LMFDB - Embedded newform 387.2.f.d.259.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			259.2
Character	$\chi$	$=$	387.259
Dual form			387.2.f.d.130.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04491 + 1.80984i) q^{2} +(1.25718 - 1.19142i) q^{3} +(-1.18368 - 2.05019i) q^{4} +(-0.136674 - 0.236726i) q^{5} +(0.842638 + 3.52023i) q^{6} +(1.21012 - 2.09599i) q^{7} +0.767710 q^{8} +(0.161024 - 2.99568i) q^{9} +O(q^{10})$	\(q+(-1.04491 + 1.80984i) q^{2} +(1.25718 - 1.19142i) q^{3} +(-1.18368 - 2.05019i) q^{4} +(-0.136674 - 0.236726i) q^{5} +(0.842638 + 3.52023i) q^{6} +(1.21012 - 2.09599i) q^{7} +0.767710 q^{8} +(0.161024 - 2.99568i) q^{9} +0.571248 q^{10} +(0.799468 - 1.38472i) q^{11} +(-3.93075 - 1.16721i) q^{12} +(-1.73339 - 3.00232i) q^{13} +(2.52893 + 4.38024i) q^{14} +(-0.453865 - 0.134772i) q^{15} +(1.56517 - 2.71095i) q^{16} -3.58535 q^{17} +(5.25343 + 3.42164i) q^{18} +0.324858 q^{19} +(-0.323556 + 0.560415i) q^{20} +(-0.975863 - 4.07680i) q^{21} +(1.67075 + 2.89382i) q^{22} +(2.17572 + 3.76846i) q^{23} +(0.965152 - 0.914667i) q^{24} +(2.46264 - 4.26542i) q^{25} +7.24495 q^{26} +(-3.36668 - 3.95796i) q^{27} -5.72956 q^{28} +(2.99685 - 5.19069i) q^{29} +(0.718164 - 0.680598i) q^{30} +(0.950453 + 1.64623i) q^{31} +(4.03863 + 6.99512i) q^{32} +(-0.644707 - 2.69335i) q^{33} +(3.74637 - 6.48891i) q^{34} -0.661566 q^{35} +(-6.33231 + 3.21579i) q^{36} +2.23031 q^{37} +(-0.339448 + 0.587942i) q^{38} +(-5.75622 - 1.70927i) q^{39} +(-0.104926 - 0.181737i) q^{40} +(5.20786 + 9.02028i) q^{41} +(8.39804 + 2.49374i) q^{42} +(0.500000 - 0.866025i) q^{43} -3.78525 q^{44} +(-0.731163 + 0.371312i) q^{45} -9.09374 q^{46} +(-4.35738 + 7.54720i) q^{47} +(-1.26218 - 5.27294i) q^{48} +(0.571231 + 0.989401i) q^{49} +(5.14648 + 8.91397i) q^{50} +(-4.50745 + 4.27167i) q^{51} +(-4.10355 + 7.10756i) q^{52} +4.52956 q^{53} +(10.6812 - 1.95743i) q^{54} -0.437066 q^{55} +(0.929019 - 1.60911i) q^{56} +(0.408407 - 0.387044i) q^{57} +(6.26287 + 10.8476i) q^{58} +(-4.95329 - 8.57935i) q^{59} +(0.260922 + 1.09004i) q^{60} +(-5.50849 + 9.54098i) q^{61} -3.97256 q^{62} +(-6.08403 - 3.96262i) q^{63} -10.6194 q^{64} +(-0.473818 + 0.820677i) q^{65} +(5.54819 + 1.64750i) q^{66} +(2.86882 + 4.96894i) q^{67} +(4.24390 + 7.35065i) q^{68} +(7.22511 + 2.14544i) q^{69} +(0.691278 - 1.19733i) q^{70} +6.74222 q^{71} +(0.123620 - 2.29981i) q^{72} +0.832499 q^{73} +(-2.33048 + 4.03650i) q^{74} +(-1.98592 - 8.29646i) q^{75} +(-0.384528 - 0.666022i) q^{76} +(-1.93490 - 3.35135i) q^{77} +(9.10824 - 8.63180i) q^{78} +(4.00799 - 6.94204i) q^{79} -0.855671 q^{80} +(-8.94814 - 0.964752i) q^{81} -21.7670 q^{82} +(3.40533 - 5.89820i) q^{83} +(-7.20311 + 6.82633i) q^{84} +(0.490024 + 0.848746i) q^{85} +(1.04491 + 1.80984i) q^{86} +(-2.41672 - 10.0962i) q^{87} +(0.613759 - 1.06306i) q^{88} -9.69164 q^{89} +(0.0919848 - 1.71127i) q^{90} -8.39042 q^{91} +(5.15071 - 8.92129i) q^{92} +(3.15625 + 0.937227i) q^{93} +(-9.10615 - 15.7723i) q^{94} +(-0.0443997 - 0.0769025i) q^{95} +(13.4114 + 3.98243i) q^{96} +(-0.848918 + 1.47037i) q^{97} -2.38754 q^{98} +(-4.01943 - 2.61792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) $ 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.04491	+	1.80984i	−0.738864	+	1.27975i	0.214144	+	0.976802i	$0.431304\pi$
$2$	−1.04491	+	1.80984i	−0.738864	+	1.27975i	−0.953007	+	0.302947i	$0.902029\pi$
$3$	1.25718	−	1.19142i	0.725836	−	0.687868i
$3$	1.25718	−	1.19142i	0.725836	−	0.687868i
$4$	−1.18368	−	2.05019i	−0.591839	−	1.02510i
$5$	−0.136674	−	0.236726i	−0.0611224	−	0.105867i	0.833845	−	0.551999i	$-0.186135\pi$
$5$	−0.136674	−	0.236726i	−0.0611224	−	0.105867i	−0.894967	+	0.446132i	$0.852801\pi$
$6$	0.842638	+	3.52023i	0.344005	+	1.43713i
$7$	1.21012	−	2.09599i	0.457381	−	0.792208i	−0.541440	−	0.840739i	$-0.682121\pi$
$7$	1.21012	−	2.09599i	0.457381	−	0.792208i	0.998822	+	0.0485314i	$0.0154541\pi$
$8$	0.767710			0.271426
$9$	0.161024	−	2.99568i	0.0536747	−	0.998558i
$10$	0.571248			0.180645
$11$	0.799468	−	1.38472i	0.241049	−	0.417508i	−0.719965	−	0.694011i	$-0.755842\pi$
$11$	0.799468	−	1.38472i	0.241049	−	0.417508i	0.961013	+	0.276502i	$0.0891753\pi$
$12$	−3.93075	−	1.16721i	−1.13471	−	0.336943i
$13$	−1.73339	−	3.00232i	−0.480756	−	0.832693i	0.519000	−	0.854774i	$-0.326304\pi$
$13$	−1.73339	−	3.00232i	−0.480756	−	0.832693i	−0.999756	+	0.0220806i	$0.992971\pi$
$14$	2.52893	+	4.38024i	0.675885	+	1.17067i
$15$	−0.453865	−	0.134772i	−0.117187	−	0.0347980i
$16$	1.56517	−	2.71095i	0.391292	−	0.677738i
$17$	−3.58535			−0.869575			−0.434788	−	0.900533i	$-0.643177\pi$
$17$	−3.58535			−0.869575			−0.434788	+	0.900533i	$0.643177\pi$
$18$	5.25343	+	3.42164i	1.23825	+	0.806489i
$19$	0.324858			0.0745276			0.0372638	−	0.999305i	$-0.488136\pi$
$19$	0.324858			0.0745276			0.0372638	+	0.999305i	$0.488136\pi$
$20$	−0.323556	+	0.560415i	−0.0723493	+	0.125313i
$21$	−0.975863	−	4.07680i	−0.212951	−	0.889631i
$22$	1.67075	+	2.89382i	0.356204	+	0.616964i
$23$	2.17572	+	3.76846i	0.453669	+	0.785778i	0.998611	−	0.0526959i	$-0.0167814\pi$
$23$	2.17572	+	3.76846i	0.453669	+	0.785778i	−0.544941	+	0.838474i	$0.683448\pi$
$24$	0.965152	−	0.914667i	0.197011	−	0.186706i
$25$	2.46264	−	4.26542i	0.492528	−	0.853084i
$26$	7.24495			1.42085
$27$	−3.36668	−	3.95796i	−0.647918	−	0.761710i
$28$	−5.72956			−1.08278
$29$	2.99685	−	5.19069i	0.556500	−	0.963887i	−0.441285	−	0.897367i	$-0.645477\pi$
$29$	2.99685	−	5.19069i	0.556500	−	0.963887i	0.997785	−	0.0665197i	$-0.0211895\pi$
$30$	0.718164	−	0.680598i	0.131118	−	0.124260i
$31$	0.950453	+	1.64623i	0.170706	+	0.295672i	0.938667	−	0.344825i	$-0.112062\pi$
$31$	0.950453	+	1.64623i	0.170706	+	0.295672i	−0.767961	+	0.640497i	$0.778728\pi$
$32$	4.03863	+	6.99512i	0.713936	+	1.23657i
$33$	−0.644707	−	2.69335i	−0.112229	−	0.468852i
$34$	3.74637	−	6.48891i	0.642498	−	1.11284i
$35$	−0.661566			−0.111825
$36$	−6.33231	+	3.21579i	−1.05538	+	0.535964i
$37$	2.23031			0.366661			0.183330	−	0.983051i	$-0.441312\pi$
$37$	2.23031			0.366661			0.183330	+	0.983051i	$0.441312\pi$
$38$	−0.339448	+	0.587942i	−0.0550658	+	0.0953767i
$39$	−5.75622	−	1.70927i	−0.921733	−	0.273702i
$40$	−0.104926	−	0.181737i	−0.0165902	−	0.0287351i
$41$	5.20786	+	9.02028i	0.813331	+	1.40873i	0.910520	+	0.413465i	$0.135682\pi$
$41$	5.20786	+	9.02028i	0.813331	+	1.40873i	−0.0971886	+	0.995266i	$0.530985\pi$
$42$	8.39804	+	2.49374i	1.29585	+	0.384792i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$44$	−3.78525			−0.570648
$45$	−0.731163	+	0.371312i	−0.108995	+	0.0553519i
$46$	−9.09374			−1.34080
$47$	−4.35738	+	7.54720i	−0.635589	+	1.10087i	0.350801	+	0.936450i	$0.385909\pi$
$47$	−4.35738	+	7.54720i	−0.635589	+	1.10087i	−0.986390	+	0.164422i	$0.947424\pi$
$48$	−1.26218	−	5.27294i	−0.182180	−	0.761084i
$49$	0.571231	+	0.989401i	0.0816044	+	0.141343i
$50$	5.14648	+	8.91397i	0.727822	+	1.26063i
$51$	−4.50745	+	4.27167i	−0.631169	+	0.598153i
$52$	−4.10355	+	7.10756i	−0.569060	+	0.985641i
$53$	4.52956			0.622182			0.311091	−	0.950380i	$-0.399306\pi$
$53$	4.52956			0.622182			0.311091	+	0.950380i	$0.399306\pi$
$54$	10.6812	−	1.95743i	1.45352	−	0.266372i
$55$	−0.437066			−0.0589339
$56$	0.929019	−	1.60911i	0.124145	−	0.215026i
$57$	0.408407	−	0.387044i	0.0540948	−	0.0512652i
$58$	6.26287	+	10.8476i	0.822356	+	1.42436i
$59$	−4.95329	−	8.57935i	−0.644864	−	1.11694i	−0.984333	−	0.176320i	$-0.943581\pi$
$59$	−4.95329	−	8.57935i	−0.644864	−	1.11694i	0.339469	−	0.940617i	$-0.389753\pi$
$60$	0.260922	+	1.09004i	0.0336849	+	0.140723i
$61$	−5.50849	+	9.54098i	−0.705289	+	1.22160i	0.261298	+	0.965258i	$0.415850\pi$
$61$	−5.50849	+	9.54098i	−0.705289	+	1.22160i	−0.966587	+	0.256339i	$0.917484\pi$
$62$	−3.97256			−0.504515
$63$	−6.08403	−	3.96262i	−0.766516	−	0.499244i
$64$	−10.6194			−1.32742
$65$	−0.473818	+	0.820677i	−0.0587699	+	0.101792i
$66$	5.54819	+	1.64750i	0.682935	+	0.202793i
$67$	2.86882	+	4.96894i	0.350482	+	0.607053i	0.986334	−	0.164758i	$-0.0526844\pi$
$67$	2.86882	+	4.96894i	0.350482	+	0.607053i	−0.635852	+	0.771811i	$0.719351\pi$
$68$	4.24390	+	7.35065i	0.514649	+	0.891398i
$69$	7.22511	+	2.14544i	0.869801	+	0.258281i
$70$	0.691278	−	1.19733i	0.0826235	−	0.143108i
$71$	6.74222			0.800155			0.400077	−	0.916481i	$-0.368983\pi$
$71$	6.74222			0.800155			0.400077	+	0.916481i	$0.368983\pi$
$72$	0.123620	−	2.29981i	0.0145687	−	0.271035i
$73$	0.832499			0.0974367			0.0487183	−	0.998813i	$-0.484486\pi$
$73$	0.832499			0.0974367			0.0487183	+	0.998813i	$0.484486\pi$
$74$	−2.33048	+	4.03650i	−0.270912	+	0.469234i
$75$	−1.98592	−	8.29646i	−0.229315	−	0.957993i
$76$	−0.384528	−	0.666022i	−0.0441084	−	0.0763979i
$77$	−1.93490	−	3.35135i	−0.220502	−	0.381921i
$78$	9.10824	−	8.63180i	1.03130	−	0.977359i
$79$	4.00799	−	6.94204i	0.450934	−	0.781040i	−0.547511	−	0.836799i	$-0.684424\pi$
$79$	4.00799	−	6.94204i	0.450934	−	0.781040i	0.998444	+	0.0557587i	$0.0177578\pi$
$80$	−0.855671			−0.0956669
