LMFDB - Embedded newform 60.7.l.a.23.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.18
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.15798 - 6.11516i) q^{2} +(-20.2023 + 17.9128i) q^{3} +(-10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(213.743 + 31.1461i) q^{6} +(-261.181 - 261.181i) q^{7} +(441.424 - 259.400i) q^{8} +(87.2628 - 723.758i) q^{9} +O(q^{10})$	\(q+(-5.15798 - 6.11516i) q^{2} +(-20.2023 + 17.9128i) q^{3} +(-10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(213.743 + 31.1461i) q^{6} +(-261.181 - 261.181i) q^{7} +(441.424 - 259.400i) q^{8} +(87.2628 - 723.758i) q^{9} +(-957.155 + 289.577i) q^{10} -1357.89 q^{11} +(-912.017 - 1467.72i) q^{12} +(2086.27 + 2086.27i) q^{13} +(-249.996 + 2944.33i) q^{14} +(1056.84 + 3205.26i) q^{15} +(-3863.13 - 1361.40i) q^{16} +(204.191 + 204.191i) q^{17} +(-4876.00 + 3199.51i) q^{18} -5303.53 q^{19} +(6707.80 + 4359.52i) q^{20} +(9954.93 + 597.963i) q^{21} +(7003.97 + 8303.71i) q^{22} +(15716.7 + 15716.7i) q^{23} +(-4271.19 + 13147.6i) q^{24} +(-10730.1 - 11358.0i) q^{25} +(1996.93 - 23518.8i) q^{26} +(11201.6 + 16184.7i) q^{27} +(19294.5 - 13658.0i) q^{28} -2104.69 q^{29} +(14149.6 - 22995.4i) q^{30} +36742.8i q^{31} +(11600.8 + 30645.8i) q^{32} +(27432.4 - 24323.6i) q^{33} +(195.447 - 2301.87i) q^{34} +(-42902.9 + 17060.9i) q^{35} +(44715.8 + 13314.5i) q^{36} +(-41818.9 + 41818.9i) q^{37} +(27355.5 + 32431.9i) q^{38} +(-79518.3 - 4776.42i) q^{39} +(-7939.53 - 63505.6i) q^{40} +87984.8i q^{41} +(-47690.7 - 63960.3i) q^{42} +(-71857.2 + 71857.2i) q^{43} +(14652.2 - 85660.8i) q^{44} +(-78765.8 - 45822.7i) q^{45} +(15043.7 - 177177. i) q^{46} +(87772.4 - 87772.4i) q^{47} +(102431. - 41696.2i) q^{48} +18781.9i q^{49} +(-14110.4 + 124201. i) q^{50} +(-7782.75 - 467.487i) q^{51} +(-154121. + 109098. i) q^{52} +(34618.2 - 34618.2i) q^{53} +(41194.1 - 151980. i) q^{54} +(-67176.9 + 155877. i) q^{55} +(-183042. - 47541.2i) q^{56} +(107143. - 95001.1i) q^{57} +(10856.0 + 12870.5i) q^{58} -166041. i q^{59} +(-213604. + 32083.3i) q^{60} +132973. q^{61} +(224688. - 189519. i) q^{62} +(-211823. + 166240. i) q^{63} +(127567. - 229011. i) q^{64} +(342701. - 136279. i) q^{65} +(-290239. - 42293.0i) q^{66} +(50730.4 + 50730.4i) q^{67} +(-15084.4 + 10677.8i) q^{68} +(-599043. - 35982.7i) q^{69} +(325622. + 174359. i) q^{70} -254279. q^{71} +(-149223. - 342121. i) q^{72} +(237265. + 237265. i) q^{73} +(471430. + 40028.1i) q^{74} +(420227. + 37251.2i) q^{75} +(57227.2 - 334567. i) q^{76} +(354655. + 354655. i) q^{77} +(380945. + 510904. i) q^{78} -137456. q^{79} +(-347395. + 376112. i) q^{80} +(-516211. - 126314. i) q^{81} +(538041. - 453824. i) q^{82} +(405414. + 405414. i) q^{83} +(-145139. + 621542. i) q^{84} +(33541.5 - 13338.2i) q^{85} +(810056. + 68780.1i) q^{86} +(42519.5 - 37700.9i) q^{87} +(-599406. + 352237. i) q^{88} -163824. q^{89} +(126060. + 718018. i) q^{90} -1.08979e6i q^{91} +(-1.16106e6 + 821880. i) q^{92} +(-658167. - 742288. i) q^{93} +(-989471. - 84013.8i) q^{94} +(-262374. + 608811. i) q^{95} +(-783314. - 411311. i) q^{96} +(-240019. + 240019. i) q^{97} +(114854. - 96876.7i) q^{98} +(-118493. + 982784. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−5.15798	−	6.11516i	−0.644748	−	0.764395i
$2$	−5.15798	−	6.11516i	−0.644748	−	0.764395i
$3$	−20.2023	+	17.9128i	−0.748232	+	0.663437i
$3$	−20.2023	+	17.9128i	−0.748232	+	0.663437i
$4$	−10.7904	+	63.0838i	−0.168600	+	0.985685i
$5$	49.4715	−	114.794i	0.395772	−	0.918349i
$5$	49.4715	−	114.794i	0.395772	−	0.918349i
$6$	213.743	+	31.1461i	0.989549	+	0.144195i
$7$	−261.181	−	261.181i	−0.761460	−	0.761460i	0.215126	−	0.976586i	$-0.430984\pi$
$7$	−261.181	−	261.181i	−0.761460	−	0.761460i	−0.976586	+	0.215126i	$0.930984\pi$
$8$	441.424	−	259.400i	0.862157	−	0.506641i
$9$	87.2628	−	723.758i	0.119702	−	0.992810i
$10$	−957.155	+	289.577i	−0.957155	+	0.289577i
$11$	−1357.89			−1.02020			−0.510101	−	0.860114i	$-0.670392\pi$
$11$	−1357.89			−1.02020			−0.510101	+	0.860114i	$0.670392\pi$
$12$	−912.017	−	1467.72i	−0.527788	−	0.849376i
$13$	2086.27	+	2086.27i	0.949599	+	0.949599i	0.998789	−	0.0491908i	$-0.0156642\pi$
$13$	2086.27	+	2086.27i	0.949599	+	0.949599i	−0.0491908	+	0.998789i	$0.515664\pi$
$14$	−249.996	+	2944.33i	−0.0911066	+	1.07301i
$15$	1056.84	+	3205.26i	0.313137	+	0.949708i
$16$	−3863.13	−	1361.40i	−0.943148	−	0.332373i
$17$	204.191	+	204.191i	0.0415614	+	0.0415614i	0.727582	−	0.686021i	$-0.240644\pi$
$17$	204.191	+	204.191i	0.0415614	+	0.0415614i	−0.686021	+	0.727582i	$0.740644\pi$
$18$	−4876.00	+	3199.51i	−0.836077	+	0.548612i
$19$	−5303.53			−0.773222			−0.386611	−	0.922243i	$-0.626354\pi$
$19$	−5303.53			−0.773222			−0.386611	+	0.922243i	$0.626354\pi$
$20$	6707.80	+	4359.52i	0.838475	+	0.544940i
$21$	9954.93	+	597.963i	1.07493	+	0.0645678i
$22$	7003.97	+	8303.71i	0.657773	+	0.779838i
$23$	15716.7	+	15716.7i	1.29175	+	1.29175i	0.933705	+	0.358044i	$0.116556\pi$
$23$	15716.7	+	15716.7i	1.29175	+	1.29175i	0.358044	+	0.933705i	$0.383444\pi$
$24$	−4271.19	+	13147.6i	−0.308969	+	0.951072i
$25$	−10730.1	−	11358.0i	−0.686728	−	0.726914i
$26$	1996.93	−	23518.8i	0.113617	−	1.33812i
$27$	11201.6	+	16184.7i	0.569102	+	0.822267i
$28$	19294.5	−	13658.0i	0.878942	−	0.622177i
$29$	−2104.69			−0.0862968			−0.0431484	−	0.999069i	$-0.513739\pi$
$29$	−2104.69			−0.0862968			−0.0431484	+	0.999069i	$0.513739\pi$
$30$	14149.6	−	22995.4i	0.524058	−	0.851683i
$31$			36742.8i			1.23335i	0.787216	+	0.616677i	$0.211521\pi$
$31$			36742.8i			1.23335i	−0.787216	+	0.616677i	$0.788479\pi$
$32$	11600.8	+	30645.8i	0.354029	+	0.935235i
$33$	27432.4	−	24323.6i	0.763348	−	0.676840i
$34$	195.447	−	2301.87i	0.00497270	−	0.0585659i
$35$	−42902.9	+	17060.9i	−1.00065	+	0.397921i
$36$	44715.8	+	13314.5i	0.958416	+	0.285376i
$37$	−41818.9	+	41818.9i	−0.825595	+	0.825595i	−0.986904	−	0.161309i	$-0.948428\pi$
$37$	−41818.9	+	41818.9i	−0.825595	+	0.825595i	0.161309	+	0.986904i	$0.448428\pi$
$38$	27355.5	+	32431.9i	0.498533	+	0.591047i
$39$	−79518.3	−	4776.42i	−1.34052	−	0.0805210i
$40$	−7939.53	−	63505.6i	−0.124055	−	0.992275i
$41$			87984.8i			1.27660i	0.769786	+	0.638302i	$0.220363\pi$
$41$			87984.8i			1.27660i	−0.769786	+	0.638302i	$0.779637\pi$
$42$	−47690.7	−	63960.3i	−0.643704	−	0.863301i
$43$	−71857.2	+	71857.2i	−0.903784	+	0.903784i	−0.995761	−	0.0919770i	$-0.970681\pi$
$43$	−71857.2	+	71857.2i	−0.903784	+	0.903784i	0.0919770	+	0.995761i	$0.470681\pi$
$44$	14652.2	−	85660.8i	0.172006	−	1.00560i
$45$	−78765.8	−	45822.7i	−0.864371	−	0.502855i
$46$	15043.7	−	177177.i	0.154554	−	1.82026i
$47$	87772.4	−	87772.4i	0.845404	−	0.845404i	−0.144151	−	0.989556i	$-0.546045\pi$
$47$	87772.4	−	87772.4i	0.845404	−	0.845404i	0.989556	+	0.144151i	$0.0460452\pi$
$48$	102431.	−	41696.2i	0.926202	−	0.377028i
$49$			18781.9i			0.159643i
$50$	−14110.4	+	124201.i	−0.112883	+	0.993608i
$51$	−7782.75	−	467.487i	−0.0586709	−	0.00352418i
$52$	−154121.	+	109098.i	−1.09611	+	0.775902i
$53$	34618.2	−	34618.2i	0.232529	−	0.232529i	−0.581219	−	0.813747i	$-0.697424\pi$
$53$	34618.2	−	34618.2i	0.232529	−	0.232529i	0.813747	+	0.581219i	$0.197424\pi$
$54$	41194.1	−	151980.i	0.261609	−	0.965174i
$55$	−67176.9	+	155877.i	−0.403768	+	0.936902i
$56$	−183042.	−	47541.2i	−1.04229	−	0.270711i
$57$	107143.	−	95001.1i	0.578549	−	0.512984i
$58$	10856.0	+	12870.5i	0.0556397	+	0.0659648i
$59$		−	166041.i		−	0.808461i	−0.914657	−	0.404231i	$-0.867539\pi$
$59$		−	166041.i		−	0.808461i	0.914657	−	0.404231i	$-0.132461\pi$
$60$	−213604.	+	32083.3i	−0.988907	+	0.148534i
$61$	132973.			0.585833			0.292916	−	0.956138i	$-0.405374\pi$
$61$	132973.			0.585833			0.292916	+	0.956138i	$0.405374\pi$
$62$	224688.	−	189519.i	0.942769	−	0.795202i
$63$	−211823.	+	166240.i	−0.847134	+	0.664837i
$64$	127567.	−	229011.i	0.486630	−	0.873608i
$65$	342701.	−	136279.i	1.24789	−	0.496238i
$66$	−290239.	−	42293.0i	−1.00954	−	0.147108i
$67$	50730.4	+	50730.4i	0.168672	+	0.168672i	0.786396	−	0.617723i	$-0.211945\pi$
$67$	50730.4	+	50730.4i	0.168672	+	0.168672i	−0.617723	+	0.786396i	$0.711945\pi$
$68$	−15084.4	+	10677.8i	−0.0479736	+	0.0339591i
$69$	−599043.	−	35982.7i	−1.82352	−	0.109533i
$70$	325622.	+	174359.i	0.949337	+	0.508334i
$71$	−254279.			−0.710454			−0.355227	−	0.934780i	$-0.615596\pi$
$71$	−254279.			−0.710454			−0.355227	+	0.934780i	$0.615596\pi$
$72$	−149223.	−	342121.i	−0.399796	−	0.916604i
$73$	237265.	+	237265.i	0.609909	+	0.609909i	0.942922	−	0.333014i	$-0.108065\pi$
$73$	237265.	+	237265.i	0.609909	+	0.609909i	−0.333014	+	0.942922i	$0.608065\pi$
$74$	471430.	+	40028.1i	1.16338	+	0.0987801i
$75$	420227.	+	37251.2i	0.996094	+	0.0882991i
$76$	57227.2	−	334567.i	0.130365	−	0.762153i
$77$	354655.	+	354655.i	0.776844	+	0.776844i
$78$	380945.	+	510904.i	0.802747	+	1.07660i
$79$	−137456.			−0.278794			−0.139397	−	0.990237i	$-0.544516\pi$
$79$	−137456.			−0.278794			−0.139397	+	0.990237i	$0.544516\pi$
$80$	−347395.	+	376112.i	−0.678506	+	0.734595i
$81$	−516211.	−	126314.i	−0.971343	−	0.237683i
$82$	538041.	−	453824.i	0.975829	−	0.823087i
$83$	405414.	+	405414.i	0.709030	+	0.709030i	0.966331	−	0.257301i	$-0.0828333\pi$
$83$	405414.	+	405414.i	0.709030	+	0.709030i	−0.257301	+	0.966331i	$0.582833\pi$
$84$	−145139.	+	621542.i	−0.244877	+	1.04866i
$85$	33541.5	−	13338.2i	0.0546167	−	0.0217190i
