LMFDB - Embedded newform 403.2.g.a.87.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(87,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("403.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			87.6
Character	$\chi$	$=$	403.87
Dual form			403.2.g.a.315.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05012 + 1.81887i) q^{2} +2.74399 q^{3} +(-1.20552 - 2.08802i) q^{4} +(0.498066 - 0.862675i) q^{5} +(-2.88153 + 4.99096i) q^{6} +(1.76422 - 3.05572i) q^{7} +0.863293 q^{8} +4.52949 q^{9} +O(q^{10})$	\(q+(-1.05012 + 1.81887i) q^{2} +2.74399 q^{3} +(-1.20552 - 2.08802i) q^{4} +(0.498066 - 0.862675i) q^{5} +(-2.88153 + 4.99096i) q^{6} +(1.76422 - 3.05572i) q^{7} +0.863293 q^{8} +4.52949 q^{9} +(1.04606 + 1.81183i) q^{10} +(-0.982713 - 1.70211i) q^{11} +(-3.30794 - 5.72952i) q^{12} +(3.58208 - 0.410739i) q^{13} +(3.70530 + 6.41777i) q^{14} +(1.36669 - 2.36717i) q^{15} +(1.50448 - 2.60583i) q^{16} +(-3.08155 + 5.33741i) q^{17} +(-4.75653 + 8.23855i) q^{18} +(-2.34816 + 4.06713i) q^{19} -2.40172 q^{20} +(4.84101 - 8.38488i) q^{21} +4.12788 q^{22} +(4.08816 - 7.08091i) q^{23} +2.36887 q^{24} +(2.00386 + 3.47079i) q^{25} +(-3.01455 + 6.94666i) q^{26} +4.19692 q^{27} -8.50723 q^{28} +(-3.21532 + 5.56909i) q^{29} +(2.87039 + 4.97166i) q^{30} +(4.20362 - 3.65097i) q^{31} +(4.02307 + 6.96816i) q^{32} +(-2.69656 - 4.67057i) q^{33} +(-6.47203 - 11.2099i) q^{34} +(-1.75740 - 3.04390i) q^{35} +(-5.46040 - 9.45769i) q^{36} -5.32538 q^{37} +(-4.93172 - 8.54199i) q^{38} +(9.82920 - 1.12707i) q^{39} +(0.429977 - 0.744741i) q^{40} +(-2.00730 - 3.47675i) q^{41} +(10.1673 + 17.6103i) q^{42} +(-1.31763 + 2.28220i) q^{43} +(-2.36936 + 4.10386i) q^{44} +(2.25599 - 3.90748i) q^{45} +(8.58616 + 14.8717i) q^{46} -9.15867 q^{47} +(4.12828 - 7.15039i) q^{48} +(-2.72496 - 4.71976i) q^{49} -8.41721 q^{50} +(-8.45576 + 14.6458i) q^{51} +(-5.17591 - 6.98432i) q^{52} +(-4.78872 + 8.29431i) q^{53} +(-4.40728 + 7.63364i) q^{54} -1.95782 q^{55} +(1.52304 - 2.63798i) q^{56} +(-6.44333 + 11.1602i) q^{57} +(-6.75296 - 11.6965i) q^{58} +(-3.43066 + 5.94207i) q^{59} -6.59029 q^{60} +(6.35707 + 11.0108i) q^{61} +(2.22632 + 11.4798i) q^{62} +(7.99103 - 13.8409i) q^{63} -10.8810 q^{64} +(1.42978 - 3.29475i) q^{65} +11.3269 q^{66} +(-3.96515 - 6.86783i) q^{67} +14.8595 q^{68} +(11.2179 - 19.4300i) q^{69} +7.38194 q^{70} -0.788971 q^{71} +3.91028 q^{72} +(0.371085 - 0.642738i) q^{73} +(5.59231 - 9.68616i) q^{74} +(5.49858 + 9.52382i) q^{75} +11.3230 q^{76} -6.93489 q^{77} +(-8.27190 + 19.0616i) q^{78} +(-2.77712 - 4.81012i) q^{79} +(-1.49866 - 2.59575i) q^{80} -2.07217 q^{81} +8.43167 q^{82} +(0.678166 - 1.17462i) q^{83} -23.3438 q^{84} +(3.06963 + 5.31676i) q^{85} +(-2.76735 - 4.79320i) q^{86} +(-8.82280 + 15.2815i) q^{87} +(-0.848369 - 1.46942i) q^{88} +(1.18104 - 2.04562i) q^{89} +(4.73813 + 8.20668i) q^{90} +(5.06448 - 11.6705i) q^{91} -19.7135 q^{92} +(11.5347 - 10.0182i) q^{93} +(9.61774 - 16.6584i) q^{94} +(2.33908 + 4.05140i) q^{95} +(11.0393 + 19.1206i) q^{96} +(0.796457 + 1.37950i) q^{97} +11.4462 q^{98} +(-4.45119 - 7.70969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9}+O(q^{10}) $ 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} - 28 q^{16} + 14 q^{17} - 20 q^{18} - 2 q^{19} - 50 q^{20} - 21 q^{21} - 8 q^{22} + 2 q^{23} - 8 q^{24} - 23 q^{25} + 6 q^{26} - 38 q^{27} + 42 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} - 28 q^{36} + 24 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} - 2 q^{41} + 27 q^{42} - q^{43} + 2 q^{44} - 29 q^{45} + 14 q^{46} + q^{48} - 37 q^{49} - 14 q^{50} - 9 q^{51} - 19 q^{52} - 2 q^{53} + 24 q^{54} - 10 q^{55} - 13 q^{56} - q^{57} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 3 q^{61} - 23 q^{62} - 32 q^{63} - 14 q^{64} + 23 q^{65} - 28 q^{66} - 2 q^{67} - 84 q^{68} + 32 q^{69} - 14 q^{70} - 86 q^{71} + 10 q^{72} + 11 q^{73} - 7 q^{74} + 37 q^{75} + 56 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} + 38 q^{80} + 22 q^{81} + 34 q^{82} + 56 q^{83} + 90 q^{84} - 5 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 19 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} - 24 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 + 4 * q^13 - 10 * q^14 + q^15 - 28 * q^16 + 14 * q^17 - 20 * q^18 - 2 * q^19 - 50 * q^20 - 21 * q^21 - 8 * q^22 + 2 * q^23 - 8 * q^24 - 23 * q^25 + 6 * q^26 - 38 * q^27 + 42 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 - 28 * q^36 + 24 * q^37 - 7 * q^38 + 10 * q^39 - q^40 - 2 * q^41 + 27 * q^42 - q^43 + 2 * q^44 - 29 * q^45 + 14 * q^46 + q^48 - 37 * q^49 - 14 * q^50 - 9 * q^51 - 19 * q^52 - 2 * q^53 + 24 * q^54 - 10 * q^55 - 13 * q^56 - q^57 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 3 * q^61 - 23 * q^62 - 32 * q^63 - 14 * q^64 + 23 * q^65 - 28 * q^66 - 2 * q^67 - 84 * q^68 + 32 * q^69 - 14 * q^70 - 86 * q^71 + 10 * q^72 + 11 * q^73 - 7 * q^74 + 37 * q^75 + 56 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 + 38 * q^80 + 22 * q^81 + 34 * q^82 + 56 * q^83 + 90 * q^84 - 5 * q^85 + 54 * q^86 - 24 * q^87 + 4 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 19 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 - 24 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.05012	+	1.81887i	−0.742550	+	1.28613i	0.208781	+	0.977962i	$0.433050\pi$
$2$	−1.05012	+	1.81887i	−0.742550	+	1.28613i	−0.951331	+	0.308172i	$0.900283\pi$
$3$	2.74399			1.58424			0.792122	−	0.610362i	$-0.208976\pi$
$3$	2.74399			1.58424			0.792122	+	0.610362i	$0.208976\pi$
$4$	−1.20552	−	2.08802i	−0.602761	−	1.04401i
$5$	0.498066	−	0.862675i	0.222742	−	0.385800i	−0.732898	−	0.680339i	$-0.761833\pi$
$5$	0.498066	−	0.862675i	0.222742	−	0.385800i	0.955640	+	0.294539i	$0.0951660\pi$
$6$	−2.88153	+	4.99096i	−1.17638	+	2.03755i
$7$	1.76422	−	3.05572i	0.666813	−	1.15495i	−0.311977	−	0.950090i	$-0.600991\pi$
$7$	1.76422	−	3.05572i	0.666813	−	1.15495i	0.978790	−	0.204865i	$-0.0656754\pi$
$8$	0.863293			0.305220
$9$	4.52949			1.50983
$10$	1.04606	+	1.81183i	0.330794	+	0.572952i
$11$	−0.982713	−	1.70211i	−0.296299	−	0.513205i	0.678987	−	0.734150i	$-0.262419\pi$
$11$	−0.982713	−	1.70211i	−0.296299	−	0.513205i	−0.975286	+	0.220945i	$0.929086\pi$
$12$	−3.30794	−	5.72952i	−0.954921	−	1.65397i
$13$	3.58208	−	0.410739i	0.993490	−	0.113919i
$13$	3.58208	−	0.410739i	0.993490	−	0.113919i
$14$	3.70530	+	6.41777i	0.990284	+	1.71522i
$15$	1.36669	−	2.36717i	0.352878	−	0.611202i
$16$	1.50448	−	2.60583i	0.376120	−	0.651458i
$17$	−3.08155	+	5.33741i	−0.747387	+	1.29451i	0.201685	+	0.979450i	$0.435358\pi$
$17$	−3.08155	+	5.33741i	−0.747387	+	1.29451i	−0.949071	+	0.315061i	$0.897975\pi$
$18$	−4.75653	+	8.23855i	−1.12112	+	1.94185i
$19$	−2.34816	+	4.06713i	−0.538705	+	0.933064i	0.460269	+	0.887779i	$0.347753\pi$
$19$	−2.34816	+	4.06713i	−0.538705	+	0.933064i	−0.998974	+	0.0452850i	$0.985580\pi$
$20$	−2.40172			−0.537040
$21$	4.84101	−	8.38488i	1.05640	−	1.82973i
$22$	4.12788			0.880067
$23$	4.08816	−	7.08091i	0.852441	−	1.47647i	−0.0265580	−	0.999647i	$-0.508455\pi$
$23$	4.08816	−	7.08091i	0.852441	−	1.47647i	0.878999	−	0.476824i	$-0.158212\pi$
$24$	2.36887			0.483543
$25$	2.00386	+	3.47079i	0.400772	+	0.694158i
$26$	−3.01455	+	6.94666i	−0.591201	+	1.36235i
$27$	4.19692			0.807697
$28$	−8.50723			−1.60772
$29$	−3.21532	+	5.56909i	−0.597069	+	1.03415i	0.396182	+	0.918172i	$0.370335\pi$
$29$	−3.21532	+	5.56909i	−0.597069	+	1.03415i	−0.993251	+	0.115982i	$0.962998\pi$
$30$	2.87039	+	4.97166i	0.524058	+	0.907696i
$31$	4.20362	−	3.65097i	0.754992	−	0.655734i
$31$	4.20362	−	3.65097i	0.754992	−	0.655734i
$32$	4.02307	+	6.96816i	0.711185	+	1.23181i
$33$	−2.69656	−	4.67057i	−0.469410	−	0.813042i
$34$	−6.47203	−	11.2099i	−1.10994	−	1.92248i
$35$	−1.75740	−	3.04390i	−0.297054	−	0.514513i
$36$	−5.46040	−	9.45769i	−0.910067	−	1.57628i
$37$	−5.32538			−0.875487			−0.437743	−	0.899100i	$-0.644222\pi$
$37$	−5.32538			−0.875487			−0.437743	+	0.899100i	$0.644222\pi$
$38$	−4.93172	−	8.54199i	−0.800031	−	1.38569i
$39$	9.82920	−	1.12707i	1.57393	−	0.180475i
$40$	0.429977	−	0.744741i	0.0679853	−	0.117754i
$41$	−2.00730	−	3.47675i	−0.313488	−	0.542977i	0.665627	−	0.746285i	$-0.268164\pi$
$41$	−2.00730	−	3.47675i	−0.313488	−	0.542977i	−0.979115	+	0.203308i	$0.934831\pi$
$42$	10.1673	+	17.6103i	1.56885	+	2.71733i
$43$	−1.31763	+	2.28220i	−0.200937	+	0.348033i	−0.948831	−	0.315786i	$-0.897732\pi$
$43$	−1.31763	+	2.28220i	−0.200937	+	0.348033i	0.747894	+	0.663819i	$0.231065\pi$
$44$	−2.36936	+	4.10386i	−0.357195	+	0.618680i
$45$	2.25599	−	3.90748i	0.336303	−	0.582493i
$46$	8.58616	+	14.8717i	1.26596	+	2.19271i
$47$	−9.15867			−1.33593			−0.667965	−	0.744193i	$-0.732834\pi$
$47$	−9.15867			−1.33593			−0.667965	+	0.744193i	$0.732834\pi$
$48$	4.12828	−	7.15039i	0.595866	−	1.03207i
$49$	−2.72496	−	4.71976i	−0.389280	−	0.674252i
$50$	−8.41721			−1.19037
$51$	−8.45576	+	14.6458i	−1.18404	+	2.05082i
