LMFDB - Embedded newform 108.4.b.b.107.7

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

$q$-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	$0.0212988\pi$
$5$			1.49508i			0.133724i	−0.997762	+	0.0668622i	$0.978701\pi$
$6$		0			0
$7$		−	26.1852i		−	1.41387i	−0.707279	−	0.706935i	$-0.750077\pi$
$7$		−	26.1852i		−	1.41387i	0.707279	−	0.706935i	$-0.249923\pi$
$8$	−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	$0.118622\pi$
$17$			51.0410i			0.728192i	−0.931361	+	0.364096i	$0.881378\pi$
$18$		0			0
$19$		−	79.0640i		−	0.954659i	−0.878724	−	0.477330i	$-0.841605\pi$
$19$		−	79.0640i		−	0.954659i	0.878724	−	0.477330i	$-0.158395\pi$
$20$	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	$-0.858218\pi$
$29$		−	134.567i		−	0.861674i	0.902430	−	0.430837i	$-0.141782\pi$
$30$		0			0
$31$		−	187.192i		−	1.08454i	−0.840204	−	0.542270i	$-0.817565\pi$
$31$		−	187.192i		−	1.08454i	0.840204	−	0.542270i	$-0.182435\pi$
$32$	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	$0.192123\pi$
$41$			298.015i			1.13517i	−0.823313	+	0.567587i	$0.807877\pi$
$42$		0			0
$43$		−	465.576i		−	1.65115i	−0.564289	−	0.825577i	$-0.690850\pi$
$43$		−	465.576i		−	1.65115i	0.564289	−	0.825577i	$-0.309150\pi$
$44$	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	$-0.702942\pi$
$53$		−	620.093i		−	1.60710i	0.595237	−	0.803550i	$-0.297058\pi$
$54$		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	$0.176015\pi$
$67$			576.075i			1.05043i	−0.850970	+	0.525215i	$0.823985\pi$
$68$	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	$0.269628\pi$
$79$			1052.32i			1.49868i	−0.662187	+	0.749338i	$0.730372\pi$
$80$	−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	$-0.705702\pi$
$89$		−	1340.64i		−	1.59672i	0.602183	−	0.798358i	$-0.294298\pi$
$90$		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	$-0.981789\pi$
$101$		−	116.079i		−	0.114359i	0.998364	−	0.0571797i	$-0.0182108\pi$
$102$		0			0
$103$			165.074i			0.157915i	0.996878	+	0.0789573i	$0.0251591\pi$
$103$			165.074i			0.157915i	−0.996878	+	0.0789573i	$0.974841\pi$
$104$	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	$0.208287\pi$
$113$			1462.22i			1.21729i	−0.793443	+	0.608645i	$0.791713\pi$
$114$		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	$-0.970489\pi$
$127$		−	265.004i		−	0.185160i	0.995705	−	0.0925800i	$-0.0295114\pi$
$128$	−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	$-0.738430\pi$
$137$		−	2348.67i		−	1.46467i	0.680943	−	0.732337i	$-0.261570\pi$
$138$		0			0
$139$			215.240i			0.131341i	0.997841	+	0.0656706i	$0.0209187\pi$
$139$			215.240i			0.131341i	−0.997841	+	0.0656706i	$0.979081\pi$
$140$	−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	$-0.980741\pi$
$149$		−	219.954i		−	0.120935i	0.998170	−	0.0604674i	$-0.0192591\pi$
$150$		0			0
$151$			1148.02i			0.618703i	0.950948	+	0.309351i	$0.100112\pi$
$151$			1148.02i			0.618703i	−0.950948	+	0.309351i	$0.899888\pi$
$152$	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	$-0.889244\pi$
$163$		−	1419.15i		−	0.681941i	0.940074	−	0.340971i	$-0.110756\pi$
$164$	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	$0.0231695\pi$
$173$			330.965i			0.145450i	−0.997352	+	0.0727248i	$0.976831\pi$
$174$		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	$-0.872244\pi$
$197$		−	2160.42i		−	0.781337i	0.920531	−	0.390669i	$-0.127756\pi$
$198$		0			0
$199$		−	2656.23i		−	0.946205i	−0.881007	−	0.473103i	$-0.843134\pi$
$199$		−	2656.23i		−	0.946205i	0.881007	−	0.473103i	$-0.156866\pi$
$200$	−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	$-0.947776\pi$
$211$		−	1001.20i		−	0.326662i	0.986571	−	0.163331i	$-0.0522239\pi$
$212$	−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	$-0.840815\pi$
$223$		−	3193.62i		−	0.959015i	0.877538	−	0.479507i	$-0.159185\pi$
$224$	−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	$0.149058\pi$
$233$			3210.54i			0.902702i	−0.892346	+	0.451351i	$0.850942\pi$
$234$		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	$-0.818368\pi$
$257$		−	4450.84i		−	1.08029i	0.841570	−	0.540147i	$-0.181632\pi$
$258$		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	$0.118990\pi$
$269$			3222.22i			0.730343i	−0.930940	+	0.365171i	$0.881010\pi$
$270$		0			0
$271$			7368.93i			1.65177i	0.563837	+	0.825886i	$0.309325\pi$
$271$			7368.93i			1.65177i	−0.563837	+	0.825886i	$0.690675\pi$
