LMFDB - Embedded newform 630.2.i.h.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.5
Root			$2.48293 - 0.894932i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.h.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.31625 + 1.12583i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.31625 + 1.12583i) q^{6} +(2.64400 + 0.0963576i) q^{7} +1.00000 q^{8} +(0.465015 + 2.96374i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.31625 + 1.12583i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.31625 + 1.12583i) q^{6} +(2.64400 + 0.0963576i) q^{7} +1.00000 q^{8} +(0.465015 + 2.96374i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.10401 - 1.91220i) q^{11} +(1.31625 + 1.12583i) q^{12} +(-0.313139 - 0.542372i) q^{13} +(2.64400 + 0.0963576i) q^{14} +(1.63312 - 0.576989i) q^{15} +1.00000 q^{16} +(-1.90382 + 3.29751i) q^{17} +(0.465015 + 2.96374i) q^{18} +(-3.79362 - 6.57074i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.37167 + 3.10352i) q^{21} +(-1.10401 - 1.91220i) q^{22} +(-1.30144 + 2.25415i) q^{23} +(1.31625 + 1.12583i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.313139 - 0.542372i) q^{26} +(-2.72459 + 4.42454i) q^{27} +(2.64400 + 0.0963576i) q^{28} +(-2.01339 + 3.48730i) q^{29} +(1.63312 - 0.576989i) q^{30} +7.40725 q^{31} +1.00000 q^{32} +(0.699663 - 3.75986i) q^{33} +(-1.90382 + 3.29751i) q^{34} +(1.40545 - 2.24159i) q^{35} +(0.465015 + 2.96374i) q^{36} +(-2.81483 - 4.87543i) q^{37} +(-3.79362 - 6.57074i) q^{38} +(0.198451 - 1.06644i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.09955 - 1.90448i) q^{41} +(3.37167 + 3.10352i) q^{42} +(-4.25532 + 7.37044i) q^{43} +(-1.10401 - 1.91220i) q^{44} +(2.79918 + 1.07916i) q^{45} +(-1.30144 + 2.25415i) q^{46} -0.450314 q^{47} +(1.31625 + 1.12583i) q^{48} +(6.98143 + 0.509538i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-6.21833 + 2.19696i) q^{51} +(-0.313139 - 0.542372i) q^{52} +(-1.19348 + 2.06717i) q^{53} +(-2.72459 + 4.42454i) q^{54} -2.20802 q^{55} +(2.64400 + 0.0963576i) q^{56} +(2.40419 - 12.9197i) q^{57} +(-2.01339 + 3.48730i) q^{58} -5.80323 q^{59} +(1.63312 - 0.576989i) q^{60} -0.968707 q^{61} +7.40725 q^{62} +(0.943918 + 7.88093i) q^{63} +1.00000 q^{64} -0.626277 q^{65} +(0.699663 - 3.75986i) q^{66} +4.08122 q^{67} +(-1.90382 + 3.29751i) q^{68} +(-4.25080 + 1.50183i) q^{69} +(1.40545 - 2.24159i) q^{70} +6.99225 q^{71} +(0.465015 + 2.96374i) q^{72} +(0.696424 - 1.20624i) q^{73} +(-2.81483 - 4.87543i) q^{74} +(0.316873 - 1.70282i) q^{75} +(-3.79362 - 6.57074i) q^{76} +(-2.73474 - 5.16223i) q^{77} +(0.198451 - 1.06644i) q^{78} -11.8055 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.56752 + 2.75637i) q^{81} +(-1.09955 - 1.90448i) q^{82} +(-7.35470 + 12.7387i) q^{83} +(3.37167 + 3.10352i) q^{84} +(1.90382 + 3.29751i) q^{85} +(-4.25532 + 7.37044i) q^{86} +(-6.57623 + 2.32341i) q^{87} +(-1.10401 - 1.91220i) q^{88} +(-5.98165 - 10.3605i) q^{89} +(2.79918 + 1.07916i) q^{90} +(-0.775676 - 1.46420i) q^{91} +(-1.30144 + 2.25415i) q^{92} +(9.74978 + 8.33931i) q^{93} -0.450314 q^{94} -7.58724 q^{95} +(1.31625 + 1.12583i) q^{96} +(8.36150 - 14.4825i) q^{97} +(6.98143 + 0.509538i) q^{98} +(5.15389 - 4.16120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.31625	+	1.12583i	0.759936	+	0.649998i
$3$	1.31625	+	1.12583i	0.759936	+	0.649998i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.31625	+	1.12583i	0.537356	+	0.459618i
$7$	2.64400	+	0.0963576i	0.999337	+	0.0364197i
$7$	2.64400	+	0.0963576i	0.999337	+	0.0364197i
$8$	1.00000			0.353553
$9$	0.465015	+	2.96374i	0.155005	+	0.987914i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.10401	−	1.91220i	−0.332872	−	0.576551i	0.650202	−	0.759761i	$-0.274684\pi$
$11$	−1.10401	−	1.91220i	−0.332872	−	0.576551i	−0.983074	+	0.183211i	$0.941351\pi$
$12$	1.31625	+	1.12583i	0.379968	+	0.324999i
$13$	−0.313139	−	0.542372i	−0.0868490	−	0.150427i	0.819329	−	0.573324i	$-0.194346\pi$
$13$	−0.313139	−	0.542372i	−0.0868490	−	0.150427i	−0.906178	+	0.422897i	$0.861013\pi$
$14$	2.64400	+	0.0963576i	0.706638	+	0.0257526i
$15$	1.63312	−	0.576989i	0.421670	−	0.148978i
$16$	1.00000			0.250000
$17$	−1.90382	+	3.29751i	−0.461744	+	0.799764i	−0.999048	−	0.0436247i	$-0.986109\pi$
$17$	−1.90382	+	3.29751i	−0.461744	+	0.799764i	0.537304	+	0.843389i	$0.319443\pi$
$18$	0.465015	+	2.96374i	0.109605	+	0.698560i
$19$	−3.79362	−	6.57074i	−0.870316	−	1.50743i	−0.861670	−	0.507469i	$-0.830581\pi$
$19$	−3.79362	−	6.57074i	−0.870316	−	1.50743i	−0.00864551	−	0.999963i	$-0.502752\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	3.37167	+	3.10352i	0.735759	+	0.677244i
$22$	−1.10401	−	1.91220i	−0.235376	−	0.407683i
$23$	−1.30144	+	2.25415i	−0.271368	+	0.470023i	−0.969212	−	0.246226i	$-0.920809\pi$
$23$	−1.30144	+	2.25415i	−0.271368	+	0.470023i	0.697844	+	0.716250i	$0.254143\pi$
$24$	1.31625	+	1.12583i	0.268678	+	0.229809i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.313139	−	0.542372i	−0.0614116	−	0.106368i
$27$	−2.72459	+	4.42454i	−0.524348	+	0.851504i
$28$	2.64400	+	0.0963576i	0.499668	+	0.0182099i
$29$	−2.01339	+	3.48730i	−0.373878	+	0.647575i	−0.990158	−	0.139951i	$-0.955305\pi$
$29$	−2.01339	+	3.48730i	−0.373878	+	0.647575i	0.616281	+	0.787527i	$0.288639\pi$
$30$	1.63312	−	0.576989i	0.298166	−	0.105343i
$31$	7.40725			1.33038			0.665191	−	0.746673i	$-0.268350\pi$
$31$	7.40725			1.33038			0.665191	+	0.746673i	$0.268350\pi$
$32$	1.00000			0.176777
$33$	0.699663	−	3.75986i	0.121796	−	0.654507i
$34$	−1.90382	+	3.29751i	−0.326502	+	0.565518i
$35$	1.40545	−	2.24159i	0.237564	−	0.378898i
$36$	0.465015	+	2.96374i	0.0775024	+	0.493957i
$37$	−2.81483	−	4.87543i	−0.462755	−	0.801515i	0.536342	−	0.844001i	$-0.319806\pi$
$37$	−2.81483	−	4.87543i	−0.462755	−	0.801515i	−0.999097	+	0.0424855i	$0.986472\pi$
$38$	−3.79362	−	6.57074i	−0.615406	−	1.06591i
$39$	0.198451	−	1.06644i	0.0317775	−	0.170767i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−1.09955	−	1.90448i	−0.171722	−	0.297430i	0.767300	−	0.641288i	$-0.221600\pi$
$41$	−1.09955	−	1.90448i	−0.171722	−	0.297430i	−0.939022	+	0.343858i	$0.888266\pi$
$42$	3.37167	+	3.10352i	0.520260	+	0.478884i
$43$	−4.25532	+	7.37044i	−0.648931	+	1.12398i	0.334448	+	0.942414i	$0.391450\pi$
$43$	−4.25532	+	7.37044i	−0.648931	+	1.12398i	−0.983379	+	0.181567i	$0.941883\pi$
$44$	−1.10401	−	1.91220i	−0.166436	−	0.288275i
$45$	2.79918	+	1.07916i	0.417277	+	0.160871i
$46$	−1.30144	+	2.25415i	−0.191886	+	0.332357i
$47$	−0.450314			−0.0656851			−0.0328425	−	0.999461i	$-0.510456\pi$
$47$	−0.450314			−0.0656851			−0.0328425	+	0.999461i	$0.510456\pi$
$48$	1.31625	+	1.12583i	0.189984	+	0.162500i
$49$	6.98143	+	0.509538i	0.997347	+	0.0727912i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−6.21833	+	2.19696i	−0.870741	+	0.307637i
$52$	−0.313139	−	0.542372i	−0.0434245	−	0.0752135i
$53$	−1.19348	+	2.06717i	−0.163937	+	0.283948i	−0.936277	−	0.351261i	$-0.885753\pi$
$53$	−1.19348	+	2.06717i	−0.163937	+	0.283948i	0.772340	+	0.635209i	$0.219086\pi$
$54$	−2.72459	+	4.42454i	−0.370770	+	0.602104i
$55$	−2.20802			−0.297729
$56$	2.64400	+	0.0963576i	0.353319	+	0.0128763i
$57$	2.40419	−	12.9197i	0.318443	−	1.71125i
$58$	−2.01339	+	3.48730i	−0.264371	+	0.457905i
$59$	−5.80323			−0.755516			−0.377758	−	0.925904i	$-0.623305\pi$
$59$	−5.80323			−0.755516			−0.377758	+	0.925904i	$0.623305\pi$
$60$	1.63312	−	0.576989i	0.210835	−	0.0744889i
$61$	−0.968707			−0.124030			−0.0620151	−	0.998075i	$-0.519753\pi$
$61$	−0.968707			−0.124030			−0.0620151	+	0.998075i	$0.519753\pi$
$62$	7.40725			0.940722
$63$	0.943918	+	7.88093i	0.118922	+	0.992904i
$64$	1.00000			0.125000
$65$	−0.626277			−0.0776802
$66$	0.699663	−	3.75986i	0.0861226	−	0.462807i
$67$	4.08122			0.498601			0.249300	−	0.968426i	$-0.419799\pi$
$67$	4.08122			0.498601			0.249300	+	0.968426i	$0.419799\pi$
$68$	−1.90382	+	3.29751i	−0.230872	+	0.399882i
$69$	−4.25080	+	1.50183i	−0.511737	+	0.180799i
$70$	1.40545	−	2.24159i	0.167983	−	0.267921i
$71$	6.99225			0.829828			0.414914	−	0.909861i	$-0.363812\pi$
$71$	6.99225			0.829828			0.414914	+	0.909861i	$0.363812\pi$
$72$	0.465015	+	2.96374i	0.0548025	+	0.349280i
$73$	0.696424	−	1.20624i	0.0815103	−	0.141180i	−0.822389	−	0.568926i	$-0.807359\pi$
$73$	0.696424	−	1.20624i	0.0815103	−	0.141180i	0.903899	+	0.427746i	$0.140692\pi$
$74$	−2.81483	−	4.87543i	−0.327217	−	0.566757i
$75$	0.316873	−	1.70282i	0.0365894	−	0.196625i
$76$	−3.79362	−	6.57074i	−0.435158	−	0.753716i
$77$	−2.73474	−	5.16223i	−0.311653	−	0.588291i
$78$	0.198451	−	1.06644i	0.0224701	−	0.120750i
$79$	−11.8055			−1.32822			−0.664110	−	0.747634i	$-0.731190\pi$
$79$	−11.8055			−1.32822			−0.664110	+	0.747634i	$0.731190\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.56752	+	2.75637i	−0.951947	+	0.306263i
