LMFDB - Embedded newform 189.4.g.a.100.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(100,189)]

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([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.g (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			100.20
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10738 + 3.65009i) q^{2} +(-4.88211 + 8.45607i) q^{4} +7.82402 q^{5} +(16.1743 + 9.02169i) q^{7} -7.43579 q^{8} +O(q^{10})$	\(q+(2.10738 + 3.65009i) q^{2} +(-4.88211 + 8.45607i) q^{4} +7.82402 q^{5} +(16.1743 + 9.02169i) q^{7} -7.43579 q^{8} +(16.4882 + 28.5584i) q^{10} +12.8427 q^{11} +(6.74197 + 11.6774i) q^{13} +(1.15547 + 78.0499i) q^{14} +(23.3869 + 40.5072i) q^{16} +(-35.5009 - 61.4893i) q^{17} +(-46.2187 + 80.0532i) q^{19} +(-38.1977 + 66.1604i) q^{20} +(27.0646 + 46.8772i) q^{22} -3.94125 q^{23} -63.7847 q^{25} +(-28.4158 + 49.2176i) q^{26} +(-155.253 + 92.7263i) q^{28} +(90.3269 - 156.451i) q^{29} +(-135.261 + 234.280i) q^{31} +(-128.313 + 222.245i) q^{32} +(149.628 - 259.163i) q^{34} +(126.548 + 70.5859i) q^{35} +(110.157 - 190.798i) q^{37} -389.602 q^{38} -58.1778 q^{40} +(33.6506 + 58.2845i) q^{41} +(237.806 - 411.893i) q^{43} +(-62.6997 + 108.599i) q^{44} +(-8.30572 - 14.3859i) q^{46} +(-256.429 - 444.148i) q^{47} +(180.218 + 291.840i) q^{49} +(-134.419 - 232.820i) q^{50} -131.660 q^{52} +(238.528 + 413.142i) q^{53} +100.482 q^{55} +(-120.269 - 67.0835i) q^{56} +761.413 q^{58} +(358.835 - 621.520i) q^{59} +(-188.346 - 326.224i) q^{61} -1140.19 q^{62} -707.430 q^{64} +(52.7493 + 91.3644i) q^{65} +(-347.181 + 601.335i) q^{67} +693.277 q^{68} +(9.04045 + 610.664i) q^{70} +230.757 q^{71} +(-258.027 - 446.916i) q^{73} +928.573 q^{74} +(-451.290 - 781.658i) q^{76} +(207.723 + 115.863i) q^{77} +(471.831 + 817.236i) q^{79} +(182.979 + 316.929i) q^{80} +(-141.829 + 245.655i) q^{82} +(84.4915 - 146.344i) q^{83} +(-277.760 - 481.094i) q^{85} +2004.60 q^{86} -95.4960 q^{88} +(149.467 - 258.885i) q^{89} +(3.69661 + 249.699i) q^{91} +(19.2416 - 33.3275i) q^{92} +(1080.79 - 1871.98i) q^{94} +(-361.616 + 626.338i) q^{95} +(389.330 - 674.339i) q^{97} +(-685.454 + 1272.83i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.10738	+	3.65009i	0.745072	+	1.29050i	0.950161	+	0.311759i	$0.100918\pi$
$2$	2.10738	+	3.65009i	0.745072	+	1.29050i	−0.205089	+	0.978743i	$0.565748\pi$
$3$		0			0
$3$		0			0
$4$	−4.88211	+	8.45607i	−0.610264	+	1.05701i
$5$	7.82402			0.699802			0.349901	−	0.936787i	$-0.386215\pi$
$5$	7.82402			0.699802			0.349901	+	0.936787i	$0.386215\pi$
$6$		0			0
$7$	16.1743	+	9.02169i	0.873332	+	0.487126i
$7$	16.1743	+	9.02169i	0.873332	+	0.487126i
$8$	−7.43579			−0.328619
$9$		0			0
$10$	16.4882	+	28.5584i	0.521402	+	0.903095i
$11$	12.8427			0.352021			0.176011	−	0.984388i	$-0.443681\pi$
$11$	12.8427			0.352021			0.176011	+	0.984388i	$0.443681\pi$
$12$		0			0
$13$	6.74197	+	11.6774i	0.143837	+	0.249134i	0.928939	−	0.370234i	$-0.120722\pi$
$13$	6.74197	+	11.6774i	0.143837	+	0.249134i	−0.785101	+	0.619367i	$0.787389\pi$
$14$	1.15547	+	78.0499i	0.0220581	+	1.48998i
$15$		0			0
$16$	23.3869	+	40.5072i	0.365420	+	0.632925i
$17$	−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
$23$	−3.94125			−0.0357308			−0.0178654	−	0.999840i	$-0.505687\pi$
$23$	−3.94125			−0.0357308			−0.0178654	+	0.999840i	$0.505687\pi$
$24$		0			0
$25$	−63.7847			−0.510278
$26$	−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	−0.417275	−	0.908780i	$-0.637015\pi$
$29$	90.3269	−	156.451i	0.578389	−	1.00180i	0.995664	−	0.0930193i	$-0.0296518\pi$
$30$		0			0
$31$	−135.261	+	234.280i	−0.783667	+	1.35735i	0.146125	+	0.989266i	$0.453320\pi$
$31$	−135.261	+	234.280i	−0.783667	+	1.35735i	−0.929792	+	0.368085i	$0.880014\pi$
$32$	−128.313	+	222.245i	−0.708837	+	1.22774i
$33$		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	$0.00386339\pi$
$38$	−389.602			−1.66321
$39$		0			0
$40$	−58.1778			−0.229968
$41$	33.6506	+	58.2845i	0.128179	+	0.222012i	0.922971	−	0.384869i	$-0.125753\pi$
$41$	33.6506	+	58.2845i	0.128179	+	0.222012i	−0.794792	+	0.606882i	$0.792420\pi$
$42$		0			0
$43$	237.806	−	411.893i	0.843375	−	1.46077i	−0.0436494	−	0.999047i	$-0.513898\pi$
$43$	237.806	−	411.893i	0.843375	−	1.46077i	0.887025	−	0.461722i	$-0.152768\pi$
$44$	−62.6997	+	108.599i	−0.214826	+	0.372089i
$45$		0			0
$46$	−8.30572	−	14.3859i	−0.0266220	−	0.0461107i
$47$	−256.429	−	444.148i	−0.795829	−	1.37842i	−0.922311	−	0.386448i	$-0.873702\pi$
$47$	−256.429	−	444.148i	−0.795829	−	1.37842i	0.126482	−	0.991969i	$-0.459631\pi$
$48$		0			0
$49$	180.218	+	291.840i	0.525417	+	0.850845i
$50$	−134.419	−	232.820i	−0.380194	−	0.658515i
$51$		0			0
$52$	−131.660			−0.351115
$53$	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
$56$	−120.269	−	67.0835i	−0.286993	−	0.160079i
$57$		0			0
$58$	761.413			1.72377
$59$	358.835	−	621.520i	0.791802	−	1.37144i	−0.133049	−	0.991109i	$-0.542477\pi$
$59$	358.835	−	621.520i	0.791802	−	1.37144i	0.924850	−	0.380331i	$-0.124190\pi$
$60$		0			0
$61$	−188.346	−	326.224i	−0.395331	−	0.684733i	0.597813	−	0.801636i	$-0.296037\pi$
$61$	−188.346	−	326.224i	−0.395331	−	0.684733i	−0.993143	+	0.116903i	$0.962703\pi$
$62$	−1140.19			−2.33555
$63$		0			0
$64$	−707.430			−1.38170
$65$	52.7493	+	91.3644i	0.100658	+	0.174344i
$66$		0			0
