LMFDB - Embedded newform 144.3.w.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26432 + 1.54968i) q^{2} +(-2.98386 - 0.310733i) q^{3} +(-0.803013 - 3.91857i) q^{4} +(2.23236 + 8.33129i) q^{5} +(4.25408 - 4.23117i) q^{6} +(-3.69610 + 2.13394i) q^{7} +(7.08778 + 3.70989i) q^{8} +(8.80689 + 1.85437i) q^{9} +O(q^{10})$	\(q+(-1.26432 + 1.54968i) q^{2} +(-2.98386 - 0.310733i) q^{3} +(-0.803013 - 3.91857i) q^{4} +(2.23236 + 8.33129i) q^{5} +(4.25408 - 4.23117i) q^{6} +(-3.69610 + 2.13394i) q^{7} +(7.08778 + 3.70989i) q^{8} +(8.80689 + 1.85437i) q^{9} +(-15.7332 - 7.07393i) q^{10} +(-15.6229 - 4.18615i) q^{11} +(1.17845 + 11.9420i) q^{12} +(-5.18329 - 19.3443i) q^{13} +(1.36611 - 8.42575i) q^{14} +(-4.07226 - 25.5531i) q^{15} +(-14.7103 + 6.29332i) q^{16} -10.6727i q^{17} +(-14.0084 + 11.3033i) q^{18} +(-12.2363 + 12.2363i) q^{19} +(30.8541 - 15.4378i) q^{20} +(11.6917 - 5.21890i) q^{21} +(26.2395 - 18.9179i) q^{22} +(9.25997 - 16.0387i) q^{23} +(-19.9962 - 13.2722i) q^{24} +(-42.7763 + 24.6969i) q^{25} +(36.5308 + 16.4249i) q^{26} +(-25.7023 - 8.26978i) q^{27} +(11.3300 + 12.7698i) q^{28} +(-6.80700 + 25.4041i) q^{29} +(44.7477 + 25.9965i) q^{30} +(6.33170 - 10.9668i) q^{31} +(8.84588 - 30.7531i) q^{32} +(45.3159 + 17.3455i) q^{33} +(16.5392 + 13.4936i) q^{34} +(-26.0295 - 26.0295i) q^{35} +(0.194430 - 35.9995i) q^{36} +(-18.0450 - 18.0450i) q^{37} +(-3.49179 - 34.4328i) q^{38} +(9.45532 + 59.3314i) q^{39} +(-15.0857 + 67.3322i) q^{40} +(-7.43075 + 12.8704i) q^{41} +(-6.69444 + 24.7168i) q^{42} +(4.70515 - 17.5598i) q^{43} +(-3.85830 + 64.5810i) q^{44} +(4.21087 + 77.5124i) q^{45} +(13.1474 + 34.6280i) q^{46} +(-16.1577 + 9.32866i) q^{47} +(45.8492 - 14.2074i) q^{48} +(-15.3926 + 26.6607i) q^{49} +(15.8105 - 97.5143i) q^{50} +(-3.31635 + 31.8458i) q^{51} +(-71.6397 + 35.8448i) q^{52} +(-38.0269 + 38.0269i) q^{53} +(45.3114 - 29.3748i) q^{54} -139.504i q^{55} +(-34.1139 + 1.41280i) q^{56} +(40.3136 - 32.7091i) q^{57} +(-30.7620 - 42.6674i) q^{58} +(16.9990 + 63.4412i) q^{59} +(-96.8615 + 36.4769i) q^{60} +(-11.9218 - 3.19445i) q^{61} +(8.98980 + 23.6776i) q^{62} +(-36.5083 + 11.9395i) q^{63} +(36.4734 + 52.5898i) q^{64} +(149.592 - 86.3670i) q^{65} +(-84.1735 + 48.2950i) q^{66} +(8.10824 + 30.2604i) q^{67} +(-41.8216 + 8.57029i) q^{68} +(-32.6143 + 44.9801i) q^{69} +(73.2470 - 7.42790i) q^{70} +38.1082 q^{71} +(55.5418 + 45.8160i) q^{72} -127.821i q^{73} +(50.7786 - 5.14939i) q^{74} +(135.313 - 60.4002i) q^{75} +(57.7745 + 38.1227i) q^{76} +(66.6769 - 17.8660i) q^{77} +(-103.899 - 60.3609i) q^{78} +(7.54888 + 13.0750i) q^{79} +(-85.2703 - 108.507i) q^{80} +(74.1226 + 32.6625i) q^{81} +(-10.5502 - 27.7876i) q^{82} +(-29.3816 + 109.654i) q^{83} +(-29.8392 - 41.6241i) q^{84} +(88.9171 - 23.8253i) q^{85} +(21.2633 + 29.4927i) q^{86} +(28.2050 - 73.6871i) q^{87} +(-95.2018 - 87.6299i) q^{88} -102.393 q^{89} +(-125.443 - 91.4746i) q^{90} +(60.4377 + 60.4377i) q^{91} +(-70.2848 - 23.4065i) q^{92} +(-22.3007 + 30.7561i) q^{93} +(5.97202 - 36.8337i) q^{94} +(-129.260 - 74.6281i) q^{95} +(-35.9509 + 89.0142i) q^{96} +(40.9773 + 70.9747i) q^{97} +(-21.8545 - 57.5611i) q^{98} +(-129.827 - 65.8377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.26432	+	1.54968i	−0.632158	+	0.774840i
$2$	−1.26432	+	1.54968i	−0.632158	+	0.774840i
$3$	−2.98386	−	0.310733i	−0.994621	−	0.103578i
$3$	−2.98386	−	0.310733i	−0.994621	−	0.103578i
$4$	−0.803013	−	3.91857i	−0.200753	−	0.979642i
$5$	2.23236	+	8.33129i	0.446472	+	1.66626i	0.712019	+	0.702160i	$0.247781\pi$
$5$	2.23236	+	8.33129i	0.446472	+	1.66626i	−0.265547	+	0.964098i	$0.585552\pi$
$6$	4.25408	−	4.23117i	0.709014	−	0.705195i
$7$	−3.69610	+	2.13394i	−0.528014	+	0.304849i	−0.740208	−	0.672378i	$-0.765273\pi$
$7$	−3.69610	+	2.13394i	−0.528014	+	0.304849i	0.212193	+	0.977228i	$0.431939\pi$
$8$	7.08778	+	3.70989i	0.885973	+	0.463737i
$9$	8.80689	+	1.85437i	0.978543	+	0.206041i
$10$	−15.7332	−	7.07393i	−1.57332	−	0.707393i
$11$	−15.6229	−	4.18615i	−1.42027	−	0.380559i	−0.534688	−	0.845050i	$-0.679571\pi$
$11$	−15.6229	−	4.18615i	−1.42027	−	0.380559i	−0.885578	+	0.464491i	$0.846237\pi$
$12$	1.17845	+	11.9420i	0.0982044	+	0.995166i
$13$	−5.18329	−	19.3443i	−0.398715	−	1.48802i	−0.815360	−	0.578954i	$-0.803461\pi$
$13$	−5.18329	−	19.3443i	−0.398715	−	1.48802i	0.416645	−	0.909069i	$-0.363206\pi$
$14$	1.36611	−	8.42575i	0.0975791	−	0.601839i
$15$	−4.07226	−	25.5531i	−0.271484	−	1.70354i
$16$	−14.7103	+	6.29332i	−0.919396	+	0.393332i
$17$		−	10.6727i		−	0.627804i	−0.949455	−	0.313902i	$-0.898364\pi$
$17$		−	10.6727i		−	0.627804i	0.949455	−	0.313902i	$-0.101636\pi$
$18$	−14.0084	+	11.3033i	−0.778243	+	0.627964i
$19$	−12.2363	+	12.2363i	−0.644014	+	0.644014i	−0.951540	−	0.307526i	$-0.900499\pi$
$19$	−12.2363	+	12.2363i	−0.644014	+	0.644014i	0.307526	+	0.951540i	$0.400499\pi$
$20$	30.8541	−	15.4378i	1.54271	−	0.771890i
$21$	11.6917	−	5.21890i	0.556750	−	0.248519i
$22$	26.2395	−	18.9179i	1.19270	−	0.859905i
$23$	9.25997	−	16.0387i	0.402608	−	0.697337i	−0.591432	−	0.806355i	$-0.701437\pi$
$23$	9.25997	−	16.0387i	0.402608	−	0.697337i	0.994040	+	0.109018i	$0.0347706\pi$
$24$	−19.9962	−	13.2722i	−0.833175	−	0.553009i
$25$	−42.7763	+	24.6969i	−1.71105	+	0.987877i
$26$	36.5308	+	16.4249i	1.40503	+	0.631726i
$27$	−25.7023	−	8.26978i	−0.951939	−	0.306288i
$28$	11.3300	+	12.7698i	0.404644	+	0.456066i
$29$	−6.80700	+	25.4041i	−0.234724	+	0.876002i	0.743549	+	0.668681i	$0.233141\pi$
$29$	−6.80700	+	25.4041i	−0.234724	+	0.876002i	−0.978273	+	0.207321i	$0.933526\pi$
$30$	44.7477	+	25.9965i	1.49159	+	0.866550i
$31$	6.33170	−	10.9668i	0.204248	−	0.353769i	−0.745645	−	0.666344i	$-0.767858\pi$
$31$	6.33170	−	10.9668i	0.204248	−	0.353769i	0.949893	+	0.312575i	$0.101192\pi$
$32$	8.84588	−	30.7531i	0.276434	−	0.961033i
$33$	45.3159	+	17.3455i	1.37321	+	0.525620i
$34$	16.5392	+	13.4936i	0.486447	+	0.396871i
$35$	−26.0295	−	26.0295i	−0.743701	−	0.743701i
$36$	0.194430	−	35.9995i	0.00540085	−	0.999985i
$37$	−18.0450	−	18.0450i	−0.487703	−	0.487703i	0.419878	−	0.907581i	$-0.362073\pi$
$37$	−18.0450	−	18.0450i	−0.487703	−	0.487703i	−0.907581	+	0.419878i	$0.862073\pi$
$38$	−3.49179	−	34.4328i	−0.0918892	−	0.906126i
$39$	9.45532	+	59.3314i	0.242444	+	1.52132i
$40$	−15.0857	+	67.3322i	−0.377142	+	1.68331i
$41$	−7.43075	+	12.8704i	−0.181238	+	0.313913i	−0.942302	−	0.334763i	$-0.891344\pi$
$41$	−7.43075	+	12.8704i	−0.181238	+	0.313913i	0.761065	+	0.648676i	$0.224677\pi$
$42$	−6.69444	+	24.7168i	−0.159391	+	0.588495i
$43$	4.70515	−	17.5598i	0.109422	−	0.408369i	−0.889387	−	0.457155i	$-0.848869\pi$
$43$	4.70515	−	17.5598i	0.109422	−	0.408369i	0.998809	+	0.0487861i	$0.0155353\pi$
$44$	−3.85830	+	64.5810i	−0.0876887	+	1.46775i
$45$	4.21087	+	77.5124i	0.0935749	+	1.72250i
$46$	13.1474	+	34.6280i	0.285813	+	0.752783i
$47$	−16.1577	+	9.32866i	−0.343781	+	0.198482i	−0.661943	−	0.749554i	$-0.730268\pi$
$47$	−16.1577	+	9.32866i	−0.343781	+	0.198482i	0.318162	+	0.948036i	$0.396935\pi$
$48$	45.8492	−	14.2074i	0.955192	−	0.295988i
$49$	−15.3926	+	26.6607i	−0.314134	+	0.544096i
$50$	15.8105	−	97.5143i	0.316209	−	1.95029i
$51$	−3.31635	+	31.8458i	−0.0650265	+	0.624427i
$52$	−71.6397	+	35.8448i	−1.37769	+	0.689323i
$53$	−38.0269	+	38.0269i	−0.717489	+	0.717489i	−0.968090	−	0.250602i	$-0.919372\pi$
$53$	−38.0269	+	38.0269i	−0.717489	+	0.717489i	0.250602	+	0.968090i	$0.419372\pi$
$54$	45.3114	−	29.3748i	0.839100	−	0.543978i
$55$		−	139.504i		−	2.53644i
$56$	−34.1139	+	1.41280i	−0.609176	+	0.0252286i
$57$	40.3136	−	32.7091i	0.707255	−	0.573844i
$58$	−30.7620	−	42.6674i	−0.530378	−	0.735645i
$59$	16.9990	+	63.4412i	0.288119	+	1.07527i	0.946530	+	0.322616i	$0.104562\pi$
$59$	16.9990	+	63.4412i	0.288119	+	1.07527i	−0.658411	+	0.752658i	$0.728771\pi$
$60$	−96.8615	+	36.4769i	−1.61436	+	0.607948i
$61$	−11.9218	−	3.19445i	−0.195440	−	0.0523680i	0.159771	−	0.987154i	$-0.448924\pi$
$61$	−11.9218	−	3.19445i	−0.195440	−	0.0523680i	−0.355211	+	0.934786i	$0.615591\pi$
$62$	8.98980	+	23.6776i	0.144997	+	0.381897i
$63$	−36.5083	+	11.9395i	−0.579496	+	0.189516i
$64$	36.4734	+	52.5898i	0.569897	+	0.821716i
$65$	149.592	−	86.3670i	2.30142	−	1.32872i
$66$	−84.1735	+	48.2950i	−1.27536	+	0.731742i
$67$	8.10824	+	30.2604i	0.121019	+	0.451647i	0.999667	−	0.0258228i	$-0.00822056\pi$
$67$	8.10824	+	30.2604i	0.121019	+	0.451647i	−0.878648	+	0.477470i	$0.841554\pi$
$68$	−41.8216	+	8.57029i	−0.615023	+	0.126034i
$69$	−32.6143	+	44.9801i	−0.472671	+	0.651885i
$70$	73.2470	−	7.42790i	1.04639	−	0.106113i
$71$	38.1082			0.536735			0.268367	−	0.963317i	$-0.413516\pi$
$71$	38.1082			0.536735			0.268367	+	0.963317i	$0.413516\pi$
$72$	55.5418	+	45.8160i	0.771414	+	0.636333i
$73$		−	127.821i		−	1.75098i	−0.483240	−	0.875488i	$-0.660540\pi$
$73$		−	127.821i		−	1.75098i	0.483240	−	0.875488i	$-0.339460\pi$
$74$	50.7786	−	5.14939i	0.686197	−	0.0695864i
$75$	135.313	−	60.4002i	1.80417	−	0.805336i
$76$	57.7745	+	38.1227i	0.760191	+	0.501615i
$77$	66.6769	−	17.8660i	0.865934	−	0.232026i
$78$	−103.899	−	60.3609i	−1.33204	−	0.773858i
$79$	7.54888	+	13.0750i	0.0955554	+	0.165507i	0.909840	−	0.414959i	$-0.136204\pi$
