LMFDB - Embedded newform 690.3.k.a.553.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.13
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.72431 + 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 - 6.04624i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.72431 + 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 - 6.04624i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(7.06040 - 0.388220i) q^{10} +6.03072 q^{11} +(2.44949 - 2.44949i) q^{12} +(-0.224734 - 0.224734i) q^{13} -12.0925i q^{14} +(0.475470 + 8.64719i) q^{15} -4.00000 q^{16} +(3.58233 - 3.58233i) q^{17} +(3.00000 + 3.00000i) q^{18} -25.3766i q^{19} +(6.67218 - 7.44862i) q^{20} +14.8102 q^{21} +(6.03072 - 6.03072i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(2.74099 + 24.8493i) q^{25} -0.449468 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-12.0925 - 12.0925i) q^{28} +37.7718i q^{29} +(9.12266 + 8.17172i) q^{30} +11.5048 q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.38610 + 7.38610i) q^{33} -7.16467i q^{34} +(42.6889 - 2.34727i) q^{35} +6.00000 q^{36} +(20.7844 - 20.7844i) q^{37} +(-25.3766 - 25.3766i) q^{38} -0.550483i q^{39} +(-0.776439 - 14.1208i) q^{40} -24.7818 q^{41} +(14.8102 - 14.8102i) q^{42} +(-19.3473 - 19.3473i) q^{43} -12.0614i q^{44} +(-10.0083 + 11.1729i) q^{45} +6.78233 q^{46} +(5.86417 - 5.86417i) q^{47} +(-4.89898 - 4.89898i) q^{48} -24.1140i q^{49} +(27.5903 + 22.1083i) q^{50} +8.77489 q^{51} +(-0.449468 + 0.449468i) q^{52} +(33.5894 + 33.5894i) q^{53} +7.34847i q^{54} +(22.4603 + 20.1190i) q^{55} -24.1849 q^{56} +(31.0798 - 31.0798i) q^{57} +(37.7718 + 37.7718i) q^{58} +20.0519i q^{59} +(17.2944 - 0.950940i) q^{60} +10.4754 q^{61} +(11.5048 - 11.5048i) q^{62} +(18.1387 + 18.1387i) q^{63} +8.00000i q^{64} +(-0.0872461 - 1.58671i) q^{65} +14.7722 q^{66} +(22.9516 - 22.9516i) q^{67} +(-7.16467 - 7.16467i) q^{68} +8.30662i q^{69} +(40.3416 - 45.0361i) q^{70} +21.4134 q^{71} +(6.00000 - 6.00000i) q^{72} +(25.3312 + 25.3312i) q^{73} -41.5687i q^{74} +(-27.0770 + 33.7910i) q^{75} -50.7531 q^{76} +(36.4632 - 36.4632i) q^{77} +(-0.550483 - 0.550483i) q^{78} +8.78027i q^{79} +(-14.8972 - 13.3444i) q^{80} -9.00000 q^{81} +(-24.7818 + 24.7818i) q^{82} +(-47.9297 - 47.9297i) q^{83} -29.6204i q^{84} +(25.2927 - 1.39073i) q^{85} -38.6945 q^{86} +(-46.2608 + 46.2608i) q^{87} +(-12.0614 - 12.0614i) q^{88} -10.7360i q^{89} +(1.16466 + 21.1812i) q^{90} -2.71759 q^{91} +(6.78233 - 6.78233i) q^{92} +(14.0904 + 14.0904i) q^{93} -11.7283i q^{94} +(84.6586 - 94.5102i) q^{95} -9.79796 q^{96} +(-63.2192 + 63.2192i) q^{97} +(-24.1140 - 24.1140i) q^{98} +18.0922i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	3.72431	+	3.33609i	0.744862	+	0.667218i
$5$	3.72431	+	3.33609i	0.744862	+	0.667218i
$6$	2.44949			0.408248
$7$	6.04624	−	6.04624i	0.863748	−	0.863748i	−0.128023	−	0.991771i	$-0.540863\pi$
$7$	6.04624	−	6.04624i	0.863748	−	0.863748i	0.991771	+	0.128023i	$0.0408632\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	7.06040	−	0.388220i	0.706040	−	0.0388220i
$11$	6.03072			0.548247			0.274124	−	0.961694i	$-0.411612\pi$
$11$	6.03072			0.548247			0.274124	+	0.961694i	$0.411612\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−0.224734	−	0.224734i	−0.0172872	−	0.0172872i	0.698410	−	0.715698i	$-0.253891\pi$
$13$	−0.224734	−	0.224734i	−0.0172872	−	0.0172872i	−0.715698	+	0.698410i	$0.753891\pi$
$14$		−	12.0925i		−	0.863748i
$15$	0.475470	+	8.64719i	0.0316980	+	0.576479i
$16$	−4.00000			−0.250000
$17$	3.58233	−	3.58233i	0.210725	−	0.210725i	−0.593850	−	0.804576i	$-0.702393\pi$
$17$	3.58233	−	3.58233i	0.210725	−	0.210725i	0.804576	+	0.593850i	$0.202393\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$		−	25.3766i		−	1.33561i	−0.744337	−	0.667804i	$-0.767234\pi$
$19$		−	25.3766i		−	1.33561i	0.744337	−	0.667804i	$-0.232766\pi$
$20$	6.67218	−	7.44862i	0.333609	−	0.372431i
$21$	14.8102			0.705247
$22$	6.03072	−	6.03072i	0.274124	−	0.274124i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	2.74099	+	24.8493i	0.109639	+	0.993971i
$26$	−0.449468			−0.0172872
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−12.0925	−	12.0925i	−0.431874	−	0.431874i
$29$			37.7718i			1.30248i	0.758874	+	0.651238i	$0.225750\pi$
$29$			37.7718i			1.30248i	−0.758874	+	0.651238i	$0.774250\pi$
$30$	9.12266	+	8.17172i	0.304089	+	0.272391i
$31$	11.5048			0.371122			0.185561	−	0.982633i	$-0.440590\pi$
$31$	11.5048			0.371122			0.185561	+	0.982633i	$0.440590\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	7.38610	+	7.38610i	0.223821	+	0.223821i
$34$		−	7.16467i		−	0.210725i
$35$	42.6889	−	2.34727i	1.21968	−	0.0670648i
$36$	6.00000			0.166667
$37$	20.7844	−	20.7844i	0.561739	−	0.561739i	−0.368062	−	0.929801i	$-0.619979\pi$
$37$	20.7844	−	20.7844i	0.561739	−	0.561739i	0.929801	+	0.368062i	$0.119979\pi$
$38$	−25.3766	−	25.3766i	−0.667804	−	0.667804i
$39$		−	0.550483i		−	0.0141150i
$40$	−0.776439	−	14.1208i	−0.0194110	−	0.353020i
$41$	−24.7818			−0.604434			−0.302217	−	0.953239i	$-0.597727\pi$
$41$	−24.7818			−0.604434			−0.302217	+	0.953239i	$0.597727\pi$
$42$	14.8102	−	14.8102i	0.352624	−	0.352624i
$43$	−19.3473	−	19.3473i	−0.449937	−	0.449937i	0.445397	−	0.895333i	$-0.353063\pi$
$43$	−19.3473	−	19.3473i	−0.449937	−	0.449937i	−0.895333	+	0.445397i	$0.853063\pi$
$44$		−	12.0614i		−	0.274124i
$45$	−10.0083	+	11.1729i	−0.222406	+	0.248287i
$46$	6.78233			0.147442
$47$	5.86417	−	5.86417i	0.124770	−	0.124770i	−0.641965	−	0.766734i	$-0.721880\pi$
$47$	5.86417	−	5.86417i	0.124770	−	0.124770i	0.766734	+	0.641965i	$0.221880\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	24.1140i		−	0.492122i
$50$	27.5903	+	22.1083i	0.551805	+	0.442166i
$51$	8.77489			0.172057
$52$	−0.449468	+	0.449468i	−0.00864361	+	0.00864361i
$53$	33.5894	+	33.5894i	0.633763	+	0.633763i	0.949010	−	0.315247i	$-0.102087\pi$
$53$	33.5894	+	33.5894i	0.633763	+	0.633763i	−0.315247	+	0.949010i	$0.602087\pi$
$54$			7.34847i			0.136083i
$55$	22.4603	+	20.1190i	0.408369	+	0.365801i
$56$	−24.1849			−0.431874
$57$	31.0798	−	31.0798i	0.545260	−	0.545260i
$58$	37.7718	+	37.7718i	0.651238	+	0.651238i
$59$			20.0519i			0.339863i	0.985456	+	0.169931i	$0.0543546\pi$
$59$			20.0519i			0.339863i	−0.985456	+	0.169931i	$0.945645\pi$
$60$	17.2944	−	0.950940i	0.288240	−	0.0158490i
$61$	10.4754			0.171727			0.0858637	−	0.996307i	$-0.472635\pi$
$61$	10.4754			0.171727			0.0858637	+	0.996307i	$0.472635\pi$
$62$	11.5048	−	11.5048i	0.185561	−	0.185561i
$63$	18.1387	+	18.1387i	0.287916	+	0.287916i
$64$			8.00000i			0.125000i
$65$	−0.0872461	−	1.58671i	−0.00134225	−	0.0244109i
$66$	14.7722			0.223821
$67$	22.9516	−	22.9516i	0.342561	−	0.342561i	−0.514769	−	0.857329i	$-0.672122\pi$
$67$	22.9516	−	22.9516i	0.342561	−	0.342561i	0.857329	+	0.514769i	$0.172122\pi$
$68$	−7.16467	−	7.16467i	−0.105363	−	0.105363i
$69$			8.30662i			0.120386i
$70$	40.3416	−	45.0361i	0.576309	−	0.643373i
$71$	21.4134			0.301597			0.150799	−	0.988565i	$-0.451815\pi$
$71$	21.4134			0.301597			0.150799	+	0.988565i	$0.451815\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	25.3312	+	25.3312i	0.347002	+	0.347002i	0.858992	−	0.511989i	$-0.171091\pi$
$73$	25.3312	+	25.3312i	0.347002	+	0.347002i	−0.511989	+	0.858992i	$0.671091\pi$
$74$		−	41.5687i		−	0.561739i
$75$	−27.0770	+	33.7910i	−0.361027	+	0.450547i
$76$	−50.7531			−0.667804
$77$	36.4632	−	36.4632i	0.473548	−	0.473548i
$78$	−0.550483	−	0.550483i	−0.00705748	−	0.00705748i
$79$			8.78027i			0.111143i	0.998455	+	0.0555713i	$0.0176980\pi$
$79$			8.78027i			0.111143i	−0.998455	+	0.0555713i	$0.982302\pi$
$80$	−14.8972	−	13.3444i	−0.186216	−	0.166805i
$81$	−9.00000			−0.111111
$82$	−24.7818	+	24.7818i	−0.302217	+	0.302217i
$83$	−47.9297	−	47.9297i	−0.577467	−	0.577467i	0.356738	−	0.934204i	$-0.383889\pi$
$83$	−47.9297	−	47.9297i	−0.577467	−	0.577467i	−0.934204	+	0.356738i	$0.883889\pi$
$84$		−	29.6204i		−	0.352624i
$85$	25.2927	−	1.39073i	0.297561	−	0.0163615i
$86$	−38.6945			−0.449937
