LMFDB - Embedded newform 1110.2.i.p.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} - 6x^{7} + 123x^{6} - 62x^{5} + 458x^{4} + 100x^{3} + 844x^{2} - 312x + 144 $ x^10 - 2x^9 + 15x^8 - 6x^7 + 123x^6 - 62x^5 + 458x^4 + 100x^3 + 844x^2 - 312*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$1.73363 - 3.00274i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.p.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(0.980808 + 1.69881i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(0.980808 + 1.69881i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.59307 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.96727 - 5.13946i) q^{13} -1.96162 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0910588 - 0.157718i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.543707 - 0.941728i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.980808 - 1.69881i) q^{21} +(-0.796533 + 1.37964i) q^{22} +7.71404 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.93454 q^{26} +1.00000 q^{27} +(0.980808 - 1.69881i) q^{28} -6.98357 q^{29} +(-0.500000 - 0.866025i) q^{30} -4.64939 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.796533 - 1.37964i) q^{33} +(0.0910588 + 0.157718i) q^{34} +(0.980808 - 1.69881i) q^{35} +1.00000 q^{36} +(5.19726 + 3.16046i) q^{37} +1.08741 q^{38} +(-2.96727 + 5.13946i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.18993 - 3.79307i) q^{41} +(0.980808 + 1.69881i) q^{42} -6.57262 q^{43} +(-0.796533 - 1.37964i) q^{44} +1.00000 q^{45} +(-3.85702 + 6.68055i) q^{46} +2.58176 q^{47} +1.00000 q^{48} +(1.57603 - 2.72977i) q^{49} +(-0.500000 - 0.866025i) q^{50} -0.182118 q^{51} +(-2.96727 + 5.13946i) q^{52} +(4.74461 - 8.21790i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.796533 - 1.37964i) q^{55} +(0.980808 + 1.69881i) q^{56} +(-0.543707 + 0.941728i) q^{57} +(3.49178 - 6.04795i) q^{58} +(5.04330 - 8.73525i) q^{59} +1.00000 q^{60} +(-7.33768 - 12.7092i) q^{61} +(2.32469 - 4.02649i) q^{62} -1.96162 q^{63} +1.00000 q^{64} +(-2.96727 + 5.13946i) q^{65} +1.59307 q^{66} +(-7.74993 - 13.4233i) q^{67} -0.182118 q^{68} +(-3.85702 - 6.68055i) q^{69} +(0.980808 + 1.69881i) q^{70} +(-2.30550 - 3.99324i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.46325 q^{73} +(-5.33567 + 2.92073i) q^{74} +1.00000 q^{75} +(-0.543707 + 0.941728i) q^{76} +(1.56249 + 2.70632i) q^{77} +(-2.96727 - 5.13946i) q^{78} +(-6.69726 - 11.6000i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +4.37985 q^{82} +(3.89857 - 6.75252i) q^{83} -1.96162 q^{84} -0.182118 q^{85} +(3.28631 - 5.69205i) q^{86} +(3.49178 + 6.04795i) q^{87} +1.59307 q^{88} +(-3.57187 + 6.18665i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(5.82064 - 10.0816i) q^{91} +(-3.85702 - 6.68055i) q^{92} +(2.32469 + 4.02649i) q^{93} +(-1.29088 + 2.23587i) q^{94} +(-0.543707 + 0.941728i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.20838 q^{97} +(1.57603 + 2.72977i) q^{98} +(-0.796533 + 1.37964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9	$ 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9} + 10 q^{10} - 2 q^{11} - 5 q^{12} + q^{13} - 5 q^{15} - 5 q^{16} - 5 q^{18} - 2 q^{19} - 5 q^{20} + q^{22} - 2 q^{23} - 5 q^{24} - 5 q^{25} - 2 q^{26} + 10 q^{27} + 18 q^{29} - 5 q^{30} - 14 q^{31} - 5 q^{32} + q^{33} + 10 q^{36} + 4 q^{38} + q^{39} - 5 q^{40} - 10 q^{41} + 6 q^{43} + q^{44} + 10 q^{45} + q^{46} + 30 q^{47} + 10 q^{48} - 11 q^{49} - 5 q^{50} + q^{52} - 2 q^{53} - 5 q^{54} + q^{55} - 2 q^{57} - 9 q^{58} - 7 q^{59} + 10 q^{60} - 6 q^{61} + 7 q^{62} + 10 q^{64} + q^{65} - 2 q^{66} - 5 q^{67} + q^{69} + 3 q^{71} - 5 q^{72} - 18 q^{73} - 3 q^{74} + 10 q^{75} - 2 q^{76} - 32 q^{77} + q^{78} - 15 q^{79} + 10 q^{80} - 5 q^{81} + 20 q^{82} - 5 q^{83} - 3 q^{86} - 9 q^{87} - 2 q^{88} - 25 q^{89} - 5 q^{90} - 18 q^{91} + q^{92} + 7 q^{93} - 15 q^{94} - 2 q^{95} - 5 q^{96} + 6 q^{97} - 11 q^{98} + q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9 + 10 * q^10 - 2 * q^11 - 5 * q^12 + q^13 - 5 * q^15 - 5 * q^16 - 5 * q^18 - 2 * q^19 - 5 * q^20 + q^22 - 2 * q^23 - 5 * q^24 - 5 * q^25 - 2 * q^26 + 10 * q^27 + 18 * q^29 - 5 * q^30 - 14 * q^31 - 5 * q^32 + q^33 + 10 * q^36 + 4 * q^38 + q^39 - 5 * q^40 - 10 * q^41 + 6 * q^43 + q^44 + 10 * q^45 + q^46 + 30 * q^47 + 10 * q^48 - 11 * q^49 - 5 * q^50 + q^52 - 2 * q^53 - 5 * q^54 + q^55 - 2 * q^57 - 9 * q^58 - 7 * q^59 + 10 * q^60 - 6 * q^61 + 7 * q^62 + 10 * q^64 + q^65 - 2 * q^66 - 5 * q^67 + q^69 + 3 * q^71 - 5 * q^72 - 18 * q^73 - 3 * q^74 + 10 * q^75 - 2 * q^76 - 32 * q^77 + q^78 - 15 * q^79 + 10 * q^80 - 5 * q^81 + 20 * q^82 - 5 * q^83 - 3 * q^86 - 9 * q^87 - 2 * q^88 - 25 * q^89 - 5 * q^90 - 18 * q^91 + q^92 + 7 * q^93 - 15 * q^94 - 2 * q^95 - 5 * q^96 + 6 * q^97 - 11 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$	0.980808	+	1.69881i	0.370711	+	0.642090i	0.989675	−	0.143329i	$-0.0457809\pi$
$7$	0.980808	+	1.69881i	0.370711	+	0.642090i	−0.618964	+	0.785419i	$0.712448\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	1.59307			0.480328			0.240164	−	0.970732i	$-0.422799\pi$
$11$	1.59307			0.480328			0.240164	+	0.970732i	$0.422799\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.96727	−	5.13946i	−0.822972	−	1.42543i	−0.903459	−	0.428674i	$-0.858981\pi$
$13$	−2.96727	−	5.13946i	−0.822972	−	1.42543i	0.0804870	−	0.996756i	$-0.474352\pi$
$14$	−1.96162			−0.524264
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0910588	−	0.157718i	0.0220850	−	0.0382523i	−0.854772	−	0.519004i	$-0.826303\pi$
$17$	0.0910588	−	0.157718i	0.0220850	−	0.0382523i	0.876857	+	0.480752i	$0.159636\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.543707	−	0.941728i	−0.124735	−	0.216047i	0.796894	−	0.604119i	$-0.206475\pi$
$19$	−0.543707	−	0.941728i	−0.124735	−	0.216047i	−0.921629	+	0.388071i	$0.873141\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.980808	−	1.69881i	0.214030	−	0.370711i
$22$	−0.796533	+	1.37964i	−0.169821	+	0.294139i
$23$	7.71404			1.60849			0.804244	−	0.594300i	$-0.202571\pi$
$23$	7.71404			1.60849			0.804244	+	0.594300i	$0.202571\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	5.93454			1.16386
$27$	1.00000			0.192450
$28$	0.980808	−	1.69881i	0.185355	−	0.321045i
$29$	−6.98357			−1.29682			−0.648408	−	0.761293i	$-0.724565\pi$
$29$	−6.98357			−1.29682			−0.648408	+	0.761293i	$0.724565\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−4.64939			−0.835054			−0.417527	−	0.908664i	$-0.637103\pi$
$31$	−4.64939			−0.835054			−0.417527	+	0.908664i	$0.637103\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.796533	−	1.37964i	−0.138659	−	0.240164i
$34$	0.0910588	+	0.157718i	0.0156164	+	0.0270485i
$35$	0.980808	−	1.69881i	0.165787	−	0.287151i
$36$	1.00000			0.166667
$37$	5.19726	+	3.16046i	0.854424	+	0.519577i
$37$	5.19726	+	3.16046i	0.854424	+	0.519577i
$38$	1.08741			0.176402
$39$	−2.96727	+	5.13946i	−0.475143	+	0.822972i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.18993	−	3.79307i	−0.342009	−	0.592377i	0.642797	−	0.766037i	$-0.277774\pi$
$41$	−2.18993	−	3.79307i	−0.342009	−	0.592377i	−0.984806	+	0.173660i	$0.944441\pi$
$42$	0.980808	+	1.69881i	0.151342	+	0.262132i
$43$	−6.57262			−1.00231			−0.501157	−	0.865356i	$-0.667092\pi$
$43$	−6.57262			−1.00231			−0.501157	+	0.865356i	$0.667092\pi$
$44$	−0.796533	−	1.37964i	−0.120082	−	0.207988i
$45$	1.00000			0.149071
$46$	−3.85702	+	6.68055i	−0.568686	+	0.984993i
$47$	2.58176			0.376589			0.188294	−	0.982113i	$-0.439704\pi$
$47$	2.58176			0.376589			0.188294	+	0.982113i	$0.439704\pi$
$48$	1.00000			0.144338
$49$	1.57603	−	2.72977i	0.225147	−	0.389967i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.182118			−0.0255016
$52$	−2.96727	+	5.13946i	−0.411486	+	0.712715i
$53$	4.74461	−	8.21790i	0.651722	−	1.12882i	−0.330983	−	0.943637i	$-0.607380\pi$
$53$	4.74461	−	8.21790i	0.651722	−	1.12882i	0.982705	−	0.185179i	$-0.0592865\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.796533	−	1.37964i	−0.107405	−	0.186030i
$56$	0.980808	+	1.69881i	0.131066	+	0.227013i
$57$	−0.543707	+	0.941728i	−0.0720157	+	0.124735i
$58$	3.49178	−	6.04795i	0.458494	−	0.794134i
$59$	5.04330	−	8.73525i	0.656582	−	1.13723i	−0.324913	−	0.945744i	$-0.605335\pi$
$59$	5.04330	−	8.73525i	0.656582	−	1.13723i	0.981495	−	0.191489i	$-0.0613316\pi$
$60$	1.00000			0.129099
$61$	−7.33768	−	12.7092i	−0.939493	−	1.62725i	−0.766419	−	0.642341i	$-0.777963\pi$
$61$	−7.33768	−	12.7092i	−0.939493	−	1.62725i	−0.173074	−	0.984909i	$-0.555370\pi$
$62$	2.32469	−	4.02649i	0.295236	−	0.511364i
$63$	−1.96162			−0.247140
$64$	1.00000			0.125000
$65$	−2.96727	+	5.13946i	−0.368044	+	0.637472i
$66$	1.59307			0.196093
