LMFDB - Embedded newform 670.2.h.c.439.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.14
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -3.40294i q^{3} +(0.500000 - 0.866025i) q^{4} +(1.60001 + 1.56204i) q^{5} +(-1.70147 - 2.94703i) q^{6} +(3.81692 + 2.20370i) q^{7} -1.00000i q^{8} -8.57997 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -3.40294i q^{3} +(0.500000 - 0.866025i) q^{4} +(1.60001 + 1.56204i) q^{5} +(-1.70147 - 2.94703i) q^{6} +(3.81692 + 2.20370i) q^{7} -1.00000i q^{8} -8.57997 q^{9} +(2.16667 + 0.552755i) q^{10} +(2.26790 - 3.92812i) q^{11} +(-2.94703 - 1.70147i) q^{12} +(-0.389955 + 0.225141i) q^{13} +4.40740 q^{14} +(5.31551 - 5.44475i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.11307 + 1.21998i) q^{17} +(-7.43048 + 4.28999i) q^{18} +(-2.49163 - 4.31562i) q^{19} +(2.15277 - 0.604635i) q^{20} +(7.49905 - 12.9887i) q^{21} -4.53580i q^{22} +(1.81352 - 1.04704i) q^{23} -3.40294 q^{24} +(0.120090 + 4.99856i) q^{25} +(-0.225141 + 0.389955i) q^{26} +18.9883i q^{27} +(3.81692 - 2.20370i) q^{28} +(2.33332 - 4.04144i) q^{29} +(1.88099 - 7.37304i) q^{30} +(-3.84677 + 6.66281i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-13.3671 - 7.71752i) q^{33} +(-1.21998 + 2.11307i) q^{34} +(2.66487 + 9.48811i) q^{35} +(-4.28999 + 7.43048i) q^{36} +(-2.64170 + 1.52519i) q^{37} +(-4.31562 - 2.49163i) q^{38} +(0.766139 + 1.32699i) q^{39} +(1.56204 - 1.60001i) q^{40} +(-2.68395 + 4.64874i) q^{41} -14.9981i q^{42} +1.96768i q^{43} +(-2.26790 - 3.92812i) q^{44} +(-13.7281 - 13.4022i) q^{45} +(1.04704 - 1.81352i) q^{46} +(7.39586 + 4.27000i) q^{47} +(-2.94703 + 1.70147i) q^{48} +(6.21258 + 10.7605i) q^{49} +(2.60328 + 4.26883i) q^{50} +(4.15153 + 7.19066i) q^{51} +0.450281i q^{52} +6.26671i q^{53} +(9.49415 + 16.4443i) q^{54} +(9.76454 - 2.74251i) q^{55} +(2.20370 - 3.81692i) q^{56} +(-14.6858 + 8.47885i) q^{57} -4.66665i q^{58} +4.27352 q^{59} +(-2.05753 - 7.32574i) q^{60} +(-6.76479 - 11.7170i) q^{61} +7.69355i q^{62} +(-32.7491 - 18.9077i) q^{63} -1.00000 q^{64} +(-0.975611 - 0.248895i) q^{65} -15.4350 q^{66} +(-1.54633 - 8.03796i) q^{67} +2.43997i q^{68} +(-3.56300 - 6.17129i) q^{69} +(7.05190 + 6.88451i) q^{70} +(-6.40231 + 11.0891i) q^{71} +8.57997i q^{72} +(-2.02350 + 1.16827i) q^{73} +(-1.52519 + 2.64170i) q^{74} +(17.0098 - 0.408660i) q^{75} -4.98325 q^{76} +(17.3128 - 9.99554i) q^{77} +(1.32699 + 0.766139i) q^{78} +(1.65104 - 2.85968i) q^{79} +(0.552755 - 2.16667i) q^{80} +38.8760 q^{81} +5.36790i q^{82} +(0.769075 - 0.444026i) q^{83} +(-7.49905 - 12.9887i) q^{84} +(-5.28661 - 1.34871i) q^{85} +(0.983840 + 1.70406i) q^{86} +(-13.7527 - 7.94015i) q^{87} +(-3.92812 - 2.26790i) q^{88} +0.369395 q^{89} +(-18.5900 - 4.74263i) q^{90} -1.98457 q^{91} -2.09407i q^{92} +(22.6731 + 13.0903i) q^{93} +8.54001 q^{94} +(2.75452 - 10.7971i) q^{95} +(-1.70147 + 2.94703i) q^{96} +(-4.39125 + 2.53529i) q^{97} +(10.7605 + 6.21258i) q^{98} +(-19.4585 + 33.7032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		−	3.40294i		−	1.96469i	−0.187089	−	0.982343i	$-0.559905\pi$
$3$		−	3.40294i		−	1.96469i	0.187089	−	0.982343i	$-0.440095\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.60001	+	1.56204i	0.715548	+	0.698563i
$5$	1.60001	+	1.56204i	0.715548	+	0.698563i
$6$	−1.70147	−	2.94703i	−0.694621	−	1.20312i
$7$	3.81692	+	2.20370i	1.44266	+	0.832920i	0.998027	−	0.0627930i	$-0.0200008\pi$
$7$	3.81692	+	2.20370i	1.44266	+	0.832920i	0.444633	+	0.895713i	$0.353334\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−8.57997			−2.85999
$10$	2.16667	+	0.552755i	0.685161	+	0.174797i
$11$	2.26790	−	3.92812i	0.683798	−	1.18437i	−0.290015	−	0.957022i	$-0.593660\pi$
$11$	2.26790	−	3.92812i	0.683798	−	1.18437i	0.973813	−	0.227351i	$-0.0730064\pi$
$12$	−2.94703	−	1.70147i	−0.850734	−	0.491172i
$13$	−0.389955	+	0.225141i	−0.108154	+	0.0624428i	−0.553101	−	0.833114i	$-0.686556\pi$
$13$	−0.389955	+	0.225141i	−0.108154	+	0.0624428i	0.444947	+	0.895557i	$0.353222\pi$
$14$	4.40740			1.17793
$15$	5.31551	−	5.44475i	1.37246	−	1.40583i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.11307	+	1.21998i	−0.512496	+	0.295890i	−0.733859	−	0.679302i	$-0.762283\pi$
$17$	−2.11307	+	1.21998i	−0.512496	+	0.295890i	0.221363	+	0.975191i	$0.428949\pi$
$18$	−7.43048	+	4.28999i	−1.75138	+	1.01116i
$19$	−2.49163	−	4.31562i	−0.571618	−	0.990072i	−0.996400	−	0.0847763i	$-0.972982\pi$
$19$	−2.49163	−	4.31562i	−0.571618	−	0.990072i	0.424782	−	0.905296i	$-0.360351\pi$
$20$	2.15277	−	0.604635i	0.481374	−	0.135201i
$21$	7.49905	−	12.9887i	1.63643	−	2.83437i
$22$		−	4.53580i		−	0.967037i
$23$	1.81352	−	1.04704i	0.378145	−	0.218322i	−0.298866	−	0.954295i	$-0.596608\pi$
$23$	1.81352	−	1.04704i	0.378145	−	0.218322i	0.677011	+	0.735973i	$0.263275\pi$
$24$	−3.40294			−0.694621
$25$	0.120090	+	4.99856i	0.0240181	+	0.999712i
$26$	−0.225141	+	0.389955i	−0.0441537	+	0.0764765i
$27$			18.9883i			3.65430i
$28$	3.81692	−	2.20370i	0.721330	−	0.416460i
$29$	2.33332	−	4.04144i	0.433287	−	0.750476i	−0.563867	−	0.825866i	$-0.690687\pi$
$29$	2.33332	−	4.04144i	0.433287	−	0.750476i	0.997154	+	0.0753900i	$0.0240202\pi$
$30$	1.88099	−	7.37304i	0.343420	−	1.34613i
$31$	−3.84677	+	6.66281i	−0.690901	+	1.19668i	0.280642	+	0.959813i	$0.409453\pi$
$31$	−3.84677	+	6.66281i	−0.690901	+	1.19668i	−0.971543	+	0.236863i	$0.923881\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−13.3671	−	7.71752i	−2.32692	−	1.34345i
$34$	−1.21998	+	2.11307i	−0.209226	+	0.362389i
$35$	2.66487	+	9.48811i	0.450445	+	1.60378i
$36$	−4.28999	+	7.43048i	−0.714998	+	1.23841i
$37$	−2.64170	+	1.52519i	−0.434293	+	0.250739i	−0.701174	−	0.712990i	$-0.747340\pi$
$37$	−2.64170	+	1.52519i	−0.434293	+	0.250739i	0.266881	+	0.963730i	$0.414007\pi$
$38$	−4.31562	−	2.49163i	−0.700087	−	0.404195i
$39$	0.766139	+	1.32699i	0.122680	+	0.212489i
$40$	1.56204	−	1.60001i	0.246979	−	0.252984i
$41$	−2.68395	+	4.64874i	−0.419162	+	0.726010i	−0.995855	−	0.0909504i	$-0.971010\pi$
$41$	−2.68395	+	4.64874i	−0.419162	+	0.726010i	0.576693	+	0.816961i	$0.304343\pi$
$42$		−	14.9981i		−	2.31426i
$43$			1.96768i			0.300069i	0.988681	+	0.150034i	$0.0479384\pi$
$43$			1.96768i			0.300069i	−0.988681	+	0.150034i	$0.952062\pi$
$44$	−2.26790	−	3.92812i	−0.341899	−	0.592187i
$45$	−13.7281	−	13.4022i	−2.04646	−	1.99789i
$46$	1.04704	−	1.81352i	0.154377	−	0.267389i
$47$	7.39586	+	4.27000i	1.07880	+	0.622844i	0.930572	−	0.366109i	$-0.119310\pi$
$47$	7.39586	+	4.27000i	1.07880	+	0.622844i	0.148226	+	0.988954i	$0.452644\pi$
$48$	−2.94703	+	1.70147i	−0.425367	+	0.245586i
$49$	6.21258	+	10.7605i	0.887511	+	1.53721i
$50$	2.60328	+	4.26883i	0.368159	+	0.603704i
$51$	4.15153	+	7.19066i	0.581330	+	1.00689i
$52$			0.450281i			0.0624428i
$53$			6.26671i			0.860799i	0.902638	+	0.430400i	$0.141627\pi$
$53$			6.26671i			0.860799i	−0.902638	+	0.430400i	$0.858373\pi$
$54$	9.49415	+	16.4443i	1.29199	+	2.23779i
$55$	9.76454	−	2.74251i	1.31665	−	0.369799i
$56$	2.20370	−	3.81692i	0.294482	−	0.510057i
$57$	−14.6858	+	8.47885i	−1.94518	+	1.12305i
$58$		−	4.66665i		−	0.612761i
$59$	4.27352			0.556365			0.278183	−	0.960528i	$-0.410268\pi$
$59$	4.27352			0.556365			0.278183	+	0.960528i	$0.410268\pi$
$60$	−2.05753	−	7.32574i	−0.265627	−	0.945749i
$61$	−6.76479	−	11.7170i	−0.866142	−	1.50020i	−0.865909	−	0.500202i	$-0.833259\pi$
$61$	−6.76479	−	11.7170i	−0.866142	−	1.50020i	−0.000233415	−	1.00000i	$-0.500074\pi$
$62$			7.69355i			0.977082i
$63$	−32.7491	−	18.9077i	−4.12599	−	2.38214i
$64$	−1.00000			−0.125000
$65$	−0.975611	−	0.248895i	−0.121010	−	0.0308717i
$66$	−15.4350			−1.89992
$67$	−1.54633	−	8.03796i	−0.188915	−	0.981994i
$67$	−1.54633	−	8.03796i	−0.188915	−	0.981994i
$68$			2.43997i			0.295890i
$69$	−3.56300	−	6.17129i	−0.428934	−	0.742936i
$70$	7.05190	+	6.88451i	0.842863	+	0.822857i
$71$	−6.40231	+	11.0891i	−0.759814	+	1.31604i	0.183131	+	0.983089i	$0.441377\pi$
$71$	−6.40231	+	11.0891i	−0.759814	+	1.31604i	−0.942945	+	0.332948i	$0.891957\pi$
$72$			8.57997i			1.01116i
$73$	−2.02350	+	1.16827i	−0.236833	+	0.136735i	−0.613720	−	0.789524i	$-0.710328\pi$
$73$	−2.02350	+	1.16827i	−0.236833	+	0.136735i	0.376887	+	0.926259i	$0.376994\pi$
$74$	−1.52519	+	2.64170i	−0.177299	+	0.307091i
$75$	17.0098	−	0.408660i	1.96412	−	0.0471880i
$76$	−4.98325			−0.571618
$77$	17.3128	−	9.99554i	1.97298	−	1.13910i
$78$	1.32699	+	0.766139i	0.150252	+	0.0867482i
$79$	1.65104	−	2.85968i	0.185756	−	0.321739i	−0.758075	−	0.652167i	$-0.773860\pi$
$79$	1.65104	−	2.85968i	0.185756	−	0.321739i	0.943831	+	0.330429i	$0.107193\pi$
