LMFDB - Embedded newform 630.2.i.h.151.1

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			151.1
Root			$0.142686 - 1.50500i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.h.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.35158 + 1.08315i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.35158 + 1.08315i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(0.653555 - 2.92795i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.35158 + 1.08315i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.35158 + 1.08315i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(0.653555 - 2.92795i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.560948 - 0.971590i) q^{11} +(-1.35158 + 1.08315i) q^{12} +(3.48320 + 6.03308i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(0.262247 + 1.71208i) q^{15} +1.00000 q^{16} +(-0.317464 + 0.549864i) q^{17} +(0.653555 - 2.92795i) q^{18} +(1.57358 + 2.72552i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.80013 - 4.21420i) q^{21} +(-0.560948 - 0.971590i) q^{22} +(-2.29090 + 3.96796i) q^{23} +(-1.35158 + 1.08315i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.48320 + 6.03308i) q^{26} +(2.28808 + 4.66526i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(-0.243093 + 0.421049i) q^{29} +(0.262247 + 1.71208i) q^{30} +2.14796 q^{31} +1.00000 q^{32} +(1.81055 + 0.705592i) q^{33} +(-0.317464 + 0.549864i) q^{34} +(1.85185 + 1.88962i) q^{35} +(0.653555 - 2.92795i) q^{36} +(-2.03399 - 3.52298i) q^{37} +(1.57358 + 2.72552i) q^{38} +(-11.2426 - 4.38136i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.96977 + 3.41175i) q^{41} +(-1.80013 - 4.21420i) q^{42} +(-4.71509 + 8.16678i) q^{43} +(-0.560948 - 0.971590i) q^{44} +(-2.20890 - 2.02997i) q^{45} +(-2.29090 + 3.96796i) q^{46} +3.61095 q^{47} +(-1.35158 + 1.08315i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.166508 - 1.08705i) q^{51} +(3.48320 + 6.03308i) q^{52} +(6.28704 - 10.8895i) q^{53} +(2.28808 + 4.66526i) q^{54} -1.12190 q^{55} +(-0.710533 + 2.54856i) q^{56} +(-5.07898 - 1.97934i) q^{57} +(-0.243093 + 0.421049i) q^{58} -9.57308 q^{59} +(0.262247 + 1.71208i) q^{60} +7.48578 q^{61} +2.14796 q^{62} +(6.99766 + 3.74603i) q^{63} +1.00000 q^{64} +6.96640 q^{65} +(1.81055 + 0.705592i) q^{66} +6.38787 q^{67} +(-0.317464 + 0.549864i) q^{68} +(-1.20156 - 7.84442i) q^{69} +(1.85185 + 1.88962i) q^{70} +12.3050 q^{71} +(0.653555 - 2.92795i) q^{72} +(4.16098 - 7.20703i) q^{73} +(-2.03399 - 3.52298i) q^{74} +(1.61383 + 0.628929i) q^{75} +(1.57358 + 2.72552i) q^{76} +(2.87473 - 0.739260i) q^{77} +(-11.2426 - 4.38136i) q^{78} -15.6422 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.14573 - 3.82715i) q^{81} +(1.96977 + 3.41175i) q^{82} +(6.68917 - 11.5860i) q^{83} +(-1.80013 - 4.21420i) q^{84} +(0.317464 + 0.549864i) q^{85} +(-4.71509 + 8.16678i) q^{86} +(-0.127501 - 0.832390i) q^{87} +(-0.560948 - 0.971590i) q^{88} +(-3.22638 - 5.58826i) q^{89} +(-2.20890 - 2.02997i) q^{90} +(-17.8506 + 4.59043i) q^{91} +(-2.29090 + 3.96796i) q^{92} +(-2.90315 + 2.32657i) q^{93} +3.61095 q^{94} +3.14716 q^{95} +(-1.35158 + 1.08315i) q^{96} +(-5.52492 + 9.56943i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(-3.21137 + 1.00744i) 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
$3$	−1.35158	+	1.08315i	−0.780337	+	0.625359i
$3$	−1.35158	+	1.08315i	−0.780337	+	0.625359i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.35158	+	1.08315i	−0.551782	+	0.442196i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$8$	1.00000			0.353553
$9$	0.653555	−	2.92795i	0.217852	−	0.975982i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.560948	−	0.971590i	−0.169132	−	0.292945i	0.768983	−	0.639269i	$-0.220763\pi$
$11$	−0.560948	−	0.971590i	−0.169132	−	0.292945i	−0.938115	+	0.346324i	$0.887430\pi$
$12$	−1.35158	+	1.08315i	−0.390169	+	0.312680i
$13$	3.48320	+	6.03308i	0.966065	+	1.67327i	0.706725	+	0.707488i	$0.250172\pi$
$13$	3.48320	+	6.03308i	0.966065	+	1.67327i	0.259340	+	0.965786i	$0.416495\pi$
$14$	−0.710533	+	2.54856i	−0.189898	+	0.681130i
$15$	0.262247	+	1.71208i	0.0677119	+	0.442058i
$16$	1.00000			0.250000
$17$	−0.317464	+	0.549864i	−0.0769963	+	0.133362i	−0.901953	−	0.431835i	$-0.857866\pi$
$17$	−0.317464	+	0.549864i	−0.0769963	+	0.133362i	0.824956	+	0.565196i	$0.191200\pi$
$18$	0.653555	−	2.92795i	0.154044	−	0.690123i
$19$	1.57358	+	2.72552i	0.361004	+	0.625277i	0.988126	−	0.153644i	$-0.0491008\pi$
$19$	1.57358	+	2.72552i	0.361004	+	0.625277i	−0.627123	+	0.778921i	$0.715767\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.80013	−	4.21420i	−0.392822	−	0.919615i
$22$	−0.560948	−	0.971590i	−0.119594	−	0.207144i
$23$	−2.29090	+	3.96796i	−0.477686	+	0.827376i	−0.999673	−	0.0255774i	$-0.991858\pi$
$23$	−2.29090	+	3.96796i	−0.477686	+	0.827376i	0.521987	+	0.852953i	$0.325191\pi$
$24$	−1.35158	+	1.08315i	−0.275891	+	0.221098i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.48320	+	6.03308i	0.683111	+	1.18318i
$27$	2.28808	+	4.66526i	0.440342	+	0.897830i
$28$	−0.710533	+	2.54856i	−0.134278	+	0.481632i
$29$	−0.243093	+	0.421049i	−0.0451412	+	0.0781869i	−0.887713	−	0.460397i	$-0.847707\pi$
$29$	−0.243093	+	0.421049i	−0.0451412	+	0.0781869i	0.842572	+	0.538584i	$0.181040\pi$
$30$	0.262247	+	1.71208i	0.0478796	+	0.312582i
$31$	2.14796			0.385785			0.192892	−	0.981220i	$-0.438213\pi$
$31$	2.14796			0.385785			0.192892	+	0.981220i	$0.438213\pi$
$32$	1.00000			0.176777
$33$	1.81055	+	0.705592i	0.315176	+	0.122828i
$34$	−0.317464	+	0.549864i	−0.0544446	+	0.0943008i
$35$	1.85185	+	1.88962i	0.313020	+	0.319404i
$36$	0.653555	−	2.92795i	0.108926	−	0.487991i
$37$	−2.03399	−	3.52298i	−0.334386	−	0.579174i	0.648980	−	0.760805i	$-0.275196\pi$
$37$	−2.03399	−	3.52298i	−0.334386	−	0.579174i	−0.983367	+	0.181631i	$0.941862\pi$
$38$	1.57358	+	2.72552i	0.255268	+	0.442138i
$39$	−11.2426	−	4.38136i	−1.80025	−	0.701580i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.96977	+	3.41175i	0.307627	+	0.532826i	0.977843	−	0.209341i	$-0.0671317\pi$
$41$	1.96977	+	3.41175i	0.307627	+	0.532826i	−0.670216	+	0.742166i	$0.733798\pi$
$42$	−1.80013	−	4.21420i	−0.277767	−	0.650266i
$43$	−4.71509	+	8.16678i	−0.719045	+	1.24542i	0.242334	+	0.970193i	$0.422087\pi$
$43$	−4.71509	+	8.16678i	−0.719045	+	1.24542i	−0.961379	+	0.275229i	$0.911246\pi$
$44$	−0.560948	−	0.971590i	−0.0845661	−	0.146473i
$45$	−2.20890	−	2.02997i	−0.329283	−	0.302610i
$46$	−2.29090	+	3.96796i	−0.337775	+	0.585043i
$47$	3.61095			0.526711			0.263356	−	0.964699i	$-0.415171\pi$
$47$	3.61095			0.526711			0.263356	+	0.964699i	$0.415171\pi$
$48$	−1.35158	+	1.08315i	−0.195084	+	0.156340i
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.166508	−	1.08705i	−0.0233158	−	0.152217i
$52$	3.48320	+	6.03308i	0.483033	+	0.836637i
$53$	6.28704	−	10.8895i	0.863591	−	1.49578i	−0.00484862	−	0.999988i	$-0.501543\pi$
$53$	6.28704	−	10.8895i	0.863591	−	1.49578i	0.868440	−	0.495795i	$-0.165123\pi$
$54$	2.28808	+	4.66526i	0.311368	+	0.634862i
$55$	−1.12190			−0.151276
$56$	−0.710533	+	2.54856i	−0.0949490	+	0.340565i
$57$	−5.07898	−	1.97934i	−0.672727	−	0.262170i
$58$	−0.243093	+	0.421049i	−0.0319197	+	0.0552865i
$59$	−9.57308			−1.24631			−0.623154	−	0.782099i	$-0.714149\pi$
$59$	−9.57308			−1.24631			−0.623154	+	0.782099i	$0.714149\pi$
$60$	0.262247	+	1.71208i	0.0338560	+	0.221029i
$61$	7.48578			0.958456			0.479228	−	0.877690i	$-0.340917\pi$
$61$	7.48578			0.958456			0.479228	+	0.877690i	$0.340917\pi$
$62$	2.14796			0.272791
$63$	6.99766	+	3.74603i	0.881623	+	0.471955i
$64$	1.00000			0.125000
$65$	6.96640			0.864075
$66$	1.81055	+	0.705592i	0.222863	+	0.0868524i
$67$	6.38787			0.780402			0.390201	−	0.920730i	$-0.372406\pi$
$67$	6.38787			0.780402			0.390201	+	0.920730i	$0.372406\pi$
$68$	−0.317464	+	0.549864i	−0.0384982	+	0.0666808i
$69$	−1.20156	−	7.84442i	−0.144651	−	0.944357i
$70$	1.85185	+	1.88962i	0.221338	+	0.225853i
$71$	12.3050			1.46034			0.730169	−	0.683267i	$-0.239441\pi$
$71$	12.3050			1.46034			0.730169	+	0.683267i	$0.239441\pi$
$72$	0.653555	−	2.92795i	0.0770222	−	0.345062i
$73$	4.16098	−	7.20703i	0.487006	−	0.843519i	−0.512882	−	0.858459i	$-0.671422\pi$
$73$	4.16098	−	7.20703i	0.487006	−	0.843519i	0.999888	+	0.0149396i	$0.00475561\pi$
$74$	−2.03399	−	3.52298i	−0.236447	−	0.409538i
$75$	1.61383	+	0.628929i	0.186349	+	0.0726224i
$76$	1.57358	+	2.72552i	0.180502	+	0.312638i
$77$	2.87473	−	0.739260i	0.327605	−	0.0842465i
$78$	−11.2426	−	4.38136i	−1.27297	−	0.496092i
$79$	−15.6422			−1.75989			−0.879945	−	0.475075i	$-0.842421\pi$
$79$	−15.6422			−1.75989			−0.879945	+	0.475075i	$0.842421\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.14573	−	3.82715i	−0.905081	−	0.425239i
$82$	1.96977	+	3.41175i	0.217525	+	0.376765i