$82$	−1.09955	−	1.90448i	−0.121425	−	0.210315i
$83$	−7.35470	+	12.7387i	−0.807283	+	1.39826i	0.107455	+	0.994210i	$0.465730\pi$
$83$	−7.35470	+	12.7387i	−0.807283	+	1.39826i	−0.914739	+	0.404046i	$0.867604\pi$
$84$	3.37167	+	3.10352i	0.367879	+	0.338622i
$85$	1.90382	+	3.29751i	0.206498	+	0.357665i
$86$	−4.25532	+	7.37044i	−0.458863	+	0.794774i
$87$	−6.57623	+	2.32341i	−0.705046	+	0.249096i
$88$	−1.10401	−	1.91220i	−0.117688	−	0.203841i
$89$	−5.98165	−	10.3605i	−0.634054	−	1.09821i	−0.986715	−	0.162462i	$-0.948056\pi$
$89$	−5.98165	−	10.3605i	−0.634054	−	1.09821i	0.352661	−	0.935751i	$-0.385277\pi$
$90$	2.79918	+	1.07916i	0.295060	+	0.113753i
$91$	−0.775676	−	1.46420i	−0.0813129	−	0.153490i
$92$	−1.30144	+	2.25415i	−0.135684	+	0.235012i
$93$	9.74978	+	8.33931i	1.01101	+	0.864746i
$94$	−0.450314			−0.0464464
$95$	−7.58724			−0.778434
$96$	1.31625	+	1.12583i	0.134339	+	0.114905i
$97$	8.36150	−	14.4825i	0.848981	−	1.47048i	−0.0331367	−	0.999451i	$-0.510550\pi$
$97$	8.36150	−	14.4825i	0.848981	−	1.47048i	0.882118	−	0.471028i	$-0.156117\pi$
$98$	6.98143	+	0.509538i	0.705231	+	0.0514711i
$99$	5.15389	−	4.16120i	0.517985	−	0.418217i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−8.02771	−	13.9044i	−0.798787	−	1.38354i	−0.920406	−	0.390963i	$-0.872142\pi$
$101$	−8.02771	−	13.9044i	−0.798787	−	1.38354i	0.121619	−	0.992577i	$-0.461191\pi$
$102$	−6.21833	+	2.19696i	−0.615707	+	0.217532i
$103$	8.17185	−	14.1541i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535393\pi$
$103$	8.17185	−	14.1541i	0.805196	−	1.39464i	0.916159	−	0.400816i	$-0.131273\pi$
$104$	−0.313139	−	0.542372i	−0.0307058	−	0.0531840i
$105$	4.37356	−	1.36819i	0.426816	−	0.133522i
$106$	−1.19348	+	2.06717i	−0.115921	+	0.200781i
$107$	1.02265	+	1.77128i	0.0988633	+	0.171236i	0.911214	−	0.411932i	$-0.135146\pi$
$107$	1.02265	+	1.77128i	0.0988633	+	0.171236i	−0.812351	+	0.583169i	$0.801813\pi$
$108$	−2.72459	+	4.42454i	−0.262174	+	0.425752i
$109$	−6.04650	+	10.4728i	−0.579150	+	1.00312i	0.416427	+	0.909169i	$0.363282\pi$
$109$	−6.04650	+	10.4728i	−0.579150	+	1.00312i	−0.995577	+	0.0939477i	$0.970051\pi$
$110$	−2.20802			−0.210527
$111$	1.78389	−	9.58629i	0.169319	−	0.909890i
$112$	2.64400	+	0.0963576i	0.249834	+	0.00910494i
$113$	−2.37424	−	4.11230i	−0.223349	−	0.386852i	0.732474	−	0.680795i	$-0.238366\pi$
$113$	−2.37424	−	4.11230i	−0.223349	−	0.386852i	−0.955823	+	0.293943i	$0.905032\pi$
$114$	2.40419	−	12.9197i	0.225173	−	1.21004i
$115$	1.30144	+	2.25415i	0.121360	+	0.210201i
$116$	−2.01339	+	3.48730i	−0.186939	+	0.323788i
$117$	1.46184	−	1.18027i	0.135147	−	0.109116i
$118$	−5.80323			−0.534231
$119$	−5.35143	+	8.53516i	−0.490565	+	0.782417i
$120$	1.63312	−	0.576989i	0.149083	−	0.0526716i
$121$	3.06232	−	5.30410i	0.278393	−	0.482191i
$122$	−0.968707			−0.0877026
$123$	0.696839	−	3.74468i	0.0628319	−	0.337647i
$124$	7.40725			0.665191
$125$	−1.00000			−0.0894427
$126$	0.943918	+	7.88093i	0.0840909	+	0.702089i
$127$	12.1160			1.07512			0.537561	−	0.843225i	$-0.319346\pi$
$127$	12.1160			1.07512			0.537561	+	0.843225i	$0.319346\pi$
$128$	1.00000			0.0883883
$129$	−13.8989	+	4.91055i	−1.22373	+	0.432350i
$130$	−0.626277			−0.0549282
$131$	9.16277	−	15.8704i	0.800555	−	1.38660i	−0.118696	−	0.992931i	$-0.537871\pi$
$131$	9.16277	−	15.8704i	0.800555	−	1.38660i	0.919251	−	0.393671i	$-0.128795\pi$
$132$	0.699663	−	3.75986i	0.0608979	−	0.327254i
$133$	−9.39717	−	17.7386i	−0.814838	−	1.53813i
$134$	4.08122			0.352564
$135$	2.46947	+	4.57184i	0.212538	+	0.393481i
$136$	−1.90382	+	3.29751i	−0.163251	+	0.282759i
$137$	6.13556	+	10.6271i	0.524196	+	0.907935i	0.999603	+	0.0281685i	$0.00896751\pi$
$137$	6.13556	+	10.6271i	0.524196	+	0.907935i	−0.475407	+	0.879766i	$0.657699\pi$
$138$	−4.25080	+	1.50183i	−0.361852	+	0.127844i
$139$	4.91134	+	8.50669i	0.416575	+	0.721528i	0.995592	−	0.0937866i	$-0.0298972\pi$
$139$	4.91134	+	8.50669i	0.416575	+	0.721528i	−0.579018	+	0.815315i	$0.696564\pi$
$140$	1.40545	−	2.24159i	0.118782	−	0.189449i
$141$	−0.592725	−	0.506977i	−0.0499164	−	0.0426952i
$142$	6.99225			0.586777
$143$	−0.691417	+	1.19757i	−0.0578192	+	0.100146i
$144$	0.465015	+	2.96374i	0.0387512	+	0.246978i
$145$	2.01339	+	3.48730i	0.167203	+	0.289604i
$146$	0.696424	−	1.20624i	0.0576365	−	0.0998293i
$147$	8.61564	+	8.53058i	0.710606	+	0.703590i
$148$	−2.81483	−	4.87543i	−0.231377	−	0.400758i
$149$	−5.53542	+	9.58762i	−0.453479	+	0.785449i	−0.998599	−	0.0529092i	$-0.983151\pi$
$149$	−5.53542	+	9.58762i	−0.453479	+	0.785449i	0.545120	+	0.838358i	$0.316484\pi$
$150$	0.316873	−	1.70282i	0.0258726	−	0.139035i
$151$	9.45819	+	16.3821i	0.769696	+	1.33315i	0.937728	+	0.347371i	$0.112926\pi$
$151$	9.45819	+	16.3821i	0.769696	+	1.33315i	−0.168031	+	0.985782i	$0.553741\pi$
$152$	−3.79362	−	6.57074i	−0.307703	−	0.532957i
$153$	−10.6583	−	4.10904i	−0.861670	−	0.332196i
$154$	−2.73474	−	5.16223i	−0.220372	−	0.415985i
$155$	3.70363	−	6.41487i	0.297482	−	0.515255i
$156$	0.198451	−	1.06644i	0.0158888	−	0.0853833i
$157$	−1.34745			−0.107538			−0.0537690	−	0.998553i	$-0.517123\pi$
$157$	−1.34745			−0.107538			−0.0537690	+	0.998553i	$0.517123\pi$
$158$	−11.8055			−0.939194
$159$	−3.89820	+	1.37725i	−0.309147	+	0.109223i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.65820	+	5.83457i	−0.288306	+	0.459828i
$162$	−8.56752	+	2.75637i	−0.673128	+	0.216561i
$163$	−2.55506	−	4.42550i	−0.200128	−	0.346632i	0.748442	−	0.663201i	$-0.230802\pi$
$163$	−2.55506	−	4.42550i	−0.200128	−	0.346632i	−0.948569	+	0.316569i	$0.897469\pi$
$164$	−1.09955	−	1.90448i	−0.0858608	−	0.148715i
$165$	−2.90630	−	2.48586i	−0.226255	−	0.193524i
$166$	−7.35470	+	12.7387i	−0.570836	+	0.988716i
$167$	−1.34245	−	2.32520i	−0.103882	−	0.179929i	0.809399	−	0.587259i	$-0.199793\pi$
$167$	−1.34245	−	2.32520i	−0.103882	−	0.179929i	−0.913281	+	0.407330i	$0.866460\pi$
$168$	3.37167	+	3.10352i	0.260130	+	0.239442i
$169$	6.30389	−	10.9187i	0.484914	−	0.839897i
$170$	1.90382	+	3.29751i	0.146016	+	0.252908i
$171$	17.7099	−	14.2988i	1.35431	−	1.09346i
$172$	−4.25532	+	7.37044i	−0.324465	+	0.561990i
$173$	−16.7364			−1.27245			−0.636224	−	0.771505i	$-0.719504\pi$
$173$	−16.7364			−1.27245			−0.636224	+	0.771505i	$0.719504\pi$
$174$	−6.57623	+	2.32341i	−0.498543	+	0.176137i
$175$	−1.23855	−	2.33795i	−0.0936256	−	0.176732i
$176$	−1.10401	−	1.91220i	−0.0832179	−	0.144138i
$177$	−7.63849	−	6.53345i	−0.574144	−	0.491084i
$178$	−5.98165	−	10.3605i	−0.448344	−	0.776554i
$179$	−9.04667	+	15.6693i	−0.676180	+	1.17118i	0.299943	+	0.953957i	$0.403032\pi$
$179$	−9.04667	+	15.6693i	−0.676180	+	1.17118i	−0.976123	+	0.217221i	$0.930301\pi$
$180$	2.79918	+	1.07916i	0.208639	+	0.0804355i
$181$	−17.8129			−1.32402			−0.662010	−	0.749495i	$-0.730296\pi$
$181$	−17.8129			−1.32402			−0.662010	+	0.749495i	$0.730296\pi$
$182$	−0.775676	−	1.46420i	−0.0574969	−	0.108534i
$183$	−1.27506	−	1.09060i	−0.0942550	−	0.0806194i
$184$	−1.30144	+	2.25415i	−0.0959431	+	0.166178i
$185$	−5.62966			−0.413901
$186$	9.74978	+	8.33931i	0.714889	+	0.611468i
$187$	8.40734			0.614806
$188$	−0.450314			−0.0328425
$189$	−7.63015	+	11.4359i	−0.555012	+	0.831842i
$190$	−7.58724			−0.550436
$191$	−16.2699			−1.17725			−0.588623	−	0.808408i	$-0.700330\pi$
$191$	−16.2699			−1.17725			−0.588623	+	0.808408i	$0.700330\pi$
$192$	1.31625	+	1.12583i	0.0949920	+	0.0812498i
$193$	17.3736			1.25058			0.625290	−	0.780392i	$-0.284981\pi$
$193$	17.3736			1.25058			0.625290	+	0.780392i	$0.284981\pi$
$194$	8.36150	−	14.4825i	0.600321	−	1.03979i
$195$	−0.824336	−	0.705082i	−0.0590319	−	0.0504920i
$196$	6.98143	+	0.509538i	0.498674	+	0.0363956i
$197$	13.0121			0.927075			0.463537	−	0.886077i	$-0.346580\pi$
$197$	13.0121			0.927075			0.463537	+	0.886077i	$0.346580\pi$
$198$	5.15389	−	4.16120i	0.366271	−	0.295724i
$199$	2.98948	−	5.17794i	0.211919	−	0.367054i	−0.740396	−	0.672171i	$-0.765362\pi$
$199$	2.98948	−	5.17794i	0.211919	−	0.367054i	0.952315	+	0.305116i	$0.0986954\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	5.37190	+	4.59476i	0.378905	+	0.324090i
$202$	−8.02771	−	13.9044i	−0.564828	−	0.978311i
$203$	−5.65943	+	9.02640i	−0.397214	+	0.633529i
$204$	−6.21833	+	2.19696i	−0.435370	+	0.153818i
$205$	−2.19911			−0.153592
$206$	8.17185	−	14.1541i	0.569359	−	0.986160i
$207$	−7.28591	−	2.80890i	−0.506406	−	0.195232i
$208$	−0.313139	−	0.542372i	−0.0217123	−	0.0376067i
$209$	−8.37639	+	14.5083i	−0.579407	+	1.00356i
$210$	4.37356	−	1.36819i	0.301804	−	0.0944143i
$211$	−2.58995	−	4.48592i	−0.178299	−	0.308824i	0.762999	−	0.646400i	$-0.223726\pi$
$211$	−2.58995	−	4.48592i	−0.178299	−	0.308824i	−0.941298	+	0.337576i	$0.890393\pi$
$212$	−1.19348	+	2.06717i	−0.0819687	+	0.141974i
$213$	9.20353	+	7.87209i	0.630616	+	0.539386i
