LMFDB - Embedded newform 147.4.c.a.146.2

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			146.2
Root			$2.70662 + 1.29391i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.4.c.a.146.12

$q$-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	$-0.673674\pi$
$5$	−11.6039			−1.03788			−0.518941	+	0.854810i	$0.673674\pi$
$6$	−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	$0.231925\pi$
$13$			62.4185i			1.33167i	−0.746097	+	0.665837i	$0.768075\pi$
$14$		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	$-0.451180\pi$
$17$	21.4164			0.305544			0.152772	+	0.988261i	$0.451180\pi$
$18$	−114.500	+	44.1834i	−1.49933	+	0.578562i
$19$		−	10.9783i		−	0.132557i	−0.997801	−	0.0662787i	$-0.978887\pi$
$19$		−	10.9783i		−	0.132557i	0.997801	−	0.0662787i	$-0.0211126\pi$
$20$	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	$0.00943286\pi$
$31$			10.2283i			0.0592598i	−0.999561	+	0.0296299i	$0.990567\pi$
$32$			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	$-0.481193\pi$
$41$	31.0035			0.118096			0.0590480	+	0.998255i	$0.481193\pi$
$42$		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	$-0.581763\pi$
$47$	−163.719			−0.508103			−0.254052	+	0.967191i	$0.581763\pi$
$48$	−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	$-0.650186\pi$
$59$	−411.956			−0.909020			−0.454510	+	0.890742i	$0.650186\pi$
$60$	431.865	−	629.552i	0.929227	−	1.35458i
$61$		−	258.431i		−	0.542437i	−0.962518	−	0.271218i	$-0.912573\pi$
$61$		−	258.431i		−	0.542437i	0.962518	−	0.271218i	$-0.0874266\pi$
$62$	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	$-0.851179\pi$
$73$		−	562.199i		−	0.901376i	0.892682	−	0.450688i	$-0.148821\pi$
$74$		−	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	$-0.595899\pi$
$83$	−448.767			−0.593477			−0.296738	+	0.954959i	$0.595899\pi$
$84$		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	$-0.608551\pi$
$89$	−561.628			−0.668904			−0.334452	+	0.942413i	$0.608551\pi$
$90$	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	$-0.964213\pi$
$97$		−	214.364i		−	0.224385i	0.993686	−	0.112192i	$-0.0357873\pi$
$98$		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	$-0.178932\pi$
$101$	1717.69			1.69224			0.846122	+	0.532990i	$0.178932\pi$
$102$	−417.126	−	286.143i	−0.404918	−	0.277769i
$103$		−	1157.71i		−	1.10750i	−0.832683	−	0.553750i	$-0.813196\pi$
$103$		−	1157.71i		−	1.10750i	0.832683	−	0.553750i	$-0.186804\pi$
$104$	−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	$-0.679557\pi$
$131$	−1603.27			−1.06930			−0.534651	+	0.845073i	$0.679557\pi$
$132$	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	$-0.810082\pi$
$139$		−	1841.57i		−	1.12374i	0.827225	−	0.561871i	$-0.189918\pi$
$140$		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	$-0.923610\pi$
$157$		−	935.164i		−	0.475377i	0.971341	−	0.237689i	$-0.0763898\pi$
$158$		−	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	$-0.162186\pi$
$167$	3767.97			1.74595			0.872977	+	0.487761i	$0.162186\pi$
$168$		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	$-0.323751\pi$
$173$	2393.06			1.05168			0.525841	+	0.850583i	$0.323751\pi$
$174$	−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	$0.331554\pi$
$181$			4204.05i			1.72643i	−0.504833	+	0.863217i	$0.668446\pi$
$182$		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	$-0.887146\pi$
$199$		−	1949.13i		−	0.694322i	0.937806	−	0.347161i	$-0.112854\pi$