$80$	0.552755	−	2.16667i	0.0617999	−	0.242241i
$81$	38.8760			4.31956
$82$			5.36790i			0.592785i
$83$	0.769075	−	0.444026i	0.0844169	−	0.0487381i	−0.457197	−	0.889365i	$-0.651147\pi$
$83$	0.769075	−	0.444026i	0.0844169	−	0.0487381i	0.541614	+	0.840627i	$0.317813\pi$
$84$	−7.49905	−	12.9887i	−0.818213	−	1.41719i
$85$	−5.28661	−	1.34871i	−0.573413	−	0.146288i
$86$	0.983840	+	1.70406i	0.106090	+	0.183754i
$87$	−13.7527	−	7.94015i	−1.47445	−	0.851274i
$88$	−3.92812	−	2.26790i	−0.418739	−	0.241759i
$89$	0.369395			0.0391558			0.0195779	−	0.999808i	$-0.493768\pi$
$89$	0.369395			0.0391558			0.0195779	+	0.999808i	$0.493768\pi$
$90$	−18.5900	−	4.74263i	−1.95956	−	0.499917i
$91$	−1.98457			−0.208039
$92$		−	2.09407i		−	0.218322i
$93$	22.6731	+	13.0903i	2.35109	+	1.35740i
$94$	8.54001			0.880835
$95$	2.75452	−	10.7971i	0.282608	−	1.10776i
$96$	−1.70147	+	2.94703i	−0.173655	+	0.300780i
$97$	−4.39125	+	2.53529i	−0.445864	+	0.257420i	−0.706082	−	0.708130i	$-0.749539\pi$
$97$	−4.39125	+	2.53529i	−0.445864	+	0.257420i	0.260218	+	0.965550i	$0.416206\pi$
$98$	10.7605	+	6.21258i	1.08697	+	0.627565i
$99$	−19.4585	+	33.7032i	−1.95566	+	3.38730i
$100$	4.38892	+	2.39528i	0.438892	+	0.239528i
$101$	0.433705	−	0.751199i	0.0431552	−	0.0747471i	−0.843641	−	0.536908i	$-0.819592\pi$
$101$	0.433705	−	0.751199i	0.0431552	−	0.0747471i	0.886796	+	0.462161i	$0.152926\pi$
$102$	7.19066	+	4.15153i	0.711981	+	0.411062i
$103$	0.327342	+	0.188991i	0.0322540	+	0.0186218i	0.516040	−	0.856564i	$-0.327405\pi$
$103$	0.327342	+	0.188991i	0.0322540	+	0.0186218i	−0.483786	+	0.875186i	$0.660739\pi$
$104$	0.225141	+	0.389955i	0.0220769	+	0.0382382i
$105$	32.2874	−	9.06837i	3.15093	−	0.884983i
$106$	3.13336	+	5.42713i	0.304338	+	0.527130i
$107$		−	2.01104i		−	0.194414i	−0.995264	−	0.0972071i	$-0.969009\pi$
$107$		−	2.01104i		−	0.194414i	0.995264	−	0.0972071i	$-0.0309909\pi$
$108$	16.4443	+	9.49415i	1.58236	+	0.913575i
$109$	16.4326			1.57395			0.786977	−	0.616982i	$-0.211645\pi$
$109$	16.4326			1.57395			0.786977	+	0.616982i	$0.211645\pi$
$110$	7.08509	−	7.25735i	0.675536	−	0.691961i
$111$	5.19011	+	8.98954i	0.492624	+	0.853249i
$112$		−	4.40740i		−	0.416460i
$113$	13.0979	+	7.56209i	1.23215	+	0.711382i	0.967478	−	0.252957i	$-0.0814031\pi$
$113$	13.0979	+	7.56209i	1.23215	+	0.711382i	0.264672	+	0.964339i	$0.414736\pi$
$114$	−8.47885	+	14.6858i	−0.794117	+	1.37545i
$115$	4.53716	+	1.15751i	0.423093	+	0.107938i
$116$	−2.33332	−	4.04144i	−0.216644	−	0.375238i
$117$	3.34580	−	1.93170i	0.309320	−	0.178586i
$118$	3.70098	−	2.13676i	0.340703	−	0.196705i
$119$	−10.7539			−0.985809
$120$	−5.44475	−	5.31551i	−0.497035	−	0.485237i
$121$	−4.78676	−	8.29090i	−0.435160	−	0.753719i
$122$	−11.7170	−	6.76479i	−1.06080	−	0.612455i
$123$	15.8193	+	9.13331i	1.42638	+	0.823522i
$124$	3.84677	+	6.66281i	0.345451	+	0.598338i
$125$	−7.61578	+	8.18535i	−0.681176	+	0.732120i
$126$	−37.8154			−3.36886
$127$	−0.528460	−	0.305106i	−0.0468932	−	0.0270738i	0.476370	−	0.879245i	$-0.341952\pi$
$127$	−0.528460	−	0.305106i	−0.0468932	−	0.0270738i	−0.523263	+	0.852171i	$0.675286\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	6.69589			0.589540
$130$	−0.969352	+	0.272256i	−0.0850178	+	0.0238784i
$131$	−3.17980			−0.277820			−0.138910	−	0.990305i	$-0.544360\pi$
$131$	−3.17980			−0.277820			−0.138910	+	0.990305i	$0.544360\pi$
$132$	−13.3671	+	7.71752i	−1.16346	+	0.671724i
$133$		−	21.9632i		−	1.90445i
$134$	−5.35815	−	6.18791i	−0.462873	−	0.534554i
$135$	−29.6604	+	30.3815i	−2.55276	+	2.61483i
$136$	1.21998	+	2.11307i	0.104613	+	0.181195i
$137$			0.310910i			0.0265628i	0.999912	+	0.0132814i	$0.00422773\pi$
$137$			0.310910i			0.0265628i	−0.999912	+	0.0132814i	$0.995772\pi$
$138$	−6.17129	−	3.56300i	−0.525335	−	0.303302i
$139$	8.53284			0.723746			0.361873	−	0.932227i	$-0.382137\pi$
$139$	8.53284			0.723746			0.361873	+	0.932227i	$0.382137\pi$
$140$	9.54938	+	2.43621i	0.807070	+	0.205898i
$141$	14.5305	−	25.1677i	1.22369	−	2.11950i
$142$			12.8046i			1.07454i
$143$			2.04239i			0.170793i
$144$	4.28999	+	7.43048i	0.357499	+	0.619206i
$145$	10.0462	−	2.82162i	0.834293	−	0.234323i
$146$	−1.16827	+	2.02350i	−0.0966866	+	0.167466i
$147$	36.6173	−	21.1410i	3.02014	−	1.74368i
$148$			3.05037i			0.250739i
$149$	−7.07581			−0.579673			−0.289836	−	0.957076i	$-0.593601\pi$
$149$	−7.07581			−0.579673			−0.289836	+	0.957076i	$0.593601\pi$
$150$	14.5266	−	8.85880i	1.18609	−	0.723318i
$151$	−6.28522	−	10.8863i	−0.511484	−	0.885916i	−0.999911	−	0.0133115i	$-0.995763\pi$
$151$	−6.28522	−	10.8863i	−0.511484	−	0.885916i	0.488428	−	0.872604i	$-0.337571\pi$
$152$	−4.31562	+	2.49163i	−0.350043	+	0.202098i
$153$	18.1301	−	10.4674i	1.46573	−	0.846242i
$154$	9.99554	−	17.3128i	0.805464	−	1.39510i
$155$	−16.5624	+	4.65179i	−1.33033	+	0.373641i
$156$	1.53228			0.122680
$157$	−12.0758	+	6.97195i	−0.963751	+	0.556422i	−0.897325	−	0.441369i	$-0.854493\pi$
$157$	−12.0758	+	6.97195i	−0.963751	+	0.556422i	−0.0664256	+	0.997791i	$0.521160\pi$
$158$		−	3.30207i		−	0.262699i
$159$	21.3252			1.69120
$160$	−0.604635	−	2.15277i	−0.0478006	−	0.170191i
$161$	9.22940			0.727379
$162$	33.6676	−	19.4380i	2.64518	−	1.52719i
$163$	−3.17714	−	1.83432i	−0.248853	−	0.143675i	0.370386	−	0.928878i	$-0.379225\pi$
$163$	−3.17714	−	1.83432i	−0.248853	−	0.143675i	−0.619239	+	0.785203i	$0.712559\pi$
$164$	2.68395	+	4.64874i	0.209581	+	0.363005i
$165$	−9.33257	−	33.2281i	−0.726540	−	2.58680i
$166$	0.444026	−	0.769075i	0.0344631	−	0.0596918i
$167$	−0.696630	−	0.402199i	−0.0539068	−	0.0311231i	0.472804	−	0.881167i	$-0.343242\pi$
$167$	−0.696630	−	0.402199i	−0.0539068	−	0.0311231i	−0.526711	+	0.850044i	$0.676575\pi$
$168$	−12.9887	−	7.49905i	−1.00210	−	0.578564i
$169$	−6.39862	+	11.0827i	−0.492202	+	0.852519i
$170$	−5.25269	+	1.47529i	−0.402863	+	0.113150i
$171$	21.3781	+	37.0279i	1.63482	+	2.83160i
$172$	1.70406	+	0.983840i	0.129933	+	0.0750171i
$173$	−4.60713	+	2.65993i	−0.350273	+	0.202230i	−0.664806	−	0.747016i	$-0.731486\pi$
$173$	−4.60713	+	2.65993i	−0.350273	+	0.202230i	0.314532	+	0.949247i	$0.398152\pi$
$174$	−15.8803			−1.20388
$175$	−10.5569	+	19.3437i	−0.798030	+	1.46225i
$176$	−4.53580			−0.341899
$177$		−	14.5425i		−	1.09308i
$178$	0.319906	−	0.184698i	0.0239779	−	0.0138437i
$179$	−7.16762			−0.535733			−0.267867	−	0.963456i	$-0.586319\pi$
$179$	−7.16762			−0.535733			−0.267867	+	0.963456i	$0.586319\pi$
$180$	−18.4707	+	5.18775i	−1.37673	+	0.386672i
$181$	9.08025	−	15.7275i	0.674930	−	1.16901i	−0.301560	−	0.953447i	$-0.597507\pi$
$181$	9.08025	−	15.7275i	0.674930	−	1.16901i	0.976489	−	0.215565i	$-0.0691594\pi$
$182$	−1.71869	+	0.992285i	−0.127398	+	0.0735530i
$183$	−39.8720	+	23.0201i	−2.94743	+	1.70170i
$184$	−1.04704	−	1.81352i	−0.0771885	−	0.133694i
$185$	−6.60915	−	1.68611i	−0.485915	−	0.123965i
$186$	26.1807			1.91966
$187$			11.0672i			0.809315i
$188$	7.39586	−	4.27000i	0.539399	−	0.311422i
$189$	−41.8445	+	72.4768i	−3.04374	+	5.27191i
$190$	−3.01305	−	10.7278i	−0.218590	−	0.778276i
$191$	−10.5336	−	18.2447i	−0.762182	−	1.32014i	−0.941724	−	0.336388i	$-0.890795\pi$
$191$	−10.5336	−	18.2447i	−0.762182	−	1.32014i	0.179542	−	0.983750i	$-0.442539\pi$
$192$			3.40294i			0.245586i
$193$		−	10.2632i		−	0.738758i	−0.929279	−	0.369379i	$-0.879570\pi$
$193$		−	10.2632i		−	0.738758i	0.929279	−	0.369379i	$-0.120430\pi$
$194$	−2.53529	+	4.39125i	−0.182023	+	0.315274i
$195$	−0.846975	+	3.31994i	−0.0606532	+	0.237746i
$196$	12.4252			0.887511
$197$	4.59395	+	2.65232i	0.327305	+	0.188970i	0.654644	−	0.755937i	$-0.272818\pi$
$197$	4.59395	+	2.65232i	0.327305	+	0.188970i	−0.327339	+	0.944907i	$0.606152\pi$
$198$			38.9171i			2.76572i
$199$	8.81786	+	15.2730i	0.625081	+	1.08267i	0.988525	+	0.151056i	$0.0482675\pi$
$199$	8.81786	+	15.2730i	0.625081	+	1.08267i	−0.363444	+	0.931616i	$0.618399\pi$
$200$	4.99856	−	0.120090i	0.353451	−	0.00849167i
$201$	−27.3527	+	5.26207i	−1.92931	+	0.371158i
$202$		−	0.867410i		−	0.0610307i
$203$	17.8122	−	10.2839i	1.25017	−	0.721787i
$204$	8.30305			0.581330
$205$	−11.5558	+	3.24562i	−0.807095	+	0.226684i
$206$	0.377982			0.0263353
$207$	−15.5599	+	8.98354i	−1.08149	+	0.624399i
$208$	0.389955	+	0.225141i	0.0270385	+	0.0156107i
$209$	−22.6031			−1.56349
$210$	23.4276	−	23.9972i	1.61665	−	1.65596i
$211$	−12.1050	−	20.9666i	−0.833346	−	1.44340i	−0.895370	−	0.445322i	$-0.853089\pi$
$211$	−12.1050	−	20.9666i	−0.833346	−	1.44340i	0.0620247	−	0.998075i	$-0.480244\pi$
$212$	5.42713	+	3.13336i	0.372737	+	0.215200i
