LMFDB - Embedded newform 93.4.c.b.92.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,4,Mod(92,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.92"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	93.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.48717763053$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			92.12
Character	$\chi$	$=$	93.92
Dual form			93.4.c.b.92.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.95427i q^{2} +(4.50778 + 2.58456i) q^{3} +4.18081 q^{4} -11.2496i q^{5} +(5.05094 - 8.80943i) q^{6} -8.06707 q^{7} -23.8046i q^{8} +(13.6401 + 23.3012i) q^{9} -21.9848 q^{10} +34.3236 q^{11} +(18.8462 + 10.8056i) q^{12} +2.46240i q^{13} +15.7653i q^{14} +(29.0753 - 50.7108i) q^{15} -13.0743 q^{16} +48.4699 q^{17} +(45.5370 - 26.6565i) q^{18} -109.439 q^{19} -47.0325i q^{20} +(-36.3646 - 20.8498i) q^{21} -67.0778i q^{22} -19.0799 q^{23} +(61.5246 - 107.306i) q^{24} -1.55398 q^{25} +4.81220 q^{26} +(1.26292 + 140.290i) q^{27} -33.7269 q^{28} -220.336 q^{29} +(-99.1028 - 56.8212i) q^{30} +(153.119 + 79.6593i) q^{31} -164.886i q^{32} +(154.723 + 88.7115i) q^{33} -94.7234i q^{34} +90.7515i q^{35} +(57.0266 + 97.4181i) q^{36} +338.536i q^{37} +213.873i q^{38} +(-6.36422 + 11.0999i) q^{39} -267.793 q^{40} -66.0955i q^{41} +(-40.7463 + 71.0663i) q^{42} +413.073i q^{43} +143.501 q^{44} +(262.130 - 153.446i) q^{45} +37.2874i q^{46} +175.739i q^{47} +(-58.9362 - 33.7914i) q^{48} -277.922 q^{49} +3.03691i q^{50} +(218.491 + 125.273i) q^{51} +10.2948i q^{52} -542.770 q^{53} +(274.166 - 2.46810i) q^{54} -386.128i q^{55} +192.034i q^{56} +(-493.325 - 282.851i) q^{57} +430.596i q^{58} +189.683i q^{59} +(121.558 - 212.012i) q^{60} -589.699i q^{61} +(155.676 - 299.236i) q^{62} +(-110.036 - 187.973i) q^{63} -426.828 q^{64} +27.7010 q^{65} +(173.367 - 302.372i) q^{66} +181.116 q^{67} +202.643 q^{68} +(-86.0081 - 49.3133i) q^{69} +177.353 q^{70} -347.339i q^{71} +(554.678 - 324.697i) q^{72} +363.492i q^{73} +661.593 q^{74} +(-7.00500 - 4.01636i) q^{75} -457.542 q^{76} -276.891 q^{77} +(21.6923 + 12.4374i) q^{78} -66.8156i q^{79} +147.081i q^{80} +(-356.896 + 635.662i) q^{81} -129.169 q^{82} +574.916 q^{83} +(-152.033 - 87.1693i) q^{84} -545.268i q^{85} +807.259 q^{86} +(-993.224 - 569.471i) q^{87} -817.062i q^{88} +103.425 q^{89} +(-299.875 - 512.274i) q^{90} -19.8643i q^{91} -79.7696 q^{92} +(484.341 + 754.832i) q^{93} +343.442 q^{94} +1231.14i q^{95} +(426.159 - 743.271i) q^{96} +1145.19 q^{97} +543.137i q^{98} +(468.177 + 799.783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) $ 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.95427i		−	0.690940i	−0.938430	−	0.345470i	$-0.887719\pi$
$2$		−	1.95427i		−	0.690940i	0.938430	−	0.345470i	$-0.112281\pi$
$3$	4.50778	+	2.58456i	0.867522	+	0.497399i
$3$	4.50778	+	2.58456i	0.867522	+	0.497399i
$4$	4.18081			0.522601
$5$		−	11.2496i		−	1.00620i	−0.864229	−	0.503098i	$-0.832193\pi$
$5$		−	11.2496i		−	1.00620i	0.864229	−	0.503098i	$-0.167807\pi$
$6$	5.05094	−	8.80943i	0.343673	−	0.599406i
$7$	−8.06707			−0.435581			−0.217791	−	0.975996i	$-0.569885\pi$
$7$	−8.06707			−0.435581			−0.217791	+	0.975996i	$0.569885\pi$
$8$		−	23.8046i		−	1.05203i
$9$	13.6401	+	23.3012i	0.505188	+	0.863009i
$10$	−21.9848			−0.695222
$11$	34.3236			0.940815			0.470407	−	0.882449i	$-0.344107\pi$
$11$	34.3236			0.940815			0.470407	+	0.882449i	$0.344107\pi$
$12$	18.8462	+	10.8056i	0.453368	+	0.259941i
$13$			2.46240i			0.0525343i	0.999655	+	0.0262672i	$0.00836206\pi$
$13$			2.46240i			0.0525343i	−0.999655	+	0.0262672i	$0.991638\pi$
$14$			15.7653i			0.300961i
$15$	29.0753	−	50.7108i	0.500481	−	0.872898i
$16$	−13.0743			−0.204287
$17$	48.4699			0.691510			0.345755	−	0.938325i	$-0.387623\pi$
$17$	48.4699			0.691510			0.345755	+	0.938325i	$0.387623\pi$
$18$	45.5370	−	26.6565i	0.596288	−	0.349055i
$19$	−109.439			−1.32142			−0.660709	−	0.750642i	$-0.729744\pi$
$19$	−109.439			−1.32142			−0.660709	+	0.750642i	$0.729744\pi$
$20$		−	47.0325i		−	0.525840i
$21$	−36.3646	−	20.8498i	−0.377876	−	0.216658i
$22$		−	67.0778i		−	0.650047i
$23$	−19.0799			−0.172976			−0.0864878	−	0.996253i	$-0.527564\pi$
$23$	−19.0799			−0.172976			−0.0864878	+	0.996253i	$0.527564\pi$
$24$	61.5246	−	107.306i	0.523277	−	0.912656i
$25$	−1.55398			−0.0124318
$26$	4.81220			0.0362981
$27$	1.26292	+	140.290i	0.00900185	+	0.999959i
$28$	−33.7269			−0.227635
$29$	−220.336			−1.41087			−0.705436	−	0.708773i	$-0.749249\pi$
$29$	−220.336			−1.41087			−0.705436	+	0.708773i	$0.749249\pi$
$30$	−99.1028	−	56.8212i	−0.603120	−	0.345803i
$31$	153.119	+	79.6593i	0.887128	+	0.461524i
$31$	153.119	+	79.6593i	0.887128	+	0.461524i
$32$		−	164.886i		−	0.910877i
$33$	154.723	+	88.7115i	0.816177	+	0.467960i
$34$		−	94.7234i		−	0.477792i
$35$			90.7515i			0.438280i
$36$	57.0266	+	97.4181i	0.264012	+	0.451010i
$37$			338.536i			1.50419i	0.659054	+	0.752095i	$0.270957\pi$
$37$			338.536i			1.50419i	−0.659054	+	0.752095i	$0.729043\pi$
$38$			213.873i			0.913021i
$39$	−6.36422	+	11.0999i	−0.0261305	+	0.0455747i
$40$	−267.793			−1.05855
$41$		−	66.0955i		−	0.251765i	−0.992045	−	0.125883i	$-0.959824\pi$
$41$		−	66.0955i		−	0.251765i	0.992045	−	0.125883i	$-0.0401763\pi$
$42$	−40.7463	+	71.0663i	−0.149698	+	0.261090i
$43$			413.073i			1.46496i	0.680791	+	0.732478i	$0.261636\pi$
$43$			413.073i			1.46496i	−0.680791	+	0.732478i	$0.738364\pi$
$44$	143.501			0.491671
$45$	262.130	−	153.446i	0.868357	−	0.508319i
$46$			37.2874i			0.119516i
$47$			175.739i			0.545408i	0.962098	+	0.272704i	$0.0879180\pi$
$47$			175.739i			0.545408i	−0.962098	+	0.272704i	$0.912082\pi$
$48$	−58.9362	−	33.7914i	−0.177223	−	0.101612i
$49$	−277.922			−0.810269
$50$			3.03691i			0.00858967i
$51$	218.491	+	125.273i	0.599900	+	0.343957i
$52$			10.2948i			0.0274545i
$53$	−542.770			−1.40670			−0.703351	−	0.710843i	$-0.748314\pi$
$53$	−542.770			−1.40670			−0.703351	+	0.710843i	$0.748314\pi$
$54$	274.166	−	2.46810i	0.690912	−	0.00621974i
$55$		−	386.128i		−	0.946645i
$56$			192.034i			0.458243i
$57$	−493.325	−	282.851i	−1.14636	−	0.657272i
$58$			430.596i			0.974829i
$59$			189.683i			0.418552i	0.977857	+	0.209276i	$0.0671107\pi$
$59$			189.683i			0.418552i	−0.977857	+	0.209276i	$0.932889\pi$
$60$	121.558	−	212.012i	0.261552	−	0.456177i
$61$		−	589.699i		−	1.23776i	−0.785486	−	0.618879i	$-0.787587\pi$
$61$		−	589.699i		−	1.23776i	0.785486	−	0.618879i	$-0.212413\pi$
$62$	155.676	−	299.236i	0.318885	−	0.612952i
$63$	−110.036	−	187.973i	−0.220050	−	0.375910i
$64$	−426.828			−0.833648
$65$	27.7010			0.0528598
$66$	173.367	−	302.372i	0.323333	−	0.563930i
$67$	181.116			0.330251			0.165125	−	0.986273i	$-0.447197\pi$
$67$	181.116			0.330251			0.165125	+	0.986273i	$0.447197\pi$
$68$	202.643			0.361384
$69$	−86.0081	−	49.3133i	−0.150060	−	0.0860380i
$70$	177.353			0.302826
$71$		−	347.339i		−	0.580586i	−0.956938	−	0.290293i	$-0.906247\pi$
$71$		−	347.339i		−	0.580586i	0.956938	−	0.290293i	$-0.0937528\pi$
$72$	554.678	−	324.697i	0.907909	−	0.531472i
$73$			363.492i			0.582788i	0.956603	+	0.291394i	$0.0941190\pi$
$73$			363.492i			0.582788i	−0.956603	+	0.291394i	$0.905881\pi$
$74$	661.593			1.03931
$75$	−7.00500	−	4.01636i	−0.0107849	−	0.00618359i
$76$	−457.542			−0.690575