$67$	−7.74993	−	13.4233i	−0.946805	−	1.63991i	−0.752096	−	0.659053i	$-0.770957\pi$
$67$	−7.74993	−	13.4233i	−0.946805	−	1.63991i	−0.194708	−	0.980861i	$-0.562376\pi$
$68$	−0.182118			−0.0220850
$69$	−3.85702	−	6.68055i	−0.464330	−	0.804244i
$70$	0.980808	+	1.69881i	0.117229	+	0.203047i
$71$	−2.30550	−	3.99324i	−0.273613	−	0.473911i	0.696172	−	0.717875i	$-0.254885\pi$
$71$	−2.30550	−	3.99324i	−0.273613	−	0.473911i	−0.969784	+	0.243965i	$0.921552\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.46325			−0.171261			−0.0856304	−	0.996327i	$-0.527290\pi$
$73$	−1.46325			−0.171261			−0.0856304	+	0.996327i	$0.527290\pi$
$74$	−5.33567	+	2.92073i	−0.620259	+	0.339528i
$75$	1.00000			0.115470
$76$	−0.543707	+	0.941728i	−0.0623675	+	0.108024i
$77$	1.56249	+	2.70632i	0.178062	+	0.308413i
$78$	−2.96727	−	5.13946i	−0.335977	−	0.581929i
$79$	−6.69726	−	11.6000i	−0.753500	−	1.30510i	−0.946116	−	0.323827i	$-0.895031\pi$
$79$	−6.69726	−	11.6000i	−0.753500	−	1.30510i	0.192616	−	0.981274i	$-0.438303\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.37985			0.483674
$83$	3.89857	−	6.75252i	0.427923	−	0.741185i	−0.568765	−	0.822500i	$-0.692579\pi$
$83$	3.89857	−	6.75252i	0.427923	−	0.741185i	0.996688	+	0.0813150i	$0.0259120\pi$
$84$	−1.96162			−0.214030
$85$	−0.182118			−0.0197534
$86$	3.28631	−	5.69205i	0.354372	−	0.613790i
$87$	3.49178	+	6.04795i	0.374358	+	0.648408i
$88$	1.59307			0.169821
$89$	−3.57187	+	6.18665i	−0.378617	+	0.655784i	−0.990861	−	0.134885i	$-0.956934\pi$
$89$	−3.57187	+	6.18665i	−0.378617	+	0.655784i	0.612244	+	0.790669i	$0.290267\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	5.82064	−	10.0816i	0.610169	−	1.05684i
$92$	−3.85702	−	6.68055i	−0.402122	−	0.696496i
$93$	2.32469	+	4.02649i	0.241059	+	0.417527i
$94$	−1.29088	+	2.23587i	−0.133144	+	0.230612i
$95$	−0.543707	+	0.941728i	−0.0557831	+	0.0966192i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−6.20838			−0.630366			−0.315183	−	0.949031i	$-0.602066\pi$
$97$	−6.20838			−0.630366			−0.315183	+	0.949031i	$0.602066\pi$
$98$	1.57603	+	2.72977i	0.159203	+	0.275748i
$99$	−0.796533	+	1.37964i	−0.0800546	+	0.138659i
$100$	1.00000			0.100000
$101$	15.6102			1.55327			0.776636	−	0.629950i	$-0.216925\pi$
$101$	15.6102			1.55327			0.776636	+	0.629950i	$0.216925\pi$
$102$	0.0910588	−	0.157718i	0.00901616	−	0.0156164i
$103$	7.02627			0.692318			0.346159	−	0.938176i	$-0.387486\pi$
$103$	7.02627			0.692318			0.346159	+	0.938176i	$0.387486\pi$
$104$	−2.96727	−	5.13946i	−0.290965	−	0.503965i
$105$	−1.96162			−0.191434
$106$	4.74461	+	8.21790i	0.460837	+	0.798193i
$107$	5.05684	+	8.75870i	0.488863	+	0.846736i	0.999918	−	0.0128124i	$-0.00407842\pi$
$107$	5.05684	+	8.75870i	0.488863	+	0.846736i	−0.511055	+	0.859548i	$0.670745\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−7.31607	+	12.6718i	−0.700752	+	1.21374i	0.267450	+	0.963572i	$0.413819\pi$
$109$	−7.31607	+	12.6718i	−0.700752	+	1.21374i	−0.968203	+	0.250167i	$0.919514\pi$
$110$	1.59307			0.151893
$111$	0.138411	−	6.08119i	0.0131374	−	0.577201i
$112$	−1.96162			−0.185355
$113$	−4.22225	+	7.31316i	−0.397196	+	0.687964i	−0.993379	−	0.114885i	$-0.963350\pi$
$113$	−4.22225	+	7.31316i	−0.397196	+	0.687964i	0.596183	+	0.802849i	$0.296683\pi$
$114$	−0.543707	−	0.941728i	−0.0509228	−	0.0882009i
$115$	−3.85702	−	6.68055i	−0.359669	−	0.622965i
$116$	3.49178	+	6.04795i	0.324204	+	0.561538i
$117$	5.93454			0.548648
$118$	5.04330	+	8.73525i	0.464273	+	0.804145i
$119$	0.357245			0.0327486
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−8.46214			−0.769285
$122$	14.6754			1.32864
$123$	−2.18993	+	3.79307i	−0.197459	+	0.342009i
$124$	2.32469	+	4.02649i	0.208764	+	0.361589i
$125$	1.00000			0.0894427
$126$	0.980808	−	1.69881i	0.0873773	−	0.151342i
$127$	−0.716857	+	1.24163i	−0.0636107	+	0.110177i	−0.896077	−	0.443899i	$-0.853595\pi$
$127$	−0.716857	+	1.24163i	−0.0636107	+	0.110177i	0.832466	+	0.554076i	$0.186928\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.28631	+	5.69205i	0.289343	+	0.501157i
$130$	−2.96727	−	5.13946i	−0.260247	−	0.450760i
$131$	−1.46742	+	2.54164i	−0.128209	+	0.222064i	−0.922983	−	0.384841i	$-0.874256\pi$
$131$	−1.46742	+	2.54164i	−0.128209	+	0.222064i	0.794774	+	0.606906i	$0.207589\pi$
$132$	−0.796533	+	1.37964i	−0.0693293	+	0.120082i
$133$	1.06654	−	1.84731i	0.0924811	−	0.160182i
$134$	15.4999			1.33898
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	0.0910588	−	0.157718i	0.00780822	−	0.0135242i
$137$	21.2169			1.81268			0.906340	−	0.422549i	$-0.138865\pi$
$137$	21.2169			1.81268			0.906340	+	0.422549i	$0.138865\pi$
$138$	7.71404			0.656662
$139$	−0.258479	+	0.447698i	−0.0219239	+	0.0379733i	−0.876779	−	0.480893i	$-0.840312\pi$
$139$	−0.258479	+	0.447698i	−0.0219239	+	0.0379733i	0.854855	+	0.518866i	$0.173646\pi$
$140$	−1.96162			−0.165787
$141$	−1.29088	−	2.23587i	−0.108712	−	0.188294i
$142$	4.61100			0.386947
$143$	−4.72706	−	8.18750i	−0.395296	−	0.684673i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.49178	+	6.04795i	0.289977	+	0.502255i
$146$	0.731627	−	1.26721i	0.0605499	−	0.104875i
$147$	−3.15206			−0.259978
$148$	0.138411	−	6.08119i	0.0113773	−	0.499871i
$149$	−8.90680			−0.729673			−0.364837	−	0.931072i	$-0.618875\pi$
$149$	−8.90680			−0.729673			−0.364837	+	0.931072i	$0.618875\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−7.60984	−	13.1806i	−0.619280	−	1.07262i	−0.989617	−	0.143727i	$-0.954091\pi$
$151$	−7.60984	−	13.1806i	−0.619280	−	1.07262i	0.370337	−	0.928897i	$-0.379242\pi$
$152$	−0.543707	−	0.941728i	−0.0441004	−	0.0763842i
$153$	0.0910588	+	0.157718i	0.00736166	+	0.0127508i
$154$	−3.12498			−0.251818
$155$	2.32469	+	4.02649i	0.186724	+	0.323415i
$156$	5.93454			0.475143
$157$	4.48357	−	7.76576i	0.357828	−	0.619776i	−0.629770	−	0.776782i	$-0.716851\pi$
$157$	4.48357	−	7.76576i	0.357828	−	0.619776i	0.987598	+	0.157006i	$0.0501842\pi$
$158$	13.3945			1.06561
$159$	−9.48922			−0.752544
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	7.56599	+	13.1047i	0.596283	+	1.03279i
$162$	1.00000			0.0785674
$163$	−1.82153	+	3.15498i	−0.142673	+	0.247117i	−0.928502	−	0.371326i	$-0.878903\pi$
$163$	−1.82153	+	3.15498i	−0.142673	+	0.247117i	0.785829	+	0.618443i	$0.212236\pi$
$164$	−2.18993	+	3.79307i	−0.171005	+	0.296189i
$165$	−0.796533	+	1.37964i	−0.0620100	+	0.107405i
$166$	3.89857	+	6.75252i	0.302587	+	0.524097i
$167$	4.18628	+	7.25085i	0.323944	+	0.561088i	0.981298	−	0.192494i	$-0.0616576\pi$
$167$	4.18628	+	7.25085i	0.323944	+	0.561088i	−0.657354	+	0.753582i	$0.728324\pi$
$168$	0.980808	−	1.69881i	0.0756710	−	0.131066i
$169$	−11.1094	+	19.2420i	−0.854566	+	1.48015i
$170$	0.0910588	−	0.157718i	0.00698389	−	0.0120964i
$171$	1.08741			0.0831566
$172$	3.28631	+	5.69205i	0.250579	+	0.434015i
$173$	4.45388	−	7.71434i	0.338622	−	0.586511i	−0.645552	−	0.763717i	$-0.723373\pi$
$173$	4.45388	−	7.71434i	0.338622	−	0.586511i	0.984174	+	0.177206i	$0.0567058\pi$
$174$	−6.98357			−0.529423
$175$	−1.96162			−0.148284
$176$	−0.796533	+	1.37964i	−0.0600409	+	0.103994i
$177$	−10.0866			−0.758155
$178$	−3.57187	−	6.18665i	−0.267723	−	0.463709i
$179$	−7.14373			−0.533948			−0.266974	−	0.963704i	$-0.586024\pi$
$179$	−7.14373			−0.533948			−0.266974	+	0.963704i	$0.586024\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	9.62049	+	16.6632i	0.715085	+	1.23856i	0.962927	+	0.269763i	$0.0869455\pi$
$181$	9.62049	+	16.6632i	0.715085	+	1.23856i	−0.247841	+	0.968801i	$0.579721\pi$
$182$	5.82064	+	10.0816i	0.431455	+	0.747301i
$183$	−7.33768	+	12.7092i	−0.542417	+	0.939493i
$184$	7.71404			0.568686
$185$	0.138411	−	6.08119i	0.0101762	−	0.447098i
$186$	−4.64939			−0.340910
$187$	0.145063	−	0.251256i	0.0106080	−	0.0183736i
$188$	−1.29088	−	2.23587i	−0.0941471	−	0.163068i
$189$	0.980808	+	1.69881i	0.0713433	+	0.123570i
$190$	−0.543707	−	0.941728i	−0.0394446	−	0.0683201i
$191$	−9.16086			−0.662856			−0.331428	−	0.943480i	$-0.607530\pi$
$191$	−9.16086			−0.662856			−0.331428	+	0.943480i	$0.607530\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	16.8757			1.21474			0.607370	−	0.794419i	$-0.292225\pi$
$193$	16.8757			1.21474			0.607370	+	0.794419i	$0.292225\pi$
$194$	3.10419	−	5.37662i	0.222868	−	0.386019i
$195$	5.93454			0.424981
$196$	−3.15206			−0.225147
$197$	−0.312230	+	0.540798i	−0.0222455	+	0.0385303i	−0.876934	−	0.480611i	$-0.840415\pi$
$197$	−0.312230	+	0.540798i	−0.0222455	+	0.0385303i	0.854688	+	0.519141i	$0.173748\pi$
$198$	−0.796533	−	1.37964i	−0.0566071	−	0.0980464i
$199$	8.13890			0.576952			0.288476	−	0.957487i	$-0.406852\pi$
$199$	8.13890			0.576952			0.288476	+	0.957487i	$0.406852\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−7.74993	+	13.4233i	−0.546638	+	0.946805i
