LMFDB - Embedded newform 108.4.b.b.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, 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("108.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.b (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:	$6.37220628062$
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} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + \cdots + 9496 $ x^12 + 3x^10 - 12x^9 + 73x^8 - 12x^7 + 589x^6 + 84x^5 + 2452x^4 + 852x^3 + 6854x^2 - 888x + 9496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.8
Root			$-2.18604 - 2.07664i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.4.b.b.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +O(q^{10})$	\(q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +(4.18188 - 0.627790i) q^{10} -56.3941 q^{11} -41.3170 q^{13} +(-73.2423 + 10.9953i) q^{14} +(52.9643 - 35.9274i) q^{16} -51.0410i q^{17} +79.0640i q^{19} +(3.51196 + 11.4335i) q^{20} +(-23.6801 - 157.739i) q^{22} -27.3688 q^{23} +122.765 q^{25} +(-17.3491 - 115.567i) q^{26} +(-61.5093 - 200.248i) q^{28} +134.567i q^{29} +187.192i q^{31} +(122.732 + 133.060i) q^{32} +(142.766 - 21.4323i) q^{34} +39.1491 q^{35} -196.585 q^{37} +(-221.149 + 33.1992i) q^{38} +(-30.5057 + 14.6242i) q^{40} -298.015i q^{41} +465.576i q^{43} +(431.267 - 132.470i) q^{44} +(-11.4922 - 76.5529i) q^{46} +373.845 q^{47} -342.667 q^{49} +(51.5492 + 343.383i) q^{50} +(315.966 - 97.0539i) q^{52} +620.093i q^{53} +84.3140i q^{55} +(534.283 - 256.131i) q^{56} +(-376.396 + 56.5052i) q^{58} +321.152 q^{59} +674.699 q^{61} +(-523.593 + 78.6026i) q^{62} +(-320.644 + 399.164i) q^{64} +61.7724i q^{65} -576.075i q^{67} +(119.896 + 390.329i) q^{68} +(16.4388 + 109.503i) q^{70} -223.813 q^{71} +70.1371 q^{73} +(-82.5465 - 549.864i) q^{74} +(-185.722 - 604.631i) q^{76} -1476.69i q^{77} -1052.32i q^{79} +(-53.7145 - 79.1862i) q^{80} +(833.574 - 125.137i) q^{82} -1219.05 q^{83} -76.3107 q^{85} +(-1302.26 + 195.497i) q^{86} +(551.621 + 1150.66i) q^{88} +1340.64i q^{89} -1081.89i q^{91} +(209.299 - 64.2895i) q^{92} +(156.979 + 1045.68i) q^{94} +118.207 q^{95} -576.059 q^{97} +(-143.887 - 958.467i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.419903	+	2.79708i	0.148458	+	0.988919i
$2$	0.419903	+	2.79708i	0.148458	+	0.988919i
$3$		0			0
$3$		0			0
$4$	−7.64736	+	2.34901i	−0.955920	+	0.293626i
$5$		−	1.49508i		−	0.133724i	−0.997762	−	0.0668622i	$-0.978701\pi$
$5$		−	1.49508i		−	0.133724i	0.997762	−	0.0668622i	$-0.0212988\pi$
$6$		0			0
$7$			26.1852i			1.41387i	0.707279	+	0.706935i	$0.249923\pi$
$7$			26.1852i			1.41387i	−0.707279	+	0.706935i	$0.750077\pi$
$8$	−9.78152	−	20.4040i	−0.432286	−	0.901736i
$9$		0			0
$10$	4.18188	−	0.627790i	0.132243	−	0.0198525i
$11$	−56.3941			−1.54577			−0.772885	−	0.634546i	$-0.781187\pi$
$11$	−56.3941			−1.54577			−0.772885	+	0.634546i	$0.781187\pi$
$12$		0			0
$13$	−41.3170			−0.881482			−0.440741	−	0.897634i	$-0.645284\pi$
$13$	−41.3170			−0.881482			−0.440741	+	0.897634i	$0.645284\pi$
$14$	−73.2423	+	10.9953i	−1.39820	+	0.209900i
$15$		0			0
$16$	52.9643	−	35.9274i	0.827568	−	0.561366i
$17$		−	51.0410i		−	0.728192i	−0.931361	−	0.364096i	$-0.881378\pi$
$17$		−	51.0410i		−	0.728192i	0.931361	−	0.364096i	$-0.118622\pi$
$18$		0			0
$19$			79.0640i			0.954659i	0.878724	+	0.477330i	$0.158395\pi$
$19$			79.0640i			0.954659i	−0.878724	+	0.477330i	$0.841605\pi$
$20$	3.51196	+	11.4335i	0.0392650	+	0.127830i
$21$		0			0
$22$	−23.6801	−	157.739i	−0.229482	−	1.52864i
$23$	−27.3688			−0.248121			−0.124061	−	0.992275i	$-0.539592\pi$
$23$	−27.3688			−0.248121			−0.124061	+	0.992275i	$0.539592\pi$
$24$		0			0
$25$	122.765			0.982118
$26$	−17.3491	−	115.567i	−0.130863	−	0.871714i
$27$		0			0
$28$	−61.5093	−	200.248i	−0.415149	−	1.35155i
$29$			134.567i			0.861674i	0.902430	+	0.430837i	$0.141782\pi$
$29$			134.567i			0.861674i	−0.902430	+	0.430837i	$0.858218\pi$
$30$		0			0
$31$			187.192i			1.08454i	0.840204	+	0.542270i	$0.182435\pi$
$31$			187.192i			1.08454i	−0.840204	+	0.542270i	$0.817565\pi$
$32$	122.732	+	133.060i	0.678004	+	0.735058i
$33$		0			0
$34$	142.766	−	21.4323i	0.720123	−	0.108106i
$35$	39.1491			0.189069
$36$		0			0
$37$	−196.585			−0.873469			−0.436734	−	0.899590i	$-0.643865\pi$
$37$	−196.585			−0.873469			−0.436734	+	0.899590i	$0.643865\pi$
$38$	−221.149	+	33.1992i	−0.944081	+	0.141727i
$39$		0			0
$40$	−30.5057	+	14.6242i	−0.120584	+	0.0578072i
$41$		−	298.015i		−	1.13517i	−0.823313	−	0.567587i	$-0.807877\pi$
$41$		−	298.015i		−	1.13517i	0.823313	−	0.567587i	$-0.192123\pi$
$42$		0			0
$43$			465.576i			1.65115i	0.564289	+	0.825577i	$0.309150\pi$
$43$			465.576i			1.65115i	−0.564289	+	0.825577i	$0.690850\pi$
$44$	431.267	−	132.470i	1.47763	−	0.453878i
$45$		0			0
$46$	−11.4922	−	76.5529i	−0.0368356	−	0.245372i
$47$	373.845			1.16023			0.580116	−	0.814534i	$-0.303007\pi$
$47$	373.845			1.16023			0.580116	+	0.814534i	$0.303007\pi$
$48$		0			0
$49$	−342.667			−0.999028
$50$	51.5492	+	343.383i	0.145803	+	0.971235i
$51$		0			0
$52$	315.966	−	97.0539i	0.842627	−	0.258826i
$53$			620.093i			1.60710i	0.595237	+	0.803550i	$0.297058\pi$
$53$			620.093i			1.60710i	−0.595237	+	0.803550i	$0.702942\pi$
$54$		0			0
$55$			84.3140i			0.206707i
$56$	534.283	−	256.131i	1.27494	−	0.611196i
$57$		0			0
$58$	−376.396	+	56.5052i	−0.852125	+	0.127922i
$59$	321.152			0.708652			0.354326	−	0.935122i	$-0.384710\pi$
$59$	321.152			0.708652			0.354326	+	0.935122i	$0.384710\pi$
$60$		0			0
$61$	674.699			1.41617			0.708085	−	0.706127i	$-0.249559\pi$
$61$	674.699			1.41617			0.708085	+	0.706127i	$0.249559\pi$
$62$	−523.593	+	78.6026i	−1.07252	+	0.161009i
$63$		0			0
$64$	−320.644	+	399.164i	−0.626257	+	0.779616i
$65$			61.7724i			0.117876i
$66$		0			0
$67$		−	576.075i		−	1.05043i	−0.850970	−	0.525215i	$-0.823985\pi$
$67$		−	576.075i		−	1.05043i	0.850970	−	0.525215i	$-0.176015\pi$
$68$	119.896	+	390.329i	0.213816	+	0.696094i
$69$		0			0
$70$	16.4388	+	109.503i	0.0280688	+	0.186974i
$71$	−223.813			−0.374110			−0.187055	−	0.982349i	$-0.559894\pi$
$71$	−223.813			−0.374110			−0.187055	+	0.982349i	$0.559894\pi$
$72$		0			0
$73$	70.1371			0.112451			0.0562255	−	0.998418i	$-0.482093\pi$
$73$	70.1371			0.112451			0.0562255	+	0.998418i	$0.482093\pi$
$74$	−82.5465	−	549.864i	−0.129673	−	0.863790i
$75$		0			0
$76$	−185.722	−	604.631i	−0.280313	−	0.912578i
$77$		−	1476.69i		−	2.18552i