$52$	−5.17591	−	6.98432i	−0.717769	−	0.968550i
$53$	−4.78872	+	8.29431i	−0.657782	+	1.13931i	0.323407	+	0.946260i	$0.395172\pi$
$53$	−4.78872	+	8.29431i	−0.657782	+	1.13931i	−0.981189	+	0.193051i	$0.938162\pi$
$54$	−4.40728	+	7.63364i	−0.599755	+	1.03881i
$55$	−1.95782			−0.263993
$56$	1.52304	−	2.63798i	0.203525	−	0.352515i
$57$	−6.44333	+	11.1602i	−0.853440	+	1.47820i
$58$	−6.75296	−	11.6965i	−0.886707	−	1.53582i
$59$	−3.43066	+	5.94207i	−0.446633	+	0.773592i	−0.998164	−	0.0605626i	$-0.980711\pi$
$59$	−3.43066	+	5.94207i	−0.446633	+	0.773592i	0.551531	+	0.834154i	$0.314044\pi$
$60$	−6.59029			−0.850803
$61$	6.35707	+	11.0108i	0.813939	+	1.40978i	0.910087	+	0.414417i	$0.136015\pi$
$61$	6.35707	+	11.0108i	0.813939	+	1.40978i	−0.0961474	+	0.995367i	$0.530652\pi$
$62$	2.22632	+	11.4798i	0.282742	+	1.45794i
$63$	7.99103	−	13.8409i	1.00678	−	1.74379i
$64$	−10.8810			−1.36012
$65$	1.42978	−	3.29475i	0.177342	−	0.408663i
$66$	11.3269			1.39424
$67$	−3.96515	−	6.86783i	−0.484420	−	0.839039i	0.515420	−	0.856938i	$-0.327636\pi$
$67$	−3.96515	−	6.86783i	−0.484420	−	0.839039i	−0.999840	+	0.0178982i	$0.994303\pi$
$68$	14.8595			1.80198
$69$	11.2179	−	19.4300i	1.35047	−	2.33909i
$70$	7.38194			0.882311
$71$	−0.788971			−0.0936336			−0.0468168	−	0.998903i	$-0.514908\pi$
$71$	−0.788971			−0.0936336			−0.0468168	+	0.998903i	$0.514908\pi$
$72$	3.91028			0.460831
$73$	0.371085	−	0.642738i	0.0434322	−	0.0752268i	−0.843492	−	0.537142i	$-0.819504\pi$
$73$	0.371085	−	0.642738i	0.0434322	−	0.0752268i	0.886924	+	0.461915i	$0.152837\pi$
$74$	5.59231	−	9.68616i	0.650092	−	1.12599i
$75$	5.49858	+	9.52382i	0.634921	+	1.09972i
$76$	11.3230			1.29884
$77$	−6.93489			−0.790304
$78$	−8.27190	+	19.0616i	−0.936608	+	2.15830i
$79$	−2.77712	−	4.81012i	−0.312451	−	0.541181i	0.666441	−	0.745557i	$-0.267817\pi$
$79$	−2.77712	−	4.81012i	−0.312451	−	0.541181i	−0.978892	+	0.204377i	$0.934483\pi$
$80$	−1.49866	−	2.59575i	−0.167555	−	0.290214i
$81$	−2.07217			−0.230241
$82$	8.43167			0.931122
$83$	0.678166	−	1.17462i	0.0744384	−	0.128931i	−0.826404	−	0.563078i	$-0.809617\pi$
$83$	0.678166	−	1.17462i	0.0744384	−	0.128931i	0.900842	+	0.434147i	$0.142950\pi$
$84$	−23.3438			−2.54701
$85$	3.06963	+	5.31676i	0.332949	+	0.576684i
$86$	−2.76735	−	4.79320i	−0.298411	−	0.516864i
$87$	−8.82280	+	15.2815i	−0.945904	+	1.63835i
$88$	−0.848369	−	1.46942i	−0.0904364	−	0.156640i
$89$	1.18104	−	2.04562i	0.125190	−	0.216835i	−0.796617	−	0.604484i	$-0.793379\pi$
$89$	1.18104	−	2.04562i	0.125190	−	0.216835i	0.921807	+	0.387649i	$0.126713\pi$
$90$	4.73813	+	8.20668i	0.499443	+	0.865060i
$91$	5.06448	−	11.6705i	0.530902	−	1.22340i
$92$	−19.7135			−2.05527
$93$	11.5347	−	10.0182i	1.19609	−	1.03884i
$94$	9.61774	−	16.6584i	0.991995	−	1.71819i
$95$	2.33908	+	4.05140i	0.239984	+	0.415665i
$96$	11.0393	+	19.1206i	1.12669	+	1.95149i
$97$	0.796457	+	1.37950i	0.0808679	+	0.140067i	0.903623	−	0.428329i	$-0.140897\pi$
$97$	0.796457	+	1.37950i	0.0808679	+	0.140067i	−0.822755	+	0.568396i	$0.807564\pi$
$98$	11.4462			1.15624
$99$	−4.45119	−	7.70969i	−0.447361	−	0.774853i
$100$	4.83139	−	8.36822i	0.483139	−	0.836822i
$101$	9.11073	−	15.7802i	0.906551	−	1.57019i	0.0877301	−	0.996144i	$-0.472039\pi$
$101$	9.11073	−	15.7802i	0.906551	−	1.57019i	0.818821	−	0.574049i	$-0.194628\pi$
$102$	−17.7592	−	30.7598i	−1.75842	−	3.04568i
$103$	2.10776	−	3.65074i	0.207683	−	0.359718i	−0.743301	−	0.668957i	$-0.766741\pi$
$103$	2.10776	−	3.65074i	0.207683	−	0.359718i	0.950984	+	0.309239i	$0.100074\pi$
$104$	3.09238	−	0.354588i	0.303233	−	0.0347702i
$105$	−4.82229	−	8.35244i	−0.470607	−	0.815115i
$106$	−10.0575	−	17.4201i	−0.976871	−	1.69199i
$107$	1.33631			0.129186			0.0645929	−	0.997912i	$-0.479425\pi$
$107$	1.33631			0.129186			0.0645929	+	0.997912i	$0.479425\pi$
$108$	−5.05947	−	8.76327i	−0.486848	−	0.843246i
$109$	−2.74132			−0.262571			−0.131285	−	0.991345i	$-0.541910\pi$
$109$	−2.74132			−0.262571			−0.131285	+	0.991345i	$0.541910\pi$
$110$	2.05596	−	3.56102i	0.196028	−	0.339530i
$111$	−14.6128			−1.38698
$112$	−5.30847	−	9.19454i	−0.501603	−	0.868802i
$113$	12.0154			1.13031			0.565155	−	0.824985i	$-0.308816\pi$
$113$	12.0154			1.13031			0.565155	+	0.824985i	$0.308816\pi$
$114$	−13.5326	−	23.4392i	−1.26744	−	2.19528i
$115$	−4.07235	−	7.05352i	−0.379749	−	0.657744i
$116$	15.5045			1.43956
$117$	16.2250	−	1.86044i	1.50000	−	0.171998i
$118$	−7.20523	−	12.4798i	−0.663295	−	1.14886i
$119$	10.8731	+	18.8327i	0.996734	+	1.72639i
$120$	1.17985	−	2.04356i	0.107705	−	0.186551i
$121$	3.56855	−	6.18091i	0.324414	−	0.561901i
$122$	−26.7029			−2.41756
$123$	−5.50802	−	9.54018i	−0.496642	−	0.860209i
$124$	−12.6909	−	4.37593i	−1.13967	−	0.392970i
$125$	8.97288			0.802559
$126$	16.7831	+	29.0693i	1.49516	+	2.58970i
$127$	−9.54224			−0.846737			−0.423369	−	0.905958i	$-0.639152\pi$
$127$	−9.54224			−0.846737			−0.423369	+	0.905958i	$0.639152\pi$
$128$	3.38024	−	5.85475i	0.298774	−	0.517492i
$129$	−3.61557	+	6.26235i	−0.318333	+	0.551369i
$130$	4.49127	+	6.06047i	0.393910	+	0.531538i
$131$	7.65368	+	13.2566i	0.668705	+	1.15823i	0.978266	+	0.207352i	$0.0664844\pi$
$131$	7.65368	+	13.2566i	0.668705	+	1.15823i	−0.309562	+	0.950879i	$0.600182\pi$
$132$	−6.50151	+	11.2610i	−0.565884	+	0.980140i
$133$	8.28535	+	14.3507i	0.718431	+	1.24436i
$134$	16.6556			1.43882
$135$	2.09034	−	3.62058i	0.179908	−	0.311610i
$136$	−2.66028	+	4.60775i	−0.228117	+	0.395111i
$137$	−3.95944			−0.338278			−0.169139	−	0.985592i	$-0.554099\pi$
$137$	−3.95944			−0.338278			−0.169139	+	0.985592i	$0.554099\pi$
$138$	23.5603	+	40.8077i	2.00559	+	3.47378i
$139$	−7.27929	−	12.6081i	−0.617421	−	1.06940i	−0.989955	−	0.141386i	$-0.954844\pi$
$139$	−7.27929	−	12.6081i	−0.617421	−	1.06940i	0.372534	−	0.928019i	$-0.378489\pi$
$140$	−4.23716	+	7.33898i	−0.358105	+	0.620257i
$141$	−25.1313			−2.11644
$142$	0.828517	−	1.43503i	0.0695276	−	0.120425i
$143$	−4.21928	−	5.69345i	−0.352834	−	0.476110i
$144$	6.81453	−	11.8031i	0.567877	−	0.983592i
$145$	3.20288	+	5.54755i	0.265985	+	0.460699i
$146$	0.779370	+	1.34991i	0.0645012	+	0.111719i
$147$	−7.47726	−	12.9510i	−0.616714	−	1.06818i
$148$	6.41986	+	11.1195i	0.527709	+	0.914019i
$149$	−7.46846	+	12.9357i	−0.611840	+	1.05974i	0.379090	+	0.925360i	$0.376237\pi$
$149$	−7.46846	+	12.9357i	−0.611840	+	1.05974i	−0.990930	+	0.134378i	$0.957096\pi$
$150$	−23.0968			−1.88584
$151$	−1.96482			−0.159895			−0.0799476	−	0.996799i	$-0.525475\pi$
$151$	−1.96482			−0.159895			−0.0799476	+	0.996799i	$0.525475\pi$
$152$	−2.02715	+	3.51113i	−0.164424	+	0.284790i
$153$	−13.9579	+	24.1758i	−1.12843	+	1.95449i
$154$	7.28250	−	12.6137i	0.586840	−	1.01644i
$155$	−1.05592	−	5.44478i	−0.0848139	−	0.437336i
$156$	−14.2027	−	19.1649i	−1.13712	−	1.53442i
$157$	−4.61957			−0.368681			−0.184341	−	0.982862i	$-0.559015\pi$
$157$	−4.61957			−0.368681			−0.184341	+	0.982862i	$0.559015\pi$
$158$	11.6653			0.928042
$159$	−13.1402	+	22.7595i	−1.04209	+	1.80495i
$160$	8.01502			0.633643
$161$	−14.4249	−	24.9846i	−1.13684	−	1.96906i
$162$	2.17604	−	3.76901i	0.170966	−	0.296121i
$163$	6.90828	+	11.9655i	0.541098	+	0.937209i	0.998841	+	0.0481249i	$0.0153246\pi$
$163$	6.90828	+	11.9655i	0.541098	+	0.937209i	−0.457743	+	0.889084i	$0.651342\pi$
$164$	−4.83969	+	8.38259i	−0.377917	+	0.654571i
$165$	−5.37225			−0.418229
$166$	1.42432	+	2.46699i	0.110548	+	0.191476i
$167$	22.6816			1.75516			0.877579	−	0.479432i	$-0.159157\pi$
$167$	22.6816			1.75516			0.877579	+	0.479432i	$0.159157\pi$
$168$	4.17921	−	7.23860i	0.322433	−	0.558470i
$169$	12.6626	−	2.94260i	0.974045	−	0.226354i
$170$	−12.8940			−0.988924
$171$	−10.6360	+	18.4221i	−0.813354	+	1.40877i
$172$	6.35373			0.484467
$173$	6.44552			0.490044			0.245022	−	0.969518i	$-0.421205\pi$
$173$	6.44552			0.490044			0.245022	+	0.969518i	$0.421205\pi$
$174$	−18.5301	−	32.0950i	−1.40476	−	2.43312i
$175$	14.1410			1.06896
$176$	−5.91388			−0.445776
$177$	−9.41369	+	16.3050i	−0.707577	+	1.22556i
$178$	2.48047	+	4.29631i	0.185919	+	0.322022i
$179$	−12.6018			−0.941900			−0.470950	−	0.882160i	$-0.656089\pi$
$179$	−12.6018			−0.941900			−0.470950	+	0.882160i	$0.656089\pi$
$180$	−10.8786			−0.810840
$181$	3.48355	−	6.03368i	0.258930	−	0.448480i	−0.707026	−	0.707188i	$-0.749963\pi$
$181$	3.48355	−	6.03368i	0.258930	−	0.448480i	0.965956	+	0.258708i	$0.0832968\pi$
$182$	15.9087	+	21.4671i	1.17923	+	1.59124i
$183$	17.4438	+	30.2135i	1.28948	+	2.23344i
$184$	3.52928	−	6.11289i	0.260182	−	0.450649i
$185$	−2.65239	+	4.59407i	−0.195007	+	0.337763i
$186$	6.10899	+	31.5005i	0.447933	+	2.30973i
$187$	12.1131			0.885800
$188$	11.0410	+	19.1235i	0.805246	+	1.39473i
$189$	7.40429	−	12.8246i	0.538583	−	0.932853i
$190$	−9.82529			−0.712801
$191$	0.784718			0.0567802			0.0283901	−	0.999597i	$-0.490962\pi$
$191$	0.784718			0.0567802			0.0283901	+	0.999597i	$0.490962\pi$
$192$	−29.8573			−2.15477
