LMFDB - Embedded newform 124.6.f.a.33.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,6,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$19.8875936568$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.13
Character	$\chi$	$=$	124.33
Dual form			124.6.f.a.109.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.8446 - 12.2383i) q^{3} +64.7441 q^{5} +(-38.0058 - 116.970i) q^{7} +(58.8724 - 181.191i) q^{9} +O(q^{10})$	\(q+(16.8446 - 12.2383i) q^{3} +64.7441 q^{5} +(-38.0058 - 116.970i) q^{7} +(58.8724 - 181.191i) q^{9} +(-153.889 - 473.622i) q^{11} +(262.902 - 191.009i) q^{13} +(1090.59 - 792.357i) q^{15} +(-410.947 + 1264.76i) q^{17} +(636.098 + 462.152i) q^{19} +(-2071.70 - 1505.18i) q^{21} +(812.410 - 2500.34i) q^{23} +1066.79 q^{25} +(337.691 + 1039.31i) q^{27} +(1181.54 + 858.437i) q^{29} +(-5198.44 - 1267.03i) q^{31} +(-8388.52 - 6094.62i) q^{33} +(-2460.65 - 7573.10i) q^{35} +8522.04 q^{37} +(2090.84 - 6434.94i) q^{39} +(6854.96 + 4980.42i) q^{41} +(-12482.0 - 9068.69i) q^{43} +(3811.64 - 11731.0i) q^{45} +(7868.50 - 5716.80i) q^{47} +(1359.67 - 987.859i) q^{49} +(8556.34 + 26333.7i) q^{51} +(-490.801 + 1510.53i) q^{53} +(-9963.41 - 30664.2i) q^{55} +16370.8 q^{57} +(36717.3 - 26676.7i) q^{59} -526.087 q^{61} -23431.3 q^{63} +(17021.3 - 12366.7i) q^{65} -42596.1 q^{67} +(-16915.2 - 52059.6i) q^{69} +(-14310.2 + 44042.3i) q^{71} +(9258.36 + 28494.3i) q^{73} +(17969.7 - 13055.7i) q^{75} +(-49550.8 + 36000.7i) q^{77} +(-30399.3 + 93559.4i) q^{79} +(55861.1 + 40585.5i) q^{81} +(22436.2 + 16300.8i) q^{83} +(-26606.4 + 81886.0i) q^{85} +30408.3 q^{87} +(20919.7 + 64384.3i) q^{89} +(-32334.1 - 23492.1i) q^{91} +(-103072. + 42277.5i) q^{93} +(41183.6 + 29921.6i) q^{95} +(13015.1 + 40056.5i) q^{97} -94875.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	$ 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	16.8446	−	12.2383i	1.08058	−	0.785087i	0.102795	−	0.994703i	$-0.467221\pi$
$3$	16.8446	−	12.2383i	1.08058	−	0.785087i	0.977784	+	0.209616i	$0.0672213\pi$
$4$		0			0
$5$	64.7441			1.15818			0.579089	−	0.815265i	$-0.303409\pi$
$5$	64.7441			1.15818			0.579089	+	0.815265i	$0.303409\pi$
$6$		0			0
$7$	−38.0058	−	116.970i	−0.293160	−	0.902253i	−0.983833	−	0.179086i	$-0.942686\pi$
$7$	−38.0058	−	116.970i	−0.293160	−	0.902253i	0.690674	−	0.723167i	$-0.257314\pi$
$8$		0			0
$9$	58.8724	−	181.191i	0.242273	−	0.745640i
$10$		0			0
$11$	−153.889	−	473.622i	−0.383466	−	1.18019i	−0.937587	−	0.347750i	$-0.886946\pi$
$11$	−153.889	−	473.622i	−0.383466	−	1.18019i	0.554122	−	0.832436i	$-0.313054\pi$
$12$		0			0
$13$	262.902	−	191.009i	0.431455	−	0.313470i	−0.350776	−	0.936460i	$-0.614082\pi$
$13$	262.902	−	191.009i	0.431455	−	0.313470i	0.782230	+	0.622989i	$0.214082\pi$
$14$		0			0
$15$	1090.59	−	792.357i	1.25150	−	0.909269i
$16$		0			0
$17$	−410.947	+	1264.76i	−0.344876	+	1.06142i	0.616774	+	0.787141i	$0.288439\pi$
$17$	−410.947	+	1264.76i	−0.344876	+	1.06142i	−0.961650	+	0.274280i	$0.911561\pi$
$18$		0			0
$19$	636.098	+	462.152i	0.404241	+	0.293698i	0.771266	−	0.636513i	$-0.219624\pi$
$19$	636.098	+	462.152i	0.404241	+	0.293698i	−0.367025	+	0.930211i	$0.619624\pi$
$20$		0			0
$21$	−2071.70	−	1505.18i	−1.02513	−	0.744800i
$22$		0			0
$23$	812.410	−	2500.34i	0.320225	−	0.985552i	−0.653325	−	0.757078i	$-0.726626\pi$
$23$	812.410	−	2500.34i	0.320225	−	0.985552i	0.973550	−	0.228474i	$-0.0733736\pi$
$24$		0			0
$25$	1066.79			0.341374
$26$		0			0
$27$	337.691	+	1039.31i	0.0891477	+	0.274368i
$28$		0			0
$29$	1181.54	+	858.437i	0.260887	+	0.189545i	0.710538	−	0.703659i	$-0.248452\pi$
$29$	1181.54	+	858.437i	0.260887	+	0.189545i	−0.449651	+	0.893204i	$0.648452\pi$
$30$		0			0
$31$	−5198.44	−	1267.03i	−0.971558	−	0.236800i
$31$	−5198.44	−	1267.03i	−0.971558	−	0.236800i
$32$		0			0
$33$	−8388.52	−	6094.62i	−1.34091	−	0.974230i
$34$		0			0
$35$	−2460.65	−	7573.10i	−0.339531	−	1.04497i
$36$		0			0
$37$	8522.04			1.02339			0.511693	−	0.859169i	$-0.329019\pi$
$37$	8522.04			1.02339			0.511693	+	0.859169i	$0.329019\pi$
$38$		0			0
$39$	2090.84	−	6434.94i	0.220120	−	0.677459i
$40$		0			0
$41$	6854.96	+	4980.42i	0.636862	+	0.462707i	0.858771	−	0.512360i	$-0.171229\pi$
$41$	6854.96	+	4980.42i	0.636862	+	0.462707i	−0.221909	+	0.975067i	$0.571229\pi$
$42$		0			0
$43$	−12482.0	−	9068.69i	−1.02947	−	0.747952i	−0.0612654	−	0.998122i	$-0.519514\pi$
$43$	−12482.0	−	9068.69i	−1.02947	−	0.747952i	−0.968202	+	0.250170i	$0.919514\pi$
$44$		0			0
$45$	3811.64	−	11731.0i	0.280595	−	0.863583i
$46$		0			0
$47$	7868.50	−	5716.80i	0.519574	−	0.377493i	−0.296869	−	0.954918i	$-0.595943\pi$
$47$	7868.50	−	5716.80i	0.519574	−	0.377493i	0.816443	+	0.577426i	$0.195943\pi$
$48$		0			0
$49$	1359.67	−	987.859i	0.0808991	−	0.0587767i
$50$		0			0
$51$	8556.34	+	26333.7i	0.460641	+	1.41771i
$52$		0			0
$53$	−490.801	+	1510.53i	−0.0240002	+	0.0738651i	−0.962339	−	0.271851i	$-0.912364\pi$
$53$	−490.801	+	1510.53i	−0.0240002	+	0.0738651i	0.938339	+	0.345716i	$0.112364\pi$
$54$		0			0
$55$	−9963.41	−	30664.2i	−0.444121	−	1.36686i
$56$		0			0
$57$	16370.8			0.667393
$58$		0			0
$59$	36717.3	−	26676.7i	1.37322	−	0.997705i	0.375746	−	0.926723i	$-0.377387\pi$
$59$	36717.3	−	26676.7i	1.37322	−	0.997705i	0.997478	−	0.0709824i	$-0.0226134\pi$
$60$		0			0
$61$	−526.087			−0.0181023			−0.00905113	−	0.999959i	$-0.502881\pi$
$61$	−526.087			−0.0181023			−0.00905113	+	0.999959i	$0.502881\pi$
$62$		0			0
$63$	−23431.3			−0.743781
$64$		0			0
$65$	17021.3	−	12366.7i	0.499701	−	0.363054i
$66$		0			0
$67$	−42596.1			−1.15927			−0.579633	−	0.814878i	$-0.696804\pi$
$67$	−42596.1			−1.15927			−0.579633	+	0.814878i	$0.696804\pi$
$68$		0			0
$69$	−16915.2	−	52059.6i	−0.427715	−	1.31637i
$70$		0			0
$71$	−14310.2	+	44042.3i	−0.336899	+	1.03687i	0.628879	+	0.777503i	$0.283514\pi$
$71$	−14310.2	+	44042.3i	−0.336899	+	1.03687i	−0.965779	+	0.259367i	$0.916486\pi$
$72$		0			0
$73$	9258.36	+	28494.3i	0.203342	+	0.625822i	0.999777	+	0.0210987i	$0.00671642\pi$
$73$	9258.36	+	28494.3i	0.203342	+	0.625822i	−0.796435	+	0.604724i	$0.793284\pi$
$74$		0			0
$75$	17969.7	−	13055.7i	0.368882	−	0.268008i
$76$		0			0
$77$	−49550.8	+	36000.7i	−0.952409	+	0.691966i
$78$		0			0
$79$	−30399.3	+	93559.4i	−0.548019	+	1.68663i	0.165682	+	0.986179i	$0.447018\pi$
$79$	−30399.3	+	93559.4i	−0.548019	+	1.68663i	−0.713701	+	0.700451i	$0.752982\pi$
$80$		0			0
$81$	55861.1	+	40585.5i	0.946013	+	0.687319i
$82$		0			0
$83$	22436.2	+	16300.8i	0.357482	+	0.259726i	0.752001	−	0.659162i	$-0.229089\pi$
$83$	22436.2	+	16300.8i	0.357482	+	0.259726i	−0.394519	+	0.918888i	$0.629089\pi$
$84$		0			0
$85$	−26606.4	+	81886.0i	−0.399428	+	1.22931i
$86$		0			0
$87$	30408.3			0.430719
$88$		0			0
$89$	20919.7	+	64384.3i	0.279951	+	0.861599i	0.987867	+	0.155303i	$0.0496353\pi$
