LMFDB - Embedded newform 147.4.c.a.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.1
Root			$-0.232749 - 2.99096i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.4.c.a.146.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.54551i q^{2} +(-2.93937 + 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(-9.72022 - 25.1896i) q^{9} +O(q^{10})$	\(q-4.54551i q^{2} +(-2.93937 + 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(-9.72022 - 25.1896i) q^{9} -52.7455i q^{10} -17.9160i q^{11} +(37.2174 - 54.2537i) q^{12} -62.4185i q^{13} +(-34.1081 + 49.7211i) q^{15} -4.97524 q^{16} -21.4164 q^{17} +(-114.500 + 44.1834i) q^{18} +10.9783i q^{19} -146.925 q^{20} -81.4374 q^{22} -69.0934i q^{23} +(-90.7953 - 62.2845i) q^{24} +9.64979 q^{25} -283.724 q^{26} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(226.008 + 155.039i) q^{30} -10.2283i q^{31} +192.133i q^{32} +(76.7677 + 52.6617i) q^{33} +97.3486i q^{34} +(123.074 + 318.943i) q^{36} +41.6514 q^{37} +49.9019 q^{38} +(267.455 + 183.471i) q^{39} +245.883i q^{40} -31.0035 q^{41} -224.550 q^{43} +226.847i q^{44} +(-112.792 - 292.297i) q^{45} -314.065 q^{46} +163.719 q^{47} +(14.6241 - 21.3182i) q^{48} -43.8633i q^{50} +(62.9508 - 91.7665i) q^{51} +790.323i q^{52} -527.220i q^{53} +(147.237 - 620.488i) q^{54} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} -1207.21 q^{58} +411.956 q^{59} +(431.865 - 629.552i) q^{60} +258.431i q^{61} -46.4928 q^{62} +833.541 q^{64} -724.296i q^{65} +(239.375 - 348.949i) q^{66} +323.474 q^{67} +271.168 q^{68} +(296.056 + 203.091i) q^{69} +45.4199i q^{71} +(533.762 - 205.969i) q^{72} +562.199i q^{73} -189.327i q^{74} +(-28.3643 + 41.3481i) q^{75} -139.004i q^{76} +(833.969 - 1215.72i) q^{78} +289.221 q^{79} -57.7320 q^{80} +(-540.035 + 489.697i) q^{81} +140.927i q^{82} +448.767 q^{83} -248.513 q^{85} +1020.70i q^{86} +(1137.99 + 780.647i) q^{87} +379.635 q^{88} +561.628 q^{89} +(-1328.64 + 512.698i) q^{90} +874.839i q^{92} +(43.8268 + 30.0647i) q^{93} -744.187i q^{94} +127.391i q^{95} +(-823.265 - 564.750i) q^{96} +214.364i q^{97} +(-451.297 + 174.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q - 28 * q^4 + 6 * q^9	$ 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) $ 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	4.54551i		−	1.60708i	−0.595250	−	0.803541i	$-0.702947\pi$
$2$		−	4.54551i		−	1.60708i	0.595250	−	0.803541i	$-0.297053\pi$
$3$	−2.93937	+	4.28487i	−0.565682	+	0.824624i
$3$	−2.93937	+	4.28487i	−0.565682	+	0.824624i
$4$	−12.6617			−1.58271
$5$	11.6039			1.03788			0.518941	−	0.854810i	$-0.326326\pi$
$5$	11.6039			1.03788			0.518941	+	0.854810i	$0.326326\pi$
$6$	19.4769	+	13.3609i	1.32524	+	0.909097i
$7$		0			0
$7$		0			0
$8$			21.1897i			0.936463i
$9$	−9.72022	−	25.1896i	−0.360008	−	0.932949i
$10$		−	52.7455i		−	1.66796i
$11$		−	17.9160i		−	0.491080i	−0.969387	−	0.245540i	$-0.921035\pi$
$11$		−	17.9160i		−	0.491080i	0.969387	−	0.245540i	$-0.0789652\pi$
$12$	37.2174	−	54.2537i	0.895311	−	1.30514i
$13$		−	62.4185i		−	1.33167i	−0.746097	−	0.665837i	$-0.768075\pi$
$13$		−	62.4185i		−	1.33167i	0.746097	−	0.665837i	$-0.231925\pi$
$14$		0			0
$15$	−34.1081	+	49.7211i	−0.587111	+	0.855862i
$16$	−4.97524			−0.0777381
$17$	−21.4164			−0.305544			−0.152772	−	0.988261i	$-0.548820\pi$
$17$	−21.4164			−0.305544			−0.152772	+	0.988261i	$0.548820\pi$
$18$	−114.500	+	44.1834i	−1.49933	+	0.578562i
$19$			10.9783i			0.132557i	0.997801	+	0.0662787i	$0.0211126\pi$
$19$			10.9783i			0.132557i	−0.997801	+	0.0662787i	$0.978887\pi$
$20$	−146.925			−1.64267
$21$		0			0
$22$	−81.4374			−0.789205
$23$		−	69.0934i		−	0.626390i	−0.949689	−	0.313195i	$-0.898601\pi$
$23$		−	69.0934i		−	0.626390i	0.949689	−	0.313195i	$-0.101399\pi$
$24$	−90.7953	−	62.2845i	−0.772230	−	0.529740i
$25$	9.64979			0.0771983
$26$	−283.724			−2.14011
$27$	136.506	+	32.3918i	0.972982	+	0.230881i
$28$		0			0
$29$		−	265.583i		−	1.70061i	−0.526294	−	0.850303i	$-0.676419\pi$
$29$		−	265.583i		−	1.70061i	0.526294	−	0.850303i	$-0.323581\pi$
$30$	226.008	+	155.039i	1.37544	+	0.943535i
$31$		−	10.2283i		−	0.0592598i	−0.999561	−	0.0296299i	$-0.990567\pi$
$31$		−	10.2283i		−	0.0592598i	0.999561	−	0.0296299i	$-0.00943286\pi$
$32$			192.133i			1.06139i
$33$	76.7677	+	52.6617i	0.404956	+	0.277795i
$34$			97.3486i			0.491034i
$35$		0			0
$36$	123.074	+	318.943i	0.569788	+	1.47659i
$37$	41.6514			0.185066			0.0925331	−	0.995710i	$-0.470504\pi$
$37$	41.6514			0.185066			0.0925331	+	0.995710i	$0.470504\pi$
$38$	49.9019			0.213031
$39$	267.455	+	183.471i	1.09813	+	0.753304i
$40$			245.883i			0.971938i
$41$	−31.0035			−0.118096			−0.0590480	−	0.998255i	$-0.518807\pi$
$41$	−31.0035			−0.118096			−0.0590480	+	0.998255i	$0.518807\pi$
$42$		0			0
$43$	−224.550			−0.796363			−0.398181	−	0.917307i	$-0.630359\pi$
$43$	−224.550			−0.796363			−0.398181	+	0.917307i	$0.630359\pi$
$44$			226.847i			0.777237i
$45$	−112.792	−	292.297i	−0.373646	−	0.968291i
$46$	−314.065			−1.00666
$47$	163.719			0.508103			0.254052	−	0.967191i	$-0.418237\pi$
$47$	163.719			0.508103			0.254052	+	0.967191i	$0.418237\pi$
$48$	14.6241	−	21.3182i	0.0439750	−	0.0641046i
$49$		0			0
$50$		−	43.8633i		−	0.124064i
$51$	62.9508	−	91.7665i	0.172841	−	0.251959i
$52$			790.323i			2.10765i
$53$		−	527.220i		−	1.36640i	−0.730231	−	0.683200i	$-0.760588\pi$
$53$		−	527.220i		−	1.36640i	0.730231	−	0.683200i	$-0.239412\pi$
$54$	147.237	−	620.488i	0.371045	−	1.56366i
$55$		−	207.895i		−	0.509682i
$56$		0			0
$57$	−47.0405	−	32.2692i	−0.109310	−	0.0749853i
$58$	−1207.21			−2.73301
$59$	411.956			0.909020			0.454510	−	0.890742i	$-0.349814\pi$
$59$	411.956			0.909020			0.454510	+	0.890742i	$0.349814\pi$
$60$	431.865	−	629.552i	0.929227	−	1.35458i
$61$			258.431i			0.542437i	0.962518	+	0.271218i	$0.0874266\pi$
$61$			258.431i			0.542437i	−0.962518	+	0.271218i	$0.912573\pi$
$62$	−46.4928			−0.0952352
$63$		0			0
$64$	833.541			1.62801
$65$		−	724.296i		−	1.38212i
$66$	239.375	−	348.949i	0.446439	−	0.650797i
$67$	323.474			0.589831			0.294915	−	0.955523i	$-0.404709\pi$
$67$	323.474			0.589831			0.294915	+	0.955523i	$0.404709\pi$
$68$	271.168			0.483587
$69$	296.056	+	203.091i	0.516536	+	0.354338i
$70$		0			0
$71$			45.4199i			0.0759205i	0.999279	+	0.0379603i	$0.0120860\pi$
$71$			45.4199i			0.0759205i	−0.999279	+	0.0379603i	$0.987914\pi$
$72$	533.762	−	205.969i	0.873673	−	0.337134i
$73$			562.199i			0.901376i	0.892682	+	0.450688i	$0.148821\pi$
$73$			562.199i			0.901376i	−0.892682	+	0.450688i	$0.851179\pi$
$74$		−	189.327i		−	0.297416i
$75$	−28.3643	+	41.3481i	−0.0436697	+	0.0636596i
$76$		−	139.004i		−	0.209800i
$77$		0			0
$78$	833.969	−	1215.72i	1.21062	−	1.76478i
$79$	289.221			0.411898			0.205949	−	0.978563i	$-0.433972\pi$
$79$	289.221			0.411898			0.205949	+	0.978563i	$0.433972\pi$