$81$	−8.94814	−	0.964752i	−0.994238	−	0.107195i
$82$	−21.7670			−2.40376
$83$	3.40533	−	5.89820i	0.373783	−	0.647412i	−0.616361	−	0.787464i	$-0.711394\pi$
$83$	3.40533	−	5.89820i	0.373783	−	0.647412i	0.990144	+	0.140052i	$0.0447270\pi$
$84$	−7.20311	+	6.82633i	−0.785924	+	0.744813i
$85$	0.490024	+	0.848746i	0.0531505	+	0.0920595i
$86$	1.04491	+	1.80984i	0.112676	+	0.195160i
$87$	−2.41672	−	10.0962i	−0.259099	−	1.08242i
$88$	0.613759	−	1.06306i	0.0654269	−	0.113323i
$89$	−9.69164			−1.02731			−0.513656	−	0.857996i	$-0.671709\pi$
$89$	−9.69164			−1.02731			−0.513656	+	0.857996i	$0.671709\pi$
$90$	0.0919848	−	1.71127i	0.00969605	−	0.180384i
$91$	−8.39042			−0.879555
$92$	5.15071	−	8.92129i	0.536998	−	0.930109i
$93$	3.15625	+	0.937227i	0.327288	+	0.0971859i
$94$	−9.10615	−	15.7723i	−0.939227	−	1.62679i
$95$	−0.0443997	−	0.0769025i	−0.00455531	−	0.00789003i
$96$	13.4114	+	3.98243i	1.36880	+	0.406455i
$97$	−0.848918	+	1.47037i	−0.0861946	+	0.149293i	−0.905900	−	0.423492i	$-0.860804\pi$
$97$	−0.848918	+	1.47037i	−0.0861946	+	0.149293i	0.819705	+	0.572786i	$0.194137\pi$
$98$	−2.38754			−0.241178
$99$	−4.01943	−	2.61792i	−0.403968	−	0.263111i
$100$	−11.6599			−1.16599
$101$	5.50615	−	9.53694i	0.547883	−	0.948961i	−0.450537	−	0.892758i	$-0.648767\pi$
$101$	5.50615	−	9.53694i	0.547883	−	0.948961i	0.998419	−	0.0562029i	$-0.0178994\pi$
$102$	−3.02115	−	12.6213i	−0.299138	−	1.24969i
$103$	−2.34516	−	4.06193i	−0.231075	−	0.400234i	0.727050	−	0.686585i	$-0.240891\pi$
$103$	−2.34516	−	4.06193i	−0.231075	−	0.400234i	−0.958125	+	0.286351i	$0.907558\pi$
$104$	−1.33074	−	2.30491i	−0.130490	−	0.226015i
$105$	−0.831710	+	0.788205i	−0.0811666	+	0.0769209i
$106$	−4.73298	+	8.19777i	−0.459708	+	0.796238i
$107$	−18.1464			−1.75427			−0.877137	−	0.480239i	$-0.840550\pi$
$107$	−18.1464			−1.75427			−0.877137	+	0.480239i	$0.840550\pi$
$108$	−4.12952	+	11.5873i	−0.397363	+	1.11499i
$109$	−2.03854			−0.195257			−0.0976285	−	0.995223i	$-0.531126\pi$
$109$	−2.03854			−0.195257			−0.0976285	+	0.995223i	$0.531126\pi$
$110$	0.456695	−	0.791018i	0.0435441	−	0.0754206i
$111$	2.80391	−	2.65724i	0.266136	−	0.252214i
$112$	−3.78807	−	6.56114i	−0.357939	−	0.619969i
$113$	0.438162	+	0.758919i	0.0412188	+	0.0713931i	0.885899	−	0.463879i	$-0.153543\pi$
$113$	0.438162	+	0.758919i	0.0412188	+	0.0713931i	−0.844680	+	0.535272i	$0.820209\pi$
$114$	0.273738	+	1.14358i	0.0256379	+	0.107106i
$115$	0.594729	−	1.03010i	0.0554587	−	0.0960574i
$116$	−14.1892			−1.31743
$117$	−9.27309	+	4.70923i	−0.857297	+	0.435368i
$118$	20.7030			1.90587
$119$	−4.33870	+	7.51484i	−0.397728	+	0.688884i
$120$	−0.348437	−	0.103466i	−0.0318078	−	0.00944509i
$121$	4.22170	+	7.31220i	0.383791	+	0.664746i
$122$	−11.5118	−	19.9389i	−1.04223	−	1.80519i
$123$	17.2942	+	5.13539i	1.55937	+	0.463043i
$124$	2.25006	−	3.89722i	0.202062	−	0.349981i
$125$	−2.71305			−0.242663
$126$	13.5290	−	6.87053i	1.20526	−	0.612076i
$127$	3.12225			0.277055			0.138527	−	0.990359i	$-0.455763\pi$
$127$	3.12225			0.277055			0.138527	+	0.990359i	$0.455763\pi$
$128$	3.01904	−	5.22913i	0.266848	−	0.462194i
$129$	−0.403210	−	1.68446i	−0.0355007	−	0.148309i
$130$	−0.990196	−	1.71507i	−0.0868459	−	0.150422i
$131$	0.763641	+	1.32266i	0.0667196	+	0.115562i	0.897455	−	0.441105i	$-0.145413\pi$
$131$	0.763641	+	1.32266i	0.0667196	+	0.115562i	−0.830736	+	0.556667i	$0.812080\pi$
$132$	−4.75876	+	4.50983i	−0.414197	+	0.392531i
$133$	0.393117	−	0.680898i	0.0340876	−	0.0590414i
$134$	−11.9907			−1.03583
$135$	−0.476816	+	1.33793i	−0.0410378	+	0.115151i
$136$	−2.75251			−0.236026
$137$	2.15844	−	3.73854i	0.184408	−	0.319405i	−0.758969	−	0.651127i	$-0.774296\pi$
$137$	2.15844	−	3.73854i	0.184408	−	0.319405i	0.943377	+	0.331722i	$0.107630\pi$
$138$	−11.4325	+	10.8345i	−0.973200	+	0.922293i
$139$	9.30729	+	16.1207i	0.789434	+	1.36734i	0.926314	+	0.376753i	$0.122959\pi$
$139$	9.30729	+	16.1207i	0.789434	+	1.36734i	−0.136880	+	0.990588i	$0.543707\pi$
$140$	0.783081	+	1.35634i	0.0661824	+	0.114631i
$141$	3.51388	+	14.6797i	0.295922	+	1.23625i
$142$	−7.04502	+	12.2023i	−0.591205	+	1.02400i
$143$	−5.54316			−0.463542
$144$	−7.86910	−	5.12526i	−0.655758	−	0.427105i
$145$	−1.63836			−0.136059
$146$	−0.869888	+	1.50669i	−0.0719924	+	0.124695i
$147$	1.89694	+	0.563282i	0.156457	+	0.0464587i
$148$	−2.63997	−	4.57256i	−0.217004	−	0.375862i
$149$	−2.55883	−	4.43203i	−0.209628	−	0.363086i	0.741969	−	0.670434i	$-0.233892\pi$
$149$	−2.55883	−	4.43203i	−0.209628	−	0.363086i	−0.951597	+	0.307348i	$0.900559\pi$
$150$	17.0904	+	5.07486i	1.39542	+	0.414361i
$151$	−6.44831	+	11.1688i	−0.524756	+	0.908904i	0.474828	+	0.880078i	$0.342510\pi$
$151$	−6.44831	+	11.1688i	−0.524756	+	0.908904i	−0.999584	+	0.0288259i	$0.990823\pi$
$152$	0.249397			0.0202288
$153$	−0.577328	+	10.7405i	−0.0466742	+	0.868322i
$154$	8.08719			0.651685
$155$	0.259804	−	0.449994i	0.0208680	−	0.0361444i
$156$	3.30919	+	13.8246i	0.264947	+	1.10685i
$157$	5.65985	+	9.80315i	0.451705	+	0.782377i	0.998492	−	0.0548952i	$-0.0174825\pi$
$157$	5.65985	+	9.80315i	0.451705	+	0.782377i	−0.546787	+	0.837272i	$0.684149\pi$
$158$	8.37598	+	14.5076i	0.666357	+	1.15416i
$159$	5.69449	−	5.39662i	0.451602	−	0.427980i
$160$	1.10395	−	1.91210i	0.0872750	−	0.151165i
$161$	10.5315			0.830000
$162$	11.0961	−	15.1866i	0.871789	−	1.19317i
$163$	9.46663			0.741484			0.370742	−	0.928736i	$-0.379103\pi$
$163$	9.46663			0.741484			0.370742	+	0.928736i	$0.379103\pi$
$164$	12.3289	−	21.3542i	0.962723	−	1.66748i
$165$	−0.549472	+	0.520730i	−0.0427763	+	0.0405388i
$166$	7.11653	+	12.3262i	0.552350	+	0.956698i
$167$	−0.882435	−	1.52842i	−0.0682849	−	0.118273i	0.829862	−	0.557969i	$-0.188419\pi$
$167$	−0.882435	−	1.52842i	−0.0682849	−	0.118273i	−0.898146	+	0.439696i	$0.855086\pi$
$168$	−0.749180	−	3.12980i	−0.0578005	−	0.241469i
$169$	0.490722	−	0.849956i	0.0377479	−	0.0653812i
$170$	−2.04813			−0.157084
$171$	0.0523101	−	0.973171i	0.00400025	−	0.0744202i
$172$	−2.36736			−0.180509
$173$	−10.5360	+	18.2490i	−0.801041	+	1.38744i	0.117891	+	0.993027i	$0.462387\pi$
$173$	−10.5360	+	18.2490i	−0.801041	+	1.38744i	−0.918932	+	0.394416i	$0.870947\pi$
$174$	20.7977	+	6.17572i	1.57667	+	0.468180i
$175$	−5.96017	−	10.3233i	−0.450546	−	0.780369i
$176$	−2.50260	−	4.33464i	−0.188641	−	0.326735i
$177$	−16.4488	−	4.88436i	−1.23637	−	0.367131i
$178$	10.1269	−	17.5403i	0.759043	−	1.31470i
$179$	7.77067			0.580807			0.290403	−	0.956904i	$-0.406210\pi$
$179$	7.77067			0.580807			0.290403	+	0.956904i	$0.406210\pi$
$180$	1.62672	+	1.05951i	0.121249	+	0.0789711i
$181$	21.4202			1.59215			0.796074	−	0.605199i	$-0.206907\pi$
$181$	21.4202			1.59215			0.796074	+	0.605199i	$0.206907\pi$
$182$	8.76724	−	15.1853i	0.649871	−	1.12561i
$183$	4.44215	+	18.5577i	0.328374	+	1.37182i
$184$	1.67032	+	2.89308i	0.123138	+	0.213281i
$185$	−0.304825	−	0.527973i	−0.0224112	−	0.0388174i
$186$	−4.99424	+	4.73299i	−0.366195	+	0.347040i
$187$	−2.86637	+	4.96470i	−0.209610	+	0.363055i
$188$	20.6309			1.50467
$189$	−12.3699	+	2.26691i	−0.899779	+	0.164893i
$190$	0.185575			0.0134630
$191$	8.60539	−	14.9050i	0.622664	−	1.07849i	−0.366324	−	0.930487i	$-0.619384\pi$
$191$	8.60539	−	14.9050i	0.622664	−	1.07849i	0.988988	−	0.147998i	$-0.0472829\pi$
$192$	−13.3505	+	12.6522i	−0.963490	+	0.913091i
$193$	2.47681	+	4.28996i	0.178285	+	0.308798i	0.941293	−	0.337590i	$-0.109612\pi$
$193$	2.47681	+	4.28996i	0.178285	+	0.308798i	−0.763008	+	0.646389i	$0.776279\pi$
$194$	−1.77409	−	3.07281i	−0.127372	−	0.220615i
$195$	0.382097	+	1.59626i	0.0273625	+	0.114311i
$196$	1.35231	−	2.34227i	0.0965934	−	0.167305i
$197$	0.691719			0.0492830			0.0246415	−	0.999696i	$-0.492156\pi$
$197$	0.691719			0.0492830			0.0246415	+	0.999696i	$0.492156\pi$
$198$	8.93796	−	4.53904i	0.635193	−	0.322575i
$199$	13.5430			0.960036			0.480018	−	0.877259i	$-0.340630\pi$
$199$	13.5430			0.960036			0.480018	+	0.877259i	$0.340630\pi$
$200$	1.89059	−	3.27460i	0.133685	−	0.231549i
$201$	9.52675	+	2.82890i	0.671965	+	0.199535i
$202$	11.5069	+	19.9305i	0.809621	+	1.40231i
$203$	−7.25307	−	12.5627i	−0.509066	−	0.881728i
$204$	14.0931	+	4.18484i	0.986714	+	0.292998i
$205$	1.42356	−	2.46567i	0.0994256	−	0.172210i
$206$	9.80192			0.682932
$207$	11.6394	−	5.91094i	0.808996	−	0.410839i
$208$	−10.8522			−0.752464
$209$	0.259714	−	0.449838i	0.0179648	−	0.0311159i
$210$	−0.557460	−	2.32887i	−0.0384684	−	0.160707i
$211$	−9.50220	−	16.4583i	−0.654159	−	1.13304i	−0.982104	−	0.188339i	$-0.939690\pi$
$211$	−9.50220	−	16.4583i	−0.654159	−	1.13304i	0.327945	−	0.944697i	$-0.393644\pi$
$212$	−5.36154	−	9.28646i	−0.368232	−	0.637796i
$213$	8.47621	−	8.03284i	0.580781	−	0.550401i
$214$	18.9613	−	32.8420i	1.29617	−	2.24503i
$215$	−0.273348			−0.0186422
$216$	−2.58463	−	3.03857i	−0.175862	−	0.206748i
$217$	4.60064			0.312312
$218$	2.13010	−	3.68943i	0.144268	−	0.249880i
$219$	1.04661	−	0.991859i	0.0707230	−	0.0670236i
$220$	0.517345	+	0.896068i	0.0348794	+	0.0604129i
