LMFDB - Embedded newform 76.5.j.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	76.53
Dual form			76.5.j.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +O(q^{10})$	\(q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +(-106.545 - 184.541i) q^{11} +(67.2882 + 11.8647i) q^{13} +(225.861 - 269.170i) q^{15} +(86.5075 + 31.4861i) q^{17} +(360.844 + 10.5981i) q^{19} +(316.044 - 868.322i) q^{21} +(152.628 + 128.070i) q^{23} +(-38.3938 + 217.742i) q^{25} +(-2175.60 + 1256.08i) q^{27} +(-125.853 - 345.779i) q^{29} +(-715.213 - 412.929i) q^{31} +(2394.78 + 2853.99i) q^{33} +(-184.444 - 1046.03i) q^{35} -2460.86i q^{37} -1194.61 q^{39} +(1695.95 - 299.042i) q^{41} +(-1341.89 + 1125.98i) q^{43} +(-2257.77 + 3910.58i) q^{45} +(1843.05 - 670.816i) q^{47} +(-196.146 - 339.734i) q^{49} +(-1585.10 - 279.496i) q^{51} +(1283.71 - 1529.86i) q^{53} +(4024.24 + 1464.70i) q^{55} +(-6245.28 + 913.057i) q^{57} +(836.628 - 2298.62i) q^{59} +(-1062.83 - 891.820i) q^{61} +(-2062.07 + 11694.6i) q^{63} +(-1189.20 + 686.584i) q^{65} +(415.368 + 1141.22i) q^{67} +(-3016.81 - 1741.76i) q^{69} +(-5933.74 - 7071.56i) q^{71} +(-258.462 - 1465.81i) q^{73} -3865.70i q^{75} +11262.1 q^{77} +(8753.63 - 1543.50i) q^{79} +(19704.9 - 16534.3i) q^{81} +(3718.48 - 6440.60i) q^{83} +(-1738.56 + 632.784i) q^{85} +(3216.77 + 5571.61i) q^{87} +(-4040.87 - 712.515i) q^{89} +(-2321.20 + 2766.30i) q^{91} +(13568.4 + 4938.48i) q^{93} +(-5692.24 + 4498.32i) q^{95} +(-2467.26 + 6778.74i) q^{97} +(-36676.7 - 30775.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−17.2182	+	3.03604i	−1.91314	+	0.337338i	−0.997854	−	0.0654748i	$-0.979144\pi$
$3$	−17.2182	+	3.03604i	−1.91314	+	0.337338i	−0.915283	+	0.402812i	$0.868033\pi$
$4$		0			0
$5$	−15.3954	+	12.9183i	−0.615815	+	0.516730i	−0.896485	−	0.443074i	$-0.853888\pi$
$5$	−15.3954	+	12.9183i	−0.615815	+	0.516730i	0.280670	+	0.959804i	$0.409443\pi$
$6$		0			0
$7$	−26.4258	+	45.7708i	−0.539302	+	0.934099i	0.459640	+	0.888105i	$0.347979\pi$
$7$	−26.4258	+	45.7708i	−0.539302	+	0.934099i	−0.998942	+	0.0459931i	$0.985355\pi$
$8$		0			0
$9$	211.135	−	76.8468i	2.60660	−	0.948726i
$10$		0			0
$11$	−106.545	−	184.541i	−0.880534	−	1.52513i	−0.850748	−	0.525574i	$-0.823851\pi$
$11$	−106.545	−	184.541i	−0.880534	−	1.52513i	−0.0297866	−	0.999556i	$-0.509483\pi$
$12$		0			0
$13$	67.2882	+	11.8647i	0.398155	+	0.0702055i	0.369141	−	0.929373i	$-0.379652\pi$
$13$	67.2882	+	11.8647i	0.398155	+	0.0702055i	0.0290144	+	0.999579i	$0.490763\pi$
$14$		0			0
$15$	225.861	−	269.170i	1.00383	−	1.19631i
$16$		0			0
$17$	86.5075	+	31.4861i	0.299334	+	0.108949i	0.487321	−	0.873223i	$-0.337974\pi$
$17$	86.5075	+	31.4861i	0.299334	+	0.108949i	−0.187987	+	0.982171i	$0.560196\pi$
$18$		0			0
$19$	360.844	+	10.5981i	0.999569	+	0.0293576i
$19$	360.844	+	10.5981i	0.999569	+	0.0293576i
$20$		0			0
$21$	316.044	−	868.322i	0.716652	−	1.96899i
$22$		0			0
$23$	152.628	+	128.070i	0.288522	+	0.242099i	0.775548	−	0.631289i	$-0.217474\pi$
$23$	152.628	+	128.070i	0.288522	+	0.242099i	−0.487026	+	0.873388i	$0.661918\pi$
$24$		0			0
$25$	−38.3938	+	217.742i	−0.0614301	+	0.348387i
$26$		0			0
$27$	−2175.60	+	1256.08i	−2.98436	+	1.72302i
$28$		0			0
$29$	−125.853	−	345.779i	−0.149647	−	0.411153i	0.842106	−	0.539312i	$-0.181315\pi$
$29$	−125.853	−	345.779i	−0.149647	−	0.411153i	−0.991754	+	0.128159i	$0.959093\pi$
$30$		0			0
$31$	−715.213	−	412.929i	−0.744238	−	0.429686i	0.0793699	−	0.996845i	$-0.474709\pi$
$31$	−715.213	−	412.929i	−0.744238	−	0.429686i	−0.823608	+	0.567159i	$0.808043\pi$
$32$		0			0
$33$	2394.78	+	2853.99i	2.19907	+	2.62075i
$34$		0			0
$35$	−184.444	−	1046.03i	−0.150567	−	0.853906i
$36$		0			0
$37$		−	2460.86i		−	1.79756i	−0.438396	−	0.898782i	$-0.644453\pi$
$37$		−	2460.86i		−	1.79756i	0.438396	−	0.898782i	$-0.355547\pi$
$38$		0			0
$39$	−1194.61			−0.785408
$40$		0			0
$41$	1695.95	−	299.042i	1.00890	−	0.177895i	0.355310	−	0.934748i	$-0.384375\pi$
$41$	1695.95	−	299.042i	1.00890	−	0.177895i	0.653585	+	0.756853i	$0.273264\pi$
$42$		0			0
$43$	−1341.89	+	1125.98i	−0.725740	+	0.608968i	−0.928967	−	0.370164i	$-0.879302\pi$
$43$	−1341.89	+	1125.98i	−0.725740	+	0.608968i	0.203227	+	0.979132i	$0.434857\pi$
$44$		0			0
$45$	−2257.77	+	3910.58i	−1.11495	+	1.93115i
$46$		0			0
$47$	1843.05	−	670.816i	0.834338	−	0.303674i	0.110700	−	0.993854i	$-0.464691\pi$
$47$	1843.05	−	670.816i	0.834338	−	0.303674i	0.723638	+	0.690180i	$0.242469\pi$
$48$		0			0
$49$	−196.146	−	339.734i	−0.0816934	−	0.141497i
$50$		0			0
$51$	−1585.10	−	279.496i	−0.609419	−	0.107457i
$52$		0			0
$53$	1283.71	−	1529.86i	0.456998	−	0.544629i	−0.487510	−	0.873118i	$-0.662095\pi$
$53$	1283.71	−	1529.86i	0.456998	−	0.544629i	0.944508	+	0.328488i	$0.106539\pi$
$54$		0			0
$55$	4024.24	+	1464.70i	1.33033	+	0.484199i
$56$		0			0
$57$	−6245.28	+	913.057i	−1.92222	+	0.281027i
$58$		0			0
$59$	836.628	−	2298.62i	0.240341	−	0.660332i	−0.759609	−	0.650380i	$-0.774610\pi$
$59$	836.628	−	2298.62i	0.240341	−	0.660332i	0.999950	−	0.00995240i	$-0.00316800\pi$
$60$		0			0
$61$	−1062.83	−	891.820i	−0.285630	−	0.239672i	0.488703	−	0.872450i	$-0.337470\pi$
$61$	−1062.83	−	891.820i	−0.285630	−	0.239672i	−0.774333	+	0.632778i	$0.781915\pi$
$62$		0			0
$63$	−2062.07	+	11694.6i	−0.519543	+	2.94647i
$64$		0			0
$65$	−1189.20	+	686.584i	−0.281467	+	0.162505i
$66$		0			0
$67$	415.368	+	1141.22i	0.0925303	+	0.254225i	0.977321	−	0.211764i	$-0.0679209\pi$
$67$	415.368	+	1141.22i	0.0925303	+	0.254225i	−0.884791	+	0.465989i	$0.845699\pi$
$68$		0			0
$69$	−3016.81	−	1741.76i	−0.633651	−	0.365838i
$70$		0			0
$71$	−5933.74	−	7071.56i	−1.17710	−	1.40281i	−0.896535	−	0.442972i	$-0.853924\pi$
$71$	−5933.74	−	7071.56i	−1.17710	−	1.40281i	−0.280561	−	0.959836i	$-0.590520\pi$
$72$		0			0
$73$	−258.462	−	1465.81i	−0.0485010	−	0.275063i	0.950907	−	0.309478i	$-0.100154\pi$
$73$	−258.462	−	1465.81i	−0.0485010	−	0.275063i	−0.999408	+	0.0344152i	$0.989043\pi$
$74$		0			0
$75$		−	3865.70i		−	0.687235i
$76$		0			0
$77$	11262.1			1.89950
$78$		0			0
$79$	8753.63	−	1543.50i	1.40260	−	0.247316i	0.579389	−	0.815051i	$-0.303291\pi$
$79$	8753.63	−	1543.50i	1.40260	−	0.247316i	0.823211	+	0.567735i	$0.192180\pi$
$80$		0			0
$81$	19704.9	−	16534.3i	3.00333	−	2.52009i
$82$		0			0
$83$	3718.48	−	6440.60i	0.539771	−	0.934911i	−0.459145	−	0.888361i	$-0.651844\pi$
$83$	3718.48	−	6440.60i	0.539771	−	0.934911i	0.998916	−	0.0465493i	$-0.0148225\pi$
$84$		0			0
$85$	−1738.56	+	632.784i	−0.240631	+	0.0875826i
$86$		0			0
$87$	3216.77	+	5571.61i	0.424993	+	0.736110i
