LMFDB - Embedded newform 124.5.o.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	124.13
Dual form			124.5.o.a.105.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38100 + 3.10178i) q^{3} +(21.1680 + 36.6640i) q^{5} +(12.2350 + 13.5884i) q^{7} +(46.4857 - 51.6276i) q^{9} +O(q^{10})$	\(q+(1.38100 + 3.10178i) q^{3} +(21.1680 + 36.6640i) q^{5} +(12.2350 + 13.5884i) q^{7} +(46.4857 - 51.6276i) q^{9} +(13.8641 + 65.2256i) q^{11} +(-228.953 - 24.0640i) q^{13} +(-84.4907 + 116.291i) q^{15} +(-47.7075 + 224.446i) q^{17} +(6.50601 + 61.9005i) q^{19} +(-25.2515 + 56.7159i) q^{21} +(487.484 - 158.393i) q^{23} +(-583.667 + 1010.94i) q^{25} +(485.895 + 157.877i) q^{27} +(332.124 + 457.130i) q^{29} +(-290.450 + 916.057i) q^{31} +(-183.169 + 133.080i) q^{33} +(-239.214 + 736.224i) q^{35} +(-311.854 - 180.049i) q^{37} +(-241.543 - 743.394i) q^{39} +(-1818.97 - 809.859i) q^{41} +(-698.258 + 73.3899i) q^{43} +(2876.89 + 611.501i) q^{45} +(942.881 + 685.043i) q^{47} +(216.025 - 2055.34i) q^{49} +(-762.066 + 161.982i) q^{51} +(1310.59 + 1180.06i) q^{53} +(-2097.96 + 1889.01i) q^{55} +(-183.017 + 105.665i) q^{57} +(2782.07 - 1238.66i) q^{59} -3323.29i q^{61} +1270.29 q^{63} +(-3964.20 - 8903.73i) q^{65} +(2914.74 + 5048.47i) q^{67} +(1164.52 + 1293.33i) q^{69} +(2178.11 - 2419.04i) q^{71} +(-771.830 - 3631.18i) q^{73} +(-3941.76 - 414.296i) q^{75} +(-716.682 + 986.428i) q^{77} +(1333.12 - 6271.81i) q^{79} +(-406.882 - 3871.22i) q^{81} +(4364.46 - 9802.73i) q^{83} +(-9238.97 + 3001.92i) q^{85} +(-959.252 + 1661.47i) q^{87} +(494.194 + 160.573i) q^{89} +(-2474.26 - 3405.52i) q^{91} +(-3242.52 + 364.164i) q^{93} +(-2131.80 + 1548.85i) q^{95} +(1810.36 - 5571.72i) q^{97} +(4011.93 + 2316.29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	$ 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) $ 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

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			0
$2$		0			0
$3$	1.38100	+	3.10178i	0.153445	+	0.344642i	0.973868	−	0.227114i	$-0.0729290\pi$
$3$	1.38100	+	3.10178i	0.153445	+	0.344642i	−0.820424	+	0.571756i	$0.806262\pi$
$4$		0			0
$5$	21.1680	+	36.6640i	0.846719	+	1.46656i	0.884120	+	0.467261i	$0.154759\pi$
$5$	21.1680	+	36.6640i	0.846719	+	1.46656i	−0.0374000	+	0.999300i	$0.511908\pi$
$6$		0			0
$7$	12.2350	+	13.5884i	0.249694	+	0.277314i	0.854942	−	0.518724i	$-0.173593\pi$
$7$	12.2350	+	13.5884i	0.249694	+	0.277314i	−0.605248	+	0.796037i	$0.706926\pi$
$8$		0			0
$9$	46.4857	−	51.6276i	0.573898	−	0.637378i
$10$		0			0
$11$	13.8641	+	65.2256i	0.114580	+	0.539055i	0.997570	+	0.0696645i	$0.0221929\pi$
$11$	13.8641	+	65.2256i	0.114580	+	0.539055i	−0.882991	+	0.469390i	$0.844474\pi$
$12$		0			0
$13$	−228.953	−	24.0640i	−1.35475	−	0.142390i	−0.600842	−	0.799368i	$-0.705168\pi$
$13$	−228.953	−	24.0640i	−1.35475	−	0.142390i	−0.753910	+	0.656977i	$0.771835\pi$
$14$		0			0
$15$	−84.4907	+	116.291i	−0.375514	+	0.516851i
$16$		0			0
$17$	−47.7075	+	224.446i	−0.165078	+	0.776630i	0.815227	+	0.579141i	$0.196612\pi$
$17$	−47.7075	+	224.446i	−0.165078	+	0.776630i	−0.980305	+	0.197489i	$0.936721\pi$
$18$		0			0
$19$	6.50601	+	61.9005i	0.0180222	+	0.171470i	0.999831	−	0.0184045i	$-0.00585868\pi$
$19$	6.50601	+	61.9005i	0.0180222	+	0.171470i	−0.981808	+	0.189874i	$0.939192\pi$
$20$		0			0
$21$	−25.2515	+	56.7159i	−0.0572597	+	0.128607i
$22$		0			0
$23$	487.484	−	158.393i	0.921519	−	0.299420i	0.190429	−	0.981701i	$-0.439012\pi$
$23$	487.484	−	158.393i	0.921519	−	0.299420i	0.731090	+	0.682281i	$0.239012\pi$
$24$		0			0
$25$	−583.667	+	1010.94i	−0.933868	+	1.61751i
$26$		0			0
$27$	485.895	+	157.877i	0.666522	+	0.216566i
$28$		0			0
$29$	332.124	+	457.130i	0.394916	+	0.543555i	0.959459	−	0.281848i	$-0.0909475\pi$
$29$	332.124	+	457.130i	0.394916	+	0.543555i	−0.564543	+	0.825404i	$0.690947\pi$
$30$		0			0
$31$	−290.450	+	916.057i	−0.302237	+	0.953233i
$31$	−290.450	+	916.057i	−0.302237	+	0.953233i
$32$		0			0
$33$	−183.169	+	133.080i	−0.168199	+	0.122204i
$34$		0			0
$35$	−239.214	+	736.224i	−0.195276	+	0.600999i
$36$		0			0
$37$	−311.854	−	180.049i	−0.227797	−	0.131519i	0.381758	−	0.924262i	$-0.375319\pi$
$37$	−311.854	−	180.049i	−0.227797	−	0.131519i	−0.609555	+	0.792744i	$0.708652\pi$
$38$		0			0
$39$	−241.543	−	743.394i	−0.158806	−	0.488754i
$40$		0			0
$41$	−1818.97	−	809.859i	−1.08208	−	0.481772i	−0.213307	−	0.976985i	$-0.568423\pi$
$41$	−1818.97	−	809.859i	−1.08208	−	0.481772i	−0.868772	+	0.495213i	$0.835090\pi$
$42$		0			0
$43$	−698.258	+	73.3899i	−0.377641	+	0.0396917i	−0.291448	−	0.956587i	$-0.594137\pi$
$43$	−698.258	+	73.3899i	−0.377641	+	0.0396917i	−0.0861932	+	0.996278i	$0.527470\pi$
$44$		0			0
$45$	2876.89	+	611.501i	1.42068	+	0.301976i
$46$		0			0
$47$	942.881	+	685.043i	0.426836	+	0.310114i	0.780382	−	0.625302i	$-0.215024\pi$
$47$	942.881	+	685.043i	0.426836	+	0.310114i	−0.353547	+	0.935417i	$0.615024\pi$
$48$		0			0
$49$	216.025	−	2055.34i	0.0899729	−	0.856035i
$50$		0			0
$51$	−762.066	+	161.982i	−0.292990	+	0.0622769i
$52$		0			0
$53$	1310.59	+	1180.06i	0.466570	+	0.420101i	0.868591	−	0.495529i	$-0.165026\pi$
$53$	1310.59	+	1180.06i	0.466570	+	0.420101i	−0.402022	+	0.915630i	$0.631692\pi$
$54$		0			0
$55$	−2097.96	+	1889.01i	−0.693540	+	0.624466i
$56$		0			0
$57$	−183.017	+	105.665i	−0.0563302	+	0.0325223i
$58$		0			0
$59$	2782.07	−	1238.66i	0.799216	−	0.355834i	0.0338480	−	0.999427i	$-0.489224\pi$
$59$	2782.07	−	1238.66i	0.799216	−	0.355834i	0.765368	+	0.643593i	$0.222557\pi$
$60$		0			0
$61$		−	3323.29i		−	0.893119i	−0.894754	−	0.446559i	$-0.852649\pi$
$61$		−	3323.29i		−	0.893119i	0.894754	−	0.446559i	$-0.147351\pi$
$62$		0			0
$63$	1270.29			0.320053
$64$		0			0
$65$	−3964.20	−	8903.73i	−0.938272	−	2.10739i
$66$		0			0
$67$	2914.74	+	5048.47i	0.649307	+	1.12463i	0.983289	+	0.182053i	$0.0582742\pi$
$67$	2914.74	+	5048.47i	0.649307	+	1.12463i	−0.333982	+	0.942579i	$0.608393\pi$
$68$		0			0
$69$	1164.52	+	1293.33i	0.244595	+	0.271650i
$70$		0			0
$71$	2178.11	−	2419.04i	0.432080	−	0.479873i	−0.487306	−	0.873232i	$-0.662020\pi$
$71$	2178.11	−	2419.04i	0.432080	−	0.479873i	0.919385	+	0.393358i	$0.128687\pi$
$72$		0			0
$73$	−771.830	−	3631.18i	−0.144836	−	0.681399i	−0.989313	−	0.145808i	$-0.953422\pi$
$73$	−771.830	−	3631.18i	−0.144836	−	0.681399i	0.844477	−	0.535592i	$-0.179911\pi$
$74$		0			0
$75$	−3941.76	−	414.296i	−0.700758	−	0.0736526i
$76$		0			0
$77$	−716.682	+	986.428i	−0.120877	+	0.166373i
$78$		0			0
$79$	1333.12	−	6271.81i	0.213606	−	1.00494i	−0.732422	−	0.680851i	$-0.761610\pi$
$79$	1333.12	−	6271.81i	0.213606	−	1.00494i	0.946028	−	0.324086i	$-0.105057\pi$
$80$		0			0
$81$	−406.882	−	3871.22i	−0.0620153	−	0.590036i
$82$		0			0
$83$	4364.46	−	9802.73i	0.633540	−	1.42295i	−0.256262	−	0.966607i	$-0.582491\pi$
$83$	4364.46	−	9802.73i	0.633540	−	1.42295i	0.889802	−	0.456347i	$-0.150842\pi$
$84$		0			0