$89$	20919.7	+	64384.3i	0.279951	+	0.861599i	−0.707916	+	0.706296i	$0.750365\pi$
$90$		0			0
$91$	−32334.1	−	23492.1i	−0.409315	−	0.297385i
$92$		0			0
$93$	−103072.	+	42277.5i	−1.23575	+	0.506876i
$94$		0			0
$95$	41183.6	+	29921.6i	0.468182	+	0.340154i
$96$		0			0
$97$	13015.1	+	40056.5i	0.140449	+	0.432258i	0.996398	−	0.0848028i	$-0.0270260\pi$
$97$	13015.1	+	40056.5i	0.140449	+	0.432258i	−0.855949	+	0.517061i	$0.827026\pi$
$98$		0			0
$99$	−94875.7			−0.972897
$100$		0			0
$101$	−13329.6	+	41024.3i	−0.130021	+	0.400164i	−0.994782	−	0.102019i	$-0.967470\pi$
$101$	−13329.6	+	41024.3i	−0.130021	+	0.400164i	0.864761	+	0.502183i	$0.167470\pi$
$102$		0			0
$103$	165528.	+	120263.i	1.53737	+	1.11697i	0.951956	+	0.306235i	$0.0990692\pi$
$103$	165528.	+	120263.i	1.53737	+	1.11697i	0.585417	+	0.810732i	$0.300931\pi$
$104$		0			0
$105$	−134130.	−	97451.3i	−1.18728	−	0.862610i
$106$		0			0
$107$	−3742.13	+	11517.1i	−0.0315980	+	0.0972486i	−0.965612	−	0.259989i	$-0.916281\pi$
$107$	−3742.13	+	11517.1i	−0.0315980	+	0.0972486i	0.934014	+	0.357237i	$0.116281\pi$
$108$		0			0
$109$	33822.7	−	24573.6i	0.272673	−	0.198108i	−0.443042	−	0.896501i	$-0.646101\pi$
$109$	33822.7	−	24573.6i	0.272673	−	0.198108i	0.715715	+	0.698392i	$0.246101\pi$
$110$		0			0
$111$	143550.	−	104295.i	1.10585	−	0.803446i
$112$		0			0
$113$	−18622.0	−	57312.5i	−0.137192	−	0.422234i	0.858732	−	0.512424i	$-0.171252\pi$
$113$	−18622.0	−	57312.5i	−0.137192	−	0.422234i	−0.995925	+	0.0901903i	$0.971252\pi$
$114$		0			0
$115$	52598.7	−	161882.i	0.370877	−	1.14144i
$116$		0			0
$117$	−19131.4	−	58880.5i	−0.129206	−	0.397655i
$118$		0			0
$119$	163558.			1.05877
$120$		0			0
$121$	−70343.1	+	51107.2i	−0.436775	+	0.317336i
$122$		0			0
$123$	176421.			1.05144
$124$		0			0
$125$	−133257.			−0.762805
$126$		0			0
$127$	112936.	−	82052.7i	0.621330	−	0.451423i	−0.232056	−	0.972702i	$-0.574545\pi$
$127$	112936.	−	82052.7i	0.621330	−	0.451423i	0.853386	+	0.521280i	$0.174545\pi$
$128$		0			0
$129$	−321239.			−1.69963
$130$		0			0
$131$	56465.6	+	173783.i	0.287479	+	0.884768i	0.985645	+	0.168832i	$0.0539997\pi$
$131$	56465.6	+	173783.i	0.287479	+	0.884768i	−0.698166	+	0.715936i	$0.746000\pi$
$132$		0			0
$133$	29882.4	−	91968.7i	0.146483	−	0.450828i
$134$		0			0
$135$	21863.5	+	67288.9i	0.103249	+	0.317767i
$136$		0			0
$137$	−223885.	+	162662.i	−1.01911	+	0.740430i	−0.966101	−	0.258164i	$-0.916883\pi$
$137$	−223885.	+	162662.i	−1.01911	+	0.740430i	−0.0530135	+	0.998594i	$0.516883\pi$
$138$		0			0
$139$	307984.	−	223764.i	1.35205	−	0.982319i	0.353139	−	0.935571i	$-0.385114\pi$
$139$	307984.	−	223764.i	1.35205	−	0.982319i	0.998907	−	0.0467483i	$-0.0148859\pi$
$140$		0			0
$141$	62577.6	−	192594.i	0.265076	−	0.815821i
$142$		0			0
$143$	−130924.	−	95121.9i	−0.535401	−	0.388992i
$144$		0			0
$145$	76497.5	+	55578.7i	0.302153	+	0.219527i
$146$		0			0
$147$	10813.4	−	33280.1i	0.0412731	−	0.127026i
$148$		0			0
$149$	−306799.			−1.13211			−0.566055	−	0.824367i	$-0.691531\pi$
$149$	−306799.			−1.13211			−0.566055	+	0.824367i	$0.691531\pi$
$150$		0			0
$151$	99396.4	+	305911.i	0.354755	+	1.09182i	0.956151	+	0.292873i	$0.0946112\pi$
$151$	99396.4	+	305911.i	0.354755	+	1.09182i	−0.601396	+	0.798951i	$0.705389\pi$
$152$		0			0
$153$	204970.	+	148919.i	0.707883	+	0.514307i
$154$		0			0
$155$	−336568.	−	82032.6i	−1.12524	−	0.274257i
$156$		0			0
$157$	−41499.7	−	30151.3i	−0.134368	−	0.0976240i	0.518571	−	0.855035i	$-0.326464\pi$
$157$	−41499.7	−	30151.3i	−0.134368	−	0.0976240i	−0.652939	+	0.757411i	$0.726464\pi$
$158$		0			0
$159$	10219.0	+	31450.8i	0.0320564	+	0.0986594i
$160$		0			0
$161$	−323340.			−0.983094
$162$		0			0
$163$	23483.6	−	72275.0i	0.0692301	−	0.213068i	−0.910456	−	0.413606i	$-0.864269\pi$
$163$	23483.6	−	72275.0i	0.0692301	−	0.213068i	0.979686	+	0.200538i	$0.0642690\pi$
$164$		0			0
$165$	−543107.	−	394590.i	−1.55301	−	1.12833i
$166$		0			0
$167$	263603.	+	191519.i	0.731406	+	0.531398i	0.890008	−	0.455945i	$-0.150699\pi$
$167$	263603.	+	191519.i	0.731406	+	0.531398i	−0.158602	+	0.987343i	$0.550699\pi$
$168$		0			0
$169$	−82103.0	+	252687.i	−0.221127	+	0.680560i
$170$		0			0
$171$	121186.	−	88047.0i	0.316930	−	0.230263i
$172$		0			0
$173$	447505.	−	325132.i	1.13680	−	0.825931i	0.150127	−	0.988667i	$-0.452032\pi$
$173$	447505.	−	325132.i	1.13680	−	0.825931i	0.986670	+	0.162736i	$0.0520318\pi$
$174$		0			0
$175$	−40544.3	−	124783.i	−0.100077	−	0.308006i
$176$		0			0
$177$	292010.	−	898715.i	0.700591	−	2.15620i
$178$		0			0
$179$	−240836.	−	741216.i	−0.561809	−	1.72907i	−0.677248	−	0.735754i	$-0.736828\pi$
$179$	−240836.	−	741216.i	−0.561809	−	1.72907i	0.115440	−	0.993314i	$-0.463172\pi$
$180$		0			0
$181$	−209039.			−0.474275			−0.237137	−	0.971476i	$-0.576209\pi$
$181$	−209039.			−0.474275			−0.237137	+	0.971476i	$0.576209\pi$
$182$		0			0
$183$	−8861.70	+	6438.40i	−0.0195609	+	0.0142118i
$184$		0			0
$185$	551751.			1.18526
$186$		0			0
$187$	662261.			1.38492
$188$		0			0
$189$	108733.	−	78999.2i	0.221415	−	0.160867i
$190$		0			0
$191$	70030.6			0.138901			0.0694503	−	0.997585i	$-0.477875\pi$
$191$	70030.6			0.138901			0.0694503	+	0.997585i	$0.477875\pi$
$192$		0			0
$193$	187760.	+	577866.i	0.362836	+	1.11669i	0.951325	+	0.308189i	$0.0997228\pi$
$193$	187760.	+	577866.i	0.362836	+	1.11669i	−0.588490	+	0.808505i	$0.700277\pi$
$194$		0			0
$195$	135369.	−	416624.i	0.254938	−	0.784617i
$196$		0			0
$197$	−71511.4	−	220089.i	−0.131283	−	0.404048i	0.863710	−	0.503989i	$-0.168135\pi$
$197$	−71511.4	−	220089.i	−0.131283	−	0.404048i	−0.994993	+	0.0999405i	$0.968135\pi$
$198$		0			0
$199$	−108261.	+	78656.6i	−0.193794	+	0.140800i	−0.680451	−	0.732793i	$-0.738216\pi$
$199$	−108261.	+	78656.6i	−0.193794	+	0.140800i	0.486657	+	0.873593i	$0.338216\pi$
$200$		0			0
$201$	−717513.	+	521304.i	−1.25268	+	0.910124i
$202$		0			0
$203$	55505.9	−	170830.i	0.0945364	−	0.290953i
$204$		0			0
$205$	443818.	+	322452.i	0.737599	+	0.535897i
$206$		0			0
$207$	−405209.	−	294402.i	−0.657285	−	0.477546i
$208$		0			0
$209$	120997.	−	372390.i	0.191606	−	0.589702i
$210$		0			0
$211$	−36881.2			−0.0570294			−0.0285147	−	0.999593i	$-0.509078\pi$
$211$	−36881.2			−0.0570294			−0.0285147	+	0.999593i	$0.509078\pi$
$212$		0			0
$213$	297953.	+	917006.i	0.449986	+	1.38492i
$214$		0			0
$215$	−808135.	−	587144.i	−1.19231	−	0.866261i
$216$		0			0
$217$	49366.7	+	656215.i	0.0711680	+	0.946012i
$218$		0			0
$219$	504675.	+	366668.i	0.711052	+	0.516609i
$220$		0			0
$221$	133543.	+	411004.i	0.183925	+	0.566063i
$222$		0			0
$223$	−625944.			−0.842894			−0.421447	−	0.906853i	$-0.638478\pi$
$223$	−625944.			−0.842894			−0.421447	+	0.906853i	$0.638478\pi$
$224$		0			0
$225$	62804.7	−	193293.i	0.0827058	−	0.254542i
$226$		0			0
$227$	−820523.	−	596145.i	−1.05688	−	0.767869i	−0.0833723	−	0.996518i	$-0.526569\pi$