$67$	−347.181	+	601.335i	−0.633058	+	1.09649i	0.353865	+	0.935296i	$0.384867\pi$
$67$	−347.181	+	601.335i	−0.633058	+	1.09649i	−0.986923	+	0.161192i	$0.948466\pi$
$68$	693.277			1.23636
$69$		0			0
$70$	9.04045	+	610.664i	0.0154363	+	1.04269i
$71$	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	$0.969096\pi$
$74$	928.573			1.45871
$75$		0			0
$76$	−451.290	−	781.658i	−0.681139	−	1.17977i
$77$	207.723	+	115.863i	0.307431	+	0.171479i
$78$		0			0
$79$	471.831	+	817.236i	0.671964	+	1.16388i	0.977346	+	0.211646i	$0.0678824\pi$
$79$	471.831	+	817.236i	0.671964	+	1.16388i	−0.305382	+	0.952230i	$0.598784\pi$
$80$	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	−0.804734	−	0.593636i	$-0.797692\pi$
$83$	84.4915	−	146.344i	0.111737	−	0.193534i	0.916471	+	0.400102i	$0.131025\pi$
$84$		0			0
$85$	−277.760	−	481.094i	−0.354438	−	0.613905i
$86$	2004.60			2.51350
$87$		0			0
$88$	−95.4960			−0.115681
$89$	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
$94$	1080.79	−	1871.98i	1.18590	−	2.05404i
$95$	−361.616	+	626.338i	−0.390537	+	0.676431i
$96$		0			0
$97$	389.330	−	674.339i	0.407531	−	0.705864i	−0.587082	−	0.809528i	$-0.699723\pi$
$97$	389.330	−	674.339i	0.407531	−	0.705864i	0.994612	+	0.103664i	$0.0330566\pi$
$98$	−685.454	+	1272.83i	−0.706544	+	1.31199i
$99$		0			0
$100$	311.404	−	539.368i	0.311404	−	0.539368i
$101$	−240.615			−0.237050			−0.118525	−	0.992951i	$-0.537817\pi$
$101$	−240.615			−0.237050			−0.118525	+	0.992951i	$0.537817\pi$
$102$		0			0
$103$	166.296			0.159083			0.0795417	−	0.996832i	$-0.474654\pi$
$103$	166.296			0.159083			0.0795417	+	0.996832i	$0.474654\pi$
$104$	−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	$0.873151\pi$
$110$	211.754	+	366.768i	0.183545	+	0.317909i
$111$		0			0
$112$	12.8230	+	866.166i	0.0108184	+	0.730759i
$113$	−235.029	−	407.082i	−0.195661	−	0.338894i	0.751456	−	0.659783i	$-0.229352\pi$
$113$	−235.029	−	407.082i	−0.195661	−	0.338894i	−0.947117	+	0.320889i	$0.896018\pi$
$114$		0			0
$115$	−30.8364			−0.0250045
$116$	881.972	+	1527.62i	0.705940	+	1.22272i
$117$		0			0
$118$	3024.81			2.35980
$119$	−19.4651	−	1314.83i	−0.0149946	−	1.01286i
$120$		0			0
$121$	−1166.06			−0.876081
$122$	793.832	−	1374.96i	0.589100	−	1.02035i
$123$		0			0
$124$	−1320.72	−	2287.56i	−0.956488	−	1.65669i
$125$	−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	$0.525720\pi$
$128$	−464.319	−	804.224i	−0.320628	−	0.555344i
$129$		0			0
$130$	−222.326	+	385.079i	−0.149994	+	0.259798i
$131$	−1700.27			−1.13400			−0.566999	−	0.823719i	$-0.691896\pi$
$131$	−1700.27			−1.13400			−0.566999	+	0.823719i	$0.691896\pi$
$132$		0			0
$133$	−1469.77	+	877.836i	−0.958237	+	0.572316i
$134$	−2926.57			−1.88669
$135$		0			0
$136$	263.977	+	457.222i	0.166440	+	0.288283i
$137$	−1308.65			−0.816096			−0.408048	−	0.912961i	$-0.633790\pi$
$137$	−1308.65			−0.816096			−0.408048	+	0.912961i	$0.633790\pi$
$138$		0			0
$139$	−1550.58	−	2685.68i	−0.946176	−	1.63883i	−0.753379	−	0.657587i	$-0.771577\pi$
$139$	−1550.58	−	2685.68i	−0.946176	−	1.63883i	−0.192798	−	0.981239i	$-0.561756\pi$
$140$	−1214.70	+	725.492i	−0.733293	+	0.437966i
$141$		0			0
$142$	486.293	+	842.283i	0.287386	+	0.497767i
$143$	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
$149$	−1093.19			−0.601059			−0.300530	−	0.953772i	$-0.597163\pi$
$149$	−1093.19			−0.601059			−0.300530	+	0.953772i	$0.597163\pi$
$150$		0			0
$151$	1990.79			1.07290			0.536451	−	0.843931i	$-0.319764\pi$
$151$	1990.79			1.07290			0.536451	+	0.843931i	$0.319764\pi$
$152$	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
$157$	−921.497	+	1596.08i	−0.468429	+	0.811344i	−0.999349	−	0.0360786i	$-0.988513\pi$
$157$	−921.497	+	1596.08i	−0.468429	+	0.811344i	0.530919	+	0.847422i	$0.321847\pi$
$158$	−1988.66	+	3444.45i	−1.00132	+	1.73434i
$159$		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	$0.119805\pi$
$164$	−657.143			−0.312892
$165$		0			0
$166$	712.224			0.333008
$167$	1136.90	+	1969.17i	0.526802	+	0.912448i	0.999512	+	0.0312300i	$0.00994244\pi$
$167$	1136.90	+	1969.17i	0.526802	+	0.912448i	−0.472710	+	0.881218i	$0.656724\pi$
$168$		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
$173$	334.903	+	580.070i	0.147181	+	0.254924i	0.930184	−	0.367093i	$-0.119647\pi$
$173$	334.903	+	580.070i	0.147181	+	0.254924i	−0.783004	+	0.622017i	$0.786313\pi$
$174$		0			0
$175$	−1031.68	−	575.446i	−0.445642	−	0.248569i
$176$	300.351	+	520.224i	0.128635	+	0.222803i
$177$		0			0
$178$	1259.94			0.530542
$179$	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	$0.623690\pi$
$182$	−903.632	+	539.703i	−0.368031	+	0.219810i
$183$		0			0
$184$	29.3063			0.0117418
$185$	861.872	−	1492.81i	0.342519	−	0.593261i
$186$		0			0
$187$	−455.929	−	789.692i	−0.178293	−	0.308813i
$188$	5007.66			1.94266
$189$		0			0
$190$	−3048.25			−1.16391
$191$	1101.18	+	1907.30i	0.417165	+	0.722551i	0.995653	−	0.0931402i	$-0.0296905\pi$
$191$	1101.18	+	1907.30i	0.417165	+	0.722551i	−0.578488	+	0.815691i	$0.696357\pi$
$192$		0			0
$193$	−345.390	+	598.233i	−0.128817	+	0.223118i	−0.923219	−	0.384275i	$-0.874451\pi$
$193$	−345.390	+	598.233i	−0.128817	+	0.223118i	0.794401	+	0.607393i	$0.207785\pi$
$194$	3281.87			1.21456
$195$		0			0
$196$	−3347.66	+	99.1412i	−1.21999	+	0.0361302i
$197$	−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	$0.798278\pi$