$202$	−7.80509	+	13.5188i	−0.549165	+	0.951181i
$203$	−6.84954	−	11.8637i	−0.480743	−	0.832672i
$204$	0.0910588	+	0.157718i	0.00637539	+	0.0110425i
$205$	−2.18993	+	3.79307i	−0.152951	+	0.264919i
$206$	−3.51313	+	6.08492i	−0.244772	+	0.423957i
$207$	−3.85702	+	6.68055i	−0.268081	+	0.464330i
$208$	5.93454			0.411486
$209$	−0.866161	−	1.50023i	−0.0599136	−	0.103773i
$210$	0.980808	−	1.69881i	0.0676822	−	0.117229i
$211$	−15.4084			−1.06076			−0.530380	−	0.847760i	$-0.677951\pi$
$211$	−15.4084			−1.06076			−0.530380	+	0.847760i	$0.677951\pi$
$212$	−9.48922			−0.651722
$213$	−2.30550	+	3.99324i	−0.157970	+	0.273613i
$214$	−10.1137			−0.691357
$215$	3.28631	+	5.69205i	0.224124	+	0.388195i
$216$	1.00000			0.0680414
$217$	−4.56015	−	7.89842i	−0.309563	−	0.536180i
$218$	−7.31607	−	12.6718i	−0.495507	−	0.858243i
$219$	0.731627	+	1.26721i	0.0494388	+	0.0856304i
$220$	−0.796533	+	1.37964i	−0.0537023	+	0.0930150i
$221$	−1.08078			−0.0727013
$222$	5.19726	+	3.16046i	0.348817	+	0.212116i
$223$	20.9025			1.39973			0.699867	−	0.714273i	$-0.253243\pi$
$223$	20.9025			1.39973			0.699867	+	0.714273i	$0.253243\pi$
$224$	0.980808	−	1.69881i	0.0655330	−	0.113506i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−4.22225	−	7.31316i	−0.280860	−	0.486464i
$227$	−13.6470	−	23.6372i	−0.905781	−	1.56886i	−0.819865	−	0.572557i	$-0.805952\pi$
$227$	−13.6470	−	23.6372i	−0.905781	−	1.56886i	−0.0859163	−	0.996302i	$-0.527382\pi$
$228$	1.08741			0.0720157
$229$	−5.44187	−	9.42559i	−0.359609	−	0.622861i	0.628287	−	0.777982i	$-0.283756\pi$
$229$	−5.44187	−	9.42559i	−0.359609	−	0.622861i	−0.987895	+	0.155121i	$0.950423\pi$
$230$	7.71404			0.508648
$231$	1.56249	−	2.70632i	0.102804	−	0.178062i
$232$	−6.98357			−0.458494
$233$	7.06762			0.463015			0.231508	−	0.972833i	$-0.425634\pi$
$233$	7.06762			0.463015			0.231508	+	0.972833i	$0.425634\pi$
$234$	−2.96727	+	5.13946i	−0.193976	+	0.335977i
$235$	−1.29088	−	2.23587i	−0.0842078	−	0.145852i
$236$	−10.0866			−0.656582
$237$	−6.69726	+	11.6000i	−0.435034	+	0.753500i
$238$	−0.178622	+	0.309383i	−0.0115784	+	0.0200543i
$239$	−4.98978	+	8.64255i	−0.322762	+	0.559040i	−0.981057	−	0.193720i	$-0.937945\pi$
$239$	−4.98978	+	8.64255i	−0.322762	+	0.559040i	0.658295	+	0.752760i	$0.271278\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	14.2806	+	24.7347i	0.919893	+	1.59330i	0.799575	+	0.600566i	$0.205058\pi$
$241$	14.2806	+	24.7347i	0.919893	+	1.59330i	0.120318	+	0.992735i	$0.461609\pi$
$242$	4.23107	−	7.32843i	0.271983	−	0.471089i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.33768	+	12.7092i	−0.469747	+	0.813625i
$245$	−3.15206			−0.201378
$246$	−2.18993	−	3.79307i	−0.139625	−	0.241837i
$247$	−3.22665	+	5.58872i	−0.205307	+	0.355602i
$248$	−4.64939			−0.295236
$249$	−7.79713			−0.494123
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	25.7808			1.62727			0.813636	−	0.581374i	$-0.197485\pi$
$251$	25.7808			1.62727			0.813636	+	0.581374i	$0.197485\pi$
$252$	0.980808	+	1.69881i	0.0617851	+	0.107015i
$253$	12.2890			0.772601
$254$	−0.716857	−	1.24163i	−0.0449796	−	0.0779069i
$255$	0.0910588	+	0.157718i	0.00570232	+	0.00987671i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.56855	−	2.71681i	0.0978435	−	0.169470i	−0.812948	−	0.582336i	$-0.802139\pi$
$257$	1.56855	−	2.71681i	0.0978435	−	0.169470i	0.910792	+	0.412866i	$0.135472\pi$
$258$	−6.57262			−0.409193
$259$	−0.271509	+	11.9290i	−0.0168707	+	0.741229i
$260$	5.93454			0.368044
$261$	3.49178	−	6.04795i	0.216136	−	0.374358i
$262$	−1.46742	−	2.54164i	−0.0906574	−	0.157023i
$263$	9.87495	+	17.1039i	0.608916	+	1.05467i	0.991419	+	0.130719i	$0.0417286\pi$
$263$	9.87495	+	17.1039i	0.608916	+	1.05467i	−0.382504	+	0.923954i	$0.624938\pi$
$264$	−0.796533	−	1.37964i	−0.0490232	−	0.0849107i
$265$	−9.48922			−0.582918
$266$	1.06654	+	1.84731i	0.0653940	+	0.113266i
$267$	7.14373			0.437189
$268$	−7.74993	+	13.4233i	−0.473402	+	0.819957i
$269$	−14.5725			−0.888499			−0.444249	−	0.895903i	$-0.646530\pi$
$269$	−14.5725			−0.888499			−0.444249	+	0.895903i	$0.646530\pi$
$270$	1.00000			0.0608581
$271$	−0.454136	+	0.786586i	−0.0275868	+	0.0477817i	−0.879489	−	0.475919i	$-0.842116\pi$
$271$	−0.454136	+	0.786586i	−0.0275868	+	0.0477817i	0.851902	+	0.523701i	$0.175449\pi$
$272$	0.0910588	+	0.157718i	0.00552125	+	0.00956308i
$273$	−11.6413			−0.704562
$274$	−10.6084	+	18.3744i	−0.640879	+	1.11004i
$275$	−0.796533	+	1.37964i	−0.0480328	+	0.0831952i
$276$	−3.85702	+	6.68055i	−0.232165	+	0.402122i
$277$	4.49959	+	7.79352i	0.270354	+	0.468267i	0.968953	−	0.247247i	$-0.0795258\pi$
$277$	4.49959	+	7.79352i	0.270354	+	0.468267i	−0.698598	+	0.715514i	$0.746192\pi$
$278$	−0.258479	−	0.447698i	−0.0155025	−	0.0268512i
$279$	2.32469	−	4.02649i	0.139176	−	0.241059i
$280$	0.980808	−	1.69881i	0.0586145	−	0.101523i
$281$	−10.3733	+	17.9671i	−0.618820	+	1.07183i	0.370881	+	0.928680i	$0.379056\pi$
$281$	−10.3733	+	17.9671i	−0.618820	+	1.07183i	−0.989701	+	0.143148i	$0.954278\pi$
$282$	2.58176			0.153742
$283$	−3.92140	−	6.79207i	−0.233103	−	0.403747i	0.725616	−	0.688099i	$-0.241555\pi$
$283$	−3.92140	−	6.79207i	−0.233103	−	0.403747i	−0.958720	+	0.284353i	$0.908221\pi$
$284$	−2.30550	+	3.99324i	−0.136806	+	0.236955i
$285$	1.08741			0.0644128
$286$	9.45411			0.559033
$287$	4.29580	−	7.44054i	0.253573	−	0.439201i
$288$	1.00000			0.0589256
$289$	8.48342	+	14.6937i	0.499025	+	0.864336i
$290$	−6.98357			−0.410089
$291$	3.10419	+	5.37662i	0.181971	+	0.315183i
$292$	0.731627	+	1.26721i	0.0428152	+	0.0741581i
$293$	6.26365	+	10.8490i	0.365926	+	0.633803i	0.988924	−	0.148420i	$-0.0474188\pi$
$293$	6.26365	+	10.8490i	0.365926	+	0.633803i	−0.622998	+	0.782223i	$0.714086\pi$
$294$	1.57603	−	2.72977i	0.0919160	−	0.159203i
$295$	−10.0866			−0.587265
$296$	5.19726	+	3.16046i	0.302084	+	0.183698i
$297$	1.59307			0.0924391
$298$	4.45340	−	7.71351i	0.257978	−	0.446832i
$299$	−22.8896	−	39.6460i	−1.32374	−	2.29279i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−6.44648	−	11.1656i	−0.371569	−	0.643576i
$302$	15.2197			0.875795
$303$	−7.80509	−	13.5188i	−0.448391	−	0.776636i
$304$	1.08741			0.0623675
$305$	−7.33768	+	12.7092i	−0.420154	+	0.727728i
$306$	−0.182118			−0.0104110
$307$	−3.70459			−0.211432			−0.105716	−	0.994396i	$-0.533713\pi$
$307$	−3.70459			−0.211432			−0.105716	+	0.994396i	$0.533713\pi$
$308$	1.56249	−	2.70632i	0.0890312	−	0.154207i
$309$	−3.51313	−	6.08492i	−0.199855	−	0.346159i
$310$	−4.64939			−0.264067
$311$	12.1914	−	21.1162i	0.691313	−	1.19739i	−0.280095	−	0.959972i	$-0.590366\pi$
$311$	12.1914	−	21.1162i	0.691313	−	1.19739i	0.971408	−	0.237416i	$-0.0763005\pi$
$312$	−2.96727	+	5.13946i	−0.167988	+	0.290965i
$313$	−10.8450	+	18.7841i	−0.612996	+	1.06174i	0.377737	+	0.925913i	$0.376702\pi$
$313$	−10.8450	+	18.7841i	−0.612996	+	1.06174i	−0.990733	+	0.135827i	$0.956631\pi$
$314$	4.48357	+	7.76576i	0.253022	+	0.438247i
$315$	0.980808	+	1.69881i	0.0552623	+	0.0957171i
$316$	−6.69726	+	11.6000i	−0.376750	+	0.652550i
$317$	7.29371	−	12.6331i	0.409656	−	0.709544i	−0.585195	−	0.810892i	$-0.698982\pi$
$317$	7.29371	−	12.6331i	0.409656	−	0.709544i	0.994851	+	0.101348i	$0.0323155\pi$
$318$	4.74461	−	8.21790i	0.266064	−	0.460837i
$319$	−11.1253			−0.622896
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	5.05684	−	8.75870i	0.282245	−	0.488863i
$322$	−15.1320			−0.843272
$323$	−0.198037			−0.0110191
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.93454			0.329189
$326$	−1.82153	−	3.15498i	−0.100885	−	0.174738i
$327$	14.6321			0.809159
$328$	−2.18993	−	3.79307i	−0.120919	−	0.209437i
$329$	2.53221	+	4.38592i	0.139605	+	0.241804i
$330$	−0.796533	−	1.37964i	−0.0438477	−	0.0759465i
$331$	11.4693	−	19.8654i	0.630408	−	1.09190i	−0.357060	−	0.934082i	$-0.616221\pi$
$331$	11.4693	−	19.8654i	0.630408	−	1.09190i	0.987468	−	0.157818i	$-0.0504459\pi$
$332$	−7.79713			−0.427923
$333$	−5.33567	+	2.92073i	−0.292393	+	0.160055i
$334$	−8.37256			−0.458126
$335$	−7.74993	+	13.4233i	−0.423424	+	0.733392i
$336$	0.980808	+	1.69881i	0.0535075	+	0.0926776i
$337$	0.206705	+	0.358024i	0.0112599	+	0.0195028i	0.871600	−	0.490217i	$-0.163082\pi$
$337$	0.206705	+	0.358024i	0.0112599	+	0.0195028i	−0.860341	+	0.509720i	$0.829749\pi$
$338$	−11.1094	−	19.2420i	−0.604270	−	1.04663i
$339$	8.44450			0.458643
$340$	0.0910588	+	0.157718i	0.00493835	+	0.00855348i
$341$	−7.40678			−0.401100
$342$	−0.543707	+	0.941728i	−0.0294003	+	0.0509228i
$343$	19.9144			1.07528
$344$	−6.57262			−0.354372
$345$	−3.85702	+	6.68055i	−0.207655	+	0.359669i
$346$	4.45388	+	7.71434i	0.239442	+	0.414726i