$227$	−820523.	−	596145.i	−1.05688	−	0.767869i	−0.973509	+	0.228649i	$0.926569\pi$
$228$		0			0
$229$	408440.	+	296749.i	0.514682	+	0.373939i	0.814597	−	0.580027i	$-0.196958\pi$
$229$	408440.	+	296749.i	0.514682	+	0.373939i	−0.299915	+	0.953966i	$0.596958\pi$
$230$		0			0
$231$	−394074.	+	1.21283e6i	−0.485900	+	1.49545i
$232$		0			0
$233$	−620816.	+	451049.i	−0.749158	+	0.544295i	−0.895566	−	0.444929i	$-0.853229\pi$
$233$	−620816.	+	451049.i	−0.749158	+	0.544295i	0.146408	+	0.989224i	$0.453229\pi$
$234$		0			0
$235$	509439.	−	370129.i	0.601759	−	0.437203i
$236$		0			0
$237$	632945.	+	1.94800e6i	0.731973	+	2.25278i
$238$		0			0
$239$	−507749.	+	1.56269e6i	−0.574982	+	1.76961i	0.0612583	+	0.998122i	$0.480489\pi$
$239$	−507749.	+	1.56269e6i	−0.574982	+	1.76961i	−0.636240	+	0.771491i	$0.719511\pi$
$240$		0			0
$241$	−378170.	−	1.16389e6i	−0.419416	−	1.29083i	−0.908241	−	0.418447i	$-0.862575\pi$
$241$	−378170.	−	1.16389e6i	−0.419416	−	1.29083i	0.488826	−	0.872382i	$-0.337425\pi$
$242$		0			0
$243$	1.17211e6			1.27336
$244$		0			0
$245$	88030.7	−	63958.0i	0.0936955	−	0.0680738i
$246$		0			0
$247$	255507.			0.266477
$248$		0			0
$249$	577422.			0.590194
$250$		0			0
$251$	−1.16611e6	+	847231.i	−1.16831	+	0.848823i	−0.990805	−	0.135298i	$-0.956801\pi$
$251$	−1.16611e6	+	847231.i	−1.16831	+	0.848823i	−0.177500	+	0.984121i	$0.556801\pi$
$252$		0			0
$253$	−1.30924e6			−1.28593
$254$		0			0
$255$	553972.	+	1.70495e6i	0.533504	+	1.64196i
$256$		0			0
$257$	413062.	−	1.27127e6i	0.390106	−	1.20062i	−0.542602	−	0.839990i	$-0.682561\pi$
$257$	413062.	−	1.27127e6i	0.390106	−	1.20062i	0.932708	−	0.360632i	$-0.117439\pi$
$258$		0			0
$259$	−323886.	−	996820.i	−0.300015	−	0.923352i
$260$		0			0
$261$	225101.	−	163545.i	0.204539	−	0.148606i
$262$		0			0
$263$	358016.	−	260114.i	0.319163	−	0.231886i	−0.416655	−	0.909065i	$-0.636798\pi$
$263$	358016.	−	260114.i	0.319163	−	0.231886i	0.735818	+	0.677179i	$0.236798\pi$
$264$		0			0
$265$	−31776.4	+	97797.8i	−0.0277965	+	0.0855489i
$266$		0			0
$267$	1.14034e6	+	828504.i	0.978939	+	0.711241i
$268$		0			0
$269$	−306046.	−	222356.i	−0.257873	−	0.187356i	0.451336	−	0.892354i	$-0.350948\pi$
$269$	−306046.	−	222356.i	−0.257873	−	0.187356i	−0.709209	+	0.704998i	$0.750948\pi$
$270$		0			0
$271$	−598121.	+	1.84083e6i	−0.494727	+	1.52261i	0.322654	+	0.946517i	$0.395425\pi$
$271$	−598121.	+	1.84083e6i	−0.494727	+	1.52261i	−0.817381	+	0.576097i	$0.804575\pi$
$272$		0			0
$273$	−832157.			−0.675770
$274$		0			0
$275$	−164168.	−	505257.i	−0.130905	−	0.402885i
$276$		0			0
$277$	−630182.	−	457854.i	−0.493476	−	0.358532i	0.313043	−	0.949739i	$-0.398652\pi$
$277$	−630182.	−	457854.i	−0.493476	−	0.358532i	−0.806520	+	0.591207i	$0.798652\pi$
$278$		0			0
$279$	−535618.	+	867315.i	−0.411950	+	0.667063i
$280$		0			0
$281$	−1.80940e6	−	1.31460e6i	−1.36700	−	0.993183i	−0.997965	−	0.0637667i	$-0.979689\pi$
$281$	−1.80940e6	−	1.31460e6i	−1.36700	−	0.993183i	−0.369034	−	0.929416i	$-0.620311\pi$
$282$		0			0
$283$	−177094.	−	545040.i	−0.131443	−	0.404541i	0.863577	−	0.504218i	$-0.168219\pi$
$283$	−177094.	−	545040.i	−0.131443	−	0.404541i	−0.995020	+	0.0996770i	$0.968219\pi$
$284$		0			0
$285$	1.05991e6			0.772959
$286$		0			0
$287$	322030.	−	991107.i	0.230777	−	0.710257i
$288$		0			0
$289$	−282063.	−	204931.i	−0.198656	−	0.144332i
$290$		0			0
$291$	709457.	+	515450.i	0.491127	+	0.356824i
$292$		0			0
$293$	−845152.	+	2.60111e6i	−0.575130	+	1.77007i	0.0606069	+	0.998162i	$0.480696\pi$
$293$	−845152.	+	2.60111e6i	−0.575130	+	1.77007i	−0.635737	+	0.771906i	$0.719304\pi$
$294$		0			0
$295$	2.37723e6	−	1.72716e6i	1.59044	−	1.15552i
$296$		0			0
$297$	440271.	−	319876.i	0.289620	−	0.210422i
$298$		0			0
$299$	−264004.	−	812522.i	−0.170778	−	0.525602i
$300$		0			0
$301$	−586375.	+	1.80468e6i	−0.373043	+	1.14811i
$302$		0			0
$303$	277536.	+	854169.i	0.173665	+	0.534487i
$304$		0			0
$305$	−34061.0			−0.0209656
$306$		0			0
$307$	2.29607e6	−	1.66819e6i	1.39040	−	1.01018i	0.394576	−	0.918863i	$-0.370891\pi$
$307$	2.29607e6	−	1.66819e6i	1.39040	−	1.01018i	0.995822	−	0.0913198i	$-0.0291085\pi$
$308$		0			0
$309$	4.26007e6			2.53817
$310$		0			0
$311$	311714.			0.182749			0.0913745	−	0.995817i	$-0.470874\pi$
$311$	311714.			0.182749			0.0913745	+	0.995817i	$0.470874\pi$
$312$		0			0
$313$	2.15492e6	−	1.56564e6i	1.24328	−	0.903297i	0.245470	−	0.969404i	$-0.421058\pi$
$313$	2.15492e6	−	1.56564e6i	1.24328	−	0.903297i	0.997813	+	0.0661069i	$0.0210578\pi$
$314$		0			0
$315$	−1.51704e6			−0.861430
$316$		0			0
$317$	−1.04442e6	−	3.21439e6i	−0.583750	−	1.79660i	−0.604234	−	0.796807i	$-0.706521\pi$
$317$	−1.04442e6	−	3.21439e6i	−0.583750	−	1.79660i	0.0204837	−	0.999790i	$-0.493479\pi$
$318$		0			0
$319$	224749.	−	691706.i	0.123658	−	0.380579i
$320$		0			0
$321$	77915.0	+	239798.i	0.0422045	+	0.129892i
$322$		0			0
$323$	−845917.	+	614594.i	−0.451150	+	0.327780i
$324$		0			0
$325$	280462.	−	203768.i	0.147287	−	0.107011i
$326$		0			0
$327$	268989.	−	827864.i	0.139112	−	0.428144i
$328$		0			0
$329$	−967741.	−	703105.i	−0.492912	−	0.358121i
$330$		0			0
$331$	−2.09922e6	−	1.52517e6i	−1.05314	−	0.765154i	−0.0803366	−	0.996768i	$-0.525600\pi$
$331$	−2.09922e6	−	1.52517e6i	−1.05314	−	0.765154i	−0.972808	+	0.231614i	$0.925600\pi$
$332$		0			0
$333$	501713.	−	1.54411e6i	0.247939	−	0.763077i
$334$		0			0
$335$	−2.75785e6			−1.34263
$336$		0			0
$337$	134674.	+	414483.i	0.0645964	+	0.198807i	0.978146	−	0.207921i	$-0.0666696\pi$
$337$	134674.	+	414483.i	0.0645964	+	0.198807i	−0.913549	+	0.406728i	$0.866670\pi$
$338$		0			0
$339$	−1.01509e6	−	737503.i	−0.479737	−	0.348550i
$340$		0			0
$341$	199891.	+	2.65708e6i	0.0930908	+	1.23742i
$342$		0			0
$343$	−1.83953e6	−	1.33650e6i	−0.844250	−	0.613384i
$344$		0			0
$345$	−1.09516e6	−	3.37055e6i	−0.495370	−	1.52459i
$346$		0			0
$347$	−1.33011e6			−0.593013			−0.296506	−	0.955031i	$-0.595822\pi$
$347$	−1.33011e6			−0.593013			−0.296506	+	0.955031i	$0.595822\pi$
$348$		0			0
$349$	−1.00390e6	+	3.08968e6i	−0.441190	+	1.35784i	0.445419	+	0.895322i	$0.353055\pi$
$349$	−1.00390e6	+	3.08968e6i	−0.441190	+	1.35784i	−0.886609	+	0.462520i	$0.846945\pi$
$350$		0			0
$351$	287297.	+	208733.i	0.124469	+	0.0904324i
$352$		0			0
$353$	−1.30893e6	−	950994.i	−0.559088	−	0.406201i	0.272037	−	0.962287i	$-0.412303\pi$
$353$	−1.30893e6	−	950994.i	−0.559088	−	0.406201i	−0.831125	+	0.556086i	$0.812303\pi$
$354$		0			0
$355$	−926502.	+	2.85148e6i	−0.390189	+	1.20088i
$356$		0			0
$357$	2.75505e6	−	2.00166e6i	1.14409	−	0.831229i
$358$		0			0
$359$	3.55455e6	−	2.58253e6i	1.45562	−	1.05757i	0.471144	−	0.882056i	$-0.343841\pi$
$359$	3.55455e6	−	2.58253e6i	1.45562	−	1.05757i	0.984477	−	0.175515i	$-0.0561589\pi$
$360$		0			0
