LMFDB - Embedded newform 189.4.s.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, degree $2$, not 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647627 - 0.373907i) q^{2} +(-3.72039 - 6.44390i) q^{4} -8.70220 q^{5} +(18.2993 - 2.85258i) q^{7} +11.5468i q^{8} +O(q^{10})$	\(q+(-0.647627 - 0.373907i) q^{2} +(-3.72039 - 6.44390i) q^{4} -8.70220 q^{5} +(18.2993 - 2.85258i) q^{7} +11.5468i q^{8} +(5.63577 + 3.25382i) q^{10} -41.5070i q^{11} +(-33.0053 - 19.0556i) q^{13} +(-12.9177 - 4.99482i) q^{14} +(-25.4456 + 44.0731i) q^{16} +(-39.9685 + 69.2274i) q^{17} +(-49.4113 + 28.5276i) q^{19} +(32.3755 + 56.0761i) q^{20} +(-15.5198 + 26.8811i) q^{22} +177.014i q^{23} -49.2718 q^{25} +(14.2501 + 24.6818i) q^{26} +(-86.4620 - 107.306i) q^{28} +(60.1430 - 34.7236i) q^{29} +(-225.864 + 130.403i) q^{31} +(112.957 - 65.2160i) q^{32} +(51.7693 - 29.8890i) q^{34} +(-159.244 + 24.8237i) q^{35} +(-74.9359 - 129.793i) q^{37} +42.6668 q^{38} -100.483i q^{40} +(54.7122 - 94.7643i) q^{41} +(124.193 + 215.108i) q^{43} +(-267.467 + 154.422i) q^{44} +(66.1867 - 114.639i) q^{46} +(-147.528 + 255.526i) q^{47} +(326.726 - 104.400i) q^{49} +(31.9097 + 18.4231i) q^{50} +283.577i q^{52} +(-263.613 - 152.197i) q^{53} +361.202i q^{55} +(32.9382 + 211.299i) q^{56} -51.9336 q^{58} +(-360.346 - 624.138i) q^{59} +(-561.494 - 324.179i) q^{61} +195.034 q^{62} +309.591 q^{64} +(287.218 + 165.826i) q^{65} +(97.4263 + 168.747i) q^{67} +594.793 q^{68} +(112.412 + 43.4659i) q^{70} -98.7349i q^{71} +(226.289 + 130.648i) q^{73} +112.076i q^{74} +(367.658 + 212.268i) q^{76} +(-118.402 - 759.548i) q^{77} +(577.124 - 999.608i) q^{79} +(221.433 - 383.533i) q^{80} +(-70.8661 + 40.9146i) q^{82} +(285.406 + 494.337i) q^{83} +(347.813 - 602.431i) q^{85} -185.746i q^{86} +479.275 q^{88} +(-89.5115 - 155.038i) q^{89} +(-658.330 - 254.553i) q^{91} +(1140.66 - 658.559i) q^{92} +(191.086 - 110.324i) q^{94} +(429.987 - 248.253i) q^{95} +(-956.569 + 552.275i) q^{97} +(-250.632 - 54.5529i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.647627	−	0.373907i	−0.228971	−	0.132196i	0.381126	−	0.924523i	$-0.375536\pi$
$2$	−0.647627	−	0.373907i	−0.228971	−	0.132196i	−0.610097	+	0.792327i	$0.708870\pi$
$3$		0			0
$3$		0			0
$4$	−3.72039	−	6.44390i	−0.465048	−	0.805487i
$5$	−8.70220			−0.778348			−0.389174	−	0.921164i	$-0.627240\pi$
$5$	−8.70220			−0.778348			−0.389174	+	0.921164i	$0.627240\pi$
$6$		0			0
$7$	18.2993	−	2.85258i	0.988067	−	0.154025i
$7$	18.2993	−	2.85258i	0.988067	−	0.154025i
$8$			11.5468i			0.510303i
$9$		0			0
$10$	5.63577	+	3.25382i	0.178219	+	0.102895i
$11$		−	41.5070i		−	1.13771i	−0.822437	−	0.568856i	$-0.807386\pi$
$11$		−	41.5070i		−	1.13771i	0.822437	−	0.568856i	$-0.192614\pi$
$12$		0			0
$13$	−33.0053	−	19.0556i	−0.704155	−	0.406544i	0.104738	−	0.994500i	$-0.466600\pi$
$13$	−33.0053	−	19.0556i	−0.704155	−	0.406544i	−0.808893	+	0.587956i	$0.799933\pi$
$14$	−12.9177	−	4.99482i	−0.246600	−	0.0953516i
$15$		0			0
$16$	−25.4456	+	44.0731i	−0.397588	+	0.688643i
$17$	−39.9685	+	69.2274i	−0.570222	+	0.987654i	0.426320	+	0.904572i	$0.359810\pi$
$17$	−39.9685	+	69.2274i	−0.570222	+	0.987654i	−0.996543	+	0.0830818i	$0.973524\pi$
$18$		0			0
$19$	−49.4113	+	28.5276i	−0.596617	+	0.344457i	−0.767710	−	0.640798i	$-0.778604\pi$
$19$	−49.4113	+	28.5276i	−0.596617	+	0.344457i	0.171092	+	0.985255i	$0.445270\pi$
$20$	32.3755	+	56.0761i	0.361969	+	0.626949i
$21$		0			0
$22$	−15.5198	+	26.8811i	−0.150401	+	0.260503i
$23$			177.014i			1.60478i	0.596802	+	0.802389i	$0.296438\pi$
$23$			177.014i			1.60478i	−0.596802	+	0.802389i	$0.703562\pi$
$24$		0			0
$25$	−49.2718			−0.394174
$26$	14.2501	+	24.6818i	0.107487	+	0.186173i
$27$		0			0
$28$	−86.4620	−	107.306i	−0.583564	−	0.724247i
$29$	60.1430	−	34.7236i	0.385113	−	0.222345i	−0.294927	−	0.955520i	$-0.595295\pi$
$29$	60.1430	−	34.7236i	0.385113	−	0.222345i	0.680041	+	0.733174i	$0.261962\pi$
$30$		0			0
$31$	−225.864	+	130.403i	−1.30859	+	0.755517i	−0.981861	−	0.189601i	$-0.939281\pi$
$31$	−225.864	+	130.403i	−1.30859	+	0.755517i	−0.326732	+	0.945117i	$0.605947\pi$
$32$	112.957	−	65.2160i	0.624007	−	0.360271i
$33$		0			0
$34$	51.7693	−	29.8890i	0.261128	−	0.150762i
$35$	−159.244	+	24.8237i	−0.769060	+	0.119885i
$36$		0			0
$37$	−74.9359	−	129.793i	−0.332957	−	0.576698i	0.650134	−	0.759820i	$-0.274713\pi$
$37$	−74.9359	−	129.793i	−0.332957	−	0.576698i	−0.983090	+	0.183122i	$0.941380\pi$
$38$	42.6668			0.182144
$39$		0			0
$40$		−	100.483i		−	0.397193i
$41$	54.7122	−	94.7643i	0.208405	−	0.360968i	−0.742807	−	0.669505i	$-0.766506\pi$
$41$	54.7122	−	94.7643i	0.208405	−	0.360968i	0.951212	+	0.308537i	$0.0998395\pi$
$42$		0			0
$43$	124.193	+	215.108i	0.440446	+	0.762875i	0.997723	−	0.0674517i	$-0.0214869\pi$
$43$	124.193	+	215.108i	0.440446	+	0.762875i	−0.557276	+	0.830327i	$0.688154\pi$
$44$	−267.467	+	154.422i	−0.916413	+	0.529092i
$45$		0			0
$46$	66.1867	−	114.639i	0.212146	−	0.367447i
$47$	−147.528	+	255.526i	−0.457855	+	0.793029i	−0.998847	−	0.0479988i	$-0.984716\pi$
$47$	−147.528	+	255.526i	−0.457855	+	0.793029i	0.540992	+	0.841028i	$0.318049\pi$
$48$		0			0
$49$	326.726	−	104.400i	0.952553	−	0.304373i
$50$	31.9097	+	18.4231i	0.0902543	+	0.0521084i
$51$		0			0
$52$			283.577i			0.756251i
$53$	−263.613	−	152.197i	−0.683208	−	0.394450i	0.117855	−	0.993031i	$-0.462398\pi$
$53$	−263.613	−	152.197i	−0.683208	−	0.394450i	−0.801062	+	0.598581i	$0.795732\pi$
$54$		0			0
$55$			361.202i			0.885537i
$56$	32.9382	+	211.299i	0.0785992	+	0.504214i
$57$		0			0
$58$	−51.9336			−0.117573
$59$	−360.346	−	624.138i	−0.795137	−	1.37722i	−0.922752	−	0.385394i	$-0.874065\pi$
$59$	−360.346	−	624.138i	−0.795137	−	1.37722i	0.127615	−	0.991824i	$-0.459268\pi$
$60$		0			0
$61$	−561.494	−	324.179i	−1.17856	−	0.680440i	−0.222876	−	0.974847i	$-0.571544\pi$
$61$	−561.494	−	324.179i	−1.17856	−	0.680440i	−0.955680	+	0.294407i	$0.904878\pi$
$62$	195.034			0.399506
$63$		0			0
$64$	309.591			0.604671
$65$	287.218	+	165.826i	0.548078	+	0.316433i
$66$		0			0
$67$	97.4263	+	168.747i	0.177649	+	0.307698i	0.941075	−	0.338198i	$-0.109817\pi$
$67$	97.4263	+	168.747i	0.177649	+	0.307698i	−0.763426	+	0.645896i	$0.776484\pi$
$68$	594.793			1.06072
$69$		0			0
$70$	112.412	+	43.4659i	0.191940	+	0.0742168i
$71$		−	98.7349i		−	0.165038i	−0.996590	−	0.0825188i	$-0.973704\pi$
$71$		−	98.7349i		−	0.165038i	0.996590	−	0.0825188i	$-0.0262965\pi$
$72$		0			0
$73$	226.289	+	130.648i	0.362809	+	0.209468i	0.670312	−	0.742079i	$-0.266160\pi$
$73$	226.289	+	130.648i	0.362809	+	0.209468i	−0.307503	+	0.951547i	$0.599493\pi$
$74$			112.076i			0.176062i
$75$		0			0
$76$	367.658	+	212.268i	0.554912	+	0.320379i
$77$	−118.402	−	759.548i	−0.175236	−	1.12414i
$78$		0			0
$79$	577.124	−	999.608i	0.821918	−	1.42360i	−0.0823344	−	0.996605i	$-0.526238\pi$
$79$	577.124	−	999.608i	0.821918	−	1.42360i	0.904252	−	0.426999i	$-0.140429\pi$
$80$	221.433	−	383.533i	0.309462	−	0.536004i
$81$		0			0
$82$	−70.8661	+	40.9146i	−0.0954372	+	0.0551007i