$86$	810056.	+	68780.1i	1.27356	+	0.108135i
$87$	42519.5	−	37700.9i	0.0645700	−	0.0572525i
$88$	−599406.	+	352237.i	−0.879575	+	0.516876i
$89$	−163824.			−0.232385			−0.116193	−	0.993227i	$-0.537069\pi$
$89$	−163824.			−0.232385			−0.116193	+	0.993227i	$0.537069\pi$
$90$	126060.	+	718018.i	0.172921	+	0.984936i
$91$		−	1.08979e6i		−	1.44616i
$92$	−1.16106e6	+	821880.i	−1.49105	+	1.05547i
$93$	−658167.	−	742288.i	−0.818253	−	0.922834i
$94$	−989471.	−	84013.8i	−1.19130	−	0.101150i
$95$	−262374.	+	608811.i	−0.306020	+	0.710087i
$96$	−783314.	−	411311.i	−0.885365	−	0.464897i
$97$	−240019.	+	240019.i	−0.262985	+	0.262985i	−0.826266	−	0.563281i	$-0.809539\pi$
$97$	−240019.	+	240019.i	−0.262985	+	0.262985i	0.563281	+	0.826266i	$0.309539\pi$
$98$	114854.	−	96876.7i	0.122031	−	0.102930i
$99$	−118493.	+	982784.i	−0.122120	+	1.01287i
$100$	832290.	−	554340.i	0.832290	−	0.554340i
$101$			743832.i			0.721956i	0.932574	+	0.360978i	$0.117557\pi$
$101$			743832.i			0.721956i	−0.932574	+	0.360978i	$0.882443\pi$
$102$	37284.6	+	50004.1i	0.0351341	+	0.0471200i
$103$	210242.	−	210242.i	0.192401	−	0.192401i	−0.604332	−	0.796733i	$-0.706560\pi$
$103$	210242.	−	210242.i	0.192401	−	0.192401i	0.796733	+	0.604332i	$0.206560\pi$
$104$	1.46211e6	+	379751.i	1.29981	+	0.337597i
$105$	561128.	−	1.11318e6i	0.484723	−	0.961606i
$106$	−390256.	−	33135.7i	−0.327666	−	0.0278214i
$107$	771000.	−	771000.i	0.629365	−	0.629365i	−0.318543	−	0.947908i	$-0.603194\pi$
$107$	771000.	−	771000.i	0.629365	−	0.629365i	0.947908	+	0.318543i	$0.103194\pi$
$108$	−1.14186e6	+	532003.i	−0.906446	+	0.422321i
$109$			1.80615e6i			1.39468i	0.716742	+	0.697339i	$0.245633\pi$
$109$			1.80615e6i			1.39468i	−0.716742	+	0.697339i	$0.754367\pi$
$110$	1.29971e6	−	393213.i	0.976492	−	0.295427i
$111$	95742.5	−	1.59393e6i	0.0700061	−	1.16547i
$112$	653405.	+	1.36455e6i	0.465081	+	0.971258i
$113$	340132.	−	340132.i	0.235728	−	0.235728i	−0.579350	−	0.815079i	$-0.696694\pi$
$113$	340132.	−	340132.i	0.235728	−	0.235728i	0.815079	+	0.579350i	$0.196694\pi$
$114$	−1.13359e6	−	165184.i	−0.765141	−	0.111495i
$115$	2.58171e6	−	1.02665e6i	1.69751	−	0.675037i
$116$	22710.5	−	132772.i	0.0145496	−	0.0850614i
$117$	1.69201e6	−	1.32790e6i	1.05644	−	0.829102i
$118$	−1.01537e6	+	856436.i	−0.617984	+	0.521254i
$119$		−	106662.i		−	0.0632947i
$120$	1.29796e6	+	1.14074e6i	0.751134	+	0.660149i
$121$	72302.8			0.0408130
$122$	−685872.	−	813151.i	−0.377715	−	0.447808i
$123$	−1.57605e6	−	1.77749e6i	−0.846946	−	0.955195i
$124$	−2.31788e6	−	396470.i	−1.21570	−	0.207943i
$125$	−1.83467e6	+	669851.i	−0.939349	+	0.342964i
$126$	2.10917e6	+	437868.i	1.05439	+	0.218893i
$127$	1.33395e6	+	1.33395e6i	0.651223	+	0.651223i	0.953288	−	0.302064i	$-0.0976757\pi$
$127$	1.33395e6	+	1.33395e6i	0.651223	+	0.651223i	−0.302064	+	0.953288i	$0.597676\pi$
$128$	−2.05843e6	+	401143.i	−0.981536	+	0.191280i
$129$	164514.	−	2.73884e6i	0.0766361	−	1.27584i
$130$	−2.60102e6	−	1.39275e6i	−1.18389	−	0.633931i
$131$	−1.57927e6			−0.702492			−0.351246	−	0.936283i	$-0.614242\pi$
$131$	−1.57927e6			−0.702492			−0.351246	+	0.936283i	$0.614242\pi$
$132$	1.23842e6	+	1.99300e6i	0.538450	+	0.866536i
$133$	1.38518e6	+	1.38518e6i	0.588778	+	0.588778i
$134$	48558.0	−	571891.i	0.0201812	−	0.237683i
$135$	2.41206e6	−	485195.i	0.980363	−	0.197204i
$136$	143102.	+	37167.7i	0.0568891	+	0.0147757i
$137$	−1.33644e6	−	1.33644e6i	−0.519743	−	0.519743i	0.397750	−	0.917494i	$-0.369791\pi$
$137$	−1.33644e6	−	1.33644e6i	−0.519743	−	0.519743i	−0.917494	+	0.397750i	$0.869791\pi$
$138$	2.86982e6	+	3.84884e6i	1.09199	+	1.46451i
$139$	−2.24891e6			−0.837391			−0.418695	−	0.908127i	$-0.637513\pi$
$139$	−2.24891e6			−0.837391			−0.418695	+	0.908127i	$0.637513\pi$
$140$	−613325.	−	2.89057e6i	−0.223515	−	1.05342i
$141$	−200951.	+	3.34545e6i	−0.0716858	+	1.19343i
$142$	1.31157e6	+	1.55496e6i	0.458064	+	0.543067i
$143$	−2.83292e6	−	2.83292e6i	−0.968783	−	0.968783i
$144$	−1.32243e6	+	2.67718e6i	−0.442880	+	0.896581i
$145$	−104122.	+	241605.i	−0.0341539	+	0.0792505i
$146$	227105.	−	2.67472e6i	0.0729738	−	0.859448i
$147$	−336436.	−	379437.i	−0.105913	−	0.119450i
$148$	−2.18685e6	−	3.08934e6i	−0.674581	−	0.952971i
$149$	2.75801e6			0.833752			0.416876	−	0.908963i	$-0.363125\pi$
$149$	2.75801e6			0.833752			0.416876	+	0.908963i	$0.363125\pi$
$150$	−1.93973e6	−	2.76190e6i	−0.574734	−	0.818340i
$151$		−	4.52508e6i		−	1.31430i	−0.753759	−	0.657151i	$-0.771762\pi$
$151$		−	4.52508e6i		−	1.31430i	0.753759	−	0.657151i	$-0.228238\pi$
$152$	−2.34111e6	+	1.37574e6i	−0.666639	+	0.391746i
$153$	165603.	−	129967.i	0.0462375	−	0.0362875i
$154$	339468.	−	3.99807e6i	0.0929472	−	1.09468i
$155$	4.21784e6	+	1.81772e6i	1.13265	+	0.488127i
$156$	1.15935e6	−	4.96477e6i	0.305380	−	1.30775i
$157$	−4.29058e6	+	4.29058e6i	−1.10871	+	1.10871i	−0.115388	+	0.993321i	$0.536811\pi$
$157$	−4.29058e6	+	4.29058e6i	−1.10871	+	1.10871i	−0.993321	+	0.115388i	$0.963189\pi$
$158$	708996.	+	840566.i	0.179752	+	0.213108i
$159$	−79256.8	+	1.31947e6i	−0.0197172	+	0.328254i
$160$	4.09185e6	+	184395.i	0.998986	+	0.0450184i
$161$		−	8.20980e6i		−	1.96723i
$162$	1.89018e6	+	3.80824e6i	0.444588	+	0.895735i
$163$	−4.93975e6	+	4.93975e6i	−1.14062	+	1.14062i	−0.152288	+	0.988336i	$0.548664\pi$
$163$	−4.93975e6	+	4.93975e6i	−1.14062	+	1.14062i	−0.988336	+	0.152288i	$0.951336\pi$
$164$	−5.55042e6	−	949391.i	−1.25833	−	0.215235i
$165$	−1.43507e6	−	4.35239e6i	−0.319463	−	0.968894i
$166$	388053.	−	4.57029e6i	0.0848334	−	0.999125i
$167$	2.31273e6	−	2.31273e6i	0.496565	−	0.496565i	−0.413802	−	0.910367i	$-0.635799\pi$
$167$	2.31273e6	−	2.31273e6i	0.496565	−	0.496565i	0.910367	+	0.413802i	$0.135799\pi$
$168$	4.54946e6	−	2.31835e6i	0.959471	−	0.488936i
$169$			3.87822e6i			0.803475i
$170$	−254571.	−	136313.i	−0.0518159	−	0.0277454i
$171$	−462801.	+	3.83847e6i	−0.0925563	+	0.767662i
$172$	−3.75766e6	−	5.30839e6i	−0.738468	−	1.04322i
$173$	−4.57544e6	+	4.57544e6i	−0.883679	+	0.883679i	−0.993906	−	0.110228i	$-0.964842\pi$
$173$	−4.57544e6	+	4.57544e6i	−0.883679	+	0.883679i	0.110228	+	0.993906i	$0.464842\pi$
$174$	−449862.	−	65553.0i	−0.0853949	−	0.0124436i
$175$	−163996.	+	5.76901e6i	−0.0305998	+	1.07643i
$176$	5.24571e6	+	1.84863e6i	0.962202	+	0.339088i
$177$	2.97426e6	+	3.35440e6i	0.536363	+	0.604916i
$178$	845004.	+	1.00181e6i	0.149830	+	0.177634i
$179$			7.83869e6i			1.36674i	0.730074	+	0.683368i	$0.239485\pi$
$179$			7.83869e6i			1.36674i	−0.730074	+	0.683368i	$0.760515\pi$
$180$	3.74058e6	−	4.47440e6i	0.641389	−	0.767216i
$181$	2.09945e6			0.354054			0.177027	−	0.984206i	$-0.443352\pi$
$181$	2.09945e6			0.354054			0.177027	+	0.984206i	$0.443352\pi$
$182$	−6.66422e6	+	5.62110e6i	−1.10544	+	0.932411i
$183$	−2.68635e6	+	2.38192e6i	−0.438339	+	0.388663i
$184$	1.10147e7	+	2.86082e6i	1.76814	+	0.459237i
$185$	2.73169e6	+	6.86938e6i	0.431436	+	1.08493i
$186$	−1.14440e6	+	7.85351e6i	−0.177844	+	1.22046i
$187$	−277269.	−	277269.i	−0.0424010	−	0.0424010i
$188$	4.58992e6	+	6.48412e6i	0.690767	+	0.975837i
$189$	1.30148e6	−	7.15278e6i	0.192775	−	1.05947i
$190$	5.07630e6	−	1.53578e6i	0.740093	−	0.223907i
$191$	−7.85594e6			−1.12745			−0.563726	−	0.825962i	$-0.690633\pi$
$191$	−7.85594e6			−1.12745			−0.563726	+	0.825962i	$0.690633\pi$
$192$	1.52509e6	+	6.91163e6i	0.215472	+	0.976510i
$193$	942578.	+	942578.i	0.131113	+	0.131113i	0.769618	−	0.638505i	$-0.220447\pi$
$193$	942578.	+	942578.i	0.131113	+	0.131113i	−0.638505	+	0.769618i	$0.720447\pi$
$194$	2.70577e6	+	229741.i	0.370583	+	0.0314654i
$195$	−4.48219e6	+	8.89189e6i	−0.604487	+	1.19920i
$196$	−1.18483e6	−	202664.i	−0.157358	−	0.0269159i
$197$	−9.30389e6	−	9.30389e6i	−1.21693	−	1.21693i	−0.968701	−	0.248230i	$-0.920151\pi$
$197$	−9.30389e6	−	9.30389e6i	−1.21693	−	1.21693i	−0.248230	−	0.968701i	$-0.579849\pi$
$198$	6.62107e6	−	4.34458e6i	0.852968	−	0.559696i
$199$	1.61487e6			0.204917			0.102458	−	0.994737i	$-0.467329\pi$
$199$	1.61487e6			0.204917			0.102458	+	0.994737i	$0.467329\pi$
$200$	−7.68282e6	−	2.23031e6i	−0.960352	−	0.278789i
$201$	−1.93359e6	−	116145.i	−0.238110	−	0.0143025i
$202$	4.54865e6	−	3.83667e6i	0.551860	−	0.465480i
$203$	549705.	+	549705.i	0.0657116	+	0.0657116i
$204$	113470.	−	485921.i	0.0133656	−	0.0572368i
$205$	1.01001e7	+	4.35274e6i	1.17237	+	0.505244i
$206$	−2.37009e6	−	201239.i	−0.271120	−	0.0230202i
$207$	1.27466e7	−	1.00036e7i	1.43709	−	1.12784i
$208$	−5.21929e6	−	1.08998e7i	−0.579991	−	1.21123i
$209$	7.20160e6			0.788843
$210$	−9.70156e6	+	2.31037e6i	−1.04757	+	0.249474i
$211$			1.30393e7i			1.38806i	0.719946	+	0.694030i	$0.244166\pi$
$211$			1.30393e7i			1.38806i	−0.719946	+	0.694030i	$0.755834\pi$
$212$	1.81030e6	+	2.55739e6i	0.189996	+	0.268404i
$213$	5.13702e6	−	4.55485e6i	0.531584	−	0.471342i
$214$	−8.69159e6	−	737984.i	−0.886866	−	0.0753018i
$215$	4.69386e6	+	1.18036e7i	0.472296	+	1.18768i
$216$	9.14299e6	+	4.23861e6i	0.907250	+	0.420593i
$217$	9.59653e6	−	9.59653e6i	0.939150	−	0.939150i
$218$	1.10449e7	−	9.31608e6i	1.06608	−	0.899216i
$219$	−9.04336e6	−	543208.i	−0.860989	−	0.0517170i
$220$	−9.10845e6	−	5.91975e6i	−0.855414	−	0.555949i
$221$			851994.i			0.0789332i
$222$	−1.02410e7	+	7.63598e6i	−0.936014	+	0.697920i
$223$	3.41634e6	−	3.41634e6i	0.308068	−	0.308068i	−0.536092	−	0.844160i	$-0.680100\pi$
