LMFDB - Embedded newform 630.2.t.b.551.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

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.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.9
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.28599 - 1.16028i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.69383 - 0.361836i) q^{6} +(-0.555567 + 2.58676i) q^{7} -1.00000i q^{8} +(0.307516 + 2.98420i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.28599 - 1.16028i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.69383 - 0.361836i) q^{6} +(-0.555567 + 2.58676i) q^{7} -1.00000i q^{8} +(0.307516 + 2.98420i) q^{9} +(-0.866025 + 0.500000i) q^{10} +4.07809i q^{11} +(-1.64782 + 0.533558i) q^{12} +(-5.20173 + 3.00322i) q^{13} +(0.812247 + 2.51799i) q^{14} +(1.28599 + 1.16028i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.641724 - 1.11150i) q^{17} +(1.75842 + 2.43063i) q^{18} +(2.90701 + 1.67836i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.71581 - 2.68193i) q^{21} +(2.03904 + 3.53173i) q^{22} -2.18864i q^{23} +(-1.16028 + 1.28599i) q^{24} +1.00000 q^{25} +(-3.00322 + 5.20173i) q^{26} +(3.06703 - 4.19444i) q^{27} +(1.96242 + 1.77452i) q^{28} +(6.21856 + 3.59029i) q^{29} +(1.69383 + 0.361836i) q^{30} +(-6.79271 - 3.92178i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.73171 - 5.24436i) q^{33} +(-1.11150 - 0.641724i) q^{34} +(0.555567 - 2.58676i) q^{35} +(2.73815 + 1.22578i) q^{36} +(-2.90160 + 5.02572i) q^{37} +3.35672 q^{38} +(10.1739 + 2.17335i) q^{39} +1.00000i q^{40} +(1.36925 + 2.37162i) q^{41} +(1.87702 - 4.18052i) q^{42} +(-2.43768 + 4.22219i) q^{43} +(3.53173 + 2.03904i) q^{44} +(-0.307516 - 2.98420i) q^{45} +(-1.09432 - 1.89542i) q^{46} +(4.13613 + 7.16398i) q^{47} +(-0.361836 + 1.69383i) q^{48} +(-6.38269 - 2.87424i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.464398 + 2.17395i) q^{51} +6.00644i q^{52} +(-7.48689 + 4.32256i) q^{53} +(0.558910 - 5.16601i) q^{54} -4.07809i q^{55} +(2.58676 + 0.555567i) q^{56} +(-1.79100 - 5.53128i) q^{57} +7.18058 q^{58} +(-0.630579 + 1.09220i) q^{59} +(1.64782 - 0.533558i) q^{60} +(-2.56956 + 1.48353i) q^{61} -7.84355 q^{62} +(-7.89026 - 0.862450i) q^{63} -1.00000 q^{64} +(5.20173 - 3.00322i) q^{65} +(1.47560 - 6.90760i) q^{66} +(4.31098 - 7.46684i) q^{67} -1.28345 q^{68} +(-2.53943 + 2.81456i) q^{69} +(-0.812247 - 2.51799i) q^{70} -14.1375i q^{71} +(2.98420 - 0.307516i) q^{72} +(-6.02332 + 3.47757i) q^{73} +5.80320i q^{74} +(-1.28599 - 1.16028i) q^{75} +(2.90701 - 1.67836i) q^{76} +(-10.5490 - 2.26565i) q^{77} +(9.89754 - 3.20478i) q^{78} +(6.09277 + 10.5530i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.81087 + 1.83538i) q^{81} +(2.37162 + 1.36925i) q^{82} +(6.87948 - 11.9156i) q^{83} +(-0.464712 - 4.55895i) q^{84} +(0.641724 + 1.11150i) q^{85} +4.87537i q^{86} +(-3.83125 - 11.8323i) q^{87} +4.07809 q^{88} +(-7.29497 + 12.6353i) q^{89} +(-1.75842 - 2.43063i) q^{90} +(-4.87871 - 15.1241i) q^{91} +(-1.89542 - 1.09432i) q^{92} +(4.18499 + 12.9248i) q^{93} +(7.16398 + 4.13613i) q^{94} +(-2.90701 - 1.67836i) q^{95} +(0.533558 + 1.64782i) q^{96} +(-16.8723 - 9.74120i) q^{97} +(-6.96469 + 0.702180i) q^{98} +(-12.1698 + 1.25408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.28599	−	1.16028i	−0.742464	−	0.669886i
$3$	−1.28599	−	1.16028i	−0.742464	−	0.669886i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.69383	−	0.361836i	−0.691505	−	0.147719i
$7$	−0.555567	+	2.58676i	−0.209985	+	0.977705i
$7$	−0.555567	+	2.58676i	−0.209985	+	0.977705i
$8$		−	1.00000i		−	0.353553i
$9$	0.307516	+	2.98420i	0.102505	+	0.994732i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$			4.07809i			1.22959i	0.788687	+	0.614795i	$0.210761\pi$
$11$			4.07809i			1.22959i	−0.788687	+	0.614795i	$0.789239\pi$
$12$	−1.64782	+	0.533558i	−0.475685	+	0.154025i
$13$	−5.20173	+	3.00322i	−1.44270	+	0.832943i	−0.998029	−	0.0627507i	$-0.980013\pi$
$13$	−5.20173	+	3.00322i	−1.44270	+	0.832943i	−0.444671	+	0.895694i	$0.646679\pi$
$14$	0.812247	+	2.51799i	0.217082	+	0.672960i
$15$	1.28599	+	1.16028i	0.332040	+	0.299582i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.641724	−	1.11150i	−0.155641	−	0.269578i	0.777651	−	0.628696i	$-0.216411\pi$
$17$	−0.641724	−	1.11150i	−0.155641	−	0.269578i	−0.933292	+	0.359118i	$0.883078\pi$
$18$	1.75842	+	2.43063i	0.414462	+	0.572906i
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	0.794906	−	0.606733i	$-0.207520\pi$
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	−0.127993	+	0.991775i	$0.540853\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.71581	−	2.68193i	0.810857	−	0.585245i
$22$	2.03904	+	3.53173i	0.434726	+	0.752967i
$23$		−	2.18864i		−	0.456363i	−0.973619	−	0.228182i	$-0.926722\pi$
$23$		−	2.18864i		−	0.456363i	0.973619	−	0.228182i	$-0.0732780\pi$
$24$	−1.16028	+	1.28599i	−0.236840	+	0.262501i
$25$	1.00000			0.200000
$26$	−3.00322	+	5.20173i	−0.588980	+	1.02014i
$27$	3.06703	−	4.19444i	0.590251	−	0.807220i
$28$	1.96242	+	1.77452i	0.370862	+	0.335352i
$29$	6.21856	+	3.59029i	1.15476	+	0.666700i	0.950042	−	0.312122i	$-0.101040\pi$
$29$	6.21856	+	3.59029i	1.15476	+	0.666700i	0.204716	+	0.978821i	$0.434373\pi$
$30$	1.69383	+	0.361836i	0.309250	+	0.0660620i
$31$	−6.79271	−	3.92178i	−1.22001	−	0.704372i	−0.255088	−	0.966918i	$-0.582104\pi$
$31$	−6.79271	−	3.92178i	−1.22001	−	0.704372i	−0.964919	+	0.262546i	$0.915438\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.73171	−	5.24436i	0.823685	−	0.912926i
$34$	−1.11150	−	0.641724i	−0.190621	−	0.110055i
$35$	0.555567	−	2.58676i	0.0939079	−	0.437243i
$36$	2.73815	+	1.22578i	0.456358	+	0.204297i
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	−0.999653	−	0.0263347i	$-0.991616\pi$
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	0.522633	+	0.852558i	$0.324950\pi$
$38$	3.35672			0.544532
$39$	10.1739	+	2.17335i	1.62913	+	0.348014i
$40$			1.00000i			0.158114i
$41$	1.36925	+	2.37162i	0.213842	+	0.370384i	0.952914	−	0.303242i	$-0.0980690\pi$
$41$	1.36925	+	2.37162i	0.213842	+	0.370384i	−0.739072	+	0.673626i	$0.764736\pi$
$42$	1.87702	−	4.18052i	0.289631	−	0.645069i
$43$	−2.43768	+	4.22219i	−0.371743	+	0.643878i	−0.989834	−	0.142229i	$-0.954573\pi$
$43$	−2.43768	+	4.22219i	−0.371743	+	0.643878i	0.618091	+	0.786107i	$0.287906\pi$
$44$	3.53173	+	2.03904i	0.532428	+	0.307397i
$45$	−0.307516	−	2.98420i	−0.0458418	−	0.444858i
$46$	−1.09432	−	1.89542i	−0.161349	−	0.279464i
$47$	4.13613	+	7.16398i	0.603316	+	1.04497i	0.992315	+	0.123736i	$0.0394876\pi$
$47$	4.13613	+	7.16398i	0.603316	+	1.04497i	−0.388999	+	0.921238i	$0.627179\pi$
$48$	−0.361836	+	1.69383i	−0.0522266	+	0.244484i
$49$	−6.38269	−	2.87424i	−0.911813	−	0.410606i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−0.464398	+	2.17395i	−0.0650288	+	0.304414i
$52$			6.00644i			0.832943i
$53$	−7.48689	+	4.32256i	−1.02840	+	0.593749i	−0.916527	−	0.399973i	$-0.869020\pi$
$53$	−7.48689	+	4.32256i	−1.02840	+	0.593749i	−0.111877	+	0.993722i	$0.535686\pi$
$54$	0.558910	−	5.16601i	0.0760581	−	0.703004i
$55$		−	4.07809i		−	0.549889i
$56$	2.58676	+	0.555567i	0.345671	+	0.0742407i
$57$	−1.79100	−	5.53128i	−0.237224	−	0.732636i
$58$	7.18058			0.942856
$59$	−0.630579	+	1.09220i	−0.0820944	+	0.142192i	−0.904149	−	0.427216i	$-0.859494\pi$
$59$	−0.630579	+	1.09220i	−0.0820944	+	0.142192i	0.822055	+	0.569408i	$0.192828\pi$
$60$	1.64782	−	0.533558i	0.212733	−	0.0688820i
$61$	−2.56956	+	1.48353i	−0.328998	+	0.189947i	−0.655396	−	0.755285i	$-0.727498\pi$
$61$	−2.56956	+	1.48353i	−0.328998	+	0.189947i	0.326398	+	0.945232i	$0.394165\pi$
$62$	−7.84355			−0.996132
$63$	−7.89026	−	0.862450i	−0.994079	−	0.108659i
$64$	−1.00000			−0.125000
$65$	5.20173	−	3.00322i	0.645195	−	0.372504i
$66$	1.47560	−	6.90760i	0.181634	−	0.850267i
$67$	4.31098	−	7.46684i	0.526670	−	0.912220i	−0.472847	−	0.881145i	$-0.656774\pi$
$67$	4.31098	−	7.46684i	0.526670	−	0.912220i	0.999517	−	0.0310753i	$-0.00989316\pi$
$68$	−1.28345			−0.155641
$69$	−2.53943	+	2.81456i	−0.305711	+	0.338833i
$70$	−0.812247	−	2.51799i	−0.0970821	−	0.300957i
$71$		−	14.1375i		−	1.67781i	−0.544277	−	0.838906i	$-0.683196\pi$
$71$		−	14.1375i		−	1.67781i	0.544277	−	0.838906i	$-0.316804\pi$
$72$	2.98420	−	0.307516i	0.351691	−	0.0362411i
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	−0.809198	−	0.587536i	$-0.800098\pi$
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	0.104222	+	0.994554i	$0.466765\pi$
$74$			5.80320i			0.674608i
$75$	−1.28599	−	1.16028i	−0.148493	−	0.133977i
$76$	2.90701	−	1.67836i	0.333457	−	0.192521i
$77$	−10.5490	−	2.26565i	−1.20218	−	0.258195i
$78$	9.89754	−	3.20478i	1.12068	−	0.362870i
$79$	6.09277	+	10.5530i	0.685490	+	1.18730i	0.973283	+	0.229610i	$0.0737452\pi$
