LMFDB - Embedded newform 189.4.h.a.37.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.17
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.93457 q^{2} +0.611720 q^{4} +(-1.84855 - 3.20179i) q^{5} +(-18.1273 + 3.79476i) q^{7} -21.6814 q^{8} +O(q^{10})$	\(q+2.93457 q^{2} +0.611720 q^{4} +(-1.84855 - 3.20179i) q^{5} +(-18.1273 + 3.79476i) q^{7} -21.6814 q^{8} +(-5.42471 - 9.39588i) q^{10} +(-32.8537 + 56.9043i) q^{11} +(2.73952 - 4.74498i) q^{13} +(-53.1960 + 11.1360i) q^{14} -68.5196 q^{16} +(25.1343 + 43.5340i) q^{17} +(0.769884 - 1.33348i) q^{19} +(-1.13080 - 1.95860i) q^{20} +(-96.4115 + 166.990i) q^{22} +(-60.0078 - 103.936i) q^{23} +(55.6657 - 96.4158i) q^{25} +(8.03931 - 13.9245i) q^{26} +(-11.0888 + 2.32133i) q^{28} +(39.2967 + 68.0640i) q^{29} -303.332 q^{31} -27.6241 q^{32} +(73.7586 + 127.754i) q^{34} +(45.6593 + 51.0250i) q^{35} +(96.6335 - 167.374i) q^{37} +(2.25928 - 3.91319i) q^{38} +(40.0793 + 69.4194i) q^{40} +(-196.671 + 340.645i) q^{41} +(-138.067 - 239.139i) q^{43} +(-20.0972 + 34.8095i) q^{44} +(-176.097 - 305.009i) q^{46} +252.760 q^{47} +(314.200 - 137.578i) q^{49} +(163.355 - 282.939i) q^{50} +(1.67582 - 2.90260i) q^{52} +(204.244 + 353.761i) q^{53} +242.927 q^{55} +(393.027 - 82.2758i) q^{56} +(115.319 + 199.739i) q^{58} -262.830 q^{59} -112.254 q^{61} -890.149 q^{62} +467.092 q^{64} -20.2566 q^{65} -98.2686 q^{67} +(15.3752 + 26.6306i) q^{68} +(133.991 + 149.737i) q^{70} +255.003 q^{71} +(344.146 + 596.078i) q^{73} +(283.578 - 491.172i) q^{74} +(0.470953 - 0.815715i) q^{76} +(379.612 - 1156.19i) q^{77} -1084.44 q^{79} +(126.662 + 219.385i) q^{80} +(-577.146 + 999.647i) q^{82} +(-152.083 - 263.415i) q^{83} +(92.9243 - 160.950i) q^{85} +(-405.167 - 701.771i) q^{86} +(712.315 - 1233.77i) q^{88} +(-550.553 + 953.585i) q^{89} +(-31.6540 + 96.4096i) q^{91} +(-36.7079 - 63.5800i) q^{92} +741.742 q^{94} -5.69269 q^{95} +(493.784 + 855.260i) q^{97} +(922.042 - 403.731i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.93457			1.03753			0.518764	−	0.854917i	$-0.326392\pi$
$2$	2.93457			1.03753			0.518764	+	0.854917i	$0.326392\pi$
$3$		0			0
$3$		0			0
$4$	0.611720			0.0764650
$5$	−1.84855	−	3.20179i	−0.165340	−	0.286377i	0.771436	−	0.636307i	$-0.219539\pi$
$5$	−1.84855	−	3.20179i	−0.165340	−	0.286377i	−0.936776	+	0.349930i	$0.886205\pi$
$6$		0			0
$7$	−18.1273	+	3.79476i	−0.978783	+	0.204898i
$7$	−18.1273	+	3.79476i	−0.978783	+	0.204898i
$8$	−21.6814			−0.958194
$9$		0			0
$10$	−5.42471	−	9.39588i	−0.171545	−	0.297124i
$11$	−32.8537	+	56.9043i	−0.900524	+	1.55975i	−0.0737076	+	0.997280i	$0.523483\pi$
$11$	−32.8537	+	56.9043i	−0.900524	+	1.55975i	−0.826816	+	0.562473i	$0.809850\pi$
$12$		0			0
$13$	2.73952	−	4.74498i	0.0584465	−	0.101232i	−0.835322	−	0.549761i	$-0.814719\pi$
$13$	2.73952	−	4.74498i	0.0584465	−	0.101232i	0.893768	+	0.448529i	$0.148052\pi$
$14$	−53.1960	+	11.1360i	−1.01552	+	0.212587i
$15$		0			0
$16$	−68.5196			−1.07062
$17$	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
$23$	−60.0078	−	103.936i	−0.544021	−	0.942272i	−0.998668	−	0.0516002i	$-0.983568\pi$
$23$	−60.0078	−	103.936i	−0.544021	−	0.942272i	0.454647	−	0.890672i	$-0.349765\pi$
$24$		0			0
$25$	55.6657	−	96.4158i	0.445326	−	0.771327i
$26$	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	0.963974	−	0.265995i	$-0.0857006\pi$
$29$	39.2967	+	68.0640i	0.251628	+	0.435833i	−0.712346	+	0.701829i	$0.752367\pi$
$30$		0			0
$31$	−303.332			−1.75742			−0.878709	−	0.477358i	$-0.841595\pi$
$31$	−303.332			−1.75742			−0.878709	+	0.477358i	$0.841595\pi$
$32$	−27.6241			−0.152603
$33$		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	$0.0254046\pi$
$38$	2.25928	−	3.91319i	0.00964484	−	0.0167053i
$39$		0			0
$40$	40.0793	+	69.4194i	0.158427	+	0.274404i
$41$	−196.671	+	340.645i	−0.749144	+	1.29756i	0.199090	+	0.979981i	$0.436202\pi$
$41$	−196.671	+	340.645i	−0.749144	+	1.29756i	−0.948233	+	0.317574i	$0.897132\pi$
$42$		0			0
$43$	−138.067	−	239.139i	−0.489651	−	0.848101i	0.510278	−	0.860010i	$-0.329543\pi$
$43$	−138.067	−	239.139i	−0.489651	−	0.848101i	−0.999929	+	0.0119087i	$0.996209\pi$
$44$	−20.0972	+	34.8095i	−0.0688585	+	0.119266i
$45$		0			0
$46$	−176.097	−	305.009i	−0.564437	−	0.977634i
$47$	252.760			0.784443			0.392221	−	0.919871i	$-0.371707\pi$
$47$	252.760			0.784443			0.392221	+	0.919871i	$0.371707\pi$
$48$		0			0
$49$	314.200	−	137.578i	0.916034	−	0.401101i
$50$	163.355	−	282.939i	0.462038	−	0.800273i
$51$		0			0
$52$	1.67582	−	2.90260i	0.00446911	−	0.00774073i
$53$	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
$56$	393.027	−	82.2758i	0.937864	−	0.196332i
$57$		0			0
$58$	115.319	+	199.739i	0.261072	+	0.452189i
$59$	−262.830			−0.579959			−0.289980	−	0.957033i	$-0.593649\pi$
$59$	−262.830			−0.579959			−0.289980	+	0.957033i	$0.593649\pi$
$60$		0			0
$61$	−112.254			−0.235617			−0.117809	−	0.993036i	$-0.537587\pi$
$61$	−112.254			−0.235617			−0.117809	+	0.993036i	$0.537587\pi$
$62$	−890.149			−1.82337
$63$		0			0
$64$	467.092			0.912288
$65$	−20.2566			−0.0386541
$66$		0			0
$67$	−98.2686			−0.179185			−0.0895926	−	0.995978i	$-0.528557\pi$
$67$	−98.2686			−0.179185			−0.0895926	+	0.995978i	$0.528557\pi$
$68$	15.3752	+	26.6306i	0.0274193	+	0.0474916i
$69$		0			0
$70$	133.991	+	149.737i	0.228785	+	0.255671i
