LMFDB - Embedded newform 92.5.f.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(5,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("92.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.f (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	92.5
Dual form			92.5.f.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.01425 - 3.47863i) q^{3} +(7.38497 + 1.06180i) q^{5} +(35.2368 - 16.0921i) q^{7} +(8.51233 + 59.2046i) q^{9} +O(q^{10})$	\(q+(3.01425 - 3.47863i) q^{3} +(7.38497 + 1.06180i) q^{5} +(35.2368 - 16.0921i) q^{7} +(8.51233 + 59.2046i) q^{9} +(-14.6909 - 50.0326i) q^{11} +(124.312 - 272.206i) q^{13} +(25.9538 - 22.4891i) q^{15} +(217.167 + 337.918i) q^{17} +(211.275 - 328.751i) q^{19} +(50.2342 - 171.082i) q^{21} +(-104.657 - 518.544i) q^{23} +(-546.273 - 160.400i) q^{25} +(545.258 + 350.416i) q^{27} +(989.558 - 635.950i) q^{29} +(905.128 + 1044.57i) q^{31} +(-218.327 - 99.7066i) q^{33} +(277.309 - 81.4254i) q^{35} +(-1086.78 + 156.255i) q^{37} +(-572.197 - 1252.94i) q^{39} +(-243.195 + 1691.46i) q^{41} +(-292.982 - 253.871i) q^{43} +446.262i q^{45} -2366.54 q^{47} +(-589.642 + 680.483i) q^{49} +(1830.09 + 263.127i) q^{51} +(-3771.18 + 1722.24i) q^{53} +(-55.3672 - 385.087i) q^{55} +(-506.767 - 1725.89i) q^{57} +(-1487.90 + 3258.04i) q^{59} +(-2727.25 + 2363.17i) q^{61} +(1252.68 + 1949.20i) q^{63} +(1207.07 - 1878.24i) q^{65} +(241.595 - 822.796i) q^{67} +(-2119.29 - 1198.96i) q^{69} +(4676.41 + 1373.12i) q^{71} +(-4910.66 - 3155.89i) q^{73} +(-2204.58 + 1416.80i) q^{75} +(-1322.79 - 1526.58i) q^{77} +(8473.74 + 3869.83i) q^{79} +(-1786.12 + 524.451i) q^{81} +(10708.1 - 1539.59i) q^{83} +(1244.97 + 2726.10i) q^{85} +(770.540 - 5359.23i) q^{87} +(327.713 + 283.965i) q^{89} -11592.1i q^{91} +6361.97 q^{93} +(1909.33 - 2203.48i) q^{95} +(-10710.3 - 1539.90i) q^{97} +(2837.10 - 1295.66i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 10 q^{3} - 318 q^{9}+O(q^{10}) $ 80 * q + 10 * q^3 - 318 * q^9	$ 80 q + 10 q^{3} - 318 q^{9} + 2 q^{13} + 1463 q^{15} - 495 q^{17} - 957 q^{19} - 1353 q^{21} + 1614 q^{23} + 1890 q^{25} + 4723 q^{27} - 1617 q^{29} - 3271 q^{31} - 6655 q^{33} - 5280 q^{35} + 3520 q^{37} + 6138 q^{39} + 11370 q^{41} + 7216 q^{43} - 270 q^{47} - 14512 q^{49} - 17424 q^{51} - 7392 q^{53} + 5746 q^{55} + 18381 q^{57} + 11772 q^{59} - 22484 q^{61} - 27775 q^{63} - 27951 q^{65} - 2926 q^{67} + 15769 q^{69} + 19779 q^{71} + 24400 q^{73} + 2809 q^{75} + 19839 q^{77} + 21604 q^{79} + 22224 q^{81} - 11253 q^{83} - 25594 q^{85} + 45506 q^{87} + 7656 q^{89} + 7970 q^{93} - 22437 q^{95} + 32439 q^{97} - 48477 q^{99}+O(q^{100}) $ 80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.01425	−	3.47863i	0.334917	−	0.386515i	−0.563164	−	0.826345i	$-0.690416\pi$
$3$	3.01425	−	3.47863i	0.334917	−	0.386515i	0.898081	+	0.439830i	$0.144961\pi$
$4$		0			0
$5$	7.38497	+	1.06180i	0.295399	+	0.0424719i	0.288421	−	0.957504i	$-0.406870\pi$
$5$	7.38497	+	1.06180i	0.295399	+	0.0424719i	0.00697779	+	0.999976i	$0.497779\pi$
$6$		0			0
$7$	35.2368	−	16.0921i	0.719119	−	0.328411i	−0.0220242	−	0.999757i	$-0.507011\pi$
$7$	35.2368	−	16.0921i	0.719119	−	0.328411i	0.741144	+	0.671347i	$0.234284\pi$
$8$		0			0
$9$	8.51233	+	59.2046i	0.105090	+	0.730920i
$10$		0			0
$11$	−14.6909	−	50.0326i	−0.121412	−	0.413492i	0.876248	−	0.481861i	$-0.160039\pi$
$11$	−14.6909	−	50.0326i	−0.121412	−	0.413492i	−0.997660	+	0.0683684i	$0.978221\pi$
$12$		0			0
$13$	124.312	−	272.206i	0.735576	−	1.61069i	−0.0551203	−	0.998480i	$-0.517554\pi$
$13$	124.312	−	272.206i	0.735576	−	1.61069i	0.790697	−	0.612208i	$-0.209718\pi$
$14$		0			0
$15$	25.9538	−	22.4891i	0.115350	−	0.0999514i
$16$		0			0
$17$	217.167	+	337.918i	0.751442	+	1.16927i	0.980627	+	0.195884i	$0.0627577\pi$
$17$	217.167	+	337.918i	0.751442	+	1.16927i	−0.229185	+	0.973383i	$0.573606\pi$
$18$		0			0
$19$	211.275	−	328.751i	0.585250	−	0.910667i	−0.414749	−	0.909936i	$-0.636131\pi$
$19$	211.275	−	328.751i	0.585250	−	0.910667i	1.00000		0.000731569i	$-0.000232866\pi$
$20$		0			0
$21$	50.2342	−	171.082i	0.113910	−	0.387941i
$22$		0			0
$23$	−104.657	−	518.544i	−0.197840	−	0.980234i
$23$	−104.657	−	518.544i	−0.197840	−	0.980234i
$24$		0			0
$25$	−546.273	−	160.400i	−0.874036	−	0.256640i
$26$		0			0
$27$	545.258	+	350.416i	0.747953	+	0.480680i
$28$		0			0
$29$	989.558	−	635.950i	1.17664	−	0.756183i	0.201878	−	0.979411i	$-0.435296\pi$
$29$	989.558	−	635.950i	1.17664	−	0.756183i	0.974766	+	0.223227i	$0.0716593\pi$
$30$		0			0
$31$	905.128	+	1044.57i	0.941860	+	1.08696i	0.996082	+	0.0884357i	$0.0281868\pi$
$31$	905.128	+	1044.57i	0.941860	+	1.08696i	−0.0542217	+	0.998529i	$0.517268\pi$
$32$		0			0
$33$	−218.327	−	99.7066i	−0.200484	−	0.0915580i
$34$		0			0
$35$	277.309	−	81.4254i	0.226375	−	0.0664697i
$36$		0			0
$37$	−1086.78	+	156.255i	−0.793850	+	0.114138i	−0.527296	−	0.849682i	$-0.676794\pi$
$37$	−1086.78	+	156.255i	−0.793850	+	0.114138i	−0.266554	+	0.963820i	$0.585885\pi$
$38$		0			0
$39$	−572.197	−	1252.94i	−0.376198	−	0.823758i
$40$		0			0
$41$	−243.195	+	1691.46i	−0.144673	+	1.00622i	0.780087	+	0.625670i	$0.215175\pi$
$41$	−243.195	+	1691.46i	−0.144673	+	1.00622i	−0.924760	+	0.380550i	$0.875735\pi$
$42$		0			0
$43$	−292.982	−	253.871i	−0.158454	−	0.137302i	0.572025	−	0.820236i	$-0.306158\pi$
$43$	−292.982	−	253.871i	−0.158454	−	0.137302i	−0.730480	+	0.682935i	$0.760703\pi$
$44$		0			0
$45$			446.262i			0.220376i
$46$		0			0
$47$	−2366.54			−1.07132			−0.535660	−	0.844434i	$-0.679937\pi$
$47$	−2366.54			−1.07132			−0.535660	+	0.844434i	$0.679937\pi$
$48$		0			0
$49$	−589.642	+	680.483i	−0.245582	+	0.283416i
$50$		0			0
$51$	1830.09	+	263.127i	0.703610	+	0.101164i
$52$		0			0
$53$	−3771.18	+	1722.24i	−1.34253	+	0.613115i	−0.951610	−	0.307309i	$-0.900572\pi$
$53$	−3771.18	+	1722.24i	−1.34253	+	0.613115i	−0.390924	+	0.920423i	$0.627844\pi$
$54$		0			0
$55$	−55.3672	−	385.087i	−0.0183032	−	0.127302i
$56$		0			0
$57$	−506.767	−	1725.89i	−0.155976	−	0.531206i
$58$		0			0
$59$	−1487.90	+	3258.04i	−0.427434	+	0.935950i	0.566302	+	0.824198i	$0.308374\pi$
$59$	−1487.90	+	3258.04i	−0.427434	+	0.935950i	−0.993736	+	0.111752i	$0.964354\pi$
$60$		0			0
$61$	−2727.25	+	2363.17i	−0.732934	+	0.635091i	−0.939186	−	0.343408i	$-0.888419\pi$
$61$	−2727.25	+	2363.17i	−0.732934	+	0.635091i	0.206252	+	0.978499i	$0.433873\pi$
$62$		0			0
$63$	1252.68	+	1949.20i	0.315615	+	0.491106i
$64$		0			0
$65$	1207.07	−	1878.24i	0.285697	−	0.444554i
$66$		0			0
$67$	241.595	−	822.796i	0.0538193	−	0.183292i	−0.928197	−	0.372090i	$-0.878641\pi$
$67$	241.595	−	822.796i	0.0538193	−	0.183292i	0.982016	+	0.188799i	$0.0604594\pi$
$68$		0			0
$69$	−2119.29	−	1198.96i	−0.445135	−	0.251829i
$70$		0			0
$71$	4676.41	+	1373.12i	0.927676	+	0.272390i	0.710463	−	0.703734i	$-0.248485\pi$
$71$	4676.41	+	1373.12i	0.927676	+	0.272390i	0.217212	+	0.976124i	$0.430304\pi$
$72$		0			0
$73$	−4910.66	−	3155.89i	−0.921498	−	0.592211i	−0.00840622	−	0.999965i	$-0.502676\pi$
