LMFDB - Embedded newform 403.2.h.b.118.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.17
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +O(q^{10})$	\(q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +(-5.67332 + 9.82648i) q^{10} +(0.129596 - 0.224467i) q^{11} +(-2.69666 - 4.67076i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.17259 - 2.03098i) q^{14} +3.80726 q^{15} +17.7275 q^{16} +(-2.06964 - 3.58471i) q^{17} +(2.96187 - 5.13011i) q^{18} +(1.04660 + 1.81277i) q^{19} +(-11.7402 + 20.3347i) q^{20} +(-0.393451 + 0.681478i) q^{21} +(0.361184 - 0.625589i) q^{22} -4.22515 q^{23} +(-4.90933 - 8.50320i) q^{24} +(-5.78767 - 10.0245i) q^{25} +(-1.39350 + 2.41361i) q^{26} -4.79311 q^{27} +(-2.42653 - 4.20287i) q^{28} -8.39075 q^{29} +10.6108 q^{30} +(-4.09017 + 3.77764i) q^{31} +28.4074 q^{32} -0.242384 q^{33} +(-5.76806 - 9.99058i) q^{34} +3.42587 q^{35} +(6.12922 - 10.6161i) q^{36} +(2.35547 + 4.07980i) q^{37} +(2.91687 + 5.05217i) q^{38} +0.935150 q^{39} +(-21.3733 + 37.0197i) q^{40} +(2.13010 - 3.68944i) q^{41} +(-1.09655 + 1.89928i) q^{42} +(-1.83814 - 3.18376i) q^{43} +(0.747425 - 1.29458i) q^{44} +(4.32675 + 7.49414i) q^{45} -11.7755 q^{46} -2.22737 q^{47} +(-8.28894 - 14.3569i) q^{48} +(3.14596 - 5.44897i) q^{49} +(-16.1302 - 27.9383i) q^{50} +(-1.93542 + 3.35225i) q^{51} +(-2.88367 + 4.99466i) q^{52} +(1.29878 - 2.24955i) q^{53} -13.3584 q^{54} +(0.527623 + 0.913870i) q^{55} +(-4.41754 - 7.65141i) q^{56} +(0.978728 - 1.69521i) q^{57} -23.3850 q^{58} +(3.65454 + 6.32984i) q^{59} +21.9578 q^{60} +13.7039 q^{61} +(-11.3993 + 10.5283i) q^{62} -1.78855 q^{63} +43.7162 q^{64} +(-2.03564 - 3.52583i) q^{65} -0.675522 q^{66} +(-2.02616 + 3.50942i) q^{67} +(-11.9363 - 20.6743i) q^{68} +(1.97557 + 3.42179i) q^{69} +9.54789 q^{70} +(-0.900818 + 1.56026i) q^{71} +(11.1584 - 19.3269i) q^{72} +(5.05129 - 8.74910i) q^{73} +(6.56469 + 11.3704i) q^{74} +(-5.41234 + 9.37445i) q^{75} +(6.03610 + 10.4548i) q^{76} -0.218103 q^{77} +2.60626 q^{78} +(8.05852 + 13.9578i) q^{79} +(-36.0869 + 62.5043i) q^{80} +(-0.947107 - 1.64044i) q^{81} +(5.93658 - 10.2825i) q^{82} +(-0.533088 + 0.923335i) q^{83} +(-2.26917 + 3.93031i) q^{84} +16.8521 q^{85} +(-5.12290 - 8.87312i) q^{86} +(3.92330 + 6.79536i) q^{87} +(1.36070 - 2.35681i) q^{88} -0.765428 q^{89} +(12.0586 + 20.8861i) q^{90} +0.841473 q^{91} -24.3679 q^{92} +(4.97183 + 1.54615i) q^{93} -6.20768 q^{94} -8.52201 q^{95} +(-13.2826 - 23.0061i) q^{96} +0.945784 q^{97} +(8.76778 - 15.1862i) q^{98} +(-0.275456 - 0.477104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.78699			1.97070			0.985351	−	0.170537i	$-0.0545501\pi$
$2$	2.78699			1.97070			0.985351	+	0.170537i	$0.0545501\pi$
$3$	−0.467575	−	0.809863i	−0.269954	−	0.467575i	0.698895	−	0.715224i	$-0.253675\pi$
$3$	−0.467575	−	0.809863i	−0.269954	−	0.467575i	−0.968850	+	0.247649i	$0.920342\pi$
$4$	5.76734			2.88367
$5$	−2.03564	+	3.52583i	−0.910366	+	1.57680i	−0.0968193	+	0.995302i	$0.530867\pi$
$5$	−2.03564	+	3.52583i	−0.910366	+	1.57680i	−0.813547	+	0.581499i	$0.802466\pi$
$6$	−1.30313	−	2.25709i	−0.532000	−	0.921451i
$7$	−0.420736	−	0.728737i	−0.159023	−	0.275437i	0.775493	−	0.631356i	$-0.217501\pi$
$7$	−0.420736	−	0.728737i	−0.159023	−	0.275437i	−0.934517	+	0.355919i	$0.884168\pi$
$8$	10.4996			3.71215
$9$	1.06275	−	1.84073i	0.354249	−	0.613578i
$10$	−5.67332	+	9.82648i	−1.79406	+	3.10741i
$11$	0.129596	−	0.224467i	0.0390747	−	0.0676794i	−0.845827	−	0.533458i	$-0.820892\pi$
$11$	0.129596	−	0.224467i	0.0390747	−	0.0676794i	0.884901	+	0.465778i	$0.154226\pi$
$12$	−2.69666	−	4.67076i	−0.778459	−	1.34833i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−1.17259	−	2.03098i	−0.313388	−	0.542804i
$15$	3.80726			0.983030
$16$	17.7275			4.43188
$17$	−2.06964	−	3.58471i	−0.501960	−	0.869421i	−0.999997	−	0.00226526i	$-0.999279\pi$
$17$	−2.06964	−	3.58471i	−0.501960	−	0.869421i	0.498037	−	0.867156i	$-0.334054\pi$
$18$	2.96187	−	5.13011i	0.698120	−	1.20918i
$19$	1.04660	+	1.81277i	0.240107	+	0.415877i	0.960744	−	0.277435i	$-0.0894843\pi$
$19$	1.04660	+	1.81277i	0.240107	+	0.415877i	−0.720638	+	0.693312i	$0.756151\pi$
$20$	−11.7402	+	20.3347i	−2.62520	+	4.54697i
$21$	−0.393451	+	0.681478i	−0.0858581	+	0.148711i
$22$	0.361184	−	0.625589i	0.0770047	−	0.133376i
$23$	−4.22515			−0.881004			−0.440502	−	0.897752i	$-0.645200\pi$
$23$	−4.22515			−0.881004			−0.440502	+	0.897752i	$0.645200\pi$
$24$	−4.90933	−	8.50320i	−1.00211	−	1.73571i
$25$	−5.78767	−	10.0245i	−1.15753	−	2.00491i
$26$	−1.39350	+	2.41361i	−0.273287	+	0.473347i
$27$	−4.79311			−0.922434
$28$	−2.42653	−	4.20287i	−0.458571	−	0.794268i
$29$	−8.39075			−1.55812			−0.779061	−	0.626948i	$-0.784304\pi$
$29$	−8.39075			−1.55812			−0.779061	+	0.626948i	$0.784304\pi$
$30$	10.6108			1.93726
$31$	−4.09017	+	3.77764i	−0.734616	+	0.678484i
$31$	−4.09017	+	3.77764i	−0.734616	+	0.678484i
$32$	28.4074			5.02176
$33$	−0.242384			−0.0421936
$34$	−5.76806	−	9.99058i	−0.989215	−	1.71337i
$35$	3.42587			0.579078
$36$	6.12922	−	10.6161i	1.02154	−	1.76935i
$37$	2.35547	+	4.07980i	0.387237	+	0.670714i	0.992077	−	0.125633i	$-0.0400961\pi$
$37$	2.35547	+	4.07980i	0.387237	+	0.670714i	−0.604840	+	0.796347i	$0.706763\pi$
$38$	2.91687	+	5.05217i	0.473179	+	0.819570i
$39$	0.935150			0.149744
$40$	−21.3733	+	37.0197i	−3.37942	+	5.85332i
$41$	2.13010	−	3.68944i	0.332666	−	0.576194i	−0.650368	−	0.759619i	$-0.725385\pi$
$41$	2.13010	−	3.68944i	0.332666	−	0.576194i	0.983034	+	0.183425i	$0.0587186\pi$
$42$	−1.09655	+	1.89928i	−0.169201	+	0.293065i
$43$	−1.83814	−	3.18376i	−0.280314	−	0.485519i	0.691148	−	0.722714i	$-0.257105\pi$
$43$	−1.83814	−	3.18376i	−0.280314	−	0.485519i	−0.971462	+	0.237195i	$0.923772\pi$
$44$	0.747425	−	1.29458i	0.112679	−	0.195165i
$45$	4.32675	+	7.49414i	0.644993	+	1.11716i
$46$	−11.7755			−1.73620
$47$	−2.22737			−0.324896			−0.162448	−	0.986717i	$-0.551939\pi$
$47$	−2.22737			−0.324896			−0.162448	+	0.986717i	$0.551939\pi$
$48$	−8.28894	−	14.3569i	−1.19641	−	2.07224i
$49$	3.14596	−	5.44897i	0.449423	−	0.778424i
$50$	−16.1302	−	27.9383i	−2.28116	−	3.95108i
$51$	−1.93542	+	3.35225i	−0.271013	+	0.469408i
$52$	−2.88367	+	4.99466i	−0.399893	+	0.692635i
$53$	1.29878	−	2.24955i	0.178401	−	0.309000i	−0.762932	−	0.646479i	$-0.776241\pi$
$53$	1.29878	−	2.24955i	0.178401	−	0.309000i	0.941333	+	0.337479i	$0.109574\pi$
$54$	−13.3584			−1.81784
$55$	0.527623	+	0.913870i	0.0711446	+	0.123226i
$56$	−4.41754	−	7.65141i	−0.590319	−	1.02246i
$57$	0.978728	−	1.69521i	0.129636	−	0.224536i
$58$	−23.3850			−3.07060
$59$	3.65454	+	6.32984i	0.475780	+	0.824076i	0.999615	−	0.0277443i	$-0.00883241\pi$
$59$	3.65454	+	6.32984i	0.475780	+	0.824076i	−0.523835	+	0.851820i	$0.675499\pi$
$60$	21.9578			2.83473
$61$	13.7039			1.75460			0.877302	−	0.479939i	$-0.159341\pi$
$61$	13.7039			1.75460			0.877302	+	0.479939i	$0.159341\pi$
$62$	−11.3993	+	10.5283i	−1.44771	+	1.33709i
$63$	−1.78855			−0.225336
$64$	43.7162			5.46452
$65$	−2.03564	−	3.52583i	−0.252490	−	0.437326i
$66$	−0.675522			−0.0831510
$67$	−2.02616	+	3.50942i	−0.247535	+	0.428744i	−0.962841	−	0.270068i	$-0.912954\pi$
$67$	−2.02616	+	3.50942i	−0.247535	+	0.428744i	0.715306	+	0.698811i	$0.246287\pi$
$68$	−11.9363	−	20.6743i	−1.44749	−	2.50712i
$69$	1.97557	+	3.42179i	0.237831	+	0.411935i
$70$	9.54789			1.14119
$71$	−0.900818	+	1.56026i	−0.106907	+	0.185169i	−0.914516	−	0.404550i	$-0.867428\pi$
$71$	−0.900818	+	1.56026i	−0.106907	+	0.185169i	0.807608	+	0.589719i	$0.200762\pi$
$72$	11.1584	−	19.3269i	1.31503	−	2.27769i
$73$	5.05129	−	8.74910i	0.591209	−	1.02400i	−0.402861	−	0.915261i	$-0.631984\pi$
$73$	5.05129	−	8.74910i	0.591209	−	1.02400i	0.994070	−	0.108743i	$-0.0346825\pi$
$74$	6.56469	+	11.3704i	0.763129	+	1.32178i
$75$	−5.41234	+	9.37445i	−0.624963	+	1.08247i
$76$	6.03610	+	10.4548i	0.692388	+	1.19925i
$77$	−0.218103			−0.0248552
$78$	2.60626			0.295101
$79$	8.05852	+	13.9578i	0.906655	+	1.57037i	0.818680	+	0.574250i	$0.194706\pi$
$79$	8.05852	+	13.9578i	0.906655	+	1.57037i	0.0879745	+	0.996123i	$0.471961\pi$
$80$	−36.0869	+	62.5043i	−4.03463	+	6.98819i
$81$	−0.947107	−	1.64044i	−0.105234	−	0.182271i
