LMFDB - Embedded newform 108.6.h.a.71.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.20
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.75408 + 4.23165i) q^{2} +(-3.81374 + 31.7719i) q^{4} +(52.1793 + 30.1257i) q^{5} +(185.316 - 106.992i) q^{7} +(-148.765 + 103.136i) q^{8} +O(q^{10})$	\(q+(3.75408 + 4.23165i) q^{2} +(-3.81374 + 31.7719i) q^{4} +(52.1793 + 30.1257i) q^{5} +(185.316 - 106.992i) q^{7} +(-148.765 + 103.136i) q^{8} +(68.4038 + 333.899i) q^{10} +(185.570 + 321.417i) q^{11} +(402.759 - 697.599i) q^{13} +(1148.44 + 382.534i) q^{14} +(-994.911 - 242.339i) q^{16} -34.0704i q^{17} +1173.48i q^{19} +(-1156.15 + 1542.95i) q^{20} +(-663.480 + 1991.90i) q^{22} +(-1980.40 + 3430.16i) q^{23} +(252.621 + 437.553i) q^{25} +(4463.99 - 914.509i) q^{26} +(2692.60 + 6295.88i) q^{28} +(382.894 - 221.064i) q^{29} +(1381.28 + 797.481i) q^{31} +(-2709.48 - 5119.88i) q^{32} +(144.174 - 127.903i) q^{34} +12892.9 q^{35} -11057.6 q^{37} +(-4965.76 + 4405.34i) q^{38} +(-10869.5 + 899.918i) q^{40} +(7969.76 + 4601.35i) q^{41} +(-1061.38 + 612.787i) q^{43} +(-10919.8 + 4670.13i) q^{44} +(-21949.8 + 4496.72i) q^{46} +(-1222.66 - 2117.71i) q^{47} +(14491.1 - 25099.3i) q^{49} +(-903.210 + 2711.61i) q^{50} +(20628.1 + 15456.9i) q^{52} -20212.4i q^{53} +22361.8i q^{55} +(-16533.7 + 35029.4i) q^{56} +(2372.88 + 790.381i) q^{58} +(1704.67 - 2952.58i) q^{59} +(-19919.9 - 34502.3i) q^{61} +(1810.77 + 8838.89i) q^{62} +(11493.9 - 30686.0i) q^{64} +(42031.4 - 24266.8i) q^{65} +(-6088.22 - 3515.04i) q^{67} +(1082.48 + 129.935i) q^{68} +(48400.9 + 54558.1i) q^{70} -25694.1 q^{71} +65431.6 q^{73} +(-41511.2 - 46792.0i) q^{74} +(-37283.7 - 4475.34i) q^{76} +(68778.2 + 39709.1i) q^{77} +(41126.9 - 23744.6i) q^{79} +(-44613.1 - 42617.5i) q^{80} +(10447.9 + 50999.1i) q^{82} +(-6605.97 - 11441.9i) q^{83} +(1026.39 - 1777.77i) q^{85} +(-6577.60 - 2190.93i) q^{86} +(-60756.1 - 28676.6i) q^{88} -85682.2i q^{89} -172368. i q^{91} +(-101430. - 76003.0i) q^{92} +(4371.44 - 13123.9i) q^{94} +(-35352.0 + 61231.4i) q^{95} +(-27944.9 - 48402.0i) q^{97} +(160612. - 32903.6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	3.75408	+	4.23165i	0.663634	+	0.748057i
$2$	3.75408	+	4.23165i	0.663634	+	0.748057i
$3$		0			0
$3$		0			0
$4$	−3.81374	+	31.7719i	−0.119179	+	0.992873i
$5$	52.1793	+	30.1257i	0.933412	+	0.538906i	0.887889	−	0.460058i	$-0.152171\pi$
$5$	52.1793	+	30.1257i	0.933412	+	0.538906i	0.0455230	+	0.998963i	$0.485505\pi$
$6$		0			0
$7$	185.316	−	106.992i	1.42944	−	0.825290i	0.432367	−	0.901698i	$-0.357679\pi$
$7$	185.316	−	106.992i	1.42944	−	0.825290i	0.997077	+	0.0764081i	$0.0243452\pi$
$8$	−148.765	+	103.136i	−0.821817	+	0.569751i
$9$		0			0
$10$	68.4038	+	333.899i	0.216312	+	1.05588i
$11$	185.570	+	321.417i	0.462410	+	0.800917i	0.999080	−	0.0428745i	$-0.0136516\pi$
$11$	185.570	+	321.417i	0.462410	+	0.800917i	−0.536671	+	0.843792i	$0.680318\pi$
$12$		0			0
$13$	402.759	−	697.599i	0.660978	−	1.14485i	−0.319381	−	0.947626i	$-0.603475\pi$
$13$	402.759	−	697.599i	0.660978	−	1.14485i	0.980359	−	0.197221i	$-0.0631917\pi$
$14$	1148.44	+	382.534i	1.56599	+	0.521615i
$15$		0			0
$16$	−994.911	−	242.339i	−0.971593	−	0.236660i
$17$		−	34.0704i		−	0.0285926i	−0.999898	−	0.0142963i	$-0.995449\pi$
$17$		−	34.0704i		−	0.0285926i	0.999898	−	0.0142963i	$-0.00455082\pi$
$18$		0			0
$19$			1173.48i			0.745747i	0.927882	+	0.372874i	$0.121627\pi$
$19$			1173.48i			0.745747i	−0.927882	+	0.372874i	$0.878373\pi$
$20$	−1156.15	+	1542.95i	−0.646308	+	0.862533i
$21$		0			0
$22$	−663.480	+	1991.90i	−0.292261	+	0.877425i
$23$	−1980.40	+	3430.16i	−0.780610	+	1.35206i	0.150977	+	0.988537i	$0.451758\pi$
$23$	−1980.40	+	3430.16i	−0.780610	+	1.35206i	−0.931587	+	0.363519i	$0.881575\pi$
$24$		0			0
$25$	252.621	+	437.553i	0.0808388	+	0.140017i
$26$	4463.99	−	914.509i	1.29506	−	0.265311i
$27$		0			0
$28$	2692.60	+	6295.88i	0.649048	+	1.51761i
$29$	382.894	−	221.064i	0.0845441	−	0.0488115i	−0.457132	−	0.889399i	$-0.651123\pi$
$29$	382.894	−	221.064i	0.0845441	−	0.0488115i	0.541676	+	0.840587i	$0.317790\pi$
$30$		0			0
$31$	1381.28	+	797.481i	0.258153	+	0.149045i	0.623492	−	0.781830i	$-0.285714\pi$
$31$	1381.28	+	797.481i	0.258153	+	0.149045i	−0.365339	+	0.930875i	$0.619047\pi$
$32$	−2709.48	−	5119.88i	−0.467747	−	0.883862i
$33$		0			0
$34$	144.174	−	127.903i	0.0213889	−	0.0189751i
$35$	12892.9			1.77901
$36$		0			0
$37$	−11057.6			−1.32787			−0.663937	−	0.747788i	$-0.731116\pi$
$37$	−11057.6			−1.32787			−0.663937	+	0.747788i	$0.731116\pi$
$38$	−4965.76	+	4405.34i	−0.557861	+	0.494903i
$39$		0			0
$40$	−10869.5	+	899.918i	−1.07414	+	0.0889310i
$41$	7969.76	+	4601.35i	0.740433	+	0.427489i	0.822227	−	0.569160i	$-0.192732\pi$
$41$	7969.76	+	4601.35i	0.740433	+	0.427489i	−0.0817937	+	0.996649i	$0.526065\pi$
$42$		0			0
$43$	−1061.38	+	612.787i	−0.0875384	+	0.0505403i	−0.543130	−	0.839648i	$-0.682761\pi$
$43$	−1061.38	+	612.787i	−0.0875384	+	0.0505403i	0.455592	+	0.890189i	$0.349428\pi$
$44$	−10919.8	+	4670.13i	−0.850319	+	0.363661i
$45$		0			0
$46$	−21949.8	+	4496.72i	−1.52945	+	0.313330i
$47$	−1222.66	−	2117.71i	−0.0807348	−	0.139837i	0.822831	−	0.568286i	$-0.192393\pi$
$47$	−1222.66	−	2117.71i	−0.0807348	−	0.139837i	−0.903566	+	0.428449i	$0.859060\pi$
$48$		0			0
$49$	14491.1	−	25099.3i	0.862206	−	1.49338i
$50$	−903.210	+	2711.61i	−0.0510933	+	0.153392i
$51$		0			0
$52$	20628.1	+	15456.9i	1.05791	+	0.792709i
$53$		−	20212.4i		−	0.988390i	−0.869351	−	0.494195i	$-0.835463\pi$
$53$		−	20212.4i		−	0.988390i	0.869351	−	0.494195i	$-0.164537\pi$
$54$		0			0
$55$			22361.8i			0.996781i
$56$	−16533.7	+	35029.4i	−0.704531	+	1.49266i
$57$		0			0
$58$	2372.88	+	790.381i	0.0926202	+	0.0308508i
$59$	1704.67	−	2952.58i	0.0637546	−	0.110426i	−0.832386	−	0.554196i	$-0.813026\pi$
$59$	1704.67	−	2952.58i	0.0637546	−	0.110426i	0.896141	+	0.443770i	$0.146359\pi$
$60$		0			0
$61$	−19919.9	−	34502.3i	−0.685430	−	1.18720i	−0.973302	−	0.229530i	$-0.926281\pi$
$61$	−19919.9	−	34502.3i	−0.685430	−	1.18720i	0.287872	−	0.957669i	$-0.407052\pi$
$62$	1810.77	+	8838.89i	0.0598251	+	0.292024i
$63$		0			0
$64$	11493.9	−	30686.0i	0.350767	−	0.936463i
$65$	42031.4	−	24266.8i	1.23393	−	0.712410i
$66$		0			0
$67$	−6088.22	−	3515.04i	−0.165693	−	0.0956627i	0.414861	−	0.909885i	$-0.363830\pi$
$67$	−6088.22	−	3515.04i	−0.165693	−	0.0956627i	−0.580553	+	0.814222i	$0.697164\pi$
$68$	1082.48	+	129.935i	0.0283889	+	0.00340765i
$69$		0			0
$70$	48400.9	+	54558.1i	1.18061	+	1.33080i
$71$	−25694.1			−0.604905			−0.302453	−	0.953164i	$-0.597805\pi$
$71$	−25694.1			−0.604905			−0.302453	+	0.953164i	$0.597805\pi$
$72$		0			0
$73$	65431.6			1.43708			0.718540	−	0.695486i	$-0.244811\pi$
$73$	65431.6			1.43708			0.718540	+	0.695486i	$0.244811\pi$
$74$	−41511.2	−	46792.0i	−0.881223	−	0.993326i
$75$		0			0
$76$	−37283.7	−	4475.34i	−0.740432	−	0.0888776i
$77$	68778.2	+	39709.1i	1.32198	+	0.763244i
$78$		0			0
$79$	41126.9	−	23744.6i	0.741409	−	0.428053i	−0.0811725	−	0.996700i	$-0.525866\pi$
$79$	41126.9	−	23744.6i	0.741409	−	0.428053i	0.822581	+	0.568647i	$0.192533\pi$
$80$	−44613.1	−	42617.5i	−0.779359	−	0.744498i
$81$		0			0
$82$	10447.9	+	50999.1i	0.171590	+	0.837583i
$83$	−6605.97	−	11441.9i	−0.105255	−	0.182306i	0.808588	−	0.588376i	$-0.200232\pi$
$83$	−6605.97	−	11441.9i	−0.105255	−	0.182306i	−0.913842	+	0.406069i	$0.866899\pi$
$84$		0			0
$85$	1026.39	−	1777.77i	0.0154087	−	0.0266887i
$86$	−6577.60	−	2190.93i	−0.0959005	−	0.0319435i
