−0.0136241	−	0.0442776i
$400$	6.96068	−	17.0661i	0.348034	−	0.853307i
$401$	5.89709	+	10.2141i	0.294487	+	0.510066i	0.974865	−	0.222795i	$-0.0715179\pi$
$401$	5.89709	+	10.2141i	0.294487	+	0.510066i	−0.680379	+	0.732861i	$0.738185\pi$
$402$	30.3005	−	2.21552i	1.51125	−	0.110500i
$403$	15.3141	+	8.84160i	0.762850	+	0.440432i
$404$	0.798430	−	1.38292i	0.0397234	−	0.0688029i
$405$	15.5584	+	12.7647i	0.773102	+	0.634282i
$406$	0.629973	−	2.05045i	0.0312651	−	0.101762i
$407$	3.52444	−	2.03484i	0.174700	−	0.100863i
$408$	−17.3418	−	25.5350i	−0.858545	−	1.26417i
$409$	33.2394			1.64358			0.821791	−	0.569789i	$-0.192975\pi$
$409$	33.2394			1.64358			0.821791	+	0.569789i	$0.192975\pi$
$410$	−0.698534	−	10.2318i	−0.0344981	−	0.505311i
$411$	21.9270	+	10.6084i	1.08158	+	0.523276i
$412$	1.43363	−	0.827708i	0.0706300	−	0.0407782i
$413$	−26.6710	+	24.8026i	−1.31240	+	1.22045i
$414$	10.1527	+	12.8262i	0.498979	+	0.630372i
$415$	−17.0860	−	8.36830i	−0.838721	−	0.410784i
$416$	−1.03790	+	1.79770i	−0.0508873	+	0.0881393i
$417$	10.0858	−	20.8468i	0.493905	−	1.02087i
$418$	−0.147915	+	0.0853988i	−0.00723476	+	0.00417699i
$419$	7.56943	−	13.1106i	0.369791	−	0.640496i	−0.619742	−	0.784806i	$-0.712763\pi$
$419$	7.56943	−	13.1106i	0.369791	−	0.640496i	0.989533	+	0.144309i	$0.0460960\pi$
$420$	−1.47974	−	0.234140i	−0.0722041	−	0.0114249i
$421$	−0.116982	−	0.202619i	−0.00570136	−	0.00987504i	0.863161	−	0.504929i	$-0.168481\pi$
$421$	−0.116982	−	0.202619i	−0.00570136	−	0.00987504i	−0.868862	+	0.495054i	$0.835148\pi$
$422$	21.1898	+	12.2340i	1.03151	+	0.595540i
$423$	0.673113	+	4.57830i	0.0327279	+	0.222605i
$424$	3.65824	+	6.33626i	0.177660	+	0.307716i
$425$	4.14428	+	30.2102i	0.201027	+	1.46541i
$426$	1.50739	+	20.6158i	0.0730332	+	0.998837i
$427$	12.9086	−	12.0043i	0.624691	−	0.580928i
$428$	2.10241	+	1.21383i	0.101624	+	0.0586726i
$429$	2.23867	−	1.52037i	0.108084	−	0.0734041i
$430$	−11.0402	+	22.5413i	−0.532404	+	1.08704i
$431$	0.544288	+	0.942735i	0.0262174	+	0.0454099i	0.878836	−	0.477123i	$-0.158320\pi$
$431$	0.544288	+	0.942735i	0.0262174	+	0.0454099i	−0.852619	+	0.522533i	$0.824987\pi$
$432$	−18.6968	+	4.16065i	−0.899550	+	0.200179i
$433$		−	26.5259i		−	1.27476i	−0.770552	−	0.637378i	$-0.780019\pi$
$433$		−	26.5259i		−	1.27476i	0.770552	−	0.637378i	$-0.219981\pi$
$434$	−17.2480	−	18.5474i	−0.827931	−	0.890302i
$435$	0.860660	−	2.13961i	0.0412655	−	0.102586i
$436$	0.378698	+	0.655924i	0.0181363	+	0.0314130i
$437$		−	0.808698i		−	0.0386853i
$438$	−1.56907	−	2.31038i	−0.0749729	−	0.110394i
$439$	−27.6764			−1.32092			−0.660460	−	0.750861i	$-0.729639\pi$
$439$	−27.6764			−1.32092			−0.660460	+	0.750861i	$0.729639\pi$
$440$	0.276478	+	4.04971i	0.0131806	+	0.193062i
$441$	−1.54022	−	20.9434i	−0.0733437	−	0.997307i
$442$			20.8836i			0.993332i
$443$			11.2635i			0.535145i	0.963538	+	0.267573i	$0.0862215\pi$
$443$			11.2635i			0.535145i	−0.963538	+	0.267573i	$0.913778\pi$
$444$	−1.49336	−	0.722501i	−0.0708718	−	0.0342884i
$445$	−8.91700	+	0.608774i	−0.422706	+	0.0288587i
$446$	18.9747	+	32.8651i	0.898477	+	1.55621i
$447$	−20.3950	−	30.0307i	−0.964651	−	1.42041i
$448$	16.4611	−	15.3079i	0.777712	−	0.723228i
$449$	−7.28739			−0.343913			−0.171957	−	0.985105i	$-0.555009\pi$
$449$	−7.28739			−0.343913			−0.171957	+	0.985105i	$0.555009\pi$
$450$	19.8315	+	4.88024i	0.934864	+	0.230057i
$451$	1.04631	+	1.81226i	0.0492688	+	0.0853361i
$452$	−0.758688	−	0.438029i	−0.0356857	−	0.0206031i
$453$	3.95377	−	8.17219i	0.185765	−	0.383963i
$454$	−8.50064	+	14.7235i	−0.398955	+	0.691010i
$455$	10.8511	+	10.1804i	0.508710	+	0.477264i
$456$	0.920020	+	0.445113i	0.0430839	+	0.0208443i
$457$		−	23.7919i		−	1.11294i	−0.830868	−	0.556469i	$-0.812156\pi$
$457$		−	23.7919i		−	1.11294i	0.830868	−	0.556469i	$-0.187844\pi$
$458$	19.4943	−	11.2550i	0.910908	−	0.525913i
$459$	23.3467	−	21.4277i	1.08973	−	1.00016i
$460$	−1.17581	−	0.575883i	−0.0548226	−	0.0268507i
$461$	6.23874	+	10.8058i	0.290567	+	0.503277i	0.973944	−	0.226789i	$-0.0728227\pi$
$461$	6.23874	+	10.8058i	0.290567	+	0.503277i	−0.683377	+	0.730066i	$0.739489\pi$
$462$	−3.70462	+	1.13990i	−0.172355	+	0.0530332i
$463$	−2.21515	−	1.27892i	−0.102947	−	0.0594364i	0.447643	−	0.894213i	$-0.352264\pi$
$463$	−2.21515	−	1.27892i	−0.102947	−	0.0594364i	−0.550590	+	0.834776i	$0.685597\pi$
$464$	1.09751	+	1.90093i	0.0509504	+	0.0882487i
$465$	−16.7978	−	21.4327i	−0.778981	−	0.993917i
$466$	7.87159	−	13.6340i	0.364645	−	0.631583i
$467$	−15.7910	−	9.11692i	−0.730719	−	0.421881i	0.0879663	−	0.996123i	$-0.471963\pi$
$467$	−15.7910	−	9.11692i	−0.730719	−	0.421881i	−0.818685	+	0.574243i	$0.805297\pi$
$468$	−1.02541	−	0.406735i	−0.0473994	−	0.0188013i
$469$	−23.2117	−	24.9603i	−1.07181	−	1.15256i
$470$	2.61964	+	3.89762i	0.120835	+	0.179784i
$471$	1.23896	+	16.9446i	0.0570884	+	0.780768i
$472$		−	40.2261i		−	1.85156i
$473$		−	5.12153i		−	0.235488i
$474$	−2.68421	−	36.7106i	−0.123290	−	1.68617i
$475$	−0.618982	−	0.797666i	−0.0284009	−	0.0365994i
$476$	−0.692833	+	2.25504i	−0.0317559	+	0.103360i
$477$	−5.88959	+	4.66198i	−0.269666	+	0.213457i
$478$	9.38333	+	5.41747i	0.429184	+	0.247789i
$479$	−3.23481	+	5.60285i	−0.147802	+	0.256001i	−0.930415	−	0.366508i	$-0.880553\pi$
$479$	−3.23481	+	5.60285i	−0.147802	+	0.256001i	0.782613	+	0.622509i	$0.213887\pi$