$82$	5.93658	−	10.2825i	0.655585	−	1.13551i
$83$	−0.533088	+	0.923335i	−0.0585140	+	0.101349i	−0.893799	−	0.448469i	$-0.851970\pi$
$83$	−0.533088	+	0.923335i	−0.0585140	+	0.101349i	0.835285	+	0.549818i	$0.185303\pi$
$84$	−2.26917	+	3.93031i	−0.247586	+	0.428832i
$85$	16.8521			1.82787
$86$	−5.12290	−	8.87312i	−0.552416	−	0.956813i
$87$	3.92330	+	6.79536i	0.420622	+	0.728539i
$88$	1.36070	−	2.35681i	0.145051	−	0.251236i
$89$	−0.765428			−0.0811352			−0.0405676	−	0.999177i	$-0.512917\pi$
$89$	−0.765428			−0.0811352			−0.0405676	+	0.999177i	$0.512917\pi$
$90$	12.0586	+	20.8861i	1.27109	+	2.20159i
$91$	0.841473			0.0882103
$92$	−24.3679			−2.54052
$93$	4.97183	+	1.54615i	0.515555	+	0.160328i
$94$	−6.20768			−0.640273
$95$	−8.52201			−0.874340
$96$	−13.2826	−	23.0061i	−1.35565	−	2.34805i
$97$	0.945784			0.0960299			0.0480149	−	0.998847i	$-0.484710\pi$
$97$	0.945784			0.0960299			0.0480149	+	0.998847i	$0.484710\pi$
$98$	8.76778	−	15.1862i	0.885679	−	1.53404i
$99$	−0.275456	−	0.477104i	−0.0276844	−	0.0479508i
$100$	−33.3795	−	57.8149i	−3.33795	−	5.78149i
$101$	−14.0197			−1.39501			−0.697507	−	0.716578i	$-0.745708\pi$
$101$	−14.0197			−1.39501			−0.697507	+	0.716578i	$0.745708\pi$
$102$	−5.39400	+	9.34269i	−0.534086	+	0.925064i
$103$	−0.594676	+	1.03001i	−0.0585951	+	0.101490i	−0.893835	−	0.448396i	$-0.851995\pi$
$103$	−0.594676	+	1.03001i	−0.0585951	+	0.101490i	0.835240	+	0.549886i	$0.185329\pi$
$104$	−5.24978	+	9.09288i	−0.514783	+	0.891630i
$105$	−1.60185	−	2.77449i	−0.156325	−	0.270762i
$106$	3.61969	−	6.26949i	0.351576	−	0.608947i
$107$	5.44753	+	9.43539i	0.526632	+	0.912154i	0.999518	+	0.0310304i	$0.00987887\pi$
$107$	5.44753	+	9.43539i	0.526632	+	0.912154i	−0.472886	+	0.881124i	$0.656788\pi$
$108$	−27.6435			−2.65999
$109$	1.54109			0.147610			0.0738050	−	0.997273i	$-0.476486\pi$
$109$	1.54109			0.147610			0.0738050	+	0.997273i	$0.476486\pi$
$110$	1.47048	+	2.54695i	0.140205	+	0.242842i
$111$	2.20272	−	3.81522i	0.209073	−	0.362125i
$112$	−7.45861	−	12.9187i	−0.704772	−	1.22070i
$113$	−4.75415	+	8.23443i	−0.447233	+	0.774630i	−0.998205	−	0.0598938i	$-0.980924\pi$
$113$	−4.75415	+	8.23443i	−0.447233	+	0.774630i	0.550972	+	0.834524i	$0.314257\pi$
$114$	2.72771	−	4.72453i	0.255473	−	0.442493i
$115$	8.60088	−	14.8972i	0.802037	−	1.38917i
$116$	−48.3923			−4.49311
$117$	1.06275	+	1.84073i	0.0982510	+	0.170176i
$118$	10.1852	+	17.6412i	0.937621	+	1.62401i
$119$	−1.74154	+	3.01644i	−0.159647	+	0.276517i
$120$	39.9745			3.64916
$121$	5.46641	+	9.46810i	0.496946	+	0.860736i
$122$	38.1927			3.45780
$123$	−3.98393			−0.359219
$124$	−23.5894	+	21.7869i	−2.11839	+	1.95652i
$125$	26.7701			2.39439
$126$	−4.98467			−0.444069
$127$	−2.54274	−	4.40416i	−0.225632	−	0.390806i	0.730877	−	0.682509i	$-0.239111\pi$
$127$	−2.54274	−	4.40416i	−0.225632	−	0.390806i	−0.956509	+	0.291703i	$0.905778\pi$
$128$	65.0220			5.74719
$129$	−1.71894	+	2.97729i	−0.151344	+	0.262136i
$130$	−5.67332	−	9.82648i	−0.497583	−	0.861839i
$131$	−6.05562	−	10.4886i	−0.529082	−	0.916397i	−0.999425	−	0.0339130i	$-0.989203\pi$
$131$	−6.05562	−	10.4886i	−0.529082	−	0.916397i	0.470343	−	0.882484i	$-0.344130\pi$
$132$	−1.39791			−0.121672
$133$	0.880686	−	1.52539i	0.0763651	−	0.132268i
$134$	−5.64691	+	9.78073i	−0.487818	+	0.844926i
$135$	9.75704	−	16.8997i	0.839753	−	1.45449i
$136$	−21.7303	−	37.6379i	−1.86335	−	3.22742i
$137$	0.518866	−	0.898703i	0.0443297	−	0.0767814i	−0.843009	−	0.537899i	$-0.819218\pi$
$137$	0.518866	−	0.898703i	0.0443297	−	0.0767814i	0.887339	+	0.461118i	$0.152551\pi$
$138$	5.50591	+	9.53652i	0.468694	+	0.811802i
$139$	17.8696			1.51568			0.757838	−	0.652443i	$-0.226256\pi$
$139$	17.8696			1.51568			0.757838	+	0.652443i	$0.226256\pi$
$140$	19.7582			1.66987
$141$	1.04146	+	1.80387i	0.0877071	+	0.151913i
$142$	−2.51058	+	4.34845i	−0.210683	+	0.364913i
$143$	0.129596	+	0.224467i	0.0108374	+	0.0187709i
$144$	18.8399	−	32.6316i	1.56999	−	2.71930i
$145$	17.0805	−	29.5844i	1.41846	−	2.45685i
$146$	14.0779	−	24.3837i	1.16510	−	2.01801i
$147$	−5.88389			−0.485295
$148$	13.5848	+	23.5296i	1.11666	+	1.93412i
$149$	−1.58004	−	2.73671i	−0.129442	−	0.224200i	0.794019	−	0.607894i	$-0.207985\pi$
$149$	−1.58004	−	2.73671i	−0.129442	−	0.224200i	−0.923461	+	0.383693i	$0.874652\pi$
$150$	−15.0842	+	26.1265i	−1.23162	+	2.13322i
$151$	−5.86679			−0.477433			−0.238716	−	0.971089i	$-0.576727\pi$
$151$	−5.86679			−0.477433			−0.238716	+	0.971089i	$0.576727\pi$
$152$	10.9888	+	19.0332i	0.891312	+	1.54380i
$153$	−8.79800			−0.711276
$154$	−0.607853			−0.0489822
$155$	−4.99321	−	22.1112i	−0.401064	−	1.77601i
$156$	5.39333			0.431812
$157$	−2.51588			−0.200789			−0.100395	−	0.994948i	$-0.532011\pi$
$157$	−2.51588			−0.200789			−0.100395	+	0.994948i	$0.532011\pi$
$158$	22.4591	+	38.9002i	1.78675	+	3.09474i
$159$	−2.42911			−0.192641
$160$	−57.8272	+	100.160i	−4.57164	+	7.91832i
$161$	1.77767	+	3.07902i	0.140100	+	0.242661i
$162$	−2.63958	−	4.57189i	−0.207385	−	0.359201i
$163$	1.72397			0.135031			0.0675157	−	0.997718i	$-0.478493\pi$
$163$	1.72397			0.135031			0.0675157	+	0.997718i	$0.478493\pi$
$164$	12.2850	−	21.2783i	0.959298	−	1.66155i
$165$	0.493406	−	0.854605i	0.0384116	−	0.0665309i
$166$	−1.48571	+	2.57333i	−0.115314	+	0.199729i
$167$	−9.54056	−	16.5247i	−0.738270	−	1.27872i	−0.953274	−	0.302108i	$-0.902310\pi$
$167$	−9.54056	−	16.5247i	−0.738270	−	1.27872i	0.215003	−	0.976613i	$-0.431024\pi$
$168$	−4.13106	+	7.15521i	−0.318718	+	0.552037i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	46.9668			3.60219
$171$	4.44909			0.340230
$172$	−10.6012	−	18.3618i	−0.808334	−	1.40008i
$173$	4.01250	−	6.94985i	0.305064	−	0.528387i	−0.672211	−	0.740359i	$-0.734655\pi$
$173$	4.01250	−	6.94985i	0.305064	−	0.528387i	0.977276	+	0.211972i	$0.0679887\pi$
$174$	10.9342	+	18.9386i	0.828921	+	1.43573i
$175$	−4.87017	+	8.43538i	−0.368150	+	0.637654i
$176$	2.29742	−	3.97925i	0.173174	−	0.299947i
$177$	3.41754	−	5.91935i	0.256878	−	0.444926i
$178$	−2.13324			−0.159893
$179$	9.72409	+	16.8426i	0.726813	+	1.25888i	0.958224	+	0.286020i	$0.0923325\pi$
$179$	9.72409	+	16.8426i	0.726813	+	1.25888i	−0.231411	+	0.972856i	$0.574334\pi$
$180$	24.9538	+	43.2213i	1.85995	+	3.22152i
$181$	−6.70159	+	11.6075i	−0.498126	+	0.862779i	−0.999998	−	0.00216311i	$-0.999311\pi$
$181$	−6.70159	+	11.6075i	−0.498126	+	0.862779i	0.501872	+	0.864942i	$0.332645\pi$
$182$	2.34518			0.173836
$183$	−6.40760	−	11.0983i	−0.473663	−	0.820409i
$184$	−44.3622			−3.27042
$185$	−19.1796			−1.41011
$186$	13.8565	+	4.30911i	1.01600	+	0.315959i
$187$	−1.07287			−0.0784559
$188$	−12.8460			−0.936893
$189$	2.01663	+	3.49291i	0.146688	+	0.254072i
$190$	−23.7508			−1.72306
$191$	−3.21016	+	5.56016i	−0.232279	+	0.402319i	−0.958478	−	0.285165i	$-0.907952\pi$
$191$	−3.21016	+	5.56016i	−0.232279	+	0.402319i	0.726199	+	0.687484i	$0.241285\pi$
$192$	−20.4406	−	35.4041i	−1.47517	−	2.55507i
$193$	7.50612	+	13.0010i	0.540302	+	0.935831i	0.998886	+	0.0471799i	$0.0150234\pi$
$193$	7.50612	+	13.0010i	0.540302	+	0.935831i	−0.458584	+	0.888651i	$0.651643\pi$
$194$	2.63590			0.189246
$195$	−1.90363	+	3.29718i	−0.136322	+	0.236116i
$196$	18.1438	−	31.4260i	1.29599	−	2.24472i
$197$	4.58822	−	7.94702i	0.326897	−	0.566202i	−0.654998	−	0.755631i	$-0.727330\pi$
$197$	4.58822	−	7.94702i	0.326897	−	0.566202i	0.981894	+	0.189429i	$0.0606637\pi$
$198$	−0.767695	−	1.32969i	−0.0545577	−	0.0944967i
$199$	2.01214	−	3.48513i	0.142637	−	0.247054i	−0.785852	−	0.618415i	$-0.787775\pi$
$199$	2.01214	−	3.48513i	0.142637	−	0.247054i	0.928489	+	0.371360i	$0.121109\pi$
$200$	−60.7679	−	105.253i	−4.29694	−	7.44252i
$201$	3.78953			0.267293
$202$	−39.0729			−2.74916
$203$	3.53029	+	6.11464i	0.247778	+	0.429164i
$204$	−11.1622	+	19.3335i	−0.781512	+	1.35362i
$205$	8.67224	+	15.0208i	0.605696	+	1.04910i
$206$	−1.65736	+	2.87063i	−0.115474	+	0.200006i
$207$	−4.49026	+	7.77737i	−0.312095	+	0.540564i
$208$	−8.86376	+	15.3525i	−0.614591	+	1.06450i
$209$	0.542542			0.0375284
$210$	−4.46435	−	7.73249i	−0.308070	−	0.533592i
$211$	−10.7226	−	18.5721i	−0.738176	−	1.27856i	−0.953316	−	0.301975i	$-0.902354\pi$