$214$	1.02265	+	1.77128i	0.0699069	+	0.121082i
$215$	4.25532	+	7.37044i	0.290211	+	0.502660i
$216$	−2.72459	+	4.42454i	−0.185385	+	0.301052i
$217$	19.5848	+	0.713745i	1.32950	+	0.0484522i
$218$	−6.04650	+	10.4728i	−0.409521	+	0.709311i
$219$	2.27469	−	0.803658i	0.153709	−	0.0543062i
$220$	−2.20802			−0.148865
$221$	2.38464			0.160408
$222$	1.78389	−	9.58629i	0.119727	−	0.643389i
$223$	−1.09620	+	1.89867i	−0.0734070	+	0.127145i	−0.900392	−	0.435079i	$-0.856721\pi$
$223$	−1.09620	+	1.89867i	−0.0734070	+	0.127145i	0.826985	+	0.562223i	$0.190054\pi$
$224$	2.64400	+	0.0963576i	0.176659	+	0.00643816i
$225$	2.33417	−	1.88459i	0.155611	−	0.125639i
$226$	−2.37424	−	4.11230i	−0.157932	−	0.273546i
$227$	5.29711	+	9.17486i	0.351581	+	0.608957i	0.986527	−	0.163600i	$-0.0523108\pi$
$227$	5.29711	+	9.17486i	0.351581	+	0.608957i	−0.634945	+	0.772557i	$0.718977\pi$
$228$	2.40419	−	12.9197i	0.159222	−	0.855627i
$229$	−9.68011	+	16.7664i	−0.639680	+	1.10796i	0.345823	+	0.938300i	$0.387600\pi$
$229$	−9.68011	+	16.7664i	−0.639680	+	1.10796i	−0.985503	+	0.169658i	$0.945734\pi$
$230$	1.30144	+	2.25415i	0.0858141	+	0.148634i
$231$	2.21220	−	9.87363i	0.145552	−	0.649637i
$232$	−2.01339	+	3.48730i	−0.132186	+	0.228952i
$233$	8.59587	+	14.8885i	0.563134	+	0.975377i	0.997221	+	0.0745060i	$0.0237380\pi$
$233$	8.59587	+	14.8885i	0.563134	+	0.975377i	−0.434086	+	0.900871i	$0.642929\pi$
$234$	1.46184	−	1.18027i	0.0955632	−	0.0771569i
$235$	−0.225157	+	0.389983i	−0.0146876	+	0.0254397i
$236$	−5.80323			−0.377758
$237$	−15.5389	−	13.2910i	−1.00936	−	0.863341i
$238$	−5.35143	+	8.53516i	−0.346882	+	0.553252i
$239$	6.64536	+	11.5101i	0.429853	+	0.744526i	0.996860	−	0.0791863i	$-0.0252322\pi$
$239$	6.64536	+	11.5101i	0.429853	+	0.744526i	−0.567007	+	0.823713i	$0.691899\pi$
$240$	1.63312	−	0.576989i	0.105418	−	0.0372445i
$241$	5.78153	+	10.0139i	0.372421	+	0.645052i	0.989937	−	0.141506i	$-0.0451945\pi$
$241$	5.78153	+	10.0139i	0.372421	+	0.645052i	−0.617517	+	0.786558i	$0.711861\pi$
$242$	3.06232	−	5.30410i	0.196854	−	0.340960i
$243$	−14.3802	−	6.01751i	−0.922489	−	0.386024i
$244$	−0.968707			−0.0620151
$245$	3.93199	−	5.79133i	0.251206	−	0.369994i
$246$	0.696839	−	3.74468i	0.0444288	−	0.238752i
$247$	−2.37586	+	4.11511i	−0.151172	+	0.261838i
$248$	7.40725			0.470361
$249$	−24.0222	+	8.48716i	−1.52235	+	0.537852i
$250$	−1.00000			−0.0632456
$251$	14.9534			0.943853			0.471927	−	0.881638i	$-0.343559\pi$
$251$	14.9534			0.943853			0.471927	+	0.881638i	$0.343559\pi$
$252$	0.943918	+	7.88093i	0.0594612	+	0.496452i
$253$	5.74719			0.361323
$254$	12.1160			0.760226
$255$	−1.20654	+	6.48372i	−0.0755564	+	0.406026i
$256$	1.00000			0.0625000
$257$	14.3276	−	24.8161i	0.893730	−	1.54799i	0.0583607	−	0.998296i	$-0.481413\pi$
$257$	14.3276	−	24.8161i	0.893730	−	1.54799i	0.835369	−	0.549690i	$-0.185254\pi$
$258$	−13.8989	+	4.91055i	−0.865309	+	0.305717i
$259$	−6.97261	−	13.1618i	−0.433257	−	0.817837i
$260$	−0.626277			−0.0388401
$261$	−11.2717	−	4.34553i	−0.697701	−	0.268982i
$262$	9.16277	−	15.8704i	0.566078	−	0.980476i
$263$	6.34216	+	10.9849i	0.391074	+	0.677361i	0.992592	−	0.121499i	$-0.0387702\pi$
$263$	6.34216	+	10.9849i	0.391074	+	0.677361i	−0.601517	+	0.798860i	$0.705437\pi$
$264$	0.699663	−	3.75986i	0.0430613	−	0.231403i
$265$	1.19348	+	2.06717i	0.0733150	+	0.126985i
$266$	−9.39717	−	17.7386i	−0.576178	−	1.08762i
$267$	3.79085	−	20.3713i	0.231996	−	1.24671i
$268$	4.08122			0.249300
$269$	−1.54280	+	2.67221i	−0.0940663	+	0.162928i	−0.909219	−	0.416319i	$-0.863320\pi$
$269$	−1.54280	+	2.67221i	−0.0940663	+	0.162928i	0.815152	+	0.579247i	$0.196653\pi$
$270$	2.46947	+	4.57184i	0.150287	+	0.278233i
$271$	13.5801	+	23.5215i	0.824935	+	1.42883i	0.901969	+	0.431801i	$0.142122\pi$
$271$	13.5801	+	23.5215i	0.824935	+	1.42883i	−0.0770338	+	0.997028i	$0.524545\pi$
$272$	−1.90382	+	3.29751i	−0.115436	+	0.199941i
$273$	0.627462	−	2.80053i	0.0379757	−	0.169496i
$274$	6.13556	+	10.6271i	0.370663	+	0.642007i
$275$	−1.10401	+	1.91220i	−0.0665743	+	0.115310i
$276$	−4.25080	+	1.50183i	−0.255868	+	0.0903994i
$277$	−6.41057	−	11.1034i	−0.385174	−	0.667141i	0.606619	−	0.794992i	$-0.292525\pi$
$277$	−6.41057	−	11.1034i	−0.385174	−	0.667141i	−0.991793	+	0.127852i	$0.959192\pi$
$278$	4.91134	+	8.50669i	0.294563	+	0.510198i
$279$	3.44448	+	21.9532i	0.206216	+	1.31430i
$280$	1.40545	−	2.24159i	0.0839915	−	0.133961i
$281$	−0.726984	+	1.25917i	−0.0433682	+	0.0751160i	−0.886895	−	0.461972i	$-0.847142\pi$
$281$	−0.726984	+	1.25917i	−0.0433682	+	0.0751160i	0.843526	+	0.537088i	$0.180476\pi$
$282$	−0.592725	−	0.506977i	−0.0352962	−	0.0301900i
$283$	23.4011			1.39105			0.695526	−	0.718500i	$-0.255171\pi$
$283$	23.4011			1.39105			0.695526	+	0.718500i	$0.255171\pi$
$284$	6.99225			0.414914
$285$	−9.98668	−	8.54194i	−0.591560	−	0.505981i
$286$	−0.691417	+	1.19757i	−0.0408843	+	0.0708137i
$287$	−2.72371	−	5.14140i	−0.160775	−	0.303487i
$288$	0.465015	+	2.96374i	0.0274013	+	0.174640i
$289$	1.25095	+	2.16671i	0.0735852	+	0.127453i
$290$	2.01339	+	3.48730i	0.118231	+	0.204781i
$291$	27.3107	−	9.64898i	1.60098	−	0.565633i
$292$	0.696424	−	1.20624i	0.0407551	−	0.0705900i
$293$	−6.19081	−	10.7228i	−0.361671	−	0.626432i	0.626565	−	0.779369i	$-0.284460\pi$
$293$	−6.19081	−	10.7228i	−0.361671	−	0.626432i	−0.988236	+	0.152937i	$0.951127\pi$
$294$	8.61564	+	8.53058i	0.502474	+	0.497514i
$295$	−2.90162	+	5.02575i	−0.168939	+	0.292610i
$296$	−2.81483	−	4.87543i	−0.163609	−	0.283378i
$297$	11.4686	+	0.325231i	0.665476	+	0.0188718i
$298$	−5.53542	+	9.58762i	−0.320658	+	0.555396i
$299$	1.63012			0.0942723
$300$	0.316873	−	1.70282i	0.0182947	−	0.0983123i
$301$	−11.9613	+	19.0774i	−0.689435	+	1.09960i
$302$	9.45819	+	16.3821i	0.544257	+	0.942682i
$303$	5.08754	−	27.3395i	0.292271	−	1.57061i
$304$	−3.79362	−	6.57074i	−0.217579	−	0.376858i
$305$	−0.484354	+	0.838925i	−0.0277340	+	0.0480367i
$306$	−10.6583	−	4.10904i	−0.609293	−	0.234898i
$307$	27.4455			1.56640			0.783198	−	0.621773i	$-0.213587\pi$
$307$	27.4455			1.56640			0.783198	+	0.621773i	$0.213587\pi$
$308$	−2.73474	−	5.16223i	−0.155826	−	0.294146i
$309$	26.6912	−	9.43013i	1.51841	−	0.536461i
$310$	3.70363	−	6.41487i	0.210352	−	0.364340i
$311$	−16.3497			−0.927106			−0.463553	−	0.886069i	$-0.653426\pi$
$311$	−16.3497			−0.927106			−0.463553	+	0.886069i	$0.653426\pi$
$312$	0.198451	−	1.06644i	0.0112351	−	0.0603751i
$313$	−25.7281			−1.45424			−0.727118	−	0.686512i	$-0.759141\pi$
$313$	−25.7281			−1.45424			−0.727118	+	0.686512i	$0.759141\pi$
$314$	−1.34745			−0.0760409
$315$	7.29704	+	3.12301i	0.411142	+	0.175962i
$316$	−11.8055			−0.664110
$317$	7.02412			0.394514			0.197257	−	0.980352i	$-0.436797\pi$
$317$	7.02412			0.394514			0.197257	+	0.980352i	$0.436797\pi$
$318$	−3.89820	+	1.37725i	−0.218600	+	0.0772324i
$319$	8.89123			0.497813
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−0.648101	+	3.48277i	−0.0361735	+	0.194389i
$322$	−3.65820	+	5.83457i	−0.203863	+	0.325148i
$323$	28.8894			1.60745
$324$	−8.56752	+	2.75637i	−0.475973	+	0.153131i
$325$	−0.313139	+	0.542372i	−0.0173698	+	0.0300854i
$326$	−2.55506	−	4.42550i	−0.141512	−	0.245106i
$327$	−19.7493	+	6.97753i	−1.09214	+	0.385858i
$328$	−1.09955	−	1.90448i	−0.0607127	−	0.105158i
$329$	−1.19063	−	0.0433912i	−0.0656415	−	0.00239223i
$330$	−2.90630	−	2.48586i	−0.159987	−	0.136842i
$331$	9.29823			0.511077			0.255538	−	0.966799i	$-0.417747\pi$
$331$	9.29823			0.511077			0.255538	+	0.966799i	$0.417747\pi$
$332$	−7.35470	+	12.7387i	−0.403642	+	0.699128i
$333$	13.1406	−	10.6096i	0.720099	−	0.581401i
$334$	−1.34245	−	2.32520i	−0.0734558	−	0.127229i
$335$	2.04061	−	3.53444i	0.111491	−	0.193107i
$336$	3.37167	+	3.10352i	0.183940	+	0.169311i
$337$	7.25900	+	12.5730i	0.395423	+	0.684893i	0.993155	−	0.116803i	$-0.0372647\pi$
$337$	7.25900	+	12.5730i	0.395423	+	0.684893i	−0.597732	+	0.801696i	$0.703931\pi$
$338$	6.30389	−	10.9187i	0.342886	−	0.593897i
$339$	1.50466	−	8.08578i	0.0817221	−	0.439159i
$340$	1.90382	+	3.29751i	0.103249	+	0.178833i
$341$	−8.17769	−	14.1642i	−0.442846	−	0.767033i
$342$	17.7099	−	14.2988i	0.957641	−	0.773190i
$343$	18.4098	+	2.01993i	0.994035	+	0.109066i
$344$	−4.25532	+	7.37044i	−0.229432	+	0.397387i
$345$	−0.824781	+	4.43222i	−0.0444047	+	0.238623i
$346$	−16.7364			−0.899756
$347$	26.2847			1.41104			0.705518	−	0.708692i	$-0.250714\pi$
$347$	26.2847			1.41104			0.705518	+	0.708692i	$0.250714\pi$
$348$	−6.57623	+	2.32341i	−0.352523	+	0.124548i
$349$	6.06179	−	10.4993i	0.324480	−	0.562016i	−0.656927	−	0.753954i	$-0.728144\pi$
$349$	6.06179	−	10.4993i	0.324480	−	0.562016i	0.981407	+	0.191938i	$0.0614774\pi$
$350$	−1.23855	−	2.33795i	−0.0662033	−	0.124969i
$351$	3.25293	+	0.0922477i	0.173628	+	0.00492382i
