LMFDB - Embedded newform 189.4.g.a.100.6

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			100.6
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46729 - 2.54141i) q^{2} +(-0.305860 + 0.529765i) q^{4} +3.69711 q^{5} +(12.3500 + 13.8013i) q^{7} -21.6814 q^{8} +O(q^{10})$	\(q+(-1.46729 - 2.54141i) q^{2} +(-0.305860 + 0.529765i) q^{4} +3.69711 q^{5} +(12.3500 + 13.8013i) q^{7} -21.6814 q^{8} +(-5.42471 - 9.39588i) q^{10} +65.7074 q^{11} +(2.73952 + 4.74498i) q^{13} +(16.9539 - 51.6370i) q^{14} +(34.2598 + 59.3397i) q^{16} +(25.1343 + 43.5340i) q^{17} +(0.769884 - 1.33348i) q^{19} +(-1.13080 + 1.95860i) q^{20} +(-96.4115 - 166.990i) q^{22} +120.016 q^{23} -111.331 q^{25} +(8.03931 - 13.9245i) q^{26} +(-11.0888 + 2.32133i) q^{28} +(39.2967 - 68.0640i) q^{29} +(151.666 - 262.693i) q^{31} +(13.8120 - 23.9231i) q^{32} +(73.7586 - 127.754i) q^{34} +(45.6593 + 51.0250i) q^{35} +(96.6335 - 167.374i) q^{37} -4.51856 q^{38} -80.1586 q^{40} +(-196.671 - 340.645i) q^{41} +(-138.067 + 239.139i) q^{43} +(-20.0972 + 34.8095i) q^{44} +(-176.097 - 305.009i) q^{46} +(-126.380 - 218.896i) q^{47} +(-37.9542 + 340.894i) q^{49} +(163.355 + 282.939i) q^{50} -3.35163 q^{52} +(204.244 + 353.761i) q^{53} +242.927 q^{55} +(-267.766 - 299.233i) q^{56} -230.638 q^{58} +(131.415 - 227.618i) q^{59} +(56.1270 + 97.2148i) q^{61} -890.149 q^{62} +467.092 q^{64} +(10.1283 + 17.5427i) q^{65} +(49.1343 - 85.1031i) q^{67} -30.7503 q^{68} +(62.6805 - 190.908i) q^{70} +255.003 q^{71} +(344.146 + 596.078i) q^{73} -567.156 q^{74} +(0.470953 + 0.815715i) q^{76} +(811.487 + 906.850i) q^{77} +(542.222 + 939.155i) q^{79} +(126.662 + 219.385i) q^{80} +(-577.146 + 999.647i) q^{82} +(-152.083 + 263.415i) q^{83} +(92.9243 + 160.950i) q^{85} +810.335 q^{86} -1424.63 q^{88} +(-550.553 + 953.585i) q^{89} +(-31.6540 + 96.4096i) q^{91} +(-36.7079 + 63.5800i) q^{92} +(-370.871 + 642.368i) q^{94} +(2.84634 - 4.93001i) q^{95} +(493.784 - 855.260i) q^{97} +(922.042 - 403.731i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.46729	−	2.54141i	−0.518764	−	0.898526i	−0.999762	−	0.0218042i	$-0.993059\pi$
$2$	−1.46729	−	2.54141i	−0.518764	−	0.898526i	0.480998	−	0.876722i	$-0.340274\pi$
$3$		0			0
$3$		0			0
$4$	−0.305860	+	0.529765i	−0.0382325	+	0.0662206i
$5$	3.69711			0.330679			0.165340	−	0.986237i	$-0.447128\pi$
$5$	3.69711			0.330679			0.165340	+	0.986237i	$0.447128\pi$
$6$		0			0
$7$	12.3500	+	13.8013i	0.666838	+	0.745203i
$7$	12.3500	+	13.8013i	0.666838	+	0.745203i
$8$	−21.6814			−0.958194
$9$		0			0
$10$	−5.42471	−	9.39588i	−0.171545	−	0.297124i
$11$	65.7074			1.80105			0.900524	−	0.434807i	$-0.143184\pi$
$11$	65.7074			1.80105			0.900524	+	0.434807i	$0.143184\pi$
$12$		0			0
$13$	2.73952	+	4.74498i	0.0584465	+	0.101232i	0.893768	−	0.448529i	$-0.148052\pi$
$13$	2.73952	+	4.74498i	0.0584465	+	0.101232i	−0.835322	+	0.549761i	$0.814719\pi$
$14$	16.9539	−	51.6370i	0.323652	−	0.985756i
$15$		0			0
$16$	34.2598	+	59.3397i	0.535309	+	0.927182i
$17$	25.1343	+	43.5340i	0.358587	+	0.621090i	0.987725	−	0.156203i	$-0.0499254\pi$
$17$	25.1343	+	43.5340i	0.358587	+	0.621090i	−0.629138	+	0.777293i	$0.716592\pi$
$18$		0			0
$19$	0.769884	−	1.33348i	0.00929597	−	0.0161011i	−0.861340	−	0.508029i	$-0.830374\pi$
$19$	0.769884	−	1.33348i	0.00929597	−	0.0161011i	0.870636	+	0.491928i	$0.163708\pi$
$20$	−1.13080	+	1.95860i	−0.0126427	+	0.0218978i
$21$		0			0
$22$	−96.4115	−	166.990i	−0.934319	−	1.61829i
$23$	120.016			1.08804			0.544021	−	0.839072i	$-0.316901\pi$
$23$	120.016			1.08804			0.544021	+	0.839072i	$0.316901\pi$
$24$		0			0
$25$	−111.331			−0.890651
$26$	8.03931	−	13.9245i	0.0606399	−	0.105031i
$27$		0			0
$28$	−11.0888	+	2.32133i	−0.0748426	+	0.0156675i
$29$	39.2967	−	68.0640i	0.251628	−	0.435833i	−0.712346	−	0.701829i	$-0.752367\pi$
$29$	39.2967	−	68.0640i	0.251628	−	0.435833i	0.963974	+	0.265995i	$0.0857006\pi$
$30$		0			0
$31$	151.666	−	262.693i	0.878709	−	1.52197i	0.0259506	−	0.999663i	$-0.491739\pi$
$31$	151.666	−	262.693i	0.878709	−	1.52197i	0.852758	−	0.522305i	$-0.174928\pi$
$32$	13.8120	−	23.9231i	0.0763014	−	0.132158i
$33$		0			0
$34$	73.7586	−	127.754i	0.372044	−	0.644399i
$35$	45.6593	+	51.0250i	0.220510	+	0.246423i
$36$		0			0
$37$	96.6335	−	167.374i	0.429363	−	0.743679i	−0.567453	−	0.823406i	$-0.692071\pi$
$37$	96.6335	−	167.374i	0.429363	−	0.743679i	0.996817	+	0.0797263i	$0.0254046\pi$
$38$	−4.51856			−0.0192897
$39$		0			0
$40$	−80.1586			−0.316855
$41$	−196.671	−	340.645i	−0.749144	−	1.29756i	−0.948233	−	0.317574i	$-0.897132\pi$
$41$	−196.671	−	340.645i	−0.749144	−	1.29756i	0.199090	−	0.979981i	$-0.436202\pi$
$42$		0			0
$43$	−138.067	+	239.139i	−0.489651	+	0.848101i	−0.999929	−	0.0119087i	$-0.996209\pi$
$43$	−138.067	+	239.139i	−0.489651	+	0.848101i	0.510278	+	0.860010i	$0.329543\pi$
$44$	−20.0972	+	34.8095i	−0.0688585	+	0.119266i
$45$		0			0
$46$	−176.097	−	305.009i	−0.564437	−	0.977634i
$47$	−126.380	−	218.896i	−0.392221	−	0.679348i	0.600521	−	0.799609i	$-0.294960\pi$
$47$	−126.380	−	218.896i	−0.392221	−	0.679348i	−0.992742	+	0.120262i	$0.961627\pi$
$48$		0			0
$49$	−37.9542	+	340.894i	−0.110654	+	0.993859i
$50$	163.355	+	282.939i	0.462038	+	0.800273i
$51$		0			0
$52$	−3.35163			−0.00893822
$53$	204.244	+	353.761i	0.529341	+	0.916845i	0.999414	+	0.0342180i	$0.0108940\pi$
$53$	204.244	+	353.761i	0.529341	+	0.916845i	−0.470074	+	0.882627i	$0.655773\pi$
$54$		0			0
$55$	242.927			0.595569
$56$	−267.766	−	299.233i	−0.638960	−	0.714048i
$57$		0			0
$58$	−230.638			−0.522143
$59$	131.415	−	227.618i	0.289980	−	0.502259i	−0.683825	−	0.729646i	$-0.739685\pi$
$59$	131.415	−	227.618i	0.289980	−	0.502259i	0.973805	+	0.227387i	$0.0730182\pi$
$60$		0			0
$61$	56.1270	+	97.2148i	0.117809	+	0.204050i	0.918899	−	0.394493i	$-0.129080\pi$
$61$	56.1270	+	97.2148i	0.117809	+	0.204050i	−0.801090	+	0.598543i	$0.795746\pi$
$62$	−890.149			−1.82337
$63$		0			0
$64$	467.092			0.912288
$65$	10.1283	+	17.5427i	0.0193271	+	0.0334754i
$66$		0			0
$67$	49.1343	−	85.1031i	0.0895926	−	0.155179i	−0.817746	−	0.575579i	$-0.804777\pi$
$67$	49.1343	−	85.1031i	0.0895926	−	0.155179i	0.907339	+	0.420400i	$0.138110\pi$
$68$	−30.7503			−0.0548386
$69$		0			0
$70$	62.6805	−	190.908i	0.107025	−	0.325969i
$71$	255.003			0.426243			0.213122	−	0.977026i	$-0.431637\pi$
$71$	255.003			0.426243			0.213122	+	0.977026i	$0.431637\pi$
$72$		0			0
$73$	344.146	+	596.078i	0.551770	+	0.955694i	0.998147	+	0.0608488i	$0.0193808\pi$
$73$	344.146	+	596.078i	0.551770	+	0.955694i	−0.446377	+	0.894845i	$0.647286\pi$
$74$	−567.156			−0.890953
$75$		0			0
$76$	0.470953	+	0.815715i	0.000710816	+	0.00123117i
$77$	811.487	+	906.850i	1.20101	+	1.34214i
$78$		0			0
$79$	542.222	+	939.155i	0.772211	+	1.33751i	0.936349	+	0.351072i	$0.114183\pi$
$79$	542.222	+	939.155i	0.772211	+	1.33751i	−0.164137	+	0.986438i	$0.552484\pi$
$80$	126.662	+	219.385i	0.177016	+	0.306600i
$81$		0			0
$82$	−577.146	+	999.647i	−0.777258	+	1.34625i
$83$	−152.083	+	263.415i	−0.201124	+	0.348356i	−0.948891	−	0.315605i	$-0.897793\pi$