$223$	3.41634e6	−	3.41634e6i	0.308068	−	0.308068i	0.844160	+	0.536092i	$0.180100\pi$
$224$	4.97418e6	−	1.10340e7i	0.442565	−	0.981723i
$225$	−9.15681e6	+	6.77489e6i	−0.803890	+	0.594778i
$226$	−3.83436e6	−	325567.i	−0.332175	−	0.0282043i
$227$	1.05014e7	−	1.05014e7i	0.897775	−	0.897775i	−0.0974638	−	0.995239i	$-0.531073\pi$
$227$	1.05014e7	−	1.05014e7i	0.897775	−	0.897775i	0.995239	+	0.0974638i	$0.0310730\pi$
$228$	4.83691e6	+	7.78411e6i	0.408097	+	0.656756i
$229$			1.14312e7i			0.951884i	0.879477	+	0.475942i	$0.157893\pi$
$229$			1.14312e7i			0.951884i	−0.879477	+	0.475942i	$0.842107\pi$
$230$	−1.95945e7	−	1.04921e7i	−1.61046	−	0.862343i
$231$	−1.35177e7	−	811967.i	−1.09665	−	0.0658722i
$232$	−929063.	+	545958.i	−0.0744014	+	0.0437215i
$233$	−4.98284e6	+	4.98284e6i	−0.393921	+	0.393921i	−0.876082	−	0.482162i	$-0.839852\pi$
$233$	−4.98284e6	+	4.98284e6i	−0.393921	+	0.393921i	0.482162	+	0.876082i	$0.339852\pi$
$234$	−1.68477e7	−	3.49761e6i	−1.31490	−	0.272976i
$235$	−5.73347e6	−	1.44179e7i	−0.441788	−	1.11096i
$236$	1.04745e7	+	1.79165e6i	0.796888	+	0.136307i
$237$	2.77692e6	−	2.46222e6i	0.208602	−	0.184962i
$238$	−652253.	+	550159.i	−0.0483821	+	0.0408091i
$239$		−	1.44812e7i		−	1.06075i	−0.847765	−	0.530373i	$-0.822052\pi$
$239$		−	1.44812e7i		−	1.06075i	0.847765	−	0.530373i	$-0.177948\pi$
$240$	280938.	−	1.38211e7i	0.0203225	−	0.999793i
$241$	−6.61637e6			−0.472682			−0.236341	−	0.971670i	$-0.575948\pi$
$241$	−6.61637e6			−0.472682			−0.236341	+	0.971670i	$0.575948\pi$
$242$	−372937.	−	442143.i	−0.0263141	−	0.0311973i
$243$	1.26913e7	−	6.69496e6i	0.884477	−	0.466583i
$244$	−1.43483e6	+	8.38844e6i	−0.0987714	+	0.577446i
$245$	2.15604e6	+	929169.i	0.146608	+	0.0631825i
$246$	−2.74039e6	+	1.88061e7i	−0.184080	+	1.26326i
$247$	−1.10646e7	−	1.10646e7i	−0.734250	−	0.734250i
$248$	9.53110e6	+	1.62192e7i	0.624868	+	1.06334i
$249$	−1.54524e7	−	928178.i	−1.00092	−	0.0601220i
$250$	1.35594e7	+	7.76420e6i	0.867803	+	0.496909i
$251$	−1.42028e7			−0.898157			−0.449079	−	0.893492i	$-0.648248\pi$
$251$	−1.42028e7			−0.898157			−0.449079	+	0.893492i	$0.648248\pi$
$252$	−8.20142e6	−	1.51564e7i	−0.512493	−	0.947098i
$253$	−2.13415e7	−	2.13415e7i	−1.31785	−	1.31785i
$254$	1.27683e6	−	1.50379e7i	0.0779170	−	0.917667i
$255$	−438689.	+	870283.i	−0.0264568	+	0.0524856i
$256$	1.30704e7	+	1.05185e7i	0.779057	+	0.626954i
$257$	5.64731e6	+	5.64731e6i	0.332692	+	0.332692i	0.853608	−	0.520916i	$-0.174410\pi$
$257$	5.64731e6	+	5.64731e6i	0.332692	+	0.332692i	−0.520916	+	0.853608i	$0.674410\pi$
$258$	−1.75970e7	+	1.31209e7i	−1.02466	+	0.764018i
$259$	2.18446e7			1.25732
$260$	4.89913e6	+	2.30894e7i	0.278740	+	1.31369i
$261$	−183661.	+	1.52329e6i	−0.0103299	+	0.0856763i
$262$	8.14583e6	+	9.65747e6i	0.452930	+	0.536982i
$263$	−2.30697e7	−	2.30697e7i	−1.26816	−	1.26816i	−0.947036	−	0.321126i	$-0.895939\pi$
$263$	−2.30697e7	−	2.30697e7i	−1.26816	−	1.26816i	−0.321126	−	0.947036i	$-0.604061\pi$
$264$	5.79980e6	−	1.78530e7i	0.315211	−	0.970286i
$265$	−2.26133e6	−	5.68656e6i	−0.121514	−	0.305571i
$266$	1.32586e6	−	1.56153e7i	0.0704456	−	0.829672i
$267$	3.30962e6	−	2.93456e6i	0.173878	−	0.154173i
$268$	−3.74767e6	+	2.65287e6i	−0.194696	+	0.137820i
$269$	6.26139e6			0.321673			0.160836	−	0.986981i	$-0.448581\pi$
$269$	6.26139e6			0.321673			0.160836	+	0.986981i	$0.448581\pi$
$270$	−1.54084e7	−	1.22475e7i	−0.782828	−	0.622238i
$271$			9.47777e6i			0.476210i	0.971239	+	0.238105i	$0.0765262\pi$
$271$			9.47777e6i			0.476210i	−0.971239	+	0.238105i	$0.923474\pi$
$272$	−510832.	−	1.06680e6i	−0.0253846	−	0.0530124i
$273$	1.95211e7	+	2.20162e7i	0.959438	+	1.08207i
$274$	−1.27921e6	+	1.50659e7i	−0.0621858	+	0.732393i
$275$	1.45703e7	+	1.54230e7i	0.700602	+	0.741600i
$276$	8.73385e6	−	3.74017e7i	0.415411	−	1.77895i
$277$	−2.37799e7	+	2.37799e7i	−1.11885	+	1.11885i	−0.126934	+	0.991911i	$0.540514\pi$
$277$	−2.37799e7	+	2.37799e7i	−1.11885	+	1.11885i	−0.991911	+	0.126934i	$0.959486\pi$
$278$	1.15999e7	+	1.37525e7i	0.539906	+	0.640098i
$279$	2.65929e7	+	3.20628e6i	1.22449	+	0.147635i
$280$	−1.45128e7	+	1.86601e7i	−0.661115	+	0.850041i
$281$			2.20213e7i			0.992484i	0.868184	+	0.496242i	$0.165287\pi$
$281$			2.20213e7i			0.992484i	−0.868184	+	0.496242i	$0.834713\pi$
$282$	2.14945e7	−	1.60269e7i	0.958472	−	0.714666i
$283$	2.67713e7	−	2.67713e7i	1.18116	−	1.18116i	0.201718	−	0.979444i	$-0.435347\pi$
$283$	2.67713e7	−	2.67713e7i	1.18116	−	1.18116i	0.979444	−	0.201718i	$-0.0646526\pi$
$284$	2.74378e6	−	1.60409e7i	0.119783	−	0.700283i
$285$	−5.60497e6	−	1.69992e7i	−0.242124	−	0.734335i
$286$	−2.71161e6	+	3.19359e7i	−0.115912	+	1.36515i
$287$	2.29799e7	−	2.29799e7i	0.972083	−	0.972083i
$288$	2.31925e7	−	5.72195e6i	0.970888	−	0.239534i
$289$		−	2.40542e7i		−	0.996545i
$290$	2.01452e6	−	609470.i	0.0825994	−	0.0249896i
$291$	549514.	−	9.14835e6i	0.0222997	−	0.371248i
$292$	−1.75277e7	+	1.24074e7i	−0.704008	+	0.498347i
$293$	2.09288e7	−	2.09288e7i	0.832036	−	0.832036i	−0.155759	−	0.987795i	$-0.549782\pi$
$293$	2.09288e7	−	2.09288e7i	0.832036	−	0.832036i	0.987795	+	0.155759i	$0.0497825\pi$
$294$	−584983.	+	4.01449e6i	−0.0230198	+	0.157975i
$295$	−1.90604e7	−	8.21430e6i	−0.742449	−	0.319967i
$296$	−7.61204e6	+	2.93077e7i	−0.293512	+	1.13007i
$297$	−1.52106e7	−	2.19770e7i	−0.580599	−	0.838879i
$298$	−1.42258e7	−	1.68657e7i	−0.537560	−	0.637316i
$299$			6.55785e7i			2.45329i
$300$	−6.88437e6	+	2.61076e7i	−0.254977	+	0.966947i
$301$	3.75354e7			1.37639
$302$	−2.76716e7	+	2.33403e7i	−1.00465	+	0.847393i
$303$	−1.33241e7	−	1.50271e7i	−0.478973	−	0.540191i
$304$	2.04882e7	+	7.22022e6i	0.729263	+	0.256998i
$305$	6.57838e6	−	1.52644e7i	0.231856	−	0.537999i
$306$	−1.64895e6	−	342325.i	−0.0575496	−	0.0119474i
$307$	5.30818e6	+	5.30818e6i	0.183455	+	0.183455i	0.792860	−	0.609404i	$-0.208591\pi$
$307$	5.30818e6	+	5.30818e6i	0.183455	+	0.183455i	−0.609404	+	0.792860i	$0.708591\pi$
$308$	−2.61998e7	+	1.85461e7i	−0.896699	+	0.634747i
$309$	−481340.	+	8.01338e6i	−0.0163146	+	0.271606i
$310$	−1.06399e7	−	3.51686e7i	−0.357151	−	1.18051i
$311$	−713162.			−0.0237087			−0.0118543	−	0.999930i	$-0.503773\pi$
$311$	−713162.			−0.0237087			−0.0118543	+	0.999930i	$0.503773\pi$
$312$	−3.63403e7	+	1.85186e7i	−1.19653	+	0.609740i
$313$	−1.25351e7	−	1.25351e7i	−0.408786	−	0.408786i	0.472529	−	0.881315i	$-0.343341\pi$
$313$	−1.25351e7	−	1.25351e7i	−0.408786	−	0.408786i	−0.881315	+	0.472529i	$0.843341\pi$
$314$	4.83684e7	+	4.10685e6i	1.56233	+	0.132654i
$315$	8.60411e6	+	3.25401e7i	0.275280	+	1.04109i
$316$	1.48321e6	−	8.67125e6i	0.0470046	−	0.274802i
$317$	4.04787e7	+	4.04787e7i	1.27072	+	1.27072i	0.945713	+	0.325004i	$0.105366\pi$
$317$	4.04787e7	+	4.04787e7i	1.27072	+	1.27072i	0.325004	+	0.945713i	$0.394634\pi$
$318$	8.47760e6	−	6.32116e6i	0.263628	−	0.196569i
$319$	2.85794e6			0.0880402
$320$	−1.99781e7	−	2.59734e7i	−0.609683	−	0.792646i
$321$	−1.76517e6	+	2.93867e7i	−0.0533669	+	0.888456i
$322$	−5.02043e7	+	4.23460e7i	−1.50374	+	1.26837i
$323$	−1.08293e6	−	1.08293e6i	−0.0321362	−	0.0321362i
$324$	1.35385e7	−	3.12016e7i	0.398049	−	0.917364i
$325$	1.30997e6	−	4.60818e7i	0.0381602	−	1.34239i
$326$	5.56866e7	+	4.72822e6i	1.60730	+	0.136472i
$327$	−3.23532e7	−	3.64883e7i	−0.925281	−	1.04354i
$328$	2.28233e7	+	3.88386e7i	0.646780	+	1.10063i
$329$	−4.58489e7			−1.28748
$330$	−1.92135e7	+	3.12253e7i	−0.534645	+	0.868889i
$331$		−	1.40494e6i		−	0.0387412i	−0.999812	−	0.0193706i	$-0.993834\pi$
$331$		−	1.40494e6i		−	0.0387412i	0.999812	−	0.0193706i	$-0.00616625\pi$
$332$	−2.99496e7	+	2.12005e7i	−0.818422	+	0.579337i
$333$	2.66175e7	+	3.39160e7i	0.720833	+	0.918484i
$334$	−2.60718e7	−	2.21370e6i	−0.699731	−	0.0594126i
$335$	8.33324e6	−	3.31381e6i	0.221656	−	0.0881442i
$336$	−3.76432e7	−	1.58626e7i	−0.992358	−	0.418175i
$337$	1.08562e7	−	1.08562e7i	0.283653	−	0.283653i	−0.550911	−	0.834564i	$-0.685720\pi$
$337$	1.08562e7	−	1.08562e7i	0.283653	−	0.283653i	0.834564	+	0.550911i	$0.185720\pi$
$338$	2.37159e7	−	2.00038e7i	0.614172	−	0.518039i
$339$	−778718.	+	1.29642e7i	−0.0199885	+	0.332771i
$340$	479497.	+	2.25985e6i	0.0121997	+	0.0574966i
$341$		−	4.98927e7i		−	1.25827i
$342$	2.58600e7	−	1.69687e7i	0.646473	−	0.424199i
$343$	−2.58222e7	+	2.58222e7i	−0.639898	+	0.639898i
$344$	−1.30797e7	+	5.03593e7i	−0.321310	+	1.23710i
$345$	−3.37662e7	+	6.69862e7i	−0.822289	+	1.63128i
$346$	5.15796e7	+	4.37951e6i	1.24523	+	0.105730i
$347$	−1.64334e7	+	1.64334e7i	−0.393315	+	0.393315i	−0.875867	−	0.482552i	$-0.839710\pi$
$347$	−1.64334e7	+	1.64334e7i	−0.393315	+	0.393315i	0.482552	+	0.875867i	$0.339710\pi$
$348$	1.91952e6	+	3.08910e6i	0.0455464	+	0.0732984i
$349$		−	1.55948e6i		−	0.0366863i	−0.999832	−	0.0183432i	$-0.994161\pi$
$349$		−	1.55948e6i		−	0.0366863i	0.999832	−	0.0183432i	$-0.00583913\pi$
$350$	3.61243e7	−	2.87536e7i	0.842549	−	0.670637i
$351$	−1.03960e7	+	5.71352e7i	−0.240405	+	1.32124i
$352$	−1.57526e7	−	4.16136e7i	−0.361181	−	0.954129i
$353$	−2.94741e7	+	2.94741e7i	−0.670065	+	0.670065i	−0.957731	−	0.287666i	$-0.907121\pi$
$353$	−2.94741e7	+	2.94741e7i	−0.670065	+	0.670065i	0.287666	+	0.957731i	$0.407121\pi$
$354$	5.17153e6	−	3.54900e7i	0.116576	−	0.800012i
$355$	−1.25796e7	+	2.91896e7i	−0.281178	+	0.652444i
$356$	1.76773e6	−	1.03347e7i	0.0391802	−	0.229059i
$357$	1.91061e6	+	2.15480e6i	0.0419920	+	0.0473591i
