LMFDB - Embedded newform 108.5.d.b.55.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(55,108)]

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, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.d (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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 $ x^16 + 38x^14 + 1016x^12 + 13512x^10 + 130640x^8 + 569472x^6 + 1783808x^4 + 352256*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.10
Root			$2.23772 + 3.87585i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.5.d.b.55.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988828 + 3.87585i) q^{2} +(-14.0444 + 7.66510i) q^{4} -20.7568 q^{5} -5.38785i q^{7} +(-43.5963 - 46.8547i) q^{8} +O(q^{10})$	\(q+(0.988828 + 3.87585i) q^{2} +(-14.0444 + 7.66510i) q^{4} -20.7568 q^{5} -5.38785i q^{7} +(-43.5963 - 46.8547i) q^{8} +(-20.5250 - 80.4504i) q^{10} -115.619i q^{11} +207.234 q^{13} +(20.8825 - 5.32765i) q^{14} +(138.493 - 215.304i) q^{16} -383.437 q^{17} -618.390i q^{19} +(291.518 - 159.103i) q^{20} +(448.121 - 114.327i) q^{22} +82.9899i q^{23} -194.153 q^{25} +(204.919 + 803.209i) q^{26} +(41.2984 + 75.6693i) q^{28} -201.949 q^{29} -196.140i q^{31} +(971.432 + 323.878i) q^{32} +(-379.153 - 1486.14i) q^{34} +111.835i q^{35} +340.480 q^{37} +(2396.79 - 611.481i) q^{38} +(904.922 + 972.556i) q^{40} -2797.22 q^{41} -254.774i q^{43} +(886.230 + 1623.80i) q^{44} +(-321.656 + 82.0627i) q^{46} -2257.41i q^{47} +2371.97 q^{49} +(-191.984 - 752.509i) q^{50} +(-2910.49 + 1588.47i) q^{52} -4111.23 q^{53} +2399.88i q^{55} +(-252.446 + 234.890i) q^{56} +(-199.693 - 782.726i) q^{58} +1598.57i q^{59} -6081.09 q^{61} +(760.210 - 193.949i) q^{62} +(-294.723 + 4085.38i) q^{64} -4301.53 q^{65} +7383.67i q^{67} +(5385.15 - 2939.08i) q^{68} +(-433.455 + 110.585i) q^{70} -9347.39i q^{71} -5320.95 q^{73} +(336.676 + 1319.65i) q^{74} +(4740.02 + 8684.94i) q^{76} -622.936 q^{77} -5971.42i q^{79} +(-2874.67 + 4469.03i) q^{80} +(-2765.97 - 10841.6i) q^{82} +10091.0i q^{83} +7958.94 q^{85} +(987.466 - 251.928i) q^{86} +(-5417.28 + 5040.55i) q^{88} +13611.5 q^{89} -1116.55i q^{91} +(-636.126 - 1165.55i) q^{92} +(8749.37 - 2232.19i) q^{94} +12835.8i q^{95} +2179.54 q^{97} +(2345.47 + 9193.41i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{4}+O(q^{10}) $ 16 * q + 28 * q^4	$ 16 q + 28 q^{4} + 176 q^{10} + 176 q^{13} + 88 q^{16} + 384 q^{22} + 2736 q^{25} + 1812 q^{28} + 1520 q^{34} + 80 q^{37} - 688 q^{40} - 1824 q^{46} - 7904 q^{49} - 5236 q^{52} - 11584 q^{58} - 1648 q^{61} + 5056 q^{64} + 26688 q^{70} + 80 q^{73} - 8388 q^{76} - 38464 q^{82} - 16832 q^{85} - 29520 q^{88} - 4512 q^{94} + 14864 q^{97}+O(q^{100}) $ 16 * q + 28 * q^4 + 176 * q^10 + 176 * q^13 + 88 * q^16 + 384 * q^22 + 2736 * q^25 + 1812 * q^28 + 1520 * q^34 + 80 * q^37 - 688 * q^40 - 1824 * q^46 - 7904 * q^49 - 5236 * q^52 - 11584 * q^58 - 1648 * q^61 + 5056 * q^64 + 26688 * q^70 + 80 * q^73 - 8388 * q^76 - 38464 * q^82 - 16832 * q^85 - 29520 * q^88 - 4512 * q^94 + 14864 * 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 $

$2$	0.988828	+	3.87585i	0.247207	+	0.968963i
$2$	0.988828	+	3.87585i	0.247207	+	0.968963i
$3$		0			0
$3$		0			0
$4$	−14.0444	+	7.66510i	−0.877777	+	0.479069i
$5$	−20.7568			−0.830274			−0.415137	−	0.909759i	$-0.636266\pi$
$5$	−20.7568			−0.830274			−0.415137	+	0.909759i	$0.636266\pi$
$6$		0			0
$7$		−	5.38785i		−	0.109956i	−0.998488	−	0.0549780i	$-0.982491\pi$
$7$		−	5.38785i		−	0.109956i	0.998488	−	0.0549780i	$-0.0175089\pi$
$8$	−43.5963	−	46.8547i	−0.681192	−	0.732104i
$9$		0			0
$10$	−20.5250	−	80.4504i	−0.205250	−	0.804504i
$11$		−	115.619i		−	0.955527i	−0.878488	−	0.477764i	$-0.841448\pi$
$11$		−	115.619i		−	0.955527i	0.878488	−	0.477764i	$-0.158552\pi$
$12$		0			0
$13$	207.234			1.22624			0.613119	−	0.789991i	$-0.289915\pi$
$13$	207.234			1.22624			0.613119	+	0.789991i	$0.289915\pi$
$14$	20.8825	−	5.32765i	0.106543	−	0.0271819i
$15$		0			0
$16$	138.493	−	215.304i	0.540986	−	0.841031i
$17$	−383.437			−1.32677			−0.663385	−	0.748278i	$-0.730881\pi$
$17$	−383.437			−1.32677			−0.663385	+	0.748278i	$0.730881\pi$
$18$		0			0
$19$		−	618.390i		−	1.71299i	−0.516155	−	0.856495i	$-0.672637\pi$
$19$		−	618.390i		−	1.71299i	0.516155	−	0.856495i	$-0.327363\pi$
$20$	291.518	−	159.103i	0.728796	−	0.397758i
$21$		0			0
$22$	448.121	−	114.327i	0.925870	−	0.236213i
$23$			82.9899i			0.156881i	0.996919	+	0.0784403i	$0.0249940\pi$
$23$			82.9899i			0.156881i	−0.996919	+	0.0784403i	$0.975006\pi$
$24$		0			0
$25$	−194.153			−0.310645
$26$	204.919	+	803.209i	0.303135	+	1.18818i
$27$		0			0
$28$	41.2984	+	75.6693i	0.0526765	+	0.0965170i
$29$	−201.949			−0.240130			−0.120065	−	0.992766i	$-0.538310\pi$
$29$	−201.949			−0.240130			−0.120065	+	0.992766i	$0.538310\pi$
$30$		0			0
$31$		−	196.140i		−	0.204100i	−0.994779	−	0.102050i	$-0.967460\pi$
$31$		−	196.140i		−	0.204100i	0.994779	−	0.102050i	$-0.0325402\pi$
$32$	971.432	+	323.878i	0.948664	+	0.316287i
$33$		0			0
$34$	−379.153	−	1486.14i	−0.327987	−	1.28559i
$35$			111.835i			0.0912937i
$36$		0			0
$37$	340.480			0.248707			0.124354	−	0.992238i	$-0.460314\pi$
$37$	340.480			0.248707			0.124354	+	0.992238i	$0.460314\pi$
$38$	2396.79	−	611.481i	1.65982	−	0.423463i
$39$		0			0
$40$	904.922	+	972.556i	0.565576	+	0.607847i
$41$	−2797.22			−1.66402			−0.832011	−	0.554758i	$-0.812811\pi$
$41$	−2797.22			−1.66402			−0.832011	+	0.554758i	$0.812811\pi$
$42$		0			0
$43$		−	254.774i		−	0.137790i	−0.997624	−	0.0688951i	$-0.978053\pi$
$43$		−	254.774i		−	0.137790i	0.997624	−	0.0688951i	$-0.0219474\pi$
$44$	886.230	+	1623.80i	0.457763	+	0.838740i
$45$		0			0
$46$	−321.656	+	82.0627i	−0.152011	+	0.0387820i
$47$		−	2257.41i		−	1.02191i	−0.859607	−	0.510956i	$-0.829291\pi$
$47$		−	2257.41i		−	1.02191i	0.859607	−	0.510956i	$-0.170709\pi$
$48$		0			0
$49$	2371.97			0.987910
$50$	−191.984	−	752.509i	−0.0767937	−	0.301004i
$51$		0			0
$52$	−2910.49	+	1588.47i	−1.07636	+	0.587452i
$53$	−4111.23			−1.46359			−0.731796	−	0.681524i	$-0.761317\pi$
$53$	−4111.23			−1.46359			−0.731796	+	0.681524i	$0.761317\pi$
$54$		0			0
$55$			2399.88i			0.793349i
$56$	−252.446	+	234.890i	−0.0804993	+	0.0749012i
$57$		0			0
$58$	−199.693	−	782.726i	−0.0593618	−	0.232677i
$59$			1598.57i			0.459226i	0.973282	+	0.229613i	$0.0737461\pi$
$59$			1598.57i			0.459226i	−0.973282	+	0.229613i	$0.926254\pi$
$60$		0			0
$61$	−6081.09			−1.63426			−0.817131	−	0.576452i	$-0.804437\pi$
$61$	−6081.09			−1.63426			−0.817131	+	0.576452i	$0.804437\pi$
$62$	760.210	−	193.949i	0.197765	−	0.0504549i
$63$		0			0
$64$	−294.723	+	4085.38i	−0.0719539	+	0.997408i