$77$	−276.891			−0.409801
$78$	21.6923	+	12.4374i	0.0314894	+	0.0180546i
$79$		−	66.8156i		−	0.0951562i	−0.998868	−	0.0475781i	$-0.984850\pi$
$79$		−	66.8156i		−	0.0951562i	0.998868	−	0.0475781i	$-0.0151503\pi$
$80$			147.081i			0.205552i
$81$	−356.896	+	635.662i	−0.489570	+	0.871964i
$82$	−129.169			−0.173955
$83$	574.916			0.760304			0.380152	−	0.924924i	$-0.375872\pi$
$83$	574.916			0.760304			0.380152	+	0.924924i	$0.375872\pi$
$84$	−152.033	−	87.1693i	−0.197479	−	0.113226i
$85$		−	545.268i		−	0.695795i
$86$	807.259			1.01220
$87$	−993.224	−	569.471i	−1.22396	−	0.701767i
$88$		−	817.062i		−	0.989762i
$89$	103.425			0.123181			0.0615903	−	0.998102i	$-0.480383\pi$
$89$	103.425			0.123181			0.0615903	+	0.998102i	$0.480383\pi$
$90$	−299.875	−	512.274i	−0.351218	−	0.599983i
$91$		−	19.8643i		−	0.0228829i
$92$	−79.7696			−0.0903973
$93$	484.341	+	754.832i	0.540041	+	0.841639i
$94$	343.442			0.376844
$95$			1231.14i			1.32961i
$96$	426.159	−	743.271i	0.453069	−	0.790206i
$97$	1145.19			1.19872			0.599361	−	0.800479i	$-0.295422\pi$
$97$	1145.19			1.19872			0.599361	+	0.800479i	$0.295422\pi$
$98$			543.137i			0.559848i
$99$	468.177	+	799.783i	0.475289	+	0.811932i
$100$	−6.49690			−0.00649690
$101$		−	1613.50i		−	1.58959i	−0.606876	−	0.794797i	$-0.707577\pi$
$101$		−	1613.50i		−	1.58959i	0.606876	−	0.794797i	$-0.292423\pi$
$102$	244.819	−	426.992i	0.237653	−	0.414495i
$103$	−94.3351			−0.0902438			−0.0451219	−	0.998981i	$-0.514368\pi$
$103$	−94.3351			−0.0902438			−0.0451219	+	0.998981i	$0.514368\pi$
$104$	58.6165			0.0552675
$105$	−234.553	+	409.088i	−0.218000	+	0.380218i
$106$			1060.72i			0.971947i
$107$		−	781.201i		−	0.705809i	−0.935659	−	0.352905i	$-0.885194\pi$
$107$		−	781.201i		−	0.705809i	0.935659	−	0.352905i	$-0.114806\pi$
$108$	5.28005	+	586.528i	0.00470438	+	0.522580i
$109$	1192.42			1.04783			0.523915	−	0.851771i	$-0.324471\pi$
$109$	1192.42			1.04783			0.523915	+	0.851771i	$0.324471\pi$
$110$	−754.600			−0.654075
$111$	−874.968	+	1526.05i	−0.748183	+	1.30492i
$112$	105.472			0.0889833
$113$		−	220.550i		−	0.183607i	−0.995777	−	0.0918037i	$-0.970737\pi$
$113$		−	220.550i		−	0.183607i	0.995777	−	0.0918037i	$-0.0292632\pi$
$114$	−552.768	+	964.092i	−0.454136	+	0.792066i
$115$			214.642i			0.174048i
$116$	−921.182			−0.737324
$117$	−57.3769	+	33.5873i	−0.0453376	+	0.0265397i
$118$	370.692			0.289195
$119$	−391.010			−0.301209
$120$	−1207.15	−	692.128i	−0.918312	−	0.526520i
$121$	−152.889			−0.114868
$122$	−1152.43			−0.855217
$123$	170.828	−	297.943i	0.125228	−	0.218412i
$124$	640.161	+	333.041i	0.463614	+	0.241193i
$125$		−	1388.72i		−	0.993688i
$126$	−367.351	+	215.040i	−0.259732	+	0.152042i
$127$		−	2450.71i		−	1.71233i	−0.516706	−	0.856163i	$-0.672842\pi$
$127$		−	2450.71i		−	1.71233i	0.516706	−	0.856163i	$-0.327158\pi$
$128$		−	484.952i		−	0.334876i
$129$	−1067.61	+	1862.04i	−0.728668	+	1.27088i
$130$		−	54.1354i		−	0.0365230i
$131$			802.813i			0.535436i	0.963497	+	0.267718i	$0.0862695\pi$
$131$			802.813i			0.535436i	−0.963497	+	0.267718i	$0.913731\pi$
$132$	646.868	+	370.886i	0.426535	+	0.244557i
$133$	882.850			0.575585
$134$		−	353.950i		−	0.228183i
$135$	1578.21	−	14.2074i	1.00616	−	0.00905763i
$136$		−	1153.81i		−	0.727487i
$137$	−2588.90			−1.61449			−0.807243	−	0.590220i	$-0.799041\pi$
$137$	−2588.90			−1.61449			−0.807243	+	0.590220i	$0.799041\pi$
$138$	−96.3717	+	168.083i	−0.0594471	+	0.103683i
$139$			837.280i			0.510915i	0.966820	+	0.255457i	$0.0822260\pi$
$139$			837.280i			0.510915i	−0.966820	+	0.255457i	$0.917774\pi$
$140$			379.415i			0.229046i
$141$	−454.208	+	792.192i	−0.271285	+	0.473153i
$142$	−678.797			−0.401150
$143$			84.5184i			0.0494250i
$144$	−178.335	−	304.648i	−0.103203	−	0.176301i
$145$			2478.69i			1.41962i
$146$	710.363			0.402672
$147$	−1252.81	−	718.307i	−0.702926	−	0.403027i
$148$			1415.36i			0.786092i
$149$			2631.00i			1.44658i	0.690546	+	0.723289i	$0.257370\pi$
$149$			2631.00i			1.44658i	−0.690546	+	0.723289i	$0.742630\pi$
$150$	−7.84907	+	13.6897i	−0.00427249	+	0.00745172i
$151$		−	2980.19i		−	1.60612i	−0.595897	−	0.803061i	$-0.703203\pi$
$151$		−	2980.19i		−	1.60612i	0.595897	−	0.803061i	$-0.296797\pi$
$152$			2605.15i			1.39017i
$153$	661.133	+	1129.41i	0.349343	+	0.596780i
$154$			541.121i			0.283148i
$155$	896.137	−	1722.53i	0.464384	−	0.892625i
$156$	−26.6076	+	46.4067i	−0.0136558	+	0.0238174i
$157$	−210.106			−0.106804			−0.0534021	−	0.998573i	$-0.517007\pi$
$157$	−210.106			−0.106804			−0.0534021	+	0.998573i	$0.517007\pi$
$158$	−130.576			−0.0657473
$159$	−2446.68	−	1402.82i	−1.22034	−	0.699692i
$160$	−1854.91			−0.916521
$161$	153.919			0.0753449
$162$	1242.26	+	697.473i	0.602475	+	0.338263i
$163$	1775.03			0.852951			0.426475	−	0.904499i	$-0.359755\pi$
$163$	1775.03			0.852951			0.426475	+	0.904499i	$0.359755\pi$
$164$		−	276.333i		−	0.131573i
$165$	997.971	−	1740.58i	0.470860	−	0.821235i
$166$		−	1123.54i		−	0.525325i
$167$	1865.90			0.864596			0.432298	−	0.901731i	$-0.357703\pi$
$167$	1865.90			0.864596			0.432298	+	0.901731i	$0.357703\pi$
$168$	−496.323	+	865.646i	−0.227930	+	0.397536i
$169$	2190.94			0.997240
$170$	−1065.60			−0.480753
$171$	−1492.75	−	2550.06i	−0.667565	−	1.14040i
$172$			1726.98i			0.765588i
$173$			622.347i			0.273504i	0.990605	+	0.136752i	$0.0436663\pi$
$173$			622.347i			0.273504i	−0.990605	+	0.136752i	$0.956334\pi$
$174$	−1112.90	+	1941.03i	−0.484879	+	0.845685i
$175$	12.5361			0.00541508
$176$	−448.759			−0.192196
$177$	−490.246	+	855.047i	−0.208187	+	0.363103i
$178$		−	202.122i		−	0.0851104i
$179$	3225.25			1.34674			0.673371	−	0.739305i	$-0.264846\pi$
$179$	3225.25			1.34674			0.673371	+	0.739305i	$0.264846\pi$
$180$	1095.92	−	641.528i	0.453805	−	0.265648i
$181$			419.537i			0.172287i	0.996283	+	0.0861436i	$0.0274544\pi$
$181$			419.537i			0.172287i	−0.996283	+	0.0861436i	$0.972546\pi$
$182$	−38.8204			−0.0158108
$183$	1524.11	−	2658.23i	0.615660	−	1.07378i
$184$			454.191i			0.181975i
$185$	3808.41			1.51351
$186$	1475.15	−	946.536i	0.581522	−	0.373136i
$187$	1663.66			0.650583
$188$			734.732i			0.285031i
$189$	−10.1881	−	1131.73i	−0.00392104	−	0.435563i
$190$	2405.99			0.918679
$191$		−	2818.82i		−	1.06787i	−0.845526	−	0.533934i	$-0.820713\pi$
$191$		−	2818.82i		−	1.06787i	0.845526	−	0.533934i	$-0.179287\pi$
$192$	−1924.04	−	1103.16i	−0.723208	−	0.414656i
$193$	−4306.94			−1.60632			−0.803162	−	0.595761i	$-0.796851\pi$
$193$	−4306.94			−1.60632			−0.803162	+	0.595761i	$0.796851\pi$
$194$		−	2238.01i		−	0.828245i
$195$	124.870	+	71.5950i	0.0458571	+	0.0262924i
$196$	−1161.94			−0.423448
$197$	−1032.98			−0.373588			−0.186794	−	0.982399i	$-0.559810\pi$
$197$	−1032.98			−0.373588			−0.186794	+	0.982399i	$0.559810\pi$
$198$	1563.00	−	914.947i	0.560996	−	0.328396i
$199$		−	5407.76i		−	1.92636i	−0.268852	−	0.963182i	$-0.586644\pi$
$199$		−	5407.76i		−	1.92636i	0.268852	−	0.963182i	$-0.413356\pi$
$200$			36.9920i			0.0130786i
$201$	816.428	+	468.104i	0.286500	+	0.164266i
$202$	−3153.22			−1.09831
$203$	1777.46			0.614549
$204$	913.471	+	523.744i	0.313509	+	0.179752i
$205$	−743.549			−0.253325
$206$			184.357i			0.0623531i
$207$	−260.252	−	444.586i	−0.0873853	−	0.149280i
$208$		−	32.1942i		−	0.0107321i