$83$	285.406	+	494.337i	0.377438	+	0.653741i	0.990689	−	0.136147i	$-0.0434719\pi$
$83$	285.406	+	494.337i	0.377438	+	0.653741i	−0.613251	+	0.789888i	$0.710139\pi$
$84$		0			0
$85$	347.813	−	602.431i	0.443831	−	0.768739i
$86$		−	185.746i		−	0.232901i
$87$		0			0
$88$	479.275			0.580578
$89$	−89.5115	−	155.038i	−0.106609	−	0.184652i	0.807785	−	0.589477i	$-0.200666\pi$
$89$	−89.5115	−	155.038i	−0.106609	−	0.184652i	−0.914394	+	0.404824i	$0.867333\pi$
$90$		0			0
$91$	−658.330	−	254.553i	−0.758370	−	0.293236i
$92$	1140.66	−	658.559i	1.29263	−	0.746299i
$93$		0			0
$94$	191.086	−	110.324i	0.209671	−	0.121054i
$95$	429.987	−	248.253i	0.464376	−	0.268108i
$96$		0			0
$97$	−956.569	+	552.275i	−1.00129	+	0.578093i	−0.908629	−	0.417605i	$-0.862870\pi$
$97$	−956.569	+	552.275i	−1.00129	+	0.578093i	−0.0926581	+	0.995698i	$0.529536\pi$
$98$	−250.632	−	54.5529i	−0.258344	−	0.0562314i
$99$		0			0
$100$	183.310	+	317.502i	0.183310	+	0.317502i
$101$	0.750795			0.000739672			0.000369836	−	1.00000i	$-0.499882\pi$
$101$	0.750795			0.000739672			0.000369836		1.00000i	$0.499882\pi$
$102$		0			0
$103$		−	753.027i		−	0.720369i	−0.932881	−	0.360184i	$-0.882714\pi$
$103$		−	753.027i		−	0.720369i	0.932881	−	0.360184i	$-0.117286\pi$
$104$	220.032	−	381.107i	0.207461	−	0.359332i
$105$		0			0
$106$	113.815	+	197.134i	0.104290	+	0.180635i
$107$	−1089.54	+	629.045i	−0.984388	+	0.568337i	−0.903592	−	0.428394i	$-0.859080\pi$
$107$	−1089.54	+	629.045i	−0.984388	+	0.568337i	−0.0807962	+	0.996731i	$0.525746\pi$
$108$		0			0
$109$	−110.812	+	191.932i	−0.0973748	+	0.168658i	−0.910597	−	0.413295i	$-0.864378\pi$
$109$	−110.812	+	191.932i	−0.0973748	+	0.168658i	0.813222	+	0.581953i	$0.197711\pi$
$110$	135.056	−	233.924i	0.117065	−	0.202762i
$111$		0			0
$112$	−339.914	+	879.091i	−0.286776	+	0.741664i
$113$	−1345.36	−	776.746i	−1.12001	−	0.646638i	−0.178607	−	0.983921i	$-0.557159\pi$
$113$	−1345.36	−	776.746i	−1.12001	−	0.646638i	−0.941404	+	0.337282i	$0.890492\pi$
$114$		0			0
$115$		−	1540.41i		−	1.24908i
$116$	−447.511	−	258.370i	−0.358192	−	0.206803i
$117$		0			0
$118$			538.945i			0.420457i
$119$	−533.917	+	1380.82i	−0.411295	+	1.06370i
$120$		0			0
$121$	−391.834			−0.294391
$122$	242.426	+	419.893i	0.179903	+	0.311601i
$123$		0			0
$124$	1680.60	+	970.297i	1.21712	+	0.702703i
$125$	1516.55			1.08515
$126$		0			0
$127$	2425.06			1.69440			0.847202	−	0.531271i	$-0.178285\pi$
$127$	2425.06			1.69440			0.847202	+	0.531271i	$0.178285\pi$
$128$	−1104.16	−	637.486i	−0.762459	−	0.440206i
$129$		0			0
$130$	−124.007	−	214.786i	−0.0836624	−	0.144908i
$131$	48.8347			0.0325703			0.0162851	−	0.999867i	$-0.494816\pi$
$131$	48.8347			0.0325703			0.0162851	+	0.999867i	$0.494816\pi$
$132$		0			0
$133$	−822.813	+	662.984i	−0.536443	+	0.432241i
$134$		−	145.714i		−	0.0939384i
$135$		0			0
$136$	−799.358	−	461.510i	−0.504003	−	0.290986i
$137$			1532.32i			0.955583i	0.878473	+	0.477792i	$0.158563\pi$
$137$			1532.32i			0.955583i	−0.878473	+	0.477792i	$0.841437\pi$
$138$		0			0
$139$	638.674	+	368.739i	0.389724	+	0.225007i	0.682040	−	0.731314i	$-0.261093\pi$
$139$	638.674	+	368.739i	0.389724	+	0.225007i	−0.292317	+	0.956322i	$0.594426\pi$
$140$	752.409	+	933.797i	0.454216	+	0.563716i
$141$		0			0
$142$	−36.9177	+	63.9433i	−0.0218174	+	0.0377888i
$143$	−790.942	+	1369.95i	−0.462531	+	0.801126i
$144$		0			0
$145$	−523.376	+	302.172i	−0.299752	+	0.173062i
$146$	−97.7003	−	169.222i	−0.0553817	−	0.0959240i
$147$		0			0
$148$	−557.581	+	965.759i	−0.309682	+	0.536385i
$149$		−	1475.76i		−	0.811400i	−0.914006	−	0.405700i	$-0.867028\pi$
$149$		−	1475.76i		−	0.811400i	0.914006	−	0.405700i	$-0.132972\pi$
$150$		0			0
$151$	−1274.88			−0.687073			−0.343536	−	0.939139i	$-0.611625\pi$
$151$	−1274.88			−0.687073			−0.343536	+	0.939139i	$0.611625\pi$
$152$	−329.404	−	570.544i	−0.175778	−	0.304456i
$153$		0			0
$154$	−207.320	+	536.175i	−0.108483	+	0.280560i
$155$	1965.51	−	1134.79i	1.01854	−	0.588055i
$156$		0			0
$157$	−1718.19	+	991.999i	−0.873418	+	0.504268i	−0.868483	−	0.495719i	$-0.834904\pi$
$157$	−1718.19	+	991.999i	−0.873418	+	0.504268i	−0.00493568	+	0.999988i	$0.501571\pi$
$158$	−747.522	+	431.582i	−0.376390	+	0.217309i
$159$		0			0
$160$	−982.977	+	567.522i	−0.485695	+	0.280416i
$161$	504.945	+	3239.22i	0.247175	+	1.58563i
$162$		0			0
$163$	−1836.59	−	3181.06i	−0.882532	−	1.52859i	−0.848517	−	0.529168i	$-0.822504\pi$
$163$	−1836.59	−	3181.06i	−0.882532	−	1.52859i	−0.0340145	−	0.999421i	$-0.510829\pi$
$164$	−814.202			−0.387674
$165$		0			0
$166$		−	426.861i		−	0.199583i
$167$	−2007.55	+	3477.17i	−0.930231	+	1.61121i	−0.147306	+	0.989091i	$0.547060\pi$
$167$	−2007.55	+	3477.17i	−0.930231	+	1.61121i	−0.782925	+	0.622116i	$0.786273\pi$
$168$		0			0
$169$	−372.268	−	644.787i	−0.169444	−	0.293485i
$170$	−450.507	+	260.100i	−0.203249	+	0.117346i
$171$		0			0
$172$	924.089	−	1600.57i	0.409658	−	0.709548i
$173$	1046.75	−	1813.03i	0.460019	−	0.796776i	−0.538943	−	0.842342i	$-0.681176\pi$
$173$	1046.75	−	1813.03i	0.460019	−	0.796776i	0.998961	+	0.0455667i	$0.0145094\pi$
$174$		0			0
$175$	−901.637	+	140.552i	−0.389471	+	0.0607125i
$176$	1829.35	+	1056.17i	0.783478	+	0.452341i
$177$		0			0
$178$			133.876i			0.0563732i
$179$	−3194.00	−	1844.06i	−1.33369	−	0.770008i	−0.347829	−	0.937558i	$-0.613081\pi$
$179$	−3194.00	−	1844.06i	−1.33369	−	0.770008i	−0.985863	+	0.167551i	$0.946414\pi$
$180$		0			0
$181$			1648.55i			0.676995i	0.940967	+	0.338497i	$0.109919\pi$
$181$			1648.55i			0.676995i	−0.940967	+	0.338497i	$0.890081\pi$
$182$	331.172	+	411.010i	0.134880	+	0.167396i
$183$		0			0
$184$	−2043.95			−0.818923
$185$	652.107	+	1129.48i	0.259156	+	0.448871i
$186$		0			0
$187$	2873.43	+	1658.97i	1.12367	+	0.648749i
$188$	2195.45			0.851700
$189$		0			0
$190$	−371.295			−0.141771
$191$	−3175.89	−	1833.60i	−1.20314	−	0.694631i	−0.241885	−	0.970305i	$-0.577766\pi$
$191$	−3175.89	−	1833.60i	−1.20314	−	0.694631i	−0.961251	+	0.275674i	$0.911099\pi$
$192$		0			0
$193$	171.063	+	296.289i	0.0637998	+	0.110504i	0.896161	−	0.443729i	$-0.146345\pi$
$193$	171.063	+	296.289i	0.0637998	+	0.110504i	−0.832361	+	0.554234i	$0.813011\pi$
$194$	825.999			0.305687
$195$		0			0
$196$	−1888.29	−	1716.98i	−0.688152	−	0.625721i
$197$		−	468.339i		−	0.169380i	−0.996407	−	0.0846898i	$-0.973010\pi$
$197$		−	468.339i		−	0.169380i	0.996407	−	0.0846898i	$-0.0269899\pi$
$198$		0			0
$199$	−1359.11	−	784.682i	−0.484144	−	0.279521i	0.237998	−	0.971266i	$-0.423509\pi$
$199$	−1359.11	−	784.682i	−0.484144	−	0.279521i	−0.722142	+	0.691745i	$0.756842\pi$
$200$		−	568.933i		−	0.201148i
$201$		0			0
$202$	−0.486235	−	0.280728i	−0.000169363	−	9.77818e-5i
$203$	1001.52	−	806.979i	0.346271	−	0.279009i
$204$		0			0
$205$	−476.116	+	824.657i	−0.162212	+	0.280959i
$206$	−281.563	+	487.681i	−0.0952300	+	0.164943i
$207$		0			0
$208$	1679.68	−	969.764i	0.559927	−	0.323274i
$209$	1184.10	+	2050.92i	0.391893	+	0.678779i
$210$		0			0
$211$	1244.68	−	2155.85i	0.406101	−	0.703387i	−0.588348	−	0.808608i	$-0.700222\pi$
$211$	1244.68	−	2155.85i	0.406101	−	0.703387i	0.994449	+	0.105221i	$0.0335549\pi$