$480$	2.51595	−	1.97187i	0.114837	−	0.0900032i
$481$	8.23808	+	14.2688i	0.375624	+	0.650600i
$482$	1.90107	+	1.09759i	0.0865916	+	0.0499937i
$483$	4.09622	−	17.8894i	0.186384	−	0.813994i
$484$	0.775915	+	1.34392i	0.0352688	+	0.0610874i
$485$	2.13797	+	1.04712i	0.0970802	+	0.0475474i
$486$	−7.57485	−	19.8266i	−0.343602	−	0.899353i
$487$	10.1016	−	5.83216i	0.457747	−	0.264280i	−0.253350	−	0.967375i	$-0.581532\pi$
$487$	10.1016	−	5.83216i	0.457747	−	0.264280i	0.711096	+	0.703095i	$0.248199\pi$
$488$			19.4692i			0.881329i
$489$	−2.15516	−	1.04268i	−0.0974597	−	0.0471518i
$490$	−10.5744	−	18.5030i	−0.477703	−	0.835881i
$491$	−6.24877	+	10.8232i	−0.282003	+	0.488444i	−0.971878	−	0.235485i	$-0.924332\pi$
$491$	−6.24877	+	10.8232i	−0.282003	+	0.488444i	0.689875	+	0.723929i	$0.257666\pi$
$492$	0.371509	−	0.767885i	0.0167489	−	0.0346189i
$493$	−3.14498	−	1.81576i	−0.141643	−	0.0817775i
$494$	−0.345739	−	0.598837i	−0.0155555	−	0.0269430i
$495$	−4.07209	+	0.885585i	−0.183027	+	0.0398041i
$496$	25.9178			1.16375
$497$	16.9824	−	15.7927i	0.761765	−	0.708399i
$498$	11.2729	+	16.5989i	0.505152	+	0.743813i
$499$	−19.1792	−	33.2193i	−0.858577	−	1.48710i	−0.873286	−	0.487207i	$-0.838016\pi$
$499$	−19.1792	−	33.2193i	−0.858577	−	1.48710i	0.0147092	−	0.999892i	$-0.495318\pi$
$500$	−1.60056	+	0.331948i	−0.0715792	+	0.0148452i
$501$	9.19789	+	4.45002i	0.410932	+	0.198812i
$502$		−	20.1843i		−	0.900869i
$503$			7.04254i			0.314012i	0.987598	+	0.157006i	$0.0501841\pi$
$503$			7.04254i			0.314012i	−0.987598	+	0.157006i	$0.949816\pi$
$504$	18.0974	+	14.5065i	0.806120	+	0.646172i
$505$	24.3658	−	1.66348i	1.08426	−	0.0740240i
$506$	−3.38734			−0.150586
$507$	−6.49512	−	9.56377i	−0.288458	−	0.424742i
$508$		−	0.924782i		−	0.0410306i
$509$	15.1566	+	26.2520i	0.671806	+	1.16360i	0.977392	+	0.211437i	$0.0678143\pi$
$509$	15.1566	+	26.2520i	0.671806	+	1.16360i	−0.305586	+	0.952164i	$0.598852\pi$
$510$	12.0016	−	29.8361i	0.531439	−	1.32116i
$511$	−0.920208	+	2.99511i	−0.0407076	+	0.132496i
$512$			24.5858i			1.08655i
$513$	−0.314721	+	1.00096i	−0.0138953	+	0.0441933i
$514$	15.3256	+	26.5447i	0.675983	+	1.17084i
$515$	22.7374	+	11.1362i	1.00193	+	0.490719i
$516$	−1.72710	+	1.17294i	−0.0760312	+	0.0516357i
$517$	−0.829859	−	0.479119i	−0.0364971	−	0.0210716i
$518$	−5.27695	−	23.0014i	−0.231856	−	1.01062i
$519$	−2.30855	−	31.5728i	−0.101334	−	1.38589i
$520$	−16.3953	+	1.11933i	−0.718983	+	0.0490858i
$521$	−4.69553	−	8.13289i	−0.205715	−	0.356308i	0.744645	−	0.667460i	$-0.232619\pi$
$521$	−4.69553	−	8.13289i	−0.205715	−	0.356308i	−0.950360	+	0.311152i	$0.899285\pi$
$522$	−1.90709	+	1.50958i	−0.0834711	+	0.0660726i
$523$	12.0758	+	6.97198i	0.528039	+	0.304864i	0.740218	−	0.672367i	$-0.234722\pi$
$523$	12.0758	+	6.97198i	0.528039	+	0.304864i	−0.212178	+	0.977231i	$0.568056\pi$
$524$	−1.28131	−	2.21929i	−0.0559741	−	0.0969500i
$525$	−9.65230	−	20.7806i	−0.421261	−	0.906940i
$526$	8.84668	−	15.3229i	0.385734	−	0.668110i
$527$	−37.1347	+	21.4398i	−1.61761	+	0.933930i
$528$	1.72739	−	3.57041i	0.0751751	−	0.155382i
$529$	−3.48075	+	6.02884i	−0.151337	+	0.262124i
$530$	−3.35291	+	6.84584i	−0.145641	+	0.297364i
$531$	40.8586	−	6.00713i	1.77311	−	0.260687i
$532$	−0.0174664	−	0.0761336i	−0.000757267	−	0.00330081i
$533$	−7.33699	+	4.23601i	−0.317800	+	0.183482i
$534$	8.48526	+	4.10524i	0.367193	+	0.177651i
$535$	2.52894	+	37.0426i	0.109336	+	1.60149i
$536$	37.6459			1.62606
$537$	17.9792	+	26.4736i	0.775860	+	1.14242i
$538$	9.36711	−	5.40811i	0.403845	−	0.233160i
$539$	3.59840	+	2.44160i	0.154994	+	0.105167i
$540$	1.23123	+	1.17038i	0.0529838	+	0.0503654i
$541$	−15.4984	+	26.8440i	−0.666328	+	1.15411i	0.312595	+	0.949886i	$0.398802\pi$
$541$	−15.4984	+	26.8440i	−0.666328	+	1.15411i	−0.978923	+	0.204228i	$0.934532\pi$
$542$	−6.72897	−	3.88498i	−0.289034	−	0.166874i
$543$	35.3833	−	2.58716i	1.51844	−	0.111026i
$544$	−2.51678	−	4.35919i	−0.107906	−	0.186899i
$545$	−5.09510	+	10.4030i	−0.218250	+	0.445614i
$546$	−4.61493	−	14.9982i	−0.197501	−	0.641865i
$547$	17.9331	−	10.3537i	0.766764	−	0.442691i	−0.0649551	−	0.997888i	$-0.520690\pi$
$547$	17.9331	−	10.3537i	0.766764	−	0.442691i	0.831719	+	0.555197i	$0.187357\pi$
$548$	1.78065	+	1.02806i	0.0760658	+	0.0439166i
$549$	−19.7753	+	2.90741i	−0.843990	+	0.124085i
$550$	−3.34113	+	2.59269i	−0.142466	+	0.110553i
$551$	0.120243			0.00512253
$552$	11.3879	+	16.7682i	0.484701	+	0.713700i
$553$	−30.2406	+	28.1221i	−1.28596	+	1.19587i
$554$	−8.42261	+	14.5884i	−0.357842	+	0.619801i
$555$	−3.56950	−	25.1199i	−0.151517	−	1.06628i
$556$	0.977416	−	1.69293i	0.0414517	−	0.0717964i
$557$	−0.264013	+	0.152428i	−0.0111866	+	0.00645859i	−0.505583	−	0.862778i	$-0.668723\pi$
$557$	−0.264013	+	0.152428i	−0.0111866	+	0.00645859i	0.494396	+	0.869237i	$0.335389\pi$
$558$	4.17744	+	28.4136i	0.176845	+	1.20284i
$559$	20.7346			0.876982
$560$	21.2341	+	4.96997i	0.897303	+	0.210019i
$561$	0.478527	+	6.54456i	0.0202034	+	0.276312i
$562$	−22.7462	+	13.1325i	−0.959488	+	0.553961i
$563$		−	14.4319i		−	0.608234i	−0.952635	−	0.304117i	$-0.901639\pi$
$563$		−	14.4319i		−	0.608234i	0.952635	−	0.304117i	$-0.0983613\pi$
$564$	0.0284850	+	0.389575i	0.00119944	+	0.0164041i
$565$	−0.912607	−	13.3674i	−0.0383936	−	0.562370i