$83$	6.68917	−	11.5860i	0.734232	−	1.27173i	−0.220828	−	0.975313i	$-0.570876\pi$
$83$	6.68917	−	11.5860i	0.734232	−	1.27173i	0.955060	−	0.296414i	$-0.0957907\pi$
$84$	−1.80013	−	4.21420i	−0.196411	−	0.459807i
$85$	0.317464	+	0.549864i	0.0344338	+	0.0596411i
$86$	−4.71509	+	8.16678i	−0.508442	+	0.880647i
$87$	−0.127501	−	0.832390i	−0.0136695	−	0.0892416i
$88$	−0.560948	−	0.971590i	−0.0597972	−	0.103572i
$89$	−3.22638	−	5.58826i	−0.341996	−	0.592354i	0.642807	−	0.766028i	$-0.277770\pi$
$89$	−3.22638	−	5.58826i	−0.341996	−	0.592354i	−0.984803	+	0.173673i	$0.944436\pi$
$90$	−2.20890	−	2.02997i	−0.232838	−	0.213977i
$91$	−17.8506	+	4.59043i	−1.87125	+	0.481207i
$92$	−2.29090	+	3.96796i	−0.238843	+	0.413688i
$93$	−2.90315	+	2.32657i	−0.301042	+	0.241254i
$94$	3.61095			0.372441
$95$	3.14716			0.322892
$96$	−1.35158	+	1.08315i	−0.137945	+	0.110549i
$97$	−5.52492	+	9.56943i	−0.560970	+	0.971629i	0.436442	+	0.899732i	$0.356238\pi$
$97$	−5.52492	+	9.56943i	−0.560970	+	0.971629i	−0.997412	+	0.0718964i	$0.977095\pi$
$98$	−5.99028	−	3.62167i	−0.605110	−	0.365844i
$99$	−3.21137	+	1.00744i	−0.322755	+	0.101251i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.66668	+	6.35088i	0.364849	+	0.631936i	0.988752	−	0.149565i	$-0.0477874\pi$
$101$	3.66668	+	6.35088i	0.364849	+	0.631936i	−0.623903	+	0.781502i	$0.714454\pi$
$102$	−0.166508	−	1.08705i	−0.0164868	−	0.107634i
$103$	0.327430	−	0.567125i	0.0322626	−	0.0558805i	−0.849443	−	0.527680i	$-0.823062\pi$
$103$	0.327430	−	0.567125i	0.0322626	−	0.0558805i	0.881706	+	0.471799i	$0.156395\pi$
$104$	3.48320	+	6.03308i	0.341556	+	0.591592i
$105$	−4.54968	−	0.548140i	−0.444003	−	0.0534930i
$106$	6.28704	−	10.8895i	0.610651	−	1.05768i
$107$	−9.03156	−	15.6431i	−0.873114	−	1.51228i	−0.858758	−	0.512381i	$-0.828763\pi$
$107$	−9.03156	−	15.6431i	−0.873114	−	1.51228i	−0.0143561	−	0.999897i	$-0.504570\pi$
$108$	2.28808	+	4.66526i	0.220171	+	0.448915i
$109$	7.80670	−	13.5216i	0.747747	−	1.29514i	−0.201154	−	0.979560i	$-0.564469\pi$
$109$	7.80670	−	13.5216i	0.747747	−	1.29514i	0.948900	−	0.315575i	$-0.102198\pi$
$110$	−1.12190			−0.106969
$111$	6.56504	+	2.55847i	0.623126	+	0.242840i
$112$	−0.710533	+	2.54856i	−0.0671391	+	0.240816i
$113$	−3.48013	−	6.02776i	−0.327383	−	0.567044i	0.654609	−	0.755968i	$-0.272833\pi$
$113$	−3.48013	−	6.02776i	−0.327383	−	0.567044i	−0.981992	+	0.188924i	$0.939500\pi$
$114$	−5.07898	−	1.97934i	−0.475690	−	0.185382i
$115$	2.29090	+	3.96796i	0.213628	+	0.370014i
$116$	−0.243093	+	0.421049i	−0.0225706	+	0.0390934i
$117$	19.9410	−	6.25567i	1.84354	−	0.578337i
$118$	−9.57308			−0.881273
$119$	−1.17579	−	1.19977i	−0.107784	−	0.109983i
$120$	0.262247	+	1.71208i	0.0239398	+	0.156291i
$121$	4.87067	−	8.43626i	0.442789	−	0.766932i
$122$	7.48578			0.677731
$123$	−6.35776	−	2.47769i	−0.573260	−	0.223406i
$124$	2.14796			0.192892
$125$	−1.00000			−0.0894427
$126$	6.99766	+	3.74603i	0.623401	+	0.333722i
$127$	9.50026			0.843012			0.421506	−	0.906826i	$-0.361502\pi$
$127$	9.50026			0.843012			0.421506	+	0.906826i	$0.361502\pi$
$128$	1.00000			0.0883883
$129$	−2.47304	−	16.1453i	−0.217739	−	1.42151i
$130$	6.96640			0.610993
$131$	−1.58959	+	2.75325i	−0.138883	+	0.240552i	−0.927074	−	0.374878i	$-0.877684\pi$
$131$	−1.58959	+	2.75325i	−0.138883	+	0.240552i	0.788191	+	0.615430i	$0.211018\pi$
$132$	1.81055	+	0.705592i	0.157588	+	0.0614139i
$133$	−8.06422	+	2.07378i	−0.699257	+	0.179820i
$134$	6.38787			0.551828
$135$	5.18428	+	0.351095i	0.446192	+	0.0302174i
$136$	−0.317464	+	0.549864i	−0.0272223	+	0.0471504i
$137$	3.14627	+	5.44949i	0.268804	+	0.465582i	0.968553	−	0.248807i	$-0.0800384\pi$
$137$	3.14627	+	5.44949i	0.268804	+	0.465582i	−0.699749	+	0.714388i	$0.746705\pi$
$138$	−1.20156	−	7.84442i	−0.102284	−	0.667761i
$139$	−6.75656	−	11.7027i	−0.573084	−	0.992611i	−0.996247	−	0.0865574i	$-0.972413\pi$
$139$	−6.75656	−	11.7027i	−0.573084	−	0.992611i	0.423163	−	0.906054i	$-0.360920\pi$
$140$	1.85185	+	1.88962i	0.156510	+	0.159702i
$141$	−4.88050	+	3.91121i	−0.411012	+	0.329384i
$142$	12.3050			1.03261
$143$	3.90778	−	6.76848i	0.326785	−	0.566009i
$144$	0.653555	−	2.92795i	0.0544629	−	0.243995i
$145$	0.243093	+	0.421049i	0.0201878	+	0.0349662i
$146$	4.16098	−	7.20703i	0.344365	−	0.596458i
$147$	12.0192	−	1.59341i	0.991326	−	0.131422i
$148$	−2.03399	−	3.52298i	−0.167193	−	0.289587i
$149$	10.2539	−	17.7602i	0.840031	−	1.45498i	−0.0498366	−	0.998757i	$-0.515870\pi$
$149$	10.2539	−	17.7602i	0.840031	−	1.45498i	0.889868	−	0.456219i	$-0.150797\pi$
$150$	1.61383	+	0.628929i	0.131769	+	0.0513518i
$151$	−3.88099	−	6.72207i	−0.315830	−	0.547034i	0.663783	−	0.747925i	$-0.268950\pi$
$151$	−3.88099	−	6.72207i	−0.315830	−	0.547034i	−0.979614	+	0.200891i	$0.935616\pi$
$152$	1.57358	+	2.72552i	0.127634	+	0.221069i
$153$	1.40249	+	1.28888i	0.113385	+	0.104200i
$154$	2.87473	−	0.739260i	0.231652	−	0.0595713i
$155$	1.07398	−	1.86019i	0.0862641	−	0.149414i
$156$	−11.2426	−	4.38136i	−0.900127	−	0.350790i
$157$	−9.44734			−0.753980			−0.376990	−	0.926217i	$-0.623041\pi$
$157$	−9.44734			−0.753980			−0.376990	+	0.926217i	$0.623041\pi$
$158$	−15.6422			−1.24443
$159$	3.29752	+	21.5279i	0.261510	+	1.70727i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−8.48480	−	8.65786i	−0.668696	−	0.682335i
$162$	−8.14573	−	3.82715i	−0.639989	−	0.300689i
$163$	9.69789	+	16.7972i	0.759597	+	1.31566i	0.943056	+	0.332634i	$0.107937\pi$
$163$	9.69789	+	16.7972i	0.759597	+	1.31566i	−0.183459	+	0.983027i	$0.558729\pi$
$164$	1.96977	+	3.41175i	0.153814	+	0.266413i
$165$	1.51634	−	1.21519i	0.118047	−	0.0946021i
$166$	6.68917	−	11.5860i	0.519180	−	0.899246i
$167$	2.76642	+	4.79158i	0.214072	+	0.370784i	0.952985	−	0.303017i	$-0.0979939\pi$
$167$	2.76642	+	4.79158i	0.214072	+	0.370784i	−0.738913	+	0.673801i	$0.764661\pi$
$168$	−1.80013	−	4.21420i	−0.138883	−	0.325133i
$169$	−17.7653	+	30.7705i	−1.36656	+	2.36696i
$170$	0.317464	+	0.549864i	0.0243484	+	0.0421726i
$171$	9.00859	−	2.82608i	0.688904	−	0.216116i
$172$	−4.71509	+	8.16678i	−0.359522	+	0.622711i
$173$	−11.7957			−0.896807			−0.448404	−	0.893831i	$-0.648007\pi$
$173$	−11.7957			−0.896807			−0.448404	+	0.893831i	$0.648007\pi$
$174$	−0.127501	−	0.832390i	−0.00966581	−	0.0631033i
$175$	2.56238	−	0.658939i	0.193698	−	0.0498111i
$176$	−0.560948	−	0.971590i	−0.0422830	−	0.0732364i
$177$	12.9388	−	10.3691i	0.972541	−	0.779391i
$178$	−3.22638	−	5.58826i	−0.241828	−	0.418858i
$179$	4.05891	−	7.03024i	0.303377	−	0.525465i	−0.673522	−	0.739168i	$-0.735219\pi$
$179$	4.05891	−	7.03024i	0.303377	−	0.525465i	0.976899	+	0.213703i	$0.0685525\pi$
$180$	−2.20890	−	2.02997i	−0.164642	−	0.151305i
$181$	−4.36357			−0.324342			−0.162171	−	0.986763i	$-0.551850\pi$
$181$	−4.36357			−0.324342			−0.162171	+	0.986763i	$0.551850\pi$
$182$	−17.8506	+	4.59043i	−1.32317	+	0.340265i
$183$	−10.1177	+	8.10825i	−0.747919	+	0.599379i
$184$	−2.29090	+	3.96796i	−0.168887	+	0.292522i
$185$	−4.06799			−0.299084
$186$	−2.90315	+	2.32657i	−0.212869	+	0.170592i
$187$	0.712323			0.0520902
$188$	3.61095			0.263356
$189$	−13.5154	+	2.51648i	−0.983104	+	0.183047i
$190$	3.14716			0.228319
$191$	19.0117			1.37564			0.687818	−	0.725883i	$-0.258569\pi$
$191$	19.0117			1.37564			0.687818	+	0.725883i	$0.258569\pi$
$192$	−1.35158	+	1.08315i	−0.0975421	+	0.0781699i
$193$	6.02865			0.433951			0.216976	−	0.976177i	$-0.430381\pi$
$193$	6.02865			0.433951			0.216976	+	0.976177i	$0.430381\pi$
$194$	−5.52492	+	9.56943i	−0.396666	+	0.687045i
$195$	−9.41566	+	7.54568i	−0.674270	+	0.540357i
$196$	−5.99028	−	3.62167i	−0.427877	−	0.258691i
$197$	−15.5057			−1.10473			−0.552367	−	0.833601i	$-0.686275\pi$
$197$	−15.5057			−1.10473			−0.552367	+	0.833601i	$0.686275\pi$
$198$	−3.21137	+	1.00744i	−0.228222	+	0.0715954i
$199$	−7.34286	+	12.7182i	−0.520522	+	0.901570i	0.479193	+	0.877709i	$0.340929\pi$
$199$	−7.34286	+	12.7182i	−0.520522	+	0.901570i	−0.999715	+	0.0238610i	$0.992404\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−8.63373	+	6.91904i	−0.608977	+	0.488032i
$202$	3.66668	+	6.35088i	0.257987	+	0.446846i
$203$	−0.900342	−	0.918706i	−0.0631916	−	0.0644805i
$204$	−0.166508	−	1.08705i	−0.0116579	−	0.0761086i
$205$	3.93955			0.275150
$206$	0.327430	−	0.567125i	0.0228131	−	0.0395135i
$207$	10.1207	+	9.30091i	0.703439	+	0.646458i
$208$	3.48320	+	6.03308i	0.241516	+	0.418319i
$209$	1.76539	−	3.05775i	0.122115	−	0.211509i
$210$	−4.54968	−	0.548140i	−0.313957	−	0.0378252i
$211$	−1.07026	−	1.85374i	−0.0736797	−	0.127617i	0.826832	−	0.562449i	$-0.190141\pi$
$211$	−1.07026	−	1.85374i	−0.0736797	−	0.127617i	−0.900511	+	0.434832i	$0.856808\pi$
$212$	6.28704	−	10.8895i	0.431795	−	0.747892i
$213$	−16.6313	+	13.3282i	−1.13956	+	0.913235i
$214$	−9.03156	−	15.6431i	−0.617385	−	1.06934i