$212$			2264.93i			0.733753i
$213$		0			0
$214$	940.818			0.300528
$215$	−1080.75	−	1871.91i	−0.342821	−	0.593783i
$216$		0			0
$217$	−3761.16	+	3030.57i	−1.17661	+	0.948057i
$218$	143.530	−	82.8668i	0.0445920	−	0.0257452i
$219$		0			0
$220$	2327.55	−	1343.81i	0.713289	−	0.411817i
$221$	2638.34	−	1523.25i	0.803050	−	0.463641i
$222$		0			0
$223$	858.894	−	495.883i	0.257918	−	0.148909i	−0.365466	−	0.930825i	$-0.619090\pi$
$223$	858.894	−	495.883i	0.257918	−	0.148909i	0.623385	+	0.781915i	$0.285757\pi$
$224$	1881.00	−	1515.62i	0.561071	−	0.452084i
$225$		0			0
$226$	580.862	+	1006.08i	0.170966	+	0.296122i
$227$	−603.465			−0.176447			−0.0882233	−	0.996101i	$-0.528119\pi$
$227$	−603.465			−0.176447			−0.0882233	+	0.996101i	$0.528119\pi$
$228$		0			0
$229$			1295.25i			0.373765i	0.982382	+	0.186883i	$0.0598384\pi$
$229$			1295.25i			0.373765i	−0.982382	+	0.186883i	$0.940162\pi$
$230$	−575.969	+	997.608i	−0.165123	+	0.286002i
$231$		0			0
$232$	400.948	+	694.462i	0.113463	+	0.196524i
$233$	3699.70	−	2136.02i	1.04024	−	0.600581i	0.120336	−	0.992733i	$-0.461603\pi$
$233$	3699.70	−	2136.02i	1.04024	−	0.600581i	0.919900	+	0.392152i	$0.128269\pi$
$234$		0			0
$235$	1283.82	−	2223.64i	0.356371	−	0.617253i
$236$	−2681.26	+	4644.07i	−0.739555	+	1.28095i
$237$		0			0
$238$	862.079	−	694.623i	0.234791	−	0.189184i
$239$	−2074.66	−	1197.80i	−0.561500	−	0.324182i	0.192247	−	0.981346i	$-0.438422\pi$
$239$	−2074.66	−	1197.80i	−0.561500	−	0.324182i	−0.753747	+	0.657164i	$0.771756\pi$
$240$		0			0
$241$			818.126i			0.218673i	0.994005	+	0.109336i	$0.0348726\pi$
$241$			818.126i			0.218673i	−0.994005	+	0.109336i	$0.965127\pi$
$242$	253.762	+	146.510i	0.0674068	+	0.0389174i
$243$		0			0
$244$			4824.28i			1.26575i
$245$	−2843.23	+	908.509i	−0.741418	+	0.236908i
$246$		0			0
$247$	2174.44			0.560148
$248$	−1505.74	−	2608.02i	−0.385542	−	0.667779i
$249$		0			0
$250$	−982.156	−	567.048i	−0.248468	−	0.143453i
$251$	7516.24			1.89012			0.945062	−	0.326891i	$-0.106001\pi$
$251$	7516.24			1.89012			0.945062	+	0.326891i	$0.106001\pi$
$252$		0			0
$253$	7347.31			1.82578
$254$	−1570.53	−	906.748i	−0.387969	−	0.223994i
$255$		0			0
$256$	−761.644	−	1319.21i	−0.185948	−	0.322072i
$257$	−5548.61			−1.34674			−0.673372	−	0.739304i	$-0.735155\pi$
$257$	−5548.61			−1.34674			−0.673372	+	0.739304i	$0.735155\pi$
$258$		0			0
$259$	−1741.52	−	2161.35i	−0.417809	−	0.518532i
$260$		−	2467.74i		−	0.588626i
$261$		0			0
$262$	−31.6267	−	18.2597i	−0.00745764	−	0.00430567i
$263$		−	6373.65i		−	1.49436i	−0.664623	−	0.747179i	$-0.731408\pi$
$263$		−	6373.65i		−	1.49436i	0.664623	−	0.747179i	$-0.268592\pi$
$264$		0			0
$265$	2294.01	+	1324.45i	0.531773	+	0.307019i
$266$	780.770	−	121.710i	0.179970	−	0.0280546i
$267$		0			0
$268$	724.927	−	1255.61i	0.165231	−	0.286189i
$269$	−2137.07	+	3701.52i	−0.484385	+	0.838979i	−0.999839	−	0.0179379i	$-0.994290\pi$
$269$	−2137.07	+	3701.52i	−0.484385	+	0.838979i	0.515454	+	0.856917i	$0.327623\pi$
$270$		0			0
$271$	−1818.38	+	1049.84i	−0.407597	+	0.235326i	−0.689757	−	0.724041i	$-0.742283\pi$
$271$	−1818.38	+	1049.84i	−0.407597	+	0.235326i	0.282160	+	0.959367i	$0.408949\pi$
$272$	−2034.05	−	3523.07i	−0.453427	−	0.785359i
$273$		0			0
$274$	572.946	−	992.371i	0.126325	−	0.218800i
$275$			2045.13i			0.448457i
$276$		0			0
$277$	4410.66			0.956718			0.478359	−	0.878164i	$-0.341232\pi$
$277$	4410.66			0.956718			0.478359	+	0.878164i	$0.341232\pi$
$278$	−275.748	−	477.610i	−0.0594902	−	0.103040i
$279$		0			0
$280$	−286.635	−	1838.76i	−0.0611775	−	0.392454i
$281$	4392.19	−	2535.83i	0.932443	−	0.538346i	0.0448593	−	0.998993i	$-0.485716\pi$
$281$	4392.19	−	2535.83i	0.932443	−	0.538346i	0.887583	+	0.460647i	$0.152383\pi$
$282$		0			0
$283$	478.561	−	276.297i	0.100521	−	0.0580360i	−0.448897	−	0.893584i	$-0.648183\pi$
$283$	478.561	−	276.297i	0.100521	−	0.0580360i	0.549418	+	0.835548i	$0.314850\pi$
$284$	−636.238	+	367.332i	−0.132936	+	0.0767505i
$285$		0			0
$286$	1024.47	−	591.478i	0.211812	−	0.122290i
$287$	730.870	−	1890.19i	0.150320	−	0.388760i
$288$		0			0
$289$	−738.458	−	1279.05i	−0.150307	−	0.260339i
$290$	451.937			0.0915125
$291$		0			0
$292$		−	1944.24i		−	0.389651i
$293$	−496.106	+	859.280i	−0.0989174	+	0.171330i	−0.911237	−	0.411883i	$-0.864871\pi$
$293$	−496.106	+	859.280i	−0.0989174	+	0.171330i	0.812319	+	0.583213i	$0.198205\pi$
$294$		0			0
$295$	3135.80	+	5431.37i	0.618894	+	1.07196i
$296$	1498.70	−	865.273i	0.294291	−	0.169909i
$297$		0			0
$298$	−551.796	+	955.739i	−0.107264	+	0.185787i
$299$	3373.10	−	5842.38i	0.652413	−	1.13001i
$300$		0			0
$301$	2886.24	+	3582.05i	0.552692	+	0.685933i
$302$	825.644	+	476.686i	0.157319	+	0.0908284i
$303$		0			0
$304$		−	2903.62i		−	0.547808i
$305$	4886.23	+	2821.07i	0.917327	+	0.529619i
$306$		0			0
$307$			256.830i			0.0477462i	0.999715	+	0.0238731i	$0.00759977\pi$
$307$			256.830i			0.0477462i	−0.999715	+	0.0238731i	$0.992400\pi$
$308$	−4453.95	+	3588.78i	−0.823985	+	0.663928i
$309$		0			0
$310$	−1697.22			−0.310955
$311$	361.742	+	626.556i	0.0659566	+	0.114240i	0.897118	−	0.441791i	$-0.145657\pi$
$311$	361.742	+	626.556i	0.0659566	+	0.114240i	−0.831161	+	0.556031i	$0.812323\pi$
$312$		0			0
$313$	−5961.98	−	3442.15i	−1.07665	−	0.621604i	−0.146659	−	0.989187i	$-0.546852\pi$
$313$	−5961.98	−	3442.15i	−1.07665	−	0.621604i	−0.929991	+	0.367584i	$0.880185\pi$
$314$	1483.66			0.266649
$315$		0			0
$316$	−8588.50			−1.52893
$317$	318.148	+	183.683i	0.0563690	+	0.0325447i	0.527920	−	0.849294i	$-0.322972\pi$
$317$	318.148	+	183.683i	0.0563690	+	0.0325447i	−0.471551	+	0.881839i	$0.656306\pi$
$318$		0			0
$319$	−1441.27	−	2496.36i	−0.252965	−	0.438148i
$320$	−2694.12			−0.470644
$321$		0			0
$322$	884.152	−	2286.61i	0.153018	−	0.395738i
$323$		−	4560.82i		−	0.785669i
$324$		0			0
$325$	1626.23	+	938.904i	0.277560	+	0.160249i
$326$			2746.85i			0.466669i
$327$		0			0
$328$	1094.23	+	631.753i	0.184203	+	0.106350i
$329$	−1970.75	+	5096.78i	−0.330246	+	0.854087i
$330$		0			0
$331$	−1912.88	+	3313.20i	−0.317647	+	0.550182i	−0.979997	−	0.199014i	$-0.936226\pi$
$331$	−1912.88	+	3313.20i	−0.317647	+	0.550182i	0.662349	+	0.749195i	$0.269560\pi$
$332$	2123.64	−	3678.25i	0.351054	−	0.608043i
$333$		0			0
$334$	2600.28	−	1501.27i	0.425991	−	0.245946i
$335$	−847.823	−	1468.47i	−0.138273	−	0.239496i
$336$		0			0
$337$	−477.374	+	826.836i	−0.0771639	+	0.133652i	−0.902025	−	0.431683i	$-0.857920\pi$
$337$	−477.374	+	826.836i	−0.0771639	+	0.133652i	0.824861	+	0.565335i	$0.191253\pi$
$338$			556.775i			0.0895993i
$339$		0			0
$340$	−5176.00			−0.825612
$341$	5412.63	+	9374.95i	0.859561	+	1.48880i
$342$		0			0
$343$	5681.03	−	2842.45i	0.894305	−	0.447458i
$344$	−2483.82	+	1434.03i	−0.389298	+	0.224761i
$345$		0			0
$346$	−1355.81	+	782.778i	−0.210662	+	0.121625i
$347$	4912.79	−	2836.40i	0.760036	−	0.438807i	−0.0692728	−	0.997598i	$-0.522068\pi$
$347$	4912.79	−	2836.40i	0.760036	−	0.438807i	0.829309	+	0.558791i	$0.188735\pi$
$348$		0			0