$209$	−3756.33			−1.24321
$210$	799.469	+	458.381i	0.262708	+	0.150625i
$211$	−280.030			−0.0913653			−0.0456827	−	0.998956i	$-0.514546\pi$
$211$	−280.030			−0.0913653			−0.0456827	+	0.998956i	$0.514546\pi$
$212$	−2269.22			−0.735144
$213$	897.720	−	1565.73i	0.288783	−	0.503671i
$214$	−1526.68			−0.487672
$215$	4646.92			1.47403
$216$	3339.56	−	30.0635i	1.05198	−	0.00947019i
$217$	−1235.22	−	642.618i	−0.386416	−	0.201031i
$218$		−	2330.32i		−	0.723988i
$219$	−939.467	+	1638.54i	−0.289878	+	0.505581i
$220$		−	1614.33i		−	0.494718i
$221$			119.352i			0.0363280i
$222$	2982.31	+	1709.93i	0.901621	+	0.516950i
$223$			4850.44i			1.45654i	0.685288	+	0.728272i	$0.259676\pi$
$223$			4850.44i			1.45654i	−0.685288	+	0.728272i	$0.740324\pi$
$224$			1330.15i			0.396761i
$225$	−21.1964	−	36.2097i	−0.00628042	−	0.0107288i
$226$	−431.016			−0.126862
$227$		−	1886.45i		−	0.551576i	−0.961218	−	0.275788i	$-0.911061\pi$
$227$		−	1886.45i		−	0.551576i	0.961218	−	0.275788i	$-0.0889389\pi$
$228$	−2062.50	−	1182.55i	−0.599089	−	0.343491i
$229$			3292.16i			0.950010i	0.879983	+	0.475005i	$0.157554\pi$
$229$			3292.16i			0.950010i	−0.879983	+	0.475005i	$0.842446\pi$
$230$	419.469			0.120257
$231$	−1248.16	−	715.642i	−0.355511	−	0.203835i
$232$			5245.01i			1.48428i
$233$			6500.93i			1.82785i	0.405880	+	0.913927i	$0.366965\pi$
$233$			6500.93i			1.82785i	−0.405880	+	0.913927i	$0.633035\pi$
$234$	65.6388	+	112.130i	0.0183374	+	0.0313256i
$235$	1977.00			0.548788
$236$			793.027i			0.218736i
$237$	172.689	−	301.190i	0.0473306	−	0.0825501i
$238$			764.141i			0.208117i
$239$	−3826.17			−1.03554			−0.517770	−	0.855520i	$-0.673238\pi$
$239$	−3826.17			−1.03554			−0.517770	+	0.855520i	$0.673238\pi$
$240$	−380.141	+	663.010i	−0.102242	+	0.178321i
$241$		−	6644.03i		−	1.77585i	−0.459989	−	0.887924i	$-0.652147\pi$
$241$		−	6644.03i		−	1.77585i	0.459989	−	0.887924i	$-0.347853\pi$
$242$			298.787i			0.0793668i
$243$	−3251.72	+	1943.00i	−0.858427	+	0.512936i
$244$		−	2465.42i		−	0.646854i
$245$			3126.52i			0.815290i
$246$	−582.263	−	333.844i	−0.150910	−	0.0865250i
$247$		−	269.481i		−	0.0694198i
$248$	1896.26	−	3644.94i	0.485535	−	0.933282i
$249$	2591.59	+	1485.91i	0.659580	+	0.378175i
$250$	−2713.94			−0.686579
$251$	2563.22			0.644577			0.322288	−	0.946642i	$-0.395548\pi$
$251$	2563.22			0.644577			0.322288	+	0.946642i	$0.395548\pi$
$252$	−460.038	−	785.879i	−0.114999	−	0.196451i
$253$	−654.892			−0.162738
$254$	−4789.36			−1.18312
$255$	1409.28	−	2457.94i	0.346088	−	0.603618i
$256$	−4362.35			−1.06503
$257$			4551.57i			1.10474i	0.833598	+	0.552371i	$0.186277\pi$
$257$			4551.57i			1.10474i	−0.833598	+	0.552371i	$0.813723\pi$
$258$	3638.94	+	2086.41i	0.878103	+	0.503466i
$259$		−	2731.00i		−	0.655197i
$260$	115.813			0.0276246
$261$	−3005.40	−	5134.10i	−0.712756	−	1.21760i
$262$	1568.92			0.369954
$263$	−1315.34			−0.308394			−0.154197	−	0.988040i	$-0.549279\pi$
$263$	−1315.34			−0.308394			−0.154197	+	0.988040i	$0.549279\pi$
$264$	2111.75	−	3683.13i	0.492307	−	0.858640i
$265$			6105.95i			1.41542i
$266$		−	1725.33i		−	0.397695i
$267$	466.218	+	267.309i	0.106862	+	0.0612699i
$268$	757.210			0.172589
$269$	−7467.48			−1.69257			−0.846283	−	0.532733i	$-0.821165\pi$
$269$	−7467.48			−1.69257			−0.846283	+	0.532733i	$0.821165\pi$
$270$	−27.7652	−	3084.26i	−0.00625829	−	0.695194i
$271$			4343.60i			0.973634i	0.873504	+	0.486817i	$0.161842\pi$
$271$			4343.60i			0.973634i	−0.873504	+	0.486817i	$0.838158\pi$
$272$	−633.712			−0.141266
$273$	51.3406	−	89.5440i	0.0113820	−	0.0198515i
$274$			5059.42i			1.11551i
$275$	−53.3383			−0.0116961
$276$	−359.583	−	206.169i	−0.0784217	−	0.0449635i
$277$			3839.72i			0.832875i	0.909164	+	0.416438i	$0.136722\pi$
$277$			3839.72i			0.832875i	−0.909164	+	0.416438i	$0.863278\pi$
$278$	1636.27			0.353012
$279$	232.393	+	4654.42i	0.0498673	+	0.998756i
$280$	2160.31			0.461083
$281$		−	4705.40i		−	0.998935i	−0.866333	−	0.499468i	$-0.833529\pi$
$281$		−	4705.40i		−	0.998935i	0.866333	−	0.499468i	$-0.166471\pi$
$282$	1548.16	+	887.648i	0.326921	+	0.187442i
$283$	−3360.51			−0.705871			−0.352936	−	0.935648i	$-0.614817\pi$
$283$	−3360.51			−0.705871			−0.352936	+	0.935648i	$0.614817\pi$
$284$		−	1452.16i		−	0.303415i
$285$	−3181.97	+	5549.72i	−0.661345	+	1.15346i
$286$	165.172			0.0341498
$287$			533.197i			0.109664i
$288$	3842.06	−	2249.06i	0.786095	−	0.460164i
$289$	−2563.67			−0.521814
$290$	4844.05			0.980870
$291$	5162.24	+	2959.80i	1.03992	+	0.596243i
$292$			1519.69i			0.304566i
$293$		−	3091.04i		−	0.616315i	−0.951335	−	0.308158i	$-0.900288\pi$
$293$		−	3091.04i		−	0.616315i	0.951335	−	0.308158i	$-0.0997125\pi$
$294$	−1403.77	+	2448.34i	−0.278468	+	0.485680i
$295$	2133.86			0.421146
$296$	8058.74			1.58245
$297$	43.3482	+	4815.28i	0.00846907	+	0.940777i
$298$	5141.70			0.999499
$299$		−	46.9824i		−	0.00908716i
$300$	−29.2866	−	16.7916i	−0.00563620	−	0.00323155i
$301$		−	3332.29i		−	0.638107i
$302$	−5824.11			−1.10973
$303$	4170.18	−	7273.28i	0.790662	−	1.37901i
$304$	1430.84			0.269948
$305$	−6633.89			−1.24543
$306$	2207.17	−	1292.04i	0.412339	−	0.241375i
$307$	1431.70			0.266162			0.133081	−	0.991105i	$-0.457513\pi$
$307$	1431.70			0.266162			0.133081	+	0.991105i	$0.457513\pi$
$308$	−1157.63			−0.214163
$309$	−425.242	−	243.815i	−0.0782885	−	0.0448872i
$310$	−3366.30	−	1751.30i	−0.616751	−	0.320861i
$311$			3650.77i			0.665646i	0.942989	+	0.332823i	$0.108001\pi$
$311$			3650.77i			0.665646i	−0.942989	+	0.332823i	$0.891999\pi$
$312$	264.230	+	151.498i	0.0479458	+	0.0274900i
$313$		−	179.991i		−	0.0325038i	−0.999868	−	0.0162519i	$-0.994827\pi$
$313$		−	179.991i		−	0.0325038i	0.999868	−	0.0162519i	$-0.00517337\pi$
$314$			410.605i			0.0737954i
$315$	−2114.62	+	1237.86i	−0.378240	+	0.221414i
$316$		−	279.343i		−	0.0497288i
$317$			62.0789i			0.0109990i	0.999985	+	0.00549952i	$0.00175056\pi$
$317$			62.0789i			0.0109990i	−0.999985	+	0.00549952i	$0.998249\pi$
$318$	−2741.50	+	4781.49i	−0.483445	+	0.843185i
$319$	−7562.72			−1.32737
$320$			4801.65i			0.838814i
$321$	2019.06	−	3521.48i	0.351069	−	0.612305i
$322$		−	300.800i		−	0.0520589i
$323$	−5304.48			−0.913774
$324$	−1492.12	+	2657.58i	−0.255850	+	0.455690i
$325$		−	3.82652i		−	0.000653098i
$326$		−	3468.89i		−	0.589338i
$327$	5375.18	+	3081.89i	0.909015	+	0.521189i
$328$	−1573.38			−0.264864
$329$		−	1417.70i		−	0.237569i
$330$	−3401.57	−	1950.31i	−0.567424	−	0.325336i
$331$		−	6127.91i		−	1.01758i	−0.860889	−	0.508792i	$-0.830092\pi$
$331$		−	6127.91i		−	1.01758i	0.860889	−	0.508792i	$-0.169908\pi$
$332$	2403.61			0.397336
$333$	−7888.32	+	4617.67i	−1.29813	+	0.759899i
$334$		−	3646.48i		−	0.597384i
$335$		−	2037.48i		−	0.332297i
$336$	475.443	+	272.598i	0.0771950	+	0.0442602i
$337$			2229.44i			0.360372i	0.983633	+	0.180186i	$0.0576700\pi$
$337$			2229.44i			0.360372i	−0.983633	+	0.180186i	$0.942330\pi$
$338$		−	4281.69i		−	0.689034i
$339$	570.026	−	994.191i	0.0913261	−	0.159283i
$340$		−	2279.66i		−	0.363623i
$341$	5255.59	+	2734.20i	0.834623	+	0.434208i
$342$	−4983.51	+	2917.25i	−0.787946	+	0.461248i
$343$	5009.03			0.788519
$344$	9833.07			1.54117
$345$	−554.756	+	967.558i	−0.0865711	+	0.150990i
$346$	1216.24			0.188975
$347$	−10464.5			−1.61891			−0.809457	−	0.587180i	$-0.800238\pi$