$73$	−4910.66	−	3155.89i	−0.921498	−	0.592211i	−0.913092	+	0.407754i	$0.866312\pi$
$74$		0			0
$75$	−2204.58	+	1416.80i	−0.391925	+	0.251875i
$76$		0			0
$77$	−1322.79	−	1526.58i	−0.223105	−	0.257477i
$78$		0			0
$79$	8473.74	+	3869.83i	1.35775	+	0.620065i	0.955372	−	0.295407i	$-0.0954552\pi$
$79$	8473.74	+	3869.83i	1.35775	+	0.620065i	0.402382	+	0.915472i	$0.368182\pi$
$80$		0			0
$81$	−1786.12	+	524.451i	−0.272233	+	0.0799347i
$82$		0			0
$83$	10708.1	−	1539.59i	1.55438	−	0.223486i	0.689058	−	0.724706i	$-0.258024\pi$
$83$	10708.1	−	1539.59i	1.55438	−	0.223486i	0.865320	+	0.501220i	$0.167115\pi$
$84$		0			0
$85$	1244.97	+	2726.10i	0.172314	+	0.377315i
$86$		0			0
$87$	770.540	−	5359.23i	0.101802	−	0.708049i
$88$		0			0
$89$	327.713	+	283.965i	0.0413727	+	0.0358496i	0.675302	−	0.737542i	$-0.264013\pi$
$89$	327.713	+	283.965i	0.0413727	+	0.0358496i	−0.633929	+	0.773391i	$0.718559\pi$
$90$		0			0
$91$		−	11592.1i		−	1.39985i
$92$		0			0
$93$	6361.97			0.735573
$94$		0			0
$95$	1909.33	−	2203.48i	0.211560	−	0.244153i
$96$		0			0
$97$	−10710.3	−	1539.90i	−1.13830	−	0.163663i	−0.452714	−	0.891656i	$-0.649544\pi$
$97$	−10710.3	−	1539.90i	−1.13830	−	0.163663i	−0.685585	+	0.727993i	$0.740453\pi$
$98$		0			0
$99$	2837.10	−	1295.66i	0.289471	−	0.132197i
$100$		0			0
$101$	802.831	+	5583.81i	0.0787012	+	0.547379i	0.990582	+	0.136923i	$0.0437213\pi$
$101$	802.831	+	5583.81i	0.0787012	+	0.547379i	−0.911881	+	0.410456i	$0.865370\pi$
$102$		0			0
$103$	668.981	+	2278.34i	0.0630578	+	0.214755i	0.984995	−	0.172585i	$-0.0552120\pi$
$103$	668.981	+	2278.34i	0.0630578	+	0.214755i	−0.921937	+	0.387340i	$0.873394\pi$
$104$		0			0
$105$	552.632	−	1210.10i	0.0501254	−	0.109759i
$106$		0			0
$107$	4671.93	−	4048.25i	0.408064	−	0.353590i	−0.426512	−	0.904482i	$-0.640258\pi$
$107$	4671.93	−	4048.25i	0.408064	−	0.353590i	0.834576	+	0.550892i	$0.185712\pi$
$108$		0			0
$109$	−8485.53	−	13203.7i	−0.714210	−	1.11133i	−0.988724	−	0.149749i	$-0.952153\pi$
$109$	−8485.53	−	13203.7i	−0.714210	−	1.11133i	0.274514	−	0.961583i	$-0.411483\pi$
$110$		0			0
$111$	−2732.28	+	4251.51i	−0.221758	+	0.345062i
$112$		0			0
$113$	10.0376	−	34.1848i	0.000786089	−	0.00267717i	−0.959099	−	0.283071i	$-0.908647\pi$
$113$	10.0376	−	34.1848i	0.000786089	−	0.00267717i	0.959885	+	0.280394i	$0.0904650\pi$
$114$		0			0
$115$	−222.301	−	3940.55i	−0.0168091	−	0.297963i
$116$		0			0
$117$	17174.0	+	5042.75i	1.25459	+	0.368380i
$118$		0			0
$119$	13090.1	+	8412.50i	0.924377	+	0.594061i
$120$		0			0
$121$	10029.4	−	6445.48i	0.685019	−	0.440235i
$122$		0			0
$123$	5150.91	+	5944.47i	0.340466	+	0.392919i
$124$		0			0
$125$	−8105.57	−	3701.69i	−0.518756	−	0.236908i
$126$		0			0
$127$	−8304.86	+	2438.53i	−0.514902	+	0.151189i	−0.528852	−	0.848714i	$-0.677378\pi$
$127$	−8304.86	+	2438.53i	−0.514902	+	0.151189i	0.0139503	+	0.999903i	$0.495559\pi$
$128$		0			0
$129$	−1766.25	+	253.948i	−0.106138	+	0.0152604i
$130$		0			0
$131$	−5546.41	−	12144.9i	−0.323198	−	0.707706i	0.676386	−	0.736548i	$-0.263545\pi$
$131$	−5546.41	−	12144.9i	−0.323198	−	0.707706i	−0.999584	+	0.0288420i	$0.990818\pi$
$132$		0			0
$133$	2154.38	−	14984.0i	0.121792	−	0.847081i
$134$		0			0
$135$	3654.64	+	3166.76i	0.200529	+	0.173759i
$136$		0			0
$137$			30695.6i			1.63544i	0.575617	+	0.817719i	$0.304762\pi$
$137$			30695.6i			1.63544i	−0.575617	+	0.817719i	$0.695238\pi$
$138$		0			0
$139$	−26324.2			−1.36247			−0.681233	−	0.732067i	$-0.738556\pi$
$139$	−26324.2			−1.36247			−0.681233	+	0.732067i	$0.738556\pi$
$140$		0			0
$141$	−7133.37	+	8232.34i	−0.358803	+	0.414081i
$142$		0			0
$143$	−15445.4	−	2220.72i	−0.755315	−	0.108598i
$144$		0			0
$145$	7983.10	−	3645.76i	0.379696	−	0.173401i
$146$		0			0
$147$	589.821	+	4102.30i	0.0272952	+	0.189842i
$148$		0			0
$149$	7525.33	+	25628.9i	0.338964	+	1.15440i	0.935944	+	0.352148i	$0.114549\pi$
$149$	7525.33	+	25628.9i	0.338964	+	1.15440i	−0.596981	+	0.802256i	$0.703633\pi$
$150$		0			0
$151$	4314.11	−	9446.58i	0.189207	−	0.414305i	−0.791127	−	0.611652i	$-0.790505\pi$
$151$	4314.11	−	9446.58i	0.189207	−	0.414305i	0.980334	+	0.197347i	$0.0632325\pi$
$152$		0			0
$153$	−18157.7	+	15733.7i	−0.775672	+	0.672123i
$154$		0			0
$155$	5575.21	+	8675.20i	0.232059	+	0.361090i
$156$		0			0
$157$	−9630.92	+	14986.0i	−0.390722	+	0.607976i	−0.979771	−	0.200122i	$-0.935866\pi$
$157$	−9630.92	+	14986.0i	−0.390722	+	0.607976i	0.589049	+	0.808098i	$0.299503\pi$
$158$		0			0
$159$	−5376.25	+	18309.8i	−0.212660	+	0.724252i
$160$		0			0
$161$	−12032.3	−	16587.7i	−0.464190	−	0.639933i
$162$		0			0
$163$	−46099.0	−	13535.9i	−1.73507	−	0.509462i	−0.747178	−	0.664624i	$-0.768592\pi$
$163$	−46099.0	−	13535.9i	−1.73507	−	0.509462i	−0.987889	+	0.155162i	$0.950410\pi$
$164$		0			0
$165$	−1506.47	−	968.149i	−0.0553340	−	0.0355610i
$166$		0			0
$167$	15065.6	−	9682.08i	0.540199	−	0.347165i	−0.241918	−	0.970297i	$-0.577776\pi$
$167$	15065.6	−	9682.08i	0.540199	−	0.347165i	0.782117	+	0.623132i	$0.214140\pi$
$168$		0			0
$169$	−39939.2	−	46092.3i	−1.39838	−	1.61382i
$170$		0			0
$171$	21262.0	+	9710.03i	0.727130	+	0.332069i
$172$		0			0
$173$	28631.8	−	8407.06i	0.956658	−	0.280900i	0.234101	−	0.972212i	$-0.424785\pi$
$173$	28631.8	−	8407.06i	0.956658	−	0.280900i	0.722556	+	0.691312i	$0.242967\pi$
$174$		0			0
$175$	−21830.1	+	3138.70i	−0.712820	+	0.102488i
$176$		0			0
$177$	6848.64	+	14996.4i	0.218604	+	0.478675i
$178$		0			0
$179$	−3952.96	+	27493.4i	−0.123372	+	0.858070i	0.830321	+	0.557286i	$0.188157\pi$
$179$	−3952.96	+	27493.4i	−0.123372	+	0.858070i	−0.953692	+	0.300784i	$0.902752\pi$
$180$		0			0
$181$	31210.9	+	27044.4i	0.952684	+	0.825506i	0.984749	−	0.173980i	$-0.0556629\pi$
$181$	31210.9	+	27044.4i	0.952684	+	0.825506i	−0.0320649	+	0.999486i	$0.510208\pi$
$182$		0			0
$183$			16610.3i			0.495993i
$184$		0			0
$185$	−8191.75			−0.239350
$186$		0			0
$187$	13716.5	−	15829.7i	0.392249	−	0.452679i
$188$		0			0
$189$	24852.1	+	3573.19i	0.695728	+	0.100031i
$190$		0			0
$191$	−31714.6	+	14483.6i	−0.869345	+	0.397016i	−0.799589	−	0.600548i	$-0.794949\pi$
$191$	−31714.6	+	14483.6i	−0.869345	+	0.397016i	−0.0697557	+	0.997564i	$0.522222\pi$
$192$		0			0
$193$	−5514.66	−	38355.3i	−0.148049	−	1.02970i	−0.919409	−	0.393302i	$-0.871333\pi$
$193$	−5514.66	−	38355.3i	−0.148049	−	1.02970i	0.771361	−	0.636398i	$-0.219576\pi$
$194$		0			0
$195$	−2895.29	−	9860.45i	−0.0761417	−	0.259315i
$196$		0			0
$197$	4062.43	−	8895.47i	0.104677	−	0.229212i	−0.850045	−	0.526711i	$-0.823425\pi$
$197$	4062.43	−	8895.47i	0.104677	−	0.229212i	0.954722	+	0.297499i	$0.0961525\pi$
$198$		0			0
$199$	−6359.44	+	5510.48i	−0.160588	+	0.139150i	−0.731448	−	0.681897i	$-0.761155\pi$
$199$	−6359.44	+	5510.48i	−0.160588	+	0.139150i	0.570860	+	0.821047i	$0.306610\pi$
$200$		0			0
$201$	−2133.98	−	3320.53i	−0.0528199	−	0.0821894i
$202$		0			0
$203$	24635.1	−	38333.0i	0.597809	−	0.930209i
$204$		0			0