$79$	6.09277	+	10.5530i	0.685490	+	1.18730i	−0.287793	+	0.957693i	$0.592921\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−8.81087	+	1.83538i	−0.978985	+	0.203931i
$82$	2.37162	+	1.36925i	0.261901	+	0.151209i
$83$	6.87948	−	11.9156i	0.755121	−	1.30791i	−0.190194	−	0.981747i	$-0.560912\pi$
$83$	6.87948	−	11.9156i	0.755121	−	1.30791i	0.945314	−	0.326161i	$-0.105755\pi$
$84$	−0.464712	−	4.55895i	−0.0507042	−	0.497422i
$85$	0.641724	+	1.11150i	0.0696048	+	0.120559i
$86$			4.87537i			0.525724i
$87$	−3.83125	−	11.8323i	−0.410753	−	1.26856i
$88$	4.07809			0.434726
$89$	−7.29497	+	12.6353i	−0.773265	+	1.33933i	0.162499	+	0.986709i	$0.448045\pi$
$89$	−7.29497	+	12.6353i	−0.773265	+	1.33933i	−0.935764	+	0.352626i	$0.885289\pi$
$90$	−1.75842	−	2.43063i	−0.185353	−	0.256211i
$91$	−4.87871	−	15.1241i	−0.511428	−	1.58544i
$92$	−1.89542	−	1.09432i	−0.197611	−	0.114091i
$93$	4.18499	+	12.9248i	0.433963	+	1.34024i
$94$	7.16398	+	4.13613i	0.738908	+	0.426609i
$95$	−2.90701	−	1.67836i	−0.298253	−	0.172196i
$96$	0.533558	+	1.64782i	0.0544560	+	0.168180i
$97$	−16.8723	−	9.74120i	−1.71312	−	0.989069i	−0.930285	−	0.366837i	$-0.880441\pi$
$97$	−16.8723	−	9.74120i	−1.71312	−	0.989069i	−0.782832	−	0.622233i	$-0.786226\pi$
$98$	−6.96469	+	0.702180i	−0.703540	+	0.0709309i
$99$	−12.1698	+	1.25408i	−1.22311	+	0.126039i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	8.53717			0.849480			0.424740	−	0.905315i	$-0.360365\pi$
$101$	8.53717			0.849480			0.424740	+	0.905315i	$0.360365\pi$
$102$	0.684794	+	2.11489i	0.0678047	+	0.209406i
$103$		−	3.61248i		−	0.355948i	−0.984035	−	0.177974i	$-0.943046\pi$
$103$		−	3.61248i		−	0.355948i	0.984035	−	0.177974i	$-0.0569543\pi$
$104$	3.00322	+	5.20173i	0.294490	+	0.510072i
$105$	−3.71581	+	2.68193i	−0.362626	+	0.261729i
$106$	−4.32256	+	7.48689i	−0.419844	+	0.727191i
$107$	11.5596	+	6.67392i	1.11751	+	0.645192i	0.940763	−	0.339065i	$-0.110111\pi$
$107$	11.5596	+	6.67392i	1.11751	+	0.645192i	0.176743	+	0.984257i	$0.443444\pi$
$108$	−2.09897	−	4.75335i	−0.201974	−	0.457391i
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	0.999830	+	0.0184222i	$0.00586429\pi$
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	−0.483961	+	0.875090i	$0.660802\pi$
$110$	−2.03904	−	3.53173i	−0.194415	−	0.336737i
$111$	9.56264	−	3.09634i	0.907646	−	0.293892i
$112$	2.51799	−	0.812247i	0.237927	−	0.0767501i
$113$	−2.45659	+	1.41832i	−0.231097	+	0.133424i	−0.611078	−	0.791570i	$-0.709264\pi$
$113$	−2.45659	+	1.41832i	−0.231097	+	0.133424i	0.379981	+	0.924994i	$0.375930\pi$
$114$	−4.31670	−	3.89473i	−0.404296	−	0.364775i
$115$			2.18864i			0.204092i
$116$	6.21856	−	3.59029i	0.577379	−	0.333350i
$117$	−10.5618	−	14.5994i	−0.976440	−	1.34972i
$118$			1.26116i			0.116099i
$119$	3.23171	−	1.04248i	0.296250	−	0.0955637i
$120$	1.16028	−	1.28599i	0.105918	−	0.117394i
$121$	−5.63079			−0.511890
$122$	−1.48353	+	2.56956i	−0.134313	+	0.232637i
$123$	0.990892	−	4.63858i	0.0893457	−	0.418247i
$124$	−6.79271	+	3.92178i	−0.610004	+	0.352186i
$125$	−1.00000			−0.0894427
$126$	−7.26439	+	3.19823i	−0.647163	+	0.284921i
$127$	−10.9625			−0.972768			−0.486384	−	0.873745i	$-0.661684\pi$
$127$	−10.9625			−0.972768			−0.486384	+	0.873745i	$0.661684\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	8.03373	−	2.60129i	0.707331	−	0.229031i
$130$	3.00322	−	5.20173i	0.263400	−	0.456222i
$131$	20.7312			1.81129			0.905647	−	0.424032i	$-0.139386\pi$
$131$	20.7312			1.81129			0.905647	+	0.424032i	$0.139386\pi$
$132$	−2.17589	−	6.71996i	−0.189387	−	0.584897i
$133$	−5.95656	+	6.58730i	−0.516499	+	0.571191i
$134$		−	8.62197i		−	0.744825i
$135$	−3.06703	+	4.19444i	−0.263968	+	0.361000i
$136$	−1.11150	+	0.641724i	−0.0953103	+	0.0550274i
$137$		−	9.67432i		−	0.826533i	−0.910610	−	0.413267i	$-0.864388\pi$
$137$		−	9.67432i		−	0.826533i	0.910610	−	0.413267i	$-0.135612\pi$
$138$	−0.791930	+	3.70719i	−0.0674136	+	0.315577i
$139$	−4.57137	+	2.63928i	−0.387739	+	0.223861i	−0.681180	−	0.732116i	$-0.738533\pi$
$139$	−4.57137	+	2.63928i	−0.387739	+	0.223861i	0.293441	+	0.955977i	$0.405200\pi$
$140$	−1.96242	−	1.77452i	−0.165855	−	0.149974i
$141$	2.99320	−	14.0118i	0.252073	−	1.18001i
$142$	−7.06874	−	12.2434i	−0.593196	−	1.02745i
$143$	−12.2474	−	21.2131i	−1.02418	−	1.77393i
$144$	2.43063	−	1.75842i	0.202553	−	0.146535i
$145$	−6.21856	−	3.59029i	−0.516423	−	0.298157i
$146$	−3.47757	+	6.02332i	−0.287806	+	0.498494i
$147$	4.87313	+	11.1019i	0.401929	+	0.915671i
$148$	2.90160	+	5.02572i	0.238510	+	0.413112i
$149$			4.37779i			0.358642i	0.983791	+	0.179321i	$0.0573901\pi$
$149$			4.37779i			0.358642i	−0.983791	+	0.179321i	$0.942610\pi$
$150$	−1.69383	−	0.361836i	−0.138301	−	0.0295438i
$151$	−5.57316			−0.453538			−0.226769	−	0.973949i	$-0.572816\pi$
$151$	−5.57316			−0.453538			−0.226769	+	0.973949i	$0.572816\pi$
$152$	1.67836	−	2.90701i	0.136133	−	0.235789i
$153$	3.11959	−	2.25684i	0.252204	−	0.182454i
$154$	−10.2686	+	3.31241i	−0.827465	+	0.266922i
$155$	6.79271	+	3.92178i	0.545604	+	0.315005i
$156$	6.96913	−	7.72419i	0.557977	−	0.618430i
$157$	−0.243649	−	0.140671i	−0.0194453	−	0.0112267i	0.490246	−	0.871584i	$-0.336907\pi$
$157$	−0.243649	−	0.140671i	−0.0194453	−	0.0112267i	−0.509691	+	0.860357i	$0.670240\pi$
$158$	10.5530	+	6.09277i	0.839550	+	0.484714i
$159$	14.6434	+	3.12812i	1.16130	+	0.248076i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	5.66149	+	1.21594i	0.446188	+	0.0958292i
$162$	−6.71275	+	5.99492i	−0.527403	+	0.471005i
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	−0.974975	−	0.222314i	$-0.928639\pi$
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	0.680017	+	0.733196i	$0.261972\pi$
$164$	2.73851			0.213842
$165$	−4.73171	+	5.24436i	−0.368363	+	0.408273i
$166$		−	13.7590i		−	1.06790i
$167$	−4.87241	−	8.43926i	−0.377039	−	0.653050i	0.613591	−	0.789624i	$-0.289724\pi$
$167$	−4.87241	−	8.43926i	−0.377039	−	0.653050i	−0.990630	+	0.136574i	$0.956391\pi$
$168$	−2.68193	−	3.71581i	−0.206915	−	0.286681i
$169$	11.5387	−	19.9855i	0.887589	−	1.53735i
$170$	1.11150	+	0.641724i	0.0852481	+	0.0492180i
$171$	−4.11461	+	9.19121i	−0.314652	+	0.702869i
$172$	2.43768	+	4.22219i	0.185872	+	0.321939i
$173$	7.13345	+	12.3555i	0.542346	+	0.939370i	0.998769	+	0.0496076i	$0.0157971\pi$
$173$	7.13345	+	12.3555i	0.542346	+	0.939370i	−0.456423	+	0.889763i	$0.650870\pi$
$174$	−9.23412	−	8.33146i	−0.700036	−	0.631606i
$175$	−0.555567	+	2.58676i	−0.0419969	+	0.195541i
$176$	3.53173	−	2.03904i	0.266214	−	0.153699i
$177$	2.07816	−	0.672901i	0.156204	−	0.0505783i
$178$			14.5899i			1.09356i
$179$	7.42444	−	4.28650i	0.554928	−	0.320388i	−0.196179	−	0.980568i	$-0.562853\pi$
$179$	7.42444	−	4.28650i	0.554928	−	0.320388i	0.751107	+	0.660180i	$0.229520\pi$
$180$	−2.73815	−	1.22578i	−0.204090	−	0.0913644i
$181$		−	1.70947i		−	0.127064i	−0.997980	−	0.0635319i	$-0.979764\pi$
$181$		−	1.70947i		−	0.127064i	0.997980	−	0.0635319i	$-0.0202365\pi$
$182$	−11.7872	−	10.6585i	−0.873722	−	0.790063i
$183$	5.02572	+	1.07359i	0.371512	+	0.0793623i
$184$	−2.18864			−0.161349
$185$	2.90160	−	5.02572i	0.213330	−	0.369498i
$186$	10.0867	+	9.10069i	0.739592	+	0.667295i
$187$	4.53279	−	2.61701i	0.331470	−	0.191375i
$188$	8.27225			0.603316
$189$	9.14607	+	10.2640i	0.665279	+	0.746595i
$190$	−3.35672			−0.243522
$191$	−8.02069	+	4.63075i	−0.580357	+	0.335069i	−0.761275	−	0.648429i	$-0.775426\pi$
$191$	−8.02069	+	4.63075i	−0.580357	+	0.335069i	0.180918	+	0.983498i	$0.442093\pi$
$192$	1.28599	+	1.16028i	0.0928080	+	0.0837358i
$193$	12.1247	−	21.0006i	0.872756	−	1.51166i	0.0136221	−	0.999907i	$-0.495664\pi$
$193$	12.1247	−	21.0006i	0.872756	−	1.51166i	0.859134	−	0.511751i	$-0.171003\pi$
$194$	−19.4824			−1.39875
$195$	−10.1739	−	2.17335i	−0.728569	−	0.155637i
$196$	−5.68051	+	4.09045i	−0.405751	+	0.292175i
$197$			18.8947i			1.34619i	0.739554	+	0.673097i	$0.235036\pi$
$197$			18.8947i			1.34619i	−0.739554	+	0.673097i	$0.764964\pi$
$198$	−9.91233	+	7.17097i	−0.704439	+	0.509619i
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	−0.417939	−	0.908475i	$-0.637247\pi$
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	0.577793	+	0.816183i	$0.303914\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−14.2075	+	4.60032i	−1.00212	+	0.324481i
$202$	7.39341	−	4.26859i	0.520198	−	0.300337i
$203$	−12.7421	+	14.0913i	−0.894317	+	0.989016i
$204$	1.65050	+	1.48916i	0.115558	+	0.104262i
$205$	−1.36925	−	2.37162i	−0.0956329	−	0.165641i
$206$	−1.80624	−	3.12850i	−0.125847	−	0.217973i
$207$	6.53133	−	0.673042i	0.453959	−	0.0467796i
$208$	5.20173	+	3.00322i	0.360675	+	0.208236i
$209$	−6.84450	+	11.8550i	−0.473444	+	0.820029i
$210$	−1.87702	+	4.18052i	−0.129527	+	0.288484i
$211$	−3.12513	−	5.41288i	−0.215143	−	0.372638i	0.738174	−	0.674610i	$-0.235688\pi$
$211$	−3.12513	−	5.41288i	−0.215143	−	0.372638i	−0.953317	+	0.301972i	$0.902355\pi$