$79$	7.54888	+	13.0750i	0.0955554	+	0.165507i	−0.814285	+	0.580465i	$0.802871\pi$
$80$	−85.2703	−	108.507i	−1.06588	−	1.35634i
$81$	74.1226	+	32.6625i	0.915094	+	0.403240i
$82$	−10.5502	−	27.7876i	−0.128661	−	0.338873i
$83$	−29.3816	+	109.654i	−0.353996	+	1.32113i	0.527748	+	0.849401i	$0.323037\pi$
$83$	−29.3816	+	109.654i	−0.353996	+	1.32113i	−0.881744	+	0.471729i	$0.843630\pi$
$84$	−29.8392	−	41.6241i	−0.355229	−	0.495525i
$85$	88.9171	−	23.8253i	1.04608	−	0.280297i
$86$	21.2633	+	29.4927i	0.247248	+	0.342938i
$87$	28.2050	−	73.6871i	0.324196	−	0.846978i
$88$	−95.2018	−	87.6299i	−1.08184	−	0.995794i
$89$	−102.393			−1.15049			−0.575243	−	0.817983i	$-0.695092\pi$
$89$	−102.393			−1.15049			−0.575243	+	0.817983i	$0.695092\pi$
$90$	−125.443	−	91.4746i	−1.39381	−	1.01638i
$91$	60.4377	+	60.4377i	0.664150	+	0.664150i
$92$	−70.2848	−	23.4065i	−0.763965	−	0.254419i
$93$	−22.3007	+	30.7561i	−0.239792	+	0.330710i
$94$	5.97202	−	36.8337i	0.0635321	−	0.391847i
$95$	−129.260	−	74.6281i	−1.36063	−	0.785559i
$96$	−35.9509	+	89.0142i	−0.374489	+	0.927232i
$97$	40.9773	+	70.9747i	0.422446	+	0.731698i	0.996178	−	0.0873452i	$-0.0278383\pi$
$97$	40.9773	+	70.9747i	0.422446	+	0.731698i	−0.573732	+	0.819043i	$0.694505\pi$
$98$	−21.8545	−	57.5611i	−0.223005	−	0.587358i
$99$	−129.827	−	65.8377i	−1.31138	−	0.665027i
$100$	131.126	+	147.790i	1.31126	+	1.47790i
$101$	−95.5779	−	25.6100i	−0.946316	−	0.253565i	−0.247518	−	0.968883i	$-0.579615\pi$
$101$	−95.5779	−	25.6100i	−0.946316	−	0.253565i	−0.698798	+	0.715319i	$0.746282\pi$
$102$	−45.1579	−	45.4024i	−0.442724	−	0.445122i
$103$	−171.623	−	99.0866i	−1.66624	−	0.962006i	−0.969636	−	0.244554i	$-0.921359\pi$
$103$	−171.623	−	99.0866i	−1.66624	−	0.962006i	−0.696608	−	0.717452i	$-0.745308\pi$
$104$	35.0273	−	156.338i	0.336801	−	1.50325i
$105$	69.5804	+	85.7569i	0.662670	+	0.816732i
$106$	−10.8515	−	107.007i	−0.102373	−	1.00950i
$107$	−49.9526	+	49.9526i	−0.466846	+	0.466846i	−0.900891	−	0.434045i	$-0.857086\pi$
$107$	−49.9526	+	49.9526i	−0.466846	+	0.466846i	0.434045	+	0.900891i	$0.357086\pi$
$108$	−11.7664	+	107.357i	−0.108948	+	0.994047i
$109$	−85.4760	+	85.4760i	−0.784184	+	0.784184i	−0.980534	−	0.196350i	$-0.937091\pi$
$109$	−85.4760	+	85.4760i	−0.784184	+	0.784184i	0.196350	+	0.980534i	$0.437091\pi$
$110$	216.187	+	176.377i	1.96533	+	1.60343i
$111$	48.2367	+	59.4510i	0.434565	+	0.535595i
$112$	40.9413	−	54.6518i	0.365547	−	0.487962i
$113$	17.2776	+	9.97525i	0.152899	+	0.0882765i	0.574498	−	0.818506i	$-0.305197\pi$
$113$	17.2776	+	9.97525i	0.152899	+	0.0882765i	−0.421598	+	0.906783i	$0.638531\pi$
$114$	−0.280381	+	103.828i	−0.00245948	+	0.910770i
$115$	154.295	+	41.3432i	1.34170	+	0.359506i
$116$	105.014	+	6.27389i	0.905290	+	0.0540853i
$117$	−9.77716	−	179.975i	−0.0835655	−	1.53825i
$118$	−119.806	−	53.8666i	−1.01530	−	0.456497i
$119$	22.7749	+	39.4473i	0.191386	+	0.331490i
$120$	65.9360	−	196.223i	0.549467	−	1.63519i
$121$	121.763	+	70.2998i	1.00630	+	0.580990i
$122$	20.0233	−	14.4362i	0.164126	−	0.118330i
$123$	26.1716	−	36.0946i	0.212777	−	0.293452i
$124$	−48.0587	−	16.0047i	−0.387570	−	0.129070i
$125$	−148.776	−	148.776i	−1.19021	−	1.19021i
$126$	27.6556	−	71.6714i	0.219489	−	0.568821i
$127$	76.3214			0.600956			0.300478	−	0.953789i	$-0.402854\pi$
$127$	76.3214			0.600956			0.300478	+	0.953789i	$0.402854\pi$
$128$	−127.611	−	9.96809i	−0.996963	−	0.0778757i
$129$	−19.4959	+	50.9342i	−0.151131	+	0.394838i
$130$	−55.2904	+	341.015i	−0.425310	+	2.62319i
$131$	−26.4201	+	7.07925i	−0.201680	+	0.0540401i	−0.358245	−	0.933628i	$-0.616625\pi$
$131$	−26.4201	+	7.07925i	−0.201680	+	0.0540401i	0.156565	+	0.987668i	$0.449958\pi$
$132$	31.5801	−	191.502i	0.239243	−	1.45077i
$133$	19.1150	−	71.3380i	0.143721	−	0.536376i
$134$	−57.1453	−	25.6935i	−0.426457	−	0.191742i
$135$	11.5210	−	232.595i	0.0853407	−	1.72292i
$136$	39.5945	−	75.6456i	0.291136	−	0.556217i
$137$	103.573	+	179.394i	0.756009	+	1.30945i	0.944871	+	0.327442i	$0.106187\pi$
$137$	103.573	+	179.394i	0.756009	+	1.30945i	−0.188863	+	0.982003i	$0.560480\pi$
$138$	−28.4699	−	107.411i	−0.206304	−	0.778338i
$139$	35.0078	−	9.38031i	0.251855	−	0.0674842i	−0.130683	−	0.991424i	$-0.541717\pi$
$139$	35.0078	−	9.38031i	0.251855	−	0.0674842i	0.382537	+	0.923940i	$0.375050\pi$
$140$	−81.0965	+	122.901i	−0.579261	+	0.877861i
$141$	51.1112	−	22.8147i	0.362490	−	0.161807i
$142$	−48.1807	+	59.0554i	−0.339301	+	0.415883i
$143$			323.913i			2.26512i
$144$	−141.222	+	28.1462i	−0.980712	+	0.195459i
$145$	−226.844			−1.56444
$146$	198.082	+	161.606i	1.35673	+	1.10689i
$147$	54.2137	−	74.7689i	0.368800	−	0.508632i
$148$	−56.2202	+	85.2009i	−0.379866	+	0.575682i
$149$	−24.5447	−	91.6021i	−0.164730	−	0.614779i	−0.998075	−	0.0620258i	$-0.980244\pi$
$149$	−24.5447	−	91.6021i	−0.164730	−	0.614779i	0.833345	−	0.552753i	$-0.186423\pi$
$150$	−77.4772	+	286.057i	−0.516514	+	1.90704i
$151$	85.7840	−	49.5274i	0.568106	−	0.327996i	−0.188286	−	0.982114i	$-0.560293\pi$
$151$	85.7840	−	49.5274i	0.568106	−	0.327996i	0.756393	+	0.654118i	$0.226960\pi$
$152$	−132.123	+	41.3328i	−0.869232	+	0.271926i
$153$	19.7911	−	93.9930i	0.129353	−	0.614333i
$154$	−56.6140	+	125.916i	−0.367624	+	0.817637i
$155$	105.502	+	28.2693i	0.680661	+	0.182383i
$156$	224.901	−	84.6952i	1.44168	−	0.542918i
$157$	9.17060	+	34.2252i	0.0584115	+	0.217995i	0.988962	−	0.148169i	$-0.0473378\pi$
$157$	9.17060	+	34.2252i	0.0584115	+	0.217995i	−0.930551	+	0.366163i	$0.880671\pi$
$158$	−29.8063	−	4.83263i	−0.188647	−	0.0305863i
$159$	125.283	−	101.651i	0.787945	−	0.639314i
$160$	275.960	+	5.04566i	1.72475	+	0.0315354i
$161$			79.0411i			0.490938i
$162$	−144.331	+	73.5706i	−0.890930	+	0.454140i
$163$	79.4058	−	79.4058i	0.487152	−	0.487152i	−0.420254	−	0.907406i	$-0.638059\pi$
$163$	79.4058	−	79.4058i	0.487152	−	0.487152i	0.907406	+	0.420254i	$0.138059\pi$
$164$	56.4007	+	18.7828i	0.343906	+	0.114529i
$165$	−43.3485	+	416.261i	−0.262718	+	2.52280i
$166$	−132.781	−	184.169i	−0.799883	−	1.10945i
$167$	−148.694	+	257.546i	−0.890384	+	1.54219i	−0.0509694	+	0.998700i	$0.516231\pi$
$167$	−148.694	+	257.546i	−0.890384	+	1.54219i	−0.839415	+	0.543491i	$0.817102\pi$
$168$	102.230	+	6.38470i	0.608513	+	0.0380041i
$169$	−200.977	+	116.034i	−1.18922	+	0.686594i
$170$	−75.4977	+	167.916i	−0.444104	+	0.987739i
$171$	−130.454	+	85.0729i	−0.762889	+	0.497502i
$172$	−72.5877	−	4.33665i	−0.422022	−	0.0252131i
$173$	7.21216	−	26.9161i	0.0416888	−	0.155585i	−0.941944	−	0.335771i	$-0.891003\pi$
$173$	7.21216	−	26.9161i	0.0416888	−	0.155585i	0.983633	+	0.180186i	$0.0576700\pi$
$174$	78.5313	+	136.872i	0.451329	+	0.786623i
$175$	105.404	−	182.565i	0.602307	−	1.04323i
$176$	256.163	−	36.7404i	1.45547	−	0.208752i
$177$	−31.0095	−	194.582i	−0.175195	−	1.09933i
$178$	129.457	−	158.677i	0.727288	−	0.891442i
$179$	38.8769	+	38.8769i	0.217190	+	0.217190i	0.807313	−	0.590123i	$-0.200921\pi$
$179$	38.8769	+	38.8769i	0.217190	+	0.217190i	−0.590123	+	0.807313i	$0.700921\pi$
$180$	300.356	−	78.7440i	1.66865	−	0.437467i
$181$	−174.343	−	174.343i	−0.963219	−	0.963219i	0.0361282	−	0.999347i	$-0.488498\pi$
$181$	−174.343	−	174.343i	−0.963219	−	0.963219i	−0.999347	+	0.0361282i	$0.988498\pi$
$182$	−170.071	+	17.2467i	−0.934457	+	0.0947622i
$183$	34.5805	+	13.2363i	0.188965	+	0.0723295i
$184$	125.135	−	79.3257i	0.680080	−	0.431118i
$185$	110.055	−	190.621i	0.594893	−	1.03038i
$186$	−19.4669	−	73.4443i	−0.104661	−	0.394862i
$187$	−44.6774	+	166.738i	−0.238917	+	0.891649i
$188$	49.5298	+	55.8241i	0.263457	+	0.296937i
$189$	112.646	−	24.2814i	0.596009	−	0.128473i
$190$	279.075	−	105.958i	1.46881	−	0.557671i
$191$	−18.5440	+	10.7064i	−0.0970889	+	0.0560543i	−0.547758	−	0.836637i	$-0.684519\pi$
$191$	−18.5440	+	10.7064i	−0.0970889	+	0.0560543i	0.450669	+	0.892691i	$0.351185\pi$
$192$	−92.4902	−	168.254i	−0.481720	−	0.876325i
$193$	62.0847	−	107.534i	0.321683	−	0.557171i	−0.659153	−	0.752009i	$-0.729085\pi$
$193$	62.0847	−	107.534i	0.321683	−	0.557171i	0.980835	+	0.194839i	$0.0624183\pi$
$194$	−161.796	−	26.2328i	−0.834001	−	0.135221i
$195$	−473.199	+	211.224i	−2.42666	+	1.08320i
$196$	116.832	+	38.9079i	0.596082	+	0.198510i
$197$	234.620	−	234.620i	1.19096	−	1.19096i	0.214168	−	0.976797i	$-0.431296\pi$
$197$	234.620	−	234.620i	1.19096	−	1.19096i	0.976797	−	0.214168i	$-0.0687040\pi$
$198$	266.169	−	117.950i	1.34429	−	0.595708i
$199$			202.984i			1.02002i	0.860169	+	0.510010i	$0.170358\pi$
$199$			202.984i			1.02002i	−0.860169	+	0.510010i	$0.829642\pi$
$200$	−394.812	+	16.3509i	−1.97406	+	0.0817544i
$201$	−14.7910	−	92.8123i	−0.0735870	−	0.461753i
$202$	160.528	−	115.736i	0.794693	−	0.572951i
$203$	−29.0515	−	108.422i	−0.143111	−	0.534097i
$204$	127.453	−	12.5772i	0.624769	−	0.0616531i
$205$	−123.815	−	33.1763i	−0.603978	−	0.161835i
$206$	370.538	−	140.684i	1.79873	−	0.682932i
$207$	111.293	−	124.080i	0.537649	−	0.599420i
$208$	197.988	+	251.941i	0.951865	+	1.21126i
$209$	242.389	−	139.943i	1.15976	−	0.669586i
$210$	−220.867	−	0.596439i	−1.05175	−	0.00284019i
$211$	50.6135	+	188.892i	0.239875	+	0.895224i	0.975891	+	0.218260i	$0.0700381\pi$