$85$	−9238.97	+	3001.92i	−1.27875	+	0.415491i
$86$		0			0
$87$	−959.252	+	1661.47i	−0.126734	+	0.219510i
$88$		0			0
$89$	494.194	+	160.573i	0.0623904	+	0.0202719i	0.340046	−	0.940409i	$-0.389557\pi$
$89$	494.194	+	160.573i	0.0623904	+	0.0202719i	−0.277656	+	0.960681i	$0.589557\pi$
$90$		0			0
$91$	−2474.26	−	3405.52i	−0.298787	−	0.411245i
$92$		0			0
$93$	−3242.52	+	364.164i	−0.374901	+	0.0421048i
$94$		0			0
$95$	−2131.80	+	1548.85i	−0.236211	+	0.171617i
$96$		0			0
$97$	1810.36	−	5571.72i	0.192407	−	0.592169i	−0.807590	−	0.589745i	$-0.799228\pi$
$97$	1810.36	−	5571.72i	0.192407	−	0.592169i	0.999997	−	0.00242440i	$-0.000771711\pi$
$98$		0			0
$99$	4011.93	+	2316.29i	0.409338	+	0.236332i
$100$		0			0
$101$	3596.57	+	11069.1i	0.352571	+	1.08510i	0.957405	+	0.288749i	$0.0932395\pi$
$101$	3596.57	+	11069.1i	0.352571	+	1.08510i	−0.604834	+	0.796352i	$0.706761\pi$
$102$		0			0
$103$	17517.6	+	7799.34i	1.65120	+	0.735162i	0.999724	−	0.0235058i	$-0.00748283\pi$
$103$	17517.6	+	7799.34i	1.65120	+	0.735162i	0.651477	+	0.758668i	$0.274149\pi$
$104$		0			0
$105$	−2613.96	+	274.738i	−0.237094	+	0.0249195i
$106$		0			0
$107$	14579.9	+	3099.05i	1.27347	+	0.270683i	0.794561	−	0.607184i	$-0.207701\pi$
$107$	14579.9	+	3099.05i	1.27347	+	0.270683i	0.478904	+	0.877867i	$0.341034\pi$
$108$		0			0
$109$	1398.20	+	1015.85i	0.117683	+	0.0855019i	0.645070	−	0.764123i	$-0.276828\pi$
$109$	1398.20	+	1015.85i	0.117683	+	0.0855019i	−0.527387	+	0.849625i	$0.676828\pi$
$110$		0			0
$111$	127.801	−	1215.95i	0.0103726	−	0.0986891i
$112$		0			0
$113$	−17508.8	+	3721.61i	−1.37119	+	0.291456i	−0.833889	−	0.551932i	$-0.813891\pi$
$113$	−17508.8	+	3721.61i	−1.37119	+	0.291456i	−0.537305	+	0.843388i	$0.680558\pi$
$114$		0			0
$115$	16126.4	+	14520.3i	1.21939	+	1.09794i
$116$		0			0
$117$	−11885.4	+	10701.7i	−0.868246	+	0.781772i
$118$		0			0
$119$	−3633.56	+	2097.84i	−0.256589	+	0.148142i
$120$		0			0
$121$	9313.05	−	4146.44i	0.636094	−	0.283207i
$122$		0			0
$123$		−	6760.47i		−	0.446855i
$124$		0			0
$125$	−22960.3			−1.46946
$126$		0			0
$127$	−4923.87	−	11059.2i	−0.305281	−	0.685671i	0.694135	−	0.719844i	$-0.255787\pi$
$127$	−4923.87	−	11059.2i	−0.305281	−	0.685671i	−0.999416	+	0.0341731i	$0.989120\pi$
$128$		0			0
$129$	−1191.93	−	2064.49i	−0.0716263	−	0.124060i
$130$		0			0
$131$	976.488	+	1084.50i	0.0569016	+	0.0631956i	0.770924	−	0.636928i	$-0.219795\pi$
$131$	976.488	+	1084.50i	0.0569016	+	0.0631956i	−0.714022	+	0.700123i	$0.753128\pi$
$132$		0			0
$133$	−761.526	+	845.760i	−0.0430508	+	0.0478128i
$134$		0			0
$135$	4497.01	+	21156.8i	0.246750	+	1.16087i
$136$		0			0
$137$	−29405.5	−	3090.64i	−1.56670	−	0.164667i	−0.718952	−	0.695059i	$-0.755378\pi$
$137$	−29405.5	−	3090.64i	−1.56670	−	0.164667i	−0.847753	+	0.530392i	$0.822045\pi$
$138$		0			0
$139$	−19998.9	+	27526.1i	−1.03509	+	1.42467i	−0.134025	+	0.990978i	$0.542790\pi$
$139$	−19998.9	+	27526.1i	−1.03509	+	1.42467i	−0.901060	+	0.433694i	$0.857210\pi$
$140$		0			0
$141$	−822.732	+	3870.65i	−0.0413828	+	0.194691i
$142$		0			0
$143$	−1604.65	−	15267.2i	−0.0784709	−	0.746601i
$144$		0			0
$145$	−9729.83	+	21853.5i	−0.462774	+	1.03941i
$146$		0			0
$147$	6673.54	−	2168.36i	0.308831	−	0.100345i
$148$		0			0
$149$	20201.7	−	34990.4i	0.909946	−	1.57607i	0.0958085	−	0.995400i	$-0.469456\pi$
$149$	20201.7	−	34990.4i	0.909946	−	1.57607i	0.814137	−	0.580673i	$-0.197210\pi$
$150$		0			0
$151$	41850.7	+	13598.1i	1.83548	+	0.596383i	0.998815	+	0.0486640i	$0.0154963\pi$
$151$	41850.7	+	13598.1i	1.83548	+	0.596383i	0.836662	+	0.547719i	$0.184504\pi$
$152$		0			0
$153$	9369.90	+	12896.6i	0.400269	+	0.550923i
$154$		0			0
$155$	−39734.6	+	8742.02i	−1.65388	+	0.363872i
$156$		0			0
$157$	32459.5	−	23583.2i	1.31687	−	0.956761i	0.316903	−	0.948458i	$-0.397357\pi$
$157$	32459.5	−	23583.2i	1.31687	−	0.956761i	0.999966	−	0.00830292i	$-0.00264293\pi$
$158$		0			0
$159$	−1850.37	+	5694.84i	−0.0731920	+	0.225262i
$160$		0			0
$161$	8116.68	+	4686.16i	0.313131	+	0.180786i
$162$		0			0
$163$	8658.21	+	26647.2i	0.325876	+	1.00294i	0.971043	+	0.238903i	$0.0767878\pi$
$163$	8658.21	+	26647.2i	0.325876	+	1.00294i	−0.645167	+	0.764042i	$0.723212\pi$
$164$		0			0
$165$	−8756.57	−	3898.68i	−0.321637	−	0.143202i
$166$		0			0
$167$	−22693.2	+	2385.15i	−0.813698	+	0.0855231i	−0.502230	−	0.864734i	$-0.667487\pi$
$167$	−22693.2	+	2385.15i	−0.813698	+	0.0855231i	−0.311467	+	0.950257i	$0.600820\pi$
$168$		0			0
$169$	23903.6	+	5080.87i	0.836932	+	0.177895i
$170$		0			0
$171$	3498.21	+	2541.60i	0.119634	+	0.0869191i
$172$		0			0
$173$	−2632.52	+	25046.8i	−0.0879588	+	0.836872i	0.858232	+	0.513262i	$0.171563\pi$
$173$	−2632.52	+	25046.8i	−0.0879588	+	0.836872i	−0.946191	+	0.323610i	$0.895103\pi$
$174$		0			0
$175$	−20878.2	+	4437.80i	−0.681738	+	0.144908i
$176$		0			0
$177$	7684.08	+	6918.78i	0.245271	+	0.220843i
$178$		0			0
$179$	17004.3	−	15310.8i	0.530705	−	0.477849i	−0.359668	−	0.933080i	$-0.617110\pi$
$179$	17004.3	−	15310.8i	0.530705	−	0.477849i	0.890373	+	0.455231i	$0.150443\pi$
$180$		0			0
$181$	25058.0	−	14467.2i	0.764872	−	0.441599i	−0.0661700	−	0.997808i	$-0.521078\pi$
$181$	25058.0	−	14467.2i	0.764872	−	0.441599i	0.831042	+	0.556209i	$0.187745\pi$
$182$		0			0
$183$	10308.1	−	4589.47i	0.307806	−	0.137044i
$184$		0			0
$185$		−	15245.1i		−	0.445437i
$186$		0			0
$187$	−15301.1			−0.437561
$188$		0			0
$189$	3799.64	+	8534.14i	0.106370	+	0.238911i
$190$		0			0
$191$	−28641.7	−	49608.9i	−0.785114	−	1.35986i	−0.928931	−	0.370253i	$-0.879271\pi$
$191$	−28641.7	−	49608.9i	−0.785114	−	1.35986i	0.143817	−	0.989604i	$-0.454062\pi$
$192$		0			0
$193$	−18446.0	−	20486.3i	−0.495207	−	0.549983i	0.442791	−	0.896625i	$-0.353988\pi$
$193$	−18446.0	−	20486.3i	−0.495207	−	0.549983i	−0.937997	+	0.346642i	$0.887322\pi$
$194$		0			0
$195$	22142.8	−	24592.1i	0.582323	−	0.646736i
$196$		0			0
$197$	−6576.14	−	30938.3i	−0.169449	−	0.797194i	−0.977973	−	0.208731i	$-0.933067\pi$
$197$	−6576.14	−	30938.3i	−0.169449	−	0.797194i	0.808524	−	0.588463i	$-0.200267\pi$
$198$		0			0
$199$	−33151.9	−	3484.40i	−0.837147	−	0.0879877i	−0.323754	−	0.946141i	$-0.604945\pi$
$199$	−33151.9	−	3484.40i	−0.837147	−	0.0879877i	−0.513393	+	0.858154i	$0.671612\pi$
$200$		0			0
$201$	−11634.0	+	16012.8i	−0.287963	+	0.396347i
$202$		0			0
$203$	−2148.10	+	10106.0i	−0.0521270	+	0.245238i
$204$		0			0
$205$	−8811.31	−	83834.0i	−0.209668	−	1.99486i
$206$		0			0
$207$	14483.6	−	32530.6i	0.338014	−	0.759192i
$208$		0			0
$209$	−3947.30	+	1282.56i	−0.0903665	+	0.0293619i
$210$		0			0
$211$	8116.52	−	14058.2i	0.182308	−	0.315766i	−0.760358	−	0.649504i	$-0.774977\pi$
$211$	8116.52	−	14058.2i	0.182308	−	0.315766i	0.942666	+	0.333738i	$0.108310\pi$
$212$		0			0
$213$	10511.3	+	3415.33i	0.231685	+	0.0752789i
$214$		0			0
$215$	−17471.5	−	24047.4i	−0.377966	−	0.520226i
$216$		0			0
$217$	−16001.4	+	7261.24i	−0.339811	+	0.154202i
$218$		0			0