$78$		0			0
$79$		−	1052.32i		−	1.49868i	−0.662187	−	0.749338i	$-0.730372\pi$
$79$		−	1052.32i		−	1.49868i	0.662187	−	0.749338i	$-0.269628\pi$
$80$	−53.7145	−	79.1862i	−0.0750684	−	0.110666i
$81$		0			0
$82$	833.574	−	125.137i	1.12260	−	0.168526i
$83$	−1219.05			−1.61214			−0.806070	−	0.591820i	$-0.798409\pi$
$83$	−1219.05			−1.61214			−0.806070	+	0.591820i	$0.798409\pi$
$84$		0			0
$85$	−76.3107			−0.0973771
$86$	−1302.26	+	195.497i	−1.63286	+	0.245127i
$87$		0			0
$88$	551.621	+	1150.66i	0.668215	+	1.39388i
$89$			1340.64i			1.59672i	0.602183	+	0.798358i	$0.294298\pi$
$89$			1340.64i			1.59672i	−0.602183	+	0.798358i	$0.705702\pi$
$90$		0			0
$91$		−	1081.89i		−	1.24630i
$92$	209.299	−	64.2895i	0.237184	−	0.0728548i
$93$		0			0
$94$	156.979	+	1045.68i	0.172246	+	1.14737i
$95$	118.207			0.127661
$96$		0			0
$97$	−576.059			−0.602989			−0.301494	−	0.953468i	$-0.597485\pi$
$97$	−576.059			−0.602989			−0.301494	+	0.953468i	$0.597485\pi$
$98$	−143.887	−	958.467i	−0.148314	−	0.987957i
$99$		0			0
$100$	−938.826	+	288.375i	−0.938826	+	0.288375i
$101$			116.079i			0.114359i	0.998364	+	0.0571797i	$0.0182108\pi$
$101$			116.079i			0.114359i	−0.998364	+	0.0571797i	$0.981789\pi$
$102$		0			0
$103$		−	165.074i		−	0.157915i	−0.996878	−	0.0789573i	$-0.974841\pi$
$103$		−	165.074i		−	0.157915i	0.996878	−	0.0789573i	$-0.0251591\pi$
$104$	404.143	+	843.030i	0.381052	+	0.794864i
$105$		0			0
$106$	−1734.45	+	260.379i	−1.58929	+	0.238587i
$107$	−936.718			−0.846318			−0.423159	−	0.906056i	$-0.639079\pi$
$107$	−936.718			−0.846318			−0.423159	+	0.906056i	$0.639079\pi$
$108$		0			0
$109$	346.957			0.304885			0.152443	−	0.988312i	$-0.451286\pi$
$109$	346.957			0.304885			0.152443	+	0.988312i	$0.451286\pi$
$110$	−235.833	+	35.4037i	−0.204417	+	0.0306874i
$111$		0			0
$112$	940.768	+	1386.88i	0.793698	+	1.17007i
$113$		−	1462.22i		−	1.21729i	−0.793443	−	0.608645i	$-0.791713\pi$
$113$		−	1462.22i		−	1.21729i	0.793443	−	0.608645i	$-0.208287\pi$
$114$		0			0
$115$			40.9187i			0.0331799i
$116$	−316.100	−	1029.09i	−0.253010	−	0.823691i
$117$		0			0
$118$	134.853	+	898.290i	0.105205	+	0.700799i
$119$	1336.52			1.02957
$120$		0			0
$121$	1849.30			1.38941
$122$	283.308	+	1887.19i	0.210242	+	1.40048i
$123$		0			0
$124$	−439.716	−	1431.53i	−0.318449	−	1.03673i
$125$		−	370.429i		−	0.265058i
$126$		0			0
$127$			265.004i			0.185160i	0.995705	+	0.0925800i	$0.0295114\pi$
$127$			265.004i			0.185160i	−0.995705	+	0.0925800i	$0.970489\pi$
$128$	−1251.13	−	729.258i	−0.863950	−	0.503577i
$129$		0			0
$130$	−172.783	+	25.9384i	−0.116569	+	0.0174996i
$131$	−1151.86			−0.768231			−0.384115	−	0.923285i	$-0.625493\pi$
$131$	−1151.86			−0.768231			−0.384115	+	0.923285i	$0.625493\pi$
$132$		0			0
$133$	−2070.31			−1.34976
$134$	1611.33	−	241.896i	1.03879	−	0.155945i
$135$		0			0
$136$	−1041.44	+	499.259i	−0.656637	+	0.314787i
$137$			2348.67i			1.46467i	0.680943	+	0.732337i	$0.261570\pi$
$137$			2348.67i			1.46467i	−0.680943	+	0.732337i	$0.738430\pi$
$138$		0			0
$139$		−	215.240i		−	0.131341i	−0.997841	−	0.0656706i	$-0.979081\pi$
$139$		−	215.240i		−	0.131341i	0.997841	−	0.0656706i	$-0.0209187\pi$
$140$	−299.388	+	91.9616i	−0.180735	+	0.0555155i
$141$		0			0
$142$	−93.9799	−	626.025i	−0.0555396	−	0.369964i
$143$	2330.04			1.36257
$144$		0			0
$145$	201.190			0.115227
$146$	29.4508	+	196.179i	0.0166943	+	0.111205i
$147$		0			0
$148$	1503.36	−	461.779i	0.834967	−	0.256473i
$149$			219.954i			0.120935i	0.998170	+	0.0604674i	$0.0192591\pi$
$149$			219.954i			0.120935i	−0.998170	+	0.0604674i	$0.980741\pi$
$150$		0			0
$151$		−	1148.02i		−	0.618703i	−0.950948	−	0.309351i	$-0.899888\pi$
$151$		−	1148.02i		−	0.618703i	0.950948	−	0.309351i	$-0.100112\pi$
$152$	1613.22	−	773.366i	0.860851	−	0.412686i
$153$		0			0
$154$	4130.44	−	620.068i	2.16130	−	0.324458i
$155$	279.869			0.145030
$156$		0			0
$157$	−276.320			−0.140463			−0.0702316	−	0.997531i	$-0.522374\pi$
$157$	−276.320			−0.140463			−0.0702316	+	0.997531i	$0.522374\pi$
$158$	2943.43	−	441.873i	1.48207	−	0.222491i
$159$		0			0
$160$	198.936	−	183.495i	0.0982952	−	0.0906658i
$161$		−	716.659i		−	0.350811i
$162$		0			0
$163$			1419.15i			0.681941i	0.940074	+	0.340971i	$0.110756\pi$
$163$			1419.15i			0.681941i	−0.940074	+	0.340971i	$0.889244\pi$
$164$	700.040	+	2279.03i	0.333317	+	1.08514i
$165$		0			0
$166$	−511.880	−	3409.77i	−0.239335	−	1.59428i
$167$	3508.69			1.62581			0.812906	−	0.582394i	$-0.197884\pi$
$167$	3508.69			1.62581			0.812906	+	0.582394i	$0.197884\pi$
$168$		0			0
$169$	−489.908			−0.222990
$170$	−32.0431	−	213.447i	−0.0144564	−	0.0962980i
$171$		0			0
$172$	−1093.64	−	3560.43i	−0.484822	−	1.57837i
$173$		−	330.965i		−	0.145450i	−0.997352	−	0.0727248i	$-0.976831\pi$
$173$		−	330.965i		−	0.145450i	0.997352	−	0.0727248i	$-0.0231695\pi$
$174$		0			0
$175$			3214.62i			1.38859i
$176$	−2986.88	+	2026.10i	−1.27923	+	0.867743i
$177$		0			0
$178$	−3749.89	+	562.939i	−1.57902	+	0.237045i
$179$	−1136.75			−0.474662			−0.237331	−	0.971429i	$-0.576273\pi$
$179$	−1136.75			−0.474662			−0.237331	+	0.971429i	$0.576273\pi$
$180$		0			0
$181$	2056.92			0.844692			0.422346	−	0.906435i	$-0.361207\pi$
$181$	2056.92			0.844692			0.422346	+	0.906435i	$0.361207\pi$
$182$	3026.15	−	454.291i	1.23249	−	0.185023i
$183$		0			0
$184$	267.709	+	558.432i	0.107259	+	0.223740i
$185$			293.911i			0.116804i
$186$		0			0
$187$			2878.42i			1.12562i
$188$	−2858.93	+	878.164i	−1.10909	+	0.340674i
$189$		0			0
$190$	49.6356	+	330.636i	0.0189523	+	0.126247i
$191$	−1983.23			−0.751316			−0.375658	−	0.926758i	$-0.622583\pi$
$191$	−1983.23			−0.751316			−0.375658	+	0.926758i	$0.622583\pi$
$192$		0			0
$193$	−189.908			−0.0708283			−0.0354141	−	0.999373i	$-0.511275\pi$
$193$	−189.908			−0.0708283			−0.0354141	+	0.999373i	$0.511275\pi$
$194$	−241.889	−	1611.29i	−0.0895185	−	0.596307i
$195$		0			0
$196$	2620.50	−	804.926i	0.954991	−	0.293340i
$197$			2160.42i			0.781337i	0.920531	+	0.390669i	$0.127756\pi$
$197$			2160.42i			0.781337i	−0.920531	+	0.390669i	$0.872244\pi$
$198$		0			0
$199$			2656.23i			0.946205i	0.881007	+	0.473103i	$0.156866\pi$
$199$			2656.23i			0.946205i	−0.881007	+	0.473103i	$0.843134\pi$
$200$	−1200.83	−	2504.89i	−0.424556	−	0.885611i
$201$		0			0
$202$	−324.683	+	48.7419i	−0.113092	+	0.0169776i
$203$	−3523.68			−1.21829
$204$		0			0
$205$	−445.558			−0.151801
$206$	461.725	−	69.3149i	0.156165	−	0.0234437i