$361$	−574121.	−	1.76696e6i	−0.231865	−	0.713607i
$362$		0			0
$363$	−559433.	+	1.72176e6i	−0.222834	+	0.685813i
$364$		0			0
$365$	599424.	+	1.84484e6i	0.235506	+	0.724813i
$366$		0			0
$367$	2.28526e6			0.885666			0.442833	−	0.896604i	$-0.353974\pi$
$367$	2.28526e6			0.885666			0.442833	+	0.896604i	$0.353974\pi$
$368$		0			0
$369$	1.30597e6	−	948844.i	0.499307	−	0.362768i
$370$		0			0
$371$	195339.			0.0736810
$372$		0			0
$373$	201557.			0.0750110			0.0375055	−	0.999296i	$-0.488059\pi$
$373$	201557.			0.0750110			0.0375055	+	0.999296i	$0.488059\pi$
$374$		0			0
$375$	−2.24465e6	+	1.63083e6i	−0.824272	+	0.598868i
$376$		0			0
$377$	474598.			0.171978
$378$		0			0
$379$	−668.216	−	2056.56i	−0.000238956	−	0.000735432i	0.950937	−	0.309385i	$-0.100123\pi$
$379$	−668.216	−	2056.56i	−0.000238956	−	0.000735432i	−0.951176	+	0.308649i	$0.900123\pi$
$380$		0			0
$381$	898170.	−	2.76428e6i	0.316990	−	0.975596i
$382$		0			0
$383$	−1.06869e6	−	3.28908e6i	−0.372266	−	1.14572i	−0.945305	−	0.326188i	$-0.894236\pi$
$383$	−1.06869e6	−	3.28908e6i	−0.372266	−	1.14572i	0.573039	−	0.819528i	$-0.305764\pi$
$384$		0			0
$385$	−3.20812e6	+	2.33083e6i	−1.10306	+	0.801419i
$386$		0			0
$387$	−2.37801e6	+	1.72772e6i	−0.807115	+	0.586404i
$388$		0			0
$389$	130437.	−	401443.i	0.0437045	−	0.134509i	−0.926823	−	0.375498i	$-0.877472\pi$
$389$	130437.	−	401443.i	0.0437045	−	0.134509i	0.970528	+	0.240989i	$0.0774718\pi$
$390$		0			0
$391$	2.82848e6	+	2.05501e6i	0.935647	+	0.679787i
$392$		0			0
$393$	3.07795e6	+	2.23626e6i	1.00526	+	0.730367i
$394$		0			0
$395$	−1.96817e6	+	6.05742e6i	−0.634703	+	1.95342i
$396$		0			0
$397$	2.88798e6			0.919641			0.459821	−	0.888012i	$-0.347914\pi$
$397$	2.88798e6			0.919641			0.459821	+	0.888012i	$0.347914\pi$
$398$		0			0
$399$	−622183.	−	1.91488e6i	−0.195653	−	0.602157i
$400$		0			0
$401$	−2.90173e6	−	2.10823e6i	−0.901148	−	0.654722i	0.0376126	−	0.999292i	$-0.488025\pi$
$401$	−2.90173e6	−	2.10823e6i	−0.901148	−	0.654722i	−0.938761	+	0.344570i	$0.888025\pi$
$402$		0			0
$403$	−1.60869e6	+	659847.i	−0.493413	+	0.202386i
$404$		0			0
$405$	3.61668e6	+	2.62767e6i	1.09565	+	0.796037i
$406$		0			0
$407$	−1.31145e6	−	4.03622e6i	−0.392433	−	1.20778i
$408$		0			0
$409$	4.86958e6			1.43941			0.719703	−	0.694282i	$-0.244278\pi$
$409$	4.86958e6			1.43941			0.719703	+	0.694282i	$0.244278\pi$
$410$		0			0
$411$	−1.78054e6	+	5.47993e6i	−0.519932	+	1.60019i
$412$		0			0
$413$	−4.51584e6	−	3.28095e6i	−1.30276	−	0.946508i
$414$		0			0
$415$	1.45261e6	+	1.05538e6i	0.414027	+	0.300808i
$416$		0			0
$417$	2.44938e6	−	7.53840e6i	0.689787	−	2.12295i
$418$		0			0
$419$	793529.	−	576533.i	0.220815	−	0.160431i	−0.471879	−	0.881663i	$-0.656424\pi$
$419$	793529.	−	576533.i	0.220815	−	0.160431i	0.692693	+	0.721232i	$0.256424\pi$
$420$		0			0
$421$	2.23304e6	−	1.62240e6i	0.614033	−	0.446121i	−0.236799	−	0.971559i	$-0.576098\pi$
$421$	2.23304e6	−	1.62240e6i	0.614033	−	0.446121i	0.850832	+	0.525438i	$0.176098\pi$
$422$		0			0
$423$	−572593.	−	1.76226e6i	−0.155595	−	0.478871i
$424$		0			0
$425$	−438396.	+	1.34924e6i	−0.117732	+	0.362341i
$426$		0			0
$427$	19994.3	+	61536.2i	0.00530685	+	0.0163328i
$428$		0			0
$429$	−3.36949e6			−0.883935
$430$		0			0
$431$	−1.80279e6	+	1.30980e6i	−0.467467	+	0.339635i	−0.796453	−	0.604700i	$-0.793293\pi$
$431$	−1.80279e6	+	1.30980e6i	−0.467467	+	0.339635i	0.328986	+	0.944335i	$0.393293\pi$
$432$		0			0
$433$	3.13565e6			0.803726			0.401863	−	0.915700i	$-0.368363\pi$
$433$	3.13565e6			0.803726			0.401863	+	0.915700i	$0.368363\pi$
$434$		0			0
$435$	1.96876e6			0.498848
$436$		0			0
$437$	1.67231e6	−	1.21500e6i	0.418903	−	0.304351i
$438$		0			0
$439$	937043.			0.232059			0.116029	−	0.993246i	$-0.462983\pi$
$439$	937043.			0.232059			0.116029	+	0.993246i	$0.462983\pi$
$440$		0			0
$441$	−98943.7	−	304517.i	−0.0242265	−	0.0745616i
$442$		0			0
$443$	1.55200e6	−	4.77657e6i	0.375736	−	1.15640i	−0.567245	−	0.823549i	$-0.691991\pi$
$443$	1.55200e6	−	4.77657e6i	0.375736	−	1.15640i	0.942981	−	0.332847i	$-0.108009\pi$
$444$		0			0
$445$	1.35443e6	+	4.16850e6i	0.324232	+	0.997884i
$446$		0			0
$447$	−5.16790e6	+	3.75470e6i	−1.22334	+	0.888805i
$448$		0			0
$449$	−10402.4	+	7557.77i	−0.00243510	+	0.00176920i	−0.589002	−	0.808131i	$-0.700479\pi$
$449$	−10402.4	+	7557.77i	−0.00243510	+	0.00176920i	0.586567	+	0.809901i	$0.300479\pi$
$450$		0			0
$451$	1.30393e6	−	4.01309e6i	0.301866	−	0.929047i
$452$		0			0
$453$	5.41811e6	+	3.93649e6i	1.24052	+	0.901288i
$454$		0			0
$455$	−2.09344e6	−	1.52097e6i	−0.474059	−	0.344424i
$456$		0			0
$457$	−1.84218e6	+	5.66964e6i	−0.412611	+	1.26989i	0.501759	+	0.865007i	$0.332686\pi$
$457$	−1.84218e6	+	5.66964e6i	−0.412611	+	1.26989i	−0.914370	+	0.404879i	$0.867314\pi$
$458$		0			0
$459$	−1.45325e6			−0.321965
$460$		0			0
$461$	946888.	+	2.91422e6i	0.207513	+	0.638661i	0.999601	+	0.0282531i	$0.00899442\pi$
$461$	946888.	+	2.91422e6i	0.207513	+	0.638661i	−0.792087	+	0.610408i	$0.791006\pi$
$462$		0			0
$463$	759977.	+	552156.i	0.164759	+	0.119704i	0.667109	−	0.744960i	$-0.267531\pi$
$463$	759977.	+	552156.i	0.164759	+	0.119704i	−0.502351	+	0.864664i	$0.667531\pi$
$464$		0			0
$465$	−6.67328e6	+	2.73722e6i	−1.43122	+	0.587052i
$466$		0			0
$467$	621146.	+	451289.i	0.131796	+	0.0957553i	0.651730	−	0.758451i	$-0.274044\pi$
$467$	621146.	+	451289.i	0.131796	+	0.0957553i	−0.519934	+	0.854206i	$0.674044\pi$
$468$		0			0
$469$	1.61890e6	+	4.98245e6i	0.339850	+	1.04595i
$470$		0			0
$471$	−1.06804e6			−0.221839
$472$		0			0
$473$	−2.37429e6	+	7.30732e6i	−0.487957	+	1.50178i
$474$		0			0
$475$	678586.	+	493021.i	0.137997	+	0.100261i
$476$		0			0
$477$	244799.	+	177857.i	0.0492622	+	0.0357911i
$478$		0			0
$479$	903083.	−	2.77940e6i	0.179841	−	0.553494i	−0.819980	−	0.572392i	$-0.806016\pi$
$479$	903083.	−	2.77940e6i	0.179841	−	0.553494i	0.999821	+	0.0188977i	$0.00601569\pi$
$480$		0			0
$481$	2.24046e6	−	1.62779e6i	0.441544	−	0.320801i
$482$		0			0
$483$	−5.44653e6	+	3.95713e6i	−1.06231	+	0.771814i
$484$		0			0
$485$	842652.	+	2.59342e6i	0.162665	+	0.500631i
$486$		0			0
$487$	−2.81923e6	+	8.67670e6i	−0.538652	+	1.65780i	0.196971	+	0.980409i	$0.436890\pi$
$487$	−2.81923e6	+	8.67670e6i	−0.538652	+	1.65780i	−0.735623	+	0.677391i	$0.763110\pi$
$488$		0			0
$489$	−488952.	−	1.50484e6i	−0.0924686	−	0.284589i
$490$		0			0
$491$	−6.47839e6			−1.21273			−0.606364	−	0.795187i	$-0.707373\pi$
$491$	−6.47839e6			−1.21273			−0.606364	+	0.795187i	$0.707373\pi$
$492$		0			0
$493$	−1.57127e6	+	1.14159e6i	−0.291161	+	0.211541i
$494$		0			0
$495$	−6.14264e6			−1.12679
$496$		0			0
$497$	5.69549e6			1.03428
$498$		0			0
$499$	3.94216e6	−	2.86415e6i	0.708733	−	0.514925i	−0.174031	−	0.984740i	$-0.555679\pi$
$499$	3.94216e6	−	2.86415e6i	0.708733	−	0.514925i	0.882765	+	0.469815i	$0.155679\pi$
