LMFDB - Embedded newform 349.2.c.a.122.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.9
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736999 + 1.27652i) q^{2} +(-0.677079 - 1.17273i) q^{3} +(-0.0863339 - 0.149535i) q^{4} +(1.59482 + 2.76232i) q^{5} +1.99602 q^{6} +(-0.744222 + 1.28903i) q^{7} -2.69348 q^{8} +(0.583129 - 1.01001i) q^{9} +O(q^{10})$	\(q+(-0.736999 + 1.27652i) q^{2} +(-0.677079 - 1.17273i) q^{3} +(-0.0863339 - 0.149535i) q^{4} +(1.59482 + 2.76232i) q^{5} +1.99602 q^{6} +(-0.744222 + 1.28903i) q^{7} -2.69348 q^{8} +(0.583129 - 1.01001i) q^{9} -4.70153 q^{10} +0.709495 q^{11} +(-0.116910 + 0.202493i) q^{12} +(-2.39034 + 4.14019i) q^{13} +(-1.09698 - 1.90003i) q^{14} +(2.15964 - 3.74061i) q^{15} +(2.15776 - 3.73735i) q^{16} +2.91020 q^{17} +(0.859531 + 1.48875i) q^{18} +(0.276792 + 0.479418i) q^{19} +(0.275375 - 0.476963i) q^{20} +2.01559 q^{21} +(-0.522897 + 0.905684i) q^{22} +(-3.33382 + 5.77435i) q^{23} +(1.82370 + 3.15874i) q^{24} +(-2.58692 + 4.48068i) q^{25} +(-3.52335 - 6.10263i) q^{26} -5.64177 q^{27} +0.257006 q^{28} +(0.388932 + 0.673649i) q^{29} +(3.18331 + 5.51365i) q^{30} -9.39553 q^{31} +(0.487051 + 0.843596i) q^{32} +(-0.480384 - 0.832049i) q^{33} +(-2.14482 + 3.71493i) q^{34} -4.74761 q^{35} -0.201375 q^{36} -3.72503 q^{37} -0.815981 q^{38} +6.47379 q^{39} +(-4.29563 - 7.44025i) q^{40} +8.42551 q^{41} +(-1.48548 + 2.57294i) q^{42} +(3.87891 + 6.71848i) q^{43} +(-0.0612535 - 0.106094i) q^{44} +3.71995 q^{45} +(-4.91405 - 8.51138i) q^{46} +5.07636 q^{47} -5.84389 q^{48} +(2.39227 + 4.14353i) q^{49} +(-3.81312 - 6.60451i) q^{50} +(-1.97044 - 3.41290i) q^{51} +0.825469 q^{52} +13.5028 q^{53} +(4.15798 - 7.20182i) q^{54} +(1.13152 + 1.95985i) q^{55} +(2.00455 - 3.47198i) q^{56} +(0.374820 - 0.649207i) q^{57} -1.14657 q^{58} +(-7.15972 - 12.4010i) q^{59} -0.745801 q^{60} -6.83965 q^{61} +(6.92449 - 11.9936i) q^{62} +(0.867955 + 1.50334i) q^{63} +7.19522 q^{64} -15.2487 q^{65} +1.41617 q^{66} -2.51335 q^{67} +(-0.251249 - 0.435176i) q^{68} +9.02904 q^{69} +(3.49898 - 6.06042i) q^{70} +(6.65052 - 11.5190i) q^{71} +(-1.57065 + 2.72044i) q^{72} +(3.51537 + 6.08880i) q^{73} +(2.74534 - 4.75507i) q^{74} +7.00620 q^{75} +(0.0477930 - 0.0827800i) q^{76} +(-0.528022 + 0.914561i) q^{77} +(-4.77117 + 8.26392i) q^{78} +12.7389 q^{79} +13.7650 q^{80} +(2.07053 + 3.58627i) q^{81} +(-6.20959 + 10.7553i) q^{82} +(2.63876 - 4.57046i) q^{83} +(-0.174013 - 0.301400i) q^{84} +(4.64126 + 8.03890i) q^{85} -11.4350 q^{86} +(0.526675 - 0.912227i) q^{87} -1.91101 q^{88} +(5.97132 + 10.3426i) q^{89} +(-2.74160 + 4.74859i) q^{90} +(-3.55789 - 6.16244i) q^{91} +1.15129 q^{92} +(6.36151 + 11.0185i) q^{93} +(-3.74127 + 6.48008i) q^{94} +(-0.882869 + 1.52917i) q^{95} +(0.659543 - 1.14236i) q^{96} +(7.31528 - 12.6704i) q^{97} -7.05239 q^{98} +(0.413727 - 0.716597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.736999	+	1.27652i	−0.521137	+	0.902635i	0.478561	+	0.878054i	$0.341159\pi$
$2$	−0.736999	+	1.27652i	−0.521137	+	0.902635i	−0.999698	+	0.0245810i	$0.992175\pi$
$3$	−0.677079	−	1.17273i	−0.390911	−	0.677079i	0.601659	−	0.798753i	$-0.294507\pi$
$3$	−0.677079	−	1.17273i	−0.390911	−	0.677079i	−0.992570	+	0.121675i	$0.961173\pi$
$4$	−0.0863339	−	0.149535i	−0.0431669	−	0.0747673i
$5$	1.59482	+	2.76232i	0.713227	+	1.23534i	0.963639	+	0.267206i	$0.0861003\pi$
$5$	1.59482	+	2.76232i	0.713227	+	1.23534i	−0.250413	+	0.968139i	$0.580566\pi$
$6$	1.99602			0.814873
$7$	−0.744222	+	1.28903i	−0.281290	+	0.487208i	−0.971703	−	0.236208i	$-0.924095\pi$
$7$	−0.744222	+	1.28903i	−0.281290	+	0.487208i	0.690413	+	0.723415i	$0.257429\pi$
$8$	−2.69348			−0.952290
$9$	0.583129	−	1.01001i	0.194376	−	0.336670i
$10$	−4.70153			−1.48675
$11$	0.709495			0.213921			0.106960	−	0.994263i	$-0.465888\pi$
$11$	0.709495			0.213921			0.106960	+	0.994263i	$0.465888\pi$
$12$	−0.116910	+	0.202493i	−0.0337489	+	0.0584548i
$13$	−2.39034	+	4.14019i	−0.662961	+	1.14828i	0.316873	+	0.948468i	$0.397367\pi$
$13$	−2.39034	+	4.14019i	−0.662961	+	1.14828i	−0.979834	+	0.199814i	$0.935966\pi$
$14$	−1.09698	−	1.90003i	−0.293181	−	0.507804i
$15$	2.15964	−	3.74061i	0.557617	−	0.965821i
$16$	2.15776	−	3.73735i	0.539440	−	0.934338i
$17$	2.91020			0.705828			0.352914	−	0.935656i	$-0.385191\pi$
$17$	2.91020			0.705828			0.352914	+	0.935656i	$0.385191\pi$
$18$	0.859531	+	1.48875i	0.202593	+	0.350902i
$19$	0.276792	+	0.479418i	0.0635004	+	0.109986i	0.896028	−	0.443998i	$-0.146440\pi$
$19$	0.276792	+	0.479418i	0.0635004	+	0.109986i	−0.832527	+	0.553984i	$0.813107\pi$
$20$	0.275375	−	0.476963i	0.0615756	−	0.106652i
$21$	2.01559			0.439837
$22$	−0.522897	+	0.905684i	−0.111482	+	0.193092i
$23$	−3.33382	+	5.77435i	−0.695150	+	1.20404i	0.274980	+	0.961450i	$0.411329\pi$
$23$	−3.33382	+	5.77435i	−0.695150	+	1.20404i	−0.970130	+	0.242586i	$0.922004\pi$
$24$	1.82370	+	3.15874i	0.372261	+	0.644775i
$25$	−2.58692	+	4.48068i	−0.517385	+	0.896137i
$26$	−3.52335	−	6.10263i	−0.690986	−	1.19682i
$27$	−5.64177			−1.08576
$28$	0.257006			0.0485696
$29$	0.388932	+	0.673649i	0.0722228	+	0.125094i	0.899875	−	0.436147i	$-0.143657\pi$
$29$	0.388932	+	0.673649i	0.0722228	+	0.125094i	−0.827652	+	0.561241i	$0.810324\pi$
$30$	3.18331	+	5.51365i	0.581189	+	1.00665i
$31$	−9.39553			−1.68749			−0.843743	−	0.536747i	$-0.819653\pi$
$31$	−9.39553			−1.68749			−0.843743	+	0.536747i	$0.819653\pi$
$32$	0.487051	+	0.843596i	0.0860992	+	0.149128i
$33$	−0.480384	−	0.832049i	−0.0836241	−	0.144841i
$34$	−2.14482	+	3.71493i	−0.367833	+	0.637105i
$35$	−4.74761			−0.802493
$36$	−0.201375			−0.0335625
$37$	−3.72503			−0.612390			−0.306195	−	0.951969i	$-0.599056\pi$
$37$	−3.72503			−0.612390			−0.306195	+	0.951969i	$0.599056\pi$
$38$	−0.815981			−0.132370
$39$	6.47379			1.03664
$40$	−4.29563	−	7.44025i	−0.679199	−	1.17641i
$41$	8.42551			1.31584			0.657922	−	0.753086i	$-0.271436\pi$
$41$	8.42551			1.31584			0.657922	+	0.753086i	$0.271436\pi$
$42$	−1.48548	+	2.57294i	−0.229215	+	0.397013i
$43$	3.87891	+	6.71848i	0.591529	+	1.02456i	0.994027	+	0.109137i	$0.0348088\pi$
$43$	3.87891	+	6.71848i	0.591529	+	1.02456i	−0.402498	+	0.915421i	$0.631858\pi$
$44$	−0.0612535	−	0.106094i	−0.00923431	−	0.0159943i
$45$	3.71995			0.554538
$46$	−4.91405	−	8.51138i	−0.724537	−	1.25493i
$47$	5.07636			0.740464			0.370232	−	0.928939i	$-0.379278\pi$
$47$	5.07636			0.740464			0.370232	+	0.928939i	$0.379278\pi$
$48$	−5.84389			−0.843493
$49$	2.39227	+	4.14353i	0.341752	+	0.591933i
$50$	−3.81312	−	6.60451i	−0.539256	−	0.934019i
$51$	−1.97044	−	3.41290i	−0.275916	−	0.477901i
$52$	0.825469			0.114472
$53$	13.5028			1.85476			0.927379	−	0.374122i	$-0.122056\pi$
$53$	13.5028			1.85476			0.927379	+	0.374122i	$0.122056\pi$
$54$	4.15798	−	7.20182i	0.565829	−	0.980044i
$55$	1.13152	+	1.95985i	0.152574	+	0.264266i
$56$	2.00455	−	3.47198i	0.267869	−	0.463963i
$57$	0.374820	−	0.649207i	0.0496461	−	0.0859896i
$58$	−1.14657			−0.150552
$59$	−7.15972	−	12.4010i	−0.932116	−	1.61447i	−0.779698	−	0.626155i	$-0.784628\pi$
$59$	−7.15972	−	12.4010i	−0.932116	−	1.61447i	−0.152417	−	0.988316i	$-0.548706\pi$
$60$	−0.745801			−0.0962825
$61$	−6.83965			−0.875727			−0.437864	−	0.899041i	$-0.644265\pi$
$61$	−6.83965			−0.875727			−0.437864	+	0.899041i	$0.644265\pi$
$62$	6.92449	−	11.9936i	0.879411	−	1.52318i
$63$	0.867955	+	1.50334i	0.109352	+	0.189403i
$64$	7.19522			0.899403
$65$	−15.2487			−1.89137
$66$	1.41617			0.174318
$67$	−2.51335			−0.307055			−0.153527	−	0.988144i	$-0.549063\pi$
$67$	−2.51335			−0.307055			−0.153527	+	0.988144i	$0.549063\pi$
$68$	−0.251249	−	0.435176i	−0.0304684	−	0.0527729i
$69$	9.02904			1.08697
$70$	3.49898	−	6.06042i	0.418208	−	0.724358i
$71$	6.65052	−	11.5190i	0.789272	−	1.36706i	−0.137142	−	0.990551i	$-0.543792\pi$
$71$	6.65052	−	11.5190i	0.789272	−	1.36706i	0.926414	−	0.376507i	$-0.122875\pi$
$72$	−1.57065	+	2.72044i	−0.185103	+	0.320607i
$73$	3.51537	+	6.08880i	0.411443	+	0.712640i	0.995048	−	0.0993979i	$-0.0316917\pi$
$73$	3.51537	+	6.08880i	0.411443	+	0.712640i	−0.583605	+	0.812038i	$0.698358\pi$
$74$	2.74534	−	4.75507i	0.319139	−	0.552765i
$75$	7.00620			0.809006
$76$	0.0477930	−	0.0827800i	0.00548224	−	0.00949552i
$77$	−0.528022	+	0.914561i	−0.0601737	+	0.104224i
$78$	−4.77117	+	8.26392i	−0.540229	+	0.935704i