$80$	−57.7320			−0.0806829
$81$	−540.035	+	489.697i	−0.740789	+	0.671738i
$82$			140.927i			0.189790i
$83$	448.767			0.593477			0.296738	−	0.954959i	$-0.404101\pi$
$83$	448.767			0.593477			0.296738	+	0.954959i	$0.404101\pi$
$84$		0			0
$85$	−248.513			−0.317118
$86$			1020.70i			1.27982i
$87$	1137.99	+	780.647i	1.40236	+	0.962002i
$88$	379.635			0.459878
$89$	561.628			0.668904			0.334452	−	0.942413i	$-0.391449\pi$
$89$	561.628			0.668904			0.334452	+	0.942413i	$0.391449\pi$
$90$	−1328.64	+	512.698i	−1.55612	+	0.600479i
$91$		0			0
$92$			874.839i			0.991394i
$93$	43.8268	+	30.0647i	0.0488670	+	0.0335222i
$94$		−	744.187i		−	0.816564i
$95$			127.391i			0.137579i
$96$	−823.265	−	564.750i	−0.875251	−	0.600412i
$97$			214.364i			0.224385i	0.993686	+	0.112192i	$0.0357873\pi$
$97$			214.364i			0.224385i	−0.993686	+	0.112192i	$0.964213\pi$
$98$		0			0
$99$	−451.297	+	174.147i	−0.458152	+	0.176793i
$100$	−122.183			−0.122183
$101$	−1717.69			−1.69224			−0.846122	−	0.532990i	$-0.821068\pi$
$101$	−1717.69			−1.69224			−0.846122	+	0.532990i	$0.821068\pi$
$102$	−417.126	−	286.143i	−0.404918	−	0.277769i
$103$			1157.71i			1.10750i	0.832683	+	0.553750i	$0.186804\pi$
$103$			1157.71i			1.10750i	−0.832683	+	0.553750i	$0.813196\pi$
$104$	1322.63			1.24706
$105$		0			0
$106$	−2396.48			−2.19592
$107$			1217.79i			1.10027i	0.835077	+	0.550134i	$0.185423\pi$
$107$			1217.79i			1.10027i	−0.835077	+	0.550134i	$0.814577\pi$
$108$	−1728.39	−	410.134i	−1.53995	−	0.365418i
$109$	1298.26			1.14084			0.570418	−	0.821355i	$-0.306781\pi$
$109$	1298.26			1.14084			0.570418	+	0.821355i	$0.306781\pi$
$110$	−944.989			−0.819101
$111$	−122.429	+	178.471i	−0.104689	+	0.152610i
$112$		0			0
$113$			1437.86i			1.19701i	0.801118	+	0.598506i	$0.204239\pi$
$113$			1437.86i			1.19701i	−0.801118	+	0.598506i	$0.795761\pi$
$114$	−146.680	+	213.823i	−0.120508	+	0.175670i
$115$		−	801.751i		−	0.650119i
$116$			3362.73i			2.69157i
$117$	−1572.30	+	606.721i	−1.24238	+	0.479413i
$118$		−	1872.55i		−	1.46087i
$119$		0			0
$120$	−1053.58	−	722.741i	−0.801483	−	0.549808i
$121$	1010.02			0.758841
$122$	1174.70			0.871740
$123$	91.1308	−	132.846i	0.0668048	−	0.0973848i
$124$			129.507i			0.0937910i
$125$	−1338.51			−0.957759
$126$		0			0
$127$	2686.32			1.87695			0.938475	−	0.345347i	$-0.112239\pi$
$127$	2686.32			1.87695			0.938475	+	0.345347i	$0.112239\pi$
$128$		−	2251.81i		−	1.55495i
$129$	660.036	−	962.169i	0.450488	−	0.656699i
$130$	−3292.29			−2.22118
$131$	1603.27			1.06930			0.534651	−	0.845073i	$-0.320443\pi$
$131$	1603.27			1.06930			0.534651	+	0.845073i	$0.320443\pi$
$132$	−972.008	−	666.786i	−0.640928	−	0.439669i
$133$		0			0
$134$		−	1470.36i		−	0.947906i
$135$	1583.99	+	375.870i	1.00984	+	0.239628i
$136$		−	453.808i		−	0.286130i
$137$		−	2318.52i		−	1.44588i	−0.690913	−	0.722938i	$-0.742791\pi$
$137$		−	2318.52i		−	1.44588i	0.690913	−	0.722938i	$-0.257209\pi$
$138$	923.153	−	1345.73i	0.569449	−	0.830116i
$139$			1841.57i			1.12374i	0.827225	+	0.561871i	$0.189918\pi$
$139$			1841.57i			1.12374i	−0.827225	+	0.561871i	$0.810082\pi$
$140$		0			0
$141$	−481.230	+	701.514i	−0.287425	+	0.418994i
$142$	206.457			0.122010
$143$	−1118.29			−0.653958
$144$	48.3604	+	125.324i	0.0279863	+	0.0725257i
$145$		−	3081.79i		−	1.76503i
$146$	2555.48			1.44858
$147$		0			0
$148$	−527.377			−0.292906
$149$		−	1300.98i		−	0.715302i	−0.933855	−	0.357651i	$-0.883578\pi$
$149$		−	1300.98i		−	0.715302i	0.933855	−	0.357651i	$-0.116422\pi$
$150$	187.948	+	128.930i	0.102306	+	0.0701808i
$151$	−2616.49			−1.41011			−0.705055	−	0.709152i	$-0.749078\pi$
$151$	−2616.49			−1.41011			−0.705055	+	0.709152i	$0.749078\pi$
$152$	−232.627			−0.124135
$153$	208.172	+	539.472i	0.109998	+	0.285057i
$154$		0			0
$155$		−	118.688i		−	0.0615046i
$156$	−3386.43	−	2323.05i	−1.73802	−	1.19226i
$157$			935.164i			0.475377i	0.971341	+	0.237689i	$0.0763898\pi$
$157$			935.164i			0.475377i	−0.971341	+	0.237689i	$0.923610\pi$
$158$		−	1314.66i		−	0.661953i
$159$	2259.07	+	1549.69i	1.12677	+	0.772948i
$160$			2229.49i			1.10160i
$161$		0			0
$162$	2225.92	+	2454.74i	1.07954	+	1.19051i
$163$	−518.158			−0.248989			−0.124495	−	0.992220i	$-0.539731\pi$
$163$	−518.158			−0.248989			−0.124495	+	0.992220i	$0.539731\pi$
$164$	392.557			0.186912
$165$	890.802	+	611.080i	0.420296	+	0.288318i
$166$		−	2039.88i		−	0.953765i
$167$	−3767.97			−1.74595			−0.872977	−	0.487761i	$-0.837814\pi$
$167$	−3767.97			−1.74595			−0.872977	+	0.487761i	$0.837814\pi$
$168$		0			0
$169$	−1699.06			−0.773356
$170$			1129.62i			0.509635i
$171$	276.539	−	106.711i	0.123669	−	0.0477217i
$172$	2843.18			1.26041
$173$	−2393.06			−1.05168			−0.525841	−	0.850583i	$-0.676249\pi$
$173$	−2393.06			−1.05168			−0.525841	+	0.850583i	$0.676249\pi$
$174$	3548.44	−	5172.74i	1.54602	−	2.25371i
$175$		0			0
$176$			89.1363i			0.0381756i
$177$	−1210.89	+	1765.18i	−0.514216	+	0.749599i
$178$		−	2552.89i		−	1.07498i
$179$		−	640.144i		−	0.267299i	−0.991029	−	0.133650i	$-0.957330\pi$
$179$		−	640.144i		−	0.267299i	0.991029	−	0.133650i	$-0.0426697\pi$
$180$	1428.14	+	3700.97i	0.591373	+	1.53252i
$181$		−	4204.05i		−	1.72643i	−0.504833	−	0.863217i	$-0.668446\pi$
$181$		−	4204.05i		−	1.72643i	0.504833	−	0.863217i	$-0.331554\pi$
$182$		0			0
$183$	−1107.34	−	759.623i	−0.447306	−	0.306847i
$184$	1464.07			0.586591
$185$	483.318			0.192077
$186$	136.659	−	199.215i	0.0538729	−	0.0785332i
$187$			383.696i			0.150046i
$188$	−2072.96			−0.804181
$189$		0			0
$190$	579.056			0.221101
$191$		−	1457.06i		−	0.551985i	−0.961160	−	0.275993i	$-0.910993\pi$
$191$		−	1457.06i		−	0.551985i	0.961160	−	0.275993i	$-0.0890066\pi$
$192$	−2450.08	+	3571.61i	−0.920935	+	1.34249i
$193$	1829.27			0.682246			0.341123	−	0.940019i	$-0.389193\pi$
$193$	1829.27			0.682246			0.341123	+	0.940019i	$0.389193\pi$
$194$	974.393			0.360605
$195$	3103.51	+	2128.97i	1.13973	+	0.781840i
$196$		0			0
$197$		−	661.168i		−	0.239118i	−0.992827	−	0.119559i	$-0.961852\pi$
$197$		−	661.168i		−	0.239118i	0.992827	−	0.119559i	$-0.0381481\pi$
$198$	791.589	+	2051.38i	0.284120	+	0.736288i
$199$			1949.13i			0.694322i	0.937806	+	0.347161i	$0.112854\pi$
$199$			1949.13i			0.694322i	−0.937806	+	0.347161i	$0.887146\pi$
$200$			204.477i			0.0722934i
$201$	−950.810	+	1386.04i	−0.333657	+	0.486388i
$202$			7807.78i			2.71957i
$203$		0			0
$204$	−797.063	+	1161.92i	−0.273557	+	0.398777i
$205$	−359.761			−0.122570
$206$	5262.38			1.77984
$207$	−1740.44	+	671.603i	−0.584390	+	0.225505i
$208$			310.547i			0.103522i
$209$	196.687			0.0650963
$210$		0			0
$211$	3341.96			1.09038			0.545189	−	0.838313i	$-0.316458\pi$
$211$	3341.96			1.09038			0.545189	+	0.838313i	$0.316458\pi$
$212$			6675.49i			2.16262i
$213$	−194.619	−	133.506i	−0.0626058	−	0.0429469i
$214$	5535.50			1.76822