$352$	−1.10401	−	1.91220i	−0.0588439	−	0.101921i
$353$	9.39893	+	16.2794i	0.500255	+	0.866466i	1.00000		0.000294070i	$9.36053e-5\pi$
$353$	9.39893	+	16.2794i	0.500255	+	0.866466i	−0.499745	+	0.866172i	$0.666573\pi$
$354$	−7.63849	−	6.53345i	−0.405981	−	0.347249i
$355$	3.49613	−	6.05547i	0.185555	−	0.321391i
$356$	−5.98165	−	10.3605i	−0.317027	−	0.549107i
$357$	−16.6529	+	5.20958i	−0.881367	+	0.275720i
$358$	−9.04667	+	15.6693i	−0.478131	+	0.828148i
$359$	3.01200	+	5.21694i	0.158967	+	0.275340i	0.934497	−	0.355972i	$-0.115850\pi$
$359$	3.01200	+	5.21694i	0.158967	+	0.275340i	−0.775529	+	0.631312i	$0.782517\pi$
$360$	2.79918	+	1.07916i	0.147530	+	0.0568765i
$361$	−19.2831	+	33.3993i	−1.01490	+	1.75786i
$362$	−17.8129			−0.936224
$363$	10.0023	−	3.53385i	0.524984	−	0.185479i
$364$	−0.775676	−	1.46420i	−0.0406565	−	0.0767451i
$365$	−0.696424	−	1.20624i	−0.0364525	−	0.0631376i
$366$	−1.27506	−	1.09060i	−0.0666484	−	0.0570066i
$367$	3.08373	+	5.34118i	0.160969	+	0.278807i	0.935217	−	0.354076i	$-0.115205\pi$
$367$	3.08373	+	5.34118i	0.160969	+	0.278807i	−0.774247	+	0.632883i	$0.781871\pi$
$368$	−1.30144	+	2.25415i	−0.0678420	+	0.117506i
$369$	5.13309	−	4.14441i	0.267218	−	0.215749i
$370$	−5.62966			−0.292672
$371$	−3.35475	+	5.35059i	−0.174170	+	0.277789i
$372$	9.74978	+	8.33931i	0.505503	+	0.432373i
$373$	7.70539	−	13.3461i	0.398970	−	0.691036i	−0.594629	−	0.804000i	$-0.702701\pi$
$373$	7.70539	−	13.3461i	0.398970	−	0.691036i	0.993599	+	0.112964i	$0.0360345\pi$
$374$	8.40734			0.434733
$375$	−1.31625	−	1.12583i	−0.0679707	−	0.0581376i
$376$	−0.450314			−0.0232232
$377$	2.52188			0.129884
$378$	−7.63015	+	11.4359i	−0.392453	+	0.588201i
$379$	−17.4280			−0.895217			−0.447608	−	0.894230i	$-0.647724\pi$
$379$	−17.4280			−0.895217			−0.447608	+	0.894230i	$0.647724\pi$
$380$	−7.58724			−0.389217
$381$	15.9477	+	13.6406i	0.817024	+	0.698827i
$382$	−16.2699			−0.832438
$383$	13.7024	−	23.7333i	0.700162	−	1.21272i	−0.268248	−	0.963350i	$-0.586445\pi$
$383$	13.7024	−	23.7333i	0.700162	−	1.21272i	0.968409	−	0.249365i	$-0.0802220\pi$
$384$	1.31625	+	1.12583i	0.0671695	+	0.0574523i
$385$	−5.83800	−	0.212760i	−0.297532	−	0.0108432i
$386$	17.3736			0.884294
$387$	−23.8228	−	9.18431i	−1.21098	−	0.466865i
$388$	8.36150	−	14.4825i	0.424491	−	0.735240i
$389$	0.458225	+	0.793669i	0.0232329	+	0.0402406i	0.877408	−	0.479745i	$-0.159271\pi$
$389$	0.458225	+	0.793669i	0.0232329	+	0.0402406i	−0.854175	+	0.519985i	$0.825937\pi$
$390$	−0.824336	−	0.705082i	−0.0417419	−	0.0357032i
$391$	−4.95540	−	8.58300i	−0.250605	−	0.434061i
$392$	6.98143	+	0.509538i	0.352615	+	0.0257356i
$393$	29.9278	−	10.5736i	1.50966	−	0.533369i
$394$	13.0121			0.655541
$395$	−5.90274	+	10.2239i	−0.296999	+	0.514418i
$396$	5.15389	−	4.16120i	0.258993	−	0.209108i
$397$	0.748527	+	1.29649i	0.0375675	+	0.0650688i	0.884198	−	0.467113i	$-0.154706\pi$
$397$	0.748527	+	1.29649i	0.0375675	+	0.0650688i	−0.846630	+	0.532181i	$0.821372\pi$
$398$	2.98948	−	5.17794i	0.149849	−	0.259547i
$399$	7.60159	−	33.9279i	0.380555	−	1.69852i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	17.7157	−	30.6844i	0.884678	−	1.53231i	0.0385961	−	0.999255i	$-0.487711\pi$
$401$	17.7157	−	30.6844i	0.884678	−	1.53231i	0.846082	−	0.533053i	$-0.178955\pi$
$402$	5.37190	+	4.59476i	0.267926	+	0.229166i
$403$	−2.31950	−	4.01749i	−0.115542	−	0.200125i
$404$	−8.02771	−	13.9044i	−0.399394	−	0.691770i
$405$	−1.89668	+	8.79788i	−0.0942467	+	0.437170i
$406$	−5.65943	+	9.02640i	−0.280873	+	0.447973i
$407$	−6.21520	+	10.7650i	−0.308076	+	0.533603i
$408$	−6.21833	+	2.19696i	−0.307853	+	0.108766i
$409$	−19.1602			−0.947410			−0.473705	−	0.880684i	$-0.657084\pi$
$409$	−19.1602			−0.947410			−0.473705	+	0.880684i	$0.657084\pi$
$410$	−2.19911			−0.108606
$411$	−3.88839	+	20.8955i	−0.191800	+	1.03070i
$412$	8.17185	−	14.1541i	0.402598	−	0.697320i
$413$	−15.3437	−	0.559185i	−0.755015	−	0.0275157i
$414$	−7.28591	−	2.80890i	−0.358083	−	0.138050i
$415$	7.35470	+	12.7387i	0.361028	+	0.625319i
$416$	−0.313139	−	0.542372i	−0.0153529	−	0.0265920i
$417$	−3.11255	+	16.7262i	−0.152422	+	0.819088i
$418$	−8.37639	+	14.5083i	−0.409703	+	0.709626i
$419$	20.0164	+	34.6694i	0.977864	+	1.69371i	0.670142	+	0.742233i	$0.266233\pi$
$419$	20.0164	+	34.6694i	0.977864	+	1.69371i	0.307722	+	0.951476i	$0.400433\pi$
$420$	4.37356	−	1.36819i	0.213408	−	0.0667610i
$421$	−16.9666	+	29.3870i	−0.826900	+	1.43223i	0.0735583	+	0.997291i	$0.476565\pi$
$421$	−16.9666	+	29.3870i	−0.826900	+	1.43223i	−0.900458	+	0.434942i	$0.856769\pi$
$422$	−2.58995	−	4.48592i	−0.126077	−	0.218371i
$423$	−0.209403	−	1.33461i	−0.0101815	−	0.0648912i
$424$	−1.19348	+	2.06717i	−0.0579606	+	0.100391i
$425$	3.80764			0.184698
$426$	9.20353	+	7.87209i	0.445913	+	0.381404i
$427$	−2.56126	−	0.0933423i	−0.123948	−	0.00451715i
$428$	1.02265	+	1.77128i	0.0494316	+	0.0856181i
$429$	−2.25833	+	0.797879i	−0.109033	+	0.0385220i
$430$	4.25532	+	7.37044i	0.205210	+	0.355434i
$431$	−14.7886	+	25.6145i	−0.712340	+	1.23381i	0.251637	+	0.967822i	$0.419031\pi$
$431$	−14.7886	+	25.6145i	−0.712340	+	1.23381i	−0.963977	+	0.265987i	$0.914302\pi$
$432$	−2.72459	+	4.42454i	−0.131087	+	0.212876i
$433$	−23.5420			−1.13136			−0.565678	−	0.824627i	$-0.691385\pi$
$433$	−23.5420			−1.13136			−0.565678	+	0.824627i	$0.691385\pi$
$434$	19.5848	+	0.713745i	0.940098	+	0.0342609i
$435$	−1.27598	+	6.85689i	−0.0611786	+	0.328763i
$436$	−6.04650	+	10.4728i	−0.289575	+	0.501558i
$437$	19.7486			0.944704
$438$	2.27469	−	0.803658i	0.108689	−	0.0384003i
$439$	19.7911			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$439$	19.7911			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$440$	−2.20802			−0.105263
$441$	1.73633	+	20.9281i	0.0826823	+	0.996576i
$442$	2.38464			0.113426
$443$	16.8478			0.800463			0.400232	−	0.916414i	$-0.368930\pi$
$443$	16.8478			0.800463			0.400232	+	0.916414i	$0.368930\pi$
$444$	1.78389	−	9.58629i	0.0846596	−	0.454945i
$445$	−11.9633			−0.567115
$446$	−1.09620	+	1.89867i	−0.0519066	+	0.0899048i
$447$	−18.0800	+	6.38775i	−0.855155	+	0.302130i
$448$	2.64400	+	0.0963576i	0.124917	+	0.00455247i
$449$	14.7590			0.696520			0.348260	−	0.937398i	$-0.386773\pi$
$449$	14.7590			0.696520			0.348260	+	0.937398i	$0.386773\pi$
$450$	2.33417	−	1.88459i	0.110034	−	0.0888402i
$451$	−2.42784	+	4.20514i	−0.114322	+	0.198012i
$452$	−2.37424	−	4.11230i	−0.111675	−	0.193426i
$453$	−5.99410	+	32.2112i	−0.281627	+	1.51341i
$454$	5.29711	+	9.17486i	0.248605	+	0.430597i
$455$	−1.65587	−	0.0603466i	−0.0776286	−	0.00282909i
$456$	2.40419	−	12.9197i	0.112587	−	0.605020i
$457$	−38.4372			−1.79801			−0.899007	−	0.437934i	$-0.855710\pi$
$457$	−38.4372			−1.79801			−0.899007	+	0.437934i	$0.855710\pi$
$458$	−9.68011	+	16.7664i	−0.452322	+	0.783444i
$459$	−9.40285	−	17.4079i	−0.438887	−	0.812531i
$460$	1.30144	+	2.25415i	0.0606798	+	0.105100i
$461$	13.2005	−	22.8639i	0.614808	−	1.06488i	−0.375610	−	0.926778i	$-0.622567\pi$
$461$	13.2005	−	22.8639i	0.614808	−	1.06488i	0.990418	−	0.138102i	$-0.0441000\pi$
$462$	2.21220	−	9.87363i	0.102921	−	0.459363i
$463$	−10.8568	−	18.8046i	−0.504560	−	0.873923i	−0.999986	−	0.00527304i	$-0.998322\pi$
$463$	−10.8568	−	18.8046i	−0.504560	−	0.873923i	0.495426	−	0.868650i	$-0.335012\pi$
$464$	−2.01339	+	3.48730i	−0.0934694	+	0.161894i
$465$	12.0969	−	4.27390i	0.560982	−	0.198198i
$466$	8.59587	+	14.8885i	0.398196	+	0.689696i
$467$	10.6164	+	18.3882i	0.491269	+	0.850903i	0.999949	−	0.0100521i	$-0.00319975\pi$
$467$	10.6164	+	18.3882i	0.491269	+	0.850903i	−0.508680	+	0.860956i	$0.669866\pi$
$468$	1.46184	−	1.18027i	0.0675734	−	0.0545581i
$469$	10.7907	+	0.393257i	0.498270	+	0.0181589i
$470$	−0.225157	+	0.389983i	−0.0103857	+	0.0179886i
$471$	−1.77357	−	1.51700i	−0.0817220	−	0.0698995i
$472$	−5.80323			−0.267115
$473$	18.7917			0.864042
$474$	−15.5389	−	13.2910i	−0.713727	−	0.610474i
$475$	−3.79362	+	6.57074i	−0.174063	+	0.301486i
$476$	−5.35143	+	8.53516i	−0.245282	+	0.391208i
$477$	−6.68155	−	2.57591i	−0.305927	−	0.117943i
$478$	6.64536	+	11.5101i	0.303952	+	0.526460i
$479$	−5.69955	−	9.87192i	−0.260419	−	0.451059i	0.705934	−	0.708278i	$-0.250527\pi$
$479$	−5.69955	−	9.87192i	−0.260419	−	0.451059i	−0.966353	+	0.257218i	$0.917194\pi$
$480$	1.63312	−	0.576989i	0.0745414	−	0.0263358i
$481$	−1.76286	+	3.05337i	−0.0803797	+	0.139222i
$482$	5.78153	+	10.0139i	0.263341	+	0.456121i
$483$	−11.3838	+	3.56123i	−0.517982	+	0.162042i
$484$	3.06232	−	5.30410i	0.139196	−	0.241095i
$485$	−8.36150	−	14.4825i	−0.379676	−	0.657618i
$486$	−14.3802	−	6.01751i	−0.652298	−	0.272960i
$487$	1.93204	−	3.34640i	0.0875493	−	0.151640i	−0.818925	−	0.573900i	$-0.805430\pi$
$487$	1.93204	−	3.34640i	0.0875493	−	0.151640i	0.906475	+	0.422260i	$0.138763\pi$
$488$	−0.968707			−0.0438513