$358$	4.79349e7	−	4.04318e7i	1.04473	−	0.881200i
$359$		−	5.84946e7i		−	1.26425i	−0.774867	−	0.632124i	$-0.782183\pi$
$359$		−	5.84946e7i		−	1.26425i	0.774867	−	0.632124i	$-0.217817\pi$
$360$	−4.66556e7	+	204623.i	−0.999990	+	0.00438577i
$361$	−1.89185e7			−0.402128
$362$	−1.08289e7	−	1.28385e7i	−0.228276	−	0.270637i
$363$	−1.46068e6	+	1.29515e6i	−0.0305376	+	0.0270769i
$364$	6.87479e7	+	1.17592e7i	1.42546	+	0.243823i
$365$	3.89743e7	−	1.54986e7i	0.801494	−	0.318724i
$366$	2.84220e7	+	4.14159e6i	0.579711	+	0.0844742i
$367$	2.14583e7	+	2.14583e7i	0.434108	+	0.434108i	0.890023	−	0.455915i	$-0.150688\pi$
$367$	2.14583e7	+	2.14583e7i	0.434108	+	0.434108i	−0.455915	+	0.890023i	$0.650688\pi$
$368$	−3.93190e7	−	8.21125e7i	−0.788968	−	1.64765i
$369$	6.36797e7	+	7.67780e6i	1.26742	+	0.152812i
$370$	2.79173e7	−	5.21369e7i	0.551149	−	1.02930i
$371$	−1.80832e7			−0.354123
$372$	5.39283e7	−	3.35101e7i	1.04758	−	0.650949i
$373$	−3.74921e7	−	3.74921e7i	−0.722459	−	0.722459i	0.246646	−	0.969106i	$-0.420671\pi$
$373$	−3.74921e7	−	3.74921e7i	−0.722459	−	0.722459i	−0.969106	+	0.246646i	$0.920671\pi$
$374$	−265395.	+	3.12569e6i	−0.00507316	+	0.0597491i
$375$	2.50655e7	−	4.63965e7i	0.475316	−	0.879815i
$376$	1.59767e7	−	6.15131e7i	0.300555	−	1.15719i
$377$	−4.39095e6	−	4.39095e6i	−0.0819473	−	0.0819473i
$378$	−5.04534e7	+	2.89352e7i	−0.934147	+	0.535736i
$379$	−4.92407e7			−0.904495			−0.452248	−	0.891892i	$-0.649378\pi$
$379$	−4.92407e7			−0.904495			−0.452248	+	0.891892i	$0.649378\pi$
$380$	−3.55750e7	−	2.31209e7i	−0.648327	−	0.421360i
$381$	−5.08438e7	−	3.05403e6i	−0.919312	−	0.0552203i
$382$	4.05208e7	+	4.80404e7i	0.726923	+	0.861819i
$383$	−1.15608e7	−	1.15608e7i	−0.205775	−	0.205775i	0.596694	−	0.802469i	$-0.296481\pi$
$383$	−1.15608e7	−	1.15608e7i	−0.205775	−	0.205775i	−0.802469	+	0.596694i	$0.796481\pi$
$384$	3.43993e7	−	4.49762e7i	0.607514	−	0.794309i
$385$	5.82574e7	−	2.31668e7i	1.02087	−	0.405960i
$386$	902215.	−	1.06258e7i	0.0156873	−	0.184757i
$387$	4.57368e7	+	5.82777e7i	0.789101	+	1.00547i
$388$	−1.25514e7	−	1.77312e7i	−0.214881	−	0.303559i
$389$	−9.27101e7			−1.57499			−0.787496	−	0.616320i	$-0.788623\pi$
$389$	−9.27101e7			−1.57499			−0.787496	+	0.616320i	$0.788623\pi$
$390$	7.74944e7	−	1.84549e7i	1.30640	−	0.311112i
$391$			6.41842e6i			0.107374i
$392$	4.87203e6	+	8.29078e6i	0.0808819	+	0.137638i
$393$	3.19048e7	−	2.82891e7i	0.525627	−	0.466059i
$394$	−8.90548e6	+	1.04884e8i	−0.145602	+	1.71483i
$395$	−6.80016e6	+	1.57791e7i	−0.110339	+	0.256030i
$396$	−6.07192e7	−	1.80796e7i	−0.977778	−	0.291142i
$397$	−1.34098e7	+	1.34098e7i	−0.214314	+	0.214314i	−0.806097	−	0.591783i	$-0.798424\pi$
$397$	−1.34098e7	+	1.34098e7i	−0.214314	+	0.214314i	0.591783	+	0.806097i	$0.298424\pi$
$398$	−8.32946e6	−	9.87517e6i	−0.132120	−	0.156637i
$399$	−5.27962e7	−	3.17131e6i	−0.831159	−	0.0499252i
$400$	2.59891e7	+	5.84856e7i	0.406080	+	0.913838i
$401$		−	6.24439e6i		−	0.0968405i	−0.998827	−	0.0484203i	$-0.984581\pi$
$401$		−	6.24439e6i		−	0.0968405i	0.998827	−	0.0484203i	$-0.0154187\pi$
$402$	9.26319e6	+	1.24233e7i	0.142588	+	0.191231i
$403$	−7.66554e7	+	7.66554e7i	−1.17119	+	1.17119i
$404$	−4.69238e7	−	8.02625e6i	−0.711621	−	0.121722i
$405$	−4.00379e7	+	5.30088e7i	−0.602706	+	0.797963i
$406$	526166.	−	6.19691e6i	0.00786220	−	0.0925970i
$407$	5.67854e7	−	5.67854e7i	0.842274	−	0.842274i
$408$	−3.55676e6	+	1.81249e6i	−0.0523690	+	0.0266867i
$409$			4.69396e7i			0.686071i	0.939322	+	0.343036i	$0.111455\pi$
$409$			4.69396e7i			0.686071i	−0.939322	+	0.343036i	$0.888545\pi$
$410$	−2.54784e7	−	8.42150e7i	−0.369675	−	1.22191i
$411$	5.09386e7	+	3.05973e6i	0.733706	+	0.0440715i
$412$	1.09943e7	+	1.55314e7i	0.157208	+	0.222085i
$413$	−4.33667e7	+	4.33667e7i	−0.615611	+	0.615611i
$414$	−1.26920e8	−	2.63489e7i	−1.78867	−	0.371332i
$415$	6.65954e7	−	2.64825e7i	0.931751	−	0.370522i
$416$	−3.97329e7	+	8.81377e7i	−0.551912	+	1.22428i
$417$	4.54331e7	−	4.02843e7i	0.626563	−	0.555556i
$418$	−3.71458e7	−	4.40390e7i	−0.508605	−	0.602988i
$419$			4.27331e7i			0.580928i	0.956886	+	0.290464i	$0.0938097\pi$
$419$			4.27331e7i			0.580928i	−0.956886	+	0.290464i	$0.906190\pi$
$420$	6.41688e7	+	4.74097e7i	0.866116	+	0.639911i
$421$	7.23166e7			0.969152			0.484576	−	0.874749i	$-0.338974\pi$
$421$	7.23166e7			0.969152			0.484576	+	0.874749i	$0.338974\pi$
$422$	7.97377e7	−	6.72567e7i	1.06103	−	0.894949i
$423$	−5.58667e7	−	7.11853e7i	−0.738129	−	0.940522i
$424$	6.30134e6	−	2.42613e7i	0.0826677	−	0.318285i
$425$	128212.	−	4.51020e6i	0.00167017	−	0.0587529i
$426$	−5.43503e7	−	7.91982e6i	−0.703029	−	0.102444i
$427$	−3.47300e7	−	3.47300e7i	−0.446088	−	0.446088i
$428$	4.03182e7	+	5.69570e7i	0.514245	+	0.726467i
$429$	1.07977e8	+	6.48585e6i	1.36760	+	0.0821477i
$430$	4.79702e7	−	8.95866e7i	0.603346	−	1.12678i
$431$	−5.82751e6			−0.0727865			−0.0363933	−	0.999338i	$-0.511587\pi$
$431$	−5.82751e6			−0.0727865			−0.0363933	+	0.999338i	$0.511587\pi$
$432$	−2.12396e7	−	7.77735e7i	−0.263448	−	0.964674i
$433$	−2.49460e7	−	2.49460e7i	−0.307283	−	0.307283i	0.536572	−	0.843855i	$-0.319719\pi$
$433$	−2.49460e7	−	2.49460e7i	−0.307283	−	0.307283i	−0.843855	+	0.536572i	$0.819719\pi$
$434$	−1.08183e8	−	9.18558e6i	−1.32340	−	0.112367i
$435$	−2.22432e6	−	6.74609e6i	−0.0270227	−	0.0819567i
$436$	−1.13939e8	−	1.94891e7i	−1.37471	−	0.235143i
$437$	−8.33540e7	−	8.33540e7i	−0.998808	−	0.998808i
$438$	4.33237e7	+	5.81035e7i	0.515589	+	0.691480i
$439$	−1.92253e7			−0.227237			−0.113618	−	0.993524i	$-0.536244\pi$
$439$	−1.92253e7			−0.227237			−0.113618	+	0.993524i	$0.536244\pi$
$440$	1.07810e7	+	8.62336e7i	0.126561	+	1.01232i
$441$	1.35935e7	+	1.63896e6i	0.158496	+	0.0191097i
$442$	5.21008e6	−	4.39457e6i	0.0603362	−	0.0508920i
$443$	9.90369e7	+	9.90369e7i	1.13916	+	1.13916i	0.988600	+	0.150563i	$0.0481085\pi$
$443$	9.90369e7	+	9.90369e7i	1.13916	+	1.13916i	0.150563	+	0.988600i	$0.451892\pi$
$444$	9.95180e7	+	2.32389e7i	1.13698	+	0.265502i
$445$	−8.10465e6	+	1.88060e7i	−0.0919717	+	0.213411i
$446$	−3.85129e7	−	3.27005e6i	−0.434112	−	0.0368595i
$447$	−5.57180e7	+	4.94037e7i	−0.623840	+	0.553142i
$448$	−9.31314e7	+	2.64953e7i	−1.03577	+	0.294669i
$449$	1.07108e8			1.18327			0.591634	−	0.806207i	$-0.298483\pi$
$449$	1.07108e8			1.18327			0.591634	+	0.806207i	$0.298483\pi$
$450$	8.86602e7	+	2.10506e7i	0.972952	+	0.231008i
$451$		−	1.19474e8i		−	1.30239i
$452$	1.77867e7	+	2.51270e7i	0.192610	+	0.272098i
$453$	8.10568e7	+	9.14168e7i	0.871956	+	0.983402i
$454$	−1.18383e8	−	1.00517e7i	−1.26509	−	0.107416i
$455$	−1.25101e8	−	5.39134e7i	−1.32808	−	0.572351i
$456$	2.26524e7	−	6.97288e7i	0.238901	−	0.735390i
$457$	−157114.	+	157114.i	−0.00164614	+	0.00164614i	−0.707929	−	0.706283i	$-0.750371\pi$
$457$	−157114.	+	157114.i	−0.00164614	+	0.00164614i	0.706283	+	0.707929i	$0.250371\pi$
$458$	6.99034e7	−	5.89618e7i	0.727616	−	0.613725i
$459$	−1.01749e6	+	5.59204e6i	−0.0105219	+	0.0578272i
$460$	3.69072e7	+	1.73942e8i	0.379173	+	1.78702i
$461$			4.16732e6i			0.0425357i	0.999774	+	0.0212679i	$0.00677028\pi$
$461$			4.16732e6i			0.0425357i	−0.999774	+	0.0212679i	$0.993230\pi$
$462$	6.47587e7	+	8.68510e7i	0.656708	+	0.880742i
$463$	3.68969e7	−	3.68969e7i	0.371746	−	0.371746i	−0.496367	−	0.868113i	$-0.665333\pi$
$463$	3.68969e7	−	3.68969e7i	0.371746	−	0.371746i	0.868113	+	0.496367i	$0.165333\pi$
$464$	8.13071e6	+	2.86533e6i	0.0813906	+	0.0286827i
$465$	−1.17770e8	+	3.88312e7i	−1.17133	+	0.386209i
$466$	5.61722e7	+	4.76946e6i	0.555091	+	0.0471315i
$467$	−1.27299e8	+	1.27299e8i	−1.24989	+	1.24989i	−0.294127	+	0.955766i	$0.595029\pi$
$467$	−1.27299e8	+	1.27299e8i	−1.24989	+	1.24989i	−0.955766	+	0.294127i	$0.904971\pi$
$468$	6.55116e7	+	1.21067e8i	0.639117	+	1.18110i
$469$		−	2.64996e7i		−	0.256875i
$470$	−5.85949e7	+	1.09429e8i	−0.564373	+	1.05399i
$471$	9.82311e6	−	1.63536e8i	0.0940126	−	1.56513i
$472$	−4.30711e7	−	7.32945e7i	−0.409600	−	0.697020i
$473$	9.75741e7	−	9.75741e7i	0.922043	−	0.922043i
$474$	−2.93802e7	−	4.28123e6i	−0.275880	−	0.0402007i
$475$	5.69076e7	+	6.02376e7i	0.530993	+	0.562066i
$476$	6.72862e6	+	1.15092e6i	0.0623886	+	0.0106715i
$477$	−2.20343e7	−	2.80761e7i	−0.203023	−	0.258691i
$478$	−8.85549e7	+	7.46938e7i	−0.810828	+	0.683913i
$479$		−	1.27478e8i		−	1.15993i	−0.814643	−	0.579963i	$-0.803067\pi$
$479$		−	1.27478e8i		−	1.15993i	0.814643	−	0.579963i	$-0.196933\pi$
$480$	−8.59676e7	+	6.95713e7i	−0.777340	+	0.629080i
$481$	−1.74491e8			−1.56797
$482$	3.41271e7	+	4.04602e7i	0.304761	+	0.361316i
$483$	1.47061e8	+	1.65857e8i	1.30513	+	1.47194i
$484$	−780176.	+	4.56114e6i	−0.00688108	+	0.0402288i
$485$	1.56785e7	+	3.94268e7i	0.137430	+	0.345594i
$486$	−1.06402e8	−	4.30768e7i	−0.926919	−	0.375262i
$487$	9.86694e7	+	9.86694e7i	0.854270	+	0.854270i	0.990656	−	0.136385i	$-0.0435485\pi$
$487$	9.86694e7	+	9.86694e7i	0.854270	+	0.854270i	−0.136385	+	0.990656i	$0.543549\pi$
$488$	5.86975e7	−	3.44932e7i	0.505080	−	0.296807i
$489$	1.13094e7	−	1.88279e8i	0.0967189	−	1.61018i
$490$	−5.43880e6	−	1.79772e7i	−0.0462291	−	0.152803i
$491$	1.23576e8			1.04398			0.521988	−	0.852953i	$-0.325191\pi$
$491$	1.23576e8			1.04398			0.521988	+	0.852953i	$0.325191\pi$
$492$	1.29137e8	−	8.02437e7i	1.08432	−	0.673776i
$493$	−429759.	−	429759.i	−0.00358661	−	0.00358661i
$494$	−1.05908e7	+	1.24733e8i	−0.0878510	+	1.03466i