$79$	12.7389			1.43324			0.716621	−	0.697463i	$-0.245688\pi$
$79$	12.7389			1.43324			0.716621	+	0.697463i	$0.245688\pi$
$80$	13.7650			1.53897
$81$	2.07053	+	3.58627i	0.230059	+	0.398474i
$82$	−6.20959	+	10.7553i	−0.685734	+	1.18773i
$83$	2.63876	−	4.57046i	0.289641	−	0.501673i	−0.684083	−	0.729404i	$-0.739797\pi$
$83$	2.63876	−	4.57046i	0.289641	−	0.501673i	0.973724	+	0.227731i	$0.0731307\pi$
$84$	−0.174013	−	0.301400i	−0.0189864	−	0.0328854i
$85$	4.64126	+	8.03890i	0.503416	+	0.871941i
$86$	−11.4350			−1.23307
$87$	0.526675	−	0.912227i	0.0564654	−	0.0978010i
$88$	−1.91101			−0.203715
$89$	5.97132	+	10.3426i	0.632959	+	1.09632i	0.986944	+	0.161065i	$0.0514930\pi$
$89$	5.97132	+	10.3426i	0.632959	+	1.09632i	−0.353985	+	0.935251i	$0.615174\pi$
$90$	−2.74160	+	4.74859i	−0.288990	+	0.500545i
$91$	−3.55789	−	6.16244i	−0.372968	−	0.645999i
$92$	1.15129			0.120030
$93$	6.36151	+	11.0185i	0.659658	+	1.14256i
$94$	−3.74127	+	6.48008i	−0.385883	+	0.668369i
$95$	−0.882869	+	1.52917i	−0.0905804	+	0.156890i
$96$	0.659543	−	1.14236i	0.0673143	−	0.116592i
$97$	7.31528	−	12.6704i	0.742755	−	1.28649i	−0.208482	−	0.978026i	$-0.566852\pi$
$97$	7.31528	−	12.6704i	0.742755	−	1.28649i	0.951237	−	0.308462i	$-0.0998144\pi$
$98$	−7.05239			−0.712399
$99$	0.413727	−	0.716597i	0.0415812	−	0.0720207i
$100$	0.893356			0.0893356
$101$	0.740934			0.0737257			0.0368628	−	0.999320i	$-0.488264\pi$
$101$	0.740934			0.0737257			0.0368628	+	0.999320i	$0.488264\pi$
$102$	5.80884			0.575161
$103$	2.00525			0.197583			0.0987914	−	0.995108i	$-0.468502\pi$
$103$	2.00525			0.197583			0.0987914	+	0.995108i	$0.468502\pi$
$104$	6.43834	−	11.1515i	0.631331	−	1.09350i
$105$	3.21451	+	5.56769i	0.313704	+	0.543351i
$106$	−9.95158	+	17.2366i	−0.966583	+	1.67417i
$107$	3.05585	−	5.29289i	0.295421	−	0.511683i	−0.679662	−	0.733525i	$-0.737874\pi$
$107$	3.05585	−	5.29289i	0.295421	−	0.511683i	0.975083	+	0.221842i	$0.0712069\pi$
$108$	0.487076	+	0.843640i	0.0468689	+	0.0811793i
$109$	−3.18580	−	5.51796i	−0.305144	−	0.528525i	0.672149	−	0.740416i	$-0.265371\pi$
$109$	−3.18580	−	5.51796i	−0.305144	−	0.528525i	−0.977293	+	0.211891i	$0.932038\pi$
$110$	−3.33571			−0.318048
$111$	2.52213	+	4.36847i	0.239390	+	0.414636i
$112$	3.21171	+	5.56284i	0.303478	+	0.525639i
$113$	0.774183	−	1.34092i	0.0728290	−	0.126144i	−0.827311	−	0.561744i	$-0.810131\pi$
$113$	0.774183	−	1.34092i	0.0728290	−	0.126144i	0.900140	+	0.435600i	$0.143464\pi$
$114$	0.552483	+	0.956929i	0.0517448	+	0.0896246i
$115$	−21.2674			−1.98320
$116$	0.0671559	−	0.116318i	0.00623527	−	0.0107998i
$117$	2.78775	+	4.82853i	0.257728	+	0.446398i
$118$	21.1068			1.94304
$119$	−2.16584	+	3.75134i	−0.198542	+	0.343885i
$120$	−5.81696	+	10.0753i	−0.531013	+	0.919742i
$121$	−10.4966			−0.954238
$122$	5.04081	−	8.73094i	0.456374	−	0.790462i
$123$	−5.70473	−	9.88089i	−0.514378	−	0.890929i
$124$	0.811152	+	1.40496i	0.0728436	+	0.126169i
$125$	−0.554511			−0.0495970
$126$	−2.55873			−0.227950
$127$	9.93228			0.881347			0.440674	−	0.897667i	$-0.354740\pi$
$127$	9.93228			0.881347			0.440674	+	0.897667i	$0.354740\pi$
$128$	−6.27697	+	10.8720i	−0.554811	+	0.960961i
$129$	5.25266	−	9.09787i	0.462471	−	0.801023i
$130$	11.2383	−	19.4652i	0.985660	−	1.70721i
$131$	3.75270			0.327875			0.163938	−	0.986471i	$-0.447580\pi$
$131$	3.75270			0.327875			0.163938	+	0.986471i	$0.447580\pi$
$132$	−0.0829468	+	0.143668i	−0.00721959	+	0.0125047i
$133$	−0.823979			−0.0714480
$134$	1.85234	−	3.20834i	0.160018	−	0.277158i
$135$	−8.99762	−	15.5843i	−0.774392	−	1.34129i
$136$	−7.83858			−0.672153
$137$	0.913860	+	1.58285i	0.0780763	+	0.135232i	0.902420	−	0.430858i	$-0.141789\pi$
$137$	0.913860	+	1.58285i	0.0780763	+	0.135232i	−0.824344	+	0.566090i	$0.808456\pi$
$138$	−6.65439	+	11.5257i	−0.566459	+	0.981137i
$139$	9.85568			0.835948			0.417974	−	0.908459i	$-0.362740\pi$
$139$	9.85568			0.835948			0.417974	+	0.908459i	$0.362740\pi$
$140$	0.409880	+	0.709932i	0.0346412	+	0.0600002i
$141$	−3.43710	−	5.95323i	−0.289456	−	0.501352i
$142$	9.80285	+	16.9790i	0.822637	+	1.42485i
$143$	−1.69593	+	2.93744i	−0.141821	+	0.245641i
$144$	−2.51651	−	4.35872i	−0.209709	−	0.363227i
$145$	−1.24055	+	2.14870i	−0.103022	+	0.178440i
$146$	−10.3633			−0.857672
$147$	3.23951	−	5.61099i	0.267190	−	0.462786i
$148$	0.321596	+	0.557020i	0.0264350	+	0.0457868i
$149$	−6.38420	+	11.0578i	−0.523014	+	0.905887i	0.476627	+	0.879105i	$0.341859\pi$
$149$	−6.38420	+	11.0578i	−0.523014	+	0.905887i	−0.999641	+	0.0267812i	$0.991474\pi$
$150$	−5.16356	+	8.94355i	−0.421603	+	0.730238i
$151$	7.06245	+	12.2325i	0.574734	+	0.995468i	0.996070	+	0.0885640i	$0.0282278\pi$
$151$	7.06245	+	12.2325i	0.574734	+	0.995468i	−0.421337	+	0.906904i	$0.638439\pi$
$152$	−0.745534	−	1.29130i	−0.0604708	−	0.104739i
$153$	1.69703	−	2.93933i	0.137196	−	0.237631i
$154$	−0.778303	−	1.34806i	−0.0627174	−	0.108630i
$155$	−14.9842	−	25.9534i	−1.20356	−	2.08463i
$156$	−0.558907	−	0.968056i	−0.0447484	−	0.0775065i
$157$	−1.04094	−	1.80297i	−0.0830764	−	0.143893i	0.821493	−	0.570218i	$-0.193141\pi$
$157$	−1.04094	−	1.80297i	−0.0830764	−	0.143893i	−0.904570	+	0.426325i	$0.859808\pi$
$158$	−9.38857	+	16.2615i	−0.746915	+	1.29369i
$159$	−9.14249	−	15.8353i	−0.725047	−	1.25582i
$160$	−1.55352	+	2.69077i	−0.122816	+	0.212724i
$161$	−4.96221	−	8.59480i	−0.391077	−	0.677365i
$162$	−6.10392			−0.479569
$163$	−10.2110			−0.799785			−0.399892	−	0.916562i	$-0.630952\pi$
$163$	−10.2110			−0.799785			−0.399892	+	0.916562i	$0.630952\pi$
$164$	−0.727407	−	1.25991i	−0.0568009	−	0.0983821i
$165$	1.53225	−	2.65394i	0.119286	−	0.206609i
$166$	3.88952	+	6.73684i	0.301885	+	0.522880i
$167$	−2.90414			−0.224729			−0.112365	−	0.993667i	$-0.535842\pi$
$167$	−2.90414			−0.224729			−0.112365	+	0.993667i	$0.535842\pi$
$168$	−5.42895			−0.418853
$169$	−4.92744	−	8.53458i	−0.379034	−	0.656506i
$170$	−13.6824			−1.04939
$171$	0.645622			0.0493720
$172$	0.669763	−	1.16006i	0.0510690	−	0.0884541i
$173$	2.58705	−	4.48089i	0.196689	−	0.340676i	−0.750764	−	0.660571i	$-0.770314\pi$
$173$	2.58705	−	4.48089i	0.196689	−	0.340676i	0.947453	+	0.319895i	$0.103648\pi$
$174$	0.776317	+	1.34462i	0.0588524	+	0.101935i
$175$	−3.85049	−	6.66925i	−0.291070	−	0.504148i
$176$	1.53092	−	2.65163i	0.115397	−	0.199874i
$177$	−9.69538	+	16.7929i	−0.728749	+	1.26223i
$178$	−17.6034			−1.31943
$179$	−9.89215			−0.739374			−0.369687	−	0.929156i	$-0.620535\pi$
$179$	−9.89215			−0.739374			−0.369687	+	0.929156i	$0.620535\pi$
$180$	−0.321158	−	0.556262i	−0.0239377	−	0.0414613i
$181$	0.838764			0.0623448			0.0311724	−	0.999514i	$-0.490076\pi$
$181$	0.838764			0.0623448			0.0311724	+	0.999514i	$0.490076\pi$
$182$	10.4886			0.777469
$183$	4.63098	+	8.02109i	0.342332	+	0.592936i
$184$	8.97960	−	15.5531i	0.661985	−	1.14659i
$185$	−5.94076	−	10.2897i	−0.436773	−	0.756513i
$186$	−18.7537			−1.37509
$187$	2.06478			0.150991
$188$	−0.438262	−	0.759092i	−0.0319636	−	0.0553625i
$189$	4.19873	−	7.27241i	0.305413	−	0.528990i
$190$	−1.30135	−	2.25400i	−0.0944096	−	0.163522i
$191$	−1.66669	+	2.88678i	−0.120597	+	0.208880i	−0.920003	−	0.391911i	$-0.871814\pi$
$191$	−1.66669	+	2.88678i	−0.120597	+	0.208880i	0.799406	+	0.600791i	$0.205148\pi$
$192$	−4.87173	−	8.43808i	−0.351587	−	0.608966i
$193$	3.03388	+	5.25483i	0.218383	+	0.378251i	0.954314	−	0.298806i	$-0.0965883\pi$
$193$	3.03388	+	5.25483i	0.218383	+	0.378251i	−0.735931	+	0.677057i	$0.763255\pi$
$194$	10.7827	+	18.6762i	0.774153	+	1.34087i
$195$	10.3246	+	17.8826i	0.739356	+	1.28060i
$196$	0.413067	−	0.715454i	0.0295048	−	0.0511038i
$197$	−2.40400	−	4.16384i	−0.171278	−	0.296661i	0.767589	−	0.640942i	$-0.221456\pi$
$197$	−2.40400	−	4.16384i	−0.171278	−	0.296661i	−0.938867	+	0.344281i	$0.888123\pi$
$198$	0.609833	+	1.05626i	0.0433389	+	0.0750653i
$199$	−7.93434	+	13.7427i	−0.562451	+	0.974193i	0.434831	+	0.900512i	$0.356808\pi$
$199$	−7.93434	+	13.7427i	−0.562451	+	0.974193i	−0.997282	+	0.0736812i	$0.976525\pi$
$200$	6.96783	−	12.0686i	0.492700	−	0.853382i
$201$	1.70174	+	2.94749i	0.120031	+	0.207900i
$202$	−0.546067	+	0.945816i	−0.0384212	+	0.0665474i
$203$	−1.15781			−0.0812621
$204$	−0.340231	+	0.589297i	−0.0238209	+	0.0412591i
$205$	13.4372	+	23.2739i	0.938495	+	1.62552i
$206$	−1.47786	+	2.55973i	−0.102968	+	0.178345i
