LMFDB - Embedded newform 62.7.f.a.15.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	62.15
Dual form			62.7.f.a.29.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.57649 + 3.32502i) q^{2} +(-16.9719 + 23.3599i) q^{3} +(9.88854 - 30.4338i) q^{4} +12.8309 q^{5} -163.338i q^{6} +(-163.532 + 503.299i) q^{7} +(55.9381 + 172.160i) q^{8} +(-32.3638 - 99.6054i) q^{9} +(-58.7205 + 42.6630i) q^{10} +(-1681.74 - 546.431i) q^{11} +(543.102 + 747.516i) q^{12} +(-1574.85 + 2167.59i) q^{13} +(-925.076 - 2847.09i) q^{14} +(-217.765 + 299.728i) q^{15} +(-828.433 - 601.892i) q^{16} +(3011.85 - 978.609i) q^{17} +(479.302 + 348.233i) q^{18} +(9317.89 - 6769.84i) q^{19} +(126.879 - 390.493i) q^{20} +(-8981.56 - 12362.1i) q^{21} +(9513.37 - 3091.08i) q^{22} +(15039.2 - 4886.53i) q^{23} +(-4971.01 - 1615.18i) q^{24} -15460.4 q^{25} -15156.4i q^{26} +(-17143.2 - 5570.15i) q^{27} +(13700.2 + 9953.80i) q^{28} +(-22150.0 - 30486.8i) q^{29} -2095.78i q^{30} +(7585.90 + 28809.0i) q^{31} +5792.62 q^{32} +(41307.0 - 30011.3i) q^{33} +(-10529.8 + 14493.0i) q^{34} +(-2098.26 + 6457.79i) q^{35} -3351.40 q^{36} -73715.5i q^{37} +(-20133.4 + 61964.2i) q^{38} +(-23906.5 - 73576.6i) q^{39} +(717.736 + 2208.96i) q^{40} +(-58912.7 + 42802.6i) q^{41} +(82208.1 + 26711.0i) q^{42} +(-16365.6 - 22525.3i) q^{43} +(-33259.9 + 45778.4i) q^{44} +(-415.256 - 1278.03i) q^{45} +(-52578.9 + 72368.7i) q^{46} +(154652. + 112361. i) q^{47} +(28120.3 - 9136.83i) q^{48} +(-131388. - 95458.6i) q^{49} +(70754.2 - 51406.0i) q^{50} +(-28256.8 + 86965.4i) q^{51} +(50395.2 + 69363.0i) q^{52} +(7937.23 - 2578.96i) q^{53} +(96976.4 - 31509.5i) q^{54} +(-21578.3 - 7011.20i) q^{55} -95795.5 q^{56} +332562. i q^{57} +(202738. + 65873.6i) q^{58} +(-82905.0 - 60234.0i) q^{59} +(6968.50 + 9591.31i) q^{60} +71955.9i q^{61} +(-130507. - 106621. i) q^{62} +55423.8 q^{63} +(-26509.9 + 19260.5i) q^{64} +(-20206.7 + 27812.2i) q^{65} +(-89253.1 + 274693. i) q^{66} -241060. q^{67} -101339. i q^{68} +(-141096. + 434248. i) q^{69} +(-11869.6 - 36530.8i) q^{70} +(-12458.9 - 38344.4i) q^{71} +(15337.7 - 11143.5i) q^{72} +(-634817. - 206265. i) q^{73} +(245105. + 337359. i) q^{74} +(262393. - 361152. i) q^{75} +(-113892. - 350523. i) q^{76} +(550037. - 757060. i) q^{77} +(354051. + 257233. i) q^{78} +(88175.3 - 28649.9i) q^{79} +(-10629.6 - 7722.82i) q^{80} +(482839. - 350803. i) q^{81} +(127294. - 391771. i) q^{82} +(613155. + 843935. i) q^{83} +(-465039. + 151100. i) q^{84} +(38644.8 - 12556.4i) q^{85} +(149794. + 48670.9i) q^{86} +1.08810e6 q^{87} -320094. i q^{88} +(-748295. - 243136. i) q^{89} +(6149.88 + 4468.15i) q^{90} +(-833411. - 1.14709e6i) q^{91} -506020. i q^{92} +(-801722. - 311739. i) q^{93} -1.08137e6 q^{94} +(119557. - 86863.2i) q^{95} +(-98312.0 + 135315. i) q^{96} +(-262340. + 807401. i) q^{97} +918695. q^{98} +185195. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−4.57649	+	3.32502i	−0.572061	+	0.415627i
$2$	−4.57649	+	3.32502i	−0.572061	+	0.415627i
$3$	−16.9719	+	23.3599i	−0.628591	+	0.865181i	−0.997943	−	0.0641086i	$-0.979580\pi$
$3$	−16.9719	+	23.3599i	−0.628591	+	0.865181i	0.369352	+	0.929289i	$0.379580\pi$
$4$	9.88854	−	30.4338i	0.154508	−	0.475528i
$5$	12.8309			0.102647			0.0513236	−	0.998682i	$-0.483656\pi$
$5$	12.8309			0.102647			0.0513236	+	0.998682i	$0.483656\pi$
$6$		−	163.338i		−	0.756196i
$7$	−163.532	+	503.299i	−0.476769	+	1.46735i	0.366787	+	0.930305i	$0.380458\pi$
$7$	−163.532	+	503.299i	−0.476769	+	1.46735i	−0.843557	+	0.537040i	$0.819542\pi$
$8$	55.9381	+	172.160i	0.109254	+	0.336249i
$9$	−32.3638	−	99.6054i	−0.0443947	−	0.136633i
$10$	−58.7205	+	42.6630i	−0.0587205	+	0.0426630i
$11$	−1681.74	−	546.431i	−1.26352	−	0.410542i	−0.400771	−	0.916178i	$-0.631258\pi$
$11$	−1681.74	−	546.431i	−1.26352	−	0.410542i	−0.862746	+	0.505637i	$0.831258\pi$
$12$	543.102	+	747.516i	0.314295	+	0.432590i
$13$	−1574.85	+	2167.59i	−0.716818	+	0.986615i	0.282805	+	0.959177i	$0.408735\pi$
$13$	−1574.85	+	2167.59i	−0.716818	+	0.986615i	−0.999624	+	0.0274381i	$0.991265\pi$
$14$	−925.076	−	2847.09i	−0.337127	−	1.03757i
$15$	−217.765	+	299.728i	−0.0645231	+	0.0888084i
$16$	−828.433	−	601.892i	−0.202254	−	0.146946i
$17$	3011.85	−	978.609i	0.613037	−	0.199188i	0.0139905	−	0.999902i	$-0.495547\pi$
$17$	3011.85	−	978.609i	0.613037	−	0.199188i	0.599046	+	0.800714i	$0.295547\pi$
$18$	479.302	+	348.233i	0.0821848	+	0.0597108i
$19$	9317.89	−	6769.84i	1.35849	−	0.987001i	0.359951	−	0.932971i	$-0.382793\pi$
$19$	9317.89	−	6769.84i	1.35849	−	0.987001i	0.998539	−	0.0540301i	$-0.0172067\pi$
$20$	126.879	−	390.493i	0.0158599	−	0.0488117i
$21$	−8981.56	−	12362.1i	−0.969826	−	1.33485i
$22$	9513.37	−	3091.08i	0.893442	−	0.290297i
$23$	15039.2	−	4886.53i	1.23606	−	0.401621i	0.383156	−	0.923684i	$-0.374837\pi$
$23$	15039.2	−	4886.53i	1.23606	−	0.401621i	0.852907	+	0.522062i	$0.174837\pi$
$24$	−4971.01	−	1615.18i	−0.359592	−	0.116839i
$25$	−15460.4			−0.989464
$26$		−	15156.4i		−	0.862333i
$27$	−17143.2	−	5570.15i	−0.870963	−	0.282993i
$28$	13700.2	+	9953.80i	0.624099	+	0.453435i
$29$	−22150.0	−	30486.8i	−0.908195	−	1.25002i	−0.967779	−	0.251800i	$-0.918978\pi$
$29$	−22150.0	−	30486.8i	−0.908195	−	1.25002i	0.0595846	−	0.998223i	$-0.481022\pi$
$30$		−	2095.78i		−	0.0776214i
$31$	7585.90	+	28809.0i	0.254637	+	0.967037i
$31$	7585.90	+	28809.0i	0.254637	+	0.967037i
$32$	5792.62			0.176777
$33$	41307.0	−	30011.3i	1.14943	−	0.835108i
$34$	−10529.8	+	14493.0i	−0.267907	+	0.368742i
$35$	−2098.26	+	6457.79i	−0.0489391	+	0.150619i
$36$	−3351.40			−0.0718322
$37$		−	73715.5i		−	1.45530i	−0.685946	−	0.727652i	$-0.740611\pi$
$37$		−	73715.5i		−	1.45530i	0.685946	−	0.727652i	$-0.259389\pi$
$38$	−20133.4	+	61964.2i	−0.366916	+	1.12925i
$39$	−23906.5	−	73576.6i	−0.403016	−	1.24035i
$40$	717.736	+	2208.96i	0.0112146	+	0.0345151i
$41$	−58912.7	+	42802.6i	−0.854786	+	0.621038i	−0.926461	−	0.376390i	$-0.877165\pi$
$41$	−58912.7	+	42802.6i	−0.854786	+	0.621038i	0.0716755	+	0.997428i	$0.477165\pi$
$42$	82208.1	+	26711.0i	1.10960	+	0.360531i
$43$	−16365.6	−	22525.3i	−0.205838	−	0.283312i	0.693600	−	0.720361i	$-0.256024\pi$
$43$	−16365.6	−	22525.3i	−0.205838	−	0.283312i	−0.899438	+	0.437049i	$0.856024\pi$
$44$	−33259.9	+	45778.4i	−0.390448	+	0.537406i
$45$	−415.256	−	1278.03i	−0.00455700	−	0.0140250i
$46$	−52578.9	+	72368.7i	−0.540180	+	0.743493i
$47$	154652.	+	112361.i	1.48957	+	1.08224i	0.974311	+	0.225206i	$0.0723056\pi$
$47$	154652.	+	112361.i	1.48957	+	1.08224i	0.515262	+	0.857032i	$0.327694\pi$
$48$	28120.3	−	9136.83i	0.254270	−	0.0826174i
$49$	−131388.	−	95458.6i	−1.11678	−	0.811385i
$50$	70754.2	−	51406.0i	0.566034	−	0.411248i
$51$	−28256.8	+	86965.4i	−0.213016	+	0.655595i
$52$	50395.2	+	69363.0i	0.358409	+	0.493308i
$53$	7937.23	−	2578.96i	0.0533140	−	0.0173228i	−0.282239	−	0.959344i	$-0.591077\pi$
$53$	7937.23	−	2578.96i	0.0533140	−	0.0173228i	0.335553	+	0.942021i	$0.391077\pi$
$54$	96976.4	−	31509.5i	0.615864	−	0.200106i
$55$	−21578.3	−	7011.20i	−0.129697	−	0.0421410i
$56$	−95795.5			−0.545483
$57$			332562.i			1.79576i
$58$	202738.	+	65873.6i	1.03909	+	0.337620i
$59$	−82905.0	−	60234.0i	−0.403669	−	0.293282i	0.367365	−	0.930077i	$-0.380260\pi$
$59$	−82905.0	−	60234.0i	−0.403669	−	0.293282i	−0.771034	+	0.636794i	$0.780260\pi$
$60$	6968.50	+	9591.31i	0.0322616	+	0.0444042i
$61$			71955.9i			0.317013i	0.987358	+	0.158507i	$0.0506679\pi$
$61$			71955.9i			0.317013i	−0.987358	+	0.158507i	$0.949332\pi$
$62$	−130507.	−	106621.i	−0.547595	−	0.447370i
$63$	55423.8			0.221654
$64$	−26509.9	+	19260.5i	−0.101127	+	0.0734732i
$65$	−20206.7	+	27812.2i	−0.0735794	+	0.101273i
$66$	−89253.1	+	274693.i	−0.310450	+	0.955466i
$67$	−241060.			−0.801494			−0.400747	−	0.916189i	$-0.631249\pi$
$67$	−241060.			−0.801494			−0.400747	+	0.916189i	$0.631249\pi$
$68$		−	101339.i		−	0.322292i
$69$	−141096.	+	434248.i	−0.429503	+	1.32187i
$70$	−11869.6	−	36530.8i	−0.0346051	−	0.106504i
$71$	−12458.9	−	38344.4i	−0.0348099	−	0.107134i	0.932142	−	0.362093i	$-0.117938\pi$
$71$	−12458.9	−	38344.4i	−0.0348099	−	0.107134i	−0.966952	+	0.254959i	$0.917938\pi$
$72$	15337.7	−	11143.5i	0.0410924	−	0.0298554i
$73$	−634817.	−	206265.i	−1.63185	−	0.530220i	−0.657154	−	0.753756i	$-0.728240\pi$
$73$	−634817.	−	206265.i	−1.63185	−	0.530220i	−0.974696	+	0.223536i	$0.928240\pi$
$74$	245105.	+	337359.i	0.604864	+	0.832523i
$75$	262393.	−	361152.i	0.621968	−	0.856065i
$76$	−113892.	−	350523.i	−0.259449	−	0.798501i
$77$	550037.	−	757060.i	1.20481	−	1.65828i
$78$	354051.	+	257233.i	0.746074	+	0.542055i
$79$	88175.3	−	28649.9i	0.178841	−	0.0581088i	−0.218228	−	0.975898i	$-0.570028\pi$
$79$	88175.3	−	28649.9i	0.178841	−	0.0581088i	0.397068	+	0.917789i	$0.370028\pi$
$80$	−10629.6	−	7722.82i	−0.0207608	−	0.0150836i
$81$	482839.	−	350803.i	0.908546	−	0.660097i
$82$	127294.	−	391771.i	0.230870	−	0.710544i
$83$	613155.	+	843935.i	1.07235	+	1.47596i	0.867676	+	0.497129i	$0.165613\pi$
$83$	613155.	+	843935.i	1.07235	+	1.47596i	0.204671	+	0.978831i	$0.434387\pi$
$84$	−465039.	+	151100.i	−0.784606	+	0.254934i
$85$	38644.8	−	12556.4i	0.0629265	−	0.0204461i
$86$	149794.	+	48670.9i	0.235504	+	0.0765199i