$207$		0			0
$208$	−2188.33	+	1484.41i	−0.729486	+	0.494834i
$209$		−	4458.75i		−	1.47568i
$210$		0			0
$211$			1001.20i			0.326662i	0.986571	+	0.163331i	$0.0522239\pi$
$211$			1001.20i			0.326662i	−0.986571	+	0.163331i	$0.947776\pi$
$212$	−1456.60	−	4742.07i	−0.471886	−	1.53626i
$213$		0			0
$214$	−393.331	−	2620.08i	−0.125643	−	0.836939i
$215$	696.075			0.220800
$216$		0			0
$217$	−4901.68			−1.53340
$218$	145.688	+	970.469i	0.0452626	+	0.301507i
$219$		0			0
$220$	−198.054	−	644.780i	−0.0606946	−	0.197596i
$221$			2108.86i			0.641888i
$222$		0			0
$223$			3193.62i			0.959015i	0.877538	+	0.479507i	$0.159185\pi$
$223$			3193.62i			0.959015i	−0.877538	+	0.479507i	$0.840815\pi$
$224$	−3484.20	+	3213.76i	−1.03928	+	0.958610i
$225$		0			0
$226$	4089.94	−	613.989i	1.20380	−	0.180717i
$227$	−1714.72			−0.501366			−0.250683	−	0.968069i	$-0.580655\pi$
$227$	−1714.72			−0.501366			−0.250683	+	0.968069i	$0.580655\pi$
$228$		0			0
$229$	−407.497			−0.117590			−0.0587951	−	0.998270i	$-0.518726\pi$
$229$	−407.497			−0.117590			−0.0587951	+	0.998270i	$0.518726\pi$
$230$	−114.453	+	17.1819i	−0.0328122	+	0.00492582i
$231$		0			0
$232$	2745.71	−	1316.27i	0.777003	−	0.372490i
$233$		−	3210.54i		−	0.902702i	−0.892346	−	0.451351i	$-0.850942\pi$
$233$		−	3210.54i		−	0.902702i	0.892346	−	0.451351i	$-0.149058\pi$
$234$		0			0
$235$		−	558.930i		−	0.155151i
$236$	−2455.97	+	754.389i	−0.677415	+	0.208079i
$237$		0			0
$238$	561.209	+	3738.36i	0.152848	+	1.01816i
$239$	1561.19			0.422532			0.211266	−	0.977429i	$-0.432241\pi$
$239$	1561.19			0.422532			0.211266	+	0.977429i	$0.432241\pi$
$240$		0			0
$241$	1460.89			0.390475			0.195238	−	0.980756i	$-0.437452\pi$
$241$	1460.89			0.390475			0.195238	+	0.980756i	$0.437452\pi$
$242$	776.526	+	5172.65i	0.206269	+	1.37401i
$243$		0			0
$244$	−5159.67	+	1584.87i	−1.35375	+	0.415824i
$245$			512.316i			0.133594i
$246$		0			0
$247$		−	3266.69i		−	0.841515i
$248$	3819.47	−	1831.03i	0.977970	−	0.468832i
$249$		0			0
$250$	1036.12	−	155.544i	0.262120	−	0.0393499i
$251$	−6868.44			−1.72722			−0.863609	−	0.504162i	$-0.831802\pi$
$251$	−6868.44			−1.72722			−0.863609	+	0.504162i	$0.831802\pi$
$252$		0			0
$253$	1543.44			0.383539
$254$	−741.239	+	111.276i	−0.183108	+	0.0274885i
$255$		0			0
$256$	1514.44	−	3805.74i	0.369737	−	0.929137i
$257$			4450.84i			1.08029i	0.841570	+	0.540147i	$0.181632\pi$
$257$			4450.84i			1.08029i	−0.841570	+	0.540147i	$0.818368\pi$
$258$		0			0
$259$		−	5147.62i		−	1.23497i
$260$	−145.104	−	472.396i	−0.0346114	−	0.112680i
$261$		0			0
$262$	−483.668	−	3221.84i	−0.114050	−	0.759718i
$263$	6525.31			1.52991			0.764957	−	0.644081i	$-0.222760\pi$
$263$	6525.31			1.52991			0.764957	+	0.644081i	$0.222760\pi$
$264$		0			0
$265$	927.091			0.214909
$266$	−869.329	−	5790.83i	−0.200383	−	1.33481i
$267$		0			0
$268$	1353.20	+	4405.46i	0.308433	+	1.00413i
$269$		−	3222.22i		−	0.730343i	−0.930940	−	0.365171i	$-0.881010\pi$
$269$		−	3222.22i		−	0.730343i	0.930940	−	0.365171i	$-0.118990\pi$
$270$		0			0
$271$		−	7368.93i		−	1.65177i	−0.563837	−	0.825886i	$-0.690675\pi$
$271$		−	7368.93i		−	1.65177i	0.563837	−	0.825886i	$-0.309325\pi$
$272$	−1833.77	−	2703.35i	−0.408782	−	0.602628i
$273$		0			0
$274$	−6569.42	+	986.212i	−1.44844	+	0.217443i
$275$	−6923.21			−1.51813
$276$		0			0
$277$	9078.61			1.96924			0.984622	−	0.174699i	$-0.0558952\pi$
$277$	9078.61			1.96924			0.984622	+	0.174699i	$0.0558952\pi$
$278$	602.045	−	90.3800i	0.129886	−	0.0194987i
$279$		0			0
$280$	−382.938	−	798.798i	−0.0817319	−	0.170490i
$281$		−	2613.34i		−	0.554801i	−0.960754	−	0.277400i	$-0.910527\pi$
$281$		−	2613.34i		−	0.554801i	0.960754	−	0.277400i	$-0.0894729\pi$
$282$		0			0
$283$		−	927.970i		−	0.194919i	−0.995239	−	0.0974596i	$-0.968928\pi$
$283$		−	927.970i		−	0.194919i	0.995239	−	0.0974596i	$-0.0310717\pi$
$284$	1711.58	−	525.739i	0.357619	−	0.109848i
$285$		0			0
$286$	978.388	+	6517.31i	0.202284	+	1.34747i
$287$	7803.60			1.60499
$288$		0			0
$289$	2307.81			0.469736
$290$	84.4801	+	562.745i	0.0171064	+	0.113950i
$291$		0			0
$292$	−536.364	+	164.753i	−0.107494	+	0.0330185i
$293$			5351.73i			1.06707i	0.845778	+	0.533535i	$0.179137\pi$
$293$			5351.73i			1.06707i	−0.845778	+	0.533535i	$0.820863\pi$
$294$		0			0
$295$		−	480.150i		−	0.0947641i
$296$	1922.90	+	4011.11i	0.377589	+	0.787639i
$297$		0			0
$298$	−615.229	+	92.3591i	−0.119595	+	0.0179538i
$299$	1130.80			0.218714
$300$		0			0
$301$	−12191.2			−2.33452
$302$	3211.10	−	482.055i	0.611847	−	0.0918514i
$303$		0			0
$304$	2840.57	+	4187.57i	0.535913	+	0.790045i
$305$		−	1008.73i		−	0.189377i
$306$		0			0
$307$			1892.38i			0.351804i	0.984408	+	0.175902i	$0.0562842\pi$
$307$			1892.38i			0.351804i	−0.984408	+	0.175902i	$0.943716\pi$
$308$	3468.76	+	11292.8i	0.641725	+	2.08918i
$309$		0			0
$310$	117.518	+	782.816i	0.0215308	+	0.143422i
$311$	5645.22			1.02930			0.514648	−	0.857402i	$-0.327923\pi$
$311$	5645.22			1.02930			0.514648	+	0.857402i	$0.327923\pi$
$312$		0			0
$313$	−818.001			−0.147719			−0.0738597	−	0.997269i	$-0.523532\pi$
$313$	−818.001			−0.147719			−0.0738597	+	0.997269i	$0.523532\pi$
$314$	−116.027	−	772.890i	−0.0208529	−	0.138907i
$315$		0			0
$316$	2471.91	+	8047.49i	0.440050	+	1.43262i
$317$		−	1946.72i		−	0.344917i	−0.985017	−	0.172458i	$-0.944829\pi$
$317$		−	1946.72i		−	0.344917i	0.985017	−	0.172458i	$-0.0551710\pi$
$318$		0			0
$319$		−	7588.81i		−	1.33195i
$320$	596.784	+	479.390i	0.104254	+	0.0837459i
$321$		0			0
$322$	2004.55	−	300.927i	0.346924	−	0.0520807i
$323$	4035.51			0.695176
$324$		0			0
$325$	−5072.27			−0.865719
$326$	−3969.48	+	595.905i	−0.674385	+	0.101240i
$327$		0			0
$328$	−6080.69	+	2915.04i	−1.02363	+	0.490720i
$329$			9789.22i			1.64042i
$330$		0			0
$331$		−	3404.83i		−	0.565396i	−0.959209	−	0.282698i	$-0.908771\pi$
$331$		−	3404.83i		−	0.565396i	0.959209	−	0.282698i	$-0.0912295\pi$
$332$	9322.48	−	2863.55i	1.54108	−	0.473366i
$333$		0			0
$334$	1473.31	+	9814.11i	0.241365	+	1.60780i
$335$	−861.281			−0.140468
$336$		0			0
$337$	7072.15			1.14316			0.571579	−	0.820547i	$-0.306331\pi$
$337$	7072.15			1.14316			0.571579	+	0.820547i	$0.306331\pi$
$338$	−205.714	−	1370.31i	−0.0331046	−	0.220519i
$339$		0			0
$340$	583.575	−	179.254i	0.0930848	−	0.0285924i
$341$		−	10556.6i		−	1.67645i
$342$		0			0
$343$			8.73194i			0.00137458i
$344$	9499.60	−	4554.04i	1.48891	−	0.713771i
$345$		0			0