$87$		0			0
$88$	−60756.1	−	28676.6i	−0.836340	−	0.394749i
$89$		−	85682.2i		−	1.14661i	−0.819342	−	0.573305i	$-0.805661\pi$
$89$		−	85682.2i		−	1.14661i	0.819342	−	0.573305i	$-0.194339\pi$
$90$		0			0
$91$		−	172368.i		−	2.18199i
$92$	−101430.	−	76003.0i	−1.24939	−	0.936183i
$93$		0			0
$94$	4371.44	−	13123.9i	0.0510275	−	0.153195i
$95$	−35352.0	+	61231.4i	−0.401887	+	0.696089i
$96$		0			0
$97$	−27944.9	−	48402.0i	−0.301560	−	0.522317i	0.674929	−	0.737882i	$-0.264174\pi$
$97$	−27944.9	−	48402.0i	−0.301560	−	0.522317i	−0.976490	+	0.215565i	$0.930841\pi$
$98$	160612.	−	32903.6i	1.68933	−	0.346082i
$99$		0			0
$100$	−14865.3	+	6357.56i	−0.148653	+	0.0635756i
$101$	−79337.0	+	45805.2i	−0.773878	+	0.446799i	−0.834256	−	0.551377i	$-0.814103\pi$
$101$	−79337.0	+	45805.2i	−0.773878	+	0.446799i	0.0603784	+	0.998176i	$0.480769\pi$
$102$		0			0
$103$	91488.4	+	52820.9i	0.849715	+	0.490583i	0.860555	−	0.509358i	$-0.170117\pi$
$103$	91488.4	+	52820.9i	0.849715	+	0.490583i	−0.0108398	+	0.999941i	$0.503450\pi$
$104$	12031.2	+	145317.i	0.109076	+	1.31745i
$105$		0			0
$106$	85531.8	−	75879.0i	0.739372	−	0.655929i
$107$	−3806.62			−0.0321426			−0.0160713	−	0.999871i	$-0.505116\pi$
$107$	−3806.62			−0.0321426			−0.0160713	+	0.999871i	$0.505116\pi$
$108$		0			0
$109$	−85149.1			−0.686458			−0.343229	−	0.939252i	$-0.611521\pi$
$109$	−85149.1			−0.686458			−0.343229	+	0.939252i	$0.611521\pi$
$110$	−94627.3	+	83948.0i	−0.745649	+	0.661498i
$111$		0			0
$112$	−210301.	+	61538.3i	−1.58415	+	0.463554i
$113$	36754.5	+	21220.2i	0.270778	+	0.156334i	0.629241	−	0.777210i	$-0.283366\pi$
$113$	36754.5	+	21220.2i	0.270778	+	0.156334i	−0.358463	+	0.933544i	$0.616699\pi$
$114$		0			0
$115$	−206672.	+	119322.i	−1.45726	+	0.841350i
$116$	5563.37	+	13008.3i	0.0383877	+	0.0897588i
$117$		0			0
$118$	18893.8	−	3870.65i	0.124915	−	0.0255905i
$119$	−3645.26	−	6313.77i	−0.0235972	−	0.0408716i
$120$		0			0
$121$	11652.7	−	20183.1i	0.0723543	−	0.125321i
$122$	71220.7	−	213819.i	0.433218	−	1.30061i
$123$		0			0
$124$	−30605.3	+	40844.5i	−0.178749	+	0.238550i
$125$		−	157844.i		−	0.903553i
$126$		0			0
$127$			37078.8i			0.203994i	0.994785	+	0.101997i	$0.0325232\pi$
$127$			37078.8i			0.203994i	−0.994785	+	0.101997i	$0.967477\pi$
$128$	173002.	−	66559.6i	0.933309	−	0.359075i
$129$		0			0
$130$	260478.	+	86762.5i	1.35180	+	0.450271i
$131$	83730.6	−	145026.i	0.426291	−	0.738357i	−0.570249	−	0.821472i	$-0.693153\pi$
$131$	83730.6	−	145026.i	0.426291	−	0.738357i	0.996540	+	0.0831144i	$0.0264867\pi$
$132$		0			0
$133$	125553.	+	217464.i	0.615457	+	1.06600i
$134$	−7981.28	−	38959.0i	−0.0383982	−	0.187433i
$135$		0			0
$136$	3513.88	+	5068.47i	0.0162907	+	0.0234979i
$137$	−298026.	+	172065.i	−1.35660	+	0.783234i	−0.989164	−	0.146814i	$-0.953098\pi$
$137$	−298026.	+	172065.i	−1.35660	+	0.783234i	−0.367438	+	0.930048i	$0.619765\pi$
$138$		0			0
$139$	239133.	+	138064.i	1.04979	+	0.606097i	0.922591	−	0.385780i	$-0.126068\pi$
$139$	239133.	+	138064.i	1.04979	+	0.606097i	0.127200	+	0.991877i	$0.459401\pi$
$140$	−49170.0	+	409631.i	−0.212021	+	1.76633i
$141$		0			0
$142$	−96457.7	−	108728.i	−0.401436	−	0.452504i
$143$	298961.			1.22257
$144$		0			0
$145$	26638.8			0.105219
$146$	245636.	+	276884.i	0.953695	+	1.07502i
$147$		0			0
$148$	42170.8	−	351322.i	0.158255	−	1.31841i
$149$	−33899.5	−	19571.9i	−0.125091	−	0.0722216i	0.436149	−	0.899875i	$-0.356342\pi$
$149$	−33899.5	−	19571.9i	−0.125091	−	0.0722216i	−0.561240	+	0.827653i	$0.689676\pi$
$150$		0			0
$151$	−372275.	+	214933.i	−1.32868	+	0.767115i	−0.985096	−	0.172006i	$-0.944975\pi$
$151$	−372275.	+	214933.i	−1.32868	+	0.767115i	−0.343587	+	0.939121i	$0.611642\pi$
$152$	−121028.	−	174572.i	−0.424890	−	0.612868i
$153$		0			0
$154$	90163.9	+	440117.i	0.306359	+	1.49543i
$155$	48049.4	+	83224.0i	0.160642	+	0.278240i
$156$		0			0
$157$	−283488.	+	491016.i	−0.917881	+	1.58982i	−0.115252	+	0.993336i	$0.536768\pi$
$157$	−283488.	+	491016.i	−0.917881	+	1.58982i	−0.802628	+	0.596479i	$0.796566\pi$
$158$	254872.	+	84895.3i	0.812232	+	0.270546i
$159$		0			0
$160$	12861.2	−	348777.i	0.0397176	−	1.07708i
$161$			847550.i			2.57692i
$162$		0			0
$163$		−	50545.5i		−	0.149009i	−0.997221	−	0.0745047i	$-0.976262\pi$
$163$		−	50545.5i		−	0.149009i	0.997221	−	0.0745047i	$-0.0237376\pi$
$164$	−176588.	+	235666.i	−0.512687	+	0.684208i
$165$		0			0
$166$	23618.7	−	70907.9i	0.0665250	−	0.199721i
$167$	−155078.	+	268602.i	−0.430287	+	0.745279i	−0.996898	−	0.0787068i	$-0.974921\pi$
$167$	−155078.	+	268602.i	−0.430287	+	0.745279i	0.566611	+	0.823985i	$0.308254\pi$
$168$		0			0
$169$	−138783.	−	240380.i	−0.373784	−	0.647413i
$170$	11376.1	−	2330.54i	0.0301905	−	0.00618493i
$171$		0			0
$172$	−15421.6	−	36059.0i	−0.0397474	−	0.0929379i
$173$	140517.	−	81127.6i	0.356955	−	0.206088i	−0.310789	−	0.950479i	$-0.600593\pi$
$173$	140517.	−	81127.6i	0.356955	−	0.206088i	0.667744	+	0.744391i	$0.267260\pi$
$174$		0			0
$175$	93629.4	+	54056.9i	0.231109	+	0.133431i
$176$	−106734.	−	364753.i	−0.259729	−	0.887599i
$177$		0			0
$178$	362577.	−	321658.i	0.857729	−	0.760929i
$179$	−313216.			−0.730653			−0.365326	−	0.930880i	$-0.619043\pi$
$179$	−313216.			−0.730653			−0.365326	+	0.930880i	$0.619043\pi$
$180$		0			0
$181$	241414.			0.547729			0.273865	−	0.961768i	$-0.411698\pi$
$181$	241414.			0.547729			0.273865	+	0.961768i	$0.411698\pi$
$182$	729402.	−	647084.i	1.63226	−	1.44805i
$183$		0			0
$184$	−59158.7	−	714538.i	−0.128817	−	1.55590i
$185$	−576979.	−	333119.i	−1.23945	−	0.715599i
$186$		0			0
$187$	10950.8	−	6322.45i	0.0229003	−	0.0132215i
$188$	71946.6	−	30769.9i	0.148462	−	0.0634938i
$189$		0			0
$190$	−391824.	+	80270.5i	−0.787421	+	0.161314i
$191$	−378078.	−	654851.i	−0.749891	−	1.29885i	−0.947874	−	0.318644i	$-0.896773\pi$
$191$	−378078.	−	654851.i	−0.749891	−	1.29885i	0.197983	−	0.980205i	$-0.436561\pi$
$192$		0			0
$193$	−210750.	+	365029.i	−0.407262	+	0.705398i	−0.994582	−	0.103957i	$-0.966850\pi$
$193$	−210750.	+	365029.i	−0.407262	+	0.705398i	0.587320	+	0.809355i	$0.300183\pi$
$194$	99913.0	−	299958.i	0.190598	−	0.572212i
$195$		0			0
$196$	742188.	+	556132.i	1.37998	+	1.03404i
$197$		−	796004.i		−	1.46133i	−0.682734	−	0.730667i	$-0.739209\pi$
$197$		−	796004.i		−	1.46133i	0.682734	−	0.730667i	$-0.260791\pi$
$198$		0			0
$199$		−	1.10972e6i		−	1.98646i	−0.116163	−	0.993230i	$-0.537060\pi$
$199$		−	1.10972e6i		−	1.98646i	0.116163	−	0.993230i	$-0.462940\pi$
$200$	−82708.6	−	39038.1i	−0.146210	−	0.0690103i
$201$		0			0
$202$	−491669.	−	163770.i	−0.847803	−	0.282394i
$203$	47304.1	−	81933.1i	0.0805673	−	0.139547i
$204$		0			0
$205$	277238.	+	480190.i	0.460753	+	0.798047i
$206$	119936.	+	585441.i	0.196916	+	0.961203i
$207$		0			0
$208$	−569765.	+	596445.i	−0.913141	+	0.955899i
$209$	−377177.	+	217763.i	−0.597282	+	0.344841i
$210$		0			0
$211$	−179473.	−	103619.i	−0.277520	−	0.160226i	0.354780	−	0.934950i	$-0.384556\pi$
$211$	−179473.	−	103619.i	−0.277520	−	0.160226i	−0.632300	+	0.774724i	$0.717889\pi$
$212$	642187.	+	77084.7i	0.981345	+	0.117796i
$213$		0			0
$214$	−14290.4	−	16108.3i	−0.0213309	−	0.0240445i
$215$	−73842.6			−0.108946
$216$		0			0
$217$	341296.			0.492020
$218$	−319657.	−	360321.i	−0.455557	−	0.513510i
$219$		0			0
$220$	−710477.	−	85282.0i	−0.989677	−	0.118796i
$221$	−23767.5	−	13722.1i	−0.0327342	−	0.0188991i
$222$		0			0
$223$	557586.	−	321922.i	0.750844	−	0.433500i	−0.0751547	−	0.997172i	$-0.523945\pi$
