LMFDB - Embedded newform 189.4.h.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(37,189)]

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([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, 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 $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.21476 q^{2} +9.76423 q^{4} +(-3.91201 - 6.77580i) q^{5} +(-15.9002 + 9.49654i) q^{7} -7.43579 q^{8} +O(q^{10})$	\(q-4.21476 q^{2} +9.76423 q^{4} +(-3.91201 - 6.77580i) q^{5} +(-15.9002 + 9.49654i) q^{7} -7.43579 q^{8} +(16.4882 + 28.5584i) q^{10} +(-6.42137 + 11.1221i) q^{11} +(6.74197 - 11.6774i) q^{13} +(67.0155 - 40.0256i) q^{14} -46.7737 q^{16} +(-35.5009 - 61.4893i) q^{17} +(-46.2187 + 80.0532i) q^{19} +(-38.1977 - 66.1604i) q^{20} +(27.0646 - 46.8772i) q^{22} +(1.97063 + 3.41322i) q^{23} +(31.8924 - 55.2392i) q^{25} +(-28.4158 + 49.2176i) q^{26} +(-155.253 + 92.7263i) q^{28} +(90.3269 + 156.451i) q^{29} +270.523 q^{31} +256.626 q^{32} +(149.628 + 259.163i) q^{34} +(126.548 + 70.5859i) q^{35} +(110.157 - 190.798i) q^{37} +(194.801 - 337.405i) q^{38} +(29.0889 + 50.3834i) q^{40} +(33.6506 - 58.2845i) q^{41} +(237.806 + 411.893i) q^{43} +(-62.6997 + 108.599i) q^{44} +(-8.30572 - 14.3859i) q^{46} +512.858 q^{47} +(162.632 - 301.993i) q^{49} +(-134.419 + 232.820i) q^{50} +(65.8301 - 114.021i) q^{52} +(238.528 + 413.142i) q^{53} +100.482 q^{55} +(118.230 - 70.6143i) q^{56} +(-380.707 - 659.403i) q^{58} -717.669 q^{59} +376.691 q^{61} -1140.19 q^{62} -707.430 q^{64} -105.499 q^{65} +694.361 q^{67} +(-346.639 - 600.396i) q^{68} +(-533.371 - 297.503i) q^{70} +230.757 q^{71} +(-258.027 - 446.916i) q^{73} +(-464.287 + 804.168i) q^{74} +(-451.290 + 781.658i) q^{76} +(-3.52083 - 237.825i) q^{77} -943.662 q^{79} +(182.979 + 316.929i) q^{80} +(-141.829 + 245.655i) q^{82} +(84.4915 + 146.344i) q^{83} +(-277.760 + 481.094i) q^{85} +(-1002.30 - 1736.03i) q^{86} +(47.7480 - 82.7020i) q^{88} +(149.467 - 258.885i) q^{89} +(3.69661 + 249.699i) q^{91} +(19.2416 + 33.3275i) q^{92} -2161.57 q^{94} +723.233 q^{95} +(389.330 + 674.339i) q^{97} +(-685.454 + 1272.83i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−4.21476			−1.49014			−0.745072	−	0.666984i	$-0.767585\pi$
$2$	−4.21476			−1.49014			−0.745072	+	0.666984i	$0.767585\pi$
$3$		0			0
$3$		0			0
$4$	9.76423			1.22053
$5$	−3.91201	−	6.77580i	−0.349901	−	0.606046i	0.636331	−	0.771416i	$-0.280451\pi$
$5$	−3.91201	−	6.77580i	−0.349901	−	0.606046i	−0.986232	+	0.165370i	$0.947118\pi$
$6$		0			0
$7$	−15.9002	+	9.49654i	−0.858529	+	0.512765i
$7$	−15.9002	+	9.49654i	−0.858529	+	0.512765i
$8$	−7.43579			−0.328619
$9$		0			0
$10$	16.4882	+	28.5584i	0.521402	+	0.903095i
$11$	−6.42137	+	11.1221i	−0.176011	+	0.304859i	−0.940511	−	0.339764i	$-0.889653\pi$
$11$	−6.42137	+	11.1221i	−0.176011	+	0.304859i	0.764500	+	0.644624i	$0.222986\pi$
$12$		0			0
$13$	6.74197	−	11.6774i	0.143837	−	0.249134i	−0.785101	−	0.619367i	$-0.787389\pi$
$13$	6.74197	−	11.6774i	0.143837	−	0.249134i	0.928939	+	0.370234i	$0.120722\pi$
$14$	67.0155	−	40.0256i	1.27933	−	0.764093i
$15$		0			0
$16$	−46.7737			−0.730839
$17$	−35.5009	−	61.4893i	−0.506484	−	0.877256i	−0.999972	−	0.00750336i	$-0.997612\pi$
$17$	−35.5009	−	61.4893i	−0.506484	−	0.877256i	0.493488	−	0.869753i	$-0.335722\pi$
$18$		0			0
$19$	−46.2187	+	80.0532i	−0.558069	+	0.966604i	0.439589	+	0.898199i	$0.355124\pi$
$19$	−46.2187	+	80.0532i	−0.558069	+	0.966604i	−0.997658	+	0.0684045i	$0.978209\pi$
$20$	−38.1977	−	66.1604i	−0.427064	−	0.739696i
$21$		0			0
$22$	27.0646	−	46.8772i	0.262281	−	0.454284i
$23$	1.97063	+	3.41322i	0.0178654	+	0.0309438i	0.874820	−	0.484448i	$-0.160980\pi$
$23$	1.97063	+	3.41322i	0.0178654	+	0.0309438i	−0.856954	+	0.515392i	$0.827646\pi$
$24$		0			0
$25$	31.8924	−	55.2392i	0.255139	−	0.441914i
$26$	−28.4158	+	49.2176i	−0.214338	+	0.371245i
$27$		0			0
$28$	−155.253	+	92.7263i	−1.04786	+	0.625844i
$29$	90.3269	+	156.451i	0.578389	+	1.00180i	0.995664	+	0.0930193i	$0.0296518\pi$
$29$	90.3269	+	156.451i	0.578389	+	1.00180i	−0.417275	+	0.908780i	$0.637015\pi$
$30$		0			0
$31$	270.523			1.56733			0.783667	−	0.621181i	$-0.213347\pi$
$31$	270.523			1.56733			0.783667	+	0.621181i	$0.213347\pi$
$32$	256.626			1.41767
$33$		0			0
$34$	149.628	+	259.163i	0.754734	+	1.30724i
$35$	126.548	+	70.5859i	0.611159	+	0.340891i
$36$		0			0
$37$	110.157	−	190.798i	0.489452	−	0.847756i	−0.510474	−	0.859893i	$-0.670530\pi$
$37$	110.157	−	190.798i	0.489452	−	0.847756i	0.999926	+	0.0121369i	$0.00386339\pi$
$38$	194.801	−	337.405i	0.831603	−	1.44038i
$39$		0			0
$40$	29.0889	+	50.3834i	0.114984	+	0.199158i
$41$	33.6506	−	58.2845i	0.128179	−	0.222012i	−0.794792	−	0.606882i	$-0.792420\pi$
$41$	33.6506	−	58.2845i	0.128179	−	0.222012i	0.922971	+	0.384869i	$0.125753\pi$
$42$		0			0
$43$	237.806	+	411.893i	0.843375	+	1.46077i	0.887025	+	0.461722i	$0.152768\pi$
$43$	237.806	+	411.893i	0.843375	+	1.46077i	−0.0436494	+	0.999047i	$0.513898\pi$
$44$	−62.6997	+	108.599i	−0.214826	+	0.372089i
$45$		0			0
$46$	−8.30572	−	14.3859i	−0.0266220	−	0.0461107i
$47$	512.858			1.59166			0.795829	−	0.605521i	$-0.207035\pi$
$47$	512.858			1.59166			0.795829	+	0.605521i	$0.207035\pi$
$48$		0			0
$49$	162.632	−	301.993i	0.474145	−	0.880447i
$50$	−134.419	+	232.820i	−0.380194	+	0.658515i
$51$		0			0
$52$	65.8301	−	114.021i	0.175557	−	0.304074i
$53$	238.528	+	413.142i	0.618195	+	1.07074i	0.989815	+	0.142360i	$0.0454689\pi$
$53$	238.528	+	413.142i	0.618195	+	1.07074i	−0.371621	+	0.928385i	$0.621198\pi$
$54$		0			0
$55$	100.482			0.246345
$56$	118.230	−	70.6143i	0.282129	−	0.168504i
$57$		0			0
$58$	−380.707	−	659.403i	−0.861883	−	1.49283i
$59$	−717.669			−1.58360			−0.791802	−	0.610778i	$-0.790857\pi$
$59$	−717.669			−1.58360			−0.791802	+	0.610778i	$0.790857\pi$
$60$		0			0
$61$	376.691			0.790662			0.395331	−	0.918539i	$-0.370630\pi$
$61$	376.691			0.790662			0.395331	+	0.918539i	$0.370630\pi$
$62$	−1140.19			−2.33555
$63$		0			0
$64$	−707.430			−1.38170
$65$	−105.499			−0.201315
$66$		0			0
$67$	694.361			1.26612			0.633058	−	0.774104i	$-0.281800\pi$
$67$	694.361			1.26612			0.633058	+	0.774104i	$0.281800\pi$
$68$	−346.639	−	600.396i	−0.618178	−	1.07072i
$69$		0			0
$70$	−533.371	−	297.503i	−0.910715	−	0.507977i
$71$	230.757			0.385715			0.192858	−	0.981227i	$-0.438224\pi$
$71$	230.757			0.385715			0.192858	+	0.981227i	$0.438224\pi$
$72$		0			0
$73$	−258.027	−	446.916i	−0.413696	−	0.716542i	0.581595	−	0.813479i	$-0.302429\pi$
$73$	−258.027	−	446.916i	−0.413696	−	0.716542i	−0.995291	+	0.0969364i	$0.969096\pi$
$74$	−464.287	+	804.168i	−0.729354	+	1.26328i
$75$		0			0
$76$	−451.290	+	781.658i	−0.681139	+	1.17977i
$77$	−3.52083	−	237.825i	−0.00521085	−	0.351983i
$78$		0			0
$79$	−943.662			−1.34393			−0.671964	−	0.740584i	$-0.734549\pi$
$79$	−943.662			−1.34393			−0.671964	+	0.740584i	$0.734549\pi$
$80$	182.979	+	316.929i	0.255721	+	0.442922i
$81$		0			0
$82$	−141.829	+	245.655i	−0.191005	+	0.330830i