$87$	1.08810e6			1.65238
$88$		−	320094.i		−	0.469710i
$89$	−748295.	−	243136.i	−1.06146	−	0.344889i	−0.274303	−	0.961643i	$-0.588447\pi$
$89$	−748295.	−	243136.i	−1.06146	−	0.344889i	−0.787155	+	0.616755i	$0.788447\pi$
$90$	6149.88	+	4468.15i	0.00843605	+	0.00612915i
$91$	−833411.	−	1.14709e6i	−1.10595	−	1.52221i
$92$		−	506020.i		−	0.649837i
$93$	−801722.	−	311739.i	−0.996724	−	0.387563i
$94$	−1.08137e6			−1.30194
$95$	119557.	−	86863.2i	0.139445	−	0.101313i
$96$	−98312.0	+	135315.i	−0.111120	+	0.152944i
$97$	−262340.	+	807401.i	−0.287442	+	0.884655i	0.698214	+	0.715889i	$0.253978\pi$
$97$	−262340.	+	807401.i	−0.287442	+	0.884655i	−0.985656	+	0.168766i	$0.946022\pi$
$98$	918695.			0.976098
$99$			185195.i			0.190864i
$100$	−152881.	+	470518.i	−0.152881	+	0.470518i
$101$	42433.4	+	130597.i	0.0411854	+	0.126756i	0.969535	−	0.244952i	$-0.0787723\pi$
$101$	42433.4	+	130597.i	0.0411854	+	0.126756i	−0.928350	+	0.371708i	$0.878772\pi$
$102$	−159844.	−	491950.i	−0.150625	−	0.463576i
$103$	−451374.	+	327943.i	−0.413071	+	0.300114i	−0.774844	−	0.632152i	$-0.782172\pi$
$103$	−451374.	+	327943.i	−0.413071	+	0.300114i	0.361773	+	0.932266i	$0.382172\pi$
$104$	−461266.	−	149874.i	−0.410064	−	0.133238i
$105$	−115242.	−	158616.i	−0.0995500	−	0.137019i
$106$	−27749.6	+	38194.0i	−0.0232991	+	0.0320684i
$107$	60563.6	+	186396.i	0.0494379	+	0.152154i	0.972728	−	0.231950i	$-0.0745104\pi$
$107$	60563.6	+	186396.i	0.0494379	+	0.152154i	−0.923290	+	0.384104i	$0.874510\pi$
$108$	−339042.	+	466651.i	−0.269142	+	0.370443i
$109$	−401490.	−	291700.i	−0.310024	−	0.225246i	0.421883	−	0.906650i	$-0.361369\pi$
$109$	−401490.	−	291700.i	−0.310024	−	0.225246i	−0.731907	+	0.681405i	$0.761369\pi$
$110$	122065.	−	39661.4i	0.0917093	−	0.0297982i
$111$	1.72199e6	+	1.25110e6i	1.25910	+	0.914791i
$112$	438407.	−	318521.i	0.312050	−	0.226717i
$113$	494202.	−	1.52100e6i	0.342507	−	1.05413i	−0.620398	−	0.784287i	$-0.713029\pi$
$113$	494202.	−	1.52100e6i	0.342507	−	1.05413i	0.962905	−	0.269840i	$-0.0869710\pi$
$114$	−1.10577e6	−	1.52197e6i	−0.746366	−	1.02728i
$115$	192966.	−	62698.6i	0.126879	−	0.0412253i
$116$	−1.14686e6	+	372638.i	−0.734745	+	0.238733i
$117$	266872.	+	86712.0i	0.166627	+	0.0541404i
$118$	579693.			0.352819
$119$			1.67590e6i			0.994503i
$120$	−63782.5	−	20724.2i	−0.0369112	−	0.0119932i
$121$	1.09644e6	+	796613.i	0.618914	+	0.449667i
$122$	−239255.	−	329306.i	−0.131759	−	0.181351i
$123$		−	2.10264e6i		−	1.12992i
$124$	951781.	+	54011.2i	0.499197	+	0.0283282i
$125$	−398853.			−0.204213
$126$	−253647.	+	184285.i	−0.126800	+	0.0921252i
$127$	612346.	−	842822.i	0.298941	−	0.411457i	−0.632951	−	0.774191i	$-0.718157\pi$
$127$	612346.	−	842822.i	0.298941	−	0.411457i	0.931893	+	0.362734i	$0.118157\pi$
$128$	57280.6	−	176291.i	0.0273135	−	0.0840623i
$129$	803943.			0.374504
$130$		−	194470.i		−	0.0885162i
$131$	−270217.	+	831642.i	−0.120198	+	0.369932i	−0.992996	−	0.118150i	$-0.962304\pi$
$131$	−270217.	+	831642.i	−0.120198	+	0.369932i	0.872797	+	0.488083i	$0.162304\pi$
$132$	−504892.	−	1.55390e6i	−0.219521	−	0.675617i
$133$	1.88349e6	+	5.79677e6i	0.800585	+	2.46395i
$134$	1.10321e6	−	801527.i	0.458504	−	0.333123i
$135$	−219962.	−	71470.1i	−0.0894019	−	0.0290485i
$136$	336954.	+	463777.i	0.133953	+	0.184371i
$137$	−649864.	+	894461.i	−0.252732	+	0.347856i	−0.916466	−	0.400113i	$-0.868971\pi$
$137$	−649864.	+	894461.i	−0.252732	+	0.347856i	0.663734	+	0.747969i	$0.268971\pi$
$138$	−798157.	−	2.45648e6i	−0.303704	−	0.934706i
$139$	−2.21477e6	+	3.04838e6i	−0.824679	+	1.13507i	0.164211	+	0.986425i	$0.447492\pi$
$139$	−2.21477e6	+	3.04838e6i	−0.824679	+	1.13507i	−0.988890	+	0.148649i	$0.952508\pi$
$140$	175786.	+	127716.i	0.0640621	+	0.0465438i
$141$	−5.24949e6	+	1.70566e6i	−1.87266	+	0.608466i
$142$	184514.	+	134057.i	0.0644412	+	0.0468193i
$143$	3.83293e6	−	2.78479e6i	1.31076	−	0.952322i
$144$	−33140.5	+	101996.i	−0.0110987	+	0.0341582i
$145$	−284204.	−	391173.i	−0.0932237	−	0.128311i
$146$	3.59107e6	−	1.16681e6i	1.15389	−	0.374922i
$147$	4.45981e6	−	1.44908e6i	1.40399	−	0.456184i
$148$	−2.24344e6	−	728939.i	−0.692038	−	0.224857i
$149$	3.55412e6			1.07442			0.537209	−	0.843449i	$-0.319479\pi$
$149$	3.55412e6			1.07442			0.537209	+	0.843449i	$0.319479\pi$
$150$			2.52527e6i			0.748228i
$151$	−3.62766e6	−	1.17870e6i	−1.05365	−	0.342351i	−0.269550	−	0.962987i	$-0.586875\pi$
$151$	−3.62766e6	−	1.17870e6i	−1.05365	−	0.342351i	−0.784099	+	0.620635i	$0.786875\pi$
$152$	1.68672e6	+	1.22547e6i	0.480299	+	0.348958i
$153$	−194949.	−	268325.i	−0.0544312	−	0.0749181i
$154$			5.29356e6i			1.44939i
$155$	97333.9	+	369645.i	0.0261378	+	0.0992636i
$156$	−2.47562e6			−0.652093
$157$	−4.65190e6	+	3.37981e6i	−1.20208	+	0.873359i	−0.994487	−	0.104857i	$-0.966561\pi$
$157$	−4.65190e6	+	3.37981e6i	−1.20208	+	0.873359i	−0.207588	+	0.978216i	$0.566561\pi$
$158$	−308272.	+	424300.i	−0.0781562	+	0.107573i
$159$	−74466.0	+	229183.i	−0.0185254	+	0.0570152i
$160$	74324.5			0.0181456
$161$			8.36832e6i			2.00521i
$162$	−1.04328e6	+	3.21089e6i	−0.245390	+	0.755233i
$163$	208742.	+	642441.i	0.0481999	+	0.148344i	0.972260	−	0.233904i	$-0.0751501\pi$
$163$	208742.	+	642441.i	0.0481999	+	0.148344i	−0.924060	+	0.382248i	$0.875150\pi$
$164$	720085.	+	2.21619e6i	0.163250	+	0.502431i
$165$	530006.	−	385072.i	0.117986	−	0.0857216i
$166$	−5.61219e6	−	1.82351e6i	−1.22690	−	0.398643i
$167$	−2.32116e6	−	3.19480e6i	−0.498373	−	0.685952i	0.483531	−	0.875327i	$-0.339354\pi$
$167$	−2.32116e6	−	3.19480e6i	−0.498373	−	0.685952i	−0.981905	+	0.189375i	$0.939354\pi$
$168$	1.62584e6	−	2.23777e6i	0.342885	−	0.471941i
$169$	−726748.	−	2.23670e6i	−0.150565	−	0.463391i
$170$	−135107.	+	185959.i	−0.0274999	+	0.0378504i
$171$	−975874.	−	709014.i	−0.195167	−	0.141797i
$172$	−847361.	+	275324.i	−0.166526	+	0.0541077i
$173$	−5.65921e6	−	4.11166e6i	−1.09299	−	0.794106i	−0.113091	−	0.993585i	$-0.536075\pi$
$173$	−5.65921e6	−	4.11166e6i	−1.09299	−	0.794106i	−0.979902	+	0.199478i	$0.936075\pi$
$174$	−4.97966e6	+	3.61794e6i	−0.945262	+	0.686773i
$175$	2.52826e6	−	7.78119e6i	0.471746	−	1.45188i
$176$	1.06432e6	+	1.46491e6i	0.195224	+	0.268703i
$177$	2.81412e6	−	914363.i	0.507485	−	0.164892i
$178$	4.23300e6	−	1.37538e6i	0.750564	−	0.243873i
$179$	4.82375e6	+	1.56733e6i	0.841058	+	0.273276i	0.697696	−	0.716394i	$-0.254209\pi$
$179$	4.82375e6	+	1.56733e6i	0.841058	+	0.273276i	0.143362	+	0.989670i	$0.454209\pi$
$180$	−43001.5			−0.00737337
$181$		−	6.60330e6i		−	1.11359i	−0.830650	−	0.556795i	$-0.812031\pi$
$181$		−	6.60330e6i		−	1.11359i	0.830650	−	0.556795i	$-0.187969\pi$
$182$	7.62819e6	+	2.47855e6i	1.26534	+	0.411134i
$183$	−1.68088e6	−	1.22123e6i	−0.274274	−	0.199271i
$184$	1.68253e6	+	2.31580e6i	0.270090	+	0.371747i
$185$		−	945837.i		−	0.149383i
$186$	4.70561e6	−	1.23907e6i	0.731269	−	0.192556i
$187$	−5.59989e6			−0.856357
$188$	4.94886e6	−	3.59556e6i	0.744787	−	0.541119i
$189$	5.60691e6	−	7.71725e6i	0.830497	−	1.14308i
$190$	−258330.	+	795057.i	−0.0376629	+	0.115914i
$191$	−6.50064e6			−0.932945			−0.466473	−	0.884536i	$-0.654475\pi$
$191$	−6.50064e6			−0.932945			−0.466473	+	0.884536i	$0.654475\pi$
$192$		−	946157.i		−	0.133678i
$193$	−266207.	+	819301.i	−0.0370295	+	0.113965i	−0.967863	−	0.251479i	$-0.919083\pi$
$193$	−266207.	+	819301.i	−0.0370295	+	0.113965i	0.930833	+	0.365444i	$0.119083\pi$
$194$	−1.48402e6	−	4.56735e6i	−0.203252	−	0.625545i
$195$	−306742.	−	944054.i	−0.0413684	−	0.127319i
$196$	−4.20440e6	+	3.05468e6i	−0.558388	+	0.405693i
$197$	−485659.	−	157800.i	−0.0635232	−	0.0206400i	0.277083	−	0.960846i	$-0.410632\pi$
$197$	−485659.	−	157800.i	−0.0635232	−	0.0206400i	−0.340606	+	0.940206i	$0.610632\pi$
$198$	−615776.	−	847543.i	−0.0793282	−	0.109186i
$199$	4.62491e6	−	6.36564e6i	0.586872	−	0.807761i	−0.407555	−	0.913180i	$-0.633619\pi$
$199$	4.62491e6	−	6.36564e6i	0.586872	−	0.807761i	0.994428	+	0.105420i	$0.0336187\pi$
$200$	−864823.	−	2.66165e6i	−0.108103	−	0.332706i
$201$	4.09125e6	−	5.63113e6i	0.503812	−	0.693437i
$202$	−628432.	−	456582.i	−0.0762437	−	0.0553943i
$203$	1.89662e7	−	6.16250e6i	2.26721	−	0.736663i
$204$	2.36727e6	+	1.71992e6i	0.278841	+	0.202590i
$205$	−755903.	+	549196.i	−0.0877414	+	0.0637479i
$206$	975296.	−	3.00165e6i	0.111567	−	0.343367i
$207$	−973449.	−	1.33984e6i	−0.109749	−	0.151057i
$208$	2.60932e6	−	847818.i	0.289959	−	0.0942134i
$209$	−1.93695e7	+	6.29354e6i	−2.12168	+	0.689376i
$210$	1.05480e6	+	342727.i	0.113897	+	0.0370075i
$211$	−1.61955e7			−1.72404			−0.862021	−	0.506873i	$-0.830801\pi$
$211$	−1.61955e7			−1.72404			−0.862021	+	0.506873i	$0.830801\pi$
$212$		−	267062.i		−	0.0280288i
$213$	1.10717e6	+	359742.i	0.114571	+	0.0372265i
$214$	−896937.	−	651663.i	−0.0915210	−	0.0664939i
$215$	−209985.	−	289020.i	−0.0211287	−	0.0290812i
$216$		−	3.26294e6i		−	0.323779i
$217$	−1.57401e7	−	893210.i	−1.54038	−	0.0874127i
$218$	2.80732e6			0.270971
$219$	1.55924e7	−	1.13285e7i	1.48450	−	1.07855i
$220$	−426755.	+	587378.i	−0.0400784	+	0.0551632i
$221$	−2.62198e6	+	8.06963e6i	−0.242914	+	0.747613i
$222$	−1.20406e7			−1.10050
$223$			1.05287e7i			0.949428i	0.880140	+	0.474714i	$0.157448\pi$