$215$	4.71509	+	8.16678i	0.321567	+	0.556970i
$216$	2.28808	+	4.66526i	0.155684	+	0.317431i
$217$	−1.52620	+	5.47420i	−0.103605	+	0.371613i
$218$	7.80670	−	13.5216i	0.528737	−	0.915799i
$219$	2.18241	+	14.2479i	0.147474	+	0.962783i
$220$	−1.12190			−0.0756382
$221$	−4.42316			−0.297534
$222$	6.56504	+	2.55847i	0.440617	+	0.171713i
$223$	−4.88316	+	8.45788i	−0.327001	+	0.566382i	−0.981915	−	0.189321i	$-0.939371\pi$
$223$	−4.88316	+	8.45788i	−0.327001	+	0.566382i	0.654915	+	0.755703i	$0.272705\pi$
$224$	−0.710533	+	2.54856i	−0.0474745	+	0.170283i
$225$	−2.86245	+	0.897978i	−0.190830	+	0.0598652i
$226$	−3.48013	−	6.02776i	−0.231495	−	0.400961i
$227$	5.72579	+	9.91736i	0.380034	+	0.658238i	0.991067	−	0.133367i	$-0.0425789\pi$
$227$	5.72579	+	9.91736i	0.380034	+	0.658238i	−0.611033	+	0.791605i	$0.709246\pi$
$228$	−5.07898	−	1.97934i	−0.336364	−	0.131085i
$229$	−6.17050	+	10.6876i	−0.407758	+	0.706257i	−0.994638	−	0.103416i	$-0.967023\pi$
$229$	−6.17050	+	10.6876i	−0.407758	+	0.706257i	0.586880	+	0.809674i	$0.300356\pi$
$230$	2.29090	+	3.96796i	0.151058	+	0.261639i
$231$	−3.08470	+	4.11294i	−0.202958	+	0.270612i
$232$	−0.243093	+	0.421049i	−0.0159598	+	0.0276432i
$233$	5.68350	+	9.84410i	0.372338	+	0.644909i	0.989925	−	0.141594i	$-0.0452228\pi$
$233$	5.68350	+	9.84410i	0.372338	+	0.644909i	−0.617587	+	0.786503i	$0.711890\pi$
$234$	19.9410	−	6.25567i	1.30358	−	0.408946i
$235$	1.80547	−	3.12717i	0.117776	−	0.203994i
$236$	−9.57308			−0.623154
$237$	21.1418	−	16.9430i	1.37331	−	1.10056i
$238$	−1.17579	−	1.19977i	−0.0762151	−	0.0777696i
$239$	−0.393008	−	0.680710i	−0.0254216	−	0.0440315i	0.853035	−	0.521854i	$-0.174759\pi$
$239$	−0.393008	−	0.680710i	−0.0254216	−	0.0440315i	−0.878456	+	0.477823i	$0.841426\pi$
$240$	0.262247	+	1.71208i	0.0169280	+	0.110514i
$241$	−2.48195	−	4.29887i	−0.159877	−	0.276915i	0.774947	−	0.632026i	$-0.217776\pi$
$241$	−2.48195	−	4.29887i	−0.159877	−	0.276915i	−0.934824	+	0.355111i	$0.884443\pi$
$242$	4.87067	−	8.43626i	0.313099	−	0.542303i
$243$	15.1550	−	3.65037i	0.972195	−	0.234172i
$244$	7.48578			0.479228
$245$	−6.13160	+	3.37690i	−0.391734	+	0.215742i
$246$	−6.35776	−	2.47769i	−0.405356	−	0.157972i
$247$	−10.9622	+	18.9870i	−0.697506	+	1.20812i
$248$	2.14796			0.136396
$249$	3.50843	+	22.9048i	0.222338	+	1.45153i
$250$	−1.00000			−0.0632456
$251$	27.1323			1.71258			0.856288	−	0.516499i	$-0.172765\pi$
$251$	27.1323			1.71258			0.856288	+	0.516499i	$0.172765\pi$
$252$	6.99766	+	3.74603i	0.440811	+	0.235977i
$253$	5.14030			0.323168
$254$	9.50026			0.596099
$255$	−1.02467	−	0.399324i	−0.0641671	−	0.0250067i
$256$	1.00000			0.0625000
$257$	−0.319583	+	0.553535i	−0.0199351	+	0.0345285i	−0.875821	−	0.482636i	$-0.839679\pi$
$257$	−0.319583	+	0.553535i	−0.0199351	+	0.0345285i	0.855886	+	0.517165i	$0.173013\pi$
$258$	−2.47304	−	16.1453i	−0.153965	−	1.00516i
$259$	10.4237	−	2.68055i	0.647699	−	0.166561i
$260$	6.96640			0.432038
$261$	1.07393	+	0.986942i	0.0664749	+	0.0610901i
$262$	−1.58959	+	2.75325i	−0.0982050	+	0.170096i
$263$	−3.12847	−	5.41867i	−0.192910	−	0.334129i	0.753304	−	0.657673i	$-0.228459\pi$
$263$	−3.12847	−	5.41867i	−0.192910	−	0.334129i	−0.946213	+	0.323544i	$0.895126\pi$
$264$	1.81055	+	0.705592i	0.111432	+	0.0434262i
$265$	−6.28704	−	10.8895i	−0.386210	−	0.668935i
$266$	−8.06422	+	2.07378i	−0.494449	+	0.127152i
$267$	10.4137	+	4.05833i	0.637307	+	0.248366i
$268$	6.38787			0.390201
$269$	−7.71092	+	13.3557i	−0.470143	+	0.814312i	−0.999417	−	0.0341389i	$-0.989131\pi$
$269$	−7.71092	+	13.3557i	−0.470143	+	0.814312i	0.529274	+	0.848451i	$0.322464\pi$
$270$	5.18428	+	0.351095i	0.315505	+	0.0213669i
$271$	−2.67346	−	4.63057i	−0.162401	−	0.281287i	0.773328	−	0.634006i	$-0.218590\pi$
$271$	−2.67346	−	4.63057i	−0.162401	−	0.281287i	−0.935729	+	0.352719i	$0.885257\pi$
$272$	−0.317464	+	0.549864i	−0.0192491	+	0.0333404i
$273$	19.1544	−	25.5393i	1.15928	−	1.54571i
$274$	3.14627	+	5.44949i	0.190073	+	0.329216i
$275$	−0.560948	+	0.971590i	−0.0338264	+	0.0585891i
$276$	−1.20156	−	7.84442i	−0.0723257	−	0.472179i
$277$	−6.19954	−	10.7379i	−0.372494	−	0.645179i	0.617455	−	0.786607i	$-0.288164\pi$
$277$	−6.19954	−	10.7379i	−0.372494	−	0.645179i	−0.989949	+	0.141428i	$0.954831\pi$
$278$	−6.75656	−	11.7027i	−0.405232	−	0.701882i
$279$	1.40381	−	6.28911i	0.0840439	−	0.376519i
$280$	1.85185	+	1.88962i	0.110669	+	0.112926i
$281$	−8.91636	+	15.4436i	−0.531906	+	0.921288i	0.467401	+	0.884046i	$0.345191\pi$
$281$	−8.91636	+	15.4436i	−0.531906	+	0.921288i	−0.999306	+	0.0372419i	$0.988143\pi$
$282$	−4.88050	+	3.91121i	−0.290629	+	0.232909i
$283$	−13.7561			−0.817716			−0.408858	−	0.912598i	$-0.634073\pi$
$283$	−13.7561			−0.817716			−0.408858	+	0.912598i	$0.634073\pi$
$284$	12.3050			0.730169
$285$	−4.25365	+	3.40886i	−0.251964	+	0.201923i
$286$	3.90778	−	6.76848i	0.231072	−	0.400229i
$287$	−10.0946	+	2.59592i	−0.595867	+	0.153232i
$288$	0.653555	−	2.92795i	0.0385111	−	0.172531i
$289$	8.29843	+	14.3733i	0.488143	+	0.845489i
$290$	0.243093	+	0.421049i	0.0142749	+	0.0247249i
$291$	−2.89779	−	18.9182i	−0.169871	−	1.10901i
$292$	4.16098	−	7.20703i	0.243503	−	0.421760i
$293$	−7.62190	−	13.2015i	−0.445276	−	0.771241i	0.552795	−	0.833317i	$-0.313561\pi$
$293$	−7.62190	−	13.2015i	−0.445276	−	0.771241i	−0.998071	+	0.0620764i	$0.980228\pi$
$294$	12.0192	−	1.59341i	0.700974	−	0.0929297i
$295$	−4.78654	+	8.29053i	−0.278683	+	0.482693i
$296$	−2.03399	−	3.52298i	−0.118223	−	0.204769i
$297$	3.24923	−	4.84005i	0.188539	−	0.280848i
$298$	10.2539	−	17.7602i	0.593992	−	1.02882i
$299$	−31.9186			−1.84590
$300$	1.61383	+	0.628929i	0.0931745	+	0.0363112i
$301$	−17.4633	−	17.8195i	−1.00657	−	1.02710i
$302$	−3.88099	−	6.72207i	−0.223326	−	0.386811i
$303$	−11.8348	−	4.61216i	−0.679892	−	0.264962i
$304$	1.57358	+	2.72552i	0.0902509	+	0.156319i
$305$	3.74289	−	6.48288i	0.214317	−	0.371208i
$306$	1.40249	+	1.28888i	0.0801751	+	0.0736805i
$307$	−1.96740			−0.112285			−0.0561426	−	0.998423i	$-0.517880\pi$
$307$	−1.96740			−0.112285			−0.0561426	+	0.998423i	$0.517880\pi$
$308$	2.87473	−	0.739260i	0.163803	−	0.0421233i
$309$	0.171735	+	1.12117i	0.00976966	+	0.0637813i
$310$	1.07398	−	1.86019i	0.0609980	−	0.105652i
$311$	−3.14312			−0.178230			−0.0891151	−	0.996021i	$-0.528404\pi$
$311$	−3.14312			−0.178230			−0.0891151	+	0.996021i	$0.528404\pi$
$312$	−11.2426	−	4.38136i	−0.636486	−	0.248046i
$313$	18.3452			1.03693			0.518467	−	0.855098i	$-0.326503\pi$
$313$	18.3452			1.03693			0.518467	+	0.855098i	$0.326503\pi$
$314$	−9.44734			−0.533144
$315$	6.74298	−	4.18714i	0.379924	−	0.235919i
$316$	−15.6422			−0.879945
$317$	32.2944			1.81384			0.906918	−	0.421307i	$-0.138429\pi$
$317$	32.2944			1.81384			0.906918	+	0.421307i	$0.138429\pi$
$318$	3.29752	+	21.5279i	0.184915	+	1.20722i
$319$	0.545450			0.0305393
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	29.1508	+	11.3604i	1.62704	+	0.634077i
$322$	−8.48480	−	8.65786i	−0.472839	−	0.482483i
$323$	−1.99822			−0.111184
$324$	−8.14573	−	3.82715i	−0.452541	−	0.212619i
$325$	3.48320	−	6.03308i	0.193213	−	0.334655i
$326$	9.69789	+	16.7972i	0.537116	+	0.930313i
$327$	4.09457	+	26.7314i	0.226430	+	1.47825i
$328$	1.96977	+	3.41175i	0.108763	+	0.188382i
$329$	−2.56570	+	9.20271i	−0.141452	+	0.507362i
$330$	1.51634	−	1.21519i	0.0834715	−	0.0668938i
$331$	−4.51014			−0.247900			−0.123950	−	0.992288i	$-0.539556\pi$
$331$	−4.51014			−0.247900			−0.123950	+	0.992288i	$0.539556\pi$
$332$	6.68917	−	11.5860i	0.367116	−	0.635863i
$333$	−11.6444	+	3.65296i	−0.638110	+	0.200181i
$334$	2.76642	+	4.79158i	0.151372	+	0.262184i
$335$	3.19393	−	5.53205i	0.174503	−	0.302248i
$336$	−1.80013	−	4.21420i	−0.0982054	−	0.229904i
$337$	11.0152	+	19.0789i	0.600037	+	1.03930i	0.992815	+	0.119662i	$0.0381810\pi$
$337$	11.0152	+	19.0789i	0.600037	+	1.03930i	−0.392777	+	0.919634i	$0.628486\pi$
$338$	−17.7653	+	30.7705i	−0.966307	+	1.67369i
$339$	11.2327	+	4.37750i	0.610075	+	0.237753i
$340$	0.317464	+	0.549864i	0.0172169	+	0.0298205i
$341$	−1.20489	−	2.08694i	−0.0652486	−	0.113014i
$342$	9.00859	−	2.82608i	0.487129	−	0.152817i
$343$	13.4863	−	12.6933i	0.728193	−	0.685372i
$344$	−4.71509	+	8.16678i	−0.254221	+	0.440323i
$345$	−7.39425	−	2.88163i	−0.398093	−	0.155141i
$346$	−11.7957			−0.634138
$347$	−22.1257			−1.18777			−0.593886	−	0.804549i	$-0.702407\pi$
$347$	−22.1257			−1.18777			−0.593886	+	0.804549i	$0.702407\pi$
$348$	−0.127501	−	0.832390i	−0.00683476	−	0.0446208i
$349$	15.9115	−	27.5596i	0.851726	−	1.47523i	−0.0279243	−	0.999610i	$-0.508890\pi$
$349$	15.9115	−	27.5596i	0.851726	−	1.47523i	0.879650	−	0.475622i	$-0.157777\pi$
$350$	2.56238	−	0.658939i	0.136965	−	0.0352217i
$351$	−20.1760	+	30.0542i	−1.07692	+	1.60417i
$352$	−0.560948	−	0.971590i	−0.0298986	−	0.0517859i