$65$	−4301.53			−1.01811
$66$		0			0
$67$			7383.67i			1.64484i	0.568884	+	0.822418i	$0.307375\pi$
$67$			7383.67i			1.64484i	−0.568884	+	0.822418i	$0.692625\pi$
$68$	5385.15	−	2939.08i	1.16461	−	0.635614i
$69$		0			0
$70$	−433.455	+	110.585i	−0.0884602	+	0.0225684i
$71$		−	9347.39i		−	1.85427i	−0.374723	−	0.927137i	$-0.622262\pi$
$71$		−	9347.39i		−	1.85427i	0.374723	−	0.927137i	$-0.377738\pi$
$72$		0			0
$73$	−5320.95			−0.998490			−0.499245	−	0.866461i	$-0.666389\pi$
$73$	−5320.95			−0.998490			−0.499245	+	0.866461i	$0.666389\pi$
$74$	336.676	+	1319.65i	0.0614822	+	0.240988i
$75$		0			0
$76$	4740.02	+	8684.94i	0.820640	+	1.50362i
$77$	−622.936			−0.105066
$78$		0			0
$79$		−	5971.42i		−	0.956806i	−0.878141	−	0.478403i	$-0.841216\pi$
$79$		−	5971.42i		−	0.956806i	0.878141	−	0.478403i	$-0.158784\pi$
$80$	−2874.67	+	4469.03i	−0.449167	+	0.698286i
$81$		0			0
$82$	−2765.97	−	10841.6i	−0.411358	−	1.61238i
$83$			10091.0i			1.46480i	0.680876	+	0.732399i	$0.261599\pi$
$83$			10091.0i			1.46480i	−0.680876	+	0.732399i	$0.738401\pi$
$84$		0			0
$85$	7958.94			1.10158
$86$	987.466	−	251.928i	0.133514	−	0.0340627i
$87$		0			0
$88$	−5417.28	+	5040.55i	−0.699546	+	0.650898i
$89$	13611.5			1.71841			0.859206	−	0.511631i	$-0.170958\pi$
$89$	13611.5			1.71841			0.859206	+	0.511631i	$0.170958\pi$
$90$		0			0
$91$		−	1116.55i		−	0.134832i
$92$	−636.126	−	1165.55i	−0.0751566	−	0.137706i
$93$		0			0
$94$	8749.37	−	2232.19i	0.990195	−	0.252624i
$95$			12835.8i			1.42225i
$96$		0			0
$97$	2179.54			0.231645			0.115822	−	0.993270i	$-0.463050\pi$
$97$	2179.54			0.231645			0.115822	+	0.993270i	$0.463050\pi$
$98$	2345.47	+	9193.41i	0.244218	+	0.957248i
$99$		0			0
$100$	2726.77	−	1488.20i	0.272677	−	0.148820i
$101$	3242.55			0.317866			0.158933	−	0.987289i	$-0.449195\pi$
$101$	3242.55			0.317866			0.158933	+	0.987289i	$0.449195\pi$
$102$		0			0
$103$		−	3261.34i		−	0.307412i	−0.988117	−	0.153706i	$-0.950879\pi$
$103$		−	3261.34i		−	0.307412i	0.988117	−	0.153706i	$-0.0491209\pi$
$104$	−9034.65	−	9709.89i	−0.835304	−	0.897734i
$105$		0			0
$106$	−4065.30	−	15934.5i	−0.361810	−	1.41817i
$107$		−	15927.7i		−	1.39119i	−0.718434	−	0.695595i	$-0.755141\pi$
$107$		−	15927.7i		−	1.39119i	0.718434	−	0.695595i	$-0.244859\pi$
$108$		0			0
$109$	7377.06			0.620913			0.310456	−	0.950588i	$-0.399518\pi$
$109$	7377.06			0.620913			0.310456	+	0.950588i	$0.399518\pi$
$110$	−9301.58	+	2373.07i	−0.768726	+	0.196122i
$111$		0			0
$112$	−1160.03	−	746.177i	−0.0924765	−	0.0594847i
$113$	7121.69			0.557733			0.278867	−	0.960330i	$-0.410041\pi$
$113$	7121.69			0.557733			0.278867	+	0.960330i	$0.410041\pi$
$114$		0			0
$115$		−	1722.61i		−	0.130254i
$116$	2836.27	−	1547.96i	0.210781	−	0.115039i
$117$		0			0
$118$	−6195.80	+	1580.71i	−0.444973	+	0.113524i
$119$			2065.90i			0.145886i
$120$		0			0
$121$	1273.29			0.0869676
$122$	−6013.15	−	23569.4i	−0.404001	−	1.58354i
$123$		0			0
$124$	1503.43	+	2754.68i	0.0977779	+	0.179154i
$125$	17003.0			1.08819
$126$		0			0
$127$		−	16366.5i		−	1.01472i	−0.861733	−	0.507362i	$-0.830621\pi$
$127$		−	16366.5i		−	1.01472i	0.861733	−	0.507362i	$-0.169379\pi$
$128$	−16125.8	+	2897.44i	−0.984239	+	0.176846i
$129$		0			0
$130$	−4253.47	−	16672.1i	−0.251685	−	0.986514i
$131$			17497.0i			1.01958i	0.860299	+	0.509790i	$0.170277\pi$
$131$			17497.0i			1.01958i	−0.860299	+	0.509790i	$0.829723\pi$
$132$		0			0
$133$	−3331.79			−0.188354
$134$	−28618.0	+	7301.18i	−1.59378	+	0.406615i
$135$		0			0
$136$	16716.4	+	17965.8i	0.903786	+	0.971334i
$137$	8028.61			0.427759			0.213880	−	0.976860i	$-0.431390\pi$
$137$	8028.61			0.427759			0.213880	+	0.976860i	$0.431390\pi$
$138$		0			0
$139$		−	15001.1i		−	0.776417i	−0.921572	−	0.388208i	$-0.873094\pi$
$139$		−	15001.1i		−	0.776417i	0.921572	−	0.388208i	$-0.126906\pi$
$140$	−857.224	−	1570.66i	−0.0437359	−	0.0801355i
$141$		0			0
$142$	36229.1	−	9242.96i	1.79672	−	0.458389i
$143$		−	23960.2i		−	1.17170i
$144$		0			0
$145$	4191.83			0.199374
$146$	−5261.50	−	20623.2i	−0.246834	−	0.967499i
$147$		0			0
$148$	−4781.85	+	2609.81i	−0.218310	+	0.119148i
$149$	1457.01			0.0656279			0.0328140	−	0.999461i	$-0.489553\pi$
$149$	1457.01			0.0656279			0.0328140	+	0.999461i	$0.489553\pi$
$150$		0			0
$151$			15413.9i			0.676019i	0.941143	+	0.338009i	$0.109754\pi$
$151$			15413.9i			0.676019i	−0.941143	+	0.338009i	$0.890246\pi$
$152$	−28974.5	+	26959.5i	−1.25409	+	1.16688i
$153$		0			0
$154$	−615.977	−	2414.41i	−0.0259731	−	0.101805i
$155$			4071.25i			0.169459i
$156$		0			0
$157$	−23328.9			−0.946443			−0.473222	−	0.880943i	$-0.656909\pi$
$157$	−23328.9			−0.946443			−0.473222	+	0.880943i	$0.656909\pi$
$158$	23144.3	−	5904.71i	0.927109	−	0.236529i
$159$		0			0
$160$	−20163.9	−	6722.68i	−0.787651	−	0.262605i
$161$	447.137			0.0172500
$162$		0			0
$163$			31514.9i			1.18615i	0.805146	+	0.593077i	$0.202087\pi$
$163$			31514.9i			1.18615i	−0.805146	+	0.593077i	$0.797913\pi$
$164$	39285.4	−	21441.0i	1.46064	−	0.797181i
$165$		0			0
$166$	−39111.2	+	9978.26i	−1.41933	+	0.362108i
$167$			45156.1i			1.61914i	0.587025	+	0.809569i	$0.300299\pi$
$167$			45156.1i			1.61914i	−0.587025	+	0.809569i	$0.699701\pi$
$168$		0			0
$169$	14385.0			0.503659
$170$	7870.02	+	30847.6i	0.272319	+	1.06739i
$171$		0			0
$172$	1952.87	+	3578.16i	0.0660109	+	0.120949i
$173$	39788.6			1.32943			0.664716	−	0.747096i	$-0.268553\pi$
$173$	39788.6			1.32943			0.664716	+	0.747096i	$0.268553\pi$
$174$		0			0
$175$			1046.07i			0.0341573i
$176$	−24893.2	−	16012.3i	−0.803628	−	0.516927i
$177$		0			0
$178$	13459.5	+	52756.3i	0.424803	+	1.66508i
$179$		−	22082.3i		−	0.689188i	−0.938752	−	0.344594i	$-0.888017\pi$
$179$		−	22082.3i		−	0.689188i	0.938752	−	0.344594i	$-0.111983\pi$
$180$		0			0
$181$	−9867.01			−0.301181			−0.150591	−	0.988596i	$-0.548118\pi$
$181$	−9867.01			−0.301181			−0.150591	+	0.988596i	$0.548118\pi$
$182$	4327.57	−	1104.07i	0.130647	−	0.0333315i
$183$		0			0
$184$	3888.46	−	3618.05i	0.114853	−	0.106866i
$185$	−7067.30			−0.206495
$186$		0			0
$187$			44332.5i			1.26777i
$188$	17303.2	+	31704.0i	0.489566	+	0.897012i
$189$		0			0
$190$	−49749.7	+	12692.4i	−1.37811	+	0.351590i
$191$		−	6985.96i		−	0.191496i	−0.995406	−	0.0957479i	$-0.969476\pi$
$191$		−	6985.96i		−	0.191496i	0.995406	−	0.0957479i	$-0.0305243\pi$
$192$		0			0
$193$	−39647.8			−1.06440			−0.532199	−	0.846619i	$-0.678634\pi$
$193$	−39647.8			−1.06440			−0.532199	+	0.846619i	$0.678634\pi$
$194$	2155.19	+	8447.59i	0.0572642	+	0.224455i
$195$		0			0
$196$	−33313.0	+	18181.4i	−0.867165	+	0.473277i
$197$	−25520.9			−0.657602			−0.328801	−	0.944399i	$-0.606645\pi$