$347$	−9.92539			−0.532823			−0.266412	−	0.963859i	$-0.585838\pi$
$347$	−9.92539			−0.532823			−0.266412	+	0.963859i	$0.585838\pi$
$348$	3.49178	−	6.04795i	0.187179	−	0.324204i
$349$	−1.42738	+	2.47230i	−0.0764060	+	0.132339i	−0.901697	−	0.432369i	$-0.857678\pi$
$349$	−1.42738	+	2.47230i	−0.0764060	+	0.132339i	0.825291	+	0.564708i	$0.191011\pi$
$350$	0.980808	−	1.69881i	0.0524264	−	0.0908052i
$351$	−2.96727	−	5.13946i	−0.158381	−	0.274324i
$352$	−0.796533	−	1.37964i	−0.0424554	−	0.0735348i
$353$	−15.0834	+	26.1252i	−0.802807	+	1.39050i	0.114955	+	0.993371i	$0.463328\pi$
$353$	−15.0834	+	26.1252i	−0.802807	+	1.39050i	−0.917762	+	0.397131i	$0.870006\pi$
$354$	5.04330	−	8.73525i	0.268048	−	0.464273i
$355$	−2.30550	+	3.99324i	−0.122363	+	0.211939i
$356$	7.14373			0.378617
$357$	−0.178622	−	0.309383i	−0.00945369	−	0.0163743i
$358$	3.57187	−	6.18665i	0.188779	−	0.326975i
$359$	1.64818			0.0869878			0.0434939	−	0.999054i	$-0.486151\pi$
$359$	1.64818			0.0869878			0.0434939	+	0.999054i	$0.486151\pi$
$360$	1.00000			0.0527046
$361$	8.90877	−	15.4304i	0.468882	−	0.812128i
$362$	−19.2410			−1.01128
$363$	4.23107	+	7.32843i	0.222074	+	0.384643i
$364$	−11.6413			−0.610169
$365$	0.731627	+	1.26721i	0.0382951	+	0.0663291i
$366$	−7.33768	−	12.7092i	−0.383546	−	0.664322i
$367$	−3.53823	−	6.12840i	−0.184694	−	0.319900i	0.758779	−	0.651348i	$-0.225796\pi$
$367$	−3.53823	−	6.12840i	−0.184694	−	0.319900i	−0.943473	+	0.331448i	$0.892463\pi$
$368$	−3.85702	+	6.68055i	−0.201061	+	0.348248i
$369$	4.37985			0.228006
$370$	5.19726	+	3.16046i	0.270193	+	0.164305i
$371$	18.6142			0.966401
$372$	2.32469	−	4.02649i	0.120530	−	0.208764i
$373$	7.73018	+	13.3891i	0.400254	+	0.693260i	0.993756	−	0.111572i	$-0.0355887\pi$
$373$	7.73018	+	13.3891i	0.400254	+	0.693260i	−0.593503	+	0.804832i	$0.702255\pi$
$374$	0.145063	+	0.251256i	0.00750101	+	0.0129921i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	2.58176			0.133144
$377$	20.7221	+	35.8918i	1.06724	+	1.84852i
$378$	−1.96162			−0.100895
$379$	−16.1340	+	27.9450i	−0.828749	+	1.43544i	0.0702704	+	0.997528i	$0.477614\pi$
$379$	−16.1340	+	27.9450i	−0.828749	+	1.43544i	−0.899020	+	0.437908i	$0.855720\pi$
$380$	1.08741			0.0557831
$381$	1.43371			0.0734513
$382$	4.58043	−	7.93353i	0.234355	−	0.405915i
$383$	6.26812	+	10.8567i	0.320286	+	0.554751i	0.980547	−	0.196285i	$-0.0628877\pi$
$383$	6.26812	+	10.8567i	0.320286	+	0.554751i	−0.660261	+	0.751036i	$0.729554\pi$
$384$	1.00000			0.0510310
$385$	1.56249	−	2.70632i	0.0796320	−	0.137927i
$386$	−8.43785	+	14.6148i	−0.429475	+	0.743873i
$387$	3.28631	−	5.69205i	0.167052	−	0.289343i
$388$	3.10419	+	5.37662i	0.157591	+	0.272956i
$389$	11.5941	+	20.0817i	0.587847	+	1.01818i	0.994514	+	0.104604i	$0.0333575\pi$
$389$	11.5941	+	20.0817i	0.587847	+	1.01818i	−0.406667	+	0.913576i	$0.633309\pi$
$390$	−2.96727	+	5.13946i	−0.150253	+	0.260247i
$391$	0.702430	−	1.21665i	0.0355234	−	0.0615284i
$392$	1.57603	−	2.72977i	0.0796016	−	0.137874i
$393$	2.93484			0.148043
$394$	−0.312230	−	0.540798i	−0.0157299	−	0.0272450i
$395$	−6.69726	+	11.6000i	−0.336976	+	0.583659i
$396$	1.59307			0.0800546
$397$	−14.5838			−0.731938			−0.365969	−	0.930627i	$-0.619262\pi$
$397$	−14.5838			−0.731938			−0.365969	+	0.930627i	$0.619262\pi$
$398$	−4.06945	+	7.04850i	−0.203983	+	0.353309i
$399$	−2.13309			−0.106788
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−34.7849			−1.73707			−0.868537	−	0.495625i	$-0.834939\pi$
$401$	−34.7849			−1.73707			−0.868537	+	0.495625i	$0.834939\pi$
$402$	−7.74993	−	13.4233i	−0.386531	−	0.669492i
$403$	13.7960	+	23.8953i	0.687227	+	1.19031i
$404$	−7.80509	−	13.5188i	−0.388318	−	0.672586i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	13.6991			0.679874
$407$	8.27958	+	5.03482i	0.410403	+	0.249567i
$408$	−0.182118			−0.00901616
$409$	18.5995	−	32.2152i	0.919685	−	1.59294i	0.119791	−	0.992799i	$-0.461778\pi$
$409$	18.5995	−	32.2152i	0.919685	−	1.59294i	0.799894	−	0.600141i	$-0.204889\pi$
$410$	−2.18993	−	3.79307i	−0.108153	−	0.187326i
$411$	−10.6084	−	18.3744i	−0.523276	−	0.906340i
$412$	−3.51313	−	6.08492i	−0.173080	−	0.299783i
$413$	19.7860			0.973607
$414$	−3.85702	−	6.68055i	−0.189562	−	0.328331i
$415$	−7.79713			−0.382746
$416$	−2.96727	+	5.13946i	−0.145482	+	0.251983i
$417$	0.516958			0.0253155
$418$	1.73232			0.0847306
$419$	−3.43878	+	5.95614i	−0.167995	+	0.290976i	−0.937715	−	0.347406i	$-0.887063\pi$
$419$	−3.43878	+	5.95614i	−0.167995	+	0.290976i	0.769720	+	0.638382i	$0.220396\pi$
$420$	0.980808	+	1.69881i	0.0478585	+	0.0828934i
$421$	34.2161			1.66759			0.833794	−	0.552075i	$-0.186164\pi$
$421$	34.2161			1.66759			0.833794	+	0.552075i	$0.186164\pi$
$422$	7.70422	−	13.3441i	0.375035	−	0.649580i
$423$	−1.29088	+	2.23587i	−0.0627648	+	0.108712i
$424$	4.74461	−	8.21790i	0.230419	−	0.399097i
$425$	0.0910588	+	0.157718i	0.00441700	+	0.00765047i
$426$	−2.30550	−	3.99324i	−0.111702	−	0.193473i
$427$	14.3937	−	24.9306i	0.696560	−	1.20648i
$428$	5.05684	−	8.75870i	0.244432	−	0.423368i
$429$	−4.72706	+	8.18750i	−0.228224	+	0.395296i
$430$	−6.57262			−0.316960
$431$	−7.78920	−	13.4913i	−0.375193	−	0.649853i	0.615163	−	0.788400i	$-0.289090\pi$
$431$	−7.78920	−	13.4913i	−0.375193	−	0.649853i	−0.990356	+	0.138547i	$0.955757\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−0.876055			−0.0421005			−0.0210503	−	0.999778i	$-0.506701\pi$
$433$	−0.876055			−0.0421005			−0.0210503	+	0.999778i	$0.506701\pi$
$434$	9.12031			0.437789
$435$	3.49178	−	6.04795i	0.167418	−	0.289977i
$436$	14.6321			0.700752
$437$	−4.19417	−	7.26452i	−0.200635	−	0.347509i
$438$	−1.46325			−0.0699170
$439$	8.51381	+	14.7464i	0.406342	+	0.703805i	0.994477	−	0.104958i	$-0.0334708\pi$
$439$	8.51381	+	14.7464i	0.406342	+	0.703805i	−0.588135	+	0.808763i	$0.700137\pi$
$440$	−0.796533	−	1.37964i	−0.0379732	−	0.0657716i
$441$	1.57603	+	2.72977i	0.0750491	+	0.129989i
$442$	0.540392	−	0.935986i	0.0257038	−	0.0445203i
$443$	4.85294			0.230570			0.115285	−	0.993332i	$-0.463222\pi$
$443$	4.85294			0.230570			0.115285	+	0.993332i	$0.463222\pi$
$444$	−5.33567	+	2.92073i	−0.253220	+	0.138612i
$445$	7.14373			0.338645
$446$	−10.4512	+	18.1021i	−0.494881	+	0.857158i
$447$	4.45340	+	7.71351i	0.210639	+	0.364837i
$448$	0.980808	+	1.69881i	0.0463388	+	0.0802612i
$449$	−10.8563	−	18.8036i	−0.512339	−	0.887397i	−0.999898	−	0.0143068i	$-0.995446\pi$
$449$	−10.8563	−	18.8036i	−0.512339	−	0.887397i	0.487559	−	0.873090i	$-0.337887\pi$
$450$	1.00000			0.0471405
$451$	−3.48870	−	6.04260i	−0.164276	−	0.284535i
$452$	8.44450			0.397196
$453$	−7.60984	+	13.1806i	−0.357542	+	0.619280i
$454$	27.2939			1.28097
$455$	−11.6413			−0.545752
$456$	−0.543707	+	0.941728i	−0.0254614	+	0.0441004i
$457$	−13.9075	−	24.0884i	−0.650563	−	1.12681i	−0.982986	−	0.183679i	$-0.941199\pi$
$457$	−13.9075	−	24.0884i	−0.650563	−	1.12681i	0.332423	−	0.943130i	$-0.392134\pi$
$458$	10.8837			0.508564
$459$	0.0910588	−	0.157718i	0.00425026	−	0.00736166i
$460$	−3.85702	+	6.68055i	−0.179834	+	0.311482i
$461$	−5.67822	+	9.83496i	−0.264461	+	0.458060i	−0.967422	−	0.253168i	$-0.918527\pi$
$461$	−5.67822	+	9.83496i	−0.264461	+	0.458060i	0.702961	+	0.711228i	$0.251861\pi$
$462$	1.56249	+	2.70632i	0.0726937	+	0.125909i
$463$	12.6691	+	21.9435i	0.588783	+	1.01980i	0.994392	+	0.105755i	$0.0337260\pi$
$463$	12.6691	+	21.9435i	0.588783	+	1.01980i	−0.405609	+	0.914047i	$0.632941\pi$
$464$	3.49178	−	6.04795i	0.162102	−	0.280769i
$465$	2.32469	−	4.02649i	0.107805	−	0.186724i
$466$	−3.53381	+	6.12074i	−0.163701	+	0.283538i
$467$	1.27369			0.0589394			0.0294697	−	0.999566i	$-0.490618\pi$
$467$	1.27369			0.0589394			0.0294697	+	0.999566i	$0.490618\pi$
$468$	−2.96727	−	5.13946i	−0.137162	−	0.237572i
$469$	15.2024	−	26.3313i	0.701981	−	1.21587i
$470$	2.58176			0.119088
$471$	−8.96713			−0.413184
$472$	5.04330	−	8.73525i	0.232137	−	0.402073i
$473$	−10.4706			−0.481439
$474$	−6.69726	−	11.6000i	−0.307615	−	0.532805i
$475$	1.08741			0.0498940
$476$	−0.178622	−	0.309383i	−0.00818714	−	0.0141805i
$477$	4.74461	+	8.21790i	0.217241	+	0.376272i
$478$	−4.98978	−	8.64255i	−0.228227	−	0.395301i
$479$	7.38387	−	12.7892i	0.337378	−	0.584355i	−0.646561	−	0.762862i	$-0.723793\pi$
$479$	7.38387	−	12.7892i	0.337378	−	0.584355i	0.983939	+	0.178507i	$0.0571268\pi$
$480$	1.00000			0.0456435
$481$	0.821403	−	36.0890i	0.0374528	−	1.64552i
$482$	−28.5612			−1.30093
$483$	7.56599	−	13.1047i	0.344264	−	0.596283i
$484$	4.23107	+	7.32843i	0.192321	+	0.333110i
$485$	3.10419	+	5.37662i	0.140954	+	0.244140i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−25.0969			−1.13725			−0.568626	−	0.822596i	$-0.692525\pi$
$487$	−25.0969			−1.13725			−0.568626	+	0.822596i	$0.692525\pi$