$200$			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	$0.104289\pi$
$223$			2143.28i			0.643608i	−0.946806	+	0.321804i	$0.895711\pi$
$224$		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	$-0.377440\pi$
$227$	2569.11			0.751178			0.375589	+	0.926786i	$0.377440\pi$
$228$	595.612	+	408.583i	0.173006	+	0.118680i
$229$		−	105.173i		−	0.0303495i	−0.999885	−	0.0151748i	$-0.995170\pi$
$229$		−	105.173i		−	0.0303495i	0.999885	−	0.0151748i	$-0.00483046\pi$
$230$	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	$0.212306\pi$
$241$			4628.89i			1.23723i	−0.785693	+	0.618616i	$0.787694\pi$
$242$		−	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	$-0.770126\pi$
$251$	−5967.85			−1.50075			−0.750373	+	0.661015i	$0.770126\pi$
$252$		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	$-0.739931\pi$
$257$	−5639.40			−1.36878			−0.684389	+	0.729117i	$0.739931\pi$
$258$	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	$-0.641498\pi$
$269$	−3794.55			−0.860066			−0.430033	+	0.902813i	$0.641498\pi$
$270$	1708.52	−	7200.06i	0.385101	−	1.62290i
$271$			7457.62i			1.67165i	0.548993	+	0.835827i	$0.315011\pi$
$271$			7457.62i			1.67165i	−0.548993	+	0.835827i	$0.684989\pi$
$272$	−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	$-0.803763\pi$
$283$		−	5505.20i		−	1.15636i	0.815909	−	0.578181i	$-0.196237\pi$
$284$		−	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	$-0.634071\pi$
$293$	−4101.08			−0.817705			−0.408853	+	0.912600i	$0.634071\pi$
$294$		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	$-0.720365\pi$
$307$		−	8281.42i		−	1.53956i	0.638308	−	0.769781i	$-0.279635\pi$
$308$		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	$-0.715473\pi$
$311$	−6871.05			−1.25280			−0.626401	+	0.779501i	$0.715473\pi$
$312$	−3887.70	+	5667.30i	−0.705441	+	1.02836i
$313$			3374.49i			0.609386i	0.952451	+	0.304693i	$0.0985538\pi$
$313$			3374.49i			0.609386i	−0.952451	+	0.304693i	$0.901446\pi$
$314$	−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	$0.190852\pi$
$349$			7358.26i			1.12859i	−0.825573	+	0.564296i	$0.809148\pi$
$350$		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	$-0.419832\pi$
$353$	3305.55			0.498405			0.249202	+	0.968451i	$0.419832\pi$
$354$	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	$-0.998277\pi$
$367$		−	76.1227i		−	0.0108272i	0.999985	−	0.00541359i	$-0.00172321\pi$
$368$			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	$-0.389257\pi$
$383$	5110.90			0.681866			0.340933	+	0.940088i	$0.389257\pi$
$384$	−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	$-0.815151\pi$
$397$		−	8679.44i		−	1.09725i	0.836068	−	0.548625i	$-0.184849\pi$
$398$	−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	$0.0656819\pi$
$409$			3389.41i			0.409769i	−0.978786	+	0.204885i	$0.934318\pi$
$410$			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	$-0.767496\pi$
$419$	−12777.4			−1.48977			−0.744887	+	0.667191i	$0.767496\pi$
$420$		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	$-0.943323\pi$
$433$		−	3191.67i		−	0.354230i	0.984190	−	0.177115i	$-0.0566765\pi$
$434$		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	$0.0577159\pi$
$439$			3317.34i			0.360656i	−0.983607	+	0.180328i	$0.942284\pi$
$440$	−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	$-0.479246\pi$
$461$	1289.80			0.130308			0.0651542	+	0.997875i	$0.479246\pi$
$462$		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	$-0.627387\pi$