$223$	557586.	−	321922.i	0.750844	−	0.433500i	0.825999	+	0.563672i	$0.190612\pi$
$224$	−1.04990e6	−	658901.i	−1.39806	−	0.877404i
$225$		0			0
$226$	48182.8	+	235194.i	0.0627511	+	0.306306i
$227$	596328.	+	1.03287e6i	0.768105	+	1.33040i	0.938589	+	0.345036i	$0.112133\pi$
$227$	596328.	+	1.03287e6i	0.768105	+	1.33040i	−0.170485	+	0.985360i	$0.554533\pi$
$228$		0			0
$229$	538232.	−	932245.i	0.678236	−	1.17474i	−0.297276	−	0.954792i	$-0.596078\pi$
$229$	538232.	−	932245.i	0.678236	−	1.17474i	0.975512	−	0.219947i	$-0.0705886\pi$
$230$	−1.28079e6	−	426619.i	−1.59647	−	0.531766i
$231$		0			0
$232$	−34161.4	+	72376.6i	−0.0416693	+	0.0882833i
$233$			178167.i			0.214999i	0.994205	+	0.107500i	$0.0342845\pi$
$233$			178167.i			0.214999i	−0.994205	+	0.107500i	$0.965716\pi$
$234$		0			0
$235$		−	147334.i		−	0.174034i
$236$	87308.1	+	65421.2i	0.102041	+	0.0764607i
$237$		0			0
$238$	13033.1	−	39127.9i	0.0149144	−	0.0447758i
$239$	336873.	−	583482.i	0.381480	−	0.660743i	−0.609794	−	0.792560i	$-0.708748\pi$
$239$	336873.	−	583482.i	0.381480	−	0.660743i	0.991274	+	0.131817i	$0.0420811\pi$
$240$		0			0
$241$	−162984.	−	282297.i	−0.180760	−	0.313086i	0.761379	−	0.648307i	$-0.224522\pi$
$241$	−162984.	−	282297.i	−0.180760	−	0.313086i	−0.942140	+	0.335221i	$0.891189\pi$
$242$	129153.	−	26458.8i	0.141764	−	0.0290424i
$243$		0			0
$244$	1.17217e6	−	501311.i	1.26043	−	0.539055i
$245$	1.51227e6	−	873110.i	1.60959	−	0.929296i
$246$		0			0
$247$	818619.	+	472630.i	0.853767	+	0.492922i
$248$	−287734.	+	23822.4i	−0.297073	+	0.0245955i
$249$		0			0
$250$	667942.	−	592560.i	0.675910	−	0.599629i
$251$	−1.32110e6			−1.32358			−0.661789	−	0.749690i	$-0.730203\pi$
$251$	−1.32110e6			−1.32358			−0.661789	+	0.749690i	$0.730203\pi$
$252$		0			0
$253$	−1.47002e6			−1.44385
$254$	−156905.	+	139197.i	−0.152599	+	0.135377i
$255$		0			0
$256$	931119.	+	482212.i	0.887984	+	0.459873i
$257$	1.15605e6	+	667444.i	1.09180	+	0.630350i	0.934055	−	0.357130i	$-0.116245\pi$
$257$	1.15605e6	+	667444.i	1.09180	+	0.630350i	0.157744	+	0.987480i	$0.449578\pi$
$258$		0			0
$259$	−2.04915e6	+	1.18308e6i	−1.89812	+	1.09588i
$260$	610708.	+	1.42797e6i	0.560273	+	1.31004i
$261$		0			0
$262$	928030.	−	190120.i	0.835235	−	0.171109i
$263$	−457251.	−	791982.i	−0.407629	−	0.706035i	0.586994	−	0.809591i	$-0.300311\pi$
$263$	−457251.	−	791982.i	−0.407629	−	0.706035i	−0.994624	+	0.103556i	$0.966978\pi$
$264$		0			0
$265$	608914.	−	1.05467e6i	0.532649	−	0.922575i
$266$	−448896.	+	1.34767e6i	−0.388993	+	1.16783i
$267$		0			0
$268$	134898.	−	180029.i	0.114728	−	0.153111i
$269$			1.86227e6i			1.56914i	0.620038	+	0.784572i	$0.287117\pi$
$269$			1.86227e6i			1.56914i	−0.620038	+	0.784572i	$0.712883\pi$
$270$		0			0
$271$			517756.i			0.428254i	0.976806	+	0.214127i	$0.0686907\pi$
$271$			517756.i			0.428254i	−0.976806	+	0.214127i	$0.931309\pi$
$272$	−8256.59	+	33897.0i	−0.00676672	+	0.0277804i
$273$		0			0
$274$	−1.84693e6	−	615194.i	−1.48619	−	0.495035i
$275$	−93758.1	+	162394.i	−0.0747613	+	0.129490i
$276$		0			0
$277$	−311881.	−	540194.i	−0.244225	−	0.423010i	0.717689	−	0.696364i	$-0.245200\pi$
$277$	−311881.	−	540194.i	−0.244225	−	0.423010i	−0.961913	+	0.273354i	$0.911867\pi$
$278$	313489.	+	1.53023e6i	0.243282	+	1.18753i
$279$		0			0
$280$	−1.91800e6	+	1.32972e6i	−1.46202	+	1.01360i
$281$	1.53273e6	−	884922.i	1.15798	−	0.668558i	0.207159	−	0.978307i	$-0.433578\pi$
$281$	1.53273e6	−	884922.i	1.15798	−	0.668558i	0.950818	+	0.309749i	$0.100245\pi$
$282$		0			0
$283$	1.28654e6	+	742782.i	0.954895	+	0.551309i	0.894598	−	0.446871i	$-0.147462\pi$
$283$	1.28654e6	+	742782.i	0.954895	+	0.551309i	0.0602971	+	0.998180i	$0.480795\pi$
$284$	97990.5	−	816351.i	0.0720921	−	0.600594i
$285$		0			0
$286$	1.12232e6	+	1.26510e6i	0.811340	+	0.914553i
$287$	1.96923e6			1.41121
$288$		0			0
$289$	1.41870e6			0.999182
$290$	100004.	+	112726.i	0.0698271	+	0.0787100i
$291$		0			0
$292$	−249539.	+	2.07889e6i	−0.171270	+	1.42684i
$293$	−1.40797e6	−	812891.i	−0.958129	−	0.553176i	−0.0625325	−	0.998043i	$-0.519918\pi$
$293$	−1.40797e6	−	812891.i	−0.958129	−	0.553176i	−0.895597	+	0.444867i	$0.853251\pi$
$294$		0			0
$295$	177898.	−	102709.i	0.119019	−	0.0687154i
$296$	1.64498e6	−	1.14044e6i	1.09127	−	0.756559i
$297$		0			0
$298$	−44440.1	−	216925.i	−0.0289891	−	0.141504i
$299$	1.59525e6	+	2.76306e6i	1.03193	+	1.78736i
$300$		0			0
$301$	−131127.	+	227118.i	−0.0834208	+	0.144489i
$302$	−2.30707e6	−	768461.i	−1.45561	−	0.484847i
$303$		0			0
$304$	284380.	−	1.16751e6i	0.176488	−	0.724562i
$305$		−	2.40041e6i		−	1.47753i
$306$		0			0
$307$			29930.7i			0.0181247i	0.999959	+	0.00906235i	$0.00288467\pi$
$307$			29930.7i			0.0181247i	−0.999959	+	0.00906235i	$0.997115\pi$
$308$	−1.52394e6	+	2.03378e6i	−0.915357	+	1.22159i
$309$		0			0
$310$	−171794.	+	515758.i	−0.101532	+	0.304819i
$311$	828429.	−	1.43488e6i	0.485685	−	0.841231i	−0.514180	−	0.857682i	$-0.671904\pi$
$311$	828429.	−	1.43488e6i	0.485685	−	0.841231i	0.999865	+	0.0164516i	$0.00523694\pi$
$312$		0			0
$313$	−1.49316e6	−	2.58623e6i	−0.861482	−	1.49213i	−0.870498	−	0.492171i	$-0.836203\pi$
$313$	−1.49316e6	−	2.58623e6i	−0.861482	−	1.49213i	0.00901652	−	0.999959i	$-0.497130\pi$
$314$	−3.14205e6	+	643692.i	−1.79841	+	0.368429i
$315$		0			0
$316$	597565.	+	1.39724e6i	0.336641	+	0.787140i
$317$	−748156.	+	431948.i	−0.418162	+	0.241426i	−0.694290	−	0.719695i	$-0.744282\pi$
$317$	−748156.	+	431948.i	−0.418162	+	0.241426i	0.276129	+	0.961121i	$0.410948\pi$
$318$		0			0
$319$	142107.	+	82045.8i	0.0781880	+	0.0451419i
$320$	1.52418e6	−	1.25491e6i	0.832075	−	0.685076i
$321$		0			0
$322$	−3.58653e6	+	3.18177e6i	−1.92768	+	1.71013i
$323$	39980.9			0.0213229
$324$		0			0
$325$	406982.			0.213731
$326$	213891.	−	189752.i	0.111468	−	0.0988877i
$327$		0			0
$328$	−1.66018e6	+	137452.i	−0.852063	+	0.0705449i
$329$	−453156.	−	261630.i	−0.230812	−	0.133259i
$330$		0			0
$331$	−1828.81	+	1055.86i	−0.000917484	+	0.000529710i	−0.500459	−	0.865760i	$-0.666835\pi$
$331$	−1828.81	+	1055.86i	−0.000917484	+	0.000529710i	0.499541	+	0.866290i	$0.333502\pi$
$332$	388724.	−	166248.i	0.193551	−	0.0827773i
$333$		0			0
$334$	−1.71881e6	+	352121.i	−0.843064	+	0.172713i
$335$	−211786.	−	366824.i	−0.103106	−	0.178586i
$336$		0			0
$337$	−1.24422e6	+	2.15505e6i	−0.596790	+	1.03367i	0.396501	+	0.918034i	$0.370224\pi$
$337$	−1.24422e6	+	2.15505e6i	−0.596790	+	1.03367i	−0.993292	+	0.115637i	$0.963109\pi$
$338$	496200.	−	1.48969e6i	0.236246	−	0.709257i
$339$		0			0
$340$	52568.7	+	39390.5i	0.0246621	+	0.0184797i
$341$			591955.i			0.275679i
$342$		0			0
$343$		−	2.60530e6i		−	1.19570i
$344$	94695.2	−	200627.i	0.0431451	−	0.0914100i
$345$		0			0
$346$	870816.	+	290060.i	0.391054	+	0.130256i
$347$	−1.65555e6	+	2.86750e6i	−0.738106	+	1.27844i	0.215241	+	0.976561i	$0.430946\pi$
$347$	−1.65555e6	+	2.86750e6i	−0.738106	+	1.27844i	−0.953347	+	0.301877i	$0.902387\pi$
$348$		0			0
$349$	−131505.	−	227773.i	−0.0577934	−	0.100101i	0.835681	−	0.549215i	$-0.185073\pi$
$349$	−131505.	−	227773.i	−0.0577934	−	0.100101i	−0.893475	+	0.449114i	$0.851740\pi$
$350$	122742.	+	599141.i	0.0535580	+	0.261432i
$351$		0			0
$352$	1.14282e6	−	1.82097e6i	0.491610	−	0.783333i
$353$	−127875.	+	73828.9i	−0.0546198	+	0.0315347i	−0.527061	−	0.849827i	$-0.676706\pi$
$353$	−127875.	+	73828.9i	−0.0546198	+	0.0315347i	0.472441	+	0.881362i	$0.343373\pi$
$354$		0			0
$355$	−1.34070e6	−	774054.i	−0.564626	−	0.325987i
$356$	2.72229e6	+	326769.i	1.13844	+	0.136652i