$221$	6.21481	+	10.7644i	0.418053	+	0.724089i
$222$	1.87934	+	7.85121i	0.126133	+	0.526939i
$223$	−2.19760	+	3.80635i	−0.147162	+	0.254892i	−0.930177	−	0.367110i	$-0.880347\pi$
$223$	−2.19760	+	3.80635i	−0.147162	+	0.254892i	0.783016	+	0.622002i	$0.213681\pi$
$224$	19.5489			1.30616
$225$	−12.3813	−	8.06411i	−0.825418	−	0.537607i
$226$	−1.83136			−0.121820
$227$	−14.1508	+	24.5099i	−0.939223	+	1.62678i	−0.172298	+	0.985045i	$0.555119\pi$
$227$	−14.1508	+	24.5099i	−0.939223	+	1.62678i	−0.766925	+	0.641737i	$0.778214\pi$
$228$	−1.27694	−	0.379177i	−0.0845671	−	0.0251116i
$229$	13.1976	+	22.8589i	0.872120	+	1.51056i	0.859799	+	0.510632i	$0.170588\pi$
$229$	13.1976	+	22.8589i	0.872120	+	1.51056i	0.0123204	+	0.999924i	$0.496078\pi$
$230$	1.24288	+	2.15273i	0.0819529	+	0.141947i
$231$	−6.42539	−	1.90797i	−0.422760	−	0.125536i
$232$	2.30071	−	3.98494i	0.151049	−	0.261624i
$233$	−28.1007			−1.84094			−0.920470	−	0.390814i	$-0.872194\pi$
$233$	−28.1007			−1.84094			−0.920470	+	0.390814i	$0.872194\pi$
$234$	1.16661	−	21.7035i	0.0762638	−	1.41880i
$235$	2.38216			0.155395
$236$	−11.7262	+	20.3104i	−0.763311	+	1.32209i
$237$	−3.23212	−	13.5026i	−0.209949	−	0.877090i
$238$	−9.06710	−	15.7047i	−0.587733	−	1.01798i
$239$	2.79192	+	4.83574i	0.180594	+	0.312798i	0.942083	−	0.335380i	$-0.108865\pi$
$239$	2.79192	+	4.83574i	0.180594	+	0.312798i	−0.761489	+	0.648178i	$0.775531\pi$
$240$	−1.07574	+	1.01947i	−0.0694384	+	0.0658062i
$241$	−3.59718	+	6.23050i	−0.231715	+	0.401342i	−0.958313	−	0.285721i	$-0.907767\pi$
$241$	−3.59718	+	6.23050i	−0.231715	+	0.401342i	0.726598	+	0.687063i	$0.241100\pi$
$242$	−17.6452			−1.13428
$243$	−12.3989	+	9.44815i	−0.795389	+	0.606099i
$244$	26.0811			1.66967
$245$	0.156145	−	0.270451i	0.00997572	−	0.0172785i
$246$	−27.3651	+	25.9337i	−1.74474	+	1.65347i
$247$	−0.563106	−	0.975329i	−0.0358296	−	0.0620587i
$248$	0.729672	+	1.26383i	0.0463342	+	0.0802532i
$249$	−2.74613	−	11.4723i	−0.174029	−	0.727028i
$250$	2.83490	−	4.91019i	0.179295	−	0.310548i
$251$	5.34271			0.337229			0.168614	−	0.985682i	$-0.446071\pi$
$251$	5.34271			0.337229			0.168614	+	0.985682i	$0.446071\pi$
$252$	−0.922598	+	17.1639i	−0.0581182	+	1.08122i
$253$	6.95768			0.437425
$254$	−3.26247	+	5.65077i	−0.204706	+	0.354561i
$255$	1.62727	+	0.483205i	0.101903	+	0.0302595i
$256$	−4.31012	−	7.46535i	−0.269383	−	0.466585i
$257$	8.34743	+	14.4582i	0.520698	+	0.901876i	0.999710	+	0.0240677i	$0.00766174\pi$
$257$	8.34743	+	14.4582i	0.520698	+	0.901876i	−0.479012	+	0.877808i	$0.659005\pi$
$258$	3.46993	+	1.03037i	0.216028	+	0.0641481i
$259$	2.69894	−	4.67470i	0.167704	−	0.290472i
$260$	2.24339			0.139129
$261$	−15.0671	−	9.81340i	−0.932627	−	0.607434i
$262$	−3.19175			−0.197187
$263$	8.74573	−	15.1480i	0.539285	−	0.934069i	−0.459658	−	0.888096i	$-0.652028\pi$
$263$	8.74573	−	15.1480i	0.539285	−	0.934069i	0.998943	−	0.0459725i	$-0.0146387\pi$
$264$	−0.494948	−	2.06771i	−0.0304619	−	0.127259i
$265$	−0.619072	−	1.07226i	−0.0380293	−	0.0658687i
$266$	0.821544	+	1.42296i	0.0503721	+	0.0872471i
$267$	−12.1842	+	11.5468i	−0.745660	+	0.706655i
$268$	6.79152	−	11.7633i	0.414858	−	0.718555i
$269$	32.3234			1.97079			0.985395	−	0.170286i	$-0.0544690\pi$
$269$	32.3234			1.97079			0.985395	+	0.170286i	$0.0544690\pi$
$270$	−1.92321	−	2.26098i	−0.117043	−	0.137599i
$271$	3.81719			0.231878			0.115939	−	0.993256i	$-0.463012\pi$
$271$	3.81719			0.231878			0.115939	+	0.993256i	$0.463012\pi$
$272$	−5.61168	+	9.71971i	−0.340258	+	0.589344i
$273$	−10.5483	+	9.99654i	−0.638412	+	0.605018i
$274$	4.51077	+	7.81288i	0.272505	+	0.471993i
$275$	−3.93760	−	6.82013i	−0.237446	−	0.411269i
$276$	−4.15364	−	17.3524i	−0.250020	−	1.04449i
$277$	−14.2015	+	24.5976i	−0.853283	+	1.47793i	0.0249458	+	0.999689i	$0.492059\pi$
$277$	−14.2015	+	24.5976i	−0.853283	+	1.47793i	−0.878229	+	0.478241i	$0.841275\pi$
$278$	−38.9012			−2.33314
$279$	5.08463	−	2.58217i	0.304409	−	0.154590i
$280$	−0.507891			−0.0303523
$281$	3.36279	−	5.82452i	0.200607	−	0.347461i	−0.748117	−	0.663567i	$-0.769042\pi$
$281$	3.36279	−	5.82452i	0.200607	−	0.347461i	0.948724	+	0.316105i	$0.102375\pi$
$282$	−30.2396	−	8.97943i	−1.80074	−	0.534717i
$283$	−15.3979	−	26.6700i	−0.915312	−	1.58537i	−0.806444	−	0.591310i	$-0.798611\pi$
$283$	−15.3979	−	26.6700i	−0.915312	−	1.58537i	−0.108868	−	0.994056i	$-0.534722\pi$
$284$	−7.98062	−	13.8228i	−0.473563	−	0.820235i
$285$	−0.147442	−	0.0437818i	−0.00873371	−	0.00259341i
$286$	5.79211	−	10.0322i	0.342494	−	0.593218i
$287$	25.2085			1.48801
$288$	21.6054	−	10.9720i	1.27311	−	0.646534i
$289$	−4.14526			−0.243839
$290$	1.71194	−	2.96517i	0.100529	−	0.174121i
$291$	0.684585	+	2.85994i	0.0401311	+	0.167653i
$292$	−0.985411	−	1.70678i	−0.0576668	−	0.0998819i
$293$	2.23699	+	3.87458i	0.130686	+	0.226355i	0.923941	−	0.382534i	$-0.124949\pi$
$293$	2.23699	+	3.87458i	0.130686	+	0.226355i	−0.793255	+	0.608889i	$0.791615\pi$
$294$	−3.00158	+	2.84457i	−0.175056	+	0.165899i
$295$	−1.35397	+	2.34515i	−0.0788313	+	0.136540i
$296$	1.71223			0.0995214
$297$	−8.17222	+	1.49764i	−0.474200	+	0.0869018i
$298$	10.6950			0.619546
$299$	7.54275	−	13.0644i	0.436208	−	0.755535i
$300$	−14.6586	+	13.8919i	−0.846317	+	0.802047i
$301$	−1.21012	−	2.09599i	−0.0697500	−	0.120811i
$302$	−13.4758	−	23.3408i	−0.775447	−	1.34311i
$303$	−4.44027	−	18.5498i	−0.255087	−	1.06566i
$304$	0.508458	−	0.880675i	0.0291621	−	0.0505102i
$305$	3.01147			0.172436
$306$	−18.8354	−	12.2678i	−1.07675	−	0.701303i
$307$	15.8569			0.904999			0.452500	−	0.891765i	$-0.350532\pi$
$307$	15.8569			0.904999			0.452500	+	0.891765i	$0.350532\pi$
$308$	−4.58060	+	7.93383i	−0.261004	+	0.452072i
$309$	−7.78777	−	2.31252i	−0.443031	−	0.131555i
$310$	0.542945	+	0.940408i	0.0308372	+	0.0534116i
$311$	−4.27370	−	7.40227i	−0.242339	−	0.419744i	0.719041	−	0.694968i	$-0.244581\pi$
$311$	−4.27370	−	7.40227i	−0.242339	−	0.419744i	−0.961380	+	0.275224i	$0.911248\pi$
$312$	−4.41911	−	1.31222i	−0.250183	−	0.0742899i
$313$	−11.4403	+	19.8152i	−0.646644	+	1.12002i	0.337275	+	0.941406i	$0.390495\pi$
$313$	−11.4403	+	19.8152i	−0.646644	+	1.12002i	−0.983919	+	0.178614i	$0.942839\pi$
$314$	−23.6562			−1.33500
$315$	−0.106528	+	1.98184i	−0.00600218	+	0.111664i
$316$	−18.9767			−1.06752
$317$	13.6986	−	23.7267i	0.769391	−	1.33262i	−0.168503	−	0.985701i	$-0.553893\pi$
$317$	13.6986	−	23.7267i	0.769391	−	1.33262i	0.937894	−	0.346923i	$-0.112773\pi$
$318$	3.81677	+	15.9451i	0.214034	+	0.894156i
$319$	−4.79176	−	8.29958i	−0.268287	−	0.464687i
$320$	1.45139	+	2.51388i	0.0811353	+	0.140530i
$321$	−22.8133	+	21.6200i	−1.27332	+	1.20671i
$322$	−11.0045	+	19.0603i	−0.613257	+	1.06219i
$323$	−1.16473			−0.0648074
$324$	8.61379	+	19.4874i	0.478544	+	1.08263i
$325$	−17.0749			−0.947143
$326$	−9.89179	+	17.1331i	−0.547855	+	0.948913i
$327$	−2.56282	+	2.42877i	−0.141724	+	0.134311i
$328$	3.99813	+	6.92496i	0.220760	+	0.382367i
$329$	10.5459	+	18.2660i	0.581413	+	1.00704i
$330$	−0.368288	−	1.53857i	−0.0202736	−	0.0846956i
$331$	11.5499	−	20.0051i	0.634841	−	1.09958i	−0.351707	−	0.936110i	$-0.614399\pi$
$331$	11.5499	−	20.0051i	0.634841	−	1.09958i	0.986549	−	0.163467i	$-0.0522678\pi$
$332$	−16.1233			−0.884878
$333$	0.359134	−	6.68129i	0.0196804	−	0.366132i
$334$	3.68826			0.201813
$335$	0.784186	−	1.35825i	0.0428447	−	0.0742091i
$336$	−12.5794	−	3.73536i	−0.686262	−	0.203781i
$337$	−11.0031	−	19.0580i	−0.599378	−	1.03815i	−0.992913	−	0.118843i	$-0.962081\pi$
$337$	−11.0031	−	19.0580i	−0.599378	−	1.03815i	0.393535	−	0.919310i	$-0.371252\pi$
$338$	1.02552	+	1.77626i	0.0557810	+	0.0966156i
$339$	1.45504	+	0.432065i	0.0790272	+	0.0234665i
$340$	1.16006	−	2.00928i	0.0629131	−	0.108969i
$341$	3.03943			0.164594
$342$	1.70662	+	1.11155i	0.0922836	+	0.0601057i
$343$	19.7067			1.06406
$344$	0.383855	−	0.664856i	0.0206961	−	0.0358466i
$345$	−0.479601	−	2.00360i	−0.0258209	−	0.107870i
$346$	−22.0185	−	38.1371i	−1.18372	−	2.05026i
$347$	−2.70165	−	4.67940i	−0.145032	−	0.251203i	0.784353	−	0.620315i	$-0.212995\pi$
$347$	−2.70165	−	4.67940i	−0.145032	−	0.251203i	−0.929385	+	0.369112i	$0.879662\pi$
$348$	−17.8384	+	16.9053i	−0.956241	+	0.906221i
$349$	−2.35604	+	4.08078i	−0.126116	+	0.218439i	−0.922169	−	0.386788i	$-0.873584\pi$
$349$	−2.35604	+	4.08078i	−0.126116	+	0.218439i	0.796053	+	0.605227i	$0.206918\pi$
$350$	24.9114			1.33157
$351$	−6.04730	+	16.9685i	−0.322781	+	0.905713i
$352$	12.9150			0.688373
$353$	12.5130	−	21.6732i	0.666001	−	1.15355i	−0.313012	−	0.949749i	$-0.601338\pi$
$353$	12.5130	−	21.6732i	0.666001	−	1.15355i	0.979013	−	0.203799i	$-0.0653288\pi$
$354$	26.0275	−	24.6660i	1.38335	−	1.31098i
$355$	−0.921486	−	1.59606i	−0.0489074	−	0.0847101i
$356$	11.4718	+	19.8697i	0.608003	+	1.05309i
$357$	3.49881	+	14.6168i	0.185177	+	0.773601i
$358$	−8.11966	+	14.0637i	−0.429137	+	0.743287i
$359$	11.4471			0.604156			0.302078	−	0.953283i	$-0.402320\pi$
$359$	11.4471			0.604156			0.302078	+	0.953283i	$0.402320\pi$