$200$	474.290			0.167687
$201$		0			0
$202$	−507.067	−	878.266i	−0.176619	−	0.305914i
$203$	2872.43	−	1715.59i	0.993128	−	0.593155i
$204$		0			0
$205$	263.283	+	456.019i	0.0896998	+	0.155365i
$206$	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	0.980365	+	0.197191i	$0.0631820\pi$
$211$	2025.80	+	3508.78i	0.660955	+	1.14481i	−0.319410	+	0.947617i	$0.603485\pi$
$212$	−4658.08			−1.50905
$213$		0			0
$214$	9083.47			2.90156
$215$	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
$220$	−490.564	+	849.682i	−0.150336	+	0.260389i
$221$	478.691	−	829.118i	0.145703	−	0.252364i
$222$		0			0
$223$	−1678.34	+	2906.97i	−0.503990	+	0.872937i	0.495999	+	0.868323i	$0.334802\pi$
$223$	−1678.34	+	2906.97i	−0.503990	+	0.872937i	−0.999989	+	0.00461387i	$0.998531\pi$
$224$	−4080.41	+	2437.06i	−1.21711	+	0.726933i
$225$		0			0
$226$	990.591	−	1715.75i	0.291562	−	0.505001i
$227$	−5152.65			−1.50658			−0.753289	−	0.657690i	$-0.771534\pi$
$227$	−5152.65			−1.50658			−0.753289	+	0.657690i	$0.771534\pi$
$228$		0			0
$229$	1168.12			0.337081			0.168540	−	0.985695i	$-0.446095\pi$
$229$	1168.12			0.337081			0.168540	+	0.985695i	$0.446095\pi$
$230$	−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
$236$	3503.74	+	6068.66i	0.966416	+	1.67388i
$237$		0			0
$238$	4758.22	−	2841.89i	1.29592	−	0.774002i
$239$	−3121.45	−	5406.50i	−0.844810	−	1.46325i	−0.885786	−	0.464094i	$-0.846380\pi$
$239$	−3121.45	−	5406.50i	−0.844810	−	1.46325i	0.0409763	−	0.999160i	$-0.486953\pi$
$240$		0			0
$241$	−2923.15			−0.781313			−0.390657	−	0.920536i	$-0.627752\pi$
$241$	−2923.15			−0.781313			−0.390657	+	0.920536i	$0.627752\pi$
$242$	−2457.34	−	4256.24i	−0.652743	−	1.13058i
$243$		0			0
$244$	3678.10			0.965025
$245$	1410.03	+	2283.36i	0.367688	+	0.595423i
$246$		0			0
$247$	−1246.42			−0.321084
$248$	1005.78	−	1742.06i	0.257528	−	0.446051i
$249$		0			0
$250$	−3112.72	−	5391.39i	−0.787463	−	1.36393i
$251$	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
$254$	−486.883	−	843.306i	−0.120275	−	0.208322i
$255$		0			0
$256$	−872.726	+	1511.61i	−0.213068	+	0.369044i
$257$	−2198.52			−0.533618			−0.266809	−	0.963749i	$-0.585969\pi$
$257$	−2198.52			−0.533618			−0.266809	+	0.963749i	$0.585969\pi$
$258$		0			0
$259$	3503.04	−	2092.22i	0.840418	−	0.501948i
$260$	−1030.11			−0.245711
$261$		0			0
$262$	−3583.13	−	6206.16i	−0.844910	−	1.46343i
$263$	3979.88			0.933117			0.466559	−	0.884490i	$-0.345494\pi$
$263$	3979.88			0.933117			0.466559	+	0.884490i	$0.345494\pi$
$264$		0			0
$265$	1866.25	+	3232.43i	0.432613	+	0.749308i
$266$	−6301.55	−	3514.87i	−1.45253	−	0.810190i
$267$		0			0
$268$	−3389.95	−	5871.57i	−0.772665	−	1.33829i
$269$	−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
$275$	−819.171			−0.179629
$276$		0			0
$277$	3872.52			0.839990			0.419995	−	0.907526i	$-0.362032\pi$
$277$	3872.52			0.839990			0.419995	+	0.907526i	$0.362032\pi$
$278$	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	−0.307103	−	0.951676i	$-0.599360\pi$
$281$	3158.92	−	5471.41i	0.670624	−	1.16156i	0.977727	−	0.209879i	$-0.0673071\pi$
$282$		0			0
$283$	−1924.63	+	3333.55i	−0.404265	+	0.700208i	−0.994236	−	0.107217i	$-0.965806\pi$
$283$	−1924.63	+	3333.55i	−0.404265	+	0.700208i	0.589970	+	0.807425i	$0.299139\pi$
$284$	−1126.58	+	1951.30i	−0.235388	+	0.407704i
$285$		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
$290$	5957.31			1.20629
$291$		0			0
$292$	5038.87			1.00985
$293$	1683.32	+	2915.59i	0.335633	+	0.581333i	0.983606	−	0.180330i	$-0.0577165\pi$
$293$	1683.32	+	2915.59i	0.335633	+	0.581333i	−0.647973	+	0.761663i	$0.724383\pi$
$294$		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
$299$	−26.5718	−	46.0237i	−0.00513942	−	0.00890173i
$300$		0			0
$301$	7562.33	−	4516.67i	1.44812	−	0.864906i
$302$	4195.36	+	7266.57i	0.799390	+	1.38458i
$303$		0			0
$304$	−4323.64			−0.815717
$305$	−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	$0.291286\pi$
$308$	−1993.87	+	1190.86i	−0.368869	+	0.220310i
$309$		0			0
$310$	−8920.87			−1.63442
$311$	−4126.50	+	7147.32i	−0.752388	+	1.30317i	0.194275	+	0.980947i	$0.437765\pi$
$311$	−4126.50	+	7147.32i	−0.752388	+	1.30317i	−0.946663	+	0.322227i	$0.895569\pi$
$312$		0			0
$313$	500.746	+	867.317i	0.0904275	+	0.156625i	0.907691	−	0.419639i	$-0.137843\pi$
$313$	500.746	+	867.317i	0.0904275	+	0.156625i	−0.817264	+	0.576264i	$0.804510\pi$
$314$	−7767.78			−1.39605
$315$		0			0
$316$	−9214.13			−1.64030
$317$	3151.70	+	5458.90i	0.558413	+	0.967200i	0.997629	+	0.0688184i	$0.0219229\pi$
$317$	3151.70	+	5458.90i	0.558413	+	0.967200i	−0.439216	+	0.898381i	$0.644744\pi$
$318$		0			0
$319$	1160.05	−	2009.26i	0.203605	−	0.352655i
$320$	−5534.94			−0.966915
$321$		0			0
$322$	−4.55401	−	307.615i	−0.000788153	−	0.0532382i
$323$	6563.23			1.13061
$324$		0			0
$325$	−430.034	−	744.842i	−0.0733970	−	0.127127i
$326$	2573.28			0.437180
$327$		0			0
$328$	−250.219	−	433.391i	−0.0421220	−	0.0729574i
$329$	−140.599	−	9497.21i	−0.0235608	−	1.59148i
$330$		0			0
$331$	2496.78	+	4324.56i	0.414609	+	0.718124i	0.995387	−	0.0959377i	$-0.0305849\pi$
$331$	2496.78	+	4324.56i	0.414609	+	0.718124i	−0.580778	+	0.814062i	$0.697252\pi$
$332$	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	0.934376	−	0.356289i	$-0.115958\pi$
$337$	981.382	+	1699.80i	0.158633	+	0.274760i	−0.775743	+	0.631049i	$0.782625\pi$