$488$	−7.33768	−	12.7092i	−0.332161	−	0.575320i
$489$	3.64306			0.164745
$490$	1.57603	−	2.72977i	0.0711978	−	0.123318i
$491$	40.8137			1.84190			0.920949	−	0.389683i	$-0.127415\pi$
$491$	40.8137			1.84190			0.920949	+	0.389683i	$0.127415\pi$
$492$	4.37985			0.197459
$493$	−0.635915	+	1.10144i	−0.0286402	+	0.0496062i
$494$	−3.22665	−	5.58872i	−0.145174	−	0.251448i
$495$	1.59307			0.0716030
$496$	2.32469	−	4.02649i	0.104382	−	0.180795i
$497$	4.52251	−	7.83321i	0.202862	−	0.351368i
$498$	3.89857	−	6.75252i	0.174699	−	0.302587i
$499$	−1.53731	−	2.66269i	−0.0688193	−	0.119199i	0.829563	−	0.558414i	$-0.188590\pi$
$499$	−1.53731	−	2.66269i	−0.0688193	−	0.119199i	−0.898382	+	0.439215i	$0.855257\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	4.18628	−	7.25085i	0.187029	−	0.323944i
$502$	−12.8904	+	22.3269i	−0.575328	+	0.996497i
$503$	11.6983	−	20.2620i	0.521600	−	0.903438i	−0.478084	−	0.878314i	$-0.658669\pi$
$503$	11.6983	−	20.2620i	0.521600	−	0.903438i	0.999684	−	0.0251236i	$-0.00799794\pi$
$504$	−1.96162			−0.0873773
$505$	−7.80509	−	13.5188i	−0.347322	−	0.601580i
$506$	−6.14448	+	10.6426i	−0.273156	+	0.473119i
$507$	22.2187			0.986768
$508$	1.43371			0.0636107
$509$	−8.04282	+	13.9306i	−0.356492	+	0.617462i	−0.987372	−	0.158418i	$-0.949361\pi$
$509$	−8.04282	+	13.9306i	−0.356492	+	0.617462i	0.630880	+	0.775880i	$0.282694\pi$
$510$	−0.182118			−0.00806430
$511$	−1.43517	−	2.48579i	−0.0634882	−	0.109965i
$512$	1.00000			0.0441942
$513$	−0.543707	−	0.941728i	−0.0240052	−	0.0415783i
$514$	1.56855	+	2.71681i	0.0691858	+	0.119833i
$515$	−3.51313	−	6.08492i	−0.154807	−	0.268134i
$516$	3.28631	−	5.69205i	0.144672	−	0.250579i
$517$	4.11292			0.180886
$518$	−10.1950	−	6.19961i	−0.447944	−	0.272395i
$519$	−8.90776			−0.391007
$520$	−2.96727	+	5.13946i	−0.130123	+	0.225380i
$521$	−17.7572	−	30.7563i	−0.777956	−	1.34746i	−0.933118	−	0.359571i	$-0.882923\pi$
$521$	−17.7572	−	30.7563i	−0.777956	−	1.34746i	0.155161	−	0.987889i	$-0.450410\pi$
$522$	3.49178	+	6.04795i	0.152831	+	0.264711i
$523$	−17.8026	−	30.8350i	−0.778454	−	1.34832i	−0.932833	−	0.360310i	$-0.882671\pi$
$523$	−17.8026	−	30.8350i	−0.778454	−	1.34832i	0.154379	−	0.988012i	$-0.450662\pi$
$524$	2.93484			0.128209
$525$	0.980808	+	1.69881i	0.0428060	+	0.0741421i
$526$	−19.7499			−0.861137
$527$	−0.423367	+	0.733294i	−0.0184422	+	0.0319428i
$528$	1.59307			0.0693293
$529$	36.5063			1.58723
$530$	4.74461	−	8.21790i	0.206093	−	0.356963i
$531$	5.04330	+	8.73525i	0.218861	+	0.379078i
$532$	−2.13309			−0.0924811
$533$	−12.9962	+	22.5101i	−0.562928	+	0.975020i
$534$	−3.57187	+	6.18665i	−0.154570	+	0.267723i
$535$	5.05684	−	8.75870i	0.218626	−	0.378672i
$536$	−7.74993	−	13.4233i	−0.334746	−	0.579797i
$537$	3.57187	+	6.18665i	0.154137	+	0.266974i
$538$	7.28623	−	12.6201i	0.314132	−	0.544092i
$539$	2.51072	−	4.34870i	0.108144	−	0.187312i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	6.46102			0.277781			0.138890	−	0.990308i	$-0.455646\pi$
$541$	6.46102			0.277781			0.138890	+	0.990308i	$0.455646\pi$
$542$	−0.454136	−	0.786586i	−0.0195068	−	0.0337868i
$543$	9.62049	−	16.6632i	0.412855	−	0.715085i
$544$	−0.182118			−0.00780822
$545$	14.6321			0.626772
$546$	5.82064	−	10.0816i	0.249100	−	0.431455i
$547$	−32.7159			−1.39883			−0.699415	−	0.714715i	$-0.746556\pi$
$547$	−32.7159			−1.39883			−0.699415	+	0.714715i	$0.746556\pi$
$548$	−10.6084	−	18.3744i	−0.453170	−	0.784913i
$549$	14.6754			0.626329
$550$	−0.796533	−	1.37964i	−0.0339643	−	0.0588279i
$551$	3.79701	+	6.57662i	0.161758	+	0.280173i
$552$	−3.85702	−	6.68055i	−0.164166	−	0.284343i
$553$	13.1374	−	22.7547i	0.558661	−	0.967629i
$554$	−8.99919			−0.382339
$555$	−5.33567	+	2.92073i	−0.226487	+	0.123978i
$556$	0.516958			0.0219239
$557$	5.11590	−	8.86100i	0.216768	−	0.375453i	−0.737050	−	0.675838i	$-0.763782\pi$
$557$	5.11590	−	8.86100i	0.216768	−	0.375453i	0.953818	+	0.300385i	$0.0971152\pi$
$558$	2.32469	+	4.02649i	0.0984121	+	0.170455i
$559$	19.5027	+	33.7797i	0.824877	+	1.42873i
$560$	0.980808	+	1.69881i	0.0414467	+	0.0717878i
$561$	−0.290125			−0.0122491
$562$	−10.3733	−	17.9671i	−0.437572	−	0.757897i
$563$	7.15869			0.301703			0.150851	−	0.988556i	$-0.451798\pi$
$563$	7.15869			0.301703			0.150851	+	0.988556i	$0.451798\pi$
$564$	−1.29088	+	2.23587i	−0.0543559	+	0.0941471i
$565$	8.44450			0.355263
$566$	7.84281			0.329658
$567$	0.980808	−	1.69881i	0.0411901	−	0.0713433i
$568$	−2.30550	−	3.99324i	−0.0967367	−	0.167553i
$569$	−34.1066			−1.42982			−0.714911	−	0.699216i	$-0.753533\pi$
$569$	−34.1066			−1.42982			−0.714911	+	0.699216i	$0.753533\pi$
$570$	−0.543707	+	0.941728i	−0.0227734	+	0.0394446i
$571$	0.324363	−	0.561814i	0.0135742	−	0.0235112i	−0.859159	−	0.511710i	$-0.829012\pi$
$571$	0.324363	−	0.561814i	0.0135742	−	0.0235112i	0.872733	+	0.488198i	$0.162346\pi$
$572$	−4.72706	+	8.18750i	−0.197648	+	0.342337i
$573$	4.58043	+	7.93353i	0.191350	+	0.331428i
$574$	4.29580	+	7.44054i	0.179303	+	0.310562i
$575$	−3.85702	+	6.68055i	−0.160849	+	0.278598i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.55818	−	7.89499i	0.189759	−	0.328673i	−0.755411	−	0.655252i	$-0.772563\pi$
$577$	4.55818	−	7.89499i	0.189759	−	0.328673i	0.945170	+	0.326579i	$0.105896\pi$
$578$	−16.9668			−0.705727
$579$	−8.43785	−	14.6148i	−0.350665	−	0.607370i
$580$	3.49178	−	6.04795i	0.144988	−	0.251127i
$581$	15.2950			0.634543
$582$	−6.20838			−0.257346
$583$	7.55848	−	13.0917i	0.313040	−	0.542201i
$584$	−1.46325			−0.0605499
$585$	−2.96727	−	5.13946i	−0.122681	−	0.212491i
$586$	−12.5273			−0.517498
$587$	8.79071	+	15.2259i	0.362831	+	0.628442i	0.988426	−	0.151706i	$-0.0484768\pi$
$587$	8.79071	+	15.2259i	0.362831	+	0.628442i	−0.625594	+	0.780148i	$0.715143\pi$
$588$	1.57603	+	2.72977i	0.0649944	+	0.112574i
$589$	2.52790	+	4.37846i	0.104160	+	0.180411i
$590$	5.04330	−	8.73525i	0.207629	−	0.359625i
$591$	0.624460			0.0256868
$592$	−5.33567	+	2.92073i	−0.219295	+	0.120041i
$593$	21.8082			0.895556			0.447778	−	0.894145i	$-0.352215\pi$
$593$	21.8082			0.895556			0.447778	+	0.894145i	$0.352215\pi$
$594$	−0.796533	+	1.37964i	−0.0326821	+	0.0566071i
$595$	−0.178622	−	0.309383i	−0.00732280	−	0.0126835i
$596$	4.45340	+	7.71351i	0.182418	+	0.315958i
$597$	−4.06945	−	7.04850i	−0.166552	−	0.288476i
$598$	45.7792			1.87205
$599$	21.4481	+	37.1492i	0.876346	+	1.51788i	0.855321	+	0.518098i	$0.173360\pi$
$599$	21.4481	+	37.1492i	0.876346	+	1.51788i	0.0210250	+	0.999779i	$0.493307\pi$
$600$	1.00000			0.0408248
$601$	−2.41151	+	4.17685i	−0.0983674	+	0.170377i	−0.911009	−	0.412386i	$-0.864695\pi$
$601$	−2.41151	+	4.17685i	−0.0983674	+	0.170377i	0.812642	+	0.582764i	$0.198029\pi$
$602$	12.8930			0.525477
$603$	15.4999			0.631203
$604$	−7.60984	+	13.1806i	−0.309640	+	0.536312i
$605$	4.23107	+	7.32843i	0.172017	+	0.297943i
$606$	15.6102			0.634121
$607$	10.7952	−	18.6979i	0.438165	−	0.758924i	−0.559383	−	0.828909i	$-0.688962\pi$
$607$	10.7952	−	18.6979i	0.438165	−	0.758924i	0.997548	+	0.0699850i	$0.0222951\pi$
$608$	−0.543707	+	0.941728i	−0.0220502	+	0.0381921i
$609$	−6.84954	+	11.8637i	−0.277557	+	0.480743i
$610$	−7.33768	−	12.7092i	−0.297094	−	0.514582i
$611$	−7.66078	−	13.2689i	−0.309922	−	0.536801i
$612$	0.0910588	−	0.157718i	0.00368083	−	0.00637539i
$613$	−18.3069	+	31.7085i	−0.739410	+	1.28069i	0.213352	+	0.976975i	$0.431562\pi$
$613$	−18.3069	+	31.7085i	−0.739410	+	1.28069i	−0.952761	+	0.303720i	$0.901771\pi$
$614$	1.85230	−	3.20827i	0.0747526	−	0.129475i
$615$	4.37985			0.176613
$616$	1.56249	+	2.70632i	0.0629546	+	0.109041i
$617$	14.3971	−	24.9365i	0.579605	−	1.00390i	−0.415920	−	0.909401i	$-0.636540\pi$
$617$	14.3971	−	24.9365i	0.579605	−	1.00390i	0.995525	−	0.0945034i	$-0.0301263\pi$
$618$	7.02627			0.282638
$619$	32.5322			1.30758			0.653789	−	0.756677i	$-0.273178\pi$
$619$	32.5322			1.30758			0.653789	+	0.756677i	$0.273178\pi$
$620$	2.32469	−	4.02649i	0.0933619	−	0.161708i
$621$	7.71404			0.309554
$622$	12.1914	+	21.1162i	0.488832	+	0.846681i
$623$	−14.0133			−0.561429
$624$	−2.96727	−	5.13946i	−0.118786	−	0.205743i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.8450	−	18.7841i	−0.433454	−	0.750764i
$627$	−0.866161	+	1.50023i	−0.0345911	+	0.0599136i
$628$	−8.96713			−0.357828
$629$	0.971719	−	0.531915i	0.0387450	−	0.0212089i
$630$	−1.96162			−0.0781526
$631$	8.44685	−	14.6304i	0.336264	−	0.582426i	−0.647463	−	0.762097i	$-0.724170\pi$
$631$	8.44685	−	14.6304i	0.336264	−	0.582426i	0.983727	+	0.179671i	$0.0575034\pi$
$632$	−6.69726	−	11.6000i	−0.266403	−	0.461423i
$633$	7.70422	+	13.3441i	0.306215	+	0.530380i
$634$	7.29371	+	12.6331i	0.289670	+	0.501724i
$635$	1.43371			0.0568952