$360$	−0.561321	+	0.285060i	−0.0295842	+	0.0150240i
$361$	−18.8945			−0.994446
$362$	−22.3822	+	38.7670i	−1.17638	+	2.03755i
$363$	14.0194	+	4.16295i	0.735827	+	0.218498i
$364$	9.93156	+	17.2020i	0.520555	+	0.901628i
$365$	−0.113781	−	0.197074i	−0.00595557	−	0.0103153i
$366$	−38.2281	−	11.3516i	−1.99822	−	0.593356i
$367$	8.16377	−	14.1401i	0.426146	−	0.738106i	−0.570381	−	0.821380i	$-0.693204\pi$
$367$	8.16377	−	14.1401i	0.426146	−	0.738106i	0.996527	+	0.0832745i	$0.0265378\pi$
$368$	13.6215			0.710069
$369$	27.8604	−	14.1486i	1.45036	−	0.736546i
$370$	1.27406			0.0662353
$371$	5.48130	−	9.49388i	0.284575	−	0.492898i
$372$	−1.81450	−	7.58030i	−0.0940772	−	0.393020i
$373$	−8.14914	−	14.1147i	−0.421946	−	0.730833i	0.574183	−	0.818727i	$-0.305320\pi$
$373$	−8.14914	−	14.1147i	−0.421946	−	0.730833i	−0.996130	+	0.0878940i	$0.971986\pi$
$374$	−5.99021	−	10.3753i	−0.309746	−	0.536496i
$375$	−3.41081	+	3.23239i	−0.176133	+	0.166920i
$376$	−3.34520	+	5.79406i	−0.172516	+	0.298806i
$377$	−20.7788			−1.07016
$378$	8.82272	−	24.7563i	0.453792	−	1.27332i
$379$	34.9308			1.79427			0.897136	−	0.441754i	$-0.145644\pi$
$379$	34.9308			1.79427			0.897136	+	0.441754i	$0.145644\pi$
$380$	−0.105110	+	0.182056i	−0.00539202	+	0.00933926i
$381$	3.92524	−	3.71992i	0.201096	−	0.190577i
$382$	17.9837	+	31.1487i	0.920128	+	1.59371i
$383$	13.7964	+	23.8960i	0.704962	+	1.22103i	0.966705	+	0.255892i	$0.0823692\pi$
$383$	13.7964	+	23.8960i	0.704962	+	1.22103i	−0.261744	+	0.965137i	$0.584297\pi$
$384$	−2.43461	−	10.1709i	−0.124241	−	0.519033i
$385$	−0.528901	+	0.916083i	−0.0269553	+	0.0466879i
$386$	−10.3522			−0.526913
$387$	−2.51382	−	1.63729i	−0.127785	−	0.0832281i
$388$	4.01938			0.204053
$389$	7.06235	−	12.2324i	0.358075	−	0.620205i	−0.629564	−	0.776949i	$-0.716766\pi$
$389$	7.06235	−	12.2324i	0.358075	−	0.620205i	0.987639	+	0.156744i	$0.0500997\pi$
$390$	−3.28823	−	0.976417i	−0.166506	−	0.0494428i
$391$	−7.80072	−	13.5112i	−0.394500	−	0.683293i
$392$	0.438540	+	0.759573i	0.0221496	+	0.0383642i
$393$	2.53589	+	0.753014i	0.127919	+	0.0379845i
$394$	−0.722785	+	1.25190i	−0.0364134	+	0.0630698i
$395$	−2.19115			−0.110249
$396$	−0.609517	+	11.3394i	−0.0306294	+	0.569825i
$397$	29.4385			1.47748			0.738738	−	0.673993i	$-0.235422\pi$
$397$	29.4385			1.47748			0.738738	+	0.673993i	$0.235422\pi$
$398$	−14.1512	+	24.5106i	−0.709336	+	1.22861i
$399$	−0.317017	−	1.32438i	−0.0158707	−	0.0663021i
$400$	−7.70889	−	13.3522i	−0.385445	−	0.667610i
$401$	8.52898	+	14.7726i	0.425917	+	0.737710i	0.996506	−	0.0835263i	$-0.0266183\pi$
$401$	8.52898	+	14.7726i	0.425917	+	0.737710i	−0.570589	+	0.821236i	$0.693285\pi$
$402$	−15.0745	+	14.2859i	−0.751846	+	0.712518i
$403$	3.29501	−	5.70713i	0.164136	−	0.284292i
$404$	−26.0701			−1.29703
$405$	0.994596	+	2.25012i	0.0494218	+	0.111809i
$406$	30.3153			1.50452
$407$	1.78306	−	3.08835i	0.0883831	−	0.153084i
$408$	−3.46041	+	3.27940i	−0.171316	+	0.162355i
$409$	18.7113	+	32.4089i	0.925215	+	1.60252i	0.791216	+	0.611537i	$0.209449\pi$
$409$	18.7113	+	32.4089i	0.925215	+	1.60252i	0.133999	+	0.990981i	$0.457218\pi$
$410$	2.97498	+	5.15282i	0.146924	+	0.254480i
$411$	−1.74061	−	7.27165i	−0.0858582	−	0.358684i
$412$	−5.55182	+	9.61604i	−0.273519	+	0.473748i
$413$	−23.9763			−1.17979
$414$	−1.46431	+	27.2419i	−0.0719670	+	1.33887i
$415$	−1.86168			−0.0913862
$416$	14.0010	−	24.2505i	0.686458	−	1.18898i
$417$	30.9076	+	9.17778i	1.51355	+	0.449438i
$418$	0.542756	+	0.940081i	0.0265471	+	0.0459808i
$419$	−17.0673	−	29.5615i	−0.833794	−	1.44417i	−0.895008	−	0.446049i	$-0.852831\pi$
$419$	−17.0673	−	29.5615i	−0.833794	−	1.44417i	0.0612141	−	0.998125i	$-0.480503\pi$
$420$	2.60045	+	0.772184i	0.126889	+	0.0376787i
$421$	−11.2844	+	19.5451i	−0.549966	+	0.952569i	0.448310	+	0.893878i	$0.352026\pi$
$421$	−11.2844	+	19.5451i	−0.549966	+	0.952569i	−0.998276	+	0.0586909i	$0.981307\pi$
$422$	39.7158			1.93334
$423$	21.9073	+	14.2686i	1.06517	+	0.693762i
$424$	3.47738			0.168877
$425$	−8.82943	+	15.2930i	−0.428290	+	0.741820i
$426$	5.68125	+	23.7342i	0.275257	+	1.14992i
$427$	13.3318	+	23.0914i	0.645172	+	1.11747i
$428$	21.4795	+	37.2035i	1.03825	+	1.79830i
$429$	−6.96877	+	6.60424i	−0.336455	+	0.318856i
$430$	0.285624	−	0.494716i	0.0137740	−	0.0238573i
$431$	−2.17813			−0.104917			−0.0524583	−	0.998623i	$-0.516706\pi$
$431$	−2.17813			−0.104917			−0.0524583	+	0.998623i	$0.516706\pi$
$432$	−15.9993	+	2.93202i	−0.769765	+	0.141067i
$433$	−29.5089			−1.41811			−0.709054	−	0.705154i	$-0.750878\pi$
$433$	−29.5089			−1.41811			−0.709054	+	0.705154i	$0.750878\pi$
$434$	−4.80726	+	8.32642i	−0.230756	+	0.399681i
$435$	−2.05972	+	1.95198i	−0.0987562	+	0.0935904i
$436$	2.41298	+	4.17940i	0.115561	+	0.200157i
$437$	0.706802	+	1.22422i	0.0338109	+	0.0585622i
$438$	0.701495	+	2.93059i	0.0335187	+	0.140029i
$439$	−5.32696	+	9.22656i	−0.254242	+	0.440360i	−0.964689	−	0.263391i	$-0.915159\pi$
$439$	−5.32696	+	9.22656i	−0.254242	+	0.440360i	0.710448	+	0.703750i	$0.248493\pi$
$440$	−0.335539			−0.0159962
$441$	3.05591	−	1.55191i	0.145519	−	0.0739002i
$442$	−25.9757			−1.23554
$443$	−7.10985	+	12.3146i	−0.337799	+	0.585085i	−0.984018	−	0.178067i	$-0.943016\pi$
$443$	−7.10985	+	12.3146i	−0.337799	+	0.585085i	0.646219	+	0.763152i	$0.276349\pi$
$444$	−8.76679	−	2.60323i	−0.416053	−	0.123544i
$445$	1.32459	+	2.29427i	0.0627918	+	0.108759i
$446$	−4.59259	−	7.95459i	−0.217465	−	0.376661i
$447$	−8.49735	−	2.52323i	−0.401911	−	0.119344i
$448$	−12.8507	+	22.2581i	−0.607138	+	1.05159i
$449$	−11.9133			−0.562221			−0.281111	−	0.959675i	$-0.590703\pi$
$449$	−11.9133			−0.562221			−0.281111	+	0.959675i	$0.590703\pi$
$450$	27.5321	−	13.9818i	1.29787	−	0.659109i
$451$	16.6541			0.784210
$452$	1.03729	−	1.79663i	0.0487898	−	0.0845065i
$453$	5.20005	+	21.7239i	0.244320	+	1.02068i
$454$	−29.5727	−	51.2214i	−1.38792	−	2.40394i
$455$	1.14675	+	1.98623i	0.0537605	+	0.0931160i
$456$	0.313538	−	0.297137i	0.0146828	−	0.0139147i
$457$	−7.68042	+	13.3029i	−0.359275	+	0.622283i	−0.987840	−	0.155474i	$-0.950309\pi$
$457$	−7.68042	+	13.3029i	−0.359275	+	0.622283i	0.628565	+	0.777757i	$0.283643\pi$
$458$	−55.1611			−2.57751
$459$	12.0707	+	14.1907i	0.563413	+	0.662365i
$460$	−2.81587			−0.131291
$461$	7.88703	−	13.6607i	0.367336	−	0.636244i	−0.621812	−	0.783166i	$-0.713603\pi$
$461$	7.88703	−	13.6607i	0.367336	−	0.636244i	0.989148	+	0.146922i	$0.0469367\pi$
$462$	10.1671	−	9.63527i	0.473016	−	0.448273i
$463$	2.36131	+	4.08992i	0.109740	+	0.190075i	0.915665	−	0.401943i	$-0.131665\pi$
$463$	2.36131	+	4.08992i	0.109740	+	0.190075i	−0.805925	+	0.592017i	$0.798332\pi$
$464$	−9.38114	−	16.2486i	−0.435508	−	0.754322i
$465$	−0.209512	−	0.875263i	−0.00971586	−	0.0405893i
$466$	29.3628	−	50.8578i	1.36020	−	2.35594i
$467$	−24.0572			−1.11324			−0.556618	−	0.830768i	$-0.687901\pi$
$467$	−24.0572			−1.11324			−0.556618	+	0.830768i	$0.687901\pi$
$468$	20.6312	+	13.4374i	0.953676	+	0.621144i
$469$	13.8864			0.641216
$470$	−2.48915	+	4.31133i	−0.114816	+	0.198867i
$471$	18.7952	+	5.58109i	0.866036	+	0.257163i
$472$	−3.80269	−	6.58645i	−0.175033	−	0.303166i
$473$	−0.799468	−	1.38472i	−0.0367596	−	0.0636694i
$474$	27.8149	+	8.25942i	1.27758	+	0.379368i
$475$	0.800010	−	1.38566i	0.0367070	−	0.0635783i
$476$	20.5425			0.941563
$477$	0.729368	−	13.5691i	0.0333955	−	0.621286i
$478$	−11.6692			−0.533738
$479$	12.1281	−	21.0065i	0.554148	−	0.959812i	−0.443822	−	0.896115i	$-0.646378\pi$
$479$	12.1281	−	21.0065i	0.554148	−	0.959812i	0.997969	−	0.0636966i	$-0.0202890\pi$
$480$	−0.890249	−	3.71913i	−0.0406341	−	0.169755i
$481$	−3.86600	−	6.69611i	−0.176274	−	0.305316i
$482$	−7.51746	−	13.0206i	−0.342411	−	0.593073i
$483$	13.2401	−	12.5475i	0.602443	−	0.570930i
$484$	9.99427	−	17.3106i	0.454285	−	0.786845i
$485$	0.464100			0.0210737
$486$	−4.14389	−	32.3125i	−0.187971	−	1.46572i
$487$	−32.1708			−1.45780			−0.728899	−	0.684621i	$-0.759968\pi$
$487$	−32.1708			−1.45780			−0.728899	+	0.684621i	$0.759968\pi$
$488$	−4.22892	+	7.32470i	−0.191434	+	0.331574i
$489$	11.9013	−	11.2788i	0.538195	−	0.510043i
$490$	0.326315	+	0.565194i	0.0147414	+	0.0255329i
$491$	−3.59674	−	6.22973i	−0.162319	−	0.281144i	0.773381	−	0.633941i	$-0.218564\pi$
$491$	−3.59674	−	6.22973i	−0.162319	−	0.281144i	−0.935700	+	0.352797i	$0.885231\pi$
$492$	−9.94225	−	41.5351i	−0.448231	−	1.87255i
$493$	−10.7447	+	18.6104i	−0.483919	+	0.838172i
$494$	2.35358			0.105893
$495$	−0.0703781	+	1.30931i	−0.00316326	+	0.0588490i
$496$	5.95048			0.267184
$497$	8.15888	−	14.1316i	0.365976	−	0.633889i
$498$	23.6325	+	7.01750i	1.05900	+	0.314462i
$499$	−20.0166	−	34.6698i	−0.896066	−	1.55203i	−0.832479	−	0.554056i	$-0.813079\pi$
$499$	−20.0166	−	34.6698i	−0.896066	−	1.55203i	−0.0635872	−	0.997976i	$-0.520254\pi$
$500$	3.21138	+	5.56228i	0.143617	+	0.248753i
$501$	−2.93038	−	0.870155i	−0.130920	−	0.0388757i
$502$	−5.58266	+	9.66945i	−0.249166	+	0.431569i
$503$	−31.2924			−1.39526			−0.697630	−	0.716458i	$-0.745762\pi$