$87$	−46.2608	+	46.2608i	−0.531733	+	0.531733i
$88$	−12.0614	−	12.0614i	−0.137062	−	0.137062i
$89$		−	10.7360i		−	0.120629i	−0.998179	−	0.0603145i	$-0.980790\pi$
$89$		−	10.7360i		−	0.120629i	0.998179	−	0.0603145i	$-0.0192104\pi$
$90$	1.16466	+	21.1812i	0.0129407	+	0.235347i
$91$	−2.71759			−0.0298636
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	14.0904	+	14.0904i	0.151510	+	0.151510i
$94$		−	11.7283i		−	0.124770i
$95$	84.6586	−	94.5102i	0.891143	−	0.994845i
$96$	−9.79796			−0.102062
$97$	−63.2192	+	63.2192i	−0.651745	+	0.651745i	−0.953413	−	0.301668i	$-0.902456\pi$
$97$	−63.2192	+	63.2192i	−0.651745	+	0.651745i	0.301668	+	0.953413i	$0.402456\pi$
$98$	−24.1140	−	24.1140i	−0.246061	−	0.246061i
$99$			18.0922i			0.182749i
$100$	49.6986	−	5.48197i	0.496986	−	0.0548197i
$101$	−6.89640			−0.0682812			−0.0341406	−	0.999417i	$-0.510869\pi$
$101$	−6.89640			−0.0682812			−0.0341406	+	0.999417i	$0.510869\pi$
$102$	8.77489	−	8.77489i	0.0860283	−	0.0860283i
$103$	−88.5287	−	88.5287i	−0.859502	−	0.859502i	0.131777	−	0.991279i	$-0.457932\pi$
$103$	−88.5287	−	88.5287i	−0.859502	−	0.859502i	−0.991279	+	0.131777i	$0.957932\pi$
$104$			0.898935i			0.00864361i
$105$	55.1578	+	49.4082i	0.525312	+	0.470554i
$106$	67.1788			0.633763
$107$	87.3608	−	87.3608i	0.816456	−	0.816456i	−0.169137	−	0.985593i	$-0.554098\pi$
$107$	87.3608	−	87.3608i	0.816456	−	0.816456i	0.985593	+	0.169137i	$0.0540980\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			8.33514i			0.0764692i	0.999269	+	0.0382346i	$0.0121734\pi$
$109$			8.33514i			0.0764692i	−0.999269	+	0.0382346i	$0.987827\pi$
$110$	42.5793	−	2.34124i	0.387085	−	0.0212840i
$111$	50.9111			0.458658
$112$	−24.1849	+	24.1849i	−0.215937	+	0.215937i
$113$	−50.5727	−	50.5727i	−0.447546	−	0.447546i	0.446992	−	0.894538i	$-0.352495\pi$
$113$	−50.5727	−	50.5727i	−0.447546	−	0.447546i	−0.894538	+	0.446992i	$0.852495\pi$
$114$		−	62.1596i		−	0.545260i
$115$	1.31652	+	23.9430i	0.0114480	+	0.208200i
$116$	75.5436			0.651238
$117$	0.674201	−	0.674201i	0.00576240	−	0.00576240i
$118$	20.0519	+	20.0519i	0.169931	+	0.169931i
$119$		−	43.3193i		−	0.364027i
$120$	16.3434	−	18.2453i	0.136195	−	0.152044i
$121$	−84.6304			−0.699425
$122$	10.4754	−	10.4754i	0.0858637	−	0.0858637i
$123$	−30.3514	−	30.3514i	−0.246759	−	0.246759i
$124$		−	23.0095i		−	0.185561i
$125$	−72.6912	+	101.691i	−0.581530	+	0.813525i
$126$	36.2774			0.287916
$127$	−171.315	+	171.315i	−1.34893	+	1.34893i	−0.462111	+	0.886822i	$0.652908\pi$
$127$	−171.315	+	171.315i	−1.34893	+	1.34893i	−0.886822	+	0.462111i	$0.847092\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	47.3910i		−	0.367372i
$130$	−1.67396	−	1.49946i	−0.0128766	−	0.0115343i
$131$	−9.31847			−0.0711333			−0.0355667	−	0.999367i	$-0.511324\pi$
$131$	−9.31847			−0.0711333			−0.0355667	+	0.999367i	$0.511324\pi$
$132$	14.7722	−	14.7722i	0.111911	−	0.111911i
$133$	−153.433	−	153.433i	−1.15363	−	1.15363i
$134$		−	45.9031i		−	0.342561i
$135$	−25.9416	+	1.42641i	−0.192160	+	0.0105660i
$136$	−14.3293			−0.105363
$137$	−108.397	+	108.397i	−0.791218	+	0.791218i	−0.981692	−	0.190474i	$-0.938997\pi$
$137$	−108.397	+	108.397i	−0.791218	+	0.791218i	0.190474	+	0.981692i	$0.438997\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$			126.720i			0.911653i	0.890069	+	0.455827i	$0.150656\pi$
$139$			126.720i			0.911653i	−0.890069	+	0.455827i	$0.849344\pi$
$140$	−4.69454	−	85.3777i	−0.0335324	−	0.609841i
$141$	14.3642			0.101874
$142$	21.4134	−	21.4134i	0.150799	−	0.150799i
$143$	−1.35531	−	1.35531i	−0.00947767	−	0.00947767i
$144$		−	12.0000i		−	0.0833333i
$145$	−126.010	+	140.674i	−0.869035	+	0.970165i
$146$	50.6624			0.347002
$147$	29.5334	−	29.5334i	0.200908	−	0.200908i
$148$	−41.5687	−	41.5687i	−0.280870	−	0.280870i
$149$		−	61.5397i		−	0.413018i	−0.978445	−	0.206509i	$-0.933790\pi$
$149$		−	61.5397i		−	0.413018i	0.978445	−	0.206509i	$-0.0662103\pi$
$150$	6.71402	+	60.8681i	0.0447601	+	0.405787i
$151$	−100.953			−0.668560			−0.334280	−	0.942474i	$-0.608493\pi$
$151$	−100.953			−0.668560			−0.334280	+	0.942474i	$0.608493\pi$
$152$	−50.7531	+	50.7531i	−0.333902	+	0.333902i
$153$	10.7470	+	10.7470i	0.0702418	+	0.0702418i
$154$		−	72.9263i		−	0.473548i
$155$	42.8473	+	38.3810i	0.276434	+	0.247619i
$156$	−1.10097			−0.00705748
$157$	−63.0830	+	63.0830i	−0.401803	+	0.401803i	−0.878868	−	0.477065i	$-0.841701\pi$
$157$	−63.0830	+	63.0830i	−0.401803	+	0.401803i	0.477065	+	0.878868i	$0.341701\pi$
$158$	8.78027	+	8.78027i	0.0555713	+	0.0555713i
$159$			82.2769i			0.517465i
$160$	−28.2416	+	1.55288i	−0.176510	+	0.00970549i
$161$	41.0076			0.254705
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−35.1517	−	35.1517i	−0.215655	−	0.215655i	0.591010	−	0.806664i	$-0.298729\pi$
$163$	−35.1517	−	35.1517i	−0.215655	−	0.215655i	−0.806664	+	0.591010i	$0.798729\pi$
$164$			49.5636i			0.302217i
$165$	2.86743	+	52.1488i	0.0173783	+	0.316053i
$166$	−95.8594			−0.577467
$167$	65.9932	−	65.9932i	0.395169	−	0.395169i	−0.481356	−	0.876525i	$-0.659856\pi$
$167$	65.9932	−	65.9932i	0.395169	−	0.395169i	0.876525	+	0.481356i	$0.159856\pi$
$168$	−29.6204	−	29.6204i	−0.176312	−	0.176312i
$169$		−	168.899i		−	0.999402i
$170$	23.9020	−	26.6834i	0.140600	−	0.156961i
$171$	76.1297			0.445203
$172$	−38.6945	+	38.6945i	−0.224968	+	0.224968i
$173$	153.430	+	153.430i	0.886880	+	0.886880i	0.994222	−	0.107343i	$-0.0342341\pi$
$173$	153.430	+	153.430i	0.886880	+	0.886880i	−0.107343	+	0.994222i	$0.534234\pi$
$174$			92.5216i			0.531733i
$175$	166.817	+	133.672i	0.953242	+	0.763840i
$176$	−24.1229			−0.137062
$177$	−24.5585	+	24.5585i	−0.138748	+	0.138748i
$178$	−10.7360	−	10.7360i	−0.0603145	−	0.0603145i
$179$			17.5087i			0.0978139i	0.998803	+	0.0489069i	$0.0155738\pi$
$179$			17.5087i			0.0978139i	−0.998803	+	0.0489069i	$0.984426\pi$
$180$	22.3459	+	20.0165i	0.124144	+	0.111203i
$181$	−345.567			−1.90921			−0.954606	−	0.297871i	$-0.903723\pi$
$181$	−345.567			−1.90921			−0.954606	+	0.297871i	$0.903723\pi$
$182$	−2.71759	+	2.71759i	−0.0149318	+	0.0149318i
$183$	12.8297	+	12.8297i	0.0701074	+	0.0701074i
$184$		−	13.5647i		−	0.0737210i
$185$	146.746	−	8.06889i	0.793221	−	0.0436156i
$186$	28.1808			0.151510
$187$	21.6041	−	21.6041i	0.115530	−	0.115530i
$188$	−11.7283	−	11.7283i	−0.0623848	−	0.0623848i
$189$			44.4306i			0.235082i
$190$	−9.85168	−	179.169i	−0.0518510	−	0.942994i
$191$	109.218			0.571822			0.285911	−	0.958256i	$-0.407704\pi$
$191$	109.218			0.571822			0.285911	+	0.958256i	$0.407704\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	24.0047	+	24.0047i	0.124377	+	0.124377i	0.766555	−	0.642178i	$-0.221969\pi$
$193$	24.0047	+	24.0047i	0.124377	+	0.124377i	−0.642178	+	0.766555i	$0.721969\pi$
$194$			126.438i			0.651745i
$195$	1.83646	−	2.05017i	0.00941775	−	0.0105137i
$196$	−48.2279			−0.246061
$197$	−141.884	+	141.884i	−0.720223	+	0.720223i	−0.968650	−	0.248428i	$-0.920086\pi$
$197$	−141.884	+	141.884i	−0.720223	+	0.720223i	0.248428	+	0.968650i	$0.420086\pi$
$198$	18.0922	+	18.0922i	0.0913746	+	0.0913746i
$199$			176.579i			0.887330i	0.896193	+	0.443665i	$0.146322\pi$
$199$			176.579i			0.887330i	−0.896193	+	0.443665i	$0.853678\pi$
$200$	44.2166	−	55.1805i	0.221083	−	0.275903i
$201$	56.2196			0.279700
$202$	−6.89640	+	6.89640i	−0.0341406	+	0.0341406i
$203$	228.377	+	228.377i	1.12501	+	1.12501i
$204$		−	17.5498i		−	0.0860283i
$205$	−92.2950	−	82.6743i	−0.450220	−	0.403289i
$206$	−177.057			−0.859502
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	0.898935	+	0.898935i	0.00432180	+	0.00432180i
$209$		−	153.039i		−	0.732244i
$210$	104.566	−	5.74961i	0.497933	−	0.0273791i
$211$	−126.385			−0.598980			−0.299490	−	0.954099i	$-0.596817\pi$
$211$	−126.385			−0.598980			−0.299490	+	0.954099i	$0.596817\pi$
$212$	67.1788	−	67.1788i	0.316881	−	0.316881i
$213$	26.2260	+	26.2260i	0.123127	+	0.123127i
$214$		−	174.722i		−	0.816456i
$215$	−7.51099	−	136.600i	−0.0349348	−	0.635347i
$216$	14.6969			0.0680414
$217$	69.5605	−	69.5605i	0.320555	−	0.320555i
$218$	8.33514	+	8.33514i	0.0382346	+	0.0382346i