$346$	925.736	−	138.973i	0.143838	−	0.0215932i
$347$	5783.02			0.894665			0.447332	−	0.894368i	$-0.352374\pi$
$347$	5783.02			0.894665			0.447332	+	0.894368i	$0.352374\pi$
$348$		0			0
$349$	1748.60			0.268196			0.134098	−	0.990968i	$-0.457186\pi$
$349$	1748.60			0.268196			0.134098	+	0.990968i	$0.457186\pi$
$350$	−8991.57	+	1349.83i	−1.37320	+	0.206147i
$351$		0			0
$352$	−6921.36	−	7503.79i	−1.04804	−	1.13623i
$353$			9552.31i			1.44028i	0.693830	+	0.720139i	$0.255922\pi$
$353$			9552.31i			1.44028i	−0.693830	+	0.720139i	$0.744078\pi$
$354$		0			0
$355$			334.620i			0.0500276i
$356$	−3149.18	−	10252.4i	−0.468837	−	1.52633i
$357$		0			0
$358$	−477.323	−	3179.58i	−0.0704673	−	0.469402i
$359$	921.392			0.135457			0.0677287	−	0.997704i	$-0.478425\pi$
$359$	921.392			0.135457			0.0677287	+	0.997704i	$0.478425\pi$
$360$		0			0
$361$	607.881			0.0886254
$362$	863.704	+	5753.37i	0.125401	+	0.835332i
$363$		0			0
$364$	2541.38	+	8273.64i	0.365946	+	1.19136i
$365$		−	104.861i		−	0.0150375i
$366$		0			0
$367$			8490.66i			1.20765i	0.797115	+	0.603827i	$0.206358\pi$
$367$			8490.66i			1.20765i	−0.797115	+	0.603827i	$0.793642\pi$
$368$	−1449.57	+	983.291i	−0.205337	+	0.139287i
$369$		0			0
$370$	−822.094	+	123.414i	−0.115510	+	0.0173405i
$371$	−16237.3			−2.27223
$372$		0			0
$373$	2824.92			0.392142			0.196071	−	0.980590i	$-0.437182\pi$
$373$	2824.92			0.392142			0.196071	+	0.980590i	$0.437182\pi$
$374$	−8051.17	+	1208.65i	−1.11314	+	0.167107i
$375$		0			0
$376$	−3656.77	−	7627.92i	−0.501552	−	1.04622i
$377$		−	5559.92i		−	0.759550i
$378$		0			0
$379$		−	5322.35i		−	0.721348i	−0.932692	−	0.360674i	$-0.882547\pi$
$379$		−	5322.35i		−	0.721348i	0.932692	−	0.360674i	$-0.117453\pi$
$380$	−903.975	+	277.670i	−0.122034	+	0.0374847i
$381$		0			0
$382$	−832.763	−	5547.26i	−0.111539	−	0.742990i
$383$	−8320.49			−1.11007			−0.555035	−	0.831827i	$-0.687295\pi$
$383$	−8320.49			−1.11007			−0.555035	+	0.831827i	$0.687295\pi$
$384$		0			0
$385$	−2207.78			−0.292257
$386$	−79.7428	−	531.188i	−0.0105150	−	0.0700434i
$387$		0			0
$388$	4405.33	−	1353.17i	0.576409	−	0.177053i
$389$		−	8358.52i		−	1.08944i	−0.838617	−	0.544722i	$-0.816635\pi$
$389$		−	8358.52i		−	1.08944i	0.838617	−	0.544722i	$-0.183365\pi$
$390$		0			0
$391$			1396.93i			0.180680i
$392$	3351.80	+	6991.76i	0.431866	+	0.900860i
$393$		0			0
$394$	−6042.87	+	907.166i	−0.772679	+	0.115996i
$395$	−1573.31			−0.200410
$396$		0			0
$397$	7283.17			0.920735			0.460367	−	0.887728i	$-0.347718\pi$
$397$	7283.17			0.920735			0.460367	+	0.887728i	$0.347718\pi$
$398$	−7429.69	+	1115.36i	−0.935720	+	0.140472i
$399$		0			0
$400$	6502.15	−	4410.62i	0.812769	−	0.551327i
$401$		−	1549.41i		−	0.192952i	−0.995335	−	0.0964759i	$-0.969243\pi$
$401$		−	1549.41i		−	0.192952i	0.995335	−	0.0964759i	$-0.0307571\pi$
$402$		0			0
$403$		−	7734.22i		−	0.956003i
$404$	−272.671	−	887.699i	−0.0335789	−	0.109318i
$405$		0			0
$406$	−1479.60	−	9856.03i	−0.180866	−	1.20479i
$407$	11086.2			1.35018
$408$		0			0
$409$	3291.67			0.397952			0.198976	−	0.980004i	$-0.436238\pi$
$409$	3291.67			0.397952			0.198976	+	0.980004i	$0.436238\pi$
$410$	−187.091	−	1246.26i	−0.0225360	−	0.150118i
$411$		0			0
$412$	387.759	+	1262.38i	0.0463678	+	0.150954i
$413$			8409.45i			1.00194i
$414$		0			0
$415$			1822.58i			0.215583i
$416$	−5070.91	−	5497.62i	−0.597649	−	0.647940i
$417$		0			0
$418$	12471.5	−	1872.24i	1.45933	−	0.219077i
$419$	−5299.78			−0.617927			−0.308964	−	0.951074i	$-0.599982\pi$
$419$	−5299.78			−0.617927			−0.308964	+	0.951074i	$0.599982\pi$
$420$		0			0
$421$	−10681.4			−1.23653			−0.618265	−	0.785970i	$-0.712164\pi$
$421$	−10681.4			−1.23653			−0.618265	+	0.785970i	$0.712164\pi$
$422$	−2800.45	+	420.408i	−0.323042	+	0.0484956i
$423$		0			0
$424$	12652.4	−	6065.45i	1.44918	−	0.694727i
$425$		−	6266.04i		−	0.715170i
$426$		0			0
$427$			17667.2i			2.00228i
$428$	7163.43	−	2200.36i	0.809012	−	0.248501i
$429$		0			0
$430$	292.284	+	1946.98i	0.0327795	+	0.218353i
$431$	−9866.13			−1.10263			−0.551316	−	0.834296i	$-0.685874\pi$
$431$	−9866.13			−1.10263			−0.551316	+	0.834296i	$0.685874\pi$
$432$		0			0
$433$	−12560.2			−1.39400			−0.697002	−	0.717069i	$-0.745483\pi$
$433$	−12560.2			−1.39400			−0.697002	+	0.717069i	$0.745483\pi$
$434$	−2058.23	−	13710.4i	−0.227645	−	1.51641i
$435$		0			0
$436$	−2653.31	+	815.005i	−0.291446	+	0.0895221i
$437$		−	2163.89i		−	0.236871i
$438$		0			0
$439$			929.228i			0.101024i	0.998723	+	0.0505121i	$0.0160854\pi$
$439$			929.228i			0.101024i	−0.998723	+	0.0505121i	$0.983915\pi$
$440$	1720.34	−	824.719i	0.186396	−	0.0893567i
$441$		0			0
$442$	−5898.66	+	885.516i	−0.634775	+	0.0952935i
$443$	4373.85			0.469092			0.234546	−	0.972105i	$-0.424640\pi$
$443$	4373.85			0.469092			0.234546	+	0.972105i	$0.424640\pi$
$444$		0			0
$445$	2004.37			0.213520
$446$	−8932.81	+	1341.01i	−0.948388	+	0.142373i
$447$		0			0
$448$	−10452.2	−	8396.13i	−1.10228	−	0.885446i
$449$			14149.5i			1.48721i	0.668618	+	0.743606i	$0.266886\pi$
$449$			14149.5i			1.48721i	−0.668618	+	0.743606i	$0.733114\pi$
$450$		0			0
$451$			16806.3i			1.75472i
$452$	3434.76	+	11182.1i	0.357428	+	1.16363i
$453$		0			0
$454$	−720.017	−	4796.22i	−0.0744319	−	0.495810i
$455$	−1617.52			−0.166661
$456$		0			0
$457$	−12582.4			−1.28792			−0.643960	−	0.765059i	$-0.722710\pi$
$457$	−12582.4			−1.28792			−0.643960	+	0.765059i	$0.722710\pi$
$458$	−171.109	−	1139.80i	−0.0174572	−	0.116287i
$459$		0			0
$460$	−96.1183	−	312.920i	−0.00974247	−	0.0317173i
$461$			10602.2i			1.07114i	0.844492	+	0.535568i	$0.179902\pi$
$461$			10602.2i			1.07114i	−0.844492	+	0.535568i	$0.820098\pi$
$462$		0			0
$463$			5080.88i			0.509997i	0.966941	+	0.254999i	$0.0820750\pi$
$463$			5080.88i			0.509997i	−0.966941	+	0.254999i	$0.917925\pi$
$464$	4834.66	+	7127.27i	0.483714	+	0.713093i
$465$		0			0
$466$	8980.16	−	1348.12i	0.892699	−	0.134013i
$467$	−6903.92			−0.684102			−0.342051	−	0.939681i	$-0.611121\pi$
$467$	−6903.92			−0.684102			−0.342051	+	0.939681i	$0.611121\pi$
$468$		0			0
$469$	15084.7			1.48517
$470$	1563.37	−	234.696i	0.153432	−	0.0230335i
$471$		0			0
$472$	−3141.36	−	6552.78i	−0.306341	−	0.639017i
$473$		−	26255.8i		−	2.55231i
$474$		0			0
$475$			9706.27i			0.937588i
$476$	−10220.9	+	3139.50i	−0.984186	+	0.302308i
$477$		0			0
$478$	655.548	+	4366.78i	0.0627282	+	0.417849i
$479$	5114.56			0.487871			0.243936	−	0.969791i	$-0.421561\pi$
