LMFDB - Embedded newform 196.4.d.b.195.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,4,Mod(195,196)] 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("196.195"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] 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:	$11.5643743611$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 $ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{34}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.16
Root			$-2.82600 - 0.117237i$ of defining polynomial
Character	$\chi$	$=$	196.195
Dual form			196.4.d.b.195.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.51453 + 2.38877i) q^{2} +0.0938614 q^{3} +(-3.41241 + 7.23571i) q^{4} +14.4177i q^{5} +(0.142156 + 0.224213i) q^{6} +(-22.4526 + 2.80725i) q^{8} -26.9912 q^{9} +(-34.4404 + 21.8360i) q^{10} -36.5134i q^{11} +(-0.320293 + 0.679154i) q^{12} +15.3232i q^{13} +1.35326i q^{15} +(-40.7110 - 49.3824i) q^{16} +62.5279i q^{17} +(-40.8789 - 64.4756i) q^{18} +69.3558 q^{19} +(-104.322 - 49.1989i) q^{20} +(87.2219 - 55.3005i) q^{22} -14.2997i q^{23} +(-2.10743 + 0.263492i) q^{24} -82.8691 q^{25} +(-36.6035 + 23.2074i) q^{26} -5.06769 q^{27} -157.182 q^{29} +(-3.23263 + 2.04955i) q^{30} -331.140 q^{31} +(56.3050 - 172.040i) q^{32} -3.42720i q^{33} +(-149.365 + 94.7003i) q^{34} +(92.1049 - 195.300i) q^{36} +76.1258 q^{37} +(105.041 + 165.675i) q^{38} +1.43825i q^{39} +(-40.4739 - 323.714i) q^{40} +335.509i q^{41} +484.545i q^{43} +(264.200 + 124.598i) q^{44} -389.150i q^{45} +(34.1587 - 21.6574i) q^{46} +374.813 q^{47} +(-3.82119 - 4.63510i) q^{48} +(-125.508 - 197.955i) q^{50} +5.86896i q^{51} +(-110.874 - 52.2889i) q^{52} -141.769 q^{53} +(-7.67516 - 12.1055i) q^{54} +526.438 q^{55} +6.50983 q^{57} +(-238.057 - 375.471i) q^{58} +319.890 q^{59} +(-9.79181 - 4.61788i) q^{60} +246.970i q^{61} +(-501.521 - 791.016i) q^{62} +(496.239 - 126.060i) q^{64} -220.924 q^{65} +(8.18677 - 5.19059i) q^{66} +205.547i q^{67} +(-452.434 - 213.371i) q^{68} -1.34219i q^{69} -82.4401i q^{71} +(606.022 - 75.7709i) q^{72} +663.980i q^{73} +(115.295 + 181.847i) q^{74} -7.77821 q^{75} +(-236.670 + 501.838i) q^{76} +(-3.43565 + 2.17828i) q^{78} +651.401i q^{79} +(711.978 - 586.957i) q^{80} +728.286 q^{81} +(-801.453 + 508.138i) q^{82} +790.194 q^{83} -901.506 q^{85} +(-1157.46 + 733.857i) q^{86} -14.7533 q^{87} +(102.502 + 819.820i) q^{88} +728.973i q^{89} +(929.588 - 589.379i) q^{90} +(103.469 + 48.7965i) q^{92} -31.0813 q^{93} +(567.664 + 895.339i) q^{94} +999.949i q^{95} +(5.28487 - 16.1479i) q^{96} -386.693i q^{97} +985.539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9} + 208 q^{16} - 136 q^{18} - 184 q^{22} + 72 q^{25} - 352 q^{29} - 1288 q^{30} + 80 q^{32} + 208 q^{36} - 516 q^{37} + 2496 q^{44} - 464 q^{46} - 864 q^{50} - 1140 q^{53}+ \cdots + 612 q^{93}+O(q^{100}) $ 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9 + 208 * q^16 - 136 * q^18 - 184 * q^22 + 72 * q^25 - 352 * q^29 - 1288 * q^30 + 80 * q^32 + 208 * q^36 - 516 * q^37 + 2496 * q^44 - 464 * q^46 - 864 * q^50 - 1140 * q^53 + 1452 * q^57 - 4488 * q^58 + 1472 * q^60 + 2560 * q^64 + 248 * q^65 + 9344 * q^72 - 1664 * q^74 - 4056 * q^78 + 2524 * q^81 - 2980 * q^85 - 11392 * q^86 + 2792 * q^88 + 3312 * q^92 + 612 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.51453	+	2.38877i	0.535467	+	0.844556i
$2$	1.51453	+	2.38877i	0.535467	+	0.844556i
$3$	0.0938614			0.0180636			0.00903182	−	0.999959i	$-0.497125\pi$
$3$	0.0938614			0.0180636			0.00903182	+	0.999959i	$0.497125\pi$
$4$	−3.41241	+	7.23571i	−0.426551	+	0.904464i
$5$			14.4177i			1.28956i	0.764370	+	0.644778i	$0.223050\pi$
$5$			14.4177i			1.28956i	−0.764370	+	0.644778i	$0.776950\pi$
$6$	0.142156	+	0.224213i	0.00967247	+	0.0152558i
$7$		0			0
$7$		0			0
$8$	−22.4526	+	2.80725i	−0.992274	+	0.124064i
$9$	−26.9912			−0.999674
$10$	−34.4404	+	21.8360i	−1.08910	+	0.690514i
$11$		−	36.5134i		−	1.00084i	−0.865784	−	0.500418i	$-0.833180\pi$
$11$		−	36.5134i		−	1.00084i	0.865784	−	0.500418i	$-0.166820\pi$
$12$	−0.320293	+	0.679154i	−0.00770506	+	0.0163379i
$13$			15.3232i			0.326914i	0.986550	+	0.163457i	$0.0522645\pi$
$13$			15.3232i			0.326914i	−0.986550	+	0.163457i	$0.947735\pi$
$14$		0			0
$15$			1.35326i			0.0232941i
$16$	−40.7110	−	49.3824i	−0.636109	−	0.771599i
$17$			62.5279i			0.892073i	0.895015	+	0.446037i	$0.147165\pi$
$17$			62.5279i			0.892073i	−0.895015	+	0.446037i	$0.852835\pi$
$18$	−40.8789	−	64.4756i	−0.535292	−	0.844281i
$19$	69.3558			0.837438			0.418719	−	0.908116i	$-0.362479\pi$
$19$	69.3558			0.837438			0.418719	+	0.908116i	$0.362479\pi$
$20$	−104.322	−	49.1989i	−1.16636	−	0.550061i
$21$		0			0
$22$	87.2219	−	55.3005i	0.845262	−	0.535914i
$23$		−	14.2997i		−	0.129639i	−0.997897	−	0.0648196i	$-0.979353\pi$
$23$		−	14.2997i		−	0.129639i	0.997897	−	0.0648196i	$-0.0206472\pi$
$24$	−2.10743	+	0.263492i	−0.0179241	+	0.00224104i
$25$	−82.8691			−0.662953
$26$	−36.6035	+	23.2074i	−0.276097	+	0.175052i
$27$	−5.06769			−0.0361214
$28$		0			0
$29$	−157.182			−1.00648			−0.503241	−	0.864146i	$-0.667859\pi$
$29$	−157.182			−1.00648			−0.503241	+	0.864146i	$0.667859\pi$
$30$	−3.23263	+	2.04955i	−0.0196731	+	0.0124732i
$31$	−331.140			−1.91853			−0.959266	−	0.282505i	$-0.908835\pi$
$31$	−331.140			−1.91853			−0.959266	+	0.282505i	$0.908835\pi$
$32$	56.3050	−	172.040i	0.311044	−	0.950395i
$33$		−	3.42720i		−	0.0180787i
$34$	−149.365	+	94.7003i	−0.753406	+	0.477675i
$35$		0			0
$36$	92.1049	−	195.300i	0.426412	−	0.904168i
$37$	76.1258			0.338243			0.169122	−	0.985595i	$-0.445907\pi$
$37$	76.1258			0.338243			0.169122	+	0.985595i	$0.445907\pi$
$38$	105.041	+	165.675i	0.448420	+	0.707263i
$39$			1.43825i			0.00590526i
$40$	−40.4739	−	323.714i	−0.159987	−	1.27959i
$41$			335.509i			1.27799i	0.769209	+	0.638997i	$0.220650\pi$
$41$			335.509i			1.27799i	−0.769209	+	0.638997i	$0.779350\pi$
$42$		0			0
$43$			484.545i			1.71843i	0.511617	+	0.859213i	$0.329047\pi$
$43$			484.545i			1.71843i	−0.511617	+	0.859213i	$0.670953\pi$
$44$	264.200	+	124.598i	0.905220	+	0.426907i
$45$		−	389.150i		−	1.28913i
$46$	34.1587	−	21.6574i	0.109488	−	0.0694175i
$47$	374.813			1.16323			0.581617	−	0.813463i	$-0.302420\pi$
$47$	374.813			1.16323			0.581617	+	0.813463i	$0.302420\pi$
$48$	−3.82119	−	4.63510i	−0.0114904	−	0.0139379i
$49$		0			0
$50$	−125.508	−	197.955i	−0.354989	−	0.559901i
$51$			5.86896i			0.0161141i
$52$	−110.874	−	52.2889i	−0.295682	−	0.139446i
$53$	−141.769			−0.367425			−0.183712	−	0.982980i	$-0.558812\pi$
$53$	−141.769			−0.367425			−0.183712	+	0.982980i	$0.558812\pi$
$54$	−7.67516	−	12.1055i	−0.0193418	−	0.0305065i
$55$	526.438			1.29063
$56$		0			0
$57$	6.50983			0.0151272
$58$	−238.057	−	375.471i	−0.538938	−	0.850031i
$59$	319.890			0.705866			0.352933	−	0.935649i	$-0.385184\pi$
$59$	319.890			0.705866			0.352933	+	0.935649i	$0.385184\pi$
$60$	−9.79181	−	4.61788i	−0.0210686	−	0.00993610i
$61$			246.970i			0.518382i	0.965826	+	0.259191i	$0.0834559\pi$
$61$			246.970i			0.518382i	−0.965826	+	0.259191i	$0.916544\pi$
$62$	−501.521	−	791.016i	−1.02731	−	1.62031i
$63$		0			0
$64$	496.239	−	126.060i	0.969216	−	0.246211i
$65$	−220.924			−0.421574
$66$	8.18677	−	5.19059i	0.0152685	−	0.00968056i
$67$			205.547i			0.374800i	0.982284	+	0.187400i	$0.0600060\pi$
$67$			205.547i			0.374800i	−0.982284	+	0.187400i	$0.939994\pi$
$68$	−452.434	−	213.371i	−0.806848	−	0.380515i