$211$	50.6135	+	188.892i	0.239875	+	0.895224i	−0.736016	+	0.676964i	$0.763295\pi$
$212$	179.547	+	118.475i	0.846920	+	0.558844i
$213$	−113.710	−	11.8415i	−0.533848	−	0.0555937i
$214$	−14.2547	−	140.566i	−0.0666106	−	0.656852i
$215$	156.800			0.729301
$216$	−151.493	−	153.967i	−0.701355	−	0.712812i
$217$			54.0460i			0.249060i
$218$	−24.3918	−	240.529i	−0.111889	−	1.10334i
$219$	−39.7183	+	381.401i	−0.181362	+	1.74156i
$220$	−546.656	+	112.024i	−2.48480	+	0.509198i
$221$	−206.455	+	55.3196i	−0.934187	+	0.250315i
$222$	−153.116	−	0.413482i	−0.689713	−	0.00186253i
$223$	98.9068	+	171.312i	0.443528	+	0.768214i	0.997948	−	0.0640232i	$-0.0203932\pi$
$223$	98.9068	+	171.312i	0.443528	+	0.768214i	−0.554420	+	0.832237i	$0.687060\pi$
$224$	32.9300	+	132.543i	0.147009	+	0.591710i
$225$	−422.524	+	138.180i	−1.87788	+	0.614133i
$226$	−37.3028	+	14.1629i	−0.165057	+	0.0626679i
$227$	67.3687	−	251.423i	0.296778	−	1.10759i	−0.643016	−	0.765853i	$-0.722317\pi$
$227$	67.3687	−	251.423i	0.296778	−	1.10759i	0.939795	−	0.341740i	$-0.111016\pi$
$228$	−160.545	−	131.706i	−0.704146	−	0.577656i
$229$	108.797	−	29.1520i	0.475095	−	0.127301i	−0.0133229	−	0.999911i	$-0.504241\pi$
$229$	108.797	−	29.1520i	0.475095	−	0.127301i	0.488418	+	0.872610i	$0.337574\pi$
$230$	−259.146	+	186.837i	−1.12672	+	0.812335i
$231$	−204.506	+	32.5911i	−0.885309	+	0.141087i
$232$	−142.493	+	154.805i	−0.614193	+	0.667264i
$233$	−281.212			−1.20692			−0.603460	−	0.797394i	$-0.706212\pi$
$233$	−281.212			−1.20692			−0.603460	+	0.797394i	$0.706212\pi$
$234$	291.265	+	212.394i	1.24472	+	0.907665i
$235$	−113.790	−	113.790i	−0.484211	−	0.484211i
$236$	234.948	−	117.556i	0.995543	−	0.498118i
$237$	−18.4620	−	41.3598i	−0.0778986	−	0.174514i
$238$	−89.9252	−	14.5800i	−0.377837	−	0.0612605i
$239$	−237.936	−	137.372i	−0.995546	−	0.574779i	−0.0886186	−	0.996066i	$-0.528245\pi$
$239$	−237.936	−	137.372i	−0.995546	−	0.574779i	−0.906927	+	0.421287i	$0.861579\pi$
$240$	220.718	+	350.267i	0.919659	+	1.45945i
$241$	−58.8394	−	101.913i	−0.244147	−	0.422875i	0.717745	−	0.696306i	$-0.245175\pi$
$241$	−58.8394	−	101.913i	−0.244147	−	0.422875i	−0.961891	+	0.273432i	$0.911841\pi$
$242$	−262.889	+	99.8122i	−1.08632	+	0.412447i
$243$	−211.023	−	120.493i	−0.868405	−	0.495855i
$244$	−2.94427	+	49.2817i	−0.0120667	+	0.201974i
$245$	−256.480	−	68.7235i	−1.04686	−	0.280504i
$246$	22.8460	+	86.1926i	0.0928698	+	0.350377i
$247$	300.126	+	173.278i	1.21509	+	0.701530i
$248$	85.5635	−	54.2406i	0.345014	−	0.218712i
$249$	121.744	−	318.062i	0.488931	−	1.27736i
$250$	418.656	−	42.4554i	1.67462	−	0.169822i
$251$	162.917	−	162.917i	0.649070	−	0.649070i	−0.303698	−	0.952768i	$-0.598222\pi$
$251$	162.917	−	162.917i	0.649070	−	0.649070i	0.952768	+	0.303698i	$0.0982215\pi$
$252$	76.1023	+	133.473i	0.301993	+	0.529653i
$253$	−211.808	+	211.808i	−0.837188	+	0.837188i
$254$	−96.4944	+	118.274i	−0.379899	+	0.465645i
$255$	−272.720	+	43.4619i	−1.06949	+	0.170439i
$256$	176.788	−	185.154i	0.690579	−	0.723257i
$257$	128.327	+	74.0896i	0.499327	+	0.288286i	0.728435	−	0.685114i	$-0.240248\pi$
$257$	128.327	+	74.0896i	0.499327	+	0.288286i	−0.229109	+	0.973401i	$0.573581\pi$
$258$	−54.2826	−	94.6093i	−0.210398	−	0.366703i
$259$	105.203	+	28.1891i	0.406190	+	0.108838i
$260$	−458.559	−	516.833i	−1.76369	−	1.98782i
$261$	−107.057	+	211.108i	−0.410180	+	0.808843i
$262$	22.4328	−	49.8931i	0.0856214	−	0.190432i
$263$	−116.549	−	201.869i	−0.443153	−	0.767563i	0.554769	−	0.832005i	$-0.312807\pi$
$263$	−116.549	−	201.869i	−0.443153	−	0.767563i	−0.997921	+	0.0644415i	$0.979473\pi$
$264$	256.840	+	291.058i	0.972877	+	1.10249i
$265$	−401.703	−	231.923i	−1.51586	−	0.875182i
$266$	86.3837	+	119.816i	0.324751	+	0.450435i
$267$	305.527	+	31.8170i	1.14430	+	0.119165i
$268$	112.066	−	56.0722i	0.418158	−	0.209224i
$269$	105.443	+	105.443i	0.391983	+	0.391983i	0.875394	−	0.483411i	$-0.160602\pi$
$269$	105.443	+	105.443i	0.391983	+	0.391983i	−0.483411	+	0.875394i	$0.660602\pi$
$270$	345.881	+	311.927i	1.28104	+	1.15529i
$271$	95.2203			0.351367			0.175683	−	0.984447i	$-0.443787\pi$
$271$	95.2203			0.351367			0.175683	+	0.984447i	$0.443787\pi$
$272$	67.1665	+	156.999i	0.246936	+	0.577201i
$273$	−161.558	−	199.118i	−0.591787	−	0.729369i
$274$	−408.952	−	66.3054i	−1.49253	−	0.241990i
$275$	771.676	−	206.770i	2.80610	−	0.751891i
$276$	202.447	+	91.6817i	0.733504	+	0.332180i
$277$	48.0221	−	179.221i	0.173365	−	0.647007i	−0.823459	−	0.567375i	$-0.807959\pi$
$277$	48.0221	−	179.221i	0.173365	−	0.647007i	0.996824	−	0.0796318i	$-0.0253745\pi$
$278$	−29.7244	+	66.1105i	−0.106922	+	0.237808i
$279$	76.0991	−	84.8423i	0.272757	−	0.304094i
$280$	−87.9250	−	281.059i	−0.314018	−	1.00378i
$281$	121.707	+	210.803i	0.433123	+	0.750190i	0.997140	−	0.0755723i	$-0.0240784\pi$
$281$	121.707	+	210.803i	0.433123	+	0.750190i	−0.564018	+	0.825763i	$0.690745\pi$
$282$	−29.2651	+	108.051i	−0.103777	+	0.383159i
$283$	103.140	−	27.6363i	0.364453	−	0.0976548i	−0.0719452	−	0.997409i	$-0.522921\pi$
$283$	103.140	−	27.6363i	0.364453	−	0.0976548i	0.436398	+	0.899754i	$0.356254\pi$
$284$	−30.6013	−	149.329i	−0.107751	−	0.525808i
$285$	362.504	+	262.845i	1.27194	+	0.922264i
$286$	−501.961	−	409.528i	−1.75511	−	1.43192i
$287$		−	63.4272i		−	0.221001i
$288$	134.932	−	254.435i	0.468515	−	0.883456i
$289$	175.094			0.605862
$290$	286.803	−	351.536i	0.988975	−	1.21219i
$291$	−100.216	−	224.512i	−0.344386	−	0.771518i
$292$	−500.876	+	102.642i	−1.71533	+	0.351514i
$293$	−65.6590	−	245.043i	−0.224092	−	0.836324i	−0.982766	−	0.184853i	$-0.940819\pi$
$293$	−65.6590	−	245.043i	−0.224092	−	0.836324i	0.758674	−	0.651471i	$-0.225848\pi$
$294$	47.3247	+	178.545i	0.160968	+	0.607297i
$295$	−490.599	+	283.247i	−1.66305	+	0.960160i
$296$	−60.9541	−	194.844i	−0.205926	−	0.658257i
$297$	366.927	+	236.792i	1.23545	+	0.797280i
$298$	172.986	+	77.7775i	0.580490	+	0.260998i
$299$	−358.256	−	95.9943i	−1.19818	−	0.321051i
$300$	−345.340	−	481.730i	−1.15113	−	1.60577i
$301$	20.0810	+	74.9435i	0.0667144	+	0.248982i
$302$	−31.7064	+	195.556i	−0.104988	+	0.647537i
$303$	277.234	+	106.116i	0.914963	+	0.350218i
$304$	102.993	−	257.006i	0.338792	−	0.845415i
$305$		−	106.455i		−	0.349034i
$306$	120.637	+	149.507i	0.394238	+	0.488584i
$307$	−62.8799	+	62.8799i	−0.204821	+	0.204821i	−0.802062	−	0.597241i	$-0.796264\pi$
$307$	−62.8799	+	62.8799i	−0.204821	+	0.204821i	0.597241	+	0.802062i	$0.296264\pi$
$308$	−123.552	−	246.931i	−0.401142	−	0.801725i
$309$	481.310	+	348.990i	1.55764	+	1.12942i
$310$	−177.197	+	127.754i	−0.571602	+	0.412109i
$311$	−146.124	+	253.095i	−0.469853	+	0.813809i	−0.999406	−	0.0344676i	$-0.989026\pi$
$311$	−146.124	+	253.095i	−0.469853	+	0.813809i	0.529553	+	0.848277i	$0.322360\pi$
$312$	−153.096	+	455.606i	−0.490692	+	1.46028i
$313$	−118.420	+	68.3697i	−0.378338	+	0.218434i	−0.677095	−	0.735896i	$-0.736761\pi$
$313$	−118.420	+	68.3697i	−0.378338	+	0.218434i	0.298757	+	0.954329i	$0.403428\pi$
$314$	−64.6326	−	29.0599i	−0.205836	−	0.0925474i
$315$	−180.971	−	277.508i	−0.574511	−	0.880977i
$316$	45.1736	−	40.0802i	0.142954	−	0.126836i
$317$	34.1866	−	127.586i	0.107844	−	0.402480i	−0.890808	−	0.454380i	$-0.849861\pi$
$317$	34.1866	−	127.586i	0.107844	−	0.402480i	0.998652	+	0.0518996i	$0.0165276\pi$
$318$	−0.871345	+	322.668i	−0.00274008	+	1.01468i
$319$	212.690	−	368.391i	0.666741	−	1.15483i
$320$	−356.719	+	421.270i	−1.11475	+	1.31647i
$321$	164.574	−	133.530i	0.512690	−	0.415980i
$322$	−122.488	−	99.9329i	−0.380399	−	0.310351i
$323$	130.594	+	130.594i	0.404314	+	0.404314i
$324$	68.4687	−	316.683i	0.211323	−	0.977416i
$325$	699.467	+	699.467i	2.15221	+	2.15221i
$326$	22.6596	+	223.448i	0.0695078	+	0.685422i
$327$	281.609	−	228.489i	0.861190	−	0.698742i
$328$	−100.415	+	63.6556i	−0.306145	+	0.194072i
$329$	39.8137	−	68.9594i	0.121014	−	0.209603i
$330$	−590.265	−	593.462i	−1.78868	−	1.79837i
$331$	−54.4461	+	203.196i	−0.164490	+	0.613884i	0.833615	+	0.552346i	$0.186267\pi$
$331$	−54.4461	+	203.196i	−0.164490	+	0.613884i	−0.998105	+	0.0615381i	$0.980399\pi$
$332$	453.280	+	27.0806i	1.36530	+	0.0815679i
$333$	−125.458	−	192.383i	−0.376752	−	0.577725i
$334$	−211.117	−	556.048i	−0.632088	−	1.66481i
$335$	−234.007	+	135.104i	−0.698530	+	0.403296i
$336$	−139.145	+	150.352i	−0.414123	+	0.447475i
$337$	−214.471	+	371.475i	−0.636414	+	1.10230i	0.349800	+	0.936824i	$0.386249\pi$
$337$	−214.471	+	371.475i	−0.636414	+	1.10230i	−0.986214	+	0.165476i	$0.947084\pi$
$338$	74.2828	−	458.155i	0.219772	−	1.35549i
$339$	−48.4545	−	35.1335i	−0.142934	−	0.103639i
$340$	−164.762	−	329.296i	−0.484595	−	0.968517i
$341$	−144.828	+	144.828i	−0.424717	+	0.424717i
$342$	33.0993	−	309.721i	0.0967817	−	0.905616i
$343$		−	340.514i		−	0.992752i
$344$	98.4942	−	107.005i	0.286320	−	0.311061i
$345$	−447.549	−	171.307i	−1.29724	−	0.496543i
$346$	32.5929	+	45.2070i	0.0941993	+	0.130656i
$347$	−75.0550	−	280.109i	−0.216297	−	0.807231i	−0.985706	−	0.168475i	$-0.946116\pi$
$347$	−75.0550	−	280.109i	−0.216297	−	0.807231i	0.769409	−	0.638756i	$-0.220551\pi$
$348$	−311.397	−	51.3516i	−0.894818	−	0.147562i
$349$	359.896	+	96.4340i	1.03122	+	0.276315i	0.734471	−	0.678640i	$-0.237430\pi$