$479$	5114.56			0.487871			0.243936	+	0.969791i	$0.421561\pi$
$480$		0			0
$481$	8122.29			0.769947
$482$	613.434	+	4086.25i	0.0579692	+	0.386148i
$483$		0			0
$484$	−14142.3	+	4344.02i	−1.32816	+	0.407966i
$485$			861.257i			0.0806344i
$486$		0			0
$487$			15594.2i			1.45101i	0.688218	+	0.725504i	$0.258393\pi$
$487$			15594.2i			1.45101i	−0.688218	+	0.725504i	$0.741607\pi$
$488$	−6599.58	−	13766.5i	−0.612191	−	1.27701i
$489$		0			0
$490$	−1432.99	+	215.123i	−0.132114	+	0.0198332i
$491$	10521.0			0.967023			0.483511	−	0.875338i	$-0.339361\pi$
$491$	10521.0			0.967023			0.483511	+	0.875338i	$0.339361\pi$
$492$		0			0
$493$	6868.46			0.627464
$494$	9137.20	−	1371.69i	0.832190	−	0.124930i
$495$		0			0
$496$	6725.34	+	9914.52i	0.608824	+	0.897531i
$497$		−	5860.61i		−	0.528942i
$498$		0			0
$499$		−	8984.43i		−	0.806009i	−0.915198	−	0.403004i	$-0.867966\pi$
$499$		−	8984.43i		−	0.806009i	0.915198	−	0.403004i	$-0.132034\pi$
$500$	870.141	+	2832.81i	0.0778278	+	0.253374i
$501$		0			0
$502$	−2884.08	−	19211.6i	−0.256420	−	1.70808i
$503$	4299.12			0.381090			0.190545	−	0.981678i	$-0.438974\pi$
$503$	4299.12			0.381090			0.190545	+	0.981678i	$0.438974\pi$
$504$		0			0
$505$	173.548			0.0152926
$506$	648.095	+	4317.13i	0.0569394	+	0.379288i
$507$		0			0
$508$	−622.497	−	2026.58i	−0.0543678	−	0.176998i
$509$			2984.83i			0.259922i	0.991519	+	0.129961i	$0.0414853\pi$
$509$			2984.83i			0.259922i	−0.991519	+	0.129961i	$0.958515\pi$
$510$		0			0
$511$			1836.56i			0.158991i
$512$	11280.9	+	2637.98i	0.973731	+	0.227702i
$513$		0			0
$514$	−12449.4	+	1868.92i	−1.06832	+	0.160378i
$515$	−246.799			−0.0211170
$516$		0			0
$517$	−21082.7			−1.79345
$518$	14398.3	−	2161.50i	1.22129	−	0.183341i
$519$		0			0
$520$	1260.40	−	604.228i	0.106293	−	0.0509560i
$521$			12255.7i			1.03058i	0.857016	+	0.515290i	$0.172316\pi$
$521$			12255.7i			1.03058i	−0.857016	+	0.515290i	$0.827684\pi$
$522$		0			0
$523$		−	15148.5i		−	1.26654i	−0.773932	−	0.633269i	$-0.781713\pi$
$523$		−	15148.5i		−	1.26654i	0.773932	−	0.633269i	$-0.218287\pi$
$524$	8808.67	−	2705.72i	0.734367	−	0.225572i
$525$		0			0
$526$	2739.99	+	18251.8i	0.227128	+	1.51296i
$527$	9554.49			0.789754
$528$		0			0
$529$	−11417.9			−0.938436
$530$	389.288	+	2593.15i	0.0319049	+	0.212527i
$531$		0			0
$532$	15832.4	−	4863.17i	1.29027	−	0.396326i
$533$			12313.1i			1.00064i
$534$		0			0
$535$			1400.47i			0.113173i
$536$	−11754.2	+	5634.89i	−0.947211	+	0.454086i
$537$		0			0
$538$	9012.82	−	1353.02i	0.722250	−	0.108425i
$539$	19324.4			1.54427
$540$		0			0
$541$	5723.84			0.454875			0.227437	−	0.973793i	$-0.426965\pi$
$541$	5723.84			0.454875			0.227437	+	0.973793i	$0.426965\pi$
$542$	20611.5	−	3094.23i	1.63347	−	0.245219i
$543$		0			0
$544$	6791.50	−	6264.36i	0.535263	−	0.493717i
$545$		−	518.730i		−	0.0407706i
$546$		0			0
$547$			8367.43i			0.654051i	0.945016	+	0.327025i	$0.106046\pi$
$547$			8367.43i			0.654051i	−0.945016	+	0.327025i	$0.893954\pi$
$548$	−5517.04	−	17961.1i	−0.430066	−	1.40011i
$549$		0			0
$550$	−2907.08	−	19364.8i	−0.225378	−	1.50131i
$551$	−10639.4			−0.822605
$552$		0			0
$553$	27555.3			2.11893
$554$	3812.13	+	25393.6i	0.292350	+	1.94742i
$555$		0			0
$556$	505.601	+	1646.02i	0.0385652	+	0.125552i
$557$			15824.2i			1.20375i	0.798589	+	0.601877i	$0.205580\pi$
$557$			15824.2i			1.20375i	−0.798589	+	0.601877i	$0.794420\pi$
$558$		0			0
$559$		−	19236.2i		−	1.45546i
$560$	2073.51	−	1406.53i	0.156467	−	0.106137i
$561$		0			0
$562$	7309.74	−	1097.35i	0.548653	−	0.0823647i
$563$	2781.72			0.208233			0.104117	−	0.994565i	$-0.466798\pi$
$563$	2781.72			0.208233			0.104117	+	0.994565i	$0.466798\pi$
$564$		0			0
$565$	−2186.14			−0.162781
$566$	2595.61	−	389.657i	0.192759	−	0.0289373i
$567$		0			0
$568$	2189.24	+	4566.68i	0.161722	+	0.337348i
$569$			4687.63i			0.345370i	0.984977	+	0.172685i	$0.0552443\pi$
$569$			4687.63i			0.345370i	−0.984977	+	0.172685i	$0.944756\pi$
$570$		0			0
$571$		−	15169.4i		−	1.11177i	−0.831259	−	0.555885i	$-0.812379\pi$
$571$		−	15169.4i		−	1.11177i	0.831259	−	0.555885i	$-0.187621\pi$
$572$	−17818.6	+	5473.27i	−1.30251	+	0.400085i
$573$		0			0
$574$	3276.75	+	21827.3i	0.238274	+	1.58720i
$575$	−3359.92			−0.243684
$576$		0			0
$577$	−14452.3			−1.04273			−0.521367	−	0.853332i	$-0.674578\pi$
$577$	−14452.3			−1.04273			−0.521367	+	0.853332i	$0.674578\pi$
$578$	969.057	+	6455.15i	0.0697361	+	0.464531i
$579$		0			0
$580$	−1538.57	+	472.596i	−0.110148	+	0.0338336i
$581$		−	31921.0i		−	2.27936i
$582$		0			0
$583$		−	34969.6i		−	2.48421i
$584$	−686.047	−	1431.07i	−0.0486110	−	0.101401i
$585$		0			0
$586$	−14969.3	+	2247.21i	−1.05525	+	0.158415i
$587$	7405.55			0.520715			0.260358	−	0.965512i	$-0.416160\pi$
$587$	7405.55			0.520715			0.260358	+	0.965512i	$0.416160\pi$
$588$		0			0
$589$	−14800.2			−1.03537
$590$	1343.02	−	201.616i	0.0937140	−	0.0140685i
$591$		0			0
$592$	−10412.0	+	7062.79i	−0.722855	+	0.490336i
$593$		−	19888.1i		−	1.37725i	−0.725120	−	0.688623i	$-0.758216\pi$
$593$		−	19888.1i		−	1.37725i	0.725120	−	0.688623i	$-0.241784\pi$
$594$		0			0
$595$		−	1998.21i		−	0.137679i
$596$	−516.672	−	1682.06i	−0.0355096	−	0.115604i
$597$		0			0
$598$	474.824	+	3162.93i	0.0324699	+	0.216291i
$599$	2335.49			0.159308			0.0796539	−	0.996823i	$-0.474618\pi$
$599$	2335.49			0.159308			0.0796539	+	0.996823i	$0.474618\pi$
$600$		0			0
$601$	24547.9			1.66611			0.833054	−	0.553192i	$-0.186590\pi$
$601$	24547.9			1.66611			0.833054	+	0.553192i	$0.186590\pi$
$602$	−5119.12	−	34099.9i	−0.346578	−	2.30865i
$603$		0			0
$604$	2696.70	+	8779.29i	0.181667	+	0.591431i
$605$		−	2764.86i		−	0.185798i
$606$		0			0
$607$			18328.9i			1.22561i	0.790233	+	0.612806i	$0.209959\pi$
$607$			18328.9i			1.22561i	−0.790233	+	0.612806i	$0.790041\pi$
$608$	−10520.2	+	9703.68i	−0.701730	+	0.647263i
$609$		0			0
$610$	2821.51	−	423.570i	0.187278	−	0.0281145i
$611$	−15446.1			−1.02272
$612$		0			0
$613$	6450.01			0.424981			0.212491	−	0.977163i	$-0.431843\pi$
$613$	6450.01			0.424981			0.212491	+	0.977163i	$0.431843\pi$
$614$	−5293.15	+	794.616i	−0.347906	+	0.0522282i
$615$		0			0
$616$	−30130.4	+	14444.3i	−1.97076	+	0.944769i
$617$			6724.96i			0.438795i	0.975636	+	0.219398i	$0.0704092\pi$
$617$			6724.96i			0.438795i	−0.975636	+	0.219398i	$0.929591\pi$
$618$		0			0
$619$		−	3136.55i		−	0.203665i	−0.994802	−	0.101832i	$-0.967529\pi$