$338$	8493.52			1.36682
$339$		0			0
$340$	5424.21			0.865204
$341$	−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
$346$	−1411.54	+	2444.86i	−0.219320	+	0.379874i
$347$	293.074	−	507.619i	0.0453402	−	0.0785315i	−0.842465	−	0.538752i	$-0.818896\pi$
$347$	293.074	−	507.619i	0.0453402	−	0.0785315i	0.887805	+	0.460220i	$0.152229\pi$
$348$		0			0
$349$	−4666.91	+	8083.33i	−0.715800	+	1.23980i	0.246851	+	0.969054i	$0.420604\pi$
$349$	−4666.91	+	8083.33i	−0.715800	+	1.23980i	−0.962650	+	0.270748i	$0.912729\pi$
$350$	−73.7016	−	4978.39i	−0.0112558	−	0.760304i
$351$		0			0
$352$	−1647.89	+	2854.24i	−0.249526	+	0.432191i
$353$	−2846.38			−0.429171			−0.214586	−	0.976705i	$-0.568840\pi$
$353$	−2846.38			−0.429171			−0.214586	+	0.976705i	$0.568840\pi$
$354$		0			0
$355$	1805.45			0.269924
$356$	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
$362$	−3888.59	−	6735.23i	−0.564584	−	0.977889i
$363$		0			0
$364$	−2129.52	−	1187.80i	−0.306640	−	0.171037i
$365$	−2018.81	−	3496.68i	−0.289505	−	0.501437i
$366$		0			0
$367$	1434.55			0.204041			0.102020	−	0.994782i	$-0.467469\pi$
$367$	1434.55			0.204041			0.102020	+	0.994782i	$0.467469\pi$
$368$	−92.1735	−	159.649i	−0.0130567	−	0.0226149i
$369$		0			0
$370$	7265.17			1.02081
$371$	130.784	+	8834.22i	0.0183018	+	1.23625i
$372$		0			0
$373$	−2732.50			−0.379313			−0.189656	−	0.981851i	$-0.560737\pi$
$373$	−2732.50			−0.379313			−0.189656	+	0.981851i	$0.560737\pi$
$374$	1921.63	−	3328.36i	0.265682	−	0.460175i
$375$		0			0
$376$	1906.75	+	3302.59i	0.261524	+	0.452974i
$377$	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	$0.165687\pi$
$380$	−3530.90	−	6115.70i	−0.476662	−	0.825603i
$381$		0			0
$382$	−4641.21	+	8038.80i	−0.621635	+	1.07670i
$383$	9086.56			1.21228			0.606138	−	0.795360i	$-0.292718\pi$
$383$	9086.56			1.21228			0.606138	+	0.795360i	$0.292718\pi$
$384$		0			0
$385$	1625.23	+	906.517i	0.215141	+	0.120001i
$386$	−2911.47			−0.383912
$387$		0			0
$388$	3801.51	+	6584.40i	0.497403	+	0.861527i
$389$	−4459.15			−0.581203			−0.290602	−	0.956844i	$-0.593855\pi$
$389$	−4459.15			−0.581203			−0.290602	+	0.956844i	$0.593855\pi$
$390$		0			0
$391$	139.918	+	242.345i	0.0180971	+	0.0313450i
$392$	−1340.06	−	2170.06i	−0.172662	−	0.279604i
$393$		0			0
$394$	−3273.20	−	5669.34i	−0.418531	−	0.724917i
$395$	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
$401$	−8896.59			−1.10792			−0.553958	−	0.832544i	$-0.686883\pi$
$401$	−8896.59			−1.10792			−0.553958	+	0.832544i	$0.686883\pi$
$402$		0			0
$403$	−3647.71			−0.450882
$404$	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
$409$	1023.95	−	1773.53i	0.123792	−	0.214414i	−0.797468	−	0.603361i	$-0.793828\pi$
$409$	1023.95	−	1773.53i	0.123792	−	0.214414i	0.921260	+	0.388947i	$0.127161\pi$
$410$	−1109.67	+	1922.01i	−0.133666	+	0.231516i
$411$		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
$416$	−3460.33			−0.407829
$417$		0			0
$418$	−5003.56			−0.585484
$419$	1185.50	+	2053.34i	0.138223	+	0.239409i	0.926824	−	0.375496i	$-0.122528\pi$
$419$	1185.50	+	2053.34i	0.138223	+	0.239409i	−0.788601	+	0.614905i	$0.789194\pi$
$420$		0			0
$421$	−5061.24	+	8766.33i	−0.585914	+	1.01483i	0.408847	+	0.912603i	$0.365931\pi$
$421$	−5061.24	+	8766.33i	−0.585914	+	1.01483i	−0.994761	+	0.102230i	$0.967402\pi$
$422$	−8538.25	+	14788.7i	−0.984918	+	1.70593i
$423$		0			0
$424$	−1773.64	−	3072.04i	−0.203150	−	0.351867i
$425$	2264.41	+	3922.08i	0.258448	+	0.447644i
$426$		0			0
$427$	−103.270	−	6975.65i	−0.0117039	−	0.790575i
$428$	10521.7	+	18224.1i	1.18829	+	2.05817i
$429$		0			0
$430$	15684.0			1.75895
$431$	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	$0.435491\pi$
$434$	−18441.8	−	10286.4i	−2.03971	−	1.13771i
$435$		0			0
$436$	2772.69			0.304559
$437$	182.160	−	315.510i	0.0199402	−	0.0345375i
$438$		0			0
$439$	−4789.23	−	8295.20i	−0.520678	−	0.901841i	−0.999711	−	0.0240439i	$-0.992346\pi$
$439$	−4789.23	−	8295.20i	−0.520678	−	0.901841i	0.479033	−	0.877797i	$-0.340987\pi$
$440$	−747.163			−0.0809536
$441$		0			0
$442$	4035.14			0.434236
$443$	−8422.93	−	14588.9i	−0.903353	−	1.56465i	−0.823113	−	0.567878i	$-0.807765\pi$
$443$	−8422.93	−	14588.9i	−0.903353	−	1.56465i	−0.0802401	−	0.996776i	$-0.525569\pi$
$444$		0			0
$445$	1169.44	−	2025.52i	0.124577	−	0.215773i
$446$	−14147.6			−1.50204
$447$		0			0
$448$	−11442.2	−	6382.22i	−1.20668	−	0.673061i
$449$	−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
$452$	4589.75			0.477619
$453$		0			0
$454$	−10858.6	−	18807.6i	−1.12251	−	1.94424i
$455$	28.9223	+	1953.65i	0.00298000	+	0.201293i
$456$		0			0
$457$	5198.19	+	9003.54i	0.532082	+	0.921592i	0.999299	+	0.0374496i	$0.0119234\pi$
$457$	5198.19	+	9003.54i	0.532082	+	0.921592i	−0.467217	+	0.884143i	$0.654743\pi$
$458$	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	−0.947748	−	0.319021i	$-0.896646\pi$
$461$	−1955.80	+	3387.54i	−0.197593	+	0.342241i	0.750154	+	0.661263i	$0.229979\pi$
$462$		0			0
$463$	1630.69	+	2824.43i	0.163681	+	0.283504i	0.936186	−	0.351505i	$-0.114330\pi$
$463$	1630.69	+	2824.43i	0.163681	+	0.283504i	−0.772505	+	0.635009i	$0.780997\pi$
$464$	8449.85			0.845419
$465$		0			0
$466$	−15016.2			−1.49273
$467$	−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
$472$	−2668.22	+	4621.49i	−0.260201	+	0.450681i