$357$		0			0
$358$	−1.17584e6	−	1.32542e6i	−0.484886	−	0.546570i
$359$	−1.46738e6			−0.600905			−0.300453	−	0.953797i	$-0.597138\pi$
$359$	−1.46738e6			−0.600905			−0.300453	+	0.953797i	$0.597138\pi$
$360$		0			0
$361$	1.09904e6			0.443861
$362$	906288.	+	1.02158e6i	0.363492	+	0.409733i
$363$		0			0
$364$	5.47647e6	+	657366.i	2.16644	+	0.260048i
$365$	3.41418e6	+	1.97118e6i	1.34139	+	0.774450i
$366$		0			0
$367$	1.76458e6	−	1.01878e6i	0.683874	−	0.394835i	−0.117439	−	0.993080i	$-0.537468\pi$
$367$	1.76458e6	−	1.01878e6i	0.683874	−	0.394835i	0.801313	+	0.598245i	$0.204135\pi$
$368$	2.80159e6	−	2.93277e6i	1.07841	−	1.12891i
$369$		0			0
$370$	−756383.	−	3.69213e6i	−0.287235	−	1.40208i
$371$	−2.16257e6	−	3.74567e6i	−0.815708	−	1.41285i
$372$		0			0
$373$	629011.	−	1.08948e6i	0.234092	−	0.405459i	−0.724917	−	0.688837i	$-0.758122\pi$
$373$	629011.	−	1.08948e6i	0.234092	−	0.405459i	0.959008	+	0.283378i	$0.0914551\pi$
$374$	67864.6	+	22605.0i	0.0250879	+	0.00835652i
$375$		0			0
$376$	400301.	+	188940.i	0.146021	+	0.0689215i
$377$		−	356142.i		−	0.129053i
$378$		0			0
$379$			3.51959e6i			1.25862i	0.777154	+	0.629310i	$0.216662\pi$
$379$			3.51959e6i			1.25862i	−0.777154	+	0.629310i	$0.783338\pi$
$380$	−1.81062e6	−	1.35672e6i	−0.643232	−	0.481982i
$381$		0			0
$382$	1.35176e6	−	4.05826e6i	0.473960	−	1.42292i
$383$	−1.45304e6	+	2.51675e6i	−0.506153	+	0.876683i	0.493822	+	0.869563i	$0.335600\pi$
$383$	−1.45304e6	+	2.51675e6i	−0.506153	+	0.876683i	−0.999975	+	0.00711941i	$0.997734\pi$
$384$		0			0
$385$	2.39253e6	+	4.14399e6i	0.822633	+	1.42484i
$386$	−2.33585e6	+	478530.i	−0.797951	+	0.163471i
$387$		0			0
$388$	1.64440e6	−	703272.i	0.554534	−	0.237161i
$389$	−3.99038e6	+	2.30384e6i	−1.33703	+	0.771932i	−0.986365	−	0.164570i	$-0.947376\pi$
$389$	−3.99038e6	+	2.30384e6i	−1.33703	+	0.771932i	−0.350660	+	0.936503i	$0.614043\pi$
$390$		0			0
$391$	116867.	+	67473.0i	0.0386589	+	0.0223197i
$392$	432879.	+	5.22845e6i	0.142282	+	1.71853i
$393$		0			0
$394$	3.36841e6	−	2.98826e6i	1.09316	−	0.969791i
$395$	2.86130e6			0.922720
$396$		0			0
$397$	−1.37551e6			−0.438012			−0.219006	−	0.975723i	$-0.570281\pi$
$397$	−1.37551e6			−0.438012			−0.219006	+	0.975723i	$0.570281\pi$
$398$	4.69594e6	−	4.16597e6i	1.48599	−	1.31828i
$399$		0			0
$400$	−145299.	−	496546.i	−0.0454060	−	0.155171i
$401$	−93720.9	−	54109.8i	−0.0291055	−	0.0168041i	0.485377	−	0.874305i	$-0.338682\pi$
$401$	−93720.9	−	54109.8i	−0.0291055	−	0.0168041i	−0.514482	+	0.857501i	$0.672016\pi$
$402$		0			0
$403$	1.11264e6	−	642385.i	0.341266	−	0.197030i
$404$	−1.15275e6	−	2.69538e6i	−0.351384	−	0.821611i
$405$		0			0
$406$	524296.	−	107409.i	0.157856	−	0.0323390i
$407$	−2.05197e6	−	3.55411e6i	−0.614022	−	1.06352i
$408$		0			0
$409$	−903457.	+	1.56483e6i	−0.267054	+	0.462551i	−0.968100	−	0.250565i	$-0.919384\pi$
$409$	−903457.	+	1.56483e6i	−0.267054	+	0.462551i	0.701046	+	0.713116i	$0.252717\pi$
$410$	−991223.	+	2.97585e6i	−0.291214	+	0.874281i
$411$		0			0
$412$	−2.02713e6	+	2.70532e6i	−0.588355	+	0.785191i
$413$		−	729546.i		−	0.210464i
$414$		0			0
$415$		−	796039.i		−	0.226889i
$416$	−4.66289e6	−	171945.i	−1.32106	−	0.0487144i
$417$		0			0
$418$	−2.33745e6	−	778580.i	−0.654337	−	0.217953i
$419$	926212.	−	1.60425e6i	0.257736	−	0.446412i	−0.707899	−	0.706314i	$-0.750357\pi$
$419$	926212.	−	1.60425e6i	0.257736	−	0.446412i	0.965635	+	0.259902i	$0.0836901\pi$
$420$		0			0
$421$	1.85582e6	+	3.21437e6i	0.510305	+	0.883874i	0.999929	+	0.0119403i	$0.00380082\pi$
$421$	1.85582e6	+	3.21437e6i	0.510305	+	0.883874i	−0.489624	+	0.871934i	$0.662866\pi$
$422$	−235278.	−	1.14846e6i	−0.0643133	−	0.313932i
$423$		0			0
$424$	2.08463e6	+	3.00689e6i	0.563137	+	0.812276i
$425$	14907.6	−	8606.90i	0.00400346	−	0.00231140i
$426$		0			0
$427$	−7.38295e6	−	4.26255e6i	−1.95957	−	1.13136i
$428$	14517.5	−	120944.i	0.00383073	−	0.0319135i
$429$		0			0
$430$	−277211.	−	312476.i	−0.0723002	−	0.0814978i
$431$	−277886.			−0.0720565			−0.0360283	−	0.999351i	$-0.511471\pi$
$431$	−277886.			−0.0720565			−0.0360283	+	0.999351i	$0.511471\pi$
$432$		0			0
$433$	−2.49224e6			−0.638807			−0.319403	−	0.947619i	$-0.603482\pi$
$433$	−2.49224e6			−0.638807			−0.319403	+	0.947619i	$0.603482\pi$
$434$	1.28125e6	+	1.44425e6i	0.326521	+	0.368059i
$435$		0			0
$436$	324736.	−	2.70535e6i	0.0818115	−	0.681565i
$437$	−4.02522e6	−	2.32396e6i	−1.00829	−	0.582138i
$438$		0			0
$439$	1.04465e6	−	603126.i	0.258707	−	0.149364i	−0.365038	−	0.930993i	$-0.618944\pi$
$439$	1.04465e6	−	603126.i	0.258707	−	0.149364i	0.623744	+	0.781628i	$0.285611\pi$
$440$	−2.30631e6	−	3.32665e6i	−0.567918	−	0.819172i
$441$		0			0
$442$	−31157.6	−	152090.i	−0.00758593	−	0.0370292i
$443$	1.30812e6	+	2.26572e6i	0.316692	+	0.548526i	0.979796	−	0.200001i	$-0.0640946\pi$
$443$	1.30812e6	+	2.26572e6i	0.316692	+	0.548526i	−0.663104	+	0.748527i	$0.730761\pi$
$444$		0			0
$445$	2.58124e6	−	4.47084e6i	0.617914	−	1.07026i
$446$	3.45549e6	+	1.15099e6i	0.822569	+	0.273989i
$447$		0			0
$448$	−1.15316e6	−	6.91636e6i	−0.271452	−	1.62810i
$449$		−	348912.i		−	0.0816770i	−0.999166	−	0.0408385i	$-0.986997\pi$
$449$		−	348912.i		−	0.0816770i	0.999166	−	0.0408385i	$-0.0130029\pi$
$450$		0			0
$451$			3.41549e6i			0.790701i
$452$	−814379.	+	1.08683e6i	−0.187491	+	0.250217i
$453$		0			0
$454$	−2.13208e6	+	6.40093e6i	−0.485472	+	1.45748i
$455$	5.19272e6	−	8.99405e6i	1.17589	−	2.03670i
$456$		0			0
$457$	1.71163e6	+	2.96463e6i	0.383371	+	0.664018i	0.991542	−	0.129788i	$-0.0414297\pi$
$457$	1.71163e6	+	2.96463e6i	0.383371	+	0.664018i	−0.608171	+	0.793806i	$0.708096\pi$
$458$	5.96550e6	−	1.22211e6i	1.32887	−	0.272238i
$459$		0			0
$460$	−3.00291e6	−	7.02144e6i	−0.661679	−	1.54715i
$461$	−4.70141e6	+	2.71436e6i	−1.03033	+	0.594861i	−0.917079	−	0.398705i	$-0.869460\pi$
$461$	−4.70141e6	+	2.71436e6i	−1.03033	+	0.594861i	−0.113251	+	0.993566i	$0.536126\pi$
$462$		0			0
$463$	3.74259e6	+	2.16079e6i	0.811373	+	0.468446i	0.847432	−	0.530903i	$-0.178147\pi$
$463$	3.74259e6	+	2.16079e6i	0.811373	+	0.468446i	−0.0360597	+	0.999350i	$0.511481\pi$
$464$	−434517.	+	127148.i	−0.0936941	+	0.0274168i
$465$		0			0
$466$	−753940.	+	668853.i	−0.160832	+	0.142681i
$467$	−3.41339e6			−0.724258			−0.362129	−	0.932128i	$-0.617950\pi$
$467$	−3.41339e6			−0.724258			−0.362129	+	0.932128i	$0.617950\pi$
$468$		0			0
$469$	−1.50432e6			−0.315798
$470$	623466.	−	553104.i	0.130187	−	0.115495i
$471$		0			0
$472$	50922.1	+	615054.i	0.0105209	+	0.127074i
$473$	−393921.	−	227430.i	−0.0809572	−	0.0467407i
$474$		0			0
$475$	−513459.	+	296446.i	−0.104417	+	0.0602853i
$476$	214503.	−	91737.8i	0.0433926	−	0.0185580i
$477$		0			0
$478$	3.73374e6	−	764908.i	0.747437	−	0.153123i
$479$	1.30808e6	+	2.26567e6i	0.260493	+	0.451188i	0.966373	−	0.257144i	$-0.0827814\pi$
$479$	1.30808e6	+	2.26567e6i	0.260493	+	0.451188i	−0.705880	+	0.708332i	$0.749448\pi$
$480$		0			0
$481$	−4.45356e6	+	7.71378e6i	−0.877696	+	1.52021i
$482$	582726.	−	1.74946e6i	0.114247	−	0.342994i
$483$		0			0
$484$	596816.	+	447203.i	0.115805	+	0.0867743i
$485$		−	3.36745e6i		−	0.650050i
$486$		0			0
$487$			8.58357e6i			1.64001i	0.572359	+	0.820003i	$0.306029\pi$
$487$			8.58357e6i			1.64001i	−0.572359	+	0.820003i	$0.693971\pi$
$488$	6.52181e6	+	3.07827e6i	1.23971	+	0.585136i
$489$		0			0
$490$	9.37189e6	+	3.12168e6i	1.76334	+	0.587351i
$491$	−4.45187e6	+	7.71087e6i	−0.833372	+	1.44344i	0.0619764	+	0.998078i	$0.480260\pi$