$500$		0			0
$501$	6.78413e6			1.20754
$502$		0			0
$503$	1.29003e6	+	3.97031e6i	0.227343	+	0.699689i	0.998045	+	0.0624939i	$0.0199054\pi$
$503$	1.29003e6	+	3.97031e6i	0.227343	+	0.699689i	−0.770703	+	0.637195i	$0.780095\pi$
$504$		0			0
$505$	−863014.	+	2.65608e6i	−0.150588	+	0.463461i
$506$		0			0
$507$	1.70947e6	+	5.26121e6i	0.295353	+	0.909003i
$508$		0			0
$509$	−8.22864e6	+	5.97846e6i	−1.40778	+	1.02281i	−0.414136	+	0.910215i	$0.635916\pi$
$509$	−8.22864e6	+	5.97846e6i	−1.40778	+	1.02281i	−0.993641	+	0.112594i	$0.964084\pi$
$510$		0			0
$511$	2.98110e6	−	2.16590e6i	0.505038	−	0.366932i
$512$		0			0
$513$	−265513.	+	817165.i	−0.0445443	+	0.137093i
$514$		0			0
$515$	1.07170e7	+	7.78634e6i	1.78055	+	1.29365i
$516$		0			0
$517$	−3.91848e6	−	2.84694e6i	−0.644750	−	0.468438i
$518$		0			0
$519$	3.55897e6	−	1.09534e7i	0.579971	−	1.78497i
$520$		0			0
$521$	−1.00640e7			−1.62434			−0.812170	−	0.583421i	$-0.801714\pi$
$521$	−1.00640e7			−1.62434			−0.812170	+	0.583421i	$0.801714\pi$
$522$		0			0
$523$	1.65172e6	+	5.08347e6i	0.264048	+	0.812655i	0.991911	+	0.126933i	$0.0405134\pi$
$523$	1.65172e6	+	5.08347e6i	0.264048	+	0.812655i	−0.727864	+	0.685722i	$0.759487\pi$
$524$		0			0
$525$	−2.21008e6	−	1.60571e6i	−0.349952	−	0.254255i
$526$		0			0
$527$	3.73878e6	−	6.05412e6i	0.586412	−	0.949565i
$528$		0			0
$529$	−384579.	−	279413.i	−0.0597511	−	0.0434117i
$530$		0			0
$531$	−2.67193e6	−	8.22336e6i	−0.411234	−	1.26565i
$532$		0			0
$533$	2.75349e6			0.419822
$534$		0			0
$535$	−242281.	+	745663.i	−0.0365961	+	0.112631i
$536$		0			0
$537$	−1.31280e7	−	9.53804e6i	−1.96455	−	1.42733i
$538$		0			0
$539$	−677111.	−	491950.i	−0.100389	−	0.0729372i
$540$		0			0
$541$	2.51060e6	−	7.72682e6i	0.368794	−	1.13503i	−0.578777	−	0.815486i	$-0.696470\pi$
$541$	2.51060e6	−	7.72682e6i	0.368794	−	1.13503i	0.947571	−	0.319545i	$-0.103530\pi$
$542$		0			0
$543$	−3.52116e6	+	2.55828e6i	−0.512492	+	0.372347i
$544$		0			0
$545$	2.18982e6	−	1.59100e6i	0.315803	−	0.229445i
$546$		0			0
$547$	−2.43352e6	−	7.48959e6i	−0.347749	−	1.07026i	−0.960096	−	0.279672i	$-0.909774\pi$
$547$	−2.43352e6	−	7.48959e6i	−0.347749	−	1.07026i	0.612347	−	0.790589i	$-0.290226\pi$
$548$		0			0
$549$	−30972.0	+	95321.9i	−0.00438569	+	0.0134978i
$550$		0			0
$551$	354845.	+	1.09210e6i	0.0497920	+	0.153244i
$552$		0			0
$553$	1.20990e7			1.68242
$554$		0			0
$555$	9.29401e6	−	6.75249e6i	1.28077	−	0.930533i
$556$		0			0
$557$	−1.26381e6			−0.172602			−0.0863009	−	0.996269i	$-0.527505\pi$
$557$	−1.26381e6			−0.172602			−0.0863009	+	0.996269i	$0.527505\pi$
$558$		0			0
$559$	−5.01374e6			−0.678629
$560$		0			0
$561$	1.11555e7	−	8.10494e6i	1.49652	−	1.08728i
$562$		0			0
$563$	4.08071e6			0.542581			0.271290	−	0.962498i	$-0.412550\pi$
$563$	4.08071e6			0.542581			0.271290	+	0.962498i	$0.412550\pi$
$564$		0			0
$565$	−1.20566e6	−	3.71064e6i	−0.158893	−	0.489022i
$566$		0			0
$567$	2.62423e6	−	8.07655e6i	0.342803	−	1.05504i
$568$		0			0
$569$	−3.44465e6	−	1.06015e7i	−0.446031	−	1.37274i	−0.881350	−	0.472465i	$-0.843364\pi$
$569$	−3.44465e6	−	1.06015e7i	−0.446031	−	1.37274i	0.435319	−	0.900276i	$-0.356636\pi$
$570$		0			0
$571$	−4.15046e6	+	3.01549e6i	−0.532729	+	0.387050i	−0.821378	−	0.570385i	$-0.806794\pi$
$571$	−4.15046e6	+	3.01549e6i	−0.532729	+	0.387050i	0.288649	+	0.957435i	$0.406794\pi$
$572$		0			0
$573$	1.17963e6	−	857055.i	0.150093	−	0.109049i
$574$		0			0
$575$	866674.	−	2.66735e6i	0.109317	−	0.336442i
$576$		0			0
$577$	−747508.	−	543096.i	−0.0934708	−	0.0679105i	0.540068	−	0.841621i	$-0.318398\pi$
$577$	−747508.	−	543096.i	−0.0934708	−	0.0679105i	−0.633539	+	0.773711i	$0.718398\pi$
$578$		0			0
$579$	1.02348e7	+	7.43604e6i	1.26877	+	0.921818i
$580$		0			0
$581$	1.05400e6	−	3.24388e6i	0.129539	−	0.398680i
$582$		0			0
$583$	790949.			0.0963778
$584$		0			0
$585$	−1.23865e6	−	3.81216e6i	−0.149644	−	0.460555i
$586$		0			0
$587$	2.08591e6	+	1.51550e6i	0.249862	+	0.181535i	0.705665	−	0.708545i	$-0.250648\pi$
$587$	2.08591e6	+	1.51550e6i	0.249862	+	0.181535i	−0.455804	+	0.890080i	$0.650648\pi$
$588$		0			0
$589$	−2.72116e6	−	3.20843e6i	−0.323196	−	0.381069i
$590$		0			0
$591$	−3.89810e6	−	2.83213e6i	−0.459075	−	0.333538i
$592$		0			0
$593$	2.99501e6	+	9.21770e6i	0.349753	+	1.07643i	0.958990	+	0.283441i	$0.0914761\pi$
$593$	2.99501e6	+	9.21770e6i	0.349753	+	1.07643i	−0.609236	+	0.792989i	$0.708524\pi$
$594$		0			0
$595$	1.05894e7			1.22625
$596$		0			0
$597$	−860995.	+	2.64987e6i	−0.0988701	+	0.304291i
$598$		0			0
$599$	−653478.	−	474780.i	−0.0744156	−	0.0540661i	0.549955	−	0.835194i	$-0.314645\pi$
$599$	−653478.	−	474780.i	−0.0744156	−	0.0540661i	−0.624371	+	0.781128i	$0.714645\pi$
$600$		0			0
$601$	−7.22704e6	−	5.25075e6i	−0.816158	−	0.592974i	0.0994511	−	0.995042i	$-0.468291\pi$
$601$	−7.22704e6	−	5.25075e6i	−0.816158	−	0.592974i	−0.915610	+	0.402069i	$0.868291\pi$
$602$		0			0
$603$	−2.50773e6	+	7.71801e6i	−0.280859	+	0.864395i
$604$		0			0
$605$	−4.55430e6	+	3.30889e6i	−0.505863	+	0.367531i
$606$		0			0
$607$	−4.71642e6	+	3.42668e6i	−0.519566	+	0.377487i	−0.816440	−	0.577430i	$-0.804056\pi$
$607$	−4.71642e6	+	3.42668e6i	−0.519566	+	0.377487i	0.296875	+	0.954916i	$0.404056\pi$
$608$		0			0
$609$	−1.15569e6	−	3.55685e6i	−0.126269	−	0.388617i
$610$		0			0
$611$	976681.	−	3.00591e6i	0.105840	−	0.325742i
$612$		0			0
$613$	1.69539e6	+	5.21787e6i	0.182229	+	0.560844i	0.999890	−	0.0148570i	$-0.00472930\pi$
$613$	1.69539e6	+	5.21787e6i	0.182229	+	0.560844i	−0.817660	+	0.575701i	$0.804729\pi$
$614$		0			0
$615$	1.14222e7			1.21776
$616$		0			0
$617$	−2.21330e6	+	1.60806e6i	−0.234060	+	0.170055i	−0.698633	−	0.715480i	$-0.746208\pi$
$617$	−2.21330e6	+	1.60806e6i	−0.234060	+	0.170055i	0.464573	+	0.885535i	$0.346208\pi$
$618$		0			0
$619$	−1.08492e7			−1.13808			−0.569040	−	0.822310i	$-0.692685\pi$
$619$	−1.08492e7			−1.13808			−0.569040	+	0.822310i	$0.692685\pi$
$620$		0			0
$621$	2.87296e6			0.298951
$622$		0			0
$623$	6.73595e6	−	4.89395e6i	0.695310	−	0.505172i
$624$		0			0
$625$	−1.19613e7			−1.22484
$626$		0			0
$627$	−2.51928e6	−	7.75355e6i	−0.255922	−	0.787647i
$628$		0			0
$629$	−3.50210e6	+	1.07784e7i	−0.352941	+	1.08624i
$630$		0			0
$631$	−6.16837e6	−	1.89843e7i	−0.616733	−	1.89811i	−0.370050	−	0.929012i	$-0.620660\pi$
$631$	−6.16837e6	−	1.89843e7i	−0.616733	−	1.89811i	−0.246682	−	0.969096i	$-0.579340\pi$
$632$		0			0
$633$	−621248.	+	451363.i	−0.0616248	+	0.0447731i
$634$		0			0
$635$	7.31192e6	−	5.31242e6i	0.719610	−	0.522827i
$636$		0			0
$637$	168770.	−	519420.i	0.0164796	−	0.0507189i
$638$		0			0
$639$	7.13758e6	+	5.18575e6i	0.691510	+	0.502412i
$640$		0			0
$641$	−2.15333e6	−	1.56449e6i	−0.206998	−	0.150393i	0.479457	−	0.877566i	$-0.340834\pi$
$641$	−2.15333e6	−	1.56449e6i	−0.206998	−	0.150393i	−0.686454	+	0.727173i	$0.740834\pi$