$212$			8.64512i			0.593749i
$213$	−16.4034	+	18.1806i	−1.12394	+	1.24571i
$214$	13.3478			0.912440
$215$	2.43768	−	4.22219i	0.166249	−	0.287951i
$216$	−4.19444	−	3.06703i	−0.285395	−	0.208685i
$217$	13.9185	−	15.3923i	0.944850	−	1.04490i
$218$	9.32854	+	5.38583i	0.631808	+	0.364775i
$219$	11.7808	+	2.51662i	0.796076	+	0.170058i
$220$	−3.53173	−	2.03904i	−0.238109	−	0.137472i
$221$	6.67615	+	3.85448i	0.449087	+	0.259280i
$222$	6.73332	−	7.46283i	0.451911	−	0.500872i
$223$	4.24320	+	2.44981i	0.284145	+	0.164051i	0.635299	−	0.772267i	$-0.280877\pi$
$223$	4.24320	+	2.44981i	0.284145	+	0.164051i	−0.351153	+	0.936318i	$0.614210\pi$
$224$	1.77452	−	1.96242i	0.118565	−	0.131120i
$225$	0.307516	+	2.98420i	0.0205011	+	0.198946i
$226$	−1.41832	+	2.45659i	−0.0943449	+	0.163410i
$227$	17.4808			1.16024			0.580121	−	0.814531i	$-0.303005\pi$
$227$	17.4808			1.16024			0.580121	+	0.814531i	$0.303005\pi$
$228$	−5.68573	−	1.21458i	−0.376547	−	0.0804378i
$229$			14.5924i			0.964292i	0.876091	+	0.482146i	$0.160143\pi$
$229$			14.5924i			0.964292i	−0.876091	+	0.482146i	$0.839857\pi$
$230$	1.09432	+	1.89542i	0.0721573	+	0.124980i
$231$	10.9371	+	15.1534i	0.719611	+	0.997021i
$232$	3.59029	−	6.21856i	0.235714	−	0.408269i
$233$	3.42360	+	1.97662i	0.224288	+	0.129493i	0.607934	−	0.793988i	$-0.291998\pi$
$233$	3.42360	+	1.97662i	0.224288	+	0.129493i	−0.383646	+	0.923480i	$0.625332\pi$
$234$	−16.4465	−	7.36259i	−1.07514	−	0.481307i
$235$	−4.13613	−	7.16398i	−0.269811	−	0.467327i
$236$	0.630579	+	1.09220i	0.0410472	+	0.0710959i
$237$	4.40917	−	20.6403i	0.286406	−	1.34073i
$238$	2.27750	−	2.51866i	0.147628	−	0.163261i
$239$	16.0317	−	9.25590i	1.03700	−	0.598714i	0.118021	−	0.993011i	$-0.462345\pi$
$239$	16.0317	−	9.25590i	1.03700	−	0.598714i	0.918983	+	0.394297i	$0.129012\pi$
$240$	0.361836	−	1.69383i	0.0233564	−	0.109337i
$241$			21.9366i			1.41306i	0.707681	+	0.706532i	$0.249741\pi$
$241$			21.9366i			1.41306i	−0.707681	+	0.706532i	$0.750259\pi$
$242$	−4.87641	+	2.81540i	−0.313468	+	0.180981i
$243$	13.4602	+	7.86278i	0.863472	+	0.504397i
$244$			2.96707i			0.189947i
$245$	6.38269	+	2.87424i	0.407775	+	0.183628i
$246$	−1.46115	−	4.51257i	−0.0931596	−	0.287711i
$247$	−20.1620			−1.28287
$248$	−3.92178	+	6.79271i	−0.249033	+	0.431338i
$249$	−22.6723	+	7.34119i	−1.43680	+	0.465229i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	15.6773			0.989540			0.494770	−	0.869024i	$-0.335252\pi$
$251$	15.6773			0.989540			0.494770	+	0.869024i	$0.335252\pi$
$252$	−4.69203	+	6.40194i	−0.295570	+	0.403284i
$253$	8.92547			0.561139
$254$	−9.49383	+	5.48127i	−0.595696	+	0.343925i
$255$	0.464398	−	2.17395i	0.0290818	−	0.136138i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.5872			−0.660411			−0.330206	−	0.943909i	$-0.607118\pi$
$257$	−10.5872			−0.660411			−0.330206	+	0.943909i	$0.607118\pi$
$258$	5.65677	−	6.26965i	0.352175	−	0.390331i
$259$	−11.3883	−	10.2979i	−0.707635	−	0.639879i
$260$		−	6.00644i		−	0.372504i
$261$	−8.80182	+	19.6615i	−0.544819	+	1.21702i
$262$	17.9538	−	10.3656i	1.10919	−	0.640389i
$263$		−	24.2649i		−	1.49624i	−0.663564	−	0.748120i	$-0.730957\pi$
$263$		−	24.2649i		−	1.49624i	0.663564	−	0.748120i	$-0.269043\pi$
$264$	−5.24436	−	4.73171i	−0.322768	−	0.291217i
$265$	7.48689	−	4.32256i	0.459916	−	0.265533i
$266$	−1.86488	+	8.68305i	−0.114343	+	0.532392i
$267$	24.0416	−	7.78457i	1.47132	−	0.476408i
$268$	−4.31098	−	7.46684i	−0.263335	−	0.456110i
$269$	−9.04616	−	15.6684i	−0.551554	−	0.955320i	−0.998163	−	0.0605906i	$-0.980702\pi$
$269$	−9.04616	−	15.6684i	−0.551554	−	0.955320i	0.446608	−	0.894730i	$-0.352632\pi$
$270$	−0.558910	+	5.16601i	−0.0340142	+	0.314393i
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	0.403723	−	0.914881i	$-0.367716\pi$
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	−0.590449	+	0.807075i	$0.701049\pi$
$272$	−0.641724	+	1.11150i	−0.0389102	+	0.0673945i
$273$	−11.2742	+	25.1101i	−0.682347	+	1.51973i
$274$	−4.83716	−	8.37821i	−0.292224	−	0.506146i
$275$			4.07809i			0.245918i
$276$	1.16777	+	3.60649i	0.0702912	+	0.217085i
$277$	2.30895			0.138732			0.0693658	−	0.997591i	$-0.477902\pi$
$277$	2.30895			0.138732			0.0693658	+	0.997591i	$0.477902\pi$
$278$	−2.63928	+	4.57137i	−0.158294	+	0.274173i
$279$	9.61448	−	21.4768i	0.575604	−	1.28578i
$280$	−2.58676	−	0.555567i	−0.154589	−	0.0332015i
$281$	−0.186637	−	0.107755i	−0.0111338	−	0.00642812i	0.494423	−	0.869222i	$-0.335379\pi$
$281$	−0.186637	−	0.107755i	−0.0111338	−	0.00642812i	−0.505557	+	0.862793i	$0.668713\pi$
$282$	−4.41372	−	13.6312i	−0.262833	−	0.811726i
$283$	13.3787	+	7.72421i	0.795283	+	0.459157i	0.841819	−	0.539760i	$-0.181485\pi$
$283$	13.3787	+	7.72421i	0.795283	+	0.459157i	−0.0465363	+	0.998917i	$0.514818\pi$
$284$	−12.2434	−	7.06874i	−0.726514	−	0.419453i
$285$	1.79100	+	5.53128i	0.106090	+	0.327645i
$286$	−21.2131	−	12.2474i	−1.25436	−	0.724203i
$287$	−6.89553	+	2.22434i	−0.407030	+	0.131299i
$288$	1.22578	−	2.73815i	0.0722299	−	0.161347i
$289$	7.67638	−	13.2959i	0.451552	−	0.782111i
$290$	−7.18058			−0.421658
$291$	10.3950	+	32.1035i	0.609365	+	1.88194i
$292$			6.95513i			0.407018i
$293$	0.347292	+	0.601528i	0.0202890	+	0.0351417i	0.875992	−	0.482326i	$-0.160208\pi$
$293$	0.347292	+	0.601528i	0.0202890	+	0.0351417i	−0.855703	+	0.517468i	$0.826875\pi$
$294$	9.77122	+	7.17798i	0.569869	+	0.418628i
$295$	0.630579	−	1.09220i	0.0367137	−	0.0635901i
$296$	5.02572	+	2.90160i	0.292114	+	0.168652i
$297$	17.1053	+	12.5076i	0.992549	+	0.725766i
$298$	2.18889	+	3.79127i	0.126799	+	0.219623i
$299$	6.57297	+	11.3847i	0.380125	+	0.658395i
$300$	−1.64782	+	0.533558i	−0.0951370	+	0.0308050i
$301$	−9.56751	−	8.65142i	−0.551462	−	0.498659i
$302$	−4.82650	+	2.78658i	−0.277734	+	0.160350i
$303$	−10.9787	−	9.90548i	−0.630709	−	0.569055i
$304$		−	3.35672i		−	0.192521i
$305$	2.56956	−	1.48353i	0.147132	−	0.0849469i
$306$	1.57323	−	3.51427i	0.0899355	−	0.200898i
$307$			34.0796i			1.94502i	0.232853	+	0.972512i	$0.425194\pi$
$307$			34.0796i			1.94502i	−0.232853	+	0.972512i	$0.574806\pi$
$308$	−7.23663	+	8.00292i	−0.412345	+	0.456009i
$309$	−4.19147	+	4.64559i	−0.238444	+	0.264278i
$310$	7.84355			0.445484
$311$	−4.24381	+	7.35049i	−0.240644	+	0.416808i	−0.960898	−	0.276903i	$-0.910692\pi$
$311$	−4.24381	+	7.35049i	−0.240644	+	0.416808i	0.720254	+	0.693711i	$0.244025\pi$
$312$	2.17335	−	10.1739i	0.123042	−	0.575984i
$313$	23.6250	−	13.6399i	1.33536	−	0.770973i	0.349248	−	0.937030i	$-0.386437\pi$
$313$	23.6250	−	13.6399i	1.33536	−	0.770973i	0.986116	+	0.166057i	$0.0531037\pi$
$314$	−0.281341			−0.0158770
$315$	7.89026	+	0.862450i	0.444566	+	0.0485936i
$316$	12.1855			0.685490
$317$	0.0390775	−	0.0225614i	0.00219481	−	0.00126717i	−0.498902	−	0.866658i	$-0.666263\pi$
$317$	0.0390775	−	0.0225614i	0.00219481	−	0.00126717i	0.501097	+	0.865391i	$0.332930\pi$
$318$	14.2456	−	4.61267i	0.798854	−	0.258666i
$319$	−14.6415	+	25.3598i	−0.819767	+	1.41988i
$320$	1.00000			0.0559017
$321$	−7.12184	−	21.9949i	−0.397503	−	1.22763i
$322$	5.51097	−	1.77772i	0.307114	−	0.0990682i
$323$		−	4.30818i		−	0.239714i
$324$	−2.81595	+	8.54812i	−0.156442	+	0.474896i
$325$	−5.20173	+	3.00322i	−0.288540	+	0.166589i
$326$			7.53154i			0.417134i
$327$	3.89758	−	18.2454i	0.215537	−	1.00897i
$328$	2.37162	−	1.36925i	0.130951	−	0.0756044i
$329$	−20.8294	+	6.71911i	−1.14836	+	0.370437i
$330$	−1.47560	+	6.90760i	−0.0812291	+	0.380251i
$331$	−9.23258	−	15.9913i	−0.507468	−	0.878961i	−0.999963	−	0.00864533i	$-0.997248\pi$
$331$	−9.23258	−	15.9913i	−0.507468	−	0.878961i	0.492494	−	0.870316i	$-0.336085\pi$
$332$	−6.87948	−	11.9156i	−0.377560	−	0.653954i
$333$	−15.8900	−	7.11346i	−0.870768	−	0.389815i
$334$	−8.43926	−	4.87241i	−0.461776	−	0.266607i
$335$	−4.31098	+	7.46684i	−0.235534	+	0.407957i
$336$	−4.18052	−	1.87702i	−0.228066	−	0.102400i
$337$	11.5293	+	19.9693i	0.628041	+	1.08780i	0.987944	+	0.154810i	$0.0494764\pi$
$337$	11.5293	+	19.9693i	0.628041	+	1.08780i	−0.359903	+	0.932990i	$0.617190\pi$
$338$		−	23.0773i		−	1.25524i
$339$	4.80478	+	1.02640i	0.260960	+	0.0557462i
$340$	1.28345			0.0696048
$341$	15.9933	−	27.7013i	0.866088	−	1.50011i
$342$	1.03225	+	10.0171i	0.0558175	+	0.541664i
$343$	10.9810	−	14.9137i	0.592918	−	0.805263i
$344$	4.22219	+	2.43768i	0.227645	+	0.131431i
$345$	2.53943	−	2.81456i	0.136718	−	0.151531i
$346$	12.3555	+	7.13345i	0.664235	+	0.383496i
$347$	−19.3393	−	11.1655i	−1.03819	−	0.599398i	−0.118868	−	0.992910i	$-0.537927\pi$
$347$	−19.3393	−	11.1655i	−1.03819	−	0.599398i	−0.919319	+	0.393512i	$0.871260\pi$
$348$	−12.1627	−	2.59819i	−0.651989	−	0.139278i
$349$	−8.01876	−	4.62963i	−0.429235	−	0.247819i	0.269786	−	0.962920i	$-0.413047\pi$
$349$	−8.01876	−	4.62963i	−0.429235	−	0.247819i	−0.699020	+	0.715102i	$0.746380\pi$