$566$	6.32329			0.265788
$567$	−12.0321	+	20.5482i	−0.505299	+	0.862944i
$568$			25.6134i			1.07472i
$569$	0.202702			0.00849769			0.00424885	−	0.999991i	$-0.498648\pi$
$569$	0.202702			0.00849769			0.00424885	+	0.999991i	$0.498648\pi$
$570$	0.149806	+	1.05424i	0.00627469	+	0.0441573i
$571$	−33.1593			−1.38768			−0.693838	−	0.720132i	$-0.744081\pi$
$571$	−33.1593			−1.38768			−0.693838	+	0.720132i	$0.744081\pi$
$572$	0.197825	−	0.114214i	0.00827148	−	0.00477554i
$573$	−10.0755	+	0.736704i	−0.420911	+	0.0307763i
$574$	11.8273	−	2.71340i	0.493662	−	0.113255i
$575$	−2.72144	−	19.8382i	−0.113492	−	0.827312i
$576$	−25.2175	+	3.70753i	−1.05073	+	0.154481i
$577$	12.7694	−	7.37241i	0.531596	−	0.306917i	−0.210070	−	0.977686i	$-0.567369\pi$
$577$	12.7694	−	7.37241i	0.531596	−	0.306917i	0.741666	+	0.670769i	$0.234036\pi$
$578$	−23.8104	−	13.7469i	−0.990381	−	0.571797i
$579$	0.914755	+	12.5106i	0.0380159	+	0.519924i
$580$	0.0856266	−	0.174829i	0.00355545	−	0.00725937i
$581$	6.61122	−	21.5183i	0.274280	−	0.892730i
$582$	−1.41058	−	2.07701i	−0.0584703	−	0.0860948i
$583$		−	1.55542i		−	0.0644188i
$584$	−1.73031	−	2.99698i	−0.0716005	−	0.124016i
$585$	−3.58531	−	16.4860i	−0.148234	−	0.681611i
$586$	20.6557	−	35.7768i	0.853280	−	1.47792i
$587$	−9.38322	+	5.41741i	−0.387287	+	0.223600i	−0.680984	−	0.732298i	$-0.738448\pi$
$587$	−9.38322	+	5.41741i	−0.387287	+	0.223600i	0.293697	+	0.955899i	$0.405114\pi$
$588$	−0.000746857	−	1.77264i	−3.07999e−5	−	0.0731024i
$589$	0.709892	−	1.22957i	0.0292506	−	0.0506635i
$590$	34.7839	−	23.3787i	1.43203	−	0.962487i
$591$	−1.92080	−	26.2697i	−0.0790110	−	1.08059i
$592$	20.9134	+	12.0743i	0.859535	+	0.496253i
$593$	−3.46118	−	1.99831i	−0.142134	−	0.0820608i	0.427247	−	0.904135i	$-0.359484\pi$
$593$	−3.46118	−	1.99831i	−0.142134	−	0.0820608i	−0.569380	+	0.822074i	$0.692817\pi$
$594$	4.19264	+	1.31825i	0.172026	+	0.0540886i
$595$	−34.5352	+	10.4443i	−1.41580	+	0.428176i
$596$	−1.53213	−	2.65373i	−0.0627585	−	0.108701i
$597$	−1.50301	−	2.21311i	−0.0615141	−	0.0905767i
$598$		−	13.7137i		−	0.560796i
$599$	2.32965			0.0951871			0.0475935	−	0.998867i	$-0.484845\pi$
$599$	2.32965			0.0951871			0.0475935	+	0.998867i	$0.484845\pi$
$600$	24.0670	+	7.82305i	0.982531	+	0.319375i
$601$	−9.73443	−	16.8605i	−0.397076	−	0.687755i	0.596288	−	0.802771i	$-0.296642\pi$
$601$	−9.73443	−	16.8605i	−0.397076	−	0.687755i	−0.993364	+	0.115015i	$0.963308\pi$
$602$	−28.3888	−	8.72208i	−1.15704	−	0.355485i
$603$	5.62182	+	38.2378i	0.228938	+	1.55717i
$604$	0.383159	−	0.663651i	0.0155905	−	0.0270036i
$605$	−10.4394	+	21.3146i	−0.424420	+	0.866563i
$606$	−23.1861	−	11.2176i	−0.941870	−	0.455684i
$607$	14.4303	−	8.33135i	0.585708	−	0.338159i	−0.177690	−	0.984086i	$-0.556863\pi$
$607$	14.4303	−	8.33135i	0.585708	−	0.338159i	0.763399	+	0.645928i	$0.223529\pi$
$608$	0.144337	+	0.0833331i	0.00585364	+	0.00337960i
$609$	2.65992	+	0.609056i	0.107786	+	0.0246802i
$610$	−16.8352	+	11.3152i	−0.681636	+	0.458137i
$611$	1.93972	−	3.35970i	0.0784728	−	0.135919i
$612$	2.09738	−	1.66021i	0.0847817	−	0.0671100i
$613$	−24.0303	+	13.8739i	−0.970573	+	0.560361i	−0.899411	−	0.437104i	$-0.856004\pi$
$613$	−24.0303	+	13.8739i	−0.970573	+	0.560361i	−0.0711621	+	0.997465i	$0.522671\pi$
$614$	−6.98419			−0.281859
$615$	12.9166	−	1.83543i	0.520848	−	0.0740119i
$616$	−4.68122	+	1.07396i	−0.188612	+	0.0432710i
$617$	3.67819	+	2.12360i	0.148078	+	0.0854931i	0.572209	−	0.820108i	$-0.306087\pi$
$617$	3.67819	+	2.12360i	0.148078	+	0.0854931i	−0.424130	+	0.905601i	$0.639420\pi$
$618$	−15.0016	−	22.0891i	−0.603451	−	0.888554i
$619$	−15.8863	+	27.5158i	−0.638523	+	1.10595i	0.347234	+	0.937779i	$0.387121\pi$
$619$	−15.8863	+	27.5158i	−0.638523	+	1.10595i	−0.985757	+	0.168176i	$0.946212\pi$
$620$	−1.28222	−	1.90775i	−0.0514953	−	0.0766169i
$621$	−15.3312	+	14.0710i	−0.615220	+	0.564650i
$622$			11.2740i			0.452044i
$623$	−2.36473	−	10.3075i	−0.0947411	−	0.412962i
$624$	14.4549	+	6.99338i	0.578658	+	0.279959i
$625$	−17.8686	−	17.4846i	−0.714746	−	0.699385i
$626$	−27.6234			−1.10405
$627$	−0.122070	−	0.179743i	−0.00487502	−	0.00717825i
$628$			1.43414i			0.0572284i
$629$	−39.9526			−1.59301
$630$	−2.02605	+	24.0799i	−0.0807197	+	0.959365i
$631$	−11.3375			−0.451340			−0.225670	−	0.974204i	$-0.572457\pi$
$631$	−11.3375			−0.451340			−0.225670	+	0.974204i	$0.572457\pi$
$632$		−	45.6099i		−	1.81427i
$633$	−13.5560	+	28.0193i	−0.538801	+	1.11367i
$634$	−32.3339			−1.28414
$635$	11.7387	−	7.88973i	0.465835	−	0.313094i
$636$	−0.524521	+	0.356222i	−0.0207986	+	0.0141251i
$637$	−9.88486	+	14.5682i	−0.391652	+	0.577213i
$638$		−	0.503655i		−	0.0199399i
$639$	−26.0162	+	3.82496i	−1.02918	+	0.151313i
$640$	−18.4048	+	12.3701i	−0.727512	+	0.488971i
$641$	−6.50717	+	11.2708i	−0.257018	+	0.445168i	−0.965442	−	0.260619i	$-0.916073\pi$
$641$	−6.50717	+	11.2708i	−0.257018	+	0.445168i	0.708424	+	0.705787i	$0.249407\pi$
$642$	17.0538	−	35.2491i	0.673059	−	1.39117i
$643$	−39.0292	−	22.5335i	−1.53916	−	0.888635i	−0.998888	−	0.0471444i	$-0.984988\pi$
$643$	−39.0292	−	22.5335i	−1.53916	−	0.888635i	−0.540272	−	0.841490i	$-0.681679\pi$
$644$	0.454966	−	1.48083i	0.0179282	−	0.0583529i
$645$	−29.6232	−	11.9160i	−1.16641	−	0.469191i
$646$	1.67674			0.0659706