$489$	1.61926	−	8.70161i	0.0732256	−	0.393501i
$490$	3.93199	−	5.79133i	0.177629	−	0.261625i
$491$	−19.2103	−	33.2733i	−0.866950	−	1.50160i	−0.865098	−	0.501603i	$-0.832744\pi$
$491$	−19.2103	−	33.2733i	−0.866950	−	1.50160i	−0.00185222	−	0.999998i	$-0.500590\pi$
$492$	0.696839	−	3.74468i	0.0314159	−	0.168823i
$493$	−7.66627	−	13.2784i	−0.345271	−	0.598028i
$494$	−2.37586	+	4.11511i	−0.106895	+	0.185147i
$495$	−1.02676	−	6.54400i	−0.0461495	−	0.294131i
$496$	7.40725			0.332596
$497$	18.4875	+	0.673757i	0.829277	+	0.0302221i
$498$	−24.0222	+	8.48716i	−1.07646	+	0.380319i
$499$	5.54076	−	9.59687i	0.248038	−	0.429615i	−0.714943	−	0.699183i	$-0.753547\pi$
$499$	5.54076	−	9.59687i	0.248038	−	0.429615i	0.962981	+	0.269568i	$0.0868808\pi$
$500$	−1.00000			−0.0447214
$501$	0.850776	−	4.57191i	0.0380099	−	0.204258i
$502$	14.9534			0.667405
$503$	−0.309909			−0.0138182			−0.00690909	−	0.999976i	$-0.502199\pi$
$503$	−0.309909			−0.0138182			−0.00690909	+	0.999976i	$0.502199\pi$
$504$	0.943918	+	7.88093i	0.0420454	+	0.351044i
$505$	−16.0554			−0.714457
$506$	5.74719			0.255494
$507$	20.5900	−	7.27455i	0.914435	−	0.323074i
$508$	12.1160			0.537561
$509$	17.2889	−	29.9452i	0.766317	−	1.32730i	−0.173231	−	0.984881i	$-0.555421\pi$
$509$	17.2889	−	29.9452i	0.766317	−	1.32730i	0.939548	−	0.342418i	$-0.111246\pi$
$510$	−1.20654	+	6.48372i	−0.0534265	+	0.287104i
$511$	1.95757	−	3.12219i	0.0865979	−	0.138118i
$512$	1.00000			0.0441942
$513$	39.4086	+	1.11756i	1.73993	+	0.0493417i
$514$	14.3276	−	24.8161i	0.631962	−	1.09459i
$515$	−8.17185	−	14.1541i	−0.360095	−	0.623702i
$516$	−13.8989	+	4.91055i	−0.611866	+	0.216175i
$517$	0.497151	+	0.861091i	0.0218647	+	0.0378708i
$518$	−6.97261	−	13.1618i	−0.306359	−	0.578298i
$519$	−22.0293	−	18.8424i	−0.966978	−	0.827088i
$520$	−0.626277			−0.0274641
$521$	2.53462	−	4.39009i	0.111044	−	0.192333i	−0.805148	−	0.593074i	$-0.797914\pi$
$521$	2.53462	−	4.39009i	0.111044	−	0.192333i	0.916191	+	0.400741i	$0.131247\pi$
$522$	−11.2717	−	4.34553i	−0.493349	−	0.190199i
$523$	14.4435	+	25.0168i	0.631568	+	1.09391i	0.987231	+	0.159294i	$0.0509217\pi$
$523$	14.4435	+	25.0168i	0.631568	+	1.09391i	−0.355663	+	0.934614i	$0.615745\pi$
$524$	9.16277	−	15.8704i	0.400278	−	0.693301i
$525$	1.00189	−	4.47171i	0.0437261	−	0.195162i
$526$	6.34216	+	10.9849i	0.276531	+	0.478966i
$527$	−14.1021	+	24.4255i	−0.614296	+	1.06399i
$528$	0.699663	−	3.75986i	0.0304489	−	0.163627i
$529$	8.11253	+	14.0513i	0.352719	+	0.610927i
$530$	1.19348	+	2.06717i	0.0518415	+	0.0897922i
$531$	−2.69859	−	17.1993i	−0.117109	−	0.746385i
$532$	−9.39717	−	17.7386i	−0.407419	−	0.769064i
$533$	−0.688626	+	1.19274i	−0.0298277	+	0.0516631i
$534$	3.79085	−	20.3713i	0.164046	−	0.881554i
$535$	2.04530			0.0884260
$536$	4.08122			0.176282
$537$	−29.5486	+	10.4397i	−1.27512	+	0.450504i
$538$	−1.54280	+	2.67221i	−0.0665149	+	0.115207i
$539$	−6.73323	−	13.9124i	−0.290021	−	0.599251i
$540$	2.46947	+	4.57184i	0.106269	+	0.196741i
$541$	−21.3756	−	37.0236i	−0.919008	−	1.59177i	−0.800925	−	0.598764i	$-0.795659\pi$
$541$	−21.3756	−	37.0236i	−0.919008	−	1.59177i	−0.118082	−	0.993004i	$-0.537675\pi$
$542$	13.5801	+	23.5215i	0.583317	+	1.01034i
$543$	−23.4461	−	20.0543i	−1.00617	−	0.860611i
$544$	−1.90382	+	3.29751i	−0.0816256	+	0.141380i
$545$	6.04650	+	10.4728i	0.259004	+	0.448607i
$546$	0.627462	−	2.80053i	0.0268529	−	0.119852i
$547$	−19.7066	+	34.1329i	−0.842594	+	1.45942i	0.0451006	+	0.998982i	$0.485639\pi$
$547$	−19.7066	+	34.1329i	−0.842594	+	1.45942i	−0.887694	+	0.460433i	$0.847694\pi$
$548$	6.13556	+	10.6271i	0.262098	+	0.453967i
$549$	−0.450463	−	2.87100i	−0.0192253	−	0.122531i
$550$	−1.10401	+	1.91220i	−0.0470752	+	0.0815366i
$551$	30.5522			1.30157
$552$	−4.25080	+	1.50183i	−0.180926	+	0.0639220i
$553$	−31.2137	−	1.13755i	−1.32734	−	0.0483735i
$554$	−6.41057	−	11.1034i	−0.272359	−	0.471740i
$555$	−7.41002	−	6.33804i	−0.314538	−	0.269035i
$556$	4.91134	+	8.50669i	0.208287	+	0.360764i
$557$	10.0496	−	17.4065i	0.425817	−	0.737536i	−0.570680	−	0.821173i	$-0.693320\pi$
$557$	10.0496	−	17.4065i	0.425817	−	0.737536i	0.996496	+	0.0836366i	$0.0266535\pi$
$558$	3.44448	+	21.9532i	0.145817	+	0.929352i
$559$	5.33003			0.225436
$560$	1.40545	−	2.24159i	0.0593909	−	0.0947244i
$561$	11.0661	+	9.46524i	0.467213	+	0.399623i
$562$	−0.726984	+	1.25917i	−0.0306660	+	0.0531150i
$563$	−24.8542			−1.04748			−0.523739	−	0.851879i	$-0.675463\pi$
$563$	−24.8542			−1.04748			−0.523739	+	0.851879i	$0.675463\pi$
$564$	−0.592725	−	0.506977i	−0.0249582	−	0.0213476i
$565$	−4.74847			−0.199770
$566$	23.4011			0.983623
$567$	−22.9181	+	6.46228i	−0.962469	+	0.271390i
$568$	6.99225			0.293388
$569$	18.2088			0.763351			0.381675	−	0.924296i	$-0.375347\pi$
$569$	18.2088			0.763351			0.381675	+	0.924296i	$0.375347\pi$
$570$	−9.98668	−	8.54194i	−0.418296	−	0.357782i
$571$	−26.5069			−1.10928			−0.554640	−	0.832090i	$-0.687144\pi$
$571$	−26.5069			−1.10928			−0.554640	+	0.832090i	$0.687144\pi$
$572$	−0.691417	+	1.19757i	−0.0289096	+	0.0500729i
$573$	−21.4152	−	18.3171i	−0.894631	−	0.765207i
$574$	−2.72371	−	5.14140i	−0.113685	−	0.214598i
$575$	2.60287			0.108547
$576$	0.465015	+	2.96374i	0.0193756	+	0.123489i
$577$	5.92260	−	10.2582i	0.246561	−	0.427056i	−0.716008	−	0.698092i	$-0.754033\pi$
$577$	5.92260	−	10.2582i	0.246561	−	0.427056i	0.962569	+	0.271035i	$0.0873661\pi$
$578$	1.25095	+	2.16671i	0.0520326	+	0.0901231i
$579$	22.8680	+	19.5597i	0.950361	+	0.812875i
$580$	2.01339	+	3.48730i	0.0836016	+	0.144802i
$581$	−20.6733	+	32.9724i	−0.857672	+	1.36793i
$582$	27.3107	−	9.64898i	1.13206	−	0.399963i
$583$	5.27047			0.218280
$584$	0.696424	−	1.20624i	0.0288182	−	0.0499147i
$585$	−0.291228	−	1.85612i	−0.0120408	−	0.0767413i
$586$	−6.19081	−	10.7228i	−0.255740	−	0.442955i
$587$	−15.7634	+	27.3029i	−0.650623	+	1.12691i	0.332348	+	0.943157i	$0.392159\pi$
$587$	−15.7634	+	27.3029i	−0.650623	+	1.12691i	−0.982972	+	0.183756i	$0.941174\pi$
$588$	8.61564	+	8.53058i	0.355303	+	0.351795i
$589$	−28.1003	−	48.6711i	−1.15785	−	2.00546i
$590$	−2.90162	+	5.02575i	−0.119458	+	0.206907i
$591$	17.1272	+	14.6494i	0.704517	+	0.602597i
$592$	−2.81483	−	4.87543i	−0.115689	−	0.200379i
$593$	−9.72613	−	16.8462i	−0.399404	−	0.691789i	0.594248	−	0.804282i	$-0.297450\pi$
$593$	−9.72613	−	16.8462i	−0.399404	−	0.691789i	−0.993653	+	0.112493i	$0.964116\pi$
$594$	11.4686	+	0.325231i	0.470562	+	0.0133444i
$595$	4.71595	+	8.90205i	0.193335	+	0.364949i
$596$	−5.53542	+	9.58762i	−0.226739	+	0.392724i
$597$	9.76438	−	3.44980i	0.399629	−	0.141191i
$598$	1.63012			0.0666606
$599$	−30.8759			−1.26156			−0.630778	−	0.775963i	$-0.717264\pi$
$599$	−30.8759			−1.26156			−0.630778	+	0.775963i	$0.717264\pi$
$600$	0.316873	−	1.70282i	0.0129363	−	0.0695173i
$601$	−7.08394	+	12.2698i	−0.288960	+	0.500494i	−0.973562	−	0.228424i	$-0.926643\pi$
$601$	−7.08394	+	12.2698i	−0.288960	+	0.500494i	0.684602	+	0.728917i	$0.259976\pi$
$602$	−11.9613	+	19.0774i	−0.487504	+	0.777536i
$603$	1.89783	+	12.0957i	0.0772856	+	0.492575i
$604$	9.45819	+	16.3821i	0.384848	+	0.666577i
$605$	−3.06232	−	5.30410i	−0.124501	−	0.215642i
$606$	5.08754	−	27.3395i	0.206667	−	1.11059i
$607$	−19.4242	+	33.6437i	−0.788404	+	1.36555i	0.138541	+	0.990357i	$0.455759\pi$
$607$	−19.4242	+	33.6437i	−0.788404	+	1.36555i	−0.926945	+	0.375198i	$0.877575\pi$
$608$	−3.79362	−	6.57074i	−0.153852	−	0.266479i
$609$	−17.6114	+	5.50942i	−0.713650	+	0.223253i
$610$	−0.484354	+	0.838925i	−0.0196109	+	0.0339671i
$611$	0.141011	+	0.244238i	0.00570469	+	0.00988080i
$612$	−10.6583	−	4.10904i	−0.430835	−	0.166098i
$613$	−6.13797	+	10.6313i	−0.247910	+	0.429393i	−0.962946	−	0.269695i	$-0.913077\pi$
$613$	−6.13797	+	10.6313i	−0.247910	+	0.429393i	0.715036	+	0.699088i	$0.246410\pi$
$614$	27.4455			1.10761
$615$	−2.89457	−	2.47582i	−0.116720	−	0.0998348i
$616$	−2.73474	−	5.16223i	−0.110186	−	0.207992i
$617$	−16.4450	−	28.4836i	−0.662052	−	1.14671i	−0.980075	−	0.198626i	$-0.936352\pi$
$617$	−16.4450	−	28.4836i	−0.662052	−	1.14671i	0.318023	−	0.948083i	$-0.396981\pi$
$618$	26.6912	−	9.43013i	1.07368	−	0.379335i
$619$	−7.89528	−	13.6750i	−0.317338	−	0.549645i	0.662594	−	0.748979i	$-0.269456\pi$
$619$	−7.89528	−	13.6750i	−0.317338	−	0.549645i	−0.979932	+	0.199334i	$0.936122\pi$
$620$	3.70363	−	6.41487i	0.148741	−	0.257627i
$621$	−6.42772	−	11.8999i	−0.257935	−	0.477527i
$622$	−16.3497			−0.655563
$623$	−14.8171	−	27.9696i	−0.593636	−	1.12058i
$624$	0.198451	−	1.06644i	0.00794439	−	0.0426916i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−25.7281			−1.02830
$627$	−27.3593	+	9.66616i	−1.09263	+	0.386029i
$628$	−1.34745			−0.0537690
$629$	21.4357			0.854697
$630$	7.29704	+	3.12301i	0.290721	+	0.124424i
$631$	−17.8503			−0.710609			−0.355304	−	0.934751i	$-0.615623\pi$