$219$	10197.2	−	7408.70i	0.212615	−	0.154473i
$220$		0			0
$221$	16323.8	−	50239.6i	0.334224	−	1.02864i
$222$		0			0
$223$	41443.6	+	23927.5i	0.833390	+	0.481158i	0.855012	−	0.518608i	$-0.173550\pi$
$223$	41443.6	+	23927.5i	0.833390	+	0.481158i	−0.0216220	+	0.999766i	$0.506883\pi$
$224$		0			0
$225$	25060.3	+	77127.7i	0.495018	+	1.52351i
$226$		0			0
$227$	33948.2	+	15114.7i	0.658818	+	0.293325i	0.708783	−	0.705426i	$-0.249244\pi$
$227$	33948.2	+	15114.7i	0.658818	+	0.293325i	−0.0499653	+	0.998751i	$0.515911\pi$
$228$		0			0
$229$	−61924.4	+	6508.51i	−1.18084	+	0.124111i	−0.674534	−	0.738243i	$-0.735656\pi$
$229$	−61924.4	+	6508.51i	−1.18084	+	0.124111i	−0.506305	+	0.862355i	$0.668989\pi$
$230$		0			0
$231$	−4049.42	−	860.730i	−0.0758872	−	0.0161303i
$232$		0			0
$233$	−12629.2	−	9175.66i	−0.232629	−	0.169015i	0.465364	−	0.885119i	$-0.345923\pi$
$233$	−12629.2	−	9175.66i	−0.232629	−	0.169015i	−0.697993	+	0.716104i	$0.745923\pi$
$234$		0			0
$235$	−5157.55	+	49070.8i	−0.0933915	+	0.888561i
$236$		0			0
$237$	21294.8	−	4526.35i	0.379120	−	0.0805845i
$238$		0			0
$239$	2261.27	+	2036.06i	0.0395874	+	0.0356447i	0.688687	−	0.725059i	$-0.258187\pi$
$239$	2261.27	+	2036.06i	0.0395874	+	0.0356447i	−0.649100	+	0.760704i	$0.724854\pi$
$240$		0			0
$241$	−39991.7	+	36008.7i	−0.688550	+	0.619974i	−0.937271	−	0.348602i	$-0.886657\pi$
$241$	−39991.7	+	36008.7i	−0.688550	+	0.619974i	0.248720	+	0.968575i	$0.419990\pi$
$242$		0			0
$243$	47284.4	−	27299.7i	0.800766	−	0.462322i
$244$		0			0
$245$	79929.8	−	35587.1i	1.33161	−	0.592870i
$246$		0			0
$247$		−	14328.9i		−	0.234865i
$248$		0			0
$249$	36433.2			0.587623
$250$		0			0
$251$	−50379.1	−	113153.i	−0.799656	−	1.79606i	−0.567488	−	0.823382i	$-0.692085\pi$
$251$	−50379.1	−	113153.i	−0.799656	−	1.79606i	−0.232169	−	0.972676i	$-0.574582\pi$
$252$		0			0
$253$	17089.8	+	29600.4i	0.266991	+	0.462442i
$254$		0			0
$255$	−22070.3	−	24511.6i	−0.339413	−	0.376956i
$256$		0			0
$257$	−49711.3	+	55210.0i	−0.752643	+	0.835894i	−0.990800	−	0.135332i	$-0.956790\pi$
$257$	−49711.3	+	55210.0i	−0.752643	+	0.835894i	0.238158	+	0.971227i	$0.423457\pi$
$258$		0			0
$259$	−1368.97	−	6440.49i	−0.0204077	−	0.0960106i
$260$		0			0
$261$	39039.6	+	4103.23i	0.573092	+	0.0602344i
$262$		0			0
$263$	21133.9	−	29088.3i	0.305540	−	0.420540i	−0.628444	−	0.777855i	$-0.716308\pi$
$263$	21133.9	−	29088.3i	0.305540	−	0.420540i	0.933984	+	0.357315i	$0.116308\pi$
$264$		0			0
$265$	−15523.3	+	73031.3i	−0.221051	+	1.03996i
$266$		0			0
$267$	184.419	+	1754.63i	0.00258693	+	0.0246130i
$268$		0			0
$269$	−11745.5	+	26380.9i	−0.162319	+	0.364574i	−0.976333	−	0.216270i	$-0.930611\pi$
$269$	−11745.5	+	26380.9i	−0.162319	+	0.364574i	0.814015	+	0.580844i	$0.197277\pi$
$270$		0			0
$271$	−94497.3	+	30704.0i	−1.28671	+	0.418078i	−0.870939	−	0.491391i	$-0.836489\pi$
$271$	−94497.3	+	30704.0i	−1.28671	+	0.418078i	−0.415772	+	0.909469i	$0.636489\pi$
$272$		0			0
$273$	7146.23	−	12377.6i	0.0958852	−	0.166078i
$274$		0			0
$275$	−74031.3	−	24054.2i	−0.978927	−	0.318073i
$276$		0			0
$277$	16899.5	+	23260.2i	0.220249	+	0.303147i	0.904816	−	0.425803i	$-0.140008\pi$
$277$	16899.5	+	23260.2i	0.220249	+	0.303147i	−0.684566	+	0.728951i	$0.740008\pi$
$278$		0			0
$279$	33792.1	+	57578.8i	0.434116	+	0.739697i
$280$		0			0
$281$	−48683.8	+	35370.9i	−0.616556	+	0.447954i	−0.851717	−	0.524003i	$-0.824438\pi$
$281$	−48683.8	+	35370.9i	−0.616556	+	0.447954i	0.235161	+	0.971956i	$0.424438\pi$
$282$		0			0
$283$	−7745.53	+	23838.3i	−0.0967116	+	0.297648i	−0.987696	−	0.156386i	$-0.950016\pi$
$283$	−7745.53	+	23838.3i	−0.0967116	+	0.297648i	0.890984	+	0.454034i	$0.150016\pi$
$284$		0			0
$285$	−7748.20	−	4473.42i	−0.0953918	−	0.0550745i
$286$		0			0
$287$	−11250.5	−	34625.5i	−0.136587	−	0.420371i
$288$		0			0
$289$	28200.2	+	12555.5i	0.337642	+	0.150328i
$290$		0			0
$291$	19782.4	−	2079.21i	0.233610	−	0.0245534i
$292$		0			0
$293$	9460.56	+	2010.90i	0.110200	+	0.0234237i	0.262682	−	0.964883i	$-0.415393\pi$
$293$	9460.56	+	2010.90i	0.110200	+	0.0234237i	−0.152482	+	0.988306i	$0.548726\pi$
$294$		0			0
$295$	104305.	+	75782.0i	1.19856	+	0.870807i
$296$		0			0
$297$	−3561.10	+	33881.6i	−0.0403712	+	0.384106i
$298$		0			0
$299$	−115423.	+	24533.8i	−1.29107	+	0.274424i
$300$		0			0
$301$	−9540.45	−	8590.26i	−0.105302	−	0.0948142i
$302$		0			0
$303$	−29367.1	+	26442.2i	−0.319871	+	0.288013i
$304$		0			0
$305$	121845.	−	70347.5i	1.30981	−	0.756221i
$306$		0			0
$307$	−106059.	+	47220.6i	−1.12531	+	0.501020i	−0.883091	−	0.469202i	$-0.844541\pi$
$307$	−106059.	+	47220.6i	−1.12531	+	0.501020i	−0.242218	+	0.970222i	$0.577875\pi$
$308$		0			0
$309$			65106.6i			0.681880i
$310$		0			0
$311$	22545.5			0.233099			0.116549	−	0.993185i	$-0.462817\pi$
$311$	22545.5			0.233099			0.116549	+	0.993185i	$0.462817\pi$
$312$		0			0
$313$	57608.6	+	129391.i	0.588029	+	1.32073i	0.925267	+	0.379315i	$0.123840\pi$
$313$	57608.6	+	129391.i	0.588029	+	1.32073i	−0.337239	+	0.941419i	$0.609493\pi$
$314$		0			0
$315$	26889.5	+	46573.9i	0.270995	+	0.469377i
$316$		0			0
$317$	49355.2	+	54814.5i	0.491150	+	0.545478i	0.936862	−	0.349699i	$-0.113716\pi$
$317$	49355.2	+	54814.5i	0.491150	+	0.545478i	−0.445712	+	0.895177i	$0.647049\pi$
$318$		0			0
$319$	−25212.0	+	28000.7i	−0.247757	+	0.275162i
$320$		0			0
$321$	10522.3	+	49503.4i	0.102117	+	0.480424i
$322$		0			0
$323$	−14203.7	−	1492.87i	−0.136143	−	0.0143093i
$324$		0			0
$325$	157960.	−	217413.i	1.49548	−	2.05835i
$326$		0			0
$327$	−1220.03	+	5739.78i	−0.0114097	+	0.0536784i
$328$		0			0
$329$	2227.55	+	21193.7i	0.0205795	+	0.195801i
$330$		0			0
$331$	10577.6	−	23757.7i	0.0965456	−	0.216845i	−0.858816	−	0.512284i	$-0.828799\pi$
$331$	10577.6	−	23757.7i	0.0965456	−	0.216845i	0.955361	+	0.295439i	$0.0954661\pi$
$332$		0			0
$333$	−23792.2	+	7730.57i	−0.214559	+	0.0697145i
$334$		0			0
$335$	−123398.	+	213732.i	−1.09956	+	1.90450i
$336$		0			0
$337$	11542.6	+	3750.43i	0.101635	+	0.0330234i	0.359393	−	0.933186i	$-0.382984\pi$
$337$	11542.6	+	3750.43i	0.101635	+	0.0330234i	−0.257758	+	0.966210i	$0.582984\pi$
$338$		0			0
$339$	−35723.2	−	49168.8i	−0.310850	−	0.427849i
$340$		0			0
$341$	−63777.2	−	6244.43i	−0.548475	−	0.0537012i
$342$		0			0
$343$	66089.4	−	48016.7i	0.561750	−	0.408136i
$344$		0			0
$345$	−22768.1	+	70072.9i	−0.191288	+	0.588724i
$346$		0			0
$347$	−139923.	−	80784.3i	−1.16206	−	0.670916i	−0.210264	−	0.977645i	$-0.567432\pi$
$347$	−139923.	−	80784.3i	−1.16206	−	0.670916i	−0.951797	+	0.306729i	$0.900766\pi$
$348$		0			0
$349$	−18069.9	−	55613.4i	−0.148356	−	0.456592i	0.849071	−	0.528278i	$-0.177162\pi$
$349$	−18069.9	−	55613.4i	−0.148356	−	0.456592i	−0.997427	+	0.0716857i	$0.977162\pi$
$350$		0			0
$351$	−107448.	−	47838.9i	−0.872136	−	0.388300i
$352$		0			0
$353$	−115967.	+	12188.6i	−0.930645	+	0.0978147i	−0.557704	−	0.830040i	$-0.688317\pi$