$347$	−10464.5			−1.61891			−0.809457	+	0.587180i	$0.800238\pi$
$348$	−4152.48	−	2380.85i	−0.639645	−	0.366744i
$349$	11439.0			1.75448			0.877239	−	0.480053i	$-0.159383\pi$
$349$	11439.0			1.75448			0.877239	+	0.480053i	$0.159383\pi$
$350$		−	24.4989i		−	0.00374150i
$351$	−345.451	+	3.10982i	−0.0525322	+	0.000472906i
$352$		−	5659.50i		−	0.856966i
$353$	9272.63			1.39811			0.699054	−	0.715069i	$-0.253605\pi$
$353$	9272.63			1.39811			0.699054	+	0.715069i	$0.253605\pi$
$354$	1671.00	+	958.076i	0.250883	+	0.143845i
$355$	−3907.44			−0.584184
$356$	432.402			0.0643743
$357$	−1762.59	−	1010.59i	−0.261305	−	0.149821i
$358$		−	6303.03i		−	0.930518i
$359$		−	12563.5i		−	1.84701i	−0.383585	−	0.923506i	$-0.625311\pi$
$359$		−	12563.5i		−	1.84701i	0.383585	−	0.923506i	$-0.374689\pi$
$360$	−3652.72	−	6239.92i	−0.534765	−	0.913535i
$361$	5117.82			0.746146
$362$	819.891			0.119040
$363$	−689.189	−	395.151i	−0.0996503	−	0.0571351i
$364$		−	83.0490i		−	0.0119587i
$365$	4089.15			0.586399
$366$	−5194.92	−	2978.54i	−0.741920	−	0.425384i
$367$			1583.71i			0.225256i	0.993637	+	0.112628i	$0.0359268\pi$
$367$			1583.71i			0.225256i	−0.993637	+	0.112628i	$0.964073\pi$
$368$	249.457			0.0353366
$369$	1540.11	−	901.547i	0.217276	−	0.127189i
$370$		−	7442.67i		−	1.04575i
$371$	4378.56			0.612732
$372$	2024.94	+	3155.81i	0.282226	+	0.439841i
$373$	−12615.3			−1.75119			−0.875596	−	0.483045i	$-0.839531\pi$
$373$	−12615.3			−1.75119			−0.875596	+	0.483045i	$0.839531\pi$
$374$		−	3251.25i		−	0.449514i
$375$	3589.23	−	6260.04i	0.494259	−	0.862046i
$376$	4183.41			0.573784
$377$		−	542.554i		−	0.0741192i
$378$	−2211.72	+	19.9104i	−0.300948	+	0.00270920i
$379$	13736.5			1.86173			0.930867	−	0.365357i	$-0.119053\pi$
$379$	13736.5			1.86173			0.930867	+	0.365357i	$0.119053\pi$
$380$			5147.18i			0.694854i
$381$	6334.01	−	11047.3i	0.851710	−	1.48548i
$382$	−5508.75			−0.737833
$383$	7946.90			1.06023			0.530115	−	0.847926i	$-0.322149\pi$
$383$	7946.90			1.06023			0.530115	+	0.847926i	$0.322149\pi$
$384$	1253.39	−	2186.05i	0.166567	−	0.290512i
$385$			3114.92i			0.412340i
$386$			8416.95i			1.10987i
$387$	−9625.13	+	5634.36i	−1.26427	+	0.740078i
$388$	4787.80			0.626453
$389$	−8638.48			−1.12593			−0.562967	−	0.826479i	$-0.690340\pi$
$389$	−8638.48			−1.12593			−0.562967	+	0.826479i	$0.690340\pi$
$390$	139.916	−	244.030i	0.0181665	−	0.0316845i
$391$	−924.802			−0.119614
$392$			6615.84i			0.852425i
$393$	−2074.92	+	3618.90i	−0.266325	+	0.464502i
$394$			2018.73i			0.258127i
$395$	−751.650			−0.0957458
$396$	1957.36	+	3343.74i	0.248386	+	0.424317i
$397$	2779.75			0.351415			0.175707	−	0.984442i	$-0.443779\pi$
$397$	2779.75			0.351415			0.175707	+	0.984442i	$0.443779\pi$
$398$	−10568.3			−1.33100
$399$	3979.69	+	2281.78i	0.499332	+	0.286295i
$400$	20.3173			0.00253966
$401$	7797.66			0.971064			0.485532	−	0.874219i	$-0.338626\pi$
$401$	7797.66			0.971064			0.485532	+	0.874219i	$0.338626\pi$
$402$	914.804	−	1595.53i	0.113498	−	0.197954i
$403$	−196.153	+	377.039i	−0.0242458	+	0.0466046i
$404$		−	6745.72i		−	0.830724i
$405$	7150.96	+	4014.95i	0.877368	+	0.492603i
$406$		−	3473.65i		−	0.424617i
$407$			11619.8i			1.41516i
$408$	2982.09	−	5201.11i	0.361851	−	0.631111i
$409$			12450.1i			1.50518i	0.658488	+	0.752591i	$0.271196\pi$
$409$			12450.1i			1.50518i	−0.658488	+	0.752591i	$0.728804\pi$
$410$			1453.10i			0.175033i
$411$	−11670.2	−	6691.17i	−1.40060	−	0.803044i
$412$	−394.397			−0.0471615
$413$		−	1530.18i		−	0.182313i
$414$	−868.844	+	508.604i	−0.103143	+	0.0603780i
$415$		−	6467.59i		−	0.765015i
$416$	406.016			0.0478523
$417$	−2164.00	+	3774.27i	−0.254129	+	0.443230i
$418$			7340.90i			0.858984i
$419$			4038.34i			0.470850i	0.971893	+	0.235425i	$0.0756481\pi$
$419$			4038.34i			0.470850i	−0.971893	+	0.235425i	$0.924352\pi$
$420$	−980.621	+	1710.32i	−0.113927	+	0.198702i
$421$	−831.019			−0.0962028			−0.0481014	−	0.998842i	$-0.515317\pi$
$421$	−831.019			−0.0962028			−0.0481014	+	0.998842i	$0.515317\pi$
$422$			547.256i			0.0631280i
$423$	−4094.94	+	2397.09i	−0.470692	+	0.275534i
$424$			12920.4i			1.47989i
$425$	−75.3213			−0.00859675
$426$	−3059.86	−	1754.39i	−0.348007	−	0.199532i
$427$			4757.15i			0.539144i
$428$		−	3266.05i		−	0.368857i
$429$	−218.443	+	380.990i	−0.0245840	+	0.0428773i
$430$		−	9081.36i		−	1.01847i
$431$		−	4275.47i		−	0.477824i	−0.971041	−	0.238912i	$-0.923209\pi$
$431$		−	4275.47i		−	0.477824i	0.971041	−	0.238912i	$-0.0767908\pi$
$432$	−16.5119	−	1834.20i	−0.00183896	−	0.204278i
$433$		−	10655.8i		−	1.18264i	−0.806436	−	0.591322i	$-0.798606\pi$
$433$		−	10655.8i		−	1.18264i	0.806436	−	0.591322i	$-0.201394\pi$
$434$	−1255.85	+	2413.96i	−0.138900	+	0.266990i
$435$	−6406.33	+	11173.4i	−0.706115	+	1.23155i
$436$	4985.30			0.547597
$437$	2088.08			0.228573
$438$	3202.16	+	1835.98i	0.349326	+	0.200288i
$439$	1211.24			0.131684			0.0658421	−	0.997830i	$-0.479027\pi$
$439$	1211.24			0.131684			0.0658421	+	0.997830i	$0.479027\pi$
$440$	−9191.64			−0.995896
$441$	−3790.88	−	6475.94i	−0.409338	−	0.699270i
$442$	233.247			0.0251005
$443$			18271.0i			1.95955i	0.200099	+	0.979776i	$0.435874\pi$
$443$			18271.0i			1.95955i	−0.200099	+	0.979776i	$0.564126\pi$
$444$	−3658.08	+	6380.11i	−0.391001	+	0.681952i
$445$		−	1163.50i		−	0.123944i
$446$	9479.09			1.00639
$447$	−6799.98	+	11860.0i	−0.719526	+	1.25494i
$448$	3443.25			0.363121
$449$	−17438.8			−1.83294			−0.916470	−	0.400105i	$-0.868974\pi$
$449$	−17438.8			−1.83294			−0.916470	+	0.400105i	$0.868974\pi$
$450$	−70.7637	+	41.4236i	−0.00741296	+	0.00433940i
$451$		−	2268.64i		−	0.236864i
$452$		−	922.079i		−	0.0959534i
$453$	7702.48	−	13434.0i	0.798883	−	1.39335i
$454$	−3686.63			−0.381107
$455$	−223.466			−0.0230247
$456$	−6733.17	+	11743.4i	−0.691468	+	1.20600i
$457$			6227.50i			0.637441i	0.947849	+	0.318720i	$0.103253\pi$
$457$			6227.50i			0.637441i	−0.947849	+	0.318720i	$0.896747\pi$
$458$	6433.79			0.656400
$459$	61.2138	+	6799.86i	0.00622487	+	0.691482i
$460$			897.378i			0.0909575i
$461$	5151.35			0.520439			0.260219	−	0.965549i	$-0.416205\pi$
$461$	5151.35			0.520439			0.260219	+	0.965549i	$0.416205\pi$
$462$	−1398.56	+	2439.25i	−0.140838	+	0.245637i
$463$		−	4276.73i		−	0.429280i	−0.976693	−	0.214640i	$-0.931142\pi$
$463$		−	4276.73i		−	0.429280i	0.976693	−	0.214640i	$-0.0688577\pi$
$464$	2880.74			0.288222
$465$	8491.57	−	5448.65i	0.846854	−	0.543388i
$466$	12704.6			1.26294
$467$		−	10353.0i		−	1.02587i	−0.858428	−	0.512934i	$-0.828559\pi$
$467$		−	10353.0i		−	1.02587i	0.858428	−	0.512934i	$-0.171441\pi$
$468$	−239.882	+	140.422i	−0.0236935	+	0.0138697i
$469$	−1461.07			−0.143851
$470$		−	3863.60i		−	0.379180i
$471$	−947.110	−	543.031i	−0.0926550	−	0.0531244i
$472$	4515.33			0.440328
$473$			14178.2i			1.37825i
$474$	−588.607	−	337.482i	−0.0570372	−	0.0327026i
$475$	170.066			0.0164277
$476$	−1634.74			−0.157412
$477$	−7403.42	−	12647.2i	−0.710649	−	1.21400i
$478$			7477.38i			0.715497i
$479$		−	6267.87i		−	0.597884i	−0.954271	−	0.298942i	$-0.903366\pi$
$479$		−	6267.87i		−	0.597884i	0.954271	−	0.298942i	$-0.0966337\pi$
$480$	−8361.51	−	4794.13i	−0.795102	−	0.455877i
$481$	−833.611			−0.0790216
$482$	−12984.3			−1.22701