$223$			1.05287e7i			0.949428i	−0.880140	+	0.474714i	$0.842552\pi$
$224$	−947278.	+	2.91542e6i	−0.0842817	+	0.259392i
$225$	500355.	+	1.53994e6i	0.0439270	+	0.135193i
$226$	2.79563e6	+	8.60406e6i	0.242189	+	0.745381i
$227$	1.25416e7	−	9.11198e6i	1.07220	−	0.778996i	0.0958900	−	0.995392i	$-0.469430\pi$
$227$	1.25416e7	−	9.11198e6i	1.07220	−	0.778996i	0.976306	+	0.216396i	$0.0694303\pi$
$228$	1.01211e7	+	3.28856e6i	0.853935	+	0.277460i
$229$	−1.13446e6	−	1.56144e6i	−0.0944672	−	0.130023i	0.759167	−	0.650896i	$-0.225607\pi$
$229$	−1.13446e6	−	1.56144e6i	−0.0944672	−	0.130023i	−0.853634	+	0.520873i	$0.825607\pi$
$230$	−674635.	+	928556.i	−0.0554479	+	0.0763175i
$231$	8.34965e6	+	2.56976e7i	0.677380	+	2.08476i
$232$	4.00957e6	−	5.51870e6i	0.321095	−	0.441950i
$233$	−7.11883e6	−	5.17214e6i	−0.562783	−	0.408886i	0.269693	−	0.962946i	$-0.413078\pi$
$233$	−7.11883e6	−	5.17214e6i	−0.562783	−	0.408886i	−0.832476	+	0.554060i	$0.813078\pi$
$234$	−1.50966e6	+	490517.i	−0.117823	+	0.0382831i
$235$	1.98433e6	+	1.44170e6i	0.152901	+	0.111089i
$236$	−2.65296e6	+	1.92749e6i	−0.201834	+	0.146641i
$237$	−827249.	+	2.54601e6i	−0.0621429	+	0.191256i
$238$	−5.57238e6	−	7.66972e6i	−0.413342	−	0.568917i
$239$	218834.	−	71103.6i	0.0160296	−	0.00520832i	−0.300991	−	0.953627i	$-0.597317\pi$
$239$	218834.	−	71103.6i	0.0160296	−	0.00520832i	0.317021	+	0.948419i	$0.397317\pi$
$240$	360808.	−	117234.i	0.0261001	−	0.00848045i
$241$	7.31451e6	+	2.37663e6i	0.522558	+	0.169789i	0.558406	−	0.829568i	$-0.311413\pi$
$241$	7.31451e6	+	2.37663e6i	0.522558	+	0.169789i	−0.0358480	+	0.999357i	$0.511413\pi$
$242$	−7.66662e6			−0.540951
$243$			4.09236e6i			0.285203i
$244$	2.18989e6	+	711539.i	0.150749	+	0.0489812i
$245$	−1.68582e6	−	1.22482e6i	−0.114634	−	0.0832864i
$246$	6.99130e6	+	9.62270e6i	0.469627	+	0.646386i
$247$			3.08589e7i			2.04781i
$248$	−4.53540e6	+	2.91750e6i	−0.297345	+	0.191274i
$249$	−3.01206e7			−1.95104
$250$	1.82535e6	−	1.32619e6i	0.116822	−	0.0848764i
$251$	1.28727e7	−	1.77177e7i	0.814043	−	1.12043i	−0.176645	−	0.984275i	$-0.556524\pi$
$251$	1.28727e7	−	1.77177e7i	0.814043	−	1.12043i	0.990687	−	0.136159i	$-0.0434757\pi$
$252$	548061.	−	1.68676e6i	0.0342474	−	0.105403i
$253$	−2.79622e7			−1.72667
$254$			5.89323e6i			0.359627i
$255$	−362560.	+	1.11584e6i	−0.0218655	+	0.0672950i
$256$	324028.	+	997255.i	0.0193136	+	0.0594410i
$257$	2.15976e6	+	6.64706e6i	0.127235	+	0.391589i	0.994302	−	0.106603i	$-0.0339975\pi$
$257$	2.15976e6	+	6.64706e6i	0.127235	+	0.391589i	−0.867067	+	0.498192i	$0.833997\pi$
$258$	−3.67924e6	+	2.67312e6i	−0.214239	+	0.155654i
$259$	3.71010e7	+	1.20548e7i	2.13543	+	0.693845i
$260$	646616.	+	889990.i	0.0367897	+	0.0506367i
$261$	−2.31979e6	+	3.19292e6i	−0.130475	+	0.179584i
$262$	−1.52858e6	−	4.70448e6i	−0.0849930	−	0.261582i
$263$	−1.24720e7	+	1.71662e7i	−0.685597	+	0.943644i	−0.999984	−	0.00565120i	$-0.998201\pi$
$263$	−1.24720e7	+	1.71662e7i	−0.685597	+	0.943644i	0.314387	+	0.949295i	$0.398201\pi$
$264$	7.47736e6	+	5.43262e6i	0.406384	+	0.295255i
$265$	101842.	−	33090.4i	0.00547253	−	0.00177813i
$266$	−2.78941e7	−	2.02663e7i	−1.48207	−	1.07678i
$267$	1.83797e7	−	1.33536e7i	0.965614	−	0.701560i
$268$	−2.38373e6	+	7.33637e6i	−0.123838	+	0.381133i
$269$	1.11157e7	+	1.52995e7i	0.571058	+	0.785994i	0.992680	−	0.120778i	$-0.0385389\pi$
$269$	1.11157e7	+	1.52995e7i	0.571058	+	0.785994i	−0.421622	+	0.906772i	$0.638539\pi$
$270$	1.24429e6	−	404296.i	0.0632167	−	0.0205404i
$271$	−3.04027e7	+	9.87842e6i	−1.52758	+	0.496340i	−0.947917	−	0.318517i	$-0.896815\pi$
$271$	−3.04027e7	+	9.87842e6i	−1.52758	+	0.496340i	−0.579662	+	0.814857i	$0.696815\pi$
$272$	−3.08413e6	−	1.00210e6i	−0.153259	−	0.0497969i
$273$	4.09405e7			2.01217
$274$		−	6.25430e6i		−	0.304037i
$275$	2.60003e7	+	8.44802e6i	1.25020	+	0.406216i
$276$	1.18206e7	+	8.58815e6i	0.562227	+	0.408482i
$277$	−5.54201e6	−	7.62792e6i	−0.260752	−	0.358894i	0.658489	−	0.752591i	$-0.271196\pi$
$277$	−5.54201e6	−	7.62792e6i	−0.260752	−	0.358894i	−0.919241	+	0.393696i	$0.871196\pi$
$278$		−	2.13150e7i		−	0.992091i
$279$	2.62402e6	−	1.68796e6i	0.120824	−	0.0777231i
$280$	−1.22914e6			−0.0559923
$281$	9.10326e6	−	6.61391e6i	0.410278	−	0.298084i	−0.363436	−	0.931619i	$-0.618397\pi$
$281$	9.10326e6	−	6.61391e6i	0.410278	−	0.298084i	0.773714	+	0.633535i	$0.218397\pi$
$282$	1.83529e7	−	2.52606e7i	0.818384	−	1.12641i
$283$	9.12995e6	−	2.80991e7i	0.402818	−	1.23975i	−0.519885	−	0.854236i	$-0.674025\pi$
$283$	9.12995e6	−	2.80991e7i	0.402818	−	1.23975i	0.922703	−	0.385511i	$-0.125975\pi$
$284$	−1.29017e6			−0.0563236
$285$			4.26707e6i			0.184330i
$286$	−8.28191e6	+	2.54891e7i	−0.354024	+	1.08957i
$287$	−1.19084e7	−	3.66503e7i	−0.503742	−	1.55036i
$288$	−187471.	−	576976.i	−0.00784795	−	0.0241535i
$289$	−1.14141e7	+	8.29286e6i	−0.472879	+	0.343567i
$290$	2.60131e6	+	845218.i	0.106659	+	0.0346557i
$291$	−1.44084e7	−	1.98314e7i	−0.584703	−	0.804775i
$292$	−1.25548e7	+	1.72803e7i	−0.504269	+	0.694067i
$293$	1.85009e6	+	5.69400e6i	0.0735513	+	0.226368i	0.981073	−	0.193637i	$-0.0620284\pi$
$293$	1.85009e6	+	5.69400e6i	0.0735513	+	0.226368i	−0.907522	+	0.420005i	$0.862028\pi$
$294$	−1.55921e7	+	2.14606e7i	−0.613566	+	0.844501i
$295$	−1.06375e6	−	772857.i	−0.0414355	−	0.0301046i
$296$	1.26908e7	−	4.12350e6i	0.489345	−	0.158998i
$297$	2.57867e7	+	1.87351e7i	0.984296	+	0.715133i
$298$	−1.62654e7	+	1.18175e7i	−0.614633	+	0.446557i
$299$	−1.30924e7	+	4.02944e7i	−0.489787	+	1.50741i
$300$	−8.39656e6	−	1.15569e7i	−0.310984	−	0.428032i
$301$	1.40132e7	−	4.55318e6i	0.513853	−	0.166961i
$302$	2.05212e7	−	6.66773e6i	0.745042	−	0.242079i
$303$	−3.77090e6	−	1.22524e6i	−0.135555	−	0.0440446i
$304$	−1.17940e7			−0.419797
$305$			923260.i			0.0325405i
$306$	1.78437e6	+	579777.i	0.0622760	+	0.0202347i
$307$	−2.14945e7	−	1.56166e7i	−0.742868	−	0.539725i	0.150740	−	0.988573i	$-0.451834\pi$
$307$	−2.14945e7	−	1.56166e7i	−0.742868	−	0.539725i	−0.893608	+	0.448848i	$0.851834\pi$
$308$	−1.76012e7	−	2.42259e7i	−0.602406	−	0.829141i
$309$		−	1.61099e7i		−	0.546030i
$310$	−1.67452e6	−	1.36804e6i	−0.0562091	−	0.0459213i
$311$	−2.23080e7			−0.741617			−0.370808	−	0.928709i	$-0.620919\pi$
$311$	−2.23080e7			−0.741617			−0.370808	+	0.928709i	$0.620919\pi$
$312$	1.13296e7	−	8.23146e6i	0.373037	−	0.271027i
$313$	8.28388e6	−	1.14018e7i	0.270147	−	0.371826i	−0.652292	−	0.757968i	$-0.726192\pi$
$313$	8.28388e6	−	1.14018e7i	0.270147	−	0.371826i	0.922439	+	0.386142i	$0.126192\pi$
$314$	1.00515e7	−	3.09353e7i	0.324670	−	0.999230i
$315$	711138.			0.0227521
$316$		−	2.96682e6i		−	0.0940220i
$317$	−3.54448e6	+	1.09088e7i	−0.111269	+	0.342451i	−0.991151	−	0.132742i	$-0.957622\pi$
$317$	−3.54448e6	+	1.09088e7i	−0.111269	+	0.342451i	0.879881	+	0.475193i	$0.157622\pi$
$318$	−421243.	−	1.29645e6i	−0.0130994	−	0.0403158i
$319$	2.05916e7	+	6.33743e7i	0.634333	+	1.95228i
$320$	−340146.	+	247130.i	−0.0103804	+	0.00754182i
$321$	−5.38206e6	−	1.74874e6i	−0.162717	−	0.0528701i
$322$	−2.78248e7	−	3.82975e7i	−0.833420	−	1.14710i
$323$	2.14390e7	−	2.95083e7i	0.636206	−	0.875663i
$324$	−5.90170e6	−	1.81636e7i	−0.173517	−	0.534030i
$325$	2.43477e7	−	3.35118e7i	0.709265	−	0.976220i
$326$	−3.09143e6	−	2.24605e6i	−0.0892291	−	0.0648287i
$327$	1.36281e7	−	4.42805e6i	0.389757	−	0.126640i
$328$	−1.06643e7	−	7.74810e6i	−0.302212	−	0.219570i
$329$	−8.18419e7	+	5.94616e7i	−2.29820	+	1.66974i
$330$	−1.14520e6	+	3.52456e6i	−0.0318668	+	0.0980760i
$331$	−3.10930e7	−	4.27959e7i	−0.857391	−	1.18010i	−0.982185	−	0.187915i	$-0.939827\pi$
$331$	−3.10930e7	−	4.27959e7i	−0.857391	−	1.18010i	0.124795	−	0.992183i	$-0.460173\pi$
$332$	3.17474e7	−	1.03153e7i	0.867548	−	0.281883i
$333$	−7.34246e6	+	2.38571e6i	−0.198842	+	0.0646078i
$334$	2.12455e7	+	6.90308e6i	0.570200	+	0.185269i
$335$	−3.09302e6			−0.0822712
$336$			1.56471e7i			0.412492i
$337$	4.54234e6	+	1.47590e6i	0.118683	+	0.0385626i	0.367757	−	0.929922i	$-0.380126\pi$
$337$	4.54234e6	+	1.47590e6i	0.118683	+	0.0385626i	−0.249073	+	0.968485i	$0.580126\pi$
$338$	1.07630e7	+	7.81979e6i	0.278730	+	0.202509i
$339$	2.71427e7	+	3.73588e7i	0.696714	+	0.958945i
$340$		−	1.30027e6i		−	0.0330824i
$341$	2.98460e6	−	5.25944e7i	0.0752702	−	1.32641i
$342$	6.82356e6			0.170582
$343$	1.91610e7	−	1.39213e7i	0.474828	−	0.344983i
$344$	2.96248e6	−	4.07751e6i	0.0727747	−	0.100166i
$345$	−1.81038e6	+	5.57179e6i	−0.0440873	+	0.135687i
$346$	3.95707e7			0.955312
$347$			370331.i			0.00886344i	0.999990	+	0.00443172i	$0.00141066\pi$
$347$			370331.i			0.00886344i	−0.999990	+	0.00443172i	$0.998589\pi$
$348$	1.07597e7	−	3.31149e7i	0.255307	−	0.785753i
$349$	7.21517e6	+	2.22060e7i	0.169735	+	0.522389i	0.999354	−	0.0359400i	$-0.0114425\pi$
$349$	7.21517e6	+	2.22060e7i	0.169735	+	0.522389i	−0.829619	+	0.558329i	$0.811443\pi$
$350$	1.43020e7	+	4.40171e7i	0.333575	+	1.02664i
$351$	3.90717e7	−	2.83873e7i	0.903527	−	0.656451i
$352$	−9.74169e6	−	3.16527e6i	−0.223360	−	0.0725742i
$353$	1.66298e7	+	2.28890e7i	0.378063	+	0.520359i	0.955070	−	0.296380i	$-0.0957795\pi$
$353$	1.66298e7	+	2.28890e7i	0.378063	+	0.520359i	−0.577007	+	0.816739i	$0.695780\pi$