$71$	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	$0.647286\pi$
$74$	283.578	−	491.172i	0.445477	−	0.771588i
$75$		0			0
$76$	0.470953	−	0.815715i	0.000710816	−	0.00123117i
$77$	379.612	−	1156.19i	0.561828	−	1.71117i
$78$		0			0
$79$	−1084.44			−1.54442			−0.772211	−	0.635366i	$-0.780849\pi$
$79$	−1084.44			−1.54442			−0.772211	+	0.635366i	$0.780849\pi$
$80$	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	0.747767	−	0.663961i	$-0.231126\pi$
$83$	−152.083	−	263.415i	−0.201124	−	0.348356i	−0.948891	+	0.315605i	$0.897793\pi$
$84$		0			0
$85$	92.9243	−	160.950i	0.118577	−	0.205382i
$86$	−405.167	−	701.771i	−0.508027	−	0.879929i
$87$		0			0
$88$	712.315	−	1233.77i	0.862876	−	1.49455i
$89$	−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
$94$	741.742			0.813882
$95$	−5.69269			−0.00614797
$96$		0			0
$97$	493.784	+	855.260i	0.516868	+	0.895242i	0.999808	+	0.0195884i	$0.00623557\pi$
$97$	493.784	+	855.260i	0.516868	+	0.895242i	−0.482940	+	0.875653i	$0.660431\pi$
$98$	922.042	−	403.731i	0.950411	−	0.416153i
$99$		0			0
$100$	34.0518	−	58.9795i	0.0340518	−	0.0589795i
$101$	375.784	−	650.877i	0.370217	−	0.641235i	−0.619382	−	0.785090i	$-0.712617\pi$
$101$	375.784	−	650.877i	0.370217	−	0.641235i	0.989599	+	0.143855i	$0.0459500\pi$
$102$		0			0
$103$	276.520	+	478.947i	0.264528	+	0.458175i	0.967440	−	0.253102i	$-0.0814507\pi$
$103$	276.520	+	478.947i	0.264528	+	0.458175i	−0.702912	+	0.711277i	$0.748117\pi$
$104$	−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	$0.894889\pi$
$110$	712.888			0.617920
$111$		0			0
$112$	1242.08	−	260.015i	1.04790	−	0.219367i
$113$	−157.658	+	273.071i	−0.131250	+	0.227331i	−0.924159	−	0.382009i	$-0.875232\pi$
$113$	−157.658	+	273.071i	−0.131250	+	0.227331i	0.792909	+	0.609340i	$0.208566\pi$
$114$		0			0
$115$	−221.855	+	384.264i	−0.179896	+	0.311590i
$116$	24.0386	+	41.6361i	0.0192408	+	0.0333260i
$117$		0			0
$118$	−771.295			−0.601724
$119$	−620.819	−	693.775i	−0.478238	−	0.534439i
$120$		0			0
$121$	−1493.23	−	2586.35i	−1.12189	−	1.94316i
$122$	−329.417			−0.244459
$123$		0			0
$124$	−185.554			−0.134381
$125$	−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	$0.464910\pi$
$128$	1591.71			1.09913
$129$		0			0
$130$	−59.4444			−0.0401047
$131$	854.346	+	1479.77i	0.569806	+	0.986932i	0.996585	+	0.0825765i	$0.0263149\pi$
$131$	854.346	+	1479.77i	0.569806	+	0.986932i	−0.426779	+	0.904356i	$0.640352\pi$
$132$		0			0
$133$	−8.89571	+	27.0939i	−0.00579967	+	0.0176642i
$134$	−288.376			−0.185910
$135$		0			0
$136$	−544.949	−	943.879i	−0.343595	−	0.595125i
$137$	−438.080	+	758.777i	−0.273195	+	0.473188i	−0.969678	−	0.244385i	$-0.921414\pi$
$137$	−438.080	+	758.777i	−0.273195	+	0.473188i	0.696483	+	0.717573i	$0.254747\pi$
$138$		0			0
$139$	−368.183	+	637.712i	−0.224668	+	0.389137i	−0.956220	−	0.292649i	$-0.905463\pi$
$139$	−368.183	+	637.712i	−0.224668	+	0.389137i	0.731552	+	0.681786i	$0.238797\pi$
$140$	27.9307	+	31.2130i	0.0168613	+	0.0188427i
$141$		0			0
$142$	748.324			0.442239
$143$	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
$149$	−161.831	−	280.300i	−0.0889781	−	0.154115i	0.818101	−	0.575074i	$-0.195027\pi$
$149$	−161.831	−	280.300i	−0.0889781	−	0.154115i	−0.907079	+	0.420959i	$0.861693\pi$
$150$		0			0
$151$	1375.69	−	2382.76i	0.741404	−	1.28415i	−0.210452	−	0.977604i	$-0.567494\pi$
$151$	1375.69	−	2382.76i	0.741404	−	1.28415i	0.951856	−	0.306545i	$-0.0991732\pi$
$152$	−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
$157$	−1710.03			−0.869267			−0.434634	−	0.900607i	$-0.643122\pi$
$157$	−1710.03			−0.869267			−0.434634	+	0.900607i	$0.643122\pi$
$158$	−3182.38			−1.60238
$159$		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	$0.863770\pi$
$164$	−120.308	+	208.379i	−0.0572833	+	0.0992175i
$165$		0			0
$166$	−446.298	−	773.011i	−0.208672	−	0.361430i
$167$	−782.792	+	1355.83i	−0.362720	+	0.628249i	−0.988407	−	0.151824i	$-0.951485\pi$
$167$	−782.792	+	1355.83i	−0.362720	+	0.628249i	0.625688	+	0.780074i	$0.284819\pi$
$168$		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
$173$	−2848.83			−1.25198			−0.625991	−	0.779830i	$-0.715305\pi$
$173$	−2848.83			−1.25198			−0.625991	+	0.779830i	$0.715305\pi$
$174$		0			0
$175$	−643.196	+	1959.00i	−0.277834	+	0.846208i
$176$	2251.12	−	3899.05i	0.964117	−	1.66990i
$177$		0			0
$178$	−1615.64	+	2798.37i	−0.680321	+	1.17835i
$179$	−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	$0.928850\pi$
$182$	−92.8911	+	282.921i	−0.0378327	+	0.115228i
$183$		0			0
$184$	1301.06	+	2253.49i	0.521278	+	0.902879i
$185$	−714.529			−0.283963
$186$		0			0
$187$	−3303.02			−1.29166
$188$	154.618			0.0599824
$189$		0			0
$190$	−16.7056			−0.00637869
$191$	−3102.96			−1.17551			−0.587755	−	0.809039i	$-0.699988\pi$
$191$	−3102.96			−1.17551			−0.587755	+	0.809039i	$0.699988\pi$
$192$		0			0
$193$	−2664.98			−0.993934			−0.496967	−	0.867769i	$-0.665553\pi$
$193$	−2664.98			−0.993934			−0.496967	+	0.867769i	$0.665553\pi$
$194$	1449.05	+	2509.82i	0.536265	+	0.928839i
$195$		0			0
$196$	192.202	−	84.1589i	0.0700445	−	0.0306701i
$197$	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	$0.715076\pi$
$200$	−1206.91	+	2090.43i	−0.426708	+	0.739080i
$201$		0			0
$202$	1102.77	−	1910.05i	0.384111	−	0.665299i
$203$	−970.631	−	1084.70i	−0.335591	−	0.375028i
$204$		0			0
$205$	1454.23			0.495453