$483$	693.833	+	397.814i	0.0653634	+	0.0374765i
$484$	−639.200			−0.0600301
$485$		−	12882.9i		−	1.20615i
$486$	3797.16	+	6354.75i	0.354409	+	0.593122i
$487$			5429.25i			0.505180i	0.967573	+	0.252590i	$0.0812824\pi$
$487$			5429.25i			0.505180i	−0.967573	+	0.252590i	$0.918718\pi$
$488$	−14037.6			−1.30215
$489$	8001.43	+	4587.67i	0.739953	+	0.424257i
$490$	6110.08			0.563317
$491$	−9007.79			−0.827935			−0.413967	−	0.910292i	$-0.635857\pi$
$491$	−9007.79			−0.827935			−0.413967	+	0.910292i	$0.635857\pi$
$492$	714.199	−	1245.65i	0.0654442	−	0.114142i
$493$	−10679.6			−0.975633
$494$	−526.641			−0.0479649
$495$	8997.26	−	5266.81i	0.816963	−	0.478234i
$496$	−2001.93	−	1041.49i	−0.181228	−	0.0942831i
$497$			2802.01i			0.252892i
$498$	2903.87	−	5064.68i	0.261296	−	0.455731i
$499$		−	14189.2i		−	1.27293i	−0.771304	−	0.636467i	$-0.780395\pi$
$499$		−	14189.2i		−	1.27293i	0.771304	−	0.636467i	$-0.219605\pi$
$500$		−	5805.98i		−	0.519303i
$501$	8411.05	+	4822.53i	0.750056	+	0.430049i
$502$		−	5009.23i		−	0.445364i
$503$		−	692.902i		−	0.0614214i	−0.999528	−	0.0307107i	$-0.990223\pi$
$503$		−	692.902i		−	0.0614214i	0.999528	−	0.0307107i	$-0.00977706\pi$
$504$	−4474.63	+	2619.36i	−0.395468	+	0.231499i
$505$	−18151.2			−1.59944
$506$			1279.84i			0.112442i
$507$	9876.25	+	5662.61i	0.865128	+	0.496026i
$508$		−	10246.0i		−	0.894864i
$509$	894.904			0.0779291			0.0389646	−	0.999241i	$-0.487594\pi$
$509$	894.904			0.0779291			0.0389646	+	0.999241i	$0.487594\pi$
$510$	−4803.50	−	2754.12i	−0.417064	−	0.239126i
$511$		−	2932.32i		−	0.253851i
$512$			4645.62i			0.400995i
$513$	−138.213	−	15353.2i	−0.0118952	−	1.32136i
$514$	8895.01			0.763311
$515$			1061.23i			0.0908030i
$516$	−4463.49	+	7784.85i	−0.380803	+	0.664164i
$517$			6032.00i			0.513128i
$518$	−5337.12			−0.452702
$519$	−1608.49	+	2805.40i	−0.136041	+	0.237271i
$520$		−	659.413i		−	0.0556100i
$521$		−	13969.9i		−	1.17473i	−0.809324	−	0.587363i	$-0.800166\pi$
$521$		−	13969.9i		−	1.17473i	0.809324	−	0.587363i	$-0.199834\pi$
$522$	−10033.4	+	5873.37i	−0.841286	+	0.492472i
$523$			7206.75i			0.602542i	0.953539	+	0.301271i	$0.0974108\pi$
$523$			7206.75i			0.602542i	−0.953539	+	0.301271i	$0.902589\pi$
$524$			3356.41i			0.279819i
$525$	56.5098	+	32.4003i	0.00469770	+	0.00269345i
$526$			2570.54i			0.213082i
$527$	7421.65	+	3861.08i	0.613458	+	0.319148i
$528$	−2022.90	−	1159.84i	−0.166734	−	0.0955980i
$529$	−11803.0			−0.970079
$530$	11932.7			0.977970
$531$	−4419.84	+	2587.29i	−0.361214	+	0.211448i
$532$	3691.03			0.300801
$533$	162.753			0.0132263
$534$	522.396	−	911.119i	0.0423338	−	0.0738351i
$535$	−8788.22			−0.710183
$536$		−	4311.39i		−	0.347432i
$537$	14538.7	+	8335.86i	1.16833	+	0.669868i
$538$			14593.5i			1.16946i
$539$	−9539.30			−0.762313
$540$	6598.21	−	59.3986i	0.525818	−	0.00473353i
$541$	2264.67			0.179973			0.0899867	−	0.995943i	$-0.471318\pi$
$541$	2264.67			0.179973			0.0899867	+	0.995943i	$0.471318\pi$
$542$	8488.58			0.672723
$543$	−1084.32	+	1891.18i	−0.0856955	+	0.149463i
$544$		−	7992.02i		−	0.629881i
$545$		−	13414.3i		−	1.05432i
$546$	−174.993	−	100.334i	−0.0137162	−	0.00786425i
$547$	14585.5			1.14010			0.570048	−	0.821612i	$-0.306925\pi$
$547$	14585.5			1.14010			0.570048	+	0.821612i	$0.306925\pi$
$548$	−10823.7			−0.843732
$549$	13740.7	−	8043.55i	1.06820	−	0.625301i
$550$			104.238i			0.00808128i
$551$	24113.2			1.86435
$552$	−1173.88	+	2047.39i	−0.0905142	+	0.157867i
$553$			539.006i			0.0414482i
$554$	7503.87			0.575467
$555$	17167.4	+	9843.06i	1.31300	+	0.752819i
$556$			3500.51i			0.267005i
$557$	17430.3			1.32594			0.662968	−	0.748647i	$-0.269296\pi$
$557$	17430.3			1.32594			0.662968	+	0.748647i	$0.269296\pi$
$558$	9096.02	−	454.159i	0.690081	−	0.0344553i
$559$	−1017.15			−0.0769604
$560$		−	1186.52i		−	0.0895347i
$561$	7499.41	+	4299.84i	0.564395	+	0.323599i
$562$	−9195.65			−0.690205
$563$		−	12819.5i		−	0.959640i	−0.877367	−	0.479820i	$-0.840702\pi$
$563$		−	12819.5i		−	0.959640i	0.877367	−	0.479820i	$-0.159298\pi$
$564$	−1898.96	+	3312.01i	−0.141774	+	0.247271i
$565$	−2481.11			−0.184745
$566$			6567.36i			0.487715i
$567$	2879.11	−	5127.93i	0.213247	−	0.379811i
$568$	−8268.29			−0.610792
$569$	21992.6			1.62035			0.810175	−	0.586188i	$-0.199372\pi$
$569$	21992.6			1.62035			0.810175	+	0.586188i	$0.199372\pi$
$570$	10845.7	+	6218.43i	0.796974	+	0.456950i
$571$			18045.6i			1.32257i	0.750135	+	0.661284i	$0.229988\pi$
$571$			18045.6i			1.32257i	−0.750135	+	0.661284i	$0.770012\pi$
$572$			353.355i			0.0258296i
$573$	7285.42	−	12706.6i	0.531157	−	0.926399i
$574$	1042.01			0.0757714
$575$	29.6499			0.00215041
$576$	−5821.97	−	9945.62i	−0.421149	−	0.719446i
$577$	−4924.71			−0.355318			−0.177659	−	0.984092i	$-0.556852\pi$
$577$	−4924.71			−0.355318			−0.177659	+	0.984092i	$0.556852\pi$
$578$			5010.12i			0.360542i
$579$	−19414.7	−	11131.6i	−1.39352	−	0.798984i
$580$			10362.9i			0.741893i
$581$	−4637.89			−0.331174
$582$	5784.27	−	10088.4i	0.411968	−	0.718521i
$583$	−18629.8			−1.32345
$584$	8652.80			0.613108
$585$	377.844	+	645.469i	0.0267042	+	0.0456185i
$586$	−6040.74			−0.425837
$587$	−17317.8			−1.21769			−0.608844	−	0.793290i	$-0.708367\pi$
$587$	−17317.8			−1.21769			−0.608844	+	0.793290i	$0.708367\pi$
$588$	−5237.77	−	3003.11i	−0.367350	−	0.210623i
$589$	−16757.1	−	8717.81i	−1.17227	−	0.609866i
$590$		−	4170.14i		−	0.290987i
$591$	−4656.44	−	2669.80i	−0.324095	−	0.185822i
$592$		−	4426.14i		−	0.307286i
$593$			3406.20i			0.235878i	0.993021	+	0.117939i	$0.0376287\pi$
$593$			3406.20i			0.235878i	−0.993021	+	0.117939i	$0.962371\pi$
$594$	9410.37	−	84.7142i	0.650021	−	0.00585163i
$595$			4398.72i			0.303075i
$596$			10999.7i			0.755983i
$597$	13976.7	−	24377.0i	0.958171	−	1.67116i
$598$	−91.8164			−0.00627868
$599$		−	8411.23i		−	0.573746i	−0.957969	−	0.286873i	$-0.907384\pi$
$599$		−	8411.23i		−	0.573746i	0.957969	−	0.286873i	$-0.0926157\pi$
$600$	−95.6080	+	166.752i	−0.00650530	+	0.0113460i
$601$		−	17562.3i		−	1.19198i	−0.802990	−	0.595992i	$-0.796759\pi$
$601$		−	17562.3i		−	1.19198i	0.802990	−	0.595992i	$-0.203241\pi$
$602$	−6512.22			−0.440894
$603$	2470.43	+	4220.22i	0.166839	+	0.285009i
$604$		−	12459.6i		−	0.839361i
$605$			1719.94i			0.115580i
$606$	−14214.0	−	8149.68i	−0.952812	−	0.546301i
$607$	18148.3			1.21353			0.606767	−	0.794880i	$-0.292466\pi$
$607$	18148.3			1.21353			0.606767	+	0.794880i	$0.292466\pi$
$608$			18044.9i			1.20365i
$609$	8012.41	+	4593.97i	0.533135	+	0.305676i
$610$			12964.4i			0.860517i
$611$	−432.739			−0.0286526
$612$	2764.07	+	4721.84i	0.182567	+	0.311878i
$613$		−	13269.9i		−	0.874335i	−0.899380	−	0.437168i	$-0.855982\pi$
$613$		−	13269.9i		−	0.874335i	0.899380	−	0.437168i	$-0.144018\pi$
$614$		−	2797.94i		−	0.183902i
$615$	−3351.75	−	1921.75i	−0.219765	−	0.126004i
$616$			6591.30i			0.431122i
$617$		−	25906.3i		−	1.69035i	−0.534486	−	0.845177i	$-0.679495\pi$
$617$		−	25906.3i		−	1.69035i	0.534486	−	0.845177i	$-0.320505\pi$
$618$	−476.481	+	831.039i	−0.0310144	+	0.0540927i
$619$		−	10725.3i		−	0.696427i	−0.937415	−	0.348213i	$-0.886788\pi$
$619$		−	10725.3i		−	0.696427i	0.937415	−	0.348213i	$-0.113212\pi$
$620$	3746.58	−	7201.57i	0.242688	−	0.466487i
$621$	−24.0965	−	2676.73i	−0.00155710	−	0.172969i