$491$	−4.45187e6	+	7.71087e6i	−0.833372	+	1.44344i	−0.895349	+	0.445366i	$0.853074\pi$
$492$		0			0
$493$	−7531.72	−	13045.3i	−0.00139565	−	0.00241734i
$494$	1.07316e6	+	5.23840e6i	0.197855	+	0.965787i
$495$		0			0
$496$	−1.18099e6	−	1.12816e6i	−0.215546	−	0.205905i
$497$	−4.76152e6	+	2.74906e6i	−0.864678	+	0.499222i
$498$		0			0
$499$	−9.00734e6	−	5.20039e6i	−1.61937	−	0.934942i	−0.987084	−	0.160205i	$-0.948784\pi$
$499$	−9.00734e6	−	5.20039e6i	−1.61937	−	0.934942i	−0.632284	−	0.774737i	$-0.717882\pi$
$500$	5.01502e6	+	601976.i	0.897114	+	0.107685i
$501$		0			0
$502$	−4.95950e6	−	5.59041e6i	−0.878372	−	0.990113i
$503$	−3.07909e6			−0.542628			−0.271314	−	0.962491i	$-0.587458\pi$
$503$	−3.07909e6			−0.542628			−0.271314	+	0.962491i	$0.587458\pi$
$504$		0			0
$505$	−5.51967e6			−0.963129
$506$	−5.51857e6	−	6.22060e6i	−0.958186	−	1.08008i
$507$		0			0
$508$	−1.17807e6	−	141409.i	−0.202540	−	0.0243118i
$509$	8.39198e6	+	4.84511e6i	1.43572	+	0.828914i	0.997549	−	0.0699775i	$-0.0222928\pi$
$509$	8.39198e6	+	4.84511e6i	1.43572	+	0.828914i	0.438172	+	0.898891i	$0.355626\pi$
$510$		0			0
$511$	1.21255e7	−	7.00067e6i	2.05422	−	1.18601i
$512$	1.45494e6	+	5.75044e6i	0.245285	+	0.969451i
$513$		0			0
$514$	1.51550e6	+	7.39762e6i	0.253017	+	1.23505i
$515$	3.18254e6	+	5.51232e6i	0.528756	+	0.915832i
$516$		0			0
$517$	453779.	−	785968.i	0.0746651	−	0.129324i
$518$	−1.26990e7	−	4.22992e6i	−2.07944	−	0.692640i
$519$		0			0
$520$	−3.75001e6	+	7.94500e6i	−0.608168	+	1.28850i
$521$			7.69134e6i			1.24139i	0.784053	+	0.620694i	$0.213149\pi$
$521$			7.69134e6i			1.24139i	−0.784053	+	0.620694i	$0.786851\pi$
$522$		0			0
$523$			1.02773e6i			0.164295i	0.996620	+	0.0821476i	$0.0261779\pi$
$523$			1.02773e6i			0.164295i	−0.996620	+	0.0821476i	$0.973822\pi$
$524$	4.28842e6	+	3.21337e6i	0.682290	+	0.511249i
$525$		0			0
$526$	1.63483e6	−	4.90809e6i	0.257638	−	0.773479i
$527$	27170.5	−	47060.6i	0.00426158	−	0.00738127i
$528$		0			0
$529$	−4.62582e6	−	8.01216e6i	−0.718704	−	1.24483i
$530$	6.74890e6	−	1.38261e6i	1.04362	−	0.213800i
$531$		0			0
$532$	−7.38808e6	+	3.15971e6i	−1.13176	+	0.484025i
$533$	6.41979e6	−	3.70647e6i	0.978820	−	0.565122i
$534$		0			0
$535$	−198627.	−	114677.i	−0.0300023	−	0.0173218i
$536$	1.26824e6	−	105001.i	0.190673	−	0.0157864i
$537$		0			0
$538$	−7.88049e6	+	6.99113e6i	−1.17381	+	1.04134i
$539$	1.07565e7			1.59477
$540$		0			0
$541$	9.97892e6			1.46585			0.732926	−	0.680308i	$-0.238154\pi$
$541$	9.97892e6			1.46585			0.732926	+	0.680308i	$0.238154\pi$
$542$	−2.19096e6	+	1.94370e6i	−0.320359	+	0.284204i
$543$		0			0
$544$	−174436.	+	92313.0i	−0.0252720	+	0.0133741i
$545$	−4.44302e6	−	2.56518e6i	−0.640748	−	0.369936i
$546$		0			0
$547$	−6.89166e6	+	3.97890e6i	−0.984817	+	0.568584i	−0.903721	−	0.428122i	$-0.859175\pi$
$547$	−6.89166e6	+	3.97890e6i	−0.984817	+	0.568584i	−0.0810959	+	0.996706i	$0.525842\pi$
$548$	−4.33025e6	−	1.01251e7i	−0.615973	−	1.44028i
$549$		0			0
$550$	−1.03917e6	+	212888.i	−0.146480	+	0.0300085i
$551$	259414.	+	449318.i	0.0364011	+	0.0630485i
$552$		0			0
$553$	5.08097e6	−	8.80049e6i	0.706535	−	1.22375i
$554$	1.11508e6	−	3.34770e6i	0.154360	−	0.463418i
$555$		0			0
$556$	−5.29854e6	+	7.07119e6i	−0.726891	+	0.970075i
$557$		−	968143.i		−	0.132221i	−0.997812	−	0.0661107i	$-0.978941\pi$
$557$		−	968143.i		−	0.132221i	0.997812	−	0.0661107i	$-0.0210590\pi$
$558$		0			0
$559$			987222.i			0.133624i
$560$	−1.28272e7	−	3.12445e6i	−1.72848	−	0.421021i
$561$		0			0
$562$	9.49868e6	+	3.16391e6i	1.26859	+	0.422555i
$563$	−3.58742e6	+	6.21360e6i	−0.476993	+	0.826176i	−0.999652	−	0.0263657i	$-0.991607\pi$
$563$	−3.58742e6	+	6.21360e6i	−0.476993	+	0.826176i	0.522660	+	0.852541i	$0.324940\pi$
$564$		0			0
$565$	1.27855e6	+	2.21451e6i	0.168499	+	0.291848i
$566$	1.68657e6	+	8.23263e6i	0.221290	+	1.08018i
$567$		0			0
$568$	3.82238e6	−	2.64999e6i	0.497121	−	0.344646i
$569$	1.01785e7	−	5.87656e6i	1.31796	−	0.760926i	0.334561	−	0.942374i	$-0.391412\pi$
$569$	1.01785e7	−	5.87656e6i	1.31796	−	0.760926i	0.983400	+	0.181448i	$0.0580785\pi$
$570$		0			0
$571$	9.11184e6	+	5.26072e6i	1.16954	+	0.675235i	0.953572	−	0.301165i	$-0.0973755\pi$
$571$	9.11184e6	+	5.26072e6i	1.16954	+	0.675235i	0.215970	+	0.976400i	$0.430709\pi$
$572$	−1.14016e6	+	9.49856e6i	−0.145705	+	1.21386i
$573$		0			0
$574$	7.39265e6	+	8.33309e6i	0.936527	+	1.05567i
$575$	−2.00117e6			−0.252414
$576$		0			0
$577$	1.46593e6			0.183305			0.0916526	−	0.995791i	$-0.470785\pi$
$577$	1.46593e6			0.183305			0.0916526	+	0.995791i	$0.470785\pi$
$578$	5.32590e6	+	6.00343e6i	0.663092	+	0.747446i
$579$		0			0
$580$	−101593.	+	846367.i	−0.0125400	+	0.104469i
$581$	−2.44838e6	−	1.41357e6i	−0.300911	−	0.173731i
$582$		0			0
$583$	6.49662e6	−	3.75082e6i	0.791618	−	0.457041i
$584$	−9.73392e6	+	6.74836e6i	−1.18102	+	0.818778i
$585$		0			0
$586$	−1.84576e6	−	9.00970e6i	−0.222040	−	1.08384i
$587$	−523994.	−	907585.i	−0.0627670	−	0.108716i	0.832934	−	0.553372i	$-0.186659\pi$
$587$	−523994.	−	907585.i	−0.0627670	−	0.108716i	−0.895701	+	0.444656i	$0.853326\pi$
$588$		0			0
$589$	−935827.	+	1.62090e6i	−0.111150	+	0.192517i
$590$	1.10247e6	+	367221.i	0.130388	+	0.0434308i
$591$		0			0
$592$	1.10013e7	+	2.67970e6i	1.29015	+	0.314254i
$593$		−	8.50755e6i		−	0.993500i	−0.867894	−	0.496750i	$-0.834527\pi$
$593$		−	8.50755e6i		−	0.993500i	0.867894	−	0.496750i	$-0.165473\pi$
$594$		0			0
$595$		−	439264.i		−	0.0508667i
$596$	751120.	−	1.00241e6i	0.0866151	−	0.115593i
$597$		0			0
$598$	−5.70358e6	+	1.71233e7i	−0.652221	+	1.95810i
$599$	4.39728e6	−	7.61632e6i	0.500746	−	0.867317i	−0.499254	−	0.866456i	$-0.666392\pi$
$599$	4.39728e6	−	7.61632e6i	0.500746	−	0.867317i	1.00000		0.000861327i	$-0.000274169\pi$
$600$		0			0
$601$	−2.32237e6	−	4.02246e6i	−0.262268	−	0.454261i	0.704576	−	0.709628i	$-0.251137\pi$
$601$	−2.32237e6	−	4.02246e6i	−0.262268	−	0.454261i	−0.966844	+	0.255367i	$0.917804\pi$
$602$	−1.45334e6	+	297737.i	−0.163447	+	0.0334844i
$603$		0			0
$604$	−5.40908e6	−	1.26476e7i	−0.603297	−	1.41064i
$605$	1.21606e6	−	702095.i	0.135073	−	0.0779843i
$606$		0			0
$607$	−1.45173e6	−	838155.i	−0.159924	−	0.0923320i	0.417902	−	0.908492i	$-0.362765\pi$
$607$	−1.45173e6	−	838155.i	−0.159924	−	0.0923320i	−0.577826	+	0.816160i	$0.696099\pi$
$608$	6.00807e6	−	3.17952e6i	0.659138	−	0.348821i
$609$		0			0
$610$	1.01577e7	−	9.01133e6i	1.10528	−	0.980538i
$611$	−1.96975e6			−0.213456
$612$		0			0
$613$	615822.			0.0661918			0.0330959	−	0.999452i	$-0.489463\pi$
$613$	615822.			0.0661918			0.0330959	+	0.999452i	$0.489463\pi$
$614$	−126656.	+	112362.i	−0.0135583	+	0.0120282i
$615$		0			0
$616$	−1.43272e7	+	1.18619e6i	−1.52128	+	0.125952i
$617$	3.65601e6	+	2.11080e6i	0.386629	+	0.223220i	0.680698	−	0.732564i	$-0.261676\pi$
$617$	3.65601e6	+	2.11080e6i	0.386629	+	0.223220i	−0.294070	+	0.955784i	$0.595010\pi$
$618$		0			0
$619$	−1.47506e7	+	8.51629e6i	−1.54733	+	0.893354i	−0.548991	+	0.835829i	$0.684988\pi$
$619$	−1.47506e7	+	8.51629e6i	−1.54733	+	0.893354i	−0.998344	+	0.0575254i	$0.981679\pi$
$620$	−2.82744e6	+	1.20923e6i	−0.295402	+	0.126337i
$621$		0			0
$622$	9.18191e6	−	1.88104e6i	0.951606	−	0.194950i
$623$	−9.16731e6	−	1.58782e7i	−0.946285	−	1.63901i
$624$		0			0
$625$	5.54462e6	−	9.60356e6i	0.567769	−	0.983405i
$626$	5.33858e6	−	1.60275e7i	0.544490	−	1.63467i
$627$		0			0
$628$	−1.45194e7	−	1.08796e7i	−1.46909	−	1.10081i
$629$			376737.i			0.0379674i
$630$		0			0
$631$		−	1.01556e7i		−	1.01539i	−0.861538	−	0.507693i	$-0.830498\pi$