$219$			62.0485i			0.283326i
$220$	40.2381	−	44.9206i	0.182900	−	0.204184i
$221$	−1.61014			−0.00728571
$222$	50.9111	−	50.9111i	0.229329	−	0.229329i
$223$	100.240	+	100.240i	0.449507	+	0.449507i	0.895191	−	0.445683i	$-0.147039\pi$
$223$	100.240	+	100.240i	0.449507	+	0.449507i	−0.445683	+	0.895191i	$0.647039\pi$
$224$			48.3699i			0.215937i
$225$	−74.5479	+	8.22296i	−0.331324	+	0.0365465i
$226$	−101.145			−0.447546
$227$	−260.102	+	260.102i	−1.14582	+	1.14582i	−0.158457	+	0.987366i	$0.550652\pi$
$227$	−260.102	+	260.102i	−1.14582	+	1.14582i	−0.987366	+	0.158457i	$0.949348\pi$
$228$	−62.1596	−	62.1596i	−0.272630	−	0.272630i
$229$		−	328.074i		−	1.43264i	−0.697773	−	0.716319i	$-0.745826\pi$
$229$		−	328.074i		−	1.43264i	0.697773	−	0.716319i	$-0.254174\pi$
$230$	25.2595	+	22.6265i	0.109824	+	0.0983760i
$231$	89.3162			0.386650
$232$	75.5436	−	75.5436i	0.325619	−	0.325619i
$233$	−133.968	−	133.968i	−0.574970	−	0.574970i	0.358543	−	0.933513i	$-0.383274\pi$
$233$	−133.968	−	133.968i	−0.574970	−	0.574970i	−0.933513	+	0.358543i	$0.883274\pi$
$234$		−	1.34840i		−	0.00576240i
$235$	41.4034	−	2.27659i	0.176185	−	0.00968760i
$236$	40.1038			0.169931
$237$	−10.7536	+	10.7536i	−0.0453738	+	0.0453738i
$238$	−43.3193	−	43.3193i	−0.182014	−	0.182014i
$239$		−	28.2933i		−	0.118382i	−0.998247	−	0.0591910i	$-0.981148\pi$
$239$		−	28.2933i		−	0.118382i	0.998247	−	0.0591910i	$-0.0188521\pi$
$240$	−1.90188	−	34.5888i	−0.00792450	−	0.144120i
$241$	−298.141			−1.23710			−0.618550	−	0.785746i	$-0.712279\pi$
$241$	−298.141			−1.23710			−0.618550	+	0.785746i	$0.712279\pi$
$242$	−84.6304	+	84.6304i	−0.349712	+	0.349712i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	20.9508i		−	0.0858637i
$245$	80.4464	−	89.8079i	0.328352	−	0.366563i
$246$	−60.7027			−0.246759
$247$	−5.70297	+	5.70297i	−0.0230890	+	0.0230890i
$248$	−23.0095	−	23.0095i	−0.0927804	−	0.0927804i
$249$		−	117.403i		−	0.471499i
$250$	28.9994	+	174.382i	0.115998	+	0.697527i
$251$	−338.924			−1.35030			−0.675148	−	0.737682i	$-0.735920\pi$
$251$	−338.924			−1.35030			−0.675148	+	0.737682i	$0.735920\pi$
$252$	36.2774	−	36.2774i	0.143958	−	0.143958i
$253$	20.4512	+	20.4512i	0.0808347	+	0.0808347i
$254$			342.629i			1.34893i
$255$	32.6804	+	29.2738i	0.128158	+	0.114799i
$256$	16.0000			0.0625000
$257$	166.864	−	166.864i	0.649277	−	0.649277i	−0.303541	−	0.952818i	$-0.598169\pi$
$257$	166.864	−	166.864i	0.649277	−	0.649277i	0.952818	+	0.303541i	$0.0981690\pi$
$258$	−47.3910	−	47.3910i	−0.183686	−	0.183686i
$259$		−	251.334i		−	0.970403i
$260$	−3.17342	+	0.174492i	−0.0122055	+	0.000671124i
$261$	−113.315			−0.434158
$262$	−9.31847	+	9.31847i	−0.0355667	+	0.0355667i
$263$	302.953	+	302.953i	1.15191	+	1.15191i	0.986169	+	0.165744i	$0.0530024\pi$
$263$	302.953	+	302.953i	1.15191	+	1.15191i	0.165744	+	0.986169i	$0.446998\pi$
$264$		−	29.5444i		−	0.111911i
$265$	13.0401	+	237.155i	0.0492078	+	0.894924i
$266$	−306.865			−1.15363
$267$	13.1488	−	13.1488i	0.0492466	−	0.0492466i
$268$	−45.9031	−	45.9031i	−0.171280	−	0.171280i
$269$		−	259.411i		−	0.964354i	−0.876074	−	0.482177i	$-0.839846\pi$
$269$		−	259.411i		−	0.964354i	0.876074	−	0.482177i	$-0.160154\pi$
$270$	−24.5152	+	27.3680i	−0.0907969	+	0.101363i
$271$	−430.196			−1.58744			−0.793719	−	0.608284i	$-0.791858\pi$
$271$	−430.196			−1.58744			−0.793719	+	0.608284i	$0.791858\pi$
$272$	−14.3293	+	14.3293i	−0.0526814	+	0.0526814i
$273$	−3.32835	−	3.32835i	−0.0121918	−	0.0121918i
$274$			216.794i			0.791218i
$275$	16.5301	+	149.859i	0.0601096	+	0.544942i
$276$	16.6132			0.0601929
$277$	−171.893	+	171.893i	−0.620553	+	0.620553i	−0.945673	−	0.325120i	$-0.894595\pi$
$277$	−171.893	+	171.893i	−0.620553	+	0.620553i	0.325120	+	0.945673i	$0.394595\pi$
$278$	126.720	+	126.720i	0.455827	+	0.455827i
$279$			34.5143i			0.123707i
$280$	−90.0723	−	80.6832i	−0.321687	−	0.288154i
$281$	349.790			1.24481			0.622403	−	0.782697i	$-0.286157\pi$
$281$	349.790			1.24481			0.622403	+	0.782697i	$0.286157\pi$
$282$	14.3642	−	14.3642i	0.0509370	−	0.0509370i
$283$	370.808	+	370.808i	1.31028	+	1.31028i	0.921210	+	0.389065i	$0.127202\pi$
$283$	370.808	+	370.808i	1.31028	+	1.31028i	0.389065	+	0.921210i	$0.372798\pi$
$284$		−	42.8268i		−	0.150799i
$285$	219.436	−	12.0658i	0.769951	−	0.0423361i
$286$	−2.71061			−0.00947767
$287$	−149.836	+	149.836i	−0.522078	+	0.522078i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			263.334i			0.911190i
$290$	14.6637	+	266.684i	0.0505646	+	0.919600i
$291$	−154.855			−0.532147
$292$	50.6624	−	50.6624i	0.173501	−	0.173501i
$293$	−50.6461	−	50.6461i	−0.172854	−	0.172854i	0.615378	−	0.788232i	$-0.289003\pi$
$293$	−50.6461	−	50.6461i	−0.172854	−	0.172854i	−0.788232	+	0.615378i	$0.789003\pi$
$294$		−	59.0669i		−	0.200908i
$295$	−66.8950	+	74.6795i	−0.226763	+	0.253151i
$296$	−83.1374			−0.280870
$297$	−22.1583	+	22.1583i	−0.0746070	+	0.0746070i
$298$	−61.5397	−	61.5397i	−0.206509	−	0.206509i
$299$		−	1.52422i		−	0.00509772i
$300$	67.5821	+	54.1541i	0.225274	+	0.180514i
$301$	−233.956			−0.777264
$302$	−100.953	+	100.953i	−0.334280	+	0.334280i
$303$	−8.44633	−	8.44633i	−0.0278757	−	0.0278757i
$304$			101.506i			0.333902i
$305$	39.0136	+	34.9468i	0.127913	+	0.114580i
$306$	21.4940			0.0702418
$307$	218.758	−	218.758i	0.712568	−	0.712568i	−0.254504	−	0.967072i	$-0.581912\pi$
$307$	218.758	−	218.758i	0.712568	−	0.712568i	0.967072	+	0.254504i	$0.0819121\pi$
$308$	−72.9263	−	72.9263i	−0.236774	−	0.236774i
$309$		−	216.850i		−	0.701781i
$310$	81.2283	−	4.46638i	0.262027	−	0.0144077i
$311$	162.318			0.521924			0.260962	−	0.965349i	$-0.415960\pi$
$311$	162.318			0.521924			0.260962	+	0.965349i	$0.415960\pi$
$312$	−1.10097	+	1.10097i	−0.00352874	+	0.00352874i
$313$	64.2791	+	64.2791i	0.205365	+	0.205365i	0.802294	−	0.596929i	$-0.203613\pi$
$313$	64.2791	+	64.2791i	0.205365	+	0.205365i	−0.596929	+	0.802294i	$0.703613\pi$
$314$			126.166i			0.401803i
$315$	7.04180	+	128.067i	0.0223549	+	0.406561i
$316$	17.5605			0.0555713
$317$	−340.744	+	340.744i	−1.07490	+	1.07490i	−0.0779433	+	0.996958i	$0.524835\pi$
$317$	−340.744	+	340.744i	−1.07490	+	1.07490i	−0.996958	+	0.0779433i	$0.975165\pi$
$318$	82.2769	+	82.2769i	0.258732	+	0.258732i
$319$			227.791i			0.714079i
$320$	−26.6887	+	29.7945i	−0.0834023	+	0.0931078i
$321$	213.989			0.666633
$322$	41.0076	−	41.0076i	0.127353	−	0.127353i
$323$	−90.9073	−	90.9073i	−0.281447	−	0.281447i
$324$			18.0000i			0.0555556i
$325$	4.96848	−	6.20047i	0.0152876	−	0.0190784i
$326$	−70.3034			−0.215655
$327$	−10.2084	+	10.2084i	−0.0312184	+	0.0312184i
$328$	49.5636	+	49.5636i	0.151108	+	0.151108i
$329$		−	70.9123i		−	0.215539i
$330$	55.0162	+	49.2814i	0.166716	+	0.149338i
$331$	−482.017			−1.45624			−0.728122	−	0.685447i	$-0.759607\pi$
$331$	−482.017			−1.45624			−0.728122	+	0.685447i	$0.759607\pi$
$332$	−95.8594	+	95.8594i	−0.288733	+	0.288733i
$333$	62.3531	+	62.3531i	0.187246	+	0.187246i
$334$		−	131.986i		−	0.395169i
$335$	162.047	−	8.91025i	0.483723	−	0.0265978i
$336$	−59.2408			−0.176312
$337$	299.309	−	299.309i	0.888158	−	0.888158i	−0.106188	−	0.994346i	$-0.533865\pi$
$337$	299.309	−	299.309i	0.888158	−	0.888158i	0.994346	+	0.106188i	$0.0338646\pi$
$338$	−168.899	−	168.899i	−0.499701	−	0.499701i
$339$		−	123.877i		−	0.365420i
$340$	−2.78146	−	50.5854i	−0.00818077	−	0.148781i
$341$	69.3821			0.203466
$342$	76.1297	−	76.1297i	0.222601	−	0.222601i
$343$	150.467	+	150.467i	0.438679	+	0.438679i
$344$			77.3891i			0.224968i
$345$	−27.7117	+	30.9365i	−0.0803236	+	0.0896709i
$346$	306.860			0.886880
$347$	−34.8305	+	34.8305i	−0.100376	+	0.100376i	−0.755512	−	0.655135i	$-0.772612\pi$
$347$	−34.8305	+	34.8305i	−0.100376	+	0.100376i	0.655135	+	0.755512i	$0.272612\pi$
$348$	92.5216	+	92.5216i	0.265867	+	0.265867i
$349$		−	455.518i		−	1.30521i	−0.757699	−	0.652604i	$-0.773676\pi$
$349$		−	455.518i		−	1.30521i	0.757699	−	0.652604i	$-0.226324\pi$
$350$	300.489	−	33.1453i	0.858541	−	0.0947009i
$351$	1.65145			0.00470498
$352$	−24.1229	+	24.1229i	−0.0685309	+	0.0685309i
