LMFDB - Embedded newform 62.6.g.b.41.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	62.41
Dual form			62.6.g.b.59.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.23607 + 2.35114i) q^{2} +(2.19008 + 20.8372i) q^{3} +(4.94427 + 15.2169i) q^{4} +(6.52504 + 11.3017i) q^{5} +(-41.9041 + 72.5799i) q^{6} +(167.742 + 35.6546i) q^{7} +(-19.7771 + 60.8676i) q^{8} +(-191.705 + 40.7481i) q^{9} +(-5.45642 + 51.9143i) q^{10} +(-232.511 + 258.230i) q^{11} +(-306.250 + 136.351i) q^{12} +(-333.975 - 148.695i) q^{13} +(458.995 + 509.766i) q^{14} +(-221.206 + 160.715i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1336.22 - 1484.02i) q^{17} +(-716.174 - 318.861i) q^{18} +(1299.90 - 578.752i) q^{19} +(-139.715 + 155.170i) q^{20} +(-375.576 + 3573.37i) q^{21} +(-1359.56 + 288.983i) q^{22} +(-526.706 + 1621.04i) q^{23} +(-1311.63 - 278.795i) q^{24} +(1477.35 - 2558.84i) q^{25} +(-731.163 - 1266.41i) q^{26} +(304.384 + 936.799i) q^{27} +(286.808 + 2728.80i) q^{28} +(4916.13 + 3571.78i) q^{29} -1093.70 q^{30} +(5039.89 + 1796.83i) q^{31} -1024.00 q^{32} +(-5890.01 - 4279.35i) q^{33} +(-834.953 - 7944.05i) q^{34} +(691.564 + 2128.42i) q^{35} +(-1567.90 - 2715.68i) q^{36} +(-403.596 + 699.049i) q^{37} +(5567.28 + 1183.36i) q^{38} +(2366.97 - 7284.78i) q^{39} +(-816.954 + 173.649i) q^{40} +(-454.140 + 4320.85i) q^{41} +(-9616.88 + 10680.6i) q^{42} +(2960.01 - 1317.88i) q^{43} +(-5079.05 - 2261.34i) q^{44} +(-1711.40 - 1900.70i) q^{45} +(-5515.74 + 4007.42i) q^{46} +(15530.5 - 11283.6i) q^{47} +(-3589.03 - 3986.02i) q^{48} +(11512.1 + 5125.54i) q^{49} +(10797.0 - 4807.13i) q^{50} +(27996.6 - 31093.3i) q^{51} +(611.419 - 5817.26i) q^{52} +(4019.83 - 854.442i) q^{53} +(-1217.54 + 3747.20i) q^{54} +(-4435.58 - 942.811i) q^{55} +(-5487.66 + 9504.91i) q^{56} +(14906.5 + 25818.8i) q^{57} +(7511.18 + 23117.0i) q^{58} +(-4233.62 - 40280.2i) q^{59} +(-3539.29 - 2571.45i) q^{60} -15350.8 q^{61} +(12084.8 + 17664.2i) q^{62} -33609.8 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-498.691 - 4744.73i) q^{65} +(-8999.14 - 27696.5i) q^{66} +(26598.2 + 46069.5i) q^{67} +(15975.6 - 27670.6i) q^{68} +(-34931.4 - 7424.91i) q^{69} +(-2766.26 + 8513.67i) q^{70} +(-45050.4 + 9575.75i) q^{71} +(1311.12 - 12474.5i) q^{72} +(17390.1 - 19313.7i) q^{73} +(-2949.63 + 1313.26i) q^{74} +(56554.7 + 25179.8i) q^{75} +(15233.9 + 16918.9i) q^{76} +(-48208.9 + 35025.8i) q^{77} +(24787.2 - 18009.0i) q^{78} +(-30142.7 - 33476.9i) q^{79} +(-3051.99 - 1358.83i) q^{80} +(-62361.2 + 27765.0i) q^{81} +(-11628.6 + 12914.8i) q^{82} +(-1454.08 + 13834.7i) q^{83} +(-56232.5 + 11952.6i) q^{84} +(8053.10 - 24784.9i) q^{85} +(12677.3 + 2694.64i) q^{86} +(-63659.3 + 110261. i) q^{87} +(-11119.4 - 19259.4i) q^{88} +(17358.9 + 53425.1i) q^{89} +(-1069.39 - 10174.6i) q^{90} +(-50720.0 - 36850.2i) q^{91} -27271.3 q^{92} +(-26403.3 + 108953. i) q^{93} +76787.2 q^{94} +(15022.8 + 10914.7i) q^{95} +(-2242.65 - 21337.3i) q^{96} +(-189.967 - 584.658i) q^{97} +(25203.2 + 43653.3i) q^{98} +(34051.1 - 58978.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) $ 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	2.19008	+	20.8372i	0.140494	+	1.33671i	0.806708	+	0.590950i	$0.201247\pi$
$3$	2.19008	+	20.8372i	0.140494	+	1.33671i	−0.666214	+	0.745760i	$0.732086\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	6.52504	+	11.3017i	0.116723	+	0.202171i	0.918467	−	0.395497i	$-0.129428\pi$
$5$	6.52504	+	11.3017i	0.116723	+	0.202171i	−0.801744	+	0.597668i	$0.796094\pi$
$6$	−41.9041	+	72.5799i	−0.475202	+	0.823073i
$7$	167.742	+	35.6546i	1.29389	+	0.275024i	0.802885	−	0.596134i	$-0.203297\pi$
$7$	167.742	+	35.6546i	1.29389	+	0.275024i	0.491003	+	0.871158i	$0.336631\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−191.705	+	40.7481i	−0.788908	+	0.167688i
$10$	−5.45642	+	51.9143i	−0.0172547	+	0.164168i
$11$	−232.511	+	258.230i	−0.579378	+	0.643464i	−0.959579	−	0.281440i	$-0.909188\pi$
$11$	−232.511	+	258.230i	−0.579378	+	0.643464i	0.380201	+	0.924904i	$0.375855\pi$
$12$	−306.250	+	136.351i	−0.613936	+	0.273342i
$13$	−333.975	−	148.695i	−0.548095	−	0.244028i	0.113957	−	0.993486i	$-0.463647\pi$
$13$	−333.975	−	148.695i	−0.548095	−	0.244028i	−0.662052	+	0.749458i	$0.730314\pi$
$14$	458.995	+	509.766i	0.625876	+	0.695105i
$15$	−221.206	+	160.715i	−0.253845	+	0.184429i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−1336.22	−	1484.02i	−1.12139	−	1.24543i	−0.966269	−	0.257533i	$-0.917090\pi$
$17$	−1336.22	−	1484.02i	−1.12139	−	1.24543i	−0.155120	−	0.987896i	$-0.549576\pi$
$18$	−716.174	−	318.861i	−0.520999	−	0.231964i
$19$	1299.90	−	578.752i	0.826085	−	0.367797i	0.0502535	−	0.998736i	$-0.483997\pi$
$19$	1299.90	−	578.752i	0.826085	−	0.367797i	0.775832	+	0.630940i	$0.217330\pi$
$20$	−139.715	+	155.170i	−0.0781032	+	0.0867424i
$21$	−375.576	+	3573.37i	−0.185844	+	1.76819i
$22$	−1359.56	+	288.983i	−0.598881	+	0.127296i
$23$	−526.706	+	1621.04i	−0.207610	+	0.638959i	0.791986	+	0.610540i	$0.209047\pi$
$23$	−526.706	+	1621.04i	−0.207610	+	0.638959i	−0.999596	+	0.0284193i	$0.990953\pi$
$24$	−1311.63	−	278.795i	−0.464817	−	0.0988000i
$25$	1477.35	−	2558.84i	0.472751	−	0.818829i
$26$	−731.163	−	1266.41i	−0.212120	−	0.367402i
$27$	304.384	+	936.799i	0.0803550	+	0.247307i
$28$	286.808	+	2728.80i	0.0691348	+	0.657774i
$29$	4916.13	+	3571.78i	1.08550	+	0.788659i	0.978633	−	0.205614i	$-0.0659192\pi$
$29$	4916.13	+	3571.78i	1.08550	+	0.788659i	0.106864	+	0.994274i	$0.465919\pi$
$30$	−1093.70			−0.221869
$31$	5039.89	+	1796.83i	0.941927	+	0.335818i
$31$	5039.89	+	1796.83i	0.941927	+	0.335818i
$32$	−1024.00			−0.176777
$33$	−5890.01	−	4279.35i	−0.941524	−	0.684057i
$34$	−834.953	−	7944.05i	−0.123870	−	1.17854i
$35$	691.564	+	2128.42i	0.0954251	+	0.293688i
$36$	−1567.90	−	2715.68i	−0.201633	−	0.349239i
$37$	−403.596	+	699.049i	−0.0484666	+	0.0839467i	−0.889241	−	0.457439i	$-0.848767\pi$
$37$	−403.596	+	699.049i	−0.0484666	+	0.0839467i	0.840774	+	0.541386i	$0.182100\pi$
$38$	5567.28	+	1183.36i	0.625438	+	0.132941i
$39$	2366.97	−	7284.78i	0.249190	−	0.766929i
$40$	−816.954	+	173.649i	−0.0807323	+	0.0171602i
$41$	−454.140	+	4320.85i	−0.0421920	+	0.401430i	0.952961	+	0.303093i	$0.0980191\pi$
$41$	−454.140	+	4320.85i	−0.0421920	+	0.401430i	−0.995153	+	0.0983375i	$0.968648\pi$
$42$	−9616.88	+	10680.6i	−0.841223	+	0.934272i
$43$	2960.01	−	1317.88i	0.244130	−	0.108694i	−0.281024	−	0.959701i	$-0.590674\pi$
$43$	2960.01	−	1317.88i	0.244130	−	0.108694i	0.525155	+	0.851007i	$0.324008\pi$
$44$	−5079.05	−	2261.34i	−0.395504	−	0.176090i
$45$	−1711.40	−	1900.70i	−0.125986	−	0.139921i
$46$	−5515.74	+	4007.42i	−0.384334	+	0.279235i
$47$	15530.5	−	11283.6i	1.02551	−	0.745080i	0.0581084	−	0.998310i	$-0.481493\pi$
$47$	15530.5	−	11283.6i	1.02551	−	0.745080i	0.967406	+	0.253230i	$0.0814931\pi$
$48$	−3589.03	−	3986.02i	−0.224840	−	0.249710i
$49$	11512.1	+	5125.54i	0.684961	+	0.304964i
$50$	10797.0	−	4807.13i	0.610770	−	0.271932i
$51$	27996.6	−	31093.3i	1.50723	−	1.67395i
$52$	611.419	−	5817.26i	0.0313567	−	0.298339i
$53$	4019.83	−	854.442i	0.196571	−	0.0417824i	−0.108574	−	0.994088i	$-0.534628\pi$
$53$	4019.83	−	854.442i	0.196571	−	0.0417824i	0.305145	+	0.952306i	$0.401295\pi$
$54$	−1217.54	+	3747.20i	−0.0568196	+	0.174873i
$55$	−4435.58	−	942.811i	−0.197717	−	0.0420260i
$56$	−5487.66	+	9504.91i	−0.233839	+	0.405021i
$57$	14906.5	+	25818.8i	0.607698	+	1.05256i
$58$	7511.18	+	23117.0i	0.293183	+	0.902323i
$59$	−4233.62	−	40280.2i	−0.158337	−	1.50647i	−0.728559	−	0.684983i	$-0.759810\pi$
$59$	−4233.62	−	40280.2i	−0.158337	−	1.50647i	0.570223	−	0.821490i	$-0.306857\pi$
$60$	−3539.29	−	2571.45i	−0.126922	−	0.0922146i
$61$	−15350.8			−0.528210			−0.264105	−	0.964494i	$-0.585077\pi$
$61$	−15350.8			−0.528210			−0.264105	+	0.964494i	$0.585077\pi$
$62$	12084.8	+	17664.2i	0.399265	+	0.583599i
$63$	−33609.8			−1.06688
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−498.691	−	4744.73i	−0.0146402	−	0.139293i
$66$	−8999.14	−	27696.5i	−0.254297	−	0.782646i
$67$	26598.2	+	46069.5i	0.723879	+	1.25380i	0.959434	+	0.281934i	$0.0909759\pi$
$67$	26598.2	+	46069.5i	0.723879	+	1.25380i	−0.235555	+	0.971861i	$0.575691\pi$
$68$	15975.6	−	27670.6i	0.418972	−	0.725682i
$69$	−34931.4	−	7424.91i	−0.883271	−	0.187745i
$70$	−2766.26	+	8513.67i	−0.0674757	+	0.207669i
$71$	−45050.4	+	9575.75i	−1.06060	+	0.225438i	−0.705006	−	0.709202i	$-0.749056\pi$
$71$	−45050.4	+	9575.75i	−1.06060	+	0.225438i	−0.355596	+	0.934640i	$0.615722\pi$
$72$	1311.12	−	12474.5i	0.0298065	−	0.283590i
$73$	17390.1	−	19313.7i	0.381941	−	0.424188i	−0.521266	−	0.853394i	$-0.674540\pi$
$73$	17390.1	−	19313.7i	0.381941	−	0.424188i	0.903206	+	0.429206i	$0.141207\pi$
$74$	−2949.63	+	1313.26i	−0.0626164	+	0.0278786i
$75$	56554.7	+	25179.8i	1.16096	+	0.516891i
$76$	15233.9	+	16918.9i	0.302535	+	0.335999i
$77$	−48208.9	+	35025.8i	−0.926618	+	0.673228i
$78$	24787.2	−	18009.0i	0.461308	−	0.335160i
$79$	−30142.7	−	33476.9i	−0.543394	−	0.603500i	0.407428	−	0.913237i	$-0.366426\pi$
$79$	−30142.7	−	33476.9i	−0.543394	−	0.603500i	−0.950822	+	0.309737i	$0.899759\pi$
$80$	−3051.99	−	1358.83i	−0.0533161	−	0.0237378i
$81$	−62361.2	+	27765.0i	−1.05609	+	0.470203i
$82$	−11628.6	+	12914.8i	−0.190982	+	0.212106i
$83$	−1454.08	+	13834.7i	−0.0231683	+	0.220432i	0.976812	+	0.214100i	$0.0686820\pi$
$83$	−1454.08	+	13834.7i	−0.0231683	+	0.220432i	−0.999980	+	0.00633127i	$0.997985\pi$
$84$	−56232.5	+	11952.6i	−0.869540	+	0.184826i
$85$	8053.10	−	24784.9i	0.120897	−	0.372083i
$86$	12677.3	+	2694.64i	0.184833	+	0.0392876i
$87$	−63659.3	+	110261.i	−0.901703	+	1.56180i