$349$	−163.883	+	94.6178i	−0.0251360	+	0.0145123i	−0.512515	−	0.858678i	$-0.671286\pi$
$349$	−163.883	+	94.6178i	−0.0251360	+	0.0145123i	0.487379	+	0.873190i	$0.337953\pi$
$350$	636.478	+	246.104i	0.0972033	+	0.0375852i
$351$		0			0
$352$	−2706.92	−	4688.53i	−0.409885	−	0.709941i
$353$	10440.7			1.57422			0.787110	−	0.616812i	$-0.211576\pi$
$353$	10440.7			1.57422			0.787110	+	0.616812i	$0.211576\pi$
$354$		0			0
$355$			859.210i			0.128457i
$356$	−666.035	+	1153.61i	−0.0991566	+	0.171744i
$357$		0			0
$358$	1379.01	+	2388.52i	0.203584	+	0.352618i
$359$	−9191.43	+	5306.67i	−1.35127	+	0.780155i	−0.988427	−	0.151697i	$-0.951526\pi$
$359$	−9191.43	+	5306.67i	−1.35127	+	0.780155i	−0.362840	+	0.931851i	$0.618193\pi$
$360$		0			0
$361$	−1801.85	+	3120.89i	−0.262698	+	0.455007i
$362$	616.407	−	1067.65i	0.0894962	−	0.155012i
$363$		0			0
$364$	808.924	+	5189.25i	0.116481	+	0.747226i
$365$	−1969.21	−	1136.92i	−0.282392	−	0.163039i
$366$		0			0
$367$			882.734i			0.125554i	0.998028	+	0.0627770i	$0.0199957\pi$
$367$			882.734i			0.125554i	−0.998028	+	0.0627770i	$0.980004\pi$
$368$	−7801.55	−	4504.22i	−1.10512	−	0.638041i
$369$		0			0
$370$		−	975.311i		−	0.137038i
$371$	−5258.07	−	2033.11i	−0.735810	−	0.284512i
$372$		0			0
$373$	2616.16			0.363162			0.181581	−	0.983376i	$-0.441879\pi$
$373$	2616.16			0.363162			0.181581	+	0.983376i	$0.441879\pi$
$374$	−1240.60	−	2148.79i	−0.171524	−	0.297089i
$375$		0			0
$376$	−2950.52	−	1703.48i	−0.404685	−	0.233645i
$377$	−2646.72			−0.361573
$378$		0			0
$379$	636.672			0.0862892			0.0431446	−	0.999069i	$-0.486262\pi$
$379$	636.672			0.0862892			0.0431446	+	0.999069i	$0.486262\pi$
$380$	−3199.43	−	1847.19i	−0.431915	−	0.249366i
$381$		0			0
$382$	1371.19	+	2374.97i	0.183655	+	0.318100i
$383$	7569.77			1.00991			0.504957	−	0.863145i	$-0.331508\pi$
$383$	7569.77			1.00991			0.504957	+	0.863145i	$0.331508\pi$
$384$		0			0
$385$	1030.36	+	6609.73i	0.136394	+	0.874970i
$386$		−	255.846i		−	0.0337364i
$387$		0			0
$388$	7117.61	+	4109.35i	0.931294	+	0.537683i
$389$			11135.5i			1.45139i	0.688015	+	0.725697i	$0.258482\pi$
$389$			11135.5i			1.45139i	−0.688015	+	0.725697i	$0.741518\pi$
$390$		0			0
$391$	−12254.2	−	7074.96i	−1.58496	−	0.915080i
$392$	1205.49	+	3772.65i	0.155323	+	0.486091i
$393$		0			0
$394$	−175.115	+	303.309i	−0.0223913	+	0.0387829i
$395$	−5022.24	+	8698.78i	−0.639738	+	1.10806i
$396$		0			0
$397$	−777.013	+	448.609i	−0.0982297	+	0.0567129i	−0.548310	−	0.836275i	$-0.684729\pi$
$397$	−777.013	+	448.609i	−0.0982297	+	0.0567129i	0.450080	+	0.892988i	$0.351395\pi$
$398$	586.797	+	1016.36i	0.0739032	+	0.128004i
$399$		0			0
$400$	1253.75	−	2171.56i	0.156719	−	0.271445i
$401$			4026.51i			0.501432i	0.968061	+	0.250716i	$0.0806660\pi$
$401$			4026.51i			0.501432i	−0.968061	+	0.250716i	$0.919334\pi$
$402$		0			0
$403$	9939.61			1.22860
$404$	−2.79325	−	4.83804i	−0.000343983	−	0.000595796i
$405$		0			0
$406$	−950.347	+	148.145i	−0.116170	+	0.0181091i
$407$	−5387.32	+	3110.37i	−0.656116	+	0.378809i
$408$		0			0
$409$	−9468.68	+	5466.74i	−1.14473	+	0.660912i	−0.947598	−	0.319464i	$-0.896497\pi$
$409$	−9468.68	+	5466.74i	−1.14473	+	0.660912i	−0.197135	+	0.980376i	$0.563164\pi$
$410$	616.691	−	356.047i	0.0742834	−	0.0428875i
$411$		0			0
$412$	−4852.43	+	2801.55i	−0.580248	+	0.335006i
$413$	−8374.47	−	10393.4i	−0.997774	−	1.23831i
$414$		0			0
$415$	−2483.66	−	4301.82i	−0.293778	−	0.508838i
$416$	−4970.92			−0.585864
$417$		0			0
$418$		−	1770.97i		−	0.207227i
$419$	2433.63	−	4215.18i	0.283749	−	0.491467i	−0.688556	−	0.725183i	$-0.741755\pi$
$419$	2433.63	−	4215.18i	0.283749	−	0.491467i	0.972305	+	0.233716i	$0.0750885\pi$
$420$		0			0
$421$	−5868.66	−	10164.8i	−0.679385	−	1.17673i	−0.975166	−	0.221474i	$-0.928913\pi$
$421$	−5868.66	−	10164.8i	−0.679385	−	1.17673i	0.295781	−	0.955256i	$-0.404420\pi$
$422$	−1612.17	+	930.789i	−0.185970	+	0.107370i
$423$		0			0
$424$	1757.39	−	3043.89i	0.201289	−	0.348643i
$425$	1969.32	−	3410.96i	0.224767	−	0.389308i
$426$		0			0
$427$	−11199.7	−	4330.52i	−1.26930	−	0.490793i
$428$	8107.00	+	4680.58i	0.915576	+	0.528608i
$429$		0			0
$430$			1616.40i			0.181278i
$431$	−8093.99	−	4673.07i	−0.904580	−	0.522260i	−0.0258967	−	0.999665i	$-0.508244\pi$
$431$	−8093.99	−	4673.07i	−0.904580	−	0.522260i	−0.878683	+	0.477405i	$0.841577\pi$
$432$		0			0
$433$			582.680i			0.0646693i	0.999477	+	0.0323346i	$0.0102942\pi$
$433$			582.680i			0.0646693i	−0.999477	+	0.0323346i	$0.989706\pi$
$434$	3568.98	−	556.350i	0.394738	−	0.0615337i
$435$		0			0
$436$	1649.05			0.181136
$437$	−5049.78	−	8746.47i	−0.552777	−	0.957438i
$438$		0			0
$439$	5577.42	+	3220.13i	0.606369	+	0.350087i	0.771543	−	0.636177i	$-0.219485\pi$
$439$	5577.42	+	3220.13i	0.606369	+	0.350087i	−0.165174	+	0.986264i	$0.552819\pi$
$440$	−4170.75			−0.451892
$441$		0			0
$442$	−2278.21			−0.245166
$443$	10151.6	+	5861.05i	1.08876	+	0.628593i	0.933245	−	0.359241i	$-0.116964\pi$
$443$	10151.6	+	5861.05i	1.08876	+	0.628593i	0.155511	+	0.987834i	$0.450298\pi$
$444$		0			0
$445$	778.946	+	1349.17i	0.0829789	+	0.143724i
$446$	−741.657			−0.0787409
$447$		0			0
$448$	5665.29	−	883.133i	0.597455	−	0.0931341i
$449$			10126.0i			1.06431i	0.846648	+	0.532153i	$0.178617\pi$
$449$			10126.0i			1.06431i	−0.846648	+	0.532153i	$0.821383\pi$
$450$		0			0
$451$	−3933.38	−	2270.94i	−0.410678	−	0.237105i
$452$			11559.2i			1.20287i
$453$		0			0
$454$	390.820	+	225.640i	0.0404011	+	0.0233256i
$455$	5728.91	+	2215.17i	0.590276	+	0.228239i
$456$		0			0
$457$	3527.39	−	6109.61i	0.361059	−	0.625373i	−0.627076	−	0.778958i	$-0.715748\pi$
$457$	3527.39	−	6109.61i	0.361059	−	0.625373i	0.988135	+	0.153585i	$0.0490818\pi$
$458$	484.302	−	838.835i	0.0494104	−	0.0855812i
$459$		0			0
$460$	−9926.22	+	5730.91i	−1.00611	+	0.580880i
$461$	−1300.85	−	2253.14i	−0.131425	−	0.227634i	0.792801	−	0.609480i	$-0.208622\pi$
$461$	−1300.85	−	2253.14i	−0.131425	−	0.227634i	−0.924226	+	0.381846i	$0.875288\pi$
$462$		0			0
$463$	−4858.94	+	8415.93i	−0.487719	+	0.844755i	−0.999900	−	0.0141228i	$-0.995504\pi$
$463$	−4858.94	+	8415.93i	−0.487719	+	0.844755i	0.512181	+	0.858878i	$0.328838\pi$
$464$			3534.26i			0.353607i
$465$		0			0
$466$	−3194.70			−0.317578
$467$	4239.34	+	7342.76i	0.420072	+	0.727585i	0.995946	−	0.0899527i	$-0.0286716\pi$
$467$	4239.34	+	7342.76i	0.420072	+	0.727585i	−0.575874	+	0.817538i	$0.695338\pi$
$468$		0			0
$469$	2264.19	+	2810.03i	0.222923	+	0.276664i
$470$	−1662.87	+	960.059i	−0.163197	+	0.0942218i
$471$		0			0
$472$	7206.82	−	4160.86i	0.702799	−	0.405761i
$473$	8928.49	−	5154.87i	0.867933	−	0.501102i
$474$		0			0
$475$	2434.58	−	1405.61i	0.235171	−	0.135776i
$476$	10884.3	−	1696.69i	1.04807	−	0.163378i
$477$		0			0
$478$	895.736	+	1551.46i	0.0857113	+	0.148456i
$479$	19701.4			1.87929			0.939645	−	0.342150i	$-0.111155\pi$
$479$	19701.4			1.87929			0.939645	+	0.342150i	$0.111155\pi$
$480$		0			0
$481$			5711.80i			0.541446i
$482$	305.903	−	529.840i	0.0289077	−	0.0500696i
$483$		0			0
$484$	1457.77	+	2524.94i	0.136906	+	0.237128i