$213$	37.7356	+	21.7866i	2.58560	+	1.49280i
$214$	−1.00552	−	1.74161i	−0.0687358	−	0.119054i
$215$	−3.07359	+	3.14832i	−0.209617	+	0.214713i
$216$	18.9883			1.29199
$217$	−29.3657	+	16.9543i	−1.99347	+	1.15093i
$218$	14.2310	−	8.21628i	0.963846	−	0.556477i
$219$	3.97554	+	6.88584i	0.268642	+	0.465302i
$220$	2.50719	−	9.82759i	0.169035	−	0.662576i
$221$	0.549336	−	0.951478i	0.0369523	−	0.0640033i
$222$	8.98954	+	5.19011i	0.603338	+	0.348338i
$223$			15.5389i			1.04056i	0.853995	+	0.520282i	$0.174173\pi$
$223$			15.5389i			1.04056i	−0.853995	+	0.520282i	$0.825827\pi$
$224$	−2.20370	−	3.81692i	−0.147241	−	0.255029i
$225$	−1.03037	−	42.8875i	−0.0686915	−	2.85917i
$226$	15.1242			1.00605
$227$	−2.44608	−	1.41224i	−0.162352	−	0.0937339i	0.416623	−	0.909079i	$-0.363214\pi$
$227$	−2.44608	−	1.41224i	−0.162352	−	0.0937339i	−0.578975	+	0.815346i	$0.696547\pi$
$228$			16.9577i			1.12305i
$229$	−10.2057	−	17.6767i	−0.674409	−	1.16811i	−0.976641	−	0.214876i	$-0.931065\pi$
$229$	−10.2057	−	17.6767i	−0.674409	−	1.16811i	0.302233	−	0.953234i	$-0.402268\pi$
$230$	4.50805	−	1.26615i	0.297252	−	0.0834874i
$231$	−34.0142	−	58.9143i	−2.23797	−	3.87628i
$232$	−4.04144	−	2.33332i	−0.265333	−	0.153190i
$233$	0.440689	+	0.254432i	0.0288705	+	0.0166684i	0.514366	−	0.857571i	$-0.328027\pi$
$233$	0.440689	+	0.254432i	0.0288705	+	0.0166684i	−0.485495	+	0.874239i	$0.661361\pi$
$234$	1.93170	−	3.34580i	0.126279	−	0.218722i
$235$	5.16359	+	18.3847i	0.336835	+	1.19928i
$236$	2.13676	−	3.70098i	0.139091	−	0.240913i
$237$	−9.73130	−	5.61837i	−0.632116	−	0.364952i
$238$	−9.31316	+	5.37695i	−0.603682	+	0.348536i
$239$	−0.995100	+	1.72356i	−0.0643676	+	0.111488i	−0.896413	−	0.443219i	$-0.853836\pi$
$239$	−0.995100	+	1.72356i	−0.0643676	+	0.111488i	0.832046	+	0.554707i	$0.187170\pi$
$240$	−7.37304	−	1.88099i	−0.475928	−	0.121417i
$241$	27.6844			1.78331			0.891655	−	0.452715i	$-0.149545\pi$
$241$	27.6844			1.78331			0.891655	+	0.452715i	$0.149545\pi$
$242$	−8.29090	−	4.78676i	−0.532960	−	0.307704i
$243$		−	75.3278i		−	4.83228i
$244$	−13.5296			−0.866142
$245$	−6.86807	+	26.9212i	−0.438785	+	1.71993i
$246$	18.2666			1.16464
$247$	1.94325	+	1.12193i	0.123646	+	0.0713869i
$248$	6.66281	+	3.84677i	0.423089	+	0.244270i
$249$	−1.51099	−	2.61711i	−0.0957551	−	0.165853i
$250$	−2.50278	+	10.8966i	−0.158290	+	0.689162i
$251$	11.8117	+	20.4584i	0.745546	+	1.29132i	0.949939	+	0.312435i	$0.101145\pi$
$251$	11.8117	+	20.4584i	0.745546	+	1.29132i	−0.204393	+	0.978889i	$0.565522\pi$
$252$	−32.7491	+	18.9077i	−2.06300	+	1.19107i
$253$		−	9.49829i		−	0.597153i
$254$	−0.610213			−0.0382882
$255$	−4.58956	+	17.9900i	−0.287409	+	1.12658i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.49777	+	2.01944i	0.218185	+	0.125969i	0.605110	−	0.796142i	$-0.293129\pi$
$257$	3.49777	+	2.01944i	0.218185	+	0.125969i	−0.386925	+	0.922111i	$0.626463\pi$
$258$	5.79881	−	3.34795i	0.361018	−	0.208434i
$259$	−13.4442			−0.835382
$260$	−0.703355	+	0.720457i	−0.0436203	+	0.0446808i
$261$	−20.0199	+	34.6754i	−1.23920	+	2.14635i
$262$	−2.75378	+	1.58990i	−0.170129	+	0.0982242i
$263$		−	4.50853i		−	0.278008i	−0.990292	−	0.139004i	$-0.955610\pi$
$263$		−	4.50853i		−	0.278008i	0.990292	−	0.139004i	$-0.0443901\pi$
$264$	−7.71752	+	13.3671i	−0.474981	+	0.822691i
$265$	−9.78883	+	10.0268i	−0.601323	+	0.615943i
$266$	−10.9816	−	19.0207i	−0.673325	−	1.16623i
$267$		−	1.25703i		−	0.0769289i
$268$	−7.73425	−	2.67982i	−0.472444	−	0.163696i
$269$	7.18777			0.438246			0.219123	−	0.975697i	$-0.429680\pi$
$269$	7.18777			0.438246			0.219123	+	0.975697i	$0.429680\pi$
$270$	−10.4959	+	41.1414i	−0.638759	+	2.50378i
$271$	−13.1874			−0.801076			−0.400538	−	0.916280i	$-0.631177\pi$
$271$	−13.1874			−0.801076			−0.400538	+	0.916280i	$0.631177\pi$
$272$	2.11307	+	1.21998i	0.128124	+	0.0739724i
$273$			6.75336i			0.408732i
$274$	0.155455	+	0.269256i	0.00939138	+	0.0162664i
$275$	19.9073	+	10.8645i	1.20045	+	0.655154i
$276$	−7.12599			−0.428934
$277$		−	24.2717i		−	1.45835i	−0.684329	−	0.729174i	$-0.739905\pi$
$277$		−	24.2717i		−	1.45835i	0.684329	−	0.729174i	$-0.260095\pi$
$278$	7.38965	−	4.26642i	0.443202	−	0.255883i
$279$	33.0052	−	57.1667i	1.97597	−	3.42248i
$280$	9.48811	−	2.66487i	0.567023	−	0.159256i
$281$	5.28366	+	9.15157i	0.315197	+	0.545937i	0.979479	−	0.201545i	$-0.0645961\pi$
$281$	5.28366	+	9.15157i	0.315197	+	0.545937i	−0.664282	+	0.747482i	$0.731263\pi$
$282$		−	29.0611i		−	1.73056i
$283$			21.3774i			1.27075i	0.772203	+	0.635376i	$0.219155\pi$
$283$			21.3774i			1.27075i	−0.772203	+	0.635376i	$0.780845\pi$
$284$	6.40231	+	11.0891i	0.379907	+	0.658018i
$285$	−36.7417	−	9.37346i	−2.17639	−	0.555236i
$286$	1.02119	+	1.76876i	0.0603845	+	0.104589i
$287$	−20.4888	+	11.8292i	−1.20942	+	0.698257i
$288$	7.43048	+	4.28999i	0.437845	+	0.252790i
$289$	−5.52328	+	9.56660i	−0.324899	+	0.562741i
$290$	7.28947	−	7.46670i	0.428052	−	0.438460i
$291$	8.62743	+	14.9432i	0.505749	+	0.875983i
$292$			2.33654i			0.136735i
$293$			11.2534i			0.657433i	0.944429	+	0.328717i	$0.106616\pi$
$293$			11.2534i			0.657433i	−0.944429	+	0.328717i	$0.893384\pi$
$294$	21.1410	−	36.6173i	1.23297	−	2.13556i
$295$	6.83770	+	6.67539i	0.398106	+	0.388656i
$296$	1.52519	+	2.64170i	0.0886497	+	0.153546i
$297$	74.5883	+	43.0636i	4.32805	+	2.49880i
$298$	−6.12783	+	3.53790i	−0.354976	+	0.204945i
$299$	−0.471461	+	0.816594i	−0.0272653	+	0.0472248i
$300$	8.15098	−	14.9352i	0.470597	−	0.862286i
$301$	−4.33618	+	7.51048i	−0.249933	+	0.432897i
$302$	−10.8863	−	6.28522i	−0.626437	−	0.361674i
$303$	−2.55628	−	1.47587i	−0.146855	−	0.0847865i
$304$	−2.49163	+	4.31562i	−0.142905	+	0.247518i
$305$	7.47854	−	29.3141i	0.428220	−	1.67852i
$306$	10.4674	−	18.1301i	0.598383	−	1.03643i
$307$	−11.9503	+	6.89949i	−0.682038	+	0.393775i	−0.800623	−	0.599169i	$-0.795498\pi$
$307$	−11.9503	+	6.89949i	−0.682038	+	0.393775i	0.118584	+	0.992944i	$0.462164\pi$
$308$		−	19.9911i		−	1.13910i
$309$	0.643124	−	1.11392i	0.0365861	−	0.0633689i
$310$	−12.0176	+	12.3098i	−0.682554	+	0.699149i
$311$	12.4373			0.705254			0.352627	−	0.935764i	$-0.385288\pi$
$311$	12.4373			0.705254			0.352627	+	0.935764i	$0.385288\pi$
$312$	1.32699	−	0.766139i	0.0751261	−	0.0433741i
$313$		−	33.0764i		−	1.86959i	−0.355189	−	0.934794i	$-0.615584\pi$
$313$		−	33.0764i		−	1.86959i	0.355189	−	0.934794i	$-0.384416\pi$
$314$	−6.97195	+	12.0758i	−0.393450	+	0.681475i
$315$	−22.8645	−	81.4077i	−1.28827	−	4.58681i
$316$	−1.65104	−	2.85968i	−0.0928780	−	0.160869i
$317$	−2.88616	+	1.66632i	−0.162103	+	0.0935901i	−0.578857	−	0.815429i	$-0.696501\pi$
$317$	−2.88616	+	1.66632i	−0.162103	+	0.0935901i	0.416754	+	0.909019i	$0.363168\pi$
$318$	18.4682	−	10.6626i	1.03564	−	0.597930i
$319$	−10.5835	−	18.3312i	−0.592562	−	1.02635i
$320$	−1.60001	−	1.56204i	−0.0894435	−	0.0873204i
$321$	−6.84343			−0.381963
$322$	7.99290	−	4.61470i	0.445427	−	0.257167i
$323$	10.5300	+	6.07949i	0.585904	+	0.338272i
$324$	19.4380	−	33.6676i	1.07989	−	1.87042i
$325$	−1.17221	−	1.92218i	−0.0650224	−	0.106623i
$326$	−3.66865			−0.203188
$327$		−	55.9190i		−	3.09233i
$328$	4.64874	+	2.68395i	0.256683	+	0.148196i
$329$	18.8196	+	32.5965i	1.03756	+	1.79710i
$330$	−24.6963	−	24.1101i	−1.35949	−	1.32722i
$331$	−5.74745	+	9.95487i	−0.315908	+	0.547169i	−0.979630	−	0.200810i	$-0.935642\pi$
$331$	−5.74745	+	9.95487i	−0.315908	+	0.547169i	0.663722	+	0.747979i	$0.268976\pi$
$332$		−	0.888051i		−	0.0487381i
$333$	22.6657	−	13.0861i	1.24207	−	0.717112i
$334$	−0.804399			−0.0440147
$335$	10.0814	−	15.2763i	0.550807	−	0.834632i
$336$	−14.9981			−0.818213
$337$	−8.58400	+	4.95597i	−0.467600	+	0.269969i	−0.715235	−	0.698885i	$-0.753680\pi$
$337$	−8.58400	+	4.95597i	−0.467600	+	0.269969i	0.247634	+	0.968854i	$0.420347\pi$
$338$			12.7972i			0.696078i
$339$	25.7333	−	44.5714i	1.39764	−	2.42079i
$340$	−3.81132	+	3.90398i	−0.206698	+	0.211723i
$341$	17.4482	+	30.2212i	0.944874	+	1.63657i
$342$	37.0279	+	21.3781i	2.00224	+	1.15600i
$343$			23.9108i			1.29106i
$344$	1.96768			0.106090
$345$	3.93893	−	15.4397i	0.212065	−	0.831244i
$346$	−2.65993	+	4.60713i	−0.142999	+	0.247681i
$347$	12.8627	+	7.42629i	0.690507	+	0.398664i	0.803802	−	0.594897i	$-0.202807\pi$
$347$	12.8627	+	7.42629i	0.690507	+	0.398664i	−0.113295	+	0.993561i	$0.536141\pi$
$348$	−13.7527	+	7.94015i	−0.737225	+	0.425637i
$349$	3.64088			0.194892			0.0974459	−	0.995241i	$-0.468933\pi$
$349$	3.64088			0.194892			0.0974459	+	0.995241i	$0.468933\pi$
$350$	0.529286	+	22.0306i	0.0282915	+	1.17759i