$83$	84.4915	+	146.344i	0.111737	+	0.193534i	0.916471	−	0.400102i	$-0.131025\pi$
$83$	84.4915	+	146.344i	0.111737	+	0.193534i	−0.804734	+	0.593636i	$0.797692\pi$
$84$		0			0
$85$	−277.760	+	481.094i	−0.354438	+	0.613905i
$86$	−1002.30	−	1736.03i	−1.25675	−	2.17676i
$87$		0			0
$88$	47.7480	−	82.7020i	0.0578404	−	0.100183i
$89$	149.467	−	258.885i	0.178017	−	0.308334i	−0.763184	−	0.646181i	$-0.776365\pi$
$89$	149.467	−	258.885i	0.178017	−	0.308334i	0.941201	+	0.337847i	$0.109698\pi$
$90$		0			0
$91$	3.69661	+	249.699i	0.00425835	+	0.287643i
$92$	19.2416	+	33.3275i	0.0218052	+	0.0377677i
$93$		0			0
$94$	−2161.57			−2.37180
$95$	723.233			0.781075
$96$		0			0
$97$	389.330	+	674.339i	0.407531	+	0.705864i	0.994612	−	0.103664i	$-0.0330566\pi$
$97$	389.330	+	674.339i	0.407531	+	0.705864i	−0.587082	+	0.809528i	$0.699723\pi$
$98$	−685.454	+	1272.83i	−0.706544	+	1.31199i
$99$		0			0
$100$	311.404	−	539.368i	0.311404	−	0.539368i
$101$	120.307	−	208.379i	0.118525	−	0.205292i	−0.800658	−	0.599121i	$-0.795517\pi$
$101$	120.307	−	208.379i	0.118525	−	0.205292i	0.919183	+	0.393830i	$0.128850\pi$
$102$		0			0
$103$	−83.1478	−	144.016i	−0.0795417	−	0.137770i	0.823511	−	0.567301i	$-0.192012\pi$
$103$	−83.1478	−	144.016i	−0.0795417	−	0.137770i	−0.903052	+	0.429531i	$0.858679\pi$
$104$	−50.1319	+	86.8309i	−0.0472676	+	0.0818699i
$105$		0			0
$106$	−1005.34	−	1741.30i	−0.921199	−	1.59556i
$107$	1077.58	−	1866.42i	0.973583	−	1.68629i	0.289047	−	0.957315i	$-0.406662\pi$
$107$	1077.58	−	1866.42i	0.973583	−	1.68629i	0.684535	−	0.728980i	$-0.260005\pi$
$108$		0			0
$109$	−141.982	−	245.920i	−0.124765	−	0.216100i	0.796876	−	0.604143i	$-0.206484\pi$
$109$	−141.982	−	245.920i	−0.124765	−	0.216100i	−0.921641	+	0.388043i	$0.873151\pi$
$110$	−423.507			−0.367090
$111$		0			0
$112$	743.710	−	444.188i	0.627447	−	0.374748i
$113$	−235.029	+	407.082i	−0.195661	+	0.338894i	−0.947117	−	0.320889i	$-0.896018\pi$
$113$	−235.029	+	407.082i	−0.195661	+	0.338894i	0.751456	+	0.659783i	$0.229352\pi$
$114$		0			0
$115$	15.4182	−	26.7051i	0.0125022	−	0.0216545i
$116$	881.972	+	1527.62i	0.705940	+	1.22272i
$117$		0			0
$118$	3024.81			2.35980
$119$	1148.41	+	640.556i	0.884657	+	0.493443i
$120$		0			0
$121$	583.032	+	1009.84i	0.438040	+	0.758708i
$122$	−1587.66			−1.17820
$123$		0			0
$124$	2641.45			1.91298
$125$	−1477.06			−1.05689
$126$		0			0
$127$	−231.037			−0.161427			−0.0807135	−	0.996737i	$-0.525720\pi$
$127$	−231.037			−0.161427			−0.0807135	+	0.996737i	$0.525720\pi$
$128$	928.638			0.641256
$129$		0			0
$130$	444.651			0.299988
$131$	850.137	+	1472.48i	0.566999	+	0.982071i	0.996861	+	0.0791760i	$0.0252289\pi$
$131$	850.137	+	1472.48i	0.566999	+	0.982071i	−0.429862	+	0.902895i	$0.641438\pi$
$132$		0			0
$133$	−25.3417	−	1711.78i	−0.0165218	−	1.11602i
$134$	−2926.57			−1.88669
$135$		0			0
$136$	263.977	+	457.222i	0.166440	+	0.288283i
$137$	654.323	−	1133.32i	0.408048	−	0.706759i	−0.586623	−	0.809860i	$-0.699543\pi$
$137$	654.323	−	1133.32i	0.408048	−	0.706759i	0.994671	+	0.103101i	$0.0328763\pi$
$138$		0			0
$139$	−1550.58	+	2685.68i	−0.946176	+	1.63883i	−0.192798	+	0.981239i	$0.561756\pi$
$139$	−1550.58	+	2685.68i	−0.946176	+	1.63883i	−0.753379	+	0.657587i	$0.771577\pi$
$140$	1235.65	+	689.217i	0.745937	+	0.416067i
$141$		0			0
$142$	−972.585			−0.574771
$143$	86.5854	+	149.970i	0.0506338	+	0.0877003i
$144$		0			0
$145$	706.720	−	1224.07i	0.404758	−	0.701061i
$146$	1087.52	+	1883.65i	0.616466	+	1.06775i
$147$		0			0
$148$	1075.60	−	1862.99i	0.597390	−	1.03471i
$149$	546.596	+	946.733i	0.300530	+	0.520533i	0.976256	−	0.216620i	$-0.0695032\pi$
$149$	546.596	+	946.733i	0.300530	+	0.520533i	−0.675726	+	0.737153i	$0.736170\pi$
$150$		0			0
$151$	−995.396	+	1724.08i	−0.536451	+	0.929161i	0.462640	+	0.886546i	$0.346902\pi$
$151$	−995.396	+	1724.08i	−0.536451	+	0.929161i	−0.999092	+	0.0426149i	$0.986431\pi$
$152$	343.673	−	595.259i	0.183392	−	0.317644i
$153$		0			0
$154$	14.8395	+	1002.38i	0.00776492	+	0.524505i
$155$	−1058.29	−	1833.01i	−0.548411	−	0.949876i
$156$		0			0
$157$	1842.99			0.936859			0.468429	−	0.883501i	$-0.344820\pi$
$157$	1842.99			0.936859			0.468429	+	0.883501i	$0.344820\pi$
$158$	3977.31			2.00265
$159$		0			0
$160$	−1003.92	−	1738.85i	−0.496045	−	0.859176i
$161$	−63.7471	−	35.5568i	−0.0312048	−	0.0174054i
$162$		0			0
$163$	305.269	−	528.742i	0.146690	−	0.254075i	−0.783312	−	0.621629i	$-0.786471\pi$
$163$	305.269	−	528.742i	0.146690	−	0.254075i	0.930002	+	0.367554i	$0.119805\pi$
$164$	328.572	−	569.103i	0.156446	−	0.270972i
$165$		0			0
$166$	−356.112	−	616.804i	−0.166504	−	0.288393i
$167$	1136.90	−	1969.17i	0.526802	−	0.912448i	−0.472710	−	0.881218i	$-0.656724\pi$
$167$	1136.90	−	1969.17i	0.526802	−	0.912448i	0.999512	−	0.0312300i	$-0.00994244\pi$
$168$		0			0
$169$	1007.59	+	1745.20i	0.458622	+	0.794356i
$170$	1170.69	−	2027.70i	0.528164	−	0.914807i
$171$		0			0
$172$	2322.00	+	4021.81i	1.02936	+	1.78291i
$173$	−669.807			−0.294361			−0.147181	−	0.989110i	$-0.547020\pi$
$173$	−669.807			−0.294361			−0.147181	+	0.989110i	$0.547020\pi$
$174$		0			0
$175$	17.4865	+	1181.18i	0.00755347	+	0.510222i
$176$	300.351	−	520.224i	0.128635	−	0.222803i
$177$		0			0
$178$	−629.969	+	1091.14i	−0.265271	+	0.459463i
$179$	1111.53	+	1925.22i	0.464131	+	0.803898i	0.999162	−	0.0409341i	$-0.0130334\pi$
$179$	1111.53	+	1925.22i	0.464131	+	0.803898i	−0.535031	+	0.844832i	$0.679700\pi$
$180$		0			0
$181$	−1845.22			−0.757758			−0.378879	−	0.925446i	$-0.623690\pi$
$181$	−1845.22			−0.757758			−0.378879	+	0.925446i	$0.623690\pi$
$182$	−15.5803	−	1052.42i	−0.00634555	−	0.428630i
$183$		0			0
$184$	−14.6532	−	25.3800i	−0.00587090	−	0.0101687i
$185$	−1723.74			−0.685039
$186$		0			0
$187$	911.858			0.356586
$188$	5007.66			1.94266
$189$		0			0
$190$	−3048.25			−1.16391
$191$	−2202.36			−0.834330			−0.417165	−	0.908831i	$-0.636976\pi$
$191$	−2202.36			−0.834330			−0.417165	+	0.908831i	$0.636976\pi$
$192$		0			0
$193$	690.780			0.257634			0.128817	−	0.991668i	$-0.458882\pi$
$193$	690.780			0.257634			0.128817	+	0.991668i	$0.458882\pi$
$194$	−1640.93	−	2842.18i	−0.607279	−	1.05184i
$195$		0			0
$196$	1587.97	−	2948.73i	0.578707	−	1.07461i
$197$	−1553.21			−0.561733			−0.280866	−	0.959747i	$-0.590622\pi$
$197$	−1553.21			−0.561733			−0.280866	+	0.959747i	$0.590622\pi$
$198$		0			0
$199$	308.538	+	534.404i	0.109908	+	0.190366i	0.915733	−	0.401788i	$-0.131611\pi$
$199$	308.538	+	534.404i	0.109908	+	0.190366i	−0.805825	+	0.592154i	$0.798278\pi$
$200$	−237.145	+	410.747i	−0.0838434	+	0.145221i
$201$		0			0
$202$	−507.067	+	878.266i	−0.176619	+	0.305914i
$203$	−2921.96	−	1629.80i	−1.01025	−	0.563497i
$204$		0			0
$205$	−526.565			−0.179400
$206$	350.448	+	606.994i	0.118529	+	0.205298i
$207$		0			0
$208$	−315.347	+	546.197i	−0.105122	+	0.182077i
$209$	−593.576	−	1028.10i	−0.196452	−	0.340265i
$210$		0			0
$211$	2025.80	−	3508.78i	0.660955	−	1.14481i	−0.319410	−	0.947617i	$-0.603485\pi$
$211$	2025.80	−	3508.78i	0.660955	−	1.14481i	0.980365	−	0.197191i	$-0.0631820\pi$