$619$		−	3136.55i		−	0.203665i	0.994802	−	0.101832i	$-0.0324705\pi$
$620$	−2140.26	+	657.413i	−0.138637	+	0.0425844i
$621$		0			0
$622$	2370.44	+	15790.2i	0.152807	+	1.01789i
$623$	−35105.0			−2.25755
$624$		0			0
$625$	14791.8			0.946673
$626$	−343.481	−	2288.02i	−0.0219301	−	0.146082i
$627$		0			0
$628$	2113.12	−	649.077i	0.134272	−	0.0412436i
$629$			10033.9i			0.636053i
$630$		0			0
$631$			6061.57i			0.382420i	0.981549	+	0.191210i	$0.0612412\pi$
$631$			6061.57i			0.382420i	−0.981549	+	0.191210i	$0.938759\pi$
$632$	−21471.5	+	10293.3i	−1.35141	+	0.647857i
$633$		0			0
$634$	5445.14	−	817.433i	0.341095	−	0.0512057i
$635$	396.204			0.0247604
$636$		0			0
$637$	14157.9			0.880625
$638$	21226.6	−	3186.56i	1.31719	−	0.197739i
$639$		0			0
$640$	−1090.30	+	1870.55i	−0.0673406	+	0.115531i
$641$			18603.3i			1.14631i	0.819446	+	0.573157i	$0.194281\pi$
$641$			18603.3i			1.14631i	−0.819446	+	0.573157i	$0.805719\pi$
$642$		0			0
$643$		−	21602.4i		−	1.32491i	−0.749103	−	0.662453i	$-0.769515\pi$
$643$		−	21602.4i		−	1.32491i	0.749103	−	0.662453i	$-0.230485\pi$
$644$	1683.44	+	5480.55i	0.103007	+	0.335348i
$645$		0			0
$646$	1694.52	+	11287.7i	0.103204	+	0.687472i
$647$	−672.754			−0.0408790			−0.0204395	−	0.999791i	$-0.506507\pi$
$647$	−672.754			−0.0408790			−0.0204395	+	0.999791i	$0.506507\pi$
$648$		0			0
$649$	−18111.1			−1.09541
$650$	−2129.86	−	14187.6i	−0.128523	−	0.856126i
$651$		0			0
$652$	−3333.59	−	10852.8i	−0.200236	−	0.651882i
$653$		−	3322.88i		−	0.199134i	−0.995031	−	0.0995668i	$-0.968254\pi$
$653$		−	3322.88i		−	0.199134i	0.995031	−	0.0995668i	$-0.0317457\pi$
$654$		0			0
$655$			1722.12i			0.102731i
$656$	−10706.9	−	15784.2i	−0.637248	−	0.939434i
$657$		0			0
$658$	−27381.3	+	4110.52i	−1.62224	+	0.243533i
$659$	25093.7			1.48332			0.741662	−	0.670773i	$-0.234038\pi$
$659$	25093.7			1.48332			0.741662	+	0.670773i	$0.234038\pi$
$660$		0			0
$661$	−28966.3			−1.70447			−0.852237	−	0.523157i	$-0.824754\pi$
$661$	−28966.3			−1.70447			−0.852237	+	0.523157i	$0.824754\pi$
$662$	9523.59	−	1429.70i	0.559131	−	0.0839376i
$663$		0			0
$664$	11924.1	+	24873.4i	0.696906	+	1.45373i
$665$			3095.29i			0.180496i
$666$		0			0
$667$		−	3682.95i		−	0.213800i
$668$	−26832.2	+	8241.94i	−1.55415	+	0.477381i
$669$		0			0
$670$	−361.654	−	2409.08i	−0.0208536	−	0.138912i
$671$	−38049.1			−2.18907
$672$		0			0
$673$	−4710.36			−0.269793			−0.134897	−	0.990860i	$-0.543070\pi$
$673$	−4710.36			−0.269793			−0.134897	+	0.990860i	$0.543070\pi$
$674$	2969.62	+	19781.4i	0.169711	+	1.13049i
$675$		0			0
$676$	3746.51	−	1150.80i	0.213160	−	0.0654755i
$677$			4784.53i			0.271617i	0.990735	+	0.135808i	$0.0433631\pi$
$677$			4784.53i			0.271617i	−0.990735	+	0.135808i	$0.956637\pi$
$678$		0			0
$679$		−	15084.2i		−	0.852548i
$680$	746.434	+	1557.04i	0.0420948	+	0.0878085i
$681$		0			0
$682$	29527.6	−	4432.73i	1.65787	−	0.248883i
$683$	18019.8			1.00953			0.504764	−	0.863258i	$-0.331580\pi$
$683$	18019.8			1.00953			0.504764	+	0.863258i	$0.331580\pi$
$684$		0			0
$685$	3511.46			0.195863
$686$	−24.4240	+	3.66657i	−0.00135935	+	0.000204067i
$687$		0			0
$688$	16726.9	+	24658.9i	0.926902	+	1.36644i
$689$		−	25620.4i		−	1.41663i
$690$		0			0
$691$			16956.5i			0.933511i	0.884386	+	0.466756i	$0.154577\pi$
$691$			16956.5i			0.933511i	−0.884386	+	0.466756i	$0.845423\pi$
$692$	777.439	+	2531.01i	0.0427078	+	0.139038i
$693$		0			0
$694$	2428.31	+	16175.6i	0.132820	+	0.884751i
$695$	−321.802			−0.0175635
$696$		0			0
$697$	−15211.0			−0.826625
$698$	734.243	+	4890.99i	0.0398159	+	0.265225i
$699$		0			0
$700$	−7551.17	−	24583.4i	−0.407725	−	1.32738i
$701$		−	30620.5i		−	1.64982i	−0.565266	−	0.824909i	$-0.691226\pi$
$701$		−	30620.5i		−	1.64982i	0.565266	−	0.824909i	$-0.308774\pi$
$702$		0			0
$703$		−	15542.8i		−	0.833865i
$704$	18082.4	−	22510.5i	0.968050	−	1.20511i
$705$		0			0
$706$	−26718.6	+	4011.04i	−1.42432	+	0.213821i
$707$	−3039.56			−0.161689
$708$		0			0
$709$	24192.8			1.28149			0.640747	−	0.767752i	$-0.278625\pi$
$709$	24192.8			1.28149			0.640747	+	0.767752i	$0.278625\pi$
$710$	−935.961	+	140.508i	−0.0494732	+	0.00742700i
$711$		0			0
$712$	27354.4	−	13113.5i	1.43982	−	0.690238i
$713$		−	5123.23i		−	0.269098i
$714$		0			0
$715$		−	3483.60i		−	0.182209i
$716$	8693.11	−	2670.23i	0.453739	−	0.139373i
$717$		0			0
$718$	386.895	+	2577.21i	0.0201098	+	0.133956i
$719$	−37146.6			−1.92675			−0.963377	−	0.268151i	$-0.913588\pi$
$719$	−37146.6			−1.92675			−0.963377	+	0.268151i	$0.913588\pi$
$720$		0			0
$721$	4322.49			0.223271
$722$	255.251	+	1700.30i	0.0131571	+	0.0876433i
$723$		0			0
$724$	−15730.0	+	4831.71i	−0.807459	+	0.248024i
$725$			16520.1i			0.846265i
$726$		0			0
$727$			14614.3i			0.745551i	0.927922	+	0.372775i	$0.121594\pi$
$727$			14614.3i			0.745551i	−0.927922	+	0.372775i	$0.878406\pi$
$728$	−22074.9	+	10582.6i	−1.12383	+	0.538759i
$729$		0			0
$730$	293.305	−	44.0314i	0.0148708	−	0.00223243i
$731$	23763.5			1.20236
$732$		0			0
$733$	−8044.73			−0.405374			−0.202687	−	0.979244i	$-0.564967\pi$
$733$	−8044.73			−0.405374			−0.202687	+	0.979244i	$0.564967\pi$
$734$	−23749.1	+	3565.25i	−1.19427	+	0.179286i
$735$		0			0
$736$	−3359.03	−	3641.68i	−0.168227	−	0.182384i
$737$			32487.3i			1.62372i
$738$		0			0
$739$		−	7025.01i		−	0.349688i	−0.984596	−	0.174844i	$-0.944058\pi$
$739$		−	7025.01i		−	0.349688i	0.984596	−	0.174844i	$-0.0559420\pi$
$740$	−690.399	−	2247.64i	−0.0342967	−	0.111655i
$741$		0			0
$742$	−6818.08	−	45417.0i	−0.337331	−	2.24705i
$743$	27063.4			1.33629			0.668143	−	0.744033i	$-0.267089\pi$
$743$	27063.4			1.33629			0.668143	+	0.744033i	$0.267089\pi$
$744$		0			0
$745$	328.849			0.0161719
$746$	1186.19	+	7901.54i	0.0582166	+	0.387796i
$747$		0			0
$748$	−6761.42	−	22012.3i	−0.330511	−	1.07600i
$749$		−	24528.2i		−	1.19658i
$750$		0			0
$751$		−	11434.2i		−	0.555579i	−0.960642	−	0.277789i	$-0.910398\pi$
$751$		−	11434.2i		−	0.555579i	0.960642	−	0.277789i	$-0.0896017\pi$
$752$	19800.4	−	13431.3i	0.960170	−	0.651315i
$753$		0			0
$754$	15551.6	−	2334.62i	0.751133	−	0.112761i
$755$	−1716.38			−0.0827357
$756$		0			0
$757$	22087.2			1.06046			0.530232	−	0.847853i	$-0.322105\pi$
$757$	22087.2			1.06046			0.530232	+	0.847853i	$0.322105\pi$
$758$	14887.1	−	2234.87i	0.713354	−	0.107090i
$759$		0			0
$760$	−1156.25	−	2411.90i	−0.0551862	−	0.115117i
$761$			35524.0i			1.69218i	0.533043	+	0.846088i	$0.321048\pi$