$495$	1.06955e8	+	6.22221e7i	0.881833	+	0.513014i
$496$	5.00217e7	−	1.41943e8i	0.409933	−	1.16323i
$497$	6.64129e7	+	6.64129e7i	0.540982	+	0.540982i
$498$	7.40272e7	+	9.92813e7i	0.599381	+	0.803859i
$499$	1.55195e8			1.24904			0.624521	−	0.781008i	$-0.285294\pi$
$499$	1.55195e8			1.24904			0.624521	+	0.781008i	$0.285294\pi$
$500$	−2.24600e7	−	1.22966e8i	−0.179680	−	0.983725i
$501$	−5.29491e6	+	8.81500e7i	−0.0421061	+	0.700986i
$502$	7.32577e7	+	8.68523e7i	0.579085	+	0.686547i
$503$	8.27616e7	+	8.27616e7i	0.650317	+	0.650317i	0.953069	−	0.302753i	$-0.0979056\pi$
$503$	8.27616e7	+	8.27616e7i	0.650317	+	0.650317i	−0.302753	+	0.953069i	$0.597906\pi$
$504$	−5.03811e7	+	1.28330e8i	−0.393529	+	1.00239i
$505$	8.53872e7	+	3.67985e7i	0.663007	+	0.285730i
$506$	−2.04277e7	+	2.40586e8i	−0.157676	+	1.85703i
$507$	−6.94698e7	−	7.83488e7i	−0.533055	−	0.601186i
$508$	−9.85449e7	+	6.97570e7i	−0.751697	+	0.532104i
$509$	−8.10897e7			−0.614911			−0.307455	−	0.951562i	$-0.599478\pi$
$509$	−8.10897e7			−0.614911			−0.307455	+	0.951562i	$0.599478\pi$
$510$	7.58467e6	−	1.80625e6i	0.0571776	−	0.0136165i
$511$		−	1.23938e8i		−	0.928842i
$512$	−3.09436e6	−	1.34182e8i	−0.0230547	−	0.999734i
$513$	−5.94082e7	−	8.58359e7i	−0.440042	−	0.635795i
$514$	5.40548e6	−	6.36629e7i	0.0398056	−	0.468810i
$515$	−1.37334e7	−	3.45354e7i	−0.100544	−	0.252838i
$516$	1.71001e8	+	3.99314e7i	1.24466	+	0.290646i
$517$	−1.19185e8	+	1.19185e8i	−0.862483	+	0.862483i
$518$	−1.12674e8	−	1.33583e8i	−0.810652	−	0.961086i
$519$	1.04753e7	−	1.74393e8i	0.0749313	−	1.24746i
$520$	1.15926e8	−	1.49054e8i	0.824461	−	1.06007i
$521$		−	1.79621e8i		−	1.27012i	−0.772463	−	0.635060i	$-0.780976\pi$
$521$		−	1.79621e8i		−	1.27012i	0.772463	−	0.635060i	$-0.219024\pi$
$522$	1.02625e7	−	6.73398e6i	0.0721507	−	0.0473435i
$523$	8.73949e7	−	8.73949e7i	0.610916	−	0.610916i	−0.332269	−	0.943185i	$-0.607814\pi$
$523$	8.73949e7	−	8.73949e7i	0.610916	−	0.610916i	0.943185	+	0.332269i	$0.107814\pi$
$524$	1.70409e7	−	9.96261e7i	0.118440	−	0.692436i
$525$	−1.00026e8	−	1.19485e8i	−0.691250	−	0.825722i
$526$	−2.20818e7	+	2.60068e8i	−0.151732	+	1.78702i
$527$	−7.50256e6	+	7.50256e6i	−0.0512599	+	0.0512599i
$528$	−1.39089e8	+	5.66189e7i	−0.944914	+	0.384644i
$529$			3.45994e8i			2.33723i
$530$	−2.31103e7	+	4.31596e7i	−0.155231	+	0.289901i
$531$	−1.20174e8	−	1.44892e7i	−0.802648	−	0.0967745i
$532$	−1.02329e8	+	7.24358e7i	−0.679617	+	0.481081i
$533$	−1.83560e8	+	1.83560e8i	−1.21226	+	1.21226i
$534$	−3.50163e7	−	5.10250e6i	−0.229957	−	0.0335088i
$535$	−5.03633e7	−	1.26648e8i	−0.328891	−	0.827062i
$536$	3.55531e7	+	9.23416e6i	0.230878	+	0.0599657i
$537$	−1.40413e8	−	1.58359e8i	−0.906743	−	1.02263i
$538$	−3.22962e7	−	3.82894e7i	−0.207398	−	0.245885i
$539$		−	2.55037e7i		−	0.162869i
$540$	4.58084e6	+	1.57397e8i	0.0290914	+	0.999577i
$541$	1.77523e8			1.12115			0.560573	−	0.828105i	$-0.310581\pi$
$541$	1.77523e8			1.12115			0.560573	+	0.828105i	$0.310581\pi$
$542$	5.79581e7	−	4.88862e7i	0.364012	−	0.307035i
$543$	−4.24137e7	+	3.76070e7i	−0.264915	+	0.234893i
$544$	−3.88881e6	+	8.62637e6i	−0.0241557	+	0.0535835i
$545$	2.07334e8	+	8.93529e7i	1.28080	+	0.551975i
$546$	3.39426e7	−	2.32934e8i	0.208530	−	1.43105i
$547$	−5.70174e7	−	5.70174e7i	−0.348374	−	0.348374i	0.511130	−	0.859504i	$-0.329227\pi$
$547$	−5.70174e7	−	5.70174e7i	−0.348374	−	0.348374i	−0.859504	+	0.511130i	$0.829227\pi$
$548$	9.87287e7	−	6.98872e7i	0.599932	−	0.424674i
$549$	1.16036e7	−	9.62403e7i	0.0701254	−	0.581621i
$550$	1.91603e7	−	1.68651e8i	0.115163	−	1.01368i
$551$	1.11623e7			0.0667265
$552$	−2.73766e8	+	1.39508e8i	−1.62766	+	0.829436i
$553$	3.59009e7	+	3.59009e7i	0.212290	+	0.212290i
$554$	2.68074e8	+	2.27615e7i	1.57661	+	0.133867i
$555$	−1.78236e8	−	8.98447e7i	−1.04260	−	0.525550i
$556$	2.42667e7	−	1.41870e8i	0.141184	−	0.825403i
$557$	2.29505e8	+	2.29505e8i	1.32809	+	1.32809i	0.907036	+	0.421054i	$0.138340\pi$
$557$	2.29505e8	+	2.29505e8i	1.32809	+	1.32809i	0.421054	+	0.907036i	$0.361660\pi$
$558$	−1.17559e8	−	1.79158e8i	−0.676633	−	1.03118i
$559$	−2.99827e8			−1.71646
$560$	1.88966e8	−	7.50042e6i	1.07602	−	0.0427092i
$561$	1.05681e7	+	634795.i	0.0598562	+	0.00359538i
$562$	1.34664e8	−	1.13585e8i	0.758650	−	0.639902i
$563$	−1.21751e8	−	1.21751e8i	−0.682256	−	0.682256i	0.278252	−	0.960508i	$-0.410245\pi$
$563$	−1.21751e8	−	1.21751e8i	−0.682256	−	0.682256i	−0.960508	+	0.278252i	$0.910245\pi$
$564$	−2.08875e8	−	4.87755e7i	−1.16426	−	0.271872i
$565$	−2.22181e7	−	5.58718e7i	−0.123186	−	0.309776i
$566$	−3.01796e8	−	2.56248e7i	−1.66443	−	0.141323i
$567$	1.01834e8	+	1.67815e8i	0.558653	+	0.920625i
$568$	−1.12245e8	+	6.59601e7i	−0.612523	+	0.359945i
$569$	−2.18270e8			−1.18483			−0.592417	−	0.805631i	$-0.701826\pi$
$569$	−2.18270e8			−1.18483			−0.592417	+	0.805631i	$0.701826\pi$
$570$	−7.50426e7	+	1.21957e8i	−0.405213	+	0.658540i
$571$			1.74583e8i			0.937763i	0.883261	+	0.468882i	$0.155343\pi$
$571$			1.74583e8i			0.937763i	−0.883261	+	0.468882i	$0.844657\pi$
$572$	2.09280e8	−	1.48143e8i	1.11825	−	0.791577i
$573$	1.58708e8	−	1.40722e8i	0.843596	−	0.747994i
$574$	−2.59056e8	−	2.19959e7i	−1.36980	−	0.116307i
$575$	9.86852e6	−	3.47153e8i	0.0519097	−	1.82607i
$576$	−1.54617e8	−	1.12312e8i	−0.809076	−	0.587703i
$577$	1.14387e8	−	1.14387e8i	0.595454	−	0.595454i	−0.343645	−	0.939099i	$-0.611662\pi$
$577$	1.14387e8	−	1.14387e8i	0.595454	−	0.595454i	0.939099	+	0.343645i	$0.111662\pi$
$578$	−1.47095e8	+	1.24071e8i	−0.761754	+	0.642521i
$579$	−3.59264e7	−	2.15799e6i	−0.185088	−	0.0111177i
$580$	−1.41179e7	−	9.17545e6i	−0.0723577	−	0.0470266i
$581$		−	2.11773e8i		−	1.07980i
$582$	−5.87780e7	+	4.38267e7i	−0.298158	+	0.222315i
$583$	−4.70077e7	+	4.70077e7i	−0.237226	+	0.237226i
$584$	1.66281e8	+	4.31879e7i	0.834842	+	0.216832i
$585$	−6.87282e7	−	2.59925e8i	−0.343295	−	1.29832i
$586$	−2.35934e8	−	2.00326e7i	−1.17246	−	0.0995507i
$587$	−1.69603e8	+	1.69603e8i	−0.838533	+	0.838533i	−0.988666	−	0.150133i	$-0.952030\pi$
$587$	−1.69603e8	+	1.69603e8i	−0.838533	+	0.838533i	0.150133	+	0.988666i	$0.452030\pi$
$588$	2.75666e7	−	1.71294e7i	0.135597	−	0.0842579i
$589$		−	1.94867e8i		−	0.953656i
$590$	4.80816e7	+	1.58927e8i	0.234112	+	0.773822i
$591$	3.54618e8	+	2.13009e7i	1.71790	+	0.103189i
$592$	2.18484e8	−	1.04620e8i	1.05306	−	0.504253i
$593$	−1.04281e8	+	1.04281e8i	−0.500082	+	0.500082i	−0.911463	−	0.411381i	$-0.865047\pi$
$593$	−1.04281e8	+	1.04281e8i	−0.500082	+	0.500082i	0.411381	+	0.911463i	$0.365047\pi$
$594$	−5.59370e7	+	2.06372e8i	−0.266895	+	0.984673i
$595$	−1.22441e7	−	5.27671e6i	−0.0581266	−	0.0250503i
$596$	−2.97600e7	+	1.73986e8i	−0.140571	+	0.821816i
$597$	−3.26240e7	+	2.89268e7i	−0.153325	+	0.135949i
$598$	4.01023e8	−	3.38253e8i	1.87528	−	1.58175i
$599$			1.14196e8i			0.531335i	0.964065	+	0.265668i	$0.0855924\pi$
$599$			1.14196e8i			0.531335i	−0.964065	+	0.265668i	$0.914408\pi$
$600$	1.95161e8	−	9.25634e7i	0.903525	−	0.428534i
$601$	9.52213e7			0.438643			0.219321	−	0.975653i	$-0.429616\pi$
$601$	9.52213e7			0.438643			0.219321	+	0.975653i	$0.429616\pi$
$602$	−1.93607e8	−	2.29535e8i	−0.887426	−	1.05211i
$603$	4.11434e7	−	3.22897e7i	0.187650	−	0.147269i
$604$	2.85459e8	+	4.88274e7i	1.29549	+	0.221591i
$605$	3.57693e6	−	8.29990e6i	0.0161527	−	0.0374806i
$606$	−2.31675e7	+	1.58989e8i	−0.104103	+	0.714411i
$607$	5.11312e6	+	5.11312e6i	0.0228623	+	0.0228623i	0.718446	−	0.695583i	$-0.244854\pi$
$607$	5.11312e6	+	5.11312e6i	0.0228623	+	0.0228623i	−0.695583	+	0.718446i	$0.744854\pi$
$608$	−6.15252e7	−	1.62531e8i	−0.273743	−	0.723144i
$609$	−2.09521e7	−	1.25853e6i	−0.0927630	−	0.00557199i
$610$	−1.27276e8	+	3.85059e7i	−0.560733	+	0.169644i
$611$	3.66234e8			1.60559
$612$	6.41187e6	+	1.18493e7i	0.0279724	+	0.0516937i
$613$	2.53063e8	+	2.53063e8i	1.09862	+	1.09862i	0.994573	+	0.104046i	$0.0331789\pi$
$613$	2.53063e8	+	2.53063e8i	1.09862	+	1.09862i	0.104046	+	0.994573i	$0.466821\pi$
$614$	5.08087e6	−	5.98398e7i	0.0219499	−	0.258515i
$615$	−2.82014e8	+	9.29856e7i	−1.21240	+	0.399752i
$616$	2.48551e8	+	6.45557e7i	1.06334	+	0.276180i
$617$	1.38214e8	+	1.38214e8i	0.588431	+	0.588431i	0.937206	−	0.348775i	$-0.113402\pi$
$617$	1.38214e8	+	1.38214e8i	0.588431	+	0.588431i	−0.348775	+	0.937206i	$0.613402\pi$
$618$	5.14858e7	−	3.83894e7i	0.218133	−	0.162647i
$619$	2.23588e8			0.942706			0.471353	−	0.881945i	$-0.343766\pi$
$619$	2.23588e8			0.942706			0.471353	+	0.881945i	$0.343766\pi$
$620$	−1.60181e8	+	2.46464e8i	−0.672104	+	1.03414i
$621$	−7.83170e7	+	4.30423e8i	−0.327025	+	1.79730i
$622$	3.67848e6	+	4.36110e6i	0.0152861	+	0.0181228i
$623$	4.27878e7	+	4.27878e7i	0.176952	+	0.176952i
$624$	3.00687e8	+	1.26708e8i	1.23754	+	0.521495i
$625$	−1.38692e7	+	2.43746e8i	−0.0568081	+	0.998385i
$626$	−1.19983e7	+	1.41310e8i	−0.0489100	+	0.576037i
$627$	−1.45489e8	+	1.29001e8i	−0.590237	+	0.523348i
$628$	−2.24369e8	−	3.16963e8i	−0.905908	−	1.27976i
$629$	−1.70781e7			−0.0686257
$630$	1.54608e8	−	2.20457e8i	0.618317	−	0.881662i
$631$			3.67203e8i			1.46156i	0.682611	+	0.730782i	$0.260844\pi$
$631$			3.67203e8i			1.46156i	−0.682611	+	0.730782i	$0.739156\pi$
$632$	−6.06765e7	+	3.56561e7i	−0.240364	+	0.141248i
$633$	−2.33571e8	−	2.63424e8i	−0.920891	−	1.03859i
$634$	3.87453e7	−	4.56322e8i	0.152038	−	1.79062i
$635$	2.19122e8	−	8.71366e7i	0.855786	−	0.340314i