$350$	0.812247	+	2.51799i	0.0434164	+	0.134592i
$351$	−3.35706	+	31.0293i	−0.179187	+	1.65622i
$352$	2.03904	−	3.53173i	0.108681	−	0.188242i
$353$	13.1868			0.701860			0.350930	−	0.936402i	$-0.385865\pi$
$353$	13.1868			0.701860			0.350930	+	0.936402i	$0.385865\pi$
$354$	1.46329	−	1.62183i	0.0777731	−	0.0861993i
$355$			14.1375i			0.750340i
$356$	7.29497	+	12.6353i	0.386633	+	0.669667i
$357$	−5.36549	−	2.40906i	−0.283972	−	0.127501i
$358$	4.28650	−	7.42444i	0.226549	−	0.392394i
$359$	9.81294	+	5.66550i	0.517907	+	0.299014i	0.736078	−	0.676897i	$-0.236676\pi$
$359$	9.81294	+	5.66550i	0.517907	+	0.299014i	−0.218171	+	0.975911i	$0.570009\pi$
$360$	−2.98420	+	0.307516i	−0.157281	+	0.0162075i
$361$	−3.86621	−	6.69647i	−0.203485	−	0.352446i
$362$	−0.854734	−	1.48044i	−0.0449238	−	0.0778104i
$363$	7.24112	+	6.53328i	0.380060	+	0.342908i
$364$	−15.5372	−	3.33698i	−0.814373	−	0.174905i
$365$	6.02332	−	3.47757i	0.315275	−	0.182024i
$366$	4.88920	−	1.58310i	0.255563	−	0.0827500i
$367$			24.3474i			1.27092i	0.772133	+	0.635461i	$0.219190\pi$
$367$			24.3474i			1.27092i	−0.772133	+	0.635461i	$0.780810\pi$
$368$	−1.89542	+	1.09432i	−0.0988055	+	0.0570454i
$369$	−6.65631	+	4.81543i	−0.346514	+	0.250682i
$370$		−	5.80320i		−	0.301694i
$371$	−7.02197	−	21.7683i	−0.364563	−	1.13015i
$372$	13.2857	+	2.83808i	0.688830	+	0.147148i
$373$	−27.4626			−1.42196			−0.710979	−	0.703214i	$-0.751748\pi$
$373$	−27.4626			−1.42196			−0.710979	+	0.703214i	$0.751748\pi$
$374$	2.61701	−	4.53279i	0.135322	−	0.234385i
$375$	1.28599	+	1.16028i	0.0664080	+	0.0599164i
$376$	7.16398	−	4.13613i	0.369454	−	0.213304i
$377$	−43.1297			−2.22129
$378$	13.0527	+	4.31583i	0.671360	+	0.221982i
$379$	32.0033			1.64390			0.821948	−	0.569562i	$-0.192887\pi$
$379$	32.0033			1.64390			0.821948	+	0.569562i	$0.192887\pi$
$380$	−2.90701	+	1.67836i	−0.149126	+	0.0860981i
$381$	14.0977	+	12.7196i	0.722245	+	0.651643i
$382$	−4.63075	+	8.02069i	−0.236930	+	0.410374i
$383$	14.2705			0.729191			0.364595	−	0.931166i	$-0.381207\pi$
$383$	14.2705			0.729191			0.364595	+	0.931166i	$0.381207\pi$
$384$	1.69383	+	0.361836i	0.0864381	+	0.0184649i
$385$	10.5490	+	2.26565i	0.537629	+	0.115468i
$386$		−	24.2494i		−	1.23426i
$387$	−13.3495	−	5.97614i	−0.678592	−	0.303784i
$388$	−16.8723	+	9.74120i	−0.856559	+	0.494535i
$389$		−	10.7610i		−	0.545604i	−0.962070	−	0.272802i	$-0.912050\pi$
$389$		−	10.7610i		−	0.545604i	0.962070	−	0.272802i	$-0.0879504\pi$
$390$	−9.89754	+	3.20478i	−0.501182	+	0.162280i
$391$	−2.43267	+	1.40450i	−0.123025	+	0.0710288i
$392$	−2.87424	+	6.38269i	−0.145171	+	0.322375i
$393$	−26.6600	−	24.0539i	−1.34482	−	1.21336i
$394$	9.44736	+	16.3633i	0.475951	+	0.824372i
$395$	−6.09277	−	10.5530i	−0.306560	−	0.530978i
$396$	−4.99885	+	11.1664i	−0.251201	+	0.561133i
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.899587	−	0.436742i	$-0.143868\pi$
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.0715634	+	0.997436i	$0.477201\pi$
$398$	1.30194	−	2.25502i	0.0652602	−	0.113034i
$399$	15.3031	−	1.55991i	0.766115	−	0.0780931i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$			18.9839i			0.948009i	0.880522	+	0.474005i	$0.157192\pi$
$401$			18.9839i			0.948009i	−0.880522	+	0.474005i	$0.842808\pi$
$402$	−10.0039	+	11.0877i	−0.498948	+	0.553005i
$403$	47.1118			2.34681
$404$	4.26859	−	7.39341i	0.212370	−	0.367836i
$405$	8.81087	−	1.83538i	0.437816	−	0.0912006i
$406$	−3.98929	+	18.5745i	−0.197985	+	0.921835i
$407$	−20.4953	−	11.8330i	−1.01592	−	0.586539i
$408$	2.17395	+	0.464398i	0.107627	+	0.0229912i
$409$	22.5328	+	13.0093i	1.11418	+	0.643270i	0.939908	−	0.341428i	$-0.110910\pi$
$409$	22.5328	+	13.0093i	1.11418	+	0.643270i	0.174269	+	0.984698i	$0.444244\pi$
$410$	−2.37162	−	1.36925i	−0.117126	−	0.0676226i
$411$	−11.2249	+	12.4410i	−0.553683	+	0.613671i
$412$	−3.12850	−	1.80624i	−0.154130	−	0.0889869i
$413$	−2.47492	−	2.23795i	−0.121783	−	0.110122i
$414$	5.31978	−	3.84854i	0.261453	−	0.189145i
$415$	−6.87948	+	11.9156i	−0.337700	+	0.584914i
$416$	6.00644			0.294490
$417$	8.94101	+	1.90998i	0.437843	+	0.0935320i
$418$			13.6890i			0.669551i
$419$	3.75114	+	6.49717i	0.183255	+	0.317407i	0.942987	−	0.332829i	$-0.108003\pi$
$419$	3.75114	+	6.49717i	0.183255	+	0.317407i	−0.759732	+	0.650236i	$0.774670\pi$
$420$	0.464712	+	4.55895i	0.0226756	+	0.222454i
$421$	−7.94926	+	13.7685i	−0.387423	+	0.671037i	−0.992102	−	0.125433i	$-0.959968\pi$
$421$	−7.94926	+	13.7685i	−0.387423	+	0.671037i	0.604679	+	0.796469i	$0.293301\pi$
$422$	−5.41288	−	3.12513i	−0.263495	−	0.152129i
$423$	−20.1068	+	14.5461i	−0.977626	+	0.707253i
$424$	4.32256	+	7.48689i	0.209922	+	0.363596i
$425$	−0.641724	−	1.11150i	−0.0311282	−	0.0539156i
$426$	−5.11546	+	23.9466i	−0.247845	+	1.16021i
$427$	−2.40999	−	7.47104i	−0.116628	−	0.361549i
$428$	11.5596	−	6.67392i	0.558753	−	0.322596i
$429$	−8.86311	+	41.4901i	−0.427915	+	2.00316i
$430$		−	4.87537i		−	0.235111i
$431$	−19.4232	+	11.2140i	−0.935581	+	0.540158i	−0.888572	−	0.458737i	$-0.848302\pi$
$431$	−19.4232	+	11.2140i	−0.935581	+	0.540158i	−0.0470087	+	0.998894i	$0.514969\pi$
$432$	−5.16601	−	0.558910i	−0.248550	−	0.0268906i
$433$		−	1.97195i		−	0.0947659i	−0.998877	−	0.0473830i	$-0.984912\pi$
$433$		−	1.97195i		−	0.0947659i	0.998877	−	0.0473830i	$-0.0150881\pi$
$434$	4.35762	−	20.2894i	0.209172	−	0.973923i
$435$	3.83125	+	11.8323i	0.183694	+	0.567316i
$436$	10.7717			0.515869
$437$	3.67333	−	6.36239i	0.175719	−	0.304355i
$438$	11.4608	−	3.71096i	0.547619	−	0.177317i
$439$	9.15130	−	5.28351i	0.436768	−	0.252168i	−0.265458	−	0.964122i	$-0.585523\pi$
$439$	9.15130	−	5.28351i	0.436768	−	0.252168i	0.702226	+	0.711954i	$0.252190\pi$
$440$	−4.07809			−0.194415
$441$	6.61452	−	19.9311i	0.314977	−	0.949099i
$442$	7.70896			0.366678
$443$	−5.85561	+	3.38074i	−0.278208	+	0.160624i	−0.632612	−	0.774469i	$-0.718017\pi$
$443$	−5.85561	+	3.38074i	−0.278208	+	0.160624i	0.354404	+	0.935093i	$0.384684\pi$
$444$	2.09981	−	9.82966i	0.0996525	−	0.466495i
$445$	7.29497	−	12.6353i	0.345815	−	0.598969i
$446$	4.89962			0.232004
$447$	5.07944	−	5.62977i	0.240249	−	0.266279i
$448$	0.555567	−	2.58676i	0.0262481	−	0.122213i
$449$			3.97534i			0.187608i	0.995591	+	0.0938039i	$0.0299027\pi$
$449$			3.97534i			0.187608i	−0.995591	+	0.0938039i	$0.970097\pi$
$450$	1.75842	+	2.43063i	0.0828925	+	0.114581i
$451$	−9.67166	+	5.58394i	−0.455421	+	0.262937i
$452$			2.83663i			0.133424i
$453$	7.16700	+	6.46641i	0.336735	+	0.303818i
$454$	15.1388	−	8.74040i	0.710500	−	0.410207i
$455$	4.87871	+	15.1241i	0.228717	+	0.709030i
$456$	−5.53128	+	1.79100i	−0.259026	+	0.0838715i
$457$	3.26014	+	5.64673i	0.152503	+	0.264143i	0.932147	−	0.362080i	$-0.117933\pi$
$457$	3.26014	+	5.64673i	0.152503	+	0.264143i	−0.779644	+	0.626223i	$0.784600\pi$
$458$	7.29619	+	12.6374i	0.340929	+	0.590506i
$459$	−6.63030	−	0.717333i	−0.309476	−	0.0334822i
$460$	1.89542	+	1.09432i	0.0883743	+	0.0510229i
$461$	4.69303	−	8.12857i	0.218576	−	0.378585i	−0.735797	−	0.677203i	$-0.763192\pi$
$461$	4.69303	−	8.12857i	0.218576	−	0.378585i	0.954373	+	0.298617i	$0.0965254\pi$
$462$	17.0485	+	7.65467i	0.793170	+	0.356127i
$463$	16.8709	+	29.2212i	0.784056	+	1.35803i	0.929561	+	0.368668i	$0.120186\pi$
$463$	16.8709	+	29.2212i	0.784056	+	1.35803i	−0.145505	+	0.989357i	$0.546481\pi$
$464$		−	7.18058i		−	0.333350i
$465$	−4.18499	−	12.9248i	−0.194074	−	0.599372i
$466$	3.95324			0.183130
$467$	17.9147	−	31.0293i	0.828996	−	1.43586i	−0.0698312	−	0.997559i	$-0.522246\pi$
$467$	17.9147	−	31.0293i	0.828996	−	1.43586i	0.898827	−	0.438304i	$-0.144421\pi$
$468$	−17.9244	+	1.84708i	−0.828556	+	0.0853811i
$469$	16.9199	+	15.2998i	0.781289	+	0.706480i
$470$	−7.16398	−	4.13613i	−0.330450	−	0.190785i
$471$	0.150112	+	0.463600i	0.00691678	+	0.0213616i
$472$	1.09220	+	0.630579i	0.0502724	+	0.0290248i
$473$	−17.2185	−	9.94108i	−0.791706	−	0.457092i
$474$	−6.50168	−	20.0796i	−0.298632	−	0.922286i
$475$	2.90701	+	1.67836i	0.133383	+	0.0770085i
$476$	0.713041	−	3.31998i	0.0326822	−	0.152171i
$477$	−15.2017	−	21.0131i	−0.696039	−	0.962124i
$478$	9.25590	−	16.0317i	0.423355	−	0.733272i
$479$	−13.8779			−0.634096			−0.317048	−	0.948409i	$-0.602692\pi$
$479$	−13.8779			−0.634096			−0.317048	+	0.948409i	$0.602692\pi$
$480$	−0.533558	−	1.64782i	−0.0243535	−	0.0752124i
$481$		−	34.8566i		−	1.58932i
$482$	10.9683	+	18.9977i	0.499593	+	0.865321i
$483$	−5.86978	−	8.13258i	−0.267084	−	0.370045i
$484$	−2.81540	+	4.87641i	−0.127973	+	0.221655i
$485$	16.8723	+	9.74120i	0.766130	+	0.442325i
$486$	15.5883	+	0.0792697i	0.707098	+	0.00359575i
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	0.988474	+	0.151390i	$0.0483750\pi$
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	−0.363129	+	0.931739i	$0.618292\pi$
$488$	1.48353	+	2.56956i	0.0671564	+	0.116318i