$354$	−9.83852e6	+	1.35416e7i	−0.221779	+	0.305252i
$355$	−159858.	−	491994.i	−0.00357314	−	0.0109970i
$356$	−1.47991e7	+	2.03692e7i	−0.328009	+	0.451465i
$357$	−3.91487e7	−	2.84432e7i	−0.860425	−	0.625135i
$358$	−2.72873e7	+	8.86617e6i	−0.594718	+	0.193236i
$359$	−5.81911e7	−	4.22783e7i	−1.25769	−	0.913764i	−0.259047	−	0.965865i	$-0.583408\pi$
$359$	−5.81911e7	−	4.22783e7i	−1.25769	−	0.913764i	−0.998642	+	0.0521002i	$0.983408\pi$
$360$	196796.	−	142981.i	0.00421802	−	0.00306457i
$361$	2.64543e7	−	8.14179e7i	0.562308	−	1.73061i
$362$	2.19561e7	+	3.02200e7i	0.462838	+	0.637042i
$363$	−3.72176e7	+	1.20927e7i	−0.778087	+	0.252816i
$364$	−4.31516e7	+	1.40208e7i	−0.894731	+	0.290716i
$365$	−8.14528e6	−	2.64656e6i	−0.167505	−	0.0544256i
$366$	1.17532e7			0.239724
$367$		−	494150.i		−	0.00999680i	−0.999988	−	0.00499840i	$-0.998409\pi$
$367$		−	494150.i		−	0.00999680i	0.999988	−	0.00499840i	$-0.00159105\pi$
$368$	−1.54001e7	−	5.00380e6i	−0.309016	−	0.100405i
$369$	6.17000e6	+	4.48277e6i	0.122802	+	0.0892211i
$370$	3.14492e6	+	4.32862e6i	0.0620876	+	0.0854562i
$371$			4.41654e6i			0.0864890i
$372$	−1.74153e7	+	2.13168e7i	−0.338300	+	0.414089i
$373$	−3.62516e7			−0.698554			−0.349277	−	0.937019i	$-0.613573\pi$
$373$	−3.62516e7			−0.698554			−0.349277	+	0.937019i	$0.613573\pi$
$374$	2.56279e7	−	1.86197e7i	0.489889	−	0.355925i
$375$	6.76932e6	−	9.31717e6i	0.128366	−	0.176681i
$376$	−1.06931e7	+	3.29101e7i	−0.201160	+	0.619107i
$377$	1.00966e8			1.88430
$378$			5.39610e7i			0.999089i
$379$	−2.84683e7	+	8.76165e7i	−0.522931	+	1.60942i	0.245440	+	0.969412i	$0.421068\pi$
$379$	−2.84683e7	+	8.76165e7i	−0.522931	+	1.60942i	−0.768371	+	0.640005i	$0.778932\pi$
$380$	−1.46133e6	−	4.49752e6i	−0.0266317	−	0.0819639i
$381$	9.29552e6	+	2.86087e7i	0.168073	+	0.517276i
$382$	2.97501e7	−	2.16147e7i	0.533702	−	0.387757i
$383$	−1.78291e6	−	579303.i	−0.0317346	−	0.0103112i	0.293107	−	0.956080i	$-0.405311\pi$
$383$	−1.78291e6	−	579303.i	−0.0317346	−	0.0103112i	−0.324841	+	0.945769i	$0.605311\pi$
$384$	3.14599e6	+	4.33008e6i	0.0555601	+	0.0764719i
$385$	7.05747e6	−	9.71377e6i	0.123671	−	0.170218i
$386$	−1.50590e6	−	4.63467e6i	−0.0261838	−	0.0805855i
$387$	−1.71399e6	+	2.35910e6i	−0.0295716	+	0.0407018i
$388$	2.19781e7	+	1.59680e7i	0.376266	+	0.273373i
$389$	−3.10798e7	+	1.00985e7i	−0.527995	+	0.171556i	−0.560871	−	0.827903i	$-0.689534\pi$
$389$	−3.10798e7	+	1.00985e7i	−0.527995	+	0.171556i	0.0328754	+	0.999459i	$0.489534\pi$
$390$	4.54280e6	+	3.30053e6i	0.0765825	+	0.0556404i
$391$	4.05138e7	−	2.94350e7i	0.677754	−	0.492417i
$392$	9.08456e6	−	2.79594e7i	0.150815	−	0.464162i
$393$	−1.48409e7	−	2.04268e7i	−0.244503	−	0.336529i
$394$	2.74730e6	−	892652.i	0.0449177	−	0.0145946i
$395$	1.13137e6	−	367604.i	0.0183575	−	0.00596471i
$396$	5.63619e6	+	1.83131e6i	0.0907612	+	0.0294901i
$397$	7.60268e7			1.21505			0.607526	−	0.794300i	$-0.292162\pi$
$397$	7.60268e7			1.21505			0.607526	+	0.794300i	$0.292162\pi$
$398$			4.45102e7i			0.706009i
$399$	−1.67378e8	−	5.43845e7i	−2.63500	−	0.856163i
$400$	1.28079e7	+	9.30547e6i	0.200123	+	0.145398i
$401$	4.75592e7	+	6.54597e7i	0.737568	+	1.01517i	0.998755	+	0.0498865i	$0.0158859\pi$
$401$	4.75592e7	+	6.54597e7i	0.737568	+	1.01517i	−0.261187	+	0.965288i	$0.584114\pi$
$402$			3.93743e7i			0.606087i
$403$	−7.43928e7	−	2.89267e7i	−1.13662	−	0.441960i
$404$	4.39415e6			0.0666394
$405$	6.19526e6	−	4.50112e6i	0.0932598	−	0.0677572i
$406$	−6.63083e7	+	9.12656e7i	−0.990809	+	1.36373i
$407$	−4.02804e7	+	1.23970e8i	−0.597463	+	1.83880i
$408$	−1.65526e7			−0.243716
$409$			2.74112e6i			0.0400644i	0.999799	+	0.0200322i	$0.00637687\pi$
$409$			2.74112e6i			0.0400644i	−0.999799	+	0.0200322i	$0.993623\pi$
$410$	1.63330e6	−	5.02678e6i	0.0236981	−	0.0729354i
$411$	−9.86505e6	−	3.03615e7i	−0.142093	−	0.437318i
$412$	5.51711e6	+	1.69799e7i	0.0788896	+	0.242797i
$413$	4.38734e7	−	3.18759e7i	0.622803	−	0.452493i
$414$	8.90996e6	+	2.89502e6i	0.125567	+	0.0407991i
$415$	7.86733e6	+	1.08284e7i	0.110074	+	0.151503i
$416$	−9.12250e6	+	1.25560e7i	−0.126717	+	0.174411i
$417$	−3.36207e7	−	1.03474e8i	−0.463658	−	1.42699i
$418$	6.77183e7	−	9.32063e7i	0.927209	−	1.27619i
$419$	3.31990e7	+	2.41205e7i	0.451319	+	0.327902i	0.790116	−	0.612957i	$-0.210020\pi$
$419$	3.31990e7	+	2.41205e7i	0.451319	+	0.327902i	−0.338797	+	0.940859i	$0.610020\pi$
$420$	−5.96687e6	+	1.93875e6i	−0.0805376	+	0.0261683i
$421$	5.49113e7	+	3.98954e7i	0.735894	+	0.534659i	0.891423	−	0.453173i	$-0.149708\pi$
$421$	5.49113e7	+	3.98954e7i	0.735894	+	0.534659i	−0.155528	+	0.987831i	$0.549708\pi$
$422$	7.41187e7	−	5.38504e7i	0.986258	−	0.716558i
$423$	6.18667e6	−	1.90406e7i	0.0817402	−	0.251570i
$424$	887986.	+	1.22221e6i	0.0116495	+	0.0160342i
$425$	−4.65643e7	+	1.51297e7i	−0.606577	+	0.197089i
$426$	−6.26311e6	+	2.03501e6i	−0.0810142	+	0.0263231i
$427$	−3.62154e7	−	1.17671e7i	−0.465168	−	0.151142i
$428$	6.27161e6			0.0799923
$429$			1.36800e8i			1.73266i
$430$	1.92199e6	+	624492.i	0.0241738	+	0.00785456i
$431$	−2.71886e7	−	1.97537e7i	−0.339590	−	0.246727i	0.404899	−	0.914362i	$-0.367307\pi$
$431$	−2.71886e7	−	1.97537e7i	−0.339590	−	0.246727i	−0.744489	+	0.667635i	$0.767307\pi$
$432$	1.08493e7	+	1.49328e7i	0.134571	+	0.185221i
$433$			6.17329e7i			0.760418i	0.924900	+	0.380209i	$0.124148\pi$
$433$			6.17329e7i			0.760418i	−0.924900	+	0.380209i	$0.875852\pi$
$434$	7.50043e7	−	4.82482e7i	0.917523	−	0.590218i
$435$	1.39613e7			0.169612
$436$	−1.28477e7	+	9.33439e6i	−0.155012	+	0.112623i
$437$	1.07052e8	−	1.47345e8i	1.28278	−	1.76560i
$438$	−3.36909e7	+	1.03690e8i	−0.400950	+	1.23400i
$439$	5.89654e7			0.696954			0.348477	−	0.937317i	$-0.386699\pi$
$439$	5.89654e7			0.696954			0.348477	+	0.937317i	$0.386699\pi$
$440$		−	4.10710e6i		−	0.0482144i
$441$	−5.25600e6	+	1.61763e7i	−0.0612829	+	0.188610i
$442$	−1.48322e7	−	4.56487e7i	−0.171766	−	0.528642i
$443$	1.31982e7	+	4.06199e7i	0.151811	+	0.467227i	0.997824	−	0.0659357i	$-0.0210032\pi$
$443$	1.31982e7	+	4.06199e7i	0.151811	+	0.467227i	−0.846013	+	0.533163i	$0.821003\pi$
$444$	5.51036e7	−	4.00351e7i	0.629551	−	0.457395i
$445$	−9.60131e6	−	3.11965e6i	−0.108956	−	0.0354019i
$446$	−3.50082e7	−	4.81847e7i	−0.394608	−	0.543131i
$447$	−6.03203e7	+	8.30238e7i	−0.675369	+	0.929565i
$448$	−5.35861e6	−	1.64921e7i	−0.0595962	−	0.183418i
$449$	−4.70627e7	+	6.47762e7i	−0.519921	+	0.715610i	−0.985553	−	0.169368i	$-0.945827\pi$
$449$	−4.70627e7	+	6.47762e7i	−0.519921	+	0.715610i	0.465632	+	0.884979i	$0.345827\pi$
$450$	−7.41018e6	−	5.38381e6i	−0.0813189	−	0.0590816i
$451$	1.22465e8	−	3.97912e7i	1.33500	−	0.433767i
$452$	−4.14028e7	−	3.00809e7i	−0.448347	−	0.325743i
$453$	8.91028e7	−	6.47370e7i	0.958510	−	0.696398i
$454$	−2.70989e7	+	8.34018e7i	−0.289590	+	0.891267i
$455$	−1.06934e7	−	1.47182e7i	−0.113523	−	0.156250i
$456$	−5.72538e7	+	1.86029e7i	−0.603823	+	0.196194i
$457$	2.84401e7	−	9.24076e6i	0.297977	−	0.0968187i	−0.156213	−	0.987723i	$-0.549929\pi$
$457$	2.84401e7	−	9.24076e6i	0.297977	−	0.0968187i	0.454190	+	0.890905i	$0.349929\pi$
$458$	1.03837e7	+	3.37385e6i	0.108082	+	0.0351180i
$459$	−5.70836e7			−0.590301
$460$		−	6.49270e6i		−	0.0667040i
$461$	−8.82976e7	−	2.86896e7i	−0.901252	−	0.292835i	−0.178498	−	0.983940i	$-0.557124\pi$
$461$	−8.82976e7	−	2.86896e7i	−0.901252	−	0.292835i	−0.722754	+	0.691106i	$0.757124\pi$
$462$	−1.23657e8	−	8.98421e7i	−1.25399	−	0.911074i
$463$	−1.77706e7	−	2.44592e7i	−0.179044	−	0.246433i	0.710057	−	0.704144i	$-0.248669\pi$
$463$	−1.77706e7	−	2.44592e7i	−0.179044	−	0.246433i	−0.889101	+	0.457711i	$0.848669\pi$
$464$			3.85882e7i			0.386278i
$465$	−1.02868e7	−	3.99989e6i	−0.102311	−	0.0397823i
$466$	4.97767e7			0.491890
$467$	−1.44251e8	+	1.04804e8i	−1.41634	+	1.02903i	−0.423976	+	0.905673i	$0.639366\pi$
$467$	−1.44251e8	+	1.04804e8i	−1.41634	+	1.02903i	−0.992362	+	0.123357i	$0.960634\pi$
$468$	5.27795e6	−	7.26448e6i	0.0514906	−	0.0708707i
$469$	3.94210e7	−	1.21325e8i	0.382128	−	1.17607i
$470$	−1.38749e7			−0.133640
$471$		−	1.66030e8i		−	1.58900i
$472$	5.73232e6	−	1.76423e7i	0.0545136	−	0.167776i
$473$	1.52141e7	+	4.68243e7i	0.143769	+	0.442474i
$474$	−4.67963e6	−	1.44024e7i	−0.0439416	−	0.135238i
$475$	−1.44058e8	+	1.04664e8i	−1.34418	+	0.976602i
$476$	5.10039e7	+	1.65722e7i	0.472914	+	0.153659i
$477$	−513757.	−	707126.i	−0.00473372	−	0.00651541i
$478$	−765073.	+	1.05303e6i	−0.00700518	+	0.00964180i
$479$	6.29622e7	+	1.93778e8i	0.572893	+	1.76318i	0.643245	+	0.765660i	$0.277588\pi$
$479$	6.29622e7	+	1.93778e8i	0.572893	+	1.76318i	−0.0703526	+	0.997522i	$0.522412\pi$
$480$	−1.26143e6	+	1.73621e6i	−0.0114062	+	0.0156993i
$481$	1.59785e8	+	1.16091e8i	1.43583	+	1.04319i
$482$	−4.13771e7	+	1.34442e7i	−0.369504	+	0.120059i
$483$	−1.95483e8	−	1.42027e8i	−1.73487	−	1.26046i
$484$	3.50862e7	−	2.54916e7i	0.309457	−	0.224834i
$485$	−3.36606e6	+	1.03597e7i	−0.0295051	+	0.0908074i
$486$	−1.36072e7	−	1.87286e7i	−0.118538	−	0.163154i
$487$	1.12079e8	−	3.64165e7i	0.970366	−	0.315291i	0.219403	−	0.975634i	$-0.429589\pi$
$487$	1.12079e8	−	3.64165e7i	0.970366	−	0.315291i	0.750964	+	0.660343i	$0.229589\pi$
$488$	−1.23879e7	+	4.02507e6i	−0.106595	+	0.0346349i