$88$	−11119.4	−	19259.4i	−0.153065	−	0.265116i
$89$	17358.9	+	53425.1i	0.232298	+	0.714941i	0.997468	+	0.0711127i	$0.0226550\pi$
$89$	17358.9	+	53425.1i	0.232298	+	0.714941i	−0.765170	+	0.643829i	$0.777345\pi$
$90$	−1069.39	−	10174.6i	−0.0139165	−	0.132406i
$91$	−50720.0	−	36850.2i	−0.642060	−	0.466484i
$92$	−27271.3			−0.335921
$93$	−26403.3	+	108953.i	−0.316556	+	1.30626i
$94$	76787.2			0.896332
$95$	15022.8	+	10914.7i	0.170781	+	0.124080i
$96$	−2242.65	−	21337.3i	−0.0248360	−	0.236299i
$97$	−189.967	−	584.658i	−0.00204998	−	0.00630918i	0.950026	−	0.312170i	$-0.101056\pi$
$97$	−189.967	−	584.658i	−0.00204998	−	0.00630918i	−0.952076	+	0.305861i	$0.901056\pi$
$98$	25203.2	+	43653.3i	0.265089	+	0.459147i
$99$	34051.1	−	58978.2i	0.349175	−	0.604789i
$100$	46242.1	+	9829.05i	0.462421	+	0.0982905i
$101$	−11740.7	+	36134.1i	−0.114522	+	0.352463i	−0.991847	−	0.127434i	$-0.959326\pi$
$101$	−11740.7	+	36134.1i	−0.114522	+	0.352463i	0.877325	+	0.479897i	$0.159326\pi$
$102$	163704.	−	34796.3i	1.55797	−	0.331156i
$103$	−3990.53	+	37967.3i	−0.0370627	+	0.352628i	0.960237	+	0.279187i	$0.0900648\pi$
$103$	−3990.53	+	37967.3i	−0.0370627	+	0.352628i	−0.997300	+	0.0734413i	$0.976602\pi$
$104$	15655.8	−	17387.5i	0.141936	−	0.157636i
$105$	−42835.8	+	19071.7i	−0.379169	+	0.168817i
$106$	15017.4	+	6686.16i	0.129816	+	0.0577979i
$107$	−91456.1	−	101572.i	−0.772242	−	0.857661i	0.220813	−	0.975316i	$-0.429129\pi$
$107$	−91456.1	−	101572.i	−0.772242	−	0.857661i	−0.993055	+	0.117655i	$0.962462\pi$
$108$	−12750.2	+	9263.58i	−0.105186	+	0.0764222i
$109$	166008.	−	120612.i	1.33833	−	0.972355i	0.338828	−	0.940848i	$-0.389970\pi$
$109$	166008.	−	120612.i	1.33833	−	0.972355i	0.999504	−	0.0315061i	$-0.0100304\pi$
$110$	−12137.1	−	13479.7i	−0.0956390	−	0.106218i
$111$	−15450.2	−	6878.86i	−0.119022	−	0.0529919i
$112$	−40105.8	+	17856.3i	−0.302108	+	0.134507i
$113$	162983.	−	181011.i	1.20073	−	1.33355i	0.272223	−	0.962234i	$-0.412241\pi$
$113$	162983.	−	181011.i	1.20073	−	1.33355i	0.928508	−	0.371313i	$-0.121092\pi$
$114$	−12465.2	+	118599.i	−0.0898333	+	0.854707i
$115$	−21757.2	+	4624.64i	−0.153412	+	0.0326087i
$116$	−30044.7	+	92468.1i	−0.207311	+	0.638039i
$117$	70083.7	+	14896.7i	0.473317	+	0.100607i
$118$	81004.1	−	140303.i	0.535552	−	0.927604i
$119$	−171228.	−	296576.i	−1.10843	−	1.91985i
$120$	−5407.56	−	16642.8i	−0.0342806	−	0.105505i
$121$	4213.23	+	40086.2i	0.0261609	+	0.248904i
$122$	−49676.2	−	36091.9i	−0.302168	−	0.219538i
$123$	−91029.3			−0.542523
$124$	−2423.64	+	85575.6i	−0.0141551	+	0.499800i
$125$	79340.5			0.454171
$126$	−108763.	−	79021.3i	−0.610319	−	0.443423i
$127$	−24578.2	−	233846.i	−0.135220	−	1.28653i	−0.826083	−	0.563548i	$-0.809436\pi$
$127$	−24578.2	−	233846.i	−0.135220	−	1.28653i	0.690863	−	0.722986i	$-0.257231\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	33943.6	+	58792.1i	0.179591	+	0.311060i
$130$	9541.73	−	16526.8i	0.0495186	−	0.0857688i
$131$	35479.5	+	7541.40i	0.180634	+	0.0383949i	0.297340	−	0.954772i	$-0.403900\pi$
$131$	35479.5	+	7541.40i	0.180634	+	0.0383949i	−0.116707	+	0.993166i	$0.537234\pi$
$132$	35996.6	−	110786.i	0.179815	−	0.553414i
$133$	238682.	−	50733.5i	1.17001	−	0.248694i
$134$	−22242.2	+	211620.i	−0.107008	+	1.01811i
$135$	−8601.30	+	9552.71i	−0.0406190	+	0.0451120i
$136$	116756.	−	51983.0i	0.541291	−	0.240998i
$137$	−83236.7	−	37059.4i	−0.378890	−	0.168693i	0.208450	−	0.978033i	$-0.433158\pi$
$137$	−83236.7	−	37059.4i	−0.378890	−	0.168693i	−0.587340	+	0.809340i	$0.699825\pi$
$138$	−95583.5	−	106156.i	−0.427253	−	0.474513i
$139$	95169.8	−	69144.9i	0.417794	−	0.303545i	−0.358956	−	0.933355i	$-0.616867\pi$
$139$	95169.8	−	69144.9i	0.417794	−	0.303545i	0.776750	+	0.629810i	$0.216867\pi$
$140$	−28968.6	+	21046.9i	−0.124913	+	0.0907546i
$141$	269132.	+	298902.i	1.14003	+	1.26614i
$142$	−168300.	−	74932.0i	−0.700427	−	0.311850i
$143$	116051.	−	51669.0i	0.474577	−	0.211295i
$144$	33572.1	−	37285.6i	0.134919	−	0.149843i
$145$	−8289.21	+	78866.6i	−0.0327411	+	0.311511i
$146$	101685.	−	21613.8i	0.394797	−	0.0839168i
$147$	−81589.5	+	251107.i	−0.311416	+	0.958440i
$148$	−12632.9	−	2685.20i	−0.0474075	−	0.0100768i
$149$	−251071.	+	434868.i	−0.926470	+	1.60469i	−0.137290	+	0.990531i	$0.543839\pi$
$149$	−251071.	+	434868.i	−0.926470	+	1.60469i	−0.789180	+	0.614162i	$0.789494\pi$
$150$	123814.	+	214452.i	0.449304	+	0.778218i
$151$	−47915.3	−	147468.i	−0.171014	−	0.526327i	0.828415	−	0.560115i	$-0.189243\pi$
$151$	−47915.3	−	147468.i	−0.171014	−	0.526327i	−0.999429	+	0.0337876i	$0.989243\pi$
$152$	9519.04	+	90567.7i	0.0334183	+	0.317954i
$153$	316631.	+	230046.i	1.09352	+	0.794486i
$154$	−238358.			−0.809894
$155$	12578.2	+	68683.8i	0.0420524	+	0.229628i
$156$	122555.			0.403198
$157$	−50293.9	−	36540.6i	−0.162842	−	0.118312i	0.503380	−	0.864065i	$-0.332090\pi$
$157$	−50293.9	−	36540.6i	−0.162842	−	0.118312i	−0.666222	+	0.745754i	$0.732090\pi$
$158$	−18835.0	−	179203.i	−0.0600238	−	0.571089i
$159$	26608.0	+	81891.0i	0.0834679	+	0.256888i
$160$	−6681.64	−	11572.9i	−0.0206340	−	0.0357391i
$161$	−146148.	+	253136.i	−0.444354	+	0.769643i
$162$	−267085.	−	56770.6i	−0.799579	−	0.169956i
$163$	−13464.8	+	41440.3i	−0.0396945	+	0.122167i	−0.968940	−	0.247295i	$-0.920458\pi$
$163$	−13464.8	+	41440.3i	−0.0396945	+	0.122167i	0.929246	+	0.369462i	$0.120458\pi$
$164$	−67995.4	+	14452.9i	−0.197410	+	0.0419609i
$165$	9931.30	−	94490.1i	0.0283986	−	0.270194i
$166$	−37232.8	+	41351.2i	−0.104871	+	0.116471i
$167$	−549097.	+	244474.i	−1.52355	+	0.678330i	−0.986280	−	0.165079i	$-0.947212\pi$
$167$	−549097.	+	244474.i	−1.52355	+	0.678330i	−0.537273	+	0.843408i	$0.680546\pi$
$168$	−210075.	−	93531.2i	−0.574249	−	0.255672i
$169$	−159014.	−	176603.i	−0.428272	−	0.475644i
$170$	84333.2	−	61271.6i	0.223808	−	0.162606i
$171$	−225613.	+	163918.i	−0.590030	+	0.428682i
$172$	34689.1	+	38526.2i	0.0894071	+	0.0992967i
$173$	488123.	+	217326.i	1.23998	+	0.552074i	0.918717	−	0.394916i	$-0.129226\pi$
$173$	488123.	+	217326.i	1.23998	+	0.552074i	0.321262	+	0.946990i	$0.395893\pi$
$174$	−465245.	+	207141.i	−1.16495	+	0.518671i
$175$	339048.	−	376551.i	0.836885	−	0.929455i
$176$	9298.38	−	88468.2i	0.0226269	−	0.215281i
$177$	830056.	−	176434.i	1.99147	−	0.423301i
$178$	−69435.5	+	213700.i	−0.164260	+	0.505540i
$179$	−374612.	−	79626.3i	−0.873876	−	0.185748i	−0.250922	−	0.968007i	$-0.580734\pi$
$179$	−374612.	−	79626.3i	−0.873876	−	0.185748i	−0.622953	+	0.782259i	$0.714067\pi$
$180$	20461.2	−	35439.8i	0.0470706	−	0.0815287i
$181$	−404943.	−	701382.i	−0.918751	−	1.59132i	−0.801315	−	0.598243i	$-0.795866\pi$
$181$	−404943.	−	701382.i	−0.918751	−	1.59132i	−0.117436	−	0.993080i	$-0.537467\pi$
$182$	−77493.2	−	238500.i	−0.173414	−	0.533715i
$183$	−33619.5	−	319869.i	−0.0742103	−	0.706064i
$184$	−88251.8	−	64118.7i	−0.192167	−	0.139618i
$185$	−10533.9			−0.0226288
$186$	−341606.	+	290501.i	−0.724008	+	0.615694i
$187$	693906.			1.45110
$188$	248489.	+	180538.i	0.512757	+	0.372540i
$189$	17656.8	+	167993.i	0.0359548	+	0.342088i
$190$	22952.7	+	70641.2i	0.0461265	+	0.141963i
$191$	−492534.	−	853094.i	−0.976907	−	1.69205i	−0.673494	−	0.739192i	$-0.735207\pi$
$191$	−492534.	−	853094.i	−0.976907	−	1.69205i	−0.303412	−	0.952859i	$-0.598126\pi$
$192$	42909.8	−	74321.9i	0.0840046	−	0.145500i
$193$	−871688.	−	185283.i	−1.68449	−	0.358049i	−0.736519	−	0.676417i	$-0.763532\pi$
$193$	−871688.	−	185283.i	−1.68449	−	0.358049i	−0.947967	+	0.318368i	$0.896865\pi$
$194$	759.868	−	2338.63i	0.00144955	−	0.00446126i
$195$	97774.9	−	20782.7i	0.184137	−	0.0391395i
$196$	−21075.6	+	200521.i	−0.0391869	+	0.372838i
$197$	−278939.	+	309793.i	−0.512086	+	0.568729i	−0.942630	−	0.333841i	$-0.891655\pi$
$197$	−278939.	+	309793.i	−0.512086	+	0.568729i	0.430543	+	0.902570i	$0.358322\pi$
$198$	248858.	−	110799.i	0.451116	−	0.200850i
$199$	586158.	+	260974.i	1.04926	+	0.467159i	0.857608	−	0.514304i	$-0.171950\pi$
$199$	586158.	+	260974.i	1.04926	+	0.467159i	0.191649	+	0.981463i	$0.438616\pi$
$200$	126533.	+	140529.i	0.223681	+	0.248423i
$201$	−901709.	+	655130.i	−1.57426	+	1.14377i
$202$	−122950.	+	89328.4i	−0.212007	+	0.154032i
$203$	697291.	+	774420.i	1.18761	+	1.31897i
$204$	611567.	+	272287.i	1.02889	+	0.458091i
$205$	−51796.2	+	23061.2i	−0.0860823	+	0.0383263i
$206$	−102180.	+	113483.i	−0.167764	+	0.186321i
$207$	34918.0	−	332222.i	0.0566400	−	0.538893i
$208$	91543.7	−	19458.2i	0.146714	−	0.0311849i
$209$	−152790.	+	470238.i	−0.241951	+	0.744650i
$210$	−183460.	−	38995.6i	−0.287073	−	0.0610193i
$211$	423942.	−	734289.i	0.655541	−	1.13543i	−0.326217	−	0.945295i	$-0.605774\pi$
$211$	423942.	−	734289.i	0.655541	−	1.13543i	0.981758	−	0.190136i	$-0.0608928\pi$
$212$	32877.1	+	56944.8i	0.0502405	+	0.0870191i
$213$	−298196.	−	917754.i	−0.450353	−	1.38604i
$214$	−57147.4	−	543721.i	−0.0853025	−	0.811599i
$215$	34208.4	+	24853.9i	0.0504704	+	0.0366689i
$216$	−63040.6			−0.0919360
$217$	781336.	+	481100.i	1.12639	+	0.693563i
$218$	820790.			1.16974
$219$	440530.	+	320064.i	0.620677	+	0.450948i
$220$	−7584.03	−	72157.3i	−0.0105644	−	0.100513i
$221$	225597.	+	694318.i	0.310709	+	0.956263i
$222$	−33824.7	−	58586.0i	−0.0460629	−	0.0797832i
$223$	626453.	−	1.08505e6i	0.843581	−	1.46112i	−0.0432673	−	0.999064i	$-0.513777\pi$
$223$	626453.	−	1.08505e6i	0.843581	−	1.46112i	0.886848	−	0.462061i	$-0.152890\pi$
$224$	−171768.	−	36510.4i	−0.228729	−	0.0486179i
$225$	−178947.	+	550741.i	−0.235650	+	0.725255i
$226$	953005.	−	202568.i	1.24115	−	0.263815i
$227$	−118782.	+	1.13013e6i	−0.152998	+	1.45568i	0.601236	+	0.799071i	$0.294675\pi$