$351$	−4.27504	−	7.40458i	−0.228185	−	0.395227i
$352$	−3.92812	+	2.26790i	−0.209370	+	0.120880i
$353$	−3.72064	+	2.14811i	−0.198030	+	0.114332i	−0.595736	−	0.803180i	$-0.703140\pi$
$353$	−3.72064	+	2.14811i	−0.198030	+	0.114332i	0.397706	+	0.917513i	$0.369806\pi$
$354$	−7.27126	−	12.5942i	−0.386463	−	0.669374i
$355$	−27.5654	+	7.74212i	−1.46302	+	0.410909i
$356$	0.184698	−	0.319906i	0.00978895	−	0.0169550i
$357$			36.5949i			1.93681i
$358$	−6.20734	+	3.58381i	−0.328068	+	0.189410i
$359$	31.1007			1.64143			0.820717	−	0.571335i	$-0.193574\pi$
$359$	31.1007			1.64143			0.820717	+	0.571335i	$0.193574\pi$
$360$	−13.4022	+	13.7281i	−0.706359	+	0.723533i
$361$	−2.91641	+	5.05137i	−0.153495	+	0.265862i
$362$		−	18.1605i		−	0.954495i
$363$	−28.2134	+	16.2890i	−1.48082	+	0.854952i
$364$	−0.992285	+	1.71869i	−0.0520098	+	0.0900837i
$365$	−5.06250	−	1.29153i	−0.264984	−	0.0676019i
$366$	−23.0201	+	39.8720i	−1.20328	+	2.08415i
$367$	−2.06615	−	1.19289i	−0.107852	−	0.0622685i	0.445104	−	0.895479i	$-0.353167\pi$
$367$	−2.06615	−	1.19289i	−0.107852	−	0.0622685i	−0.552956	+	0.833211i	$0.686500\pi$
$368$	−1.81352	−	1.04704i	−0.0945362	−	0.0545805i
$369$	23.0282	−	39.8860i	1.19880	−	2.07638i
$370$	−6.56675	+	1.84436i	−0.341389	+	0.0958838i
$371$	−13.8099	+	23.9195i	−0.716977	+	1.24184i
$372$	22.6731	−	13.0903i	1.17555	−	0.678702i
$373$	−24.8507	−	14.3476i	−1.28672	−	0.742889i	−0.308653	−	0.951175i	$-0.599878\pi$
$373$	−24.8507	−	14.3476i	−1.28672	−	0.742889i	−0.978068	+	0.208286i	$0.933212\pi$
$374$	5.53361	+	9.58449i	0.286136	+	0.495602i
$375$	27.8542	+	25.9160i	1.43839	+	1.33830i
$376$	4.27000	−	7.39586i	0.220209	−	0.381413i
$377$			2.10130i			0.108223i
$378$			83.6890i			4.30450i
$379$	−8.44996	−	14.6358i	−0.434045	−	0.751789i	0.563172	−	0.826340i	$-0.309581\pi$
$379$	−8.44996	−	14.6358i	−0.434045	−	0.751789i	−0.997217	+	0.0745512i	$0.976248\pi$
$380$	−7.97328	−	7.78402i	−0.409020	−	0.399312i
$381$	−1.03826	+	1.79831i	−0.0531915	+	0.0921305i
$382$	−18.2447	−	10.5336i	−0.933479	−	0.538944i
$383$	16.2285	−	9.36950i	0.829235	−	0.478759i	−0.0243556	−	0.999703i	$-0.507753\pi$
$383$	16.2285	−	9.36950i	0.829235	−	0.478759i	0.853591	+	0.520944i	$0.174420\pi$
$384$	1.70147	+	2.94703i	0.0868277	+	0.150390i
$385$	43.3141	+	11.0502i	2.20749	+	0.563169i
$386$	−5.13158	−	8.88816i	−0.261190	−	0.452395i
$387$		−	16.8827i		−	0.858193i
$388$			5.07058i			0.257420i
$389$	0.00228831	+	0.00396347i	0.000116022	+	0.000200956i	0.866083	−	0.499900i	$-0.166630\pi$
$389$	0.00228831	+	0.00396347i	0.000116022	+	0.000200956i	−0.865967	+	0.500100i	$0.833296\pi$
$390$	0.926470	+	3.29864i	0.0469136	+	0.167033i
$391$	−2.55473	+	4.42493i	−0.129198	+	0.223778i
$392$	10.7605	−	6.21258i	0.543487	−	0.313783i
$393$			10.8206i			0.545829i
$394$	5.30464			0.267244
$395$	7.10860	−	1.99655i	0.357672	−	0.100457i
$396$	19.4585	+	33.7032i	0.977828	+	1.69365i
$397$		−	0.543684i		−	0.0272867i	−0.999907	−	0.0136434i	$-0.995657\pi$
$397$		−	0.543684i		−	0.0272867i	0.999907	−	0.0136434i	$-0.00434295\pi$
$398$	15.2730	+	8.81786i	0.765565	+	0.441999i
$399$	−74.7393			−3.74165
$400$	4.26883	−	2.60328i	0.213442	−	0.130164i
$401$	−24.9471			−1.24580			−0.622900	−	0.782301i	$-0.714046\pi$
$401$	−24.9471			−1.24580			−0.622900	+	0.782301i	$0.714046\pi$
$402$	−21.0571	+	18.2334i	−1.05023	+	0.909401i
$403$		−	3.46426i		−	0.172567i
$404$	−0.433705	−	0.751199i	−0.0215776	−	0.0373735i
$405$	62.2022	+	60.7257i	3.09085	+	3.01749i
$406$	10.2839	−	17.8122i	0.510381	−	0.884005i
$407$			13.8359i			0.685820i
$408$	7.19066	−	4.15153i	0.355991	−	0.205531i
$409$	−5.21871	+	9.03907i	−0.258049	+	0.446953i	−0.965719	−	0.259589i	$-0.916413\pi$
$409$	−5.21871	+	9.03907i	−0.258049	+	0.446953i	0.707671	+	0.706543i	$0.249746\pi$
$410$	−8.38485	+	8.58871i	−0.414098	+	0.424166i
$411$	1.05801			0.0521876
$412$	0.327342	−	0.188991i	0.0161270	−	0.00931092i
$413$	16.3117	+	9.41756i	0.802646	+	0.463408i
$414$	−8.98354	+	15.5599i	−0.441517	+	0.764730i
$415$	1.92411	+	0.490875i	0.0944510	+	0.0240961i
$416$	0.450281			0.0220769
$417$		−	29.0367i		−	1.42193i
$418$	−19.5748	+	11.3015i	−0.957436	+	0.552776i
$419$	1.10195	+	1.90863i	0.0538337	+	0.0932426i	0.891686	−	0.452654i	$-0.149523\pi$
$419$	1.10195	+	1.90863i	0.0538337	+	0.0932426i	−0.837853	+	0.545896i	$0.816189\pi$
$420$	8.29028	−	32.4959i	0.404524	−	1.58564i
$421$	−17.0281	−	29.4935i	−0.829899	−	1.43743i	−0.898117	−	0.439756i	$-0.855065\pi$
$421$	−17.0281	−	29.4935i	−0.829899	−	1.43743i	0.0682183	−	0.997670i	$-0.478269\pi$
$422$	−20.9666	−	12.1050i	−1.02064	−	0.589264i
$423$	−63.4563	−	36.6365i	−3.08535	−	1.78133i
$424$	6.26671			0.304338
$425$	−6.35192	−	10.4158i	−0.308113	−	0.505241i
$426$	43.5733			2.11113
$427$		−	59.6302i		−	2.88571i
$428$	−1.74161	−	1.00552i	−0.0841838	−	0.0486036i
$429$	6.95011			0.335555
$430$	−1.08765	+	4.26332i	−0.0524510	+	0.205595i
$431$	−3.07913	+	5.33321i	−0.148316	+	0.256891i	−0.930605	−	0.366024i	$-0.880719\pi$
$431$	−3.07913	+	5.33321i	−0.148316	+	0.256891i	0.782289	+	0.622916i	$0.214052\pi$
$432$	16.4443	−	9.49415i	0.791179	−	0.456787i
$433$	−35.4415	−	20.4622i	−1.70321	−	0.983349i	−0.942468	−	0.334295i	$-0.891502\pi$
$433$	−35.4415	−	20.4622i	−1.70321	−	0.983349i	−0.760742	−	0.649054i	$-0.775165\pi$
$434$	−16.9543	+	29.3657i	−0.813831	+	1.40960i
$435$	−9.60179	−	34.1866i	−0.460371	−	1.63912i
$436$	8.21628	−	14.2310i	0.393489	−	0.681542i
$437$	−9.03723	−	5.21764i	−0.432309	−	0.249594i
$438$	6.88584	+	3.97554i	0.329018	+	0.189959i
$439$	8.57929	+	14.8598i	0.409467	+	0.709218i	0.994830	−	0.101553i	$-0.0323813\pi$
$439$	8.57929	+	14.8598i	0.409467	+	0.709218i	−0.585363	+	0.810771i	$0.699048\pi$
$440$	−2.74251	−	9.76454i	−0.130744	−	0.465506i
$441$	−53.3038	−	92.3248i	−2.53827	−	4.39642i
$442$		−	1.09867i		−	0.0522585i
$443$	−8.04964	−	4.64746i	−0.382450	−	0.220808i	0.296434	−	0.955053i	$-0.404203\pi$
$443$	−8.04964	−	4.64746i	−0.382450	−	0.220808i	−0.678884	+	0.734246i	$0.737536\pi$
$444$	10.3802			0.492624
$445$	0.591037	+	0.577008i	0.0280179	+	0.0273528i
$446$	7.76946	+	13.4571i	0.367895	+	0.637212i
$447$			24.0785i			1.13888i
$448$	−3.81692	−	2.20370i	−0.180332	−	0.104115i
$449$	−6.61239	+	11.4530i	−0.312058	+	0.540500i	−0.978808	−	0.204781i	$-0.934352\pi$
$449$	−6.61239	+	11.4530i	−0.312058	+	0.540500i	0.666750	+	0.745282i	$0.267685\pi$
$450$	−22.3361	−	36.6265i	−1.05293	−	1.72659i
$451$	12.1739	+	21.0857i	0.573245	+	0.992889i
$452$	13.0979	−	7.56209i	0.616075	−	0.355691i
$453$	−37.0454	+	21.3882i	−1.74055	+	1.00491i
$454$	−2.82449			−0.132560
$455$	−3.17534	−	3.09997i	−0.148862	−	0.145329i
$456$	8.47885	+	14.6858i	0.397058	+	0.687725i
$457$	−27.5818	−	15.9244i	−1.29022	−	0.744911i	−0.311529	−	0.950237i	$-0.600841\pi$
$457$	−27.5818	−	15.9244i	−1.29022	−	0.744911i	−0.978694	+	0.205326i	$0.934175\pi$
$458$	−17.6767	−	10.2057i	−0.825979	−	0.476879i
$459$	−23.1654	−	40.1237i	−1.08127	−	1.87281i
$460$	3.27101	−	3.35054i	0.152512	−	0.156220i
$461$	31.8104			1.48156			0.740778	−	0.671750i	$-0.234457\pi$
$461$	31.8104			1.48156			0.740778	+	0.671750i	$0.234457\pi$
$462$	−58.9143	−	34.0142i	−2.74094	−	1.58248i
$463$	34.4229	−	19.8741i	1.59977	−	0.923625i	0.608235	−	0.793757i	$-0.291878\pi$
$463$	34.4229	−	19.8741i	1.59977	−	0.923625i	0.991531	−	0.129868i	$-0.0414555\pi$
$464$	−4.66665			−0.216644
$465$	15.8297	+	56.3609i	0.734087	+	2.61368i
$466$	0.508863			0.0235726
$467$	−26.9140	+	15.5388i	−1.24543	+	0.719050i	−0.970195	−	0.242326i	$-0.922089\pi$
$467$	−26.9140	+	15.5388i	−1.24543	+	0.719050i	−0.275237	+	0.961377i	$0.588756\pi$
$468$		−	3.86340i		−	0.178586i
$469$	11.8110	−	34.0879i	0.545382	−	1.57403i
$470$	13.6641	+	13.3398i	0.630279	+	0.615319i
$471$	23.7251	+	41.0931i	1.09319	+	1.89347i
$472$		−	4.27352i		−	0.196705i
$473$	7.72929	+	4.46251i	0.355393	+	0.205186i
$474$	−11.2367			−0.516120
$475$	21.2727	−	12.9728i	0.976057	−	0.595233i
$476$	−5.37695	+	9.31316i	−0.246452	+	0.426868i
$477$		−	53.7682i		−	2.46188i
$478$			1.99020i			0.0910296i
$479$	−3.44528	−	5.96740i	−0.157419	−	0.272658i	0.776518	−	0.630095i	$-0.216984\pi$
$479$	−3.44528	−	5.96740i	−0.157419	−	0.272658i	−0.933937	+	0.357437i	$0.883651\pi$
$480$	−7.32574	+	2.05753i	−0.334373	+	0.0939132i
$481$	0.686763	−	1.18951i	0.0313137	−	0.0542369i
$482$	23.9754	−	13.8422i	1.09205	−	0.630495i
$483$		−	31.4071i		−	1.42907i
$484$	−9.57351			−0.435160
$485$	−10.9863	−	2.80279i	−0.498861	−	0.127268i
$486$	−37.6639	−	65.2358i	−1.70847	−	2.95915i