$211$	−10.7226	−	18.5721i	−0.738176	−	1.27856i	0.215140	−	0.976583i	$-0.430979\pi$
$212$	7.49051	−	12.9739i	0.514450	−	0.891054i
$213$	1.68480			0.115441
$214$	15.1822	+	26.2964i	1.03784	+	1.79758i
$215$	14.9672			1.02076
$216$	−50.3255			−3.42421
$217$	4.47378	+	1.39126i	0.303700	+	0.0944452i
$218$	4.29502			0.290895
$219$	−9.44743			−0.638398
$220$	3.04298	+	5.27059i	0.205158	+	0.355343i
$221$	4.13927			0.278438
$222$	6.13896	−	10.6330i	0.412020	−	0.713640i
$223$	−5.78526	−	10.0204i	−0.387410	−	0.671013i	0.604691	−	0.796460i	$-0.293297\pi$
$223$	−5.78526	−	10.0204i	−0.387410	−	0.671013i	−0.992100	+	0.125447i	$0.959963\pi$
$224$	−11.9520	−	20.7015i	−0.798578	−	1.38318i
$225$	−24.6033			−1.64022
$226$	−13.2498	+	22.9493i	−0.881363	+	1.52657i
$227$	−4.94543	+	8.56573i	−0.328239	+	0.568527i	−0.982163	−	0.188034i	$-0.939789\pi$
$227$	−4.94543	+	8.56573i	−0.328239	+	0.568527i	0.653923	+	0.756561i	$0.273122\pi$
$228$	5.64466	−	9.77683i	0.373827	−	0.647487i
$229$	8.58258	+	14.8655i	0.567153	+	0.982338i	0.996846	+	0.0793625i	$0.0252885\pi$
$229$	8.58258	+	14.8655i	0.567153	+	0.982338i	−0.429693	+	0.902975i	$0.641378\pi$
$230$	23.9706	−	41.5183i	1.58058	−	2.73764i
$231$	0.101980	+	0.176634i	0.00670977	+	0.0116217i
$232$	−88.0991			−5.78399
$233$	19.7483			1.29376			0.646878	−	0.762594i	$-0.276074\pi$
$233$	19.7483			1.29376			0.646878	+	0.762594i	$0.276074\pi$
$234$	2.96187	+	5.13011i	0.193624	+	0.335366i
$235$	4.53414	−	7.85335i	0.295774	−	0.512296i
$236$	21.0770	+	36.5064i	1.37199	+	2.37636i
$237$	7.53593	−	13.0526i	0.489511	−	0.847858i
$238$	−4.85367	+	8.40680i	−0.314617	+	0.544932i
$239$	−13.1299	+	22.7416i	−0.849300	+	1.47103i	0.0325342	+	0.999471i	$0.489642\pi$
$239$	−13.1299	+	22.7416i	−0.849300	+	1.47103i	−0.881834	+	0.471560i	$0.843691\pi$
$240$	67.4932			4.35667
$241$	−9.23442	−	15.9945i	−0.594841	−	1.03029i	−0.993569	−	0.113226i	$-0.963882\pi$
$241$	−9.23442	−	15.9945i	−0.594841	−	1.03029i	0.398728	−	0.917069i	$-0.369452\pi$
$242$	15.2349	+	26.3875i	0.979333	+	1.69626i
$243$	−8.07534	+	13.9869i	−0.518034	+	0.897261i
$244$	79.0350			5.05970
$245$	12.8081	+	22.1843i	0.818279	+	1.41730i
$246$	−11.1032			−0.707913
$247$	−2.09320			−0.133187
$248$	−42.9449	+	39.6635i	−2.72700	+	2.51863i
$249$	0.997034			0.0631845
$250$	74.6080			4.71863
$251$	5.60248	+	9.70379i	0.353626	+	0.612498i	0.986882	−	0.161445i	$-0.0516153\pi$
$251$	5.60248	+	9.70379i	0.353626	+	0.612498i	−0.633256	+	0.773942i	$0.718282\pi$
$252$	−10.3151			−0.649793
$253$	−0.547563	+	0.948407i	−0.0344250	+	0.0596258i
$254$	−7.08662	−	12.2744i	−0.444654	−	0.770163i
$255$	−7.87964	−	13.6479i	−0.493442	−	0.854667i
$256$	93.7836			5.86148
$257$	−2.36984	+	4.10468i	−0.147826	+	0.256043i	−0.930424	−	0.366485i	$-0.880561\pi$
$257$	−2.36984	+	4.10468i	−0.147826	+	0.256043i	0.782597	+	0.622528i	$0.213894\pi$
$258$	−4.79068	+	8.29770i	−0.298255	+	0.516592i
$259$	1.98206	−	3.43304i	0.123160	−	0.213319i
$260$	−11.7402	−	20.3347i	−0.728098	−	1.26110i
$261$	−8.91724	+	15.4451i	−0.551964	+	0.956029i
$262$	−16.8770	−	29.2318i	−1.04266	−	1.80595i
$263$	19.0671			1.17573			0.587865	−	0.808959i	$-0.299968\pi$
$263$	19.0671			1.17573			0.587865	+	0.808959i	$0.299968\pi$
$264$	−2.54492			−0.156629
$265$	5.28770	+	9.15857i	0.324821	+	0.562606i
$266$	2.45447	−	4.25126i	0.150493	−	0.260661i
$267$	0.357895	+	0.619892i	0.0219028	+	0.0379368i
$268$	−11.6856	+	20.2400i	−0.713810	+	1.23635i
$269$	3.48183	−	6.03071i	0.212291	−	0.367699i	−0.740140	−	0.672453i	$-0.765241\pi$
$269$	3.48183	−	6.03071i	0.212291	−	0.367699i	0.952431	+	0.304754i	$0.0985742\pi$
$270$	27.1928	−	47.0994i	1.65490	−	2.86638i
$271$	5.35133			0.325070			0.162535	−	0.986703i	$-0.448033\pi$
$271$	5.35133			0.325070			0.162535	+	0.986703i	$0.448033\pi$
$272$	−36.6895	−	63.5481i	−2.22463	−	3.85317i
$273$	−0.393451	−	0.681478i	−0.0238128	−	0.0412449i
$274$	1.44608	−	2.50468i	0.0873608	−	0.151313i
$275$	−3.00024			−0.180921
$276$	11.3938	+	19.7346i	0.685826	+	1.18789i
$277$	−0.0361715			−0.00217334			−0.00108667	−	0.999999i	$-0.500346\pi$
$277$	−0.0361715			−0.00217334			−0.00108667	+	0.999999i	$0.500346\pi$
$278$	49.8023			2.98695
$279$	2.60681	+	11.5436i	0.156065	+	0.691096i
$280$	35.9701			2.14963
$281$	−10.3402			−0.616843			−0.308422	−	0.951250i	$-0.599801\pi$
$281$	−10.3402			−0.616843			−0.308422	+	0.951250i	$0.599801\pi$
$282$	2.90256	+	5.02737i	0.172845	+	0.299376i
$283$	−29.7841			−1.77048			−0.885241	−	0.465132i	$-0.846007\pi$
$283$	−29.7841			−1.77048			−0.885241	+	0.465132i	$0.846007\pi$
$284$	−5.19532	+	8.99857i	−0.308286	+	0.533967i
$285$	3.98468	+	6.90167i	0.236032	+	0.408819i
$286$	0.361184	+	0.625589i	0.0213573	+	0.0369918i
$287$	−3.58484			−0.211607
$288$	30.1899	−	52.2904i	1.77896	−	3.08124i
$289$	−0.0667873	+	0.115679i	−0.00392866	+	0.00680464i
$290$	47.6034	−	82.4515i	2.79537	−	4.84172i
$291$	−0.442225	−	0.765956i	−0.0259237	−	0.0449011i
$292$	29.1325	−	50.4590i	1.70485	−	2.95289i
$293$	4.01720	+	6.95800i	0.234687	+	0.406491i	0.959182	−	0.282790i	$-0.0912600\pi$
$293$	4.01720	+	6.95800i	0.234687	+	0.406491i	−0.724494	+	0.689281i	$0.757927\pi$
$294$	−16.3984			−0.956373
$295$	−29.7573			−1.73254
$296$	24.7314	+	42.8360i	1.43748	+	2.48979i
$297$	−0.621168	+	1.07590i	−0.0360438	+	0.0624298i
$298$	−4.40357	−	7.62720i	−0.255092	−	0.441832i
$299$	2.11257	−	3.65909i	0.122173	−	0.211610i
$300$	−31.2148	+	54.0656i	−1.80219	+	3.12148i
$301$	−1.54675	+	2.67905i	−0.0891531	+	0.154418i
$302$	−16.3507			−0.940878
$303$	6.55527	+	11.3541i	0.376590	+	0.652274i
$304$	18.5536	+	32.1358i	1.06412	+	1.84312i
$305$	−27.8962	+	48.3177i	−1.59733	+	2.76666i
$306$	−24.5200			−1.40171
$307$	−2.32545	−	4.02780i	−0.132720	−	0.229879i	0.792004	−	0.610516i	$-0.209038\pi$
$307$	−2.32545	−	4.02780i	−0.132720	−	0.229879i	−0.924724	+	0.380637i	$0.875705\pi$
$308$	−1.25788			−0.0716741
$309$	1.11222			0.0632721
$310$	−13.9160	−	61.6237i	−0.790378	−	3.49999i
$311$	−6.67669			−0.378600			−0.189300	−	0.981919i	$-0.560622\pi$
$311$	−6.67669			−0.378600			−0.189300	+	0.981919i	$0.560622\pi$
$312$	9.81865			0.555872
$313$	−6.39968	−	11.0846i	−0.361731	−	0.626537i	0.626515	−	0.779410i	$-0.284481\pi$
$313$	−6.39968	−	11.0846i	−0.361731	−	0.626537i	−0.988246	+	0.152873i	$0.951148\pi$
$314$	−7.01175			−0.395696
$315$	3.64084	−	6.30612i	0.205138	−	0.355309i
$316$	46.4762	+	80.4992i	2.61449	+	4.52843i
$317$	−5.06486	−	8.77260i	−0.284471	−	0.492718i	0.688010	−	0.725701i	$-0.258485\pi$
$317$	−5.06486	−	8.77260i	−0.284471	−	0.492718i	−0.972481	+	0.232983i	$0.925151\pi$
$318$	−6.76991			−0.379638
$319$	−1.08741	+	1.88345i	−0.0608832	+	0.105453i
$320$	−88.9905	+	154.136i	−4.97472	+	8.61647i
$321$	5.09425	−	8.82351i	0.284334	−	0.492480i
$322$	4.95436	+	8.58121i	0.276096	+	0.478212i
$323$	4.33216	−	7.50353i	0.241048	−	0.417508i
$324$	−5.46228	−	9.46095i	−0.303460	−	0.525609i
$325$	11.5753			0.642084
$326$	4.80468			0.266107
$327$	−0.720577	−	1.24808i	−0.0398480	−	0.0690187i
$328$	22.3651	−	38.7375i	1.23491	−	2.13892i
$329$	0.937137	+	1.62317i	0.0516661	+	0.0894882i
$330$	1.37512	−	2.38178i	0.0756979	−	0.131113i
$331$	−0.693958	+	1.20197i	−0.0381434	+	0.0660663i	−0.884467	−	0.466603i	$-0.845478\pi$
$331$	−0.693958	+	1.20197i	−0.0381434	+	0.0660663i	0.846323	+	0.532669i	$0.178811\pi$
$332$	−3.07450	+	5.32519i	−0.168735	+	0.292258i
$333$	10.0131			0.548714
$334$	−26.5895	−	46.0543i	−1.45491	−	2.51998i
$335$	−8.24908	−	14.2878i	−0.450695	−	0.780627i
$336$	−6.97492	+	12.0809i	−0.380513	+	0.659068i
$337$	9.17340			0.499707			0.249853	−	0.968284i	$-0.419618\pi$
$337$	9.17340			0.499707			0.249853	+	0.968284i	$0.419618\pi$
$338$	−1.39350	−	2.41361i	−0.0757963	−	0.131283i
$339$	8.89168			0.482930
$340$	97.1920			5.27098
$341$	0.317886	+	1.40768i	0.0172145	+	0.0762299i
$342$	12.3996			0.670493
$343$	−11.1848			−0.603922
$344$	−19.2997	−	33.4280i	−1.04057	−	1.80232i
$345$	−16.0862			−0.866054
$346$	11.1828	−	19.3692i	0.601191	−	1.04129i
$347$	−16.6974	−	28.9207i	−0.896362	−	1.55254i	−0.832110	−	0.554611i	$-0.812867\pi$
$347$	−16.6974	−	28.9207i	−0.896362	−	1.55254i	−0.0642526	−	0.997934i	$-0.520466\pi$