$631$	−17.8503			−0.710609			−0.355304	+	0.934751i	$0.615623\pi$
$632$	−11.8055			−0.469597
$633$	1.64137	−	8.82042i	0.0652387	−	0.350580i
$634$	7.02412			0.278963
$635$	6.05800	−	10.4928i	0.240405	−	0.416393i
$636$	−3.89820	+	1.37725i	−0.154574	+	0.0546116i
$637$	−1.90980	−	3.94609i	−0.0756689	−	0.156350i
$638$	8.89123			0.352007
$639$	3.25150	+	20.7232i	0.128627	+	0.819798i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−7.87123	−	13.6334i	−0.310895	−	0.538486i	0.667661	−	0.744465i	$-0.267295\pi$
$641$	−7.87123	−	13.6334i	−0.310895	−	0.538486i	−0.978556	+	0.205979i	$0.933962\pi$
$642$	−0.648101	+	3.48277i	−0.0255785	+	0.137454i
$643$	−3.38986	−	5.87141i	−0.133683	−	0.231546i	0.791411	−	0.611285i	$-0.209347\pi$
$643$	−3.38986	−	5.87141i	−0.133683	−	0.231546i	−0.925094	+	0.379739i	$0.876014\pi$
$644$	−3.65820	+	5.83457i	−0.144153	+	0.229914i
$645$	−2.69680	+	14.4921i	−0.106186	+	0.570625i
$646$	28.8894			1.13664
$647$	−12.2841	+	21.2766i	−0.482936	+	0.836470i	−0.999808	−	0.0195929i	$-0.993763\pi$
$647$	−12.2841	+	21.2766i	−0.482936	+	0.836470i	0.516872	+	0.856063i	$0.327096\pi$
$648$	−8.56752	+	2.75637i	−0.336564	+	0.108280i
$649$	6.40683	+	11.0970i	0.251490	+	0.435593i
$650$	−0.313139	+	0.542372i	−0.0122823	+	0.0212736i
$651$	24.9748	+	22.9886i	0.978841	+	0.900993i
$652$	−2.55506	−	4.42550i	−0.100064	−	0.173316i
$653$	−1.70432	+	2.95197i	−0.0666952	+	0.115520i	−0.897445	−	0.441127i	$-0.854579\pi$
$653$	−1.70432	+	2.95197i	−0.0666952	+	0.115520i	0.830749	+	0.556646i	$0.187912\pi$
$654$	−19.7493	+	6.97753i	−0.772260	+	0.272843i
$655$	−9.16277	−	15.8704i	−0.358019	−	0.620107i
$656$	−1.09955	−	1.90448i	−0.0429304	−	0.0743576i
$657$	3.89884	+	1.50310i	0.152108	+	0.0586415i
$658$	−1.19063	−	0.0433912i	−0.0464155	−	0.00169156i
$659$	4.00164	−	6.93104i	0.155882	−	0.269995i	−0.777498	−	0.628885i	$-0.783511\pi$
$659$	4.00164	−	6.93104i	0.155882	−	0.269995i	0.933380	+	0.358890i	$0.116845\pi$
$660$	−2.90630	−	2.48586i	−0.113128	−	0.0967618i
$661$	−15.7492			−0.612573			−0.306287	−	0.951939i	$-0.599087\pi$
$661$	−15.7492			−0.612573			−0.306287	+	0.951939i	$0.599087\pi$
$662$	9.29823			0.361386
$663$	3.13877	+	2.68470i	0.121900	+	0.104265i
$664$	−7.35470	+	12.7387i	−0.285418	+	0.494358i
$665$	−20.0606	−	0.731088i	−0.777918	−	0.0283504i
$666$	13.1406	−	10.6096i	0.509187	−	0.411112i
$667$	−5.24060	−	9.07699i	−0.202917	−	0.351463i
$668$	−1.34245	−	2.32520i	−0.0519411	−	0.0899646i
$669$	−3.58045	+	1.26499i	−0.138428	+	0.0489074i
$670$	2.04061	−	3.53444i	0.0788357	−	0.136547i
$671$	1.06946	+	1.85236i	0.0412862	+	0.0715097i
$672$	3.37167	+	3.10352i	0.130065	+	0.119721i
$673$	11.5505	−	20.0061i	0.445240	−	0.771178i	−0.552829	−	0.833295i	$-0.686452\pi$
$673$	11.5505	−	20.0061i	0.445240	−	0.771178i	0.998069	+	0.0621165i	$0.0197850\pi$
$674$	7.25900	+	12.5730i	0.279606	+	0.484292i
$675$	5.19406	+	0.147295i	0.199920	+	0.00566940i
$676$	6.30389	−	10.9187i	0.242457	−	0.419948i
$677$	−10.5359			−0.404927			−0.202464	−	0.979290i	$-0.564895\pi$
$677$	−10.5359			−0.404927			−0.202464	+	0.979290i	$0.564895\pi$
$678$	1.50466	−	8.08578i	0.0577863	−	0.310533i
$679$	23.5033	−	37.4861i	0.901973	−	1.43858i
$680$	1.90382	+	3.29751i	0.0730081	+	0.126454i
$681$	−3.35702	+	18.0400i	−0.128641	+	0.691295i
$682$	−8.17769	−	14.1642i	−0.313140	−	0.542374i
$683$	22.7696	−	39.4381i	0.871254	−	1.50906i	0.0105545	−	0.999944i	$-0.496640\pi$
$683$	22.7696	−	39.4381i	0.871254	−	1.50906i	0.860700	−	0.509113i	$-0.170026\pi$
$684$	17.7099	−	14.2988i	0.677154	−	0.546728i
$685$	12.2711			0.468855
$686$	18.4098	+	2.01993i	0.702889	+	0.0771213i
$687$	−31.6176	+	11.1706i	−1.20629	+	0.426186i
$688$	−4.25532	+	7.37044i	−0.162233	+	0.280995i
$689$	1.49490			0.0569512
$690$	−0.824781	+	4.43222i	−0.0313989	+	0.168732i
$691$	39.0260			1.48462			0.742309	−	0.670057i	$-0.233731\pi$
$691$	39.0260			1.48462			0.742309	+	0.670057i	$0.233731\pi$
$692$	−16.7364			−0.636224
$693$	14.0278	−	10.5056i	0.532873	−	0.399074i
$694$	26.2847			0.997753
$695$	9.82268			0.372596
$696$	−6.57623	+	2.32341i	−0.249271	+	0.0880686i
$697$	8.37341			0.317165
$698$	6.06179	−	10.4993i	0.229442	−	0.397405i
$699$	−5.44761	+	29.2744i	−0.206047	+	1.10726i
$700$	−1.23855	−	2.33795i	−0.0468128	−	0.0883661i
$701$	13.5798			0.512900			0.256450	−	0.966557i	$-0.417447\pi$
$701$	13.5798			0.512900			0.256450	+	0.966557i	$0.417447\pi$
$702$	3.25293	+	0.0922477i	0.122774	+	0.00348167i
$703$	−21.3568	+	36.9910i	−0.805486	+	1.39514i
$704$	−1.10401	−	1.91220i	−0.0416090	−	0.0720688i
$705$	−0.735417	+	0.259826i	−0.0276974	+	0.00978562i
$706$	9.39893	+	16.2794i	0.353733	+	0.612684i
$707$	−19.8854	−	37.5367i	−0.747869	−	1.41171i
$708$	−7.63849	−	6.53345i	−0.287072	−	0.245542i
$709$	−41.4414			−1.55637			−0.778183	−	0.628038i	$-0.783858\pi$
$709$	−41.4414			−1.55637			−0.778183	+	0.628038i	$0.783858\pi$
$710$	3.49613	−	6.05547i	0.131207	−	0.227258i
$711$	−5.48972	−	34.9884i	−0.205881	−	1.31217i
$712$	−5.98165	−	10.3605i	−0.224172	−	0.388277i
$713$	−9.64007	+	16.6971i	−0.361023	+	0.625311i
$714$	−16.6529	+	5.20958i	−0.623221	+	0.194964i
$715$	0.691417	+	1.19757i	0.0258575	+	0.0447865i
$716$	−9.04667	+	15.6693i	−0.338090	+	0.585589i
$717$	−4.21148	+	22.6317i	−0.157280	+	0.845196i
$718$	3.01200	+	5.21694i	0.112407	+	0.194695i
$719$	−10.6812	−	18.5004i	−0.398341	−	0.689947i	0.595180	−	0.803592i	$-0.297081\pi$
$719$	−10.6812	−	18.5004i	−0.398341	−	0.689947i	−0.993521	+	0.113645i	$0.963747\pi$
$720$	2.79918	+	1.07916i	0.104319	+	0.0402178i
$721$	22.9702	−	36.6358i	0.855454	−	1.36439i
$722$	−19.2831	+	33.3993i	−0.717642	+	1.24299i
$723$	−3.66402	+	19.6898i	−0.136267	+	0.732271i
$724$	−17.8129			−0.662010
$725$	4.02679			0.149551
$726$	10.0023	−	3.53385i	0.371220	−	0.131154i
$727$	7.94143	−	13.7550i	0.294531	−	0.510143i	−0.680344	−	0.732893i	$-0.738170\pi$
$727$	7.94143	−	13.7550i	0.294531	−	0.510143i	0.974876	+	0.222749i	$0.0715031\pi$
$728$	−0.775676	−	1.46420i	−0.0287485	−	0.0542670i
$729$	−12.1532	−	24.1102i	−0.450118	−	0.892969i
$730$	−0.696424	−	1.20624i	−0.0257758	−	0.0446450i
$731$	−16.2027	−	28.0639i	−0.599279	−	1.03798i
$732$	−1.27506	−	1.09060i	−0.0471275	−	0.0403097i
$733$	−11.3802	+	19.7111i	−0.420339	+	0.728048i	−0.995972	−	0.0896598i	$-0.971422\pi$
$733$	−11.3802	+	19.7111i	−0.420339	+	0.728048i	0.575634	+	0.817708i	$0.304755\pi$
$734$	3.08373	+	5.34118i	0.113823	+	0.197147i
$735$	11.6955	−	3.19607i	0.431396	−	0.117889i
$736$	−1.30144	+	2.25415i	−0.0479716	+	0.0830892i
$737$	−4.50571	−	7.80412i	−0.165970	−	0.287469i
$738$	5.13309	−	4.14441i	0.188952	−	0.152558i
$739$	2.16907	−	3.75695i	0.0797907	−	0.138201i	−0.823369	−	0.567507i	$-0.807908\pi$
$739$	2.16907	−	3.75695i	0.0797907	−	0.138201i	0.903160	+	0.429305i	$0.141241\pi$
$740$	−5.62966			−0.206950
$741$	−7.76013	+	2.74169i	−0.285075	+	0.100718i
$742$	−3.35475	+	5.35059i	−0.123157	+	0.196426i
$743$	8.40145	+	14.5517i	0.308219	+	0.533852i	0.977973	−	0.208732i	$-0.0669336\pi$
$743$	8.40145	+	14.5517i	0.308219	+	0.533852i	−0.669754	+	0.742583i	$0.733600\pi$
$744$	9.74978	+	8.33931i	0.357444	+	0.305734i
$745$	5.53542	+	9.58762i	0.202802	+	0.351263i
$746$	7.70539	−	13.3461i	0.282114	−	0.488636i
$747$	−41.1743	−	15.8737i	−1.50649	−	0.580790i
$748$	8.40734			0.307403
$749$	2.53320	+	4.78180i	0.0925613	+	0.174723i
$750$	−1.31625	−	1.12583i	−0.0480626	−	0.0411095i
$751$	11.2014	−	19.4014i	0.408746	−	0.707968i	−0.586004	−	0.810308i	$-0.699300\pi$
$751$	11.2014	−	19.4014i	0.408746	−	0.707968i	0.994749	+	0.102340i	$0.0326330\pi$
$752$	−0.450314			−0.0164213
$753$	19.6824	+	16.8350i	0.717268	+	0.613503i
$754$	2.52188			0.0918416
$755$	18.9164			0.688437
$756$	−7.63015	+	11.4359i	−0.277506	+	0.415921i
$757$	−9.32122			−0.338786			−0.169393	−	0.985549i	$-0.554181\pi$
$757$	−9.32122			−0.338786			−0.169393	+	0.985549i	$0.554181\pi$
$758$	−17.4280			−0.633014
$759$	7.56473	+	6.47036i	0.274582	+	0.234859i
$760$	−7.58724			−0.275218
$761$	−14.5224	+	25.1536i	−0.526438	+	0.911817i	0.473088	+	0.881015i	$0.343139\pi$
$761$	−14.5224	+	25.1536i	−0.526438	+	0.911817i	−0.999526	+	0.0308015i	$0.990194\pi$
$762$	15.9477	+	13.6406i	0.577723	+	0.494145i
$763$	−16.9961	+	27.1075i	−0.615299	+	0.981359i
$764$	−16.2699			−0.588623
$765$	−8.88766	+	7.17582i	−0.321334	+	0.259442i
$766$	13.7024	−	23.7333i	0.495089	−	0.857519i
$767$	1.81722	+	3.14751i	0.0656159	+	0.113650i
$768$	1.31625	+	1.12583i	0.0474960	+	0.0406249i
$769$	8.79286	+	15.2297i	0.317079	+	0.549196i	0.979877	−	0.199602i	$-0.0639648\pi$
$769$	8.79286	+	15.2297i	0.317079	+	0.549196i	−0.662799	+	0.748798i	$0.730631\pi$
$770$	−5.83800	−	0.212760i	−0.210387	−	0.00766732i
$771$	46.7973	−	16.5337i	1.68536	−	0.595447i
$772$	17.3736			0.625290