$467$	−7863.66			−0.779201			−0.389600	+	0.920984i	$0.627387\pi$
$468$	−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	$-0.443621\pi$
$479$	3694.27			0.352391			0.176196	+	0.984355i	$0.443621\pi$
$480$	−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	$-0.247168\pi$
$503$	16095.2			1.42674			0.713370	+	0.700788i	$0.247168\pi$
$504$		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	$-0.456196\pi$
$509$	3150.63			0.274360			0.137180	+	0.990546i	$0.456196\pi$
$510$	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	$-0.567135\pi$
$521$	−4979.20			−0.418700			−0.209350	+	0.977841i	$0.567135\pi$
$522$	11734.4	+	30409.2i	0.983906	+	2.54976i
$523$		−	13829.8i		−	1.15628i	−0.815936	−	0.578142i	$-0.803778\pi$
$523$		−	13829.8i		−	1.15628i	0.815936	−	0.578142i	$-0.196222\pi$
$524$	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	$-0.453173\pi$
$563$	3916.24			0.293161			0.146581	+	0.989199i	$0.453173\pi$
$564$	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	$0.156721\pi$
$577$			13103.3i			0.945405i	−0.881222	+	0.472703i	$0.843279\pi$
$578$			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	$-0.718608\pi$
$587$	−18034.7			−1.26809			−0.634047	+	0.773294i	$0.718608\pi$
$588$		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	$-0.211867\pi$
$593$	22716.2			1.57309			0.786547	+	0.617531i	$0.211867\pi$
$594$	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	$0.0397250\pi$
$601$			3667.98i			0.248952i	−0.992223	+	0.124476i	$0.960275\pi$
$602$		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	$0.0863758\pi$
$607$			8017.00i			0.536079i	−0.963408	+	0.268039i	$0.913624\pi$
$608$	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	$-0.926660\pi$
$619$		−	7034.12i		−	0.456745i	0.973574	−	0.228373i	$-0.0733404\pi$
$620$			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	$-0.997128\pi$
$643$		−	294.191i		−	0.0180432i	0.999959	−	0.00902160i	$-0.00287170\pi$
$644$		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	$-0.575349\pi$
$647$	−7718.79			−0.469021			−0.234511	+	0.972114i	$0.575349\pi$
$648$	−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	$0.366837\pi$
$661$			31057.5i			1.82753i	−0.406247	+	0.913763i	$0.633163\pi$
$662$		−	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	$-0.750578\pi$
$677$	−24956.6			−1.41678			−0.708389	+	0.705822i	$0.750578\pi$
$678$	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	$0.0973469\pi$
$691$			10937.8i			0.602159i	−0.953599	+	0.301079i	$0.902653\pi$
$692$	−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	$-0.430940\pi$
$719$	8300.21			0.430522			0.215261	+	0.976557i	$0.430940\pi$
$720$	−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	$-0.820530\pi$
$727$		−	20951.5i		−	1.06884i	0.845218	−	0.534421i	$-0.179470\pi$
$728$		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	$-0.954602\pi$
$733$		−	5641.56i		−	0.284278i	0.989847	−	0.142139i	$-0.0453980\pi$
$734$	−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	$-0.320605\pi$
$761$	22429.9			1.06844			0.534221	+	0.845345i	$0.320605\pi$
$762$	−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	$-0.782883\pi$
$769$		−	26887.4i		−	1.26084i	0.776254	−	0.630420i	$-0.217117\pi$
$770$		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	$-0.327163\pi$
$773$	22209.1			1.03339			0.516693	+	0.856171i	$0.327163\pi$
$774$	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	$-0.849603\pi$