$215$	−2605.65			−0.826530
$216$	−686.373	+	2892.52i	−0.216212	+	0.911162i
$217$		0			0
$218$		−	5901.27i		−	1.83342i
$219$	−2408.95	−	1652.51i	−0.743296	−	0.509892i
$220$			2632.30i			0.806680i
$221$			1336.78i			0.406885i
$222$	811.242	+	556.502i	0.245257	+	0.168243i
$223$		−	2143.28i		−	0.643608i	−0.946806	−	0.321804i	$-0.895711\pi$
$223$		−	2143.28i		−	0.643608i	0.946806	−	0.321804i	$-0.104289\pi$
$224$		0			0
$225$	−93.7981	−	243.075i	−0.0277920	−	0.0720221i
$226$	6535.80			1.92370
$227$	−2569.11			−0.751178			−0.375589	−	0.926786i	$-0.622560\pi$
$227$	−2569.11			−0.751178			−0.375589	+	0.926786i	$0.622560\pi$
$228$	595.612	+	408.583i	0.173006	+	0.118680i
$229$			105.173i			0.0303495i	0.999885	+	0.0151748i	$0.00483046\pi$
$229$			105.173i			0.0303495i	−0.999885	+	0.0151748i	$0.995170\pi$
$230$	−3644.37			−1.04479
$231$		0			0
$232$	5627.64			1.59255
$233$			2625.72i			0.738270i	0.929376	+	0.369135i	$0.120346\pi$
$233$			2625.72i			0.738270i	−0.929376	+	0.369135i	$0.879654\pi$
$234$	2757.86	+	7146.90i	0.770456	+	1.99661i
$235$	1899.77			0.527351
$236$	−5216.06			−1.43872
$237$	−850.127	+	1239.27i	−0.233003	+	0.339660i
$238$		0			0
$239$		−	6080.85i		−	1.64576i	−0.568212	−	0.822882i	$-0.692365\pi$
$239$		−	6080.85i		−	1.64576i	0.568212	−	0.822882i	$-0.307635\pi$
$240$	169.696	−	247.374i	0.0456409	−	0.0665330i
$241$		−	4628.89i		−	1.23723i	−0.785693	−	0.618616i	$-0.787694\pi$
$241$		−	4628.89i		−	1.23723i	0.785693	−	0.618616i	$-0.212306\pi$
$242$		−	4591.05i		−	1.21952i
$243$	−510.927	−	3753.38i	−0.134881	−	0.990862i
$244$		−	3272.17i		−	0.858521i
$245$		0			0
$246$	−603.853	−	414.236i	−0.156505	−	0.107361i
$247$	685.248			0.176523
$248$	216.735			0.0554946
$249$	−1319.09	+	1922.91i	−0.335719	+	0.489395i
$250$			6084.21i			1.53920i
$251$	5967.85			1.50075			0.750373	−	0.661015i	$-0.229874\pi$
$251$	5967.85			1.50075			0.750373	+	0.661015i	$0.229874\pi$
$252$		0			0
$253$	−1237.88			−0.307607
$254$		−	12210.7i		−	3.01641i
$255$	730.472	−	1064.85i	0.179388	−	0.261503i
$256$	−3567.29			−0.870920
$257$	5639.40			1.36878			0.684389	−	0.729117i	$-0.260069\pi$
$257$	5639.40			1.36878			0.684389	+	0.729117i	$0.260069\pi$
$258$	−4373.55	−	3000.20i	−1.05537	−	0.723971i
$259$		0			0
$260$			9170.80i			2.18750i
$261$	−6689.94	+	2581.53i	−1.58658	+	0.612232i
$262$		−	7287.70i		−	1.71846i
$263$			3485.62i			0.817234i	0.912706	+	0.408617i	$0.133989\pi$
$263$			3485.62i			0.817234i	−0.912706	+	0.408617i	$0.866011\pi$
$264$	−1115.89	+	1626.69i	−0.260145	+	0.379226i
$265$		−	6117.79i		−	1.41816i
$266$		0			0
$267$	−1650.83	+	2406.50i	−0.378387	+	0.551594i
$268$	−4095.73			−0.933531
$269$	3794.55			0.860066			0.430033	−	0.902813i	$-0.358502\pi$
$269$	3794.55			0.860066			0.430033	+	0.902813i	$0.358502\pi$
$270$	1708.52	−	7200.06i	0.385101	−	1.62290i
$271$		−	7457.62i		−	1.67165i	−0.548993	−	0.835827i	$-0.684989\pi$
$271$		−	7457.62i		−	1.67165i	0.548993	−	0.835827i	$-0.315011\pi$
$272$	106.552			0.0237524
$273$		0			0
$274$	−10538.9			−2.32364
$275$		−	172.886i		−	0.0379105i
$276$	−3748.57	−	2571.48i	−0.817527	−	0.560814i
$277$	−3415.49			−0.740856			−0.370428	−	0.928861i	$-0.620789\pi$
$277$	−3415.49			−0.740856			−0.370428	+	0.928861i	$0.620789\pi$
$278$	8370.89			1.80595
$279$	−257.646	+	99.4210i	−0.0552863	+	0.0213340i
$280$		0			0
$281$			2762.14i			0.586390i	0.956053	+	0.293195i	$0.0947185\pi$
$281$			2762.14i			0.586390i	−0.956053	+	0.293195i	$0.905281\pi$
$282$	3188.74	+	2187.44i	0.673358	+	0.461915i
$283$			5505.20i			1.15636i	0.815909	+	0.578181i	$0.196237\pi$
$283$			5505.20i			1.15636i	−0.815909	+	0.578181i	$0.803763\pi$
$284$		−	575.093i		−	0.120160i
$285$	−545.852	−	374.448i	−0.113451	−	0.0778259i
$286$			5083.19i			1.05096i
$287$		0			0
$288$	4839.76	−	1867.57i	0.990227	−	0.382110i
$289$	−4454.34			−0.906643
$290$	−14008.3			−2.83654
$291$	−918.520	−	630.094i	−0.185033	−	0.126930i
$292$		−	7118.39i		−	1.42662i
$293$	4101.08			0.817705			0.408853	−	0.912600i	$-0.365929\pi$
$293$	4101.08			0.817705			0.408853	+	0.912600i	$0.365929\pi$
$294$		0			0
$295$	4780.29			0.943455
$296$			882.583i			0.173308i
$297$	580.331	−	2445.63i	0.113381	−	0.477812i
$298$	−5913.60			−1.14955
$299$	−4312.70			−0.834148
$300$	359.140	−	523.537i	0.0691165	−	0.100755i
$301$		0			0
$302$			11893.3i			2.26616i
$303$	5048.93	−	7360.08i	0.957271	−	1.39546i
$304$		−	54.6196i		−	0.0103048i
$305$			2998.80i			0.562985i
$306$	2452.17	−	946.249i	0.458109	−	0.176776i
$307$			8281.42i			1.53956i	0.638308	+	0.769781i	$0.279635\pi$
$307$			8281.42i			1.53956i	−0.638308	+	0.769781i	$0.720365\pi$
$308$		0			0
$309$	−4960.63	−	3402.94i	−0.913270	−	0.626493i
$310$	−539.496			−0.0988429
$311$	6871.05			1.25280			0.626401	−	0.779501i	$-0.284527\pi$
$311$	6871.05			1.25280			0.626401	+	0.779501i	$0.284527\pi$
$312$	−3887.70	+	5667.30i	−0.705441	+	1.02836i
$313$		−	3374.49i		−	0.609386i	−0.952451	−	0.304693i	$-0.901446\pi$
$313$		−	3374.49i		−	0.609386i	0.952451	−	0.304693i	$-0.0985538\pi$
$314$	4250.80			0.763970
$315$		0			0
$316$	−3662.02			−0.651914
$317$			2369.77i			0.419872i	0.977715	+	0.209936i	$0.0673255\pi$
$317$			2369.77i			0.419872i	−0.977715	+	0.209936i	$0.932674\pi$
$318$	7044.15	−	10268.6i	1.24219	−	1.81080i
$319$	−4758.19			−0.835133
$320$	9672.30			1.68968
$321$	−5218.09	−	3579.55i	−0.907306	−	0.622401i
$322$		0			0
$323$		−	235.116i		−	0.0405021i
$324$	6837.75	−	6200.39i	1.17245	−	1.06317i
$325$		−	602.325i		−	0.102803i
$326$			2355.29i			0.400146i
$327$	−3816.08	+	5562.89i	−0.645350	+	0.940760i
$328$		−	656.957i		−	0.110593i
$329$		0			0
$330$	2777.67	−	4049.15i	0.463351	−	0.675450i
$331$	3803.61			0.631617			0.315808	−	0.948823i	$-0.397724\pi$
$331$	3803.61			0.631617			0.315808	+	0.948823i	$0.397724\pi$
$332$	−5682.14			−0.939302
$333$	−404.861	−	1049.18i	−0.0666253	−	0.172657i
$334$			17127.4i			2.80589i
$335$	3753.55			0.612175
$336$		0			0
$337$	−592.955			−0.0958466			−0.0479233	−	0.998851i	$-0.515260\pi$
$337$	−592.955			−0.0958466			−0.0479233	+	0.998851i	$0.515260\pi$
$338$			7723.11i			1.24285i
$339$	−6161.04	−	4226.40i	−0.987084	−	0.677128i
$340$	3146.60			0.501906
$341$	−183.250			−0.0291013
$342$	−485.058	−	1257.01i	−0.0766927	−	0.198747i
$343$		0			0
$344$		−	4758.16i		−	0.745764i
$345$	3435.40	+	2356.64i	0.536103	+	0.367760i
$346$			10877.7i			1.69014i
$347$			4777.16i			0.739054i	0.929220	+	0.369527i	$0.120480\pi$
$347$			4777.16i			0.739054i	−0.929220	+	0.369527i	$0.879520\pi$
$348$	−14408.9	−	9884.31i	−2.21953	−	1.52257i
$349$		−	7358.26i		−	1.12859i	−0.825573	−	0.564296i	$-0.809148\pi$
$349$		−	7358.26i		−	1.12859i	0.825573	−	0.564296i	$-0.190852\pi$
$350$		0			0
$351$	2021.84	−	8520.47i	0.307459	−	1.29569i
$352$	3442.25			0.521229
$353$	−3305.55			−0.498405			−0.249202	−	0.968451i	$-0.580168\pi$