$485$	8324.25	−	4806.01i	0.779350	−	0.449958i
$486$		0			0
$487$	−7141.08	+	12368.7i	−0.664463	+	1.15088i	0.314968	+	0.949102i	$0.398006\pi$
$487$	−7141.08	+	12368.7i	−0.664463	+	1.15088i	−0.979431	+	0.201781i	$0.935327\pi$
$488$	3743.24	−	6483.48i	0.347230	−	0.601421i
$489$		0			0
$490$	2181.05	+	474.730i	0.201081	+	0.0437676i
$491$	−9090.51	−	5248.41i	−0.835537	−	0.482398i	0.0202074	−	0.999796i	$-0.493567\pi$
$491$	−9090.51	−	5248.41i	−0.835537	−	0.482398i	−0.855745	+	0.517398i	$0.826901\pi$
$492$		0			0
$493$			5551.40i			0.507145i
$494$	−1408.23	−	813.041i	−0.128257	−	0.0740495i
$495$		0			0
$496$		−	13272.7i		−	1.20154i
$497$	−281.649	−	1806.77i	−0.0254199	−	0.163068i
$498$		0			0
$499$	16828.4			1.50970			0.754850	−	0.655897i	$-0.227710\pi$
$499$	16828.4			1.50970			0.754850	+	0.655897i	$0.227710\pi$
$500$	−5642.14	−	9772.48i	−0.504649	−	0.874077i
$501$		0			0
$502$	−4867.72	−	2810.38i	−0.432783	−	0.249867i
$503$	−12335.3			−1.09344			−0.546722	−	0.837314i	$-0.684125\pi$
$503$	−12335.3			−1.09344			−0.546722	+	0.837314i	$0.684125\pi$
$504$		0			0
$505$	−6.53356			−0.000575722
$506$	−4758.31	−	2747.21i	−0.418049	−	0.241361i
$507$		0			0
$508$	−9022.16	−	15626.8i	−0.787980	−	1.36482i
$509$	−14453.1			−1.25859			−0.629295	−	0.777166i	$-0.716656\pi$
$509$	−14453.1			−1.25859			−0.629295	+	0.777166i	$0.716656\pi$
$510$		0			0
$511$	4513.59	+	1745.25i	0.390743	+	0.151087i
$512$			11338.9i			0.978739i
$513$		0			0
$514$	3593.43	+	2074.67i	0.308365	+	0.178034i
$515$			6552.99i			0.560698i
$516$		0			0
$517$	10606.1	+	6123.46i	0.902239	+	0.520908i
$518$	319.706	+	2050.91i	0.0271179	+	0.173961i
$519$		0			0
$520$	−1914.76	+	3316.46i	−0.161477	+	0.279686i
$521$	−3797.90	+	6578.16i	−0.319365	+	0.553156i	−0.980356	−	0.197238i	$-0.936803\pi$
$521$	−3797.90	+	6578.16i	−0.319365	+	0.553156i	0.660991	+	0.750394i	$0.270136\pi$
$522$		0			0
$523$	15947.4	−	9207.24i	1.33333	−	0.769799i	0.347522	−	0.937672i	$-0.387023\pi$
$523$	15947.4	−	9207.24i	1.33333	−	0.769799i	0.985809	+	0.167873i	$0.0536900\pi$
$524$	−181.684	−	314.686i	−0.0151468	−	0.0262350i
$525$		0			0
$526$	−2383.15	+	4127.74i	−0.197548	+	0.342164i
$527$		−	20848.0i		−	1.72325i
$528$		0			0
$529$	−19166.8			−1.57531
$530$	−990.441	−	1715.49i	−0.0811736	−	0.140597i
$531$		0			0
$532$	7333.38	+	2835.57i	0.597636	+	0.231085i
$533$	−3611.58	+	2085.15i	−0.293499	+	0.169452i
$534$		0			0
$535$	9481.37	−	5474.07i	0.766197	−	0.442364i
$536$	−1948.50	+	1124.97i	−0.157019	+	0.0906551i
$537$		0			0
$538$	2768.05	−	1598.13i	0.221820	−	0.128068i
$539$	−4333.34	−	13561.4i	−0.346289	−	1.08373i
$540$		0			0
$541$	10525.6	+	18230.9i	0.836474	+	1.44882i	0.892825	+	0.450405i	$0.148720\pi$
$541$	10525.6	+	18230.9i	0.836474	+	1.44882i	−0.0563503	+	0.998411i	$0.517946\pi$
$542$	1570.18			0.124437
$543$		0			0
$544$			10426.3i			0.821738i
$545$	964.307	−	1670.23i	0.0757915	−	0.131275i
$546$		0			0
$547$	−8242.69	−	14276.8i	−0.644300	−	1.11596i	−0.984463	−	0.175594i	$-0.943815\pi$
$547$	−8242.69	−	14276.8i	−0.644300	−	1.11596i	0.340163	−	0.940367i	$-0.389518\pi$
$548$	9874.11	−	5700.82i	0.769710	−	0.444392i
$549$		0			0
$550$	764.688	−	1324.48i	0.0592844	−	0.102684i
$551$	−1981.16	+	3431.48i	−0.153177	+	0.265310i
$552$		0			0
$553$	7709.48	−	19938.4i	0.592840	−	1.53321i
$554$	−2856.46	−	1649.18i	−0.219060	−	0.126474i
$555$		0			0
$556$		−	5487.40i		−	0.418557i
$557$	5731.63	+	3309.16i	0.436009	+	0.251730i	0.701903	−	0.712272i	$-0.252334\pi$
$557$	5731.63	+	3309.16i	0.436009	+	0.251730i	−0.265894	+	0.964002i	$0.585667\pi$
$558$		0			0
$559$		−	9466.26i		−	0.716243i
$560$	2958.00	−	7650.03i	0.223211	−	0.577272i
$561$		0			0
$562$	−3792.67			−0.284669
$563$	−8503.32	−	14728.2i	−0.636540	−	1.10252i	−0.986187	−	0.165638i	$-0.947032\pi$
$563$	−8503.32	−	14728.2i	−0.636540	−	1.10252i	0.349647	−	0.936882i	$-0.386302\pi$
$564$		0			0
$565$	11707.6	+	6759.40i	0.871758	+	0.503310i
$566$	−413.239			−0.0306885
$567$		0			0
$568$	1140.08			0.0842192
$569$	9769.80	+	5640.60i	0.719809	+	0.415582i	0.814682	−	0.579907i	$-0.196911\pi$
$569$	9769.80	+	5640.60i	0.719809	+	0.415582i	−0.0948734	+	0.995489i	$0.530245\pi$
$570$		0			0
$571$	12233.2	+	21188.5i	0.896571	+	1.55291i	0.831848	+	0.555004i	$0.187283\pi$
$571$	12233.2	+	21188.5i	0.896571	+	1.55291i	0.0647233	+	0.997903i	$0.479384\pi$
$572$	11770.4			0.860396
$573$		0			0
$574$	−1180.09	+	950.857i	−0.0858115	+	0.0691429i
$575$		−	8721.78i		−	0.632562i
$576$		0			0
$577$	−14445.8	−	8340.28i	−1.04226	−	0.601751i	−0.121790	−	0.992556i	$-0.538863\pi$
$577$	−14445.8	−	8340.28i	−1.04226	−	0.601751i	−0.920474	+	0.390805i	$0.872197\pi$
$578$			1104.46i			0.0794801i
$579$		0			0
$580$	3894.33	+	2248.39i	0.278798	+	0.160964i
$581$	6632.84	+	8231.86i	0.473626	+	0.587806i
$582$		0			0
$583$	−6317.24	+	10941.8i	−0.448771	+	0.777294i
$584$	−1508.57	+	2612.92i	−0.106892	+	0.185143i
$585$		0			0
$586$	642.582	−	370.995i	0.0452984	−	0.0261530i
$587$	−7866.86	−	13625.8i	−0.553152	−	0.958087i	−0.998045	−	0.0625029i	$-0.980092\pi$
$587$	−7866.86	−	13625.8i	−0.553152	−	0.958087i	0.444893	−	0.895584i	$-0.353242\pi$
$588$		0			0
$589$	7440.16	−	12886.7i	0.520486	−	0.901509i
$590$		−	4690.00i		−	0.327262i
$591$		0			0
$592$	7627.17			0.529518
$593$	−2335.26	−	4044.79i	−0.161716	−	0.280101i	0.773768	−	0.633469i	$-0.218370\pi$
$593$	−2335.26	−	4044.79i	−0.161716	−	0.280101i	−0.935484	+	0.353368i	$0.885036\pi$
$594$		0			0
$595$	4646.25	−	12016.2i	0.320131	−	0.827926i
$596$	−9509.62	+	5490.38i	−0.653573	+	0.377340i
$597$		0			0
$598$	−4369.02	+	2522.45i	−0.298767	+	0.172493i
$599$	11047.3	−	6378.15i	0.753556	−	0.435066i	−0.0734215	−	0.997301i	$-0.523392\pi$
$599$	11047.3	−	6378.15i	0.753556	−	0.435066i	0.826977	+	0.562235i	$0.190059\pi$
$600$		0			0
$601$	17937.2	−	10356.0i	1.21743	−	0.702882i	0.253060	−	0.967451i	$-0.418563\pi$
$601$	17937.2	−	10356.0i	1.21743	−	0.702882i	0.964367	+	0.264569i	$0.0852297\pi$
$602$	−529.855	−	3399.02i	−0.0358725	−	0.230122i
$603$		0			0
$604$	4743.03	+	8215.17i	0.319522	+	0.553428i
$605$	3409.82			0.229139
$606$		0			0
$607$		−	24485.0i		−	1.63726i	−0.574325	−	0.818628i	$-0.694735\pi$
$607$		−	24485.0i		−	1.63726i	0.574325	−	0.818628i	$-0.305265\pi$
$608$	−3720.91	+	6444.81i	−0.248196	+	0.429888i
$609$		0			0
$610$	−2109.63	−	3653.99i	−0.140027	−	0.242534i
$611$	9738.42	−	5622.48i	0.644803	−	0.372277i
$612$		0			0
$613$	−2415.65	+	4184.03i	−0.159164	+	0.275679i	−0.934567	−	0.355786i	$-0.884213\pi$
$613$	−2415.65	+	4184.03i	−0.159164	+	0.275679i	0.775404	+	0.631466i	$0.217546\pi$
$614$	96.0308	−	166.330i	0.00631187	−	0.0109325i
$615$		0			0
$616$	8770.38	−	1367.17i	0.573650	−	0.0894233i
$617$	5042.06	+	2911.04i	0.328988	+	0.189942i	0.655392	−	0.755289i	$-0.272503\pi$
$617$	5042.06	+	2911.04i	0.328988	+	0.189942i	−0.326404	+	0.945231i	$0.605837\pi$
$618$		0			0
$619$			1448.25i			0.0940388i	0.998894	+	0.0470194i	$0.0149723\pi$
$619$			1448.25i			0.0940388i	−0.998894	+	0.0470194i	$0.985028\pi$
$620$	−14624.9	−	8443.71i	−0.947341	−	0.546948i