$227$	−118782.	+	1.13013e6i	−0.152998	+	1.45568i	−0.754234	+	0.656606i	$0.771992\pi$
$228$	−319180.	+	354485.i	−0.406629	+	0.451608i
$229$	458434.	−	204108.i	0.577681	−	0.257200i	−0.0970311	−	0.995281i	$-0.530935\pi$
$229$	458434.	−	204108.i	0.577681	−	0.257200i	0.674712	+	0.738081i	$0.264268\pi$
$230$	−81281.0	−	36188.7i	−0.101314	−	0.0451079i
$231$	−835424.	−	927832.i	−1.03009	−	1.14404i
$232$	−314632.	+	228594.i	−0.383781	+	0.278833i
$233$	−476372.	+	346104.i	−0.574852	+	0.417654i	−0.836865	−	0.547410i	$-0.815614\pi$
$233$	−476372.	+	346104.i	−0.574852	+	0.417654i	0.262013	+	0.965064i	$0.415614\pi$
$234$	191771.	+	212983.i	0.228952	+	0.254276i
$235$	228861.	+	101896.i	0.270335	+	0.120361i
$236$	592007.	−	263579.i	0.691906	−	0.308056i
$237$	631552.	−	701409.i	0.730362	−	0.811149i
$238$	143186.	−	1.36232e6i	0.163854	−	1.55897i
$239$	−1.30441e6	+	277260.i	−1.47713	+	0.313974i	−0.874882	−	0.484336i	$-0.839061\pi$
$239$	−1.30441e6	+	277260.i	−1.47713	+	0.313974i	−0.602247	+	0.798309i	$0.705728\pi$
$240$	21630.2	−	66571.0i	0.0242400	−	0.0746032i
$241$	−83168.2	−	17678.0i	−0.0922390	−	0.0196060i	0.161561	−	0.986863i	$-0.448347\pi$
$241$	−83168.2	−	17678.0i	−0.0922390	−	0.0196060i	−0.253800	+	0.967257i	$0.581680\pi$
$242$	−80614.1	+	139628.i	−0.0884856	+	0.153261i
$243$	−595444.	−	1.03134e6i	−0.646882	−	1.12043i
$244$	−75898.5	−	233592.i	−0.0816129	−	0.251179i
$245$	17189.9	+	163551.i	0.0182961	+	0.174076i
$246$	−294577.	−	214023.i	−0.310357	−	0.225487i
$247$	−520191.			−0.542526
$248$	−209043.	+	271230.i	−0.215828	+	0.280033i
$249$	−291461.			−0.297908
$250$	256751.	+	186541.i	0.259814	+	0.188766i
$251$	8436.08	+	80264.0i	0.00845194	+	0.0804149i	0.997935	−	0.0642356i	$-0.0204609\pi$
$251$	8436.08	+	80264.0i	0.00845194	+	0.0804149i	−0.989483	+	0.144650i	$0.953794\pi$
$252$	−166176.	−	511437.i	−0.164841	−	0.507330i
$253$	−296134.	−	512920.i	−0.290862	−	0.503788i
$254$	470269.	−	814530.i	0.457364	−	0.792178i
$255$	534086.	+	113523.i	0.514352	+	0.109329i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	661751.	−	140659.i	0.624974	−	0.132842i	0.115470	−	0.993311i	$-0.463163\pi$
$257$	661751.	−	140659.i	0.624974	−	0.132842i	0.509503	+	0.860469i	$0.329829\pi$
$258$	−28384.6	+	270062.i	−0.0265481	+	0.252588i
$259$	−92624.4	+	102870.i	−0.0857978	+	0.0952881i
$260$	69734.4	−	31047.8i	0.0639755	−	0.0284837i
$261$	−1.08799e6	−	484404.i	−0.988605	−	0.440155i
$262$	97083.1	+	107822.i	0.0873757	+	0.0970405i
$263$	1.26833e6	−	921497.i	1.13069	−	0.821495i	0.144895	−	0.989447i	$-0.453716\pi$
$263$	1.26833e6	−	921497.i	1.13069	−	0.821495i	0.985795	+	0.167952i	$0.0537155\pi$
$264$	376961.	−	273878.i	0.332879	−	0.241851i
$265$	35886.2	+	39855.7i	0.0313916	+	0.0348639i
$266$	891674.	+	396999.i	0.772684	+	0.344021i
$267$	−1.07521e6	+	478716.i	−0.923033	+	0.410961i
$268$	−569526.	+	632523.i	−0.484370	+	0.537947i
$269$	−37683.5	+	358534.i	−0.0317519	+	0.302100i	0.967108	+	0.254366i	$0.0818667\pi$
$269$	−37683.5	+	358534.i	−0.0317519	+	0.302100i	−0.998860	+	0.0477340i	$0.984800\pi$
$270$	−50294.2	+	10690.4i	−0.0419863	+	0.00892447i
$271$	−290633.	+	894476.i	−0.240393	+	0.739853i	0.755967	+	0.654609i	$0.227167\pi$
$271$	−290633.	+	894476.i	−0.240393	+	0.739853i	−0.996360	+	0.0852437i	$0.972833\pi$
$272$	500048.	+	106289.i	0.409817	+	0.0871093i
$273$	656776.	−	1.13757e6i	0.533348	−	0.923786i
$274$	−182228.	−	315628.i	−0.146635	−	0.253980i
$275$	317269.	+	976454.i	0.252986	+	0.778610i
$276$	−59726.5	−	568259.i	−0.0471948	−	0.449028i
$277$	1.46444e6	+	1.06398e6i	1.14676	+	0.833167i	0.988046	−	0.154158i	$-0.0492665\pi$
$277$	1.46444e6	+	1.06398e6i	1.14676	+	0.833167i	0.158710	+	0.987325i	$0.449266\pi$
$278$	470545.			0.365165
$279$	−1.03939e6	−	139095.i	−0.799406	−	0.106980i
$280$	−143229.			−0.109178
$281$	−1.91445e6	−	1.39093e6i	−1.44637	−	1.05085i	−0.986664	−	0.162773i	$-0.947956\pi$
$281$	−1.91445e6	−	1.39093e6i	−1.44637	−	1.05085i	−0.459702	−	0.888073i	$-0.652044\pi$
$282$	168170.	+	1.60003e6i	0.125929	+	1.19814i
$283$	713927.	+	2.19724e6i	0.529892	+	1.63084i	0.754434	+	0.656376i	$0.227911\pi$
$283$	713927.	+	2.19724e6i	0.529892	+	1.63084i	−0.224542	+	0.974464i	$0.572089\pi$
$284$	−368454.	−	638182.i	−0.271074	−	0.469514i
$285$	−194531.	+	336937.i	−0.141865	+	0.245718i
$286$	497028.	+	105647.i	0.359307	+	0.0763731i
$287$	−230237.	+	708596.i	−0.164995	+	0.507801i
$288$	196306.	−	41726.0i	0.139461	−	0.0296433i
$289$	−268425.	+	2.55389e6i	−0.189051	+	1.79870i
$290$	−212251.	+	235729.i	−0.148202	+	0.164595i
$291$	11766.6	−	5238.84i	0.00814554	−	0.00362663i
$292$	379876.	+	169132.i	0.260726	+	0.116083i
$293$	−369360.	−	410216.i	−0.251351	−	0.279154i	0.604244	−	0.796799i	$-0.293475\pi$
$293$	−369360.	−	410216.i	−0.251351	−	0.279154i	−0.855595	+	0.517645i	$0.826809\pi$
$294$	−854417.	+	620770.i	−0.576503	+	0.418854i
$295$	427610.	−	310677.i	0.286083	−	0.207852i
$296$	−34567.5	−	38391.1i	−0.0229318	−	0.0254684i
$297$	−312682.	−	139215.i	−0.205689	−	0.0915788i
$298$	−1.83492e6	+	816959.i	−1.19695	+	0.532917i
$299$	416947.	−	463067.i	0.269714	−	0.299548i
$300$	−103536.	+	985084.i	−0.0664187	+	0.631931i
$301$	543506.	−	115526.i	0.345770	−	0.0734958i
$302$	191661.	−	589873.i	0.120925	−	0.372170i
$303$	−778648.	−	165507.i	−0.487231	−	0.103564i
$304$	−182133.	+	315464.i	−0.113033	+	0.195779i
$305$	−100165.	−	173490.i	−0.0616545	−	0.106789i
$306$	483769.	+	1.48889e6i	0.295348	+	0.908989i
$307$	−149505.	−	1.42244e6i	−0.0905334	−	0.861368i	−0.941696	−	0.336465i	$-0.890769\pi$
$307$	−149505.	−	1.42244e6i	−0.0905334	−	0.861368i	0.851162	−	0.524902i	$-0.175898\pi$
$308$	−771343.	−	560414.i	−0.463309	−	0.336614i
$309$	−799874.			−0.476569
$310$	−120781.	+	251839.i	−0.0713831	+	0.148839i
$311$	−518938.			−0.304239			−0.152119	−	0.988362i	$-0.548610\pi$
$311$	−518938.			−0.304239			−0.152119	+	0.988362i	$0.548610\pi$
$312$	396596.	+	288144.i	0.230654	+	0.167580i
$313$	−254943.	−	2.42563e6i	−0.147090	−	1.39947i	−0.780260	−	0.625455i	$-0.784913\pi$
$313$	−254943.	−	2.42563e6i	−0.147090	−	1.39947i	0.633170	−	0.774013i	$-0.281753\pi$
$314$	−76842.2	−	236496.i	−0.0439821	−	0.135363i
$315$	−219305.	−	379847.i	−0.124529	−	0.215691i
$316$	360381.	−	624198.i	0.203022	−	0.351645i
$317$	164707.	+	35009.6i	0.0920585	+	0.0195676i	0.253711	−	0.967280i	$-0.418349\pi$
$317$	164707.	+	35009.6i	0.0920585	+	0.0195676i	−0.161652	+	0.986848i	$0.551682\pi$
$318$	−106432.	+	327564.i	−0.0590207	+	0.181647i
$319$	−2.06539e6	+	439013.i	−1.13639	+	0.241547i
$320$	5587.37	−	53160.3i	0.00305023	−	0.0290210i
$321$	1.91619e6	−	2.12814e6i	1.03795	−	1.15276i
$322$	−1.06810e6	+	475551.i	−0.574082	+	0.255598i
$323$	−2.59583e6	−	1.15574e6i	−1.38443	−	0.616387i
$324$	−730828.	−	811667.i	−0.386770	−	0.429552i
$325$	−873885.	+	634915.i	−0.458930	+	0.333432i
$326$	−141005.	+	102446.i	−0.0734836	+	0.0533889i
$327$	2.87680e6	+	3.19501e6i	1.48778	+	1.65235i
$328$	−254018.	−	113096.i	−0.130371	−	0.0580449i
$329$	3.00743e6	−	1.33900e6i	1.53182	−	0.682008i
$330$	254298.	−	282426.i	0.128546	−	0.142765i
$331$	−156706.	+	1.49096e6i	−0.0786168	+	0.747989i	0.882213	+	0.470850i	$0.156053\pi$
$331$	−156706.	+	1.49096e6i	−0.0786168	+	0.747989i	−0.960830	+	0.277138i	$0.910614\pi$
$332$	−217710.	+	46275.8i	−0.108401	+	0.0230414i
$333$	48886.4	−	150457.i	0.0241589	−	0.0743535i
$334$	−2.35171e6	−	499871.i	−1.15350	−	0.245184i
$335$	−347109.	+	601210.i	−0.168987	+	0.292694i
$336$	−459910.	−	796588.i	−0.222241	−	0.384933i
$337$	1.17524e6	+	3.61702e6i	0.563705	+	1.73490i	0.671769	+	0.740761i	$0.265535\pi$
$337$	1.17524e6	+	3.61702e6i	0.563705	+	1.73490i	−0.108064	+	0.994144i	$0.534465\pi$
$338$	−99361.9	−	945366.i	−0.0473073	−	0.450099i
$339$	4.12871e6	+	2.99969e6i	1.95126	+	1.41767i
$340$	416966.			0.195616
$341$	−1.63583e6	+	883667.i	−0.761818	+	0.411531i
$342$	−1.11549e6			−0.515705
$343$	−583446.	−	423899.i	−0.267772	−	0.194548i
$344$	21675.9	+	206232.i	0.00987599	+	0.0939638i
$345$	−144015.	−	443232.i	−0.0651418	−	0.200486i
$346$	1.06863e6	+	1.85093e6i	0.479887	+	0.831189i
$347$	1.35482e6	−	2.34662e6i	0.604030	−	1.04621i	−0.388174	−	0.921586i	$-0.626894\pi$
$347$	1.35482e6	−	2.34662e6i	0.604030	−	1.04621i	0.992204	−	0.124624i	$-0.0397725\pi$
$348$	−1.99258e6	−	423536.i	−0.881999	−	0.187475i
$349$	1.14629e6	−	3.52792e6i	0.503769	−	1.55044i	−0.299061	−	0.954234i	$-0.596674\pi$
$349$	1.14629e6	−	3.52792e6i	0.503769	−	1.55044i	0.802830	−	0.596207i	$-0.203326\pi$
$350$	1.98251e6	−	421395.i	0.865056	−	0.183873i
$351$	37640.8	−	358128.i	0.0163076	−	0.155157i
$352$	238091.	−	264427.i	0.102421	−	0.113749i
$353$	−3.01994e6	+	1.34457e6i	−1.28992	+	0.574308i	−0.933017	−	0.359834i	$-0.882833\pi$
$353$	−3.01994e6	+	1.34457e6i	−1.28992	+	0.574308i	−0.356901	+	0.934142i	$0.616167\pi$
$354$	3.10094e6	+	1.38063e6i	1.31518	+	0.585556i
$355$	−402177.	−	446663.i	−0.169374	−	0.188109i
$356$	−727138.	+	528296.i	−0.304083	+	0.220929i
$357$	5.80482e6	−	4.21745e6i	2.41056	−	1.75138i
$358$	−1.02506e6	−	1.13844e6i	−0.422709	−	0.469465i
$359$	2.33677e6	+	1.04040e6i	0.956928	+	0.426052i	0.824953	−	0.565201i	$-0.191201\pi$
$359$	2.33677e6	+	1.04040e6i	0.956928	+	0.426052i	0.131975	+	0.991253i	$0.457868\pi$
$360$	149538.	−	66578.6i	0.0608128	−	0.0270756i
$361$	−302054.	+	335465.i	−0.121988	+	0.135481i
$362$	338625.	−	3.22180e6i	0.135815	−	1.29219i
$363$	−826059.	+	175584.i	−0.329037	+	0.0699390i
$364$	309973.	−	953999.i	0.122623	−	0.377393i
$365$	331749.	+	70515.4i	0.130340	+	0.0277046i
$366$	643261.	−	1.11416e6i	0.251006	−	0.434755i
$367$	504476.	+	873779.i	0.195513	+	0.338638i	0.947069	−	0.321031i	$-0.104029\pi$