$761$			35524.0i			1.69218i	−0.533043	+	0.846088i	$0.678952\pi$
$762$		0			0
$763$			9085.16i			0.431068i
$764$	15166.5	−	4658.62i	0.718198	−	0.220606i
$765$		0			0
$766$	−3493.79	−	23273.1i	−0.164799	−	1.09777i
$767$	−13269.0			−0.624664
$768$		0			0
$769$	21213.0			0.994745			0.497372	−	0.867537i	$-0.334298\pi$
$769$	21213.0			0.994745			0.497372	+	0.867537i	$0.334298\pi$
$770$	−927.054	−	6175.36i	−0.0433879	−	0.289019i
$771$		0			0
$772$	1452.29	−	446.095i	0.0677062	−	0.0207970i
$773$			14370.7i			0.668663i	0.942456	+	0.334332i	$0.108511\pi$
$773$			14370.7i			0.668663i	−0.942456	+	0.334332i	$0.891489\pi$
$774$		0			0
$775$			22980.6i			1.06515i
$776$	5634.73	+	11753.9i	0.260664	+	0.543737i
$777$		0			0
$778$	23379.5	−	3509.77i	1.07737	−	0.161737i
$779$	23562.3			1.08371
$780$		0			0
$781$	12621.8			0.578287
$782$	−3907.34	+	586.575i	−0.178678	+	0.0268234i
$783$		0			0
$784$	−18149.1	+	12311.1i	−0.826763	+	0.560820i
$785$			413.122i			0.0187834i
$786$		0			0
$787$			41642.9i			1.88616i	0.332564	+	0.943081i	$0.392086\pi$
$787$			41642.9i			1.88616i	−0.332564	+	0.943081i	$0.607914\pi$
$788$	−5074.84	−	16521.5i	−0.229421	−	0.746896i
$789$		0			0
$790$	−660.637	−	4400.68i	−0.0297524	−	0.198189i
$791$	38288.5			1.72109
$792$		0			0
$793$	−27876.5			−1.24833
$794$	3058.22	+	20371.6i	0.136691	+	0.910532i
$795$		0			0
$796$	−6239.49	−	20313.1i	−0.277830	−	0.904497i
$797$		−	23527.1i		−	1.04564i	−0.852445	−	0.522818i	$-0.824881\pi$
$797$		−	23527.1i		−	1.04564i	0.852445	−	0.522818i	$-0.175119\pi$
$798$		0			0
$799$		−	19081.4i		−	0.844872i
$800$	15067.1	+	16335.0i	0.665880	+	0.721913i
$801$		0			0
$802$	4333.82	−	650.600i	0.190814	−	0.0286453i
$803$	−3955.32			−0.173823
$804$		0			0
$805$	−1071.47			−0.0469120
$806$	21633.3	−	3247.62i	0.945409	−	0.141926i
$807$		0			0
$808$	2368.47	−	1135.43i	0.103122	−	0.0494360i
$809$		−	7508.22i		−	0.326298i	−0.986601	−	0.163149i	$-0.947835\pi$
$809$		−	7508.22i		−	0.326298i	0.986601	−	0.163149i	$-0.0521651\pi$
$810$		0			0
$811$			15834.0i			0.685581i	0.939412	+	0.342791i	$0.111372\pi$
$811$			15834.0i			0.685581i	−0.939412	+	0.342791i	$0.888628\pi$
$812$	26946.9	−	8277.15i	1.16459	−	0.357723i
$813$		0			0
$814$	4655.14	+	31009.1i	0.200445	+	1.33522i
$815$	2121.75			0.0911923
$816$		0			0
$817$	−36810.3			−1.57629
$818$	1382.18	+	9207.07i	0.0590792	+	0.393542i
$819$		0			0
$820$	3407.35	−	1046.62i	0.145109	−	0.0445726i
$821$		−	13279.1i		−	0.564486i	−0.959343	−	0.282243i	$-0.908922\pi$
$821$		−	13279.1i		−	0.564486i	0.959343	−	0.282243i	$-0.0910784\pi$
$822$		0			0
$823$			27997.4i			1.18582i	0.805270	+	0.592909i	$0.202021\pi$
$823$			27997.4i			1.18582i	−0.805270	+	0.592909i	$0.797979\pi$
$824$	−3368.16	+	1614.67i	−0.142397	+	0.0682643i
$825$		0			0
$826$	−23521.9	+	3531.15i	−0.990839	+	0.148746i
$827$	35177.8			1.47914			0.739571	−	0.673078i	$-0.235028\pi$
$827$	35177.8			1.47914			0.739571	+	0.673078i	$0.235028\pi$
$828$		0			0
$829$	−13390.3			−0.560996			−0.280498	−	0.959855i	$-0.590500\pi$
$829$	−13390.3			−0.560996			−0.280498	+	0.959855i	$0.590500\pi$
$830$	−5097.90	+	765.305i	−0.213194	+	0.0320050i
$831$		0			0
$832$	13248.0	−	16492.2i	0.552034	−	0.687218i
$833$			17490.1i			0.727484i
$834$		0			0
$835$		−	5245.79i		−	0.217411i
$836$	10473.6	+	34097.7i	0.433299	+	1.41064i
$837$		0			0
$838$	−2225.39	−	14823.9i	−0.0917362	−	0.611080i
$839$	−8466.38			−0.348381			−0.174191	−	0.984712i	$-0.555731\pi$
$839$	−8466.38			−0.348381			−0.174191	+	0.984712i	$0.555731\pi$
$840$		0			0
$841$	6280.62			0.257518
$842$	−4485.15	−	29876.8i	−0.183573	−	1.22283i
$843$		0			0
$844$	−2351.83	−	7656.57i	−0.0959164	−	0.312263i
$845$			732.454i			0.0298192i
$846$		0			0
$847$			48424.4i			1.96444i
$848$	22278.3	+	32842.8i	0.902171	+	1.32998i
$849$		0			0
$850$	17526.6	−	2631.13i	0.707245	−	0.106173i
$851$	5380.29			0.216726
$852$		0			0
$853$	−16448.2			−0.660229			−0.330114	−	0.943941i	$-0.607087\pi$
$853$	−16448.2			−0.660229			−0.330114	+	0.943941i	$0.607087\pi$
$854$	−49416.5	+	7418.49i	−1.98009	+	0.297255i
$855$		0			0
$856$	9162.53	+	19112.8i	0.365851	+	0.763155i
$857$		−	13593.7i		−	0.541832i	−0.962603	−	0.270916i	$-0.912673\pi$
$857$		−	13593.7i		−	0.541832i	0.962603	−	0.270916i	$-0.0873266\pi$
$858$		0			0
$859$			15107.9i			0.600086i	0.953926	+	0.300043i	$0.0970011\pi$
$859$			15107.9i			0.600086i	−0.953926	+	0.300043i	$0.902999\pi$
$860$	−5323.14	+	1635.09i	−0.211067	+	0.0648325i
$861$		0			0
$862$	−4142.81	−	27596.4i	−0.163695	−	1.09041i
$863$	−43717.5			−1.72440			−0.862202	−	0.506565i	$-0.830915\pi$
$863$	−43717.5			−1.72440			−0.862202	+	0.506565i	$0.830915\pi$
$864$		0			0
$865$	−494.820			−0.0194502
$866$	−5274.06	−	35131.9i	−0.206951	−	1.37856i
$867$		0			0
$868$	37484.9	−	11514.1i	1.46581	−	0.450246i
$869$			59344.8i			2.31661i
$870$		0			0
$871$			23801.7i			0.925935i
$872$	−3393.77	−	7079.30i	−0.131798	−	0.274926i
$873$		0			0
$874$	6052.58	−	908.622i	0.234247	−	0.0351655i
$875$	9699.78			0.374757
$876$		0			0
$877$	−23868.3			−0.919012			−0.459506	−	0.888175i	$-0.651974\pi$
$877$	−23868.3			−0.919012			−0.459506	+	0.888175i	$0.651974\pi$
$878$	−2599.13	+	390.185i	−0.0999048	+	0.0149979i
$879$		0			0
$880$	3029.19	+	4465.64i	0.116038	+	0.171064i
$881$		−	48039.2i		−	1.83710i	−0.395310	−	0.918548i	$-0.629363\pi$
$881$		−	48039.2i		−	1.83710i	0.395310	−	0.918548i	$-0.370637\pi$
$882$		0			0
$883$		−	10091.3i		−	0.384595i	−0.981337	−	0.192298i	$-0.938406\pi$
$883$		−	10091.3i		−	0.384595i	0.981337	−	0.192298i	$-0.0615939\pi$
$884$	−4953.73	−	16127.2i	−0.188475	−	0.613594i
$885$		0			0
$886$	1836.59	+	12234.0i	0.0696405	+	0.463894i
$887$	−37951.2			−1.43661			−0.718307	−	0.695726i	$-0.755083\pi$
$887$	−37951.2			−1.43661			−0.718307	+	0.695726i	$0.755083\pi$
$888$		0			0
$889$	−6939.20			−0.261792
$890$	841.642	+	5606.40i	0.0316988	+	0.211154i
$891$		0			0
$892$	−7501.83	−	24422.7i	−0.281592	−	0.916742i
$893$			29557.7i			1.10763i
$894$		0			0
$895$			1699.53i			0.0634739i
$896$	19095.8	−	32761.2i	0.711993	−	1.22151i
$897$		0			0
$898$	−39577.5	+	5941.43i	−1.47073	+	0.220789i
$899$	−25190.0			−0.934520
$900$		0			0
$901$	31650.2			1.17028
$902$	−47008.7	+	7057.02i	−1.73528	+	0.260502i
$903$		0			0
$904$	−29835.0	+	14302.7i	−1.09768	+	0.526218i
$905$		−	3075.26i		−	0.112956i
$906$		0			0
$907$			23697.4i			0.867540i	0.901024	+	0.433770i	$0.142817\pi$