$193$	−18.1949			−1.30970			−0.654850	−	0.755759i	$-0.727268\pi$
$193$	−18.1949			−1.30970			−0.654850	+	0.755759i	$0.727268\pi$
$194$	−3.34551			−0.240194
$195$	3.92330	−	9.04076i	0.280953	−	0.647422i
$196$	−6.56999	+	11.3796i	−0.469285	+	0.812825i
$197$	2.01627	+	3.49228i	0.143653	+	0.248815i	0.928870	−	0.370407i	$-0.120782\pi$
$197$	2.01627	+	3.49228i	0.143653	+	0.248815i	−0.785216	+	0.619222i	$0.787448\pi$
$198$	18.6972			1.32875
$199$	−19.7990			−1.40351			−0.701757	−	0.712417i	$-0.747601\pi$
$199$	−19.7990			−1.40351			−0.701757	+	0.712417i	$0.747601\pi$
$200$	1.72992	+	2.99631i	0.122324	+	0.211871i
$201$	−10.8803	−	18.8453i	−0.767439	−	1.32924i
$202$	19.1348	+	33.1424i	1.34632	+	2.33189i
$203$	11.3451	+	19.6502i	0.796267	+	1.37918i
$204$	40.7744			2.85478
$205$	−3.99908			−0.279308
$206$	4.42681	+	7.66746i	0.308431	+	0.534217i
$207$	18.5173	−	32.0729i	1.28704	−	2.22922i
$208$	4.31884	−	9.95225i	0.299458	−	0.690064i
$209$	9.23027			0.638471
$210$	20.2560			1.39780
$211$	−9.80601			−0.675073			−0.337537	−	0.941312i	$-0.609594\pi$
$211$	−9.80601			−0.675073			−0.337537	+	0.941312i	$0.609594\pi$
$212$	23.0916			1.58594
$213$	−2.16493			−0.148339
$214$	−1.40329	+	2.43057i	−0.0959269	+	0.166150i
$215$	1.31253	+	2.27338i	0.0895141	+	0.155043i
$216$	3.62317			0.246525
$217$	−3.74024	−	19.2862i	−0.253904	−	1.30923i
$218$	2.87873	−	4.98610i	0.194972	−	0.337701i
$219$	1.01825	−	1.76367i	0.0688072	−	0.119178i
$220$	2.36020	+	4.08798i	0.159124	+	0.275612i
$221$	−8.84609	+	20.3847i	−0.595052	+	1.37123i
$222$	15.3452	−	26.5787i	1.02991	−	1.78385i
$223$	21.4490			1.43633			0.718164	−	0.695873i	$-0.244983\pi$
$223$	21.4490			1.43633			0.718164	+	0.695873i	$0.244983\pi$
$224$	28.3904			1.89691
$225$	9.07647	+	15.7209i	0.605098	+	1.04806i
$226$	−12.6176	+	21.8544i	−0.839312	+	1.45373i
$227$	−1.20088			−0.0797055			−0.0398528	−	0.999206i	$-0.512689\pi$
$227$	−1.20088			−0.0797055			−0.0398528	+	0.999206i	$0.512689\pi$
$228$	31.0703			2.05768
$229$	0.943285	+	1.63382i	0.0623340	+	0.107966i	0.895508	−	0.445045i	$-0.146812\pi$
$229$	0.943285	+	1.63382i	0.0623340	+	0.107966i	−0.833174	+	0.553011i	$0.813479\pi$
$230$	17.1059			1.12793
$231$	−19.0293			−1.25204
$232$	−2.77576	+	4.80776i	−0.182238	+	0.315645i
$233$	6.03784			0.395552			0.197776	−	0.980247i	$-0.436628\pi$
$233$	6.03784			0.395552			0.197776	+	0.980247i	$0.436628\pi$
$234$	−13.6544	+	31.4648i	−0.892614	+	2.05692i
$235$	−4.56162	+	7.90096i	−0.297568	+	0.515402i
$236$	16.5429			1.07685
$237$	−7.62041	−	13.1989i	−0.494999	−	0.857363i
$238$	−45.6724			−2.96050
$239$	8.01117	−	13.8758i	0.518199	−	0.897548i	−0.481577	−	0.876404i	$-0.659936\pi$
$239$	8.01117	−	13.8758i	0.518199	−	0.897548i	0.999776	−	0.0211440i	$-0.00673084\pi$
$240$	−4.11231	−	7.12273i	−0.265448	−	0.459770i
$241$	−3.34896	+	5.80057i	−0.215726	+	0.373648i	−0.953497	−	0.301403i	$-0.902545\pi$
$241$	−3.34896	+	5.80057i	−0.215726	+	0.373648i	0.737771	+	0.675051i	$0.235878\pi$
$242$	7.49484	+	12.9815i	0.481787	+	0.834479i
$243$	−18.2768			−1.17246
$244$	15.3272	−	26.5474i	0.981222	−	1.69953i
$245$	−5.42883			−0.346835
$246$	23.1364			1.47512
$247$	−6.74077	+	15.5333i	−0.428905	+	0.988359i
$248$	3.62895	−	3.15186i	0.230439	−	0.200143i
$249$	1.86088	−	3.22314i	0.117929	−	0.204258i
$250$	−9.42264	+	16.3205i	−0.595940	+	1.03220i
$251$	4.23511	−	7.33542i	0.267318	−	0.463008i	−0.700851	−	0.713308i	$-0.747196\pi$
$251$	4.23511	−	7.33542i	0.267318	−	0.463008i	0.968168	+	0.250300i	$0.0805294\pi$
$252$	−38.5334			−2.42738
$253$	−16.0700			−1.01031
$254$	10.0205	−	17.3561i	0.628745	−	1.08902i
$255$	8.42305	+	14.5892i	0.527472	+	0.913608i
$256$	−3.78164	−	6.54999i	−0.236352	−	0.409374i
$257$	−10.7590	−	18.6351i	−0.671126	−	1.16242i	−0.977585	−	0.210540i	$-0.932478\pi$
$257$	−10.7590	−	18.6351i	−0.671126	−	1.16242i	0.306459	−	0.951884i	$-0.400856\pi$
$258$	−7.59359	−	13.1525i	−0.472757	−	0.818838i
$259$	−9.39515	+	16.2729i	−0.583786	+	1.01115i
$260$	−8.60314	+	0.986479i	−0.533544	+	0.0611789i
$261$	−14.5638	+	25.2252i	−0.901474	+	1.56140i
$262$	−32.1492			−1.98619
$263$	−2.04699	+	3.54550i	−0.126223	+	0.218625i	−0.922210	−	0.386689i	$-0.873619\pi$
$263$	−2.04699	+	3.54550i	−0.126223	+	0.218625i	0.795987	+	0.605313i	$0.206952\pi$
$264$	−2.32792	−	4.03207i	−0.143273	−	0.248157i
$265$	4.77020	+	8.26223i	0.293031	+	0.507545i
$266$	−34.8026			−2.13388
$267$	3.24076	−	5.61316i	0.198331	−	0.343520i
$268$	−9.56014	+	16.5586i	−0.583978	+	1.01148i
$269$	−26.1379			−1.59366			−0.796829	−	0.604205i	$-0.793491\pi$
$269$	−26.1379			−1.59366			−0.796829	+	0.604205i	$0.793491\pi$
$270$	4.39024	+	7.60411i	0.267181	+	0.462772i
$271$	−13.9052	+	24.0845i	−0.844681	+	1.46303i	0.0412168	+	0.999150i	$0.486877\pi$
$271$	−13.9052	+	24.0845i	−0.844681	+	1.46303i	−0.885898	+	0.463880i	$0.846457\pi$
$272$	9.27226	+	16.0600i	0.562214	+	0.973783i
$273$	13.8969	−	32.0237i	0.841078	−	1.93816i
$274$	4.15790	−	7.20170i	0.251188	−	0.435071i
$275$	3.93844	−	6.82158i	0.237497	−	0.411356i
$276$	−54.0936			−3.25605
$277$	9.02907	+	15.6388i	0.542504	+	0.939644i	0.998759	+	0.0497956i	$0.0158570\pi$
$277$	9.02907	+	15.6388i	0.542504	+	0.939644i	−0.456255	+	0.889849i	$0.650810\pi$
$278$	30.5766			1.83386
$279$	19.0403	−	16.5371i	1.13991	−	0.990047i
$280$	−1.51715	−	2.62778i	−0.0906670	−	0.157040i
$281$	−21.0516			−1.25583			−0.627917	−	0.778281i	$-0.716092\pi$
$281$	−21.0516			−1.25583			−0.627917	+	0.778281i	$0.716092\pi$
$282$	26.3910	−	45.7106i	1.57156	−	2.72203i
$283$	14.5972	−	25.2832i	0.867716	−	1.50293i	0.00339019	−	0.999994i	$-0.498921\pi$
$283$	14.5972	−	25.2832i	0.867716	−	1.50293i	0.864325	−	0.502933i	$-0.167746\pi$
$284$	0.951121	+	1.64739i	0.0564387	+	0.0977546i
$285$	6.41841	+	11.1170i	0.380194	+	0.658515i
$286$	14.7864	−	1.69548i	0.874338	−	0.100256i
$287$	−14.1653			−0.836152
$288$	18.2225	+	31.5623i	1.07377	+	1.85982i
$289$	−10.4919	−	18.1726i	−0.617174	−	1.06898i
$290$	−13.4537			−0.790027
$291$	2.18547	+	3.78535i	0.128115	+	0.221901i
$292$	−1.78940			−0.104717
$293$	−5.50225	+	9.53017i	−0.321445	+	0.556759i	−0.980786	−	0.195085i	$-0.937502\pi$
$293$	−5.50225	+	9.53017i	−0.321445	+	0.556759i	0.659342	+	0.751843i	$0.270835\pi$
$294$	31.4082			1.83176
$295$	3.41739	+	5.91909i	0.198968	+	0.344623i
$296$	−4.59736			−0.267216
$297$	−4.12436	−	7.14361i	−0.239320	−	0.414514i
$298$	−15.6856	−	27.1683i	−0.908643	−	1.57382i
$299$	11.7357	−	27.0435i	0.678694	−	1.56397i
$300$	13.2573	−	22.9623i	0.765411	−	1.32573i
$301$	4.64919	+	8.05263i	0.267975	+	0.464146i
$302$	2.06331	−	3.57376i	0.118730	−	0.205647i
$303$	24.9998	−	43.3009i	1.43620	−	2.48757i
$304$	7.06551	+	12.2378i	0.405235	+	0.701888i
$305$	12.6650			0.725194
$306$	−29.3150	−	50.7751i	−1.67583	−	2.90262i
$307$	−6.58812	−	11.4110i	−0.376004	−	0.651258i	0.614473	−	0.788938i	$-0.289369\pi$
$307$	−6.58812	−	11.4110i	−0.376004	−	0.651258i	−0.990477	+	0.137680i	$0.956035\pi$
$308$	8.36016	+	14.4802i	0.476364	+	0.825087i
$309$	5.78367	−	10.0176i	0.329021	−	0.569882i
$310$	11.0122	+	3.79711i	0.625451	+	0.215661i
$311$	−14.1854			−0.804382			−0.402191	−	0.915556i	$-0.631751\pi$
$311$	−14.1854			−0.804382			−0.402191	+	0.915556i	$0.631751\pi$
$312$	8.48547	−	0.972987i	0.480395	−	0.0550846i
$313$	−10.0487	−	17.4049i	−0.567986	−	0.983781i	−0.996765	−	0.0803714i	$-0.974389\pi$
$313$	−10.0487	−	17.4049i	−0.567986	−	0.983781i	0.428779	−	0.903409i	$-0.358944\pi$
$314$	4.85112	−	8.40238i	0.273764	−	0.474174i
$315$	−7.96012	−	13.7873i	−0.448502	−	0.776828i
$316$	−6.69577	+	11.5974i	−0.376666	+	0.652405i
$317$	9.81146	+	16.9939i	0.551067	+	0.954475i	0.998198	+	0.0600070i	$0.0191123\pi$
$317$	9.81146	+	16.9939i	0.551067	+	0.954475i	−0.447131	+	0.894468i	$0.647554\pi$
$318$	−27.5977	−	47.8006i	−1.54760	−	2.68053i
$319$	12.6389			0.707644
$320$	−5.41945	+	9.38676i	−0.302956	+	0.524736i
$321$	3.66682			0.204662
$322$	60.5915			3.37663
$323$	−14.4720	−	25.0662i	−0.805242	−	1.39472i
$324$	2.49805	+	4.32674i	0.138780	+	0.240375i
$325$	8.60358	+	11.6096i	0.477241	+	0.643983i
$326$	−29.0182			−1.60717
$327$	−7.52216			−0.415976
$328$	−1.73289	−	3.00145i	−0.0956828	−	0.165728i
$329$	−16.1579	+	27.9864i	−0.890816	+	1.54294i
$330$	5.64153	−	9.77142i	0.310556	−	0.537899i
$331$	16.5809			0.911367			0.455684	−	0.890142i	$-0.349395\pi$
$331$	16.5809			0.911367			0.455684	+	0.890142i	$0.349395\pi$
$332$	−3.27018			−0.179474
$333$	−24.1213			−1.32184
$334$	−23.8185	+	41.2549i	−1.30329	+	2.25737i
$335$	−7.89961			−0.431602
$336$	−14.5664	−	25.2297i	−0.794662	−	1.37639i
$337$	26.9798			1.46968			0.734842	−	0.678238i	$-0.237256\pi$
$337$	26.9798			1.46968			0.734842	+	0.678238i	$0.237256\pi$
$338$	−7.94508	+	26.1217i	−0.432156	+	1.42083i
$339$	32.9701			1.79069
$340$	7.40102	−	12.8189i	0.401377	−	0.695205i
$341$	−10.3453	−	3.56716i	−0.560229	−	0.193172i
$342$	−22.3382	−	38.6909i	−1.20791	−	2.09216i
$343$	5.46939			0.295319