$367$	504476.	+	873779.i	0.195513	+	0.338638i	−0.751556	+	0.659670i	$0.770696\pi$
$368$	−134837.	−	414985.i	−0.0519026	−	0.159740i
$369$	−89005.7	−	846833.i	−0.0340292	−	0.323766i
$370$	−34088.5	−	24766.7i	−0.0129450	−	0.00940513i
$371$	704760.			0.265831
$372$	−1.78847e6	+	136916.i	−0.670076	+	0.0512975i
$373$	−3.21299e6			−1.19574			−0.597870	−	0.801593i	$-0.703986\pi$
$373$	−3.21299e6			−1.19574			−0.597870	+	0.801593i	$0.703986\pi$
$374$	2.24553e6	+	1.63147e6i	0.830117	+	0.603115i
$375$	173762.	+	1.65324e6i	0.0638083	+	0.607096i
$376$	379657.	+	1.16846e6i	0.138491	+	0.426231i
$377$	−1.11076e6	−	1.92389e6i	−0.402501	−	0.697152i
$378$	−337837.	+	585151.i	−0.121612	+	0.210639i
$379$	924297.	+	196465.i	0.330532	+	0.0702568i	0.370189	−	0.928957i	$-0.379293\pi$
$379$	924297.	+	196465.i	0.330532	+	0.0702568i	−0.0396565	+	0.999213i	$0.512626\pi$
$380$	−91810.9	+	282565.i	−0.0326163	+	0.100383i
$381$	4.81889e6	−	1.02429e6i	1.70073	−	0.361500i
$382$	411871.	−	3.91869e6i	0.144412	−	1.37399i
$383$	494139.	−	548797.i	0.172128	−	0.191168i	−0.650908	−	0.759157i	$-0.725612\pi$
$383$	494139.	−	548797.i	0.172128	−	0.191168i	0.823036	+	0.567989i	$0.192278\pi$
$384$	313600.	−	139624.i	0.108530	−	0.0483205i
$385$	−710417.	−	316298.i	−0.244265	−	0.108754i
$386$	−2.38521e6	−	2.64905e6i	−0.814815	−	0.904944i
$387$	−513746.	+	373258.i	−0.174370	+	0.126687i
$388$	7957.44	−	5781.42i	0.00268345	−	0.00194964i
$389$	−1.35224e6	−	1.50181e6i	−0.453085	−	0.503202i	0.472715	−	0.881215i	$-0.343274\pi$
$389$	−1.35224e6	−	1.50181e6i	−0.453085	−	0.503202i	−0.925800	+	0.378013i	$0.876607\pi$
$390$	365269.	+	162628.i	0.121605	+	0.0541421i
$391$	3.10945e6	−	1.38442e6i	1.02859	−	0.457958i
$392$	−539656.	+	599349.i	−0.177379	+	0.196999i
$393$	−79438.9	+	755811.i	−0.0259449	+	0.246849i
$394$	−1.63103e6	+	346686.i	−0.529324	+	0.112511i
$395$	181663.	−	559102.i	0.0585834	−	0.180301i
$396$	1.06582e6	+	226548.i	0.341545	+	0.0725975i
$397$	1.21595e6	−	2.10609e6i	0.387204	−	0.670658i	−0.604868	−	0.796326i	$-0.706774\pi$
$397$	1.21595e6	−	2.10609e6i	0.387204	−	0.670658i	0.992072	+	0.125668i	$0.0401074\pi$
$398$	1.28326e6	+	2.22267e6i	0.406076	+	0.703343i
$399$	1.57988e6	+	4.86238e6i	0.496812	+	1.52903i
$400$	79065.5	+	752258.i	0.0247080	+	0.235081i
$401$	−1.06676e6	−	775043.i	−0.331287	−	0.240694i	0.409690	−	0.912225i	$-0.365637\pi$
$401$	−1.06676e6	−	775043.i	−0.331287	−	0.240694i	−0.740976	+	0.671531i	$0.765637\pi$
$402$	−4.45830e6			−1.37595
$403$	−1.41602e6	−	1.34951e6i	−0.434317	−	0.413916i
$404$	−607898.			−0.185301
$405$	−720701.	−	523620.i	−0.218332	−	0.158628i
$406$	435710.	+	4.14550e6i	0.131185	+	1.24814i
$407$	−86674.7	−	266757.i	−0.0259362	−	0.0798234i
$408$	1.33889e6	+	2.31902e6i	0.398193	+	0.689690i
$409$	−2.57112e6	+	4.45331e6i	−0.760001	+	1.31636i	0.182849	+	0.983141i	$0.441468\pi$
$409$	−2.57112e6	+	4.45331e6i	−0.760001	+	1.31636i	−0.942849	+	0.333219i	$0.891865\pi$
$410$	−221836.	−	47152.7i	−0.0651738	−	0.0138531i
$411$	589920.	−	1.81559e6i	0.172262	−	0.530167i
$412$	−597475.	+	126997.i	−0.173411	+	0.0368597i
$413$	726020.	−	6.90762e6i	0.209447	−	1.99275i
$414$	894098.	−	992997.i	0.256380	−	0.284739i
$415$	−165843.	+	73838.2i	−0.0472692	+	0.0210456i
$416$	341991.	+	152264.i	0.0968904	+	0.0431384i
$417$	1.64922e6	+	1.83164e6i	0.464449	+	0.515823i
$418$	−1.60003e6	+	1.16249e6i	−0.447908	+	0.325424i
$419$	−345983.	+	251372.i	−0.0962765	+	0.0699490i	−0.634882	−	0.772609i	$-0.718951\pi$
$419$	−345983.	+	251372.i	−0.0962765	+	0.0699490i	0.538606	+	0.842558i	$0.318951\pi$
$420$	−502004.	−	557532.i	−0.138862	−	0.154222i
$421$	−2.89717e6	−	1.28990e6i	−0.796652	−	0.354692i	−0.0322889	−	0.999479i	$-0.510280\pi$
$421$	−2.89717e6	−	1.28990e6i	−0.796652	−	0.354692i	−0.764363	+	0.644786i	$0.776946\pi$
$422$	3.09832e6	−	1.37946e6i	0.846926	−	0.377076i
$423$	−2.51749e6	+	2.79596e6i	−0.684096	+	0.759765i
$424$	−27492.8	+	261576.i	−0.00742683	+	0.0706616i
$425$	−5.77145e6	+	1.22676e6i	−1.54993	+	0.329448i
$426$	1.19279e6	−	3.67102e6i	0.318448	−	0.980082i
$427$	−2.57497e6	−	547328.i	−0.683444	−	0.145271i
$428$	1.09343e6	−	1.89388e6i	0.288524	−	0.499739i
$429$	1.33080e6	+	2.30501e6i	0.349116	+	0.604687i
$430$	52265.8	+	160858.i	0.0136316	+	0.0419537i
$431$	251957.	+	2.39721e6i	0.0653331	+	0.621603i	0.977376	+	0.211508i	$0.0678376\pi$
$431$	251957.	+	2.39721e6i	0.0653331	+	0.621603i	−0.912043	+	0.410094i	$0.865496\pi$
$432$	−204004.	−	148217.i	−0.0525930	−	0.0382111i
$433$	−3.13649e6			−0.803942			−0.401971	−	0.915652i	$-0.631675\pi$
$433$	−3.13649e6			−0.803942			−0.401971	+	0.915652i	$0.631675\pi$
$434$	1.39732e6	+	3.39390e6i	0.356100	+	0.864919i
$435$	−1.66152e6			−0.421000
$436$	2.65613e6	+	1.92979e6i	0.669166	+	0.486177i
$437$	253513.	+	2.41201e6i	0.0635032	+	0.604193i
$438$	673070.	+	2.07150e6i	0.167639	+	0.515940i
$439$	1.48372e6	+	2.56987e6i	0.367443	+	0.636429i	0.989165	−	0.146808i	$-0.0469001\pi$
$439$	1.48372e6	+	2.56987e6i	0.367443	+	0.636429i	−0.621722	+	0.783238i	$0.713567\pi$
$440$	145109.	−	251337.i	0.0357325	−	0.0618906i
$441$	−2.41579e6	−	513491.i	−0.591510	−	0.125729i
$442$	−902390.	+	2.77727e6i	−0.219704	+	0.676180i
$443$	3.08641e6	−	656036.i	0.747213	−	0.158825i	0.181458	−	0.983399i	$-0.441918\pi$
$443$	3.08641e6	−	656036.i	0.747213	−	0.158825i	0.565754	+	0.824574i	$0.308585\pi$
$444$	28285.1	−	269115.i	0.00680927	−	0.0647859i
$445$	−490527.	+	544785.i	−0.117426	+	0.130414i
$446$	4.57835e6	−	2.03841e6i	1.08986	−	0.485238i
$447$	−9.61132e6	−	4.27924e6i	−2.27517	−	1.01297i
$448$	−470011.	−	522000.i	−0.110640	−	0.122878i
$449$	−1.79156e6	+	1.30165e6i	−0.419388	+	0.304703i	−0.777392	−	0.629017i	$-0.783458\pi$
$449$	−1.79156e6	+	1.30165e6i	−0.419388	+	0.304703i	0.358003	+	0.933720i	$0.383458\pi$
$450$	−1.87395e6	+	1.36151e6i	−0.436242	+	0.316948i
$451$	−1.01018e6	−	1.12192e6i	−0.233861	−	0.259729i
$452$	3.56026e6	+	1.58513e6i	0.819662	+	0.364937i
$453$	2.96789e6	−	1.32139e6i	0.679521	−	0.302542i
$454$	−3.04149e6	+	3.37792e6i	−0.692543	+	0.769147i
$455$	85520.2	−	813671.i	0.0193660	−	0.184255i
$456$	−1.86633e6	+	396701.i	−0.420317	+	0.0893412i
$457$	−2.31868e6	+	7.13618e6i	−0.519339	+	1.59836i	0.255906	+	0.966702i	$0.417626\pi$
$457$	−2.31868e6	+	7.13618e6i	−0.519339	+	1.59836i	−0.775245	+	0.631660i	$0.782374\pi$
$458$	1.96341e6	+	417335.i	0.437368	+	0.0929655i
$459$	983508.	−	1.70349e6i	0.217894	−	0.377404i
$460$	−177946.	−	308212.i	−0.0392098	−	0.0679134i
$461$	666470.	+	2.05118e6i	0.146059	+	0.449523i	0.997146	−	0.0755020i	$-0.0240559\pi$
$461$	666470.	+	2.05118e6i	0.146059	+	0.449523i	−0.851087	+	0.525025i	$0.824056\pi$
$462$	−522024.	−	4.96673e6i	−0.113785	−	1.08259i
$463$	4.51483e6	+	3.28022e6i	0.978789	+	0.711132i	0.957438	−	0.288640i	$-0.0932032\pi$
$463$	4.51483e6	+	3.28022e6i	0.978789	+	0.711132i	0.0213512	+	0.999772i	$0.493203\pi$
$464$	−1.55563e6			−0.335437
$465$	−1.40363e6	+	412519.i	−0.301038	+	0.0884731i
$466$	−2.35531e6			−0.502439
$467$	−241787.	−	175669.i	−0.0513028	−	0.0372737i	0.561838	−	0.827247i	$-0.310094\pi$
$467$	−241787.	−	175669.i	−0.0513028	−	0.0372737i	−0.613141	+	0.789973i	$0.710094\pi$
$468$	119830.	+	1.14011e6i	0.0252902	+	0.240620i
$469$	2.81905e6	+	8.67614e6i	0.591794	+	1.82135i
$470$	501039.	+	867825.i	0.104623	+	0.181212i
$471$	651259.	−	1.12801e6i	0.135270	−	0.234294i
$472$	2.53549e6	+	538934.i	0.523849	+	0.111348i
$473$	−347918.	+	1.07078e6i	−0.0715030	+	0.220064i
$474$	3.69286e6	−	784941.i	0.754947	−	0.160469i
$475$	439467.	−	4.18125e6i	0.0893701	−	0.850299i
$476$	3.66637e6	−	4.07191e6i	0.741683	−	0.823723i
$477$	−735804.	+	327601.i	−0.148070	+	0.0659249i
$478$	−4.87303e6	−	2.16961e6i	−0.975505	−	0.434323i
$479$	4.82472e6	+	5.35840e6i	0.960802	+	1.06708i	0.997702	+	0.0677592i	$0.0215850\pi$
$479$	4.82472e6	+	5.35840e6i	0.960802	+	1.06708i	−0.0369002	+	0.999319i	$0.511748\pi$
$480$	226515.	−	164573.i	0.0448739	−	0.0326028i
$481$	238737.	−	173452.i	0.0470496	−	0.0341836i
$482$	−227575.	−	252747.i	−0.0446176	−	0.0495529i
$483$	−5.59474e6	−	2.49094e6i	−1.09122	−	0.485842i
$484$	−589157.	+	262310.i	−0.114319	+	0.0508980i
$485$	5368.09	−	5961.87i	0.00103625	−	0.00115087i
$486$	497927.	−	4.73746e6i	0.0956258	−	0.909818i
$487$	5.31586e6	−	1.12992e6i	1.01567	−	0.215886i	0.330138	−	0.943933i	$-0.392905\pi$
$487$	5.31586e6	−	1.12992e6i	1.01567	−	0.215886i	0.685528	+	0.728046i	$0.259571\pi$
$488$	303594.	−	934367.i	0.0577090	−	0.177610i
$489$	−892991.	−	189811.i	−0.168879	−	0.0358963i
$490$	−328904.	+	569678.i	−0.0618841	+	0.107186i
$491$	753813.	+	1.30564e6i	0.141111	+	0.244411i	0.927915	−	0.372791i	$-0.121599\pi$
$491$	753813.	+	1.30564e6i	0.141111	+	0.244411i	−0.786804	+	0.617202i	$0.788266\pi$
$492$	−450074.	−	1.38518e6i	−0.0838245	−	0.257985i
$493$	−1.26843e6	−	1.20684e7i	−0.235045	−	2.23630i
$494$	−1.68337e6	−	1.22304e6i	−0.310358	−	0.225488i
$495$	888738.			0.163028
$496$	−1.31418e6	+	386229.i	−0.239856	+	0.0704921i
$497$	−7.89825e6			−1.43430
$498$	−943189.	−	685267.i	−0.170422	−	0.123819i
$499$	642058.	+	6.10878e6i	0.115431	+	1.09825i	0.886892	+	0.461977i	$0.152860\pi$
$499$	642058.	+	6.10878e6i	0.115431	+	1.09825i	−0.771461	+	0.636277i	$0.780474\pi$
$500$	392281.	+	1.20732e6i	0.0701733	+	0.215971i
$501$	−6.29672e6	−	1.09062e7i	−1.12078	−	1.94125i
$502$	−161412.	+	279574.i	−0.0285876	+	0.0495151i
$503$	−2.91278e6	−	619131.i	−0.513320	−	0.109109i	−0.0560331	−	0.998429i	$-0.517845\pi$
$503$	−2.91278e6	−	619131.i	−0.513320	−	0.109109i	−0.457286	+	0.889319i	$0.651179\pi$
$504$	664703.	−	2.04575e6i	0.116561	−	0.358736i
$505$	−484985.	+	103087.i	−0.0846252	+	0.0179876i
$506$	247636.	−	2.35610e6i	0.0429969	−	0.409088i