$489$	−1.85501e7	−	6.02729e6i	−0.158642	−	0.0515461i
$490$	1.17877e7			0.100194
$491$		−	5.87355e7i		−	0.496199i	−0.968735	−	0.248100i	$-0.920194\pi$
$491$		−	5.87355e7i		−	0.496199i	0.968735	−	0.248100i	$-0.0798060\pi$
$492$	−6.39913e7	−	2.07920e7i	−0.537311	−	0.174583i
$493$	−9.65470e7	−	7.01455e7i	−0.805746	−	0.585409i
$494$	−1.02606e8	−	1.41225e8i	−0.851124	−	1.17147i
$495$			2.37622e6i			0.0195917i
$496$	1.10555e7	−	2.84322e7i	0.0906010	−	0.233005i
$497$	2.13361e7			0.173799
$498$	1.37847e8	−	1.00152e8i	1.11611	−	0.810905i
$499$	2.61425e7	−	3.59821e7i	0.210400	−	0.289591i	−0.690754	−	0.723090i	$-0.742721\pi$
$499$	2.61425e7	−	3.59821e7i	0.210400	−	0.289591i	0.901154	+	0.433499i	$0.142721\pi$
$500$	−3.94408e6	+	1.21386e7i	−0.0315526	+	0.0971090i
$501$	1.14025e8			0.906746
$502$			1.23887e8i			0.979295i
$503$	−2.74693e7	+	8.45418e7i	−0.215846	+	0.664305i	0.783247	+	0.621711i	$0.213562\pi$
$503$	−2.74693e7	+	8.45418e7i	−0.215846	+	0.664305i	−0.999092	+	0.0425938i	$0.986438\pi$
$504$	3.10030e6	+	9.54175e6i	0.0242165	+	0.0745309i
$505$	544459.	+	1.67567e6i	0.00422757	+	0.0130111i
$506$	1.27969e8	−	9.29746e7i	0.987761	−	0.717650i
$507$	6.45834e7	+	2.09844e7i	0.495561	+	0.161017i
$508$	−1.95951e7	−	2.69703e7i	−0.149471	−	0.205729i
$509$	−2.06511e7	+	2.84239e7i	−0.156600	+	0.215541i	−0.880107	−	0.474776i	$-0.842529\pi$
$509$	−2.06511e7	+	2.84239e7i	−0.156600	+	0.215541i	0.723507	+	0.690317i	$0.242529\pi$
$510$	−2.05095e6	−	6.31217e6i	−0.0154612	−	0.0475848i
$511$	2.07626e8	−	2.85772e8i	1.55603	−	2.14169i
$512$	−4.79880e6	−	3.48653e6i	−0.0357538	−	0.0259767i
$513$	−1.97447e8	+	6.41544e7i	−1.46251	+	0.475198i
$514$	−3.19857e7	−	2.32390e7i	−0.235541	−	0.171131i
$515$	−5.79154e6	+	4.20780e6i	−0.0424006	+	0.0308059i
$516$	7.94983e6	−	2.44671e7i	0.0578640	−	0.178087i
$517$	−1.98687e8	−	2.73469e8i	−1.43780	−	1.97896i
$518$	−2.09875e8	+	6.81925e7i	−1.50998	+	0.490622i
$519$	1.92096e8	−	6.24157e7i	1.37409	−	0.446469i
$520$	−5.91846e6	−	1.92303e6i	−0.0420919	−	0.0136765i
$521$	2.15156e8			1.52139			0.760695	−	0.649109i	$-0.224858\pi$
$521$	2.15156e8			1.52139			0.760695	+	0.649109i	$0.224858\pi$
$522$		−	2.23257e7i		−	0.156962i
$523$	4.14263e7	+	1.34602e7i	0.289582	+	0.0940908i	0.450206	−	0.892925i	$-0.351351\pi$
$523$	4.14263e7	+	1.34602e7i	0.289582	+	0.0940908i	−0.160624	+	0.987016i	$0.551351\pi$
$524$	2.26380e7	+	1.64474e7i	0.157342	+	0.114315i
$525$	1.38858e8	+	1.91122e8i	0.959608	+	1.32079i
$526$		−	1.20031e8i		−	0.824775i
$527$	5.10403e7	+	7.93447e7i	0.348724	+	0.542108i
$528$	−5.22836e7			−0.355193
$529$	8.25354e7	−	5.99655e7i	0.557536	−	0.405074i
$530$	−356052.	+	490064.i	−0.00239158	+	0.00329173i
$531$	−3.31652e6	+	1.02072e7i	−0.0221513	+	0.0681746i
$532$	1.95043e8			1.29537
$533$		−	1.95106e8i		−	1.28852i
$534$	−3.97134e7	+	1.22225e8i	−0.260803	+	0.802670i
$535$	777086.	+	2.39162e6i	0.00507467	+	0.0156182i
$536$	−1.34844e7	−	4.15008e7i	−0.0875664	−	0.269502i
$537$	−1.18481e8	+	8.60816e7i	−0.765115	+	0.555888i
$538$	−1.01742e8	−	3.30579e7i	−0.653360	−	0.212290i
$539$	1.68798e8	+	2.32331e8i	1.07796	+	1.48368i
$540$	−4.35021e6	+	5.98756e6i	−0.0276267	+	0.0380249i
$541$	−5.55239e7	−	1.70885e8i	−0.350662	−	1.07923i	−0.958482	−	0.285152i	$-0.907956\pi$
$541$	−5.55239e7	−	1.70885e8i	−0.350662	−	1.07923i	0.607820	−	0.794074i	$-0.292044\pi$
$542$	1.06292e8	−	1.46298e8i	0.667576	−	0.918840i
$543$	1.54252e8	+	1.12071e8i	0.963457	+	0.699993i
$544$	1.74465e7	−	5.66871e6i	0.108371	−	0.0352117i
$545$	−5.15149e6	−	3.74277e6i	−0.0318231	−	0.0231209i
$546$	−1.87364e8	+	1.36128e8i	−1.15109	+	0.836314i
$547$	−7.07739e7	+	2.17820e8i	−0.432426	+	1.33087i	0.463276	+	0.886214i	$0.346674\pi$
$547$	−7.07739e7	+	2.17820e8i	−0.432426	+	1.33087i	−0.895702	+	0.444655i	$0.853326\pi$
$548$	2.07956e7	+	2.86227e7i	0.126366	+	0.173928i
$549$	7.16720e6	−	2.32876e6i	0.0433144	−	0.0140737i
$550$	−1.47080e8	+	4.77892e7i	−0.884028	+	0.287238i
$551$	−4.12782e8	−	1.34121e8i	−2.46755	−	0.801755i
$552$	−8.26525e7			−0.491404
$553$			4.90638e7i			0.290125i
$554$	5.07259e7	+	1.64818e7i	0.298332	+	0.0969340i
$555$	2.20946e7	+	1.60527e7i	0.129243	+	0.0939008i
$556$	7.08728e7	+	9.75480e7i	0.412340	+	0.567537i
$557$		−	5.65390e7i		−	0.327177i	−0.986529	−	0.163588i	$-0.947693\pi$
$557$		−	5.65390e7i		−	0.327177i	0.986529	−	0.163588i	$-0.0523069\pi$
$558$	−6.39631e6	+	1.64499e7i	−0.0368152	+	0.0946803i
$559$	7.45989e7			0.427068
$560$	5.62516e6	−	4.08692e6i	0.0320310	−	0.0232719i
$561$	9.50411e7	−	1.30813e8i	0.538298	−	0.740904i
$562$	−1.96697e7	+	6.05370e7i	−0.110812	+	0.341045i
$563$	1.41456e7			0.0792678			0.0396339	−	0.999214i	$-0.487381\pi$
$563$	1.41456e7			0.0792678			0.0396339	+	0.999214i	$0.487381\pi$
$564$			1.76629e8i			0.984518i
$565$	6.34106e6	−	1.95158e7i	0.0351574	−	0.108203i
$566$	5.16468e7	+	1.58952e8i	0.284835	+	0.876633i
$567$	9.75993e7	+	3.00380e8i	0.535424	+	1.64787i
$568$	5.90444e6	−	4.28982e6i	0.0322206	−	0.0234096i
$569$	2.25964e8	+	7.34201e7i	1.22660	+	0.398546i	0.849481	−	0.527620i	$-0.176915\pi$
$569$	2.25964e8	+	7.34201e7i	1.22660	+	0.398546i	0.377117	+	0.926166i	$0.376915\pi$
$570$	−1.41881e7	−	1.95282e7i	−0.0766124	−	0.105448i
$571$	−1.23148e8	+	1.69499e8i	−0.661486	+	0.910457i	−0.999529	−	0.0306732i	$-0.990235\pi$
$571$	−1.23148e8	+	1.69499e8i	−0.661486	+	0.910457i	0.338044	+	0.941130i	$0.390235\pi$
$572$	−4.68496e7	−	1.44188e8i	−0.250333	−	0.770445i
$573$	1.10329e8	−	1.51854e8i	0.586441	−	0.807167i
$574$	1.76362e8	+	1.28134e8i	0.932542	+	0.677531i
$575$	−2.32511e8	+	7.55475e7i	−1.22304	+	0.397390i
$576$	2.77641e6	+	2.01718e6i	0.0145284	+	0.0105555i
$577$	−1.40806e8	+	1.02301e8i	−0.732981	+	0.532542i	−0.890505	−	0.454973i	$-0.849649\pi$
$577$	−1.40806e8	+	1.02301e8i	−0.732981	+	0.532542i	0.157524	+	0.987515i	$0.449649\pi$
$578$	2.46628e7	−	7.59044e7i	0.127720	−	0.393082i
$579$	−1.46207e7	−	2.01237e7i	−0.0753240	−	0.103675i
$580$	−1.47153e7	+	4.78128e6i	−0.0754196	+	0.0245053i
$581$	−5.25022e8	+	1.70590e8i	−2.67701	+	0.869812i
$582$	1.31879e8	+	4.28502e7i	0.668972	+	0.217362i
$583$	−1.47576e7			−0.0744749
$584$		−	1.20828e8i		−	0.606637i
$585$	3.42421e6	+	1.11259e6i	0.0171038	+	0.00555736i
$586$	−2.73995e7	−	1.99069e7i	−0.136160	−	0.0989263i
$587$	5.02187e6	+	6.91201e6i	0.0248285	+	0.0341735i	0.821251	−	0.570567i	$-0.193277\pi$
$587$	5.02187e6	+	6.91201e6i	0.0248285	+	0.0341735i	−0.796422	+	0.604741i	$0.793277\pi$
$588$		−	1.50058e8i		−	0.738121i
$589$	2.65717e8	+	2.17084e8i	1.30039	+	1.06238i
$590$	7.43799e6			0.0362159
$591$	1.19288e7	−	8.66676e6i	0.0577874	−	0.0419850i
$592$	−4.43688e7	+	6.10684e7i	−0.213852	+	0.294342i
$593$	−3.63313e7	+	1.11816e8i	−0.174228	+	0.536218i	−0.999597	−	0.0283750i	$-0.990967\pi$
$593$	−3.63313e7	+	1.11816e8i	−0.174228	+	0.536218i	0.825370	+	0.564593i	$0.190967\pi$
$594$	−1.80307e8			−0.860306
$595$			2.15033e7i			0.102083i
$596$	3.51451e7	−	1.08165e8i	0.166007	−	0.510916i
$597$	7.02069e7	+	2.16075e8i	0.329956	+	1.01550i
$598$	−7.40620e7	−	2.27940e8i	−0.346332	−	1.06590i
$599$	−1.71292e8	+	1.24451e8i	−0.796995	+	0.579051i	−0.910031	−	0.414540i	$-0.863942\pi$
$599$	−1.71292e8	+	1.24451e8i	−0.796995	+	0.579051i	0.113036	+	0.993591i	$0.463942\pi$
$600$	7.68536e7	+	2.49712e7i	0.355804	+	0.115608i
$601$	−7.30243e7	−	1.00509e8i	−0.336391	−	0.463002i	0.606992	−	0.794708i	$-0.292376\pi$
$601$	−7.30243e7	−	1.00509e8i	−0.336391	−	0.463002i	−0.943383	+	0.331706i	$0.892376\pi$
$602$	−4.89921e7	+	6.74318e7i	−0.224562	+	0.309083i
$603$	7.80160e6	+	2.40109e7i	0.0355821	+	0.109510i
$604$	−7.17446e7	+	9.87480e7i	−0.325595	+	0.448144i
$605$	1.40684e7	+	1.02213e7i	0.0635298	+	0.0461571i
$606$	2.13314e7	−	6.93100e6i	0.0958521	−	0.0311442i
$607$	1.43337e8	+	1.04140e8i	0.640902	+	0.465643i	0.860160	−	0.510024i	$-0.170364\pi$
$607$	1.43337e8	+	1.04140e8i	0.640902	+	0.465643i	−0.219258	+	0.975667i	$0.570364\pi$
$608$	5.39750e7	−	3.92151e7i	0.240149	−	0.174479i
$609$	−1.77938e8	+	5.47638e8i	−0.787804	+	2.42461i
$610$	−3.06985e6	−	4.22529e6i	−0.0135247	−	0.0186152i
$611$	−4.87107e8	+	1.58271e8i	−2.13551	+	0.693868i
$612$	−1.00939e7	+	3.27971e6i	−0.0440358	+	0.0143081i
$613$	2.01871e8	+	6.55920e7i	0.876382	+	0.284754i	0.712454	−	0.701718i	$-0.247584\pi$
$613$	2.01871e8	+	6.55920e7i	0.876382	+	0.284754i	0.163928	+	0.986472i	$0.447584\pi$
$614$	1.50295e8			0.649290
$615$		−	2.69787e7i		−	0.115984i
$616$	1.61103e8	+	5.23456e7i	0.689227	+	0.223943i
$617$	−2.86577e8	−	2.08210e8i	−1.22007	−	0.886434i	−0.223966	−	0.974597i	$-0.571900\pi$
$617$	−2.86577e8	−	2.08210e8i	−1.22007	−	0.886434i	−0.996106	+	0.0881626i	$0.971900\pi$
$618$	5.35656e7	+	7.37267e7i	0.226945	+	0.312363i
$619$		−	1.77180e8i		−	0.747038i	−0.927622	−	0.373519i	$-0.878151\pi$
$619$		−	1.77180e8i		−	0.747038i	0.927622	−	0.373519i	$-0.121849\pi$
$620$	1.22122e7	+	693012.i	0.0512412	+	0.00290781i
$621$	−2.85038e8			−1.19022
$622$	1.02092e8	−	7.41745e7i	0.424250	−	0.308236i
$623$	2.44740e8	−	3.36856e8i	1.01214	−	1.39309i
$624$	−2.44802e7	+	7.53424e7i	−0.100754	+	0.310089i
$625$	2.36451e8			0.968502
$626$			7.97242e7i			0.324988i
$627$	1.81722e8	−	5.59284e8i	0.737234	−	2.26897i
$628$	5.68598e7	+	1.74997e8i	0.229576	+	0.706562i