$353$	14.9564	+	25.9053i	0.796051	+	1.37880i	0.922170	+	0.386786i	$0.126415\pi$
$353$	14.9564	+	25.9053i	0.796051	+	1.37880i	−0.126119	+	0.992015i	$0.540252\pi$
$354$	12.9388	−	10.3691i	0.687690	−	0.551112i
$355$	6.15251	−	10.6565i	0.326541	−	0.565586i
$356$	−3.22638	−	5.58826i	−0.170998	−	0.296177i
$357$	2.88872	+	0.348029i	0.152887	+	0.0184197i
$358$	4.05891	−	7.03024i	0.214520	−	0.371560i
$359$	−13.8924	−	24.0623i	−0.733212	−	1.26996i	−0.955503	−	0.294980i	$-0.904687\pi$
$359$	−13.8924	−	24.0623i	−0.733212	−	1.26996i	0.222292	−	0.974980i	$-0.428646\pi$
$360$	−2.20890	−	2.02997i	−0.116419	−	0.106989i
$361$	4.54770	−	7.87685i	0.239353	−	0.414571i
$362$	−4.36357			−0.229344
$363$	2.55464	+	16.6780i	0.134084	+	0.875368i
$364$	−17.8506	+	4.59043i	−0.935624	+	0.240604i
$365$	−4.16098	−	7.20703i	−0.217796	−	0.377233i
$366$	−10.1177	+	8.10825i	−0.528858	+	0.423825i
$367$	−15.6472	−	27.1017i	−0.816775	−	1.41470i	−0.908047	−	0.418869i	$-0.862427\pi$
$367$	−15.6472	−	27.1017i	−0.816775	−	1.41470i	0.0912718	−	0.995826i	$-0.470907\pi$
$368$	−2.29090	+	3.96796i	−0.119421	+	0.206844i
$369$	11.2768	−	3.53763i	0.587045	−	0.184161i
$370$	−4.06799			−0.211485
$371$	23.2853	+	23.7602i	1.20891	+	1.23357i
$372$	−2.90315	+	2.32657i	−0.150521	+	0.120627i
$373$	−5.75771	+	9.97265i	−0.298123	+	0.516364i	−0.975707	−	0.219082i	$-0.929694\pi$
$373$	−5.75771	+	9.97265i	−0.298123	+	0.516364i	0.677583	+	0.735446i	$0.263027\pi$
$374$	0.712323			0.0368333
$375$	1.35158	−	1.08315i	0.0697955	−	0.0559338i
$376$	3.61095			0.186220
$377$	−3.38696			−0.174437
$378$	−13.5154	+	2.51648i	−0.695160	+	0.129434i
$379$	25.7056			1.32041			0.660203	−	0.751087i	$-0.270470\pi$
$379$	25.7056			1.32041			0.660203	+	0.751087i	$0.270470\pi$
$380$	3.14716			0.161446
$381$	−12.8404	+	10.2902i	−0.657833	+	0.527185i
$382$	19.0117			0.972722
$383$	−6.56073	+	11.3635i	−0.335238	+	0.580649i	−0.983530	−	0.180742i	$-0.942150\pi$
$383$	−6.56073	+	11.3635i	−0.335238	+	0.580649i	0.648293	+	0.761391i	$0.275483\pi$
$384$	−1.35158	+	1.08315i	−0.0689727	+	0.0552745i
$385$	0.797144	−	2.85922i	0.0406262	−	0.145719i
$386$	6.02865			0.306850
$387$	20.8303	+	19.1430i	1.05886	+	0.973092i
$388$	−5.52492	+	9.56943i	−0.280485	+	0.485814i
$389$	3.38153	+	5.85697i	0.171450	+	0.296960i	0.938927	−	0.344116i	$-0.111821\pi$
$389$	3.38153	+	5.85697i	0.171450	+	0.296960i	−0.767477	+	0.641077i	$0.778488\pi$
$390$	−9.41566	+	7.54568i	−0.476781	+	0.382090i
$391$	−1.45456	−	2.51937i	−0.0735601	−	0.127410i
$392$	−5.99028	−	3.62167i	−0.302555	−	0.182922i
$393$	−0.833729	−	5.44301i	−0.0420561	−	0.274563i
$394$	−15.5057			−0.781165
$395$	−7.82112	+	13.5466i	−0.393523	+	0.681603i
$396$	−3.21137	+	1.00744i	−0.161378	+	0.0506256i
$397$	−5.05120	−	8.74893i	−0.253512	−	0.439096i	0.710978	−	0.703214i	$-0.248253\pi$
$397$	−5.05120	−	8.74893i	−0.253512	−	0.439096i	−0.964490	+	0.264118i	$0.914919\pi$
$398$	−7.34286	+	12.7182i	−0.368065	+	0.637506i
$399$	8.65324	−	11.5377i	0.433204	−	0.577607i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−13.5515	+	23.4719i	−0.676730	+	1.17213i	0.299230	+	0.954181i	$0.403270\pi$
$401$	−13.5515	+	23.4719i	−0.676730	+	1.17213i	−0.975960	+	0.217949i	$0.930063\pi$
$402$	−8.63373	+	6.91904i	−0.430611	+	0.345090i
$403$	7.48177	+	12.9588i	0.372693	+	0.645524i
$404$	3.66668	+	6.35088i	0.182424	+	0.315968i
$405$	−7.38727	+	5.14084i	−0.367077	+	0.255450i
$406$	−0.900342	−	0.918706i	−0.0446832	−	0.0455946i
$407$	−2.28193	+	3.95242i	−0.113111	+	0.195914i
$408$	−0.166508	−	1.08705i	−0.00824338	−	0.0538169i
$409$	9.52808			0.471133			0.235567	−	0.971858i	$-0.424305\pi$
$409$	9.52808			0.471133			0.235567	+	0.971858i	$0.424305\pi$
$410$	3.93955			0.194560
$411$	−10.1551	−	3.95755i	−0.500913	−	0.195212i
$412$	0.327430	−	0.567125i	0.0161313	−	0.0279402i
$413$	6.80199	−	24.3975i	0.334704	−	1.20052i
$414$	10.1207	+	9.30091i	0.497407	+	0.457115i
$415$	−6.68917	−	11.5860i	−0.328358	−	0.568733i
$416$	3.48320	+	6.03308i	0.170778	+	0.295796i
$417$	21.8079	+	8.49879i	1.06794	+	0.416188i
$418$	1.76539	−	3.05775i	0.0863481	−	0.149559i
$419$	−20.0930	−	34.8022i	−0.981609	−	1.70020i	−0.656129	−	0.754649i	$-0.727807\pi$
$419$	−20.0930	−	34.8022i	−0.981609	−	1.70020i	−0.325480	−	0.945549i	$-0.605526\pi$
$420$	−4.54968	−	0.548140i	−0.222001	−	0.0267465i
$421$	6.20666	−	10.7503i	0.302494	−	0.523935i	−0.674206	−	0.738543i	$-0.735514\pi$
$421$	6.20666	−	10.7503i	0.302494	−	0.523935i	0.976700	+	0.214608i	$0.0688474\pi$
$422$	−1.07026	−	1.85374i	−0.0520994	−	0.0902389i
$423$	2.35995	−	10.5727i	0.114745	−	0.514060i
$424$	6.28704	−	10.8895i	0.305325	−	0.528839i
$425$	0.634928			0.0307985
$426$	−16.6313	+	13.3282i	−0.805787	+	0.645755i
$427$	−5.31890	+	19.0779i	−0.257400	+	0.923246i
$428$	−9.03156	−	15.6431i	−0.436557	−	0.756139i
$429$	2.04961	+	13.3809i	0.0989561	+	0.646036i
$430$	4.71509	+	8.16678i	0.227382	+	0.393837i
$431$	−5.13091	+	8.88700i	−0.247147	+	0.428072i	−0.962733	−	0.270453i	$-0.912826\pi$
$431$	−5.13091	+	8.88700i	−0.247147	+	0.428072i	0.715586	+	0.698525i	$0.246160\pi$
$432$	2.28808	+	4.66526i	0.110085	+	0.224458i
$433$	29.3085			1.40848			0.704238	−	0.709964i	$-0.251289\pi$
$433$	29.3085			1.40848			0.704238	+	0.709964i	$0.251289\pi$
$434$	−1.52620	+	5.47420i	−0.0732598	+	0.262770i
$435$	−0.784621	−	0.305776i	−0.0376197	−	0.0146608i
$436$	7.80670	−	13.5216i	0.373873	−	0.647568i
$437$	−14.4197			−0.689785
$438$	2.18241	+	14.2479i	0.104280	+	0.680790i
$439$	18.8441			0.899381			0.449690	−	0.893185i	$-0.351534\pi$
$439$	18.8441			0.899381			0.449690	+	0.893185i	$0.351534\pi$
$440$	−1.12190			−0.0534843
$441$	−14.5190	+	15.1723i	−0.691382	+	0.722489i
$442$	−4.42316			−0.210388
$443$	10.9196			0.518808			0.259404	−	0.965769i	$-0.416474\pi$
$443$	10.9196			0.518808			0.259404	+	0.965769i	$0.416474\pi$
$444$	6.56504	+	2.55847i	0.311563	+	0.121420i
$445$	−6.45277			−0.305891
$446$	−4.88316	+	8.45788i	−0.231224	+	0.400492i
$447$	5.37810	+	35.1110i	0.254376	+	1.66069i
$448$	−0.710533	+	2.54856i	−0.0335695	+	0.120408i
$449$	−14.4079			−0.679949			−0.339975	−	0.940435i	$-0.610418\pi$
$449$	−14.4079			−0.679949			−0.339975	+	0.940435i	$0.610418\pi$
$450$	−2.86245	+	0.897978i	−0.134937	+	0.0423311i
$451$	2.20988	−	3.82763i	0.104059	−	0.180236i
$452$	−3.48013	−	6.02776i	−0.163691	−	0.283522i
$453$	12.5265	+	4.88173i	0.588547	+	0.229364i
$454$	5.72579	+	9.91736i	0.268725	+	0.465445i
$455$	−4.94986	+	17.7543i	−0.232053	+	0.832332i
$456$	−5.07898	−	1.97934i	−0.237845	−	0.0926910i
$457$	1.49735			0.0700429			0.0350214	−	0.999387i	$-0.488850\pi$
$457$	1.49735			0.0700429			0.0350214	+	0.999387i	$0.488850\pi$
$458$	−6.17050	+	10.6876i	−0.288328	+	0.499399i
$459$	−3.29164	−	0.222920i	−0.153641	−	0.0104050i
$460$	2.29090	+	3.96796i	0.106814	+	0.185007i
$461$	8.47082	−	14.6719i	0.394526	−	0.683338i	−0.598515	−	0.801112i	$-0.704242\pi$
$461$	8.47082	−	14.6719i	0.394526	−	0.683338i	0.993041	+	0.117773i	$0.0375756\pi$
$462$	−3.08470	+	4.11294i	−0.143513	+	0.191351i
$463$	5.08561	+	8.80854i	0.236349	+	0.409368i	0.959664	−	0.281150i	$-0.0907160\pi$
$463$	5.08561	+	8.80854i	0.236349	+	0.409368i	−0.723315	+	0.690518i	$0.757383\pi$
$464$	−0.243093	+	0.421049i	−0.0112853	+	0.0195467i
$465$	0.563296	+	3.67748i	0.0261222	+	0.170539i
$466$	5.68350	+	9.84410i	0.263283	+	0.456019i
$467$	−13.0827	−	22.6599i	−0.605395	−	1.04857i	−0.991989	−	0.126324i	$-0.959682\pi$
$467$	−13.0827	−	22.6599i	−0.605395	−	1.04857i	0.386594	−	0.922250i	$-0.373651\pi$
$468$	19.9410	−	6.25567i	0.921772	−	0.289168i
$469$	−4.53879	+	16.2798i	−0.209582	+	0.751733i
$470$	1.80547	−	3.12717i	0.0832803	−	0.144246i
$471$	12.7689	−	10.2329i	0.588359	−	0.471508i
$472$	−9.57308			−0.440637
$473$	10.5797			0.486454
$474$	21.1418	−	16.9430i	0.971075	−	0.778216i
$475$	1.57358	−	2.72552i	0.0722008	−	0.125055i
$476$	−1.17579	−	1.19977i	−0.0538922	−	0.0549914i
$477$	−27.7748	−	25.5250i	−1.27172	−	1.16871i
$478$	−0.393008	−	0.680710i	−0.0179758	−	0.0311350i
$479$	−5.33351	−	9.23791i	−0.243694	−	0.422091i	0.718070	−	0.695971i	$-0.245026\pi$
$479$	−5.33351	−	9.23791i	−0.243694	−	0.422091i	−0.961764	+	0.273881i	$0.911693\pi$
$480$	0.262247	+	1.71208i	0.0119699	+	0.0781455i
$481$	14.1696	−	24.5425i	0.646078	−	1.11904i
$482$	−2.48195	−	4.29887i	−0.113050	−	0.195808i
$483$	20.8457	+	2.51147i	0.948512	+	0.114276i
$484$	4.87067	−	8.43626i	0.221394	−	0.383466i
$485$	5.52492	+	9.56943i	0.250873	+	0.434526i
$486$	15.1550	−	3.65037i	0.687446	−	0.165584i
$487$	−10.0410	+	17.3916i	−0.455002	+	0.788086i	−0.998688	−	0.0512021i	$-0.983695\pi$
$487$	−10.0410	+	17.3916i	−0.455002	+	0.788086i	0.543686	+	0.839288i	$0.317028\pi$
$488$	7.48578			0.338865
$489$	−31.3015	−	12.1986i	−1.41550	−	0.551638i