$353$	31.7609	+	31.7609i	0.0899741	+	0.0899741i	0.750661	−	0.660687i	$-0.229735\pi$
$353$	31.7609	+	31.7609i	0.0899741	+	0.0899741i	−0.660687	+	0.750661i	$0.729735\pi$
$354$			49.1169i			0.138748i
$355$	79.7502	+	71.4371i	0.224648	+	0.201231i
$356$	−21.4720			−0.0603145
$357$	53.0550	−	53.0550i	0.148614	−	0.148614i
$358$	17.5087	+	17.5087i	0.0489069	+	0.0489069i
$359$			39.3142i			0.109510i	0.998500	+	0.0547551i	$0.0174378\pi$
$359$			39.3142i			0.109510i	−0.998500	+	0.0547551i	$0.982562\pi$
$360$	42.3624	−	2.32932i	0.117673	−	0.00647033i
$361$	−282.970			−0.783851
$362$	−345.567	+	345.567i	−0.954606	+	0.954606i
$363$	−103.651	−	103.651i	−0.285539	−	0.285539i
$364$			5.43517i			0.0149318i
$365$	9.83406	+	178.848i	0.0269426	+	0.489995i
$366$	25.6593			0.0701074
$367$	421.823	−	421.823i	1.14938	−	1.14938i	0.162708	−	0.986674i	$-0.447977\pi$
$367$	421.823	−	421.823i	1.14938	−	1.14938i	0.986674	−	0.162708i	$-0.0520227\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	74.3453i		−	0.201478i
$370$	138.677	−	154.815i	0.374803	−	0.418418i
$371$	406.179			1.09482
$372$	28.1808	−	28.1808i	0.0757549	−	0.0757549i
$373$	−324.873	−	324.873i	−0.870973	−	0.870973i	0.121605	−	0.992579i	$-0.461196\pi$
$373$	−324.873	−	324.873i	−0.870973	−	0.870973i	−0.992579	+	0.121605i	$0.961196\pi$
$374$		−	43.2081i		−	0.115530i
$375$	−213.573	+	35.5169i	−0.569529	+	0.0947118i
$376$	−23.4567			−0.0623848
$377$	8.48860	−	8.48860i	0.0225162	−	0.0225162i
$378$	44.4306	+	44.4306i	0.117541	+	0.117541i
$379$		−	188.177i		−	0.496509i	−0.968695	−	0.248255i	$-0.920143\pi$
$379$		−	188.177i		−	0.496509i	0.968695	−	0.248255i	$-0.0798570\pi$
$380$	−189.020	−	169.317i	−0.497422	−	0.445571i
$381$	−419.633			−1.10140
$382$	109.218	−	109.218i	0.285911	−	0.285911i
$383$	231.954	+	231.954i	0.605624	+	0.605624i	0.941799	−	0.336175i	$-0.109133\pi$
$383$	231.954	+	231.954i	0.605624	+	0.605624i	−0.336175	+	0.941799i	$0.609133\pi$
$384$			19.5959i			0.0510310i
$385$	257.445	−	14.1557i	0.668687	−	0.0367681i
$386$	48.0095			0.124377
$387$	58.0418	−	58.0418i	0.149979	−	0.149979i
$388$	126.438	+	126.438i	0.325872	+	0.325872i
$389$		−	645.912i		−	1.66044i	−0.557435	−	0.830220i	$-0.688214\pi$
$389$		−	645.912i		−	1.66044i	0.557435	−	0.830220i	$-0.311786\pi$
$390$	−0.213708	−	3.88663i	−0.000547970	−	0.00996572i
$391$	24.2966			0.0621395
$392$	−48.2279	+	48.2279i	−0.123030	+	0.123030i
$393$	−11.4127	−	11.4127i	−0.0290401	−	0.0290401i
$394$			283.768i			0.720223i
$395$	−29.2918	+	32.7005i	−0.0741564	+	0.0827860i
$396$	36.1843			0.0913746
$397$	−192.099	+	192.099i	−0.483877	+	0.483877i	−0.906367	−	0.422491i	$-0.861156\pi$
$397$	−192.099	+	192.099i	−0.483877	+	0.483877i	0.422491	+	0.906367i	$0.361156\pi$
$398$	176.579	+	176.579i	0.443665	+	0.443665i
$399$		−	375.832i		−	0.941935i
$400$	−10.9639	−	99.3971i	−0.0274099	−	0.248493i
$401$	143.800			0.358602			0.179301	−	0.983794i	$-0.442616\pi$
$401$	143.800			0.358602			0.179301	+	0.983794i	$0.442616\pi$
$402$	56.2196	−	56.2196i	0.139850	−	0.139850i
$403$	−2.58551	−	2.58551i	−0.00641566	−	0.00641566i
$404$			13.7928i			0.0341406i
$405$	−33.5188	−	30.0248i	−0.0827625	−	0.0741354i
$406$	456.754			1.12501
$407$	125.345	−	125.345i	0.307972	−	0.307972i
$408$	−17.5498	−	17.5498i	−0.0430142	−	0.0430142i
$409$			174.989i			0.427846i	0.976851	+	0.213923i	$0.0686241\pi$
$409$			174.989i			0.427846i	−0.976851	+	0.213923i	$0.931376\pi$
$410$	−174.969	+	9.62077i	−0.426754	+	0.0234653i
$411$	−265.517			−0.646027
$412$	−177.057	+	177.057i	−0.429751	+	0.429751i
$413$	121.239	+	121.239i	0.293556	+	0.293556i
$414$			20.3470i			0.0491473i
$415$	−18.6073	−	338.403i	−0.0448368	−	0.815429i
$416$	1.79787			0.00432180
$417$	−155.199	+	155.199i	−0.372181	+	0.372181i
$418$	−153.039	−	153.039i	−0.366122	−	0.366122i
$419$		−	677.602i		−	1.61719i	−0.588366	−	0.808595i	$-0.700229\pi$
$419$		−	677.602i		−	1.61719i	0.588366	−	0.808595i	$-0.299771\pi$
$420$	98.8163	−	110.316i	0.235277	−	0.262656i
$421$	−647.109			−1.53708			−0.768538	−	0.639805i	$-0.779015\pi$
$421$	−647.109			−1.53708			−0.768538	+	0.639805i	$0.779015\pi$
$422$	−126.385	+	126.385i	−0.299490	+	0.299490i
$423$	17.5925	+	17.5925i	0.0415899	+	0.0415899i
$424$		−	134.358i		−	0.316881i
$425$	98.8375	+	79.1993i	0.232559	+	0.186351i
$426$	52.4519			0.123127
$427$	63.3366	−	63.3366i	0.148329	−	0.148329i
$428$	−174.722	−	174.722i	−0.408228	−	0.408228i
$429$		−	3.31981i		−	0.00773849i
$430$	−144.111	−	129.089i	−0.335141	−	0.300206i
$431$	79.7599			0.185058			0.0925289	−	0.995710i	$-0.470505\pi$
$431$	79.7599			0.185058			0.0925289	+	0.995710i	$0.470505\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−32.7197	−	32.7197i	−0.0755652	−	0.0755652i	0.668314	−	0.743879i	$-0.267016\pi$
$433$	−32.7197	−	32.7197i	−0.0755652	−	0.0755652i	−0.743879	+	0.668314i	$0.767016\pi$
$434$		−	139.121i		−	0.320555i
$435$	−326.620	+	17.9594i	−0.750850	+	0.0412859i
$436$	16.6703			0.0382346
$437$	86.0561	−	86.0561i	0.196925	−	0.196925i
$438$	62.0485	+	62.0485i	0.141663	+	0.141663i
$439$		−	701.466i		−	1.59787i	−0.601416	−	0.798936i	$-0.705397\pi$
$439$		−	701.466i		−	1.59787i	0.601416	−	0.798936i	$-0.294603\pi$
$440$	−4.68249	−	85.1587i	−0.0106420	−	0.193542i
$441$	72.3419			0.164041
$442$	−1.61014	+	1.61014i	−0.00364286	+	0.00364286i
$443$	150.926	+	150.926i	0.340691	+	0.340691i	0.856627	−	0.515936i	$-0.172556\pi$
$443$	150.926	+	150.926i	0.340691	+	0.340691i	−0.515936	+	0.856627i	$0.672556\pi$
$444$		−	101.822i		−	0.229329i
$445$	35.8162	−	39.9841i	0.0804858	−	0.0898519i
$446$	200.480			0.449507
$447$	75.3704	−	75.3704i	0.168614	−	0.168614i
$448$	48.3699	+	48.3699i	0.107969	+	0.107969i
$449$		−	233.234i		−	0.519451i	−0.965682	−	0.259726i	$-0.916368\pi$
$449$		−	233.234i		−	0.519451i	0.965682	−	0.259726i	$-0.0836321\pi$
$450$	−66.3249	+	82.7708i	−0.147389	+	0.183935i
$451$	−149.452			−0.331379
$452$	−101.145	+	101.145i	−0.223773	+	0.223773i
$453$	−123.641	−	123.641i	−0.272938	−	0.272938i
$454$			520.204i			1.14582i
$455$	−10.1211	−	9.06612i	−0.0222443	−	0.0199255i
$456$	−124.319			−0.272630
$457$	323.809	−	323.809i	0.708554	−	0.708554i	−0.257677	−	0.966231i	$-0.582957\pi$
$457$	323.809	−	323.809i	0.708554	−	0.708554i	0.966231	+	0.257677i	$0.0829570\pi$
$458$	−328.074	−	328.074i	−0.716319	−	0.716319i
$459$			26.3247i			0.0573522i
$460$	47.8860	−	2.63303i	0.104100	−	0.00572399i
$461$	461.068			1.00015			0.500074	−	0.865983i	$-0.333306\pi$
$461$	461.068			1.00015			0.500074	+	0.865983i	$0.333306\pi$
$462$	89.3162	−	89.3162i	0.193325	−	0.193325i
$463$	168.651	+	168.651i	0.364258	+	0.364258i	0.865378	−	0.501120i	$-0.167079\pi$
$463$	168.651	+	168.651i	0.364258	+	0.364258i	−0.501120	+	0.865378i	$0.667079\pi$
$464$		−	151.087i		−	0.325619i
$465$	5.47017	+	99.4839i	0.0117638	+	0.213944i
$466$	−267.936			−0.574970
$467$	616.116	−	616.116i	1.31931	−	1.31931i	0.404980	−	0.914325i	$-0.367278\pi$
$467$	616.116	−	616.116i	1.31931	−	1.31931i	0.914325	−	0.404980i	$-0.132722\pi$
$468$	−1.34840	−	1.34840i	−0.00288120	−	0.00288120i
$469$		−	277.541i		−	0.591772i
$470$	39.1268	−	43.6800i	0.0832486	−	0.0929362i
$471$	−154.521			−0.328070
$472$	40.1038	−	40.1038i	0.0849657	−	0.0849657i
$473$	−116.678	−	116.678i	−0.246677	−	0.246677i
$474$			21.5072i			0.0453738i
$475$	630.590	−	69.5568i	1.32756	−	0.146435i
$476$	−86.6385			−0.182014
$477$	−100.768	+	100.768i	−0.211254	+	0.211254i
$478$	−28.2933	−	28.2933i	−0.0591910	−	0.0591910i
$479$		−	465.174i		−	0.971136i	−0.874199	−	0.485568i	$-0.838613\pi$
$479$		−	465.174i		−	0.971136i	0.874199	−	0.485568i	$-0.161387\pi$
$480$	−36.4906	−	32.6869i	−0.0760222	−	0.0680977i
$481$	−9.34189			−0.0194218
$482$	−298.141	+	298.141i	−0.618550	+	0.618550i
$483$	50.2238	+	50.2238i	0.103983	+	0.103983i
$484$			169.261i			0.349712i
$485$	−446.353	+	24.5429i	−0.920316	+	0.0506040i
$486$	−22.0454			−0.0453609
$487$	−326.491	+	326.491i	−0.670412	+	0.670412i	−0.957811	−	0.287399i	$-0.907209\pi$
$487$	−326.491	+	326.491i	−0.670412	+	0.670412i	0.287399	+	0.957811i	$0.407209\pi$