$348$	22.6270	+	39.1911i	1.21294	+	2.10087i
$349$	21.1587			1.13260			0.566299	−	0.824200i	$-0.308375\pi$
$349$	21.1587			1.13260			0.566299	+	0.824200i	$0.308375\pi$
$350$	−13.5731	+	23.5093i	−0.725514	+	1.25663i
$351$	2.39655	−	4.15095i	0.127919	−	0.221561i
$352$	3.68149	−	6.37653i	0.196224	−	0.339870i
$353$	−4.29571	−	7.44040i	−0.228638	−	0.396012i	0.728767	−	0.684762i	$-0.240094\pi$
$353$	−4.29571	−	7.44040i	−0.228638	−	0.396012i	−0.957405	+	0.288750i	$0.906760\pi$
$354$	9.52467	−	16.4972i	0.506230	−	0.876817i
$355$	−3.66749	−	6.35227i	−0.194650	−	0.337144i
$356$	−4.41448			−0.233967
$357$	3.25721			0.172390
$358$	27.1010	+	46.9403i	1.43233	+	2.48087i
$359$	9.22732	−	15.9822i	0.486999	−	0.843508i	−0.512889	−	0.858455i	$-0.671425\pi$
$359$	9.22732	−	15.9822i	0.486999	−	0.843508i	0.999888	+	0.0149472i	$0.00475802\pi$
$360$	45.4289	+	78.6851i	2.39431	+	4.14707i
$361$	7.30925	−	12.6600i	0.384698	−	0.666316i
$362$	−18.6773	+	32.3500i	−0.981657	+	1.70028i
$363$	5.11191	−	8.85409i	0.268306	−	0.464719i
$364$	4.85306			0.254369
$365$	20.5652	+	35.6200i	1.07643	+	1.86444i
$366$	−17.8579	−	30.9309i	−0.933449	−	1.61678i
$367$	5.55113	−	9.61483i	0.289766	−	0.501890i	−0.683987	−	0.729494i	$-0.739756\pi$
$367$	5.55113	−	9.61483i	0.289766	−	0.501890i	0.973754	+	0.227604i	$0.0730891\pi$
$368$	−74.9014			−3.90450
$369$	−4.52752	−	7.84189i	−0.235693	−	0.408233i
$370$	−53.4534			−2.77891
$371$	−2.18578			−0.113480
$372$	28.6742	+	8.91716i	1.48669	+	0.462333i
$373$	−23.4406			−1.21371			−0.606853	−	0.794814i	$-0.707569\pi$
$373$	−23.4406			−1.21371			−0.606853	+	0.794814i	$0.707569\pi$
$374$	−2.99008			−0.154613
$375$	−12.5170	−	21.6801i	−0.646376	−	1.11956i
$376$	−23.3864			−1.20606
$377$	4.19537	−	7.26660i	0.216073	−	0.374249i
$378$	5.62035	+	9.73473i	0.289079	+	0.500700i
$379$	−12.2716	−	21.2551i	−0.630352	−	1.09180i	−0.987480	−	0.157746i	$-0.949577\pi$
$379$	−12.2716	−	21.2551i	−0.630352	−	1.09180i	0.357127	−	0.934056i	$-0.383756\pi$
$380$	−49.1493			−2.52131
$381$	−2.37785	+	4.11855i	−0.121821	+	0.211000i
$382$	−8.94669	+	15.4961i	−0.457753	+	0.792851i
$383$	−18.0042	+	31.1842i	−0.919973	+	1.59344i	−0.120520	+	0.992711i	$0.538456\pi$
$383$	−18.0042	+	31.1842i	−0.919973	+	1.59344i	−0.799453	+	0.600729i	$0.794877\pi$
$384$	−30.4027	−	52.6590i	−1.55148	−	2.68724i
$385$	0.443980	−	0.768996i	0.0226273	−	0.0391917i
$386$	20.9195	+	36.2337i	1.06478	+	1.84424i
$387$	−7.81393			−0.397205
$388$	5.45466			0.276918
$389$	2.97808	+	5.15818i	0.150994	+	0.261530i	0.931593	−	0.363502i	$-0.118419\pi$
$389$	2.97808	+	5.15818i	0.150994	+	0.261530i	−0.780599	+	0.625032i	$0.785086\pi$
$390$	−5.30540	+	9.18923i	−0.268650	+	0.465315i
$391$	8.74452	+	15.1459i	0.442229	+	0.765964i
$392$	33.0312	−	57.2117i	1.66833	−	2.88963i
$393$	−5.66291	+	9.80845i	−0.285656	+	0.494771i
$394$	12.7873	−	22.1483i	0.644217	−	1.11582i
$395$	−65.6171			−3.30155
$396$	−1.58865	−	2.75162i	−0.0798326	−	0.138274i
$397$	−9.66422	−	16.7389i	−0.485033	−	0.840102i	0.514819	−	0.857299i	$-0.327859\pi$
$397$	−9.66422	−	16.7389i	−0.485033	−	0.840102i	−0.999852	+	0.0171967i	$0.994526\pi$
$398$	5.60783	−	9.71304i	0.281095	−	0.486871i
$399$	−1.64715			−0.0824604
$400$	−102.601	−	177.710i	−5.13005	−	8.88551i
$401$	17.5378			0.875796			0.437898	−	0.899025i	$-0.355723\pi$
$401$	17.5378			0.875796			0.437898	+	0.899025i	$0.355723\pi$
$402$	10.5614			0.526755
$403$	−1.22645	−	5.43101i	−0.0610937	−	0.270538i
$404$	−80.8565			−4.02276
$405$	7.71188			0.383206
$406$	9.83890	+	17.0415i	0.488297	+	0.845754i
$407$	1.22104			0.0605247
$408$	−20.3210	+	35.1971i	−1.00604	+	1.74251i
$409$	3.34471	+	5.79321i	0.165385	+	0.286456i	0.936792	−	0.349887i	$-0.113780\pi$
$409$	3.34471	+	5.79321i	0.165385	+	0.286456i	−0.771407	+	0.636342i	$0.780447\pi$
$410$	24.1695	+	41.8628i	1.19365	+	2.06746i
$411$	−0.970436			−0.0478681
$412$	−3.42969	+	5.94041i	−0.168969	+	0.292663i
$413$	3.07519	−	5.32639i	0.151320	−	0.262095i
$414$	−12.5143	+	21.6755i	−0.615046	+	1.06529i
$415$	−2.17035	−	3.75916i	−0.106538	−	0.184530i
$416$	−14.2037	+	24.6015i	−0.696393	+	1.20619i
$417$	−8.35535	−	14.4719i	−0.409163	−	0.708692i
$418$	1.51206			0.0739573
$419$	30.3574			1.48306			0.741528	−	0.670922i	$-0.234101\pi$
$419$	30.3574			1.48306			0.741528	+	0.670922i	$0.234101\pi$
$420$	−9.23842	−	16.0014i	−0.450789	−	0.780789i
$421$	15.8850	−	27.5136i	0.774187	−	1.34093i	−0.161064	−	0.986944i	$-0.551493\pi$
$421$	15.8850	−	27.5136i	0.774187	−	1.34093i	0.935251	−	0.353986i	$-0.115174\pi$
$422$	−29.8839	−	51.7604i	−1.45472	−	2.51966i
$423$	−2.36714	+	4.10000i	−0.115094	+	0.199349i
$424$	13.6366	−	23.6193i	0.662252	−	1.14705i
$425$	−23.9567	+	41.4943i	−1.16207	+	2.01277i
$426$	4.69553			0.227499
$427$	−5.76573	−	9.98653i	−0.279023	−	0.483282i
$428$	31.4177	+	54.4171i	1.51863	+	2.63035i
$429$	0.121192	−	0.209910i	0.00585120	−	0.0101346i
$430$	41.7135			2.01161
$431$	−12.9211	−	22.3801i	−0.622389	−	1.07801i	−0.989040	−	0.147651i	$-0.952829\pi$
$431$	−12.9211	−	22.3801i	−0.622389	−	1.07801i	0.366650	−	0.930359i	$-0.380505\pi$
$432$	−84.9698			−4.08811
$433$	−27.9846			−1.34485			−0.672426	−	0.740164i	$-0.734748\pi$
$433$	−27.9846			−1.34485			−0.672426	+	0.740164i	$0.734748\pi$
$434$	12.4684	+	3.87745i	0.598503	+	0.186123i
$435$	−31.9457			−1.53168
$436$	8.88801			0.425658
$437$	−4.42204	−	7.65920i	−0.211535	−	0.366389i
$438$	−26.3299			−1.25809
$439$	−3.22950	+	5.59365i	−0.154135	+	0.266970i	−0.932744	−	0.360540i	$-0.882593\pi$
$439$	−3.22950	+	5.59365i	−0.154135	+	0.266970i	0.778608	+	0.627510i	$0.215926\pi$
$440$	5.53980	+	9.59522i	0.264100	+	0.457434i
$441$	−6.68673	−	11.5817i	−0.318416	−	0.551512i
$442$	11.5361			0.548718
$443$	9.65475	−	16.7225i	0.458711	−	0.794511i	−0.540182	−	0.841548i	$-0.681645\pi$
$443$	9.65475	−	16.7225i	0.458711	−	0.794511i	0.998893	+	0.0470371i	$0.0149779\pi$
$444$	12.7038	−	22.0037i	0.602897	−	1.04425i
$445$	1.55814	−	2.69877i	0.0738627	−	0.127934i
$446$	−16.1235	−	27.9267i	−0.763469	−	1.32237i
$447$	−1.47758	+	2.55924i	−0.0698869	+	0.121048i
$448$	−18.3930	−	31.8576i	−0.868987	−	1.50513i
$449$	−17.6398			−0.832473			−0.416237	−	0.909256i	$-0.636651\pi$
$449$	−17.6398			−0.832473			−0.416237	+	0.909256i	$0.636651\pi$
$450$	−68.5693			−3.23239
$451$	−0.552106	−	0.956276i	−0.0259977	−	0.0450293i
$452$	−27.4188	+	47.4907i	−1.28967	+	2.23378i
$453$	2.74316	+	4.75130i	0.128885	+	0.223236i
$454$	−13.7829	+	23.8726i	−0.646862	+	1.12040i
$455$	−1.71294	+	2.96689i	−0.0803037	+	0.139090i
$456$	10.2762	−	17.7989i	0.481227	−	0.833510i
$457$	33.2079			1.55340			0.776701	−	0.629870i	$-0.216892\pi$
$457$	33.2079			1.55340			0.776701	+	0.629870i	$0.216892\pi$
$458$	23.9196	+	41.4300i	1.11769	+	1.93590i
$459$	9.91998	+	17.1819i	0.463025	+	0.801983i
$460$	49.6042	−	85.9170i	2.31281	−	4.00590i
$461$	15.5365			0.723608			0.361804	−	0.932254i	$-0.382161\pi$
$461$	15.5365			0.723608			0.361804	+	0.932254i	$0.382161\pi$
$462$	0.284217	+	0.492278i	0.0132230	+	0.0229028i
$463$	−15.1329			−0.703287			−0.351643	−	0.936134i	$-0.614377\pi$
$463$	−15.1329			−0.703287			−0.351643	+	0.936134i	$0.614377\pi$
$464$	−148.747			−6.90541
$465$	−15.5723	+	14.3824i	−0.722149	+	0.666970i
$466$	55.0385			2.54961
$467$	3.92039			0.181414			0.0907069	−	0.995878i	$-0.471087\pi$
$467$	3.92039			0.181414			0.0907069	+	0.995878i	$0.471087\pi$
$468$	6.12922	+	10.6161i	0.283323	+	0.490731i
$469$	3.40992			0.157456
$470$	12.6366	−	21.8873i	0.582883	−	1.00958i
$471$	1.17636	+	2.03752i	0.0542040	+	0.0938840i
$472$	38.3710	+	66.4605i	1.76617	+	3.05909i
$473$	−0.952866			−0.0438128
$474$	21.0026	−	36.3775i	0.964681	−	1.67088i
$475$	12.1148	−	20.9834i	0.555863	−	0.962783i
$476$	−10.0441	+	17.3968i	−0.460369	+	0.797382i
$477$	−2.76055	−	4.78141i	−0.126397	−	0.218926i
$478$	−36.5928	+	63.3807i	−1.67372	+	2.89896i
$479$	19.7978	+	34.2907i	0.904582	+	1.56678i	0.821477	+	0.570242i	$0.193151\pi$
$479$	19.7978	+	34.2907i	0.904582	+	1.56678i	0.0831055	+	0.996541i	$0.473516\pi$
$480$	108.154			4.93654
$481$	−4.71094			−0.214801
$482$	−25.7363	−	44.5765i	−1.17225	−	2.03040i
$483$	1.66239	−	2.87934i	0.0756414	−	0.131015i