$490$	−6.13160	+	3.37690i	−0.276997	+	0.152553i
$491$	−8.48718	−	14.7002i	−0.383021	−	0.663412i	0.608472	−	0.793576i	$-0.291783\pi$
$491$	−8.48718	−	14.7002i	−0.383021	−	0.663412i	−0.991492	+	0.130164i	$0.958450\pi$
$492$	−6.35776	−	2.47769i	−0.286630	−	0.111703i
$493$	−0.154346	−	0.267336i	−0.00695141	−	0.0120402i
$494$	−10.9622	+	18.9870i	−0.493211	+	0.854267i
$495$	−0.733221	+	3.28485i	−0.0329558	+	0.147643i
$496$	2.14796			0.0964462
$497$	−8.74313	+	31.3600i	−0.392183	+	1.40669i
$498$	3.50843	+	22.9048i	0.157217	+	1.02639i
$499$	7.40677	−	12.8289i	0.331573	−	0.574301i	−0.651248	−	0.758865i	$-0.725754\pi$
$499$	7.40677	−	12.8289i	0.331573	−	0.574301i	0.982820	+	0.184565i	$0.0590875\pi$
$500$	−1.00000			−0.0447214
$501$	−8.92907	−	3.47976i	−0.398922	−	0.155464i
$502$	27.1323			1.21097
$503$	6.45793			0.287945			0.143972	−	0.989582i	$-0.454012\pi$
$503$	6.45793			0.287945			0.143972	+	0.989582i	$0.454012\pi$
$504$	6.99766	+	3.74603i	0.311701	+	0.166861i
$505$	7.33337			0.326331
$506$	5.14030			0.228514
$507$	−9.31782	−	60.8314i	−0.413819	−	2.70162i
$508$	9.50026			0.421506
$509$	−8.59741	+	14.8912i	−0.381074	+	0.660039i	−0.991216	−	0.132253i	$-0.957779\pi$
$509$	−8.59741	+	14.8912i	−0.381074	+	0.660039i	0.610142	+	0.792292i	$0.291112\pi$
$510$	−1.02467	−	0.399324i	−0.0453730	−	0.0176824i
$511$	15.4110	+	15.7253i	0.681743	+	0.695648i
$512$	1.00000			0.0441942
$513$	−9.11478	+	13.5774i	−0.402428	+	0.599456i
$514$	−0.319583	+	0.553535i	−0.0140962	+	0.0244154i
$515$	−0.327430	−	0.567125i	−0.0144283	−	0.0249905i
$516$	−2.47304	−	16.1453i	−0.108870	−	0.710755i
$517$	−2.02555	−	3.50836i	−0.0890838	−	0.154298i
$518$	10.4237	−	2.68055i	0.457993	−	0.117777i
$519$	15.9428	−	12.7765i	0.699812	−	0.560827i
$520$	6.96640			0.305497
$521$	−17.9671	+	31.1199i	−0.787153	+	1.36339i	0.140552	+	0.990073i	$0.455112\pi$
$521$	−17.9671	+	31.1199i	−0.787153	+	1.36339i	−0.927705	+	0.373315i	$0.878221\pi$
$522$	1.07393	+	0.986942i	0.0470048	+	0.0431973i
$523$	−18.7536	−	32.4822i	−0.820039	−	1.42035i	−0.905653	−	0.424020i	$-0.860619\pi$
$523$	−18.7536	−	32.4822i	−0.820039	−	1.42035i	0.0856140	−	0.996328i	$-0.472715\pi$
$524$	−1.58959	+	2.75325i	−0.0694414	+	0.120276i
$525$	−2.74954	+	3.66606i	−0.120000	+	0.160000i
$526$	−3.12847	−	5.41867i	−0.136408	−	0.236265i
$527$	−0.681900	+	1.18108i	−0.0297040	+	0.0514489i
$528$	1.81055	+	0.705592i	0.0787941	+	0.0307070i
$529$	1.00355	+	1.73820i	0.0436326	+	0.0755739i
$530$	−6.28704	−	10.8895i	−0.273091	−	0.473008i
$531$	−6.25653	+	28.0295i	−0.271510	+	1.21637i
$532$	−8.06422	+	2.07378i	−0.349628	+	0.0899099i
$533$	−13.7222	+	23.7676i	−0.594376	+	1.02949i
$534$	10.4137	+	4.05833i	0.450644	+	0.175621i
$535$	−18.0631			−0.780937
$536$	6.38787			0.275914
$537$	2.12887	+	13.8984i	0.0918677	+	0.599759i
$538$	−7.71092	+	13.3557i	−0.332442	+	0.575806i
$539$	−0.158541	+	7.85167i	−0.00682884	+	0.338195i
$540$	5.18428	+	0.351095i	0.223096	+	0.0151087i
$541$	−16.1141	−	27.9104i	−0.692797	−	1.19996i	−0.970918	−	0.239414i	$-0.923045\pi$
$541$	−16.1141	−	27.9104i	−0.692797	−	1.19996i	0.278120	−	0.960546i	$-0.410289\pi$
$542$	−2.67346	−	4.63057i	−0.114835	−	0.198900i
$543$	5.89773	−	4.72642i	0.253096	−	0.202830i
$544$	−0.317464	+	0.549864i	−0.0136112	+	0.0235752i
$545$	−7.80670	−	13.5216i	−0.334402	−	0.579202i
$546$	19.1544	−	25.5393i	0.819732	−	1.09298i
$547$	4.64483	−	8.04509i	0.198599	−	0.343983i	−0.749476	−	0.662032i	$-0.769694\pi$
$547$	4.64483	−	8.04509i	0.198599	−	0.343983i	0.948074	+	0.318049i	$0.103028\pi$
$548$	3.14627	+	5.44949i	0.134402	+	0.232791i
$549$	4.89237	−	21.9180i	0.208801	−	0.935436i
$550$	−0.560948	+	0.971590i	−0.0239189	+	0.0414287i
$551$	−1.53010			−0.0651846
$552$	−1.20156	−	7.84442i	−0.0511420	−	0.333881i
$553$	11.1143	−	39.8652i	0.472630	−	1.69524i
$554$	−6.19954	−	10.7379i	−0.263393	−	0.456210i
$555$	5.49822	−	4.40626i	0.233387	−	0.187035i
$556$	−6.75656	−	11.7027i	−0.286542	−	0.496306i
$557$	−1.45996	+	2.52873i	−0.0618607	+	0.107146i	−0.895297	−	0.445469i	$-0.853037\pi$
$557$	−1.45996	+	2.52873i	−0.0618607	+	0.107146i	0.833436	+	0.552615i	$0.186370\pi$
$558$	1.40381	−	6.28911i	0.0594280	−	0.266239i
$559$	−65.6944			−2.77858
$560$	1.85185	+	1.88962i	0.0782549	+	0.0798509i
$561$	−0.962764	+	0.771555i	−0.0406479	+	0.0325751i
$562$	−8.91636	+	15.4436i	−0.376114	+	0.651449i
$563$	8.14308			0.343190			0.171595	−	0.985168i	$-0.445108\pi$
$563$	8.14308			0.343190			0.171595	+	0.985168i	$0.445108\pi$
$564$	−4.88050	+	3.91121i	−0.205506	+	0.164692i
$565$	−6.96026			−0.292820
$566$	−13.7561			−0.578213
$567$	15.5415	−	18.0405i	0.652682	−	0.757632i
$568$	12.3050			0.516307
$569$	−16.0444			−0.672615			−0.336308	−	0.941752i	$-0.609178\pi$
$569$	−16.0444			−0.672615			−0.336308	+	0.941752i	$0.609178\pi$
$570$	−4.25365	+	3.40886i	−0.178166	+	0.142781i
$571$	18.4453			0.771912			0.385956	−	0.922517i	$-0.373872\pi$
$571$	18.4453			0.771912			0.385956	+	0.922517i	$0.373872\pi$
$572$	3.90778	−	6.76848i	0.163393	−	0.283004i
$573$	−25.6959	+	20.5926i	−1.07346	+	0.860267i
$574$	−10.0946	+	2.59592i	−0.421342	+	0.108352i
$575$	4.58180			0.191074
$576$	0.653555	−	2.92795i	0.0272315	−	0.121998i
$577$	7.62510	−	13.2071i	0.317437	−	0.549817i	−0.662515	−	0.749048i	$-0.730511\pi$
$577$	7.62510	−	13.2071i	0.317437	−	0.549817i	0.979953	+	0.199231i	$0.0638444\pi$
$578$	8.29843	+	14.3733i	0.345169	+	0.597851i
$579$	−8.14822	+	6.52995i	−0.338628	+	0.271376i
$580$	0.243093	+	0.421049i	0.0100939	+	0.0174831i
$581$	24.7747	+	25.2800i	1.02783	+	1.04879i
$582$	−2.89779	−	18.9182i	−0.120117	−	0.784186i
$583$	−14.1068			−0.584244
$584$	4.16098	−	7.20703i	0.172183	−	0.298229i
$585$	4.55292	−	20.3972i	0.188240	−	0.843322i
$586$	−7.62190	−	13.2015i	−0.314858	−	0.545349i
$587$	0.345203	−	0.597908i	0.0142480	−	0.0246783i	−0.858813	−	0.512288i	$-0.828798\pi$
$587$	0.345203	−	0.597908i	0.0142480	−	0.0246783i	0.873062	+	0.487610i	$0.162131\pi$
$588$	12.0192	−	1.59341i	0.495663	−	0.0657112i
$589$	3.37998	+	5.85430i	0.139270	+	0.241222i
$590$	−4.78654	+	8.29053i	−0.197059	+	0.341316i
$591$	20.9572	−	16.7950i	0.862065	−	0.690856i
$592$	−2.03399	−	3.52298i	−0.0835966	−	0.144794i
$593$	−12.4639	−	21.5882i	−0.511832	−	0.886520i	−0.999906	−	0.0137171i	$-0.995634\pi$
$593$	−12.4639	−	21.5882i	−0.511832	−	0.886520i	0.488074	−	0.872802i	$-0.337700\pi$
$594$	3.24923	−	4.84005i	0.133318	−	0.198590i
$595$	−1.62693	+	0.418378i	−0.0666975	+	0.0171518i
$596$	10.2539	−	17.7602i	0.420015	−	0.727488i
$597$	−3.85129	−	25.1432i	−0.157623	−	1.02904i
$598$	−31.9186			−1.30525
$599$	30.2126			1.23445			0.617226	−	0.786786i	$-0.288256\pi$
$599$	30.2126			1.23445			0.617226	+	0.786786i	$0.288256\pi$
$600$	1.61383	+	0.628929i	0.0658844	+	0.0256759i
$601$	18.0478	−	31.2597i	0.736185	−	1.27511i	−0.218016	−	0.975945i	$-0.569958\pi$
$601$	18.0478	−	31.2597i	0.736185	−	1.27511i	0.954201	−	0.299165i	$-0.0967082\pi$
$602$	−17.4633	−	17.8195i	−0.711750	−	0.726267i
$603$	4.17482	−	18.7033i	0.170012	−	0.761658i
$604$	−3.88099	−	6.72207i	−0.157915	−	0.273517i
$605$	−4.87067	−	8.43626i	−0.198021	−	0.342983i
$606$	−11.8348	−	4.61216i	−0.480756	−	0.187356i
$607$	−12.9990	+	22.5150i	−0.527614	+	0.913854i	0.471868	+	0.881669i	$0.343580\pi$
$607$	−12.9990	+	22.5150i	−0.527614	+	0.913854i	−0.999482	+	0.0321847i	$0.989754\pi$
$608$	1.57358	+	2.72552i	0.0638171	+	0.110534i
$609$	2.21199	+	0.266498i	0.0896342	+	0.0107990i
$610$	3.74289	−	6.48288i	0.151545	−	0.262484i
$611$	12.5776	+	21.7851i	0.508837	+	0.881332i
$612$	1.40249	+	1.28888i	0.0566923	+	0.0521000i
$613$	3.68506	−	6.38271i	0.148838	−	0.257795i	−0.781960	−	0.623328i	$-0.785780\pi$
$613$	3.68506	−	6.38271i	0.148838	−	0.257795i	0.930798	+	0.365533i	$0.119113\pi$
$614$	−1.96740			−0.0793977
$615$	−5.32463	+	4.26714i	−0.214710	+	0.172068i
$616$	2.87473	−	0.739260i	0.115826	−	0.0297856i
$617$	−0.467264	−	0.809325i	−0.0188113	−	0.0325822i	0.856466	−	0.516203i	$-0.172655\pi$
$617$	−0.467264	−	0.809325i	−0.0188113	−	0.0325822i	−0.875278	+	0.483620i	$0.839322\pi$
$618$	0.171735	+	1.12117i	0.00690820	+	0.0451002i
$619$	15.3271	+	26.5473i	0.616049	+	1.06703i	0.990200	+	0.139660i	$0.0446009\pi$
$619$	15.3271	+	26.5473i	0.616049	+	1.06703i	−0.374151	+	0.927368i	$0.622066\pi$
$620$	1.07398	−	1.86019i	0.0431321	−	0.0747069i
$621$	−23.7533	−	1.60865i	−0.953188	−	0.0645527i
$622$	−3.14312			−0.126028
$623$	16.5345	−	4.25198i	0.662439	−	0.170352i
$624$	−11.2426	−	4.38136i	−0.450063	−	0.175395i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	18.3452			0.733223
$627$	0.925938	+	6.04499i	0.0369784	+	0.241414i
$628$	−9.44734			−0.376990
$629$	2.58288			0.102986
$630$	6.74298	−	4.18714i	0.268647	−	0.166820i
$631$	18.1446			0.722325			0.361162	−	0.932503i	$-0.382380\pi$