$207$	3.88810	+	6.73439i	0.270242	+	0.468072i
$208$	10.3156	+	17.8671i	0.715255	+	1.23886i
$209$	0.196383	+	0.340145i	0.0135841	+	0.0235283i
$210$	−9.47635			−0.653930
$211$	3.09292	−	5.35710i	0.212926	−	0.368798i	−0.739703	−	0.672933i	$-0.765034\pi$
$211$	3.09292	−	5.35710i	0.212926	−	0.368798i	0.952629	+	0.304135i	$0.0983675\pi$
$212$	−1.16575	−	2.01914i	−0.0800643	−	0.138675i
$213$	−18.0117			−1.23414
$214$	4.50432	+	7.80171i	0.307909	+	0.533314i
$215$	−12.3724	+	21.4296i	−0.843788	+	1.46148i
$216$	15.1960			1.03396
$217$	6.99236	−	12.1111i	0.474672	−	0.822156i
$218$	9.39171			0.636087
$219$	4.76036	−	8.24519i	0.321675	−	0.557158i
$220$	0.195377	−	0.338403i	0.0131723	−	0.0228151i
$221$	−6.95638	+	12.0488i	−0.467936	+	0.810490i
$222$	−7.43524			−0.499021
$223$	−11.1754			−0.748357			−0.374179	−	0.927357i	$-0.622075\pi$
$223$	−11.1754			−0.748357			−0.374179	+	0.927357i	$0.622075\pi$
$224$	−1.44990			−0.0968752
$225$	3.01702	+	5.22564i	0.201135	+	0.348376i
$226$	1.14114	+	1.97652i	0.0759077	+	0.131476i
$227$	−8.12581	+	14.0743i	−0.539329	+	0.934145i	0.459611	+	0.888120i	$0.347989\pi$
$227$	−8.12581	+	14.0743i	−0.539329	+	0.934145i	−0.998940	+	0.0460251i	$0.985345\pi$
$228$	−0.129439			−0.00857228
$229$	−6.62830	+	11.4806i	−0.438011	+	0.758656i	−0.997536	−	0.0701567i	$-0.977650\pi$
$229$	−6.62830	+	11.4806i	−0.438011	+	0.758656i	0.559525	+	0.828813i	$0.310983\pi$
$230$	15.6741	−	27.1483i	1.03352	−	1.79011i
$231$	1.43005			0.0940903
$232$	−1.04758	−	1.81446i	−0.0687770	−	0.119125i
$233$	14.0752	−	24.3790i	0.922097	−	1.59712i	0.125933	−	0.992039i	$-0.459807\pi$
$233$	14.0752	−	24.3790i	0.922097	−	1.59712i	0.796164	−	0.605081i	$-0.206859\pi$
$234$	−8.21828			−0.537246
$235$	8.09591	+	14.0225i	0.528119	+	0.914728i
$236$	−1.23625	+	2.14125i	−0.0804731	+	0.139384i
$237$	−8.62525	−	14.9394i	−0.560270	−	0.970417i
$238$	−3.19244	−	5.52947i	−0.206935	−	0.358422i
$239$	21.6292			1.39908			0.699539	−	0.714594i	$-0.253389\pi$
$239$	21.6292			1.39908			0.699539	+	0.714594i	$0.253389\pi$
$240$	−9.31998	−	16.1427i	−0.601602	−	1.04201i
$241$	−5.31778	−	9.21066i	−0.342548	−	0.593311i	0.642357	−	0.766406i	$-0.277957\pi$
$241$	−5.31778	−	9.21066i	−0.342548	−	0.593311i	−0.984905	+	0.173095i	$0.944623\pi$
$242$	7.73599	−	13.3991i	0.497288	−	0.861329i
$243$	−5.65883	+	9.80138i	−0.363014	+	0.628759i
$244$	0.590493	+	1.02276i	0.0378025	+	0.0654758i
$245$	−7.63049	+	13.2164i	−0.487494	+	0.844364i
$246$	16.8175			1.07225
$247$	−2.64651			−0.168393
$248$	25.3067			1.60698
$249$	−7.14658			−0.452896
$250$	0.408674	−	0.707844i	0.0258468	−	0.0447680i
$251$	8.96705			0.565995			0.282998	−	0.959121i	$-0.408671\pi$
$251$	8.96705			0.565995			0.282998	+	0.959121i	$0.408671\pi$
$252$	0.149868	−	0.259579i	0.00944079	−	0.0163519i
$253$	−2.36533	+	4.09687i	−0.148707	+	0.257568i
$254$	−7.32007	+	12.6787i	−0.459302	+	0.795535i
$255$	6.28500	−	10.8859i	0.393582	−	0.681704i
$256$	−2.05701	−	3.56285i	−0.128563	−	0.222678i
$257$	−16.6300			−1.03735			−0.518677	−	0.854971i	$-0.673575\pi$
$257$	−16.6300			−1.03735			−0.518677	+	0.854971i	$0.673575\pi$
$258$	7.74240	+	13.4102i	0.482021	+	0.834885i
$259$	2.77225	−	4.80167i	0.172259	−	0.298361i
$260$	1.31648	+	2.28021i	0.0816445	+	0.141412i
$261$	0.907190			0.0561536
$262$	−2.76574	+	4.79039i	−0.170868	+	0.295952i
$263$	1.78190			0.109877			0.0549384	−	0.998490i	$-0.482504\pi$
$263$	1.78190			0.109877			0.0549384	+	0.998490i	$0.482504\pi$
$264$	1.29391	+	2.24111i	0.0796344	+	0.137931i
$265$	21.5347	+	37.2991i	1.32286	+	2.29127i
$266$	0.607271	−	1.05182i	0.0372342	−	0.0644915i
$267$	8.08610	−	14.0055i	0.494862	−	0.857125i
$268$	0.216987	+	0.375833i	0.0132546	+	0.0229577i
$269$	26.9422			1.64269			0.821347	−	0.570429i	$-0.193223\pi$
$269$	26.9422			1.64269			0.821347	+	0.570429i	$0.193223\pi$
$270$	26.5249			1.61426
$271$	8.45090	−	14.6374i	0.513355	−	0.889158i	−0.486525	−	0.873667i	$-0.661736\pi$
$271$	8.45090	−	14.6374i	0.513355	−	0.889158i	0.999880	−	0.0154907i	$-0.00493105\pi$
$272$	6.27952	−	10.8765i	0.380752	−	0.659482i
$273$	−4.81794	+	8.34491i	−0.291595	+	0.505057i
$274$	−2.69405			−0.162754
$275$	−1.83541	+	3.17902i	−0.110679	+	0.191702i
$276$	−0.779512	−	1.35015i	−0.0469211	−	0.0812698i
$277$	9.47961	−	16.4192i	0.569575	−	0.986532i	−0.427033	−	0.904236i	$-0.640441\pi$
$277$	9.47961	−	16.4192i	0.569575	−	0.986532i	0.996608	−	0.0822964i	$-0.0262254\pi$
$278$	−7.26362	+	12.5810i	−0.435643	+	0.754556i
$279$	−5.47881	+	9.48957i	−0.328008	+	0.568126i
$280$	12.7876			0.764206
$281$	−6.91876	−	11.9836i	−0.412738	−	0.714884i	0.582450	−	0.812867i	$-0.302094\pi$
$281$	−6.91876	−	11.9836i	−0.412738	−	0.714884i	−0.995188	+	0.0979829i	$0.968761\pi$
$282$	10.1325			0.603384
$283$	−18.6412			−1.10811			−0.554053	−	0.832481i	$-0.686920\pi$
$283$	−18.6412			−1.10811			−0.554053	+	0.832481i	$0.686920\pi$
$284$	−2.29666			−0.136282
$285$	2.39109			0.141636
$286$	−2.49980	−	4.32978i	−0.147816	−	0.256025i
$287$	−6.27045	+	10.8607i	−0.370133	+	0.641089i
$288$	1.13605			0.0669426
$289$	−8.53071			−0.501807
$290$	−1.82857	−	3.16718i	−0.107378	−	0.185983i
$291$	−19.8121			−1.16141
$292$	0.606991	−	1.05134i	0.0355214	−	0.0615249i
$293$	−15.4828	+	26.8169i	−0.904513	+	1.56666i	−0.0829440	+	0.996554i	$0.526432\pi$
$293$	−15.4828	+	26.8169i	−0.904513	+	1.56666i	−0.821569	+	0.570109i	$0.806901\pi$
$294$	4.77502	+	8.27058i	0.278485	+	0.482350i
$295$	22.8370	−	39.5548i	1.32962	−	2.30297i
$296$	10.0333			0.583173
$297$	−4.00281			−0.232266
$298$	−9.41029	−	16.2991i	−0.545123	−	0.944182i
$299$	−15.9379	−	27.6053i	−0.921715	−	1.59646i
$300$	−0.604873	−	1.04767i	−0.0349223	−	0.0604873i
$301$	−11.5471			−0.665563
$302$	−20.8201			−1.19806
$303$	−0.501670	−	0.868919i	−0.0288202	−	0.0499181i
$304$	2.38900			0.137019
$305$	−10.9080	−	18.8933i	−0.624592	−	1.08183i
$306$	2.50141	+	4.33257i	0.142996	+	0.247677i
$307$	−2.63926	+	4.57133i	−0.150631	+	0.260900i	−0.931459	−	0.363845i	$-0.881464\pi$
$307$	−2.63926	+	4.57133i	−0.150631	+	0.260900i	0.780829	+	0.624745i	$0.214797\pi$
$308$	0.182345			0.0103901
$309$	−1.35771	−	2.35162i	−0.0772374	−	0.133779i
$310$	44.1734			2.50888
$311$	24.3300			1.37963			0.689813	−	0.723988i	$-0.257693\pi$
$311$	24.3300			1.37963			0.689813	+	0.723988i	$0.257693\pi$
$312$	−17.4370			−0.987178
$313$	−14.2820			−0.807267			−0.403633	−	0.914921i	$-0.632253\pi$
$313$	−14.2820			−0.807267			−0.403633	+	0.914921i	$0.632253\pi$
$314$	3.06870			0.173177
$315$	−2.76847	+	4.79513i	−0.155986	+	0.270175i
$316$	−1.09980	−	1.90491i	−0.0618686	−	0.107160i
$317$	7.15973	+	12.4010i	0.402131	+	0.696511i	0.993983	−	0.109536i	$-0.0349364\pi$
$317$	7.15973	+	12.4010i	0.402131	+	0.696511i	−0.591852	+	0.806046i	$0.701603\pi$
$318$	26.9520			1.51139
$319$	0.275945	+	0.477951i	0.0154500	+	0.0267601i
$320$	11.4751	+	19.8755i	0.641478	+	1.11107i
$321$	−8.27621			−0.461933
$322$	14.6286			0.815218
$323$	0.805521	+	1.39520i	0.0448204	+	0.0776312i
$324$	0.357514	−	0.619233i	0.0198619	−	0.0344018i
$325$	−12.3673	−	21.4207i	−0.686012	−	1.18821i
$326$	7.52547	−	13.0345i	0.416797	−	0.721914i
$327$	−4.31407	+	7.47219i	−0.238569	+	0.413213i
$328$	−22.6940			−1.25306
$329$	−3.77794	+	6.54359i	−0.208285	+	0.360760i
$330$	2.25854	+	3.91191i	0.124329	+	0.215343i
$331$	−2.49084	−	4.31427i	−0.136909	−	0.237134i	0.789416	−	0.613859i	$-0.210384\pi$
$331$	−2.49084	−	4.31427i	−0.136909	−	0.237134i	−0.926325	+	0.376725i	$0.877050\pi$
$332$	−0.911256			−0.0500117
$333$	−2.17217	+	3.76231i	−0.119034	+	0.206173i
$334$	2.14035	−	3.70719i	0.117115	−	0.202849i
$335$	−4.00835	−	6.94267i	−0.219000	−	0.379319i
$336$	4.34915	−	7.53296i	0.237266	−	0.410957i
$337$	−5.47598	+	9.48468i	−0.298296	+	0.516663i	−0.975746	−	0.218905i	$-0.929751\pi$
$337$	−5.47598	+	9.48468i	−0.298296	+	0.516663i	0.677450	+	0.735568i	$0.263085\pi$
$338$	14.5261			0.790114
$339$	−2.09673			−0.113879
$340$	0.801396	−	1.38806i	0.0434618	−	0.0752781i
$341$	−6.66608			−0.360988
$342$	−0.475823	+	0.824149i	−0.0257295	+	0.0445649i
$343$	−17.5406			−0.947105
$344$	−10.4478	−	18.0961i	−0.563307	−	0.975676i
$345$	14.3997	+	24.9411i	0.775255	+	1.34278i
$346$	3.81330	+	6.60483i	0.205004	+	0.355078i
$347$	10.6471	−	18.4413i	0.571566	−	0.989981i	−0.424840	−	0.905268i	$-0.639670\pi$