$647$	15.7349	−	9.08453i	0.618602	−	0.357150i	−0.157723	−	0.987483i	$-0.550415\pi$
$647$	15.7349	−	9.08453i	0.618602	−	0.357150i	0.776324	+	0.630334i	$0.217082\pi$
$648$	−7.56956	−	25.1864i	−0.297360	−	0.989416i
$649$	−4.27585	+	7.40599i	−0.167842	+	0.290711i
$650$	−10.4966	−	13.5267i	−0.411709	−	0.530559i
$651$	21.9317	−	23.6038i	0.859571	−	0.925106i
$652$	−0.175017	−	0.101046i	−0.00685421	−	0.00395728i
$653$	−29.8254	+	17.2197i	−1.16716	+	0.673860i	−0.953009	−	0.302941i	$-0.902032\pi$
$653$	−29.8254	+	17.2197i	−1.16716	+	0.673860i	−0.214150	+	0.976801i	$0.568698\pi$
$654$	10.1063	−	6.86360i	0.395189	−	0.268388i
$655$	17.2390	−	35.1979i	0.673584	−	1.37530i
$656$	−6.20862	+	10.7536i	−0.242406	+	0.419859i
$657$	2.78571	−	2.20506i	0.108681	−	0.0860277i
$658$	−4.06903	+	3.78397i	−0.158627	+	0.147515i
$659$	20.7037	+	35.8598i	0.806501	+	1.39690i	0.915273	+	0.402834i	$0.131975\pi$
$659$	20.7037	+	35.8598i	0.806501	+	1.39690i	−0.108772	+	0.994067i	$0.534692\pi$
$660$	−0.348267	+	0.0494883i	−0.0135563	+	0.00192633i
$661$	31.0105			1.20617			0.603083	−	0.797678i	$-0.293939\pi$
$661$	31.0105			1.20617			0.603083	+	0.797678i	$0.293939\pi$
$662$			37.3274i			1.45077i
$663$	−26.4958	+	1.93733i	−1.02901	+	0.0752395i
$664$	12.4313	+	21.5317i	0.482430	+	0.835593i
$665$	0.817384	−	0.871239i	0.0316968	−	0.0337852i
$666$	−9.86624	+	24.8734i	−0.382309	+	0.963825i
$667$	2.06523	+	1.19236i	0.0799660	+	0.0461684i
$668$	0.746947	+	0.431250i	0.0289002	+	0.0166856i
$669$	−39.9369	+	27.1227i	−1.54405	+	1.04862i
$670$	21.8792	+	32.5528i	0.845266	+	1.25762i
$671$	2.06948	−	3.58445i	0.0798916	−	0.138376i
$672$	2.77081	+	2.57452i	0.106886	+	0.0993144i
$673$	−22.6091	+	13.0533i	−0.871515	+	0.503169i	−0.867851	−	0.496824i	$-0.834499\pi$
$673$	−22.6091	+	13.0533i	−0.871515	+	0.503169i	−0.00366358	+	0.999993i	$0.501166\pi$
$674$	3.75177	−	6.49825i	0.144513	−	0.250303i
$675$	−4.35203	+	25.6137i	−0.167510	+	0.985870i
$676$	−0.487932	−	0.845122i	−0.0187666	−	0.0325047i
$677$			14.7483i			0.566823i	0.958998	+	0.283412i	$0.0914662\pi$
$677$			14.7483i			0.566823i	−0.958998	+	0.283412i	$0.908534\pi$
$678$	−6.15412	+	12.7202i	−0.236348	+	0.488515i
$679$	−0.827259	+	2.69258i	−0.0317473	+	0.103332i
$680$	17.5277	−	35.7873i	0.672156	−	1.37238i
$681$	−19.4689	−	9.41922i	−0.746050	−	0.360945i
$682$	−5.15022	−	2.97348i	−0.197212	−	0.113861i
$683$	−8.69914	+	5.02245i	−0.332863	+	0.192179i	−0.657112	−	0.753793i	$-0.728222\pi$
$683$	−8.69914	+	5.02245i	−0.332863	+	0.192179i	0.324248	+	0.945972i	$0.394889\pi$
$684$	−0.0326568	+	0.0823298i	−0.00124866	+	0.00314796i
$685$	2.14190	+	31.3735i	0.0818380	+	1.19872i
$686$	19.6620	−	15.7879i	0.750698	−	0.602786i
$687$	16.0881	+	23.6890i	0.613800	+	0.903793i
$688$	26.3187	−	15.1951i	1.00339	−	0.579309i
$689$	6.29714			0.239902
$690$	−7.88113	+	19.5926i	−0.300029	+	0.745877i
$691$	−35.1164			−1.33589			−0.667946	−	0.744210i	$-0.732826\pi$
$691$	−35.1164			−1.33589			−0.667946	+	0.744210i	$0.732826\pi$
$692$		−	2.67222i		−	0.101582i
$693$	−1.78991	−	4.59445i	−0.0679930	−	0.174529i
$694$	0.517909			0.0196595
$695$	29.8279	−	2.03639i	1.13144	−	0.0772446i
$696$	−2.49321	+	1.69324i	−0.0945050	+	0.0641820i
$697$		−	20.5436i		−	0.778143i
$698$	0.983935	−	0.568075i	0.0372425	−	0.0215020i
$699$	18.0282	+	8.72219i	0.681889	+	0.329904i
$700$	−0.684678	−	1.80886i	−0.0258784	−	0.0683686i
$701$	−19.0065			−0.717865			−0.358933	−	0.933363i	$-0.616859\pi$
$701$	−19.0065			−0.717865			−0.358933	+	0.933363i	$0.616859\pi$
$702$	−5.33698	+	16.9740i	−0.201431	+	0.640643i
$703$	1.14564	−	0.661435i	0.0432086	−	0.0249465i
$704$	2.63901	−	4.57089i	0.0994613	−	0.172272i
$705$	−4.70204	+	3.68521i	−0.177089	+	0.138793i
$706$	10.0029	−	17.3255i	0.376464	−	0.652055i
$707$	6.46166	+	28.1654i	0.243016	+	1.05927i
$708$	3.47673	−	0.254212i	0.130663	−	0.00955387i
$709$	20.5284			0.770961			0.385481	−	0.922716i	$-0.374036\pi$
$709$	20.5284			0.770961			0.385481	+	0.922716i	$0.374036\pi$
$710$	−22.1482	+	14.8861i	−0.831206	+	0.558665i
$711$	46.3271	−	6.81112i	1.73740	−	0.255437i
$712$	10.1152	+	5.84004i	0.379085	+	0.218865i
$713$	24.3854	−	14.0789i	0.913242	−	0.527260i
$714$	37.0916	+	8.49305i	1.38812	+	0.317844i
$715$	3.13751	+	1.53667i	0.117336	+	0.0574682i
$716$	1.35065	+	2.33939i	0.0504761	+	0.0874272i
$717$	−6.00288	+	12.4076i	−0.224182	+	0.463369i
$718$	23.4095	+	13.5155i	0.873633	+	0.504392i
$719$	21.9283	−	37.9809i	0.817786	−	1.41645i	−0.0895237	−	0.995985i	$-0.528534\pi$
$719$	21.9283	−	37.9809i	0.817786	−	1.41645i	0.907310	−	0.420463i	$-0.138132\pi$
$720$	−16.6324	−	18.2984i	−0.619853	−	0.681941i
$721$	−8.79794	+	28.6357i	−0.327653	+	1.06645i
$722$	22.3554	−	12.9069i	0.831981	−	0.480345i
$723$	−1.21619	+	2.51379i	−0.0452306	+	0.0934887i
$724$	2.99473			0.111298
$725$	2.94970	−	0.404644i	0.109549	−	0.0150281i
$726$	20.7069	−	14.0628i	0.768505	−	0.521921i
$727$	8.29739	−	4.79050i	0.307733	−	0.177670i	−0.338178	−	0.941082i	$-0.609811\pi$
$727$	8.29739	−	4.79050i	0.307733	−	0.177670i	0.645912	+	0.763412i	$0.276477\pi$
$728$	−4.34794	−	18.9520i	−0.161145	−	0.702408i
$729$	24.4521	−	11.4498i	0.905631	−	0.424066i
$730$	1.58589	−	3.23800i	0.0586964	−	0.119844i
$731$	−25.1394	+	43.5428i	−0.929815	+	1.61049i
$732$	−1.68271	+	0.123037i	−0.0621949	+	0.00454758i