$636$	−8.23822e7	−	1.92375e7i	−0.320230	−	0.0747785i
$637$	−3.91841e7	+	3.91841e7i	−0.151597	+	0.151597i
$638$	−1.47412e7	−	1.74768e7i	−0.0567637	−	0.0672975i
$639$	−2.21891e7	+	1.84037e8i	−0.0850428	+	0.705346i
$640$	−5.57850e7	+	2.56140e8i	−0.212803	+	0.977095i
$641$			7.77280e7i			0.295123i	0.989053	+	0.147562i	$0.0471425\pi$
$641$			7.77280e7i			0.295123i	−0.989053	+	0.147562i	$0.952858\pi$
$642$	1.88809e8	−	1.40782e8i	0.713540	−	0.532037i
$643$	−1.86163e8	+	1.86163e8i	−0.700261	+	0.700261i	−0.964466	−	0.264206i	$-0.914890\pi$
$643$	−1.86163e8	+	1.86163e8i	−0.700261	+	0.700261i	0.264206	+	0.964466i	$0.414890\pi$
$644$	5.17906e8	+	8.85871e7i	1.93907	+	0.331675i
$645$	−3.06263e8	−	1.54380e8i	−1.14134	−	0.575323i
$646$	−1.03656e6	+	1.22081e7i	−0.00384500	+	0.0452844i
$647$	−3.29523e8	+	3.29523e8i	−1.21667	+	1.21667i	−0.247881	+	0.968790i	$0.579734\pi$
$647$	−3.29523e8	+	3.29523e8i	−1.21667	+	1.21667i	−0.968790	+	0.247881i	$0.920266\pi$
$648$	−2.60634e8	+	7.81471e7i	−0.957870	+	0.287202i
$649$			2.25465e8i			0.824794i
$650$	−2.88555e8	+	2.29679e8i	−1.05072	+	0.836336i
$651$	−2.19708e7	+	3.65772e8i	−0.0796349	+	1.32577i
$652$	−2.58317e8	−	3.64920e8i	−0.931986	−	1.31660i
$653$	2.73103e8	−	2.73103e8i	0.980815	−	0.980815i	−0.0190042	−	0.999819i	$-0.506050\pi$
$653$	2.73103e8	−	2.73103e8i	0.980815	−	0.980815i	0.999819	+	0.0190042i	$0.00604959\pi$
$654$	−5.62545e7	+	3.86051e8i	−0.201106	+	1.38010i
$655$	−7.81288e7	+	1.81290e8i	−0.278027	+	0.645133i
$656$	1.19782e8	−	3.39897e8i	0.424308	−	1.20403i
$657$	1.92427e8	−	1.51018e8i	0.678531	−	0.532516i
$658$	2.36488e8	+	2.80374e8i	0.830102	+	0.984146i
$659$			2.84879e7i			0.0995417i	0.998761	+	0.0497708i	$0.0158491\pi$
$659$			2.84879e7i			0.0995417i	−0.998761	+	0.0497708i	$0.984151\pi$
$660$	2.90051e8	−	4.35655e7i	1.00889	−	0.151534i
$661$	−1.91780e8			−0.664047			−0.332024	−	0.943271i	$-0.607731\pi$
$661$	−1.91780e8			−0.664047			−0.332024	+	0.943271i	$0.607731\pi$
$662$	−8.59143e6	+	7.24665e6i	−0.0296136	+	0.0249783i
$663$	−1.52616e7	−	1.72122e7i	−0.0523672	−	0.0590604i
$664$	2.84124e8	+	7.37952e7i	0.970519	+	0.252071i
$665$	2.27537e8	−	9.04828e7i	0.773725	−	0.307681i
$666$	7.01090e7	−	3.37709e8i	0.237329	−	1.14319i
$667$	−3.30788e7	−	3.30788e7i	−0.111474	−	0.111474i
$668$	1.20941e8	+	1.70851e8i	0.405736	+	0.573178i
$669$	−7.82157e6	+	1.30214e8i	−0.0261225	+	0.434890i
$670$	−6.32472e7	−	3.38665e7i	−0.210289	−	0.112602i
$671$	−1.80563e8			−0.597668
$672$	9.71602e7	+	3.12013e8i	0.320170	+	1.02817i
$673$	−3.12667e8	−	3.12667e8i	−1.02574	−	1.02574i	−0.999660	−	0.0260794i	$-0.991698\pi$
$673$	−3.12667e8	−	3.12667e8i	−1.02574	−	1.02574i	−0.0260794	−	0.999660i	$-0.508302\pi$
$674$	−1.22383e8	−	1.03913e7i	−0.399708	−	0.0339383i
$675$	6.36311e7	−	3.00892e8i	0.206899	−	0.978362i
$676$	−2.44653e8	−	4.18476e7i	−0.791973	−	0.135466i
$677$	−2.08606e8	−	2.08606e8i	−0.672297	−	0.672297i	0.285948	−	0.958245i	$-0.407692\pi$
$677$	−2.08606e8	−	2.08606e8i	−0.672297	−	0.672297i	−0.958245	+	0.285948i	$0.907692\pi$
$678$	8.32945e7	−	6.21069e7i	0.267256	−	0.199274i
$679$	1.25377e8			0.400505
$680$	1.13461e7	−	1.45885e7i	0.0360844	−	0.0463962i
$681$	−2.40424e7	+	4.00260e8i	−0.0761266	+	1.26736i
$682$	−3.05102e8	+	2.57346e8i	−0.961816	+	0.811267i
$683$	7.53661e7	+	7.53661e7i	0.236545	+	0.236545i	0.815418	−	0.578873i	$-0.196507\pi$
$683$	7.53661e7	+	7.53661e7i	0.236545	+	0.236545i	−0.578873	+	0.815418i	$0.696507\pi$
$684$	−2.37152e8	−	7.06139e7i	−0.741068	−	0.220659i
$685$	−2.19531e8	+	8.72992e7i	−0.683006	+	0.271606i
$686$	2.91097e8	+	2.47164e7i	0.901708	+	0.0765620i
$687$	−2.04764e8	−	2.30935e8i	−0.631515	−	0.712230i
$688$	3.75420e8	−	1.79768e8i	1.15280	−	0.552009i
$689$	1.44446e8			0.441618
$690$	5.83797e8	−	1.39028e8i	1.77711	−	0.423209i
$691$		−	1.73004e8i		−	0.524351i	−0.965020	−	0.262176i	$-0.915560\pi$
$691$		−	1.73004e8i		−	0.524351i	0.965020	−	0.262176i	$-0.0844400\pi$
$692$	−2.39265e8	−	3.38007e8i	−0.722040	−	1.02002i
$693$	2.87633e8	−	2.25736e8i	0.864248	−	0.678268i
$694$	1.85257e8	+	1.57297e7i	0.554237	+	0.0470590i
$695$	−1.11257e8	+	2.58161e8i	−0.331416	+	0.769017i
$696$	8.98953e6	−	2.76717e7i	0.0266630	−	0.0820745i
$697$	−1.79657e7	+	1.79657e7i	−0.0530574	+	0.0530574i
$698$	−9.53648e6	+	8.04378e6i	−0.0280428	+	0.0236534i
$699$	1.14080e7	−	1.89921e8i	0.0334024	−	0.556086i
$700$	−3.62161e8	−	7.25954e7i	−1.05586	−	0.211648i
$701$		−	4.15307e8i		−	1.20563i	−0.797880	−	0.602816i	$-0.794045\pi$
$701$		−	4.15307e8i		−	1.20563i	0.797880	−	0.602816i	$-0.205955\pi$
$702$	4.03013e8	−	2.31129e8i	1.16495	−	0.668104i
$703$	2.21787e8	−	2.21787e8i	0.638368	−	0.638368i
$704$	−1.73222e8	+	3.10972e8i	−0.496461	+	0.891257i
$705$	3.74095e8	+	1.88573e8i	1.06761	+	0.538160i
$706$	3.32266e8	+	2.82120e7i	0.944218	+	0.0801714i
$707$	1.94275e8	−	1.94275e8i	0.549741	−	0.549741i
$708$	−2.43702e8	+	1.51432e8i	−0.686688	+	0.426696i
$709$		−	3.93832e8i		−	1.10503i	−0.833504	−	0.552513i	$-0.813669\pi$
$709$		−	3.93832e8i		−	1.10503i	0.833504	−	0.552513i	$-0.186331\pi$
$710$	2.43385e8	−	7.36334e7i	0.680014	−	0.205731i
$711$	−1.19948e7	+	9.94850e7i	−0.0333722	+	0.276789i
$712$	−7.23161e7	+	4.24961e7i	−0.200353	+	0.117736i
$713$	−5.77476e8	+	5.77476e8i	−1.59318	+	1.59318i
$714$	3.32210e6	−	2.27981e7i	0.00912678	−	0.0626332i
$715$	−4.65350e8	+	1.85052e8i	−1.27310	+	0.506263i
$716$	−4.94494e8	−	8.45826e7i	−1.34717	−	0.230432i
$717$	2.59399e8	+	2.92553e8i	0.703738	+	0.793683i
$718$	−3.57704e8	+	3.01714e8i	−0.966385	+	0.815121i
$719$		−	1.92397e8i		−	0.517620i	−0.965928	−	0.258810i	$-0.916670\pi$
$719$		−	1.92397e8i		−	0.517620i	0.965928	−	0.258810i	$-0.0833304\pi$
$720$	2.41900e8	+	2.84251e8i	0.648094	+	0.761560i
$721$	−1.09822e8			−0.293011
$722$	9.75812e7	+	1.15690e8i	0.259271	+	0.307385i
$723$	1.33666e8	−	1.18518e8i	0.353675	−	0.313595i
$724$	−2.26539e7	+	1.32441e8i	−0.0596936	+	0.348986i
$725$	2.25836e7	+	2.39052e7i	0.0592625	+	0.0627303i
$726$	1.54542e7	+	2.25195e6i	0.0403865	+	0.00588504i
$727$	−1.19250e8	−	1.19250e8i	−0.310352	−	0.310352i	0.534694	−	0.845046i	$-0.320427\pi$
$727$	−1.19250e8	−	1.19250e8i	−0.310352	−	0.310352i	−0.845046	+	0.534694i	$0.820427\pi$
$728$	−2.82691e8	−	4.81058e8i	−0.732686	−	1.24682i
$729$	−1.36467e8	+	3.62590e8i	−0.352246	+	0.935908i
$730$	−2.95806e8	−	1.58393e8i	−0.760392	−	0.407161i
$731$	−2.93452e7			−0.0751250
$732$	−1.21274e8	−	1.95167e8i	−0.309196	−	0.497593i
$733$	2.50488e8	+	2.50488e8i	0.636027	+	0.636027i	0.949573	−	0.313546i	$-0.101517\pi$
$733$	2.50488e8	+	2.50488e8i	0.636027	+	0.636027i	−0.313546	+	0.949573i	$0.601517\pi$
$734$	2.05394e7	−	2.41903e8i	0.0519398	−	0.611721i
$735$	−6.02009e7	+	1.98494e7i	−0.151615	+	0.0499903i
$736$	−2.99324e8	+	6.63977e8i	−0.750772	+	1.66540i
$737$	−6.88863e7	−	6.88863e7i	−0.172080	−	0.172080i
$738$	−2.81508e8	−	4.29014e8i	−0.700360	−	1.06734i
$739$	4.02436e7			0.0997157			0.0498578	−	0.998756i	$-0.484123\pi$
$739$	4.02436e7			0.0997157			0.0498578	+	0.998756i	$0.484123\pi$
$740$	−4.62823e8	+	9.82022e7i	−1.14214	+	0.242341i
$741$	4.21727e8	+	2.53319e7i	1.03652	+	0.0622606i
$742$	9.32729e7	+	1.10582e8i	0.228320	+	0.270690i
$743$	1.93136e8	+	1.93136e8i	0.470865	+	0.470865i	0.902194	−	0.431329i	$-0.141955\pi$
$743$	1.93136e8	+	1.93136e8i	0.470865	+	0.470865i	−0.431329	+	0.902194i	$0.641955\pi$
$744$	−4.83081e8	−	1.56935e8i	−1.17301	−	0.381068i
$745$	1.36443e8	−	3.16602e8i	0.329976	−	0.765675i
$746$	−3.58866e7	+	4.22654e8i	−0.0864402	+	1.01805i
$747$	3.28799e8	−	2.58044e8i	0.788804	−	0.619059i
$748$	2.04830e7	−	1.44993e7i	0.0489428	−	0.0346452i
$749$	−4.02741e8			−0.958474
$750$	−4.13010e8	+	8.60329e7i	−0.978985	+	0.203930i
$751$		−	2.28465e8i		−	0.539386i	−0.962946	−	0.269693i	$-0.913078\pi$
$751$		−	2.28465e8i		−	0.539386i	0.962946	−	0.269693i	$-0.0869223\pi$
$752$	−4.58570e8	+	2.19583e8i	−1.07833	+	0.516352i
$753$	2.86928e8	−	2.54412e8i	0.672030	−	0.595871i
$754$	−4.20292e6	+	4.94998e7i	−0.00980476	+	0.115475i
$755$	−5.19450e8	−	2.23862e8i	−1.20699	−	0.520164i
$756$	4.37181e8	+	1.59283e8i	1.01180	+	0.368642i
$757$	−1.63256e7	+	1.63256e7i	−0.0376342	+	0.0376342i	−0.725673	−	0.688039i	$-0.758472\pi$
$757$	−1.63256e7	+	1.63256e7i	−0.0376342	+	0.0376342i	0.688039	+	0.725673i	$0.258472\pi$
$758$	2.53983e8	+	3.01115e8i	0.583171	+	0.691392i
$759$	8.13435e8	+	4.88606e7i	1.86036	+	0.111746i
$760$	4.21075e7	+	3.36804e8i	0.0959222	+	0.767249i
$761$		−	3.86040e8i		−	0.875948i	−0.898988	−	0.437974i	$-0.855696\pi$
$761$		−	3.86040e8i		−	0.875948i	0.898988	−	0.437974i	$-0.144304\pi$
$762$	2.43575e8	+	3.26671e8i	0.550514	+	0.738321i
$763$	4.71731e8	−	4.71731e8i	1.06199	−	1.06199i
$764$	8.47688e7	−	4.95583e8i	0.190089	−	1.11131i
$765$	−6.72669e6	−	2.54398e7i	−0.0150251	−	0.0568238i
$766$	−1.10658e7	+	1.30327e8i	−0.0246204	+	0.289966i
$767$	3.46406e8	−	3.46406e8i	0.767714	−	0.767714i
$768$	−4.52468e8	+	2.16293e7i	−0.998859	+	0.0477483i
$769$		−	6.66598e8i		−	1.46584i	−0.680317	−	0.732918i	$-0.738158\pi$
$769$		−	6.66598e8i		−	1.46584i	0.680317	−	0.732918i	$-0.261842\pi$
$770$	−4.42159e8	−	2.36760e8i	−0.968516	−	0.518604i
$771$	−2.15248e8	−	1.29293e7i	−0.469651	−	0.0282105i
$772$	−6.96322e7	+	4.92906e7i	−0.151342	+	0.107130i
$773$	−2.30960e8	+	2.30960e8i	−0.500032	+	0.500032i	−0.911448	−	0.411416i	$-0.865034\pi$
$773$	−2.30960e8	+	2.30960e8i	−0.500032	+	0.500032i	0.411416	+	0.911448i	$0.365034\pi$