$629$	−7.21387e7	−	2.22020e8i	−0.289879	−	0.892155i
$630$	−3.25452e6	+	2.36454e6i	−0.0130156	+	0.00945640i
$631$	2.37257e8	+	7.70895e7i	0.944347	+	0.306837i	0.740416	−	0.672149i	$-0.234628\pi$
$631$	2.37257e8	+	7.70895e7i	0.944347	+	0.306837i	0.203930	+	0.978985i	$0.434628\pi$
$632$	9.86471e6	+	1.35776e7i	0.0390781	+	0.0537864i
$633$	2.74870e8	−	3.78326e8i	1.08372	−	1.49161i
$634$	−2.00506e7	−	6.17095e7i	−0.0786792	−	0.242150i
$635$	7.85695e6	−	1.08142e7i	0.0306855	−	0.0422349i
$636$	6.23854e6	+	4.53257e6i	0.0242500	+	0.0176187i
$637$	4.13831e8	−	1.34462e8i	1.60105	−	0.520213i
$638$	−3.04958e8	−	2.21565e8i	−1.17430	−	0.853176i
$639$	−3.41610e6	+	2.48194e6i	−0.0130926	+	0.00951236i
$640$	734961.	−	2.26198e6i	0.00280366	−	0.00862876i
$641$	−1.84679e8	−	2.54189e8i	−0.701204	−	0.965125i	−0.999942	−	0.0107895i	$-0.996566\pi$
$641$	−1.84679e8	−	2.54189e8i	−0.701204	−	0.965125i	0.298738	−	0.954335i	$-0.403434\pi$
$642$	3.04455e7	−	9.89236e6i	0.115058	−	0.0373848i
$643$	1.50229e8	−	4.88125e7i	0.565096	−	0.183611i	−0.0125170	−	0.999922i	$-0.503984\pi$
$643$	1.50229e8	−	4.88125e7i	0.565096	−	0.183611i	0.577613	+	0.816311i	$0.303984\pi$
$644$	2.54680e8	+	8.27505e7i	0.953535	+	0.309822i
$645$	1.03153e7			0.0384418
$646$			2.06330e8i			0.765357i
$647$	−1.89065e8	−	6.14308e7i	−0.698067	−	0.226816i	−0.0615790	−	0.998102i	$-0.519614\pi$
$647$	−1.89065e8	−	6.14308e7i	−0.698067	−	0.226816i	−0.636488	+	0.771286i	$0.719614\pi$
$648$	8.74031e7	+	6.35021e7i	0.321220	+	0.233380i
$649$	1.06511e8	+	1.46600e8i	0.389637	+	0.536290i
$650$			2.34323e8i			0.853248i
$651$	2.88005e8	−	3.52527e8i	1.04390	−	1.27776i
$652$	2.16161e7			0.0779891
$653$	−1.04433e8	+	7.58748e7i	−0.375057	+	0.272495i	−0.759305	−	0.650735i	$-0.774461\pi$
$653$	−1.04433e8	+	7.58748e7i	−0.375057	+	0.272495i	0.384248	+	0.923230i	$0.374461\pi$
$654$	−4.76458e7	+	6.55788e7i	−0.170330	+	0.234439i
$655$	−3.46713e6	+	1.06707e7i	−0.0123380	+	0.0379725i
$656$	7.45678e7			0.264143
$657$			6.99067e7i			0.246503i
$658$	1.76838e8	−	5.44251e8i	0.620723	−	1.91039i
$659$	8.46809e6	+	2.60621e7i	0.0295889	+	0.0910653i	0.964760	−	0.263130i	$-0.0847548\pi$
$659$	8.46809e6	+	2.60621e7i	0.0295889	+	0.0910653i	−0.935171	+	0.354195i	$0.884755\pi$
$660$	−6.47822e6	−	1.99379e7i	−0.0225332	−	0.0693502i
$661$	2.02205e8	−	1.46910e8i	0.700144	−	0.508684i	−0.179835	−	0.983697i	$-0.557556\pi$
$661$	2.02205e8	−	1.46910e8i	0.700144	−	0.508684i	0.879979	+	0.475012i	$0.157556\pi$
$662$	2.84594e8	+	9.24701e7i	0.980960	+	0.318733i
$663$	−1.44005e8	−	1.98207e8i	−0.494127	−	0.680107i
$664$	−1.10993e8	+	1.52769e8i	−0.379132	+	0.521831i
$665$	2.41668e7	+	7.43778e7i	0.0821778	+	0.252917i
$666$	2.56702e7	−	3.53320e7i	0.0868973	−	0.119604i
$667$	−4.82092e8	−	3.50260e8i	−1.62462	−	1.18036i
$668$	−1.20183e8	+	3.90497e7i	−0.403193	+	0.131005i
$669$	−2.45950e8	−	1.78693e8i	−0.821427	−	0.596802i
$670$	1.41552e7	−	1.02843e7i	0.0470642	−	0.0341941i
$671$	3.93189e7	−	1.21011e8i	0.130147	−	0.400551i
$672$	−5.20268e7	−	7.16087e7i	−0.171443	−	0.235971i
$673$	−4.31220e8	+	1.40112e8i	−1.41467	+	0.459653i	−0.913904	−	0.405931i	$-0.866947\pi$
$673$	−4.31220e8	+	1.40112e8i	−1.41467	+	0.459653i	−0.500763	+	0.865584i	$0.666947\pi$
$674$	−2.56954e7	+	8.34893e6i	−0.0839219	+	0.0272679i
$675$	2.65040e8	+	8.61166e7i	0.861786	+	0.280011i
$676$	−7.52578e7			−0.243619
$677$		−	5.24354e8i		−	1.68989i	−0.534852	−	0.844946i	$-0.679633\pi$
$677$		−	5.24354e8i		−	1.68989i	0.534852	−	0.844946i	$-0.320367\pi$
$678$	−2.48437e8	−	8.07221e7i	−0.797127	−	0.259002i
$679$	−3.63463e8	−	2.64071e8i	−1.16105	−	0.843553i
$680$	4.32342e6	+	5.95068e6i	0.0137500	+	0.0189252i
$681$			4.47617e8i			1.41731i
$682$	1.61218e8	+	2.50622e8i	0.508231	+	0.790070i
$683$	2.06495e8			0.648109			0.324054	−	0.946038i	$-0.394954\pi$
$683$	2.06495e8			0.648109			0.324054	+	0.946038i	$0.394954\pi$
$684$	−3.12280e7	+	2.26885e7i	−0.0975833	+	0.0708984i
$685$	−8.33834e6	+	1.14767e7i	−0.0259423	+	0.0357065i
$686$	−4.14017e7	+	1.27421e8i	−0.128247	+	0.394703i
$687$	5.57291e7			0.171875
$688$			2.85110e7i			0.0875482i
$689$	−6.90979e6	+	2.12662e7i	−0.0211255	+	0.0650177i
$690$	−1.02411e7	−	3.15188e7i	−0.0311744	−	0.0959450i
$691$	5.18264e7	+	1.59505e8i	0.157079	+	0.483438i	0.998366	−	0.0571505i	$-0.0182015\pi$
$691$	5.18264e7	+	1.59505e8i	0.157079	+	0.483438i	−0.841287	+	0.540589i	$0.818201\pi$
$692$	−1.81095e8	+	1.31573e8i	−0.546497	+	0.397053i
$693$	−9.32085e7	−	3.02853e7i	−0.280063	−	0.0909980i
$694$	−1.23136e6	−	1.69482e6i	−0.00368388	−	0.00507043i
$695$	−2.84176e7	+	3.91134e7i	−0.0846511	+	0.116512i
$696$	6.08660e7	+	1.87326e8i	0.180529	+	0.555611i
$697$	−1.35549e8	+	1.86567e8i	−0.400312	+	0.550982i
$698$	−1.06856e8	−	7.76351e7i	−0.314218	−	0.228293i
$699$	2.41641e8	−	7.85139e7i	0.707521	−	0.229887i
$700$	−2.11811e8	−	1.53889e8i	−0.617523	−	0.448657i
$701$	9.77682e7	−	7.10328e7i	0.283820	−	0.206208i	−0.436762	−	0.899577i	$-0.643875\pi$
$701$	9.77682e7	−	7.10328e7i	0.283820	−	0.206208i	0.720582	+	0.693370i	$0.243875\pi$
$702$	−8.44233e7	+	2.59828e8i	−0.244034	+	0.751060i
$703$	−4.99042e8	−	6.86873e8i	−1.43639	−	1.97702i
$704$	5.51073e7	−	1.79054e7i	0.157940	−	0.0513177i
$705$	−6.73557e7	+	2.18852e7i	−0.192224	+	0.0624573i
$706$	−1.52213e8	−	4.94569e7i	−0.432550	−	0.140544i
$707$	−7.26684e7			−0.205630
$708$		−	9.46861e7i		−	0.266800i
$709$	−2.84401e8	−	9.24074e7i	−0.797980	−	0.259279i	−0.118482	−	0.992956i	$-0.537803\pi$
$709$	−2.84401e8	−	9.24074e7i	−0.797980	−	0.259279i	−0.679499	+	0.733677i	$0.737803\pi$
$710$	2.36748e6	+	1.72007e6i	0.00661471	+	0.00480587i
$711$	−5.70737e6	−	7.85552e6i	−0.0158791	−	0.0218558i
$712$		−	1.42427e8i		−	0.394595i
$713$	2.54862e8	+	3.96195e8i	0.703130	+	1.09305i
$714$	2.73738e8			0.752039
$715$	4.91800e7	−	3.57313e7i	0.134546	−	0.0977532i
$716$	9.53998e7	−	1.31307e8i	0.259901	−	0.357723i
$717$	−2.05307e6	+	6.31871e6i	−0.00556990	+	0.0171424i
$718$	4.06887e8			1.09926
$719$			2.85441e7i			0.0767944i	0.999263	+	0.0383972i	$0.0122252\pi$
$719$			2.85441e7i			0.0767944i	−0.999263	+	0.0383972i	$0.987775\pi$
$720$	−425222.	+	1.30870e6i	−0.00113925	+	0.00350625i
$721$	−9.12392e7	−	2.80805e8i	−0.243431	−	0.749203i
$722$	1.49648e8	+	4.60569e8i	0.397612	+	1.22372i
$723$	−1.79659e8	+	1.30530e8i	−0.475374	+	0.345379i
$724$	−2.00964e8	−	6.52971e7i	−0.529544	−	0.172059i
$725$	3.42447e8	+	4.71337e8i	0.898626	+	1.23685i
$726$	1.30117e8	−	1.79091e8i	0.340037	−	0.468020i
$727$	2.13598e8	+	6.57387e8i	0.555897	+	1.71087i	0.693564	+	0.720395i	$0.256039\pi$
$727$	2.13598e8	+	6.57387e8i	0.555897	+	1.71087i	−0.137668	+	0.990478i	$0.543961\pi$
$728$	1.50863e8	−	2.07646e8i	0.391012	−	0.538182i
$729$	2.56392e8	+	1.86280e8i	0.661794	+	0.480821i
$730$	4.60767e7	−	1.49712e7i	0.118444	−	0.0384847i
$731$	−7.13341e7	−	5.18272e7i	−0.182619	−	0.132680i
$732$	−5.37882e7	+	3.90794e7i	−0.137137	+	0.0996357i
$733$	−4.67635e7	+	1.43923e8i	−0.118739	+	0.365443i	−0.992709	−	0.120539i	$-0.961538\pi$
$733$	−4.67635e7	+	1.43923e8i	−0.118739	+	0.365443i	0.873969	+	0.485981i	$0.161538\pi$
$734$	1.64306e6	+	2.26147e6i	0.00415494	+	0.00571878i
$735$	5.72233e7	−	1.85930e7i	0.144116	−	0.0468260i
$736$	8.71163e7	−	2.83058e7i	0.218507	−	0.0709973i
$737$	4.05400e8	+	1.31723e8i	1.01270	+	0.329047i
$738$	−4.31422e7			−0.107333
$739$			4.13777e8i			1.02526i	0.858610	+	0.512629i	$0.171328\pi$
$739$			4.13777e8i			1.02526i	−0.858610	+	0.512629i	$0.828672\pi$
$740$	−2.87854e7	−	9.35295e6i	−0.0710358	−	0.0230809i
$741$	−7.20860e8	−	5.23735e8i	−1.77172	−	1.28723i
$742$	−1.46851e7	−	2.02123e7i	−0.0359471	−	0.0494770i
$743$		−	2.93400e8i		−	0.715310i	−0.933854	−	0.357655i	$-0.883576\pi$
$743$		−	2.93400e8i		−	0.715310i	0.933854	−	0.357655i	$-0.116424\pi$
$744$	8.82209e6	−	1.55462e8i	0.0214216	−	0.377491i
$745$	4.56026e7			0.110286
$746$	1.65905e8	−	1.20537e8i	0.399616	−	0.290338i
$747$	6.42165e7	−	8.83864e7i	0.154058	−	0.212043i
$748$	−5.53748e7	+	1.70426e8i	−0.132314	+	0.407222i
$749$	−1.03717e8			−0.246833
$750$			6.51480e7i			0.154425i
$751$	−1.50218e8	+	4.62322e8i	−0.354651	+	1.09150i	0.601561	+	0.798827i	$0.294546\pi$
$751$	−1.50218e8	+	4.62322e8i	−0.354651	+	1.09150i	−0.956212	+	0.292676i	$0.905454\pi$
$752$	−6.04895e7	−	1.86168e8i	−0.142242	−	0.437775i
$753$	1.95409e8	+	6.01408e8i	0.457678	+	1.40859i
$754$	−4.62069e8	+	3.35713e8i	−1.07794	+	0.783167i
$755$	−4.65462e7	−	1.51238e7i	−0.108154	−	0.0351414i
$756$	−1.79421e8	−	2.46952e8i	−0.415248	−	0.571540i
$757$	−1.65696e6	+	2.28061e6i	−0.00381965	+	0.00525730i	−0.810923	−	0.585154i	$-0.801034\pi$
$757$	−1.65696e6	+	2.28061e6i	−0.00381965	+	0.00525730i	0.807103	+	0.590411i	$0.201034\pi$
$758$	−1.61041e8	−	4.95634e8i	−0.369768	−	1.13803i
$759$	4.74573e8	−	6.53193e8i	1.08537	−	1.49388i
$760$	2.16421e7	+	1.57239e7i	0.0493014	+	0.0358195i
$761$	5.99693e8	−	1.94852e8i	1.36074	−	0.442131i	0.464450	−	0.885600i	$-0.346252\pi$
$761$	5.99693e8	−	1.94852e8i	1.36074	−	0.442131i	0.896290	+	0.443468i	$0.146252\pi$
$762$	−1.37665e8	−	1.00020e8i	−0.311142	−	0.226058i
$763$	2.12469e8	−	1.54368e8i	0.478323	−	0.347522i
$764$	−6.42819e7	+	1.97839e8i	−0.144148	+	0.443642i