$622$	7134.60			0.459922
$623$	−834.340			−0.0536551
$624$	83.2079	−	145.124i	0.00533811	−	0.00931029i
$625$	−15816.8			−1.01228
$626$	−351.752			−0.0224582
$627$	−16932.7	−	9708.47i	−1.07851	−	0.618371i
$628$	−878.413			−0.0558161
$629$			16408.8i			1.04016i
$630$	2419.12	+	4132.56i	0.152984	+	0.261341i
$631$			2817.33i			0.177743i	0.996043	+	0.0888717i	$0.0283261\pi$
$631$			2817.33i			0.177743i	−0.996043	+	0.0888717i	$0.971674\pi$
$632$	−1590.52			−0.100107
$633$	−1262.31	−	723.756i	−0.0792614	−	0.0454450i
$634$	121.319			0.00759969
$635$	−27569.6			−1.72294
$636$	−10229.1	−	5864.93i	−0.637753	−	0.365660i
$637$		−	684.355i		−	0.0425669i
$638$			14779.6i			0.917133i
$639$	8093.44	−	4737.74i	0.501051	−	0.293305i
$640$	−5455.52			−0.336951
$641$	−10955.4			−0.675060			−0.337530	−	0.941315i	$-0.609591\pi$
$641$	−10955.4			−0.675060			−0.337530	+	0.941315i	$0.609591\pi$
$642$	−6881.94	−	3945.80i	−0.423066	−	0.242568i
$643$			26329.3i			1.61481i	0.589995	+	0.807407i	$0.299130\pi$
$643$			26329.3i			1.61481i	−0.589995	+	0.807407i	$0.700870\pi$
$644$	643.507			0.0393754
$645$	20947.3	+	12010.2i	1.27876	+	0.733183i
$646$			10366.4i			0.631363i
$647$	4671.03			0.283828			0.141914	−	0.989879i	$-0.454674\pi$
$647$	4671.03			0.283828			0.141914	+	0.989879i	$0.454674\pi$
$648$	15131.7	+	8495.79i	0.917330	+	0.515040i
$649$			6510.60i			0.393780i
$650$	−7.47807			−0.000451252
$651$	−3907.22	−	6089.28i	−0.235232	−	0.366602i
$652$	7421.06			0.445753
$653$			20641.5i			1.23701i	0.785782	+	0.618503i	$0.212261\pi$
$653$			20641.5i			1.23701i	−0.785782	+	0.618503i	$0.787739\pi$
$654$	6022.86	−	10504.6i	0.360111	−	0.628075i
$655$	9031.34			0.538754
$656$			864.154i			0.0514323i
$657$	−8469.81	+	4958.06i	−0.502951	+	0.294417i
$658$	−2770.57			−0.164146
$659$			15196.0i			0.898255i	0.893468	+	0.449128i	$0.148265\pi$
$659$			15196.0i			0.898255i	−0.893468	+	0.449128i	$0.851735\pi$
$660$	4172.33	−	7277.02i	0.246072	−	0.429178i
$661$	−16877.9			−0.993151			−0.496575	−	0.867994i	$-0.665409\pi$
$661$	−16877.9			−0.993151			−0.496575	+	0.867994i	$0.665409\pi$
$662$	−11975.6			−0.703090
$663$	−308.473	+	538.012i	−0.0180695	+	0.0315153i
$664$		−	13685.7i		−	0.799860i
$665$		−	9931.72i		−	0.579151i
$666$	9024.19	+	15415.9i	0.525045	+	0.896931i
$667$	4203.99			0.244047
$668$	7800.96			0.451839
$669$	−12536.3	+	21864.7i	−0.724484	+	1.26358i
$670$	−3981.80			−0.229597
$671$		−	20240.6i		−	1.16450i
$672$	−3437.86	+	5996.02i	−0.197348	+	0.344199i
$673$			2489.02i			0.142563i	0.997456	+	0.0712814i	$0.0227088\pi$
$673$			2489.02i			0.142563i	−0.997456	+	0.0712814i	$0.977291\pi$
$674$	4356.94			0.248996
$675$	−1.96256	−	218.009i	−0.000111910	−	0.0124313i
$676$	9159.89			0.521159
$677$	1660.59			0.0942713			0.0471356	−	0.998888i	$-0.484991\pi$
$677$	1660.59			0.0942713			0.0471356	+	0.998888i	$0.484991\pi$
$678$	−1942.92	−	1113.99i	−0.110055	−	0.0631009i
$679$	−9238.30			−0.522140
$680$	−12979.9			−0.731995
$681$	4875.64	−	8503.68i	0.274354	−	0.478505i
$682$	5343.37	−	10270.9i	0.300012	−	0.576675i
$683$			16771.9i			0.939617i	0.882768	+	0.469808i	$0.155677\pi$
$683$			16771.9i			0.939617i	−0.882768	+	0.469808i	$0.844323\pi$
$684$	−6240.91	−	10661.3i	−0.348870	−	0.595972i
$685$			29124.1i			1.62449i
$686$		−	9789.01i		−	0.544820i
$687$	−8508.80	+	14840.3i	−0.472534	+	0.824154i
$688$		−	5400.66i		−	0.299271i
$689$		−	1336.51i		−	0.0739001i
$690$	1890.87	+	1084.14i	0.104325	+	0.0598155i
$691$	23763.0			1.30823			0.654114	−	0.756396i	$-0.273042\pi$
$691$	23763.0			1.30823			0.654114	+	0.756396i	$0.273042\pi$
$692$			2601.91i			0.142933i
$693$	−3776.82	−	6451.91i	−0.207027	−	0.353662i
$694$			20450.5i			1.11857i
$695$	9419.08			0.514081
$696$	−13556.1	+	23643.3i	−0.738277	+	1.28764i
$697$		−	3203.64i		−	0.174098i
$698$		−	22354.9i		−	1.21224i
$699$	−16802.0	+	29304.7i	−0.909172	+	1.58570i
$700$	52.4110			0.00282993
$701$			15621.6i			0.841680i	0.907135	+	0.420840i	$0.138265\pi$
$701$			15621.6i			0.841680i	−0.907135	+	0.420840i	$0.861735\pi$
$702$	6.07745	+	675.105i	0.000326750	+	0.0362966i
$703$		−	37049.0i		−	1.98766i
$704$	−14650.3			−0.784309
$705$	8911.86	+	5109.67i	0.476085	+	0.272966i
$706$		−	18121.3i		−	0.966009i
$707$			13016.2i			0.692397i
$708$	−2049.63	+	3574.79i	−0.108799	+	0.189758i
$709$			33595.5i			1.77955i	0.456395	+	0.889777i	$0.349140\pi$
$709$			33595.5i			1.77955i	−0.456395	+	0.889777i	$0.650860\pi$
$710$			7636.21i			0.403636i
$711$	1556.89	−	911.370i	0.0821207	−	0.0480718i
$712$		−	2462.00i		−	0.129589i
$713$	−2921.50	−	1519.89i	−0.153452	−	0.0798324i
$714$	−1974.97	+	3444.58i	−0.103517	+	0.180546i
$715$	950.800			0.0497313
$716$	13484.2			0.703809
$717$	−17247.5	−	9888.96i	−0.898354	−	0.515077i
$718$	−24552.6			−1.27617
$719$	−10260.6			−0.532206			−0.266103	−	0.963945i	$-0.585736\pi$
$719$	−10260.6			−0.532206			−0.266103	+	0.963945i	$0.585736\pi$
$720$	−3427.18	+	2006.20i	−0.177394	+	0.103843i
$721$	761.008			0.0393085
$722$		−	10001.6i		−	0.515542i
$723$	17171.9	−	29949.8i	0.883306	−	1.54059i
$724$			1754.01i			0.0900375i
$725$	342.397			0.0175398
$726$	−772.234	+	1346.87i	−0.0394770	+	0.0688524i
$727$	29023.7			1.48065			0.740323	−	0.672251i	$-0.234672\pi$
$727$	29023.7			1.48065			0.740323	+	0.672251i	$0.234672\pi$
$728$	−472.863			−0.0240735
$729$	−19679.8	+	354.353i	−0.999838	+	0.0180030i
$730$		−	7991.31i		−	0.405167i
$731$			20021.6i			1.01303i
$732$	6372.03	−	11113.6i	0.321745	−	0.561160i
$733$	−16596.9			−0.836319			−0.418160	−	0.908374i	$-0.637325\pi$
$733$	−16596.9			−0.836319			−0.418160	+	0.908374i	$0.637325\pi$
$734$	3095.00			0.155638
$735$	−8080.69	+	14093.7i	−0.405525	+	0.707282i
$736$			3146.02i			0.157560i
$737$	6216.54			0.310705
$738$	−1761.87	−	3009.79i	−0.0878799	−	0.150125i
$739$			14480.6i			0.720808i	0.932796	+	0.360404i	$0.117361\pi$
$739$			14480.6i			0.720808i	−0.932796	+	0.360404i	$0.882639\pi$
$740$	15922.2			0.790963
$741$	696.491	−	1214.76i	0.0345293	−	0.0602232i
$742$		−	8556.92i		−	0.423362i
$743$	1263.67			0.0623950			0.0311975	−	0.999513i	$-0.490068\pi$
$743$	1263.67			0.0623950			0.0311975	+	0.999513i	$0.490068\pi$
$744$	17968.5	−	11529.6i	0.885426	−	0.568138i
$745$	29597.8			1.45554
$746$			24653.7i			1.20997i
$747$	7841.90	+	13396.3i	0.384097	+	0.656149i
$748$	6955.45			0.339995
$749$			6302.01i			0.307437i
$750$	−12233.8	−	7014.35i	−0.595622	−	0.341504i
$751$	31412.1			1.52629			0.763145	−	0.646227i	$-0.223654\pi$
$751$	31412.1			1.52629			0.763145	+	0.646227i	$0.223654\pi$
$752$		−	2297.67i		−	0.111419i
$753$	11554.4	+	6624.79i	0.559184	+	0.320612i
$754$	−1060.30			−0.0512120
$755$	−33526.0			−1.61607
$756$	−42.5945	−	4731.56i	−0.00204914	−	0.227626i
$757$			6922.57i			0.332371i	0.986094	+	0.166186i	$0.0531451\pi$
$757$			6922.57i			0.332371i	−0.986094	+	0.166186i	$0.946855\pi$
$758$		−	26844.9i		−	1.28635i
$759$	−2952.11	−	1692.61i	−0.141179	−	0.0809458i
$760$	29306.9			1.39878
$761$	−3112.56			−0.148266			−0.0741328	−	0.997248i	$-0.523619\pi$
$761$	−3112.56			−0.148266			−0.0741328	+	0.997248i	$0.523619\pi$
$762$	−21589.4	−	12378.4i	−1.02638	−	0.588481i
$763$	−9619.36			−0.456415
$764$		−	11785.0i		−	0.558069i
$765$	12705.4	−	7437.50i	0.600478	−	0.351508i