$484$	31.5266	+	54.6057i	1.43303	+	2.48208i
$485$	−1.92528	+	3.33468i	−0.0874224	+	0.151420i
$486$	−22.5059	+	38.9814i	−1.02089	+	1.76823i
$487$	−0.338825	+	0.586863i	−0.0153536	+	0.0265933i	−0.873600	−	0.486644i	$-0.838221\pi$
$487$	−0.338825	+	0.586863i	−0.0153536	+	0.0265933i	0.858246	+	0.513238i	$0.171554\pi$
$488$	143.885			6.51336
$489$	−0.806083	−	1.39618i	−0.0364523	−	0.0631373i
$490$	35.6961	+	61.8275i	1.61259	+	2.79308i
$491$	−9.36279	+	16.2168i	−0.422537	+	0.731855i	−0.996187	−	0.0872455i	$-0.972194\pi$
$491$	−9.36279	+	16.2168i	−0.422537	+	0.731855i	0.573650	+	0.819100i	$0.305527\pi$
$492$	−22.9766			−1.03587
$493$	17.3658	+	30.0784i	0.782116	+	1.35466i
$494$	−5.83374			−0.262472
$495$	2.24292			0.100812
$496$	−72.5085	+	66.9681i	−3.25573	+	3.00696i
$497$	1.51603			0.0680032
$498$	2.77873			0.124518
$499$	12.2804	+	21.2704i	0.549748	+	0.952192i	0.998291	+	0.0584307i	$0.0186097\pi$
$499$	12.2804	+	21.2704i	0.549748	+	0.952192i	−0.448543	+	0.893761i	$0.648057\pi$
$500$	154.392			6.90462
$501$	−8.92185	+	15.4531i	−0.398599	+	0.690393i
$502$	15.6141	+	27.0444i	0.696891	+	1.20705i
$503$	−3.09597	−	5.36238i	−0.138043	−	0.239097i	0.788713	−	0.614762i	$-0.210748\pi$
$503$	−3.09597	−	5.36238i	−0.138043	−	0.239097i	−0.926756	+	0.375665i	$0.877414\pi$
$504$	−18.7789			−0.836480
$505$	28.5391	−	49.4312i	1.26997	−	2.19966i
$506$	−1.52606	+	2.64321i	−0.0678414	+	0.117505i
$507$	−0.467575	+	0.809863i	−0.0207657	+	0.0359673i
$508$	−14.6649	−	25.4003i	−0.650648	−	1.12696i
$509$	−9.86807	+	17.0920i	−0.437395	+	0.757590i	−0.997488	−	0.0708400i	$-0.977432\pi$
$509$	−9.86807	+	17.0920i	−0.437395	+	0.757590i	0.560093	+	0.828430i	$0.310765\pi$
$510$	−21.9605	−	38.0367i	−0.972428	−	1.68429i
$511$	−8.50105			−0.376064
$512$	131.330			5.80404
$513$	−5.01647	−	8.68877i	−0.221482	−	0.383619i
$514$	−6.60472	+	11.4397i	−0.291322	+	0.504584i
$515$	−2.42109	−	4.19345i	−0.106686	−	0.184786i
$516$	−9.91371	+	17.1711i	−0.436427	+	0.755913i
$517$	−0.288659	+	0.499973i	−0.0126952	+	0.0219888i
$518$	5.52400	−	9.56785i	0.242711	−	0.420387i
$519$	−7.50457			−0.329414
$520$	−21.3733	−	37.0197i	−0.937282	−	1.62342i
$521$	−18.3647	−	31.8085i	−0.804571	−	1.39356i	−0.916580	−	0.399850i	$-0.869062\pi$
$521$	−18.3647	−	31.8085i	−0.804571	−	1.39356i	0.112010	−	0.993707i	$-0.464271\pi$
$522$	−24.8523	+	43.0455i	−1.08776	+	1.88405i
$523$	−6.90952			−0.302132			−0.151066	−	0.988524i	$-0.548271\pi$
$523$	−6.90952			−0.302132			−0.151066	+	0.988524i	$0.548271\pi$
$524$	−34.9248	−	60.4915i	−1.52570	−	2.64259i
$525$	9.10867			0.397535
$526$	53.1400			2.31702
$527$	22.0069	+	6.84375i	0.958636	+	0.298118i
$528$	−4.29686			−0.186997
$529$	−5.14813			−0.223832
$530$	14.7368	+	25.5249i	0.640126	+	1.10873i
$531$	15.5354			0.674179
$532$	5.07921	−	8.79745i	0.220212	−	0.381418i
$533$	2.13010	+	3.68944i	0.0922649	+	0.159807i
$534$	0.997451	+	1.72764i	0.0431639	+	0.0747621i
$535$	−44.3568			−1.91771
$536$	−21.2738	+	36.8473i	−0.918888	+	1.59156i
$537$	9.09348	−	15.7504i	0.392413	−	0.679679i
$538$	9.70384	−	16.8075i	0.418362	−	0.724625i
$539$	−0.815410	−	1.41233i	−0.0351222	−	0.0608334i
$540$	56.2722	−	97.4663i	2.42157	−	4.19428i
$541$	7.91889	+	13.7159i	0.340460	+	0.589693i	0.984518	−	0.175283i	$-0.0560840\pi$
$541$	7.91889	+	13.7159i	0.340460	+	0.589693i	−0.644059	+	0.764976i	$0.722751\pi$
$542$	14.9141			0.640617
$543$	12.5340			0.537885
$544$	−58.7929	−	101.832i	−2.52073	−	4.36603i
$545$	−3.13711	+	5.43364i	−0.134379	+	0.232752i
$546$	−1.09655	−	1.89928i	−0.0469279	−	0.0812815i
$547$	−14.0110	+	24.2678i	−0.599069	+	1.03762i	0.393890	+	0.919158i	$0.371129\pi$
$547$	−14.0110	+	24.2678i	−0.599069	+	1.03762i	−0.992959	+	0.118460i	$0.962204\pi$
$548$	2.99248	−	5.18312i	0.127832	−	0.221412i
$549$	14.5638	−	25.2252i	0.621567	−	1.07659i
$550$	−8.36165			−0.356542
$551$	−8.78176	−	15.2105i	−0.374116	−	0.647987i
$552$	20.7426	+	35.9273i	0.882865	+	1.52917i
$553$	6.78103	−	11.7451i	0.288359	−	0.499452i
$554$	−0.100810			−0.00428300
$555$	8.96789	+	15.5328i	0.380666	+	0.659332i
$556$	103.060			4.37071
$557$	−27.3296			−1.15799			−0.578996	−	0.815331i	$-0.696555\pi$
$557$	−27.3296			−1.15799			−0.578996	+	0.815331i	$0.696555\pi$
$558$	7.26515	+	32.1719i	0.307558	+	1.36194i
$559$	3.67629			0.155490
$560$	60.7322			2.56640
$561$	0.501646	+	0.868877i	0.0211795	+	0.0366840i
$562$	−28.8180			−1.21562
$563$	−0.831984	+	1.44104i	−0.0350640	+	0.0607326i	−0.883025	−	0.469326i	$-0.844497\pi$
$563$	−0.831984	+	1.44104i	−0.0350640	+	0.0607326i	0.847961	+	0.530059i	$0.177830\pi$
$564$	6.00648	+	10.4035i	0.252918	+	0.438067i
$565$	−19.3555	−	33.5247i	−0.814291	−	1.41039i
$566$	−83.0082			−3.48909
$567$	−0.796964	+	1.38038i	−0.0334693	+	0.0579706i
$568$	−9.45819	+	16.3821i	−0.396857	+	0.687376i
$569$	−15.7435	+	27.2685i	−0.660001	+	1.14316i	0.320614	+	0.947210i	$0.396111\pi$
$569$	−15.7435	+	27.2685i	−0.660001	+	1.14316i	−0.980615	+	0.195946i	$0.937222\pi$
$570$	11.1053	+	19.2349i	0.465149	+	0.805662i
$571$	8.90650	−	15.4265i	0.372725	−	0.645579i	−0.617258	−	0.786761i	$-0.711757\pi$
$571$	8.90650	−	15.4265i	0.372725	−	0.645579i	0.989984	+	0.141181i	$0.0450900\pi$
$572$	0.747425	+	1.29458i	0.0312514	+	0.0541290i
$573$	6.00396			0.250819
$574$	−9.99094			−0.417014
$575$	24.4538	+	42.3552i	1.01979	+	1.76633i
$576$	46.4593	−	80.4698i	1.93580	−	3.35291i
$577$	1.03045	+	1.78479i	0.0428982	+	0.0743018i	0.886677	−	0.462389i	$-0.153008\pi$
$577$	1.03045	+	1.78479i	0.0428982	+	0.0743018i	−0.843779	+	0.536691i	$0.819674\pi$
$578$	−0.186136	+	0.322397i	−0.00774223	+	0.0134099i
$579$	7.01934	−	12.1579i	0.291714	−	0.505264i
$580$	98.5093	−	170.623i	4.09038	−	7.08474i
$581$	0.897158			0.0372204
$582$	−1.23248	−	2.13472i	−0.0510879	−	0.0884868i
$583$	−0.336634	−	0.583067i	−0.0139420	−	0.0241482i
$584$	53.0363	−	91.8616i	2.19466	−	3.80126i
$585$	−8.65349			−0.357778
$586$	11.1959	+	19.3919i	0.462499	+	0.801072i
$587$	27.3716			1.12975			0.564873	−	0.825178i	$-0.308925\pi$
$587$	27.3716			1.12975			0.564873	+	0.825178i	$0.308925\pi$
$588$	−33.9344			−1.39943
$589$	−11.1287	−	3.46083i	−0.458552	−	0.142601i
$590$	−82.9335			−3.41432
$591$	−8.58134			−0.352989
$592$	41.7567	+	72.3246i	1.71619	+	2.97252i
$593$	9.88958			0.406117			0.203058	−	0.979167i	$-0.434912\pi$
$593$	9.88958			0.406117			0.203058	+	0.979167i	$0.434912\pi$
$594$	−1.73119	+	2.99851i	−0.0710317	+	0.123031i
$595$	−7.09031	−	12.2808i	−0.290674	−	0.503463i
$596$	−9.11263	−	15.7835i	−0.373268	−	0.646519i
$597$	−3.76331			−0.154022
$598$	5.88773	−	10.1979i	0.240767	−	0.417021i
$599$	18.0061	−	31.1874i	0.735709	−	1.27428i	−0.218703	−	0.975791i	$-0.570183\pi$
$599$	18.0061	−	31.1874i	0.735709	−	1.27428i	0.954412	−	0.298493i	$-0.0964840\pi$
$600$	−56.8271	+	98.4275i	−2.31996	+	4.01828i
$601$	−4.41298	−	7.64350i	−0.180009	−	0.311785i	0.761874	−	0.647725i	$-0.224279\pi$
$601$	−4.41298	−	7.64350i	−0.180009	−	0.311785i	−0.941883	+	0.335940i	$0.890946\pi$
$602$	−4.31078	+	7.46649i	−0.175694	+	0.304311i
$603$	4.30660	+	7.45925i	0.175378	+	0.303764i
$604$	−33.8358			−1.37676
$605$	−44.5106			−1.80961
$606$	18.2695	+	31.6437i	0.742148	+	1.28544i
$607$	−8.96622	+	15.5299i	−0.363928	+	0.630341i	−0.988603	−	0.150543i	$-0.951898\pi$
$607$	−8.96622	+	15.5299i	−0.363928	+	0.630341i	0.624676	+	0.780884i	$0.285231\pi$
$608$	29.7312	+	51.4959i	1.20576	+	2.08844i
$609$	3.30135	−	5.71811i	0.133778	−	0.231709i
$610$	−77.7466	+	134.661i	−3.14787	+	5.45227i
$611$	1.11369	−	1.92896i	0.0450550	−	0.0780375i
$612$	−50.7411			−2.05109
$613$	−13.4523	−	23.3000i	−0.543333	−	0.941080i	−0.998710	−	0.0507811i	$-0.983829\pi$
$613$	−13.4523	−	23.3000i	−0.543333	−	0.941080i	0.455377	−	0.890299i	$-0.349504\pi$
$614$	−6.48102	−	11.2255i	−0.261553	−	0.453022i
$615$	8.10984	−	14.0467i	0.327020	−	0.566416i
$616$	−2.28999			−0.0922662
$617$	16.9002	+	29.2720i	0.680375	+	1.17844i	0.974866	+	0.222791i	$0.0715166\pi$
$617$	16.9002	+	29.2720i	0.680375	+	1.17844i	−0.294491	+	0.955654i	$0.595150\pi$
$618$	3.09975			0.124690
$619$	−22.6135			−0.908912			−0.454456	−	0.890769i	$-0.650166\pi$
$619$	−22.6135			−0.908912			−0.454456	+	0.890769i	$0.650166\pi$