$503$	−31.2924			−1.39526			−0.697630	+	0.716458i	$0.745762\pi$
$504$	−4.67077	−	3.04214i	−0.208053	−	0.135508i
$505$	−3.01019			−0.133952
$506$	−7.27015	+	12.5923i	−0.323198	+	0.559795i
$507$	−0.395728	−	1.65321i	−0.0175749	−	0.0734216i
$508$	−3.69574	−	6.40121i	−0.163972	−	0.284008i
$509$	21.4060	+	37.0762i	0.948803	+	1.64338i	0.747951	+	0.663754i	$0.231038\pi$
$509$	21.4060	+	37.0762i	0.948803	+	1.64338i	0.200852	+	0.979621i	$0.435629\pi$
$510$	−2.57487	+	2.44018i	−0.114017	+	0.108053i
$511$	1.00742	−	1.74491i	0.0445657	−	0.0771901i
$512$	30.0909			1.32984
$513$	−1.09369	−	1.28578i	−0.0482878	−	0.0567685i
$514$	−34.8893			−1.53890
$515$	−0.641043	+	1.11032i	−0.0282477	+	0.0489265i
$516$	−2.97620	+	2.82052i	−0.131020	+	0.124167i
$517$	6.96717	+	12.0675i	0.306416	+	0.530728i
$518$	5.64030	+	9.76929i	0.247821	+	0.429238i
$519$	8.49648	+	35.4952i	0.372954	+	1.55807i
$520$	−0.363755	+	0.630042i	−0.0159517	+	0.0276292i
$521$	−2.79772			−0.122570			−0.0612851	−	0.998120i	$-0.519520\pi$
$521$	−2.79772			−0.122570			−0.0612851	+	0.998120i	$0.519520\pi$
$522$	33.5044	−	17.0148i	1.46645	−	0.744718i
$523$	−7.44564			−0.325575			−0.162788	−	0.986661i	$-0.552049\pi$
$523$	−7.44564			−0.325575			−0.162788	+	0.986661i	$0.552049\pi$
$524$	1.80781	−	3.13122i	0.0789745	−	0.136788i
$525$	−19.7925	−	5.87723i	−0.863814	−	0.256503i
$526$	18.2770	+	31.6567i	0.796916	+	1.38030i
$527$	−3.40771	−	5.90232i	−0.148442	−	0.257109i
$528$	−8.31062	−	2.46778i	−0.361673	−	0.107396i
$529$	2.03247	−	3.52034i	0.0883683	−	0.153058i
$530$	2.58750			0.112394
$531$	−26.4986	+	13.4570i	−1.14994	+	0.583983i
$532$	−1.86130			−0.0806974
$533$	18.0545	−	31.2713i	0.782027	−	1.35451i
$534$	−8.16654	−	34.1168i	−0.353401	−	1.47638i
$535$	2.48013	+	4.29572i	0.107226	+	0.185720i
$536$	2.20242	+	3.81471i	0.0951301	+	0.164770i
$537$	9.76916	−	9.25815i	0.421570	−	0.399519i
$538$	−33.7750	+	58.5001i	−1.45614	+	2.52212i
$539$	1.82672			0.0786825
$540$	3.30741	−	0.606115i	0.142328	−	0.0260831i
$541$	−36.9090			−1.58684			−0.793421	−	0.608673i	$-0.791702\pi$
$541$	−36.9090			−1.58684			−0.793421	+	0.608673i	$0.791702\pi$
$542$	−3.98862	+	6.90850i	−0.171326	+	0.296745i
$543$	26.9291	−	25.5205i	1.15564	−	1.09519i
$544$	−14.4799	−	25.0799i	−0.620821	−	1.07529i
$545$	0.278616	+	0.482576i	0.0119346	+	0.0206713i
$546$	−7.07008	−	29.5362i	−0.302572	−	1.26403i
$547$	−19.8177	+	34.3252i	−0.847343	+	1.46764i	0.0362277	+	0.999344i	$0.488466\pi$
$547$	−19.8177	+	34.3252i	−0.847343	+	1.46764i	−0.883571	+	0.468298i	$0.844867\pi$
$548$	−10.2196			−0.436560
$549$	27.6947	+	18.0380i	1.18198	+	0.769841i
$550$	16.4578			0.701762
$551$	0.973551	−	1.68624i	0.0414747	−	0.0718362i
$552$	5.54679	+	1.64708i	0.236087	+	0.0701043i
$553$	−9.70027	−	16.8014i	−0.412497	−	0.714466i
$554$	−29.6785	−	51.4047i	−1.26092	−	2.18398i
$555$	−1.01226	−	0.300584i	−0.0429681	−	0.0127591i
$556$	22.0337	−	38.1635i	0.934436	−	1.61849i
$557$	24.8972			1.05493			0.527464	−	0.849578i	$-0.323143\pi$
$557$	24.8972			1.05493			0.527464	+	0.849578i	$0.323143\pi$
$558$	−0.639678	+	11.9005i	−0.0270797	+	0.503788i
$559$	−3.46678			−0.146629
$560$	−1.03546	+	1.79347i	−0.0437563	+	0.0757881i
$561$	2.31150	+	9.65661i	0.0975916	+	0.407702i
$562$	7.02762	+	12.1722i	0.296442	+	0.513453i
$563$	−6.80608	−	11.7885i	−0.286842	−	0.496825i	0.686212	−	0.727401i	$-0.259272\pi$
$563$	−6.80608	−	11.7885i	−0.286842	−	0.496825i	−0.973054	+	0.230576i	$0.925939\pi$
$564$	25.9369	−	24.5802i	1.09214	−	1.03501i
$565$	0.119771	−	0.207449i	0.00503879	−	0.00872744i
$566$	64.3579			2.70516
$567$	−12.8504	+	17.5877i	−0.539667	+	0.738614i
$568$	5.17607			0.217183
$569$	−5.30680	+	9.19165i	−0.222473	+	0.385334i	−0.955558	−	0.294802i	$-0.904746\pi$
$569$	−5.30680	+	9.19165i	−0.222473	+	0.385334i	0.733086	+	0.680136i	$0.238079\pi$
$570$	0.233302	−	0.221098i	0.00977194	−	0.00926078i
$571$	−17.4674	−	30.2545i	−0.730990	−	1.26611i	−0.956461	−	0.291861i	$-0.905725\pi$
$571$	−17.4674	−	30.2545i	−0.730990	−	1.26611i	0.225471	−	0.974250i	$-0.427608\pi$
$572$	6.56131	+	11.3645i	0.274342	+	0.475175i
$573$	−6.93956	−	28.9909i	−0.289904	−	1.21111i
$574$	−26.3406	+	45.6233i	−1.09944	+	1.90428i
$575$	21.4321			0.893780
$576$	−1.70998	+	31.8122i	−0.0712490	+	1.32551i
$577$	−17.0364			−0.709236			−0.354618	−	0.935011i	$-0.615389\pi$
$577$	−17.0364			−0.709236			−0.354618	+	0.935011i	$0.615389\pi$
$578$	4.33143	−	7.50226i	0.180164	−	0.312053i
$579$	8.22497	+	2.44234i	0.341818	+	0.101500i
$580$	1.93929	+	3.35896i	0.0805248	+	0.139473i
$581$	−8.24169	−	14.2750i	−0.341923	−	0.592228i
$582$	−5.89137	−	1.74940i	−0.244205	−	0.0725149i
$583$	3.62124	−	6.27216i	0.149976	−	0.259766i
$584$	0.639118			0.0264469
$585$	2.38219	+	1.55155i	0.0984913	+	0.0641489i
$586$	−9.34981			−0.386237
$587$	0.824967	−	1.42888i	0.0340500	−	0.0589764i	−0.848498	−	0.529198i	$-0.822493\pi$
$587$	0.824967	−	1.42888i	0.0340500	−	0.0589764i	0.882548	+	0.470222i	$0.155826\pi$
$588$	−1.09053	−	4.55583i	−0.0449726	−	0.187879i
$589$	0.308763	+	0.534793i	0.0127223	+	0.0220358i
$590$	−2.82956	−	4.90094i	−0.116491	−	0.201769i
$591$	0.869618	−	0.824130i	0.0357713	−	0.0339002i
$592$	3.49081	−	6.04626i	0.143472	−	0.248500i
$593$	−2.89587			−0.118919			−0.0594596	−	0.998231i	$-0.518938\pi$
$593$	−2.89587			−0.118919			−0.0594596	+	0.998231i	$0.518938\pi$
$594$	5.82876	−	16.3553i	0.239157	−	0.671066i
$595$	2.37195			0.0972403
$596$	−6.05767	+	10.4922i	−0.248132	+	0.429777i
$597$	17.0260	−	16.1354i	0.696828	−	0.660378i
$598$	15.7630	+	27.3023i	0.644597	+	1.11647i
$599$	−4.20198	−	7.27804i	−0.171688	−	0.297373i	0.767322	−	0.641262i	$-0.221589\pi$
$599$	−4.20198	−	7.27804i	−0.171688	−	0.297373i	−0.939010	+	0.343889i	$0.888256\pi$
$600$	−1.52461	−	6.36927i	−0.0622420	−	0.260025i
$601$	−15.2704	+	26.4491i	−0.622892	+	1.07888i	0.366053	+	0.930594i	$0.380709\pi$
$601$	−15.2704	+	26.4491i	−0.622892	+	1.07888i	−0.988945	+	0.148286i	$0.952624\pi$
$602$	5.05786			0.206143
$603$	15.3473	−	7.79394i	0.624990	−	0.317394i
$604$	30.5309			1.24229
$605$	1.15399	−	1.99877i	0.0469165	−	0.0812618i
$606$	38.2119	+	11.3468i	1.55225	+	0.460930i
$607$	18.6263	+	32.2616i	0.756017	+	1.30946i	0.944867	+	0.327454i	$0.106191\pi$
$607$	18.6263	+	32.2616i	0.756017	+	1.30946i	−0.188850	+	0.982006i	$0.560476\pi$
$608$	1.31198	+	2.27242i	0.0532080	+	0.0921589i
$609$	−24.0859	−	7.15214i	−0.976011	−	0.289819i
$610$	−3.14671	+	5.45027i	−0.127407	+	0.220675i
$611$	30.2121			1.22225
$612$	22.7035	−	11.5297i	0.917736	−	0.466061i
$613$	−15.5040			−0.626199			−0.313099	−	0.949720i	$-0.601367\pi$
$613$	−15.5040			−0.626199			−0.313099	+	0.949720i	$0.601367\pi$
$614$	−16.5690	+	28.6984i	−0.668671	+	1.15817i
$615$	−1.14799	−	4.79587i	−0.0462913	−	0.193388i
$616$	−1.48544	−	2.57286i	−0.0598501	−	0.103663i
$617$	18.6789	+	32.3528i	0.751985	+	1.30248i	0.946859	+	0.321648i	$0.104237\pi$
$617$	18.6789	+	32.3528i	0.751985	+	1.30248i	−0.194874	+	0.980828i	$0.562430\pi$
$618$	12.3228	−	11.6782i	0.495696	−	0.469767i
$619$	20.4282	−	35.3827i	0.821079	−	1.42215i	−0.0838006	−	0.996483i	$-0.526706\pi$
$619$	20.4282	−	35.3827i	0.821079	−	1.42215i	0.904879	−	0.425668i	$-0.139961\pi$
$620$	−1.23010			−0.0494020
$621$	7.59047	−	21.2986i	0.304595	−	0.854684i
$622$	17.8626			0.716223
$623$	−11.7280	+	20.3135i	−0.469873	+	0.813845i
$624$	−13.6432	+	12.9295i	−0.546165	+	0.517596i
$625$	−11.9424	−	20.6848i	−0.477696	−	0.827394i
$626$	−23.9082	−	41.4102i	−0.955564	−	1.65509i
$627$	−0.209439	−	0.874958i	−0.00836417	−	0.0349424i
$628$	13.3989	−	23.2076i	0.534674	−	0.926082i
$629$	−7.99645			−0.318839
$630$	−3.47549	−	2.26364i	−0.138467	−	0.0901857i
$631$	−22.1435			−0.881520			−0.440760	−	0.897625i	$-0.645291\pi$
$631$	−22.1435			−0.881520			−0.440760	+	0.897625i	$0.645291\pi$
$632$	3.07697	−	5.32947i	0.122395	−	0.211995i
$633$	−31.5548	−	9.36997i	−1.25419	−	0.372423i
$634$	28.6277	+	49.5846i	1.13695	+	1.96926i
$635$	−0.426730	−	0.739118i	−0.0169343	−	0.0293310i
$636$	−17.8045	−	5.28693i	−0.705996	−	0.209640i
$637$	1.98033	−	3.43004i	0.0784636	−	0.135903i
$638$	20.0279			0.792911
$639$	1.08566	−	20.1975i	0.0429481	−	0.799001i
$640$	−1.65049			−0.0652415
$641$	−5.25836	+	9.10774i	−0.207693	+	0.359734i	−0.950987	−	0.309230i	$-0.899929\pi$
$641$	−5.25836	+	9.10774i	−0.207693	+	0.359734i	0.743295	+	0.668964i	$0.233262\pi$
$642$	−15.2908	−	63.8794i	−0.603480	−	2.52112i
$643$	3.31908	+	5.74882i	0.130892	+	0.226711i	0.924021	−	0.382343i	$-0.124883\pi$
$643$	3.31908	+	5.74882i	0.130892	+	0.226711i	−0.793129	+	0.609054i	$0.791549\pi$
$644$	−12.4659	−	21.5916i	−0.491226	−	0.850829i
$645$	−0.343649	+	0.325673i	−0.0135311	+	0.0128234i
$646$	1.21704	−	2.10798i	0.0478838	−	0.0829372i
$647$	−41.0456			−1.61367			−0.806834	−	0.590779i	$-0.798821\pi$
$647$	−41.0456			−1.61367			−0.806834	+	0.590779i	$0.798821\pi$
$648$	−6.86958	−	0.740650i	−0.269862	−	0.0290955i
$649$	−15.8400			−0.621774
$650$	17.8417	−	30.9027i	0.699809	−	1.21211i