$347$	10.6471	−	18.4413i	0.571566	−	0.989981i	0.996405	−	0.0847121i	$-0.0269970\pi$
$348$	−0.181879			−0.00974976
$349$	15.5950	+	10.2858i	0.834780	+	0.550584i
$349$	15.5950	+	10.2858i	0.834780	+	0.550584i
$350$	11.3512			0.606749
$351$	13.4857	−	23.3580i	0.719816	−	1.24676i
$352$	0.345560	+	0.598527i	0.0184184	+	0.0319016i
$353$	−10.4793	−	18.1506i	−0.557755	−	0.966060i	−0.997683	−	0.0680275i	$-0.978329\pi$
$353$	−10.4793	−	18.1506i	−0.557755	−	0.966060i	0.439928	−	0.898033i	$-0.355004\pi$
$354$	−14.2910	−	24.7527i	−0.759556	−	1.31559i
$355$	42.4256			2.25172
$356$	1.03105	−	1.78584i	0.0546458	−	0.0946492i
$357$	5.86577			0.310449
$358$	7.29050	−	12.6275i	0.385315	−	0.667385i
$359$	28.6454			1.51185			0.755924	−	0.654659i	$-0.227188\pi$
$359$	28.6454			1.51185			0.755924	+	0.654659i	$0.227188\pi$
$360$	−10.0196			−0.528081
$361$	9.34677	−	16.1891i	0.491935	−	0.852057i
$362$	−0.618168	+	1.07070i	−0.0324902	+	0.0562746i
$363$	7.10703	+	12.3097i	0.373023	+	0.646094i
$364$	−0.614332	+	1.06405i	−0.0321998	+	0.0557716i
$365$	−11.2128	+	19.4211i	−0.586904	+	1.01655i
$366$	−13.6521			−0.713607
$367$	−16.4953	−	28.5706i	−0.861046	−	1.49138i	−0.870920	−	0.491424i	$-0.836476\pi$
$367$	−16.4953	−	28.5706i	−0.861046	−	1.49138i	0.00987410	−	0.999951i	$-0.496857\pi$
$368$	14.3872	+	24.9193i	0.749984	+	1.29901i
$369$	4.91316	−	8.50985i	0.255769	−	0.443005i
$370$	17.5133			0.910474
$371$	−10.0491	+	17.4056i	−0.521724	+	0.903653i
$372$	1.09843	−	1.90253i	0.0569508	−	0.0986417i
$373$	7.42456	+	12.8597i	0.384429	+	0.665851i	0.991690	−	0.128652i	$-0.0410650\pi$
$373$	7.42456	+	12.8597i	0.384429	+	0.665851i	−0.607261	+	0.794503i	$0.707732\pi$
$374$	−1.52174	+	2.63573i	−0.0786871	+	0.136290i
$375$	0.375448	+	0.650295i	0.0193880	+	0.0335811i
$376$	−13.6731			−0.705136
$377$	−3.71871			−0.191524
$378$	6.18891	+	10.7195i	0.318323	+	0.551352i
$379$	−8.54614	−	14.8024i	−0.438986	−	0.760346i	0.558626	−	0.829420i	$-0.311329\pi$
$379$	−8.54614	−	14.8024i	−0.438986	−	0.760346i	−0.997612	+	0.0690741i	$0.977996\pi$
$380$	0.304886			0.0156403
$381$	−6.72493	−	11.6479i	−0.344529	−	0.596741i
$382$	−2.45669	−	4.25511i	−0.125695	−	0.217710i
$383$	−3.96587	+	6.86909i	−0.202647	+	0.350994i	−0.949380	−	0.314129i	$-0.898288\pi$
$383$	−3.96587	+	6.86909i	−0.202647	+	0.350994i	0.746734	+	0.665123i	$0.231621\pi$
$384$	17.0000			0.867528
$385$	−3.36841			−0.171670
$386$	−8.94386			−0.455230
$387$	9.04763			0.459917
$388$	−2.52623			−0.128250
$389$	−11.4239	−	19.7868i	−0.579216	−	1.00323i	−0.995570	−	0.0940285i	$-0.970026\pi$
$389$	−11.4239	−	19.7868i	−0.579216	−	1.00323i	0.416354	−	0.909203i	$-0.363308\pi$
$390$	−30.4367			−1.54122
$391$	−9.70211	+	16.8045i	−0.490657	+	0.849842i
$392$	−6.44353	−	11.1605i	−0.325447	−	0.563691i
$393$	−2.54087	−	4.40092i	−0.128170	−	0.221997i
$394$	7.08697			0.357036
$395$	20.3163	+	35.1889i	1.02223	+	1.77055i
$396$	−0.142875			−0.00717973
$397$	−38.3633			−1.92540			−0.962699	−	0.270575i	$-0.912786\pi$
$397$	−38.3633			−1.92540			−0.962699	+	0.270575i	$0.912786\pi$
$398$	−11.6952	−	20.2567i	−0.586227	−	1.01538i
$399$	0.557898	+	0.966308i	0.0279299	+	0.0483759i
$400$	11.1639	+	19.3365i	0.558196	+	0.966824i
$401$	−26.1168			−1.30421			−0.652104	−	0.758129i	$-0.726114\pi$
$401$	−26.1168			−1.30421			−0.652104	+	0.758129i	$0.726114\pi$
$402$	−5.01671			−0.250211
$403$	22.4585	−	38.8993i	1.11874	−	1.93771i
$404$	−0.0639677	−	0.110795i	−0.00318251	−	0.00551227i
$405$	−6.60427	+	11.4389i	−0.328169	+	0.568405i
$406$	0.853302	−	1.47796i	0.0423486	−	0.0733500i
$407$	−2.64289			−0.131003
$408$	5.30734	+	9.19258i	0.262752	+	0.455100i
$409$	−3.17490			−0.156988			−0.0784942	−	0.996915i	$-0.525011\pi$
$409$	−3.17490			−0.156988			−0.0784942	+	0.996915i	$0.525011\pi$
$410$	−39.6128			−1.95634
$411$	1.23751	−	2.14343i	0.0610419	−	0.105728i
$412$	−0.173121	−	0.299854i	−0.00852904	−	0.0147727i
$413$	21.3137			1.04878
$414$	−11.4621			−0.563332
$415$	16.8334			0.826319
$416$	−4.65686			−0.228322
$417$	−6.67307	−	11.5581i	−0.326782	−	0.566002i
$418$	−0.578935			−0.0283166
$419$	−15.0001	+	25.9810i	−0.732805	+	1.26926i	0.222875	+	0.974847i	$0.428456\pi$
$419$	−15.0001	+	25.9810i	−0.732805	+	1.26926i	−0.955680	+	0.294408i	$0.904878\pi$
$420$	0.555041	−	0.961360i	0.0270832	−	0.0469096i
$421$	10.5643	−	18.2979i	0.514872	−	0.891784i	−0.484980	−	0.874525i	$-0.661173\pi$
$421$	10.5643	−	18.2979i	0.514872	−	0.891784i	0.999851	−	0.0172581i	$-0.00549371\pi$
$422$	4.55896	+	7.89635i	0.221927	+	0.384388i
$423$	2.96018	−	5.12718i	0.143929	−	0.249292i
$424$	−36.3697			−1.76627
$425$	−7.52848	+	13.0397i	−0.365185	+	0.632518i
$426$	13.2746	−	22.9923i	0.643157	−	1.11398i
$427$	5.09022	−	8.81652i	0.246333	−	0.426661i
$428$	−1.05529			−0.0510096
$429$	4.59312			0.221758
$430$	−18.2368	−	31.5871i	−0.879458	−	1.52327i
$431$	−1.80682	+	3.12950i	−0.0870314	+	0.150743i	−0.906255	−	0.422731i	$-0.861071\pi$
$431$	−1.80682	+	3.12950i	−0.0870314	+	0.150743i	0.819224	+	0.573474i	$0.194405\pi$
$432$	−12.1736	+	21.0853i	−0.585702	+	1.01447i
$433$	−0.755244	−	1.30812i	−0.0362947	−	0.0628643i	0.847307	−	0.531103i	$-0.178222\pi$
$433$	−0.755244	−	1.30812i	−0.0362947	−	0.0628643i	−0.883602	+	0.468238i	$0.844889\pi$
$434$	10.3067	+	17.8518i	0.494738	+	0.856912i
$435$	3.35981			0.161091
$436$	−0.550084	+	0.952774i	−0.0263443	+	0.0456296i
$437$	−3.69110			−0.176569
$438$	7.01676	+	12.1534i	0.335274	+	0.580711i
$439$	−0.0918674	+	0.159119i	−0.00438459	+	0.00759434i	−0.868209	−	0.496198i	$-0.834729\pi$
$439$	−0.0918674	+	0.159119i	−0.00438459	+	0.00759434i	0.863825	+	0.503792i	$0.168062\pi$
$440$	−3.04773	−	5.27882i	−0.145295	−	0.251658i
$441$	5.58000			0.265714
$442$	−10.2537	−	17.7599i	−0.487718	−	0.844752i
$443$	−3.52676	+	6.10853i	−0.167561	+	0.290225i	−0.937562	−	0.347818i	$-0.886923\pi$
$443$	−3.52676	+	6.10853i	−0.167561	+	0.290225i	0.770001	+	0.638043i	$0.220256\pi$
$444$	0.435491	−	0.754293i	0.0206675	−	0.0357972i
$445$	−19.0464	+	32.9893i	−0.902886	+	1.56384i
$446$	8.23622	−	14.2656i	0.389996	−	0.675494i
$447$	17.2904			0.817808
$448$	−5.35484	+	9.27486i	−0.252993	+	0.438196i
$449$	16.4832			0.777891			0.388945	−	0.921261i	$-0.372840\pi$
$449$	16.4832			0.777891			0.388945	+	0.921261i	$0.372840\pi$
$450$	−8.89416			−0.419275
$451$	5.97786			0.281486
$452$	−0.267353			−0.0125752
$453$	9.56366	−	16.5648i	0.449340	−	0.778280i
$454$	−11.9774	−	20.7455i	−0.562128	−	0.973635i
$455$	11.3484	−	19.6560i	0.532021	−	0.921488i
$456$	−1.00957	+	1.74863i	−0.0472775	+	0.0818870i
$457$	6.96015	+	12.0553i	0.325582	+	0.563925i	0.981630	−	0.190795i	$-0.0611065\pi$
$457$	6.96015	+	12.0553i	0.325582	+	0.563925i	−0.656048	+	0.754719i	$0.727773\pi$
$458$	−9.77010	−	16.9223i	−0.456527	−	0.790727i
$459$	−16.4187			−0.766359
$460$	1.83610	+	3.18022i	0.0856086	+	0.148279i
$461$	18.8342	+	32.6218i	0.877196	+	1.51935i	0.854405	+	0.519608i	$0.173922\pi$
$461$	18.8342	+	32.6218i	0.877196	+	1.51935i	0.0227914	+	0.999740i	$0.492745\pi$
$462$	−1.05394	+	1.82549i	−0.0490339	+	0.0849292i
$463$	−14.4260	−	24.9865i	−0.670432	−	1.16122i	−0.977782	−	0.209626i	$-0.932775\pi$
$463$	−14.4260	−	24.9865i	−0.670432	−	1.16122i	0.307350	−	0.951597i	$-0.400558\pi$
$464$	3.35689			0.155840
$465$	−20.2910	+	35.1450i	−0.940971	+	1.62981i
$466$	20.7468	+	35.9345i	0.961078	+	1.66464i
$467$	−2.14454			−0.0992376			−0.0496188	−	0.998768i	$-0.515801\pi$
$467$	−2.14454			−0.0992376			−0.0496188	+	0.998768i	$0.515801\pi$
$468$	0.481355	−	0.833732i	0.0222506	−	0.0385393i
$469$	1.87049	−	3.23979i	0.0863713	−	0.149599i
$470$	−23.8667			−1.10089
$471$	−1.40960	+	2.44150i	−0.0649511	+	0.112499i
$472$	19.2846	+	33.4019i	0.887644	+	1.53744i
$473$	2.75207	+	4.76673i	0.126540	+	0.219174i
$474$	25.4272			1.16791
$475$	−2.86416			−0.131417
$476$	0.747941			0.0342818
$477$	7.87391	−	13.6380i	0.360521	−	0.624441i
$478$	−15.9407	+	27.6101i	−0.729111	+	1.26286i
$479$	−20.9544	+	36.2941i	−0.957430	+	1.65832i	−0.228724	+	0.973491i	$0.573455\pi$
$479$	−20.9544	+	36.2941i	−0.957430	+	1.65832i	−0.728706	+	0.684826i	$0.759878\pi$
$480$	4.20742			0.192041
$481$	8.90407	−	15.4223i	0.405991	−	0.703197i
$482$	15.6768			0.714058
$483$	−6.71961	+	11.6387i	−0.305753	+	0.529580i
$484$	0.906214	+	1.56961i	0.0411915	+	0.0713458i
$485$	46.6663			2.11901