$489$	12.4106	−	4.01851i	0.561229	−	0.181723i
$490$	6.96469	−	0.702180i	0.314633	−	0.0317213i
$491$	−18.1949	+	10.5048i	−0.821122	+	0.474075i	−0.850803	−	0.525484i	$-0.823884\pi$
$491$	−18.1949	+	10.5048i	−0.821122	+	0.474075i	0.0296811	+	0.999559i	$0.490551\pi$
$492$	−3.52168	−	3.17743i	−0.158770	−	0.143249i
$493$		−	9.21590i		−	0.415063i
$494$	−17.4608	+	10.0810i	−0.785597	+	0.453565i
$495$	12.1698	−	1.25408i	0.546993	−	0.0563666i
$496$			7.84355i			0.352186i
$497$	36.5703	+	7.85432i	1.64040	+	0.352314i
$498$	−15.9642	+	17.6938i	−0.715372	+	0.792878i
$499$	0.395326			0.0176972			0.00884862	−	0.999961i	$-0.497183\pi$
$499$	0.395326			0.0176972			0.00884862	+	0.999961i	$0.497183\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−3.52603	+	16.5061i	−0.157532	+	0.737439i
$502$	13.5769	−	7.83863i	0.605967	−	0.349855i
$503$	−10.3934			−0.463418			−0.231709	−	0.972785i	$-0.574432\pi$
$503$	−10.3934			−0.463418			−0.231709	+	0.972785i	$0.574432\pi$
$504$	−0.862450	+	7.89026i	−0.0384166	+	0.351460i
$505$	−8.53717			−0.379899
$506$	7.72968	−	4.46273i	0.343626	−	0.198393i
$507$	−38.0273	+	12.3131i	−1.68885	+	0.546843i
$508$	−5.48127	+	9.49383i	−0.243192	+	0.421221i
$509$	−40.5347			−1.79667			−0.898334	−	0.439313i	$-0.855222\pi$
$509$	−40.5347			−1.79667			−0.898334	+	0.439313i	$0.855222\pi$
$510$	−0.684794	−	2.11489i	−0.0303232	−	0.0936491i
$511$	−5.64928	−	17.5129i	−0.249910	−	0.774727i
$512$			1.00000i			0.0441942i
$513$	15.9557	−	7.04567i	0.704460	−	0.311074i
$514$	−9.16878	+	5.29360i	−0.404417	+	0.233491i
$515$			3.61248i			0.159185i
$516$	1.76409	−	8.25806i	0.0776595	−	0.363541i
$517$	−29.2153	+	16.8675i	−1.28489	+	0.741831i
$518$	−15.0115	−	3.22407i	−0.659568	−	0.141657i
$519$	5.16228	−	24.1657i	0.226599	−	1.06076i
$520$	−3.00322	−	5.20173i	−0.131700	−	0.228111i
$521$	4.80694	+	8.32586i	0.210596	+	0.364763i	0.951901	−	0.306405i	$-0.0991263\pi$
$521$	4.80694	+	8.32586i	0.210596	+	0.364763i	−0.741305	+	0.671168i	$0.765793\pi$
$522$	2.20814	+	21.4283i	0.0966477	+	0.937889i
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	0.155393	−	0.987853i	$-0.450336\pi$
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	−0.777809	+	0.628501i	$0.783669\pi$
$524$	10.3656	−	17.9538i	0.452824	−	0.784313i
$525$	3.71581	−	2.68193i	0.162171	−	0.117049i
$526$	−12.1325	−	21.0140i	−0.529001	−	0.916256i
$527$			10.0668i			0.438516i
$528$	−6.90760	−	1.47560i	−0.300615	−	0.0642173i
$529$	18.2099			0.791733
$530$	4.32256	−	7.48689i	0.187760	−	0.325210i
$531$	−3.45324	−	1.54591i	−0.149858	−	0.0670866i
$532$	2.72649	+	8.45218i	0.118208	+	0.366449i
$533$	−14.2450	−	8.22434i	−0.617019	−	0.356236i
$534$	16.9284	−	18.7624i	0.732562	−	0.811930i
$535$	−11.5596	−	6.67392i	−0.499764	−	0.288539i
$536$	−7.46684	−	4.31098i	−0.322518	−	0.186206i
$537$	−14.5212	−	3.10202i	−0.626638	−	0.133862i
$538$	−15.6684	−	9.04616i	−0.675513	−	0.390008i
$539$	11.7214	−	26.0292i	0.504877	−	1.12116i
$540$	2.09897	+	4.75335i	0.0903254	+	0.204552i
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	−0.275612	−	0.961269i	$-0.588880\pi$
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	0.970289	−	0.241948i	$-0.0777863\pi$
$542$	−3.54942			−0.152461
$543$	−1.98346	+	2.19835i	−0.0851183	+	0.0943403i
$544$			1.28345i			0.0550274i
$545$	−5.38583	−	9.32854i	−0.230704	−	0.399591i
$546$	2.79126	+	27.3831i	0.119455	+	1.17189i
$547$	−3.41985	+	5.92335i	−0.146222	+	0.253264i	−0.929828	−	0.367994i	$-0.880045\pi$
$547$	−3.41985	+	5.92335i	−0.146222	+	0.253264i	0.783606	+	0.621258i	$0.213378\pi$
$548$	−8.37821	−	4.83716i	−0.357899	−	0.206633i
$549$	−5.21734	−	7.21185i	−0.222671	−	0.307794i
$550$	2.03904	+	3.53173i	0.0869451	+	0.150593i
$551$	12.0516	+	20.8740i	0.513416	+	0.889262i
$552$	2.81456	+	2.53943i	0.119796	+	0.108085i
$553$	−30.6830	+	9.89766i	−1.30477	+	0.420891i
$554$	1.99961	−	1.15448i	0.0849554	−	0.0490490i
$555$	−9.56264	+	3.09634i	−0.405911	+	0.131432i
$556$			5.27856i			0.223861i
$557$	−5.91206	+	3.41333i	−0.250502	+	0.144627i	−0.619994	−	0.784607i	$-0.712865\pi$
$557$	−5.91206	+	3.41333i	−0.250502	+	0.144627i	0.369492	+	0.929234i	$0.379532\pi$
$558$	−2.41202	−	23.4067i	−0.102109	−	0.990885i
$559$		−	29.2836i		−	1.23856i
$560$	−2.51799	+	0.812247i	−0.106404	+	0.0343237i
$561$	−8.86555	−	1.89386i	−0.374304	−	0.0799587i
$562$	−0.215510			−0.00909074
$563$	−5.41857	+	9.38524i	−0.228366	+	0.395541i	−0.957324	−	0.289017i	$-0.906671\pi$
$563$	−5.41857	+	9.38524i	−0.228366	+	0.395541i	0.728958	+	0.684558i	$0.240005\pi$
$564$	−10.6380	−	9.59810i	−0.447940	−	0.404153i
$565$	2.45659	−	1.41832i	0.103350	−	0.0596690i
$566$	15.4484			0.649346
$567$	0.147341	−	23.8113i	0.00618775	−	0.999981i
$568$	−14.1375			−0.593196
$569$	−12.0811	+	6.97501i	−0.506465	+	0.292408i	−0.731379	−	0.681971i	$-0.761123\pi$
$569$	−12.0811	+	6.97501i	−0.506465	+	0.292408i	0.224914	+	0.974379i	$0.427790\pi$
$570$	4.31670	+	3.89473i	0.180806	+	0.163132i
$571$	13.6060	−	23.5662i	0.569393	−	0.986217i	−0.427234	−	0.904141i	$-0.640512\pi$
$571$	13.6060	−	23.5662i	0.569393	−	0.986217i	0.996626	−	0.0820756i	$-0.0261549\pi$
$572$	−24.4948			−1.02418
$573$	15.6874	+	3.35115i	0.655352	+	0.139996i
$574$	−4.85953	+	5.37410i	−0.202833	+	0.224311i
$575$		−	2.18864i		−	0.0912726i
$576$	−0.307516	−	2.98420i	−0.0128132	−	0.124342i
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	−0.198318	−	0.980138i	$-0.563548\pi$
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	0.749665	+	0.661818i	$0.230215\pi$
$578$		−	15.3528i		−	0.638591i
$579$	−39.9587	+	12.9385i	−1.66063	+	0.537704i
$580$	−6.21856	+	3.59029i	−0.258212	+	0.149079i
$581$	27.0008	+	24.4155i	1.12018	+	1.01293i
$582$	25.0541	+	22.6050i	1.03853	+	0.937006i
$583$	−17.6278	−	30.5322i	−0.730068	−	1.26451i
$584$	3.47757	+	6.02332i	0.143903	+	0.249247i
$585$	10.5618	+	14.5994i	0.436677	+	0.603613i
$586$	0.601528	+	0.347292i	0.0248489	+	0.0143465i
$587$	−7.16231	+	12.4055i	−0.295620	+	0.512029i	−0.975129	−	0.221638i	$-0.928860\pi$
$587$	−7.16231	+	12.4055i	−0.295620	+	0.512029i	0.679509	+	0.733667i	$0.262193\pi$
$588$	12.0511	+	1.33070i	0.496979	+	0.0548773i
$589$	−13.1643	−	22.8013i	−0.542426	−	0.939509i
$590$		−	1.26116i		−	0.0519211i
$591$	21.9231	−	24.2983i	0.901796	−	0.999500i
$592$	5.80320			0.238510
$593$	0.594674	−	1.03001i	0.0244203	−	0.0422973i	−0.853557	−	0.521000i	$-0.825559\pi$
$593$	0.594674	−	1.03001i	0.0244203	−	0.0422973i	0.877977	+	0.478702i	$0.158893\pi$
$594$	21.0674	+	2.27929i	0.864407	+	0.0935202i
$595$	−3.23171	+	1.04248i	−0.132487	+	0.0427374i
$596$	3.79127	+	2.18889i	0.155297	+	0.0896606i
$597$	−4.41053	−	0.942177i	−0.180511	−	0.0385607i
$598$	11.3847	+	6.57297i	0.465556	+	0.268789i
$599$	−39.8059	−	22.9819i	−1.62642	−	0.939016i	−0.985148	−	0.171706i	$-0.945072\pi$
$599$	−39.8059	−	22.9819i	−1.62642	−	0.939016i	−0.641276	−	0.767310i	$-0.721595\pi$
$600$	−1.16028	+	1.28599i	−0.0473681	+	0.0525001i
$601$	−14.0543	−	8.11427i	−0.573288	−	0.330988i	0.185173	−	0.982706i	$-0.440715\pi$
$601$	−14.0543	−	8.11427i	−0.573288	−	0.330988i	−0.758462	+	0.651718i	$0.774049\pi$
$602$	−12.6114	−	2.70859i	−0.514003	−	0.110394i
$603$	23.6082	+	10.5687i	0.961401	+	0.430389i
$604$	−2.78658	+	4.82650i	−0.113384	+	0.196387i
$605$	5.63079			0.228924
$606$	−14.4606	−	3.08906i	−0.587420	−	0.125485i
$607$			6.95304i			0.282215i	0.989994	+	0.141108i	$0.0450664\pi$
$607$			6.95304i			0.282215i	−0.989994	+	0.141108i	$0.954934\pi$
$608$	−1.67836	−	2.90701i	−0.0680665	−	0.117895i
$609$	32.7359	−	3.33690i	1.32653	−	0.135218i
$610$	1.48353	−	2.56956i	0.0600665	−	0.104038i
$611$	−43.0300	−	24.8434i	−1.74081	−	1.00506i
$612$	−0.394681	−	3.83006i	−0.0159540	−	0.154821i
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	−0.914073	−	0.405549i	$-0.867080\pi$
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	0.105821	−	0.994385i	$-0.466253\pi$
$614$	17.0398	+	29.5138i	0.687670	+	1.19108i
$615$	−0.990892	+	4.63858i	−0.0399566	+	0.187046i
$616$	−2.26565	+	10.5490i	−0.0912856	+	0.425033i
$617$	7.94775	−	4.58864i	0.319964	−	0.184732i	−0.331412	−	0.943486i	$-0.607525\pi$
$617$	7.94775	−	4.58864i	0.319964	−	0.184732i	0.651377	+	0.758754i	$0.274192\pi$
$618$	−1.30713	+	6.11893i	−0.0525803	+	0.246140i
$619$			38.3260i			1.54045i	0.637770	+	0.770227i	$0.279857\pi$
$619$			38.3260i			1.54045i	−0.637770	+	0.770227i	$0.720143\pi$
$620$	6.79271	−	3.92178i	0.272802	−	0.157502i
$621$	−9.18011	−	6.71263i	−0.368385	−	0.269369i
$622$			8.48761i			0.340322i
$623$	−28.6316	−	25.8901i	−1.14710	−	1.03726i
$624$	−3.20478	−	9.89754i	−0.128294	−	0.396219i
$625$	1.00000			0.0400000
$626$	13.6399	−	23.6250i	0.545160	−	0.944245i
$627$	22.5570	−	7.30387i	0.900842	−	0.291689i
$628$	−0.243649	+	0.140671i	−0.00972264	+	0.00561337i
$629$	7.44811			0.296976
$630$	7.26439	−	3.19823i	0.289420	−	0.127420i