$212$	2329.04	+	4034.01i	0.754524	+	1.30687i
$213$		0			0
$214$	−4541.73	+	7866.51i	−1.45078	+	2.51282i
$215$	1860.60	−	3222.66i	0.590195	−	1.02225i
$216$		0			0
$217$	−4301.36	+	2569.03i	−1.34560	+	0.803674i
$218$	598.420	+	1036.49i	0.185918	+	0.322020i
$219$		0			0
$220$	981.128			0.300671
$221$	−957.383			−0.291405
$222$		0			0
$223$	−1678.34	−	2906.97i	−0.503990	−	0.872937i	−0.999989	−	0.00461387i	$-0.998531\pi$
$223$	−1678.34	−	2906.97i	−0.503990	−	0.872937i	0.495999	−	0.868323i	$-0.334802\pi$
$224$	−4080.41	+	2437.06i	−1.21711	+	0.726933i
$225$		0			0
$226$	990.591	−	1715.75i	0.291562	−	0.505001i
$227$	2576.32	−	4462.32i	0.753289	−	1.30473i	−0.192932	−	0.981212i	$-0.561800\pi$
$227$	2576.32	−	4462.32i	0.753289	−	1.30473i	0.946221	−	0.323522i	$-0.104867\pi$
$228$		0			0
$229$	−584.060	−	1011.62i	−0.168540	−	0.291921i	0.769367	−	0.638808i	$-0.220572\pi$
$229$	−584.060	−	1011.62i	−0.168540	−	0.291921i	−0.937907	+	0.346887i	$0.887239\pi$
$230$	−64.9841	+	112.556i	−0.0186301	+	0.0322683i
$231$		0			0
$232$	−671.652	−	1163.34i	−0.190070	−	0.329210i
$233$	−1781.39	+	3085.45i	−0.500869	+	0.867530i	0.499131	+	0.866527i	$0.333653\pi$
$233$	−1781.39	+	3085.45i	−0.500869	+	0.867530i	−0.999999	+	0.00100361i	$0.999681\pi$
$234$		0			0
$235$	−2006.30	−	3475.02i	−0.556923	−	0.964618i
$236$	−7007.48			−1.93283
$237$		0			0
$238$	−4840.26	−	2699.79i	−1.31827	−	0.735301i
$239$	−3121.45	+	5406.50i	−0.844810	+	1.46325i	0.0409763	+	0.999160i	$0.486953\pi$
$239$	−3121.45	+	5406.50i	−0.844810	+	1.46325i	−0.885786	+	0.464094i	$0.846380\pi$
$240$		0			0
$241$	1461.57	−	2531.52i	0.390657	−	0.676637i	−0.601880	−	0.798587i	$-0.705581\pi$
$241$	1461.57	−	2531.52i	0.390657	−	0.676637i	0.992536	+	0.121950i	$0.0389147\pi$
$242$	−2457.34	−	4256.24i	−0.652743	−	1.13058i
$243$		0			0
$244$	3678.10			0.965025
$245$	−2682.46	+	79.4413i	−0.699495	+	0.0207156i
$246$		0			0
$247$	623.210	+	1079.43i	0.160542	+	0.278067i
$248$	−2011.55			−0.515055
$249$		0			0
$250$	6225.44			1.57493
$251$	6272.12			1.57726			0.788631	−	0.614867i	$-0.210790\pi$
$251$	6272.12			1.57726			0.788631	+	0.614867i	$0.210790\pi$
$252$		0			0
$253$	−50.6165			−0.0125780
$254$	973.766			0.240549
$255$		0			0
$256$	1745.45			0.426136
$257$	1099.26	+	1903.97i	0.266809	+	0.462127i	0.968036	−	0.250811i	$-0.0806974\pi$
$257$	1099.26	+	1903.97i	0.266809	+	0.462127i	−0.701227	+	0.712938i	$0.747364\pi$
$258$		0			0
$259$	60.3990	+	4079.83i	0.0144904	+	0.978797i
$260$	−1030.11			−0.245711
$261$		0			0
$262$	−3583.13	−	6206.16i	−0.844910	−	1.46343i
$263$	−1989.94	+	3446.68i	−0.466559	+	0.808103i	−0.999270	−	0.0381935i	$-0.987840\pi$
$263$	−1989.94	+	3446.68i	−0.466559	+	0.808103i	0.532712	+	0.846297i	$0.321173\pi$
$264$		0			0
$265$	1866.25	−	3232.43i	0.432613	−	0.749308i
$266$	106.809	+	7214.74i	0.0246199	+	1.66302i
$267$		0			0
$268$	6779.90			1.54533
$269$	−533.462	−	923.984i	−0.120914	−	0.209429i	0.799215	−	0.601046i	$-0.205249\pi$
$269$	−533.462	−	923.984i	−0.120914	−	0.209429i	−0.920128	+	0.391617i	$0.871916\pi$
$270$		0			0
$271$	1680.55	−	2910.80i	0.376702	−	0.652467i	−0.613878	−	0.789401i	$-0.710391\pi$
$271$	1680.55	−	2910.80i	0.376702	−	0.652467i	0.990580	+	0.136934i	$0.0437248\pi$
$272$	1660.51	+	2876.08i	0.370158	+	0.641133i
$273$		0			0
$274$	−2757.81	+	4776.67i	−0.608050	+	1.05317i
$275$	409.586	+	709.423i	0.0898143	+	0.155563i
$276$		0			0
$277$	−1936.26	+	3353.70i	−0.419995	+	0.727453i	−0.995938	−	0.0900370i	$-0.971301\pi$
$277$	−1936.26	+	3353.70i	−0.419995	+	0.727453i	0.575944	+	0.817489i	$0.304635\pi$
$278$	6535.33	−	11319.5i	1.40994	−	2.44209i
$279$		0			0
$280$	−940.987	−	524.862i	−0.200838	−	0.112023i
$281$	3158.92	+	5471.41i	0.670624	+	1.16156i	0.977727	+	0.209879i	$0.0673071\pi$
$281$	3158.92	+	5471.41i	0.670624	+	1.16156i	−0.307103	+	0.951676i	$0.599360\pi$
$282$		0			0
$283$	3849.25			0.808531			0.404265	−	0.914642i	$-0.367527\pi$
$283$	3849.25			0.808531			0.404265	+	0.914642i	$0.367527\pi$
$284$	2253.16			0.470777
$285$		0			0
$286$	−364.937	−	632.089i	−0.0754516	−	0.130686i
$287$	18.4505	+	1246.30i	0.00379478	+	0.256330i
$288$		0			0
$289$	−64.1252	+	111.068i	−0.0130521	+	0.0226070i
$290$	−2978.66	+	5159.18i	−0.603147	+	1.04468i
$291$		0			0
$292$	−2519.44	−	4363.79i	−0.504927	−	0.874560i
$293$	1683.32	−	2915.59i	0.335633	−	0.581333i	−0.647973	−	0.761663i	$-0.724383\pi$
$293$	1683.32	−	2915.59i	0.335633	−	0.581333i	0.983606	+	0.180330i	$0.0577165\pi$
$294$		0			0
$295$	2807.53	+	4862.78i	0.554104	+	0.959736i
$296$	−819.106	+	1418.73i	−0.160843	+	0.278589i
$297$		0			0
$298$	−2303.77	−	3990.25i	−0.447832	−	0.775668i
$299$	53.1436			0.0102788
$300$		0			0
$301$	−7692.72	−	4290.83i	−1.47309	−	0.821660i
$302$	4195.36	−	7266.57i	0.799390	−	1.38458i
$303$		0			0
$304$	2161.82	−	3744.39i	0.407859	−	0.706432i
$305$	−1473.62	−	2552.38i	−0.276653	−	0.479177i
$306$		0			0
$307$	6559.35			1.21942			0.609710	−	0.792625i	$-0.291286\pi$
$307$	6559.35			1.21942			0.609710	+	0.792625i	$0.291286\pi$
$308$	−34.3782	−	2322.18i	−0.00635999	−	0.429605i
$309$		0			0
$310$	4460.43	+	7725.70i	0.817212	+	1.41545i
$311$	8253.01			1.50478			0.752388	−	0.658720i	$-0.228902\pi$
$311$	8253.01			1.50478			0.752388	+	0.658720i	$0.228902\pi$
$312$		0			0
$313$	−1001.49			−0.180855			−0.0904275	−	0.995903i	$-0.528823\pi$
$313$	−1001.49			−0.180855			−0.0904275	+	0.995903i	$0.528823\pi$
$314$	−7767.78			−1.39605
$315$		0			0
$316$	−9214.13			−1.64030
$317$	−6303.39			−1.11683			−0.558413	−	0.829563i	$-0.688590\pi$
$317$	−6303.39			−1.11683			−0.558413	+	0.829563i	$0.688590\pi$
$318$		0			0
$319$	−2320.09			−0.407211
$320$	2767.47	+	4793.40i	0.483457	+	0.837373i
$321$		0			0
$322$	268.679	+	149.863i	0.0464997	+	0.0259365i
$323$	6563.23			1.13061
$324$		0			0
$325$	−430.034	−	744.842i	−0.0733970	−	0.127127i
$326$	−1286.64	+	2228.52i	−0.218590	+	0.378609i
$327$		0			0
$328$	−250.219	+	433.391i	−0.0421220	+	0.0729574i
$329$	−8154.53	+	4870.37i	−1.36649	+	0.816146i
$330$		0			0
$331$	−4993.57			−0.829218			−0.414609	−	0.910000i	$-0.636082\pi$
$331$	−4993.57			−0.829218			−0.414609	+	0.910000i	$0.636082\pi$
$332$	824.994	+	1428.93i	0.136378	+	0.236213i
$333$		0			0
$334$	−4791.76	+	8299.58i	−0.785011	+	1.35968i
$335$	−2716.35	−	4704.85i	−0.443015	−	0.767324i
$336$		0			0
$337$	981.382	−	1699.80i	0.158633	−	0.274760i	−0.775743	−	0.631049i	$-0.782625\pi$
$337$	981.382	−	1699.80i	0.158633	−	0.274760i	0.934376	+	0.356289i	$0.115958\pi$
$338$	−4246.76	−	7355.60i	−0.683412	−	1.18370i
$339$		0			0
$340$	−2712.11	+	4697.51i	−0.432602	+	0.749289i
$341$	−1737.13	+	3008.80i	−0.275868	+	0.477817i
$342$		0			0
$343$	282.017	+	6346.19i	0.0443950	+	0.999014i
$344$	−1768.28	−	3062.75i	−0.277149	−	0.480036i
$345$		0			0
$346$	2823.08			0.438640
$347$	−586.148			−0.0906804			−0.0453402	−	0.998972i	$-0.514437\pi$
$347$	−586.148			−0.0906804			−0.0453402	+	0.998972i	$0.514437\pi$
$348$		0			0