$88$		0			0
$89$	−4040.87	−	712.515i	−0.510147	−	0.0899526i	−0.0873508	−	0.996178i	$-0.527840\pi$
$89$	−4040.87	−	712.515i	−0.510147	−	0.0899526i	−0.422796	+	0.906225i	$0.638951\pi$
$90$		0			0
$91$	−2321.20	+	2766.30i	−0.280305	+	0.334054i
$92$		0			0
$93$	13568.4	+	4938.48i	1.56878	+	0.570989i
$94$		0			0
$95$	−5692.24	+	4498.32i	−0.630720	+	0.498429i
$96$		0			0
$97$	−2467.26	+	6778.74i	−0.262224	+	0.720453i	0.736793	+	0.676118i	$0.236339\pi$
$97$	−2467.26	+	6778.74i	−0.262224	+	0.720453i	−0.999017	+	0.0443351i	$0.985883\pi$
$98$		0			0
$99$	−36676.7	−	30775.4i	−3.74213	−	3.14002i
$100$		0			0
$101$	−1197.57	+	6791.76i	−0.117397	+	0.665794i	0.868138	+	0.496323i	$0.165317\pi$
$101$	−1197.57	+	6791.76i	−0.117397	+	0.665794i	−0.985535	+	0.169470i	$0.945794\pi$
$102$		0			0
$103$	5231.12	−	3020.19i	0.493083	−	0.284682i	−0.232770	−	0.972532i	$-0.574779\pi$
$103$	5231.12	−	3020.19i	0.493083	−	0.284682i	0.725853	+	0.687850i	$0.241445\pi$
$104$		0			0
$105$	6351.60	+	17450.9i	0.576109	+	1.58285i
$106$		0			0
$107$	−3388.86	−	1956.56i	−0.295996	−	0.170894i	0.344647	−	0.938733i	$-0.387999\pi$
$107$	−3388.86	−	1956.56i	−0.295996	−	0.170894i	−0.640643	+	0.767839i	$0.721332\pi$
$108$		0			0
$109$	−9566.05	−	11400.4i	−0.805155	−	0.959547i	0.194617	−	0.980879i	$-0.437654\pi$
$109$	−9566.05	−	11400.4i	−0.805155	−	0.959547i	−0.999772	+	0.0213326i	$0.993209\pi$
$110$		0			0
$111$	7471.28	+	42371.7i	0.606386	+	3.43898i
$112$		0			0
$113$		−	9372.48i		−	0.734002i	−0.930220	−	0.367001i	$-0.880384\pi$
$113$		−	9372.48i		−	0.734002i	0.930220	−	0.367001i	$-0.119616\pi$
$114$		0			0
$115$	−4004.21			−0.302776
$116$		0			0
$117$	15118.7	−	2665.83i	1.10444	−	0.194742i
$118$		0			0
$119$	−3727.18	+	3127.47i	−0.263200	+	0.220851i
$120$		0			0
$121$	−15383.0	+	26644.2i	−1.05068	+	1.81983i
$122$		0			0
$123$	−28293.4	+	10298.0i	−1.87014	+	0.680677i
$124$		0			0
$125$	−8502.15	−	14726.2i	−0.544137	−	0.942474i
$126$		0			0
$127$	7087.92	+	1249.79i	0.439452	+	0.0774872i	0.388997	−	0.921239i	$-0.372822\pi$
$127$	7087.92	+	1249.79i	0.439452	+	0.0774872i	0.0504549	+	0.998726i	$0.483933\pi$
$128$		0			0
$129$	19686.5	−	23461.5i	1.18301	−	1.40986i
$130$		0			0
$131$	22572.5	+	8215.72i	1.31534	+	0.478744i	0.901961	−	0.431817i	$-0.142127\pi$
$131$	22572.5	+	8215.72i	1.31534	+	0.478744i	0.413376	+	0.910560i	$0.364349\pi$
$132$		0			0
$133$	−10020.7	+	16236.1i	−0.566492	+	0.917863i
$134$		0			0
$135$	17267.8	−	47442.8i	0.947478	−	2.60317i
$136$		0			0
$137$	5433.87	+	4559.56i	0.289513	+	0.242930i	0.775963	−	0.630778i	$-0.217264\pi$
$137$	5433.87	+	4559.56i	0.289513	+	0.242930i	−0.486450	+	0.873708i	$0.661709\pi$
$138$		0			0
$139$	−3348.80	+	18992.0i	−0.173324	+	0.982971i	0.766736	+	0.641962i	$0.221880\pi$
$139$	−3348.80	+	18992.0i	−0.173324	+	0.982971i	−0.940060	+	0.341008i	$0.889232\pi$
$140$		0			0
$141$	−29697.5	+	17145.8i	−1.49376	+	0.862423i
$142$		0			0
$143$	−4979.68	−	13681.5i	−0.243517	−	0.669057i
$144$		0			0
$145$	6404.43	+	3697.60i	0.304610	+	0.175867i
$146$		0			0
$147$	4408.73	+	5254.12i	0.204023	+	0.243145i
$148$		0			0
$149$	−4717.58	−	26754.7i	−0.212494	−	1.20511i	−0.885203	−	0.465205i	$-0.845980\pi$
$149$	−4717.58	−	26754.7i	−0.212494	−	1.20511i	0.672709	−	0.739907i	$-0.265131\pi$
$150$		0			0
$151$			5119.66i			0.224537i	0.993678	+	0.112268i	$0.0358116\pi$
$151$			5119.66i			0.224537i	−0.993678	+	0.112268i	$0.964188\pi$
$152$		0			0
$153$	20684.3			0.883607
$154$		0			0
$155$	16345.3	−	2882.12i	0.680345	−	0.119963i
$156$		0			0
$157$	−24723.3	+	20745.3i	−1.00301	+	0.841628i	−0.987399	−	0.158250i	$-0.949415\pi$
$157$	−24723.3	+	20745.3i	−1.00301	+	0.841628i	−0.0156143	+	0.999878i	$0.504970\pi$
$158$		0			0
$159$	−17458.5	+	30238.9i	−0.690576	+	1.19611i
$160$		0			0
$161$	−9895.19	+	3601.56i	−0.381744	+	0.138944i
$162$		0			0
$163$	16504.3	+	28586.3i	0.621186	+	1.07593i	0.989265	+	0.146132i	$0.0466824\pi$
$163$	16504.3	+	28586.3i	0.621186	+	1.07593i	−0.368079	+	0.929795i	$0.619984\pi$
$164$		0			0
$165$	−73737.2	−	13001.9i	−2.70844	−	0.477570i
$166$		0			0
$167$	28254.6	−	33672.6i	1.01311	−	1.20738i	0.0349797	−	0.999388i	$-0.488863\pi$
$167$	28254.6	−	33672.6i	1.01311	−	1.20738i	0.978131	−	0.207990i	$-0.0666922\pi$
$168$		0			0
$169$	−22451.6	−	8171.72i	−0.786094	−	0.286115i
$170$		0			0
$171$	77001.3	−	25492.1i	2.63333	−	0.871793i
$172$		0			0
$173$	5571.00	−	15306.2i	0.186141	−	0.511417i	−0.811162	−	0.584822i	$-0.801164\pi$
$173$	5571.00	−	15306.2i	0.186141	−	0.511417i	0.997302	+	0.0734051i	$0.0233866\pi$
$174$		0			0
$175$	−8951.65	−	7511.33i	−0.292299	−	0.245268i
$176$		0			0
$177$	−7426.56	+	42118.1i	−0.237051	+	1.34438i
$178$		0			0
$179$	13361.2	−	7714.08i	0.417003	−	0.240757i	−0.276792	−	0.960930i	$-0.589271\pi$
$179$	13361.2	−	7714.08i	0.417003	−	0.240757i	0.693794	+	0.720173i	$0.255938\pi$
$180$		0			0
$181$	2005.49	+	5510.03i	0.0612156	+	0.168189i	0.966530	−	0.256554i	$-0.0825870\pi$
$181$	2005.49	+	5510.03i	0.0612156	+	0.168189i	−0.905314	+	0.424742i	$0.860365\pi$
$182$		0			0
$183$	21007.6	+	12128.8i	0.627300	+	0.362172i
$184$		0			0
$185$	31790.1	+	37885.9i	0.928855	+	1.10697i
$186$		0			0
$187$	−3406.43	−	19318.8i	−0.0974129	−	0.552456i
$188$		0			0
$189$		−	132772.i		−	3.71692i
$190$		0			0
$191$	−25118.6			−0.688538			−0.344269	−	0.938871i	$-0.611873\pi$
$191$	−25118.6			−0.688538			−0.344269	+	0.938871i	$0.611873\pi$
$192$		0			0
$193$	−14788.4	+	2607.59i	−0.397014	+	0.0700043i	−0.368591	−	0.929592i	$-0.620160\pi$
$193$	−14788.4	+	2607.59i	−0.397014	+	0.0700043i	−0.0284232	+	0.999596i	$0.509049\pi$
$194$		0			0
$195$	18391.4	−	15432.2i	0.483666	−	0.405844i
$196$		0			0
$197$	−9000.57	+	15589.4i	−0.231920	+	0.401697i	−0.958373	−	0.285519i	$-0.907834\pi$
$197$	−9000.57	+	15589.4i	−0.231920	+	0.401697i	0.726453	+	0.687216i	$0.241167\pi$
$198$		0			0
$199$	31587.8	−	11497.0i	0.797650	−	0.290321i	0.0891380	−	0.996019i	$-0.471589\pi$
$199$	31587.8	−	11497.0i	0.797650	−	0.290321i	0.708513	+	0.705698i	$0.249367\pi$
$200$		0			0
$201$	−10616.7	−	18388.6i	−0.262783	−	0.455153i
$202$		0			0
$203$	19152.4	+	3377.08i	0.464762	+	0.0819501i
$204$		0			0
$205$	−22246.7	+	26512.6i	−0.529369	+	0.630877i
$206$		0			0
$207$	42066.9	+	15311.1i	0.981747	+	0.357327i
$208$		0			0
$209$	−36490.3	−	67719.7i	−0.835381	−	1.55032i
$210$		0			0
$211$	16937.1	−	46534.2i	0.380428	−	1.04522i	−0.590748	−	0.806856i	$-0.701167\pi$
$211$	16937.1	−	46534.2i	0.380428	−	1.04522i	0.971176	−	0.238362i	$-0.0766106\pi$
$212$		0			0
$213$	123638.	+	103745.i	2.72517	+	2.28669i