$766$		−	15530.4i		−	0.732555i
$767$	−467.074			−0.0219883
$768$	−19664.5	−	11274.8i	−0.923935	−	0.529744i
$769$	303.063			0.0142116			0.00710580	−	0.999975i	$-0.497738\pi$
$769$	303.063			0.0142116			0.00710580	+	0.999975i	$0.497738\pi$
$770$	6087.41			0.284903
$771$	−11763.8	+	20517.4i	−0.549498	+	0.958388i
$772$	−18006.5			−0.839467
$773$	30419.8			1.41542			0.707712	−	0.706501i	$-0.249727\pi$
$773$	30419.8			1.41542			0.707712	+	0.706501i	$0.249727\pi$
$774$	11011.1	+	18810.1i	0.511350	+	0.873535i
$775$	−237.944	−	123.789i	−0.0110286	−	0.00573759i
$776$		−	27260.7i		−	1.26109i
$777$	7058.43	−	12310.7i	0.325894	−	0.568398i
$778$			16882.0i			0.777953i
$779$			7233.40i			0.332687i
$780$	522.058	+	299.325i	0.0239650	+	0.0137405i
$781$		−	11921.9i		−	0.546224i
$782$			1807.32i			0.0826465i
$783$	−278.267	−	30911.0i	−0.0127005	−	1.41082i
$784$	3633.65			0.165527
$785$			2363.61i			0.107466i
$786$	7072.32	+	4054.96i	0.320943	+	0.184015i
$787$		−	13429.0i		−	0.608249i	−0.952632	−	0.304124i	$-0.901636\pi$
$787$		−	13429.0i		−	0.608249i	0.952632	−	0.304124i	$-0.0983638\pi$
$788$	−4318.69			−0.195237
$789$	−5929.27	−	3399.58i	−0.267538	−	0.153395i
$790$			1468.93i			0.0661547i
$791$			1779.20i			0.0799759i
$792$	19038.6	−	11144.8i	0.854174	−	0.500016i
$793$	1452.07			0.0650248
$794$		−	5432.40i		−	0.242807i
$795$	−15781.2	+	27524.3i	−0.704028	+	1.22791i
$796$		−	22608.8i		−	1.00672i
$797$	18964.0			0.842833			0.421417	−	0.906867i	$-0.361533\pi$
$797$	18964.0			0.842833			0.421417	+	0.906867i	$0.361533\pi$
$798$	4459.22	−	7777.40i	0.197813	−	0.345009i
$799$			8518.05i			0.377155i
$800$			256.230i			0.0113239i
$801$	1410.73	+	2409.94i	0.0622294	+	0.106306i
$802$		−	15238.8i		−	0.670947i
$803$			12476.4i			0.548295i
$804$	3413.33	+	1957.06i	0.149725	+	0.0858458i
$805$		−	1731.53i		−	0.0758118i
$806$	736.839	+	383.337i	0.0322010	+	0.0167524i
$807$	−33661.7	−	19300.2i	−1.46834	−	0.841881i
$808$	−38408.7			−1.67229
$809$	16627.5			0.722608			0.361304	−	0.932448i	$-0.382332\pi$
$809$	16627.5			0.722608			0.361304	+	0.932448i	$0.382332\pi$
$810$	7846.31	−	13974.9i	0.340360	−	0.606209i
$811$	−362.356			−0.0156893			−0.00784466	−	0.999969i	$-0.502497\pi$
$811$	−362.356			−0.0156893			−0.00784466	+	0.999969i	$0.502497\pi$
$812$	7431.24			0.321164
$813$	−11226.3	+	19580.0i	−0.484284	+	0.844648i
$814$	22708.3			0.977794
$815$		−	19968.4i		−	0.858236i
$816$	−2856.63	−	1637.87i	−0.122552	−	0.0702657i
$817$		−	45206.2i		−	1.93582i
$818$	24331.0			1.03999
$819$	462.864	−	270.951i	0.0197482	−	0.0115602i
$820$	−3108.64			−0.132388
$821$	−7911.36			−0.336307			−0.168154	−	0.985761i	$-0.553780\pi$
$821$	−7911.36			−0.336307			−0.168154	+	0.985761i	$0.553780\pi$
$822$	−13076.4	+	22806.7i	−0.554855	+	0.967732i
$823$			19678.1i			0.833457i	0.909031	+	0.416729i	$0.136823\pi$
$823$			19678.1i			0.833457i	−0.909031	+	0.416729i	$0.863177\pi$
$824$			2245.61i			0.0949389i
$825$	−240.437	−	137.856i	−0.0101466	−	0.00581761i
$826$	−2990.40			−0.125968
$827$	3014.86			0.126768			0.0633838	−	0.997989i	$-0.479811\pi$
$827$	3014.86			0.126768			0.0633838	+	0.997989i	$0.479811\pi$
$828$	−1088.06	−	1858.73i	−0.0456677	−	0.0780137i
$829$		−	18132.4i		−	0.759668i	−0.925055	−	0.379834i	$-0.875981\pi$
$829$		−	18132.4i		−	0.759668i	0.925055	−	0.379834i	$-0.124019\pi$
$830$	−12639.4			−0.528580
$831$	−9924.00	+	17308.6i	−0.414272	+	0.722538i
$832$		−	1051.02i		−	0.0437951i
$833$	−13470.9			−0.560309
$834$	7375.96	+	4229.05i	0.306245	+	0.175588i
$835$		−	20990.6i		−	0.869953i
$836$	−15704.5			−0.649703
$837$	−10982.1	+	21581.7i	−0.453519	+	0.891246i
$838$	7892.03			0.325329
$839$			10654.5i			0.438419i	0.975678	+	0.219209i	$0.0703478\pi$
$839$			10654.5i			0.438419i	−0.975678	+	0.219209i	$0.929652\pi$
$840$	9738.18	+	5583.45i	0.399999	+	0.229342i
$841$	24158.8			0.990561
$842$			1624.04i			0.0664704i
$843$	12161.4	−	21210.9i	0.496869	−	0.866598i
$844$	−1170.75			−0.0477476
$845$		−	24647.2i		−	1.00342i
$846$	4684.58	+	8002.63i	0.190377	+	0.325220i
$847$	1233.37			0.0500342
$848$	7096.36			0.287370
$849$	−15148.4	−	8685.44i	−0.612359	−	0.351100i
$850$			147.198i			0.00593984i
$851$		−	6459.25i		−	0.260188i
$852$	3753.20	−	6546.01i	0.150918	−	0.263219i
$853$	2346.87			0.0942033			0.0471017	−	0.998890i	$-0.485002\pi$
$853$	2346.87			0.0942033			0.0471017	+	0.998890i	$0.485002\pi$
$854$	9296.77			0.372516
$855$	−28687.2	+	16792.9i	−1.14746	+	0.671702i
$856$	−18596.2			−0.742530
$857$		−	28584.4i		−	1.13935i	−0.821869	−	0.569676i	$-0.807069\pi$
$857$		−	28584.4i		−	1.13935i	0.821869	−	0.569676i	$-0.192931\pi$
$858$	744.559	+	426.897i	0.0296257	+	0.0169861i
$859$		−	5232.57i		−	0.207838i	−0.994586	−	0.103919i	$-0.966862\pi$
$859$		−	5232.57i		−	0.207838i	0.994586	−	0.103919i	$-0.0331383\pi$
$860$	19427.9			0.770332
$861$	−1378.08	+	2403.53i	−0.0545469	+	0.0951361i
$862$	−8355.45			−0.330148
$863$	22024.3			0.868731			0.434366	−	0.900737i	$-0.356973\pi$
$863$	22024.3			0.868731			0.434366	+	0.900737i	$0.356973\pi$
$864$	23132.0	−	208.239i	0.910840	−	0.00819958i
$865$	7001.17			0.275199
$866$	−20824.3			−0.817136
$867$	−11556.5	−	6625.97i	−0.452685	−	0.259550i
$868$	−5164.23	−	2686.66i	−0.201942	−	0.105059i
$869$		−	2293.35i		−	0.0895243i
$870$	21835.9	+	12519.7i	0.850926	+	0.487884i
$871$			445.978i			0.0173495i
$872$		−	28385.2i		−	1.10234i
$873$	15620.4	+	26684.3i	0.605580	+	1.03451i
$874$		−	4080.69i		−	0.157930i
$875$			11202.9i			0.432832i
$876$	−3927.73	+	6850.42i	−0.151491	+	0.264217i
$877$	−33249.9			−1.28024			−0.640119	−	0.768275i	$-0.721115\pi$
$877$	−33249.9			−1.28024			−0.640119	+	0.768275i	$0.721115\pi$
$878$		−	2367.10i		−	0.0909860i
$879$	7988.98	−	13933.7i	0.306555	−	0.534667i
$880$			5048.36i			0.193387i
$881$	−24488.6			−0.936484			−0.468242	−	0.883600i	$-0.655112\pi$
$881$	−24488.6			−0.936484			−0.468242	+	0.883600i	$0.655112\pi$
$882$	−12655.8	+	7408.43i	−0.483154	+	0.282828i
$883$			21164.1i			0.806600i	0.915068	+	0.403300i	$0.132137\pi$
$883$			21164.1i			0.806600i	−0.915068	+	0.403300i	$0.867863\pi$
$884$			498.988i			0.0189851i
$885$	9618.95	+	5515.09i	0.365353	+	0.209478i
$886$	35706.5			1.35393
$887$			43717.6i			1.65490i	0.561543	+	0.827448i	$0.310208\pi$
$887$			43717.6i			1.65490i	−0.561543	+	0.827448i	$0.689792\pi$
$888$	36327.0	+	20828.3i	1.37281	+	0.787109i
$889$			19770.1i			0.745857i
$890$	−2273.79			−0.0856378
$891$	−12250.0	+	21818.2i	−0.460594	+	0.820357i
$892$			20278.8i			0.761192i
$893$		−	19232.6i		−	0.720712i
$894$	23177.6	+	13289.0i	0.867087	+	0.497150i
$895$		−	36282.9i		−	1.35509i
$896$			3912.14i			0.145865i
$897$	121.429	−	211.786i	0.00451994	−	0.00788331i
$898$			34080.3i			1.26645i
$899$	−33737.6	−	17551.8i	−1.25162	−	0.651151i
$900$	−88.6183	−	151.386i	−0.00328216	−	0.00560688i
$901$	−26308.0			−0.972748
$902$	−4433.54			−0.163659
$903$	8612.52	−	15021.2i	0.317394	−	0.553572i
$904$	−5250.12			−0.193160
$905$	4719.64			0.173355
$906$	−26253.8	−	15052.8i	−0.962719	−	0.551981i
$907$	32604.5			1.19362			0.596811	−	0.802382i	$-0.296434\pi$
$907$	32604.5			1.19362			0.596811	+	0.802382i	$0.296434\pi$
$908$		−	7886.88i		−	0.288255i
$909$	37596.5	−	22008.2i	1.37183	−	0.803044i
$910$			436.714i			0.0159087i