$349$	359.896	+	96.4340i	1.03122	+	0.276315i	0.296751	+	0.954955i	$0.404097\pi$
$350$	149.653	+	394.161i	0.427580	+	1.12617i
$351$	−26.7504	+	540.059i	−0.0762121	+	1.53863i
$352$	−266.935	+	443.422i	−0.758339	+	1.25972i
$353$	−364.255	+	210.302i	−1.03188	+	0.595758i	−0.917523	−	0.397682i	$-0.869815\pi$
$353$	−364.255	+	210.302i	−1.03188	+	0.595758i	−0.114359	+	0.993439i	$0.536481\pi$
$354$	340.745	+	197.958i	0.962558	+	0.559204i
$355$	85.0712	+	317.490i	0.239637	+	0.894339i
$356$	82.2231	+	401.235i	0.230964	+	1.12706i
$357$	−55.6996	−	124.782i	−0.156021	−	0.349530i
$358$	−109.399	+	11.0941i	−0.305585	+	0.0309890i
$359$	626.317			1.74462			0.872308	−	0.488956i	$-0.162622\pi$
$359$	626.317			1.74462			0.872308	+	0.488956i	$0.162622\pi$
$360$	−257.717	+	565.013i	−0.715880	+	1.56948i
$361$			61.5478i			0.170492i
$362$	490.599	−	49.7511i	1.35525	−	0.137434i
$363$	−341.479	−	247.601i	−0.940714	−	0.682096i
$364$	188.297	−	285.361i	0.517299	−	0.783959i
$365$	1064.92	−	285.343i	2.91758	−	0.781762i
$366$	−64.2327	+	36.8539i	−0.175499	+	0.100694i
$367$	−112.057	−	194.088i	−0.305331	−	0.528849i	0.672004	−	0.740548i	$-0.265434\pi$
$367$	−112.057	−	194.088i	−0.305331	−	0.528849i	−0.977335	+	0.211699i	$0.932101\pi$
$368$	−35.2804	+	294.211i	−0.0958707	+	0.799487i
$369$	−89.3083	+	99.5691i	−0.242028	+	0.269835i
$370$	156.257	+	411.556i	0.422317	+	1.11231i
$371$	59.4039	−	221.699i	0.160118	−	0.597570i
$372$	138.427	+	62.6892i	0.372117	+	0.168519i
$373$	306.789	−	82.2039i	0.822491	−	0.220386i	0.177056	−	0.984201i	$-0.443343\pi$
$373$	306.789	−	82.2039i	0.822491	−	0.220386i	0.645435	+	0.763815i	$0.276676\pi$
$374$	−201.905	−	280.045i	−0.539852	−	0.748785i
$375$	397.698	+	490.158i	1.06053	+	1.30709i
$376$	−149.131	+	6.17615i	−0.396624	+	0.0164259i
$377$	526.706			1.39710
$378$	−104.791	+	205.264i	−0.277226	+	0.543027i
$379$	−275.758	−	275.758i	−0.727594	−	0.727594i	0.242546	−	0.970140i	$-0.422017\pi$
$379$	−275.758	−	275.758i	−0.727594	−	0.727594i	−0.970140	+	0.242546i	$0.922017\pi$
$380$	−188.638	+	566.440i	−0.496416	+	1.49063i
$381$	−227.733	−	23.7156i	−0.597724	−	0.0622456i
$382$	6.85400	−	42.2735i	0.0179424	−	0.110664i
$383$	153.374	+	88.5508i	0.400456	+	0.231203i	0.686681	−	0.726959i	$-0.259067\pi$
$383$	153.374	+	88.5508i	0.400456	+	0.231203i	−0.286225	+	0.958162i	$0.592400\pi$
$384$	377.677	+	69.3965i	0.983535	+	0.180720i
$385$	297.694	+	515.621i	0.773231	+	1.33928i
$386$	88.1484	+	232.168i	0.228364	+	0.601472i
$387$	74.0002	−	145.923i	0.191215	−	0.377061i
$388$	245.214	−	217.566i	0.631994	−	0.560736i
$389$	−239.507	−	64.1757i	−0.615699	−	0.164976i	−0.0625273	−	0.998043i	$-0.519916\pi$
$389$	−239.507	−	64.1757i	−0.615699	−	0.164976i	−0.553172	+	0.833067i	$0.686583\pi$
$390$	270.944	−	1000.36i	0.694727	−	2.56503i
$391$	−171.176	−	98.8286i	−0.437791	−	0.252759i
$392$	−208.007	+	131.861i	−0.530631	+	0.336379i
$393$	81.0338	−	12.9139i	0.206193	−	0.0328598i
$394$	66.9521	+	660.220i	0.169929	+	1.67568i
$395$	−92.0801	+	92.0801i	−0.233114	+	0.233114i
$396$	−153.737	+	561.603i	−0.388224	+	1.41819i
$397$	264.780	−	264.780i	0.666953	−	0.666953i	−0.290057	−	0.957009i	$-0.593674\pi$
$397$	264.780	−	264.780i	0.666953	−	0.666953i	0.957009	+	0.290057i	$0.0936742\pi$
$398$	−314.560	−	256.636i	−0.790352	−	0.644813i
$399$	−79.2035	+	206.923i	−0.198505	+	0.518604i
$400$	473.829	−	632.505i	1.18457	−	1.58126i
$401$	424.888	+	245.309i	1.05957	+	0.611744i	0.925314	−	0.379202i	$-0.123802\pi$
$401$	424.888	+	245.309i	1.05957	+	0.611744i	0.134258	+	0.990946i	$0.457135\pi$
$402$	162.530	+	94.4228i	0.404303	+	0.234883i
$403$	−244.965	−	65.6381i	−0.607853	−	0.162874i
$404$	−23.6043	+	395.094i	−0.0584266	+	0.977955i
$405$	−106.652	+	690.452i	−0.263338	+	1.70482i
$406$	204.749	+	92.0587i	0.504308	+	0.226746i
$407$	206.377	+	357.455i	0.507068	+	0.878267i
$408$	−141.650	+	213.413i	−0.347182	+	0.523071i
$409$	472.092	+	272.563i	1.15426	+	0.666412i	0.949922	−	0.312488i	$-0.101162\pi$
$409$	472.092	+	272.563i	1.15426	+	0.666412i	0.204338	+	0.978900i	$0.434496\pi$
$410$	207.954	−	149.929i	0.507206	−	0.365681i
$411$	−253.305	−	567.471i	−0.616313	−	1.38071i
$412$	−250.462	+	752.084i	−0.607918	+	1.82545i
$413$	−198.210	−	198.210i	−0.479927	−	0.479927i
$414$	51.5744	+	329.345i	0.124576	+	0.795520i
$415$	−979.148			−2.35939
$416$	−640.747	−	11.7154i	−1.54026	−	0.0281621i
$417$	−107.373	+	17.1115i	−0.257490	+	0.0410348i
$418$	−89.5888	+	552.558i	−0.214327	+	1.32191i
$419$	−746.051	+	199.904i	−1.78055	+	0.477097i	−0.990684	−	0.136181i	$-0.956517\pi$
$419$	−746.051	+	199.904i	−1.78055	+	0.477097i	−0.789867	+	0.613278i	$0.789850\pi$
$420$	280.170	−	341.519i	0.667072	−	0.813141i
$421$	76.7375	−	286.388i	0.182274	−	0.680257i	−0.812923	−	0.582371i	$-0.802125\pi$
$421$	76.7375	−	286.388i	0.182274	−	0.680257i	0.995198	−	0.0978865i	$-0.0312082\pi$
$422$	−356.714	−	160.385i	−0.845294	−	0.380059i
$423$	−159.598	+	52.1941i	−0.377300	+	0.123390i
$424$	−410.602	+	128.451i	−0.968401	+	0.302950i
$425$	263.582	+	456.537i	0.620193	+	1.07421i
$426$	162.115	−	161.242i	0.380552	−	0.378503i
$427$	50.8811	−	13.6335i	0.119159	−	0.0319287i
$428$	235.855	+	155.630i	0.551063	+	0.363621i
$429$	100.650	−	966.511i	0.234616	−	2.25294i
$430$	−198.244	+	242.989i	−0.461033	+	0.565092i
$431$		−	629.535i		−	1.46064i	−0.683107	−	0.730318i	$-0.739372\pi$
$431$		−	629.535i		−	1.46064i	0.683107	−	0.730318i	$-0.260628\pi$
$432$	430.135	−	40.1018i	0.995682	−	0.0928282i
$433$	−848.660			−1.95995			−0.979977	−	0.199112i	$-0.936194\pi$
$433$	−848.660			−1.95995			−0.979977	+	0.199112i	$0.936194\pi$
$434$	−83.7540	−	68.3312i	−0.192981	−	0.157445i
$435$	676.872	+	70.4880i	1.55603	+	0.162041i
$436$	403.582	+	266.305i	0.925647	+	0.610792i
$437$	82.9468	+	309.562i	0.189810	+	0.708379i
$438$	−540.833	−	543.762i	−1.23478	−	1.24147i
$439$	−395.202	+	228.170i	−0.900233	+	0.519750i	−0.877276	−	0.479987i	$-0.840641\pi$
$439$	−395.202	+	228.170i	−0.900233	+	0.519750i	−0.0229572	+	0.999736i	$0.507308\pi$
$440$	517.545	−	988.775i	1.17624	−	2.24722i
$441$	−184.999	+	206.254i	−0.419500	+	0.467697i
$442$	175.297	−	389.881i	0.396600	−	0.882084i
$443$	−64.7626	−	17.3531i	−0.146191	−	0.0391718i	0.184981	−	0.982742i	$-0.440778\pi$
$443$	−64.7626	−	17.3531i	−0.146191	−	0.0391718i	−0.331172	+	0.943570i	$0.607444\pi$
$444$	194.228	−	236.759i	0.437451	−	0.533240i
$445$	−228.579	−	853.068i	−0.513660	−	1.91701i
$446$	−390.528	−	63.3181i	−0.875623	−	0.141969i
$447$	44.7743	+	280.955i	0.100166	+	0.628535i
$448$	−247.033	−	116.545i	−0.551413	−	0.260145i
$449$		−	692.689i		−	1.54274i	−0.636388	−	0.771369i	$-0.719572\pi$
$449$		−	692.689i		−	1.54274i	0.636388	−	0.771369i	$-0.280428\pi$
$450$	320.069	−	829.479i	0.711263	−	1.84329i
$451$	169.968	−	169.968i	0.376868	−	0.376868i
$452$	25.2145	−	75.7138i	0.0557843	−	0.167508i
$453$	−271.358	+	121.127i	−0.599024	+	0.267389i
$454$	304.450	+	422.278i	0.670596	+	0.930129i
$455$	−368.605	+	638.442i	−0.810121	+	1.40317i
$456$	407.081	−	82.2763i	0.892722	−	0.180431i
$457$	−17.1245	+	9.88683i	−0.0374715	+	0.0216342i	−0.518619	−	0.855006i	$-0.673554\pi$
$457$	−17.1245	+	9.88683i	−0.0374715	+	0.0216342i	0.481147	+	0.876640i	$0.340220\pi$
$458$	−92.3771	+	205.457i	−0.201697	+	0.448597i
$459$	−88.2606	+	274.313i	−0.192289	+	0.597631i
$460$	38.1053	−	637.815i	0.0828377	−	1.38655i
$461$	−117.395	+	438.124i	−0.254653	+	0.950376i	0.713631	+	0.700522i	$0.247049\pi$
$461$	−117.395	+	438.124i	−0.254653	+	0.950376i	−0.968283	+	0.249854i	$0.919617\pi$
$462$	208.055	−	358.125i	0.450335	−	0.775162i
$463$	250.824	−	434.441i	0.541737	−	0.938316i	−0.457067	−	0.889432i	$-0.651100\pi$
$463$	250.824	−	434.441i	0.541737	−	0.938316i	0.998804	−	0.0488843i	$-0.0155666\pi$
$464$	−59.7426	−	416.541i	−0.128756	−	0.897717i
$465$	−306.021	−	117.135i	−0.658109	−	0.251903i
$466$	355.541	−	435.789i	0.762963	−	0.935169i
$467$	−233.073	−	233.073i	−0.499086	−	0.499086i	0.412067	−	0.911153i	$-0.364807\pi$
$467$	−233.073	−	233.073i	−0.499086	−	0.499086i	−0.911153	+	0.412067i	$0.864807\pi$
$468$	−697.393	+	182.835i	−1.49016	+	0.390672i
$469$	−94.5428	−	94.5428i	−0.201584	−	0.201584i
$470$	320.204	−	32.4715i	0.681284	−	0.0690882i
$471$	−16.7289	−	104.973i	−0.0355179	−	0.222872i
$472$	−114.875	+	512.722i	−0.243378	+	1.08628i
$473$	−147.016	+	254.640i	−0.310817	+	0.538350i
$474$	87.4362	+	23.6817i	0.184465	+	0.0499614i
$475$	221.224	−	825.620i	0.465735	−	1.73815i
$476$	136.288	−	120.922i	0.286320	−	0.254037i
$477$	−405.415	+	264.383i	−0.849926	+	0.554261i
$478$	513.708	−	195.042i	1.07470	−	0.408038i
$479$	−90.3640	+	52.1717i	−0.188651	+	0.108918i	−0.591351	−	0.806414i	$-0.701405\pi$
$479$	−90.3640	+	52.1717i	−0.188651	+	0.108918i	0.402700	+	0.915332i	$0.368072\pi$
$480$	−821.859	−	100.805i	−1.71221	−	0.210011i
$481$	−255.536	+	442.601i	−0.531259	+	0.920168i
$482$	232.324	+	37.6677i	0.481999	+	0.0781488i
$483$	24.5607	−	235.848i	0.0508503	−	0.488298i
$484$	177.697	−	533.588i	0.367143	−	1.10245i
$485$	−499.835	+	499.835i	−1.03059	+	1.03059i
$486$	453.524	−	174.676i	0.933177	−	0.359417i
$487$		−	29.0400i		−	0.0596304i	−0.999555	−	0.0298152i	$-0.990508\pi$