$642$		0			0
$643$	−4.26965e6	+	1.31406e7i	−0.407253	+	1.25340i	0.511746	+	0.859137i	$0.328999\pi$
$643$	−4.26965e6	+	1.31406e7i	−0.407253	+	1.25340i	−0.918999	+	0.394260i	$0.871001\pi$
$644$		0			0
$645$	−2.07983e7			−1.96847
$646$		0			0
$647$	−3.11639e6	−	9.59126e6i	−0.292679	−	0.900773i	−0.983991	−	0.178217i	$-0.942967\pi$
$647$	−3.11639e6	−	9.59126e6i	−0.292679	−	0.900773i	0.691313	−	0.722556i	$-0.257033\pi$
$648$		0			0
$649$	−1.82851e7	−	1.32849e7i	−1.70406	−	1.23807i
$650$		0			0
$651$	8.86251e6	+	1.04495e7i	0.819604	+	0.966368i
$652$		0			0
$653$	1.26474e6	+	918886.i	0.116069	+	0.0843293i	0.644306	−	0.764768i	$-0.277146\pi$
$653$	1.26474e6	+	918886.i	0.116069	+	0.0843293i	−0.528236	+	0.849097i	$0.677146\pi$
$654$		0			0
$655$	3.65581e6	+	1.12514e7i	0.332951	+	1.02472i
$656$		0			0
$657$	5.70796e6			0.515903
$658$		0			0
$659$	−4.27246e6	+	1.31493e7i	−0.383235	+	1.17948i	0.554518	+	0.832172i	$0.312903\pi$
$659$	−4.27246e6	+	1.31493e7i	−0.383235	+	1.17948i	−0.937753	+	0.347304i	$0.887097\pi$
$660$		0			0
$661$	1.42832e7	+	1.03774e7i	1.27152	+	0.923812i	0.999262	−	0.0384129i	$-0.0122302\pi$
$661$	1.42832e7	+	1.03774e7i	1.27152	+	0.923812i	0.272256	+	0.962225i	$0.412230\pi$
$662$		0			0
$663$	7.27946e6	+	5.28884e6i	0.643154	+	0.467279i
$664$		0			0
$665$	1.93471e6	−	5.95443e6i	0.169653	−	0.522139i
$666$		0			0
$667$	3.10628e6	−	2.25684e6i	0.270349	−	0.196420i
$668$		0			0
$669$	−1.05437e7	+	7.66048e6i	−0.910814	+	0.661745i
$670$		0			0
$671$	80959.0	+	249166.i	0.00694159	+	0.0213640i
$672$		0			0
$673$	2.70104e6	−	8.31294e6i	0.229876	−	0.707485i	−0.767884	−	0.640589i	$-0.778690\pi$
$673$	2.70104e6	−	8.31294e6i	0.229876	−	0.707485i	0.997760	−	0.0668961i	$-0.0213096\pi$
$674$		0			0
$675$	360247.	+	1.10872e6i	0.0304327	+	0.0936622i
$676$		0			0
$677$	1.92570e7			1.61479			0.807397	−	0.590009i	$-0.200876\pi$
$677$	1.92570e7			1.61479			0.807397	+	0.590009i	$0.200876\pi$
$678$		0			0
$679$	4.19074e6	−	3.04475e6i	0.348832	−	0.253441i
$680$		0			0
$681$	−2.11171e7			−1.74489
$682$		0			0
$683$	−1.44017e7			−1.18131			−0.590653	−	0.806926i	$-0.701130\pi$
$683$	−1.44017e7			−1.18131			−0.590653	+	0.806926i	$0.701130\pi$
$684$		0			0
$685$	−1.44952e7	+	1.05314e7i	−1.18032	+	0.857549i
$686$		0			0
$687$	1.05117e7			0.849729
$688$		0			0
$689$	159493.	+	490869.i	0.0127995	+	0.0393928i
$690$		0			0
$691$	7.08866e6	−	2.18166e7i	0.564766	−	1.73817i	−0.103878	−	0.994590i	$-0.533125\pi$
$691$	7.08866e6	−	2.18166e7i	0.564766	−	1.73817i	0.668645	−	0.743582i	$-0.266875\pi$
$692$		0			0
$693$	3.60582e6	+	1.10976e7i	0.285214	+	0.877799i
$694$		0			0
$695$	1.99402e7	−	1.44874e7i	1.56591	−	1.13770i
$696$		0			0
$697$	−9.11608e6	+	6.62322e6i	−0.710765	+	0.516401i
$698$		0			0
$699$	−4.93730e6	+	1.51955e7i	−0.382205	+	1.17631i
$700$		0			0
$701$	1.85069e6	+	1.34460e6i	0.142245	+	0.103347i	0.656632	−	0.754211i	$-0.271980\pi$
$701$	1.85069e6	+	1.34460e6i	0.142245	+	0.103347i	−0.514387	+	0.857558i	$0.671980\pi$
$702$		0			0
$703$	5.42085e6	+	3.93848e6i	0.413694	+	0.300566i
$704$		0			0
$705$	4.05153e6	−	1.24693e7i	0.307005	−	0.944865i
$706$		0			0
$707$	5.30521e6			0.399166
$708$		0			0
$709$	−3.32246e6	−	1.02255e7i	−0.248225	−	0.763957i	−0.995089	−	0.0989807i	$-0.968442\pi$
$709$	−3.32246e6	−	1.02255e7i	−0.248225	−	0.763957i	0.746865	−	0.664976i	$-0.231558\pi$
$710$		0			0
$711$	1.51624e7	+	1.10161e7i	1.12485	+	0.817250i
$712$		0			0
$713$	−7.39127e6	+	1.19685e7i	−0.544496	+	0.881692i
$714$		0			0
$715$	−8.47655e6	−	6.15858e6i	−0.620089	−	0.450521i
$716$		0			0
$717$	1.05719e7	+	3.25368e7i	0.767986	+	2.36362i
$718$		0			0
$719$	−2.99354e6			−0.215955			−0.107977	−	0.994153i	$-0.534437\pi$
$719$	−2.99354e6			−0.215955			−0.107977	+	0.994153i	$0.534437\pi$
$720$		0			0
$721$	7.77614e6	−	2.39325e7i	0.557091	−	1.71455i
$722$		0			0
$723$	−2.06141e7	−	1.49770e7i	−1.46662	−	1.06556i
$724$		0			0
$725$	1.26046e6	+	915775.i	0.0890600	+	0.0647059i
$726$		0			0
$727$	−7.81500e6	+	2.40521e7i	−0.548395	+	1.68779i	0.164384	+	0.986396i	$0.447436\pi$
$727$	−7.81500e6	+	2.40521e7i	−0.548395	+	1.68779i	−0.712779	+	0.701389i	$0.752564\pi$
$728$		0			0
$729$	6.16935e6	−	4.48229e6i	0.429952	−	0.312379i
$730$		0			0
$731$	1.65992e7	−	1.20600e7i	1.14893	−	0.834747i
$732$		0			0
$733$	−2.50365e6	−	7.70544e6i	−0.172113	−	0.529709i	0.827377	−	0.561647i	$-0.189832\pi$
$733$	−2.50365e6	−	7.70544e6i	−0.172113	−	0.529709i	−0.999490	+	0.0319380i	$0.989832\pi$
$734$		0			0
$735$	700101.	−	2.15469e6i	0.0478016	−	0.147118i
$736$		0			0
$737$	6.55508e6	+	2.01745e7i	0.444538	+	1.36815i
$738$		0			0
$739$	1.46897e7			0.989471			0.494735	−	0.869044i	$-0.335265\pi$
$739$	1.46897e7			0.989471			0.494735	+	0.869044i	$0.335265\pi$
$740$		0			0
$741$	4.30390e6	−	3.12697e6i	0.287950	−	0.209208i
$742$		0			0
$743$	−1.39830e7			−0.929239			−0.464619	−	0.885511i	$-0.653809\pi$
$743$	−1.39830e7			−0.929239			−0.464619	+	0.885511i	$0.653809\pi$
$744$		0			0
$745$	−1.98634e7			−1.31118
$746$		0			0
$747$	4.27443e6	−	3.10556e6i	0.280270	−	0.203628i
$748$		0			0
$749$	1.48937e6			0.0970061
$750$		0			0
$751$	5.88241e6	+	1.81042e7i	0.380588	+	1.17133i	0.939631	+	0.342191i	$0.111169\pi$
$751$	5.88241e6	+	1.81042e7i	0.380588	+	1.17133i	−0.559043	+	0.829139i	$0.688831\pi$
$752$		0			0
$753$	−9.27401e6	+	2.85425e7i	−0.596046	+	1.83444i
$754$		0			0
$755$	6.43533e6	+	1.98059e7i	0.410869	+	1.26452i
$756$		0			0
$757$	−1.09625e7	+	7.96471e6i	−0.695295	+	0.505161i	−0.878396	−	0.477933i	$-0.841386\pi$
$757$	−1.09625e7	+	7.96471e6i	−0.695295	+	0.505161i	0.183102	+	0.983094i	$0.441386\pi$
$758$		0			0
$759$	−2.20535e7	+	1.60228e7i	−1.38955	+	1.00957i
$760$		0			0
$761$	615478.	−	1.89425e6i	0.0385257	−	0.118570i	−0.929944	−	0.367701i	$-0.880145\pi$
$761$	615478.	−	1.89425e6i	0.0385257	−	0.118570i	0.968470	+	0.249131i	$0.0801450\pi$
$762$		0			0
$763$	−4.15983e6	−	3.02229e6i	−0.258681	−	0.187942i
$764$		0			0
$765$	1.32706e7	+	9.64165e6i	0.819854	+	0.595659i
$766$		0			0
$767$	4.55756e6	−	1.40267e7i	0.279733	−	0.860929i
$768$		0			0
$769$	1.83590e7			1.11952			0.559761	−	0.828654i	$-0.310893\pi$
$769$	1.83590e7			1.11952			0.559761	+	0.828654i	$0.310893\pi$
$770$		0			0
$771$	−8.60037e6	−	2.64692e7i	−0.521052	−	1.60363i
$772$		0			0
$773$	1.18536e7	+	8.61214e6i	0.713512	+	0.518397i	0.884305	−	0.466910i	$-0.154633\pi$
$773$	1.18536e7	+	8.61214e6i	0.713512	+	0.518397i	−0.170793	+	0.985307i	$0.554633\pi$
$774$		0			0
$775$	−5.54566e6	−	1.35166e6i	−0.331665	−	0.0808375i
$776$		0			0
$777$	−1.76551e7	−	1.28272e7i	−1.04910	−	0.762217i
$778$		0			0
$779$	2.05871e6	+	6.33607e6i	0.121549	+	0.374090i
$780$		0			0
$781$	2.30616e7			1.35289
$782$		0			0
$783$	−493184.	+	1.51786e6i	−0.0287478	+	0.0884766i
$784$		0			0
$785$	−2.68686e6	−	1.95212e6i	−0.155622	−	0.113066i