$631$		−	1.01556e7i		−	1.01539i	0.861538	−	0.507693i	$-0.169502\pi$
$632$	−3.66930e6	+	7.77402e6i	−0.365419	+	0.774200i
$633$		0			0
$634$	−4.63649e6	−	1.54437e6i	−0.458107	−	0.152590i
$635$	−1.11703e6	+	1.93475e6i	−0.109933	+	0.190410i
$636$		0			0
$637$	−1.16728e7	−	2.02180e7i	−1.13980	−	1.97419i
$638$	186294.	+	909356.i	0.0181195	+	0.0884468i
$639$		0			0
$640$	1.10323e7	+	1.73877e6i	1.06467	+	0.167800i
$641$	1.77251e7	−	1.02336e7i	1.70389	−	0.983744i	0.762160	−	0.647389i	$-0.224139\pi$
$641$	1.77251e7	−	1.02336e7i	1.70389	−	0.983744i	0.941735	−	0.336355i	$-0.109194\pi$
$642$		0			0
$643$	−1.99881e6	−	1.15401e6i	−0.190653	−	0.110074i	0.401635	−	0.915800i	$-0.368442\pi$
$643$	−1.99881e6	−	1.15401e6i	−0.190653	−	0.110074i	−0.592288	+	0.805726i	$0.701775\pi$
$644$	−2.69283e7	−	3.23233e6i	−2.55855	−	0.307115i
$645$		0			0
$646$	150091.	+	169185.i	0.0141506	+	0.0159507i
$647$	−4.18696e6			−0.393222			−0.196611	−	0.980482i	$-0.562994\pi$
$647$	−4.18696e6			−0.393222			−0.196611	+	0.980482i	$0.562994\pi$
$648$		0			0
$649$	1.26535e6			0.117923
$650$	1.52784e6	+	1.72221e6i	0.141839	+	0.159883i
$651$		0			0
$652$	1.60593e6	+	192767.i	0.147947	+	0.0177588i
$653$	1.70167e6	+	982460.i	0.156168	+	0.0901638i	0.576048	−	0.817416i	$-0.304594\pi$
$653$	1.70167e6	+	982460.i	0.156168	+	0.0901638i	−0.419879	+	0.907580i	$0.637928\pi$
$654$		0			0
$655$	8.73801e6	−	5.04489e6i	0.795810	−	0.459461i
$656$	−6.81412e6	−	6.50932e6i	−0.618230	−	0.590576i
$657$		0			0
$658$	−594059.	−	2.89978e6i	−0.0534890	−	0.261096i
$659$	2.30212e6	+	3.98739e6i	0.206497	+	0.357664i	0.950609	−	0.310391i	$-0.100460\pi$
$659$	2.30212e6	+	3.98739e6i	0.206497	+	0.357664i	−0.744111	+	0.668056i	$0.767127\pi$
$660$		0			0
$661$	−2.73544e6	+	4.73792e6i	−0.243514	+	0.421778i	−0.961713	−	0.274060i	$-0.911633\pi$
$661$	−2.73544e6	+	4.73792e6i	−0.243514	+	0.421778i	0.718199	+	0.695838i	$0.244967\pi$
$662$	−11333.5	−	3775.08i	−0.00100513	−	0.000334797i
$663$		0			0
$664$	2.16280e6	+	1.02083e6i	0.190369	+	0.0898535i
$665$			1.51295e7i			1.32669i
$666$		0			0
$667$			1.75118e6i			0.152411i
$668$	−7.94259e6	−	5.95149e6i	−0.688686	−	0.516042i
$669$		0			0
$670$	757210.	−	2.27329e6i	0.0651673	−	0.195645i
$671$	7.39309e6	−	1.28052e7i	0.633899	−	1.09795i
$672$		0			0
$673$	1.03102e7	+	1.78577e7i	0.877460	+	1.51981i	0.854119	+	0.520078i	$0.174097\pi$
$673$	1.03102e7	+	1.78577e7i	0.877460	+	1.51981i	0.0233415	+	0.999728i	$0.492569\pi$
$674$	−1.37903e7	+	2.82513e6i	−1.16930	+	0.239546i
$675$		0			0
$676$	8.16662e6	−	3.49267e6i	0.687346	−	0.293962i
$677$	−2.59618e6	+	1.49891e6i	−0.217702	+	0.125691i	−0.604886	−	0.796312i	$-0.706781\pi$
$677$	−2.59618e6	+	1.49891e6i	−0.217702	+	0.125691i	0.387184	+	0.922003i	$0.373448\pi$
$678$		0			0
$679$	−1.03573e7	−	5.97977e6i	−0.862126	−	0.497749i
$680$	30660.5	+	370328.i	0.00254277	+	0.0307124i
$681$		0			0
$682$	−2.50495e6	+	2.22225e6i	−0.206223	+	0.182950i
$683$	−3.24667e6			−0.266310			−0.133155	−	0.991095i	$-0.542511\pi$
$683$	−3.24667e6			−0.266310			−0.133155	+	0.991095i	$0.542511\pi$
$684$		0			0
$685$	−2.07344e7			−1.68836
$686$	1.10247e7	−	9.78050e6i	0.894452	−	0.793507i
$687$		0			0
$688$	1.20448e6	−	352454.i	0.0970125	−	0.0283878i
$689$	−1.41002e7	−	8.14073e6i	−1.13156	−	0.653304i
$690$		0			0
$691$	1.27793e7	−	7.37815e6i	1.01815	−	0.587831i	0.104584	−	0.994516i	$-0.466649\pi$
$691$	1.27793e7	−	7.37815e6i	1.01815	−	0.587831i	0.913568	+	0.406685i	$0.133315\pi$
$692$	2.04169e6	+	4.77390e6i	0.162078	+	0.378973i
$693$		0			0
$694$	−1.83493e7	+	3.75911e6i	−1.44618	+	0.296269i
$695$	8.31854e6	+	1.44081e7i	0.653259	+	1.13148i
$696$		0			0
$697$	156769.	−	271533.i	0.0122230	−	0.0211709i
$698$	470177.	−	1.41156e6i	0.0365277	−	0.109663i
$699$		0			0
$700$	−2.07457e6	+	2.76863e6i	−0.160023	+	0.213560i
$701$		−	571089.i		−	0.0438944i	−0.999759	−	0.0219472i	$-0.993013\pi$
$701$		−	571089.i		−	0.0438944i	0.999759	−	0.0219472i	$-0.00698656\pi$
$702$		0			0
$703$		−	1.29759e7i		−	0.990259i
$704$	1.19960e7	−	2.00007e6i	0.912227	−	0.152095i
$705$		0			0
$706$	−792472.	−	263964.i	−0.0598374	−	0.0199312i
$707$	−9.80159e6	+	1.69769e7i	−0.737476	+	1.27735i
$708$		0			0
$709$	9.31781e6	+	1.61389e7i	0.696143	+	1.20576i	0.969794	+	0.243926i	$0.0784354\pi$
$709$	9.31781e6	+	1.61389e7i	0.696143	+	1.20576i	−0.273651	+	0.961829i	$0.588231\pi$
$710$	−1.75757e6	−	8.57924e6i	−0.130848	−	0.638709i
$711$		0			0
$712$	8.83692e6	+	1.27465e7i	0.653282	+	0.942303i
$713$	−5.47097e6	+	3.15867e6i	−0.403033	+	0.232691i
$714$		0			0
$715$	1.55996e7	+	9.00642e6i	1.14116	+	0.658851i
$716$	1.19452e6	−	9.95147e6i	0.0870786	−	0.725445i
$717$		0			0
$718$	−5.50866e6	−	6.20943e6i	−0.398781	−	0.449511i
$719$	7.72155e6			0.557035			0.278517	−	0.960431i	$-0.410157\pi$
$719$	7.72155e6			0.557035			0.278517	+	0.960431i	$0.410157\pi$
$720$		0			0
$721$	2.26057e7			1.61949
$722$	4.12590e6	+	4.65077e6i	0.294562	+	0.332034i
$723$		0			0
$724$	−920689.	+	7.67019e6i	−0.0652780	+	0.543825i
$725$	193454.	+	111691.i	0.0136689	+	0.00789173i
$726$		0			0
$727$	−1.28498e7	+	7.41886e6i	−0.901700	+	0.520596i	−0.877751	−	0.479117i	$-0.840957\pi$
$727$	−1.28498e7	+	7.41886e6i	−0.901700	+	0.520596i	−0.0239484	+	0.999713i	$0.507624\pi$
$728$	1.77774e7	+	2.56423e7i	1.24319	+	1.79320i
$729$		0			0
$730$	4.47577e6	+	2.18476e7i	0.310857	+	1.51739i
$731$	20877.9	+	36161.5i	0.00144508	+	0.00250296i
$732$		0			0
$733$	−1.71343e6	+	2.96776e6i	−0.117790	+	0.204018i	−0.918891	−	0.394510i	$-0.870914\pi$
$733$	−1.71343e6	+	2.96776e6i	−0.117790	+	0.204018i	0.801102	+	0.598528i	$0.204248\pi$
$734$	1.09355e7	+	3.64250e6i	0.749201	+	0.249551i
$735$		0			0
$736$	2.29279e7	+	845471.i	1.56016	+	0.0575313i
$737$		−	2.60915e6i		−	0.176942i
$738$		0			0
$739$			1.26632e7i			0.852970i	0.904495	+	0.426485i	$0.140248\pi$
$739$			1.26632e7i			0.852970i	−0.904495	+	0.426485i	$0.859752\pi$
$740$	1.27843e7	−	1.70613e7i	0.858216	−	1.14534i
$741$		0			0
$742$	7.73194e6	−	2.32128e7i	0.515559	−	1.54781i
$743$	6.02221e6	−	1.04308e7i	0.400206	−	0.693178i	−0.593544	−	0.804801i	$-0.702272\pi$
$743$	6.02221e6	−	1.04308e7i	0.400206	−	0.693178i	0.993751	+	0.111624i	$0.0356052\pi$
$744$		0			0
$745$	−1.17924e6	−	2.04250e6i	−0.0778413	−	0.134825i
$746$	6.97165e6	−	1.42824e6i	0.458658	−	0.0939623i
$747$		0			0
$748$	159113.	+	372040.i	0.0103980	+	0.0243129i
$749$	−705427.	+	407278.i	−0.0459460	+	0.0265269i
$750$		0			0
$751$	1.01719e7	+	5.87273e6i	0.658114	+	0.379962i	0.791558	−	0.611094i	$-0.209270\pi$
$751$	1.01719e7	+	5.87273e6i	0.658114	+	0.379962i	−0.133444	+	0.991056i	$0.542604\pi$
$752$	703233.	+	2.40323e6i	0.0453476	+	0.154971i
$753$		0			0
$754$	1.50707e6	−	1.33699e6i	0.0965393	−	0.0856443i
$755$	−2.59001e7			−1.65361
$756$		0			0
$757$	5.08821e6			0.322719			0.161360	−	0.986896i	$-0.448412\pi$
$757$	5.08821e6			0.322719			0.161360	+	0.986896i	$0.448412\pi$
$758$	−1.48937e7	+	1.32128e7i	−0.941520	+	0.835263i
$759$		0			0
$760$	−1.05604e6	−	1.27551e7i	−0.0663200	−	0.801034i
$761$	6.60390e6	+	3.81276e6i	0.413370	+	0.238659i	0.692237	−	0.721671i	$-0.256625\pi$
$761$	6.60390e6	+	3.81276e6i	0.413370	+	0.238659i	−0.278867	+	0.960330i	$0.589959\pi$
$762$		0			0
$763$	−1.57795e7	+	9.11027e6i	−0.981252	+	0.566526i
$764$	2.22478e7	−	9.51485e6i	1.37896	−	0.589751i
$765$		0			0
$766$	−1.61048e7	+	3.29930e6i	−0.991709	+	0.203165i
$767$	−1.37315e6	−	2.37836e6i	−0.0842808	−	0.145979i
$768$		0			0