$473$	3054.09	−	5289.84i	0.296886	−	0.514222i
$474$		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
$479$	638.794			0.0609337			0.0304669	−	0.999536i	$-0.490301\pi$
$479$	638.794			0.0609337			0.0304669	+	0.999536i	$0.490301\pi$
$480$		0			0
$481$	2970.70			0.281606
$482$	−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	$0.915739\pi$
$488$	1400.50	+	2425.73i	0.129913	+	0.225016i
$489$		0			0
$490$	−5363.00	+	9958.65i	−0.494440	+	0.918134i
$491$	442.623	+	766.646i	0.0406829	+	0.0704649i	0.885650	−	0.464354i	$-0.153713\pi$
$491$	442.623	+	766.646i	0.0406829	+	0.0704649i	−0.844967	+	0.534819i	$0.820380\pi$
$492$		0			0
$493$	−12826.7			−1.17178
$494$	−2626.68	−	4549.55i	−0.239231	−	0.414360i
$495$		0			0
$496$	−12653.4			−1.14547
$497$	3732.34	+	2081.82i	0.336858	+	0.187892i
$498$		0			0
$499$	−486.372			−0.0436333			−0.0218166	−	0.999762i	$-0.506945\pi$
$499$	−486.372			−0.0436333			−0.0218166	+	0.999762i	$0.506945\pi$
$500$	7211.15	−	12490.1i	0.644985	−	1.11715i
$501$		0			0
$502$	13217.8	+	22893.8i	1.17517	+	2.03546i
$503$	−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
$506$	−106.668	−	184.755i	−0.00937151	−	0.0162319i
$507$		0			0
$508$	1127.95	−	1953.66i	0.0985131	−	0.170630i
$509$	−15024.6			−1.30835			−0.654177	−	0.756342i	$-0.726985\pi$
$509$	−15024.6			−1.30835			−0.654177	+	0.756342i	$0.726985\pi$
$510$		0			0
$511$	−141.476	−	9556.41i	−0.0122476	−	0.827301i
$512$	−14785.8			−1.27626
$513$		0			0
$514$	−4633.12	−	8024.79i	−0.397584	−	0.688635i
$515$	1301.10			0.111327
$516$		0			0
$517$	−3293.25	−	5704.08i	−0.280149	−	0.485232i
$518$	15019.0	+	8377.30i	1.27394	+	0.710574i
$519$		0			0
$520$	−392.233	−	679.367i	−0.0330780	−	0.0572927i
$521$	−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
$527$	19207.6			1.58766
$528$		0			0
$529$	−12151.5			−0.998723
$530$	−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
$535$	8430.99	−	14602.9i	0.681315	−	1.18007i
$536$	2581.56	−	4471.40i	0.208035	−	0.360327i
$537$		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	$0.778999\pi$
$542$	14166.2			1.12268
$543$		0			0
$544$	18220.9			1.43606
$545$	−1110.87	−	1924.08i	−0.0873109	−	0.151227i
$546$		0			0
$547$	8677.56	−	15030.0i	0.678292	−	1.17484i	−0.297203	−	0.954814i	$-0.596054\pi$
$547$	8677.56	−	15030.0i	0.678292	−	1.17484i	0.975495	−	0.220022i	$-0.0706128\pi$
$548$	6388.95	−	11066.0i	0.498034	−	0.862620i
$549$		0			0
$550$	−1726.31	−	2990.05i	−0.133836	−	0.231811i
$551$	8349.59	+	14461.9i	0.645562	+	1.11815i
$552$		0			0
$553$	258.704	+	17475.0i	0.0198937	+	1.34378i
$554$	8160.88	+	14135.1i	0.625853	+	1.08401i
$555$		0			0
$556$	30280.4			2.30967
$557$	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
$560$	100.327	+	6776.90i	0.00757071	+	0.511386i
$561$		0			0
$562$	26628.2			1.99865
$563$	−3014.56	+	5221.37i	−0.225663	+	0.390861i	−0.956518	−	0.291672i	$-0.905788\pi$
$563$	−3014.56	+	5221.37i	−0.225663	+	0.390861i	0.730855	+	0.682533i	$0.239122\pi$
$564$		0			0
$565$	−1838.87	−	3185.02i	−0.136924	−	0.237159i
$566$	−16223.7			−1.20483
$567$		0			0
$568$	−1715.86			−0.126753
$569$	−1381.13	−	2392.18i	−0.101757	−	0.176249i	0.810652	−	0.585529i	$-0.199113\pi$
$569$	−1381.13	−	2392.18i	−0.101757	−	0.176249i	−0.912409	+	0.409280i	$0.865780\pi$
$570$		0			0
$571$	−838.416	+	1452.18i	−0.0614477	+	0.106431i	−0.895113	−	0.445840i	$-0.852905\pi$
$571$	−838.416	+	1452.18i	−0.0614477	+	0.106431i	0.833665	+	0.552270i	$0.186238\pi$
$572$	−1690.88			−0.123600
$573$		0			0
$574$	−4510.22	+	2693.77i	−0.327967	+	0.195881i
$575$	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	$0.790400\pi$
$578$	−540.545			−0.0388991
$579$		0			0
$580$	6900.57	+	11952.1i	0.494018	+	0.855665i
$581$	2686.86	−	1604.75i	0.191859	−	0.114589i
$582$		0			0
$583$	3063.35	+	5305.88i	0.217618	+	0.376925i
$584$	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	−0.958513	−	0.285047i	$-0.907991\pi$
$587$	−3305.15	+	5724.68i	−0.232399	+	0.402526i	0.726115	+	0.687573i	$0.241324\pi$
$588$		0			0
$589$	−12503.2	−	21656.2i	−0.874680	−	1.51499i
$590$	23666.1			1.65139
$591$		0			0
$592$	10304.9			0.715422
$593$	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
$598$	111.994	−	193.979i	0.00765847	−	0.0132649i
$599$	6828.02	−	11826.5i	0.465752	−	0.806706i	−0.533483	−	0.845811i	$-0.679117\pi$
$599$	6828.02	−	11826.5i	0.465752	−	0.806706i	0.999235	+	0.0391047i	$0.0124506\pi$
$600$		0			0
$601$	−3519.77	+	6096.42i	−0.238893	+	0.413774i	−0.960397	−	0.278636i	$-0.910118\pi$
$601$	−3519.77	+	6096.42i	−0.238893	+	0.413774i	0.721504	+	0.692410i	$0.243451\pi$
$602$	32423.0	+	18084.8i	2.19512	+	1.22439i
$603$		0			0
$604$	−9719.27	+	16834.3i	−0.654754	+	1.13407i
$605$	−9123.31			−0.613083
$606$		0			0
$607$	−16957.8			−1.13393			−0.566964	−	0.823743i	$-0.691882\pi$
$607$	−16957.8			−1.13393			−0.566964	+	0.823743i	$0.691882\pi$
$608$	−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	$-0.384950\pi$
$614$	13823.1	+	23942.2i	0.908555	+	1.57366i
$615$		0			0
$616$	−1544.58	−	861.536i	−0.101028	−	0.0563511i
$617$	−279.127	−	483.463i	−0.0182127	−	0.0315454i	0.856775	−	0.515690i	$-0.172464\pi$
$617$	−279.127	−	483.463i	−0.0182127	−	0.0315454i	−0.874988	+	0.484144i	$0.839131\pi$
$618$		0			0
$619$	−7895.95			−0.512706			−0.256353	−	0.966583i	$-0.582521\pi$