$205$	−3591.97	+	12233.1i	−0.0854722	+	0.291092i
$206$		0			0
$207$	29809.3	−	10610.2i	0.695682	−	0.247618i
$208$		0			0
$209$	−19552.1	−	5741.00i	−0.447610	−	0.131430i
$210$		0			0
$211$	33477.5	+	21514.7i	0.751948	+	0.483248i	0.859617	−	0.510939i	$-0.170702\pi$
$211$	33477.5	+	21514.7i	0.751948	+	0.483248i	−0.107669	+	0.994187i	$0.534339\pi$
$212$		0			0
$213$	18872.5	−	12128.6i	0.415977	−	0.267332i
$214$		0			0
$215$	−1894.10	−	2185.91i	−0.0409758	−	0.0472885i
$216$		0			0
$217$	48703.2	+	22242.0i	1.03428	+	0.472340i
$218$		0			0
$219$	−25780.2	+	7569.74i	−0.537524	+	0.157831i
$220$		0			0
$221$	118980.	−	17106.7i	2.43607	−	0.350254i
$222$		0			0
$223$	−17721.5	−	38804.7i	−0.356362	−	0.780324i	−0.999889	−	0.0149006i	$-0.995257\pi$
$223$	−17721.5	−	38804.7i	−0.356362	−	0.780324i	0.643527	−	0.765424i	$-0.277470\pi$
$224$		0			0
$225$	4846.37	−	33707.2i	0.0957307	−	0.665822i
$226$		0			0
$227$	−5659.74	−	4904.19i	−0.109836	−	0.0951734i	0.598211	−	0.801338i	$-0.295878\pi$
$227$	−5659.74	−	4904.19i	−0.109836	−	0.0951734i	−0.708047	+	0.706165i	$0.750424\pi$
$228$		0			0
$229$		−	1952.71i		−	0.0372362i	−0.999827	−	0.0186181i	$-0.994073\pi$
$229$		−	1952.71i		−	0.0372362i	0.999827	−	0.0186181i	$-0.00592667\pi$
$230$		0			0
$231$	−9297.65			−0.174241
$232$		0			0
$233$	−3908.08	+	4510.17i	−0.0719866	+	0.0830770i	−0.790600	−	0.612332i	$-0.790231\pi$
$233$	−3908.08	+	4510.17i	−0.0719866	+	0.0830770i	0.718614	+	0.695409i	$0.244777\pi$
$234$		0			0
$235$	−17476.9	−	2512.79i	−0.316466	−	0.0455010i
$236$		0			0
$237$	39003.7	−	17812.4i	0.694399	−	0.317122i
$238$		0			0
$239$	−3611.29	−	25117.1i	−0.0632218	−	0.439717i	−0.996706	−	0.0810987i	$-0.974157\pi$
$239$	−3611.29	−	25117.1i	−0.0632218	−	0.439717i	0.933484	−	0.358618i	$-0.116752\pi$
$240$		0			0
$241$	−3657.11	−	12455.0i	−0.0629657	−	0.214441i	0.922001	−	0.387189i	$-0.126554\pi$
$241$	−3657.11	−	12455.0i	−0.0629657	−	0.214441i	−0.984966	+	0.172747i	$0.944736\pi$
$242$		0			0
$243$	−25368.8	+	55549.8i	−0.429622	+	0.940741i
$244$		0			0
$245$	−5077.02	+	4399.26i	−0.0845818	+	0.0732905i
$246$		0			0
$247$	−63223.9	−	98378.3i	−1.03630	−	1.61252i
$248$		0			0
$249$	26921.3	−	41890.3i	0.434207	−	0.675640i
$250$		0			0
$251$	−19219.4	+	65455.3i	−0.305065	+	1.03896i	0.654170	+	0.756347i	$0.273018\pi$
$251$	−19219.4	+	65455.3i	−0.305065	+	1.03896i	−0.959235	+	0.282609i	$0.908800\pi$
$252$		0			0
$253$	−24406.6	+	12854.1i	−0.381299	+	0.200818i
$254$		0			0
$255$	13235.8	+	3886.37i	0.203549	+	0.0597673i
$256$		0			0
$257$	19413.1	+	12476.1i	0.293920	+	0.188891i	0.679288	−	0.733872i	$-0.262289\pi$
$257$	19413.1	+	12476.1i	0.293920	+	0.188891i	−0.385367	+	0.922763i	$0.625925\pi$
$258$		0			0
$259$	−35780.2	+	22994.6i	−0.533388	+	0.342788i
$260$		0			0
$261$	46074.6	+	53172.9i	0.676364	+	0.780566i
$262$		0			0
$263$	66081.6	+	30178.5i	0.955365	+	0.436300i	0.831208	−	0.555962i	$-0.187650\pi$
$263$	66081.6	+	30178.5i	0.955365	+	0.436300i	0.124157	+	0.992263i	$0.460377\pi$
$264$		0			0
$265$	−29678.7	+	8714.45i	−0.422623	+	0.124093i
$266$		0			0
$267$	1975.62	−	284.051i	0.0277128	−	0.00398451i
$268$		0			0
$269$	−185.303	−	405.758i	−0.00256082	−	0.00560741i	0.908347	−	0.418217i	$-0.137345\pi$
$269$	−185.303	−	405.758i	−0.00256082	−	0.00560741i	−0.910908	+	0.412609i	$0.864617\pi$
$270$		0			0
$271$	15242.1	−	106011.i	0.207542	−	1.44349i	−0.573600	−	0.819136i	$-0.694454\pi$
$271$	15242.1	−	106011.i	0.207542	−	1.44349i	0.781142	−	0.624353i	$-0.214637\pi$
$272$		0			0
$273$	−40324.8	−	34941.7i	−0.541062	−	0.468833i
$274$		0			0
$275$			29687.8i			0.392567i
$276$		0			0
$277$	−67656.5			−0.881759			−0.440880	−	0.897566i	$-0.645333\pi$
$277$	−67656.5			−0.881759			−0.440880	+	0.897566i	$0.645333\pi$
$278$		0			0
$279$	−54138.7	+	62479.4i	−0.695504	+	0.802655i
$280$		0			0
$281$	−60050.3	−	8633.93i	−0.760506	−	0.109344i	−0.248859	−	0.968540i	$-0.580055\pi$
$281$	−60050.3	−	8633.93i	−0.760506	−	0.109344i	−0.511647	+	0.859196i	$0.670965\pi$
$282$		0			0
$283$	128831.	−	58835.3i	1.60860	−	0.734624i	0.610260	−	0.792201i	$-0.291065\pi$
$283$	128831.	−	58835.3i	1.60860	−	0.734624i	0.998341	+	0.0575774i	$0.0183376\pi$
$284$		0			0
$285$	−1909.91	−	13283.7i	−0.0235138	−	0.163542i
$286$		0			0
$287$	18649.7	+	63515.1i	0.226417	+	0.771105i
$288$		0			0
$289$	−32331.4	+	70795.9i	−0.387105	+	0.847642i
$290$		0			0
$291$	−37640.2	+	32615.4i	−0.444494	+	0.385156i
$292$		0			0
$293$	77411.8	+	120455.i	0.901720	+	1.40310i	0.915115	+	0.403194i	$0.132100\pi$
$293$	77411.8	+	120455.i	0.901720	+	1.40310i	−0.0133943	+	0.999910i	$0.504264\pi$
$294$		0			0
$295$	−14447.5	+	22480.7i	−0.166015	+	0.258324i
$296$		0			0
$297$	9521.88	−	32428.5i	0.107947	−	0.367633i
$298$		0			0
$299$	−154161.	−	35973.1i	−1.72438	−	0.402379i
$300$		0			0
$301$	−14409.1	−	4230.89i	−0.159039	−	0.0466980i
$302$		0			0
$303$	21844.0	+	14038.3i	0.237928	+	0.152907i
$304$		0			0
$305$	−22649.9	+	14556.2i	−0.243481	+	0.156476i
$306$		0			0
$307$	12012.7	+	13863.4i	0.127457	+	0.147093i	0.815891	−	0.578206i	$-0.196247\pi$
$307$	12012.7	+	13863.4i	0.127457	+	0.147093i	−0.688434	+	0.725299i	$0.741702\pi$
$308$		0			0
$309$	9941.99	+	4540.35i	0.104125	+	0.0475524i
$310$		0			0
$311$	−117535.	+	34511.5i	−1.21520	+	0.356815i	−0.825646	−	0.564189i	$-0.809189\pi$
$311$	−117535.	+	34511.5i	−1.21520	+	0.356815i	−0.389554	+	0.921004i	$0.627371\pi$
$312$		0			0
$313$	62686.5	−	9012.96i	0.639861	−	0.0919981i	0.185255	−	0.982691i	$-0.440689\pi$
$313$	62686.5	−	9012.96i	0.639861	−	0.0919981i	0.454606	+	0.890692i	$0.349780\pi$
$314$		0			0
$315$	7181.31	+	15724.9i	0.0723740	+	0.158477i
$316$		0			0
$317$	4929.91	−	34288.3i	0.0490592	−	0.341214i	−0.950478	−	0.310792i	$-0.899406\pi$
$317$	4929.91	−	34288.3i	0.0490592	−	0.341214i	0.999537	−	0.0304221i	$-0.00968516\pi$
$318$		0			0
$319$	−46355.7	−	40167.4i	−0.455535	−	0.394723i
$320$		0			0
$321$		−	28454.4i		−	0.276146i
$322$		0			0
$323$	156973.			1.50460
$324$		0			0
$325$	−111570.	+	128759.i	−1.05629	+	1.21902i
$326$		0			0
$327$	−71508.5	−	10281.4i	−0.668748	−	0.0961514i
$328$		0			0
$329$	−83389.6	+	38082.7i	−0.770407	+	0.351833i
$330$		0			0
$331$	−16695.4	−	116119.i	−0.152384	−	1.05985i	−0.912208	−	0.409726i	$-0.865624\pi$
$331$	−16695.4	−	116119.i	−0.152384	−	1.05985i	0.759824	−	0.650128i	$-0.225285\pi$
$332$		0			0
$333$	−18502.1	−	63012.2i	−0.166852	−	0.568246i
$334$		0			0
$335$	2657.81	−	5819.79i	0.0236829	−	0.0518583i
$336$		0			0
$337$	−119637.	+	103666.i	−1.05343	+	0.912806i	−0.996333	−	0.0855629i	$-0.972731\pi$
$337$	−119637.	+	103666.i	−1.05343	+	0.912806i	−0.0571010	+	0.998368i	$0.518186\pi$
$338$		0			0
$339$	−88.6607	−	137.959i	−0.000771493	−	0.00120047i
$340$		0			0
$341$	38965.5	−	60631.5i	0.335098	−	0.521423i
$342$		0			0
$343$	−36030.3	+	122708.i	−0.306252	+	1.04300i
$344$		0			0
$345$	−14377.8	−	11104.5i	−0.120797	−	0.0932958i
$346$		0			0
$347$	−21575.6	−	6335.16i	−0.179186	−	0.0526137i	0.190909	−	0.981608i	$-0.438857\pi$