$631$	−21.4220			−0.852797			−0.426399	−	0.904535i	$-0.640218\pi$
$631$	−21.4220			−0.852797			−0.426399	+	0.904535i	$0.640218\pi$
$632$	10.5530	−	6.09277i	0.419775	−	0.242357i
$633$	−2.26157	+	10.5869i	−0.0898893	+	0.420791i
$634$	0.0225614	−	0.0390775i	0.000896027	−	0.00155196i
$635$	10.9625			0.435035
$636$	10.0307	−	11.1175i	0.397744	−	0.440837i
$637$	41.8330	−	4.21760i	1.65748	−	0.167108i
$638$			29.2830i			1.15933i
$639$	42.1891	−	4.34750i	1.66897	−	0.171985i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$		−	23.8349i		−	0.941421i	−0.882288	−	0.470710i	$-0.843998\pi$
$641$		−	23.8349i		−	0.941421i	0.882288	−	0.470710i	$-0.156002\pi$
$642$	−17.1651	−	15.4872i	−0.677454	−	0.611231i
$643$	10.6419	−	6.14411i	0.419676	−	0.242300i	−0.275263	−	0.961369i	$-0.588765\pi$
$643$	10.6419	−	6.14411i	0.419676	−	0.242300i	0.694939	+	0.719069i	$0.255432\pi$
$644$	3.88378	−	4.29503i	0.153042	−	0.169248i
$645$	−8.03373	+	2.60129i	−0.316328	+	0.102426i
$646$	−2.15409	−	3.73099i	−0.0847516	−	0.146794i
$647$	8.50175	+	14.7255i	0.334238	+	0.578917i	0.983338	−	0.181786i	$-0.0581877\pi$
$647$	8.50175	+	14.7255i	0.334238	+	0.578917i	−0.649100	+	0.760703i	$0.724854\pi$
$648$	1.83538	+	8.81087i	0.0721004	+	0.346124i
$649$	−4.45407	−	2.57156i	−0.174837	−	0.100942i
$650$	−3.00322	+	5.20173i	−0.117796	+	0.204029i
$651$	−35.7584	+	3.64499i	−1.40148	+	0.142858i
$652$	3.76577	+	6.52251i	0.147479	+	0.255441i
$653$		−	11.0926i		−	0.434087i	−0.976162	−	0.217044i	$-0.930359\pi$
$653$		−	11.0926i		−	0.434087i	0.976162	−	0.217044i	$-0.0696414\pi$
$654$	−5.74730	−	17.7498i	−0.224737	−	0.694071i
$655$	−20.7312			−0.810035
$656$	1.36925	−	2.37162i	0.0534604	−	0.0925961i
$657$	−12.2300	−	16.9054i	−0.477138	−	0.659542i
$658$	−14.6793	+	16.2336i	−0.572257	+	0.632853i
$659$	−39.7712	−	22.9619i	−1.54927	−	0.894470i	−0.998198	−	0.0600103i	$-0.980887\pi$
$659$	−39.7712	−	22.9619i	−1.54927	−	0.894470i	−0.551069	−	0.834459i	$-0.685780\pi$
$660$	2.17589	+	6.71996i	0.0846966	+	0.261574i
$661$	−18.0299	−	10.4096i	−0.701281	−	0.404885i	0.106543	−	0.994308i	$-0.466022\pi$
$661$	−18.0299	−	10.4096i	−0.701281	−	0.404885i	−0.807824	+	0.589423i	$0.799355\pi$
$662$	−15.9913	−	9.23258i	−0.621519	−	0.358834i
$663$	−4.11317	−	12.7030i	−0.159742	−	0.493343i
$664$	−11.9156	−	6.87948i	−0.462415	−	0.266975i
$665$	5.95656	−	6.58730i	0.230986	−	0.255444i
$666$	−17.3179	+	1.78458i	−0.671055	+	0.0691509i
$667$	7.85785	−	13.6102i	0.304257	−	0.526989i
$668$	−9.74482			−0.377039
$669$	−2.61423	−	8.07370i	−0.101072	−	0.312147i
$670$			8.62197i			0.333096i
$671$	−6.04998	−	10.4789i	−0.233557	−	0.404532i
$672$	−4.55895	+	0.464712i	−0.175865	+	0.0179267i
$673$	14.6307	−	25.3410i	0.563970	−	0.976825i	−0.433175	−	0.901310i	$-0.642607\pi$
$673$	14.6307	−	25.3410i	0.563970	−	0.976825i	0.997145	−	0.0755149i	$-0.0240600\pi$
$674$	19.9693	+	11.5293i	0.769190	+	0.444092i
$675$	3.06703	−	4.19444i	0.118050	−	0.161444i
$676$	−11.5387	−	19.9855i	−0.443795	−	0.768675i
$677$	12.3058	+	21.3142i	0.472949	+	0.819172i	0.999521	−	0.0309588i	$-0.00985606\pi$
$677$	12.3058	+	21.3142i	0.472949	+	0.819172i	−0.526571	+	0.850131i	$0.676523\pi$
$678$	4.67426	−	1.51351i	0.179514	−	0.0581258i
$679$	34.5718	−	38.2326i	1.32675	−	1.46723i
$680$	1.11150	−	0.641724i	0.0426240	−	0.0246090i
$681$	−22.4801	−	20.2826i	−0.861437	−	0.777230i
$682$		−	31.9867i		−	1.22483i
$683$	−4.84830	+	2.79917i	−0.185515	+	0.107107i	−0.589881	−	0.807490i	$-0.700825\pi$
$683$	−4.84830	+	2.79917i	−0.185515	+	0.107107i	0.404366	+	0.914597i	$0.367492\pi$
$684$	5.90251	+	8.15896i	0.225688	+	0.311966i
$685$			9.67432i			0.369637i
$686$	2.05298	−	18.4061i	0.0783831	−	0.702749i
$687$	16.9312	−	18.7656i	0.645966	−	0.715952i
$688$	4.87537			0.185872
$689$	25.9632	−	44.9696i	0.989119	−	1.71320i
$690$	0.791930	−	3.70719i	0.0301483	−	0.141130i
$691$	−28.6519	+	16.5422i	−1.08997	+	0.629294i	−0.933568	−	0.358399i	$-0.883323\pi$
$691$	−28.6519	+	16.5422i	−1.08997	+	0.629294i	−0.156401	+	0.987694i	$0.549989\pi$
$692$	14.2669			0.542346
$693$	3.51715	−	32.1772i	0.133605	−	1.22231i
$694$	−22.3311			−0.847677
$695$	4.57137	−	2.63928i	0.173402	−	0.100114i
$696$	−11.8323	+	3.83125i	−0.448503	+	0.145223i
$697$	1.75737	−	3.04385i	0.0665650	−	0.115294i
$698$	−9.25927			−0.350469
$699$	−2.10928	−	6.51423i	−0.0797803	−	0.246391i
$700$	1.96242	+	1.77452i	0.0741725	+	0.0670704i
$701$		−	3.12417i		−	0.117998i	−0.998258	−	0.0589992i	$-0.981209\pi$
$701$		−	3.12417i		−	0.117998i	0.998258	−	0.0589992i	$-0.0187909\pi$
$702$	12.6074	+	28.5507i	0.475834	+	1.07758i
$703$	−16.8699	+	9.73987i	−0.636262	+	0.367346i
$704$		−	4.07809i		−	0.153699i
$705$	−2.99320	+	14.0118i	−0.112731	+	0.527716i
$706$	11.4201	−	6.59338i	0.429800	−	0.248145i
$707$	−4.74297	+	22.0836i	−0.178378	+	0.830541i
$708$	0.456333	−	2.13619i	0.0171500	−	0.0802831i
$709$	21.7411	+	37.6567i	0.816504	+	1.41423i	0.908243	+	0.418443i	$0.137424\pi$
$709$	21.7411	+	37.6567i	0.816504	+	1.41423i	−0.0917396	+	0.995783i	$0.529243\pi$
$710$	7.06874	+	12.2434i	0.265285	+	0.459487i
$711$	−29.6186	+	21.4272i	−1.11078	+	0.803584i
$712$	12.6353	+	7.29497i	0.473526	+	0.273391i
$713$	−8.58336	+	14.8668i	−0.321449	+	0.556766i
$714$	−5.85118	+	0.596434i	−0.218975	+	0.0223210i
$715$	12.2474	+	21.2131i	0.458026	+	0.793325i
$716$		−	8.57300i		−	0.320388i
$717$	−31.3559	−	6.69824i	−1.17101	−	0.250151i
$718$	11.3310			0.422869
$719$	−2.21764	+	3.84106i	−0.0827039	+	0.143247i	−0.904411	−	0.426663i	$-0.859689\pi$
$719$	−2.21764	+	3.84106i	−0.0827039	+	0.143247i	0.821707	+	0.569911i	$0.193022\pi$
$720$	−2.43063	+	1.75842i	−0.0905843	+	0.0655323i
$721$	9.34462	+	2.00697i	0.348012	+	0.0747435i
$722$	−6.69647	−	3.86621i	−0.249217	−	0.143885i
$723$	25.4526	−	28.2102i	0.946591	−	1.04915i
$724$	−1.48044	−	0.854734i	−0.0550202	−	0.0317659i
$725$	6.21856	+	3.59029i	0.230952	+	0.133340i
$726$	9.53763	+	2.03743i	0.353975	+	0.0756160i
$727$	36.5068	+	21.0772i	1.35396	+	0.781711i	0.988802	−	0.149233i	$-0.0476803\pi$
$727$	36.5068	+	21.0772i	1.35396	+	0.781711i	0.365162	+	0.930944i	$0.381014\pi$
$728$	−15.1241	+	4.87871i	−0.560538	+	0.180817i
$729$	−8.18661	−	25.7290i	−0.303208	−	0.952924i
$730$	3.47757	−	6.02332i	0.128711	−	0.222933i
$731$	6.25728			0.231434
$732$	3.44262	−	3.81561i	0.127243	−	0.141029i
$733$			46.2254i			1.70738i	0.520785	+	0.853688i	$0.325639\pi$
$733$			46.2254i			1.70738i	−0.520785	+	0.853688i	$0.674361\pi$
$734$	12.1737	+	21.0854i	0.449339	+	0.778278i
$735$	−4.87313	−	11.1019i	−0.179748	−	0.409500i
$736$	−1.09432	+	1.89542i	−0.0403372	+	0.0698660i
$737$	30.4504	+	17.5806i	1.12166	+	0.647589i
$738$	−3.35681	+	7.49844i	−0.123566	+	0.276021i
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	−0.999563	−	0.0295478i	$-0.990593\pi$
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	0.474193	−	0.880421i	$-0.342740\pi$
$740$	−2.90160	−	5.02572i	−0.106665	−	0.184749i
$741$	25.9280	+	23.3934i	0.952488	+	0.859380i
$742$	−16.9654	−	15.3409i	−0.622818	−	0.563183i
$743$	3.36454	−	1.94252i	0.123433	−	0.0712640i	−0.437012	−	0.899456i	$-0.643963\pi$
$743$	3.36454	−	1.94252i	0.123433	−	0.0712640i	0.560445	+	0.828192i	$0.310630\pi$
$744$	12.9248	−	4.18499i	0.473845	−	0.153429i
$745$		−	4.37779i		−	0.160390i
$746$	−23.7833	+	13.7313i	−0.870767	+	0.502738i
$747$	37.6741	+	16.8655i	1.37842	+	0.617075i
$748$		−	5.23401i		−	0.191375i
$749$	−23.6860	+	26.1941i	−0.865467	+	0.957111i
$750$	1.69383	+	0.361836i	0.0618501	+	0.0132124i
$751$	21.2885			0.776829			0.388415	−	0.921485i	$-0.373023\pi$
$751$	21.2885			0.776829			0.388415	+	0.921485i	$0.373023\pi$
$752$	4.13613	−	7.16398i	0.150829	−	0.261244i
$753$	−20.1607	−	18.1900i	−0.734698	−	0.662879i
$754$	−37.3514	+	21.5649i	−1.36026	+	0.785346i
$755$	5.57316			0.202828
$756$	13.4619	−	2.78874i	0.489605	−	0.101426i
$757$	−42.1251			−1.53106			−0.765531	−	0.643399i	$-0.777524\pi$
$757$	−42.1251			−1.53106			−0.765531	+	0.643399i	$0.777524\pi$
$758$	27.7156	−	16.0016i	1.00668	−	0.581205i
$759$	−11.4780	−	10.3560i	−0.416626	−	0.375899i
$760$	−1.67836	+	2.90701i	−0.0608806	+	0.105448i
$761$	48.8379			1.77037			0.885187	−	0.465236i	$-0.154030\pi$
$761$	48.8379			1.77037			0.885187	+	0.465236i	$0.154030\pi$
$762$	18.5687	+	3.96665i	0.672674	+	0.143696i
$763$	−27.1229	+	8.74925i	−0.981915	+	0.316744i
$764$			9.26150i			0.335069i
$765$	−3.11959	+	2.25684i	−0.112789	+	0.0815961i
$766$	12.3587	−	7.13527i	0.446536	−	0.257808i
$767$		−	7.57507i		−	0.273520i
$768$	1.64782	−	0.533558i	0.0594606	−	0.0192531i
$769$	−41.1583	+	23.7627i	−1.48420	+	0.856906i	−0.999839	−	0.0179596i	$-0.994283\pi$
$769$	−41.1583	+	23.7627i	−1.48420	+	0.856906i	−0.484366	+	0.874866i	$0.660950\pi$
$770$	10.2686	−	3.31241i	0.370053	−	0.119371i
$771$	13.6150	+	12.2841i	0.490331	+	0.442400i