$487$	1.41542	−	0.817195i	0.0641390	−	0.0370307i	−0.467588	−	0.883947i	$-0.654877\pi$
$487$	1.41542	−	0.817195i	0.0641390	−	0.0370307i	0.531727	+	0.846916i	$0.321543\pi$
$488$	−11.7170	+	6.76479i	−0.530402	+	0.306227i
$489$	−6.24209	+	10.8116i	−0.282277	+	0.488918i
$490$	7.51269	+	26.7485i	0.339389	+	1.20837i
$491$	24.4665			1.10416			0.552079	−	0.833792i	$-0.313835\pi$
$491$	24.4665			1.10416			0.552079	+	0.833792i	$0.313835\pi$
$492$	15.8193	−	9.13331i	0.713191	−	0.411761i
$493$			11.3865i			0.512821i
$494$	2.24387			0.100956
$495$	−83.7795	+	23.5306i	−3.76561	+	1.05762i
$496$	7.69355			0.345451
$497$	−48.8742	+	28.2175i	−2.19231	+	1.26573i
$498$	−2.61711	−	1.51099i	−0.117276	−	0.0677091i
$499$	13.5328	+	23.4395i	0.605811	+	1.04930i	0.991923	+	0.126843i	$0.0404846\pi$
$499$	13.5328	+	23.4395i	0.605811	+	1.04930i	−0.386112	+	0.922452i	$0.626182\pi$
$500$	3.28083	+	10.6881i	0.146723	+	0.477988i
$501$	−1.36866	+	2.37059i	−0.0611472	+	0.105910i
$502$	20.4584	+	11.8117i	0.913104	+	0.527181i
$503$	−1.36689	−	0.789177i	−0.0609468	−	0.0351877i	0.469217	−	0.883083i	$-0.344536\pi$
$503$	−1.36689	−	0.789177i	−0.0609468	−	0.0351877i	−0.530164	+	0.847895i	$0.677870\pi$
$504$	−18.9077	+	32.7491i	−0.842215	+	1.45876i
$505$	1.86733	−	0.524466i	0.0830952	−	0.0233384i
$506$	−4.74915	−	8.22576i	−0.211125	−	0.365680i
$507$	37.7139	+	21.7741i	1.67493	+	0.967022i
$508$	−0.528460	+	0.305106i	−0.0234466	+	0.0135369i
$509$	−28.6334			−1.26915			−0.634577	−	0.772860i	$-0.718826\pi$
$509$	−28.6334			−1.26915			−0.634577	+	0.772860i	$0.718826\pi$
$510$	5.02032	+	17.8746i	0.222303	+	0.791499i
$511$	−10.2980			−0.455559
$512$			1.00000i			0.0441942i
$513$	81.9464	−	47.3118i	3.61802	−	2.08886i
$514$	4.03888			0.178147
$515$	0.228541	+	0.813708i	0.0100707	+	0.0358563i
$516$	3.34795	−	5.79881i	0.147385	−	0.255278i
$517$	33.5462	−	19.3679i	1.47536	−	0.851799i
$518$	−11.6430	+	6.72210i	−0.511565	+	0.295352i
$519$	9.05156	+	15.6778i	0.397319	+	0.688177i
$520$	−0.248895	+	0.975611i	−0.0109148	+	0.0427834i
$521$	−39.8939			−1.74778			−0.873892	−	0.486119i	$-0.838412\pi$
$521$	−39.8939			−1.74778			−0.873892	+	0.486119i	$0.838412\pi$
$522$			40.0397i			1.75249i
$523$	−14.0358	+	8.10359i	−0.613744	+	0.354345i	−0.774429	−	0.632660i	$-0.781963\pi$
$523$	−14.0358	+	8.10359i	−0.613744	+	0.354345i	0.160685	+	0.987006i	$0.448630\pi$
$524$	−1.58990	+	2.75378i	−0.0694550	+	0.120300i
$525$	65.8255	+	35.9246i	2.87286	+	1.56788i
$526$	−2.25427	−	3.90450i	−0.0982906	−	0.170244i
$527$		−	18.7720i		−	0.817722i
$528$			15.4350i			0.671724i
$529$	−9.30743	+	16.1209i	−0.404671	+	0.700911i
$530$	−3.46396	+	13.5779i	−0.150465	+	0.589786i
$531$	−36.6667			−1.59120
$532$	−19.0207	−	10.9816i	−0.824651	−	0.476112i
$533$		−	2.41706i		−	0.104695i
$534$	−0.628514	−	1.08862i	−0.0271985	−	0.0471091i
$535$	3.14131	−	3.21769i	0.135811	−	0.139113i
$536$	−8.03796	+	1.54633i	−0.347187	+	0.0667914i
$537$			24.3910i			1.05255i
$538$	6.22479	−	3.59389i	0.268370	−	0.154943i
$539$	56.3581			2.42751
$540$	11.4810	+	40.8774i	0.494063	+	1.75908i
$541$	−16.2637			−0.699229			−0.349615	−	0.936894i	$-0.613688\pi$
$541$	−16.2637			−0.699229			−0.349615	+	0.936894i	$0.613688\pi$
$542$	−11.4206	+	6.59369i	−0.490557	+	0.283223i
$543$	−53.5195	−	30.8995i	−2.29674	−	1.32602i
$544$	2.43997			0.104613
$545$	26.2923	+	25.6682i	1.12624	+	1.09951i
$546$	3.37668	+	5.84858i	0.144509	+	0.250296i
$547$	−21.9142	−	12.6522i	−0.936984	−	0.540968i	−0.0479703	−	0.998849i	$-0.515275\pi$
$547$	−21.9142	−	12.6522i	−0.936984	−	0.540968i	−0.889014	+	0.457881i	$0.848609\pi$
$548$	0.269256	+	0.155455i	0.0115020	+	0.00664071i
$549$	58.0417	+	100.531i	2.47716	+	4.29057i
$550$	22.6725	−	0.544706i	0.966758	−	0.0232264i
$551$	−23.2551			−0.990700
$552$	−6.17129	+	3.56300i	−0.262667	+	0.151651i
$553$	12.6037	−	7.27677i	0.535965	−	0.309440i
$554$	−12.1359	−	21.0199i	−0.515604	−	0.893052i
$555$	−5.73772	+	22.4905i	−0.243553	+	0.954670i
$556$	4.26642	−	7.38965i	0.180936	−	0.313391i
$557$	16.8071	+	9.70358i	0.712139	+	0.411154i	0.811853	−	0.583862i	$-0.198459\pi$
$557$	16.8071	+	9.70358i	0.712139	+	0.411154i	−0.0997134	+	0.995016i	$0.531793\pi$
$558$		−	66.0105i		−	2.79445i
$559$	−0.443005	−	0.767307i	−0.0187371	−	0.0324536i
$560$	6.88451	−	7.05190i	0.290924	−	0.297997i
$561$	37.6610			1.59005
$562$	9.15157	+	5.28366i	0.386036	+	0.222878i
$563$		−	8.81730i		−	0.371605i	−0.982587	−	0.185802i	$-0.940512\pi$
$563$		−	8.81730i		−	0.371605i	0.982587	−	0.185802i	$-0.0594884\pi$
$564$	−14.5305	−	25.1677i	−0.611847	−	1.05975i
$565$	9.14461	+	32.5589i	0.384717	+	1.36976i
$566$	10.6887	+	18.5133i	0.449279	+	0.778173i
$567$	148.387	+	85.6711i	6.23165	+	3.59785i
$568$	11.0891	+	6.40231i	0.465289	+	0.268635i
$569$	7.71974	−	13.3710i	0.323628	−	0.560541i	−0.657605	−	0.753363i	$-0.728431\pi$
$569$	7.71974	−	13.3710i	0.323628	−	0.560541i	0.981234	+	0.192822i	$0.0617639\pi$
$570$	−36.5060	+	10.2532i	−1.52907	+	0.429460i
$571$	5.94247	−	10.2927i	0.248685	−	0.430734i	−0.714477	−	0.699659i	$-0.753335\pi$
$571$	5.94247	−	10.2927i	0.248685	−	0.430734i	0.963161	+	0.268925i	$0.0866684\pi$
$572$	1.76876	+	1.02119i	0.0739556	+	0.0426983i
$573$	−62.0854	+	35.8450i	−2.59366	+	1.49745i
$574$	−11.8292	+	20.4888i	−0.493742	+	0.855187i
$575$	5.45145	+	8.93924i	0.227341	+	0.372792i
$576$	8.57997			0.357499
$577$	−10.5513	−	6.09178i	−0.439255	−	0.253604i	0.264027	−	0.964515i	$-0.414949\pi$
$577$	−10.5513	−	6.09178i	−0.439255	−	0.253604i	−0.703282	+	0.710911i	$0.748283\pi$
$578$			11.0466i			0.459476i
$579$	−34.9249			−1.45143
$580$	2.57951	−	10.1111i	0.107109	−	0.419840i
$581$	3.91399			0.162380
$582$	14.9432	+	8.62743i	0.619414	+	0.357619i
$583$	24.6164	+	14.2123i	1.01951	+	0.588613i
$584$	1.16827	+	2.02350i	0.0483433	+	0.0837330i
$585$	8.37072	+	2.13552i	0.346087	+	0.0882927i
$586$	5.62672	+	9.74577i	0.232438	+	0.402594i
$587$	−13.8706	+	8.00820i	−0.572501	+	0.330534i	−0.758148	−	0.652083i	$-0.773895\pi$
$587$	−13.8706	+	8.00820i	−0.572501	+	0.330534i	0.185646	+	0.982617i	$0.440562\pi$
$588$		−	42.2820i		−	1.74368i
$589$	38.3389			1.57973
$590$	9.25932	+	2.36221i	0.381200	+	0.0972507i
$591$	9.02567	−	15.6329i	0.371266	−	0.643052i
$592$	2.64170	+	1.52519i	0.108573	+	0.0626848i
$593$	42.0481	−	24.2765i	1.72671	−	0.996916i	0.824114	−	0.566425i	$-0.191674\pi$
$593$	42.0481	−	24.2765i	1.72671	−	0.996916i	0.902595	−	0.430491i	$-0.141660\pi$
$594$	86.1272			3.53384
$595$	−17.2064	−	16.7980i	−0.705394	−	0.688650i
$596$	−3.53790	+	6.12783i	−0.144918	+	0.251006i
$597$	51.9730	−	30.0066i	2.12711	−	1.22809i
$598$			0.942921i			0.0385589i
$599$	12.7026	−	22.0016i	0.519014	−	0.898959i	−0.480742	−	0.876862i	$-0.659632\pi$
$599$	12.7026	−	22.0016i	0.519014	−	0.898959i	0.999756	−	0.0220967i	$-0.00703417\pi$
$600$	−0.408660	−	17.0098i	−0.0166835	−	0.694421i
$601$	−12.1339	−	21.0165i	−0.494950	−	0.857279i	0.505033	−	0.863100i	$-0.331480\pi$
$601$	−12.1339	−	21.0165i	−0.494950	−	0.857279i	−0.999983	+	0.00582099i	$0.998147\pi$
$602$			8.67235i			0.353459i
$603$	13.2675	+	68.9655i	0.540294	+	2.80849i
$604$	−12.5704			−0.511484
$605$	5.29181	−	20.7426i	0.215143	−	0.843309i
$606$	−2.95174			−0.119906
$607$	27.0640	+	15.6254i	1.09849	+	0.634215i	0.935825	−	0.352466i	$-0.114657\pi$
$607$	27.0640	+	15.6254i	1.09849	+	0.634215i	0.162668	+	0.986681i	$0.447990\pi$
$608$			4.98325i			0.202098i
$609$	−34.9954	−	60.6138i	−1.41809	−	2.45620i
$610$	−8.18045	−	29.1260i	−0.331217	−	1.17928i
$611$	−3.84541			−0.155568
$612$		−	20.9349i		−	0.846242i
$613$	−16.0574	+	9.27076i	−0.648554	+	0.374443i	−0.787902	−	0.615801i	$-0.788833\pi$
$613$	−16.0574	+	9.27076i	−0.648554	+	0.374443i	0.139348	+	0.990243i	$0.455499\pi$
$614$	−6.89949	+	11.9503i	−0.278441	+	0.482274i
$615$	11.0446	+	39.3238i	0.445363	+	1.58569i
$616$	−9.99554	−	17.3128i	−0.402732	−	0.697552i
$617$		−	40.7534i		−	1.64067i	−0.571884	−	0.820335i	$-0.693787\pi$
$617$		−	40.7534i		−	1.64067i	0.571884	−	0.820335i	$-0.306213\pi$
$618$		−	1.28625i		−	0.0517405i
$619$	14.1320	+	24.4774i	0.568014	+	0.983829i	0.996762	+	0.0804050i	$0.0256214\pi$
$619$	14.1320	+	24.4774i	0.568014	+	0.983829i	−0.428748	+	0.903424i	$0.641045\pi$
$620$	−4.25265	+	16.6694i	−0.170791	+	0.669459i
$621$	19.8814	+	34.4356i	0.797814	+	1.38185i
$622$	10.7710	−	6.21864i	0.431878	−	0.249345i
$623$	1.40995	+	0.814036i	0.0564885	+	0.0326137i
$624$	0.766139	−	1.32699i	0.0306701	−	0.0531222i
$625$	−24.9712	+	1.20056i	−0.998846	+	0.0480223i
$626$	−16.5382	−	28.6450i	−0.660999	−	1.14488i
$627$			76.9168i			3.07176i
$628$			13.9439i			0.556422i