$347$	−21575.6	−	6335.16i	−0.179186	−	0.0526137i	−0.370095	+	0.928994i	$0.620675\pi$
$348$		0			0
$349$	157654.	+	101318.i	1.29435	+	0.831831i	0.992585	−	0.121550i	$-0.0387866\pi$
$349$	157654.	+	101318.i	1.29435	+	0.831831i	0.301769	+	0.953381i	$0.402423\pi$
$350$		0			0
$351$	163168.	−	104861.i	1.32440	−	0.851141i
$352$		0			0
$353$	−100889.	−	116432.i	−0.809644	−	0.934379i	0.189224	−	0.981934i	$-0.439403\pi$
$353$	−100889.	−	116432.i	−0.809644	−	0.934379i	−0.998869	+	0.0475545i	$0.984857\pi$
$354$		0			0
$355$	33077.2	+	15105.8i	0.262465	+	0.119864i
$356$		0			0
$357$	68720.9	−	20178.3i	0.539203	−	0.158324i
$358$		0			0
$359$	215770.	−	31023.0i	1.67418	−	0.240711i	0.761142	−	0.648586i	$-0.224639\pi$
$359$	215770.	−	31023.0i	1.67418	−	0.240711i	0.913038	+	0.407875i	$0.133730\pi$
$360$		0			0
$361$	−9302.56	−	20369.8i	−0.0713819	−	0.156305i
$362$		0			0
$363$	7809.57	−	54316.8i	0.0592672	−	0.412212i
$364$		0			0
$365$	−32914.2	−	28520.3i	−0.247057	−	0.214076i
$366$		0			0
$367$			264461.i			1.96349i	0.190198	+	0.981746i	$0.439087\pi$
$367$			264461.i			1.96349i	−0.190198	+	0.981746i	$0.560913\pi$
$368$		0			0
$369$	−102212.			−0.750671
$370$		0			0
$371$	−105170.	+	121373.i	−0.764088	+	0.881805i
$372$		0			0
$373$	86574.1	+	12447.5i	0.622258	+	0.0894672i	0.446231	−	0.894918i	$-0.352766\pi$
$373$	86574.1	+	12447.5i	0.622258	+	0.0894672i	0.176027	+	0.984385i	$0.443675\pi$
$374$		0			0
$375$	−37309.1	+	17038.5i	−0.265309	+	0.121163i
$376$		0			0
$377$	−50095.3	−	348420.i	−0.352463	−	2.45144i
$378$		0			0
$379$	−32652.0	−	111202.i	−0.227316	−	0.774169i	−0.991606	−	0.129296i	$-0.958728\pi$
$379$	−32652.0	−	111202.i	−0.227316	−	0.774169i	0.764290	−	0.644873i	$-0.223090\pi$
$380$		0			0
$381$	−16550.2	+	36239.9i	−0.114013	+	0.249653i
$382$		0			0
$383$	182848.	−	158439.i	1.24650	−	1.08010i	0.252864	−	0.967502i	$-0.418628\pi$
$383$	182848.	−	158439.i	1.24650	−	1.08010i	0.993640	−	0.112600i	$-0.0359178\pi$
$384$		0			0
$385$	−8147.84	−	12678.3i	−0.0549694	−	0.0855341i
$386$		0			0
$387$	12536.3	−	19506.9i	0.0837044	−	0.130247i
$388$		0			0
$389$	−33538.8	+	114223.i	−0.221640	+	0.754836i	0.771326	+	0.636440i	$0.219594\pi$
$389$	−33538.8	+	114223.i	−0.221640	+	0.754836i	−0.992966	+	0.118397i	$0.962225\pi$
$390$		0			0
$391$	152497.	−	147976.i	0.997491	−	0.967917i
$392$		0			0
$393$	−58966.1	−	17314.0i	−0.381784	−	0.112102i
$394$		0			0
$395$	58469.3	+	37575.9i	0.374743	+	0.240833i
$396$		0			0
$397$	142697.	−	91705.7i	0.905385	−	0.581856i	−0.00299732	−	0.999996i	$-0.500954\pi$
$397$	142697.	−	91705.7i	0.905385	−	0.581856i	0.908383	+	0.418140i	$0.137318\pi$
$398$		0			0
$399$	−45630.1	−	52659.9i	−0.286619	−	0.330776i
$400$		0			0
$401$	126252.	+	57657.2i	0.785142	+	0.358562i	0.767308	−	0.641279i	$-0.221596\pi$
$401$	126252.	+	57657.2i	0.785142	+	0.358562i	0.0178340	+	0.999841i	$0.494323\pi$
$402$		0			0
$403$	396858.	−	116528.i	2.44357	−	0.717497i
$404$		0			0
$405$	−13747.3	+	1976.56i	−0.0838121	+	0.0120504i
$406$		0			0
$407$	23783.6	+	52078.9i	0.143578	+	0.314393i
$408$		0			0
$409$	−17151.8	+	119294.i	−0.102533	+	0.713133i	0.872101	+	0.489327i	$0.162757\pi$
$409$	−17151.8	+	119294.i	−0.102533	+	0.713133i	−0.974634	+	0.223806i	$0.928152\pi$
$410$		0			0
$411$	106779.	+	92524.2i	0.632122	+	0.547737i
$412$		0			0
$413$			138747.i			0.813434i
$414$		0			0
$415$	80713.8			0.468653
$416$		0			0
$417$	−79347.8	+	91572.3i	−0.456313	+	0.526613i
$418$		0			0
$419$	−183466.	−	26378.4i	−1.04503	−	0.150252i	−0.401643	−	0.915796i	$-0.631561\pi$
$419$	−183466.	−	26378.4i	−1.04503	−	0.150252i	−0.643383	+	0.765545i	$0.722470\pi$
$420$		0			0
$421$	139693.	−	63795.9i	0.788155	−	0.359939i	0.0196706	−	0.999807i	$-0.493738\pi$
$421$	139693.	−	63795.9i	0.788155	−	0.359939i	0.768485	+	0.639868i	$0.221011\pi$
$422$		0			0
$423$	−20144.8	−	140110.i	−0.112585	−	0.783049i
$424$		0			0
$425$	−64430.2	−	219429.i	−0.356707	−	1.21483i
$426$		0			0
$427$	−58071.1	+	127158.i	−0.318496	+	0.697410i
$428$		0			0
$429$	−54281.5	+	47035.2i	−0.294943	+	0.255569i
$430$		0			0
$431$	19616.6	+	30524.1i	0.105602	+	0.164319i	0.890033	−	0.455897i	$-0.150681\pi$
$431$	19616.6	+	30524.1i	0.105602	+	0.164319i	−0.784431	+	0.620216i	$0.787045\pi$
$432$		0			0
$433$	32761.1	−	50977.2i	0.174736	−	0.271894i	−0.742828	−	0.669482i	$-0.766516\pi$
$433$	32761.1	−	50977.2i	0.174736	−	0.271894i	0.917564	+	0.397588i	$0.130153\pi$
$434$		0			0
$435$	11380.8	−	38759.5i	0.0601444	−	0.204833i
$436$		0			0
$437$	−192583.	−	75149.4i	−1.00845	−	0.393516i
$438$		0			0
$439$	−187411.	−	55028.9i	−0.972448	−	0.285536i	−0.243344	−	0.969940i	$-0.578244\pi$
$439$	−187411.	−	55028.9i	−0.972448	−	0.285536i	−0.729103	+	0.684404i	$0.760063\pi$
$440$		0			0
$441$	−45306.9	−	29117.0i	−0.232963	−	0.149716i
$442$		0			0
$443$	−30346.6	+	19502.6i	−0.154633	+	0.0993767i	−0.615669	−	0.788005i	$-0.711114\pi$
$443$	−30346.6	+	19502.6i	−0.154633	+	0.0993767i	0.461036	+	0.887381i	$0.347478\pi$
$444$		0			0
$445$	2118.64	+	2445.04i	0.0106988	+	0.0123471i
$446$		0			0
$447$	111837.	+	51074.2i	0.559719	+	0.255615i
$448$		0			0
$449$	−330476.	+	97036.4i	−1.63926	+	0.481329i	−0.966099	−	0.258171i	$-0.916880\pi$
$449$	−330476.	+	97036.4i	−1.63926	+	0.481329i	−0.673157	+	0.739500i	$0.735062\pi$
$450$		0			0
$451$	88200.7	−	12681.3i	0.433629	−	0.0623465i
$452$		0			0
$453$	−19857.4	−	43481.6i	−0.0967666	−	0.211889i
$454$		0			0
$455$	12308.5	−	85607.6i	0.0594542	−	0.413513i
$456$		0			0
$457$	−53588.5	−	46434.7i	−0.256590	−	0.222336i	0.517061	−	0.855949i	$-0.327026\pi$
$457$	−53588.5	−	46434.7i	−0.256590	−	0.222336i	−0.773651	+	0.633612i	$0.781571\pi$
$458$		0			0
$459$			260351.i			1.23576i
$460$		0			0
$461$	−23429.3			−0.110245			−0.0551223	−	0.998480i	$-0.517555\pi$
$461$	−23429.3			−0.110245			−0.0551223	+	0.998480i	$0.517555\pi$
$462$		0			0
$463$	−171103.	+	197464.i	−0.798172	+	0.921140i	−0.998280	−	0.0586344i	$-0.981325\pi$
$463$	−171103.	+	197464.i	−0.798172	+	0.921140i	0.200108	+	0.979774i	$0.435871\pi$
$464$		0			0
$465$	46982.9	+	6755.13i	0.217287	+	0.0312412i
$466$		0			0
$467$	388074.	−	177227.i	1.77943	−	0.812638i	0.803260	−	0.595628i	$-0.203097\pi$
$467$	388074.	−	177227.i	1.77943	−	0.812638i	0.976169	−	0.217010i	$-0.0696304\pi$
$468$		0			0
$469$	−4727.50	−	32880.5i	−0.0214925	−	0.149483i
$470$		0			0
$471$	23100.8	+	78674.0i	0.104132	+	0.354642i
$472$		0			0
$473$	−8397.62	+	18388.2i	−0.0375348	+	0.0821898i
$474$		0			0
$475$	−168146.	+	145699.i	−0.745244	+	0.645758i
$476$		0			0
$477$	−134066.	−	208611.i	−0.589225	−	0.916853i
$478$		0			0
$479$	−72143.9	+	112258.i	−0.314433	+	0.489268i	−0.962115	−	0.272643i	$-0.912102\pi$
$479$	−72143.9	+	112258.i	−0.314433	+	0.489268i	0.647682	+	0.761911i	$0.275739\pi$
$480$		0			0
$481$	−92566.6	+	315253.i	−0.400096	+	1.36260i
$482$		0			0
$483$	−93970.9	−	8143.69i	−0.402809	−	0.0349081i
$484$		0			0
$485$	−77459.8	−	22744.2i	−0.329301	−	0.0966915i