$353$	−115967.	+	12188.6i	−0.930645	+	0.0978147i	−0.372941	+	0.927855i	$0.621651\pi$
$354$		0			0
$355$	134798.	+	28652.2i	1.06961	+	0.227353i
$356$		0			0
$357$	−11525.0	−	8373.38i	−0.0904281	−	0.0656998i
$358$		0			0
$359$	24113.9	−	229428.i	0.187102	−	1.78016i	−0.350110	−	0.936709i	$-0.613856\pi$
$359$	24113.9	−	229428.i	0.187102	−	1.78016i	0.537211	−	0.843448i	$-0.319478\pi$
$360$		0			0
$361$	123684.	−	26289.8i	0.949071	−	0.201731i
$362$		0			0
$363$	25722.7	+	23160.8i	0.195210	+	0.175768i
$364$		0			0
$365$	116795.	−	105163.i	0.876678	−	0.789365i
$366$		0			0
$367$	−101499.	+	58600.3i	−0.753579	+	0.435079i	−0.826986	−	0.562223i	$-0.809946\pi$
$367$	−101499.	+	58600.3i	−0.753579	+	0.435079i	0.0734068	+	0.997302i	$0.476613\pi$
$368$		0			0
$369$	−126367.	+	56262.4i	−0.928073	+	0.413205i
$370$		0			0
$371$			32247.0i			0.234283i
$372$		0			0
$373$	197608.			1.42032			0.710160	−	0.704041i	$-0.248623\pi$
$373$	197608.			1.42032			0.710160	+	0.704041i	$0.248623\pi$
$374$		0			0
$375$	−31708.1	−	71217.7i	−0.225480	−	0.506437i
$376$		0			0
$377$	−65040.6	−	112654.i	−0.457617	−	0.792615i
$378$		0			0
$379$	−111481.	−	123812.i	−0.776110	−	0.861957i	0.217355	−	0.976093i	$-0.430257\pi$
$379$	−111481.	−	123812.i	−0.776110	−	0.861957i	−0.993465	+	0.114135i	$0.963590\pi$
$380$		0			0
$381$	27503.3	−	30545.5i	0.189468	−	0.210425i
$382$		0			0
$383$	8786.97	+	41339.5i	0.0599021	+	0.281817i	0.997896	−	0.0648345i	$-0.0206520\pi$
$383$	8786.97	+	41339.5i	0.0599021	+	0.281817i	−0.937994	+	0.346652i	$0.887319\pi$
$384$		0			0
$385$	−51337.1	−	5395.75i	−0.346346	−	0.0364024i
$386$		0			0
$387$	−28670.1	+	39461.0i	−0.191429	+	0.263479i
$388$		0			0
$389$	−17429.2	+	81998.1i	−0.115181	+	0.541882i	0.882284	+	0.470717i	$0.156005\pi$
$389$	−17429.2	+	81998.1i	−0.115181	+	0.541882i	−0.997465	+	0.0711644i	$0.977328\pi$
$390$		0			0
$391$	12294.1	+	116970.i	0.0804160	+	0.765107i
$392$		0			0
$393$	−2015.35	+	4526.54i	−0.0130486	+	0.0293077i
$394$		0			0
$395$	258169.	−	83884.3i	1.65467	−	0.537634i
$396$		0			0
$397$	−35266.4	+	61083.2i	−0.223759	+	0.387562i	−0.955946	−	0.293541i	$-0.905166\pi$
$397$	−35266.4	+	61083.2i	−0.223759	+	0.387562i	0.732187	+	0.681103i	$0.238499\pi$
$398$		0			0
$399$	−3675.03	−	1194.09i	−0.0230842	−	0.00750051i
$400$		0			0
$401$	−37615.0	−	51772.7i	−0.233923	−	0.321967i	0.675877	−	0.737014i	$-0.263765\pi$
$401$	−37615.0	−	51772.7i	−0.233923	−	0.321967i	−0.909800	+	0.415047i	$0.863765\pi$
$402$		0			0
$403$	88543.4	−	202745.i	0.545188	−	1.24836i
$404$		0			0
$405$	133322.	−	96864.0i	0.812814	−	0.590544i
$406$		0			0
$407$	7420.21	−	22837.1i	0.0447948	−	0.137864i
$408$		0			0
$409$	−61638.2	−	35586.8i	−0.368471	−	0.212737i	0.304319	−	0.952570i	$-0.401571\pi$
$409$	−61638.2	−	35586.8i	−0.368471	−	0.212737i	−0.672790	+	0.739833i	$0.734904\pi$
$410$		0			0
$411$	−31022.5	−	95477.5i	−0.183651	−	0.565220i
$412$		0			0
$413$	50870.0	+	22648.8i	0.298237	+	0.132784i
$414$		0			0
$415$	451794.	−	47485.5i	2.62328	−	0.275718i
$416$		0			0
$417$	−112998.	−	24018.5i	−0.649830	−	0.138126i
$418$		0			0
$419$	191881.	+	139410.i	1.09296	+	0.794081i	0.979896	−	0.199507i	$-0.0639341\pi$
$419$	191881.	+	139410.i	1.09296	+	0.794081i	0.113062	+	0.993588i	$0.463934\pi$
$420$		0			0
$421$	6894.52	−	65596.9i	0.0388991	−	0.370100i	−0.957705	−	0.287753i	$-0.907092\pi$
$421$	6894.52	−	65596.9i	0.0388991	−	0.370100i	0.996604	−	0.0823471i	$-0.0262416\pi$
$422$		0			0
$423$	79197.6	−	16834.0i	0.442620	−	0.0940819i
$424$		0			0
$425$	−199057.	−	179231.i	−1.10204	−	0.992284i
$426$		0			0
$427$	45158.2	−	40660.6i	0.247674	−	0.223007i
$428$		0			0
$429$	45139.6	−	26061.3i	0.245269	−	0.141606i
$430$		0			0
$431$	−289508.	+	128897.i	−1.55850	+	0.693887i	−0.991533	−	0.129855i	$-0.958549\pi$
$431$	−289508.	+	128897.i	−1.55850	+	0.693887i	−0.566964	+	0.823743i	$0.691882\pi$
$432$		0			0
$433$			268504.i			1.43211i	0.698045	+	0.716054i	$0.254053\pi$
$433$			268504.i			1.43211i	−0.698045	+	0.716054i	$0.745947\pi$
$434$		0			0
$435$	−81221.8			−0.429234
$436$		0			0
$437$	12976.2	+	29145.0i	0.0679492	+	0.152616i
$438$		0			0
$439$	−96918.4	−	167868.i	−0.502895	−	0.871040i	−0.999994	−	0.00334606i	$-0.998935\pi$
$439$	−96918.4	−	167868.i	−0.502895	−	0.871040i	0.497099	−	0.867694i	$-0.334398\pi$
$440$		0			0
$441$	−96070.2	−	106697.i	−0.493982	−	0.548623i
$442$		0			0
$443$	−240368.	+	266956.i	−1.22481	+	1.36029i	−0.312966	+	0.949764i	$0.601323\pi$
$443$	−240368.	+	266956.i	−1.22481	+	1.36029i	−0.911847	+	0.410529i	$0.865344\pi$
$444$		0			0
$445$	4573.83	+	21518.2i	0.0230972	+	0.108664i
$446$		0			0
$447$	136431.	+	14339.5i	0.682807	+	0.0717659i
$448$		0			0
$449$	200711.	−	276255.i	0.995585	−	1.37031i	0.0675905	−	0.997713i	$-0.478469\pi$
$449$	200711.	−	276255.i	0.995585	−	1.37031i	0.927995	−	0.372593i	$-0.121531\pi$
$450$		0			0
$451$	27605.1	−	129872.i	0.135717	−	0.638501i
$452$		0			0
$453$	15617.5	+	148591.i	0.0761054	+	0.724094i
$454$		0			0
$455$	72485.2	−	162804.i	0.350128	−	0.786399i
$456$		0			0
$457$	−233401.	+	75836.5i	−1.11756	+	0.363117i	−0.808835	−	0.588035i	$-0.799902\pi$
$457$	−233401.	+	75836.5i	−1.11756	+	0.363117i	−0.308723	+	0.951152i	$0.599902\pi$
$458$		0			0
$459$	−58615.6	+	101525.i	−0.278220	+	0.481891i
$460$		0			0
$461$	−290492.	−	94386.5i	−1.36689	−	0.444128i	−0.468549	−	0.883437i	$-0.655223\pi$
$461$	−290492.	−	94386.5i	−1.36689	−	0.444128i	−0.898336	+	0.439309i	$0.855223\pi$
$462$		0			0
$463$	−113749.	−	156562.i	−0.530623	−	0.730340i	0.456602	−	0.889671i	$-0.349066\pi$
$463$	−113749.	−	156562.i	−0.530623	−	0.730340i	−0.987225	+	0.159331i	$0.949066\pi$
$464$		0			0
$465$	−81989.3	−	111175.i	−0.379185	−	0.514164i
$466$		0			0
$467$	210162.	−	152691.i	0.963651	−	0.700133i	0.00965484	−	0.999953i	$-0.496927\pi$
$467$	210162.	−	152691.i	0.963651	−	0.700133i	0.953996	+	0.299820i	$0.0969267\pi$
$468$		0			0
$469$	−32938.6	+	101375.i	−0.149748	+	0.460876i
$470$		0			0
$471$	117976.	+	68113.7i	0.531806	+	0.307038i
$472$		0			0
$473$	−14467.6	−	44526.8i	−0.0646659	−	0.199021i
$474$		0			0
$475$	−66375.1	−	29552.1i	−0.294183	−	0.130979i
$476$		0			0
$477$	121848.	−	12806.7i	0.535527	−	0.0562861i
$478$		0			0
$479$	56160.9	+	11937.4i	0.244773	+	0.0520280i	0.328664	−	0.944447i	$-0.393402\pi$
$479$	56160.9	+	11937.4i	0.244773	+	0.0520280i	−0.0838915	+	0.996475i	$0.526735\pi$
$480$		0			0
$481$	67067.2	+	48727.2i	0.289881	+	0.210611i
$482$		0			0
$483$	−3326.31	+	31647.7i	−0.0142583	+	0.135659i
$484$		0			0
$485$	242603.	−	51567.0i	1.03137	−	0.219224i
$486$		0			0
$487$	−204842.	−	184441.i	−0.863697	−	0.777676i	0.112707	−	0.993628i	$-0.464048\pi$
$487$	−204842.	−	184441.i	−0.863697	−	0.777676i	−0.976404	+	0.215952i	$0.930715\pi$
$488$		0			0
$489$	−70696.8	+	63655.7i	−0.295653	+	0.266207i
$490$		0			0
$491$	−100477.	+	58010.7i	−0.416779	+	0.240627i	−0.693698	−	0.720266i	$-0.744020\pi$