$487$		−	29.0400i		−	0.0596304i	0.999555	−	0.0298152i	$-0.00949188\pi$
$488$	−72.6484	−	66.8703i	−0.148870	−	0.137029i
$489$	−261.610	+	212.262i	−0.534990	+	0.434074i
$490$	430.771	−	310.573i	0.879124	−	0.633823i
$491$	205.184	+	765.757i	0.417890	+	1.55959i	0.778976	+	0.627054i	$0.215739\pi$
$491$	205.184	+	765.757i	0.417890	+	1.55959i	−0.361086	+	0.932533i	$0.617594\pi$
$492$	−162.455	−	73.5708i	−0.330194	−	0.149534i
$493$	271.129	+	72.6488i	0.549957	+	0.147361i
$494$	−647.979	+	246.021i	−1.31170	+	0.498019i
$495$	258.692	−	1228.60i	0.522611	−	2.48202i
$496$	−24.1237	+	201.173i	−0.0486365	+	0.405591i
$497$	−140.852	+	81.3207i	−0.283404	+	0.163623i
$498$	338.972	+	590.795i	0.680666	+	1.18634i
$499$	192.975	+	720.192i	0.386723	+	1.44327i	0.835432	+	0.549593i	$0.185217\pi$
$499$	192.975	+	720.192i	0.386723	+	1.44327i	−0.448709	+	0.893678i	$0.648116\pi$
$500$	−463.521	+	702.459i	−0.927041	+	1.40492i
$501$	523.711	−	722.278i	1.04533	−	1.44167i
$502$	46.4905	+	458.446i	0.0926106	+	0.913239i
$503$	22.4731			0.0446781			0.0223390	−	0.999750i	$-0.492889\pi$
$503$	22.4731			0.0446781			0.0223390	+	0.999750i	$0.492889\pi$
$504$	−303.057	−	50.8174i	−0.601304	−	0.100828i
$505$		−	853.458i		−	1.69002i
$506$	−60.4425	−	596.028i	−0.119452	−	1.17792i
$507$	635.745	−	283.780i	1.25393	−	0.559725i
$508$	−61.2871	−	299.071i	−0.120644	−	0.588722i
$509$	−810.744	+	217.238i	−1.59282	+	0.426794i	−0.942863	−	0.333180i	$-0.891878\pi$
$509$	−810.744	+	217.238i	−1.59282	+	0.426794i	−0.649954	+	0.759974i	$0.725212\pi$
$510$	277.452	−	477.578i	0.544023	−	0.936427i
$511$	272.763	+	472.440i	0.533784	+	0.924540i
$512$	63.4128	+	508.058i	0.123853	+	0.992301i
$513$	415.692	−	213.309i	0.810316	−	0.415808i
$514$	−277.061	+	105.193i	−0.539029	+	0.204656i
$515$	442.394	−	1651.04i	0.859018	−	3.20590i
$516$	215.244	+	35.4954i	0.417140	+	0.0687895i
$517$	291.482	−	78.1024i	0.563795	−	0.151068i
$518$	−176.694	+	127.391i	−0.341108	+	0.245929i
$519$	−29.8838	+	78.0731i	−0.0575796	+	0.150430i
$520$	1380.69	−	57.1803i	2.65517	−	0.109962i
$521$	−860.751			−1.65211			−0.826057	−	0.563587i	$-0.809421\pi$
$521$	−860.751			−1.65211			−0.826057	+	0.563587i	$0.809421\pi$
$522$	−191.796	−	432.811i	−0.367425	−	0.829140i
$523$	590.670	+	590.670i	1.12939	+	1.12939i	0.990277	+	0.139112i	$0.0444248\pi$
$523$	590.670	+	590.670i	1.12939	+	1.12939i	0.139112	+	0.990277i	$0.455575\pi$
$524$	48.9562	+	97.8443i	0.0934279	+	0.186726i
$525$	−371.239	+	511.996i	−0.707122	+	0.975230i
$526$	460.187	+	74.6124i	0.874881	+	0.141849i
$527$	−117.045	−	67.5761i	−0.222097	−	0.128228i
$528$	−775.773	+	30.0298i	−1.46927	+	0.0568747i
$529$	93.0058	+	161.091i	0.175814	+	0.304519i
$530$	867.286	−	329.287i	1.63639	−	0.621295i
$531$	32.0650	+	590.242i	0.0603860	+	1.11157i
$532$	−294.892	−	17.6179i	−0.554309	−	0.0331164i
$533$	287.485	+	77.0315i	0.539372	+	0.144524i
$534$	−435.589	+	433.243i	−0.815710	+	0.811316i
$535$	−527.681	−	304.657i	−0.986320	−	0.569452i
$536$	−54.7933	+	244.560i	−0.102226	+	0.456268i
$537$	−103.923	−	128.084i	−0.193525	−	0.238517i
$538$	−296.717	+	30.0897i	−0.551519	+	0.0559289i
$539$	352.082	−	352.082i	0.653214	−	0.653214i
$540$	−920.690	+	141.631i	−1.70498	+	0.262279i
$541$	709.094	−	709.094i	1.31071	−	1.31071i	0.389817	−	0.920892i	$-0.372538\pi$
$541$	709.094	−	709.094i	1.31071	−	1.31071i	0.920892	−	0.389817i	$-0.127462\pi$
$542$	−120.389	+	147.561i	−0.222119	+	0.272253i
$543$	466.041	+	574.389i	0.858270	+	1.05781i
$544$	−328.217	−	94.4092i	−0.603340	−	0.173546i
$545$	−902.939	−	521.312i	−1.65677	−	0.956536i
$546$	512.829	+	1.38486i	0.939247	+	0.00253638i
$547$	−376.806	−	100.965i	−0.688860	−	0.184579i	−0.102624	−	0.994720i	$-0.532724\pi$
$547$	−376.806	−	100.965i	−0.688860	−	0.184579i	−0.586235	+	0.810141i	$0.699391\pi$
$548$	619.797	−	549.914i	1.13102	−	1.00349i
$549$	−99.0706	−	50.2406i	−0.180456	−	0.0915130i
$550$	−655.215	+	1457.27i	−1.19130	+	2.64959i
$551$	−227.558	−	394.143i	−0.412992	−	0.715323i
$552$	−398.034	+	197.813i	−0.721076	+	0.358358i
$553$	−55.8028	−	32.2178i	−0.100909	−	0.0582600i
$554$	217.020	+	301.011i	0.391733	+	0.543341i
$555$	−387.622	+	534.590i	−0.698418	+	0.963225i
$556$	−64.8691	−	129.648i	−0.116671	−	0.233180i
$557$	121.809	+	121.809i	0.218688	+	0.218688i	0.807946	−	0.589257i	$-0.200580\pi$
$557$	121.809	+	121.809i	0.218688	+	0.218688i	−0.589257	+	0.807946i	$0.700580\pi$
$558$	35.2651	+	225.197i	0.0631990	+	0.403578i
$559$	−364.071			−0.651290
$560$	546.716	+	219.091i	0.976278	+	0.391234i
$561$	185.122	−	483.642i	0.329986	−	0.862106i
$562$	−480.554	−	77.9146i	−0.855079	−	0.138638i
$563$	−701.738	+	188.030i	−1.24643	+	0.333979i	−0.820955	−	0.570993i	$-0.806558\pi$
$563$	−701.738	+	188.030i	−1.24643	+	0.333979i	−0.425472	+	0.904972i	$0.639892\pi$
$564$	−130.444	−	181.962i	−0.231284	−	0.322628i
$565$	−44.5367	+	166.213i	−0.0788261	+	0.294183i
$566$	−87.5742	+	194.775i	−0.154725	+	0.344126i
$567$	−343.665	+	37.4498i	−0.606110	+	0.0660490i
$568$	270.102	+	141.377i	0.475533	+	0.248904i
$569$	−114.358	−	198.073i	−0.200980	−	0.348108i	0.747864	−	0.663852i	$-0.231079\pi$
$569$	−114.358	−	198.073i	−0.200980	−	0.348108i	−0.948845	+	0.315744i	$0.897746\pi$
$570$	−865.645	+	229.445i	−1.51868	+	0.402536i
$571$	−277.397	+	74.3283i	−0.485809	+	0.130172i	−0.493406	−	0.869799i	$-0.664248\pi$
$571$	−277.397	+	74.3283i	−0.485809	+	0.130172i	0.00759710	+	0.999971i	$0.497582\pi$
$572$	1269.27	−	260.106i	2.21901	−	0.454731i
$573$	58.6596	−	26.1841i	0.102373	−	0.0456966i
$574$	98.2919	+	80.1920i	0.171240	+	0.139707i
$575$			914.771i			1.59091i
$576$	223.696	+	530.788i	0.388361	+	0.921507i
$577$	1015.70			1.76031			0.880156	−	0.474685i	$-0.157438\pi$
$577$	1015.70			1.76031			0.880156	+	0.474685i	$0.157438\pi$
$578$	−221.374	+	271.340i	−0.383000	+	0.469446i
$579$	−218.667	+	301.575i	−0.377663	+	0.520855i
$580$	182.159	+	888.904i	0.314067	+	1.53259i
$581$	−125.398	−	467.990i	−0.215831	−	0.805491i
$582$	474.626	+	128.550i	0.815509	+	0.220877i
$583$	753.278	−	434.905i	1.29207	−	0.745978i
$584$	474.203	−	905.969i	0.811991	−	1.55132i
$585$	1477.60	−	483.226i	2.52581	−	0.826027i
$586$	462.752	+	208.061i	0.789678	+	0.355053i
$587$	19.9763	+	5.35264i	0.0340312	+	0.00911864i	0.275794	−	0.961217i	$-0.411059\pi$
$587$	19.9763	+	5.35264i	0.0340312	+	0.00911864i	−0.241763	+	0.970335i	$0.577726\pi$
$588$	−336.521	−	152.400i	−0.572315	−	0.259183i
$589$	56.7166	+	211.669i	0.0962931	+	0.359371i
$590$	181.329	−	1118.38i	0.307337	−	1.89557i
$591$	−772.979	+	627.170i	−1.30792	+	1.06120i
$592$	379.011	+	151.885i	0.640222	+	0.256563i
$593$			938.907i			1.58332i	0.610964	+	0.791659i	$0.290782\pi$
$593$			938.907i			1.58332i	−0.610964	+	0.791659i	$0.709218\pi$
$594$	−830.864	+	269.240i	−1.39876	+	0.453266i
$595$	−277.805	+	277.805i	−0.466899	+	0.466899i
$596$	−339.239	+	169.738i	−0.569193	+	0.284795i
$597$	63.0738	−	605.676i	0.105651	−	1.01453i
$598$	601.708	−	433.814i	1.00620	−	0.725442i
$599$	337.675	−	584.869i	0.563730	−	0.976410i	−0.433436	−	0.901184i	$-0.642699\pi$
$599$	337.675	−	584.869i	0.563730	−	0.976410i	0.997167	−	0.0752255i	$-0.0239677\pi$
$600$	1183.15	+	73.8924i	1.97191	+	0.123154i
$601$	−744.438	+	429.801i	−1.23866	+	0.715144i	−0.968821	−	0.247761i	$-0.920305\pi$
$601$	−744.438	+	429.801i	−1.23866	+	0.715144i	−0.269844	+	0.962904i	$0.586972\pi$
$602$	−141.527	−	63.6330i	−0.235095	−	0.105703i
$603$	15.2945	+	281.535i	0.0253639	+	0.466891i
$604$	−262.962	−	296.379i	−0.435368	−	0.490694i
$605$	−313.869	+	1171.38i	−0.518792	+	1.93616i
$606$	−514.957	+	295.459i	−0.849764	+	0.487556i
$607$	−46.7213	+	80.9237i	−0.0769708	+	0.133317i	−0.901942	−	0.431858i	$-0.857858\pi$
$607$	−46.7213	+	80.9237i	−0.0769708	+	0.133317i	0.824971	+	0.565175i	$0.191192\pi$
$608$	268.062	+	484.543i	0.440891	+	0.796946i
$609$	52.9955	+	332.543i	0.0870206	+	0.546047i
$610$	164.972	+	134.593i	0.270446	+	0.220645i
$611$	264.207	+	264.207i	0.432417	+	0.432417i
$612$	−384.210	−	2.07509i	−0.627795	−	0.00339067i
$613$	74.1488	+	74.1488i	0.120960	+	0.120960i	0.764996	−	0.644035i	$-0.222741\pi$
$613$	74.1488	+	74.1488i	0.120960	+	0.120960i	−0.644035	+	0.764996i	$0.722741\pi$
$614$	−17.9437	−	176.944i	−0.0292242	−	0.288182i
$615$	359.140	+	137.467i	0.583967	+	0.223524i
$616$	538.873	+	120.734i	0.874793	+	0.195996i
$617$	−386.923	+	670.170i	−0.627103	+	1.08617i	0.361027	+	0.932555i	$0.382426\pi$
$617$	−386.923	+	670.170i	−0.627103	+	1.08617i	−0.988130	+	0.153619i	$0.950907\pi$
$618$	−1149.35	+	304.643i	−1.85979	+	0.492951i
$619$	187.068	−	698.147i	0.302210	−	1.12786i	−0.633111	−	0.774061i	$-0.718222\pi$
$619$	187.068	−	698.147i	0.302210	−	1.12786i	0.935321	−	0.353802i	$-0.115111\pi$
$620$	26.0553	−	436.119i	0.0420247	−	0.703418i
$621$	−370.640	+	335.655i	−0.596844	+	0.540508i
$622$	−207.468	−	546.437i	−0.333551	−	0.878517i
$623$	378.456	−	218.501i	0.607473	−	0.350725i
$624$	−512.482	−	813.280i	−0.821286	−	1.30333i
$625$	289.953	−	502.213i	0.463924	−	0.803540i
$626$	43.7689	−	269.954i	0.0699183	−	0.431236i
$627$	−766.741	+	342.254i	−1.22287	+	0.545859i
$628$	126.749	−	63.4189i	0.201830	−	0.100985i
$629$	−192.588	+	192.588i	−0.306182	+	0.306182i