$488$	−20.9508	−	20.9508i	−0.0429319	−	0.0429319i
$489$		−	86.1038i		−	0.176081i
$490$	−9.36151	−	170.254i	−0.0191051	−	0.347458i
$491$	520.742			1.06057			0.530287	−	0.847818i	$-0.322084\pi$
$491$	520.742			1.06057			0.530287	+	0.847818i	$0.322084\pi$
$492$	−60.7027	+	60.7027i	−0.123379	+	0.123379i
$493$	135.311	+	135.311i	0.274465	+	0.274465i
$494$			11.4059i			0.0230890i
$495$	−60.3571	+	67.3809i	−0.121934	+	0.136123i
$496$	−46.0191			−0.0927804
$497$	129.471	−	129.471i	0.260504	−	0.260504i
$498$	−117.403	−	117.403i	−0.235750	−	0.235750i
$499$			153.945i			0.308506i	0.988031	+	0.154253i	$0.0492971\pi$
$499$			153.945i			0.308506i	−0.988031	+	0.154253i	$0.950703\pi$
$500$	203.381	+	145.382i	0.406763	+	0.290765i
$501$	161.650			0.322654
$502$	−338.924	+	338.924i	−0.675148	+	0.675148i
$503$	413.457	+	413.457i	0.821982	+	0.821982i	0.986392	−	0.164410i	$-0.0525721\pi$
$503$	413.457	+	413.457i	0.821982	+	0.821982i	−0.164410	+	0.986392i	$0.552572\pi$
$504$		−	72.5548i		−	0.143958i
$505$	−25.6843	−	23.0070i	−0.0508601	−	0.0455585i
$506$	40.9023			0.0808347
$507$	206.858	−	206.858i	0.408004	−	0.408004i
$508$	342.629	+	342.629i	0.674467	+	0.674467i
$509$		−	528.261i		−	1.03784i	−0.854823	−	0.518920i	$-0.826334\pi$
$509$		−	528.261i		−	1.03784i	0.854823	−	0.518920i	$-0.173666\pi$
$510$	61.9542	−	3.40658i	0.121479	−	0.00667957i
$511$	306.317			0.599445
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	93.2395	+	93.2395i	0.181753	+	0.181753i
$514$		−	333.729i		−	0.649277i
$515$	−34.3686	−	625.048i	−0.0667351	−	1.21369i
$516$	−94.7819			−0.183686
$517$	35.3652	−	35.3652i	0.0684046	−	0.0684046i
$518$	−251.334	−	251.334i	−0.485201	−	0.485201i
$519$			375.826i			0.724134i
$520$	−2.99893	+	3.34791i	−0.00576717	+	0.00643830i
$521$	630.082			1.20937			0.604685	−	0.796464i	$-0.293299\pi$
$521$	630.082			1.20937			0.604685	+	0.796464i	$0.293299\pi$
$522$	−113.315	+	113.315i	−0.217079	+	0.217079i
$523$	325.068	+	325.068i	0.621545	+	0.621545i	0.945927	−	0.324381i	$-0.105156\pi$
$523$	325.068	+	325.068i	0.621545	+	0.621545i	−0.324381	+	0.945927i	$0.605156\pi$
$524$			18.6369i			0.0355667i
$525$	40.5945	+	368.023i	0.0773229	+	0.700996i
$526$	605.906			1.15191
$527$	41.2139	−	41.2139i	0.0782047	−	0.0782047i
$528$	−29.5444	−	29.5444i	−0.0559553	−	0.0559553i
$529$			23.0000i			0.0434783i
$530$	250.195	+	224.115i	0.472066	+	0.422858i
$531$	−60.1557			−0.113288
$532$	−306.865	+	306.865i	−0.576815	+	0.576815i
$533$	5.56930	+	5.56930i	0.0104490	+	0.0104490i
$534$		−	26.2977i		−	0.0492466i
$535$	616.802	−	33.9152i	1.15290	−	0.0633928i
$536$	−91.8063			−0.171280
$537$	−21.4437	+	21.4437i	−0.0399323	+	0.0399323i
$538$	−259.411	−	259.411i	−0.482177	−	0.482177i
$539$		−	145.425i		−	0.269804i
$540$	2.85282	+	51.8832i	0.00528300	+	0.0960799i
$541$	242.869			0.448926			0.224463	−	0.974483i	$-0.427937\pi$
$541$	242.869			0.448926			0.224463	+	0.974483i	$0.427937\pi$
$542$	−430.196	+	430.196i	−0.793719	+	0.793719i
$543$	−423.232	−	423.232i	−0.779433	−	0.779433i
$544$			28.6587i			0.0526814i
$545$	−27.8068	+	31.0426i	−0.0510216	+	0.0569590i
$546$	−6.65670			−0.0121918
$547$	139.082	−	139.082i	0.254263	−	0.254263i	−0.568453	−	0.822716i	$-0.692458\pi$
$547$	139.082	−	139.082i	0.254263	−	0.254263i	0.822716	+	0.568453i	$0.192458\pi$
$548$	216.794	+	216.794i	0.395609	+	0.395609i
$549$			31.4261i			0.0572425i
$550$	166.389	+	133.329i	0.302526	+	0.242416i
$551$	958.518			1.73960
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	53.0876	+	53.0876i	0.0959992	+	0.0959992i
$554$			343.787i			0.620553i
$555$	189.609	+	169.844i	0.341637	+	0.306025i
$556$	253.440			0.455827
$557$	−501.877	+	501.877i	−0.901036	+	0.901036i	−0.995526	−	0.0944902i	$-0.969878\pi$
$557$	−501.877	+	501.877i	−0.901036	+	0.901036i	0.0944902	+	0.995526i	$0.469878\pi$
$558$	34.5143	+	34.5143i	0.0618536	+	0.0618536i
$559$			8.69597i			0.0155563i
$560$	−170.755	+	9.38907i	−0.304920	+	0.0167662i
$561$	52.9189			0.0943296
$562$	349.790	−	349.790i	0.622403	−	0.622403i
$563$	592.906	+	592.906i	1.05312	+	1.05312i	0.998508	+	0.0546116i	$0.0173921\pi$
$563$	592.906	+	592.906i	1.05312	+	1.05312i	0.0546116	+	0.998508i	$0.482608\pi$
$564$		−	28.7285i		−	0.0509370i
$565$	−19.6333	−	357.064i	−0.0347492	−	0.631971i
$566$	741.616			1.31028
$567$	−54.4161	+	54.4161i	−0.0959720	+	0.0959720i
$568$	−42.8268	−	42.8268i	−0.0753993	−	0.0753993i
$569$		−	204.295i		−	0.359043i	−0.983754	−	0.179521i	$-0.942545\pi$
$569$		−	204.295i		−	0.359043i	0.983754	−	0.179521i	$-0.0574549\pi$
$570$	207.370	−	231.502i	0.363807	−	0.406144i
$571$	106.932			0.187271			0.0936357	−	0.995607i	$-0.470151\pi$
$571$	106.932			0.187271			0.0936357	+	0.995607i	$0.470151\pi$
$572$	−2.71061	+	2.71061i	−0.00473884	+	0.00473884i
$573$	133.764	+	133.764i	0.233445	+	0.233445i
$574$			299.673i			0.522078i
$575$	−74.9729	+	93.5632i	−0.130388	+	0.162719i
$576$	−24.0000			−0.0416667
$577$	−258.933	+	258.933i	−0.448757	+	0.448757i	−0.894941	−	0.446184i	$-0.852783\pi$
$577$	−258.933	+	258.933i	−0.448757	+	0.448757i	0.446184	+	0.894941i	$0.352783\pi$
$578$	263.334	+	263.334i	0.455595	+	0.455595i
$579$			58.7993i			0.101553i
$580$	281.348	+	252.020i	0.485082	+	0.434518i
$581$	−579.589			−0.997571
$582$	−154.855	+	154.855i	−0.266074	+	0.266074i
$583$	202.568	+	202.568i	0.347459	+	0.347459i
$584$		−	101.325i		−	0.173501i
$585$	4.76013	−	0.261738i	0.00813698	−	0.000447416i
$586$	−101.292			−0.172854
$587$	−668.767	+	668.767i	−1.13930	+	1.13930i	−0.150719	+	0.988577i	$0.548159\pi$
$587$	−668.767	+	668.767i	−1.13930	+	1.13930i	−0.988577	+	0.150719i	$0.951841\pi$
$588$	−59.0669	−	59.0669i	−0.100454	−	0.100454i
$589$		−	291.952i		−	0.495673i
$590$	7.78454	+	141.574i	0.0131941	+	0.239957i
$591$	−347.543			−0.588059
$592$	−83.1374	+	83.1374i	−0.140435	+	0.140435i
$593$	31.4468	+	31.4468i	0.0530300	+	0.0530300i	0.733124	−	0.680094i	$-0.238061\pi$
$593$	31.4468	+	31.4468i	0.0530300	+	0.0530300i	−0.680094	+	0.733124i	$0.738061\pi$
$594$			44.3166i			0.0746070i
$595$	144.517	−	161.334i	0.242886	−	0.271150i
$596$	−123.079			−0.206509
$597$	−216.264	+	216.264i	−0.362251	+	0.362251i
$598$	−1.52422	−	1.52422i	−0.00254886	−	0.00254886i
$599$		−	789.984i		−	1.31884i	−0.751776	−	0.659419i	$-0.770802\pi$
$599$		−	789.984i		−	1.31884i	0.751776	−	0.659419i	$-0.229198\pi$
$600$	121.736	−	13.4280i	0.202894	−	0.0223801i
$601$	490.719			0.816503			0.408252	−	0.912869i	$-0.366139\pi$
$601$	490.719			0.816503			0.408252	+	0.912869i	$0.366139\pi$
$602$	−233.956	+	233.956i	−0.388632	+	0.388632i
$603$	68.8547	+	68.8547i	0.114187	+	0.114187i
$604$			201.905i			0.334280i
$605$	−315.190	−	282.335i	−0.520975	−	0.466669i
$606$	−16.8927			−0.0278757
$607$	268.721	−	268.721i	0.442703	−	0.442703i	−0.450216	−	0.892920i	$-0.648653\pi$
$607$	268.721	−	268.721i	0.442703	−	0.442703i	0.892920	+	0.450216i	$0.148653\pi$
$608$	101.506	+	101.506i	0.166951	+	0.166951i
$609$			559.408i			0.918567i
$610$	73.9604	−	4.06675i	0.121247	−	0.00666680i
$611$	−2.63575			−0.00431384
$612$	21.4940	−	21.4940i	0.0351209	−	0.0351209i
$613$	754.006	+	754.006i	1.23003	+	1.23003i	0.963953	+	0.266073i	$0.0857261\pi$
$613$	754.006	+	754.006i	1.23003	+	1.23003i	0.266073	+	0.963953i	$0.414274\pi$
$614$		−	437.517i		−	0.712568i
$615$	−11.7830	−	214.293i	−0.0191593	−	0.348444i
$616$	−145.853			−0.236774
$617$	−577.903	+	577.903i	−0.936634	+	0.936634i	−0.998109	−	0.0614748i	$-0.980420\pi$
$617$	−577.903	+	577.903i	−0.936634	+	0.936634i	0.0614748	+	0.998109i	$0.480420\pi$
$618$	−216.850	−	216.850i	−0.350890	−	0.350890i
$619$		−	71.5819i		−	0.115641i	−0.998327	−	0.0578206i	$-0.981585\pi$
$619$		−	71.5819i		−	0.115641i	0.998327	−	0.0578206i	$-0.0184151\pi$
$620$	76.7619	−	85.6947i	0.123810	−	0.138217i
$621$	−24.9199			−0.0401286
$622$	162.318	−	162.318i	0.260962	−	0.260962i
$623$	−64.9123	−	64.9123i	−0.104193	−	0.104193i
$624$			2.20193i			0.00352874i
$625$	−609.974	+	136.223i	−0.975958	+	0.217957i
$626$	128.558			0.205365