$769$	8.36212e6	−	1.44836e7i	0.509918	−	0.883205i	−0.490016	−	0.871714i	$-0.663009\pi$
$769$	8.36212e6	−	1.44836e7i	0.509918	−	0.883205i	0.999934	−	0.0114909i	$-0.00365776\pi$
$770$	−8.55415e6	+	2.56812e7i	−0.519936	+	1.56095i
$771$		0			0
$772$	−1.07939e7	−	8.08804e6i	−0.651833	−	0.488428i
$773$			610007.i			0.0367186i	0.999831	+	0.0183593i	$0.00584428\pi$
$773$			610007.i			0.0367186i	−0.999831	+	0.0183593i	$0.994156\pi$
$774$		0			0
$775$			805843.i			0.0481943i
$776$	9.14922e6	+	4.31839e6i	0.545418	+	0.257435i
$777$		0			0
$778$	−2.47293e7	−	8.23705e6i	−1.46475	−	0.487891i
$779$	−5.39958e6	+	9.35236e6i	−0.318799	+	0.552176i
$780$		0			0
$781$	−4.76806e6	−	8.25853e6i	−0.279714	−	0.484479i
$782$	153205.	+	747839.i	0.00895893	+	0.0437312i
$783$		0			0
$784$	−2.04999e7	+	2.14598e7i	−1.19114	+	1.24691i
$785$	−2.95845e7	+	1.70806e7i	−1.71352	+	0.989302i
$786$		0			0
$787$	−1.47383e7	−	8.50913e6i	−0.848221	−	0.489721i	0.0118291	−	0.999930i	$-0.496235\pi$
$787$	−1.47383e7	−	8.50913e6i	−0.848221	−	0.489721i	−0.860050	+	0.510209i	$0.829568\pi$
$788$	2.52906e7	+	3.03575e6i	1.45092	+	0.174161i
$789$		0			0
$790$	1.07415e7	+	1.21080e7i	0.612349	+	0.690247i
$791$	9.08157e6			0.516083
$792$		0			0
$793$	−3.20917e7			−1.81222
$794$	−5.16376e6	−	5.82066e6i	−0.290680	−	0.327658i
$795$		0			0
$796$	3.52579e7	+	4.23217e6i	1.97230	+	0.236745i
$797$	−1.38609e7	−	8.00260e6i	−0.772941	−	0.446257i	0.0609820	−	0.998139i	$-0.480577\pi$
$797$	−1.38609e7	−	8.00260e6i	−0.772941	−	0.446257i	−0.833923	+	0.551881i	$0.813910\pi$
$798$		0			0
$799$	−72151.1	+	41656.4i	−0.00399830	+	0.00230842i
$800$	1.55574e6	−	2.47893e6i	0.0859436	−	0.136943i
$801$		0			0
$802$	−122862.	−	599727.i	−0.00674501	−	0.0329244i
$803$	1.21422e7	+	2.10309e7i	0.664519	+	1.15098i
$804$		0			0
$805$	−2.55331e7	+	4.42246e7i	−1.38872	+	2.40533i
$806$	6.89531e6	+	2.29675e6i	0.373866	+	0.124531i
$807$		0			0
$808$	7.07838e6	−	1.49967e7i	0.381422	−	0.808105i
$809$			2.13263e7i			1.14563i	0.819686	+	0.572813i	$0.194148\pi$
$809$			2.13263e7i			1.14563i	−0.819686	+	0.572813i	$0.805852\pi$
$810$		0			0
$811$		−	8.01640e6i		−	0.427984i	−0.976835	−	0.213992i	$-0.931353\pi$
$811$		−	8.01640e6i		−	0.427984i	0.976835	−	0.213992i	$-0.0686466\pi$
$812$	2.42277e6	+	1.81541e6i	0.128950	+	0.0966242i
$813$		0			0
$814$	7.33650e6	−	2.20256e7i	0.388086	−	1.16511i
$815$	1.52272e6	−	2.63743e6i	0.0803020	−	0.139087i
$816$		0			0
$817$	−719093.	−	1.24550e6i	−0.0376903	−	0.0652815i
$818$	−1.00135e7	+	2.05140e6i	−0.523241	+	0.107193i
$819$		0			0
$820$	−1.63139e7	+	6.97707e6i	−0.847272	+	0.362358i
$821$	−1.96434e6	+	1.13411e6i	−0.101709	+	0.0587215i	−0.549992	−	0.835170i	$-0.685369\pi$
$821$	−1.96434e6	+	1.13411e6i	−0.101709	+	0.0587215i	0.448283	+	0.893892i	$0.352036\pi$
$822$		0			0
$823$	3.22738e7	+	1.86333e7i	1.66093	+	0.958936i	0.972274	+	0.233844i	$0.0751304\pi$
$823$	3.22738e7	+	1.86333e7i	1.66093	+	0.958936i	0.688652	+	0.725092i	$0.258203\pi$
$824$	−1.90580e7	+	1.57787e6i	−0.977821	+	0.0809567i
$825$		0			0
$826$	3.08719e6	−	2.73878e6i	0.157439	−	0.139671i
$827$	3.20117e7			1.62759			0.813794	−	0.581153i	$-0.197398\pi$
$827$	3.20117e7			1.62759			0.813794	+	0.581153i	$0.197398\pi$
$828$		0			0
$829$	1.94310e7			0.981994			0.490997	−	0.871161i	$-0.336633\pi$
$829$	1.94310e7			0.981994			0.490997	+	0.871161i	$0.336633\pi$
$830$	3.36856e6	−	2.98839e6i	0.169726	−	0.150571i
$831$		0			0
$832$	−1.67773e7	−	2.03772e7i	−0.840258	−	1.02056i
$833$	−855143.	−	493717.i	−0.0426998	−	0.0246528i
$834$		0			0
$835$	−1.61837e7	+	9.34366e6i	−0.803270	+	0.463768i
$836$	−5.48030e6	−	1.28141e7i	−0.271199	−	0.634123i
$837$		0			0
$838$	1.02657e7	−	2.10307e6i	0.504984	−	0.103453i
$839$	−4.00186e6	−	6.93143e6i	−0.196272	−	0.339952i	0.751045	−	0.660251i	$-0.229550\pi$
$839$	−4.00186e6	−	6.93143e6i	−0.196272	−	0.339952i	−0.947317	+	0.320299i	$0.896217\pi$
$840$		0			0
$841$	−1.01578e7	+	1.75939e7i	−0.495235	+	0.857772i
$842$	−6.63520e6	+	1.99202e7i	−0.322533	+	0.968306i
$843$		0			0
$844$	3.97664e6	−	5.30704e6i	0.192159	−	0.256446i
$845$		−	1.67238e7i		−	0.805738i
$846$		0			0
$847$		−	4.98700e6i		−	0.238853i
$848$	−4.89826e6	+	2.01095e7i	−0.233912	+	0.960312i
$849$		0			0
$850$	92385.7	+	30772.7i	0.00438589	+	0.00146089i
$851$	2.18985e7	−	3.79294e7i	1.03655	−	1.79536i
$852$		0			0
$853$	7.09314e6	+	1.22857e7i	0.333784	+	0.578131i	0.983251	−	0.182259i	$-0.0583410\pi$
$853$	7.09314e6	+	1.22857e7i	0.333784	+	0.578131i	−0.649466	+	0.760390i	$0.725008\pi$
$854$	−9.67858e6	−	4.72440e7i	−0.454116	−	2.21667i
$855$		0			0
$856$	566291.	−	392600.i	0.0264153	−	0.0183133i
$857$	−3.07075e7	+	1.77290e7i	−1.42821	+	0.824578i	−0.996980	−	0.0776628i	$-0.975254\pi$
$857$	−3.07075e7	+	1.77290e7i	−1.42821	+	0.824578i	−0.431232	+	0.902241i	$0.641921\pi$
$858$		0			0
$859$	−1.51108e7	−	8.72423e6i	−0.698723	−	0.403408i	0.108149	−	0.994135i	$-0.465508\pi$
$859$	−1.51108e7	−	8.72423e6i	−0.698723	−	0.403408i	−0.806872	+	0.590727i	$0.798841\pi$
$860$	281616.	−	2.34612e6i	0.0129841	−	0.108169i
$861$		0			0
$862$	−1.04321e6	−	1.17592e6i	−0.0478192	−	0.0539024i
$863$	−7.28107e6			−0.332788			−0.166394	−	0.986059i	$-0.553212\pi$
$863$	−7.28107e6			−0.332788			−0.166394	+	0.986059i	$0.553212\pi$
$864$		0			0
$865$	9.77612e6			0.444249
$866$	−9.35606e6	−	1.05463e7i	−0.423934	−	0.477864i
$867$		0			0
$868$	−1.30161e6	+	1.08436e7i	−0.0586385	+	0.488513i
$869$	1.52639e7	+	8.81259e6i	0.685669	+	0.395871i
$870$		0			0
$871$	−4.90417e6	+	2.83143e6i	−0.219039	+	0.126462i
$872$	1.26672e7	−	8.78194e6i	0.564143	−	0.391110i
$873$		0			0
$874$	−5.27681e6	−	2.57577e7i	−0.233665	−	1.14059i
$875$	−1.68881e7	−	2.92510e7i	−0.745693	−	1.29158i
$876$		0			0
$877$	−432760.	+	749562.i	−0.0189998	+	0.0329085i	−0.875369	−	0.483455i	$-0.839382\pi$
$877$	−432760.	+	749562.i	−0.0189998	+	0.0329085i	0.856369	+	0.516364i	$0.172715\pi$
$878$	6.47391e6	+	2.15639e6i	0.283420	+	0.0944041i
$879$		0			0
$880$	5.41914e6	−	2.22480e7i	0.235898	−	0.968465i
$881$		−	8.64368e6i		−	0.375197i	−0.982246	−	0.187598i	$-0.939930\pi$
$881$		−	8.64368e6i		−	0.375197i	0.982246	−	0.187598i	$-0.0600703\pi$
$882$		0			0
$883$		−	6.19117e6i		−	0.267221i	−0.991034	−	0.133611i	$-0.957343\pi$
$883$		−	6.19117e6i		−	0.267221i	0.991034	−	0.133611i	$-0.0426572\pi$
$884$	526622.	−	702805.i	0.0226657	−	0.0302485i
$885$		0			0
$886$	−4.67697e6	+	1.40412e7i	−0.200162	+	0.600924i
$887$	−1.36675e7	+	2.36728e7i	−0.583285	+	1.01028i	0.411802	+	0.911273i	$0.364900\pi$
$887$	−1.36675e7	+	2.36728e7i	−0.583285	+	1.01028i	−0.995087	+	0.0990058i	$0.968434\pi$
$888$		0			0
$889$	3.96714e6	+	6.87129e6i	0.168354	+	0.291598i
$890$	2.86092e7	−	5.86099e6i	1.21068	−	0.248025i
$891$		0			0
$892$	8.10161e6	+	1.89433e7i	0.340925	+	0.797157i
$893$	2.48509e6	−	1.43477e6i	0.104283	−	0.0602077i
$894$		0			0
$895$	−1.63434e7	−	9.43586e6i	−0.682000	−	0.393753i
$896$	2.49386e7	−	3.08443e7i	1.03777	−	1.28353i
$897$		0			0
$898$	1.47647e6	−	1.30984e6i	0.0610991	−	0.0542037i
$899$	705176.			0.0291004
$900$		0			0
$901$	−688644.			−0.0282607
$902$	−1.44532e7	+	1.28220e7i	−0.591489	+	0.524736i
$903$		0			0
$904$	−7.65634e6	+	633891.i	−0.311602	+	0.0257985i
$905$	1.25968e7	+	7.27278e6i	0.511257	+	0.295174i
$906$		0			0
$907$	2.71438e6	−	1.56715e6i	0.109560	−	0.0632545i	−0.444219	−	0.895918i	$-0.646519\pi$
$907$	2.71438e6	−	1.56715e6i	0.109560	−	0.0632545i	0.553779	+	0.832664i	$0.313185\pi$
$908$	−3.50905e7	+	1.50074e7i	−1.41246	+	0.604075i
$909$		0			0