$344$	−1.13750	+	1.97021i	−0.0613300	+	0.106227i
$345$	−11.1745	−	19.3548i	−0.601615	−	1.04203i
$346$	−6.76860	+	11.7236i	−0.363882	+	0.630262i
$347$	−1.62994	+	2.82313i	−0.0874996	+	0.151554i	−0.906454	−	0.422305i	$-0.861221\pi$
$347$	−1.62994	+	2.82313i	−0.0874996	+	0.151554i	0.818954	+	0.573859i	$0.194554\pi$
$348$	42.5443			2.28061
$349$	−6.15819	+	10.6663i	−0.329640	+	0.570953i	−0.982440	−	0.186577i	$-0.940261\pi$
$349$	−6.15819	+	10.6663i	−0.329640	+	0.570953i	0.652800	+	0.757530i	$0.273594\pi$
$350$	−14.8498	+	25.7207i	−0.793757	+	1.37483i
$351$	15.0337	−	1.72384i	0.802439	−	0.0920117i
$352$	7.90705	−	13.6954i	0.421447	−	0.729968i
$353$	9.61364			0.511682			0.255841	−	0.966719i	$-0.417648\pi$
$353$	9.61364			0.511682			0.255841	+	0.966719i	$0.417648\pi$
$354$	−19.7711	−	34.2445i	−1.05082	−	1.82008i
$355$	−0.392959	+	0.680626i	−0.0208561	+	0.0361239i
$356$	−5.69507			−0.301838
$357$	29.8357	+	51.6769i	1.57907	+	2.73503i
$358$	13.2334	−	22.9209i	0.699408	−	1.21141i
$359$	9.60723	−	16.6402i	0.507050	−	0.878237i	−0.492916	−	0.870077i	$-0.664069\pi$
$359$	9.60723	−	16.6402i	0.507050	−	0.878237i	0.999967	−	0.00816010i	$-0.00259747\pi$
$360$	1.94758	−	3.37330i	0.102646	−	0.177789i
$361$	−1.52772	−	2.64608i	−0.0804061	−	0.139267i
$362$	7.31631	+	12.6722i	0.384537	+	0.666037i
$363$	9.79208	−	16.9604i	0.513951	−	0.890189i
$364$	−30.4736	+	3.49425i	−1.59725	+	0.183149i
$365$	−0.369649	−	0.640252i	−0.0193483	−	0.0335123i
$366$	−73.2724			−3.83001
$367$	8.18117	+	14.1702i	0.427054	+	0.739679i	0.996610	−	0.0822738i	$-0.0262182\pi$
$367$	8.18117	+	14.1702i	0.427054	+	0.739679i	−0.569556	+	0.821952i	$0.692885\pi$
$368$	−12.3011	−	21.3061i	−0.641240	−	1.11066i
$369$	−9.09206	−	15.7479i	−0.473314	−	0.819804i
$370$	−5.57067	−	9.64869i	−0.289606	−	0.501612i
$371$	16.8967	+	29.2660i	0.877235	+	1.51942i
$372$	−34.8237	−	12.0075i	−1.80552	−	0.622561i
$373$	−0.970464	−	1.68089i	−0.0502487	−	0.0870333i	0.839807	−	0.542885i	$-0.182668\pi$
$373$	−0.970464	−	1.68089i	−0.0502487	−	0.0870333i	−0.890056	+	0.455852i	$0.849335\pi$
$374$	−12.7203	+	22.0322i	−0.657750	+	1.13926i
$375$	24.6215			1.27145
$376$	−7.90662			−0.407753
$377$	−9.23007	+	21.2696i	−0.475373	+	1.09544i
$378$	15.5509	+	26.9349i	0.799850	+	1.38538i
$379$	11.3389			0.582441			0.291221	−	0.956656i	$-0.405939\pi$
$379$	11.3389			0.582441			0.291221	+	0.956656i	$0.405939\pi$
$380$	5.63962	−	9.76810i	0.289306	−	0.501093i
$381$	−26.1838			−1.34144
$382$	−0.824051	+	1.42730i	−0.0421621	+	0.0730270i
$383$	10.8825			0.556072			0.278036	−	0.960571i	$-0.410317\pi$
$383$	10.8825			0.556072			0.278036	+	0.960571i	$0.410317\pi$
$384$	9.27536	−	16.0654i	0.473331	−	0.819833i
$385$	−3.45403	+	5.98256i	−0.176034	+	0.304900i
$386$	19.1070	−	33.0942i	0.972518	−	1.68445i
$387$	−5.96820	+	10.3372i	−0.303381	+	0.525471i
$388$	1.92029	−	3.32604i	0.0974880	−	0.168854i
$389$	−16.8886	−	29.2519i	−0.856286	−	1.48313i	−0.875447	−	0.483314i	$-0.839433\pi$
$389$	−16.8886	−	29.2519i	−0.856286	−	1.48313i	0.0191613	−	0.999816i	$-0.493900\pi$
$390$	12.3240	+	16.6299i	0.624050	+	0.842087i
$391$	25.1958	+	43.6404i	1.27421	+	2.20699i
$392$	−2.35244	−	4.07454i	−0.118816	−	0.205795i
$393$	21.0016	+	36.3759i	1.05939	+	1.83492i
$394$	−8.46934			−0.426679
$395$	−5.53276			−0.278384
$396$	−10.7320	+	18.5884i	−0.539304	+	0.934102i
$397$	15.4027	−	26.6783i	0.773041	−	1.33895i	−0.162848	−	0.986651i	$-0.552068\pi$
$397$	15.4027	−	26.6783i	0.773041	−	1.33895i	0.935889	−	0.352295i	$-0.114599\pi$
$398$	20.7914	−	36.0118i	1.04218	−	1.80511i
$399$	22.7349	+	39.3781i	1.13817	+	1.97137i
$400$	12.0591			0.602953
$401$	6.02302	−	10.4322i	0.300775	−	0.520958i	−0.675537	−	0.737326i	$-0.736088\pi$
$401$	6.02302	−	10.4322i	0.300775	−	0.520958i	0.976312	+	0.216369i	$0.0694213\pi$
$402$	45.7028			2.27945
$403$	13.5581	−	14.8047i	0.675377	−	0.737473i
$404$	−43.9327			−2.18573
$405$	−1.03208	+	1.78761i	−0.0512844	+	0.0888271i
$406$	−47.6549			−2.36507
$407$	5.23332	+	9.06437i	0.259406	+	0.449304i
$408$	−7.29980	+	12.6436i	−0.361394	+	0.625952i
$409$	−6.38380	+	11.0571i	−0.315659	+	0.546737i	−0.979577	−	0.201068i	$-0.935559\pi$
$409$	−6.38380	+	11.0571i	−0.315659	+	0.546737i	0.663919	+	0.747805i	$0.268892\pi$
$410$	4.19953	−	7.27379i	0.207400	−	0.359227i
$411$	−10.8647			−0.535915
$412$	−10.1638			−0.500734
$413$	12.1049	+	20.9663i	0.595642	+	1.03168i
$414$	38.8909	+	67.3611i	1.91139	+	3.31062i
$415$	−0.675543	−	1.17007i	−0.0331611	−	0.0574367i
$416$	17.2731	+	23.3081i	0.846881	+	1.14277i
$417$	−19.9743	−	34.5965i	−0.978146	−	1.69420i
$418$	−9.69293	+	16.7886i	−0.474097	+	0.821159i
$419$	6.65154	−	11.5208i	0.324949	−	0.562828i	−0.656553	−	0.754280i	$-0.727986\pi$
$419$	6.65154	−	11.5208i	0.324949	−	0.562828i	0.981502	+	0.191452i	$0.0613195\pi$
$420$	−11.6267	+	20.1381i	−0.567327	+	0.982639i
$421$	−9.45129	+	16.3701i	−0.460628	+	0.797830i	−0.998992	−	0.0448816i	$-0.985709\pi$
$421$	−9.45129	+	16.3701i	−0.460628	+	0.797830i	0.538365	+	0.842712i	$0.319042\pi$
$422$	10.2975	−	17.8358i	0.501276	−	0.868235i
$423$	−41.4842			−2.01703
$424$	−4.13407	+	7.16042i	−0.200768	+	0.347741i
$425$	−24.7000			−1.19813
$426$	2.27344	−	3.93772i	0.110149	−	0.190783i
$427$	44.8611			2.17098
$428$	−1.61095	−	2.79024i	−0.0778681	−	0.134872i
$429$	−11.5777	−	15.6228i	−0.558975	−	0.754275i
$430$	−5.51330			−0.265875
$431$	1.13234			0.0545427			0.0272714	−	0.999628i	$-0.491318\pi$
$431$	1.13234			0.0545427			0.0272714	+	0.999628i	$0.491318\pi$
$432$	6.31417	−	10.9365i	0.303791	−	0.526181i
$433$	12.0474	+	20.8667i	0.578961	+	1.00279i	0.995599	+	0.0937168i	$0.0298748\pi$
$433$	12.0474	+	20.8667i	0.578961	+	1.00279i	−0.416638	+	0.909072i	$0.636792\pi$
$434$	39.0068	+	13.4499i	1.87239	+	0.645617i
$435$	8.78867	+	15.2224i	0.421385	+	0.729860i
$436$	3.30472	+	5.72394i	0.158267	+	0.274127i
$437$	19.1993	+	33.2542i	0.918428	+	1.59076i
$438$	2.13859	+	3.70414i	0.102186	+	0.176991i
$439$	16.0674	+	27.8295i	0.766854	+	1.32823i	0.939261	+	0.343205i	$0.111513\pi$
$439$	16.0674	+	27.8295i	0.766854	+	1.32823i	−0.172406	+	0.985026i	$0.555154\pi$
$440$	−1.69017			−0.0805759
$441$	−12.3427	−	21.3781i	−0.587746	−	1.01801i
$442$	−27.7877	−	37.4964i	−1.32172	−	1.78352i
$443$	13.7492	−	23.8144i	0.653246	−	1.13146i	−0.329084	−	0.944301i	$-0.606740\pi$
$443$	13.7492	−	23.8144i	0.653246	−	1.13146i	0.982330	−	0.187155i	$-0.0599268\pi$
$444$	17.6160	+	30.5119i	0.836020	+	1.44803i
$445$	−1.17647	−	2.03771i	−0.0557700	−	0.0965965i
$446$	−22.5241	+	39.0128i	−1.06655	+	1.84731i
$447$	−20.4934	+	35.4956i	−0.969304	+	1.67888i
$448$	−19.1965	+	33.2493i	−0.906948	+	1.57088i
$449$	−15.8669	−	27.4823i	−0.748805	−	1.29697i	−0.948396	−	0.317088i	$-0.897295\pi$
$449$	−15.8669	−	27.4823i	−0.748805	−	1.29697i	0.199591	−	0.979879i	$-0.436039\pi$
$450$	−38.1257			−1.79726
$451$	−3.94520	+	6.83329i	−0.185772	+	0.321767i
$452$	−14.4848	−	25.0884i	−0.681307	−	1.18006i
$453$	−5.39146			−0.253313
$454$	1.26108	−	2.18425i	0.0591853	−	0.102512i
$455$	−7.54539	−	10.1817i	−0.353733	−	0.477324i
$456$	−5.56248	+	9.63450i	−0.260487	+	0.451177i
$457$	−8.10164	+	14.0324i	−0.378979	+	0.656410i	−0.990914	−	0.134498i	$-0.957058\pi$
$457$	−8.10164	+	14.0324i	−0.378979	+	0.656410i	0.611935	+	0.790908i	$0.290391\pi$
$458$	−3.96226			−0.185144
$459$	−12.9330	+	22.4007i	−0.603662	+	1.04557i
$460$	−9.81861	+	17.0063i	−0.457795	+	0.792924i
$461$	−10.2752	−	17.7971i	−0.478562	−	0.828893i	0.521136	−	0.853474i	$-0.325508\pi$
$461$	−10.2752	−	17.7971i	−0.478562	−	0.828893i	−0.999698	+	0.0245804i	$0.992175\pi$
$462$	19.9831	−	34.6118i	0.929699	−	1.61029i
$463$	−5.40882			−0.251369			−0.125685	−	0.992070i	$-0.540113\pi$
$463$	−5.40882			−0.251369			−0.125685	+	0.992070i	$0.540113\pi$
$464$	9.67475	+	16.7572i	0.449139	+	0.777931i
$465$	−2.89745	−	14.9404i	−0.134366	−	0.692846i
$466$	−6.34048	+	10.9820i	−0.293717	+	0.508733i
$467$	−9.88546			−0.457444			−0.228722	−	0.973492i	$-0.573455\pi$
$467$	−9.88546			−0.457444			−0.228722	+	0.973492i	$0.573455\pi$
$468$	−23.4442	−	31.6354i	−1.08371	−	1.46235i
$469$	−27.9816			−1.29207
$470$	−9.58054	−	16.5940i	−0.441917	−	0.765423i
$471$	−12.6761			−0.584082
$472$	−2.96166	+	5.12975i	−0.136321	+	0.236116i
$473$	5.17941			0.238150
$474$	32.0095			1.47024
$475$	−18.8215			−0.863592
$476$	26.2155	−	45.4066i	1.20158	−	2.08121i
$477$	−21.6905	+	37.5690i	−0.993139	+	1.72017i
$478$	16.8254	+	29.1425i	0.769578	+	1.33295i
$479$	24.3692			1.11346			0.556729	−	0.830694i	$-0.312056\pi$
$479$	24.3692			1.11346			0.556729	+	0.830694i	$0.312056\pi$
$480$	21.9932			1.00385
$481$	−19.0759	+	2.18734i	−0.869787	+	0.0997342i
$482$	−7.03365	−	12.1826i	−0.320374	−	0.554904i
$483$	−39.5817	−	68.5575i	−1.80103	−	3.11947i
$484$	−17.2079			−0.782176
$485$	1.58675			0.0720507
$486$	19.1929	−	33.2430i	0.870607	−	1.50794i
$487$	−0.478488			−0.0216823			−0.0108412	−	0.999941i	$-0.503451\pi$