$214$		0			0
$215$	6113.23	−	34669.8i	0.132249	−	0.750023i
$216$		0			0
$217$	37800.2	−	21823.9i	0.802739	−	0.463461i
$218$		0			0
$219$	8900.51	+	24453.9i	0.185578	+	0.509871i
$220$		0			0
$221$	5447.36	+	3145.03i	0.111533	+	0.0643933i
$222$		0			0
$223$	−45306.7	−	53994.4i	−0.911071	−	1.08577i	−0.995997	−	0.0893853i	$-0.971510\pi$
$223$	−45306.7	−	53994.4i	−0.911071	−	1.08577i	0.0849257	−	0.996387i	$-0.472935\pi$
$224$		0			0
$225$	8626.51	+	48923.4i	0.170400	+	0.966388i
$226$		0			0
$227$			35715.4i			0.693112i	0.938029	+	0.346556i	$0.112649\pi$
$227$			35715.4i			0.693112i	−0.938029	+	0.346556i	$0.887351\pi$
$228$		0			0
$229$	−5528.47			−0.105423			−0.0527113	−	0.998610i	$-0.516786\pi$
$229$	−5528.47			−0.105423			−0.0527113	+	0.998610i	$0.516786\pi$
$230$		0			0
$231$	−193914.	+	34192.2i	−3.63400	+	0.640772i
$232$		0			0
$233$	32484.7	−	27257.9i	0.598367	−	0.502090i	−0.292553	−	0.956249i	$-0.594505\pi$
$233$	32484.7	−	27257.9i	0.598367	−	0.502090i	0.890920	+	0.454160i	$0.150060\pi$
$234$		0			0
$235$	−19708.7	+	34136.5i	−0.356880	+	0.618134i
$236$		0			0
$237$	−146036.	+	53152.7i	−2.59994	+	0.946300i
$238$		0			0
$239$	−45449.9	−	78721.5i	−0.795677	−	1.37815i	−0.922408	−	0.386216i	$-0.873782\pi$
$239$	−45449.9	−	78721.5i	−0.795677	−	1.37815i	0.126732	−	0.991937i	$-0.459551\pi$
$240$		0			0
$241$	91025.9	+	16050.3i	1.56722	+	0.276344i	0.888789	−	0.458318i	$-0.151548\pi$
$241$	91025.9	+	16050.3i	1.56722	+	0.276344i	0.678434	+	0.734661i	$0.262659\pi$
$242$		0			0
$243$	−158286.	+	188638.i	−2.68059	+	3.19460i
$244$		0			0
$245$	7408.51	+	2696.48i	0.123424	+	0.0449226i
$246$		0			0
$247$	24154.8	+	4994.45i	0.395923	+	0.0818641i
$248$		0			0
$249$	−44471.8	+	122185.i	−0.717275	+	1.97070i
$250$		0			0
$251$	14358.0	+	12047.8i	0.227901	+	0.191231i	0.749587	−	0.661906i	$-0.230252\pi$
$251$	14358.0	+	12047.8i	0.227901	+	0.191231i	−0.521686	+	0.853138i	$0.674697\pi$
$252$		0			0
$253$	7372.46	−	41811.3i	0.115178	−	0.653209i
$254$		0			0
$255$	28013.8	−	16173.8i	0.430816	−	0.248731i
$256$		0			0
$257$	−33686.6	−	92553.2i	−0.510025	−	1.40128i	−0.881211	−	0.472723i	$-0.843271\pi$
$257$	−33686.6	−	92553.2i	−0.510025	−	1.40128i	0.371187	−	0.928558i	$-0.378951\pi$
$258$		0			0
$259$	112636.	+	65030.3i	1.67910	+	0.969430i
$260$		0			0
$261$	−53144.1	−	63334.6i	−0.780142	−	0.929737i
$262$		0			0
$263$	11343.4	+	64331.7i	0.163996	+	0.930065i	0.950094	+	0.311964i	$0.100987\pi$
$263$	11343.4	+	64331.7i	0.163996	+	0.930065i	−0.786098	+	0.618102i	$0.787902\pi$
$264$		0			0
$265$			40136.1i			0.571536i
$266$		0			0
$267$	71739.9			1.00632
$268$		0			0
$269$	5882.67	−	1037.27i	0.0812961	−	0.0143347i	−0.132852	−	0.991136i	$-0.542414\pi$
$269$	5882.67	−	1037.27i	0.0812961	−	0.0143347i	0.214148	+	0.976801i	$0.431302\pi$
$270$		0			0
$271$	97484.4	−	81799.1i	1.32738	−	1.11381i	0.342703	−	0.939444i	$-0.388658\pi$
$271$	97484.4	−	81799.1i	1.32738	−	1.11381i	0.984681	−	0.174364i	$-0.0557868\pi$
$272$		0			0
$273$	31568.4	−	54678.1i	0.423572	−	0.733649i
$274$		0			0
$275$	44273.0	−	16114.0i	0.585428	−	0.213078i
$276$		0			0
$277$	−12794.5	−	22160.8i	−0.166750	−	0.288819i	0.770526	−	0.637409i	$-0.219994\pi$
$277$	−12794.5	−	22160.8i	−0.166750	−	0.288819i	−0.937275	+	0.348590i	$0.886661\pi$
$278$		0			0
$279$	−182739.	−	32221.8i	−2.34759	−	0.413943i
$280$		0			0
$281$	−34639.1	+	41281.2i	−0.438686	+	0.522806i	−0.939407	−	0.342803i	$-0.888624\pi$
$281$	−34639.1	+	41281.2i	−0.438686	+	0.522806i	0.500721	+	0.865609i	$0.333068\pi$
$282$		0			0
$283$	−73639.8	−	26802.7i	−0.919474	−	0.334661i	−0.161445	−	0.986882i	$-0.551615\pi$
$283$	−73639.8	−	26802.7i	−0.919474	−	0.334661i	−0.758029	+	0.652220i	$0.773838\pi$
$284$		0			0
$285$	84353.3	−	94734.9i	1.03851	−	1.16633i
$286$		0			0
$287$	−31129.5	+	85527.6i	−0.377927	+	1.03835i
$288$		0			0
$289$	−57488.6	−	48238.7i	−0.688314	−	0.577564i
$290$		0			0
$291$	21901.3	−	124209.i	0.258633	−	1.46678i
$292$		0			0
$293$	7217.48	−	4167.01i	0.0840718	−	0.0485389i	−0.457375	−	0.889274i	$-0.651210\pi$
$293$	7217.48	−	4167.01i	0.0840718	−	0.0485389i	0.541447	+	0.840735i	$0.317877\pi$
$294$		0			0
$295$	16813.9	+	46195.8i	0.193208	+	0.530834i
$296$		0			0
$297$	463597.	+	267658.i	5.25567	+	3.03436i
$298$		0			0
$299$	8750.55	+	10428.5i	0.0978798	+	0.116649i
$300$		0			0
$301$	−16076.5	−	91174.5i	−0.177443	−	1.00633i
$302$		0			0
$303$		−	120578.i		−	1.31336i
$304$		0			0
$305$	27883.4			0.299741
$306$		0			0
$307$	−70590.5	+	12447.0i	−0.748979	+	0.132065i	−0.535092	−	0.844793i	$-0.679723\pi$
$307$	−70590.5	+	12447.0i	−0.748979	+	0.132065i	−0.213886	+	0.976859i	$0.568612\pi$
$308$		0			0
$309$	−80901.2	+	67884.1i	−0.847301	+	0.710970i
$310$		0			0
$311$	45054.1	−	78036.0i	0.465815	−	0.806815i	−0.533423	−	0.845849i	$-0.679095\pi$
$311$	45054.1	−	78036.0i	0.465815	−	0.806815i	0.999238	+	0.0390334i	$0.0124279\pi$
$312$		0			0
$313$	−80691.9	+	29369.4i	−0.823647	+	0.299783i	−0.719249	−	0.694752i	$-0.755514\pi$
$313$	−80691.9	+	29369.4i	−0.823647	+	0.299783i	−0.104398	+	0.994536i	$0.533292\pi$
$314$		0			0
$315$	−119327.	−	206680.i	−1.20259	−	2.08295i
$316$		0			0
$317$	−32268.5	−	5689.81i	−0.321115	−	0.0566213i	0.0107673	−	0.999942i	$-0.496573\pi$
$317$	−32268.5	−	5689.81i	−0.321115	−	0.0566213i	−0.331882	+	0.943321i	$0.607684\pi$
$318$		0			0
$319$	−50401.4	+	60066.0i	−0.495292	+	0.590266i
$320$		0			0
$321$	64290.4	+	23399.8i	0.623931	+	0.227092i
$322$		0			0
$323$	30882.0	+	12278.4i	0.296006	+	0.117689i
$324$		0			0
$325$	−5166.90	+	14196.0i	−0.0489174	+	0.134400i
$326$		0			0
$327$	199322.	+	167251.i	1.86406	+	1.56413i
$328$		0			0
$329$	−18000.3	+	102085.i	−0.166298	+	0.943126i
$330$		0			0
$331$	−39905.3	+	23039.4i	−0.364229	+	0.210288i	−0.670934	−	0.741517i	$-0.734107\pi$
$331$	−39905.3	+	23039.4i	−0.364229	+	0.210288i	0.306705	+	0.951805i	$0.400773\pi$
$332$		0			0
$333$	−189110.	−	519574.i	−1.70539	−	4.68553i
$334$		0			0
$335$	−21137.3	−	12203.6i	−0.188347	−	0.108742i
$336$		0			0
$337$	−35283.6	−	42049.4i	−0.310680	−	0.370254i	0.587998	−	0.808862i	$-0.299916\pi$
$337$	−35283.6	−	42049.4i	−0.310680	−	0.370254i	−0.898678	+	0.438608i	$0.855472\pi$
$338$		0			0
$339$	28455.2	+	161377.i	0.247607	+	1.40425i
$340$		0			0
$341$			175981.i			1.51341i
$342$		0			0
$343$	−106163.			−0.902374
$344$		0			0
$345$	68945.4	−	12156.9i	0.579251	−	0.102138i
$346$		0			0
$347$	−46603.3	+	39104.8i	−0.387041	+	0.324766i	−0.815459	−	0.578814i	$-0.803516\pi$
$347$	−46603.3	+	39104.8i	−0.387041	+	0.324766i	0.428418	+	0.903581i	$0.359071\pi$