$631$	18.1446			0.722325			0.361162	+	0.932503i	$0.382380\pi$
$632$	−15.6422			−0.622215
$633$	3.45444	+	1.34623i	0.137301	+	0.0535080i
$634$	32.2944			1.28258
$635$	4.75013	−	8.22746i	0.188503	−	0.326497i
$636$	3.29752	+	21.5279i	0.130755	+	0.853635i
$637$	0.984457	−	48.7548i	0.0390056	−	1.93174i
$638$	0.545450			0.0215946
$639$	8.04201	−	36.0284i	0.318137	−	1.42526i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−22.5677	−	39.0884i	−0.891370	−	1.54390i	−0.838234	−	0.545311i	$-0.816412\pi$
$641$	−22.5677	−	39.0884i	−0.891370	−	1.54390i	−0.0531361	−	0.998587i	$-0.516922\pi$
$642$	29.1508	+	11.3604i	1.15049	+	0.448360i
$643$	−8.38623	−	14.5254i	−0.330721	−	0.572825i	0.651933	−	0.758277i	$-0.273958\pi$
$643$	−8.38623	−	14.5254i	−0.330721	−	0.572825i	−0.982653	+	0.185452i	$0.940625\pi$
$644$	−8.48480	−	8.65786i	−0.334348	−	0.341167i
$645$	−15.2187	−	5.93091i	−0.599237	−	0.233529i
$646$	−1.99822			−0.0786188
$647$	−10.5306	+	18.2396i	−0.414002	+	0.717072i	−0.995323	−	0.0966021i	$-0.969203\pi$
$647$	−10.5306	+	18.2396i	−0.414002	+	0.717072i	0.581321	+	0.813674i	$0.302536\pi$
$648$	−8.14573	−	3.82715i	−0.319995	−	0.150345i
$649$	5.37000	+	9.30111i	0.210791	+	0.365101i
$650$	3.48320	−	6.03308i	0.136622	−	0.236637i
$651$	−3.86662	−	9.05194i	−0.151545	−	0.354774i
$652$	9.69789	+	16.7972i	0.379799	+	0.657831i
$653$	1.42546	−	2.46897i	0.0557825	−	0.0966182i	−0.836786	−	0.547531i	$-0.815568\pi$
$653$	1.42546	−	2.46897i	0.0557825	−	0.0966182i	0.892568	+	0.450912i	$0.148901\pi$
$654$	4.09457	+	26.7314i	0.160110	+	1.04528i
$655$	1.58959	+	2.75325i	0.0621103	+	0.107578i
$656$	1.96977	+	3.41175i	0.0769068	+	0.133206i
$657$	−18.3824	−	16.8933i	−0.717164	−	0.659071i
$658$	−2.56570	+	9.20271i	−0.100021	+	0.358759i
$659$	23.0667	−	39.9527i	0.898551	−	1.55634i	0.0692038	−	0.997603i	$-0.477954\pi$
$659$	23.0667	−	39.9527i	0.898551	−	1.55634i	0.829347	−	0.558734i	$-0.188713\pi$
$660$	1.51634	−	1.21519i	0.0590233	−	0.0473010i
$661$	15.2060			0.591445			0.295723	−	0.955274i	$-0.404440\pi$
$661$	15.2060			0.591445			0.295723	+	0.955274i	$0.404440\pi$
$662$	−4.51014			−0.175292
$663$	5.97827	−	4.79096i	0.232177	−	0.186066i
$664$	6.68917	−	11.5860i	0.259590	−	0.449623i
$665$	−2.23616	+	8.02071i	−0.0867146	+	0.311030i
$666$	−11.6444	+	3.65296i	−0.451212	+	0.141549i
$667$	−1.11380	−	1.92916i	−0.0431266	−	0.0746975i
$668$	2.76642	+	4.79158i	0.107036	+	0.185392i
$669$	−2.56119	−	16.7207i	−0.0990213	−	0.646462i
$670$	3.19393	−	5.53205i	0.123392	−	0.213722i
$671$	−4.19913	−	7.27311i	−0.162106	−	0.280775i
$672$	−1.80013	−	4.21420i	−0.0694417	−	0.162566i
$673$	−23.4191	+	40.5631i	−0.902741	+	1.56359i	−0.0788206	+	0.996889i	$0.525115\pi$
$673$	−23.4191	+	40.5631i	−0.902741	+	1.56359i	−0.823921	+	0.566705i	$0.808218\pi$
$674$	11.0152	+	19.0789i	0.424291	+	0.734893i
$675$	2.89620	−	4.31417i	0.111475	−	0.166052i
$676$	−17.7653	+	30.7705i	−0.683282	+	1.18348i
$677$	−42.6898			−1.64070			−0.820352	−	0.571859i	$-0.806222\pi$
$677$	−42.6898			−1.64070			−0.820352	+	0.571859i	$0.806222\pi$
$678$	11.2327	+	4.37750i	0.431388	+	0.168117i
$679$	−20.4626	−	20.8800i	−0.785283	−	0.801299i
$680$	0.317464	+	0.549864i	0.0121742	+	0.0210863i
$681$	−18.4809	−	7.20223i	−0.708190	−	0.275990i
$682$	−1.20489	−	2.08694i	−0.0461378	−	0.0799129i
$683$	−7.54185	+	13.0629i	−0.288581	+	0.499837i	−0.973471	−	0.228809i	$-0.926517\pi$
$683$	−7.54185	+	13.0629i	−0.288581	+	0.499837i	0.684890	+	0.728646i	$0.259850\pi$
$684$	9.00859	−	2.82608i	0.344452	−	0.108058i
$685$	6.29253			0.240425
$686$	13.4863	−	12.6933i	0.514910	−	0.484631i
$687$	−3.23639	−	21.1288i	−0.123476	−	0.806114i
$688$	−4.71509	+	8.16678i	−0.179761	+	0.311356i
$689$	87.5960			3.33714
$690$	−7.39425	−	2.88163i	−0.281494	−	0.109702i
$691$	35.3479			1.34470			0.672349	−	0.740235i	$-0.265286\pi$
$691$	35.3479			1.34470			0.672349	+	0.740235i	$0.265286\pi$
$692$	−11.7957			−0.448404
$693$	−0.285723	−	8.90019i	−0.0108537	−	0.338090i
$694$	−22.1257			−0.839881
$695$	−13.5131			−0.512582
$696$	−0.127501	−	0.832390i	−0.00483291	−	0.0315517i
$697$	−2.50133			−0.0947446
$698$	15.9115	−	27.5596i	0.602261	−	1.04315i
$699$	−18.3444	−	7.14902i	−0.693849	−	0.270401i
$700$	2.56238	−	0.658939i	0.0968489	−	0.0249055i
$701$	45.3237			1.71185			0.855927	−	0.517097i	$-0.172987\pi$
$701$	45.3237			1.71185			0.855927	+	0.517097i	$0.172987\pi$
$702$	−20.1760	+	30.0542i	−0.761496	+	1.13432i
$703$	6.40130	−	11.0874i	0.241430	−	0.418168i
$704$	−0.560948	−	0.971590i	−0.0211415	−	0.0366182i
$705$	0.946961	+	6.18224i	0.0356646	+	0.232837i
$706$	14.9564	+	25.9053i	0.562893	+	0.974959i
$707$	−18.7909	+	4.83224i	−0.706704	+	0.181735i
$708$	12.9388	−	10.3691i	0.486270	−	0.389695i
$709$	7.40111			0.277955			0.138977	−	0.990296i	$-0.455619\pi$
$709$	7.40111			0.277955			0.138977	+	0.990296i	$0.455619\pi$
$710$	6.15251	−	10.6565i	0.230900	−	0.399930i
$711$	−10.2231	+	45.7997i	−0.383395	+	1.71762i
$712$	−3.22638	−	5.58826i	−0.120914	−	0.209429i
$713$	−4.92076	+	8.52301i	−0.184284	+	0.319189i
$714$	2.88872	+	0.348029i	0.108107	+	0.0130247i
$715$	−3.90778	−	6.76848i	−0.146143	−	0.253127i
$716$	4.05891	−	7.03024i	0.151689	−	0.262732i
$717$	1.26850	+	0.494348i	0.0473729	+	0.0184618i
$718$	−13.8924	−	24.0623i	−0.518459	−	0.897997i
$719$	−6.55906	−	11.3606i	−0.244612	−	0.423680i	0.717411	−	0.696650i	$-0.245327\pi$
$719$	−6.55906	−	11.3606i	−0.244612	−	0.423680i	−0.962022	+	0.272971i	$0.911994\pi$
$720$	−2.20890	−	2.02997i	−0.0823208	−	0.0756524i
$721$	1.21270	+	1.23743i	0.0451633	+	0.0460845i
$722$	4.54770	−	7.87685i	0.169248	−	0.293146i
$723$	8.01090	+	3.12194i	0.297929	+	0.116106i
$724$	−4.36357			−0.162171
$725$	0.486186			0.0180565
$726$	2.55464	+	16.6780i	0.0948116	+	0.618978i
$727$	−21.8998	+	37.9315i	−0.812217	+	1.40680i	0.0990919	+	0.995078i	$0.468406\pi$
$727$	−21.8998	+	37.9315i	−0.812217	+	1.40680i	−0.911309	+	0.411723i	$0.864927\pi$
$728$	−17.8506	+	4.59043i	−0.661586	+	0.170133i
$729$	−16.5294	+	21.3490i	−0.612199	+	0.790704i
$730$	−4.16098	−	7.20703i	−0.154005	−	0.266744i
$731$	−2.99374	−	5.18532i	−0.110728	−	0.191786i
$732$	−10.1177	+	8.10825i	−0.373959	+	0.299690i
$733$	14.1338	−	24.4805i	0.522044	−	0.904207i	−0.477627	−	0.878563i	$-0.658503\pi$
$733$	14.1338	−	24.4805i	0.522044	−	0.904207i	0.999671	−	0.0256443i	$-0.00816374\pi$
$734$	−15.6472	−	27.1017i	−0.577547	−	1.00034i
$735$	4.62966	−	11.2056i	0.170768	−	0.413326i
$736$	−2.29090	+	3.96796i	−0.0844437	+	0.146261i
$737$	−3.58326	−	6.20639i	−0.131991	−	0.228615i
$738$	11.2768	−	3.53763i	0.415104	−	0.130222i
$739$	15.5762	−	26.9788i	0.572980	−	0.992431i	−0.423277	−	0.906000i	$-0.639120\pi$
$739$	15.5762	−	26.9788i	0.572980	−	0.992431i	0.996258	−	0.0864312i	$-0.0275463\pi$
$740$	−4.06799			−0.149542
$741$	−5.74960	−	37.5363i	−0.211217	−	1.37893i
$742$	23.2853	+	23.7602i	0.854829	+	0.872264i
$743$	−15.5646	−	26.9588i	−0.571011	−	0.989021i	−0.996462	−	0.0840394i	$-0.973218\pi$
$743$	−15.5646	−	26.9588i	−0.571011	−	0.989021i	0.425451	−	0.904981i	$-0.360115\pi$
$744$	−2.90315	+	2.32657i	−0.106435	+	0.0852962i
$745$	−10.2539	−	17.7602i	−0.375673	−	0.650685i
$746$	−5.75771	+	9.97265i	−0.210805	+	0.365125i
$747$	−29.5514	−	27.1576i	−1.08123	−	0.993645i
$748$	0.712323			0.0260451
$749$	46.2846	−	11.9025i	1.69120	−	0.434908i
$750$	1.35158	−	1.08315i	0.0493528	−	0.0395512i
$751$	1.35636	−	2.34929i	0.0494944	−	0.0857268i	−0.840217	−	0.542251i	$-0.817572\pi$
$751$	1.35636	−	2.34929i	0.0494944	−	0.0857268i	0.889711	+	0.456524i	$0.150906\pi$
$752$	3.61095			0.131678
$753$	−36.6716	+	29.3885i	−1.33639	+	1.07097i
$754$	−3.38696			−0.123346
$755$	−7.76197			−0.282487
$756$	−13.5154	+	2.51648i	−0.491552	+	0.0915236i
$757$	51.8066			1.88294			0.941472	−	0.337091i	$-0.109443\pi$
$757$	51.8066			1.88294			0.941472	+	0.337091i	$0.109443\pi$
$758$	25.7056			0.933668
$759$	−6.94755	+	5.56774i	−0.252180	+	0.202096i
$760$	3.14716			0.114159
$761$	−13.8395	+	23.9708i	−0.501682	+	0.868939i	0.498316	+	0.866996i	$0.333952\pi$
$761$	−13.8395	+	23.9708i	−0.501682	+	0.868939i	−0.999998	+	0.00194355i	$0.999381\pi$
$762$	−12.8404	+	10.2902i	−0.465158	+	0.372776i
$763$	28.9137	+	29.5034i	1.04674	+	1.06809i
$764$	19.0117			0.687818
$765$	1.81745	−	0.570151i	0.0657101	−	0.0206139i
$766$	−6.56073	+	11.3635i	−0.237049	+	0.410581i
$767$	−33.3449	−	57.7551i	−1.20402	−	2.08542i
$768$	−1.35158	+	1.08315i	−0.0487711	+	0.0390850i
$769$	22.1158	+	38.3057i	0.797517	+	1.38134i	0.921229	+	0.389021i	$0.127187\pi$
$769$	22.1158	+	38.3057i	0.797517	+	1.38134i	−0.123712	+	0.992318i	$0.539480\pi$
$770$	0.797144	−	2.85922i	0.0287271	−	0.103039i
$771$	−0.167620	−	1.09431i	−0.00603667	−	0.0394105i
$772$	6.02865			0.216976
$773$	−0.0327643	+	0.0567494i	−0.00117845	+	0.00204113i	−0.866614	−	0.498979i	$-0.833708\pi$