$636$	4.74461	+	8.21790i	0.188136	+	0.325861i
$637$	−18.7060			−0.741160
$638$	5.56264	−	9.63478i	0.220227	−	0.381445i
$639$	4.61100			0.182408
$640$	1.00000			0.0395285
$641$	−22.3988	+	38.7958i	−0.884698	+	1.53234i	−0.0386384	+	0.999253i	$0.512302\pi$
$641$	−22.3988	+	38.7958i	−0.884698	+	1.53234i	−0.846060	+	0.533088i	$0.821031\pi$
$642$	5.05684	+	8.75870i	0.199578	+	0.345678i
$643$	−1.48720			−0.0586496			−0.0293248	−	0.999570i	$-0.509336\pi$
$643$	−1.48720			−0.0586496			−0.0293248	+	0.999570i	$0.509336\pi$
$644$	7.56599	−	13.1047i	0.298142	−	0.516397i
$645$	3.28631	−	5.69205i	0.129398	−	0.224124i
$646$	0.0990185	−	0.171505i	0.00389583	−	0.00674778i
$647$	−21.0229	−	36.4126i	−0.826494	−	1.43153i	−0.900772	−	0.434291i	$-0.856999\pi$
$647$	−21.0229	−	36.4126i	−0.826494	−	1.43153i	0.0742789	−	0.997238i	$-0.476335\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.03431	−	13.9158i	0.315374	−	0.546244i
$650$	−2.96727	+	5.13946i	−0.116386	+	0.201586i
$651$	−4.56015	+	7.89842i	−0.178727	+	0.309563i
$652$	3.64306			0.142673
$653$	8.02270	+	13.8957i	0.313953	+	0.543782i	0.979214	−	0.202828i	$-0.0650134\pi$
$653$	8.02270	+	13.8957i	0.313953	+	0.543782i	−0.665262	+	0.746610i	$0.731680\pi$
$654$	−7.31607	+	12.6718i	−0.286081	+	0.495507i
$655$	2.93484			0.114674
$656$	4.37985			0.171005
$657$	0.731627	−	1.26721i	0.0285435	−	0.0494388i
$658$	−5.06442			−0.197432
$659$	2.10043	+	3.63806i	0.0818213	+	0.141719i	0.904032	−	0.427464i	$-0.140593\pi$
$659$	2.10043	+	3.63806i	0.0818213	+	0.141719i	−0.822211	+	0.569183i	$0.807260\pi$
$660$	1.59307			0.0620100
$661$	8.92207	+	15.4535i	0.347028	+	0.601071i	0.985720	−	0.168392i	$-0.0538574\pi$
$661$	8.92207	+	15.4535i	0.347028	+	0.601071i	−0.638692	+	0.769463i	$0.720524\pi$
$662$	11.4693	+	19.8654i	0.445766	+	0.772089i
$663$	0.540392	+	0.935986i	0.0209871	+	0.0363507i
$664$	3.89857	−	6.75252i	0.151294	−	0.262048i
$665$	−2.13309			−0.0827176
$666$	0.138411	−	6.08119i	0.00536330	−	0.235641i
$667$	−53.8715			−2.08591
$668$	4.18628	−	7.25085i	0.161972	−	0.280544i
$669$	−10.4512	−	18.1021i	−0.404068	−	0.699867i
$670$	−7.74993	−	13.4233i	−0.299406	−	0.518586i
$671$	−11.6894	−	20.2466i	−0.451264	−	0.781613i
$672$	−1.96162			−0.0756710
$673$	13.3669	+	23.1522i	0.515257	+	0.892451i	0.999843	+	0.0177075i	$0.00563677\pi$
$673$	13.3669	+	23.1522i	0.515257	+	0.892451i	−0.484586	+	0.874743i	$0.661030\pi$
$674$	−0.413410			−0.0159240
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	22.2187			0.854566
$677$	12.7426			0.489737			0.244869	−	0.969556i	$-0.421255\pi$
$677$	12.7426			0.489737			0.244869	+	0.969556i	$0.421255\pi$
$678$	−4.22225	+	7.31316i	−0.162155	+	0.280860i
$679$	−6.08923	−	10.5469i	−0.233683	−	0.404751i
$680$	−0.182118			−0.00698389
$681$	−13.6470	+	23.6372i	−0.522953	+	0.905781i
$682$	3.70339	−	6.41446i	0.141810	−	0.245622i
$683$	5.97292	−	10.3454i	0.228547	−	0.395856i	−0.728830	−	0.684694i	$-0.759936\pi$
$683$	5.97292	−	10.3454i	0.228547	−	0.395856i	0.957378	+	0.288838i	$0.0932691\pi$
$684$	−0.543707	−	0.941728i	−0.0207892	−	0.0360079i
$685$	−10.6084	−	18.3744i	−0.405328	−	0.702048i
$686$	−9.95722	+	17.2464i	−0.380169	+	0.658471i
$687$	−5.44187	+	9.42559i	−0.207620	+	0.359609i
$688$	3.28631	−	5.69205i	0.125289	−	0.217008i
$689$	−56.3141			−2.14540
$690$	−3.85702	−	6.68055i	−0.146834	−	0.254324i
$691$	8.28924	−	14.3574i	0.315338	−	0.546181i	−0.664172	−	0.747580i	$-0.731216\pi$
$691$	8.28924	−	14.3574i	0.315338	−	0.546181i	0.979509	+	0.201399i	$0.0645489\pi$
$692$	−8.90776			−0.338622
$693$	−3.12498			−0.118708
$694$	4.96270	−	8.59564i	0.188381	−	0.326286i
$695$	0.516958			0.0196093
$696$	3.49178	+	6.04795i	0.132356	+	0.229247i
$697$	−0.797648			−0.0302131
$698$	−1.42738	−	2.47230i	−0.0540272	−	0.0935779i
$699$	−3.53381	−	6.12074i	−0.133661	−	0.231508i
$700$	0.980808	+	1.69881i	0.0370711	+	0.0642090i
$701$	7.95134	−	13.7721i	0.300318	−	0.520166i	−0.675890	−	0.737003i	$-0.736241\pi$
$701$	7.95134	−	13.7721i	0.300318	−	0.520166i	0.976208	+	0.216837i	$0.0695739\pi$
$702$	5.93454			0.223985
$703$	0.150510	−	6.61277i	0.00567658	−	0.249405i
$704$	1.59307			0.0600409
$705$	−1.29088	+	2.23587i	−0.0486174	+	0.0842078i
$706$	−15.0834	−	26.1252i	−0.567670	−	0.983233i
$707$	15.3106	+	26.5187i	0.575814	+	0.997340i
$708$	5.04330	+	8.73525i	0.189539	+	0.328291i
$709$	36.2623			1.36186			0.680929	−	0.732349i	$-0.261576\pi$
$709$	36.2623			1.36186			0.680929	+	0.732349i	$0.261576\pi$
$710$	−2.30550	−	3.99324i	−0.0865239	−	0.149864i
$711$	13.3945			0.502334
$712$	−3.57187	+	6.18665i	−0.133861	+	0.231855i
$713$	−35.8655			−1.34317
$714$	0.357245			0.0133695
$715$	−4.72706	+	8.18750i	−0.176782	+	0.306195i
$716$	3.57187	+	6.18665i	0.133487	+	0.231206i
$717$	9.97955			0.372693
$718$	−0.824092	+	1.42737i	−0.0307548	+	0.0532689i
$719$	3.78341	−	6.55307i	0.141098	−	0.244388i	−0.786813	−	0.617192i	$-0.788270\pi$
$719$	3.78341	−	6.55307i	0.141098	−	0.244388i	0.927910	+	0.372804i	$0.121604\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	6.89142	+	11.9363i	0.256650	+	0.444530i
$722$	8.90877	+	15.4304i	0.331550	+	0.574261i
$723$	14.2806	−	24.7347i	0.531100	−	0.919893i
$724$	9.62049	−	16.6632i	0.357543	−	0.619282i
$725$	3.49178	−	6.04795i	0.129682	−	0.224615i
$726$	−8.46214			−0.314059
$727$	11.9360	+	20.6738i	0.442683	+	0.766749i	0.997888	−	0.0649648i	$-0.0206935\pi$
$727$	11.9360	+	20.6738i	0.442683	+	0.766749i	−0.555205	+	0.831714i	$0.687360\pi$
$728$	5.82064	−	10.0816i	0.215727	−	0.373651i
$729$	1.00000			0.0370370
$730$	−1.46325			−0.0541574
$731$	−0.598494	+	1.03662i	−0.0221361	+	0.0383409i
$732$	14.6754			0.542417
$733$	−20.7314	−	35.9079i	−0.765732	−	1.32629i	−0.939859	−	0.341564i	$-0.889043\pi$
$733$	−20.7314	−	35.9079i	−0.765732	−	1.32629i	0.174126	−	0.984723i	$-0.444290\pi$
$734$	7.07647			0.261197
$735$	1.57603	+	2.72977i	0.0581328	+	0.100689i
$736$	−3.85702	−	6.68055i	−0.142172	−	0.246248i
$737$	−12.3462	−	21.3842i	−0.454776	−	0.787696i
$738$	−2.18993	+	3.79307i	−0.0806123	+	0.139625i
$739$	29.5101			1.08555			0.542774	−	0.839879i	$-0.317374\pi$
$739$	29.5101			1.08555			0.542774	+	0.839879i	$0.317374\pi$
$740$	−5.33567	+	2.92073i	−0.196143	+	0.107368i
$741$	6.45330			0.237068
$742$	−9.30710	+	16.1204i	−0.341674	+	0.591798i
$743$	−5.90686	−	10.2310i	−0.216702	−	0.375338i	0.737096	−	0.675788i	$-0.236197\pi$
$743$	−5.90686	−	10.2310i	−0.216702	−	0.375338i	−0.953798	+	0.300450i	$0.902863\pi$
$744$	2.32469	+	4.02649i	0.0852274	+	0.147618i
$745$	4.45340	+	7.71351i	0.163160	+	0.282601i
$746$	−15.4604			−0.566044
$747$	3.89857	+	6.75252i	0.142641	+	0.247062i
$748$	−0.290125			−0.0106080
$749$	−9.91958	+	17.1812i	−0.362453	+	0.627788i
$750$	1.00000			0.0365148
$751$	38.7531			1.41412			0.707060	−	0.707153i	$-0.250021\pi$
$751$	38.7531			1.41412			0.707060	+	0.707153i	$0.250021\pi$
$752$	−1.29088	+	2.23587i	−0.0470736	+	0.0815338i
$753$	−12.8904	−	22.3269i	−0.469753	−	0.813636i
$754$	−41.4442			−1.50931
$755$	−7.60984	+	13.1806i	−0.276951	+	0.479692i
$756$	0.980808	−	1.69881i	0.0356716	−	0.0617851i
$757$	25.3568	−	43.9193i	0.921609	−	1.59627i	0.124682	−	0.992197i	$-0.460209\pi$
$757$	25.3568	−	43.9193i	0.921609	−	1.59627i	0.796926	−	0.604076i	$-0.206458\pi$
$758$	−16.1340	−	27.9450i	−0.586014	−	1.01501i
$759$	−6.14448	−	10.6426i	−0.223031	−	0.386300i
$760$	−0.543707	+	0.941728i	−0.0197223	+	0.0341601i
$761$	−16.1286	+	27.9355i	−0.584660	+	1.01266i	0.410257	+	0.911970i	$0.365439\pi$
$761$	−16.1286	+	27.9355i	−0.584660	+	1.01266i	−0.994918	+	0.100691i	$0.967894\pi$
$762$	−0.716857	+	1.24163i	−0.0259690	+	0.0449796i
$763$	−28.7026			−1.03911
$764$	4.58043	+	7.93353i	0.165714	+	0.287025i
$765$	0.0910588	−	0.157718i	0.00329224	−	0.00570232i
$766$	−12.5362			−0.452952
$767$	−59.8593			−2.16139
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−47.2434			−1.70364			−0.851821	−	0.523833i	$-0.824502\pi$
$769$	−47.2434			−1.70364			−0.851821	+	0.523833i	$0.824502\pi$
$770$	1.56249	+	2.70632i	0.0563083	+	0.0975288i
$771$	−3.13710			−0.112980
$772$	−8.43785	−	14.6148i	−0.303685	−	0.525998i
$773$	9.89161	+	17.1328i	0.355776	+	0.616223i	0.987251	−	0.159174i	$-0.0508831\pi$
$773$	9.89161	+	17.1328i	0.355776	+	0.616223i	−0.631474	+	0.775397i	$0.717550\pi$
$774$	3.28631	+	5.69205i	0.118124	+	0.204597i
$775$	2.32469	−	4.02649i	0.0835054	−	0.144636i
$776$	−6.20838			−0.222868
$777$	10.4665	−	5.72934i	0.375485	−	0.205539i
$778$	−23.1883			−0.831341
$779$	−2.38136	+	4.12463i	−0.0853210	+	0.147780i
$780$	−2.96727	−	5.13946i	−0.106245	−	0.184022i
$781$	−3.67282	−	6.36150i	−0.131424	−	0.227632i
$782$	0.702430	+	1.21665i	0.0251189	+	0.0435071i
$783$	−6.98357			−0.249572