$621$		0			0
$622$		−	541.032i		−	0.0348769i
$623$	−2080.25	−	2581.75i	−0.133778	−	0.166028i
$624$		0			0
$625$	−7038.32			−0.450452
$626$	2574.09	+	4458.46i	0.164347	+	0.284658i
$627$		0			0
$628$	12784.7	+	7381.24i	0.812363	+	0.469018i
$629$	11980.3			0.759437
$630$		0			0
$631$	−22632.9			−1.42790			−0.713948	−	0.700199i	$-0.753095\pi$
$631$	−22632.9			−1.42790			−0.713948	+	0.700199i	$0.753095\pi$
$632$	11542.3	+	6663.96i	0.726469	+	0.419427i
$633$		0			0
$634$	−137.361	−	237.916i	−0.00860456	−	0.0149035i
$635$	−21103.4			−1.31884
$636$		0			0
$637$	−12773.1	−	2780.20i	−0.794486	−	0.172929i
$638$			2155.61i			0.133764i
$639$		0			0
$640$	9608.61	+	5547.53i	0.593459	+	0.342633i
$641$			15231.9i			0.938571i	0.883046	+	0.469286i	$0.155489\pi$
$641$			15231.9i			0.938571i	−0.883046	+	0.469286i	$0.844511\pi$
$642$		0			0
$643$	−12428.6	−	7175.65i	−0.762264	−	0.440093i	0.0678441	−	0.997696i	$-0.478388\pi$
$643$	−12428.6	−	7175.65i	−0.762264	−	0.440093i	−0.830108	+	0.557603i	$0.811721\pi$
$644$	18994.6	−	15305.0i	1.16225	−	0.936490i
$645$		0			0
$646$	−1705.33	+	2953.71i	−0.103862	+	0.179895i
$647$	−14009.3	+	24264.9i	−0.851258	+	1.47442i	0.0288151	+	0.999585i	$0.490827\pi$
$647$	−14009.3	+	24264.9i	−0.851258	+	1.47442i	−0.880073	+	0.474838i	$0.842507\pi$
$648$		0			0
$649$	−25906.1	+	14956.9i	−1.56688	+	0.904638i
$650$	−702.126	−	1216.12i	−0.0423687	−	0.0733847i
$651$		0			0
$652$	−13665.6	+	23669.6i	−0.820840	+	1.42174i
$653$			12216.5i			0.732113i	0.930593	+	0.366057i	$0.119292\pi$
$653$			12216.5i			0.732113i	−0.930593	+	0.366057i	$0.880708\pi$
$654$		0			0
$655$	−424.969			−0.0253510
$656$	2784.37	+	4822.67i	0.165719	+	0.287033i
$657$		0			0
$658$	3182.03	−	2563.93i	0.188524	−	0.151903i
$659$	−5703.43	+	3292.88i	−0.337138	+	0.194647i	−0.659006	−	0.752138i	$-0.729023\pi$
$659$	−5703.43	+	3292.88i	−0.337138	+	0.194647i	0.321868	+	0.946785i	$0.395689\pi$
$660$		0			0
$661$	−6336.72	+	3658.51i	−0.372874	+	0.215279i	−0.674713	−	0.738080i	$-0.735733\pi$
$661$	−6336.72	+	3658.51i	−0.372874	+	0.215279i	0.301839	+	0.953359i	$0.402399\pi$
$662$	2477.66	−	1430.48i	0.145464	−	0.0839836i
$663$		0			0
$664$	−5708.03	+	3295.53i	−0.333606	+	0.192608i
$665$	7160.28	−	5769.42i	0.417539	−	0.336434i
$666$		0			0
$667$	6146.55	+	10646.1i	0.356815	+	0.618021i
$668$	29875.4			1.73041
$669$		0			0
$670$			1268.03i			0.0731167i
$671$	−13455.7	+	23305.9i	−0.774145	+	1.34086i
$672$		0			0
$673$	1486.23	+	2574.23i	0.0851263	+	0.147443i	0.905445	−	0.424464i	$-0.139537\pi$
$673$	1486.23	+	2574.23i	0.0851263	+	0.147443i	−0.820319	+	0.571907i	$0.806204\pi$
$674$	618.320	−	356.987i	0.0353365	−	0.0204015i
$675$		0			0
$676$	−2769.96	+	4797.71i	−0.157599	+	0.272970i
$677$	−8554.38	+	14816.6i	−0.485630	+	0.841136i	−0.999864	−	0.0165140i	$-0.994743\pi$
$677$	−8554.38	+	14816.6i	−0.485630	+	0.841136i	0.514233	+	0.857650i	$0.328077\pi$
$678$		0			0
$679$	−15929.1	+	12834.9i	−0.900298	+	0.725418i
$680$	6956.17	+	4016.15i	0.392290	+	0.226488i
$681$		0			0
$682$		−	8095.29i		−	0.454523i
$683$	−4555.42	−	2630.07i	−0.255210	−	0.147346i	0.366938	−	0.930246i	$-0.380406\pi$
$683$	−4555.42	−	2630.07i	−0.255210	−	0.147346i	−0.622147	+	0.782900i	$0.713740\pi$
$684$		0			0
$685$		−	13334.5i		−	0.743776i
$686$	−4742.00	−	283.330i	−0.263922	−	0.0157691i
$687$		0			0
$688$	−12640.6			−0.700465
$689$	5800.41	+	10046.6i	0.320723	+	0.555508i
$690$		0			0
$691$	−16770.2	−	9682.26i	−0.923252	−	0.533040i	−0.0385810	−	0.999255i	$-0.512284\pi$
$691$	−16770.2	−	9682.26i	−0.923252	−	0.533040i	−0.884671	+	0.466216i	$0.845617\pi$
$692$	−15577.3			−0.855724
$693$		0			0
$694$	−4242.21			−0.232034
$695$	−5557.87	−	3208.84i	−0.303341	−	0.175134i
$696$		0			0
$697$	4373.52	+	7575.17i	0.237674	+	0.411664i
$698$	141.513			0.00767386
$699$		0			0
$700$	4260.14	+	5287.15i	0.230026	+	0.285479i
$701$			23797.7i			1.28221i	0.767455	+	0.641103i	$0.221523\pi$
$701$			23797.7i			1.28221i	−0.767455	+	0.641103i	$0.778477\pi$
$702$		0			0
$703$	7405.36	+	4275.49i	0.397295	+	0.229379i
$704$		−	12850.2i		−	0.687942i
$705$		0			0
$706$	−6761.64	−	3903.84i	−0.360450	−	0.208106i
$707$	13.7390	−	2.14170i	0.000730845	−	0.000113928i
$708$		0			0
$709$	−7213.51	+	12494.2i	−0.382100	+	0.661817i	−0.991362	−	0.131152i	$-0.958132\pi$
$709$	−7213.51	+	12494.2i	−0.382100	+	0.661817i	0.609262	+	0.792969i	$0.291466\pi$
$710$	321.265	−	556.447i	0.0169815	−	0.0294128i
$711$		0			0
$712$	1790.20	−	1033.57i	0.0942285	−	0.0544029i
$713$	−23083.0	−	39981.0i	−1.21244	−	2.10000i
$714$		0			0
$715$	6882.93	−	11921.6i	0.360010	−	0.623555i
$716$			27442.4i			1.43236i
$717$		0			0
$718$	7936.82			0.412534
$719$	−2139.85	−	3706.33i	−0.110992	−	0.192243i	0.805179	−	0.593032i	$-0.202069\pi$
$719$	−2139.85	−	3706.33i	−0.110992	−	0.192243i	−0.916170	+	0.400789i	$0.868736\pi$
$720$		0			0
$721$	−2148.07	−	13779.8i	−0.110955	−	0.711773i
$722$	2333.85	−	1347.45i	0.120300	−	0.0694555i
$723$		0			0
$724$	10623.1	−	6133.26i	0.545311	−	0.314835i
$725$	−2963.36	+	1710.89i	−0.151802	+	0.0876428i
$726$		0			0
$727$	8438.47	−	4871.95i	0.430489	−	0.248543i	−0.269066	−	0.963122i	$-0.586715\pi$
$727$	8438.47	−	4871.95i	0.430489	−	0.248543i	0.699555	+	0.714579i	$0.253382\pi$
$728$	2939.29	−	7601.62i	0.149639	−	0.386999i
$729$		0			0
$730$	850.207	+	1472.60i	0.0431063	+	0.0746623i
$731$	−19855.2			−1.00461
$732$		0			0
$733$			4535.45i			0.228541i	0.993450	+	0.114271i	$0.0364531\pi$
$733$			4535.45i			0.228541i	−0.993450	+	0.114271i	$0.963547\pi$
$734$	330.061	−	571.682i	0.0165978	−	0.0287482i
$735$		0			0
$736$	11544.1	+	19995.0i	0.578154	+	1.00139i
$737$	7004.20	−	4043.88i	0.350072	−	0.202114i
$738$		0			0
$739$	15942.1	−	27612.6i	0.793561	−	1.37449i	−0.130189	−	0.991489i	$-0.541558\pi$
$739$	15942.1	−	27612.6i	0.793561	−	1.37449i	0.923749	−	0.382998i	$-0.125108\pi$
$740$	4852.18	−	8404.22i	0.241040	−	0.417494i
$741$		0			0
$742$	2645.07	+	3282.73i	0.130867	+	0.162416i
$743$	10135.3	+	5851.64i	0.500444	+	0.288931i	0.728897	−	0.684624i	$-0.240033\pi$
$743$	10135.3	+	5851.64i	0.500444	+	0.288931i	−0.228453	+	0.973555i	$0.573367\pi$
$744$		0			0
$745$			12842.3i			0.631552i
$746$	−1694.29	−	978.200i	−0.0831534	−	0.0480086i
$747$		0			0
$748$		−	24688.1i		−	1.20680i
$749$	−18143.3	+	14619.0i	−0.885104	+	0.713175i
$750$		0			0
$751$	−16580.5			−0.805635			−0.402817	−	0.915280i	$-0.631969\pi$
$751$	−16580.5			−0.805635			−0.402817	+	0.915280i	$0.631969\pi$
$752$	−7507.90	−	13004.1i	−0.364076	−	0.630598i
$753$		0			0
$754$	1714.08	+	989.627i	0.0827895	+	0.0477985i
$755$	11094.2			0.534782
$756$		0			0
$757$	−16410.7			−0.787923			−0.393962	−	0.919127i	$-0.628896\pi$
$757$	−16410.7			−0.787923			−0.393962	+	0.919127i	$0.628896\pi$
$758$	−412.325	−	238.056i	−0.0197577	−	0.0114071i
$759$		0			0
$760$	2866.54	+	4964.99i	0.136816	+	0.236972i
$761$	−21191.0			−1.00943			−0.504713	−	0.863287i	$-0.668402\pi$
$761$	−21191.0			−1.00943			−0.504713	+	0.863287i	$0.668402\pi$
$762$		0			0
$763$	−1480.28	+	3828.31i	−0.0702354	+	0.181644i