$486$	−8.34109	−	14.4472i	−0.378360	−	0.655338i
$487$	13.6823	−	23.6984i	0.620004	−	1.07388i	−0.369480	−	0.929239i	$-0.620464\pi$
$487$	13.6823	−	23.6984i	0.620004	−	1.07388i	0.989484	−	0.144640i	$-0.0462025\pi$
$488$	18.4225			0.833946
$489$	6.91363	+	11.9748i	0.312645	+	0.541517i
$490$	−11.2473	−	19.4809i	−0.508102	−	0.880058i
$491$	9.46965	+	16.4019i	0.427359	+	0.740208i	0.996638	−	0.0819371i	$-0.0261107\pi$
$491$	9.46965	+	16.4019i	0.427359	+	0.740208i	−0.569278	+	0.822145i	$0.692777\pi$
$492$	−0.985023	+	1.70611i	−0.0444083	+	0.0769174i
$493$	1.13187	+	1.96046i	0.0509769	+	0.0882946i
$494$	1.95047	−	3.37832i	0.0877559	−	0.151998i
$495$	2.63929			0.118627
$496$	−20.2733	+	35.1144i	−0.910298	+	1.57668i
$497$	9.89893	+	17.1455i	0.444028	+	0.769079i
$498$	5.26702	−	9.12274i	0.236021	−	0.408800i
$499$	16.3157	−	28.2597i	0.730393	−	1.26508i	−0.226323	−	0.974052i	$-0.572670\pi$
$499$	16.3157	−	28.2597i	0.730393	−	1.26508i	0.956715	−	0.291025i	$-0.0939963\pi$
$500$	0.0478731	+	0.0829187i	0.00214095	+	0.00370824i
$501$	1.96633	+	3.40579i	0.0878493	+	0.152159i
$502$	−6.60870	+	11.4466i	−0.294961	+	0.510887i
$503$	2.68609	+	4.65245i	0.119767	+	0.207442i	0.919675	−	0.392680i	$-0.128452\pi$
$503$	2.68609	+	4.65245i	0.119767	+	0.207442i	−0.799908	+	0.600122i	$0.795119\pi$
$504$	−2.33782	−	4.04923i	−0.104135	−	0.180367i
$505$	1.18166	+	2.04669i	0.0525831	+	0.0910766i
$506$	−3.48649	−	6.03878i	−0.154993	−	0.268457i
$507$	−6.67253	+	11.5572i	−0.296338	+	0.513272i
$508$	−0.857492	−	1.48522i	−0.0380450	−	0.0658960i
$509$	−2.08160	+	3.60544i	−0.0922654	+	0.159808i	−0.908464	−	0.417963i	$-0.862744\pi$
$509$	−2.08160	+	3.60544i	−0.0922654	+	0.159808i	0.816199	+	0.577771i	$0.196077\pi$
$510$	9.26407	+	16.0458i	0.410220	+	0.710522i
$511$	−10.4649			−0.462938
$512$	−19.0438			−0.841625
$513$	−1.56160	−	2.70476i	−0.0689462	−	0.119418i
$514$	12.2563	−	21.2286i	0.540603	−	0.936352i
$515$	3.19801	+	5.53912i	0.140921	+	0.244083i
$516$	−1.81393			−0.0798538
$517$	3.60166			0.158401
$518$	4.08628	+	7.07765i	0.179541	+	0.310974i
$519$	−7.00653			−0.307553
$520$	41.0720			1.80113
$521$	16.7819	−	29.0671i	0.735227	−	1.27345i	−0.219396	−	0.975636i	$-0.570409\pi$
$521$	16.7819	−	29.0671i	0.735227	−	1.27345i	0.954624	−	0.297815i	$-0.0962580\pi$
$522$	−0.668598	+	1.15805i	−0.0292637	+	0.0506863i
$523$	−6.32802	−	10.9605i	−0.276705	−	0.479267i	0.693859	−	0.720111i	$-0.255909\pi$
$523$	−6.32802	−	10.9605i	−0.276705	−	0.479267i	−0.970564	+	0.240844i	$0.922576\pi$
$524$	−0.323985	−	0.561159i	−0.0141534	−	0.0245143i
$525$	−5.21417	+	9.03121i	−0.227565	+	0.394154i
$526$	−1.31326	+	2.27463i	−0.0572608	+	0.0991787i
$527$	−27.3429			−1.19108
$528$	−4.14621			−0.180441
$529$	−10.7288	−	18.5828i	−0.466468	−	0.807947i
$530$	−63.4841			−2.75757
$531$	−16.7002			−0.724725
$532$	0.0711373	+	0.123213i	0.00308419	+	0.00534198i
$533$	−20.1398	+	34.8832i	−0.872353	+	1.51096i
$534$	11.9189	+	20.6441i	0.515781	+	0.893359i
$535$	19.4942			0.842807
$536$	6.76967			0.292405
$537$	6.69776	+	11.6009i	0.289030	+	0.500614i
$538$	−19.8563	+	34.3922i	−0.856068	+	1.48275i
$539$	1.69730	+	2.93981i	0.0731080	+	0.126627i
$540$	−1.55360	+	2.69091i	−0.0668563	+	0.115798i
$541$	6.80577	+	11.7879i	0.292603	+	0.506803i	0.974424	−	0.224715i	$-0.0721452\pi$
$541$	6.80577	+	11.7879i	0.292603	+	0.506803i	−0.681821	+	0.731519i	$0.738812\pi$
$542$	12.4566	+	21.5755i	0.535057	+	0.926745i
$543$	−0.567909	−	0.983647i	−0.0243713	−	0.0422123i
$544$	1.41742	+	2.45504i	0.0607712	+	0.105259i
$545$	10.1616	−	17.6003i	0.435274	−	0.753916i
$546$	−7.10163	−	12.3004i	−0.303922	−	0.526408i
$547$	3.34904	+	5.80070i	0.143194	+	0.248020i	0.928698	−	0.370837i	$-0.120929\pi$
$547$	3.34904	+	5.80070i	0.143194	+	0.248020i	−0.785503	+	0.618857i	$0.787596\pi$
$548$	0.157794	−	0.273308i	0.00674063	−	0.0116751i
$549$	−3.98840	+	6.90811i	−0.170221	+	0.294831i
$550$	−2.70539	−	4.68587i	−0.115358	−	0.199806i
$551$	−0.215306	+	0.372921i	−0.00917236	+	0.0158870i
$552$	−24.3196			−1.03511
$553$	−9.48059	+	16.4209i	−0.403156	+	0.698286i
$554$	13.9729	+	24.2018i	0.593653	+	1.02824i
$555$	−8.04472	+	13.9339i	−0.341479	+	0.591459i
$556$	−0.850879	−	1.47377i	−0.0360853	−	0.0625016i
$557$	−3.81075	−	6.60041i	−0.161467	−	0.279668i	0.773928	−	0.633273i	$-0.218289\pi$
$557$	−3.81075	−	6.60041i	−0.161467	−	0.279668i	−0.935395	+	0.353605i	$0.884956\pi$
$558$	−8.07575	−	13.9876i	−0.341874	−	0.592142i
$559$	−37.0877			−1.56864
$560$	−10.2442	+	17.7435i	−0.432897	+	0.749799i
$561$	−1.39802	−	2.42143i	−0.0590242	−	0.102233i
$562$	20.3965			0.860373
$563$	7.38279	+	12.7874i	0.311148	+	0.538923i	0.978611	−	0.205719i	$-0.0659533\pi$
$563$	7.38279	+	12.7874i	0.311148	+	0.538923i	−0.667464	+	0.744642i	$0.732620\pi$
$564$	−0.593476	+	1.02793i	−0.0249898	+	0.0432837i
$565$	4.93874			0.207774
$566$	13.7386	−	23.7959i	0.577475	−	1.00022i
$567$	−6.16374			−0.258853
$568$	−17.9131	+	31.0263i	−0.751616	+	1.30184i
$569$	17.5320	−	30.3663i	0.734980	−	1.27302i	−0.219752	−	0.975556i	$-0.570525\pi$
$569$	17.5320	−	30.3663i	0.734980	−	1.27302i	0.954732	−	0.297467i	$-0.0961419\pi$
$570$	−1.76223	+	3.05227i	−0.0738116	+	0.127845i
$571$	6.93973			0.290419			0.145209	−	0.989401i	$-0.453614\pi$
$571$	6.93973			0.290419			0.145209	+	0.989401i	$0.453614\pi$
$572$	0.585666			0.0244879
$573$	4.51391			0.188571
$574$	−9.24263	−	16.0087i	−0.385780	−	0.668190i
$575$	−17.2487	−	29.8756i	−0.719320	−	1.24590i
$576$	4.19574	−	7.26724i	0.174823	−	0.302802i
$577$	5.99522			0.249584			0.124792	−	0.992183i	$-0.460174\pi$
$577$	5.99522			0.249584			0.124792	+	0.992183i	$0.460174\pi$
$578$	6.28712	−	10.8896i	0.261510	−	0.452948i
$579$	4.10835	−	7.11587i	0.170737	−	0.295725i
$580$	0.428408			0.0177887
$581$	3.92764	+	6.80287i	0.162946	+	0.282231i
$582$	14.6015	−	25.2905i	0.605251	−	1.04833i
$583$	9.58020			0.396772
$584$	−9.46858	−	16.4001i	−0.391813	−	0.678640i
$585$	−8.89195	+	15.4013i	−0.367637	+	0.636766i
$586$	−22.8216	−	39.5281i	−0.942750	−	1.63289i
$587$	−22.2729	−	38.5778i	−0.919302	−	1.59228i	−0.800478	−	0.599362i	$-0.795421\pi$
$587$	−22.2729	−	38.5778i	−0.919302	−	1.59228i	−0.118824	−	0.992915i	$-0.537912\pi$
$588$	−1.11872			−0.0461351
$589$	−2.60061	−	4.50438i	−0.107156	−	0.185600i
$590$	33.6616	+	58.3036i	1.38583	+	2.40032i
$591$	−3.25539	+	5.63850i	−0.133909	+	0.231937i
$592$	−8.03771	+	13.9217i	−0.330348	+	0.572179i
$593$	−9.60913	−	16.6435i	−0.394600	−	0.683467i	0.598450	−	0.801160i	$-0.295783\pi$
$593$	−9.60913	−	16.6435i	−0.394600	−	0.683467i	−0.993050	+	0.117693i	$0.962450\pi$
$594$	2.95006	−	5.10966i	0.121043	−	0.209652i
$595$	−13.8165			−0.566422
$596$	2.20469			0.0903076
$597$	21.4887			0.879474
$598$	46.9850			1.92136
$599$	−14.4157	+	24.9686i	−0.589008	+	1.02019i	0.405355	+	0.914159i	$0.367148\pi$
$599$	−14.4157	+	24.9686i	−0.589008	+	1.02019i	−0.994363	+	0.106032i	$0.966185\pi$
$600$	−18.8711			−0.770409
$601$	24.2247	−	41.9584i	0.988146	−	1.71152i	0.361123	−	0.932518i	$-0.382394\pi$
$601$	24.2247	−	41.9584i	0.988146	−	1.71152i	0.627023	−	0.779001i	$-0.284273\pi$
$602$	8.51019	−	14.7401i	0.346850	−	0.600761i
$603$	−1.46561	+	2.53851i	−0.0596842	+	0.103376i
$604$	1.21946	−	2.11216i	0.0496190	−	0.0859426i
$605$	−16.7403	−	28.9950i	−0.680588	−	1.17881i
$606$	1.47892			0.0600771
$607$	−1.48984	−	2.58048i	−0.0604707	−	0.104738i	0.834205	−	0.551454i	$-0.185927\pi$
$607$	−1.48984	−	2.58048i	−0.0604707	−	0.104738i	−0.894676	+	0.446716i	$0.852594\pi$
$608$	−0.269623	+	0.467001i	−0.0109347	+	0.0189394i
$609$	0.783926	+	1.35780i	0.0317663	+	0.0550208i
$610$	32.1568			1.30199
$611$	−12.1342	+	21.0171i	−0.490899	+	0.850261i
$612$	−0.586043			−0.0236894
$613$	8.73781	+	15.1343i	0.352917	+	0.611270i	0.986759	−	0.162192i	$-0.0518565\pi$
$613$	8.73781	+	15.1343i	0.352917	+	0.611270i	−0.633842	+	0.773462i	$0.718523\pi$
$614$	−3.89026	−	6.73813i	−0.156998	−	0.271929i
$615$	18.1961	−	31.5165i	0.733737	−	1.27087i
$616$	1.42222	−	2.46335i	0.0573028	−	0.0992513i
$617$	1.33225	+	2.30753i	0.0536345	+	0.0928976i	0.891596	−	0.452832i	$-0.149586\pi$
$617$	1.33225	+	2.30753i	0.0536345	+	0.0928976i	−0.837962	+	0.545729i	$0.816253\pi$
$618$	4.00252			0.161005
$619$	−2.12671			−0.0854795			−0.0427397	−	0.999086i	$-0.513609\pi$
$619$	−2.12671			−0.0854795			−0.0427397	+	0.999086i	$0.513609\pi$