$83$	−152.083	+	263.415i	−0.201124	+	0.348356i	0.747767	+	0.663961i	$0.231126\pi$
$84$		0			0
$85$	92.9243	+	160.950i	0.118577	+	0.205382i
$86$	810.335			1.01605
$87$		0			0
$88$	−1424.63			−1.72575
$89$	−550.553	+	953.585i	−0.655713	+	1.13573i	0.326002	+	0.945369i	$0.394299\pi$
$89$	−550.553	+	953.585i	−0.655713	+	1.13573i	−0.981715	+	0.190359i	$0.939035\pi$
$90$		0			0
$91$	−31.6540	+	96.4096i	−0.0364642	+	0.111060i
$92$	−36.7079	+	63.5800i	−0.0415985	+	0.0720508i
$93$		0			0
$94$	−370.871	+	642.368i	−0.406941	+	0.704842i
$95$	2.84634	−	4.93001i	0.00307399	−	0.00532430i
$96$		0			0
$97$	493.784	−	855.260i	0.516868	−	0.895242i	−0.482940	−	0.875653i	$-0.660431\pi$
$97$	493.784	−	855.260i	0.516868	−	0.895242i	0.999808	−	0.0195884i	$-0.00623557\pi$
$98$	922.042	−	403.731i	0.950411	−	0.416153i
$99$		0			0
$100$	34.0518	−	58.9795i	0.0340518	−	0.0589795i
$101$	−751.568			−0.740434			−0.370217	−	0.928945i	$-0.620717\pi$
$101$	−751.568			−0.740434			−0.370217	+	0.928945i	$0.620717\pi$
$102$		0			0
$103$	−553.040			−0.529055			−0.264528	−	0.964378i	$-0.585216\pi$
$103$	−553.040			−0.529055			−0.264528	+	0.964378i	$0.585216\pi$
$104$	−59.3967	−	102.878i	−0.0560031	−	0.0970002i
$105$		0			0
$106$	599.369	−	1038.14i	0.549206	−	0.951253i
$107$	−136.170	+	235.853i	−0.123028	+	0.213091i	−0.920960	−	0.389656i	$-0.872594\pi$
$107$	−136.170	+	235.853i	−0.123028	+	0.213091i	0.797932	+	0.602747i	$0.205927\pi$
$108$		0			0
$109$	−218.698	−	378.796i	−0.192179	−	0.332863i	0.753793	−	0.657112i	$-0.228222\pi$
$109$	−218.698	−	378.796i	−0.192179	−	0.332863i	−0.945972	+	0.324248i	$0.894889\pi$
$110$	−356.444	−	617.379i	−0.308960	−	0.535134i
$111$		0			0
$112$	−395.859	+	1205.68i	−0.333974	+	1.01719i
$113$	−157.658	−	273.071i	−0.131250	−	0.227331i	0.792909	−	0.609340i	$-0.208566\pi$
$113$	−157.658	−	273.071i	−0.131250	−	0.227331i	−0.924159	+	0.382009i	$0.875232\pi$
$114$		0			0
$115$	443.710			0.359793
$116$	24.0386	+	41.6361i	0.0192408	+	0.0333260i
$117$		0			0
$118$	−771.295			−0.601724
$119$	−290.418	+	884.533i	−0.223719	+	0.681386i
$120$		0			0
$121$	2986.46			2.24377
$122$	164.709	−	285.284i	0.122230	−	0.211708i
$123$		0			0
$124$	92.7770	+	160.694i	0.0671905	+	0.116377i
$125$	−873.742			−0.625199
$126$		0			0
$127$	314.914			0.220032			0.110016	−	0.993930i	$-0.464910\pi$
$127$	314.914			0.220032			0.110016	+	0.993930i	$0.464910\pi$
$128$	−795.854	−	1378.46i	−0.549564	−	0.951873i
$129$		0			0
$130$	29.7222	−	51.4803i	0.0200524	−	0.0347317i
$131$	−1708.69			−1.13961			−0.569806	−	0.821779i	$-0.692982\pi$
$131$	−1708.69			−1.13961			−0.569806	+	0.821779i	$0.692982\pi$
$132$		0			0
$133$	27.9119	−	5.84304i	0.0181975	−	0.00380944i
$134$	−288.376			−0.185910
$135$		0			0
$136$	−544.949	−	943.879i	−0.343595	−	0.595125i
$137$	876.161			0.546390			0.273195	−	0.961959i	$-0.411920\pi$
$137$	876.161			0.546390			0.273195	+	0.961959i	$0.411920\pi$
$138$		0			0
$139$	−368.183	−	637.712i	−0.224668	−	0.389137i	0.731552	−	0.681786i	$-0.238797\pi$
$139$	−368.183	−	637.712i	−0.224668	−	0.389137i	−0.956220	+	0.292649i	$0.905463\pi$
$140$	−40.9966	+	8.58219i	−0.0247489	+	0.00518091i
$141$		0			0
$142$	−374.162	−	648.068i	−0.221120	−	0.382991i
$143$	180.006	+	311.780i	0.105265	+	0.182324i
$144$		0			0
$145$	145.284	−	251.640i	0.0832083	−	0.144121i
$146$	1009.92	−	1749.23i	0.572477	−	0.991559i
$147$		0			0
$148$	59.1126	+	102.386i	0.0328313	+	0.0568654i
$149$	323.663			0.177956			0.0889781	−	0.996034i	$-0.471640\pi$
$149$	323.663			0.177956			0.0889781	+	0.996034i	$0.471640\pi$
$150$		0			0
$151$	−2751.38			−1.48281			−0.741404	−	0.671059i	$-0.765840\pi$
$151$	−2751.38			−1.48281			−0.741404	+	0.671059i	$0.765840\pi$
$152$	−16.6922	+	28.9117i	−0.00890734	+	0.0154280i
$153$		0			0
$154$	1114.00	−	3392.93i	0.582913	−	1.77539i
$155$	560.725	−	971.203i	0.290571	−	0.503283i
$156$		0			0
$157$	855.013	−	1480.93i	0.434634	−	0.752807i	−0.562632	−	0.826707i	$-0.690211\pi$
$157$	855.013	−	1480.93i	0.434634	−	0.752807i	0.997266	+	0.0739000i	$0.0235446\pi$
$158$	1591.19	−	2756.02i	0.801191	−	1.38770i
$159$		0			0
$160$	51.0645	−	88.4464i	0.0252313	−	0.0437019i
$161$	1482.19	+	1656.38i	0.725548	+	0.810812i
$162$		0			0
$163$	−1694.66	+	2935.24i	−0.814332	+	1.41046i	0.0954751	+	0.995432i	$0.469563\pi$
$163$	−1694.66	+	2935.24i	−0.814332	+	1.41046i	−0.909807	+	0.415032i	$0.863770\pi$
$164$	240.615			0.114567
$165$		0			0
$166$	892.597			0.417343
$167$	−782.792	−	1355.83i	−0.362720	−	0.628249i	0.625688	−	0.780074i	$-0.284819\pi$
$167$	−782.792	−	1355.83i	−0.362720	−	0.628249i	−0.988407	+	0.151824i	$0.951485\pi$
$168$		0			0
$169$	1083.49	−	1876.66i	0.493168	−	0.854192i
$170$	272.693	−	472.319i	0.123027	−	0.213089i
$171$		0			0
$172$	−84.4583	−	146.286i	−0.0374412	−	0.0648500i
$173$	1424.42	+	2467.16i	0.625991	+	1.08425i	0.988348	+	0.152209i	$0.0486386\pi$
$173$	1424.42	+	2467.16i	0.625991	+	1.08425i	−0.362358	+	0.932039i	$0.618028\pi$
$174$		0			0
$175$	−1374.94	−	1536.52i	−0.593920	−	0.663716i
$176$	2251.12	+	3899.05i	0.964117	+	1.66990i
$177$		0			0
$178$	3231.27			1.36064
$179$	−2004.75	−	3472.33i	−0.837106	−	1.44991i	−0.892304	−	0.451435i	$-0.850912\pi$
$179$	−2004.75	−	3472.33i	−0.837106	−	1.44991i	0.0551975	−	0.998475i	$-0.482421\pi$
$180$		0			0
$181$	−4749.05			−1.95024			−0.975122	−	0.221668i	$-0.928850\pi$
$181$	−4749.05			−1.95024			−0.975122	+	0.221668i	$0.928850\pi$
$182$	291.462	−	61.0144i	0.118707	−	0.0248499i
$183$		0			0
$184$	−2602.11			−1.04256
$185$	357.264	−	618.800i	0.141982	−	0.245919i
$186$		0			0
$187$	1651.51	+	2860.50i	0.645831	+	1.11861i
$188$	154.618			0.0599824
$189$		0			0
$190$	−16.7056			−0.00637869
$191$	1551.48	+	2687.24i	0.587755	+	1.01802i	0.994526	+	0.104492i	$0.0333215\pi$
$191$	1551.48	+	2687.24i	0.587755	+	1.01802i	−0.406771	+	0.913530i	$0.633345\pi$
$192$		0			0
$193$	1332.49	−	2307.94i	0.496967	−	0.860772i	−0.503027	−	0.864271i	$-0.667780\pi$
$193$	1332.49	−	2307.94i	0.496967	−	0.860772i	0.999994	+	0.00349846i	$0.00111360\pi$
$194$	−2898.09			−1.07253
$195$		0			0
$196$	−168.985	−	124.372i	−0.0615834	−	0.0453253i
$197$	1434.52			0.518810			0.259405	−	0.965769i	$-0.416474\pi$
$197$	1434.52			0.518810			0.259405	+	0.965769i	$0.416474\pi$
$198$		0			0
$199$	1019.11	+	1765.15i	0.363030	+	0.628786i	0.988458	−	0.151496i	$-0.0484089\pi$
$199$	1019.11	+	1765.15i	0.363030	+	0.628786i	−0.625428	+	0.780282i	$0.715076\pi$
$200$	2413.83			0.853416
$201$		0			0
$202$	1102.77	+	1910.05i	0.384111	+	0.665299i
$203$	1424.69	−	298.243i	0.492579	−	0.103116i
$204$		0			0
$205$	−727.115	−	1259.40i	−0.247726	−	0.429075i
$206$	811.468	+	1405.50i	0.274455	+	0.475370i
$207$		0			0
$208$	−187.710	+	325.124i	−0.0625739	+	0.108381i
$209$	50.5871	−	87.6193i	0.0167425	−	0.0289988i
$210$		0			0
$211$	463.774	+	803.279i	0.151315	+	0.262085i	0.931711	−	0.363200i	$-0.118316\pi$
$211$	463.774	+	803.279i	0.151315	+	0.262085i	−0.780396	+	0.625286i	$0.784983\pi$
$212$	−249.880			−0.0809521
$213$		0			0