$349$	−4666.91	−	8083.33i	−0.715800	−	1.23980i	−0.962650	−	0.270748i	$-0.912729\pi$
$349$	−4666.91	−	8083.33i	−0.715800	−	1.23980i	0.246851	−	0.969054i	$-0.420604\pi$
$350$	−73.7016	−	4978.39i	−0.0112558	−	0.760304i
$351$		0			0
$352$	−1647.89	+	2854.24i	−0.249526	+	0.432191i
$353$	1423.19	−	2465.04i	0.214586	−	0.371673i	−0.738559	−	0.674189i	$-0.764493\pi$
$353$	1423.19	−	2465.04i	0.214586	−	0.371673i	0.953144	+	0.302516i	$0.0978266\pi$
$354$		0			0
$355$	−902.723	−	1563.56i	−0.134962	−	0.233761i
$356$	1459.43	−	2527.81i	0.217275	−	0.376331i
$357$		0			0
$358$	−4684.82	−	8114.35i	−0.691622	−	1.19792i
$359$	−3171.73	+	5493.59i	−0.466288	+	0.807635i	−0.999259	−	0.0384991i	$-0.987742\pi$
$359$	−3171.73	+	5493.59i	−0.466288	+	0.807635i	0.532971	+	0.846134i	$0.321076\pi$
$360$		0			0
$361$	−842.846	−	1459.85i	−0.122882	−	0.212837i
$362$	7777.17			1.12917
$363$		0			0
$364$	36.0945	+	2438.11i	0.00519744	+	0.351077i
$365$	−2018.81	+	3496.68i	−0.289505	+	0.501437i
$366$		0			0
$367$	−717.276	+	1242.36i	−0.102020	+	0.176704i	−0.912517	−	0.409039i	$-0.865864\pi$
$367$	−717.276	+	1242.36i	−0.102020	+	0.176704i	0.810497	+	0.585743i	$0.199197\pi$
$368$	−92.1735	−	159.649i	−0.0130567	−	0.0226149i
$369$		0			0
$370$	7265.17			1.02081
$371$	−7716.05	−	4303.85i	−1.07978	−	0.602277i
$372$		0			0
$373$	1366.25	+	2366.42i	0.189656	+	0.328494i	0.945136	−	0.326678i	$-0.105929\pi$
$373$	1366.25	+	2366.42i	0.189656	+	0.328494i	−0.755479	+	0.655172i	$0.772596\pi$
$374$	−3843.26			−0.531365
$375$		0			0
$376$	−3813.50			−0.523049
$377$	2435.92			0.332776
$378$		0			0
$379$	12802.3			1.73512			0.867560	−	0.497332i	$-0.165687\pi$
$379$	12802.3			1.73512			0.867560	+	0.497332i	$0.165687\pi$
$380$	7061.81			0.953324
$381$		0			0
$382$	9282.41			1.24327
$383$	−4543.28	−	7869.19i	−0.606138	−	1.04986i	−0.991871	−	0.127251i	$-0.959385\pi$
$383$	−4543.28	−	7869.19i	−0.606138	−	1.04986i	0.385733	−	0.922611i	$-0.373949\pi$
$384$		0			0
$385$	−1597.68	+	954.230i	−0.211494	+	0.126317i
$386$	−2911.47			−0.383912
$387$		0			0
$388$	3801.51	+	6584.40i	0.497403	+	0.861527i
$389$	2229.58	−	3861.74i	0.290602	−	0.503337i	−0.683350	−	0.730091i	$-0.739478\pi$
$389$	2229.58	−	3861.74i	0.290602	−	0.503337i	0.973952	+	0.226754i	$0.0728112\pi$
$390$		0			0
$391$	139.918	−	242.345i	0.0180971	−	0.0313450i
$392$	−1209.30	+	2245.56i	−0.155813	+	0.289331i
$393$		0			0
$394$	6546.40			0.837063
$395$	3691.62	+	6394.07i	0.470241	+	0.814482i
$396$		0			0
$397$	−19.8448	+	34.3721i	−0.00250877	+	0.00434531i	−0.867277	−	0.497826i	$-0.834132\pi$
$397$	−19.8448	+	34.3721i	−0.00250877	+	0.00434531i	0.864768	+	0.502171i	$0.167465\pi$
$398$	−1300.42	−	2252.39i	−0.163779	−	0.283673i
$399$		0			0
$400$	−1491.72	+	2583.74i	−0.186465	+	0.322968i
$401$	4448.30	+	7704.67i	0.553958	+	0.959484i	0.997984	+	0.0634697i	$0.0202166\pi$
$401$	4448.30	+	7704.67i	0.553958	+	0.959484i	−0.444026	+	0.896014i	$0.646450\pi$
$402$		0			0
$403$	1823.86	−	3159.01i	0.225441	−	0.390475i
$404$	1174.71	−	2034.66i	0.144663	−	0.250564i
$405$		0			0
$406$	12315.3	+	6869.24i	1.50542	+	0.839691i
$407$	1414.72	+	2450.37i	0.172298	+	0.298428i
$408$		0			0
$409$	−2047.90			−0.247584			−0.123792	−	0.992308i	$-0.539506\pi$
$409$	−2047.90			−0.247584			−0.123792	+	0.992308i	$0.539506\pi$
$410$	2219.35			0.267331
$411$		0			0
$412$	−811.874	−	1406.21i	−0.0970829	−	0.168153i
$413$	11411.1	−	6815.37i	1.35957	−	0.812016i
$414$		0			0
$415$	661.063	−	1145.00i	0.0781936	−	0.135435i
$416$	1730.17	−	2996.74i	0.203914	−	0.353190i
$417$		0			0
$418$	2501.78	+	4333.21i	0.292742	+	0.507044i
$419$	1185.50	−	2053.34i	0.138223	−	0.239409i	−0.788601	−	0.614905i	$-0.789194\pi$
$419$	1185.50	−	2053.34i	0.138223	−	0.239409i	0.926824	+	0.375496i	$0.122528\pi$
$420$		0			0
$421$	−5061.24	−	8766.33i	−0.585914	−	1.01483i	−0.994761	−	0.102230i	$-0.967402\pi$
$421$	−5061.24	−	8766.33i	−0.585914	−	1.01483i	0.408847	−	0.912603i	$-0.365931\pi$
$422$	−8538.25	+	14788.7i	−0.984918	+	1.70593i
$423$		0			0
$424$	−1773.64	−	3072.04i	−0.203150	−	0.351867i
$425$	−4528.83			−0.516895
$426$		0			0
$427$	−5989.46	+	3577.26i	−0.678806	+	0.405423i
$428$	10521.7	−	18224.1i	1.18829	−	2.05817i
$429$		0			0
$430$	−7842.00	+	13582.7i	−0.879476	+	1.52330i
$431$	2720.32	+	4711.74i	0.304022	+	0.526581i	0.977043	−	0.213042i	$-0.0683371\pi$
$431$	2720.32	+	4711.74i	0.304022	+	0.526581i	−0.673021	+	0.739623i	$0.735004\pi$
$432$		0			0
$433$	3627.07			0.402554			0.201277	−	0.979534i	$-0.435491\pi$
$433$	3627.07			0.402554			0.201277	+	0.979534i	$0.435491\pi$
$434$	18129.2	−	10827.9i	2.00514	−	1.19759i
$435$		0			0
$436$	−1386.34	−	2401.22i	−0.152279	−	0.263756i
$437$	−364.319			−0.0398805
$438$		0			0
$439$	9578.47			1.04136			0.520678	−	0.853753i	$-0.325679\pi$
$439$	9578.47			1.04136			0.520678	+	0.853753i	$0.325679\pi$
$440$	−747.163			−0.0809536
$441$		0			0
$442$	4035.14			0.434236
$443$	16845.9			1.80671			0.903353	−	0.428898i	$-0.141098\pi$
$443$	16845.9			1.80671			0.903353	+	0.428898i	$0.141098\pi$
$444$		0			0
$445$	−2338.87			−0.249153
$446$	7073.80	+	12252.2i	0.751018	+	1.30080i
$447$		0			0
$448$	11248.3	−	6718.13i	1.18623	−	0.708486i
$449$	−16837.7			−1.76976			−0.884879	−	0.465820i	$-0.845759\pi$
$449$	−16837.7			−1.76976			−0.884879	+	0.465820i	$0.845759\pi$
$450$		0			0
$451$	432.166	+	748.533i	0.0451217	+	0.0781531i
$452$	−2294.87	+	3974.84i	−0.238809	+	0.413630i
$453$		0			0
$454$	−10858.6	+	18807.6i	−1.12251	+	1.94424i
$455$	1677.45	−	1001.87i	0.172835	−	0.103227i
$456$		0			0
$457$	−10396.4			−1.06416			−0.532082	−	0.846693i	$-0.678590\pi$
$457$	−10396.4			−1.06416			−0.532082	+	0.846693i	$0.678590\pi$
$458$	2461.67	+	4263.74i	0.251149	+	0.435003i
$459$		0			0
$460$	150.547	−	260.755i	0.0152593	−	0.0264299i
$461$	−1955.80	−	3387.54i	−0.197593	−	0.342241i	0.750154	−	0.661263i	$-0.229979\pi$
$461$	−1955.80	−	3387.54i	−0.197593	−	0.342241i	−0.947748	+	0.319021i	$0.896646\pi$
$462$		0			0
$463$	1630.69	−	2824.43i	0.163681	−	0.283504i	−0.772505	−	0.635009i	$-0.780997\pi$
$463$	1630.69	−	2824.43i	0.163681	−	0.283504i	0.936186	+	0.351505i	$0.114330\pi$
$464$	−4224.92	−	7317.78i	−0.422709	−	0.732154i
$465$		0			0
$466$	7508.12	−	13004.4i	0.746367	−	1.29274i
$467$	−1995.37	+	3456.08i	−0.197719	+	0.342459i	−0.947788	−	0.318900i	$-0.896687\pi$
$467$	−1995.37	+	3456.08i	−0.197719	+	0.342459i	0.750069	+	0.661359i	$0.230020\pi$
$468$		0			0
$469$	−11040.5	+	6594.03i	−1.08700	+	0.649219i
$470$	8456.09	+	14646.4i	0.829895	+	1.43742i
$471$		0			0
$472$	5336.44			0.520402
$473$	−6108.18			−0.593772
$474$		0			0
$475$	2948.05	+	5106.17i	0.284770	+	0.493236i
$476$	11213.3	+	6254.54i	1.07975	+	0.602261i
$477$		0			0
$478$	13156.2	−	22787.1i	1.25889	−	2.18046i
$479$	−319.397	+	553.212i	−0.0304669	+	0.0527702i	−0.880857	−	0.473383i	$-0.843033\pi$
$479$	−319.397	+	553.212i	−0.0304669	+	0.0527702i	0.850390	+	0.526153i	$0.176366\pi$
$480$		0			0
$481$	−1485.35	−	2572.71i	−0.140803	−	0.243878i
$482$	−6160.19	+	10669.8i	−0.582134	+	1.00829i