$733$	−34.7728	+	20.0761i	−1.28436	+	0.741528i	−0.977643	−	0.210271i	$-0.932565\pi$
$733$	−34.7728	+	20.0761i	−1.28436	+	0.741528i	−0.306721	+	0.951799i	$0.599232\pi$
$734$	12.8556	−	22.2666i	0.474510	−	0.821876i
$735$	22.4945	−	15.1326i	0.829723	−	0.558176i
$736$	1.65270	+	2.86257i	0.0609194	+	0.105516i
$737$	−6.93095	−	4.00159i	−0.255305	−	0.147400i
$738$	−12.7899	−	5.07321i	−0.470802	−	0.186747i
$739$	−1.19273	−	2.06588i	−0.0438755	−	0.0759945i	0.843254	−	0.537516i	$-0.180637\pi$
$739$	−1.19273	−	2.06588i	−0.0438755	−	0.0759945i	−0.887129	+	0.461521i	$0.847304\pi$
$740$	−0.145877	−	2.13673i	−0.00536255	−	0.0785478i
$741$	0.727694	−	0.494205i	0.0267325	−	0.0181551i
$742$	−8.62171	−	2.64891i	−0.316513	−	0.0972444i
$743$	0.855753	+	0.494069i	0.0313945	+	0.0181256i	0.515615	−	0.856820i	$-0.327563\pi$
$743$	0.855753	+	0.494069i	0.0313945	+	0.0181256i	−0.484221	+	0.874946i	$0.660897\pi$
$744$	2.59507	+	35.4914i	0.0951397	+	1.30118i
$745$	20.6137	−	42.0882i	0.755227	−	1.54199i
$746$	−3.68532	−	6.38317i	−0.134929	−	0.233704i
$747$	−20.0138	+	15.8422i	−0.732268	+	0.579637i
$748$			0.553910i			0.0202530i
$749$	−42.8190	+	9.82346i	−1.56457	+	0.358942i
$750$	7.22267	+	25.3576i	0.263734	+	0.925928i
$751$	13.4998	+	23.3824i	0.492615	+	0.853234i	0.999964	−	0.00850648i	$-0.00270773\pi$
$751$	13.4998	+	23.3824i	0.492615	+	0.853234i	−0.507349	+	0.861741i	$0.669374\pi$
$752$		−	5.68601i		−	0.207348i
$753$	25.6086	−	1.87245i	0.933228	−	0.0682359i
$754$	2.03906			0.0742581
$755$	11.6929	−	0.798290i	0.425549	−	0.0290527i
$756$	−1.13942	+	1.65582i	−0.0414405	+	0.0602216i
$757$			40.0695i			1.45635i	0.685391	+	0.728175i	$0.259631\pi$
$757$			40.0695i			1.45635i	−0.685391	+	0.728175i	$0.740369\pi$
$758$			49.1834i			1.78642i
$759$	−0.314236	−	4.29765i	−0.0114061	−	0.155995i
$760$	0.0898709	+	1.31638i	0.00325996	+	0.0477502i
$761$	−5.88610	−	10.1950i	−0.213371	−	0.369569i	0.739397	−	0.673270i	$-0.235111\pi$
$761$	−5.88610	−	10.1950i	−0.213371	−	0.369569i	−0.952767	+	0.303701i	$0.901778\pi$
$762$	−14.8769	+	1.08777i	−0.538932	+	0.0394058i
$763$	−13.1016	−	4.02529i	−0.474309	−	0.145725i
$764$	−0.852759			−0.0308517
$765$	38.9675	+	12.4590i	1.40887	+	0.450457i
$766$	−23.6990	−	41.0479i	−0.856280	−	1.48312i
$767$	−29.9833	−	17.3109i	−1.08264	−	0.625060i
$768$	−6.02825	+	0.440775i	−0.217526	+	0.0159051i
$769$	−16.4254	+	28.4496i	−0.592314	+	1.02592i	0.401606	+	0.915813i	$0.368452\pi$
$769$	−16.4254	+	28.4496i	−0.592314	+	1.02592i	−0.993920	+	0.110106i	$0.964881\pi$
$770$	−3.64930	−	3.42373i	−0.131512	−	0.123383i
$771$	−32.2565	+	21.9066i	−1.16169	+	0.788949i
$772$			1.05886i			0.0381091i
$773$	−3.24032	+	1.87080i	−0.116546	+	0.0672879i	−0.557140	−	0.830419i	$-0.688101\pi$
$773$	−3.24032	+	1.87080i	−0.116546	+	0.0672879i	0.440594	+	0.897707i	$0.354768\pi$
$774$	20.9004	+	26.4040i	0.751249	+	0.949071i
$775$	13.2767	−	32.5516i	0.476912	−	1.16929i
$776$	−1.55553	−	2.69426i	−0.0558402	−	0.0967181i
$777$	28.6932	−	8.82885i	1.02936	−	0.316733i
$778$	−32.8066	−	18.9409i	−1.17617	−	0.679063i
$779$	0.340109	+	0.589087i	0.0121857	+	0.0211062i
$780$	−0.200354	−	1.40997i	−0.00717384	−	0.0504849i
$781$	2.72259	−	4.71566i	0.0974219	−	0.168740i
$782$	28.7988	+	16.6270i	1.02984	+	0.594581i
$783$	−2.09218	−	2.27956i	−0.0747685	−	0.0814647i
$784$	−1.87084	+	25.7356i	−0.0668157	+	0.919128i
$785$	−18.2042	+	12.2353i	−0.649735	+	0.436696i
$786$	−34.1943	+	23.2227i	−1.21967	+	0.828325i
$787$			15.6470i			0.557756i	0.960327	+	0.278878i	$0.0899625\pi$
$787$			15.6470i			0.557756i	−0.960327	+	0.278878i	$0.910037\pi$
$788$		−	2.22338i		−	0.0792048i
$789$	20.2614	+	9.80265i	0.721326	+	0.348983i
$790$	39.4393	−	26.5077i	1.40319	−	0.943102i
$791$	15.4519	−	3.54495i	0.549406	−	0.126044i
$792$	5.06220	+	2.00796i	0.179878	+	0.0713499i
$793$	14.5117	+	8.37835i	0.515327	+	0.297524i
$794$	17.8118	−	30.8510i	0.632118	−	1.09486i
$795$	−8.99661	−	3.61889i	−0.319077	−	0.128349i
$796$	−0.112910	−	0.195566i	−0.00400200	−	0.00693166i
$797$	−1.28952	−	0.744503i	−0.0456771	−	0.0263717i	0.476988	−	0.878910i	$-0.341729\pi$
$797$	−1.28952	−	0.744503i	−0.0456771	−	0.0263717i	−0.522665	+	0.852538i	$0.675062\pi$
$798$	−1.20421	+	0.370533i	−0.0426285	+	0.0131167i
$799$	4.70358	+	8.14684i	0.166401	+	0.288215i
$800$	3.82118	+	1.55853i	0.135099	+	0.0551022i
$801$	−4.42131	+	11.1464i	−0.156219	+	0.393839i
$802$	13.9069	−	8.02914i	0.491069	−	0.283519i
$803$			0.735694i			0.0259621i
$804$	0.237906	+	3.25372i	0.00839030	+	0.114750i
$805$	22.6784	−	6.85853i	0.799307	−	0.241731i
$806$	12.0382	−	20.8508i	0.424028	−	0.734438i
$807$	7.73044	+	11.3827i	0.272124	+	0.400691i
$808$	−27.6400	−	15.9580i	−0.972372	−	0.561399i
$809$	−17.6030	−	30.4893i	−0.618889	−	1.07195i	−0.989689	−	0.143234i	$-0.954250\pi$
$809$	−17.6030	−	30.4893i	−0.618889	−	1.07195i	0.370800	−	0.928713i	$-0.379083\pi$
$810$	17.3796	−	21.1834i	0.610658	−	0.744308i
$811$	−26.5990			−0.934017			−0.467008	−	0.884253i	$-0.654668\pi$
$811$	−26.5990			−0.934017			−0.467008	+	0.884253i	$0.654668\pi$
$812$	0.220181	+	0.0676477i	0.00772683	+	0.00237397i
$813$	4.30478	−	8.89771i	0.150975	−	0.312056i
$814$	−2.77051	−	4.79867i	−0.0971064	−	0.168193i
$815$	−0.210524	−	3.08364i	−0.00737433	−	0.108015i
$816$	−32.2117	+	21.8762i	−1.12764	+	0.765820i