$629$	3.72141	−	6.44566i	0.148382	−	0.257005i
$630$	−60.5051	−	59.0689i	−2.41058	−	2.35336i
$631$	−17.9007	−	31.0049i	−0.712615	−	1.23429i	−0.963872	−	0.266365i	$-0.914177\pi$
$631$	−17.9007	−	31.0049i	−0.712615	−	1.23429i	0.251257	−	0.967920i	$-0.419156\pi$
$632$	−2.85968	−	1.65104i	−0.113752	−	0.0656747i
$633$	−71.3478	+	41.1927i	−2.83582	+	1.63726i
$634$	−1.66632	+	2.88616i	−0.0661782	+	0.114624i
$635$	−0.368956	−	1.31365i	−0.0146416	−	0.0521305i
$636$	10.6626	−	18.4682i	0.422800	−	0.732311i
$637$	−4.84525	−	2.79741i	−0.191976	−	0.110837i
$638$	−18.3312	−	10.5835i	−0.725738	−	0.419005i
$639$	54.9316	−	95.1444i	2.17306	−	3.76385i
$640$	−2.16667	−	0.552755i	−0.0856452	−	0.0218496i
$641$	4.96105	−	8.59279i	0.195950	−	0.339395i	−0.751262	−	0.660004i	$-0.770554\pi$
$641$	4.96105	−	8.59279i	0.195950	−	0.339395i	0.947211	+	0.320610i	$0.103888\pi$
$642$	−5.92658	+	3.42171i	−0.233904	+	0.135044i
$643$			43.4522i			1.71359i	0.515658	+	0.856795i	$0.327548\pi$
$643$			43.4522i			1.71359i	−0.515658	+	0.856795i	$0.672452\pi$
$644$	4.61470	−	7.99290i	0.181845	−	0.314964i
$645$	10.7135	+	10.4592i	0.421845	+	0.411831i
$646$	12.1590			0.478389
$647$	−22.1659	+	12.7975i	−0.871432	+	0.503121i	−0.867824	−	0.496872i	$-0.834482\pi$
$647$	−22.1659	+	12.7975i	−0.871432	+	0.503121i	−0.00360789	+	0.999993i	$0.501148\pi$
$648$		−	38.8760i		−	1.52719i
$649$	9.69193	−	16.7869i	0.380441	−	0.658944i
$650$	−1.97625	−	1.07855i	−0.0775149	−	0.0423042i
$651$	57.6943	+	99.9294i	2.26122	+	3.91654i
$652$	−3.17714	+	1.83432i	−0.124427	+	0.0718377i
$653$	6.80288	−	3.92765i	0.266217	−	0.153701i	−0.360950	−	0.932585i	$-0.617548\pi$
$653$	6.80288	−	3.92765i	0.266217	−	0.153701i	0.627167	+	0.778884i	$0.284214\pi$
$654$	−27.9595	−	48.4272i	−1.09330	−	1.89366i
$655$	−5.08772	−	4.96695i	−0.198794	−	0.194075i
$656$	5.36790			0.209581
$657$	17.3616	−	10.0237i	0.677340	−	0.391062i
$658$	32.5965	+	18.8196i	1.27074	+	0.733665i
$659$	−10.0450	+	17.3984i	−0.391296	+	0.677745i	−0.992621	−	0.121260i	$-0.961307\pi$
$659$	−10.0450	+	17.3984i	−0.391296	+	0.677745i	0.601325	+	0.799005i	$0.294640\pi$
$660$	−33.4427	−	8.53181i	−1.30175	−	0.332100i
$661$	−20.5364			−0.798772			−0.399386	−	0.916783i	$-0.630777\pi$
$661$	−20.5364			−0.798772			−0.399386	+	0.916783i	$0.630777\pi$
$662$			11.4949i			0.446762i
$663$	−3.23782	−	1.86936i	−0.125746	−	0.0725997i
$664$	−0.444026	−	0.769075i	−0.0172315	−	0.0298459i
$665$	34.3073	−	35.1414i	1.33038	−	1.36273i
$666$	13.0861	−	22.6657i	0.507075	−	0.878279i
$667$		−	9.77229i		−	0.378385i
$668$	−0.696630	+	0.402199i	−0.0269534	+	0.0155616i
$669$	52.8779			2.04438
$670$	1.09263	−	18.2704i	0.0422121	−	0.705846i
$671$	−61.3675			−2.36907
$672$	−12.9887	+	7.49905i	−0.501051	+	0.289282i
$673$		−	27.6875i		−	1.06727i	−0.845714	−	0.533637i	$-0.820825\pi$
$673$		−	27.6875i		−	1.06727i	0.845714	−	0.533637i	$-0.179175\pi$
$674$	−4.95597	+	8.58400i	−0.190897	+	0.330643i
$675$	−94.9141	+	2.28031i	−3.65324	+	0.0877693i
$676$	6.39862	+	11.0827i	0.246101	+	0.426259i
$677$	15.6292	+	9.02350i	0.600678	+	0.346801i	0.769308	−	0.638878i	$-0.220601\pi$
$677$	15.6292	+	9.02350i	0.600678	+	0.346801i	−0.168631	+	0.985679i	$0.553934\pi$
$678$		−	51.4666i		−	1.97656i
$679$	−22.3481			−0.857640
$680$	−1.34871	+	5.28661i	−0.0517205	+	0.202732i
$681$	−4.80578	+	8.32385i	−0.184158	+	0.318971i
$682$	30.2212	+	17.4482i	1.15723	+	0.668127i
$683$	7.62080	−	4.39987i	0.291602	−	0.168356i	−0.347062	−	0.937842i	$-0.612821\pi$
$683$	7.62080	−	4.39987i	0.291602	−	0.168356i	0.638664	+	0.769486i	$0.279487\pi$
$684$	42.7562			1.63482
$685$	−0.485653	+	0.497460i	−0.0185558	+	0.0190070i
$686$	11.9554	+	20.7074i	0.456460	+	0.790611i
$687$	−60.1527	+	34.7292i	−2.29497	+	1.32500i
$688$	1.70406	−	0.983840i	0.0649667	−	0.0375086i
$689$	−1.41089	−	2.44374i	−0.0537507	−	0.0930989i
$690$	−4.30862	−	15.3406i	−0.164027	−	0.584007i
$691$	1.81451	−	3.14282i	0.0690272	−	0.119559i	−0.829446	−	0.558587i	$-0.811344\pi$
$691$	1.81451	−	3.14282i	0.0690272	−	0.119559i	0.898473	+	0.439028i	$0.144677\pi$
$692$			5.31985i			0.202230i
$693$	−148.543	+	85.7615i	−5.64269	+	3.25781i
$694$	14.8526			0.563797
$695$	13.6527	+	13.3286i	0.517875	+	0.505582i
$696$	−7.94015	+	13.7527i	−0.300971	+	0.521297i
$697$		−	13.0975i		−	0.496103i
$698$	3.15309	−	1.82044i	0.119346	−	0.0689046i
$699$	0.865815	−	1.49963i	0.0327481	−	0.0567214i
$700$	11.4737	+	18.8144i	0.433665	+	0.711119i
$701$	1.59835	−	2.76842i	0.0603688	−	0.104562i	−0.834262	−	0.551369i	$-0.814106\pi$
$701$	1.59835	−	2.76842i	0.0603688	−	0.104562i	0.894630	+	0.446807i	$0.147439\pi$
$702$	−7.40458	−	4.27504i	−0.279468	−	0.161351i
$703$	13.1643	+	7.60039i	0.496500	+	0.286654i
$704$	−2.26790	+	3.92812i	−0.0854748	+	0.148047i
$705$	62.5618	−	17.5714i	2.35622	−	0.661776i
$706$	−2.14811	+	3.72064i	−0.0808453	+	0.140028i
$707$	3.31083	−	1.91151i	0.124517	−	0.0718897i
$708$	−12.5942	−	7.27126i	−0.473319	−	0.273271i
$709$	−16.4482	−	28.4891i	−0.617725	−	1.06993i	−0.989900	−	0.141768i	$-0.954721\pi$
$709$	−16.4482	−	28.4891i	−0.617725	−	1.06993i	0.372175	−	0.928163i	$-0.378612\pi$
$710$	−20.0013	+	20.4876i	−0.750634	+	0.768885i
$711$	−14.1658	+	24.5360i	−0.531261	+	0.920170i
$712$		−	0.369395i		−	0.0138437i
$713$			16.1108i			0.603356i
$714$	18.2974	+	31.6921i	0.684764	+	1.18605i
$715$	−3.19028	+	3.26785i	−0.119310	+	0.122211i
$716$	−3.58381	+	6.20734i	−0.133933	+	0.231979i
$717$	5.86518	+	3.38626i	0.219039	+	0.126462i
$718$	26.9340	−	15.5504i	1.00517	−	0.580335i
$719$	−17.4214	−	30.1748i	−0.649710	−	1.12533i	−0.983192	−	0.182574i	$-0.941557\pi$
$719$	−17.4214	−	30.1748i	−0.649710	−	1.12533i	0.333482	−	0.942756i	$-0.391776\pi$
$720$	−4.74263	+	18.5900i	−0.176747	+	0.692808i
$721$	0.832959	+	1.44273i	0.0310210	+	0.0537300i
$722$			5.83282i			0.217075i
$723$		−	94.2083i		−	3.50365i
$724$	−9.08025	−	15.7275i	−0.337465	−	0.584506i
$725$	20.4816	+	11.1779i	0.760666	+	0.415137i
$726$	−16.2890	+	28.2134i	−0.604542	+	1.04710i
$727$	−1.44271	+	0.832949i	−0.0535071	+	0.0308924i	−0.526515	−	0.850166i	$-0.676502\pi$
$727$	−1.44271	+	0.832949i	−0.0535071	+	0.0308924i	0.473008	+	0.881058i	$0.343168\pi$
$728$			1.98457i			0.0735530i
$729$	−139.707			−5.17435
$730$	−5.03002	+	1.41275i	−0.186170	+	0.0522883i
$731$	−2.40054	−	4.15786i	−0.0887871	−	0.153784i
$732$			46.0403i			1.70170i
$733$	−5.29705	−	3.05826i	−0.195651	−	0.112959i	0.398974	−	0.916962i	$-0.369366\pi$
$733$	−5.29705	−	3.05826i	−0.195651	−	0.112959i	−0.594625	+	0.804003i	$0.702700\pi$
$734$	−2.38578			−0.0880609
$735$	91.6112	+	23.3716i	3.37913	+	0.862075i
$736$	−2.09407			−0.0771885
$737$	−35.0810	−	12.1551i	−1.29223	−	0.447740i
$738$		−	46.0564i		−	1.69536i
$739$	12.9978	+	22.5128i	0.478131	+	0.828146i	0.999686	−	0.0250712i	$-0.00798126\pi$
$739$	12.9978	+	22.5128i	0.478131	+	0.828146i	−0.521555	+	0.853218i	$0.674648\pi$
$740$	−4.76479	+	4.88064i	−0.175157	+	0.179416i
$741$	3.81787	−	6.61274i	0.140253	−	0.242925i
$742$			27.6199i			1.01396i
$743$	9.73258	−	5.61911i	0.357054	−	0.206145i	−0.310734	−	0.950497i	$-0.600575\pi$
$743$	9.73258	−	5.61911i	0.357054	−	0.206145i	0.667788	+	0.744352i	$0.267241\pi$
$744$	13.0903	−	22.6731i	0.479915	−	0.831237i
$745$	−11.3214	−	11.0527i	−0.414784	−	0.404938i
$746$	−28.6951			−1.05060
$747$	−6.59864	+	3.80973i	−0.241432	+	0.139391i
$748$	9.58449	+	5.53361i	0.350444	+	0.202329i
$749$	4.43172	−	7.67596i	0.161931	−	0.280474i
$750$	37.0805	+	8.51681i	1.35399	+	0.310990i
$751$	3.41451			0.124597			0.0622986	−	0.998058i	$-0.480157\pi$
$751$	3.41451			0.124597			0.0622986	+	0.998058i	$0.480157\pi$
$752$		−	8.54001i		−	0.311422i
$753$	69.6187	−	40.1944i	2.53705	−	1.46476i
$754$	1.05065	+	1.81978i	0.0382625	+	0.0662726i
$755$	6.94838	−	27.2360i	0.252877	−	0.991219i
$756$	41.8445	+	72.4768i	1.52187	+	2.63595i
$757$	17.5951	+	10.1585i	0.639504	+	0.369218i	0.784423	−	0.620226i	$-0.212959\pi$
$757$	17.5951	+	10.1585i	0.639504	+	0.369218i	−0.144920	+	0.989443i	$0.546292\pi$
$758$	−14.6358	−	8.44996i	−0.531595	−	0.306916i
$759$	−32.3221			−1.17322
$760$	−10.7971	−	2.75452i	−0.391651	−	0.0999170i
$761$	1.25070			0.0453379			0.0226690	−	0.999743i	$-0.492784\pi$
$761$	1.25070			0.0453379			0.0226690	+	0.999743i	$0.492784\pi$
$762$			2.07652i			0.0752242i
$763$	62.7218	+	36.2124i	2.27068	+	1.31098i
$764$	−21.0671			−0.762182
$765$	45.3589	+	11.5719i	1.63996	+	0.418381i
$766$	9.36950	−	16.2285i	0.338534	−	0.586358i
$767$	−1.66648	+	0.962144i	−0.0601732	+	0.0347410i
$768$	2.94703	+	1.70147i	0.106342	+	0.0613964i