$483$		0			0
$484$	5692.86	+	9860.31i	0.534641	+	0.926025i
$485$	3046.13	−	5276.04i	0.285191	−	0.493965i
$486$		0			0
$487$	−2751.31	−	4765.41i	−0.256003	−	0.443411i	0.709164	−	0.705043i	$-0.249073\pi$
$487$	−2751.31	−	4765.41i	−0.256003	−	0.443411i	−0.965168	+	0.261632i	$0.915739\pi$
$488$	−2801.00			−0.259826
$489$		0			0
$490$	11305.9	−	334.826i	1.04235	−	0.0308692i
$491$	442.623	−	766.646i	0.0406829	−	0.0704649i	−0.844967	−	0.534819i	$-0.820380\pi$
$491$	442.623	−	766.646i	0.0406829	−	0.0704649i	0.885650	+	0.464354i	$0.153713\pi$
$492$		0			0
$493$	6413.37	−	11108.3i	0.585890	−	1.01479i
$494$	−2626.68	−	4549.55i	−0.239231	−	0.414360i
$495$		0			0
$496$	−12653.4			−1.14547
$497$	−3669.08	+	2191.39i	−0.331148	+	0.197781i
$498$		0			0
$499$	243.186	+	421.210i	0.0218166	+	0.0377875i	0.876728	−	0.480987i	$-0.159722\pi$
$499$	243.186	+	421.210i	0.0218166	+	0.0377875i	−0.854911	+	0.518775i	$0.826388\pi$
$500$	−14422.3			−1.28997
$501$		0			0
$502$	−26435.5			−2.35035
$503$	−1146.99			−0.101673			−0.0508366	−	0.998707i	$-0.516189\pi$
$503$	−1146.99			−0.101673			−0.0508366	+	0.998707i	$0.516189\pi$
$504$		0			0
$505$	−1882.58			−0.165888
$506$	213.337			0.0187430
$507$		0			0
$508$	−2255.90			−0.197026
$509$	7512.28	+	13011.6i	0.654177	+	1.13307i	0.982100	+	0.188363i	$0.0603181\pi$
$509$	7512.28	+	13011.6i	0.654177	+	1.13307i	−0.327923	+	0.944705i	$0.606349\pi$
$510$		0			0
$511$	8346.83	+	4655.69i	0.722588	+	0.403044i
$512$	−14785.8			−1.27626
$513$		0			0
$514$	−4633.12	−	8024.79i	−0.397584	−	0.688635i
$515$	−650.550	+	1126.79i	−0.0556634	+	0.0964119i
$516$		0			0
$517$	−3293.25	+	5704.08i	−0.280149	+	0.485232i
$518$	−254.567	−	17195.5i	−0.0215928	−	1.45855i
$519$		0			0
$520$	784.465			0.0661559
$521$	−7697.96	−	13333.3i	−0.647320	−	1.12119i	−0.983760	−	0.179486i	$-0.942556\pi$
$521$	−7697.96	−	13333.3i	−0.647320	−	1.12119i	0.336440	−	0.941705i	$-0.390777\pi$
$522$		0			0
$523$	−4010.52	+	6946.43i	−0.335311	+	0.580776i	−0.983545	−	0.180665i	$-0.942175\pi$
$523$	−4010.52	+	6946.43i	−0.335311	+	0.580776i	0.648233	+	0.761442i	$0.275508\pi$
$524$	8300.93	+	14377.6i	0.692038	+	1.19864i
$525$		0			0
$526$	8387.12	−	14526.9i	0.695239	−	1.20419i
$527$	−9603.80	−	16634.3i	−0.793830	−	1.37495i
$528$		0			0
$529$	6075.73	−	10523.5i	0.499362	−	0.864920i
$530$	−7865.78	+	13623.9i	−0.644656	+	1.11658i
$531$		0			0
$532$	−247.442	−	16714.2i	−0.0201653	−	1.36213i
$533$	−453.742	−	785.904i	−0.0368738	−	0.0638673i
$534$		0			0
$535$	−16862.0			−1.36263
$536$	−5163.13			−0.416069
$537$		0			0
$538$	2248.42	+	3894.37i	0.180179	+	0.312079i
$539$	2314.50	+	3748.02i	0.184958	+	0.299516i
$540$		0			0
$541$	−11807.9	+	20451.8i	−0.938373	+	1.62531i	−0.169868	+	0.985467i	$0.554334\pi$
$541$	−11807.9	+	20451.8i	−0.938373	+	1.62531i	−0.768506	+	0.639843i	$0.778999\pi$
$542$	−7083.12	+	12268.3i	−0.561340	+	0.972269i
$543$		0			0
$544$	−9110.46	−	15779.8i	−0.718029	−	1.24366i
$545$	−1110.87	+	1924.08i	−0.0873109	+	0.151227i
$546$		0			0
$547$	8677.56	+	15030.0i	0.678292	+	1.17484i	0.975495	+	0.220022i	$0.0706128\pi$
$547$	8677.56	+	15030.0i	0.678292	+	1.17484i	−0.297203	+	0.954814i	$0.596054\pi$
$548$	6388.95	−	11066.0i	0.498034	−	0.862620i
$549$		0			0
$550$	−1726.31	−	2990.05i	−0.133836	−	0.231811i
$551$	−16699.2			−1.29112
$552$		0			0
$553$	15004.4	−	8961.52i	1.15380	−	0.689119i
$554$	8160.88	−	14135.1i	0.625853	−	1.08401i
$555$		0			0
$556$	−15140.2	+	26223.6i	−1.15483	+	2.00023i
$557$	134.682	+	233.276i	0.0102454	+	0.0177455i	0.871103	−	0.491101i	$-0.163405\pi$
$557$	134.682	+	233.276i	0.0102454	+	0.0177455i	−0.860857	+	0.508846i	$0.830072\pi$
$558$		0			0
$559$	6413.13			0.485235
$560$	−5919.13	−	3301.56i	−0.446659	−	0.249137i
$561$		0			0
$562$	−13314.1	−	23060.7i	−0.999327	−	1.73088i
$563$	6029.12			0.451327			0.225663	−	0.974205i	$-0.427545\pi$
$563$	6029.12			0.451327			0.225663	+	0.974205i	$0.427545\pi$
$564$		0			0
$565$	3677.74			0.273847
$566$	−16223.7			−1.20483
$567$		0			0
$568$	−1715.86			−0.126753
$569$	2762.25			0.203514			0.101757	−	0.994809i	$-0.467554\pi$
$569$	2762.25			0.203514			0.101757	+	0.994809i	$0.467554\pi$
$570$		0			0
$571$	1676.83			0.122895			0.0614477	−	0.998110i	$-0.480428\pi$
$571$	1676.83			0.122895			0.0614477	+	0.998110i	$0.480428\pi$
$572$	845.439	+	1464.34i	0.0618000	+	0.107041i
$573$		0			0
$574$	−77.7647	−	5252.85i	−0.00565476	−	0.381968i
$575$	251.392			0.0182326
$576$		0			0
$577$	1863.78	+	3228.16i	0.134471	+	0.232911i	0.925395	−	0.379003i	$-0.123733\pi$
$577$	1863.78	+	3228.16i	0.134471	+	0.232911i	−0.790924	+	0.611914i	$0.790400\pi$
$578$	270.272	−	468.126i	0.0194496	−	0.0336876i
$579$		0			0
$580$	6900.57	−	11952.1i	0.494018	−	0.855665i
$581$	−2733.19	−	1524.51i	−0.195167	−	0.108860i
$582$		0			0
$583$	−6126.70			−0.435235
$584$	1918.64	+	3323.18i	0.135948	+	0.235469i
$585$		0			0
$586$	−7094.78	+	12288.5i	−0.500141	+	0.866270i
$587$	−3305.15	−	5724.68i	−0.232399	−	0.402526i	0.726115	−	0.687573i	$-0.241324\pi$
$587$	−3305.15	−	5724.68i	−0.232399	−	0.402526i	−0.958513	+	0.285047i	$0.907991\pi$
$588$		0			0
$589$	−12503.2	+	21656.2i	−0.874680	+	1.51499i
$590$	−11833.1	−	20495.5i	−0.825694	−	1.43014i
$591$		0			0
$592$	−5152.46	+	8924.32i	−0.357711	+	0.619573i
$593$	2387.35	−	4135.01i	0.165323	−	0.286348i	−0.771447	−	0.636294i	$-0.780467\pi$
$593$	2387.35	−	4135.01i	0.165323	−	0.286348i	0.936770	+	0.349946i	$0.113800\pi$
$594$		0			0
$595$	−152.295	−	10287.2i	−0.0104933	−	0.708799i
$596$	5337.09	+	9244.11i	0.366805	+	0.635325i
$597$		0			0
$598$	−223.988			−0.0153169
$599$	−13656.0			−0.931504			−0.465752	−	0.884915i	$-0.654216\pi$
$599$	−13656.0			−0.931504			−0.465752	+	0.884915i	$0.654216\pi$
$600$		0			0
$601$	−3519.77	−	6096.42i	−0.238893	−	0.413774i	0.721504	−	0.692410i	$-0.243451\pi$
$601$	−3519.77	−	6096.42i	−0.238893	−	0.413774i	−0.960397	+	0.278636i	$0.910118\pi$
$602$	32423.0	+	18084.8i	2.19512	+	1.22439i
$603$		0			0
$604$	−9719.27	+	16834.3i	−0.654754	+	1.13407i
$605$	4561.65	−	7901.01i	0.306541	−	0.530945i
$606$		0			0
$607$	8478.88	+	14685.8i	0.566964	+	0.982010i	0.996864	+	0.0791336i	$0.0252154\pi$
$607$	8478.88	+	14685.8i	0.566964	+	0.982010i	−0.429900	+	0.902876i	$0.641451\pi$
$608$	−11861.0	+	20543.8i	−0.791160	+	1.37033i
$609$		0			0
$610$	6210.96	+	10757.7i	0.412253	+	0.714043i
$611$	3457.67	−	5988.86i	0.228940	−	0.396536i
$612$		0			0
$613$	−9611.09	−	16646.9i	−0.633260	−	1.09684i	−0.986881	−	0.161450i	$-0.948383\pi$
$613$	−9611.09	−	16646.9i	−0.633260	−	1.09684i	0.353621	−	0.935389i	$-0.384950\pi$
$614$	−27646.1			−1.81711
$615$		0			0
$616$	26.1801	+	1768.42i	0.00171238	+	0.115668i
$617$	−279.127	+	483.463i	−0.0182127	+	0.0315454i	−0.874988	−	0.484144i	$-0.839131\pi$
$617$	−279.127	+	483.463i	−0.0182127	+	0.0315454i	0.856775	+	0.515690i	$0.172464\pi$
$618$		0			0
$619$	3947.97	−	6838.09i	0.256353	−	0.444016i	−0.708909	−	0.705300i	$-0.750812\pi$
$619$	3947.97	−	6838.09i	0.256353	−	0.444016i	0.965262	+	0.261283i	$0.0841457\pi$