$214$	799.200			0.255291
$215$	−510.448	+	884.122i	−0.161918	+	0.280449i
$216$		0			0
$217$	5498.59	−	1151.07i	1.72013	−	0.360091i
$218$	−641.785	+	1111.60i	−0.199391	+	0.345355i
$219$		0			0
$220$	−74.3017	+	128.694i	−0.0227701	+	0.0394389i
$221$	−137.712	+	238.524i	−0.0419163	+	0.0726012i
$222$		0			0
$223$	−2033.70	+	3522.47i	−0.610702	+	1.05777i	0.380421	+	0.924814i	$0.375779\pi$
$223$	−2033.70	+	3522.47i	−0.610702	+	1.05777i	−0.991122	+	0.132953i	$0.957554\pi$
$224$	500.750	−	104.827i	0.149365	−	0.0312679i
$225$		0			0
$226$	−462.658	+	801.348i	−0.136175	+	0.235862i
$227$	−761.568			−0.222674			−0.111337	−	0.993783i	$-0.535513\pi$
$227$	−761.568			−0.222674			−0.111337	+	0.993783i	$0.535513\pi$
$228$		0			0
$229$	−5133.84			−1.48146			−0.740729	−	0.671804i	$-0.765520\pi$
$229$	−5133.84			−1.48146			−0.740729	+	0.671804i	$0.765520\pi$
$230$	−651.050	−	1127.65i	−0.186648	−	0.323283i
$231$		0			0
$232$	−852.010	+	1475.73i	−0.241109	+	0.417613i
$233$	718.366	−	1244.25i	0.201982	−	0.349843i	−0.747185	−	0.664616i	$-0.768595\pi$
$233$	718.366	−	1244.25i	0.201982	−	0.349843i	0.949167	+	0.314773i	$0.101929\pi$
$234$		0			0
$235$	−467.240	−	809.284i	−0.129700	−	0.224646i
$236$	80.3892	+	139.238i	0.0221733	+	0.0384052i
$237$		0			0
$238$	2674.09	−	559.791i	0.728301	−	0.152462i
$239$	−1361.15	−	2357.57i	−0.368390	−	0.638070i	0.620924	−	0.783871i	$-0.286758\pi$
$239$	−1361.15	−	2357.57i	−0.368390	−	0.638070i	−0.989314	+	0.145801i	$0.953424\pi$
$240$		0			0
$241$	−6189.93			−1.65447			−0.827237	−	0.561853i	$-0.810089\pi$
$241$	−6189.93			−1.65447			−0.827237	+	0.561853i	$0.810089\pi$
$242$	−4381.99	−	7589.83i	−1.16399	−	2.01609i
$243$		0			0
$244$	−68.6680			−0.0180165
$245$	−140.321	+	1260.32i	−0.0365909	+	0.328649i
$246$		0			0
$247$	8.43644			0.00217327
$248$	−3288.33	+	5695.56i	−0.841973	+	1.45834i
$249$		0			0
$250$	1282.03	+	2220.54i	0.324331	+	0.561758i
$251$	4822.76			1.21279			0.606394	−	0.795164i	$-0.292615\pi$
$251$	4822.76			1.21279			0.606394	+	0.795164i	$0.292615\pi$
$252$		0			0
$253$	7885.90			1.95961
$254$	−462.069	−	800.327i	−0.114145	−	0.197705i
$255$		0			0
$256$	−467.124	+	809.082i	−0.114044	+	0.197530i
$257$	−5982.91			−1.45216			−0.726078	−	0.687613i	$-0.758659\pi$
$257$	−5982.91			−1.45216			−0.726078	+	0.687613i	$0.758659\pi$
$258$		0			0
$259$	3503.41	−	733.401i	0.840508	−	0.175951i
$260$	−12.3913			−0.00295569
$261$		0			0
$262$	2507.14	+	4342.50i	0.591190	+	1.02397i
$263$	−3749.90			−0.879197			−0.439598	−	0.898194i	$-0.644879\pi$
$263$	−3749.90			−0.879197			−0.439598	+	0.898194i	$0.644879\pi$
$264$		0			0
$265$	755.112	+	1307.89i	0.175042	+	0.303182i
$266$	−55.8043	−	62.3622i	−0.0128631	−	0.0143747i
$267$		0			0
$268$	30.0564	+	52.0592i	0.00685070	+	0.0118658i
$269$	599.355	+	1038.11i	0.135849	+	0.235297i	0.925921	−	0.377716i	$-0.123291\pi$
$269$	599.355	+	1038.11i	0.135849	+	0.235297i	−0.790073	+	0.613013i	$0.789957\pi$
$270$		0			0
$271$	2007.66	−	3477.37i	0.450024	−	0.779465i	−0.548362	−	0.836241i	$-0.684749\pi$
$271$	2007.66	−	3477.37i	0.450024	−	0.779465i	0.998387	+	0.0567755i	$0.0180819\pi$
$272$	−1722.19	+	2982.93i	−0.383909	+	0.664950i
$273$		0			0
$274$	−1285.58	−	2226.69i	−0.283448	−	0.490946i
$275$	−7315.29			−1.60410
$276$		0			0
$277$	−4418.65			−0.958452			−0.479226	−	0.877692i	$-0.659083\pi$
$277$	−4418.65			−0.958452			−0.479226	+	0.877692i	$0.659083\pi$
$278$	−1080.46	+	1871.41i	−0.233100	+	0.403741i
$279$		0			0
$280$	−989.960	−	1106.30i	−0.211291	−	0.236121i
$281$	−786.552	+	1362.35i	−0.166981	+	0.289220i	−0.937357	−	0.348370i	$-0.886735\pi$
$281$	−786.552	+	1362.35i	−0.166981	+	0.289220i	0.770376	+	0.637590i	$0.220069\pi$
$282$		0			0
$283$	−2434.17	+	4216.11i	−0.511296	+	0.885590i	0.488619	+	0.872497i	$0.337501\pi$
$283$	−2434.17	+	4216.11i	−0.511296	+	0.885590i	−0.999914	+	0.0130925i	$0.995832\pi$
$284$	−77.9951	+	135.092i	−0.0162963	+	0.0282261i
$285$		0			0
$286$	528.242	−	914.942i	0.109215	−	0.189167i
$287$	2272.46	−	6921.30i	0.467384	−	1.42352i
$288$		0			0
$289$	1193.03	−	2066.39i	0.242831	−	0.420596i
$290$	−852.695			−0.172662
$291$		0			0
$292$	−421.042			−0.0843822
$293$	4379.03	+	7584.70i	0.873125	+	1.51230i	0.858747	+	0.512401i	$0.171244\pi$
$293$	4379.03	+	7584.70i	0.873125	+	1.51230i	0.0143787	+	0.999897i	$0.495423\pi$
$294$		0			0
$295$	485.856	−	841.527i	0.0958902	−	0.166087i
$296$	−2095.15	+	3628.91i	−0.411413	+	0.712589i
$297$		0			0
$298$	−474.906	−	822.561i	−0.0923173	−	0.159898i
$299$	328.784	+	569.471i	0.0635923	+	0.110145i
$300$		0			0
$301$	−5005.57	+	1047.86i	−0.958525	+	0.200657i
$302$	4037.06	+	6992.40i	0.769228	+	1.33234i
$303$		0			0
$304$	105.504			0.0199049
$305$	207.507	+	359.413i	0.0389569	+	0.0674752i
$306$		0			0
$307$	−5488.53			−1.02035			−0.510174	−	0.860071i	$-0.670419\pi$
$307$	−5488.53			−1.02035			−0.510174	+	0.860071i	$0.670419\pi$
$308$	−728.619	+	152.528i	−0.134795	+	0.0282179i
$309$		0			0
$310$	−3290.97			−0.602951
$311$	852.450	−	1476.49i	0.155428	−	0.269209i	−0.777787	−	0.628528i	$-0.783658\pi$
$311$	852.450	−	1476.49i	0.155428	−	0.269209i	0.933215	+	0.359319i	$0.116991\pi$
$312$		0			0
$313$	3326.29	+	5761.31i	0.600681	+	1.04041i	0.992718	+	0.120461i	$0.0384373\pi$
$313$	3326.29	+	5761.31i	0.600681	+	1.04041i	−0.392037	+	0.919950i	$0.628229\pi$
$314$	−5018.20			−0.901889
$315$		0			0
$316$	−663.375			−0.118094
$317$	−2112.92	−	3659.68i	−0.374364	−	0.648417i	0.615868	−	0.787850i	$-0.288806\pi$
$317$	−2112.92	−	3659.68i	−0.374364	−	0.648417i	−0.990232	+	0.139432i	$0.955472\pi$
$318$		0			0
$319$	2582.09	−	4472.30i	0.453195	−	0.784956i
$320$	1726.89			0.301675
$321$		0			0
$322$	2034.73	−	6197.25i	0.352147	−	1.07254i
$323$	77.4021			0.0133336
$324$		0			0
$325$	−304.994	−	528.265i	−0.0520555	−	0.0901627i
$326$	9946.21			1.68978
$327$		0			0
$328$	4264.12	+	7385.67i	0.717825	+	1.24331i
$329$	1460.27	−	4447.59i	0.244703	−	0.745299i
$330$		0			0
$331$	−2207.40	−	3823.33i	−0.366555	−	0.634891i	0.622470	−	0.782644i	$-0.286129\pi$
$331$	−2207.40	−	3823.33i	−0.366555	−	0.634891i	−0.989024	+	0.147753i	$0.952796\pi$
$332$	−93.0321	−	161.136i	−0.0153789	−	0.0266371i
$333$		0			0
$334$	−2297.16	+	3978.80i	−0.376332	+	0.651827i
$335$	181.655	−	314.635i	0.0296264	−	0.0513145i
$336$		0			0
$337$	1290.74	+	2235.63i	0.208638	+	0.361372i	0.951286	−	0.308311i	$-0.0997636\pi$
$337$	1290.74	+	2235.63i	0.208638	+	0.361372i	−0.742648	+	0.669682i	$0.766430\pi$
$338$	−6359.16			−1.02335
$339$		0			0
$340$	−113.687			−0.0181340
$341$	9965.56	−	17260.9i	1.58260	−	2.74114i
$342$		0			0
$343$	−5173.53	+	3686.22i	−0.814414	+	0.580284i
$344$	2993.49	−	5184.88i	0.469181	−	0.812645i
$345$		0			0
$346$	4180.06	−	7240.07i	0.649483	−	1.12494i
$347$	3024.09	−	5237.87i	0.467843	−	0.810327i	−0.531482	−	0.847070i	$-0.678365\pi$
$347$	3024.09	−	5237.87i	0.467843	−	0.810327i	0.999325	+	0.0367422i	$0.0116980\pi$
$348$		0			0
$349$	5649.71	−	9785.58i	0.866538	−	1.50089i	0.00102701	−	0.999999i	$-0.499673\pi$