$487$	−0.478488			−0.0216823			−0.0108412	+	0.999941i	$0.503451\pi$
$488$	5.48801	+	9.50552i	0.248431	+	0.430295i
$489$	18.9563	+	32.8332i	0.857232	+	1.48477i
$490$	5.70095	−	9.87433i	0.257543	−	0.446077i
$491$	6.39372	+	11.0742i	0.288545	+	0.499774i	0.973463	−	0.228846i	$-0.0734953\pi$
$491$	6.39372	+	11.0742i	0.288545	+	0.499774i	−0.684918	+	0.728620i	$0.740162\pi$
$492$	−13.2801	+	23.0018i	−0.598712	+	1.03700i
$493$	−19.8163	−	34.3229i	−0.892483	−	1.54583i
$494$	−21.1743	−	28.5724i	−0.952679	−	1.28553i
$495$	−8.86795			−0.398584
$496$	−3.18957	−	16.4467i	−0.143216	−	0.738480i
$497$	−1.39192	+	2.41087i	−0.0624361	+	0.108143i
$498$	3.90832	+	6.76940i	0.175136	+	0.303344i
$499$	4.95811	+	8.58770i	0.221956	+	0.384438i	0.955402	−	0.295309i	$-0.0954227\pi$
$499$	4.95811	+	8.58770i	0.221956	+	0.384438i	−0.733446	+	0.679748i	$0.762089\pi$
$500$	−10.8170	−	18.7356i	−0.483751	−	0.837881i
$501$	62.2383			2.78060
$502$	8.89478	+	15.4062i	0.396993	+	0.687613i
$503$	17.5605	−	30.4157i	0.782986	−	1.35617i	−0.147209	−	0.989105i	$-0.547029\pi$
$503$	17.5605	−	30.4157i	0.782986	−	1.35617i	0.930195	−	0.367066i	$-0.119638\pi$
$504$	6.89860	−	11.9487i	0.307288	−	0.532238i
$505$	−9.07549	−	15.7192i	−0.403854	−	0.699495i
$506$	16.8755	−	29.2291i	0.750205	−	1.29939i
$507$	34.7460	−	8.07447i	1.54313	−	0.358600i
$508$	11.5034	+	19.9244i	0.510380	+	0.884004i
$509$	−0.437868	−	0.758410i	−0.0194082	−	0.0336159i	0.856158	−	0.516714i	$-0.172845\pi$
$509$	−0.437868	−	0.758410i	−0.0194082	−	0.0336159i	−0.875566	+	0.483098i	$0.839512\pi$
$510$	−35.3810			−1.56670
$511$	−1.30935	−	2.26786i	−0.0579223	−	0.100324i
$512$	29.4057			1.29956
$513$	−9.85504	+	17.0694i	−0.435110	+	0.753633i
$514$	45.1930			1.99338
$515$	−2.09960	−	3.63662i	−0.0925196	−	0.160249i
$516$	17.4346			0.767515
$517$	9.00035	+	15.5891i	0.395835	+	0.685606i
$518$	−19.7321	−	34.1771i	−0.866980	−	1.50165i
$519$	17.6865			0.776349
$520$	1.23432	−	2.84433i	0.0541283	−	0.124732i
$521$	12.9258	+	22.3881i	0.566289	+	0.980841i	0.996929	+	0.0783170i	$0.0249546\pi$
$521$	12.9258	+	22.3881i	0.566289	+	0.980841i	−0.430640	+	0.902524i	$0.641712\pi$
$522$	−30.5875	−	52.9791i	−1.33878	−	2.31883i
$523$	−6.26531	+	10.8518i	−0.273963	+	0.474518i	−0.969873	−	0.243611i	$-0.921668\pi$
$523$	−6.26531	+	10.8518i	−0.273963	+	0.474518i	0.695910	+	0.718129i	$0.255001\pi$
$524$	18.4533	−	31.9621i	0.806138	−	1.39627i
$525$	38.8028			1.69350
$526$	−4.29919	−	7.44642i	−0.187454	−	0.324680i
$527$	6.53305	+	33.6871i	0.284584	+	1.46743i
$528$	−16.2276			−0.706218
$529$	−21.9262	−	37.9772i	−0.953311	−	1.65118i
$530$	−20.0372			−0.870361
$531$	−15.5391	+	26.9146i	−0.674341	+	1.16799i
$532$	19.9763	−	34.6000i	0.866084	−	1.50010i
$533$	−8.61836	−	11.6295i	−0.373302	−	0.503730i
$534$	6.80640	+	11.7890i	0.294542	+	0.510161i
$535$	0.665570	−	1.15280i	0.0287751	−	0.0498399i
$536$	−3.42308	−	5.92895i	−0.147855	−	0.256092i
$537$	−34.5791			−1.49220
$538$	27.4481	−	47.5415i	1.18337	−	2.04966i
$539$	−5.35570	+	9.27634i	−0.230686	+	0.399560i
$540$	−10.0798			−0.433766
$541$	−1.00472	−	1.74022i	−0.0431963	−	0.0748181i	0.843619	−	0.536942i	$-0.180421\pi$
$541$	−1.00472	−	1.74022i	−0.0431963	−	0.0748181i	−0.886815	+	0.462124i	$0.847087\pi$
$542$	−29.2044	−	50.5835i	−1.25444	−	2.17275i
$543$	9.55882	−	16.5564i	0.410208	−	0.710502i
$544$	−49.5892			−2.12612
$545$	−1.36536	+	2.36487i	−0.0584855	+	0.101300i
$546$	43.6534	+	58.9055i	1.86819	+	2.52092i
$547$	8.18986	−	14.1852i	0.350173	−	0.606517i	−0.636107	−	0.771601i	$-0.719456\pi$
$547$	8.18986	−	14.1852i	0.350173	−	0.606517i	0.986280	+	0.165084i	$0.0527895\pi$
$548$	4.77319	+	8.26741i	0.203901	+	0.353166i
$549$	28.7943	+	49.8732i	1.22891	+	2.12854i
$550$	8.27170	+	14.3270i	0.352706	+	0.610905i
$551$	−15.1002	−	26.1542i	−0.643288	−	1.11421i
$552$	9.68432	−	16.7737i	0.412192	−	0.713938i
$553$	−19.5979			−0.833386
$554$	−37.9266			−1.61135
$555$	−7.27813	+	12.6061i	−0.308940	+	0.535099i
$556$	−17.5507	+	30.3987i	−0.744314	+	1.28919i
$557$	6.01193	−	10.4130i	0.254734	−	0.441212i	−0.710090	−	0.704111i	$-0.751346\pi$
$557$	6.01193	−	10.4130i	0.254734	−	0.441212i	0.964823	+	0.262900i	$0.0846789\pi$
$558$	10.0841	+	51.9977i	0.426893	+	2.20124i
$559$	−3.78247	+	8.71624i	−0.159981	+	0.368658i
$560$	−10.5759			−0.446912
$561$	33.2383			1.40332
$562$	22.1068	−	38.2901i	0.932519	−	1.61517i
$563$	−26.8506			−1.13162			−0.565808	−	0.824537i	$-0.691436\pi$
$563$	−26.8506			−1.13162			−0.565808	+	0.824537i	$0.691436\pi$
$564$	30.2964	+	52.4748i	1.27571	+	2.20959i
$565$	5.98444	−	10.3654i	0.251767	−	0.436074i
$566$	30.6578	+	53.1009i	1.28864	+	2.23200i
$567$	−3.65577	+	6.33198i	−0.153528	+	0.265918i
$568$	−0.681113			−0.0285788
$569$	−6.60240	−	11.4357i	−0.276787	−	0.479409i	0.693797	−	0.720170i	$-0.255936\pi$
$569$	−6.60240	−	11.4357i	−0.276787	−	0.479409i	−0.970584	+	0.240761i	$0.922603\pi$
$570$	−26.9605			−1.12925
$571$	−3.23857	+	5.60936i	−0.135530	+	0.234745i	−0.925800	−	0.378014i	$-0.876607\pi$
$571$	−3.23857	+	5.60936i	−0.135530	+	0.234745i	0.790270	+	0.612759i	$0.209940\pi$
$572$	−6.80163	+	15.6735i	−0.284390	+	0.655343i
$573$	2.15326			0.0899537
$574$	14.8753	−	25.7648i	0.620884	−	1.07540i
$575$	32.7684			1.36654
$576$	−49.2853			−2.05356
$577$	7.62327	+	13.2039i	0.317361	+	0.549685i	0.979937	−	0.199310i	$-0.0638700\pi$
$577$	7.62327	+	13.2039i	0.317361	+	0.549685i	−0.662576	+	0.748995i	$0.730537\pi$
$578$	44.0714			1.83313
$579$	−49.9268			−2.07489
$580$	7.72228	−	13.3754i	0.320650	−	0.555382i
$581$	−2.39287	−	4.14457i	−0.0992730	−	0.171946i
$582$	−9.18006			−0.380526
$583$	18.8238			0.779600
$584$	0.320355	−	0.554871i	0.0132564	−	0.0229607i
$585$	6.47617	−	14.9235i	0.267756	−	0.617012i
$586$	−11.5561	−	20.0157i	−0.477378	−	0.826842i
$587$	10.2240	−	17.7085i	0.421991	−	0.730909i	−0.574143	−	0.818755i	$-0.694665\pi$
$587$	10.2240	−	17.7085i	0.421991	−	0.730909i	0.996134	+	0.0878454i	$0.0279981\pi$
$588$	−18.0280	+	31.2254i	−0.743462	+	1.28771i
$589$	4.97822	+	25.6697i	0.205124	+	1.05770i
$590$	−14.3547			−0.590974
$591$	5.53263	+	9.58280i	0.227582	+	0.394184i
$592$	−8.01192	+	13.8770i	−0.329288	+	0.570343i
$593$	−26.3941			−1.08388			−0.541938	−	0.840418i	$-0.682309\pi$
$593$	−26.3941			−1.08388			−0.541938	+	0.840418i	$0.682309\pi$
$594$	17.3244			0.710828
$595$	21.6621			0.888058
$596$	36.0135			1.47517
$597$	−54.3283			−2.22351
$598$	36.8647	+	49.7448i	1.50751	+	2.03422i
$599$	18.1823	−	31.4926i	0.742907	−	1.28675i	−0.208259	−	0.978074i	$-0.566780\pi$
$599$	18.1823	−	31.4926i	0.742907	−	1.28675i	0.951166	−	0.308679i	$-0.0998870\pi$
$600$	4.74688	+	8.22184i	0.193791	+	0.335655i
$601$	26.3931			1.07660			0.538300	−	0.842754i	$-0.319067\pi$
$601$	26.3931			1.07660			0.538300	+	0.842754i	$0.319067\pi$
$602$	−19.5289			−0.795938
$603$	−17.9601	−	31.1078i	−0.731392	−	1.26681i
$604$	2.36864	+	4.10260i	0.0963785	+	0.166932i
$605$	−3.55475	−	6.15700i	−0.144521	−	0.250318i
$606$	52.5057	+	90.9426i	2.13290	+	3.69429i
$607$	−34.0308			−1.38127			−0.690634	−	0.723205i	$-0.742668\pi$
$607$	−34.0308			−1.38127			−0.690634	+	0.723205i	$0.742668\pi$
$608$	−37.7873			−1.53248
$609$	31.1308	+	53.9201i	1.26148	+	2.18495i
$610$	−13.2998	+	23.0359i	−0.538492	+	0.932696i
$611$	−32.8071	+	3.76183i	−1.32723	+	0.152187i
$612$	67.3061			2.72069
$613$	−15.2684			−0.616684			−0.308342	−	0.951276i	$-0.599774\pi$
$613$	−15.2684			−0.616684			−0.308342	+	0.951276i	$0.599774\pi$
$614$	27.6734			1.11681
$615$	−10.9734			−0.442492
$616$	−5.98684			−0.241217
$617$	2.79341	−	4.83833i	0.112458	−	0.194784i	−0.804303	−	0.594220i	$-0.797461\pi$
$617$	2.79341	−	4.83833i	0.112458	−	0.194784i	0.916761	+	0.399436i	$0.130794\pi$
$618$	12.1471	+	21.0395i	0.488629	+	0.846331i
$619$	−44.1697			−1.77533			−0.887666	−	0.460488i	$-0.847674\pi$
$619$	−44.1697			−1.77533			−0.887666	+	0.460488i	$0.847674\pi$
$620$	−10.0959	+	8.76860i	−0.405461	+	0.352155i
$621$	17.1577	−	29.7180i	0.688514	−	1.19254i
$622$	14.8965	−	25.8014i	0.597294	−	1.03454i
$623$	−4.16723	−	7.21785i	−0.166956	−	0.289177i
$624$	11.8509	−	27.3089i	0.474415	−	1.09323i
$625$	−5.55022	+	9.61326i	−0.222009	+	0.384530i
$626$	42.2095			1.68703
$627$	25.3278			1.01149
$628$	5.56899	+	9.64577i	0.222227	+	0.384908i
$629$	16.4104	−	28.4237i	0.654327	−	1.13333i
$630$	33.4365			1.33214
$631$	31.0170			1.23477			0.617383	−	0.786662i	$-0.288193\pi$
$631$	31.0170			1.23477			0.617383	+	0.786662i	$0.288193\pi$
$632$	−2.39747	−	4.15254i	−0.0953663	−	0.165179i
$633$	−26.9076			−1.06948
$634$	−41.2130			−1.63678
$635$	−4.75267	+	8.23186i	−0.188604	+	0.326671i
$636$	63.3633			2.51252
$637$	−11.6996	−	15.7873i	−0.463555	−	0.625517i
$638$	−13.2724	+	22.9885i	−0.525461	+	0.910125i
$639$	−3.57364			−0.141371
$640$	−3.36717	−	5.83210i	−0.133099	−	0.230534i
$641$	−0.862129			−0.0340521			−0.0170260	−	0.999855i	$-0.505420\pi$