$197$	−25520.9			−0.657602			−0.328801	+	0.944399i	$0.606645\pi$
$198$		0			0
$199$		−	20635.7i		−	0.521091i	−0.965462	−	0.260546i	$-0.916098\pi$
$199$		−	20635.7i		−	0.521091i	0.965462	−	0.260546i	$-0.0839024\pi$
$200$	8464.36	+	9096.99i	0.211609	+	0.227425i
$201$		0			0
$202$	3206.32	+	12567.6i	0.0785786	+	0.308000i
$203$			1088.07i			0.0264038i
$204$		0			0
$205$	58061.5			1.38159
$206$	12640.5	−	3224.90i	0.297871	−	0.0759944i
$207$		0			0
$208$	28700.4	−	44618.4i	0.663378	−	1.03130i
$209$	−71497.5			−1.63681
$210$		0			0
$211$			37403.1i			0.840123i	0.907496	+	0.420062i	$0.137992\pi$
$211$			37403.1i			0.840123i	−0.907496	+	0.420062i	$0.862008\pi$
$212$	57739.9	−	31513.0i	1.28471	−	0.701161i
$213$		0			0
$214$	61733.5	−	15749.8i	1.34801	−	0.343912i
$215$			5288.31i			0.114404i
$216$		0			0
$217$	−1056.77			−0.0224420
$218$	7294.65	+	28592.4i	0.153494	+	0.601641i
$219$		0			0
$220$	−18395.3	−	33705.0i	−0.380069	−	0.696384i
$221$	−79461.2			−1.62694
$222$		0			0
$223$		−	63893.4i		−	1.28483i	−0.766356	−	0.642416i	$-0.777932\pi$
$223$		−	63893.4i		−	1.28483i	0.766356	−	0.642416i	$-0.222068\pi$
$224$	1745.00	−	5233.92i	0.0347777	−	0.104311i
$225$		0			0
$226$	7042.13	+	27602.6i	0.137876	+	0.540423i
$227$		−	52128.0i		−	1.01162i	−0.862644	−	0.505812i	$-0.831193\pi$
$227$		−	52128.0i		−	1.01162i	0.862644	−	0.505812i	$-0.168807\pi$
$228$		0			0
$229$	−30234.6			−0.576545			−0.288272	−	0.957548i	$-0.593081\pi$
$229$	−30234.6			−0.576545			−0.288272	+	0.957548i	$0.593081\pi$
$230$	6676.57	−	1703.36i	0.126211	−	0.0321997i
$231$		0			0
$232$	8804.25	+	9462.28i	0.163575	+	0.175800i
$233$	−5080.01			−0.0935735			−0.0467868	−	0.998905i	$-0.514898\pi$
$233$	−5080.01			−0.0935735			−0.0467868	+	0.998905i	$0.514898\pi$
$234$		0			0
$235$			46856.6i			0.848468i
$236$	−12253.2	−	22451.0i	−0.220001	−	0.403098i
$237$		0			0
$238$	−8007.11	+	2042.82i	−0.141359	+	0.0360641i
$239$		−	40740.6i		−	0.713234i	−0.934251	−	0.356617i	$-0.883930\pi$
$239$		−	40740.6i		−	0.713234i	0.934251	−	0.356617i	$-0.116070\pi$
$240$		0			0
$241$	−34834.0			−0.599749			−0.299875	−	0.953979i	$-0.596945\pi$
$241$	−34834.0			−0.599749			−0.299875	+	0.953979i	$0.596945\pi$
$242$	1259.07	+	4935.09i	0.0214990	+	0.0842684i
$243$		0			0
$244$	85405.5	−	46612.2i	1.43452	−	0.782924i
$245$	−49234.6			−0.820236
$246$		0			0
$247$		−	128151.i		−	2.10053i
$248$	−9190.08	+	8550.98i	−0.149422	+	0.139031i
$249$		0			0
$250$	16813.1	+	65901.2i	0.269009	+	1.05442i
$251$		−	71105.6i		−	1.12864i	−0.825555	−	0.564321i	$-0.809138\pi$
$251$		−	71105.6i		−	1.12864i	0.825555	−	0.564321i	$-0.190862\pi$
$252$		0			0
$253$	9595.19			0.149904
$254$	63434.1	−	16183.6i	0.983230	−	0.250847i
$255$		0			0
$256$	−27175.6	−	59636.0i	−0.414667	−	0.909973i
$257$	4341.02			0.0657242			0.0328621	−	0.999460i	$-0.489538\pi$
$257$	4341.02			0.0657242			0.0328621	+	0.999460i	$0.489538\pi$
$258$		0			0
$259$		−	1834.46i		−	0.0273469i
$260$	60412.6	−	32971.6i	0.893677	−	0.487746i
$261$		0			0
$262$	−67815.8	+	17301.5i	−0.987934	+	0.252047i
$263$			112382.i			1.62475i	0.583135	+	0.812375i	$0.301826\pi$
$263$			112382.i			1.62475i	−0.583135	+	0.812375i	$0.698174\pi$
$264$		0			0
$265$	85336.1			1.21518
$266$	−3294.57	−	12913.5i	−0.0465624	−	0.182508i
$267$		0			0
$268$	−56596.5	−	103699.i	−0.787989	−	1.44380i
$269$	−67178.9			−0.928385			−0.464193	−	0.885734i	$-0.653655\pi$
$269$	−67178.9			−0.928385			−0.464193	+	0.885734i	$0.653655\pi$
$270$		0			0
$271$		−	30451.7i		−	0.414641i	−0.978273	−	0.207321i	$-0.933526\pi$
$271$		−	30451.7i		−	0.414641i	0.978273	−	0.207321i	$-0.0664744\pi$
$272$	−53103.1	+	82555.4i	−0.717765	+	1.11586i
$273$		0			0
$274$	7938.92	+	31117.7i	0.105745	+	0.414483i
$275$			22447.8i			0.296830i
$276$		0			0
$277$	16480.0			0.214782			0.107391	−	0.994217i	$-0.465750\pi$
$277$	16480.0			0.214782			0.107391	+	0.994217i	$0.465750\pi$
$278$	58142.2	−	14833.6i	0.752319	−	0.191936i
$279$		0			0
$280$	5239.98	−	4875.58i	0.0668365	−	0.0621885i
$281$	−22525.2			−0.285270			−0.142635	−	0.989775i	$-0.545558\pi$
$281$	−22525.2			−0.285270			−0.142635	+	0.989775i	$0.545558\pi$
$282$		0			0
$283$			69282.8i			0.865073i	0.901616	+	0.432537i	$0.142381\pi$
$283$			69282.8i			0.865073i	−0.901616	+	0.432537i	$0.857619\pi$
$284$	71648.7	+	131279.i	0.888324	+	1.62764i
$285$		0			0
$286$	92866.0	−	23692.5i	1.13534	−	0.289653i
$287$			15071.0i			0.182969i
$288$		0			0
$289$	63502.6			0.760319
$290$	4145.00	+	16246.9i	0.0492866	+	0.193186i
$291$		0			0
$292$	74729.8	−	40785.6i	0.876452	−	0.478345i
$293$	92504.8			1.07753			0.538764	−	0.842456i	$-0.318891\pi$
$293$	92504.8			1.07753			0.538764	+	0.842456i	$0.318891\pi$
$294$		0			0
$295$		−	33181.2i		−	0.381283i
$296$	−14843.7	−	15953.1i	−0.169417	−	0.182080i
$297$		0			0
$298$	1440.73	+	5647.13i	0.0162237	+	0.0635910i
$299$			17198.3i			0.192373i
$300$		0			0
$301$	−1372.68			−0.0151509
$302$	−59742.0	+	15241.7i	−0.655037	+	0.167117i
$303$		0			0
$304$	−133142.	−	85642.3i	−1.44068	−	0.926705i
$305$	126224.			1.35689
$306$		0			0
$307$		−	79741.9i		−	0.846077i	−0.906112	−	0.423038i	$-0.860964\pi$
$307$		−	79741.9i		−	0.846077i	0.906112	−	0.423038i	$-0.139036\pi$
$308$	8748.79	−	4774.87i	0.0922246	−	0.0503338i
$309$		0			0
$310$	−15779.6	+	4025.76i	−0.164199	+	0.0418914i
$311$		−	115631.i		−	1.19551i	−0.801679	−	0.597755i	$-0.796060\pi$
$311$		−	115631.i		−	1.19551i	0.801679	−	0.597755i	$-0.203940\pi$
$312$		0			0
$313$	−25857.6			−0.263936			−0.131968	−	0.991254i	$-0.542130\pi$
$313$	−25857.6			−0.263936			−0.131968	+	0.991254i	$0.542130\pi$
$314$	−23068.2	−	90419.2i	−0.233967	−	0.917068i
$315$		0			0
$316$	45771.6	+	83865.3i	0.458376	+	0.839862i
$317$	78300.9			0.779198			0.389599	−	0.920985i	$-0.372614\pi$
$317$	78300.9			0.779198			0.389599	+	0.920985i	$0.372614\pi$
$318$		0			0
$319$			23349.1i			0.229451i
$320$	6117.53	−	84799.7i	0.0597415	−	0.828122i
$321$		0			0
$322$	442.141	+	1733.04i	0.00426432	+	0.0167146i
$323$			237113.i			2.27274i
$324$		0			0
$325$	−40235.2			−0.380925
$326$	−122147.	+	31162.8i	−1.14934	+	0.293226i
$327$		0			0
$328$	121949.	+	131063.i	1.13352	+	1.21824i
$329$	−12162.6			−0.112366
$330$		0			0
$331$			159345.i			1.45439i	0.686429	+	0.727197i	$0.259177\pi$
$331$			159345.i			1.45439i	−0.686429	+	0.727197i	$0.740823\pi$
$332$	−77348.5	−	141722.i	−0.701739	−	1.28577i
$333$		0			0
$334$	−175018.	+	44651.6i	−1.56888	+	0.400262i
$335$		−	153262.i		−	1.36566i
$336$		0			0
$337$	32887.8			0.289584			0.144792	−	0.989462i	$-0.453749\pi$
$337$	32887.8			0.289584			0.144792	+	0.989462i	$0.453749\pi$