$69$		−	1.34219i		−	0.00234176i
$70$		0			0
$71$		−	82.4401i		−	0.137801i	−0.997624	−	0.0689003i	$-0.978051\pi$
$71$		−	82.4401i		−	0.137801i	0.997624	−	0.0689003i	$-0.0219490\pi$
$72$	606.022	−	75.7709i	0.991950	−	0.124023i
$73$			663.980i			1.06456i	0.846568	+	0.532280i	$0.178665\pi$
$73$			663.980i			1.06456i	−0.846568	+	0.532280i	$0.821335\pi$
$74$	115.295	+	181.847i	0.181118	+	0.285666i
$75$	−7.77821			−0.0119753
$76$	−236.670	+	501.838i	−0.357210	+	0.757432i
$77$		0			0
$78$	−3.43565	+	2.17828i	−0.00498732	+	0.00316207i
$79$			651.401i			0.927700i	0.885914	+	0.463850i	$0.153532\pi$
$79$			651.401i			0.927700i	−0.885914	+	0.463850i	$0.846468\pi$
$80$	711.978	−	586.957i	0.995020	−	0.820297i
$81$	728.286			0.999021
$82$	−801.453	+	508.138i	−1.07934	+	0.684323i
$83$	790.194			1.04500			0.522500	−	0.852639i	$-0.324999\pi$
$83$	790.194			1.04500			0.522500	+	0.852639i	$0.324999\pi$
$84$		0			0
$85$	−901.506			−1.15038
$86$	−1157.46	+	733.857i	−1.45131	+	0.920160i
$87$	−14.7533			−0.0181807
$88$	102.502	+	819.820i	0.124168	+	0.993104i
$89$			728.973i			0.868214i	0.900861	+	0.434107i	$0.142936\pi$
$89$			728.973i			0.868214i	−0.900861	+	0.434107i	$0.857064\pi$
$90$	929.588	−	589.379i	1.08875	−	0.690289i
$91$		0			0
$92$	103.469	+	48.7965i	0.117254	+	0.0552977i
$93$	−31.0813			−0.0346557
$94$	567.664	+	895.339i	0.622873	+	0.982417i
$95$			999.949i			1.07992i
$96$	5.28487	−	16.1479i	0.00561859	−	0.0171676i
$97$		−	386.693i		−	0.404771i	−0.979306	−	0.202385i	$-0.935131\pi$
$97$		−	386.693i		−	0.404771i	0.979306	−	0.202385i	$-0.0648694\pi$
$98$		0			0
$99$			985.539i			1.00051i
$100$	282.783	−	599.617i	0.282783	−	0.599617i
$101$		−	1308.90i		−	1.28951i	−0.764391	−	0.644753i	$-0.776960\pi$
$101$		−	1308.90i		−	1.28951i	0.764391	−	0.644753i	$-0.223040\pi$
$102$	−14.0196	+	8.88870i	−0.0136093	+	0.00862855i
$103$	119.667			0.114478			0.0572388	−	0.998361i	$-0.481770\pi$
$103$	119.667			0.114478			0.0572388	+	0.998361i	$0.481770\pi$
$104$	−43.0159	−	344.045i	−0.0405582	−	0.324389i
$105$		0			0
$106$	−214.714	−	338.654i	−0.196744	−	0.310311i
$107$		−	777.048i		−	0.702057i	−0.936365	−	0.351028i	$-0.885832\pi$
$107$		−	777.048i		−	0.702057i	0.936365	−	0.351028i	$-0.114168\pi$
$108$	17.2930	−	36.6683i	0.0154076	−	0.0326705i
$109$	−1253.24			−1.10127			−0.550636	−	0.834746i	$-0.685615\pi$
$109$	−1253.24			−1.10127			−0.550636	+	0.834746i	$0.685615\pi$
$110$	797.305	+	1257.54i	0.691091	+	1.09001i
$111$	7.14527			0.00610990
$112$		0			0
$113$	1151.72			0.958799			0.479400	−	0.877597i	$-0.340854\pi$
$113$	1151.72			0.958799			0.479400	+	0.877597i	$0.340854\pi$
$114$	9.85933	+	15.5505i	0.00810009	+	0.0127757i
$115$	206.169			0.167177
$116$	536.369	−	1137.32i	0.429316	−	0.910327i
$117$		−	413.591i		−	0.326808i
$118$	484.482	+	764.142i	0.377968	+	0.596143i
$119$		0			0
$120$	−3.79894	−	30.3843i	−0.00288995	−	0.0231141i
$121$	−2.22648			−0.00167279
$122$	−589.954	+	374.043i	−0.437803	+	0.277576i
$123$			31.4914i			0.0230852i
$124$	1129.98	−	2396.03i	0.818351	−	1.73524i
$125$			607.429i			0.434641i
$126$		0			0
$127$		−	146.370i		−	0.102270i	−0.998692	−	0.0511348i	$-0.983716\pi$
$127$		−	146.370i		−	0.102270i	0.998692	−	0.0511348i	$-0.0162838\pi$
$128$	1052.70	+	994.477i	0.726922	+	0.686720i
$129$			45.4800i			0.0310410i
$130$	−334.596	−	527.737i	−0.225739	−	0.356043i
$131$	−1424.66			−0.950175			−0.475088	−	0.879938i	$-0.657584\pi$
$131$	−1424.66			−0.950175			−0.475088	+	0.879938i	$0.657584\pi$
$132$	24.7982	+	11.6950i	0.0163516	+	0.00771150i
$133$		0			0
$134$	−491.004	+	311.307i	−0.316539	+	0.200693i
$135$		−	73.0642i		−	0.0465805i
$136$	−175.531	−	1403.91i	−0.110674	−	0.885181i
$137$	1369.02			0.853745			0.426872	−	0.904312i	$-0.359615\pi$
$137$	1369.02			0.853745			0.426872	+	0.904312i	$0.359615\pi$
$138$	3.20619	−	2.03279i	0.00197774	−	0.00125393i
$139$	−1844.54			−1.12556			−0.562778	−	0.826608i	$-0.690267\pi$
$139$	−1844.54			−1.12556			−0.562778	+	0.826608i	$0.690267\pi$
$140$		0			0
$141$	35.1804			0.0210122
$142$	196.930	−	124.858i	0.116380	−	0.0737876i
$143$	559.501			0.327188
$144$	1098.84	+	1332.89i	0.635901	+	0.771348i
$145$		−	2266.20i		−	1.29791i
$146$	−1586.09	+	1005.62i	−0.899081	+	0.570037i
$147$		0			0
$148$	−259.772	+	550.824i	−0.144278	+	0.305929i
$149$	1462.79			0.804269			0.402135	−	0.915581i	$-0.368268\pi$
$149$	1462.79			0.804269			0.402135	+	0.915581i	$0.368268\pi$
$150$	−11.7803	−	18.5803i	−0.00641239	−	0.0101138i
$151$		−	2387.86i		−	1.28689i	−0.765490	−	0.643447i	$-0.777504\pi$
$151$		−	2387.86i		−	1.28689i	0.765490	−	0.643447i	$-0.222496\pi$
$152$	−1557.22	+	194.699i	−0.830968	+	0.103896i
$153$		−	1687.70i		−	0.891782i
$154$		0			0
$155$		−	4774.27i		−	2.47405i
$156$	−10.4068	−	4.90791i	−0.00534109	−	0.00251889i
$157$			2212.46i			1.12467i	0.826909	+	0.562335i	$0.190097\pi$
$157$			2212.46i			1.12467i	−0.826909	+	0.562335i	$0.809903\pi$
$158$	−1556.04	+	986.565i	−0.783495	+	0.496753i
$159$	−13.3067			−0.00663703
$160$	2480.41	+	811.787i	1.22559	+	0.401109i
$161$		0			0
$162$	1103.01	+	1739.71i	0.534943	+	0.843730i
$163$			1023.96i			0.492044i	0.969264	+	0.246022i	$0.0791235\pi$
$163$			1023.96i			0.492044i	−0.969264	+	0.246022i	$0.920876\pi$
$164$	−2427.65	−	1144.89i	−1.15590	−	0.545129i
$165$	49.4122			0.0233135
$166$	1196.77	+	1887.59i	0.559563	+	0.882562i
$167$	−3232.62			−1.49789			−0.748945	−	0.662632i	$-0.769439\pi$
$167$	−3232.62			−1.49789			−0.748945	+	0.662632i	$0.769439\pi$
$168$		0			0
$169$	1962.20			0.893127
$170$	−1365.36	−	2153.49i	−0.615989	−	0.971559i
$171$	−1872.00			−0.837164
$172$	−3506.02	−	1653.46i	−1.55425	−	0.732996i
$173$		−	49.7782i		−	0.0218761i	−0.999940	−	0.0109381i	$-0.996518\pi$
$173$		−	49.7782i		−	0.0218761i	0.999940	−	0.0109381i	$-0.00348176\pi$
$174$	−22.3443	−	35.2423i	−0.00973518	−	0.0153547i
$175$		0			0
$176$	−1803.12	+	1486.49i	−0.772245	+	0.636641i
$177$	30.0253			0.0127505
$178$	−1741.35	+	1104.05i	−0.733255	+	0.464899i
$179$		−	2911.41i		−	1.21569i	−0.794054	−	0.607847i	$-0.792033\pi$
$179$		−	2911.41i		−	1.21569i	0.794054	−	0.607847i	$-0.207967\pi$
$180$	2815.78	+	1327.94i	1.16598	+	0.549881i
$181$			1071.48i			0.440015i	0.975498	+	0.220008i	$0.0706082\pi$
$181$			1071.48i			0.440015i	−0.975498	+	0.220008i	$0.929392\pi$
$182$		0			0
$183$			23.1810i			0.00936386i
$184$	40.1429	+	321.066i	0.0160835	+	0.128638i
$185$			1097.56i			0.436183i
$186$	−47.0734	−	74.2459i	−0.0185570	−	0.0292687i
$187$	2283.10			0.892819
$188$	−1279.01	+	2712.03i	−0.496179	+	1.05210i
$189$		0			0
$190$	−2388.64	+	1514.45i	−0.912055	+	0.578262i
$191$		−	3067.23i		−	1.16197i	−0.813913	−	0.580987i	$-0.802667\pi$
$191$		−	3067.23i		−	1.16197i	0.813913	−	0.580987i	$-0.197333\pi$
$192$	46.5777	−	11.8322i	0.0175076	−	0.00444746i
$193$	−1080.23			−0.402882			−0.201441	−	0.979501i	$-0.564562\pi$
$193$	−1080.23			−0.402882			−0.201441	+	0.979501i	$0.564562\pi$
$194$	923.720	−	585.658i	0.341852	−	0.216741i
$195$	−20.7363			−0.00761516
$196$		0			0
$197$	−1207.76			−0.436798			−0.218399	−	0.975860i	$-0.570083\pi$
$197$	−1207.76			−0.436798			−0.218399	+	0.975860i	$0.570083\pi$
$198$	−2354.22	+	1492.63i	−0.844987	+	0.535739i
$199$	2056.94			0.732728			0.366364	−	0.930472i	$-0.380603\pi$
$199$	2056.94			0.732728			0.366364	+	0.930472i	$0.380603\pi$
$200$	1860.63	−	232.634i	0.657831	−	0.0822485i
$201$			19.2929i			0.00677024i