$774$	1.20468e8	−	5.80283e8i	0.259806	−	1.25146i
$775$	4.17326e8	−	3.94255e8i	0.896542	−	0.846979i
$776$	−4.36893e7	+	1.68211e8i	−0.0934953	+	0.359973i
$777$	−4.41310e8	+	3.91298e8i	−0.940764	+	0.834150i
$778$	4.78197e8	+	5.66937e8i	1.01547	+	1.20392i
$779$		−	4.66630e8i		−	0.987097i
$780$	−5.12569e8	−	3.78701e8i	−1.08011	−	0.798018i
$781$	3.45283e8			0.724807
$782$	3.92497e7	−	3.31061e7i	0.0820759	−	0.0692290i
$783$	−2.35760e7	−	3.40638e7i	−0.0491117	−	0.0709590i
$784$	2.55697e7	−	7.25570e7i	0.0530611	−	0.150567i
$785$	2.80270e8	+	7.04793e8i	0.579385	+	1.45698i
$786$	−3.37557e8	−	4.91880e7i	−0.695151	−	0.101296i
$787$	6.81594e7	+	6.81594e7i	0.139830	+	0.139830i	0.773557	−	0.633727i	$-0.218476\pi$
$787$	6.81594e7	+	6.81594e7i	0.139830	+	0.139830i	−0.633727	+	0.773557i	$0.718476\pi$
$788$	6.87318e8	−	4.86532e8i	1.40468	−	0.994335i
$789$	8.79304e8	+	5.28171e7i	1.79023	+	0.107534i
$790$	1.31567e8	−	3.98041e7i	0.266849	−	0.0807322i
$791$	−1.77672e8			−0.358996
$792$	2.02629e8	+	4.64562e8i	0.407873	+	0.935122i
$793$	2.77417e8	+	2.77417e8i	0.556306	+	0.556306i
$794$	1.51171e8	+	1.28356e7i	0.301999	+	0.0256421i
$795$	1.47546e8	+	7.43746e7i	0.293648	+	0.148021i
$796$	−1.74251e7	+	1.01872e8i	−0.0345490	+	0.201983i
$797$	−5.25947e8	−	5.25947e8i	−1.03888	−	1.03888i	−0.999213	−	0.0396706i	$-0.987369\pi$
$797$	−5.25947e8	−	5.25947e8i	−1.03888	−	1.03888i	−0.0396706	−	0.999213i	$-0.512631\pi$
$798$	2.52929e8	+	3.39215e8i	0.497726	+	0.667523i
$799$	3.58447e7			0.0702723
$800$	2.23597e8	−	4.60595e8i	0.436714	−	0.899601i
$801$	−1.42958e7	+	1.18569e8i	−0.0278170	+	0.230714i
$802$	−3.81855e7	+	3.22085e7i	−0.0740244	+	0.0624377i
$803$	−3.22179e8	−	3.22179e8i	−0.622230	−	0.622230i
$804$	2.81911e7	−	1.20725e8i	0.0542431	−	0.232290i
$805$	−9.42433e8	−	4.06152e8i	−1.80660	−	0.778575i
$806$	8.64148e8	+	7.33728e7i	1.65038	+	0.140130i
$807$	−1.26494e8	+	1.12159e8i	−0.240686	+	0.213410i
$808$	1.92950e8	+	3.28346e8i	0.365773	+	0.622440i
$809$	−8.10218e7			−0.153023			−0.0765114	−	0.997069i	$-0.524378\pi$
$809$	−8.10218e7			−0.153023			−0.0765114	+	0.997069i	$0.524378\pi$
$810$	5.30672e8	−	2.85805e7i	0.998553	−	0.0537792i
$811$			2.88768e8i			0.541360i	0.962669	+	0.270680i	$0.0872485\pi$
$811$			2.88768e8i			0.541360i	−0.962669	+	0.270680i	$0.912751\pi$
$812$	−4.06090e7	+	2.87460e7i	−0.0758498	+	0.0536919i
$813$	−1.69773e8	−	1.91472e8i	−0.315935	−	0.356315i
$814$	−6.40150e8	−	5.43537e7i	−1.18688	−	0.100776i
$815$	3.22675e8	+	8.11429e8i	0.596063	+	1.49892i
$816$	2.94294e7	+	1.24014e7i	0.0541640	+	0.0228244i
$817$	3.81096e8	−	3.81096e8i	0.698826	−	0.698826i
$818$	2.87043e8	−	2.42114e8i	0.524429	−	0.442343i
$819$	−7.88742e8	−	9.50979e7i	−1.43577	−	0.173109i
$820$	−3.83572e8	+	5.90184e8i	−0.695673	+	1.07040i
$821$		−	6.88823e8i		−	1.24474i	−0.782724	−	0.622370i	$-0.786170\pi$
$821$		−	6.88823e8i		−	1.24474i	0.782724	−	0.622370i	$-0.213830\pi$
$822$	−2.44030e8	−	3.27280e8i	−0.439367	−	0.589256i
$823$	4.20517e7	−	4.20517e7i	0.0754369	−	0.0754369i	−0.668382	−	0.743819i	$-0.733013\pi$
$823$	4.20517e7	−	4.20517e7i	0.0754369	−	0.0754369i	0.743819	+	0.668382i	$0.233013\pi$
$824$	3.82691e7	−	1.47343e8i	0.0684016	−	0.263358i
$825$	−5.70622e8	−	5.05830e7i	−1.01622	−	0.0900830i
$826$	4.88879e8	+	4.15096e7i	0.867484	+	0.0736561i
$827$	3.50042e8	−	3.50042e8i	0.618875	−	0.618875i	−0.326368	−	0.945243i	$-0.605825\pi$
$827$	3.50042e8	−	3.50042e8i	0.618875	−	0.618875i	0.945243	+	0.326368i	$0.105825\pi$
$828$	4.93525e8	+	9.12046e8i	0.869397	+	1.60667i
$829$		−	2.32683e8i		−	0.408415i	−0.978928	−	0.204207i	$-0.934538\pi$
$829$		−	2.32683e8i		−	0.408415i	0.978928	−	0.204207i	$-0.0654617\pi$
$830$	−5.05443e8	−	2.70645e8i	−0.883970	−	0.473333i
$831$	5.44430e7	−	9.06371e8i	0.0948722	−	1.57944i
$832$	7.43918e8	−	2.11640e8i	1.29168	−	0.367475i
$833$	−3.83509e6	+	3.83509e6i	−0.00663500	+	0.00663500i
$834$	−4.80689e8	−	7.00450e7i	−0.828640	−	0.120748i
$835$	−1.51072e8	−	3.79902e8i	−0.259493	−	0.652547i
$836$	−7.77082e7	+	4.54305e8i	−0.132999	+	0.777550i
$837$	−5.94671e8	+	4.11580e8i	−1.01415	+	0.701904i
$838$	2.61320e8	−	2.20417e8i	0.444059	−	0.374552i
$839$			7.66640e8i			1.29809i	0.760749	+	0.649046i	$0.224832\pi$
$839$			7.66640e8i			1.29809i	−0.760749	+	0.649046i	$0.775168\pi$
$840$	−4.10635e7	−	6.36941e8i	−0.0692816	−	1.07464i
$841$	−5.90394e8			−0.992553
$842$	−3.73008e8	−	4.42228e8i	−0.624859	−	0.740815i
$843$	−3.94463e8	−	4.44880e8i	−0.658451	−	0.742608i
$844$	−8.22571e8	−	1.40700e8i	−1.36819	−	0.234027i
$845$	4.45195e8	+	1.91862e8i	0.737870	+	0.317993i
$846$	−1.47150e8	+	7.08807e8i	−0.243024	+	1.17062i
$847$	−1.88841e7	−	1.88841e7i	−0.0310775	−	0.0310775i
$848$	−1.80864e8	+	8.66055e7i	−0.296595	+	0.142023i
$849$	−6.12917e7	+	1.02039e9i	−0.100156	+	1.66741i
$850$	−2.82419e7	+	2.24795e7i	−0.0459873	+	0.0366042i
$851$	−1.31451e9			−2.13292
$852$	2.31907e8	+	3.73211e8i	0.374969	+	0.603443i
$853$	−1.21093e8	−	1.21093e8i	−0.195107	−	0.195107i	0.602792	−	0.797898i	$-0.294055\pi$
$853$	−1.21093e8	−	1.21093e8i	−0.195107	−	0.195107i	−0.797898	+	0.602792i	$0.794055\pi$
$854$	−3.32428e7	+	3.91516e8i	−0.0533732	+	0.628603i
$855$	4.17737e8	+	2.43022e8i	0.668350	+	0.388818i
$856$	1.40341e8	−	5.40336e8i	0.223749	−	0.861474i
$857$	6.56327e8	+	6.56327e8i	1.04274	+	1.04274i	0.999045	+	0.0436995i	$0.0139144\pi$
$857$	6.56327e8	+	6.56327e8i	1.04274	+	1.04274i	0.0436995	+	0.999045i	$0.486086\pi$
$858$	−5.17282e8	−	6.93751e8i	−0.818965	−	1.09835i
$859$	−3.63159e8			−0.572952			−0.286476	−	0.958087i	$-0.592484\pi$
$859$	−3.63159e8			−0.572952			−0.286476	+	0.958087i	$0.592484\pi$
$860$	−7.95266e8	+	1.68740e8i	−1.25031	+	0.265292i
$861$	−5.26116e7	+	8.75882e8i	−0.0824275	+	1.37226i
$862$	3.00582e7	+	3.56361e7i	0.0469290	+	0.0556377i
$863$	5.75037e8	+	5.75037e8i	0.894671	+	0.894671i	0.994958	−	0.100288i	$-0.0319764\pi$
$863$	5.75037e8	+	5.75037e8i	0.894671	+	0.894671i	−0.100288	+	0.994958i	$0.531976\pi$
$864$	−3.66044e8	+	5.31038e8i	−0.567534	+	0.823350i
$865$	2.98877e8	+	7.51585e8i	0.461790	+	1.16126i
$866$	−2.38778e7	+	2.81220e8i	−0.0367655	+	0.433005i
$867$	4.30878e8	+	4.85949e8i	0.661145	+	0.745647i
$868$	5.01835e8	+	7.08936e8i	0.767365	+	1.08405i
$869$	1.86650e8			0.284426
$870$	−2.97805e7	+	4.83983e7i	−0.0452245	+	0.0734975i
$871$			2.11674e8i			0.320342i
$872$	4.68515e8	+	7.97278e8i	0.706601	+	1.20243i
$873$	1.52771e8	+	1.94661e8i	0.229614	+	0.292574i
$874$	−7.97846e7	+	9.39662e8i	−0.119505	+	1.40746i
$875$	6.54132e8	+	3.04227e8i	0.976430	+	0.454124i
$876$	1.31849e8	−	5.64628e8i	0.196139	−	0.839944i
$877$	1.90408e8	−	1.90408e8i	0.282283	−	0.282283i	−0.551736	−	0.834019i	$-0.686034\pi$
$877$	1.90408e8	−	1.90408e8i	0.282283	−	0.282283i	0.834019	+	0.551736i	$0.186034\pi$
$878$	9.91636e7	+	1.17566e8i	0.146511	+	0.173699i
$879$	−4.79156e7	+	7.97703e8i	−0.0705522	+	1.17456i
$880$	4.71724e8	−	5.10719e8i	0.692214	−	0.749435i
$881$		−	5.16585e8i		−	0.755465i	−0.925915	−	0.377732i	$-0.876704\pi$
$881$		−	5.16585e8i		−	0.755465i	0.925915	−	0.377732i	$-0.123296\pi$
$882$	−6.00928e7	−	9.15805e7i	−0.0875824	−	0.133474i
$883$	−2.64049e8	+	2.64049e8i	−0.383532	+	0.383532i	−0.872373	−	0.488841i	$-0.837420\pi$
$883$	−2.64049e8	+	2.64049e8i	−0.383532	+	0.383532i	0.488841	+	0.872373i	$0.337420\pi$
$884$	−5.37470e7	−	9.19336e6i	−0.0778033	−	0.0133081i
$885$	5.32205e8	−	1.75478e8i	0.767802	−	0.253159i
$886$	9.47959e7	−	1.11646e9i	0.136298	−	1.60524i
$887$	1.43878e8	−	1.43878e8i	0.206169	−	0.206169i	−0.596468	−	0.802637i	$-0.703430\pi$
$887$	1.43878e8	−	1.43878e8i	0.206169	−	0.206169i	0.802637	+	0.596468i	$0.203430\pi$
$888$	−3.71202e8	−	7.28435e8i	−0.530117	−	1.04028i
$889$		−	6.96807e8i		−	0.991761i
$890$	1.56805e8	−	4.74398e7i	0.222429	−	0.0672934i
$891$	7.00958e8	+	1.71521e8i	0.990966	+	0.242485i
$892$	1.78652e8	+	2.52380e8i	0.251718	+	0.355598i
$893$	−4.65503e8	+	4.65503e8i	−0.653685	+	0.653685i
$894$	5.89504e8	+	8.59013e7i	0.825039	+	0.120223i
$895$	8.99831e8	+	3.87792e8i	1.25514	+	0.540916i
$896$	6.42393e8	+	4.32851e8i	0.893052	+	0.601748i
$897$	−1.17470e9	−	1.32483e9i	−1.62760	−	1.83563i
$898$	−5.52462e8	−	6.54983e8i	−0.762910	−	0.904484i
$899$		−	7.73324e7i		−	0.106434i
$900$	−3.28580e8	−	6.50750e8i	−0.450727	−	0.892662i
$901$	1.41374e7			0.0193284
$902$	−7.30600e8	+	6.16243e8i	−0.995544	+	0.839716i
$903$	−7.58301e8	+	6.72365e8i	−1.02986	+	0.913149i
$904$	6.19122e7	−	2.38373e8i	0.0838052	−	0.322665i
$905$	1.03863e8	−	2.41003e8i	0.140125	−	0.325145i
$906$	1.40939e8	−	9.67202e8i	0.189516	−	1.30057i
$907$	−1.25387e8	−	1.25387e8i	−0.168047	−	0.168047i	0.618074	−	0.786120i	$-0.287913\pi$
$907$	−1.25387e8	−	1.25387e8i	−0.168047	−	0.168047i	−0.786120	+	0.618074i	$0.787913\pi$
$908$	5.49152e8	+	7.75779e8i	0.733558	+	1.03629i
$909$	5.38355e8	+	6.49089e7i	0.716765	+	0.0864197i
$910$	3.15577e8	+	1.04309e9i	0.418776	+	1.38420i
$911$	2.00672e8			0.265419			0.132710	−	0.991155i	$-0.457632\pi$
$911$	2.00672e8			0.265419			0.132710	+	0.991155i	$0.457632\pi$
$912$	−5.43243e8	+	2.21137e8i	−0.716160	+	0.291526i
$913$	−5.50507e8	−	5.50507e8i	−0.723354	−	0.723354i
$914$	1.77117e6	+	150386.i	0.00231964	+	0.000196956i
$915$	1.40531e8	+	4.26213e8i	0.183446	+	0.556370i
$916$	−7.21121e8	−	1.23347e8i	−0.938257	−	0.160488i
$917$	4.12474e8	+	4.12474e8i	0.534920	+	0.534920i