$786$		0			0
$787$	−1.55783e7	−	1.13183e7i	−0.896569	−	0.651396i	0.0410134	−	0.999159i	$-0.486941\pi$
$787$	−1.55783e7	−	1.13183e7i	−0.896569	−	0.651396i	−0.937582	+	0.347763i	$0.886941\pi$
$788$		0			0
$789$	2.84727e6	−	8.76300e6i	0.162831	−	0.501141i
$790$		0			0
$791$	−5.99609e6	+	4.35641e6i	−0.340743	+	0.247564i
$792$		0			0
$793$	−138309.	+	100487.i	−0.00781031	+	0.00567452i
$794$		0			0
$795$	661618.	+	2.03625e6i	0.0371270	+	0.114265i
$796$		0			0
$797$	−83637.6	+	257410.i	−0.00466397	+	0.0143542i	−0.953361	−	0.301831i	$-0.902402\pi$
$797$	−83637.6	+	257410.i	−0.00466397	+	0.0143542i	0.948697	+	0.316185i	$0.102402\pi$
$798$		0			0
$799$	3.99687e6	+	1.23011e7i	0.221489	+	0.681674i
$800$		0			0
$801$	1.28974e7			0.710267
$802$		0			0
$803$	1.20708e7	−	8.76993e6i	0.660612	−	0.479963i
$804$		0			0
$805$	−2.09344e7			−1.13860
$806$		0			0
$807$	−7.87647e6			−0.425743
$808$		0			0
$809$	−5.64237e6	+	4.09942e6i	−0.303103	+	0.220217i	−0.728931	−	0.684587i	$-0.759983\pi$
$809$	−5.64237e6	+	4.09942e6i	−0.303103	+	0.220217i	0.425829	+	0.904804i	$0.359983\pi$
$810$		0			0
$811$	1.10982e7			0.592515			0.296258	−	0.955108i	$-0.404261\pi$
$811$	1.10982e7			0.592515			0.296258	+	0.955108i	$0.404261\pi$
$812$		0			0
$813$	1.24535e7	+	3.83279e7i	0.660792	+	2.03371i
$814$		0			0
$815$	1.52042e6	−	4.67938e6i	0.0801807	−	0.246771i
$816$		0			0
$817$	−3.74865e6	−	1.15372e7i	−0.196481	−	0.604705i
$818$		0			0
$819$	−6.16013e6	+	4.47560e6i	−0.320908	+	0.233153i
$820$		0			0
$821$	1.72641e7	−	1.25431e7i	0.893896	−	0.649453i	−0.0429951	−	0.999075i	$-0.513690\pi$
$821$	1.72641e7	−	1.25431e7i	0.893896	−	0.649453i	0.936891	+	0.349622i	$0.113690\pi$
$822$		0			0
$823$	−4.94486e6	+	1.52187e7i	−0.254481	+	0.783210i	0.739451	+	0.673210i	$0.235085\pi$
$823$	−4.94486e6	+	1.52187e7i	−0.254481	+	0.783210i	−0.993932	+	0.110000i	$0.964915\pi$
$824$		0			0
$825$	−8.94882e6	−	6.50170e6i	−0.457753	−	0.332577i
$826$		0			0
$827$	−2.19953e7	−	1.59805e7i	−1.11832	−	0.812508i	−0.134368	−	0.990932i	$-0.542900\pi$
$827$	−2.19953e7	−	1.59805e7i	−1.11832	−	0.812508i	−0.983954	+	0.178424i	$0.942900\pi$
$828$		0			0
$829$	4.06501e6	−	1.25108e7i	0.205436	−	0.632266i	−0.794260	−	0.607579i	$-0.792141\pi$
$829$	4.06501e6	−	1.25108e7i	0.205436	−	0.632266i	0.999695	−	0.0246873i	$-0.00785901\pi$
$830$		0			0
$831$	−1.62185e7			−0.814719
$832$		0			0
$833$	690656.	+	2.12562e6i	0.0344865	+	0.106139i
$834$		0			0
$835$	1.70667e7	+	1.23997e7i	0.847098	+	0.615453i
$836$		0			0
$837$	−438636.	−	5.83063e6i	−0.0216416	−	0.287675i
$838$		0			0
$839$	−3.91807e6	−	2.84665e6i	−0.192162	−	0.139614i	0.487544	−	0.873098i	$-0.337893\pi$
$839$	−3.91807e6	−	2.84665e6i	−0.192162	−	0.139614i	−0.679706	+	0.733484i	$0.737893\pi$
$840$		0			0
$841$	−5.67918e6	−	1.74787e7i	−0.276882	−	0.852157i
$842$		0			0
$843$	−4.65670e7			−2.25688
$844$		0			0
$845$	−5.31568e6	+	1.63600e7i	−0.256105	+	0.788209i
$846$		0			0
$847$	8.65144e6	+	6.28564e6i	0.414362	+	0.301052i
$848$		0			0
$849$	−9.65343e6	−	7.01363e6i	−0.459634	−	0.333944i
$850$		0			0
$851$	6.92338e6	−	2.13080e7i	0.327714	−	1.00860i
$852$		0			0
$853$	−1.90336e7	+	1.38287e7i	−0.895669	+	0.650741i	−0.937350	−	0.348390i	$-0.886729\pi$
$853$	−1.90336e7	+	1.38287e7i	−0.895669	+	0.650741i	0.0416812	+	0.999131i	$0.486729\pi$
$854$		0			0
$855$	7.84609e6	−	5.70052e6i	0.367061	−	0.266685i
$856$		0			0
$857$	9.28192e6	+	2.85668e7i	0.431704	+	1.32865i	0.896427	+	0.443192i	$0.146154\pi$
$857$	9.28192e6	+	2.85668e7i	0.431704	+	1.32865i	−0.464723	+	0.885456i	$0.653846\pi$
$858$		0			0
$859$	8.25525e6	−	2.54070e7i	0.381722	−	1.17482i	−0.557108	−	0.830440i	$-0.688089\pi$
$859$	8.25525e6	−	2.54070e7i	0.381722	−	1.17482i	0.938830	−	0.344380i	$-0.111911\pi$
$860$		0			0
$861$	−6.70500e6	−	2.06359e7i	−0.308241	−	0.948669i
$862$		0			0
$863$	−7.18729e6			−0.328502			−0.164251	−	0.986419i	$-0.552521\pi$
$863$	−7.18729e6			−0.328502			−0.164251	+	0.986419i	$0.552521\pi$
$864$		0			0
$865$	2.89733e7	−	2.10503e7i	1.31661	−	0.956574i
$866$		0			0
$867$	−7.25924e6			−0.327977
$868$		0			0
$869$	4.89899e7			2.20068
$870$		0			0
$871$	−1.11986e7	+	8.13626e6i	−0.500171	+	0.363395i
$872$		0			0
$873$	8.02408e6			0.356336
$874$		0			0
$875$	5.06452e6	+	1.55870e7i	0.223624	+	0.688244i
$876$		0			0
$877$	−5.40687e6	+	1.66406e7i	−0.237381	+	0.730585i	0.759415	+	0.650606i	$0.225485\pi$
$877$	−5.40687e6	+	1.66406e7i	−0.237381	+	0.730585i	−0.996797	+	0.0799787i	$0.974515\pi$
$878$		0			0
$879$	1.75969e7	+	5.41578e7i	0.768183	+	2.36423i
$880$		0			0
$881$	2.49113e7	−	1.80991e7i	1.08133	−	0.785631i	0.103414	−	0.994638i	$-0.467023\pi$
$881$	2.49113e7	−	1.80991e7i	1.08133	−	0.785631i	0.977914	+	0.209008i	$0.0670234\pi$
$882$		0			0
$883$	−2.43436e7	+	1.76866e7i	−1.05071	+	0.763385i	−0.972347	−	0.233540i	$-0.924969\pi$
$883$	−2.43436e7	+	1.76866e7i	−1.05071	+	0.763385i	−0.0783620	+	0.996925i	$0.524969\pi$
$884$		0			0
$885$	1.89059e7	−	5.81865e7i	0.811409	−	2.49726i
$886$		0			0
$887$	−2.82696e7	−	2.05391e7i	−1.20645	−	0.876540i	−0.211549	−	0.977367i	$-0.567851\pi$
$887$	−2.82696e7	−	2.05391e7i	−1.20645	−	0.876540i	−0.994904	+	0.100828i	$0.967851\pi$
$888$		0			0
$889$	−1.38899e7	−	1.00916e7i	−0.589446	−	0.428258i
$890$		0			0
$891$	1.06258e7	−	3.27027e7i	0.448400	−	1.38003i
$892$		0			0
$893$	7.64717e6			0.320902
$894$		0			0
$895$	−1.55927e7	−	4.79893e7i	−0.650674	−	2.00257i
$896$		0			0
$897$	−1.43909e7	−	1.04556e7i	−0.597183	−	0.433879i
$898$		0			0
$899$	−5.05449e6	−	5.95957e6i	−0.208582	−	0.245933i
$900$		0			0
$901$	−1.70877e6	−	1.24149e6i	−0.0701248	−	0.0509487i
$902$		0			0
$903$	1.22089e7	+	3.75752e7i	0.498263	+	1.53349i
$904$		0			0
$905$	−1.35340e7			−0.549294
$906$		0			0
$907$	−7.70753e6	+	2.37213e7i	−0.311098	+	0.957461i	0.666233	+	0.745744i	$0.267906\pi$
$907$	−7.70753e6	+	2.37213e7i	−0.311098	+	0.957461i	−0.977331	+	0.211717i	$0.932094\pi$
$908$		0			0
$909$	6.64848e6	+	4.83040e6i	0.266878	+	0.193898i
$910$		0			0
$911$	−2.25913e7	−	1.64136e7i	−0.901875	−	0.655250i	0.0370722	−	0.999313i	$-0.488197\pi$
$911$	−2.25913e7	−	1.64136e7i	−0.901875	−	0.655250i	−0.938947	+	0.344062i	$0.888197\pi$
$912$		0			0
$913$	4.26775e6	−	1.31348e7i	0.169443	−	0.521491i
$914$		0			0
$915$	−573742.	+	416848.i	−0.0226550	+	0.0164598i
$916$		0			0
$917$	1.81814e7	−	1.32095e7i	0.714008	−	0.518757i
$918$		0			0
$919$	5.98403e6	+	1.84169e7i	0.233725	+	0.719331i	0.997288	+	0.0735978i	$0.0234481\pi$
$919$	5.98403e6	+	1.84169e7i	0.233725	+	0.719331i	−0.763563	+	0.645733i	$0.776552\pi$
$920$		0			0
$921$	1.82605e7	−	5.61999e7i	0.709353	−	2.18317i
$922$		0			0
$923$	4.65031e6	+	1.43122e7i	0.179671	+	0.552970i
$924$		0			0
$925$	9.09126e6			0.349357
$926$		0			0
$927$	3.15356e7	−	2.29120e7i	1.20532	−	0.875716i
$928$		0			0