$620$	−10333.4	−	17897.9i	−0.669352	−	1.15935i
$621$		0			0
$622$	−34784.5			−2.24233
$623$	81.9527	+	5535.74i	0.00527025	+	0.355995i
$624$		0			0
$625$	1791.71	+	3103.33i	0.114669	+	0.198613i
$626$	4221.05			0.269500
$627$		0			0
$628$	17995.4			1.14346
$629$	−15642.7			−0.991599
$630$		0			0
$631$	709.050			0.0447335			0.0223667	−	0.999750i	$-0.492880\pi$
$631$	709.050			0.0447335			0.0223667	+	0.999750i	$0.492880\pi$
$632$	7016.88			0.441640
$633$		0			0
$634$	26567.3			1.66423
$635$	903.819	+	1565.46i	0.0564834	+	0.0978321i
$636$		0			0
$637$	−2430.05	−	3935.15i	−0.151149	−	0.244766i
$638$	9778.64			0.606802
$639$		0			0
$640$	−3632.84	−	6292.26i	−0.224376	−	0.388630i
$641$	3261.23	−	5648.61i	0.200953	−	0.348060i	−0.747883	−	0.663831i	$-0.768930\pi$
$641$	3261.23	−	5648.61i	0.200953	−	0.348060i	0.948836	+	0.315770i	$0.102263\pi$
$642$		0			0
$643$	5565.74	−	9640.15i	0.341355	−	0.591245i	−0.643329	−	0.765590i	$-0.722447\pi$
$643$	5565.74	−	9640.15i	0.341355	−	0.591245i	0.984685	+	0.174345i	$0.0557807\pi$
$644$	−622.441	−	347.184i	−0.0380864	−	0.0212438i
$645$		0			0
$646$	−27662.4			−1.68477
$647$	9778.93	+	16937.6i	0.594203	+	1.02919i	0.993659	+	0.112438i	$0.0358659\pi$
$647$	9778.93	+	16937.6i	0.594203	+	1.02919i	−0.399456	+	0.916753i	$0.630801\pi$
$648$		0			0
$649$	4608.42	−	7982.02i	0.278731	−	0.482776i
$650$	1812.49	+	3139.33i	0.109372	+	0.189438i
$651$		0			0
$652$	2980.72	−	5162.76i	0.179040	−	0.310106i
$653$	590.302	+	1022.43i	0.0353756	+	0.0612724i	0.883171	−	0.469051i	$-0.155404\pi$
$653$	590.302	+	1022.43i	0.0353756	+	0.0612724i	−0.847796	+	0.530323i	$0.822071\pi$
$654$		0			0
$655$	6651.49	−	11520.7i	0.396787	−	0.687255i
$656$	−1573.96	+	2726.18i	−0.0936781	+	0.162255i
$657$		0			0
$658$	34369.4	−	20527.5i	2.03626	−	1.21618i
$659$	4039.50	+	6996.61i	0.238781	+	0.413580i	0.960365	−	0.278747i	$-0.0899190\pi$
$659$	4039.50	+	6996.61i	0.238781	+	0.413580i	−0.721584	+	0.692327i	$0.756586\pi$
$660$		0			0
$661$	−1145.24			−0.0673898			−0.0336949	−	0.999432i	$-0.510727\pi$
$661$	−1145.24			−0.0673898			−0.0336949	+	0.999432i	$0.510727\pi$
$662$	21046.7			1.23565
$663$		0			0
$664$	−628.262	−	1088.18i	−0.0367188	−	0.0635988i
$665$	−11499.5	+	6868.21i	−0.670576	+	0.400508i
$666$		0			0
$667$	−356.001	+	616.612i	−0.0206663	+	0.0357951i
$668$	11100.9	−	19227.4i	0.642977	−	1.11367i
$669$		0			0
$670$	11448.8	+	19829.8i	0.660156	+	1.14342i
$671$	−2418.87	+	4189.61i	−0.139165	+	0.241041i
$672$		0			0
$673$	10900.3	+	18879.9i	0.624333	+	1.08138i	0.988669	+	0.150109i	$0.0479625\pi$
$673$	10900.3	+	18879.9i	0.624333	+	1.08138i	−0.364337	+	0.931267i	$0.618704\pi$
$674$	−4136.29	+	7164.27i	−0.236386	+	0.409432i
$675$		0			0
$676$	9838.35	+	17040.5i	0.559761	+	0.969534i
$677$	19232.8			1.09184			0.545922	−	0.837836i	$-0.316179\pi$
$677$	19232.8			1.09184			0.545922	+	0.837836i	$0.316179\pi$
$678$		0			0
$679$	−12594.3	−	7024.83i	−0.711819	−	0.397037i
$680$	2065.36	−	3577.31i	0.116475	−	0.201741i
$681$		0			0
$682$	7321.59	−	12681.4i	0.411082	−	0.712015i
$683$	−5221.24	−	9043.46i	−0.292512	−	0.506645i	0.681891	−	0.731453i	$-0.261158\pi$
$683$	−5221.24	−	9043.46i	−0.292512	−	0.506645i	−0.974403	+	0.224809i	$0.927824\pi$
$684$		0			0
$685$	−10238.9			−0.571105
$686$	−1188.63	−	26747.7i	−0.0661549	−	1.48867i
$687$		0			0
$688$	−11123.1	−	19265.8i	−0.616372	−	1.06759i
$689$	6432.58			0.355678
$690$		0			0
$691$	−3888.90			−0.214096			−0.107048	−	0.994254i	$-0.534140\pi$
$691$	−3888.90			−0.214096			−0.107048	+	0.994254i	$0.534140\pi$
$692$	−6540.15			−0.359276
$693$		0			0
$694$	2470.48			0.135127
$695$	24263.5			1.32427
$696$		0			0
$697$	−4778.50			−0.259682
$698$	19669.9	+	34069.3i	1.06664	+	1.84748i
$699$		0			0
$700$	170.742	+	11533.3i	0.00921922	+	0.622740i
$701$	32491.0			1.75060			0.875298	−	0.483584i	$-0.160665\pi$
$701$	32491.0			1.75060			0.875298	+	0.483584i	$0.160665\pi$
$702$		0			0
$703$	10182.7	+	17636.9i	0.546296	+	0.946213i
$704$	4542.67	−	7868.14i	0.243194	−	0.421224i
$705$		0			0
$706$	−5998.41	+	10389.5i	−0.319763	+	0.553846i
$707$	65.9643	+	4455.76i	0.00350897	+	0.237024i
$708$		0			0
$709$	6744.02			0.357231			0.178616	−	0.983919i	$-0.442838\pi$
$709$	6744.02			0.357231			0.178616	+	0.983919i	$0.442838\pi$
$710$	3804.76	+	6590.04i	0.201113	+	0.348338i
$711$		0			0
$712$	−1111.41	+	1925.02i	−0.0584997	+	0.101324i
$713$	533.100	+	923.356i	0.0280010	+	0.0484992i
$714$		0			0
$715$	677.446	−	1173.37i	0.0354336	−	0.0613728i
$716$	10853.2	+	18798.3i	0.566485	+	0.981181i
$717$		0			0
$718$	13368.1	−	23154.2i	0.694836	−	1.20349i
$719$	10740.5	−	18603.0i	0.557095	−	0.964918i	−0.440642	−	0.897683i	$-0.645249\pi$
$719$	10740.5	−	18603.0i	0.557095	−	0.964918i	0.997737	−	0.0672346i	$-0.0214176\pi$
$720$		0			0
$721$	2689.72	+	1500.27i	0.138933	+	0.0774936i
$722$	3552.39	+	6152.93i	0.183111	+	0.317158i
$723$		0			0
$724$	−18017.2			−0.924865
$725$	11523.0			0.590278
$726$		0			0
$727$	13189.8	+	22845.5i	0.672880	+	1.16546i	0.977084	+	0.212856i	$0.0682765\pi$
$727$	13189.8	+	22845.5i	0.672880	+	1.16546i	−0.304203	+	0.952607i	$0.598390\pi$
$728$	−27.4872	−	1856.71i	−0.00139937	−	0.0945249i
$729$		0			0
$730$	8508.80	−	14737.7i	0.431404	−	0.747214i
$731$	16884.7	−	29245.1i	0.854312	−	1.47971i
$732$		0			0
$733$	971.629	+	1682.91i	0.0489604	+	0.0848018i	0.889467	−	0.456999i	$-0.151076\pi$
$733$	971.629	+	1682.91i	0.0489604	+	0.0848018i	−0.840507	+	0.541801i	$0.817743\pi$
$734$	3023.15	−	5236.24i	0.152025	−	0.263315i
$735$		0			0
$736$	505.715	+	875.924i	0.0253273	+	0.0438682i
$737$	−4458.75	+	7722.79i	−0.222850	+	0.385987i
$738$		0			0
$739$	19615.3	+	33974.7i	0.976400	+	1.69118i	0.675234	+	0.737603i	$0.264043\pi$
$739$	19615.3	+	33974.7i	0.976400	+	1.69118i	0.301166	+	0.953572i	$0.402624\pi$
$740$	−16831.0			−0.836109
$741$		0			0
$742$	32521.3	+	18139.7i	1.60902	+	0.897479i
$743$	9461.21	−	16387.3i	0.467158	−	0.809141i	−0.532138	−	0.846658i	$-0.678611\pi$
$743$	9461.21	−	16387.3i	0.467158	−	0.809141i	0.999296	+	0.0375164i	$0.0119447\pi$
$744$		0			0
$745$	4276.58	−	7407.26i	0.210311	−	0.364270i
$746$	−5758.42	−	9973.88i	−0.282615	−	0.489504i
$747$		0			0
$748$	8903.59			0.435224
$749$	590.834	+	39909.7i	0.0288232	+	1.94695i
$750$		0			0
$751$	13190.2	+	22846.2i	0.640903	+	1.11008i	0.985231	+	0.171228i	$0.0547734\pi$
$751$	13190.2	+	22846.2i	0.640903	+	1.11008i	−0.344328	+	0.938849i	$0.611893\pi$
$752$	−23988.2			−1.16325
$753$		0			0
$754$	−10266.8			−0.495884
$755$	15576.0			0.750819
$756$		0			0
$757$	21186.2			1.01721			0.508603	−	0.861001i	$-0.330162\pi$
$757$	21186.2			1.01721			0.508603	+	0.861001i	$0.330162\pi$
$758$	−53958.7			−2.58558
$759$		0			0
$760$	−5377.81			−0.256676
$761$	14261.4	+	24701.4i	0.679335	+	1.17664i	0.975182	+	0.221407i	$0.0710648\pi$
$761$	14261.4	+	24701.4i	0.679335	+	1.17664i	−0.295847	+	0.955235i	$0.595602\pi$
$762$		0			0
$763$	4592.93	+	2561.84i	0.217923	+	0.121553i
$764$	−21504.3			−1.01832
$765$		0			0