$206$	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	−0.780396	−	0.625286i	$-0.784983\pi$
$211$	463.774	−	803.279i	0.151315	−	0.262085i	0.931711	+	0.363200i	$0.118316\pi$
$212$	124.940	+	216.403i	0.0404760	+	0.0701065i
$213$		0			0
$214$	−399.600	+	692.128i	−0.127645	+	0.221088i
$215$	−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
$220$	148.603			0.0455402
$221$	275.424			0.0838326
$222$		0			0
$223$	−2033.70	−	3522.47i	−0.610702	−	1.05777i	−0.991122	−	0.132953i	$-0.957554\pi$
$223$	−2033.70	−	3522.47i	−0.610702	−	1.05777i	0.380421	−	0.924814i	$-0.375779\pi$
$224$	500.750	−	104.827i	0.149365	−	0.0312679i
$225$		0			0
$226$	−462.658	+	801.348i	−0.136175	+	0.235862i
$227$	380.784	−	659.537i	0.111337	−	0.192842i	−0.804972	−	0.593312i	$-0.797820\pi$
$227$	380.784	−	659.537i	0.111337	−	0.192842i	0.916310	+	0.400471i	$0.131153\pi$
$228$		0			0
$229$	2566.92	+	4446.04i	0.740729	+	1.28298i	0.952164	+	0.305588i	$0.0988531\pi$
$229$	2566.92	+	4446.04i	0.740729	+	1.28298i	−0.211435	+	0.977392i	$0.567814\pi$
$230$	−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
$236$	−160.778			−0.0443466
$237$		0			0
$238$	−1821.84	−	2035.93i	−0.496186	−	0.554496i
$239$	−1361.15	+	2357.57i	−0.368390	+	0.638070i	−0.989314	−	0.145801i	$-0.953424\pi$
$239$	−1361.15	+	2357.57i	−0.368390	+	0.638070i	0.620924	+	0.783871i	$0.286758\pi$
$240$		0			0
$241$	3094.96	−	5360.63i	0.827237	−	1.43282i	−0.0729607	−	0.997335i	$-0.523245\pi$
$241$	3094.96	−	5360.63i	0.827237	−	1.43282i	0.900198	−	0.435482i	$-0.143422\pi$
$242$	−4381.99	−	7589.83i	−1.16399	−	2.01609i
$243$		0			0
$244$	−68.6680			−0.0180165
$245$	−1021.31	−	751.681i	−0.266323	−	0.196013i
$246$		0			0
$247$	−4.21822	−	7.30617i	−0.00108663	−	0.00188211i
$248$	6576.67			1.68395
$249$		0			0
$250$	−2564.06			−0.648662
$251$	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
$254$	924.137			0.228290
$255$		0			0
$256$	934.248			0.228088
$257$	2991.46	+	5181.36i	0.726078	+	1.25760i	0.958529	+	0.284995i	$0.0919921\pi$
$257$	2991.46	+	5181.36i	0.726078	+	1.25760i	−0.232451	+	0.972608i	$0.574675\pi$
$258$		0			0
$259$	−1116.56	+	3400.74i	−0.267876	+	0.815876i
$260$	−12.3913			−0.00295569
$261$		0			0
$262$	2507.14	+	4342.50i	0.591190	+	1.02397i
$263$	1874.95	−	3247.51i	0.439598	−	0.761407i	−0.558060	−	0.829801i	$-0.688454\pi$
$263$	1874.95	−	3247.51i	0.439598	−	0.761407i	0.997658	+	0.0683939i	$0.0217875\pi$
$264$		0			0
$265$	755.112	−	1307.89i	0.175042	−	0.303182i
$266$	−26.1051	+	79.5091i	−0.00601732	+	0.0183271i
$267$		0			0
$268$	−60.1128			−0.0137014
$269$	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
$275$	3657.65	+	6335.23i	0.802052	+	1.38920i
$276$		0			0
$277$	2209.33	−	3826.67i	0.479226	−	0.830044i	−0.520490	−	0.853868i	$-0.674251\pi$
$277$	2209.33	−	3826.67i	0.479226	−	0.830044i	0.999716	+	0.0238239i	$0.00758409\pi$
$278$	−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	0.770376	−	0.637590i	$-0.220069\pi$
$281$	−786.552	−	1362.35i	−0.166981	−	0.289220i	−0.937357	+	0.348370i	$0.886735\pi$
$282$		0			0
$283$	4868.35			1.02259			0.511296	−	0.859405i	$-0.329166\pi$
$283$	4868.35			1.02259			0.511296	+	0.859405i	$0.329166\pi$
$284$	155.990			0.0325927
$285$		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
$290$	426.347	−	738.455i	0.0863310	−	0.149530i
$291$		0			0
$292$	210.521	+	364.633i	0.0421911	+	0.0730771i
$293$	4379.03	−	7584.70i	0.873125	−	1.51230i	0.0143787	−	0.999897i	$-0.495423\pi$
$293$	4379.03	−	7584.70i	0.873125	−	1.51230i	0.858747	−	0.512401i	$-0.171244\pi$
$294$		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
$299$	−657.569			−0.127185
$300$		0			0
$301$	3410.26	+	3811.02i	0.653036	+	0.729779i
$302$	4037.06	−	6992.40i	0.769228	−	1.33234i
$303$		0			0
$304$	−52.7521	+	91.3693i	−0.00995244	+	0.0172381i
$305$	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	$0.670419\pi$
$308$	232.216	−	707.266i	0.0429602	−	0.130845i
$309$		0			0
$310$	1645.49	+	2850.07i	0.301475	+	0.522171i
$311$	−1704.90			−0.310855			−0.155428	−	0.987847i	$-0.549676\pi$
$311$	−1704.90			−0.310855			−0.155428	+	0.987847i	$0.549676\pi$
$312$		0			0
$313$	−6652.59			−1.20136			−0.600681	−	0.799488i	$-0.705104\pi$
$313$	−6652.59			−1.20136			−0.600681	+	0.799488i	$0.705104\pi$
$314$	−5018.20			−0.901889
$315$		0			0
$316$	−663.375			−0.118094
$317$	4225.84			0.748728			0.374364	−	0.927282i	$-0.377861\pi$
$317$	4225.84			0.748728			0.374364	+	0.927282i	$0.377861\pi$
$318$		0			0
$319$	−5164.17			−0.906389
$320$	−863.444	−	1495.53i	−0.150837	−	0.261258i
$321$		0			0
$322$	4349.61	+	4860.76i	0.752777	+	0.841240i
$323$	77.4021			0.0133336
$324$		0			0
$325$	−304.994	−	528.265i	−0.0520555	−	0.0901627i
$326$	−4973.11	+	8613.67i	−0.844892	+	1.46340i
$327$		0			0
$328$	4264.12	−	7385.67i	0.717825	−	1.24331i
$329$	−4581.86	+	959.162i	−0.767800	+	0.160730i
$330$		0			0
$331$	4414.80			0.733109			0.366555	−	0.930396i	$-0.380537\pi$
$331$	4414.80			0.733109			0.366555	+	0.930396i	$0.380537\pi$
$332$	−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	−0.742648	−	0.669682i	$-0.766430\pi$
$337$	1290.74	−	2235.63i	0.208638	−	0.361372i	0.951286	+	0.308311i	$0.0997636\pi$
$338$	3179.58	+	5507.20i	0.511676	+	0.886248i
$339$		0			0
$340$	56.8436	−	98.4561i	0.00906700	−	0.0157045i
$341$	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