$627$	187.434	−	187.434i	0.298937	−	0.298937i
$628$	126.166	+	126.166i	0.200901	+	0.200901i
$629$		−	148.913i		−	0.236746i
$630$	135.108	+	121.025i	0.214458	+	0.192103i
$631$	568.739			0.901330			0.450665	−	0.892693i	$-0.351187\pi$
$631$	568.739			0.901330			0.450665	+	0.892693i	$0.351187\pi$
$632$	17.5605	−	17.5605i	0.0277857	−	0.0277857i
$633$	−154.789	−	154.789i	−0.244533	−	0.244533i
$634$			681.487i			1.07490i
$635$	−1209.55	+	66.5077i	−1.90480	+	0.104736i
$636$	164.554			0.258732
$637$	−5.41922	+	5.41922i	−0.00850741	+	0.00850741i
$638$	227.791	+	227.791i	0.357039	+	0.357039i
$639$			64.2402i			0.100532i
$640$	3.10576	+	56.4832i	0.00485275	+	0.0882550i
$641$	−1051.81			−1.64089			−0.820445	−	0.571726i	$-0.806274\pi$
$641$	−1051.81			−1.64089			−0.820445	+	0.571726i	$0.806274\pi$
$642$	213.989	−	213.989i	0.333317	−	0.333317i
$643$	−64.6780	−	64.6780i	−0.100588	−	0.100588i	0.655022	−	0.755610i	$-0.272659\pi$
$643$	−64.6780	−	64.6780i	−0.100588	−	0.100588i	−0.755610	+	0.655022i	$0.772659\pi$
$644$		−	82.0151i		−	0.127353i
$645$	158.101	−	176.499i	0.245117	−	0.273641i
$646$	−181.815			−0.281447
$647$	682.188	−	682.188i	1.05439	−	1.05439i	0.0559524	−	0.998433i	$-0.482181\pi$
$647$	682.188	−	682.188i	1.05439	−	1.05439i	0.998433	−	0.0559524i	$-0.0178195\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			120.927i			0.186329i
$650$	−1.23198	−	11.1689i	−0.00189536	−	0.0171830i
$651$	170.388			0.261732
$652$	−70.3034	+	70.3034i	−0.107827	+	0.107827i
$653$	−740.977	−	740.977i	−1.13473	−	1.13473i	−0.989381	−	0.145346i	$-0.953571\pi$
$653$	−740.977	−	740.977i	−1.13473	−	1.13473i	−0.145346	−	0.989381i	$-0.546429\pi$
$654$			20.4168i			0.0312184i
$655$	−34.7049	−	31.0873i	−0.0529845	−	0.0474615i
$656$	99.1271			0.151108
$657$	−75.9935	+	75.9935i	−0.115667	+	0.115667i
$658$	−70.9123	−	70.9123i	−0.107770	−	0.107770i
$659$			985.952i			1.49613i	0.663623	+	0.748067i	$0.269018\pi$
$659$			985.952i			1.49613i	−0.663623	+	0.748067i	$0.730982\pi$
$660$	104.298	−	5.73485i	0.158027	−	0.00868917i
$661$	649.680			0.982875			0.491438	−	0.870913i	$-0.336472\pi$
$661$	649.680			0.982875			0.491438	+	0.870913i	$0.336472\pi$
$662$	−482.017	+	482.017i	−0.728122	+	0.728122i
$663$	−1.97201	−	1.97201i	−0.00297438	−	0.00297438i
$664$			191.719i			0.288733i
$665$	−59.5656	−	1083.30i	−0.0895723	−	1.62902i
$666$	124.706			0.187246
$667$	−128.090	+	128.090i	−0.192040	+	0.192040i
$668$	−131.986	−	131.986i	−0.197584	−	0.197584i
$669$			245.537i			0.367021i
$670$	153.137	−	170.958i	0.228563	−	0.255160i
$671$	63.1741			0.0941492
$672$	−59.2408	+	59.2408i	−0.0881559	+	0.0881559i
$673$	634.795	+	634.795i	0.943232	+	0.943232i	0.998473	−	0.0552411i	$-0.0175927\pi$
$673$	634.795	+	634.795i	0.943232	+	0.943232i	−0.0552411	+	0.998473i	$0.517593\pi$
$674$		−	598.618i		−	0.888158i
$675$	−101.373	−	81.2311i	−0.150182	−	0.120342i
$676$	−337.798			−0.499701
$677$	−500.696	+	500.696i	−0.739580	+	0.739580i	−0.972497	−	0.232916i	$-0.925173\pi$
$677$	−500.696	+	500.696i	−0.739580	+	0.739580i	0.232916	+	0.972497i	$0.425173\pi$
$678$	−123.877	−	123.877i	−0.182710	−	0.182710i
$679$			764.477i			1.12589i
$680$	−53.3669	−	47.8040i	−0.0784807	−	0.0702999i
$681$	−637.117			−0.935560
$682$	69.3821	−	69.3821i	0.101733	−	0.101733i
$683$	−457.846	−	457.846i	−0.670345	−	0.670345i	0.287450	−	0.957796i	$-0.407192\pi$
$683$	−457.846	−	457.846i	−0.670345	−	0.670345i	−0.957796	+	0.287450i	$0.907192\pi$
$684$		−	152.259i		−	0.222601i
$685$	−765.325	+	42.0818i	−1.11726	+	0.0614333i
$686$	300.934			0.438679
$687$	401.807	−	401.807i	0.584872	−	0.584872i
$688$	77.3891	+	77.3891i	0.112484	+	0.112484i
$689$		−	15.0974i		−	0.0219120i
$690$	3.22479	+	58.6481i	0.00467361	+	0.0849973i
$691$	182.546			0.264176			0.132088	−	0.991238i	$-0.457832\pi$
$691$	182.546			0.264176			0.132088	+	0.991238i	$0.457832\pi$
$692$	306.860	−	306.860i	0.443440	−	0.443440i
$693$	109.390	+	109.390i	0.157849	+	0.157849i
$694$			69.6610i			0.100376i
$695$	−422.749	+	471.944i	−0.608272	+	0.679056i
$696$	185.043			0.265867
$697$	−88.7766	+	88.7766i	−0.127370	+	0.127370i
$698$	−455.518	−	455.518i	−0.652604	−	0.652604i
$699$		−	328.153i		−	0.469461i
$700$	267.344	−	333.635i	0.381920	−	0.476621i
$701$	336.087			0.479440			0.239720	−	0.970842i	$-0.422944\pi$
$701$	336.087			0.479440			0.239720	+	0.970842i	$0.422944\pi$
$702$	1.65145	−	1.65145i	0.00235249	−	0.00235249i
$703$	−527.436	−	527.436i	−0.750264	−	0.750264i
$704$			48.2458i			0.0685309i
$705$	53.4969	+	47.9204i	0.0758821	+	0.0679722i
$706$	63.5217			0.0899741
$707$	−41.6973	+	41.6973i	−0.0589777	+	0.0589777i
$708$	49.1169	+	49.1169i	0.0693742	+	0.0693742i
$709$			607.338i			0.856612i	0.903634	+	0.428306i	$0.140890\pi$
$709$			607.338i			0.856612i	−0.903634	+	0.428306i	$0.859110\pi$
$710$	151.187	−	8.31310i	0.212940	−	0.0117086i
$711$	−26.3408			−0.0370475
$712$	−21.4720	+	21.4720i	−0.0301572	+	0.0301572i
$713$	39.0146	+	39.0146i	0.0547189	+	0.0547189i
$714$		−	106.110i		−	0.148614i
$715$	−0.526157	−	9.56901i	−0.000735884	−	0.0133832i
$716$	35.0174			0.0489069
$717$	34.6521	−	34.6521i	0.0483293	−	0.0483293i
$718$	39.3142	+	39.3142i	0.0547551	+	0.0547551i
$719$			916.546i			1.27475i	0.770553	+	0.637376i	$0.219980\pi$
$719$			916.546i			1.27475i	−0.770553	+	0.637376i	$0.780020\pi$
$720$	40.0331	−	44.6917i	0.0556015	−	0.0620719i
$721$	−1070.53			−1.48479
$722$	−282.970	+	282.970i	−0.391926	+	0.391926i
$723$	−365.147	−	365.147i	−0.505044	−	0.505044i
$724$			691.135i			0.954606i
$725$	−938.602	+	103.532i	−1.29462	+	0.142803i
$726$	−207.301			−0.285539
$727$	246.536	−	246.536i	0.339114	−	0.339114i	−0.516920	−	0.856034i	$-0.672922\pi$
$727$	246.536	−	246.536i	0.339114	−	0.339114i	0.856034	+	0.516920i	$0.172922\pi$
$728$	5.43517	+	5.43517i	0.00746590	+	0.00746590i
$729$		−	27.0000i		−	0.0370370i
$730$	188.682	+	169.014i	0.258469	+	0.231526i
$731$	−138.617			−0.189626
$732$	25.6593	−	25.6593i	0.0350537	−	0.0350537i
$733$	730.190	+	730.190i	0.996166	+	0.996166i	0.999993	−	0.00382636i	$-0.00121797\pi$
$733$	730.190	+	730.190i	0.996166	+	0.996166i	−0.00382636	+	0.999993i	$0.501218\pi$
$734$		−	843.646i		−	1.14938i
$735$	208.518	−	11.4655i	0.283698	−	0.0155993i
$736$	−27.1293			−0.0368605
$737$	138.414	−	138.414i	0.187808	−	0.187808i
$738$	−74.3453	−	74.3453i	−0.100739	−	0.100739i
$739$			865.300i			1.17091i	0.810706	+	0.585453i	$0.199083\pi$
$739$			865.300i			1.17091i	−0.810706	+	0.585453i	$0.800917\pi$
$740$	−16.1378	−	293.492i	−0.0218078	−	0.396611i
$741$	−13.9694			−0.0188521
$742$	406.179	−	406.179i	0.547411	−	0.547411i
$743$	791.656	+	791.656i	1.06549	+	1.06549i	0.997700	+	0.0677859i	$0.0215935\pi$
$743$	791.656	+	791.656i	1.06549	+	1.06549i	0.0677859	+	0.997700i	$0.478407\pi$
$744$		−	56.3616i		−	0.0757549i
$745$	205.302	−	229.193i	0.275573	−	0.307641i
$746$	−649.746			−0.870973
$747$	143.789	−	143.789i	0.192489	−	0.192489i
$748$	−43.2081	−	43.2081i	−0.0577648	−	0.0577648i
$749$		−	1056.41i		−	1.41042i
$750$	−178.056	+	249.090i	−0.237408	+	0.332120i
$751$	1140.21			1.51825			0.759125	−	0.650944i	$-0.225627\pi$
$751$	1140.21			1.51825			0.759125	+	0.650944i	$0.225627\pi$
$752$	−23.4567	+	23.4567i	−0.0311924	+	0.0311924i
$753$	−415.096	−	415.096i	−0.551256	−	0.551256i
$754$		−	16.9772i		−	0.0225162i
$755$	−375.979	−	336.787i	−0.497985	−	0.446075i
$756$	88.8612			0.117541
$757$	171.242	−	171.242i	0.226212	−	0.226212i	−0.584896	−	0.811108i	$-0.698865\pi$
$757$	171.242	−	171.242i	0.226212	−	0.226212i	0.811108	+	0.584896i	$0.198865\pi$
$758$	−188.177	−	188.177i	−0.248255	−	0.248255i
$759$			50.0949i			0.0660012i
$760$	−358.338	+	19.7034i	−0.471497	+	0.0259255i
$761$	82.4693			0.108370			0.0541848	−	0.998531i	$-0.482744\pi$
$761$	82.4693			0.108370			0.0541848	+	0.998531i	$0.482744\pi$
$762$	−419.633	+	419.633i	−0.550700	+	0.550700i
$763$	50.3962	+	50.3962i	0.0660501	+	0.0660501i
$764$		−	218.436i		−	0.285911i
$765$	4.17220	+	75.8781i	0.00545385	+	0.0991871i
$766$	463.908			0.605624