$491$	−100477.	+	58010.7i	−0.416779	+	0.240627i	0.276919	+	0.960893i	$0.410687\pi$
$492$		0			0
$493$	−118446.	+	52735.5i	−0.487333	+	0.216975i
$494$		0			0
$495$			196125.i			0.800427i
$496$		0			0
$497$	59520.1			0.240963
$498$		0			0
$499$	34523.1	+	77540.1i	0.138646	+	0.311405i	0.969502	−	0.245083i	$-0.0788152\pi$
$499$	34523.1	+	77540.1i	0.138646	+	0.311405i	−0.830856	+	0.556488i	$0.812149\pi$
$500$		0			0
$501$	−38737.6	−	67095.4i	−0.154332	−	0.267311i
$502$		0			0
$503$	214802.	+	238562.i	0.848991	+	0.942900i	0.998951	−	0.0457917i	$-0.0145811\pi$
$503$	214802.	+	238562.i	0.848991	+	0.942900i	−0.149960	+	0.988692i	$0.547914\pi$
$504$		0			0
$505$	−329706.	+	366176.i	−1.29284	+	1.43584i
$506$		0			0
$507$	17251.2	+	81160.4i	0.0671124	+	0.315739i
$508$		0			0
$509$	177585.	+	18664.9i	0.685441	+	0.0720428i	0.440846	−	0.897583i	$-0.354678\pi$
$509$	177585.	+	18664.9i	0.685441	+	0.0720428i	0.244595	+	0.969625i	$0.421345\pi$
$510$		0			0
$511$	39898.4	−	54915.4i	0.152797	−	0.210306i
$512$		0			0
$513$	−6611.42	+	31104.3i	−0.0251223	+	0.118191i
$514$		0			0
$515$	84857.1	+	807362.i	0.319944	+	3.04406i
$516$		0			0
$517$	−31610.1	+	70997.5i	−0.118262	+	0.265621i
$518$		0			0
$519$	−81325.0	+	26424.1i	−0.301918	+	0.0980992i
$520$		0			0
$521$	38504.8	−	66692.3i	0.141853	−	0.245697i	−0.786341	−	0.617792i	$-0.788027\pi$
$521$	38504.8	−	66692.3i	0.141853	−	0.245697i	0.928195	+	0.372095i	$0.121361\pi$
$522$		0			0
$523$	61376.7	+	19942.5i	0.224388	+	0.0729082i	0.419053	−	0.907962i	$-0.362362\pi$
$523$	61376.7	+	19942.5i	0.224388	+	0.0729082i	−0.194665	+	0.980870i	$0.562362\pi$
$524$		0			0
$525$	−42597.9	−	58631.0i	−0.154550	−	0.212720i
$526$		0			0
$527$	−191749.	−	108893.i	−0.690417	−	0.392084i
$528$		0			0
$529$	−13844.2	+	10058.4i	−0.0494716	+	0.0359432i
$530$		0			0
$531$	65377.6	−	201212.i	0.231867	−	0.713615i
$532$		0			0
$533$	396971.	+	229192.i	1.39735	+	0.806760i
$534$		0			0
$535$	195003.	+	600159.i	0.681294	+	2.09681i
$536$		0			0
$537$	70973.6	+	31599.5i	0.246121	+	0.109580i
$538$		0			0
$539$	137056.	−	14405.1i	0.471758	−	0.0495838i
$540$		0			0
$541$	−336521.	−	71529.8i	−1.14979	−	0.244395i	−0.406683	−	0.913569i	$-0.633315\pi$
$541$	−336521.	−	71529.8i	−1.14979	−	0.244395i	−0.743106	+	0.669174i	$0.766648\pi$
$542$		0			0
$543$	79479.2	+	57745.1i	0.269559	+	0.195846i
$544$		0			0
$545$	−7648.11	+	72766.9i	−0.0257491	+	0.244986i
$546$		0			0
$547$	290151.	−	61673.4i	0.969726	−	0.206122i	0.304292	−	0.952579i	$-0.401580\pi$
$547$	290151.	−	61673.4i	0.969726	−	0.206122i	0.665433	+	0.746457i	$0.268247\pi$
$548$		0			0
$549$	−171574.	−	154486.i	−0.569254	−	0.512559i
$550$		0			0
$551$	−26135.8	+	23532.8i	−0.0860860	+	0.0775122i
$552$		0			0
$553$	101534.	−	58620.9i	0.332019	−	0.191691i
$554$		0			0
$555$	47286.9	−	21053.5i	0.153516	−	0.0683499i
$556$		0			0
$557$		−	160712.i		−	0.518010i	−0.965876	−	0.259005i	$-0.916605\pi$
$557$		−	160712.i		−	0.518010i	0.965876	−	0.259005i	$-0.0833945\pi$
$558$		0			0
$559$	161634.			0.517262
$560$		0			0
$561$	−21130.8	−	47460.5i	−0.0671413	−	0.150802i
$562$		0			0
$563$	170868.	+	295951.i	0.539067	+	0.933692i	0.998955	+	0.0457148i	$0.0145565\pi$
$563$	170868.	+	295951.i	0.539067	+	0.933692i	−0.459887	+	0.887977i	$0.652110\pi$
$564$		0			0
$565$	−507075.	−	563163.i	−1.58846	−	1.76416i
$566$		0			0
$567$	47625.4	−	52893.4i	0.148140	−	0.164526i
$568$		0			0
$569$	90973.6	+	427997.i	0.280990	+	1.32195i	0.861524	+	0.507717i	$0.169511\pi$
$569$	90973.6	+	427997.i	0.280990	+	1.32195i	−0.580534	+	0.814236i	$0.697156\pi$
$570$		0			0
$571$	−626668.	−	65865.5i	−1.92205	−	0.202016i	−0.934128	−	0.356939i	$-0.883820\pi$
$571$	−626668.	−	65865.5i	−1.92205	−	0.202016i	−0.987926	+	0.154923i	$0.950487\pi$
$572$		0			0
$573$	114322.	−	157350.i	0.348192	−	0.479246i
$574$		0			0
$575$	−124402.	+	585266.i	−0.376264	+	1.77018i
$576$		0			0
$577$	19081.7	+	181551.i	0.0573148	+	0.545313i	0.985074	+	0.172133i	$0.0550660\pi$
$577$	19081.7	+	181551.i	0.0573148	+	0.545313i	−0.927759	+	0.373180i	$0.878267\pi$
$578$		0			0
$579$	38070.1	−	85506.9i	0.113560	−	0.255061i
$580$		0			0
$581$	186602.	−	60630.8i	0.552796	−	0.179614i
$582$		0			0
$583$	−58800.2	+	101845.i	−0.172998	+	0.299642i
$584$		0			0
$585$	−643957.	−	209234.i	−1.88168	−	0.611394i
$586$		0			0
$587$	−284284.	−	391283.i	−0.825043	−	1.13557i	−0.988826	−	0.149077i	$-0.952370\pi$
$587$	−284284.	−	391283.i	−0.825043	−	1.13557i	0.163783	−	0.986496i	$-0.447630\pi$
$588$		0			0
$589$	−58594.1	−	12019.1i	−0.168897	−	0.0346451i
$590$		0			0
$591$	86882.1	−	63123.5i	0.248746	−	0.180724i
$592$		0			0
$593$	−41258.0	+	126979.i	−0.117327	+	0.361096i	−0.992425	−	0.122849i	$-0.960797\pi$
$593$	−41258.0	+	126979.i	−0.117327	+	0.361096i	0.875098	+	0.483946i	$0.160797\pi$
$594$		0			0
$595$	−153830.	−	88813.9i	−0.434518	−	0.250869i
$596$		0			0
$597$	−34974.9	−	107642.i	−0.0981314	−	0.302017i
$598$		0			0
$599$	51838.6	+	23080.0i	0.144477	+	0.0643255i	0.477702	−	0.878522i	$-0.341470\pi$
$599$	51838.6	+	23080.0i	0.144477	+	0.0643255i	−0.333224	+	0.942848i	$0.608137\pi$
$600$		0			0
$601$	−404133.	+	42476.1i	−1.11886	+	0.117597i	−0.645853	−	0.763462i	$-0.723498\pi$
$601$	−404133.	+	42476.1i	−1.11886	+	0.117597i	−0.473006	+	0.881059i	$0.656831\pi$
$602$		0			0
$603$	396134.	+	84201.0i	1.08945	+	0.231570i
$604$		0			0
$605$	349164.	+	253682.i	0.953934	+	0.693074i
$606$		0			0
$607$	59975.8	−	570632.i	0.162779	−	1.54874i	−0.542649	−	0.839959i	$-0.682579\pi$
$607$	59975.8	−	570632.i	0.162779	−	1.54874i	0.705428	−	0.708781i	$-0.250755\pi$
$608$		0			0
$609$	−34313.2	+	7293.49i	−0.0925180	+	0.0196653i
$610$		0			0
$611$	−199391.	−	179532.i	−0.534100	−	0.480906i
$612$		0			0
$613$	91569.6	−	82449.7i	0.243686	−	0.219416i	−0.538233	−	0.842796i	$-0.680908\pi$
$613$	91569.6	−	82449.7i	0.243686	−	0.219416i	0.781919	+	0.623380i	$0.214241\pi$
$614$		0			0
$615$	247866.	−	143106.i	0.655340	−	0.378361i
$616$		0			0
$617$	−123208.	+	54855.6i	−0.323644	+	0.144096i	−0.562127	−	0.827051i	$-0.690017\pi$
$617$	−123208.	+	54855.6i	−0.323644	+	0.144096i	0.238483	+	0.971147i	$0.423350\pi$
$618$		0			0
$619$			61355.1i			0.160129i	0.996790	+	0.0800644i	$0.0255126\pi$
$619$			61355.1i			0.160129i	−0.996790	+	0.0800644i	$0.974487\pi$
$620$		0			0
$621$	261872.			0.679057
$622$		0			0
$623$	3864.55	+	8679.92i	0.00995686	+	0.0223635i
$624$		0			0
$625$	−121231.	−	209978.i	−0.310350	−	0.537542i
$626$		0			0
$627$	−9429.42	−	10472.4i	−0.0239856	−	0.0266387i
$628$		0			0
$629$	55289.0	−	61404.7i	0.139745	−	0.155203i
$630$		0			0
$631$	−65914.2	−	310102.i	−0.165547	−	0.778836i	−0.980062	−	0.198693i	$-0.936330\pi$
$631$	−65914.2	−	310102.i	−0.165547	−	0.778836i	0.814515	−	0.580142i	$-0.197003\pi$
$632$		0			0
$633$	54814.4	+	5761.23i	0.136800	+	0.0143783i
$634$		0			0
$635$	301246.	−	414630.i	0.747092	−	1.02828i
$636$		0			0
$637$	−98919.2	+	465378.i	−0.243782	+	1.14690i