$346$	−8360.11			−1.29897
$347$	−6048.17			−0.935685			−0.467843	−	0.883812i	$-0.654969\pi$
$347$	−6048.17			−0.935685			−0.467843	+	0.883812i	$0.654969\pi$
$348$		0			0
$349$	5649.71	+	9785.58i	0.866538	+	1.50089i	0.865511	+	0.500889i	$0.166994\pi$
$349$	5649.71	+	9785.58i	0.866538	+	1.50089i	0.00102701	+	0.999999i	$0.499673\pi$
$350$	−1887.50	+	5748.82i	−0.288261	+	0.877965i
$351$		0			0
$352$	907.552	−	1571.93i	0.137422	−	0.238023i
$353$	518.102	−	897.379i	0.0781183	−	0.135305i	−0.824320	−	0.566125i	$-0.808442\pi$
$353$	518.102	−	897.379i	0.0781183	−	0.135305i	0.902438	+	0.430820i	$0.141775\pi$
$354$		0			0
$355$	−471.386	−	816.465i	−0.0704749	−	0.122066i
$356$	−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
$362$	−13936.4			−2.02343
$363$		0			0
$364$	−19.3634	+	58.9756i	−0.00278824	+	0.00849221i
$365$	1272.34	−	2203.76i	0.182459	−	0.316028i
$366$		0			0
$367$	1033.03	−	1789.26i	0.146931	−	0.254493i	−0.783160	−	0.621820i	$-0.786394\pi$
$367$	1033.03	−	1789.26i	0.146931	−	0.254493i	0.930092	+	0.367327i	$0.119727\pi$
$368$	4111.71	+	7121.68i	0.582439	+	1.00881i
$369$		0			0
$370$	−2096.84			−0.294620
$371$	−5044.83	−	5637.68i	−0.705969	−	0.788932i
$372$		0			0
$373$	−2409.82	−	4173.92i	−0.334519	−	0.579404i	0.648873	−	0.760896i	$-0.275240\pi$
$373$	−2409.82	−	4173.92i	−0.334519	−	0.579404i	−0.983392	+	0.181493i	$0.941907\pi$
$374$	−9692.96			−1.34014
$375$		0			0
$376$	−5480.20			−0.751648
$377$	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	$0.597715\pi$
$380$	−3.48233			−0.000470104
$381$		0			0
$382$	−9105.87			−1.21963
$383$	4505.18	+	7803.19i	0.601054	+	1.04106i	0.992662	+	0.120924i	$0.0385857\pi$
$383$	4505.18	+	7803.19i	0.601054	+	1.04106i	−0.391608	+	0.920132i	$0.628081\pi$
$384$		0			0
$385$	−4403.62	+	921.849i	−0.582933	+	0.122031i
$386$	−7820.57			−1.03124
$387$		0			0
$388$	302.058	+	523.179i	0.0395223	+	0.0684546i
$389$	694.134	−	1202.28i	0.0904730	−	0.156704i	−0.817237	−	0.576301i	$-0.804495\pi$
$389$	694.134	−	1202.28i	0.0904730	−	0.156704i	0.907710	+	0.419598i	$0.137829\pi$
$390$		0			0
$391$	3016.51	−	5224.75i	0.390157	−	0.675772i
$392$	−6812.30	+	2982.88i	−0.877738	+	0.384332i
$393$		0			0
$394$	4209.71			0.538280
$395$	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
$401$	−7681.86	−	13305.4i	−0.956642	−	1.65695i	−0.730564	−	0.682844i	$-0.760743\pi$
$401$	−7681.86	−	13305.4i	−0.956642	−	1.65695i	−0.226078	−	0.974109i	$-0.572591\pi$
$402$		0			0
$403$	−830.982	+	1439.30i	−0.102715	+	0.177908i
$404$	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
$409$	2526.36			0.305429			0.152714	−	0.988270i	$-0.451199\pi$
$409$	2526.36			0.305429			0.152714	+	0.988270i	$0.451199\pi$
$410$	4267.54			0.514046
$411$		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
$416$	−75.6765	+	131.076i	−0.00891911	+	0.0154483i
$417$		0			0
$418$	148.451	+	257.125i	0.0173708	+	0.0300871i
$419$	−7146.27	+	12377.7i	−0.833217	+	1.44317i	0.0622570	+	0.998060i	$0.480170\pi$
$419$	−7146.27	+	12377.7i	−0.833217	+	1.44317i	−0.895474	+	0.445114i	$0.853163\pi$
$420$		0			0
$421$	4922.61	+	8526.22i	0.569866	+	0.987036i	0.996579	+	0.0826493i	$0.0263381\pi$
$421$	4922.61	+	8526.22i	0.569866	+	0.987036i	−0.426713	+	0.904387i	$0.640329\pi$
$422$	1360.98	−	2357.28i	0.156994	−	0.271921i
$423$		0			0
$424$	−4428.30	−	7670.05i	−0.507211	−	0.878515i
$425$	5596.48			0.638751
$426$		0			0
$427$	2034.86	−	425.976i	0.230618	−	0.0482774i
$428$	−83.2977	+	144.276i	−0.00940735	+	0.0162940i
$429$		0			0
$430$	−1497.95	+	2594.52i	−0.167994	+	0.290974i
$431$	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	$0.520779\pi$
$434$	16136.0	−	3377.90i	1.78469	−	0.373604i
$435$		0			0
$436$	−133.782	−	231.717i	−0.0146949	−	0.0254524i
$437$	−184.796			−0.0202288
$438$		0			0
$439$	13454.2			1.46272			0.731358	−	0.681994i	$-0.238887\pi$
$439$	13454.2			1.46272			0.731358	+	0.681994i	$0.238887\pi$
$440$	−5267.01			−0.570670
$441$		0			0
$442$	808.251			0.0869787
$443$	−6329.65			−0.678851			−0.339425	−	0.940633i	$-0.610233\pi$
$443$	−6329.65			−0.678851			−0.339425	+	0.940633i	$0.610233\pi$
$444$		0			0
$445$	4070.90			0.433661
$446$	−5968.03	−	10336.9i	−0.633620	−	1.09746i
$447$		0			0
$448$	−8467.12	+	1772.50i	−0.892933	+	0.186926i
$449$	−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
$452$	−96.4424	+	167.043i	−0.0100360	+	0.0173828i
$453$		0			0
$454$	1117.44	−	1935.46i	0.115515	−	0.200079i
$455$	367.197	−	76.8687i	0.0378340	−	0.00792013i
$456$		0			0
$457$	2638.21			0.270044			0.135022	−	0.990843i	$-0.456889\pi$
$457$	2638.21			0.270044			0.135022	+	0.990843i	$0.456889\pi$
$458$	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	0.759307	−	0.650733i	$-0.225538\pi$
$461$	−1820.24	−	3152.75i	−0.183898	−	0.318521i	−0.943205	+	0.332212i	$0.892205\pi$
$462$		0			0
$463$	−3186.10	+	5518.49i	−0.319807	+	0.553923i	−0.980448	−	0.196780i	$-0.936952\pi$
$463$	−3186.10	+	5518.49i	−0.319807	+	0.553923i	0.660640	+	0.750703i	$0.270285\pi$
$464$	−2692.60	−	4663.71i	−0.269398	−	0.466611i
$465$		0			0
$466$	2108.10	−	3651.33i	0.209562	−	0.362972i
$467$	−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
$472$	5698.54			0.555713
$473$	18144.0			1.76377
$474$		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