$348$		0			0
$349$	−33423.1	+	57890.4i	−0.274407	+	0.475287i	−0.969985	−	0.243163i	$-0.921815\pi$
$349$	−33423.1	+	57890.4i	−0.274407	+	0.475287i	0.695578	+	0.718450i	$0.255148\pi$
$350$		0			0
$351$	−161295.	+	58706.7i	−1.30921	+	0.476512i
$352$		0			0
$353$	−16958.4	−	29372.8i	−0.136093	−	0.235719i	0.789922	−	0.613208i	$-0.210121\pi$
$353$	−16958.4	−	29372.8i	−0.136093	−	0.235719i	−0.926014	+	0.377488i	$0.876788\pi$
$354$		0			0
$355$	182704.	+	32215.7i	1.44975	+	0.255630i
$356$		0			0
$357$	54680.2	−	65165.4i	0.429036	−	0.511306i
$358$		0			0
$359$	188763.	+	68704.0i	1.46463	+	0.533081i	0.946636	−	0.322305i	$-0.104458\pi$
$359$	188763.	+	68704.0i	1.46463	+	0.533081i	0.517991	+	0.855386i	$0.326680\pi$
$360$		0			0
$361$	130096.	+	7648.53i	0.998276	+	0.0586899i
$362$		0			0
$363$	183976.	−	505469.i	1.39620	−	3.83603i
$364$		0			0
$365$	22914.8	+	19227.8i	0.172001	+	0.144326i
$366$		0			0
$367$	26055.5	−	147768.i	0.193450	−	1.09711i	−0.721160	−	0.692769i	$-0.756391\pi$
$367$	26055.5	−	147768.i	0.193450	−	1.09711i	0.914610	−	0.404338i	$-0.132498\pi$
$368$		0			0
$369$	335094.	−	193467.i	2.46102	−	1.42087i
$370$		0			0
$371$	36100.1	+	99184.3i	0.262277	+	0.720601i
$372$		0			0
$373$	−50978.3	−	29432.3i	−0.366410	−	0.211547i	0.305479	−	0.952199i	$-0.401183\pi$
$373$	−50978.3	−	29432.3i	−0.366410	−	0.211547i	−0.671889	+	0.740652i	$0.734517\pi$
$374$		0			0
$375$	191101.	+	227745.i	1.35894	+	1.61952i
$376$		0			0
$377$	−4365.87	−	24760.1i	−0.0307177	−	0.174209i
$378$		0			0
$379$		−	177467.i		−	1.23549i	−0.786380	−	0.617743i	$-0.788047\pi$
$379$		−	177467.i		−	1.23549i	0.786380	−	0.617743i	$-0.211953\pi$
$380$		0			0
$381$	−125836.			−0.866870
$382$		0			0
$383$	−199006.	+	35090.1i	−1.35665	+	0.239214i	−0.804214	−	0.594340i	$-0.797413\pi$
$383$	−199006.	+	35090.1i	−1.35665	+	0.239214i	−0.552438	+	0.833554i	$0.686302\pi$
$384$		0			0
$385$	−173384.	+	145487.i	−1.16974	+	0.981527i
$386$		0			0
$387$	−196792.	+	340854.i	−1.31397	+	2.27587i
$388$		0			0
$389$	55021.1	−	20026.0i	0.363605	−	0.132341i	−0.153756	−	0.988109i	$-0.549137\pi$
$389$	55021.1	−	20026.0i	0.363605	−	0.132341i	0.517361	+	0.855768i	$0.326915\pi$
$390$		0			0
$391$	9171.03	+	15884.7i	0.0599880	+	0.103902i
$392$		0			0
$393$	−413602.	−	72929.2i	−2.67792	−	0.472189i
$394$		0			0
$395$	−114826.	+	136844.i	−0.735946	+	0.877067i
$396$		0			0
$397$	120480.	+	43851.3i	0.764426	+	0.278228i	0.694663	−	0.719335i	$-0.255554\pi$
$397$	120480.	+	43851.3i	0.764426	+	0.278228i	0.0697628	+	0.997564i	$0.477776\pi$
$398$		0			0
$399$	123245.	−	309980.i	0.774148	−	1.94710i
$400$		0			0
$401$	−18921.1	+	51985.4i	−0.117668	+	0.323290i	−0.984519	−	0.175277i	$-0.943918\pi$
$401$	−18921.1	+	51985.4i	−0.117668	+	0.323290i	0.866851	+	0.498567i	$0.166140\pi$
$402$		0			0
$403$	−43226.1	−	36271.0i	−0.266156	−	0.223331i
$404$		0			0
$405$	−89768.9	+	509105.i	−0.547288	+	3.10382i
$406$		0			0
$407$	−454130.	+	262192.i	−2.74152	+	1.58282i
$408$		0			0
$409$	49191.2	+	135152.i	0.294064	+	0.807933i	0.995462	+	0.0951633i	$0.0303373\pi$
$409$	49191.2	+	135152.i	0.294064	+	0.807933i	−0.701398	+	0.712770i	$0.747440\pi$
$410$		0			0
$411$	−107405.	−	62010.1i	−0.635828	−	0.367095i
$412$		0			0
$413$	83101.0	+	99035.9i	0.487199	+	0.580621i
$414$		0			0
$415$	25953.9	+	147192.i	0.150697	+	0.854648i
$416$		0			0
$417$		−	337175.i		−	1.93903i
$418$		0			0
$419$	−317161.			−1.80656			−0.903278	−	0.429055i	$-0.858847\pi$
$419$	−317161.			−1.80656			−0.903278	+	0.429055i	$0.858847\pi$
$420$		0			0
$421$	164298.	−	28970.2i	0.926976	−	0.163451i	0.310274	−	0.950647i	$-0.399579\pi$
$421$	164298.	−	28970.2i	0.926976	−	0.163451i	0.616703	+	0.787196i	$0.288468\pi$
$422$		0			0
$423$	337582.	−	283265.i	1.88668	−	1.58312i
$424$		0			0
$425$	−10177.2	+	17627.4i	−0.0563444	+	0.0975914i
$426$		0			0
$427$	68905.4	−	25079.5i	0.377918	−	0.137551i
$428$		0			0
$429$	127279.	+	220454.i	0.691579	+	1.19785i
$430$		0			0
$431$	−134617.	−	23736.6i	−0.724678	−	0.127780i	−0.200872	−	0.979618i	$-0.564377\pi$
$431$	−134617.	−	23736.6i	−0.724678	−	0.127780i	−0.523806	+	0.851837i	$0.675488\pi$
$432$		0			0
$433$	−16853.3	+	20085.0i	−0.0898895	+	0.107126i	−0.809114	−	0.587651i	$-0.800053\pi$
$433$	−16853.3	+	20085.0i	−0.0898895	+	0.107126i	0.719225	+	0.694777i	$0.244497\pi$
$434$		0			0
$435$	−121499.	−	44222.0i	−0.642087	−	0.233701i
$436$		0			0
$437$	53717.7	+	47831.0i	0.281290	+	0.250464i
$438$		0			0
$439$	−54851.0	+	150702.i	−0.284613	+	0.781969i	0.712183	+	0.701993i	$0.247706\pi$
$439$	−54851.0	+	150702.i	−0.284613	+	0.781969i	−0.996797	+	0.0799755i	$0.974516\pi$
$440$		0			0
$441$	−67520.7	−	56656.6i	−0.347184	−	0.291322i
$442$		0			0
$443$	−46580.2	+	264169.i	−0.237353	+	1.34609i	0.600250	+	0.799813i	$0.295068\pi$
$443$	−46580.2	+	264169.i	−0.237353	+	1.34609i	−0.837602	+	0.546280i	$0.816043\pi$
$444$		0			0
$445$	71415.2	−	41231.6i	0.360637	−	0.208214i
$446$		0			0
$447$	162457.	+	446346.i	0.813060	+	2.23386i
$448$		0			0
$449$	−25539.6	−	14745.3i	−0.126684	−	0.0731409i	0.435319	−	0.900276i	$-0.356636\pi$
$449$	−25539.6	−	14745.3i	−0.126684	−	0.0731409i	−0.562003	+	0.827135i	$0.689969\pi$
$450$		0			0
$451$	−235880.	−	281111.i	−1.15968	−	1.38205i
$452$		0			0
$453$	−15543.5	−	88151.5i	−0.0757447	−	0.429570i
$454$		0			0
$455$		−	72574.2i		−	0.350558i
$456$		0			0
$457$	257900.			1.23486			0.617431	−	0.786625i	$-0.288174\pi$
$457$	257900.			1.23486			0.617431	+	0.786625i	$0.288174\pi$
$458$		0			0
$459$	−227755.	+	40159.3i	−1.08104	+	0.190617i
$460$		0			0
$461$	54610.5	−	45823.6i	0.256965	−	0.215619i	−0.505200	−	0.863003i	$-0.668581\pi$
$461$	54610.5	−	45823.6i	0.256965	−	0.215619i	0.762165	+	0.647383i	$0.224137\pi$
$462$		0			0
$463$	90318.2	−	156436.i	0.421321	−	0.729749i	−0.574748	−	0.818331i	$-0.694900\pi$
$463$	90318.2	−	156436.i	0.421321	−	0.729749i	0.996069	+	0.0885810i	$0.0282332\pi$
$464$		0			0
$465$	−272687.	+	99249.9i	−1.26113	+	0.459012i
$466$		0			0
$467$	81.5564	+	141.260i	0.000373959	+	0.000647716i	0.866212	−	0.499676i	$-0.166548\pi$
$467$	81.5564	+	141.260i	0.000373959	+	0.000647716i	−0.865838	+	0.500324i	$0.833214\pi$
$468$		0			0
$469$	−63210.8	−	11145.8i	−0.287373	−	0.0506716i
$470$		0			0
$471$	362708.	−	432258.i	1.63499	−	1.94850i
$472$		0			0
$473$	350761.	+	127667.i	1.56779	+	0.570631i
$474$		0			0
$475$	−16161.8	+	78164.1i	−0.0716314	+	0.346434i
$476$		0			0
$477$	153470.	−	421656.i	0.674509	−	1.85320i
$478$		0			0
$479$	−8694.79	−	7295.79i	−0.0378955	−	0.0317981i	0.623643	−	0.781709i	$-0.285652\pi$