$764$			27286.8i			1.29215i
$765$		0			0
$766$	−4902.38	−	2830.39i	−0.231241	−	0.133507i
$767$			27466.5i			1.29303i
$768$		0			0
$769$	−4457.86	−	2573.75i	−0.209044	−	0.120691i	0.391823	−	0.920041i	$-0.371844\pi$
$769$	−4457.86	−	2573.75i	−0.209044	−	0.120691i	−0.600867	+	0.799349i	$0.705178\pi$
$770$	1804.14	−	4665.90i	0.0844374	−	0.218373i
$771$		0			0
$772$	1272.84	−	2204.62i	0.0593400	−	0.102780i
$773$	13537.8	−	23448.2i	0.629912	−	1.09104i	−0.357657	−	0.933853i	$-0.616424\pi$
$773$	13537.8	−	23448.2i	0.629912	−	1.09104i	0.987569	−	0.157187i	$-0.0502425\pi$
$774$		0			0
$775$	11128.7	−	6425.17i	0.515814	−	0.297805i
$776$	−6377.03	−	11045.3i	−0.295003	−	0.510960i
$777$		0			0
$778$	4163.64	−	7211.64i	0.191869	−	0.332326i
$779$			6243.23i			0.287146i
$780$		0			0
$781$	−4098.19			−0.187765
$782$	5290.76	+	9163.87i	0.241940	+	0.419053i
$783$		0			0
$784$	−3712.51	+	17056.4i	−0.169119	+	0.776984i
$785$	14952.0	−	8632.57i	0.679823	−	0.392496i
$786$		0			0
$787$	−9407.72	+	5431.55i	−0.426110	+	0.246015i	−0.697688	−	0.716401i	$-0.745788\pi$
$787$	−9407.72	+	5431.55i	−0.426110	+	0.246015i	0.271578	+	0.962416i	$0.412455\pi$
$788$	−3017.93	+	1742.40i	−0.136433	+	0.0787697i
$789$		0			0
$790$	6505.08	−	3755.71i	0.292962	−	0.169142i
$791$	−26834.9	−	10376.1i	−1.20624	−	0.466413i
$792$		0			0
$793$	12354.8	+	21399.2i	0.553257	+	0.958270i
$794$	670.953			0.0299889
$795$		0			0
$796$			11677.3i			0.519963i
$797$	−3869.66	+	6702.44i	−0.171983	+	0.297883i	−0.939113	−	0.343608i	$-0.888351\pi$
$797$	−3869.66	+	6702.44i	−0.171983	+	0.297883i	0.767130	+	0.641491i	$0.221684\pi$
$798$		0			0
$799$	−11793.0	−	20426.0i	−0.522159	−	0.904406i
$800$	−5565.61	+	3213.31i	−0.245968	+	0.142010i
$801$		0			0
$802$	1505.54	−	2607.67i	0.0662874	−	0.114813i
$803$	5422.80	−	9392.57i	0.238314	−	0.412773i
$804$		0			0
$805$	−4394.13	−	28188.3i	−0.192388	−	1.23417i
$806$	−6437.15	−	3716.49i	−0.281314	−	0.162417i
$807$		0			0
$808$			8.66930i			0.000377457i
$809$	18111.7	+	10456.8i	0.787114	+	0.454440i	0.838945	−	0.544215i	$-0.183173\pi$
$809$	18111.7	+	10456.8i	0.787114	+	0.454440i	−0.0518317	+	0.998656i	$0.516506\pi$
$810$		0			0
$811$			31359.1i			1.35779i	0.734235	+	0.678895i	$0.237541\pi$
$811$			31359.1i			1.35779i	−0.734235	+	0.678895i	$0.762459\pi$
$812$	−8926.13	−	3451.43i	−0.385771	−	0.149164i
$813$		0			0
$814$	4651.96			0.200308
$815$	15982.3	+	27682.2i	0.686917	+	1.18977i
$816$		0			0
$817$	−12273.0	−	7085.84i	−0.525556	−	0.303430i
$818$	8176.22			0.349480
$819$		0			0
$820$	7085.34			0.301745
$821$	−16357.5	−	9444.03i	−0.695349	−	0.401460i	0.110264	−	0.993902i	$-0.464831\pi$
$821$	−16357.5	−	9444.03i	−0.695349	−	0.401460i	−0.805613	+	0.592442i	$0.798164\pi$
$822$		0			0
$823$	6742.64	+	11678.6i	0.285582	+	0.494642i	0.972750	−	0.231856i	$-0.0744799\pi$
$823$	6742.64	+	11678.6i	0.285582	+	0.494642i	−0.687168	+	0.726498i	$0.741147\pi$
$824$	8695.09			0.367606
$825$		0			0
$826$	1537.38	+	9862.29i	0.0647607	+	0.415439i
$827$		−	17296.9i		−	0.727292i	−0.931537	−	0.363646i	$-0.881532\pi$
$827$		−	17296.9i		−	0.727292i	0.931537	−	0.363646i	$-0.118468\pi$
$828$		0			0
$829$	−4067.89	−	2348.59i	−0.170426	−	0.0983957i	0.412360	−	0.911021i	$-0.364704\pi$
$829$	−4067.89	−	2348.59i	−0.170426	−	0.0983957i	−0.582787	+	0.812625i	$0.698038\pi$
$830$			3714.63i			0.155345i
$831$		0			0
$832$	−10218.1	−	5899.45i	−0.425782	−	0.245825i
$833$	−5831.38	+	26791.1i	−0.242551	+	1.11435i
$834$		0			0
$835$	17470.1	−	30259.0i	0.724043	−	1.25408i
$836$	8810.60	−	15260.4i	0.364499	−	0.631330i
$837$		0			0
$838$	−3152.17	+	1819.91i	−0.129940	+	0.0750210i
$839$	−1606.27	−	2782.14i	−0.0660960	−	0.114482i	0.831084	−	0.556147i	$-0.187721\pi$
$839$	−1606.27	−	2782.14i	−0.0660960	−	0.114482i	−0.897180	+	0.441666i	$0.854388\pi$
$840$		0			0
$841$	−9783.04	+	16944.7i	−0.401125	+	0.694769i
$842$			8777.35i			0.359249i
$843$		0			0
$844$	−18522.7			−0.755425
$845$	3239.55	+	5611.06i	0.131886	+	0.228434i
$846$		0			0
$847$	−7170.28	+	1117.74i	−0.290878	+	0.0453434i
$848$	13415.6	−	7745.50i	0.543270	−	0.313657i
$849$		0			0
$850$	−2550.77	+	1472.69i	−0.102930	+	0.0594267i
$851$	22975.1	−	13264.7i	0.925471	−	0.534321i
$852$		0			0
$853$	−34142.7	+	19712.3i	−1.37048	+	0.791249i	−0.990989	−	0.133945i	$-0.957235\pi$
$853$	−34142.7	+	19712.3i	−1.37048	+	0.791249i	−0.379495	+	0.925194i	$0.623902\pi$
$854$	5633.99	+	6992.20i	0.225751	+	0.280173i
$855$		0			0
$856$	−7263.48	−	12580.7i	−0.290024	−	0.502336i
$857$	1759.78			0.0701435			0.0350718	−	0.999385i	$-0.488834\pi$
$857$	1759.78			0.0701435			0.0350718	+	0.999385i	$0.488834\pi$
$858$		0			0
$859$		−	5140.46i		−	0.204179i	−0.994775	−	0.102090i	$-0.967447\pi$
$859$		−	5140.46i		−	0.204179i	0.994775	−	0.102090i	$-0.0325529\pi$
$860$	−8041.60	+	13928.5i	−0.318856	+	0.552275i
$861$		0			0
$862$	3494.59	+	6052.81i	0.138081	+	0.239164i
$863$	30321.8	−	17506.3i	1.19602	−	0.690523i	0.236355	−	0.971667i	$-0.424047\pi$
$863$	30321.8	−	17506.3i	1.19602	−	0.690523i	0.959666	+	0.281144i	$0.0907139\pi$
$864$		0			0
$865$	−9109.06	+	15777.4i	−0.358055	+	0.620169i
$866$	217.868	−	377.359i	0.00854903	−	0.0148074i
$867$		0			0
$868$	33521.6	+	12961.7i	1.31083	+	0.506852i
$869$	−41490.8	−	23954.7i	−1.61965	−	0.935107i
$870$		0			0
$871$		−	7426.07i		−	0.288889i
$872$	−2216.21	−	1279.53i	−0.0860668	−	0.0496907i
$873$		0			0
$874$			7552.60i			0.292300i
$875$	27751.7	−	4326.07i	1.07220	−	0.167140i
$876$		0			0
$877$	17341.8			0.667721			0.333860	−	0.942623i	$-0.391649\pi$
$877$	17341.8			0.667721			0.333860	+	0.942623i	$0.391649\pi$
$878$	−2408.06	−	4170.88i	−0.0925604	−	0.160319i
$879$		0			0
$880$	−15919.3	−	9191.03i	−0.609819	−	0.352079i
$881$	38797.9			1.48369			0.741846	−	0.670570i	$-0.233950\pi$
$881$	38797.9			1.48369			0.741846	+	0.670570i	$0.233950\pi$
$882$		0			0
$883$	27338.7			1.04193			0.520963	−	0.853579i	$-0.325573\pi$
$883$	27338.7			1.04193			0.520963	+	0.853579i	$0.325573\pi$
$884$	−19631.3	−	11334.1i	−0.746914	−	0.431231i
$885$		0			0
$886$	−4382.98	−	7591.54i	−0.166195	−	0.287859i
$887$	43410.3			1.64326			0.821631	−	0.570019i	$-0.193064\pi$
$887$	43410.3			1.64326			0.821631	+	0.570019i	$0.193064\pi$
$888$		0			0
$889$	44376.8	−	6917.67i	1.67418	−	0.260980i
$890$		−	1165.02i		−	0.0438780i
$891$		0			0
$892$	−6390.83	−	3689.75i	−0.239889	−	0.138500i
$893$		−	16834.5i		−	0.630847i
$894$		0			0
$895$	27794.8	+	16047.4i	1.03808	+	0.599334i
$896$	−22023.8	−	8515.83i	−0.821163	−	0.317516i
$897$		0			0
$898$	3786.17	−	6557.84i	0.140697	−	0.243695i
$899$	−9056.10	+	15685.6i	−0.335971	+	0.581919i
$900$		0			0
$901$	21072.4	−	12166.2i	0.779160	−	0.449848i
$902$	1698.24	+	2941.44i	0.0626888	+	0.108580i
$903$		0			0
$904$	8968.96	−	15534.7i	0.329981	−	0.571545i
$905$		−	14346.0i		−	0.526938i
$906$		0			0
$907$	−5130.22			−0.187813			−0.0939064	−	0.995581i	$-0.529935\pi$
$907$	−5130.22			−0.187813			−0.0939064	+	0.995581i	$0.529935\pi$
$908$	2245.12	+	3888.67i	0.0820562	+	0.142125i
$909$		0			0
$910$	−2881.93	−	3576.69i	−0.104983	−	0.130292i