$479$	5969.99	−	10340.3i	0.569470	−	0.986350i	−0.427149	−	0.904181i	$-0.640482\pi$
$479$	5969.99	−	10340.3i	0.569470	−	0.986350i	0.996618	−	0.0821690i	$-0.0261847\pi$
$480$		0			0
$481$	−529.458	−	917.048i	−0.0501896	−	0.0869310i
$482$	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	$0.691435\pi$
$488$	2433.83			0.225767
$489$		0			0
$490$	−2997.11	−	2205.86i	−0.276317	−	0.203369i
$491$	−2769.69	+	4797.25i	−0.254571	+	0.440931i	−0.964779	−	0.263062i	$-0.915268\pi$
$491$	−2769.69	+	4797.25i	−0.254571	+	0.440931i	0.710208	+	0.703992i	$0.248601\pi$
$492$		0			0
$493$	−1975.40	+	3421.49i	−0.180461	+	0.312568i
$494$	−12.3787	−	21.4405i	−0.00112741	−	0.00195274i
$495$		0			0
$496$	20784.1			1.88152
$497$	−4622.52	+	967.673i	−0.417200	+	0.0873362i
$498$		0			0
$499$	−2601.07	−	4505.19i	−0.233347	−	0.404168i	0.725444	−	0.688281i	$-0.241634\pi$
$499$	−2601.07	−	4505.19i	−0.233347	−	0.404168i	−0.958791	+	0.284113i	$0.908301\pi$
$500$	−534.485			−0.0478058
$501$		0			0
$502$	14152.7			1.25830
$503$	−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
$506$	23141.8			2.03316
$507$		0			0
$508$	192.639			0.0168247
$509$	441.724	+	765.088i	0.0384658	+	0.0666246i	0.884617	−	0.466318i	$-0.154420\pi$
$509$	441.724	+	765.088i	0.0384658	+	0.0666246i	−0.846152	+	0.532942i	$0.821086\pi$
$510$		0			0
$511$	−8500.41	−	9499.35i	−0.735883	−	0.822361i
$512$	−9992.04			−0.862480
$513$		0			0
$514$	8778.65	+	15205.1i	0.753326	+	1.30480i
$515$	1022.32	−	1770.72i	0.0874738	−	0.151509i
$516$		0			0
$517$	−8304.09	+	14383.1i	−0.706409	+	1.22354i
$518$	−3276.63	+	9979.73i	−0.277929	+	0.846495i
$519$		0			0
$520$	439.192			0.0370381
$521$	−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
$527$	−7624.04	−	13205.2i	−0.630187	−	1.09152i
$528$		0			0
$529$	−1118.36	+	1937.06i	−0.0919177	+	0.159206i
$530$	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
$535$	1006.87			0.0813658
$536$	2130.60			0.171694
$537$		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	$0.153368\pi$
$542$	5891.62	−	10204.6i	0.466913	−	0.808717i
$543$		0			0
$544$	−694.312	−	1202.58i	−0.0547213	−	0.0947801i
$545$	−808.550	+	1400.45i	−0.0635495	+	0.110071i
$546$		0			0
$547$	−8242.51	−	14276.4i	−0.644286	−	1.11594i	−0.984466	−	0.175575i	$-0.943821\pi$
$547$	−8242.51	−	14276.4i	−0.644286	−	1.11594i	0.340180	−	0.940360i	$-0.389512\pi$
$548$	−267.982	+	464.159i	−0.0208899	+	0.0361823i
$549$		0			0
$550$	10733.6	+	18591.2i	0.832152	+	1.44133i
$551$	121.016			0.00935652
$552$		0			0
$553$	19658.1	−	4115.20i	1.51166	−	0.316448i
$554$	6483.43	−	11229.6i	0.497211	−	0.861194i
$555$		0			0
$556$	−225.225	+	390.101i	−0.0171793	+	0.0297553i
$557$	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
$560$	−3128.56	−	3496.21i	−0.236082	−	0.263825i
$561$		0			0
$562$	−2308.19	−	3997.91i	−0.173248	−	0.300074i
$563$	−19540.3			−1.46275			−0.731373	−	0.681977i	$-0.761120\pi$
$563$	−19540.3			−1.46275			−0.731373	+	0.681977i	$0.761120\pi$
$564$		0			0
$565$	1165.76			0.0868030
$566$	14286.5			1.06097
$567$		0			0
$568$	−5528.83			−0.408424
$569$	−18980.7			−1.39844			−0.699220	−	0.714906i	$-0.746469\pi$
$569$	−18980.7			−1.39844			−0.699220	+	0.714906i	$0.746469\pi$
$570$		0			0
$571$	19907.7			1.45904			0.729519	−	0.683960i	$-0.239744\pi$
$571$	19907.7			1.45904			0.729519	+	0.683960i	$0.239744\pi$
$572$	110.113	+	190.722i	0.00804908	+	0.0139414i
$573$		0			0
$574$	6668.70	−	20311.1i	0.484924	−	1.47695i
$575$	−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	$0.815892\pi$
$578$	3501.03	−	6063.97i	0.251944	−	0.436380i
$579$		0			0
$580$	88.8733	−	153.933i	0.00636252	−	0.0110202i
$581$	3756.45	+	4197.90i	0.268234	+	0.299756i
$582$		0			0
$583$	−26840.7			−1.90674
$584$	−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	0.864275	−	0.503019i	$-0.167777\pi$
$587$	−49.6245	−	85.9522i	−0.00348931	−	0.00604366i	−0.867765	+	0.496975i	$0.834444\pi$
$588$		0			0
$589$	−233.530	+	404.486i	−0.0163369	+	0.0282964i
$590$	1425.78	+	2469.52i	0.0994888	+	0.172320i
$591$		0			0
$592$	−6621.28	+	11468.4i	−0.459684	+	0.796196i
$593$	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
$598$	−1929.68			−0.131958
$599$	19758.0			1.34773			0.673866	−	0.738854i	$-0.264632\pi$
$599$	19758.0			1.34773			0.673866	+	0.738854i	$0.264632\pi$
$600$		0			0
$601$	745.047	+	1290.46i	0.0505676	+	0.0875856i	0.890201	−	0.455568i	$-0.150564\pi$
$601$	745.047	+	1290.46i	0.0505676	+	0.0875856i	−0.839634	+	0.543153i	$0.817230\pi$
$602$	10007.6	+	11183.7i	0.677544	+	0.757166i
$603$		0			0
$604$	841.536	−	1457.58i	0.0566914	−	0.0981925i
$605$	−5520.63	+	9562.01i	−0.370984	+	0.642563i
$606$		0			0
$607$	1207.26	+	2091.04i	0.0807269	+	0.139823i	0.903562	−	0.428457i	$-0.140942\pi$
$607$	1207.26	+	2091.04i	0.0807269	+	0.139823i	−0.822835	+	0.568280i	$0.807609\pi$
$608$	−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	$0.684720\pi$
$614$	−16106.5			−1.05864
$615$		0			0
$616$	−8230.53	+	25067.9i	−0.538340	+	1.63964i
$617$	−1876.84	+	3250.78i	−0.122461	+	0.212109i	−0.920738	−	0.390182i	$-0.872412\pi$
$617$	−1876.84	+	3250.78i	−0.122461	+	0.212109i	0.798276	+	0.602291i	$0.205745\pi$
$618$		0			0
$619$	−12799.7	+	22169.7i	−0.831118	+	1.43954i	0.0660345	+	0.997817i	$0.478965\pi$
$619$	−12799.7	+	22169.7i	−0.831118	+	1.43954i	−0.897152	+	0.441721i	$0.854368\pi$