$772$	−12.1247	−	21.0006i	−0.436378	−	0.755829i
$773$	2.07497	+	3.59395i	0.0746314	+	0.129265i	0.900926	−	0.433973i	$-0.142889\pi$
$773$	2.07497	+	3.59395i	0.0746314	+	0.129265i	−0.826295	+	0.563238i	$0.809555\pi$
$774$	−14.5491	+	1.49925i	−0.522955	+	0.0538895i
$775$	−6.79271	−	3.92178i	−0.244001	−	0.140874i
$776$	−9.74120	+	16.8723i	−0.349689	+	0.605679i
$777$	2.69682	+	26.4565i	0.0967477	+	0.949122i
$778$	−5.38049	−	9.31929i	−0.192900	−	0.334113i
$779$			9.19241i			0.329352i
$780$	−6.96913	+	7.72419i	−0.249535	+	0.276570i
$781$	57.6539			2.06302
$782$	−1.40450	+	2.43267i	−0.0502249	+	0.0869922i
$783$	34.1318	−	15.0718i	1.21977	−	0.538623i
$784$	0.702180	+	6.96469i	0.0250779	+	0.248739i
$785$	0.243649	+	0.140671i	0.00869619	+	0.00502075i
$786$	−35.1152	−	7.50131i	−1.25252	−	0.267563i
$787$	23.6630	+	13.6618i	0.843495	+	0.486992i	0.858451	−	0.512896i	$-0.171427\pi$
$787$	23.6630	+	13.6618i	0.843495	+	0.486992i	−0.0149557	+	0.999888i	$0.504761\pi$
$788$	16.3633	+	9.44736i	0.582919	+	0.336548i
$789$	−28.1540	+	31.2043i	−1.00231	+	1.11090i
$790$	−10.5530	−	6.09277i	−0.375458	−	0.216771i
$791$	−2.30404	−	7.14260i	−0.0819224	−	0.253961i
$792$	1.25408	+	12.1698i	0.0445617	+	0.432436i
$793$	8.91076	−	15.4339i	0.316430	−	0.548073i
$794$	22.3435			0.792941
$795$	−14.6434	−	3.12812i	−0.519348	−	0.110943i
$796$		−	2.60387i		−	0.0922919i
$797$	14.7404	+	25.5311i	0.522132	+	0.904359i	0.999668	+	0.0257473i	$0.00819652\pi$
$797$	14.7404	+	25.5311i	0.522132	+	0.904359i	−0.477536	+	0.878612i	$0.658470\pi$
$798$	12.4730	−	9.00249i	0.441538	−	0.318685i
$799$	5.30850	−	9.19460i	0.187801	−	0.325282i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−39.9494	−	17.8841i	−1.41154	−	0.631903i
$802$	9.49194	+	16.4405i	0.335172	+	0.580535i
$803$	−14.1818	−	24.5636i	−0.500466	−	0.866832i
$804$	−3.11974	+	14.6042i	−0.110025	+	0.515050i
$805$	−5.66149	−	1.21594i	−0.199541	−	0.0428561i
$806$	40.8000	−	23.5559i	1.43712	−	0.829721i
$807$	−6.54646	+	30.6454i	−0.230446	+	1.07877i
$808$		−	8.53717i		−	0.300337i
$809$	1.53294	−	0.885046i	0.0538955	−	0.0311166i	−0.472810	−	0.881164i	$-0.656760\pi$
$809$	1.53294	−	0.885046i	0.0538955	−	0.0311166i	0.526706	+	0.850048i	$0.323427\pi$
$810$	6.71275	−	5.99492i	0.235862	−	0.210640i
$811$		−	21.7821i		−	0.764872i	−0.923982	−	0.382436i	$-0.875085\pi$
$811$		−	21.7821i		−	0.764872i	0.923982	−	0.382436i	$-0.124915\pi$
$812$	5.83240	+	18.0806i	0.204677	+	0.634504i
$813$	1.89382	+	5.84881i	0.0664191	+	0.205127i
$814$	−23.6660			−0.829491
$815$	3.76577	−	6.52251i	0.131909	−	0.228473i
$816$	2.11489	−	0.684794i	0.0740361	−	0.0239726i
$817$	−14.1727	+	8.18263i	−0.495841	+	0.286274i
$818$	26.0187			0.909722
$819$	43.6331	−	19.2099i	1.52466	−	0.671250i
$820$	−2.73851			−0.0956329
$821$	−21.5112	+	12.4195i	−0.750746	+	0.433443i	−0.825963	−	0.563724i	$-0.809368\pi$
$821$	−21.5112	+	12.4195i	−0.750746	+	0.433443i	0.0752177	+	0.997167i	$0.476035\pi$
$822$	−3.50052	+	16.3867i	−0.122095	+	0.571552i
$823$	−22.3540	+	38.7182i	−0.779210	+	1.34963i	0.153187	+	0.988197i	$0.451046\pi$
$823$	−22.3540	+	38.7182i	−0.779210	+	1.34963i	−0.932398	+	0.361434i	$0.882287\pi$
$824$	−3.61248			−0.125847
$825$	4.73171	−	5.24436i	0.164737	−	0.182585i
$826$	−3.26232	−	0.700658i	−0.113511	−	0.0243790i
$827$			43.9883i			1.52962i	0.644255	+	0.764811i	$0.277168\pi$
$827$			43.9883i			1.52962i	−0.644255	+	0.764811i	$0.722832\pi$
$828$	2.68280	−	5.99282i	0.0932336	−	0.208265i
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	−0.0372876	−	0.999305i	$-0.511872\pi$
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	0.846779	+	0.531944i	$0.178538\pi$
$830$			13.7590i			0.477580i
$831$	−2.96928	−	2.67902i	−0.103003	−	0.0929343i
$832$	5.20173	−	3.00322i	0.180338	−	0.104118i
$833$	0.901212	+	8.93882i	0.0312252	+	0.309712i
$834$	8.69813	−	2.81642i	0.301192	−	0.0975246i
$835$	4.87241	+	8.43926i	0.168617	+	0.292053i
$836$	6.84450	+	11.8550i	0.236722	+	0.410015i
$837$	−37.2831	+	16.4634i	−1.28869	+	0.569058i
$838$	6.49717	+	3.75114i	0.224441	+	0.129581i
$839$	7.52241	−	13.0292i	0.259702	−	0.449818i	−0.706460	−	0.707753i	$-0.749709\pi$
$839$	7.52241	−	13.0292i	0.259702	−	0.449818i	0.966162	+	0.257935i	$0.0830422\pi$
$840$	2.68193	+	3.71581i	0.0925353	+	0.128208i
$841$	11.2803	+	19.5381i	0.388977	+	0.673728i
$842$			15.8985i			0.547899i
$843$	0.114987	+	0.355122i	0.00396036	+	0.0122310i
$844$	−6.25025			−0.215143
$845$	−11.5387	+	19.9855i	−0.396942	+	0.687524i
$846$	−10.1400	+	22.6507i	−0.348620	+	0.778746i
$847$	3.12828	−	14.5655i	0.107489	−	0.500478i
$848$	7.48689	+	4.32256i	0.257101	+	0.148437i
$849$	−8.24262	−	25.4562i	−0.282886	−	0.873656i
$850$	−1.11150	−	0.641724i	−0.0381241	−	0.0220110i
$851$	10.9995	+	6.35056i	0.377058	+	0.217694i
$852$	7.54316	+	23.2961i	0.258424	+	0.798110i
$853$	11.0905	+	6.40312i	0.379732	+	0.219239i	0.677702	−	0.735337i	$-0.262976\pi$
$853$	11.0905	+	6.40312i	0.379732	+	0.219239i	−0.297970	+	0.954575i	$0.596309\pi$
$854$	−5.82263	−	5.26511i	−0.199246	−	0.180168i
$855$	4.11461	−	9.19121i	0.140717	−	0.314333i
$856$	6.67392	−	11.5596i	0.228110	−	0.395098i
$857$	−42.5215			−1.45251			−0.726254	−	0.687426i	$-0.758740\pi$
$857$	−42.5215			−1.45251			−0.726254	+	0.687426i	$0.758740\pi$
$858$	13.0694	+	40.3630i	0.446181	+	1.37797i
$859$			7.34964i			0.250767i	0.992108	+	0.125383i	$0.0400161\pi$
$859$			7.34964i			0.250767i	−0.992108	+	0.125383i	$0.959984\pi$
$860$	−2.43768	−	4.22219i	−0.0831243	−	0.143976i
$861$	11.4484	+	5.14024i	0.390160	+	0.175179i
$862$	−11.2140	+	19.4232i	−0.381949	+	0.661556i
$863$	3.64790	+	2.10612i	0.124176	+	0.0716930i	0.560801	−	0.827950i	$-0.310493\pi$
$863$	3.64790	+	2.10612i	0.124176	+	0.0716930i	−0.436625	+	0.899643i	$0.643826\pi$
$864$	−4.75335	+	2.09897i	−0.161712	+	0.0714085i
$865$	−7.13345	−	12.3555i	−0.242544	−	0.420099i
$866$	−0.985975	−	1.70776i	−0.0335048	−	0.0580320i
$867$	−25.2986	+	8.19158i	−0.859186	+	0.278201i
$868$	−6.37090	−	19.7500i	−0.216242	−	0.670357i
$869$	−43.0360	+	24.8468i	−1.45990	+	0.842871i
$870$	9.23412	+	8.33146i	0.313066	+	0.282463i
$871$			51.7873i			1.75475i
$872$	9.32854	−	5.38583i	0.315904	−	0.182387i
$873$	23.8812	−	53.3457i	0.808255	−	1.80548i
$874$		−	7.34666i		−	0.248504i
$875$	0.555567	−	2.58676i	0.0187816	−	0.0874486i
$876$	8.06988	−	8.94420i	0.272656	−	0.302197i
$877$	−26.7236			−0.902390			−0.451195	−	0.892425i	$-0.649002\pi$
$877$	−26.7236			−0.902390			−0.451195	+	0.892425i	$0.649002\pi$
$878$	5.28351	−	9.15130i	0.178310	−	0.308842i
$879$	0.251326	−	1.17651i	0.00847702	−	0.0396828i
$880$	−3.53173	+	2.03904i	−0.119054	+	0.0687361i
$881$	5.40270			0.182022			0.0910109	−	0.995850i	$-0.470990\pi$
$881$	5.40270			0.182022			0.0910109	+	0.995850i	$0.470990\pi$
$882$	−4.23720	−	20.5681i	−0.142674	−	0.692563i
$883$	−27.9671			−0.941169			−0.470584	−	0.882355i	$-0.655957\pi$
$883$	−27.9671			−0.941169			−0.470584	+	0.882355i	$0.655957\pi$
$884$	6.67615	−	3.85448i	0.224543	−	0.129640i
$885$	−2.07816	+	0.672901i	−0.0698567	+	0.0226193i
$886$	−3.38074	+	5.85561i	−0.113578	+	0.196723i
$887$	21.4552			0.720395			0.360198	−	0.932876i	$-0.382709\pi$
$887$	21.4552			0.720395			0.360198	+	0.932876i	$0.382709\pi$
$888$	−3.09634	−	9.56264i	−0.103906	−	0.320901i
$889$	6.09042	−	28.3575i	0.204266	−	0.951079i
$890$		−	14.5899i		−	0.489056i
$891$	−7.48483	−	35.9315i	−0.250751	−	1.20375i
$892$	4.24320	−	2.44981i	0.142073	−	0.0820257i
$893$			27.7677i			0.929209i
$894$	1.58404	−	7.41524i	0.0529783	−	0.248003i
$895$	−7.42444	+	4.28650i	−0.248172	+	0.143282i
$896$	−0.812247	−	2.51799i	−0.0271353	−	0.0841200i
$897$	4.75668	−	22.2670i	0.158821	−	0.743475i
$898$	1.98767	+	3.44275i	0.0663294	+	0.114886i
$899$	−28.1606	−	48.7756i	−0.939209	−	1.62676i
$900$	2.73815	+	1.22578i	0.0912716	+	0.0408594i
$901$	9.60904	+	5.54778i	0.320124	+	0.184823i
$902$	−5.58394	+	9.67166i	−0.185925	+	0.322031i
$903$	2.26564	+	22.2266i	0.0753958	+	0.739654i
$904$	1.41832	+	2.45659i	0.0471725	+	0.0817051i
$905$			1.70947i			0.0568247i
$906$	9.44001	+	2.01657i	0.313623	+	0.0669962i
$907$	−21.1006			−0.700634			−0.350317	−	0.936631i	$-0.613926\pi$
$907$	−21.1006			−0.700634			−0.350317	+	0.936631i	$0.613926\pi$
$908$	8.74040	−	15.1388i	0.290060	−	0.502399i
$909$	2.62532	+	25.4766i	0.0870763	+	0.845006i
$910$	11.7872	+	10.6585i	0.390740	+	0.353327i
$911$	18.9423	+	10.9363i	0.627585	+	0.362337i	0.779816	−	0.626008i	$-0.215312\pi$
$911$	18.9423	+	10.9363i	0.627585	+	0.362337i	−0.152231	+	0.988345i	$0.548646\pi$
$912$	−3.89473	+	4.31670i	−0.128967	+	0.142940i
$913$	48.5929	+	28.0551i	1.60819	+	0.928488i
$914$	5.64673	+	3.26014i	0.186777	+	0.107836i
$915$	−5.02572	−	1.07359i	−0.166145	−	0.0354919i
$916$	12.6374	+	7.29619i	0.417551	+	0.241073i
$917$	−11.5176	+	53.6267i	−0.380344	+	1.77091i