$911$	−20476.8	+	11822.3i	−0.744707	+	0.429957i	−0.823778	−	0.566912i	$-0.808138\pi$
$911$	−20476.8	+	11822.3i	−0.744707	+	0.429957i	0.0790715	+	0.996869i	$0.474804\pi$
$912$		0			0
$913$	20518.5	−	11846.3i	0.743770	−	0.429416i
$914$	−4568.86	+	2637.83i	−0.165344	+	0.0954614i
$915$		0			0
$916$	8346.43	−	4818.81i	0.301063	−	0.173819i
$917$	893.639	−	139.305i	0.0321816	−	0.00501663i
$918$		0			0
$919$	−22890.0	−	39646.7i	−0.821623	−	1.42309i	−0.904473	−	0.426531i	$-0.859735\pi$
$919$	−22890.0	−	39646.7i	−0.821623	−	1.42309i	0.0828494	−	0.996562i	$-0.473598\pi$
$920$	17786.8			0.637407
$921$		0			0
$922$			1945.59i			0.0694953i
$923$	−1881.45	+	3258.77i	−0.0670951	+	0.116212i
$924$		0			0
$925$	3692.23	+	6395.13i	0.131243	+	0.227319i
$926$	6293.56	−	3633.59i	0.223347	−	0.128949i
$927$		0			0
$928$	4529.07	−	7844.57i	0.160209	−	0.277490i
$929$	14332.6	−	24824.8i	0.506176	−	0.876723i	−0.493798	−	0.869577i	$-0.664392\pi$
$929$	14332.6	−	24824.8i	0.506176	−	0.876723i	0.999974	−	0.00714671i	$-0.00227489\pi$
$930$		0			0
$931$	−13165.7	+	14479.2i	−0.463466	+	0.509708i
$932$	−27528.6	−	15893.6i	−0.967521	−	0.558598i
$933$		0			0
$934$		−	6340.49i		−	0.222128i
$935$	−25005.1	−	14436.7i	−0.874604	−	0.504953i
$936$		0			0
$937$			20013.0i			0.697754i	0.937168	+	0.348877i	$0.113437\pi$
$937$			20013.0i			0.697754i	−0.937168	+	0.348877i	$0.886563\pi$
$938$	−415.659	−	2666.45i	−0.0144688	−	0.0928174i
$939$		0			0
$940$	−19105.2			−0.662919
$941$	−11943.4	−	20686.6i	−0.413757	−	0.716647i	0.581540	−	0.813517i	$-0.302450\pi$
$941$	−11943.4	−	20686.6i	−0.413757	−	0.716647i	−0.995297	+	0.0968701i	$0.969117\pi$
$942$		0			0
$943$	16774.6	+	9684.80i	0.579273	+	0.334444i
$944$	36677.0			1.26455
$945$		0			0
$946$	−7709.77			−0.264975
$947$	−8161.37	−	4711.97i	−0.280052	−	0.161688i	0.353395	−	0.935474i	$-0.385027\pi$
$947$	−8161.37	−	4711.97i	−0.280052	−	0.161688i	−0.633447	+	0.773786i	$0.718360\pi$
$948$		0			0
$949$	−4979.14	−	8624.13i	−0.170316	−	0.294996i
$950$	−2102.27			−0.0717964
$951$		0			0
$952$	−15944.1	−	6165.05i	−0.542808	−	0.209885i
$953$		−	42523.4i		−	1.44540i	−0.691161	−	0.722701i	$-0.742900\pi$
$953$		−	42523.4i		−	1.44540i	0.691161	−	0.722701i	$-0.257100\pi$
$954$		0			0
$955$	27637.2	+	15956.3i	0.936459	+	0.540665i
$956$			17825.2i			0.603041i
$957$		0			0
$958$	−12759.2	−	7366.50i	−0.430302	−	0.248435i
$959$	4371.06	+	28040.3i	0.147183	+	0.944180i
$960$		0			0
$961$	19114.2	−	33106.8i	0.641611	−	1.11130i
$962$	2135.68	−	3699.11i	0.0715771	−	0.123975i
$963$		0			0
$964$	5271.92	−	3043.75i	0.176138	−	0.101693i
$965$	−1488.62	−	2578.37i	−0.0496584	−	0.0860109i
$966$		0			0
$967$	−2110.16	+	3654.91i	−0.0701739	+	0.121545i	−0.898977	−	0.437995i	$-0.855689\pi$
$967$	−2110.16	+	3654.91i	−0.0701739	+	0.121545i	0.828803	+	0.559540i	$0.189022\pi$
$968$		−	4524.45i		−	0.150229i
$969$		0			0
$970$	−7188.01			−0.237931
$971$	−5026.42	−	8706.01i	−0.166123	−	0.287733i	0.770931	−	0.636919i	$-0.219792\pi$
$971$	−5026.42	−	8706.01i	−0.166123	−	0.287733i	−0.937054	+	0.349186i	$0.886458\pi$
$972$		0			0
$973$	12739.1	+	4925.78i	0.419730	+	0.162295i
$974$	9249.51	−	5340.21i	0.304285	−	0.175679i
$975$		0			0
$976$	28575.1	−	16497.9i	0.937160	−	0.541070i
$977$	18918.6	−	10922.7i	0.619509	−	0.357674i	−0.157169	−	0.987572i	$-0.550237\pi$
$977$	18918.6	−	10922.7i	0.619509	−	0.357674i	0.776678	+	0.629898i	$0.216903\pi$
$978$		0			0
$979$	−6435.19	+	3715.36i	−0.210081	+	0.121290i
$980$	16432.3	+	14941.5i	0.535622	+	0.487029i
$981$		0			0
$982$	3924.84	+	6798.02i	0.127542	+	0.220910i
$983$	−44724.2			−1.45115			−0.725575	−	0.688143i	$-0.758426\pi$
$983$	−44724.2			−1.45115			−0.725575	+	0.688143i	$0.758426\pi$
$984$		0			0
$985$			4075.58i			0.131836i
$986$	2075.71	−	3595.23i	0.0670426	−	0.116121i
$987$		0			0
$988$	−8089.78	−	14011.9i	−0.260496	−	0.451192i
$989$	−38077.0	+	21983.8i	−1.22425	+	0.706818i
$990$		0			0
$991$	−8670.77	+	15018.2i	−0.277937	+	0.481402i	−0.970872	−	0.239599i	$-0.922984\pi$
$991$	−8670.77	+	15018.2i	−0.277937	+	0.481402i	0.692935	+	0.721000i	$0.256317\pi$
$992$	−17008.7	+	29459.9i	−0.544381	+	0.942896i
$993$		0			0
$994$	−493.163	+	1275.43i	−0.0157366	+	0.0406982i
$995$	11827.2	+	6828.46i	0.376833	+	0.217565i
$996$		0			0
$997$			56296.2i			1.78828i	0.447783	+	0.894142i	$0.352214\pi$
$997$			56296.2i			1.78828i	−0.447783	+	0.894142i	$0.647786\pi$
$998$	−10898.5	−	6292.25i	−0.345677	−	0.199577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.11		44
3.2	odd	2		63.4.s.a.59.12	yes	44
7.5	odd	6		189.4.i.a.152.12		44
9.2	odd	6		189.4.i.a.143.11		44
9.7	even	3		63.4.i.a.38.12	yes	44
21.5	even	6		63.4.i.a.5.11	✓	44
63.47	even	6	inner	189.4.s.a.89.11		44
63.61	odd	6		63.4.s.a.47.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.11	✓	44	21.5	even	6
63.4.i.a.38.12	yes	44	9.7	even	3
63.4.s.a.47.12	yes	44	63.61	odd	6
63.4.s.a.59.12	yes	44	3.2	odd	2
189.4.i.a.143.11		44	9.2	odd	6
189.4.i.a.152.12		44	7.5	odd	6
189.4.s.a.17.11		44	1.1	even	1	trivial
189.4.s.a.89.11		44	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.647627 - 0.373907i) q^{2} +(-3.72039 - 6.44390i) q^{4} -8.70220 q^{5} +(18.2993 - 2.85258i) q^{7} +11.5468i q^{8} +O(q^{10})\)	\(q+(-0.647627 - 0.373907i) q^{2} +(-3.72039 - 6.44390i) q^{4} -8.70220 q^{5} +(18.2993 - 2.85258i) q^{7} +11.5468i q^{8} +(5.63577 + 3.25382i) q^{10} -41.5070i q^{11} +(-33.0053 - 19.0556i) q^{13} +(-12.9177 - 4.99482i) q^{14} +(-25.4456 + 44.0731i) q^{16} +(-39.9685 + 69.2274i) q^{17} +(-49.4113 + 28.5276i) q^{19} +(32.3755 + 56.0761i) q^{20} +(-15.5198 + 26.8811i) q^{22} +177.014i q^{23} -49.2718 q^{25} +(14.2501 + 24.6818i) q^{26} +(-86.4620 - 107.306i) q^{28} +(60.1430 - 34.7236i) q^{29} +(-225.864 + 130.403i) q^{31} +(112.957 - 65.2160i) q^{32} +(51.7693 - 29.8890i) q^{34} +(-159.244 + 24.8237i) q^{35} +(-74.9359 - 129.793i) q^{37} +42.6668 q^{38} -100.483i q^{40} +(54.7122 - 94.7643i) q^{41} +(124.193 + 215.108i) q^{43} +(-267.467 + 154.422i) q^{44} +(66.1867 - 114.639i) q^{46} +(-147.528 + 255.526i) q^{47} +(326.726 - 104.400i) q^{49} +(31.9097 + 18.4231i) q^{50} +283.577i q^{52} +(-263.613 - 152.197i) q^{53} +361.202i q^{55} +(32.9382 + 211.299i) q^{56} -51.9336 q^{58} +(-360.346 - 624.138i) q^{59} +(-561.494 - 324.179i) q^{61} +195.034 q^{62} +309.591 q^{64} +(287.218 + 165.826i) q^{65} +(97.4263 + 168.747i) q^{67} +594.793 q^{68} +(112.412 + 43.4659i) q^{70} -98.7349i q^{71} +(226.289 + 130.648i) q^{73} +112.076i q^{74} +(367.658 + 212.268i) q^{76} +(-118.402 - 759.548i) q^{77} +(577.124 - 999.608i) q^{79} +(221.433 - 383.533i) q^{80} +(-70.8661 + 40.9146i) q^{82} +(285.406 + 494.337i) q^{83} +(347.813 - 602.431i) q^{85} -185.746i q^{86} +479.275 q^{88} +(-89.5115 - 155.038i) q^{89} +(-658.330 - 254.553i) q^{91} +(1140.66 - 658.559i) q^{92} +(191.086 - 110.324i) q^{94} +(429.987 - 248.253i) q^{95} +(-956.569 + 552.275i) q^{97} +(-250.632 - 54.5529i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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