$353$	−3305.55			−0.498405			−0.249202	+	0.968451i	$0.580168\pi$
$354$	8023.65	+	5504.13i	1.20467	+	0.826387i
$355$			527.047i			0.0787965i
$356$	−7111.16			−1.05868
$357$		0			0
$358$	−2909.78			−0.429572
$359$		−	414.716i		−	0.0609689i	−0.999535	−	0.0304845i	$-0.990295\pi$
$359$		−	414.716i		−	0.0609689i	0.999535	−	0.0304845i	$-0.00970501\pi$
$360$	6193.70	−	2390.04i	0.906769	−	0.349905i
$361$	6738.48			0.982429
$362$	−19109.6			−2.77452
$363$	−2968.81	+	4327.79i	−0.429263	+	0.625758i
$364$		0			0
$365$			6523.69i			0.935522i
$366$	−3452.88	+	5033.43i	−0.493128	+	0.718858i
$367$			76.1227i			0.0108272i	0.999985	+	0.00541359i	$0.00172321\pi$
$367$			76.1227i			0.0108272i	−0.999985	+	0.00541359i	$0.998277\pi$
$368$			343.756i			0.0486944i
$369$	301.361	+	780.967i	0.0425155	+	0.110178i
$370$		−	2196.93i		−	0.308683i
$371$		0			0
$372$	−554.921	−	380.669i	−0.0773423	−	0.0530559i
$373$	−12301.0			−1.70756			−0.853781	−	0.520632i	$-0.825696\pi$
$373$	−12301.0			−1.70756			−0.853781	+	0.520632i	$0.825696\pi$
$374$	1744.10			0.241137
$375$	3934.37	−	5735.34i	0.541787	−	0.789791i
$376$			3469.16i			0.475820i
$377$	−16577.3			−2.26465
$378$		0			0
$379$	−1429.02			−0.193678			−0.0968389	−	0.995300i	$-0.530873\pi$
$379$	−1429.02			−0.193678			−0.0968389	+	0.995300i	$0.530873\pi$
$380$		−	1612.98i		−	0.217748i
$381$	−7896.10	+	11510.5i	−1.06176	+	1.54778i
$382$	−6623.09			−0.887086
$383$	−5110.90			−0.681866			−0.340933	−	0.940088i	$-0.610743\pi$
$383$	−5110.90			−0.681866			−0.340933	+	0.940088i	$0.610743\pi$
$384$	9648.70	+	6618.89i	1.28225	+	0.879606i
$385$		0			0
$386$		−	8314.95i		−	1.09642i
$387$	2182.68	+	5656.34i	0.286697	+	0.742966i
$388$		−	2714.20i		−	0.355136i
$389$		−	7320.62i		−	0.954165i	−0.878858	−	0.477083i	$-0.841694\pi$
$389$		−	7320.62i		−	0.954165i	0.878858	−	0.477083i	$-0.158306\pi$
$390$	9677.27	−	14107.1i	1.25648	−	1.83164i
$391$			1479.73i			0.191390i
$392$		0			0
$393$	−4712.61	+	6869.82i	−0.604885	+	0.881772i
$394$	−3005.35			−0.384283
$395$	3356.08			0.427501
$396$	5714.18	−	2205.00i	0.725122	−	0.279811i
$397$			8679.44i			1.09725i	0.836068	+	0.548625i	$0.184849\pi$
$397$			8679.44i			1.09725i	−0.836068	+	0.548625i	$0.815151\pi$
$398$	8859.79			1.11583
$399$		0			0
$400$	−48.0100			−0.00600125
$401$			9754.54i			1.21476i	0.794412	+	0.607379i	$0.207779\pi$
$401$			9754.54i			1.21476i	−0.794412	+	0.607379i	$0.792221\pi$
$402$	6300.28	+	4321.92i	0.781666	+	0.536213i
$403$	−638.433			−0.0789147
$404$	21748.9			2.67833
$405$	−6266.49	+	5682.38i	−0.768851	+	0.697185i
$406$		0			0
$407$		−	746.226i		−	0.0908822i
$408$	1944.51	+	1333.91i	0.235950	+	0.161859i
$409$		−	3389.41i		−	0.409769i	−0.978786	−	0.204885i	$-0.934318\pi$
$409$		−	3389.41i		−	0.409769i	0.978786	−	0.204885i	$-0.0656819\pi$
$410$			1635.30i			0.196979i
$411$	9934.58	+	6815.00i	1.19230	+	0.817906i
$412$		−	14658.5i		−	1.75285i
$413$		0			0
$414$	3052.78	+	7911.18i	0.362406	+	0.939163i
$415$	5207.43			0.615959
$416$	11992.6			1.41343
$417$	−7890.90	−	5413.06i	−0.926664	−	0.635681i
$418$		−	894.043i		−	0.104615i
$419$	12777.4			1.48977			0.744887	−	0.667191i	$-0.232504\pi$
$419$	12777.4			1.48977			0.744887	+	0.667191i	$0.232504\pi$
$420$		0			0
$421$	11005.4			1.27404			0.637020	−	0.770848i	$-0.280167\pi$
$421$	11005.4			1.27404			0.637020	+	0.770848i	$0.280167\pi$
$422$		−	15190.9i		−	1.75233i
$423$	−1591.38	−	4124.02i	−0.182921	−	0.474035i
$424$	11171.6			1.27958
$425$	−206.664			−0.0235875
$426$	−606.853	+	884.641i	−0.0690191	+	0.100613i
$427$		0			0
$428$		−	15419.3i		−	1.74140i
$429$	3287.06	−	4791.72i	0.369932	−	0.539269i
$430$			11844.0i			1.32830i
$431$		−	3786.41i		−	0.423167i	−0.977360	−	0.211584i	$-0.932138\pi$
$431$		−	3786.41i		−	0.423167i	0.977360	−	0.211584i	$-0.0678621\pi$
$432$	−679.147	−	161.157i	−0.0756377	−	0.0179483i
$433$			3191.67i			0.354230i	0.984190	+	0.177115i	$0.0566765\pi$
$433$			3191.67i			0.354230i	−0.984190	+	0.177115i	$0.943323\pi$
$434$		0			0
$435$	13205.1	+	9058.53i	1.45548	+	0.998444i
$436$	−16438.2			−1.80561
$437$	758.527			0.0830327
$438$	−7511.51	+	10949.9i	−0.819438	+	1.19454i
$439$		−	3317.34i		−	0.360656i	−0.983607	−	0.180328i	$-0.942284\pi$
$439$		−	3317.34i		−	0.360656i	0.983607	−	0.180328i	$-0.0577159\pi$
$440$	4405.24			0.477299
$441$		0			0
$442$	6076.35			0.653897
$443$		−	10700.5i		−	1.14763i	−0.818986	−	0.573813i	$-0.805464\pi$
$443$		−	10700.5i		−	1.14763i	0.818986	−	0.573813i	$-0.194536\pi$
$444$	1550.16	−	2259.74i	0.165692	−	0.241537i
$445$	6517.06			0.694243
$446$	−9742.29			−1.03433
$447$	5574.51	+	3824.05i	0.589855	+	0.404634i
$448$		0			0
$449$			4017.92i			0.422310i	0.977453	+	0.211155i	$0.0677225\pi$
$449$			4017.92i			0.422310i	−0.977453	+	0.211155i	$0.932278\pi$
$450$	−1104.90	+	426.360i	−0.115745	+	0.0446640i
$451$			555.459i			0.0579945i
$452$		−	18205.7i		−	1.89452i
$453$	7690.82	−	11211.3i	0.797674	−	1.16281i
$454$			11677.9i			1.20720i
$455$		0			0
$456$	683.777	−	996.777i	0.0702210	−	0.102365i
$457$	9169.65			0.938596			0.469298	−	0.883040i	$-0.344507\pi$
$457$	9169.65			0.938596			0.469298	+	0.883040i	$0.344507\pi$
$458$	478.066			0.0487742
$459$	−2923.46	−	693.716i	−0.297289	−	0.0705444i
$460$			10151.5i			1.02895i
$461$	−1289.80			−0.130308			−0.0651542	−	0.997875i	$-0.520754\pi$
$461$	−1289.80			−0.130308			−0.0651542	+	0.997875i	$0.520754\pi$
$462$		0			0
$463$	6976.52			0.700273			0.350137	−	0.936699i	$-0.386135\pi$
$463$	6976.52			0.700273			0.350137	+	0.936699i	$0.386135\pi$
$464$			1321.34i			0.132202i
$465$	508.561	+	348.867i	0.0507182	+	0.0347920i
$466$	11935.3			1.18646
$467$	7863.66			0.779201			0.389600	−	0.920984i	$-0.372613\pi$
$467$	7863.66			0.779201			0.389600	+	0.920984i	$0.372613\pi$
$468$	19907.9	−	7682.11i	1.96633	−	0.758772i
$469$		0			0
$470$		−	8635.44i		−	0.847496i
$471$	−4007.06	−	2748.79i	−0.392007	−	0.268912i
$472$			8729.25i			0.851263i
$473$			4023.04i			0.391077i
$474$	5633.14	+	3864.26i	0.545862	+	0.374455i
$475$			105.938i			0.0102332i
$476$		0			0
$477$	−13280.5	+	5124.69i	−1.27478	+	0.491915i
$478$	−27640.6			−2.64488
$479$	−3694.27			−0.352391			−0.176196	−	0.984355i	$-0.556379\pi$
$479$	−3694.27			−0.352391			−0.176196	+	0.984355i	$0.556379\pi$
$480$	−9553.05	−	6553.28i	−0.908407	−	0.623156i
$481$		−	2599.82i		−	0.246448i
$482$	−21040.7			−1.98833
$483$		0			0
$484$	−12788.5			−1.20103
$485$			2487.45i			0.232885i
$486$	−17061.0	+	2322.42i	−1.59240	+	0.216764i
$487$	−1052.72			−0.0979533			−0.0489766	−	0.998800i	$-0.515596\pi$
$487$	−1052.72			−0.0979533			−0.0489766	+	0.998800i	$0.515596\pi$
$488$	−5476.08			−0.507972
$489$	1523.06	−	2220.24i	0.140849	−	0.205322i
$490$		0			0
$491$		−	2378.40i		−	0.218607i	−0.994008	−	0.109303i	$-0.965138\pi$