$202$	3126.65	−	1982.36i	1.08906	−	0.690487i
$203$		0			0
$204$	−42.4661	−	20.0273i	−0.0145746	−	0.00687348i
$205$	−4837.26			−1.64804
$206$	181.240	+	285.858i	0.0612989	+	0.0966827i
$207$			385.967i			0.129597i
$208$	756.695	−	623.821i	0.252247	−	0.207953i
$209$		−	2532.41i		−	0.838138i
$210$		0			0
$211$			762.431i			0.248758i	0.992235	+	0.124379i	$0.0396938\pi$
$211$			762.431i			0.248758i	−0.992235	+	0.124379i	$0.960306\pi$
$212$	483.775	−	1025.80i	0.156725	−	0.332322i
$213$		−	7.73794i		−	0.00248918i
$214$	1856.19	−	1176.86i	0.592927	−	0.375928i
$215$	−6986.00			−2.21601
$216$	113.783	−	14.2262i	0.0358423	−	0.00448136i
$217$		0			0
$218$	−1898.07	−	2993.70i	−0.589694	−	0.930086i
$219$			62.3220i			0.0192298i
$220$	−1796.42	+	3809.15i	−0.550521	+	1.16733i
$221$	−958.126			−0.291631
$222$	10.8217	+	17.0684i	0.00327165	+	0.00516016i
$223$	−1016.07			−0.305118			−0.152559	−	0.988294i	$-0.548751\pi$
$223$	−1016.07			−0.305118			−0.152559	+	0.988294i	$0.548751\pi$
$224$		0			0
$225$	2236.74			0.662736
$226$	1744.31	+	2751.18i	0.513405	+	0.809760i
$227$	−1139.76			−0.333253			−0.166627	−	0.986020i	$-0.553287\pi$
$227$	−1139.76			−0.333253			−0.166627	+	0.986020i	$0.553287\pi$
$228$	−22.2142	+	47.1033i	−0.00645251	+	0.0136820i
$229$			3418.58i			0.986491i	0.869890	+	0.493245i	$0.164190\pi$
$229$			3418.58i			0.986491i	−0.869890	+	0.493245i	$0.835810\pi$
$230$	312.249	+	492.489i	0.0895177	+	0.141190i
$231$		0			0
$232$	3529.15	−	441.249i	0.998707	−	0.124868i
$233$	2676.22			0.752467			0.376234	−	0.926525i	$-0.377219\pi$
$233$	2676.22			0.752467			0.376234	+	0.926525i	$0.377219\pi$
$234$	987.972	−	626.395i	0.276007	−	0.174995i
$235$			5403.92i			1.50006i
$236$	−1091.59	+	2314.63i	−0.301088	+	0.638430i
$237$			61.1414i			0.0167576i
$238$		0			0
$239$		−	747.415i		−	0.202285i	−0.994872	−	0.101143i	$-0.967750\pi$
$239$		−	747.415i		−	0.202285i	0.994872	−	0.101143i	$-0.0322499\pi$
$240$	66.8273	−	55.0926i	0.0179737	−	0.0148176i
$241$		−	1714.96i		−	0.458383i	−0.973381	−	0.229192i	$-0.926392\pi$
$241$		−	1714.96i		−	0.458383i	0.973381	−	0.229192i	$-0.0736082\pi$
$242$	−3.37207	−	5.31854i	−0.000895722	−	0.00141276i
$243$	205.186			0.0541673
$244$	−1787.00	−	842.763i	−0.468857	−	0.221116i
$245$		0			0
$246$	−75.2255	+	47.6946i	−0.0194968	+	0.0123614i
$247$			1062.75i			0.273770i
$248$	7434.95	−	929.591i	1.90371	−	0.238021i
$249$	74.1687			0.0188765
$250$	−1451.01	+	919.969i	−0.367079	+	0.232736i
$251$	−1604.07			−0.403379			−0.201690	−	0.979449i	$-0.564643\pi$
$251$	−1604.07			−0.403379			−0.201690	+	0.979449i	$0.564643\pi$
$252$		0			0
$253$	−522.132			−0.129748
$254$	349.644	−	221.682i	0.0863725	−	0.0547620i
$255$	−84.6166			−0.0207800
$256$	−781.236	+	4020.81i	−0.190731	+	0.981642i
$257$		−	5179.48i		−	1.25715i	−0.777749	−	0.628575i	$-0.783639\pi$
$257$		−	5179.48i		−	1.25715i	0.777749	−	0.628575i	$-0.216361\pi$
$258$	−108.641	+	68.8808i	−0.0262159	+	0.0166214i
$259$		0			0
$260$	753.884	−	1598.54i	0.179823	−	0.381298i
$261$	4242.53			1.00615
$262$	−2157.69	−	3403.17i	−0.508787	−	0.802477i
$263$		−	958.592i		−	0.224750i	−0.993666	−	0.112375i	$-0.964154\pi$
$263$		−	958.592i		−	0.224750i	0.993666	−	0.112375i	$-0.0358458\pi$
$264$	9.62098	+	76.9495i	0.00224292	+	0.0179391i
$265$		−	2043.98i		−	0.473815i
$266$		0			0
$267$			68.4224i			0.0156831i
$268$	−1487.28	−	701.410i	−0.338993	−	0.159871i
$269$		−	2293.88i		−	0.519927i	−0.965618	−	0.259963i	$-0.916289\pi$
$269$		−	2293.88i		−	0.519927i	0.965618	−	0.259963i	$-0.0837105\pi$
$270$	174.533	−	110.658i	0.0393399	−	0.0249423i
$271$	6273.87			1.40631			0.703156	−	0.711036i	$-0.251774\pi$
$271$	6273.87			1.40631			0.703156	+	0.711036i	$0.251774\pi$
$272$	3087.78	−	2545.57i	0.688323	−	0.567456i
$273$		0			0
$274$	2073.42	+	3270.26i	0.457152	+	0.721035i
$275$			3025.83i			0.663507i
$276$	9.71172	+	4.58011i	0.00211803	+	0.000998878i
$277$	7261.82			1.57516			0.787582	−	0.616210i	$-0.211333\pi$
$277$	7261.82			1.57516			0.787582	+	0.616210i	$0.211333\pi$
$278$	−2793.61	−	4406.18i	−0.602697	−	0.950595i
$279$	8937.86			1.91791
$280$		0			0
$281$	−3850.59			−0.817463			−0.408732	−	0.912655i	$-0.634029\pi$
$281$	−3850.59			−0.817463			−0.408732	+	0.912655i	$0.634029\pi$
$282$	53.2818	+	84.0378i	0.0112514	+	0.0177460i
$283$	4941.52			1.03796			0.518980	−	0.854786i	$-0.326312\pi$
$283$	4941.52			1.03796			0.518980	+	0.854786i	$0.326312\pi$
$284$	596.512	+	281.319i	0.124636	+	0.0587789i
$285$			93.8566i			0.0195073i
$286$	847.380	+	1336.52i	0.175198	+	0.276328i
$287$		0			0
$288$	−1519.74	+	4643.56i	−0.310943	+	0.950085i
$289$	1003.26			0.204205
$290$	5413.42	−	3432.22i	1.09616	−	0.694990i
$291$		−	36.2956i		−	0.00731163i
$292$	−4804.36	−	2265.77i	−0.962856	−	0.454089i
$293$			6898.69i			1.37551i	0.725941	+	0.687757i	$0.241405\pi$
$293$			6898.69i			1.37551i	−0.725941	+	0.687757i	$0.758595\pi$
$294$		0			0
$295$			4612.06i			0.910253i
$296$	−1709.22	+	213.704i	−0.335630	+	0.0419638i
$297$			185.038i			0.0361516i
$298$	2215.43	+	3494.25i	0.430659	+	0.679251i
$299$	219.117			0.0423809
$300$	26.5424	−	56.2808i	0.00510809	−	0.0108313i
$301$		0			0
$302$	5704.03	−	3616.48i	1.08686	−	0.689089i
$303$		−	122.855i		−	0.0232931i
$304$	−2823.54	−	3424.95i	−0.532701	−	0.646166i
$305$	−3560.73			−0.668482
$306$	4031.53	−	2556.07i	0.753160	−	0.477520i
$307$	7512.51			1.39662			0.698308	−	0.715797i	$-0.253936\pi$
$307$	7512.51			1.39662			0.698308	+	0.715797i	$0.253936\pi$
$308$		0			0
$309$	11.2322			0.00206788
$310$	11404.6	−	7230.76i	2.08948	−	1.32477i
$311$	767.233			0.139890			0.0699450	−	0.997551i	$-0.477718\pi$
$311$	767.233			0.139890			0.0699450	+	0.997551i	$0.477718\pi$
$312$	−4.03753	−	32.2926i	−0.000732629	−	0.00585964i
$313$			2841.04i			0.513051i	0.966537	+	0.256525i	$0.0825777\pi$
$313$			2841.04i			0.513051i	−0.966537	+	0.256525i	$0.917422\pi$
$314$	−5285.04	+	3350.83i	−0.949847	+	0.602223i
$315$		0			0
$316$	−4713.35	−	2222.84i	−0.839071	−	0.395711i
$317$	−5719.70			−1.01341			−0.506704	−	0.862120i	$-0.669136\pi$
$317$	−5719.70			−1.01341			−0.506704	+	0.862120i	$0.669136\pi$
$318$	−20.1533	−	31.7865i	−0.00355391	−	0.00560534i
$319$			5739.25i			1.00732i
$320$	1817.49	+	7154.60i	0.317502	+	1.24986i
$321$		−	72.9348i		−	0.0126817i
$322$		0			0
$323$			4336.67i			0.747056i
$324$	−2485.21	+	5269.67i	−0.426133	+	0.903578i
$325$		−	1269.82i		−	0.216729i
$326$	−2446.01	+	1550.82i	−0.415559	+	0.263473i
$327$	−117.631			−0.0198930
$328$	−941.857	−	7533.06i	−0.158553	−	1.26812i
$329$		0			0
$330$	74.8361	+	118.034i	0.0124836	+	0.0196896i
$331$			1925.09i			0.319675i	0.987143	+	0.159838i	$0.0510971\pi$
$331$			1925.09i			0.319675i	−0.987143	+	0.159838i	$0.948903\pi$
$332$	−2696.46	+	5717.61i	−0.445746	+	0.945165i
$333$	−2054.73			−0.338133
$334$	−4895.89	−	7721.97i	−0.802070	−	1.26505i
$335$	−2963.51			−0.483325
$336$		0			0
$337$	4006.13			0.647561			0.323780	−	0.946132i	$-0.395046\pi$
$337$	4006.13			0.647561			0.323780	+	0.946132i	$0.395046\pi$
$338$	2971.81	+	4687.24i	0.478240	+	0.754296i
$339$	108.102			0.0173194
$340$	3076.31	−	6523.04i	0.490695	−	1.04047i
$341$			12091.0i			1.92014i
$342$	−2835.19	−	4471.76i	−0.448274	−	0.707032i
$343$		0			0
$344$	−1360.24	−	10879.3i	−0.213195	−	1.70515i
$345$	19.3513			0.00301982
$346$	118.908	−	75.3905i	0.0184756	−	0.0117139i
$347$		−	1939.80i		−	0.300098i	−0.988679	−	0.150049i	$-0.952057\pi$