$620$	343.006	+	594.104i	0.0222185	+	0.0384836i
$621$		0			0
$622$	−5003.15			−0.322521
$623$	6361.42	−	19375.2i	0.409093	−	1.24599i
$624$		0			0
$625$	−5343.05	−	9254.44i	−0.341955	−	0.592284i
$626$	−19522.5			−1.24645
$627$		0			0
$628$	−1046.06			−0.0664685
$629$	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	$0.492785\pi$
$632$	23512.3			1.47986
$633$		0			0
$634$	12401.0			0.776826
$635$	−582.135	−	1008.29i	−0.0363800	−	0.0630121i
$636$		0			0
$637$	207.952	−	1867.77i	0.0129347	−	0.116175i
$638$	−15154.6			−0.940404
$639$		0			0
$640$	−2942.36	−	5096.31i	−0.181729	−	0.314765i
$641$	4421.16	−	7657.67i	0.272426	−	0.471856i	−0.697056	−	0.717016i	$-0.745507\pi$
$641$	4421.16	−	7657.67i	0.272426	−	0.471856i	0.969483	+	0.245160i	$0.0788406\pi$
$642$		0			0
$643$	−15033.0	+	26037.9i	−0.921997	+	1.59695i	−0.125676	+	0.992071i	$0.540110\pi$
$643$	−15033.0	+	26037.9i	−0.921997	+	1.59695i	−0.796321	+	0.604874i	$0.793224\pi$
$644$	906.687	+	1013.24i	0.0554790	+	0.0619987i
$645$		0			0
$646$	227.142			0.0138340
$647$	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
$653$	−9099.17	−	15760.2i	−0.545296	−	0.944480i	−0.998588	−	0.0531181i	$-0.983084\pi$
$653$	−9099.17	−	15760.2i	−0.545296	−	0.944480i	0.453292	−	0.891362i	$-0.350249\pi$
$654$		0			0
$655$	3158.61	−	5470.87i	0.188423	−	0.326358i
$656$	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	0.985138	−	0.171762i	$-0.0549461\pi$
$659$	5816.45	+	10074.4i	0.343819	+	0.595512i	−0.641320	+	0.767274i	$0.721613\pi$
$660$		0			0
$661$	−8940.79			−0.526107			−0.263053	−	0.964781i	$-0.584730\pi$
$661$	−8940.79			−0.526107			−0.263053	+	0.964781i	$0.584730\pi$
$662$	12955.5			0.760622
$663$		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
$668$	−478.849	+	829.391i	−0.0277354	+	0.0480391i
$669$		0			0
$670$	533.079	+	923.320i	0.0307383	+	0.0532402i
$671$	3687.96	−	6387.73i	0.212179	−	0.367504i
$672$		0			0
$673$	5154.45	+	8927.77i	0.295229	+	0.511352i	0.975038	−	0.222037i	$-0.0712706\pi$
$673$	5154.45	+	8927.77i	0.295229	+	0.511352i	−0.679809	+	0.733389i	$0.737937\pi$
$674$	3787.77	−	6560.61i	0.216468	−	0.374933i
$675$		0			0
$676$	662.792	+	1147.99i	0.0377101	+	0.0653158i
$677$	−19108.4			−1.08478			−0.542389	−	0.840128i	$-0.682480\pi$
$677$	−19108.4			−1.08478			−0.542389	+	0.840128i	$0.682480\pi$
$678$		0			0
$679$	−12196.5	−	13629.8i	−0.689335	−	0.770343i
$680$	−2014.73	+	3489.62i	−0.113620	+	0.196795i
$681$		0			0
$682$	29244.7	−	50653.2i	1.64199	−	2.84401i
$683$	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
$686$	−15182.1	+	10817.5i	−0.844978	+	0.602061i
$687$		0			0
$688$	9460.28	+	16385.7i	0.524230	+	0.907992i
$689$	2238.12			0.123753
$690$		0			0
$691$	13845.9			0.762261			0.381131	−	0.924521i	$-0.375535\pi$
$691$	13845.9			0.762261			0.381131	+	0.924521i	$0.375535\pi$
$692$	−1742.69			−0.0957327
$693$		0			0
$694$	−17748.8			−0.970800
$695$	2722.43			0.148586
$696$		0			0
$697$	−19772.8			−1.07453
$698$	16579.5	+	28716.5i	0.899058	+	1.55721i
$699$		0			0
$700$	−393.455	+	1198.36i	−0.0212446	+	0.0647052i
$701$	−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
$704$	−15345.7	+	26579.5i	−0.821537	+	1.42294i
$705$		0			0
$706$	1520.41	−	2633.42i	0.0810500	−	0.140383i
$707$	−4342.04	+	13224.7i	−0.230975	+	0.703486i
$708$		0			0
$709$	490.782			0.0259968			0.0129984	−	0.999916i	$-0.495862\pi$
$709$	490.782			0.0259968			0.0129984	+	0.999916i	$0.495862\pi$
$710$	−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
$716$	−1226.34	−	2124.09i	−0.0640093	−	0.110867i
$717$		0			0
$718$	−15133.0	+	26211.1i	−0.786572	+	1.36238i
$719$	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
$724$	−2905.09			−0.149125
$725$	8749.92			0.448226
$726$		0			0
$727$	−9687.53	−	16779.3i	−0.494210	−	0.855997i	0.505768	−	0.862670i	$-0.331209\pi$
$727$	−9687.53	−	16779.3i	−0.494210	−	0.855997i	−0.999978	+	0.00667304i	$0.997876\pi$
$728$	686.306	−	2090.30i	0.0349398	−	0.106417i
$729$		0			0
$730$	3733.79	−	6467.11i	0.189306	−	0.327888i
$731$	6940.44	−	12021.2i	0.351165	−	0.608235i
$732$		0			0
$733$	−4090.20	−	7084.44i	−0.206105	−	0.356985i	0.744379	−	0.667757i	$-0.232746\pi$
$733$	−4090.20	−	7084.44i	−0.206105	−	0.356985i	−0.950484	+	0.310773i	$0.899412\pi$
$734$	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	$0.897055\pi$
$740$	−437.091			−0.0217132
$741$		0			0
$742$	−14804.4	−	16544.2i	−0.732463	−	0.818540i
$743$	−11091.9	+	19211.7i	−0.547674	+	0.948599i	0.450760	+	0.892645i	$0.351153\pi$
$743$	−11091.9	+	19211.7i	−0.547674	+	0.948599i	−0.998433	+	0.0559534i	$0.982180\pi$
$744$		0			0
$745$	−598.308	+	1036.30i	−0.0294232	+	0.0509625i
$746$	−7071.78	−	12248.7i	−0.347073	−	0.601148i
$747$		0			0
$748$	−2020.52			−0.0987669
$749$	1573.39	−	4792.11i	0.0767562	−	0.233778i
$750$		0			0
$751$	−6605.32	−	11440.7i	−0.320947	−	0.555897i	0.659736	−	0.751497i	$-0.270668\pi$
$751$	−6605.32	−	11440.7i	−0.320947	−	0.555897i	−0.980684	+	0.195600i	$0.937335\pi$
$752$	−17319.0			−0.839839
$753$		0			0
$754$	1263.67			0.0610349
$755$	−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	$0.545589\pi$
$758$	−13085.8			−0.627044
$759$		0			0
$760$	123.426			0.00589095
$761$	3981.91	+	6896.87i	0.189677	+	0.328530i	0.945142	−	0.326658i	$-0.105923\pi$
$761$	3981.91	+	6896.87i	0.189677	+	0.328530i	−0.755466	+	0.655188i	$0.772589\pi$