$773$	−12.6362	+	21.8865i	−0.454492	+	0.787202i	−0.998659	−	0.0517743i	$-0.983512\pi$
$773$	−12.6362	+	21.8865i	−0.454492	+	0.787202i	0.544167	+	0.838977i	$0.316846\pi$
$774$	−23.8228	−	9.18431i	−0.856295	−	0.330123i
$775$	−3.70363	−	6.41487i	−0.133038	−	0.230429i
$776$	8.36150	−	14.4825i	0.300160	−	0.519893i
$777$	5.64031	−	25.1742i	0.202345	−	0.903120i
$778$	0.458225	+	0.793669i	0.0164282	+	0.0284544i
$779$	−8.34258	+	14.4498i	−0.298904	+	0.517717i
$780$	−0.824336	−	0.705082i	−0.0295160	−	0.0252460i
$781$	−7.71952	−	13.3706i	−0.276226	−	0.478438i
$782$	−4.95540	−	8.58300i	−0.177205	−	0.306927i
$783$	−9.94403	−	18.4098i	−0.355371	−	0.657913i
$784$	6.98143	+	0.509538i	0.249337	+	0.0181978i
$785$	−0.673724	+	1.16692i	−0.0240462	+	0.0416493i
$786$	29.9278	−	10.5736i	1.06749	−	0.377149i
$787$	3.58955			0.127954			0.0639768	−	0.997951i	$-0.479622\pi$
$787$	3.58955			0.127954			0.0639768	+	0.997951i	$0.479622\pi$
$788$	13.0121			0.463537
$789$	−4.01932	+	21.5991i	−0.143092	+	0.768948i
$790$	−5.90274	+	10.2239i	−0.210010	+	0.363748i
$791$	−5.88122	−	11.1017i	−0.209112	−	0.394730i
$792$	5.15389	−	4.16120i	0.183136	−	0.147862i
$793$	0.303340	+	0.525400i	0.0107719	+	0.0186575i
$794$	0.748527	+	1.29649i	0.0265642	+	0.0460106i
$795$	−0.756366	+	4.06457i	−0.0268255	+	0.144155i
$796$	2.98948	−	5.17794i	0.105959	−	0.183527i
$797$	13.1208	+	22.7258i	0.464761	+	0.804990i	0.999191	−	0.0402229i	$-0.0128068\pi$
$797$	13.1208	+	22.7258i	0.464761	+	0.804990i	−0.534429	+	0.845213i	$0.679473\pi$
$798$	7.60159	−	33.9279i	0.269093	−	1.20104i
$799$	0.857316	−	1.48492i	0.0303297	−	0.0525325i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	27.9244	−	22.5459i	0.986658	−	0.796619i
$802$	17.7157	−	30.6844i	0.625562	−	1.08351i
$803$	−3.07544			−0.108530
$804$	5.37190	+	4.59476i	0.189452	+	0.162045i
$805$	3.22379	+	6.08537i	0.113624	+	0.214481i
$806$	−2.31950	−	4.01749i	−0.0817008	−	0.141510i
$807$	−5.03917	+	1.78036i	−0.177387	+	0.0626716i
$808$	−8.02771	−	13.9044i	−0.282414	−	0.489155i
$809$	−1.43999	+	2.49413i	−0.0506272	+	0.0876889i	−0.890228	−	0.455514i	$-0.849455\pi$
$809$	−1.43999	+	2.49413i	−0.0506272	+	0.0876889i	0.839601	+	0.543203i	$0.182789\pi$
$810$	−1.89668	+	8.79788i	−0.0666425	+	0.309126i
$811$	−21.9486			−0.770718			−0.385359	−	0.922767i	$-0.625922\pi$
$811$	−21.9486			−0.770718			−0.385359	+	0.922767i	$0.625922\pi$
$812$	−5.65943	+	9.02640i	−0.198607	+	0.316764i
$813$	−8.60638	+	46.2490i	−0.301839	+	1.62202i
$814$	−6.21520	+	10.7650i	−0.217843	+	0.377315i
$815$	−5.11012			−0.179000
$816$	−6.21833	+	2.19696i	−0.217685	+	0.0769091i
$817$	64.5723			2.25910
$818$	−19.1602			−0.669920
$819$	3.97882	−	2.97978i	0.139031	−	0.104122i
$820$	−2.19911			−0.0767962
$821$	−25.1037			−0.876123			−0.438062	−	0.898945i	$-0.644335\pi$
$821$	−25.1037			−0.876123			−0.438062	+	0.898945i	$0.644335\pi$
$822$	−3.88839	+	20.8955i	−0.135623	+	0.728814i
$823$	52.0715			1.81510			0.907549	−	0.419947i	$-0.137951\pi$
$823$	52.0715			1.81510			0.907549	+	0.419947i	$0.137951\pi$
$824$	8.17185	−	14.1541i	0.284680	−	0.493080i
$825$	−3.60596	+	1.27400i	−0.125544	+	0.0443551i
$826$	−15.3437	−	0.559185i	−0.533876	−	0.0194566i
$827$	−32.9641			−1.14627			−0.573137	−	0.819459i	$-0.694274\pi$
$827$	−32.9641			−1.14627			−0.573137	+	0.819459i	$0.694274\pi$
$828$	−7.28591	−	2.80890i	−0.253203	−	0.0976162i
$829$	21.1297	−	36.5978i	0.733866	−	1.27109i	−0.221353	−	0.975194i	$-0.571047\pi$
$829$	21.1297	−	36.5978i	0.733866	−	1.27109i	0.955219	−	0.295899i	$-0.0956192\pi$
$830$	7.35470	+	12.7387i	0.255285	+	0.442167i
$831$	4.06268	−	21.8321i	0.140933	−	0.757347i
$832$	−0.313139	−	0.542372i	−0.0108561	−	0.0188034i
$833$	−14.9716	+	22.0513i	−0.518735	+	0.764031i
$834$	−3.11255	+	16.7262i	−0.107779	+	0.579183i
$835$	−2.68491			−0.0929151
$836$	−8.37639	+	14.5083i	−0.289703	+	0.501781i
$837$	−20.1818	+	32.7737i	−0.697584	+	1.13283i
$838$	20.0164	+	34.6694i	0.691454	+	1.19763i
$839$	−20.4420	+	35.4066i	−0.705738	+	1.22237i	0.260687	+	0.965423i	$0.416051\pi$
$839$	−20.4420	+	35.4066i	−0.705738	+	1.22237i	−0.966425	+	0.256950i	$0.917282\pi$
$840$	4.37356	−	1.36819i	0.150902	−	0.0472071i
$841$	6.39250	+	11.0721i	0.220431	+	0.381798i
$842$	−16.9666	+	29.3870i	−0.584707	+	1.01274i
$843$	−2.37451	+	0.838924i	−0.0817824	+	0.0288941i
$844$	−2.58995	−	4.48592i	−0.0891497	−	0.154412i
$845$	−6.30389	−	10.9187i	−0.216860	−	0.375613i
$846$	−0.209403	−	1.33461i	−0.00719941	−	0.0458850i
$847$	8.60786	−	13.7289i	0.295770	−	0.471732i
$848$	−1.19348	+	2.06717i	−0.0409843	+	0.0709870i
$849$	30.8017	+	26.3457i	1.05711	+	0.904182i
$850$	3.80764			0.130601
$851$	14.6533			0.502308
$852$	9.20353	+	7.87209i	0.315308	+	0.269693i
$853$	17.5373	−	30.3754i	0.600464	−	1.04003i	−0.392287	−	0.919843i	$-0.628316\pi$
$853$	17.5373	−	30.3754i	0.600464	−	1.04003i	0.992751	−	0.120191i	$-0.0383508\pi$
$854$	−2.56126	−	0.0933423i	−0.0876445	−	0.00319411i
$855$	−3.52818	−	22.4866i	−0.120661	−	0.769026i
$856$	1.02265	+	1.77128i	0.0349534	+	0.0605411i
$857$	−14.6490	−	25.3728i	−0.500400	−	0.866719i	−1.00000		0.000462348i	$-0.999853\pi$
$857$	−14.6490	−	25.3728i	−0.500400	−	0.866719i	0.499600	−	0.866256i	$-0.333481\pi$
$858$	−2.25833	+	0.797879i	−0.0770983	+	0.0272392i
$859$	23.0323	−	39.8932i	0.785853	−	1.36114i	−0.142636	−	0.989775i	$-0.545558\pi$
$859$	23.0323	−	39.8932i	0.785853	−	1.36114i	0.928488	−	0.371362i	$-0.121109\pi$
$860$	4.25532	+	7.37044i	0.145105	+	0.251330i
$861$	2.20327	−	9.83378i	0.0750872	−	0.335134i
$862$	−14.7886	+	25.6145i	−0.503700	+	0.872434i
$863$	−26.4489	−	45.8109i	−0.900331	−	1.55942i	−0.827064	−	0.562107i	$-0.809991\pi$
$863$	−26.4489	−	45.8109i	−0.900331	−	1.55942i	−0.0732671	−	0.997312i	$-0.523343\pi$
$864$	−2.72459	+	4.42454i	−0.0926926	+	0.150526i
$865$	−8.36821	+	14.4942i	−0.284528	+	0.492817i
$866$	−23.5420			−0.799989
$867$	−0.792785	+	4.26028i	−0.0269244	+	0.144687i
$868$	19.5848	+	0.713745i	0.664750	+	0.0242261i
$869$	13.0334	+	22.5745i	0.442127	+	0.765787i
$870$	−1.27598	+	6.85689i	−0.0432598	+	0.232470i
$871$	−1.27799	−	2.21354i	−0.0433030	−	0.0750030i
$872$	−6.04650	+	10.4728i	−0.204760	+	0.354655i
$873$	46.8107	+	18.0467i	1.58430	+	0.610789i
$874$	19.7486			0.668007
$875$	−2.64400	−	0.0963576i	−0.0893834	−	0.00325748i
$876$	2.27469	−	0.803658i	0.0768546	−	0.0271531i
$877$	−5.01493	+	8.68611i	−0.169342	+	0.293309i	−0.938189	−	0.346124i	$-0.887498\pi$
$877$	−5.01493	+	8.68611i	−0.169342	+	0.293309i	0.768847	+	0.639433i	$0.220831\pi$
$878$	19.7911			0.667917
$879$	3.92341	−	21.0837i	0.132333	−	0.711134i
$880$	−2.20802			−0.0744324
$881$	−14.3989			−0.485110			−0.242555	−	0.970138i	$-0.577985\pi$
$881$	−14.3989			−0.485110			−0.242555	+	0.970138i	$0.577985\pi$
$882$	1.73633	+	20.9281i	0.0584652	+	0.704686i
$883$	−19.6842			−0.662426			−0.331213	−	0.943556i	$-0.607458\pi$
$883$	−19.6842			−0.662426			−0.331213	+	0.943556i	$0.607458\pi$
$884$	2.38464			0.0802040
$885$	−9.47738	+	3.34840i	−0.318579	+	0.112555i
$886$	16.8478			0.566013
$887$	−27.5378	+	47.6968i	−0.924628	+	1.60150i	−0.132469	+	0.991187i	$0.542291\pi$
$887$	−27.5378	+	47.6968i	−0.924628	+	1.60150i	−0.792159	+	0.610315i	$0.791043\pi$
$888$	1.78389	−	9.58629i	0.0598634	−	0.321695i
$889$	32.0347	+	1.16747i	1.07441	+	0.0391557i
$890$	−11.9633			−0.401011
$891$	14.7294	+	13.3398i	0.493452	+	0.446899i
$892$	−1.09620	+	1.89867i	−0.0367035	+	0.0635723i
$893$	1.70832	+	2.95890i	0.0571667	+	0.0990157i
$894$	−18.0800	+	6.38775i	−0.604686	+	0.213638i
$895$	9.04667	+	15.6693i	0.302397	+	0.523767i
$896$	2.64400	+	0.0963576i	0.0883297	+	0.00321908i
$897$	2.14564	+	1.83524i	0.0716409	+	0.0612768i
$898$	14.7590			0.492514
$899$	−14.9137	+	25.8313i	−0.497400	+	0.861522i
$900$	2.33417	−	1.88459i	0.0778056	−	0.0628195i
$901$	−4.54435	−	7.87104i	−0.151394	−	0.262222i
$902$	−2.42784	+	4.20514i	−0.0808382	+	0.140016i
$903$	−37.2218	+	11.6442i	−1.23867	+	0.387495i
$904$	−2.37424	−	4.11230i	−0.0789659	−	0.136773i
$905$	−8.90644	+	15.4264i	−0.296060	+	0.512791i
$906$	−5.99410	+	32.2112i	−0.199141	+	1.07014i
$907$	0.626051	+	1.08435i	0.0207877	+	0.0360053i	0.876232	−	0.481889i	$-0.160049\pi$
$907$	0.626051	+	1.08435i	0.0207877	+	0.0360053i	−0.855444	+	0.517895i	$0.826716\pi$
$908$	5.29711	+	9.17486i	0.175791	+	0.304478i
$909$	37.4761	−	30.2578i	1.24300	−	1.00359i
$910$	−1.65587	−	0.0603466i	−0.0548917	−	0.00200047i
$911$	−8.81127	+	15.2616i	−0.291930	+	0.505638i	−0.974266	−	0.225401i	$-0.927631\pi$
$911$	−8.81127	+	15.2616i	−0.291930	+	0.505638i	0.682336	+	0.731039i	$0.260964\pi$
$912$	2.40419	−	12.9197i	0.0796108	−	0.427814i
$913$	32.4787			1.07489
$914$	−38.4372			−1.27139
$915$	−1.58202	+	0.558933i	−0.0522998	+	0.0184778i
$916$	−9.68011	+	16.7664i	−0.319840	+	0.553979i
$917$	25.7556	−	41.0783i	0.850524	−	1.35653i