$347$		−	1939.80i		−	0.300098i	0.988679	−	0.150049i	$-0.0479431\pi$
$348$	50.3444	−	106.751i	0.00775501	−	0.0164438i
$349$			1677.48i			0.257288i	0.991691	+	0.128644i	$0.0410624\pi$
$349$			1677.48i			0.257288i	−0.991691	+	0.128644i	$0.958938\pi$
$350$		0			0
$351$		−	77.6531i		−	0.0118086i
$352$	−6281.76	−	2055.89i	−0.951190	−	0.311304i
$353$		−	2399.66i		−	0.361817i	−0.983500	−	0.180908i	$-0.942096\pi$
$353$		−	2399.66i		−	0.361817i	0.983500	−	0.180908i	$-0.0579037\pi$
$354$	45.4742	+	71.7234i	0.00682747	+	0.0107685i
$355$	1188.59			0.177701
$356$	−5274.64	−	2487.55i	−0.785268	−	0.370337i
$357$		0			0
$358$	6954.68	−	4409.42i	1.02672	−	0.650964i
$359$			1500.05i			0.220528i	0.993902	+	0.110264i	$0.0351697\pi$
$359$			1500.05i			0.220528i	−0.993902	+	0.110264i	$0.964830\pi$
$360$	1092.44	+	8737.43i	0.159935	+	1.27917i
$361$	−2048.77			−0.298698
$362$	−2559.52	+	1622.79i	−0.371618	+	0.235614i
$363$	−0.208981			−3.02166e−5
$364$		0			0
$365$	−9573.04			−1.37281
$366$	−55.3739	+	35.1082i	−0.00790831	+	0.00501403i
$367$	−9207.02			−1.30954			−0.654772	−	0.755826i	$-0.727235\pi$
$367$	−9207.02			−1.30954			−0.654772	+	0.755826i	$0.727235\pi$
$368$	−706.155	+	582.156i	−0.100030	+	0.0824646i
$369$		−	9055.80i		−	1.27758i
$370$	−2621.81	+	1662.28i	−0.368382	+	0.233562i
$371$		0			0
$372$	106.062	−	224.895i	0.0147824	−	0.0313448i
$373$	−437.476			−0.0607283			−0.0303642	−	0.999539i	$-0.509667\pi$
$373$	−437.476			−0.0607283			−0.0303642	+	0.999539i	$0.509667\pi$
$374$	3457.83	+	5453.80i	0.478075	+	0.754036i
$375$			57.0142i			0.00785120i
$376$	−8415.52	+	1052.19i	−1.15425	+	0.144315i
$377$		−	2408.53i		−	0.329033i
$378$		0			0
$379$			8880.19i			1.20355i	0.798667	+	0.601774i	$0.205539\pi$
$379$			8880.19i			1.20355i	−0.798667	+	0.601774i	$0.794461\pi$
$380$	−7235.34	−	3412.23i	−0.976750	−	0.460642i
$381$		−	13.7385i		−	0.00184736i
$382$	7326.90	−	4645.41i	0.981353	−	0.622199i
$383$	6355.65			0.847933			0.423967	−	0.905678i	$-0.360637\pi$
$383$	6355.65			0.847933			0.423967	+	0.905678i	$0.360637\pi$
$384$	98.8075	+	93.3430i	0.0131309	+	0.0124047i
$385$		0			0
$386$	−1636.03	−	2580.41i	−0.215730	−	0.340257i
$387$		−	13078.4i		−	1.71787i
$388$	2798.00	+	1319.56i	0.366101	+	0.172655i
$389$	−2866.03			−0.373556			−0.186778	−	0.982402i	$-0.559805\pi$
$389$	−2866.03			−0.373556			−0.186778	+	0.982402i	$0.559805\pi$
$390$	−31.4057	−	49.5341i	−0.00407766	−	0.00643143i
$391$	894.133			0.115648
$392$		0			0
$393$	−133.720			−0.0171636
$394$	−1829.18	−	2885.05i	−0.233891	−	0.368900i
$395$	−9391.68			−1.19632
$396$	−7131.08	−	3363.06i	−0.904924	−	0.426768i
$397$			5626.02i			0.711239i	0.934631	+	0.355619i	$0.115730\pi$
$397$			5626.02i			0.711239i	−0.934631	+	0.355619i	$0.884270\pi$
$398$	3115.30	+	4913.55i	0.392351	+	0.618830i
$399$		0			0
$400$	3373.68	+	4092.27i	0.421710	+	0.511534i
$401$	−3919.55			−0.488112			−0.244056	−	0.969761i	$-0.578478\pi$
$401$	−3919.55			−0.488112			−0.244056	+	0.969761i	$0.578478\pi$
$402$	−46.0863	+	29.2197i	−0.00571785	+	0.00362524i
$403$		−	5074.12i		−	0.627195i
$404$	9470.79	+	4466.49i	1.16631	+	0.550040i
$405$			10500.2i			1.28829i
$406$		0			0
$407$		−	2779.61i		−	0.338526i
$408$	−16.4756	−	131.773i	−0.00199918	−	0.0159896i
$409$			10534.9i			1.27364i	0.771014	+	0.636818i	$0.219750\pi$
$409$			10534.9i			1.27364i	−0.771014	+	0.636818i	$0.780250\pi$
$410$	−7326.17	−	11555.1i	−0.882473	−	1.39187i
$411$	128.498			0.0154217
$412$	−408.354	+	865.879i	−0.0488305	+	0.103541i
$413$		0			0
$414$	−921.985	+	584.558i	−0.109452	+	0.0693948i
$415$			11392.7i			1.34759i
$416$	2636.20	+	862.772i	0.310698	+	0.101685i
$417$	−173.131			−0.0203316
$418$	6049.35	−	3835.41i	0.707855	−	0.448795i
$419$	−2243.25			−0.261551			−0.130776	−	0.991412i	$-0.541747\pi$
$419$	−2243.25			−0.261551			−0.130776	+	0.991412i	$0.541747\pi$
$420$		0			0
$421$	−14402.2			−1.66727			−0.833635	−	0.552316i	$-0.813744\pi$
$421$	−14402.2			−1.66727			−0.833635	+	0.552316i	$0.813744\pi$
$422$	−1821.27	+	1154.72i	−0.210090	+	0.133202i
$423$	−10116.6			−1.16285
$424$	3183.09	−	397.981i	0.364586	−	0.0455842i
$425$		−	5181.63i		−	0.591402i
$426$	18.4841	−	11.7193i	0.00210225	−	0.00133287i
$427$		0			0
$428$	5622.50	+	2651.60i	0.634985	+	0.299463i
$429$	52.5155			0.00591020
$430$	−10580.5	−	16687.9i	−1.18660	−	1.87154i
$431$		−	2208.01i		−	0.246766i	−0.992359	−	0.123383i	$-0.960626\pi$
$431$		−	2208.01i		−	0.246766i	0.992359	−	0.123383i	$-0.0393744\pi$
$432$	206.310	+	250.254i	0.0229771	+	0.0278712i
$433$		−	12802.5i		−	1.42089i	−0.703751	−	0.710446i	$-0.748493\pi$
$433$		−	12802.5i		−	1.42089i	0.703751	−	0.710446i	$-0.251507\pi$
$434$		0			0
$435$		−	212.709i		−	0.0234451i
$436$	4276.56	−	9068.08i	0.469748	−	0.996060i
$437$		−	991.770i		−	0.108565i
$438$	−148.873	+	94.3885i	−0.0162407	+	0.0102969i
$439$	13800.5			1.50037			0.750183	−	0.661230i	$-0.229965\pi$
$439$	13800.5			1.50037			0.750183	+	0.661230i	$0.229965\pi$
$440$	−11819.9	+	1477.84i	−1.28066	+	0.160121i
$441$		0			0
$442$	−1451.11	−	2288.74i	−0.156159	−	0.246299i
$443$		−	5393.43i		−	0.578441i	−0.957262	−	0.289221i	$-0.906604\pi$
$443$		−	5393.43i		−	0.578441i	0.957262	−	0.289221i	$-0.0933961\pi$
$444$	−24.3826	+	51.7011i	−0.00260618	+	0.00552619i
$445$	−10510.1			−1.11961
$446$	−1538.87	−	2427.16i	−0.163380	−	0.257689i
$447$	137.299			0.0145280
$448$		0			0
$449$	15602.5			1.63992			0.819962	−	0.572417i	$-0.193994\pi$
$449$	15602.5			1.63992			0.819962	+	0.572417i	$0.193994\pi$
$450$	3387.60	+	5343.04i	0.354873	+	0.559718i
$451$	12250.6			1.27906
$452$	−3930.12	+	8333.48i	−0.408977	+	0.867199i
$453$		−	224.128i		−	0.0232460i
$454$	−1726.20	−	2722.62i	−0.178446	−	0.281451i
$455$		0			0
$456$	−146.163	+	18.2747i	−0.0150103	+	0.00187673i
$457$	5467.58			0.559655			0.279828	−	0.960050i	$-0.409723\pi$
$457$	5467.58			0.559655			0.279828	+	0.960050i	$0.409723\pi$
$458$	−8166.20	+	5177.54i	−0.833147	+	0.528233i
$459$		−	316.872i		−	0.0322229i
$460$	−703.532	+	1491.78i	−0.0713095	+	0.151205i
$461$			14746.1i			1.48979i	0.667182	+	0.744895i	$0.267500\pi$
$461$			14746.1i			1.48979i	−0.667182	+	0.744895i	$0.732500\pi$
$462$		0			0
$463$		−	8510.80i		−	0.854278i	−0.904186	−	0.427139i	$-0.859522\pi$
$463$		−	8510.80i		−	0.854278i	0.904186	−	0.427139i	$-0.140478\pi$
$464$	6399.04	+	7762.03i	0.640232	+	0.776601i
$465$		−	448.119i		−	0.0446904i
$466$	4053.21	+	6392.86i	0.402921	+	0.635501i
$467$	−15756.2			−1.56126			−0.780632	−	0.624991i	$-0.785103\pi$
$467$	−15756.2			−1.56126			−0.780632	+	0.624991i	$0.785103\pi$
$468$	2992.62	+	1411.34i	0.295586	+	0.139400i
$469$		0			0
$470$	−12908.7	+	8184.39i	−1.26688	+	0.803230i
$471$			207.664i			0.0203156i
$472$	−7182.36	+	898.009i	−0.700413	+	0.0875725i
$473$	17692.4			1.71986
$474$	−146.052	+	92.6004i	−0.0141528	+	0.00897316i
$475$	−5747.45			−0.555182
$476$		0			0
$477$	3826.52			0.367305
$478$	1785.40	−	1131.98i	0.170841	−	0.108317i
$479$	14445.5			1.37794			0.688969	−	0.724791i	$-0.258063\pi$
$479$	14445.5			1.37794			0.688969	+	0.724791i	$0.258063\pi$
$480$	232.815	+	76.1954i	0.0221386	+	0.00724548i
$481$			1166.49i			0.110577i
$482$	4096.64	−	2597.36i	0.387130	−	0.245449i
$483$		0			0
$484$	7.59766	−	16.1102i	0.000713529	−	0.00151298i
$485$	5575.22			0.521974
$486$	310.759	+	490.140i	0.0290048	+	0.0457474i
$487$		−	7607.54i		−	0.707865i	−0.935271	−	0.353933i	$-0.884844\pi$