$491$		−	2378.40i		−	0.218607i	0.994008	−	0.109303i	$-0.0348620\pi$
$492$	−1153.87	+	1682.05i	−0.105733	+	0.154132i
$493$			5687.84i			0.519609i
$494$		−	3114.80i		−	0.283687i
$495$	−5236.79	+	2020.78i	−0.475508	+	0.183490i
$496$			50.8881i			0.00460674i
$497$		0			0
$498$	8740.60	+	5995.95i	0.786497	+	0.539528i
$499$	18771.5			1.68402			0.842011	−	0.539461i	$-0.181372\pi$
$499$	18771.5			1.68402			0.842011	+	0.539461i	$0.181372\pi$
$500$	16947.8			1.51586
$501$	11075.5	−	16145.3i	0.987655	−	1.43975i
$502$		−	27126.9i		−	2.41182i
$503$	−16095.2			−1.42674			−0.713370	−	0.700788i	$-0.752832\pi$
$503$	−16095.2			−1.42674			−0.713370	+	0.700788i	$0.752832\pi$
$504$		0			0
$505$	−19931.9			−1.75635
$506$			5626.79i			0.494350i
$507$	4994.17	−	7280.26i	0.437473	−	0.637728i
$508$	−34013.4			−2.97067
$509$	−3150.63			−0.274360			−0.137180	−	0.990546i	$-0.543804\pi$
$509$	−3150.63			−0.274360			−0.137180	+	0.990546i	$0.543804\pi$
$510$	−4840.28	−	3320.37i	−0.420257	−	0.288291i
$511$		0			0
$512$		−	1799.30i		−	0.155310i
$513$	−355.606	+	1498.60i	−0.0306051	+	0.128976i
$514$		−	25633.9i		−	2.19974i
$515$			13433.9i			1.14945i
$516$	−8357.17	+	12182.7i	−0.712992	+	1.03937i
$517$		−	2933.19i		−	0.249519i
$518$		0			0
$519$	7034.08	−	10253.9i	0.594917	−	0.867241i
$520$	15347.6			1.29430
$521$	4979.20			0.418700			0.209350	−	0.977841i	$-0.432865\pi$
$521$	4979.20			0.418700			0.209350	+	0.977841i	$0.432865\pi$
$522$	11734.4	+	30409.2i	0.983906	+	2.54976i
$523$			13829.8i			1.15628i	0.815936	+	0.578142i	$0.196222\pi$
$523$			13829.8i			1.15628i	−0.815936	+	0.578142i	$0.803778\pi$
$524$	−20300.1			−1.69240
$525$		0			0
$526$	15843.9			1.31336
$527$			219.053i			0.0181064i
$528$	−381.937	−	262.005i	−0.0314805	−	0.0215952i
$529$	7393.10			0.607635
$530$	−27808.5			−2.27910
$531$	−4004.31	−	10377.0i	−0.327254	−	0.848069i
$532$		0			0
$533$			1935.19i			0.157265i
$534$	10938.8	+	7503.88i	0.886456	+	0.608098i
$535$			14131.1i			1.14195i
$536$			6854.33i			0.552355i
$537$	2742.93	+	1881.62i	0.220421	+	0.151206i
$538$		−	17248.2i		−	1.38220i
$539$		0			0
$540$	−20056.0	−	4759.15i	−1.59828	−	0.379261i
$541$	5317.95			0.422618			0.211309	−	0.977419i	$-0.432227\pi$
$541$	5317.95			0.422618			0.211309	+	0.977419i	$0.432227\pi$
$542$	−33898.7			−2.68648
$543$	18013.8	+	12357.3i	1.42366	+	0.976613i
$544$		−	4114.80i		−	0.324302i
$545$	15064.9			1.18405
$546$		0			0
$547$	−9266.96			−0.724363			−0.362181	−	0.932108i	$-0.617968\pi$
$547$	−9266.96			−0.724363			−0.362181	+	0.932108i	$0.617968\pi$
$548$			29356.4i			2.28840i
$549$	6509.77	−	2512.00i	0.506066	−	0.195282i
$550$	−785.854			−0.0609253
$551$	2915.65			0.225428
$552$	−4303.45	+	6273.36i	−0.331824	+	0.483717i
$553$		0			0
$554$			15525.2i			1.19062i
$555$	−1420.65	+	2070.95i	−0.108654	+	0.158391i
$556$		−	23317.4i		−	1.77856i
$557$			145.400i			0.0110607i	0.999985	+	0.00553033i	$0.00176037\pi$
$557$			145.400i			0.0110607i	−0.999985	+	0.00553033i	$0.998240\pi$
$558$	451.920	+	1171.14i	0.0342854	+	0.0888497i
$559$			14016.1i			1.06050i
$560$		0			0
$561$	−1644.09	−	1127.83i	−0.123732	−	0.0848785i
$562$	12555.4			0.942376
$563$	−3916.24			−0.293161			−0.146581	−	0.989199i	$-0.546827\pi$
$563$	−3916.24			−0.293161			−0.146581	+	0.989199i	$0.546827\pi$
$564$	6093.19	−	8882.35i	0.454910	−	0.663146i
$565$			16684.7i			1.24236i
$566$	25024.0			1.85837
$567$		0			0
$568$	−962.437			−0.0710968
$569$		−	8550.53i		−	0.629977i	−0.949096	−	0.314988i	$-0.897999\pi$
$569$		−	8550.53i		−	0.629977i	0.949096	−	0.314988i	$-0.102001\pi$
$570$	−1702.06	+	2481.18i	−0.125073	+	0.182325i
$571$	−23913.7			−1.75264			−0.876318	−	0.481733i	$-0.840007\pi$
$571$	−23913.7			−1.75264			−0.876318	+	0.481733i	$0.840007\pi$
$572$	14159.4			1.03503
$573$	6243.32	+	4282.84i	0.455180	+	0.312248i
$574$		0			0
$575$		−	666.737i		−	0.0483563i
$576$	−8102.20	−	20996.6i	−0.586096	−	1.51885i
$577$		−	13103.3i		−	0.945405i	−0.881222	−	0.472703i	$-0.843279\pi$
$577$		−	13103.3i		−	0.945405i	0.881222	−	0.472703i	$-0.156721\pi$
$578$			20247.2i			1.45705i
$579$	−5376.89	+	7838.16i	−0.385934	+	0.562596i
$580$			39020.7i			2.79353i
$581$		0			0
$582$	−2864.10	+	4175.15i	−0.203988	+	0.297363i
$583$	−9445.66			−0.671011
$584$	−11912.9			−0.844106
$585$	−18244.7	+	7040.31i	−1.28945	+	0.497574i
$586$		−	18641.5i		−	1.31412i
$587$	18034.7			1.26809			0.634047	−	0.773294i	$-0.281392\pi$
$587$	18034.7			1.26809			0.634047	+	0.773294i	$0.281392\pi$
$588$		0			0
$589$	112.289			0.00785532
$590$		−	21728.9i		−	1.51621i
$591$	2833.02	+	1943.42i	0.197183	+	0.135265i
$592$	−207.226			−0.0143867
$593$	−22716.2			−1.57309			−0.786547	−	0.617531i	$-0.788133\pi$
$593$	−22716.2			−1.57309			−0.786547	+	0.617531i	$0.788133\pi$
$594$	−11116.7	−	2637.90i	−0.767882	−	0.182213i
$595$		0			0
$596$			16472.5i			1.13212i
$597$	−8351.76	−	5729.21i	−0.572554	−	0.392765i
$598$			19603.5i			1.34054i
$599$		−	13533.6i		−	0.923149i	−0.887101	−	0.461575i	$-0.847285\pi$
$599$		−	13533.6i		−	0.923149i	0.887101	−	0.461575i	$-0.152715\pi$
$600$	−876.156	−	601.032i	−0.0596148	−	0.0408951i
$601$		−	3667.98i		−	0.248952i	−0.992223	−	0.124476i	$-0.960275\pi$
$601$		−	3667.98i		−	0.248952i	0.992223	−	0.124476i	$-0.0397250\pi$
$602$		0			0
$603$	−3144.24	−	8148.20i	−0.212344	−	0.550282i
$604$	33129.1			2.23180
$605$	11720.1			0.787587
$606$	−33455.3	−	22950.0i	−2.24262	−	1.53841i
$607$		−	8017.00i		−	0.536079i	−0.963408	−	0.268039i	$-0.913624\pi$
$607$		−	8017.00i		−	0.536079i	0.963408	−	0.268039i	$-0.0863758\pi$
$608$	−2109.29			−0.140696
$609$		0			0
$610$	13631.1			0.904763
$611$		−	10219.1i		−	0.676628i
$612$	−2635.81	−	6830.62i	−0.174095	−	0.451162i
$613$	9396.52			0.619122			0.309561	−	0.950880i	$-0.399818\pi$
$613$	9396.52			0.619122			0.309561	+	0.950880i	$0.399818\pi$
$614$	37643.3			2.47420
$615$	1057.47	−	1541.53i	0.0693355	−	0.101074i
$616$		0			0
$617$		−	8906.76i		−	0.581155i	−0.956851	−	0.290578i	$-0.906153\pi$
$617$		−	8906.76i		−	0.581155i	0.956851	−	0.290578i	$-0.0938474\pi$
$618$	−15468.1	+	22548.6i	−1.00682	+	1.46770i
$619$			7034.12i			0.456745i	0.973574	+	0.228373i	$0.0733404\pi$
$619$			7034.12i			0.456745i	−0.973574	+	0.228373i	$0.926660\pi$
$620$			1502.78i			0.0973440i
$621$	2238.06	−	9431.64i	0.144622	−	0.609466i
$622$		−	31232.4i		−	2.01335i
$623$		0			0
$624$	−1330.65	−	912.811i	−0.0853665	−	0.0585604i
$625$	−16738.1			−1.07124
$626$	−15338.8			−0.979332
$627$	−578.135	+	842.778i	−0.0368238	+	0.0536799i
$628$		−	11840.8i		−	0.752385i
$629$	−892.024			−0.0565458
$630$		0			0
$631$	−12628.6			−0.796728			−0.398364	−	0.917227i	$-0.630422\pi$
$631$	−12628.6			−0.796728			−0.398364	+	0.917227i	$0.630422\pi$
$632$			6128.52i			0.385727i
$633$	−9823.25	+	14319.9i	−0.616808	+	0.899152i
$634$	10771.8			0.674768
$635$	31171.8			1.94805