$918$	−6.10068	+	2.69392i	−0.201352	+	0.0889127i
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	−0.988194	−	0.153205i	$-0.951040\pi$
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	0.626777	+	0.779199i	$0.284374\pi$
$920$	2.18864			0.0721573
$921$	39.5417	−	43.8258i	1.30294	−	1.44411i
$922$		−	9.38607i		−	0.309114i
$923$	42.4580	+	73.5394i	1.39752	+	2.42058i
$924$	18.5918	−	1.89514i	0.611625	−	0.0623454i
$925$	−2.90160	+	5.02572i	−0.0954040	+	0.165245i
$926$	29.2212	+	16.8709i	0.960269	+	0.554411i
$927$	10.7803	−	1.11089i	0.354073	−	0.0364865i
$928$	−3.59029	−	6.21856i	−0.117857	−	0.204134i
$929$	12.1080	+	20.9717i	0.397251	+	0.688059i	0.993386	−	0.114826i	$-0.0366310\pi$
$929$	12.1080	+	20.9717i	0.397251	+	0.688059i	−0.596135	+	0.802884i	$0.703298\pi$
$930$	−10.0867	−	9.10069i	−0.330756	−	0.298423i
$931$	−13.7305	−	19.0679i	−0.449999	−	0.624925i
$932$	3.42360	−	1.97662i	0.112144	−	0.0647463i
$933$	13.9861	−	4.52863i	0.457883	−	0.148261i
$934$		−	35.8295i		−	1.17238i
$935$	−4.53279	+	2.61701i	−0.148238	+	0.0855853i
$936$	−14.5994	+	10.5618i	−0.477198	+	0.345224i
$937$			38.1815i			1.24733i	0.781690	+	0.623667i	$0.214358\pi$
$937$			38.1815i			1.24733i	−0.781690	+	0.623667i	$0.785642\pi$
$938$	22.3030	+	4.79008i	0.728218	+	0.156402i
$939$	−46.2075	−	9.87083i	−1.50792	−	0.322122i
$940$	−8.27225			−0.269811
$941$	3.96611	−	6.86950i	0.129291	−	0.223939i	−0.794111	−	0.607773i	$-0.792063\pi$
$941$	3.96611	−	6.86950i	0.129291	−	0.223939i	0.923402	+	0.383834i	$0.125396\pi$
$942$	0.361801	+	0.326434i	0.0117881	+	0.0106358i
$943$	5.19062	−	2.99680i	0.169030	−	0.0975894i
$944$	1.26116			0.0410472
$945$	−9.14607	−	10.2640i	−0.297522	−	0.333887i
$946$	−19.8822			−0.646425
$947$	−2.86322	+	1.65308i	−0.0930421	+	0.0537179i	−0.545799	−	0.837916i	$-0.683774\pi$
$947$	−2.86322	+	1.65308i	−0.0930421	+	0.0537179i	0.452757	+	0.891634i	$0.350440\pi$
$948$	−15.6704	−	14.1386i	−0.508951	−	0.459200i
$949$	20.8878	−	36.1787i	0.678047	−	1.17441i
$950$	3.35672			0.108906
$951$	−0.0764305	−	0.0163271i	−0.00247843	−	0.000529441i
$952$	−1.04248	−	3.23171i	−0.0337869	−	0.104740i
$953$			53.6699i			1.73854i	0.494339	+	0.869269i	$0.335410\pi$
$953$			53.6699i			1.73854i	−0.494339	+	0.869269i	$0.664590\pi$
$954$	−23.6716	−	10.5970i	−0.766397	−	0.343092i
$955$	8.02069	−	4.63075i	0.259543	−	0.149847i
$956$		−	18.5118i		−	0.598714i
$957$	48.2532	−	15.6242i	1.55980	−	0.505058i
$958$	−12.0186	+	6.93894i	−0.388303	+	0.224187i
$959$	25.0252	+	5.37473i	0.808105	+	0.173559i
$960$	−1.28599	−	1.16028i	−0.0415050	−	0.0374478i
$961$	15.2606	+	26.4322i	0.492279	+	0.852652i
$962$	−17.4283	−	30.1867i	−0.561910	−	0.973257i
$963$	−16.3616	+	36.5484i	−0.527244	+	1.17776i
$964$	18.9977	+	10.9683i	0.611874	+	0.353266i
$965$	−12.1247	+	21.0006i	−0.390308	+	0.676034i
$966$	−9.14966	−	4.10813i	−0.294386	−	0.132177i
$967$	8.76620	+	15.1835i	0.281902	+	0.488268i	0.971853	−	0.235587i	$-0.0757014\pi$
$967$	8.76620	+	15.1835i	0.281902	+	0.488268i	−0.689951	+	0.723856i	$0.742368\pi$
$968$			5.63079i			0.180981i
$969$	−4.99868	+	5.54026i	−0.160581	+	0.177979i
$970$	19.4824			0.625542
$971$	1.13150	−	1.95981i	0.0363115	−	0.0628933i	−0.847299	−	0.531117i	$-0.821772\pi$
$971$	1.13150	−	1.95981i	0.0363115	−	0.0628933i	0.883610	+	0.468224i	$0.155106\pi$
$972$	13.5395	−	7.72548i	0.434278	−	0.247795i
$973$	−4.28750	−	13.2914i	−0.137451	−	0.426101i
$974$	23.9026	+	13.8002i	0.765888	+	0.442186i
$975$	10.1739	+	2.17335i	0.325826	+	0.0696029i
$976$	2.56956	+	1.48353i	0.0822495	+	0.0474868i
$977$	39.2275	+	22.6480i	1.25500	+	0.724574i	0.972098	−	0.234575i	$-0.0753700\pi$
$977$	39.2275	+	22.6480i	1.25500	+	0.724574i	0.282901	+	0.959149i	$0.408703\pi$
$978$	8.73867	−	9.68545i	0.279432	−	0.309707i
$979$	−51.5277	−	29.7495i	−1.64683	−	0.950799i
$980$	5.68051	−	4.09045i	0.181457	−	0.130665i
$981$	−26.1820	+	18.9411i	−0.835926	+	0.604742i
$982$	−10.5048	+	18.1949i	−0.335222	+	0.580621i
$983$	27.1875			0.867145			0.433572	−	0.901119i	$-0.357253\pi$
$983$	27.1875			0.867145			0.433572	+	0.901119i	$0.357253\pi$
$984$	−4.63858	−	0.990892i	−0.147872	−	0.0315885i
$985$		−	18.8947i		−	0.602036i
$986$	−4.60795	−	7.98120i	−0.146747	−	0.254173i
$987$	34.5824	+	15.5272i	1.10077	+	0.494237i
$988$	−10.0810	+	17.4608i	−0.320719	+	0.555501i
$989$	9.24086	+	5.33521i	0.293842	+	0.169650i
$990$	9.91233	−	7.17097i	0.315035	−	0.227908i
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	0.577150	−	0.816638i	$-0.304165\pi$
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	−0.995804	+	0.0915077i	$0.970831\pi$
$992$	3.92178	+	6.79271i	0.124516	+	0.215669i
$993$	−6.68137	+	31.2769i	−0.212027	+	0.992543i
$994$	35.5980	−	11.4831i	1.12910	−	0.364223i
$995$	−2.25502	+	1.30194i	−0.0714890	+	0.0412742i
$996$	−4.97849	+	23.3054i	−0.157750	+	0.738459i
$997$			51.3611i			1.62662i	0.581828	+	0.813312i	$0.302338\pi$
$997$			51.3611i			1.62662i	−0.581828	+	0.813312i	$0.697662\pi$
$998$	0.342363	−	0.197663i	0.0108373	−	0.00625692i
$999$	12.1808	+	27.5846i	0.385382	+	0.872739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.551.9	yes	28
3.2	odd	2		1890.2.t.b.1601.1		28
7.3	odd	6		630.2.bk.b.101.12	yes	28
9.4	even	3		1890.2.bk.b.341.13		28
9.5	odd	6		630.2.bk.b.131.5	yes	28
21.17	even	6		1890.2.bk.b.521.13		28
63.31	odd	6		1890.2.t.b.1151.1		28
63.59	even	6	inner	630.2.t.b.311.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.9	✓	28	63.59	even	6	inner
630.2.t.b.551.9	yes	28	1.1	even	1	trivial
630.2.bk.b.101.12	yes	28	7.3	odd	6
630.2.bk.b.131.5	yes	28	9.5	odd	6
1890.2.t.b.1151.1		28	63.31	odd	6
1890.2.t.b.1601.1		28	3.2	odd	2
1890.2.bk.b.341.13		28	9.4	even	3
1890.2.bk.b.521.13		28	21.17	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.28599 - 1.16028i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.69383 - 0.361836i) q^{6} +(-0.555567 + 2.58676i) q^{7} -1.00000i q^{8} +(0.307516 + 2.98420i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.28599 - 1.16028i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-1.69383 - 0.361836i) q^{6} +(-0.555567 + 2.58676i) q^{7} -1.00000i q^{8} +(0.307516 + 2.98420i) q^{9} +(-0.866025 + 0.500000i) q^{10} +4.07809i q^{11} +(-1.64782 + 0.533558i) q^{12} +(-5.20173 + 3.00322i) q^{13} +(0.812247 + 2.51799i) q^{14} +(1.28599 + 1.16028i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.641724 - 1.11150i) q^{17} +(1.75842 + 2.43063i) q^{18} +(2.90701 + 1.67836i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.71581 - 2.68193i) q^{21} +(2.03904 + 3.53173i) q^{22} -2.18864i q^{23} +(-1.16028 + 1.28599i) q^{24} +1.00000 q^{25} +(-3.00322 + 5.20173i) q^{26} +(3.06703 - 4.19444i) q^{27} +(1.96242 + 1.77452i) q^{28} +(6.21856 + 3.59029i) q^{29} +(1.69383 + 0.361836i) q^{30} +(-6.79271 - 3.92178i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.73171 - 5.24436i) q^{33} +(-1.11150 - 0.641724i) q^{34} +(0.555567 - 2.58676i) q^{35} +(2.73815 + 1.22578i) q^{36} +(-2.90160 + 5.02572i) q^{37} +3.35672 q^{38} +(10.1739 + 2.17335i) q^{39} +1.00000i q^{40} +(1.36925 + 2.37162i) q^{41} +(1.87702 - 4.18052i) q^{42} +(-2.43768 + 4.22219i) q^{43} +(3.53173 + 2.03904i) q^{44} +(-0.307516 - 2.98420i) q^{45} +(-1.09432 - 1.89542i) q^{46} +(4.13613 + 7.16398i) q^{47} +(-0.361836 + 1.69383i) q^{48} +(-6.38269 - 2.87424i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-0.464398 + 2.17395i) q^{51} +6.00644i q^{52} +(-7.48689 + 4.32256i) q^{53} +(0.558910 - 5.16601i) q^{54} -4.07809i q^{55} +(2.58676 + 0.555567i) q^{56} +(-1.79100 - 5.53128i) q^{57} +7.18058 q^{58} +(-0.630579 + 1.09220i) q^{59} +(1.64782 - 0.533558i) q^{60} +(-2.56956 + 1.48353i) q^{61} -7.84355 q^{62} +(-7.89026 - 0.862450i) q^{63} -1.00000 q^{64} +(5.20173 - 3.00322i) q^{65} +(1.47560 - 6.90760i) q^{66} +(4.31098 - 7.46684i) q^{67} -1.28345 q^{68} +(-2.53943 + 2.81456i) q^{69} +(-0.812247 - 2.51799i) q^{70} -14.1375i q^{71} +(2.98420 - 0.307516i) q^{72} +(-6.02332 + 3.47757i) q^{73} +5.80320i q^{74} +(-1.28599 - 1.16028i) q^{75} +(2.90701 - 1.67836i) q^{76} +(-10.5490 - 2.26565i) q^{77} +(9.89754 - 3.20478i) q^{78} +(6.09277 + 10.5530i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.81087 + 1.83538i) q^{81} +(2.37162 + 1.36925i) q^{82} +(6.87948 - 11.9156i) q^{83} +(-0.464712 - 4.55895i) q^{84} +(0.641724 + 1.11150i) q^{85} +4.87537i q^{86} +(-3.83125 - 11.8323i) q^{87} +4.07809 q^{88} +(-7.29497 + 12.6353i) q^{89} +(-1.75842 - 2.43063i) q^{90} +(-4.87871 - 15.1241i) q^{91} +(-1.89542 - 1.09432i) q^{92} +(4.18499 + 12.9248i) q^{93} +(7.16398 + 4.13613i) q^{94} +(-2.90701 - 1.67836i) q^{95} +(0.533558 + 1.64782i) q^{96} +(-16.8723 - 9.74120i) q^{97} +(-6.96469 + 0.702180i) q^{98} +(-12.1698 + 1.25408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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