$765$	−2.50138e6	−	3.44285e6i	−0.00558721	−	0.00769014i
$766$	1.00857e7	−	3.27703e6i	0.0224398	−	0.00729112i
$767$	2.61126e8	−	8.48449e7i	0.578714	−	0.188035i
$768$	−2.87951e7	−	9.35611e6i	−0.0635676	−	0.0206544i
$769$	−2.44170e8			−0.536925			−0.268463	−	0.963290i	$-0.586516\pi$
$769$	−2.44170e8			−0.536925			−0.268463	+	0.963290i	$0.586516\pi$
$770$			6.79212e7i			0.148776i
$771$	−1.91930e8	−	6.23618e7i	−0.418774	−	0.136068i
$772$	2.23021e7	+	1.62034e7i	0.0484722	+	0.0352171i
$773$	−4.92540e7	−	6.77923e7i	−0.106636	−	0.146772i	0.752364	−	0.658748i	$-0.228914\pi$
$773$	−4.92540e7	−	6.77923e7i	−0.106636	−	0.146772i	−0.859000	+	0.511976i	$0.828914\pi$
$774$		−	1.64954e7i		−	0.0355747i
$775$	−1.17281e8	−	4.45398e8i	−0.251954	−	0.956848i
$776$	−1.53677e8			−0.328869
$777$	−9.11276e8	+	6.62081e8i	−1.94261	+	1.41139i
$778$	1.08659e8	−	1.49556e8i	0.230742	−	0.317590i
$779$	−2.59175e8	+	7.97659e8i	−0.548253	+	1.68735i
$780$	−3.17644e7			−0.0669355
$781$			7.12933e7i			0.149656i
$782$	−8.75391e7	+	2.69418e8i	−0.183055	+	0.563386i
$783$	2.09904e8	+	6.46019e8i	0.437256	+	1.34574i
$784$	5.13900e7	+	1.58162e8i	0.106643	+	0.328212i
$785$	−5.96881e7	+	4.33660e7i	−0.123390	+	0.0896479i
$786$	1.35839e8	+	4.41367e7i	0.279741	+	0.0908935i
$787$	5.02442e8	+	6.91551e8i	1.03077	+	1.41873i	0.904368	+	0.426753i	$0.140342\pi$
$787$	5.02442e8	+	6.91551e8i	1.03077	+	1.41873i	0.126401	+	0.991979i	$0.459658\pi$
$788$	−9.60492e6	+	1.32200e7i	−0.0196298	+	0.0270180i
$789$	−1.89327e8	−	5.82689e8i	−0.385462	−	1.18633i
$790$	−3.95541e6	+	5.44416e6i	−0.00802252	+	0.0110420i
$791$	6.84699e8	+	4.97463e8i	1.38347	+	1.00515i
$792$	−3.18831e7	+	1.03594e7i	−0.0641778	+	0.0208526i
$793$	−1.55971e8	−	1.13320e8i	−0.312770	−	0.227241i
$794$	−3.47936e8	+	2.52790e8i	−0.695085	+	0.505009i
$795$	−955466.	+	2.94062e6i	−0.00190158	+	0.00585245i
$796$	−1.47997e8	−	2.03700e8i	−0.293436	−	0.403880i
$797$	7.67236e7	−	2.49290e7i	0.151549	−	0.0492413i	−0.232260	−	0.972654i	$-0.574612\pi$
$797$	7.67236e7	−	2.49290e7i	0.151549	−	0.0492413i	0.383809	+	0.923412i	$0.374612\pi$
$798$	9.46835e8	−	3.07645e8i	1.86323	−	0.605399i
$799$	5.75746e8	+	1.87071e8i	1.12873	+	0.366747i
$800$	−8.95560e7			−0.174914
$801$			8.24030e7i			0.160341i
$802$	−4.35309e8	−	1.41440e8i	−0.843868	−	0.274189i
$803$	9.54889e8	+	6.93768e8i	1.84419	+	1.33988i
$804$	−1.30920e8	−	1.80196e8i	−0.251906	−	0.346719i
$805$			1.07373e8i			0.205830i
$806$	4.36640e8	−	1.14975e8i	0.833908	−	0.219582i
$807$	−5.46049e8			−1.03899
$808$	−2.01098e7	+	1.46106e7i	−0.0381218	+	0.0276971i
$809$	4.58729e7	−	6.31386e7i	0.0866384	−	0.119247i	−0.763498	−	0.645811i	$-0.776520\pi$
$809$	4.58729e7	−	6.31386e7i	0.0866384	−	0.119247i	0.850136	+	0.526563i	$0.176520\pi$
$810$	−1.33863e7	+	4.11987e7i	−0.0251886	+	0.0775225i
$811$	2.05533e8			0.385318			0.192659	−	0.981266i	$-0.438289\pi$
$811$	2.05533e8			0.385318			0.192659	+	0.981266i	$0.438289\pi$
$812$		−	6.38152e8i		−	1.19195i
$813$	2.85234e8	−	8.77859e8i	0.530798	−	1.63363i
$814$	−2.27861e8	−	7.01283e8i	−0.422470	−	1.30023i
$815$	2.67834e6	+	8.24310e6i	0.00494759	+	0.0152271i
$816$	7.57526e7	−	5.50375e7i	0.139421	−	0.101295i
$817$	−3.04985e8	−	9.90956e7i	−0.559258	−	0.181714i
$818$	−9.11428e6	−	1.25447e7i	−0.0166518	−	0.0229193i
$819$	−8.72842e7	+	1.20136e8i	−0.158885	+	0.218687i
$820$	9.23934e6	+	2.84358e7i	0.0167571	+	0.0515731i
$821$	−2.97054e8	+	4.08860e8i	−0.536792	+	0.738831i	−0.988146	−	0.153514i	$-0.950941\pi$
$821$	−2.97054e8	+	4.08860e8i	−0.536792	+	0.738831i	0.451355	+	0.892345i	$0.350941\pi$
$822$	1.46100e8	+	1.06148e8i	0.263047	+	0.191115i
$823$	8.25753e8	−	2.68304e8i	1.48133	−	0.481312i	0.546818	−	0.837252i	$-0.315839\pi$
$823$	8.25753e8	−	2.68304e8i	1.48133	−	0.481312i	0.934509	+	0.355939i	$0.115839\pi$
$824$	−8.17074e7	−	5.93639e7i	−0.146043	−	0.106106i
$825$	−6.38621e8	+	4.63986e8i	−1.13732	+	0.826309i
$826$	−9.47983e7	+	2.91759e8i	−0.168213	+	0.517708i
$827$	8.87224e7	+	1.22116e8i	0.156862	+	0.215902i	0.880213	−	0.474578i	$-0.157399\pi$
$827$	8.87224e7	+	1.22116e8i	0.156862	+	0.215902i	−0.723352	+	0.690480i	$0.757399\pi$
$828$	−5.04023e7	+	1.63767e7i	−0.0887891	+	0.0288493i
$829$	−5.46508e8	+	1.77571e8i	−0.959253	+	0.311680i	−0.746470	−	0.665419i	$-0.768253\pi$
$829$	−5.46508e8	+	1.77571e8i	−0.959253	+	0.311680i	−0.212783	+	0.977099i	$0.568253\pi$
$830$	−7.20095e7	−	2.33973e7i	−0.125938	−	0.0409196i
$831$	2.72246e8			0.474415
$832$		−	8.77951e7i		−	0.152440i
$833$	−4.89136e8	−	1.58930e8i	−0.846242	−	0.274961i
$834$	4.97917e8	+	3.61758e8i	0.858338	+	0.623619i
$835$	−2.97825e7	−	4.09921e7i	−0.0511567	−	0.0704111i
$836$			6.51722e8i			1.11543i
$837$	3.04241e7	−	5.36132e8i	0.0518850	−	0.914314i
$838$	−2.32136e8			−0.394467
$839$	6.11136e8	−	4.44017e8i	1.03479	−	0.751819i	0.0655282	−	0.997851i	$-0.479127\pi$
$839$	6.11136e8	−	4.44017e8i	1.03479	−	0.751819i	0.969262	+	0.246032i	$0.0791268\pi$
$840$	2.08609e7	−	2.87126e7i	0.0351962	−	0.0484435i
$841$	−2.55014e8	+	7.84853e8i	−0.428722	+	1.31947i
$842$	−3.83954e8			−0.643195
$843$			3.24902e8i			0.542338i
$844$	−1.60150e8	+	4.92892e8i	−0.266379	+	0.819830i
$845$	−9.32483e6	−	2.86989e7i	−0.0154551	−	0.0475658i
$846$	3.49971e7	+	1.07710e8i	0.0577990	+	0.177887i
$847$	−5.80239e8	+	4.21568e8i	−0.954897	+	0.693773i
$848$	−8.12772e6	−	2.64086e6i	−0.0133285	−	0.00433069i
$849$	5.01438e8	+	6.90171e8i	0.819397	+	1.12780i
$850$	1.62795e8	−	2.24068e8i	0.265084	−	0.364857i
$851$	−3.60213e8	−	1.10862e9i	−0.584481	−	1.79885i
$852$	2.18966e7	−	3.01381e7i	0.0354045	−	0.0487301i
$853$	−8.05069e8	−	5.84917e8i	−1.29714	−	0.942425i	−0.297213	−	0.954811i	$-0.596057\pi$
$853$	−8.05069e8	−	5.84917e8i	−1.29714	−	0.942425i	−0.999923	+	0.0123861i	$0.996057\pi$
$854$	2.04865e8	−	6.65647e7i	0.328923	−	0.106874i
$855$	−1.25214e7	−	9.09730e6i	−0.0200333	−	0.0145551i
$856$	−2.87020e7	+	2.08532e7i	−0.0457605	+	0.0332469i
$857$	−1.87229e8	+	5.76231e8i	−0.297461	+	0.915491i	0.684923	+	0.728616i	$0.259836\pi$
$857$	−1.87229e8	+	5.76231e8i	−0.297461	+	0.915491i	−0.982384	+	0.186875i	$0.940164\pi$
$858$	−4.54862e8	−	6.26064e8i	−0.720142	−	0.991190i
$859$	−1.04065e9	+	3.38129e8i	−1.64182	+	0.533461i	−0.976945	−	0.213492i	$-0.931516\pi$
$859$	−1.04065e9	+	3.38129e8i	−1.64182	+	0.533461i	−0.664878	+	0.746952i	$0.731516\pi$
$860$	−1.08724e7	+	3.53266e6i	−0.0170935	+	0.00555401i
$861$	1.05826e9	+	3.43848e8i	1.65799	+	0.538713i
$862$	1.90110e8			0.296813
$863$		−	4.93008e8i		−	0.767046i	−0.923531	−	0.383523i	$-0.874711\pi$
$863$		−	4.93008e8i		−	0.767046i	0.923531	−	0.383523i	$-0.125289\pi$
$864$	−9.93038e7	−	3.22658e7i	−0.153966	−	0.0500266i
$865$	−7.26128e7	−	5.27563e7i	−0.112193	−	0.0815128i
$866$	−2.05263e8	−	2.82520e8i	−0.316050	−	0.435006i
$867$		−	4.07379e8i		−	0.625088i
$868$	−1.82830e8	+	4.70198e8i	−0.279569	+	0.718988i
$869$	−1.63943e8			−0.249824
$870$	−6.38936e7	+	4.64214e7i	−0.0970286	+	0.0704954i
$871$	3.79633e8	−	5.22520e8i	0.574525	−	0.790766i
$872$	2.77603e7	−	8.54376e7i	0.0418673	−	0.128854i
$873$	8.89118e7			0.133634
$874$			1.03027e9i			1.54319i
$875$	6.52252e7	−	2.00743e8i	0.0973625	−	0.299651i
$876$	−1.90585e8	−	5.86559e8i	−0.283515	−	0.872569i
$877$	−2.60044e7	−	8.00334e7i	−0.0385521	−	0.118651i	0.929928	−	0.367741i	$-0.119869\pi$
$877$	−2.60044e7	−	8.00334e7i	−0.0385521	−	0.118651i	−0.968480	+	0.249090i	$0.919869\pi$
$878$	−2.69855e8	+	1.96061e8i	−0.398700	+	0.289673i
$879$	−1.64411e8	−	5.34203e7i	−0.242083	−	0.0786574i
$880$	1.36562e7	+	1.87961e7i	0.0200392	+	0.0275816i
$881$	−4.93118e7	+	6.78719e7i	−0.0721146	+	0.0992572i	−0.843551	−	0.537050i	$-0.819539\pi$
$881$	−4.93118e7	+	6.78719e7i	−0.0721146	+	0.0992572i	0.771436	+	0.636307i	$0.219539\pi$
$882$	−2.97324e7	−	9.15070e7i	−0.0433336	−	0.133367i
$883$	7.91816e8	−	1.08984e9i	1.15012	−	1.58300i	0.407621	−	0.913151i	$-0.366358\pi$
$883$	7.91816e8	−	1.08984e9i	1.15012	−	1.58300i	0.742496	−	0.669850i	$-0.233642\pi$
$884$	2.19662e8	+	1.59594e8i	0.317979	+	0.231025i
$885$	3.61077e7	−	1.17321e7i	0.0520919	−	0.0169257i
$886$	−1.95464e8	−	1.42013e8i	−0.281038	−	0.204186i
$887$	7.28974e8	−	5.29631e8i	1.04458	−	0.758931i	0.0734052	−	0.997302i	$-0.476613\pi$
$887$	7.28974e8	−	5.29631e8i	1.04458	−	0.758931i	0.971174	+	0.238371i	$0.0766134\pi$
$888$	−1.19064e8	+	3.66440e8i	−0.170036	+	0.523317i
$889$	3.24054e8	+	4.46022e8i	0.461224	+	0.634820i
$890$	5.43132e7	−	1.76474e7i	0.0770434	−	0.0250329i
$891$	−1.00370e9	+	3.26122e8i	−1.41896	+	0.461048i
$892$	3.20430e8	+	1.04114e8i	0.451480	+	0.146695i
$893$	2.20170e9			3.09174
$894$		−	5.80524e8i		−	0.812470i
$895$	6.18931e7	+	2.01103e7i	0.0863323	+	0.0280511i
$896$	7.93602e7	+	5.76585e7i	0.110326	+	0.0801567i
$897$	−7.19068e8	−	9.89712e8i	−0.996306	−	1.37130i
$898$		−	4.52932e8i		−	0.625466i
$899$	7.10267e8	−	8.69388e8i	0.977558	−	1.19656i
$900$	5.18139e7			0.0710753
$901$	2.13819e7	−	1.55349e7i	0.0292329	−	0.0212390i
$902$	−4.28152e8	+	5.89300e8i	−0.583416	+	0.803003i
$903$	−1.31470e8	+	4.04624e8i	−0.178552	+	0.549526i
$904$	2.89499e8			0.391870
$905$		−	8.47264e7i		−	0.114307i
$906$	−1.92527e8	+	5.92536e8i	−0.258885	+	0.796765i
$907$	3.82590e7	+	1.17749e8i	0.0512757	+	0.157810i	0.973415	−	0.229046i	$-0.0735608\pi$