$620$	−28.7975	−	127.523i	−1.15654	−	5.12143i
$621$	20.2516			0.812668
$622$	−18.6079			−0.746108
$623$	0.322043	+	0.557795i	0.0129024	+	0.0223476i
$624$	16.5779			0.663646
$625$	−25.5559	+	44.2641i	−1.02224	+	1.77057i
$626$	−17.8359	−	30.8926i	−0.712865	−	1.23472i
$627$	−0.253679	−	0.439385i	−0.0101310	−	0.0175473i
$628$	−14.5099			−0.579010
$629$	9.74994	−	16.8874i	0.388755	−	0.673344i
$630$	10.1470	−	17.5751i	0.404266	−	0.700209i
$631$	16.8310	−	29.1522i	0.670032	−	1.16053i	−0.307863	−	0.951431i	$-0.599614\pi$
$631$	16.8310	−	29.1522i	0.670032	−	1.16053i	0.977895	−	0.209099i	$-0.0670529\pi$
$632$	84.6109	+	146.550i	3.36564	+	5.82946i
$633$	−10.0273	+	17.3677i	−0.398548	+	0.690305i
$634$	−14.1157	−	24.4492i	−0.560608	−	0.971001i
$635$	20.7045			0.821632
$636$	−14.0095			−0.555512
$637$	3.14596	+	5.44897i	0.124648	+	0.215896i
$638$	−3.03060	+	5.24916i	−0.119983	+	0.207816i
$639$	1.91469	+	3.31633i	0.0757438	+	0.131192i
$640$	−132.362	+	229.257i	−5.23205	+	9.06217i
$641$	1.64265	−	2.84515i	0.0648807	−	0.112377i	−0.831760	−	0.555135i	$-0.812667\pi$
$641$	1.64265	−	2.84515i	0.0648807	−	0.112377i	0.896641	+	0.442758i	$0.146000\pi$
$642$	14.1977	−	24.5911i	0.560337	−	0.970532i
$643$	24.7246			0.975041			0.487521	−	0.873111i	$-0.337901\pi$
$643$	24.7246			0.975041			0.487521	+	0.873111i	$0.337901\pi$
$644$	10.2524	+	17.7577i	0.404003	+	0.699753i
$645$	−6.99829	−	12.1214i	−0.275557	−	0.477280i
$646$	12.0737	−	20.9123i	0.475034	−	0.822783i
$647$	−4.02193			−0.158118			−0.0790591	−	0.996870i	$-0.525192\pi$
$647$	−4.02193			−0.158118			−0.0790591	+	0.996870i	$0.525192\pi$
$648$	−9.94419	−	17.2238i	−0.390645	−	0.676617i
$649$	1.89446			0.0743639
$650$	32.2604			1.26536
$651$	−0.965094	−	4.27367i	−0.0378250	−	0.167499i
$652$	9.94269			0.389386
$653$	−39.6923			−1.55328			−0.776640	−	0.629945i	$-0.783077\pi$
$653$	−39.6923			−1.55328			−0.776640	+	0.629945i	$0.783077\pi$
$654$	−2.00824	−	3.47838i	−0.0785285	−	0.136015i
$655$	49.3083			1.92663
$656$	37.7614	−	65.4046i	1.47433	−	2.55362i
$657$	−10.7365	−	18.5962i	−0.418871	−	0.725505i
$658$	2.61180	+	4.52376i	0.101818	+	0.176355i
$659$	−17.6062			−0.685840			−0.342920	−	0.939365i	$-0.611416\pi$
$659$	−17.6062			−0.685840			−0.342920	+	0.939365i	$0.611416\pi$
$660$	2.84564	−	4.92880i	0.110766	−	0.191853i
$661$	10.4738	−	18.1411i	0.407383	−	0.705609i	−0.587212	−	0.809433i	$-0.699775\pi$
$661$	10.4738	−	18.1411i	0.407383	−	0.705609i	0.994596	+	0.103824i	$0.0331080\pi$
$662$	−1.93406	+	3.34988i	−0.0751693	+	0.130197i
$663$	−1.93542	−	3.35225i	−0.0751655	−	0.130190i
$664$	−5.59718	+	9.69460i	−0.217213	+	0.376224i
$665$	3.58552	+	6.21030i	0.139041	+	0.240825i
$666$	27.9064			1.08135
$667$	35.4521			1.37271
$668$	−55.0236	−	95.3037i	−2.12893	−	3.68741i
$669$	−5.41008	+	9.37054i	−0.209166	+	0.362286i
$670$	−22.9901	−	39.8201i	−0.888187	−	1.53838i
$671$	1.77597	−	3.07608i	0.0685607	−	0.118751i
$672$	−11.1769	+	19.3590i	−0.431159	+	0.746790i
$673$	8.52900	−	14.7727i	0.328769	−	0.569445i	−0.653499	−	0.756927i	$-0.726700\pi$
$673$	8.52900	−	14.7727i	0.328769	−	0.569445i	0.982268	+	0.187483i	$0.0600329\pi$
$674$	25.5662			0.984774
$675$	27.7409	+	48.0487i	1.06775	+	1.84939i
$676$	−2.88367	−	4.99466i	−0.110910	−	0.192102i
$677$	16.6304	−	28.8046i	0.639156	−	1.10705i	−0.346462	−	0.938064i	$-0.612617\pi$
$677$	16.6304	−	28.8046i	0.639156	−	1.10705i	0.985618	−	0.168987i	$-0.0540497\pi$
$678$	24.7811			0.951711
$679$	−0.397926	−	0.689228i	−0.0152710	−	0.0264501i
$680$	176.940			6.78534
$681$	9.24943			0.354439
$682$	0.885946	+	3.92318i	0.0339246	+	0.150226i
$683$	5.19052			0.198610			0.0993049	−	0.995057i	$-0.468338\pi$
$683$	5.19052			0.198610			0.0993049	+	0.995057i	$0.468338\pi$
$684$	25.6594			0.981112
$685$	2.11245	+	3.65887i	0.0807126	+	0.139798i
$686$	−31.1719			−1.19015
$687$	8.02600	−	13.9014i	0.306211	−	0.530373i
$688$	−32.5857	−	56.4401i	−1.24232	−	2.15176i
$689$	1.29878	+	2.24955i	0.0494796	+	0.0857012i
$690$	−44.8322			−1.70673
$691$	−24.0337	+	41.6276i	−0.914286	+	1.58359i	−0.106342	+	0.994330i	$0.533914\pi$
$691$	−24.0337	+	41.6276i	−0.914286	+	1.58359i	−0.807943	+	0.589260i	$0.799419\pi$
$692$	23.1414	−	40.0821i	0.879705	−	1.52369i
$693$	−0.231789	+	0.401470i	−0.00880493	+	0.0152506i
$694$	−46.5355	−	80.6018i	−1.76646	−	3.05960i
$695$	−36.3760	+	63.0051i	−1.37982	+	2.38992i
$696$	41.1929	+	71.3482i	1.56141	+	2.70445i
$697$	−17.6341			−0.667940
$698$	58.9691			2.23201
$699$	−9.23382	−	15.9934i	−0.349255	−	0.604928i
$700$	−28.0879	+	48.6497i	−1.06162	+	1.83878i
$701$	−11.3053	−	19.5814i	−0.426996	−	0.739579i	0.569608	−	0.821916i	$-0.307095\pi$
$701$	−11.3053	−	19.5814i	−0.426996	−	0.739579i	−0.996605	+	0.0823371i	$0.973762\pi$
$702$	6.67918	−	11.5687i	0.252089	−	0.436632i
$703$	−4.93048	+	8.53983i	−0.185956	+	0.322086i
$704$	5.66545	−	9.81285i	0.213525	−	0.369836i
$705$	−8.48019			−0.319383
$706$	−11.9721	−	20.7363i	−0.450577	−	0.780423i
$707$	5.89861	+	10.2167i	0.221840	+	0.384238i
$708$	19.7101	−	34.1389i	0.740751	−	1.28302i
$709$	19.0043			0.713720			0.356860	−	0.934158i	$-0.383847\pi$
$709$	19.0043			0.713720			0.356860	+	0.934158i	$0.383847\pi$
$710$	−10.2213	−	17.7037i	−0.383597	−	0.664410i
$711$	34.2567			1.28473
$712$	−8.03665			−0.301186
$713$	17.2816	−	15.9611i	0.647199	−	0.597747i
$714$	9.07781			0.339729
$715$	−1.05525			−0.0394639
$716$	56.0821	+	97.1371i	2.09589	+	3.63018i
$717$	24.5568			0.917089
$718$	25.7165	−	44.5423i	0.959731	−	1.66230i
$719$	14.2717	+	24.7193i	0.532245	+	0.921876i	0.999291	+	0.0376428i	$0.0119849\pi$
$719$	14.2717	+	24.7193i	0.532245	+	0.921876i	−0.467046	+	0.884233i	$0.654682\pi$
$720$	76.7024	+	132.853i	2.85853	+	4.95112i
$721$	1.00081			0.0372720
$722$	20.3709	−	35.2834i	0.758125	−	1.31311i
$723$	−8.63556	+	14.9572i	−0.321160	+	0.556265i
$724$	−38.6504	+	66.9444i	−1.43643	+	2.48797i
$725$	48.5629	+	84.1134i	1.80358	+	3.12389i
$726$	14.2469	−	24.6763i	0.528751	−	0.915823i
$727$	−14.6916	−	25.4466i	−0.544881	−	0.943761i	−0.998614	−	0.0526239i	$-0.983242\pi$
$727$	−14.6916	−	25.4466i	−0.544881	−	0.943761i	0.453734	−	0.891137i	$-0.350092\pi$
$728$	8.83508			0.327450
$729$	9.42067			0.348914
$730$	57.3152	+	99.2729i	2.12133	+	3.67425i
$731$	−7.60858	+	13.1784i	−0.281414	+	0.487422i
$732$	−36.9548	−	64.0076i	−1.36589	−	2.36579i
$733$	21.7698	−	37.7063i	0.804085	−	1.39272i	−0.112823	−	0.993615i	$-0.535989\pi$
$733$	21.7698	−	37.7063i	0.804085	−	1.39272i	0.916907	−	0.399100i	$-0.130677\pi$
$734$	15.4710	−	26.7965i	0.571043	−	0.989076i
$735$	11.9775	−	20.7456i	0.441796	−	0.765214i
$736$	−120.025			−4.42419
$737$	0.525166	+	0.909614i	0.0193447	+	0.0335061i
$738$	−12.6182	−	21.8553i	−0.464481	−	0.804505i
$739$	−12.4726	+	21.6033i	−0.458814	+	0.794689i	−0.998899	−	0.0469219i	$-0.985059\pi$
$739$	−12.4726	+	21.6033i	−0.458814	+	0.794689i	0.540085	+	0.841611i	$0.318392\pi$
$740$	−110.615			−4.06629
$741$	0.978728	+	1.69521i	0.0359545	+	0.0622750i
$742$	−6.09175			−0.223635
$743$	−43.6974			−1.60310			−0.801552	−	0.597925i	$-0.795992\pi$
$743$	−43.6974			−1.60310			−0.801552	+	0.597925i	$0.795992\pi$
$744$	52.2020	+	16.2339i	1.91382	+	0.595162i
$745$	12.8656			0.471359
$746$	−65.3288			−2.39186
$747$	1.13308	+	1.96254i	0.0414571	+	0.0718057i
$748$	−6.18759			−0.226241
$749$	4.58394	−	7.93963i	0.167494	−	0.290108i
$750$	−34.8848	−	60.4223i	−1.27381	−	2.20631i
$751$	3.42892	+	5.93906i	0.125123	+	0.216719i	0.921781	−	0.387711i	$-0.126734\pi$
$751$	3.42892	+	5.93906i	0.125123	+	0.216719i	−0.796658	+	0.604430i	$0.793401\pi$
$752$	−39.4858			−1.43990
$753$	5.23916	−	9.07449i	0.190926	−	0.330693i
$754$	11.6925	−	20.2520i	0.425815	−	0.737533i
$755$	11.9427	−	20.6853i	0.434639	−	0.752816i
$756$	11.6306	+	20.1448i	0.423001	+	0.732659i
$757$	−3.81100	+	6.60085i	−0.138513	+	0.239912i	−0.926934	−	0.375224i	$-0.877566\pi$
$757$	−3.81100	+	6.60085i	−0.138513	+	0.239912i	0.788421	+	0.615136i	$0.210899\pi$
$758$	−34.2010	−	59.2379i	−1.24224	−	2.15162i
$759$	1.02411			0.0371727
$760$	−89.4773			−3.24568
$761$	−14.7629	−	25.5701i	−0.535156	−	0.926917i	−0.999156	−	0.0410815i	$-0.986920\pi$