$619$	−7895.95			−0.512706			−0.256353	+	0.966583i	$0.582521\pi$
$620$	−10333.4	−	17897.9i	−0.669352	−	1.15935i
$621$		0			0
$622$	−34784.5			−2.24233
$623$	4753.12	−	2838.84i	0.305665	−	0.182562i
$624$		0			0
$625$	−3583.42			−0.229339
$626$	−2110.52	+	3655.53i	−0.134750	+	0.233394i
$627$		0			0
$628$	−8997.70	−	15584.5i	−0.571731	−	0.990268i
$629$	−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	$0.492880\pi$
$632$	−3508.44	−	6076.79i	−0.220820	−	0.382471i
$633$		0			0
$634$	−13283.7	+	23008.0i	−0.832116	+	1.44127i
$635$	−1807.64			−0.112967
$636$		0			0
$637$	−2192.91	+	4072.06i	−0.136399	+	0.253282i
$638$	9778.64			0.606802
$639$		0			0
$640$	−3632.84	−	6292.26i	−0.224376	−	0.388630i
$641$	−6522.45			−0.401906			−0.200953	−	0.979601i	$-0.564404\pi$
$641$	−6522.45			−0.401906			−0.200953	+	0.979601i	$0.564404\pi$
$642$		0			0
$643$	5565.74	+	9640.15i	0.341355	+	0.591245i	0.984685	−	0.174345i	$-0.0557807\pi$
$643$	5565.74	+	9640.15i	0.341355	+	0.591245i	−0.643329	+	0.765590i	$0.722447\pi$
$644$	611.891	−	365.458i	0.0374408	−	0.0223619i
$645$		0			0
$646$	13831.2	+	23956.4i	0.842387	+	1.45906i
$647$	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
$653$	−1180.60			−0.0707513			−0.0353756	−	0.999374i	$-0.511263\pi$
$653$	−1180.60			−0.0707513			−0.0353756	+	0.999374i	$0.511263\pi$
$654$		0			0
$655$	−13303.0			−0.793573
$656$	−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	−0.721584	−	0.692327i	$-0.756586\pi$
$659$	4039.50	−	6996.61i	0.238781	−	0.413580i	0.960365	+	0.278747i	$0.0899190\pi$
$660$		0			0
$661$	572.620	−	991.806i	0.0336949	−	0.0583613i	−0.848686	−	0.528897i	$-0.822606\pi$
$661$	572.620	−	991.806i	0.0336949	−	0.0583613i	0.882381	+	0.470535i	$0.155939\pi$
$662$	−10523.4	+	18227.0i	−0.617827	+	1.07011i
$663$		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
$668$	−22201.9			−1.28595
$669$		0			0
$670$	−22897.5			−1.32031
$671$	−2418.87	−	4189.61i	−0.139165	−	0.241041i
$672$		0			0
$673$	10900.3	−	18879.9i	0.624333	−	1.08138i	−0.364337	−	0.931267i	$-0.618704\pi$
$673$	10900.3	−	18879.9i	0.624333	−	1.08138i	0.988669	−	0.150109i	$-0.0479625\pi$
$674$	−4136.29	+	7164.27i	−0.236386	+	0.409432i
$675$		0			0
$676$	9838.35	+	17040.5i	0.559761	+	0.969534i
$677$	−9616.42	−	16656.1i	−0.545922	−	0.945565i	−0.998548	−	0.0538643i	$-0.982846\pi$
$677$	−9616.42	−	16656.1i	−0.545922	−	0.945565i	0.452626	−	0.891700i	$-0.350487\pi$
$678$		0			0
$679$	12380.8	−	7394.57i	0.699754	−	0.417935i
$680$	2065.36	+	3577.31i	0.116475	+	0.201741i
$681$		0			0
$682$	−14643.2			−0.822164
$683$	−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
$686$	−22569.8	+	14403.2i	−1.25615	+	0.801629i
$687$		0			0
$688$	22246.2			1.23274
$689$	−3216.29	+	5570.78i	−0.177839	+	0.308026i
$690$		0			0
$691$	1944.45	+	3367.88i	0.107048	+	0.185413i	0.914573	−	0.404420i	$-0.132527\pi$
$691$	1944.45	+	3367.88i	0.107048	+	0.185413i	−0.807525	+	0.589833i	$0.799193\pi$
$692$	−6540.15			−0.359276
$693$		0			0
$694$	2470.48			0.135127
$695$	−12131.8	−	21012.8i	−0.662136	−	1.14685i
$696$		0			0
$697$	2389.25	−	4138.30i	0.129841	−	0.224891i
$698$	−39339.9			−2.13329
$699$		0			0
$700$	9902.77	−	5914.52i	0.534699	−	0.319354i
$701$	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
$704$	−9085.34			−0.486387
$705$		0			0
$706$	−5998.41	−	10389.5i	−0.319763	−	0.553846i
$707$	−3891.78	−	2170.75i	−0.207024	−	0.115473i
$708$		0			0
$709$	−3372.01	−	5840.49i	−0.178616	−	0.309371i	0.762791	−	0.646645i	$-0.223829\pi$
$709$	−3372.01	−	5840.49i	−0.178616	−	0.309371i	−0.941407	+	0.337274i	$0.890495\pi$
$710$	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
$716$	−21706.4			−1.13297
$717$		0			0
$718$	−26736.2			−1.38967
$719$	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
$724$	9008.58	−	15603.3i	0.462433	−	0.800957i
$725$	−5761.48	+	9979.17i	−0.295139	+	0.511196i
$726$		0			0
$727$	13189.8	−	22845.5i	0.672880	−	1.16546i	−0.304203	−	0.952607i	$-0.598390\pi$
$727$	13189.8	−	22845.5i	0.672880	−	1.16546i	0.977084	−	0.212856i	$-0.0682765\pi$
$728$	−27.4872	−	1856.71i	−0.00139937	−	0.0945249i
$729$		0			0
$730$	8508.80	−	14737.7i	0.431404	−	0.747214i
$731$	−33769.3			−1.70862
$732$		0			0
$733$	−1943.26			−0.0979207			−0.0489604	−	0.998801i	$-0.515591\pi$
$733$	−1943.26			−0.0979207			−0.0489604	+	0.998801i	$0.515591\pi$
$734$	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	$0.402624\pi$
$740$	8415.51	+	14576.1i	0.418055	+	0.724092i
$741$		0			0
$742$	−31970.1	+	19094.5i	−1.58175	+	0.944716i
$743$	9461.21	+	16387.3i	0.467158	+	0.809141i	0.999296	−	0.0375164i	$-0.0119447\pi$
$743$	9461.21	+	16387.3i	0.467158	+	0.809141i	−0.532138	+	0.846658i	$0.678611\pi$
$744$		0			0
$745$	−8553.16			−0.420622
$746$	−5758.42	−	9973.88i	−0.282615	−	0.489504i
$747$		0			0
$748$	8903.59			0.435224
$749$	34267.4	−	20466.5i	1.67170	−	0.998438i
$750$		0			0
$751$	−26380.5			−1.28181			−0.640903	−	0.767622i	$-0.721440\pi$
$751$	−26380.5			−1.28181			−0.640903	+	0.767622i	$0.721440\pi$
$752$	11994.1	−	20774.4i	0.581623	−	1.00740i
$753$		0			0
$754$	5133.42	+	8891.35i	0.247942	+	0.429448i
$755$	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	$0.330162\pi$
$758$	26979.4	+	46729.6i	1.29279	+	2.23918i
$759$		0			0
$760$	2688.90	−	4657.32i	0.128338	−	0.222288i
$761$	−28522.7			−1.35867			−0.679335	−	0.733829i	$-0.737731\pi$