$349$	5649.71	−	9785.58i	0.866538	−	1.50089i	0.865511	−	0.500889i	$-0.166994\pi$
$350$	−1887.50	+	5748.82i	−0.288261	+	0.877965i
$351$		0			0
$352$	907.552	−	1571.93i	0.137422	−	0.238023i
$353$	−1036.20			−0.156237			−0.0781183	−	0.996944i	$-0.524891\pi$
$353$	−1036.20			−0.156237			−0.0781183	+	0.996944i	$0.524891\pi$
$354$		0			0
$355$	942.773			0.140950
$356$	−336.784	−	583.327i	−0.0501391	−	0.0868434i
$357$		0			0
$358$	−5883.08	+	10189.8i	−0.868522	+	1.50432i
$359$	−5156.80	+	8931.83i	−0.758121	+	1.31310i	0.185687	+	0.982609i	$0.440549\pi$
$359$	−5156.80	+	8931.83i	−0.758121	+	1.31310i	−0.943808	+	0.330495i	$0.892784\pi$
$360$		0			0
$361$	3428.31	+	5938.01i	0.499827	+	0.865726i
$362$	6968.22	+	12069.3i	1.01172	+	1.75235i
$363$		0			0
$364$	−41.3927	−	46.2570i	−0.00596035	−	0.00666079i
$365$	1272.34	+	2203.76i	0.182459	+	0.316028i
$366$		0			0
$367$	−2066.06			−0.293863			−0.146931	−	0.989147i	$-0.546940\pi$
$367$	−2066.06			−0.293863			−0.146931	+	0.989147i	$0.546940\pi$
$368$	4111.71	+	7121.68i	0.582439	+	1.00881i
$369$		0			0
$370$	−2096.84			−0.294620
$371$	−2359.96	+	7187.79i	−0.330251	+	1.00585i
$372$		0			0
$373$	4819.63			0.669038			0.334519	−	0.942389i	$-0.391426\pi$
$373$	4819.63			0.669038			0.334519	+	0.942389i	$0.391426\pi$
$374$	4846.48	−	8394.35i	0.670068	−	1.16059i
$375$		0			0
$376$	2740.10	+	4745.99i	0.375824	+	0.650947i
$377$	430.616			0.0588272
$378$		0			0
$379$	−4459.20			−0.604363			−0.302182	−	0.953250i	$-0.597715\pi$
$379$	−4459.20			−0.604363			−0.302182	+	0.953250i	$0.597715\pi$
$380$	1.74116	+	3.01578i	0.000235052	+	0.000407122i
$381$		0			0
$382$	4552.94	−	7885.92i	0.609813	−	1.05623i
$383$	−9010.35			−1.20211			−0.601054	−	0.799208i	$-0.705252\pi$
$383$	−9010.35			−1.20211			−0.601054	+	0.799208i	$0.705252\pi$
$384$		0			0
$385$	3000.15	+	3352.72i	0.397148	+	0.443819i
$386$	−7820.57			−1.03124
$387$		0			0
$388$	302.058	+	523.179i	0.0395223	+	0.0684546i
$389$	−1388.27			−0.180946			−0.0904730	−	0.995899i	$-0.528838\pi$
$389$	−1388.27			−0.180946			−0.0904730	+	0.995899i	$0.528838\pi$
$390$		0			0
$391$	3016.51	+	5224.75i	0.390157	+	0.675772i
$392$	822.902	−	7391.07i	0.106028	−	0.952309i
$393$		0			0
$394$	−2104.86	−	3645.72i	−0.269140	−	0.466164i
$395$	2004.65	+	3472.16i	0.255354	+	0.442287i
$396$		0			0
$397$	1056.07	−	1829.16i	0.133507	−	0.231242i	−0.791519	−	0.611145i	$-0.790709\pi$
$397$	1056.07	−	1829.16i	0.133507	−	0.231242i	0.925026	+	0.379903i	$0.124043\pi$
$398$	2990.66	−	5179.97i	0.376654	−	0.652384i
$399$		0			0
$400$	−3814.19	−	6606.37i	−0.476774	−	0.825796i
$401$	15363.7			1.91328			0.956642	−	0.291265i	$-0.0940761\pi$
$401$	15363.7			1.91328			0.956642	+	0.291265i	$0.0940761\pi$
$402$		0			0
$403$	1661.96			0.205430
$404$	229.875	−	398.154i	0.0283086	−	0.0490320i
$405$		0			0
$406$	−2848.39	−	3183.12i	−0.348185	−	0.389102i
$407$	6349.53	−	10997.7i	0.773304	−	1.33940i
$408$		0			0
$409$	−1263.18	+	2187.89i	−0.152714	+	0.264509i	−0.932224	−	0.361881i	$-0.882135\pi$
$409$	−1263.18	+	2187.89i	−0.152714	+	0.264509i	0.779510	+	0.626390i	$0.215468\pi$
$410$	−2133.77	+	3695.80i	−0.257023	+	0.445177i
$411$		0			0
$412$	169.153	−	292.981i	0.0202271	−	0.0350343i
$413$	4764.41	−	997.377i	0.567654	−	0.118832i
$414$		0			0
$415$	−562.267	+	973.874i	−0.0665074	+	0.115194i
$416$	151.353			0.0178382
$417$		0			0
$418$	−296.903			−0.0347416
$419$	−7146.27	−	12377.7i	−0.833217	−	1.44317i	−0.895474	−	0.445114i	$-0.853163\pi$
$419$	−7146.27	−	12377.7i	−0.833217	−	1.44317i	0.0622570	−	0.998060i	$-0.480170\pi$
$420$		0			0
$421$	4922.61	−	8526.22i	0.569866	−	0.987036i	−0.426713	−	0.904387i	$-0.640329\pi$
$421$	4922.61	−	8526.22i	0.569866	−	0.987036i	0.996579	−	0.0826493i	$-0.0263381\pi$
$422$	1360.98	−	2357.28i	0.156994	−	0.271921i
$423$		0			0
$424$	−4428.30	−	7670.05i	−0.507211	−	0.878515i
$425$	−2798.24	−	4846.70i	−0.319376	−	0.553175i
$426$		0			0
$427$	−648.526	+	1975.23i	−0.0734997	+	0.223860i
$428$	−83.2977	−	144.276i	−0.00940735	−	0.0162940i
$429$		0			0
$430$	2995.89			0.335988
$431$	185.814	+	321.839i	0.0207664	+	0.0359685i	0.876222	−	0.481908i	$-0.160056\pi$
$431$	185.814	+	321.839i	0.0207664	+	0.0359685i	−0.855455	+	0.517876i	$0.826723\pi$
$432$		0			0
$433$	−1175.51			−0.130466			−0.0652328	−	0.997870i	$-0.520779\pi$
$433$	−1175.51			−0.130466			−0.0652328	+	0.997870i	$0.520779\pi$
$434$	−10993.4	−	12285.2i	−1.21589	−	1.35878i
$435$		0			0
$436$	267.564			0.0293899
$437$	92.3980	−	160.038i	0.0101144	−	0.0175187i
$438$		0			0
$439$	−6727.08	−	11651.6i	−0.731358	−	1.26675i	−0.956303	−	0.292378i	$-0.905554\pi$
$439$	−6727.08	−	11651.6i	−0.731358	−	1.26675i	0.224945	−	0.974371i	$-0.427780\pi$
$440$	−5267.01			−0.570670
$441$		0			0
$442$	808.251			0.0869787
$443$	3164.83	+	5481.64i	0.339425	+	0.587902i	0.984325	−	0.176366i	$-0.0564341\pi$
$443$	3164.83	+	5481.64i	0.339425	+	0.587902i	−0.644899	+	0.764267i	$0.723101\pi$
$444$		0			0
$445$	−2035.45	+	3525.51i	−0.216831	+	0.375562i
$446$	11936.1			1.26724
$447$		0			0
$448$	5768.59	+	6446.49i	0.608349	+	0.679840i
$449$	−644.573			−0.0677489			−0.0338745	−	0.999426i	$-0.510785\pi$
$449$	−644.573			−0.0677489			−0.0338745	+	0.999426i	$0.510785\pi$
$450$		0			0
$451$	−12922.8	−	22382.9i	−1.34924	−	2.33696i
$452$	192.885			0.0200720
$453$		0			0
$454$	1117.44	+	1935.46i	0.115515	+	0.200079i
$455$	−117.028	+	356.437i	−0.0120580	+	0.0367253i
$456$		0			0
$457$	−1319.10	−	2284.76i	−0.135022	−	0.233865i	0.790584	−	0.612354i	$-0.209777\pi$
$457$	−1319.10	−	2284.76i	−0.135022	−	0.233865i	−0.925606	+	0.378489i	$0.876444\pi$
$458$	7532.82	+	13047.2i	0.768527	+	1.33113i
$459$		0			0
$460$	−135.713	+	235.062i	−0.0137558	+	0.0238257i
$461$	−1820.24	+	3152.75i	−0.183898	+	0.318521i	−0.943205	−	0.332212i	$-0.892205\pi$
$461$	−1820.24	+	3152.75i	−0.183898	+	0.318521i	0.759307	+	0.650733i	$0.225538\pi$
$462$		0			0
$463$	−3186.10	−	5518.49i	−0.319807	−	0.553923i	0.660640	−	0.750703i	$-0.270285\pi$
$463$	−3186.10	−	5518.49i	−0.319807	−	0.553923i	−0.980448	+	0.196780i	$0.936952\pi$
$464$	5385.19			0.538796
$465$		0			0
$466$	−4216.20			−0.419124
$467$	−2398.70	+	4154.67i	−0.237684	+	0.411681i	−0.960049	−	0.279831i	$-0.909722\pi$
$467$	−2398.70	+	4154.67i	−0.237684	+	0.411681i	0.722365	+	0.691512i	$0.243055\pi$
$468$		0			0
$469$	1781.35	−	372.905i	0.175384	−	0.0367146i
$470$	−1371.15	+	2374.90i	−0.134567	+	0.233077i
$471$		0			0
$472$	−2849.27	+	4935.08i	−0.277857	+	0.481262i
$473$	−9072.01	+	15713.2i	−0.881885	+	1.52747i
$474$		0			0
$475$	−85.7123	+	148.458i	−0.00827947	+	0.0143405i
$476$	−379.767	−	424.396i	−0.0365685	−	0.0408659i
$477$		0			0
$478$	−3994.38	+	6918.47i	−0.382215	+	0.662016i
$479$	−11940.0			−1.13894			−0.569470	−	0.822012i	$-0.692851\pi$
$479$	−11940.0			−1.13894			−0.569470	+	0.822012i	$0.692851\pi$
$480$		0			0
$481$	1058.92			0.100379
$482$	9082.40	+	15731.2i	0.858282	+	1.48659i
$483$		0			0
$484$	−913.438	+	1582.12i	−0.0857849	+	0.148584i
$485$	1825.57	−	3161.99i	0.170918	−	0.296038i
$486$		0			0