$487$		−	7607.54i		−	0.707865i	0.935271	−	0.353933i	$-0.115156\pi$
$488$	−693.306	−	5545.12i	−0.0643125	−	0.514377i
$489$			96.1108i			0.00888810i
$490$		0			0
$491$		−	7521.86i		−	0.691358i	−0.938353	−	0.345679i	$-0.887649\pi$
$491$		−	7521.86i		−	0.691358i	0.938353	−	0.345679i	$-0.112351\pi$
$492$	−227.862	−	107.461i	−0.0208797	−	0.00984702i
$493$		−	9828.27i		−	0.897856i
$494$	−2538.66	+	1609.57i	−0.231214	+	0.146595i
$495$	−14209.2			−1.29021
$496$	13481.0	+	16352.5i	1.22039	+	1.48034i
$497$		0			0
$498$	112.331	+	177.172i	0.0101077	+	0.0159423i
$499$			14262.1i			1.27948i	0.768592	+	0.639739i	$0.220958\pi$
$499$			14262.1i			1.27948i	−0.768592	+	0.639739i	$0.779042\pi$
$500$	−4395.18	−	2072.80i	−0.393117	−	0.185397i
$501$	−303.418			−0.0270573
$502$	−2429.41	−	3831.75i	−0.215996	−	0.340676i
$503$	−3887.75			−0.344625			−0.172312	−	0.985042i	$-0.555124\pi$
$503$	−3887.75			−0.344625			−0.172312	+	0.985042i	$0.555124\pi$
$504$		0			0
$505$	18871.2			1.66289
$506$	−790.783	−	1247.25i	−0.0694755	−	0.109579i
$507$	184.175			0.0161331
$508$	1059.09	+	499.474i	0.0924991	+	0.0436232i
$509$		−	16396.8i		−	1.42785i	−0.700223	−	0.713924i	$-0.746916\pi$
$509$		−	16396.8i		−	1.42785i	0.700223	−	0.713924i	$-0.253084\pi$
$510$	−128.154	−	202.129i	−0.0111270	−	0.0175499i
$511$		0			0
$512$	−10788.0	+	4223.44i	−0.931183	+	0.364553i
$513$	−351.474			−0.0302494
$514$	12372.6	−	7844.48i	1.06173	−	0.673162i
$515$			1725.33i			0.147625i
$516$	−329.080	−	155.196i	−0.0280755	−	0.0132406i
$517$		−	13685.7i		−	1.16421i
$518$		0			0
$519$		−	4.67225i		−	0.000395162i
$520$	4960.33	−	620.189i	0.418317	−	0.0523021i
$521$			3699.46i			0.311087i	0.987829	+	0.155543i	$0.0497128\pi$
$521$			3699.46i			0.311087i	−0.987829	+	0.155543i	$0.950287\pi$
$522$	6425.44	+	10134.4i	0.538762	+	0.849754i
$523$	8304.62			0.694332			0.347166	−	0.937804i	$-0.387144\pi$
$523$	8304.62			0.694332			0.347166	+	0.937804i	$0.387144\pi$
$524$	4861.51	−	10308.4i	0.405298	−	0.859399i
$525$		0			0
$526$	2289.85	−	1451.82i	0.189814	−	0.120346i
$527$		−	20705.5i		−	1.71147i
$528$	−169.243	+	139.524i	−0.0139495	+	0.0115000i
$529$	11962.5			0.983194
$530$	4882.60	−	3095.67i	0.400163	−	0.253712i
$531$	−8634.20			−0.705636
$532$		0			0
$533$	−5141.07			−0.417794
$534$	−163.445	+	103.628i	−0.0132453	+	0.00839777i
$535$	11203.2			0.905341
$536$	−577.021	−	4615.07i	−0.0464991	−	0.371904i
$537$		−	273.269i		−	0.0219599i
$538$	5479.54	−	3474.15i	0.439107	−	0.278403i
$539$		0			0
$540$	528.672	+	249.325i	0.0421304	+	0.0198690i
$541$	−9978.03			−0.792956			−0.396478	−	0.918044i	$-0.629768\pi$
$541$	−9978.03			−0.792956			−0.396478	+	0.918044i	$0.629768\pi$
$542$	9501.95	+	14986.8i	0.753033	+	1.18771i
$543$			100.571i			0.00794828i
$544$	10757.3	+	3520.63i	0.847822	+	0.277474i
$545$		−	18068.8i		−	1.42015i
$546$		0			0
$547$		−	8278.49i		−	0.647098i	−0.946211	−	0.323549i	$-0.895124\pi$
$547$		−	8278.49i		−	0.647098i	0.946211	−	0.323549i	$-0.104876\pi$
$548$	−4671.64	+	9905.81i	−0.364166	+	0.772181i
$549$		−	6666.02i		−	0.518213i
$550$	−7228.00	+	4582.71i	−0.560369	+	0.355286i
$551$	−10901.5			−0.842866
$552$	3.76787	+	30.1357i	0.000290527	+	0.00232366i
$553$		0			0
$554$	10998.2	+	17346.8i	0.843448	+	1.33031i
$555$			103.018i			0.00787906i
$556$	6294.34	−	13346.6i	0.480107	−	1.01802i
$557$	−18578.0			−1.41324			−0.706620	−	0.707593i	$-0.749781\pi$
$557$	−18578.0			−1.41324			−0.706620	+	0.707593i	$0.749781\pi$
$558$	13536.6	+	21350.5i	1.02697	+	1.61978i
$559$	−7424.76			−0.561778
$560$		0			0
$561$	214.295			0.0161276
$562$	−5831.83	−	9198.17i	−0.437724	−	0.690394i
$563$	−11970.8			−0.896107			−0.448054	−	0.894007i	$-0.647883\pi$
$563$	−11970.8			−0.896107			−0.448054	+	0.894007i	$0.647883\pi$
$564$	−120.050	+	254.555i	−0.00896279	+	0.0190048i
$565$			16605.1i			1.23642i
$566$	7484.07	+	11804.1i	0.555793	+	0.876615i
$567$		0			0
$568$	231.429	+	1850.99i	0.0170961	+	0.136736i
$569$	13172.0			0.970474			0.485237	−	0.874383i	$-0.338733\pi$
$569$	13172.0			0.970474			0.485237	+	0.874383i	$0.338733\pi$
$570$	−224.201	+	142.148i	−0.0164750	+	0.0104455i
$571$			12867.5i			0.943064i	0.881849	+	0.471532i	$0.156299\pi$
$571$			12867.5i			0.943064i	−0.881849	+	0.471532i	$0.843701\pi$
$572$	−1909.24	+	4048.39i	−0.139562	+	0.295929i
$573$		−	287.895i		−	0.0209895i
$574$		0			0
$575$			1185.01i			0.0859447i
$576$	−13394.1	+	3402.51i	−0.968900	+	0.246130i
$577$			18131.0i			1.30815i	0.756430	+	0.654075i	$0.226942\pi$
$577$			18131.0i			1.30815i	−0.756430	+	0.654075i	$0.773058\pi$
$578$	1519.47	+	2396.56i	0.109345	+	0.172463i
$579$	−101.391			−0.00727752
$580$	16397.6	+	7733.20i	1.17392	+	0.553627i
$581$		0			0
$582$	86.7017	−	54.9707i	0.00617509	−	0.00391514i
$583$			5176.48i			0.367732i
$584$	−1863.95	−	14908.1i	−0.132074	−	1.05634i
$585$	5963.01			0.421436
$586$	−16479.4	+	10448.3i	−1.16170	+	0.736542i
$587$	24252.4			1.70529			0.852644	−	0.522492i	$-0.174998\pi$
$587$	24252.4			1.70529			0.852644	+	0.522492i	$0.174998\pi$
$588$		0			0
$589$	−22966.5			−1.60665
$590$	−11017.1	+	6985.10i	−0.768760	+	0.487410i
$591$	−113.362			−0.00789016
$592$	−3099.15	−	3759.27i	−0.215160	−	0.260988i
$593$		−	7533.35i		−	0.521682i	−0.965382	−	0.260841i	$-0.916000\pi$
$593$		−	7533.35i		−	0.521682i	0.965382	−	0.260841i	$-0.0839998\pi$
$594$	−442.013	+	280.246i	−0.0305320	+	0.0193580i
$595$		0			0
$596$	−4991.62	+	10584.3i	−0.343062	+	0.727432i
$597$	193.067			0.0132357
$598$	331.860	+	523.420i	0.0226936	+	0.0357931i
$599$			23590.6i			1.60916i	0.593846	+	0.804578i	$0.297609\pi$
$599$			23590.6i			1.60916i	−0.593846	+	0.804578i	$0.702391\pi$
$600$	174.641	−	21.8353i	0.0118828	−	0.00148571i
$601$		−	585.188i		−	0.0397177i	−0.999803	−	0.0198588i	$-0.993678\pi$
$601$		−	585.188i		−	0.0397177i	0.999803	−	0.0198588i	$-0.00632168\pi$
$602$		0			0
$603$		−	5547.96i		−	0.374677i
$604$	17277.8	+	8148.34i	1.16395	+	0.548926i
$605$		−	32.1007i		−	0.00215715i
$606$	293.471	−	186.067i	0.0196724	−	0.0124727i
$607$	−23500.6			−1.57143			−0.785715	−	0.618589i	$-0.787705\pi$
$607$	−23500.6			−1.57143			−0.785715	+	0.618589i	$0.787705\pi$
$608$	3905.08	−	11932.0i	0.260480	−	0.795897i
$609$		0			0
$610$	−5392.83	−	8505.76i	−0.357950	−	0.564571i
$611$			5743.32i			0.380278i
$612$	12211.7	+	5759.13i	0.806584	+	0.380390i
$613$	5615.23			0.369978			0.184989	−	0.982741i	$-0.440775\pi$
$613$	5615.23			0.369978			0.184989	+	0.982741i	$0.440775\pi$
$614$	11377.9	+	17945.6i	0.747842	+	1.17952i
$615$	−454.032			−0.0297697
$616$		0			0
$617$	18767.7			1.22457			0.612286	−	0.790636i	$-0.290250\pi$
$617$	18767.7			1.22457			0.612286	+	0.790636i	$0.290250\pi$
$618$	17.0114	+	26.8310i	0.00110728	+	0.00174644i
$619$	21909.6			1.42265			0.711325	−	0.702863i	$-0.248095\pi$
$619$	21909.6			1.42265			0.711325	+	0.702863i	$0.248095\pi$
$620$	34545.2	+	16291.7i	2.23769	+	1.05531i
$621$			72.4666i			0.00468275i
$622$	1162.00	+	1832.74i	0.0749064	+	0.118145i
$623$		0			0
$624$	71.0244	−	58.5527i	0.00455649	−	0.00375639i
$625$	−19116.4			−1.22345
$626$	−6786.57	+	4302.83i	−0.433300	+	0.274722i
$627$		−	237.696i		−	0.0151398i
$628$	−16008.7	−	7549.80i	−1.01722	−	0.479729i
$629$			4759.99i			0.301738i
$630$		0			0
$631$			6303.66i			0.397694i	0.980031	+	0.198847i	$0.0637197\pi$
$631$			6303.66i			0.397694i	−0.980031	+	0.198847i	$0.936280\pi$
$632$	−1828.64	−	14625.6i	−0.115094	−	0.920533i