$929$	−2.77760e7			−1.05592			−0.527959	−	0.849270i	$-0.677043\pi$
$929$	−2.77760e7			−1.05592			−0.527959	+	0.849270i	$0.677043\pi$
$930$		0			0
$931$	1.32143e6			0.0499653
$932$		0			0
$933$	5.25068e6	−	3.81484e6i	0.197475	−	0.143474i
$934$		0			0
$935$	4.28775e7			1.60398
$936$		0			0
$937$	9.41493e6	+	2.89762e7i	0.350323	+	1.07818i	0.958672	+	0.284513i	$0.0918319\pi$
$937$	9.41493e6	+	2.89762e7i	0.350323	+	1.07818i	−0.608350	+	0.793669i	$0.708168\pi$
$938$		0			0
$939$	1.71379e7	−	5.27450e7i	0.634298	−	1.95217i
$940$		0			0
$941$	675284.	+	2.07831e6i	0.0248607	+	0.0765132i	0.962717	−	0.270510i	$-0.0871924\pi$
$941$	675284.	+	2.07831e6i	0.0248607	+	0.0765132i	−0.937856	+	0.347024i	$0.887192\pi$
$942$		0			0
$943$	1.80218e7	−	1.30936e7i	0.659961	−	0.479490i
$944$		0			0
$945$	7.03982e6	−	5.11473e6i	0.256438	−	0.186313i
$946$		0			0
$947$	7.36973e6	−	2.26817e7i	0.267040	−	0.821865i	−0.724176	−	0.689615i	$-0.757780\pi$
$947$	7.36973e6	−	2.26817e7i	0.267040	−	0.821865i	0.991216	−	0.132250i	$-0.0422202\pi$
$948$		0			0
$949$	7.87672e6	+	5.72277e6i	0.283910	+	0.206272i
$950$		0			0
$951$	−5.69315e7	−	4.13631e7i	−2.04127	−	1.48307i
$952$		0			0
$953$	3.63905e6	−	1.11998e7i	0.129794	−	0.399466i	−0.864950	−	0.501858i	$-0.832650\pi$
$953$	3.63905e6	−	1.11998e7i	0.129794	−	0.399466i	0.994744	+	0.102393i	$0.0326498\pi$
$954$		0			0
$955$	4.53406e6			0.160872
$956$		0			0
$957$	−4.67950e6	−	1.44020e7i	−0.165166	−	0.508328i
$958$		0			0
$959$	2.75354e7	+	2.00056e7i	0.966819	+	0.702435i
$960$		0			0
$961$	2.54184e7	+	1.31732e7i	0.887851	+	0.460131i
$962$		0			0
$963$	1.86648e6	+	1.35608e6i	0.0648571	+	0.0471215i
$964$		0			0
$965$	1.21564e7	+	3.74134e7i	0.420228	+	1.29333i
$966$		0			0
$967$	−4.35229e7			−1.49676			−0.748379	−	0.663272i	$-0.769167\pi$
$967$	−4.35229e7			−1.49676			−0.748379	+	0.663272i	$0.769167\pi$
$968$		0			0
$969$	−6.72751e6	+	2.07051e7i	−0.230168	+	0.708384i
$970$		0			0
$971$	2.53745e7	+	1.84357e7i	0.863674	+	0.627496i	0.928882	−	0.370376i	$-0.120771\pi$
$971$	2.53745e7	+	1.84357e7i	0.863674	+	0.627496i	−0.0652083	+	0.997872i	$0.520771\pi$
$972$		0			0
$973$	−3.78787e7	−	2.75205e7i	−1.28267	−	0.931911i
$974$		0			0
$975$	2.23049e6	−	6.86475e6i	0.0751432	−	0.231267i
$976$		0			0
$977$	−1.92886e7	+	1.40140e7i	−0.646494	+	0.469706i	−0.862075	−	0.506780i	$-0.830835\pi$
$977$	−1.92886e7	+	1.40140e7i	−0.646494	+	0.469706i	0.215581	+	0.976486i	$0.430835\pi$
$978$		0			0
$979$	2.72745e7	−	1.98161e7i	0.909495	−	0.660787i
$980$		0			0
$981$	−2.46129e6	−	7.57506e6i	−0.0816563	−	0.251312i
$982$		0			0
$983$	−2.76406e6	+	8.50691e6i	−0.0912356	+	0.280794i	−0.986254	−	0.165234i	$-0.947162\pi$
$983$	−2.76406e6	+	8.50691e6i	−0.0912356	+	0.280794i	0.895019	+	0.446028i	$0.147162\pi$
$984$		0			0
$985$	−4.62994e6	−	1.42495e7i	−0.152049	−	0.467960i
$986$		0			0
$987$	−2.49060e7			−0.813787
$988$		0			0
$989$	−3.28153e7	+	2.38417e7i	−1.06681	+	0.775080i
$990$		0			0
$991$	−5.57548e7			−1.80342			−0.901712	−	0.432337i	$-0.857689\pi$
$991$	−5.57548e7			−1.80342			−0.901712	+	0.432337i	$0.857689\pi$
$992$		0			0
$993$	−5.40259e7			−1.73872
$994$		0			0
$995$	−7.00929e6	+	5.09255e6i	−0.224448	+	0.163071i
$996$		0			0
$997$	−3.33914e6			−0.106389			−0.0531945	−	0.998584i	$-0.516940\pi$
$997$	−3.33914e6			−0.106389			−0.0531945	+	0.998584i	$0.516940\pi$
$998$		0			0
$999$	2.87781e6	+	8.85700e6i	0.0912324	+	0.280784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.6.f.a.33.13	✓	56
31.16	even	5	inner	124.6.f.a.109.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.6.f.a.33.13	✓	56	1.1	even	1	trivial
124.6.f.a.109.13	yes	56	31.16	even	5	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(16.8446 - 12.2383i) q^{3} +64.7441 q^{5} +(-38.0058 - 116.970i) q^{7} +(58.8724 - 181.191i) q^{9} +O(q^{10})\)	\(q+(16.8446 - 12.2383i) q^{3} +64.7441 q^{5} +(-38.0058 - 116.970i) q^{7} +(58.8724 - 181.191i) q^{9} +(-153.889 - 473.622i) q^{11} +(262.902 - 191.009i) q^{13} +(1090.59 - 792.357i) q^{15} +(-410.947 + 1264.76i) q^{17} +(636.098 + 462.152i) q^{19} +(-2071.70 - 1505.18i) q^{21} +(812.410 - 2500.34i) q^{23} +1066.79 q^{25} +(337.691 + 1039.31i) q^{27} +(1181.54 + 858.437i) q^{29} +(-5198.44 - 1267.03i) q^{31} +(-8388.52 - 6094.62i) q^{33} +(-2460.65 - 7573.10i) q^{35} +8522.04 q^{37} +(2090.84 - 6434.94i) q^{39} +(6854.96 + 4980.42i) q^{41} +(-12482.0 - 9068.69i) q^{43} +(3811.64 - 11731.0i) q^{45} +(7868.50 - 5716.80i) q^{47} +(1359.67 - 987.859i) q^{49} +(8556.34 + 26333.7i) q^{51} +(-490.801 + 1510.53i) q^{53} +(-9963.41 - 30664.2i) q^{55} +16370.8 q^{57} +(36717.3 - 26676.7i) q^{59} -526.087 q^{61} -23431.3 q^{63} +(17021.3 - 12366.7i) q^{65} -42596.1 q^{67} +(-16915.2 - 52059.6i) q^{69} +(-14310.2 + 44042.3i) q^{71} +(9258.36 + 28494.3i) q^{73} +(17969.7 - 13055.7i) q^{75} +(-49550.8 + 36000.7i) q^{77} +(-30399.3 + 93559.4i) q^{79} +(55861.1 + 40585.5i) q^{81} +(22436.2 + 16300.8i) q^{83} +(-26606.4 + 81886.0i) q^{85} +30408.3 q^{87} +(20919.7 + 64384.3i) q^{89} +(-32334.1 - 23492.1i) q^{91} +(-103072. + 42277.5i) q^{93} +(41183.6 + 29921.6i) q^{95} +(13015.1 + 40056.5i) q^{97} -94875.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9	\( 56 q + 2 q^{3} - 58 q^{5} + 104 q^{7} - 1234 q^{9} - 509 q^{11} - 117 q^{13} + 89 q^{15} - 3504 q^{17} + 262 q^{19} + 352 q^{21} - 2448 q^{23} + 49618 q^{25} + 14324 q^{27} - 9888 q^{29} - 12771 q^{31} + 27699 q^{33} + 13840 q^{35} + 76096 q^{37} + 33520 q^{39} - 4843 q^{41} - 40778 q^{43} + 56692 q^{45} + 38922 q^{47} - 17126 q^{49} - 69292 q^{51} - 41728 q^{53} - 172096 q^{55} + 57066 q^{57} - 58198 q^{59} + 176328 q^{61} - 37444 q^{63} + 143863 q^{65} + 9812 q^{67} - 9250 q^{69} - 67356 q^{71} - 63512 q^{73} - 198012 q^{75} - 74257 q^{77} + 137651 q^{79} + 196077 q^{81} + 156427 q^{83} + 238828 q^{85} - 558144 q^{87} - 99292 q^{89} - 243609 q^{91} - 325925 q^{93} - 75077 q^{95} - 476340 q^{97} + 745812 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 58 * q^5 + 104 * q^7 - 1234 * q^9 - 509 * q^11 - 117 * q^13 + 89 * q^15 - 3504 * q^17 + 262 * q^19 + 352 * q^21 - 2448 * q^23 + 49618 * q^25 + 14324 * q^27 - 9888 * q^29 - 12771 * q^31 + 27699 * q^33 + 13840 * q^35 + 76096 * q^37 + 33520 * q^39 - 4843 * q^41 - 40778 * q^43 + 56692 * q^45 + 38922 * q^47 - 17126 * q^49 - 69292 * q^51 - 41728 * q^53 - 172096 * q^55 + 57066 * q^57 - 58198 * q^59 + 176328 * q^61 - 37444 * q^63 + 143863 * q^65 + 9812 * q^67 - 9250 * q^69 - 67356 * q^71 - 63512 * q^73 - 198012 * q^75 - 74257 * q^77 + 137651 * q^79 + 196077 * q^81 + 156427 * q^83 + 238828 * q^85 - 558144 * q^87 - 99292 * q^89 - 243609 * q^91 - 325925 * q^93 - 75077 * q^95 - 476340 * q^97 + 745812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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