$817$		−	1.66478i		−	0.0582434i
$818$		−	45.2568i		−	1.58237i
$819$	18.6007	−	7.24649i	0.649961	−	0.253213i
$820$	1.09870	−	0.0750098i	0.0383684	−	0.00261946i
$821$	21.7369			0.758622			0.379311	−	0.925269i	$-0.376161\pi$
$821$	21.7369			0.758622			0.379311	+	0.925269i	$0.376161\pi$
$822$	14.4438	−	29.8545i	0.503787	−	1.04129i
$823$			21.3752i			0.745093i	0.928014	+	0.372547i	$0.121515\pi$
$823$			21.3752i			0.745093i	−0.928014	+	0.372547i	$0.878485\pi$
$824$	−16.5431	−	28.6535i	−0.576307	−	0.998194i
$825$	−3.59940	−	3.99850i	−0.125315	−	0.139210i
$826$	33.7697	+	36.3137i	1.17500	+	1.26352i
$827$		−	15.4869i		−	0.538531i	−0.963066	−	0.269265i	$-0.913219\pi$
$827$		−	15.4869i		−	0.538531i	0.963066	−	0.269265i	$-0.0867809\pi$
$828$	−1.37730	+	1.09022i	−0.0478644	+	0.0378877i
$829$	19.1032	+	33.0877i	0.663481	+	1.14918i	0.979695	+	0.200495i	$0.0642552\pi$
$829$	19.1032	+	33.0877i	0.663481	+	1.14918i	−0.316213	+	0.948688i	$0.602411\pi$
$830$	−11.3938	+	23.2634i	−0.395484	+	0.807483i
$831$	−19.2902	−	9.33275i	−0.669169	−	0.323749i
$832$	18.5054	+	10.6841i	0.641558	+	0.370404i
$833$	−18.6085	−	38.4212i	−0.644746	−	1.33122i
$834$	−28.3837	−	13.7323i	−0.982848	−	0.475510i
$835$	0.898484	+	13.1605i	0.0310933	+	0.455438i
$836$	−0.00917027	−	0.0158834i	−0.000317160	−	0.000549338i
$837$	−35.6619	+	7.93594i	−1.23266	+	0.274306i
$838$	−17.8507	−	10.3061i	−0.616641	−	0.356018i
$839$	3.17437	+	5.49817i	0.109591	+	0.189818i	0.915605	−	0.402079i	$-0.131712\pi$
$839$	3.17437	+	5.49817i	0.109591	+	0.189818i	−0.806013	+	0.591897i	$0.798379\pi$
$840$	−4.67968	+	29.5751i	−0.161464	+	1.02044i
$841$	14.3227	−	24.8077i	0.493887	−	0.855437i
$842$	−0.275874	+	0.159276i	−0.00950724	+	0.00548901i
$843$	−18.7718	−	27.6406i	−0.646535	−	0.951994i
$844$	−1.31370	+	2.27540i	−0.0452196	+	0.0783226i
$845$	6.56476	−	13.4036i	0.225834	−	0.461099i
$846$	6.23355	−	0.916472i	0.214314	−	0.0315089i
$847$	−26.8438	−	8.24742i	−0.922365	−	0.283385i
$848$	7.99303	−	4.61478i	0.274482	−	0.158472i
$849$	0.586598	+	8.02260i	0.0201320	+	0.275335i
$850$	41.1324	−	5.64261i	1.41083	−	0.193540i
$851$	26.2358			0.899353
$852$	−2.21376	+	0.161866i	−0.0758421	+	0.00554544i
$853$	−0.907008	+	0.523661i	−0.0310554	+	0.0179298i	−0.515447	−	0.856921i	$-0.672374\pi$
$853$	−0.907008	+	0.523661i	−0.0310554	+	0.0179298i	0.484392	+	0.874851i	$0.339041\pi$
$854$	−16.3443	−	17.5756i	−0.559291	−	0.601424i
$855$	−1.32366	+	0.287865i	−0.0452682	+	0.00984476i
$856$	24.2604	−	42.0202i	0.829203	−	1.43622i
$857$	−19.6042	−	11.3185i	−0.669667	−	0.386632i	0.126284	−	0.991994i	$-0.459695\pi$
$857$	−19.6042	−	11.3185i	−0.669667	−	0.386632i	−0.795950	+	0.605362i	$0.793028\pi$
$858$	−2.07004	−	3.04805i	−0.0706702	−	0.104059i
$859$	6.47432	+	11.2139i	0.220901	+	0.382612i	0.955082	−	0.296342i	$-0.0957669\pi$
$859$	6.47432	+	11.2139i	0.220901	+	0.382612i	−0.734181	+	0.678954i	$0.762434\pi$
$860$	−2.42053	−	1.18551i	−0.0825394	−	0.0404256i
$861$	4.53979	+	14.7540i	0.154716	+	0.502816i
$862$	1.28357	−	0.741071i	0.0437187	−	0.0252410i
$863$	16.5213	+	9.53859i	0.562392	+	0.324697i	0.754105	−	0.656754i	$-0.228071\pi$
$863$	16.5213	+	9.53859i	0.562392	+	0.324697i	−0.191713	+	0.981451i	$0.561404\pi$
$864$	−0.931587	−	4.18629i	−0.0316932	−	0.142421i
$865$	33.9196	−	22.7979i	1.15330	−	0.775150i
$866$	−36.1162			−1.22728
$867$	15.2324	−	31.4844i	0.517320	−	1.06927i
$868$	1.99165	−	1.85212i	0.0676010	−	0.0628651i
$869$	−4.84813	+	8.39720i	−0.164461	+	0.284855i
$870$	−2.91317	−	1.17182i	−0.0987657	−	0.0397286i
$871$	16.2005	−	28.0601i	0.548933	−	0.950780i
$872$	13.1097	−	7.56891i	0.443952	−	0.256316i
$873$	2.50432	−	1.98233i	0.0847586	−	0.0670918i
$874$	−1.10108			−0.0372444
$875$	17.1194	−	24.1231i	0.578742	−	0.815511i
$876$	0.248093	−	0.168489i	0.00838227	−	0.00569272i
$877$	−28.5236	+	16.4681i	−0.963172	+	0.556088i	−0.897148	−	0.441730i	$-0.854365\pi$
$877$	−28.5236	+	16.4681i	−0.963172	+	0.556088i	−0.0660243	+	0.997818i	$0.521031\pi$
$878$			37.6825i			1.27172i
$879$	47.3075	+	22.8878i	1.59564	+	0.771985i
$880$	5.10860	−	0.348770i	0.172211	−	0.0117570i
$881$	5.91693			0.199347			0.0996733	−	0.995020i	$-0.468220\pi$
$881$	5.91693			0.199347			0.0996733	+	0.995020i	$0.468220\pi$
$882$	−28.5154	+	2.09707i	−0.960162	+	0.0706120i
$883$		−	54.0403i		−	1.81860i	−0.416141	−	0.909300i	$-0.636618\pi$
$883$		−	54.0403i		−	1.81860i	0.416141	−	0.909300i	$-0.363382\pi$
$884$	−2.24252			−0.0754240
$885$	32.8883	+	41.9629i	1.10553	+	1.41057i
$886$	15.3357			0.515214
$887$	13.2703	−	7.66161i	0.445573	−	0.257252i	−0.260386	−	0.965505i	$-0.583850\pi$
$887$	13.2703	−	7.66161i	0.445573	−	0.257252i	0.705959	+	0.708253i	$0.250516\pi$
$888$	−14.4404	+	29.8473i	−0.484588	+	1.00161i
$889$	11.3964	+	12.2549i	0.382224	+	0.411018i
$890$	0.828871	+	12.1409i	0.0277838	+	0.406963i
$891$	−1.28358	+	5.44166i	−0.0430014	+	0.182302i
$892$	−3.52911	+	2.03753i	−0.118163	+	0.0682217i
$893$	−0.269750	−	0.155741i	−0.00902686	−	0.00521166i
$894$	−40.8881	+	27.7687i	−1.36750	+	0.928723i
$895$	−18.1720	+	37.1028i	−0.607422	+	1.24021i
$896$	−17.8681	−	19.2142i	−0.596932	−	0.641901i
$897$	17.3991	−	1.27219i	0.580940	−	0.0424773i
$898$			9.92209i			0.331104i
$899$	2.09336	+	3.62581i	0.0698175	+	0.120927i
$900$	−0.524049	+	2.12954i	−0.0174683	+	0.0709846i