$907$	3.82590e7	+	1.17749e8i	0.0512757	+	0.157810i	−0.922140	+	0.386857i	$0.873561\pi$
$908$	−1.53294e8	−	4.71792e8i	−0.204771	−	0.630221i
$909$	1.16348e7	−	8.45319e6i	0.0154906	−	0.0112546i
$910$	9.78766e7	+	3.18020e7i	0.129884	+	0.0422018i
$911$	−6.19239e8	−	8.52309e8i	−0.819036	−	1.12731i	−0.989866	−	0.142006i	$-0.954645\pi$
$911$	−6.19239e8	−	8.52309e8i	−0.819036	−	1.12731i	0.170830	−	0.985300i	$-0.445355\pi$
$912$	2.00167e8	−	2.75506e8i	0.263880	−	0.363200i
$913$	−5.70015e8	−	1.75433e9i	−0.748987	−	2.30514i
$914$	−9.94304e7	+	1.36854e8i	−0.130221	+	0.179234i
$915$	−2.15672e7	−	1.56695e7i	−0.0281534	−	0.0204547i
$916$	−5.87388e7	+	1.90854e7i	−0.0764256	+	0.0248322i
$917$	−3.74376e8	−	2.72000e8i	−0.485512	−	0.352745i
$918$	2.61243e8	−	1.89804e8i	0.337688	−	0.245345i
$919$	−4.40812e8	+	1.35668e9i	−0.567946	+	1.74796i	0.0910862	+	0.995843i	$0.470966\pi$
$919$	−4.40812e8	+	1.35668e9i	−0.567946	+	1.74796i	−0.659032	+	0.752115i	$0.729034\pi$
$920$	2.15883e7	+	2.97138e7i	0.0277240	+	0.0381588i
$921$	7.29606e8	−	2.37063e8i	0.933920	−	0.303449i
$922$	4.99487e8	−	1.62293e8i	0.637281	−	0.207065i
$923$	1.02736e8	+	3.33809e7i	0.130652	+	0.0424515i
$924$	8.64641e8			1.09602
$925$			1.13967e9i			1.43997i
$926$	1.62654e8	+	5.28496e7i	0.204848	+	0.0665593i
$927$	4.72730e7	+	3.43458e7i	0.0593436	+	0.0431157i
$928$	−1.28306e8	−	1.76598e8i	−0.160548	−	0.220975i
$929$		−	4.12255e8i		−	0.514184i	−0.966387	−	0.257092i	$-0.917236\pi$
$929$		−	4.12255e8i		−	0.514184i	0.966387	−	0.257092i	$-0.0827643\pi$
$930$	6.03773e7	−	1.58984e7i	0.0750628	−	0.0197653i
$931$	−1.87049e9			−2.31797
$932$	−2.27803e8	+	1.65508e8i	−0.281392	+	0.204443i
$933$	3.78610e8	−	5.21112e8i	0.466173	−	0.641633i
$934$	3.11686e8	−	9.59271e8i	0.382540	−	1.17734i
$935$	−7.18517e7			−0.0879027
$936$			5.07951e7i			0.0619433i
$937$	−3.32545e8	+	1.02347e9i	−0.404232	+	1.24410i	0.517302	+	0.855803i	$0.326936\pi$
$937$	−3.32545e8	+	1.02347e9i	−0.404232	+	1.24410i	−0.921534	+	0.388297i	$0.873064\pi$
$938$	2.22999e8	+	6.86319e8i	0.270205	+	0.831606i
$939$	1.25751e8	+	3.87021e8i	0.151885	+	0.467453i
$940$	6.34984e7	−	4.61343e7i	0.0764503	−	0.0555444i
$941$	−9.18753e8	−	2.98521e8i	−1.10263	−	0.358266i	−0.299516	−	0.954091i	$-0.596825\pi$
$941$	−9.18753e8	−	2.98521e8i	−1.10263	−	0.358266i	−0.803114	+	0.595825i	$0.796825\pi$
$942$	5.52052e8	+	7.59834e8i	0.660431	+	0.909005i
$943$	−6.76843e8	+	9.31594e8i	−0.807147	+	1.11094i
$944$	3.24269e7	+	9.97998e7i	0.0385469	+	0.118635i
$945$	7.19417e7	−	9.90192e7i	0.0852482	−	0.117334i
$946$	−2.25319e8	−	1.63704e8i	−0.266149	−	0.193368i
$947$	1.00475e9	−	3.26463e8i	1.18306	−	0.384400i	0.349559	−	0.936914i	$-0.386331\pi$
$947$	1.00475e9	−	3.26463e8i	1.18306	−	0.384400i	0.833504	+	0.552514i	$0.186331\pi$
$948$	6.93045e7	+	5.03527e7i	0.0813461	+	0.0591014i
$949$	1.44684e9	−	1.05119e9i	1.69286	−	1.22994i
$950$	3.11270e8	−	9.57990e8i	0.363050	−	1.11735i
$951$	−1.94671e8	−	2.67942e8i	−0.226340	−	0.311530i
$952$	−2.88522e8	+	9.37463e7i	−0.334401	+	0.108653i
$953$	−5.45347e7	+	1.77194e7i	−0.0630077	+	0.0204725i	−0.340351	−	0.940298i	$-0.610546\pi$
$953$	−5.45347e7	+	1.77194e7i	−0.0630077	+	0.0204725i	0.277344	+	0.960771i	$0.410546\pi$
$954$	4.70241e6	+	1.52790e6i	0.00541596	+	0.00175975i
$955$	−8.34091e7			−0.0957643
$956$		−	7.36308e6i		−	0.00842724i
$957$	−1.82990e9	−	5.94569e8i	−2.08781	−	0.678370i
$958$	−9.32460e8	−	6.77472e8i	−1.06056	−	0.770539i
$959$	−3.43908e8	−	4.73349e8i	−0.389930	−	0.536693i
$960$		−	1.21400e7i		−	0.0137217i
$961$	−7.72412e8	+	4.37084e8i	−0.870320	+	0.492487i
$962$	−1.11726e9			−1.25496
$963$	1.66059e7	−	1.20649e7i	0.0185945	−	0.0135097i
$964$	1.44660e8	−	1.99107e8i	0.161479	−	0.222257i
$965$	−3.41568e6	+	1.05124e7i	−0.00380098	+	0.0116982i
$966$	1.36687e9			1.51633
$967$			1.50466e9i			1.66402i	0.554759	+	0.832011i	$0.312811\pi$
$967$			1.50466e9i			1.66402i	−0.554759	+	0.832011i	$0.687189\pi$
$968$	−7.58117e7	+	2.33324e8i	−0.0835815	+	0.257237i
$969$	3.25448e8	+	1.00163e9i	0.357693	+	1.10087i
$970$	−1.90413e7	−	5.86032e7i	−0.0208633	−	0.0642105i
$971$	6.32774e8	−	4.59737e8i	0.691179	−	0.502171i	−0.185868	−	0.982575i	$-0.559510\pi$
$971$	6.32774e8	−	4.59737e8i	0.691179	−	0.502171i	0.877048	+	0.480404i	$0.159510\pi$
$972$	1.24546e8	+	4.04675e7i	0.135622	+	0.0440664i
$973$	−1.17206e9	−	1.61320e9i	−1.27236	−	1.75126i
$974$	−3.91841e8	+	5.39323e8i	−0.424066	+	0.583676i
$975$	3.69603e8	+	1.13752e9i	0.398769	+	1.22729i
$976$	4.33097e7	−	5.96107e7i	0.0465839	−	0.0641172i
$977$	8.74399e8	+	6.35288e8i	0.937619	+	0.681220i	0.947846	−	0.318728i	$-0.103256\pi$
$977$	8.74399e8	+	6.35288e8i	0.937619	+	0.681220i	−0.0102277	+	0.999948i	$0.503256\pi$
$978$	1.04935e8	−	3.40955e7i	0.112177	−	0.0364486i
$979$	1.12558e9	+	8.17783e8i	1.19958	+	0.871546i
$980$	−5.39463e7	+	3.91943e7i	−0.0573170	+	0.0416432i
$981$	−1.60611e7	+	4.94311e7i	−0.0170125	+	0.0523592i
$982$	1.95296e8	+	2.68802e8i	0.206234	+	0.283856i
$983$	−2.97870e8	+	9.67839e7i	−0.313593	+	0.101893i	−0.461585	−	0.887096i	$-0.652719\pi$
$983$	−2.97870e8	+	9.67839e7i	−0.313593	+	0.101893i	0.147992	+	0.988989i	$0.452719\pi$
$984$	3.61989e8	−	1.17617e8i	0.379936	−	0.123449i
$985$	−6.23144e6	−	2.02472e6i	−0.00652049	−	0.00211863i
$986$	6.75082e8			0.704248
$987$		−	2.92100e9i		−	3.03794i
$988$	9.39153e8	+	3.05149e8i	0.973791	+	0.316404i
$989$	−3.56195e8	−	2.58791e8i	−0.368213	−	0.267522i
$990$	−7.90097e6	−	1.08748e7i	−0.00814282	−	0.0112076i
$991$		−	4.48261e8i		−	0.460586i	−0.973121	−	0.230293i	$-0.926032\pi$
$991$		−	4.48261e8i		−	0.460586i	0.973121	−	0.230293i	$-0.0739684\pi$
$992$	4.39422e7	+	1.66879e8i	0.0450139	+	0.170950i
$993$	1.52742e9			1.55995
$994$	−9.76447e7	+	7.09430e7i	−0.0994236	+	0.0722355i
$995$	5.93417e7	−	8.16769e7i	0.0602408	−	0.0829144i
$996$	−2.97849e8	+	9.16686e8i	−0.301452	+	0.927775i
$997$	−1.42949e9			−1.44243			−0.721216	−	0.692710i	$-0.756417\pi$
$997$	−1.42949e9			−1.44243			−0.721216	+	0.692710i	$0.756417\pi$
$998$			2.51596e8i			0.253112i
$999$	−4.10607e8	+	1.26372e9i	−0.411841	+	1.26752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.15.2	✓	64
31.29	odd	10	inner	62.7.f.a.29.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.2	✓	64	1.1	even	1	trivial
62.7.f.a.29.2	yes	64	31.29	odd	10	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.57649 + 3.32502i) q^{2} +(-16.9719 + 23.3599i) q^{3} +(9.88854 - 30.4338i) q^{4} +12.8309 q^{5} -163.338i q^{6} +(-163.532 + 503.299i) q^{7} +(55.9381 + 172.160i) q^{8} +(-32.3638 - 99.6054i) q^{9} +(-58.7205 + 42.6630i) q^{10} +(-1681.74 - 546.431i) q^{11} +(543.102 + 747.516i) q^{12} +(-1574.85 + 2167.59i) q^{13} +(-925.076 - 2847.09i) q^{14} +(-217.765 + 299.728i) q^{15} +(-828.433 - 601.892i) q^{16} +(3011.85 - 978.609i) q^{17} +(479.302 + 348.233i) q^{18} +(9317.89 - 6769.84i) q^{19} +(126.879 - 390.493i) q^{20} +(-8981.56 - 12362.1i) q^{21} +(9513.37 - 3091.08i) q^{22} +(15039.2 - 4886.53i) q^{23} +(-4971.01 - 1615.18i) q^{24} -15460.4 q^{25} -15156.4i q^{26} +(-17143.2 - 5570.15i) q^{27} +(13700.2 + 9953.80i) q^{28} +(-22150.0 - 30486.8i) q^{29} -2095.78i q^{30} +(7585.90 + 28809.0i) q^{31} +5792.62 q^{32} +(41307.0 - 30011.3i) q^{33} +(-10529.8 + 14493.0i) q^{34} +(-2098.26 + 6457.79i) q^{35} -3351.40 q^{36} -73715.5i q^{37} +(-20133.4 + 61964.2i) q^{38} +(-23906.5 - 73576.6i) q^{39} +(717.736 + 2208.96i) q^{40} +(-58912.7 + 42802.6i) q^{41} +(82208.1 + 26711.0i) q^{42} +(-16365.6 - 22525.3i) q^{43} +(-33259.9 + 45778.4i) q^{44} +(-415.256 - 1278.03i) q^{45} +(-52578.9 + 72368.7i) q^{46} +(154652. + 112361. i) q^{47} +(28120.3 - 9136.83i) q^{48} +(-131388. - 95458.6i) q^{49} +(70754.2 - 51406.0i) q^{50} +(-28256.8 + 86965.4i) q^{51} +(50395.2 + 69363.0i) q^{52} +(7937.23 - 2578.96i) q^{53} +(96976.4 - 31509.5i) q^{54} +(-21578.3 - 7011.20i) q^{55} -95795.5 q^{56} +332562. i q^{57} +(202738. + 65873.6i) q^{58} +(-82905.0 - 60234.0i) q^{59} +(6968.50 + 9591.31i) q^{60} +71955.9i q^{61} +(-130507. - 106621. i) q^{62} +55423.8 q^{63} +(-26509.9 + 19260.5i) q^{64} +(-20206.7 + 27812.2i) q^{65} +(-89253.1 + 274693. i) q^{66} -241060. q^{67} -101339. i q^{68} +(-141096. + 434248. i) q^{69} +(-11869.6 - 36530.8i) q^{70} +(-12458.9 - 38344.4i) q^{71} +(15337.7 - 11143.5i) q^{72} +(-634817. - 206265. i) q^{73} +(245105. + 337359. i) q^{74} +(262393. - 361152. i) q^{75} +(-113892. - 350523. i) q^{76} +(550037. - 757060. i) q^{77} +(354051. + 257233. i) q^{78} +(88175.3 - 28649.9i) q^{79} +(-10629.6 - 7722.82i) q^{80} +(482839. - 350803. i) q^{81} +(127294. - 391771. i) q^{82} +(613155. + 843935. i) q^{83} +(-465039. + 151100. i) q^{84} +(38644.8 - 12556.4i) q^{85} +(149794. + 48670.9i) q^{86} +1.08810e6 q^{87} -320094. i q^{88} +(-748295. - 243136. i) q^{89} +(6149.88 + 4468.15i) q^{90} +(-833411. - 1.14709e6i) q^{91} -506020. i q^{92} +(-801722. - 311739. i) q^{93} -1.08137e6 q^{94} +(119557. - 86863.2i) q^{95} +(-98312.0 + 135315. i) q^{96} +(-262340. + 807401. i) q^{97} +918695. q^{98} +185195. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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