$787$		−	20095.5i		−	0.910200i	0.890440	−	0.455100i	$-0.150397\pi$
$788$			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	$-0.397059\pi$
$797$	14300.8			0.635583			0.317791	+	0.948161i	$0.397059\pi$
$798$		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	$-0.968459\pi$
$811$		−	4569.51i		−	0.197851i	0.995095	−	0.0989255i	$-0.0315405\pi$
$812$		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	$-0.842732\pi$
$829$		−	22637.9i		−	0.948430i	0.880409	−	0.474215i	$-0.157268\pi$
$830$		−	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	$-0.198228\pi$
$839$	39480.0			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$840$		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	$-0.655180\pi$
$853$		−	44021.1i		−	1.76700i	0.468430	−	0.883501i	$-0.344820\pi$
$854$		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	$-0.487214\pi$
$857$	2014.90			0.0803124			0.0401562	+	0.999193i	$0.487214\pi$
$858$	−21780.8	−	14941.4i	−0.866649	−	0.594511i
$859$		−	18295.7i		−	0.726706i	−0.931652	−	0.363353i	$-0.881632\pi$
$859$		−	18295.7i		−	0.726706i	0.931652	−	0.363353i	$-0.118368\pi$
$860$	−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	$-0.455767\pi$
$881$	7244.25			0.277032			0.138516	+	0.990360i	$0.455767\pi$
$882$		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	$-0.390186\pi$
$887$	17868.0			0.676378			0.338189	+	0.941078i	$0.390186\pi$
$888$	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	$-0.647170\pi$
$929$	−25260.3			−0.892104			−0.446052	+	0.895007i	$0.647170\pi$
$930$	−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	$0.296820\pi$
$937$			46069.3i			1.60621i	−0.595838	+	0.803105i	$0.703180\pi$
$938$		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	$-0.814721\pi$
$941$	−48224.7			−1.67065			−0.835325	+	0.549756i	$0.814721\pi$
$942$	−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	$-0.173096\pi$
$971$	51785.2			1.71150			0.855750	+	0.517389i	$0.173096\pi$
$972$	−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	$-0.247192\pi$
$983$	43968.6			1.42663			0.713317	+	0.700841i	$0.247192\pi$
$984$	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	$-0.855490\pi$
$997$		−	27611.9i		−	0.877110i	0.898704	−	0.438555i	$-0.144510\pi$
$998$		−	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.146.2		12
3.2	odd	2	inner	147.4.c.a.146.11		12
7.2	even	3		147.4.g.d.80.1		12
7.3	odd	6		147.4.g.d.68.6		12
7.4	even	3		21.4.g.a.5.6	yes	12
7.5	odd	6		21.4.g.a.17.1	yes	12
7.6	odd	2	inner	147.4.c.a.146.1		12
21.2	odd	6		147.4.g.d.80.6		12
21.5	even	6		21.4.g.a.17.6	yes	12
21.11	odd	6		21.4.g.a.5.1	✓	12
21.17	even	6		147.4.g.d.68.1		12
21.20	even	2	inner	147.4.c.a.146.12		12
28.11	odd	6		336.4.bc.d.257.6		12
28.19	even	6		336.4.bc.d.17.4		12
84.11	even	6		336.4.bc.d.257.4		12
84.47	odd	6		336.4.bc.d.17.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	21.11	odd	6
21.4.g.a.5.6	yes	12	7.4	even	3
21.4.g.a.17.1	yes	12	7.5	odd	6
21.4.g.a.17.6	yes	12	21.5	even	6
147.4.c.a.146.1		12	7.6	odd	2	inner
147.4.c.a.146.2		12	1.1	even	1	trivial
147.4.c.a.146.11		12	3.2	odd	2	inner
147.4.c.a.146.12		12	21.20	even	2	inner
147.4.g.d.68.1		12	21.17	even	6
147.4.g.d.68.6		12	7.3	odd	6
147.4.g.d.80.1		12	7.2	even	3
147.4.g.d.80.6		12	21.2	odd	6
336.4.bc.d.17.4		12	28.19	even	6
336.4.bc.d.17.6		12	84.47	odd	6
336.4.bc.d.257.4		12	84.11	even	6
336.4.bc.d.257.6		12	28.11	odd	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more