$901$	−7.63487	+	13.2240i	−0.254355	+	0.440555i
$902$	2.46747	−	1.42460i	0.0821578	−	0.0474338i
$903$	8.43247	−	36.8270i	0.280615	−	1.22553i
$904$	−8.75474	+	15.1637i	−0.291178	+	0.504335i
$905$	25.5493	+	38.0134i	0.849288	+	1.26361i
$906$	−11.1268	−	5.38323i	−0.369663	−	0.178846i
$907$	−35.9660	−	20.7650i	−1.19423	−	0.689491i	−0.234969	−	0.972003i	$-0.575499\pi$
$907$	−35.9660	−	20.7650i	−1.19423	−	0.689491i	−0.959264	+	0.282512i	$0.908832\pi$
$908$	−1.58104	−	0.912814i	−0.0524687	−	0.0302928i
$909$	12.0813	−	30.4577i	0.400711	−	1.01022i
$910$	13.8610	−	14.7743i	0.459489	−	0.489763i
$911$	8.99143	+	15.5736i	0.297899	+	0.515977i	0.975655	−	0.219310i	$-0.0703807\pi$
$911$	8.99143	+	15.5736i	0.297899	+	0.515977i	−0.677756	+	0.735287i	$0.737047\pi$
$912$	0.561499	−	1.16058i	0.0185931	−	0.0384307i
$913$		−	5.28558i		−	0.174927i
$914$	−32.3937			−1.07149
$915$	−15.9177	−	20.3097i	−0.526224	−	0.671419i
$916$	1.20858	+	2.09333i	0.0399328	+	0.0691656i
$917$	44.3285	+	13.6194i	1.46386	+	0.449751i
$918$	−29.1747	−	31.7876i	−0.962908	−	1.04915i
$919$	23.7506	−	41.1372i	0.783459	−	1.35699i	−0.146456	−	0.989217i	$-0.546787\pi$
$919$	23.7506	−	41.1372i	0.783459	−	1.35699i	0.929915	−	0.367774i	$-0.119880\pi$
$920$	−11.5100	+	23.5006i	−0.379473	+	0.774792i
$921$	−0.647908	−	8.86110i	−0.0213493	−	0.291983i
$922$	14.7126	−	8.49431i	0.484533	−	0.279745i
$923$	19.0915	+	11.0225i	0.628403	+	0.362809i
$924$	−0.122405	−	0.397809i	−0.00402683	−	0.0130869i
$925$	25.8779	−	20.0811i	0.850861	−	0.660261i
$926$	−1.74130	+	3.01602i	−0.0572227	+	0.0991127i
$927$	26.6336	−	21.0822i	0.874763	−	0.692430i
$928$	−0.425627	+	0.245736i	−0.0139719	+	0.00806668i
$929$	9.08921			0.298207			0.149104	−	0.988822i	$-0.452361\pi$
$929$	9.08921			0.298207			0.149104	+	0.988822i	$0.452361\pi$
$930$	−29.1815	+	22.8710i	−0.956899	+	0.749968i
$931$	1.16968	+	0.793655i	0.0383348	+	0.0260110i
$932$	1.46404	+	0.845266i	0.0479563	+	0.0276876i
$933$	−14.3037	+	1.04586i	−0.468282	+	0.0342399i
$934$	−12.4131	+	21.5001i	−0.406168	+	0.703503i
$935$	−7.03103	+	4.72565i	−0.229939	+	0.154545i
$936$	−8.12929	+	20.4944i	−0.265714	+	0.669882i
$937$		−	0.442145i		−	0.0144442i	−0.999974	−	0.00722212i	$-0.997701\pi$
$937$		−	0.442145i		−	0.0144442i	0.999974	−	0.00722212i	$-0.00229889\pi$
$938$	−33.9844	+	31.6036i	−1.10963	+	1.03190i
$939$	−2.56256	−	35.0468i	−0.0836259	−	1.14371i
$940$	−0.418533	+	0.281302i	−0.0136510	+	0.00917505i
$941$	−38.9689			−1.27035			−0.635175	−	0.772368i	$-0.719072\pi$
$941$	−38.9689			−1.27035			−0.635175	+	0.772368i	$0.719072\pi$
$942$	23.0708	−	1.68690i	0.751689	−	0.0549621i
$943$			13.4904i			0.439309i
$944$	−50.7443			−1.65159
$945$	−30.7390	−	0.336685i	−0.999940	−	0.0109524i
$946$	−6.97318			−0.226718
$947$		−	7.58619i		−	0.246518i	−0.992375	−	0.123259i	$-0.960665\pi$
$947$		−	7.58619i		−	0.246518i	0.992375	−	0.123259i	$-0.0393346\pi$
$948$	3.94205	−	0.288235i	0.128032	−	0.00936145i
$949$	−2.97847			−0.0966853
$950$	−1.08606	+	0.842770i	−0.0352363	+	0.0273431i
$951$	−2.99955	−	41.0232i	−0.0972669	−	1.33027i
$952$	45.0708	+	13.8474i	1.46075	+	0.448798i
$953$		−	22.6949i		−	0.735161i	−0.929992	−	0.367581i	$-0.880186\pi$
$953$		−	22.6949i		−	0.735161i	0.929992	−	0.367581i	$-0.119814\pi$
$954$	6.34748	+	8.01892i	0.205507	+	0.259622i
$955$	−7.27526	−	10.8245i	−0.235422	−	0.350271i
$956$	−0.581737	+	1.00760i	−0.0188147	+	0.0325881i
$957$	0.639006	−	0.0467230i	0.0206561	−	0.00151034i
$958$	7.62852	+	4.40433i	0.246466	+	0.142297i
$959$	−36.2659	+	8.32006i	−1.17109	+	0.268669i
$960$	−20.2983	−	25.8990i	−0.655125	−	0.835887i
$961$	18.4352			0.594683
$962$	19.4275	−	11.2165i	0.626368	−	0.361634i
$963$	46.3038	+	18.3668i	1.49212	+	0.591862i
$964$	−0.117861	+	0.204141i	−0.00379604	+	0.00657493i
$965$	−13.4406	+	9.03359i	−0.432667	+	0.290801i
$966$	−24.3571	−	5.57717i	−0.783677	−	0.179442i
$967$	−12.8032	−	7.39193i	−0.411723	−	0.237708i	0.279807	−	0.960056i	$-0.409730\pi$
$967$	−12.8032	−	7.39193i	−0.411723	−	0.237708i	−0.691530	+	0.722348i	$0.743063\pi$
$968$	26.8606	−	15.5080i	0.863331	−	0.498445i
$969$	0.155548	+	2.12735i	0.00499692	+	0.0683403i
$970$	1.42570	−	2.91093i	0.0457765	−	0.0934645i
$971$	10.2470	−	17.7483i	0.328841	−	0.569569i	−0.653441	−	0.756977i	$-0.726675\pi$
$971$	10.2470	−	17.7483i	0.328841	−	0.569569i	0.982282	+	0.187408i	$0.0600086\pi$
$972$	2.12901	−	0.813401i	0.0682882	−	0.0260898i
$973$	7.91018	+	34.4793i	0.253589	+	1.10536i
$974$	−7.94072	−	13.7537i	−0.254437	−	0.440698i
$975$	16.1880	−	14.5722i	0.518432	−	0.466685i
$976$	24.5599			0.786143
$977$		−	25.4253i		−	0.813428i	−0.913556	−	0.406714i	$-0.866675\pi$
$977$		−	25.4253i		−	0.813428i	0.913556	−	0.406714i	$-0.133325\pi$
$978$	−1.41966	+	2.93434i	−0.0453957	+	0.0938299i
$979$	−1.24154	−	2.15041i	−0.0396797	−	0.0687273i
$980$	1.98689	−	1.13550i	0.0634688	−	0.0362722i
$981$	9.64565	+	12.1856i	0.307962	+	0.389055i
$982$	14.7362	+	8.50797i	0.470252	+	0.271500i
$983$	3.96058	+	2.28664i	0.126323	+	0.0729325i	0.561830	−	0.827253i	$-0.310098\pi$
$983$	3.96058	+	2.28664i	0.126323	+	0.0729325i	−0.435507	+	0.900185i	$0.643431\pi$
$984$	−15.3475	−	7.42523i	−0.489260	−	0.236708i
$985$	28.2224	−	18.9687i	0.899241	−	0.604392i
$986$	−2.47223	+	4.28202i	−0.0787318	+	0.136367i