$636$	−28603.6	−	19621.7i	−1.78334	−	1.22335i
$637$		0			0
$638$			21628.4i			1.34213i
$639$	1144.11	−	441.492i	0.0708300	−	0.0273320i
$640$		−	26129.7i		−	1.61385i
$641$			9923.02i			0.611444i	0.952121	+	0.305722i	$0.0988978\pi$
$641$			9923.02i			0.611444i	−0.952121	+	0.305722i	$0.901102\pi$
$642$	−16270.9	+	23718.9i	−1.00025	+	1.45811i
$643$			294.191i			0.0180432i	0.999959	+	0.00902160i	$0.00287170\pi$
$643$			294.191i			0.0180432i	−0.999959	+	0.00902160i	$0.997128\pi$
$644$		0			0
$645$	7658.97	−	11164.9i	0.467553	−	0.681576i
$646$	−1068.72			−0.0650902
$647$	7718.79			0.469021			0.234511	−	0.972114i	$-0.424651\pi$
$647$	7718.79			0.469021			0.234511	+	0.972114i	$0.424651\pi$
$648$	−10376.6	−	11443.2i	−0.629058	−	0.693721i
$649$		−	7380.61i		−	0.446401i
$650$	−2737.88			−0.165213
$651$		0			0
$652$	6560.75			0.394078
$653$		−	11370.2i		−	0.681395i	−0.940173	−	0.340697i	$-0.889337\pi$
$653$		−	11370.2i		−	0.681395i	0.940173	−	0.340697i	$-0.110663\pi$
$654$	25286.2	+	17346.0i	1.51188	+	1.03713i
$655$	18604.2			1.10981
$656$	154.250			0.00918056
$657$	14161.6	−	5464.70i	0.840938	−	0.324503i
$658$		0			0
$659$			19795.1i			1.17012i	0.810990	+	0.585060i	$0.198929\pi$
$659$			19795.1i			1.17012i	−0.810990	+	0.585060i	$0.801071\pi$
$660$	−11279.1	−	7737.30i	−0.665207	−	0.456324i
$661$		−	31057.5i		−	1.82753i	−0.406247	−	0.913763i	$-0.633163\pi$
$661$		−	31057.5i		−	1.82753i	0.406247	−	0.913763i	$-0.366837\pi$
$662$		−	17289.3i		−	1.01506i
$663$	−5727.93	−	3929.29i	−0.335527	−	0.230167i
$664$			9509.25i			0.555769i
$665$		0			0
$666$	−4769.08	+	1840.30i	−0.277474	+	0.107072i
$667$	−18350.1			−1.06524
$668$	47708.9			2.76334
$669$	9183.66	+	6299.88i	0.530734	+	0.364077i
$670$		−	17061.8i		−	0.983814i
$671$	4630.04			0.266380
$672$		0			0
$673$	5340.26			0.305872			0.152936	−	0.988236i	$-0.451127\pi$
$673$	5340.26			0.305872			0.152936	+	0.988236i	$0.451127\pi$
$674$			2695.28i			0.154033i
$675$	1317.25	+	312.574i	0.0751126	+	0.0178237i
$676$	21513.0			1.22400
$677$	24956.6			1.41678			0.708389	−	0.705822i	$-0.249422\pi$
$677$	24956.6			1.41678			0.708389	+	0.705822i	$0.249422\pi$
$678$	−19211.1	+	28005.1i	−1.08820	+	1.58632i
$679$		0			0
$680$		−	5265.93i		−	0.296970i
$681$	7551.55	−	11008.3i	0.424928	−	0.619439i
$682$			832.964i			0.0467681i
$683$		−	11208.5i		−	0.627937i	−0.949433	−	0.313968i	$-0.898341\pi$
$683$		−	11208.5i		−	0.627937i	0.949433	−	0.313968i	$-0.101659\pi$
$684$	−3501.45	+	1351.14i	−0.195733	+	0.0755297i
$685$		−	26903.9i		−	1.50065i
$686$		0			0
$687$	−450.654	−	309.143i	−0.0250269	−	0.0171682i
$688$	1117.19			0.0619077
$689$	−32908.2			−1.81960
$690$	10712.1	−	15615.6i	0.591021	−	0.861562i
$691$		−	10937.8i		−	0.602159i	−0.953599	−	0.301079i	$-0.902653\pi$
$691$		−	10937.8i		−	0.602159i	0.953599	−	0.301079i	$-0.0973469\pi$
$692$	30300.2			1.66451
$693$		0			0
$694$	21714.7			1.18772
$695$			21369.4i			1.16631i
$696$	−16541.7	+	24113.7i	−0.900879	+	1.31326i
$697$	663.984			0.0360835
$698$	−33447.1			−1.81374
$699$	−11250.9	−	7717.97i	−0.608795	−	0.417626i
$700$		0			0
$701$		−	27949.3i		−	1.50589i	−0.658082	−	0.752947i	$-0.728632\pi$
$701$		−	27949.3i		−	1.50589i	0.658082	−	0.752947i	$-0.271368\pi$
$702$	−38729.9	−	9190.32i	−2.08229	−	0.494111i
$703$			457.261i			0.0245319i
$704$		−	14933.7i		−	0.799482i
$705$	−5584.14	+	8140.28i	−0.298313	+	0.434866i
$706$			15025.4i			0.800977i
$707$		0			0
$708$	15331.9	−	22350.1i	0.813855	−	1.18640i
$709$	20945.4			1.10948			0.554741	−	0.832023i	$-0.312817\pi$
$709$	20945.4			1.10948			0.554741	+	0.832023i	$0.312817\pi$
$710$	2395.70			0.126632
$711$	−2811.29	−	7285.37i	−0.148286	−	0.384279i
$712$			11900.8i			0.626404i
$713$	−706.707			−0.0371197
$714$		0			0
$715$	−12976.5			−0.678731
$716$			8105.30i			0.423058i
$717$	26055.7	+	17873.9i	1.35714	+	0.930979i
$718$	−1885.09			−0.0979820
$719$	−8300.21			−0.430522			−0.215261	−	0.976557i	$-0.569060\pi$
$719$	−8300.21			−0.430522			−0.215261	+	0.976557i	$0.569060\pi$
$720$	561.167	+	1454.25i	0.0290465	+	0.0752731i
$721$		0			0
$722$		−	30629.8i		−	1.57884i
$723$	19834.2	+	13606.0i	1.02025	+	0.699880i
$724$			53230.4i			2.73245i
$725$		−	2562.82i		−	0.131284i
$726$	19672.0	+	13494.8i	1.00564	+	0.689860i
$727$			20951.5i			1.06884i	0.845218	+	0.534421i	$0.179470\pi$
$727$			20951.5i			1.06884i	−0.845218	+	0.534421i	$0.820530\pi$
$728$		0			0
$729$	17584.5	+	8843.31i	0.893388	+	0.449287i
$730$	29653.5			1.50346
$731$	4809.06			0.243324
$732$	14020.8	+	9618.11i	0.707956	+	0.485650i
$733$			5641.56i			0.284278i	0.989847	+	0.142139i	$0.0453980\pi$
$733$			5641.56i			0.284278i	−0.989847	+	0.142139i	$0.954602\pi$
$734$	346.017			0.0174001
$735$		0			0
$736$	13275.1			0.664847
$737$		−	5795.36i		−	0.289654i
$738$	3549.90	−	1369.84i	0.177064	−	0.0683259i
$739$	−11382.2			−0.566576			−0.283288	−	0.959035i	$-0.591425\pi$
$739$	−11382.2			−0.566576			−0.283288	+	0.959035i	$0.591425\pi$
$740$	−6119.61			−0.304002
$741$	−2014.20	+	2936.20i	−0.0998560	+	0.145565i
$742$		0			0
$743$			4665.46i			0.230362i	0.993345	+	0.115181i	$0.0367449\pi$
$743$			4665.46i			0.230362i	−0.993345	+	0.115181i	$0.963255\pi$
$744$	−637.063	+	928.679i	−0.0313923	+	0.0457621i
$745$		−	15096.3i		−	0.742399i
$746$			55914.3i			2.74419i
$747$	−4362.11	−	11304.3i	−0.213656	−	0.553684i
$748$		−	4858.24i		−	0.237480i
$749$		0			0
$750$	−26070.0	−	17883.7i	−1.26926	−	0.870696i
$751$	−9560.86			−0.464555			−0.232277	−	0.972650i	$-0.574618\pi$
$751$	−9560.86			−0.464555			−0.232277	+	0.972650i	$0.574618\pi$
$752$	−814.540			−0.0394990
$753$	−17541.7	+	25571.5i	−0.848945	+	1.23755i
$754$			75352.3i			3.63948i
$755$	−30361.4			−1.46353
$756$		0			0
$757$	31574.1			1.51596			0.757979	−	0.652279i	$-0.226187\pi$
$757$	31574.1			1.51596			0.757979	+	0.652279i	$0.226187\pi$
$758$			6495.63i			0.311256i
$759$	3638.58	−	5304.14i	0.174008	−	0.253660i
$760$	−2699.37			−0.128838
$761$	−22429.9			−1.06844			−0.534221	−	0.845345i	$-0.679395\pi$
$761$	−22429.9			−1.06844			−0.534221	+	0.845345i	$0.679395\pi$
$762$	52321.3	+	35891.8i	2.48740	+	1.70633i
$763$		0			0
$764$			18448.8i			0.873633i
$765$	2415.60	+	6259.96i	0.114165	+	0.295855i
$766$			23231.6i			1.09581i
$767$		−	25713.7i		−	1.21052i
$768$	10485.6	−	15285.4i	0.492664	−	0.718181i
$769$			26887.4i			1.26084i	0.776254	+	0.630420i	$0.217117\pi$
$769$			26887.4i			1.26084i	−0.776254	+	0.630420i	$0.782883\pi$
$770$		0			0
$771$	−16576.3	+	24164.1i	−0.774293	+	1.12873i
$772$	−23161.6			−1.07980
$773$	−22209.1			−1.03339			−0.516693	−	0.856171i	$-0.672837\pi$
$773$	−22209.1			−1.03339			−0.516693	+	0.856171i	$0.672837\pi$
$774$	25711.0	−	9921.39i	1.19401	−	0.460745i
$775$		−	98.7007i		−	0.00457476i
$776$	−4542.31			−0.210128
$777$		0			0
$778$	−33276.0			−1.53342