$479$	−8694.79	−	7295.79i	−0.0378955	−	0.0317981i	−0.661539	+	0.749911i	$0.730096\pi$
$480$		0			0
$481$	29197.5	−	165587.i	0.126199	−	0.715709i
$482$		0			0
$483$	159443.	−	92054.6i	0.683458	−	0.394595i
$484$		0			0
$485$	−49585.1	−	136234.i	−0.210799	−	0.579165i
$486$		0			0
$487$	−126080.	−	72792.4i	−0.531605	−	0.306922i	0.210065	−	0.977687i	$-0.432632\pi$
$487$	−126080.	−	72792.4i	−0.531605	−	0.306922i	−0.741670	+	0.670765i	$0.765966\pi$
$488$		0			0
$489$	−370964.	−	442098.i	−1.55137	−	1.84884i
$490$		0			0
$491$	−5635.06	−	31958.0i	−0.0233741	−	0.132561i	0.970888	−	0.239535i	$-0.0769950\pi$
$491$	−5635.06	−	31958.0i	−0.0233741	−	0.132561i	−0.994262	+	0.106974i	$0.965884\pi$
$492$		0			0
$493$		−	33875.1i		−	0.139376i
$494$		0			0
$495$	962215.			3.92701
$496$		0			0
$497$	480475.	−	84720.7i	1.94517	−	0.342986i
$498$		0			0
$499$	371345.	−	311595.i	1.49134	−	1.25138i	0.598406	−	0.801193i	$-0.295801\pi$
$499$	371345.	−	311595.i	1.49134	−	1.25138i	0.892933	−	0.450189i	$-0.148643\pi$
$500$		0			0
$501$	−384264.	+	665564.i	−1.53093	+	2.65164i
$502$		0			0
$503$	−66403.3	+	24168.8i	−0.262454	+	0.0955255i	−0.469896	−	0.882722i	$-0.655709\pi$
$503$	−66403.3	+	24168.8i	−0.262454	+	0.0955255i	0.207442	+	0.978247i	$0.433486\pi$
$504$		0			0
$505$	−69300.6	−	120032.i	−0.271741	−	0.470668i
$506$		0			0
$507$	411387.	+	72538.6i	1.60042	+	0.282198i
$508$		0			0
$509$	16680.1	−	19878.6i	0.0643818	−	0.0767272i	−0.732892	−	0.680345i	$-0.761830\pi$
$509$	16680.1	−	19878.6i	0.0643818	−	0.0767272i	0.797274	+	0.603617i	$0.206275\pi$
$510$		0			0
$511$	73921.3	+	26905.2i	0.283092	+	0.103037i
$512$		0			0
$513$	−798365.	+	430193.i	−3.03366	+	1.63467i
$514$		0			0
$515$	−41519.5	+	114074.i	−0.156544	+	0.430102i
$516$		0			0
$517$	−320160.	−	268646.i	−1.19781	−	1.00508i
$518$		0			0
$519$	−49452.6	+	280459.i	−0.183592	+	1.04120i
$520$		0			0
$521$	−103676.	+	59857.4i	−0.381947	+	0.220517i	−0.678665	−	0.734448i	$-0.737441\pi$
$521$	−103676.	+	59857.4i	−0.381947	+	0.220517i	0.296718	+	0.954965i	$0.404108\pi$
$522$		0			0
$523$	131240.	+	360578.i	0.479801	+	1.31824i	0.909663	+	0.415348i	$0.136340\pi$
$523$	131240.	+	360578.i	0.479801	+	1.31824i	−0.429861	+	0.902895i	$0.641438\pi$
$524$		0			0
$525$	176936.	+	102154.i	0.641946	+	0.370627i
$526$		0			0
$527$	−48869.8	−	58240.7i	−0.175962	−	0.209703i
$528$		0			0
$529$	−41700.5	−	236495.i	−0.149015	−	0.845106i
$530$		0			0
$531$		−	549610.i		−	1.94924i
$532$		0			0
$533$	117666.			0.414186
$534$		0			0
$535$	77448.2	−	13656.2i	0.270585	−	0.0477114i
$536$		0			0
$537$	−206636.	+	173388.i	−0.716567	+	0.601271i
$538$		0			0
$539$	−41796.6	+	72393.8i	−0.143868	+	0.249186i
$540$		0			0
$541$	−420093.	+	152901.i	−1.43533	+	0.522417i	−0.938453	−	0.345406i	$-0.887741\pi$
$541$	−420093.	+	152901.i	−1.43533	+	0.522417i	−0.496874	+	0.867823i	$0.665519\pi$
$542$		0			0
$543$	−51259.6	−	88784.2i	−0.173850	−	0.301117i
$544$		0			0
$545$	294546.	+	51936.4i	0.991653	+	0.174855i
$546$		0			0
$547$	220234.	−	262465.i	0.736055	−	0.877196i	−0.260030	−	0.965601i	$-0.583732\pi$
$547$	220234.	−	262465.i	0.736055	−	0.877196i	0.996085	+	0.0884048i	$0.0281769\pi$
$548$		0			0
$549$	−292934.	−	106619.i	−0.971907	−	0.353745i
$550$		0			0
$551$	−41748.9	−	126106.i	−0.137512	−	0.415369i
$552$		0			0
$553$	−160674.	+	441449.i	−0.525407	+	1.44354i
$554$		0			0
$555$	−662392.	−	555813.i	−2.15045	−	1.80444i
$556$		0			0
$557$	78672.7	−	446175.i	0.253579	−	1.43812i	−0.546115	−	0.837711i	$-0.683894\pi$
$557$	78672.7	−	446175.i	0.253579	−	1.43812i	0.799694	−	0.600408i	$-0.204995\pi$
$558$		0			0
$559$	−103653.	+	59844.1i	−0.331710	+	0.191513i
$560$		0			0
$561$	117305.	+	322294.i	0.372728	+	1.02406i
$562$		0			0
$563$	100361.	+	57943.2i	0.316626	+	0.182804i	0.649888	−	0.760030i	$-0.274816\pi$
$563$	100361.	+	57943.2i	0.316626	+	0.182804i	−0.333262	+	0.942834i	$0.608149\pi$
$564$		0			0
$565$	121076.	+	144293.i	0.379281	+	0.452010i
$566$		0			0
$567$	236074.	+	1.33884e6i	0.734314	+	4.16450i
$568$		0			0
$569$		−	329980.i		−	1.01921i	−0.860409	−	0.509604i	$-0.829792\pi$
$569$		−	329980.i		−	1.01921i	0.860409	−	0.509604i	$-0.170208\pi$
$570$		0			0
$571$	240069.			0.736315			0.368158	−	0.929763i	$-0.379989\pi$
$571$	240069.			0.736315			0.368158	+	0.929763i	$0.379989\pi$
$572$		0			0
$573$	432497.	−	76260.9i	1.31727	−	0.232270i
$574$		0			0
$575$	−33746.2	+	28316.5i	−0.102068	+	0.0856452i
$576$		0			0
$577$	132930.	−	230241.i	0.399273	−	0.691561i	−0.594363	−	0.804197i	$-0.702596\pi$
$577$	132930.	−	230241.i	0.399273	−	0.691561i	0.993636	+	0.112635i	$0.0359292\pi$
$578$		0			0
$579$	246713.	−	89796.2i	0.735927	−	0.267856i
$580$		0			0
$581$	196528.	+	340396.i	0.582199	+	1.00840i
$582$		0			0
$583$	−419095.	−	73897.7i	−1.23303	−	0.217417i
$584$		0			0
$585$	−198320.	+	236348.i	−0.579501	+	0.690622i
$586$		0			0
$587$	−43133.2	−	15699.2i	−0.125180	−	0.0455619i	0.278670	−	0.960387i	$-0.410106\pi$
$587$	−43133.2	−	15699.2i	−0.125180	−	0.0455619i	−0.403851	+	0.914825i	$0.632328\pi$
$588$		0			0
$589$	−253704.	−	156583.i	−0.731303	−	0.451350i
$590$		0			0
$591$	107644.	−	295749.i	0.308187	−	0.846736i
$592$		0			0
$593$	−249153.	−	209064.i	−0.708527	−	0.594525i	0.215659	−	0.976469i	$-0.430810\pi$
$593$	−249153.	−	209064.i	−0.708527	−	0.594525i	−0.924185	+	0.381944i	$0.875255\pi$
$594$		0			0
$595$	16979.8	−	96297.2i	0.0479621	−	0.272007i
$596$		0			0
$597$	−508980.	+	293860.i	−1.42808	+	0.824501i
$598$		0			0
$599$	−89235.2	−	245172.i	−0.248704	−	0.683308i	−0.999735	−	0.0230408i	$-0.992665\pi$
$599$	−89235.2	−	245172.i	−0.248704	−	0.683308i	0.751031	−	0.660267i	$-0.229557\pi$
$600$		0			0
$601$	312353.	+	180337.i	0.864763	+	0.499271i	0.865605	−	0.500728i	$-0.166934\pi$
$601$	312353.	+	180337.i	0.864763	+	0.499271i	−0.000841159		1.00000i	$0.500268\pi$
$602$		0			0
$603$	175397.	+	209031.i	0.482379	+	0.574877i
$604$		0			0
$605$	−107369.	−	608919.i	−0.293338	−	1.66360i
$606$		0			0
$607$			700138.i			1.90023i	0.311898	+	0.950116i	$0.399035\pi$
$607$			700138.i			1.90023i	−0.311898	+	0.950116i	$0.600965\pi$
$608$		0			0
$609$	−340023.			−0.916799
$610$		0			0
$611$	131975.	−	23270.7i	0.353515	−	0.0623343i
$612$		0			0
$613$	349037.	−	292877.i	0.928860	−	0.779406i	−0.0467526	−	0.998907i	$-0.514887\pi$
$613$	349037.	−	292877.i	0.928860	−	0.779406i	0.975612	+	0.219501i	$0.0704428\pi$
$614$		0			0
$615$	302556.	−	524042.i	0.799937	−	1.38553i
$616$		0			0
$617$	262002.	−	95360.9i	0.688231	−	0.250496i	0.0258534	−	0.999666i	$-0.491770\pi$