$272$	−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	$0.0894729\pi$
$281$			2613.34i			0.554801i	−0.960754	+	0.277400i	$0.910527\pi$
$282$		0			0
$283$			927.970i			0.194919i	0.995239	+	0.0974596i	$0.0310717\pi$
$283$			927.970i			0.194919i	−0.995239	+	0.0974596i	$0.968928\pi$
$284$	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	$-0.820863\pi$
$293$		−	5351.73i		−	1.06707i	0.845778	−	0.533535i	$-0.179137\pi$
$294$		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	$-0.943716\pi$
$307$		−	1892.38i		−	0.351804i	0.984408	−	0.175902i	$-0.0562842\pi$
$308$	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	$0.0551710\pi$
$317$			1946.72i			0.344917i	−0.985017	+	0.172458i	$0.944829\pi$
$318$		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	$0.0912295\pi$
$331$			3404.83i			0.565396i	−0.959209	+	0.282698i	$0.908771\pi$
$332$	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	$-0.744078\pi$
$353$		−	9552.31i		−	1.44028i	0.693830	−	0.720139i	$-0.255922\pi$
$354$		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	$-0.793642\pi$
$367$		−	8490.66i		−	1.20765i	0.797115	−	0.603827i	$-0.206358\pi$
$368$	−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	$0.117453\pi$
$379$			5322.35i			0.721348i	−0.932692	+	0.360674i	$0.882547\pi$
$380$	−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	$0.183365\pi$
$389$			8358.52i			1.08944i	−0.838617	+	0.544722i	$0.816635\pi$
$390$		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	$0.0307571\pi$
$401$			1549.41i			0.192952i	−0.995335	+	0.0964759i	$0.969243\pi$
$402$		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	$-0.983915\pi$
$439$		−	929.228i		−	0.101024i	0.998723	−	0.0505121i	$-0.0160854\pi$
$440$	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	$-0.733114\pi$
$449$		−	14149.5i		−	1.48721i	0.668618	−	0.743606i	$-0.266886\pi$
$450$		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	$-0.820098\pi$
$461$		−	10602.2i		−	1.07114i	0.844492	−	0.535568i	$-0.179902\pi$
$462$		0			0
$463$		−	5080.88i		−	0.509997i	−0.966941	−	0.254999i	$-0.917925\pi$
$463$		−	5080.88i		−	0.509997i	0.966941	−	0.254999i	$-0.0820750\pi$
$464$	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	$-0.741607\pi$
$487$		−	15594.2i		−	1.45101i	0.688218	−	0.725504i	$-0.258393\pi$
$488$	−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	$0.132034\pi$
$499$			8984.43i			0.806009i	−0.915198	+	0.403004i	$0.867966\pi$
$500$	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	$-0.958515\pi$
$509$		−	2984.83i		−	0.259922i	0.991519	−	0.129961i	$-0.0414853\pi$
$510$		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	$-0.827684\pi$
$521$		−	12255.7i		−	1.03058i	0.857016	−	0.515290i	$-0.172316\pi$
$522$		0			0
$523$			15148.5i			1.26654i	0.773932	+	0.633269i	$0.218287\pi$
$523$			15148.5i			1.26654i	−0.773932	+	0.633269i	$0.781713\pi$
$524$	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	$-0.893954\pi$
$547$		−	8367.43i		−	0.654051i	0.945016	−	0.327025i	$-0.106046\pi$
$548$	−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	$-0.794420\pi$
$557$		−	15824.2i		−	1.20375i	0.798589	−	0.601877i	$-0.205580\pi$
$558$		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	$-0.944756\pi$
$569$		−	4687.63i		−	0.345370i	0.984977	−	0.172685i	$-0.0552443\pi$
$570$		0			0
$571$			15169.4i			1.11177i	0.831259	+	0.555885i	$0.187621\pi$
$571$			15169.4i			1.11177i	−0.831259	+	0.555885i	$0.812379\pi$
$572$	−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	$0.241784\pi$
$593$			19888.1i			1.37725i	−0.725120	+	0.688623i	$0.758216\pi$
$594$		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	$-0.790041\pi$
$607$		−	18328.9i		−	1.22561i	0.790233	−	0.612806i	$-0.209959\pi$
$608$	−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	$-0.929591\pi$
$617$		−	6724.96i		−	0.438795i	0.975636	−	0.219398i	$-0.0704092\pi$
$618$		0			0
$619$			3136.55i			0.203665i	0.994802	+	0.101832i	$0.0324705\pi$
$619$			3136.55i			0.203665i	−0.994802	+	0.101832i	$0.967529\pi$
$620$	−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	$-0.938759\pi$
$631$		−	6061.57i		−	0.382420i	0.981549	−	0.191210i	$-0.0612412\pi$
$632$	−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	$-0.805719\pi$
$641$		−	18603.3i		−	1.14631i	0.819446	−	0.573157i	$-0.194281\pi$
$642$		0			0