$507$	3.33167e6	−	3.70020e6i	0.575629	−	0.639300i
$508$	3.43690e6	−	1.53020e6i	0.590891	−	0.263081i
$509$	−2.36631e6	−	1.05355e6i	−0.404835	−	0.180244i	0.194209	−	0.980960i	$-0.437786\pi$
$509$	−2.36631e6	−	1.05355e6i	−0.404835	−	0.180244i	−0.599044	+	0.800716i	$0.704453\pi$
$510$	1.46143e6	+	1.62308e6i	0.248801	+	0.276322i
$511$	3.60568e6	−	2.61968e6i	0.610850	−	0.443809i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	937842.	+	1.04158e6i	0.157339	+	0.174743i
$514$	2.47218e6	+	1.10069e6i	0.412736	+	0.183762i
$515$	−455133.	+	202638.i	−0.0756172	+	0.0336669i
$516$	−726807.	+	807201.i	−0.120170	+	0.133462i
$517$	−697262.	+	6.63401e6i	−0.114728	+	1.09156i
$518$	−541600.	+	115121.i	−0.0886859	+	0.0188508i
$519$	−3.45946e6	+	1.06471e7i	−0.563754	+	1.73506i
$520$	298663.	+	63482.8i	0.0484365	+	0.0102955i
$521$	3.34615e6	−	5.79569e6i	0.540071	−	0.935430i	−0.458829	−	0.888525i	$-0.651731\pi$
$521$	3.34615e6	−	5.79569e6i	0.540071	−	0.935430i	0.998899	−	0.0469051i	$-0.0149358\pi$
$522$	−2.38190e6	−	4.12558e6i	−0.382602	−	0.662687i
$523$	−675952.	−	2.08037e6i	−0.108059	−	0.332572i	0.882377	−	0.470543i	$-0.155942\pi$
$523$	−675952.	−	2.08037e6i	−0.108059	−	0.332572i	−0.990436	+	0.137971i	$0.955942\pi$
$524$	60663.5	+	577175.i	0.00965160	+	0.0918288i
$525$	8.58882e6	+	6.24015e6i	1.35999	+	0.988090i
$526$	6.27098e6			0.988259
$527$	−4.06787e6	−	9.88030e6i	−0.638029	−	1.54969i
$528$	1.86380e6			0.290947
$529$	2.85678e6	+	2.07557e6i	0.443851	+	0.322476i
$530$	22423.9	+	213349.i	0.00346754	+	0.0329914i
$531$	2.45294e6	+	7.54938e6i	0.377530	+	1.16192i
$532$	1.95212e6	+	3.38117e6i	0.299038	+	0.517950i
$533$	794162.	−	1.37553e6i	0.121085	−	0.209726i
$534$	−4.60500e6	−	978823.i	−0.698838	−	0.148543i
$535$	551185.	−	1.69637e6i	0.0832554	−	0.256234i
$536$	−3.33018e6	+	707851.i	−0.500674	+	0.106422i
$537$	838761.	−	7.98028e6i	0.125517	−	1.19421i
$538$	−964911.	+	1.07164e6i	−0.143725	+	0.159623i
$539$	−4.00027e6	+	1.78103e6i	−0.593085	+	0.264059i
$540$	−187890.	−	83653.9i	−0.0277280	−	0.0123453i
$541$	169797.	+	188578.i	0.0249423	+	0.0277012i	0.755487	−	0.655164i	$-0.227400\pi$
$541$	169797.	+	188578.i	0.0249423	+	0.0277012i	−0.730545	+	0.682865i	$0.760734\pi$
$542$	−3.04355e6	+	2.21127e6i	−0.445022	+	0.323328i
$543$	1.37280e7	−	9.97399e6i	1.99806	−	1.45167i
$544$	1.36829e6	+	1.51964e6i	0.198235	+	0.220163i
$545$	2.44633e6	+	1.08918e6i	0.352796	+	0.157075i
$546$	4.79996e6	−	2.13708e6i	0.689058	−	0.306789i
$547$	−2.88999e6	+	3.20966e6i	−0.412979	+	0.458660i	−0.913364	−	0.407143i	$-0.866525\pi$
$547$	−2.88999e6	+	3.20966e6i	−0.412979	+	0.458660i	0.500385	+	0.865803i	$0.333192\pi$
$548$	152384.	−	1.44984e6i	0.0216764	−	0.206237i
$549$	2.94282e6	−	625516.i	0.416709	−	0.0885742i
$550$	−1.26908e6	+	3.90582e6i	−0.178888	+	0.550560i
$551$	8.45764e6	+	1.79773e6i	1.18678	+	0.252258i
$552$	1.14278e6	−	1.97935e6i	0.159630	−	0.276487i
$553$	−3.86259e6	−	6.69021e6i	−0.537114	−	0.930308i
$554$	2.23746e6	+	6.88619e6i	0.309728	+	0.953246i
$555$	−23070.2	−	219498.i	−0.00317920	−	0.0302481i
$556$	1.52272e6	+	1.10632e6i	0.208897	+	0.151772i
$557$	1.23758e6			0.169019			0.0845094	−	0.996423i	$-0.473068\pi$
$557$	1.23758e6			0.169019			0.0845094	+	0.996423i	$0.473068\pi$
$558$	−3.03650e6	−	2.89387e6i	−0.412846	−	0.393454i
$559$	−1.18453e6			−0.160331
$560$	−463498.	−	336751.i	−0.0624565	−	0.0453773i
$561$	1.51971e6	+	1.44591e7i	0.203870	+	1.93970i
$562$	−2.92502e6	−	9.00228e6i	−0.390650	−	1.20230i
$563$	2.95124e6	+	5.11171e6i	0.392405	+	0.679665i	0.992766	−	0.120064i	$-0.0383100\pi$
$563$	2.95124e6	+	5.11171e6i	0.392405	+	0.679665i	−0.600361	+	0.799729i	$0.704977\pi$
$564$	−3.21769e6	+	5.57321e6i	−0.425939	+	0.737747i
$565$	3.10920e6	+	660880.i	0.409758	+	0.0870967i
$566$	−2.85571e6	+	8.78896e6i	−0.374690	+	1.15318i
$567$	−1.14505e7	+	2.43389e6i	−1.49578	+	0.317938i
$568$	308112.	−	2.93149e6i	0.0400717	−	0.381257i
$569$	815216.	−	905389.i	0.105558	−	0.117234i	−0.688050	−	0.725663i	$-0.741533\pi$
$569$	815216.	−	905389.i	0.105558	−	0.117234i	0.793609	+	0.608429i	$0.208200\pi$
$570$	−1.42170e6	+	632982.i	−0.183282	+	0.0816026i
$571$	−1.16425e7	−	5.18356e6i	−1.49436	−	0.665331i	−0.513153	−	0.858297i	$-0.671522\pi$
$571$	−1.16425e7	−	5.18356e6i	−1.49436	−	0.665331i	−0.981205	+	0.192966i	$0.938189\pi$
$572$	1.36003e6	+	1.51046e6i	0.173803	+	0.193028i
$573$	1.66974e7	−	1.21314e7i	2.12453	−	1.54356i
$574$	−2.41107e6	+	1.75175e6i	−0.305443	+	0.221917i
$575$	3.36984e6	+	3.74259e6i	0.425050	+	0.472066i
$576$	733362.	+	326514.i	0.0921005	+	0.0410058i
$577$	4.42463e6	−	1.96997e6i	0.553271	−	0.246332i	−0.111005	−	0.993820i	$-0.535407\pi$
$577$	4.42463e6	−	1.96997e6i	0.553271	−	0.246332i	0.664275	+	0.747488i	$0.268740\pi$
$578$	−6.87321e6	+	7.63347e6i	−0.855736	+	0.950391i
$579$	1.95172e6	−	1.85694e7i	0.241947	−	2.30197i
$580$	−1.24109e6	+	263802.i	−0.153191	+	0.0325617i
$581$	−737182.	+	2.26881e6i	−0.0906013	+	0.278842i
$582$	50394.9	+	10711.8i	0.00616707	+	0.00131085i
$583$	−714013.	+	1.23671e6i	−0.0870032	+	0.150694i
$584$	831653.	+	1.44046e6i	0.100904	+	0.174771i
$585$	288940.	+	889266.i	0.0349074	+	0.107434i
$586$	−230799.	−	2.19591e6i	−0.0277645	−	0.264162i
$587$	9.63647e6	+	7.00130e6i	1.15431	+	0.838656i	0.989048	−	0.147594i	$-0.0471529\pi$
$587$	9.63647e6	+	7.00130e6i	1.15431	+	0.838656i	0.165262	+	0.986250i	$0.447153\pi$
$588$	−4.22447e6			−0.503882
$589$	7.59127e6	−	581147.i	0.901625	−	0.0690237i
$590$	2.11422e6			0.250046
$591$	−7.06612e6	−	5.13384e6i	−0.832171	−	0.604608i
$592$	−21599.9	−	205509.i	−0.00253307	−	0.0241006i
$593$	2.26105e6	+	6.95880e6i	0.264043	+	0.812639i	0.991912	+	0.126924i	$0.0405105\pi$
$593$	2.26105e6	+	6.95880e6i	0.264043	+	0.812639i	−0.727870	+	0.685715i	$0.759490\pi$
$594$	−684546.	−	1.18567e6i	−0.0796043	−	0.137879i
$595$	2.23454e6	−	3.87034e6i	0.258759	−	0.448184i
$596$	−7.85871e6	−	1.67042e6i	−0.906224	−	0.192624i
$597$	−4.15425e6	+	1.27855e7i	−0.477043	+	1.46819i
$598$	2.43801e6	−	518214.i	0.278793	−	0.0592593i
$599$	905208.	−	8.61248e6i	0.103082	−	0.980756i	−0.813678	−	0.581316i	$-0.802538\pi$
$599$	905208.	−	8.61248e6i	0.103082	−	0.980756i	0.916759	−	0.399440i	$-0.130795\pi$
$600$	−2.65112e6	+	2.94437e6i	−0.300643	+	0.333898i
$601$	6.55204e6	−	2.91716e6i	0.739930	−	0.329438i	−0.00192540	−	0.999998i	$-0.500613\pi$
$601$	6.55204e6	−	2.91716e6i	0.739930	−	0.329438i	0.741855	+	0.670560i	$0.233946\pi$
$602$	2.03044e6	+	904009.i	0.228349	+	0.101667i
$603$	−6.97625e6	−	7.74791e6i	−0.781320	−	0.867743i
$604$	2.00710e6	−	1.45825e6i	0.223860	−	0.162644i
$605$	−425551.	+	309181.i	−0.0472675	+	0.0343419i
$606$	−2.13063e6	−	2.36630e6i	−0.235682	−	0.261751i
$607$	3.48984e6	+	1.55378e6i	0.384445	+	0.171166i	0.589853	−	0.807510i	$-0.299186\pi$
$607$	3.48984e6	+	1.55378e6i	0.384445	+	0.171166i	−0.205408	+	0.978676i	$0.565852\pi$
$608$	−1.33109e6	+	592642.i	−0.146033	+	0.0650179i
$609$	−1.46097e7	+	1.62257e7i	−1.59623	+	1.77280i
$610$	83760.4	−	796927.i	0.00911411	−	0.0867149i
$611$	−6.86463e6	+	1.45912e6i	−0.743900	+	0.158121i
$612$	−1.93508e6	+	5.95555e6i	−0.208843	+	0.642752i
$613$	1.43676e6	+	305393.i	0.154430	+	0.0328252i	0.284478	−	0.958683i	$-0.408180\pi$
$613$	1.43676e6	+	305393.i	0.154430	+	0.0328252i	−0.130048	+	0.991508i	$0.541513\pi$
$614$	2.86055e6	−	4.95462e6i	0.306217	−	0.530383i
$615$	−593970.	−	1.02879e6i	−0.0633252	−	0.109682i
$616$	−1.17851e6	−	3.62707e6i	−0.125136	−	0.385127i
$617$	−831089.	−	7.90728e6i	−0.0878890	−	0.836208i	−0.946310	−	0.323262i	$-0.895221\pi$
$617$	−831089.	−	7.90728e6i	−0.0878890	−	0.836208i	0.858421	−	0.512946i	$-0.171446\pi$
$618$	−2.58845e6	−	1.88062e6i	−0.272626	−	0.198075i
$619$	−1.51943e7			−1.59387			−0.796935	−	0.604065i	$-0.793547\pi$
$619$	−1.51943e7			−1.59387			−0.796935	+	0.604065i	$0.793547\pi$
$620$	−982964.	+	530993.i	−0.102697	+	0.0554766i
$621$	−1.67891e6			−0.174702
$622$	−1.67932e6	−	1.22010e6i	−0.174043	−	0.126450i
$623$	1.00696e6	+	9.58055e6i	0.103942	+	0.988941i
$624$	605944.	+	1.86490e6i	0.0622976	+	0.191732i
$625$	−4.09901e6	−	7.09970e6i	−0.419739	−	0.727009i
$626$	4.87797e6	−	8.44890e6i	0.497512	−	0.861716i
$627$	−1.01331e7	−	2.15386e6i	−1.02937	−	0.218800i
$628$	307369.	−	945984.i	0.0311000	−	0.0957161i
$629$	1.57670e6	−	335138.i	0.158900	−	0.0337752i
$630$	183389.	−	1.74483e6i	0.0184086	−	0.175146i
$631$	−6.65450e6	+	7.39057e6i	−0.665337	+	0.738932i	−0.977463	−	0.211109i	$-0.932293\pi$
$631$	−6.65450e6	+	7.39057e6i	−0.665337	+	0.738932i	0.312125	+	0.950041i	$0.398959\pi$
$632$	2.63380e6	−	1.17264e6i	0.262295	−	0.116781i
$633$	1.62290e7	+	7.22563e6i	1.60984	+	0.716748i
$634$	450691.	+	500543.i	0.0445303	+	0.0494559i
$635$	2.48249e6	−	1.80363e6i	0.244316	−	0.177506i
$636$	−1.11457e6	+	809783.i	−0.109261	+	0.0793827i
$637$	−3.08263e6	−	3.42361e6i	−0.301004	−	0.334299i
$638$	−7.71594e6	−	3.43536e6i	−0.750476	−	0.334134i
$639$	8.24617e6	−	3.67143e6i	0.798914	−	0.355699i
$640$	143068.	−	158894.i	0.0138068	−	0.0153340i
$641$	−1.47960e6	+	1.40775e7i	−0.142233	+	1.35325i	0.657753	+	0.753234i	$0.271507\pi$
$641$	−1.47960e6	+	1.40775e7i	−0.142233	+	1.35325i	−0.799986	+	0.600019i	$0.795160\pi$
$642$	1.12045e7	−	2.38159e6i	1.07289	−	0.228049i
$643$	6.31406e6	−	1.94327e7i	0.602256	−	1.85355i	0.0876037	−	0.996155i	$-0.472079\pi$
$643$	6.31406e6	−	1.94327e7i	0.602256	−	1.85355i	0.514653	−	0.857399i	$-0.327921\pi$
$644$	−4.57454e6	−	972349.i	−0.434643	−	0.0923863i
$645$	−442967.	+	767241.i	−0.0419249	+	0.0726161i
$646$	−5.68299e6	−	9.84322e6i	−0.535791	−	0.928017i
$647$	−4.91174e6	−	1.51168e7i	−0.461291	−	1.41971i	−0.863588	−	0.504198i	$-0.831788\pi$