$338$	14224.3	+	55754.2i	0.124508	+	0.488027i
$339$		0			0
$340$	−111779.	+	61006.0i	−0.966944	+	0.527734i
$341$	−22677.5			−0.195023
$342$		0			0
$343$		−	25716.0i		−	0.218583i
$344$	−11937.4	+	11107.2i	−0.100877	+	0.0938616i
$345$		0			0
$346$	39344.0	+	154215.i	0.328645	+	1.28817i
$347$		−	68679.4i		−	0.570385i	−0.958470	−	0.285192i	$-0.907943\pi$
$347$		−	68679.4i		−	0.570385i	0.958470	−	0.285192i	$-0.0920575\pi$
$348$		0			0
$349$	−228554.			−1.87645			−0.938226	−	0.346024i	$-0.887532\pi$
$349$	−228554.			−1.87645			−0.938226	+	0.346024i	$0.887532\pi$
$350$	−4054.40	+	1034.38i	−0.0330972	+	0.00844393i
$351$		0			0
$352$	37446.4	−	112316.i	0.302221	−	0.906474i
$353$	46025.5			0.369359			0.184680	−	0.982799i	$-0.440875\pi$
$353$	46025.5			0.369359			0.184680	+	0.982799i	$0.440875\pi$
$354$		0			0
$355$			194022.i			1.53956i
$356$	−191166.	+	104334.i	−1.50838	+	0.823237i
$357$		0			0
$358$	85587.6	−	21835.6i	0.667797	−	0.170372i
$359$			131445.i			1.01990i	0.860205	+	0.509948i	$0.170335\pi$
$359$			131445.i			1.01990i	−0.860205	+	0.509948i	$0.829665\pi$
$360$		0			0
$361$	−252085.			−1.93434
$362$	−9756.77	−	38243.0i	−0.0744542	−	0.291834i
$363$		0			0
$364$	8558.44	+	15681.3i	0.0645939	+	0.118353i
$365$	110446.			0.829020
$366$		0			0
$367$		−	120649.i		−	0.895756i	−0.894095	−	0.447878i	$-0.852180\pi$
$367$		−	120649.i		−	0.895756i	0.894095	−	0.447878i	$-0.147820\pi$
$368$	17868.1	+	11493.5i	0.131942	+	0.0848703i
$369$		0			0
$370$	−6988.34	−	27391.8i	−0.0510470	−	0.200086i
$371$			22150.7i			0.160931i
$372$		0			0
$373$	183241.			1.31706			0.658530	−	0.752555i	$-0.271179\pi$
$373$	183241.			1.31706			0.658530	+	0.752555i	$0.271179\pi$
$374$	−171826.	+	43837.2i	−1.22842	+	0.313400i
$375$		0			0
$376$	−105770.	+	98414.6i	−0.748147	+	0.696119i
$377$	−41850.8			−0.294457
$378$		0			0
$379$			210539.i			1.46573i	0.680374	+	0.732865i	$0.261817\pi$
$379$			210539.i			1.46573i	−0.680374	+	0.732865i	$0.738183\pi$
$380$	−98387.8	−	180272.i	−0.681356	−	1.24842i
$381$		0			0
$382$	27076.5	−	6907.91i	0.185552	−	0.0473391i
$383$		−	115027.i		−	0.784153i	−0.919933	−	0.392076i	$-0.871757\pi$
$383$		−	115027.i		−	0.784153i	0.919933	−	0.392076i	$-0.128243\pi$
$384$		0			0
$385$	12930.2			0.0872336
$386$	−39204.8	−	153669.i	−0.263127	−	1.03136i
$387$		0			0
$388$	−30610.5	+	16706.4i	−0.203332	+	0.110974i
$389$	227952.			1.50641			0.753206	−	0.657785i	$-0.228507\pi$
$389$	227952.			1.50641			0.753206	+	0.657785i	$0.228507\pi$
$390$		0			0
$391$		−	31821.4i		−	0.208145i
$392$	−103409.	−	111138.i	−0.672957	−	0.723253i
$393$		0			0
$394$	−25235.8	−	98915.2i	−0.162564	−	0.637192i
$395$			123948.i			0.794411i
$396$		0			0
$397$	253211.			1.60657			0.803287	−	0.595592i	$-0.203082\pi$
$397$	253211.			1.60657			0.803287	+	0.595592i	$0.203082\pi$
$398$	79981.0	−	20405.2i	0.504918	−	0.128817i
$399$		0			0
$400$	−26888.8	+	41802.0i	−0.168055	+	0.261262i
$401$	113054.			0.703071			0.351535	−	0.936175i	$-0.385660\pi$
$401$	113054.			0.703071			0.351535	+	0.936175i	$0.385660\pi$
$402$		0			0
$403$		−	40646.9i		−	0.250275i
$404$	−45539.7	+	24854.4i	−0.279015	+	0.152279i
$405$		0			0
$406$	−4217.21	+	1075.92i	−0.0255843	+	0.00652719i
$407$		−	39365.9i		−	0.237647i
$408$		0			0
$409$	77602.4			0.463905			0.231952	−	0.972727i	$-0.425489\pi$
$409$	77602.4			0.463905			0.231952	+	0.972727i	$0.425489\pi$
$410$	57412.9	+	225038.i	0.341540	+	1.33871i
$411$		0			0
$412$	24998.5	+	45803.6i	0.147272	+	0.269839i
$413$	8612.83			0.0504947
$414$		0			0
$415$		−	209457.i		−	1.21618i
$416$	201314.	+	67118.5i	1.16329	+	0.387843i
$417$		0			0
$418$	−70698.7	−	277114.i	−0.404631	−	1.58601i
$419$		−	46895.2i		−	0.267116i	−0.991041	−	0.133558i	$-0.957360\pi$
$419$		−	46895.2i		−	0.267116i	0.991041	−	0.133558i	$-0.0426403\pi$
$420$		0			0
$421$	40148.2			0.226518			0.113259	−	0.993566i	$-0.463871\pi$
$421$	40148.2			0.226518			0.113259	+	0.993566i	$0.463871\pi$
$422$	−144969.	+	36985.3i	−0.814048	+	0.207684i
$423$		0			0
$424$	179234.	+	192630.i	0.996987	+	1.07150i
$425$	74445.5			0.412155
$426$		0			0
$427$			32764.0i			0.179697i
$428$	122088.	+	223696.i	0.666475	+	1.22115i
$429$		0			0
$430$	−20496.7	+	5229.22i	−0.110853	+	0.0282814i
$431$			257425.i			1.38579i	0.721040	+	0.692893i	$0.243664\pi$
$431$			257425.i			1.38579i	−0.721040	+	0.692893i	$0.756336\pi$
$432$		0			0
$433$	−29760.6			−0.158732			−0.0793661	−	0.996846i	$-0.525290\pi$
$433$	−29760.6			−0.158732			−0.0793661	+	0.996846i	$0.525290\pi$
$434$	−1044.97	−	4095.89i	−0.00554783	−	0.0217455i
$435$		0			0
$436$	−103607.	+	56545.9i	−0.545023	+	0.297460i
$437$	51320.1			0.268735
$438$		0			0
$439$		−	249198.i		−	1.29305i	−0.762892	−	0.646526i	$-0.776221\pi$
$439$		−	249198.i		−	1.29305i	0.762892	−	0.646526i	$-0.223779\pi$
$440$	112446.	−	104626.i	0.580815	−	0.540424i
$441$		0			0
$442$	−78573.4	−	307980.i	−0.402190	−	1.57644i
$443$		−	53833.8i		−	0.274314i	−0.990549	−	0.137157i	$-0.956204\pi$
$443$		−	53833.8i		−	0.274314i	0.990549	−	0.137157i	$-0.0437964\pi$
$444$		0			0
$445$	−282533.			−1.42675
$446$	247641.	−	63179.6i	1.24495	−	0.317619i
$447$		0			0
$448$	22011.4	+	1587.92i	0.109671	+	0.00791177i
$449$	−127961.			−0.634726			−0.317363	−	0.948304i	$-0.602797\pi$
$449$	−127961.			−0.634726			−0.317363	+	0.948304i	$0.602797\pi$
$450$		0			0
$451$			323412.i			1.59002i
$452$	−100020.	+	54588.5i	−0.489566	+	0.267192i
$453$		0			0
$454$	202040.	−	51545.6i	0.980227	−	0.250081i
$455$			23176.0i			0.111948i
$456$		0			0
$457$	138874.			0.664951			0.332475	−	0.943112i	$-0.392116\pi$
$457$	138874.			0.664951			0.332475	+	0.943112i	$0.392116\pi$
$458$	−29896.8	−	117185.i	−0.142526	−	0.558650i
$459$		0			0
$460$	13204.0	+	24193.1i	0.0624006	+	0.114334i
$461$	−242960.			−1.14323			−0.571613	−	0.820523i	$-0.693682\pi$
$461$	−242960.			−1.14323			−0.571613	+	0.820523i	$0.693682\pi$
$462$		0			0
$463$		−	277264.i		−	1.29340i	−0.762746	−	0.646699i	$-0.776149\pi$
$463$		−	277264.i		−	1.29340i	0.762746	−	0.646699i	$-0.223851\pi$
$464$	−27968.5	+	43480.5i	−0.129907	+	0.201957i
$465$		0			0
$466$	−5023.26	−	19689.4i	−0.0231320	−	0.0906692i
$467$			123580.i			0.566649i	0.959024	+	0.283325i	$0.0914374\pi$
$467$			123580.i			0.566649i	−0.959024	+	0.283325i	$0.908563\pi$
$468$		0			0
$469$	39782.1			0.180860
$470$	−181609.	+	46333.1i	−0.822133	+	0.209747i
$471$		0			0
$472$	74900.3	−	69691.6i	0.336202	−	0.312821i
$473$	−29456.7			−0.131662
$474$		0			0
$475$			120062.i			0.532132i
$476$	−15835.3	−	29014.4i	−0.0698896	−	0.128056i
$477$		0			0
$478$	157905.	−	40285.5i	0.691097	−	0.176316i
$479$		−	56214.6i		−	0.245007i	−0.992468	−	0.122503i	$-0.960908\pi$