$761$	−28522.7			−1.35867			−0.679335	+	0.733829i	$0.737731\pi$
$762$		0			0
$763$	−77.8485	−	5258.51i	−0.00369371	−	0.249503i
$764$	−21504.3			−1.01832
$765$		0			0
$766$	19148.9	+	33166.8i	0.903233	+	1.56444i
$767$	9677.00			0.455562
$768$		0			0
$769$	20000.8	+	34642.4i	0.937903	+	1.62450i	0.769373	+	0.638799i	$0.220569\pi$
$769$	20000.8	+	34642.4i	0.937903	+	1.62450i	0.168530	+	0.985697i	$0.446098\pi$
$770$	116.104	+	7842.61i	0.00543390	+	0.367049i
$771$		0			0
$772$	−3372.46	−	5841.28i	−0.157225	−	0.272322i
$773$	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
$779$	−6221.15			−0.286131
$780$		0			0
$781$	2963.55			0.135780
$782$	−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
$787$	−7125.05	+	12341.0i	−0.322720	+	0.558968i	−0.981048	−	0.193763i	$-0.937931\pi$
$787$	−7125.05	+	12341.0i	−0.322720	+	0.558968i	0.658328	+	0.752731i	$0.271264\pi$
$788$	7582.93	−	13134.0i	0.342805	−	0.593756i
$789$		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
$794$	−167.282			−0.00747685
$795$		0			0
$796$	−6025.27			−0.268292
$797$	16294.3	+	28222.5i	0.724181	+	1.25432i	0.959310	+	0.282354i	$0.0911154\pi$
$797$	16294.3	+	28222.5i	0.724181	+	1.25432i	−0.235129	+	0.971964i	$0.575551\pi$
$798$		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
$803$	−3313.78	−	5739.63i	−0.145630	−	0.252238i
$804$		0			0
$805$	−498.759	−	278.197i	−0.0218372	−	0.0121803i
$806$	−7687.12	−	13314.5i	−0.335940	−	0.581865i
$807$		0			0
$808$	1789.16			0.0778991
$809$	−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	$0.592716\pi$
$812$	483.584	+	32665.1i	0.0208996	+	1.41173i
$813$		0			0
$814$	11925.4			0.513496
$815$	2388.43	−	4136.89i	0.102654	−	0.177802i
$816$		0			0
$817$	21982.2	+	38074.3i	0.941323	+	1.63042i
$818$	8631.39			0.368936
$819$		0			0
$820$	−5141.50			−0.218962
$821$	8004.17	+	13863.6i	0.340253	+	0.589335i	0.984480	−	0.175499i	$-0.0561540\pi$
$821$	8004.17	+	13863.6i	0.340253	+	0.589335i	−0.644227	+	0.764835i	$0.722821\pi$
$822$		0			0
$823$	15315.5	−	26527.2i	0.648680	−	1.12355i	−0.334759	−	0.942304i	$-0.608655\pi$
$823$	15315.5	−	26527.2i	0.648680	−	1.12355i	0.983438	−	0.181242i	$-0.0580119\pi$
$824$	−1236.54			−0.0522778
$825$		0			0
$826$	48924.2	+	27288.9i	2.06089	+	1.14952i
$827$	−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	$0.816989\pi$
$830$	5572.45			0.233039
$831$		0			0
$832$	−4769.47	−	8260.96i	−0.198740	−	0.344227i
$833$	11547.1	−	21442.1i	0.480293	−	0.891865i
$834$		0			0
$835$	8895.13	+	15406.8i	0.368657	+	0.638532i
$836$	−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	−0.651425	−	0.758713i	$-0.725829\pi$
$839$	8052.53	−	13947.4i	0.331352	−	0.573918i	0.982777	+	0.184794i	$0.0591619\pi$
$840$		0			0
$841$	−4123.40	−	7141.94i	−0.169068	−	0.292835i
$842$	−42663.9			−1.74619
$843$		0			0
$844$	−39560.7			−1.61343
$845$	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
$850$	−9543.97	+	16530.6i	−0.385124	+	0.667054i
$851$	−434.157	+	751.983i	−0.0174885	+	0.0302910i
$852$		0			0
$853$	18952.1	−	32826.1i	0.760737	−	1.31764i	−0.181734	−	0.983348i	$-0.558171\pi$
$853$	18952.1	−	32826.1i	0.760737	−	1.31764i	0.942471	−	0.334288i	$-0.108496\pi$
$854$	25244.1	−	15077.3i	1.01152	−	0.604139i
$855$		0			0
$856$	−8012.64	+	13878.3i	−0.319937	+	0.554148i
$857$	31991.8			1.27517			0.637585	−	0.770380i	$-0.279934\pi$
$857$	31991.8			1.27517			0.637585	+	0.770380i	$0.279934\pi$
$858$		0			0
$859$	26825.6			1.06552			0.532758	−	0.846268i	$-0.321156\pi$
$859$	26825.6			1.06552			0.532758	+	0.846268i	$0.321156\pi$
$860$	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
$866$	7643.62	+	13239.1i	0.299932	+	0.519497i
$867$		0			0
$868$	−724.150	−	48914.9i	−0.0283171	−	1.91277i
$869$	6059.61	+	10495.6i	0.236546	+	0.409709i
$870$		0			0
$871$	−9362.72			−0.364229
$872$	1055.75	+	1828.61i	0.0410002	+	0.0710144i
$873$		0			0
$874$	1535.52			0.0594276
$875$	−23890.4	−	13325.5i	−0.923020	−	0.514841i
$876$		0			0
$877$	−42453.1			−1.63460			−0.817298	−	0.576216i	$-0.804529\pi$
$877$	−42453.1			−1.63460			−0.817298	+	0.576216i	$0.804529\pi$
$878$	20185.5	−	34962.3i	0.775885	−	1.34387i
$879$		0			0
$880$	2349.96	+	4070.24i	0.0900193	+	0.155918i
$881$	−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	$0.567157\pi$
$884$	4674.05	+	8095.69i	0.177834	+	0.308018i
$885$		0			0
$886$	35500.6	−	61488.9i	1.34613	−	2.33156i
$887$	21316.4			0.806916			0.403458	−	0.914998i	$-0.367808\pi$
$887$	21316.4			0.806916			0.403458	+	0.914998i	$0.367808\pi$
$888$		0			0
$889$	−3736.87	−	2084.35i	−0.140979	−	0.0786352i
$890$	9857.79			0.371274
$891$		0			0
$892$	−16387.7	−	28384.3i	−0.615135	−	1.06544i
$893$	47407.3			1.77651
$894$		0			0
$895$	8696.61	+	15063.0i	0.324800	+	0.562569i
$896$	−254.585	−	17196.7i	−0.00949229	−	0.641186i
$897$		0			0
$898$	−35483.5	−	61459.3i	−1.31860	−	2.28388i
$899$	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
$905$	−14437.0			−0.530280
$906$		0			0
$907$	15117.8			0.553450			0.276725	−	0.960949i	$-0.410751\pi$
$907$	15117.8			0.553450			0.276725	+	0.960949i	$0.410751\pi$
$908$	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	−0.693131	−	0.720812i	$-0.743769\pi$
$911$	7635.12	−	13224.4i	0.277676	−	0.480949i	0.970807	+	0.239863i	$0.0771025\pi$
$912$		0			0
$913$	1085.10	−	1879.45i	0.0393337	−	0.0681280i