$633$			71.5628i			0.00449347i
$634$	−8662.65	−	13663.0i	−0.542647	−	0.855881i
$635$	2110.31			0.131882
$636$	45.4078	−	96.2832i	0.00283103	−	0.00600295i
$637$		0			0
$638$	−13709.7	+	8692.26i	−0.850742	+	0.539388i
$639$			2225.16i			0.137756i
$640$	−14338.0	+	15177.4i	−0.885564	+	0.937406i
$641$	7758.16			0.478048			0.239024	−	0.971014i	$-0.423172\pi$
$641$	7758.16			0.478048			0.239024	+	0.971014i	$0.423172\pi$
$642$	174.224	−	110.462i	0.0107104	−	0.00679063i
$643$	−31588.3			−1.93735			−0.968677	−	0.248323i	$-0.920121\pi$
$643$	−31588.3			−1.93735			−0.968677	+	0.248323i	$0.920121\pi$
$644$		0			0
$645$	−655.716			−0.0400291
$646$	−10359.3	+	6568.02i	−0.630931	+	0.400023i
$647$	−2713.67			−0.164892			−0.0824461	−	0.996596i	$-0.526273\pi$
$647$	−2713.67			−0.164892			−0.0824461	+	0.996596i	$0.526273\pi$
$648$	−16351.9	+	2044.48i	−0.991303	+	0.123942i
$649$		−	11680.3i		−	0.706456i
$650$	3033.30	−	1923.18i	0.183040	−	0.116051i
$651$		0			0
$652$	−7409.11	−	3494.19i	−0.445036	−	0.209882i
$653$	15005.9			0.899274			0.449637	−	0.893211i	$-0.351553\pi$
$653$	15005.9			0.899274			0.449637	+	0.893211i	$0.351553\pi$
$654$	−178.155	−	280.992i	−0.0106520	−	0.0168007i
$655$		−	20540.2i		−	1.22530i
$656$	16568.2	−	13658.9i	0.986099	−	0.812943i
$657$		−	17921.6i		−	1.06421i
$658$		0			0
$659$		−	16279.4i		−	0.962301i	−0.876638	−	0.481150i	$-0.840219\pi$
$659$		−	16279.4i		−	0.962301i	0.876638	−	0.481150i	$-0.159781\pi$
$660$	−168.614	+	357.532i	−0.00994441	+	0.0210862i
$661$		−	11274.5i		−	0.663428i	−0.943380	−	0.331714i	$-0.892373\pi$
$661$		−	11274.5i		−	0.663428i	0.943380	−	0.331714i	$-0.107627\pi$
$662$	−4598.59	+	2915.61i	−0.269984	+	0.171176i
$663$	−89.9310			−0.00526792
$664$	−17741.9	+	2218.27i	−1.03693	+	0.129647i
$665$		0			0
$666$	−3111.94	−	4908.26i	−0.181059	−	0.285572i
$667$			2247.66i			0.130480i
$668$	11031.0	−	23390.3i	0.638926	−	1.35479i
$669$	−95.3700			−0.00551153
$670$	−4488.32	−	7079.13i	−0.258804	−	0.408195i
$671$	9017.71			0.518815
$672$		0			0
$673$	17159.1			0.982813			0.491406	−	0.870930i	$-0.336483\pi$
$673$	17159.1			0.982813			0.491406	+	0.870930i	$0.336483\pi$
$674$	6067.40	+	9569.71i	0.346747	+	0.546902i
$675$	419.955			0.0239468
$676$	−6695.83	+	14197.9i	−0.380964	+	0.807801i
$677$			16158.1i			0.917289i	0.888620	+	0.458644i	$0.151665\pi$
$677$			16158.1i			0.917289i	−0.888620	+	0.458644i	$0.848335\pi$
$678$	163.723	+	258.230i	0.00927396	+	0.0146272i
$679$		0			0
$680$	20241.2	−	2530.75i	1.14149	−	0.142720i
$681$	−106.979			−0.00601976
$682$	−28882.7	+	18312.2i	−1.62166	+	1.02817i
$683$		−	30880.5i		−	1.73003i	−0.501746	−	0.865015i	$-0.667309\pi$
$683$		−	30880.5i		−	1.73003i	0.501746	−	0.865015i	$-0.332691\pi$
$684$	6388.01	−	13545.2i	0.357093	−	0.757185i
$685$			19738.0i			1.10095i
$686$		0			0
$687$			320.873i			0.0178196i
$688$	23928.0	−	19726.3i	1.32594	−	1.09311i
$689$		−	2172.36i		−	0.120116i
$690$	29.3081	+	46.2257i	0.00161701	+	0.00255041i
$691$	24465.0			1.34688			0.673438	−	0.739244i	$-0.264817\pi$
$691$	24465.0			1.34688			0.673438	+	0.739244i	$0.264817\pi$
$692$	360.181	+	169.864i	0.0197861	+	0.00933127i
$693$		0			0
$694$	4633.73	−	2937.88i	0.253449	−	0.160692i
$695$		−	26594.0i		−	1.45147i
$696$	331.251	−	41.4162i	0.0180403	−	0.00225557i
$697$	−20978.7			−1.14006
$698$	−4007.11	+	2540.59i	−0.217294	+	0.137769i
$699$	251.194			0.0135923
$700$		0			0
$701$	19017.1			1.02463			0.512316	−	0.858797i	$-0.328788\pi$
$701$	19017.1			1.02463			0.512316	+	0.858797i	$0.328788\pi$
$702$	185.495	−	117.608i	0.00997302	−	0.00632311i
$703$	5279.77			0.283258
$704$	−4602.87	−	18119.4i	−0.246417	−	0.970027i
$705$			507.220i			0.0270964i
$706$	5732.24	−	3634.36i	0.305575	−	0.193741i
$707$		0			0
$708$	−102.459	+	217.254i	−0.00543874	+	0.0115324i
$709$	−14819.9			−0.785011			−0.392506	−	0.919750i	$-0.628392\pi$
$709$	−14819.9			−0.785011			−0.392506	+	0.919750i	$0.628392\pi$
$710$	1800.16	+	2839.27i	0.0951532	+	0.150079i
$711$		−	17582.1i		−	0.927398i
$712$	−2046.41	−	16367.3i	−0.107714	−	0.861506i
$713$			4735.21i			0.248717i
$714$		0			0
$715$			8066.70i			0.421926i
$716$	21066.1	+	9934.93i	1.09955	+	0.518555i
$717$		−	70.1534i		−	0.00365401i
$718$	−3583.27	+	2271.87i	−0.186248	+	0.118085i
$719$	15993.1			0.829542			0.414771	−	0.909926i	$-0.363862\pi$
$719$	15993.1			0.829542			0.414771	+	0.909926i	$0.363862\pi$
$720$	−19217.1	+	15842.7i	−0.994695	+	0.820030i
$721$		0			0
$722$	−3102.92	−	4894.03i	−0.159943	−	0.252267i
$723$		−	160.969i		−	0.00828007i
$724$	−7752.95	−	3656.34i	−0.397978	−	0.187689i
$725$	13025.5			0.667250
$726$	−0.316507	−	0.499206i	−1.61800e−5	−	2.55196e-5i
$727$	−11418.3			−0.582503			−0.291252	−	0.956646i	$-0.594072\pi$
$727$	−11418.3			−0.582503			−0.291252	+	0.956646i	$0.594072\pi$
$728$		0			0
$729$	−19644.5			−0.998043
$730$	−14498.6	−	22867.7i	−0.735094	−	1.15942i
$731$	−30297.6			−1.53296
$732$	−167.731	−	79.1029i	−0.00846927	−	0.00399416i
$733$		−	4263.33i		−	0.214829i	−0.994214	−	0.107414i	$-0.965743\pi$
$733$		−	4263.33i		−	0.214829i	0.994214	−	0.107414i	$-0.0342572\pi$
$734$	−13944.3	−	21993.4i	−0.701217	−	1.10598i
$735$		0			0
$736$	−2460.13	−	805.147i	−0.123209	−	0.0403235i
$737$	7505.22			0.375113
$738$	21632.2	−	13715.3i	1.07899	−	0.684100i
$739$			29624.7i			1.47464i	0.675542	+	0.737321i	$0.263910\pi$
$739$			29624.7i			1.47464i	−0.675542	+	0.737321i	$0.736090\pi$
$740$	−7941.60	−	3745.31i	−0.394512	−	0.186054i
$741$			99.7513i			0.00494529i
$742$		0			0
$743$			9471.33i			0.467657i	0.972278	+	0.233829i	$0.0751255\pi$
$743$			9471.33i			0.467657i	−0.972278	+	0.233829i	$0.924875\pi$
$744$	697.855	−	87.2527i	0.0343879	−	0.00429952i
$745$			21090.0i			1.03715i
$746$	−662.571	−	1045.03i	−0.0325180	−	0.0512885i
$747$	−21328.3			−1.04466
$748$	−7790.88	+	16519.9i	−0.380833	+	0.807522i
$749$		0			0
$750$	−136.194	+	86.3496i	−0.00663078	+	0.00420405i
$751$			18747.1i			0.910906i	0.890260	+	0.455453i	$0.150523\pi$
$751$			18747.1i			0.910906i	−0.890260	+	0.455453i	$0.849477\pi$
$752$	−15259.0	−	18509.1i	−0.739944	−	0.897551i
$753$	−150.560			−0.00728649
$754$	5753.41	−	3647.79i	0.277887	−	0.176186i
$755$	34427.3			1.65952
$756$		0			0
$757$	−28442.9			−1.36562			−0.682809	−	0.730597i	$-0.739242\pi$
$757$	−28442.9			−1.36562			−0.682809	+	0.730597i	$0.739242\pi$
$758$	−21212.7	+	13449.3i	−1.01646	+	0.644460i
$759$	−49.0080			−0.00234371
$760$	−2807.10	−	22451.5i	−0.133979	−	1.07158i
$761$		−	27490.5i		−	1.30950i	−0.755846	−	0.654749i	$-0.772774\pi$
$761$		−	27490.5i		−	1.30950i	0.755846	−	0.654749i	$-0.227226\pi$
$762$	32.8181	−	20.8073i	0.00156020	−	0.000989200i
$763$		0			0
$764$	22193.6	+	10466.6i	1.05096	+	0.495641i
$765$	24332.7			1.15000
$766$	9625.81	+	15182.2i	0.454040	+	0.716128i
$767$			4901.73i			0.230758i
$768$	−73.3279	+	377.399i	−0.00344530	+	0.0177320i
$769$			36762.3i			1.72390i	0.506991	+	0.861952i	$0.330758\pi$
$769$			36762.3i			1.72390i	−0.506991	+	0.861952i	$0.669242\pi$
$770$		0			0
$771$		−	486.154i		−	0.0227087i
$772$	3686.17	−	7816.19i	0.171850	−	0.364392i
$773$		−	8170.80i		−	0.380185i	−0.981766	−	0.190093i	$-0.939121\pi$
$773$		−	8170.80i		−	0.380185i	0.981766	−	0.190093i	$-0.0608788\pi$
$774$	31241.3	−	19807.7i	1.45083	−	0.919860i
$775$	27441.3			1.27190
$776$	1085.54	+	8682.28i	0.0502174	+	0.401644i
$777$		0			0
$778$	−4340.68	−	6846.27i	−0.200027	−	0.315489i
$779$			23269.5i			1.07024i