$638$		0			0
$639$	−23638.1	−	224902.i	−0.0578910	−	0.550796i
$640$		0			0
$641$	−225789.	+	507131.i	−0.549525	+	1.23425i	0.398825	+	0.917027i	$0.369418\pi$
$641$	−225789.	+	507131.i	−0.549525	+	1.23425i	−0.948350	+	0.317226i	$0.897248\pi$
$642$		0			0
$643$	485224.	−	157659.i	1.17360	−	0.381326i	0.343615	−	0.939111i	$-0.388348\pi$
$643$	485224.	−	157659.i	1.17360	−	0.381326i	0.829986	+	0.557785i	$0.188348\pi$
$644$		0			0
$645$	50461.7	−	87402.2i	0.121295	−	0.210089i
$646$		0			0
$647$	325674.	+	105818.i	0.777992	+	0.252785i	0.670983	−	0.741473i	$-0.265873\pi$
$647$	325674.	+	105818.i	0.777992	+	0.252785i	0.107009	+	0.994258i	$0.465873\pi$
$648$		0			0
$649$	119363.	+	164289.i	0.283388	+	0.390050i
$650$		0			0
$651$	−44620.7	−	39604.9i	−0.105287	−	0.0934518i
$652$		0			0
$653$	590946.	−	429348.i	1.38587	−	1.00689i	0.389563	−	0.921000i	$-0.372626\pi$
$653$	590946.	−	429348.i	1.38587	−	1.00689i	0.996305	−	0.0858914i	$-0.0273738\pi$
$654$		0			0
$655$	−19091.8	+	58758.7i	−0.0445005	+	0.136959i
$656$		0			0
$657$	−223348.	−	128950.i	−0.517430	−	0.298738i
$658$		0			0
$659$	15582.1	+	47956.6i	0.0358801	+	0.110428i	0.967392	−	0.253282i	$-0.0815100\pi$
$659$	15582.1	+	47956.6i	0.0358801	+	0.110428i	−0.931512	+	0.363710i	$0.881510\pi$
$660$		0			0
$661$	−416133.	−	185274.i	−0.952421	−	0.424045i	−0.129107	−	0.991631i	$-0.541211\pi$
$661$	−416133.	−	185274.i	−0.952421	−	0.424045i	−0.823315	+	0.567585i	$0.807878\pi$
$662$		0			0
$663$	178375.	−	18748.0i	0.405796	−	0.0426509i
$664$		0			0
$665$	−47128.9	−	10017.6i	−0.106572	−	0.0226526i
$666$		0			0
$667$	234311.	+	170237.i	0.526674	+	0.382651i
$668$		0			0
$669$	−16984.1	+	161593.i	−0.0379481	+	0.361052i
$670$		0			0
$671$	216764.	−	46074.6i	0.481440	−	0.102333i
$672$		0			0
$673$	561053.	+	505174.i	1.23872	+	1.11535i	0.989137	+	0.146996i	$0.0469605\pi$
$673$	561053.	+	505174.i	1.23872	+	1.11535i	0.249584	+	0.968353i	$0.419706\pi$
$674$		0			0
$675$	−443205.	+	399064.i	−0.972741	+	0.875860i
$676$		0			0
$677$	703448.	−	406136.i	1.53481	−	0.886123i	0.535679	−	0.844422i	$-0.320056\pi$
$677$	703448.	−	406136.i	1.53481	−	0.886123i	0.999130	−	0.0417011i	$-0.0132777\pi$
$678$		0			0
$679$	97860.4	−	43570.3i	0.212260	−	0.0945041i
$680$		0			0
$681$			126173.i			0.272065i
$682$		0			0
$683$	−34750.4			−0.0744935			−0.0372467	−	0.999306i	$-0.511859\pi$
$683$	−34750.4			−0.0744935			−0.0372467	+	0.999306i	$0.511859\pi$
$684$		0			0
$685$	−509140.	−	1.14355e6i	−1.08506	−	2.43710i
$686$		0			0
$687$	−105706.	−	183087.i	−0.223967	−	0.387923i
$688$		0			0
$689$	−271668.	−	301718.i	−0.572268	−	0.635568i
$690$		0			0
$691$	−2676.93	+	2973.04i	−0.00560637	+	0.00622650i	−0.745941	−	0.666011i	$-0.768000\pi$
$691$	−2676.93	+	2973.04i	−0.00560637	+	0.00622650i	0.740335	+	0.672238i	$0.234667\pi$
$692$		0			0
$693$	17611.4	+	82855.4i	0.0366715	+	0.172526i
$694$		0			0
$695$	−1.43255e6	−	150567.i	−2.96580	−	0.311718i
$696$		0			0
$697$	268548.	−	369625.i	0.552786	−	0.760845i
$698$		0			0
$699$	11019.9	−	51844.6i	0.0225540	−	0.106108i
$700$		0			0
$701$	−96388.0	−	917071.i	−0.196149	−	1.86624i	−0.442114	−	0.896959i	$-0.645771\pi$
$701$	−96388.0	−	917071.i	−0.196149	−	1.86624i	0.245965	−	0.969279i	$-0.420895\pi$
$702$		0			0
$703$	9116.19	−	20475.3i	0.0184460	−	0.0414305i
$704$		0			0
$705$	−159329.	+	51769.2i	−0.320566	+	0.104158i
$706$		0			0
$707$	−106407.	+	184302.i	−0.212878	+	0.368716i
$708$		0			0
$709$	−417403.	−	135623.i	−0.830354	−	0.269798i	−0.137160	−	0.990549i	$-0.543797\pi$
$709$	−417403.	−	135623.i	−0.830354	−	0.269798i	−0.693195	+	0.720750i	$0.743797\pi$
$710$		0			0
$711$	−261828.	−	360375.i	−0.517937	−	0.712879i
$712$		0			0
$713$	3507.49	+	492568.i	0.00689949	+	0.968918i
$714$		0			0
$715$	525791.	−	382010.i	1.02849	−	0.747244i
$716$		0			0
$717$	−3192.58	+	9825.77i	−0.00621018	+	0.0191130i
$718$		0			0
$719$	343437.	+	198283.i	0.664338	+	0.383556i	0.793928	−	0.608012i	$-0.208033\pi$
$719$	343437.	+	198283.i	0.664338	+	0.383556i	−0.129590	+	0.991568i	$0.541366\pi$
$720$		0			0
$721$	108348.	+	333461.i	0.208425	+	0.641466i
$722$		0			0
$723$	−166920.	−	74317.4i	−0.319323	−	0.142172i
$724$		0			0
$725$	−655982.	+	68946.5i	−1.24800	+	0.131171i
$726$		0			0
$727$	615940.	+	130922.i	1.16538	+	0.247710i	0.749687	−	0.661793i	$-0.230204\pi$
$727$	615940.	+	130922.i	1.16538	+	0.247710i	0.415698	+	0.909503i	$0.363537\pi$
$728$		0			0
$729$	−105103.	−	76361.7i	−0.197770	−	0.143688i
$730$		0			0
$731$	16840.1	−	160223.i	0.0315144	−	0.299839i
$732$		0			0
$733$	20771.0	−	4415.02i	0.0386589	−	0.00821721i	−0.188542	−	0.982065i	$-0.560376\pi$
$733$	20771.0	−	4415.02i	0.0386589	−	0.00821721i	0.227201	+	0.973848i	$0.427043\pi$
$734$		0			0
$735$	220766.	+	198779.i	0.408656	+	0.367956i
$736$		0			0
$737$	−288879.	+	260108.i	−0.531841	+	0.478872i
$738$		0			0
$739$	−71287.3	+	41157.7i	−0.130534	+	0.0753638i	−0.563845	−	0.825881i	$-0.690678\pi$
$739$	−71287.3	+	41157.7i	−0.130534	+	0.0753638i	0.433311	+	0.901244i	$0.357345\pi$
$740$		0			0
$741$	44445.0	−	19788.2i	0.0809444	−	0.0360388i
$742$		0			0
$743$		−	272328.i		−	0.493303i	−0.969104	−	0.246652i	$-0.920670\pi$
$743$		−	272328.i		−	0.493303i	0.969104	−	0.246652i	$-0.0793303\pi$
$744$		0			0
$745$	1.71052e6			3.08188
$746$		0			0
$747$	−303207.	−	681013.i	−0.543372	−	1.22043i
$748$		0			0
$749$	136274.	+	236034.i	0.242913	+	0.420737i
$750$		0			0
$751$	−45622.3	−	50668.7i	−0.0808905	−	0.0898380i	0.701341	−	0.712826i	$-0.252585\pi$
$751$	−45622.3	−	50668.7i	−0.0808905	−	0.0898380i	−0.782231	+	0.622988i	$0.785918\pi$
$752$		0			0
$753$	281403.	−	312530.i	0.496294	−	0.551190i
$754$		0			0
$755$	387334.	+	1.82226e6i	0.679503	+	3.19681i
$756$		0			0
$757$	−392511.	−	41254.5i	−0.684951	−	0.0719913i	−0.244340	−	0.969689i	$-0.578571\pi$
$757$	−392511.	−	41254.5i	−0.684951	−	0.0719913i	−0.440611	+	0.897698i	$0.645238\pi$
$758$		0			0
$759$	−68212.9	+	93887.0i	−0.118409	+	0.162975i
$760$		0			0
$761$	−129714.	+	610258.i	−0.223985	+	1.05377i	0.712124	+	0.702054i	$0.247733\pi$
$761$	−129714.	+	610258.i	−0.223985	+	1.05377i	−0.936108	+	0.351711i	$0.885600\pi$
$762$		0			0
$763$	3303.23	+	31428.1i	0.00567400	+	0.0539845i
$764$		0			0
$765$	−274498.	+	616533.i	−0.469047	+	1.05350i
$766$		0			0
$767$	−666771.	+	216647.i	−1.13341	+	0.368266i
$768$		0			0
$769$	487202.	−	843859.i	0.823866	−	1.42698i	−0.0789162	−	0.996881i	$-0.525146\pi$
$769$	487202.	−	843859.i	0.823866	−	1.42698i	0.902783	−	0.430097i	$-0.141521\pi$
$770$		0			0
$771$	−239900.	−	77948.4i	−0.403573	−	0.131129i
$772$		0			0
$773$	363005.	+	499634.i	0.607510	+	0.836166i	0.996370	−	0.0851307i	$-0.0271308\pi$
$773$	363005.	+	499634.i	0.607510	+	0.836166i	−0.388859	+	0.921297i	$0.627131\pi$
$774$		0			0
$775$	−756554.	−	828300.i	−1.25961	−	1.37906i
$776$		0			0
$777$	18086.4	−	13140.5i	0.0299578	−	0.0217656i
$778$		0			0
$779$	38296.4	−	117864.i	0.0631079	−	0.194226i