$651$	5.78385	−	5.48131i	0.226687	−	0.214829i
$652$	−11.2054	−	19.4084i	−0.438839	−	0.760092i
$653$	13.0373	+	22.5812i	0.510188	+	0.883671i	0.999930	+	0.0118041i	$0.00375746\pi$
$653$	13.0373	+	22.5812i	0.510188	+	0.883671i	−0.489742	+	0.871867i	$0.662909\pi$
$654$	−1.71775	−	7.17614i	−0.0671694	−	0.280609i
$655$	0.208740	−	0.361547i	0.00815613	−	0.0141268i
$656$	32.6047			1.27300
$657$	0.134053	−	2.49390i	0.00522989	−	0.0972962i
$658$	−44.0780			−1.71834
$659$	−0.483468	+	0.837391i	−0.0188332	+	0.0326201i	−0.875288	−	0.483601i	$-0.839328\pi$
$659$	−0.483468	+	0.837391i	−0.0188332	+	0.0326201i	0.856455	+	0.516221i	$0.172662\pi$
$660$	1.71799	+	0.510146i	0.0668728	+	0.0198574i
$661$	9.02772	+	15.6365i	0.351138	+	0.608188i	0.986449	−	0.164068i	$-0.0524616\pi$
$661$	9.02772	+	15.6365i	0.351138	+	0.608188i	−0.635311	+	0.772256i	$0.719128\pi$
$662$	24.1373	+	41.8070i	0.938122	+	1.62488i
$663$	20.6381	+	6.12832i	0.801516	+	0.238004i
$664$	2.61430	−	4.52811i	0.101455	−	0.175725i
$665$	−0.214915			−0.00833406
$666$	11.7168	+	7.63133i	0.454017	+	0.295708i
$667$	26.0812			1.00987
$668$	−2.08904	+	3.61832i	−0.0808273	+	0.139997i
$669$	1.77219	+	7.40355i	0.0685167	+	0.286238i
$670$	1.63881	+	2.83850i	0.0633127	+	0.109661i
$671$	8.80771	+	15.2554i	0.340018	+	0.588928i
$672$	24.5765	−	23.2910i	0.948061	−	0.898469i
$673$	5.43861	−	9.41994i	0.209643	−	0.363112i	−0.741959	−	0.670445i	$-0.766103\pi$
$673$	5.43861	−	9.41994i	0.209643	−	0.363112i	0.951602	+	0.307333i	$0.0994365\pi$
$674$	45.9891			1.77143
$675$	−25.1733	+	4.61325i	−0.968920	+	0.177564i
$676$	−2.32343			−0.0893626
$677$	6.68319	−	11.5756i	0.256856	−	0.444888i	−0.708542	−	0.705669i	$-0.750647\pi$
$677$	6.68319	−	11.5756i	0.256856	−	0.444888i	0.965398	+	0.260781i	$0.0839800\pi$
$678$	−2.30236	+	2.18193i	−0.0884216	+	0.0837964i
$679$	2.05458	+	3.55864i	0.0788476	+	0.136568i
$680$	0.376196	+	0.651591i	0.0144265	+	0.0249874i
$681$	11.4115	+	47.6731i	0.437290	+	1.82684i
$682$	−3.17593	+	5.50087i	−0.121613	+	0.210639i
$683$	−19.4039			−0.742471			−0.371236	−	0.928539i	$-0.621066\pi$
$683$	−19.4039			−0.742471			−0.371236	+	0.928539i	$0.621066\pi$
$684$	−2.05710	+	1.04468i	−0.0786553	+	0.0399442i
$685$	−1.18001			−0.0450860
$686$	−20.5917	+	35.6659i	−0.786196	+	1.36173i
$687$	43.8263	+	13.0139i	1.67208	+	0.496512i
$688$	−1.56517	−	2.71095i	−0.0596715	−	0.103354i
$689$	−7.85149	−	13.5992i	−0.299118	−	0.518087i
$690$	4.12733	+	1.22558i	0.157125	+	0.0466571i
$691$	12.4326	−	21.5339i	0.472959	−	0.819189i	−0.526562	−	0.850137i	$-0.676519\pi$
$691$	12.4326	−	21.5339i	0.472959	−	0.819189i	0.999521	+	0.0309479i	$0.00985261\pi$
$692$	49.8851			1.89635
$693$	−10.3511	+	5.25669i	−0.393206	+	0.199685i
$694$	11.2919			0.428637
$695$	2.54413	−	4.40656i	0.0965043	−	0.167150i
$696$	−1.85534	−	7.75092i	−0.0703264	−	0.293798i
$697$	−18.6720	−	32.3409i	−0.707253	−	1.22500i
$698$	−4.92370	−	8.52810i	−0.186365	−	0.322793i
$699$	−35.3278	+	33.4798i	−1.33622	+	1.26632i
$700$	−14.1098	+	24.4390i	−0.533302	+	0.923706i
$701$	33.5387			1.26674			0.633369	−	0.773850i	$-0.281672\pi$
$701$	33.5387			1.26674			0.633369	+	0.773850i	$0.281672\pi$
$702$	−24.3914	−	28.6753i	−0.920595	−	1.08228i
$703$	0.724536			0.0273264
$704$	−8.48985	+	14.7048i	−0.319973	+	0.554210i
$705$	2.99481	−	2.83816i	0.112791	−	0.106891i
$706$	26.1500	+	45.2931i	0.984168	+	1.70463i
$707$	−13.3262	−	23.0816i	−0.501183	−	0.868074i
$708$	9.45625	+	39.5048i	0.355388	+	1.48468i
$709$	−3.61137	+	6.25507i	−0.135628	+	0.234914i	−0.925837	−	0.377923i	$-0.876638\pi$
$709$	−3.61137	+	6.25507i	−0.135628	+	0.234914i	0.790209	+	0.612837i	$0.209972\pi$
$710$	3.85148			0.144544
$711$	−20.1507	−	13.1245i	−0.755710	−	0.492206i
$712$	−7.44037			−0.278840
$713$	−4.13584	+	7.16349i	−0.154889	+	0.268275i
$714$	−30.1099	−	8.94093i	−1.12684	−	0.334606i
$715$	0.757605	+	1.31221i	0.0283328	+	0.0490739i
$716$	−9.19797	−	15.9314i	−0.343744	−	0.595383i
$717$	9.27137	+	2.75307i	0.346246	+	0.102815i
$718$	−11.9612	+	20.7174i	−0.446389	+	0.773168i
$719$	−17.6476			−0.658144			−0.329072	−	0.944305i	$-0.606736\pi$
$719$	−17.6476			−0.658144			−0.329072	+	0.944305i	$0.606736\pi$
$720$	−0.137784	+	2.56331i	−0.00513489	+	0.0955290i
$721$	−11.3517			−0.422758
$722$	19.7430	−	34.1959i	0.734760	−	1.27264i
$723$	2.90084	+	12.1186i	0.107883	+	0.450697i
$724$	−25.3546	−	43.9154i	−0.942295	−	1.63210i
$725$	−14.7603	−	25.5656i	−0.548184	−	0.949483i
$726$	−22.1833	+	21.0229i	−0.823299	+	0.780233i
$727$	−3.51589	+	6.08970i	−0.130397	+	0.225855i	−0.923830	−	0.382804i	$-0.874959\pi$
$727$	−3.51589	+	6.08970i	−0.130397	+	0.225855i	0.793433	+	0.608658i	$0.208292\pi$
$728$	−6.44141			−0.238734
$729$	−4.33095	+	26.6504i	−0.160406	+	0.987051i
$730$	0.475564			0.0176014
$731$	−1.79268	+	3.10500i	−0.0663045	+	0.114843i
$732$	32.7887	−	31.0736i	1.21191	−	1.14851i
$733$	−20.0560	−	34.7379i	−0.740784	−	1.28307i	−0.952139	−	0.305666i	$-0.901121\pi$
$733$	−20.0560	−	34.7379i	−0.740784	−	1.28307i	0.211355	−	0.977409i	$-0.432212\pi$
$734$	17.0608	+	29.5502i	0.629727	+	1.09072i
$735$	−0.125918	−	0.526041i	−0.00464457	−	0.0194033i
$736$	−17.5739	+	30.4389i	−0.647782	+	1.12199i
$737$	9.17412			0.337933
$738$	−3.50502	+	65.2069i	−0.129021	+	2.40030i
$739$	−48.1715			−1.77202			−0.886008	−	0.463670i	$-0.846532\pi$
$739$	−48.1715			−1.77202			−0.886008	+	0.463670i	$0.846532\pi$
$740$	−0.721630	+	1.24990i	−0.0265277	+	0.0459473i
$741$	−1.86996	−	0.555270i	−0.0686946	−	0.0203984i
$742$	11.4549	+	19.8405i	0.420524	+	0.728369i
$743$	−16.6656	−	28.8656i	−0.611400	−	1.05898i	−0.991005	−	0.133827i	$-0.957273\pi$
$743$	−16.6656	−	28.8656i	−0.611400	−	1.05898i	0.379604	−	0.925149i	$-0.376060\pi$
$744$	2.42309	+	0.719518i	0.0888347	+	0.0263788i
$745$	−0.699452	+	1.21149i	−0.0256259	+	0.0443854i
$746$	34.0605			1.24704
$747$	−17.1208	−	11.1510i	−0.626416	−	0.407994i
$748$	13.5714			0.496221
$749$	−21.9592	+	38.0345i	−0.802373	+	1.38975i
$750$	−2.28612	−	9.55058i	−0.0834773	−	0.348738i
$751$	19.6490	+	34.0332i	0.717004	+	1.24189i	0.962182	+	0.272409i	$0.0878204\pi$
$751$	19.6490	+	34.0332i	0.717004	+	1.24189i	−0.245177	+	0.969478i	$0.578846\pi$
$752$	13.6401	+	23.6253i	0.497402	+	0.861525i
$753$	6.71677	−	6.36543i	0.244773	−	0.231969i
$754$	21.7120	−	37.6063i	0.790704	−	1.36954i
$755$	3.52526			0.128298
$756$	19.2896	+	22.6774i	0.701555	+	0.824769i
$757$	23.7890			0.864627			0.432313	−	0.901723i	$-0.357697\pi$
$757$	23.7890			0.864627			0.432313	+	0.901723i	$0.357697\pi$
$758$	−36.4995	+	63.2190i	−1.32572	+	2.29622i
$759$	8.74708	−	8.28953i	0.317499	−	0.300891i
$760$	−0.0340861	−	0.0590388i	−0.00123643	−	0.00214156i
$761$	12.2868	+	21.2813i	0.445395	+	0.771448i	0.998080	−	0.0619432i	$-0.0197298\pi$
$761$	12.2868	+	21.2813i	0.445395	+	0.771448i	−0.552684	+	0.833391i	$0.686396\pi$
$762$	2.63092	+	10.9910i	0.0953083	+	0.398163i
$763$	−2.46688	+	4.27275i	−0.0893069	+	0.154684i
$764$	−40.7440			−1.47407
$765$	2.62147	−	1.33128i	0.0947796	−	0.0481327i
$766$	−57.6639			−2.08348
$767$	−17.1720	+	29.7427i	−0.620044	+	1.07395i
$768$	−14.3130	−	4.25015i	−0.516476	−	0.153364i
$769$	12.0908	+	20.9418i	0.436005	+	0.755182i	0.997377	−	0.0723810i	$-0.0230597\pi$
$769$	12.0908	+	20.9418i	0.436005	+	0.755182i	−0.561372	+	0.827563i	$0.689726\pi$
$770$	−1.10531	−	1.91445i	−0.0398326	−	0.0689920i
$771$	27.7201	+	8.23127i	0.998313	+	0.296442i
$772$	5.86350	−	10.1559i	0.211032	−	0.365518i
$773$	7.66684			0.275757			0.137878	−	0.990449i	$-0.455972\pi$
$773$	7.66684			0.275757			0.137878	+	0.990449i	$0.455972\pi$
$774$	5.58995	−	2.83879i	0.200926	−	0.102038i
$775$	9.36250			0.336311
$776$	−0.651722	+	1.12882i	−0.0233955	+	0.0405221i
$777$	−2.17648	−	9.09254i	−0.0780808	−	0.326193i
$778$	14.7591	+	25.5634i	0.529138	+	0.916494i
$779$	1.69182	+	2.93031i	0.0606157	+	0.104989i
$780$	2.82036	−	2.67283i	0.100985	−	0.0957027i
$781$	5.39019	−	9.33608i	0.192876	−	0.334071i
$782$	32.6043			1.16593
$783$	−30.6340	+	5.61397i	−1.09477	+	0.200627i
$784$	3.57629			0.127725
$785$	1.54711	−	2.67967i	0.0552187	−	0.0956415i
$786$	−4.01261	+	3.80272i	−0.143125	+	0.135638i
$787$	7.00049	+	12.1252i	0.249540	+	0.432217i	0.963398	−	0.268074i	$-0.0863871\pi$
$787$	7.00049	+	12.1252i	0.249540	+	0.432217i	−0.713858	+	0.700291i	$0.753054\pi$
$788$	−0.818773	−	1.41816i	−0.0291676	−	0.0505197i
$789$	−7.05273	−	29.4637i	−0.251084	−	1.04894i
$790$	2.28956	−	3.96563i	0.0814587	−	0.141091i
$791$	2.12091			0.0754109
$792$	−3.08576	−	2.00980i	−0.109648	−	0.0714152i
$793$	38.1934			1.35629
$794$	−30.7606	+	53.2789i	−1.09165	+	1.89080i
$795$	−2.05581	−	0.610457i	−0.0729120	−	0.0216507i
$796$	−16.0305	−	27.7657i	−0.568187	−	0.984129i
$797$	3.56346	+	6.17210i	0.126224	+	0.218627i	0.922211	−	0.386687i	$-0.126381\pi$
$797$	3.56346	+	6.17210i	0.126224	+	0.218627i	−0.795987	+	0.605314i	$0.793047\pi$
$798$	2.72818	+	0.810112i	0.0965764	+	0.0286777i
$799$	15.6227	−	27.0594i	0.552692	−	0.957291i
$800$	39.7828			1.40653