$907$			23697.4i			0.867540i	−0.901024	+	0.433770i	$0.857183\pi$
$908$	13113.1	−	4027.90i	0.479266	−	0.147214i
$909$		0			0
$910$	−679.203	−	4524.35i	−0.0247421	−	0.164814i
$911$	11833.0			0.430347			0.215174	−	0.976576i	$-0.430968\pi$
$911$	11833.0			0.430347			0.215174	+	0.976576i	$0.430968\pi$
$912$		0			0
$913$	68747.0			2.49200
$914$	−5283.38	−	35194.0i	−0.191202	−	1.27365i
$915$		0			0
$916$	3116.28	−	957.214i	0.112407	−	0.0345276i
$917$		−	30161.6i		−	1.08618i
$918$		0			0
$919$		−	51576.2i		−	1.85130i	−0.378386	−	0.925648i	$-0.623521\pi$
$919$		−	51576.2i		−	1.85130i	0.378386	−	0.925648i	$-0.376479\pi$
$920$	834.903	−	400.247i	0.0299195	−	0.0143432i
$921$		0			0
$922$	−29655.3	+	4451.89i	−1.05927	+	0.159019i
$923$	9247.29			0.329771
$924$		0			0
$925$	−24133.7			−0.857849
$926$	−14211.7	+	2133.48i	−0.504346	+	0.0757132i
$927$		0			0
$928$	−17905.5	+	16515.7i	−0.633380	+	0.584219i
$929$		−	46577.3i		−	1.64494i	−0.568807	−	0.822471i	$-0.692595\pi$
$929$		−	46577.3i		−	1.64494i	0.568807	−	0.822471i	$-0.307405\pi$
$930$		0			0
$931$		−	27092.6i		−	0.953731i
$932$	7541.59	+	24552.2i	0.265057	+	0.862912i
$933$		0			0
$934$	−2898.98	−	19310.9i	−0.101560	−	0.676521i
$935$	4303.47			0.150523
$936$		0			0
$937$	11409.2			0.397783			0.198891	−	0.980022i	$-0.436266\pi$
$937$	11409.2			0.397783			0.198891	+	0.980022i	$0.436266\pi$
$938$	6334.09	+	42193.1i	0.220486	+	1.46871i
$939$		0			0
$940$	1312.93	+	4274.34i	0.0455565	+	0.148312i
$941$			32444.9i			1.12399i	0.827141	+	0.561994i	$0.189966\pi$
$941$			32444.9i			1.12399i	−0.827141	+	0.561994i	$0.810034\pi$
$942$		0			0
$943$			8156.32i			0.281661i
$944$	17009.6	−	11538.2i	0.586458	−	0.397813i
$945$		0			0
$946$	73439.6	−	11024.9i	2.52402	−	0.378910i
$947$	−22327.6			−0.766154			−0.383077	−	0.923716i	$-0.625136\pi$
$947$	−22327.6			−0.766154			−0.383077	+	0.923716i	$0.625136\pi$
$948$		0			0
$949$	−2897.85			−0.0991236
$950$	−27149.3	+	4075.69i	−0.927198	+	0.139192i
$951$		0			0
$952$	−13073.2	−	27270.3i	−0.445068	−	0.928400i
$953$		−	15314.3i		−	0.520546i	−0.965535	−	0.260273i	$-0.916187\pi$
$953$		−	15314.3i		−	0.520546i	0.965535	−	0.260273i	$-0.0838126\pi$
$954$		0			0
$955$			2965.09i			0.100469i
$956$	−11939.0	+	3667.25i	−0.403907	+	0.124066i
$957$		0			0
$958$	2147.62	+	14305.9i	0.0724284	+	0.482465i
$959$	−61500.4			−2.07086
$960$		0			0
$961$	−5250.01			−0.176228
$962$	3410.57	+	22718.7i	0.114305	+	0.761415i
$963$		0			0
$964$	−11172.0	+	3431.65i	−0.373263	+	0.114654i
$965$			283.928i			0.00947147i
$966$		0			0
$967$		−	16913.6i		−	0.562465i	−0.959640	−	0.281232i	$-0.909257\pi$
$967$		−	16913.6i		−	0.562465i	0.959640	−	0.281232i	$-0.0907431\pi$
$968$	−18089.0	−	37733.1i	−0.600621	−	1.25288i
$969$		0			0
$970$	−2409.01	+	361.644i	−0.0797408	+	0.0119708i
$971$	56451.5			1.86572			0.932861	−	0.360237i	$-0.117304\pi$
$971$	56451.5			1.86572			0.932861	+	0.360237i	$0.117304\pi$
$972$		0			0
$973$	5636.12			0.185699
$974$	−43618.3	+	6548.05i	−1.43493	+	0.215414i
$975$		0			0
$976$	35735.0	−	24240.2i	1.17198	−	0.794990i
$977$			7397.50i			0.242238i	0.992638	+	0.121119i	$0.0386483\pi$
$977$			7397.50i			0.242238i	−0.992638	+	0.121119i	$0.961352\pi$
$978$		0			0
$979$		−	75604.3i		−	2.46816i
$980$	−1203.43	−	3917.86i	−0.0392268	−	0.127706i
$981$		0			0
$982$	4417.82	+	29428.3i	0.143562	+	0.956307i
$983$	18261.7			0.592532			0.296266	−	0.955105i	$-0.404258\pi$
$983$	18261.7			0.592532			0.296266	+	0.955105i	$0.404258\pi$
$984$		0			0
$985$	3230.01			0.104484
$986$	2884.08	+	19211.7i	0.0931521	+	0.620511i
$987$		0			0
$988$	7673.47	+	24981.5i	0.247091	+	0.804421i
$989$		−	12742.3i		−	0.409687i
$990$		0			0
$991$		−	7020.98i		−	0.225054i	−0.993649	−	0.112527i	$-0.964105\pi$
$991$		−	7020.98i		−	0.225054i	0.993649	−	0.112527i	$-0.0358945\pi$
$992$	−24907.8	+	22974.5i	−0.797200	+	0.735323i
$993$		0			0
$994$	16392.6	−	2460.89i	0.523081	−	0.0785257i
$995$	3971.28			0.126531
$996$		0			0
$997$	6983.34			0.221830			0.110915	−	0.993830i	$-0.464622\pi$
$997$	6983.34			0.221830			0.110915	+	0.993830i	$0.464622\pi$
$998$	25130.2	−	3772.59i	0.797077	−	0.119658i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.b.b.107.8	yes	12
3.2	odd	2	inner	108.4.b.b.107.5	✓	12
4.3	odd	2	inner	108.4.b.b.107.6	yes	12
8.3	odd	2		1728.4.c.j.1727.7		12
8.5	even	2		1728.4.c.j.1727.8		12
12.11	even	2	inner	108.4.b.b.107.7	yes	12
24.5	odd	2		1728.4.c.j.1727.6		12
24.11	even	2		1728.4.c.j.1727.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.b.b.107.5	✓	12	3.2	odd	2	inner
108.4.b.b.107.6	yes	12	4.3	odd	2	inner
108.4.b.b.107.7	yes	12	12.11	even	2	inner
108.4.b.b.107.8	yes	12	1.1	even	1	trivial
1728.4.c.j.1727.5		12	24.11	even	2
1728.4.c.j.1727.6		12	24.5	odd	2
1728.4.c.j.1727.7		12	8.3	odd	2
1728.4.c.j.1727.8		12	8.5	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +O(q^{10})\)	\(q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +(4.18188 - 0.627790i) q^{10} -56.3941 q^{11} -41.3170 q^{13} +(-73.2423 + 10.9953i) q^{14} +(52.9643 - 35.9274i) q^{16} -51.0410i q^{17} +79.0640i q^{19} +(3.51196 + 11.4335i) q^{20} +(-23.6801 - 157.739i) q^{22} -27.3688 q^{23} +122.765 q^{25} +(-17.3491 - 115.567i) q^{26} +(-61.5093 - 200.248i) q^{28} +134.567i q^{29} +187.192i q^{31} +(122.732 + 133.060i) q^{32} +(142.766 - 21.4323i) q^{34} +39.1491 q^{35} -196.585 q^{37} +(-221.149 + 33.1992i) q^{38} +(-30.5057 + 14.6242i) q^{40} -298.015i q^{41} +465.576i q^{43} +(431.267 - 132.470i) q^{44} +(-11.4922 - 76.5529i) q^{46} +373.845 q^{47} -342.667 q^{49} +(51.5492 + 343.383i) q^{50} +(315.966 - 97.0539i) q^{52} +620.093i q^{53} +84.3140i q^{55} +(534.283 - 256.131i) q^{56} +(-376.396 + 56.5052i) q^{58} +321.152 q^{59} +674.699 q^{61} +(-523.593 + 78.6026i) q^{62} +(-320.644 + 399.164i) q^{64} +61.7724i q^{65} -576.075i q^{67} +(119.896 + 390.329i) q^{68} +(16.4388 + 109.503i) q^{70} -223.813 q^{71} +70.1371 q^{73} +(-82.5465 - 549.864i) q^{74} +(-185.722 - 604.631i) q^{76} -1476.69i q^{77} -1052.32i q^{79} +(-53.7145 - 79.1862i) q^{80} +(833.574 - 125.137i) q^{82} -1219.05 q^{83} -76.3107 q^{85} +(-1302.26 + 195.497i) q^{86} +(551.621 + 1150.66i) q^{88} +1340.64i q^{89} -1081.89i q^{91} +(209.299 - 64.2895i) q^{92} +(156.979 + 1045.68i) q^{94} +118.207 q^{95} -576.059 q^{97} +(-143.887 - 958.467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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