$780$		0			0
$781$	187981.	+	108531.i	0.308185	+	0.177931i
$782$		0			0
$783$	89207.3	+	274552.i	0.145505	+	0.447817i
$784$		0			0
$785$	1.55176e6	+	690887.i	2.51817	+	1.12116i
$786$		0			0
$787$	−1.03208e6	+	108476.i	−1.66634	+	0.175139i	−0.890247	−	0.455478i	$-0.849468\pi$
$787$	−1.03208e6	+	108476.i	−1.66634	+	0.175139i	−0.776094	+	0.630618i	$0.782802\pi$
$788$		0			0
$789$	119412.	+	25381.7i	0.191819	+	0.0407724i
$790$		0			0
$791$	−264791.	−	192382.i	−0.423204	−	0.307476i
$792$		0			0
$793$	−79971.6	+	760879.i	−0.127171	+	1.20996i
$794$		0			0
$795$	−247964.	+	52706.5i	−0.392333	+	0.0833930i
$796$		0			0
$797$	319918.	+	288055.i	0.503642	+	0.453481i	0.881364	−	0.472438i	$-0.156626\pi$
$797$	319918.	+	288055.i	0.503642	+	0.453481i	−0.377722	+	0.925919i	$0.623293\pi$
$798$		0			0
$799$	−198738.	+	178944.i	−0.311305	+	0.280301i
$800$		0			0
$801$	31263.0	−	18049.7i	0.0487266	−	0.0281323i
$802$		0			0
$803$	226145.	−	100686.i	0.350716	−	0.156149i
$804$		0			0
$805$			396787.i			0.612302i
$806$		0			0
$807$	−98048.3			−0.150554
$808$		0			0
$809$	−396738.	−	891088.i	−0.606187	−	1.36152i	−0.912300	−	0.409524i	$-0.865695\pi$
$809$	−396738.	−	891088.i	−0.606187	−	1.36152i	0.306112	−	0.951995i	$-0.400972\pi$
$810$		0			0
$811$	414429.	+	717812.i	0.630098	+	1.09136i	0.987531	+	0.157423i	$0.0503187\pi$
$811$	414429.	+	717812.i	0.630098	+	1.09136i	−0.357433	+	0.933939i	$0.616348\pi$
$812$		0			0
$813$	−225738.	−	250707.i	−0.341526	−	0.379303i
$814$		0			0
$815$	−793718.	+	881513.i	−1.19495	+	1.32713i
$816$		0			0
$817$	−9085.74	−	42745.1i	−0.0136118	−	0.0640386i
$818$		0			0
$819$	−290837.	−	30568.2i	−0.433592	−	0.0455724i
$820$		0			0
$821$	200859.	−	276459.i	0.297992	−	0.410151i	−0.633597	−	0.773663i	$-0.718422\pi$
$821$	200859.	−	276459.i	0.297992	−	0.410151i	0.931590	+	0.363512i	$0.118422\pi$
$822$		0			0
$823$	−187188.	+	880651.i	−0.276362	+	1.30018i	0.592678	+	0.805440i	$0.298071\pi$
$823$	−187188.	+	880651.i	−0.276362	+	1.30018i	−0.869040	+	0.494742i	$0.835263\pi$
$824$		0			0
$825$	−27626.4	−	262848.i	−0.0405898	−	0.386186i
$826$		0			0
$827$	241889.	−	543292.i	0.353676	−	0.794368i	−0.645847	−	0.763467i	$-0.723496\pi$
$827$	241889.	−	543292.i	0.353676	−	0.794368i	0.999522	−	0.0309015i	$-0.00983781\pi$
$828$		0			0
$829$	−523757.	+	170179.i	−0.762116	+	0.247626i	−0.664186	−	0.747567i	$-0.731222\pi$
$829$	−523757.	+	170179.i	−0.762116	+	0.247626i	−0.0979292	+	0.995193i	$0.531222\pi$
$830$		0			0
$831$	−48809.7	+	84540.9i	−0.0706813	+	0.122424i
$832$		0			0
$833$	451007.	+	146541.i	0.649970	+	0.211188i
$834$		0			0
$835$	−567819.	−	781536.i	−0.814399	−	1.12092i
$836$		0			0
$837$	−285752.	+	399252.i	−0.407886	+	0.569896i
$838$		0			0
$839$	430080.	−	312472.i	0.610978	−	0.443902i	−0.238781	−	0.971074i	$-0.576748\pi$
$839$	430080.	−	312472.i	0.610978	−	0.443902i	0.849759	+	0.527172i	$0.176748\pi$
$840$		0			0
$841$	119901.	−	369016.i	0.169523	−	0.521739i
$842$		0			0
$843$	−176945.	−	102159.i	−0.248991	−	0.143755i
$844$		0			0
$845$	319706.	+	983955.i	0.447752	+	1.37804i
$846$		0			0
$847$	170289.	+	75817.4i	0.237366	+	0.105682i
$848$		0			0
$849$	−84637.7	+	8895.78i	−0.117422	+	0.0123415i
$850$		0			0
$851$	−180542.	−	38375.4i	−0.249298	−	0.0529900i
$852$		0			0
$853$	907217.	+	659132.i	1.24685	+	0.905888i	0.998035	−	0.0626640i	$-0.0199596\pi$
$853$	907217.	+	659132.i	1.24685	+	0.905888i	0.248813	+	0.968552i	$0.419960\pi$
$854$		0			0
$855$	−19135.2	+	182059.i	−0.0261758	+	0.249046i
$856$		0			0
$857$	−210134.	+	44665.5i	−0.286112	+	0.0608149i	−0.348732	−	0.937223i	$-0.613388\pi$
$857$	−210134.	+	44665.5i	−0.286112	+	0.0608149i	0.0626203	+	0.998037i	$0.480054\pi$
$858$		0			0
$859$	169993.	+	153062.i	0.230380	+	0.207435i	0.776233	−	0.630446i	$-0.217128\pi$
$859$	169993.	+	153062.i	0.230380	+	0.207435i	−0.545854	+	0.837881i	$0.683795\pi$
$860$		0			0
$861$	91863.7	−	82714.5i	0.123919	−	0.111577i
$862$		0			0
$863$	545328.	−	314845.i	0.732211	−	0.422742i	−0.0870196	−	0.996207i	$-0.527734\pi$
$863$	545328.	−	314845.i	0.732211	−	0.422742i	0.819230	+	0.573464i	$0.194401\pi$
$864$		0			0
$865$	−974040.	+	433671.i	−1.30180	+	0.579599i
$866$		0			0
$867$			104810.i			0.139433i
$868$		0			0
$869$	427565.			0.566191
$870$		0			0
$871$	−545852.	−	1.22600e6i	−0.719513	−	1.61605i
$872$		0			0
$873$	−203499.	−	352470.i	−0.267013	−	0.462481i
$874$		0			0
$875$	−280919.	−	311993.i	−0.366915	−	0.407501i
$876$		0			0
$877$	−262606.	+	291654.i	−0.341433	+	0.379200i	−0.889268	−	0.457387i	$-0.848786\pi$
$877$	−262606.	+	291654.i	−0.341433	+	0.379200i	0.547835	+	0.836587i	$0.315452\pi$
$878$		0			0
$879$	6827.66	+	32121.6i	0.00883679	+	0.0415738i
$880$		0			0
$881$	−965916.	−	101522.i	−1.24448	−	0.130800i	−0.540698	−	0.841217i	$-0.681840\pi$
$881$	−965916.	−	101522.i	−1.24448	−	0.130800i	−0.703781	+	0.710417i	$0.748506\pi$
$882$		0			0
$883$	18463.6	−	25412.9i	0.0236807	−	0.0325936i	−0.797013	−	0.603963i	$-0.793588\pi$
$883$	18463.6	−	25412.9i	0.0236807	−	0.0325936i	0.820693	+	0.571369i	$0.193588\pi$
$884$		0			0
$885$	−91013.7	+	428186.i	−0.116204	+	0.546696i
$886$		0			0
$887$	6939.22	+	66022.3i	0.00881990	+	0.0839157i	0.998046	−	0.0624775i	$-0.0199002\pi$
$887$	6939.22	+	66022.3i	0.00881990	+	0.0839157i	−0.989226	+	0.146393i	$0.953234\pi$
$888$		0			0
$889$	90032.7	−	202217.i	0.113919	−	0.255867i
$890$		0			0
$891$	246862.	−	80210.3i	0.310956	−	0.101036i
$892$		0			0
$893$	−36270.1	+	62821.7i	−0.0454827	+	0.0787783i
$894$		0			0
$895$	921302.	+	299349.i	1.15015	+	0.373707i
$896$		0			0
$897$	−235497.	−	324134.i	−0.292685	−	0.402846i
$898$		0			0
$899$	−515223.	+	171472.i	−0.637493	+	0.212164i
$900$		0			0
$901$	−327386.	+	237860.i	−0.403284	+	0.293003i
$902$		0			0
$903$	13469.7	−	41455.5i	0.0165190	−	0.0508401i
$904$		0			0
$905$	1.06085e6	+	612484.i	1.29526	+	0.747821i
$906$		0			0
$907$	453565.	+	1.39593e6i	0.551346	+	1.69687i	0.705402	+	0.708808i	$0.250767\pi$
$907$	453565.	+	1.39593e6i	0.551346	+	1.69687i	−0.154055	+	0.988062i	$0.549233\pi$
$908$		0			0
$909$	738661.	+	328873.i	0.893959	+	0.398016i
$910$		0			0
$911$	1.46090e6	−	153547.i	1.76029	−	0.185014i	0.831475	−	0.555563i	$-0.187497\pi$
$911$	1.46090e6	−	153547.i	1.76029	−	0.185014i	0.928813	+	0.370549i	$0.120830\pi$
$912$		0			0
$913$	699898.	+	148768.i	0.839641	+	0.178471i
$914$		0			0
$915$	386471.	+	280787.i	0.461609	+	0.335379i
$916$		0			0
$917$	−2789.23	+	26537.8i	−0.00331700	+	0.0315592i
$918$		0			0
$919$	−1.12921e6	+	240020.i	−1.33703	+	0.284195i	−0.820291	−	0.571946i	$-0.806189\pi$
$919$	−1.12921e6	+	240020.i	−1.33703	+	0.284195i	−0.516742	+	0.856141i	$0.672855\pi$
$920$		0			0
$921$	−292936.	−	263760.i	−0.345345	−	0.310950i
$922$		0			0
$923$	−556898.	+	501433.i	−0.653690	+	0.588585i
$924$		0			0
$925$	364038.	−	210177.i	0.425464	−	0.245642i
$926$		0			0
$927$	1.21698e6	−	541834.i	1.41620	−	0.630531i