$630$	658.853	+	70.4105i	1.04580	+	0.111763i
$631$			232.499i			0.368461i	0.982883	+	0.184231i	$0.0589793\pi$
$631$			232.499i			0.368461i	−0.982883	+	0.184231i	$0.941021\pi$
$632$	4.99782	+	120.679i	0.00790795	+	0.190947i
$633$	−92.3288	−	579.356i	−0.145859	−	0.915255i
$634$	154.495	+	214.288i	0.243683	+	0.337993i
$635$	170.377	+	635.856i	0.268310	+	1.00135i
$636$	−498.930	−	409.304i	−0.784481	−	0.643560i
$637$	595.517	+	159.568i	0.934877	+	0.250500i
$638$	301.979	+	795.364i	0.473322	+	1.24665i
$639$	335.614	+	70.6667i	0.525218	+	0.110589i
$640$	−201.828	−	1085.42i	−0.315356	−	1.69597i
$641$	−154.261	+	89.0624i	−0.240656	+	0.138943i	−0.615478	−	0.788154i	$-0.711037\pi$
$641$	−154.261	+	89.0624i	−0.240656	+	0.138943i	0.374822	+	0.927097i	$0.377704\pi$
$642$	−1.14461	+	423.860i	−0.00178288	+	0.660218i
$643$	119.295	+	445.215i	0.185529	+	0.692402i	0.994517	+	0.104577i	$0.0333489\pi$
$643$	119.295	+	445.215i	0.185529	+	0.692402i	−0.808988	+	0.587825i	$0.799984\pi$
$644$	309.728	−	63.4710i	0.480944	−	0.0985575i
$645$	−467.869	−	48.7229i	−0.725379	−	0.0755393i
$646$	−367.490	+	37.2667i	−0.568869	+	0.0576884i
$647$	−978.908			−1.51300			−0.756498	−	0.653996i	$-0.773091\pi$
$647$	−978.908			−1.51300			−0.756498	+	0.653996i	$0.773091\pi$
$648$	404.191	+	506.492i	0.623751	+	0.781623i
$649$		−	1062.30i		−	1.63682i
$650$	−1968.30	+	199.603i	−3.02815	+	0.307081i
$651$	16.7939	−	161.266i	0.0257970	−	0.247720i
$652$	−374.921	−	247.393i	−0.575032	−	0.379437i
$653$	−123.593	+	33.1167i	−0.189270	+	0.0507148i	−0.352209	−	0.935921i	$-0.614569\pi$
$653$	−123.593	+	33.1167i	−0.189270	+	0.0507148i	0.162939	+	0.986636i	$0.447903\pi$
$654$	−1.95859	+	725.286i	−0.00299479	+	1.10900i
$655$	−117.959	−	204.310i	−0.180089	−	0.311924i
$656$	28.3111	−	236.093i	0.0431572	−	0.359897i
$657$	237.028	−	1125.71i	0.360773	−	1.71341i
$658$	56.5278	+	148.885i	0.0859085	+	0.226269i
$659$	119.886	−	447.422i	0.181922	−	0.678941i	−0.813347	−	0.581779i	$-0.802357\pi$
$659$	119.886	−	447.422i	0.181922	−	0.678941i	0.995269	−	0.0971622i	$-0.0309766\pi$
$660$	1665.96	−	164.399i	2.52418	−	0.249089i
$661$	−1025.09	+	274.672i	−1.55082	+	0.415541i	−0.929743	−	0.368210i	$-0.879971\pi$
$661$	−1025.09	+	274.672i	−1.55082	+	0.415541i	−0.621076	+	0.783750i	$0.713304\pi$
$662$	−246.051	−	341.277i	−0.371678	−	0.515525i
$663$	633.224	−	100.914i	0.955090	−	0.152207i
$664$	−615.055	+	668.200i	−0.926287	+	1.00632i
$665$	637.009			0.957908
$666$	456.750	+	48.8121i	0.685811	+	0.0732914i
$667$	344.417	+	344.417i	0.516367	+	0.516367i
$668$	1128.61	+	375.856i	1.68954	+	0.562658i
$669$	−241.892	−	541.904i	−0.361573	−	0.810022i
$670$	86.4909	−	533.451i	0.129091	−	0.796195i
$671$	172.882	+	99.8132i	0.257648	+	0.148753i
$672$	−57.0733	−	405.723i	−0.0849305	−	0.603754i
$673$	−477.904	−	827.754i	−0.710110	−	1.22995i	−0.964815	−	0.262928i	$-0.915312\pi$
$673$	−477.904	−	827.754i	−0.710110	−	1.22995i	0.254705	−	0.967019i	$-0.418021\pi$
$674$	−304.508	−	802.024i	−0.451793	−	1.18995i
$675$	1303.69	−	281.018i	1.93139	−	0.416323i
$676$	616.076	+	694.366i	0.911355	+	1.02717i
$677$	903.751	+	242.159i	1.33493	+	0.357695i	0.854553	−	0.519365i	$-0.173831\pi$
$677$	903.751	+	242.159i	1.33493	+	0.357695i	0.480382	+	0.877060i	$0.340498\pi$
$678$	115.707	−	30.6691i	0.170660	−	0.0452346i
$679$	−302.912	−	174.886i	−0.446115	−	0.257565i
$680$	718.614	+	161.005i	1.05679	+	0.236771i
$681$	−279.145	+	729.280i	−0.409904	+	1.07090i
$682$	−41.3288	−	407.547i	−0.0605995	−	0.597576i
$683$	−393.319	+	393.319i	−0.575870	+	0.575870i	−0.933763	−	0.357893i	$-0.883495\pi$
$683$	−393.319	+	393.319i	−0.575870	+	0.575870i	0.357893	+	0.933763i	$0.383495\pi$
$684$	438.120	+	442.878i	0.640526	+	0.647483i
$685$	−1263.37	+	1263.37i	−1.84434	+	1.84434i
$686$	527.688	+	430.517i	0.769224	+	0.627576i
$687$	−333.693	+	53.1788i	−0.485725	+	0.0774073i
$688$	41.2954	+	287.922i	0.0600224	+	0.418492i
$689$	932.708	+	538.499i	1.35371	+	0.781567i
$690$	831.314	−	476.971i	1.20480	−	0.691262i
$691$	358.967	+	96.1850i	0.519489	+	0.139197i	0.509030	−	0.860749i	$-0.330004\pi$
$691$	358.967	+	96.1850i	0.519489	+	0.139197i	0.0104590	+	0.999945i	$0.496671\pi$
$692$	−111.264	−	6.64732i	−0.160786	−	0.00960596i
$693$	620.346	−	33.7004i	0.895161	−	0.0486297i
$694$	528.972	+	237.835i	0.762208	+	0.342702i
$695$	156.300	+	270.720i	0.224892	+	0.389525i
$696$	473.282	−	417.641i	0.680003	−	0.600058i
$697$	137.362	+	79.3059i	0.197076	+	0.113782i
$698$	−604.464	+	435.801i	−0.865995	+	0.624357i
$699$	839.099	+	87.3819i	1.20043	+	0.125010i
$700$	−800.032	−	266.430i	−1.14290	−	0.380614i
$701$	314.121	+	314.121i	0.448105	+	0.448105i	0.894724	−	0.446619i	$-0.147372\pi$
$701$	314.121	+	314.121i	0.448105	+	0.448105i	−0.446619	+	0.894724i	$0.647372\pi$
$702$	−803.097	−	724.259i	−1.14401	−	1.03171i
$703$	441.607			0.628175
$704$	−349.672	−	974.290i	−0.496693	−	1.38394i
$705$	304.175	+	374.891i	0.431453	+	0.531760i
$706$	134.631	−	830.366i	0.190696	−	1.17616i
$707$	407.916	−	109.301i	0.576968	−	0.154598i
$708$	−737.582	+	277.764i	−1.04178	+	0.392323i
$709$	158.573	−	591.802i	0.223657	−	0.834699i	−0.759281	−	0.650763i	$-0.774449\pi$
$709$	158.573	−	591.802i	0.223657	−	0.834699i	0.982938	−	0.183936i	$-0.0588840\pi$
$710$	−599.565	−	269.575i	−0.844458	−	0.379683i
$711$	42.2362	+	129.149i	0.0594039	+	0.181644i
$712$	−725.741	−	379.868i	−1.01930	−	0.533522i
$713$	−117.263	−	203.105i	−0.164464	−	0.284860i
$714$	263.794	+	71.4475i	0.369460	+	0.100067i
$715$	−2698.61	+	723.091i	−3.77428	+	1.01132i
$716$	121.123	−	183.561i	0.169166	−	0.256369i
$717$	667.281	+	483.834i	0.930657	+	0.674804i
$718$	−791.863	+	970.591i	−1.10287	+	1.35180i
$719$		−	1339.60i		−	1.86314i	−0.363563	−	0.931570i	$-0.618440\pi$
$719$		−	1339.60i		−	1.86314i	0.363563	−	0.931570i	$-0.381560\pi$
$720$	−549.754	−	1113.73i	−0.763547	−	1.54685i
$721$	845.782			1.17307
$722$	−95.3793	−	77.8158i	−0.132104	−	0.107778i
$723$	143.901	+	322.377i	0.199033	+	0.445888i
$724$	−543.174	+	823.173i	−0.750240	+	1.13698i
$725$	−336.224	−	1254.80i	−0.463757	−	1.73076i
$726$	815.439	−	216.138i	1.12319	−	0.297711i
$727$	89.3724	−	51.5992i	0.122933	−	0.0709755i	−0.437272	−	0.899329i	$-0.644055\pi$
$727$	89.3724	−	51.5992i	0.122933	−	0.0709755i	0.560206	+	0.828354i	$0.310722\pi$
$728$	204.152	+	652.586i	0.280428	+	0.896410i
$729$	592.221	+	425.106i	0.812375	+	0.583135i
$730$	−904.199	+	2011.04i	−1.23863	+	2.75485i
$731$	−187.410	−	50.2165i	−0.256375	−	0.0686956i
$732$	24.0987	−	146.135i	0.0329218	−	0.199638i
$733$	−95.9769	−	358.191i	−0.130937	−	0.488664i	0.869045	−	0.494734i	$-0.164734\pi$
$733$	−95.9769	−	358.191i	−0.130937	−	0.488664i	−0.999982	+	0.00607015i	$0.998068\pi$
$734$	442.448	+	71.7363i	0.602791	+	0.0977333i
$735$	743.946	+	284.758i	1.01217	+	0.387426i
$736$	−411.328	−	426.649i	−0.558869	−	0.579687i
$737$		−	506.698i		−	0.687514i
$738$	−41.3863	−	264.286i	−0.0560790	−	0.358111i
$739$	499.501	−	499.501i	0.675915	−	0.675915i	−0.283158	−	0.959073i	$-0.591382\pi$
$739$	499.501	−	499.501i	0.675915	−	0.675915i	0.959073	+	0.283158i	$0.0913821\pi$
$740$	−835.338	−	278.187i	−1.12883	−	0.375929i
$741$	−841.692	−	610.297i	−1.13589	−	0.823612i
$742$	268.456	+	372.354i	0.361801	+	0.501825i
$743$	347.803	−	602.412i	0.468106	−	0.810784i	−0.531229	−	0.847228i	$-0.678270\pi$
$743$	347.803	−	602.412i	0.468106	−	0.810784i	0.999336	+	0.0364442i	$0.0116031\pi$
$744$	−272.164	+	135.259i	−0.365812	+	0.181800i
$745$	708.371	−	408.978i	0.950833	−	0.548964i
$746$	−260.489	+	579.356i	−0.349180	+	0.776617i
$747$	−462.100	+	911.224i	−0.618607	+	1.21985i
$748$	689.252	+	41.1784i	0.921460	+	0.0550513i
$749$	78.0337	−	291.226i	0.104184	−	0.388819i
$750$	−1262.40	−	3.40905i	−1.68320	−	0.00454540i
$751$	68.1628	−	118.062i	0.0907628	−	0.157206i	−0.817070	−	0.576539i	$-0.804403\pi$
$751$	68.1628	−	118.062i	0.0907628	−	0.157206i	0.907832	+	0.419333i	$0.137736\pi$
$752$	178.977	−	238.913i	0.238002	−	0.317704i
$753$	−536.744	+	435.497i	−0.712808	+	0.578349i
$754$	−665.923	+	816.226i	−0.883187	+	1.08253i
$755$	604.128	+	604.128i	0.800170	+	0.800170i
$756$	−185.604	−	421.912i	−0.245509	−	0.558084i
$757$	−490.578	−	490.578i	−0.648056	−	0.648056i	0.304467	−	0.952523i	$-0.401522\pi$
$757$	−490.578	−	490.578i	−0.648056	−	0.648056i	−0.952523	+	0.304467i	$0.901522\pi$
$758$	775.981	−	78.6914i	1.02372	−	0.103814i
$759$	697.824	−	566.192i	0.919399	−	0.745971i
$760$	−639.302	−	1008.49i	−0.841187	−	1.32696i
$761$	219.368	−	379.956i	0.288263	−	0.499286i	−0.685132	−	0.728418i	$-0.740256\pi$
$761$	219.368	−	379.956i	0.288263	−	0.499286i	0.973395	+	0.229133i	$0.0735890\pi$
$762$	324.678	−	322.929i	0.426086	−	0.423791i
$763$	133.527	−	498.329i	0.175003	−	0.653118i
$764$	56.8447	+	64.0685i	0.0744041	+	0.0838593i
$765$	827.264	−	44.9412i	1.08139	−	0.0587467i
$766$	−331.139	+	125.725i	−0.432296	+	0.164132i
$767$	1139.11	−	657.668i	1.48516	−	0.857455i
$768$	−585.046	+	497.540i	−0.761778	+	0.647838i
$769$	−4.71464	+	8.16600i	−0.00613087	+	0.0106190i	−0.869075	−	0.494681i	$-0.835285\pi$
$769$	−4.71464	+	8.16600i	−0.00613087	+	0.0106190i	0.862944	+	0.505300i	$0.168618\pi$
$770$	−1175.43	−	190.578i	−1.52653	−	0.247503i