$647$	−4.91174e6	−	1.51168e7i	−0.461291	−	1.41971i	0.402297	−	0.915509i	$-0.368212\pi$
$648$	−456666.	−	4.34489e6i	−0.0427230	−	0.406482i
$649$	1.13859e7	+	8.27234e6i	1.06110	+	0.770933i
$650$	−4.32073e6			−0.401119
$651$	−8.31361e6	+	1.73345e7i	−0.768842	+	1.60310i
$652$	−697167.			−0.0642270
$653$	−2.44820e6	−	1.77872e6i	−0.224680	−	0.163240i	0.469751	−	0.882799i	$-0.344344\pi$
$653$	−2.44820e6	−	1.77872e6i	−0.224680	−	0.163240i	−0.694431	+	0.719560i	$0.744344\pi$
$654$	1.79760e6	+	1.71030e7i	0.164342	+	1.56361i
$655$	146274.	+	450186.i	0.0133219	+	0.0410005i
$656$	−556116.	−	963221.i	−0.0504552	−	0.0873909i
$657$	−2.54677e6	+	4.41114e6i	−0.230185	+	0.398692i
$658$	1.28804e7	+	2.73782e6i	1.15975	+	0.246513i
$659$	−3.03204e6	+	9.33165e6i	−0.271970	+	0.837038i	0.718035	+	0.696007i	$0.245042\pi$
$659$	−3.03204e6	+	9.33165e6i	−0.271970	+	0.837038i	−0.990005	+	0.141031i	$0.954958\pi$
$660$	1.48695e6	−	316061.i	0.132873	−	0.0282430i
$661$	−667257.	+	6.34853e6i	−0.0594005	+	0.565158i	0.923832	+	0.382799i	$0.125040\pi$
$661$	−667257.	+	6.34853e6i	−0.0594005	+	0.565158i	−0.983232	+	0.182359i	$0.941627\pi$
$662$	−4.01256e6	+	4.45640e6i	−0.355858	+	0.395220i
$663$	−1.39736e7	+	6.22144e6i	−1.23459	+	0.549677i
$664$	−813327.	−	362116.i	−0.0715888	−	0.0318734i
$665$	2.13079e6	+	2.36648e6i	0.186847	+	0.207514i
$666$	511945.	−	371950.i	0.0447237	−	0.0324937i
$667$	−8.37934e6	+	6.08794e6i	−0.729281	+	0.529854i
$668$	−6.43501e6	−	7.14681e6i	−0.557967	−	0.619685i
$669$	2.39814e7	+	1.06772e7i	2.07162	+	0.922344i
$670$	−2.53680e6	+	1.12946e6i	−0.218323	+	0.0972036i
$671$	3.56923e6	−	3.96403e6i	0.306033	−	0.339884i
$672$	384590.	−	3.65913e6i	0.0328530	−	0.312575i
$673$	−7.39990e6	+	1.57290e6i	−0.629779	+	0.133864i	−0.511733	−	0.859145i	$-0.670996\pi$
$673$	−7.39990e6	+	1.57290e6i	−0.629779	+	0.133864i	−0.118046	+	0.993008i	$0.537663\pi$
$674$	−4.70096e6	+	1.44681e7i	−0.398599	+	1.22676i
$675$	2.84680e6	+	605106.i	0.240490	+	0.0511178i
$676$	1.90115e6	−	3.29288e6i	0.160011	−	0.277146i
$677$	1.81958e6	+	3.15161e6i	0.152581	+	0.264278i	0.932176	−	0.362007i	$-0.117908\pi$
$677$	1.81958e6	+	3.15161e6i	0.152581	+	0.264278i	−0.779595	+	0.626284i	$0.784575\pi$
$678$	6.30811e6	+	1.94144e7i	0.527018	+	1.62199i
$679$	−11019.6	−	104845.i	−0.000917262	−	0.00872716i
$680$	1.34933e6	+	980346.i	0.111904	+	0.0813031i
$681$	−2.38090e7			−1.96731
$682$	−7.37127e6	−	986455.i	−0.606850	−	0.0812113i
$683$	6.11789e6			0.501822			0.250911	−	0.968010i	$-0.419270\pi$
$683$	6.11789e6			0.501822			0.250911	+	0.968010i	$0.419270\pi$
$684$	−3.60981e6	−	2.62268e6i	−0.295015	−	0.214341i
$685$	−124289.	−	1.18253e6i	−0.0101206	−	0.0962909i
$686$	−891427.	−	2.74353e6i	−0.0723228	−	0.222587i
$687$	5.25705e6	+	9.10548e6i	0.424962	+	0.736057i
$688$	−414737.	+	718345.i	−0.0334042	+	0.0578578i
$689$	−1.46958e6	−	312368.i	−0.117935	−	0.0250679i
$690$	576060.	−	1.77293e6i	0.0460622	−	0.141765i
$691$	2.11030e7	−	4.48559e6i	1.68132	−	0.357375i	0.734366	−	0.678754i	$-0.237480\pi$
$691$	2.11030e7	−	4.48559e6i	1.68132	−	0.357375i	0.946951	+	0.321379i	$0.104146\pi$
$692$	−893622.	+	8.50225e6i	−0.0709396	+	0.674945i
$693$	7.81464e6	−	8.67904e6i	0.618125	−	0.686497i
$694$	9.90153e6	−	4.40844e6i	0.780375	−	0.347445i
$695$	1.40244e6	+	624407.i	0.110134	+	0.0490349i
$696$	−5.45234e6	−	6.05543e6i	−0.426638	−	0.473830i
$697$	7.01908e6	−	5.09966e6i	0.547266	−	0.397612i
$698$	1.20041e7	−	8.72150e6i	0.932592	−	0.677568i
$699$	−8.25515e6	−	9.16828e6i	−0.639046	−	0.709733i
$700$	7.40628e6	+	3.29749e6i	0.571288	+	0.254354i
$701$	−4.99511e6	+	2.22397e6i	−0.383928	+	0.170936i	−0.589620	−	0.807681i	$-0.700722\pi$
$701$	−4.99511e6	+	2.22397e6i	−0.383928	+	0.170936i	0.205692	+	0.978617i	$0.434056\pi$
$702$	963818.	−	1.07043e6i	0.0738163	−	0.0819813i
$703$	−120058.	+	1.14227e6i	−0.00916225	+	0.0871730i
$704$	1.39219e6	−	295918.i	0.105868	−	0.0225030i
$705$	−1.62200e6	+	4.99199e6i	−0.122907	+	0.378270i
$706$	−1.29340e7	−	2.74921e6i	−0.976610	−	0.207585i
$707$	−3.25775e6	+	5.64259e6i	−0.245115	+	0.424551i
$708$	6.78880e6	+	1.17585e7i	0.508991	+	0.881598i
$709$	−1.59945e6	−	4.92260e6i	−0.119496	−	0.367772i	0.873362	−	0.487072i	$-0.161935\pi$
$709$	−1.59945e6	−	4.92260e6i	−0.119496	−	0.367772i	−0.992858	+	0.119300i	$0.961935\pi$
$710$	−251305.	−	2.39101e6i	−0.0187092	−	0.178006i
$711$	7.14262e6	+	5.18942e6i	0.529888	+	0.384986i
$712$	−3.59517e6			−0.265778
$713$	−5.56728e6	+	7.22344e6i	−0.410127	+	0.532133i
$714$	2.87006e7			2.10691
$715$	1.34118e6	+	974425.i	0.0981121	+	0.0712826i
$716$	−640519.	−	6.09414e6i	−0.0466928	−	0.444252i
$717$	−8.63411e6	−	2.65730e7i	−0.627219	−	1.93038i
$718$	5.11582e6	+	8.86086e6i	0.370343	+	0.641453i
$719$	1.06995e7	−	1.85321e7i	0.771865	−	1.33691i	−0.164674	−	0.986348i	$-0.552657\pi$
$719$	1.06995e7	−	1.85321e7i	0.771865	−	1.33691i	0.936539	−	0.350562i	$-0.114009\pi$
$720$	640450.	+	136132.i	0.0460420	+	0.00978653i
$721$	−2.02309e6	+	6.22643e6i	−0.144936	+	0.446068i
$722$	−1.76619e6	+	375416.i	−0.126094	+	0.0268022i
$723$	186215.	−	1.77171e6i	0.0132485	−	0.126051i
$724$	8.67072e6	−	9.62981e6i	0.614764	−	0.682765i
$725$	1.64025e7	−	7.30284e6i	1.15895	−	0.515997i
$726$	−3.08601e6	−	1.37398e6i	−0.217298	−	0.0967473i
$727$	−8.37792e6	−	9.30462e6i	−0.587895	−	0.652924i	0.373650	−	0.927570i	$-0.378106\pi$
$727$	−8.37792e6	−	9.30462e6i	−0.587895	−	0.652924i	−0.961545	+	0.274646i	$0.911439\pi$
$728$	3.24608e6	−	2.35841e6i	0.227002	−	0.164927i
$729$	6.76633e6	−	4.91603e6i	0.471557	−	0.342606i
$730$	907770.	+	1.00818e6i	0.0630476	+	0.0700215i
$731$	−5.91099e6	−	2.63174e6i	−0.409135	−	0.182159i
$732$	4.70118e6	−	2.09310e6i	0.324287	−	0.144382i
$733$	996267.	−	1.10647e6i	0.0684882	−	0.0760639i	−0.707927	−	0.706286i	$-0.750369\pi$
$733$	996267.	−	1.10647e6i	0.0684882	−	0.0760639i	0.776415	+	0.630222i	$0.217036\pi$
$734$	−421857.	+	4.01370e6i	−0.0289018	+	0.274982i
$735$	−3.37031e6	+	716381.i	−0.230118	+	0.0489132i
$736$	539347.	−	1.65994e6i	0.0367007	−	0.112953i
$737$	−1.80809e7	−	3.84321e6i	−1.22617	−	0.260631i
$738$	1.70299e6	−	2.94967e6i	0.115099	−	0.199358i
$739$	−6.14280e6	−	1.06396e7i	−0.413766	−	0.716664i	0.581532	−	0.813524i	$-0.302454\pi$
$739$	−6.14280e6	−	1.06396e7i	−0.413766	−	0.716664i	−0.995298	+	0.0968595i	$0.969120\pi$
$740$	−52082.6	−	160294.i	−0.00349634	−	0.0107606i
$741$	−1.13926e6	−	1.08394e7i	−0.0762216	−	0.725200i
$742$	2.28065e6	+	1.65699e6i	0.152072	+	0.110487i
$743$	−2.04853e7			−1.36135			−0.680677	−	0.732583i	$-0.738314\pi$
$743$	−2.04853e7			−1.36135			−0.680677	+	0.732583i	$0.738314\pi$
$744$	−6.10951e6	−	3.76187e6i	−0.404645	−	0.249156i
$745$	−6.55300e6			−0.432563
$746$	−1.03974e7	−	7.55419e6i	−0.684037	−	0.496982i
$747$	−284982.	−	2.71142e6i	−0.0186860	−	0.177785i
$748$	3.43086e6	+	1.05591e7i	0.224207	+	0.690038i
$749$	−1.17195e7	−	2.02988e7i	−0.763316	−	1.32210i
$750$	−3.32469e6	+	5.75853e6i	−0.215823	+	0.373816i
$751$	−1.97792e7	−	4.20419e6i	−1.27970	−	0.272009i	−0.482592	−	0.875845i	$-0.660305\pi$
$751$	−1.97792e7	−	4.20419e6i	−1.27970	−	0.272009i	−0.797108	+	0.603837i	$0.793638\pi$
$752$	−1.51863e6	+	4.67385e6i	−0.0979279	+	0.301391i
$753$	−1.65400e6	+	351570.i	−0.106304	+	0.0225956i
$754$	928848.	−	8.83740e6i	0.0594999	−	0.566104i
$755$	1.35399e6	−	1.50376e6i	0.0864467	−	0.0960088i
$756$	−2.46904e6	+	1.09929e6i	−0.157117	+	0.0699530i
$757$	6.21569e6	+	2.76740e6i	0.394230	+	0.175523i	0.594271	−	0.804265i	$-0.297441\pi$
$757$	6.21569e6	+	2.76740e6i	0.394230	+	0.175523i	−0.200041	+	0.979788i	$0.564107\pi$
$758$	2.52917e6	+	2.80893e6i	0.159884	+	0.177569i
$759$	1.00393e7	−	7.29396e6i	0.632555	−	0.459578i
$760$	−961456.	+	698539.i	−0.0603803	+	0.0438689i
$761$	5.18484e6	+	5.75834e6i	0.324544	+	0.360442i	0.883233	−	0.468935i	$-0.155362\pi$
$761$	5.18484e6	+	5.75834e6i	0.324544	+	0.360442i	−0.558689	+	0.829377i	$0.688695\pi$
$762$	1.80025e7	+	8.01522e6i	1.12317	+	0.500067i
$763$	3.21469e7	−	1.43127e7i	1.99907	−	0.890044i
$764$	1.05462e7	−	1.17128e7i	0.653678	−	0.725983i
$765$	−533880.	+	5.07953e6i	−0.0329830	+	0.313812i
$766$	2.88936e6	−	614153.i	0.177922	−	0.0378186i
$767$	−4.57555e6	+	1.40821e7i	−0.280838	+	0.864329i
$768$	1.34311e6	+	285486.i	0.0821689	+	0.0174655i
$769$	−1.53181e7	+	2.65318e7i	−0.934092	+	1.61789i	−0.157846	+	0.987464i	$0.550455\pi$
$769$	−1.53181e7	+	2.65318e7i	−0.934092	+	1.61789i	−0.776246	+	0.630430i	$0.782879\pi$
$770$	−1.55530e6	−	2.69385e6i	−0.0945336	−	0.163737i
$771$	4.38025e6	+	1.34810e7i	0.265377	+	0.816745i
$772$	−1.49043e6	−	1.41805e7i	−0.0900052	−	0.856343i
$773$	−4.12847e6	−	2.99951e6i	−0.248508	−	0.180552i	0.456557	−	0.889694i	$-0.349082\pi$
$773$	−4.12847e6	−	2.99951e6i	−0.248508	−	0.180552i	−0.705065	+	0.709142i	$0.749082\pi$
$774$	−2.54010e6			−0.152405
$775$	1.20435e7	−	1.02417e7i	0.720275	−	0.612519i
$776$	39343.8			0.00234543
$777$	−2.34638e6	−	1.70474e6i	−0.139427	−	0.101299i
$778$	−844962.	−	8.03928e6i	−0.0500482	−	0.476177i
$779$	1.91036e6	+	5.87950e6i	0.112791	+	0.347134i
$780$	799674.	+	1.38508e6i	0.0470627	+	0.0815150i
$781$	8.00196e6	−	1.38598e7i	0.469428	−	0.813073i
$782$	1.33174e7	+	2.83069e6i	0.778756	+	0.165530i
$783$	−1.84964e6	+	5.69262e6i	−0.107816	+	0.331824i
$784$	−3.15552e6	+	670726.i	−0.183350	+	0.0389722i
$785$	84801.8	−	806835.i	0.00491169	−	0.0467316i
$786$	−2.03409e6	+	2.25908e6i	−0.117439	+	0.130430i
$787$	2.16012e7	−	9.61748e6i	1.24320	−	0.553508i	0.323537	−	0.946216i	$-0.395128\pi$
$787$	2.16012e7	−	9.61748e6i	1.24320	−	0.553508i	0.919664	+	0.392707i	$0.128461\pi$
$788$	−6.09323e6	−	2.71288e6i	−0.349568	−	0.155638i
$789$	2.19792e7	+	2.44104e7i	1.25696	+	1.39599i