$486$		0			0
$487$	211873.	+	136162.i	0.893341	+	0.574116i	0.904808	−	0.425819i	$-0.140014\pi$
$487$	211873.	+	136162.i	0.893341	+	0.574116i	−0.0114673	+	0.999934i	$0.503650\pi$
$488$		0			0
$489$	−186040.	+	119561.i	−0.778018	+	0.500002i
$490$		0			0
$491$	−199287.	−	229990.i	−0.826639	−	0.953993i	0.172882	−	0.984943i	$-0.444692\pi$
$491$	−199287.	−	229990.i	−0.826639	−	0.953993i	−0.999521	+	0.0309499i	$0.990147\pi$
$492$		0			0
$493$	429798.	+	196282.i	1.76836	+	0.807583i
$494$		0			0
$495$	22327.6	−	6555.98i	0.0911239	−	0.0267564i
$496$		0			0
$497$	186878.	−	26869.1i	0.756565	−	0.108778i
$498$		0			0
$499$	−9282.70	−	20326.3i	−0.0372798	−	0.0816313i	0.890076	−	0.455812i	$-0.150651\pi$
$499$	−9282.70	−	20326.3i	−0.0372798	−	0.0816313i	−0.927356	+	0.374181i	$0.877924\pi$
$500$		0			0
$501$	11731.2	−	81592.0i	0.0467375	−	0.325066i
$502$		0			0
$503$	−234549.	−	203238.i	−0.927037	−	0.803282i	0.0537120	−	0.998556i	$-0.482895\pi$
$503$	−234549.	−	203238.i	−0.927037	−	0.803282i	−0.980749	+	0.195275i	$0.937440\pi$
$504$		0			0
$505$			42088.7i			0.165037i
$506$		0			0
$507$	−280725.			−1.09211
$508$		0			0
$509$	−152366.	+	175840.i	−0.588103	+	0.678707i	−0.969327	−	0.245776i	$-0.920957\pi$
$509$	−152366.	+	175840.i	−0.588103	+	0.678707i	0.381224	+	0.924483i	$0.375503\pi$
$510$		0			0
$511$	−223821.	−	32180.6i	−0.857156	−	0.123240i
$512$		0			0
$513$	230399.	−	105220.i	0.875479	−	0.399818i
$514$		0			0
$515$	2521.26	+	17535.8i	0.00950613	+	0.0661166i
$516$		0			0
$517$	34766.6	+	118404.i	0.130071	+	0.442982i
$518$		0			0
$519$	57058.5	−	124941.i	0.211829	−	0.463841i
$520$		0			0
$521$	58138.4	−	50377.2i	0.214184	−	0.185592i	−0.541161	−	0.840919i	$-0.682015\pi$
$521$	58138.4	−	50377.2i	0.214184	−	0.185592i	0.755345	+	0.655328i	$0.227469\pi$
$522$		0			0
$523$	−18558.1	−	28877.0i	−0.0678470	−	0.105572i	0.805672	−	0.592361i	$-0.201804\pi$
$523$	−18558.1	−	28877.0i	−0.0678470	−	0.105572i	−0.873519	+	0.486789i	$0.838168\pi$
$524$		0			0
$525$	−54883.1	+	85399.8i	−0.199122	+	0.309841i
$526$		0			0
$527$	−156417.	+	532706.i	−0.563198	+	1.91808i
$528$		0			0
$529$	−257935.	+	108539.i	−0.921719	+	0.387858i
$530$		0			0
$531$	−205556.	−	60356.8i	−0.729024	−	0.214061i
$532$		0			0
$533$	430193.	+	276468.i	1.51429	+	0.973175i
$534$		0			0
$535$	38800.4	−	24935.5i	0.135559	−	0.0871186i
$536$		0			0
$537$	83724.3	+	96623.0i	0.290337	+	0.335067i
$538$		0			0
$539$	42708.7	+	19504.4i	0.147007	+	0.0671359i
$540$		0			0
$541$	−219113.	+	64337.4i	−0.748641	+	0.219821i	−0.633729	−	0.773555i	$-0.718477\pi$
$541$	−219113.	+	64337.4i	−0.748641	+	0.219821i	−0.114912	+	0.993376i	$0.536658\pi$
$542$		0			0
$543$	188155.	−	27052.6i	0.638141	−	0.0917508i
$544$		0			0
$545$	−48645.6	−	106519.i	−0.163776	−	0.358620i
$546$		0			0
$547$	30049.0	−	208995.i	0.100428	−	0.698492i	−0.875947	−	0.482408i	$-0.839762\pi$
$547$	30049.0	−	208995.i	0.100428	−	0.698492i	0.976375	−	0.216084i	$-0.0693286\pi$
$548$		0			0
$549$	−163126.	−	141349.i	−0.541226	−	0.468975i
$550$		0			0
$551$		−	459679.i		−	1.51409i
$552$		0			0
$553$	360862.			1.18002
$554$		0			0
$555$	−24692.0	+	28496.1i	−0.0801623	+	0.0925123i
$556$		0			0
$557$	−99470.4	−	14301.7i	−0.320615	−	0.0460975i	−0.0198714	−	0.999803i	$-0.506326\pi$
$557$	−99470.4	−	14301.7i	−0.320615	−	0.0460975i	−0.300743	+	0.953705i	$0.597235\pi$
$558$		0			0
$559$	−105526.	+	48192.3i	−0.337705	+	0.154225i
$560$		0			0
$561$	−13720.7	−	95429.7i	−0.0435964	−	0.303220i
$562$		0			0
$563$	48704.5	+	165872.i	0.153657	+	0.523308i	0.999956	−	0.00940083i	$-0.00299242\pi$
$563$	48704.5	+	165872.i	0.153657	+	0.523308i	−0.846299	+	0.532708i	$0.821174\pi$
$564$		0			0
$565$	110.424	−	241.796i	0.000345914	−	0.000757446i
$566$		0			0
$567$	−54497.6	+	47222.5i	−0.169516	+	0.146887i
$568$		0			0
$569$	−165194.	−	257046.i	−0.510234	−	0.793939i	0.486586	−	0.873633i	$-0.338242\pi$
$569$	−165194.	−	257046.i	−0.510234	−	0.793939i	−0.996819	+	0.0796938i	$0.974606\pi$
$570$		0			0
$571$	188477.	−	293275.i	0.578076	−	0.899504i	−0.421898	−	0.906643i	$-0.638636\pi$
$571$	188477.	−	293275.i	0.578076	−	0.899504i	0.999975	+	0.00713892i	$0.00227241\pi$
$572$		0			0
$573$	−45212.8	+	153980.i	−0.137706	+	0.468982i
$574$		0			0
$575$	−26003.2	+	300054.i	−0.0786486	+	0.907534i
$576$		0			0
$577$	107618.	+	31599.5i	0.323246	+	0.0949136i	0.439330	−	0.898326i	$-0.355216\pi$
$577$	107618.	+	31599.5i	0.323246	+	0.0949136i	−0.116084	+	0.993239i	$0.537034\pi$
$578$		0			0
$579$	−150047.	−	96429.1i	−0.447578	−	0.287641i
$580$		0			0
$581$	352545.	−	226567.i	1.04439	−	0.671187i
$582$		0			0
$583$	141570.	+	163380.i	0.416518	+	0.480687i
$584$		0			0
$585$	121475.	+	55475.9i	0.354957	+	0.162104i
$586$		0			0
$587$	363536.	−	106744.i	1.05505	−	0.309789i	0.292191	−	0.956360i	$-0.405616\pi$
$587$	363536.	−	106744.i	1.05505	−	0.309789i	0.762854	+	0.646571i	$0.223797\pi$
$588$		0			0
$589$	534635.	−	76869.0i	1.54109	−	0.221575i
$590$		0			0
$591$	−18698.9	−	40944.9i	−0.0535355	−	0.117226i
$592$		0			0
$593$	86277.1	−	600071.i	0.245350	−	1.70645i	−0.379077	−	0.925365i	$-0.623759\pi$
$593$	86277.1	−	600071.i	0.245350	−	1.70645i	0.624428	−	0.781083i	$-0.285332\pi$
$594$		0			0
$595$	87737.6	+	76025.0i	0.247829	+	0.214745i
$596$		0			0
$597$			38732.2i			0.108673i
$598$		0			0
$599$	−588328.			−1.63970			−0.819852	−	0.572575i	$-0.805944\pi$
$599$	−588328.			−1.63970			−0.819852	+	0.572575i	$0.805944\pi$
$600$		0			0
$601$	−70594.7	+	81470.6i	−0.195444	+	0.225555i	−0.845010	−	0.534751i	$-0.820405\pi$
$601$	−70594.7	+	81470.6i	−0.195444	+	0.225555i	0.649565	+	0.760306i	$0.274951\pi$
$602$		0			0
$603$	50769.8	+	7299.59i	0.139627	+	0.0200754i
$604$		0			0
$605$	80910.3	−	36950.5i	0.221051	−	0.100951i
$606$		0			0
$607$	−76514.6	−	532171.i	−0.207667	−	1.44435i	−0.780743	−	0.624852i	$-0.785159\pi$
$607$	−76514.6	−	532171.i	−0.207667	−	1.44435i	0.573076	−	0.819502i	$-0.305750\pi$
$608$		0			0
$609$	−59089.9	−	201242.i	−0.159323	−	0.542605i
$610$		0			0
$611$	−294191.	+	644188.i	−0.788037	+	1.72556i
$612$		0			0
$613$	−82039.9	+	71088.0i	−0.218325	+	0.189180i	−0.757156	−	0.653234i	$-0.773412\pi$
$613$	−82039.9	+	71088.0i	−0.218325	+	0.189180i	0.538831	+	0.842414i	$0.318866\pi$
$614$		0			0
$615$	31727.5	+	49368.9i	0.0838852	+	0.130528i
$616$		0			0
$617$	67880.0	−	105623.i	0.178308	−	0.277453i	−0.740582	−	0.671966i	$-0.765450\pi$
$617$	67880.0	−	105623.i	0.178308	−	0.277453i	0.918890	+	0.394513i	$0.129087\pi$
$618$		0			0
$619$	76857.0	−	261751.i	0.200587	−	0.683135i	−0.796344	−	0.604844i	$-0.793235\pi$
$619$	76857.0	−	261751.i	0.200587	−	0.683135i	0.996931	−	0.0782912i	$-0.0249464\pi$
$620$		0			0
$621$	124641.	−	319414.i	0.323204	−	0.828267i
$622$		0			0
$623$	16117.2	+	4732.43i	0.0415253	+	0.0121929i
$624$		0			0
$625$	243418.	+	156435.i	0.623150	+	0.400474i
$626$		0			0
$627$	−78905.8	+	50709.7i	−0.200712	+	0.128990i
$628$		0			0
$629$	−288814.	−	333309.i	−0.729991	−	0.842454i