$617$	262002.	−	95360.9i	0.688231	−	0.250496i	0.662378	+	0.749170i	$0.269547\pi$
$618$		0			0
$619$	144826.	+	250846.i	0.377977	+	0.654675i	0.990768	−	0.135570i	$-0.0432865\pi$
$619$	144826.	+	250846.i	0.377977	+	0.654675i	−0.612791	+	0.790245i	$0.709953\pi$
$620$		0			0
$621$	−492924.	−	86915.9i	−1.27819	−	0.225380i
$622$		0			0
$623$	139396.	−	166125.i	0.359148	−	0.428016i
$624$		0			0
$625$	191275.	+	69618.6i	0.489665	+	0.178224i
$626$		0			0
$627$	833897.	+	1.05523e6i	2.12118	+	2.68418i
$628$		0			0
$629$	77483.1	−	212883.i	0.195842	−	0.538071i
$630$		0			0
$631$	153557.	+	128850.i	0.385666	+	0.323612i	0.814922	−	0.579571i	$-0.196780\pi$
$631$	153557.	+	128850.i	0.385666	+	0.323612i	−0.429256	+	0.903183i	$0.641224\pi$
$632$		0			0
$633$	−150347.	+	852658.i	−0.375220	+	2.12798i
$634$		0			0
$635$	−125266.	+	72322.5i	−0.310661	+	0.179360i
$636$		0			0
$637$	−9167.45	−	25187.4i	−0.0225928	−	0.0620731i
$638$		0			0
$639$	−1.79625e6	−	1.03706e6i	−4.39910	−	2.53982i
$640$		0			0
$641$	158129.	+	188451.i	0.384854	+	0.458651i	0.923340	−	0.383983i	$-0.125448\pi$
$641$	158129.	+	188451.i	0.384854	+	0.458651i	−0.538486	+	0.842634i	$0.681004\pi$
$642$		0			0
$643$	246.266	+	1396.64i	0.000595638	+	0.00337803i	0.985104	−	0.171959i	$-0.0550096\pi$
$643$	246.266	+	1396.64i	0.000595638	+	0.00337803i	−0.984508	+	0.175337i	$0.943899\pi$
$644$		0			0
$645$			615513.i			1.47951i
$646$		0			0
$647$	−740265.			−1.76839			−0.884196	−	0.467116i	$-0.845293\pi$
$647$	−740265.			−1.76839			−0.884196	+	0.467116i	$0.845293\pi$
$648$		0			0
$649$	−513327.	+	90513.3i	−1.21872	+	0.214893i
$650$		0			0
$651$	−584594.	+	490532.i	−1.37941	+	1.15746i
$652$		0			0
$653$	−232390.	+	402512.i	−0.544994	+	0.943957i	0.453614	+	0.891199i	$0.350135\pi$
$653$	−232390.	+	402512.i	−0.544994	+	0.943957i	−0.998607	+	0.0527584i	$0.983199\pi$
$654$		0			0
$655$	−453645.	+	165113.i	−1.05739	+	0.384857i
$656$		0			0
$657$	−167213.	−	289621.i	−0.387382	−	0.670965i
$658$		0			0
$659$	570323.	+	100563.i	1.31326	+	0.231563i	0.786044	−	0.618170i	$-0.212126\pi$
$659$	570323.	+	100563.i	1.31326	+	0.231563i	0.527213	+	0.849733i	$0.323237\pi$
$660$		0			0
$661$	307277.	−	366198.i	0.703278	−	0.838134i	−0.289616	−	0.957143i	$-0.593527\pi$
$661$	307277.	−	366198.i	0.703278	−	0.838134i	0.992893	+	0.119010i	$0.0379719\pi$
$662$		0			0
$663$	−103342.	−	37613.5i	−0.235099	−	0.0855691i
$664$		0			0
$665$	−55469.6	−	379410.i	−0.125433	−	0.857958i
$666$		0			0
$667$	25075.3	−	68893.7i	0.0563629	−	0.154856i
$668$		0			0
$669$	944030.	+	792135.i	2.10928	+	1.76989i
$670$		0			0
$671$	−51338.3	+	291154.i	−0.114024	+	0.646662i
$672$		0			0
$673$	−174278.	+	100620.i	−0.384781	+	0.222153i	−0.679896	−	0.733308i	$-0.737975\pi$
$673$	−174278.	+	100620.i	−0.384781	+	0.222153i	0.295115	+	0.955462i	$0.404642\pi$
$674$		0			0
$675$	−189973.	−	521946.i	−0.416950	−	1.14556i
$676$		0			0
$677$	113461.	+	65506.5i	0.247553	+	0.142925i	0.618643	−	0.785672i	$-0.287683\pi$
$677$	113461.	+	65506.5i	0.247553	+	0.142925i	−0.371090	+	0.928597i	$0.621016\pi$
$678$		0			0
$679$	−245069.	−	292062.i	−0.531557	−	0.633485i
$680$		0			0
$681$	−108433.	−	614956.i	−0.233813	−	1.32602i
$682$		0			0
$683$			322919.i			0.692232i	0.938192	+	0.346116i	$0.112500\pi$
$683$			322919.i			0.692232i	−0.938192	+	0.346116i	$0.887500\pi$
$684$		0			0
$685$	−142558.			−0.303816
$686$		0			0
$687$	95190.5	−	16784.6i	0.201688	−	0.0355630i
$688$		0			0
$689$	104530.	−	87711.0i	0.220192	−	0.184763i
$690$		0			0
$691$	−210030.	+	363782.i	−0.439870	+	0.761877i	−0.997679	−	0.0680920i	$-0.978309\pi$
$691$	−210030.	+	363782.i	−0.439870	+	0.761877i	0.557809	+	0.829969i	$0.311642\pi$
$692$		0			0
$693$	2.37782e6	−	865457.i	4.95123	−	1.80210i
$694$		0			0
$695$	−193787.	−	335649.i	−0.401195	−	0.694890i
$696$		0			0
$697$	156128.	+	27529.6i	0.321378	+	0.0566676i
$698$		0			0
$699$	−476574.	+	567958.i	−0.975384	+	1.16242i
$700$		0			0
$701$	441203.	+	160585.i	0.897847	+	0.326790i	0.749390	−	0.662129i	$-0.230347\pi$
$701$	441203.	+	160585.i	0.897847	+	0.326790i	0.148457	+	0.988919i	$0.452569\pi$
$702$		0			0
$703$	26080.5	−	887989.i	0.0527722	−	1.79679i
$704$		0			0
$705$	235709.	−	647606.i	0.474240	−	1.30296i
$706$		0			0
$707$	−279218.	−	234291.i	−0.558604	−	0.468724i
$708$		0			0
$709$	−17147.2	+	97246.8i	−0.0341116	+	0.193456i	−0.997102	−	0.0760804i	$-0.975759\pi$
$709$	−17147.2	+	97246.8i	−0.0341116	+	0.193456i	0.962990	+	0.269537i	$0.0868706\pi$
$710$		0			0
$711$	1.72958e6	−	998575.i	3.42139	−	1.97534i
$712$		0			0
$713$	−56277.8	−	154622.i	−0.110703	−	0.304153i
$714$		0			0
$715$	253406.	+	146304.i	0.495683	+	0.286183i
$716$		0			0
$717$	1.02157e6	+	1.21746e6i	1.98714	+	2.36818i
$718$		0			0
$719$	−138945.	−	787996.i	−0.268773	−	1.52429i	−0.758073	−	0.652170i	$-0.773859\pi$
$719$	−138945.	−	787996.i	−0.268773	−	1.52429i	0.489300	−	0.872115i	$-0.337252\pi$
$720$		0			0
$721$			319243.i			0.614117i
$722$		0			0
$723$	−1.61603e6			−3.09153
$724$		0			0
$725$	80122.7	−	14127.8i	0.152433	−	0.0268781i
$726$		0			0
$727$	−665887.	+	558745.i	−1.25989	+	1.05717i	−0.264193	+	0.964470i	$0.585105\pi$
$727$	−665887.	+	558745.i	−1.25989	+	1.05717i	−0.995694	+	0.0927005i	$0.970450\pi$
$728$		0			0
$729$	1.11092e6	−	1.92416e6i	2.09038	−	3.62065i
$730$		0			0
$731$	−151537.	+	55154.8i	−0.283585	+	0.103216i
$732$		0			0
$733$	26777.0	+	46379.1i	0.0498372	+	0.0863206i	0.889868	−	0.456218i	$-0.150796\pi$
$733$	26777.0	+	46379.1i	0.0498372	+	0.0863206i	−0.840031	+	0.542539i	$0.817463\pi$
$734$		0			0
$735$	−135748.	−	23936.1i	−0.251281	−	0.0443076i
$736$		0			0
$737$	166345.	−	198243.i	0.306250	−	0.364974i
$738$		0			0
$739$	392557.	+	142879.i	0.718809	+	0.261625i	0.675420	−	0.737433i	$-0.263962\pi$
$739$	392557.	+	142879.i	0.718809	+	0.261625i	0.0433888	+	0.999058i	$0.486185\pi$
$740$		0			0
$741$	−431067.	−	12660.6i	−0.785070	−	0.0230577i
$742$		0			0
$743$	−269615.	+	740760.i	−0.488389	+	1.34184i	0.413750	+	0.910391i	$0.364219\pi$
$743$	−269615.	+	740760.i	−0.488389	+	1.34184i	−0.902139	+	0.431446i	$0.858003\pi$
$744$		0			0
$745$	418253.	+	350956.i	0.753575	+	0.632324i
$746$		0			0
$747$	290162.	−	1.64559e6i	0.519994	−	2.94904i
$748$		0			0
$749$	179107.	−	103407.i	0.319263	−	0.184327i
$750$		0			0
$751$	−26385.3	−	72493.1i	−0.0467824	−	0.128534i	0.914101	−	0.405486i	$-0.132898\pi$
$751$	−26385.3	−	72493.1i	−0.0467824	−	0.128534i	−0.960884	+	0.276953i	$0.910676\pi$
$752$		0			0
$753$	−283797.	−	163850.i	−0.500515	−	0.288972i
$754$		0			0
$755$	−66137.1	−	78819.1i	−0.116025	−	0.138273i
$756$		0			0