$790$	1.90240e6	−	1.38218e6i	0.108451	−	0.0787945i
$791$	3.37929e7	−	2.45520e7i	1.92037	−	1.39523i
$792$	2.91643e6	+	3.23903e6i	0.165211	+	0.183485i
$793$	5.12679e6	+	2.28259e6i	0.289509	+	0.128898i
$794$	8.88662e6	−	3.95658e6i	0.500248	−	0.222725i
$795$	−751889.	+	835057.i	−0.0421926	+	0.0468596i
$796$	−1.07310e6	+	1.02098e7i	−0.0600283	+	0.571132i
$797$	4.88475e6	−	1.03828e6i	0.272393	−	0.0578990i	−0.0696898	−	0.997569i	$-0.522201\pi$
$797$	4.88475e6	−	1.03828e6i	0.272393	−	0.0578990i	0.342083	+	0.939670i	$0.388868\pi$
$798$	−6.31953e6	+	1.94495e7i	−0.351299	+	1.08119i
$799$	−3.74974e7	−	7.97031e6i	−2.07794	−	0.441681i
$800$	−1.51280e6	+	2.62025e6i	−0.0835714	+	0.144750i
$801$	−5.50475e6	−	9.53450e6i	−0.303149	−	0.525069i
$802$	−1.62986e6	−	5.01619e6i	−0.0894775	−	0.275383i
$803$	943972.	+	8.98130e6i	0.0516619	+	0.491530i
$804$	−1.44274e7	−	1.04821e7i	−0.787130	−	0.571883i
$805$	−3.81449e6			−0.207466
$806$	−1.40945e6	−	7.69636e6i	−0.0764211	−	0.417299i
$807$	−7.55340e6			−0.408281
$808$	−1.96720e6	−	1.42925e6i	−0.106003	−	0.0770160i
$809$	3.47855e6	+	3.30962e7i	0.186864	+	1.77790i	0.539352	+	0.842080i	$0.318669\pi$
$809$	3.47855e6	+	3.30962e7i	0.186864	+	1.77790i	−0.352488	+	0.935816i	$0.614664\pi$
$810$	−1.10113e6	−	3.38894e6i	−0.0589695	−	0.181489i
$811$	1.63175e7	+	2.82627e7i	0.871167	+	1.50890i	0.860791	+	0.508959i	$0.169969\pi$
$811$	1.63175e7	+	2.82627e7i	0.871167	+	1.50890i	0.0103758	+	0.999946i	$0.496697\pi$
$812$	−8.33668e6	+	1.44396e7i	−0.443714	+	0.768535i
$813$	−1.92749e7	−	4.09701e6i	−1.02274	−	0.217391i
$814$	346699.	−	1.06703e6i	0.0183397	−	0.0564437i
$815$	−556204.	+	118225.i	−0.0293319	+	0.00623469i
$816$	−1.11961e6	+	1.06524e7i	−0.0588631	+	0.560045i
$817$	3.08498e6	−	3.42622e6i	0.161695	−	0.179581i
$818$	−1.87907e7	+	8.36615e6i	−0.981882	+	0.437162i
$819$	1.12248e7	+	4.99762e6i	0.584750	+	0.260347i
$820$	−607014.	−	674158.i	−0.0315257	−	0.0350128i
$821$	−1.82680e7	+	1.32725e7i	−0.945874	+	0.687218i	−0.949827	−	0.312774i	$-0.898742\pi$
$821$	−1.82680e7	+	1.32725e7i	−0.945874	+	0.687218i	0.00395338	+	0.999992i	$0.498742\pi$
$822$	6.17772e6	−	4.48838e6i	0.318896	−	0.231691i
$823$	9.78492e6	+	1.08672e7i	0.503567	+	0.559268i	0.940310	−	0.340318i	$-0.110535\pi$
$823$	9.78492e6	+	1.08672e7i	0.503567	+	0.559268i	−0.436743	+	0.899586i	$0.643868\pi$
$824$	−2.23206e6	−	993777.i	−0.114522	−	0.0509883i
$825$	−1.96518e7	+	8.74953e6i	−1.00523	+	0.447559i
$826$	1.85902e7	−	2.06466e7i	0.948058	−	1.05293i
$827$	−3.12631e6	+	2.97448e7i	−0.158953	+	1.51233i	0.566500	+	0.824062i	$0.308297\pi$
$827$	−3.12631e6	+	2.97448e7i	−0.158953	+	1.51233i	−0.725452	+	0.688272i	$0.758369\pi$
$828$	5.22804e6	−	1.11125e6i	0.265010	−	0.0563297i
$829$	−6.66200e6	+	2.05035e7i	−0.336681	+	1.03620i	0.629207	+	0.777238i	$0.283380\pi$
$829$	−6.66200e6	+	2.05035e7i	−0.336681	+	1.03620i	−0.965888	+	0.258960i	$0.916620\pi$
$830$	−710284.	−	150976.i	−0.0357880	−	0.00760697i
$831$	−1.89631e7	+	3.28450e7i	−0.952591	+	1.64994i
$832$	748711.	+	1.29681e6i	0.0374978	+	0.0649481i
$833$	−7.77636e6	−	2.39332e7i	−0.388297	−	1.19505i
$834$	1.03053e6	+	9.80487e6i	0.0513035	+	0.488120i
$835$	−6.34584e6	−	4.61052e6i	−0.314973	−	0.228841i
$836$	−7.91100e6			−0.391486
$837$	−149207.	+	5.26830e6i	−0.00736164	+	0.259930i
$838$	−1.71064e6			−0.0841487
$839$	−5.14128e6	−	3.73536e6i	−0.252154	−	0.183201i	0.454527	−	0.890733i	$-0.349808\pi$
$839$	−5.14128e6	−	3.73536e6i	−0.252154	−	0.183201i	−0.706681	+	0.707532i	$0.749808\pi$
$840$	−313683.	−	2.98449e6i	−0.0153388	−	0.145939i
$841$	5.07245e6	+	1.56114e7i	0.247302	+	0.761118i
$842$	−6.34269e6	−	1.09859e7i	−0.308314	−	0.534016i
$843$	2.47903e7	−	4.29381e7i	1.20147	−	2.08101i
$844$	1.32697e7	+	2.82056e6i	0.641216	+	0.136295i
$845$	958343.	−	2.94948e6i	0.0461720	−	0.142103i
$846$	−1.47205e7	+	3.12893e6i	−0.707124	+	0.150304i
$847$	−722525.	+	6.87436e6i	−0.0346054	+	0.329249i
$848$	−703971.	+	781839.i	−0.0336175	+	0.0373360i
$849$	−4.42209e7	+	1.96884e7i	−2.10551	+	0.937435i
$850$	−2.15611e7	−	9.59961e6i	−1.02358	−	0.455729i
$851$	−920607.	−	1.02244e6i	−0.0435763	−	0.0483964i
$852$	1.24910e7	−	9.07525e6i	0.589520	−	0.428311i
$853$	−3.19855e6	+	2.32388e6i	−0.150515	+	0.109356i	−0.660494	−	0.750831i	$-0.729653\pi$
$853$	−3.19855e6	+	2.32388e6i	−0.150515	+	0.109356i	0.509979	+	0.860187i	$0.329653\pi$
$854$	−7.04594e6	−	7.82531e6i	−0.330594	−	0.367161i
$855$	−3.32468e6	−	1.48024e6i	−0.155537	−	0.0692497i
$856$	7.99120e6	−	3.55791e6i	0.372758	−	0.165963i
$857$	1.86670e7	−	2.07317e7i	0.868203	−	0.964237i	−0.131430	−	0.991325i	$-0.541957\pi$
$857$	1.86670e7	−	2.07317e7i	0.868203	−	0.964237i	0.999633	+	0.0270882i	$0.00862351\pi$
$858$	−1.11285e6	+	1.05881e7i	−0.0516083	+	0.491020i
$859$	−1.13225e6	+	240667.i	−0.0523551	+	0.0111284i	−0.234015	−	0.972233i	$-0.575186\pi$
$859$	−1.13225e6	+	240667.i	−0.0523551	+	0.0111284i	0.181660	+	0.983361i	$0.441853\pi$
$860$	−209063.	+	643430.i	−0.00963899	+	0.0296658i
$861$	−1.52694e7	−	3.24562e6i	−0.701964	−	0.149207i
$862$	−4.82083e6	+	8.34992e6i	−0.220980	+	0.382749i
$863$	−1.87558e6	−	3.24860e6i	−0.0857253	−	0.148481i	0.819975	−	0.572400i	$-0.193987\pi$
$863$	−1.87558e6	−	3.24860e6i	−0.0857253	−	0.148481i	−0.905700	+	0.423919i	$0.860654\pi$
$864$	−311690.	−	959282.i	−0.0142049	−	0.0437182i
$865$	728865.	+	6.93468e6i	0.0331212	+	0.315128i
$866$	−1.01499e7	−	7.37434e6i	−0.459904	−	0.334140i
$867$	−5.38040e7			−2.43090
$868$	−3.45772e6	+	1.42682e7i	−0.155772	+	0.642791i
$869$	1.56533e7			0.703162
$870$	−5.37678e6	−	3.90646e6i	−0.240838	−	0.174979i
$871$	−2.03283e6	−	1.93411e7i	−0.0907938	−	0.863845i
$872$	4.05821e6	+	1.24899e7i	0.180735	+	0.556247i
$873$	60241.3	+	104341.i	0.00267521	+	0.00463361i
$874$	−4.85059e6	+	8.40148e6i	−0.214791	+	0.372029i
$875$	1.33087e7	+	2.82886e6i	0.587647	+	0.124908i
$876$	−2.69228e6	+	8.28599e6i	−0.118539	+	0.364825i
$877$	3.46902e7	−	7.37364e6i	1.52303	−	0.323730i	0.631027	−	0.775761i	$-0.282634\pi$
$877$	3.46902e7	−	7.37364e6i	1.52303	−	0.323730i	0.892002	+	0.452031i	$0.149300\pi$
$878$	−1.24072e6	+	1.18047e7i	−0.0543174	+	0.516796i
$879$	7.73885e6	−	8.59486e6i	0.337835	−	0.375203i
$880$	1.06051e6	−	472171.i	0.0461646	−	0.0205538i
$881$	1.21534e7	+	5.41104e6i	0.527543	+	0.234877i	0.653185	−	0.757198i	$-0.273432\pi$
$881$	1.21534e7	+	5.41104e6i	0.527543	+	0.234877i	−0.125642	+	0.992076i	$0.540099\pi$
$882$	−6.61036e6	−	7.34155e6i	−0.286124	−	0.317772i
$883$	−3.84120e6	+	2.79080e6i	−0.165793	+	0.120455i	−0.667588	−	0.744531i	$-0.732673\pi$
$883$	−3.84120e6	+	2.79080e6i	−0.165793	+	0.120455i	0.501795	+	0.864987i	$0.332673\pi$
$884$	−9.44995e6	+	6.86579e6i	−0.406723	+	0.295502i
$885$	7.41015e6	+	8.22980e6i	0.318030	+	0.353209i
$886$	1.15303e7	+	5.13360e6i	0.493463	+	0.219704i
$887$	−4.02588e6	+	1.79244e6i	−0.171811	+	0.0764953i	−0.490840	−	0.871250i	$-0.663310\pi$
$887$	−4.02588e6	+	1.79244e6i	−0.171811	+	0.0764953i	0.319029	+	0.947745i	$0.396643\pi$
$888$	724259.	−	804372.i	0.0308221	−	0.0342314i
$889$	4.21491e6	−	4.01022e7i	0.178868	−	1.70182i
$890$	−2.86825e6	+	609664.i	−0.121378	+	0.0257998i
$891$	7.32993e6	−	2.25592e7i	0.309318	−	0.951983i
$892$	1.96084e7	+	4.16790e6i	0.825146	+	0.175390i
$893$	1.36577e7	−	2.36558e7i	0.573124	−	0.992681i
$894$	−2.10418e7	−	3.64455e7i	−0.880520	−	1.52511i
$895$	−1.54445e6	−	4.75332e6i	−0.0644489	−	0.198353i
$896$	−293692.	−	2.79429e6i	−0.0122214	−	0.116279i
$897$	1.05622e7	+	7.67388e6i	0.438301	+	0.318445i
$898$	−8.85797e6			−0.366559
$899$	1.83589e7	+	2.68349e7i	0.757613	+	1.10739i
$900$	−9.26533e6			−0.381289
$901$	−6.63940e6	−	4.82381e6i	−0.272469	−	0.197960i
$902$	−631222.	−	6.00568e6i	−0.0258325	−	0.245780i
$903$	3.59756e6	+	1.10721e7i	0.146821	+	0.451869i
$904$	7.79437e6	+	1.35002e7i	0.317219	+	0.549440i
$905$	5.28454e6	−	9.15309e6i	0.214479	−	0.371489i
$906$	1.27111e7	+	2.70182e6i	0.514472	+	0.109354i
$907$	−8.36139e6	+	2.57337e7i	−0.337490	+	1.03869i	0.627993	+	0.778219i	$0.283877\pi$
$907$	−8.36139e6	+	2.57337e7i	−0.337490	+	1.03869i	−0.965483	+	0.260467i	$0.916123\pi$
$908$	−1.77844e7	+	3.78020e6i	−0.715855	+	0.152160i
$909$	778348.	−	7.40548e6i	0.0312438	−	0.297265i
$910$	2.18980e6	−	2.43202e6i	0.0876601	−	0.0973564i
$911$	1.69382e6	−	754138.i	0.0676195	−	0.0301061i	−0.372648	−	0.927973i	$-0.621550\pi$
$911$	1.69382e6	−	754138.i	0.0676195	−	0.0301061i	0.440268	+	0.897867i	$0.354884\pi$
$912$	−6.97228e6	−	3.10426e6i	−0.277580	−	0.123587i
$913$	−3.23444e6	−	3.59221e6i	−0.128417	−	0.142621i
$914$	−2.42816e7	+	1.76416e7i	−0.961416	+	0.698510i
$915$	3.39569e6	−	2.46711e6i	0.134083	−	0.0974173i
$916$	5.37251e6	+	5.96678e6i	0.211562	+	0.234964i
$917$	5.68251e6	+	2.53002e6i	0.223160	+	0.0993574i
$918$	7.18783e6	−	3.20023e6i	0.281508	−	0.125336i
$919$	−2.62656e7	+	2.91709e7i	−1.02588	+	1.13936i	−0.0357313	+	0.999361i	$0.511376\pi$
$919$	−2.62656e7	+	2.91709e7i	−1.02588	+	1.13936i	−0.990152	+	0.139997i	$0.955291\pi$
$920$	148804.	−	1.41577e6i	0.00579621	−	0.0551473i
$921$	2.93123e7	−	6.23053e6i	1.13868	−	0.242034i
$922$	−2.66588e6	+	8.20473e6i	−0.103279	+	0.317861i
$923$	1.64696e7	+	3.50072e6i	0.636324	+	0.135255i
$924$	9.98817e6	−	1.73000e7i	0.384863	−	0.666602i
$925$	1.19250e6	+	2.06548e6i	0.0458253	+	0.0793718i
$926$	6.89805e6	+	2.12300e7i	0.264362	+	0.813622i
$927$	−782093.	−	7.44112e6i	−0.0298923	−	0.284406i
$928$	−5.03412e6	−	3.65750e6i	−0.191891	−	0.139417i
$929$	−9.94914e6			−0.378221			−0.189111	−	0.981956i	$-0.560561\pi$
$929$	−9.94914e6			−0.378221			−0.189111	+	0.981956i	$0.560561\pi$
$930$	−5.51214e6	−	1.96520e6i	−0.208984	−	0.0745074i
$931$	1.79310e7			0.678002