$987$	−5.17835	−	4.81151i	−0.164829	−	0.153152i
$988$	0.0643042	−	0.0371260i	0.00204579	−	0.00118114i
$989$	16.5084	−	28.5934i	0.524937	−	0.909218i
$990$	1.20576	+	5.54433i	0.0383216	+	0.176210i
$991$	11.3064	+	19.5833i	0.359161	+	0.622085i	0.987821	−	0.155595i	$-0.0497296\pi$
$991$	11.3064	+	19.5833i	0.359161	+	0.622085i	−0.628660	+	0.777680i	$0.716396\pi$
$992$			5.80311i			0.184249i
$993$	−47.3587	+	3.46278i	−1.50288	+	0.109888i
$994$	−21.5024	−	23.1223i	−0.682015	−	0.733393i
$995$	1.51912	−	3.10168i	0.0481595	−	0.0983300i
$996$	−1.78242	+	1.21051i	−0.0564780	+	0.0383564i
$997$	22.7515	+	13.1356i	0.720548	+	0.416008i	0.814954	−	0.579525i	$-0.196762\pi$
$997$	22.7515	+	13.1356i	0.720548	+	0.416008i	−0.0944065	+	0.995534i	$0.530095\pi$
$998$	−45.2294	+	26.1132i	−1.43171	+	0.826600i
$999$	−32.4731	−	10.2102i	−1.02740	−	0.323037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.13	✓	84
3.2	odd	2		945.2.r.b.604.30		84
5.4	even	2	inner	315.2.r.b.184.30	yes	84
7.4	even	3		315.2.bo.b.4.30	yes	84
9.2	odd	6		945.2.bo.b.289.30		84
9.7	even	3		315.2.bo.b.79.13	yes	84
15.14	odd	2		945.2.r.b.604.13		84
21.11	odd	6		945.2.bo.b.739.13		84
35.4	even	6		315.2.bo.b.4.13	yes	84
45.29	odd	6		945.2.bo.b.289.13		84
45.34	even	6		315.2.bo.b.79.30	yes	84
63.11	odd	6		945.2.r.b.424.30		84
63.25	even	3	inner	315.2.r.b.214.13	yes	84
105.74	odd	6		945.2.bo.b.739.30		84
315.74	odd	6		945.2.r.b.424.13		84
315.214	even	6	inner	315.2.r.b.214.30	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.13	✓	84	1.1	even	1	trivial
315.2.r.b.184.30	yes	84	5.4	even	2	inner
315.2.r.b.214.13	yes	84	63.25	even	3	inner
315.2.r.b.214.30	yes	84	315.214	even	6	inner
315.2.bo.b.4.13	yes	84	35.4	even	6
315.2.bo.b.4.30	yes	84	7.4	even	3
315.2.bo.b.79.13	yes	84	9.7	even	3
315.2.bo.b.79.30	yes	84	45.34	even	6
945.2.r.b.424.13		84	315.74	odd	6
945.2.r.b.424.30		84	63.11	odd	6
945.2.r.b.604.13		84	15.14	odd	2
945.2.r.b.604.30		84	3.2	odd	2
945.2.bo.b.289.13		84	45.29	odd	6
945.2.bo.b.289.30		84	9.2	odd	6
945.2.bo.b.739.13		84	21.11	odd	6
945.2.bo.b.739.30		84	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.36154i q^{2} +(1.72744 - 0.126307i) q^{3} +0.146205 q^{4} +(1.24734 + 1.85584i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(-1.93746 + 1.80173i) q^{7} -2.92215i q^{8} +(2.96809 - 0.436376i) q^{9} +O(q^{10})\)	\(q-1.36154i q^{2} +(1.72744 - 0.126307i) q^{3} +0.146205 q^{4} +(1.24734 + 1.85584i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(-1.93746 + 1.80173i) q^{7} -2.92215i q^{8} +(2.96809 - 0.436376i) q^{9} +(2.52681 - 1.69830i) q^{10} +(-0.310611 + 0.537993i) q^{11} +(0.252560 - 0.0184667i) q^{12} +(-2.17808 - 1.25751i) q^{13} +(2.45313 + 2.63794i) q^{14} +(2.38911 + 3.04831i) q^{15} -3.68621 q^{16} +(5.28156 - 3.04931i) q^{17} +(-0.594144 - 4.04118i) q^{18} +(-0.100966 + 0.174878i) q^{19} +(0.182367 + 0.271333i) q^{20} +(-3.11928 + 3.35710i) q^{21} +(0.732500 + 0.422909i) q^{22} +(-3.46827 + 2.00240i) q^{23} +(-0.369088 - 5.04783i) q^{24} +(-1.88830 + 4.62972i) q^{25} +(-1.71216 + 2.96554i) q^{26} +(5.07208 - 1.12870i) q^{27} +(-0.283266 + 0.263422i) q^{28} +(-0.297732 - 0.515687i) q^{29} +(4.15040 - 3.25287i) q^{30} -7.03102 q^{31} -0.825359i q^{32} +(-0.468609 + 0.968583i) q^{33} +(-4.15176 - 7.19106i) q^{34} +(-5.76040 - 1.34826i) q^{35} +(0.433949 - 0.0638003i) q^{36} +(-5.67340 - 3.27554i) q^{37} +(0.238104 + 0.137469i) q^{38} +(-3.92133 - 1.89717i) q^{39} +(5.42304 - 3.64490i) q^{40} +(1.68428 - 2.91726i) q^{41} +(4.57083 + 4.24703i) q^{42} +(-7.13977 + 4.12215i) q^{43} +(-0.0454127 + 0.0786572i) q^{44} +(4.51206 + 4.96400i) q^{45} +(2.72636 + 4.72219i) q^{46} +1.54251i q^{47} +(-6.36771 + 0.465596i) q^{48} +(0.507523 - 6.98158i) q^{49} +(6.30356 + 2.57100i) q^{50} +(8.73843 - 5.93460i) q^{51} +(-0.318445 - 0.183854i) q^{52} +(-2.16836 + 1.25190i) q^{53} +(-1.53678 - 6.90585i) q^{54} +(-1.38587 + 0.0946147i) q^{55} +(5.26493 + 5.66155i) q^{56} +(-0.152324 + 0.314844i) q^{57} +(-0.702130 + 0.405375i) q^{58} +13.7660 q^{59} +(0.349298 + 0.445677i) q^{60} -6.66263 q^{61} +9.57302i q^{62} +(-4.96434 + 6.19317i) q^{63} -8.49619 q^{64} +(-0.383050 - 5.61071i) q^{65} +(1.31877 + 0.638030i) q^{66} +12.8830i q^{67} +(0.772189 - 0.445824i) q^{68} +(-5.73830 + 3.89710i) q^{69} +(-1.83571 + 7.84302i) q^{70} -8.76528 q^{71} +(-1.27516 - 8.67320i) q^{72} +(1.02561 - 0.592135i) q^{73} +(-4.45978 + 7.72457i) q^{74} +(-2.67716 + 8.23607i) q^{75} +(-0.0147617 + 0.0255680i) q^{76} +(-0.367523 - 1.60198i) q^{77} +(-2.58308 + 5.33905i) q^{78} +15.6084 q^{79} +(-4.59795 - 6.84103i) q^{80} +(8.61915 - 2.59041i) q^{81} +(-3.97197 - 2.29322i) q^{82} +(-7.36846 + 4.25418i) q^{83} +(-0.456053 + 0.490824i) q^{84} +(12.2469 + 5.99823i) q^{85} +(5.61248 + 9.72109i) q^{86} +(-0.579449 - 0.853213i) q^{87} +(1.57210 + 0.907650i) q^{88} +(-1.99854 + 3.46158i) q^{89} +(6.75870 - 6.14335i) q^{90} +(6.48565 - 1.48793i) q^{91} +(-0.507077 + 0.292761i) q^{92} +(-12.1457 + 0.888068i) q^{93} +2.10019 q^{94} +(-0.450484 + 0.0307551i) q^{95} +(-0.104249 - 1.42576i) q^{96} +(0.922012 - 0.532324i) q^{97} +(-9.50571 - 0.691014i) q^{98} +(-0.687154 + 1.73236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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