$780$	70.7606	−	150.042i	0.00324825	−	0.00688763i
$781$	−3010.16			−0.137916
$782$	1354.19	+	2135.87i	0.0619255	+	0.0976710i
$783$	796.550			0.0363555
$784$		0			0
$785$	−31898.5			−1.45032
$786$	−202.523	−	319.427i	−0.00919055	−	0.0144956i
$787$	−33766.4			−1.52941			−0.764703	−	0.644383i	$-0.777114\pi$
$787$	−33766.4			−1.52941			−0.764703	+	0.644383i	$0.777114\pi$
$788$	4121.36	−	8738.98i	0.186316	−	0.395068i
$789$		−	89.9748i		−	0.00405981i
$790$	−14224.0	−	22434.5i	−0.640590	−	1.01036i
$791$		0			0
$792$	−2766.65	−	22127.9i	−0.124127	−	0.992780i
$793$	−3784.37			−0.169466
$794$	−13439.2	+	8520.77i	−0.600681	+	0.380845i
$795$		−	191.851i		−	0.00855881i
$796$	−7019.12	+	14883.4i	−0.312546	+	0.662725i
$797$			3635.92i			0.161595i	0.996731	+	0.0807973i	$0.0257466\pi$
$797$			3635.92i			0.161595i	−0.996731	+	0.0807973i	$0.974253\pi$
$798$		0			0
$799$			23436.2i			1.03769i
$800$	−4665.94	+	14256.8i	−0.206208	+	0.630067i
$801$		−	19675.9i		−	0.867930i
$802$	−5936.27	−	9362.89i	−0.261368	−	0.412238i
$803$	24244.1			1.06545
$804$	−139.598	−	65.8353i	−0.00612344	−	0.00288785i
$805$		0			0
$806$	12120.9	−	7684.89i	0.529702	−	0.335842i
$807$		−	215.307i		−	0.00939177i
$808$	3674.39	+	29388.1i	0.159981	+	1.27954i
$809$	−36212.3			−1.57374			−0.786871	−	0.617118i	$-0.788300\pi$
$809$	−36212.3			−1.57374			−0.786871	+	0.617118i	$0.788300\pi$
$810$	−25082.5	+	15902.8i	−1.08804	+	0.689838i
$811$	−3940.47			−0.170615			−0.0853074	−	0.996355i	$-0.527187\pi$
$811$	−3940.47			−0.170615			−0.0853074	+	0.996355i	$0.527187\pi$
$812$		0			0
$813$	588.874			0.0254031
$814$	6639.84	−	4209.80i	0.285904	−	0.181269i
$815$	−14763.2			−0.634518
$816$	289.823	−	238.931i	0.0124336	−	0.0102503i
$817$			33606.0i			1.43908i
$818$	−25165.4	+	15955.4i	−1.07566	+	0.681989i
$819$		0			0
$820$	16506.7	−	35001.0i	0.702974	−	1.49060i
$821$	−12795.9			−0.543947			−0.271973	−	0.962305i	$-0.587676\pi$
$821$	−12795.9			−0.543947			−0.271973	+	0.962305i	$0.587676\pi$
$822$	194.614	+	306.951i	0.00825782	+	0.0130245i
$823$			14489.4i			0.613691i	0.951759	+	0.306845i	$0.0992735\pi$
$823$			14489.4i			0.613691i	−0.951759	+	0.306845i	$0.900727\pi$
$824$	−2686.85	+	335.936i	−0.113593	+	0.0142025i
$825$			284.009i			0.0119853i
$826$		0			0
$827$			42110.7i			1.77066i	0.464965	+	0.885329i	$0.346067\pi$
$827$			42110.7i			1.77066i	−0.464965	+	0.885329i	$0.653933\pi$
$828$	−2792.74	−	1317.08i	−0.117216	−	0.0552797i
$829$			22763.6i			0.953693i	0.878987	+	0.476846i	$0.158220\pi$
$829$			22763.6i			0.953693i	−0.878987	+	0.476846i	$0.841780\pi$
$830$	−27214.6	+	17254.6i	−1.13811	+	0.721587i
$831$	681.604			0.0284532
$832$	1931.64	+	7603.95i	0.0804898	+	0.316851i
$833$		0			0
$834$	−262.213	−	413.571i	−0.0108869	−	0.0171712i
$835$		−	46606.8i		−	1.93161i
$836$	18323.8	+	8641.63i	0.758065	+	0.357508i
$837$	1678.11			0.0693000
$838$	−3397.46	−	5358.60i	−0.140052	−	0.220895i
$839$	5492.90			0.226026			0.113013	−	0.993594i	$-0.463950\pi$
$839$	5492.90			0.226026			0.113013	+	0.993594i	$0.463950\pi$
$840$		0			0
$841$	317.228			0.0130070
$842$	−21812.5	−	34403.5i	−0.892767	−	1.40810i
$843$	−361.422			−0.0147664
$844$	−5516.73	−	2601.72i	−0.224992	−	0.106108i
$845$			28290.3i			1.15174i
$846$	−15321.9	−	24166.3i	−0.622670	−	0.982097i
$847$		0			0
$848$	5771.57	+	7000.90i	0.233722	+	0.283505i
$849$	463.818			0.0187493
$850$	12377.7	−	7847.73i	0.499473	−	0.316676i
$851$		−	1088.58i		−	0.0438496i
$852$	55.9895	+	26.4050i	0.00225137	+	0.00106176i
$853$		−	14715.4i		−	0.590675i	−0.955393	−	0.295338i	$-0.904568\pi$
$853$		−	14715.4i		−	0.590675i	0.955393	−	0.295338i	$-0.0954321\pi$
$854$		0			0
$855$		−	26989.8i		−	1.07957i
$856$	2181.37	+	17446.8i	0.0870999	+	0.696633i
$857$		−	16617.5i		−	0.662360i	−0.943568	−	0.331180i	$-0.892553\pi$
$857$		−	16617.5i		−	0.662360i	0.943568	−	0.331180i	$-0.107447\pi$
$858$	79.5363	+	125.447i	0.00316471	+	0.00499149i
$859$	−23427.3			−0.930536			−0.465268	−	0.885170i	$-0.654042\pi$
$859$	−23427.3			−0.930536			−0.465268	+	0.885170i	$0.654042\pi$
$860$	23839.1	−	50548.7i	0.945239	−	2.00430i
$861$		0			0
$862$	5274.43	−	3344.10i	0.208408	−	0.132135i
$863$			18685.1i			0.737020i	0.929624	+	0.368510i	$0.120132\pi$
$863$			18685.1i			0.737020i	−0.929624	+	0.368510i	$0.879868\pi$
$864$	−285.336	+	871.845i	−0.0112353	+	0.0343296i
$865$	717.686			0.0282105
$866$	30582.1	−	19389.7i	1.20002	−	0.760841i
$867$	94.1675			0.00368869
$868$		0			0
$869$	23784.8			0.928476
$870$	508.111	−	322.153i	0.0198007	−	0.0125540i
$871$	−3149.63			−0.122527
$872$	28138.5	−	3518.15i	1.09276	−	0.136628i
$873$			10437.3i			0.404639i
$874$	2369.11	−	1502.06i	0.0916891	−	0.0581328i
$875$		0			0
$876$	−450.944	−	212.668i	−0.0173927	−	0.00820250i
$877$	−42981.9			−1.65495			−0.827477	−	0.561499i	$-0.810225\pi$
$877$	−42981.9			−1.65495			−0.827477	+	0.561499i	$0.810225\pi$
$878$	20901.2	+	32966.1i	0.803396	+	1.26714i
$879$			647.521i			0.0248468i
$880$	−21431.8	−	25996.7i	−0.820983	−	0.995852i
$881$		−	36788.9i		−	1.40687i	−0.710761	−	0.703434i	$-0.751649\pi$
$881$		−	36788.9i		−	1.40687i	0.710761	−	0.703434i	$-0.248351\pi$
$882$		0			0
$883$			6006.92i			0.228934i	0.993427	+	0.114467i	$0.0365161\pi$
$883$			6006.92i			0.228934i	−0.993427	+	0.114467i	$0.963484\pi$
$884$	3269.52	−	6932.72i	0.124396	−	0.263770i
$885$			432.895i			0.0164425i
$886$	12883.6	−	8168.50i	0.488526	−	0.309736i
$887$	11334.9			0.429073			0.214536	−	0.976716i	$-0.431176\pi$
$887$	11334.9			0.429073			0.214536	+	0.976716i	$0.431176\pi$
$888$	−160.430	+	20.0585i	−0.00606270	+	0.000758018i
$889$		0			0
$890$	−15917.8	−	25106.2i	−0.599514	−	0.945573i
$891$		−	26592.2i		−	0.999856i
$892$	3467.25	−	7352.00i	0.130148	−	0.275968i
$893$	25995.4			0.974136
$894$	207.944	+	327.976i	0.00777927	+	0.0122697i
$895$	41975.8			1.56770
$896$		0			0
$897$	20.5667			0.000765553
$898$	23630.4	+	37270.7i	0.878125	+	1.38501i
$899$	52049.3			1.93097
$900$	−7632.65	+	16184.4i	−0.282691	+	0.599421i
$901$		−	8864.54i		−	0.327770i
$902$	18553.8	+	29263.8i	0.684895	+	1.08024i
$903$		0			0
$904$	−25859.0	+	3233.15i	−0.951392	+	0.118952i
$905$	−15448.3			−0.567424
$906$	535.389	−	339.448i	0.0196326	−	0.0124475i
$907$		−	26762.3i		−	0.979742i	−0.871795	−	0.489871i	$-0.837044\pi$
$907$		−	26762.3i		−	0.979742i	0.871795	−	0.489871i	$-0.162956\pi$
$908$	3889.32	−	8246.96i	0.142149	−	0.301415i
$909$			35328.7i			1.28908i
$910$		0			0
$911$			26600.8i			0.967425i	0.875227	+	0.483712i	$0.160712\pi$
$911$			26600.8i			0.967425i	−0.875227	+	0.483712i	$0.839288\pi$
$912$	−265.022	−	321.471i	−0.00962252	−	0.0116721i
$913$		−	28852.6i		−	1.04587i
$914$	8280.80	+	13060.8i	0.299677	+	0.472660i
$915$	−334.215			−0.0120752
$916$	−24735.9	−	11665.6i	−0.892245	−	0.420788i
$917$		0			0
$918$	756.933	−	479.912i	0.0272141	−	0.0172543i
$919$			37146.5i			1.33335i	0.745348	+	0.666675i	$0.232283\pi$
$919$			37146.5i			1.33335i	−0.745348	+	0.666675i	$0.767717\pi$
$920$	−4629.03	+	578.767i	−0.165885	+	0.0207406i
$921$	705.134			0.0252280
$922$	−35224.9	+	22333.4i	−1.25821	+	0.797733i
$923$	1263.24			0.0450489
$924$		0			0
$925$	−6308.47			−0.224239
$926$	20330.3	−	12889.9i	0.721485	−	0.457437i
$927$	−3229.97			−0.114440
$928$	−8850.14	+	27041.6i	−0.313061	+	0.956556i
$929$			9713.77i			0.343055i	0.985179	+	0.171528i	$0.0548703\pi$
$929$			9713.77i			0.343055i	−0.985179	+	0.171528i	$0.945130\pi$