$620$	−2.58729	+	4.48132i	−0.103908	+	0.179974i
$621$	18.8087	−	32.5776i	0.754766	−	1.30729i
$622$	−17.9311	+	31.0577i	−0.718973	+	1.24530i
$623$	−17.7760			−0.712178
$624$	13.9689	−	24.1948i	0.559203	−	0.968568i
$625$	12.0503	+	20.8717i	0.482011	+	0.834867i
$626$	10.5258	−	18.2313i	0.420696	−	0.728667i
$627$	0.265933	−	0.460609i	0.0106203	−	0.0183950i
$628$	−0.179738	+	0.311315i	−0.00717231	+	0.0124228i
$629$	−10.8406			−0.432242
$630$	−4.08072	−	7.06801i	−0.162580	−	0.281596i
$631$	−22.3814			−0.890991			−0.445495	−	0.895284i	$-0.646972\pi$
$631$	−22.3814			−0.890991			−0.445495	+	0.895284i	$0.646972\pi$
$632$	−34.3121			−1.36486
$633$	−8.37660			−0.332940
$634$	−21.1068			−0.838260
$635$	15.8402	+	27.4361i	0.628600	+	1.08877i
$636$	−1.57861	+	2.73424i	−0.0625961	+	0.108420i
$637$	−22.8733			−0.906274
$638$	−0.813485			−0.0322062
$639$	−7.75623	−	13.4342i	−0.306832	−	0.531448i
$640$	−40.0426			−1.58282
$641$	−0.962051	+	1.66632i	−0.0379987	+	0.0658157i	−0.884399	−	0.466731i	$-0.845432\pi$
$641$	−0.962051	+	1.66632i	−0.0379987	+	0.0658157i	0.846401	+	0.532547i	$0.178765\pi$
$642$	6.09956	−	10.5647i	0.240730	−	0.416957i
$643$	17.7677	+	30.7746i	0.700690	+	1.21363i	0.968224	+	0.250083i	$0.0804579\pi$
$643$	17.7677	+	30.7746i	0.700690	+	1.21363i	−0.267534	+	0.963548i	$0.586209\pi$
$644$	−0.856814	+	1.48405i	−0.0337632	+	0.0584796i
$645$	33.5083			1.31939
$646$	−2.37467			−0.0934302
$647$	−12.3712	−	21.4276i	−0.486363	−	0.842405i	0.513514	−	0.858081i	$-0.328343\pi$
$647$	−12.3712	−	21.4276i	−0.486363	−	0.842405i	−0.999877	+	0.0156761i	$0.995010\pi$
$648$	−5.57694	−	9.65955i	−0.219083	−	0.379463i
$649$	−5.07978	−	8.79844i	−0.199399	−	0.345369i
$650$	36.4586			1.43002
$651$	−18.9375			−0.742219
$652$	0.881552	+	1.52689i	0.0345242	+	0.0597978i
$653$	−19.3124			−0.755752			−0.377876	−	0.925856i	$-0.623345\pi$
$653$	−19.3124			−0.755752			−0.377876	+	0.925856i	$0.623345\pi$
$654$	−6.35892	−	11.0140i	−0.248654	−	0.430681i
$655$	5.98490	+	10.3661i	0.233849	+	0.405039i
$656$	18.1802	−	31.4891i	0.709819	−	1.22944i
$657$	8.19966			0.319899
$658$	−5.56868	−	9.64523i	−0.217090	−	0.376010i
$659$	−13.4095			−0.522361			−0.261180	−	0.965290i	$-0.584112\pi$
$659$	−13.4095			−0.522361			−0.261180	+	0.965290i	$0.584112\pi$
$660$	−0.529142			−0.0205968
$661$	−15.3819			−0.598286			−0.299143	−	0.954208i	$-0.596701\pi$
$661$	−15.3819			−0.598286			−0.299143	+	0.954208i	$0.596701\pi$
$662$	7.34299			0.285394
$663$	18.8400			0.731687
$664$	−7.10744	+	12.3105i	−0.275822	+	0.477738i
$665$	−1.31410	−	2.27609i	−0.0509586	−	0.0882630i
$666$	−3.20177	−	5.54564i	−0.124066	−	0.214889i
$667$	−5.18652			−0.200823
$668$	0.250726	+	0.434270i	0.00970088	+	0.0168024i
$669$	7.56660	+	13.1057i	0.292541	+	0.506697i
$670$	11.8166			0.456515
$671$	−4.85270			−0.187336
$672$	0.981693	+	1.70034i	0.0378696	+	0.0655921i
$673$	8.95444	−	15.5095i	0.345168	−	0.597849i	−0.640216	−	0.768195i	$-0.721155\pi$
$673$	8.95444	−	15.5095i	0.345168	−	0.597849i	0.985384	+	0.170346i	$0.0544885\pi$
$674$	−8.07158	−	13.9804i	−0.310906	−	0.538504i
$675$	14.5948	−	25.2790i	0.561755	−	0.972988i
$676$	−0.850811	+	1.47365i	−0.0327235	+	0.0566787i
$677$	−18.2801			−0.702560			−0.351280	−	0.936271i	$-0.614253\pi$
$677$	−18.2801			−0.702560			−0.351280	+	0.936271i	$0.614253\pi$
$678$	1.54529	−	2.67652i	0.0593464	−	0.102791i
$679$	10.8884	+	18.8592i	0.417858	+	0.723751i
$680$	−12.5012	−	21.6526i	−0.479398	−	0.830341i
$681$	22.0073			0.843320
$682$	4.91289	−	8.50938i	0.188124	−	0.325841i
$683$	−10.8332	+	18.7637i	−0.414522	+	0.717973i	−0.995378	−	0.0960332i	$-0.969385\pi$
$683$	−10.8332	+	18.7637i	−0.414522	+	0.717973i	0.580856	+	0.814006i	$0.302718\pi$
$684$	−0.0557391	−	0.0965429i	−0.00213124	−	0.00369141i
$685$	−2.91489	+	5.04874i	−0.111372	+	0.192902i
$686$	12.9274	−	22.3909i	0.493571	−	0.854890i
$687$	17.9515			0.684893
$688$	33.4791			1.27638
$689$	−32.2764	+	55.9043i	−1.22963	+	2.12979i
$690$	−42.4503			−1.61606
$691$	−21.5344	+	37.2986i	−0.819205	+	1.41891i	0.0870631	+	0.996203i	$0.472252\pi$
$691$	−21.5344	+	37.2986i	−0.819205	+	1.41891i	−0.906268	+	0.422703i	$0.861082\pi$
$692$	−0.893399			−0.0339619
$693$	0.615810	+	1.06661i	0.0233927	+	0.0405173i
$694$	15.6938	+	27.1824i	0.595728	+	1.03183i
$695$	15.7181	+	27.2245i	0.596220	+	1.03268i
$696$	−1.41859	+	2.45707i	−0.0537715	+	0.0931349i
$697$	24.5200			0.928760
$698$	−24.6234	+	12.3267i	−0.932011	+	0.466572i
$699$	−38.1201			−1.44183
$700$	−0.664856	+	1.15156i	−0.0251292	+	0.0435250i
$701$	−23.1263	−	40.0558i	−0.873466	−	1.51289i	−0.858387	−	0.513002i	$-0.828533\pi$
$701$	−23.1263	−	40.0558i	−0.873466	−	1.51289i	−0.0150790	−	0.999886i	$-0.504800\pi$
$702$	19.8779	+	34.4296i	0.750245	+	1.29946i
$703$	−1.03106	−	1.78584i	−0.0388871	−	0.0673544i
$704$	5.10497			0.192401
$705$	10.9631	−	18.9887i	0.412895	−	0.715156i
$706$	30.8928			1.16267
$707$	−0.551419	+	0.955086i	−0.0207383	+	0.0359197i
$708$	3.34816			0.125832
$709$	30.2542			1.13622			0.568110	−	0.822952i	$-0.307675\pi$
$709$	30.2542			1.13622			0.568110	+	0.822952i	$0.307675\pi$
$710$	−31.2676	+	54.1571i	−1.17345	+	2.03248i
$711$	7.42844	−	12.8664i	0.278588	−	0.482529i
$712$	−16.0836	−	27.8577i	−0.602760	−	1.04401i
$713$	31.3230	−	54.2531i	1.17306	−	2.03179i
$714$	−4.32306	+	7.48777i	−0.161787	+	0.280223i
$715$	−10.8189			−0.404602
$716$	0.854028	+	1.47922i	0.0319165	+	0.0552810i
$717$	−14.6447	−	25.3653i	−0.546916	−	0.947286i
$718$	−21.1116	+	36.5664i	−0.787880	+	1.36465i
$719$	13.0254			0.485767			0.242884	−	0.970055i	$-0.421907\pi$
$719$	13.0254			0.485767			0.242884	+	0.970055i	$0.421907\pi$
$720$	8.02677	−	13.9028i	0.299140	−	0.518126i
$721$	−1.49235	+	2.58482i	−0.0555780	+	0.0962638i
$722$	13.7771	+	23.8627i	0.512731	+	0.888076i
$723$	−7.20111	+	12.4727i	−0.267812	+	0.463864i
$724$	−0.0724137	−	0.125424i	−0.00269123	−	0.00466135i
$725$	−4.02455			−0.149468
$726$	−20.9515			−0.777583
$727$	−1.07072	−	1.85453i	−0.0397107	−	0.0687809i	0.845487	−	0.533996i	$-0.179310\pi$
$727$	−1.07072	−	1.85453i	−0.0397107	−	0.0687809i	−0.885198	+	0.465215i	$0.845977\pi$
$728$	9.58311	+	16.5984i	0.355174	+	0.615179i
$729$	27.7491			1.02774
$730$	−16.5276	−	28.6267i	−0.611714	−	1.05952i
$731$	11.2884	+	19.5521i	0.417518	+	0.723162i
$732$	0.799621	−	1.38498i	0.0295548	−	0.0511905i
$733$	37.6534			1.39076			0.695380	−	0.718642i	$-0.255236\pi$
$733$	37.6534			1.39076			0.695380	+	0.718642i	$0.255236\pi$
$734$	48.6280			1.79489
$735$	20.6658			0.762268
$736$	−6.49496			−0.239408
$737$	−1.78321			−0.0656854
$738$	7.24199	+	12.5435i	0.266581	+	0.461732i
$739$	−47.9648			−1.76441			−0.882207	−	0.470863i	$-0.843943\pi$
$739$	−47.9648			−1.76441			−0.882207	+	0.470863i	$0.843943\pi$
$740$	−1.02578	+	1.77670i	−0.0377083	+	0.0653127i
$741$	1.79189	+	3.10365i	0.0658268	+	0.114015i
$742$	−14.8124	−	25.6558i	−0.543779	−	0.941853i
$743$	26.2131			0.961666			0.480833	−	0.876812i	$-0.340334\pi$
$743$	26.2131			0.961666			0.480833	+	0.876812i	$0.340334\pi$
$744$	−17.1346	−	29.6780i	−0.628185	−	1.08805i
$745$	−40.7267			−1.49211
$746$	−21.8876			−0.801361
$747$	−3.07747	−	5.33034i	−0.112599	−	0.195027i
$748$	−0.178260	−	0.308755i	−0.00651783	−	0.0112892i
$749$	4.54847	+	7.87818i	0.166197	+	0.287862i
$750$	−1.10682			−0.0404153
$751$	47.8502			1.74608			0.873039	−	0.487651i	$-0.162146\pi$
$751$	47.8502			1.74608			0.873039	+	0.487651i	$0.162146\pi$
$752$	10.9536	−	18.9722i	0.399436	−	0.691843i
$753$	−6.07140	−	10.5160i	−0.221254	−	0.383223i
$754$	2.74069	−	4.74701i	0.0998099	−	0.172876i
$755$	−22.5267	+	39.0174i	−0.819831	+	1.41999i
$756$	−1.44997			−0.0527349
$757$	4.74071	+	8.21115i	0.172304	+	0.298439i	0.939225	−	0.343302i	$-0.111546\pi$
$757$	4.74071	+	8.21115i	0.172304	+	0.298439i	−0.766921	+	0.641742i	$0.778212\pi$
$758$	25.1940			0.915087
$759$	6.40606			0.232525
$760$	2.37799	−	4.11880i	0.0862588	−	0.149405i
$761$	18.2289	+	31.5735i	0.660799	+	1.14454i	0.980406	+	0.196987i	$0.0631157\pi$
$761$	18.2289	+	31.5735i	0.660799	+	1.14454i	−0.319607	+	0.947550i	$0.603551\pi$
$762$	19.8251			0.718186
$763$	9.48376			0.343335
$764$	0.575566			0.0208232
$765$	10.8258			0.391408
$766$	−5.84569	−	10.1250i	−0.211213	−	0.365832i
$767$	68.4566			2.47182
$768$	−2.78552	+	4.82466i	−0.100514	+	0.174095i