$630$		0			0
$631$	432652.	+	197586.i	1.08663	+	0.496246i	0.876487	−	0.481425i	$-0.159881\pi$
$631$	432652.	+	197586.i	1.08663	+	0.496246i	0.210140	+	0.977671i	$0.432608\pi$
$632$		0			0
$633$	175751.	−	51605.2i	0.438623	−	0.128791i
$634$		0			0
$635$	−63920.3	+	9190.35i	−0.158523	+	0.0227921i
$636$		0			0
$637$	111932.	+	245097.i	0.275851	+	0.604030i
$638$		0			0
$639$	−41487.7	+	288553.i	−0.101606	+	0.706683i
$640$		0			0
$641$	567906.	+	492093.i	1.38217	+	1.19765i	0.956128	+	0.292949i	$0.0946366\pi$
$641$	567906.	+	492093.i	1.38217	+	1.19765i	0.426038	+	0.904705i	$0.359909\pi$
$642$		0			0
$643$			251000.i			0.607088i	0.952817	+	0.303544i	$0.0981699\pi$
$643$			251000.i			0.607088i	−0.952817	+	0.303544i	$0.901830\pi$
$644$		0			0
$645$	−13313.3			−0.0320012
$646$		0			0
$647$	165754.	−	191290.i	0.395963	−	0.456966i	−0.522402	−	0.852699i	$-0.674964\pi$
$647$	165754.	−	191290.i	0.395963	−	0.456966i	0.918365	+	0.395733i	$0.129510\pi$
$648$		0			0
$649$	184867.	+	26579.8i	0.438904	+	0.0631048i
$650$		0			0
$651$	224176.	−	102378.i	0.528965	−	0.241570i
$652$		0			0
$653$	−49384.0	−	343473.i	−0.115814	−	0.805502i	−0.962085	−	0.272750i	$-0.912067\pi$
$653$	−49384.0	−	343473.i	−0.115814	−	0.805502i	0.846271	−	0.532752i	$-0.178842\pi$
$654$		0			0
$655$	−28064.6	−	95579.1i	−0.0654147	−	0.222782i
$656$		0			0
$657$	145042.	−	317598.i	0.336018	−	0.735778i
$658$		0			0
$659$	−210655.	+	182534.i	−0.485066	+	0.420312i	−0.862756	−	0.505620i	$-0.831264\pi$
$659$	−210655.	+	182534.i	−0.485066	+	0.420312i	0.377690	+	0.925932i	$0.376718\pi$
$660$		0			0
$661$	221815.	+	345151.i	0.507678	+	0.789962i	0.996602	−	0.0823643i	$-0.0262471\pi$
$661$	221815.	+	345151.i	0.507678	+	0.789962i	−0.488925	+	0.872326i	$0.662611\pi$
$662$		0			0
$663$	299128.	−	465452.i	0.680503	−	1.05888i
$664$		0			0
$665$	31820.0	−	108369.i	0.0719543	−	0.245054i
$666$		0			0
$667$	−433332.	−	446573.i	−0.974024	−	1.00378i
$668$		0			0
$669$	−188405.	−	55320.6i	−0.420959	−	0.123605i
$670$		0			0
$671$	158301.	+	101734.i	0.351592	+	0.225955i
$672$		0			0
$673$	121900.	−	78340.6i	0.269138	−	0.172964i	−0.399110	−	0.916903i	$-0.630681\pi$
$673$	121900.	−	78340.6i	0.269138	−	0.172964i	0.668248	+	0.743939i	$0.267045\pi$
$674$		0			0
$675$	−241653.	−	278882.i	−0.530376	−	0.612087i
$676$		0			0
$677$	−48253.1	−	22036.4i	−0.105280	−	0.0480800i	0.362079	−	0.932148i	$-0.382067\pi$
$677$	−48253.1	−	22036.4i	−0.105280	−	0.0480800i	−0.467359	+	0.884068i	$0.654794\pi$
$678$		0			0
$679$	−402176.	+	118089.i	−0.872321	+	0.256137i
$680$		0			0
$681$	−34119.8	+	4905.68i	−0.0735719	+	0.0105780i
$682$		0			0
$683$	−133425.	−	292160.i	−0.286020	−	0.626296i	0.711021	−	0.703171i	$-0.248233\pi$
$683$	−133425.	−	292160.i	−0.286020	−	0.626296i	−0.997041	+	0.0768749i	$0.975506\pi$
$684$		0			0
$685$	−32592.5	+	226686.i	−0.0694602	+	0.483106i
$686$		0			0
$687$	−6792.75	−	5885.95i	−0.0143924	−	0.0124711i
$688$		0			0
$689$			1.24063e6i			2.61339i
$690$		0			0
$691$	−90963.0			−0.190506			−0.0952530	−	0.995453i	$-0.530366\pi$
$691$	−90963.0			−0.190506			−0.0952530	+	0.995453i	$0.530366\pi$
$692$		0			0
$693$	79120.6	−	91310.0i	0.164749	−	0.190131i
$694$		0			0
$695$	−194403.	−	27951.0i	−0.402471	−	0.0578665i
$696$		0			0
$697$	−624388.	+	285148.i	−1.28525	+	0.586956i
$698$		0			0
$699$	3909.27	+	27189.6i	0.00800095	+	0.0556478i
$700$		0			0
$701$	−125192.	−	426363.i	−0.254764	−	0.867648i	−0.983200	−	0.182533i	$-0.941570\pi$
$701$	−125192.	−	426363.i	−0.254764	−	0.867648i	0.728435	−	0.685115i	$-0.240248\pi$
$702$		0			0
$703$	−178241.	+	390293.i	−0.360659	+	0.789732i
$704$		0			0
$705$	−61420.8	+	53221.4i	−0.123577	+	0.107080i
$706$		0			0
$707$	118145.	+	183837.i	0.236361	+	0.367784i
$708$		0			0
$709$	−281263.	+	437653.i	−0.559525	+	0.870638i	−0.999627	−	0.0273098i	$-0.991306\pi$
$709$	−281263.	+	437653.i	−0.559525	+	0.870638i	0.440102	+	0.897948i	$0.354942\pi$
$710$		0			0
$711$	−156980.	+	534625.i	−0.310531	+	1.05757i
$712$		0			0
$713$	446929.	−	578671.i	0.879143	−	1.13829i
$714$		0			0
$715$	−111706.	−	32799.8i	−0.218507	−	0.0641593i
$716$		0			0
$717$	−98258.5	−	63146.9i	−0.191131	−	0.122833i
$718$		0			0
$719$	227207.	−	146017.i	0.439505	−	0.282452i	−0.302117	−	0.953271i	$-0.597693\pi$
$719$	227207.	−	146017.i	0.439505	−	0.282452i	0.741622	+	0.670818i	$0.234057\pi$
$720$		0			0
$721$	60236.1	+	69516.1i	0.115874	+	0.133726i
$722$		0			0
$723$	−54349.7	−	24820.7i	−0.103973	−	0.0474829i
$724$		0			0
$725$	−642575.	+	188677.i	−1.22250	+	0.358958i
$726$		0			0
$727$	157147.	−	22594.3i	0.297328	−	0.0427494i	0.00796369	−	0.999968i	$-0.497465\pi$
$727$	157147.	−	22594.3i	0.297328	−	0.0427494i	0.289365	+	0.957219i	$0.406556\pi$
$728$		0			0
$729$	54132.0	+	118533.i	0.101859	+	0.223040i
$730$		0			0
$731$	22161.5	−	154136.i	0.0414728	−	0.288450i
$732$		0			0
$733$	−451001.	−	390795.i	−0.839402	−	0.727346i	0.124895	−	0.992170i	$-0.460141\pi$
$733$	−451001.	−	390795.i	−0.839402	−	0.727346i	−0.964297	+	0.264824i	$0.914686\pi$
$734$		0			0
$735$			30921.6i			0.0572384i
$736$		0			0
$737$	−44715.8			−0.0823239
$738$		0			0
$739$	−383862.	+	443000.i	−0.702888	+	0.811176i	−0.989140	−	0.146979i	$-0.953045\pi$
$739$	−383862.	+	443000.i	−0.702888	+	0.811176i	0.286252	+	0.958154i	$0.407591\pi$
$740$		0			0
$741$	−532795.	−	76604.4i	−0.970339	−	0.139514i
$742$		0			0
$743$	−775713.	+	354256.i	−1.40515	+	0.641711i	−0.966434	−	0.256914i	$-0.917294\pi$
$743$	−775713.	+	354256.i	−1.40515	+	0.641711i	−0.438717	+	0.898625i	$0.644567\pi$
$744$		0			0
$745$	28361.6	+	197259.i	0.0510996	+	0.355406i
$746$		0			0
$747$	182302.	+	620863.i	0.326701	+	1.11264i
$748$		0			0
$749$	99479.1	−	217829.i	0.177324	−	0.388286i
$750$		0			0
$751$	56876.3	−	49283.6i	0.100844	−	0.0873821i	−0.602979	−	0.797757i	$-0.706020\pi$
$751$	56876.3	−	49283.6i	0.100844	−	0.0873821i	0.703824	+	0.710375i	$0.251474\pi$
$752$		0			0
$753$	169763.	+	264156.i	0.299401	+	0.465876i
$754$		0			0
$755$	41889.9	−	65182.0i	0.0734878	−	0.114349i
$756$		0			0
$757$	268172.	−	913309.i	0.467974	−	1.59377i	−0.300429	−	0.953804i	$-0.597130\pi$
$757$	268172.	−	913309.i	0.467974	−	1.59377i	0.768402	−	0.639967i	$-0.221052\pi$
$758$		0			0
$759$	−28852.8	+	123647.i	−0.0500846	+	0.214635i
$760$		0			0
$761$	121033.	+	35538.5i	0.208994	+	0.0613662i	0.384554	−	0.923103i	$-0.374355\pi$
$761$	121033.	+	35538.5i	0.208994	+	0.0613662i	−0.175560	+	0.984469i	$0.556173\pi$
$762$		0			0
$763$	−511480.	−	328708.i	−0.878576	−	0.564626i
$764$		0			0
$765$	−150800.	+	96913.3i	−0.257679	+	0.165600i
$766$		0			0
$767$	701895.	+	810030.i	1.19311	+	1.37693i
$768$		0			0
$769$	−184004.	−	84031.6i	−0.311153	−	0.142099i	0.253718	−	0.967278i	$-0.418347\pi$
$769$	−184004.	−	84031.6i	−0.311153	−	0.142099i	−0.564870	+	0.825180i	$0.691074\pi$
$770$		0			0
$771$	101916.	−	29925.2i	0.171448	−	0.0503417i
$772$		0			0
$773$	−245088.	+	35238.3i	−0.410169	+	0.0589734i	−0.344311	−	0.938856i	$-0.611888\pi$