$914$	−21909.2	+	37947.8i	−0.792878	+	1.37330i
$915$		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	$0.133203\pi$
$920$	229.293			0.00821693
$921$		0			0
$922$	−16486.4			−0.588885
$923$	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
$929$	21273.7	+	36847.0i	0.751309	+	1.30131i	0.947189	+	0.320677i	$0.103910\pi$
$929$	21273.7	+	36847.0i	0.751309	+	1.30131i	−0.195880	+	0.980628i	$0.562756\pi$
$930$		0			0
$931$	−31692.2	+	938.565i	−1.11565	+	0.0330400i
$932$	−17393.9	−	30127.0i	−0.611325	−	1.05885i
$933$		0			0
$934$	−16820.0			−0.589259
$935$	−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	$0.454692\pi$
$938$	−47335.3	−	26402.6i	−1.64771	−	0.919057i
$939$		0			0
$940$	39180.0			1.35948
$941$	4523.59	−	7835.09i	0.156711	−	0.271431i	−0.776970	−	0.629538i	$-0.783244\pi$
$941$	4523.59	−	7835.09i	0.156711	−	0.271431i	0.933681	+	0.358107i	$0.116578\pi$
$942$		0			0
$943$	−132.625	−	229.714i	−0.00457993	−	0.00793267i
$944$	33568.0			1.15736
$945$		0			0
$946$	25744.5			0.884806
$947$	−2683.02	−	4647.12i	−0.0920658	−	0.159463i	0.816314	−	0.577608i	$-0.196014\pi$
$947$	−2683.02	−	4647.12i	−0.0920658	−	0.159463i	−0.908380	+	0.418145i	$0.862680\pi$
$948$		0			0
$949$	3479.22	−	6026.19i	0.119010	−	0.206131i
$950$	24850.7			0.848697
$951$		0			0
$952$	144.738	+	9776.78i	0.00492751	+	0.332844i
$953$	−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
$956$	60957.0			2.06223
$957$		0			0
$958$	1346.18	+	2331.66i	0.0454000	+	0.0786351i
$959$	−21166.5	−	11806.2i	−0.712722	−	0.397541i
$960$		0			0
$961$	−21695.8	−	37578.3i	−0.728268	−	1.26140i
$962$	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	0.858894	+	0.512153i	$0.171152\pi$
$967$	26251.0	+	45468.1i	0.872985	+	1.51205i	0.0140902	+	0.999901i	$0.495515\pi$
$968$	8670.61			0.287897
$969$		0			0
$970$	25677.4			0.849950
$971$	−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
$976$	8809.62	−	15258.7i	0.288923	−	0.500430i
$977$	6879.13	−	11915.0i	0.225264	−	0.390169i	−0.731135	−	0.682233i	$-0.761009\pi$
$977$	6879.13	−	11915.0i	0.225264	−	0.390169i	0.956399	+	0.292065i	$0.0943422\pi$
$978$		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
$983$	−4831.35			−0.156761			−0.0783806	−	0.996924i	$-0.524975\pi$
$983$	−4831.35			−0.156761			−0.0783806	+	0.996924i	$0.524975\pi$
$984$		0			0
$985$	−12152.3			−0.393101
$986$	−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	$-0.520392\pi$
$992$	−34711.7	−	60122.4i	−1.11098	−	1.92428i
$993$		0			0
$994$	266.633	+	18010.6i	0.00850815	+	0.574708i
$995$	2414.01	+	4181.19i	0.0769138	+	0.133219i
$996$		0			0
$997$	18274.5			0.580500			0.290250	−	0.956951i	$-0.406261\pi$
$997$	18274.5			0.580500			0.290250	+	0.956951i	$0.406261\pi$
$998$	−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.g.a.100.20		44
3.2	odd	2		63.4.g.a.16.3	yes	44
7.4	even	3		189.4.h.a.46.3		44
9.4	even	3		189.4.h.a.37.3		44
9.5	odd	6		63.4.h.a.58.20	yes	44
21.11	odd	6		63.4.h.a.25.20	yes	44
63.4	even	3	inner	189.4.g.a.172.20		44
63.32	odd	6		63.4.g.a.4.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.3	✓	44	63.32	odd	6
63.4.g.a.16.3	yes	44	3.2	odd	2
63.4.h.a.25.20	yes	44	21.11	odd	6
63.4.h.a.58.20	yes	44	9.5	odd	6
189.4.g.a.100.20		44	1.1	even	1	trivial
189.4.g.a.172.20		44	63.4	even	3	inner
189.4.h.a.37.3		44	9.4	even	3
189.4.h.a.46.3		44	7.4	even	3

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10738 + 3.65009i) q^{2} +(-4.88211 + 8.45607i) q^{4} +7.82402 q^{5} +(16.1743 + 9.02169i) q^{7} -7.43579 q^{8} +O(q^{10})\)	\(q+(2.10738 + 3.65009i) q^{2} +(-4.88211 + 8.45607i) q^{4} +7.82402 q^{5} +(16.1743 + 9.02169i) q^{7} -7.43579 q^{8} +(16.4882 + 28.5584i) q^{10} +12.8427 q^{11} +(6.74197 + 11.6774i) q^{13} +(1.15547 + 78.0499i) q^{14} +(23.3869 + 40.5072i) q^{16} +(-35.5009 - 61.4893i) q^{17} +(-46.2187 + 80.0532i) q^{19} +(-38.1977 + 66.1604i) q^{20} +(27.0646 + 46.8772i) q^{22} -3.94125 q^{23} -63.7847 q^{25} +(-28.4158 + 49.2176i) q^{26} +(-155.253 + 92.7263i) q^{28} +(90.3269 - 156.451i) q^{29} +(-135.261 + 234.280i) q^{31} +(-128.313 + 222.245i) q^{32} +(149.628 - 259.163i) q^{34} +(126.548 + 70.5859i) q^{35} +(110.157 - 190.798i) q^{37} -389.602 q^{38} -58.1778 q^{40} +(33.6506 + 58.2845i) q^{41} +(237.806 - 411.893i) q^{43} +(-62.6997 + 108.599i) q^{44} +(-8.30572 - 14.3859i) q^{46} +(-256.429 - 444.148i) q^{47} +(180.218 + 291.840i) q^{49} +(-134.419 - 232.820i) q^{50} -131.660 q^{52} +(238.528 + 413.142i) q^{53} +100.482 q^{55} +(-120.269 - 67.0835i) q^{56} +761.413 q^{58} +(358.835 - 621.520i) q^{59} +(-188.346 - 326.224i) q^{61} -1140.19 q^{62} -707.430 q^{64} +(52.7493 + 91.3644i) q^{65} +(-347.181 + 601.335i) q^{67} +693.277 q^{68} +(9.04045 + 610.664i) q^{70} +230.757 q^{71} +(-258.027 - 446.916i) q^{73} +928.573 q^{74} +(-451.290 - 781.658i) q^{76} +(207.723 + 115.863i) q^{77} +(471.831 + 817.236i) q^{79} +(182.979 + 316.929i) q^{80} +(-141.829 + 245.655i) q^{82} +(84.4915 - 146.344i) q^{83} +(-277.760 - 481.094i) q^{85} +2004.60 q^{86} -95.4960 q^{88} +(149.467 - 258.885i) q^{89} +(3.69661 + 249.699i) q^{91} +(19.2416 - 33.3275i) q^{92} +(1080.79 - 1871.98i) q^{94} +(-361.616 + 626.338i) q^{95} +(389.330 - 674.339i) q^{97} +(-685.454 + 1272.83i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

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