$767$	4.50634	−	4.50634i	0.00587528	−	0.00587528i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	643.087i		−	0.836264i	−0.908386	−	0.418132i	$-0.862685\pi$
$769$		−	643.087i		−	0.836264i	0.908386	−	0.418132i	$-0.137315\pi$
$770$	243.289	−	271.600i	0.315960	−	0.352728i
$771$	408.732			0.530133
$772$	48.0095	−	48.0095i	0.0621884	−	0.0621884i
$773$	−815.269	−	815.269i	−1.05468	−	1.05468i	−0.998416	−	0.0562666i	$-0.982080\pi$
$773$	−815.269	−	815.269i	−1.05468	−	1.05468i	−0.0562666	−	0.998416i	$-0.517920\pi$
$774$		−	116.084i		−	0.149979i
$775$	31.5344	+	285.885i	0.0406896	+	0.368884i
$776$	252.877			0.325872
$777$	307.820	−	307.820i	0.396165	−	0.396165i
$778$	−645.912	−	645.912i	−0.830220	−	0.830220i
$779$			628.876i			0.807287i
$780$	−4.10034	−	3.67292i	−0.00525685	−	0.00470888i
$781$	129.138			0.165350
$782$	24.2966	−	24.2966i	0.0310698	−	0.0310698i
$783$	−138.782	−	138.782i	−0.177244	−	0.177244i
$784$			96.4558i			0.123030i
$785$	−445.391	+	24.4901i	−0.567378	+	0.0311975i
$786$	−22.8255			−0.0290401
$787$	410.159	−	410.159i	0.521168	−	0.521168i	−0.396756	−	0.917924i	$-0.629864\pi$
$787$	410.159	−	410.159i	0.521168	−	0.521168i	0.917924	+	0.396756i	$0.129864\pi$
$788$	283.768	+	283.768i	0.360111	+	0.360111i
$789$			742.080i			0.940533i
$790$	3.40867	+	61.9922i	0.00431478	+	0.0784712i
$791$	−611.549			−0.773134
$792$	36.1843	−	36.1843i	0.0456873	−	0.0456873i
$793$	−2.35417	−	2.35417i	−0.00296869	−	0.00296869i
$794$			384.198i			0.483877i
$795$	−274.483	+	306.425i	−0.345262	+	0.385440i
$796$	353.157			0.443665
$797$	−274.683	+	274.683i	−0.344646	+	0.344646i	−0.858111	−	0.513465i	$-0.828362\pi$
$797$	−274.683	+	274.683i	−0.344646	+	0.344646i	0.513465	+	0.858111i	$0.328362\pi$
$798$	−375.832	−	375.832i	−0.470967	−	0.470967i
$799$		−	42.0148i		−	0.0525843i
$800$	−110.361	−	88.4332i	−0.137951	−	0.110541i
$801$	32.2079			0.0402096
$802$	143.800	−	143.800i	0.179301	−	0.179301i
$803$	152.765	+	152.765i	0.190243	+	0.190243i
$804$		−	112.439i		−	0.139850i
$805$	152.725	+	136.805i	0.189720	+	0.169944i
$806$	−5.17102			−0.00641566
$807$	317.712	−	317.712i	0.393696	−	0.393696i
$808$	13.7928	+	13.7928i	0.0170703	+	0.0170703i
$809$		−	1089.04i		−	1.34616i	−0.739569	−	0.673080i	$-0.764971\pi$
$809$		−	1089.04i		−	1.34616i	0.739569	−	0.673080i	$-0.235029\pi$
$810$	−63.5436	+	3.49398i	−0.0784489	+	0.00431355i
$811$	−396.301			−0.488657			−0.244329	−	0.969693i	$-0.578568\pi$
$811$	−396.301			−0.488657			−0.244329	+	0.969693i	$0.578568\pi$
$812$	456.754	−	456.754i	0.562505	−	0.562505i
$813$	−526.880	−	526.880i	−0.648069	−	0.648069i
$814$		−	250.689i		−	0.307972i
$815$	−13.6466	−	248.185i	−0.0167443	−	0.304522i
$816$	−35.0995			−0.0430142
$817$	−490.967	+	490.967i	−0.600939	+	0.600939i
$818$	174.989	+	174.989i	0.213923	+	0.213923i
$819$		−	8.15276i		−	0.00995453i
$820$	−165.349	+	184.590i	−0.201645	+	0.225110i
$821$	−771.453			−0.939651			−0.469825	−	0.882759i	$-0.655683\pi$
$821$	−771.453			−0.939651			−0.469825	+	0.882759i	$0.655683\pi$
$822$	−265.517	+	265.517i	−0.323013	+	0.323013i
$823$	−1097.89	−	1097.89i	−1.33401	−	1.33401i	−0.901744	−	0.432271i	$-0.857712\pi$
$823$	−1097.89	−	1097.89i	−1.33401	−	1.33401i	−0.432271	−	0.901744i	$-0.642288\pi$
$824$			354.115i			0.429751i
$825$	−163.294	+	203.784i	−0.197932	+	0.247011i
$826$	242.477			0.293556
$827$	324.200	−	324.200i	0.392020	−	0.392020i	−0.483387	−	0.875407i	$-0.660594\pi$
$827$	324.200	−	324.200i	0.392020	−	0.392020i	0.875407	+	0.483387i	$0.160594\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	749.329i		−	0.903895i	−0.892045	−	0.451947i	$-0.850729\pi$
$829$		−	749.329i		−	0.903895i	0.892045	−	0.451947i	$-0.149271\pi$
$830$	−357.010	−	319.796i	−0.430133	−	0.385296i
$831$	−421.051			−0.506680
$832$	1.79787	−	1.79787i	0.00216090	−	0.00216090i
$833$	−86.3842	−	86.3842i	−0.103703	−	0.103703i
$834$			310.399i			0.372181i
$835$	465.938	−	25.6198i	0.558010	−	0.0306824i
$836$	−306.078			−0.366122
$837$	−42.2712	+	42.2712i	−0.0505032	+	0.0505032i
$838$	−677.602	−	677.602i	−0.808595	−	0.808595i
$839$			1522.91i			1.81514i	0.419897	+	0.907572i	$0.362066\pi$
$839$			1522.91i			1.81514i	−0.419897	+	0.907572i	$0.637934\pi$
$840$	−11.4992	−	209.132i	−0.0136895	−	0.248967i
$841$	−585.708			−0.696442
$842$	−647.109	+	647.109i	−0.768538	+	0.768538i
$843$	428.404	+	428.404i	0.508190	+	0.508190i
$844$			252.770i			0.299490i
$845$	563.462	−	629.032i	0.666820	−	0.744417i
$846$	35.1850			0.0415899
$847$	−511.695	+	511.695i	−0.604127	+	0.604127i
$848$	−134.358	−	134.358i	−0.158441	−	0.158441i
$849$			908.290i			1.06984i
$850$	178.037	−	19.6383i	0.209455	−	0.0231038i
$851$	140.966			0.165648
$852$	52.4519	−	52.4519i	0.0615633	−	0.0615633i
$853$	897.399	+	897.399i	1.05205	+	1.05205i	0.998569	+	0.0534821i	$0.0170320\pi$
$853$	897.399	+	897.399i	1.05205	+	1.05205i	0.0534821	+	0.998569i	$0.482968\pi$
$854$		−	126.673i		−	0.148329i
$855$	283.531	+	253.976i	0.331615	+	0.297048i
$856$	−349.443			−0.408228
$857$	−627.513	+	627.513i	−0.732220	+	0.732220i	−0.971059	−	0.238839i	$-0.923233\pi$
$857$	−627.513	+	627.513i	−0.732220	+	0.732220i	0.238839	+	0.971059i	$0.423233\pi$
$858$	−3.31981	−	3.31981i	−0.00386924	−	0.00386924i
$859$			692.193i			0.805813i	0.915241	+	0.402906i	$0.132000\pi$
$859$			692.193i			0.805813i	−0.915241	+	0.402906i	$0.868000\pi$
$860$	−273.199	+	15.0220i	−0.317673	+	0.0174674i
$861$	−367.023			−0.426275
$862$	79.7599	−	79.7599i	0.0925289	−	0.0925289i
$863$	−193.607	−	193.607i	−0.224341	−	0.224341i	0.585982	−	0.810324i	$-0.300709\pi$
$863$	−193.607	−	193.607i	−0.224341	−	0.224341i	−0.810324	+	0.585982i	$0.800709\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	59.5646	+	1083.28i	0.0688608	+	1.25235i
$866$	−65.4395			−0.0755652
$867$	−322.517	+	322.517i	−0.371992	+	0.371992i
$868$	−139.121	−	139.121i	−0.160278	−	0.160278i
$869$			52.9514i			0.0609337i
$870$	−308.661	+	344.579i	−0.354782	+	0.396068i
$871$	−10.3160			−0.0118438
$872$	16.6703	−	16.6703i	0.0191173	−	0.0191173i
$873$	−189.658	−	189.658i	−0.217248	−	0.217248i
$874$		−	172.112i		−	0.196925i
$875$	175.338	+	1054.35i	0.200386	+	1.20498i
$876$	124.097			0.141663
$877$	477.056	−	477.056i	0.543964	−	0.543964i	−0.380725	−	0.924688i	$-0.624325\pi$
$877$	477.056	−	477.056i	0.543964	−	0.543964i	0.924688	+	0.380725i	$0.124325\pi$
$878$	−701.466	−	701.466i	−0.798936	−	0.798936i
$879$		−	124.057i		−	0.141134i
$880$	−89.8411	−	80.4762i	−0.102092	−	0.0914502i
$881$	−193.133			−0.219220			−0.109610	−	0.993975i	$-0.534960\pi$
$881$	−193.133			−0.219220			−0.109610	+	0.993975i	$0.534960\pi$
$882$	72.3419	−	72.3419i	0.0820203	−	0.0820203i
$883$	−278.043	−	278.043i	−0.314885	−	0.314885i	0.531914	−	0.846799i	$-0.321473\pi$
$883$	−278.043	−	278.043i	−0.314885	−	0.314885i	−0.846799	+	0.531914i	$0.821473\pi$
$884$			3.22028i			0.00364286i
$885$	−173.393	+	9.53407i	−0.195924	+	0.0107730i
$886$	301.852			0.340691
$887$	556.774	−	556.774i	0.627704	−	0.627704i	−0.319786	−	0.947490i	$-0.603611\pi$
$887$	556.774	−	556.774i	0.627704	−	0.627704i	0.947490	+	0.319786i	$0.103611\pi$
$888$	−101.822	−	101.822i	−0.114665	−	0.114665i
$889$			2071.62i			2.33028i
$890$	−4.16792	−	75.8003i	−0.00468305	−	0.0851689i
$891$	−54.2765			−0.0609164
$892$	200.480	−	200.480i	0.224754	−	0.224754i
$893$	−148.813	−	148.813i	−0.166643	−	0.166643i
$894$		−	150.741i		−	0.168614i
$895$	−58.4106	+	65.2078i	−0.0652632	+	0.0728578i
$896$	96.7398			0.107969
$897$	1.86678	−	1.86678i	0.00208114	−	0.00208114i
$898$	−233.234	−	233.234i	−0.259726	−	0.259726i
$899$			434.556i			0.483377i
$900$	16.4459	+	149.096i	0.0182732	+	0.165662i
$901$	240.657			0.267100
$902$	−149.452	+	149.452i	−0.165690	+	0.165690i
$903$	−286.537	−	286.537i	−0.317317	−	0.317317i
$904$			202.291i			0.223773i
$905$	−1287.00	−	1152.84i	−1.42210	−	1.27386i
$906$	−247.282			−0.272938
$907$	−241.525	+	241.525i	−0.266290	+	0.266290i	−0.827604	−	0.561313i	$-0.810296\pi$
$907$	−241.525	+	241.525i	−0.266290	+	0.266290i	0.561313	+	0.827604i	$0.310296\pi$
$908$	520.204	+	520.204i	0.572911	+	0.572911i