$487$	4633.83	+	8026.04i	0.431168	+	0.746806i	0.996974	−	0.0777329i	$-0.0247681\pi$
$487$	4633.83	+	8026.04i	0.431168	+	0.746806i	−0.565806	+	0.824539i	$0.691435\pi$
$488$	−1216.91	−	2107.76i	−0.112883	−	0.195520i
$489$		0			0
$490$	3408.89	−	1492.64i	0.314281	−	0.137613i
$491$	−2769.69	−	4797.25i	−0.254571	−	0.440931i	0.710208	−	0.703992i	$-0.248601\pi$
$491$	−2769.69	−	4797.25i	−0.254571	−	0.440931i	−0.964779	+	0.263062i	$0.915268\pi$
$492$		0			0
$493$	3950.79			0.360922
$494$	−12.3787	−	21.4405i	−0.00112741	−	0.00195274i
$495$		0			0
$496$	20784.1			1.88152
$497$	3149.29	+	3519.38i	0.284235	+	0.317638i
$498$		0			0
$499$	5202.14			0.466693			0.233347	−	0.972394i	$-0.425032\pi$
$499$	5202.14			0.466693			0.233347	+	0.972394i	$0.425032\pi$
$500$	267.243	−	462.878i	0.0239029	−	0.0414011i
$501$		0			0
$502$	−7076.37	−	12256.6i	−0.629151	−	1.08972i
$503$	−8925.34			−0.791176			−0.395588	−	0.918428i	$-0.629459\pi$
$503$	−8925.34			−0.791176			−0.395588	+	0.918428i	$0.629459\pi$
$504$		0			0
$505$	−2778.63			−0.244846
$506$	−11570.9	−	20041.4i	−1.01658	−	1.76076i
$507$		0			0
$508$	−96.3195	+	166.830i	−0.00841237	+	0.0145707i
$509$	−883.448			−0.0769315			−0.0384658	−	0.999260i	$-0.512247\pi$
$509$	−883.448			−0.0769315			−0.0384658	+	0.999260i	$0.512247\pi$
$510$		0			0
$511$	−3976.47	+	12111.2i	−0.344244	+	1.04847i
$512$	−9992.04			−0.862480
$513$		0			0
$514$	8778.65	+	15205.1i	0.753326	+	1.30480i
$515$	−2044.65			−0.174948
$516$		0			0
$517$	−8304.09	−	14383.1i	−0.706409	−	1.22354i
$518$	−7004.39	−	7827.52i	−0.594122	−	0.663941i
$519$		0			0
$520$	−219.596	−	380.351i	−0.0185191	−	0.0320760i
$521$	−3383.38	−	5860.18i	−0.284507	−	0.492781i	0.687982	−	0.725728i	$-0.258497\pi$
$521$	−3383.38	−	5860.18i	−0.284507	−	0.492781i	−0.972490	+	0.232946i	$0.925163\pi$
$522$		0			0
$523$	−2074.51	+	3593.15i	−0.173445	+	0.300416i	−0.939622	−	0.342214i	$-0.888823\pi$
$523$	−2074.51	+	3593.15i	−0.173445	+	0.300416i	0.766177	+	0.642630i	$0.222157\pi$
$524$	522.620	−	905.205i	0.0435702	−	0.0754658i
$525$		0			0
$526$	5502.18	+	9530.05i	0.456096	+	0.789981i
$527$	15248.1			1.26037
$528$		0			0
$529$	2236.73			0.183835
$530$	2215.93	−	3838.10i	0.181611	−	0.314560i
$531$		0			0
$532$	−5.44168	+	16.5739i	−0.000443472	+	0.00135069i
$533$	1077.57	−	1866.40i	0.0875697	−	0.151675i
$534$		0			0
$535$	−503.434	+	871.973i	−0.0406829	+	0.0704649i
$536$	−1065.30	+	1845.16i	−0.0858471	+	0.148692i
$537$		0			0
$538$	1758.85	−	3046.42i	0.140947	−	0.244127i
$539$	−2493.87	+	22399.2i	−0.199293	+	1.78999i
$540$		0			0
$541$	525.578	−	910.327i	0.0417677	−	0.0723439i	−0.844386	−	0.535736i	$-0.820034\pi$
$541$	525.578	−	910.327i	0.0417677	−	0.0723439i	0.886154	+	0.463392i	$0.153368\pi$
$542$	−11783.2			−0.933826
$543$		0			0
$544$	1388.62			0.109443
$545$	−808.550	−	1400.45i	−0.0635495	−	0.110071i
$546$		0			0
$547$	−8242.51	+	14276.4i	−0.644286	+	1.11594i	0.340180	+	0.940360i	$0.389512\pi$
$547$	−8242.51	+	14276.4i	−0.644286	+	1.11594i	−0.984466	+	0.175575i	$0.943821\pi$
$548$	−267.982	+	464.159i	−0.0208899	+	0.0361823i
$549$		0			0
$550$	10733.6	+	18591.2i	0.832152	+	1.44133i
$551$	−60.5079	−	104.803i	−0.00467826	−	0.00810299i
$552$		0			0
$553$	−6265.16	+	19082.0i	−0.481775	+	1.46736i
$554$	6483.43	+	11229.6i	0.497211	+	0.861194i
$555$		0			0
$556$	450.450			0.0343585
$557$	4592.38	+	7954.23i	0.349345	+	0.605084i	0.986133	−	0.165955i	$-0.0530707\pi$
$557$	4592.38	+	7954.23i	0.349345	+	0.605084i	−0.636788	+	0.771039i	$0.719737\pi$
$558$		0			0
$559$	−1512.95			−0.114474
$560$	−1463.53	+	4457.52i	−0.110438	+	0.336365i
$561$		0			0
$562$	4616.39			0.346496
$563$	9770.16	−	16922.4i	0.731373	−	1.26678i	−0.224923	−	0.974377i	$-0.572213\pi$
$563$	9770.16	−	16922.4i	0.731373	−	1.26678i	0.956296	−	0.292399i	$-0.0944536\pi$
$564$		0			0
$565$	−582.878	−	1009.57i	−0.0434015	−	0.0751736i
$566$	14286.5			1.06097
$567$		0			0
$568$	−5528.83			−0.408424
$569$	9490.35	+	16437.8i	0.699220	+	1.21108i	0.968737	+	0.248089i	$0.0798026\pi$
$569$	9490.35	+	16437.8i	0.699220	+	1.21108i	−0.269517	+	0.962996i	$0.586864\pi$
$570$		0			0
$571$	−9953.84	+	17240.6i	−0.729519	+	1.26356i	0.227568	+	0.973762i	$0.426923\pi$
$571$	−9953.84	+	17240.6i	−0.729519	+	1.26356i	−0.957087	+	0.289802i	$0.906411\pi$
$572$	−220.227			−0.0160982
$573$		0			0
$574$	−20924.2	+	4380.26i	−1.52153	+	0.318516i
$575$	−13361.5			−0.969066
$576$		0			0
$577$	759.050	+	1314.71i	0.0547655	+	0.0948566i	0.892108	−	0.451821i	$-0.149226\pi$
$577$	759.050	+	1314.71i	0.0547655	+	0.0948566i	−0.837343	+	0.546678i	$0.815892\pi$
$578$	−7002.07			−0.503889
$579$		0			0
$580$	88.8733	+	153.933i	0.00636252	+	0.0110202i
$581$	−5513.71	+	1154.23i	−0.393713	+	0.0824195i
$582$		0			0
$583$	13420.3	+	23244.7i	0.953368	+	1.65128i
$584$	−7461.58	−	12923.8i	−0.528703	−	0.915740i
$585$		0			0
$586$	12850.6	−	22257.9i	0.905892	−	1.56905i
$587$	−49.6245	+	85.9522i	−0.00348931	+	0.00604366i	−0.867765	−	0.496975i	$-0.834444\pi$
$587$	−49.6245	+	85.9522i	−0.00348931	+	0.00604366i	0.864275	+	0.503019i	$0.167777\pi$
$588$		0			0
$589$	−233.530	−	404.486i	−0.0163369	−	0.0282964i
$590$	−2851.56			−0.198978
$591$		0			0
$592$	13242.6			0.919368
$593$	1602.40	−	2775.44i	0.110966	−	0.192199i	−0.805194	−	0.593011i	$-0.797939\pi$
$593$	1602.40	−	2775.44i	0.110966	−	0.192199i	0.916160	+	0.400813i	$0.131272\pi$
$594$		0			0
$595$	−1073.70	+	3270.21i	−0.0739792	+	0.225320i
$596$	−98.9954	+	171.465i	−0.00680371	+	0.0117844i
$597$		0			0
$598$	964.842	−	1671.16i	0.0659788	−	0.114279i
$599$	−9879.02	+	17111.0i	−0.673866	+	1.16717i	0.302933	+	0.953012i	$0.402034\pi$
$599$	−9879.02	+	17111.0i	−0.673866	+	1.16717i	−0.976799	+	0.214158i	$0.931299\pi$
$600$		0			0
$601$	745.047	−	1290.46i	0.0505676	−	0.0875856i	−0.839634	−	0.543153i	$-0.817230\pi$
$601$	745.047	−	1290.46i	0.0505676	−	0.0875856i	0.890201	+	0.455568i	$0.150564\pi$
$602$	10007.6	+	11183.7i	0.677544	+	0.757166i
$603$		0			0
$604$	841.536	−	1457.58i	0.0566914	−	0.0981925i
$605$	11041.3			0.741968
$606$		0			0
$607$	−2414.52			−0.161454			−0.0807269	−	0.996736i	$-0.525724\pi$
$607$	−2414.52			−0.161454			−0.0807269	+	0.996736i	$0.525724\pi$
$608$	−21.2673	−	36.8361i	−0.00141859	−	0.00245707i
$609$		0			0
$610$	608.946	−	1054.72i	0.0404188	−	0.0700075i
$611$	692.440	−	1199.34i	0.0458480	−	0.0794110i
$612$		0			0
$613$	6831.31	+	11832.2i	0.450105	+	0.779604i	0.998392	−	0.0566858i	$-0.0180533\pi$
$613$	6831.31	+	11832.2i	0.450105	+	0.779604i	−0.548287	+	0.836290i	$0.684720\pi$
$614$	8053.25	+	13948.6i	0.529320	+	0.916809i
$615$		0			0
$616$	−17594.2	−	19661.8i	−1.15080	−	1.28603i
$617$	−1876.84	−	3250.78i	−0.122461	−	0.212109i	0.798276	−	0.602291i	$-0.205745\pi$
$617$	−1876.84	−	3250.78i	−0.122461	−	0.212109i	−0.920738	+	0.390182i	$0.872412\pi$
$618$		0			0
$619$	25599.3			1.66224			0.831118	−	0.556096i	$-0.187701\pi$
$619$	25599.3			1.66224			0.831118	+	0.556096i	$0.187701\pi$
$620$	343.006	+	594.104i	0.0222185	+	0.0384836i
$621$		0			0
$622$	−5003.15			−0.322521