$641$	−0.862129			−0.0340521			−0.0170260	+	0.999855i	$0.505420\pi$
$642$	−3.85062	+	6.66946i	−0.151972	+	0.263223i
$643$	6.86286	+	11.8868i	0.270645	+	0.468771i	0.969027	−	0.246954i	$-0.0794298\pi$
$643$	6.86286	+	11.8868i	0.270645	+	0.468771i	−0.698382	+	0.715725i	$0.746096\pi$
$644$	−34.7789	+	60.2389i	−1.37048	+	2.37374i
$645$	3.60158	+	6.23813i	0.141812	+	0.245626i
$646$	60.7894			2.39173
$647$	6.26860	−	10.8575i	0.246444	−	0.426854i	−0.716093	−	0.698005i	$-0.754071\pi$
$647$	6.26860	−	10.8575i	0.246444	−	0.426854i	0.962537	+	0.271152i	$0.0874045\pi$
$648$	−1.78889			−0.0702742
$649$	13.4854			0.529348
$650$	−30.1511	+	3.45728i	−1.18262	+	0.135606i
$651$	−10.2632	−	52.9212i	−0.402246	−	2.07415i
$652$	16.6562	−	28.8493i	0.652305	−	1.12983i
$653$	10.2881	−	17.8195i	0.402604	−	0.697331i	−0.591435	−	0.806353i	$-0.701438\pi$
$653$	10.2881	−	17.8195i	0.402604	−	0.697331i	0.994039	+	0.109021i	$0.0347717\pi$
$654$	7.89920	−	13.6818i	0.308883	−	0.535001i
$655$	15.2481			0.595794
$656$	−12.0798			−0.471636
$657$	1.68083	−	2.91128i	0.0655753	−	0.113580i
$658$	−33.9357	−	58.7783i	−1.32295	−	2.29142i
$659$	8.04636	+	13.9367i	0.313442	+	0.542897i	0.979105	−	0.203355i	$-0.0651847\pi$
$659$	8.04636	+	13.9367i	0.313442	+	0.542897i	−0.665663	+	0.746252i	$0.731851\pi$
$660$	6.47636	+	11.2174i	0.252092	+	0.436636i
$661$	−14.6064	−	25.2989i	−0.568121	−	0.984015i	−0.996752	−	0.0805351i	$-0.974337\pi$
$661$	−14.6064	−	25.2989i	−0.568121	−	0.984015i	0.428630	−	0.903480i	$-0.358996\pi$
$662$	−17.4120	+	30.1584i	−0.676736	+	1.17214i
$663$	−24.2736	+	55.9356i	−0.942708	+	2.17236i
$664$	0.585456	−	1.01404i	0.0227201	−	0.0393524i
$665$	16.5066			0.640099
$666$	25.3303	−	43.8734i	0.981530	−	1.70006i
$667$	26.2895	+	45.5347i	1.01793	+	1.76311i
$668$	−27.3432	−	47.3598i	−1.05794	−	1.83241i
$669$	58.8558			2.27550
$670$	8.29558	−	14.3684i	0.320486	−	0.555098i
$671$	12.4943	−	21.6408i	0.482339	−	0.835436i
$672$	77.9029			3.00517
$673$	12.0889	+	20.9385i	0.465991	+	0.807121i	0.999246	−	0.0388342i	$-0.0123644\pi$
$673$	12.0889	+	20.9385i	0.465991	+	0.807121i	−0.533254	+	0.845955i	$0.679031\pi$
$674$	−28.3322	+	49.0727i	−1.09131	+	1.89021i
$675$	8.41004	+	14.5666i	0.323702	+	0.560669i
$676$	−21.4092	−	22.8924i	−0.823433	−	0.880478i
$677$	2.45640	−	4.25462i	0.0944072	−	0.163518i	−0.814954	−	0.579526i	$-0.803238\pi$
$677$	2.45640	−	4.25462i	0.0944072	−	0.163518i	0.909361	+	0.416008i	$0.136571\pi$
$678$	−34.6227	+	59.9682i	−1.32967	+	2.30306i
$679$	5.62051			0.215695
$680$	2.64999	+	4.58992i	0.101623	+	0.176015i
$681$	−3.29522			−0.126273
$682$	17.3520	−	15.0708i	0.664444	−	0.577090i
$683$	10.1393	+	17.5618i	0.387971	+	0.671985i	0.992176	−	0.124843i	$-0.0398429\pi$
$683$	10.1393	+	17.5618i	0.387971	+	0.671985i	−0.604206	+	0.796828i	$0.706510\pi$
$684$	51.2876			1.96103
$685$	−1.97206	+	3.41571i	−0.0753486	+	0.130508i
$686$	−5.74354	+	9.94810i	−0.219289	+	0.379820i
$687$	2.58837	+	4.48318i	0.0987523	+	0.171044i
$688$	3.96470	+	6.86705i	0.151153	+	0.261804i
$689$	−13.7468	+	31.6778i	−0.523711	+	1.20683i
$690$	46.9384			1.78692
$691$	−3.40044	−	5.88974i	−0.129359	−	0.224056i	0.794069	−	0.607827i	$-0.207959\pi$
$691$	−3.40044	−	5.88974i	−0.129359	−	0.224056i	−0.923428	+	0.383771i	$0.874625\pi$
$692$	−7.77021	−	13.4584i	−0.295379	−	0.511612i
$693$	−31.4115			−1.19323
$694$	−3.42327	−	5.92928i	−0.129946	−	0.225072i
$695$	−14.5023			−0.550102
$696$	−7.61666	+	13.1924i	−0.288709	+	0.500058i
$697$	24.7424			0.937187
$698$	−12.9337	−	22.4019i	−0.489549	−	0.847923i
$699$	16.5678			0.626651
$700$	−17.0473	−	29.5268i	−0.644327	−	1.11601i
$701$	−6.89677	−	11.9456i	−0.260487	−	0.451177i	0.705884	−	0.708327i	$-0.250550\pi$
$701$	−6.89677	−	11.9456i	−0.260487	−	0.451177i	−0.966372	+	0.257150i	$0.917217\pi$
$702$	−12.6518	+	29.1546i	−0.477512	+	1.10037i
$703$	12.5048	−	21.6590i	0.471629	−	0.816885i
$704$	10.6929	+	18.5206i	0.403003	+	0.698022i
$705$	−12.5171	+	21.6802i	−0.471420	+	0.816523i
$706$	−10.0955	+	17.4859i	−0.379950	+	0.658092i
$707$	−32.1467	−	55.6797i	−1.20900	−	2.09405i
$708$	45.3936			1.70600
$709$	−18.7706	−	32.5116i	−0.704943	−	1.22100i	−0.966712	−	0.255867i	$-0.917639\pi$
$709$	−18.7706	−	32.5116i	−0.704943	−	1.22100i	0.261769	−	0.965131i	$-0.415694\pi$
$710$	−0.825312	−	1.42948i	−0.0309734	−	0.0536475i
$711$	−12.5790	−	21.7874i	−0.471748	−	0.817092i
$712$	1.01958	−	1.76597i	0.0382104	−	0.0661824i
$713$	−8.66711	−	44.6912i	−0.324586	−	1.67370i
$714$	−125.325			−4.69016
$715$	−7.01308	+	0.804155i	−0.262274	+	0.0300737i
$716$	15.1917	+	26.3128i	0.567740	+	0.983355i
$717$	21.9826	−	38.0750i	0.820955	−	1.42194i
$718$	20.1776	+	34.9486i	0.753020	+	1.30427i
$719$	22.5031	−	38.9766i	0.839226	−	1.45358i	−0.0513174	−	0.998682i	$-0.516342\pi$
$719$	22.5031	−	38.9766i	0.839226	−	1.45358i	0.890543	−	0.454899i	$-0.150325\pi$
$720$	−6.78817	−	11.7574i	−0.252980	−	0.438174i
$721$	−7.43710	−	12.8814i	−0.276972	−	0.479730i
$722$	6.41717			0.238822
$723$	−9.18952	+	15.9167i	−0.341762	+	0.591949i
$724$	−16.7980			−0.624291
$725$	−25.7722			−0.957155
$726$	20.5658	+	35.6210i	0.763268	+	1.32202i
$727$	17.0132	+	29.4678i	0.630985	+	1.09290i	0.987351	+	0.158552i	$0.0506825\pi$
$727$	17.0132	+	29.4678i	0.630985	+	1.09290i	−0.356365	+	0.934347i	$0.615984\pi$
$728$	4.37213	−	10.0750i	0.162042	−	0.373406i
$729$	−43.9348			−1.62722
$730$	1.55271			0.0574684
$731$	−8.12070	−	14.0655i	−0.300355	−	0.520230i
$732$	42.0576	−	72.8460i	1.55450	−	2.69246i
$733$	24.0328	−	41.6261i	0.887672	−	1.53749i	0.0450523	−	0.998985i	$-0.485655\pi$
$733$	24.0328	−	41.6261i	0.887672	−	1.53749i	0.842620	−	0.538509i	$-0.181012\pi$
$734$	−34.3650			−1.26843
$735$	−14.8967			−0.549472
$736$	65.7879			2.42497
$737$	−7.79320	+	13.4982i	−0.287066	+	0.497213i
$738$	38.1912			1.40584
$739$	26.6651	+	46.1853i	0.980892	+	1.69895i	0.658936	+	0.752199i	$0.271007\pi$
$739$	26.6651	+	46.1853i	0.980892	+	1.69895i	0.321956	+	0.946755i	$0.395660\pi$
$740$	12.7900			0.470171
$741$	−18.4966	+	42.6232i	−0.679490	+	1.56580i
$742$	−70.9747			−2.60556
$743$	−8.85493	+	15.3372i	−0.324856	+	0.562667i	−0.981483	−	0.191548i	$-0.938649\pi$
$743$	−8.85493	+	15.3372i	−0.324856	+	0.562667i	0.656627	+	0.754215i	$0.271982\pi$
$744$	9.95782	−	8.64867i	0.365071	−	0.317076i
$745$	7.43957	+	12.8857i	0.272565	+	0.472096i
$746$	4.07643			0.149249
$747$	3.07175	−	5.32042i	0.112389	−	0.194664i
$748$	−14.6026	−	25.2925i	−0.533925	−	0.924786i
$749$	2.35754	−	4.08339i	0.0861428	−	0.149204i
$750$	−25.8556	+	44.7833i	−0.944115	+	1.63525i
$751$	−23.1600			−0.845122			−0.422561	−	0.906335i	$-0.638869\pi$
$751$	−23.1600			−0.845122			−0.422561	+	0.906335i	$0.638869\pi$
$752$	−13.7790	+	23.8660i	−0.502469	+	0.870303i
$753$	11.6211	−	20.1283i	0.423496	−	0.733517i
$754$	−28.9939	−	39.1240i	−1.05589	−	1.42481i
$755$	−0.978612	+	1.69501i	−0.0356153	+	0.0616876i
$756$	−35.7041			−1.29855
$757$	3.41405	+	5.91331i	0.124086	+	0.214923i	0.921375	−	0.388674i	$-0.127067\pi$
$757$	3.41405	+	5.91331i	0.124086	+	0.214923i	−0.797289	+	0.603597i	$0.793734\pi$
$758$	−11.9073	+	20.6240i	−0.432492	+	0.749098i
$759$	−44.0958			−1.60058
$760$	2.01931	+	3.49754i	0.0732480	+	0.126869i
$761$	3.85623	−	6.67918i	0.139788	−	0.242120i	−0.787628	−	0.616151i	$-0.788691\pi$
$761$	3.85623	−	6.67918i	0.139788	−	0.242120i	0.927416	+	0.374031i	$0.122024\pi$
$762$	27.4963	−	47.6250i	0.996085	−	1.72527i
$763$	−4.83629	+	8.37671i	−0.175086	+	0.303257i
$764$	−0.945994	−	1.63851i	−0.0342249	−	0.0592792i
$765$	13.9039	+	24.0822i	0.502696	+	0.870695i
$766$	−11.4280	+	19.7939i	−0.412911	+	0.715183i
$767$	−9.84824	+	22.6941i	−0.355599	+	0.819436i
$768$	−10.3768	−	17.9731i	−0.374440	−	0.648549i
$769$	−53.3227			−1.92286			−0.961432	−	0.275042i	$-0.911308\pi$
$769$	−53.3227			−1.92286			−0.961432	+	0.275042i	$0.911308\pi$
$770$	−7.25433	−	12.5649i	−0.261428	−	0.452806i
$771$	−29.5225	−	51.1345i	−1.06323	−	1.84156i
$772$	21.9344	+	37.9915i	0.789436	+	1.36734i
$773$	27.2049	+	47.1202i	0.978491	+	1.69480i	0.667897	+	0.744253i	$0.267194\pi$
$773$	27.2049	+	47.1202i	0.978491	+	1.69480i	0.310594	+	0.950543i	$0.399472\pi$
$774$	−12.5347	−	21.7107i	−0.450551	−	0.780377i
$775$	21.0952	+	7.27383i	0.757762	+	0.261284i
$776$	0.687575	+	1.19092i	0.0246825	+	0.0427514i
$777$	−25.7802	+	44.6526i	−0.924860	+	1.60190i
$778$	70.9405			2.54334
$779$	18.8539			0.675510
$780$	−23.6070	+	2.70689i	−0.845264	+	0.0969223i
$781$	0.775331	+	1.34291i	0.0277435	+	0.0480532i
$782$	−105.835			−3.78465
$783$	−13.4944	+	23.3730i	−0.482251	+	0.835283i
$784$	−16.3986			−0.585663
$785$	−2.30085	+	3.98519i	−0.0821208	+	0.142237i
$786$	−88.2173			−3.14661
$787$	12.1268	−	21.0042i	0.432272	−	0.748717i	−0.564796	−	0.825230i	$-0.691045\pi$
$787$	12.1268	−	21.0042i	0.432272	−	0.748717i	0.997069	+	0.0765130i	$0.0243787\pi$
$788$	4.86132	−	8.42005i	0.173177	−	0.299952i
$789$	−5.61693	+	9.72882i	−0.199968	+	0.346355i