$773$	−245088.	+	35238.3i	−0.410169	+	0.0589734i	−0.0658579	+	0.997829i	$0.520978\pi$
$774$		0			0
$775$	−326897.	−	715804.i	−0.544261	−	1.19177i
$776$		0			0
$777$	−27861.0	+	193778.i	−0.0461483	+	0.320968i
$778$		0			0
$779$	504687.	+	437314.i	0.831663	+	0.720640i
$780$		0			0
$781$		−	254145.i		−	0.416658i
$782$		0			0
$783$	762411.			1.24356
$784$		0			0
$785$	−87036.1	+	100445.i	−0.141241	+	0.163001i
$786$		0			0
$787$	−36420.9	−	5236.54i	−0.0588033	−	0.00845464i	0.112850	−	0.993612i	$-0.464002\pi$
$787$	−36420.9	−	5236.54i	−0.0588033	−	0.00845464i	−0.171654	+	0.985157i	$0.554911\pi$
$788$		0			0
$789$	304167.	−	138908.i	0.488605	−	0.223138i
$790$		0			0
$791$	−196.414	−	1366.09i	−0.000313921	−	0.00218337i
$792$		0			0
$793$	304240.	+	1.03615e6i	0.483804	+	1.64769i
$794$		0			0
$795$	−59144.7	+	129509.i	−0.0935797	+	0.204911i
$796$		0			0
$797$	−249888.	+	216530.i	−0.393396	+	0.340879i	−0.828990	−	0.559264i	$-0.811084\pi$
$797$	−249888.	+	216530.i	−0.393396	+	0.340879i	0.435594	+	0.900143i	$0.356538\pi$
$798$		0			0
$799$	−513935.	−	799699.i	−0.805035	−	1.25266i
$800$		0			0
$801$	−14022.4	+	21819.3i	−0.0218554	+	0.0340076i
$802$		0			0
$803$	−85755.3	+	292056.i	−0.132993	+	0.452934i
$804$		0			0
$805$	−71245.1	−	135275.i	−0.109942	−	0.208750i
$806$		0			0
$807$	−1970.03	−	578.454i	−0.00302501	−	0.000888223i
$808$		0			0
$809$	630162.	+	404981.i	0.962842	+	0.618781i	0.924783	−	0.380494i	$-0.124246\pi$
$809$	630162.	+	404981.i	0.962842	+	0.618781i	0.0380591	+	0.999275i	$0.487882\pi$
$810$		0			0
$811$	770103.	−	494915.i	1.17087	−	0.752470i	0.197181	−	0.980367i	$-0.436821\pi$
$811$	770103.	−	494915.i	1.17087	−	0.752470i	0.973685	+	0.227897i	$0.0731850\pi$
$812$		0			0
$813$	−322831.	−	372567.i	−0.488421	−	0.563667i
$814$		0			0
$815$	−326067.	−	148910.i	−0.490899	−	0.224186i
$816$		0			0
$817$	−145360.	+	42681.6i	−0.217772	+	0.0639435i
$818$		0			0
$819$	686308.	−	98676.1i	1.02318	−	0.147111i
$820$		0			0
$821$	194066.	+	424946.i	0.287915	+	0.630445i	0.997225	−	0.0744517i	$-0.0237207\pi$
$821$	194066.	+	424946.i	0.287915	+	0.630445i	−0.709310	+	0.704897i	$0.750993\pi$
$822$		0			0
$823$	121332.	−	843881.i	0.179133	−	1.24590i	−0.679643	−	0.733543i	$-0.737865\pi$
$823$	121332.	−	843881.i	0.179133	−	1.24590i	0.858775	−	0.512352i	$-0.171226\pi$
$824$		0			0
$825$	103273.	+	89486.7i	0.151733	+	0.131477i
$826$		0			0
$827$		−	468602.i		−	0.685162i	−0.939488	−	0.342581i	$-0.888699\pi$
$827$		−	468602.i		−	0.685162i	0.939488	−	0.342581i	$-0.111301\pi$
$828$		0			0
$829$	−348348.			−0.506878			−0.253439	−	0.967351i	$-0.581562\pi$
$829$	−348348.			−0.506878			−0.253439	+	0.967351i	$0.581562\pi$
$830$		0			0
$831$	−203934.	+	235352.i	−0.295316	+	0.340813i
$832$		0			0
$833$	−357998.	−	51472.4i	−0.515930	−	0.0741796i
$834$		0			0
$835$	121539.	−	55505.2i	0.174319	−	0.0796087i
$836$		0			0
$837$	127493.	+	886732.i	0.181985	+	1.26573i
$838$		0			0
$839$	−124574.	−	424260.i	−0.176972	−	0.602710i	−0.999426	−	0.0338790i	$-0.989214\pi$
$839$	−124574.	−	424260.i	−0.176972	−	0.602710i	0.822454	−	0.568831i	$-0.192604\pi$
$840$		0			0
$841$	280977.	−	615253.i	0.397263	−	0.869885i
$842$		0			0
$843$	−211041.	+	182868.i	−0.296970	+	0.257326i
$844$		0			0
$845$	−246009.	−	382797.i	−0.344538	−	0.536112i
$846$		0			0
$847$	249682.	−	388512.i	0.348032	−	0.541549i
$848$		0			0
$849$	183664.	−	625501.i	0.254805	−	0.867787i
$850$		0			0
$851$	194765.	+	547190.i	0.268937	+	0.755578i
$852$		0			0
$853$	172594.	+	50678.1i	0.237207	+	0.0696502i	0.398175	−	0.917309i	$-0.369644\pi$
$853$	172594.	+	50678.1i	0.237207	+	0.0696502i	−0.160968	+	0.986960i	$0.551462\pi$
$854$		0			0
$855$	146709.	+	94284.2i	0.200689	+	0.128975i
$856$		0			0
$857$	−291942.	+	187620.i	−0.397498	+	0.255457i	−0.724085	−	0.689711i	$-0.757738\pi$
$857$	−291942.	+	187620.i	−0.397498	+	0.255457i	0.326587	+	0.945167i	$0.394101\pi$
$858$		0			0
$859$	−235559.	−	271850.i	−0.319238	−	0.368420i	0.573337	−	0.819320i	$-0.305649\pi$
$859$	−235559.	−	271850.i	−0.319238	−	0.368420i	−0.892575	+	0.450900i	$0.851103\pi$
$860$		0			0
$861$	277161.	+	126575.i	0.373874	+	0.170743i
$862$		0			0
$863$	935690.	−	274743.i	1.25635	−	0.368897i	0.415215	−	0.909723i	$-0.363706\pi$
$863$	935690.	−	274743.i	1.25635	−	0.368897i	0.841134	+	0.540826i	$0.181888\pi$
$864$		0			0
$865$	220372.	−	31684.6i	0.294526	−	0.0423464i
$866$		0			0
$867$	148818.	+	325866.i	0.197978	+	0.433512i
$868$		0			0
$869$	69130.6	−	480814.i	0.0915442	−	0.636704i
$870$		0			0
$871$	−193937.	−	168047.i	−0.255637	−	0.221511i
$872$		0			0
$873$		−	647204.i		−	0.849205i
$874$		0			0
$875$	−345183.			−0.450851
$876$		0			0
$877$	230456.	−	265960.i	0.299632	−	0.345794i	−0.585890	−	0.810390i	$-0.699255\pi$
$877$	230456.	−	265960.i	0.299632	−	0.345794i	0.885523	+	0.464596i	$0.153801\pi$
$878$		0			0
$879$	652358.	+	93794.9i	0.844322	+	0.121395i
$880$		0			0
$881$	1.29574e6	−	591743.i	1.66942	−	0.762397i	0.669610	−	0.742713i	$-0.266461\pi$
$881$	1.29574e6	−	591743.i	1.66942	−	0.762397i	0.999806	−	0.0196835i	$-0.00626586\pi$
$882$		0			0
$883$	49345.8	+	343208.i	0.0632891	+	0.440185i	0.996686	+	0.0813407i	$0.0259202\pi$
$883$	49345.8	+	343208.i	0.0632891	+	0.440185i	−0.933397	+	0.358845i	$0.883171\pi$
$884$		0			0
$885$	34653.8	+	118020.i	0.0442450	+	0.150685i
$886$		0			0
$887$	88526.3	−	193846.i	0.112519	−	0.246382i	−0.844992	−	0.534779i	$-0.820395\pi$
$887$	88526.3	−	193846.i	0.112519	−	0.246382i	0.957511	+	0.288397i	$0.0931222\pi$
$888$		0			0
$889$	−253396.	+	219569.i	−0.320624	+	0.277822i
$890$		0			0
$891$	52479.3	+	81659.4i	0.0661047	+	0.102861i
$892$		0			0
$893$	−499993.	+	778004.i	−0.626990	+	0.975615i
$894$		0			0
$895$	−58384.9	+	198841.i	−0.0728877	+	0.248233i
$896$		0			0
$897$	−589818.	+	427838.i	−0.733049	+	0.531734i
$898$		0			0
$899$	1.55997e6	+	458049.i	1.93018	+	0.566752i
$900$		0			0
$901$	−1.40095e6	−	900336.i	−1.72573	−	1.10906i
$902$		0			0
$903$	−58150.4	+	37371.0i	−0.0713144	+	0.0458310i
$904$		0			0
$905$	201776.	+	232862.i	0.246361	+	0.284316i
$906$		0			0
$907$	−299719.	−	136877.i	−0.364334	−	0.166386i	0.224833	−	0.974397i	$-0.427816\pi$
$907$	−299719.	−	136877.i	−0.364334	−	0.166386i	−0.589166	+	0.808012i	$0.700544\pi$
$908$		0			0
$909$	−323753.	+	95062.5i	−0.391819	+	0.115049i
$910$		0			0
$911$	−487597.	+	70105.9i	−0.587523	+	0.0844730i	−0.429664	−	0.902989i	$-0.641368\pi$
$911$	−487597.	+	70105.9i	−0.587523	+	0.0844730i	−0.157858	+	0.987462i	$0.550459\pi$
$912$		0			0
$913$	−234341.	−	513136.i	−0.281130	−	0.615589i
$914$		0			0
$915$	−17636.8	+	122667.i	−0.0210658	+	0.146516i
$916$		0			0
$917$	−390876.	−	338696.i	−0.464836	−	0.402783i
$918$		0			0
$919$		−	834929.i		−	0.988595i	−0.869293	−	0.494297i	$-0.835425\pi$
$919$		−	834929.i		−	0.988595i	0.869293	−	0.494297i	$-0.164575\pi$
$920$		0			0
$921$	84434.8			0.0995411
$922$		0			0
$923$	955108.	−	1.10225e6i	1.12111	−	1.29383i