$784$	1.57603	+	2.72977i	0.0562868	+	0.0974917i
$785$	−8.96713			−0.320051
$786$	−1.46742	+	2.54164i	−0.0523411	+	0.0906574i
$787$	6.13590			0.218721			0.109361	−	0.994002i	$-0.465120\pi$
$787$	6.13590			0.218721			0.109361	+	0.994002i	$0.465120\pi$
$788$	0.624460			0.0222455
$789$	9.87495	−	17.1039i	0.351558	−	0.608916i
$790$	−6.69726	−	11.6000i	−0.238278	−	0.412709i
$791$	−16.5649			−0.588979
$792$	−0.796533	+	1.37964i	−0.0283036	+	0.0490232i
$793$	−43.5457	+	75.4234i	−1.54635	+	2.67836i
$794$	7.29188	−	12.6299i	0.258779	−	0.448219i
$795$	4.74461	+	8.21790i	0.168274	+	0.291459i
$796$	−4.06945	−	7.04850i	−0.144238	−	0.249827i
$797$	−2.34407	+	4.06006i	−0.0830314	+	0.143815i	−0.904551	−	0.426366i	$-0.859794\pi$
$797$	−2.34407	+	4.06006i	−0.0830314	+	0.143815i	0.821519	+	0.570181i	$0.193127\pi$
$798$	1.06654	−	1.84731i	0.0377552	−	0.0653940i
$799$	0.235092	−	0.407191i	0.00831696	−	0.0144054i
$800$	1.00000			0.0353553
$801$	−3.57187	−	6.18665i	−0.126206	−	0.218595i
$802$	17.3924	−	30.1246i	0.614148	−	1.06374i
$803$	−2.33106			−0.0822613
$804$	15.4999			0.546638
$805$	7.56599	−	13.1047i	0.266666	−	0.461879i
$806$	−27.5920			−0.971885
$807$	7.28623	+	12.6201i	0.256488	+	0.444249i
$808$	15.6102			0.549165
$809$	17.4519	+	30.2276i	0.613576	+	1.06274i	0.990633	+	0.136554i	$0.0436028\pi$
$809$	17.4519	+	30.2276i	0.613576	+	1.06274i	−0.377057	+	0.926190i	$0.623064\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−21.9928	−	38.0926i	−0.772271	−	1.33761i	−0.936315	−	0.351160i	$-0.885787\pi$
$811$	−21.9928	−	38.0926i	−0.772271	−	1.33761i	0.164044	−	0.986453i	$-0.447546\pi$
$812$	−6.84954	+	11.8637i	−0.240372	+	0.416336i
$813$	0.908272			0.0318545
$814$	−8.50007	+	4.65291i	−0.297927	+	0.163084i
$815$	3.64306			0.127611
$816$	0.0910588	−	0.157718i	0.00318769	−	0.00552125i
$817$	3.57358	+	6.18962i	0.125024	+	0.216547i
$818$	18.5995	+	32.2152i	0.650315	+	1.12638i
$819$	5.82064	+	10.0816i	0.203390	+	0.352281i
$820$	4.37985			0.152951
$821$	0.763088	+	1.32171i	0.0266319	+	0.0461279i	0.879034	−	0.476759i	$-0.158188\pi$
$821$	0.763088	+	1.32171i	0.0266319	+	0.0461279i	−0.852402	+	0.522887i	$0.824855\pi$
$822$	21.2169			0.740024
$823$	−27.1228	+	46.9780i	−0.945440	+	1.63755i	−0.190573	+	0.981673i	$0.561035\pi$
$823$	−27.1228	+	46.9780i	−0.945440	+	1.63755i	−0.754867	+	0.655878i	$0.772299\pi$
$824$	7.02627			0.244772
$825$	1.59307			0.0554634
$826$	−9.89302	+	17.1352i	−0.344222	+	0.596210i
$827$	−20.3990	−	35.3320i	−0.709341	−	1.22861i	−0.965102	−	0.261875i	$-0.915659\pi$
$827$	−20.3990	−	35.3320i	−0.709341	−	1.22861i	0.255761	−	0.966740i	$-0.417674\pi$
$828$	7.71404			0.268081
$829$	−1.34828	+	2.33528i	−0.0468276	+	0.0811078i	−0.888489	−	0.458898i	$-0.848244\pi$
$829$	−1.34828	+	2.33528i	−0.0468276	+	0.0811078i	0.841662	+	0.540005i	$0.181578\pi$
$830$	3.89857	−	6.75252i	0.135321	−	0.234383i
$831$	4.49959	−	7.79352i	0.156089	−	0.270354i
$832$	−2.96727	−	5.13946i	−0.102872	−	0.178179i
$833$	−0.287023	−	0.497138i	−0.00994476	−	0.0172248i
$834$	−0.258479	+	0.447698i	−0.00895039	+	0.0155025i
$835$	4.18628	−	7.25085i	0.144872	−	0.250926i
$836$	−0.866161	+	1.50023i	−0.0299568	+	0.0518867i
$837$	−4.64939			−0.160706
$838$	−3.43878	−	5.95614i	−0.118791	−	0.205751i
$839$	8.07775	−	13.9911i	0.278875	−	0.483026i	−0.692230	−	0.721676i	$-0.743372\pi$
$839$	8.07775	−	13.9911i	0.278875	−	0.483026i	0.971105	+	0.238651i	$0.0767052\pi$
$840$	−1.96162			−0.0676822
$841$	19.7702			0.681731
$842$	−17.1080	+	29.6320i	−0.589582	+	1.02119i
$843$	20.7466			0.714552
$844$	7.70422	+	13.3441i	0.265190	+	0.459323i
$845$	22.2187			0.764347
$846$	−1.29088	−	2.23587i	−0.0443814	−	0.0768708i
$847$	−8.29973	−	14.3756i	−0.285182	−	0.493950i
$848$	4.74461	+	8.21790i	0.162931	+	0.282204i
$849$	−3.92140	+	6.79207i	−0.134582	+	0.233103i
$850$	−0.182118			−0.00624658
$851$	40.0918	+	24.3799i	1.37433	+	0.835732i
$852$	4.61100			0.157970
$853$	−12.6385	+	21.8906i	−0.432735	+	0.749519i	−0.997108	−	0.0760011i	$-0.975785\pi$
$853$	−12.6385	+	21.8906i	−0.432735	+	0.749519i	0.564373	+	0.825520i	$0.309118\pi$
$854$	14.3937	+	24.9306i	0.492542	+	0.853108i
$855$	−0.543707	−	0.941728i	−0.0185944	−	0.0322064i
$856$	5.05684	+	8.75870i	0.172839	+	0.299366i
$857$	5.19427			0.177433			0.0887164	−	0.996057i	$-0.471724\pi$
$857$	5.19427			0.177433			0.0887164	+	0.996057i	$0.471724\pi$
$858$	−4.72706	−	8.18750i	−0.161379	−	0.279517i
$859$	20.5501			0.701160			0.350580	−	0.936533i	$-0.385985\pi$
$859$	20.5501			0.701160			0.350580	+	0.936533i	$0.385985\pi$
$860$	3.28631	−	5.69205i	0.112062	−	0.194097i
$861$	−8.59159			−0.292801
$862$	15.5784			0.530603
$863$	7.71895	−	13.3696i	0.262756	−	0.455107i	−0.704217	−	0.709985i	$-0.748702\pi$
$863$	7.71895	−	13.3696i	0.262756	−	0.455107i	0.966973	+	0.254878i	$0.0820352\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−8.90776			−0.302873
$866$	0.438028	−	0.758686i	0.0148848	−	0.0257812i
$867$	8.48342	−	14.6937i	0.288112	−	0.499025i
$868$	−4.56015	+	7.89842i	−0.154782	+	0.268090i
$869$	−10.6692	−	18.4796i	−0.361927	−	0.626876i
$870$	3.49178	+	6.04795i	0.118383	+	0.205045i
$871$	−45.9923	+	79.6609i	−1.55839	+	2.69921i
$872$	−7.31607	+	12.6718i	−0.247753	+	0.429121i
$873$	3.10419	−	5.37662i	0.105061	−	0.181971i
$874$	8.38835			0.283740
$875$	0.980808	+	1.69881i	0.0331574	+	0.0574302i
$876$	0.731627	−	1.26721i	0.0247194	−	0.0428152i
$877$	−21.4995			−0.725986			−0.362993	−	0.931792i	$-0.618245\pi$
$877$	−21.4995			−0.725986			−0.362993	+	0.931792i	$0.618245\pi$
$878$	−17.0276			−0.574654
$879$	6.26365	−	10.8490i	0.211268	−	0.365926i
$880$	1.59307			0.0537023
$881$	−15.3006	−	26.5014i	−0.515489	−	0.892853i	−0.999838	−	0.0179785i	$-0.994277\pi$
$881$	−15.3006	−	26.5014i	−0.515489	−	0.892853i	0.484349	−	0.874875i	$-0.339056\pi$
$882$	−3.15206			−0.106135
$883$	−10.4743	−	18.1420i	−0.352487	−	0.610526i	0.634197	−	0.773171i	$-0.281331\pi$
$883$	−10.4743	−	18.1420i	−0.352487	−	0.610526i	−0.986685	+	0.162645i	$0.947997\pi$
$884$	0.540392	+	0.935986i	0.0181753	+	0.0314806i
$885$	5.04330	+	8.73525i	0.169529	+	0.293632i
$886$	−2.42647	+	4.20277i	−0.0815189	+	0.141195i
$887$	−6.49053			−0.217931			−0.108965	−	0.994046i	$-0.534754\pi$
$887$	−6.49053			−0.217931			−0.108965	+	0.994046i	$0.534754\pi$
$888$	0.138411	−	6.08119i	0.00464476	−	0.204071i
$889$	−2.81239			−0.0943247
$890$	−3.57187	+	6.18665i	−0.119729	+	0.207377i
$891$	−0.796533	−	1.37964i	−0.0266849	−	0.0462195i
$892$	−10.4512	−	18.1021i	−0.349933	−	0.606103i
$893$	−1.40372	−	2.43132i	−0.0469737	−	0.0813609i
$894$	−8.90680			−0.297888
$895$	3.57187	+	6.18665i	0.119394	+	0.206797i
$896$	−1.96162			−0.0655330
$897$	−22.8896	+	39.6460i	−0.764262	+	1.32374i
$898$	21.7125			0.724557
$899$	32.4693			1.08291
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−0.864076	−	1.49662i	−0.0287866	−	0.0498598i
$902$	6.97740			0.232322
$903$	−6.44648	+	11.1656i	−0.214525	+	0.371569i
$904$	−4.22225	+	7.31316i	−0.140430	+	0.243232i
$905$	9.62049	−	16.6632i	0.319796	−	0.553903i
$906$	−7.60984	−	13.1806i	−0.252820	−	0.437897i
$907$	3.78765	+	6.56040i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$907$	3.78765	+	6.56040i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$908$	−13.6470	+	23.6372i	−0.452891	+	0.784430i
$909$	−7.80509	+	13.5188i	−0.258879	+	0.448391i
$910$	5.82064	−	10.0816i	0.192952	−	0.334203i
$911$	−2.11048			−0.0699232			−0.0349616	−	0.999389i	$-0.511131\pi$
$911$	−2.11048			−0.0699232			−0.0349616	+	0.999389i	$0.511131\pi$
$912$	−0.543707	−	0.941728i	−0.0180039	−	0.0311837i
$913$	6.21068	−	10.7572i	0.205543	−	0.356012i
$914$	27.8149			0.920036
$915$	14.6754			0.485152
$916$	−5.44187	+	9.42559i	−0.179804	+	0.311430i
$917$	−5.75702			−0.190114
$918$	0.0910588	+	0.157718i	0.00300539	+	0.00520548i
$919$	44.4029			1.46471			0.732357	−	0.680920i	$-0.238420\pi$
$919$	44.4029			1.46471			0.732357	+	0.680920i	$0.238420\pi$
$920$	−3.85702	−	6.68055i	−0.127162	−	0.220251i
$921$	1.85230	+	3.20827i	0.0610352	+	0.105716i
$922$	−5.67822	−	9.83496i	−0.187002	−	0.323897i
$923$	−13.6821	+	23.6981i	−0.450351	+	0.780031i
$924$	−3.12498			−0.102804
$925$	−5.33567	+	2.92073i	−0.175436	+	0.0960329i
$926$	−25.3382			−0.832665
$927$	−3.51313	+	6.08492i	−0.115386	+	0.199855i
$928$	3.49178	+	6.04795i	0.114623	+	0.198534i
$929$	−14.8562	−	25.7317i	−0.487416	−	0.844230i	0.512479	−	0.858700i	$-0.328727\pi$
$929$	−14.8562	−	25.7317i	−0.487416	−	0.844230i	−0.999895	+	0.0144700i	$0.995394\pi$
$930$	2.32469	+	4.02649i	0.0762297	+	0.132034i
$931$	−3.42760			−0.112335
$932$	−3.53381	−	6.12074i	−0.115754	−	0.200492i
$933$	−24.3829			−0.798259
$934$	−0.636846	+	1.10305i	−0.0208382	+	0.0360929i