$790$	5.81009	−	10.0634i	0.206714	−	0.358039i
$791$	21.1978	−	36.7156i	0.753706	−	1.30546i
$792$	−3.84268	−	6.65572i	−0.136544	−	0.236501i
$793$	27.2941	+	36.8304i	0.969241	+	1.30788i
$794$	32.3496	+	56.0311i	1.14804	+	1.98847i
$795$	13.0894	+	22.6715i	0.464233	+	0.804075i
$796$	23.8681	+	41.3408i	0.845983	+	1.46529i
$797$	53.1026			1.88099			0.940495	−	0.339807i	$-0.110362\pi$
$797$	53.1026			1.88099			0.940495	+	0.339807i	$0.110362\pi$
$798$	−95.4980			−3.38059
$799$	28.2229	−	48.8836i	0.998456	−	1.72938i
$800$	−16.1233	+	27.9265i	−0.570046	+	0.987349i
$801$	5.34950	−	9.26561i	0.189015	−	0.327384i
$802$	12.6498	+	21.9101i	0.446681	+	0.773674i
$803$	−1.45868			−0.0514757
$804$	−26.2329	+	45.4368i	−0.925164	+	1.60243i
$805$	−28.7381			−1.01289
$806$	12.6900	+	40.2071i	0.446988	+	1.41624i
$807$	−71.7223			−2.52474
$808$	7.86522	−	13.6230i	0.276698	−	0.479254i
$809$	12.2659			0.431245			0.215622	−	0.976477i	$-0.430822\pi$
$809$	12.2659			0.431245			0.215622	+	0.976477i	$0.430822\pi$
$810$	−2.16762	−	3.75443i	−0.0761624	−	0.131917i
$811$	−0.262781	+	0.455150i	−0.00922748	+	0.0159825i	−0.870602	−	0.491987i	$-0.836271\pi$
$811$	−0.262781	+	0.455150i	−0.00922748	+	0.0159825i	0.861375	+	0.507970i	$0.169604\pi$
$812$	27.3534	−	47.3775i	0.959917	−	1.66263i
$813$	−38.1558	+	66.0877i	−1.33818	+	2.31780i
$814$	−21.9825			−0.770487
$815$	13.7631			0.482101
$816$	25.4430	+	44.0686i	0.890684	+	1.54271i
$817$	−6.18802	−	10.7180i	−0.216491	−	0.374974i
$818$	−13.4076	−	23.2226i	−0.468785	−	0.811959i
$819$	22.9395	−	52.8613i	0.801572	−	1.84712i
$820$	4.82097	+	8.35017i	0.168356	+	0.291601i
$821$	18.7571	−	32.4882i	0.654626	−	1.13384i	−0.327362	−	0.944899i	$-0.606160\pi$
$821$	18.7571	−	32.4882i	0.654626	−	1.13384i	0.981988	−	0.188946i	$-0.0605071\pi$
$822$	11.4093	−	19.7614i	0.397943	−	0.689258i
$823$	5.61623	−	9.72759i	0.195769	−	0.339082i	−0.751383	−	0.659866i	$-0.770613\pi$
$823$	5.61623	−	9.72759i	0.195769	−	0.339082i	0.947152	+	0.320784i	$0.103946\pi$
$824$	1.81961	−	3.15166i	0.0633891	−	0.109793i
$825$	10.8070	−	18.7184i	0.376253	−	0.651689i
$826$	−50.8465			−1.76918
$827$	−12.6640	+	21.9347i	−0.440371	+	0.762745i	−0.997717	−	0.0675357i	$-0.978486\pi$
$827$	−12.6640	+	21.9347i	−0.440371	+	0.762745i	0.557346	+	0.830280i	$0.311820\pi$
$828$	−89.2920			−3.10311
$829$	25.2959	−	43.8138i	0.878562	−	1.52171i	0.0256433	−	0.999671i	$-0.491837\pi$
$829$	25.2959	−	43.8138i	0.878562	−	1.52171i	0.852919	−	0.522043i	$-0.174830\pi$
$830$	2.83762			0.0984951
$831$	24.7757	+	42.9127i	0.859459	+	1.48863i
$832$	−38.9765	+	4.46925i	−1.35127	+	0.154943i
$833$	33.5884			1.16377
$834$	83.9020			2.90529
$835$	11.2970	−	19.5669i	0.390947	−	0.677140i
$836$	−11.1273	−	19.2730i	−0.384845	−	0.666572i
$837$	17.6422	−	15.3228i	0.609805	−	0.529634i
$838$	13.9699	+	24.1966i	0.482582	+	0.835856i
$839$	16.0110	+	27.7319i	0.552762	+	0.957412i	0.998074	+	0.0620361i	$0.0197594\pi$
$839$	16.0110	+	27.7319i	0.552762	+	0.957412i	−0.445312	+	0.895375i	$0.646907\pi$
$840$	−4.16304	−	7.21060i	−0.143639	−	0.248789i
$841$	−6.17652	−	10.6980i	−0.212983	−	0.368898i
$842$	−19.8500	−	34.3813i	−0.684078	−	1.18486i
$843$	−57.7654			−1.98955
$844$	11.8214	+	20.4752i	0.406908	+	0.704785i
$845$	3.76829	−	12.3893i	0.129633	−	0.426205i
$846$	43.5635	−	75.4542i	1.49774	−	2.59417i
$847$	−12.5914	−	21.8090i	−0.432647	−	0.749366i
$848$	14.4091	+	24.9572i	0.494809	+	0.857035i
$849$	40.0547	−	69.3768i	1.37467	−	2.38100i
$850$	25.9381	−	44.9261i	0.889669	−	1.54095i
$851$	−21.7710	+	37.7085i	−0.746301	+	1.29263i
$852$	2.60987	+	4.52043i	0.0894126	+	0.154867i
$853$	10.1015			0.345867			0.172934	−	0.984933i	$-0.444675\pi$
$853$	10.1015			0.345867			0.172934	+	0.984933i	$0.444675\pi$
$854$	−47.1098	+	81.5965i	−1.61206	+	2.79217i
$855$	10.5948	+	18.3508i	0.362336	+	0.627584i
$856$	1.15363			0.0394301
$857$	−9.91759	+	17.1778i	−0.338778	+	0.586781i	−0.984203	−	0.177042i	$-0.943347\pi$
$857$	−9.91759	+	17.1778i	−0.338778	+	0.586781i	0.645425	+	0.763824i	$0.276680\pi$
$858$	40.5738	−	4.65239i	1.38517	−	0.158830i
$859$	−11.3829	+	19.7157i	−0.388378	+	0.672691i	−0.992232	−	0.124404i	$-0.960298\pi$
$859$	−11.3829	+	19.7157i	−0.388378	+	0.672691i	0.603853	+	0.797096i	$0.293631\pi$
$860$	3.16458	−	5.48121i	0.107911	−	0.186908i
$861$	−38.8695			−1.32467
$862$	−1.18909	+	2.05957i	−0.0405007	+	0.0701493i
$863$	−19.4772	+	33.7356i	−0.663013	+	1.14837i	0.316807	+	0.948490i	$0.397389\pi$
$863$	−19.4772	+	33.7356i	−0.663013	+	1.14837i	−0.979820	+	0.199882i	$0.935944\pi$
$864$	16.8845	+	29.2448i	0.574422	+	0.994929i
$865$	3.21029	−	5.56039i	0.109153	−	0.189059i
$866$	−50.6050			−1.71963
$867$	−28.7898	−	49.8654i	−0.977754	−	1.69352i
$868$	−35.7611	+	31.0597i	−1.21381	+	1.05423i
$869$	−5.45823	+	9.45393i	−0.185158	+	0.320703i
$870$	−36.9168			−1.25160
$871$	−17.0244	−	22.9725i	−0.576848	−	0.778393i
$872$	−2.36656			−0.0801418
$873$	3.60755	+	6.24845i	0.122097	+	0.211478i
$874$	−80.6467			−2.72792
$875$	15.8301	−	27.4186i	0.535157	−	0.926919i
$876$	−4.91011			−0.165897
$877$	3.17953			0.107365			0.0536826	−	0.998558i	$-0.482904\pi$
$877$	3.17953			0.107365			0.0536826	+	0.998558i	$0.482904\pi$
$878$	−67.4910			−2.27771
$879$	−15.0981	+	26.1507i	−0.509247	+	0.882042i
$880$	−2.94550	+	5.10176i	−0.0992929	+	0.171980i
$881$	−7.06534	−	12.2375i	−0.238037	−	0.412293i	0.722114	−	0.691774i	$-0.243171\pi$
$881$	−7.06534	−	12.2375i	−0.238037	−	0.412293i	−0.960151	+	0.279482i	$0.909837\pi$
$882$	51.8454			1.74572
$883$	51.2183			1.72363			0.861816	−	0.507222i	$-0.169327\pi$
$883$	51.2183			1.72363			0.861816	+	0.507222i	$0.169327\pi$
$884$	53.2280	−	6.10339i	1.79025	−	0.205279i
$885$	9.37728	+	16.2419i	0.315214	+	0.545966i
$886$	28.8768	+	50.0161i	0.970136	+	1.68033i
$887$	43.1241			1.44797			0.723983	−	0.689818i	$-0.242309\pi$
$887$	43.1241			1.44797			0.723983	+	0.689818i	$0.242309\pi$
$888$	−12.6151			−0.423336
$889$	−16.8346	+	29.1584i	−0.564615	+	0.977943i
$890$	4.94176			0.165648
$891$	2.03635	+	3.52706i	0.0682203	+	0.118161i
$892$	−25.8572	−	44.7860i	−0.865763	−	1.49955i
$893$	21.5060	−	37.2495i	0.719672	−	1.24651i
$894$	−43.0412	−	74.5496i	−1.43951	−	2.49331i
$895$	−6.27651	+	10.8712i	−0.209801	+	0.363385i
$896$	−11.9270	−	20.6582i	−0.398453	−	0.690140i
$897$	32.2027	−	74.2073i	1.07522	−	2.47771i
$898$	66.6488			2.22410
$899$	6.81663	+	35.1494i	0.227347	+	1.17230i
$900$	21.8838	−	37.9038i	0.729459	−	1.26346i
$901$	−29.5134	−	51.1187i	−0.983234	−	1.70301i
$902$	−8.28591	−	14.3516i	−0.275891	−	0.477856i
$903$	12.7573	+	22.0963i	0.424537	+	0.735320i
$904$	10.3728			0.344993
$905$	−3.47007	−	6.01034i	−0.115349	−	0.199790i
$906$	5.66171	−	9.80636i	0.188098	−	0.325795i
$907$	10.6158	−	18.3870i	0.352491	−	0.610532i	−0.634195	−	0.773174i	$-0.718668\pi$
$907$	10.6158	−	18.3870i	0.352491	−	0.610532i	0.986685	+	0.162642i	$0.0520015\pi$
$908$	1.44769	+	2.50748i	0.0480434	+	0.0832136i
$909$	41.2670	−	71.4765i	1.36874	−	2.37073i
$910$	26.4427	−	3.03205i	0.876567	−	0.100512i
$911$	−23.2925	−	40.3437i	−0.771714	−	1.33665i	−0.936623	−	0.350339i	$-0.886066\pi$
$911$	−23.2925	−	40.3437i	−0.771714	−	1.33665i	0.164909	−	0.986309i	$-0.447267\pi$
$912$	19.3877	+	33.5805i	0.641991	+	1.11196i
$913$	−2.66577			−0.0882241
$914$	−17.0154	−	29.4716i	−0.562821	−	0.974835i
$915$	34.7526			1.14888
$916$	2.27430	−	3.93920i	0.0751450	−	0.130155i
$917$	54.0111			1.78361
$918$	−27.1626	−	47.0470i	−0.896498	−	1.55278i
$919$	−19.1512			−0.631740			−0.315870	−	0.948802i	$-0.602296\pi$
$919$	−19.1512			−0.631740			−0.315870	+	0.948802i	$0.602296\pi$
$920$	−3.51563	−	6.08925i	−0.115907	−	0.200757i
$921$	−18.0777	−	31.3116i	−0.595682	−	1.03175i
$922$	43.1608			1.42142
$923$	−2.82616	+	0.324061i	−0.0930240	+	0.0106666i
$924$	22.9402	+	39.7336i	0.754678	+	1.30714i
$925$	−10.6713	−	18.4833i	−0.350871	−	0.607726i
$926$	5.67993	−	9.83793i	0.186654	−	0.323295i
$927$	9.54707	−	16.5360i	0.313567	−	0.543114i
$928$	−51.7418			−1.69851
$929$	16.6700	+	28.8732i	0.546924	+	0.947300i	0.998483	+	0.0550588i	$0.0175346\pi$
$929$	16.6700	+	28.8732i	0.546924	+	0.947300i	−0.451559	+	0.892241i	$0.649132\pi$
$930$	30.2174	+	10.4192i	0.990867	+	0.341660i
$931$	25.5945			0.838827
$932$	−7.27874	−	12.6072i	−0.238423	−	0.412961i
$933$	−38.9247			−1.27434
$934$	10.3810	−	17.9803i	0.339675	−	0.588335i
$935$	6.03314	−	10.4497i	0.197305	−	0.341742i
$936$	14.0069	−	1.60610i	0.457831	−	0.0524972i
$937$	−10.1309	−	17.5473i	−0.330963	−	0.573245i	0.651738	−	0.758444i	$-0.274040\pi$
$937$	−10.1309	−	17.5473i	−0.330963	−	0.573245i	−0.982701	+	0.185199i	$0.940707\pi$
$938$	29.3841	−	50.8948i	0.959426	−	1.66177i
$939$	−27.5736	−	47.7588i	−0.899829	−	1.55855i
$940$	21.9965			0.717448
$941$	−21.2179	+	36.7505i	−0.691683	+	1.19803i	0.279603	+	0.960116i	$0.409797\pi$
$941$	−21.2179	+	36.7505i	−0.691683	+	1.19803i	−0.971286	+	0.237915i	$0.923536\pi$
$942$	13.3114	−	23.0561i	0.433710	−	0.751207i