$779$		−	340.366i		−	0.0156545i
$780$	−39295.7	−	26956.4i	−1.80386	−	1.23743i
$781$	813.743			0.0372830
$782$	6726.15			0.307579
$783$	8602.71	−	36253.6i	0.392638	−	1.65466i
$784$		0			0
$785$			10851.5i			0.493385i
$786$	31226.8	+	21421.2i	1.41708	+	0.972100i
$787$			20095.5i			0.910200i	0.890440	+	0.455100i	$0.150397\pi$
$787$			20095.5i			0.910200i	−0.890440	+	0.455100i	$0.849603\pi$
$788$			8371.51i			0.378455i
$789$	−14935.4	−	10245.5i	−0.673910	−	0.462294i
$790$		−	15255.1i		−	0.687029i
$791$		0			0
$792$	−3690.14	−	9562.87i	−0.165560	−	0.429043i
$793$	16130.8			0.722349
$794$	39452.5			1.76337
$795$	26213.9	+	17982.4i	1.16945	+	0.802228i
$796$		−	24679.2i		−	1.09891i
$797$	−14300.8			−0.635583			−0.317791	−	0.948161i	$-0.602941\pi$
$797$	−14300.8			−0.635583			−0.317791	+	0.948161i	$0.602941\pi$
$798$		0			0
$799$	−3506.27			−0.155248
$800$			1854.04i			0.0819379i
$801$	−5459.15	−	14147.2i	−0.240811	−	0.624053i
$802$	44339.4			1.95222
$803$	10072.4			0.442647
$804$	12038.9	−	17549.7i	0.528082	−	0.769812i
$805$		0			0
$806$			2902.01i			0.126822i
$807$	−11153.6	+	16259.2i	−0.486524	+	0.709231i
$808$		−	36397.4i		−	1.58472i
$809$		−	14748.9i		−	0.640967i	−0.947254	−	0.320483i	$-0.896155\pi$
$809$		−	14748.9i		−	0.640967i	0.947254	−	0.320483i	$-0.103845\pi$
$810$	25829.3	+	28484.4i	1.12043	+	1.23561i
$811$			4569.51i			0.197851i	0.995095	+	0.0989255i	$0.0315405\pi$
$811$			4569.51i			0.197851i	−0.995095	+	0.0989255i	$0.968459\pi$
$812$		0			0
$813$	31954.9	+	21920.7i	1.37848	+	0.945624i
$814$	−3391.98			−0.146055
$815$	−6012.63			−0.258421
$816$	−313.195	+	456.560i	−0.0134363	+	0.0195868i
$817$		−	2465.18i		−	0.105564i
$818$	−15406.6			−0.658532
$819$		0			0
$820$	4555.18			0.193992
$821$			46797.8i			1.98935i	0.103070	+	0.994674i	$0.467133\pi$
$821$			46797.8i			1.98935i	−0.103070	+	0.994674i	$0.532867\pi$
$822$	30977.7	−	45157.7i	1.31444	−	1.91613i
$823$	−26173.4			−1.10856			−0.554281	−	0.832330i	$-0.687007\pi$
$823$	−26173.4			−1.10856			−0.554281	+	0.832330i	$0.687007\pi$
$824$	−24531.6			−1.03713
$825$	740.792	+	508.175i	0.0312619	+	0.0214453i
$826$		0			0
$827$		−	42212.0i		−	1.77492i	−0.460888	−	0.887458i	$-0.652469\pi$
$827$		−	42212.0i		−	1.77492i	0.460888	−	0.887458i	$-0.347531\pi$
$828$	22036.9	−	8503.62i	0.924921	−	0.356910i
$829$			22637.9i			0.948430i	0.880409	+	0.474215i	$0.157268\pi$
$829$			22637.9i			0.948430i	−0.880409	+	0.474215i	$0.842732\pi$
$830$		−	23670.5i		−	0.989896i
$831$	10039.4	−	14634.9i	0.419089	−	0.610927i
$832$		−	52028.3i		−	2.16798i
$833$		0			0
$834$	−24605.1	+	35868.2i	−1.02159	+	1.48923i
$835$	−43723.0			−1.81209
$836$	−2490.39			−0.103029
$837$	331.312	−	1396.22i	0.0136820	−	0.0576587i
$838$		−	58079.7i		−	2.39419i
$839$	−39480.0			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$839$	−39480.0			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$840$		0			0
$841$	−46145.4			−1.89206
$842$		−	50025.2i		−	2.04748i
$843$	−11835.4	−	8118.96i	−0.483551	−	0.331710i
$844$	−42314.8			−1.72575
$845$	−19715.7			−0.802652
$846$	−18745.8	+	7233.65i	−0.761812	+	0.293969i
$847$		0			0
$848$			2623.04i			0.106221i
$849$	−23589.1	−	16181.8i	−0.953563	−	0.654133i
$850$			939.394i			0.0379070i
$851$		−	2877.84i		−	0.115924i
$852$	2464.20	+	1690.41i	0.0990869	+	0.0679724i
$853$			44021.1i			1.76700i	0.468430	+	0.883501i	$0.344820\pi$
$853$			44021.1i			1.76700i	−0.468430	+	0.883501i	$0.655180\pi$
$854$		0			0
$855$	3208.92	−	1238.26i	0.128354	−	0.0495295i
$856$	−25804.7			−1.03036
$857$	−2014.90			−0.0803124			−0.0401562	−	0.999193i	$-0.512786\pi$
$857$	−2014.90			−0.0803124			−0.0401562	+	0.999193i	$0.512786\pi$
$858$	−21780.8	−	14941.4i	−0.866649	−	0.594511i
$859$			18295.7i			0.726706i	0.931652	+	0.363353i	$0.118368\pi$
$859$			18295.7i			0.726706i	−0.931652	+	0.363353i	$0.881632\pi$
$860$	32991.9			1.30816
$861$		0			0
$862$	−17211.2			−0.680064
$863$		−	6904.01i		−	0.272323i	−0.990687	−	0.136162i	$-0.956523\pi$
$863$		−	6904.01i		−	0.272323i	0.990687	−	0.136162i	$-0.0434767\pi$
$864$	−6223.53	+	26227.2i	−0.245056	+	1.03272i
$865$	−27768.7			−1.09152
$866$	14507.8			0.569277
$867$	13092.9	−	19086.3i	0.512872	−	0.747639i
$868$		0			0
$869$		−	5181.68i		−	0.202274i
$870$	41175.6	−	60023.9i	1.60458	−	2.33908i
$871$		−	20190.8i		−	0.785462i
$872$			27509.9i			1.06835i
$873$	5399.74	−	2083.66i	0.209340	−	0.0807803i
$874$		−	3447.90i		−	0.133440i
$875$		0			0
$876$	30501.4	+	20923.6i	1.17642	+	0.807012i
$877$	417.193			0.0160634			0.00803171	−	0.999968i	$-0.497443\pi$
$877$	417.193			0.0160634			0.00803171	+	0.999968i	$0.497443\pi$
$878$	−15079.0			−0.579603
$879$	−12054.6	+	17572.6i	−0.462561	+	0.674299i
$880$			1034.33i			0.0396217i
$881$	−7244.25			−0.277032			−0.138516	−	0.990360i	$-0.544233\pi$
$881$	−7244.25			−0.277032			−0.138516	+	0.990360i	$0.544233\pi$
$882$		0			0
$883$	38284.4			1.45908			0.729542	−	0.683936i	$-0.239733\pi$
$883$	38284.4			1.45908			0.729542	+	0.683936i	$0.239733\pi$
$884$		−	16925.9i		−	0.643981i
$885$	−14051.0	+	20482.9i	−0.533695	+	0.777995i
$886$	−48639.5			−1.84433
$887$	−17868.0			−0.676378			−0.338189	−	0.941078i	$-0.609814\pi$
$887$	−17868.0			−0.676378			−0.338189	+	0.941078i	$0.609814\pi$
$888$	−3781.75	−	2594.24i	−0.142914	−	0.0980370i
$889$		0			0
$890$		−	29623.4i		−	1.11571i
$891$	8773.41	+	9675.26i	0.329877	+	0.363786i
$892$			27137.5i			1.01864i
$893$			1797.35i			0.0673529i
$894$	17382.3	−	25339.0i	0.650279	−	0.947945i
$895$		−	7428.15i		−	0.277425i
$896$		0			0
$897$	12676.6	−	18479.4i	0.471862	−	0.687858i
$898$	18263.5			0.678687
$899$	−2716.46			−0.100777
$900$	1187.64	+	3077.74i	0.0439867	+	0.113990i
$901$			11291.2i			0.417495i
$902$	2524.85			0.0932020
$903$		0			0
$904$	−30467.9			−1.12096
$905$		−	48783.3i		−	1.79183i
$906$	−50961.1	−	34958.7i	−1.86873	−	1.28193i
$907$	−6562.99			−0.240265			−0.120132	−	0.992758i	$-0.538332\pi$
$907$	−6562.99			−0.240265			−0.120132	+	0.992758i	$0.538332\pi$
$908$	32529.2			1.18890
$909$	16696.3	+	43268.0i	0.609221	+	1.57878i
$910$		0			0
$911$			41084.1i			1.49416i	0.664735	+	0.747079i	$0.268544\pi$
$911$			41084.1i			1.49416i	−0.664735	+	0.747079i	$0.731456\pi$
$912$	234.038	+	160.547i	0.00849755	+	0.00582922i
$913$		−	8040.11i		−	0.291444i
$914$		−	41680.8i		−	1.50840i
$915$	−12849.4	−	8814.57i	−0.464251	−	0.318471i
$916$		−	1331.67i		−	0.0480345i
$917$		0			0
$918$	−3153.29	+	13288.6i	−0.113371	+	0.477767i
$919$	5524.67			0.198305			0.0991524	−	0.995072i	$-0.468387\pi$
$919$	5524.67			0.198305			0.0991524	+	0.995072i	$0.468387\pi$
$920$	16988.9			0.608812
$921$	−35484.8	−	24342.2i	−1.26956	−	0.870903i
$922$			5862.82i			0.209416i
$923$	2835.04			0.101101
$924$		0			0
$925$	401.928			0.0142868
$926$		−	31711.9i		−	1.12540i
$927$	29162.3	−	11253.2i	1.03324	−	0.398709i