$479$		−	56214.6i		−	0.245007i	0.992468	−	0.122503i	$-0.0390922\pi$
$480$		0			0
$481$	70559.1			0.304974
$482$	−34444.9	−	135011.i	−0.148262	−	0.581134i
$483$		0			0
$484$	−17882.7	+	9759.92i	−0.0763382	+	0.0416635i
$485$	−45240.5			−0.192328
$486$		0			0
$487$		−	271980.i		−	1.14678i	−0.819283	−	0.573389i	$-0.805628\pi$
$487$		−	271980.i		−	1.14678i	0.819283	−	0.573389i	$-0.194372\pi$
$488$	265113.	+	284928.i	1.11325	+	1.19645i
$489$		0			0
$490$	−48684.6	−	190826.i	−0.202768	−	0.794778i
$491$		−	335208.i		−	1.39044i	−0.718798	−	0.695219i	$-0.755307\pi$
$491$		−	335208.i		−	1.39044i	0.718798	−	0.695219i	$-0.244693\pi$
$492$		0			0
$493$	77434.8			0.318597
$494$	496696.	−	126720.i	2.03534	−	0.519267i
$495$		0			0
$496$	−42229.7	−	27163.9i	−0.171654	−	0.110415i
$497$	−50362.3			−0.203889
$498$		0			0
$499$		−	287692.i		−	1.15538i	−0.816255	−	0.577692i	$-0.803953\pi$
$499$		−	287692.i		−	1.15538i	0.816255	−	0.577692i	$-0.196047\pi$
$500$	−238798.	+	130330.i	−0.955193	+	0.521320i
$501$		0			0
$502$	275595.	−	70311.2i	1.09361	−	0.279008i
$503$		−	338788.i		−	1.33903i	−0.742797	−	0.669517i	$-0.766501\pi$
$503$		−	338788.i		−	1.33903i	0.742797	−	0.669517i	$-0.233499\pi$
$504$		0			0
$505$	−67305.0			−0.263915
$506$	9487.99	+	37189.5i	0.0370572	+	0.145251i
$507$		0			0
$508$	125451.	+	229858.i	0.486123	+	0.890702i
$509$	−444920.			−1.71730			−0.858651	−	0.512561i	$-0.828697\pi$
$509$	−444920.			−1.71730			−0.858651	+	0.512561i	$0.828697\pi$
$510$		0			0
$511$			28668.5i			0.109790i
$512$	204268.	−	164298.i	0.779221	−	0.626749i
$513$		0			0
$514$	4292.52	+	16825.1i	0.0162475	+	0.0636843i
$515$			67695.1i			0.255236i
$516$		0			0
$517$	−260999.			−0.976466
$518$	7110.08	−	1813.96i	0.0264981	−	0.00676034i
$519$		0			0
$520$	187531.	+	201547.i	0.693531	+	0.745365i
$521$	−275911.			−1.01647			−0.508233	−	0.861220i	$-0.669701\pi$
$521$	−275911.			−1.01647			−0.508233	+	0.861220i	$0.669701\pi$
$522$		0			0
$523$		−	85712.3i		−	0.313357i	−0.987650	−	0.156679i	$-0.949921\pi$
$523$		−	85712.3i		−	0.313357i	0.987650	−	0.156679i	$-0.0500787\pi$
$524$	−134116.	−	245736.i	−0.488448	−	0.894964i
$525$		0			0
$526$	−435577.	+	111127.i	−1.57432	+	0.401650i
$527$			75207.3i			0.270794i
$528$		0			0
$529$	272954.			0.975388
$530$	84382.7	+	330750.i	0.300401	+	1.17747i
$531$		0			0
$532$	46793.1	−	25538.5i	0.165333	−	0.0902344i
$533$	−579680.			−2.04049
$534$		0			0
$535$			330610.i			1.15507i
$536$	345959.	−	321901.i	1.20419	−	1.12045i
$537$		0			0
$538$	−66428.4	−	260375.i	−0.229503	−	0.899571i
$539$		−	274244.i		−	0.943975i
$540$		0			0
$541$	250046.			0.854331			0.427165	−	0.904174i	$-0.359512\pi$
$541$	250046.			0.854331			0.427165	+	0.904174i	$0.359512\pi$
$542$	118026.	−	30111.5i	0.401772	−	0.102502i
$543$		0			0
$544$	−372482.	−	124187.i	−1.25866	−	0.419640i
$545$	−153125.			−0.515528
$546$		0			0
$547$			435437.i			1.45529i	0.685951	+	0.727647i	$0.259386\pi$
$547$			435437.i			1.45529i	−0.685951	+	0.727647i	$0.740614\pi$
$548$	−112757.	+	61540.1i	−0.375477	+	0.204926i
$549$		0			0
$550$	−87004.2	+	22197.0i	−0.287617	+	0.0733784i
$551$			124883.i			0.411341i
$552$		0			0
$553$	−32173.1			−0.105207
$554$	16295.9	+	63874.2i	0.0530957	+	0.208116i
$555$		0			0
$556$	114985.	+	210683.i	0.371957	+	0.681521i
$557$	466836.			1.50471			0.752356	−	0.658756i	$-0.228917\pi$
$557$	466836.			1.50471			0.752356	+	0.658756i	$0.228917\pi$
$558$		0			0
$559$		−	52797.9i		−	0.168964i
$560$	24078.5	+	15488.3i	0.0767808	+	0.0493886i
$561$		0			0
$562$	−22273.6	−	87304.4i	−0.0705208	−	0.276416i
$563$			75191.2i			0.237219i	0.992941	+	0.118610i	$0.0378437\pi$
$563$			75191.2i			0.237219i	−0.992941	+	0.118610i	$0.962156\pi$
$564$		0			0
$565$	−147824.			−0.463071
$566$	−268530.	+	68508.8i	−0.838224	+	0.213852i
$567$		0			0
$568$	−437969.	+	407512.i	−1.35752	+	1.26312i
$569$	66289.8			0.204749			0.102375	−	0.994746i	$-0.467356\pi$
$569$	66289.8			0.204749			0.102375	+	0.994746i	$0.467356\pi$
$570$		0			0
$571$			377844.i			1.15888i	0.815014	+	0.579442i	$0.196729\pi$
$571$			377844.i			1.15888i	−0.815014	+	0.579442i	$0.803271\pi$
$572$	183657.	+	336507.i	0.561327	+	1.02850i
$573$		0			0
$574$	−58413.0	+	14902.6i	−0.177291	+	0.0452313i
$575$		−	16112.8i		−	0.0487342i
$576$		0			0
$577$	−415556.			−1.24818			−0.624091	−	0.781352i	$-0.714530\pi$
$577$	−415556.			−1.24818			−0.624091	+	0.781352i	$0.714530\pi$
$578$	62793.2	+	246127.i	0.187956	+	0.736721i
$579$		0			0
$580$	−58872.0	+	32130.8i	−0.175006	+	0.0955137i
$581$	54368.7			0.161063
$582$		0			0
$583$			475335.i			1.39850i
$584$	231974.	+	249311.i	0.680163	+	0.730999i
$585$		0			0
$586$	91471.3	+	358535.i	0.266373	+	1.04409i
$587$			342605.i			0.994301i	0.867664	+	0.497151i	$0.165620\pi$
$587$			342605.i			0.994301i	−0.867664	+	0.497151i	$0.834380\pi$
$588$		0			0
$589$	−121291.			−0.349621
$590$	128605.	−	32810.5i	0.369449	−	0.0942559i
$591$		0			0
$592$	47154.0	−	73306.8i	0.134547	−	0.209171i
$593$	−125568.			−0.357082			−0.178541	−	0.983932i	$-0.557138\pi$
$593$	−125568.			−0.357082			−0.178541	+	0.983932i	$0.557138\pi$
$594$		0			0
$595$		−	42881.5i		−	0.121126i
$596$	−20462.8	+	11168.1i	−0.0576067	+	0.0314403i
$597$		0			0
$598$	−66658.2	+	17006.2i	−0.186402	+	0.0475559i
$599$			317723.i			0.885512i	0.896642	+	0.442756i	$0.145999\pi$
$599$			317723.i			0.885512i	−0.896642	+	0.442756i	$0.854001\pi$
$600$		0			0
$601$	−168972.			−0.467806			−0.233903	−	0.972260i	$-0.575150\pi$
$601$	−168972.			−0.467806			−0.233903	+	0.972260i	$0.575150\pi$
$602$	−1357.35	−	5320.32i	−0.00374540	−	0.0146806i
$603$		0			0
$604$	−118149.	−	216480.i	−0.323859	−	0.593394i
$605$	−26429.5			−0.0722070
$606$		0			0
$607$		−	644373.i		−	1.74888i	−0.485135	−	0.874440i	$-0.661229\pi$
$607$		−	644373.i		−	1.74888i	0.485135	−	0.874440i	$-0.338771\pi$
$608$	200283.	−	600723.i	0.541796	−	1.62505i
$609$		0			0
$610$	124814.	+	489227.i	0.335432	+	1.31477i
$611$		−	467812.i		−	1.25311i
$612$		0			0
$613$	228892.			0.609129			0.304564	−	0.952492i	$-0.401489\pi$
$613$	228892.			0.609129			0.304564	+	0.952492i	$0.401489\pi$
$614$	309068.	−	78851.0i	0.819817	−	0.209156i
$615$		0			0
$616$	27157.7	+	29187.5i	0.0715702	+	0.0769193i
$617$	329605.			0.865813			0.432906	−	0.901439i	$-0.357488\pi$
$617$	329605.			0.865813			0.432906	+	0.901439i	$0.357488\pi$
$618$		0			0
$619$		−	223932.i		−	0.584434i	−0.956352	−	0.292217i	$-0.905607\pi$
$619$		−	223932.i		−	0.584434i	0.956352	−	0.292217i	$-0.0943930\pi$
$620$	−31206.5	−	57178.4i	−0.0811824	−	0.148747i
$621$		0			0
$622$	448168.	−	114339.i	1.15840	−	0.295538i