$769$	−22.4237	+	38.8391i	−0.808621	+	1.40057i	0.105198	+	0.994451i	$0.466452\pi$
$769$	−22.4237	+	38.8391i	−0.808621	+	1.40057i	−0.913819	+	0.406122i	$0.866881\pi$
$770$	2.48251	−	4.29984i	0.0894635	−	0.154955i
$771$	11.2598	+	19.5026i	0.405513	+	0.702370i
$772$	0.523853	−	0.907340i	0.0188539	−	0.0326559i
$773$	−23.4285			−0.842664			−0.421332	−	0.906906i	$-0.638437\pi$
$773$	−23.4285			−0.842664			−0.421332	+	0.906906i	$0.638437\pi$
$774$	−6.66809	+	11.5495i	−0.239680	+	0.415137i
$775$	24.3055	−	42.0984i	0.873080	−	1.51222i
$776$	−19.7036	+	34.1276i	−0.707318	+	1.22511i
$777$	−7.50811			−0.269352
$778$	33.6777			1.20740
$779$	2.33211	+	4.03934i	0.0835566	+	0.144724i
$780$	1.78272	−	3.08776i	0.0638315	−	0.110559i
$781$	4.71851	−	8.17270i	0.168842	−	0.292442i
$782$	−14.3009	−	24.7699i	−0.511398	−	0.885768i
$783$	−2.19426	−	3.80057i	−0.0784165	−	0.135821i
$784$	20.6478			0.737420
$785$	3.32025	−	5.75083i	0.118505	−	0.205256i
$786$	7.49048			0.267177
$787$	−23.3107	−	40.3753i	−0.830937	−	1.43922i	−0.897296	−	0.441429i	$-0.854472\pi$
$787$	−23.3107	−	40.3753i	−0.830937	−	1.43922i	0.0663598	−	0.997796i	$-0.478861\pi$
$788$	−0.415092	+	0.718961i	−0.0147871	+	0.0256119i
$789$	−1.20649	−	2.08970i	−0.0429521	−	0.0743952i
$790$	−59.8924			−2.13088
$791$	1.15233	+	1.99589i	0.0409721	+	0.0709657i
$792$	−1.11437	+	1.93014i	−0.0395973	+	0.0685846i
$793$	16.3491	−	28.3174i	0.580573	−	1.00558i
$794$	28.2737	−	48.9715i	1.00340	−	1.73793i
$795$	29.1613	−	50.5089i	1.03425	−	1.79137i
$796$	2.74001			0.0971171
$797$	−5.00343	+	8.66619i	−0.177230	+	0.306972i	−0.940931	−	0.338599i	$-0.890047\pi$
$797$	−5.00343	+	8.66619i	−0.177230	+	0.306972i	0.763700	+	0.645571i	$0.223380\pi$
$798$	−1.64468			−0.0582211
$799$	14.7733			0.522640
$800$	−5.03985			−0.178186
$801$	13.9282			0.492129
$802$	19.2480	−	33.3385i	0.679671	−	1.17722i
$803$	2.49414	+	4.31997i	0.0880162	+	0.152448i
$804$	0.293835	−	0.508937i	0.0103628	−	0.0179488i
$805$	15.8277	−	27.4144i	0.557853	−	0.966230i
$806$	33.1038	+	57.3374i	1.16603	+	2.01962i
$807$	−18.2420	−	31.5960i	−0.642148	−	1.11223i
$808$	−1.99569			−0.0702082
$809$	21.5845	+	37.3855i	0.758872	+	1.31441i	0.943426	+	0.331583i	$0.107583\pi$
$809$	21.5845	+	37.3855i	0.758872	+	1.31441i	−0.184554	+	0.982822i	$0.559084\pi$
$810$	−9.73467	−	16.8609i	−0.342041	−	0.592433i
$811$	−11.7259	+	20.3099i	−0.411753	+	0.713177i	−0.995082	−	0.0990594i	$-0.968417\pi$
$811$	−11.7259	+	20.3099i	−0.411753	+	0.713177i	0.583329	+	0.812236i	$0.301750\pi$
$812$	0.0999579	+	0.173132i	0.00350783	+	0.00607575i
$813$	−22.8877			−0.802706
$814$	1.94780	−	3.37370i	0.0682705	−	0.118248i
$815$	−16.2847	−	28.2059i	−0.570428	−	0.988010i
$816$	−17.0069			−0.595361
$817$	−2.14730	+	3.71924i	−0.0751247	+	0.130120i
$818$	2.33989	−	4.05281i	0.0818125	−	0.141703i
$819$	−8.29883			−0.289985
$820$	2.32017	−	4.01865i	0.0810239	−	0.140337i
$821$	−25.3295	−	43.8719i	−0.884005	−	1.53114i	−0.846850	−	0.531831i	$-0.821504\pi$
$821$	−25.3295	−	43.8719i	−0.884005	−	1.53114i	−0.0371541	−	0.999310i	$-0.511829\pi$
$822$	1.82409	+	3.15941i	0.0636223	+	0.110197i
$823$	13.5641			0.472814			0.236407	−	0.971654i	$-0.424030\pi$
$823$	13.5641			0.472814			0.236407	+	0.971654i	$0.424030\pi$
$824$	−5.40109			−0.188156
$825$	4.97087			0.173063
$826$	−15.7081	+	27.2073i	−0.546556	+	0.946663i
$827$	−15.2217	+	26.3647i	−0.529310	+	0.916791i	0.470106	+	0.882610i	$0.344216\pi$
$827$	−15.2217	+	26.3647i	−0.529310	+	0.916791i	−0.999416	+	0.0341813i	$0.989118\pi$
$828$	0.671350	−	1.16281i	0.0233310	−	0.0404105i
$829$	−48.9583			−1.70039			−0.850195	−	0.526468i	$-0.823516\pi$
$829$	−48.9583			−1.70039			−0.850195	+	0.526468i	$0.823516\pi$
$830$	−12.4062	+	21.4882i	−0.430625	+	0.745865i
$831$	−25.6738			−0.890613
$832$	−17.1990	+	29.7896i	−0.596269	+	1.03277i
$833$	6.96199	+	12.0585i	0.241218	+	0.417803i
$834$	19.6722			0.681192
$835$	−4.63159	−	8.02216i	−0.160283	−	0.277618i
$836$	0.0339089	−	0.0587320i	0.00117276	−	0.00203129i
$837$	53.0074			1.83220
$838$	−22.1102	−	38.2959i	−0.763783	−	1.32291i
$839$	−2.36545	−	4.09708i	−0.0816644	−	0.141447i	0.822301	−	0.569053i	$-0.192690\pi$
$839$	−2.36545	−	4.09708i	−0.0816644	−	0.141447i	−0.903965	+	0.427607i	$0.859357\pi$
$840$	−8.65822	−	14.9965i	−0.298737	−	0.517427i
$841$	14.1975	−	24.5907i	0.489568	−	0.847956i
$842$	15.5717	+	26.9710i	0.536637	+	0.929482i
$843$	−9.36908	+	16.2277i	−0.322688	+	0.558913i
$844$	−1.06810			−0.0367654
$845$	15.7168	−	27.2223i	0.540675	−	0.936476i
$846$	4.36329	+	7.55744i	0.150013	+	0.259830i
$847$	7.81181	−	13.5305i	0.268417	−	0.464912i
$848$	29.1359	−	50.4649i	1.00053	−	1.73297i
$849$	12.6216	+	21.8612i	0.433171	+	0.750275i
$850$	−11.0970	−	19.2205i	−0.380622	−	0.659257i
$851$	12.4186	−	21.5096i	0.425703	−	0.737340i
$852$	1.55502	+	2.69337i	0.0532741	+	0.0922735i
$853$	5.58340	+	9.67073i	0.191172	+	0.331119i	0.945639	−	0.325219i	$-0.105438\pi$
$853$	5.58340	+	9.67073i	0.191172	+	0.331119i	−0.754467	+	0.656338i	$0.772105\pi$
$854$	7.50297	+	12.9955i	0.256746	+	0.444698i
$855$	1.02965	+	1.78341i	0.0352134	+	0.0609914i
$856$	−8.23089	+	14.2563i	−0.281326	+	0.487271i
$857$	3.30253	+	5.72015i	0.112812	+	0.195397i	0.916903	−	0.399110i	$-0.130681\pi$
$857$	3.30253	+	5.72015i	0.112812	+	0.195397i	−0.804091	+	0.594507i	$0.797347\pi$
$858$	−3.38512	+	5.86321i	−0.115566	+	0.200167i
$859$	18.1416	+	31.4221i	0.618982	+	1.07211i	0.989672	+	0.143352i	$0.0457880\pi$
$859$	18.1416	+	31.4221i	0.618982	+	1.07211i	−0.370690	+	0.928757i	$0.620879\pi$
$860$	4.27262			0.145695
$861$	16.9824			0.578757
$862$	−2.66324	−	4.61287i	−0.0907105	−	0.157115i
$863$	−11.1197	+	19.2599i	−0.378520	+	0.655616i	−0.990847	−	0.134989i	$-0.956900\pi$
$863$	−11.1197	+	19.2599i	−0.378520	+	0.655616i	0.612327	+	0.790604i	$0.290234\pi$
$864$	−2.74783	−	4.75937i	−0.0934830	−	0.161917i
$865$	16.5035			0.561137
$866$	2.22645			0.0756580
$867$	5.77596	+	10.0043i	0.196162	+	0.339762i
$868$	−2.41471			−0.0819606
$869$	9.03820			0.306600
$870$	−2.47618	+	4.28886i	−0.0839502	+	0.145406i
$871$	6.00776	−	10.4058i	0.203565	−	0.352585i
$872$	8.58089	+	14.8625i	0.290585	+	0.503309i
$873$	−8.53151	−	14.7770i	−0.288748	−	0.500126i
$874$	2.72034	−	4.71176i	0.0920168	−	0.159378i
$875$	0.412680	−	0.714782i	0.0139511	−	0.0241640i
$876$	−1.64392			−0.0555430
$877$	−48.2283			−1.62856			−0.814278	−	0.580475i	$-0.802867\pi$
$877$	−48.2283			−1.62856			−0.814278	+	0.580475i	$0.802867\pi$
$878$	−0.135412	−	0.234541i	−0.00456994	−	0.00791537i
$879$	41.9322			1.41434
$880$	9.76619			0.329218
$881$	20.1699	+	34.9352i	0.679540	+	1.17700i	0.975119	+	0.221680i	$0.0711540\pi$
$881$	20.1699	+	34.9352i	0.679540	+	1.17700i	−0.295579	+	0.955318i	$0.595513\pi$
$882$	−4.11246	+	7.12298i	−0.138474	+	0.239843i
$883$	−4.91185	−	8.50758i	−0.165297	−	0.286303i	0.771464	−	0.636273i	$-0.219525\pi$
$883$	−4.91185	−	8.50758i	−0.165297	−	0.286303i	−0.936761	+	0.349971i	$0.886192\pi$
$884$	2.40228			0.0807975
$885$	−61.8497			−2.07905
$886$	−5.19843	−	9.00395i	−0.174645	−	0.302494i
$887$	14.9472	−	25.8893i	0.501877	−	0.869276i	−0.498121	−	0.867108i	$-0.665976\pi$
$887$	14.9472	−	25.8893i	0.501877	−	0.869276i	0.999998	−	0.00216860i	$-0.000690286\pi$
$888$	−6.79333	−	11.7664i	−0.227969	−	0.394854i
$889$	−7.39182	+	12.8030i	−0.247914	+	0.429399i
$890$	−28.0743	−	48.6262i	−0.941054	−	1.62995i
$891$	1.46903	+	2.54444i	0.0492144	+	0.0852419i
$892$	0.964812	+	1.67110i	0.0323043	+	0.0559527i
$893$	1.40510	+	2.43370i	0.0470198	+	0.0814406i
$894$	−12.7430	+	22.0715i	−0.426190	+	0.738183i
$895$	−15.7762	−	27.3252i	−0.527341	−	0.913382i
$896$	−9.34292	−	16.1824i	−0.312125	−	0.540616i
$897$	−21.5825	+	37.3819i	−0.720618	+	1.24815i
$898$	−12.1481	+	21.0411i	−0.405387	+	0.702152i
$899$	−3.65422	−	6.32929i	−0.121875	−	0.211094i
$900$	0.520942	−	0.902299i	0.0173647	−	0.0300766i
$901$	39.2960			1.30914
$902$	−4.40567	+	7.63085i	−0.146693	+	0.254079i
$903$	7.81829	+	13.5417i	0.260176	+	0.450639i
$904$	−2.08525	+	3.61176i	−0.0693543	+	0.120125i
$905$	1.33768	+	2.31693i	0.0444660	+	0.0770173i
$906$	14.0968	+	24.4164i	0.468335	+	0.811181i
$907$	4.70250	+	8.14498i	0.156144	+	0.270450i	0.933475	−	0.358642i	$-0.116760\pi$
$907$	4.70250	+	8.14498i	0.156144	+	0.270450i	−0.777331	+	0.629092i	$0.783427\pi$