$623$	−19960.1	+	4178.42i	−1.28360	+	0.268708i
$624$		0			0
$625$	10686.1			0.683911
$626$	9761.26	−	16907.0i	0.623224	−	1.07946i
$627$		0			0
$628$	523.028	+	905.912i	0.0332342	+	0.0575634i
$629$	9715.27			0.615856
$630$		0			0
$631$	718.485			0.0453288			0.0226644	−	0.999743i	$-0.492785\pi$
$631$	718.485			0.0453288			0.0226644	+	0.999743i	$0.492785\pi$
$632$	−11756.1	−	20362.2i	−0.739928	−	1.28159i
$633$		0			0
$634$	−6200.51	+	10739.6i	−0.388413	+	0.672751i
$635$	1164.27			0.0727601
$636$		0			0
$637$	−1721.51	+	753.792i	−0.107078	+	0.0468859i
$638$	−15154.6			−0.940404
$639$		0			0
$640$	−2942.36	−	5096.31i	−0.181729	−	0.314765i
$641$	−8842.32			−0.544853			−0.272426	−	0.962177i	$-0.587826\pi$
$641$	−8842.32			−0.544853			−0.272426	+	0.962177i	$0.587826\pi$
$642$		0			0
$643$	−15033.0	−	26037.9i	−0.921997	−	1.59695i	−0.796321	−	0.604874i	$-0.793224\pi$
$643$	−15033.0	−	26037.9i	−0.921997	−	1.59695i	−0.125676	−	0.992071i	$-0.540110\pi$
$644$	−1330.83	+	278.595i	−0.0814319	+	0.0170469i
$645$		0			0
$646$	−113.571	−	196.711i	−0.00691702	−	0.0119806i
$647$	2937.46	+	5087.84i	0.178491	+	0.309155i	0.941364	−	0.337393i	$-0.109545\pi$
$647$	2937.46	+	5087.84i	0.178491	+	0.309155i	−0.762873	+	0.646548i	$0.776212\pi$
$648$		0			0
$649$	8634.94	−	14956.2i	0.522267	−	0.904593i
$650$	−895.028	+	1550.23i	−0.0540090	+	0.0935464i
$651$		0			0
$652$	−1036.66	−	1795.54i	−0.0622678	−	0.107851i
$653$	18198.3			1.09059			0.545296	−	0.838244i	$-0.316417\pi$
$653$	18198.3			1.09059			0.545296	+	0.838244i	$0.316417\pi$
$654$		0			0
$655$	−6317.22			−0.376846
$656$	13475.8	−	23340.8i	0.802047	−	1.38919i
$657$		0			0
$658$	−13445.8	+	2814.73i	−0.796614	+	0.166762i
$659$	5816.45	−	10074.4i	0.343819	−	0.595512i	−0.641320	−	0.767274i	$-0.721613\pi$
$659$	5816.45	−	10074.4i	0.343819	−	0.595512i	0.985138	+	0.171762i	$0.0549461\pi$
$660$		0			0
$661$	4470.40	−	7742.95i	0.263053	−	0.455622i	−0.703998	−	0.710201i	$-0.748604\pi$
$661$	4470.40	−	7742.95i	0.263053	−	0.455622i	0.967052	+	0.254580i	$0.0819372\pi$
$662$	−6477.77	+	11219.8i	−0.380311	+	0.658718i
$663$		0			0
$664$	3297.38	−	5711.22i	0.192715	−	0.333793i
$665$	103.193	−	21.6024i	0.00601753	−	0.00125970i
$666$		0			0
$667$	4716.22	−	8168.73i	0.273782	−	0.474205i
$668$	957.698			0.0554707
$669$		0			0
$670$	−1066.16			−0.0614765
$671$	3687.96	+	6387.73i	0.212179	+	0.367504i
$672$		0			0
$673$	5154.45	−	8927.77i	0.295229	−	0.511352i	−0.679809	−	0.733389i	$-0.737937\pi$
$673$	5154.45	−	8927.77i	0.295229	−	0.511352i	0.975038	+	0.222037i	$0.0712706\pi$
$674$	3787.77	−	6560.61i	0.216468	−	0.374933i
$675$		0			0
$676$	662.792	+	1147.99i	0.0377101	+	0.0653158i
$677$	9554.19	+	16548.3i	0.542389	+	0.939445i	0.998766	+	0.0496586i	$0.0158133\pi$
$677$	9554.19	+	16548.3i	0.542389	+	0.939445i	−0.456378	+	0.889786i	$0.650853\pi$
$678$		0			0
$679$	17902.0	−	3747.58i	1.01180	−	0.211810i
$680$	−2014.73	−	3489.62i	−0.113620	−	0.196795i
$681$		0			0
$682$	−58489.3			−3.28398
$683$	7772.25	+	13461.9i	0.435427	+	0.754182i	0.997330	−	0.0730208i	$-0.0232639\pi$
$683$	7772.25	+	13461.9i	0.435427	+	0.754182i	−0.561903	+	0.827203i	$0.689931\pi$
$684$		0			0
$685$	3239.26			0.180680
$686$	16959.3	+	7739.33i	0.943889	+	0.430742i
$687$		0			0
$688$	−18920.6			−1.04846
$689$	−1119.06	+	1938.27i	−0.0618763	+	0.107173i
$690$		0			0
$691$	−6922.94	−	11990.9i	−0.381131	−	0.660137i	0.610094	−	0.792329i	$-0.291132\pi$
$691$	−6922.94	−	11990.9i	−0.381131	−	0.660137i	−0.991224	+	0.132192i	$0.957798\pi$
$692$	−1742.69			−0.0957327
$693$		0			0
$694$	−17748.8			−0.970800
$695$	−1361.21	−	2357.69i	−0.0742932	−	0.128680i
$696$		0			0
$697$	9886.41	−	17123.8i	0.537266	−	0.930572i
$698$	−33159.0			−1.79812
$699$		0			0
$700$	1234.54	−	258.437i	0.0666587	−	0.0139543i
$701$	−21818.9			−1.17559			−0.587794	−	0.809011i	$-0.700003\pi$
$701$	−21818.9			−1.17559			−0.587794	+	0.809011i	$0.700003\pi$
$702$		0			0
$703$	−148.793	−	257.717i	−0.00798270	−	0.0138264i
$704$	30691.4			1.64307
$705$		0			0
$706$	1520.41	+	2633.42i	0.0810500	+	0.140383i
$707$	−9281.88	−	10372.7i	−0.493750	−	0.551773i
$708$		0			0
$709$	−245.391	−	425.030i	−0.0129984	−	0.0225138i	0.859453	−	0.511215i	$-0.170804\pi$
$709$	−245.391	−	425.030i	−0.0129984	−	0.0225138i	−0.872451	+	0.488701i	$0.837471\pi$
$710$	−1383.32	−	2395.98i	−0.0731197	−	0.126647i
$711$		0			0
$712$	11936.8	−	20675.1i	0.628300	−	1.08825i
$713$	18202.2	−	31527.2i	0.956072	−	1.65597i
$714$		0			0
$715$	665.503	+	1152.68i	0.0348089	+	0.0602909i
$716$	2452.69			0.128019
$717$		0			0
$718$	30266.0			1.57314
$719$	3069.85	−	5317.13i	0.159229	−	0.275794i	−0.775362	−	0.631518i	$-0.782432\pi$
$719$	3069.85	−	5317.13i	0.159229	−	0.275794i	0.934591	+	0.355724i	$0.115766\pi$
$720$		0			0
$721$	−6830.05	−	7632.70i	−0.352794	−	0.394253i
$722$	10060.6	−	17425.5i	0.518585	−	0.898215i
$723$		0			0
$724$	1452.54	−	2515.88i	0.0745627	−	0.129146i
$725$	−4374.96	+	7577.66i	−0.224113	+	0.388175i
$726$		0			0
$727$	−9687.53	+	16779.3i	−0.494210	+	0.855997i	−0.999978	−	0.00667304i	$-0.997876\pi$
$727$	−9687.53	+	16779.3i	−0.494210	+	0.855997i	0.505768	+	0.862670i	$0.331209\pi$
$728$	686.306	−	2090.30i	0.0349398	−	0.106417i
$729$		0			0
$730$	3733.79	−	6467.11i	0.189306	−	0.327888i
$731$	−13880.9			−0.702330
$732$		0			0
$733$	8180.41			0.412210			0.206105	−	0.978530i	$-0.433921\pi$
$733$	8180.41			0.412210			0.206105	+	0.978530i	$0.433921\pi$
$734$	3031.51	+	5250.72i	0.152445	+	0.264043i
$735$		0			0
$736$	1657.66	−	2871.15i	0.0830191	−	0.143793i
$737$	3228.48	−	5591.90i	0.161361	−	0.279485i
$738$		0			0
$739$	−3994.83	−	6919.24i	−0.198853	−	0.344423i	0.749304	−	0.662226i	$-0.230388\pi$
$739$	−3994.83	−	6919.24i	−0.198853	−	0.344423i	−0.948157	+	0.317803i	$0.897055\pi$
$740$	218.546	+	378.532i	0.0108566	+	0.0188042i
$741$		0			0
$742$	21729.9	−	4548.92i	1.07511	−	0.225062i
$743$	−11091.9	−	19211.7i	−0.547674	−	0.948599i	−0.998433	−	0.0559534i	$-0.982180\pi$
$743$	−11091.9	−	19211.7i	−0.547674	−	0.948599i	0.450760	−	0.892645i	$-0.351153\pi$
$744$		0			0
$745$	1196.62			0.0588464
$746$	−7071.78	−	12248.7i	−0.347073	−	0.601148i
$747$		0			0
$748$	−2020.52			−0.0987669
$749$	−4936.79	+	1033.46i	−0.240836	+	0.0504164i
$750$		0			0
$751$	13210.6			0.641895			0.320947	−	0.947097i	$-0.395999\pi$
$751$	13210.6			0.641895			0.320947	+	0.947097i	$0.395999\pi$
$752$	8659.50	−	14998.7i	0.419919	−	0.727322i
$753$		0			0
$754$	−631.837	−	1094.37i	−0.0305175	−	0.0528578i
$755$	−10172.1			−0.490334
$756$		0			0
$757$	−5945.66			−0.285467			−0.142734	−	0.989761i	$-0.545589\pi$
$757$	−5945.66			−0.285467			−0.142734	+	0.989761i	$0.545589\pi$
$758$	6542.92	+	11332.7i	0.313522	+	0.543036i
$759$		0			0
$760$	−61.7128	+	106.890i	−0.00294547	+	0.00510171i
$761$	−7963.82			−0.379354			−0.189677	−	0.981847i	$-0.560744\pi$
$761$	−7963.82			−0.379354			−0.189677	+	0.981847i	$0.560744\pi$
$762$		0			0
$763$	2526.97	−	7696.46i	0.119898	−	0.365178i
$764$	−1898.14			−0.0898854
$765$		0			0
$766$	13220.8	+	22899.0i	0.623611	+	1.08013i