$928$		0			0
$929$		−	1.38931e6i		−	1.60978i	−0.593422	−	0.804892i	$-0.702223\pi$
$929$		−	1.38931e6i		−	1.60978i	0.593422	−	0.804892i	$-0.297777\pi$
$930$		0			0
$931$	128632.			0.148405
$932$		0			0
$933$	31135.4	+	69931.3i	0.0357677	+	0.0803356i
$934$		0			0
$935$	−323893.	−	560998.i	−0.370491	−	0.641709i
$936$		0			0
$937$	−1.12350e6	−	1.24778e6i	−1.27966	−	1.42121i	−0.857332	−	0.514765i	$-0.827879\pi$
$937$	−1.12350e6	−	1.24778e6i	−1.27966	−	1.42121i	−0.422329	−	0.906443i	$-0.638787\pi$
$938$		0			0
$939$	−321785.	+	357378.i	−0.364951	+	0.405319i
$940$		0			0
$941$	341973.	+	1.60886e6i	0.386200	+	1.81693i	0.555680	+	0.831396i	$0.312458\pi$
$941$	341973.	+	1.60886e6i	0.386200	+	1.81693i	−0.169479	+	0.985534i	$0.554209\pi$
$942$		0			0
$943$	−1.01500e6	−	106680.i	−1.14141	−	0.119967i
$944$		0			0
$945$	−232465.	+	319961.i	−0.260312	+	0.358289i
$946$		0			0
$947$	129696.	−	610171.i	0.144619	−	0.680380i	−0.844775	−	0.535122i	$-0.820266\pi$
$947$	129696.	−	610171.i	0.144619	−	0.680380i	0.989394	−	0.145258i	$-0.0464011\pi$
$948$		0			0
$949$	89332.6	+	849943.i	0.0991922	+	0.943751i
$950$		0			0
$951$	−101863.	+	228788.i	−0.112630	+	0.252972i
$952$		0			0
$953$	799021.	−	259618.i	0.879777	−	0.285857i	0.165912	−	0.986141i	$-0.446943\pi$
$953$	799021.	−	259618.i	0.879777	−	0.285857i	0.713865	+	0.700284i	$0.246943\pi$
$954$		0			0
$955$	1.21258e6	−	2.10024e6i	1.32954	−	2.30283i
$956$		0			0
$957$	−121670.	−	39532.9i	−0.132849	−	0.0431653i
$958$		0			0
$959$	−317780.	−	437387.i	−0.345533	−	0.475585i
$960$		0			0
$961$	−754799.	−	532137.i	−0.817306	−	0.576204i
$962$		0			0
$963$	837754.	−	608664.i	0.903366	−	0.656334i
$964$		0			0
$965$	360647.	−	1.10996e6i	0.387282	−	1.19193i
$966$		0			0
$967$	277.615	+	160.281i	0.000296886	+	0.000171407i	0.500148	−	0.865940i	$-0.333279\pi$
$967$	277.615	+	160.281i	0.000296886	+	0.000171407i	−0.499852	+	0.866111i	$0.666612\pi$
$968$		0			0
$969$	−14984.8	−	46118.4i	−0.0159589	−	0.0491164i
$970$		0			0
$971$	−1.50388e6	−	669568.i	−1.59505	−	0.710161i	−0.599148	−	0.800638i	$-0.704494\pi$
$971$	−1.50388e6	−	669568.i	−1.59505	−	0.710161i	−0.995898	+	0.0904777i	$0.971161\pi$
$972$		0			0
$973$	−618721.	+	65030.2i	−0.653536	+	0.0686894i
$974$		0			0
$975$	892509.	+	189709.i	0.938866	+	0.199562i
$976$		0			0
$977$	−583959.	−	424271.i	−0.611778	−	0.444482i	0.238262	−	0.971201i	$-0.423422\pi$
$977$	−583959.	−	424271.i	−0.611778	−	0.444482i	−0.850040	+	0.526718i	$0.823422\pi$
$978$		0			0
$979$	−3621.93	+	34460.3i	−0.00377898	+	0.0359546i
$980$		0			0
$981$	117442.	−	24963.1i	0.122035	−	0.0259394i
$982$		0			0
$983$	−713914.	−	642811.i	−0.738820	−	0.665237i	0.211194	−	0.977444i	$-0.432265\pi$
$983$	−713914.	−	642811.i	−0.738820	−	0.665237i	−0.950014	+	0.312207i	$0.898932\pi$
$984$		0			0
$985$	995119.	−	896009.i	1.02566	−	0.923507i
$986$		0			0
$987$	−62662.0	+	36177.9i	−0.0643235	+	0.0371372i
$988$		0			0
$989$	−328765.	+	146376.i	−0.336119	+	0.149650i
$990$		0			0
$991$		−	805226.i		−	0.819918i	−0.912104	−	0.409959i	$-0.865543\pi$
$991$		−	805226.i		−	0.819918i	0.912104	−	0.409959i	$-0.134457\pi$
$992$		0			0
$993$	88299.0			0.0895483
$994$		0			0
$995$	−574006.	−	1.28924e6i	−0.579790	−	1.30223i
$996$		0			0
$997$	−192670.	−	333714.i	−0.193831	−	0.335725i	0.752686	−	0.658380i	$-0.228758\pi$
$997$	−192670.	−	333714.i	−0.193831	−	0.335725i	−0.946517	+	0.322655i	$0.895425\pi$
$998$		0			0
$999$	−123103.	−	136719.i	−0.123349	−	0.136993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.o.a.13.6	✓	88
31.12	odd	30	inner	124.5.o.a.105.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.o.a.13.6	✓	88	1.1	even	1	trivial
124.5.o.a.105.6	yes	88	31.12	odd	30	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38100 + 3.10178i) q^{3} +(21.1680 + 36.6640i) q^{5} +(12.2350 + 13.5884i) q^{7} +(46.4857 - 51.6276i) q^{9} +O(q^{10})\)	\(q+(1.38100 + 3.10178i) q^{3} +(21.1680 + 36.6640i) q^{5} +(12.2350 + 13.5884i) q^{7} +(46.4857 - 51.6276i) q^{9} +(13.8641 + 65.2256i) q^{11} +(-228.953 - 24.0640i) q^{13} +(-84.4907 + 116.291i) q^{15} +(-47.7075 + 224.446i) q^{17} +(6.50601 + 61.9005i) q^{19} +(-25.2515 + 56.7159i) q^{21} +(487.484 - 158.393i) q^{23} +(-583.667 + 1010.94i) q^{25} +(485.895 + 157.877i) q^{27} +(332.124 + 457.130i) q^{29} +(-290.450 + 916.057i) q^{31} +(-183.169 + 133.080i) q^{33} +(-239.214 + 736.224i) q^{35} +(-311.854 - 180.049i) q^{37} +(-241.543 - 743.394i) q^{39} +(-1818.97 - 809.859i) q^{41} +(-698.258 + 73.3899i) q^{43} +(2876.89 + 611.501i) q^{45} +(942.881 + 685.043i) q^{47} +(216.025 - 2055.34i) q^{49} +(-762.066 + 161.982i) q^{51} +(1310.59 + 1180.06i) q^{53} +(-2097.96 + 1889.01i) q^{55} +(-183.017 + 105.665i) q^{57} +(2782.07 - 1238.66i) q^{59} -3323.29i q^{61} +1270.29 q^{63} +(-3964.20 - 8903.73i) q^{65} +(2914.74 + 5048.47i) q^{67} +(1164.52 + 1293.33i) q^{69} +(2178.11 - 2419.04i) q^{71} +(-771.830 - 3631.18i) q^{73} +(-3941.76 - 414.296i) q^{75} +(-716.682 + 986.428i) q^{77} +(1333.12 - 6271.81i) q^{79} +(-406.882 - 3871.22i) q^{81} +(4364.46 - 9802.73i) q^{83} +(-9238.97 + 3001.92i) q^{85} +(-959.252 + 1661.47i) q^{87} +(494.194 + 160.573i) q^{89} +(-2474.26 - 3405.52i) q^{91} +(-3242.52 + 364.164i) q^{93} +(-2131.80 + 1548.85i) q^{95} +(1810.36 - 5571.72i) q^{97} +(4011.93 + 2316.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9}+O(q^{10}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9	\( 88 q - 9 q^{3} + 3 q^{5} - 215 q^{7} - 254 q^{9} - 42 q^{11} + 6 q^{13} + 665 q^{15} - 585 q^{17} - 153 q^{19} - 402 q^{21} - 1365 q^{23} - 5933 q^{25} - 9225 q^{27} - 1140 q^{29} + 117 q^{31} + 5151 q^{33} + 2898 q^{35} + 6594 q^{37} + 3173 q^{39} - 9393 q^{41} - 5322 q^{43} + 2010 q^{45} - 5112 q^{47} - 5210 q^{49} - 1829 q^{51} + 7395 q^{53} + 10585 q^{55} + 40485 q^{57} + 5625 q^{59} - 14954 q^{63} - 17094 q^{65} + 8909 q^{67} - 35370 q^{69} - 11811 q^{71} - 22105 q^{73} + 79377 q^{75} + 71490 q^{77} + 219 q^{79} - 5422 q^{81} + 10545 q^{83} - 53630 q^{85} + 13732 q^{87} - 40305 q^{89} + 42760 q^{91} - 1028 q^{93} + 62319 q^{95} + 35201 q^{97} + 16197 q^{99}+O(q^{100}) \) 88 * q - 9 * q^3 + 3 * q^5 - 215 * q^7 - 254 * q^9 - 42 * q^11 + 6 * q^13 + 665 * q^15 - 585 * q^17 - 153 * q^19 - 402 * q^21 - 1365 * q^23 - 5933 * q^25 - 9225 * q^27 - 1140 * q^29 + 117 * q^31 + 5151 * q^33 + 2898 * q^35 + 6594 * q^37 + 3173 * q^39 - 9393 * q^41 - 5322 * q^43 + 2010 * q^45 - 5112 * q^47 - 5210 * q^49 - 1829 * q^51 + 7395 * q^53 + 10585 * q^55 + 40485 * q^57 + 5625 * q^59 - 14954 * q^63 - 17094 * q^65 + 8909 * q^67 - 35370 * q^69 - 11811 * q^71 - 22105 * q^73 + 79377 * q^75 + 71490 * q^77 + 219 * q^79 - 5422 * q^81 + 10545 * q^83 - 53630 * q^85 + 13732 * q^87 - 40305 * q^89 + 42760 * q^91 - 1028 * q^93 + 62319 * q^95 + 35201 * q^97 + 16197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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