$918$	−9.40285	−	17.4079i	−0.310340	−	0.574547i
$919$	15.7983	+	27.3635i	0.521139	+	0.902639i	0.999698	+	0.0245836i	$0.00782600\pi$
$919$	15.7983	+	27.3635i	0.521139	+	0.902639i	−0.478559	+	0.878055i	$0.658841\pi$
$920$	1.30144	+	2.25415i	0.0429071	+	0.0743172i
$921$	36.1250	+	30.8989i	1.19036	+	1.01815i
$922$	13.2005	−	22.8639i	0.434735	−	0.752984i
$923$	−2.18954	−	3.79240i	−0.0720697	−	0.124828i
$924$	2.21220	−	9.87363i	0.0727760	−	0.324819i
$925$	−2.81483	+	4.87543i	−0.0925510	+	0.160303i
$926$	−10.8568	−	18.8046i	−0.356778	−	0.617957i
$927$	45.7490	+	17.6374i	1.50259	+	0.579288i
$928$	−2.01339	+	3.48730i	−0.0660929	+	0.114476i
$929$	26.2275			0.860495			0.430248	−	0.902711i	$-0.358426\pi$
$929$	26.2275			0.860495			0.430248	+	0.902711i	$0.358426\pi$
$930$	12.0969	−	4.27390i	0.396674	−	0.140147i
$931$	−23.1368	−	47.8062i	−0.758279	−	1.56678i
$932$	8.59587	+	14.8885i	0.281567	+	0.487689i
$933$	−21.5202	−	18.4070i	−0.704541	−	0.602617i
$934$	10.6164	+	18.3882i	0.347380	+	0.601680i
$935$	4.20367	−	7.28097i	0.137475	−	0.238113i
$936$	1.46184	−	1.18027i	0.0477816	−	0.0385784i
$937$	−10.3380			−0.337726			−0.168863	−	0.985639i	$-0.554010\pi$
$937$	−10.3380			−0.337726			−0.168863	+	0.985639i	$0.554010\pi$
$938$	10.7907	+	0.393257i	0.352330	+	0.0128403i
$939$	−33.8645	−	28.9654i	−1.10513	−	0.945251i
$940$	−0.225157	+	0.389983i	−0.00734381	+	0.0127199i
$941$	29.9320			0.975755			0.487878	−	0.872912i	$-0.337771\pi$
$941$	29.9320			0.975755			0.487878	+	0.872912i	$0.337771\pi$
$942$	−1.77357	−	1.51700i	−0.0577862	−	0.0494264i
$943$	5.72400			0.186399
$944$	−5.80323			−0.188879
$945$	6.08874	+	12.3259i	0.198067	+	0.400961i
$946$	18.7917			0.610970
$947$	36.1895			1.17600			0.588000	−	0.808861i	$-0.299916\pi$
$947$	36.1895			1.17600			0.588000	+	0.808861i	$0.299916\pi$
$948$	−15.5389	−	13.2910i	−0.504681	−	0.431671i
$949$	−0.872309			−0.0283164
$950$	−3.79362	+	6.57074i	−0.123081	+	0.213183i
$951$	9.24548	+	7.90796i	0.299805	+	0.256433i
$952$	−5.35143	+	8.53516i	−0.173441	+	0.276626i
$953$	58.6636			1.90030			0.950149	−	0.311795i	$-0.100930\pi$
$953$	58.6636			1.90030			0.950149	+	0.311795i	$0.100930\pi$
$954$	−6.68155	−	2.57591i	−0.216323	−	0.0833981i
$955$	−8.13493	+	14.0901i	−0.263240	+	0.455945i
$956$	6.64536	+	11.5101i	0.214926	+	0.372263i
$957$	11.7031	+	10.0100i	0.378306	+	0.323578i
$958$	−5.69955	−	9.87192i	−0.184144	−	0.318947i
$959$	15.1984	+	28.6892i	0.490782	+	0.926423i
$960$	1.63312	−	0.576989i	0.0527088	−	0.0186222i
$961$	23.8674			0.769917
$962$	−1.76286	+	3.05337i	−0.0568370	+	0.0984446i
$963$	−4.77407	+	3.85454i	−0.153842	+	0.124211i
$964$	5.78153	+	10.0139i	0.186210	+	0.322526i
$965$	8.68681	−	15.0460i	0.279638	−	0.484348i
$966$	−11.3838	+	3.56123i	−0.366268	+	0.114581i
$967$	2.68655	+	4.65325i	0.0863938	+	0.149638i	0.905984	−	0.423311i	$-0.139132\pi$
$967$	2.68655	+	4.65325i	0.0863938	+	0.149638i	−0.819591	+	0.572950i	$0.805799\pi$
$968$	3.06232	−	5.30410i	0.0984268	−	0.170480i
$969$	38.0257	+	32.5246i	1.22156	+	1.04484i
$970$	−8.36150	−	14.4825i	−0.268472	−	0.465006i
$971$	23.4680	+	40.6478i	0.753124	+	1.30445i	0.946302	+	0.323285i	$0.104787\pi$
$971$	23.4680	+	40.6478i	0.753124	+	1.30445i	−0.193177	+	0.981164i	$0.561879\pi$
$972$	−14.3802	−	6.01751i	−0.461244	−	0.193012i
$973$	12.1659	+	22.9649i	0.390020	+	0.736221i
$974$	1.93204	−	3.34640i	0.0619067	−	0.107226i
$975$	−1.02279	+	0.361355i	−0.0327554	+	0.0115726i
$976$	−0.968707			−0.0310076
$977$	38.2405			1.22342			0.611711	−	0.791081i	$-0.290482\pi$
$977$	38.2405			1.22342			0.611711	+	0.791081i	$0.290482\pi$
$978$	1.61926	−	8.70161i	0.0517783	−	0.278247i
$979$	−13.2076	+	22.8762i	−0.422117	+	0.731128i
$980$	3.93199	−	5.79133i	0.125603	−	0.184997i
$981$	−33.8505	−	13.0502i	−1.08076	−	0.416662i
$982$	−19.2103	−	33.2733i	−0.613026	−	1.06179i
$983$	−20.1795	−	34.9520i	−0.643627	−	1.11479i	−0.984617	−	0.174728i	$-0.944096\pi$
$983$	−20.1795	−	34.9520i	−0.643627	−	1.11479i	0.340990	−	0.940067i	$-0.389238\pi$
$984$	0.696839	−	3.74468i	0.0222144	−	0.119376i
$985$	6.50606	−	11.2688i	0.207300	−	0.359055i
$986$	−7.66627	−	13.2784i	−0.244144	−	0.422869i
$987$	−1.51831	−	1.39756i	−0.0483284	−	0.0444848i
$988$	−2.37586	+	4.11511i	−0.0755861	+	0.130919i
$989$	−11.0761	−	19.1843i	−0.352198	−	0.610025i
$990$	−1.02676	−	6.54400i	−0.0326326	−	0.207982i
$991$	24.3231	−	42.1288i	0.772648	−	1.33827i	−0.163459	−	0.986550i	$-0.552265\pi$
$991$	24.3231	−	42.1288i	0.772648	−	1.33827i	0.936107	−	0.351715i	$-0.114401\pi$
$992$	7.40725			0.235181
$993$	12.2388	+	10.4682i	0.388386	+	0.332199i
$994$	18.4875	+	0.673757i	0.586388	+	0.0213703i
$995$	−2.98948	−	5.17794i	−0.0947730	−	0.164152i
$996$	−24.0222	+	8.48716i	−0.761174	+	0.268926i
$997$	−0.650034	−	1.12589i	−0.0205868	−	0.0356573i	0.855548	−	0.517723i	$-0.173220\pi$
$997$	−0.650034	−	1.12589i	−0.0205868	−	0.0356573i	−0.876135	+	0.482065i	$0.839887\pi$
$998$	5.54076	−	9.59687i	0.175390	−	0.303784i
$999$	29.2408	+	0.829222i	0.925138	+	0.0262354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.151.5	yes	12
3.2	odd	2		1890.2.i.f.991.5		12
7.2	even	3		630.2.l.f.331.2	yes	12
9.4	even	3		630.2.l.f.571.2	yes	12
9.5	odd	6		1890.2.l.h.361.4		12
21.2	odd	6		1890.2.l.h.1801.4		12
63.23	odd	6		1890.2.i.f.1171.5		12
63.58	even	3	inner	630.2.i.h.121.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.5	✓	12	63.58	even	3	inner
630.2.i.h.151.5	yes	12	1.1	even	1	trivial
630.2.l.f.331.2	yes	12	7.2	even	3
630.2.l.f.571.2	yes	12	9.4	even	3
1890.2.i.f.991.5		12	3.2	odd	2
1890.2.i.f.1171.5		12	63.23	odd	6
1890.2.l.h.361.4		12	9.5	odd	6
1890.2.l.h.1801.4		12	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.31625 + 1.12583i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.31625 + 1.12583i) q^{6} +(2.64400 + 0.0963576i) q^{7} +1.00000 q^{8} +(0.465015 + 2.96374i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.31625 + 1.12583i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(1.31625 + 1.12583i) q^{6} +(2.64400 + 0.0963576i) q^{7} +1.00000 q^{8} +(0.465015 + 2.96374i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.10401 - 1.91220i) q^{11} +(1.31625 + 1.12583i) q^{12} +(-0.313139 - 0.542372i) q^{13} +(2.64400 + 0.0963576i) q^{14} +(1.63312 - 0.576989i) q^{15} +1.00000 q^{16} +(-1.90382 + 3.29751i) q^{17} +(0.465015 + 2.96374i) q^{18} +(-3.79362 - 6.57074i) q^{19} +(0.500000 - 0.866025i) q^{20} +(3.37167 + 3.10352i) q^{21} +(-1.10401 - 1.91220i) q^{22} +(-1.30144 + 2.25415i) q^{23} +(1.31625 + 1.12583i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.313139 - 0.542372i) q^{26} +(-2.72459 + 4.42454i) q^{27} +(2.64400 + 0.0963576i) q^{28} +(-2.01339 + 3.48730i) q^{29} +(1.63312 - 0.576989i) q^{30} +7.40725 q^{31} +1.00000 q^{32} +(0.699663 - 3.75986i) q^{33} +(-1.90382 + 3.29751i) q^{34} +(1.40545 - 2.24159i) q^{35} +(0.465015 + 2.96374i) q^{36} +(-2.81483 - 4.87543i) q^{37} +(-3.79362 - 6.57074i) q^{38} +(0.198451 - 1.06644i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.09955 - 1.90448i) q^{41} +(3.37167 + 3.10352i) q^{42} +(-4.25532 + 7.37044i) q^{43} +(-1.10401 - 1.91220i) q^{44} +(2.79918 + 1.07916i) q^{45} +(-1.30144 + 2.25415i) q^{46} -0.450314 q^{47} +(1.31625 + 1.12583i) q^{48} +(6.98143 + 0.509538i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-6.21833 + 2.19696i) q^{51} +(-0.313139 - 0.542372i) q^{52} +(-1.19348 + 2.06717i) q^{53} +(-2.72459 + 4.42454i) q^{54} -2.20802 q^{55} +(2.64400 + 0.0963576i) q^{56} +(2.40419 - 12.9197i) q^{57} +(-2.01339 + 3.48730i) q^{58} -5.80323 q^{59} +(1.63312 - 0.576989i) q^{60} -0.968707 q^{61} +7.40725 q^{62} +(0.943918 + 7.88093i) q^{63} +1.00000 q^{64} -0.626277 q^{65} +(0.699663 - 3.75986i) q^{66} +4.08122 q^{67} +(-1.90382 + 3.29751i) q^{68} +(-4.25080 + 1.50183i) q^{69} +(1.40545 - 2.24159i) q^{70} +6.99225 q^{71} +(0.465015 + 2.96374i) q^{72} +(0.696424 - 1.20624i) q^{73} +(-2.81483 - 4.87543i) q^{74} +(0.316873 - 1.70282i) q^{75} +(-3.79362 - 6.57074i) q^{76} +(-2.73474 - 5.16223i) q^{77} +(0.198451 - 1.06644i) q^{78} -11.8055 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.56752 + 2.75637i) q^{81} +(-1.09955 - 1.90448i) q^{82} +(-7.35470 + 12.7387i) q^{83} +(3.37167 + 3.10352i) q^{84} +(1.90382 + 3.29751i) q^{85} +(-4.25532 + 7.37044i) q^{86} +(-6.57623 + 2.32341i) q^{87} +(-1.10401 - 1.91220i) q^{88} +(-5.98165 - 10.3605i) q^{89} +(2.79918 + 1.07916i) q^{90} +(-0.775676 - 1.46420i) q^{91} +(-1.30144 + 2.25415i) q^{92} +(9.74978 + 8.33931i) q^{93} -0.450314 q^{94} -7.58724 q^{95} +(1.31625 + 1.12583i) q^{96} +(8.36150 - 14.4825i) q^{97} +(6.98143 + 0.509538i) q^{98} +(5.15389 - 4.16120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

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