$771$	−359.888	−	260.949i	−0.466781	−	0.338455i
$772$	−471.234	−	156.932i	−0.610406	−	0.203280i
$773$	−99.7597	+	99.7597i	−0.129055	+	0.129055i	−0.768684	−	0.639629i	$-0.779088\pi$
$773$	−99.7597	+	99.7597i	−0.129055	+	0.129055i	0.639629	+	0.768684i	$0.279088\pi$
$774$	132.574	+	299.169i	0.171284	+	0.386523i
$775$			625.494i			0.807089i
$776$	27.1295	+	655.075i	0.0349607	+	0.844168i
$777$	−305.153	−	116.803i	−0.392732	−	0.150325i
$778$	402.264	−	290.021i	0.517049	−	0.372777i
$779$	−66.5614	−	248.411i	−0.0854447	−	0.318884i
$780$	1207.68	+	1684.65i	1.54831	+	2.15981i
$781$	−595.361	−	159.527i	−0.762306	−	0.204259i
$782$	369.573	−	140.318i	0.472600	−	0.179434i
$783$	385.042	−	596.651i	0.491752	−	0.762007i
$784$	58.6455	−	489.058i	0.0748030	−	0.623799i
$785$	−264.668	+	152.806i	−0.337156	+	0.194657i
$786$	−82.4399	+	141.904i	−0.104885	+	0.180539i
$787$	−381.041	−	1422.06i	−0.484169	−	1.80694i	−0.583774	−	0.811916i	$-0.698425\pi$
$787$	−381.041	−	1422.06i	−0.484169	−	1.80694i	0.0996051	−	0.995027i	$-0.468242\pi$
$788$	−1107.78	−	730.972i	−1.40581	−	0.927629i
$789$	285.040	+	638.566i	0.361267	+	0.809335i
$790$	−26.2763	−	259.113i	−0.0332612	−	0.327991i
$791$	−85.1465			−0.107644
$792$	−675.933	−	948.286i	−0.853451	−	1.19733i
$793$			247.177i			0.311699i
$794$	75.5587	+	745.090i	0.0951621	+	0.938401i
$795$	1126.56	+	816.850i	1.41706	+	1.02748i
$796$	795.406	−	162.999i	0.999254	−	0.204772i
$797$	405.134	−	108.555i	0.508324	−	0.136205i	0.00446366	−	0.999990i	$-0.498579\pi$
$797$	405.134	−	108.555i	0.508324	−	0.136205i	0.503861	+	0.863785i	$0.331913\pi$
$798$	−220.526	−	384.356i	−0.276349	−	0.481649i
$799$	99.5617	+	172.446i	0.124608	+	0.215827i
$800$	381.111	+	1533.97i	0.476389	+	1.91746i
$801$	−901.766	−	189.875i	−1.12580	−	0.237047i
$802$	−917.344	+	348.292i	−1.14382	+	0.434280i
$803$	−535.079	+	1996.94i	−0.666350	+	2.48685i
$804$	−351.814	+	132.489i	−0.437580	+	0.164787i
$805$	−658.514	+	176.448i	−0.818030	+	0.219191i
$806$	411.431	−	296.630i	0.510460	−	0.368027i
$807$	−281.864	−	347.393i	−0.349274	−	0.430475i
$808$	−582.425	−	536.102i	−0.720824	−	0.663493i
$809$	550.664			0.680673			0.340336	−	0.940304i	$-0.389459\pi$
$809$	550.664			0.680673			0.340336	+	0.940304i	$0.389459\pi$
$810$	−935.137	−	1038.22i	−1.15449	−	1.28176i
$811$	722.538	+	722.538i	0.890923	+	0.890923i	0.994610	−	0.103687i	$-0.0330640\pi$
$811$	722.538	+	722.538i	0.890923	+	0.890923i	−0.103687	+	0.994610i	$0.533064\pi$
$812$	−401.529	+	200.904i	−0.494494	+	0.247419i
$813$	−284.125	−	29.5881i	−0.349477	−	0.0363937i
$814$	−814.866	−	132.118i	−1.00106	−	0.162307i
$815$	838.815	+	484.290i	1.02922	+	0.594221i
$816$	−151.631	−	489.333i	−0.185822	−	0.599673i
$817$	157.293	+	272.440i	0.192526	+	0.333464i
$818$	−1019.26	+	386.987i	−1.24604	+	0.473089i
$819$	420.194	+	644.342i	0.513057	+	0.786742i
$820$	−30.5780	+	511.820i	−0.0372902	+	0.624171i
$821$	−562.850	−	150.815i	−0.685566	−	0.183697i	−0.100810	−	0.994906i	$-0.532143\pi$
$821$	−562.850	−	150.815i	−0.685566	−	0.183697i	−0.584757	+	0.811209i	$0.698810\pi$
$822$	1199.65	+	324.921i	1.45943	+	0.395281i
$823$	1297.92	+	749.355i	1.57706	+	0.910516i	0.995267	+	0.0971789i	$0.0309819\pi$
$823$	1297.92	+	749.355i	1.57706	+	0.910516i	0.581793	+	0.813337i	$0.302351\pi$
$824$	−848.827	−	1339.01i	−1.03013	−	1.62501i
$825$	−2366.83	+	377.188i	−2.86888	+	0.457198i
$826$	557.762	−	56.5620i	0.675257	−	0.0684770i
$827$	724.214	−	724.214i	0.875712	−	0.875712i	−0.117375	−	0.993088i	$-0.537448\pi$
$827$	724.214	−	724.214i	0.875712	−	0.875712i	0.993088	+	0.117375i	$0.0374481\pi$
$828$	−575.586	−	336.473i	−0.695152	−	0.406368i
$829$	−191.121	+	191.121i	−0.230544	+	0.230544i	−0.812920	−	0.582375i	$-0.802123\pi$
$829$	−191.121	+	191.121i	−0.230544	+	0.230544i	0.582375	+	0.812920i	$0.302123\pi$
$830$	1237.95	−	1517.37i	1.49151	−	1.82815i
$831$	−198.981	+	519.849i	−0.239448	+	0.625570i
$832$	828.262	−	978.141i	0.995507	−	1.17565i
$833$	284.541	+	164.280i	0.341586	+	0.197214i
$834$	109.236	−	188.028i	0.130979	−	0.225454i
$835$	−2477.63	−	663.879i	−2.96722	−	0.795064i
$836$	−743.019	−	837.441i	−0.888779	−	1.00172i
$837$	−253.433	+	229.511i	−0.302787	+	0.274207i
$838$	633.457	−	1408.88i	0.755915	−	1.68124i
$839$	−316.759	−	548.642i	−0.377543	−	0.653924i	0.613161	−	0.789958i	$-0.289898\pi$
$839$	−316.759	−	548.642i	−0.377543	−	0.653924i	−0.990704	+	0.136034i	$0.956564\pi$
$840$	175.022	+	865.962i	0.208360	+	1.03091i
$841$	129.297	+	74.6494i	0.153741	+	0.0887627i
$842$	346.790	+	481.004i	0.411864	+	0.571264i
$843$	−297.655	−	666.827i	−0.353090	−	0.791017i
$844$	699.544	−	350.016i	0.828844	−	0.414710i
$845$	−1415.37	−	1415.37i	−1.67499	−	1.67499i
$846$	120.898	−	313.316i	0.142906	−	0.370349i
$847$	−600.064			−0.708458
$848$	320.073	−	798.704i	0.377445	−	0.941868i
$849$	−316.344	+	50.4140i	−0.372607	+	0.0593804i
$850$	−1040.74	−	168.740i	−1.22440	−	0.198517i
$851$	−456.516	+	122.323i	−0.536446	+	0.143740i
$852$	44.9087	+	455.088i	0.0527097	+	0.534140i
$853$	−77.8998	+	290.726i	−0.0913245	+	0.340828i	−0.996437	−	0.0843454i	$-0.973120\pi$
$853$	−77.8998	+	290.726i	−0.0913245	+	0.340828i	0.905112	+	0.425173i	$0.139787\pi$
$854$	−43.2021	+	96.0865i	−0.0505880	+	0.112513i
$855$	−999.987	−	896.937i	−1.16958	−	1.04905i
$856$	−539.372	+	168.734i	−0.630107	+	0.197120i
$857$	26.3700	+	45.6742i	0.0307701	+	0.0532955i	0.881000	−	0.473116i	$-0.156871\pi$
$857$	26.3700	+	45.6742i	0.0307701	+	0.0532955i	−0.850230	+	0.526411i	$0.823537\pi$
$858$	1370.53	+	1377.95i	1.59735	+	1.60600i
$859$	1519.02	−	407.020i	1.76836	−	0.473830i	0.779975	−	0.625811i	$-0.215232\pi$
$859$	1519.02	−	407.020i	1.76836	−	0.473830i	0.988383	+	0.151981i	$0.0485652\pi$
$860$	−125.912	−	614.431i	−0.146410	−	0.714454i
$861$	−19.7089	+	189.258i	−0.0228908	+	0.219812i
$862$	975.577	+	795.930i	1.13176	+	0.923353i
$863$			1189.26i			1.37805i	0.724738	+	0.689025i	$0.241961\pi$
$863$			1189.26i			1.37805i	−0.724738	+	0.689025i	$0.758039\pi$
$864$	−481.681	+	717.272i	−0.557501	+	0.830176i
$865$	240.346			0.277857
$866$	1072.97	−	1315.15i	1.23900	−	1.51865i
$867$	−522.457	−	54.4075i	−0.602603	−	0.0627538i
$868$	211.783	−	43.3996i	0.243989	−	0.0499996i
$869$	−63.2015	−	235.871i	−0.0727289	−	0.271428i
$870$	−965.014	+	959.816i	−1.10921	+	1.10324i
$871$	543.339	−	313.697i	0.623810	−	0.360157i
$872$	−922.943	+	288.729i	−1.05842	+	0.331111i
$873$	229.269	+	701.053i	0.262622	+	0.803039i
$874$	−584.592	−	262.843i	−0.668870	−	0.300735i
$875$	867.372	+	232.412i	0.991283	+	0.265613i
$876$	1526.44	−	150.631i	1.74251	−	0.171953i
$877$	103.814	+	387.439i	0.118374	+	0.441778i	0.999517	−	0.0310718i	$-0.00989206\pi$
$877$	103.814	+	387.439i	0.118374	+	0.441778i	−0.881143	+	0.472850i	$0.843225\pi$
$878$	146.070	−	900.916i	0.166366	−	1.02610i
$879$	119.775	+	751.577i	0.136262	+	0.855036i
$880$	877.944	+	2052.15i	0.997664	+	2.33199i
$881$			557.459i			0.632757i	0.948633	+	0.316379i	$0.102467\pi$
$881$			557.459i			0.632757i	−0.948633	+	0.316379i	$0.897533\pi$
$882$	−85.7305	−	547.460i	−0.0972001	−	0.620703i
$883$	−6.13732	+	6.13732i	−0.00695053	+	0.00695053i	−0.710574	−	0.703623i	$-0.751564\pi$
$883$	−6.13732	+	6.13732i	−0.00695053	+	0.00695053i	0.703623	+	0.710574i	$0.251564\pi$
$884$	382.560	+	764.587i	0.432760	+	0.864917i
$885$	1551.89	−	692.726i	1.75355	−	0.782742i
$886$	108.772	−	78.4215i	0.122768	−	0.0885118i
$887$	51.9793	−	90.0309i	0.0586013	−	0.101500i	−0.835236	−	0.549891i	$-0.814669\pi$
$887$	51.9793	−	90.0309i	0.0586013	−	0.101500i	0.893838	+	0.448391i	$0.148003\pi$
$888$	121.334	+	600.329i	0.136638	+	0.676046i
$889$	−282.092	+	162.866i	−0.317313	+	0.183201i
$890$	1610.98	+	724.323i	1.81009	+	0.813846i
$891$	−1021.28	−	820.572i	−1.14622	−	0.920956i
$892$	591.873	−	525.139i	0.663535	−	0.588720i
$893$	83.5621	−	311.858i	0.0935746	−	0.349225i
$894$	−491.999	−	285.830i	−0.550334	−	0.319720i
$895$	−237.108	+	410.682i	−0.264925	+	0.458863i
$896$	492.935	−	235.472i	0.550151	−	0.262804i
$897$	1039.16	+	397.756i	1.15848	+	0.443429i
$898$	1073.45	+	875.778i	1.19537	+	0.975254i
$899$	235.502	+	235.502i	0.261960	+	0.261960i
$900$	880.759	+	1544.73i	0.978621	+	1.71636i
$901$	405.848	+	405.848i	0.450442	+	0.450442i
$902$	48.5026	+	478.288i	0.0537723	+	0.530253i
$903$	−36.6317	−	229.861i	−0.0405667	−	0.254553i
$904$	85.4531	+	134.801i	0.0945277	+	0.149116i
$905$	1063.30	−	1841.70i	1.17492	−	2.03502i
$906$	155.373	−	573.660i	0.171494	−	0.633179i
$907$	−333.971	+	1246.40i	−0.368215	+	1.37420i	0.494795	+	0.869010i	$0.335243\pi$
$907$	−333.971	+	1246.40i	−0.368215	+	1.37420i	−0.863010	+	0.505187i	$0.831424\pi$
$908$	−1039.32	−	62.0926i	−1.14462	−	0.0683839i
$909$	−794.254	−	402.782i	−0.873767	−	0.443104i
$910$	−523.348	−	1378.41i	−0.575108	−	1.51474i
$911$	−852.908	+	492.427i	−0.936233	+	0.540535i	−0.888778	−	0.458339i	$-0.848445\pi$
$911$	−852.908	+	492.427i	−0.936233	+	0.540535i	−0.0474557	+	0.998873i	$0.515111\pi$
$912$	−387.177	+	734.869i	−0.424536	+	0.805777i
$913$	918.054	−	1590.12i	1.00554	−	1.74164i
$914$	6.32934	−	39.0375i	0.00692488	−	0.0427106i
$915$	−33.0792	+	317.649i	−0.0361522	+	0.347157i