$909$		−	20.6892i		−	0.0227604i
$910$	−19.1873	+	1.05502i	−0.0210849	+	0.00115936i
$911$	−614.690			−0.674742			−0.337371	−	0.941372i	$-0.609538\pi$
$911$	−614.690			−0.674742			−0.337371	+	0.941372i	$0.609538\pi$
$912$	−124.319	+	124.319i	−0.136315	+	0.136315i
$913$	−289.051	−	289.051i	−0.316595	−	0.316595i
$914$		−	647.619i		−	0.708554i
$915$	4.98073	+	90.5826i	0.00544342	+	0.0989974i
$916$	−656.148			−0.716319
$917$	−56.3417	+	56.3417i	−0.0614413	+	0.0614413i
$918$	26.3247	+	26.3247i	0.0286761	+	0.0286761i
$919$		−	555.649i		−	0.604623i	−0.953209	−	0.302312i	$-0.902242\pi$
$919$		−	555.649i		−	0.604623i	0.953209	−	0.302312i	$-0.0977583\pi$
$920$	45.2529	−	50.5190i	0.0491880	−	0.0549120i
$921$	535.847			0.581809
$922$	461.068	−	461.068i	0.500074	−	0.500074i
$923$	−4.81231	−	4.81231i	−0.00521378	−	0.00521378i
$924$		−	178.632i		−	0.193325i
$925$	573.446	+	459.507i	0.619942	+	0.496764i
$926$	337.303			0.364258
$927$	265.586	−	265.586i	0.286501	−	0.286501i
$928$	−151.087	−	151.087i	−0.162809	−	0.162809i
$929$			1272.33i			1.36957i	0.728743	+	0.684787i	$0.240105\pi$
$929$			1272.33i			1.36957i	−0.728743	+	0.684787i	$0.759895\pi$
$930$	104.954	+	94.0138i	0.112854	+	0.101090i
$931$	−611.929			−0.657282
$932$	−267.936	+	267.936i	−0.287485	+	0.287485i
$933$	198.798	+	198.798i	0.213074	+	0.213074i
$934$		−	1232.23i		−	1.31931i
$935$	152.533	−	8.38712i	0.163137	−	0.00897018i
$936$	−2.69681			−0.00288120
$937$	191.429	−	191.429i	0.204300	−	0.204300i	−0.597539	−	0.801840i	$-0.703855\pi$
$937$	191.429	−	191.429i	0.204300	−	0.204300i	0.801840	+	0.597539i	$0.203855\pi$
$938$	−277.541	−	277.541i	−0.295886	−	0.295886i
$939$			157.451i			0.167680i
$940$	−4.55317	−	82.8068i	−0.00484380	−	0.0880924i
$941$	603.570			0.641414			0.320707	−	0.947179i	$-0.396080\pi$
$941$	603.570			0.641414			0.320707	+	0.947179i	$0.396080\pi$
$942$	−154.521	+	154.521i	−0.164035	+	0.164035i
$943$	−84.0391	−	84.0391i	−0.0891189	−	0.0891189i
$944$		−	80.2076i		−	0.0849657i
$945$	−148.224	+	165.473i	−0.156851	+	0.175104i
$946$	−233.356			−0.246677
$947$	−528.634	+	528.634i	−0.558219	+	0.558219i	−0.928800	−	0.370581i	$-0.879159\pi$
$947$	−528.634	+	528.634i	−0.558219	+	0.558219i	0.370581	+	0.928800i	$0.379159\pi$
$948$	21.5072	+	21.5072i	0.0226869	+	0.0226869i
$949$		−	11.3855i		−	0.0119974i
$950$	561.033	−	700.146i	0.590561	−	0.736996i
$951$	−834.648			−0.877653
$952$	−86.6385	+	86.6385i	−0.0910069	+	0.0910069i
$953$	−10.8666	−	10.8666i	−0.0114025	−	0.0114025i	0.701383	−	0.712785i	$-0.252566\pi$
$953$	−10.8666	−	10.8666i	−0.0114025	−	0.0114025i	−0.712785	+	0.701383i	$0.752566\pi$
$954$			201.536i			0.211254i
$955$	406.762	+	364.361i	0.425929	+	0.381530i
$956$	−56.5866			−0.0591910
$957$	−278.986	+	278.986i	−0.291521	+	0.291521i
$958$	−465.174	−	465.174i	−0.485568	−	0.485568i
$959$			1310.79i			1.36683i
$960$	−69.1775	+	3.80376i	−0.0720599	+	0.00396225i
$961$	−828.640			−0.862269
$962$	−9.34189	+	9.34189i	−0.00971091	+	0.00971091i
$963$	262.082	+	262.082i	0.272152	+	0.272152i
$964$			596.282i			0.618550i
$965$	9.31911	+	169.483i	0.00965711	+	0.175630i
$966$	100.448			0.103983
$967$	781.887	−	781.887i	0.808570	−	0.808570i	−0.175847	−	0.984417i	$-0.556266\pi$
$967$	781.887	−	781.887i	0.808570	−	0.808570i	0.984417	+	0.175847i	$0.0562665\pi$
$968$	169.261	+	169.261i	0.174856	+	0.174856i
$969$		−	222.677i		−	0.229800i
$970$	−421.810	+	470.896i	−0.434856	+	0.485460i
$971$	−756.547			−0.779142			−0.389571	−	0.920996i	$-0.627377\pi$
$971$	−756.547			−0.779142			−0.389571	+	0.920996i	$0.627377\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	766.178	+	766.178i	0.787439	+	0.787439i
$974$			652.981i			0.670412i
$975$	13.6791	−	1.50887i	0.0140299	−	0.00154756i
$976$	−41.9015			−0.0429319
$977$	207.633	−	207.633i	0.212521	−	0.212521i	−0.592817	−	0.805338i	$-0.701984\pi$
$977$	207.633	−	207.633i	0.212521	−	0.212521i	0.805338	+	0.592817i	$0.201984\pi$
$978$	−86.1038	−	86.1038i	−0.0880407	−	0.0880407i
$979$		−	64.7457i		−	0.0661345i
$980$	−179.616	−	160.893i	−0.183281	−	0.164176i
$981$	−25.0054			−0.0254897
$982$	520.742	−	520.742i	0.530287	−	0.530287i
$983$	986.181	+	986.181i	1.00324	+	1.00324i	0.999995	+	0.00324109i	$0.00103167\pi$
$983$	986.181	+	986.181i	1.00324	+	1.00324i	0.00324109	+	0.999995i	$0.498968\pi$
$984$			121.405i			0.123379i
$985$	−1001.76	+	55.0821i	−1.01701	+	0.0559209i
$986$	270.622			0.274465
$987$	86.8495	−	86.8495i	0.0879934	−	0.0879934i
$988$	11.4059	+	11.4059i	0.0115445	+	0.0115445i
$989$		−	131.220i		−	0.132679i
$990$	7.02373	+	127.738i	0.00709468	+	0.129028i
$991$	−1417.92			−1.43080			−0.715398	−	0.698717i	$-0.753755\pi$
$991$	−1417.92			−1.43080			−0.715398	+	0.698717i	$0.753755\pi$
$992$	−46.0191	+	46.0191i	−0.0463902	+	0.0463902i
$993$	−590.348	−	590.348i	−0.594509	−	0.594509i
$994$		−	258.941i		−	0.260504i
$995$	−589.083	+	657.634i	−0.592043	+	0.660939i
$996$	−234.807			−0.235750
$997$	−1322.30	+	1322.30i	−1.32628	+	1.32628i	−0.417696	+	0.908587i	$0.637162\pi$
$997$	−1322.30	+	1322.30i	−1.32628	+	1.32628i	−0.908587	+	0.417696i	$0.862838\pi$
$998$	153.945	+	153.945i	0.154253	+	0.154253i
$999$			152.733i			0.152886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.13	yes	40
5.2	odd	4	inner	690.3.k.a.277.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.13	✓	40	5.2	odd	4	inner
690.3.k.a.553.13	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.72431 + 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 - 6.04624i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.72431 + 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 - 6.04624i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(7.06040 - 0.388220i) q^{10} +6.03072 q^{11} +(2.44949 - 2.44949i) q^{12} +(-0.224734 - 0.224734i) q^{13} -12.0925i q^{14} +(0.475470 + 8.64719i) q^{15} -4.00000 q^{16} +(3.58233 - 3.58233i) q^{17} +(3.00000 + 3.00000i) q^{18} -25.3766i q^{19} +(6.67218 - 7.44862i) q^{20} +14.8102 q^{21} +(6.03072 - 6.03072i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(2.74099 + 24.8493i) q^{25} -0.449468 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-12.0925 - 12.0925i) q^{28} +37.7718i q^{29} +(9.12266 + 8.17172i) q^{30} +11.5048 q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.38610 + 7.38610i) q^{33} -7.16467i q^{34} +(42.6889 - 2.34727i) q^{35} +6.00000 q^{36} +(20.7844 - 20.7844i) q^{37} +(-25.3766 - 25.3766i) q^{38} -0.550483i q^{39} +(-0.776439 - 14.1208i) q^{40} -24.7818 q^{41} +(14.8102 - 14.8102i) q^{42} +(-19.3473 - 19.3473i) q^{43} -12.0614i q^{44} +(-10.0083 + 11.1729i) q^{45} +6.78233 q^{46} +(5.86417 - 5.86417i) q^{47} +(-4.89898 - 4.89898i) q^{48} -24.1140i q^{49} +(27.5903 + 22.1083i) q^{50} +8.77489 q^{51} +(-0.449468 + 0.449468i) q^{52} +(33.5894 + 33.5894i) q^{53} +7.34847i q^{54} +(22.4603 + 20.1190i) q^{55} -24.1849 q^{56} +(31.0798 - 31.0798i) q^{57} +(37.7718 + 37.7718i) q^{58} +20.0519i q^{59} +(17.2944 - 0.950940i) q^{60} +10.4754 q^{61} +(11.5048 - 11.5048i) q^{62} +(18.1387 + 18.1387i) q^{63} +8.00000i q^{64} +(-0.0872461 - 1.58671i) q^{65} +14.7722 q^{66} +(22.9516 - 22.9516i) q^{67} +(-7.16467 - 7.16467i) q^{68} +8.30662i q^{69} +(40.3416 - 45.0361i) q^{70} +21.4134 q^{71} +(6.00000 - 6.00000i) q^{72} +(25.3312 + 25.3312i) q^{73} -41.5687i q^{74} +(-27.0770 + 33.7910i) q^{75} -50.7531 q^{76} +(36.4632 - 36.4632i) q^{77} +(-0.550483 - 0.550483i) q^{78} +8.78027i q^{79} +(-14.8972 - 13.3444i) q^{80} -9.00000 q^{81} +(-24.7818 + 24.7818i) q^{82} +(-47.9297 - 47.9297i) q^{83} -29.6204i q^{84} +(25.2927 - 1.39073i) q^{85} -38.6945 q^{86} +(-46.2608 + 46.2608i) q^{87} +(-12.0614 - 12.0614i) q^{88} -10.7360i q^{89} +(1.16466 + 21.1812i) q^{90} -2.71759 q^{91} +(6.78233 - 6.78233i) q^{92} +(14.0904 + 14.0904i) q^{93} -11.7283i q^{94} +(84.6586 - 94.5102i) q^{95} -9.79796 q^{96} +(-63.2192 + 63.2192i) q^{97} +(-24.1140 - 24.1140i) q^{98} +18.0922i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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