$911$	−40833.7			−1.48505			−0.742526	−	0.669818i	$-0.766372\pi$
$911$	−40833.7			−1.48505			−0.742526	+	0.669818i	$0.766372\pi$
$912$	6449.90	+	3698.09i	0.234186	+	0.134272i
$913$	19733.2			0.715305
$914$	12170.3			0.440433
$915$	−29904.1	−	17145.7i	−1.08044	−	0.619475i
$916$			13763.9i			0.496476i
$917$		−	6476.35i		−	0.233226i
$918$	13288.8	−	119.629i	0.477773	−	0.00430102i
$919$	−1795.92			−0.0644634			−0.0322317	−	0.999480i	$-0.510261\pi$
$919$	−1795.92			−0.0644634			−0.0322317	+	0.999480i	$0.510261\pi$
$920$	5109.48			0.183103
$921$	6453.80	+	3700.33i	0.230901	+	0.132389i
$922$		−	10067.2i		−	0.359592i
$923$	855.287			0.0305007
$924$	−5218.33	−	2991.96i	−0.185791	−	0.106524i
$925$		−	526.079i		−	0.0186999i
$926$	−8357.90			−0.296607
$927$	−1286.74	−	2198.13i	−0.0455901	−	0.0778813i
$928$			36330.3i			1.28513i
$929$	−24120.5			−0.851850			−0.425925	−	0.904759i	$-0.640051\pi$
$929$	−24120.5			−0.851850			−0.425925	+	0.904759i	$0.640051\pi$
$930$	−10648.2	−	16594.9i	−0.375449	−	0.585126i
$931$	30415.4			1.07070
$932$			27179.1i			0.955238i
$933$	−9435.63	+	16456.8i	−0.331092	+	0.577463i
$934$	−20232.6			−0.708813
$935$		−	18715.6i		−	0.654614i
$936$	799.534	+	1365.84i	0.0279205	+	0.0476964i
$937$	24179.2			0.843009			0.421504	−	0.906826i	$-0.361502\pi$
$937$	24179.2			0.843009			0.421504	+	0.906826i	$0.361502\pi$
$938$			2855.34i			0.0993924i
$939$	465.198	−	811.359i	0.0161674	−	0.0281978i
$940$	8265.45			0.286797
$941$	9608.96			0.332883			0.166442	−	0.986051i	$-0.446772\pi$
$941$	9608.96			0.332883			0.166442	+	0.986051i	$0.446772\pi$
$942$	−1061.23	+	1850.91i	−0.0367058	+	0.0640191i
$943$			1261.10i			0.0435493i
$944$		−	2479.98i		−	0.0855046i
$945$	−12731.6	+	114.612i	−0.438262	+	0.00394533i
$946$	27708.0			0.952290
$947$	6277.62			0.215412			0.107706	−	0.994183i	$-0.465649\pi$
$947$	6277.62			0.215412			0.107706	+	0.994183i	$0.465649\pi$
$948$	721.980	−	1259.22i	0.0247350	−	0.0431408i
$949$	−895.061			−0.0306163
$950$		−	332.355i		−	0.0113505i
$951$	−160.447	+	279.838i	−0.00547092	+	0.00954191i
$952$			9307.86i			0.316880i
$953$	5533.32			0.188082			0.0940409	−	0.995568i	$-0.470022\pi$
$953$	5533.32			0.188082			0.0940409	+	0.995568i	$0.470022\pi$
$954$	−24716.1	+	14468.3i	−0.838799	+	0.491016i
$955$	−31710.7			−1.07449
$956$	−15996.5			−0.541175
$957$	−34091.0	−	19546.3i	−1.15152	−	0.660232i
$958$	−12249.1			−0.413102
$959$	20884.8			0.703239
$960$	−12410.2	+	21644.8i	−0.417225	+	0.727690i
$961$	17099.8	+	24394.7i	0.573992	+	0.818861i
$962$			1629.10i			0.0545992i
$963$	18203.0	−	10655.7i	0.609120	−	0.356566i
$964$		−	27777.4i		−	0.928061i
$965$			48451.5i			1.61628i
$966$	777.437	−	1355.94i	0.0258940	−	0.0451622i
$967$		−	33479.8i		−	1.11338i	−0.830721	−	0.556689i	$-0.812071\pi$
$967$		−	33479.8i		−	1.11338i	0.830721	−	0.556689i	$-0.187929\pi$
$968$			3639.47i			0.120844i
$969$	−23911.4	−	13709.7i	−0.792719	−	0.454510i
$970$	−25176.7			−0.833377
$971$			30574.1i			1.01047i	0.862981	+	0.505237i	$0.168595\pi$
$971$			30574.1i			1.01047i	−0.862981	+	0.505237i	$0.831405\pi$
$972$	−13594.8	+	8123.32i	−0.448615	+	0.268061i
$973$		−	6754.40i		−	0.222545i
$974$	10610.2			0.349049
$975$	9.88987	−	17.2491i	0.000324851	−	0.000566577i
$976$			7709.93i			0.252857i
$977$			30140.9i			0.986993i	0.869748	+	0.493496i	$0.164281\pi$
$977$			30140.9i			0.986993i	−0.869748	+	0.493496i	$0.835719\pi$
$978$	8965.57	−	15637.0i	0.293136	−	0.511264i
$979$	3549.93			0.115890
$980$			13071.4i			0.426072i
$981$	16264.8	+	27784.9i	0.529351	+	0.904286i
$982$			17603.7i			0.572054i
$983$	41311.0			1.34040			0.670201	−	0.742180i	$-0.266208\pi$
$983$	41311.0			1.34040			0.670201	+	0.742180i	$0.266208\pi$
$984$	−7092.44	−	4066.50i	−0.229775	−	0.131743i
$985$			11620.6i			0.375903i
$986$			20871.0i			0.674104i
$987$	3664.13	−	6390.67i	0.118167	−	0.206097i
$988$		−	1126.65i		−	0.0362789i
$989$		−	7881.41i		−	0.253402i
$990$	−10292.8	−	17583.1i	−0.330431	−	0.564473i
$991$			2929.34i			0.0938988i	0.998897	+	0.0469494i	$0.0149500\pi$
$991$			2929.34i			0.0938988i	−0.998897	+	0.0469494i	$0.985050\pi$
$992$	13134.7	−	25247.2i	0.420391	−	0.808064i
$993$	15838.0	−	27623.2i	0.506146	−	0.882777i
$994$	5475.90			0.174733
$995$	−60835.3			−1.93830
$996$	10835.0	+	6212.29i	0.344698	+	0.197635i
$997$	5523.90			0.175470			0.0877350	−	0.996144i	$-0.472037\pi$
$997$	5523.90			0.175470			0.0877350	+	0.996144i	$0.472037\pi$
$998$	−27729.5			−0.879521
$999$	−47493.4	+	427.546i	−1.50413	+	0.0135405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.4.c.b.92.12	yes	28
3.2	odd	2	inner	93.4.c.b.92.17	yes	28
31.30	odd	2	inner	93.4.c.b.92.11	✓	28
93.92	even	2	inner	93.4.c.b.92.18	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.4.c.b.92.11	✓	28	31.30	odd	2	inner
93.4.c.b.92.12	yes	28	1.1	even	1	trivial
93.4.c.b.92.17	yes	28	3.2	odd	2	inner
93.4.c.b.92.18	yes	28	93.92	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	93.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.95427i q^{2} +(4.50778 + 2.58456i) q^{3} +4.18081 q^{4} -11.2496i q^{5} +(5.05094 - 8.80943i) q^{6} -8.06707 q^{7} -23.8046i q^{8} +(13.6401 + 23.3012i) q^{9} -21.9848 q^{10} +34.3236 q^{11} +(18.8462 + 10.8056i) q^{12} +2.46240i q^{13} +15.7653i q^{14} +(29.0753 - 50.7108i) q^{15} -13.0743 q^{16} +48.4699 q^{17} +(45.5370 - 26.6565i) q^{18} -109.439 q^{19} -47.0325i q^{20} +(-36.3646 - 20.8498i) q^{21} -67.0778i q^{22} -19.0799 q^{23} +(61.5246 - 107.306i) q^{24} -1.55398 q^{25} +4.81220 q^{26} +(1.26292 + 140.290i) q^{27} -33.7269 q^{28} -220.336 q^{29} +(-99.1028 - 56.8212i) q^{30} +(153.119 + 79.6593i) q^{31} -164.886i q^{32} +(154.723 + 88.7115i) q^{33} -94.7234i q^{34} +90.7515i q^{35} +(57.0266 + 97.4181i) q^{36} +338.536i q^{37} +213.873i q^{38} +(-6.36422 + 11.0999i) q^{39} -267.793 q^{40} -66.0955i q^{41} +(-40.7463 + 71.0663i) q^{42} +413.073i q^{43} +143.501 q^{44} +(262.130 - 153.446i) q^{45} +37.2874i q^{46} +175.739i q^{47} +(-58.9362 - 33.7914i) q^{48} -277.922 q^{49} +3.03691i q^{50} +(218.491 + 125.273i) q^{51} +10.2948i q^{52} -542.770 q^{53} +(274.166 - 2.46810i) q^{54} -386.128i q^{55} +192.034i q^{56} +(-493.325 - 282.851i) q^{57} +430.596i q^{58} +189.683i q^{59} +(121.558 - 212.012i) q^{60} -589.699i q^{61} +(155.676 - 299.236i) q^{62} +(-110.036 - 187.973i) q^{63} -426.828 q^{64} +27.7010 q^{65} +(173.367 - 302.372i) q^{66} +181.116 q^{67} +202.643 q^{68} +(-86.0081 - 49.3133i) q^{69} +177.353 q^{70} -347.339i q^{71} +(554.678 - 324.697i) q^{72} +363.492i q^{73} +661.593 q^{74} +(-7.00500 - 4.01636i) q^{75} -457.542 q^{76} -276.891 q^{77} +(21.6923 + 12.4374i) q^{78} -66.8156i q^{79} +147.081i q^{80} +(-356.896 + 635.662i) q^{81} -129.169 q^{82} +574.916 q^{83} +(-152.033 - 87.1693i) q^{84} -545.268i q^{85} +807.259 q^{86} +(-993.224 - 569.471i) q^{87} -817.062i q^{88} +103.425 q^{89} +(-299.875 - 512.274i) q^{90} -19.8643i q^{91} -79.7696 q^{92} +(484.341 + 754.832i) q^{93} +343.442 q^{94} +1231.14i q^{95} +(426.159 - 743.271i) q^{96} +1145.19 q^{97} +543.137i q^{98} +(468.177 + 799.783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) \) 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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