$762$		0			0
$763$	5401.85	+	6036.65i	0.256304	+	0.286424i
$764$	−1898.14			−0.0898854
$765$		0			0
$766$	13220.8	+	22899.0i	0.623611	+	1.08013i
$767$	−720.028	+	1247.12i	−0.0338966	+	0.0587106i
$768$		0			0
$769$	11183.7	−	19370.7i	0.524439	−	0.908355i	−0.475156	−	0.879902i	$-0.657608\pi$
$769$	11183.7	−	19370.7i	0.524439	−	0.908355i	0.999595	−	0.0284535i	$-0.00905826\pi$
$770$	−12922.7	+	2705.23i	−0.604809	+	0.126610i
$771$		0			0
$772$	−1630.22			−0.0760012
$773$	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
$779$	302.828	+	524.514i	0.0139280	+	0.0241241i
$780$		0			0
$781$	−8377.78	+	14510.7i	−0.383842	+	0.664834i
$782$	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
$787$	−28114.7			−1.27342			−0.636711	−	0.771103i	$-0.719705\pi$
$787$	−28114.7			−1.27342			−0.636711	+	0.771103i	$0.719705\pi$
$788$	877.526			0.0396708
$789$		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
$794$	3099.10	−	5367.80i	0.138518	−	0.239920i
$795$		0			0
$796$	623.411	+	1079.78i	0.0277591	+	0.0480801i
$797$	−798.238	+	1382.59i	−0.0354769	+	0.0614477i	−0.883219	−	0.468961i	$-0.844628\pi$
$797$	−798.238	+	1382.59i	−0.0354769	+	0.0614477i	0.847742	+	0.530409i	$0.177962\pi$
$798$		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
$803$	−45225.8			−1.98753
$804$		0			0
$805$	2563.45	−	7807.57i	0.112236	−	0.341839i
$806$	−2438.58	+	4223.74i	−0.106570	+	0.184584i
$807$		0			0
$808$	−8147.54	+	14112.0i	−0.354740	+	0.614427i
$809$	−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	$0.408587\pi$
$812$	−593.754	−	663.530i	−0.0256609	−	0.0286765i
$813$		0			0
$814$	18633.2	+	32273.6i	0.802324	+	1.38967i
$815$	12530.7			0.538565
$816$		0			0
$817$	−425.182			−0.0182071
$818$	7413.79			0.316891
$819$		0			0
$820$	889.581			0.0378848
$821$	−27720.8			−1.17839			−0.589197	−	0.807990i	$-0.700556\pi$
$821$	−27720.8			−1.17839			−0.589197	+	0.807990i	$0.700556\pi$
$822$		0			0
$823$	42033.0			1.78029			0.890144	−	0.455679i	$-0.150603\pi$
$823$	42033.0			1.78029			0.890144	+	0.455679i	$0.150603\pi$
$824$	−5995.36	−	10384.3i	−0.253469	−	0.439020i
$825$		0			0
$826$	13981.5	−	2926.87i	0.588957	−	0.123292i
$827$	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	$-0.402201\pi$
$830$	−1650.01	+	2857.91i	−0.0690033	+	0.119517i
$831$		0			0
$832$	1279.60	−	2216.34i	0.0533201	−	0.0923531i
$833$	13886.5	+	10220.4i	0.577597	+	0.425110i
$834$		0			0
$835$	5788.13			0.239888
$836$	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	0.998409	−	0.0563819i	$-0.0179564\pi$
$839$	10945.1	+	18957.4i	0.450376	+	0.780075i	−0.548033	+	0.836457i	$0.684623\pi$
$840$		0			0
$841$	9106.03	−	15772.1i	0.373366	−	0.646689i
$842$	14445.8	+	25020.8i	0.591252	+	1.02408i
$843$		0			0
$844$	283.699	−	491.382i	0.0115703	−	0.0200404i
$845$	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
$850$	16423.3			0.662722
$851$	−23195.0			−0.934331
$852$		0			0
$853$	−4501.76	−	7797.27i	−0.180700	−	0.312982i	0.761419	−	0.648260i	$-0.224503\pi$
$853$	−4501.76	−	7797.27i	−0.180700	−	0.312982i	−0.942119	+	0.335278i	$0.891170\pi$
$854$	5971.46	−	1250.06i	0.239273	−	0.0500891i
$855$		0			0
$856$	2952.36	−	5113.63i	0.117885	−	0.204183i
$857$	−14264.5	+	24706.8i	−0.568571	+	0.984794i	0.428136	+	0.903714i	$0.359170\pi$
$857$	−14264.5	+	24706.8i	−0.568571	+	0.984794i	−0.996708	+	0.0810802i	$0.974163\pi$
$858$		0			0
$859$	−6163.02	−	10674.7i	−0.244796	−	0.423999i	0.717278	−	0.696787i	$-0.245388\pi$
$859$	−6163.02	−	10674.7i	−0.244796	−	0.423999i	−0.962074	+	0.272788i	$0.912054\pi$
$860$	−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
$866$	−3449.63			−0.135362
$867$		0			0
$868$	3363.60	−	704.132i	0.131530	−	0.0275343i
$869$	35628.0	−	61709.4i	1.39079	−	2.40892i
$870$		0			0
$871$	−269.208	+	466.282i	−0.0104728	+	0.0181394i
$872$	4741.69	+	8212.85i	0.184144	+	0.318947i
$873$		0			0
$874$	−542.298			−0.0209880
$875$	15838.6	−	3315.64i	0.611935	−	0.128102i
$876$		0			0
$877$	7105.35	+	12306.8i	0.273581	+	0.473856i	0.969776	−	0.243996i	$-0.0784585\pi$
$877$	7105.35	+	12306.8i	0.273581	+	0.473856i	−0.696195	+	0.717853i	$0.745125\pi$
$878$	39482.2			1.51761
$879$		0			0
$880$	−16645.3			−0.637627
$881$	−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	$0.727422\pi$
$884$	168.482			0.00641026
$885$		0			0
$886$	−18574.8			−0.704327
$887$	−4300.61	−	7448.88i	−0.162796	−	0.281972i	0.773074	−	0.634316i	$-0.218718\pi$
$887$	−4300.61	−	7448.88i	−0.162796	−	0.281972i	−0.935871	+	0.352344i	$0.885385\pi$
$888$		0			0
$889$	−5708.54	+	1195.02i	−0.215364	+	0.0450840i
$890$	11946.4			0.449936
$891$		0			0
$892$	−1244.05	−	2154.76i	−0.0466973	−	0.0808820i
$893$	194.596	−	337.050i	0.00729216	−	0.0126304i
$894$		0			0
$895$	−7411.77	+	12837.6i	−0.276814	+	0.479455i
$896$	−28853.4	+	6040.14i	−1.07581	+	0.225209i
$897$		0			0
$898$	−1891.55			−0.0702914
$899$	−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
$905$	8778.88	+	15205.5i	0.322453	+	0.558504i
$906$		0			0
$907$	−4418.11	+	7652.40i	−0.161743	+	0.280147i	−0.935494	−	0.353343i	$-0.885045\pi$
$907$	−4418.11	+	7652.40i	−0.161743	+	0.280147i	0.773751	+	0.633490i	$0.218378\pi$
$908$	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	0.846084	−	0.533050i	$-0.178954\pi$
$911$	−1061.16	−	1837.99i	−0.0385926	−	0.0668443i	−0.884677	+	0.466205i	$0.845621\pi$