$916$	−201.599	−	402.918i	−0.220086	−	0.439867i
$917$	82.5447	−	82.5447i	0.0900161	−	0.0900161i
$918$	−313.507	−	483.593i	−0.341511	−	0.526790i
$919$			273.336i			0.297428i	0.988880	+	0.148714i	$0.0475133\pi$
$919$			273.336i			0.297428i	−0.988880	+	0.148714i	$0.952487\pi$
$920$	940.231	+	865.450i	1.02199	+	0.940707i
$921$	207.164	−	168.086i	0.224934	−	0.182504i
$922$	−530.527	−	735.851i	−0.575409	−	0.798103i
$923$	−197.526	−	737.176i	−0.214004	−	0.798674i
$924$	291.932	+	775.201i	0.315943	+	0.838962i
$925$	1217.55	+	326.243i	1.31628	+	0.352695i
$926$	356.122	+	937.967i	0.384581	+	1.01292i
$927$	−1327.72	−	1190.90i	−1.43228	−	1.28468i
$928$	721.038	+	434.057i	0.776981	+	0.467734i
$929$	−392.453	+	226.583i	−0.422447	+	0.243900i	−0.696124	−	0.717922i	$-0.745093\pi$
$929$	−392.453	+	226.583i	−0.422447	+	0.243900i	0.273677	+	0.961822i	$0.411760\pi$
$930$	568.428	−	326.139i	0.611213	−	0.350687i
$931$	−137.880	−	514.575i	−0.148099	−	0.552712i
$932$	225.817	+	1101.95i	0.242293	+	1.18235i
$933$	514.660	−	709.795i	0.551618	−	0.760766i
$934$	655.867	−	66.5107i	0.702213	−	0.0712106i
$935$	−1488.88			−1.59239
$936$	598.389	−	1311.90i	0.639305	−	1.40160i
$937$			1234.45i			1.31744i	0.752386	+	0.658722i	$0.228903\pi$
$937$			1234.45i			1.31744i	−0.752386	+	0.658722i	$0.771097\pi$
$938$	266.043	−	26.9791i	0.283628	−	0.0287624i
$939$	374.593	−	167.209i	0.398928	−	0.178071i
$940$	−354.518	+	537.267i	−0.377147	+	0.571561i
$941$	496.355	−	132.998i	0.527476	−	0.141337i	0.0147534	−	0.999891i	$-0.495304\pi$
$941$	496.355	−	132.998i	0.527476	−	0.141337i	0.512722	+	0.858554i	$0.328637\pi$
$942$	183.825	+	106.794i	0.195143	+	0.113370i
$943$	137.617	+	238.360i	0.145935	+	0.252768i
$944$	−649.317	−	826.261i	−0.687836	−	0.875276i
$945$	453.762	+	884.279i	0.480171	+	0.935745i
$946$	−208.735	−	549.773i	−0.220650	−	0.581156i
$947$	−192.442	+	718.202i	−0.203212	+	0.758397i	0.786775	+	0.617240i	$0.211749\pi$
$947$	−192.442	+	718.202i	−0.203212	+	0.758397i	−0.989987	+	0.141158i	$0.954918\pi$
$948$	−147.246	+	105.557i	−0.155323	+	0.111347i
$949$	−2472.61	+	662.535i	−2.60549	+	0.698140i
$950$	999.749	+	1386.67i	1.05237	+	1.45965i
$951$	−141.654	+	370.077i	−0.148952	+	0.389145i
$952$	15.0784	+	364.086i	0.0158386	+	0.382443i
$953$	−1054.90			−1.10693			−0.553463	−	0.832874i	$-0.686694\pi$
$953$	−1054.90			−1.10693			−0.553463	+	0.832874i	$0.686694\pi$
$954$	102.864	−	962.526i	0.107823	−	1.00894i
$955$	−130.595	−	130.595i	−0.136749	−	0.136749i
$956$	−347.237	+	1042.68i	−0.363218	+	1.09067i
$957$	−749.110	+	1033.14i	−0.782769	+	1.07956i
$958$	33.3992	−	205.997i	0.0348635	−	0.215028i
$959$	−765.634	−	442.039i	−0.798367	−	0.460937i
$960$	1195.30	−	1146.17i	1.24511	−	1.19392i
$961$	400.319	+	693.373i	0.416565	+	0.721512i
$962$	−362.812	−	955.585i	−0.377143	−	0.993332i
$963$	−532.557	+	347.296i	−0.553019	+	0.360640i
$964$	−352.103	+	312.403i	−0.365252	+	0.324070i
$965$	1034.49	+	277.191i	1.07201	+	0.287245i
$966$	334.436	+	336.247i	0.346207	+	0.348082i
$967$	−1491.54	−	861.139i	−1.54244	−	0.890527i	−0.998684	−	0.0512814i	$-0.983669\pi$
$967$	−1491.54	−	861.139i	−1.54244	−	0.890527i	−0.543753	−	0.839245i	$-0.682997\pi$
$968$	602.224	+	949.997i	0.622132	+	0.981402i
$969$	−349.094	−	430.253i	−0.360262	−	0.444018i
$970$	−142.635	−	1406.53i	−0.147046	−	1.45003i
$971$	43.2692	−	43.2692i	0.0445615	−	0.0445615i	−0.684475	−	0.729036i	$-0.739968\pi$
$971$	43.2692	−	43.2692i	0.0445615	−	0.0445615i	0.729036	+	0.684475i	$0.239968\pi$
$972$	−302.705	+	923.663i	−0.311425	+	0.950271i
$973$	−109.375	+	109.375i	−0.112410	+	0.112410i
$974$	45.0027	+	36.7157i	0.0462040	+	0.0376958i
$975$	−1869.77	−	2304.46i	−1.91771	−	2.36355i
$976$	195.478	−	28.0365i	0.200285	−	0.0287260i
$977$	505.899	+	292.081i	0.517809	+	0.298957i	0.736038	−	0.676941i	$-0.236695\pi$
$977$	505.899	+	292.081i	0.517809	+	0.298957i	−0.218229	+	0.975898i	$0.570028\pi$
$978$	1.81950	−	673.778i	0.00186043	−	0.688935i
$979$	1599.68	+	428.633i	1.63400	+	0.437828i
$980$	−63.3413	+	1060.22i	−0.0646340	+	1.08186i
$981$	−911.282	+	594.274i	−0.928932	+	0.605784i
$982$	−1446.10	−	650.189i	−1.47260	−	0.662107i
$983$	−501.229	−	868.153i	−0.509897	−	0.883167i	−0.999934	−	0.0114659i	$-0.996350\pi$
$983$	−501.229	−	868.153i	−0.509897	−	0.883167i	0.490037	−	0.871701i	$-0.336983\pi$
$984$	319.406	−	158.737i	0.324600	−	0.161318i
$985$	2478.45	+	1430.93i	2.51619	+	1.45272i
$986$	−455.375	+	328.312i	−0.461841	+	0.332974i
$987$	−140.227	+	193.394i	−0.142074	+	0.195941i
$988$	437.996	−	1315.21i	0.443316	−	1.33118i
$989$	−238.068	−	238.068i	−0.240716	−	0.240716i
$990$	1576.86	+	1954.22i	1.59279	+	1.97396i
$991$	−560.194			−0.565281			−0.282641	−	0.959226i	$-0.591210\pi$
$991$	−560.194			−0.565281			−0.282641	+	0.959226i	$0.591210\pi$
$992$	−281.254	−	291.730i	−0.283522	−	0.294083i
$993$	225.599	−	589.390i	0.227190	−	0.593545i
$994$	52.0598	−	321.090i	0.0523741	−	0.323028i
$995$	−1691.12	+	453.134i	−1.69962	+	0.455411i
$996$	−1344.11	−	221.654i	−1.34951	−	0.222544i
$997$	440.930	−	1645.57i	0.442257	−	1.65053i	−0.280821	−	0.959760i	$-0.590607\pi$
$997$	440.930	−	1645.57i	0.442257	−	1.65053i	0.723078	−	0.690766i	$-0.242727\pi$
$998$	−1360.05	−	611.501i	−1.36277	−	0.612726i
$999$	314.571	+	613.027i	0.314886	+	0.613641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.13	✓	184
3.2	odd	2		432.3.x.a.341.34		184
9.2	odd	6	inner	144.3.w.a.101.3	yes	184
9.7	even	3		432.3.x.a.197.44		184
16.13	even	4	inner	144.3.w.a.77.3	yes	184
48.29	odd	4		432.3.x.a.125.44		184
144.29	odd	12	inner	144.3.w.a.29.13	yes	184
144.61	even	12		432.3.x.a.413.34		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.13	✓	184	1.1	even	1	trivial
144.3.w.a.29.13	yes	184	144.29	odd	12	inner
144.3.w.a.77.3	yes	184	16.13	even	4	inner
144.3.w.a.101.3	yes	184	9.2	odd	6	inner
432.3.x.a.125.44		184	48.29	odd	4
432.3.x.a.197.44		184	9.7	even	3
432.3.x.a.341.34		184	3.2	odd	2
432.3.x.a.413.34		184	144.61	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26432 + 1.54968i) q^{2} +(-2.98386 - 0.310733i) q^{3} +(-0.803013 - 3.91857i) q^{4} +(2.23236 + 8.33129i) q^{5} +(4.25408 - 4.23117i) q^{6} +(-3.69610 + 2.13394i) q^{7} +(7.08778 + 3.70989i) q^{8} +(8.80689 + 1.85437i) q^{9} +O(q^{10})\)	\(q+(-1.26432 + 1.54968i) q^{2} +(-2.98386 - 0.310733i) q^{3} +(-0.803013 - 3.91857i) q^{4} +(2.23236 + 8.33129i) q^{5} +(4.25408 - 4.23117i) q^{6} +(-3.69610 + 2.13394i) q^{7} +(7.08778 + 3.70989i) q^{8} +(8.80689 + 1.85437i) q^{9} +(-15.7332 - 7.07393i) q^{10} +(-15.6229 - 4.18615i) q^{11} +(1.17845 + 11.9420i) q^{12} +(-5.18329 - 19.3443i) q^{13} +(1.36611 - 8.42575i) q^{14} +(-4.07226 - 25.5531i) q^{15} +(-14.7103 + 6.29332i) q^{16} -10.6727i q^{17} +(-14.0084 + 11.3033i) q^{18} +(-12.2363 + 12.2363i) q^{19} +(30.8541 - 15.4378i) q^{20} +(11.6917 - 5.21890i) q^{21} +(26.2395 - 18.9179i) q^{22} +(9.25997 - 16.0387i) q^{23} +(-19.9962 - 13.2722i) q^{24} +(-42.7763 + 24.6969i) q^{25} +(36.5308 + 16.4249i) q^{26} +(-25.7023 - 8.26978i) q^{27} +(11.3300 + 12.7698i) q^{28} +(-6.80700 + 25.4041i) q^{29} +(44.7477 + 25.9965i) q^{30} +(6.33170 - 10.9668i) q^{31} +(8.84588 - 30.7531i) q^{32} +(45.3159 + 17.3455i) q^{33} +(16.5392 + 13.4936i) q^{34} +(-26.0295 - 26.0295i) q^{35} +(0.194430 - 35.9995i) q^{36} +(-18.0450 - 18.0450i) q^{37} +(-3.49179 - 34.4328i) q^{38} +(9.45532 + 59.3314i) q^{39} +(-15.0857 + 67.3322i) q^{40} +(-7.43075 + 12.8704i) q^{41} +(-6.69444 + 24.7168i) q^{42} +(4.70515 - 17.5598i) q^{43} +(-3.85830 + 64.5810i) q^{44} +(4.21087 + 77.5124i) q^{45} +(13.1474 + 34.6280i) q^{46} +(-16.1577 + 9.32866i) q^{47} +(45.8492 - 14.2074i) q^{48} +(-15.3926 + 26.6607i) q^{49} +(15.8105 - 97.5143i) q^{50} +(-3.31635 + 31.8458i) q^{51} +(-71.6397 + 35.8448i) q^{52} +(-38.0269 + 38.0269i) q^{53} +(45.3114 - 29.3748i) q^{54} -139.504i q^{55} +(-34.1139 + 1.41280i) q^{56} +(40.3136 - 32.7091i) q^{57} +(-30.7620 - 42.6674i) q^{58} +(16.9990 + 63.4412i) q^{59} +(-96.8615 + 36.4769i) q^{60} +(-11.9218 - 3.19445i) q^{61} +(8.98980 + 23.6776i) q^{62} +(-36.5083 + 11.9395i) q^{63} +(36.4734 + 52.5898i) q^{64} +(149.592 - 86.3670i) q^{65} +(-84.1735 + 48.2950i) q^{66} +(8.10824 + 30.2604i) q^{67} +(-41.8216 + 8.57029i) q^{68} +(-32.6143 + 44.9801i) q^{69} +(73.2470 - 7.42790i) q^{70} +38.1082 q^{71} +(55.5418 + 45.8160i) q^{72} -127.821i q^{73} +(50.7786 - 5.14939i) q^{74} +(135.313 - 60.4002i) q^{75} +(57.7745 + 38.1227i) q^{76} +(66.6769 - 17.8660i) q^{77} +(-103.899 - 60.3609i) q^{78} +(7.54888 + 13.0750i) q^{79} +(-85.2703 - 108.507i) q^{80} +(74.1226 + 32.6625i) q^{81} +(-10.5502 - 27.7876i) q^{82} +(-29.3816 + 109.654i) q^{83} +(-29.8392 - 41.6241i) q^{84} +(88.9171 - 23.8253i) q^{85} +(21.2633 + 29.4927i) q^{86} +(28.2050 - 73.6871i) q^{87} +(-95.2018 - 87.6299i) q^{88} -102.393 q^{89} +(-125.443 - 91.4746i) q^{90} +(60.4377 + 60.4377i) q^{91} +(-70.2848 - 23.4065i) q^{92} +(-22.3007 + 30.7561i) q^{93} +(5.97202 - 36.8337i) q^{94} +(-129.260 - 74.6281i) q^{95} +(-35.9509 + 89.0142i) q^{96} +(40.9773 + 70.9747i) q^{97} +(-21.8545 - 57.5611i) q^{98} +(-129.827 - 65.8377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more