$935$	−0.290125			−0.00948811
$936$	5.93454			0.193976
$937$	−5.68513	+	9.84694i	−0.185725	+	0.321685i	−0.943821	−	0.330458i	$-0.892797\pi$
$937$	−5.68513	+	9.84694i	−0.185725	+	0.321685i	0.758095	+	0.652144i	$0.226130\pi$
$938$	15.2024	+	26.3313i	0.496376	+	0.859748i
$939$	21.6900			0.707827
$940$	−1.29088	+	2.23587i	−0.0421039	+	0.0729261i
$941$	9.84604	−	17.0538i	0.320972	−	0.555939i	−0.659717	−	0.751514i	$-0.729324\pi$
$941$	9.84604	−	17.0538i	0.320972	−	0.555939i	0.980689	+	0.195575i	$0.0626572\pi$
$942$	4.48357	−	7.76576i	0.146082	−	0.253022i
$943$	−16.8932	−	29.2598i	−0.550118	−	0.952832i
$944$	5.04330	+	8.73525i	0.164145	+	0.284308i
$945$	0.980808	−	1.69881i	0.0319057	−	0.0552623i
$946$	5.23531	−	9.06782i	0.170215	−	0.294820i
$947$	−7.16029	+	12.4020i	−0.232678	+	0.403010i	−0.958595	−	0.284772i	$-0.908082\pi$
$947$	−7.16029	+	12.4020i	−0.232678	+	0.403010i	0.725917	+	0.687782i	$0.241416\pi$
$948$	13.3945			0.435034
$949$	4.34187	+	7.52033i	0.140943	+	0.244120i
$950$	−0.543707	+	0.941728i	−0.0176402	+	0.0305537i
$951$	−14.5874			−0.473030
$952$	0.357245			0.0115784
$953$	−10.3072	+	17.8525i	−0.333881	+	0.578300i	−0.983269	−	0.182158i	$-0.941692\pi$
$953$	−10.3072	+	17.8525i	−0.333881	+	0.578300i	0.649388	+	0.760457i	$0.275025\pi$
$954$	−9.48922			−0.307225
$955$	4.58043	+	7.93353i	0.148219	+	0.256723i
$956$	9.97955			0.322762
$957$	5.56264	+	9.63478i	0.179815	+	0.311448i
$958$	7.38387	+	12.7892i	0.238562	+	0.413202i
$959$	20.8097	+	36.0434i	0.671980	+	1.16390i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−9.38321			−0.302684
$962$	30.8433	+	18.7559i	0.994428	+	0.604714i
$963$	−10.1137			−0.325909
$964$	14.2806	−	24.7347i	0.459946	−	0.796651i
$965$	−8.43785	−	14.6148i	−0.271624	−	0.470467i
$966$	7.56599	+	13.1047i	0.243432	+	0.421636i
$967$	−15.7047	−	27.2014i	−0.505030	−	0.874738i	−0.999983	−	0.00581828i	$-0.998148\pi$
$967$	−15.7047	−	27.2014i	−0.505030	−	0.874738i	0.494953	−	0.868920i	$-0.335185\pi$
$968$	−8.46214			−0.271983
$969$	0.0990185	+	0.171505i	0.00318093	+	0.00550954i
$970$	−6.20838			−0.199339
$971$	−22.8854	+	39.6388i	−0.734429	+	1.27207i	0.220545	+	0.975377i	$0.429217\pi$
$971$	−22.8854	+	39.6388i	−0.734429	+	1.27207i	−0.954973	+	0.296691i	$0.904117\pi$
$972$	1.00000			0.0320750
$973$	−1.01407			−0.0325097
$974$	12.5485	−	21.7346i	0.402079	−	0.696421i
$975$	−2.96727	−	5.13946i	−0.0950286	−	0.164594i
$976$	14.6754			0.469747
$977$	−15.9631	+	27.6488i	−0.510704	+	0.884565i	0.489219	+	0.872161i	$0.337282\pi$
$977$	−15.9631	+	27.6488i	−0.510704	+	0.884565i	−0.999923	+	0.0124040i	$0.996052\pi$
$978$	−1.82153	+	3.15498i	−0.0582460	+	0.100885i
$979$	−5.69022	+	9.85575i	−0.181860	+	0.314991i
$980$	1.57603	+	2.72977i	0.0503445	+	0.0871992i
$981$	−7.31607	−	12.6718i	−0.233584	−	0.404580i
$982$	−20.4069	+	35.3457i	−0.651209	+	1.12793i
$983$	3.95423	−	6.84893i	0.126120	−	0.218447i	−0.796050	−	0.605231i	$-0.793081\pi$
$983$	3.95423	−	6.84893i	0.126120	−	0.218447i	0.922170	+	0.386784i	$0.126414\pi$
$984$	−2.18993	+	3.79307i	−0.0698123	+	0.120919i
$985$	0.624460			0.0198969
$986$	−0.635915	−	1.10144i	−0.0202517	−	0.0350769i
$987$	2.53221	−	4.38592i	0.0806012	−	0.139605i
$988$	6.45330			0.205307
$989$	−50.7014			−1.61221
$990$	−0.796533	+	1.37964i	−0.0253155	+	0.0438477i
$991$	−17.3308			−0.550529			−0.275265	−	0.961368i	$-0.588766\pi$
$991$	−17.3308			−0.550529			−0.275265	+	0.961368i	$0.588766\pi$
$992$	2.32469	+	4.02649i	0.0738091	+	0.127841i
$993$	−22.9386			−0.727933
$994$	4.52251	+	7.83321i	0.143445	+	0.248454i
$995$	−4.06945	−	7.04850i	−0.129010	−	0.223452i
$996$	3.89857	+	6.75252i	0.123531	+	0.213962i
$997$	6.47342	−	11.2123i	0.205015	−	0.355097i	−0.745122	−	0.666928i	$-0.767609\pi$
$997$	6.47342	−	11.2123i	0.205015	−	0.355097i	0.950138	+	0.311831i	$0.100942\pi$
$998$	3.07462			0.0973252
$999$	5.19726	+	3.16046i	0.164434	+	0.0999926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.p.121.4	✓	10
37.26	even	3	inner	1110.2.i.p.211.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.p.121.4	✓	10	1.1	even	1	trivial
1110.2.i.p.211.4	yes	10	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(0.980808 + 1.69881i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(0.980808 + 1.69881i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +1.59307 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.96727 - 5.13946i) q^{13} -1.96162 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0910588 - 0.157718i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.543707 - 0.941728i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.980808 - 1.69881i) q^{21} +(-0.796533 + 1.37964i) q^{22} +7.71404 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.93454 q^{26} +1.00000 q^{27} +(0.980808 - 1.69881i) q^{28} -6.98357 q^{29} +(-0.500000 - 0.866025i) q^{30} -4.64939 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.796533 - 1.37964i) q^{33} +(0.0910588 + 0.157718i) q^{34} +(0.980808 - 1.69881i) q^{35} +1.00000 q^{36} +(5.19726 + 3.16046i) q^{37} +1.08741 q^{38} +(-2.96727 + 5.13946i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.18993 - 3.79307i) q^{41} +(0.980808 + 1.69881i) q^{42} -6.57262 q^{43} +(-0.796533 - 1.37964i) q^{44} +1.00000 q^{45} +(-3.85702 + 6.68055i) q^{46} +2.58176 q^{47} +1.00000 q^{48} +(1.57603 - 2.72977i) q^{49} +(-0.500000 - 0.866025i) q^{50} -0.182118 q^{51} +(-2.96727 + 5.13946i) q^{52} +(4.74461 - 8.21790i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.796533 - 1.37964i) q^{55} +(0.980808 + 1.69881i) q^{56} +(-0.543707 + 0.941728i) q^{57} +(3.49178 - 6.04795i) q^{58} +(5.04330 - 8.73525i) q^{59} +1.00000 q^{60} +(-7.33768 - 12.7092i) q^{61} +(2.32469 - 4.02649i) q^{62} -1.96162 q^{63} +1.00000 q^{64} +(-2.96727 + 5.13946i) q^{65} +1.59307 q^{66} +(-7.74993 - 13.4233i) q^{67} -0.182118 q^{68} +(-3.85702 - 6.68055i) q^{69} +(0.980808 + 1.69881i) q^{70} +(-2.30550 - 3.99324i) q^{71} +(-0.500000 + 0.866025i) q^{72} -1.46325 q^{73} +(-5.33567 + 2.92073i) q^{74} +1.00000 q^{75} +(-0.543707 + 0.941728i) q^{76} +(1.56249 + 2.70632i) q^{77} +(-2.96727 - 5.13946i) q^{78} +(-6.69726 - 11.6000i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +4.37985 q^{82} +(3.89857 - 6.75252i) q^{83} -1.96162 q^{84} -0.182118 q^{85} +(3.28631 - 5.69205i) q^{86} +(3.49178 + 6.04795i) q^{87} +1.59307 q^{88} +(-3.57187 + 6.18665i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(5.82064 - 10.0816i) q^{91} +(-3.85702 - 6.68055i) q^{92} +(2.32469 + 4.02649i) q^{93} +(-1.29088 + 2.23587i) q^{94} +(-0.543707 + 0.941728i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.20838 q^{97} +(1.57603 + 2.72977i) q^{98} +(-0.796533 + 1.37964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9	\( 10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} + 10 q^{6} + 10 q^{8} - 5 q^{9} + 10 q^{10} - 2 q^{11} - 5 q^{12} + q^{13} - 5 q^{15} - 5 q^{16} - 5 q^{18} - 2 q^{19} - 5 q^{20} + q^{22} - 2 q^{23} - 5 q^{24} - 5 q^{25} - 2 q^{26} + 10 q^{27} + 18 q^{29} - 5 q^{30} - 14 q^{31} - 5 q^{32} + q^{33} + 10 q^{36} + 4 q^{38} + q^{39} - 5 q^{40} - 10 q^{41} + 6 q^{43} + q^{44} + 10 q^{45} + q^{46} + 30 q^{47} + 10 q^{48} - 11 q^{49} - 5 q^{50} + q^{52} - 2 q^{53} - 5 q^{54} + q^{55} - 2 q^{57} - 9 q^{58} - 7 q^{59} + 10 q^{60} - 6 q^{61} + 7 q^{62} + 10 q^{64} + q^{65} - 2 q^{66} - 5 q^{67} + q^{69} + 3 q^{71} - 5 q^{72} - 18 q^{73} - 3 q^{74} + 10 q^{75} - 2 q^{76} - 32 q^{77} + q^{78} - 15 q^{79} + 10 q^{80} - 5 q^{81} + 20 q^{82} - 5 q^{83} - 3 q^{86} - 9 q^{87} - 2 q^{88} - 25 q^{89} - 5 q^{90} - 18 q^{91} + q^{92} + 7 q^{93} - 15 q^{94} - 2 q^{95} - 5 q^{96} + 6 q^{97} - 11 q^{98} + q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 + 10 * q^6 + 10 * q^8 - 5 * q^9 + 10 * q^10 - 2 * q^11 - 5 * q^12 + q^13 - 5 * q^15 - 5 * q^16 - 5 * q^18 - 2 * q^19 - 5 * q^20 + q^22 - 2 * q^23 - 5 * q^24 - 5 * q^25 - 2 * q^26 + 10 * q^27 + 18 * q^29 - 5 * q^30 - 14 * q^31 - 5 * q^32 + q^33 + 10 * q^36 + 4 * q^38 + q^39 - 5 * q^40 - 10 * q^41 + 6 * q^43 + q^44 + 10 * q^45 + q^46 + 30 * q^47 + 10 * q^48 - 11 * q^49 - 5 * q^50 + q^52 - 2 * q^53 - 5 * q^54 + q^55 - 2 * q^57 - 9 * q^58 - 7 * q^59 + 10 * q^60 - 6 * q^61 + 7 * q^62 + 10 * q^64 + q^65 - 2 * q^66 - 5 * q^67 + q^69 + 3 * q^71 - 5 * q^72 - 18 * q^73 - 3 * q^74 + 10 * q^75 - 2 * q^76 - 32 * q^77 + q^78 - 15 * q^79 + 10 * q^80 - 5 * q^81 + 20 * q^82 - 5 * q^83 - 3 * q^86 - 9 * q^87 - 2 * q^88 - 25 * q^89 - 5 * q^90 - 18 * q^91 + q^92 + 7 * q^93 - 15 * q^94 - 2 * q^95 - 5 * q^96 + 6 * q^97 - 11 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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