$773$	−0.0327643	+	0.0567494i	−0.00117845	+	0.00204113i	0.865436	+	0.501020i	$0.167042\pi$
$774$	20.8303	+	19.1430i	0.748730	+	0.688080i
$775$	−1.07398	−	1.86019i	−0.0385785	−	0.0668199i
$776$	−5.52492	+	9.56943i	−0.198333	+	0.343523i
$777$	−11.1851	+	14.9135i	−0.401263	+	0.535019i
$778$	3.38153	+	5.85697i	0.121234	+	0.209983i
$779$	−6.19919	+	10.7373i	−0.222109	+	0.384704i
$780$	−9.41566	+	7.54568i	−0.337135	+	0.270179i
$781$	−6.90247	−	11.9554i	−0.246990	−	0.427799i
$782$	−1.45456	−	2.51937i	−0.0520148	−	0.0900923i
$783$	−2.52052	−	0.170697i	−0.0900761	−	0.00610022i
$784$	−5.99028	−	3.62167i	−0.213939	−	0.129345i
$785$	−4.72367	+	8.18164i	−0.168595	+	0.292015i
$786$	−0.833729	−	5.44301i	−0.0297381	−	0.194146i
$787$	−40.0563			−1.42785			−0.713927	−	0.700220i	$-0.753085\pi$
$787$	−40.0563			−1.42785			−0.713927	+	0.700220i	$0.753085\pi$
$788$	−15.5057			−0.552367
$789$	10.0976	+	3.93517i	0.359485	+	0.140096i
$790$	−7.82112	+	13.5466i	−0.278263	+	0.481966i
$791$	17.8348	−	4.58638i	0.634134	−	0.163073i
$792$	−3.21137	+	1.00744i	−0.114111	+	0.0357977i
$793$	26.0745	+	45.1623i	0.925931	+	1.60376i
$794$	−5.05120	−	8.74893i	−0.179260	−	0.310488i
$795$	20.2924	+	7.90819i	0.719698	+	0.280475i
$796$	−7.34286	+	12.7182i	−0.260261	+	0.450785i
$797$	8.70717	+	15.0813i	0.308424	+	0.534205i	0.978018	−	0.208522i	$-0.0668652\pi$
$797$	8.70717	+	15.0813i	0.308424	+	0.534205i	−0.669594	+	0.742727i	$0.733532\pi$
$798$	8.65324	−	11.5377i	0.306321	−	0.408430i
$799$	−1.14635	+	1.98553i	−0.0405548	+	0.0702430i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−18.4707	+	5.79444i	−0.652632	+	0.204737i
$802$	−13.5515	+	23.4719i	−0.478520	+	0.828821i
$803$	−9.33638			−0.329474
$804$	−8.63373	+	6.91904i	−0.304488	+	0.244016i
$805$	−11.7403	+	3.01913i	−0.413792	+	0.106410i
$806$	7.48177	+	12.9588i	0.263534	+	0.456454i
$807$	−4.04434	−	26.4035i	−0.142367	−	0.929446i
$808$	3.66668	+	6.35088i	0.128993	+	0.223423i
$809$	−3.71971	+	6.44272i	−0.130778	+	0.226514i	−0.923977	−	0.382449i	$-0.875081\pi$
$809$	−3.71971	+	6.44272i	−0.130778	+	0.226514i	0.793199	+	0.608963i	$0.208414\pi$
$810$	−7.38727	+	5.14084i	−0.259562	+	0.180631i
$811$	−4.37460			−0.153613			−0.0768065	−	0.997046i	$-0.524472\pi$
$811$	−4.37460			−0.153613			−0.0768065	+	0.997046i	$0.524472\pi$
$812$	−0.900342	−	0.918706i	−0.0315958	−	0.0322402i
$813$	8.62902	+	3.36283i	0.302633	+	0.117940i
$814$	−2.28193	+	3.95242i	−0.0799816	+	0.138532i
$815$	19.3958			0.679405
$816$	−0.166508	−	1.08705i	−0.00582895	−	0.0380543i
$817$	−29.6783			−1.03831
$818$	9.52808			0.333142
$819$	1.77419	+	55.2656i	0.0619953	+	1.93114i
$820$	3.93955			0.137575
$821$	−12.4569			−0.434748			−0.217374	−	0.976088i	$-0.569749\pi$
$821$	−12.4569			−0.434748			−0.217374	+	0.976088i	$0.569749\pi$
$822$	−10.1551	−	3.95755i	−0.354199	−	0.138036i
$823$	−55.6771			−1.94078			−0.970391	−	0.241538i	$-0.922348\pi$
$823$	−55.6771			−1.94078			−0.970391	+	0.241538i	$0.922348\pi$
$824$	0.327430	−	0.567125i	0.0114066	−	0.0197567i
$825$	−0.294214	−	1.92078i	−0.0102432	−	0.0668729i
$826$	6.80199	−	24.3975i	0.236672	−	0.848899i
$827$	20.0104			0.695830			0.347915	−	0.937526i	$-0.386890\pi$
$827$	20.0104			0.695830			0.347915	+	0.937526i	$0.386890\pi$
$828$	10.1207	+	9.30091i	0.351720	+	0.323229i
$829$	−8.00600	+	13.8668i	−0.278060	+	0.481614i	−0.970903	−	0.239475i	$-0.923025\pi$
$829$	−8.00600	+	13.8668i	−0.278060	+	0.481614i	0.692843	+	0.721089i	$0.256358\pi$
$830$	−6.68917	−	11.5860i	−0.232184	−	0.402155i
$831$	20.0100	+	7.79813i	0.694139	+	0.270514i
$832$	3.48320	+	6.03308i	0.120758	+	0.209159i
$833$	3.89312	−	2.14409i	0.134889	−	0.0742883i
$834$	21.8079	+	8.49879i	0.755146	+	0.294289i
$835$	5.53284			0.191472
$836$	1.76539	−	3.05775i	0.0610573	−	0.105754i
$837$	4.91471	+	10.0208i	0.169877	+	0.346369i
$838$	−20.0930	−	34.8022i	−0.694103	−	1.20222i
$839$	−18.0548	+	31.2719i	−0.623322	+	1.07962i	0.365541	+	0.930795i	$0.380884\pi$
$839$	−18.0548	+	31.2719i	−0.623322	+	1.07962i	−0.988863	+	0.148830i	$0.952449\pi$
$840$	−4.54968	−	0.548140i	−0.156979	−	0.0189126i
$841$	14.3818	+	24.9100i	0.495925	+	0.858967i
$842$	6.20666	−	10.7503i	0.213896	−	0.370478i
$843$	−4.67658	−	30.5311i	−0.161070	−	1.05155i
$844$	−1.07026	−	1.85374i	−0.0368399	−	0.0638085i
$845$	17.7653	+	30.7705i	0.611146	+	1.05854i
$846$	2.35995	−	10.5727i	0.0811369	−	0.363496i
$847$	18.0395	+	18.4074i	0.619845	+	0.632487i
$848$	6.28704	−	10.8895i	0.215898	−	0.373946i
$849$	18.5925	−	14.9000i	0.638094	−	0.511367i
$850$	0.634928			0.0217778
$851$	18.6387			0.638927
$852$	−16.6313	+	13.3282i	−0.569778	+	0.456618i
$853$	8.92954	−	15.4664i	0.305742	−	0.529560i	−0.671684	−	0.740837i	$-0.734429\pi$
$853$	8.92954	−	15.4664i	0.305742	−	0.529560i	0.977426	+	0.211277i	$0.0677622\pi$
$854$	−5.31890	+	19.0779i	−0.182009	+	0.652834i
$855$	2.05684	−	9.21471i	0.0703425	−	0.315136i
$856$	−9.03156	−	15.6431i	−0.308692	−	0.534671i
$857$	2.70675	+	4.68823i	0.0924608	+	0.160147i	0.908546	−	0.417785i	$-0.137193\pi$
$857$	2.70675	+	4.68823i	0.0924608	+	0.160147i	−0.816085	+	0.577932i	$0.803860\pi$
$858$	2.04961	+	13.3809i	0.0699726	+	0.456816i
$859$	−15.9742	+	27.6681i	−0.545032	+	0.944023i	0.453573	+	0.891219i	$0.350149\pi$
$859$	−15.9742	+	27.6681i	−0.545032	+	0.944023i	−0.998605	+	0.0528036i	$0.983184\pi$
$860$	4.71509	+	8.16678i	0.160783	+	0.278485i
$861$	10.8319	−	14.4426i	0.369152	−	0.492204i
$862$	−5.13091	+	8.88700i	−0.174759	+	0.302692i
$863$	−19.3645	−	33.5402i	−0.659174	−	1.14172i	−0.980830	−	0.194866i	$-0.937573\pi$
$863$	−19.3645	−	33.5402i	−0.659174	−	1.14172i	0.321656	−	0.946857i	$-0.395760\pi$
$864$	2.28808	+	4.66526i	0.0778421	+	0.158715i
$865$	−5.89783	+	10.2153i	−0.200532	+	0.347332i
$866$	29.3085			0.995943
$867$	−26.7845	−	10.4382i	−0.909650	−	0.354501i
$868$	−1.52620	+	5.47420i	−0.0518025	+	0.185806i
$869$	8.77449	+	15.1979i	0.297654	+	0.515552i
$870$	−0.784621	−	0.305776i	−0.0266012	−	0.0103668i
$871$	22.2502	+	38.5385i	0.753919	+	1.30583i
$872$	7.80670	−	13.5216i	0.264368	−	0.457899i
$873$	24.4079	+	22.4308i	0.826084	+	0.759168i
$874$	−14.4197			−0.487752
$875$	0.710533	−	2.54856i	0.0240204	−	0.0861569i
$876$	2.18241	+	14.2479i	0.0737369	+	0.481392i
$877$	−12.9894	+	22.4982i	−0.438620	+	0.759712i	−0.997583	−	0.0694806i	$-0.977866\pi$
$877$	−12.9894	+	22.4982i	−0.438620	+	0.759712i	0.558964	+	0.829192i	$0.311199\pi$
$878$	18.8441			0.635958
$879$	24.6009	+	9.58726i	0.829768	+	0.323370i
$880$	−1.12190			−0.0378191
$881$	31.9946			1.07793			0.538963	−	0.842330i	$-0.318816\pi$
$881$	31.9946			1.07793			0.538963	+	0.842330i	$0.318816\pi$
$882$	−14.5190	+	15.1723i	−0.488881	+	0.510877i
$883$	−36.8306			−1.23945			−0.619724	−	0.784820i	$-0.712756\pi$
$883$	−36.8306			−1.23945			−0.619724	+	0.784820i	$0.712756\pi$
$884$	−4.42316			−0.148767
$885$	−2.51051	−	16.3899i	−0.0843900	−	0.550941i
$886$	10.9196			0.366853
$887$	−2.75742	+	4.77599i	−0.0925850	+	0.160362i	−0.908598	−	0.417671i	$-0.862846\pi$
$887$	−2.75742	+	4.77599i	−0.0925850	+	0.160362i	0.816013	+	0.578033i	$0.196180\pi$
$888$	6.56504	+	2.55847i	0.220308	+	0.0858567i
$889$	−6.75025	+	24.2119i	−0.226396	+	0.812043i
$890$	−6.45277			−0.216297
$891$	0.850912	+	10.0611i	0.0285066	+	0.337061i
$892$	−4.88316	+	8.45788i	−0.163500	+	0.283191i
$893$	5.68211	+	9.84171i	0.190145	+	0.329340i
$894$	5.37810	+	35.1110i	0.179871	+	1.17429i
$895$	−4.05891	−	7.03024i	−0.135674	−	0.234995i
$896$	−0.710533	+	2.54856i	−0.0237373	+	0.0851413i
$897$	43.1407	−	34.5728i	1.44043	−	1.15435i
$898$	−14.4079			−0.480797
$899$	−0.522154	+	0.904397i	−0.0174148	+	0.0301633i
$900$	−2.86245	+	0.897978i	−0.0954151	+	0.0299326i
$901$	3.99181	+	6.91403i	0.132987	+	0.230340i
$902$	2.20988	−	3.82763i	0.0735810	−	0.127446i
$903$	42.9043	+	5.16906i	1.42777	+	0.172016i
$904$	−3.48013	−	6.02776i	−0.115747	−	0.200480i
$905$	−2.18179	+	3.77896i	−0.0725250	+	0.125617i
$906$	12.5265	+	4.88173i	0.416165	+	0.162184i
$907$	−2.35137	−	4.07270i	−0.0780761	−	0.135232i	0.824344	−	0.566090i	$-0.191544\pi$
$907$	−2.35137	−	4.07270i	−0.0780761	−	0.135232i	−0.902420	+	0.430858i	$0.858211\pi$
$908$	5.72579	+	9.91736i	0.190017	+	0.329119i
$909$	20.9914	−	6.58520i	0.696241	−	0.218417i
$910$	−4.94986	+	17.7543i	−0.164086	+	0.588548i
$911$	9.43488	−	16.3417i	0.312591	−	0.541424i	−0.666331	−	0.745656i	$-0.732136\pi$
$911$	9.43488	−	16.3417i	0.312591	−	0.541424i	0.978923	+	0.204232i	$0.0654696\pi$
$912$	−5.07898	−	1.97934i	−0.168182	−	0.0655424i
$913$	−15.0091			−0.496729
$914$	1.49735			0.0495278
$915$	1.96313	+	12.8163i	0.0648989	+	0.423693i
$916$	−6.17050	+	10.6876i	−0.203879	+	0.353129i
$917$	−5.88735	−	6.00742i	−0.194417	−	0.198383i
$918$	−3.29164	−	0.222920i	−0.108640	−	0.00735745i