$918$	3.94444e7	−	2.26215e7i	0.0509868	−	0.0292411i
$919$	−4.61364e8			−0.594425			−0.297212	−	0.954811i	$-0.596057\pi$
$919$	−4.61364e8			−0.594425			−0.297212	+	0.954811i	$0.596057\pi$
$920$	8.73316e8	−	1.12288e9i	1.12152	−	1.44202i
$921$	−2.02321e8	−	1.21528e7i	−0.258978	−	0.0155560i
$922$	2.54838e7	−	2.14950e7i	0.0325141	−	0.0274248i
$923$	−5.30495e8	−	5.30495e8i	−0.674646	−	0.674646i
$924$	1.97083e8	−	8.43986e8i	0.249824	−	1.06984i
$925$	9.23702e8	+	2.62581e7i	1.16710	+	0.0331770i
$926$	−4.15944e8	−	3.53169e7i	−0.523844	−	0.0444784i
$927$	−1.33818e8	−	1.70510e8i	−0.167987	−	0.214048i
$928$	−2.44161e7	−	6.44999e7i	−0.0305515	−	0.0807077i
$929$	5.98439e8			0.746402			0.373201	−	0.927751i	$-0.378260\pi$
$929$	5.98439e8			0.746402			0.373201	+	0.927751i	$0.378260\pi$
$930$	8.44917e8	+	5.19895e8i	1.05043	+	0.646348i
$931$		−	9.96103e7i		−	0.123440i
$932$	−2.60570e8	−	3.68103e8i	−0.321867	−	0.454697i
$933$	1.44075e7	−	1.27747e7i	0.0177396	−	0.0157292i
$934$	1.43506e9	+	1.21847e8i	1.76128	+	0.149546i
$935$	−4.55456e7	+	1.81118e7i	−0.0557201	+	0.0221578i
$936$	4.02436e8	−	1.02507e9i	0.490760	−	1.25005i
$937$	1.14784e9	−	1.14784e9i	1.39528	−	1.39528i	0.582334	−	0.812949i	$-0.302139\pi$
$937$	1.14784e9	−	1.14784e9i	1.39528	−	1.39528i	0.812949	−	0.582334i	$-0.197861\pi$
$938$	−1.62049e8	+	1.36685e8i	−0.196354	+	0.165619i
$939$	4.77777e8	+	2.86986e7i	0.577070	+	0.0346629i
$940$	9.71405e8	−	2.06114e8i	1.16954	−	0.248155i
$941$			1.53112e8i			0.183755i	0.995770	+	0.0918775i	$0.0292868\pi$
$941$			1.53112e8i			0.183755i	−0.995770	+	0.0918775i	$0.970713\pi$
$942$	−1.05072e9	+	7.83445e8i	−1.25699	+	0.937251i
$943$	−1.38283e9	+	1.38283e9i	−1.64905	+	1.64905i
$944$	−2.26048e8	+	6.41438e8i	−0.268711	+	0.762499i
$945$	−7.56707e8	−	5.03260e8i	−0.896670	−	0.596344i
$946$	−1.09997e9	−	9.33957e7i	−1.29929	−	0.110320i
$947$	8.55786e8	−	8.55786e8i	1.00766	−	1.00766i	0.00769273	−	0.999970i	$-0.497551\pi$
$947$	8.55786e8	−	8.55786e8i	1.00766	−	1.00766i	0.999970	−	0.00769273i	$-0.00244870\pi$
$948$	1.25362e8	+	2.01747e8i	0.147144	+	0.236801i
$949$			9.89996e8i			1.15834i
$950$	7.48347e7	−	6.58704e8i	0.0872835	−	0.768280i
$951$	−1.54285e9	−	9.26743e7i	−1.79383	−	0.107750i
$952$	−2.76680e7	−	4.70830e7i	−0.0320677	−	0.0545699i
$953$	8.11319e8	−	8.11319e8i	0.937375	−	0.937375i	−0.0607767	−	0.998151i	$-0.519358\pi$
$953$	8.11319e8	−	8.11319e8i	0.937375	−	0.937375i	0.998151	+	0.0607767i	$0.0193578\pi$
$954$	−5.80371e7	+	2.79559e8i	−0.0668437	+	0.321980i
$955$	−3.88646e8	+	9.01812e8i	−0.446215	+	1.03539i
$956$	9.13530e8	+	1.56258e8i	1.04556	+	0.178842i
$957$	−5.77368e7	+	5.11937e7i	−0.0658745	+	0.0584091i
$958$	−7.79551e8	+	6.57531e8i	−0.886641	+	0.747859i
$959$			6.98107e8i			0.791528i
$960$	8.68859e8	+	1.66858e8i	0.982055	+	0.188597i
$961$	−4.62532e8			−0.521161
$962$	9.00020e8	+	1.06704e9i	1.01094	+	1.19855i
$963$	−4.90738e8	−	6.25297e8i	−0.549504	−	0.700177i
$964$	7.13933e7	−	4.17386e8i	0.0796941	−	0.465915i
$965$	1.54833e8	−	6.15711e7i	0.172298	−	0.0685165i
$966$	2.55704e8	−	1.75479e9i	0.283665	−	1.94667i
$967$	2.43796e8	+	2.43796e8i	0.269617	+	0.269617i	0.828946	−	0.559329i	$-0.188941\pi$
$967$	2.43796e8	+	2.43796e8i	0.269617	+	0.269617i	−0.559329	+	0.828946i	$0.688941\pi$
$968$	3.19162e7	−	1.87554e7i	0.0351873	−	0.0206776i
$969$	4.12760e7	+	2.47933e6i	0.0453656	+	0.00272498i
$970$	1.60231e8	−	2.99240e8i	0.175563	−	0.327872i
$971$	−1.86629e7			−0.0203855			−0.0101928	−	0.999948i	$-0.503245\pi$
$971$	−1.86629e7			−0.0203855			−0.0101928	+	0.999948i	$0.503245\pi$
$972$	2.85399e8	+	8.72856e8i	0.310781	+	0.950482i
$973$	5.87373e8	+	5.87373e8i	0.637640	+	0.637640i
$974$	9.44441e7	−	1.11231e9i	0.102211	−	1.20379i
$975$	7.98991e8	+	9.54423e8i	0.862041	+	1.02974i
$976$	−5.13692e8	−	1.81029e8i	−0.552527	−	0.194715i
$977$	6.44397e8	+	6.44397e8i	0.690987	+	0.690987i	0.962449	−	0.271462i	$-0.0875072\pi$
$977$	6.44397e8	+	6.44397e8i	0.690987	+	0.690987i	−0.271462	+	0.962449i	$0.587507\pi$
$978$	−1.20969e9	+	9.01982e8i	−1.29318	+	0.964231i
$979$	2.22456e8			0.237080
$980$	−8.18801e7	+	1.25985e8i	−0.0869961	+	0.133857i
$981$	1.30721e9	+	1.57610e8i	1.38465	+	0.166946i
$982$	−6.37404e8	−	7.55689e8i	−0.673101	−	0.798010i
$983$	−1.21423e9	−	1.21423e9i	−1.27832	−	1.27832i	−0.941605	−	0.336718i	$-0.890683\pi$
$983$	−1.21423e9	−	1.21423e9i	−1.27832	−	1.27832i	−0.336718	−	0.941605i	$-0.609317\pi$
$984$	−1.15679e9	−	3.75799e8i	−1.21414	−	0.394431i
$985$	−1.52830e9	+	6.07749e8i	−1.59919	+	0.635939i
$986$	−411356.	+	4.84474e6i	−0.000429128	+	0.00505405i
$987$	9.26252e8	−	8.21283e8i	0.963336	−	0.854164i
$988$	8.17387e8	−	5.78605e8i	0.847534	−	0.599945i
$989$	−2.25872e9			−2.33492
$990$	−1.71175e8	−	9.74989e8i	−0.176415	−	1.00483i
$991$		−	1.07909e9i		−	1.10875i	−0.832265	−	0.554377i	$-0.812956\pi$
$991$		−	1.07909e9i		−	1.10875i	0.832265	−	0.554377i	$-0.187044\pi$
$992$	−1.12601e9	+	4.26247e8i	−1.15347	+	0.436642i
$993$	2.51664e7	+	2.83830e7i	0.0257024	+	0.0289874i
$994$	6.35689e7	−	7.48682e8i	0.0647270	−	0.762322i
$995$	7.98899e7	−	1.85376e8i	0.0811004	−	0.188185i
$996$	2.25290e8	−	9.64780e8i	0.228016	−	0.976450i
$997$	−6.82326e8	+	6.82326e8i	−0.688504	+	0.688504i	−0.961901	−	0.273397i	$-0.911853\pi$
$997$	−6.82326e8	+	6.82326e8i	−0.688504	+	0.688504i	0.273397	+	0.961901i	$0.411853\pi$
$998$	−8.00495e8	−	9.49044e8i	−0.805317	−	0.954761i
$999$	−1.14526e9	−	2.08385e8i	−1.14871	−	0.209012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.18	yes	136
3.2	odd	2	inner	60.7.l.a.23.51	yes	136
4.3	odd	2	inner	60.7.l.a.23.17	✓	136
5.2	odd	4	inner	60.7.l.a.47.52	yes	136
12.11	even	2	inner	60.7.l.a.23.52	yes	136
15.2	even	4	inner	60.7.l.a.47.17	yes	136
20.7	even	4	inner	60.7.l.a.47.51	yes	136
60.47	odd	4	inner	60.7.l.a.47.18	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.17	✓	136	4.3	odd	2	inner
60.7.l.a.23.18	yes	136	1.1	even	1	trivial
60.7.l.a.23.51	yes	136	3.2	odd	2	inner
60.7.l.a.23.52	yes	136	12.11	even	2	inner
60.7.l.a.47.17	yes	136	15.2	even	4	inner
60.7.l.a.47.18	yes	136	60.47	odd	4	inner
60.7.l.a.47.51	yes	136	20.7	even	4	inner
60.7.l.a.47.52	yes	136	5.2	odd	4	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.15798 - 6.11516i) q^{2} +(-20.2023 + 17.9128i) q^{3} +(-10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(213.743 + 31.1461i) q^{6} +(-261.181 - 261.181i) q^{7} +(441.424 - 259.400i) q^{8} +(87.2628 - 723.758i) q^{9} +O(q^{10})\)	\(q+(-5.15798 - 6.11516i) q^{2} +(-20.2023 + 17.9128i) q^{3} +(-10.7904 + 63.0838i) q^{4} +(49.4715 - 114.794i) q^{5} +(213.743 + 31.1461i) q^{6} +(-261.181 - 261.181i) q^{7} +(441.424 - 259.400i) q^{8} +(87.2628 - 723.758i) q^{9} +(-957.155 + 289.577i) q^{10} -1357.89 q^{11} +(-912.017 - 1467.72i) q^{12} +(2086.27 + 2086.27i) q^{13} +(-249.996 + 2944.33i) q^{14} +(1056.84 + 3205.26i) q^{15} +(-3863.13 - 1361.40i) q^{16} +(204.191 + 204.191i) q^{17} +(-4876.00 + 3199.51i) q^{18} -5303.53 q^{19} +(6707.80 + 4359.52i) q^{20} +(9954.93 + 597.963i) q^{21} +(7003.97 + 8303.71i) q^{22} +(15716.7 + 15716.7i) q^{23} +(-4271.19 + 13147.6i) q^{24} +(-10730.1 - 11358.0i) q^{25} +(1996.93 - 23518.8i) q^{26} +(11201.6 + 16184.7i) q^{27} +(19294.5 - 13658.0i) q^{28} -2104.69 q^{29} +(14149.6 - 22995.4i) q^{30} +36742.8i q^{31} +(11600.8 + 30645.8i) q^{32} +(27432.4 - 24323.6i) q^{33} +(195.447 - 2301.87i) q^{34} +(-42902.9 + 17060.9i) q^{35} +(44715.8 + 13314.5i) q^{36} +(-41818.9 + 41818.9i) q^{37} +(27355.5 + 32431.9i) q^{38} +(-79518.3 - 4776.42i) q^{39} +(-7939.53 - 63505.6i) q^{40} +87984.8i q^{41} +(-47690.7 - 63960.3i) q^{42} +(-71857.2 + 71857.2i) q^{43} +(14652.2 - 85660.8i) q^{44} +(-78765.8 - 45822.7i) q^{45} +(15043.7 - 177177. i) q^{46} +(87772.4 - 87772.4i) q^{47} +(102431. - 41696.2i) q^{48} +18781.9i q^{49} +(-14110.4 + 124201. i) q^{50} +(-7782.75 - 467.487i) q^{51} +(-154121. + 109098. i) q^{52} +(34618.2 - 34618.2i) q^{53} +(41194.1 - 151980. i) q^{54} +(-67176.9 + 155877. i) q^{55} +(-183042. - 47541.2i) q^{56} +(107143. - 95001.1i) q^{57} +(10856.0 + 12870.5i) q^{58} -166041. i q^{59} +(-213604. + 32083.3i) q^{60} +132973. q^{61} +(224688. - 189519. i) q^{62} +(-211823. + 166240. i) q^{63} +(127567. - 229011. i) q^{64} +(342701. - 136279. i) q^{65} +(-290239. - 42293.0i) q^{66} +(50730.4 + 50730.4i) q^{67} +(-15084.4 + 10677.8i) q^{68} +(-599043. - 35982.7i) q^{69} +(325622. + 174359. i) q^{70} -254279. q^{71} +(-149223. - 342121. i) q^{72} +(237265. + 237265. i) q^{73} +(471430. + 40028.1i) q^{74} +(420227. + 37251.2i) q^{75} +(57227.2 - 334567. i) q^{76} +(354655. + 354655. i) q^{77} +(380945. + 510904. i) q^{78} -137456. q^{79} +(-347395. + 376112. i) q^{80} +(-516211. - 126314. i) q^{81} +(538041. - 453824. i) q^{82} +(405414. + 405414. i) q^{83} +(-145139. + 621542. i) q^{84} +(33541.5 - 13338.2i) q^{85} +(810056. + 68780.1i) q^{86} +(42519.5 - 37700.9i) q^{87} +(-599406. + 352237. i) q^{88} -163824. q^{89} +(126060. + 718018. i) q^{90} -1.08979e6i q^{91} +(-1.16106e6 + 821880. i) q^{92} +(-658167. - 742288. i) q^{93} +(-989471. - 84013.8i) q^{94} +(-262374. + 608811. i) q^{95} +(-783314. - 411311. i) q^{96} +(-240019. + 240019. i) q^{97} +(114854. - 96876.7i) q^{98} +(-118493. + 982784. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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