$761$	−14.7629	−	25.5701i	−0.535156	−	0.926917i	0.464000	−	0.885835i	$-0.346414\pi$
$762$	−6.62705	+	11.4784i	−0.240073	+	0.415818i
$763$	−0.648394	−	1.12305i	−0.0234734	−	0.0406572i
$764$	−18.5141	+	32.0673i	−0.669815	+	1.16015i
$765$	17.9096	−	31.0203i	0.647522	−	1.12154i
$766$	−50.1777	+	86.9103i	−1.81299	+	3.14020i
$767$	−7.30908			−0.263915
$768$	−43.8509	−	75.9519i	−1.58233	−	2.74068i
$769$	21.0746	+	36.5022i	0.759968	+	1.31630i	0.942866	+	0.333171i	$0.108119\pi$
$769$	21.0746	+	36.5022i	0.759968	+	1.31630i	−0.182898	+	0.983132i	$0.558548\pi$
$770$	1.23737	−	2.14319i	0.0445917	−	0.0772351i
$771$	4.43230			0.159626
$772$	43.2903	+	74.9810i	1.55805	+	2.69863i
$773$	−14.7440			−0.530306			−0.265153	−	0.964206i	$-0.585423\pi$
$773$	−14.7440			−0.530306			−0.265153	+	0.964206i	$0.585423\pi$
$774$	−21.7774			−0.782772
$775$	61.5416	+	19.1383i	2.21064	+	0.687469i
$776$	9.93031			0.356477
$777$	−3.70705			−0.132990
$778$	8.29988	+	14.3758i	0.297565	+	0.515398i
$779$	8.91746			0.319501
$780$	−10.9789	+	19.0160i	−0.393107	+	0.680881i
$781$	0.233485	+	0.404408i	0.00835476	+	0.0144709i
$782$	24.3709	+	42.2117i	0.871502	+	1.50949i
$783$	40.2177			1.43726
$784$	55.7701	−	96.5966i	1.99179	−	3.44988i
$785$	5.12143	−	8.87059i	0.182792	−	0.316605i
$786$	−15.7825	+	27.3361i	−0.562943	+	0.975046i
$787$	19.1135	+	33.1055i	0.681321	+	1.18008i	0.974578	+	0.224050i	$0.0719277\pi$
$787$	19.1135	+	33.1055i	0.681321	+	1.18008i	−0.293256	+	0.956034i	$0.594739\pi$
$788$	26.4618	−	45.8332i	0.942662	−	1.63274i
$789$	−8.91532	−	15.4418i	−0.317394	−	0.549742i
$790$	−182.874			−6.50638
$791$	8.00097			0.284482
$792$	−2.89217	−	5.00938i	−0.102769	−	0.178000i
$793$	−6.85195	+	11.8679i	−0.243320	+	0.421442i
$794$	−26.9341	−	46.6513i	−0.955856	−	1.65559i
$795$	4.94479	−	8.56463i	0.175374	−	0.303756i
$796$	11.6047	−	20.0999i	0.411318	−	0.712423i
$797$	−23.8960	+	41.3891i	−0.846439	+	1.46608i	0.0379258	+	0.999281i	$0.487925\pi$
$797$	−23.8960	+	41.3891i	−0.846439	+	1.46608i	−0.884365	+	0.466796i	$0.845408\pi$
$798$	−4.59059			−0.162505
$799$	4.60986	+	7.98450i	0.163085	+	0.282471i
$800$	−164.413	−	284.771i	−5.81286	−	10.0682i
$801$	−0.813456	+	1.40895i	−0.0287421	+	0.0497827i
$802$	48.8778			1.72593
$803$	−1.30926	−	2.26770i	−0.0462027	−	0.0800254i
$804$	21.8555			0.770784
$805$	−14.4748			−0.510170
$806$	−3.41810	−	15.1362i	−0.120397	−	0.533149i
$807$	−6.51207			−0.229236
$808$	−147.201			−5.17851
$809$	7.72721	+	13.3839i	0.271674	+	0.470553i	0.969291	−	0.245918i	$-0.0790894\pi$
$809$	7.72721	+	13.3839i	0.271674	+	0.470553i	−0.697617	+	0.716471i	$0.745756\pi$
$810$	21.4930			0.755186
$811$	−10.3999	+	18.0132i	−0.365191	+	0.632530i	−0.988807	−	0.149201i	$-0.952330\pi$
$811$	−10.3999	+	18.0132i	−0.365191	+	0.632530i	0.623616	+	0.781731i	$0.285663\pi$
$812$	20.3604	+	35.2652i	0.714509	+	1.23757i
$813$	−2.50215	−	4.33385i	−0.0877542	−	0.151995i
$814$	3.40303			0.119276
$815$	−3.50938	+	6.07842i	−0.122928	+	0.212918i
$816$	−34.3102	+	59.4270i	−1.20110	+	2.08036i
$817$	3.84761	−	6.66425i	0.134611	−	0.233153i
$818$	9.32169	+	16.1456i	0.325925	+	0.564519i
$819$	0.894273	−	1.54893i	0.0312484	−	0.0541239i
$820$	50.0157	+	86.6298i	1.74663	+	3.02524i
$821$	30.8594			1.07700			0.538500	−	0.842626i	$-0.318991\pi$
$821$	30.8594			1.07700			0.538500	+	0.842626i	$0.318991\pi$
$822$	−2.70460			−0.0943337
$823$	20.7278	+	35.9016i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903518\pi$
$823$	20.7278	+	35.9016i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$824$	−6.24383	+	10.8146i	−0.217514	+	0.376745i
$825$	1.40284	+	2.42979i	0.0488405	+	0.0845943i
$826$	8.57055	−	14.8446i	0.298207	−	0.516510i
$827$	15.7638	−	27.3037i	0.548161	−	0.949443i	−0.450240	−	0.892908i	$-0.648661\pi$
$827$	15.7638	−	27.3037i	0.548161	−	0.949443i	0.998401	−	0.0565349i	$-0.0180052\pi$
$828$	−25.8969	+	44.8547i	−0.899979	+	1.55881i
$829$	0.671471			0.0233212			0.0116606	−	0.999932i	$-0.496288\pi$
$829$	0.671471			0.0233212			0.0116606	+	0.999932i	$0.496288\pi$
$830$	−6.04876	−	10.4768i	−0.209955	−	0.363653i
$831$	0.0169129	+	0.0292940i	0.000586702	+	0.00101620i
$832$	−21.8581	+	37.8593i	−0.757793	+	1.31254i
$833$	−26.0440			−0.902371
$834$	−23.2863	−	40.3331i	−0.806339	−	1.39662i
$835$	77.6846			2.68839
$836$	3.12902			0.108220
$837$	19.6046	−	18.1066i	0.677634	−	0.625856i
$838$	84.6059			2.92266
$839$	33.9195			1.17103			0.585516	−	0.810661i	$-0.300892\pi$
$839$	33.9195			1.17103			0.585516	+	0.810661i	$0.300892\pi$
$840$	−16.8187	−	29.1309i	−0.580301	−	1.00511i
$841$	41.4046			1.42775
$842$	44.2713	−	76.6802i	1.52569	−	2.64258i
$843$	4.83481	+	8.37413i	0.166520	+	0.288421i
$844$	−61.8410	−	107.112i	−2.12865	−	3.68694i
$845$	4.07128			0.140056
$846$	−6.59720	+	11.4267i	−0.226816	+	0.392857i
$847$	4.59983	−	7.96715i	0.158052	−	0.273754i
$848$	23.0241	−	39.8790i	0.790653	−	1.36945i
$849$	13.9263	+	24.1211i	0.477950	+	0.827833i
$850$	−66.7673	+	115.644i	−2.29010	+	3.96657i
$851$	−9.95221	−	17.2377i	−0.341158	−	0.590902i
$852$	9.71681			0.332893
$853$	9.67616			0.331305			0.165653	−	0.986184i	$-0.447027\pi$
$853$	9.67616			0.331305			0.165653	+	0.986184i	$0.447027\pi$
$854$	−16.0690	−	27.8324i	−0.549871	−	0.952405i
$855$	−9.05675	+	15.6867i	−0.309734	+	0.536475i
$856$	57.1966	+	99.0674i	1.95494	+	3.38605i
$857$	−7.04521	+	12.2027i	−0.240660	+	0.416835i	−0.960902	−	0.276887i	$-0.910697\pi$
$857$	−7.04521	+	12.2027i	−0.240660	+	0.416835i	0.720242	+	0.693722i	$0.244031\pi$
$858$	0.337761	−	0.585019i	0.0115310	−	0.0199722i
$859$	−2.83084	+	4.90317i	−0.0965871	+	0.167294i	−0.910270	−	0.414015i	$-0.864126\pi$
$859$	−2.83084	+	4.90317i	−0.0965871	+	0.167294i	0.813683	+	0.581309i	$0.197459\pi$
$860$	86.3210			2.94352
$861$	1.67618	+	2.90323i	0.0571241	+	0.0989419i
$862$	−36.0111	−	62.3731i	−1.22654	−	2.12444i
$863$	0.615440	−	1.06597i	0.0209498	−	0.0362861i	−0.855360	−	0.518033i	$-0.826664\pi$
$863$	0.615440	−	1.06597i	0.0209498	−	0.0362861i	0.876310	+	0.481747i	$0.159998\pi$
$864$	−136.160			−4.63224
$865$	16.3360	+	28.2948i	0.555441	+	0.962052i
$866$	−77.9928			−2.65030
$867$	0.124912			0.00424224
$868$	25.8018	+	8.02390i	0.875771	+	0.272349i
$869$	4.17742			0.141709
$870$	−89.0326			−3.01849
$871$	−2.02616	−	3.50942i	−0.0686539	−	0.118912i
$872$	16.1808			0.547951
$873$	1.00513	−	1.74094i	0.0340185	−	0.0589218i
$874$	−12.3242	−	21.3462i	−0.416872	−	0.722044i
$875$	−11.2631	−	19.5083i	−0.380764	−	0.659502i
$876$	−54.4865			−1.84093
$877$	20.3609	−	35.2661i	0.687538	−	1.19085i	−0.285094	−	0.958499i	$-0.592025\pi$
$877$	20.3609	−	35.2661i	0.687538	−	1.19085i	0.972632	−	0.232351i	$-0.0746418\pi$
$878$	−9.00059	+	15.5895i	−0.303755	+	0.526119i
$879$	3.75669	−	6.50677i	0.126710	−	0.219468i
$880$	9.35344	+	16.2006i	0.315304	+	0.546123i
$881$	4.89783	−	8.48330i	0.165012	−	0.285810i	−0.771647	−	0.636051i	$-0.780567\pi$
$881$	4.89783	−	8.48330i	0.165012	−	0.285810i	0.936660	+	0.350241i	$0.113900\pi$
$882$	−18.6359	−	32.2783i	−0.627502	−	1.08687i
$883$	25.4991			0.858113			0.429057	−	0.903278i	$-0.358846\pi$
$883$	25.4991			0.858113			0.429057	+	0.903278i	$0.358846\pi$
$884$	23.8726			0.802922
$885$	13.9138	+	24.0994i	0.467706	+	0.810091i
$886$	26.9077	−	46.6056i	0.903983	−	1.56575i
$887$	−17.8476	−	30.9129i	−0.599263	−	1.03795i	−0.992930	−	0.118701i	$-0.962127\pi$
$887$	−17.8476	−	30.9129i	−0.599263	−	1.03795i	0.393667	−	0.919253i	$-0.371206\pi$
$888$	23.1276	−	40.0581i	0.776110	−	1.34426i
$889$	−2.13965	+	3.70598i	−0.0717616	+	0.124295i
$890$	4.34252	−	7.52146i	0.145561	−	0.252120i
$891$	−0.490966			−0.0164480
$892$	−33.3655	−	57.7908i	−1.11716	−	1.93498i
$893$	−2.33117	−	4.03771i	−0.0780097	−	0.135117i
$894$	−4.11799	+	7.13258i	−0.137726	+	0.238549i
$895$	−79.1790			−2.64666
$896$	−27.3571	−	47.3839i	−0.913937	−	1.58299i
$897$	−3.95115			−0.131925
$898$	−49.1620			−1.64056
$899$	34.3195	−	31.6972i	1.14462	−	1.05716i
$900$	−141.896			−4.72986
$901$	−10.7520			−0.358201
$902$	−1.53872	−	2.66513i	−0.0512336	−	0.0887393i
$903$	2.89288			0.0962691
$904$	−49.9164	+	86.4578i	−1.66020	+	2.87554i
$905$	−27.2841	−	47.2574i	−0.906954	−	1.57089i
$906$	7.64518	+	13.2418i	0.253994	+	0.439931i