$910$	5.75536e7	−	1.17906e7i	2.30393	−	0.471991i
$911$	−2.15693e7	−	3.73592e7i	−0.861074	−	1.49142i	−0.870893	−	0.491472i	$-0.836459\pi$
$911$	−2.15693e7	−	3.73592e7i	−0.861074	−	1.49142i	0.00981891	−	0.999952i	$-0.496874\pi$
$912$		0			0
$913$	2.45174e6	−	4.24655e6i	0.0973415	−	0.168600i
$914$	−6.11968e6	+	1.83725e7i	−0.242305	+	0.727448i
$915$		0			0
$916$	2.75665e7	+	2.06560e7i	1.08553	+	0.813406i
$917$		−	3.58340e7i		−	1.40725i
$918$		0			0
$919$		−	9.73606e6i		−	0.380272i	−0.981758	−	0.190136i	$-0.939107\pi$
$919$		−	9.73606e6i		−	0.380272i	0.981758	−	0.190136i	$-0.0608929\pi$
$920$	1.84391e7	−	3.90663e7i	0.718242	−	1.52171i
$921$		0			0
$922$	−2.91357e7	−	9.70480e6i	−1.12875	−	0.375975i
$923$	−1.03485e7	+	1.79242e7i	−0.399829	+	0.692524i
$924$		0			0
$925$	−2.79339e6	−	4.83829e6i	−0.107344	−	0.185925i
$926$	4.90631e6	+	2.39491e7i	0.188030	+	0.917830i
$927$		0			0
$928$	−2.16926e6	−	1.36140e6i	−0.0826879	−	0.0518938i
$929$	3.71782e7	−	2.14649e7i	1.41335	−	0.815997i	0.417647	−	0.908610i	$-0.362855\pi$
$929$	3.71782e7	−	2.14649e7i	1.41335	−	0.815997i	0.995702	+	0.0926123i	$0.0295217\pi$
$930$		0			0
$931$	2.94535e7	+	1.70050e7i	1.11369	+	0.642988i
$932$	−5.66071e6	−	679482.i	−0.213467	−	0.0256235i
$933$		0			0
$934$	−1.28141e7	−	1.44443e7i	−0.480642	−	0.541786i
$935$	761874.			0.0285006
$936$		0			0
$937$	−2.31461e7			−0.861250			−0.430625	−	0.902531i	$-0.641707\pi$
$937$	−2.31461e7			−0.861250			−0.430625	+	0.902531i	$0.641707\pi$
$938$	−5.64736e6	−	6.36577e6i	−0.209574	−	0.236235i
$939$		0			0
$940$	4.68109e6	+	561893.i	0.172793	+	0.0207412i
$941$	1.44508e7	+	8.34315e6i	0.532006	+	0.307154i	0.741833	−	0.670585i	$-0.233957\pi$
$941$	1.44508e7	+	8.34315e6i	0.532006	+	0.307154i	−0.209827	+	0.977739i	$0.567290\pi$
$942$		0			0
$943$	−3.15667e7	+	1.82250e7i	−1.15598	+	0.667405i
$944$	−2.41153e6	+	2.52445e6i	−0.0880769	+	0.0922011i
$945$		0			0
$946$	−516405.	−	2.52073e6i	−0.0187613	−	0.0915794i
$947$	4.97026e6	+	8.60874e6i	0.180096	+	0.311936i	0.941913	−	0.335857i	$-0.109026\pi$
$947$	4.97026e6	+	8.60874e6i	0.180096	+	0.311936i	−0.761817	+	0.647792i	$0.775692\pi$
$948$		0			0
$949$	2.63532e7	−	4.56451e7i	0.949878	−	1.64524i
$950$	−3.18202e6	−	1.05990e6i	−0.114392	−	0.0381027i
$951$		0			0
$952$	1.19346e6	+	563309.i	0.0426792	+	0.0201444i
$953$			1.33255e7i			0.475283i	0.971353	+	0.237641i	$0.0763743\pi$
$953$			1.33255e7i			0.475283i	−0.971353	+	0.237641i	$0.923626\pi$
$954$		0			0
$955$		−	4.55595e7i		−	1.61648i
$956$	1.72536e7	+	1.29284e7i	0.610569	+	0.457508i
$957$		0			0
$958$	−4.67686e6	+	1.40409e7i	−0.164642	+	0.494288i
$959$	−3.68192e7	+	6.37728e7i	−1.29279	+	2.23918i
$960$		0			0
$961$	−1.30426e7	−	2.25905e7i	−0.455571	−	0.789073i
$962$	−4.93610e7	+	1.01123e7i	−1.71968	+	0.352299i
$963$		0			0
$964$	9.59070e6	−	4.10172e6i	0.332397	−	0.142159i
$965$	−2.19935e7	+	1.26980e7i	−0.760286	+	0.438951i
$966$		0			0
$967$	4.52649e7	+	2.61337e7i	1.55667	+	0.898742i	0.997572	+	0.0696376i	$0.0221843\pi$
$967$	4.52649e7	+	2.61337e7i	1.55667	+	0.898742i	0.559094	+	0.829104i	$0.311149\pi$
$968$	348091.	+	4.20436e6i	0.0119400	+	0.144215i
$969$		0			0
$970$	1.42499e7	−	1.26417e7i	0.486274	−	0.431395i
$971$	−2.52629e7			−0.859874			−0.429937	−	0.902859i	$-0.641464\pi$
$971$	−2.52629e7			−0.859874			−0.429937	+	0.902859i	$0.641464\pi$
$972$		0			0
$973$	5.90868e7			2.00082
$974$	−3.63227e7	+	3.22234e7i	−1.22682	+	1.08836i
$975$		0			0
$976$	1.14573e7	+	3.91541e7i	0.384996	+	1.31569i
$977$	−2.99055e7	−	1.72660e7i	−1.00234	−	0.578701i	−0.0934002	−	0.995629i	$-0.529774\pi$
$977$	−2.99055e7	−	1.72660e7i	−1.00234	−	0.578701i	−0.908940	+	0.416927i	$0.863107\pi$
$978$		0			0
$979$	2.75397e7	−	1.59001e7i	0.918339	−	0.530203i
$980$	2.19730e7	+	5.13776e7i	0.730843	+	1.70887i
$981$		0			0
$982$	−4.93424e7	+	1.01085e7i	−1.63283	+	0.334508i
$983$	1.02022e7	+	1.76708e7i	0.336753	+	0.583273i	0.983820	−	0.179160i	$-0.0573381\pi$
$983$	1.02022e7	+	1.76708e7i	0.336753	+	0.583273i	−0.647067	+	0.762433i	$0.724005\pi$
$984$		0			0
$985$	2.39802e7	−	4.15349e7i	0.787521	−	1.36403i
$986$	26928.5	−	80844.8i	0.000882106	−	0.00264826i
$987$		0			0
$988$	−1.81384e7	+	2.42066e7i	−0.591161	+	0.788936i
$989$		−	4.85426e6i		−	0.157809i
$990$		0			0
$991$		−	2.57219e7i		−	0.831991i	−0.909367	−	0.415996i	$-0.863433\pi$
$991$		−	2.57219e7i		−	0.831991i	0.909367	−	0.415996i	$-0.136567\pi$
$992$	340459.	−	9.23273e6i	0.0109846	−	0.297887i
$993$		0			0
$994$	−2.95082e7	−	9.82887e6i	−0.947277	−	0.315528i
$995$	3.34311e7	−	5.79043e7i	1.07051	−	1.85419i
$996$		0			0
$997$	−4.80332e6	−	8.31959e6i	−0.153040	−	0.265072i	0.779304	−	0.626646i	$-0.215573\pi$
$997$	−4.80332e6	−	8.31959e6i	−0.153040	−	0.265072i	−0.932343	+	0.361574i	$0.882240\pi$
$998$	−1.18081e7	−	5.76386e7i	−0.375277	−	1.83184i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.71.20		56
3.2	odd	2		36.6.h.a.23.9	yes	56
4.3	odd	2	inner	108.6.h.a.71.11		56
9.2	odd	6	inner	108.6.h.a.35.11		56
9.7	even	3		36.6.h.a.11.18	yes	56
12.11	even	2		36.6.h.a.23.18	yes	56
36.7	odd	6		36.6.h.a.11.9	✓	56
36.11	even	6	inner	108.6.h.a.35.20		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.9	✓	56	36.7	odd	6
36.6.h.a.11.18	yes	56	9.7	even	3
36.6.h.a.23.9	yes	56	3.2	odd	2
36.6.h.a.23.18	yes	56	12.11	even	2
108.6.h.a.35.11		56	9.2	odd	6	inner
108.6.h.a.35.20		56	36.11	even	6	inner
108.6.h.a.71.11		56	4.3	odd	2	inner
108.6.h.a.71.20		56	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.75408 + 4.23165i) q^{2} +(-3.81374 + 31.7719i) q^{4} +(52.1793 + 30.1257i) q^{5} +(185.316 - 106.992i) q^{7} +(-148.765 + 103.136i) q^{8} +O(q^{10})\)	\(q+(3.75408 + 4.23165i) q^{2} +(-3.81374 + 31.7719i) q^{4} +(52.1793 + 30.1257i) q^{5} +(185.316 - 106.992i) q^{7} +(-148.765 + 103.136i) q^{8} +(68.4038 + 333.899i) q^{10} +(185.570 + 321.417i) q^{11} +(402.759 - 697.599i) q^{13} +(1148.44 + 382.534i) q^{14} +(-994.911 - 242.339i) q^{16} -34.0704i q^{17} +1173.48i q^{19} +(-1156.15 + 1542.95i) q^{20} +(-663.480 + 1991.90i) q^{22} +(-1980.40 + 3430.16i) q^{23} +(252.621 + 437.553i) q^{25} +(4463.99 - 914.509i) q^{26} +(2692.60 + 6295.88i) q^{28} +(382.894 - 221.064i) q^{29} +(1381.28 + 797.481i) q^{31} +(-2709.48 - 5119.88i) q^{32} +(144.174 - 127.903i) q^{34} +12892.9 q^{35} -11057.6 q^{37} +(-4965.76 + 4405.34i) q^{38} +(-10869.5 + 899.918i) q^{40} +(7969.76 + 4601.35i) q^{41} +(-1061.38 + 612.787i) q^{43} +(-10919.8 + 4670.13i) q^{44} +(-21949.8 + 4496.72i) q^{46} +(-1222.66 - 2117.71i) q^{47} +(14491.1 - 25099.3i) q^{49} +(-903.210 + 2711.61i) q^{50} +(20628.1 + 15456.9i) q^{52} -20212.4i q^{53} +22361.8i q^{55} +(-16533.7 + 35029.4i) q^{56} +(2372.88 + 790.381i) q^{58} +(1704.67 - 2952.58i) q^{59} +(-19919.9 - 34502.3i) q^{61} +(1810.77 + 8838.89i) q^{62} +(11493.9 - 30686.0i) q^{64} +(42031.4 - 24266.8i) q^{65} +(-6088.22 - 3515.04i) q^{67} +(1082.48 + 129.935i) q^{68} +(48400.9 + 54558.1i) q^{70} -25694.1 q^{71} +65431.6 q^{73} +(-41511.2 - 46792.0i) q^{74} +(-37283.7 - 4475.34i) q^{76} +(68778.2 + 39709.1i) q^{77} +(41126.9 - 23744.6i) q^{79} +(-44613.1 - 42617.5i) q^{80} +(10447.9 + 50999.1i) q^{82} +(-6605.97 - 11441.9i) q^{83} +(1026.39 - 1777.77i) q^{85} +(-6577.60 - 2190.93i) q^{86} +(-60756.1 - 28676.6i) q^{88} -85682.2i q^{89} -172368. i q^{91} +(-101430. - 76003.0i) q^{92} +(4371.44 - 13123.9i) q^{94} +(-35352.0 + 61231.4i) q^{95} +(-27944.9 - 48402.0i) q^{97} +(160612. - 32903.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more