$623$		−	73336.9i		−	0.188950i
$624$		0			0
$625$	−231584.			−0.592854
$626$	−25568.7	−	100220.i	−0.0652468	−	0.255744i
$627$		0			0
$628$	327641.	−	178818.i	0.830766	−	0.453411i
$629$	−130553.			−0.329977
$630$		0			0
$631$			681430.i			1.71144i	0.517437	+	0.855721i	$0.326886\pi$
$631$			681430.i			1.71144i	−0.517437	+	0.855721i	$0.673114\pi$
$632$	−279789.	+	260332.i	−0.700482	+	0.651769i
$633$		0			0
$634$	77426.1	+	303482.i	0.192623	+	0.755014i
$635$			339717.i			0.842499i
$636$		0			0
$637$	491554.			1.21141
$638$	−90497.8	+	23088.3i	−0.222329	+	0.0567219i
$639$		0			0
$640$	334720.	−	60141.7i	0.817188	−	0.146830i
$641$	346761.			0.843945			0.421973	−	0.906609i	$-0.361338\pi$
$641$	346761.			0.843945			0.421973	+	0.906609i	$0.361338\pi$
$642$		0			0
$643$		−	124932.i		−	0.302169i	−0.988521	−	0.151085i	$-0.951723\pi$
$643$		−	124932.i		−	0.302169i	0.988521	−	0.151085i	$-0.0482766\pi$
$644$	−6279.78	+	3427.35i	−0.0151416	+	0.00826392i
$645$		0			0
$646$	−919015.	+	234464.i	−2.20221	+	0.561838i
$647$		−	43450.9i		−	0.103798i	−0.998652	−	0.0518992i	$-0.983473\pi$
$647$		−	43450.9i		−	0.103798i	0.998652	−	0.0518992i	$-0.0165274\pi$
$648$		0			0
$649$	184824.			0.438803
$650$	−39785.7	−	155946.i	−0.0941673	−	0.369102i
$651$		0			0
$652$	−241565.	−	442609.i	−0.568249	−	1.04118i
$653$	344790.			0.808589			0.404294	−	0.914629i	$-0.367517\pi$
$653$	344790.			0.808589			0.404294	+	0.914629i	$0.367517\pi$
$654$		0			0
$655$		−	363183.i		−	0.846530i
$656$	−387394.	+	602253.i	−0.900214	+	1.39950i
$657$		0			0
$658$	−12026.7	−	47140.3i	−0.0277775	−	0.108878i
$659$		−	670185.i		−	1.54321i	−0.636105	−	0.771603i	$-0.719455\pi$
$659$		−	670185.i		−	1.54321i	0.636105	−	0.771603i	$-0.280545\pi$
$660$		0			0
$661$	−619584.			−1.41807			−0.709034	−	0.705174i	$-0.750869\pi$
$661$	−619584.			−1.41807			−0.709034	+	0.705174i	$0.750869\pi$
$662$	−617597.	+	157565.i	−1.40925	+	0.359536i
$663$		0			0
$664$	472810.	−	439930.i	1.07239	−	0.997809i
$665$	69157.4			0.156385
$666$		0			0
$667$		−	16759.8i		−	0.0376718i
$668$	−346126.	−	634193.i	−0.775678	−	1.42124i
$669$		0			0
$670$	594019.	−	151549.i	1.32328	−	0.337602i
$671$			703088.i			1.56158i
$672$		0			0
$673$	−233848.			−0.516302			−0.258151	−	0.966105i	$-0.583113\pi$
$673$	−233848.			−0.516302			−0.258151	+	0.966105i	$0.583113\pi$
$674$	32520.3	+	127468.i	0.0715872	+	0.280596i
$675$		0			0
$676$	−202029.	+	110263.i	−0.442101	+	0.241287i
$677$	703621.			1.53519			0.767594	−	0.640936i	$-0.221454\pi$
$677$	703621.			1.53519			0.767594	+	0.640936i	$0.221454\pi$
$678$		0			0
$679$		−	11743.0i		−	0.0254707i
$680$	−346980.	−	372913.i	−0.750390	−	0.806474i
$681$		0			0
$682$	−22424.1	−	87894.5i	−0.0482111	−	0.188970i
$683$			8903.15i			0.0190855i	0.999954	+	0.00954273i	$0.00303759\pi$
$683$			8903.15i			0.0190855i	−0.999954	+	0.00954273i	$0.996962\pi$
$684$		0			0
$685$	−166649.			−0.355157
$686$	99671.5	−	25428.7i	0.211799	−	0.0540352i
$687$		0			0
$688$	−54853.9	−	35284.3i	−0.115886	−	0.0745426i
$689$	−851987.			−1.79471
$690$		0			0
$691$		−	186507.i		−	0.390606i	−0.980743	−	0.195303i	$-0.937431\pi$
$691$		−	186507.i		−	0.390606i	0.980743	−	0.195303i	$-0.0625690\pi$
$692$	−558808.	+	304983.i	−1.16694	+	0.636889i
$693$		0			0
$694$	266191.	−	67912.1i	0.552681	−	0.141003i
$695$			311376.i			0.644638i
$696$		0			0
$697$	1.07256e6			2.20778
$698$	−226000.	−	885840.i	−0.463872	−	1.81821i
$699$		0			0
$700$	−8018.21	−	14691.4i	−0.0163637	−	0.0299825i
$701$	498328.			1.01410			0.507048	−	0.861918i	$-0.330736\pi$
$701$	498328.			1.01410			0.507048	+	0.861918i	$0.330736\pi$
$702$		0			0
$703$		−	210549.i		−	0.426033i
$704$	472347.	+	34075.5i	0.953051	+	0.0687539i
$705$		0			0
$706$	45511.3	+	178388.i	0.0913082	+	0.357895i
$707$		−	17470.3i		−	0.0349512i
$708$		0			0
$709$	84448.4			0.167996			0.0839980	−	0.996466i	$-0.473231\pi$
$709$	84448.4			0.167996			0.0839980	+	0.996466i	$0.473231\pi$
$710$	−752002.	+	191855.i	−1.49177	+	0.380589i
$711$		0			0
$712$	−593413.	−	637764.i	−1.17057	−	1.25806i
$713$	16277.6			0.0320193
$714$		0			0
$715$			497338.i			0.972835i
$716$	169263.	+	310133.i	0.330168	+	0.604954i
$717$		0			0
$718$	−509462.	+	129977.i	−0.988241	+	0.252125i
$719$		−	563153.i		−	1.08935i	−0.838646	−	0.544677i	$-0.816652\pi$
$719$		−	563153.i		−	1.08935i	0.838646	−	0.544677i	$-0.183348\pi$
$720$		0			0
$721$	−17571.6			−0.0338018
$722$	−249268.	−	977043.i	−0.478182	−	1.87430i
$723$		0			0
$724$	138577.	−	75631.6i	0.264370	−	0.144287i
$725$	39209.1			0.0745953
$726$		0			0
$727$		−	829063.i		−	1.56862i	−0.620367	−	0.784312i	$-0.713016\pi$
$727$		−	829063.i		−	1.56862i	0.620367	−	0.784312i	$-0.286984\pi$
$728$	−52315.4	+	48677.3i	−0.0987113	+	0.0918467i
$729$		0			0
$730$	109212.	+	428073.i	0.204939	+	0.803289i
$731$			97689.7i			0.182816i
$732$		0			0
$733$	345658.			0.643338			0.321669	−	0.946852i	$-0.395756\pi$
$733$	345658.			0.643338			0.321669	+	0.946852i	$0.395756\pi$
$734$	467616.	−	119301.i	0.867954	−	0.221437i
$735$		0			0
$736$	−26878.6	+	80619.0i	−0.0496193	+	0.148827i
$737$	853691.			1.57169
$738$		0			0
$739$		−	662859.i		−	1.21376i	−0.794794	−	0.606879i	$-0.792421\pi$
$739$		−	662859.i		−	1.21376i	0.794794	−	0.606879i	$-0.207579\pi$
$740$	99256.2	−	54171.5i	0.181257	−	0.0989253i
$741$		0			0
$742$	−85852.7	+	21903.2i	−0.155936	+	0.0397832i
$743$		−	346708.i		−	0.628039i	−0.949417	−	0.314019i	$-0.898324\pi$
$743$		−	346708.i		−	0.628039i	0.949417	−	0.314019i	$-0.101676\pi$
$744$		0			0
$745$	−30242.8			−0.0544891
$746$	181194.	+	710216.i	0.325586	+	1.27618i
$747$		0			0
$748$	−339813.	−	622625.i	−0.607347	−	1.11282i
$749$	−85816.2			−0.152970
$750$		0			0
$751$			218129.i			0.386752i	0.981125	+	0.193376i	$0.0619438\pi$
$751$			218129.i			0.386752i	−0.981125	+	0.193376i	$0.938056\pi$
$752$	−486028.	−	312634.i	−0.859461	−	0.552841i
$753$		0			0
$754$	−41383.3	−	162208.i	−0.0727917	−	0.285318i
$755$		−	319944.i		−	0.561281i
$756$		0			0
$757$	454177.			0.792563			0.396281	−	0.918129i	$-0.370300\pi$
$757$	454177.			0.792563			0.396281	+	0.918129i	$0.370300\pi$
$758$	−816017.	+	208187.i	−1.42024	+	0.362339i
$759$		0			0
$760$	601418.	−	559594.i	1.04124	−	0.968827i
$761$	779754.			1.34644			0.673222	−	0.739441i	$-0.264910\pi$
$761$	779754.			1.34644			0.673222	+	0.739441i	$0.264910\pi$
$762$		0			0
$763$		−	39746.5i		−	0.0682731i
$764$	53548.1	+	98113.9i	0.0917396	+	0.168091i
$765$		0			0
$766$	445826.	−	113742.i	0.759815	−	0.193848i
$767$			331278.i			0.563120i
$768$		0			0
$769$	1.04561e6			1.76814			0.884072	−	0.467350i	$-0.154791\pi$