$908$	2.80613			0.0931247
$909$	0.432060	−	0.748350i	0.0143305	−	0.0248212i
$910$	16.7275	+	28.9729i	0.554512	+	0.960442i
$911$	51.5762			1.70880			0.854398	−	0.519619i	$-0.173926\pi$
$911$	51.5762			1.70880			0.854398	+	0.519619i	$0.173926\pi$
$912$	−1.61754	−	2.80167i	−0.0535622	−	0.0927724i
$913$	1.87218	−	3.24272i	0.0619603	−	0.107318i
$914$	−20.5185			−0.678691
$915$	−14.7712	+	25.5845i	−0.488321	+	0.845796i
$916$	2.28899			0.0756303
$917$	−2.79284	+	4.83735i	−0.0922278	+	0.159743i
$918$	12.1006	−	20.9588i	0.399378	−	0.691743i
$919$	15.3701	−	26.6219i	0.507014	−	0.878174i	−0.492953	−	0.870056i	$-0.664082\pi$
$919$	15.3701	−	26.6219i	0.507014	−	0.878174i	0.999967	−	0.00811836i	$-0.00258418\pi$
$920$	57.2835			1.88858
$921$	7.14794			0.235533
$922$	−55.5231			−1.82856
$923$	31.7940	+	55.0688i	1.04651	+	1.81261i
$924$	−0.123462	−	0.213842i	−0.00406159	−	0.00703488i
$925$	9.63636	−	16.6907i	0.316841	−	0.548785i
$926$	42.5277			1.39755
$927$	1.16932	−	2.02532i	0.0384054	−	0.0665202i
$928$	−0.378859	+	0.656203i	−0.0124366	+	0.0215409i
$929$	−47.0155			−1.54253			−0.771264	−	0.636516i	$-0.780375\pi$
$929$	−47.0155			−1.54253			−0.771264	+	0.636516i	$0.780375\pi$
$930$	−29.9088	−	51.8036i	−0.980749	−	1.69871i
$931$	−1.32432	+	2.29379i	−0.0434029	+	0.0751759i
$932$	−4.86067			−0.159216
$933$	−16.4733	−	28.5326i	−0.539311	−	0.934115i
$934$	1.58052	−	2.73755i	0.0517163	−	0.0895753i
$935$	3.29295	+	5.70356i	0.107691	+	0.186526i
$936$	−7.50877	−	13.0056i	−0.245432	−	0.425100i
$937$	50.6012			1.65307			0.826535	−	0.562885i	$-0.190309\pi$
$937$	50.6012			1.65307			0.826535	+	0.562885i	$0.190309\pi$
$938$	2.75710	+	4.77544i	0.0900225	+	0.155924i
$939$	9.67004	+	16.7490i	0.315570	+	0.546583i
$940$	1.39790	−	2.42124i	0.0455945	−	0.0789720i
$941$	11.2093	−	19.4151i	0.365414	−	0.632915i	−0.623429	−	0.781880i	$-0.714261\pi$
$941$	11.2093	−	19.4151i	0.365414	−	0.632915i	0.988842	+	0.148965i	$0.0475942\pi$
$942$	−2.07775	−	3.59877i	−0.0676968	−	0.117254i
$943$	−28.0892	+	48.6519i	−0.914709	+	1.58432i
$944$	−61.7958			−2.01128
$945$	26.7849			0.871314
$946$	−8.11309			−0.263779
$947$	42.7585			1.38947			0.694733	−	0.719268i	$-0.255523\pi$
$947$	42.7585			1.38947			0.694733	+	0.719268i	$0.255523\pi$
$948$	−1.48930	+	2.57955i	−0.0483703	+	0.0837798i
$949$	−33.6117			−1.09108
$950$	2.11088	−	3.65615i	0.0684860	−	0.118621i
$951$	9.69540	−	16.7929i	0.314395	−	0.544548i
$952$	5.83365	−	10.1042i	0.189070	−	0.327478i
$953$	−11.2317	+	19.4539i	−0.363830	+	0.630173i	−0.988588	−	0.150646i	$-0.951865\pi$
$953$	−11.2317	+	19.4539i	−0.363830	+	0.630173i	0.624757	+	0.780819i	$0.285198\pi$
$954$	11.6061	+	20.1024i	0.375762	+	0.650839i
$955$	−10.6323			−0.344052
$956$	−1.86734	−	3.23432i	−0.0603939	−	0.104605i
$957$	0.373673	−	0.647221i	0.0120791	−	0.0209217i
$958$	−30.8867	−	53.4973i	−0.997904	−	1.72842i
$959$	−2.72046			−0.0878482
$960$	15.5391	−	26.9145i	0.501522	−	0.868662i
$961$	57.2759			1.84761
$962$	13.1246	+	22.7324i	0.423153	+	0.732923i
$963$	−3.56392	−	6.17288i	−0.114846	−	0.198918i
$964$	−0.918209	+	1.59038i	−0.0295735	+	0.0512228i
$965$	−9.67700	+	16.7611i	−0.311514	+	0.539558i
$966$	−9.90469	−	17.1554i	−0.318678	−	0.551967i
$967$	7.91327			0.254474			0.127237	−	0.991872i	$-0.459389\pi$
$967$	7.91327			0.254474			0.127237	+	0.991872i	$0.459389\pi$
$968$	28.2725			0.908711
$969$	1.09080	−	1.88932i	0.0350416	−	0.0606939i
$970$	−34.3930	+	59.5705i	−1.10429	+	1.91269i
$971$	−1.92023	+	3.32593i	−0.0616231	+	0.106734i	−0.895191	−	0.445683i	$-0.852961\pi$
$971$	−1.92023	+	3.32593i	−0.0616231	+	0.106734i	0.833568	+	0.552417i	$0.186294\pi$
$972$	1.95419			0.0626808
$973$	−7.33482	+	12.7043i	−0.235143	+	0.407280i
$974$	20.1677	+	34.9314i	0.646214	+	1.11928i
$975$	−16.7472	+	29.0070i	−0.536340	+	0.928967i
$976$	−14.7583	+	25.5622i	−0.472403	+	0.818225i
$977$	20.1657	−	34.9280i	0.645158	−	1.11745i	−0.339107	−	0.940748i	$-0.610125\pi$
$977$	20.1657	−	34.9280i	0.645158	−	1.11745i	0.984265	−	0.176699i	$-0.0565418\pi$
$978$	−20.3813			−0.651723
$979$	4.23662	+	7.33804i	0.135403	+	0.234525i
$980$	2.63508			0.0841745
$981$	−7.43092			−0.237251
$982$	−27.9165			−0.890850
$983$	29.1814			0.930741			0.465371	−	0.885116i	$-0.345921\pi$
$983$	29.1814			0.930741			0.465371	+	0.885116i	$0.345921\pi$
$984$	15.3656	+	26.6140i	0.489837	+	0.848423i
$985$	7.66790	−	13.2812i	0.244320	−	0.423174i
$986$	−3.33675			−0.106264
$987$	10.2319			0.325684
$988$	0.228483	+	0.395744i	0.00726902	+	0.0125903i
$989$	−51.7265			−1.64481
$990$	−1.94515	+	3.36910i	−0.0618210	+	0.107077i
$991$	−14.4491	+	25.0266i	−0.458991	+	0.794997i	−0.998908	−	0.0467220i	$-0.985122\pi$
$991$	−14.4491	+	25.0266i	−0.458991	+	0.794997i	0.539916	+	0.841719i	$0.318456\pi$
$992$	−4.57610	−	7.92603i	−0.145291	−	0.251652i
$993$	−3.37299	+	5.84220i	−0.107039	+	0.185397i
$994$	−29.1820			−0.925597
$995$	−50.6155			−1.60462
$996$	0.616992	+	1.06866i	0.0195501	+	0.0338618i
$997$	−3.68660	−	6.38539i	−0.116756	−	0.202227i	0.801724	−	0.597694i	$-0.203916\pi$
$997$	−3.68660	−	6.38539i	−0.116756	−	0.202227i	−0.918480	+	0.395467i	$0.870583\pi$
$998$	24.0494	+	41.6547i	0.761269	+	1.31856i
$999$	21.0157			0.664908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.9	✓	56
349.226	even	3	inner	349.2.c.a.226.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.9	✓	56	1.1	even	1	trivial
349.2.c.a.226.9	yes	56	349.226	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736999 + 1.27652i) q^{2} +(-0.677079 - 1.17273i) q^{3} +(-0.0863339 - 0.149535i) q^{4} +(1.59482 + 2.76232i) q^{5} +1.99602 q^{6} +(-0.744222 + 1.28903i) q^{7} -2.69348 q^{8} +(0.583129 - 1.01001i) q^{9} +O(q^{10})\)	\(q+(-0.736999 + 1.27652i) q^{2} +(-0.677079 - 1.17273i) q^{3} +(-0.0863339 - 0.149535i) q^{4} +(1.59482 + 2.76232i) q^{5} +1.99602 q^{6} +(-0.744222 + 1.28903i) q^{7} -2.69348 q^{8} +(0.583129 - 1.01001i) q^{9} -4.70153 q^{10} +0.709495 q^{11} +(-0.116910 + 0.202493i) q^{12} +(-2.39034 + 4.14019i) q^{13} +(-1.09698 - 1.90003i) q^{14} +(2.15964 - 3.74061i) q^{15} +(2.15776 - 3.73735i) q^{16} +2.91020 q^{17} +(0.859531 + 1.48875i) q^{18} +(0.276792 + 0.479418i) q^{19} +(0.275375 - 0.476963i) q^{20} +2.01559 q^{21} +(-0.522897 + 0.905684i) q^{22} +(-3.33382 + 5.77435i) q^{23} +(1.82370 + 3.15874i) q^{24} +(-2.58692 + 4.48068i) q^{25} +(-3.52335 - 6.10263i) q^{26} -5.64177 q^{27} +0.257006 q^{28} +(0.388932 + 0.673649i) q^{29} +(3.18331 + 5.51365i) q^{30} -9.39553 q^{31} +(0.487051 + 0.843596i) q^{32} +(-0.480384 - 0.832049i) q^{33} +(-2.14482 + 3.71493i) q^{34} -4.74761 q^{35} -0.201375 q^{36} -3.72503 q^{37} -0.815981 q^{38} +6.47379 q^{39} +(-4.29563 - 7.44025i) q^{40} +8.42551 q^{41} +(-1.48548 + 2.57294i) q^{42} +(3.87891 + 6.71848i) q^{43} +(-0.0612535 - 0.106094i) q^{44} +3.71995 q^{45} +(-4.91405 - 8.51138i) q^{46} +5.07636 q^{47} -5.84389 q^{48} +(2.39227 + 4.14353i) q^{49} +(-3.81312 - 6.60451i) q^{50} +(-1.97044 - 3.41290i) q^{51} +0.825469 q^{52} +13.5028 q^{53} +(4.15798 - 7.20182i) q^{54} +(1.13152 + 1.95985i) q^{55} +(2.00455 - 3.47198i) q^{56} +(0.374820 - 0.649207i) q^{57} -1.14657 q^{58} +(-7.15972 - 12.4010i) q^{59} -0.745801 q^{60} -6.83965 q^{61} +(6.92449 - 11.9936i) q^{62} +(0.867955 + 1.50334i) q^{63} +7.19522 q^{64} -15.2487 q^{65} +1.41617 q^{66} -2.51335 q^{67} +(-0.251249 - 0.435176i) q^{68} +9.02904 q^{69} +(3.49898 - 6.06042i) q^{70} +(6.65052 - 11.5190i) q^{71} +(-1.57065 + 2.72044i) q^{72} +(3.51537 + 6.08880i) q^{73} +(2.74534 - 4.75507i) q^{74} +7.00620 q^{75} +(0.0477930 - 0.0827800i) q^{76} +(-0.528022 + 0.914561i) q^{77} +(-4.77117 + 8.26392i) q^{78} +12.7389 q^{79} +13.7650 q^{80} +(2.07053 + 3.58627i) q^{81} +(-6.20959 + 10.7553i) q^{82} +(2.63876 - 4.57046i) q^{83} +(-0.174013 - 0.301400i) q^{84} +(4.64126 + 8.03890i) q^{85} -11.4350 q^{86} +(0.526675 - 0.912227i) q^{87} -1.91101 q^{88} +(5.97132 + 10.3426i) q^{89} +(-2.74160 + 4.74859i) q^{90} +(-3.55789 - 6.16244i) q^{91} +1.15129 q^{92} +(6.36151 + 11.0185i) q^{93} +(-3.74127 + 6.48008i) q^{94} +(-0.882869 + 1.52917i) q^{95} +(0.659543 - 1.14236i) q^{96} +(7.31528 - 12.6704i) q^{97} -7.05239 q^{98} +(0.413727 - 0.716597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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