$757$	8647.11	+	49040.2i	0.0150897	+	0.0855777i	0.991423	−	0.130695i	$-0.0417210\pi$
$757$	8647.11	+	49040.2i	0.0150897	+	0.0855777i	−0.976333	+	0.216273i	$0.930610\pi$
$758$		0			0
$759$			742299.i			1.28853i
$760$		0			0
$761$	−146035.			−0.252166			−0.126083	−	0.992020i	$-0.540241\pi$
$761$	−146035.			−0.252166			−0.126083	+	0.992020i	$0.540241\pi$
$762$		0			0
$763$	774595.	−	136582.i	1.33053	−	0.234609i
$764$		0			0
$765$	−318443.	+	267206.i	−0.544138	+	0.456586i
$766$		0			0
$767$	83567.7	−	144743.i	0.142052	−	0.246041i
$768$		0			0
$769$	−730202.	+	265772.i	−1.23478	+	0.449424i	−0.875233	−	0.483702i	$-0.839292\pi$
$769$	−730202.	+	265772.i	−1.23478	+	0.449424i	−0.359549	+	0.933126i	$0.617070\pi$
$770$		0			0
$771$	861019.	+	1.49133e6i	1.44845	+	2.50879i
$772$		0			0
$773$	266882.	+	47058.4i	0.446642	+	0.0787551i	0.392446	−	0.919775i	$-0.371629\pi$
$773$	266882.	+	47058.4i	0.446642	+	0.0787551i	0.0541966	+	0.998530i	$0.482740\pi$
$774$		0			0
$775$	117372.	−	139878.i	0.195416	−	0.232888i
$776$		0			0
$777$	−2.13682e6	−	777740.i	−3.53938	−	1.28823i
$778$		0			0
$779$	615145.	−	89933.9i	1.01368	−	0.148200i
$780$		0			0
$781$	−672782.	+	1.84845e6i	−1.10299	+	3.03045i
$782$		0			0
$783$	708134.	+	594195.i	1.15503	+	0.969183i
$784$		0			0
$785$	112631.	−	638763.i	0.182776	−	1.03657i
$786$		0			0
$787$	−755514.	+	436196.i	−1.21981	+	0.704259i	−0.964878	−	0.262700i	$-0.915387\pi$
$787$	−755514.	+	436196.i	−1.21981	+	0.704259i	−0.254934	+	0.966958i	$0.582054\pi$
$788$		0			0
$789$	−390627.	−	1.07324e6i	−0.627492	−	1.72402i
$790$		0			0
$791$	428986.	+	247675.i	0.685631	+	0.395849i
$792$		0			0
$793$	−60934.7	−	72619.1i	−0.0968988	−	0.115479i
$794$		0			0
$795$	−121855.	−	691073.i	−0.192801	−	1.09343i
$796$		0			0
$797$		−	225568.i		−	0.355108i	−0.984111	−	0.177554i	$-0.943182\pi$
$797$		−	225568.i		−	0.355108i	0.984111	−	0.177554i	$-0.0568185\pi$
$798$		0			0
$799$	180559.			0.282830
$800$		0			0
$801$	−907923.	+	160091.i	−1.41509	+	0.249519i
$802$		0			0
$803$	−242964.	+	203871.i	−0.376800	+	0.316172i
$804$		0			0
$805$	105814.	−	183276.i	0.163288	−	0.282822i
$806$		0			0
$807$	−98139.9	+	35720.0i	−0.150695	+	0.0548485i
$808$		0			0
$809$	152999.	+	265002.i	0.233771	+	0.404903i	0.958915	−	0.283694i	$-0.0915600\pi$
$809$	152999.	+	265002.i	0.233771	+	0.404903i	−0.725144	+	0.688598i	$0.758227\pi$
$810$		0			0
$811$	415121.	+	73197.0i	0.631151	+	0.111289i	0.480067	−	0.877232i	$-0.340613\pi$
$811$	415121.	+	73197.0i	0.631151	+	0.111289i	0.151084	+	0.988521i	$0.451724\pi$
$812$		0			0
$813$	−1.43016e6	+	1.70440e6i	−2.16374	+	2.57864i
$814$		0			0
$815$	−623375.	−	226890.i	−0.938500	−	0.341586i
$816$		0			0
$817$	−496148.	+	392083.i	−0.743305	+	0.587400i
$818$		0			0
$819$	−277505.	+	762440.i	−0.413717	+	1.13668i
$820$		0			0
$821$	−85862.3	−	72047.0i	−0.127384	−	0.106888i	0.576870	−	0.816836i	$-0.304274\pi$
$821$	−85862.3	−	72047.0i	−0.127384	−	0.106888i	−0.704254	+	0.709948i	$0.748718\pi$
$822$		0			0
$823$	149285.	−	846640.i	0.220403	−	1.24997i	−0.650877	−	0.759183i	$-0.725599\pi$
$823$	149285.	−	846640.i	0.220403	−	1.24997i	0.871281	−	0.490785i	$-0.163290\pi$
$824$		0			0
$825$	−713379.	+	411870.i	−1.04812	+	0.605134i
$826$		0			0
$827$	114574.	+	314789.i	0.167523	+	0.460265i	0.994838	−	0.101472i	$-0.0323554\pi$
$827$	114574.	+	314789.i	0.167523	+	0.460265i	−0.827316	+	0.561737i	$0.810133\pi$
$828$		0			0
$829$	−465779.	−	268918.i	−0.677752	−	0.391300i	0.121255	−	0.992621i	$-0.461308\pi$
$829$	−465779.	−	268918.i	−0.677752	−	0.391300i	−0.799008	+	0.601321i	$0.794641\pi$
$830$		0			0
$831$	287580.	+	342725.i	0.416445	+	0.496299i
$832$		0			0
$833$	−6271.15	−	35565.4i	−0.00903768	−	0.0512552i
$834$		0			0
$835$			883402.i			1.26703i
$836$		0			0
$837$	2.07469e6			2.96144
$838$		0			0
$839$	−1.08093e6	+	190598.i	−1.53559	+	0.270766i	−0.876538	−	0.481332i	$-0.840153\pi$
$839$	−1.08093e6	+	190598.i	−1.53559	+	0.270766i	−0.659051	+	0.752098i	$0.729042\pi$
$840$		0			0
$841$	438084.	−	367596.i	0.619392	−	0.519732i
$842$		0			0
$843$	471092.	−	815956.i	0.662904	−	1.14818i
$844$		0			0
$845$	451216.	−	164229.i	0.631933	−	0.230005i
$846$		0			0
$847$	−813018.	−	1.40819e6i	−1.13327	−	1.96288i
$848$		0			0
$849$	1.34932e6	+	237922.i	1.87197	+	0.330080i
$850$		0			0
$851$	315163.	−	375597.i	0.435187	−	0.518636i
$852$		0			0
$853$	1.05145e6	+	382698.i	1.44508	+	0.525967i	0.941213	−	0.337814i	$-0.109687\pi$
$853$	1.05145e6	+	382698.i	1.44508	+	0.525967i	0.503868	+	0.863781i	$0.331910\pi$
$854$		0			0
$855$	−856150.	+	1.38718e6i	−1.17116	+	1.89759i
$856$		0			0
$857$	−37226.5	+	102279.i	−0.0506864	+	0.139260i	−0.962453	−	0.271450i	$-0.912497\pi$
$857$	−37226.5	+	102279.i	−0.0506864	+	0.139260i	0.911766	+	0.410710i	$0.134719\pi$
$858$		0			0
$859$	428009.	+	359142.i	0.580052	+	0.486721i	0.884964	−	0.465659i	$-0.154183\pi$
$859$	428009.	+	359142.i	0.580052	+	0.486721i	−0.304913	+	0.952380i	$0.598627\pi$
$860$		0			0
$861$	276330.	−	1.56714e6i	0.372753	−	2.11399i
$862$		0			0
$863$	398333.	−	229978.i	0.534841	−	0.308790i	−0.208145	−	0.978098i	$-0.566742\pi$
$863$	398333.	−	229978.i	0.534841	−	0.308790i	0.742985	+	0.669308i	$0.233409\pi$
$864$		0			0
$865$	111962.	+	307612.i	0.149636	+	0.411123i
$866$		0			0
$867$	1.13631e6	+	656047.i	1.51167	+	0.872764i
$868$		0			0
$869$	−1.21749e6	−	1.45095e6i	−1.61223	−	1.92138i
$870$		0			0
$871$	14409.2	+	81718.6i	0.0189934	+	0.107717i
$872$		0			0
$873$			1.62083e6i			2.12671i
$874$		0			0
$875$	898704.			1.17382
$876$		0			0
$877$	−564381.	+	99515.7i	−0.733793	+	0.129387i	−0.528044	−	0.849217i	$-0.677074\pi$
$877$	−564381.	+	99515.7i	−0.733793	+	0.129387i	−0.205749	+	0.978605i	$0.565963\pi$
$878$		0			0
$879$	−111621.	+	93661.2i	−0.144467	+	0.121222i
$880$		0			0
$881$	212439.	−	367955.i	0.273705	−	0.474071i	−0.696103	−	0.717942i	$-0.745084\pi$
$881$	212439.	−	367955.i	0.273705	−	0.474071i	0.969808	+	0.243871i	$0.0784174\pi$
$882$		0			0
$883$	816881.	−	297320.i	1.04770	−	0.381332i	0.239906	−	0.970796i	$-0.422883\pi$
$883$	816881.	−	297320.i	1.04770	−	0.381332i	0.807795	+	0.589464i	$0.200661\pi$
$884$		0			0
$885$	−429758.	−	744363.i	−0.548703	−	0.950382i
$886$		0			0
$887$	746594.	+	131645.i	0.948937	+	0.167323i	0.626634	−	0.779314i	$-0.284432\pi$
$887$	746594.	+	131645.i	0.948937	+	0.167323i	0.322302	+	0.946637i	$0.395543\pi$
$888$		0			0
$889$	−244508.	+	291393.i	−0.309378	+	0.368702i
$890$		0			0
$891$	−5.15071e6	−	1.87470e6i	−6.48801	−	2.36144i
$892$		0			0
$893$	672164.	−	222527.i	0.842893	−	0.279049i