$907$	−46.2981			−1.53730			−0.768652	−	0.639667i	$-0.779072\pi$
$907$	−46.2981			−1.53730			−0.768652	+	0.639667i	$0.779072\pi$
$908$	−28.5219	+	49.4014i	−0.946534	+	1.63944i
$909$	−14.8994	+	25.8066i	−0.494183	+	0.855950i
$910$	−4.77394	+	8.26871i	−0.158255	+	0.274105i
$911$	−5.40701	−	9.36522i	−0.179142	−	0.310284i	0.762445	−	0.647053i	$-0.223999\pi$
$911$	−5.40701	−	9.36522i	−0.179142	−	0.310284i	−0.941587	+	0.336770i	$0.890666\pi$
$912$	17.3504	−	30.0518i	0.574530	−	0.995115i
$913$	0.138172	+	0.239321i	0.00457284	+	0.00792039i
$914$	92.5503			3.06129
$915$	52.1743			1.72483
$916$	49.4986	+	85.7342i	1.63548	+	2.83274i
$917$	−5.09564	+	8.82590i	−0.168273	+	0.291457i
$918$	27.6469	+	47.8859i	0.912485	+	1.58047i
$919$	−24.5952	+	42.6001i	−0.811321	+	1.40525i	0.100619	+	0.994925i	$0.467918\pi$
$919$	−24.5952	+	42.6001i	−0.811321	+	1.40525i	−0.911940	+	0.410323i	$0.865416\pi$
$920$	90.3054	−	156.414i	2.97728	−	5.15680i
$921$	−2.17464	+	3.76659i	−0.0716570	+	0.124114i
$922$	43.3002			1.42602
$923$	−0.900818	−	1.56026i	−0.0296508	−	0.0513567i
$924$	0.588151	+	1.01871i	0.0193488	+	0.0335130i
$925$	27.2654	−	47.2250i	0.896480	−	1.55275i
$926$	−42.1754			−1.38597
$927$	1.26398	+	2.18928i	0.0415145	+	0.0719053i
$928$	−238.359			−7.82452
$929$	−29.6457			−0.972643			−0.486321	−	0.873780i	$-0.661662\pi$
$929$	−29.6457			−0.972643			−0.486321	+	0.873780i	$0.661662\pi$
$930$	−43.4000	+	40.0838i	−1.42314	+	1.31440i
$931$	13.1703			0.431638
$932$	113.895			3.73076
$933$	3.12185	+	5.40720i	0.102205	+	0.177024i
$934$	10.9261			0.357513
$935$	2.18397	−	3.78275i	0.0714236	−	0.123709i
$936$	11.1584	+	19.3269i	0.364723	+	0.631718i
$937$	−10.7198	−	18.5672i	−0.350201	−	0.606565i	0.636084	−	0.771620i	$-0.280553\pi$
$937$	−10.7198	−	18.5672i	−0.350201	−	0.606565i	−0.986284	+	0.165055i	$0.947220\pi$
$938$	9.50343			0.310298
$939$	−5.98466	+	10.3657i	−0.195302	+	0.338273i
$940$	26.1499	−	45.2929i	0.852916	−	1.47729i
$941$	9.36725	−	16.2246i	0.305364	−	0.528906i	−0.671978	−	0.740571i	$-0.734555\pi$
$941$	9.36725	−	16.2246i	0.305364	−	0.528906i	0.977342	+	0.211665i	$0.0678886\pi$
$942$	3.27852	+	5.67856i	0.106820	+	0.185018i
$943$	−8.99999	+	15.5884i	−0.293080	+	0.507629i
$944$	64.7859	+	112.212i	2.10860	+	3.65220i
$945$	−16.4206			−0.534161
$946$	−2.65563			−0.0863421
$947$	−18.9349	−	32.7962i	−0.615302	−	1.06573i	−0.990331	−	0.138722i	$-0.955701\pi$
$947$	−18.9349	−	32.7962i	−0.615302	−	1.06573i	0.375029	−	0.927013i	$-0.377633\pi$
$948$	43.4622	−	75.2788i	1.41159	−	2.44494i
$949$	5.05129	+	8.74910i	0.163972	+	0.284008i
$950$	33.7638	−	58.4806i	1.09544	−	1.89736i
$951$	−4.73640	+	8.20369i	−0.153588	+	0.266023i
$952$	−18.2854	+	31.6713i	−0.592634	+	1.02647i
$953$	31.5233			1.02114			0.510570	−	0.859836i	$-0.329435\pi$
$953$	31.5233			1.02114			0.510570	+	0.859836i	$0.329435\pi$
$954$	−7.69364	−	13.3258i	−0.249091	−	0.431438i
$955$	−13.0695	−	22.6370i	−0.422918	−	0.732515i
$956$	−75.7243	+	131.158i	−2.44910	+	4.24197i
$957$	2.03378			0.0657428
$958$	55.1762	+	95.5680i	1.78266	+	3.08766i
$959$	−0.873224			−0.0281979
$960$	166.439			5.37179
$961$	2.45892	−	30.9023i	0.0793199	−	0.996849i
$962$	−13.1294			−0.423308
$963$	23.1574			0.746236
$964$	−53.2580	−	92.2456i	−1.71532	−	2.97103i
$965$	−61.1191			−1.96749
$966$	4.63307	−	8.02472i	0.149067	−	0.258191i
$967$	−23.6774	−	41.0105i	−0.761415	−	1.31881i	−0.942121	−	0.335272i	$-0.891172\pi$
$967$	−23.6774	−	41.0105i	−0.761415	−	1.31881i	0.180706	−	0.983537i	$-0.442162\pi$
$968$	57.3948	+	99.4108i	1.84474	+	3.19518i
$969$	−8.10245			−0.260288
$970$	−5.36574	+	9.29373i	−0.172283	+	0.298404i
$971$	−12.6334	+	21.8817i	−0.405425	+	0.702217i	−0.994371	−	0.105956i	$-0.966210\pi$
$971$	−12.6334	+	21.8817i	−0.405425	+	0.702217i	0.588946	+	0.808173i	$0.299543\pi$
$972$	−46.5732	+	80.6672i	−1.49384	+	2.58740i
$973$	−7.51837	−	13.0222i	−0.241028	−	0.417472i
$974$	−0.944305	+	1.63558i	−0.0302575	+	0.0524075i
$975$	−5.41234	−	9.37445i	−0.173334	−	0.300223i
$976$	242.936			7.77619
$977$	−14.5751			−0.466298			−0.233149	−	0.972441i	$-0.574903\pi$
$977$	−14.5751			−0.466298			−0.233149	+	0.972441i	$0.574903\pi$
$978$	−2.24655	−	3.89114i	−0.0718367	−	0.124425i
$979$	−0.0991965	+	0.171813i	−0.00317033	+	0.00549118i
$980$	73.8686	+	127.944i	2.35965	+	4.08703i
$981$	1.63779	−	2.83674i	0.0522907	−	0.0905702i
$982$	−26.0940	+	45.1962i	−0.832694	+	1.44227i
$983$	−5.64016	+	9.76904i	−0.179893	+	0.311584i	−0.941844	−	0.336051i	$-0.890908\pi$
$983$	−5.64016	+	9.76904i	−0.179893	+	0.311584i	0.761951	+	0.647635i	$0.224242\pi$
$984$	−41.8294			−1.33347
$985$	18.6799	+	32.3546i	0.595192	+	1.03090i
$986$	48.3984	+	83.8284i	1.54132	+	2.66964i
$987$	0.876364	−	1.51791i	0.0278950	−	0.0483155i
$988$	−12.0722			−0.384068
$989$	7.76643	+	13.4519i	0.246958	+	0.427744i
$990$	6.25100			0.198670
$991$	−54.6438			−1.73582			−0.867908	−	0.496725i	$-0.834536\pi$
$991$	−54.6438			−1.73582			−0.867908	+	0.496725i	$0.834536\pi$
$992$	−116.191	+	107.313i	−3.68907	+	3.40718i
$993$	1.29791			0.0411879
$994$	4.22516			0.134014
$995$	8.19200	+	14.1890i	0.259704	+	0.449820i
$996$	5.75023			0.182203
$997$	22.5604	−	39.0757i	0.714494	−	1.23754i	−0.248660	−	0.968591i	$-0.579990\pi$
$997$	22.5604	−	39.0757i	0.714494	−	1.23754i	0.963154	−	0.268949i	$-0.0866763\pi$
$998$	34.2255	+	59.2804i	1.08339	+	1.87649i
$999$	−11.2900	−	19.5549i	−0.357201	−	0.618689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.17	✓	34
31.5	even	3	inner	403.2.h.b.222.17	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.17	✓	34	1.1	even	1	trivial
403.2.h.b.222.17	yes	34	31.5	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +O(q^{10})\)	\(q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +(-5.67332 + 9.82648i) q^{10} +(0.129596 - 0.224467i) q^{11} +(-2.69666 - 4.67076i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.17259 - 2.03098i) q^{14} +3.80726 q^{15} +17.7275 q^{16} +(-2.06964 - 3.58471i) q^{17} +(2.96187 - 5.13011i) q^{18} +(1.04660 + 1.81277i) q^{19} +(-11.7402 + 20.3347i) q^{20} +(-0.393451 + 0.681478i) q^{21} +(0.361184 - 0.625589i) q^{22} -4.22515 q^{23} +(-4.90933 - 8.50320i) q^{24} +(-5.78767 - 10.0245i) q^{25} +(-1.39350 + 2.41361i) q^{26} -4.79311 q^{27} +(-2.42653 - 4.20287i) q^{28} -8.39075 q^{29} +10.6108 q^{30} +(-4.09017 + 3.77764i) q^{31} +28.4074 q^{32} -0.242384 q^{33} +(-5.76806 - 9.99058i) q^{34} +3.42587 q^{35} +(6.12922 - 10.6161i) q^{36} +(2.35547 + 4.07980i) q^{37} +(2.91687 + 5.05217i) q^{38} +0.935150 q^{39} +(-21.3733 + 37.0197i) q^{40} +(2.13010 - 3.68944i) q^{41} +(-1.09655 + 1.89928i) q^{42} +(-1.83814 - 3.18376i) q^{43} +(0.747425 - 1.29458i) q^{44} +(4.32675 + 7.49414i) q^{45} -11.7755 q^{46} -2.22737 q^{47} +(-8.28894 - 14.3569i) q^{48} +(3.14596 - 5.44897i) q^{49} +(-16.1302 - 27.9383i) q^{50} +(-1.93542 + 3.35225i) q^{51} +(-2.88367 + 4.99466i) q^{52} +(1.29878 - 2.24955i) q^{53} -13.3584 q^{54} +(0.527623 + 0.913870i) q^{55} +(-4.41754 - 7.65141i) q^{56} +(0.978728 - 1.69521i) q^{57} -23.3850 q^{58} +(3.65454 + 6.32984i) q^{59} +21.9578 q^{60} +13.7039 q^{61} +(-11.3993 + 10.5283i) q^{62} -1.78855 q^{63} +43.7162 q^{64} +(-2.03564 - 3.52583i) q^{65} -0.675522 q^{66} +(-2.02616 + 3.50942i) q^{67} +(-11.9363 - 20.6743i) q^{68} +(1.97557 + 3.42179i) q^{69} +9.54789 q^{70} +(-0.900818 + 1.56026i) q^{71} +(11.1584 - 19.3269i) q^{72} +(5.05129 - 8.74910i) q^{73} +(6.56469 + 11.3704i) q^{74} +(-5.41234 + 9.37445i) q^{75} +(6.03610 + 10.4548i) q^{76} -0.218103 q^{77} +2.60626 q^{78} +(8.05852 + 13.9578i) q^{79} +(-36.0869 + 62.5043i) q^{80} +(-0.947107 - 1.64044i) q^{81} +(5.93658 - 10.2825i) q^{82} +(-0.533088 + 0.923335i) q^{83} +(-2.26917 + 3.93031i) q^{84} +16.8521 q^{85} +(-5.12290 - 8.87312i) q^{86} +(3.92330 + 6.79536i) q^{87} +(1.36070 - 2.35681i) q^{88} -0.765428 q^{89} +(12.0586 + 20.8861i) q^{90} +0.841473 q^{91} -24.3679 q^{92} +(4.97183 + 1.54615i) q^{93} -6.20768 q^{94} -8.52201 q^{95} +(-13.2826 - 23.0061i) q^{96} +0.945784 q^{97} +(8.76778 - 15.1862i) q^{98} +(-0.275456 - 0.477104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more