$919$	24.1217	+	41.7799i	0.795700	+	1.37819i	0.922394	+	0.386251i	$0.126230\pi$
$919$	24.1217	+	41.7799i	0.795700	+	1.37819i	−0.126693	+	0.991942i	$0.540436\pi$
$920$	2.29090	+	3.96796i	0.0755288	+	0.130820i
$921$	2.65910	−	2.13099i	0.0876203	−	0.0702186i
$922$	8.47082	−	14.6719i	0.278972	−	0.483193i
$923$	42.8608	+	74.2371i	1.41078	+	2.44354i
$924$	−3.08470	+	4.11294i	−0.101479	+	0.135306i
$925$	−2.03399	+	3.52298i	−0.0668773	+	0.115835i
$926$	5.08561	+	8.80854i	0.167124	+	0.289467i
$927$	−1.44652	−	1.32934i	−0.0475099	−	0.0436614i
$928$	−0.243093	+	0.421049i	−0.00797991	+	0.0138216i
$929$	−46.0943			−1.51230			−0.756152	−	0.654396i	$-0.772923\pi$
$929$	−46.0943			−1.51230			−0.756152	+	0.654396i	$0.772923\pi$
$930$	0.563296	+	3.67748i	0.0184712	+	0.120589i
$931$	0.444741	−	22.0256i	0.0145758	−	0.721860i
$932$	5.68350	+	9.84410i	0.186169	+	0.322454i
$933$	4.24819	−	3.40449i	0.139080	−	0.111458i
$934$	−13.0827	−	22.6599i	−0.428079	−	0.741454i
$935$	0.356161	−	0.616890i	0.0116477	−	0.0201744i
$936$	19.9410	−	6.25567i	0.651791	−	0.204473i
$937$	−29.3325			−0.958250			−0.479125	−	0.877747i	$-0.659046\pi$
$937$	−29.3325			−0.958250			−0.479125	+	0.877747i	$0.659046\pi$
$938$	−4.53879	+	16.2798i	−0.148197	+	0.531556i
$939$	−24.7951	+	19.8707i	−0.809158	+	0.648456i
$940$	1.80547	−	3.12717i	0.0588881	−	0.101997i
$941$	−34.7270			−1.13207			−0.566033	−	0.824382i	$-0.691523\pi$
$941$	−34.7270			−1.13207			−0.566033	+	0.824382i	$0.691523\pi$
$942$	12.7689	−	10.2329i	0.416032	−	0.333407i
$943$	−18.0502			−0.587796
$944$	−9.57308			−0.311577
$945$	−4.57839	+	12.9630i	−0.148935	+	0.421685i
$946$	10.5797			0.343975
$947$	19.8198			0.644056			0.322028	−	0.946730i	$-0.395636\pi$
$947$	19.8198			0.644056			0.322028	+	0.946730i	$0.395636\pi$
$948$	21.1418	−	16.9430i	0.686654	−	0.550282i
$949$	57.9741			1.88192
$950$	1.57358	−	2.72552i	0.0510536	−	0.0884275i
$951$	−43.6486	+	34.9798i	−1.41540	+	1.13430i
$952$	−1.17579	−	1.19977i	−0.0381076	−	0.0388848i
$953$	10.0049			0.324092			0.162046	−	0.986783i	$-0.448191\pi$
$953$	10.0049			0.324092			0.162046	+	0.986783i	$0.448191\pi$
$954$	−27.7748	−	25.5250i	−0.899244	−	0.826401i
$955$	9.50584	−	16.4646i	0.307602	−	0.532782i
$956$	−0.393008	−	0.680710i	−0.0127108	−	0.0220157i
$957$	−0.737221	+	0.590806i	−0.0238310	+	0.0190980i
$958$	−5.33351	−	9.23791i	−0.172318	−	0.298463i
$959$	−16.1239	+	4.14639i	−0.520667	+	0.133894i
$960$	0.262247	+	1.71208i	0.00846399	+	0.0552572i
$961$	−26.3863			−0.851170
$962$	14.1696	−	24.5425i	0.456846	−	0.791281i
$963$	−51.7048	+	16.2203i	−1.66617	+	0.522691i
$964$	−2.48195	−	4.29887i	−0.0799383	−	0.138457i
$965$	3.01432	−	5.22096i	0.0970345	−	0.168069i
$966$	20.8457	+	2.51147i	0.670700	+	0.0808051i
$967$	−9.26371	−	16.0452i	−0.297901	−	0.515980i	0.677755	−	0.735288i	$-0.262953\pi$
$967$	−9.26371	−	16.0452i	−0.297901	−	0.515980i	−0.975656	+	0.219309i	$0.929620\pi$
$968$	4.87067	−	8.43626i	0.156549	−	0.271152i
$969$	2.70076	−	2.16438i	0.0867609	−	0.0695298i
$970$	5.52492	+	9.56943i	0.177394	+	0.307256i
$971$	−15.3742	−	26.6289i	−0.493381	−	0.854561i	0.506590	−	0.862187i	$-0.330906\pi$
$971$	−15.3742	−	26.6289i	−0.493381	−	0.854561i	−0.999971	+	0.00762627i	$0.997572\pi$
$972$	15.1550	−	3.65037i	0.486098	−	0.117086i
$973$	34.6258	−	8.90432i	1.11005	−	0.285459i
$974$	−10.0410	+	17.3916i	−0.321735	+	0.557261i
$975$	1.82692	+	11.9270i	0.0585082	+	0.381971i
$976$	7.48578			0.239614
$977$	−8.64990			−0.276735			−0.138367	−	0.990381i	$-0.544185\pi$
$977$	−8.64990			−0.276735			−0.138367	+	0.990381i	$0.544185\pi$
$978$	−31.3015	−	12.1986i	−1.00091	−	0.390067i
$979$	−3.61967	+	6.26945i	−0.115685	+	0.200372i
$980$	−6.13160	+	3.37690i	−0.195867	+	0.107871i
$981$	−34.4884	−	31.6947i	−1.10113	−	1.01193i
$982$	−8.48718	−	14.7002i	−0.270837	−	0.469103i
$983$	−31.0750	−	53.8235i	−0.991139	−	1.71670i	−0.610602	−	0.791938i	$-0.709073\pi$
$983$	−31.0750	−	53.8235i	−0.991139	−	1.71670i	−0.380537	−	0.924766i	$-0.624261\pi$
$984$	−6.35776	−	2.47769i	−0.202678	−	0.0789860i
$985$	−7.75284	+	13.4283i	−0.247026	+	0.427862i
$986$	−0.154346	−	0.267336i	−0.00491539	−	0.00851371i
$987$	−6.50019	−	15.2173i	−0.206903	−	0.484371i
$988$	−10.9622	+	18.9870i	−0.348753	+	0.604058i
$989$	−21.6036	−	37.4186i	−0.686955	−	1.18984i
$990$	−0.733221	+	3.28485i	−0.0233033	+	0.104399i
$991$	−27.8376	+	48.2161i	−0.884289	+	1.53163i	−0.0377633	+	0.999287i	$0.512023\pi$
$991$	−27.8376	+	48.2161i	−0.884289	+	1.53163i	−0.846526	+	0.532347i	$0.821310\pi$
$992$	2.14796			0.0681978
$993$	6.09583	−	4.88517i	0.193445	−	0.155026i
$994$	−8.74313	+	31.3600i	−0.277315	+	0.994680i
$995$	7.34286	+	12.7182i	0.232784	+	0.403194i
$996$	3.50843	+	22.9048i	0.111169	+	0.725767i
$997$	13.0620	+	22.6240i	0.413676	+	0.716509i	0.995289	−	0.0969577i	$-0.0309111\pi$
$997$	13.0620	+	22.6240i	0.413676	+	0.716509i	−0.581612	+	0.813466i	$0.697578\pi$
$998$	7.40677	−	12.8289i	0.234457	−	0.406092i
$999$	11.7817	−	17.5500i	0.372756	−	0.555257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.151.1	yes	12
3.2	odd	2		1890.2.i.f.991.2		12
7.2	even	3		630.2.l.f.331.5	yes	12
9.4	even	3		630.2.l.f.571.5	yes	12
9.5	odd	6		1890.2.l.h.361.1		12
21.2	odd	6		1890.2.l.h.1801.1		12
63.23	odd	6		1890.2.i.f.1171.2		12
63.58	even	3	inner	630.2.i.h.121.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.1	✓	12	63.58	even	3	inner
630.2.i.h.151.1	yes	12	1.1	even	1	trivial
630.2.l.f.331.5	yes	12	7.2	even	3
630.2.l.f.571.5	yes	12	9.4	even	3
1890.2.i.f.991.2		12	3.2	odd	2
1890.2.i.f.1171.2		12	63.23	odd	6
1890.2.l.h.361.1		12	9.5	odd	6
1890.2.l.h.1801.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.35158 + 1.08315i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.35158 + 1.08315i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(0.653555 - 2.92795i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.35158 + 1.08315i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.35158 + 1.08315i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(0.653555 - 2.92795i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.560948 - 0.971590i) q^{11} +(-1.35158 + 1.08315i) q^{12} +(3.48320 + 6.03308i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(0.262247 + 1.71208i) q^{15} +1.00000 q^{16} +(-0.317464 + 0.549864i) q^{17} +(0.653555 - 2.92795i) q^{18} +(1.57358 + 2.72552i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.80013 - 4.21420i) q^{21} +(-0.560948 - 0.971590i) q^{22} +(-2.29090 + 3.96796i) q^{23} +(-1.35158 + 1.08315i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.48320 + 6.03308i) q^{26} +(2.28808 + 4.66526i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(-0.243093 + 0.421049i) q^{29} +(0.262247 + 1.71208i) q^{30} +2.14796 q^{31} +1.00000 q^{32} +(1.81055 + 0.705592i) q^{33} +(-0.317464 + 0.549864i) q^{34} +(1.85185 + 1.88962i) q^{35} +(0.653555 - 2.92795i) q^{36} +(-2.03399 - 3.52298i) q^{37} +(1.57358 + 2.72552i) q^{38} +(-11.2426 - 4.38136i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.96977 + 3.41175i) q^{41} +(-1.80013 - 4.21420i) q^{42} +(-4.71509 + 8.16678i) q^{43} +(-0.560948 - 0.971590i) q^{44} +(-2.20890 - 2.02997i) q^{45} +(-2.29090 + 3.96796i) q^{46} +3.61095 q^{47} +(-1.35158 + 1.08315i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.166508 - 1.08705i) q^{51} +(3.48320 + 6.03308i) q^{52} +(6.28704 - 10.8895i) q^{53} +(2.28808 + 4.66526i) q^{54} -1.12190 q^{55} +(-0.710533 + 2.54856i) q^{56} +(-5.07898 - 1.97934i) q^{57} +(-0.243093 + 0.421049i) q^{58} -9.57308 q^{59} +(0.262247 + 1.71208i) q^{60} +7.48578 q^{61} +2.14796 q^{62} +(6.99766 + 3.74603i) q^{63} +1.00000 q^{64} +6.96640 q^{65} +(1.81055 + 0.705592i) q^{66} +6.38787 q^{67} +(-0.317464 + 0.549864i) q^{68} +(-1.20156 - 7.84442i) q^{69} +(1.85185 + 1.88962i) q^{70} +12.3050 q^{71} +(0.653555 - 2.92795i) q^{72} +(4.16098 - 7.20703i) q^{73} +(-2.03399 - 3.52298i) q^{74} +(1.61383 + 0.628929i) q^{75} +(1.57358 + 2.72552i) q^{76} +(2.87473 - 0.739260i) q^{77} +(-11.2426 - 4.38136i) q^{78} -15.6422 q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.14573 - 3.82715i) q^{81} +(1.96977 + 3.41175i) q^{82} +(6.68917 - 11.5860i) q^{83} +(-1.80013 - 4.21420i) q^{84} +(0.317464 + 0.549864i) q^{85} +(-4.71509 + 8.16678i) q^{86} +(-0.127501 - 0.832390i) q^{87} +(-0.560948 - 0.971590i) q^{88} +(-3.22638 - 5.58826i) q^{89} +(-2.20890 - 2.02997i) q^{90} +(-17.8506 + 4.59043i) q^{91} +(-2.29090 + 3.96796i) q^{92} +(-2.90315 + 2.32657i) q^{93} +3.61095 q^{94} +3.14716 q^{95} +(-1.35158 + 1.08315i) q^{96} +(-5.52492 + 9.56943i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(-3.21137 + 1.00744i) 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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