$912$		0			0
$913$	19985.9			0.724466
$914$	7742.01			0.280178
$915$		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	$0.0621370\pi$
$920$	4810.14	−	8331.41i	0.172376	−	0.298563i
$921$		0			0
$922$	−5341.63	−	9251.97i	−0.190800	−	0.330474i
$923$	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
$929$	48328.7			1.70680			0.853398	−	0.521260i	$-0.174538\pi$
$929$	48328.7			1.70680			0.853398	+	0.521260i	$0.174538\pi$
$930$		0			0
$931$	58.4407	−	524.897i	0.00205727	−	0.0184778i
$932$	439.439	−	761.130i	0.0154445	−	0.0267507i
$933$		0			0
$934$	−7039.16	+	12192.2i	−0.246604	+	0.427131i
$935$	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	$0.255355\pi$
$938$	5227.49	−	1094.32i	0.181965	−	0.0380925i
$939$		0			0
$940$	−285.820	−	495.055i	−0.00991747	−	0.0171776i
$941$	28111.7			0.973874			0.486937	−	0.873437i	$-0.338114\pi$
$941$	28111.7			0.973874			0.486937	+	0.873437i	$0.338114\pi$
$942$		0			0
$943$	47207.2			1.63020
$944$	18009.0			0.620915
$945$		0			0
$946$	53245.0			1.82996
$947$	31844.6			1.09273			0.546363	−	0.837549i	$-0.316012\pi$
$947$	31844.6			1.09273			0.546363	+	0.837549i	$0.316012\pi$
$948$		0			0
$949$	3771.17			0.128996
$950$	−251.529	−	435.661i	−0.00859018	−	0.0148786i
$951$		0			0
$952$	13460.3	+	15042.1i	0.458245	+	0.512096i
$953$	−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
$956$	−832.640	+	1442.17i	−0.0281689	+	0.0487900i
$957$		0			0
$958$	17519.4	−	30344.5i	0.590841	−	1.02337i
$959$	5061.85	−	15417.0i	0.170444	−	0.519125i
$960$		0			0
$961$	62219.0			2.08852
$962$	−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	−0.918944	−	0.394388i	$-0.870957\pi$
$967$	−3545.97	+	6141.80i	−0.117922	+	0.204247i	0.801022	+	0.598635i	$0.204290\pi$
$968$	32375.4	+	56075.8i	1.07498	+	1.86193i
$969$		0			0
$970$	5357.28	−	9279.08i	0.177332	−	0.307148i
$971$	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
$976$	7691.59			0.252256
$977$	−11732.9			−0.384205			−0.192103	−	0.981375i	$-0.561531\pi$
$977$	−11732.9			−0.384205			−0.192103	+	0.981375i	$0.561531\pi$
$978$		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
$983$	20528.6	−	35556.6i	0.666084	−	1.15369i	−0.312906	−	0.949784i	$-0.601303\pi$
$983$	20528.6	−	35556.6i	0.666084	−	1.15369i	0.978990	−	0.203907i	$-0.0653642\pi$
$984$		0			0
$985$	−2651.79	−	4593.04i	−0.0857799	−	0.148575i
$986$	−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	$0.959660\pi$
$992$	8379.25			0.268187
$993$		0			0
$994$	−13565.1	+	2839.71i	−0.432857	+	0.0906138i
$995$	3767.77	−	6525.96i	0.120046	−	0.207927i
$996$		0			0
$997$	5507.96	−	9540.06i	0.174964	−	0.303046i	−0.765185	−	0.643810i	$-0.777353\pi$
$997$	5507.96	−	9540.06i	0.174964	−	0.303046i	0.940149	+	0.340764i	$0.110686\pi$
$998$	−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.h.a.37.17		44
3.2	odd	2		63.4.h.a.58.6	yes	44
7.4	even	3		189.4.g.a.172.6		44
9.2	odd	6		63.4.g.a.16.17	yes	44
9.7	even	3		189.4.g.a.100.6		44
21.11	odd	6		63.4.g.a.4.17	✓	44
63.11	odd	6		63.4.h.a.25.6	yes	44
63.25	even	3	inner	189.4.h.a.46.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.17	✓	44	21.11	odd	6
63.4.g.a.16.17	yes	44	9.2	odd	6
63.4.h.a.25.6	yes	44	63.11	odd	6
63.4.h.a.58.6	yes	44	3.2	odd	2
189.4.g.a.100.6		44	9.7	even	3
189.4.g.a.172.6		44	7.4	even	3
189.4.h.a.37.17		44	1.1	even	1	trivial
189.4.h.a.46.17		44	63.25	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.93457 q^{2} +0.611720 q^{4} +(-1.84855 - 3.20179i) q^{5} +(-18.1273 + 3.79476i) q^{7} -21.6814 q^{8} +O(q^{10})\)	\(q+2.93457 q^{2} +0.611720 q^{4} +(-1.84855 - 3.20179i) q^{5} +(-18.1273 + 3.79476i) q^{7} -21.6814 q^{8} +(-5.42471 - 9.39588i) q^{10} +(-32.8537 + 56.9043i) q^{11} +(2.73952 - 4.74498i) q^{13} +(-53.1960 + 11.1360i) q^{14} -68.5196 q^{16} +(25.1343 + 43.5340i) q^{17} +(0.769884 - 1.33348i) q^{19} +(-1.13080 - 1.95860i) q^{20} +(-96.4115 + 166.990i) q^{22} +(-60.0078 - 103.936i) q^{23} +(55.6657 - 96.4158i) q^{25} +(8.03931 - 13.9245i) q^{26} +(-11.0888 + 2.32133i) q^{28} +(39.2967 + 68.0640i) q^{29} -303.332 q^{31} -27.6241 q^{32} +(73.7586 + 127.754i) q^{34} +(45.6593 + 51.0250i) q^{35} +(96.6335 - 167.374i) q^{37} +(2.25928 - 3.91319i) q^{38} +(40.0793 + 69.4194i) q^{40} +(-196.671 + 340.645i) q^{41} +(-138.067 - 239.139i) q^{43} +(-20.0972 + 34.8095i) q^{44} +(-176.097 - 305.009i) q^{46} +252.760 q^{47} +(314.200 - 137.578i) q^{49} +(163.355 - 282.939i) q^{50} +(1.67582 - 2.90260i) q^{52} +(204.244 + 353.761i) q^{53} +242.927 q^{55} +(393.027 - 82.2758i) q^{56} +(115.319 + 199.739i) q^{58} -262.830 q^{59} -112.254 q^{61} -890.149 q^{62} +467.092 q^{64} -20.2566 q^{65} -98.2686 q^{67} +(15.3752 + 26.6306i) q^{68} +(133.991 + 149.737i) q^{70} +255.003 q^{71} +(344.146 + 596.078i) q^{73} +(283.578 - 491.172i) q^{74} +(0.470953 - 0.815715i) q^{76} +(379.612 - 1156.19i) q^{77} -1084.44 q^{79} +(126.662 + 219.385i) q^{80} +(-577.146 + 999.647i) q^{82} +(-152.083 - 263.415i) q^{83} +(92.9243 - 160.950i) q^{85} +(-405.167 - 701.771i) q^{86} +(712.315 - 1233.77i) q^{88} +(-550.553 + 953.585i) q^{89} +(-31.6540 + 96.4096i) q^{91} +(-36.7079 - 63.5800i) q^{92} +741.742 q^{94} -5.69269 q^{95} +(493.784 + 855.260i) q^{97} +(922.042 - 403.731i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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