$894$		0			0
$895$	−106048.	+	291364.i	−0.132390	+	0.363739i
$896$		0			0
$897$	−182330.	−	152993.i	−0.226607	−	0.190146i
$898$		0			0
$899$	−52770.2	+	299274.i	−0.0652934	+	0.370297i
$900$		0			0
$901$	159220.	−	91925.6i	0.196132	−	0.113237i
$902$		0			0
$903$	553619.	+	1.52106e6i	0.678946	+	1.86539i
$904$		0			0
$905$	−102055.	−	58921.5i	−0.124606	−	0.0719411i
$906$		0			0
$907$	−663552.	−	790790.i	−0.806604	−	0.961273i	0.193199	−	0.981160i	$-0.438114\pi$
$907$	−663552.	−	790790.i	−0.806604	−	0.961273i	−0.999802	+	0.0198870i	$0.993669\pi$
$908$		0			0
$909$	269076.	+	1.52601e6i	0.325647	+	1.84684i
$910$		0			0
$911$			389820.i			0.469708i	0.972031	+	0.234854i	$0.0754612\pi$
$911$			389820.i			0.469708i	−0.972031	+	0.234854i	$0.924539\pi$
$912$		0			0
$913$	−1.58474e6			−1.90115
$914$		0			0
$915$	−480103.	+	84655.1i	−0.573446	+	0.101114i
$916$		0			0
$917$	−972537.	+	816055.i	−1.15656	+	0.970467i
$918$		0			0
$919$	−110440.	+	191287.i	−0.130766	+	0.226493i	−0.923972	−	0.382460i	$-0.875077\pi$
$919$	−110440.	+	191287.i	−0.130766	+	0.226493i	0.793206	+	0.608953i	$0.208410\pi$
$920$		0			0
$921$	1.17765e6	−	428631.i	1.38835	−	0.505317i
$922$		0			0
$923$	−315369.	−	546235.i	−0.370182	−	0.641174i
$924$		0			0
$925$	535834.	+	94482.0i	0.626248	+	0.110424i
$926$		0			0
$927$	872379.	−	1.03966e6i	1.01519	−	1.20985i
$928$		0			0
$929$	1.37672e6	+	501086.i	1.59520	+	0.580606i	0.978438	−	0.206543i	$-0.0662213\pi$
$929$	1.37672e6	+	501086.i	1.59520	+	0.580606i	0.616763	+	0.787149i	$0.288444\pi$
$930$		0			0
$931$	−67177.6	−	124670.i	−0.0775041	−	0.143834i
$932$		0			0
$933$	−538832.	+	1.48043e6i	−0.618999	+	1.70069i
$934$		0			0
$935$	302009.	+	253416.i	0.345459	+	0.289875i
$936$		0			0
$937$	252427.	−	1.43158e6i	0.287512	−	1.63056i	−0.408658	−	0.912687i	$-0.634003\pi$
$937$	252427.	−	1.43158e6i	0.287512	−	1.63056i	0.696171	−	0.717876i	$-0.254886\pi$
$938$		0			0
$939$	1.30020e6	−	750674.i	1.47462	−	0.851373i
$940$		0			0
$941$	121779.	+	334584.i	0.137528	+	0.377856i	0.989269	−	0.146108i	$-0.0466748\pi$
$941$	121779.	+	334584.i	0.137528	+	0.377856i	−0.851740	+	0.523964i	$0.824453\pi$
$942$		0			0
$943$	297148.	+	171559.i	0.334157	+	0.192925i
$944$		0			0
$945$	1.71518e6	+	2.04408e6i	1.92064	+	2.28893i
$946$		0			0
$947$	−159612.	−	905207.i	−0.177978	−	1.00936i	−0.934650	−	0.355569i	$-0.884287\pi$
$947$	−159612.	−	905207.i	−0.177978	−	1.00936i	0.756672	−	0.653795i	$-0.226824\pi$
$948$		0			0
$949$		−	101698.i		−	0.112923i
$950$		0			0
$951$	572882.			0.633438
$952$		0			0
$953$	−261112.	+	46041.2i	−0.287502	+	0.0506944i	−0.315540	−	0.948912i	$-0.602185\pi$
$953$	−261112.	+	46041.2i	−0.287502	+	0.0506944i	0.0280370	+	0.999607i	$0.491074\pi$
$954$		0			0
$955$	386710.	−	324488.i	0.424012	−	0.355788i
$956$		0			0
$957$	685460.	−	1.18725e6i	0.748442	−	1.29634i
$958$		0			0
$959$	−352289.	+	128223.i	−0.383056	+	0.139421i
$960$		0			0
$961$	−120741.	−	209129.i	−0.130739	−	0.226447i
$962$		0			0
$963$	−865863.	−	152675.i	−0.933676	−	0.164632i
$964$		0			0
$965$	193987.	−	231185.i	0.208314	−	0.248259i
$966$		0			0
$967$	176538.	+	64254.6i	0.188793	+	0.0687149i	0.434686	−	0.900582i	$-0.356859\pi$
$967$	176538.	+	64254.6i	0.188793	+	0.0687149i	−0.245894	+	0.969297i	$0.579081\pi$
$968$		0			0
$969$	−569012.	−	117653.i	−0.606002	−	0.125302i
$970$		0			0
$971$	358173.	−	984073.i	0.379887	−	1.04373i	−0.591515	−	0.806294i	$-0.701470\pi$
$971$	358173.	−	984073.i	0.379887	−	1.04373i	0.971403	−	0.237438i	$-0.0763076\pi$
$972$		0			0
$973$	−780784.	−	655155.i	−0.824717	−	0.692020i
$974$		0			0
$975$	45865.5	−	260116.i	0.0482477	−	0.273626i
$976$		0			0
$977$	−1.48943e6	+	859926.i	−1.56039	+	0.900890i	−0.563170	+	0.826341i	$0.690418\pi$
$977$	−1.48943e6	+	859926.i	−1.56039	+	0.900890i	−0.997217	+	0.0745486i	$0.976248\pi$
$978$		0			0
$979$	299045.	+	821620.i	0.312012	+	0.857246i
$980$		0			0
$981$	−2.89581e6	−	1.67190e6i	−3.00907	−	1.73729i
$982$		0			0
$983$	−175464.	−	209110.i	−0.181586	−	0.216405i	0.667571	−	0.744546i	$-0.267334\pi$
$983$	−175464.	−	209110.i	−0.181586	−	0.216405i	−0.849157	+	0.528140i	$0.822889\pi$
$984$		0			0
$985$	−62821.2	−	356277.i	−0.0647491	−	0.367211i
$986$		0			0
$987$		−	1.81237e6i		−	1.86043i
$988$		0			0
$989$	−349015.			−0.356822
$990$		0			0
$991$	952749.	−	167995.i	0.970133	−	0.171061i	0.333943	−	0.942593i	$-0.391621\pi$
$991$	952749.	−	167995.i	0.970133	−	0.171061i	0.636190	+	0.771533i	$0.280510\pi$
$992$		0			0
$993$	617151.	−	517851.i	0.625883	−	0.525178i
$994$		0			0
$995$	−337784.	+	585059.i	−0.341188	+	0.590954i
$996$		0			0
$997$	82851.7	−	30155.6i	0.0833511	−	0.0303373i	−0.300008	−	0.953937i	$-0.596989\pi$
$997$	82851.7	−	30155.6i	0.0833511	−	0.0303373i	0.383359	+	0.923599i	$0.374767\pi$
$998$		0			0
$999$	3.09105e6	+	5.35386e6i	3.09724	+	5.36458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.53.1	yes	42
19.14	odd	18	inner	76.5.j.a.33.1	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.1	✓	42	19.14	odd	18	inner
76.5.j.a.53.1	yes	42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +O(q^{10})\)	\(q+(-17.2182 + 3.03604i) q^{3} +(-15.3954 + 12.9183i) q^{5} +(-26.4258 + 45.7708i) q^{7} +(211.135 - 76.8468i) q^{9} +(-106.545 - 184.541i) q^{11} +(67.2882 + 11.8647i) q^{13} +(225.861 - 269.170i) q^{15} +(86.5075 + 31.4861i) q^{17} +(360.844 + 10.5981i) q^{19} +(316.044 - 868.322i) q^{21} +(152.628 + 128.070i) q^{23} +(-38.3938 + 217.742i) q^{25} +(-2175.60 + 1256.08i) q^{27} +(-125.853 - 345.779i) q^{29} +(-715.213 - 412.929i) q^{31} +(2394.78 + 2853.99i) q^{33} +(-184.444 - 1046.03i) q^{35} -2460.86i q^{37} -1194.61 q^{39} +(1695.95 - 299.042i) q^{41} +(-1341.89 + 1125.98i) q^{43} +(-2257.77 + 3910.58i) q^{45} +(1843.05 - 670.816i) q^{47} +(-196.146 - 339.734i) q^{49} +(-1585.10 - 279.496i) q^{51} +(1283.71 - 1529.86i) q^{53} +(4024.24 + 1464.70i) q^{55} +(-6245.28 + 913.057i) q^{57} +(836.628 - 2298.62i) q^{59} +(-1062.83 - 891.820i) q^{61} +(-2062.07 + 11694.6i) q^{63} +(-1189.20 + 686.584i) q^{65} +(415.368 + 1141.22i) q^{67} +(-3016.81 - 1741.76i) q^{69} +(-5933.74 - 7071.56i) q^{71} +(-258.462 - 1465.81i) q^{73} -3865.70i q^{75} +11262.1 q^{77} +(8753.63 - 1543.50i) q^{79} +(19704.9 - 16534.3i) q^{81} +(3718.48 - 6440.60i) q^{83} +(-1738.56 + 632.784i) q^{85} +(3216.77 + 5571.61i) q^{87} +(-4040.87 - 712.515i) q^{89} +(-2321.20 + 2766.30i) q^{91} +(13568.4 + 4938.48i) q^{93} +(-5692.24 + 4498.32i) q^{95} +(-2467.26 + 6778.74i) q^{97} +(-36676.7 - 30775.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more