$801$	−1.56059	+	29.0330i	−0.0551407	+	1.02583i
$802$	−35.6481			−1.25878
$803$	0.665556	−	1.15278i	0.0234870	−	0.0406806i
$804$	−5.47682	−	22.8802i	−0.193153	−	0.806921i
$805$	−1.43938	−	2.49309i	−0.0507316	−	0.0878697i
$806$	6.88599	+	11.9269i	0.242549	+	0.420106i
$807$	40.6364	−	38.5108i	1.43047	−	1.35564i
$808$	4.22713	−	7.32160i	0.148710	−	0.257573i
$809$	28.5298			1.00306			0.501528	−	0.865141i	$-0.332771\pi$
$809$	28.5298			1.00306			0.501528	+	0.865141i	$0.332771\pi$
$810$	−5.11161	−	0.551113i	−0.179604	−	0.0193641i
$811$	21.0869			0.740463			0.370231	−	0.928940i	$-0.379278\pi$
$811$	21.0869			0.740463			0.370231	+	0.928940i	$0.379278\pi$
$812$	−17.1706	+	29.7404i	−0.602570	+	1.04368i
$813$	4.79891	−	4.54789i	0.168305	−	0.159501i
$814$	3.72628	+	6.45411i	0.130606	+	0.226216i
$815$	−1.29384	−	2.24100i	−0.0453213	−	0.0784988i
$816$	4.52537	+	18.9053i	0.158420	+	0.661819i
$817$	0.162429	−	0.281336i	0.00568268	−	0.00984269i
$818$	−78.2066			−2.73443
$819$	−1.35106	+	25.1350i	−0.0472099	+	0.878287i
$820$	−6.74014			−0.235376
$821$	−3.38052	+	5.85524i	−0.117981	+	0.204349i	−0.918968	−	0.394333i	$-0.870976\pi$
$821$	−3.38052	+	5.85524i	−0.117981	+	0.204349i	0.800986	+	0.598683i	$0.204309\pi$
$822$	14.9793	+	4.44800i	0.522463	+	0.155142i
$823$	−25.7399	−	44.5828i	−0.897237	−	1.55406i	−0.831012	−	0.556255i	$-0.812238\pi$
$823$	−25.7399	−	44.5828i	−0.897237	−	1.55406i	−0.0662248	−	0.997805i	$-0.521095\pi$
$824$	−1.80040	−	3.11838i	−0.0627199	−	0.108634i
$825$	−13.0760	−	3.88281i	−0.455246	−	0.135182i
$826$	25.0531	−	43.3932i	0.871708	−	1.50984i
$827$	−32.7541			−1.13897			−0.569486	−	0.822001i	$-0.692858\pi$
$827$	−32.7541			−1.13897			−0.569486	+	0.822001i	$0.692858\pi$
$828$	−25.8959	−	16.8664i	−0.899945	−	0.586148i
$829$	−31.7417			−1.10243			−0.551217	−	0.834362i	$-0.685836\pi$
$829$	−31.7417			−1.10243			−0.551217	+	0.834362i	$0.685836\pi$
$830$	1.94529	−	3.36934i	0.0675219	−	0.116951i
$831$	11.4523	+	47.8437i	0.397277	+	1.65968i
$832$	18.4075	+	31.8827i	0.638166	+	1.10534i
$833$	−2.04806	−	3.54735i	−0.0709612	−	0.122908i
$834$	−48.9059	+	46.3477i	−1.69347	+	1.60489i
$835$	−0.241212	+	0.417791i	−0.00834748	+	0.0144583i
$836$	−1.22967			−0.0425291
$837$	3.31586	−	9.30420i	0.114613	−	0.321600i
$838$	71.3354			2.46424
$839$	−14.5744	+	25.2436i	−0.503164	+	0.871506i	0.496829	+	0.867848i	$0.334498\pi$
$839$	−14.5744	+	25.2436i	−0.503164	+	0.871506i	−0.999993	+	0.00365762i	$0.998836\pi$
$840$	−0.638512	+	0.605112i	−0.0220308	+	0.0208784i
$841$	−3.46217	−	5.99666i	−0.119385	−	0.206781i
$842$	−23.5823	−	40.8457i	−0.812700	−	1.40764i
$843$	−2.71182	−	11.3290i	−0.0934000	−	0.390191i
$844$	−22.4951	+	38.9627i	−0.774313	+	1.34115i
$845$	−0.268276			−0.00922896
$846$	−48.7150	+	24.7393i	−1.67486	+	0.850556i
$847$	20.4350			0.702156
$848$	7.08952	−	12.2794i	0.243455	−	0.421677i
$849$	−51.1333	−	15.1837i	−1.75489	−	0.521102i
$850$	−18.4519	−	31.9597i	−0.632896	−	1.09621i
$851$	4.85254	+	8.40484i	0.166343	+	0.288114i
$852$	−26.5020	−	7.86956i	−0.907942	−	0.269607i
$853$	27.0832	−	46.9095i	0.927312	−	1.60615i	0.139511	−	0.990220i	$-0.455447\pi$
$853$	27.0832	−	46.9095i	0.927312	−	1.60615i	0.787800	−	0.615931i	$-0.211220\pi$
$854$	−55.7223			−1.90678
$855$	−0.237524	+	0.120624i	−0.00812316	+	0.00412525i
$856$	−13.9311			−0.476156
$857$	0.862497	−	1.49389i	0.0294623	−	0.0510302i	−0.850918	−	0.525298i	$-0.823954\pi$
$857$	0.862497	−	1.49389i	0.0294623	−	0.0510302i	0.880381	+	0.474268i	$0.157287\pi$
$858$	−4.67087	−	19.5132i	−0.159461	−	0.666170i
$859$	−7.64074	−	13.2341i	−0.260699	−	0.451543i	0.705729	−	0.708482i	$-0.250620\pi$
$859$	−7.64074	−	13.2341i	−0.260699	−	0.451543i	−0.966428	+	0.256939i	$0.917286\pi$
$860$	0.323556	+	0.560415i	0.0110332	+	0.0191100i
$861$	31.6917	−	30.0340i	1.08005	−	1.02356i
$862$	2.27595	−	3.94206i	0.0775191	−	0.134267i
$863$	31.2885			1.06507			0.532537	−	0.846407i	$-0.321239\pi$
$863$	31.2885			1.06507			0.532537	+	0.846407i	$0.321239\pi$
$864$	14.0896	−	39.5351i	0.479339	−	1.34501i
$865$	5.76001			0.195846
$866$	30.8342	−	53.4064i	1.04779	−	1.81482i
$867$	−5.21136	+	4.93876i	−0.176987	+	0.167729i
$868$	−5.44568	−	9.43219i	−0.184838	−	0.320149i
$869$	−6.40851	−	11.0999i	−0.217394	−	0.376537i
$870$	−1.38055	−	5.76742i	−0.0468049	−	0.195534i
$871$	9.94557	−	17.2262i	0.336993	−	0.583688i
$872$	−1.56501			−0.0529979
$873$	4.26805	+	2.77985i	0.144452	+	0.0940836i
$874$	−2.95418			−0.0999266
$875$	−3.28311	+	5.68652i	−0.110990	+	0.192239i
$876$	−3.27234	−	0.971699i	−0.110562	−	0.0328307i
$877$	−5.27153	−	9.13056i	−0.178007	−	0.308317i	0.763191	−	0.646173i	$-0.223632\pi$
$877$	−5.27153	−	9.13056i	−0.178007	−	0.308317i	−0.941198	+	0.337856i	$0.890298\pi$
$878$	−11.1324	−	19.2819i	−0.375700	−	0.650731i
$879$	7.42857	+	2.20586i	0.250559	+	0.0744018i
$880$	−0.684081	+	1.18486i	−0.0230604	+	0.0399417i
$881$	−42.4065			−1.42871			−0.714356	−	0.699783i	$-0.753280\pi$
$881$	−42.4065			−1.42871			−0.714356	+	0.699783i	$0.753280\pi$
$882$	−0.384452	+	7.15230i	−0.0129452	+	0.240831i
$883$	−40.6960			−1.36953			−0.684765	−	0.728764i	$-0.740095\pi$
$883$	−40.6960			−1.36953			−0.684765	+	0.728764i	$0.740095\pi$
$884$	14.7127	−	25.4831i	0.494841	−	0.857089i
$885$	1.09187	+	4.56144i	0.0367028	+	0.153331i
$886$	−14.8583	−	25.7354i	−0.499175	−	0.864596i
$887$	12.2660	+	21.2454i	0.411853	+	0.713351i	0.995092	−	0.0989498i	$-0.0315483\pi$
$887$	12.2660	+	21.2454i	0.411853	+	0.713351i	−0.583239	+	0.812300i	$0.698215\pi$
$888$	2.15259	−	2.03999i	0.0722362	−	0.0684576i
$889$	3.77829	−	6.54419i	0.126720	−	0.219485i
$890$	−5.53633			−0.185578
$891$	−8.48966	+	11.6194i	−0.284414	+	0.389264i
$892$	10.4050			0.348385
$893$	−1.41553	+	2.45177i	−0.0473690	+	0.0820454i
$894$	13.4456	−	12.7423i	0.449688	−	0.426166i
$895$	−1.06205	−	1.83952i	−0.0355003	−	0.0614884i
$896$	−7.30678	−	12.6557i	−0.244102	−	0.422798i
$897$	−6.08262	−	25.4110i	−0.203093	−	0.848448i
$898$	12.4483	−	21.5611i	0.415405	−	0.719502i
$899$	11.3934			0.379993
$900$	−1.87753	+	34.9293i	−0.0625842	+	1.16431i
$901$	−16.2400			−0.541034
$902$	−17.4020	+	30.1412i	−0.579424	+	1.00359i
$903$	−4.01854	−	1.19328i	−0.133729	−	0.0397098i
$904$	0.336381	+	0.582630i	0.0111879	+	0.0193780i
$905$	−2.92758	−	5.07071i	−0.0973160	−	0.168556i
$906$	−44.7504	−	13.2883i	−1.48673	−	0.441474i
$907$	15.0814	−	26.1218i	0.500770	−	0.867359i	−0.499230	−	0.866470i	$-0.666384\pi$
$907$	15.0814	−	26.1218i	0.500770	−	0.867359i	1.00000		0.000888993i	$-0.000282975\pi$
$908$	67.0001			2.22348
$909$	−27.6829	−	18.0303i	−0.918185	−	0.598028i
$910$	−4.79301			−0.158887
$911$	3.73340	−	6.46644i	0.123693	−	0.214243i	−0.797528	−	0.603282i	$-0.793860\pi$
$911$	3.73340	−	6.46644i	0.123693	−	0.214243i	0.921221	+	0.389039i	$0.127193\pi$
$912$	−0.410031	−	1.71296i	−0.0135775	−	0.0567218i
$913$	−5.44490	−	9.43084i	−0.180200	−	0.312115i
$914$	−16.0507	−	27.8007i	−0.530911	−	0.919564i
$915$	3.78597	−	3.58793i	0.125160	−	0.118613i
$916$	31.2433	−	54.1151i	1.03231	−	1.78801i
$917$	3.69638			0.122065
$918$	−38.2957	+	7.01806i	−1.26395	+	0.231630i
$919$	28.7562			0.948579			0.474289	−	0.880369i	$-0.342705\pi$
$919$	28.7562			0.948579			0.474289	+	0.880369i	$0.342705\pi$
$920$	0.456579	−	0.790818i	0.0150530	−	0.0260725i
$921$	19.9350	−	18.8922i	0.656881	−	0.622520i
$922$	16.4825	+	28.5485i	0.542822	+	0.940195i
$923$	−11.6869	−	20.2423i	−0.384679	−	0.666283i
$924$	3.69389	+	15.4317i	0.121520	+	0.507666i
$925$	5.49246	−	9.51321i	0.180591	−	0.312792i
$926$	−9.86945			−0.324330
$927$	−12.5459	+	6.37126i	−0.412060	+	0.209260i
$928$	48.4126			1.58922
$929$	−17.7359	+	30.7195i	−0.581896	+	1.00787i	0.413359	+	0.910568i	$0.364355\pi$
$929$	−17.7359	+	30.7195i	−0.581896	+	1.00787i	−0.995255	+	0.0973047i	$0.968978\pi$
$930$	1.80301	+	0.535389i	0.0591229	+	0.0175561i
$931$	0.185569	+	0.321415i	0.00608179	+	0.0105340i
$932$	33.2622	+	57.6118i	1.08954	+	1.88714i
$933$	−14.1921	−	4.21423i	−0.464627	−	0.137968i
$934$	25.1377	−	43.5397i	0.822530	−	1.42466i
$935$	1.56703			0.0512475
$936$	−7.11904	+	3.61532i	−0.232693	+	0.118170i
$937$	−37.7639			−1.23369			−0.616847	−	0.787083i	$-0.711590\pi$
$937$	−37.7639			−1.23369			−0.616847	+	0.787083i	$0.711590\pi$
$938$	−14.5101	+	25.1322i	−0.473771	+	0.820596i
$939$	9.22569	+	38.5416i	0.301069	+	1.25776i
$940$	−2.81971	−	4.88388i	−0.0919688	−	0.159295i
$941$	−9.21120	−	15.9543i	−0.300277	−	0.520094i	0.675922	−	0.736973i	$-0.263746\pi$
$941$	−9.21120	−	15.9543i	−0.300277	−	0.520094i	−0.976199	+	0.216879i	$0.930412\pi$
$942$	−29.7402	+	28.1845i	−0.968987	+	0.918301i
$943$	−22.6617	+	39.2512i	−0.737967	+	1.27820i
$944$	−31.0109			−1.00932
$945$	2.22728	+	2.61845i	0.0724534	+	0.0851783i
$946$	3.34149			0.108641
$947$	8.26337	−	14.3126i	0.268523	−	0.465096i	−0.699957	−	0.714185i	$-0.746798\pi$
$947$	8.26337	−	14.3126i	0.268523	−	0.465096i	0.968481	+	0.249089i	$0.0801310\pi$
$948$	−23.8572	+	22.6092i	−0.774845	+	0.734314i