$924$		0			0
$925$	618742.	+	88961.7i	0.723146	+	0.103973i
$926$		0			0
$927$	−129193.	+	59000.7i	−0.150342	+	0.0686590i
$928$		0			0
$929$	−90821.8	−	631680.i	−0.105235	−	0.731923i	−0.972301	−	0.233731i	$-0.924906\pi$
$929$	−90821.8	−	631680.i	−0.105235	−	0.731923i	0.867067	−	0.498192i	$-0.166003\pi$
$930$		0			0
$931$	99132.6	+	337615.i	0.114371	+	0.389513i
$932$		0			0
$933$	−234229.	+	512889.i	−0.269077	+	0.589197i
$934$		0			0
$935$	118104.	−	102338.i	0.135096	−	0.117061i
$936$		0			0
$937$	138772.	+	215934.i	0.158061	+	0.245947i	0.911247	−	0.411860i	$-0.135121\pi$
$937$	138772.	+	215934.i	0.158061	+	0.245947i	−0.753187	+	0.657807i	$0.771484\pi$
$938$		0			0
$939$	157600.	−	245231.i	0.178742	−	0.278128i
$940$		0			0
$941$	59016.1	−	200991.i	0.0666487	−	0.226985i	−0.919433	−	0.393247i	$-0.871352\pi$
$941$	59016.1	−	200991.i	0.0666487	−	0.226985i	0.986082	+	0.166262i	$0.0531699\pi$
$942$		0			0
$943$	902547.	−	50915.9i	1.01495	−	0.0572572i
$944$		0			0
$945$	179738.	+	52775.8i	0.201269	+	0.0590978i
$946$		0			0
$947$	−50247.8	−	32292.3i	−0.0560295	−	0.0360080i	0.512326	−	0.858791i	$-0.328784\pi$
$947$	−50247.8	−	32292.3i	−0.0560295	−	0.0360080i	−0.568356	+	0.822783i	$0.692420\pi$
$948$		0			0
$949$	−1.46951e6	+	944397.i	−1.63170	+	1.04863i
$950$		0			0
$951$	−104416.	−	120503.i	−0.115454	−	0.133241i
$952$		0			0
$953$	759114.	+	346676.i	0.835836	+	0.381714i	0.786894	−	0.617088i	$-0.211688\pi$
$953$	759114.	+	346676.i	0.835836	+	0.381714i	0.0489421	+	0.998802i	$0.484415\pi$
$954$		0			0
$955$	−249590.	+	73286.1i	−0.273665	+	0.0803554i
$956$		0			0
$957$	−279456.	+	40179.7i	−0.305133	+	0.0438715i
$958$		0			0
$959$	493957.	+	1.08161e6i	0.537096	+	1.17608i
$960$		0			0
$961$	−140446.	+	976823.i	−0.152077	+	1.05772i
$962$		0			0
$963$	279444.	+	242139.i	0.301330	+	0.261104i
$964$		0			0
$965$		−	289108.i		−	0.310460i
$966$		0			0
$967$	476046.			0.509092			0.254546	−	0.967061i	$-0.418074\pi$
$967$	476046.			0.509092			0.254546	+	0.967061i	$0.418074\pi$
$968$		0			0
$969$	473156.	−	546051.i	0.503915	−	0.581549i
$970$		0			0
$971$	523153.	+	75218.0i	0.554868	+	0.0797780i	0.414044	−	0.910257i	$-0.364116\pi$
$971$	523153.	+	75218.0i	0.554868	+	0.0797780i	0.140824	+	0.990035i	$0.455025\pi$
$972$		0			0
$973$	−927582.	+	423612.i	−0.979775	+	0.447448i
$974$		0			0
$975$	111604.	+	776225.i	0.117401	+	0.816542i
$976$		0			0
$977$	−60380.4	−	205637.i	−0.0632567	−	0.215433i	0.921799	−	0.387668i	$-0.126719\pi$
$977$	−60380.4	−	205637.i	−0.0632567	−	0.215433i	−0.985056	+	0.172235i	$0.944901\pi$
$978$		0			0
$979$	9393.10	−	20568.0i	0.00980039	−	0.0214599i
$980$		0			0
$981$	709490.	−	614777.i	0.737239	−	0.638821i
$982$		0			0
$983$	−220920.	−	343759.i	−0.228627	−	0.355751i	0.707920	−	0.706293i	$-0.249634\pi$
$983$	−220920.	−	343759.i	−0.228627	−	0.355751i	−0.936547	+	0.350542i	$0.885998\pi$
$984$		0			0
$985$	39446.1	−	61379.3i	0.0406566	−	0.0632629i
$986$		0			0
$987$	−118881.	+	404873.i	−0.122034	+	0.415609i
$988$		0			0
$989$	−100980.	+	178494.i	−0.103239	+	0.182486i
$990$		0			0
$991$	−1.19205e6	−	350018.i	−1.21380	−	0.356405i	−0.388688	−	0.921369i	$-0.627072\pi$
$991$	−1.19205e6	−	350018.i	−1.21380	−	0.356405i	−0.825115	+	0.564965i	$0.808890\pi$
$992$		0			0
$993$	−454259.	−	291934.i	−0.460686	−	0.296065i
$994$		0			0
$995$	−52815.2	+	33942.3i	−0.0533474	+	0.0342843i
$996$		0			0
$997$	−505726.	−	583639.i	−0.508774	−	0.587156i	0.442010	−	0.897010i	$-0.354265\pi$
$997$	−505726.	−	583639.i	−0.508774	−	0.587156i	−0.950784	+	0.309854i	$0.899720\pi$
$998$		0			0
$999$	−647330.	−	295626.i	−0.648626	−	0.296218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.f.a.5.5	✓	80
23.14	odd	22	inner	92.5.f.a.37.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.f.a.5.5	✓	80	1.1	even	1	trivial
92.5.f.a.37.5	yes	80	23.14	odd	22	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(3.01425 - 3.47863i) q^{3} +(7.38497 + 1.06180i) q^{5} +(35.2368 - 16.0921i) q^{7} +(8.51233 + 59.2046i) q^{9} +O(q^{10})\)	\(q+(3.01425 - 3.47863i) q^{3} +(7.38497 + 1.06180i) q^{5} +(35.2368 - 16.0921i) q^{7} +(8.51233 + 59.2046i) q^{9} +(-14.6909 - 50.0326i) q^{11} +(124.312 - 272.206i) q^{13} +(25.9538 - 22.4891i) q^{15} +(217.167 + 337.918i) q^{17} +(211.275 - 328.751i) q^{19} +(50.2342 - 171.082i) q^{21} +(-104.657 - 518.544i) q^{23} +(-546.273 - 160.400i) q^{25} +(545.258 + 350.416i) q^{27} +(989.558 - 635.950i) q^{29} +(905.128 + 1044.57i) q^{31} +(-218.327 - 99.7066i) q^{33} +(277.309 - 81.4254i) q^{35} +(-1086.78 + 156.255i) q^{37} +(-572.197 - 1252.94i) q^{39} +(-243.195 + 1691.46i) q^{41} +(-292.982 - 253.871i) q^{43} +446.262i q^{45} -2366.54 q^{47} +(-589.642 + 680.483i) q^{49} +(1830.09 + 263.127i) q^{51} +(-3771.18 + 1722.24i) q^{53} +(-55.3672 - 385.087i) q^{55} +(-506.767 - 1725.89i) q^{57} +(-1487.90 + 3258.04i) q^{59} +(-2727.25 + 2363.17i) q^{61} +(1252.68 + 1949.20i) q^{63} +(1207.07 - 1878.24i) q^{65} +(241.595 - 822.796i) q^{67} +(-2119.29 - 1198.96i) q^{69} +(4676.41 + 1373.12i) q^{71} +(-4910.66 - 3155.89i) q^{73} +(-2204.58 + 1416.80i) q^{75} +(-1322.79 - 1526.58i) q^{77} +(8473.74 + 3869.83i) q^{79} +(-1786.12 + 524.451i) q^{81} +(10708.1 - 1539.59i) q^{83} +(1244.97 + 2726.10i) q^{85} +(770.540 - 5359.23i) q^{87} +(327.713 + 283.965i) q^{89} -11592.1i q^{91} +6361.97 q^{93} +(1909.33 - 2203.48i) q^{95} +(-10710.3 - 1539.90i) q^{97} +(2837.10 - 1295.66i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 10 q^{3} - 318 q^{9}+O(q^{10}) \) 80 * q + 10 * q^3 - 318 * q^9	\( 80 q + 10 q^{3} - 318 q^{9} + 2 q^{13} + 1463 q^{15} - 495 q^{17} - 957 q^{19} - 1353 q^{21} + 1614 q^{23} + 1890 q^{25} + 4723 q^{27} - 1617 q^{29} - 3271 q^{31} - 6655 q^{33} - 5280 q^{35} + 3520 q^{37} + 6138 q^{39} + 11370 q^{41} + 7216 q^{43} - 270 q^{47} - 14512 q^{49} - 17424 q^{51} - 7392 q^{53} + 5746 q^{55} + 18381 q^{57} + 11772 q^{59} - 22484 q^{61} - 27775 q^{63} - 27951 q^{65} - 2926 q^{67} + 15769 q^{69} + 19779 q^{71} + 24400 q^{73} + 2809 q^{75} + 19839 q^{77} + 21604 q^{79} + 22224 q^{81} - 11253 q^{83} - 25594 q^{85} + 45506 q^{87} + 7656 q^{89} + 7970 q^{93} - 22437 q^{95} + 32439 q^{97} - 48477 q^{99}+O(q^{100}) \) 80 * q + 10 * q^3 - 318 * q^9 + 2 * q^13 + 1463 * q^15 - 495 * q^17 - 957 * q^19 - 1353 * q^21 + 1614 * q^23 + 1890 * q^25 + 4723 * q^27 - 1617 * q^29 - 3271 * q^31 - 6655 * q^33 - 5280 * q^35 + 3520 * q^37 + 6138 * q^39 + 11370 * q^41 + 7216 * q^43 - 270 * q^47 - 14512 * q^49 - 17424 * q^51 - 7392 * q^53 + 5746 * q^55 + 18381 * q^57 + 11772 * q^59 - 22484 * q^61 - 27775 * q^63 - 27951 * q^65 - 2926 * q^67 + 15769 * q^69 + 19779 * q^71 + 24400 * q^73 + 2809 * q^75 + 19839 * q^77 + 21604 * q^79 + 22224 * q^81 - 11253 * q^83 - 25594 * q^85 + 45506 * q^87 + 7656 * q^89 + 7970 * q^93 - 22437 * q^95 + 32439 * q^97 - 48477 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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