$943$	−32.8247			−1.06892
$944$	10.3227	+	17.8794i	0.335975	+	0.581926i
$945$	−7.37565	−	12.7750i	−0.239930	−	0.415571i
$946$	−5.43902	+	9.42067i	−0.176838	+	0.306292i
$947$	26.4752			0.860330			0.430165	−	0.902750i	$-0.358455\pi$
$947$	26.4752			0.860330			0.430165	+	0.902750i	$0.358455\pi$
$948$	−18.3731	+	31.8232i	−0.596732	+	1.03357i
$949$	1.06526	−	2.45476i	0.0345797	−	0.0796848i
$950$	19.7650	−	34.2339i	0.641260	−	1.11069i
$951$	26.9226	+	46.6313i	0.873024	+	1.51212i
$952$	9.38666	+	16.2582i	0.304223	+	0.526930i
$953$	−7.55443	−	13.0847i	−0.244712	−	0.423854i	0.717339	−	0.696725i	$-0.245360\pi$
$953$	−7.55443	−	13.0847i	−0.244712	−	0.423854i	−0.962051	+	0.272871i	$0.912027\pi$
$954$	−45.5554	−	78.9043i	−1.47491	−	2.55462i
$955$	0.390841	−	0.676957i	0.0126473	−	0.0219058i
$956$	−38.6305			−1.24940
$957$	34.6811			1.12108
$958$	−25.5907	+	44.3244i	−0.826799	+	1.43206i
$959$	−6.98533	+	12.0989i	−0.225568	+	0.390695i
$960$	−14.8709	+	25.7572i	−0.479957	+	0.831310i
$961$	4.34082	−	30.6946i	0.140026	−	0.990148i
$962$	16.0536	−	36.9936i	0.517589	−	1.19272i
$963$	6.05280			0.195049
$964$	16.1490			0.520124
$965$	−9.06228	+	15.6963i	−0.291725	+	0.505283i
$966$	166.263			5.34942
$967$	10.2534	+	17.7593i	0.329726	+	0.571102i	0.982457	−	0.186488i	$-0.0597104\pi$
$967$	10.2534	+	17.7593i	0.329726	+	0.571102i	−0.652732	+	0.757589i	$0.726377\pi$
$968$	3.08070	−	5.33594i	0.0990176	−	0.171503i
$969$	−39.7110	−	68.7814i	−1.27570	−	2.20958i
$970$	−1.66629	+	2.88609i	−0.0535012	+	0.0926669i
$971$	33.6360			1.07943			0.539716	−	0.841847i	$-0.318532\pi$
$971$	33.6360			1.07943			0.539716	+	0.841847i	$0.318532\pi$
$972$	22.0330	+	38.1624i	0.706710	+	1.22406i
$973$	−51.3691			−1.64682
$974$	0.502472	−	0.870306i	0.0161002	−	0.0278864i
$975$	23.6081	+	31.8566i	0.756066	+	1.02023i
$976$	38.2563			1.22455
$977$	−3.13436	+	5.42888i	−0.100277	+	0.173685i	−0.911799	−	0.410637i	$-0.865306\pi$
$977$	−3.13436	+	5.42888i	−0.100277	+	0.173685i	0.811522	+	0.584322i	$0.198640\pi$
$978$	−79.6257			−2.54615
$979$	−4.64249			−0.148374
$980$	6.54458	+	11.3355i	0.209059	+	0.362100i
$981$	−12.4168			−0.396437
$982$	−26.8568			−0.857035
$983$	5.48768	−	9.50493i	0.175030	−	0.303160i	−0.765142	−	0.643862i	$-0.777331\pi$
$983$	5.48768	−	9.50493i	0.175030	−	0.303160i	0.940172	+	0.340701i	$0.110665\pi$
$984$	−4.75504	−	8.23596i	−0.151585	−	0.262553i
$985$	4.01694			0.127990
$986$	83.2385			2.65085
$987$	−44.3372	+	76.7944i	−1.41127	+	2.44439i
$988$	40.5600	−	4.65081i	1.29039	−	0.147962i
$989$	10.7734	+	18.6600i	0.342574	+	0.593355i
$990$	9.31244	−	16.1296i	0.295969	−	0.512633i
$991$	−3.94401	+	6.83122i	−0.125286	+	0.217001i	−0.921845	−	0.387560i	$-0.873318\pi$
$991$	−3.94401	+	6.83122i	−0.125286	+	0.217001i	0.796559	+	0.604561i	$0.206651\pi$
$992$	42.3520	+	14.6034i	1.34468	+	0.463658i
$993$	45.4978			1.44383
$994$	−2.92338	−	5.06344i	−0.0927239	−	0.160602i
$995$	−9.86120	+	17.0801i	−0.312621	+	0.541476i
$996$	−8.97334			−0.284331
$997$	11.7148			0.371010			0.185505	−	0.982643i	$-0.440608\pi$
$997$	11.7148			0.371010			0.185505	+	0.982643i	$0.440608\pi$
$998$	−20.8265			−0.659252
$999$	−22.3502			−0.707128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.g.a.87.6	yes	70
13.3	even	3		403.2.e.a.211.6	yes	70
31.5	even	3		403.2.e.a.191.6	✓	70
403.315	even	3	inner	403.2.g.a.315.6	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.e.a.191.6	✓	70	31.5	even	3
403.2.e.a.211.6	yes	70	13.3	even	3
403.2.g.a.87.6	yes	70	1.1	even	1	trivial
403.2.g.a.315.6	yes	70	403.315	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05012 + 1.81887i) q^{2} +2.74399 q^{3} +(-1.20552 - 2.08802i) q^{4} +(0.498066 - 0.862675i) q^{5} +(-2.88153 + 4.99096i) q^{6} +(1.76422 - 3.05572i) q^{7} +0.863293 q^{8} +4.52949 q^{9} +O(q^{10})\)	\(q+(-1.05012 + 1.81887i) q^{2} +2.74399 q^{3} +(-1.20552 - 2.08802i) q^{4} +(0.498066 - 0.862675i) q^{5} +(-2.88153 + 4.99096i) q^{6} +(1.76422 - 3.05572i) q^{7} +0.863293 q^{8} +4.52949 q^{9} +(1.04606 + 1.81183i) q^{10} +(-0.982713 - 1.70211i) q^{11} +(-3.30794 - 5.72952i) q^{12} +(3.58208 - 0.410739i) q^{13} +(3.70530 + 6.41777i) q^{14} +(1.36669 - 2.36717i) q^{15} +(1.50448 - 2.60583i) q^{16} +(-3.08155 + 5.33741i) q^{17} +(-4.75653 + 8.23855i) q^{18} +(-2.34816 + 4.06713i) q^{19} -2.40172 q^{20} +(4.84101 - 8.38488i) q^{21} +4.12788 q^{22} +(4.08816 - 7.08091i) q^{23} +2.36887 q^{24} +(2.00386 + 3.47079i) q^{25} +(-3.01455 + 6.94666i) q^{26} +4.19692 q^{27} -8.50723 q^{28} +(-3.21532 + 5.56909i) q^{29} +(2.87039 + 4.97166i) q^{30} +(4.20362 - 3.65097i) q^{31} +(4.02307 + 6.96816i) q^{32} +(-2.69656 - 4.67057i) q^{33} +(-6.47203 - 11.2099i) q^{34} +(-1.75740 - 3.04390i) q^{35} +(-5.46040 - 9.45769i) q^{36} -5.32538 q^{37} +(-4.93172 - 8.54199i) q^{38} +(9.82920 - 1.12707i) q^{39} +(0.429977 - 0.744741i) q^{40} +(-2.00730 - 3.47675i) q^{41} +(10.1673 + 17.6103i) q^{42} +(-1.31763 + 2.28220i) q^{43} +(-2.36936 + 4.10386i) q^{44} +(2.25599 - 3.90748i) q^{45} +(8.58616 + 14.8717i) q^{46} -9.15867 q^{47} +(4.12828 - 7.15039i) q^{48} +(-2.72496 - 4.71976i) q^{49} -8.41721 q^{50} +(-8.45576 + 14.6458i) q^{51} +(-5.17591 - 6.98432i) q^{52} +(-4.78872 + 8.29431i) q^{53} +(-4.40728 + 7.63364i) q^{54} -1.95782 q^{55} +(1.52304 - 2.63798i) q^{56} +(-6.44333 + 11.1602i) q^{57} +(-6.75296 - 11.6965i) q^{58} +(-3.43066 + 5.94207i) q^{59} -6.59029 q^{60} +(6.35707 + 11.0108i) q^{61} +(2.22632 + 11.4798i) q^{62} +(7.99103 - 13.8409i) q^{63} -10.8810 q^{64} +(1.42978 - 3.29475i) q^{65} +11.3269 q^{66} +(-3.96515 - 6.86783i) q^{67} +14.8595 q^{68} +(11.2179 - 19.4300i) q^{69} +7.38194 q^{70} -0.788971 q^{71} +3.91028 q^{72} +(0.371085 - 0.642738i) q^{73} +(5.59231 - 9.68616i) q^{74} +(5.49858 + 9.52382i) q^{75} +11.3230 q^{76} -6.93489 q^{77} +(-8.27190 + 19.0616i) q^{78} +(-2.77712 - 4.81012i) q^{79} +(-1.49866 - 2.59575i) q^{80} -2.07217 q^{81} +8.43167 q^{82} +(0.678166 - 1.17462i) q^{83} -23.3438 q^{84} +(3.06963 + 5.31676i) q^{85} +(-2.76735 - 4.79320i) q^{86} +(-8.82280 + 15.2815i) q^{87} +(-0.848369 - 1.46942i) q^{88} +(1.18104 - 2.04562i) q^{89} +(4.73813 + 8.20668i) q^{90} +(5.06448 - 11.6705i) q^{91} -19.7135 q^{92} +(11.5347 - 10.0182i) q^{93} +(9.61774 - 16.6584i) q^{94} +(2.33908 + 4.05140i) q^{95} +(11.0393 + 19.1206i) q^{96} +(0.796457 + 1.37950i) q^{97} +11.4462 q^{98} +(-4.45119 - 7.70969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9}+O(q^{10}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9	\( 70 q - 2 q^{2} - 8 q^{3} - 34 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 58 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} - 28 q^{16} + 14 q^{17} - 20 q^{18} - 2 q^{19} - 50 q^{20} - 21 q^{21} - 8 q^{22} + 2 q^{23} - 8 q^{24} - 23 q^{25} + 6 q^{26} - 38 q^{27} + 42 q^{28} + 6 q^{29} + 31 q^{30} + 22 q^{31} + 14 q^{32} + 2 q^{33} - 11 q^{34} + 4 q^{35} - 28 q^{36} + 24 q^{37} - 7 q^{38} + 10 q^{39} - q^{40} - 2 q^{41} + 27 q^{42} - q^{43} + 2 q^{44} - 29 q^{45} + 14 q^{46} + q^{48} - 37 q^{49} - 14 q^{50} - 9 q^{51} - 19 q^{52} - 2 q^{53} + 24 q^{54} - 10 q^{55} - 13 q^{56} - q^{57} + 6 q^{58} + 21 q^{59} + 18 q^{60} - 3 q^{61} - 23 q^{62} - 32 q^{63} - 14 q^{64} + 23 q^{65} - 28 q^{66} - 2 q^{67} - 84 q^{68} + 32 q^{69} - 14 q^{70} - 86 q^{71} + 10 q^{72} + 11 q^{73} - 7 q^{74} + 37 q^{75} + 56 q^{76} - 10 q^{77} - 64 q^{78} + 2 q^{79} + 38 q^{80} + 22 q^{81} + 34 q^{82} + 56 q^{83} + 90 q^{84} - 5 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} + 30 q^{89} - 23 q^{90} - 36 q^{91} + 74 q^{92} + 19 q^{93} + 47 q^{94} - 9 q^{95} + 26 q^{96} + 29 q^{97} - 24 q^{98} + 3 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 8 * q^3 - 34 * q^4 - 2 * q^5 - 4 * q^7 - 6 * q^8 + 58 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 + 4 * q^13 - 10 * q^14 + q^15 - 28 * q^16 + 14 * q^17 - 20 * q^18 - 2 * q^19 - 50 * q^20 - 21 * q^21 - 8 * q^22 + 2 * q^23 - 8 * q^24 - 23 * q^25 + 6 * q^26 - 38 * q^27 + 42 * q^28 + 6 * q^29 + 31 * q^30 + 22 * q^31 + 14 * q^32 + 2 * q^33 - 11 * q^34 + 4 * q^35 - 28 * q^36 + 24 * q^37 - 7 * q^38 + 10 * q^39 - q^40 - 2 * q^41 + 27 * q^42 - q^43 + 2 * q^44 - 29 * q^45 + 14 * q^46 + q^48 - 37 * q^49 - 14 * q^50 - 9 * q^51 - 19 * q^52 - 2 * q^53 + 24 * q^54 - 10 * q^55 - 13 * q^56 - q^57 + 6 * q^58 + 21 * q^59 + 18 * q^60 - 3 * q^61 - 23 * q^62 - 32 * q^63 - 14 * q^64 + 23 * q^65 - 28 * q^66 - 2 * q^67 - 84 * q^68 + 32 * q^69 - 14 * q^70 - 86 * q^71 + 10 * q^72 + 11 * q^73 - 7 * q^74 + 37 * q^75 + 56 * q^76 - 10 * q^77 - 64 * q^78 + 2 * q^79 + 38 * q^80 + 22 * q^81 + 34 * q^82 + 56 * q^83 + 90 * q^84 - 5 * q^85 + 54 * q^86 - 24 * q^87 + 4 * q^88 + 30 * q^89 - 23 * q^90 - 36 * q^91 + 74 * q^92 + 19 * q^93 + 47 * q^94 - 9 * q^95 + 26 * q^96 + 29 * q^97 - 24 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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