$949$	−1.44305	−	2.49943i	−0.0468432	−	0.0811349i
$950$	1.67188	+	2.89578i	0.0542429	+	0.0939514i
$951$	−11.0468	−	46.1497i	−0.358218	−	1.49651i
$952$	−3.33086	+	5.76922i	−0.107954	+	0.186981i
$953$	−25.4326			−0.823842			−0.411921	−	0.911219i	$-0.635142\pi$
$953$	−25.4326			−0.823842			−0.411921	+	0.911219i	$0.635142\pi$
$954$	23.7957	+	15.4985i	0.770415	+	0.501783i
$955$	−4.70453			−0.152235
$956$	6.60947	−	11.4479i	0.213765	−	0.370253i
$957$	−15.9124	−	4.72508i	−0.514376	−	0.152740i
$958$	25.3456	+	43.8999i	0.818879	+	1.41834i
$959$	−5.22394	−	9.04814i	−0.168690	−	0.292180i
$960$	4.81976	+	1.43119i	0.155557	+	0.0461916i
$961$	13.6933	−	23.7175i	0.441719	−	0.765079i
$962$	16.1585			0.520971
$963$	−2.92200	+	54.3606i	−0.0941602	+	1.75175i
$964$	17.0316			0.548551
$965$	0.677031	−	1.17265i	0.0217944	−	0.0377490i
$966$	8.87425	+	37.0734i	0.285524	+	1.19282i
$967$	7.07071	+	12.2468i	0.227379	+	0.393832i	0.957030	−	0.289987i	$-0.0936511\pi$
$967$	7.07071	+	12.2468i	0.227379	+	0.393832i	−0.729652	+	0.683819i	$0.760318\pi$
$968$	3.24104	+	5.61365i	0.104171	+	0.180430i
$969$	−1.46428	+	1.38769i	−0.0470395	+	0.0445789i
$970$	−0.484943	+	0.839946i	−0.0155706	+	0.0269690i
$971$	−27.1607			−0.871627			−0.435814	−	0.900037i	$-0.643539\pi$
$971$	−27.1607			−0.871627			−0.435814	+	0.900037i	$0.643539\pi$
$972$	34.0468	+	14.2365i	1.09205	+	0.456637i
$973$	45.0517			1.44429
$974$	33.6156	−	58.2240i	1.07711	−	1.86562i
$975$	−21.4662	+	20.3434i	−0.687470	+	0.651509i
$976$	17.2434	+	29.8665i	0.551948	+	0.956002i
$977$	3.63720	+	6.29981i	0.116364	+	0.201549i	0.918324	−	0.395829i	$-0.129543\pi$
$977$	3.63720	+	6.29981i	0.116364	+	0.201549i	−0.801960	+	0.597378i	$0.796209\pi$
$978$	7.97694	+	33.3247i	0.255074	+	1.06561i
$979$	−7.74816	+	13.4202i	−0.247632	+	0.428911i
$980$	−0.739301			−0.0236161
$981$	−0.328255	+	6.10681i	−0.0104804	+	0.194975i
$982$	15.0331			0.479725
$983$	−19.8887	+	34.4483i	−0.634351	+	1.09873i	0.352301	+	0.935887i	$0.385399\pi$
$983$	−19.8887	+	34.4483i	−0.634351	+	1.09873i	−0.986652	+	0.162842i	$0.947934\pi$
$984$	13.2769	+	3.94249i	0.423253	+	0.125682i
$985$	−0.0945400	−	0.163748i	−0.00301229	−	0.00521745i
$986$	−22.4546	−	38.8925i	−0.715100	−	1.23859i
$987$	35.0206	+	10.3991i	1.11472	+	0.331008i
$988$	−1.33307	+	2.30895i	−0.0424107	+	0.0734575i
$989$	4.35144			0.138368
$990$	−2.29610	−	1.49548i	−0.0729747	−	0.0475295i
$991$	−7.74113			−0.245905			−0.122953	−	0.992413i	$-0.539236\pi$
$991$	−7.74113			−0.245905			−0.122953	+	0.992413i	$0.539236\pi$
$992$	−7.67706	+	13.2971i	−0.243747	+	0.422182i
$993$	−9.31409	−	38.9109i	−0.295574	−	1.23480i
$994$	17.0506	+	29.5325i	0.540812	+	0.936715i
$995$	−1.85097	−	3.20598i	−0.0586797	−	0.101636i
$996$	−20.2699	+	19.2096i	−0.642276	+	0.608680i
$997$	2.18933	−	3.79204i	0.0693369	−	0.120095i	−0.829273	−	0.558844i	$-0.811245\pi$
$997$	2.18933	−	3.79204i	0.0693369	−	0.120095i	0.898610	+	0.438749i	$0.144578\pi$
$998$	83.6623			2.64828
$999$	−7.50874	−	8.82749i	−0.237566	−	0.279289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.d.259.2	yes	40
3.2	odd	2		1161.2.f.d.775.19		40
9.2	odd	6		3483.2.a.u.1.2		20
9.4	even	3	inner	387.2.f.d.130.2	✓	40
9.5	odd	6		1161.2.f.d.388.19		40
9.7	even	3		3483.2.a.t.1.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.2	✓	40	9.4	even	3	inner
387.2.f.d.259.2	yes	40	1.1	even	1	trivial
1161.2.f.d.388.19		40	9.5	odd	6
1161.2.f.d.775.19		40	3.2	odd	2
3483.2.a.t.1.19		20	9.7	even	3
3483.2.a.u.1.2		20	9.2	odd	6

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04491 + 1.80984i) q^{2} +(1.25718 - 1.19142i) q^{3} +(-1.18368 - 2.05019i) q^{4} +(-0.136674 - 0.236726i) q^{5} +(0.842638 + 3.52023i) q^{6} +(1.21012 - 2.09599i) q^{7} +0.767710 q^{8} +(0.161024 - 2.99568i) q^{9} +O(q^{10})\)	\(q+(-1.04491 + 1.80984i) q^{2} +(1.25718 - 1.19142i) q^{3} +(-1.18368 - 2.05019i) q^{4} +(-0.136674 - 0.236726i) q^{5} +(0.842638 + 3.52023i) q^{6} +(1.21012 - 2.09599i) q^{7} +0.767710 q^{8} +(0.161024 - 2.99568i) q^{9} +0.571248 q^{10} +(0.799468 - 1.38472i) q^{11} +(-3.93075 - 1.16721i) q^{12} +(-1.73339 - 3.00232i) q^{13} +(2.52893 + 4.38024i) q^{14} +(-0.453865 - 0.134772i) q^{15} +(1.56517 - 2.71095i) q^{16} -3.58535 q^{17} +(5.25343 + 3.42164i) q^{18} +0.324858 q^{19} +(-0.323556 + 0.560415i) q^{20} +(-0.975863 - 4.07680i) q^{21} +(1.67075 + 2.89382i) q^{22} +(2.17572 + 3.76846i) q^{23} +(0.965152 - 0.914667i) q^{24} +(2.46264 - 4.26542i) q^{25} +7.24495 q^{26} +(-3.36668 - 3.95796i) q^{27} -5.72956 q^{28} +(2.99685 - 5.19069i) q^{29} +(0.718164 - 0.680598i) q^{30} +(0.950453 + 1.64623i) q^{31} +(4.03863 + 6.99512i) q^{32} +(-0.644707 - 2.69335i) q^{33} +(3.74637 - 6.48891i) q^{34} -0.661566 q^{35} +(-6.33231 + 3.21579i) q^{36} +2.23031 q^{37} +(-0.339448 + 0.587942i) q^{38} +(-5.75622 - 1.70927i) q^{39} +(-0.104926 - 0.181737i) q^{40} +(5.20786 + 9.02028i) q^{41} +(8.39804 + 2.49374i) q^{42} +(0.500000 - 0.866025i) q^{43} -3.78525 q^{44} +(-0.731163 + 0.371312i) q^{45} -9.09374 q^{46} +(-4.35738 + 7.54720i) q^{47} +(-1.26218 - 5.27294i) q^{48} +(0.571231 + 0.989401i) q^{49} +(5.14648 + 8.91397i) q^{50} +(-4.50745 + 4.27167i) q^{51} +(-4.10355 + 7.10756i) q^{52} +4.52956 q^{53} +(10.6812 - 1.95743i) q^{54} -0.437066 q^{55} +(0.929019 - 1.60911i) q^{56} +(0.408407 - 0.387044i) q^{57} +(6.26287 + 10.8476i) q^{58} +(-4.95329 - 8.57935i) q^{59} +(0.260922 + 1.09004i) q^{60} +(-5.50849 + 9.54098i) q^{61} -3.97256 q^{62} +(-6.08403 - 3.96262i) q^{63} -10.6194 q^{64} +(-0.473818 + 0.820677i) q^{65} +(5.54819 + 1.64750i) q^{66} +(2.86882 + 4.96894i) q^{67} +(4.24390 + 7.35065i) q^{68} +(7.22511 + 2.14544i) q^{69} +(0.691278 - 1.19733i) q^{70} +6.74222 q^{71} +(0.123620 - 2.29981i) q^{72} +0.832499 q^{73} +(-2.33048 + 4.03650i) q^{74} +(-1.98592 - 8.29646i) q^{75} +(-0.384528 - 0.666022i) q^{76} +(-1.93490 - 3.35135i) q^{77} +(9.10824 - 8.63180i) q^{78} +(4.00799 - 6.94204i) q^{79} -0.855671 q^{80} +(-8.94814 - 0.964752i) q^{81} -21.7670 q^{82} +(3.40533 - 5.89820i) q^{83} +(-7.20311 + 6.82633i) q^{84} +(0.490024 + 0.848746i) q^{85} +(1.04491 + 1.80984i) q^{86} +(-2.41672 - 10.0962i) q^{87} +(0.613759 - 1.06306i) q^{88} -9.69164 q^{89} +(0.0919848 - 1.71127i) q^{90} -8.39042 q^{91} +(5.15071 - 8.92129i) q^{92} +(3.15625 + 0.937227i) q^{93} +(-9.10615 - 15.7723i) q^{94} +(-0.0443997 - 0.0769025i) q^{95} +(13.4114 + 3.98243i) q^{96} +(-0.848918 + 1.47037i) q^{97} -2.38754 q^{98} +(-4.01943 - 2.61792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8}+O(q^{10}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8	\( 40 q + 6 q^{2} + 2 q^{3} - 22 q^{4} + 17 q^{5} - 6 q^{6} - 3 q^{7} - 30 q^{8} - 4 q^{10} + 10 q^{11} - 17 q^{12} + q^{13} + 10 q^{14} + 7 q^{15} - 22 q^{16} - 40 q^{17} + 3 q^{18} + 16 q^{19} + 30 q^{20} + 6 q^{21} - 15 q^{22} + 19 q^{23} + 33 q^{24} - 19 q^{25} - 50 q^{26} + 8 q^{27} - 6 q^{28} + 25 q^{29} - 54 q^{30} + 11 q^{31} + 36 q^{32} - 6 q^{33} - 9 q^{34} + 44 q^{36} + 18 q^{37} + 28 q^{38} - 35 q^{39} - 12 q^{40} + 12 q^{41} + 37 q^{42} + 20 q^{43} - 10 q^{44} - 25 q^{45} + 8 q^{46} + 38 q^{47} - 7 q^{48} - 37 q^{49} + 36 q^{50} - 4 q^{51} + 8 q^{52} - 138 q^{53} + 33 q^{54} - 18 q^{55} + 30 q^{56} - 53 q^{57} + 27 q^{58} + 31 q^{59} + 38 q^{60} - 19 q^{61} - 64 q^{62} - 35 q^{63} + 22 q^{64} + 47 q^{65} - 33 q^{66} - 9 q^{67} + 68 q^{68} + 26 q^{69} + 6 q^{70} - 42 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} - 56 q^{75} - 37 q^{76} + 85 q^{77} + 43 q^{78} + 4 q^{79} - 122 q^{80} - 36 q^{81} + 2 q^{82} + 19 q^{83} - 83 q^{84} + 6 q^{85} - 6 q^{86} + 49 q^{87} - 60 q^{88} - 108 q^{89} + 3 q^{90} - 6 q^{91} + 85 q^{92} - 10 q^{93} + 19 q^{94} - 11 q^{95} + 93 q^{96} - 2 q^{97} - 10 q^{98} + 19 q^{99}+O(q^{100}) \) 40 * q + 6 * q^2 + 2 * q^3 - 22 * q^4 + 17 * q^5 - 6 * q^6 - 3 * q^7 - 30 * q^8 - 4 * q^10 + 10 * q^11 - 17 * q^12 + q^13 + 10 * q^14 + 7 * q^15 - 22 * q^16 - 40 * q^17 + 3 * q^18 + 16 * q^19 + 30 * q^20 + 6 * q^21 - 15 * q^22 + 19 * q^23 + 33 * q^24 - 19 * q^25 - 50 * q^26 + 8 * q^27 - 6 * q^28 + 25 * q^29 - 54 * q^30 + 11 * q^31 + 36 * q^32 - 6 * q^33 - 9 * q^34 + 44 * q^36 + 18 * q^37 + 28 * q^38 - 35 * q^39 - 12 * q^40 + 12 * q^41 + 37 * q^42 + 20 * q^43 - 10 * q^44 - 25 * q^45 + 8 * q^46 + 38 * q^47 - 7 * q^48 - 37 * q^49 + 36 * q^50 - 4 * q^51 + 8 * q^52 - 138 * q^53 + 33 * q^54 - 18 * q^55 + 30 * q^56 - 53 * q^57 + 27 * q^58 + 31 * q^59 + 38 * q^60 - 19 * q^61 - 64 * q^62 - 35 * q^63 + 22 * q^64 + 47 * q^65 - 33 * q^66 - 9 * q^67 + 68 * q^68 + 26 * q^69 + 6 * q^70 - 42 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 - 56 * q^75 - 37 * q^76 + 85 * q^77 + 43 * q^78 + 4 * q^79 - 122 * q^80 - 36 * q^81 + 2 * q^82 + 19 * q^83 - 83 * q^84 + 6 * q^85 - 6 * q^86 + 49 * q^87 - 60 * q^88 - 108 * q^89 + 3 * q^90 - 6 * q^91 + 85 * q^92 - 10 * q^93 + 19 * q^94 - 11 * q^95 + 93 * q^96 - 2 * q^97 - 10 * q^98 + 19 * q^99

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