$769$	1.04561e6			1.76814			0.884072	+	0.467350i	$0.154791\pi$
$770$	12785.7	+	50115.5i	0.0215647	+	0.0845261i
$771$		0			0
$772$	556831.	−	303904.i	0.934305	−	0.509920i
$773$	−240697.			−0.402820			−0.201410	−	0.979507i	$-0.564552\pi$
$773$	−240697.			−0.402820			−0.201410	+	0.979507i	$0.564552\pi$
$774$		0			0
$775$			38081.2i			0.0634027i
$776$	−95020.1	−	102122.i	−0.157795	−	0.169588i
$777$		0			0
$778$	225405.	+	883506.i	0.372395	+	1.45966i
$779$			1.72977e6i			2.85046i
$780$		0			0
$781$	−1.08073e6			−1.77181
$782$	123335.	−	31465.8i	0.201684	−	0.0514548i
$783$		0			0
$784$	328500.	−	510695.i	0.534446	−	0.830863i
$785$	484234.			0.785807
$786$		0			0
$787$		−	453844.i		−	0.732753i	−0.930467	−	0.366376i	$-0.880598\pi$
$787$		−	453844.i		−	0.732753i	0.930467	−	0.366376i	$-0.119402\pi$
$788$	358427.	−	195620.i	0.577229	−	0.315037i
$789$		0			0
$790$	−480404.	+	122563.i	−0.769754	+	0.196384i
$791$		−	38370.6i		−	0.0613261i
$792$		0			0
$793$	−1.26021e6			−2.00399
$794$	250382.	+	981406.i	0.397156	+	1.55671i
$795$		0			0
$796$	158175.	+	289817.i	0.249638	+	0.457402i
$797$	595530.			0.937534			0.468767	−	0.883322i	$-0.344698\pi$
$797$	595530.			0.937534			0.468767	+	0.883322i	$0.344698\pi$
$798$		0			0
$799$			865572.i			1.35584i
$800$	−188607.	−	62881.9i	−0.294698	−	0.0982530i
$801$		0			0
$802$	111791.	+	438182.i	0.173804	+	0.681249i
$803$			615202.i			0.954084i
$804$		0			0
$805$	−9281.15			−0.0143222
$806$	157541.	−	40192.8i	0.242507	−	0.0618697i
$807$		0			0
$808$	−141363.	−	151928.i	−0.216528	−	0.232711i
$809$	−238455.			−0.364342			−0.182171	−	0.983267i	$-0.558312\pi$
$809$	−238455.			−0.364342			−0.182171	+	0.983267i	$0.558312\pi$
$810$		0			0
$811$			325863.i			0.495443i	0.968831	+	0.247721i	$0.0796817\pi$
$811$			325863.i			0.495443i	−0.968831	+	0.247721i	$0.920318\pi$
$812$	−8340.18	−	15281.4i	−0.0126492	−	0.0231766i
$813$		0			0
$814$	152576.	−	38926.1i	0.230271	−	0.0587479i
$815$		−	654151.i		−	0.984833i
$816$		0			0
$817$	−157550.			−0.236033
$818$	76735.4	+	300775.i	0.114680	+	0.449506i
$819$		0			0
$820$	−815442.	+	445047.i	−1.21273	+	0.661879i
$821$	−376943.			−0.559228			−0.279614	−	0.960113i	$-0.590206\pi$
$821$	−376943.			−0.559228			−0.279614	+	0.960113i	$0.590206\pi$
$822$		0			0
$823$			1.10349e6i			1.62918i	0.580040	+	0.814588i	$0.303037\pi$
$823$			1.10349e6i			1.62918i	−0.580040	+	0.814588i	$0.696963\pi$
$824$	−152809.	+	142182.i	−0.225058	+	0.209407i
$825$		0			0
$826$	8516.61	+	33382.0i	0.0124826	+	0.0489275i
$827$		−	251807.i		−	0.368177i	−0.982910	−	0.184089i	$-0.941067\pi$
$827$		−	251807.i		−	0.368177i	0.982910	−	0.184089i	$-0.0589334\pi$
$828$		0			0
$829$	595280.			0.866189			0.433094	−	0.901349i	$-0.357422\pi$
$829$	595280.			0.866189			0.433094	+	0.901349i	$0.357422\pi$
$830$	811825.	−	207117.i	1.17844	−	0.300649i
$831$		0			0
$832$	−61076.7	+	846631.i	−0.0882326	+	1.22306i
$833$	−909501.			−1.31073
$834$		0			0
$835$		−	937299.i		−	1.34433i
$836$	1.00414e6	−	548035.i	1.43675	−	0.784144i
$837$		0			0
$838$	181759.	−	46371.3i	0.258826	−	0.0660330i
$839$		−	937926.i		−	1.33243i	−0.745760	−	0.666215i	$-0.767913\pi$
$839$		−	937926.i		−	1.33243i	0.745760	−	0.666215i	$-0.232087\pi$
$840$		0			0
$841$	−666497.			−0.942338
$842$	39699.7	+	155609.i	0.0559967	+	0.219487i
$843$		0			0
$844$	−286699.	−	525306.i	−0.402477	−	0.737441i
$845$	−298588.			−0.418175
$846$		0			0
$847$		−	6860.31i		−	0.00956262i
$848$	−569374.	+	885164.i	−0.791783	+	1.23093i
$849$		0			0
$850$	73613.7	+	288539.i	0.101888	+	0.399363i
$851$			28256.4i			0.0390174i
$852$		0			0
$853$	−17614.3			−0.0242085			−0.0121042	−	0.999927i	$-0.503853\pi$
$853$	−17614.3			−0.0242085			−0.0121042	+	0.999927i	$0.503853\pi$
$854$	−126988.	+	32397.9i	−0.174120	+	0.0444224i
$855$		0			0
$856$	−746289.	+	694390.i	−1.01850	+	0.947668i
$857$	−203626.			−0.277251			−0.138625	−	0.990345i	$-0.544268\pi$
$857$	−203626.			−0.277251			−0.138625	+	0.990345i	$0.544268\pi$
$858$		0			0
$859$		−	110138.i		−	0.149262i	−0.997211	−	0.0746310i	$-0.976222\pi$
$859$		−	110138.i		−	0.149262i	0.997211	−	0.0746310i	$-0.0237779\pi$
$860$	−40535.4	−	74271.3i	−0.0548072	−	0.100421i
$861$		0			0
$862$	−997741.	+	254549.i	−1.34278	+	0.342576i
$863$		−	366628.i		−	0.492271i	−0.969235	−	0.246136i	$-0.920839\pi$
$863$		−	366628.i		−	0.492271i	0.969235	−	0.246136i	$-0.0791609\pi$
$864$		0			0
$865$	−825885.			−1.10379
$866$	−29428.1	−	115347.i	−0.0392397	−	0.153806i
$867$		0			0
$868$	14841.8	−	8100.27i	0.0196991	−	0.0107513i
$869$	−690409.			−0.914254
$870$		0			0
$871$			1.53015e6i			2.01696i
$872$	−321613.	−	345650.i	−0.422961	−	0.454573i
$873$		0			0
$874$	50746.7	+	198909.i	0.0664332	+	0.260394i
$875$		−	91609.8i		−	0.119654i
$876$		0			0
$877$	−556086.			−0.723007			−0.361503	−	0.932371i	$-0.617736\pi$
$877$	−556086.			−0.723007			−0.361503	+	0.932371i	$0.617736\pi$
$878$	965855.	−	246414.i	1.25292	−	0.319651i
$879$		0			0
$880$	516704.	+	332366.i	0.667232	+	0.429191i
$881$	246117.			0.317096			0.158548	−	0.987351i	$-0.449319\pi$
$881$	246117.			0.317096			0.158548	+	0.987351i	$0.449319\pi$
$882$		0			0
$883$		−	317186.i		−	0.406810i	−0.979095	−	0.203405i	$-0.934799\pi$
$883$		−	317186.i		−	0.406810i	0.979095	−	0.203405i	$-0.0652009\pi$
$884$	1.11599e6	−	609078.i	1.42809	−	0.779414i
$885$		0			0
$886$	208652.	−	53232.3i	0.265800	−	0.0678122i
$887$			84967.8i			0.107996i	0.998541	+	0.0539979i	$0.0171964\pi$
$887$			84967.8i			0.107996i	−0.998541	+	0.0539979i	$0.982804\pi$
$888$		0			0
$889$	−88180.2			−0.111575
$890$	−279376.	−	1.09505e6i	−0.352703	−	1.38247i
$891$		0			0
$892$	489749.	+	897347.i	0.615523	+	1.12780i
$893$	−1.39596e6			−1.75053
$894$		0			0
$895$			458358.i			0.572215i
$896$	15610.9	+	86883.2i	0.0194452	+	0.108223i
$897$		0			0
$898$	−126532.	−	495959.i	−0.156909	−	0.615026i
$899$			39610.4i			0.0490105i
$900$		0			0
$901$	1.57640e6			1.94185
$902$	−1.25349e6	+	319798.i	−1.54067	+	0.393064i
$903$		0			0
$904$	−310480.	−	333685.i	−0.379924	−	0.408319i
$905$	204808.			0.250063
$906$		0			0
$907$			384478.i			0.467366i	0.972313	+	0.233683i	$0.0750778\pi$
$907$			384478.i			0.467366i	−0.972313	+	0.233683i	$0.924922\pi$
$908$	399566.	+	732109.i	0.484638	+	0.887981i
$909$		0			0
$910$	−89826.7	+	22917.1i	−0.108473	+	0.0276743i
$911$			1.24116e6i			1.49552i	0.663972	+	0.747758i	$0.268870\pi$
$911$			1.24116e6i			1.49552i	−0.663972	+	0.747758i	$0.731130\pi$
$912$		0			0
$913$	1.16671e6			1.39965
$914$	137323.	+	538256.i	0.164380	+	0.644312i
$915$		0			0
$916$	424628.	−	231751.i	0.506078	−	0.276205i
$917$	94271.2			0.112109
$918$		0			0