$643$			21602.4i			1.32491i	0.749103	+	0.662453i	$0.230485\pi$
$643$			21602.4i			1.32491i	−0.749103	+	0.662453i	$0.769515\pi$
$644$	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	$0.0317457\pi$
$653$			3322.88i			0.199134i	−0.995031	+	0.0995668i	$0.968254\pi$
$654$		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	$-0.956637\pi$
$677$		−	4784.53i		−	0.271617i	0.990735	−	0.135808i	$-0.0433631\pi$
$678$		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	$-0.845423\pi$
$691$		−	16956.5i		−	0.933511i	0.884386	−	0.466756i	$-0.154577\pi$
$692$	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	$0.308774\pi$
$701$			30620.5i			1.64982i	−0.565266	+	0.824909i	$0.691226\pi$
$702$		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	$-0.878406\pi$
$727$		−	14614.3i		−	0.745551i	0.927922	−	0.372775i	$-0.121594\pi$
$728$	−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	$0.0559420\pi$
$739$			7025.01i			0.349688i	−0.984596	+	0.174844i	$0.944058\pi$
$740$	−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	$0.0896017\pi$
$751$			11434.2i			0.555579i	−0.960642	+	0.277789i	$0.910398\pi$
$752$	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	$-0.678952\pi$
$761$		−	35524.0i		−	1.69218i	0.533043	−	0.846088i	$-0.321048\pi$
$762$		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	$-0.891489\pi$
$773$		−	14370.7i		−	0.668663i	0.942456	−	0.334332i	$-0.108511\pi$
$774$		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	$-0.607914\pi$
$787$		−	41642.9i		−	1.88616i	0.332564	−	0.943081i	$-0.392086\pi$
$788$	−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	$0.175119\pi$
$797$			23527.1i			1.04564i	−0.852445	+	0.522818i	$0.824881\pi$
$798$		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	$0.0521651\pi$
$809$			7508.22i			0.326298i	−0.986601	+	0.163149i	$0.947835\pi$
$810$		0			0
$811$		−	15834.0i		−	0.685581i	−0.939412	−	0.342791i	$-0.888628\pi$
$811$		−	15834.0i		−	0.685581i	0.939412	−	0.342791i	$-0.111372\pi$
$812$	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	$0.0910784\pi$
$821$			13279.1i			0.564486i	−0.959343	+	0.282243i	$0.908922\pi$
$822$		0			0
$823$		−	27997.4i		−	1.18582i	−0.805270	−	0.592909i	$-0.797979\pi$
$823$		−	27997.4i		−	1.18582i	0.805270	−	0.592909i	$-0.202021\pi$
$824$	−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	$0.0873266\pi$
$857$			13593.7i			0.541832i	−0.962603	+	0.270916i	$0.912673\pi$
$858$		0			0
$859$		−	15107.9i		−	0.600086i	−0.953926	−	0.300043i	$-0.902999\pi$
$859$		−	15107.9i		−	0.600086i	0.953926	−	0.300043i	$-0.0970011\pi$
$860$	−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	$0.370637\pi$
$881$			48039.2i			1.83710i	−0.395310	+	0.918548i	$0.629363\pi$
$882$		0			0
$883$			10091.3i			0.384595i	0.981337	+	0.192298i	$0.0615939\pi$
$883$			10091.3i			0.384595i	−0.981337	+	0.192298i	$0.938406\pi$
$884$	−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	$-0.857183\pi$
$907$		−	23697.4i		−	0.867540i	0.901024	−	0.433770i	$-0.142817\pi$
$908$	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	$0.376479\pi$
$919$			51576.2i			1.85130i	−0.378386	+	0.925648i	$0.623521\pi$
$920$	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	$0.307405\pi$
$929$			46577.3i			1.64494i	−0.568807	+	0.822471i	$0.692595\pi$
$930$		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	$-0.810034\pi$
$941$		−	32444.9i		−	1.12399i	0.827141	−	0.561994i	$-0.189966\pi$
$942$		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	$0.0838126\pi$
$953$			15314.3i			0.520546i	−0.965535	+	0.260273i	$0.916187\pi$
$954$		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	$0.0907431\pi$
$967$			16913.6i			0.562465i	−0.959640	+	0.281232i	$0.909257\pi$
$968$	−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	$-0.961352\pi$
$977$		−	7397.50i		−	0.242238i	0.992638	−	0.121119i	$-0.0386483\pi$
$978$		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	$0.0358945\pi$
$991$			7020.98i			0.225054i	−0.993649	+	0.112527i	$0.964105\pi$
$992$	−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.107.7	yes	12
3.2	odd	2	inner	108.4.b.b.107.6	yes	12
4.3	odd	2	inner	108.4.b.b.107.5	✓	12
8.3	odd	2		1728.4.c.j.1727.6		12
8.5	even	2		1728.4.c.j.1727.5		12
12.11	even	2	inner	108.4.b.b.107.8	yes	12
24.5	odd	2		1728.4.c.j.1727.7		12
24.11	even	2		1728.4.c.j.1727.8		12

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