$932$	−7.62195e6	−	5.53767e6i	−0.287426	−	0.208827i
$933$	−1.13652e6	−	1.08132e7i	−0.0427437	−	0.406679i
$934$	−369418.	−	1.13695e6i	−0.0138564	−	0.0426457i
$935$	4.52776e6	+	7.84231e6i	0.169377	+	0.293370i
$936$	−2.29278e6	+	3.97121e6i	−0.0855407	+	0.148161i
$937$	−2.80654e7	−	5.96549e6i	−1.04429	−	0.221971i	−0.346336	−	0.938111i	$-0.612574\pi$
$937$	−2.80654e7	−	5.96549e6i	−1.04429	−	0.221971i	−0.697957	+	0.716139i	$0.745907\pi$
$938$	−1.12762e7	+	3.47046e7i	−0.418461	+	1.28789i
$939$	4.99850e7	−	1.06246e7i	1.85002	−	0.393233i
$940$	−418983.	+	3.98636e6i	−0.0154660	+	0.147149i
$941$	1.83533e7	−	2.03834e7i	0.675678	−	0.750416i	−0.303631	−	0.952790i	$-0.598199\pi$
$941$	1.83533e7	−	2.03834e7i	0.675678	−	0.750416i	0.979308	+	0.202374i	$0.0648656\pi$
$942$	4.75964e6	−	2.11913e6i	0.174762	−	0.0778090i
$943$	−6.76506e6	−	3.01200e6i	−0.247738	−	0.110300i
$944$	6.93790e6	+	7.70532e6i	0.253395	+	0.281424i
$945$	−1.78340e6	+	1.29571e6i	−0.0649634	+	0.0471986i
$946$	−3.64345e6	+	2.64712e6i	−0.132369	+	0.0961714i
$947$	6.90489e6	+	7.66865e6i	0.250197	+	0.277872i	0.855140	−	0.518397i	$-0.173471\pi$
$947$	6.90489e6	+	7.66865e6i	0.250197	+	0.277872i	−0.604943	+	0.796268i	$0.706804\pi$
$948$	1.37958e7	+	6.14230e6i	0.498571	+	0.221978i
$949$	−8.67973e6	+	3.86447e6i	−0.312853	+	0.139291i
$950$	1.12528e7	−	1.24976e7i	0.404533	−	0.449279i
$951$	−368781.	+	3.50872e6i	−0.0132226	+	0.125805i
$952$	2.14383e7	−	4.55684e6i	0.766650	−	0.162956i
$953$	1.13113e7	−	3.48125e7i	0.403440	−	1.24166i	−0.518750	−	0.854926i	$-0.673603\pi$
$953$	1.13113e7	−	3.48125e7i	0.403440	−	1.24166i	0.922191	−	0.386736i	$-0.126397\pi$
$954$	−3.15135e6	−	669840.i	−0.112105	−	0.0238287i
$955$	6.42761e6	−	1.11329e7i	0.228056	−	0.395004i
$956$	−1.06684e7	−	1.84782e7i	−0.377532	−	0.653905i
$957$	−1.36712e7	−	4.20757e7i	−0.482533	−	1.48508i
$958$	3.01478e6	+	2.86837e7i	0.106131	+	1.00977i
$959$	−1.26409e7	−	9.18418e6i	−0.443847	−	0.322473i
$960$	1.11995e6			0.0392212
$961$	2.21719e7	+	1.81117e7i	0.774453	+	0.632632i
$962$	1.18038e6			0.0411229
$963$	2.16714e7	+	1.57452e7i	0.753047	+	0.547120i
$964$	−142203.	−	1.35297e6i	−0.00492850	−	0.0468916i
$965$	−3.59378e6	−	1.10605e7i	−0.124232	−	0.382347i
$966$	−1.22484e7	−	2.12149e7i	−0.422315	−	0.731471i
$967$	9.10177e6	−	1.57647e7i	0.313011	−	0.542151i	−0.666002	−	0.745950i	$-0.731996\pi$
$967$	9.10177e6	−	1.57647e7i	0.313011	−	0.542151i	0.979013	+	0.203799i	$0.0653289\pi$
$968$	−2.52328e6	−	536339.i	−0.0865519	−	0.0183972i
$969$	1.83973e7	−	5.66212e7i	0.629427	−	1.93718i
$970$	31388.7	−	6671.87i	0.00107113	−	0.000227677i
$971$	−2.33954e6	+	2.22593e7i	−0.0796312	+	0.757640i	0.879733	+	0.475468i	$0.157721\pi$
$971$	−2.33954e6	+	2.22593e7i	−0.0796312	+	0.757640i	−0.959364	+	0.282172i	$0.908945\pi$
$972$	1.27498e7	−	1.41600e7i	0.432849	−	0.480727i
$973$	1.84293e7	−	8.20525e6i	0.624060	−	0.277850i
$974$	1.98591e7	+	8.84183e6i	0.670751	+	0.298638i
$975$	−1.51438e7	−	1.68189e7i	−0.510179	−	0.566611i
$976$	3.17928e6	−	2.30988e6i	0.106833	−	0.0776185i
$977$	1.43741e6	−	1.04434e6i	0.0481776	−	0.0350031i	−0.563436	−	0.826160i	$-0.690521\pi$
$977$	1.43741e6	−	1.04434e6i	0.0481776	−	0.0350031i	0.611613	+	0.791157i	$0.290521\pi$
$978$	−2.44351e6	−	2.71379e6i	−0.0816895	−	0.0907254i
$979$	−1.78321e7	−	7.93935e6i	−0.594628	−	0.264745i
$980$	−2.40375e6	+	1.07022e6i	−0.0799510	+	0.0355965i
$981$	−2.69099e7	+	2.98864e7i	−0.892768	+	0.991520i
$982$	−630359.	+	5.99747e6i	−0.0208598	+	0.198467i
$983$	2.89837e7	−	6.16067e6i	0.956686	−	0.203350i	0.296988	−	0.954881i	$-0.404018\pi$
$983$	2.89837e7	−	6.16067e6i	0.956686	−	0.203350i	0.659697	+	0.751531i	$0.270684\pi$
$984$	1.80029e6	−	5.54074e6i	0.0592728	−	0.182423i
$985$	−5.32127e6	−	1.13107e6i	−0.174753	−	0.0371449i
$986$	2.42697e7	−	4.20363e7i	0.795008	−	1.37699i
$987$	3.44875e7	+	5.97342e7i	1.12686	+	1.95178i
$988$	−2.57197e6	−	7.91570e6i	−0.0838249	−	0.257986i
$989$	577275.	+	5.49241e6i	0.0187669	+	0.178555i
$990$	2.87602e6	+	2.08955e6i	0.0932617	+	0.0677586i
$991$	2.91734e7			0.943633			0.471817	−	0.881697i	$-0.343598\pi$
$991$	2.91734e7			0.943633			0.471817	+	0.881697i	$0.343598\pi$
$992$	−5.16085e6	−	1.83996e6i	−0.166511	−	0.0593648i
$993$	−3.14106e7			−1.01089
$994$	−2.55593e7	−	1.85699e7i	−0.820508	−	0.596134i
$995$	875250.	+	8.32745e6i	0.0280269	+	0.266658i
$996$	−1.44106e6	−	4.43514e6i	−0.0460294	−	0.141664i
$997$	1.12181e7	+	1.94303e7i	0.357423	+	0.619074i	0.987529	−	0.157434i	$-0.0503222\pi$
$997$	1.12181e7	+	1.94303e7i	0.357423	+	0.619074i	−0.630107	+	0.776508i	$0.716989\pi$
$998$	−1.22848e7	+	2.12780e7i	−0.390430	+	0.676245i
$999$	−777717.	−	165309.i	−0.0246552	−	0.00524062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.g.b.41.7	✓	56
31.28	even	15	inner	62.6.g.b.59.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.g.b.41.7	✓	56	1.1	even	1	trivial
62.6.g.b.59.7	yes	56	31.28	even	15	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(2.19008 + 20.8372i) q^{3} +(4.94427 + 15.2169i) q^{4} +(6.52504 + 11.3017i) q^{5} +(-41.9041 + 72.5799i) q^{6} +(167.742 + 35.6546i) q^{7} +(-19.7771 + 60.8676i) q^{8} +(-191.705 + 40.7481i) q^{9} +(-5.45642 + 51.9143i) q^{10} +(-232.511 + 258.230i) q^{11} +(-306.250 + 136.351i) q^{12} +(-333.975 - 148.695i) q^{13} +(458.995 + 509.766i) q^{14} +(-221.206 + 160.715i) q^{15} +(-207.108 + 150.473i) q^{16} +(-1336.22 - 1484.02i) q^{17} +(-716.174 - 318.861i) q^{18} +(1299.90 - 578.752i) q^{19} +(-139.715 + 155.170i) q^{20} +(-375.576 + 3573.37i) q^{21} +(-1359.56 + 288.983i) q^{22} +(-526.706 + 1621.04i) q^{23} +(-1311.63 - 278.795i) q^{24} +(1477.35 - 2558.84i) q^{25} +(-731.163 - 1266.41i) q^{26} +(304.384 + 936.799i) q^{27} +(286.808 + 2728.80i) q^{28} +(4916.13 + 3571.78i) q^{29} -1093.70 q^{30} +(5039.89 + 1796.83i) q^{31} -1024.00 q^{32} +(-5890.01 - 4279.35i) q^{33} +(-834.953 - 7944.05i) q^{34} +(691.564 + 2128.42i) q^{35} +(-1567.90 - 2715.68i) q^{36} +(-403.596 + 699.049i) q^{37} +(5567.28 + 1183.36i) q^{38} +(2366.97 - 7284.78i) q^{39} +(-816.954 + 173.649i) q^{40} +(-454.140 + 4320.85i) q^{41} +(-9616.88 + 10680.6i) q^{42} +(2960.01 - 1317.88i) q^{43} +(-5079.05 - 2261.34i) q^{44} +(-1711.40 - 1900.70i) q^{45} +(-5515.74 + 4007.42i) q^{46} +(15530.5 - 11283.6i) q^{47} +(-3589.03 - 3986.02i) q^{48} +(11512.1 + 5125.54i) q^{49} +(10797.0 - 4807.13i) q^{50} +(27996.6 - 31093.3i) q^{51} +(611.419 - 5817.26i) q^{52} +(4019.83 - 854.442i) q^{53} +(-1217.54 + 3747.20i) q^{54} +(-4435.58 - 942.811i) q^{55} +(-5487.66 + 9504.91i) q^{56} +(14906.5 + 25818.8i) q^{57} +(7511.18 + 23117.0i) q^{58} +(-4233.62 - 40280.2i) q^{59} +(-3539.29 - 2571.45i) q^{60} -15350.8 q^{61} +(12084.8 + 17664.2i) q^{62} -33609.8 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-498.691 - 4744.73i) q^{65} +(-8999.14 - 27696.5i) q^{66} +(26598.2 + 46069.5i) q^{67} +(15975.6 - 27670.6i) q^{68} +(-34931.4 - 7424.91i) q^{69} +(-2766.26 + 8513.67i) q^{70} +(-45050.4 + 9575.75i) q^{71} +(1311.12 - 12474.5i) q^{72} +(17390.1 - 19313.7i) q^{73} +(-2949.63 + 1313.26i) q^{74} +(56554.7 + 25179.8i) q^{75} +(15233.9 + 16918.9i) q^{76} +(-48208.9 + 35025.8i) q^{77} +(24787.2 - 18009.0i) q^{78} +(-30142.7 - 33476.9i) q^{79} +(-3051.99 - 1358.83i) q^{80} +(-62361.2 + 27765.0i) q^{81} +(-11628.6 + 12914.8i) q^{82} +(-1454.08 + 13834.7i) q^{83} +(-56232.5 + 11952.6i) q^{84} +(8053.10 - 24784.9i) q^{85} +(12677.3 + 2694.64i) q^{86} +(-63659.3 + 110261. i) q^{87} +(-11119.4 - 19259.4i) q^{88} +(17358.9 + 53425.1i) q^{89} +(-1069.39 - 10174.6i) q^{90} +(-50720.0 - 36850.2i) q^{91} -27271.3 q^{92} +(-26403.3 + 108953. i) q^{93} +76787.2 q^{94} +(15022.8 + 10914.7i) q^{95} +(-2242.65 - 21337.3i) q^{96} +(-189.967 - 584.658i) q^{97} +(25203.2 + 43653.3i) q^{98} +(34051.1 - 58978.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 7 q^{3} - 224 q^{4} + 91 q^{5} - 152 q^{6} - 94 q^{7} + 896 q^{8} + 896 q^{9} - 944 q^{10} - 31 q^{11} - 112 q^{12} - 1244 q^{13} + 856 q^{14} + 518 q^{15} - 3584 q^{16} + 1064 q^{17}+ \cdots - 625437 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 7 * q^3 - 224 * q^4 + 91 * q^5 - 152 * q^6 - 94 * q^7 + 896 * q^8 + 896 * q^9 - 944 * q^10 - 31 * q^11 - 112 * q^12 - 1244 * q^13 + 856 * q^14 + 518 * q^15 - 3584 * q^16 + 1064 * q^17 - 1724 * q^18 + 619 * q^19 - 1024 * q^20 + 9541 * q^21 + 124 * q^22 - 1717 * q^23 + 768 * q^24 - 24033 * q^25 - 1344 * q^26 + 22754 * q^27 + 1776 * q^28 + 11733 * q^29 + 13928 * q^30 + 57065 * q^31 - 57344 * q^32 - 11248 * q^33 - 10456 * q^34 - 7296 * q^35 - 42464 * q^36 - 1504 * q^37 - 29736 * q^38 - 19566 * q^39 + 4096 * q^40 + 35891 * q^41 + 40636 * q^42 + 66400 * q^43 + 23344 * q^44 - 27014 * q^45 - 7612 * q^46 + 36521 * q^47 - 3072 * q^48 + 121465 * q^49 - 13108 * q^50 - 236890 * q^51 - 19904 * q^52 - 143661 * q^53 - 91016 * q^54 + 106359 * q^55 + 5056 * q^56 + 13060 * q^57 + 59468 * q^58 + 230112 * q^59 + 8288 * q^60 - 49860 * q^61 + 26740 * q^62 + 66726 * q^63 - 57344 * q^64 + 201094 * q^65 - 30508 * q^66 + 74372 * q^67 - 4656 * q^68 - 599733 * q^69 + 29184 * q^70 + 23383 * q^71 - 27584 * q^72 - 66915 * q^73 + 186916 * q^74 + 553648 * q^75 - 152736 * q^76 + 120895 * q^77 + 142024 * q^78 - 452529 * q^79 - 50944 * q^80 - 365276 * q^81 - 14324 * q^82 - 469160 * q^83 - 50464 * q^84 - 127377 * q^85 + 215540 * q^86 + 217461 * q^87 + 39744 * q^88 - 155746 * q^89 + 820796 * q^90 - 142152 * q^91 - 5952 * q^92 + 342224 * q^93 + 29656 * q^94 + 756444 * q^95 + 7168 * q^96 + 325303 * q^97 + 533540 * q^98 - 625437 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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