$919$			698308.i			0.826829i	0.910543	+	0.413415i	$0.135664\pi$
$919$			698308.i			0.826829i	−0.910543	+	0.413415i	$0.864336\pi$
$920$	−80712.3	+	75099.4i	−0.0953595	+	0.0887280i
$921$		0			0
$922$	−240245.	−	941675.i	−0.282614	−	1.10774i
$923$		−	1.93710e6i		−	2.27378i
$924$		0			0
$925$	−66105.3			−0.0772597
$926$	1.07463e6	−	274167.i	1.25325	−	0.319737i
$927$		0			0
$928$	−196180.	−	65406.9i	−0.227803	−	0.0759500i
$929$	−1.40938e6			−1.63304			−0.816519	−	0.577318i	$-0.804099\pi$
$929$	−1.40938e6			−1.63304			−0.816519	+	0.577318i	$0.804099\pi$
$930$		0			0
$931$		−	1.46680e6i		−	1.69228i
$932$	71345.9	−	38938.8i	0.0821367	−	0.0448281i
$933$		0			0
$934$	−478978.	+	122199.i	−0.549062	+	0.140080i
$935$		−	920203.i		−	1.05259i
$936$		0			0
$937$	−98815.5			−0.112550			−0.0562751	−	0.998415i	$-0.517922\pi$
$937$	−98815.5			−0.112550			−0.0562751	+	0.998415i	$0.517922\pi$
$938$	39337.6	+	154189.i	0.0447098	+	0.175246i
$939$		0			0
$940$	−359161.	−	658075.i	−0.406474	−	0.744766i
$941$	−1.30446e6			−1.47316			−0.736581	−	0.676350i	$-0.763561\pi$
$941$	−1.30446e6			−1.47316			−0.736581	+	0.676350i	$0.763561\pi$
$942$		0			0
$943$		−	232141.i		−	0.261053i
$944$	344178.	+	221389.i	0.386224	+	0.248435i
$945$		0			0
$946$	−29127.6	−	114170.i	−0.0325478	−	0.127576i
$947$		−	146295.i		−	0.163128i	−0.996668	−	0.0815641i	$-0.974008\pi$
$947$		−	146295.i		−	0.163128i	0.996668	−	0.0815641i	$-0.0259915\pi$
$948$		0			0
$949$	−1.10268e6			−1.22439
$950$	−465344.	+	118721.i	−0.515616	+	0.131547i
$951$		0			0
$952$	96797.0	−	90065.5i	0.106804	−	0.0993767i
$953$	−1.65688e6			−1.82433			−0.912167	−	0.409818i	$-0.865592\pi$
$953$	−1.65688e6			−1.82433			−0.912167	+	0.409818i	$0.865592\pi$
$954$		0			0
$955$			145006.i			0.158994i
$956$	312281.	+	572179.i	0.341688	+	0.626061i
$957$		0			0
$958$	217879.	−	55586.5i	0.237402	−	0.0605674i
$959$		−	43256.9i		−	0.0470347i
$960$		0			0
$961$	885050.			0.958343
$962$	69770.8	+	273477.i	0.0753918	+	0.295509i
$963$		0			0
$964$	489224.	−	267006.i	0.526446	−	0.287321i
$965$	822963.			0.883742
$966$		0			0
$967$			532588.i			0.569559i	0.958593	+	0.284780i	$0.0919204\pi$
$967$			532588.i			0.569559i	−0.958593	+	0.284780i	$0.908080\pi$
$968$	−55510.9	−	59659.7i	−0.0592417	−	0.0636694i
$969$		0			0
$970$	−44735.0	−	175345.i	−0.0475449	−	0.186359i
$971$			1.26243e6i			1.33896i	0.742828	+	0.669482i	$0.233484\pi$
$971$			1.26243e6i			1.33896i	−0.742828	+	0.669482i	$0.766516\pi$
$972$		0			0
$973$	−80823.9			−0.0853717
$974$	1.05416e6	−	268942.i	1.11119	−	0.283492i
$975$		0			0
$976$	−842186.	+	1.30928e6i	−0.884114	+	1.37447i
$977$	995130.			1.04254			0.521268	−	0.853393i	$-0.325459\pi$
$977$	995130.			1.04254			0.521268	+	0.853393i	$0.325459\pi$
$978$		0			0
$979$		−	1.57375e6i		−	1.64199i
$980$	691473.	−	377388.i	0.719984	−	0.392949i
$981$		0			0
$982$	1.29922e6	−	331463.i	1.34728	−	0.343726i
$983$		−	706269.i		−	0.730909i	−0.930829	−	0.365454i	$-0.880914\pi$
$983$		−	706269.i		−	0.730909i	0.930829	−	0.365454i	$-0.119086\pi$
$984$		0			0
$985$	529733.			0.545990
$986$	76569.7	+	300126.i	0.0787595	+	0.308709i
$987$		0			0
$988$	982294.	+	1.79982e6i	1.00630	+	1.84380i
$989$	21143.7			0.0216166
$990$		0			0
$991$		−	6734.63i		−	0.00685751i	−0.999994	−	0.00342875i	$-0.998909\pi$
$991$		−	6734.63i		−	0.00685751i	0.999994	−	0.00342875i	$-0.00109141\pi$
$992$	63525.4	−	190537.i	0.0645541	−	0.193622i
$993$		0			0
$994$	−49799.7	−	195197.i	−0.0504027	−	0.197560i
$995$			428333.i			0.432648i
$996$		0			0
$997$	−525528.			−0.528696			−0.264348	−	0.964427i	$-0.585157\pi$
$997$	−525528.			−0.528696			−0.264348	+	0.964427i	$0.585157\pi$
$998$	1.11505e6	−	284478.i	1.11952	−	0.285619i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.d.b.55.10	yes	16
3.2	odd	2	inner	108.5.d.b.55.7	✓	16
4.3	odd	2	inner	108.5.d.b.55.9	yes	16
12.11	even	2	inner	108.5.d.b.55.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.d.b.55.7	✓	16	3.2	odd	2	inner
108.5.d.b.55.8	yes	16	12.11	even	2	inner
108.5.d.b.55.9	yes	16	4.3	odd	2	inner
108.5.d.b.55.10	yes	16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988828 + 3.87585i) q^{2} +(-14.0444 + 7.66510i) q^{4} -20.7568 q^{5} -5.38785i q^{7} +(-43.5963 - 46.8547i) q^{8} +O(q^{10})\)	\(q+(0.988828 + 3.87585i) q^{2} +(-14.0444 + 7.66510i) q^{4} -20.7568 q^{5} -5.38785i q^{7} +(-43.5963 - 46.8547i) q^{8} +(-20.5250 - 80.4504i) q^{10} -115.619i q^{11} +207.234 q^{13} +(20.8825 - 5.32765i) q^{14} +(138.493 - 215.304i) q^{16} -383.437 q^{17} -618.390i q^{19} +(291.518 - 159.103i) q^{20} +(448.121 - 114.327i) q^{22} +82.9899i q^{23} -194.153 q^{25} +(204.919 + 803.209i) q^{26} +(41.2984 + 75.6693i) q^{28} -201.949 q^{29} -196.140i q^{31} +(971.432 + 323.878i) q^{32} +(-379.153 - 1486.14i) q^{34} +111.835i q^{35} +340.480 q^{37} +(2396.79 - 611.481i) q^{38} +(904.922 + 972.556i) q^{40} -2797.22 q^{41} -254.774i q^{43} +(886.230 + 1623.80i) q^{44} +(-321.656 + 82.0627i) q^{46} -2257.41i q^{47} +2371.97 q^{49} +(-191.984 - 752.509i) q^{50} +(-2910.49 + 1588.47i) q^{52} -4111.23 q^{53} +2399.88i q^{55} +(-252.446 + 234.890i) q^{56} +(-199.693 - 782.726i) q^{58} +1598.57i q^{59} -6081.09 q^{61} +(760.210 - 193.949i) q^{62} +(-294.723 + 4085.38i) q^{64} -4301.53 q^{65} +7383.67i q^{67} +(5385.15 - 2939.08i) q^{68} +(-433.455 + 110.585i) q^{70} -9347.39i q^{71} -5320.95 q^{73} +(336.676 + 1319.65i) q^{74} +(4740.02 + 8684.94i) q^{76} -622.936 q^{77} -5971.42i q^{79} +(-2874.67 + 4469.03i) q^{80} +(-2765.97 - 10841.6i) q^{82} +10091.0i q^{83} +7958.94 q^{85} +(987.466 - 251.928i) q^{86} +(-5417.28 + 5040.55i) q^{88} +13611.5 q^{89} -1116.55i q^{91} +(-636.126 - 1165.55i) q^{92} +(8749.37 - 2232.19i) q^{94} +12835.8i q^{95} +2179.54 q^{97} +(2345.47 + 9193.41i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{4}+O(q^{10}) \) 16 * q + 28 * q^4	\( 16 q + 28 q^{4} + 176 q^{10} + 176 q^{13} + 88 q^{16} + 384 q^{22} + 2736 q^{25} + 1812 q^{28} + 1520 q^{34} + 80 q^{37} - 688 q^{40} - 1824 q^{46} - 7904 q^{49} - 5236 q^{52} - 11584 q^{58} - 1648 q^{61} + 5056 q^{64} + 26688 q^{70} + 80 q^{73} - 8388 q^{76} - 38464 q^{82} - 16832 q^{85} - 29520 q^{88} - 4512 q^{94} + 14864 q^{97}+O(q^{100}) \) 16 * q + 28 * q^4 + 176 * q^10 + 176 * q^13 + 88 * q^16 + 384 * q^22 + 2736 * q^25 + 1812 * q^28 + 1520 * q^34 + 80 * q^37 - 688 * q^40 - 1824 * q^46 - 7904 * q^49 - 5236 * q^52 - 11584 * q^58 - 1648 * q^61 + 5056 * q^64 + 26688 * q^70 + 80 * q^73 - 8388 * q^76 - 38464 * q^82 - 16832 * q^85 - 29520 * q^88 - 4512 * q^94 + 14864 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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