$767$	1440.06			0.0677932
$768$		0			0
$769$	11183.7	+	19370.7i	0.524439	+	0.908355i	0.999595	+	0.0284535i	$0.00905826\pi$
$769$	11183.7	+	19370.7i	0.524439	+	0.908355i	−0.475156	+	0.879902i	$0.657608\pi$
$770$	4118.57	−	12544.0i	0.192757	−	0.587085i
$771$		0			0
$772$	815.110	+	1411.81i	0.0380006	+	0.0658189i
$773$	14269.9	+	24716.1i	0.663974	+	1.15004i	0.979562	+	0.201140i	$0.0644647\pi$
$773$	14269.9	+	24716.1i	0.663974	+	1.15004i	−0.315589	+	0.948896i	$0.602202\pi$
$774$		0			0
$775$	−16885.2	+	29246.0i	−0.782623	+	1.35554i
$776$	−10706.0	+	18543.3i	−0.495260	+	0.857815i
$777$		0			0
$778$	2036.99	+	3528.17i	0.0938683	+	0.162585i
$779$	−605.656			−0.0278561
$780$		0			0
$781$	16755.6			0.767684
$782$	8852.17	−	15332.4i	0.404799	−	0.701133i
$783$		0			0
$784$	−21528.8	+	9426.75i	−0.980723	+	0.429426i
$785$	3161.07	−	5475.14i	0.143724	−	0.248938i
$786$		0			0
$787$	14057.4	−	24348.1i	0.636711	−	1.10282i	−0.349439	−	0.936959i	$-0.613628\pi$
$787$	14057.4	−	24348.1i	0.636711	−	1.10282i	0.986150	−	0.165856i	$-0.0530388\pi$
$788$	−438.763	+	759.960i	−0.0198354	+	0.0343559i
$789$		0			0
$790$	5882.80	−	10189.3i	0.264937	−	0.458885i
$791$	1821.67	−	5548.32i	0.0818853	−	0.249400i
$792$		0			0
$793$	−307.521	+	532.643i	−0.0137710	+	0.0238521i
$794$	−6198.21			−0.277035
$795$		0			0
$796$	−1246.82			−0.0555181
$797$	−798.238	−	1382.59i	−0.0354769	−	0.0614477i	0.847742	−	0.530409i	$-0.177962\pi$
$797$	−798.238	−	1382.59i	−0.0354769	−	0.0614477i	−0.883219	+	0.468961i	$0.844628\pi$
$798$		0			0
$799$	6352.95	−	11003.6i	0.281291	−	0.487210i
$800$	−1537.71	+	2663.40i	−0.0679579	+	0.117707i
$801$		0			0
$802$	−22543.0	−	39045.6i	−0.992544	−	1.71914i
$803$	22612.9	+	39166.7i	0.993764	+	1.72125i
$804$		0			0
$805$	5479.83	+	6123.80i	0.239924	+	0.268119i
$806$	−2438.58	−	4223.74i	−0.106570	−	0.184584i
$807$		0			0
$808$	16295.1			0.709479
$809$	−17244.2	−	29867.8i	−0.749411	−	1.29802i	−0.948105	−	0.317956i	$-0.897004\pi$
$809$	−17244.2	−	29867.8i	−0.749411	−	1.29802i	0.198695	−	0.980061i	$-0.436330\pi$
$810$		0			0
$811$	13083.8			0.566504			0.283252	−	0.959046i	$-0.408587\pi$
$811$	13083.8			0.566504			0.283252	+	0.959046i	$0.408587\pi$
$812$	−277.757	+	845.971i	−0.0120041	+	0.0365613i
$813$		0			0
$814$	−37266.3			−1.60465
$815$	−6265.34	+	10851.9i	−0.269283	+	0.466411i
$816$		0			0
$817$	212.591	+	368.218i	0.00910357	+	0.0157678i
$818$	7413.79			0.316891
$819$		0			0
$820$	889.581			0.0378848
$821$	13860.4	+	24006.9i	0.589197	+	1.02052i	0.994338	+	0.106265i	$0.0338891\pi$
$821$	13860.4	+	24006.9i	0.589197	+	1.02052i	−0.405141	+	0.914254i	$0.632778\pi$
$822$		0			0
$823$	−21016.5	+	36401.6i	−0.890144	+	1.54178i	−0.0504427	+	0.998727i	$0.516063\pi$
$823$	−21016.5	+	36401.6i	−0.890144	+	1.54178i	−0.839702	+	0.543048i	$0.817270\pi$
$824$	11990.7			0.506937
$825$		0			0
$826$	−9525.50	−	10644.9i	−0.401253	−	0.448406i
$827$	37151.6			1.56214			0.781069	−	0.624444i	$-0.214675\pi$
$827$	37151.6			1.56214			0.781069	+	0.624444i	$0.214675\pi$
$828$		0			0
$829$	−16093.7	−	27875.1i	−0.674254	−	1.16784i	−0.976686	−	0.214671i	$-0.931132\pi$
$829$	−16093.7	−	27875.1i	−0.674254	−	1.16784i	0.302432	−	0.953171i	$-0.402201\pi$
$830$	3300.03			0.138007
$831$		0			0
$832$	1279.60	+	2216.34i	0.0533201	+	0.0923531i
$833$	−15794.4	+	6915.84i	−0.656955	+	0.287659i
$834$		0			0
$835$	−2894.06	−	5012.67i	−0.119944	−	0.207749i
$836$	30.9451	+	53.5985i	0.00128021	+	0.00221739i
$837$		0			0
$838$	−20971.2	+	36323.2i	−0.864486	+	1.49733i
$839$	10945.1	−	18957.4i	0.450376	−	0.780075i	−0.548033	−	0.836457i	$-0.684623\pi$
$839$	10945.1	−	18957.4i	0.450376	−	0.780075i	0.998409	+	0.0563819i	$0.0179564\pi$
$840$		0			0
$841$	9106.03	+	15772.1i	0.373366	+	0.646689i
$842$	−28891.5			−1.18250
$843$		0			0
$844$	−567.399			−0.0231406
$845$	4005.78	−	6938.21i	0.163080	−	0.282464i
$846$		0			0
$847$	36882.8	+	41217.1i	1.49623	+	1.67206i
$848$	−13994.7	+	24239.5i	−0.566722	+	0.981591i
$849$		0			0
$850$	−8211.64	+	14223.0i	−0.331361	+	0.573934i
$851$	11597.5	−	20087.5i	0.467165	−	0.809154i
$852$		0			0
$853$	−4501.76	+	7797.27i	−0.180700	+	0.312982i	−0.942119	−	0.335278i	$-0.891170\pi$
$853$	−4501.76	+	7797.27i	−0.180700	+	0.312982i	0.761419	+	0.648260i	$0.224503\pi$
$854$	5971.46	−	1250.06i	0.239273	−	0.0500891i
$855$		0			0
$856$	2952.36	−	5113.63i	0.117885	−	0.204183i
$857$	28529.0			1.13714			0.568571	−	0.822634i	$-0.307496\pi$
$857$	28529.0			1.13714			0.568571	+	0.822634i	$0.307496\pi$
$858$		0			0
$859$	12326.0			0.489591			0.244796	−	0.969575i	$-0.421279\pi$
$859$	12326.0			0.489591			0.244796	+	0.969575i	$0.421279\pi$
$860$	−312.251	−	540.835i	−0.0123810	−	0.0214446i
$861$		0			0
$862$	545.284	−	944.459i	0.0215458	−	0.0373183i
$863$	−1048.43	+	1815.93i	−0.0413544	+	0.0716280i	−0.885962	−	0.463758i	$-0.846501\pi$
$863$	−1048.43	+	1815.93i	−0.0413544	+	0.0716280i	0.844607	+	0.535386i	$0.179834\pi$
$864$		0			0
$865$	5266.22	+	9121.36i	0.207002	+	0.358538i
$866$	1724.82	+	2987.47i	0.0676809	+	0.117227i
$867$		0			0
$868$	−1072.00	+	3265.02i	−0.0419195	+	0.127675i
$869$	35628.0	+	61709.4i	1.39079	+	2.40892i
$870$		0			0
$871$	538.417			0.0209455
$872$	4741.69	+	8212.85i	0.184144	+	0.318947i
$873$		0			0
$874$	−542.298			−0.0209880
$875$	−10790.7	−	12058.8i	−0.416907	−	0.465900i
$876$		0			0
$877$	−14210.7			−0.547162			−0.273581	−	0.961849i	$-0.588208\pi$
$877$	−14210.7			−0.547162			−0.273581	+	0.961849i	$0.588208\pi$
$878$	−19741.1	+	34192.6i	−0.758805	+	1.31429i
$879$		0			0
$880$	8322.63	+	14415.2i	0.318813	+	0.552201i
$881$	−19902.7			−0.761112			−0.380556	−	0.924758i	$-0.624267\pi$
$881$	−19902.7			−0.761112			−0.380556	+	0.924758i	$0.624267\pi$
$882$		0			0
$883$	−34383.9			−1.31043			−0.655216	−	0.755442i	$-0.727422\pi$
$883$	−34383.9			−1.31043			−0.655216	+	0.755442i	$0.727422\pi$
$884$	−84.2410	−	145.910i	−0.00320513	−	0.00555144i
$885$		0			0
$886$	9287.41	−	16086.3i	0.352163	−	0.609965i
$887$	8601.22			0.325593			0.162796	−	0.986660i	$-0.447949\pi$
$887$	8601.22			0.325593			0.162796	+	0.986660i	$0.447949\pi$
$888$		0			0
$889$	3889.19	+	4346.23i	0.146726	+	0.163968i
$890$	11946.4			0.449936
$891$		0			0
$892$	−1244.05	−	2154.76i	−0.0466973	−	0.0808820i
$893$	−389.192			−0.0145843
$894$		0			0
$895$	−7411.77	−	12837.6i	−0.276814	−	0.479455i
$896$	9195.78	−	28007.8i	0.342868	−	1.04428i
$897$		0			0
$898$	945.773	+	1638.13i	0.0351457	+	0.0608742i
$899$	−11919.9	−	20646.0i	−0.442216	−	0.765941i
$900$		0			0
$901$	−10267.1	+	17783.1i	−0.379629	+	0.657537i
$902$	−37922.8	+	65684.2i	−1.39988	+	2.42466i
$903$		0			0
$904$	3418.25	+	5920.58i	0.125762	+	0.217827i
$905$	−17557.8			−0.644905
$906$		0			0
$907$	8836.23			0.323486			0.161743	−	0.986833i	$-0.448288\pi$
$907$	8836.23			0.323486			0.161743	+	0.986833i	$0.448288\pi$
$908$	232.933	−	403.452i	0.00851339	−	0.0147456i
$909$		0			0
$910$	1077.57	−	225.577i	0.0392539	−	0.00821736i
$911$	−1061.16	+	1837.99i	−0.0385926	+	0.0668443i	−0.884677	−	0.466205i	$-0.845621\pi$