$769$	−8.55304	+	14.8143i	−0.308430	+	0.534217i	−0.978019	−	0.208515i	$-0.933137\pi$
$769$	−8.55304	+	14.8143i	−0.308430	+	0.534217i	0.669589	+	0.742732i	$0.266470\pi$
$770$	43.0362	−	12.0873i	1.55092	−	0.435597i
$771$	6.87202	−	11.9027i	0.247490	−	0.428665i
$772$	−8.88816	−	5.13158i	−0.319892	−	0.184690i
$773$	−28.6133	−	16.5199i	−1.02915	−	0.594180i	−0.112409	−	0.993662i	$-0.535857\pi$
$773$	−28.6133	−	16.5199i	−1.02915	−	0.594180i	−0.916741	+	0.399482i	$0.869190\pi$
$774$	−8.44133	−	14.6208i	−0.303417	−	0.525534i
$775$	−33.7664	−	18.4282i	−1.21292	−	0.661960i
$776$	2.53529	+	4.39125i	0.0910117	+	0.157637i
$777$			45.7498i			1.64126i
$778$	0.00396347	+	0.00228831i	0.000142097	+	8.20400e-5i
$779$	26.7496			0.958404
$780$	2.45167	+	2.39347i	0.0877838	+	0.0857001i
$781$	29.0396	+	50.2981i	1.03912	+	1.79981i
$782$			5.10947i			0.182714i
$783$	76.7400	+	44.3058i	2.74246	+	1.58336i
$784$	6.21258	−	10.7605i	0.221878	−	0.384304i
$785$	−30.2118	−	7.70756i	−1.07831	−	0.275095i
$786$	5.41032	+	9.37095i	0.192980	+	0.334251i
$787$	−24.6593	+	14.2370i	−0.879009	+	0.507496i	−0.870331	−	0.492466i	$-0.836095\pi$
$787$	−24.6593	+	14.2370i	−0.879009	+	0.507496i	−0.00867737	+	0.999962i	$0.502762\pi$
$788$	4.59395	−	2.65232i	0.163653	−	0.0944849i
$789$	−15.3422			−0.546198
$790$	5.15795	−	5.28336i	0.183512	−	0.187974i
$791$	33.3291	+	57.7278i	1.18505	+	2.05256i
$792$	33.7032	+	19.4585i	1.19759	+	0.691429i
$793$	5.27593	+	3.04606i	0.187354	+	0.108169i
$794$	−0.271842	−	0.470844i	−0.00964731	−	0.0167096i
$795$	34.1207	+	33.3108i	1.21013	+	1.18141i
$796$	17.6357			0.625081
$797$	−28.4255	−	16.4115i	−1.00688	−	0.581325i	−0.0966060	−	0.995323i	$-0.530799\pi$
$797$	−28.4255	−	16.4115i	−1.00688	−	0.581325i	−0.910278	+	0.413998i	$0.864132\pi$
$798$	−64.7261	+	37.3697i	−2.29128	+	1.32287i
$799$	−20.8373			−0.737172
$800$	2.39528	−	4.38892i	0.0846858	−	0.155172i
$801$	−3.16940			−0.111985
$802$	−21.6049	+	12.4736i	−0.762894	+	0.440457i
$803$			10.5981i			0.373998i
$804$	−9.11925	+	26.3191i	−0.321611	+	0.928205i
$805$	14.7672	+	14.4167i	0.520475	+	0.508120i
$806$	−1.73213	−	3.00014i	−0.0610117	−	0.105675i
$807$		−	24.4595i		−	0.861016i
$808$	−0.751199	−	0.433705i	−0.0264271	−	0.0152577i
$809$	12.5233			0.440297			0.220149	−	0.975466i	$-0.429346\pi$
$809$	12.5233			0.440297			0.220149	+	0.975466i	$0.429346\pi$
$810$	84.2316	+	21.4889i	2.95960	+	0.755044i
$811$	15.2301	−	26.3793i	0.534800	−	0.926301i	−0.464373	−	0.885640i	$-0.653720\pi$
$811$	15.2301	−	26.3793i	0.534800	−	0.926301i	0.999173	−	0.0406615i	$-0.0129465\pi$
$812$		−	20.5678i		−	0.721787i
$813$			44.8758i			1.57386i
$814$	6.91795	+	11.9822i	0.242474	+	0.419977i
$815$	−2.21819	−	7.89776i	−0.0777000	−	0.276646i
$816$	4.15153	−	7.19066i	0.145333	−	0.251723i
$817$	8.49177	−	4.90273i	0.297090	−	0.171525i
$818$			10.4374i			0.364936i
$819$	17.0276			0.594991
$820$	−2.96713	+	11.6305i	−0.103617	+	0.406153i
$821$	23.9423	+	41.4694i	0.835594	+	1.44729i	0.893546	+	0.448971i	$0.148209\pi$
$821$	23.9423	+	41.4694i	0.835594	+	1.44729i	−0.0579526	+	0.998319i	$0.518457\pi$
$822$	0.916261	−	0.529004i	0.0319583	−	0.0184511i
$823$	−2.68474	+	1.55003i	−0.0935841	+	0.0540308i	−0.546062	−	0.837745i	$-0.683874\pi$
$823$	−2.68474	+	1.55003i	−0.0935841	+	0.0540308i	0.452478	+	0.891776i	$0.350540\pi$
$824$	0.188991	−	0.327342i	0.00658382	−	0.0114035i
$825$	36.9712	−	67.7432i	1.28717	−	2.35852i
$826$	18.8351			0.655357
$827$	22.5999	−	13.0481i	0.785877	−	0.453726i	−0.0526323	−	0.998614i	$-0.516761\pi$
$827$	22.5999	−	13.0481i	0.785877	−	0.453726i	0.838509	+	0.544888i	$0.183428\pi$
$828$			17.9671i			0.624399i
$829$	13.8250			0.480162			0.240081	−	0.970753i	$-0.422826\pi$
$829$	13.8250			0.480162			0.240081	+	0.970753i	$0.422826\pi$
$830$	1.91177	−	0.536947i	0.0663585	−	0.0186377i
$831$	−82.5952			−2.86520
$832$	0.389955	−	0.225141i	0.0135193	−	0.00780535i
$833$	−26.2553	−	15.1585i	−0.909691	−	0.525211i
$834$	−14.5184	−	25.1465i	−0.502729	−	0.870753i
$835$	−0.486368	−	1.73168i	−0.0168314	−	0.0599274i
$836$	−11.3015	+	19.5748i	−0.390872	+	0.677009i
$837$	−126.515	−	73.0437i	−4.37301	−	2.52476i
$838$	1.90863	+	1.10195i	0.0659325	+	0.0380661i
$839$	13.3406	−	23.1066i	0.460568	−	0.797728i	−0.538421	−	0.842676i	$-0.680979\pi$
$839$	13.3406	−	23.1066i	0.460568	−	0.797728i	0.998989	+	0.0449482i	$0.0143123\pi$
$840$	−9.06837	−	32.2874i	−0.312889	−	1.11402i
$841$	3.61120	+	6.25478i	0.124524	+	0.215682i
$842$	−29.4935	−	17.0281i	−1.01641	−	0.586827i
$843$	31.1422	−	17.9800i	1.07259	−	0.619263i
$844$	−24.2101			−0.833346
$845$	−27.5495	+	7.73767i	−0.947732	+	0.266184i
$846$	−73.2730			−2.51918
$847$		−	42.1943i		−	1.44981i
$848$	5.42713	−	3.13336i	0.186368	−	0.107600i
$849$	72.7458			2.49663
$850$	−10.7088	−	5.84440i	−0.367310	−	0.200461i
$851$	−3.19385	+	5.53191i	−0.109484	+	0.189631i
$852$	37.7356	−	21.7866i	1.29280	−	0.746398i
$853$	3.21839	−	1.85814i	0.110196	−	0.0636215i	−0.443889	−	0.896082i	$-0.646402\pi$
$853$	3.21839	−	1.85814i	0.110196	−	0.0636215i	0.554085	+	0.832460i	$0.313068\pi$
$854$	−29.8151	−	51.6413i	−1.02025	−	1.76713i
$855$	−23.6337	+	92.6386i	−0.808256	+	3.16817i
$856$	−2.01104			−0.0687358
$857$			17.4406i			0.595761i	0.954603	+	0.297880i	$0.0962797\pi$
$857$			17.4406i			0.595761i	−0.954603	+	0.297880i	$0.903720\pi$
$858$	6.01898	−	3.47506i	0.205484	−	0.118637i
$859$	26.5931	−	46.0607i	0.907346	−	1.57157i	0.0896090	−	0.995977i	$-0.471438\pi$
$859$	26.5931	−	46.0607i	0.907346	−	1.57157i	0.817737	−	0.575592i	$-0.195228\pi$
$860$	1.18973	+	4.23596i	0.0405694	+	0.144445i
$861$	40.2541	+	69.7222i	1.37186	+	2.37612i
$862$			6.15826i			0.209751i
$863$			8.95327i			0.304773i	0.988321	+	0.152386i	$0.0486958\pi$
$863$			8.95327i			0.304773i	−0.988321	+	0.152386i	$0.951304\pi$
$864$	9.49415	−	16.4443i	0.322997	−	0.559448i
$865$	−11.5264	−	2.94058i	−0.391908	−	0.0999826i
$866$	−40.9243			−1.39067
$867$	32.5545	+	18.7954i	1.10561	+	0.638324i
$868$			33.9085i			1.15093i
$869$	−7.48877	−	12.9709i	−0.254039	−	0.440009i
$870$	−25.4087	−	24.8056i	−0.861436	−	0.840989i
$871$	2.41267	+	2.78630i	0.0817503	+	0.0944103i
$872$		−	16.4326i		−	0.556477i
$873$	37.6768	−	21.7527i	1.27517	−	0.736218i
$874$	−10.4353			−0.352979
$875$	−47.1068	+	14.4599i	−1.59250	+	0.488835i
$876$	7.95108			0.268642
$877$	−35.8124	+	20.6763i	−1.20930	+	0.698190i	−0.962606	−	0.270904i	$-0.912678\pi$
$877$	−35.8124	+	20.6763i	−1.20930	+	0.698190i	−0.246694	+	0.969093i	$0.579344\pi$
$878$	14.8598	+	8.57929i	0.501493	+	0.289537i
$879$	38.2948			1.29165
$880$	−7.25735	−	7.08509i	−0.244645	−	0.238838i
$881$	0.485693	+	0.841244i	0.0163634	+	0.0283422i	0.874091	−	0.485762i	$-0.161458\pi$
$881$	0.485693	+	0.841244i	0.0163634	+	0.0283422i	−0.857728	+	0.514104i	$0.828124\pi$
$882$	−92.3248	−	53.3038i	−3.10874	−	1.79483i
$883$	−19.0115	−	10.9763i	−0.639788	−	0.369382i	0.144745	−	0.989469i	$-0.453764\pi$
$883$	−19.0115	−	10.9763i	−0.639788	−	0.369382i	−0.784533	+	0.620087i	$0.787097\pi$
$884$	−0.549336	−	0.951478i	−0.0184762	−	0.0320017i
$885$	22.7159	−	23.2682i	0.763588	−	0.782153i
$886$	−9.29492			−0.312269
$887$	−3.72894	+	2.15290i	−0.125205	+	0.0722874i	−0.561295	−	0.827616i	$-0.689697\pi$
$887$	−3.72894	+	2.15290i	−0.125205	+	0.0722874i	0.436089	+	0.899903i	$0.356363\pi$
$888$	8.98954	−	5.19011i	0.301669	−	0.174169i
$889$	−1.34473	−	2.32913i	−0.0451006	−	0.0781166i
$890$	0.800358	+	0.204185i	0.0268280	+	0.00684430i
$891$	88.1670	−	152.710i	2.95371	−	5.11597i
$892$	13.4571	+	7.76946i	0.450577	+	0.260141i
$893$		−	42.5570i		−	1.42412i
$894$	12.0393	+	20.8526i	0.402653	+	0.697416i
$895$	−11.4683	−	11.1961i	−0.383343	−	0.374244i
$896$	−4.40740			−0.147241
$897$	2.77882	+	1.60435i	0.0927820	+	0.0535677i
$898$			13.2248i			0.441317i
$899$	17.9515	+	31.0930i	0.598718	+	1.03701i
$900$	−37.6568	−	20.5514i	−1.25523	−	0.685047i
$901$	−7.64529	−	13.2420i	−0.254701	−	0.441156i
$902$	21.0857	+	12.1739i	0.702079	+	0.405345i
$903$	25.5577	+	14.7557i	0.850506	+	0.491040i
$904$	7.56209	−	13.0979i	0.251511	−	0.435630i
$905$	39.0954	−	10.9805i	1.29957	−	0.365003i
$906$	−21.3882	+	37.0454i	−0.710575	+	1.23075i
$907$	−13.9362	−	8.04605i	−0.462743	−	0.267165i	0.250454	−	0.968128i	$-0.419420\pi$
$907$	−13.9362	−	8.04605i	−0.462743	−	0.267165i	−0.713197	+	0.700964i	$0.752753\pi$
$908$	−2.44608	+	1.41224i	−0.0811760	+	0.0468670i
$909$	−3.72118	+	6.44527i	−0.123424	+	0.213776i
$910$	−4.29991	−	1.09698i	−0.142541	−	0.0363646i
$911$	50.6907			1.67946			0.839729	−	0.543006i	$-0.182714\pi$