$930$	1070.45	−	678.689i	0.0377435	−	0.0239302i
$931$		0			0
$932$	−9132.34	+	19364.3i	−0.320966	+	0.680579i
$933$	72.0135			0.00252692
$934$	−23863.2	−	37637.9i	−0.836005	−	1.31858i
$935$			32917.0i			1.15134i
$936$	1161.05	+	9286.19i	0.0405450	+	0.324283i
$937$			26889.4i			0.937501i	0.883331	+	0.468750i	$0.155296\pi$
$937$			26889.4i			0.937501i	−0.883331	+	0.468750i	$0.844704\pi$
$938$		0			0
$939$			266.664i			0.00926756i
$940$	−39101.2	−	18440.4i	−1.35675	−	0.639850i
$941$			34727.2i			1.20305i	0.798852	+	0.601527i	$0.205441\pi$
$941$			34727.2i			1.20305i	−0.798852	+	0.601527i	$0.794559\pi$
$942$	−496.061	+	314.513i	−0.0171577	+	0.0108783i
$943$	4797.70			0.165678
$944$	−13023.0	−	15796.9i	−0.449007	−	0.544646i
$945$		0			0
$946$	26795.6	+	42262.9i	0.920930	+	1.45252i
$947$			25396.3i			0.871454i	0.900079	+	0.435727i	$0.143509\pi$
$947$			25396.3i			0.871454i	−0.900079	+	0.435727i	$0.856491\pi$
$948$	−442.401	−	208.639i	−0.0151567	−	0.00714799i
$949$	−10174.3			−0.348020
$950$	−8704.68	−	13729.3i	−0.297281	−	0.468882i
$951$	−536.859			−0.0183058
$952$		0			0
$953$	−23212.4			−0.789005			−0.394503	−	0.918895i	$-0.629083\pi$
$953$	−23212.4			−0.789005			−0.394503	+	0.918895i	$0.629083\pi$
$954$	5795.38	+	9140.67i	0.196680	+	0.310210i
$955$	44222.3			1.49843
$956$	5408.07	+	2550.48i	0.182960	+	0.0862851i
$957$			538.694i			0.0181959i
$958$	21878.1	+	34507.0i	0.737840	+	1.16375i
$959$		0			0
$960$	170.592	+	671.541i	0.00573525	+	0.0225770i
$961$	79862.7			2.68076
$962$	−2786.47	+	1766.68i	−0.0933881	+	0.0592101i
$963$			20973.5i			0.701828i
$964$	12409.0	+	5852.14i	0.414591	+	0.195524i
$965$		−	15574.3i		−	0.519539i
$966$		0			0
$967$		−	57399.1i		−	1.90882i	−0.298494	−	0.954412i	$-0.596484\pi$
$967$		−	57399.1i		−	1.90882i	0.298494	−	0.954412i	$-0.403516\pi$
$968$	49.9903	−	6.25028i	0.00165986	−	0.000207533i
$969$			407.046i			0.0134945i
$970$	8443.83	+	13317.9i	0.279500	+	0.440837i
$971$	−10388.1			−0.343326			−0.171663	−	0.985156i	$-0.554914\pi$
$971$	−10388.1			−0.343326			−0.171663	+	0.985156i	$0.554914\pi$
$972$	−700.177	+	1484.66i	−0.0231051	+	0.0489924i
$973$		0			0
$974$	18172.6	−	11521.8i	0.597832	−	0.379038i
$975$		−	119.187i		−	0.00391491i
$976$	12196.0	−	10054.4i	0.399983	−	0.329747i
$977$	46989.5			1.53872			0.769358	−	0.638817i	$-0.220576\pi$
$977$	46989.5			1.53872			0.769358	+	0.638817i	$0.220576\pi$
$978$	−229.586	+	145.563i	−0.00750650	+	0.00475928i
$979$	26617.3			0.868940
$980$		0			0
$981$	33826.4			1.10091
$982$	17968.0	−	11392.1i	0.583891	−	0.370199i
$983$	−16852.9			−0.546818			−0.273409	−	0.961898i	$-0.588151\pi$
$983$	−16852.9			−0.546818			−0.273409	+	0.961898i	$0.588151\pi$
$984$	−88.4040	−	707.063i	−0.00286404	−	0.0229069i
$985$		−	17413.0i		−	0.563275i
$986$	23477.4	−	14885.2i	0.758290	−	0.480772i
$987$		0			0
$988$	−7689.76	−	3626.54i	−0.247615	−	0.116777i
$989$	6928.86			0.222776
$990$	−21520.2	−	33942.4i	−0.690866	−	1.08966i
$991$		−	1407.09i		−	0.0451035i	−0.999746	−	0.0225518i	$-0.992821\pi$
$991$		−	1407.09i		−	0.0451035i	0.999746	−	0.0225518i	$-0.00717906\pi$
$992$	−18644.8	+	56969.3i	−0.596748	+	1.82336i
$993$			180.692i			0.00577450i
$994$		0			0
$995$			29656.3i			0.944893i
$996$	−253.094	+	536.663i	−0.00805179	+	0.0170731i
$997$		−	7537.49i		−	0.239433i	−0.992808	−	0.119717i	$-0.961801\pi$
$997$		−	7537.49i		−	0.239433i	0.992808	−	0.119717i	$-0.0381986\pi$
$998$	−34068.8	+	21600.4i	−1.08059	+	0.685118i
$999$	−385.782			−0.0122178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.d.b.195.16		20
4.3	odd	2	inner	196.4.d.b.195.13		20
7.2	even	3		28.4.f.a.3.7	yes	20
7.3	odd	6		28.4.f.a.19.1	yes	20
7.4	even	3		196.4.f.d.19.1		20
7.5	odd	6		196.4.f.d.31.7		20
7.6	odd	2	inner	196.4.d.b.195.15		20
28.3	even	6		28.4.f.a.19.7	yes	20
28.11	odd	6		196.4.f.d.19.7		20
28.19	even	6		196.4.f.d.31.1		20
28.23	odd	6		28.4.f.a.3.1	✓	20
28.27	even	2	inner	196.4.d.b.195.14		20
56.3	even	6		448.4.p.h.383.6		20
56.37	even	6		448.4.p.h.255.6		20
56.45	odd	6		448.4.p.h.383.5		20
56.51	odd	6		448.4.p.h.255.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.1	✓	20	28.23	odd	6
28.4.f.a.3.7	yes	20	7.2	even	3
28.4.f.a.19.1	yes	20	7.3	odd	6
28.4.f.a.19.7	yes	20	28.3	even	6
196.4.d.b.195.13		20	4.3	odd	2	inner
196.4.d.b.195.14		20	28.27	even	2	inner
196.4.d.b.195.15		20	7.6	odd	2	inner
196.4.d.b.195.16		20	1.1	even	1	trivial
196.4.f.d.19.1		20	7.4	even	3
196.4.f.d.19.7		20	28.11	odd	6
196.4.f.d.31.1		20	28.19	even	6
196.4.f.d.31.7		20	7.5	odd	6
448.4.p.h.255.5		20	56.51	odd	6
448.4.p.h.255.6		20	56.37	even	6
448.4.p.h.383.5		20	56.45	odd	6
448.4.p.h.383.6		20	56.3	even	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51453 + 2.38877i) q^{2} +0.0938614 q^{3} +(-3.41241 + 7.23571i) q^{4} +14.4177i q^{5} +(0.142156 + 0.224213i) q^{6} +(-22.4526 + 2.80725i) q^{8} -26.9912 q^{9} +(-34.4404 + 21.8360i) q^{10} -36.5134i q^{11} +(-0.320293 + 0.679154i) q^{12} +15.3232i q^{13} +1.35326i q^{15} +(-40.7110 - 49.3824i) q^{16} +62.5279i q^{17} +(-40.8789 - 64.4756i) q^{18} +69.3558 q^{19} +(-104.322 - 49.1989i) q^{20} +(87.2219 - 55.3005i) q^{22} -14.2997i q^{23} +(-2.10743 + 0.263492i) q^{24} -82.8691 q^{25} +(-36.6035 + 23.2074i) q^{26} -5.06769 q^{27} -157.182 q^{29} +(-3.23263 + 2.04955i) q^{30} -331.140 q^{31} +(56.3050 - 172.040i) q^{32} -3.42720i q^{33} +(-149.365 + 94.7003i) q^{34} +(92.1049 - 195.300i) q^{36} +76.1258 q^{37} +(105.041 + 165.675i) q^{38} +1.43825i q^{39} +(-40.4739 - 323.714i) q^{40} +335.509i q^{41} +484.545i q^{43} +(264.200 + 124.598i) q^{44} -389.150i q^{45} +(34.1587 - 21.6574i) q^{46} +374.813 q^{47} +(-3.82119 - 4.63510i) q^{48} +(-125.508 - 197.955i) q^{50} +5.86896i q^{51} +(-110.874 - 52.2889i) q^{52} -141.769 q^{53} +(-7.67516 - 12.1055i) q^{54} +526.438 q^{55} +6.50983 q^{57} +(-238.057 - 375.471i) q^{58} +319.890 q^{59} +(-9.79181 - 4.61788i) q^{60} +246.970i q^{61} +(-501.521 - 791.016i) q^{62} +(496.239 - 126.060i) q^{64} -220.924 q^{65} +(8.18677 - 5.19059i) q^{66} +205.547i q^{67} +(-452.434 - 213.371i) q^{68} -1.34219i q^{69} -82.4401i q^{71} +(606.022 - 75.7709i) q^{72} +663.980i q^{73} +(115.295 + 181.847i) q^{74} -7.77821 q^{75} +(-236.670 + 501.838i) q^{76} +(-3.43565 + 2.17828i) q^{78} +651.401i q^{79} +(711.978 - 586.957i) q^{80} +728.286 q^{81} +(-801.453 + 508.138i) q^{82} +790.194 q^{83} -901.506 q^{85} +(-1157.46 + 733.857i) q^{86} -14.7533 q^{87} +(102.502 + 819.820i) q^{88} +728.973i q^{89} +(929.588 - 589.379i) q^{90} +(103.469 + 48.7965i) q^{92} -31.0813 q^{93} +(567.664 + 895.339i) q^{94} +999.949i q^{95} +(5.28487 - 16.1479i) q^{96} -386.693i q^{97} +985.539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{4} + 72 q^{8} + 112 q^{9} + 208 q^{16} - 136 q^{18} - 184 q^{22} + 72 q^{25} - 352 q^{29} - 1288 q^{30} + 80 q^{32} + 208 q^{36} - 516 q^{37} + 2496 q^{44} - 464 q^{46} - 864 q^{50} - 1140 q^{53}+ \cdots + 612 q^{93}+O(q^{100}) \) 20 * q - 8 * q^4 + 72 * q^8 + 112 * q^9 + 208 * q^16 - 136 * q^18 - 184 * q^22 + 72 * q^25 - 352 * q^29 - 1288 * q^30 + 80 * q^32 + 208 * q^36 - 516 * q^37 + 2496 * q^44 - 464 * q^46 - 864 * q^50 - 1140 * q^53 + 1452 * q^57 - 4488 * q^58 + 1472 * q^60 + 2560 * q^64 + 248 * q^65 + 9344 * q^72 - 1664 * q^74 - 4056 * q^78 + 2524 * q^81 - 2980 * q^85 - 11392 * q^86 + 2792 * q^88 + 3312 * q^92 + 612 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more