$911$	−1061.16	+	1837.99i	−0.0385926	+	0.0668443i	0.846084	+	0.533050i	$0.178954\pi$
$912$		0			0
$913$	−9992.97	+	17308.3i	−0.362233	+	0.627406i
$914$	−3871.01	+	6704.78i	−0.140089	+	0.242642i
$915$		0			0
$916$	1570.24	−	2719.73i	0.0566398	−	0.0981030i
$917$	−21102.4	−	23582.2i	−0.759936	−	0.849241i
$918$		0			0
$919$	8985.22	−	15562.9i	0.322519	−	0.558620i	−0.658488	−	0.752591i	$-0.728804\pi$
$919$	8985.22	−	15562.9i	0.322519	−	0.558620i	0.981007	+	0.193972i	$0.0621370\pi$
$920$	−9620.28			−0.344751
$921$		0			0
$922$	10683.3			0.381599
$923$	698.584	+	1209.98i	0.0249124	+	0.0431496i
$924$		0			0
$925$	−10758.3	+	18634.0i	−0.382413	+	0.662359i
$926$	−9349.85	+	16194.4i	−0.331809	+	0.574710i
$927$		0			0
$928$	−1085.54	−	1880.20i	−0.0383992	−	0.0665094i
$929$	−24164.3	−	41853.9i	−0.853398	−	1.47813i	−0.878123	−	0.478434i	$-0.841205\pi$
$929$	−24164.3	−	41853.9i	−0.853398	−	1.47813i	0.0247257	−	0.999694i	$-0.492129\pi$
$930$		0			0
$931$	425.354	+	313.060i	0.0149736	+	0.0110205i
$932$	439.439	+	761.130i	0.0154445	+	0.0267507i
$933$		0			0
$934$	14078.3			0.493208
$935$	6105.81	+	10575.6i	0.213563	+	0.369902i
$936$		0			0
$937$	39874.3			1.39022			0.695111	−	0.718903i	$-0.255355\pi$
$937$	39874.3			1.39022			0.695111	+	0.718903i	$0.255355\pi$
$938$	−3561.45	−	3979.98i	−0.123972	−	0.138540i
$939$		0			0
$940$	571.640			0.0198349
$941$	−14055.9	+	24345.5i	−0.486937	+	0.843400i	−0.999887	−	0.0150185i	$-0.995219\pi$
$941$	−14055.9	+	24345.5i	−0.486937	+	0.843400i	0.512950	+	0.858418i	$0.328553\pi$
$942$		0			0
$943$	−23603.6	−	40882.7i	−0.815100	−	1.41179i
$944$	18009.0			0.620915
$945$		0			0
$946$	53245.0			1.82996
$947$	−15922.3	−	27578.3i	−0.546363	−	0.946328i	−0.998520	−	0.0543899i	$-0.982679\pi$
$947$	−15922.3	−	27578.3i	−0.546363	−	0.946328i	0.452157	−	0.891938i	$-0.350655\pi$
$948$		0			0
$949$	−1885.59	+	3265.93i	−0.0644981	+	0.111714i
$950$	503.058			0.0171804
$951$		0			0
$952$	6296.67	−	19177.9i	0.214366	−	0.652900i
$953$	−20409.8			−0.693745			−0.346872	−	0.937912i	$-0.612756\pi$
$953$	−20409.8			−0.693745			−0.346872	+	0.937912i	$0.612756\pi$
$954$		0			0
$955$	5735.99	+	9935.03i	0.194358	+	0.336639i
$956$	1665.28			0.0563379
$957$		0			0
$958$	17519.4	+	30344.5i	0.590841	+	1.02337i
$959$	10820.6	+	12092.2i	0.364354	+	0.407171i
$960$		0			0
$961$	−31109.5	−	53883.3i	−1.04426	−	1.80871i
$962$	−1553.73	−	2691.14i	−0.0520731	−	0.0901933i
$963$		0			0
$964$	1893.25	−	3279.20i	0.0632546	−	0.109560i
$965$	4926.35	−	8532.70i	0.164337	−	0.284640i
$966$		0			0
$967$	−3545.97	−	6141.80i	−0.117922	−	0.204247i	0.801022	−	0.598635i	$-0.204290\pi$
$967$	−3545.97	−	6141.80i	−0.117922	−	0.204247i	−0.918944	+	0.394388i	$0.870957\pi$
$968$	−64750.7			−2.14997
$969$		0			0
$970$	−10714.6			−0.354664
$971$	23512.6	−	40725.1i	0.777092	−	1.34596i	−0.156519	−	0.987675i	$-0.550027\pi$
$971$	23512.6	−	40725.1i	0.777092	−	1.34596i	0.933611	−	0.358289i	$-0.116640\pi$
$972$		0			0
$973$	4254.22	−	12957.2i	0.140168	−	0.426915i
$974$	13598.3	−	23553.0i	0.447349	−	0.774832i
$975$		0			0
$976$	−3845.80	+	6661.11i	−0.126128	+	0.218460i
$977$	5866.45	−	10161.0i	0.192103	−	0.332732i	−0.753844	−	0.657053i	$-0.771803\pi$
$977$	5866.45	−	10161.0i	0.192103	−	0.332732i	0.945947	+	0.324322i	$0.105136\pi$
$978$		0			0
$979$	−36175.4	+	62657.6i	−1.18097	+	2.04550i
$980$	−624.755	−	459.818i	−0.0203643	−	0.0149881i
$981$		0			0
$982$	−8127.87	+	14077.9i	−0.264125	+	0.457478i
$983$	−41057.2			−1.33217			−0.666084	−	0.745877i	$-0.732031\pi$
$983$	−41057.2			−1.33217			−0.666084	+	0.745877i	$0.732031\pi$
$984$		0			0
$985$	5303.59			0.171560
$986$	−5796.94	−	10040.6i	−0.187234	−	0.324298i
$987$		0			0
$988$	−2.58037	+	4.46933i	−8.30895e−5	+	0.000143915i
$989$	−16570.2	+	28700.4i	−0.532761	+	0.922770i
$990$		0			0
$991$	−12058.6	−	20886.1i	−0.386532	−	0.669493i	0.605449	−	0.795884i	$-0.292994\pi$
$991$	−12058.6	−	20886.1i	−0.386532	−	0.669493i	−0.991980	+	0.126392i	$0.959660\pi$
$992$	−4189.62	−	7256.64i	−0.134093	−	0.232257i
$993$		0			0
$994$	4323.30	−	13167.6i	0.137954	−	0.420172i
$995$	3767.77	+	6525.96i	0.120046	+	0.207927i
$996$		0			0
$997$	−11015.9			−0.349927			−0.174964	−	0.984575i	$-0.555981\pi$
$997$	−11015.9			−0.349927			−0.174964	+	0.984575i	$0.555981\pi$
$998$	−7633.04	−	13220.8i	−0.242104	−	0.419336i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.6		44
3.2	odd	2		63.4.g.a.16.17	yes	44
7.4	even	3		189.4.h.a.46.17		44
9.4	even	3		189.4.h.a.37.17		44
9.5	odd	6		63.4.h.a.58.6	yes	44
21.11	odd	6		63.4.h.a.25.6	yes	44
63.4	even	3	inner	189.4.g.a.172.6		44
63.32	odd	6		63.4.g.a.4.17	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.17	✓	44	63.32	odd	6
63.4.g.a.16.17	yes	44	3.2	odd	2
63.4.h.a.25.6	yes	44	21.11	odd	6
63.4.h.a.58.6	yes	44	9.5	odd	6
189.4.g.a.100.6		44	1.1	even	1	trivial
189.4.g.a.172.6		44	63.4	even	3	inner
189.4.h.a.37.17		44	9.4	even	3
189.4.h.a.46.17		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)

\(f(q)\)	\(=\)	\(q+(-1.46729 - 2.54141i) q^{2} +(-0.305860 + 0.529765i) q^{4} +3.69711 q^{5} +(12.3500 + 13.8013i) q^{7} -21.6814 q^{8} +O(q^{10})\)	\(q+(-1.46729 - 2.54141i) q^{2} +(-0.305860 + 0.529765i) q^{4} +3.69711 q^{5} +(12.3500 + 13.8013i) q^{7} -21.6814 q^{8} +(-5.42471 - 9.39588i) q^{10} +65.7074 q^{11} +(2.73952 + 4.74498i) q^{13} +(16.9539 - 51.6370i) q^{14} +(34.2598 + 59.3397i) q^{16} +(25.1343 + 43.5340i) q^{17} +(0.769884 - 1.33348i) q^{19} +(-1.13080 + 1.95860i) q^{20} +(-96.4115 - 166.990i) q^{22} +120.016 q^{23} -111.331 q^{25} +(8.03931 - 13.9245i) q^{26} +(-11.0888 + 2.32133i) q^{28} +(39.2967 - 68.0640i) q^{29} +(151.666 - 262.693i) q^{31} +(13.8120 - 23.9231i) q^{32} +(73.7586 - 127.754i) q^{34} +(45.6593 + 51.0250i) q^{35} +(96.6335 - 167.374i) q^{37} -4.51856 q^{38} -80.1586 q^{40} +(-196.671 - 340.645i) q^{41} +(-138.067 + 239.139i) q^{43} +(-20.0972 + 34.8095i) q^{44} +(-176.097 - 305.009i) q^{46} +(-126.380 - 218.896i) q^{47} +(-37.9542 + 340.894i) q^{49} +(163.355 + 282.939i) q^{50} -3.35163 q^{52} +(204.244 + 353.761i) q^{53} +242.927 q^{55} +(-267.766 - 299.233i) q^{56} -230.638 q^{58} +(131.415 - 227.618i) q^{59} +(56.1270 + 97.2148i) q^{61} -890.149 q^{62} +467.092 q^{64} +(10.1283 + 17.5427i) q^{65} +(49.1343 - 85.1031i) q^{67} -30.7503 q^{68} +(62.6805 - 190.908i) q^{70} +255.003 q^{71} +(344.146 + 596.078i) q^{73} -567.156 q^{74} +(0.470953 + 0.815715i) q^{76} +(811.487 + 906.850i) q^{77} +(542.222 + 939.155i) q^{79} +(126.662 + 219.385i) q^{80} +(-577.146 + 999.647i) q^{82} +(-152.083 + 263.415i) q^{83} +(92.9243 + 160.950i) q^{85} +810.335 q^{86} -1424.63 q^{88} +(-550.553 + 953.585i) q^{89} +(-31.6540 + 96.4096i) q^{91} +(-36.7079 + 63.5800i) q^{92} +(-370.871 + 642.368i) q^{94} +(2.84634 - 4.93001i) q^{95} +(493.784 - 855.260i) q^{97} +(922.042 - 403.731i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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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