$766$	19148.9	+	33166.8i	0.903233	+	1.56444i
$767$	−4838.50	+	8380.53i	−0.227781	+	0.394529i
$768$		0			0
$769$	20000.8	−	34642.4i	0.937903	−	1.62450i	0.168530	−	0.985697i	$-0.446098\pi$
$769$	20000.8	−	34642.4i	0.937903	−	1.62450i	0.769373	−	0.638799i	$-0.220569\pi$
$770$	6733.85	−	4021.85i	0.315157	−	0.188231i
$771$		0			0
$772$	6744.93			0.314450
$773$	513.456	+	889.332i	0.0238910	+	0.0413804i	0.877724	−	0.479167i	$-0.159061\pi$
$773$	513.456	+	889.332i	0.0238910	+	0.0413804i	−0.853833	+	0.520547i	$0.825728\pi$
$774$		0			0
$775$	8627.62	−	14943.5i	0.399888	−	0.692626i
$776$	−2894.98	−	5014.25i	−0.133922	−	0.231960i
$777$		0			0
$778$	−9397.14	+	16276.3i	−0.433038	+	0.750044i
$779$	3110.57	+	5387.67i	0.143065	+	0.247796i
$780$		0			0
$781$	−1481.78	+	2566.51i	−0.0678900	+	0.117589i
$782$	−589.721	+	1021.43i	−0.0269672	+	0.0467086i
$783$		0			0
$784$	−7606.88	+	14125.3i	−0.346524	+	0.643465i
$785$	−7209.81	−	12487.8i	−0.327808	−	0.567780i
$786$		0			0
$787$	14250.1			0.645440			0.322720	−	0.946494i	$-0.395403\pi$
$787$	14250.1			0.645440			0.322720	+	0.946494i	$0.395403\pi$
$788$	−15165.9			−0.685611
$789$		0			0
$790$	−15559.3	−	26949.5i	−0.700727	−	1.21370i
$791$	−128.866	−	8704.63i	−0.00579259	−	0.391278i
$792$		0			0
$793$	2539.64	−	4398.78i	0.113727	−	0.196980i
$794$	83.6410	−	144.870i	0.00373842	−	0.00647514i
$795$		0			0
$796$	3012.64	+	5218.04i	0.134146	+	0.232347i
$797$	16294.3	−	28222.5i	0.724181	−	1.25432i	−0.235129	−	0.971964i	$-0.575551\pi$
$797$	16294.3	−	28222.5i	0.724181	−	1.25432i	0.959310	−	0.282354i	$-0.0911154\pi$
$798$		0			0
$799$	−18206.9	−	31535.3i	−0.806150	−	1.39629i
$800$	8184.42	−	14175.8i	0.361704	−	0.626489i
$801$		0			0
$802$	−18748.5	−	32473.4i	−0.825477	−	1.42977i
$803$	6627.56			0.291260
$804$		0			0
$805$	8.45378	+	571.036i	0.000370132	+	0.0250017i
$806$	−7687.12	+	13314.5i	−0.335940	+	0.581865i
$807$		0			0
$808$	−894.581	+	1549.46i	−0.0389496	+	0.0674626i
$809$	−7697.24	−	13332.0i	−0.334512	−	0.579393i	0.648879	−	0.760892i	$-0.275238\pi$
$809$	−7697.24	−	13332.0i	−0.334512	−	0.579393i	−0.983391	+	0.181499i	$0.941905\pi$
$810$		0			0
$811$	−13264.9			−0.574346			−0.287173	−	0.957879i	$-0.592716\pi$
$811$	−13264.9			−0.574346			−0.287173	+	0.957879i	$0.592716\pi$
$812$	−28530.6	−	15913.8i	−1.23304	−	0.687763i
$813$		0			0
$814$	−5962.72	−	10327.7i	−0.256748	−	0.444701i
$815$	−4776.87			−0.205308
$816$		0			0
$817$	−43964.5			−1.88265
$818$	8631.39			0.368936
$819$		0			0
$820$	−5141.50			−0.218962
$821$	−16008.3			−0.680506			−0.340253	−	0.940334i	$-0.610513\pi$
$821$	−16008.3			−0.680506			−0.340253	+	0.940334i	$0.610513\pi$
$822$		0			0
$823$	−30630.9			−1.29736			−0.648680	−	0.761061i	$-0.724679\pi$
$823$	−30630.9			−1.29736			−0.648680	+	0.761061i	$0.724679\pi$
$824$	618.270	+	1070.87i	0.0261389	+	0.0452739i
$825$		0			0
$826$	−48095.0	+	28725.2i	−2.02595	+	1.21002i
$827$	−3670.92			−0.154354			−0.0771769	−	0.997017i	$-0.524591\pi$
$827$	−3670.92			−0.154354			−0.0771769	+	0.997017i	$0.524591\pi$
$828$		0			0
$829$	1225.07	+	2121.88i	0.0513250	+	0.0888976i	0.890547	−	0.454892i	$-0.150322\pi$
$829$	1225.07	+	2121.88i	0.0513250	+	0.0888976i	−0.839221	+	0.543790i	$0.816989\pi$
$830$	−2786.23	+	4825.88i	−0.116520	+	0.201818i
$831$		0			0
$832$	−4769.47	+	8260.96i	−0.198740	+	0.344227i
$833$	−24342.9	+	720.917i	−1.01252	+	0.0299860i
$834$		0			0
$835$	−17790.3			−0.737314
$836$	−5795.81	−	10038.6i	−0.239775	−	0.415303i
$837$		0			0
$838$	−4996.60	+	8654.36i	−0.205972	+	0.356754i
$839$	8052.53	+	13947.4i	0.331352	+	0.573918i	0.982777	−	0.184794i	$-0.0591619\pi$
$839$	8052.53	+	13947.4i	0.331352	+	0.573918i	−0.651425	+	0.758713i	$0.725829\pi$
$840$		0			0
$841$	−4123.40	+	7141.94i	−0.169068	+	0.292835i
$842$	21331.9	+	36948.0i	0.873096	+	1.51225i
$843$		0			0
$844$	19780.3	−	34260.5i	0.806715	−	1.39727i
$845$	7883.42	−	13654.5i	0.320944	−	0.555892i
$846$		0			0
$847$	−18860.3	−	10519.9i	−0.765109	−	0.426762i
$848$	−11156.8	−	19324.2i	−0.451801	−	0.782542i
$849$		0			0
$850$	19087.9			0.770248
$851$	868.315			0.0349770
$852$		0			0
$853$	18952.1	+	32826.1i	0.760737	+	1.31764i	0.942471	+	0.334288i	$0.108496\pi$
$853$	18952.1	+	32826.1i	0.760737	+	1.31764i	−0.181734	+	0.983348i	$0.558171\pi$
$854$	25244.1	−	15077.3i	1.01152	−	0.604139i
$855$		0			0
$856$	−8012.64	+	13878.3i	−0.319937	+	0.554148i
$857$	−15995.9	+	27705.7i	−0.637585	+	1.10433i	0.348377	+	0.937355i	$0.386733\pi$
$857$	−15995.9	+	27705.7i	−0.637585	+	1.10433i	−0.985961	+	0.166974i	$0.946600\pi$
$858$		0			0
$859$	−13412.8	−	23231.7i	−0.532758	−	0.922764i	−0.999268	−	0.0382479i	$-0.987822\pi$
$859$	−13412.8	−	23231.7i	−0.532758	−	0.922764i	0.466510	−	0.884516i	$-0.345511\pi$
$860$	18167.3	−	31466.8i	0.720350	−	1.24768i
$861$		0			0
$862$	−11465.5	−	19858.9i	−0.453036	−	0.784682i
$863$	−803.365	+	1391.47i	−0.0316882	+	0.0548855i	−0.881435	−	0.472306i	$-0.843422\pi$
$863$	−803.365	+	1391.47i	−0.0316882	+	0.0548855i	0.849746	+	0.527192i	$0.176755\pi$
$864$		0			0
$865$	2620.29	+	4538.48i	0.102997	+	0.178396i
$866$	−15287.2			−0.599863
$867$		0			0
$868$	−41999.5	+	25084.6i	−1.64235	+	0.980906i
$869$	6059.61	−	10495.6i	0.236546	−	0.409709i
$870$		0			0
$871$	4681.36	−	8108.36i	0.182115	−	0.315432i
$872$	1055.75	+	1828.61i	0.0410002	+	0.0710144i
$873$		0			0
$874$	1535.52			0.0594276
$875$	23485.4	−	14026.9i	0.907375	−	0.541938i
$876$		0			0
$877$	21226.6	+	36765.5i	0.817298	+	1.41560i	0.907666	+	0.419692i	$0.137862\pi$
$877$	21226.6	+	36765.5i	0.817298	+	1.41560i	−0.0903689	+	0.995908i	$0.528805\pi$
$878$	−40371.0			−1.55177
$879$		0			0
$880$	−4699.91			−0.180039
$881$	−18106.4			−0.692418			−0.346209	−	0.938157i	$-0.612531\pi$
$881$	−18106.4			−0.692418			−0.346209	+	0.938157i	$0.612531\pi$
$882$		0			0
$883$	−10989.7			−0.418837			−0.209418	−	0.977826i	$-0.567157\pi$
$883$	−10989.7			−0.418837			−0.209418	+	0.977826i	$0.567157\pi$
$884$	−9348.10			−0.355668
$885$		0			0
$886$	−71001.3			−2.69225
$887$	−10658.2	−	18460.6i	−0.403458	−	0.698810i	0.590682	−	0.806904i	$-0.298859\pi$
$887$	−10658.2	−	18460.6i	−0.403458	−	0.698810i	−0.994141	+	0.108094i	$0.965525\pi$
$888$		0			0
$889$	3673.53	−	2194.05i	0.138590	−	0.0827740i
$890$	9857.79			0.371274
$891$		0			0
$892$	−16387.7	−	28384.3i	−0.615135	−	1.06544i
$893$	−23703.6	+	41055.9i	−0.888255	+	1.53850i
$894$		0			0
$895$	8696.61	−	15063.0i	0.324800	−	0.562569i
$896$	−14765.5	+	8818.84i	−0.550537	+	0.328813i
$897$		0			0
$898$	70967.0			2.63719
$899$	24435.5	+	42323.5i	0.906529	+	1.57015i
$900$		0			0
$901$	16935.9	−	29333.8i	0.626211	−	1.08463i
$902$	−1821.48	−	3154.89i	−0.0672378	−	0.116459i
$903$		0			0
$904$	1747.63	−	3026.98i	0.0642977	−	0.111367i
$905$	7218.52	+	12502.9i	0.265140	+	0.459236i
$906$		0			0
$907$	−7558.91	+	13092.4i	−0.276725	+	0.479301i	−0.970569	−	0.240824i	$-0.922582\pi$
$907$	−7558.91	+	13092.4i	−0.276725	+	0.479301i	0.693844	+	0.720125i	$0.255916\pi$
$908$	25155.8	−	43571.1i	0.919410	−	1.59247i