$911$	50.6907			1.67946			0.839729	+	0.543006i	$0.182714\pi$
$912$	14.6858	+	8.47885i	0.486295	+	0.280763i
$913$		−	4.02802i		−	0.133308i
$914$	−31.8487			−1.05346
$915$	−99.7541	−	25.4490i	−3.29777	−	0.841318i
$916$	−20.4113			−0.674409
$917$	−12.1370	−	7.00731i	−0.400800	−	0.231402i
$918$	−40.1237	−	23.1654i	−1.32428	−	0.764573i
$919$	12.5081	+	21.6647i	0.412606	+	0.714654i	0.995174	−	0.0981279i	$-0.0312854\pi$
$919$	12.5081	+	21.6647i	0.412606	+	0.714654i	−0.582568	+	0.812782i	$0.697952\pi$
$920$	1.15751	−	4.53716i	0.0381619	−	0.149586i
$921$	23.4785	+	40.6660i	0.773644	+	1.33999i
$922$	27.5486	−	15.9052i	0.907264	−	0.523809i
$923$		−	5.76568i		−	0.189780i
$924$	−68.0284			−2.23797
$925$	−7.94098	−	13.0215i	−0.261098	−	0.428145i
$926$	19.8741	−	34.4229i	0.653102	−	1.13121i
$927$	−2.80859	−	1.62154i	−0.0922461	−	0.0532583i
$928$	−4.04144	+	2.33332i	−0.132667	+	0.0765951i
$929$	18.2247			0.597933			0.298967	−	0.954264i	$-0.403358\pi$
$929$	18.2247			0.597933			0.298967	+	0.954264i	$0.403358\pi$
$930$	41.8894	+	40.8951i	1.37361	+	1.34100i
$931$	30.9589	−	53.6223i	1.01464	−	1.75740i
$932$	0.440689	−	0.254432i	0.0144352	−	0.00833419i
$933$		−	42.3233i		−	1.38560i
$934$	−15.5388	+	26.9140i	−0.508445	+	0.880653i
$935$	−17.2874	+	17.7077i	−0.565358	+	0.579104i
$936$	−1.93170	−	3.34580i	−0.0631396	−	0.109361i
$937$			15.1212i			0.493988i	0.969017	+	0.246994i	$0.0794429\pi$
$937$			15.1212i			0.493988i	−0.969017	+	0.246994i	$0.920557\pi$
$938$	−6.81531	−	35.4265i	−0.222528	−	1.15672i
$939$	−112.557			−3.67316
$940$	18.5034	+	4.72053i	0.603514	+	0.153967i
$941$	−48.5846			−1.58381			−0.791907	−	0.610642i	$-0.790912\pi$
$941$	−48.5846			−1.58381			−0.791907	+	0.610642i	$0.790912\pi$
$942$	41.0931	+	23.7251i	1.33888	+	0.773005i
$943$			11.2408i			0.366049i
$944$	−2.13676	−	3.70098i	−0.0695457	−	0.120457i
$945$	−180.163	+	50.6013i	−5.86070	+	1.64606i
$946$	8.92501			0.290177
$947$			46.6869i			1.51712i	0.651602	+	0.758561i	$0.274097\pi$
$947$			46.6869i			1.51712i	−0.651602	+	0.758561i	$0.725903\pi$
$948$	−9.73130	+	5.61837i	−0.316058	+	0.182476i
$949$	0.526049	−	0.911144i	0.0170763	−	0.0295770i
$950$	11.9363	−	21.8711i	0.387264	−	0.709593i
$951$	5.67039	+	9.82141i	0.183875	+	0.318481i
$952$			10.7539i			0.348536i
$953$		−	34.2056i		−	1.10803i	−0.832507	−	0.554015i	$-0.813095\pi$
$953$		−	34.2056i		−	1.10803i	0.832507	−	0.554015i	$-0.186905\pi$
$954$	−26.8841	−	46.5647i	−0.870405	−	1.50759i
$955$	11.6450	−	45.6455i	0.376822	−	1.47705i
$956$	0.995100	+	1.72356i	0.0321838	+	0.0557440i
$957$	−62.3798	+	36.0150i	−2.01645	+	1.16420i
$958$	−5.96740	−	3.44528i	−0.192798	−	0.111312i
$959$	−0.685152	+	1.18672i	−0.0221247	+	0.0383211i
$960$	−5.31551	+	5.44475i	−0.171557	+	0.175728i
$961$	−14.0954	−	24.4139i	−0.454689	−	0.787544i
$962$		−	1.37353i		−	0.0442843i
$963$			17.2546i			0.556023i
$964$	13.8422	−	23.9754i	0.445828	−	0.772196i
$965$	16.0314	−	16.4212i	0.516070	−	0.528617i
$966$	−15.7035	−	27.1993i	−0.505253	−	0.875124i
$967$	38.6171	+	22.2956i	1.24184	+	0.716978i	0.969469	−	0.245213i	$-0.0788580\pi$
$967$	38.6171	+	22.2956i	1.24184	+	0.716978i	0.272374	+	0.962192i	$0.412191\pi$
$968$	−8.29090	+	4.78676i	−0.266480	+	0.153852i
$969$	20.6881	−	35.8329i	0.664598	−	1.15112i
$970$	−10.9158	+	3.06585i	−0.350485	+	0.0984386i
$971$	−2.05272	+	3.55541i	−0.0658748	+	0.114098i	−0.897082	−	0.441865i	$-0.854317\pi$
$971$	−2.05272	+	3.55541i	−0.0658748	+	0.114098i	0.831207	+	0.555963i	$0.187650\pi$
$972$	−65.2358	−	37.6639i	−2.09244	−	1.20807i
$973$	32.5691	+	18.8038i	1.04412	+	0.602822i
$974$	0.817195	−	1.41542i	0.0261846	−	0.0453531i
$975$	−6.54104	+	3.98895i	−0.209481	+	0.127749i
$976$	−6.76479	+	11.7170i	−0.216536	+	0.375051i
$977$	−29.8440	+	17.2304i	−0.954793	+	0.551250i	−0.894567	−	0.446935i	$-0.852516\pi$
$977$	−29.8440	+	17.2304i	−0.954793	+	0.551250i	−0.0602264	+	0.998185i	$0.519182\pi$
$978$			12.4842i			0.399200i
$979$	0.837752	−	1.45103i	0.0267747	−	0.0463751i
$980$	19.8804	+	19.4085i	0.635057	+	0.619983i
$981$	−140.991			−4.50150
$982$	21.1886	−	12.2332i	0.676155	−	0.390379i
$983$		−	10.4523i		−	0.333377i	−0.986010	−	0.166689i	$-0.946693\pi$
$983$		−	10.4523i		−	0.333377i	0.986010	−	0.166689i	$-0.0533075\pi$
$984$	9.13331	−	15.8193i	0.291159	−	0.504302i
$985$	3.20737	+	11.4197i	0.102195	+	0.363861i
$986$	5.69324	+	9.86097i	0.181310	+	0.314037i
$987$	110.924	−	64.0419i	3.53074	−	2.03848i
$988$	1.94325	−	1.12193i	0.0618229	−	0.0356935i
$989$	2.06023	+	3.56843i	0.0655116	+	0.113469i
$990$	−60.7899	+	62.2679i	−1.93203	+	1.97900i
$991$	−11.0240			−0.350190			−0.175095	−	0.984552i	$-0.556023\pi$
$991$	−11.0240			−0.350190			−0.175095	+	0.984552i	$0.556023\pi$
$992$	6.66281	−	3.84677i	0.211544	−	0.122135i
$993$	33.8758	+	19.5582i	1.07502	+	0.620660i
$994$	−28.2175	+	48.8742i	−0.895005	+	1.55019i
$995$	−9.74823	+	38.2108i	−0.309040	+	1.21136i
$996$	−3.02198			−0.0957551
$997$			54.5265i			1.72687i	0.504459	+	0.863436i	$0.331692\pi$
$997$			54.5265i			1.72687i	−0.504459	+	0.863436i	$0.668308\pi$
$998$	23.4395	+	13.5328i	0.741964	+	0.428373i
$999$	−28.9607	−	50.1614i	−0.916276	−	1.58704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.14	yes	52
5.4	even	2	inner	670.2.h.c.439.13	yes	52
67.29	even	3	inner	670.2.h.c.29.1	✓	52
335.29	even	6	inner	670.2.h.c.29.26	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.1	✓	52	67.29	even	3	inner
670.2.h.c.29.26	yes	52	335.29	even	6	inner
670.2.h.c.439.13	yes	52	5.4	even	2	inner
670.2.h.c.439.14	yes	52	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -3.40294i q^{3} +(0.500000 - 0.866025i) q^{4} +(1.60001 + 1.56204i) q^{5} +(-1.70147 - 2.94703i) q^{6} +(3.81692 + 2.20370i) q^{7} -1.00000i q^{8} -8.57997 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -3.40294i q^{3} +(0.500000 - 0.866025i) q^{4} +(1.60001 + 1.56204i) q^{5} +(-1.70147 - 2.94703i) q^{6} +(3.81692 + 2.20370i) q^{7} -1.00000i q^{8} -8.57997 q^{9} +(2.16667 + 0.552755i) q^{10} +(2.26790 - 3.92812i) q^{11} +(-2.94703 - 1.70147i) q^{12} +(-0.389955 + 0.225141i) q^{13} +4.40740 q^{14} +(5.31551 - 5.44475i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.11307 + 1.21998i) q^{17} +(-7.43048 + 4.28999i) q^{18} +(-2.49163 - 4.31562i) q^{19} +(2.15277 - 0.604635i) q^{20} +(7.49905 - 12.9887i) q^{21} -4.53580i q^{22} +(1.81352 - 1.04704i) q^{23} -3.40294 q^{24} +(0.120090 + 4.99856i) q^{25} +(-0.225141 + 0.389955i) q^{26} +18.9883i q^{27} +(3.81692 - 2.20370i) q^{28} +(2.33332 - 4.04144i) q^{29} +(1.88099 - 7.37304i) q^{30} +(-3.84677 + 6.66281i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-13.3671 - 7.71752i) q^{33} +(-1.21998 + 2.11307i) q^{34} +(2.66487 + 9.48811i) q^{35} +(-4.28999 + 7.43048i) q^{36} +(-2.64170 + 1.52519i) q^{37} +(-4.31562 - 2.49163i) q^{38} +(0.766139 + 1.32699i) q^{39} +(1.56204 - 1.60001i) q^{40} +(-2.68395 + 4.64874i) q^{41} -14.9981i q^{42} +1.96768i q^{43} +(-2.26790 - 3.92812i) q^{44} +(-13.7281 - 13.4022i) q^{45} +(1.04704 - 1.81352i) q^{46} +(7.39586 + 4.27000i) q^{47} +(-2.94703 + 1.70147i) q^{48} +(6.21258 + 10.7605i) q^{49} +(2.60328 + 4.26883i) q^{50} +(4.15153 + 7.19066i) q^{51} +0.450281i q^{52} +6.26671i q^{53} +(9.49415 + 16.4443i) q^{54} +(9.76454 - 2.74251i) q^{55} +(2.20370 - 3.81692i) q^{56} +(-14.6858 + 8.47885i) q^{57} -4.66665i q^{58} +4.27352 q^{59} +(-2.05753 - 7.32574i) q^{60} +(-6.76479 - 11.7170i) q^{61} +7.69355i q^{62} +(-32.7491 - 18.9077i) q^{63} -1.00000 q^{64} +(-0.975611 - 0.248895i) q^{65} -15.4350 q^{66} +(-1.54633 - 8.03796i) q^{67} +2.43997i q^{68} +(-3.56300 - 6.17129i) q^{69} +(7.05190 + 6.88451i) q^{70} +(-6.40231 + 11.0891i) q^{71} +8.57997i q^{72} +(-2.02350 + 1.16827i) q^{73} +(-1.52519 + 2.64170i) q^{74} +(17.0098 - 0.408660i) q^{75} -4.98325 q^{76} +(17.3128 - 9.99554i) q^{77} +(1.32699 + 0.766139i) q^{78} +(1.65104 - 2.85968i) q^{79} +(0.552755 - 2.16667i) q^{80} +38.8760 q^{81} +5.36790i q^{82} +(0.769075 - 0.444026i) q^{83} +(-7.49905 - 12.9887i) q^{84} +(-5.28661 - 1.34871i) q^{85} +(0.983840 + 1.70406i) q^{86} +(-13.7527 - 7.94015i) q^{87} +(-3.92812 - 2.26790i) q^{88} +0.369395 q^{89} +(-18.5900 - 4.74263i) q^{90} -1.98457 q^{91} -2.09407i q^{92} +(22.6731 + 13.0903i) q^{93} +8.54001 q^{94} +(2.75452 - 10.7971i) q^{95} +(-1.70147 + 2.94703i) q^{96} +(-4.39125 + 2.53529i) q^{97} +(10.7605 + 6.21258i) q^{98} +(-19.4585 + 33.7032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Introduction

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