$928$	51027.3			1.80501
$929$	25260.3			0.892104			0.446052	−	0.895007i	$-0.352830\pi$
$929$	25260.3			0.892104			0.446052	+	0.895007i	$0.352830\pi$
$930$	1585.78	−	2311.67i	0.0559136	−	0.0815082i
$931$		0			0
$932$		−	33246.1i		−	1.16847i
$933$	−20196.5	+	29441.5i	−0.708687	+	1.03309i
$934$		−	35744.4i		−	1.25224i
$935$			4452.36i			0.155730i
$936$	−12856.3	−	33316.6i	−0.448953	−	1.16345i
$937$		−	46069.3i		−	1.60621i	−0.595838	−	0.803105i	$-0.703180\pi$
$937$		−	46069.3i		−	1.60621i	0.595838	−	0.803105i	$-0.296820\pi$
$938$		0			0
$939$	14459.3	+	9918.89i	0.502514	+	0.344718i
$940$	−24054.3			−0.834644
$941$	48224.7			1.67065			0.835325	−	0.549756i	$-0.185279\pi$
$941$	48224.7			1.67065			0.835325	+	0.549756i	$0.185279\pi$
$942$	−12494.7	+	18214.1i	−0.432164	+	0.629988i
$943$			2142.14i			0.0739742i
$944$	−2049.58			−0.0706654
$945$		0			0
$946$	18286.8			0.628493
$947$			24641.6i			0.845559i	0.906233	+	0.422779i	$0.138945\pi$
$947$			24641.6i			0.845559i	−0.906233	+	0.422779i	$0.861055\pi$
$948$	10764.0	−	15691.3i	0.368776	−	0.537584i
$949$	35091.6			1.20034
$950$	481.543			0.0164456
$951$	−10154.1	−	6965.62i	−0.346236	−	0.237514i
$952$		0			0
$953$			13271.1i			0.451095i	0.974232	+	0.225548i	$0.0724171\pi$
$953$			13271.1i			0.451095i	−0.974232	+	0.225548i	$0.927583\pi$
$954$	23294.3	+	60366.5i	0.790547	+	2.04868i
$955$		−	16907.5i		−	0.572896i
$956$			76993.9i			2.60477i
$957$	13986.1	−	20388.2i	0.472419	−	0.688670i
$958$			16792.3i			0.566321i
$959$		0			0
$960$	−28430.5	+	41444.5i	−0.955822	+	1.39335i
$961$	29686.4			0.996488
$962$	−11817.5			−0.396062
$963$	30675.8	−	11837.2i	1.02649	−	0.396105i
$964$			58609.5i			1.95818i
$965$	21226.6			0.708090
$966$		0			0
$967$	−15785.8			−0.524959			−0.262480	−	0.964938i	$-0.584540\pi$
$967$	−15785.8			−0.524959			−0.262480	+	0.964938i	$0.584540\pi$
$968$			21402.0i			0.710626i
$969$	1007.44	+	691.091i	0.0333990	+	0.0229113i
$970$	11306.7			0.374265
$971$	−51785.2			−1.71150			−0.855750	−	0.517389i	$-0.826904\pi$
$971$	−51785.2			−1.71150			−0.855750	+	0.517389i	$0.826904\pi$
$972$	6469.20	+	47524.1i	0.213477	+	1.56825i
$973$		0			0
$974$			4785.15i			0.157419i
$975$	2580.88	+	1770.46i	0.0847738	+	0.0581538i
$976$		−	1285.75i		−	0.0421680i
$977$			28631.9i			0.937581i	0.883309	+	0.468790i	$0.155310\pi$
$977$			28631.9i			0.937581i	−0.883309	+	0.468790i	$0.844690\pi$
$978$	−10092.1	−	6923.07i	−0.329970	−	0.226355i
$979$		−	10062.1i		−	0.328485i
$980$		0			0
$981$	−12619.4	−	32702.8i	−0.410710	−	1.06434i
$982$	−10811.1			−0.351319
$983$	−43968.6			−1.42663			−0.713317	−	0.700841i	$-0.752808\pi$
$983$	−43968.6			−1.42663			−0.713317	+	0.700841i	$0.752808\pi$
$984$	2814.97	+	1931.04i	0.0911972	+	0.0625602i
$985$		−	7672.11i		−	0.248176i
$986$	25854.1			0.835055
$987$		0			0
$988$	−8676.39			−0.279385
$989$			15514.9i			0.498834i
$990$	9185.49	+	23803.9i	0.294883	+	0.764180i
$991$	−15154.7			−0.485776			−0.242888	−	0.970054i	$-0.578095\pi$
$991$	−15154.7			−0.485776			−0.242888	+	0.970054i	$0.578095\pi$
$992$	1965.19			0.0628980
$993$	−11180.2	+	16298.0i	−0.357294	+	0.520846i
$994$		0			0
$995$			22617.4i			0.720624i
$996$	16701.9	−	24347.2i	0.531346	−	0.774570i
$997$			27611.9i			0.877110i	0.898704	+	0.438555i	$0.144510\pi$
$997$			27611.9i			0.877110i	−0.898704	+	0.438555i	$0.855490\pi$
$998$		−	85326.0i		−	2.70636i
$999$	5685.65	+	1349.16i	0.180066	+	0.0427284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.a.146.1		12
3.2	odd	2	inner	147.4.c.a.146.12		12
7.2	even	3		21.4.g.a.17.1	yes	12
7.3	odd	6		21.4.g.a.5.6	yes	12
7.4	even	3		147.4.g.d.68.6		12
7.5	odd	6		147.4.g.d.80.1		12
7.6	odd	2	inner	147.4.c.a.146.2		12
21.2	odd	6		21.4.g.a.17.6	yes	12
21.5	even	6		147.4.g.d.80.6		12
21.11	odd	6		147.4.g.d.68.1		12
21.17	even	6		21.4.g.a.5.1	✓	12
21.20	even	2	inner	147.4.c.a.146.11		12
28.3	even	6		336.4.bc.d.257.6		12
28.23	odd	6		336.4.bc.d.17.4		12
84.23	even	6		336.4.bc.d.17.6		12
84.59	odd	6		336.4.bc.d.257.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	21.17	even	6
21.4.g.a.5.6	yes	12	7.3	odd	6
21.4.g.a.17.1	yes	12	7.2	even	3
21.4.g.a.17.6	yes	12	21.2	odd	6
147.4.c.a.146.1		12	1.1	even	1	trivial
147.4.c.a.146.2		12	7.6	odd	2	inner
147.4.c.a.146.11		12	21.20	even	2	inner
147.4.c.a.146.12		12	3.2	odd	2	inner
147.4.g.d.68.1		12	21.11	odd	6
147.4.g.d.68.6		12	7.4	even	3
147.4.g.d.80.1		12	7.5	odd	6
147.4.g.d.80.6		12	21.5	even	6
336.4.bc.d.17.4		12	28.23	odd	6
336.4.bc.d.17.6		12	84.23	even	6
336.4.bc.d.257.4		12	84.59	odd	6
336.4.bc.d.257.6		12	28.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.54551i q^{2} +(-2.93937 + 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(-9.72022 - 25.1896i) q^{9} +O(q^{10})\)	\(q-4.54551i q^{2} +(-2.93937 + 4.28487i) q^{3} -12.6617 q^{4} +11.6039 q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(-9.72022 - 25.1896i) q^{9} -52.7455i q^{10} -17.9160i q^{11} +(37.2174 - 54.2537i) q^{12} -62.4185i q^{13} +(-34.1081 + 49.7211i) q^{15} -4.97524 q^{16} -21.4164 q^{17} +(-114.500 + 44.1834i) q^{18} +10.9783i q^{19} -146.925 q^{20} -81.4374 q^{22} -69.0934i q^{23} +(-90.7953 - 62.2845i) q^{24} +9.64979 q^{25} -283.724 q^{26} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(226.008 + 155.039i) q^{30} -10.2283i q^{31} +192.133i q^{32} +(76.7677 + 52.6617i) q^{33} +97.3486i q^{34} +(123.074 + 318.943i) q^{36} +41.6514 q^{37} +49.9019 q^{38} +(267.455 + 183.471i) q^{39} +245.883i q^{40} -31.0035 q^{41} -224.550 q^{43} +226.847i q^{44} +(-112.792 - 292.297i) q^{45} -314.065 q^{46} +163.719 q^{47} +(14.6241 - 21.3182i) q^{48} -43.8633i q^{50} +(62.9508 - 91.7665i) q^{51} +790.323i q^{52} -527.220i q^{53} +(147.237 - 620.488i) q^{54} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} -1207.21 q^{58} +411.956 q^{59} +(431.865 - 629.552i) q^{60} +258.431i q^{61} -46.4928 q^{62} +833.541 q^{64} -724.296i q^{65} +(239.375 - 348.949i) q^{66} +323.474 q^{67} +271.168 q^{68} +(296.056 + 203.091i) q^{69} +45.4199i q^{71} +(533.762 - 205.969i) q^{72} +562.199i q^{73} -189.327i q^{74} +(-28.3643 + 41.3481i) q^{75} -139.004i q^{76} +(833.969 - 1215.72i) q^{78} +289.221 q^{79} -57.7320 q^{80} +(-540.035 + 489.697i) q^{81} +140.927i q^{82} +448.767 q^{83} -248.513 q^{85} +1020.70i q^{86} +(1137.99 + 780.647i) q^{87} +379.635 q^{88} +561.628 q^{89} +(-1328.64 + 512.698i) q^{90} +874.839i q^{92} +(43.8268 + 30.0647i) q^{93} -744.187i q^{94} +127.391i q^{95} +(-823.265 - 564.750i) q^{96} +214.364i q^{97} +(-451.297 + 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q - 28 * q^4 + 6 * q^9	\( 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) \) 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Introduction

L-functions

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