$909$		0			0
$910$	−7070.04	+	4222.65i	−0.257549	+	0.153823i
$911$	7635.12	+	13224.4i	0.277676	+	0.480949i	0.970807	−	0.239863i	$-0.0771025\pi$
$911$	7635.12	+	13224.4i	0.277676	+	0.480949i	−0.693131	+	0.720812i	$0.743769\pi$
$912$		0			0
$913$	−2170.21			−0.0786674
$914$	43818.3			1.58576
$915$		0			0
$916$	−5702.89	−	9877.70i	−0.205708	−	0.356297i
$917$	−27500.8	−	15339.4i	−0.990356	−	0.552399i
$918$		0			0
$919$	2923.46	−	5063.57i	0.104936	−	0.181754i	−0.808776	−	0.588116i	$-0.799870\pi$
$919$	2923.46	−	5063.57i	0.104936	−	0.181754i	0.913712	+	0.406363i	$0.133203\pi$
$920$	−114.647	+	198.574i	−0.00410847	+	0.00711607i
$921$		0			0
$922$	8243.21	+	14277.7i	0.294442	+	0.509989i
$923$	1555.75	−	2694.65i	0.0554803	−	0.0960946i
$924$		0			0
$925$	−7026.35	−	12170.0i	−0.249757	−	0.432591i
$926$	−6872.95	+	11904.3i	−0.243908	+	0.422462i
$927$		0			0
$928$	23180.3	+	40149.4i	0.819967	+	1.42023i
$929$	−42547.3			−1.50262			−0.751309	−	0.659951i	$-0.770577\pi$
$929$	−42547.3			−1.50262			−0.751309	+	0.659951i	$0.770577\pi$
$930$		0			0
$931$	16658.9	+	26976.9i	0.586438	+	0.949660i
$932$	−17393.9	+	30127.0i	−0.611325	+	1.05885i
$933$		0			0
$934$	8410.02	−	14566.6i	0.294630	−	0.510314i
$935$	−3567.20	−	6178.57i	−0.124770	−	0.216108i
$936$		0			0
$937$	8137.69			0.283721			0.141861	−	0.989887i	$-0.454692\pi$
$937$	8137.69			0.283721			0.141861	+	0.989887i	$0.454692\pi$
$938$	46533.0	−	27792.3i	1.61978	−	0.967430i
$939$		0			0
$940$	−19590.0	−	33930.9i	−0.679740	−	1.17734i
$941$	−9047.18			−0.313422			−0.156711	−	0.987645i	$-0.550089\pi$
$941$	−9047.18			−0.313422			−0.156711	+	0.987645i	$0.550089\pi$
$942$		0			0
$943$	265.251			0.00915986
$944$	33568.0			1.15736
$945$		0			0
$946$	25744.5			0.884806
$947$	5366.03			0.184132			0.0920658	−	0.995753i	$-0.470653\pi$
$947$	5366.03			0.184132			0.0920658	+	0.995753i	$0.470653\pi$
$948$		0			0
$949$	−6958.44			−0.238020
$950$	−12425.3	−	21521.3i	−0.424348	−	0.734993i
$951$		0			0
$952$	−8539.31	−	4763.04i	−0.290715	−	0.162155i
$953$	−24743.1			−0.841035			−0.420518	−	0.907284i	$-0.638152\pi$
$953$	−24743.1			−0.841035			−0.420518	+	0.907284i	$0.638152\pi$
$954$		0			0
$955$	8615.64	+	14922.7i	0.291933	+	0.505642i
$956$	−30478.5	+	52790.3i	−1.03111	+	1.78594i
$957$		0			0
$958$	1346.18	−	2331.66i	0.0454000	−	0.0786351i
$959$	358.764	+	24233.8i	0.0120804	+	0.816006i
$960$		0			0
$961$	43391.7			1.45654
$962$	6260.41	+	10843.3i	0.209817	+	0.363413i
$963$		0			0
$964$	14271.1	−	24718.3i	0.476807	−	0.825855i
$965$	−2702.34	−	4680.58i	−0.0901464	−	0.156138i
$966$		0			0
$967$	26251.0	−	45468.1i	0.872985	−	1.51205i	0.0140902	−	0.999901i	$-0.495515\pi$
$967$	26251.0	−	45468.1i	0.872985	−	1.51205i	0.858894	−	0.512153i	$-0.171152\pi$
$968$	−4335.30	−	7508.97i	−0.143948	−	0.249326i
$969$		0			0
$970$	−12838.7	+	22237.3i	−0.424975	+	0.736078i
$971$	−12710.1	+	22014.6i	−0.420069	+	0.727581i	−0.995946	−	0.0899554i	$-0.971328\pi$
$971$	−12710.1	+	22014.6i	−0.420069	+	0.727581i	0.575877	+	0.817537i	$0.304661\pi$
$972$		0			0
$973$	−850.180	−	57428.0i	−0.0280119	−	1.89215i
$974$	11596.1	+	20085.1i	0.381482	+	0.660746i
$975$		0			0
$976$	−17619.2			−0.577846
$977$	−13758.3			−0.450528			−0.225264	−	0.974298i	$-0.572324\pi$
$977$	−13758.3			−0.450528			−0.225264	+	0.974298i	$0.572324\pi$
$978$		0			0
$979$	1919.57	+	3324.80i	0.0626658	+	0.108540i
$980$	−26192.2	+	775.683i	−0.853753	+	0.0252839i
$981$		0			0
$982$	−1865.55	+	3231.23i	−0.0606234	+	0.105003i
$983$	2415.68	−	4184.07i	0.0783806	−	0.135759i	−0.824171	−	0.566341i	$-0.808358\pi$
$983$	2415.68	−	4184.07i	0.0783806	−	0.135759i	0.902551	+	0.430582i	$0.141692\pi$
$984$		0			0
$985$	6076.16	+	10524.2i	0.196551	+	0.340436i
$986$	−27030.8	+	46818.8i	−0.873060	+	1.51218i
$987$		0			0
$988$	6085.17	+	10539.8i	0.195946	+	0.339389i
$989$	−937.255	+	1623.37i	−0.0301345	+	0.0521944i
$990$		0			0
$991$	−27960.4	−	48428.9i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$991$	−27960.4	−	48428.9i	−0.896258	−	1.55236i	−0.0640186	−	0.997949i	$-0.520392\pi$
$992$	69423.3			2.22197
$993$		0			0
$994$	15464.3	−	9236.19i	0.493458	−	0.294722i
$995$	2414.01	−	4181.19i	0.0769138	−	0.133219i
$996$		0			0
$997$	−9137.24	+	15826.2i	−0.290250	+	0.502728i	−0.973869	−	0.227111i	$-0.927072\pi$
$997$	−9137.24	+	15826.2i	−0.290250	+	0.502728i	0.683619	+	0.729839i	$0.260405\pi$
$998$	−1024.97	−	1775.30i	−0.0325099	−	0.0563088i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.h.a.37.3		44
3.2	odd	2		63.4.h.a.58.20	yes	44
7.4	even	3		189.4.g.a.172.20		44
9.2	odd	6		63.4.g.a.16.3	yes	44
9.7	even	3		189.4.g.a.100.20		44
21.11	odd	6		63.4.g.a.4.3	✓	44
63.11	odd	6		63.4.h.a.25.20	yes	44
63.25	even	3	inner	189.4.h.a.46.3		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.3	✓	44	21.11	odd	6
63.4.g.a.16.3	yes	44	9.2	odd	6
63.4.h.a.25.20	yes	44	63.11	odd	6
63.4.h.a.58.20	yes	44	3.2	odd	2
189.4.g.a.100.20		44	9.7	even	3
189.4.g.a.172.20		44	7.4	even	3
189.4.h.a.37.3		44	1.1	even	1	trivial
189.4.h.a.46.3		44	63.25	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.21476 q^{2} +9.76423 q^{4} +(-3.91201 - 6.77580i) q^{5} +(-15.9002 + 9.49654i) q^{7} -7.43579 q^{8} +O(q^{10})\)	\(q-4.21476 q^{2} +9.76423 q^{4} +(-3.91201 - 6.77580i) q^{5} +(-15.9002 + 9.49654i) q^{7} -7.43579 q^{8} +(16.4882 + 28.5584i) q^{10} +(-6.42137 + 11.1221i) q^{11} +(6.74197 - 11.6774i) q^{13} +(67.0155 - 40.0256i) q^{14} -46.7737 q^{16} +(-35.5009 - 61.4893i) q^{17} +(-46.2187 + 80.0532i) q^{19} +(-38.1977 - 66.1604i) q^{20} +(27.0646 - 46.8772i) q^{22} +(1.97063 + 3.41322i) q^{23} +(31.8924 - 55.2392i) q^{25} +(-28.4158 + 49.2176i) q^{26} +(-155.253 + 92.7263i) q^{28} +(90.3269 + 156.451i) q^{29} +270.523 q^{31} +256.626 q^{32} +(149.628 + 259.163i) q^{34} +(126.548 + 70.5859i) q^{35} +(110.157 - 190.798i) q^{37} +(194.801 - 337.405i) q^{38} +(29.0889 + 50.3834i) q^{40} +(33.6506 - 58.2845i) q^{41} +(237.806 + 411.893i) q^{43} +(-62.6997 + 108.599i) q^{44} +(-8.30572 - 14.3859i) q^{46} +512.858 q^{47} +(162.632 - 301.993i) q^{49} +(-134.419 + 232.820i) q^{50} +(65.8301 - 114.021i) q^{52} +(238.528 + 413.142i) q^{53} +100.482 q^{55} +(118.230 - 70.6143i) q^{56} +(-380.707 - 659.403i) q^{58} -717.669 q^{59} +376.691 q^{61} -1140.19 q^{62} -707.430 q^{64} -105.499 q^{65} +694.361 q^{67} +(-346.639 - 600.396i) q^{68} +(-533.371 - 297.503i) q^{70} +230.757 q^{71} +(-258.027 - 446.916i) q^{73} +(-464.287 + 804.168i) q^{74} +(-451.290 + 781.658i) q^{76} +(-3.52083 - 237.825i) q^{77} -943.662 q^{79} +(182.979 + 316.929i) q^{80} +(-141.829 + 245.655i) q^{82} +(84.4915 + 146.344i) q^{83} +(-277.760 + 481.094i) q^{85} +(-1002.30 - 1736.03i) q^{86} +(47.7480 - 82.7020i) q^{88} +(149.467 - 258.885i) q^{89} +(3.69661 + 249.699i) q^{91} +(19.2416 + 33.3275i) q^{92} -2161.57 q^{94} +723.233 q^{95} +(389.330 + 674.339i) q^{97} +(-685.454 + 1272.83i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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